LMFDB - Embedded newform 98.10.c.m.79.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not 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:	$50.4735119441$
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} - 4 x^{7} - 4806 x^{6} + 14432 x^{5} + 8678459 x^{4} - 17380976 x^{3} - 6978412850 x^{2} + \cdots + 2108388231292 $ x^8 - 4x^7 - 4806x^6 + 14432x^5 + 8678459x^4 - 17380976x^3 - 6978412850x^2 + 6987105744*x + 2108388231292
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.4
Root			$-34.9094 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.10.c.m.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(95.8886 + 166.084i) q^{3} +(-128.000 - 221.703i) q^{4} +(16.7949 - 29.0896i) q^{5} +3068.43 q^{6} -4096.00 q^{8} +(-8547.74 + 14805.1i) q^{9} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(95.8886 + 166.084i) q^{3} +(-128.000 - 221.703i) q^{4} +(16.7949 - 29.0896i) q^{5} +3068.43 q^{6} -4096.00 q^{8} +(-8547.74 + 14805.1i) q^{9} +(-268.719 - 465.434i) q^{10} +(25770.2 + 44635.3i) q^{11} +(24547.5 - 42517.5i) q^{12} -113303. q^{13} +6441.76 q^{15} +(-32768.0 + 56755.8i) q^{16} +(-230833. - 399815. i) q^{17} +(136764. + 236882. i) q^{18} +(-418329. + 724566. i) q^{19} -8598.99 q^{20} +824646. q^{22} +(-149702. + 259291. i) q^{23} +(-392760. - 680280. i) q^{24} +(975998. + 1.69048e6i) q^{25} +(-906420. + 1.56997e6i) q^{26} +496229. q^{27} +2.58319e6 q^{29} +(51534.1 - 89259.6i) q^{30} +(-3.42162e6 - 5.92642e6i) q^{31} +(524288. + 908093. i) q^{32} +(-4.94213e6 + 8.56003e6i) q^{33} -7.38666e6 q^{34} +4.37644e6 q^{36} +(-6.97734e6 + 1.20851e7i) q^{37} +(6.69326e6 + 1.15931e7i) q^{38} +(-1.08644e7 - 1.88177e7i) q^{39} +(-68791.9 + 119151. i) q^{40} -2.22245e7 q^{41} -3.24518e7 q^{43} +(6.59717e6 - 1.14266e7i) q^{44} +(287117. + 497301. i) q^{45} +(2.39523e6 + 4.14866e6i) q^{46} +(-1.59026e6 + 2.75442e6i) q^{47} -1.25683e7 q^{48} +3.12319e7 q^{50} +(4.42685e7 - 7.66754e7i) q^{51} +(1.45027e7 + 2.51195e7i) q^{52} +(-4.41456e7 - 7.64625e7i) q^{53} +(3.96983e6 - 6.87595e6i) q^{54} +1.73123e6 q^{55} -1.60452e8 q^{57} +(2.06656e7 - 3.57938e7i) q^{58} +(-6.99559e6 - 1.21167e7i) q^{59} +(-824545. - 1.42815e6i) q^{60} +(-5.69654e7 + 9.86669e7i) q^{61} -1.09492e8 q^{62} +1.67772e7 q^{64} +(-1.90291e6 + 3.29593e6i) q^{65} +(7.90741e7 + 1.36960e8i) q^{66} +(1.52746e8 + 2.64565e8i) q^{67} +(-5.90933e7 + 1.02353e8i) q^{68} -5.74188e7 q^{69} -2.86664e8 q^{71} +(3.50115e7 - 6.06417e7i) q^{72} +(2.39428e7 + 4.14702e7i) q^{73} +(1.11637e8 + 1.93362e8i) q^{74} +(-1.87174e8 + 3.24195e8i) q^{75} +2.14184e8 q^{76} -3.47661e8 q^{78} +(5.37908e7 - 9.31683e7i) q^{79} +(1.10067e6 + 1.90642e6i) q^{80} +(2.15828e8 + 3.73825e8i) q^{81} +(-1.77796e8 + 3.07952e8i) q^{82} -5.67595e7 q^{83} -1.55073e7 q^{85} +(-2.59614e8 + 4.49665e8i) q^{86} +(2.47699e8 + 4.29027e8i) q^{87} +(-1.05555e8 - 1.82826e8i) q^{88} +(-4.24334e8 + 7.34969e8i) q^{89} +9.18774e6 q^{90} +7.66474e7 q^{92} +(6.56188e8 - 1.13655e9i) q^{93} +(2.54442e7 + 4.40707e7i) q^{94} +(1.40516e7 + 2.43380e7i) q^{95} +(-1.00546e8 + 1.74152e8i) q^{96} -8.99384e8 q^{97} -8.81107e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9}+O(q^{10}) $ 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9	$ 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9} - 9548 q^{11} - 834624 q^{15} - 262144 q^{16} + 254592 q^{18} - 305536 q^{22} + 2836736 q^{23} - 966144 q^{25} + 33339944 q^{29} - 6676992 q^{30} + 4194304 q^{32} + 8146944 q^{36} - 3226372 q^{37} - 69110568 q^{39} - 152960408 q^{43} - 2444288 q^{44} - 45387776 q^{46} - 30916608 q^{50} + 97261596 q^{51} - 13708112 q^{53} - 743115384 q^{57} + 266719552 q^{58} + 106831872 q^{60} + 134217728 q^{64} + 515731188 q^{65} + 814420776 q^{67} - 2649337488 q^{71} + 65175552 q^{72} + 51621952 q^{74} - 2211538176 q^{78} + 668411176 q^{79} + 1111307688 q^{81} - 3318529928 q^{85} - 1223683264 q^{86} + 39108608 q^{88} - 1452408832 q^{92} + 3706577496 q^{93} - 977188688 q^{95} - 5583163320 q^{99}+O(q^{100}) $ 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9 - 9548 * q^11 - 834624 * q^15 - 262144 * q^16 + 254592 * q^18 - 305536 * q^22 + 2836736 * q^23 - 966144 * q^25 + 33339944 * q^29 - 6676992 * q^30 + 4194304 * q^32 + 8146944 * q^36 - 3226372 * q^37 - 69110568 * q^39 - 152960408 * q^43 - 2444288 * q^44 - 45387776 * q^46 - 30916608 * q^50 + 97261596 * q^51 - 13708112 * q^53 - 743115384 * q^57 + 266719552 * q^58 + 106831872 * q^60 + 134217728 * q^64 + 515731188 * q^65 + 814420776 * q^67 - 2649337488 * q^71 + 65175552 * q^72 + 51621952 * q^74 - 2211538176 * q^78 + 668411176 * q^79 + 1111307688 * q^81 - 3318529928 * q^85 - 1223683264 * q^86 + 39108608 * q^88 - 1452408832 * q^92 + 3706577496 * q^93 - 977188688 * q^95 - 5583163320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	95.8886	+	166.084i	0.683473	+	1.18381i	0.973914	+	0.226917i	$0.0728645\pi$
$3$	95.8886	+	166.084i	0.683473	+	1.18381i	−0.290441	+	0.956893i	$0.593802\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	16.7949	−	29.0896i	0.0120175	−	0.0208148i	−0.859954	−	0.510371i	$-0.829508\pi$
$5$	16.7949	−	29.0896i	0.0120175	−	0.0208148i	0.871972	+	0.489556i	$0.162841\pi$
$6$	3068.43			0.966576
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	−8547.74	+	14805.1i	−0.434270	+	0.752178i
$10$	−268.719	−	465.434i	−0.00849763	−	0.0147183i
$11$	25770.2	+	44635.3i	0.530702	+	0.919202i	0.999358	+	0.0358219i	$0.0114049\pi$
$11$	25770.2	+	44635.3i	0.530702	+	0.919202i	−0.468656	+	0.883381i	$0.655262\pi$
$12$	24547.5	−	42517.5i	0.341736	−	0.591905i
$13$	−113303.			−1.10026			−0.550129	−	0.835080i	$-0.685421\pi$
$13$	−113303.			−1.10026			−0.550129	+	0.835080i	$0.685421\pi$
$14$		0			0
$15$	6441.76			0.0328544
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−230833.	−	399815.i	−0.670314	−	1.16102i	−0.977815	−	0.209470i	$-0.932826\pi$
$17$	−230833.	−	399815.i	−0.670314	−	1.16102i	0.307501	−	0.951548i	$-0.400507\pi$
$18$	136764.	+	236882.i	0.307075	+	0.531870i
$19$	−418329.	+	724566.i	−0.736421	+	1.27552i	0.217676	+	0.976021i	$0.430152\pi$
$19$	−418329.	+	724566.i	−0.736421	+	1.27552i	−0.954097	+	0.299498i	$0.903181\pi$
$20$	−8598.99			−0.0120175
$21$		0			0
$22$	824646.			0.750526
$23$	−149702.	+	259291.i	−0.111546	+	0.193202i	−0.916394	−	0.400278i	$-0.868913\pi$
$23$	−149702.	+	259291.i	−0.111546	+	0.193202i	0.804848	+	0.593481i	$0.202247\pi$
$24$	−392760.	−	680280.i	−0.241644	−	0.418540i
$25$	975998.	+	1.69048e6i	0.499711	+	0.865525i
$26$	−906420.	+	1.56997e6i	−0.389000	+	0.673768i
$27$	496229.			0.179699
$28$		0			0
$29$	2.58319e6			0.678213			0.339106	−	0.940748i	$-0.389875\pi$
$29$	2.58319e6			0.678213			0.339106	+	0.940748i	$0.389875\pi$
$30$	51534.1	−	89259.6i	0.0116158	−	0.0201191i
$31$	−3.42162e6	−	5.92642e6i	−0.665433	−	1.15256i	−0.979168	−	0.203053i	$-0.934914\pi$
$31$	−3.42162e6	−	5.92642e6i	−0.665433	−	1.15256i	0.313735	−	0.949511i	$-0.398420\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	−4.94213e6	+	8.56003e6i	−0.725440	+	1.25650i
$34$	−7.38666e6			−0.947967
$35$		0			0
$36$	4.37644e6			0.434270
$37$	−6.97734e6	+	1.20851e7i	−0.612043	+	1.06009i	0.378853	+	0.925457i	$0.376319\pi$
$37$	−6.97734e6	+	1.20851e7i	−0.612043	+	1.06009i	−0.990896	+	0.134632i	$0.957015\pi$
$38$	6.69326e6	+	1.15931e7i	0.520728	+	0.901928i
$39$	−1.08644e7	−	1.88177e7i	−0.751996	−	1.30250i
$40$	−68791.9	+	119151.i	−0.00424881	+	0.00735916i
$41$	−2.22245e7			−1.22830			−0.614151	−	0.789188i	$-0.710502\pi$
$41$	−2.22245e7			−1.22830			−0.614151	+	0.789188i	$0.710502\pi$
$42$		0			0
$43$	−3.24518e7			−1.44754			−0.723770	−	0.690042i	$-0.757592\pi$
$43$	−3.24518e7			−1.44754			−0.723770	+	0.690042i	$0.757592\pi$
$44$	6.59717e6	−	1.14266e7i	0.265351	−	0.459601i
$45$	287117.	+	497301.i	0.0104376	+	0.0180785i
$46$	2.39523e6	+	4.14866e6i	0.0788746	+	0.136615i
$47$	−1.59026e6	+	2.75442e6i	−0.0475367	+	0.0823360i	−0.888815	−	0.458267i	$-0.848470\pi$
$47$	−1.59026e6	+	2.75442e6i	−0.0475367	+	0.0823360i	0.841278	+	0.540603i	$0.181804\pi$
$48$	−1.25683e7			−0.341736
$49$		0			0
$50$	3.12319e7			0.706698
$51$	4.42685e7	−	7.66754e7i	0.916283	−	1.58705i
$52$	1.45027e7	+	2.51195e7i	0.275065	+	0.476426i
$53$	−4.41456e7	−	7.64625e7i	−0.768504	−	1.33109i	−0.938374	−	0.345622i	$-0.887668\pi$
$53$	−4.41456e7	−	7.64625e7i	−0.768504	−	1.33109i	0.169870	−	0.985467i	$-0.445665\pi$
$54$	3.96983e6	−	6.87595e6i	0.0635331	−	0.110043i
$55$	1.73123e6			0.0255107
$56$		0			0
$57$	−1.60452e8			−2.01330
$58$	2.06656e7	−	3.57938e7i	0.239784	−	0.415319i
$59$	−6.99559e6	−	1.21167e7i	−0.0751606	−	0.130182i	0.825995	−	0.563677i	$-0.190614\pi$
$59$	−6.99559e6	−	1.21167e7i	−0.0751606	−	0.130182i	−0.901156	+	0.433495i	$0.857280\pi$
$60$	−824545.	−	1.42815e6i	−0.00821360	−	0.0142264i
$61$	−5.69654e7	+	9.86669e7i	−0.526777	+	0.912404i	0.472736	+	0.881204i	$0.343266\pi$
$61$	−5.69654e7	+	9.86669e7i	−0.526777	+	0.912404i	−0.999513	+	0.0312003i	$0.990067\pi$
$62$	−1.09492e8			−0.941064
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.90291e6	+	3.29593e6i	−0.0132223	+	0.0229017i
$66$	7.90741e7	+	1.36960e8i	0.512964	+	0.888479i
$67$	1.52746e8	+	2.64565e8i	0.926050	+	1.60397i	0.789863	+	0.613283i	$0.210152\pi$
$67$	1.52746e8	+	2.64565e8i	0.926050	+	1.60397i	0.136187	+	0.990683i	$0.456515\pi$
$68$	−5.90933e7	+	1.02353e8i	−0.335157	+	0.580509i
$69$	−5.74188e7			−0.304953
$70$		0			0
$71$	−2.86664e8			−1.33878			−0.669392	−	0.742909i	$-0.733445\pi$
$71$	−2.86664e8			−1.33878			−0.669392	+	0.742909i	$0.733445\pi$
$72$	3.50115e7	−	6.06417e7i	0.153538	−	0.265935i
$73$	2.39428e7	+	4.14702e7i	0.0986785	+	0.170916i	0.911138	−	0.412102i	$-0.135205\pi$
$73$	2.39428e7	+	4.14702e7i	0.0986785	+	0.170916i	−0.812459	+	0.583018i	$0.801872\pi$
$74$	1.11637e8	+	1.93362e8i	0.432780	+	0.749596i
$75$	−1.87174e8	+	3.24195e8i	−0.683078	+	1.18313i
$76$	2.14184e8			0.736421
$77$		0			0
$78$	−3.47661e8			−1.06348
$79$	5.37908e7	−	9.31683e7i	0.155377	−	0.269120i	−0.777819	−	0.628488i	$-0.783674\pi$
$79$	5.37908e7	−	9.31683e7i	0.155377	−	0.269120i	0.933196	+	0.359367i	$0.117008\pi$
$80$	1.10067e6	+	1.90642e6i	0.00300436	+	0.00520371i
$81$	2.15828e8	+	3.73825e8i	0.557089	+	0.964907i
$82$	−1.77796e8	+	3.07952e8i	−0.434271	+	0.752179i
$83$	−5.67595e7			−0.131277			−0.0656383	−	0.997843i	$-0.520908\pi$
$83$	−5.67595e7			−0.131277			−0.0656383	+	0.997843i	$0.520908\pi$
$84$		0			0
$85$	−1.55073e7			−0.0322219
$86$	−2.59614e8	+	4.49665e8i	−0.511782	+	0.886433i
$87$	2.47699e8	+	4.29027e8i	0.463540	+	0.802875i
$88$	−1.05555e8	−	1.82826e8i	−0.187631	−	0.324987i
$89$	−4.24334e8	+	7.34969e8i	−0.716891	+	1.24169i	0.245334	+	0.969438i	$0.421102\pi$
$89$	−4.24334e8	+	7.34969e8i	−0.716891	+	1.24169i	−0.962226	+	0.272253i	$0.912231\pi$
$90$	9.18774e6			0.0147611
$91$		0			0
$92$	7.66474e7			0.111546
$93$	6.56188e8	−	1.13655e9i	0.909610	−	1.57549i
$94$	2.54442e7	+	4.40707e7i	0.0336135	+	0.0582203i
$95$	1.40516e7	+	2.43380e7i	0.0176998	+	0.0306570i
$96$	−1.00546e8	+	1.74152e8i	−0.120822	+	0.209270i
$97$	−8.99384e8			−1.03151			−0.515754	−	0.856737i	$-0.672488\pi$
$97$	−8.99384e8			−1.03151			−0.515754	+	0.856737i	$0.672488\pi$
$98$		0			0
$99$	−8.81107e8			−0.921871
$100$	2.49856e8	−	4.32763e8i	0.249856	−	0.432763i
$101$	3.16101e7	+	5.47503e7i	0.0302259	+	0.0523529i	0.880743	−	0.473595i	$-0.157044\pi$
$101$	3.16101e7	+	5.47503e7i	0.0302259	+	0.0523529i	−0.850517	+	0.525948i	$0.823711\pi$
$102$	−7.08297e8	−	1.22681e9i	−0.647910	−	1.12221i
$103$	6.07898e8	−	1.05291e9i	0.532185	−	0.921772i	−0.467108	−	0.884200i	$-0.654704\pi$
$103$	6.07898e8	−	1.05291e9i	0.532185	−	0.921772i	0.999294	−	0.0375722i	$-0.0119624\pi$
$104$	4.64087e8			0.389000
$105$		0			0
$106$	−1.41266e9			−1.08683
$107$	6.41212e8	−	1.11061e9i	0.472906	−	0.819097i	−0.526613	−	0.850105i	$-0.676538\pi$
$107$	6.41212e8	−	1.11061e9i	0.472906	−	0.819097i	0.999519	+	0.0310082i	$0.00987180\pi$
$108$	−6.35173e7	−	1.10015e8i	−0.0449247	−	0.0778118i
$109$	2.53284e8	+	4.38700e8i	0.171865	+	0.297679i	0.939072	−	0.343721i	$-0.111687\pi$
$109$	2.53284e8	+	4.38700e8i	0.171865	+	0.297679i	−0.767207	+	0.641400i	$0.778354\pi$
$110$	1.38499e7	−	2.39887e7i	0.00901941	−	0.0156221i
$111$	−2.67619e9			−1.67326
$112$		0			0
$113$	1.15512e9			0.666462			0.333231	−	0.942845i	$-0.391861\pi$
$113$	1.15512e9			0.666462			0.333231	+	0.942845i	$0.391861\pi$
$114$	−1.28361e9	+	2.22328e9i	−0.711807	+	1.23289i
$115$	5.02846e6	+	8.70955e6i	0.00268099	+	0.00464361i
$116$	−3.30649e8	−	5.72701e8i	−0.169553	−	0.293675i
$117$	9.68480e8	−	1.67746e9i	0.477809	−	0.827590i
$118$	−2.23859e8			−0.106293
$119$		0			0
$120$	−2.63854e7			−0.0116158
$121$	−1.49232e8	+	2.58477e8i	−0.0632888	+	0.109619i
$122$	9.11446e8	+	1.57867e9i	0.372487	+	0.645167i
$123$	−2.13108e9	−	3.69114e9i	−0.839511	−	1.45408i
$124$	−8.75935e8	+	1.51716e9i	−0.332716	+	0.576282i
$125$	1.31172e8			0.0480559
$126$		0			0
$127$	3.41280e9			1.16411			0.582055	−	0.813150i	$-0.302249\pi$
$127$	3.41280e9			1.16411			0.582055	+	0.813150i	$0.302249\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	−3.11175e9	−	5.38972e9i	−0.989354	−	1.71361i
$130$	3.04465e7	+	5.27349e7i	0.00934958	+	0.0161940i
$131$	3.58994e8	−	6.21795e8i	0.106504	−	0.184470i	−0.807848	−	0.589391i	$-0.799368\pi$
$131$	3.58994e8	−	6.21795e8i	0.106504	−	0.184470i	0.914352	+	0.404921i	$0.132701\pi$
$132$	2.53037e9			0.725440
$133$		0			0
$134$	4.88789e9			1.30963
$135$	8.33412e6	−	1.44351e7i	0.00215952	−	0.00374040i
$136$	9.45493e8	+	1.63764e9i	0.236992	+	0.410482i
$137$	3.65685e9	+	6.33385e9i	0.886880	+	1.53612i	0.843544	+	0.537061i	$0.180465\pi$
$137$	3.65685e9	+	6.33385e9i	0.886880	+	1.53612i	0.0433362	+	0.999061i	$0.486201\pi$
$138$	−4.59350e8	+	7.95618e8i	−0.107817	+	0.186745i
$139$	4.88666e9			1.11031			0.555157	−	0.831746i	$-0.312658\pi$
$139$	4.88666e9			1.11031			0.555157	+	0.831746i	$0.312658\pi$
$140$		0			0
$141$	−6.09953e8			−0.129960
$142$	−2.29331e9	+	3.97213e9i	−0.473332	+	0.819834i
$143$	−2.91983e9	−	5.05729e9i	−0.583909	−	1.01136i
$144$	−5.60184e8	−	9.70268e8i	−0.108567	−	0.188044i
$145$	4.33845e7	−	7.51442e7i	0.00815039	−	0.0141169i
$146$	7.66170e8			0.139552
$147$		0			0
$148$	3.57240e9			0.612043
$149$	−3.45145e9	+	5.97808e9i	−0.573671	+	0.993627i	0.422514	+	0.906356i	$0.361148\pi$
$149$	−3.45145e9	+	5.97808e9i	−0.573671	+	0.993627i	−0.996185	+	0.0872706i	$0.972186\pi$
$150$	2.99479e9	+	5.18712e9i	0.483009	+	0.836596i
$151$	2.82774e9	+	4.89778e9i	0.442632	+	0.766660i	0.997884	−	0.0650215i	$-0.0207116\pi$
$151$	2.82774e9	+	4.89778e9i	0.442632	+	0.766660i	−0.555252	+	0.831682i	$0.687378\pi$
$152$	1.71347e9	−	2.96782e9i	0.260364	−	0.450964i
$153$	7.89241e9			1.16439
$154$		0			0
$155$	−2.29863e8			−0.0319872
$156$	−2.78129e9	+	4.81734e9i	−0.375998	+	0.651248i
$157$	−3.29987e9	−	5.71555e9i	−0.433460	−	0.750775i	0.563709	−	0.825974i	$-0.309374\pi$
$157$	−3.29987e9	−	5.71555e9i	−0.433460	−	0.750775i	−0.997169	+	0.0751991i	$0.976041\pi$
$158$	−8.60652e8	−	1.49069e9i	−0.109868	−	0.190297i
$159$	8.46612e9	−	1.46638e10i	1.05050	−	1.81952i
$160$	3.52215e7			0.00424881
$161$		0			0
$162$	6.90649e9			0.787843
$163$	3.99398e9	−	6.91778e9i	0.443162	−	0.767578i	−0.554761	−	0.832010i	$-0.687190\pi$
$163$	3.99398e9	−	6.91778e9i	0.443162	−	0.767578i	0.997922	+	0.0644317i	$0.0205235\pi$
$164$	2.84474e9	+	4.92724e9i	0.307076	+	0.531871i
$165$	1.66005e8	+	2.87530e8i	0.0174359	+	0.0301999i
$166$	−4.54076e8	+	7.86483e8i	−0.0464133	+	0.0803902i
$167$	−4.34905e9			−0.432683			−0.216342	−	0.976318i	$-0.569412\pi$
$167$	−4.34905e9			−0.432683			−0.216342	+	0.976318i	$0.569412\pi$
$168$		0			0
$169$	2.23297e9			0.210568
$170$	−1.24058e8	+	2.14875e8i	−0.0113922	+	0.0197318i
$171$	−7.15152e9	−	1.23868e10i	−0.639611	−	1.10784i
$172$	4.15383e9	+	7.19464e9i	0.361885	+	0.626803i
$173$	6.92455e9	−	1.19937e10i	0.587739	−	1.01799i	−0.406789	−	0.913522i	$-0.633352\pi$
$173$	6.92455e9	−	1.19937e10i	0.587739	−	1.01799i	0.994528	−	0.104471i	$-0.0333150\pi$
$174$	7.92636e9			0.655545
$175$		0			0
$176$	−3.37775e9			−0.265351
$177$	1.34159e9	−	2.32371e9i	0.102740	−	0.177952i
$178$	6.78935e9	+	1.17595e10i	0.506919	+	0.878009i
$179$	−9.97712e9	−	1.72809e10i	−0.726384	−	1.25813i	−0.958402	−	0.285423i	$-0.907866\pi$
$179$	−9.97712e9	−	1.72809e10i	−0.726384	−	1.25813i	0.232017	−	0.972712i	$-0.425467\pi$
$180$	7.35019e7	−	1.27309e8i	0.00521882	−	0.00903926i
$181$	3.33705e9			0.231105			0.115552	−	0.993301i	$-0.463136\pi$
$181$	3.33705e9			0.231105			0.115552	+	0.993301i	$0.463136\pi$
$182$		0			0
$183$	−2.18493e10			−1.44015
$184$	6.13179e8	−	1.06206e9i	0.0394373	−	0.0683074i
$185$	2.34367e8	+	4.05936e8i	0.0147104	+	0.0254792i
$186$	−1.04990e10	−	1.81848e10i	−0.643191	−	1.11404i
$187$	1.18972e10	−	2.06066e10i	0.711474	−	1.23231i
$188$	8.14216e8			0.0475367
$189$		0			0
$190$	4.49650e8			0.0250313
$191$	1.22946e10	−	2.12948e10i	0.668441	−	1.15777i	−0.309899	−	0.950770i	$-0.600295\pi$
$191$	1.22946e10	−	2.12948e10i	0.668441	−	1.15777i	0.978340	−	0.207005i	$-0.0663716\pi$
$192$	1.60874e9	+	2.78643e9i	0.0854341	+	0.147976i
$193$	9.00593e9	+	1.55987e10i	0.467219	+	0.809247i	0.999299	−	0.0374471i	$-0.0119226\pi$
$193$	9.00593e9	+	1.55987e10i	0.467219	+	0.809247i	−0.532079	+	0.846694i	$0.678589\pi$
$194$	−7.19507e9	+	1.24622e10i	−0.364693	+	0.631666i
$195$	−7.29868e8			−0.0361483
$196$		0			0
$197$	4.02716e10			1.90503			0.952514	−	0.304496i	$-0.0984880\pi$
$197$	4.02716e10			1.90503			0.952514	+	0.304496i	$0.0984880\pi$
$198$	−7.04886e9	+	1.22090e10i	−0.325931	+	0.564529i
$199$	1.88426e10	+	3.26363e10i	0.851730	+	1.47524i	0.879646	+	0.475630i	$0.157780\pi$
$199$	1.88426e10	+	3.26363e10i	0.851730	+	1.47524i	−0.0279153	+	0.999610i	$0.508887\pi$
$200$	−3.99769e9	−	6.92420e9i	−0.176675	−	0.306009i
$201$	−2.92933e10	+	5.07375e10i	−1.26586	+	2.19253i
$202$	1.01152e9			0.0427459
$203$		0			0
$204$	−2.26655e10			−0.916283
$205$	−3.73259e8	+	6.46504e8i	−0.0147611	+	0.0255669i
$206$	−9.72636e9	−	1.68466e10i	−0.376312	−	0.651791i
$207$	−2.55922e9	−	4.43271e9i	−0.0968817	−	0.167804i
$208$	3.71270e9	−	6.43058e9i	0.137532	−	0.238213i
$209$	−4.31216e10			−1.56328
$210$		0			0
$211$	−1.57268e10			−0.546223			−0.273111	−	0.961982i	$-0.588053\pi$
$211$	−1.57268e10			−0.546223			−0.273111	+	0.961982i	$0.588053\pi$
$212$	−1.13013e10	+	1.95744e10i	−0.384252	+	0.665544i
$213$	−2.74878e10	−	4.76103e10i	−0.915022	−	1.58487i
$214$	−1.02594e10	−	1.77698e10i	−0.334395	−	0.579189i
$215$	−5.45025e8	+	9.44010e8i	−0.0173957	+	0.0301303i
$216$	−2.03255e9			−0.0635331
$217$		0			0
$218$	8.10508e9			0.243054
$219$	−4.59169e9	+	7.95303e9i	−0.134888	+	0.233633i
$220$	−2.21598e8	−	3.83818e8i	−0.00637769	−	0.0110465i
$221$	2.61540e10	+	4.53000e10i	0.737518	+	1.27742i
$222$	−2.14095e10	+	3.70823e10i	−0.591586	+	1.02466i
$223$	−6.29667e10			−1.70506			−0.852528	−	0.522681i	$-0.824932\pi$
$223$	−6.29667e10			−1.70506			−0.852528	+	0.522681i	$0.824932\pi$
$224$		0			0
$225$	−3.33703e10			−0.868038
$226$	9.24098e9	−	1.60058e10i	0.235630	−	0.408123i
$227$	2.74005e10	+	4.74591e10i	0.684925	+	1.18632i	0.973460	+	0.228855i	$0.0734982\pi$
$227$	2.74005e10	+	4.74591e10i	0.684925	+	1.18632i	−0.288536	+	0.957469i	$0.593168\pi$
$228$	2.05378e10	+	3.55725e10i	0.503324	+	0.871782i
$229$	−3.07059e10	+	5.31842e10i	−0.737840	+	1.27798i	0.215627	+	0.976476i	$0.430821\pi$
$229$	−3.07059e10	+	5.31842e10i	−0.737840	+	1.27798i	−0.953466	+	0.301500i	$0.902513\pi$
$230$	1.60911e8			0.00379149
$231$		0			0
$232$	−1.05808e10			−0.239784
$233$	4.21455e9	−	7.29981e9i	0.0936806	−	0.162259i	−0.815377	−	0.578931i	$-0.803470\pi$
$233$	4.21455e9	−	7.29981e9i	0.0936806	−	0.162259i	0.909057	+	0.416671i	$0.136803\pi$
$234$	−1.54957e10	−	2.68393e10i	−0.337862	−	0.585194i
$235$	5.34167e7	+	9.25204e7i	0.00114254	+	0.00197894i
$236$	−1.79087e9	+	3.10188e9i	−0.0375803	+	0.0650910i
$237$	2.06317e10			0.424783
$238$		0			0
$239$	3.13951e10			0.622402			0.311201	−	0.950344i	$-0.399269\pi$
$239$	3.13951e10			0.622402			0.311201	+	0.950344i	$0.399269\pi$
$240$	−2.11084e8	+	3.65607e8i	−0.00410680	+	0.00711319i
$241$	7.29330e9	+	1.26324e10i	0.139267	+	0.241217i	0.927219	−	0.374519i	$-0.122192\pi$
$241$	7.29330e9	+	1.26324e10i	0.139267	+	0.241217i	−0.787953	+	0.615736i	$0.788859\pi$
$242$	2.38771e9	+	4.13563e9i	0.0447519	+	0.0775126i
$243$	−3.65072e10	+	6.32323e10i	−0.671661	+	1.16335i
$244$	2.91663e10			0.526777
$245$		0			0
$246$	−6.81945e10			−1.18725
$247$	4.73977e10	−	8.20952e10i	0.810253	−	1.40340i
$248$	1.40150e10	+	2.42746e10i	0.235266	+	0.407493i
$249$	−5.44259e9	−	9.42684e9i	−0.0897240	−	0.155406i
$250$	1.04938e9	−	1.81758e9i	0.0169903	−	0.0294281i
$251$	3.56389e10			0.566752			0.283376	−	0.959009i	$-0.408546\pi$
$251$	3.56389e10			0.566752			0.283376	+	0.959009i	$0.408546\pi$
$252$		0			0
$253$	−1.54314e10			−0.236790
$254$	2.73024e10	−	4.72891e10i	0.411575	−	0.712869i
$255$	−1.48697e9	−	2.57551e9i	−0.0220228	−	0.0381446i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	3.47285e10	−	6.01515e10i	0.496577	−	0.860096i	−0.503415	−	0.864045i	$-0.667923\pi$
$257$	3.47285e10	−	6.01515e10i	0.496577	−	0.860096i	0.999992	+	0.00394818i	$0.00125675\pi$
$258$	−9.95761e10			−1.39916
$259$		0			0
$260$	9.74288e8			0.0132223
$261$	−2.20805e10	+	3.82445e10i	−0.294527	+	0.510137i
$262$	−5.74390e9	−	9.94873e9i	−0.0753097	−	0.130440i
$263$	−3.61510e10	−	6.26154e10i	−0.465929	−	0.807012i	0.533314	−	0.845917i	$-0.320946\pi$
$263$	−3.61510e10	−	6.26154e10i	−0.465929	−	0.807012i	−0.999243	+	0.0389051i	$0.987613\pi$
$264$	2.02430e10	−	3.50619e10i	0.256482	−	0.444240i
$265$	−2.96569e9			−0.0369419
$266$		0			0
$267$	−1.62755e11			−1.95990
$268$	3.91031e10	−	6.77286e10i	0.463025	−	0.801983i
$269$	4.51533e10	+	7.82078e10i	0.525780	+	0.910678i	0.999549	+	0.0300285i	$0.00955980\pi$
$269$	4.51533e10	+	7.82078e10i	0.525780	+	0.910678i	−0.473769	+	0.880649i	$0.657107\pi$
$270$	−1.33346e8	−	2.30962e8i	−0.00152701	−	0.00264486i
$271$	2.01115e10	−	3.48341e10i	0.226507	−	0.392322i	−0.730264	−	0.683166i	$-0.760603\pi$
$271$	2.01115e10	−	3.48341e10i	0.226507	−	0.392322i	0.956771	+	0.290844i	$0.0939361\pi$
$272$	3.02558e10			0.335157
$273$		0			0
$274$	1.17019e11			1.25424
$275$	−5.03033e10	+	8.71279e10i	−0.530395	+	0.918671i
$276$	7.34961e9	+	1.27299e10i	0.0762383	+	0.132049i
$277$	1.03358e10	+	1.79022e10i	0.105484	+	0.182704i	0.913936	−	0.405859i	$-0.133027\pi$
$277$	1.03358e10	+	1.79022e10i	0.105484	+	0.182704i	−0.808452	+	0.588562i	$0.799694\pi$
$278$	3.90933e10	−	6.77116e10i	0.392555	−	0.679926i
$279$	1.16988e11			1.15591
$280$		0			0
$281$	−3.46833e10			−0.331850			−0.165925	−	0.986138i	$-0.553061\pi$
$281$	−3.46833e10			−0.331850			−0.165925	+	0.986138i	$0.553061\pi$
$282$	−4.87962e9	+	8.45175e9i	−0.0459479	+	0.0795840i
$283$	5.23196e10	+	9.06203e10i	0.484870	+	0.839820i	0.999849	−	0.0173829i	$-0.00553342\pi$
$283$	5.23196e10	+	9.06203e10i	0.484870	+	0.839820i	−0.514978	+	0.857203i	$0.672200\pi$
$284$	3.66930e10	+	6.35541e10i	0.334696	+	0.579711i
$285$	−2.69477e9	+	4.66748e9i	−0.0241947	+	0.0419064i
$286$	−9.34345e10			−0.825772
$287$		0			0
$288$	−1.79259e10			−0.153538
$289$	−4.72740e10	+	8.18810e10i	−0.398641	+	0.690467i
$290$	−6.94152e8	−	1.20231e9i	−0.00576320	−	0.00998215i
$291$	−8.62406e10	−	1.49373e11i	−0.705007	−	1.22111i
$292$	6.12936e9	−	1.06164e10i	0.0493392	−	0.0854581i
$293$	1.60760e11			1.27431			0.637153	−	0.770737i	$-0.280112\pi$
$293$	1.60760e11			1.27431			0.637153	+	0.770737i	$0.280112\pi$
$294$		0			0
$295$	−4.69961e8			−0.00361296
$296$	2.85792e10	−	4.95006e10i	0.216390	−	0.374798i
$297$	1.27879e10	+	2.21493e10i	0.0953664	+	0.165180i
$298$	5.52231e10	+	9.56493e10i	0.405647	+	0.702600i
$299$	1.69616e10	−	2.93784e10i	0.122729	−	0.212573i
$300$	9.58332e10			0.683078
$301$		0			0
$302$	9.04875e10			0.625976
$303$	−6.06210e9	+	1.04999e10i	−0.0413172	+	0.0715635i
$304$	−2.74156e10	−	4.74852e10i	−0.184105	−	0.318880i
$305$	1.91346e9	+	3.31420e9i	0.0126610	+	0.0219296i
$306$	6.31393e10	−	1.09360e11i	0.411674	−	0.713040i
$307$	−1.45170e11			−0.932725			−0.466362	−	0.884594i	$-0.654436\pi$
$307$	−1.45170e11			−0.932725			−0.466362	+	0.884594i	$0.654436\pi$
$308$		0			0
$309$	2.33162e11			1.45494
$310$	−1.83891e9	+	3.18508e9i	−0.0113092	+	0.0195881i
$311$	−1.31545e11	−	2.27842e11i	−0.797356	−	1.38106i	−0.921333	−	0.388775i	$-0.872898\pi$
$311$	−1.31545e11	−	2.27842e11i	−0.797356	−	1.38106i	0.123977	−	0.992285i	$-0.460435\pi$
$312$	4.45007e10	+	7.70774e10i	0.265871	+	0.460502i
$313$	−4.19102e10	+	7.25905e10i	−0.246814	+	0.427495i	−0.962640	−	0.270784i	$-0.912717\pi$
$313$	−4.19102e10	+	7.25905e10i	−0.246814	+	0.427495i	0.715826	+	0.698279i	$0.246050\pi$
$314$	−1.05596e11			−0.613005
$315$		0			0
$316$	−2.75409e10			−0.155377
$317$	−1.35358e11	+	2.34447e11i	−0.752865	+	1.30400i	0.193564	+	0.981088i	$0.437995\pi$
$317$	−1.35358e11	+	2.34447e11i	−0.752865	+	1.30400i	−0.946429	+	0.322913i	$0.895338\pi$
$318$	−1.35458e11	−	2.34620e11i	−0.742818	−	1.28660i
$319$	6.65694e10	+	1.15302e11i	0.359929	+	0.623415i
$320$	2.81772e8	−	4.88043e8i	0.00150218	−	0.00260186i
$321$	2.45940e11			1.29287
$322$		0			0
$323$	3.86257e11			1.97453
$324$	5.52519e10	−	9.56991e10i	0.278545	−	0.482453i
$325$	−1.10583e11	−	1.91536e11i	−0.549811	−	0.952301i
$326$	−6.39037e10	−	1.10685e11i	−0.313363	−	0.542760i
$327$	−4.85740e10	+	8.41327e10i	−0.234930	+	0.406911i
$328$	9.10317e10			0.434271
$329$		0			0
$330$	5.31217e9			0.0246581
$331$	−9.68704e10	+	1.67784e11i	−0.443573	+	0.768291i	−0.997952	−	0.0639738i	$-0.979623\pi$
$331$	−9.68704e10	+	1.67784e11i	−0.443573	+	0.768291i	0.554379	+	0.832265i	$0.312956\pi$
$332$	7.26522e9	+	1.25837e10i	0.0328191	+	0.0568444i
$333$	−1.19281e11	−	2.06600e11i	−0.531584	−	0.920730i
$334$	−3.47924e10	+	6.02622e10i	−0.152977	+	0.264963i
$335$	1.02615e10			0.0445151
$336$		0			0
$337$	2.23909e11			0.945665			0.472832	−	0.881152i	$-0.343232\pi$
$337$	2.23909e11			0.945665			0.472832	+	0.881152i	$0.343232\pi$
$338$	1.78637e10	−	3.09409e10i	0.0744470	−	0.128946i
$339$	1.10763e11	+	1.91847e11i	0.455508	+	0.788964i
$340$	1.98493e9	+	3.43801e9i	0.00805547	+	0.0139525i
$341$	1.76352e11	−	3.05450e11i	0.706293	−	1.22333i
$342$	−2.28849e11			−0.904547
$343$		0			0
$344$	1.32922e11			0.511782
$345$	−9.64344e8	+	1.67029e9i	−0.00366476	+	0.00634756i
$346$	−1.10793e11	−	1.91899e11i	−0.415594	−	0.719830i
$347$	1.28864e11	+	2.23200e11i	0.477145	+	0.826439i	0.999657	−	0.0261929i	$-0.00833841\pi$
$347$	1.28864e11	+	2.23200e11i	0.477145	+	0.826439i	−0.522512	+	0.852632i	$0.675005\pi$
$348$	6.34109e10	−	1.09831e11i	0.231770	−	0.401437i
$349$	−1.38744e11			−0.500609			−0.250304	−	0.968167i	$-0.580531\pi$
$349$	−1.38744e11			−0.500609			−0.250304	+	0.968167i	$0.580531\pi$
$350$		0			0
$351$	−5.62240e10			−0.197715
$352$	−2.70220e10	+	4.68035e10i	−0.0938157	+	0.162494i
$353$	9.34902e10	+	1.61930e11i	0.320464	+	0.555061i	0.980584	−	0.196100i	$-0.0628277\pi$
$353$	9.34902e10	+	1.61930e11i	0.320464	+	0.555061i	−0.660119	+	0.751161i	$0.729494\pi$
$354$	−2.14655e10	−	3.71794e10i	−0.0726485	−	0.125831i
$355$	−4.81450e9	+	8.33895e9i	−0.0160888	+	0.0278666i
$356$	2.17259e11			0.716891
$357$		0			0
$358$	−3.19268e11			−1.02726
$359$	−1.03782e11	+	1.79755e11i	−0.329758	+	0.571157i	−0.982464	−	0.186454i	$-0.940300\pi$
$359$	−1.03782e11	+	1.79755e11i	−0.329758	+	0.571157i	0.652706	+	0.757611i	$0.273634\pi$
$360$	−1.17603e9	−	2.03694e9i	−0.00369026	−	0.00639172i
$361$	−1.88654e11	−	3.26758e11i	−0.584632	−	1.01261i
$362$	2.66964e10	−	4.62395e10i	0.0817079	−	0.141522i
$363$	−5.72384e10			−0.173025
$364$		0			0
$365$	1.60847e9			0.00474346
$366$	−1.74794e11	+	3.02753e11i	−0.509170	+	0.881908i
$367$	8.96653e10	+	1.55305e11i	0.258004	+	0.446877i	0.965707	−	0.259634i	$-0.0836018\pi$
$367$	8.96653e10	+	1.55305e11i	0.258004	+	0.446877i	−0.707703	+	0.706510i	$0.750268\pi$
$368$	−9.81086e9	−	1.69929e10i	−0.0278864	−	0.0483006i
$369$	1.89969e11	−	3.29037e11i	0.533415	−	0.923902i
$370$	7.49976e9			0.0208036
$371$		0			0
$372$	−3.35968e11			−0.909610
$373$	2.72418e11	−	4.71842e11i	0.728696	−	1.26214i	−0.228738	−	0.973488i	$-0.573460\pi$
$373$	2.72418e11	−	4.71842e11i	0.728696	−	1.26214i	0.957434	−	0.288651i	$-0.0932066\pi$
$374$	−1.90356e11	−	3.29706e11i	−0.503088	−	0.871374i
$375$	1.25779e10	+	2.17856e10i	0.0328449	+	0.0568891i
$376$	6.51372e9	−	1.12821e10i	0.0168068	−	0.0291102i
$377$	−2.92682e11			−0.746209
$378$		0			0
$379$	−1.24662e11			−0.310353			−0.155177	−	0.987887i	$-0.549595\pi$
$379$	−1.24662e11			−0.310353			−0.155177	+	0.987887i	$0.549595\pi$
$380$	3.59720e9	−	6.23054e9i	0.00884991	−	0.0153285i
$381$	3.27248e11	+	5.66811e11i	0.795637	+	1.37808i
$382$	−1.96713e11	−	3.40717e11i	−0.472659	−	0.818670i
$383$	−2.04123e11	+	3.53551e11i	−0.484726	+	0.839571i	−0.999846	−	0.0175476i	$-0.994414\pi$
$383$	−2.04123e11	+	3.53551e11i	−0.484726	+	0.839571i	0.515120	+	0.857118i	$0.327747\pi$
$384$	5.14798e10			0.120822
$385$		0			0
$386$	2.88190e11			0.660748
$387$	2.77389e11	−	4.80452e11i	0.628623	−	1.08881i
$388$	1.15121e11	+	1.99396e11i	0.257877	+	0.446656i
$389$	−2.56820e11	−	4.44825e11i	−0.568663	−	0.984954i	−0.996698	−	0.0811919i	$-0.974127\pi$
$389$	−2.56820e11	−	4.44825e11i	−0.568663	−	0.984954i	0.428035	−	0.903762i	$-0.359206\pi$
$390$	−5.83894e9	+	1.01133e10i	−0.0127804	+	0.0221362i
$391$	1.38225e11			0.299082
$392$		0			0
$393$	1.37694e11			0.291170
$394$	3.22173e11	−	5.58020e11i	0.673529	−	1.16659i
$395$	−1.80682e9	−	3.12951e9i	−0.00373447	−	0.00646828i
$396$	1.12782e11	+	1.95344e11i	0.230468	+	0.399182i
$397$	1.80407e11	−	3.12474e11i	0.364499	−	0.631331i	−0.624197	−	0.781267i	$-0.714574\pi$
$397$	1.80407e11	−	3.12474e11i	0.364499	−	0.631331i	0.988696	+	0.149936i	$0.0479069\pi$
$398$	6.02963e11			1.20453
$399$		0			0
$400$	−1.27926e11			−0.249856
$401$	−1.19297e11	+	2.06629e11i	−0.230399	+	0.399062i	−0.957925	−	0.287017i	$-0.907336\pi$
$401$	−1.19297e11	+	2.06629e11i	−0.230399	+	0.399062i	0.727527	+	0.686079i	$0.240670\pi$
$402$	4.68693e11	+	8.11799e11i	0.895098	+	1.55036i
$403$	3.87678e11	+	6.71478e11i	0.732148	+	1.26812i
$404$	8.09219e9	−	1.40161e10i	0.0151130	−	0.0261764i
$405$	1.44992e10			0.0267792
$406$		0			0
$407$	−7.19229e11			−1.29925
$408$	−1.81324e11	+	3.14062e11i	−0.323955	+	0.561106i
$409$	−3.87345e11	−	6.70901e11i	−0.684452	−	1.18551i	−0.973609	−	0.228224i	$-0.926708\pi$
$409$	−3.87345e11	−	6.70901e11i	−0.684452	−	1.18551i	0.289157	−	0.957282i	$-0.406625\pi$
$410$	5.97214e9	+	1.03441e10i	0.0104377	+	0.0180785i
$411$	−7.01301e11	+	1.21469e12i	−1.21232	+	2.09979i
$412$	−3.11244e11			−0.532185
$413$		0			0
$414$	−8.18952e10			−0.137011
$415$	−9.53271e8	+	1.65111e9i	−0.00157761	+	0.00273250i
$416$	−5.94032e10	−	1.02889e11i	−0.0972500	−	0.168442i
$417$	4.68575e11	+	8.11596e11i	0.758869	+	1.31440i
$418$	−3.44973e11	+	5.97511e11i	−0.552703	+	0.957310i
$419$	5.87231e11			0.930777			0.465389	−	0.885106i	$-0.345915\pi$
$419$	5.87231e11			0.930777			0.465389	+	0.885106i	$0.345915\pi$
$420$		0			0
$421$	−1.12541e12			−1.74599			−0.872993	−	0.487733i	$-0.837824\pi$
$421$	−1.12541e12			−1.74599			−0.872993	+	0.487733i	$0.837824\pi$
$422$	−1.25815e11	+	2.17917e11i	−0.193119	+	0.334492i
$423$	−2.71863e10	−	4.70881e10i	−0.0412875	−	0.0715121i
$424$	1.80820e11	+	3.13190e11i	0.271707	+	0.470611i
$425$	4.50586e11	−	7.80437e11i	0.669927	−	1.16035i
$426$	−8.79610e11			−1.29404
$427$		0			0
$428$	−3.28300e11			−0.472906
$429$	5.59956e11	−	9.69873e11i	0.798172	−	1.38247i
$430$	8.72039e9	+	1.51042e10i	0.0123006	+	0.0213053i
$431$	3.38834e11	+	5.86878e11i	0.472976	+	0.819219i	0.999522	−	0.0309282i	$-0.00984632\pi$
$431$	3.38834e11	+	5.86878e11i	0.472976	+	0.819219i	−0.526545	+	0.850147i	$0.676513\pi$
$432$	−1.62604e10	+	2.81639e10i	−0.0224623	+	0.0389059i
$433$	−5.66584e11			−0.774585			−0.387292	−	0.921957i	$-0.626590\pi$
$433$	−5.66584e11			−0.774585			−0.387292	+	0.921957i	$0.626590\pi$
$434$		0			0
$435$	1.66403e10			0.0222823
$436$	6.48406e10	−	1.12307e11i	0.0859326	−	0.148840i
$437$	−1.25249e11	−	2.16938e11i	−0.164289	−	0.284557i
$438$	7.34670e10	+	1.27249e11i	0.0953803	+	0.165203i
$439$	−3.70618e11	+	6.41930e11i	−0.476252	+	0.824892i	−0.999630	−	0.0272086i	$-0.991338\pi$
$439$	−3.70618e11	+	6.41930e11i	−0.476252	+	0.824892i	0.523378	+	0.852100i	$0.324671\pi$
$440$	−7.09113e9			−0.00901941
$441$		0			0
$442$	8.36928e11			1.04301
$443$	−4.62603e10	+	8.01252e10i	−0.0570679	+	0.0988445i	−0.893148	−	0.449763i	$-0.851508\pi$
$443$	−4.62603e10	+	8.01252e10i	−0.0570679	+	0.0988445i	0.836080	+	0.548607i	$0.184842\pi$
$444$	3.42552e11	+	5.93317e11i	0.418315	+	0.724542i
$445$	1.42533e10	+	2.46875e10i	0.0172304	+	0.0298440i
$446$	−5.03733e11	+	8.72492e11i	−0.602828	+	1.04413i
$447$	−1.32382e12			−1.56835
$448$		0			0
$449$	−1.26884e11			−0.147333			−0.0736664	−	0.997283i	$-0.523470\pi$
$449$	−1.26884e11			−0.147333			−0.0736664	+	0.997283i	$0.523470\pi$
$450$	−2.66962e11	+	4.62392e11i	−0.306898	+	0.531563i
$451$	−5.72731e11	−	9.91998e11i	−0.651862	−	1.12906i
$452$	−1.47856e11	−	2.56094e11i	−0.166615	−	0.288586i
$453$	−5.42295e11	+	9.39282e11i	−0.605053	+	1.04798i
$454$	8.76817e11			0.968630
$455$		0			0
$456$	6.57210e11			0.711807
$457$	−5.14076e11	+	8.90406e11i	−0.551321	+	0.954916i	0.446858	+	0.894605i	$0.352543\pi$
$457$	−5.14076e11	+	8.90406e11i	−0.551321	+	0.954916i	−0.998180	+	0.0603116i	$0.980791\pi$
$458$	4.91294e11	+	8.50946e11i	0.521731	+	0.903665i
$459$	−1.14546e11	−	1.98400e11i	−0.120455	−	0.208633i
$460$	1.28729e9	−	2.22964e9i	0.00134049	−	0.00232180i
$461$	8.10233e11			0.835518			0.417759	−	0.908558i	$-0.362816\pi$
$461$	8.10233e11			0.835518			0.417759	+	0.908558i	$0.362816\pi$
$462$		0			0
$463$	−1.44793e12			−1.46431			−0.732155	−	0.681139i	$-0.761485\pi$
$463$	−1.44793e12			−1.46431			−0.732155	+	0.681139i	$0.761485\pi$
$464$	−8.46461e10	+	1.46611e11i	−0.0847766	+	0.146837i
$465$	−2.20412e10	−	3.81766e10i	−0.0218624	−	0.0378668i
$466$	−6.74328e10	−	1.16797e11i	−0.0662422	−	0.114735i
$467$	−2.23517e11	+	3.87143e11i	−0.217463	+	0.376657i	−0.954032	−	0.299706i	$-0.903111\pi$
$467$	−2.23517e11	+	3.87143e11i	−0.217463	+	0.376657i	0.736569	+	0.676363i	$0.236445\pi$
$468$	−4.95862e11			−0.477809
$469$		0			0
$470$	1.70933e9			0.00161580
$471$	6.32840e11	−	1.09611e12i	0.592516	−	1.02627i
$472$	2.86539e10	+	4.96301e10i	0.0265733	+	0.0460263i
$473$	−8.36288e11	−	1.44849e12i	−0.768212	−	1.33058i
$474$	1.65053e11	−	2.85881e11i	0.150183	−	0.260125i
$475$	−1.63315e12			−1.47199
$476$		0			0
$477$	1.50938e12			1.33495
$478$	2.51161e11	−	4.35023e11i	0.220052	−	0.381142i
$479$	−4.34776e10	−	7.53054e10i	−0.0377360	−	0.0653606i	0.846541	−	0.532324i	$-0.178681\pi$
$479$	−4.34776e10	−	7.53054e10i	−0.0377360	−	0.0653606i	−0.884277	+	0.466964i	$0.845348\pi$
$480$	3.37734e9	+	5.84972e9i	0.00290395	+	0.00502979i
$481$	7.90550e11	−	1.36927e12i	0.673405	−	1.16637i
$482$	2.33386e11			0.196953
$483$		0			0
$484$	7.64066e10			0.0632888
$485$	−1.51051e10	+	2.61627e10i	−0.0123961	+	0.0214707i
$486$	5.84115e11	+	1.01172e12i	0.474936	+	0.822614i
$487$	2.40968e8	+	4.17368e8i	0.000194124	+	0.000336232i	0.866122	−	0.499832i	$-0.166605\pi$
$487$	2.40968e8	+	4.17368e8i	0.000194124	+	0.000336232i	−0.865928	+	0.500168i	$0.833272\pi$
$488$	2.33330e11	−	4.04140e11i	0.186244	−	0.322584i
$489$	1.53191e12			1.21156
$490$		0			0
$491$	−5.88640e11			−0.457070			−0.228535	−	0.973536i	$-0.573394\pi$
$491$	−5.88640e11			−0.457070			−0.228535	+	0.973536i	$0.573394\pi$
$492$	−5.45556e11	+	9.44931e11i	−0.419756	+	0.727038i
$493$	−5.96287e11	−	1.03280e12i	−0.454616	−	0.787417i
$494$	−7.58363e11	−	1.31352e12i	−0.572936	−	0.992354i
$495$	−1.47981e10	+	2.56311e10i	−0.0110786	+	0.0191886i
$496$	4.48478e11			0.332716
$497$		0			0
$498$	−1.74163e11			−0.126889
$499$	1.23973e12	−	2.14728e12i	0.895107	−	1.55037i	0.0614341	−	0.998111i	$-0.480433\pi$
$499$	1.23973e12	−	2.14728e12i	0.895107	−	1.55037i	0.833673	−	0.552259i	$-0.186234\pi$
$500$	−1.67901e10	−	2.90812e10i	−0.0120140	−	0.0208088i
$501$	−4.17024e11	−	7.22307e11i	−0.295727	−	0.512214i
$502$	2.85111e11	−	4.93828e11i	0.200377	−	0.347063i
$503$	−1.35604e12			−0.944530			−0.472265	−	0.881457i	$-0.656563\pi$
$503$	−1.35604e12			−0.944530			−0.472265	+	0.881457i	$0.656563\pi$
$504$		0			0
$505$	2.12356e9			0.00145296
$506$	−1.23451e11	+	2.13824e11i	−0.0837178	+	0.145003i
$507$	2.14116e11	+	3.70860e11i	0.143917	+	0.249272i
$508$	−4.36838e11	−	7.56626e11i	−0.291027	−	0.504074i
$509$	8.44120e11	−	1.46206e12i	0.557409	−	0.965461i	−0.440303	−	0.897849i	$-0.645129\pi$
$509$	8.44120e11	−	1.46206e12i	0.557409	−	0.965461i	0.997712	−	0.0676115i	$-0.0215379\pi$
$510$	−4.75831e10			−0.0311449
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	−2.07587e11	+	3.59551e11i	−0.132334	+	0.229209i
$514$	−5.55655e11	−	9.62423e11i	−0.351133	−	0.608180i
$515$	−2.04192e10	−	3.53670e10i	−0.0127910	−	0.0221547i
$516$	−7.96609e11	+	1.37977e12i	−0.494677	+	0.856805i
$517$	−1.63926e11			−0.100911
$518$		0			0
$519$	2.65594e12			1.60681
$520$	7.79430e9	−	1.35001e10i	0.00467479	−	0.00809698i
$521$	4.71068e11	+	8.15913e11i	0.280100	+	0.485148i	0.971409	−	0.237411i	$-0.0762990\pi$
$521$	4.71068e11	+	8.15913e11i	0.280100	+	0.485148i	−0.691309	+	0.722559i	$0.742966\pi$
$522$	3.53287e11	+	6.11912e11i	0.208262	+	0.360721i
$523$	1.22203e12	−	2.11661e12i	0.714206	−	1.23704i	−0.249060	−	0.968488i	$-0.580121\pi$
$523$	1.22203e12	−	2.11661e12i	0.714206	−	1.23704i	0.963265	−	0.268552i	$-0.0865452\pi$
$524$	−1.83805e11			−0.106504
$525$		0			0
$526$	−1.15683e12			−0.658923
$527$	−1.57965e12	+	2.73603e12i	−0.892097	+	1.54516i
$528$	−3.23888e11	−	5.60990e11i	−0.181360	−	0.314125i
$529$	8.55755e11	+	1.48221e12i	0.475115	+	0.822924i
$530$	−2.37255e10	+	4.10938e10i	−0.0130609	+	0.0226222i
$531$	2.39186e11			0.130560
$532$		0			0
$533$	2.51810e12			1.35145
$534$	−1.30204e12	+	2.25520e12i	−0.692930	+	1.20019i
$535$	−2.15382e10	−	3.73052e10i	−0.0113662	−	0.0196869i
$536$	−6.25650e11	−	1.08366e12i	−0.327408	−	0.567088i
$537$	1.91338e12	−	3.31408e12i	0.992928	−	1.71980i
$538$	1.44490e12			0.743565
$539$		0			0
$540$	−4.26707e9			−0.00215952
$541$	3.29098e11	−	5.70014e11i	0.165172	−	0.286087i	−0.771544	−	0.636176i	$-0.780515\pi$
$541$	3.29098e11	−	5.70014e11i	0.165172	−	0.286087i	0.936716	+	0.350089i	$0.113849\pi$
$542$	−3.21783e11	−	5.57345e11i	−0.160165	−	0.277413i
$543$	3.19985e11	+	5.54230e11i	0.157954	+	0.273584i
$544$	2.42046e11	−	4.19236e11i	0.118496	−	0.205241i
$545$	1.70155e10			0.00826153
$546$		0			0
$547$	−2.50775e12			−1.19768			−0.598840	−	0.800869i	$-0.704372\pi$
$547$	−2.50775e12			−1.19768			−0.598840	+	0.800869i	$0.704372\pi$
$548$	9.36154e11	−	1.62147e12i	0.443440	−	0.768061i
$549$	−9.73850e11	−	1.68676e12i	−0.457527	−	0.792460i
$550$	8.04853e11	+	1.39405e12i	0.375046	+	0.649599i
$551$	−1.08062e12	+	1.87170e12i	−0.499450	+	0.865073i
$552$	2.35187e11			0.107817
$553$		0			0
$554$	3.30747e11			0.149177
$555$	−4.49463e10	+	7.78493e10i	−0.0201083	+	0.0348286i
$556$	−6.25493e11	−	1.08339e12i	−0.277578	−	0.480780i
$557$	1.30253e12	+	2.25604e12i	0.573375	+	0.993114i	0.996216	+	0.0869103i	$0.0276993\pi$
$557$	1.30253e12	+	2.25604e12i	0.573375	+	0.993114i	−0.422842	+	0.906204i	$0.638967\pi$
$558$	9.35907e11	−	1.62104e12i	0.408676	−	0.707847i
$559$	3.67687e12			1.59267
$560$		0			0
$561$	4.56324e12			1.94509
$562$	−2.77467e11	+	4.80586e11i	−0.117327	+	0.203216i
$563$	1.29701e11	+	2.24649e11i	0.0544071	+	0.0942359i	0.891946	−	0.452141i	$-0.149340\pi$
$563$	1.29701e11	+	2.24649e11i	0.0544071	+	0.0942359i	−0.837539	+	0.546377i	$0.816006\pi$
$564$	7.80740e10	+	1.35228e11i	0.0324900	+	0.0562744i
$565$	1.94002e10	−	3.36021e10i	0.00800917	−	0.0138723i
$566$	1.67423e12			0.685710
$567$		0			0
$568$	1.17418e12			0.473332
$569$	−1.32166e12	+	2.28918e12i	−0.528585	+	0.915536i	0.470860	+	0.882208i	$0.343944\pi$
$569$	−1.32166e12	+	2.28918e12i	−0.528585	+	0.915536i	−0.999444	+	0.0333277i	$0.989389\pi$
$570$	4.31163e10	+	7.46797e10i	0.0171082	+	0.0296323i
$571$	1.03397e12	+	1.79089e12i	0.407049	+	0.705029i	0.994558	−	0.104189i	$-0.0332246\pi$
$571$	1.03397e12	+	1.79089e12i	0.407049	+	0.705029i	−0.587509	+	0.809218i	$0.699891\pi$
$572$	−7.47476e11	+	1.29467e12i	−0.291954	+	0.505680i
$573$	4.71564e12			1.82745
$574$		0			0
$575$	−5.84435e11			−0.222962
$576$	−1.43407e11	+	2.48389e11i	−0.0542837	+	0.0940222i
$577$	−1.28250e12	−	2.22135e12i	−0.481688	−	0.834309i	0.518091	−	0.855326i	$-0.326643\pi$
$577$	−1.28250e12	−	2.22135e12i	−0.481688	−	0.834309i	−0.999779	+	0.0210170i	$0.993310\pi$
$578$	7.56385e11	+	1.31010e12i	0.281882	+	0.488234i
$579$	−1.72713e12	+	2.99148e12i	−0.638663	+	1.10620i
$580$	−2.22129e10			−0.00815039
$581$		0			0
$582$	−2.75970e12			−0.997030
$583$	2.27528e12	−	3.94090e12i	0.815693	−	1.41282i
$584$	−9.80698e10	−	1.69862e11i	−0.0348881	−	0.0604280i
$585$	−3.25311e10	−	5.63455e10i	−0.0114841	−	0.0198910i
$586$	1.28608e12	−	2.22756e12i	0.450535	−	0.780350i
$587$	−1.59591e12			−0.554800			−0.277400	−	0.960755i	$-0.589473\pi$
$587$	−1.59591e12			−0.554800			−0.277400	+	0.960755i	$0.589473\pi$
$588$		0			0
$589$	5.72544e12			1.96015
$590$	−3.75969e9	+	6.51197e9i	−0.00127737	+	0.00221248i
$591$	3.86159e12	+	6.68847e12i	1.30203	+	2.25519i
$592$	−4.57267e11	−	7.92009e11i	−0.153011	−	0.265022i
$593$	−9.85581e11	+	1.70708e12i	−0.327300	+	0.566900i	−0.981975	−	0.189010i	$-0.939472\pi$
$593$	−9.85581e11	+	1.70708e12i	−0.327300	+	0.566900i	0.654675	+	0.755910i	$0.272805\pi$
$594$	4.09213e11			0.134869
$595$		0			0
$596$	1.76714e12			0.573671
$597$	−3.61358e12	+	6.25891e12i	−1.16427	+	2.01657i
$598$	−2.71386e11	−	4.70054e11i	−0.0867824	−	0.150312i
$599$	−2.48539e12	−	4.30483e12i	−0.788814	−	1.36627i	−0.926694	−	0.375817i	$-0.877362\pi$
$599$	−2.48539e12	−	4.30483e12i	−0.788814	−	1.36627i	0.137880	−	0.990449i	$-0.455971\pi$
$600$	7.66665e11	−	1.32790e12i	0.241505	−	0.418298i
$601$	−4.73669e12			−1.48095			−0.740475	−	0.672084i	$-0.765399\pi$
$601$	−4.73669e12			−1.48095			−0.740475	+	0.672084i	$0.765399\pi$
$602$		0			0
$603$	−5.22255e12			−1.60862
$604$	7.23900e11	−	1.25383e12i	0.221316	−	0.383330i
$605$	5.01266e9	+	8.68219e9i	0.00152114	+	0.00263469i
$606$	9.69935e10	+	1.67998e11i	0.0292157	+	0.0506030i
$607$	1.63452e12	−	2.83106e12i	0.488697	−	0.846449i	−0.511218	−	0.859451i	$-0.670806\pi$
$607$	1.63452e12	−	2.83106e12i	0.488697	−	0.846449i	0.999915	+	0.0130024i	$0.00413890\pi$
$608$	−8.77298e11			−0.260364
$609$		0			0
$610$	6.12306e10			0.0179054
$611$	1.80181e11	−	3.12083e11i	0.0523026	−	0.0905908i
$612$	−1.01023e12	−	1.74977e12i	−0.291097	−	0.504195i
$613$	3.26789e11	+	5.66014e11i	0.0934748	+	0.161903i	0.908971	−	0.416859i	$-0.136869\pi$
$613$	3.26789e11	+	5.66014e11i	0.0934748	+	0.161903i	−0.815496	+	0.578762i	$0.803536\pi$
$614$	−1.16136e12	+	2.01153e12i	−0.329768	+	0.571175i
$615$	−1.43165e11			−0.0403552
$616$		0			0
$617$	−6.63823e12			−1.84404			−0.922018	−	0.387148i	$-0.873460\pi$
$617$	−6.63823e12			−1.84404			−0.922018	+	0.387148i	$0.873460\pi$
$618$	1.86529e12	−	3.23078e12i	0.514398	−	0.890963i
$619$	3.62687e10	+	6.28193e10i	0.00992943	+	0.0171983i	0.870947	−	0.491376i	$-0.163506\pi$
$619$	3.62687e10	+	6.28193e10i	0.00992943	+	0.0171983i	−0.861018	+	0.508574i	$0.830173\pi$
$620$	2.94225e10	+	5.09612e10i	0.00799681	+	0.0138509i
$621$	−7.42864e10	+	1.28668e11i	−0.0200446	+	0.0347182i
$622$	−4.20943e12			−1.12763
$623$		0			0
$624$	1.42402e12			0.375998
$625$	−1.90404e12	+	3.29790e12i	−0.499134	+	0.864525i
$626$	6.70563e11	+	1.16145e12i	0.174524	+	0.302284i
$627$	−4.13487e12	−	7.16181e12i	−1.06846	−	1.85063i
$628$	−8.44768e11	+	1.46318e12i	−0.216730	+	0.375387i
$629$	6.44240e12			1.64104
$630$		0			0
$631$	−2.35325e12			−0.590930			−0.295465	−	0.955354i	$-0.595475\pi$
$631$	−2.35325e12			−0.590930			−0.295465	+	0.955354i	$0.595475\pi$
$632$	−2.20327e11	+	3.81618e11i	−0.0549340	+	0.0951484i
$633$	−1.50802e12	−	2.61197e12i	−0.373328	−	0.646624i
$634$	2.16573e12	+	3.75115e12i	0.532356	+	0.922068i
$635$	5.73176e10	−	9.92770e10i	0.0139896	−	0.0242308i
$636$	−4.33465e12			−1.05050
$637$		0			0
$638$	2.13022e12			0.509016
$639$	2.45033e12	−	4.24409e12i	0.581394	−	1.00700i
$640$	−4.50835e9	−	7.80869e9i	−0.00106220	−	0.00183979i
$641$	3.76444e11	+	6.52019e11i	0.0880722	+	0.152546i	0.906696	−	0.421784i	$-0.138596\pi$
$641$	3.76444e11	+	6.52019e11i	0.0880722	+	0.152546i	−0.818624	+	0.574330i	$0.805263\pi$
$642$	1.96752e12	−	3.40784e12i	0.457099	−	0.791719i
$643$	−4.82355e12			−1.11280			−0.556400	−	0.830915i	$-0.687818\pi$
$643$	−4.82355e12			−1.11280			−0.556400	+	0.830915i	$0.687818\pi$
$644$		0			0
$645$	−2.09047e11			−0.0475581
$646$	3.09005e12	−	5.35213e12i	0.698103	−	1.20915i
$647$	4.09586e12	+	7.09424e12i	0.918916	+	1.59161i	0.801065	+	0.598578i	$0.204267\pi$
$647$	4.09586e12	+	7.09424e12i	0.918916	+	1.59161i	0.117851	+	0.993031i	$0.462399\pi$
$648$	−8.84030e11	−	1.53119e12i	−0.196961	−	0.341146i
$649$	3.60555e11	−	6.24500e11i	0.0797758	−	0.138176i
$650$	−3.53866e12			−0.777551
$651$		0			0
$652$	−2.04492e12			−0.443162
$653$	2.90609e12	−	5.03349e12i	0.625460	−	1.08333i	−0.362992	−	0.931792i	$-0.618245\pi$
$653$	2.90609e12	−	5.03349e12i	0.625460	−	1.08333i	0.988452	−	0.151536i	$-0.0484218\pi$
$654$	7.77184e11	+	1.34612e12i	0.166121	+	0.287730i
$655$	−1.20585e10	−	2.08860e10i	−0.00255982	−	0.00443373i
$656$	7.28254e11	−	1.26137e12i	0.153538	−	0.265935i
$657$	−8.18628e11			−0.171412
$658$		0			0
$659$	−3.45418e12			−0.713446			−0.356723	−	0.934210i	$-0.616106\pi$
$659$	−3.45418e12			−0.713446			−0.356723	+	0.934210i	$0.616106\pi$
$660$	4.24974e10	−	7.36076e10i	0.00871795	−	0.0150999i
$661$	−2.72790e12	−	4.72487e12i	−0.555805	−	0.962683i	−0.997840	−	0.0656852i	$-0.979077\pi$
$661$	−2.72790e12	−	4.72487e12i	−0.555805	−	0.962683i	0.442035	−	0.896998i	$-0.354257\pi$
$662$	1.54993e12	+	2.68455e12i	0.313653	+	0.543264i
$663$	−5.01574e12	+	8.68751e12i	−1.00815	+	1.74616i
$664$	2.32487e11			0.0464133
$665$		0			0
$666$	−3.81699e12			−0.751773
$667$	−3.86709e11	+	6.69800e11i	−0.0756516	+	0.131032i
$668$	5.56678e11	+	9.64195e11i	0.108171	+	0.187357i
$669$	−6.03778e12	−	1.04577e13i	−1.16536	−	2.01846i
$670$	8.20916e10	−	1.42187e11i	0.0157385	−	0.0272598i
$671$	−5.87203e12			−1.11825
$672$		0			0
$673$	4.93782e12			0.927828			0.463914	−	0.885880i	$-0.346445\pi$
$673$	4.93782e12			0.927828			0.463914	+	0.885880i	$0.346445\pi$
$674$	1.79127e12	−	3.10258e12i	0.334343	−	0.579099i
$675$	4.84319e11	+	8.38864e11i	0.0897975	+	0.155534i
$676$	−2.85820e11	−	4.95054e11i	−0.0526420	−	0.0911785i
$677$	−4.53949e12	+	7.86262e12i	−0.830535	+	1.43853i	0.0670798	+	0.997748i	$0.478632\pi$
$677$	−4.53949e12	+	7.86262e12i	−0.830535	+	1.43853i	−0.897615	+	0.440781i	$0.854702\pi$
$678$	3.54442e12			0.644186
$679$		0			0
$680$	6.35179e10			0.0113922
$681$	−5.25480e12	+	9.10158e12i	−0.936255	+	1.62164i
$682$	−2.82163e12	−	4.88720e12i	−0.499424	−	0.865028i
$683$	2.54958e12	+	4.41601e12i	0.448308	+	0.776492i	0.998276	−	0.0586939i	$-0.0186936\pi$
$683$	2.54958e12	+	4.41601e12i	0.448308	+	0.776492i	−0.549968	+	0.835185i	$0.685360\pi$
$684$	−1.83079e12	+	3.17102e12i	−0.319806	+	0.553920i
$685$	2.45666e11			0.0426322
$686$		0			0
$687$	−1.17774e13			−2.01717
$688$	1.06338e12	−	1.84183e12i	0.180942	−	0.313401i
$689$	5.00181e12	+	8.66339e12i	0.845553	+	1.46454i
$690$	1.54295e10	+	2.67247e10i	0.00259138	+	0.00448840i
$691$	−3.42055e12	+	5.92457e12i	−0.570748	+	0.988565i	0.425741	+	0.904845i	$0.360014\pi$
$691$	−3.42055e12	+	5.92457e12i	−0.570748	+	0.988565i	−0.996489	+	0.0837201i	$0.973320\pi$
$692$	−3.54537e12			−0.587739
$693$		0			0
$694$	4.12366e12			0.674785
$695$	8.20710e10	−	1.42151e11i	0.0133431	−	0.0231110i
$696$	−1.01457e12	−	1.75729e12i	−0.163886	−	0.283859i
$697$	5.13016e12	+	8.88570e12i	0.823348	+	1.42608i
$698$	−1.10995e12	+	1.92249e12i	−0.176992	+	0.306559i
$699$	1.61651e12			0.256112
$700$		0			0
$701$	9.89108e12			1.54708			0.773539	−	0.633748i	$-0.218484\pi$
$701$	9.89108e12			1.54708			0.773539	+	0.633748i	$0.218484\pi$
$702$	−4.49792e11	+	7.79062e11i	−0.0699028	+	0.121075i
$703$	−5.83764e12	−	1.01111e13i	−0.901443	−	1.56134i
$704$	4.32352e11	+	7.48856e11i	0.0663377	+	0.114900i
$705$	−1.02441e10	+	1.77433e10i	−0.00156179	+	0.00270510i
$706$	2.99169e12			0.453205
$707$		0			0
$708$	−6.86896e11			−0.102740
$709$	5.72156e12	−	9.91004e12i	0.850368	−	1.47288i	−0.0305092	−	0.999534i	$-0.509713\pi$
$709$	5.72156e12	−	9.91004e12i	0.850368	−	1.47288i	0.880877	−	0.473345i	$-0.156954\pi$
$710$	7.70319e10	+	1.33423e11i	0.0113765	+	0.0197047i
$711$	9.19579e11	+	1.59276e12i	0.134951	+	0.233742i
$712$	1.73807e12	−	3.01043e12i	0.253459	−	0.439004i
$713$	2.04889e12			0.296904
$714$		0			0
$715$	−1.96153e11			−0.0280684
$716$	−2.55414e12	+	4.42390e12i	−0.363192	+	0.629067i
$717$	3.01043e12	+	5.21422e12i	0.425395	+	0.736806i
$718$	1.66050e12	+	2.87608e12i	0.233174	+	0.403869i
$719$	−3.60225e12	+	6.23928e12i	−0.502683	+	0.870672i	0.497313	+	0.867571i	$0.334320\pi$
$719$	−3.60225e12	+	6.23928e12i	−0.502683	+	0.870672i	−0.999995	+	0.00310036i	$0.999013\pi$
$720$	−3.76330e10			−0.00521882
$721$		0			0
$722$	−6.03692e12			−0.826795
$723$	−1.39869e12	+	2.42260e12i	−0.190370	+	0.329730i
$724$	−4.27142e11	−	7.39832e11i	−0.0577762	−	0.100071i
$725$	2.52119e12	+	4.36683e12i	0.338911	+	0.587010i
$726$	−4.57908e11	+	7.93119e11i	−0.0611735	+	0.105956i
$727$	−7.27861e12			−0.966371			−0.483185	−	0.875518i	$-0.660520\pi$
$727$	−7.27861e12			−0.966371			−0.483185	+	0.875518i	$0.660520\pi$
$728$		0			0
$729$	−5.50621e12			−0.722070
$730$	1.28678e10	−	2.22876e10i	0.00167707	−	0.00290476i
$731$	7.49095e12	+	1.29747e13i	0.970306	+	1.68062i
$732$	2.79671e12	+	4.84405e12i	0.360038	+	0.623603i
$733$	6.84727e12	−	1.18598e13i	0.876092	−	1.51744i	0.0204976	−	0.999790i	$-0.493475\pi$
$733$	6.84727e12	−	1.18598e13i	0.876092	−	1.51744i	0.855595	−	0.517646i	$-0.173192\pi$
$734$	2.86929e12			0.364873
$735$		0			0
$736$	−3.13948e11			−0.0394373
$737$	−7.87261e12	+	1.36358e13i	−0.982913	+	1.70246i
$738$	−3.03951e12	−	5.26459e12i	−0.377181	−	0.653297i
$739$	8.29933e11	+	1.43749e12i	0.102363	+	0.177298i	0.912658	−	0.408725i	$-0.134026\pi$
$739$	8.29933e11	+	1.43749e12i	0.102363	+	0.177298i	−0.810295	+	0.586023i	$0.800693\pi$
$740$	5.99981e10	−	1.03920e11i	0.00735520	−	0.0127396i
$741$	1.81796e13			2.21514
$742$		0			0
$743$	−4.66431e11			−0.0561484			−0.0280742	−	0.999606i	$-0.508937\pi$
$743$	−4.66431e11			−0.0561484			−0.0280742	+	0.999606i	$0.508937\pi$
$744$	−2.68775e12	+	4.65532e12i	−0.321596	+	0.557020i
$745$	1.15933e11	+	2.00803e11i	0.0137881	+	0.0238817i
$746$	−4.35869e12	−	7.54948e12i	−0.515266	−	0.892467i
$747$	4.85165e11	−	8.40331e11i	0.0570095	−	0.0987433i
$748$	−6.09138e12			−0.711474
$749$		0			0
$750$	4.02494e11			0.0464497
$751$	2.66801e12	−	4.62113e12i	0.306061	−	0.530113i	−0.671436	−	0.741063i	$-0.734322\pi$
$751$	2.66801e12	−	4.62113e12i	0.306061	−	0.530113i	0.977497	+	0.210949i	$0.0676555\pi$
$752$	−1.04220e11	−	1.80514e11i	−0.0118842	−	0.0205840i
$753$	3.41737e12	+	5.91905e12i	0.387359	+	0.670926i
$754$	−2.34146e12	+	4.05553e12i	−0.263825	+	0.456958i
$755$	1.89966e11			0.0212772
$756$		0			0
$757$	8.40938e12			0.930748			0.465374	−	0.885114i	$-0.345920\pi$
$757$	8.40938e12			0.930748			0.465374	+	0.885114i	$0.345920\pi$
$758$	−9.97292e11	+	1.72736e12i	−0.109726	+	0.190052i
$759$	−1.47969e12	−	2.56290e12i	−0.161839	−	0.280314i
$760$	−5.75553e10	−	9.96886e10i	−0.00625783	−	0.0108389i
$761$	3.08193e12	−	5.33806e12i	0.333113	−	0.576969i	−0.650007	−	0.759928i	$-0.725234\pi$
$761$	3.08193e12	−	5.33806e12i	0.333113	−	0.576969i	0.983121	+	0.182959i	$0.0585675\pi$
$762$	1.04719e13			1.12520
$763$		0			0
$764$	−6.29482e12			−0.668441
$765$	1.32552e11	−	2.29587e11i	0.0139930	−	0.0242366i
$766$	3.26596e12	+	5.65681e12i	0.342753	+	0.593666i
$767$	7.92618e11	+	1.37286e12i	0.0826961	+	0.143234i
$768$	4.11838e11	−	7.13325e11i	0.0427170	−	0.0739881i
$769$	−9.39193e12			−0.968470			−0.484235	−	0.874938i	$-0.660902\pi$
$769$	−9.39193e12			−0.968470			−0.484235	+	0.874938i	$0.660902\pi$
$770$		0			0
$771$	1.33203e13			1.35759
$772$	2.30552e12	−	3.99327e12i	0.233610	−	0.404624i
$773$	−2.11318e12	−	3.66014e12i	−0.212877	−	0.368714i	0.739737	−	0.672897i	$-0.234950\pi$
$773$	−2.11318e12	−	3.66014e12i	−0.212877	−	0.368714i	−0.952614	+	0.304182i	$0.901617\pi$
$774$	−4.43823e12	−	7.68723e12i	−0.444504	−	0.769903i
$775$	6.67899e12	−	1.15683e13i	0.665048	−	1.15190i
$776$	3.68388e12			0.364693
$777$		0			0
$778$	−8.21823e12			−0.804212
$779$	9.29716e12	−	1.61031e13i	0.904548	−	1.56672i
$780$	9.34231e10	+	1.61813e11i	0.00903709	+	0.0156527i
$781$	−7.38739e12	−	1.27953e13i	−0.710495	−	1.23061i
$782$	1.10580e12	−	1.91530e12i	0.105741	−	0.183150i
$783$	1.28186e12			0.121874
$784$		0			0
$785$	−2.21684e11			−0.0208363
$786$	1.10155e12	−	1.90794e12i	0.102944	−	0.178305i
$787$	−2.94913e11	−	5.10804e11i	−0.0274036	−	0.0474644i	0.851998	−	0.523544i	$-0.175391\pi$
$787$	−2.94913e11	−	5.10804e11i	−0.0274036	−	0.0474644i	−0.879402	+	0.476080i	$0.842057\pi$
$788$	−5.15477e12	−	8.92832e12i	−0.476257	−	0.824901i
$789$	6.93293e12	−	1.20082e13i	0.636899	−	1.10314i
$790$	−5.78183e10			−0.00528133
$791$		0			0
$792$	3.60901e12			0.325931
$793$	6.45432e12	−	1.11792e13i	0.579590	−	1.00388i
$794$	−2.88651e12	−	4.99959e12i	−0.257740	−	0.446418i
$795$	−2.84375e11	−	4.92553e11i	−0.0252488	−	0.0437321i
$796$	4.82371e12	−	8.35490e12i	0.425865	−	0.737620i
$797$	2.83029e12			0.248467			0.124233	−	0.992253i	$-0.460353\pi$
$797$	2.83029e12			0.248467			0.124233	+	0.992253i	$0.460353\pi$
$798$		0			0
$799$	1.46834e12			0.127458
$800$	−1.02341e12	+	1.77260e12i	−0.0883373	+	0.153005i
$801$	−7.25420e12	−	1.25646e13i	−0.622649	−	1.07846i
$802$	1.90875e12	+	3.30606e12i	0.162916	+	0.282180i
$803$	−1.23402e12	+	2.13739e12i	−0.104738	+	0.181411i
$804$	1.49982e13			1.26586
$805$		0			0
$806$	1.24057e13			1.03541
$807$	−8.65937e12	+	1.49985e13i	−0.718713	+	1.24485i
$808$	−1.29475e11	−	2.24257e11i	−0.0106865	−	0.0185095i
$809$	−5.80166e12	−	1.00488e13i	−0.476194	−	0.824793i	0.523434	−	0.852066i	$-0.324651\pi$
$809$	−5.80166e12	−	1.00488e13i	−0.476194	−	0.824793i	−0.999628	+	0.0272738i	$0.991317\pi$
$810$	1.15994e11	−	2.00907e11i	0.00946787	−	0.0163988i
$811$	4.13817e12			0.335903			0.167952	−	0.985795i	$-0.446285\pi$
$811$	4.13817e12			0.335903			0.167952	+	0.985795i	$0.446285\pi$
$812$		0			0
$813$	7.71383e12			0.619245
$814$	−5.75383e12	+	9.96593e12i	−0.459354	+	0.795624i
$815$	−1.34157e11	−	2.32367e11i	−0.0106514	−	0.0184487i
$816$	2.90118e12	+	5.02500e12i	0.229071	+	0.396762i
$817$	1.35755e13	−	2.35135e13i	1.06600	−	1.84636i
$818$	−1.23950e13			−0.967961
$819$		0			0
$820$	1.91109e11			0.0147611
$821$	9.78514e10	−	1.69484e11i	0.00751662	−	0.0130192i	−0.862243	−	0.506495i	$-0.830941\pi$
$821$	9.78514e10	−	1.69484e11i	0.00751662	−	0.0130192i	0.869759	+	0.493476i	$0.164274\pi$
$822$	1.12208e13	+	1.94350e13i	0.857237	+	1.48478i
$823$	4.25699e12	+	7.37333e12i	0.323447	+	0.560227i	0.981197	−	0.193009i	$-0.0618248\pi$
$823$	4.25699e12	+	7.37333e12i	0.323447	+	0.560227i	−0.657750	+	0.753237i	$0.728491\pi$
$824$	−2.48995e12	+	4.31272e12i	−0.188156	+	0.325896i
$825$	−1.92941e13			−1.45004
$826$		0			0
$827$	−1.19931e12			−0.0891576			−0.0445788	−	0.999006i	$-0.514195\pi$
$827$	−1.19931e12			−0.0891576			−0.0445788	+	0.999006i	$0.514195\pi$
$828$	−6.55161e11	+	1.13477e12i	−0.0484409	+	0.0839020i
$829$	−8.20420e12	−	1.42101e13i	−0.603311	−	1.04496i	−0.992316	−	0.123729i	$-0.960515\pi$
$829$	−8.20420e12	−	1.42101e13i	−0.603311	−	1.04496i	0.389005	−	0.921236i	$-0.372819\pi$
$830$	1.52523e10	+	2.64178e10i	0.00111554	+	0.00193217i
$831$	−1.98218e12	+	3.43323e12i	−0.144191	+	0.249746i
$832$	−1.90090e12			−0.137532
$833$		0			0
$834$	1.49944e13			1.07320
$835$	−7.30418e10	+	1.26512e11i	−0.00519975	+	0.00900623i
$836$	5.51957e12	+	9.56017e12i	0.390820	+	0.676920i
$837$	−1.69791e12	−	2.94086e12i	−0.119577	−	0.207114i
$838$	4.69785e12	−	8.13691e12i	0.329080	−	0.569982i
$839$	1.67670e13			1.16822			0.584111	−	0.811674i	$-0.301443\pi$
$839$	1.67670e13			1.16822			0.584111	+	0.811674i	$0.301443\pi$
$840$		0			0
$841$	−7.83425e12			−0.540027
$842$	−9.00327e12	+	1.55941e13i	−0.617299	+	1.06919i
$843$	−3.32574e12	−	5.76034e12i	−0.226811	−	0.392848i
$844$	2.01303e12	+	3.48668e12i	0.136556	+	0.236521i
$845$	3.75025e10	−	6.49562e10i	0.00253049	−	0.00438294i
$846$	−8.69962e11			−0.0583894
$847$		0			0
$848$	5.78625e12			0.384252
$849$	−1.00337e13	+	1.73789e13i	−0.662791	+	1.14799i
$850$	−7.20937e12	−	1.24870e13i	−0.473710	−	0.820489i
$851$	−2.08904e12	−	3.61833e12i	−0.136541	−	0.236496i
$852$	−7.03688e12	+	1.21882e13i	−0.457511	+	0.792433i
$853$	6.93277e12			0.448370			0.224185	−	0.974547i	$-0.428028\pi$
$853$	6.93277e12			0.448370			0.224185	+	0.974547i	$0.428028\pi$
$854$		0			0
$855$	−4.80437e11			−0.0307460
$856$	−2.62640e12	+	4.54906e12i	−0.167197	+	0.289594i
$857$	−1.30460e11	−	2.25963e11i	−0.00826158	−	0.0143095i	0.861865	−	0.507138i	$-0.169296\pi$
$857$	−1.30460e11	−	2.25963e11i	−0.00826158	−	0.0143095i	−0.870127	+	0.492828i	$0.835963\pi$
$858$	−8.95930e12	−	1.55180e13i	−0.564393	−	0.977557i
$859$	−1.27103e13	+	2.20149e13i	−0.796502	+	1.37958i	0.125379	+	0.992109i	$0.459985\pi$
$859$	−1.27103e13	+	2.20149e13i	−0.796502	+	1.37958i	−0.921881	+	0.387473i	$0.873348\pi$
$860$	2.79053e11			0.0173957
$861$		0			0
$862$	1.08427e13			0.668889
$863$	−3.59309e12	+	6.22342e12i	−0.220506	+	0.381927i	−0.954962	−	0.296729i	$-0.904104\pi$
$863$	−3.59309e12	+	6.22342e12i	−0.220506	+	0.381927i	0.734456	+	0.678656i	$0.237437\pi$
$864$	2.60167e11	+	4.50622e11i	0.0158833	+	0.0275106i
$865$	−2.32594e11	−	4.02865e11i	−0.0141262	−	0.0244674i
$866$	−4.53267e12	+	7.85082e12i	−0.273857	+	0.474334i
$867$	−1.81322e13			−1.08984
$868$		0			0
$869$	5.54479e12			0.329835
$870$	1.33122e11	−	2.30575e11i	0.00787798	−	0.0136451i
$871$	−1.73066e13	−	2.99758e13i	−1.01889	−	1.76478i
$872$	−1.03745e12	−	1.79692e12i	−0.0607635	−	0.105245i
$873$	7.68769e12	−	1.33155e13i	0.447953	−	0.775877i
$874$	−4.00797e12			−0.232340
$875$		0			0
$876$	2.35094e12			0.134888
$877$	1.34403e13	−	2.32793e13i	0.767205	−	1.32884i	−0.171868	−	0.985120i	$-0.554980\pi$
$877$	1.34403e13	−	2.32793e13i	0.767205	−	1.32884i	0.939073	−	0.343718i	$-0.111686\pi$
$878$	5.92989e12	+	1.02709e13i	0.336761	+	0.583287i
$879$	1.54151e13	+	2.66997e13i	0.870954	+	1.50854i
$880$	−5.67290e10	+	9.82575e10i	−0.00318884	+	0.00552324i
$881$	−5.33553e11			−0.0298391			−0.0149195	−	0.999889i	$-0.504749\pi$
$881$	−5.33553e11			−0.0298391			−0.0149195	+	0.999889i	$0.504749\pi$
$882$		0			0
$883$	6.42561e12			0.355706			0.177853	−	0.984057i	$-0.443085\pi$
$883$	6.42561e12			0.355706			0.177853	+	0.984057i	$0.443085\pi$
$884$	6.69542e12	−	1.15968e13i	0.368759	−	0.638710i
$885$	−4.50639e10	−	7.80530e10i	−0.00246936	−	0.00427705i
$886$	7.40165e11	+	1.28200e12i	0.0403531	+	0.0698936i
$887$	−1.44219e12	+	2.49794e12i	−0.0782285	+	0.135496i	−0.902486	−	0.430720i	$-0.858260\pi$
$887$	−1.44219e12	+	2.49794e12i	−0.0782285	+	0.135496i	0.824257	+	0.566216i	$0.191593\pi$
$888$	1.09617e13			0.591586
$889$		0			0
$890$	4.56106e11			0.0243675
$891$	−1.11238e13	+	1.92671e13i	−0.591296	+	1.02416i
$892$	8.05973e12	+	1.39599e13i	0.426264	+	0.738311i
$893$	−1.33051e12	−	2.30450e12i	−0.0700141	−	0.121268i
$894$	−1.05905e13	+	1.83433e13i	−0.554497	+	0.960416i
$895$	−6.70259e11			−0.0349172
$896$		0			0
$897$	6.50570e12			0.335527
$898$	−1.01507e12	+	1.75816e12i	−0.0520900	+	0.0902225i
$899$	−8.83871e12	−	1.53091e13i	−0.451305	−	0.781683i
$900$	4.27140e12	+	7.39828e12i	0.217010	+	0.375872i
$901$	−2.03806e13	+	3.53002e13i	−1.03028	+	1.78449i
$902$	−1.83274e13			−0.921873
$903$		0			0
$904$	−4.73138e12			−0.235630
$905$	5.60454e10	−	9.70735e10i	0.00277729	−	0.00481041i
$906$	8.67672e12	+	1.50285e13i	0.427837	+	0.741036i
$907$	8.74404e12	+	1.51451e13i	0.429022	+	0.743088i	0.996787	−	0.0801031i	$-0.0255249\pi$
$907$	8.74404e12	+	1.51451e13i	0.429022	+	0.743088i	−0.567765	+	0.823191i	$0.692192\pi$
$908$	7.01454e12	−	1.21495e13i	0.342462	−	0.593162i
$909$	−1.08078e12			−0.0525049
$910$		0			0
$911$	−1.68088e13			−0.808543			−0.404271	−	0.914639i	$-0.632475\pi$
$911$	−1.68088e13			−0.808543			−0.404271	+	0.914639i	$0.632475\pi$
$912$	5.25768e12	−	9.10657e12i	0.251662	−	0.435891i
$913$	−1.46270e12	−	2.53348e12i	−0.0696687	−	0.120670i
$914$	8.22522e12	+	1.42465e13i	0.389843	+	0.675228i
$915$	−3.66957e11	+	6.35588e11i	−0.0173069	+	0.0299765i
$916$	1.57214e13			0.737840
$917$		0			0
$918$	−3.66548e12			−0.170348
$919$	1.24473e13	−	2.15594e13i	0.575648	−	0.997051i	−0.420323	−	0.907374i	$-0.638083\pi$
$919$	1.24473e13	−	2.15594e13i	0.575648	−	0.997051i	0.995971	−	0.0896768i	$-0.0285834\pi$
$920$	−2.05966e10	−	3.56743e10i	−0.000947872	−	0.00164176i
$921$	−1.39201e13	−	2.41104e13i	−0.637492	−	1.10417i
$922$	6.48186e12	−	1.12269e13i	0.295400	−	0.511648i
$923$	3.24798e13			1.47301
$924$		0			0
$925$	−2.72395e13			−1.22338
$926$	−1.15834e13	+	2.00631e13i	−0.517711	+	0.896703i
$927$	1.03923e13	+	1.80000e13i	0.462224	+	0.800596i
$928$	1.35434e12	+	2.34578e12i	0.0599461	+	0.103830i
$929$	1.92243e13	−	3.32975e13i	0.846799	−	1.46670i	−0.0372516	−	0.999306i	$-0.511860\pi$
$929$	1.92243e13	−	3.32975e13i	0.846799	−	1.46670i	0.884050	−	0.467392i	$-0.154806\pi$
$930$	−7.05320e11			−0.0309181
$931$		0			0
$932$	−2.15785e12			−0.0936806
$933$	2.52273e13	−	4.36950e13i	1.08994	−	1.88783i
$934$	3.57627e12	+	6.19429e12i	0.153769	+	0.266336i
$935$	−3.99626e11	−	6.92172e11i	−0.0171002	−	0.0296184i
$936$	−3.96689e12	+	6.87086e12i	−0.168931	+	0.292597i
$937$	4.89574e11			0.0207486			0.0103743	−	0.999946i	$-0.496698\pi$
$937$	4.89574e11			0.0207486			0.0103743	+	0.999946i	$0.496698\pi$
$938$		0			0
$939$	−1.60748e13			−0.674763
$940$	1.36747e10	−	2.36852e10i	0.000571270	−	0.000989469i
$941$	1.10361e13	+	1.91150e13i	0.458840	+	0.794734i	0.998900	−	0.0468926i	$-0.0149319\pi$
$941$	1.10361e13	+	1.91150e13i	0.458840	+	0.794734i	−0.540060	+	0.841626i	$0.681599\pi$
$942$	−1.01254e13	−	1.75378e13i	−0.418972	−	0.725681i
$943$	3.32706e12	−	5.76263e12i	0.137012	−	0.237311i
$944$	9.16926e11			0.0375803
$945$		0			0
$946$	−2.67612e13			−1.08642
$947$	−2.43071e11	+	4.21012e11i	−0.00982108	+	0.0170106i	−0.870894	−	0.491471i	$-0.836460\pi$
$947$	−2.43071e11	+	4.21012e11i	−0.00982108	+	0.0170106i	0.861073	+	0.508481i	$0.169793\pi$
$948$	−2.64086e12	−	4.57410e12i	−0.106196	−	0.183936i
$949$	−2.71278e12	−	4.69868e12i	−0.108572	−	0.188052i
$950$	−1.30652e13	+	2.26296e13i	−0.520428	+	0.901407i
$951$	−5.19171e13			−2.05825
$952$		0			0
$953$	−2.77682e13			−1.09051			−0.545254	−	0.838271i	$-0.683567\pi$
$953$	−2.77682e13			−1.09051			−0.545254	+	0.838271i	$0.683567\pi$
$954$	1.20750e13	−	2.09146e13i	0.471977	−	0.817488i
$955$	−4.12972e11	−	7.15289e11i	−0.0160659	−	0.0278270i
$956$	−4.01857e12	−	6.96037e12i	−0.155601	−	0.269508i
$957$	−1.27665e13	+	2.21122e13i	−0.492003	+	0.852174i
$958$	−1.39128e12			−0.0533667
$959$		0			0
$960$	1.08075e11			0.00410680
$961$	−1.01951e13	+	1.76585e13i	−0.385601	+	0.667881i
$962$	−1.26488e13	−	2.19084e13i	−0.476169	−	0.824750i
$963$	1.09618e13	+	1.89864e13i	0.410737	+	0.711418i
$964$	1.86708e12	−	3.23388e12i	0.0696333	−	0.120608i
$965$	6.05015e11			0.0224591
$966$		0			0
$967$	−2.53282e12			−0.0931505			−0.0465752	−	0.998915i	$-0.514831\pi$
$967$	−2.53282e12			−0.0931505			−0.0465752	+	0.998915i	$0.514831\pi$
$968$	6.11253e11	−	1.05872e12i	0.0223760	−	0.0387563i
$969$	3.70376e13	+	6.41510e13i	1.34954	+	2.33747i
$970$	2.41681e11	+	4.18604e11i	0.00876536	+	0.0151821i
$971$	4.26211e12	−	7.38219e12i	0.153864	−	0.266501i	−0.778781	−	0.627296i	$-0.784161\pi$
$971$	4.26211e12	−	7.38219e12i	0.153864	−	0.266501i	0.932645	+	0.360795i	$0.117495\pi$
$972$	1.86917e13			0.671661
$973$		0			0
$974$	7.71096e9			0.000274532
$975$	2.12073e13	−	3.67321e13i	0.751562	−	1.30174i
$976$	−3.73328e12	−	6.46624e12i	−0.131694	−	0.228101i
$977$	1.68588e13	+	2.92003e13i	0.591972	+	1.02533i	0.993967	+	0.109684i	$0.0349839\pi$
$977$	1.68588e13	+	2.92003e13i	0.591972	+	1.02533i	−0.401994	+	0.915642i	$0.631683\pi$
$978$	1.22553e13	−	2.12268e13i	0.428350	−	0.741923i
$979$	−4.37407e13			−1.52182
$980$		0			0
$981$	−8.66001e12			−0.298544
$982$	−4.70912e12	+	8.15643e12i	−0.161599	+	0.279897i
$983$	1.63952e12	+	2.83973e12i	0.0560049	+	0.0970033i	0.892669	−	0.450714i	$-0.148830\pi$
$983$	1.63952e12	+	2.83973e12i	0.0560049	+	0.0970033i	−0.836664	+	0.547717i	$0.815497\pi$
$984$	8.72890e12	+	1.51189e13i	0.296812	+	0.514094i
$985$	6.76358e11	−	1.17149e12i	0.0228936	−	0.0396529i
$986$	−1.90812e13			−0.642923
$987$		0			0
$988$	−2.42676e13			−0.810253
$989$	4.85809e12	−	8.41446e12i	0.161467	−	0.279668i
$990$	2.36770e11	+	4.10097e11i	0.00783372	+	0.0135684i
$991$	−1.14647e13	−	1.98575e13i	−0.377600	−	0.654023i	0.613112	−	0.789996i	$-0.289917\pi$
$991$	−1.14647e13	−	1.98575e13i	−0.377600	−	0.654023i	−0.990713	+	0.135973i	$0.956584\pi$
$992$	3.58783e12	−	6.21430e12i	0.117633	−	0.203746i
$993$	−3.71550e13			−1.21268
$994$		0			0
$995$	1.26584e12			0.0409425
$996$	−1.39330e12	+	2.41327e12i	−0.0448620	+	0.0777032i
$997$	6.27545e12	+	1.08694e13i	0.201148	+	0.348399i	0.948899	−	0.315581i	$-0.102199\pi$
$997$	6.27545e12	+	1.08694e13i	0.201148	+	0.348399i	−0.747750	+	0.663980i	$0.768866\pi$
$998$	−1.98357e13	−	3.43564e13i	−0.632936	−	1.09628i
$999$	−3.46236e12	+	5.99698e12i	−0.109983	+	0.190497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.m.79.4		8
7.2	even	3		98.10.a.k.1.1	✓	4
7.3	odd	6	inner	98.10.c.m.67.1		8
7.4	even	3	inner	98.10.c.m.67.4		8
7.5	odd	6		98.10.a.k.1.4	yes	4
7.6	odd	2	inner	98.10.c.m.79.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.k.1.1	✓	4	7.2	even	3
98.10.a.k.1.4	yes	4	7.5	odd	6
98.10.c.m.67.1		8	7.3	odd	6	inner
98.10.c.m.67.4		8	7.4	even	3	inner
98.10.c.m.79.1		8	7.6	odd	2	inner
98.10.c.m.79.4		8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(95.8886 + 166.084i) q^{3} +(-128.000 - 221.703i) q^{4} +(16.7949 - 29.0896i) q^{5} +3068.43 q^{6} -4096.00 q^{8} +(-8547.74 + 14805.1i) q^{9} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(95.8886 + 166.084i) q^{3} +(-128.000 - 221.703i) q^{4} +(16.7949 - 29.0896i) q^{5} +3068.43 q^{6} -4096.00 q^{8} +(-8547.74 + 14805.1i) q^{9} +(-268.719 - 465.434i) q^{10} +(25770.2 + 44635.3i) q^{11} +(24547.5 - 42517.5i) q^{12} -113303. q^{13} +6441.76 q^{15} +(-32768.0 + 56755.8i) q^{16} +(-230833. - 399815. i) q^{17} +(136764. + 236882. i) q^{18} +(-418329. + 724566. i) q^{19} -8598.99 q^{20} +824646. q^{22} +(-149702. + 259291. i) q^{23} +(-392760. - 680280. i) q^{24} +(975998. + 1.69048e6i) q^{25} +(-906420. + 1.56997e6i) q^{26} +496229. q^{27} +2.58319e6 q^{29} +(51534.1 - 89259.6i) q^{30} +(-3.42162e6 - 5.92642e6i) q^{31} +(524288. + 908093. i) q^{32} +(-4.94213e6 + 8.56003e6i) q^{33} -7.38666e6 q^{34} +4.37644e6 q^{36} +(-6.97734e6 + 1.20851e7i) q^{37} +(6.69326e6 + 1.15931e7i) q^{38} +(-1.08644e7 - 1.88177e7i) q^{39} +(-68791.9 + 119151. i) q^{40} -2.22245e7 q^{41} -3.24518e7 q^{43} +(6.59717e6 - 1.14266e7i) q^{44} +(287117. + 497301. i) q^{45} +(2.39523e6 + 4.14866e6i) q^{46} +(-1.59026e6 + 2.75442e6i) q^{47} -1.25683e7 q^{48} +3.12319e7 q^{50} +(4.42685e7 - 7.66754e7i) q^{51} +(1.45027e7 + 2.51195e7i) q^{52} +(-4.41456e7 - 7.64625e7i) q^{53} +(3.96983e6 - 6.87595e6i) q^{54} +1.73123e6 q^{55} -1.60452e8 q^{57} +(2.06656e7 - 3.57938e7i) q^{58} +(-6.99559e6 - 1.21167e7i) q^{59} +(-824545. - 1.42815e6i) q^{60} +(-5.69654e7 + 9.86669e7i) q^{61} -1.09492e8 q^{62} +1.67772e7 q^{64} +(-1.90291e6 + 3.29593e6i) q^{65} +(7.90741e7 + 1.36960e8i) q^{66} +(1.52746e8 + 2.64565e8i) q^{67} +(-5.90933e7 + 1.02353e8i) q^{68} -5.74188e7 q^{69} -2.86664e8 q^{71} +(3.50115e7 - 6.06417e7i) q^{72} +(2.39428e7 + 4.14702e7i) q^{73} +(1.11637e8 + 1.93362e8i) q^{74} +(-1.87174e8 + 3.24195e8i) q^{75} +2.14184e8 q^{76} -3.47661e8 q^{78} +(5.37908e7 - 9.31683e7i) q^{79} +(1.10067e6 + 1.90642e6i) q^{80} +(2.15828e8 + 3.73825e8i) q^{81} +(-1.77796e8 + 3.07952e8i) q^{82} -5.67595e7 q^{83} -1.55073e7 q^{85} +(-2.59614e8 + 4.49665e8i) q^{86} +(2.47699e8 + 4.29027e8i) q^{87} +(-1.05555e8 - 1.82826e8i) q^{88} +(-4.24334e8 + 7.34969e8i) q^{89} +9.18774e6 q^{90} +7.66474e7 q^{92} +(6.56188e8 - 1.13655e9i) q^{93} +(2.54442e7 + 4.40707e7i) q^{94} +(1.40516e7 + 2.43380e7i) q^{95} +(-1.00546e8 + 1.74152e8i) q^{96} -8.99384e8 q^{97} -8.81107e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9}+O(q^{10}) \) 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9	\( 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9} - 9548 q^{11} - 834624 q^{15} - 262144 q^{16} + 254592 q^{18} - 305536 q^{22} + 2836736 q^{23} - 966144 q^{25} + 33339944 q^{29} - 6676992 q^{30} + 4194304 q^{32} + 8146944 q^{36} - 3226372 q^{37} - 69110568 q^{39} - 152960408 q^{43} - 2444288 q^{44} - 45387776 q^{46} - 30916608 q^{50} + 97261596 q^{51} - 13708112 q^{53} - 743115384 q^{57} + 266719552 q^{58} + 106831872 q^{60} + 134217728 q^{64} + 515731188 q^{65} + 814420776 q^{67} - 2649337488 q^{71} + 65175552 q^{72} + 51621952 q^{74} - 2211538176 q^{78} + 668411176 q^{79} + 1111307688 q^{81} - 3318529928 q^{85} - 1223683264 q^{86} + 39108608 q^{88} - 1452408832 q^{92} + 3706577496 q^{93} - 977188688 q^{95} - 5583163320 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9 - 9548 * q^11 - 834624 * q^15 - 262144 * q^16 + 254592 * q^18 - 305536 * q^22 + 2836736 * q^23 - 966144 * q^25 + 33339944 * q^29 - 6676992 * q^30 + 4194304 * q^32 + 8146944 * q^36 - 3226372 * q^37 - 69110568 * q^39 - 152960408 * q^43 - 2444288 * q^44 - 45387776 * q^46 - 30916608 * q^50 + 97261596 * q^51 - 13708112 * q^53 - 743115384 * q^57 + 266719552 * q^58 + 106831872 * q^60 + 134217728 * q^64 + 515731188 * q^65 + 814420776 * q^67 - 2649337488 * q^71 + 65175552 * q^72 + 51621952 * q^74 - 2211538176 * q^78 + 668411176 * q^79 + 1111307688 * q^81 - 3318529928 * q^85 - 1223683264 * q^86 + 39108608 * q^88 - 1452408832 * q^92 + 3706577496 * q^93 - 977188688 * q^95 - 5583163320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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