LMFDB - Embedded newform 91.10.h.a.16.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(16,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.h (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:	$46.8682610909$
Analytic rank:	$0$
Dimension:	$164$
Relative dimension:	$82$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.14
Character	$\chi$	$=$	91.16
Dual form			91.10.h.a.74.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-33.5094 q^{2} +(52.0738 - 90.1944i) q^{3} +610.880 q^{4} +(-1097.77 + 1901.40i) q^{5} +(-1744.96 + 3022.36i) q^{6} +(2263.61 + 5935.46i) q^{7} -3313.40 q^{8} +(4418.14 + 7652.45i) q^{9} +O(q^{10})$	\(q-33.5094 q^{2} +(52.0738 - 90.1944i) q^{3} +610.880 q^{4} +(-1097.77 + 1901.40i) q^{5} +(-1744.96 + 3022.36i) q^{6} +(2263.61 + 5935.46i) q^{7} -3313.40 q^{8} +(4418.14 + 7652.45i) q^{9} +(36785.7 - 63714.7i) q^{10} +(30811.2 - 53366.6i) q^{11} +(31810.8 - 55098.0i) q^{12} +(101284. - 18600.6i) q^{13} +(-75852.1 - 198894. i) q^{14} +(114330. + 198026. i) q^{15} -201740. q^{16} +190343. q^{17} +(-148049. - 256429. i) q^{18} +(260610. + 451389. i) q^{19} +(-670607. + 1.16153e6i) q^{20} +(653220. + 104917. i) q^{21} +(-1.03247e6 + 1.78828e6i) q^{22} -25757.1 q^{23} +(-172541. + 298851. i) q^{24} +(-1.43364e6 - 2.48315e6i) q^{25} +(-3.39398e6 + 623293. i) q^{26} +2.97021e6 q^{27} +(1.38279e6 + 3.62585e6i) q^{28} +(-1.65604e6 - 2.86834e6i) q^{29} +(-3.83114e6 - 6.63573e6i) q^{30} +(679515. + 1.17695e6i) q^{31} +8.45666e6 q^{32} +(-3.20891e6 - 5.55800e6i) q^{33} -6.37828e6 q^{34} +(-1.37706e7 - 2.21177e6i) q^{35} +(2.69896e6 + 4.67473e6i) q^{36} -4.41049e6 q^{37} +(-8.73287e6 - 1.51258e7i) q^{38} +(3.59659e6 - 1.01039e7i) q^{39} +(3.63736e6 - 6.30010e6i) q^{40} +(9.29943e6 + 1.61071e7i) q^{41} +(-2.18890e7 - 3.51571e6i) q^{42} +(1.68731e7 - 2.92251e7i) q^{43} +(1.88219e7 - 3.26006e7i) q^{44} -1.94005e7 q^{45} +863105. q^{46} +(1.84487e7 - 3.19540e7i) q^{47} +(-1.05054e7 + 1.81958e7i) q^{48} +(-3.01058e7 + 2.68711e7i) q^{49} +(4.80406e7 + 8.32087e7i) q^{50} +(9.91188e6 - 1.71679e7i) q^{51} +(6.18726e7 - 1.13627e7i) q^{52} +(-1.00698e7 - 1.74414e7i) q^{53} -9.95301e7 q^{54} +(6.76474e7 + 1.17169e8i) q^{55} +(-7.50025e6 - 1.96666e7i) q^{56} +5.42837e7 q^{57} +(5.54928e7 + 9.61163e7i) q^{58} +1.33587e8 q^{59} +(6.98421e7 + 1.20970e8i) q^{60} +(4.10585e7 + 7.11155e7i) q^{61} +(-2.27701e7 - 3.94390e7i) q^{62} +(-3.54199e7 + 4.35459e7i) q^{63} -1.80087e8 q^{64} +(-7.58201e7 + 2.13001e8i) q^{65} +(1.07529e8 + 1.86245e8i) q^{66} +(-8.61913e7 + 1.49288e8i) q^{67} +1.16277e8 q^{68} +(-1.34127e6 + 2.32315e6i) q^{69} +(4.61444e8 + 7.41150e7i) q^{70} +(1.21205e8 - 2.09934e8i) q^{71} +(-1.46391e7 - 2.53557e7i) q^{72} +(-1.29736e8 - 2.24710e8i) q^{73} +1.47793e8 q^{74} -2.98621e8 q^{75} +(1.59201e8 + 2.75744e8i) q^{76} +(3.86500e8 + 6.20777e7i) q^{77} +(-1.20520e8 + 3.38575e8i) q^{78} +(-1.55813e8 + 2.69876e8i) q^{79} +(2.21465e8 - 3.83588e8i) q^{80} +(6.77079e7 - 1.17274e8i) q^{81} +(-3.11618e8 - 5.39739e8i) q^{82} +2.05683e8 q^{83} +(3.99039e8 + 6.40917e7i) q^{84} +(-2.08953e8 + 3.61918e8i) q^{85} +(-5.65409e8 + 9.79316e8i) q^{86} -3.44944e8 q^{87} +(-1.02090e8 + 1.76825e8i) q^{88} +1.13906e9 q^{89} +6.50098e8 q^{90} +(3.39671e8 + 5.59065e8i) q^{91} -1.57345e7 q^{92} +1.41540e8 q^{93} +(-6.18204e8 + 1.07076e9i) q^{94} -1.14436e9 q^{95} +(4.40370e8 - 7.62743e8i) q^{96} +(6.09171e7 - 1.05511e8i) q^{97} +(1.00883e9 - 9.00435e8i) q^{98} +5.44514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) $ 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−33.5094			−1.48092			−0.740460	−	0.672100i	$-0.765392\pi$
$2$	−33.5094			−1.48092			−0.740460	+	0.672100i	$0.765392\pi$
$3$	52.0738	−	90.1944i	0.371170	−	0.642886i	−0.618575	−	0.785725i	$-0.712290\pi$
$3$	52.0738	−	90.1944i	0.371170	−	0.642886i	0.989746	+	0.142839i	$0.0456232\pi$
$4$	610.880			1.19312
$5$	−1097.77	+	1901.40i	−0.785502	+	1.36053i	0.143197	+	0.989694i	$0.454262\pi$
$5$	−1097.77	+	1901.40i	−0.785502	+	1.36053i	−0.928699	+	0.370835i	$0.879072\pi$
$6$	−1744.96	+	3022.36i	−0.549674	+	0.952063i
$7$	2263.61	+	5935.46i	0.356336	+	0.934358i
$7$	2263.61	+	5935.46i	0.356336	+	0.934358i
$8$	−3313.40			−0.286002
$9$	4418.14	+	7652.45i	0.224465	+	0.388785i
$10$	36785.7	−	63714.7i	1.16327	−	2.01483i
$11$	30811.2	−	53366.6i	0.634515	−	1.09901i	−0.352103	−	0.935961i	$-0.614533\pi$
$11$	30811.2	−	53366.6i	0.634515	−	1.09901i	0.986618	−	0.163050i	$-0.0521333\pi$
$12$	31810.8	−	55098.0i	0.442853	−	0.767043i
$13$	101284.	−	18600.6i	0.983552	−	0.180626i
$13$	101284.	−	18600.6i	0.983552	−	0.180626i
$14$	−75852.1	−	198894.i	−0.527705	−	1.38371i
$15$	114330.	+	198026.i	0.583110	+	1.00998i
$16$	−201740.			−0.769578
$17$	190343.			0.552735			0.276368	−	0.961052i	$-0.410869\pi$
$17$	190343.			0.552735			0.276368	+	0.961052i	$0.410869\pi$
$18$	−148049.	−	256429.i	−0.332415	−	0.575759i
$19$	260610.	+	451389.i	0.458774	+	0.794621i	0.998896	−	0.0469661i	$-0.0149553\pi$
$19$	260610.	+	451389.i	0.458774	+	0.794621i	−0.540122	+	0.841587i	$0.681622\pi$
$20$	−670607.	+	1.16153e6i	−0.937202	+	1.62328i
$21$	653220.	+	104917.i	0.732947	+	0.117722i
$22$	−1.03247e6	+	1.78828e6i	−0.939666	+	1.62755i
$23$	−25757.1			−0.0191921			−0.00959603	−	0.999954i	$-0.503055\pi$
$23$	−25757.1			−0.0191921			−0.00959603	+	0.999954i	$0.503055\pi$
$24$	−172541.	+	298851.i	−0.106156	+	0.183867i
$25$	−1.43364e6	−	2.48315e6i	−0.734026	−	1.27137i
$26$	−3.39398e6	+	623293.i	−1.45656	+	0.267493i
$27$	2.97021e6			1.07560
$28$	1.38279e6	+	3.62585e6i	0.425153	+	1.11481i
$29$	−1.65604e6	−	2.86834e6i	−0.434789	−	0.753077i	0.562489	−	0.826805i	$-0.309844\pi$
$29$	−1.65604e6	−	2.86834e6i	−0.434789	−	0.753077i	−0.997278	+	0.0737277i	$0.976510\pi$
$30$	−3.83114e6	−	6.63573e6i	−0.863539	−	1.49569i
$31$	679515.	+	1.17695e6i	0.132151	+	0.228893i	0.924506	−	0.381168i	$-0.124478\pi$
$31$	679515.	+	1.17695e6i	0.132151	+	0.228893i	−0.792354	+	0.610061i	$0.791145\pi$
$32$	8.45666e6			1.42569
$33$	−3.20891e6	−	5.55800e6i	−0.471026	−	0.815841i
$34$	−6.37828e6			−0.818557
$35$	−1.37706e7	−	2.21177e6i	−1.55112	−	0.249134i
$36$	2.69896e6	+	4.67473e6i	0.267815	+	0.463869i
$37$	−4.41049e6			−0.386883			−0.193441	−	0.981112i	$-0.561965\pi$
$37$	−4.41049e6			−0.386883			−0.193441	+	0.981112i	$0.561965\pi$
$38$	−8.73287e6	−	1.51258e7i	−0.679408	−	1.17677i
$39$	3.59659e6	−	1.01039e7i	0.248943	−	0.699355i
$40$	3.63736e6	−	6.30010e6i	0.224655	−	0.389114i
$41$	9.29943e6	+	1.61071e7i	0.513960	+	0.890205i	0.999869	+	0.0161952i	$0.00515531\pi$
$41$	9.29943e6	+	1.61071e7i	0.513960	+	0.890205i	−0.485909	+	0.874009i	$0.661511\pi$
$42$	−2.18890e7	−	3.51571e6i	−1.08544	−	0.174338i
$43$	1.68731e7	−	2.92251e7i	0.752641	−	1.30361i	−0.193898	−	0.981022i	$-0.562113\pi$
$43$	1.68731e7	−	2.92251e7i	0.752641	−	1.30361i	0.946539	−	0.322590i	$-0.104554\pi$
$44$	1.88219e7	−	3.26006e7i	0.757055	−	1.31126i
$45$	−1.94005e7			−0.705271
$46$	863105.			0.0284219
$47$	1.84487e7	−	3.19540e7i	0.551474	−	0.955180i	−0.446695	−	0.894686i	$-0.647399\pi$
$47$	1.84487e7	−	3.19540e7i	0.551474	−	0.955180i	0.998169	−	0.0604939i	$-0.0192676\pi$
$48$	−1.05054e7	+	1.81958e7i	−0.285645	+	0.494751i
$49$	−3.01058e7	+	2.68711e7i	−0.746049	+	0.665891i
$50$	4.80406e7	+	8.32087e7i	1.08703	+	1.88280i
$51$	9.91188e6	−	1.71679e7i	0.205159	−	0.355346i
$52$	6.18726e7	−	1.13627e7i	1.17350	−	0.215510i
$53$	−1.00698e7	−	1.74414e7i	−0.175299	−	0.303627i	0.764966	−	0.644071i	$-0.222756\pi$
$53$	−1.00698e7	−	1.74414e7i	−0.175299	−	0.303627i	−0.940265	+	0.340444i	$0.889423\pi$
$54$	−9.95301e7			−1.59288
$55$	6.76474e7	+	1.17169e8i	0.996825	+	1.72655i
$56$	−7.50025e6	−	1.96666e7i	−0.101913	−	0.267228i
$57$	5.42837e7			0.681134
$58$	5.54928e7	+	9.61163e7i	0.643888	+	1.11525i
$59$	1.33587e8			1.43526			0.717631	−	0.696423i	$-0.245226\pi$
$59$	1.33587e8			1.43526			0.717631	+	0.696423i	$0.245226\pi$
$60$	6.98421e7	+	1.20970e8i	0.695723	+	1.20503i
$61$	4.10585e7	+	7.11155e7i	0.379681	+	0.657627i	0.991016	−	0.133745i	$-0.0427003\pi$
$61$	4.10585e7	+	7.11155e7i	0.379681	+	0.657627i	−0.611334	+	0.791372i	$0.709367\pi$
$62$	−2.27701e7	−	3.94390e7i	−0.195705	−	0.338972i
$63$	−3.54199e7	+	4.35459e7i	−0.283279	+	0.348269i
$64$	−1.80087e8			−1.34175
$65$	−7.58201e7	+	2.13001e8i	−0.526834	+	1.48003i
$66$	1.07529e8	+	1.86245e8i	0.697552	+	1.20820i
$67$	−8.61913e7	+	1.49288e8i	−0.522549	+	0.905081i	0.477107	+	0.878845i	$0.341685\pi$
$67$	−8.61913e7	+	1.49288e8i	−0.522549	+	0.905081i	−0.999656	+	0.0262355i	$0.991648\pi$
$68$	1.16277e8			0.659482
$69$	−1.34127e6	+	2.32315e6i	−0.00712353	+	0.0123383i
$70$	4.61444e8	+	7.41150e7i	2.29709	+	0.368948i
$71$	1.21205e8	−	2.09934e8i	0.566056	−	0.980438i	−0.430894	−	0.902402i	$-0.641802\pi$
$71$	1.21205e8	−	2.09934e8i	0.566056	−	0.980438i	0.996951	−	0.0780357i	$-0.0248648\pi$
$72$	−1.46391e7	−	2.53557e7i	−0.0641975	−	0.111193i
$73$	−1.29736e8	−	2.24710e8i	−0.534697	−	0.926123i	−0.999178	−	0.0405396i	$-0.987092\pi$
$73$	−1.29736e8	−	2.24710e8i	−0.534697	−	0.926123i	0.464481	−	0.885583i	$-0.346241\pi$
$74$	1.47793e8			0.572942
$75$	−2.98621e8			−1.08980
$76$	1.59201e8	+	2.75744e8i	0.547375	+	0.948081i
$77$	3.86500e8	+	6.20777e7i	1.25297	+	0.201246i
$78$	−1.20520e8	+	3.38575e8i	−0.368665	+	1.03569i
$79$	−1.55813e8	+	2.69876e8i	−0.450073	+	0.779549i	−0.998390	−	0.0567217i	$-0.981935\pi$
$79$	−1.55813e8	+	2.69876e8i	−0.450073	+	0.779549i	0.548317	+	0.836270i	$0.315269\pi$
$80$	2.21465e8	−	3.83588e8i	0.604505	−	1.04703i
$81$	6.77079e7	−	1.17274e8i	0.174766	−	0.302703i
$82$	−3.11618e8	−	5.39739e8i	−0.761134	−	1.31832i
$83$	2.05683e8			0.475716			0.237858	−	0.971300i	$-0.423555\pi$
$83$	2.05683e8			0.475716			0.237858	+	0.971300i	$0.423555\pi$
$84$	3.99039e8	+	6.40917e7i	0.874497	+	0.140458i
$85$	−2.08953e8	+	3.61918e8i	−0.434174	+	0.752012i
$86$	−5.65409e8	+	9.79316e8i	−1.11460	+	1.93055i
$87$	−3.44944e8			−0.645523
$88$	−1.02090e8	+	1.76825e8i	−0.181473	+	0.314320i
$89$	1.13906e9			1.92439			0.962194	−	0.272365i	$-0.0878057\pi$
$89$	1.13906e9			1.92439			0.962194	+	0.272365i	$0.0878057\pi$
$90$	6.50098e8			1.04445
$91$	3.39671e8	+	5.59065e8i	0.519245	+	0.854626i
$92$	−1.57345e7			−0.0228985
$93$	1.41540e8			0.196202
$94$	−6.18204e8	+	1.07076e9i	−0.816688	+	1.41455i
$95$	−1.14436e9			−1.44147
$96$	4.40370e8	−	7.62743e8i	0.529173	−	0.916554i
$97$	6.09171e7	−	1.05511e8i	0.0698661	−	0.121012i	−0.828976	−	0.559284i	$-0.811076\pi$
$97$	6.09171e7	−	1.05511e8i	0.0698661	−	0.121012i	0.898842	+	0.438272i	$0.144409\pi$
$98$	1.00883e9	−	9.00435e8i	1.10484	−	0.986131i
$99$	5.44514e8			0.569705
$100$	−8.75785e8	−	1.51690e9i	−0.875785	−	1.51690i
$101$	4.20507e8	−	7.28340e8i	0.402094	−	0.696447i	−0.591885	−	0.806023i	$-0.701616\pi$
$101$	4.20507e8	−	7.28340e8i	0.402094	−	0.696447i	0.993978	+	0.109576i	$0.0349492\pi$
$102$	−3.32141e8	+	5.75286e8i	−0.303824	+	0.526239i
$103$	3.08852e8	−	5.34947e8i	0.270385	−	0.468321i	−0.698575	−	0.715537i	$-0.746182\pi$
$103$	3.08852e8	−	5.34947e8i	0.270385	−	0.468321i	0.968960	+	0.247216i	$0.0795156\pi$
$104$	−3.35596e8	+	6.16312e7i	−0.281298	+	0.0516595i
$105$	−9.16576e8	+	1.12686e9i	−0.735896	+	0.904725i
$106$	3.37434e8	+	5.84452e8i	0.259604	+	0.449648i
$107$	5.03991e8			0.371703			0.185852	−	0.982578i	$-0.440496\pi$
$107$	5.03991e8			0.371703			0.185852	+	0.982578i	$0.440496\pi$
$108$	1.81444e9			1.28332
$109$	−2.98095e8	−	5.16316e8i	−0.202272	−	0.350345i	0.746988	−	0.664837i	$-0.231499\pi$
$109$	−2.98095e8	−	5.16316e8i	−0.202272	−	0.350345i	−0.949260	+	0.314492i	$0.898166\pi$
$110$	−2.26682e9	−	3.92625e9i	−1.47622	−	2.55688i
$111$	−2.29671e8	+	3.97802e8i	−0.143599	+	0.248721i
$112$	−4.56661e8	−	1.19742e9i	−0.274229	−	0.719061i
$113$	−1.27598e9	+	2.21007e9i	−0.736195	+	1.27513i	0.218003	+	0.975948i	$0.430046\pi$
$113$	−1.27598e9	+	2.21007e9i	−0.736195	+	1.27513i	−0.954197	+	0.299178i	$0.903288\pi$
$114$	−1.81901e9			−1.00871
$115$	2.82754e7	−	4.89745e7i	0.0150754	−	0.0261114i
$116$	−1.01164e9	−	1.75221e9i	−0.518758	−	0.898515i
$117$	5.89829e8	+	6.92894e8i	0.290998	+	0.341846i
$118$	−4.47643e9			−2.12551
$119$	4.30862e8	+	1.12977e9i	0.196960	+	0.516452i
$120$	−3.78822e8	−	6.56140e8i	−0.166771	−	0.288855i
$121$	−7.19687e8	−	1.24653e9i	−0.305218	−	0.528652i
$122$	−1.37585e9	−	2.38304e9i	−0.562278	−	0.973894i
$123$	1.93703e9			0.763067
$124$	4.15102e8	+	7.18977e8i	0.157673	+	0.273097i
$125$	2.00709e9			0.735312
$126$	1.18690e9	−	1.45920e9i	0.419514	−	0.515758i
$127$	2.58537e9	+	4.47800e9i	0.881874	+	1.52745i	0.849255	+	0.527982i	$0.177051\pi$
$127$	2.58537e9	+	4.47800e9i	0.881874	+	1.52745i	0.0326186	+	0.999468i	$0.489615\pi$
$128$	1.70478e9			0.561337
$129$	−1.75730e9	−	3.04373e9i	−0.558716	−	0.967725i
$130$	2.54069e9	−	7.13753e9i	0.780200	−	2.19181i
$131$	−7.29043e8	+	1.26274e9i	−0.216288	+	0.374622i	−0.953670	−	0.300854i	$-0.902728\pi$
$131$	−7.29043e8	+	1.26274e9i	−0.216288	+	0.374622i	0.737382	+	0.675476i	$0.236062\pi$
$132$	−1.96026e9	−	3.39527e9i	−0.561993	−	0.973400i
$133$	−2.08928e9	+	2.56861e9i	−0.578982	+	0.711812i
$134$	2.88822e9	−	5.00254e9i	0.773853	−	1.34035i
$135$	−3.26062e9	+	5.64756e9i	−0.844886	+	1.46338i
$136$	−6.30684e8			−0.158083
$137$	1.79348e9			0.434965			0.217483	−	0.976064i	$-0.430215\pi$
$137$	1.79348e9			0.434965			0.217483	+	0.976064i	$0.430215\pi$
$138$	4.49451e7	−	7.78472e7i	0.0105494	−	0.0182721i
$139$	−2.70061e9	+	4.67759e9i	−0.613613	+	1.06281i	0.377013	+	0.926208i	$0.376951\pi$
$139$	−2.70061e9	+	4.67759e9i	−0.613613	+	1.06281i	−0.990626	+	0.136601i	$0.956382\pi$
$140$	−8.41218e9	−	1.35112e9i	−1.85068	−	0.297248i
$141$	−1.92138e9	−	3.32793e9i	−0.409381	−	0.709069i
$142$	−4.06152e9	+	7.03476e9i	−0.838284	+	1.45195i
$143$	2.12805e9	−	5.97830e9i	0.425568	−	1.19554i
$144$	−8.91318e8	−	1.54381e9i	−0.172743	−	0.299200i
$145$	7.27180e9			1.36611
$146$	4.34738e9	+	7.52988e9i	0.791844	+	1.37151i
$147$	8.55902e8	+	4.11465e9i	0.151181	+	0.726784i
$148$	−2.69428e9			−0.461599
$149$	5.19337e8	+	8.99518e8i	0.0863199	+	0.149510i	0.905953	−	0.423379i	$-0.139156\pi$
$149$	5.19337e8	+	8.99518e8i	0.0863199	+	0.149510i	−0.819633	+	0.572889i	$0.805823\pi$
$150$	1.00066e10			1.61390
$151$	4.73832e9	+	8.20702e9i	0.741700	+	1.28466i	0.951721	+	0.306965i	$0.0993136\pi$
$151$	4.73832e9	+	8.20702e9i	0.741700	+	1.28466i	−0.210020	+	0.977697i	$0.567353\pi$
$152$	−8.63505e8	−	1.49563e9i	−0.131211	−	0.227263i
$153$	8.40964e8	+	1.45659e9i	0.124070	+	0.214895i
$154$	−1.29514e10	−	2.08019e9i	−1.85555	−	0.298029i
$155$	−2.98381e9			−0.415220
$156$	2.19709e9	−	6.17226e9i	0.297020	−	0.834418i
$157$	−1.38290e8	−	2.39524e8i	−0.0181652	−	0.0314631i	0.856800	−	0.515649i	$-0.172449\pi$
$157$	−1.38290e8	−	2.39524e8i	−0.0181652	−	0.0314631i	−0.874965	+	0.484186i	$0.839116\pi$
$158$	5.22121e9	−	9.04340e9i	0.666522	−	1.15445i
$159$	−2.09749e9			−0.260264
$160$	−9.28348e9	+	1.60795e10i	−1.11988	+	1.93969i
$161$	−5.83040e7	−	1.52880e8i	−0.00683883	−	0.0179323i
$162$	−2.26885e9	+	3.92976e9i	−0.258814	+	0.448280i
$163$	1.67252e8	+	2.89689e8i	0.0185578	+	0.0321431i	0.875155	−	0.483842i	$-0.160759\pi$
$163$	1.67252e8	+	2.89689e8i	0.0185578	+	0.0321431i	−0.856597	+	0.515985i	$0.827426\pi$
$164$	5.68084e9	+	9.83950e9i	0.613218	+	1.06213i
$165$	1.40906e10			1.47997
$166$	−6.89232e9			−0.704497
$167$	7.88290e8	+	1.36536e9i	0.0784263	+	0.135838i	0.902571	−	0.430541i	$-0.141677\pi$
$167$	7.88290e8	+	1.36536e9i	0.0784263	+	0.135838i	−0.824145	+	0.566379i	$0.808344\pi$
$168$	−2.16438e9	−	3.47633e8i	−0.209625	−	0.0336689i
$169$	9.91254e9	−	3.76789e9i	0.934748	−	0.355311i
$170$	7.00190e9	−	1.21277e10i	0.642978	−	1.11367i
$171$	−2.30282e9	+	3.98860e9i	−0.205958	+	0.356729i
$172$	1.03075e10	−	1.78530e10i	0.897994	−	1.55537i
$173$	2.23151e9	+	3.86509e9i	0.189405	+	0.328059i	0.945052	−	0.326920i	$-0.106011\pi$
$173$	2.23151e9	+	3.86509e9i	0.189405	+	0.328059i	−0.755647	+	0.654979i	$0.772677\pi$
$174$	1.15589e10			0.955969
$175$	1.14934e10	−	1.41302e10i	0.926355	−	1.13888i
$176$	−6.21586e9	+	1.07662e10i	−0.488309	+	0.845775i
$177$	6.95640e9	−	1.20488e10i	0.532727	−	0.922710i
$178$	−3.81693e10			−2.84987
$179$	4.05006e9	−	7.01490e9i	0.294864	−	0.510720i	−0.680089	−	0.733130i	$-0.738059\pi$
$179$	4.05006e9	−	7.01490e9i	0.294864	−	0.510720i	0.974953	+	0.222409i	$0.0713922\pi$
$180$	−1.18514e10			−0.841476
$181$	−2.61947e10			−1.81409			−0.907047	−	0.421030i	$-0.861669\pi$
$181$	−2.61947e10			−1.81409			−0.907047	+	0.421030i	$0.861669\pi$
$182$	−1.13822e10	−	1.87339e10i	−0.768960	−	1.26563i
$183$	8.55229e9			0.563706
$184$	8.53437e7			0.00548897
$185$	4.84171e9	−	8.38609e9i	0.303897	−	0.526365i
$186$	−4.74291e9			−0.290560
$187$	5.86470e9	−	1.01580e10i	0.350719	−	0.607462i
$188$	1.12699e10	−	1.95201e10i	0.657977	−	1.13965i
$189$	6.72340e9	+	1.76296e10i	0.383275	+	1.00500i
$190$	3.83468e10			2.13471
$191$	−7.18569e9	−	1.24460e10i	−0.390678	−	0.676674i	0.601861	−	0.798601i	$-0.294426\pi$
$191$	−7.18569e9	−	1.24460e10i	−0.390678	−	0.676674i	−0.992539	+	0.121927i	$0.961093\pi$
$192$	−9.37778e9	+	1.62428e10i	−0.498018	+	0.862592i
$193$	−6.61248e9	+	1.14532e10i	−0.343049	+	0.594179i	−0.984997	−	0.172569i	$-0.944793\pi$
$193$	−6.61248e9	+	1.14532e10i	−0.343049	+	0.594179i	0.641948	+	0.766748i	$0.278126\pi$
$194$	−2.04129e9	+	3.53563e9i	−0.103466	+	0.179208i
$195$	1.52633e10	+	1.79303e10i	0.755947	+	0.888039i
$196$	−1.83910e10	+	1.64150e10i	−0.890130	+	0.794491i
$197$	−1.46779e10	−	2.54229e10i	−0.694332	−	1.20262i	−0.970405	−	0.241481i	$-0.922367\pi$
$197$	−1.46779e10	−	2.54229e10i	−0.694332	−	1.20262i	0.276074	−	0.961136i	$-0.410967\pi$
$198$	−1.82463e10			−0.843688
$199$	−2.87416e10			−1.29919			−0.649594	−	0.760281i	$-0.725061\pi$
$199$	−2.87416e10			−1.29919			−0.649594	+	0.760281i	$0.725061\pi$
$200$	4.75024e9	+	8.22766e9i	0.209933	+	0.363615i
$201$	8.97661e9	+	1.55479e10i	0.387909	+	0.671878i
$202$	−1.40909e10	+	2.44062e10i	−0.595469	+	1.03138i
$203$	1.32763e10	−	1.63221e10i	0.548712	−	0.674597i
$204$	6.05497e9	−	1.04875e10i	0.244780	−	0.423972i
$205$	−4.08346e10			−1.61487
$206$	−1.03494e10	+	1.79258e10i	−0.400419	+	0.693546i
$207$	−1.13799e8	−	1.97105e8i	−0.00430795	−	0.00746158i
$208$	−2.04331e10	+	3.75248e9i	−0.756920	+	0.139006i
$209$	3.21188e10			1.16440
$210$	3.07139e10	−	3.77602e10i	1.08980	−	1.33982i
$211$	6.06681e9	+	1.05080e10i	0.210712	+	0.364964i	0.951938	−	0.306292i	$-0.0990884\pi$
$211$	6.06681e9	+	1.05080e10i	0.210712	+	0.364964i	−0.741225	+	0.671256i	$0.765755\pi$
$212$	−6.15145e9	−	1.06546e10i	−0.209154	−	0.362265i
$213$	−1.26232e10	−	2.18641e10i	−0.420207	−	0.727819i
$214$	−1.68884e10			−0.550463
$215$	3.70457e10	+	6.41651e10i	1.18240	+	2.04798i
$216$	−9.84152e9			−0.307624
$217$	−5.44761e9	+	6.69739e9i	−0.166777	+	0.205039i
$218$	9.98899e9	+	1.73014e10i	0.299549	+	0.518834i
$219$	−2.70234e10			−0.793855
$220$	4.13244e10	+	7.15760e10i	1.18934	+	2.05999i
$221$	1.92788e10	−	3.54049e9i	0.543644	−	0.0998385i
$222$	7.69613e9	−	1.33301e10i	0.212659	−	0.368337i
$223$	3.65860e10	+	6.33688e10i	0.990701	+	1.71595i	0.613177	+	0.789946i	$0.289891\pi$
$223$	3.65860e10	+	6.33688e10i	0.990701	+	1.71595i	0.377524	+	0.926000i	$0.376775\pi$
$224$	1.91426e10	+	5.01942e10i	0.508024	+	1.33210i
$225$	1.26681e10	−	2.19418e10i	0.329526	−	0.570756i
$226$	4.27575e10	−	7.40581e10i	1.09025	−	1.88836i
$227$	−3.95057e10			−0.987514			−0.493757	−	0.869600i	$-0.664377\pi$
$227$	−3.95057e10			−0.987514			−0.493757	+	0.869600i	$0.664377\pi$
$228$	3.31608e10			0.812678
$229$	1.01141e10	−	1.75181e10i	0.243034	−	0.420947i	−0.718543	−	0.695482i	$-0.755191\pi$
$229$	1.01141e10	−	1.75181e10i	0.243034	−	0.420947i	0.961577	+	0.274535i	$0.0885240\pi$
$230$	−9.47492e8	+	1.64111e9i	−0.0223255	+	0.0386688i
$231$	2.57256e10	−	3.16275e10i	0.594444	−	0.730821i
$232$	5.48711e9	+	9.50396e9i	0.124351	+	0.215382i
$233$	−3.83735e10	+	6.64649e10i	−0.852963	+	1.47738i	0.0255586	+	0.999673i	$0.491864\pi$
$233$	−3.83735e10	+	6.64649e10i	−0.852963	+	1.47738i	−0.878522	+	0.477702i	$0.841470\pi$
$234$	−1.97648e10	−	2.32184e10i	−0.430944	−	0.506246i
$235$	4.05049e10	+	7.01565e10i	0.866367	+	1.50059i
$236$	8.16058e10			1.71245
$237$	1.62276e10	+	2.81070e10i	0.334107	+	0.578691i
$238$	−1.44379e10	−	3.78581e10i	−0.291681	−	0.764825i
$239$	−8.36249e10			−1.65785			−0.828924	−	0.559361i	$-0.811047\pi$
$239$	−8.36249e10			−1.65785			−0.828924	+	0.559361i	$0.811047\pi$
$240$	−2.30650e10	−	3.99498e10i	−0.448749	−	0.777256i
$241$	5.11323e10			0.976380			0.488190	−	0.872737i	$-0.337657\pi$
$241$	5.11323e10			0.976380			0.488190	+	0.872737i	$0.337657\pi$
$242$	2.41163e10	+	4.17706e10i	0.452003	+	0.782892i
$243$	2.21797e10	+	3.84165e10i	0.408064	+	0.706788i
$244$	2.50818e10	+	4.34430e10i	0.453007	+	0.784631i
$245$	−1.80434e10	−	8.67414e10i	−0.319941	−	1.53808i
$246$	−6.49086e10			−1.13004
$247$	3.47918e10	+	4.08712e10i	0.594758	+	0.698684i
$248$	−2.25151e9	−	3.89972e9i	−0.0377955	−	0.0654638i
$249$	1.07107e10	−	1.85515e10i	0.176572	−	0.305831i
$250$	−6.72563e10			−1.08894
$251$	5.02007e10	−	8.69502e10i	0.798323	−	1.38274i	−0.122385	−	0.992483i	$-0.539054\pi$
$251$	5.02007e10	−	8.69502e10i	0.798323	−	1.38274i	0.920708	−	0.390253i	$-0.127612\pi$
$252$	−2.16373e10	+	2.66013e10i	−0.337987	+	0.415528i
$253$	−7.93607e8	+	1.37457e9i	−0.0121776	+	0.0210923i
$254$	−8.66343e10	−	1.50055e11i	−1.30598	−	2.26203i
$255$	2.17620e10	+	3.76929e10i	0.322305	+	0.558249i
$256$	3.50781e10			0.510453
$257$	−9.34564e10			−1.33632			−0.668159	−	0.744018i	$-0.732917\pi$
$257$	−9.34564e10			−1.33632			−0.668159	+	0.744018i	$0.732917\pi$
$258$	5.88859e10	+	1.01993e11i	0.827414	+	1.43312i
$259$	−9.98362e9	−	2.61783e10i	−0.137860	−	0.361487i
$260$	−4.63170e10	+	1.30118e11i	−0.628579	+	1.76586i
$261$	1.46332e10	−	2.53455e10i	0.195190	−	0.338079i
$262$	2.44298e10	−	4.23136e10i	0.320305	−	0.554785i
$263$	−1.47623e10	+	2.55691e10i	−0.190263	+	0.329545i	−0.945337	−	0.326094i	$-0.894267\pi$
$263$	−1.47623e10	+	2.55691e10i	−0.190263	+	0.329545i	0.755074	+	0.655639i	$0.227601\pi$
$264$	1.06324e10	+	1.84159e10i	0.134715	+	0.233332i
$265$	4.42175e10			0.550792
$266$	7.00107e10	−	8.60724e10i	0.857426	−	1.05414i
$267$	5.93153e10	−	1.02737e11i	0.714276	−	1.23716i
$268$	−5.26525e10	+	9.11968e10i	−0.623466	+	1.07987i
$269$	1.71080e10			0.199211			0.0996057	−	0.995027i	$-0.468242\pi$
$269$	1.71080e10			0.199211			0.0996057	+	0.995027i	$0.468242\pi$
$270$	1.09261e11	−	1.89246e11i	1.25121	−	2.16716i
$271$	−2.36509e10			−0.266370			−0.133185	−	0.991091i	$-0.542520\pi$
$271$	−2.36509e10			−0.266370			−0.133185	+	0.991091i	$0.542520\pi$
$272$	−3.83999e10			−0.425373
$273$	6.81125e10	−	1.52380e9i	0.742155	−	0.0166034i
$274$	−6.00985e10			−0.644149
$275$	−1.76689e11			−1.86300
$276$	−8.19354e8	+	1.41916e9i	−0.00849926	+	0.0147211i
$277$	1.67010e11			1.70444			0.852221	−	0.523181i	$-0.175255\pi$
$277$	1.67010e11			1.70444			0.852221	+	0.523181i	$0.175255\pi$
$278$	9.04957e10	−	1.56743e11i	0.908712	−	1.57394i
$279$	−6.00439e9	+	1.03999e10i	−0.0593266	+	0.102757i
$280$	4.56275e10	+	7.32848e9i	0.443625	+	0.0712529i
$281$	−6.47070e10			−0.619117			−0.309559	−	0.950880i	$-0.600181\pi$
$281$	−6.47070e10			−0.619117			−0.309559	+	0.950880i	$0.600181\pi$
$282$	6.43844e10	+	1.11517e11i	0.606261	+	1.05008i
$283$	−1.00151e11	+	1.73466e11i	−0.928144	+	1.60759i	−0.141719	+	0.989907i	$0.545263\pi$
$283$	−1.00151e11	+	1.73466e11i	−0.928144	+	1.60759i	−0.786425	+	0.617686i	$0.788070\pi$
$284$	7.40420e10	−	1.28244e11i	0.675376	−	1.16978i
$285$	−5.95911e10	+	1.03215e11i	−0.535032	+	0.926703i
$286$	−7.13095e10	+	2.00329e11i	−0.630232	+	1.77051i
$287$	−7.45527e10	+	9.16566e10i	−0.648627	+	0.797435i
$288$	3.73627e10	+	6.47142e10i	0.320017	+	0.554285i
$289$	−8.23574e10			−0.694484
$290$	−2.43674e11			−2.02310
$291$	−6.34436e9	−	1.09888e10i	−0.0518644	−	0.0898318i
$292$	−7.92532e10	−	1.37271e11i	−0.637961	−	1.10498i
$293$	−4.02226e10	+	6.96676e10i	−0.318835	+	0.552239i	−0.980245	−	0.197786i	$-0.936625\pi$
$293$	−4.02226e10	+	6.96676e10i	−0.318835	+	0.552239i	0.661410	+	0.750024i	$0.269958\pi$
$294$	−2.86808e10	−	1.37880e11i	−0.223887	−	1.07631i
$295$	−1.46648e11	+	2.54003e11i	−1.12740	+	1.95272i
$296$	1.46137e10			0.110649
$297$	9.15159e10	−	1.58510e11i	0.682484	−	1.18210i
$298$	−1.74027e10	−	3.01423e10i	−0.127833	−	0.221413i
$299$	−2.60879e9	+	4.79096e8i	−0.0188764	+	0.00346659i
$300$	−1.82422e11			−1.30026
$301$	2.11659e11	+	3.39956e10i	1.48623	+	0.238712i
$302$	−1.58778e11	−	2.75012e11i	−1.09840	−	1.90248i
$303$	−4.37948e10	−	7.58548e10i	−0.298491	−	0.517001i
$304$	−5.25755e10	−	9.10634e10i	−0.353063	−	0.611523i
$305$	−1.80292e11			−1.19296
$306$	−2.81802e10	−	4.88095e10i	−0.183737	−	0.318242i
$307$	3.40004e10			0.218455			0.109227	−	0.994017i	$-0.465162\pi$
$307$	3.40004e10			0.218455			0.109227	+	0.994017i	$0.465162\pi$
$308$	2.36105e11	+	3.79220e10i	1.49495	+	0.240112i
$309$	−3.21662e10	−	5.57134e10i	−0.200718	−	0.347654i
$310$	9.99856e10			0.614908
$311$	6.99004e10	+	1.21071e11i	0.423700	+	0.733869i	0.996298	−	0.0859666i	$-0.0273978\pi$
$311$	6.99004e10	+	1.21071e11i	0.423700	+	0.733869i	−0.572598	+	0.819836i	$0.694065\pi$
$312$	−1.19170e10	+	3.34782e10i	−0.0711983	+	0.200017i
$313$	1.47249e11	−	2.55044e11i	0.867170	−	1.50198i	0.00229386	−	0.999997i	$-0.499270\pi$
$313$	1.47249e11	−	2.55044e11i	0.867170	−	1.50198i	0.864876	−	0.501985i	$-0.167397\pi$
$314$	4.63400e9	+	8.02632e9i	0.0269013	+	0.0465943i
$315$	−4.39150e10	−	1.15151e11i	−0.251313	−	0.658975i
$316$	−9.51832e10	+	1.64862e11i	−0.536993	+	0.930099i
$317$	7.63075e10	−	1.32168e11i	0.424424	−	0.735125i	−0.571942	−	0.820294i	$-0.693810\pi$
$317$	7.63075e10	−	1.32168e11i	0.424424	−	0.735125i	0.996366	+	0.0851694i	$0.0271432\pi$
$318$	7.02858e10			0.385430
$319$	−2.04098e11			−1.10352
$320$	1.97694e11	−	3.42416e11i	1.05395	−	1.82549i
$321$	2.62447e10	−	4.54572e10i	0.137965	−	0.238963i
$322$	1.95373e9	+	5.12292e9i	0.0101278	+	0.0265562i
$323$	4.96052e10	+	8.59188e10i	0.253581	+	0.439215i
$324$	4.13614e10	−	7.16400e10i	0.208518	−	0.361163i
$325$	−1.91394e11	−	2.24837e11i	−0.951596	−	1.11787i
$326$	−5.60452e9	−	9.70731e9i	−0.0274827	−	0.0476014i
$327$	−6.20918e10			−0.300310
$328$	−3.08128e10	−	5.33693e10i	−0.146994	−	0.254601i
$329$	2.31422e11	+	3.71700e10i	1.08899	+	0.174908i
$330$	−4.72168e11			−2.19171
$331$	−1.22890e11	−	2.12851e11i	−0.562717	−	0.974654i	−0.997258	−	0.0740020i	$-0.976423\pi$
$331$	−1.22890e11	−	2.12851e11i	−0.562717	−	0.974654i	0.434541	−	0.900652i	$-0.356910\pi$
$332$	1.25648e11			0.567588
$333$	−1.94862e10	−	3.37511e10i	−0.0868416	−	0.150414i
$334$	−2.64151e10	−	4.57523e10i	−0.116143	−	0.201166i
$335$	−1.89237e11	−	3.27768e11i	−0.820926	−	1.42188i
$336$	−1.31781e11	−	2.11660e10i	−0.564060	−	0.0905966i
$337$	3.78854e11			1.60006			0.800032	−	0.599957i	$-0.204816\pi$
$337$	3.78854e11			1.60006			0.800032	+	0.599957i	$0.204816\pi$
$338$	−3.32163e11	+	1.26260e11i	−1.38429	+	0.526187i
$339$	1.32891e11	+	2.30173e11i	0.546507	+	0.946578i
$340$	−1.27645e11	+	2.21088e11i	−0.518024	+	0.897244i
$341$	8.37467e10			0.335408
$342$	7.71662e10	−	1.33656e11i	0.305007	−	0.528287i
$343$	−2.27640e11	−	1.17866e11i	−0.888025	−	0.459796i
$344$	−5.59075e10	+	9.68347e10i	−0.215257	+	0.372836i
$345$	−2.94482e9	−	5.10057e9i	−0.0111911	−	0.0193835i
$346$	−7.47766e10	−	1.29517e11i	−0.280494	−	0.485830i
$347$	4.87213e11			1.80400			0.901999	−	0.431738i	$-0.142100\pi$
$347$	4.87213e11			1.80400			0.901999	+	0.431738i	$0.142100\pi$
$348$	−2.10719e11			−0.770190
$349$	−2.71249e11	−	4.69817e11i	−0.978709	−	1.69517i	−0.667107	−	0.744962i	$-0.732468\pi$
$349$	−2.71249e11	−	4.69817e11i	−0.978709	−	1.69517i	−0.311602	−	0.950213i	$-0.600866\pi$
$350$	−3.85137e11	+	4.73495e11i	−1.37186	+	1.68659i
$351$	3.00836e11	−	5.52476e10i	1.05791	−	0.194282i
$352$	2.60560e11	−	4.51303e11i	0.904619	−	1.56685i
$353$	−1.71856e11	+	2.97664e11i	−0.589087	+	1.02033i	0.405265	+	0.914199i	$0.367179\pi$
$353$	−1.71856e11	+	2.97664e11i	−0.589087	+	1.02033i	−0.994352	+	0.106129i	$0.966154\pi$
$354$	−2.33105e11	+	4.03749e11i	−0.788926	+	1.36646i
$355$	2.66112e11	+	4.60919e11i	0.889276	+	1.54027i
$356$	6.95831e11			2.29603
$357$	1.24336e11	+	1.99702e10i	0.405126	+	0.0650693i
$358$	−1.35715e11	+	2.35065e11i	−0.436671	+	0.756336i
$359$	−1.33202e11	+	2.30713e11i	−0.423239	+	0.733072i	−0.996254	−	0.0864732i	$-0.972440\pi$
$359$	−1.33202e11	+	2.30713e11i	−0.423239	+	0.733072i	0.573015	+	0.819545i	$0.305774\pi$
$360$	6.42816e10			0.201709
$361$	2.55091e10	−	4.41831e10i	0.0790521	−	0.136922i
$362$	8.77768e11			2.68653
$363$	−1.49907e11			−0.453151
$364$	2.07498e11	+	3.41521e11i	0.619524	+	1.01967i
$365$	5.69683e11			1.68002
$366$	−2.86582e11			−0.834804
$367$	−1.77581e11	+	3.07579e11i	−0.510974	+	0.885034i	0.488945	+	0.872315i	$0.337382\pi$
$367$	−1.77581e11	+	3.07579e11i	−0.510974	+	0.885034i	−0.999919	+	0.0127189i	$0.995951\pi$
$368$	5.19624e9			0.0147698
$369$	−8.21725e10	+	1.42327e11i	−0.230732	+	0.399640i
$370$	−1.62243e11	+	2.81013e11i	−0.450047	+	0.779504i
$371$	8.07288e10	−	9.92496e10i	0.221231	−	0.271986i
$372$	8.64637e10			0.234094
$373$	−5.94970e10	−	1.03052e11i	−0.159149	−	0.275655i	0.775413	−	0.631455i	$-0.217542\pi$
$373$	−5.94970e10	−	1.03052e11i	−0.159149	−	0.275655i	−0.934562	+	0.355800i	$0.884209\pi$
$374$	−1.96523e11	+	3.40387e11i	−0.519386	+	0.899603i
$375$	1.04517e11	−	1.81028e11i	0.272926	−	0.472722i
$376$	−6.11279e10	+	1.05877e11i	−0.157723	+	0.273184i
$377$	−2.21083e11	−	2.59715e11i	−0.563663	−	0.662156i
$378$	−2.25297e11	−	5.90757e11i	−0.567600	−	1.48832i
$379$	3.93560e11	+	6.81667e11i	0.979795	+	1.69705i	0.663108	+	0.748524i	$0.269237\pi$
$379$	3.93560e11	+	6.81667e11i	0.979795	+	1.69705i	0.316686	+	0.948530i	$0.397430\pi$
$380$	−6.99066e11			−1.71986
$381$	5.38520e11			1.30930
$382$	2.40788e11	+	4.17058e11i	0.578562	+	1.00210i
$383$	1.28111e11	+	2.21894e11i	0.304222	+	0.526928i	0.977088	−	0.212837i	$-0.0682703\pi$
$383$	1.28111e11	+	2.21894e11i	0.304222	+	0.526928i	−0.672866	+	0.739764i	$0.734937\pi$
$384$	8.87744e10	−	1.53762e11i	0.208352	−	0.360876i
$385$	−5.42323e11	+	6.66742e11i	−1.25801	+	1.54662i
$386$	2.21580e11	−	3.83788e11i	0.508029	−	0.879931i
$387$	2.98192e11			0.675766
$388$	3.72130e10	−	6.44548e10i	0.0833589	−	0.144382i
$389$	−8.88316e10	−	1.53861e11i	−0.196695	−	0.340686i	0.750760	−	0.660575i	$-0.229688\pi$
$389$	−8.88316e10	−	1.53861e11i	−0.196695	−	0.340686i	−0.947455	+	0.319889i	$0.896354\pi$
$390$	−5.11463e11	−	6.00834e11i	−1.11950	−	1.31511i
$391$	−4.90269e9			−0.0106081
$392$	9.97526e10	−	8.90348e10i	0.213372	−	0.190446i
$393$	7.59280e10	+	1.31511e11i	0.160559	+	0.278097i
$394$	4.91849e11	+	8.51907e11i	1.02825	+	1.78098i
$395$	−3.42095e11	−	5.92526e11i	−0.707066	−	1.22467i
$396$	3.32632e11			0.679729
$397$	3.87269e11	+	6.70770e11i	0.782448	+	1.35524i	0.930512	+	0.366262i	$0.119363\pi$
$397$	3.87269e11	+	6.70770e11i	0.782448	+	1.35524i	−0.148064	+	0.988978i	$0.547304\pi$
$398$	9.63113e11			1.92399
$399$	1.22877e11	+	3.22199e11i	0.242713	+	0.636423i
$400$	2.89224e11	+	5.00951e11i	0.564890	+	0.978419i
$401$	8.06467e11			1.55753			0.778766	−	0.627314i	$-0.215846\pi$
$401$	8.06467e11			1.55753			0.778766	+	0.627314i	$0.215846\pi$
$402$	−3.00801e11	−	5.21002e11i	−0.574462	−	0.994998i
$403$	9.07162e10	+	1.06568e11i	0.171322	+	0.201258i
$404$	2.56879e11	−	4.44928e11i	0.479748	−	0.830948i
$405$	1.48656e11	+	2.57479e11i	0.274558	+	0.475548i
$406$	−4.44881e11	+	5.46945e11i	−0.812599	+	0.999025i
$407$	−1.35893e11	+	2.35373e11i	−0.245483	+	0.425188i
$408$	−3.28421e10	+	5.68841e10i	−0.0586759	+	0.101630i
$409$	−7.22376e11			−1.27646			−0.638232	−	0.769844i	$-0.720334\pi$
$409$	−7.22376e11			−1.27646			−0.638232	+	0.769844i	$0.720334\pi$
$410$	1.36834e12			2.39149
$411$	9.33934e10	−	1.61762e11i	0.161446	−	0.279633i
$412$	1.88671e11	−	3.26789e11i	0.322603	−	0.558765i
$413$	3.02389e11	+	7.92902e11i	0.511436	+	1.34105i
$414$	3.81332e9	+	6.60487e9i	0.00637973	+	0.0110500i
$415$	−2.25793e11	+	3.91085e11i	−0.373676	+	0.647225i
$416$	8.56527e11	−	1.57299e11i	1.40224	−	0.257516i
$417$	2.81261e11	+	4.87159e11i	0.455510	+	0.788967i
$418$	−1.07628e12			−1.72438
$419$	−3.20002e11	−	5.54260e11i	−0.507213	−	0.878518i	−0.999965	−	0.00834843i	$-0.997343\pi$
$419$	−3.20002e11	−	5.54260e11i	−0.507213	−	0.878518i	0.492753	−	0.870169i	$-0.335991\pi$
$420$	−5.59918e11	+	6.88373e11i	−0.878016	+	1.07945i
$421$	−7.80808e11			−1.21136			−0.605682	−	0.795707i	$-0.707100\pi$
$421$	−7.80808e11			−1.21136			−0.605682	+	0.795707i	$0.707100\pi$
$422$	−2.03295e11	−	3.52118e11i	−0.312048	−	0.540483i
$423$	3.26036e11			0.495146
$424$	3.33654e10	+	5.77905e10i	0.0501360	+	0.0868381i
$425$	−2.72884e11	−	4.72650e11i	−0.405722	−	0.702731i
$426$	4.22997e11	+	7.32653e11i	0.622292	+	1.07784i
$427$	−3.29163e11	+	4.04679e11i	−0.479165	+	0.589095i
$428$	3.07878e11			0.443488
$429$	−4.28394e11	−	5.03251e11i	−0.610641	−	0.717342i
$430$	−1.24138e12	−	2.15013e12i	−1.75104	−	3.03289i
$431$	1.75289e11	−	3.03610e11i	0.244685	−	0.423807i	−0.717358	−	0.696705i	$-0.754649\pi$
$431$	1.75289e11	−	3.03610e11i	0.244685	−	0.423807i	0.962043	+	0.272898i	$0.0879822\pi$
$432$	−5.99212e11			−0.827758
$433$	−1.20459e11	+	2.08642e11i	−0.164681	+	0.285237i	−0.936542	−	0.350555i	$-0.885993\pi$
$433$	−1.20459e11	+	2.08642e11i	−0.164681	+	0.285237i	0.771861	+	0.635792i	$0.219326\pi$
$434$	1.82546e11	−	2.24426e11i	0.246984	−	0.303647i
$435$	3.78670e11	−	6.55876e11i	0.507060	−	0.878253i
$436$	−1.82100e11	−	3.15407e11i	−0.241336	−	0.418006i
$437$	−6.71255e9	−	1.16265e10i	−0.00880483	−	0.0152504i
$438$	9.05538e11			1.17564
$439$	−1.88428e11			−0.242133			−0.121067	−	0.992644i	$-0.538631\pi$
$439$	−1.88428e11			−0.242133			−0.121067	+	0.992644i	$0.538631\pi$
$440$	−2.24143e11	−	3.88227e11i	−0.285094	−	0.493797i
$441$	−3.38641e11	−	1.11663e11i	−0.426350	−	0.140583i
$442$	−6.46020e11	+	1.18640e11i	−0.805093	+	0.147853i
$443$	2.13227e11	−	3.69321e11i	0.263043	−	0.455603i	−0.704006	−	0.710194i	$-0.748607\pi$
$443$	2.13227e11	−	3.69321e11i	0.263043	−	0.455603i	0.967049	+	0.254590i	$0.0819406\pi$
$444$	−1.40301e11	+	2.43009e11i	−0.171332	+	0.296756i
$445$	−1.25043e12	+	2.16581e12i	−1.51161	+	2.61819i
$446$	−1.22597e12	−	2.12345e12i	−1.46715	−	2.54118i
$447$	1.08175e11			0.128158
$448$	−4.07645e11	−	1.06890e12i	−0.478114	−	1.25367i
$449$	−1.35747e11	+	2.35120e11i	−0.157623	+	0.273012i	−0.934011	−	0.357244i	$-0.883716\pi$
$449$	−1.35747e11	+	2.35120e11i	−0.157623	+	0.273012i	0.776388	+	0.630255i	$0.217050\pi$
$450$	−4.24500e11	+	7.35256e11i	−0.488002	+	0.845245i
$451$	1.14611e12			1.30446
$452$	−7.79473e11	+	1.35009e12i	−0.878372	+	1.52138i
$453$	9.86969e11			1.10119
$454$	1.32381e12			1.46243
$455$	−1.43589e12	+	3.21234e10i	−1.57061	+	0.0351374i
$456$	−1.79864e11			−0.194806
$457$	1.49292e12			1.60108			0.800541	−	0.599277i	$-0.204545\pi$
$457$	1.49292e12			1.60108			0.800541	+	0.599277i	$0.204545\pi$
$458$	−3.38917e11	+	5.87021e11i	−0.359914	+	0.623389i
$459$	5.65360e11			0.594522
$460$	1.72729e10	−	2.99175e10i	0.0179868	−	0.0311541i
$461$	8.92029e10	−	1.54504e11i	0.0919867	−	0.159326i	−0.816360	−	0.577543i	$-0.804012\pi$
$461$	8.92029e10	−	1.54504e11i	0.0919867	−	0.159326i	0.908347	+	0.418217i	$0.137345\pi$
$462$	−8.62048e11	+	1.05982e12i	−0.880324	+	1.08229i
$463$	−9.13660e11			−0.923996			−0.461998	−	0.886881i	$-0.652867\pi$
$463$	−9.13660e11			−0.923996			−0.461998	+	0.886881i	$0.652867\pi$
$464$	3.34089e11	+	5.78659e11i	0.334604	+	0.579552i
$465$	−1.55378e11	+	2.69123e11i	−0.154117	+	0.266939i
$466$	1.28587e12	−	2.22720e12i	1.26317	−	2.18788i
$467$	7.63391e11	−	1.32223e12i	0.742713	−	1.28642i	−0.208543	−	0.978013i	$-0.566872\pi$
$467$	7.63391e11	−	1.32223e12i	0.742713	−	1.28642i	0.951256	−	0.308403i	$-0.0997947\pi$
$468$	3.60314e11	+	4.23275e11i	0.347197	+	0.407865i
$469$	−1.08119e12	−	1.73656e11i	−1.03187	−	0.165734i
$470$	−1.35729e12	−	2.35090e12i	−1.28302	−	2.22226i
$471$	−2.88050e10			−0.0269696
$472$	−4.42629e11			−0.410488
$473$	−1.03976e12	−	1.80092e12i	−0.955123	−	1.65432i
$474$	−5.43776e11	−	9.41848e11i	−0.494786	−	0.856995i
$475$	7.47243e11	−	1.29426e12i	0.673505	−	1.16654i
$476$	2.63205e11	+	6.90156e11i	0.234997	+	0.616192i
$477$	8.89798e10	−	1.54118e11i	0.0786971	−	0.136307i
$478$	2.80222e12			2.45514
$479$	−3.58197e11	+	6.20416e11i	−0.310894	+	0.538484i	−0.978556	−	0.205980i	$-0.933962\pi$
$479$	−3.58197e11	+	6.20416e11i	−0.310894	+	0.538484i	0.667662	+	0.744464i	$0.267295\pi$
$480$	9.66852e11	+	1.67464e12i	0.831332	+	1.43991i
$481$	−4.46714e11	+	8.20376e10i	−0.380519	+	0.0698811i
$482$	−1.71341e12			−1.44594
$483$	−1.68250e10	−	2.70236e9i	−0.0140668	−	0.00225934i
$484$	−4.39642e11	−	7.61483e11i	−0.364163	−	0.630748i
$485$	1.33746e11	+	2.31655e11i	0.109760	+	0.190110i
$486$	−7.43230e11	−	1.28731e12i	−0.604310	−	1.04670i
$487$	1.02838e11			0.0828464			0.0414232	−	0.999142i	$-0.486811\pi$
$487$	1.02838e11			0.0828464			0.0414232	+	0.999142i	$0.486811\pi$
$488$	−1.36044e11	−	2.35634e11i	−0.108590	−	0.188083i
$489$	3.48378e10			0.0275525
$490$	6.04622e11	+	2.90665e12i	0.473807	+	2.27777i
$491$	−9.93443e11	−	1.72069e12i	−0.771394	−	1.33609i	−0.936799	−	0.349868i	$-0.886226\pi$
$491$	−9.93443e11	−	1.72069e12i	−0.771394	−	1.33609i	0.165405	−	0.986226i	$-0.447107\pi$
$492$	1.18329e12			0.910434
$493$	−3.15215e11	−	5.45968e11i	−0.240323	−	0.416252i
$494$	−1.16585e12	−	1.36957e12i	−0.880789	−	1.03470i
$495$	−5.97752e11	+	1.03534e12i	−0.447505	+	0.775101i
$496$	−1.37085e11	−	2.37439e11i	−0.101701	−	0.176151i
$497$	1.52042e12	+	2.44202e11i	1.11779	+	0.179533i
$498$	−3.58909e11	+	6.21649e11i	−0.261488	+	0.452911i
$499$	1.21587e12	−	2.10594e12i	0.877876	−	1.52053i	0.0242095	−	0.999707i	$-0.492293\pi$
$499$	1.21587e12	−	2.10594e12i	0.877876	−	1.52053i	0.853667	−	0.520819i	$-0.174374\pi$
$500$	1.22609e12			0.877318
$501$	1.64197e11			0.116438
$502$	−1.68220e12	+	2.91365e12i	−1.18225	+	2.04772i
$503$	3.02270e11	−	5.23547e11i	0.210542	−	0.364670i	−0.741342	−	0.671127i	$-0.765810\pi$
$503$	3.02270e11	−	5.23547e11i	0.210542	−	0.364670i	0.951884	+	0.306457i	$0.0991437\pi$
$504$	1.17360e11	−	1.44285e11i	0.0810185	−	0.0996056i
$505$	9.23242e11	+	1.59910e12i	0.631691	+	1.09412i
$506$	2.65933e10	−	4.60610e10i	0.0180341	−	0.0312360i
$507$	1.76341e11	−	1.09026e12i	0.118527	−	0.732817i
$508$	1.57935e12	+	2.73552e12i	1.05219	+	1.82244i
$509$	2.05811e12			1.35906			0.679529	−	0.733648i	$-0.262184\pi$
$509$	2.05811e12			1.35906			0.679529	+	0.733648i	$0.262184\pi$
$510$	−7.29231e11	−	1.26306e12i	−0.477309	−	0.826723i
$511$	1.04008e12	−	1.27870e12i	0.674798	−	0.829610i
$512$	−2.04829e12			−1.31728
$513$	7.74066e11	+	1.34072e12i	0.493458	+	0.854694i
$514$	3.13167e12			1.97898
$515$	6.78098e11	+	1.17450e12i	0.424776	+	0.735734i
$516$	−1.07350e12	−	1.85935e12i	−0.666618	−	1.15462i
$517$	−1.13685e12	−	1.96908e12i	−0.699836	−	1.21215i
$518$	3.34545e11	+	8.77219e11i	0.204160	+	0.535333i
$519$	4.64813e11			0.281206
$520$	2.51223e11	−	7.05758e11i	0.150676	−	0.423293i
$521$	−5.74118e11	−	9.94402e11i	−0.341375	−	0.591279i	0.643313	−	0.765603i	$-0.277559\pi$
$521$	−5.74118e11	−	9.94402e11i	−0.341375	−	0.591279i	−0.984688	+	0.174324i	$0.944226\pi$
$522$	−4.90350e11	+	8.49311e11i	−0.289061	+	0.500668i
$523$	−1.78814e12			−1.04507			−0.522535	−	0.852618i	$-0.675013\pi$
$523$	−1.78814e12			−1.04507			−0.522535	+	0.852618i	$0.675013\pi$
$524$	−4.45358e11	+	7.71382e11i	−0.258058	+	0.446970i
$525$	−6.75961e11	−	1.77245e12i	−0.388333	−	1.01826i
$526$	4.94677e11	−	8.56806e11i	0.281764	−	0.488030i
$527$	1.29341e11	+	2.24025e11i	0.0730446	+	0.126517i
$528$	6.47367e11	+	1.12127e12i	0.362491	+	0.627854i
$529$	−1.80049e12			−0.999632
$530$	−1.48170e12			−0.815679
$531$	5.90208e11	+	1.02227e12i	0.322166	+	0.558008i
$532$	−1.27630e12	+	1.56911e12i	−0.690798	+	0.849280i
$533$	1.24149e12	+	1.45842e12i	0.666300	+	0.782728i
$534$	−1.98762e12	+	3.44266e12i	−1.05779	+	1.83214i
$535$	−5.53268e11	+	9.58288e11i	−0.291973	+	0.505713i
$536$	2.85586e11	−	4.94650e11i	0.149450	−	0.258855i
$537$	−4.21803e11	−	7.30585e11i	−0.218890	−	0.379129i
$538$	−5.73279e11			−0.295016
$539$	5.06424e11	+	2.43457e12i	0.258443	+	1.24243i
$540$	−1.99185e12	+	3.44998e12i	−1.00805	+	1.74600i
$541$	−1.28806e12	+	2.23099e12i	−0.646473	+	1.11972i	0.337487	+	0.941330i	$0.390423\pi$
$541$	−1.28806e12	+	2.23099e12i	−0.646473	+	1.11972i	−0.983959	+	0.178393i	$0.942910\pi$
$542$	7.92527e11			0.394473
$543$	−1.36406e12	+	2.36261e12i	−0.673338	+	1.16626i
$544$	1.60967e12			0.788027
$545$	1.30896e12			0.635540
$546$	−2.28241e12	+	5.10616e10i	−1.09907	+	0.0245882i
$547$	−2.65955e12			−1.27018			−0.635089	−	0.772439i	$-0.719037\pi$
$547$	−2.65955e12			−1.27018			−0.635089	+	0.772439i	$0.719037\pi$
$548$	1.09560e12			0.518968
$549$	−3.62805e11	+	6.28397e11i	−0.170450	+	0.295229i
$550$	5.92075e12			2.75896
$551$	8.63158e11	−	1.49503e12i	0.398940	−	0.690985i
$552$	4.44417e9	−	7.69752e9i	0.00203734	−	0.00352878i
$553$	−1.95454e12	−	3.13929e11i	−0.888754	−	0.142747i
$554$	−5.59639e12			−2.52414
$555$	−5.04253e11	−	8.73391e11i	−0.225595	−	0.390742i
$556$	−1.64975e12	+	2.85744e12i	−0.732117	+	1.26806i
$557$	−3.95336e11	+	6.84741e11i	−0.174027	+	0.301424i	−0.939824	−	0.341658i	$-0.889011\pi$
$557$	−3.95336e11	+	6.84741e11i	−0.174027	+	0.301424i	0.765797	+	0.643083i	$0.222345\pi$
$558$	2.01203e11	−	3.48495e11i	0.0878580	−	0.152175i
$559$	1.16538e12	−	3.27390e12i	0.504795	−	1.41812i
$560$	2.77808e12	+	4.46202e11i	1.19371	+	0.191728i
$561$	−6.10794e11	−	1.05793e12i	−0.260353	−	0.450944i
$562$	2.16829e12			0.916863
$563$	−2.44512e11			−0.102568			−0.0512840	−	0.998684i	$-0.516331\pi$
$563$	−2.44512e11			−0.102568			−0.0512840	+	0.998684i	$0.516331\pi$
$564$	−1.17373e12	−	2.03297e12i	−0.488443	−	0.846008i
$565$	−2.80148e12	−	4.85231e12i	−1.15656	−	2.00323i
$566$	3.35599e12	−	5.81275e12i	1.37451	−	2.38072i
$567$	8.49336e11	+	1.36416e11i	0.345109	+	0.0554297i
$568$	−4.01603e11	+	6.95596e11i	−0.161893	+	0.280407i
$569$	−3.74617e11			−0.149824			−0.0749121	−	0.997190i	$-0.523868\pi$
$569$	−3.74617e11			−0.149824			−0.0749121	+	0.997190i	$0.523868\pi$
$570$	1.99686e12	−	3.45867e12i	0.792340	−	1.37237i
$571$	−8.10565e10	−	1.40394e11i	−0.0319099	−	0.0552695i	0.849629	−	0.527380i	$-0.176826\pi$
$571$	−8.10565e10	−	1.40394e11i	−0.0319099	−	0.0552695i	−0.881539	+	0.472111i	$0.843492\pi$
$572$	1.29998e12	−	3.65203e12i	0.507755	−	1.42643i
$573$	−1.49674e12			−0.580032
$574$	2.49822e12	−	3.07136e12i	0.960565	−	1.18094i
$575$	3.69265e10	+	6.39586e10i	0.0140875	+	0.0244002i
$576$	−7.95648e11	−	1.37810e12i	−0.301176	−	0.521652i
$577$	9.00256e11	+	1.55929e12i	0.338123	+	0.585646i	0.984080	−	0.177728i	$-0.0568747\pi$
$577$	9.00256e11	+	1.55929e12i	0.338123	+	0.585646i	−0.645957	+	0.763374i	$0.723541\pi$
$578$	2.75975e12			1.02848
$579$	6.88674e11	+	1.19282e12i	0.254660	+	0.441083i
$580$	4.44220e12			1.62994
$581$	4.65586e11	+	1.22082e12i	0.169515	+	0.444489i
$582$	2.12596e11	+	3.68227e11i	0.0768071	+	0.133034i
$583$	−1.24105e12			−0.444920
$584$	4.29868e11	+	7.44553e11i	0.152925	+	0.264873i
$585$	−1.96496e12	+	3.60859e11i	−0.693670	+	0.127390i
$586$	1.34784e12	−	2.33452e12i	0.472169	−	0.817821i
$587$	2.11203e11	+	3.65815e11i	0.0734225	+	0.127172i	0.900399	−	0.435065i	$-0.143274\pi$
$587$	2.11203e11	+	3.65815e11i	0.0734225	+	0.127172i	−0.826977	+	0.562236i	$0.809941\pi$
$588$	5.22854e11	+	2.51356e12i	0.180377	+	0.867143i
$589$	−3.54176e11	+	6.13451e11i	−0.121255	+	0.210020i
$590$	4.91410e12	−	8.51147e12i	1.66959	−	2.89182i
$591$	−3.05734e12			−1.03086
$592$	8.89774e11			0.297736
$593$	2.08394e12	−	3.60949e12i	0.692053	−	1.19867i	−0.279111	−	0.960259i	$-0.590040\pi$
$593$	2.08394e12	−	3.60949e12i	0.692053	−	1.19867i	0.971164	−	0.238412i	$-0.0766270\pi$
$594$	−3.06664e12	+	5.31158e12i	−1.01070	+	1.75059i
$595$	−2.62114e12	−	4.20995e11i	−0.857360	−	0.137705i
$596$	3.17252e11	+	5.49497e11i	0.102990	+	0.178385i
$597$	−1.49668e12	+	2.59233e12i	−0.482220	+	0.835230i
$598$	8.74190e10	−	1.60542e10i	0.0279544	−	0.00513374i
$599$	−1.42913e12	−	2.47533e12i	−0.453578	−	0.785619i	0.545028	−	0.838418i	$-0.316519\pi$
$599$	−1.42913e12	−	2.47533e12i	−0.453578	−	0.785619i	−0.998605	+	0.0527987i	$0.983186\pi$
$600$	9.89452e11			0.311684
$601$	−6.24164e11	−	1.08108e12i	−0.195148	−	0.338006i	0.751801	−	0.659390i	$-0.229185\pi$
$601$	−6.24164e11	−	1.08108e12i	−0.195148	−	0.338006i	−0.946949	+	0.321384i	$0.895852\pi$
$602$	−7.09256e12	−	1.13917e12i	−2.20099	−	0.353513i
$603$	−1.52322e12			−0.469175
$604$	2.89455e12	+	5.01350e12i	0.884941	+	1.53276i
$605$	3.16021e12			0.958996
$606$	1.46754e12	+	2.54185e12i	0.442041	+	0.765637i
$607$	−1.11561e11	−	1.93229e11i	−0.0333552	−	0.0577729i	0.848866	−	0.528608i	$-0.177286\pi$
$607$	−1.11561e11	−	1.93229e11i	−0.0333552	−	0.0577729i	−0.882221	+	0.470835i	$0.843953\pi$
$608$	2.20389e12	+	3.81724e12i	0.654068	+	1.13288i
$609$	−7.80818e11	−	2.04740e12i	−0.230023	−	0.603150i
$610$	6.04147e12			1.76668
$611$	1.27420e12	−	3.57960e12i	0.369872	−	1.03908i
$612$	5.13728e11	+	8.89802e11i	0.148031	+	0.256397i
$613$	7.65196e11	−	1.32536e12i	0.218877	−	0.379107i	−0.735588	−	0.677429i	$-0.763094\pi$
$613$	7.65196e11	−	1.32536e12i	0.218877	−	0.379107i	0.954465	+	0.298323i	$0.0964272\pi$
$614$	−1.13933e12			−0.323514
$615$	−2.12641e12	+	3.68306e12i	−0.599390	+	1.03817i
$616$	−1.28063e12	−	2.05689e11i	−0.358352	−	0.0575568i
$617$	−1.38978e12	+	2.40717e12i	−0.386067	+	0.668688i	−0.991917	−	0.126891i	$-0.959500\pi$
$617$	−1.38978e12	+	2.40717e12i	−0.386067	+	0.668688i	0.605849	+	0.795579i	$0.292833\pi$
$618$	1.07787e12	+	1.86692e12i	0.297247	+	0.514847i
$619$	−1.09079e12	−	1.88930e12i	−0.298629	−	0.517241i	0.677193	−	0.735805i	$-0.263196\pi$
$619$	−1.09079e12	−	1.88930e12i	−0.298629	−	0.517241i	−0.975823	+	0.218564i	$0.929863\pi$
$620$	−1.82275e12			−0.495409
$621$	−7.65041e10			−0.0206430
$622$	−2.34232e12	−	4.05702e12i	−0.627466	−	1.08680i
$623$	2.57839e12	+	6.76086e12i	0.685729	+	1.79807i
$624$	−7.25577e11	+	2.03836e12i	−0.191581	+	0.538208i
$625$	5.96762e11	−	1.03362e12i	0.156438	−	0.270958i
$626$	−4.93424e12	+	8.54636e12i	−1.28421	+	2.22432i
$627$	1.67255e12	−	2.89694e12i	0.432189	−	0.748574i
$628$	−8.44783e10	−	1.46321e11i	−0.0216734	−	0.0375394i
$629$	−8.39507e11			−0.213844
$630$	1.47157e12	+	3.85863e12i	0.372175	+	0.975890i
$631$	−5.92494e11	+	1.02623e12i	−0.148783	+	0.257699i	−0.930778	−	0.365585i	$-0.880869\pi$
$631$	−5.92494e11	+	1.02623e12i	−0.148783	+	0.257699i	0.781995	+	0.623284i	$0.214202\pi$
$632$	5.16272e11	−	8.94210e11i	0.128722	−	0.222953i
$633$	1.26369e12			0.312840
$634$	−2.55702e12	+	4.42888e12i	−0.628539	+	1.08866i
$635$	−1.13526e13			−2.77085
$636$	−1.28132e12			−0.310527
$637$	−2.54943e12	+	3.28161e12i	−0.613501	+	0.789694i
$638$	6.83920e12			1.63423
$639$	2.14201e12			0.508239
$640$	−1.87146e12	+	3.24147e12i	−0.440932	+	0.763716i
$641$	2.56558e12			0.600239			0.300119	−	0.953902i	$-0.402973\pi$
$641$	2.56558e12			0.600239			0.300119	+	0.953902i	$0.402973\pi$
$642$	−8.79445e11	+	1.52324e12i	−0.204315	+	0.353885i
$643$	−8.56270e11	+	1.48310e12i	−0.197543	+	0.342154i	−0.947731	−	0.319070i	$-0.896629\pi$
$643$	−8.56270e11	+	1.48310e12i	−0.197543	+	0.342154i	0.750188	+	0.661224i	$0.229963\pi$
$644$	−3.56167e10	−	9.33914e10i	−0.00815957	−	0.0213954i
$645$	7.71644e12			1.75549
$646$	−1.66224e12	−	2.87909e12i	−0.375533	−	0.650442i
$647$	−6.80019e11	+	1.17783e12i	−0.152564	+	0.264248i	−0.932169	−	0.362023i	$-0.882086\pi$
$647$	−6.80019e11	+	1.17783e12i	−0.152564	+	0.264248i	0.779605	+	0.626271i	$0.215420\pi$
$648$	−2.24344e11	+	3.88575e11i	−0.0499834	+	0.0865739i
$649$	4.11599e12	−	7.12910e12i	0.910695	−	1.57737i
$650$	6.41349e12	+	7.53416e12i	1.40924	+	1.65548i
$651$	3.20390e11	+	8.40102e11i	0.0699140	+	0.183323i
$652$	1.02171e11	+	1.76965e11i	0.0221418	+	0.0383507i
$653$	−8.31062e12			−1.78864			−0.894322	−	0.447423i	$-0.852342\pi$
$653$	−8.31062e12			−1.78864			−0.894322	+	0.447423i	$0.852342\pi$
$654$	2.08066e12			0.444735
$655$	−1.60065e12	−	2.77240e12i	−0.339789	−	0.588532i
$656$	−1.87607e12	−	3.24945e12i	−0.395532	−	0.685082i
$657$	1.14639e12	−	1.98560e12i	0.240042	−	0.415764i
$658$	−7.75483e12	−	1.24554e12i	−1.61271	−	0.259025i
$659$	−9.91520e11	+	1.71736e12i	−0.204794	+	0.354713i	−0.950067	−	0.312046i	$-0.898986\pi$
$659$	−9.91520e11	+	1.71736e12i	−0.204794	+	0.354713i	0.745273	+	0.666759i	$0.232319\pi$
$660$	8.60767e12			1.76579
$661$	4.18503e12	−	7.24869e12i	0.852692	−	1.47691i	−0.0260781	−	0.999660i	$-0.508302\pi$
$661$	4.18503e12	−	7.24869e12i	0.852692	−	1.47691i	0.878770	−	0.477246i	$-0.158365\pi$
$662$	4.11796e12	+	7.13252e12i	0.833338	+	1.44338i
$663$	6.84586e11	−	1.92320e12i	0.137600	−	0.386558i
$664$	−6.81512e11			−0.136056
$665$	−2.59038e12	−	6.79230e12i	−0.513649	−	1.34685i
$666$	6.52970e11	+	1.13098e12i	0.128605	+	0.222751i
$667$	4.26547e10	+	7.38801e10i	0.00834450	+	0.0144531i
$668$	4.81550e11	+	8.34070e11i	0.0935724	+	0.162072i
$669$	7.62068e12			1.47088
$670$	6.34121e12	+	1.09833e13i	1.21573	+	2.10570i
$671$	5.06025e12			0.963653
$672$	5.52406e12	+	8.87248e11i	1.04495	+	0.167835i
$673$	−4.44954e12	−	7.70683e12i	−0.836079	−	1.44813i	−0.893149	−	0.449761i	$-0.851509\pi$
$673$	−4.44954e12	−	7.70683e12i	−0.836079	−	1.44813i	0.0570702	−	0.998370i	$-0.481824\pi$
$674$	−1.26952e13			−2.36957
$675$	−4.25823e12	−	7.37547e12i	−0.789518	−	1.36749i
$676$	6.05537e12	−	2.30173e12i	1.11527	−	0.423930i
$677$	−1.78413e12	+	3.09020e12i	−0.326421	+	0.565377i	−0.981799	−	0.189924i	$-0.939176\pi$
$677$	−1.78413e12	+	3.09020e12i	−0.326421	+	0.565377i	0.655378	+	0.755301i	$0.272509\pi$
$678$	−4.45309e12	−	7.71297e12i	−0.809334	−	1.40181i
$679$	7.64152e11	+	1.22734e11i	0.137964	+	0.0221591i
$680$	6.92347e11	−	1.19918e12i	0.124175	−	0.215077i
$681$	−2.05721e12	+	3.56319e12i	−0.366536	+	0.634859i
$682$	−2.80630e12			−0.496712
$683$	2.30157e12			0.404698			0.202349	−	0.979313i	$-0.435142\pi$
$683$	2.30157e12			0.404698			0.202349	+	0.979313i	$0.435142\pi$
$684$	−1.40675e12	+	2.43656e12i	−0.245733	+	0.425622i
$685$	−1.96884e12	+	3.41012e12i	−0.341666	+	0.591783i
$686$	7.62808e12	+	3.94962e12i	1.31509	+	0.680921i
$687$	−1.05336e12	−	1.82447e12i	−0.180414	−	0.312486i
$688$	−3.40399e12	+	5.89589e12i	−0.579216	+	1.00323i
$689$	−1.34434e12	−	1.57924e12i	−0.227259	−	0.266970i
$690$	9.86790e10	+	1.70917e11i	0.0165731	+	0.0287055i
$691$	6.96202e12			1.16167			0.580837	−	0.814020i	$-0.302725\pi$
$691$	6.96202e12			1.16167			0.580837	+	0.814020i	$0.302725\pi$
$692$	1.36319e12	+	2.36111e12i	0.225984	+	0.391416i
$693$	1.23256e12	+	3.23194e12i	0.203007	+	0.532309i
$694$	−1.63262e13			−2.67158
$695$	−5.92930e12	−	1.02698e13i	−0.963988	−	1.66968i
$696$	1.14294e12			0.184621
$697$	1.77008e12	+	3.06587e12i	0.284084	+	0.492047i
$698$	9.08939e12	+	1.57433e13i	1.44939	+	2.51042i
$699$	3.99651e12	+	6.92216e12i	0.633189	+	1.09672i
$700$	7.02109e12	−	8.63186e12i	1.10526	−	1.35882i
$701$	8.63879e12			1.35121			0.675604	−	0.737265i	$-0.263883\pi$
$701$	8.63879e12			1.35121			0.675604	+	0.737265i	$0.263883\pi$
$702$	−1.00808e13	+	1.85131e12i	−1.56668	+	0.287716i
$703$	−1.14942e12	−	1.99085e12i	−0.177492	−	0.307425i
$704$	−5.54868e12	+	9.61060e12i	−0.851360	+	1.47460i
$705$	8.43697e12			1.28628
$706$	5.75880e12	−	9.97454e12i	0.872391	−	1.51102i
$707$	5.27490e12	+	8.47229e11i	0.794011	+	0.127530i
$708$	4.24952e12	−	7.36039e12i	0.635610	−	1.10091i
$709$	1.20990e12	+	2.09561e12i	0.179822	+	0.311460i	0.941819	−	0.336119i	$-0.109115\pi$
$709$	1.20990e12	+	2.09561e12i	0.179822	+	0.311460i	−0.761998	+	0.647580i	$0.775781\pi$
$710$	−8.91725e12	−	1.54451e13i	−1.31695	−	2.28102i
$711$	−2.75362e12			−0.404102
$712$	−3.77418e12			−0.550379
$713$	−1.75023e10	−	3.03149e10i	−0.00253625	−	0.00439292i
$714$	−4.16642e12	−	6.69191e11i	−0.599959	−	0.0963625i
$715$	9.03102e12	+	1.06091e13i	1.29229	+	1.51810i
$716$	2.47410e12	−	4.28526e12i	0.351810	−	0.609353i
$717$	−4.35466e12	+	7.54250e12i	−0.615344	+	1.06581i
$718$	4.46352e12	−	7.73104e12i	0.626783	−	1.08562i
$719$	1.00959e12	+	1.74865e12i	0.140885	+	0.244019i	0.927830	−	0.373003i	$-0.121672\pi$
$719$	1.00959e12	+	1.74865e12i	0.140885	+	0.244019i	−0.786945	+	0.617023i	$0.788339\pi$
$720$	3.91386e12			0.542761
$721$	3.87428e12	+	6.22268e11i	0.533927	+	0.0857568i
$722$	−8.54796e11	+	1.48055e12i	−0.117070	+	0.202771i
$723$	2.66265e12	−	4.61185e12i	0.362403	−	0.627701i
$724$	−1.60018e13			−2.16444
$725$	−4.74833e12	+	8.22435e12i	−0.638293	+	1.10556i
$726$	5.02330e12			0.671081
$727$	−1.26021e13			−1.67316			−0.836579	−	0.547846i	$-0.815448\pi$
$727$	−1.26021e13			−1.67316			−0.836579	+	0.547846i	$0.815448\pi$
$728$	−1.12547e12	−	1.85241e12i	−0.148505	−	0.244425i
$729$	7.28532e12			0.955377
$730$	−1.90897e13			−2.48798
$731$	3.21169e12	−	5.56280e12i	0.416011	−	0.720552i
$732$	5.22442e12			0.672572
$733$	−3.07177e12	+	5.32046e12i	−0.393025	+	0.680740i	−0.992847	−	0.119394i	$-0.961905\pi$
$733$	−3.07177e12	+	5.32046e12i	−0.393025	+	0.680740i	0.599822	+	0.800134i	$0.295238\pi$
$734$	5.95063e12	−	1.03068e13i	0.756712	−	1.31066i
$735$	−8.76317e12	−	2.88954e12i	−1.10756	−	0.365204i
$736$	−2.17819e11			−0.0273619
$737$	5.31131e12	+	9.19947e12i	0.663129	+	1.14857i
$738$	2.75355e12	−	4.76929e12i	0.341696	−	0.591834i
$739$	2.75491e12	−	4.77165e12i	0.339788	−	0.588530i	−0.644605	−	0.764516i	$-0.722978\pi$
$739$	2.75491e12	−	4.77165e12i	0.339788	−	0.588530i	0.984393	+	0.175986i	$0.0563113\pi$
$740$	2.95771e12	−	5.12290e12i	0.362587	−	0.628019i
$741$	5.49809e12	−	1.00971e12i	0.669931	−	0.123031i
$742$	−2.70517e12	+	3.32579e12i	−0.327626	+	0.402789i
$743$	1.93403e12	+	3.34983e12i	0.232816	+	0.403249i	0.958636	−	0.284636i	$-0.0918727\pi$
$743$	1.93403e12	+	3.34983e12i	0.232816	+	0.403249i	−0.725820	+	0.687885i	$0.758539\pi$
$744$	−4.68978e11			−0.0561144
$745$	−2.28045e12			−0.271218
$746$	1.99371e12	+	3.45320e12i	0.235688	+	0.408223i
$747$	9.08738e11	+	1.57398e12i	0.106782	+	0.184951i
$748$	3.58263e12	−	6.20529e12i	0.418451	−	0.724778i
$749$	1.14084e12	+	2.99142e12i	0.132451	+	0.347304i
$750$	−3.50229e12	+	6.06614e12i	−0.404182	+	0.700063i
$751$	−3.67458e11			−0.0421530			−0.0210765	−	0.999778i	$-0.506709\pi$
$751$	−3.67458e11			−0.0421530			−0.0210765	+	0.999778i	$0.506709\pi$
$752$	−3.72184e12	+	6.44642e12i	−0.424402	+	0.735086i
$753$	−5.22828e12	−	9.05565e12i	−0.592627	−	1.02646i
$754$	7.40836e12	+	8.70288e12i	0.834740	+	0.980600i
$755$	−2.08064e13			−2.33043
$756$	4.10719e12	+	1.07696e13i	0.457295	+	1.19908i
$757$	3.47993e12	+	6.02742e12i	0.385158	+	0.667113i	0.991791	−	0.127869i	$-0.0408136\pi$
$757$	3.47993e12	+	6.02742e12i	0.385158	+	0.667113i	−0.606633	+	0.794982i	$0.707480\pi$
$758$	−1.31880e13	−	2.28422e13i	−1.45100	−	2.51320i
$759$	8.26522e10	+	1.43158e11i	0.00903996	+	0.0156577i
$760$	3.79173e12			0.412264
$761$	−2.32837e12	−	4.03286e12i	−0.251664	−	0.435896i	0.712320	−	0.701855i	$-0.247645\pi$
$761$	−2.32837e12	−	4.03286e12i	−0.251664	−	0.435896i	−0.963984	+	0.265959i	$0.914311\pi$
$762$	−1.80455e13			−1.93897
$763$	2.38980e12	−	2.93807e12i	0.255271	−	0.313835i
$764$	−4.38960e12	−	7.60300e12i	−0.466127	−	0.807356i
$765$	−3.69275e12			−0.389828
$766$	−4.29291e12	−	7.43553e12i	−0.450528	−	0.780338i
$767$	1.35303e13	−	2.48480e12i	1.41165	−	0.259246i
$768$	1.82665e12	−	3.16385e12i	0.189465	−	0.328163i
$769$	−1.33098e12	−	2.30533e12i	−0.137247	−	0.237719i	0.789206	−	0.614128i	$-0.210492\pi$
$769$	−1.33098e12	−	2.30533e12i	−0.137247	−	0.237719i	−0.926454	+	0.376409i	$0.877159\pi$
$770$	1.81729e13	−	2.23421e13i	1.86302	−	2.29043i
$771$	−4.86663e12	+	8.42924e12i	−0.496002	+	0.859100i
$772$	−4.03943e12	+	6.99650e12i	−0.409301	+	0.708929i
$773$	4.62855e12			0.466270			0.233135	−	0.972444i	$-0.425102\pi$
$773$	4.62855e12			0.466270			0.233135	+	0.972444i	$0.425102\pi$
$774$	−9.99223e12			−1.00076
$775$	1.94836e12	−	3.37467e12i	0.194005	−	0.336026i
$776$	−2.01843e11	+	3.49602e11i	−0.0199819	+	0.0346096i
$777$	−2.88102e12	−	4.62736e11i	−0.283564	−	0.0455448i
$778$	2.97669e12	+	5.15578e12i	0.291290	+	0.504529i
$779$	−4.84704e12	+	8.39533e12i	−0.471583	+	0.816806i
$780$	9.32402e12	+	1.09533e13i	0.901939	+	1.05954i
$781$	−7.46897e12	−	1.29366e13i	−0.718342	−	1.24420i
$782$	1.64286e11			0.0157098
$783$	−4.91878e12	−	8.51958e12i	−0.467659	−	0.810009i
$784$	6.07355e12	−	5.42098e12i	0.574143	−	0.512455i
$785$	6.07242e11			0.0570753
$786$	−2.54430e12	−	4.40686e12i	−0.237776	−	0.411839i
$787$	1.62032e13			1.50561			0.752806	−	0.658242i	$-0.228700\pi$
$787$	1.62032e13			1.50561			0.752806	+	0.658242i	$0.228700\pi$
$788$	−8.96646e12	−	1.55304e13i	−0.828424	−	1.43487i
$789$	1.53746e12	+	2.66296e12i	0.141240	+	0.244635i
$790$	1.14634e13	+	1.98552e13i	1.04711	+	1.81364i
$791$	−1.60061e13	−	2.57083e12i	−1.45376	−	0.233495i
$792$	−1.80419e12			−0.162937
$793$	5.48138e12	+	6.43917e12i	0.492221	+	0.578230i
$794$	−1.29772e13	−	2.24771e13i	−1.15874	−	2.00700i
$795$	2.30257e12	−	3.98817e12i	0.204438	−	0.354096i
$796$	−1.75577e13			−1.55009
$797$	−3.64064e12	+	6.30577e12i	−0.319606	+	0.553574i	−0.980406	−	0.196988i	$-0.936884\pi$
$797$	−3.64064e12	+	6.30577e12i	−0.319606	+	0.553574i	0.660800	+	0.750562i	$0.270217\pi$
$798$	−4.11753e12	−	1.07967e13i	−0.359438	−	0.942492i
$799$	3.51158e12	−	6.08223e12i	0.304819	−	0.527962i
$800$	−1.21238e13	−	2.09991e13i	−1.04649	−	1.81258i
$801$	5.03254e12	+	8.71662e12i	0.431958	+	0.748173i
$802$	−2.70242e13			−2.30658
$803$	−1.59893e13			−1.35709
$804$	5.48363e12	+	9.49792e12i	0.462824	+	0.801635i
$805$	3.54690e11	+	5.69687e10i	0.0297693	+	0.00478140i
$806$	−3.03984e12	−	3.57102e12i	−0.253714	−	0.298047i
$807$	8.90879e11	−	1.54305e12i	0.0739414	−	0.128070i
$808$	−1.39331e12	+	2.41328e12i	−0.115000	+	0.199185i
$809$	5.53593e12	−	9.58851e12i	0.454383	−	0.787015i	−0.544269	−	0.838910i	$-0.683193\pi$
$809$	5.53593e12	−	9.58851e12i	0.454383	−	0.787015i	0.998652	+	0.0518959i	$0.0165264\pi$
$810$	−4.98136e12	−	8.62797e12i	−0.406598	−	0.704249i
$811$	1.84457e13			1.49727			0.748635	−	0.662982i	$-0.230709\pi$
$811$	1.84457e13			1.49727			0.748635	+	0.662982i	$0.230709\pi$
$812$	8.11022e12	−	9.97086e12i	0.654682	−	0.804878i
$813$	−1.23159e12	+	2.13318e12i	−0.0988688	+	0.171246i
$814$	4.55368e12	−	7.88720e12i	0.363540	−	0.629670i
$815$	−7.34419e11			−0.0583089
$816$	−1.99963e12	+	3.46345e12i	−0.157886	+	0.273466i
$817$	1.75892e13			1.38117
$818$	2.42064e13			1.89034
$819$	−2.77750e12	+	5.06934e12i	−0.215713	+	0.393708i
$820$	−2.49451e13			−1.92674
$821$	5.81248e12			0.446496			0.223248	−	0.974762i	$-0.428334\pi$
$821$	5.81248e12			0.446496			0.223248	+	0.974762i	$0.428334\pi$
$822$	−3.12956e12	+	5.42055e12i	−0.239089	+	0.414114i
$823$	3.00900e12			0.228625			0.114312	−	0.993445i	$-0.463533\pi$
$823$	3.00900e12			0.228625			0.114312	+	0.993445i	$0.463533\pi$
$824$	−1.02335e12	+	1.77250e12i	−0.0773308	+	0.133941i
$825$	−9.20088e12	+	1.59364e13i	−0.691491	+	1.19770i
$826$	−1.01329e13	−	2.65697e13i	−0.757396	−	1.98599i
$827$	8.31781e12			0.618350			0.309175	−	0.951005i	$-0.399947\pi$
$827$	8.31781e12			0.618350			0.309175	+	0.951005i	$0.399947\pi$
$828$	−6.95173e10	−	1.20407e11i	−0.00513992	−	0.00890260i
$829$	−1.29681e13	+	2.24613e13i	−0.953629	+	1.65173i	−0.216155	+	0.976359i	$0.569352\pi$
$829$	−1.29681e13	+	2.24613e13i	−0.953629	+	1.65173i	−0.737474	+	0.675375i	$0.763982\pi$
$830$	7.56620e12	−	1.31050e13i	0.553384	−	0.958489i
$831$	8.69682e12	−	1.50633e13i	0.632639	−	1.09576i
$832$	−1.82399e13	+	3.34971e12i	−1.31968	+	0.242355i
$833$	−5.73043e12	+	5.11473e12i	−0.412368	+	0.368061i
$834$	−9.42490e12	−	1.63244e13i	−0.674574	−	1.16840i
$835$	−3.46145e12			−0.246416
$836$	1.96207e13			1.38927
$837$	2.01830e12	+	3.49580e12i	0.142142	+	0.246197i
$838$	1.07231e13	+	1.85729e13i	0.751141	+	1.30101i
$839$	−1.30777e13	+	2.26512e13i	−0.911177	+	1.57820i	−0.0987718	+	0.995110i	$0.531491\pi$
$839$	−1.30777e13	+	2.26512e13i	−0.911177	+	1.57820i	−0.812405	+	0.583094i	$0.801842\pi$
$840$	3.03699e12	−	3.73373e12i	0.210468	−	0.258753i
$841$	1.76867e12	−	3.06342e12i	0.121917	−	0.211166i
$842$	2.61644e13			1.79393
$843$	−3.36954e12	+	5.83621e12i	−0.229798	+	0.398022i
$844$	3.70609e12	+	6.41914e12i	0.251406	+	0.435448i
$845$	−3.71745e12	+	2.29840e13i	−0.250836	+	1.55085i
$846$	−1.09253e13			−0.733272
$847$	5.76967e12	−	7.09334e12i	0.385190	−	0.473560i
$848$	2.03149e12	+	3.51864e12i	0.134907	+	0.233665i
$849$	1.04305e13	+	1.80661e13i	0.688999	+	1.19338i
$850$	9.14419e12	+	1.58382e13i	0.600842	+	1.04069i
$851$	1.13601e11			0.00742507
$852$	−7.71129e12	−	1.33563e13i	−0.501359	−	0.868379i
$853$	8.32182e12			0.538205			0.269102	−	0.963112i	$-0.413273\pi$
$853$	8.32182e12			0.538205			0.269102	+	0.963112i	$0.413273\pi$
$854$	1.10300e13	−	1.35605e13i	0.709605	−	0.872402i
$855$	−5.05595e12	−	8.75716e12i	−0.323560	−	0.560423i
$856$	−1.66993e12			−0.106308
$857$	−6.59359e12	−	1.14204e13i	−0.417550	−	0.723217i	0.578143	−	0.815936i	$-0.303778\pi$
$857$	−6.59359e12	−	1.14204e13i	−0.417550	−	0.723217i	−0.995692	+	0.0927184i	$0.970444\pi$
$858$	1.43552e13	+	1.68636e13i	0.904311	+	1.06233i
$859$	−1.05905e12	+	1.83433e12i	−0.0663664	+	0.114950i	−0.897299	−	0.441423i	$-0.854474\pi$
$859$	−1.05905e12	+	1.83433e12i	−0.0663664	+	0.114950i	0.830933	+	0.556373i	$0.187807\pi$
$860$	2.26305e13	+	3.91971e13i	1.41075	+	2.44349i
$861$	4.38467e12	+	1.14971e13i	0.271908	+	0.712977i
$862$	−5.87383e12	+	1.01738e13i	−0.362359	+	0.627624i
$863$	−6.44354e12	+	1.11605e13i	−0.395436	+	0.684915i	−0.993157	−	0.116789i	$-0.962740\pi$
$863$	−6.44354e12	+	1.11605e13i	−0.395436	+	0.684915i	0.597721	+	0.801704i	$0.296073\pi$
$864$	2.51181e13			1.53347
$865$	−9.79877e12			−0.595112
$866$	4.03652e12	−	6.99146e12i	0.243880	−	0.422413i
$867$	−4.28866e12	+	7.42817e12i	−0.257772	+	0.446474i
$868$	−3.32783e12	+	4.09130e12i	−0.198986	+	0.244637i
$869$	9.60159e12	+	1.66304e13i	0.571155	+	0.989270i
$870$	−1.26890e13	+	2.19780e13i	−0.750915	+	1.30062i
$871$	−5.95299e12	+	1.67237e13i	−0.350472	+	0.984580i
$872$	9.87710e11	+	1.71076e12i	0.0578502	+	0.100200i
$873$	1.07656e12			0.0627299
$874$	2.24933e11	+	3.89596e11i	0.0130392	+	0.0225846i
$875$	4.54326e12	+	1.19130e13i	0.262018	+	0.687044i
$876$	−1.65080e13			−0.947168
$877$	1.25949e13	+	2.18150e13i	0.718946	+	1.24525i	0.961418	+	0.275093i	$0.0887085\pi$
$877$	1.25949e13	+	2.18150e13i	0.718946	+	1.24525i	−0.242472	+	0.970158i	$0.577958\pi$
$878$	6.31410e12			0.358580
$879$	4.18909e12	+	7.25571e12i	0.236684	+	0.409949i
$880$	−1.36472e13	−	2.36376e13i	−0.767135	−	1.32872i
$881$	−8.24372e11	−	1.42785e12i	−0.0461033	−	0.0798532i	0.842053	−	0.539395i	$-0.181347\pi$
$881$	−8.24372e11	−	1.42785e12i	−0.0461033	−	0.0798532i	−0.888156	+	0.459542i	$0.848014\pi$
$882$	1.13477e13	+	3.74174e12i	0.631391	+	0.208193i
$883$	9.69596e12			0.536744			0.268372	−	0.963315i	$-0.413514\pi$
$883$	9.69596e12			0.536744			0.268372	+	0.963315i	$0.413514\pi$
$884$	1.17770e13	−	2.16281e12i	0.648635	−	0.119120i
$885$	1.52731e13	+	2.64537e13i	0.836916	+	1.44958i
$886$	−7.14512e12	+	1.23757e13i	−0.389545	+	0.674712i
$887$	7.44752e12			0.403976			0.201988	−	0.979388i	$-0.435260\pi$
$887$	7.44752e12			0.403976			0.201988	+	0.979388i	$0.435260\pi$
$888$	7.60992e11	−	1.31808e12i	0.0410697	−	0.0711349i
$889$	−2.07267e13	+	2.54818e13i	−1.11294	+	1.36827i
$890$	4.19012e13	−	7.25750e13i	2.23857	−	3.87732i
$891$	−4.17232e12	−	7.22668e12i	−0.221783	−	0.384140i
$892$	2.23496e13	+	3.87107e13i	1.18203	+	2.04734i
$893$	1.92316e13			1.01201
$894$	−3.62489e12			−0.189791
$895$	8.89208e12	+	1.54015e13i	0.463233	+	0.802343i
$896$	3.85896e12	+	1.01187e13i	0.200025	+	0.524490i
$897$	−9.26378e10	+	2.60247e11i	−0.00477773	+	0.0134221i
$898$	4.54879e12	−	7.87873e12i	0.233427	−	0.404308i
$899$	2.25060e12	−	3.89815e12i	0.114916	−	0.199040i
$900$	7.73869e12	−	1.34038e13i	0.393166	−	0.680984i
$901$	−1.91672e12	−	3.31986e12i	−0.0968941	−	0.167825i
$902$	−3.84054e13			−1.93180
$903$	1.40881e13	−	1.73202e13i	0.705110	−	0.866876i
$904$	4.22785e12	−	7.32286e12i	0.210553	−	0.364689i
$905$	2.87558e13	−	4.98065e13i	1.42497	−	2.46813i
$906$	−3.30728e13			−1.63077
$907$	1.55249e13	−	2.68899e13i	0.761721	−	1.31934i	−0.180242	−	0.983622i	$-0.557688\pi$
$907$	1.55249e13	−	2.68899e13i	0.761721	−	1.31934i	0.941963	−	0.335717i	$-0.108979\pi$
$908$	−2.41332e13			−1.17823
$909$	7.43145e12			0.361024
$910$	4.81157e13	−	1.07643e12i	2.32595	−	0.0520357i
$911$	2.73751e13			1.31681			0.658406	−	0.752663i	$-0.271231\pi$
$911$	2.73751e13			1.31681			0.658406	+	0.752663i	$0.271231\pi$
$912$	−1.09512e13			−0.524186
$913$	6.33735e12	−	1.09766e13i	0.301849	−	0.522817i
$914$	−5.00269e13			−2.37108
$915$	−9.38847e12	+	1.62613e13i	−0.442792	+	0.766938i
$916$	6.17849e12	−	1.07015e13i	0.289970	−	0.502242i
$917$	−9.14521e12	−	1.46886e12i	−0.427102	−	0.0685991i
$918$	−1.89449e13			−0.880439
$919$	−5.90171e12	−	1.02221e13i	−0.272934	−	0.472736i	0.696677	−	0.717384i	$-0.254661\pi$
$919$	−5.90171e12	−	1.02221e13i	−0.272934	−	0.472736i	−0.969612	+	0.244648i	$0.921328\pi$
$920$	−9.36879e10	+	1.62272e11i	−0.00431160	+	0.00746791i
$921$	1.77053e12	−	3.06665e12i	0.0810840	−	0.140442i
$922$	−2.98914e12	+	5.17734e12i	−0.136225	+	0.235948i
$923$	8.37132e12	−	2.35175e13i	0.379653	−	1.06656i
$924$	1.57152e13	−	1.93206e13i	0.709246	−	0.871960i
$925$	6.32308e12	+	1.09519e13i	0.283982	+	0.491871i
$926$	3.06162e13			1.36837
$927$	5.45821e12			0.242768
$928$	−1.40045e13	−	2.42566e13i	−0.619873	−	1.07365i
$929$	4.16356e12	+	7.21149e12i	0.183398	+	0.317654i	0.943035	−	0.332692i	$-0.107957\pi$
$929$	4.16356e12	+	7.21149e12i	0.183398	+	0.317654i	−0.759638	+	0.650346i	$0.774624\pi$
$930$	5.20663e12	−	9.01815e12i	0.228236	−	0.395316i
$931$	−1.99752e13	−	6.58655e12i	−0.871399	−	0.287332i
$932$	−2.34416e13	+	4.06021e13i	−1.01769	+	1.76269i
$933$	1.45599e13			0.629059
$934$	−2.55808e13	+	4.43072e13i	−1.09990	+	1.90508i
$935$	1.28762e13	+	2.23023e13i	0.550980	+	0.954325i
$936$	−1.95434e12	−	2.29584e12i	−0.0832260	−	0.0977686i
$937$	−9.01718e12			−0.382158			−0.191079	−	0.981575i	$-0.561199\pi$
$937$	−9.01718e12			−0.382158			−0.191079	+	0.981575i	$0.561199\pi$
$938$	3.62302e13	+	5.81911e12i	1.52812	+	0.245439i
$939$	−1.53357e13	−	2.65622e13i	−0.643736	−	1.11498i
$940$	2.47436e13	+	4.28572e13i	1.03368	+	1.79039i
$941$	−2.30356e12	−	3.98989e12i	−0.0957738	−	0.165885i	0.814157	−	0.580644i	$-0.197199\pi$
$941$	−2.30356e12	−	3.98989e12i	−0.0957738	−	0.165885i	−0.909931	+	0.414759i	$0.863866\pi$
$942$	9.65239e11			0.0399398
$943$	−2.39526e11	−	4.14872e11i	−0.00986395	−	0.0170849i
$944$	−2.69499e13			−1.10455
$945$	−4.09016e13	−	6.56942e12i	−1.66839	−	0.267969i
$946$	3.48418e13	+	6.03478e13i	1.41446	+	2.44992i
$947$	−3.60940e13			−1.45835			−0.729173	−	0.684330i	$-0.760095\pi$
$947$	−3.60940e13			−1.45835			−0.729173	+	0.684330i	$0.760095\pi$
$948$	9.91309e12	+	1.71700e13i	0.398632	+	0.690450i
$949$	−1.73200e13	−	2.03464e13i	−0.693185	−	0.814310i
$950$	−2.50397e13	+	4.33700e13i	−0.997407	+	1.72756i
$951$	−7.94723e12	−	1.37650e13i	−0.315068	−	0.545713i
$952$	−1.42762e12	−	3.74340e12i	−0.0563309	−	0.147707i
$953$	−7.98018e12	+	1.38221e13i	−0.313397	+	0.542819i	−0.979095	−	0.203402i	$-0.934800\pi$
$953$	−7.98018e12	+	1.38221e13i	−0.313397	+	0.542819i	0.665699	+	0.746221i	$0.268134\pi$
$954$	−2.98166e12	+	5.16439e12i	−0.116544	+	0.201860i
$955$	3.15530e13			1.22751
$956$	−5.10847e13			−1.97802
$957$	−1.06281e13	+	1.84085e13i	−0.409594	+	0.709438i
$958$	1.20030e13	−	2.07898e13i	0.460409	−	0.797452i
$959$	4.05974e12	+	1.06451e13i	0.154994	+	0.406413i
$960$	−2.05893e13	−	3.56618e13i	−0.782387	−	1.35513i
$961$	1.22963e13	−	2.12979e13i	0.465072	−	0.805529i
$962$	1.49691e13	−	2.74903e12i	0.563518	−	0.103488i
$963$	2.22671e12	+	3.85677e12i	0.0834343	+	0.144512i
$964$	3.12357e13			1.16494
$965$	−1.45180e13	−	2.51459e13i	−0.538932	−	0.933457i
$966$	5.63797e11	+	9.05544e10i	0.0208318	+	0.00334590i
$967$	−1.54182e13			−0.567040			−0.283520	−	0.958966i	$-0.591502\pi$
$967$	−1.54182e13			−0.567040			−0.283520	+	0.958966i	$0.591502\pi$
$968$	2.38461e12	+	4.13027e12i	0.0872929	+	0.151196i
$969$	1.03325e13			0.376487
$970$	−4.48175e12	−	7.76262e12i	−0.162546	−	0.281537i
$971$	−2.19401e13	−	3.80014e13i	−0.792050	−	1.37187i	−0.924696	−	0.380707i	$-0.875681\pi$
$971$	−2.19401e13	−	3.80014e13i	−0.792050	−	1.37187i	0.132646	−	0.991163i	$-0.457653\pi$
$972$	1.35492e13	+	2.34678e13i	0.486871	+	0.843286i
$973$	−3.38767e13	−	5.44112e12i	−1.21170	−	0.194617i
$974$	−3.44604e12			−0.122689
$975$	−3.02456e13	+	5.55452e12i	−1.07187	+	0.196846i
$976$	−8.28316e12	−	1.43469e13i	−0.292194	−	0.506096i
$977$	−7.09206e12	+	1.22838e13i	−0.249027	+	0.431328i	−0.963256	−	0.268584i	$-0.913444\pi$
$977$	−7.09206e12	+	1.22838e13i	−0.249027	+	0.431328i	0.714229	+	0.699912i	$0.246778\pi$
$978$	−1.16739e12			−0.0408030
$979$	3.50959e13	−	6.07879e13i	1.22105	−	2.11492i
$980$	−1.10223e13	−	5.29886e13i	−0.381730	−	1.83512i
$981$	2.63406e12	−	4.56232e12i	0.0908060	−	0.157281i
$982$	3.32897e13	+	5.76594e13i	1.14237	+	1.97865i
$983$	−2.77625e13	−	4.80860e13i	−0.948348	−	1.64259i	−0.748906	−	0.662677i	$-0.769420\pi$
$983$	−2.77625e13	−	4.80860e13i	−0.948348	−	1.64259i	−0.199442	−	0.979910i	$-0.563913\pi$
$984$	−6.41815e12			−0.218239
$985$	6.44521e13			2.18159
$986$	1.05627e13	+	1.82951e13i	0.355900	+	0.616436i
$987$	1.54036e13	−	1.89374e13i	0.516647	−	0.635176i
$988$	2.12536e13	+	2.49674e13i	0.709620	+	0.833617i
$989$	−4.34603e11	+	7.52754e11i	−0.0144447	+	0.0250190i
$990$	2.00303e13	−	3.46935e13i	0.662719	−	1.14786i
$991$	−3.90660e12	+	6.76643e12i	−0.128667	+	0.222858i	−0.923160	−	0.384415i	$-0.874403\pi$
$991$	−3.90660e12	+	6.76643e12i	−0.128667	+	0.222858i	0.794493	+	0.607273i	$0.207737\pi$
$992$	5.74642e12	+	9.95310e12i	0.188406	+	0.326329i
$993$	−2.55973e13			−0.835455
$994$	−5.09482e13	−	8.18306e12i	−1.65535	−	0.265875i
$995$	3.15517e13	−	5.46492e13i	1.02051	−	1.76758i
$996$	6.54295e12	−	1.13327e13i	0.210672	−	0.364894i
$997$	−3.80527e13			−1.21971			−0.609856	−	0.792512i	$-0.708773\pi$
$997$	−3.80527e13			−1.21971			−0.609856	+	0.792512i	$0.708773\pi$
$998$	−4.07429e13	+	7.05689e13i	−1.30006	+	2.25178i
$999$	−1.31001e13			−0.416131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.h.a.16.14	yes	164
7.4	even	3		91.10.g.a.81.69	yes	164
13.9	even	3		91.10.g.a.9.69	✓	164
91.74	even	3	inner	91.10.h.a.74.14	yes	164

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.g.a.9.69	✓	164	13.9	even	3
91.10.g.a.81.69	yes	164	7.4	even	3
91.10.h.a.16.14	yes	164	1.1	even	1	trivial
91.10.h.a.74.14	yes	164	91.74	even	3	inner

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-33.5094 q^{2} +(52.0738 - 90.1944i) q^{3} +610.880 q^{4} +(-1097.77 + 1901.40i) q^{5} +(-1744.96 + 3022.36i) q^{6} +(2263.61 + 5935.46i) q^{7} -3313.40 q^{8} +(4418.14 + 7652.45i) q^{9} +O(q^{10})\)	\(q-33.5094 q^{2} +(52.0738 - 90.1944i) q^{3} +610.880 q^{4} +(-1097.77 + 1901.40i) q^{5} +(-1744.96 + 3022.36i) q^{6} +(2263.61 + 5935.46i) q^{7} -3313.40 q^{8} +(4418.14 + 7652.45i) q^{9} +(36785.7 - 63714.7i) q^{10} +(30811.2 - 53366.6i) q^{11} +(31810.8 - 55098.0i) q^{12} +(101284. - 18600.6i) q^{13} +(-75852.1 - 198894. i) q^{14} +(114330. + 198026. i) q^{15} -201740. q^{16} +190343. q^{17} +(-148049. - 256429. i) q^{18} +(260610. + 451389. i) q^{19} +(-670607. + 1.16153e6i) q^{20} +(653220. + 104917. i) q^{21} +(-1.03247e6 + 1.78828e6i) q^{22} -25757.1 q^{23} +(-172541. + 298851. i) q^{24} +(-1.43364e6 - 2.48315e6i) q^{25} +(-3.39398e6 + 623293. i) q^{26} +2.97021e6 q^{27} +(1.38279e6 + 3.62585e6i) q^{28} +(-1.65604e6 - 2.86834e6i) q^{29} +(-3.83114e6 - 6.63573e6i) q^{30} +(679515. + 1.17695e6i) q^{31} +8.45666e6 q^{32} +(-3.20891e6 - 5.55800e6i) q^{33} -6.37828e6 q^{34} +(-1.37706e7 - 2.21177e6i) q^{35} +(2.69896e6 + 4.67473e6i) q^{36} -4.41049e6 q^{37} +(-8.73287e6 - 1.51258e7i) q^{38} +(3.59659e6 - 1.01039e7i) q^{39} +(3.63736e6 - 6.30010e6i) q^{40} +(9.29943e6 + 1.61071e7i) q^{41} +(-2.18890e7 - 3.51571e6i) q^{42} +(1.68731e7 - 2.92251e7i) q^{43} +(1.88219e7 - 3.26006e7i) q^{44} -1.94005e7 q^{45} +863105. q^{46} +(1.84487e7 - 3.19540e7i) q^{47} +(-1.05054e7 + 1.81958e7i) q^{48} +(-3.01058e7 + 2.68711e7i) q^{49} +(4.80406e7 + 8.32087e7i) q^{50} +(9.91188e6 - 1.71679e7i) q^{51} +(6.18726e7 - 1.13627e7i) q^{52} +(-1.00698e7 - 1.74414e7i) q^{53} -9.95301e7 q^{54} +(6.76474e7 + 1.17169e8i) q^{55} +(-7.50025e6 - 1.96666e7i) q^{56} +5.42837e7 q^{57} +(5.54928e7 + 9.61163e7i) q^{58} +1.33587e8 q^{59} +(6.98421e7 + 1.20970e8i) q^{60} +(4.10585e7 + 7.11155e7i) q^{61} +(-2.27701e7 - 3.94390e7i) q^{62} +(-3.54199e7 + 4.35459e7i) q^{63} -1.80087e8 q^{64} +(-7.58201e7 + 2.13001e8i) q^{65} +(1.07529e8 + 1.86245e8i) q^{66} +(-8.61913e7 + 1.49288e8i) q^{67} +1.16277e8 q^{68} +(-1.34127e6 + 2.32315e6i) q^{69} +(4.61444e8 + 7.41150e7i) q^{70} +(1.21205e8 - 2.09934e8i) q^{71} +(-1.46391e7 - 2.53557e7i) q^{72} +(-1.29736e8 - 2.24710e8i) q^{73} +1.47793e8 q^{74} -2.98621e8 q^{75} +(1.59201e8 + 2.75744e8i) q^{76} +(3.86500e8 + 6.20777e7i) q^{77} +(-1.20520e8 + 3.38575e8i) q^{78} +(-1.55813e8 + 2.69876e8i) q^{79} +(2.21465e8 - 3.83588e8i) q^{80} +(6.77079e7 - 1.17274e8i) q^{81} +(-3.11618e8 - 5.39739e8i) q^{82} +2.05683e8 q^{83} +(3.99039e8 + 6.40917e7i) q^{84} +(-2.08953e8 + 3.61918e8i) q^{85} +(-5.65409e8 + 9.79316e8i) q^{86} -3.44944e8 q^{87} +(-1.02090e8 + 1.76825e8i) q^{88} +1.13906e9 q^{89} +6.50098e8 q^{90} +(3.39671e8 + 5.59065e8i) q^{91} -1.57345e7 q^{92} +1.41540e8 q^{93} +(-6.18204e8 + 1.07076e9i) q^{94} -1.14436e9 q^{95} +(4.40370e8 - 7.62743e8i) q^{96} +(6.09171e7 - 1.05511e8i) q^{97} +(1.00883e9 - 9.00435e8i) q^{98} +5.44514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9}+O(q^{10}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9	\( 164 q - 2 q^{2} + 163 q^{3} + 40958 q^{4} - 2 q^{5} - 1026 q^{6} - 913 q^{7} - 1032 q^{8} - 512605 q^{9} + 38977 q^{10} - 59285 q^{11} + 44088 q^{12} + 232454 q^{13} + 17108 q^{14} - 407531 q^{15} + 10497654 q^{16} - 1395086 q^{17} - 76575 q^{18} + 1207545 q^{19} + 713618 q^{20} + 1790137 q^{21} + 199216 q^{22} + 2148062 q^{23} + 3435832 q^{24} - 29660780 q^{25} - 6096660 q^{26} - 9655538 q^{27} - 5996877 q^{28} + 996812 q^{29} + 4910674 q^{30} + 7678612 q^{31} - 13584366 q^{32} - 3082415 q^{33} + 32705872 q^{34} + 11865077 q^{35} - 134627249 q^{36} - 25237130 q^{37} + 25519874 q^{38} + 30627737 q^{39} + 45727182 q^{40} - 13667582 q^{41} - 81628563 q^{42} + 26867814 q^{43} - 75673614 q^{44} + 29593550 q^{45} - 70893356 q^{46} - 23074040 q^{47} + 29166348 q^{48} - 13541447 q^{49} + 77715962 q^{50} - 94065066 q^{51} + 139792121 q^{52} + 46529776 q^{53} - 14474550 q^{54} + 218800681 q^{55} - 649788015 q^{56} - 143710238 q^{57} + 1142701 q^{58} + 439131230 q^{59} - 557690411 q^{60} + 508694743 q^{61} + 307731320 q^{62} - 355730647 q^{63} + 1713678376 q^{64} + 148754944 q^{65} + 278425259 q^{66} + 37418955 q^{67} - 1290484830 q^{68} + 290468024 q^{69} - 182370322 q^{70} - 415622020 q^{71} + 720832393 q^{72} + 514120432 q^{73} + 128989762 q^{74} + 241348444 q^{75} + 985961470 q^{76} - 1189530907 q^{77} + 2167273673 q^{78} - 376448286 q^{79} - 482394712 q^{80} - 3131306974 q^{81} - 971561072 q^{82} + 971157612 q^{83} + 3735517629 q^{84} + 538436691 q^{85} + 1470174876 q^{86} - 912549686 q^{87} - 629673387 q^{88} + 699403942 q^{89} - 8083448244 q^{90} + 2740572083 q^{91} + 2309185554 q^{92} + 820704894 q^{93} + 419356886 q^{94} - 5283246 q^{95} - 4707829686 q^{96} + 1339771120 q^{97} - 1961676608 q^{98} + 1482300132 q^{99}+O(q^{100}) \) 164 * q - 2 * q^2 + 163 * q^3 + 40958 * q^4 - 2 * q^5 - 1026 * q^6 - 913 * q^7 - 1032 * q^8 - 512605 * q^9 + 38977 * q^10 - 59285 * q^11 + 44088 * q^12 + 232454 * q^13 + 17108 * q^14 - 407531 * q^15 + 10497654 * q^16 - 1395086 * q^17 - 76575 * q^18 + 1207545 * q^19 + 713618 * q^20 + 1790137 * q^21 + 199216 * q^22 + 2148062 * q^23 + 3435832 * q^24 - 29660780 * q^25 - 6096660 * q^26 - 9655538 * q^27 - 5996877 * q^28 + 996812 * q^29 + 4910674 * q^30 + 7678612 * q^31 - 13584366 * q^32 - 3082415 * q^33 + 32705872 * q^34 + 11865077 * q^35 - 134627249 * q^36 - 25237130 * q^37 + 25519874 * q^38 + 30627737 * q^39 + 45727182 * q^40 - 13667582 * q^41 - 81628563 * q^42 + 26867814 * q^43 - 75673614 * q^44 + 29593550 * q^45 - 70893356 * q^46 - 23074040 * q^47 + 29166348 * q^48 - 13541447 * q^49 + 77715962 * q^50 - 94065066 * q^51 + 139792121 * q^52 + 46529776 * q^53 - 14474550 * q^54 + 218800681 * q^55 - 649788015 * q^56 - 143710238 * q^57 + 1142701 * q^58 + 439131230 * q^59 - 557690411 * q^60 + 508694743 * q^61 + 307731320 * q^62 - 355730647 * q^63 + 1713678376 * q^64 + 148754944 * q^65 + 278425259 * q^66 + 37418955 * q^67 - 1290484830 * q^68 + 290468024 * q^69 - 182370322 * q^70 - 415622020 * q^71 + 720832393 * q^72 + 514120432 * q^73 + 128989762 * q^74 + 241348444 * q^75 + 985961470 * q^76 - 1189530907 * q^77 + 2167273673 * q^78 - 376448286 * q^79 - 482394712 * q^80 - 3131306974 * q^81 - 971561072 * q^82 + 971157612 * q^83 + 3735517629 * q^84 + 538436691 * q^85 + 1470174876 * q^86 - 912549686 * q^87 - 629673387 * q^88 + 699403942 * q^89 - 8083448244 * q^90 + 2740572083 * q^91 + 2309185554 * q^92 + 820704894 * q^93 + 419356886 * q^94 - 5283246 * q^95 - 4707829686 * q^96 + 1339771120 * q^97 - 1961676608 * q^98 + 1482300132 * q^99

Introduction

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