LMFDB - Embedded newform 14.14.c.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
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:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2 x^{7} + 692094 x^{6} + 445371928 x^{5} + 480078817147 x^{4} + 153633603309480 x^{3} + \cdots + 23\!\cdots\!25 $ x^8 - 2x^7 + 692094x^6 + 445371928x^5 + 480078817147x^4 + 153633603309480x^3 + 48219450150076326x^2 + 340591169755393830*x + 2353882543131872025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.4
Root			$-217.937 - 377.477i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.14.c.a.9.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.0000 - 55.4256i) q^{2} +(1142.35 - 1978.62i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-18256.5 - 31621.1i) q^{5} -146221. q^{6} +(-233961. + 205308. i) q^{7} +262144. q^{8} +(-1.81279e6 - 3.13984e6i) q^{9} +O(q^{10})$	\(q+(-32.0000 - 55.4256i) q^{2} +(1142.35 - 1978.62i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-18256.5 - 31621.1i) q^{5} -146221. q^{6} +(-233961. + 205308. i) q^{7} +262144. q^{8} +(-1.81279e6 - 3.13984e6i) q^{9} +(-1.16841e6 + 2.02375e6i) q^{10} +(1.91927e6 - 3.32427e6i) q^{11} +(4.67908e6 + 8.10441e6i) q^{12} +1.67406e7 q^{13} +(1.88661e7 + 6.39754e6i) q^{14} -8.34214e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(-8.06528e7 + 1.39695e8i) q^{17} +(-1.16018e8 + 2.00950e8i) q^{18} +(-1.29443e8 - 2.24202e8i) q^{19} +1.49557e8 q^{20} +(1.38960e8 + 6.97453e8i) q^{21} -2.45667e8 q^{22} +(4.39704e8 + 7.61589e8i) q^{23} +(2.99461e8 - 5.18682e8i) q^{24} +(-5.62445e7 + 9.74183e7i) q^{25} +(-5.35700e8 - 9.27860e8i) q^{26} -4.64082e9 q^{27} +(-2.49127e8 - 1.25039e9i) q^{28} +6.01309e8 q^{29} +(2.66948e9 + 4.62368e9i) q^{30} +(1.66816e9 - 2.88933e9i) q^{31} +(-5.36871e8 + 9.29888e8i) q^{32} +(-4.38497e9 - 7.59500e9i) q^{33} +1.03236e10 q^{34} +(1.07634e10 + 3.64989e9i) q^{35} +1.48503e10 q^{36} +(-2.94647e9 - 5.10343e9i) q^{37} +(-8.28436e9 + 1.43489e10i) q^{38} +(1.91237e10 - 3.31233e10i) q^{39} +(-4.78582e9 - 8.28928e9i) q^{40} -4.54312e10 q^{41} +(3.42100e10 - 3.00205e10i) q^{42} -2.12865e10 q^{43} +(7.86133e9 + 1.36162e10i) q^{44} +(-6.61901e10 + 1.14645e11i) q^{45} +(2.81410e10 - 4.87417e10i) q^{46} +(-3.51744e10 - 6.09238e10i) q^{47} -3.83311e10 q^{48} +(1.25860e10 - 9.60681e10i) q^{49} +7.19929e9 q^{50} +(1.84268e11 + 3.19162e11i) q^{51} +(-3.42848e10 + 5.93831e10i) q^{52} +(1.57102e10 - 2.72108e10i) q^{53} +(1.48506e11 + 2.57220e11i) q^{54} -1.40156e11 q^{55} +(-6.13313e10 + 5.38203e10i) q^{56} -5.91480e11 q^{57} +(-1.92419e10 - 3.33279e10i) q^{58} +(1.02489e11 - 1.77517e11i) q^{59} +(1.70847e11 - 2.95916e11i) q^{60} +(-2.45117e11 - 4.24555e11i) q^{61} -2.13524e11 q^{62} +(1.06876e12 + 3.62418e11i) q^{63} +6.87195e10 q^{64} +(-3.05625e11 - 5.29357e11i) q^{65} +(-2.80638e11 + 4.86080e11i) q^{66} +(-9.70566e9 + 1.68107e10i) q^{67} +(-3.30354e11 - 5.72190e11i) q^{68} +2.00919e12 q^{69} +(-1.42130e11 - 7.13363e11i) q^{70} +1.11249e12 q^{71} +(-4.75211e11 - 8.23090e11i) q^{72} +(-1.49352e11 + 2.58686e11i) q^{73} +(-1.88574e11 + 3.26620e11i) q^{74} +(1.28502e11 + 2.22572e11i) q^{75} +1.06040e12 q^{76} +(2.33467e11 + 1.17179e12i) q^{77} -2.44784e12 q^{78} +(-1.60375e12 - 2.77777e12i) q^{79} +(-3.06292e11 + 5.30514e11i) q^{80} +(-2.41129e12 + 4.17648e12i) q^{81} +(1.45380e12 + 2.51806e12i) q^{82} -2.08048e12 q^{83} +(-2.75862e12 - 9.35458e11i) q^{84} +5.88974e12 q^{85} +(6.81169e11 + 1.17982e12i) q^{86} +(6.86908e11 - 1.18976e12i) q^{87} +(5.03125e11 - 8.71438e11i) q^{88} +(-1.93546e12 - 3.35232e12i) q^{89} +8.47233e12 q^{90} +(-3.91665e12 + 3.43699e12i) q^{91} -3.60205e12 q^{92} +(-3.81125e12 - 6.60129e12i) q^{93} +(-2.25116e12 + 3.89912e12i) q^{94} +(-4.72634e12 + 8.18627e12i) q^{95} +(1.22659e12 + 2.12452e12i) q^{96} +1.42174e13 q^{97} +(-5.72739e12 + 2.37659e12i) q^{98} -1.39169e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9}+O(q^{10}) $ 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9} - 4121600 q^{10} - 1008790 q^{11} - 745472 q^{12} + 53807264 q^{13} + 23506560 q^{14} - 88888916 q^{15} - 67108864 q^{16} - 165333028 q^{17} - 254960128 q^{18} - 423405794 q^{19} + 527564800 q^{20} + 231089600 q^{21} + 129125120 q^{22} + 286233866 q^{23} - 47710208 q^{24} - 472017432 q^{25} - 1721832448 q^{26} - 10405941644 q^{27} - 1038557184 q^{28} + 18200674816 q^{29} + 2844445312 q^{30} + 1507094246 q^{31} - 4294967296 q^{32} - 16888935028 q^{33} + 21162627584 q^{34} - 4300332526 q^{35} + 32634896384 q^{36} - 18959705336 q^{37} - 27097970816 q^{38} + 35759388756 q^{39} - 16882073600 q^{40} + 113651910624 q^{41} + 25531294208 q^{42} - 91557619424 q^{43} - 4132003840 q^{44} - 119804452768 q^{45} + 18318967424 q^{46} - 81351201078 q^{47} + 6106906624 q^{48} - 60954502168 q^{49} + 60418231296 q^{50} + 14996824142 q^{51} - 110197276672 q^{52} + 87497947440 q^{53} + 332990132608 q^{54} + 701637410348 q^{55} - 29815209984 q^{56} - 1807326928264 q^{57} - 582421594112 q^{58} - 194140265102 q^{59} + 182044499968 q^{60} + 175816313120 q^{61} - 192908063488 q^{62} + 3245184239332 q^{63} + 549755813888 q^{64} - 1689866774568 q^{65} - 1080891841792 q^{66} - 243815218758 q^{67} - 677204082688 q^{68} + 6044157952784 q^{69} + 3010938632576 q^{70} - 3275394679072 q^{71} - 1044316684288 q^{72} - 3492491920596 q^{73} - 1213421141504 q^{74} - 2370218127424 q^{75} + 3468540264448 q^{76} + 6381735922240 q^{77} - 4577201760768 q^{78} - 1016380081246 q^{79} - 1080452710400 q^{80} + 17492694092 q^{81} - 3636861139968 q^{82} + 7027495743296 q^{83} - 2580545830912 q^{84} + 569114840528 q^{85} + 2929843821568 q^{86} - 9706955821052 q^{87} - 264448245760 q^{88} - 8034124428036 q^{89} + 15334969954304 q^{90} - 11436513503632 q^{91} - 2344827830272 q^{92} - 3388371390552 q^{93} - 5206476868992 q^{94} + 1429435505438 q^{95} - 195421011968 q^{96} + 54351131725632 q^{97} - 461748942592 q^{98} - 25837834576328 q^{99}+O(q^{100}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9 - 4121600 * q^10 - 1008790 * q^11 - 745472 * q^12 + 53807264 * q^13 + 23506560 * q^14 - 88888916 * q^15 - 67108864 * q^16 - 165333028 * q^17 - 254960128 * q^18 - 423405794 * q^19 + 527564800 * q^20 + 231089600 * q^21 + 129125120 * q^22 + 286233866 * q^23 - 47710208 * q^24 - 472017432 * q^25 - 1721832448 * q^26 - 10405941644 * q^27 - 1038557184 * q^28 + 18200674816 * q^29 + 2844445312 * q^30 + 1507094246 * q^31 - 4294967296 * q^32 - 16888935028 * q^33 + 21162627584 * q^34 - 4300332526 * q^35 + 32634896384 * q^36 - 18959705336 * q^37 - 27097970816 * q^38 + 35759388756 * q^39 - 16882073600 * q^40 + 113651910624 * q^41 + 25531294208 * q^42 - 91557619424 * q^43 - 4132003840 * q^44 - 119804452768 * q^45 + 18318967424 * q^46 - 81351201078 * q^47 + 6106906624 * q^48 - 60954502168 * q^49 + 60418231296 * q^50 + 14996824142 * q^51 - 110197276672 * q^52 + 87497947440 * q^53 + 332990132608 * q^54 + 701637410348 * q^55 - 29815209984 * q^56 - 1807326928264 * q^57 - 582421594112 * q^58 - 194140265102 * q^59 + 182044499968 * q^60 + 175816313120 * q^61 - 192908063488 * q^62 + 3245184239332 * q^63 + 549755813888 * q^64 - 1689866774568 * q^65 - 1080891841792 * q^66 - 243815218758 * q^67 - 677204082688 * q^68 + 6044157952784 * q^69 + 3010938632576 * q^70 - 3275394679072 * q^71 - 1044316684288 * q^72 - 3492491920596 * q^73 - 1213421141504 * q^74 - 2370218127424 * q^75 + 3468540264448 * q^76 + 6381735922240 * q^77 - 4577201760768 * q^78 - 1016380081246 * q^79 - 1080452710400 * q^80 + 17492694092 * q^81 - 3636861139968 * q^82 + 7027495743296 * q^83 - 2580545830912 * q^84 + 569114840528 * q^85 + 2929843821568 * q^86 - 9706955821052 * q^87 - 264448245760 * q^88 - 8034124428036 * q^89 + 15334969954304 * q^90 - 11436513503632 * q^91 - 2344827830272 * q^92 - 3388371390552 * q^93 - 5206476868992 * q^94 + 1429435505438 * q^95 - 195421011968 * q^96 + 54351131725632 * q^97 - 461748942592 * q^98 - 25837834576328 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−32.0000	−	55.4256i	−0.353553	−	0.612372i
$2$	−32.0000	−	55.4256i	−0.353553	−	0.612372i
$3$	1142.35	−	1978.62i	0.904717	−	1.56702i	0.0834205	−	0.996514i	$-0.473416\pi$
$3$	1142.35	−	1978.62i	0.904717	−	1.56702i	0.821297	−	0.570502i	$-0.193251\pi$
$4$	−2048.00	+	3547.24i	−0.250000	+	0.433013i
$5$	−18256.5	−	31621.1i	−0.522530	−	0.905049i	−0.999656	−	0.0262140i	$-0.991655\pi$
$5$	−18256.5	−	31621.1i	−0.522530	−	0.905049i	0.477126	−	0.878835i	$-0.341678\pi$
$6$	−146221.			−1.27946
$7$	−233961.	+	205308.i	−0.751632	+	0.659583i
$7$	−233961.	+	205308.i	−0.751632	+	0.659583i
$8$	262144.			0.353553
$9$	−1.81279e6	−	3.13984e6i	−1.13703	−	1.96939i
$10$	−1.16841e6	+	2.02375e6i	−0.369485	+	0.639966i
$11$	1.91927e6	−	3.32427e6i	0.326651	−	0.565776i	−0.655194	−	0.755460i	$-0.727413\pi$
$11$	1.91927e6	−	3.32427e6i	0.326651	−	0.565776i	0.981845	+	0.189685i	$0.0607466\pi$
$12$	4.67908e6	+	8.10441e6i	0.452359	+	0.783508i
$13$	1.67406e7			0.961923			0.480961	−	0.876742i	$-0.340288\pi$
$13$	1.67406e7			0.961923			0.480961	+	0.876742i	$0.340288\pi$
$14$	1.88661e7	+	6.39754e6i	0.669652	+	0.227081i
$15$	−8.34214e7			−1.89097
$16$	−8.38861e6	−	1.45295e7i	−0.125000	−	0.216506i
$17$	−8.06528e7	+	1.39695e8i	−0.810404	+	1.40366i	0.102177	+	0.994766i	$0.467419\pi$
$17$	−8.06528e7	+	1.39695e8i	−0.810404	+	1.40366i	−0.912582	+	0.408895i	$0.865914\pi$
$18$	−1.16018e8	+	2.00950e8i	−0.803999	+	1.39257i
$19$	−1.29443e8	−	2.24202e8i	−0.631220	−	1.09330i	−0.987303	−	0.158850i	$-0.949221\pi$
$19$	−1.29443e8	−	2.24202e8i	−0.631220	−	1.09330i	0.356083	−	0.934454i	$-0.384112\pi$
$20$	1.49557e8			0.522530
$21$	1.38960e8	+	6.97453e8i	0.353562	+	1.77456i
$22$	−2.45667e8			−0.461954
$23$	4.39704e8	+	7.61589e8i	0.619340	+	1.07273i	0.989606	+	0.143803i	$0.0459330\pi$
$23$	4.39704e8	+	7.61589e8i	0.619340	+	1.07273i	−0.370267	+	0.928926i	$0.620734\pi$
$24$	2.99461e8	−	5.18682e8i	0.319866	−	0.554024i
$25$	−5.62445e7	+	9.74183e7i	−0.0460755	+	0.0798051i
$26$	−5.35700e8	−	9.27860e8i	−0.340091	−	0.589055i
$27$	−4.64082e9			−2.30531
$28$	−2.49127e8	−	1.25039e9i	−0.0976996	−	0.490362i
$29$	6.01309e8			0.187720			0.0938600	−	0.995585i	$-0.470079\pi$
$29$	6.01309e8			0.187720			0.0938600	+	0.995585i	$0.470079\pi$
$30$	2.66948e9	+	4.62368e9i	0.668558	+	1.15798i
$31$	1.66816e9	−	2.88933e9i	0.337587	−	0.584718i	−0.646391	−	0.763006i	$-0.723723\pi$
$31$	1.66816e9	−	2.88933e9i	0.337587	−	0.584718i	0.983978	+	0.178288i	$0.0570559\pi$
$32$	−5.36871e8	+	9.29888e8i	−0.0883883	+	0.153093i
$33$	−4.38497e9	−	7.59500e9i	−0.591053	−	1.02373i
$34$	1.03236e10			1.14608
$35$	1.07634e10	+	3.64989e9i	0.989705	+	0.335612i
$36$	1.48503e10			1.13703
$37$	−2.94647e9	−	5.10343e9i	−0.188795	−	0.327003i	0.756054	−	0.654510i	$-0.227125\pi$
$37$	−2.94647e9	−	5.10343e9i	−0.188795	−	0.327003i	−0.944849	+	0.327507i	$0.893792\pi$
$38$	−8.28436e9	+	1.43489e10i	−0.446340	+	0.773083i
$39$	1.91237e10	−	3.31233e10i	0.870268	−	1.50735i
$40$	−4.78582e9	−	8.28928e9i	−0.184742	−	0.319983i
$41$	−4.54312e10			−1.49369			−0.746843	−	0.665000i	$-0.768432\pi$
$41$	−4.54312e10			−1.49369			−0.746843	+	0.665000i	$0.768432\pi$
$42$	3.42100e10	−	3.00205e10i	0.961686	−	0.843912i
$43$	−2.12865e10			−0.513523			−0.256762	−	0.966475i	$-0.582656\pi$
$43$	−2.12865e10			−0.513523			−0.256762	+	0.966475i	$0.582656\pi$
$44$	7.86133e9	+	1.36162e10i	0.163325	+	0.282888i
$45$	−6.61901e10	+	1.14645e11i	−1.18826	+	2.05813i
$46$	2.81410e10	−	4.87417e10i	0.437939	−	0.758533i
$47$	−3.51744e10	−	6.09238e10i	−0.475982	−	0.824425i	0.523639	−	0.851940i	$-0.324574\pi$
$47$	−3.51744e10	−	6.09238e10i	−0.475982	−	0.824425i	−0.999621	+	0.0275151i	$0.991241\pi$
$48$	−3.83311e10			−0.452359
$49$	1.25860e10	−	9.60681e10i	0.129902	−	0.991527i
$50$	7.19929e9			0.0651606
$51$	1.84268e11	+	3.19162e11i	1.46637	+	2.53983i
$52$	−3.42848e10	+	5.93831e10i	−0.240481	+	0.416525i
$53$	1.57102e10	−	2.72108e10i	0.0973617	−	0.168635i	−0.813230	−	0.581942i	$-0.802293\pi$
$53$	1.57102e10	−	2.72108e10i	0.0973617	−	0.168635i	0.910592	+	0.413307i	$0.135626\pi$
$54$	1.48506e11	+	2.57220e11i	0.815051	+	1.41171i
$55$	−1.40156e11			−0.682739
$56$	−6.13313e10	+	5.38203e10i	−0.265742	+	0.233198i
$57$	−5.91480e11			−2.28430
$58$	−1.92419e10	−	3.33279e10i	−0.0663691	−	0.114955i
$59$	1.02489e11	−	1.77517e11i	0.316330	−	0.547900i	−0.663389	−	0.748275i	$-0.730883\pi$
$59$	1.02489e11	−	1.77517e11i	0.316330	−	0.547900i	0.979719	+	0.200375i	$0.0642159\pi$
$60$	1.70847e11	−	2.95916e11i	0.472742	−	0.818813i
$61$	−2.45117e11	−	4.24555e11i	−0.609157	−	1.05509i	−0.991380	−	0.131020i	$-0.958175\pi$
$61$	−2.45117e11	−	4.24555e11i	−0.609157	−	1.05509i	0.382223	−	0.924070i	$-0.375159\pi$
$62$	−2.13524e11			−0.477420
$63$	1.06876e12	+	3.62418e11i	2.15360	+	0.730292i
$64$	6.87195e10			0.125000
$65$	−3.05625e11	−	5.29357e11i	−0.502634	−	0.870587i
$66$	−2.80638e11	+	4.86080e11i	−0.417938	+	0.723889i
$67$	−9.70566e9	+	1.68107e10i	−0.0131081	+	0.0227039i	−0.872505	−	0.488605i	$-0.837506\pi$
$67$	−9.70566e9	+	1.68107e10i	−0.0131081	+	0.0227039i	0.859397	+	0.511309i	$0.170839\pi$
$68$	−3.30354e11	−	5.72190e11i	−0.405202	−	0.701830i
$69$	2.00919e12			2.24131
$70$	−1.42130e11	−	7.13363e11i	−0.144394	−	0.724725i
$71$	1.11249e12			1.03067			0.515334	−	0.856989i	$-0.327668\pi$
$71$	1.11249e12			1.03067			0.515334	+	0.856989i	$0.327668\pi$
$72$	−4.75211e11	−	8.23090e11i	−0.401999	−	0.696283i
$73$	−1.49352e11	+	2.58686e11i	−0.115508	+	0.200066i	−0.917983	−	0.396620i	$-0.870183\pi$
$73$	−1.49352e11	+	2.58686e11i	−0.115508	+	0.200066i	0.802474	+	0.596686i	$0.203516\pi$
$74$	−1.88574e11	+	3.26620e11i	−0.133498	+	0.231226i
$75$	1.28502e11	+	2.22572e11i	0.0833705	+	0.144402i
$76$	1.06040e12			0.631220
$77$	2.33467e11	+	1.17179e12i	0.127655	+	0.640708i
$78$	−2.44784e12			−1.23074
$79$	−1.60375e12	−	2.77777e12i	−0.742267	−	1.28564i	−0.951461	−	0.307769i	$-0.900417\pi$
$79$	−1.60375e12	−	2.77777e12i	−0.742267	−	1.28564i	0.209194	−	0.977874i	$-0.432916\pi$
$80$	−3.06292e11	+	5.30514e11i	−0.130633	+	0.226262i
$81$	−2.41129e12	+	4.17648e12i	−0.948630	+	1.64308i
$82$	1.45380e12	+	2.51806e12i	0.528098	+	0.914693i
$83$	−2.08048e12			−0.698483			−0.349241	−	0.937033i	$-0.613561\pi$
$83$	−2.08048e12			−0.698483			−0.349241	+	0.937033i	$0.613561\pi$
$84$	−2.75862e12	−	9.35458e11i	−0.856795	−	0.290542i
$85$	5.88974e12			1.69384
$86$	6.81169e11	+	1.17982e12i	0.181558	+	0.314467i
$87$	6.86908e11	−	1.18976e12i	0.169834	−	0.294160i
$88$	5.03125e11	−	8.71438e11i	0.115488	−	0.200032i
$89$	−1.93546e12	−	3.35232e12i	−0.412810	−	0.715007i	0.582386	−	0.812912i	$-0.302119\pi$
$89$	−1.93546e12	−	3.35232e12i	−0.412810	−	0.715007i	−0.995196	+	0.0979049i	$0.968786\pi$
$90$	8.47233e12			1.68045
$91$	−3.91665e12	+	3.43699e12i	−0.723012	+	0.634467i
$92$	−3.60205e12			−0.619340
$93$	−3.81125e12	−	6.60129e12i	−0.610842	−	1.05801i
$94$	−2.25116e12	+	3.89912e12i	−0.336570	+	0.582956i
$95$	−4.72634e12	+	8.18627e12i	−0.659662	+	1.14257i
$96$	1.22659e12	+	2.12452e12i	0.159933	+	0.277012i
$97$	1.42174e13			1.73302			0.866509	−	0.499162i	$-0.166359\pi$
$97$	1.42174e13			1.73302			0.866509	+	0.499162i	$0.166359\pi$
$98$	−5.72739e12	+	2.37659e12i	−0.653111	+	0.271009i
$99$	−1.39169e13			−1.48564
$100$	−2.30377e11	−	3.99025e11i	−0.0230377	−	0.0399025i
$101$	−5.24950e12	+	9.09240e12i	−0.492072	+	0.852294i	−0.999958	−	0.00912999i	$-0.997094\pi$
$101$	−5.24950e12	+	9.09240e12i	−0.492072	+	0.852294i	0.507886	+	0.861424i	$0.330427\pi$
$102$	1.17932e13	−	2.04264e13i	1.03688	−	1.79593i
$103$	−5.59871e12	−	9.69725e12i	−0.462005	−	0.800215i	0.537056	−	0.843546i	$-0.319536\pi$
$103$	−5.59871e12	−	9.69725e12i	−0.462005	−	0.800215i	−0.999061	+	0.0433311i	$0.986203\pi$
$104$	4.38846e12			0.340091
$105$	1.95173e13	−	1.71271e13i	1.42131	−	1.24725i
$106$	−2.01090e12			−0.137690
$107$	1.16058e13	+	2.01019e13i	0.747622	+	1.29492i	0.948959	+	0.315398i	$0.102138\pi$
$107$	1.16058e13	+	2.01019e13i	0.747622	+	1.29492i	−0.201337	+	0.979522i	$0.564529\pi$
$108$	9.50439e12	−	1.64621e13i	0.576328	−	0.998230i
$109$	−4.27010e12	+	7.39604e12i	−0.243874	+	0.422403i	−0.961815	−	0.273702i	$-0.911752\pi$
$109$	−4.27010e12	+	7.39604e12i	−0.243874	+	0.422403i	0.717940	+	0.696105i	$0.245085\pi$
$110$	4.48500e12	+	7.76825e12i	0.241385	+	0.418091i
$111$	−1.34636e13			−0.683224
$112$	4.94563e12	+	1.67708e12i	0.236758	+	0.0802853i
$113$	1.63979e13			0.740934			0.370467	−	0.928846i	$-0.379198\pi$
$113$	1.63979e13			0.740934			0.370467	+	0.928846i	$0.379198\pi$
$114$	1.89273e13	+	3.27831e13i	0.807622	+	1.39884i
$115$	1.60549e13	−	2.78078e13i	0.647247	−	1.12107i
$116$	−1.23148e12	+	2.13299e12i	−0.0469300	+	0.0812852i
$117$	−3.03472e13	−	5.25629e13i	−1.09373	−	1.89440i
$118$	−1.31186e13			−0.447358
$119$	−9.81092e12	−	4.92418e13i	−0.316705	−	1.58957i
$120$	−2.18684e13			−0.668558
$121$	9.89416e12	+	1.71372e13i	0.286599	+	0.496403i
$122$	−1.56875e13	+	2.71715e13i	−0.430739	+	0.746062i
$123$	−5.18986e13	+	8.98910e13i	−1.35136	+	2.34063i
$124$	6.83277e12	+	1.18347e13i	0.168794	+	0.292359i
$125$	−4.04641e13			−0.948757
$126$	−1.41129e13	−	7.08338e13i	−0.314201	−	1.57700i
$127$	3.77685e13			0.798741			0.399371	−	0.916790i	$-0.369229\pi$
$127$	3.77685e13			0.798741			0.399371	+	0.916790i	$0.369229\pi$
$128$	−2.19902e12	−	3.80882e12i	−0.0441942	−	0.0765466i
$129$	−2.43168e13	+	4.21179e13i	−0.464593	+	0.804699i
$130$	−1.95600e13	+	3.38789e13i	−0.355416	+	0.615598i
$131$	2.22248e13	+	3.84945e13i	0.384216	+	0.665481i	0.991660	−	0.128881i	$-0.0411386\pi$
$131$	2.22248e13	+	3.84945e13i	0.384216	+	0.665481i	−0.607444	+	0.794362i	$0.707805\pi$
$132$	3.59217e13			0.591053
$133$	7.63151e13	+	2.58787e13i	1.19557	+	0.405421i
$134$	1.24232e12			0.0185376
$135$	8.47248e13	+	1.46748e14i	1.20460	+	2.08642i
$136$	−2.11427e13	+	3.66202e13i	−0.286521	+	0.496269i
$137$	5.54037e13	−	9.59620e13i	0.715904	−	1.23998i	−0.246706	−	0.969090i	$-0.579348\pi$
$137$	5.54037e13	−	9.59620e13i	0.715904	−	1.23998i	0.962610	−	0.270892i	$-0.0873186\pi$
$138$	−6.42941e13	−	1.11361e14i	−0.792423	−	1.37252i
$139$	8.82502e13			1.03781			0.518907	−	0.854831i	$-0.326339\pi$
$139$	8.82502e13			1.03781			0.518907	+	0.854831i	$0.326339\pi$
$140$	−3.49904e13	+	3.07053e13i	−0.392750	+	0.344652i
$141$	−1.60726e14			−1.72252
$142$	−3.55998e13	−	6.16607e13i	−0.364396	−	0.631153i
$143$	3.21298e13	−	5.56504e13i	0.314213	−	0.544232i
$144$	−3.04135e13	+	5.26777e13i	−0.284256	+	0.492347i
$145$	−1.09778e13	−	1.90141e13i	−0.0980894	−	0.169896i
$146$	1.91171e13			0.163353
$147$	−1.75704e14	−	1.34647e14i	−1.43621	−	1.10061i
$148$	2.41375e13			0.188795
$149$	−6.36934e13	−	1.10320e14i	−0.476852	−	0.825932i	0.522796	−	0.852458i	$-0.324889\pi$
$149$	−6.36934e13	−	1.10320e14i	−0.476852	−	0.825932i	−0.999648	+	0.0265259i	$0.991556\pi$
$150$	8.22414e12	−	1.42446e13i	0.0589519	−	0.102108i
$151$	−4.79442e13	+	8.30417e13i	−0.329144	+	0.570094i	−0.982342	−	0.187093i	$-0.940093\pi$
$151$	−4.79442e13	+	8.30417e13i	−0.329144	+	0.570094i	0.653198	+	0.757187i	$0.273427\pi$
$152$	−3.39327e13	−	5.87732e13i	−0.223170	−	0.386541i
$153$	5.84825e14			3.68580
$154$	5.74763e13	−	5.04374e13i	0.347219	−	0.304697i
$155$	−1.21819e14			−0.705598
$156$	7.83308e13	+	1.35673e14i	0.435134	+	0.753674i
$157$	1.47340e14	−	2.55201e14i	0.785189	−	1.35999i	−0.143698	−	0.989622i	$-0.545899\pi$
$157$	1.47340e14	−	2.55201e14i	0.785189	−	1.35999i	0.928886	−	0.370365i	$-0.120767\pi$
$158$	−1.02640e14	+	1.77777e14i	−0.524862	+	0.909087i
$159$	−3.58932e13	−	6.21689e13i	−0.176170	−	0.305135i
$160$	3.92054e13			0.184742
$161$	−2.59234e14	−	8.79070e13i	−1.17307	−	0.397791i
$162$	3.08645e14			1.34157
$163$	1.77089e13	+	3.06727e13i	0.0739556	+	0.128095i	0.900632	−	0.434583i	$-0.143104\pi$
$163$	1.77089e13	+	3.06727e13i	0.0739556	+	0.128095i	−0.826676	+	0.562678i	$0.809771\pi$
$164$	9.30432e13	−	1.61156e14i	0.373422	−	0.646785i
$165$	−1.60108e14	+	2.77315e14i	−0.617686	+	1.06986i
$166$	6.65753e13	+	1.15312e14i	0.246951	+	0.427732i
$167$	1.84001e14			0.656390			0.328195	−	0.944610i	$-0.393560\pi$
$167$	1.84001e14			0.656390			0.328195	+	0.944610i	$0.393560\pi$
$168$	3.64276e13	+	1.82833e14i	0.125003	+	0.627400i
$169$	−2.26262e13			−0.0747049
$170$	−1.88472e14	−	3.26442e14i	−0.598864	−	1.03726i
$171$	−4.69305e14	+	8.12861e14i	−1.43543	+	2.48623i
$172$	4.35948e13	−	7.55085e13i	0.128381	−	0.222362i
$173$	−3.25046e13	−	5.62995e13i	−0.0921817	−	0.159663i	0.816247	−	0.577703i	$-0.196051\pi$
$173$	−3.25046e13	−	5.62995e13i	−0.0921817	−	0.159663i	−0.908429	+	0.418039i	$0.862717\pi$
$174$	−8.79242e13			−0.240181
$175$	−6.84179e12	−	3.43395e13i	−0.0180062	−	0.0903746i
$176$	−6.44000e13			−0.163325
$177$	−2.34158e14	−	4.05574e14i	−0.572379	−	0.991389i
$178$	−1.23870e14	+	2.14549e14i	−0.291901	+	0.505587i
$179$	−1.31245e14	+	2.27323e14i	−0.298221	+	0.516534i	−0.975729	−	0.218982i	$-0.929727\pi$
$179$	−1.31245e14	+	2.27323e14i	−0.298221	+	0.516534i	0.677508	+	0.735515i	$0.263060\pi$
$180$	−2.71115e14	−	4.69584e14i	−0.594130	−	1.02906i
$181$	4.09833e14			0.866355			0.433178	−	0.901309i	$-0.357392\pi$
$181$	4.09833e14			0.866355			0.433178	+	0.901309i	$0.357392\pi$
$182$	3.15830e14	+	1.07099e14i	0.644154	+	0.218434i
$183$	−1.12004e15			−2.20446
$184$	1.15266e14	+	1.99646e14i	0.218970	+	0.379267i
$185$	−1.07584e14	+	1.86341e14i	−0.197302	+	0.341737i
$186$	−2.43920e14	+	4.22482e14i	−0.431930	+	0.748125i
$187$	3.09589e14	+	5.36224e14i	0.529438	+	0.917014i
$188$	2.88149e14			0.475982
$189$	1.08577e15	−	9.52798e14i	1.73275	−	1.52054i
$190$	6.04972e14			0.932904
$191$	−3.25497e13	−	5.63777e13i	−0.0485099	−	0.0840216i	0.840751	−	0.541422i	$-0.182114\pi$
$191$	−3.25497e13	−	5.63777e13i	−0.0485099	−	0.0840216i	−0.889261	+	0.457401i	$0.848781\pi$
$192$	7.85020e13	−	1.35969e14i	0.113090	−	0.195877i
$193$	1.62299e14	−	2.81110e14i	0.226044	−	0.391519i	−0.730588	−	0.682818i	$-0.760754\pi$
$193$	1.62299e14	−	2.81110e14i	0.226044	−	0.391519i	0.956632	+	0.291299i	$0.0940874\pi$
$194$	−4.54956e14	−	7.88007e14i	−0.612714	−	1.06125i
$195$	−1.39653e15			−1.81896
$196$	3.15000e14	+	2.41393e14i	0.396868	+	0.304131i
$197$	8.88338e14			1.08280			0.541399	−	0.840766i	$-0.317895\pi$
$197$	8.88338e14			1.08280			0.541399	+	0.840766i	$0.317895\pi$
$198$	4.45341e14	+	7.71353e14i	0.525253	+	0.909766i
$199$	7.84474e13	−	1.35875e14i	0.0895433	−	0.155094i	−0.817775	−	0.575538i	$-0.804793\pi$
$199$	7.84474e13	−	1.35875e14i	0.0895433	−	0.155094i	0.907318	+	0.420445i	$0.138126\pi$
$200$	−1.47441e13	+	2.55376e13i	−0.0162901	+	0.0282153i
$201$	2.21746e13	+	3.84076e13i	0.0237182	+	0.0410811i
$202$	6.71936e14			0.695895
$203$	−1.40683e14	+	1.23454e14i	−0.141096	+	0.123817i
$204$	−1.50953e15			−1.46637
$205$	8.29413e14	+	1.43659e15i	0.780496	+	1.35186i
$206$	−3.58318e14	+	6.20624e14i	−0.326687	+	0.565838i
$207$	1.59418e15	−	2.76120e15i	1.40841	−	2.43944i
$208$	−1.40431e14	−	2.43233e14i	−0.120240	−	0.208262i
$209$	−9.93745e14			−0.824753
$210$	−1.57383e15	−	5.33692e14i	−1.26629	−	0.429403i
$211$	−3.37886e14			−0.263593			−0.131797	−	0.991277i	$-0.542075\pi$
$211$	−3.37886e14			−0.263593			−0.131797	+	0.991277i	$0.542075\pi$
$212$	6.43489e13	+	1.11456e14i	0.0486809	+	0.0843177i
$213$	1.27086e15	−	2.20120e15i	0.932463	−	1.61507i
$214$	7.42774e14	−	1.28652e15i	0.528649	−	0.915647i
$215$	3.88617e14	+	6.73104e14i	0.268331	+	0.464764i
$216$	−1.21656e15			−0.815051
$217$	2.02921e14	+	1.01848e15i	0.131929	+	0.662160i
$218$	5.46573e14			0.344890
$219$	3.41227e14	+	5.91022e14i	0.209005	+	0.362007i
$220$	2.87040e14	−	4.97168e14i	0.170685	−	0.295635i
$221$	−1.35018e15	+	2.33858e15i	−0.779546	+	1.35021i
$222$	4.30837e14	+	7.46231e14i	0.241556	+	0.418388i
$223$	2.69510e15			1.46755			0.733775	−	0.679392i	$-0.237756\pi$
$223$	2.69510e15			1.46755			0.733775	+	0.679392i	$0.237756\pi$
$224$	−6.53070e13	−	3.27781e14i	−0.0345420	−	0.173369i
$225$	4.07837e14			0.209556
$226$	−5.24734e14	−	9.08867e14i	−0.261960	−	0.453728i
$227$	−1.55079e15	+	2.68604e15i	−0.752288	+	1.30300i	0.194424	+	0.980918i	$0.437716\pi$
$227$	−1.55079e15	+	2.68604e15i	−0.752288	+	1.30300i	−0.946711	+	0.322083i	$0.895617\pi$
$228$	1.21135e15	−	2.09812e15i	0.571075	−	0.989131i
$229$	−3.25208e14	−	5.63277e14i	−0.149015	−	0.258102i	0.781849	−	0.623468i	$-0.214277\pi$
$229$	−3.25208e14	−	5.63277e14i	−0.149015	−	0.258102i	−0.930864	+	0.365367i	$0.880944\pi$
$230$	−2.05502e15			−0.915346
$231$	2.58523e15	+	8.76658e14i	1.11949	+	0.379623i
$232$	1.57630e14			0.0663691
$233$	−1.81763e15	−	3.14824e15i	−0.744206	−	1.28900i	−0.950565	−	0.310526i	$-0.899495\pi$
$233$	−1.81763e15	−	3.14824e15i	−0.744206	−	1.28900i	0.206359	−	0.978476i	$-0.433839\pi$
$234$	−1.94222e15	+	3.36403e15i	−0.773385	+	1.33954i
$235$	−1.28432e15	+	2.22451e15i	−0.497430	+	0.861574i
$236$	4.19796e14	+	7.27109e14i	0.158165	+	0.273950i
$237$	−7.32819e15			−2.68617
$238$	−2.41531e15	+	2.11951e15i	−0.861434	+	0.755937i
$239$	1.13012e15			0.392228			0.196114	−	0.980581i	$-0.437168\pi$
$239$	1.13012e15			0.392228			0.196114	+	0.980581i	$0.437168\pi$
$240$	6.99789e14	+	1.21207e15i	0.236371	+	0.409407i
$241$	2.08731e15	−	3.61533e15i	0.686242	−	1.18861i	−0.286803	−	0.957989i	$-0.592593\pi$
$241$	2.08731e15	−	3.61533e15i	0.686242	−	1.18861i	0.973045	−	0.230616i	$-0.0740740\pi$
$242$	6.33226e14	−	1.09678e15i	0.202656	−	0.351010i
$243$	1.80962e15	+	3.13435e15i	0.563827	+	0.976577i
$244$	2.00800e15			0.609157
$245$	−3.26755e15	+	1.35588e15i	−0.965258	+	0.400535i
$246$	6.64302e15			1.91112
$247$	−2.16696e15	−	3.75328e15i	−0.607184	−	1.05167i
$248$	4.37297e14	−	7.57421e14i	0.119355	−	0.206729i
$249$	−2.37665e15	+	4.11647e15i	−0.631929	+	1.09453i
$250$	1.29485e15	+	2.24275e15i	0.335436	+	0.580993i
$251$	−1.57148e15			−0.396669			−0.198335	−	0.980134i	$-0.563553\pi$
$251$	−1.57148e15			−0.396669			−0.198335	+	0.980134i	$0.563553\pi$
$252$	−3.47440e15	+	3.04890e15i	−0.854625	+	0.749962i
$253$	3.37564e15			0.809231
$254$	−1.20859e15	−	2.09335e15i	−0.282398	−	0.489127i
$255$	6.72817e15	−	1.16535e16i	1.53245	−	2.65428i
$256$	−1.40737e14	+	2.43764e14i	−0.0312500	+	0.0541266i
$257$	2.14419e15	+	3.71385e15i	0.464193	+	0.804006i	0.999165	−	0.0408639i	$-0.0130110\pi$
$257$	2.14419e15	+	3.71385e15i	0.464193	+	0.804006i	−0.534972	+	0.844870i	$0.679678\pi$
$258$	3.11255e15			0.657034
$259$	1.73713e15	+	5.89068e14i	0.357590	+	0.121260i
$260$	2.50368e15			0.502634
$261$	−1.09005e15	−	1.88801e15i	−0.213443	−	0.369693i
$262$	1.42239e15	−	2.46365e15i	0.271681	−	0.470566i
$263$	5.50898e14	−	9.54183e14i	0.102650	−	0.177795i	−0.810126	−	0.586256i	$-0.800601\pi$
$263$	5.50898e14	−	9.54183e14i	0.102650	−	0.177795i	0.912776	+	0.408461i	$0.133935\pi$
$264$	−1.14949e15	−	1.99098e15i	−0.208969	−	0.361944i
$265$	−1.14725e15			−0.203498
$266$	−1.00774e15	−	5.05793e15i	−0.174429	−	0.875472i
$267$	−8.84394e15			−1.49390
$268$	−3.97544e13	−	6.88566e13i	−0.00655404	−	0.0113519i
$269$	2.82176e15	−	4.88743e15i	0.454077	−	0.786485i	−0.544557	−	0.838724i	$-0.683302\pi$
$269$	2.82176e15	−	4.88743e15i	0.454077	−	0.786485i	0.998635	+	0.0522386i	$0.0166356\pi$
$270$	5.42239e15	−	9.39185e15i	0.851778	−	1.47532i
$271$	−1.74448e15	−	3.02153e15i	−0.267526	−	0.463368i	0.700697	−	0.713459i	$-0.252873\pi$
$271$	−1.74448e15	−	3.02153e15i	−0.267526	−	0.463368i	−0.968222	+	0.250091i	$0.919539\pi$
$272$	2.70626e15			0.405202
$273$	2.32628e15	+	1.16758e16i	0.340099	+	1.70698i
$274$	−7.09167e15			−1.01244
$275$	2.15897e14	+	3.73944e14i	0.0301012	+	0.0521367i
$276$	−4.11482e15	+	7.12708e15i	−0.560327	+	0.970515i
$277$	8.95883e14	−	1.55172e15i	0.119161	−	0.206392i	−0.800275	−	0.599634i	$-0.795313\pi$
$277$	8.95883e14	−	1.55172e15i	0.119161	−	0.206392i	0.919435	+	0.393241i	$0.128646\pi$
$278$	−2.82401e15	−	4.89132e15i	−0.366923	−	0.635529i
$279$	−1.20961e16			−1.53538
$280$	2.82155e15	+	9.56797e14i	0.349913	+	0.118657i
$281$	2.57574e15			0.312112			0.156056	−	0.987748i	$-0.450122\pi$
$281$	2.57574e15			0.312112			0.156056	+	0.987748i	$0.450122\pi$
$282$	5.14325e15	+	8.90837e15i	0.609001	+	1.05482i
$283$	−7.20836e15	+	1.24852e16i	−0.834112	+	1.44472i	0.0606394	+	0.998160i	$0.480686\pi$
$283$	−7.20836e15	+	1.24852e16i	−0.834112	+	1.44472i	−0.894751	+	0.446565i	$0.852647\pi$
$284$	−2.27839e15	+	3.94629e15i	−0.257667	+	0.446292i
$285$	1.07983e16	+	1.87032e16i	1.19362	+	2.06740i
$286$	−4.11261e15			−0.444364
$287$	1.06291e16	−	9.32741e15i	1.12270	−	0.985210i
$288$	3.89293e15			0.401999
$289$	−8.05747e15	−	1.39559e16i	−0.813509	−	1.40904i
$290$	−7.02577e14	+	1.21690e15i	−0.0693597	+	0.120134i
$291$	1.62413e16	−	2.81307e16i	1.56789	−	2.71567i
$292$	−6.11747e14	−	1.05958e15i	−0.0577542	−	0.100033i
$293$	5.01501e15			0.463055			0.231527	−	0.972828i	$-0.425628\pi$
$293$	5.01501e15			0.463055			0.231527	+	0.972828i	$0.425628\pi$
$294$	−1.84035e15	+	1.40472e16i	−0.166204	+	1.26862i
$295$	−7.48437e15			−0.661168
$296$	−7.72399e14	−	1.33783e15i	−0.0667491	−	0.115613i
$297$	−8.90698e15	+	1.54273e16i	−0.753032	+	1.30429i
$298$	−4.07638e15	+	7.06049e15i	−0.337185	+	0.584022i
$299$	7.36092e15	+	1.27495e16i	0.595757	+	1.03188i
$300$	−1.05269e15			−0.0833705
$301$	4.98021e15	−	4.37030e15i	0.385981	−	0.338711i
$302$	6.13685e15			0.465479
$303$	1.19936e16	+	2.07735e16i	0.890373	+	1.54217i
$304$	−2.17169e15	+	3.76149e15i	−0.157805	+	0.273326i
$305$	−8.94993e15	+	1.55017e16i	−0.636606	+	1.10263i
$306$	−1.87144e16	−	3.24143e16i	−1.30313	−	2.25708i
$307$	−1.74053e16			−1.18654			−0.593271	−	0.805003i	$-0.702164\pi$
$307$	−1.74053e16			−1.18654			−0.593271	+	0.805003i	$0.702164\pi$
$308$	−4.63476e15	−	1.57166e15i	−0.309348	−	0.104901i
$309$	−2.55829e16			−1.67193
$310$	3.89819e15	+	6.75187e15i	0.249467	+	0.432089i
$311$	1.21253e15	−	2.10016e15i	0.0759886	−	0.131616i	−0.825527	−	0.564362i	$-0.809122\pi$
$311$	1.21253e15	−	2.10016e15i	0.0759886	−	0.131616i	0.901516	+	0.432746i	$0.142455\pi$
$312$	5.01317e15	−	8.68307e15i	0.307686	−	0.532928i
$313$	−9.15997e15	−	1.58655e16i	−0.550625	−	0.953711i	−0.998230	−	0.0594791i	$-0.981056\pi$
$313$	−9.15997e15	−	1.58655e16i	−0.550625	−	0.953711i	0.447604	−	0.894232i	$-0.352277\pi$
$314$	−1.88596e16			−1.11042
$315$	−8.05162e15	−	4.04117e16i	−0.464370	−	2.33071i
$316$	1.31379e16			0.742267
$317$	2.39436e15	+	4.14716e15i	0.132527	+	0.229544i	0.924650	−	0.380818i	$-0.124358\pi$
$317$	2.39436e15	+	4.14716e15i	0.132527	+	0.229544i	−0.792123	+	0.610362i	$0.791024\pi$
$318$	−2.29717e15	+	3.97881e15i	−0.124571	+	0.215763i
$319$	1.15407e15	−	1.99892e15i	0.0613189	−	0.106207i
$320$	−1.25457e15	−	2.17299e15i	−0.0653163	−	0.113131i
$321$	5.30320e16			2.70555
$322$	3.42318e15	+	1.71812e16i	0.171146	+	0.858995i
$323$	4.17598e16			2.04617
$324$	−9.87665e15	−	1.71069e16i	−0.474315	−	0.821538i
$325$	−9.41568e14	+	1.63084e15i	−0.0443210	+	0.0767663i
$326$	1.13337e15	−	1.96305e15i	0.0522945	−	0.0905768i
$327$	9.75594e15	+	1.68978e16i	0.441275	+	0.764310i
$328$	−1.19095e16			−0.528098
$329$	2.07376e16	+	7.03218e15i	0.901540	+	0.305715i
$330$	2.04938e16			0.873540
$331$	7.00632e15	+	1.21353e16i	0.292825	+	0.507187i	0.974477	−	0.224489i	$-0.0720714\pi$
$331$	7.00632e15	+	1.21353e16i	0.292825	+	0.507187i	−0.681652	+	0.731677i	$0.738738\pi$
$332$	4.26082e15	−	7.37996e15i	0.174621	−	0.302452i
$333$	−1.06826e16	+	1.85029e16i	−0.429330	+	0.743621i
$334$	−5.88802e15	−	1.01983e16i	−0.232069	−	0.401955i
$335$	7.08764e14			0.0273975
$336$	8.96796e15	−	7.86968e15i	0.340007	−	0.298368i
$337$	−5.03253e16			−1.87151			−0.935755	−	0.352650i	$-0.885281\pi$
$337$	−5.03253e16			−1.87151			−0.935755	+	0.352650i	$0.885281\pi$
$338$	7.24040e14	+	1.25407e15i	0.0264122	+	0.0457472i
$339$	1.87323e16	−	3.24452e16i	0.670336	−	1.16106i
$340$	−1.20622e16	+	2.08923e16i	−0.423461	+	0.733455i
$341$	−6.40329e15	−	1.10908e16i	−0.220546	−	0.381997i
$342$	6.00711e16			2.03000
$343$	1.67789e16	+	2.50602e16i	0.556356	+	0.830944i
$344$	−5.58014e15			−0.181558
$345$	−3.66807e16	−	6.35328e16i	−1.17115	−	2.02849i
$346$	−2.08029e15	+	3.60317e15i	−0.0651823	+	0.112899i
$347$	−5.30620e15	+	9.19060e15i	−0.163171	+	0.282620i	−0.936004	−	0.351989i	$-0.885505\pi$
$347$	−5.30620e15	+	9.19060e15i	−0.163171	+	0.282620i	0.772834	+	0.634609i	$0.218839\pi$
$348$	2.81358e15	+	4.87326e15i	0.0849168	+	0.147080i
$349$	1.98547e16			0.588163			0.294082	−	0.955780i	$-0.404986\pi$
$349$	1.98547e16			0.588163			0.294082	+	0.955780i	$0.404986\pi$
$350$	−1.68435e15	+	1.47807e15i	−0.0489768	+	0.0429788i
$351$	−7.76902e16			−2.21753
$352$	2.06080e15	+	3.56941e15i	0.0577442	+	0.100016i
$353$	1.07656e15	−	1.86465e15i	0.0296143	−	0.0512935i	−0.850838	−	0.525427i	$-0.823905\pi$
$353$	1.07656e15	−	1.86465e15i	0.0296143	−	0.0512935i	0.880453	+	0.474134i	$0.157239\pi$
$354$	−1.49861e16	+	2.59567e16i	−0.404733	+	0.701018i
$355$	−2.03102e16	−	3.51783e16i	−0.538555	−	0.932805i
$356$	1.58553e16			0.412810
$357$	−1.08638e17	−	3.68395e16i	−2.77740	−	0.941826i
$358$	1.67994e16			0.421748
$359$	2.00877e16	+	3.47929e16i	0.495240	+	0.857780i	0.999985	−	0.00548800i	$-0.00174689\pi$
$359$	2.00877e16	+	3.47929e16i	0.495240	+	0.857780i	−0.504745	+	0.863268i	$0.668414\pi$
$360$	−1.73513e16	+	3.00534e16i	−0.420114	+	0.727658i
$361$	−1.24845e16	+	2.16238e16i	−0.296876	+	0.514205i
$362$	−1.31147e16	−	2.27152e16i	−0.306303	−	0.530532i
$363$	4.52106e16			1.03716
$364$	−4.17054e15	−	2.09322e16i	−0.0939794	−	0.471690i
$365$	1.09066e16			0.241426
$366$	3.58413e16	+	6.20790e16i	0.779394	+	1.34995i
$367$	9.34576e15	−	1.61873e16i	0.199657	−	0.345817i	−0.748760	−	0.662841i	$-0.769350\pi$
$367$	9.34576e15	−	1.61873e16i	0.199657	−	0.345817i	0.948417	+	0.317025i	$0.102684\pi$
$368$	7.37700e15	−	1.27773e16i	0.154835	−	0.268182i
$369$	8.23571e16	+	1.42647e17i	1.69836	+	2.94165i
$370$	1.37708e16			0.279027
$371$	1.91105e15	+	9.59170e15i	0.0380488	+	0.190970i
$372$	3.12218e16			0.610842
$373$	−1.39042e16	−	2.40829e16i	−0.267325	−	0.463021i	0.700845	−	0.713314i	$-0.252806\pi$
$373$	−1.39042e16	−	2.40829e16i	−0.267325	−	0.463021i	−0.968170	+	0.250293i	$0.919473\pi$
$374$	1.98137e16	−	3.43183e16i	0.374369	−	0.648427i
$375$	−4.62244e16	+	8.00630e16i	−0.858357	+	1.48672i
$376$	−9.22075e15	−	1.59708e16i	−0.168285	−	0.291478i
$377$	1.00663e16			0.180572
$378$	−8.75540e16	−	2.96898e16i	−1.54376	−	0.523493i
$379$	5.13829e15			0.0890562			0.0445281	−	0.999008i	$-0.485822\pi$
$379$	5.13829e15			0.0890562			0.0445281	+	0.999008i	$0.485822\pi$
$380$	−1.93591e16	−	3.35309e16i	−0.329831	−	0.571284i
$381$	4.31451e16	−	7.47295e16i	0.722635	−	1.25164i
$382$	−2.08318e15	+	3.60818e15i	−0.0343017	+	0.0594122i
$383$	−3.54517e16	−	6.14041e16i	−0.573911	−	0.994044i	−0.996159	−	0.0875631i	$-0.972092\pi$
$383$	−3.54517e16	−	6.14041e16i	−0.573911	−	0.994044i	0.422248	−	0.906481i	$-0.361241\pi$
$384$	−1.00483e16			−0.159933
$385$	3.27910e16	−	2.87752e16i	0.513169	−	0.450323i
$386$	−2.07742e16			−0.319674
$387$	3.85880e16	+	6.68363e16i	0.583889	+	1.01133i
$388$	−2.91172e16	+	5.04324e16i	−0.433254	+	0.750419i
$389$	−4.07444e16	+	7.05713e16i	−0.596205	+	1.03266i	0.397171	+	0.917745i	$0.369992\pi$
$389$	−4.07444e16	+	7.05713e16i	−0.596205	+	1.03266i	−0.993376	+	0.114912i	$0.963341\pi$
$390$	4.46889e16	+	7.74034e16i	0.643101	+	1.11388i
$391$	−1.41853e17			−2.00766
$392$	3.29936e15	−	2.51837e16i	0.0459272	−	0.350558i
$393$	1.01555e17			1.39043
$394$	−2.84268e16	−	4.92367e16i	−0.382827	−	0.663076i
$395$	−5.85575e16	+	1.01425e17i	−0.775713	+	1.34357i
$396$	2.85018e16	−	4.93666e16i	0.371410	−	0.643302i
$397$	−6.29534e16	−	1.09039e17i	−0.807014	−	1.39779i	−0.914923	−	0.403628i	$-0.867749\pi$
$397$	−6.29534e16	−	1.09039e17i	−0.807014	−	1.39779i	0.107909	−	0.994161i	$-0.465584\pi$
$398$	−1.00413e16			−0.126633
$399$	1.38383e17	−	1.21436e17i	1.71695	−	1.50668i
$400$	1.88725e15			0.0230377
$401$	3.44516e16	+	5.96719e16i	0.413781	+	0.716691i	0.995300	−	0.0968428i	$-0.0308744\pi$
$401$	3.44516e16	+	5.96719e16i	0.413781	+	0.716691i	−0.581518	+	0.813533i	$0.697541\pi$
$402$	1.41918e15	−	2.45808e15i	0.0167713	−	0.0290487i
$403$	2.79260e16	−	4.83693e16i	0.324733	−	0.562454i
$404$	−2.15020e16	−	3.72425e16i	−0.246036	−	0.426147i
$405$	1.76086e17			1.98275
$406$	1.13443e16	+	3.84690e15i	0.125707	+	0.0426277i
$407$	−2.26203e16			−0.246680
$408$	4.83048e16	+	8.36664e16i	0.518441	+	0.897966i
$409$	4.70235e16	−	8.14471e16i	0.496722	−	0.860348i	−0.503271	−	0.864129i	$-0.667870\pi$
$409$	4.70235e16	−	8.14471e16i	0.496722	−	0.860348i	0.999993	+	0.00378092i	$0.00120351\pi$
$410$	5.30824e16	−	9.19415e16i	0.551894	−	0.955909i
$411$	−1.26581e17	−	2.19245e17i	−1.29538	−	2.24367i
$412$	4.58647e16			0.462005
$413$	1.24672e16	+	6.25738e16i	0.123621	+	0.620465i
$414$	−2.04055e17			−1.99179
$415$	3.79822e16	+	6.57870e16i	0.364978	+	0.632161i
$416$	−8.98756e15	+	1.55669e16i	−0.0850228	+	0.147264i
$417$	1.00813e17	−	1.74613e17i	0.938928	−	1.62627i
$418$	3.17998e16	+	5.50789e16i	0.291594	+	0.505056i
$419$	−7.38113e16			−0.666395			−0.333198	−	0.942857i	$-0.608128\pi$
$419$	−7.38113e16			−0.666395			−0.333198	+	0.942857i	$0.608128\pi$
$420$	2.07825e16	+	1.04309e17i	0.184747	+	0.927259i
$421$	1.83025e17			1.60205			0.801026	−	0.598630i	$-0.204288\pi$
$421$	1.83025e17			1.60205			0.801026	+	0.598630i	$0.204288\pi$
$422$	1.08123e16	+	1.87275e16i	0.0931942	+	0.161417i
$423$	−1.27527e17	+	2.20884e17i	−1.08241	+	1.87478i
$424$	4.11833e15	−	7.13316e15i	0.0344226	−	0.0596216i
$425$	−9.07255e15	−	1.57141e16i	−0.0746795	−	0.129349i
$426$	−1.62671e17			−1.31870
$427$	1.44512e17	+	4.90046e16i	1.15378	+	0.391251i
$428$	−9.50751e16			−0.747622
$429$	−7.34072e16	−	1.27145e17i	−0.568547	−	0.984753i
$430$	2.48715e16	−	4.30786e16i	0.189739	−	0.328637i
$431$	−1.29050e17	+	2.23521e17i	−0.969739	+	1.67964i	−0.273435	+	0.961891i	$0.588160\pi$
$431$	−1.29050e17	+	2.23521e17i	−0.969739	+	1.67964i	−0.696304	+	0.717747i	$0.745174\pi$
$432$	3.89300e16	+	6.74287e16i	0.288164	+	0.499115i
$433$	−6.73189e16			−0.490869			−0.245435	−	0.969413i	$-0.578931\pi$
$433$	−6.73189e16			−0.490869			−0.245435	+	0.969413i	$0.578931\pi$
$434$	4.99562e16	−	4.38383e16i	0.358845	−	0.314898i
$435$	−5.01620e16			−0.354973
$436$	−1.74903e16	−	3.02942e16i	−0.121937	−	0.211201i
$437$	1.13833e17	−	1.97165e17i	0.781879	−	1.35425i
$438$	2.18385e16	−	3.78254e16i	0.147789	−	0.255978i
$439$	1.30115e17	+	2.25366e17i	0.867577	+	1.50269i	0.864466	+	0.502692i	$0.167657\pi$
$439$	1.30115e17	+	2.25366e17i	0.867577	+	1.50269i	0.00311079	+	0.999995i	$0.499010\pi$
$440$	−3.67411e16			−0.241385
$441$	−3.24454e17	+	1.34633e17i	−2.10040	+	0.871565i
$442$	1.72823e17			1.10244
$443$	9.05469e16	+	1.56832e17i	0.569179	+	0.985848i	0.996647	+	0.0818172i	$0.0260724\pi$
$443$	9.05469e16	+	1.56832e17i	0.569179	+	0.985848i	−0.427468	+	0.904031i	$0.640594\pi$
$444$	2.75736e16	−	4.77588e16i	0.170806	−	0.295845i
$445$	−7.06694e16	+	1.22403e17i	−0.431411	+	0.747226i
$446$	−8.62432e16	−	1.49378e17i	−0.518858	−	0.898688i
$447$	−2.91042e17			−1.72566
$448$	−1.60776e16	+	1.41087e16i	−0.0939540	+	0.0824478i
$449$	−1.16257e17			−0.669603			−0.334801	−	0.942289i	$-0.608669\pi$
$449$	−1.16257e17			−0.669603			−0.334801	+	0.942289i	$0.608669\pi$
$450$	−1.30508e16	−	2.26046e16i	−0.0740892	−	0.128326i
$451$	−8.71948e16	+	1.51026e17i	−0.487914	+	0.845091i
$452$	−3.35830e16	+	5.81675e16i	−0.185234	+	0.320834i
$453$	1.09538e17	+	1.89726e17i	0.595564	+	1.03155i
$454$	1.98501e17			1.06390
$455$	1.80186e17	+	6.11015e16i	0.952019	+	0.322833i
$456$	−1.55053e17			−0.807622
$457$	−8.21676e16	−	1.42318e17i	−0.421935	−	0.730812i	0.574194	−	0.818719i	$-0.305315\pi$
$457$	−8.21676e16	−	1.42318e17i	−0.421935	−	0.730812i	−0.996129	+	0.0879072i	$0.971982\pi$
$458$	−2.08133e16	+	3.60497e16i	−0.105370	+	0.182506i
$459$	3.74295e17	−	6.48298e17i	1.86824	−	3.23588i
$460$	6.57607e16	+	1.13901e17i	0.323624	+	0.560533i
$461$	1.27102e17			0.616732			0.308366	−	0.951268i	$-0.400218\pi$
$461$	1.27102e17			0.616732			0.308366	+	0.951268i	$0.400218\pi$
$462$	−3.41379e16	−	1.71341e17i	−0.163329	−	0.819763i
$463$	1.15615e17			0.545427			0.272714	−	0.962095i	$-0.412079\pi$
$463$	1.15615e17			0.545427			0.272714	+	0.962095i	$0.412079\pi$
$464$	−5.04415e15	−	8.73672e15i	−0.0234650	−	0.0406426i
$465$	−1.39160e17	+	2.41032e17i	−0.638367	+	1.10568i
$466$	−1.16329e17	+	2.01487e17i	−0.526233	+	0.911462i
$467$	−5.06977e16	−	8.78109e16i	−0.226166	−	0.391732i	0.730502	−	0.682910i	$-0.239286\pi$
$467$	−5.06977e16	−	8.78109e16i	−0.226166	−	0.391732i	−0.956669	+	0.291178i	$0.905953\pi$
$468$	2.48604e17			1.09373
$469$	−1.18063e15	−	5.92569e15i	−0.00512262	−	0.0257108i
$470$	1.64393e17			0.703472
$471$	−3.36630e17	−	5.83060e17i	−1.42075	−	2.46081i
$472$	2.68670e16	−	4.65350e16i	0.111840	−	0.193712i
$473$	−4.08546e16	+	7.07623e16i	−0.167743	+	0.290539i
$474$	2.34502e17	+	4.06170e17i	0.949703	+	1.64493i
$475$	2.91218e16			0.116335
$476$	1.94765e17	+	6.60454e16i	0.767478	+	0.260254i
$477$	−1.13917e17			−0.442811
$478$	−3.61639e16	−	6.26377e16i	−0.138674	−	0.240190i
$479$	1.37053e17	−	2.37383e17i	0.518451	−	0.897983i	−0.481319	−	0.876545i	$-0.659842\pi$
$479$	1.37053e17	−	2.37383e17i	0.518451	−	0.897983i	0.999770	−	0.0214381i	$-0.00682447\pi$
$480$	4.47865e16	−	7.75725e16i	0.167140	−	0.289494i
$481$	−4.93258e16	−	8.54347e16i	−0.181606	−	0.314551i
$482$	−2.67176e17			−0.970492
$483$	−4.70071e17	+	4.12503e17i	−1.68464	+	1.47833i
$484$	−8.10530e16			−0.286599
$485$	−2.59559e17	−	4.49569e17i	−0.905554	−	1.56847i
$486$	1.15816e17	−	2.00598e17i	0.398686	−	0.690544i
$487$	1.58958e17	−	2.75324e17i	0.539939	−	0.935202i	−0.458968	−	0.888453i	$-0.651781\pi$
$487$	1.58958e17	−	2.75324e17i	0.539939	−	0.935202i	0.998907	−	0.0467486i	$-0.0148860\pi$
$488$	−6.42559e16	−	1.11294e17i	−0.215369	−	0.373031i
$489$	8.09192e16			0.267636
$490$	1.79712e17	+	1.37718e17i	0.586547	+	0.449487i
$491$	2.94376e17			0.948140			0.474070	−	0.880487i	$-0.342784\pi$
$491$	2.94376e17			0.948140			0.474070	+	0.880487i	$0.342784\pi$
$492$	−2.12577e17	−	3.68194e17i	−0.675682	−	1.17032i
$493$	−4.84973e16	+	8.39997e16i	−0.152129	+	0.263495i
$494$	−1.38685e17	+	2.40210e17i	−0.429344	+	0.743646i
$495$	2.54073e17	+	4.40068e17i	0.776292	+	1.34458i
$496$	−5.59741e16			−0.168794
$497$	−2.60280e17	+	2.28404e17i	−0.774683	+	0.679811i
$498$	3.04211e17			0.893683
$499$	2.67698e17	+	4.63666e17i	0.776232	+	1.34447i	0.934100	+	0.357012i	$0.116205\pi$
$499$	2.67698e17	+	4.63666e17i	0.776232	+	1.34447i	−0.157868	+	0.987460i	$0.550462\pi$
$500$	8.28705e16	−	1.43536e17i	0.237189	−	0.410824i
$501$	2.10194e17	−	3.64066e17i	0.593847	−	1.02857i
$502$	5.02872e16	+	8.71000e16i	0.140244	+	0.242909i
$503$	3.35892e17			0.924716			0.462358	−	0.886693i	$-0.347004\pi$
$503$	3.35892e17			0.924716			0.462358	+	0.886693i	$0.347004\pi$
$504$	2.80168e17	+	9.50058e16i	0.761412	+	0.258197i
$505$	3.83349e17			1.02849
$506$	−1.08020e17	−	1.87097e17i	−0.286106	−	0.495551i
$507$	−2.58472e16	+	4.47687e16i	−0.0675868	+	0.117064i
$508$	−7.73500e16	+	1.33974e17i	−0.199685	+	0.345865i
$509$	−1.76717e17	−	3.06083e17i	−0.450415	−	0.780142i	0.547996	−	0.836481i	$-0.315391\pi$
$509$	−1.76717e17	−	3.06083e17i	−0.450415	−	0.780142i	−0.998412	+	0.0563384i	$0.982057\pi$
$510$	−8.61206e17			−2.16721
$511$	−1.81678e16	−	9.11855e16i	−0.0451405	−	0.226564i
$512$	1.80144e16			0.0441942
$513$	6.00722e17	+	1.04048e18i	1.45516	+	2.52041i
$514$	1.37228e17	−	2.37687e17i	0.328234	−	0.568518i
$515$	−2.04425e17	+	3.54075e17i	−0.482823	+	0.836273i
$516$	−9.96015e16	−	1.72515e17i	−0.232297	−	0.402350i
$517$	−2.70037e17			−0.621919
$518$	−2.29389e16	−	1.15132e17i	−0.0521709	−	0.261850i
$519$	−1.48527e17			−0.333593
$520$	−8.01177e16	−	1.38768e17i	−0.177708	−	0.307799i
$521$	1.53433e17	−	2.65755e17i	0.336105	−	0.582151i	−0.647592	−	0.761988i	$-0.724224\pi$
$521$	1.53433e17	−	2.65755e17i	0.336105	−	0.582151i	0.983696	+	0.179837i	$0.0575570\pi$
$522$	−6.97629e16	+	1.20833e17i	−0.150927	+	0.261413i
$523$	−3.42843e17	−	5.93821e17i	−0.732544	−	1.26880i	−0.955792	−	0.294042i	$-0.904999\pi$
$523$	−3.42843e17	−	5.93821e17i	−0.732544	−	1.26880i	0.223248	−	0.974762i	$-0.428334\pi$
$524$	−1.82066e17			−0.384216
$525$	−7.57604e16	−	2.56906e16i	−0.157909	−	0.0535474i
$526$	−7.05150e16			−0.145169
$527$	2.69083e17	+	4.66066e17i	0.547164	+	0.947716i
$528$	−7.35676e16	+	1.27423e17i	−0.147763	+	0.255933i
$529$	−1.34660e17	+	2.33238e17i	−0.267164	+	0.462741i
$530$	3.67120e16	+	6.35870e16i	0.0719473	+	0.124616i
$531$	−7.43165e17			−1.43870
$532$	−2.48091e17	+	2.17708e17i	−0.474445	+	0.416341i
$533$	−7.60548e17			−1.43681
$534$	2.83006e17	+	4.90181e17i	0.528175	+	0.914826i
$535$	4.23763e17	−	7.33979e17i	0.781311	−	1.35327i
$536$	−2.54428e15	+	4.40682e15i	−0.00463441	+	0.00802703i
$537$	2.99857e17	+	5.19367e17i	0.539611	+	0.934634i
$538$	−3.61185e17			−0.642162
$539$	−2.95200e17	−	2.26220e17i	−0.518549	−	0.397378i
$540$	−6.94066e17			−1.20460
$541$	−1.64739e17	−	2.85336e17i	−0.282497	−	0.489299i	0.689502	−	0.724284i	$-0.257829\pi$
$541$	−1.64739e17	−	2.85336e17i	−0.282497	−	0.489299i	−0.971999	+	0.234985i	$0.924496\pi$
$542$	−1.11647e17	+	1.93378e17i	−0.189169	+	0.327651i
$543$	4.68174e17	−	8.10902e17i	0.783806	−	1.35759i
$544$	−8.66003e16	−	1.49996e17i	−0.143261	−	0.248135i
$545$	3.11828e17			0.509727
$546$	5.72698e17	−	5.02562e17i	0.925067	−	0.811778i
$547$	7.07530e17			1.12935			0.564673	−	0.825315i	$-0.309002\pi$
$547$	7.07530e17			1.12935			0.564673	+	0.825315i	$0.309002\pi$
$548$	2.26933e17	+	3.93060e17i	0.357952	+	0.619991i
$549$	−8.88689e17	+	1.53925e18i	−1.38525	+	2.39933i
$550$	1.38174e16	−	2.39324e16i	0.0212847	−	0.0368662i
$551$	−7.78353e16	−	1.34815e17i	−0.118493	−	0.205235i
$552$	5.26697e17			0.792423
$553$	9.45513e17	+	3.20626e17i	1.40590	+	0.476745i
$554$	−1.14673e17			−0.168519
$555$	2.45798e17	+	4.25735e17i	0.357005	+	0.618351i
$556$	−1.80736e17	+	3.13045e17i	−0.259454	+	0.449387i
$557$	4.14052e17	−	7.17159e17i	0.587484	−	1.01755i	−0.407077	−	0.913394i	$-0.633452\pi$
$557$	4.14052e17	−	7.17159e17i	0.587484	−	1.01755i	0.994561	−	0.104158i	$-0.0332147\pi$
$558$	3.87074e17	+	6.70431e17i	0.542839	+	0.940225i
$559$	−3.56350e17			−0.493970
$560$	−3.72586e16	−	1.87004e17i	−0.0510510	−	0.256229i
$561$	1.41464e18			1.91597
$562$	−8.24237e16	−	1.42762e17i	−0.110348	−	0.191129i
$563$	−4.96156e17	+	8.59368e17i	−0.656620	+	1.13730i	0.324865	+	0.945760i	$0.394681\pi$
$563$	−4.96156e17	+	8.59368e17i	−0.656620	+	1.13730i	−0.981485	+	0.191538i	$0.938652\pi$
$564$	3.29168e17	−	5.70135e17i	0.430629	−	0.745871i
$565$	−2.99368e17	−	5.18521e17i	−0.387160	−	0.670582i
$566$	9.22670e17			1.17961
$567$	−2.93319e17	−	1.47219e18i	−0.370723	−	1.86069i
$568$	2.91634e17			0.364396
$569$	−2.58716e17	−	4.48110e17i	−0.319590	−	0.553547i	0.660812	−	0.750551i	$-0.270212\pi$
$569$	−2.58716e17	−	4.48110e17i	−0.319590	−	0.553547i	−0.980403	+	0.197004i	$0.936879\pi$
$570$	6.91092e17	−	1.19701e18i	0.844014	−	1.46187i
$571$	9.51050e16	−	1.64727e17i	0.114834	−	0.198898i	−0.802880	−	0.596141i	$-0.796700\pi$
$571$	9.51050e16	−	1.64727e17i	0.114834	−	0.198898i	0.917713	+	0.397244i	$0.130033\pi$
$572$	1.31604e17	+	2.27944e17i	0.157106	+	0.272116i
$573$	−1.48733e17			−0.175551
$574$	−8.57109e17	−	2.90648e17i	−1.00025	−	0.339188i
$575$	−9.89236e16			−0.114145
$576$	−1.24574e17	−	2.15768e17i	−0.142128	−	0.246173i
$577$	−6.30548e16	+	1.09214e17i	−0.0711337	+	0.123207i	−0.899398	−	0.437130i	$-0.855995\pi$
$577$	−6.30548e16	+	1.09214e17i	−0.0711337	+	0.123207i	0.828265	+	0.560337i	$0.189328\pi$
$578$	−5.15678e17	+	8.93180e17i	−0.575238	+	0.996341i
$579$	−3.70805e17	−	6.42254e17i	−0.409011	−	0.708428i
$580$	8.99299e16			0.0980894
$581$	4.86750e17	−	4.27140e17i	0.525002	−	0.460707i
$582$	−2.07888e18			−2.21733
$583$	−6.03042e16	−	1.04450e17i	−0.0636065	−	0.110170i
$584$	−3.91518e16	+	6.78129e16i	−0.0408384	+	0.0707341i
$585$	−1.10806e18	+	1.91922e18i	−1.14301	+	1.97976i
$586$	−1.60480e17	−	2.77960e17i	−0.163715	−	0.283562i
$587$	1.15869e18			1.16902			0.584508	−	0.811388i	$-0.301288\pi$
$587$	1.15869e18			1.16902			0.584508	+	0.811388i	$0.301288\pi$
$588$	8.37466e17	−	3.47508e17i	0.835631	−	0.346747i
$589$	−8.63726e17			−0.852367
$590$	2.39500e17	+	4.14826e17i	0.233758	+	0.404881i
$591$	1.01480e18	−	1.75768e18i	0.979626	−	1.69676i
$592$	−4.94335e16	+	8.56214e16i	−0.0471988	+	0.0817507i
$593$	−7.70638e16	−	1.33478e17i	−0.0727771	−	0.126054i	0.827340	−	0.561701i	$-0.189853\pi$
$593$	−7.70638e16	−	1.33478e17i	−0.0727771	−	0.126054i	−0.900117	+	0.435647i	$0.856520\pi$
$594$	1.14009e18			1.06495
$595$	−1.37797e18	+	1.20921e18i	−1.27315	+	1.11723i
$596$	5.21776e17			0.476852
$597$	−1.79229e17	−	3.10434e17i	−0.162023	−	0.280632i
$598$	4.71099e17	−	8.15967e17i	0.421264	−	0.729650i
$599$	−7.16824e17	+	1.24158e18i	−0.634071	+	1.09824i	0.352640	+	0.935759i	$0.385284\pi$
$599$	−7.16824e17	+	1.24158e18i	−0.634071	+	1.09824i	−0.986711	+	0.162485i	$0.948049\pi$
$600$	3.36861e16	+	5.83460e16i	0.0294759	+	0.0510538i
$601$	−1.25241e18			−1.08408			−0.542040	−	0.840353i	$-0.682348\pi$
$601$	−1.25241e18			−1.08408			−0.542040	+	0.840353i	$0.682348\pi$
$602$	−4.01593e17	−	1.36182e17i	−0.343882	−	0.116611i
$603$	7.03772e16			0.0596169
$604$	−1.96379e17	−	3.40139e17i	−0.164572	−	0.285047i
$605$	3.61265e17	−	6.25729e17i	0.299513	−	0.518772i
$606$	7.67589e17	−	1.32950e18i	0.629588	−	1.09048i
$607$	5.93033e17	+	1.02716e18i	0.481230	+	0.833514i	0.999768	−	0.0215401i	$-0.00685696\pi$
$607$	5.93033e17	+	1.02716e18i	0.481230	+	0.833514i	−0.518538	+	0.855054i	$0.673524\pi$
$608$	2.77977e17			0.223170
$609$	8.35581e16	+	4.19385e17i	0.0663707	+	0.333120i
$610$	1.14559e18			0.900296
$611$	−5.88842e17	−	1.01990e18i	−0.457858	−	0.793033i
$612$	−1.19772e18	+	2.07452e18i	−0.921450	+	1.59600i
$613$	−9.49353e17	+	1.64433e18i	−0.722661	+	1.25169i	0.237268	+	0.971444i	$0.423748\pi$
$613$	−9.49353e17	+	1.64433e18i	−0.722661	+	1.25169i	−0.959929	+	0.280242i	$0.909585\pi$
$614$	5.56971e17	+	9.64701e17i	0.419506	+	0.726605i
$615$	3.78994e18			2.82451
$616$	6.12020e16	+	3.07178e17i	0.0451327	+	0.226525i
$617$	−4.94808e17			−0.361063			−0.180532	−	0.983569i	$-0.557782\pi$
$617$	−4.94808e17			−0.361063			−0.180532	+	0.983569i	$0.557782\pi$
$618$	8.18652e17	+	1.41795e18i	0.591118	+	1.02385i
$619$	−5.83734e17	+	1.01106e18i	−0.417086	+	0.722414i	−0.995645	−	0.0932266i	$-0.970282\pi$
$619$	−5.83734e17	+	1.01106e18i	−0.417086	+	0.722414i	0.578559	+	0.815640i	$0.303615\pi$
$620$	2.49484e17	−	4.32120e17i	0.176399	−	0.305533i
$621$	−2.04058e18	−	3.53439e18i	−1.42777	−	2.47297i
$622$	−1.55203e17			−0.107464
$623$	1.14108e18	+	3.86944e17i	0.781887	+	0.265140i
$624$	−6.41686e17			−0.435134
$625$	8.07389e17	+	1.39844e18i	0.541830	+	0.938476i
$626$	−5.86238e17	+	1.01539e18i	−0.389351	+	0.674375i
$627$	−1.13521e18	+	1.96624e18i	−0.746168	+	1.29240i
$628$	6.03506e17	+	1.04530e18i	0.392594	+	0.679993i
$629$	9.50564e17			0.612001
$630$	−1.98219e18	+	1.73944e18i	−1.26308	+	1.10840i
$631$	−2.58748e18			−1.63187			−0.815935	−	0.578143i	$-0.803777\pi$
$631$	−2.58748e18			−1.63187			−0.815935	+	0.578143i	$0.803777\pi$
$632$	−4.20413e17	−	7.28176e17i	−0.262431	−	0.454544i
$633$	−3.85985e17	+	6.68546e17i	−0.238477	+	0.413055i
$634$	1.53239e17	−	2.65418e17i	0.0937108	−	0.162312i
$635$	−6.89520e17	−	1.19428e18i	−0.417366	−	0.722900i
$636$	2.94037e17			0.176170
$637$	2.10698e17	−	1.60824e18i	0.124955	−	0.953772i
$638$	−1.47722e17			−0.0867180
$639$	−2.01672e18	−	3.49305e18i	−1.17190	−	2.02978i
$640$	−8.02927e16	+	1.39071e17i	−0.0461856	+	0.0799958i
$641$	−1.05191e18	+	1.82195e18i	−0.598962	+	1.03743i	0.394012	+	0.919105i	$0.371087\pi$
$641$	−1.05191e18	+	1.82195e18i	−0.598962	+	1.03743i	−0.992975	+	0.118328i	$0.962247\pi$
$642$	−1.69702e18	−	2.93933e18i	−0.956555	−	1.65680i
$643$	2.34494e18			1.30846			0.654230	−	0.756296i	$-0.272993\pi$
$643$	2.34494e18			1.30846			0.654230	+	0.756296i	$0.272993\pi$
$644$	8.42738e17	−	7.39531e17i	0.465516	−	0.408506i
$645$	1.77575e18			0.971056
$646$	−1.33631e18	−	2.31456e18i	−0.723431	−	1.25302i
$647$	−6.98459e17	+	1.20977e18i	−0.374337	+	0.648371i	−0.990228	−	0.139461i	$-0.955463\pi$
$647$	−6.98459e17	+	1.20977e18i	−0.374337	+	0.648371i	0.615890	+	0.787832i	$0.288796\pi$
$648$	−6.32105e17	+	1.09484e18i	−0.335391	+	0.580915i
$649$	−3.93409e17	−	6.81405e17i	−0.206659	−	0.357944i
$650$	1.20521e17			0.0626794
$651$	2.24698e18	+	7.61958e17i	1.15697	+	0.392333i
$652$	−1.45071e17			−0.0739556
$653$	1.03360e18	+	1.79025e18i	0.521697	+	0.903606i	0.999681	+	0.0252376i	$0.00803422\pi$
$653$	1.03360e18	+	1.79025e18i	0.521697	+	0.903606i	−0.477984	+	0.878368i	$0.658632\pi$
$654$	6.24380e17	−	1.08146e18i	0.312028	−	0.540449i
$655$	8.11493e17	−	1.40555e18i	0.401528	−	0.695468i
$656$	3.81105e17	+	6.60093e17i	0.186711	+	0.323393i
$657$	1.08298e18			0.525344
$658$	−2.73840e17	−	1.37442e18i	−0.131531	−	0.660164i
$659$	2.93883e18			1.39772			0.698858	−	0.715261i	$-0.253692\pi$
$659$	2.93883e18			1.39772			0.698858	+	0.715261i	$0.253692\pi$
$660$	−6.55803e17	−	1.13588e18i	−0.308843	−	0.534932i
$661$	1.26765e18	−	2.19564e18i	0.591141	−	1.02389i	−0.402938	−	0.915227i	$-0.632011\pi$
$661$	1.26765e18	−	2.19564e18i	0.591141	−	1.02389i	0.994079	−	0.108659i	$-0.0346556\pi$
$662$	4.48404e17	−	7.76659e17i	0.207058	−	0.358636i
$663$	3.08477e18	+	5.34297e18i	1.41054	+	2.44312i
$664$	−5.45385e17			−0.246951
$665$	−5.74930e17	−	2.88562e18i	−0.257795	−	1.29389i
$666$	1.36738e18			0.607164
$667$	2.64398e17	+	4.57950e17i	0.116263	+	0.201373i
$668$	−3.76833e17	+	6.52694e17i	−0.164098	+	0.284225i
$669$	3.07876e18	−	5.33257e18i	1.32772	−	2.29968i
$670$	−2.26804e16	−	3.92837e16i	−0.00968647	−	0.0167774i
$671$	−1.88178e18			−0.795926
$672$	−7.23157e17	−	2.45225e17i	−0.302923	−	0.102722i
$673$	−3.04015e18			−1.26124			−0.630618	−	0.776093i	$-0.717199\pi$
$673$	−3.04015e18			−1.26124			−0.630618	+	0.776093i	$0.717199\pi$
$674$	1.61041e18	+	2.78931e18i	0.661679	+	1.14606i
$675$	2.61020e17	−	4.52100e17i	0.106218	−	0.183976i
$676$	4.63386e16	−	8.02607e16i	0.0186762	−	0.0323482i
$677$	2.71270e17	+	4.69854e17i	0.108287	+	0.187558i	0.915076	−	0.403281i	$-0.132130\pi$
$677$	2.71270e17	+	4.69854e17i	0.108287	+	0.187558i	−0.806790	+	0.590839i	$0.798797\pi$
$678$	−2.39773e18			−0.947998
$679$	−3.32630e18	+	2.91894e18i	−1.30259	+	1.14307i
$680$	1.54396e18			0.598864
$681$	3.54310e18	+	6.13682e18i	1.36121	+	2.35769i
$682$	−4.09810e17	+	7.09812e17i	−0.155950	+	0.270113i
$683$	1.47214e18	−	2.54982e18i	0.554900	−	0.961115i	−0.443011	−	0.896516i	$-0.646090\pi$
$683$	1.47214e18	−	2.54982e18i	0.554900	−	0.961115i	0.997911	−	0.0645988i	$-0.0205768\pi$
$684$	−1.92227e18	−	3.32948e18i	−0.717713	−	1.24312i
$685$	−4.04590e18			−1.49633
$686$	8.52049e17	−	1.73191e18i	0.312146	−	0.634480i
$687$	−1.48601e18			−0.539266
$688$	1.78564e17	+	3.09283e17i	0.0641904	+	0.111181i
$689$	2.62999e17	−	4.55527e17i	0.0936544	−	0.162214i
$690$	−2.34756e18	+	4.06610e18i	−0.828129	+	1.43436i
$691$	7.95101e17	+	1.37715e18i	0.277853	+	0.481255i	0.970851	−	0.239684i	$-0.0770439\pi$
$691$	7.95101e17	+	1.37715e18i	0.277853	+	0.481255i	−0.692998	+	0.720939i	$0.743711\pi$
$692$	2.66277e17			0.0921817
$693$	3.25601e18	−	2.85726e18i	1.11666	−	0.979903i
$694$	6.79193e17			0.230758
$695$	−1.61114e18	−	2.79057e18i	−0.542289	−	0.939273i
$696$	1.80069e17	−	3.11888e17i	0.0600452	−	0.104001i
$697$	3.66416e18	−	6.34651e18i	1.21049	−	2.09663i
$698$	−6.35350e17	−	1.10046e18i	−0.207947	−	0.360175i
$699$	−8.30553e18			−2.69318
$700$	1.35822e17	+	4.60578e16i	0.0436349	+	0.0147967i
$701$	−3.34716e18			−1.06539			−0.532695	−	0.846307i	$-0.678821\pi$
$701$	−3.34716e18			−1.06539			−0.532695	+	0.846307i	$0.678821\pi$
$702$	2.48609e18	+	4.30603e18i	0.784016	+	1.35796i
$703$	−7.62800e17	+	1.32121e18i	−0.238342	+	0.412821i
$704$	1.31891e17	−	2.28442e17i	0.0408313	−	0.0707219i
$705$	2.93430e18	+	5.08235e18i	0.900066	+	1.55896i
$706$	−1.37799e17			−0.0418809
$707$	−6.38569e17	−	3.20503e18i	−0.192301	−	0.965174i
$708$	1.91823e18			0.572379
$709$	2.17273e18	+	3.76328e18i	0.642400	+	1.11267i	0.984895	+	0.173150i	$0.0553945\pi$
$709$	2.17273e18	+	3.76328e18i	0.642400	+	1.11267i	−0.342496	+	0.939519i	$0.611272\pi$
$710$	−1.29985e18	+	2.25141e18i	−0.380816	+	0.659593i
$711$	−5.81450e18	+	1.00710e19i	−1.68795	+	2.92362i
$712$	−5.07370e17	−	8.78791e17i	−0.145950	−	0.252793i
$713$	2.93398e18			0.836325
$714$	1.43457e18	+	7.20020e18i	0.405212	+	2.03379i
$715$	−2.34630e18			−0.656742
$716$	−5.37580e17	−	9.31115e17i	−0.149110	−	0.258267i
$717$	1.29100e18	−	2.23608e18i	0.354856	−	0.614628i
$718$	1.28561e18	−	2.22674e18i	0.350187	−	0.606542i
$719$	−1.05687e18	−	1.83055e18i	−0.285288	−	0.494133i	0.687391	−	0.726287i	$-0.258756\pi$
$719$	−1.05687e18	−	1.83055e18i	−0.285288	−	0.494133i	−0.972679	+	0.232155i	$0.925422\pi$
$720$	2.22097e18			0.594130
$721$	3.30080e18	+	1.11931e18i	0.875065	+	0.296737i
$722$	1.59802e18			0.419846
$723$	−4.76891e18	−	8.25999e18i	−1.24171	−	2.15070i
$724$	−8.39338e17	+	1.45378e18i	−0.216589	+	0.375143i
$725$	−3.38203e16	+	5.85785e16i	−0.00864929	+	0.0149810i
$726$	−1.44674e18	−	2.50582e18i	−0.366692	−	0.635130i
$727$	1.17297e18			0.294656			0.147328	−	0.989088i	$-0.452933\pi$
$727$	1.17297e18			0.294656			0.147328	+	0.989088i	$0.452933\pi$
$728$	−1.02673e18	+	9.00986e17i	−0.255623	+	0.224318i
$729$	5.80148e17			0.143156
$730$	−3.49010e17	−	6.04504e17i	−0.0853571	−	0.147843i
$731$	1.71682e18	−	2.97362e18i	0.416161	−	0.720812i
$732$	2.29384e18	−	3.97306e18i	0.551115	−	0.954559i
$733$	7.46241e17	+	1.29253e18i	0.177706	+	0.307797i	0.941095	−	0.338143i	$-0.109799\pi$
$733$	7.46241e17	+	1.29253e18i	0.177706	+	0.307797i	−0.763388	+	0.645940i	$0.776466\pi$
$734$	−1.19626e18			−0.282358
$735$	−1.04995e18	+	8.01413e18i	−0.245640	+	1.87495i
$736$	−9.44256e17			−0.218970
$737$	3.72556e16	+	6.45285e16i	0.00856352	+	0.0148325i
$738$	5.27086e18	−	9.12939e18i	1.20092	−	2.08006i
$739$	2.01374e18	−	3.48789e18i	0.454793	−	0.787724i	−0.543884	−	0.839161i	$-0.683047\pi$
$739$	2.01374e18	−	3.48789e18i	0.454793	−	0.787724i	0.998676	+	0.0514366i	$0.0163800\pi$
$740$	−4.40665e17	−	7.63253e17i	−0.0986511	−	0.170869i
$741$	−9.90174e18			−2.19732
$742$	4.70472e17	−	4.12855e17i	0.103492	−	0.0908181i
$743$	−4.29776e18			−0.937163			−0.468582	−	0.883420i	$-0.655235\pi$
$743$	−4.29776e18			−0.937163			−0.468582	+	0.883420i	$0.655235\pi$
$744$	−9.99097e17	−	1.73049e18i	−0.215965	−	0.374063i
$745$	−2.32563e18	+	4.02811e18i	−0.498339	+	0.863148i
$746$	−8.89871e17	+	1.54130e18i	−0.189027	+	0.327405i
$747$	3.77146e18	+	6.53237e18i	0.794193	+	1.37558i
$748$	−2.53615e18			−0.529438
$749$	−6.84240e18	−	2.32028e18i	−1.41604	−	0.480185i
$750$	5.91672e18			1.21390
$751$	2.85161e18	+	4.93914e18i	0.580004	+	1.00460i	0.995478	+	0.0949914i	$0.0302824\pi$
$751$	2.85161e18	+	4.93914e18i	0.580004	+	1.00460i	−0.415474	+	0.909605i	$0.636384\pi$
$752$	−5.90128e17	+	1.02213e18i	−0.118995	+	0.206106i
$753$	−1.79518e18	+	3.10935e18i	−0.358873	+	0.621587i
$754$	−3.22121e17	−	5.57931e17i	−0.0638419	−	0.110577i
$755$	3.50116e18			0.687950
$756$	1.15615e18	+	5.80281e18i	0.225228	+	1.13044i
$757$	9.41377e18			1.81819			0.909097	−	0.416584i	$-0.136773\pi$
$757$	9.41377e18			1.81819			0.909097	+	0.416584i	$0.136773\pi$
$758$	−1.64425e17	−	2.84793e17i	−0.0314861	−	0.0545355i
$759$	3.85618e18	−	6.67909e18i	0.732125	−	1.26808i
$760$	−1.23898e18	+	2.14598e18i	−0.233226	+	0.403959i
$761$	1.47511e18	+	2.55497e18i	0.275312	+	0.476854i	0.970214	−	0.242250i	$-0.0778856\pi$
$761$	1.47511e18	+	2.55497e18i	0.275312	+	0.476854i	−0.694902	+	0.719105i	$0.744552\pi$
$762$	−5.52257e18			−1.02196
$763$	−5.19432e17	−	2.60707e18i	−0.0953057	−	0.478347i
$764$	2.66647e17			0.0485099
$765$	−1.06768e19	−	1.84928e19i	−1.92594	−	3.33583i
$766$	−2.26891e18	+	3.92986e18i	−0.405817	+	0.702895i
$767$	1.71574e18	−	2.97174e18i	0.304285	−	0.527037i
$768$	3.21544e17	+	5.56931e17i	0.0565448	+	0.0979385i
$769$	6.59719e18			1.15037			0.575185	−	0.818023i	$-0.304930\pi$
$769$	6.59719e18			1.15037			0.575185	+	0.818023i	$0.304930\pi$
$770$	−2.64420e18	−	8.96656e17i	−0.457198	−	0.155037i
$771$	9.79772e18			1.67985
$772$	6.64776e17	+	1.15143e18i	0.113022	+	0.195760i
$773$	1.13715e18	−	1.96961e18i	0.191713	−	0.332057i	−0.754105	−	0.656754i	$-0.771929\pi$
$773$	1.13715e18	−	1.96961e18i	0.191713	−	0.332057i	0.945818	+	0.324697i	$0.105262\pi$
$774$	2.46963e18	−	4.27752e18i	0.412872	−	0.715115i
$775$	1.87649e17	+	3.25018e17i	0.0311090	+	0.0538823i
$776$	3.72700e18			0.612714
$777$	3.14996e18	−	2.76420e18i	0.513533	−	0.450643i
$778$	5.21528e18			0.843161
$779$	5.88076e18	+	1.01858e19i	0.942844	+	1.63305i
$780$	2.86009e18	−	4.95382e18i	0.454741	−	0.787635i
$781$	2.13518e18	−	3.69824e18i	0.336668	−	0.583127i
$782$	4.53931e18	+	7.86231e18i	0.709816	+	1.22944i
$783$	−2.79056e18			−0.432754
$784$	−1.50140e18	+	6.23008e17i	−0.230910	+	0.0958163i
$785$	−1.07596e19			−1.64114
$786$	−3.24975e18	−	5.62872e18i	−0.491590	−	0.851458i
$787$	1.92422e18	−	3.33285e18i	0.288682	−	0.500012i	−0.684813	−	0.728718i	$-0.740116\pi$
$787$	1.92422e18	−	3.33285e18i	0.288682	−	0.500012i	0.973495	+	0.228707i	$0.0734496\pi$
$788$	−1.81932e18	+	3.15115e18i	−0.270700	+	0.468865i
$789$	−1.25864e18	−	2.18003e18i	−0.185738	−	0.321708i
$790$	7.49536e18			1.09702
$791$	−3.83647e18	+	3.36663e18i	−0.556910	+	0.488707i
$792$	−3.64823e18			−0.525253
$793$	−4.10341e18	−	7.10732e18i	−0.585962	−	1.01492i
$794$	−4.02902e18	+	6.97847e18i	−0.570645	+	0.988386i
$795$	−1.31057e18	+	2.26997e18i	−0.184108	+	0.318884i
$796$	3.21320e17	+	5.56543e17i	0.0447717	+	0.0775468i
$797$	7.52899e17			0.104054			0.0520269	−	0.998646i	$-0.483432\pi$
$797$	7.52899e17			0.104054			0.0520269	+	0.998646i	$0.483432\pi$
$798$	−1.11589e19	−	3.78402e18i	−1.52969	−	0.518722i
$799$	1.13477e19			1.54295
$800$	−6.03920e16	−	1.04602e17i	−0.00814507	−	0.0141077i
$801$	−7.01716e18	+	1.21541e19i	−0.938751	+	1.62596i
$802$	2.20490e18	−	3.81900e18i	0.292588	−	0.506777i
$803$	5.73295e17	+	9.92976e17i	0.0754618	+	0.130704i
$804$	−1.81654e17			−0.0237182
$805$	1.95297e18	+	9.80213e18i	0.252943	+	1.26954i
$806$	−3.57453e18			−0.459241
$807$	−6.44690e18	−	1.11663e19i	−0.821623	−	1.42309i
$808$	−1.37612e18	+	2.38352e18i	−0.173974	+	0.301332i
$809$	−2.35644e17	+	4.08147e17i	−0.0295523	+	0.0511861i	−0.880423	−	0.474189i	$-0.842741\pi$
$809$	−2.35644e17	+	4.08147e17i	−0.0295523	+	0.0511861i	0.850871	+	0.525375i	$0.176075\pi$
$810$	−5.63477e18	−	9.75970e18i	−0.701008	−	1.21418i
$811$	−1.90998e18			−0.235719			−0.117859	−	0.993030i	$-0.537603\pi$
$811$	−1.90998e18			−0.235719			−0.117859	+	0.993030i	$0.537603\pi$
$812$	−1.49802e17	−	7.51868e17i	−0.0183402	−	0.0920508i
$813$	−7.97125e18			−0.968140
$814$	7.23849e17	+	1.25374e18i	0.0872146	+	0.151060i
$815$	6.46602e17	−	1.11995e18i	0.0772881	−	0.133867i
$816$	3.09151e18	−	5.35465e18i	0.366593	−	0.634958i
$817$	2.75539e18	+	4.77248e18i	0.324146	+	0.561437i
$818$	−6.01901e18			−0.702471
$819$	1.78916e19	+	6.06711e18i	2.07159	+	0.702484i
$820$	−6.79455e18			−0.780496
$821$	5.89897e18	+	1.02173e19i	0.672273	+	1.16441i	0.977258	+	0.212054i	$0.0680154\pi$
$821$	5.89897e18	+	1.02173e19i	0.672273	+	1.16441i	−0.304985	+	0.952357i	$0.598651\pi$
$822$	−8.10120e18	+	1.40317e19i	−0.915973	+	1.58651i
$823$	9.71790e17	−	1.68319e18i	0.109012	−	0.188814i	−0.806358	−	0.591427i	$-0.798565\pi$
$823$	9.71790e17	−	1.68319e18i	0.109012	−	0.188814i	0.915370	+	0.402613i	$0.131898\pi$
$824$	−1.46767e18	−	2.54208e18i	−0.163343	−	0.282919i
$825$	9.86522e17			0.108932
$826$	3.06924e18	−	2.69336e18i	0.336249	−	0.295070i
$827$	−1.46200e19			−1.58914			−0.794570	−	0.607173i	$-0.792304\pi$
$827$	−1.46200e19			−1.58914			−0.794570	+	0.607173i	$0.792304\pi$
$828$	6.52975e18	+	1.13099e19i	0.704205	+	1.21972i
$829$	1.50698e18	−	2.61016e18i	0.161251	−	0.279295i	−0.774067	−	0.633104i	$-0.781780\pi$
$829$	1.50698e18	−	2.61016e18i	0.161251	−	0.279295i	0.935318	+	0.353809i	$0.115114\pi$
$830$	2.43086e18	−	4.21037e18i	0.258079	−	0.447005i
$831$	−2.04683e18	−	3.54522e18i	−0.215613	−	0.373453i
$832$	1.15041e18			0.120240
$833$	1.24051e19	+	9.50637e18i	1.28649	+	0.985875i
$834$	−1.29041e19			−1.32785
$835$	−3.35920e18	−	5.81830e18i	−0.342984	−	0.594065i
$836$	2.03519e18	−	3.52505e18i	0.206188	−	0.357129i
$837$	−7.74161e18	+	1.34089e19i	−0.778244	+	1.34796i
$838$	2.36196e18	+	4.09104e18i	0.235606	+	0.408082i
$839$	−3.67263e18			−0.363517			−0.181759	−	0.983343i	$-0.558179\pi$
$839$	−3.67263e18			−0.363517			−0.181759	+	0.983343i	$0.558179\pi$
$840$	5.11634e18	−	4.48977e18i	0.502510	−	0.440969i
$841$	−9.89906e18			−0.964761
$842$	−5.85680e18	−	1.01443e19i	−0.566411	−	0.981052i
$843$	2.94241e18	−	5.09640e18i	0.282373	−	0.489085i
$844$	6.91990e17	−	1.19856e18i	0.0658983	−	0.114139i
$845$	4.13075e17	+	7.15467e17i	0.0390355	+	0.0676116i
$846$	1.63235e19			1.53076
$847$	−5.83325e18	−	1.97807e18i	−0.542836	−	0.184077i
$848$	−5.27146e17			−0.0486809
$849$	1.64690e19	+	2.85251e19i	1.50927	+	2.61413i
$850$	−5.80643e17	+	1.00570e18i	−0.0528064	+	0.0914633i
$851$	2.59115e18	−	4.48800e18i	0.233857	−	0.405052i
$852$	5.20546e18	+	9.01612e18i	0.466231	+	0.807537i
$853$	1.22672e19			1.09038			0.545189	−	0.838313i	$-0.316458\pi$
$853$	1.22672e19			1.09038			0.545189	+	0.838313i	$0.316458\pi$
$854$	−1.90828e18	−	9.57783e18i	−0.168332	−	0.844872i
$855$	3.42714e19			3.00021
$856$	3.04240e18	+	5.26960e18i	0.264324	+	0.457823i
$857$	8.00928e17	−	1.38725e18i	0.0690587	−	0.119613i	−0.829429	−	0.558613i	$-0.811334\pi$
$857$	8.00928e17	−	1.38725e18i	0.0690587	−	0.119613i	0.898487	+	0.439000i	$0.144667\pi$
$858$	−4.69806e18	+	8.13728e18i	−0.402024	+	0.696325i
$859$	−6.14645e18	−	1.06460e19i	−0.521998	−	0.904127i	−0.999673	−	0.0255901i	$-0.991854\pi$
$859$	−6.14645e18	−	1.06460e19i	−0.521998	−	0.904127i	0.477675	−	0.878537i	$-0.341480\pi$
$860$	−3.18355e18			−0.268331
$861$	−6.31314e18	−	3.16862e19i	−0.528111	−	2.65063i
$862$	1.65184e19			1.37142
$863$	1.84925e18	+	3.20299e18i	0.152379	+	0.263928i	0.932102	−	0.362197i	$-0.117973\pi$
$863$	1.84925e18	+	3.20299e18i	0.152379	+	0.263928i	−0.779723	+	0.626125i	$0.784640\pi$
$864$	2.49152e18	−	4.31544e18i	0.203763	−	0.352928i
$865$	−1.18684e18	+	2.05566e18i	−0.0963354	+	0.166858i
$866$	2.15421e18	+	3.73119e18i	0.173548	+	0.300595i
$867$	−3.68179e19			−2.94398
$868$	−4.02836e18	−	1.36603e18i	−0.319706	−	0.108413i
$869$	−1.23121e19			−0.969848
$870$	1.60518e18	+	2.78026e18i	0.125502	+	0.217375i
$871$	−1.62479e17	+	2.81422e17i	−0.0126090	+	0.0218394i
$872$	−1.11938e18	+	1.93883e18i	−0.0862226	+	0.149342i
$873$	−2.57731e19	−	4.46402e19i	−1.97049	−	3.41298i
$874$	−1.45706e19			−1.10574
$875$	9.46701e18	−	8.30762e18i	0.713116	−	0.625784i
$876$	−2.79533e18			−0.209005
$877$	−1.71080e18	−	2.96319e18i	−0.126970	−	0.219918i	0.795531	−	0.605913i	$-0.207192\pi$
$877$	−1.71080e18	−	2.96319e18i	−0.126970	−	0.219918i	−0.922501	+	0.385994i	$0.873859\pi$
$878$	8.32736e18	−	1.44234e19i	0.613469	−	1.06256i
$879$	5.72892e18	−	9.92279e18i	0.418934	−	0.725614i
$880$	1.17572e18	+	2.03640e18i	0.0853424	+	0.147817i
$881$	1.42953e19			1.03003			0.515015	−	0.857181i	$-0.327786\pi$
$881$	1.42953e19			1.03003			0.515015	+	0.857181i	$0.327786\pi$
$882$	1.78446e19	+	1.36748e19i	1.27633	+	0.978083i
$883$	−2.07001e19			−1.46970			−0.734848	−	0.678232i	$-0.762747\pi$
$883$	−2.07001e19			−1.46970			−0.734848	+	0.678232i	$0.762747\pi$
$884$	−5.53034e18	−	9.57882e18i	−0.389773	−	0.675107i
$885$	−8.54980e18	+	1.48087e19i	−0.598170	+	1.03606i
$886$	5.79500e18	−	1.00372e19i	0.402471	−	0.697100i
$887$	−6.04696e18	−	1.04737e19i	−0.416902	−	0.722095i	0.578724	−	0.815523i	$-0.303551\pi$
$887$	−6.04696e18	−	1.04737e19i	−0.416902	−	0.722095i	−0.995626	+	0.0934281i	$0.970217\pi$
$888$	−3.52941e18			−0.241556
$889$	−8.83635e18	+	7.75420e18i	−0.600360	+	0.526836i
$890$	9.04568e18			0.610107
$891$	9.25583e18	+	1.60316e19i	0.619741	+	1.07342i
$892$	−5.51956e18	+	9.56016e18i	−0.366888	+	0.635468i
$893$	−9.10616e18	+	1.57723e19i	−0.600898	+	1.04079i
$894$	9.31333e18	+	1.61312e19i	0.610114	+	1.05675i
$895$	9.58427e18			0.623318
$896$	1.29647e18	+	4.39636e17i	0.0837065	+	0.0283851i
$897$	3.36351e19			2.15597
$898$	3.72022e18	+	6.44361e18i	0.236740	+	0.410046i
$899$	1.00308e18	−	1.73738e18i	0.0633719	−	0.109763i
$900$	−8.35250e17	+	1.44670e18i	−0.0523890	+	0.0907404i
$901$	2.53414e18	+	4.38926e18i	0.157805	+	0.273326i
$902$	1.11609e19			0.690014
$903$	−2.95799e18	−	1.48464e19i	−0.181562	−	0.911275i
$904$	4.29862e18			0.261960
$905$	−7.48209e18	−	1.29594e19i	−0.452697	−	0.784094i
$906$	7.01046e18	−	1.21425e19i	0.421127	−	0.729414i
$907$	−4.37871e18	+	7.58415e18i	−0.261155	+	0.452334i	−0.966549	−	0.256481i	$-0.917437\pi$
$907$	−4.37871e18	+	7.58415e18i	−0.261155	+	0.452334i	0.705394	+	0.708815i	$0.250770\pi$
$908$	−6.35202e18	−	1.10020e19i	−0.376144	−	0.651500i
$909$	3.80649e19			2.23800
$910$	−2.37935e18	−	1.19421e19i	−0.138896	−	0.697129i
$911$	3.20011e18			0.185480			0.0927398	−	0.995690i	$-0.470438\pi$
$911$	3.20011e18			0.185480			0.0927398	+	0.995690i	$0.470438\pi$
$912$	4.96169e18	+	8.59390e18i	0.285538	+	0.494566i
$913$	−3.99300e18	+	6.91608e18i	−0.228160	+	0.395185i
$914$	−5.25872e18	+	9.10838e18i	−0.298353	+	0.516762i
$915$	2.04480e19	+	3.54169e19i	1.15190	+	1.99514i
$916$	2.66410e18			0.149015
$917$	−1.31030e19	−	4.44326e18i	−0.727728	−	0.246775i
$918$	−4.79098e19			−2.64208
$919$	−9.83842e18	−	1.70406e19i	−0.538734	−	0.933115i	−0.998973	−	0.0453198i	$-0.985569\pi$
$919$	−9.83842e18	−	1.70406e19i	−0.538734	−	0.933115i	0.460238	−	0.887795i	$-0.347764\pi$
$920$	4.20868e18	−	7.28965e18i	0.228837	−	0.396357i
$921$	−1.98831e19	+	3.44385e19i	−1.07348	+	1.85933i
$922$	−4.06727e18	−	7.04471e18i	−0.218048	−	0.377670i
$923$	1.86239e19			0.991423
$924$	−8.40426e18	+	7.37502e18i	−0.444254	+	0.389848i
$925$	6.62890e17			0.0347953
$926$	−3.69967e18	−	6.40802e18i	−0.192838	−	0.334005i
$927$	−2.02985e19	+	3.51581e19i	−1.05062	+	1.81973i
$928$	−3.22825e17	+	5.59150e17i	−0.0165923	+	0.0287387i
$929$	1.35760e19	+	2.35143e19i	0.692899	+	1.20014i	0.970884	+	0.239551i	$0.0770003\pi$
$929$	1.35760e19	+	2.35143e19i	0.692899	+	1.20014i	−0.277984	+	0.960586i	$0.589666\pi$
$930$	1.78125e19			0.902787
$931$	−2.31678e19	+	9.61353e18i	−1.16604	+	0.483849i
$932$	1.48901e19			0.744206
$933$	−2.77027e18	−	4.79825e18i	−0.137496	−	0.238151i
$934$	−3.24465e18	+	5.61990e18i	−0.159924	+	0.276996i
$935$	1.13040e19	−	1.95791e19i	0.553295	−	0.958334i
$936$	−7.95534e18	−	1.37790e19i	−0.386692	−	0.669771i
$937$	5.82871e18			0.281362			0.140681	−	0.990055i	$-0.455071\pi$
$937$	5.82871e18			0.281362			0.140681	+	0.990055i	$0.455071\pi$
$938$	−2.90655e17	+	2.55060e17i	−0.0139335	+	0.0122271i
$939$	−4.18558e19			−1.99264
$940$	−5.26057e18	−	9.11158e18i	−0.248715	−	0.430787i
$941$	7.22541e18	−	1.25148e19i	0.339258	−	0.587612i	−0.645035	−	0.764153i	$-0.723157\pi$
$941$	7.22541e18	−	1.25148e19i	0.339258	−	0.587612i	0.984293	+	0.176541i	$0.0564907\pi$
$942$	−2.15443e19	+	3.73158e19i	−1.00462	+	1.74005i
$943$	−1.99763e19	−	3.45999e19i	−0.925100	−	1.60232i
$944$	−3.43897e18			−0.158165
$945$	−4.99508e19	−	1.69385e19i	−2.28158	−	0.773691i
$946$	5.22939e18			0.237224
$947$	1.51205e19	+	2.61895e19i	0.681226	+	1.17992i	0.974607	+	0.223922i	$0.0718861\pi$
$947$	1.51205e19	+	2.61895e19i	0.681226	+	1.17992i	−0.293382	+	0.955995i	$0.594781\pi$
$948$	1.50081e19	−	2.59949e19i	0.671541	−	1.16314i
$949$	−2.50025e18	+	4.33056e18i	−0.111110	+	0.192448i
$950$	−9.31898e17	−	1.61410e18i	−0.0411306	−	0.0712403i
$951$	1.09408e19			0.479598
$952$	−2.57187e18	−	1.29084e19i	−0.111972	−	0.561996i
$953$	8.71317e18			0.376767			0.188383	−	0.982096i	$-0.439675\pi$
$953$	8.71317e18			0.376767			0.188383	+	0.982096i	$0.439675\pi$
$954$	3.64534e18	+	6.31391e18i	0.156557	+	0.271165i
$955$	−1.18848e18	+	2.05851e18i	−0.0506957	+	0.0878076i
$956$	−2.31449e18	+	4.00881e18i	−0.0980571	+	0.169840i
$957$	−2.63672e18	−	4.56694e18i	−0.110953	−	0.192175i
$958$	−1.75428e19			−0.733200
$959$	6.73951e18	+	3.38261e19i	0.279774	+	1.40421i
$960$	−5.73267e18			−0.236371
$961$	6.64328e18	+	1.15065e19i	0.272070	+	0.471239i
$962$	−3.15685e18	+	5.46782e18i	−0.128415	+	0.222421i
$963$	4.20779e19	−	7.28810e19i	1.70013	−	2.94472i
$964$	8.54964e18	+	1.48084e19i	0.343121	+	0.594303i
$965$	−1.18520e19			−0.472459
$966$	3.79055e19	+	1.28539e19i	1.50090	+	0.508959i
$967$	4.61552e19			1.81530			0.907650	−	0.419728i	$-0.137874\pi$
$967$	4.61552e19			1.81530			0.907650	+	0.419728i	$0.137874\pi$
$968$	2.59370e18	+	4.49241e18i	0.101328	+	0.175505i
$969$	4.77045e19	−	8.26266e19i	1.85121	−	3.20638i
$970$	−1.66118e19	+	2.87724e19i	−0.640323	+	1.10907i
$971$	1.54495e19	+	2.67593e19i	0.591548	+	1.02459i	0.994024	+	0.109160i	$0.0348162\pi$
$971$	1.54495e19	+	2.67593e19i	0.591548	+	1.02459i	−0.402476	+	0.915430i	$0.631850\pi$
$972$	−1.48244e19			−0.563827
$973$	−2.06471e19	+	1.81185e19i	−0.780055	+	0.684524i
$974$	−2.03466e19			−0.763589
$975$	2.15121e18	+	3.72600e18i	0.0801960	+	0.138904i
$976$	−4.11238e18	+	7.12285e18i	−0.152289	+	0.263773i
$977$	−1.18103e19	+	2.04561e19i	−0.434457	+	0.752502i	−0.997251	−	0.0740955i	$-0.976393\pi$
$977$	−1.18103e19	+	2.04561e19i	−0.434457	+	0.752502i	0.562794	+	0.826597i	$0.309726\pi$
$978$	−2.58941e18	−	4.48500e18i	−0.0946235	−	0.163893i
$979$	−1.48587e19			−0.539378
$980$	1.88233e18	−	1.43676e19i	0.0678776	−	0.518103i
$981$	3.09631e19			1.10917
$982$	−9.42002e18	−	1.63160e19i	−0.335218	−	0.580615i
$983$	−6.70975e17	+	1.16216e18i	−0.0237196	+	0.0410836i	−0.877642	−	0.479318i	$-0.840884\pi$
$983$	−6.70975e17	+	1.16216e18i	−0.0237196	+	0.0410836i	0.853922	+	0.520401i	$0.174218\pi$
$984$	−1.36049e19	+	2.35644e19i	−0.477779	+	0.827538i
$985$	−1.62179e19	−	2.80902e19i	−0.565795	−	0.979985i
$986$	6.20765e18			0.215143
$987$	3.76037e19	−	3.29985e19i	1.29470	−	1.13614i
$988$	1.77517e19			0.607184
$989$	−9.35977e18	−	1.62116e19i	−0.318045	−	0.550871i
$990$	1.62607e19	−	2.81643e19i	0.548922	−	0.950760i
$991$	7.05790e18	−	1.22246e19i	0.236699	−	0.409975i	−0.723066	−	0.690779i	$-0.757268\pi$
$991$	7.05790e18	−	1.22246e19i	0.236699	−	0.409975i	0.959765	+	0.280804i	$0.0906010\pi$
$992$	1.79117e18	+	3.10240e18i	0.0596776	+	0.103365i
$993$	3.20148e19			1.05969
$994$	2.09884e19	+	7.11724e18i	0.690189	+	0.234045i
$995$	−5.72868e18			−0.187156
$996$	−9.73474e18	−	1.68611e19i	−0.315965	−	0.547267i
$997$	−1.91620e19	+	3.31895e19i	−0.617905	+	1.07024i	0.371963	+	0.928248i	$0.378685\pi$
$997$	−1.91620e19	+	3.31895e19i	−0.617905	+	1.07024i	−0.989867	+	0.141994i	$0.954648\pi$
$998$	1.71327e19	−	2.96746e19i	0.548879	−	0.950686i
$999$	1.36740e19	+	2.36841e19i	0.435232	+	0.753843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.c.a.11.4	yes	8
3.2	odd	2		126.14.g.d.109.3		8
7.2	even	3	inner	14.14.c.a.9.4	✓	8
7.3	odd	6		98.14.a.k.1.4		4
7.4	even	3		98.14.a.l.1.1		4
7.5	odd	6		98.14.c.n.79.1		8
7.6	odd	2		98.14.c.n.67.1		8
21.2	odd	6		126.14.g.d.37.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.a.9.4	✓	8	7.2	even	3	inner
14.14.c.a.11.4	yes	8	1.1	even	1	trivial
98.14.a.k.1.4		4	7.3	odd	6
98.14.a.l.1.1		4	7.4	even	3
98.14.c.n.67.1		8	7.6	odd	2
98.14.c.n.79.1		8	7.5	odd	6
126.14.g.d.37.3		8	21.2	odd	6
126.14.g.d.109.3		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.0000 - 55.4256i) q^{2} +(1142.35 - 1978.62i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-18256.5 - 31621.1i) q^{5} -146221. q^{6} +(-233961. + 205308. i) q^{7} +262144. q^{8} +(-1.81279e6 - 3.13984e6i) q^{9} +O(q^{10})\)	\(q+(-32.0000 - 55.4256i) q^{2} +(1142.35 - 1978.62i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-18256.5 - 31621.1i) q^{5} -146221. q^{6} +(-233961. + 205308. i) q^{7} +262144. q^{8} +(-1.81279e6 - 3.13984e6i) q^{9} +(-1.16841e6 + 2.02375e6i) q^{10} +(1.91927e6 - 3.32427e6i) q^{11} +(4.67908e6 + 8.10441e6i) q^{12} +1.67406e7 q^{13} +(1.88661e7 + 6.39754e6i) q^{14} -8.34214e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(-8.06528e7 + 1.39695e8i) q^{17} +(-1.16018e8 + 2.00950e8i) q^{18} +(-1.29443e8 - 2.24202e8i) q^{19} +1.49557e8 q^{20} +(1.38960e8 + 6.97453e8i) q^{21} -2.45667e8 q^{22} +(4.39704e8 + 7.61589e8i) q^{23} +(2.99461e8 - 5.18682e8i) q^{24} +(-5.62445e7 + 9.74183e7i) q^{25} +(-5.35700e8 - 9.27860e8i) q^{26} -4.64082e9 q^{27} +(-2.49127e8 - 1.25039e9i) q^{28} +6.01309e8 q^{29} +(2.66948e9 + 4.62368e9i) q^{30} +(1.66816e9 - 2.88933e9i) q^{31} +(-5.36871e8 + 9.29888e8i) q^{32} +(-4.38497e9 - 7.59500e9i) q^{33} +1.03236e10 q^{34} +(1.07634e10 + 3.64989e9i) q^{35} +1.48503e10 q^{36} +(-2.94647e9 - 5.10343e9i) q^{37} +(-8.28436e9 + 1.43489e10i) q^{38} +(1.91237e10 - 3.31233e10i) q^{39} +(-4.78582e9 - 8.28928e9i) q^{40} -4.54312e10 q^{41} +(3.42100e10 - 3.00205e10i) q^{42} -2.12865e10 q^{43} +(7.86133e9 + 1.36162e10i) q^{44} +(-6.61901e10 + 1.14645e11i) q^{45} +(2.81410e10 - 4.87417e10i) q^{46} +(-3.51744e10 - 6.09238e10i) q^{47} -3.83311e10 q^{48} +(1.25860e10 - 9.60681e10i) q^{49} +7.19929e9 q^{50} +(1.84268e11 + 3.19162e11i) q^{51} +(-3.42848e10 + 5.93831e10i) q^{52} +(1.57102e10 - 2.72108e10i) q^{53} +(1.48506e11 + 2.57220e11i) q^{54} -1.40156e11 q^{55} +(-6.13313e10 + 5.38203e10i) q^{56} -5.91480e11 q^{57} +(-1.92419e10 - 3.33279e10i) q^{58} +(1.02489e11 - 1.77517e11i) q^{59} +(1.70847e11 - 2.95916e11i) q^{60} +(-2.45117e11 - 4.24555e11i) q^{61} -2.13524e11 q^{62} +(1.06876e12 + 3.62418e11i) q^{63} +6.87195e10 q^{64} +(-3.05625e11 - 5.29357e11i) q^{65} +(-2.80638e11 + 4.86080e11i) q^{66} +(-9.70566e9 + 1.68107e10i) q^{67} +(-3.30354e11 - 5.72190e11i) q^{68} +2.00919e12 q^{69} +(-1.42130e11 - 7.13363e11i) q^{70} +1.11249e12 q^{71} +(-4.75211e11 - 8.23090e11i) q^{72} +(-1.49352e11 + 2.58686e11i) q^{73} +(-1.88574e11 + 3.26620e11i) q^{74} +(1.28502e11 + 2.22572e11i) q^{75} +1.06040e12 q^{76} +(2.33467e11 + 1.17179e12i) q^{77} -2.44784e12 q^{78} +(-1.60375e12 - 2.77777e12i) q^{79} +(-3.06292e11 + 5.30514e11i) q^{80} +(-2.41129e12 + 4.17648e12i) q^{81} +(1.45380e12 + 2.51806e12i) q^{82} -2.08048e12 q^{83} +(-2.75862e12 - 9.35458e11i) q^{84} +5.88974e12 q^{85} +(6.81169e11 + 1.17982e12i) q^{86} +(6.86908e11 - 1.18976e12i) q^{87} +(5.03125e11 - 8.71438e11i) q^{88} +(-1.93546e12 - 3.35232e12i) q^{89} +8.47233e12 q^{90} +(-3.91665e12 + 3.43699e12i) q^{91} -3.60205e12 q^{92} +(-3.81125e12 - 6.60129e12i) q^{93} +(-2.25116e12 + 3.89912e12i) q^{94} +(-4.72634e12 + 8.18627e12i) q^{95} +(1.22659e12 + 2.12452e12i) q^{96} +1.42174e13 q^{97} +(-5.72739e12 + 2.37659e12i) q^{98} -1.39169e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9}+O(q^{10}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9	\( 8 q - 256 q^{2} - 182 q^{3} - 16384 q^{4} - 64400 q^{5} + 23296 q^{6} - 113736 q^{7} + 2097152 q^{8} - 3983752 q^{9} - 4121600 q^{10} - 1008790 q^{11} - 745472 q^{12} + 53807264 q^{13} + 23506560 q^{14} - 88888916 q^{15} - 67108864 q^{16} - 165333028 q^{17} - 254960128 q^{18} - 423405794 q^{19} + 527564800 q^{20} + 231089600 q^{21} + 129125120 q^{22} + 286233866 q^{23} - 47710208 q^{24} - 472017432 q^{25} - 1721832448 q^{26} - 10405941644 q^{27} - 1038557184 q^{28} + 18200674816 q^{29} + 2844445312 q^{30} + 1507094246 q^{31} - 4294967296 q^{32} - 16888935028 q^{33} + 21162627584 q^{34} - 4300332526 q^{35} + 32634896384 q^{36} - 18959705336 q^{37} - 27097970816 q^{38} + 35759388756 q^{39} - 16882073600 q^{40} + 113651910624 q^{41} + 25531294208 q^{42} - 91557619424 q^{43} - 4132003840 q^{44} - 119804452768 q^{45} + 18318967424 q^{46} - 81351201078 q^{47} + 6106906624 q^{48} - 60954502168 q^{49} + 60418231296 q^{50} + 14996824142 q^{51} - 110197276672 q^{52} + 87497947440 q^{53} + 332990132608 q^{54} + 701637410348 q^{55} - 29815209984 q^{56} - 1807326928264 q^{57} - 582421594112 q^{58} - 194140265102 q^{59} + 182044499968 q^{60} + 175816313120 q^{61} - 192908063488 q^{62} + 3245184239332 q^{63} + 549755813888 q^{64} - 1689866774568 q^{65} - 1080891841792 q^{66} - 243815218758 q^{67} - 677204082688 q^{68} + 6044157952784 q^{69} + 3010938632576 q^{70} - 3275394679072 q^{71} - 1044316684288 q^{72} - 3492491920596 q^{73} - 1213421141504 q^{74} - 2370218127424 q^{75} + 3468540264448 q^{76} + 6381735922240 q^{77} - 4577201760768 q^{78} - 1016380081246 q^{79} - 1080452710400 q^{80} + 17492694092 q^{81} - 3636861139968 q^{82} + 7027495743296 q^{83} - 2580545830912 q^{84} + 569114840528 q^{85} + 2929843821568 q^{86} - 9706955821052 q^{87} - 264448245760 q^{88} - 8034124428036 q^{89} + 15334969954304 q^{90} - 11436513503632 q^{91} - 2344827830272 q^{92} - 3388371390552 q^{93} - 5206476868992 q^{94} + 1429435505438 q^{95} - 195421011968 q^{96} + 54351131725632 q^{97} - 461748942592 q^{98} - 25837834576328 q^{99}+O(q^{100}) \) 8 * q - 256 * q^2 - 182 * q^3 - 16384 * q^4 - 64400 * q^5 + 23296 * q^6 - 113736 * q^7 + 2097152 * q^8 - 3983752 * q^9 - 4121600 * q^10 - 1008790 * q^11 - 745472 * q^12 + 53807264 * q^13 + 23506560 * q^14 - 88888916 * q^15 - 67108864 * q^16 - 165333028 * q^17 - 254960128 * q^18 - 423405794 * q^19 + 527564800 * q^20 + 231089600 * q^21 + 129125120 * q^22 + 286233866 * q^23 - 47710208 * q^24 - 472017432 * q^25 - 1721832448 * q^26 - 10405941644 * q^27 - 1038557184 * q^28 + 18200674816 * q^29 + 2844445312 * q^30 + 1507094246 * q^31 - 4294967296 * q^32 - 16888935028 * q^33 + 21162627584 * q^34 - 4300332526 * q^35 + 32634896384 * q^36 - 18959705336 * q^37 - 27097970816 * q^38 + 35759388756 * q^39 - 16882073600 * q^40 + 113651910624 * q^41 + 25531294208 * q^42 - 91557619424 * q^43 - 4132003840 * q^44 - 119804452768 * q^45 + 18318967424 * q^46 - 81351201078 * q^47 + 6106906624 * q^48 - 60954502168 * q^49 + 60418231296 * q^50 + 14996824142 * q^51 - 110197276672 * q^52 + 87497947440 * q^53 + 332990132608 * q^54 + 701637410348 * q^55 - 29815209984 * q^56 - 1807326928264 * q^57 - 582421594112 * q^58 - 194140265102 * q^59 + 182044499968 * q^60 + 175816313120 * q^61 - 192908063488 * q^62 + 3245184239332 * q^63 + 549755813888 * q^64 - 1689866774568 * q^65 - 1080891841792 * q^66 - 243815218758 * q^67 - 677204082688 * q^68 + 6044157952784 * q^69 + 3010938632576 * q^70 - 3275394679072 * q^71 - 1044316684288 * q^72 - 3492491920596 * q^73 - 1213421141504 * q^74 - 2370218127424 * q^75 + 3468540264448 * q^76 + 6381735922240 * q^77 - 4577201760768 * q^78 - 1016380081246 * q^79 - 1080452710400 * q^80 + 17492694092 * q^81 - 3636861139968 * q^82 + 7027495743296 * q^83 - 2580545830912 * q^84 + 569114840528 * q^85 + 2929843821568 * q^86 - 9706955821052 * q^87 - 264448245760 * q^88 - 8034124428036 * q^89 + 15334969954304 * q^90 - 11436513503632 * q^91 - 2344827830272 * q^92 - 3388371390552 * q^93 - 5206476868992 * q^94 + 1429435505438 * q^95 - 195421011968 * q^96 + 54351131725632 * q^97 - 461748942592 * q^98 - 25837834576328 * q^99

Introduction

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