LMFDB - Embedded newform 98.10.c.n.79.3

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 14308 x^{10} + 60936 x^{9} + 76758531 x^{8} - 346934000 x^{7} + \cdots + 15\!\cdots\!52 $ x^12 - 4x^11 - 14308x^10 + 60936x^9 + 76758531x^8 - 346934000x^7 - 182843353540x^6 + 875116510720x^5 + 162514720277588x^4 - 824748733066112x^3 + 1886261254314000x^2 - 2133295698229248*x + 1587609732656752
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$58.9949 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.10.c.n.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 + 13.8564i) q^{2} +(-60.6851 - 105.110i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1333.01 + 2308.84i) q^{5} +1941.92 q^{6} +4096.00 q^{8} +(2476.14 - 4288.79i) q^{9} +O(q^{10})$	\(q+(-8.00000 + 13.8564i) q^{2} +(-60.6851 - 105.110i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1333.01 + 2308.84i) q^{5} +1941.92 q^{6} +4096.00 q^{8} +(2476.14 - 4288.79i) q^{9} +(-21328.1 - 36941.4i) q^{10} +(9446.53 + 16361.9i) q^{11} +(-15535.4 + 26908.1i) q^{12} +96063.7 q^{13} +323575. q^{15} +(-32768.0 + 56755.8i) q^{16} +(-286996. - 497092. i) q^{17} +(39618.2 + 68620.7i) q^{18} +(-43870.0 + 75985.0i) q^{19} +682500. q^{20} -302289. q^{22} +(750174. - 1.29934e6i) q^{23} +(-248566. - 430529. i) q^{24} +(-2.57726e6 - 4.46394e6i) q^{25} +(-768510. + 1.33110e6i) q^{26} -2.98999e6 q^{27} -1.78997e6 q^{29} +(-2.58860e6 + 4.48359e6i) q^{30} +(4.83065e6 + 8.36693e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.14653e6 - 1.98584e6i) q^{33} +9.18388e6 q^{34} -1.26778e6 q^{36} +(1.54840e6 - 2.68192e6i) q^{37} +(-701920. - 1.21576e6i) q^{38} +(-5.82964e6 - 1.00972e7i) q^{39} +(-5.46000e6 + 9.45700e6i) q^{40} +1.17852e7 q^{41} +3.60280e7 q^{43} +(2.41831e6 - 4.18864e6i) q^{44} +(6.60142e6 + 1.14340e7i) q^{45} +(1.20028e7 + 2.07894e7i) q^{46} +(-2.95998e6 + 5.12684e6i) q^{47} +7.95412e6 q^{48} +8.24723e7 q^{50} +(-3.48328e7 + 6.03322e7i) q^{51} +(-1.22962e7 - 2.12976e7i) q^{52} +(1.50157e7 + 2.60079e7i) q^{53} +(2.39199e7 - 4.14305e7i) q^{54} -5.03692e7 q^{55} +1.06490e7 q^{57} +(1.43198e7 - 2.48026e7i) q^{58} +(7.16607e7 + 1.24120e8i) q^{59} +(-4.14176e7 - 7.17374e7i) q^{60} +(-7.53227e7 + 1.30463e8i) q^{61} -1.54581e8 q^{62} +1.67772e7 q^{64} +(-1.28054e8 + 2.21796e8i) q^{65} +(1.83444e7 + 3.17735e7i) q^{66} +(-4.97455e7 - 8.61617e7i) q^{67} +(-7.34710e7 + 1.27256e8i) q^{68} -1.82097e8 q^{69} -2.01373e8 q^{71} +(1.01422e7 - 1.75669e7i) q^{72} +(-2.32838e7 - 4.03287e7i) q^{73} +(2.47745e7 + 4.29106e7i) q^{74} +(-3.12802e8 + 5.41790e8i) q^{75} +2.24614e7 q^{76} +1.86548e8 q^{78} +(1.26611e8 - 2.19297e8i) q^{79} +(-8.73600e7 - 1.51312e8i) q^{80} +(1.32710e8 + 2.29860e8i) q^{81} +(-9.42819e7 + 1.63301e8i) q^{82} -3.16834e8 q^{83} +1.53027e9 q^{85} +(-2.88224e8 + 4.99219e8i) q^{86} +(1.08625e8 + 1.88144e8i) q^{87} +(3.86930e7 + 6.70182e7i) q^{88} +(-4.20311e8 + 7.28000e8i) q^{89} -2.11245e8 q^{90} -3.84089e8 q^{92} +(5.86297e8 - 1.01550e9i) q^{93} +(-4.73597e7 - 8.20295e7i) q^{94} +(-1.16958e8 - 2.02577e8i) q^{95} +(-6.36329e7 + 1.10215e8i) q^{96} -2.72768e8 q^{97} +9.35636e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9}+O(q^{10}) $ 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9	$ 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9} - 110664 q^{11} - 1045456 q^{15} - 393216 q^{16} - 1160800 q^{18} + 3541248 q^{22} - 243384 q^{23} - 17125446 q^{25} + 20927280 q^{29} + 8363648 q^{30} - 6291456 q^{32} + 37145600 q^{36} - 24332568 q^{37} - 42635880 q^{39} + 149517168 q^{43} - 28329984 q^{44} - 3894144 q^{46} + 548014272 q^{50} - 260246248 q^{51} - 137815308 q^{53} + 899327920 q^{57} - 167418240 q^{58} + 133818368 q^{60} + 201326592 q^{64} - 565976460 q^{65} + 202943376 q^{67} + 1228585536 q^{71} - 297164800 q^{72} - 389321088 q^{74} + 1364348160 q^{78} + 182370096 q^{79} + 432881842 q^{81} + 4140991464 q^{85} - 1196137344 q^{86} - 453279744 q^{88} + 124612608 q^{92} - 190722192 q^{93} + 1311555480 q^{95} + 10645173584 q^{99}+O(q^{100}) $ 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9 - 110664 * q^11 - 1045456 * q^15 - 393216 * q^16 - 1160800 * q^18 + 3541248 * q^22 - 243384 * q^23 - 17125446 * q^25 + 20927280 * q^29 + 8363648 * q^30 - 6291456 * q^32 + 37145600 * q^36 - 24332568 * q^37 - 42635880 * q^39 + 149517168 * q^43 - 28329984 * q^44 - 3894144 * q^46 + 548014272 * q^50 - 260246248 * q^51 - 137815308 * q^53 + 899327920 * q^57 - 167418240 * q^58 + 133818368 * q^60 + 201326592 * q^64 - 565976460 * q^65 + 202943376 * q^67 + 1228585536 * q^71 - 297164800 * q^72 - 389321088 * q^74 + 1364348160 * q^78 + 182370096 * q^79 + 432881842 * q^81 + 4140991464 * q^85 - 1196137344 * q^86 - 453279744 * q^88 + 124612608 * q^92 - 190722192 * q^93 + 1311555480 * q^95 + 10645173584 * 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
$3$	−60.6851	−	105.110i	−0.432550	−	0.749199i	0.564542	−	0.825404i	$-0.309053\pi$
$3$	−60.6851	−	105.110i	−0.432550	−	0.749199i	−0.997092	+	0.0762055i	$0.975719\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−1333.01	+	2308.84i	−0.953823	+	1.65207i	−0.216784	+	0.976220i	$0.569557\pi$
$5$	−1333.01	+	2308.84i	−0.953823	+	1.65207i	−0.737039	+	0.675850i	$0.763777\pi$
$6$	1941.92			0.611718
$7$		0			0
$7$		0			0
$8$	4096.00			0.353553
$9$	2476.14	−	4288.79i	0.125801	−	0.217893i
$10$	−21328.1	−	36941.4i	−0.674455	−	1.16819i
$11$	9446.53	+	16361.9i	0.194538	+	0.336950i	0.946749	−	0.321972i	$-0.104346\pi$
$11$	9446.53	+	16361.9i	0.194538	+	0.336950i	−0.752211	+	0.658923i	$0.771012\pi$
$12$	−15535.4	+	26908.1i	−0.216275	+	0.374599i
$13$	96063.7			0.932856			0.466428	−	0.884559i	$-0.345541\pi$
$13$	96063.7			0.932856			0.466428	+	0.884559i	$0.345541\pi$
$14$		0			0
$15$	323575.			1.65031
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−286996.	−	497092.i	−0.833405	−	1.44350i	−0.895323	−	0.445418i	$-0.853055\pi$
$17$	−286996.	−	497092.i	−0.833405	−	1.44350i	0.0619180	−	0.998081i	$-0.480278\pi$
$18$	39618.2	+	68620.7i	0.0889545	+	0.154074i
$19$	−43870.0	+	75985.0i	−0.0772282	+	0.133763i	−0.902053	−	0.431625i	$-0.857940\pi$
$19$	−43870.0	+	75985.0i	−0.0772282	+	0.133763i	0.824825	+	0.565388i	$0.191274\pi$
$20$	682500.			0.953823
$21$		0			0
$22$	−302289.			−0.275119
$23$	750174.	−	1.29934e6i	0.558967	−	0.968160i	−0.438616	−	0.898675i	$-0.644531\pi$
$23$	750174.	−	1.29934e6i	0.558967	−	0.968160i	0.997583	−	0.0694852i	$-0.0221357\pi$
$24$	−248566.	−	430529.i	−0.152930	−	0.264882i
$25$	−2.57726e6	−	4.46394e6i	−1.31956	−	2.28554i
$26$	−768510.	+	1.33110e6i	−0.329814	+	0.571255i
$27$	−2.98999e6			−1.08276
$28$		0			0
$29$	−1.78997e6			−0.469955			−0.234977	−	0.972001i	$-0.575502\pi$
$29$	−1.78997e6			−0.469955			−0.234977	+	0.972001i	$0.575502\pi$
$30$	−2.58860e6	+	4.48359e6i	−0.583471	+	1.01060i
$31$	4.83065e6	+	8.36693e6i	0.939459	+	1.62719i	0.766483	+	0.642265i	$0.222005\pi$
$31$	4.83065e6	+	8.36693e6i	0.939459	+	1.62719i	0.172977	+	0.984926i	$0.444661\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$	1.14653e6	−	1.98584e6i	0.168295	−	0.291496i
$34$	9.18388e6			1.17861
$35$		0			0
$36$	−1.26778e6			−0.125801
$37$	1.54840e6	−	2.68192e6i	0.135824	−	0.235254i	−0.790088	−	0.612994i	$-0.789965\pi$
$37$	1.54840e6	−	2.68192e6i	0.135824	−	0.235254i	0.925912	+	0.377739i	$0.123298\pi$
$38$	−701920.	−	1.21576e6i	−0.0546086	−	0.0945849i
$39$	−5.82964e6	−	1.00972e7i	−0.403507	−	0.698894i
$40$	−5.46000e6	+	9.45700e6i	−0.337227	+	0.584095i
$41$	1.17852e7			0.651345			0.325673	−	0.945483i	$-0.394409\pi$
$41$	1.17852e7			0.651345			0.325673	+	0.945483i	$0.394409\pi$
$42$		0			0
$43$	3.60280e7			1.60706			0.803530	−	0.595264i	$-0.202953\pi$
$43$	3.60280e7			1.60706			0.803530	+	0.595264i	$0.202953\pi$
$44$	2.41831e6	−	4.18864e6i	0.0972692	−	0.168475i
$45$	6.60142e6	+	1.14340e7i	0.239983	+	0.415663i
$46$	1.20028e7	+	2.07894e7i	0.395250	+	0.684593i
$47$	−2.95998e6	+	5.12684e6i	−0.0884808	+	0.153253i	−0.906869	−	0.421412i	$-0.861535\pi$
$47$	−2.95998e6	+	5.12684e6i	−0.0884808	+	0.153253i	0.818388	+	0.574666i	$0.194868\pi$
$48$	7.95412e6			0.216275
$49$		0			0
$50$	8.24723e7			1.86613
$51$	−3.48328e7	+	6.03322e7i	−0.720979	+	1.24877i
$52$	−1.22962e7	−	2.12976e7i	−0.233214	−	0.403938i
$53$	1.50157e7	+	2.60079e7i	0.261399	+	0.452755i	0.966614	−	0.256238i	$-0.0824830\pi$
$53$	1.50157e7	+	2.60079e7i	0.261399	+	0.452755i	−0.705215	+	0.708993i	$0.749150\pi$
$54$	2.39199e7	−	4.14305e7i	0.382814	−	0.663053i
$55$	−5.03692e7			−0.742221
$56$		0			0
$57$	1.06490e7			0.133620
$58$	1.43198e7	−	2.48026e7i	0.166154	−	0.287787i
$59$	7.16607e7	+	1.24120e8i	0.769922	+	1.33354i	0.937605	+	0.347703i	$0.113038\pi$
$59$	7.16607e7	+	1.24120e8i	0.769922	+	1.33354i	−0.167682	+	0.985841i	$0.553628\pi$
$60$	−4.14176e7	−	7.17374e7i	−0.412576	−	0.714603i
$61$	−7.53227e7	+	1.30463e8i	−0.696533	+	1.20643i	0.273128	+	0.961978i	$0.411942\pi$
$61$	−7.53227e7	+	1.30463e8i	−0.696533	+	1.20643i	−0.969661	+	0.244453i	$0.921392\pi$
$62$	−1.54581e8			−1.32860
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.28054e8	+	2.21796e8i	−0.889779	+	1.54114i
$66$	1.83444e7	+	3.17735e7i	0.119003	+	0.206119i
$67$	−4.97455e7	−	8.61617e7i	−0.301590	−	0.522369i	0.674906	−	0.737904i	$-0.264184\pi$
$67$	−4.97455e7	−	8.61617e7i	−0.301590	−	0.522369i	−0.976496	+	0.215534i	$0.930851\pi$
$68$	−7.34710e7	+	1.27256e8i	−0.416702	+	0.721750i
$69$	−1.82097e8			−0.967126
$70$		0			0
$71$	−2.01373e8			−0.940455			−0.470228	−	0.882545i	$-0.655828\pi$
$71$	−2.01373e8			−0.940455			−0.470228	+	0.882545i	$0.655828\pi$
$72$	1.01422e7	−	1.75669e7i	0.0444773	−	0.0770369i
$73$	−2.32838e7	−	4.03287e7i	−0.0959624	−	0.166212i	0.814047	−	0.580798i	$-0.197260\pi$
$73$	−2.32838e7	−	4.03287e7i	−0.0959624	−	0.166212i	−0.910010	+	0.414587i	$0.863926\pi$
$74$	2.47745e7	+	4.29106e7i	0.0960421	+	0.166350i
$75$	−3.12802e8	+	5.41790e8i	−1.14155	+	1.97722i
$76$	2.24614e7			0.0772282
$77$		0			0
$78$	1.86548e8			0.570645
$79$	1.26611e8	−	2.19297e8i	0.365721	−	0.633446i	−0.623171	−	0.782086i	$-0.714156\pi$
$79$	1.26611e8	−	2.19297e8i	0.365721	−	0.633446i	0.988892	+	0.148639i	$0.0474893\pi$
$80$	−8.73600e7	−	1.51312e8i	−0.238456	−	0.413017i
$81$	1.32710e8	+	2.29860e8i	0.342548	+	0.593310i
$82$	−9.42819e7	+	1.63301e8i	−0.230285	+	0.398866i
$83$	−3.16834e8			−0.732793			−0.366396	−	0.930459i	$-0.619409\pi$
$83$	−3.16834e8			−0.732793			−0.366396	+	0.930459i	$0.619409\pi$
$84$		0			0
$85$	1.53027e9			3.17968
$86$	−2.88224e8	+	4.99219e8i	−0.568181	+	0.984119i
$87$	1.08625e8	+	1.88144e8i	0.203279	+	0.352089i
$88$	3.86930e7	+	6.70182e7i	0.0687797	+	0.119130i
$89$	−4.20311e8	+	7.28000e8i	−0.710094	+	1.22992i	0.254728	+	0.967013i	$0.418014\pi$
$89$	−4.20311e8	+	7.28000e8i	−0.710094	+	1.22992i	−0.964821	+	0.262906i	$0.915319\pi$
$90$	−2.11245e8			−0.339387
$91$		0			0
$92$	−3.84089e8			−0.558967
$93$	5.86297e8	−	1.01550e9i	0.812726	−	1.40768i
$94$	−4.73597e7	−	8.20295e7i	−0.0625654	−	0.108366i
$95$	−1.16958e8	−	2.02577e8i	−0.147324	−	0.255173i
$96$	−6.36329e7	+	1.10215e8i	−0.0764648	+	0.132441i
$97$	−2.72768e8			−0.312839			−0.156419	−	0.987691i	$-0.549995\pi$
$97$	−2.72768e8			−0.312839			−0.156419	+	0.987691i	$0.549995\pi$
$98$		0			0
$99$	9.35636e7			0.0978923
$100$	−6.59778e8	+	1.14277e9i	−0.659778	+	1.14277i
$101$	1.85832e8	+	3.21871e8i	0.177695	+	0.307777i	0.941091	−	0.338155i	$-0.109803\pi$
$101$	1.85832e8	+	3.21871e8i	0.177695	+	0.307777i	−0.763396	+	0.645931i	$0.776469\pi$
$102$	−5.57325e8	−	9.65315e8i	−0.509809	−	0.883015i
$103$	4.98456e8	−	8.63352e8i	0.436375	−	0.755823i	−0.561032	−	0.827794i	$-0.689596\pi$
$103$	4.98456e8	−	8.63352e8i	0.436375	−	0.755823i	0.997407	+	0.0719710i	$0.0229289\pi$
$104$	3.93477e8			0.329814
$105$		0			0
$106$	−4.80501e8			−0.369673
$107$	−1.32686e9	+	2.29819e9i	−0.978586	+	1.69496i	−0.311032	+	0.950400i	$0.600675\pi$
$107$	−1.32686e9	+	2.29819e9i	−0.978586	+	1.69496i	−0.667554	+	0.744561i	$0.732659\pi$
$108$	3.82718e8	+	6.62888e8i	0.270690	+	0.468849i
$109$	4.94086e8	+	8.55782e8i	0.335261	+	0.580690i	0.983535	−	0.180718i	$-0.0578421\pi$
$109$	4.94086e8	+	8.55782e8i	0.335261	+	0.580690i	−0.648274	+	0.761407i	$0.724509\pi$
$110$	4.02954e8	−	6.97936e8i	0.262415	−	0.454516i
$111$	−3.75860e8			−0.235003
$112$		0			0
$113$	6.67601e8			0.385180			0.192590	−	0.981279i	$-0.438311\pi$
$113$	6.67601e8			0.385180			0.192590	+	0.981279i	$0.438311\pi$
$114$	−8.51921e7	+	1.47557e8i	−0.0472419	+	0.0818254i
$115$	1.99997e9	+	3.46406e9i	1.06631	+	1.84691i
$116$	2.29117e8	+	3.96842e8i	0.117489	+	0.203496i
$117$	2.37867e8	−	4.11997e8i	0.117354	−	0.203263i
$118$	−2.29314e9			−1.08883
$119$		0			0
$120$	1.32536e9			0.583471
$121$	1.00050e9	−	1.73292e9i	0.424310	−	0.734926i
$122$	−1.20516e9	−	2.08740e9i	−0.492523	−	0.853075i
$123$	−7.15189e8	−	1.23874e9i	−0.281739	−	0.487987i
$124$	1.23665e9	−	2.14193e9i	0.469730	−	0.813596i
$125$	8.53496e9			3.12685
$126$		0			0
$127$	−3.51915e9			−1.20039			−0.600193	−	0.799856i	$-0.704909\pi$
$127$	−3.51915e9			−1.20039			−0.600193	+	0.799856i	$0.704909\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$	−2.18636e9	−	3.78689e9i	−0.695134	−	1.20401i
$130$	−2.04886e9	−	3.54873e9i	−0.629169	−	1.08975i
$131$	−1.90130e9	+	3.29315e9i	−0.564066	+	0.976991i	0.433070	+	0.901360i	$0.357430\pi$
$131$	−1.90130e9	+	3.29315e9i	−0.564066	+	0.976991i	−0.997136	+	0.0756310i	$0.975903\pi$
$132$	−5.87022e8			−0.168295
$133$		0			0
$134$	1.59186e9			0.426513
$135$	3.98568e9	−	6.90340e9i	1.03276	−	1.78880i
$136$	−1.17554e9	−	2.03609e9i	−0.294653	−	0.510354i
$137$	3.77148e9	+	6.53239e9i	0.914680	+	1.58427i	0.807369	+	0.590047i	$0.200891\pi$
$137$	3.77148e9	+	6.53239e9i	0.914680	+	1.58427i	0.107311	+	0.994225i	$0.465776\pi$
$138$	1.45678e9	−	2.52322e9i	0.341931	−	0.592241i
$139$	1.04500e9			0.237437			0.118718	−	0.992928i	$-0.462121\pi$
$139$	1.04500e9			0.237437			0.118718	+	0.992928i	$0.462121\pi$
$140$		0			0
$141$	7.18508e8			0.153090
$142$	1.61098e9	−	2.79030e9i	0.332501	−	0.575909i
$143$	9.07469e8	+	1.57178e9i	0.181476	+	0.314326i
$144$	1.62276e8	+	2.81070e8i	0.0314502	+	0.0544733i
$145$	2.38605e9	−	4.13276e9i	0.448253	−	0.776398i
$146$	7.45082e8			0.135711
$147$		0			0
$148$	−7.92783e8			−0.135824
$149$	1.83322e8	−	3.17523e8i	0.0304703	−	0.0527761i	−0.850388	−	0.526156i	$-0.823633\pi$
$149$	1.83322e8	−	3.17523e8i	0.0304703	−	0.0527761i	0.880858	+	0.473380i	$0.156966\pi$
$150$	−5.00484e9	−	8.66863e9i	−0.807197	−	1.39811i
$151$	−2.69003e9	−	4.65926e9i	−0.421076	−	0.729325i	0.574969	−	0.818175i	$-0.305014\pi$
$151$	−2.69003e9	−	4.65926e9i	−0.421076	−	0.729325i	−0.996045	+	0.0888504i	$0.971681\pi$
$152$	−1.79691e8	+	3.11235e8i	−0.0273043	+	0.0472924i
$153$	−2.84257e9			−0.419372
$154$		0			0
$155$	−2.57572e10			−3.58431
$156$	−1.49239e9	+	2.58489e9i	−0.201753	+	0.349447i
$157$	4.18569e9	+	7.24983e9i	0.549818	+	0.952312i	0.998287	+	0.0585139i	$0.0186362\pi$
$157$	4.18569e9	+	7.24983e9i	0.549818	+	0.952312i	−0.448469	+	0.893798i	$0.648030\pi$
$158$	2.02577e9	+	3.50875e9i	0.258603	+	0.447914i
$159$	1.82245e9	−	3.15658e9i	0.226136	−	0.391679i
$160$	2.79552e9			0.337227
$161$		0			0
$162$	−4.24672e9			−0.484436
$163$	3.65750e9	−	6.33497e9i	0.405826	−	0.702911i	−0.588591	−	0.808431i	$-0.700317\pi$
$163$	3.65750e9	−	6.33497e9i	0.405826	−	0.702911i	0.994417	+	0.105519i	$0.0336505\pi$
$164$	−1.50851e9	−	2.61282e9i	−0.162836	−	0.282041i
$165$	3.05666e9	+	5.29429e9i	0.321048	+	0.556071i
$166$	2.53468e9	−	4.39019e9i	0.259081	−	0.448742i
$167$	−5.33639e9			−0.530913			−0.265457	−	0.964123i	$-0.585523\pi$
$167$	−5.33639e9			−0.530913			−0.265457	+	0.964123i	$0.585523\pi$
$168$		0			0
$169$	−1.37626e9			−0.129780
$170$	−1.22422e10	+	2.12041e10i	−1.12419	+	1.94715i
$171$	2.17256e8	+	3.76298e8i	0.0194307	+	0.0336550i
$172$	−4.61158e9	−	7.98750e9i	−0.401765	−	0.695877i
$173$	2.24257e9	−	3.88424e9i	0.190344	−	0.329685i	−0.755020	−	0.655701i	$-0.772373\pi$
$173$	2.24257e9	−	3.88424e9i	0.190344	−	0.329685i	0.945364	+	0.326016i	$0.105706\pi$
$174$	−3.47599e9			−0.287480
$175$		0			0
$176$	−1.23818e9			−0.0972692
$177$	8.69747e9	−	1.50645e10i	0.666060	−	1.15365i
$178$	−6.72498e9	−	1.16480e10i	−0.502112	−	0.869684i
$179$	3.38138e9	+	5.85672e9i	0.246181	+	0.426399i	0.962463	−	0.271413i	$-0.0874908\pi$
$179$	3.38138e9	+	5.85672e9i	0.246181	+	0.426399i	−0.716282	+	0.697811i	$0.754157\pi$
$180$	1.68996e9	−	2.92710e9i	0.119992	−	0.207832i
$181$	−4.06637e9			−0.281613			−0.140807	−	0.990037i	$-0.544970\pi$
$181$	−4.06637e9			−0.281613			−0.140807	+	0.990037i	$0.544970\pi$
$182$		0			0
$183$	1.82839e10			1.20514
$184$	3.07271e9	−	5.32209e9i	0.197625	−	0.342296i
$185$	4.12807e9	+	7.15003e9i	0.259104	+	0.448782i
$186$	9.38075e9	+	1.62479e10i	0.574684	+	0.995383i
$187$	5.42224e9	−	9.39159e9i	0.324258	−	0.561632i
$188$	1.51551e9			0.0884808
$189$		0			0
$190$	3.74266e9			0.208348
$191$	5.63713e9	−	9.76379e9i	0.306484	−	0.530846i	−0.671107	−	0.741361i	$-0.734181\pi$
$191$	5.63713e9	−	9.76379e9i	0.306484	−	0.530846i	0.977591	+	0.210515i	$0.0675141\pi$
$192$	−1.01813e9	−	1.76345e9i	−0.0540688	−	0.0936499i
$193$	1.15055e10	+	1.99282e10i	0.596896	+	1.03385i	0.993276	+	0.115768i	$0.0369330\pi$
$193$	1.15055e10	+	1.99282e10i	0.596896	+	1.03385i	−0.396380	+	0.918087i	$0.629734\pi$
$194$	2.18214e9	−	3.77958e9i	0.110605	−	0.191574i
$195$	3.10838e10			1.53950
$196$		0			0
$197$	1.63377e10			0.772844			0.386422	−	0.922322i	$-0.373711\pi$
$197$	1.63377e10			0.772844			0.386422	+	0.922322i	$0.373711\pi$
$198$	−7.48509e8	+	1.29645e9i	−0.0346101	+	0.0599465i
$199$	−1.20729e9	−	2.09108e9i	−0.0545722	−	0.0945219i	0.837449	−	0.546516i	$-0.184046\pi$
$199$	−1.20729e9	−	2.09108e9i	−0.0545722	−	0.0945219i	−0.892021	+	0.451994i	$0.850713\pi$
$200$	−1.05564e10	−	1.82843e10i	−0.466534	−	0.808060i
$201$	−6.03762e9	+	1.04575e10i	−0.260906	+	0.451902i
$202$	−5.94663e9			−0.251298
$203$		0			0
$204$	1.78344e10			0.720979
$205$	−1.57098e10	+	2.72102e10i	−0.621268	+	1.07607i
$206$	7.97530e9	+	1.38136e10i	0.308563	+	0.534448i
$207$	−3.71506e9	−	6.43468e9i	−0.140637	−	0.243590i
$208$	−3.14782e9	+	5.45218e9i	−0.116607	+	0.201969i
$209$	−1.65768e9			−0.0600954
$210$		0			0
$211$	1.58653e10			0.551034			0.275517	−	0.961296i	$-0.411151\pi$
$211$	1.58653e10			0.551034			0.275517	+	0.961296i	$0.411151\pi$
$212$	3.84401e9	−	6.65802e9i	0.130699	−	0.226378i
$213$	1.22203e10	+	2.11662e10i	0.406794	+	0.704588i
$214$	−2.12298e10	−	3.67711e10i	−0.691965	−	1.19852i
$215$	−4.80256e10	+	8.31828e10i	−1.53285	+	2.65498i
$216$	−1.22470e10			−0.382814
$217$		0			0
$218$	−1.58108e10			−0.474131
$219$	−2.82596e9	+	4.89471e9i	−0.0830171	+	0.143790i
$220$	6.44726e9	+	1.11670e10i	0.185555	+	0.321391i
$221$	−2.75699e10	−	4.77525e10i	−0.777446	−	1.34658i
$222$	3.00688e9	−	5.20807e9i	0.0830861	−	0.143909i
$223$	3.21097e10			0.869489			0.434745	−	0.900554i	$-0.356839\pi$
$223$	3.21097e10			0.869489			0.434745	+	0.900554i	$0.356839\pi$
$224$		0			0
$225$	−2.55266e10			−0.664004
$226$	−5.34081e9	+	9.25056e9i	−0.136182	+	0.235874i
$227$	−2.28370e9	−	3.95548e9i	−0.0570851	−	0.0988743i	0.836071	−	0.548622i	$-0.184847\pi$
$227$	−2.28370e9	−	3.95548e9i	−0.0570851	−	0.0988743i	−0.893156	+	0.449748i	$0.851514\pi$
$228$	−1.36307e9	−	2.36091e9i	−0.0334051	−	0.0578593i
$229$	6.61049e9	−	1.14497e10i	0.158845	−	0.275128i	−0.775607	−	0.631216i	$-0.782556\pi$
$229$	6.61049e9	−	1.14497e10i	0.158845	−	0.275128i	0.934453	+	0.356088i	$0.115890\pi$
$230$	−6.39992e10			−1.50799
$231$		0			0
$232$	−7.33174e9			−0.166154
$233$	−2.43668e10	+	4.22045e10i	−0.541622	+	0.938117i	0.457189	+	0.889369i	$0.348856\pi$
$233$	−2.43668e10	+	4.22045e10i	−0.541622	+	0.938117i	−0.998811	+	0.0487471i	$0.984477\pi$
$234$	3.80587e9	+	6.59196e9i	0.0829817	+	0.143729i
$235$	−7.89136e9	−	1.36682e10i	−0.168790	−	0.292353i
$236$	1.83451e10	−	3.17747e10i	0.384961	−	0.666772i
$237$	−3.07336e10			−0.632770
$238$		0			0
$239$	7.16988e10			1.42142			0.710708	−	0.703487i	$-0.248375\pi$
$239$	7.16988e10			1.42142			0.710708	+	0.703487i	$0.248375\pi$
$240$	−1.06029e10	+	1.83648e10i	−0.206288	+	0.357302i
$241$	3.19518e10	+	5.53422e10i	0.610125	+	1.05677i	0.991219	+	0.132231i	$0.0422141\pi$
$241$	3.19518e10	+	5.53422e10i	0.610125	+	1.05677i	−0.381094	+	0.924536i	$0.624453\pi$
$242$	1.60080e10	+	2.77267e10i	0.300032	+	0.519671i
$243$	−1.33189e10	+	2.30691e10i	−0.245042	+	0.424426i
$244$	3.85652e10			0.696533
$245$		0			0
$246$	2.28860e10			0.398440
$247$	−4.21431e9	+	7.29940e9i	−0.0720428	+	0.124782i
$248$	1.97863e10	+	3.42709e10i	0.332149	+	0.575299i
$249$	1.92271e10	+	3.33024e10i	0.316970	+	0.549007i
$250$	−6.82797e10	+	1.18264e11i	−1.10551	+	1.91479i
$251$	−9.92465e10			−1.57828			−0.789139	−	0.614215i	$-0.789473\pi$
$251$	−9.92465e10			−1.57828			−0.789139	+	0.614215i	$0.789473\pi$
$252$		0			0
$253$	2.83462e10			0.434963
$254$	2.81532e10	−	4.87627e10i	0.424400	−	0.735083i
$255$	−9.28648e10	−	1.60846e11i	−1.37537	−	2.38221i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	6.50118e9	−	1.12604e10i	0.0929593	−	0.161010i	−0.815796	−	0.578340i	$-0.803701\pi$
$257$	6.50118e9	−	1.12604e10i	0.0929593	−	0.161010i	0.908755	+	0.417330i	$0.137034\pi$
$258$	6.99636e10			0.983068
$259$		0			0
$260$	6.55635e10			0.889779
$261$	−4.43222e9	+	7.67683e9i	−0.0591206	+	0.102400i
$262$	−3.04208e10	−	5.26904e10i	−0.398855	−	0.690837i
$263$	−1.64165e10	−	2.84342e10i	−0.211582	−	0.366472i	0.740627	−	0.671916i	$-0.234528\pi$
$263$	−1.64165e10	−	2.84342e10i	−0.211582	−	0.366472i	−0.952210	+	0.305444i	$0.901195\pi$
$264$	4.69618e9	−	8.13402e9i	0.0595014	−	0.103059i
$265$	−8.00640e10			−0.997312
$266$		0			0
$267$	1.02026e11			1.22861
$268$	−1.27348e10	+	2.20574e10i	−0.150795	+	0.261185i
$269$	3.65129e10	+	6.32423e10i	0.425169	+	0.736414i	0.996436	−	0.0843500i	$-0.0268814\pi$
$269$	3.65129e10	+	6.32423e10i	0.425169	+	0.736414i	−0.571267	+	0.820764i	$0.693548\pi$
$270$	6.37709e10	+	1.10454e11i	0.730273	+	1.26487i
$271$	4.41643e10	−	7.64949e10i	0.497405	−	0.861530i	−0.502591	−	0.864524i	$-0.667620\pi$
$271$	4.41643e10	−	7.64949e10i	0.497405	−	0.861530i	0.999996	+	0.00299431i	$0.000953120\pi$
$272$	3.76172e10			0.416702
$273$		0			0
$274$	−1.20687e11			−1.29355
$275$	4.86923e10	−	8.43376e10i	0.513409	−	0.889250i
$276$	2.33085e10	+	4.03715e10i	0.241781	+	0.418778i
$277$	5.87375e10	+	1.01736e11i	0.599455	+	1.03829i	0.992902	+	0.118939i	$0.0379494\pi$
$277$	5.87375e10	+	1.01736e11i	0.599455	+	1.03829i	−0.393446	+	0.919348i	$0.628717\pi$
$278$	−8.35996e9	+	1.44799e10i	−0.0839466	+	0.145400i
$279$	4.78454e10			0.472738
$280$		0			0
$281$	−3.51607e10			−0.336418			−0.168209	−	0.985751i	$-0.553798\pi$
$281$	−3.51607e10			−0.336418			−0.168209	+	0.985751i	$0.553798\pi$
$282$	−5.74806e9	+	9.95594e9i	−0.0541253	+	0.0937478i
$283$	2.51730e10	+	4.36009e10i	0.233290	+	0.404070i	0.958774	−	0.284169i	$-0.0917176\pi$
$283$	2.51730e10	+	4.36009e10i	0.233290	+	0.404070i	−0.725485	+	0.688238i	$0.758384\pi$
$284$	2.57757e10	+	4.46448e10i	0.235114	+	0.407229i
$285$	−1.41952e10	+	2.45868e10i	−0.127450	+	0.220750i
$286$	−2.90390e10			−0.256646
$287$		0			0
$288$	−5.19283e9			−0.0444773
$289$	−1.05440e11	+	1.82627e11i	−0.889127	+	1.54001i
$290$	3.81768e10	+	6.61242e10i	0.316963	+	0.548996i
$291$	1.65529e10	+	2.86705e10i	0.135318	+	0.234378i
$292$	−5.96066e9	+	1.03242e10i	−0.0479812	+	0.0831059i
$293$	−1.70340e11			−1.35024			−0.675121	−	0.737707i	$-0.735909\pi$
$293$	−1.70340e11			−1.35024			−0.675121	+	0.737707i	$0.735909\pi$
$294$		0			0
$295$	−3.82097e11			−2.93748
$296$	6.34227e9	−	1.09851e10i	0.0480211	−	0.0831749i
$297$	−2.82450e10	−	4.89218e10i	−0.210639	−	0.364837i
$298$	2.93315e9	+	5.08037e9i	0.0215457	+	0.0373183i
$299$	7.20645e10	−	1.24819e11i	0.521436	−	0.903153i
$300$	1.60155e11			1.14155
$301$		0			0
$302$	8.60808e10			0.595491
$303$	2.25545e10	−	3.90655e10i	0.153724	−	0.266258i
$304$	−2.87506e9	−	4.97975e9i	−0.0193071	−	0.0334408i
$305$	−2.00812e11	−	3.47816e11i	−1.32874	−	2.30144i
$306$	2.27405e10	−	3.93877e10i	0.148270	−	0.256812i
$307$	5.25886e10			0.337885			0.168943	−	0.985626i	$-0.445965\pi$
$307$	5.25886e10			0.337885			0.168943	+	0.985626i	$0.445965\pi$
$308$		0			0
$309$	−1.20995e11			−0.755016
$310$	2.06057e11	−	3.56902e11i	1.26725	−	2.19493i
$311$	−3.04301e10	−	5.27065e10i	−0.184451	−	0.319479i	0.758940	−	0.651160i	$-0.225718\pi$
$311$	−3.04301e10	−	5.27065e10i	−0.184451	−	0.319479i	−0.943392	+	0.331681i	$0.892384\pi$
$312$	−2.38782e10	−	4.13583e10i	−0.142661	−	0.247096i
$313$	9.42448e10	−	1.63237e11i	0.555019	−	0.961321i	−0.442883	−	0.896579i	$-0.646044\pi$
$313$	9.42448e10	−	1.63237e11i	0.555019	−	0.961321i	0.997902	−	0.0647416i	$-0.0206223\pi$
$314$	−1.33942e11			−0.777560
$315$		0			0
$316$	−6.48248e10			−0.365721
$317$	9.59915e9	−	1.66262e10i	0.0533908	−	0.0924755i	−0.838095	−	0.545525i	$-0.816330\pi$
$317$	9.59915e9	−	1.66262e10i	0.0533908	−	0.0924755i	0.891486	+	0.453049i	$0.149664\pi$
$318$	2.91593e10	+	5.05053e10i	0.159902	+	0.276959i
$319$	−1.69091e10	−	2.92873e10i	−0.0914242	−	0.158351i
$320$	−2.23642e10	+	3.87359e10i	−0.119228	+	0.206509i
$321$	3.22083e11			1.69315
$322$		0			0
$323$	5.03621e10			0.257450
$324$	3.39738e10	−	5.88443e10i	0.171274	−	0.296655i
$325$	−2.47581e11	−	4.28823e11i	−1.23096	−	2.13208i
$326$	5.85200e10	+	1.01360e11i	0.286962	+	0.497033i
$327$	5.99673e10	−	1.03866e11i	0.290035	−	0.502355i
$328$	4.82724e10			0.230285
$329$		0			0
$330$	−9.78132e10			−0.454030
$331$	−1.55258e11	+	2.68914e11i	−0.710931	+	1.23137i	0.253577	+	0.967315i	$0.418393\pi$
$331$	−1.55258e11	+	2.68914e11i	−0.710931	+	1.23137i	−0.964508	+	0.264054i	$0.914940\pi$
$332$	4.05548e10	+	7.02430e10i	0.183198	+	0.317308i
$333$	−7.66812e9	−	1.32816e10i	−0.0341735	−	0.0591903i
$334$	4.26911e10	−	7.39432e10i	0.187706	−	0.325117i
$335$	2.65245e11			1.15065
$336$		0			0
$337$	3.29977e11			1.39363			0.696817	−	0.717249i	$-0.254599\pi$
$337$	3.29977e11			1.39363			0.696817	+	0.717249i	$0.254599\pi$
$338$	1.10101e10	−	1.90700e10i	0.0458843	−	0.0794740i
$339$	−4.05135e10	−	7.01714e10i	−0.166610	−	0.288577i
$340$	−1.95875e11	−	3.39265e11i	−0.794920	−	1.37684i
$341$	−9.12658e10	+	1.58077e11i	−0.365522	+	0.633102i
$342$	−6.95219e9			−0.0274792
$343$		0			0
$344$	1.47571e11			0.568181
$345$	2.42737e11	−	4.20433e11i	0.922467	−	1.59776i
$346$	3.58811e10	+	6.21479e10i	0.134593	+	0.233122i
$347$	1.77833e11	+	3.08016e11i	0.658460	+	1.14049i	0.981014	+	0.193936i	$0.0621253\pi$
$347$	1.77833e11	+	3.08016e11i	0.658460	+	1.14049i	−0.322554	+	0.946551i	$0.604541\pi$
$348$	2.78079e10	−	4.81648e10i	0.101639	−	0.176045i
$349$	2.61881e11			0.944907			0.472454	−	0.881356i	$-0.343368\pi$
$349$	2.61881e11			0.944907			0.472454	+	0.881356i	$0.343368\pi$
$350$		0			0
$351$	−2.87229e11			−1.01006
$352$	9.90541e9	−	1.71567e10i	0.0343899	−	0.0595650i
$353$	−5.73762e10	−	9.93785e10i	−0.196673	−	0.340648i	0.750774	−	0.660559i	$-0.229681\pi$
$353$	−5.73762e10	−	9.93785e10i	−0.196673	−	0.340648i	−0.947448	+	0.319910i	$0.896347\pi$
$354$	1.39160e11	+	2.41031e11i	0.470976	+	0.815754i
$355$	2.68432e11	−	4.64937e11i	0.897028	−	1.55370i
$356$	2.15199e11			0.710094
$357$		0			0
$358$	−1.08204e11			−0.348153
$359$	−9.25048e10	+	1.60223e11i	−0.293927	+	0.509096i	−0.974735	−	0.223366i	$-0.928296\pi$
$359$	−9.25048e10	+	1.60223e11i	−0.293927	+	0.509096i	0.680808	+	0.732462i	$0.261629\pi$
$360$	2.70394e10	+	4.68336e10i	0.0848469	+	0.146959i
$361$	1.57495e11	+	2.72789e11i	0.488072	+	0.845365i
$362$	3.25310e10	−	5.63453e10i	0.0995654	−	0.172452i
$363$	−2.42862e11			−0.734141
$364$		0			0
$365$	1.24150e11			0.366125
$366$	−1.46271e11	+	2.53349e11i	−0.426082	+	0.737996i
$367$	8.22673e10	+	1.42491e11i	0.236717	+	0.410007i	0.959770	−	0.280786i	$-0.0905951\pi$
$367$	8.22673e10	+	1.42491e11i	0.236717	+	0.410007i	−0.723053	+	0.690793i	$0.757262\pi$
$368$	4.91634e10	+	8.51535e10i	0.139742	+	0.242040i
$369$	2.91819e10	−	5.05445e10i	0.0819397	−	0.141924i
$370$	−1.32098e11			−0.366429
$371$		0			0
$372$	−3.00184e11			−0.812726
$373$	3.18061e10	−	5.50898e10i	0.0850787	−	0.147361i	−0.820346	−	0.571867i	$-0.806219\pi$
$373$	3.18061e10	−	5.50898e10i	0.0850787	−	0.147361i	0.905425	+	0.424507i	$0.139552\pi$
$374$	8.67558e10	+	1.50265e11i	0.229285	+	0.397134i
$375$	−5.17945e11	−	8.97107e11i	−1.35252	−	2.34263i
$376$	−1.21241e10	+	2.09995e10i	−0.0312827	+	0.0541832i
$377$	−1.71952e11			−0.438400
$378$		0			0
$379$	−7.53720e10			−0.187644			−0.0938218	−	0.995589i	$-0.529908\pi$
$379$	−7.53720e10			−0.187644			−0.0938218	+	0.995589i	$0.529908\pi$
$380$	−2.99413e10	+	5.18598e10i	−0.0736621	+	0.127586i
$381$	2.13560e11	+	3.69896e11i	0.519227	+	0.899327i
$382$	9.01940e10	+	1.56221e11i	0.216717	+	0.375365i
$383$	−1.95778e11	+	3.39097e11i	−0.464910	+	0.805247i	−0.999197	−	0.0400553i	$-0.987247\pi$
$383$	−1.95778e11	+	3.39097e11i	−0.464910	+	0.805247i	0.534288	+	0.845303i	$0.320580\pi$
$384$	3.25801e10			0.0764648
$385$		0			0
$386$	−3.68177e11			−0.844139
$387$	8.92102e10	−	1.54517e11i	0.202169	−	0.350167i
$388$	3.49143e10	+	6.04733e10i	0.0782097	+	0.135463i
$389$	2.03184e11	+	3.51925e11i	0.449900	+	0.779250i	0.998379	−	0.0569146i	$-0.0181263\pi$
$389$	2.03184e11	+	3.51925e11i	0.449900	+	0.779250i	−0.548479	+	0.836164i	$0.684793\pi$
$390$	−2.48671e11	+	4.30710e11i	−0.544294	+	0.942745i
$391$	−8.61188e11			−1.86338
$392$		0			0
$393$	4.61523e11			0.975948
$394$	−1.30701e11	+	2.26381e11i	−0.273242	+	0.473268i
$395$	3.37547e11	+	5.84648e11i	0.697665	+	1.20839i
$396$	−1.19761e10	−	2.07433e10i	−0.0244731	−	0.0423886i
$397$	−1.24011e11	+	2.14794e11i	−0.250555	+	0.433975i	−0.963679	−	0.267064i	$-0.913947\pi$
$397$	−1.24011e11	+	2.14794e11i	−0.250555	+	0.433975i	0.713123	+	0.701039i	$0.247280\pi$
$398$	3.86332e10			0.0771768
$399$		0			0
$400$	3.37806e11			0.659778
$401$	−2.63248e11	+	4.55959e11i	−0.508412	+	0.880595i	0.491541	+	0.870855i	$0.336434\pi$
$401$	−2.63248e11	+	4.55959e11i	−0.508412	+	0.880595i	−0.999953	+	0.00974044i	$0.996899\pi$
$402$	−9.66020e10	−	1.67319e11i	−0.184488	−	0.319543i
$403$	4.64050e11	+	8.03759e11i	0.876380	+	1.51793i
$404$	4.75731e10	−	8.23989e10i	0.0888474	−	0.153888i
$405$	−7.07614e11			−1.30692
$406$		0			0
$407$	5.85082e10			0.105692
$408$	−1.42675e11	+	2.47121e11i	−0.254904	+	0.441507i
$409$	−3.88176e11	−	6.72341e11i	−0.685921	−	1.18805i	−0.973146	−	0.230187i	$-0.926066\pi$
$409$	−3.88176e11	−	6.72341e11i	−0.685921	−	1.18805i	0.287225	−	0.957863i	$-0.407267\pi$
$410$	−2.51357e11	−	4.35363e11i	−0.439303	−	0.760895i
$411$	4.57745e11	−	7.92838e11i	0.791290	−	1.37055i
$412$	−2.55210e11			−0.436375
$413$		0			0
$414$	1.18882e11			0.198891
$415$	4.22343e11	−	7.31519e11i	0.698954	−	1.21062i
$416$	−5.03651e10	−	8.72349e10i	−0.0824536	−	0.142814i
$417$	−6.34157e10	−	1.09839e11i	−0.102703	−	0.177887i
$418$	1.32614e10	−	2.29694e10i	0.0212469	−	0.0368008i
$419$	8.55309e11			1.35569			0.677844	−	0.735205i	$-0.262914\pi$
$419$	8.55309e11			1.35569			0.677844	+	0.735205i	$0.262914\pi$
$420$		0			0
$421$	8.48099e11			1.31576			0.657881	−	0.753122i	$-0.271453\pi$
$421$	8.48099e11			1.31576			0.657881	+	0.753122i	$0.271453\pi$
$422$	−1.26923e11	+	2.19837e11i	−0.194820	+	0.337438i
$423$	1.46586e10	+	2.53895e10i	0.0222619	+	0.0385587i
$424$	6.15042e10	+	1.06528e11i	0.0924183	+	0.160073i
$425$	−1.47933e12	+	2.56227e12i	−2.19945	+	3.80956i
$426$	−3.91050e11			−0.575294
$427$		0			0
$428$	6.79354e11			0.978586
$429$	1.10140e11	−	1.90768e11i	0.156995	−	0.271924i
$430$	−7.68410e11	−	1.33092e12i	−1.08389	−	1.87735i
$431$	1.17364e11	+	2.03281e11i	0.163828	+	0.283758i	0.936238	−	0.351365i	$-0.114282\pi$
$431$	1.17364e11	+	2.03281e11i	0.163828	+	0.283758i	−0.772410	+	0.635124i	$0.780949\pi$
$432$	9.79759e10	−	1.69699e11i	0.135345	−	0.234425i
$433$	2.27943e11			0.311624			0.155812	−	0.987787i	$-0.450201\pi$
$433$	2.27943e11			0.311624			0.155812	+	0.987787i	$0.450201\pi$
$434$		0			0
$435$	−5.79191e11			−0.775568
$436$	1.26486e11	−	2.19080e11i	0.167631	−	0.290345i
$437$	6.58202e10	+	1.14004e11i	0.0863361	+	0.149539i
$438$	−4.52154e10	−	7.83153e10i	−0.0587020	−	0.101675i
$439$	−3.67059e11	+	6.35765e11i	−0.471678	+	0.816970i	−0.999475	−	0.0324002i	$-0.989685\pi$
$439$	−3.67059e11	+	6.35765e11i	−0.471678	+	0.816970i	0.527797	+	0.849371i	$0.323018\pi$
$440$	−2.06312e11			−0.262415
$441$		0			0
$442$	8.82238e11			1.09947
$443$	−6.72000e11	+	1.16394e12i	−0.828996	+	1.43586i	0.0698302	+	0.997559i	$0.477754\pi$
$443$	−6.72000e11	+	1.16394e12i	−0.828996	+	1.43586i	−0.898826	+	0.438305i	$0.855579\pi$
$444$	4.81101e10	+	8.33292e10i	0.0587507	+	0.101759i
$445$	−1.12056e12	−	1.94086e12i	−1.35461	−	2.34625i
$446$	−2.56877e11	+	4.44925e11i	−0.307411	+	0.532451i
$447$	−4.44997e10			−0.0527197
$448$		0			0
$449$	−3.61013e11			−0.419193			−0.209597	−	0.977788i	$-0.567215\pi$
$449$	−3.61013e11			−0.419193			−0.209597	+	0.977788i	$0.567215\pi$
$450$	2.04212e11	−	3.53706e11i	0.234761	−	0.406618i
$451$	1.11330e11	+	1.92829e11i	0.126712	+	0.219471i
$452$	−8.54530e10	−	1.48009e11i	−0.0962951	−	0.166788i
$453$	−3.26489e11	+	5.65496e11i	−0.364273	+	0.630939i
$454$	7.30784e10			0.0807305
$455$		0			0
$456$	4.36184e10			0.0472419
$457$	−4.24090e11	+	7.34545e11i	−0.454815	+	0.787762i	−0.998678	−	0.0514118i	$-0.983628\pi$
$457$	−4.24090e11	+	7.34545e11i	−0.454815	+	0.787762i	0.543863	+	0.839174i	$0.316961\pi$
$458$	1.05768e11	+	1.83195e11i	0.112320	+	0.194545i
$459$	8.58115e11	+	1.48630e12i	0.902378	+	1.56296i
$460$	5.11994e11	−	8.86799e11i	0.533156	−	0.923453i
$461$	2.08658e11			0.215170			0.107585	−	0.994196i	$-0.465688\pi$
$461$	2.08658e11			0.215170			0.107585	+	0.994196i	$0.465688\pi$
$462$		0			0
$463$	−5.84855e11			−0.591471			−0.295736	−	0.955270i	$-0.595565\pi$
$463$	−5.84855e11			−0.591471			−0.295736	+	0.955270i	$0.595565\pi$
$464$	5.86539e10	−	1.01592e11i	0.0587443	−	0.101748i
$465$	1.56308e12	+	2.70733e12i	1.55039	+	2.68536i
$466$	−3.89868e11	−	6.75271e11i	−0.382984	−	0.663349i
$467$	6.63460e11	−	1.14915e12i	0.645488	−	1.11802i	−0.338700	−	0.940894i	$-0.609987\pi$
$467$	6.63460e11	−	1.14915e12i	0.645488	−	1.11802i	0.984188	−	0.177124i	$-0.0566795\pi$
$468$	−1.21788e11			−0.117354
$469$		0			0
$470$	2.52524e11			0.238705
$471$	5.08018e11	−	8.79914e11i	0.475648	−	0.823846i
$472$	2.93522e11	+	5.08395e11i	0.272209	+	0.471479i
$473$	3.40340e11	+	5.89486e11i	0.312635	+	0.541500i
$474$	2.45869e11	−	4.25857e11i	0.223718	−	0.387491i
$475$	4.52257e11			0.407628
$476$		0			0
$477$	1.48723e11			0.131536
$478$	−5.73590e11	+	9.93488e11i	−0.502547	+	0.870436i
$479$	9.12671e10	+	1.58079e11i	0.0792144	+	0.137203i	0.902911	−	0.429827i	$-0.141425\pi$
$479$	9.12671e10	+	1.58079e11i	0.0792144	+	0.137203i	−0.823697	+	0.567031i	$0.808092\pi$
$480$	−1.69646e11	−	2.93836e11i	−0.145868	−	0.252650i
$481$	1.48746e11	−	2.57635e11i	0.126704	−	0.219458i
$482$	−1.02246e12			−0.862847
$483$		0			0
$484$	−5.12256e11			−0.424310
$485$	3.63602e11	−	6.29777e11i	0.298393	−	0.516831i
$486$	−2.13103e11	−	3.69105e11i	−0.173271	−	0.300114i
$487$	−8.68115e11	−	1.50362e12i	−0.699354	−	1.21132i	−0.968691	−	0.248270i	$-0.920138\pi$
$487$	−8.68115e11	−	1.50362e12i	−0.699354	−	1.21132i	0.269337	−	0.963046i	$-0.413195\pi$
$488$	−3.08522e11	+	5.34375e11i	−0.246262	+	0.426538i
$489$	−8.87823e11			−0.702161
$490$		0			0
$491$	1.43457e12			1.11392			0.556962	−	0.830538i	$-0.311967\pi$
$491$	1.43457e12			1.11392			0.556962	+	0.830538i	$0.311967\pi$
$492$	−1.83088e11	+	3.17118e11i	−0.140870	+	0.243994i
$493$	5.13716e11	+	8.89782e11i	0.391662	+	0.678379i
$494$	−6.74290e10	−	1.16790e11i	−0.0509419	−	0.0882340i
$495$	−1.24721e11	+	2.16023e11i	−0.0933719	+	0.161725i
$496$	−6.33163e11			−0.469730
$497$		0			0
$498$	−6.15268e11			−0.448263
$499$	1.00151e11	−	1.73467e11i	0.0723108	−	0.125246i	−0.827603	−	0.561314i	$-0.810296\pi$
$499$	1.00151e11	−	1.73467e11i	0.0723108	−	0.125246i	0.899914	+	0.436068i	$0.143629\pi$
$500$	−1.09248e12	−	1.89222e12i	−0.781712	−	1.35396i
$501$	3.23840e11	+	5.60906e11i	0.229647	+	0.397760i
$502$	7.93972e11	−	1.37520e12i	0.558005	−	0.966493i
$503$	2.58160e12			1.79818			0.899090	−	0.437764i	$-0.144229\pi$
$503$	2.58160e12			1.79818			0.899090	+	0.437764i	$0.144229\pi$
$504$		0			0
$505$	−9.90863e11			−0.677958
$506$	−2.26769e11	+	3.92776e11i	−0.153783	+	0.266359i
$507$	8.35183e10	+	1.44658e11i	0.0561366	+	0.0972314i
$508$	4.50451e11	+	7.80204e11i	0.300096	+	0.519782i
$509$	8.18518e11	−	1.41772e12i	0.540503	−	0.936179i	−0.458372	−	0.888761i	$-0.651567\pi$
$509$	8.18518e11	−	1.41772e12i	0.540503	−	0.936179i	0.998875	−	0.0474186i	$-0.0150995\pi$
$510$	2.97167e12			1.94507
$511$		0			0
$512$	6.87195e10			0.0441942
$513$	1.31171e11	−	2.27194e11i	0.0836197	−	0.144834i
$514$	1.04019e11	+	1.80166e11i	0.0657322	+	0.113851i
$515$	1.32889e12	+	2.30171e12i	0.832448	+	1.44184i
$516$	−5.59709e11	+	9.69444e11i	−0.347567	+	0.602004i
$517$	−1.11846e11			−0.0688517
$518$		0			0
$519$	−5.44362e11			−0.329333
$520$	−5.24508e11	+	9.08475e11i	−0.314584	+	0.544876i
$521$	−4.80212e11	−	8.31752e11i	−0.285538	−	0.494566i	0.687202	−	0.726467i	$-0.258839\pi$
$521$	−4.80212e11	−	8.31752e11i	−0.285538	−	0.494566i	−0.972739	+	0.231901i	$0.925506\pi$
$522$	−7.09155e10	−	1.22829e11i	−0.0418046	−	0.0724077i
$523$	8.35446e11	−	1.44704e12i	0.488271	−	0.845710i	−0.511638	−	0.859201i	$-0.670961\pi$
$523$	8.35446e11	−	1.44704e12i	0.488271	−	0.845710i	0.999909	+	0.0134909i	$0.00429442\pi$
$524$	9.73466e11			0.564066
$525$		0			0
$526$	5.25328e11			0.299223
$527$	2.77276e12	−	4.80255e12i	1.56590	−	2.71222i
$528$	7.51389e10	+	1.30144e11i	0.0420738	+	0.0728740i
$529$	−2.24945e11	−	3.89616e11i	−0.124889	−	0.216315i
$530$	6.40512e11	−	1.10940e12i	0.352603	−	0.610726i
$531$	7.09766e11			0.387427
$532$		0			0
$533$	1.13213e12			0.607611
$534$	−8.16212e11	+	1.41372e12i	−0.434377	+	0.752364i
$535$	−3.53744e12	−	6.12702e12i	−1.86680	−	3.23338i
$536$	−2.03758e11	−	3.52918e11i	−0.106628	−	0.184686i
$537$	4.10399e11	−	7.10832e11i	0.212972	−	0.368878i
$538$	−1.16841e12			−0.601280
$539$		0			0
$540$	−2.04067e12			−1.03276
$541$	−1.05117e12	+	1.82067e12i	−0.527575	+	0.913786i	0.471909	+	0.881647i	$0.343565\pi$
$541$	−1.05117e12	+	1.82067e12i	−0.527575	+	0.913786i	−0.999483	+	0.0321389i	$0.989768\pi$
$542$	7.06629e11	+	1.22392e12i	0.351718	+	0.609194i
$543$	2.46768e11	+	4.27415e11i	0.121812	+	0.210984i
$544$	−3.00937e11	+	5.21239e11i	−0.147327	+	0.255177i
$545$	−2.63448e12			−1.27912
$546$		0			0
$547$	1.37451e11			0.0656455			0.0328228	−	0.999461i	$-0.489550\pi$
$547$	1.37451e11			0.0656455			0.0328228	+	0.999461i	$0.489550\pi$
$548$	9.65499e11	−	1.67229e12i	0.457340	−	0.792136i
$549$	3.73018e11	+	6.46087e11i	0.175249	+	0.303540i
$550$	7.79077e11	+	1.34940e12i	0.363035	+	0.628795i
$551$	7.85261e10	−	1.36011e11i	0.0362938	−	0.0628626i
$552$	−7.45871e11			−0.341931
$553$		0			0
$554$	−1.87960e12			−0.847758
$555$	5.01025e11	−	8.67801e11i	0.224151	−	0.388241i
$556$	−1.33759e11	−	2.31678e11i	−0.0593592	−	0.102813i
$557$	−3.05883e11	−	5.29804e11i	−0.134650	−	0.233221i	0.790814	−	0.612057i	$-0.209658\pi$
$557$	−3.05883e11	−	5.29804e11i	−0.134650	−	0.233221i	−0.925464	+	0.378836i	$0.876324\pi$
$558$	−3.82763e11	+	6.62965e11i	−0.167138	+	0.289492i
$559$	3.46098e12			1.49915
$560$		0			0
$561$	−1.31620e12			−0.561032
$562$	2.81286e11	−	4.87202e11i	0.118942	−	0.206013i
$563$	7.86485e11	+	1.36223e12i	0.329916	+	0.571430i	0.982495	−	0.186290i	$-0.0596464\pi$
$563$	7.86485e11	+	1.36223e12i	0.329916	+	0.571430i	−0.652579	+	0.757720i	$0.726313\pi$
$564$	−9.19690e10	−	1.59295e11i	−0.0382724	−	0.0662897i
$565$	−8.89918e11	+	1.54138e12i	−0.367394	+	0.636345i
$566$	−8.05535e11			−0.329921
$567$		0			0
$568$	−8.24823e11			−0.332501
$569$	−1.61913e11	+	2.80441e11i	−0.0647554	+	0.112160i	−0.896585	−	0.442871i	$-0.853960\pi$
$569$	−1.61913e11	+	2.80441e11i	−0.0647554	+	0.112160i	0.831830	+	0.555030i	$0.187293\pi$
$570$	−2.27124e11	−	3.93390e11i	−0.0901209	−	0.156094i
$571$	−6.93754e11	−	1.20162e12i	−0.273113	−	0.473046i	0.696544	−	0.717514i	$-0.254720\pi$
$571$	−6.93754e11	−	1.20162e12i	−0.273113	−	0.473046i	−0.969657	+	0.244468i	$0.921387\pi$
$572$	2.32312e11	−	4.02376e11i	0.0907381	−	0.157163i
$573$	−1.36836e12			−0.530279
$574$		0			0
$575$	−7.73356e12			−2.95036
$576$	4.15427e10	−	7.19540e10i	0.0157251	−	0.0272367i
$577$	−2.21750e11	−	3.84083e11i	−0.0832862	−	0.144256i	0.821373	−	0.570391i	$-0.193208\pi$
$577$	−2.21750e11	−	3.84083e11i	−0.0832862	−	0.144256i	−0.904660	+	0.426135i	$0.859875\pi$
$578$	−1.68703e12	−	2.92203e12i	−0.628708	−	1.08895i
$579$	1.39643e12	−	2.41869e12i	0.516375	−	0.894388i
$580$	−1.22166e12			−0.448253
$581$		0			0
$582$	−5.29694e11			−0.191369
$583$	−2.83692e11	+	4.91369e11i	−0.101704	+	0.176157i
$584$	−9.53705e10	−	1.65187e11i	−0.0339278	−	0.0587647i
$585$	6.34157e11	+	1.09839e12i	0.223870	+	0.387754i
$586$	1.36272e12	−	2.36030e12i	0.477383	−	0.826851i
$587$	−3.22961e12			−1.12274			−0.561369	−	0.827565i	$-0.689725\pi$
$587$	−3.22961e12			−1.12274			−0.561369	+	0.827565i	$0.689725\pi$
$588$		0			0
$589$	−8.47682e11			−0.290211
$590$	3.05678e12	−	5.29449e12i	1.03856	−	1.79883i
$591$	−9.91452e11	−	1.71725e12i	−0.334294	−	0.579014i
$592$	1.01476e11	+	1.75762e11i	0.0339560	+	0.0588135i
$593$	−1.39338e12	+	2.41340e12i	−0.462724	+	0.801462i	−0.999096	−	0.0425200i	$-0.986461\pi$
$593$	−1.39338e12	+	2.41340e12i	−0.462724	+	0.801462i	0.536371	+	0.843982i	$0.319795\pi$
$594$	9.03841e11			0.297888
$595$		0			0
$596$	−9.38609e10			−0.0304703
$597$	−1.46529e11	+	2.53795e11i	−0.0472105	+	0.0817709i
$598$	1.15303e12	+	1.99711e12i	0.368711	+	0.638626i
$599$	−4.48074e11	−	7.76087e11i	−0.142210	−	0.246314i	0.786119	−	0.618075i	$-0.212087\pi$
$599$	−4.48074e11	−	7.76087e11i	−0.142210	−	0.246314i	−0.928328	+	0.371761i	$0.878754\pi$
$600$	−1.28124e12	+	2.21917e12i	−0.403598	+	0.699053i
$601$	2.34296e12			0.732536			0.366268	−	0.930509i	$-0.380635\pi$
$601$	2.34296e12			0.732536			0.366268	+	0.930509i	$0.380635\pi$
$602$		0			0
$603$	−4.92706e11			−0.151761
$604$	−6.88647e11	+	1.19277e12i	−0.210538	+	0.364662i
$605$	2.66735e12	+	4.61998e12i	0.809432	+	1.40198i
$606$	3.60872e11	+	6.25049e11i	0.108699	+	0.188273i
$607$	7.35311e11	−	1.27360e12i	0.219848	−	0.380788i	−0.734913	−	0.678161i	$-0.762777\pi$
$607$	7.35311e11	−	1.27360e12i	0.219848	−	0.380788i	0.954761	+	0.297373i	$0.0961106\pi$
$608$	9.20020e10			0.0273043
$609$		0			0
$610$	6.42597e12			1.87912
$611$	−2.84347e11	+	4.92504e11i	−0.0825398	+	0.142963i
$612$	3.63848e11	+	6.30204e11i	0.104843	+	0.181593i
$613$	5.88203e11	+	1.01880e12i	0.168250	+	0.291418i	0.937805	−	0.347163i	$-0.112855\pi$
$613$	5.88203e11	+	1.01880e12i	0.168250	+	0.291418i	−0.769555	+	0.638581i	$0.779522\pi$
$614$	−4.20709e11	+	7.28690e11i	−0.119460	+	0.206912i
$615$	3.81341e12			1.07492
$616$		0			0
$617$	6.76956e12			1.88052			0.940259	−	0.340461i	$-0.110583\pi$
$617$	6.76956e12			1.88052			0.940259	+	0.340461i	$0.110583\pi$
$618$	9.67964e11	−	1.67656e12i	0.266938	−	0.462351i
$619$	−2.94519e12	−	5.10121e12i	−0.806315	−	1.39658i	−0.915399	−	0.402547i	$-0.868125\pi$
$619$	−2.94519e12	−	5.10121e12i	−0.806315	−	1.39658i	0.109084	−	0.994033i	$-0.465208\pi$
$620$	3.29692e12	+	5.71043e12i	0.896078	+	1.55205i
$621$	−2.24301e12	+	3.88501e12i	−0.605228	+	1.04829i
$622$	9.73764e11			0.260854
$623$		0			0
$624$	7.64102e11			0.201753
$625$	−6.34346e12	+	1.09872e13i	−1.66290	+	2.88023i
$626$	1.50792e12	+	2.61179e12i	0.392458	+	0.679757i
$627$	1.00596e11	+	1.74238e11i	0.0259943	+	0.0450234i
$628$	1.07154e12	−	1.85596e12i	0.274909	−	0.476156i
$629$	−1.77754e12			−0.452786
$630$		0			0
$631$	2.08173e12			0.522748			0.261374	−	0.965238i	$-0.415824\pi$
$631$	2.08173e12			0.522748			0.261374	+	0.965238i	$0.415824\pi$
$632$	5.18598e11	−	8.98239e11i	0.129302	−	0.223957i
$633$	−9.62790e11	−	1.66760e12i	−0.238350	−	0.412834i
$634$	1.53586e11	+	2.66019e11i	0.0377530	+	0.0653901i
$635$	4.69105e12	−	8.12514e12i	1.14495	−	1.98312i
$636$	−9.33097e11			−0.226136
$637$		0			0
$638$	5.41090e11			0.129293
$639$	−4.98626e11	+	8.63646e11i	−0.118310	+	0.204919i
$640$	−3.57827e11	−	6.19774e11i	−0.0843068	−	0.146024i
$641$	1.02969e12	+	1.78347e12i	0.240904	+	0.417258i	0.960972	−	0.276646i	$-0.0892228\pi$
$641$	1.02969e12	+	1.78347e12i	0.240904	+	0.417258i	−0.720068	+	0.693903i	$0.755889\pi$
$642$	−2.57667e12	+	4.46292e12i	−0.598619	+	1.03684i
$643$	−3.54773e12			−0.818468			−0.409234	−	0.912429i	$-0.634204\pi$
$643$	−3.54773e12			−0.818468			−0.409234	+	0.912429i	$0.634204\pi$
$644$		0			0
$645$	1.16578e13			2.65214
$646$	−4.02896e11	+	6.97837e11i	−0.0910221	+	0.157655i
$647$	4.85324e11	+	8.40607e11i	0.108884	+	0.188592i	0.915318	−	0.402731i	$-0.131939\pi$
$647$	4.85324e11	+	8.40607e11i	0.108884	+	0.188592i	−0.806435	+	0.591323i	$0.798606\pi$
$648$	5.43580e11	+	9.41508e11i	0.121109	+	0.209767i
$649$	−1.35389e12	+	2.34501e12i	−0.299559	+	0.518851i
$650$	7.92259e12			1.74083
$651$		0			0
$652$	−1.87264e12			−0.405826
$653$	1.92552e12	−	3.33510e12i	0.414418	−	0.717793i	−0.580949	−	0.813940i	$-0.697319\pi$
$653$	1.92552e12	−	3.33510e12i	0.414418	−	0.717793i	0.995367	+	0.0961471i	$0.0306519\pi$
$654$	9.59477e11	+	1.66186e12i	0.205085	+	0.355218i
$655$	−5.06890e12	−	8.77959e12i	−1.07604	−	1.86375i
$656$	−3.86179e11	+	6.68881e11i	−0.0814181	+	0.141020i
$657$	−2.30615e11			−0.0482886
$658$		0			0
$659$	−6.97320e12			−1.44028			−0.720141	−	0.693827i	$-0.755923\pi$
$659$	−6.97320e12			−1.44028			−0.720141	+	0.693827i	$0.755923\pi$
$660$	7.82505e11	−	1.35534e12i	0.160524	−	0.278036i
$661$	−1.89428e12	−	3.28098e12i	−0.385955	−	0.668494i	0.605946	−	0.795506i	$-0.292795\pi$
$661$	−1.89428e12	−	3.28098e12i	−0.385955	−	0.668494i	−0.991901	+	0.127012i	$0.959461\pi$
$662$	−2.48413e12	−	4.30263e12i	−0.502704	−	0.870709i
$663$	−3.34617e12	+	5.79573e12i	−0.672569	+	1.16492i
$664$	−1.29775e12			−0.259081
$665$		0			0
$666$	2.45380e11			0.0483287
$667$	−1.34279e12	+	2.32578e12i	−0.262689	+	0.454991i
$668$	6.83058e11	+	1.18309e12i	0.132728	+	0.229892i
$669$	−1.94858e12	−	3.37504e12i	−0.376098	−	0.651420i
$670$	−2.12196e12	+	3.67534e12i	−0.406818	+	0.704629i
$671$	−2.84615e12			−0.542010
$672$		0			0
$673$	5.11087e12			0.960344			0.480172	−	0.877174i	$-0.340574\pi$
$673$	5.11087e12			0.960344			0.480172	+	0.877174i	$0.340574\pi$
$674$	−2.63982e12	+	4.57229e12i	−0.492724	+	0.853424i
$675$	7.70597e12	+	1.33471e13i	1.42876	+	2.47469i
$676$	1.76161e11	+	3.05120e11i	0.0324451	+	0.0561966i
$677$	2.81373e12	−	4.87353e12i	0.514795	−	0.891650i	−0.485058	−	0.874482i	$-0.661201\pi$
$677$	2.81373e12	−	4.87353e12i	0.514795	−	0.891650i	0.999853	−	0.0171685i	$-0.00546517\pi$
$678$	1.29643e12			0.235622
$679$		0			0
$680$	6.26800e12			1.12419
$681$	−2.77173e11	+	4.80078e11i	−0.0493843	+	0.0855362i
$682$	−1.46025e12	−	2.52923e12i	−0.258463	−	0.447671i
$683$	−1.20279e12	−	2.08330e12i	−0.211494	−	0.366318i	0.740688	−	0.671849i	$-0.234500\pi$
$683$	−1.20279e12	−	2.08330e12i	−0.211494	−	0.366318i	−0.952182	+	0.305530i	$0.901166\pi$
$684$	5.56175e10	−	9.63324e10i	0.00971537	−	0.0168275i
$685$	−2.01097e13			−3.48977
$686$		0			0
$687$	−1.60463e12			−0.274834
$688$	−1.18057e12	+	2.04480e12i	−0.200882	+	0.347939i
$689$	1.44246e12	+	2.49842e12i	0.243847	+	0.422355i
$690$	3.88380e12	+	6.72694e12i	0.652283	+	1.12979i
$691$	1.07262e12	−	1.85784e12i	0.178976	−	0.309996i	−0.762554	−	0.646925i	$-0.776055\pi$
$691$	1.07262e12	−	1.85784e12i	0.178976	−	0.309996i	0.941530	+	0.336929i	$0.109388\pi$
$692$	−1.14820e12			−0.190344
$693$		0			0
$694$	−5.69065e12			−0.931203
$695$	−1.39299e12	+	2.41273e12i	−0.226473	+	0.392262i
$696$	4.44927e11	+	7.70636e11i	0.0718700	+	0.124482i
$697$	−3.38232e12	−	5.85835e12i	−0.542834	−	0.940216i
$698$	−2.09505e12	+	3.62873e12i	−0.334075	+	0.578635i
$699$	5.91480e12			0.937114
$700$		0			0
$701$	3.57696e12			0.559478			0.279739	−	0.960076i	$-0.409752\pi$
$701$	3.57696e12			0.559478			0.279739	+	0.960076i	$0.409752\pi$
$702$	2.29784e12	−	3.97997e12i	0.357110	−	0.618533i
$703$	1.35857e11	+	2.35311e11i	0.0209789	+	0.0363365i
$704$	1.58487e11	+	2.74507e11i	0.0243173	+	0.0421188i
$705$	−9.57777e11	+	1.65892e12i	−0.146020	+	0.252915i
$706$	1.83604e12			0.278138
$707$		0			0
$708$	−4.45311e12			−0.666060
$709$	−2.53384e12	+	4.38873e12i	−0.376592	+	0.652276i	−0.990564	−	0.137052i	$-0.956237\pi$
$709$	−2.53384e12	+	4.38873e12i	−0.376592	+	0.652276i	0.613972	+	0.789328i	$0.289571\pi$
$710$	4.29490e12	+	7.43899e12i	0.634294	+	1.09863i
$711$	−6.27012e11	−	1.08602e12i	−0.0920158	−	0.159376i
$712$	−1.72159e12	+	2.98189e12i	−0.251056	+	0.434842i
$713$	1.44953e13			2.10051
$714$		0			0
$715$	−4.83866e12			−0.692385
$716$	8.65633e11	−	1.49932e12i	0.123091	−	0.213199i
$717$	−4.35105e12	−	7.53624e12i	−0.614834	−	1.06492i
$718$	−1.48008e12	−	2.56357e12i	−0.207838	−	0.359986i
$719$	−6.90281e12	+	1.19560e13i	−0.963265	+	1.66842i	−0.249059	+	0.968488i	$0.580121\pi$
$719$	−6.90281e12	+	1.19560e13i	−0.963265	+	1.66842i	−0.714206	+	0.699936i	$0.753212\pi$
$720$	−8.65261e11			−0.119992
$721$		0			0
$722$	−5.03983e12			−0.690237
$723$	3.87800e12	−	6.71689e12i	0.527819	−	0.914210i
$724$	5.20495e11	+	9.01524e11i	0.0704033	+	0.121942i
$725$	4.61323e12	+	7.99034e12i	0.620131	+	1.07410i
$726$	1.94289e12	−	3.36519e12i	0.259558	−	0.449568i
$727$	−1.39068e13			−1.84638			−0.923190	−	0.384343i	$-0.874428\pi$
$727$	−1.39068e13			−1.84638			−0.923190	+	0.384343i	$0.874428\pi$
$728$		0			0
$729$	8.45730e12			1.10907
$730$	−9.93200e11	+	1.72027e12i	−0.129445	+	0.224205i
$731$	−1.03399e13	−	1.79092e13i	−1.33933	−	2.31979i
$732$	−2.34033e12	−	4.05358e12i	−0.301285	−	0.521842i
$733$	−3.46688e12	+	6.00482e12i	−0.443579	+	0.768302i	−0.997952	−	0.0639666i	$-0.979625\pi$
$733$	−3.46688e12	+	6.00482e12i	−0.443579	+	0.768302i	0.554373	+	0.832269i	$0.312958\pi$
$734$	−2.63255e12			−0.334769
$735$		0			0
$736$	−1.57323e12			−0.197625
$737$	9.39845e11	−	1.62786e12i	0.117342	−	0.203242i
$738$	4.66910e11	+	8.08711e11i	0.0579401	+	0.100355i
$739$	1.20918e12	+	2.09435e12i	0.149138	+	0.258315i	0.930909	−	0.365251i	$-0.119017\pi$
$739$	1.20918e12	+	2.09435e12i	0.149138	+	0.258315i	−0.781771	+	0.623566i	$0.785683\pi$
$740$	1.05679e12	−	1.83041e12i	0.129552	−	0.224391i
$741$	1.02298e12			0.124648
$742$		0			0
$743$	−1.07681e13			−1.29626			−0.648129	−	0.761531i	$-0.724448\pi$
$743$	−1.07681e13			−1.29626			−0.648129	+	0.761531i	$0.724448\pi$
$744$	2.40147e12	−	4.15947e12i	0.287342	−	0.497691i
$745$	4.88739e11	+	8.46522e11i	0.0581265	+	0.100678i
$746$	5.08898e11	+	8.81437e11i	0.0601597	+	0.104200i
$747$	−7.84525e11	+	1.35884e12i	−0.0921858	+	0.159671i
$748$	−2.77619e12			−0.324258
$749$		0			0
$750$	1.65742e13			1.91275
$751$	1.18135e11	−	2.04616e11i	0.0135519	−	0.0234725i	−0.859170	−	0.511690i	$-0.829020\pi$
$751$	1.18135e11	−	2.04616e11i	0.0135519	−	0.0234725i	0.872722	+	0.488218i	$0.162353\pi$
$752$	−1.93986e11	−	3.35993e11i	−0.0221202	−	0.0383133i
$753$	6.02278e12	+	1.04318e13i	0.682684	+	1.18244i
$754$	1.37561e12	−	2.38263e12i	0.154998	−	0.268464i
$755$	1.43433e13			1.60653
$756$		0			0
$757$	9.94250e12			1.10043			0.550217	−	0.835022i	$-0.314545\pi$
$757$	9.94250e12			1.10043			0.550217	+	0.835022i	$0.314545\pi$
$758$	6.02976e11	−	1.04439e12i	0.0663420	−	0.114908i
$759$	−1.72019e12	−	2.97946e12i	−0.188143	−	0.325873i
$760$	−4.79060e11	−	8.29757e11i	−0.0520869	−	0.0902172i
$761$	−6.00882e12	+	1.04076e13i	−0.649469	+	1.12491i	0.333781	+	0.942651i	$0.391676\pi$
$761$	−6.00882e12	+	1.04076e13i	−0.649469	+	1.12491i	−0.983250	+	0.182263i	$0.941658\pi$
$762$	−6.83391e12			−0.734298
$763$		0			0
$764$	−2.88621e12			−0.306484
$765$	3.78916e12	−	6.56302e12i	0.400006	−	0.692831i
$766$	−3.13244e12	−	5.42555e12i	−0.328741	−	0.569396i
$767$	6.88399e12	+	1.19234e13i	0.718226	+	1.24400i
$768$	−2.60641e11	+	4.51443e11i	−0.0270344	+	0.0468249i
$769$	8.18420e12			0.843933			0.421966	−	0.906611i	$-0.361340\pi$
$769$	8.18420e12			0.843933			0.421966	+	0.906611i	$0.361340\pi$
$770$		0			0
$771$	−1.57810e12			−0.160838
$772$	2.94542e12	−	5.10161e12i	0.298448	−	0.516927i
$773$	4.49987e12	+	7.79400e12i	0.453307	+	0.785150i	0.998589	−	0.0531023i	$-0.0169110\pi$
$773$	4.49987e12	+	7.79400e12i	0.453307	+	0.785150i	−0.545283	+	0.838252i	$0.683578\pi$
$774$	1.42736e12	+	2.47227e12i	0.142955	+	0.247606i
$775$	2.48997e13	−	4.31275e13i	2.47934	−	4.29434i
$776$	−1.11726e12			−0.110605
$777$		0			0
$778$	−6.50188e12			−0.636255
$779$	−5.17018e11	+	8.95502e11i	−0.0503022	+	0.0871260i
$780$	−3.97873e12	−	6.89136e12i	−0.384874	−	0.666621i
$781$	−1.90227e12	−	3.29484e12i	−0.182955	−	0.316887i
$782$	6.88950e12	−	1.19330e13i	0.658806	−	1.14109i
$783$	5.35200e12			0.508848
$784$		0			0
$785$	−2.23182e13			−2.09772
$786$	−3.69218e12	+	6.39505e12i	−0.345050	+	0.597644i
$787$	−7.72990e11	−	1.33886e12i	−0.0718270	−	0.124408i	0.827875	−	0.560913i	$-0.189550\pi$
$787$	−7.72990e11	−	1.33886e12i	−0.0718270	−	0.124408i	−0.899702	+	0.436505i	$0.856216\pi$
$788$	−2.09122e12	−	3.62210e12i	−0.193211	−	0.334651i
$789$	−1.99247e12	+	3.45107e12i	−0.183040	+	0.317035i
$790$	−1.08015e13			−0.986648
$791$		0			0
$792$	3.83236e11			0.0346101
$793$	−7.23578e12	+	1.25327e13i	−0.649765	+	1.12543i
$794$	−1.98418e12	−	3.43670e12i	−0.177169	−	0.306867i
$795$	4.85869e12	+	8.41550e12i	0.431387	+	0.747185i
$796$	−3.09066e11	+	5.35317e11i	−0.0272861	+	0.0472609i
$797$	−6.94374e12			−0.609581			−0.304790	−	0.952419i	$-0.598586\pi$
$797$	−6.94374e12			−0.609581			−0.304790	+	0.952419i	$0.598586\pi$
$798$		0			0
$799$	3.39802e12			0.294961
$800$	−2.70245e12	+	4.68078e12i	−0.233267	+	0.404030i
$801$	2.08149e12	+	3.60525e12i	0.178661	+	0.309449i
$802$	−4.21197e12	−	7.29535e12i	−0.359501	−	0.622675i
$803$	4.39903e11	−	7.61934e11i	0.0373368	−	0.0646692i
$804$	3.09126e12			0.260906
$805$		0			0
$806$	−1.48496e13			−1.23939
$807$	4.43158e12	−	7.67573e12i	0.367814	−	0.637072i
$808$	7.61169e11	+	1.31838e12i	0.0628246	+	0.108815i
$809$	−6.01049e12	−	1.04105e13i	−0.493335	−	0.854481i	0.506636	−	0.862160i	$-0.330889\pi$
$809$	−6.01049e12	−	1.04105e13i	−0.493335	−	0.854481i	−0.999971	+	0.00767957i	$0.997555\pi$
$810$	5.66091e12	−	9.80499e12i	0.462066	−	0.800321i
$811$	−3.73568e11			−0.0303232			−0.0151616	−	0.999885i	$-0.504826\pi$
$811$	−3.73568e11			−0.0303232			−0.0151616	+	0.999885i	$0.504826\pi$
$812$		0			0
$813$	−1.07205e13			−0.860610
$814$	−4.68066e11	+	8.10714e11i	−0.0373678	+	0.0647229i
$815$	9.75095e12	+	1.68891e13i	0.774172	+	1.34091i
$816$	−2.28280e12	−	3.95393e12i	−0.180245	−	0.312193i
$817$	−1.58055e12	+	2.73759e12i	−0.124110	+	0.214966i
$818$	1.24216e13			0.970039
$819$		0			0
$820$	8.04343e12			0.621268
$821$	5.55685e12	−	9.62475e12i	0.426859	−	0.739342i	−0.569733	−	0.821830i	$-0.692953\pi$
$821$	5.55685e12	−	9.62475e12i	0.426859	−	0.739342i	0.996592	+	0.0824882i	$0.0262867\pi$
$822$	7.32393e12	+	1.26854e13i	0.559527	+	0.969128i
$823$	3.47686e12	+	6.02210e12i	0.264173	+	0.457561i	0.967347	−	0.253457i	$-0.0815677\pi$
$823$	3.47686e12	+	6.02210e12i	0.264173	+	0.457561i	−0.703174	+	0.711018i	$0.748234\pi$
$824$	2.04168e12	−	3.53629e12i	0.154282	−	0.267224i
$825$	−1.18196e13			−0.888300
$826$		0			0
$827$	−2.17166e12			−0.161442			−0.0807211	−	0.996737i	$-0.525722\pi$
$827$	−2.17166e12			−0.161442			−0.0807211	+	0.996737i	$0.525722\pi$
$828$	−9.51056e11	+	1.64728e12i	−0.0703185	+	0.121795i
$829$	−3.06803e12	−	5.31398e12i	−0.225613	−	0.390773i	0.730890	−	0.682495i	$-0.239105\pi$
$829$	−3.06803e12	−	5.31398e12i	−0.225613	−	0.390773i	−0.956503	+	0.291722i	$0.905772\pi$
$830$	6.75749e12	+	1.17043e13i	0.494235	+	0.856041i
$831$	7.12899e12	−	1.23478e13i	0.518589	−	0.898223i
$832$	1.61168e12			0.116607
$833$		0			0
$834$	2.02930e12			0.145244
$835$	7.11345e12	−	1.23209e13i	0.506397	−	0.877106i
$836$	2.12183e11	+	3.67511e11i	0.0150239	+	0.0260221i
$837$	−1.44436e13	−	2.50170e13i	−1.01721	−	1.76186i
$838$	−6.84247e12	+	1.18515e13i	−0.479308	+	0.830186i
$839$	1.85233e13			1.29059			0.645297	−	0.763932i	$-0.276734\pi$
$839$	1.85233e13			1.29059			0.645297	+	0.763932i	$0.276734\pi$
$840$		0			0
$841$	−1.13031e13			−0.779143
$842$	−6.78479e12	+	1.17516e13i	−0.465192	+	0.805736i
$843$	2.13373e12	+	3.69574e12i	0.145518	+	0.252044i
$844$	−2.03076e12	−	3.51738e12i	−0.137758	−	0.238605i
$845$	1.83456e12	−	3.17755e12i	0.123788	−	0.214406i
$846$	−4.69077e11			−0.0314831
$847$		0			0
$848$	−1.96813e12			−0.130699
$849$	3.05525e12	−	5.29185e12i	0.201819	−	0.349561i
$850$	−2.36692e13	−	4.09963e13i	−1.55525	−	2.69376i
$851$	−2.32314e12	−	4.02380e12i	−0.151842	−	0.262999i
$852$	3.12840e12	−	5.41855e12i	0.203397	−	0.352294i
$853$	2.20104e13			1.42350			0.711750	−	0.702433i	$-0.247903\pi$
$853$	2.20104e13			1.42350			0.711750	+	0.702433i	$0.247903\pi$
$854$		0			0
$855$	−1.15842e12			−0.0741339
$856$	−5.43483e12	+	9.41340e12i	−0.345982	+	0.599259i
$857$	2.88538e12	+	4.99762e12i	0.182721	+	0.316482i	0.942806	−	0.333341i	$-0.108176\pi$
$857$	2.88538e12	+	4.99762e12i	0.182721	+	0.316482i	−0.760085	+	0.649823i	$0.774843\pi$
$858$	1.76224e12	+	3.05228e12i	0.111012	+	0.192279i
$859$	−6.34305e12	+	1.09865e13i	−0.397493	+	0.688477i	−0.993416	−	0.114564i	$-0.963453\pi$
$859$	−6.34305e12	+	1.09865e13i	−0.397493	+	0.688477i	0.595923	+	0.803041i	$0.296786\pi$
$860$	2.45891e13			1.53285
$861$		0			0
$862$	−3.75566e12			−0.231688
$863$	1.30439e13	−	2.25928e13i	0.800498	−	1.38650i	−0.118790	−	0.992919i	$-0.537902\pi$
$863$	1.30439e13	−	2.25928e13i	0.800498	−	1.38650i	0.919289	−	0.393584i	$-0.128765\pi$
$864$	1.56761e12	+	2.71519e12i	0.0957034	+	0.165763i
$865$	5.97873e12	+	1.03555e13i	0.363108	+	0.628922i
$866$	−1.82355e12	+	3.15847e12i	−0.110176	+	0.190830i
$867$	2.55945e13			1.53837
$868$		0			0
$869$	4.78414e12			0.284587
$870$	4.63353e12	−	8.02550e12i	0.274205	−	0.474937i
$871$	−4.77874e12	−	8.27702e12i	−0.281340	−	0.487295i
$872$	2.02378e12	+	3.50528e12i	0.118533	+	0.205305i
$873$	−6.75410e11	+	1.16984e12i	−0.0393553	+	0.0681654i
$874$	−2.10625e12			−0.122098
$875$		0			0
$876$	1.44689e12			0.0830171
$877$	5.34707e12	−	9.26140e12i	0.305224	−	0.528663i	−0.672088	−	0.740472i	$-0.734602\pi$
$877$	5.34707e12	−	9.26140e12i	0.305224	−	0.528663i	0.977311	+	0.211809i	$0.0679355\pi$
$878$	−5.87295e12	−	1.01722e13i	−0.333527	−	0.577685i
$879$	1.03371e13	+	1.79044e13i	0.584048	+	1.01160i
$880$	1.65050e12	−	2.85875e12i	0.0927776	−	0.160696i
$881$	−2.77622e13			−1.55261			−0.776304	−	0.630359i	$-0.782908\pi$
$881$	−2.77622e13			−1.55261			−0.776304	+	0.630359i	$0.782908\pi$
$882$		0			0
$883$	2.89461e13			1.60239			0.801193	−	0.598407i	$-0.204199\pi$
$883$	2.89461e13			1.60239			0.801193	+	0.598407i	$0.204199\pi$
$884$	−7.05790e12	+	1.22246e13i	−0.388723	+	0.673288i
$885$	2.31876e13	+	4.01621e13i	1.27061	+	2.20076i
$886$	−1.07520e13	−	1.86230e13i	−0.586189	−	1.01531i
$887$	−3.16844e12	+	5.48790e12i	−0.171866	+	0.297680i	−0.939072	−	0.343720i	$-0.888313\pi$
$887$	−3.16844e12	+	5.48790e12i	−0.171866	+	0.297680i	0.767206	+	0.641400i	$0.221646\pi$
$888$	−1.53952e12			−0.0830861
$889$		0			0
$890$	3.58578e13			1.91570
$891$	−2.50730e12	+	4.34277e12i	−0.133277	+	0.230843i
$892$	−4.11004e12	−	7.11880e12i	−0.217372	−	0.376500i
$893$	−2.59709e11	−	4.49829e11i	−0.0136664	−	0.0236710i
$894$	3.55997e11	−	6.16605e11i	0.0186392	−	0.0322841i
$895$	−1.80296e13			−0.939254
$896$		0			0
$897$	−1.74930e13			−0.902189
$898$	2.88810e12	−	5.00234e12i	0.148207	−	0.256702i
$899$	−8.64674e12	−	1.49766e13i	−0.441503	−	0.764706i
$900$	3.26740e12	+	5.65930e12i	0.166001	+	0.287522i
$901$	8.61888e12	−	1.49283e13i	0.435701	−	0.754657i
$902$	−3.56255e12			−0.179197
$903$		0			0
$904$	2.73450e12			0.136182
$905$	5.42050e12	−	9.38859e12i	0.268609	−	0.465245i
$906$	−5.22382e12	−	9.04793e12i	−0.257580	−	0.446141i
$907$	−1.34446e13	−	2.32867e13i	−0.659651	−	1.14255i	−0.980706	−	0.195489i	$-0.937371\pi$
$907$	−1.34446e13	−	2.32867e13i	−0.659651	−	1.14255i	0.321055	−	0.947061i	$-0.395963\pi$
$908$	−5.84627e11	+	1.01260e12i	−0.0285425	+	0.0494371i
$909$	1.84058e12			0.0894166
$910$		0			0
$911$	1.68170e13			0.808940			0.404470	−	0.914551i	$-0.367456\pi$
$911$	1.68170e13			0.808940			0.404470	+	0.914551i	$0.367456\pi$
$912$	−3.48947e11	+	6.04394e11i	−0.0167025	+	0.0289297i
$913$	−2.99299e12	−	5.18401e12i	−0.142556	−	0.246915i
$914$	−6.78543e12	−	1.17527e13i	−0.321603	−	0.557032i
$915$	−2.43725e13	+	4.22145e13i	−1.14949	+	1.99098i
$916$	−3.38457e12			−0.158845
$917$		0			0
$918$	−2.74597e13			−1.27616
$919$	−1.77032e13	+	3.06628e13i	−0.818713	+	1.41805i	0.0879175	+	0.996128i	$0.471979\pi$
$919$	−1.77032e13	+	3.06628e13i	−0.818713	+	1.41805i	−0.906631	+	0.421925i	$0.861355\pi$
$920$	8.19190e12	+	1.41888e13i	0.376998	+	0.652980i
$921$	−3.19135e12	−	5.52758e12i	−0.146152	−	0.253143i
$922$	−1.66927e12	+	2.89126e12i	−0.0760741	+	0.131764i
$923$	−1.93446e13			−0.877309
$924$		0			0
$925$	−1.59626e13			−0.716910
$926$	4.67884e12	−	8.10399e12i	0.209117	−	0.362201i
$927$	−2.46849e12	−	4.27555e12i	−0.109792	−	0.190166i
$928$	9.38462e11	+	1.62546e12i	0.0415385	+	0.0719468i
$929$	−1.29064e13	+	2.23546e13i	−0.568506	+	0.984681i	0.428208	+	0.903680i	$0.359145\pi$
$929$	−1.29064e13	+	2.23546e13i	−0.568506	+	0.984681i	−0.996714	+	0.0810010i	$0.974188\pi$
$930$	−5.00185e13			−2.19259
$931$		0			0
$932$	1.24758e13			0.541622
$933$	−3.69331e12	+	6.39700e12i	−0.159569	+	0.276382i
$934$	1.06154e13	+	1.83863e13i	0.456429	+	0.790559i
$935$	1.44558e13	+	2.50381e13i	0.618570	+	1.07140i
$936$	9.74302e11	−	1.68754e12i	0.0414909	−	0.0718643i
$937$	2.58007e13			1.09346			0.546730	−	0.837309i	$-0.315872\pi$
$937$	2.58007e13			1.09346			0.546730	+	0.837309i	$0.315872\pi$
$938$		0			0
$939$	−2.28770e13			−0.960294
$940$	−2.02019e12	+	3.49907e12i	−0.0843950	+	0.146176i
$941$	1.66790e12	+	2.88888e12i	0.0693451	+	0.120109i	0.898613	−	0.438742i	$-0.144576\pi$
$941$	1.66790e12	+	2.88888e12i	0.0693451	+	0.120109i	−0.829268	+	0.558851i	$0.811242\pi$
$942$	8.12829e12	+	1.40786e13i	0.336334	+	0.582547i
$943$	8.84098e12	−	1.53130e13i	0.364081	−	0.630606i
$944$	−9.39271e12			−0.384961
$945$		0			0
$946$	−1.08909e13			−0.442133
$947$	−4.74470e12	+	8.21806e12i	−0.191705	+	0.332043i	−0.945815	−	0.324705i	$-0.894735\pi$
$947$	−4.74470e12	+	8.21806e12i	−0.191705	+	0.332043i	0.754110	+	0.656748i	$0.228068\pi$
$948$	3.93390e12	+	6.81371e12i	0.158192	+	0.273997i
$949$	−2.23673e12	−	3.87413e12i	−0.0895191	−	0.155052i
$950$	−3.61806e12	+	6.26666e12i	−0.144118	+	0.249620i
$951$	−2.33010e12			−0.0923767
$952$		0			0
$953$	9.71866e12			0.381670			0.190835	−	0.981622i	$-0.438880\pi$
$953$	9.71866e12			0.381670			0.190835	+	0.981622i	$0.438880\pi$
$954$	−1.18979e12	+	2.06077e12i	−0.0465052	+	0.0805493i
$955$	1.50287e13	+	2.60304e13i	0.584663	+	1.01267i
$956$	−9.17745e12	−	1.58958e13i	−0.355354	−	0.615491i
$957$	−2.05226e12	+	3.55461e12i	−0.0790911	+	0.136990i
$958$	−2.92055e12			−0.112026
$959$		0			0
$960$	5.42869e12			0.206288
$961$	−3.34505e13	+	5.79380e13i	−1.26517	+	2.19133i
$962$	2.37993e12	+	4.12216e12i	0.0895934	+	0.155180i
$963$	6.57098e12	+	1.13813e13i	0.246214	+	0.426454i
$964$	8.17966e12	−	1.41676e13i	0.305062	−	0.528384i
$965$	−6.13479e13			−2.27733
$966$		0			0
$967$	3.55171e13			1.30623			0.653113	−	0.757260i	$-0.273463\pi$
$967$	3.55171e13			1.30623			0.653113	+	0.757260i	$0.273463\pi$
$968$	4.09805e12	−	7.09803e12i	0.150016	−	0.259836i
$969$	−3.05623e12	−	5.29354e12i	−0.111360	−	0.192881i
$970$	5.81763e12	+	1.00764e13i	0.210995	+	0.365455i
$971$	−5.55055e12	+	9.61384e12i	−0.200378	+	0.347064i	−0.948650	−	0.316327i	$-0.897550\pi$
$971$	−5.55055e12	+	9.61384e12i	−0.200378	+	0.347064i	0.748272	+	0.663392i	$0.230884\pi$
$972$	6.81929e12			0.245042
$973$		0			0
$974$	2.77797e13			0.989036
$975$	−3.00490e13	+	5.20463e13i	−1.06490	+	1.84446i
$976$	−4.93635e12	−	8.55001e12i	−0.174133	−	0.301608i
$977$	1.47098e13	+	2.54780e13i	0.516511	+	0.894624i	0.999816	+	0.0191719i	$0.00610299\pi$
$977$	1.47098e13	+	2.54780e13i	0.516511	+	0.894624i	−0.483305	+	0.875452i	$0.660564\pi$
$978$	7.10258e12	−	1.23020e13i	0.248251	−	0.429984i
$979$	−1.58819e13			−0.552562
$980$		0			0
$981$	4.89370e12			0.168704
$982$	−1.14766e13	+	1.98780e13i	−0.393832	+	0.682136i
$983$	2.22871e13	+	3.86023e13i	0.761310	+	1.31863i	0.942175	+	0.335120i	$0.108777\pi$
$983$	2.22871e13	+	3.86023e13i	0.761310	+	1.31863i	−0.180865	+	0.983508i	$0.557890\pi$
$984$	−2.92941e12	−	5.07389e12i	−0.0996099	−	0.172529i
$985$	−2.17782e13	+	3.77210e13i	−0.737156	+	1.27679i
$986$	−1.64389e13			−0.553894
$987$		0			0
$988$	2.15773e12			0.0720428
$989$	2.70273e13	−	4.68126e13i	0.898294	−	1.55589i
$990$	−1.99554e12	−	3.45637e12i	−0.0660239	−	0.114357i
$991$	2.45153e13	+	4.24617e13i	0.807430	+	1.39851i	0.914638	+	0.404274i	$0.132476\pi$
$991$	2.45153e13	+	4.24617e13i	0.807430	+	1.39851i	−0.107208	+	0.994237i	$0.534191\pi$
$992$	5.06530e12	−	8.77336e12i	0.166074	−	0.287649i
$993$	3.76874e13			1.23005
$994$		0			0
$995$	6.43729e12			0.208209
$996$	4.92215e12	−	8.52541e12i	0.158485	−	0.274504i
$997$	−2.47416e13	−	4.28537e13i	−0.793047	−	1.37360i	−0.924072	−	0.382219i	$-0.875160\pi$
$997$	−2.47416e13	−	4.28537e13i	−0.793047	−	1.37360i	0.131025	−	0.991379i	$-0.458173\pi$
$998$	1.60242e12	+	2.77547e12i	0.0511315	+	0.0885623i
$999$	−4.62971e12	+	8.01890e12i	−0.147065	+	0.254724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.n.79.3		12
7.2	even	3		98.10.a.l.1.4	yes	6
7.3	odd	6	inner	98.10.c.n.67.4		12
7.4	even	3	inner	98.10.c.n.67.3		12
7.5	odd	6		98.10.a.l.1.3	✓	6
7.6	odd	2	inner	98.10.c.n.79.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.l.1.3	✓	6	7.5	odd	6
98.10.a.l.1.4	yes	6	7.2	even	3
98.10.c.n.67.3		12	7.4	even	3	inner
98.10.c.n.67.4		12	7.3	odd	6	inner
98.10.c.n.79.3		12	1.1	even	1	trivial
98.10.c.n.79.4		12	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-60.6851 - 105.110i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1333.01 + 2308.84i) q^{5} +1941.92 q^{6} +4096.00 q^{8} +(2476.14 - 4288.79i) q^{9} +O(q^{10})\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-60.6851 - 105.110i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1333.01 + 2308.84i) q^{5} +1941.92 q^{6} +4096.00 q^{8} +(2476.14 - 4288.79i) q^{9} +(-21328.1 - 36941.4i) q^{10} +(9446.53 + 16361.9i) q^{11} +(-15535.4 + 26908.1i) q^{12} +96063.7 q^{13} +323575. q^{15} +(-32768.0 + 56755.8i) q^{16} +(-286996. - 497092. i) q^{17} +(39618.2 + 68620.7i) q^{18} +(-43870.0 + 75985.0i) q^{19} +682500. q^{20} -302289. q^{22} +(750174. - 1.29934e6i) q^{23} +(-248566. - 430529. i) q^{24} +(-2.57726e6 - 4.46394e6i) q^{25} +(-768510. + 1.33110e6i) q^{26} -2.98999e6 q^{27} -1.78997e6 q^{29} +(-2.58860e6 + 4.48359e6i) q^{30} +(4.83065e6 + 8.36693e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.14653e6 - 1.98584e6i) q^{33} +9.18388e6 q^{34} -1.26778e6 q^{36} +(1.54840e6 - 2.68192e6i) q^{37} +(-701920. - 1.21576e6i) q^{38} +(-5.82964e6 - 1.00972e7i) q^{39} +(-5.46000e6 + 9.45700e6i) q^{40} +1.17852e7 q^{41} +3.60280e7 q^{43} +(2.41831e6 - 4.18864e6i) q^{44} +(6.60142e6 + 1.14340e7i) q^{45} +(1.20028e7 + 2.07894e7i) q^{46} +(-2.95998e6 + 5.12684e6i) q^{47} +7.95412e6 q^{48} +8.24723e7 q^{50} +(-3.48328e7 + 6.03322e7i) q^{51} +(-1.22962e7 - 2.12976e7i) q^{52} +(1.50157e7 + 2.60079e7i) q^{53} +(2.39199e7 - 4.14305e7i) q^{54} -5.03692e7 q^{55} +1.06490e7 q^{57} +(1.43198e7 - 2.48026e7i) q^{58} +(7.16607e7 + 1.24120e8i) q^{59} +(-4.14176e7 - 7.17374e7i) q^{60} +(-7.53227e7 + 1.30463e8i) q^{61} -1.54581e8 q^{62} +1.67772e7 q^{64} +(-1.28054e8 + 2.21796e8i) q^{65} +(1.83444e7 + 3.17735e7i) q^{66} +(-4.97455e7 - 8.61617e7i) q^{67} +(-7.34710e7 + 1.27256e8i) q^{68} -1.82097e8 q^{69} -2.01373e8 q^{71} +(1.01422e7 - 1.75669e7i) q^{72} +(-2.32838e7 - 4.03287e7i) q^{73} +(2.47745e7 + 4.29106e7i) q^{74} +(-3.12802e8 + 5.41790e8i) q^{75} +2.24614e7 q^{76} +1.86548e8 q^{78} +(1.26611e8 - 2.19297e8i) q^{79} +(-8.73600e7 - 1.51312e8i) q^{80} +(1.32710e8 + 2.29860e8i) q^{81} +(-9.42819e7 + 1.63301e8i) q^{82} -3.16834e8 q^{83} +1.53027e9 q^{85} +(-2.88224e8 + 4.99219e8i) q^{86} +(1.08625e8 + 1.88144e8i) q^{87} +(3.86930e7 + 6.70182e7i) q^{88} +(-4.20311e8 + 7.28000e8i) q^{89} -2.11245e8 q^{90} -3.84089e8 q^{92} +(5.86297e8 - 1.01550e9i) q^{93} +(-4.73597e7 - 8.20295e7i) q^{94} +(-1.16958e8 - 2.02577e8i) q^{95} +(-6.36329e7 + 1.10215e8i) q^{96} -2.72768e8 q^{97} +9.35636e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9}+O(q^{10}) \) 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9	\( 12 q - 96 q^{2} - 1536 q^{4} + 49152 q^{8} - 72550 q^{9} - 110664 q^{11} - 1045456 q^{15} - 393216 q^{16} - 1160800 q^{18} + 3541248 q^{22} - 243384 q^{23} - 17125446 q^{25} + 20927280 q^{29} + 8363648 q^{30} - 6291456 q^{32} + 37145600 q^{36} - 24332568 q^{37} - 42635880 q^{39} + 149517168 q^{43} - 28329984 q^{44} - 3894144 q^{46} + 548014272 q^{50} - 260246248 q^{51} - 137815308 q^{53} + 899327920 q^{57} - 167418240 q^{58} + 133818368 q^{60} + 201326592 q^{64} - 565976460 q^{65} + 202943376 q^{67} + 1228585536 q^{71} - 297164800 q^{72} - 389321088 q^{74} + 1364348160 q^{78} + 182370096 q^{79} + 432881842 q^{81} + 4140991464 q^{85} - 1196137344 q^{86} - 453279744 q^{88} + 124612608 q^{92} - 190722192 q^{93} + 1311555480 q^{95} + 10645173584 q^{99}+O(q^{100}) \) 12 * q - 96 * q^2 - 1536 * q^4 + 49152 * q^8 - 72550 * q^9 - 110664 * q^11 - 1045456 * q^15 - 393216 * q^16 - 1160800 * q^18 + 3541248 * q^22 - 243384 * q^23 - 17125446 * q^25 + 20927280 * q^29 + 8363648 * q^30 - 6291456 * q^32 + 37145600 * q^36 - 24332568 * q^37 - 42635880 * q^39 + 149517168 * q^43 - 28329984 * q^44 - 3894144 * q^46 + 548014272 * q^50 - 260246248 * q^51 - 137815308 * q^53 + 899327920 * q^57 - 167418240 * q^58 + 133818368 * q^60 + 201326592 * q^64 - 565976460 * q^65 + 202943376 * q^67 + 1228585536 * q^71 - 297164800 * q^72 - 389321088 * q^74 + 1364348160 * q^78 + 182370096 * q^79 + 432881842 * q^81 + 4140991464 * q^85 - 1196137344 * q^86 - 453279744 * q^88 + 124612608 * q^92 - 190722192 * q^93 + 1311555480 * q^95 + 10645173584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more