LMFDB - Embedded newform 98.13.d.b.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,13,Mod(19,98)]

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([5]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("98.19");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, 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:	$89.5713940931$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 51570 x^{14} + 1743306357 x^{12} + 34303771893750 x^{10} + \cdots + 24\!\cdots\!96 $ x^16 + 51570x^14 + 1743306357x^12 + 34303771893750x^10 + 490016452747859435x^8 + 4318992197678245462380x^6 + 27578712253339290626452398x^4 + 100997229845590062592768165320*x^2 + 243579618669480443960727421550596
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{54}\cdot 3^{8}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.7
Root			$37.6663 - 65.2399i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.13.d.b.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(22.6274 - 39.1918i) q^{2} +(88.3706 - 51.0208i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-5989.93 - 3458.29i) q^{5} -4617.87i q^{6} -92681.9 q^{8} +(-260514. + 451224. i) q^{9} +O(q^{10})$	\(q+(22.6274 - 39.1918i) q^{2} +(88.3706 - 51.0208i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-5989.93 - 3458.29i) q^{5} -4617.87i q^{6} -92681.9 q^{8} +(-260514. + 451224. i) q^{9} +(-271073. + 156504. i) q^{10} +(672699. + 1.16515e6i) q^{11} +(-180983. - 104491. i) q^{12} +5.40570e6i q^{13} -705778. q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(3.75433e7 - 2.16756e7i) q^{17} +(1.17895e7 + 2.04201e7i) q^{18} +(-4.16802e7 - 2.40641e7i) q^{19} +1.41652e7i q^{20} +6.08857e7 q^{22} +(8.06349e7 - 1.39664e8i) q^{23} +(-8.19035e6 + 4.72870e6i) q^{24} +(-9.81508e7 - 1.70002e8i) q^{25} +(2.11859e8 + 1.22317e8i) q^{26} +1.07396e8i q^{27} -7.77122e7 q^{29} +(-1.59699e7 + 2.76607e7i) q^{30} +(1.18013e8 - 6.81348e7i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(1.18893e8 + 6.86432e7i) q^{33} -1.96185e9i q^{34} +1.06707e9 q^{36} +(6.77800e8 - 1.17398e9i) q^{37} +(-1.88623e9 + 1.08902e9i) q^{38} +(2.75803e8 + 4.77705e8i) q^{39} +(5.55158e8 + 3.20521e8i) q^{40} +4.10282e9i q^{41} +2.00941e9 q^{43} +(1.37769e9 - 2.38622e9i) q^{44} +(3.12093e9 - 1.80187e9i) q^{45} +(-3.64912e9 - 6.32046e9i) q^{46} +(-1.42119e10 - 8.20527e9i) q^{47} +4.27993e8i q^{48} -8.88359e9 q^{50} +(2.21181e9 - 3.83097e9i) q^{51} +(9.58765e9 - 5.53543e9i) q^{52} +(-1.38335e10 - 2.39604e10i) q^{53} +(4.20903e9 + 2.43009e9i) q^{54} -9.30554e9i q^{55} -4.91107e9 q^{57} +(-1.75843e9 + 3.04568e9i) q^{58} +(-3.29737e10 + 1.90374e10i) q^{59} +(7.22717e8 + 1.25178e9i) q^{60} +(7.24689e10 + 4.18399e10i) q^{61} -6.16686e9i q^{62} +8.58993e9 q^{64} +(1.86945e10 - 3.23798e10i) q^{65} +(5.38051e9 - 3.10644e9i) q^{66} +(-4.96015e10 - 8.59123e10i) q^{67} +(-7.68886e10 - 4.43916e10i) q^{68} -1.64562e10i q^{69} -3.72326e10 q^{71} +(2.41450e10 - 4.18203e10i) q^{72} +(6.66093e10 - 3.84569e10i) q^{73} +(-3.06737e10 - 5.31285e10i) q^{74} +(-1.73473e10 - 1.00155e10i) q^{75} +9.85665e10i q^{76} +2.49628e10 q^{78} +(1.13765e11 - 1.97046e11i) q^{79} +(2.51236e10 - 1.45051e10i) q^{80} +(-1.32969e11 - 2.30308e11i) q^{81} +(1.60797e11 + 9.28362e10i) q^{82} +1.32152e11i q^{83} -2.99842e11 q^{85} +(4.54677e10 - 7.87523e10i) q^{86} +(-6.86747e9 + 3.96493e9i) q^{87} +(-6.23470e10 - 1.07988e11i) q^{88} +(-4.39326e11 - 2.53645e11i) q^{89} -1.63086e11i q^{90} -3.30281e11 q^{92} +(6.95258e9 - 1.20422e10i) q^{93} +(-6.43159e11 + 3.71328e11i) q^{94} +(1.66441e11 + 2.88284e11i) q^{95} +(1.67738e10 + 9.68438e9i) q^{96} -2.74033e11i q^{97} -7.00990e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16384 q^{4} + 1478904 q^{9}+O(q^{10}) $ 16 * q - 16384 * q^4 + 1478904 * q^9	$ 16 q - 16384 q^{4} + 1478904 q^{9} + 213840 q^{11} + 131764608 q^{15} - 33554432 q^{16} - 32547840 q^{18} - 442675200 q^{22} - 156731760 q^{23} - 191237000 q^{25} + 617707296 q^{29} + 2203567104 q^{30} - 6057590784 q^{36} + 3243600880 q^{37} - 13521315264 q^{39} + 42012604000 q^{43} + 437944320 q^{44} - 9664610304 q^{46} + 52518979584 q^{50} + 80965832832 q^{51} - 180445637520 q^{53} - 126291924480 q^{57} + 94193264640 q^{58} - 134926958592 q^{60} + 137438953472 q^{64} + 424890168192 q^{65} - 369211259440 q^{67} + 1148116288608 q^{71} - 66657976320 q^{72} - 450517137408 q^{74} - 502001694720 q^{78} + 607826610128 q^{79} - 919051941384 q^{81} - 494404521216 q^{85} + 413092638720 q^{86} + 453299404800 q^{88} + 641973288960 q^{92} - 2292312458880 q^{93} + 1053641981376 q^{95} - 3601908512928 q^{99}+O(q^{100}) $ 16 * q - 16384 * q^4 + 1478904 * q^9 + 213840 * q^11 + 131764608 * q^15 - 33554432 * q^16 - 32547840 * q^18 - 442675200 * q^22 - 156731760 * q^23 - 191237000 * q^25 + 617707296 * q^29 + 2203567104 * q^30 - 6057590784 * q^36 + 3243600880 * q^37 - 13521315264 * q^39 + 42012604000 * q^43 + 437944320 * q^44 - 9664610304 * q^46 + 52518979584 * q^50 + 80965832832 * q^51 - 180445637520 * q^53 - 126291924480 * q^57 + 94193264640 * q^58 - 134926958592 * q^60 + 137438953472 * q^64 + 424890168192 * q^65 - 369211259440 * q^67 + 1148116288608 * q^71 - 66657976320 * q^72 - 450517137408 * q^74 - 502001694720 * q^78 + 607826610128 * q^79 - 919051941384 * q^81 - 494404521216 * q^85 + 413092638720 * q^86 + 453299404800 * q^88 + 641973288960 * q^92 - 2292312458880 * q^93 + 1053641981376 * q^95 - 3601908512928 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$2$	22.6274	−	39.1918i	0.353553	−	0.612372i
$3$	88.3706	−	51.0208i	0.121222	−	0.0699873i	−0.438163	−	0.898895i	$-0.644371\pi$
$3$	88.3706	−	51.0208i	0.121222	−	0.0699873i	0.559385	+	0.828908i	$0.311037\pi$
$4$	−1024.00	−	1773.62i	−0.250000	−	0.433013i
$5$	−5989.93	−	3458.29i	−0.383356	−	0.221331i	0.295922	−	0.955212i	$-0.404373\pi$
$5$	−5989.93	−	3458.29i	−0.383356	−	0.221331i	−0.679277	+	0.733882i	$0.737707\pi$
$6$		−	4617.87i		−	0.0989770i
$7$		0			0
$7$		0			0
$8$	−92681.9			−0.353553
$9$	−260514.	+	451224.i	−0.490204	+	0.849057i
$10$	−271073.	+	156504.i	−0.271073	+	0.156504i
$11$	672699.	+	1.16515e6i	0.379721	+	0.657696i	0.991021	−	0.133703i	$-0.0426867\pi$
$11$	672699.	+	1.16515e6i	0.379721	+	0.657696i	−0.611301	+	0.791398i	$0.709353\pi$
$12$	−180983.	−	104491.i	−0.0606108	−	0.0349937i
$13$			5.40570e6i			1.11993i	0.828516	+	0.559966i	$0.189186\pi$
$13$			5.40570e6i			1.11993i	−0.828516	+	0.559966i	$0.810814\pi$
$14$		0			0
$15$	−705778.			−0.0619613
$16$	−2.09715e6	+	3.63237e6i	−0.125000	+	0.216506i
$17$	3.75433e7	−	2.16756e7i	1.55539	−	0.898003i	0.557699	−	0.830043i	$-0.311684\pi$
$17$	3.75433e7	−	2.16756e7i	1.55539	−	0.898003i	0.997688	−	0.0679595i	$-0.0216489\pi$
$18$	1.17895e7	+	2.04201e7i	0.346626	+	0.600374i
$19$	−4.16802e7	−	2.40641e7i	−0.885948	−	0.511502i	−0.0133331	−	0.999911i	$-0.504244\pi$
$19$	−4.16802e7	−	2.40641e7i	−0.885948	−	0.511502i	−0.872615	+	0.488409i	$0.837578\pi$
$20$			1.41652e7i			0.221331i
$21$		0			0
$22$	6.08857e7			0.537006
$23$	8.06349e7	−	1.39664e8i	0.544698	−	0.943445i	−0.453927	−	0.891039i	$-0.649977\pi$
$23$	8.06349e7	−	1.39664e8i	0.544698	−	0.943445i	0.998626	−	0.0524067i	$-0.0166892\pi$
$24$	−8.19035e6	+	4.72870e6i	−0.0428583	+	0.0247443i
$25$	−9.81508e7	−	1.70002e8i	−0.402026	−	0.696329i
$26$	2.11859e8	+	1.22317e8i	0.685816	+	0.395956i
$27$			1.07396e8i			0.277207i
$28$		0			0
$29$	−7.77122e7			−0.130647			−0.0653237	−	0.997864i	$-0.520808\pi$
$29$	−7.77122e7			−0.130647			−0.0653237	+	0.997864i	$0.520808\pi$
$30$	−1.59699e7	+	2.76607e7i	−0.0219066	+	0.0379434i
$31$	1.18013e8	−	6.81348e7i	0.132972	−	0.0767713i	−0.432038	−	0.901855i	$-0.642206\pi$
$31$	1.18013e8	−	6.81348e7i	0.132972	−	0.0767713i	0.565010	+	0.825084i	$0.308872\pi$
$32$	9.49063e7	+	1.64382e8i	0.0883883	+	0.153093i
$33$	1.18893e8	+	6.86432e7i	0.0920607	+	0.0531513i
$34$		−	1.96185e9i		−	1.26997i
$35$		0			0
$36$	1.06707e9			0.490204
$37$	6.77800e8	−	1.17398e9i	0.264175	−	0.457564i	−0.703172	−	0.711019i	$-0.748234\pi$
$37$	6.77800e8	−	1.17398e9i	0.264175	−	0.457564i	0.967347	+	0.253455i	$0.0815671\pi$
$38$	−1.88623e9	+	1.08902e9i	−0.626460	+	0.361687i
$39$	2.75803e8	+	4.77705e8i	0.0783811	+	0.135760i
$40$	5.55158e8	+	3.20521e8i	0.135537	+	0.0782522i
$41$			4.10282e9i			0.863733i	0.901938	+	0.431866i	$0.142145\pi$
$41$			4.10282e9i			0.863733i	−0.901938	+	0.431866i	$0.857855\pi$
$42$		0			0
$43$	2.00941e9			0.317875			0.158938	−	0.987289i	$-0.449193\pi$
$43$	2.00941e9			0.317875			0.158938	+	0.987289i	$0.449193\pi$
$44$	1.37769e9	−	2.38622e9i	0.189860	−	0.328848i
$45$	3.12093e9	−	1.80187e9i	0.375845	−	0.216994i
$46$	−3.64912e9	−	6.32046e9i	−0.385160	−	0.667117i
$47$	−1.42119e10	−	8.20527e9i	−1.31846	−	0.761212i	−0.334977	−	0.942226i	$-0.608729\pi$
$47$	−1.42119e10	−	8.20527e9i	−1.31846	−	0.761212i	−0.983481	+	0.181014i	$0.942062\pi$
$48$			4.27993e8i			0.0349937i
$49$		0			0
$50$	−8.88359e9			−0.568550
$51$	2.21181e9	−	3.83097e9i	0.125698	−	0.217715i
$52$	9.58765e9	−	5.53543e9i	0.484945	−	0.279983i
$53$	−1.38335e10	−	2.39604e10i	−0.624134	−	1.08103i	−0.988708	−	0.149857i	$-0.952119\pi$
$53$	−1.38335e10	−	2.39604e10i	−0.624134	−	1.08103i	0.364574	−	0.931174i	$-0.381215\pi$
$54$	4.20903e9	+	2.43009e9i	0.169754	+	0.0980074i
$55$		−	9.30554e9i		−	0.336175i
$56$		0			0
$57$	−4.91107e9			−0.143195
$58$	−1.75843e9	+	3.04568e9i	−0.0461909	+	0.0800049i
$59$	−3.29737e10	+	1.90374e10i	−0.781728	+	0.451331i	−0.837042	−	0.547138i	$-0.815717\pi$
$59$	−3.29737e10	+	1.90374e10i	−0.781728	+	0.451331i	0.0553146	+	0.998469i	$0.482384\pi$
$60$	7.22717e8	+	1.25178e9i	0.0154903	+	0.0268300i
$61$	7.24689e10	+	4.18399e10i	1.40661	+	0.812104i	0.995059	−	0.0992845i	$-0.0316554\pi$
$61$	7.24689e10	+	4.18399e10i	1.40661	+	0.812104i	0.411547	+	0.911389i	$0.364989\pi$
$62$		−	6.16686e9i		−	0.108571i
$63$		0			0
$64$	8.58993e9			0.125000
$65$	1.86945e10	−	3.23798e10i	0.247875	−	0.429332i
$66$	5.38051e9	−	3.10644e9i	0.0650968	−	0.0375836i
$67$	−4.96015e10	−	8.59123e10i	−0.548335	−	0.949744i	−0.998389	−	0.0567426i	$-0.981929\pi$
$67$	−4.96015e10	−	8.59123e10i	−0.548335	−	0.949744i	0.450054	−	0.893001i	$-0.351405\pi$
$68$	−7.68886e10	−	4.43916e10i	−0.777693	−	0.449001i
$69$		−	1.64562e10i		−	0.152488i
$70$		0			0
$71$	−3.72326e10			−0.290652			−0.145326	−	0.989384i	$-0.546423\pi$
$71$	−3.72326e10			−0.290652			−0.145326	+	0.989384i	$0.546423\pi$
$72$	2.41450e10	−	4.18203e10i	0.173313	−	0.300187i
$73$	6.66093e10	−	3.84569e10i	0.440147	−	0.254119i	−0.263513	−	0.964656i	$-0.584881\pi$
$73$	6.66093e10	−	3.84569e10i	0.440147	−	0.254119i	0.703660	+	0.710537i	$0.251548\pi$
$74$	−3.06737e10	−	5.31285e10i	−0.186800	−	0.323547i
$75$	−1.73473e10	−	1.00155e10i	−0.0974684	−	0.0562734i
$76$			9.85665e10i			0.511502i
$77$		0			0
$78$	2.49628e10			0.110848
$79$	1.13765e11	−	1.97046e11i	0.467999	−	0.810598i	−0.531332	−	0.847163i	$-0.678308\pi$
$79$	1.13765e11	−	1.97046e11i	0.467999	−	0.810598i	0.999331	+	0.0365655i	$0.0116418\pi$
$80$	2.51236e10	−	1.45051e10i	0.0958389	−	0.0553326i
$81$	−1.32969e11	−	2.30308e11i	−0.470803	−	0.815454i
$82$	1.60797e11	+	9.28362e10i	0.528926	+	0.305376i
$83$			1.32152e11i			0.404207i	0.979364	+	0.202104i	$0.0647777\pi$
$83$			1.32152e11i			0.404207i	−0.979364	+	0.202104i	$0.935222\pi$
$84$		0			0
$85$	−2.99842e11			−0.795022
$86$	4.54677e10	−	7.87523e10i	0.112386	−	0.194658i
$87$	−6.86747e9	+	3.96493e9i	−0.0158373	+	0.00914367i
$88$	−6.23470e10	−	1.07988e11i	−0.134252	−	0.232531i
$89$	−4.39326e11	−	2.53645e11i	−0.883989	−	0.510372i	−0.0120177	−	0.999928i	$-0.503825\pi$
$89$	−4.39326e11	−	2.53645e11i	−0.883989	−	0.510372i	−0.871972	+	0.489556i	$0.837159\pi$
$90$		−	1.63086e11i		−	0.306876i
$91$		0			0
$92$	−3.30281e11			−0.544698
$93$	6.95258e9	−	1.20422e10i	0.0107460	−	0.0186127i
$94$	−6.43159e11	+	3.71328e11i	−0.932291	+	0.538258i
$95$	1.66441e11	+	2.88284e11i	0.226422	+	0.392175i
$96$	1.67738e10	+	9.68438e9i	0.0214292	+	0.0123721i
$97$		−	2.74033e11i		−	0.328983i	−0.986379	−	0.164491i	$-0.947402\pi$
$97$		−	2.74033e11i		−	0.328983i	0.986379	−	0.164491i	$-0.0525983\pi$
$98$		0			0
$99$	−7.00990e11			−0.744562
$100$	−2.01013e11	+	3.48164e11i	−0.201013	+	0.348164i
$101$	6.17463e11	−	3.56492e11i	0.581678	−	0.335832i	−0.180122	−	0.983644i	$-0.557649\pi$
$101$	6.17463e11	−	3.56492e11i	0.581678	−	0.335832i	0.761800	+	0.647812i	$0.224316\pi$
$102$	−1.00095e11	−	1.73370e11i	−0.0888817	−	0.153948i
$103$	1.36326e12	+	7.87078e11i	1.14171	+	0.659165i	0.946853	−	0.321667i	$-0.104243\pi$
$103$	1.36326e12	+	7.87078e11i	1.14171	+	0.659165i	0.194855	+	0.980832i	$0.437576\pi$
$104$		−	5.01010e11i		−	0.395956i
$105$		0			0
$106$	−1.25207e12			−0.882658
$107$	−3.78869e11	+	6.56220e11i	−0.252456	+	0.437267i	−0.964201	−	0.265171i	$-0.914572\pi$
$107$	−3.78869e11	+	6.56220e11i	−0.252456	+	0.437267i	0.711745	+	0.702438i	$0.247905\pi$
$108$	1.90479e11	−	1.09973e11i	0.120034	−	0.0693017i
$109$	−9.53307e11	−	1.65118e12i	−0.568426	−	0.984542i	−0.996722	−	0.0809039i	$-0.974219\pi$
$109$	−9.53307e11	−	1.65118e12i	−0.568426	−	0.984542i	0.428296	−	0.903638i	$-0.359114\pi$
$110$	−3.64701e11	−	2.10560e11i	−0.205864	−	0.118856i
$111$		−	1.38327e11i		−	0.0739555i
$112$		0			0
$113$	−3.73652e12			−1.79472			−0.897360	−	0.441300i	$-0.854518\pi$
$113$	−3.73652e12			−1.79472			−0.897360	+	0.441300i	$0.854518\pi$
$114$	−1.11125e11	+	1.92474e11i	−0.0506270	+	0.0876885i
$115$	−9.65995e11	+	5.57718e11i	−0.417627	+	0.241117i
$116$	7.95772e10	+	1.37832e11i	0.0326619	+	0.0565720i
$117$	−2.43918e12	−	1.40826e12i	−0.950887	−	0.548995i
$118$			1.72307e12i			0.638278i
$119$		0			0
$120$	6.54129e10			0.0219066
$121$	6.64167e11	−	1.15037e12i	0.211624	−	0.366544i
$122$	3.27957e12	−	1.89346e12i	0.994620	−	0.574244i
$123$	2.09329e11	+	3.62569e11i	0.0604504	+	0.104703i
$124$	−2.41690e11	−	1.39540e11i	−0.0664859	−	0.0383856i
$125$			3.04635e12i			0.798583i
$126$		0			0
$127$	−6.59899e12			−1.57273			−0.786366	−	0.617760i	$-0.788040\pi$
$127$	−6.59899e12			−1.57273			−0.786366	+	0.617760i	$0.788040\pi$
$128$	1.94368e11	−	3.36655e11i	0.0441942	−	0.0765466i
$129$	1.77572e11	−	1.02521e11i	0.0385334	−	0.0222472i
$130$	−8.46015e11	−	1.46534e12i	−0.175274	−	0.303584i
$131$	2.90989e12	+	1.68003e12i	0.575771	+	0.332421i	0.759451	−	0.650565i	$-0.225468\pi$
$131$	2.90989e12	+	1.68003e12i	0.575771	+	0.332421i	−0.183680	+	0.982986i	$0.558801\pi$
$132$		−	2.81163e11i		−	0.0531513i
$133$		0			0
$134$	−4.48941e12			−0.775463
$135$	3.71405e11	−	6.43292e11i	0.0613543	−	0.106269i
$136$	−3.47958e12	+	2.00894e12i	−0.549912	+	0.317492i
$137$	−2.85116e12	−	4.93835e12i	−0.431219	−	0.746894i	0.565759	−	0.824570i	$-0.308583\pi$
$137$	−2.85116e12	−	4.93835e12i	−0.431219	−	0.746894i	−0.996979	+	0.0776767i	$0.975250\pi$
$138$	−6.44950e11	−	3.72362e11i	−0.0933794	−	0.0539126i
$139$		−	1.26130e13i		−	1.74876i	−0.485243	−	0.874379i	$-0.661269\pi$
$139$		−	1.26130e13i		−	1.74876i	0.485243	−	0.874379i	$-0.338731\pi$
$140$		0			0
$141$	−1.67456e12			−0.213101
$142$	−8.42477e11	+	1.45921e12i	−0.102761	+	0.177987i
$143$	−6.29844e12	+	3.63641e12i	−0.736574	+	0.425261i
$144$	−1.09268e12	−	1.89257e12i	−0.122551	−	0.212264i
$145$	4.65491e11	+	2.68751e11i	0.0500844	+	0.0289163i
$146$		−	3.48072e12i		−	0.359379i
$147$		0			0
$148$	−2.77627e12			−0.264175
$149$	8.60053e12	−	1.48966e13i	0.785973	−	1.36135i	−0.142443	−	0.989803i	$-0.545496\pi$
$149$	8.60053e12	−	1.48966e13i	0.785973	−	1.36135i	0.928416	−	0.371543i	$-0.121171\pi$
$150$	−7.85048e11	+	4.53248e11i	−0.0689206	+	0.0397913i
$151$	−8.14632e12	−	1.41098e13i	−0.687226	−	1.19031i	−0.972732	−	0.231934i	$-0.925495\pi$
$151$	−8.14632e12	−	1.41098e13i	−0.687226	−	1.19031i	0.285505	−	0.958377i	$-0.407839\pi$
$152$	3.86300e12	+	2.23030e12i	0.313230	+	0.180843i
$153$			2.25872e13i			1.76082i
$154$		0			0
$155$	−9.42519e11			−0.0679673
$156$	5.64844e11	−	9.78339e11i	0.0391905	−	0.0678800i
$157$	5.89780e12	−	3.40509e12i	0.393815	−	0.227369i	−0.289997	−	0.957028i	$-0.593654\pi$
$157$	5.89780e12	−	3.40509e12i	0.393815	−	0.227369i	0.683812	+	0.729659i	$0.260321\pi$
$158$	−5.14840e12	−	8.91729e12i	−0.330925	−	0.573179i
$159$	−2.44495e12	−	1.41159e12i	−0.151317	−	0.0873629i
$160$		−	1.31285e12i		−	0.0782522i
$161$		0			0
$162$	−1.20349e13			−0.665815
$163$	4.85016e12	−	8.40072e12i	0.258601	−	0.447910i	−0.707266	−	0.706947i	$-0.750072\pi$
$163$	4.85016e12	−	8.40072e12i	0.258601	−	0.447910i	0.965867	+	0.259037i	$0.0834051\pi$
$164$	7.27685e12	−	4.20129e12i	0.374007	−	0.215933i
$165$	−4.74776e11	−	8.22336e11i	−0.0235280	−	0.0407517i
$166$	5.17926e12	+	2.99025e12i	0.247525	+	0.142909i
$167$		−	7.66955e11i		−	0.0353567i	−0.999844	−	0.0176783i	$-0.994373\pi$
$167$		−	7.66955e11i		−	0.0353567i	0.999844	−	0.0176783i	$-0.00562748\pi$
$168$		0			0
$169$	−5.92349e12			−0.254248
$170$	−6.78465e12	+	1.17514e13i	−0.281083	+	0.486849i
$171$	2.17166e13	−	1.25381e13i	0.868590	−	0.501481i
$172$	−2.05763e12	−	3.56392e12i	−0.0794688	−	0.137644i
$173$	−2.48391e13	−	1.43409e13i	−0.926530	−	0.534933i	−0.0408177	−	0.999167i	$-0.512996\pi$
$173$	−2.48391e13	−	1.43409e13i	−0.926530	−	0.534933i	−0.885713	+	0.464234i	$0.846330\pi$
$174$			3.58865e11i			0.0129311i
$175$		0			0
$176$	−5.64300e12			−0.189860
$177$	−1.94260e12	+	3.36469e12i	−0.0631749	+	0.109422i
$178$	−1.98816e13	+	1.14787e13i	−0.625075	+	0.360887i
$179$	−4.32685e12	−	7.49433e12i	−0.131539	−	0.227832i	0.792731	−	0.609571i	$-0.208658\pi$
$179$	−4.32685e12	−	7.49433e12i	−0.131539	−	0.227832i	−0.924270	+	0.381740i	$0.875325\pi$
$180$	−6.39166e12	−	3.69022e12i	−0.187922	−	0.108497i
$181$		−	2.96628e13i		−	0.843607i	−0.906687	−	0.421803i	$-0.861397\pi$
$181$		−	2.96628e13i		−	0.843607i	0.906687	−	0.421803i	$-0.138603\pi$
$182$		0			0
$183$	8.53882e12			0.227348
$184$	−7.47340e12	+	1.29443e13i	−0.192580	+	0.333558i
$185$	−8.11995e12	+	4.68806e12i	−0.202546	+	0.116940i
$186$	−3.14638e11	−	5.44969e11i	−0.00759859	−	0.0131612i
$187$	5.05106e13	+	2.91623e13i	1.18123	+	0.681981i
$188$			3.36088e13i			0.761212i
$189$		0			0
$190$	1.50645e13			0.320209
$191$	1.50349e13	−	2.60412e13i	0.309670	−	0.536365i	−0.668620	−	0.743604i	$-0.733115\pi$
$191$	1.50349e13	−	2.60412e13i	0.309670	−	0.536365i	0.978290	+	0.207240i	$0.0664480\pi$
$192$	7.59097e11	−	4.38265e11i	0.0151527	−	0.00874842i
$193$	1.44632e13	+	2.50509e13i	0.279846	+	0.484708i	0.971346	−	0.237668i	$-0.0763831\pi$
$193$	1.44632e13	+	2.50509e13i	0.279846	+	0.484708i	−0.691500	+	0.722376i	$0.743050\pi$
$194$	−1.07399e13	−	6.20067e12i	−0.201460	−	0.116313i
$195$		−	3.81522e12i		−	0.0693925i
$196$		0			0
$197$	8.13502e13			1.39175			0.695875	−	0.718163i	$-0.255017\pi$
$197$	8.13502e13			1.39175			0.695875	+	0.718163i	$0.255017\pi$
$198$	−1.58616e13	+	2.74731e13i	−0.263242	+	0.455949i
$199$	−6.69437e13	+	3.86500e13i	−1.07793	+	0.622344i	−0.930338	−	0.366704i	$-0.880486\pi$
$199$	−6.69437e13	+	3.86500e13i	−1.07793	+	0.622344i	−0.147594	+	0.989048i	$0.547153\pi$
$200$	9.09680e12	+	1.57561e13i	0.142138	+	0.246189i
$201$	−8.76662e12	−	5.06141e12i	−0.132940	−	0.0767530i
$202$		−	3.22660e13i		−	0.474938i
$203$		0			0
$204$	−9.05958e12			−0.125698
$205$	1.41887e13	−	2.45756e13i	0.191170	−	0.331117i
$206$	6.16940e13	−	3.56191e13i	0.807309	−	0.466100i
$207$	4.20131e13	+	7.27688e13i	0.534026	+	0.924961i
$208$	−1.96355e13	−	1.13366e13i	−0.242472	−	0.139992i
$209$		−	6.47515e13i		−	0.776912i
$210$		0			0
$211$	1.50952e14			1.71059			0.855293	−	0.518145i	$-0.173377\pi$
$211$	1.50952e14			1.71059			0.855293	+	0.518145i	$0.173377\pi$
$212$	−2.83311e13	+	4.90708e13i	−0.312067	+	0.540516i
$213$	−3.29026e12	+	1.89963e12i	−0.0352333	+	0.0203419i
$214$	1.71456e13	+	2.96971e13i	0.178513	+	0.309194i
$215$	−1.20362e13	−	6.94911e12i	−0.121859	−	0.0703555i
$216$		−	9.95363e12i		−	0.0980074i
$217$		0			0
$218$	−8.62835e13			−0.803875
$219$	3.92420e12	−	6.79692e12i	0.0355702	−	0.0616095i
$220$	−1.65045e13	+	9.52888e12i	−0.145568	+	0.0840438i
$221$	1.17172e14	+	2.02948e14i	1.00570	+	1.74193i
$222$	−5.42131e12	−	3.12999e12i	−0.0452883	−	0.0261472i
$223$			2.34517e14i			1.90697i	0.301437	+	0.953486i	$0.402534\pi$
$223$			2.34517e14i			1.90697i	−0.301437	+	0.953486i	$0.597466\pi$
$224$		0			0
$225$	1.02279e14			0.788298
$226$	−8.45478e13	+	1.46441e14i	−0.634529	+	1.09904i
$227$	1.74392e14	−	1.00685e14i	1.27459	−	0.735888i	0.298746	−	0.954333i	$-0.403432\pi$
$227$	1.74392e14	−	1.00685e14i	1.27459	−	0.735888i	0.975849	+	0.218445i	$0.0700985\pi$
$228$	5.02894e12	+	8.71037e12i	0.0357987	+	0.0620051i
$229$	−1.36536e13	−	7.88290e12i	−0.0946747	−	0.0546604i	0.451915	−	0.892061i	$-0.350741\pi$
$229$	−1.36536e13	−	7.88290e12i	−0.0946747	−	0.0546604i	−0.546590	+	0.837400i	$0.684074\pi$
$230$			5.04788e13i			0.340991i
$231$		0			0
$232$	7.20251e12			0.0461909
$233$	−3.13906e13	+	5.43701e13i	−0.196184	+	0.339801i	−0.947288	−	0.320383i	$-0.896188\pi$
$233$	−3.13906e13	+	5.43701e13i	−0.196184	+	0.339801i	0.751104	+	0.660184i	$0.229522\pi$
$234$	−1.10385e14	+	6.37306e13i	−0.672378	+	0.388198i
$235$	5.67524e13	+	9.82980e13i	0.336959	+	0.583630i
$236$	6.75301e13	+	3.89885e13i	0.390864	+	0.225665i
$237$		−	2.32174e13i		−	0.131016i
$238$		0			0
$239$	2.45537e14			1.31743			0.658717	−	0.752391i	$-0.271100\pi$
$239$	2.45537e14			1.31743			0.658717	+	0.752391i	$0.271100\pi$
$240$	1.48012e12	−	2.56365e12i	0.00774517	−	0.0134150i
$241$	−4.92795e13	+	2.84515e13i	−0.251515	+	0.145212i	−0.620458	−	0.784240i	$-0.713053\pi$
$241$	−4.92795e13	+	2.84515e13i	−0.251515	+	0.145212i	0.368943	+	0.929452i	$0.379720\pi$
$242$	−3.00568e13	−	5.20599e13i	−0.149641	−	0.259186i
$243$	−7.29289e13	−	4.21055e13i	−0.354211	−	0.204504i
$244$		−	1.71376e14i		−	0.812104i
$245$		0			0
$246$	1.89463e13			0.0854897
$247$	1.30083e14	−	2.25311e14i	0.572848	−	0.992202i
$248$	−1.09377e13	+	6.31486e12i	−0.0470126	+	0.0271427i
$249$	6.74248e12	+	1.16783e13i	0.0282894	+	0.0489986i
$250$	1.19392e14	+	6.89311e13i	0.489030	+	0.282342i
$251$		−	2.56371e14i		−	1.02524i	−0.858615	−	0.512621i	$-0.828675\pi$
$251$		−	2.56371e14i		−	1.02524i	0.858615	−	0.512621i	$-0.171325\pi$
$252$		0			0
$253$	2.16972e14			0.827333
$254$	−1.49318e14	+	2.58626e14i	−0.556045	+	0.963098i
$255$	−2.64972e13	+	1.52982e13i	−0.0963738	+	0.0556415i
$256$	−8.79609e12	−	1.52353e13i	−0.0312500	−	0.0541266i
$257$	2.84187e14	+	1.64075e14i	0.986291	+	0.569436i	0.904164	−	0.427186i	$-0.140495\pi$
$257$	2.84187e14	+	1.64075e14i	0.986291	+	0.569436i	0.0821277	+	0.996622i	$0.473828\pi$
$258$		−	9.27918e12i		−	0.0314624i
$259$		0			0
$260$	−7.65725e13			−0.247875
$261$	2.02451e13	−	3.50656e13i	0.0640438	−	0.110927i
$262$	1.31687e14	−	7.60294e13i	0.407131	−	0.235057i
$263$	4.38526e13	+	7.59549e13i	0.132514	+	0.229520i	0.924645	−	0.380830i	$-0.124362\pi$
$263$	4.38526e13	+	7.59549e13i	0.132514	+	0.229520i	−0.792131	+	0.610351i	$0.791028\pi$
$264$	−1.10193e13	−	6.36198e12i	−0.0325484	−	0.0187918i
$265$			1.91361e14i			0.552559i
$266$		0			0
$267$	−5.17647e13			−0.142878
$268$	−1.01584e14	+	1.75948e14i	−0.274167	+	0.474872i
$269$	−4.19327e14	+	2.42098e14i	−1.10672	+	0.638967i	−0.937979	−	0.346693i	$-0.887305\pi$
$269$	−4.19327e14	+	2.42098e14i	−1.10672	+	0.638967i	−0.168744	+	0.985660i	$0.553971\pi$
$270$	−1.68079e13	−	2.91121e13i	−0.0433841	−	0.0751434i
$271$	−4.13686e14	−	2.38842e14i	−1.04437	−	0.602968i	−0.123303	−	0.992369i	$-0.539349\pi$
$271$	−4.13686e14	−	2.38842e14i	−1.04437	−	0.602968i	−0.921068	+	0.389401i	$0.872682\pi$
$272$			1.81828e14i			0.449001i
$273$		0			0
$274$	−2.58058e14			−0.609836
$275$	1.32052e14	−	2.28720e14i	0.305315	−	0.528821i
$276$	−2.91871e13	+	1.68512e13i	−0.0660292	+	0.0381220i
$277$	−2.68903e14	−	4.65754e14i	−0.595274	−	1.03105i	−0.993508	−	0.113762i	$-0.963710\pi$
$277$	−2.68903e14	−	4.65754e14i	−0.595274	−	1.03105i	0.398234	−	0.917284i	$-0.369623\pi$
$278$	−4.94327e14	−	2.85400e14i	−1.07089	−	0.618280i
$279$			7.10003e13i			0.150534i
$280$		0			0
$281$	1.44271e14			0.293050			0.146525	−	0.989207i	$-0.453191\pi$
$281$	1.44271e14			0.293050			0.146525	+	0.989207i	$0.453191\pi$
$282$	−3.78909e13	+	6.56289e13i	−0.0753425	+	0.130497i
$283$	7.18358e14	−	4.14744e14i	1.39837	−	0.807350i	0.404149	−	0.914693i	$-0.367568\pi$
$283$	7.18358e14	−	4.14744e14i	1.39837	−	0.807350i	0.994222	+	0.107343i	$0.0342345\pi$
$284$	3.81262e13	+	6.60364e13i	0.0726629	+	0.125856i
$285$	2.94170e13	+	1.69839e13i	0.0548945	+	0.0316934i
$286$			3.29130e14i			0.601411i
$287$		0			0
$288$	−9.88977e13			−0.173313
$289$	6.48353e14	−	1.12298e15i	1.11282	−	1.92746i
$290$	2.10657e13	−	1.21623e13i	0.0354151	−	0.0204469i
$291$	−1.39814e13	−	2.42165e13i	−0.0230246	−	0.0398798i
$292$	−1.36416e14	−	7.87598e13i	−0.220074	−	0.127060i
$293$		−	7.24824e14i		−	1.14558i	−0.819701	−	0.572792i	$-0.805860\pi$
$293$		−	7.24824e14i		−	1.14558i	0.819701	−	0.572792i	$-0.194140\pi$
$294$		0			0
$295$	2.63347e14			0.399573
$296$	−6.28198e13	+	1.08807e14i	−0.0933999	+	0.161773i
$297$	−1.25132e14	+	7.22449e13i	−0.182318	+	0.105261i
$298$	−3.89216e14	−	6.74141e14i	−0.555767	−	0.962617i
$299$	7.54980e14	+	4.35888e14i	1.05659	+	0.610025i
$300$			4.10233e13i			0.0562734i
$301$		0			0
$302$	−7.37321e14			−0.971885
$303$	3.63770e13	−	6.30068e13i	0.0470080	−	0.0814202i
$304$	1.74819e14	−	1.00932e14i	0.221487	−	0.127876i
$305$	−2.89389e14	−	5.01236e14i	−0.359487	−	0.622650i
$306$	8.85235e14	+	5.11090e14i	1.07828	+	0.622543i
$307$			3.18911e14i			0.380925i	0.981694	+	0.190462i	$0.0609987\pi$
$307$			3.18911e14i			0.380925i	−0.981694	+	0.190462i	$0.939001\pi$
$308$		0			0
$309$	1.60629e14			0.184533
$310$	−2.13268e13	+	3.69391e13i	−0.0240301	+	0.0416213i
$311$	−1.03839e15	+	5.99514e14i	−1.14762	+	0.662578i	−0.948306	−	0.317358i	$-0.897204\pi$
$311$	−1.03839e15	+	5.99514e14i	−1.14762	+	0.662578i	−0.199312	+	0.979936i	$0.563871\pi$
$312$	−2.55619e13	−	4.42746e13i	−0.0277119	−	0.0479984i
$313$	−6.62152e14	−	3.82294e14i	−0.704193	−	0.406566i	0.104714	−	0.994502i	$-0.466607\pi$
$313$	−6.62152e14	−	3.82294e14i	−0.704193	−	0.406566i	−0.808907	+	0.587936i	$0.799941\pi$
$314$		−	3.08194e14i		−	0.321548i
$315$		0			0
$316$	−4.65980e14			−0.467999
$317$	1.07587e14	−	1.86346e14i	0.106024	−	0.183638i	−0.808132	−	0.589001i	$-0.799521\pi$
$317$	1.07587e14	−	1.86346e14i	0.106024	−	0.183638i	0.914156	+	0.405363i	$0.132855\pi$
$318$	−1.10646e14	+	6.38815e13i	−0.106997	+	0.0617749i
$319$	−5.22769e13	−	9.05462e13i	−0.0496096	−	0.0859263i
$320$	−5.14531e13	−	2.97065e13i	−0.0479195	−	0.0276663i
$321$			7.73207e13i			0.0706749i
$322$		0			0
$323$	−2.08641e15			−1.83732
$324$	−2.72320e14	+	4.71671e14i	−0.235401	+	0.407727i
$325$	9.18980e14	−	5.30574e14i	0.779841	−	0.450241i
$326$	−2.19493e14	−	3.80173e14i	−0.182859	−	0.316720i
$327$	−1.68489e14	−	9.72769e13i	−0.137811	−	0.0795652i
$328$		−	3.80257e14i		−	0.305376i
$329$		0			0
$330$	−4.29718e13			−0.0332736
$331$	−4.41093e14	+	7.63996e14i	−0.335399	+	0.580929i	−0.983561	−	0.180574i	$-0.942205\pi$
$331$	−4.41093e14	+	7.63996e14i	−0.335399	+	0.580929i	0.648162	+	0.761502i	$0.275538\pi$
$332$	2.34387e14	−	1.35323e14i	0.175027	−	0.101052i
$333$	3.53153e14	+	6.11679e14i	0.258999	+	0.448599i
$334$	−3.00584e13	−	1.73542e13i	−0.0216514	−	0.0125005i
$335$			6.86145e14i			0.485453i
$336$		0			0
$337$	−1.99560e15			−1.36237			−0.681185	−	0.732111i	$-0.738535\pi$
$337$	−1.99560e15			−1.36237			−0.681185	+	0.732111i	$0.738535\pi$
$338$	−1.34033e14	+	2.32152e14i	−0.0898902	+	0.155694i
$339$	−3.30198e14	+	1.90640e14i	−0.217559	+	0.125608i
$340$	3.07038e14	+	5.31806e14i	0.198755	+	0.344255i
$341$	1.58774e14	+	9.16684e13i	0.100984	+	0.0583033i
$342$		−	1.13482e15i		−	0.709201i
$343$		0			0
$344$	−1.86236e14			−0.112386
$345$	−5.69104e13	+	9.85717e13i	−0.0337502	+	0.0584571i
$346$	−1.12409e15	+	6.48994e14i	−0.655156	+	0.378254i
$347$	−8.33185e14	−	1.44312e15i	−0.477270	−	0.826657i	0.522390	−	0.852707i	$-0.325040\pi$
$347$	−8.33185e14	−	1.44312e15i	−0.477270	−	0.826657i	−0.999661	+	0.0260499i	$0.991707\pi$
$348$	1.40646e13	+	8.12018e12i	0.00791865	+	0.00457183i
$349$			1.13921e15i			0.630450i	0.949017	+	0.315225i	$0.102080\pi$
$349$			1.13921e15i			0.630450i	−0.949017	+	0.315225i	$0.897920\pi$
$350$		0			0
$351$	−5.80548e14			−0.310453
$352$	−1.27687e14	+	2.21160e14i	−0.0671258	+	0.116265i
$353$	2.22194e15	−	1.28284e15i	1.14838	−	0.663015i	0.199885	−	0.979819i	$-0.435943\pi$
$353$	2.22194e15	−	1.28284e15i	1.14838	−	0.663015i	0.948491	+	0.316805i	$0.102610\pi$
$354$	8.79121e13	+	1.52268e14i	0.0446714	+	0.0773731i
$355$	2.23021e14	+	1.28761e14i	0.111423	+	0.0643301i
$356$			1.03893e15i			0.510372i
$357$		0			0
$358$	−3.91622e14			−0.186024
$359$	8.91753e14	−	1.54456e15i	0.416560	−	0.721503i	−0.579031	−	0.815306i	$-0.696569\pi$
$359$	8.91753e14	−	1.54456e15i	0.416560	−	0.721503i	0.995591	+	0.0938025i	$0.0299022\pi$
$360$	−2.89253e14	+	1.67000e14i	−0.132881	+	0.0767190i
$361$	5.15022e13	+	8.92044e13i	0.0232692	+	0.0403035i
$362$	−1.16254e15	−	6.71192e14i	−0.516602	−	0.298260i
$363$		−	1.35545e14i		−	0.0592441i
$364$		0			0
$365$	−5.31981e14			−0.224977
$366$	1.93211e14	−	3.34652e14i	0.0803797	−	0.139222i
$367$	−2.54183e15	+	1.46753e15i	−1.04028	+	0.600607i	−0.919913	−	0.392123i	$-0.871741\pi$
$367$	−2.54183e15	+	1.46753e15i	−1.04028	+	0.600607i	−0.120368	+	0.992729i	$0.538408\pi$
$368$	3.38207e14	+	5.85792e14i	0.136175	+	0.235861i
$369$	−1.85129e15	−	1.06884e15i	−0.733359	−	0.423405i
$370$			4.24314e14i			0.165378i
$371$		0			0
$372$	−2.84778e13			−0.0107460
$373$	−1.14986e15	+	1.99162e15i	−0.426966	+	0.739527i	−0.996602	−	0.0823703i	$-0.973751\pi$
$373$	−1.14986e15	+	1.99162e15i	−0.426966	+	0.739527i	0.569636	+	0.821897i	$0.307084\pi$
$374$	2.28585e15	−	1.31974e15i	0.835252	−	0.482233i
$375$	1.55427e14	+	2.69208e14i	0.0558907	+	0.0968055i
$376$	1.31719e15	+	7.60480e14i	0.466145	+	0.269129i
$377$		−	4.20088e14i		−	0.146316i
$378$		0			0
$379$	1.88145e15			0.634829			0.317414	−	0.948287i	$-0.397185\pi$
$379$	1.88145e15			0.634829			0.317414	+	0.948287i	$0.397185\pi$
$380$	3.40871e14	−	5.90406e14i	0.113211	−	0.196087i
$381$	−5.83156e14	+	3.36685e14i	−0.190649	+	0.110071i
$382$	−6.80401e14	−	1.17849e15i	−0.218970	−	0.379267i
$383$	1.03257e15	+	5.96152e14i	0.327134	+	0.188871i	0.654568	−	0.756003i	$-0.272851\pi$
$383$	1.03257e15	+	5.96152e14i	0.327134	+	0.188871i	−0.327434	+	0.944874i	$0.606184\pi$
$384$		−	3.96672e13i		−	0.0123721i
$385$		0			0
$386$	1.30906e15			0.395763
$387$	−5.23479e14	+	9.06692e14i	−0.155824	+	0.269894i
$388$	−4.86031e14	+	2.80610e14i	−0.142454	+	0.0822457i
$389$	8.72776e14	+	1.51169e15i	0.251887	+	0.436281i	0.964045	−	0.265738i	$-0.0856156\pi$
$389$	8.72776e14	+	1.51169e15i	0.251887	+	0.436281i	−0.712159	+	0.702019i	$0.752282\pi$
$390$	−1.49526e14	−	8.63287e13i	−0.0424940	−	0.0245339i
$391$		−	6.99124e15i		−	1.95656i
$392$		0			0
$393$	3.42865e14			0.0930611
$394$	1.84075e15	−	3.18826e15i	0.492058	−	0.852270i
$395$	−1.36289e15	+	7.86862e14i	−0.358820	+	0.207165i
$396$	7.17814e14	+	1.24329e15i	0.186140	+	0.322405i
$397$	5.19894e15	+	3.00161e15i	1.32792	+	0.766675i	0.984978	−	0.172681i	$-0.0552430\pi$
$397$	5.19894e15	+	3.00161e15i	1.32792	+	0.766675i	0.342943	+	0.939356i	$0.388576\pi$
$398$			3.49819e15i			0.880127i
$399$		0			0
$400$	8.23348e14			0.201013
$401$	−1.03231e15	+	1.78802e15i	−0.248281	+	0.430036i	−0.963049	−	0.269326i	$-0.913199\pi$
$401$	−1.03231e15	+	1.78802e15i	−0.248281	+	0.430036i	0.714768	+	0.699362i	$0.246532\pi$
$402$	−3.96732e14	+	2.29053e14i	−0.0940028	+	0.0542726i
$403$	3.68316e14	+	6.37942e14i	0.0859786	+	0.148919i
$404$	−1.26456e15	−	7.30096e14i	−0.290839	−	0.167916i
$405$			1.83937e15i			0.416812i
$406$		0			0
$407$	1.82382e15			0.401250
$408$	−2.04995e14	+	3.55062e14i	−0.0444408	+	0.0769738i
$409$	2.70946e15	−	1.56431e15i	0.578819	−	0.334181i	−0.181845	−	0.983327i	$-0.558207\pi$
$409$	2.70946e15	−	1.56431e15i	0.578819	−	0.334181i	0.760664	+	0.649146i	$0.224874\pi$
$410$	−6.42109e14	−	1.11217e15i	−0.135178	−	0.234135i
$411$	−5.03917e14	−	2.90937e14i	−0.104546	−	0.0603598i
$412$		−	3.22387e15i		−	0.659165i
$413$		0			0
$414$	3.80259e15			0.755227
$415$	4.57018e14	−	7.91579e14i	0.0894633	−	0.154955i
$416$	−8.88602e14	+	5.13035e14i	−0.171454	+	0.0989889i
$417$	−6.43525e14	−	1.11462e15i	−0.122391	−	0.211987i
$418$	−2.53773e15	−	1.46516e15i	−0.475760	−	0.274680i
$419$			3.93360e15i			0.726952i	0.931603	+	0.363476i	$0.118410\pi$
$419$			3.93360e15i			0.726952i	−0.931603	+	0.363476i	$0.881590\pi$
$420$		0			0
$421$	4.51876e15			0.811572			0.405786	−	0.913968i	$-0.366998\pi$
$421$	4.51876e15			0.811572			0.405786	+	0.913968i	$0.366998\pi$
$422$	3.41566e15	−	5.91610e15i	0.604783	−	1.04752i
$423$	7.40483e15	−	4.27518e15i	1.29263	−	0.746298i
$424$	1.28212e15	+	2.22069e15i	0.220665	+	0.382202i
$425$	−7.36980e15	−	4.25496e15i	−1.25061	−	0.722040i
$426$			1.71935e14i			0.0287678i
$427$		0			0
$428$	1.55185e15			0.252456
$429$	−3.71064e14	+	6.42702e14i	−0.0595258	+	0.103102i
$430$	−5.44696e14	+	3.14481e14i	−0.0861676	+	0.0497489i
$431$	−2.20787e15	−	3.82413e15i	−0.344436	−	0.596581i	0.640815	−	0.767695i	$-0.278597\pi$
$431$	−2.20787e15	−	3.82413e15i	−0.344436	−	0.596581i	−0.985251	+	0.171114i	$0.945263\pi$
$432$	−3.90101e14	−	2.25225e14i	−0.0600170	−	0.0346509i
$433$			8.01909e15i			1.21674i	0.793654	+	0.608370i	$0.208176\pi$
$433$			8.01909e15i			1.21674i	−0.793654	+	0.608370i	$0.791824\pi$
$434$		0			0
$435$	5.48475e13			0.00809509
$436$	−1.95237e15	+	3.38161e15i	−0.284213	+	0.492271i
$437$	−6.72176e15	+	3.88081e15i	−0.965149	+	0.557229i
$438$	−1.77589e14	−	3.07593e14i	−0.0251520	−	0.0435645i
$439$	9.17606e14	+	5.29780e14i	0.128194	+	0.0740131i	0.562726	−	0.826644i	$-0.309753\pi$
$439$	9.17606e14	+	5.29780e14i	0.128194	+	0.0740131i	−0.434531	+	0.900657i	$0.643086\pi$
$440$			8.62456e14i			0.118856i
$441$		0			0
$442$	1.06052e16			1.42228
$443$	−4.38133e15	+	7.58868e15i	−0.579674	+	1.00402i	0.415843	+	0.909436i	$0.363487\pi$
$443$	−4.38133e15	+	7.58868e15i	−0.579674	+	1.00402i	−0.995517	+	0.0945877i	$0.969847\pi$
$444$	−2.45340e14	+	1.41647e14i	−0.0320237	+	0.0184889i
$445$	1.75436e15	+	3.03863e15i	0.225922	+	0.391308i
$446$	9.19114e15	+	5.30650e15i	1.16778	+	0.674217i
$447$		−	1.75522e15i		−	0.220033i
$448$		0			0
$449$	−4.20903e15			−0.513693			−0.256847	−	0.966452i	$-0.582684\pi$
$449$	−4.20903e15			−0.513693			−0.256847	+	0.966452i	$0.582684\pi$
$450$	2.31430e15	−	4.00849e15i	0.278705	−	0.482732i
$451$	−4.78039e15	+	2.75996e15i	−0.568073	+	0.327977i
$452$	3.82620e15	+	6.62717e15i	0.448680	+	0.777136i
$453$	−1.43979e15	−	8.31263e14i	−0.166613	−	0.0961943i
$454$		−	9.11301e15i		−	1.04070i
$455$		0			0
$456$	4.55167e14			0.0506270
$457$	−4.93773e15	+	8.55239e15i	−0.542038	+	0.938838i	0.456749	+	0.889596i	$0.349014\pi$
$457$	−4.93773e15	+	8.55239e15i	−0.542038	+	0.938838i	−0.998787	+	0.0492419i	$0.984319\pi$
$458$	−6.17891e14	+	3.56739e14i	−0.0669451	+	0.0386508i
$459$	2.32787e15	+	4.03198e15i	0.248933	+	0.431164i
$460$	1.97836e15	+	1.14221e15i	0.208813	+	0.120558i
$461$		−	1.50600e16i		−	1.56898i	−0.620140	−	0.784491i	$-0.712924\pi$
$461$		−	1.50600e16i		−	1.56898i	0.620140	−	0.784491i	$-0.287076\pi$
$462$		0			0
$463$	4.17743e15			0.424056			0.212028	−	0.977264i	$-0.431993\pi$
$463$	4.17743e15			0.424056			0.212028	+	0.977264i	$0.431993\pi$
$464$	1.62974e14	−	2.82280e14i	0.0163309	−	0.0282860i
$465$	−8.32910e13	+	4.80881e13i	−0.00823911	+	0.00475685i
$466$	1.42058e15	+	2.46051e15i	0.138723	+	0.240275i
$467$	−5.15279e14	−	2.97496e14i	−0.0496753	−	0.0286801i	0.474957	−	0.880009i	$-0.342464\pi$
$467$	−5.15279e14	−	2.97496e14i	−0.0496753	−	0.0286801i	−0.524632	+	0.851329i	$0.675797\pi$
$468$			5.76824e15i			0.548995i
$469$		0			0
$470$	5.13664e15			0.476532
$471$	3.47461e14	−	6.01820e14i	0.0318259	−	0.0551241i
$472$	3.05606e15	−	1.76442e15i	0.276382	−	0.159569i
$473$	1.35172e15	+	2.34126e15i	0.120704	+	0.209065i
$474$	−9.09934e14	−	5.25351e14i	−0.0802306	−	0.0463211i
$475$			9.44763e15i			0.822548i
$476$		0			0
$477$	1.44153e16			1.22381
$478$	5.55586e15	−	9.62303e15i	0.465783	−	0.806760i
$479$	4.91871e15	−	2.83982e15i	0.407229	−	0.235114i	−0.282370	−	0.959306i	$-0.591120\pi$
$479$	4.91871e15	−	2.83982e15i	0.407229	−	0.235114i	0.689598	+	0.724192i	$0.257787\pi$
$480$	−6.69828e13	−	1.16018e14i	−0.00547666	−	0.00948585i
$481$	6.34620e15	+	3.66398e15i	0.512441	+	0.295858i
$482$			2.57514e15i			0.205361i
$483$		0			0
$484$	−2.72043e15			−0.211624
$485$	−9.47687e14	+	1.64144e15i	−0.0728139	+	0.126117i
$486$	−3.30039e15	+	1.90548e15i	−0.250465	+	0.144606i
$487$	7.23436e15	+	1.25303e16i	0.542283	+	0.939262i	0.998772	+	0.0495331i	$0.0157733\pi$
$487$	7.23436e15	+	1.25303e16i	0.542283	+	0.939262i	−0.456489	+	0.889729i	$0.650893\pi$
$488$	−6.71655e15	−	3.87780e15i	−0.497310	−	0.287122i
$489$		−	9.89835e14i		−	0.0723952i
$490$		0			0
$491$	−1.76959e16			−1.26294			−0.631472	−	0.775398i	$-0.717549\pi$
$491$	−1.76959e16			−1.26294			−0.631472	+	0.775398i	$0.717549\pi$
$492$	4.28706e14	−	7.42540e14i	0.0302252	−	0.0523515i
$493$	−2.91757e15	+	1.68446e15i	−0.203207	+	0.117322i
$494$	−5.88689e15	−	1.01964e16i	−0.405065	−	0.701592i
$495$	4.19888e15	+	2.42423e15i	0.285432	+	0.164794i
$496$			5.71556e14i			0.0383856i
$497$		0			0
$498$	6.10259e14			0.0400072
$499$	−1.04389e16	+	1.80808e16i	−0.676165	+	1.17115i	0.299962	+	0.953951i	$0.403026\pi$
$499$	−1.04389e16	+	1.80808e16i	−0.676165	+	1.17115i	−0.976127	+	0.217201i	$0.930307\pi$
$500$	5.40307e15	−	3.11947e15i	0.345797	−	0.199646i
$501$	−3.91307e13	−	6.77763e13i	−0.00247452	−	0.00428599i
$502$	−1.00476e16	−	5.80101e15i	−0.627829	−	0.362478i
$503$			1.88109e16i			1.16146i	0.814098	+	0.580728i	$0.197232\pi$
$503$			1.88109e16i			1.16146i	−0.814098	+	0.580728i	$0.802768\pi$
$504$		0			0
$505$	−4.93141e15			−0.297319
$506$	4.90952e15	−	8.50353e15i	0.292507	−	0.506636i
$507$	−5.23462e14	+	3.02221e14i	−0.0308203	+	0.0177941i
$508$	6.75736e15	+	1.17041e16i	0.393183	+	0.681013i
$509$	8.98820e15	+	5.18934e15i	0.516852	+	0.298404i	0.735646	−	0.677367i	$-0.236879\pi$
$509$	8.98820e15	+	5.18934e15i	0.516852	+	0.298404i	−0.218794	+	0.975771i	$0.570212\pi$
$510$			1.38463e15i			0.0786889i
$511$		0			0
$512$	−7.96131e14			−0.0441942
$513$	2.58438e15	−	4.47627e15i	0.141792	−	0.245591i
$514$	1.28608e16	−	7.42520e15i	0.697413	−	0.402652i
$515$	−5.44388e15	−	9.42908e15i	−0.291787	−	0.505389i
$516$	−3.63668e14	−	2.09964e14i	−0.0192667	−	0.0111236i
$517$		−	2.20787e16i		−	1.15619i
$518$		0			0
$519$	−2.92673e15			−0.149754
$520$	−1.73264e15	+	3.00102e15i	−0.0876371	+	0.151792i
$521$	4.79328e15	−	2.76740e15i	0.239666	−	0.138371i	−0.375357	−	0.926880i	$-0.622480\pi$
$521$	4.79328e15	−	2.76740e15i	0.239666	−	0.138371i	0.615023	+	0.788509i	$0.289147\pi$
$522$	−9.16190e14	−	1.58689e15i	−0.0452858	−	0.0784374i
$523$	−2.52525e16	−	1.45795e16i	−1.23394	−	0.712416i	−0.266092	−	0.963948i	$-0.585733\pi$
$523$	−2.52525e16	−	1.45795e16i	−1.23394	−	0.712416i	−0.967849	+	0.251531i	$0.919066\pi$
$524$		−	6.88140e15i		−	0.332421i
$525$		0			0
$526$	3.96908e15			0.187403
$527$	2.95373e15	−	5.11600e15i	0.137882	−	0.238818i
$528$	−4.98675e14	+	2.87910e14i	−0.0230152	+	0.0132878i
$529$	−2.04667e15	−	3.54493e15i	−0.0933928	−	0.161761i
$530$	7.49980e15	+	4.33001e15i	0.338372	+	0.195359i
$531$		−	1.98380e16i		−	0.884976i
$532$		0			0
$533$	−2.21786e16			−0.967322
$534$	−1.17130e15	+	2.02875e15i	−0.0505151	+	0.0874946i
$535$	4.53879e15	−	2.62047e15i	0.193561	−	0.111752i
$536$	4.59716e15	+	7.96252e15i	0.193866	+	0.335785i
$537$	−7.64733e14	−	4.41519e14i	−0.0318907	−	0.0184121i
$538$			2.19122e16i			0.903635i
$539$		0			0
$540$	−1.52128e15			−0.0613543
$541$	−1.27196e15	+	2.20310e15i	−0.0507329	+	0.0878720i	−0.890277	−	0.455420i	$-0.849489\pi$
$541$	−1.27196e15	+	2.20310e15i	−0.0507329	+	0.0878720i	0.839544	+	0.543292i	$0.182822\pi$
$542$	−1.87213e16	+	1.08087e16i	−0.738482	+	0.426363i
$543$	−1.51342e15	−	2.62131e15i	−0.0590418	−	0.102263i
$544$	7.12618e15	+	4.11430e15i	0.274956	+	0.158746i
$545$			1.31872e16i			0.503240i
$546$		0			0
$547$	−4.15289e16			−1.55034			−0.775169	−	0.631754i	$-0.782335\pi$
$547$	−4.15289e16			−1.55034			−0.775169	+	0.631754i	$0.782335\pi$
$548$	−5.83918e15	+	1.01137e16i	−0.215610	+	0.373447i
$549$	−3.77583e16	+	2.17998e16i	−1.37905	+	0.796193i
$550$	−5.97598e15	−	1.03507e16i	−0.215890	−	0.373933i
$551$	3.23906e15	+	1.87007e15i	0.115747	+	0.0668265i
$552$			1.52519e15i			0.0539126i
$553$		0			0
$554$	−2.43383e16			−0.841845
$555$	−4.78376e14	+	8.28572e14i	−0.0163686	+	0.0283513i
$556$	−2.23707e16	+	1.29157e16i	−0.757235	+	0.437190i
$557$	−2.43848e16	−	4.22357e16i	−0.816560	−	1.41432i	−0.908203	−	0.418531i	$-0.862545\pi$
$557$	−2.43848e16	−	4.22357e16i	−0.816560	−	1.41432i	0.0916429	−	0.995792i	$-0.470788\pi$
$558$	2.78263e15	+	1.60655e15i	0.0921830	+	0.0532219i
$559$			1.08622e16i			0.355999i
$560$		0			0
$561$	5.95153e15			0.190920
$562$	3.26449e15	−	5.65426e15i	0.103609	−	0.179456i
$563$	3.00880e16	−	1.73713e16i	0.944807	−	0.545484i	0.0533429	−	0.998576i	$-0.483012\pi$
$563$	3.00880e16	−	1.73713e16i	0.944807	−	0.545484i	0.891464	+	0.453092i	$0.149679\pi$
$564$	1.71475e15	+	2.97003e15i	0.0532752	+	0.0922754i
$565$	2.23815e16	+	1.29220e16i	0.688016	+	0.397226i
$566$		−	3.75384e16i		−	1.14176i
$567$		0			0
$568$	3.45079e15			0.102761
$569$	1.68050e16	−	2.91072e16i	0.495183	−	0.857682i	−0.504802	−	0.863235i	$-0.668434\pi$
$569$	1.68050e16	−	2.91072e16i	0.495183	−	0.857682i	0.999985	+	0.00555324i	$0.00176766\pi$
$570$	1.33126e15	−	7.68604e14i	0.0388163	−	0.0224106i
$571$	−2.13500e16	−	3.69793e16i	−0.616000	−	1.06694i	−0.990208	−	0.139599i	$-0.955419\pi$
$571$	−2.13500e16	−	3.69793e16i	−0.616000	−	1.06694i	0.374208	−	0.927345i	$-0.377915\pi$
$572$	1.28992e16	+	7.44736e15i	0.368287	+	0.212631i
$573$		−	3.06836e15i		−	0.0866920i
$574$		0			0
$575$	−3.16575e16			−0.875931
$576$	−2.23780e15	+	3.87598e15i	−0.0612754	+	0.106132i
$577$	3.37960e16	−	1.95121e16i	0.915820	−	0.528749i	0.0335206	−	0.999438i	$-0.489328\pi$
$577$	3.37960e16	−	1.95121e16i	0.915820	−	0.528749i	0.882299	+	0.470689i	$0.155995\pi$
$578$	−2.93411e16	−	5.08203e16i	−0.786882	−	1.36292i
$579$	2.55624e15	+	1.47584e15i	0.0678469	+	0.0391714i
$580$		−	1.10080e15i		−	0.0289163i
$581$		0			0
$582$	−1.26545e15			−0.0325617
$583$	1.86116e16	−	3.22362e16i	0.473993	−	0.820980i
$584$	−6.17348e15	+	3.56426e15i	−0.155616	+	0.0898447i
$585$	9.74035e15	+	1.68708e16i	0.243019	+	0.420920i
$586$	−2.84072e16	−	1.64009e16i	−0.701524	−	0.405025i
$587$		−	1.17306e16i		−	0.286741i	−0.989669	−	0.143371i	$-0.954206\pi$
$587$		−	1.17306e16i		−	0.286741i	0.989669	−	0.143371i	$-0.0457941\pi$
$588$		0			0
$589$	−6.55840e15			−0.157075
$590$	5.95886e15	−	1.03210e16i	0.141270	−	0.244687i
$591$	7.18896e15	−	4.15055e15i	0.168710	−	0.0974049i
$592$	2.84290e15	+	4.92405e15i	0.0660437	+	0.114391i
$593$	−5.13414e16	−	2.96420e16i	−1.18070	−	0.681677i	−0.224523	−	0.974469i	$-0.572082\pi$
$593$	−5.13414e16	−	2.96420e16i	−1.18070	−	0.681677i	−0.956176	+	0.292792i	$0.905416\pi$
$594$			6.53886e15i			0.148862i
$595$		0			0
$596$	−3.52278e16			−0.785973
$597$	−3.94390e15	+	6.83104e15i	−0.0871124	+	0.150883i
$598$	3.41665e16	−	1.97260e16i	0.747125	−	0.431353i
$599$	−2.10616e16	−	3.64797e16i	−0.455963	−	0.789751i	0.542780	−	0.839875i	$-0.317372\pi$
$599$	−2.10616e16	−	3.64797e16i	−0.455963	−	0.789751i	−0.998743	+	0.0501238i	$0.984038\pi$
$600$	1.60778e15	+	9.28252e14i	0.0344603	+	0.0198957i
$601$			8.27638e16i			1.75628i	0.478405	+	0.878139i	$0.341215\pi$
$601$			8.27638e16i			1.75628i	−0.478405	+	0.878139i	$0.658785\pi$
$602$		0			0
$603$	5.16876e16			1.07518
$604$	−1.66837e16	+	2.88969e16i	−0.343613	+	0.595155i
$605$	−7.95664e15	+	4.59377e15i	−0.162255	+	0.0936778i
$606$	−1.64624e15	−	2.85136e15i	−0.0332396	−	0.0575727i
$607$	2.73533e16	+	1.57924e16i	0.546862	+	0.315731i	0.747855	−	0.663862i	$-0.231084\pi$
$607$	2.73533e16	+	1.57924e16i	0.546862	+	0.315731i	−0.200994	+	0.979593i	$0.564417\pi$
$608$		−	9.13533e15i		−	0.180843i
$609$		0			0
$610$	−2.61925e16			−0.508391
$611$	4.43552e16	−	7.68255e16i	0.852506	−	1.47658i
$612$	4.00611e16	−	2.31293e16i	0.762456	−	0.440204i
$613$	3.40905e16	+	5.90465e16i	0.642497	+	1.11284i	0.984874	+	0.173275i	$0.0554348\pi$
$613$	3.40905e16	+	5.90465e16i	0.642497	+	1.11284i	−0.342377	+	0.939563i	$0.611232\pi$
$614$	1.24987e16	+	7.21614e15i	0.233268	+	0.134677i
$615$		−	2.89568e15i		−	0.0535180i
$616$		0			0
$617$	3.16558e16			0.573777			0.286888	−	0.957964i	$-0.407379\pi$
$617$	3.16558e16			0.573777			0.286888	+	0.957964i	$0.407379\pi$
$618$	3.63462e15	−	6.29535e15i	0.0652422	−	0.113003i
$619$	−6.17058e16	+	3.56259e16i	−1.09694	+	0.633318i	−0.935415	−	0.353551i	$-0.884974\pi$
$619$	−6.17058e16	+	3.56259e16i	−1.09694	+	0.633318i	−0.161523	+	0.986869i	$0.551641\pi$
$620$	9.65140e14	+	1.67167e15i	0.0169918	+	0.0294307i
$621$	1.49993e16	+	8.65984e15i	0.261530	+	0.150994i
$622$			5.42618e16i			0.937026i
$623$		0			0
$624$	−2.31360e15			−0.0391905
$625$	−1.34274e16	+	2.32570e16i	−0.225275	+	0.390187i
$626$	−2.99656e16	+	1.73006e16i	−0.497940	+	0.287486i
$627$	−3.30367e15	−	5.72212e15i	−0.0543740	−	0.0941786i
$628$	−1.20787e16	−	6.97363e15i	−0.196907	−	0.113684i
$629$		−	5.87669e16i		−	0.948919i
$630$		0			0
$631$	4.94210e16			0.782953			0.391477	−	0.920188i	$-0.371964\pi$
$631$	4.94210e16			0.782953			0.391477	+	0.920188i	$0.371964\pi$
$632$	−1.05439e16	+	1.82626e16i	−0.165463	+	0.286590i
$633$	1.33397e16	−	7.70170e15i	0.207360	−	0.119719i
$634$	−4.86882e15	−	8.43304e15i	−0.0749701	−	0.129852i
$635$	3.95275e16	+	2.28212e16i	0.602916	+	0.348094i
$636$			5.78189e15i			0.0873629i
$637$		0			0
$638$	−4.73156e15			−0.0701585
$639$	9.69962e15	−	1.68002e16i	0.142479	−	0.246780i
$640$	−2.32850e15	+	1.34436e15i	−0.0338842	+	0.0195630i
$641$	1.87234e16	+	3.24298e16i	0.269920	+	0.467516i	0.968841	−	0.247683i	$-0.0796693\pi$
$641$	1.87234e16	+	3.24298e16i	0.269920	+	0.467516i	−0.698921	+	0.715199i	$0.746336\pi$
$642$	3.03034e15	+	1.74957e15i	0.0432794	+	0.0249874i
$643$		−	1.35542e17i		−	1.91782i	−0.283717	−	0.958908i	$-0.591568\pi$
$643$		−	1.35542e17i		−	1.91782i	0.283717	−	0.958908i	$-0.408432\pi$
$644$		0			0
$645$	−1.41819e15			−0.0196960
$646$	−4.72102e16	+	8.17704e16i	−0.649592	+	1.12513i
$647$	−5.20145e16	+	3.00306e16i	−0.709085	+	0.409390i	−0.810722	−	0.585431i	$-0.800925\pi$
$647$	−5.20145e16	+	3.00306e16i	−0.709085	+	0.409390i	0.101637	+	0.994822i	$0.467592\pi$
$648$	1.23238e16	+	2.13454e16i	0.166454	+	0.288307i
$649$	−4.43627e16	−	2.56128e16i	−0.593676	−	0.342759i
$650$		−	4.80220e16i		−	0.636737i
$651$		0			0
$652$	−1.98663e16			−0.258601
$653$	3.02273e15	−	5.23552e15i	0.0389870	−	0.0675275i	−0.845873	−	0.533384i	$-0.820920\pi$
$653$	3.02273e15	−	5.23552e15i	0.0389870	−	0.0675275i	0.884860	+	0.465856i	$0.154254\pi$
$654$	−7.62492e15	+	4.40225e15i	−0.0974471	+	0.0562611i
$655$	−1.16200e16	−	2.01265e16i	−0.147150	−	0.254871i
$656$	−1.49030e16	−	8.60424e15i	−0.187004	−	0.107967i
$657$			4.00743e16i			0.498280i
$658$		0			0
$659$	−3.39399e16			−0.414379			−0.207190	−	0.978301i	$-0.566432\pi$
$659$	−3.39399e16			−0.414379			−0.207190	+	0.978301i	$0.566432\pi$
$660$	−9.72341e14	+	1.68414e15i	−0.0117640	+	0.0203758i
$661$	7.13797e15	−	4.12111e15i	0.0855787	−	0.0494089i	−0.456600	−	0.889672i	$-0.650933\pi$
$661$	7.13797e15	−	4.12111e15i	0.0855787	−	0.0494089i	0.542179	+	0.840263i	$0.317600\pi$
$662$	1.99616e16	+	3.45745e16i	0.237163	+	0.410779i
$663$	2.07091e16	+	1.19564e16i	0.243826	+	0.140773i
$664$		−	1.22481e16i		−	0.142909i
$665$		0			0
$666$	3.19638e16			0.366280
$667$	−6.26631e15	+	1.08536e16i	−0.0711635	+	0.123259i
$668$	−1.36029e15	+	7.85362e14i	−0.0153099	+	0.00883917i
$669$	1.19652e16	+	2.07244e16i	0.133464	+	0.231166i
$670$	2.68913e16	+	1.55257e16i	0.297278	+	0.171634i
$671$			1.12583e17i			1.23349i
$672$		0			0
$673$	1.68997e17			1.81881			0.909406	−	0.415909i	$-0.136537\pi$
$673$	1.68997e17			1.81881			0.909406	+	0.415909i	$0.136537\pi$
$674$	−4.51554e16	+	7.82114e16i	−0.481671	+	0.834278i
$675$	1.82575e16	−	1.05410e16i	0.193027	−	0.111444i
$676$	6.06565e15	+	1.05060e16i	0.0635619	+	0.110093i
$677$	−1.58891e16	−	9.17360e15i	−0.165032	−	0.0952813i	0.415209	−	0.909726i	$-0.363708\pi$
$677$	−1.58891e16	−	9.17360e15i	−0.165032	−	0.0952813i	−0.580241	+	0.814445i	$0.697042\pi$
$678$			1.72548e16i			0.177636i
$679$		0			0
$680$	2.77899e16			0.281083
$681$	1.02741e16	−	1.77953e16i	0.103006	−	0.178411i
$682$	7.18530e15	−	4.14844e15i	0.0714067	−	0.0412267i
$683$	8.30063e16	+	1.43771e17i	0.817686	+	1.41627i	0.907383	+	0.420305i	$0.138077\pi$
$683$	8.30063e16	+	1.43771e17i	0.817686	+	1.41627i	−0.0896963	+	0.995969i	$0.528590\pi$
$684$	−4.44755e16	−	2.56780e16i	−0.434295	−	0.250740i
$685$			3.94405e16i			0.381768i
$686$		0			0
$687$	−1.60877e15			−0.0153022
$688$	−4.21403e15	+	7.29891e15i	−0.0397344	+	0.0688220i
$689$	1.29523e17	−	7.47799e16i	1.21068	−	0.698987i
$690$	2.57547e15	+	4.46084e15i	0.0238650	+	0.0413354i
$691$	−9.75093e16	−	5.62970e16i	−0.895731	−	0.517151i	−0.0199183	−	0.999802i	$-0.506341\pi$
$691$	−9.75093e16	−	5.62970e16i	−0.895731	−	0.517151i	−0.875813	+	0.482651i	$0.839674\pi$
$692$			5.87402e16i			0.534933i
$693$		0			0
$694$	−7.54113e16			−0.674962
$695$	−4.36194e16	+	7.55511e16i	−0.387054	+	0.670397i
$696$	6.36490e14	−	3.67478e14i	0.00559933	−	0.00323277i
$697$	8.89311e16	+	1.54033e17i	0.775635	+	1.34344i
$698$	4.46476e16	+	2.57773e16i	0.386070	+	0.222898i
$699$			6.40629e15i			0.0549216i
$700$		0			0
$701$	1.67852e17			1.41455			0.707276	−	0.706937i	$-0.249924\pi$
$701$	1.67852e17			1.41455			0.707276	+	0.706937i	$0.249924\pi$
$702$	−1.31363e16	+	2.27527e16i	−0.109762	+	0.190113i
$703$	−5.65017e16	+	3.26213e16i	−0.468090	+	0.270252i
$704$	5.77844e15	+	1.00085e16i	0.0474651	+	0.0822120i
$705$	1.00305e16	+	5.79110e15i	0.0816934	+	0.0471657i
$706$		−	1.16109e17i		−	0.937645i
$707$		0			0
$708$	7.95690e15			0.0631749
$709$	−2.91003e15	+	5.04032e15i	−0.0229097	+	0.0396808i	−0.877253	−	0.480028i	$-0.840626\pi$
$709$	−2.91003e15	+	5.04032e15i	−0.0229097	+	0.0396808i	0.854343	+	0.519709i	$0.173960\pi$
$710$	1.00928e16	−	5.82706e15i	0.0787880	−	0.0454882i
$711$	5.92746e16	+	1.02667e17i	0.458830	+	0.794716i
$712$	4.07176e16	+	2.35083e16i	0.312537	+	0.180444i
$713$		−	2.19762e16i		−	0.167269i
$714$		0			0
$715$	5.03030e16			0.376493
$716$	−8.86140e15	+	1.53484e16i	−0.0657694	+	0.113916i
$717$	2.16982e16	−	1.25275e16i	0.159701	−	0.0922037i
$718$	−4.03561e16	−	6.98988e16i	−0.294552	−	0.510180i
$719$	−1.95286e16	−	1.12749e16i	−0.141351	−	0.0816090i	0.427657	−	0.903941i	$-0.359339\pi$
$719$	−1.95286e16	−	1.12749e16i	−0.141351	−	0.0816090i	−0.569008	+	0.822332i	$0.692673\pi$
$720$			1.51152e16i			0.108497i
$721$		0			0
$722$	4.66144e15			0.0329077
$723$	−2.90324e15	+	5.02856e15i	−0.0203261	+	0.0352058i
$724$	−5.26105e16	+	3.03747e16i	−0.365292	+	0.210902i
$725$	7.62751e15	+	1.32112e16i	0.0525236	+	0.0909736i
$726$	−5.31227e15	−	3.06704e15i	−0.0362794	−	0.0209459i
$727$		−	8.48651e16i		−	0.574808i	−0.957809	−	0.287404i	$-0.907208\pi$
$727$		−	8.48651e16i		−	0.574808i	0.957809	−	0.287404i	$-0.0927922\pi$
$728$		0			0
$729$	1.32737e17			0.884354
$730$	−1.20373e16	+	2.08493e16i	−0.0795415	+	0.137770i
$731$	7.54396e16	−	4.35551e16i	0.494419	−	0.285453i
$732$	−8.74375e15	−	1.51446e16i	−0.0568370	−	0.0984446i
$733$	2.38459e17	+	1.37674e17i	1.53741	+	0.887623i	0.998989	+	0.0449449i	$0.0143112\pi$
$733$	2.38459e17	+	1.37674e17i	1.53741	+	0.887623i	0.538418	+	0.842678i	$0.319022\pi$
$734$			1.32826e17i			0.849386i
$735$		0			0
$736$	3.06110e16			0.192580
$737$	6.67337e16	−	1.15586e17i	0.416428	−	0.721275i
$738$	−8.37799e16	+	4.83703e16i	−0.518563	+	0.299392i
$739$	−1.06031e17	−	1.83651e17i	−0.650976	−	1.12752i	−0.982886	−	0.184213i	$-0.941026\pi$
$739$	−1.06031e17	−	1.83651e17i	−0.650976	−	1.12752i	0.331910	−	0.943311i	$-0.392307\pi$
$740$	1.66297e16	+	9.60114e15i	0.101273	+	0.0584699i
$741$		−	2.65478e16i		−	0.160368i
$742$		0			0
$743$	−7.72077e16			−0.458910			−0.229455	−	0.973319i	$-0.573694\pi$
$743$	−7.72077e16			−0.458910			−0.229455	+	0.973319i	$0.573694\pi$
$744$	−6.44378e14	+	1.11610e15i	−0.00379930	+	0.00658058i
$745$	−1.03033e17	+	5.94863e16i	−0.602615	+	0.347920i
$746$	5.20369e16	+	9.01306e16i	0.301911	+	0.522925i
$747$	−5.96300e16	−	3.44274e16i	−0.343195	−	0.198144i
$748$		−	1.19449e17i		−	0.681981i
$749$		0			0
$750$	1.40677e16			0.0790414
$751$	1.19267e16	−	2.06577e16i	0.0664785	−	0.115144i	−0.830870	−	0.556466i	$-0.812157\pi$
$751$	1.19267e16	−	2.06577e16i	0.0664785	−	0.115144i	0.897349	+	0.441322i	$0.145490\pi$
$752$	5.96092e16	−	3.44154e16i	0.329614	−	0.190303i
$753$	−1.30802e16	−	2.26556e16i	−0.0717539	−	0.124281i
$754$	−1.64640e16	−	9.50552e15i	−0.0896001	−	0.0517306i
$755$			1.12689e17i			0.608417i
$756$		0			0
$757$	1.29851e17			0.690032			0.345016	−	0.938597i	$-0.387874\pi$
$757$	1.29851e17			0.690032			0.345016	+	0.938597i	$0.387874\pi$
$758$	4.25723e16	−	7.37373e16i	0.224446	−	0.388752i
$759$	1.91739e16	−	1.10701e16i	0.100291	−	0.0579029i
$760$	−1.54261e16	−	2.67187e16i	−0.0800523	−	0.138655i
$761$	−6.56503e16	−	3.79032e16i	−0.338009	−	0.195150i	0.321382	−	0.946950i	$-0.395853\pi$
$761$	−6.56503e16	−	3.79032e16i	−0.338009	−	0.195150i	−0.659391	+	0.751800i	$0.729186\pi$
$762$			3.04733e16i			0.155664i
$763$		0			0
$764$	−6.15828e16			−0.309670
$765$	7.81131e16	−	1.35296e17i	0.389723	−	0.675019i
$766$	4.67286e16	−	2.69788e16i	0.231318	−	0.133552i
$767$	−1.02910e17	−	1.78246e17i	−0.505460	−	0.875482i
$768$	−1.55463e15	−	8.97567e14i	−0.00757635	−	0.00437421i
$769$		−	1.28136e17i		−	0.619601i	−0.950802	−	0.309800i	$-0.899738\pi$
$769$		−	1.28136e17i		−	0.619601i	0.950802	−	0.309800i	$-0.100262\pi$
$770$		0			0
$771$	3.34850e16			0.159413
$772$	2.96206e16	−	5.13043e16i	0.139923	−	0.242354i
$773$	−3.32107e17	+	1.91742e17i	−1.55669	+	0.898754i	−0.559117	+	0.829089i	$0.688860\pi$
$773$	−3.32107e17	+	1.91742e17i	−1.55669	+	0.898754i	−0.997570	+	0.0696654i	$0.977807\pi$
$774$	2.36899e16	+	4.10322e16i	0.110184	+	0.190844i
$775$	−2.31661e16	−	1.33750e16i	−0.106916	−	0.0617280i
$776$			2.53979e16i			0.116313i
$777$		0			0
$778$	7.89947e16			0.356222
$779$	9.87306e16	−	1.71006e17i	0.441801	−	0.765222i
$780$	−6.76676e15	+	3.90679e15i	−0.0300478	+	0.0173481i
$781$	−2.50463e16	−	4.33815e16i	−0.110367	−	0.191160i
$782$	−2.74000e17	−	1.58194e17i	−1.19815	−	0.691750i
$783$		−	8.34594e15i		−	0.0362164i
$784$		0			0
$785$	−4.71032e16			−0.201295
$786$	7.75816e15	−	1.34375e16i	0.0329021	−	0.0569881i
$787$	9.58573e16	−	5.53432e16i	0.403438	−	0.232925i	−0.284528	−	0.958668i	$-0.591837\pi$
$787$	9.58573e16	−	5.53432e16i	0.403438	−	0.232925i	0.687966	+	0.725743i	$0.258504\pi$
$788$	−8.33026e16	−	1.44284e17i	−0.347938	−	0.602646i
$789$	7.75056e15	+	4.47479e15i	0.0321271	+	0.0185486i
$790$			7.12186e16i			0.292975i
$791$		0			0
$792$	6.49691e16			0.263242
$793$	−2.26174e17	+	3.91745e17i	−0.909501	+	1.57530i
$794$	2.35277e17	−	1.35837e17i	0.938982	−	0.542121i
$795$	9.76340e15	+	1.69107e16i	0.0386722	+	0.0669821i
$796$	1.37101e17	+	7.91551e16i	0.538966	+	0.311172i
$797$		−	6.75641e16i		−	0.263612i	−0.991276	−	0.131806i	$-0.957922\pi$
$797$		−	6.75641e16i		−	0.263612i	0.991276	−	0.131806i	$-0.0420776\pi$
$798$		0			0
$799$	−7.11417e17			−2.73428
$800$	1.86302e16	−	3.22685e16i	0.0710688	−	0.123095i
$801$	2.28901e17	−	1.32156e17i	0.866669	−	0.500372i
$802$	4.67171e16	+	8.09163e16i	0.175562	+	0.304081i
$803$	8.96160e16	+	5.17398e16i	0.334266	+	0.192989i
$804$			2.07315e16i			0.0767530i
$805$		0			0
$806$	3.33362e16			0.121592
$807$	−2.47041e16	+	4.27887e16i	−0.0894392	+	0.154913i
$808$	−5.72276e16	+	3.30404e16i	−0.205654	+	0.118734i
$809$	−7.40820e16	−	1.28314e17i	−0.264254	−	0.457702i	0.703114	−	0.711077i	$-0.251792\pi$
$809$	−7.40820e16	−	1.28314e17i	−0.264254	−	0.457702i	−0.967368	+	0.253376i	$0.918459\pi$
$810$	7.20885e16	+	4.16203e16i	0.255244	+	0.147365i
$811$			3.91802e17i			1.37702i	0.725226	+	0.688511i	$0.241735\pi$
$811$			3.91802e17i			1.37702i	−0.725226	+	0.688511i	$0.758265\pi$
$812$		0			0
$813$	−4.87436e16			−0.168801
$814$	4.12683e16	−	7.14789e16i	0.141863	−	0.245715i
$815$	−5.81043e16	+	3.35465e16i	−0.198272	+	0.114473i
$816$	9.27701e15	+	1.60683e16i	0.0314244	+	0.0544287i
$817$	−8.37524e16	−	4.83545e16i	−0.281621	−	0.162594i
$818$		−	1.41585e17i		−	0.472604i
$819$		0			0
$820$	−5.81171e16			−0.191170
$821$	−5.08078e16	+	8.80016e16i	−0.165909	+	0.287364i	−0.936978	−	0.349389i	$-0.886389\pi$
$821$	−5.08078e16	+	8.80016e16i	−0.165909	+	0.287364i	0.771068	+	0.636752i	$0.219723\pi$
$822$	−2.28047e16	+	1.31663e16i	−0.0739253	+	0.0426808i
$823$	−1.83207e17	−	3.17323e17i	−0.589580	−	1.02118i	−0.994287	−	0.106736i	$-0.965960\pi$
$823$	−1.83207e17	−	3.17323e17i	−0.589580	−	1.02118i	0.404708	−	0.914446i	$-0.367373\pi$
$824$	−1.26349e17	−	7.29479e16i	−0.403655	−	0.233050i
$825$		−	2.69495e16i		−	0.0854727i
$826$		0			0
$827$	−2.85422e17			−0.892183			−0.446091	−	0.894987i	$-0.647184\pi$
$827$	−2.85422e17			−0.892183			−0.446091	+	0.894987i	$0.647184\pi$
$828$	8.60428e16	−	1.49031e17i	0.267013	−	0.462480i
$829$	2.21711e17	−	1.28005e17i	0.683063	−	0.394367i	−0.117945	−	0.993020i	$-0.537631\pi$
$829$	2.21711e17	−	1.28005e17i	0.683063	−	0.394367i	0.801008	+	0.598654i	$0.204297\pi$
$830$	−2.06823e16	−	3.58228e16i	−0.0632601	−	0.109570i
$831$	−4.75262e16	−	2.74393e16i	−0.144320	−	0.0833233i
$832$			4.64346e16i			0.139992i
$833$		0			0
$834$	−5.82453e16			−0.173087
$835$	−2.65235e15	+	4.59401e15i	−0.00782551	+	0.0135542i
$836$	−1.14845e17	+	6.63055e16i	−0.336413	+	0.194228i
$837$	7.31738e15	+	1.26741e16i	0.0212815	+	0.0368607i
$838$	1.54165e17	+	8.90072e16i	0.445166	+	0.257016i
$839$		−	1.97080e17i		−	0.565028i	−0.959263	−	0.282514i	$-0.908832\pi$
$839$		−	1.97080e17i		−	0.565028i	0.959263	−	0.282514i	$-0.0911684\pi$
$840$		0			0
$841$	−3.47776e17			−0.982931
$842$	1.02248e17	−	1.77099e17i	0.286934	−	0.496984i
$843$	1.27493e16	−	7.36083e15i	0.0355240	−	0.0205098i
$844$	−1.54575e17	−	2.67732e17i	−0.427646	−	0.740705i
$845$	3.54813e16	+	2.04851e16i	0.0974673	+	0.0562728i
$846$		−	3.86945e17i		−	1.05542i
$847$		0			0
$848$	1.16044e17			0.312067
$849$	4.23211e16	−	7.33024e16i	0.113009	−	0.195736i
$850$	−3.33519e17	+	1.92557e17i	−0.884315	+	0.510560i
$851$	−1.09309e17	−	1.89328e17i	−0.287791	−	0.498469i
$852$	6.73846e15	+	3.89045e15i	0.0176166	+	0.0101710i
$853$			2.02493e16i			0.0525673i	0.999655	+	0.0262836i	$0.00836731\pi$
$853$			2.02493e16i			0.0525673i	−0.999655	+	0.0262836i	$0.991633\pi$
$854$		0			0
$855$	−1.73441e17			−0.443972
$856$	3.51143e16	−	6.08197e16i	0.0892567	−	0.154597i
$857$	−4.73881e17	+	2.73595e17i	−1.19615	+	0.690596i	−0.959694	−	0.281047i	$-0.909318\pi$
$857$	−4.73881e17	+	2.73595e17i	−1.19615	+	0.690596i	−0.236453	+	0.971643i	$0.575985\pi$
$858$	1.67925e16	+	2.90854e16i	0.0420911	+	0.0729040i
$859$	−7.51160e16	−	4.33682e16i	−0.186971	−	0.107948i	0.403593	−	0.914939i	$-0.367761\pi$
$859$	−7.51160e16	−	4.33682e16i	−0.186971	−	0.107948i	−0.590564	+	0.806991i	$0.701095\pi$
$860$			2.84635e16i			0.0703555i
$861$		0			0
$862$	−1.99833e17			−0.487106
$863$	−1.04296e17	+	1.80646e17i	−0.252465	+	0.437283i	−0.964204	−	0.265161i	$-0.914575\pi$
$863$	−1.04296e17	+	1.80646e17i	−0.252465	+	0.437283i	0.711739	+	0.702444i	$0.247908\pi$
$864$	−1.76540e16	+	1.01925e16i	−0.0424385	+	0.0245019i
$865$	9.91898e16	+	1.71802e17i	0.236794	+	0.410139i
$866$	3.14283e17	+	1.81451e17i	0.745098	+	0.430182i
$867$		−	1.32318e17i		−	0.311533i
$868$		0			0
$869$	3.06117e17			0.710836
$870$	1.24106e15	−	2.14958e15i	0.00286205	−	0.00495721i
$871$	4.64416e17	−	2.68131e17i	1.06365	−	0.614098i
$872$	8.83543e16	+	1.53034e17i	0.200969	+	0.348088i
$873$	1.23650e17	+	7.13896e16i	0.279325	+	0.161268i
$874$			3.51251e17i			0.788041i
$875$		0			0
$876$	−1.60735e16			−0.0355702
$877$	−3.33020e17	+	5.76807e17i	−0.731935	+	1.26775i	0.224120	+	0.974562i	$0.428049\pi$
$877$	−3.33020e17	+	5.76807e17i	−0.731935	+	1.26775i	−0.956055	+	0.293187i	$0.905284\pi$
$878$	4.15261e16	−	2.39751e16i	0.0906471	−	0.0523352i
$879$	−3.69811e16	−	6.40531e16i	−0.0801764	−	0.138870i
$880$	3.38012e16	+	1.95151e16i	0.0727841	+	0.0420219i
$881$		−	2.75630e16i		−	0.0589483i	−0.999566	−	0.0294742i	$-0.990617\pi$
$881$		−	2.75630e16i		−	0.0589483i	0.999566	−	0.0294742i	$-0.00938327\pi$
$882$		0			0
$883$	−9.14924e17			−1.93028			−0.965141	−	0.261730i	$-0.915707\pi$
$883$	−9.14924e17			−1.93028			−0.965141	+	0.261730i	$0.915707\pi$
$884$	2.39968e17	−	4.15636e17i	0.502851	−	0.870964i
$885$	2.32721e16	−	1.34362e16i	0.0484369	−	0.0279650i
$886$	1.98276e17	+	3.43425e17i	0.409891	+	0.709952i
$887$	2.97422e17	+	1.71717e17i	0.610705	+	0.352590i	0.773241	−	0.634112i	$-0.218634\pi$
$887$	2.97422e17	+	1.71717e17i	0.610705	+	0.352590i	−0.162537	+	0.986703i	$0.551968\pi$
$888$			1.28205e16i			0.0261472i
$889$		0			0
$890$	1.58786e17			0.319501
$891$	1.78896e17	−	3.09856e17i	0.357547	−	0.619290i
$892$	4.15943e17	−	2.40145e17i	0.825743	−	0.476743i
$893$	3.94904e17	+	6.83995e17i	0.778723	+	1.34879i
$894$	−6.87904e16	−	3.97162e16i	−0.134742	−	0.0777933i
$895$			5.98540e16i			0.116454i
$896$		0			0
$897$	8.89574e16			0.170776
$898$	−9.52395e16	+	1.64960e17i	−0.181618	+	0.314572i
$899$	−9.17104e15	+	5.29490e15i	−0.0173724	+	0.0100300i
$900$	−1.04733e17	−	1.81404e17i	−0.197074	−	0.341343i
$901$	−1.03871e18	−	5.99700e17i	−1.94154	−	1.12095i
$902$			2.49803e17i			0.463830i
$903$		0			0
$904$	3.46308e17			0.634529
$905$	−1.02582e17	+	1.77678e17i	−0.186716	+	0.323401i
$906$	−6.51574e16	+	3.76187e16i	−0.117813	+	0.0680196i
$907$	−3.27310e17	−	5.66918e17i	−0.587917	−	1.01830i	−0.994505	−	0.104690i	$-0.966615\pi$
$907$	−3.27310e17	−	5.66918e17i	−0.587917	−	1.01830i	0.406588	−	0.913612i	$-0.366718\pi$
$908$	−3.57155e17	−	2.06204e17i	−0.637297	−	0.367944i
$909$			3.71485e17i			0.658504i
$910$		0			0
$911$	−1.25928e17			−0.220298			−0.110149	−	0.993915i	$-0.535133\pi$
$911$	−1.25928e17			−0.220298			−0.110149	+	0.993915i	$0.535133\pi$
$912$	1.02993e16	−	1.78388e16i	0.0178993	−	0.0310026i
$913$	−1.53976e17	+	8.88982e16i	−0.265845	+	0.153486i
$914$	2.23456e17	+	3.87037e17i	0.383279	+	0.663859i
$915$	−5.11469e16	−	2.95297e16i	−0.0871552	−	0.0503191i
$916$			3.22884e16i			0.0546604i
$917$		0			0
$918$	2.10694e17			0.352044
$919$	−2.19066e17	+	3.79433e17i	−0.363648	+	0.629857i	−0.988558	−	0.150839i	$-0.951802\pi$
$919$	−2.19066e17	+	3.79433e17i	−0.363648	+	0.629857i	0.624910	+	0.780697i	$0.285136\pi$
$920$	8.95303e16	−	5.16903e16i	0.147653	−	0.0852477i
$921$	1.62711e16	+	2.81824e16i	0.0266599	+	0.0461763i
$922$	−5.90227e17	−	3.40768e17i	−0.960801	−	0.554719i
$923$		−	2.01268e17i		−	0.325510i
$924$		0			0
$925$	−2.66106e17			−0.424820
$926$	9.45245e16	−	1.63721e17i	0.149927	−	0.259680i
$927$	−7.10297e17	+	4.10090e17i	−1.11934	+	0.646250i
$928$	−7.37537e15	−	1.27745e16i	−0.0115477	−	0.0200012i
$929$	1.02346e18	+	5.90894e17i	1.59212	+	0.919211i	0.992943	+	0.118594i	$0.0378388\pi$
$929$	1.02346e18	+	5.90894e17i	1.59212	+	0.919211i	0.599177	+	0.800616i	$0.295495\pi$
$930$			4.35243e15i			0.00672720i
$931$		0			0
$932$	1.28576e17			0.196184
$933$	−6.11753e16	+	1.05959e17i	−0.0927441	+	0.160637i
$934$	−2.33189e16	+	1.34631e16i	−0.0351258	+	0.0202799i
$935$	−2.01703e17	−	3.49360e17i	−0.301886	−	0.522882i
$936$	2.26068e17	+	1.30520e17i	0.336189	+	0.194099i
$937$		−	2.14322e17i		−	0.316686i	−0.987384	−	0.158343i	$-0.949385\pi$
$937$		−	2.14322e17i		−	0.316686i	0.987384	−	0.158343i	$-0.0506152\pi$
$938$		0			0
$939$	−7.80197e16			−0.113818
$940$	1.16229e17	−	2.01314e17i	0.168479	−	0.291815i
$941$	6.20483e17	−	3.58236e17i	0.893701	−	0.515979i	0.0185500	−	0.999828i	$-0.494095\pi$
$941$	6.20483e17	−	3.58236e17i	0.893701	−	0.515979i	0.875151	+	0.483849i	$0.160762\pi$
$942$	−1.57243e16	−	2.72353e16i	−0.0225043	−	0.0389786i
$943$	5.73015e17	+	3.30831e17i	0.814885	+	0.470474i
$944$		−	1.59697e17i		−	0.225665i
$945$		0			0
$946$	1.22344e17			0.170701
$947$	2.14733e17	−	3.71928e17i	0.297713	−	0.515655i	−0.677899	−	0.735155i	$-0.737109\pi$
$947$	2.14733e17	−	3.71928e17i	0.297713	−	0.515655i	0.975612	+	0.219500i	$0.0704427\pi$
$948$	−4.11789e16	+	2.37747e16i	−0.0567316	+	0.0327540i
$949$	2.07886e17	+	3.60070e17i	0.284596	+	0.492935i
$950$	3.70270e17	+	2.13776e17i	0.503706	+	0.290815i
$951$		−	2.19566e16i		−	0.0296813i
$952$		0			0
$953$	1.43767e18			1.91911			0.959557	−	0.281515i	$-0.0908370\pi$
$953$	1.43767e18			1.91911			0.959557	+	0.281515i	$0.0908370\pi$
$954$	3.26182e17	−	5.64963e17i	0.432682	−	0.749428i
$955$	−1.80116e17	+	1.03990e17i	−0.237428	+	0.137079i
$956$	−2.51429e17	−	4.35489e17i	−0.329358	−	0.570465i
$957$	−9.23947e15	−	5.33441e15i	−0.0120275	−	0.00694408i
$958$		−	2.57031e17i		−	0.332501i
$959$		0			0
$960$	−6.06259e15			−0.00774517
$961$	−3.84547e17	+	6.66054e17i	−0.488212	+	0.845609i
$962$	2.87196e17	−	1.65813e17i	0.362350	−	0.209203i
$963$	−1.97401e17	−	3.41909e17i	−0.247510	−	0.428699i
$964$	1.00924e17	+	5.82688e16i	0.125758	+	0.0726062i
$965$		−	2.00071e17i		−	0.247754i
$966$		0			0
$967$	−5.69655e17			−0.696712			−0.348356	−	0.937362i	$-0.613260\pi$
$967$	−5.69655e17			−0.696712			−0.348356	+	0.937362i	$0.613260\pi$
$968$	−6.15563e16	+	1.06619e17i	−0.0748205	+	0.129593i
$969$	−1.84378e17	+	1.06450e17i	−0.222723	+	0.128589i
$970$	4.28874e16	+	7.42831e16i	0.0514872	+	0.0891784i
$971$	−5.23288e17	−	3.02120e17i	−0.624346	−	0.360466i	0.154213	−	0.988038i	$-0.450716\pi$
$971$	−5.23288e17	−	3.02120e17i	−0.624346	−	0.360466i	−0.778559	+	0.627571i	$0.784049\pi$
$972$			1.72464e17i			0.204504i
$973$		0			0
$974$	6.54779e17			0.766904
$975$	5.41405e16	−	9.37742e16i	0.0630224	−	0.109158i
$976$	−3.03956e17	+	1.75489e17i	−0.351651	+	0.203026i
$977$	4.20718e17	+	7.28705e17i	0.483753	+	0.837885i	0.999826	−	0.0186600i	$-0.00593999\pi$
$977$	4.20718e17	+	7.28705e17i	0.483753	+	0.837885i	−0.516073	+	0.856545i	$0.672607\pi$
$978$	−3.87935e16	−	2.23974e16i	−0.0443328	−	0.0255956i
$979$		−	6.82507e17i		−	0.775195i
$980$		0			0
$981$	9.93400e17			1.11458
$982$	−4.00413e17	+	6.93536e17i	−0.446518	+	0.773392i
$983$	2.30490e17	−	1.33073e17i	0.255465	−	0.147493i	−0.366799	−	0.930300i	$-0.619546\pi$
$983$	2.30490e17	−	1.33073e17i	0.255465	−	0.147493i	0.622264	+	0.782808i	$0.286213\pi$
$984$	−1.94010e16	−	3.36035e16i	−0.0213724	−	0.0370181i
$985$	−4.87282e17	−	2.81333e17i	−0.533535	−	0.308037i
$986$			1.52460e17i			0.165918i
$987$		0			0
$988$	−5.32821e17			−0.572848
$989$	1.62028e17	−	2.80641e17i	0.173146	−	0.299898i
$990$	1.90020e17	−	1.09708e17i	0.201831	−	0.116527i
$991$	6.83866e15	+	1.18449e16i	0.00721987	+	0.0125052i	0.869613	−	0.493734i	$-0.164368\pi$
$991$	6.83866e15	+	1.18449e16i	0.00721987	+	0.0125052i	−0.862393	+	0.506240i	$0.831035\pi$
$992$	2.24003e16	+	1.29328e16i	0.0235063	+	0.0135714i
$993$			9.00196e16i			0.0938949i
$994$		0			0
$995$	5.34651e17			0.550975
$996$	1.38086e16	−	2.39172e16i	0.0141447	−	0.0244993i
$997$	1.98044e17	−	1.14341e17i	0.201646	−	0.116421i	−0.395777	−	0.918347i	$-0.629525\pi$
$997$	1.98044e17	−	1.14341e17i	0.201646	−	0.116421i	0.597423	+	0.801926i	$0.296191\pi$
$998$	4.72412e17	+	8.18242e17i	0.478121	+	0.828130i
$999$	1.26081e17	+	7.27927e16i	0.126840	+	0.0732310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.13.d.b.19.7		16
7.2	even	3		14.13.b.a.13.3	yes	8
7.3	odd	6	inner	98.13.d.b.31.7		16
7.4	even	3	inner	98.13.d.b.31.6		16
7.5	odd	6		14.13.b.a.13.2	✓	8
7.6	odd	2	inner	98.13.d.b.19.6		16
21.2	odd	6		126.13.c.a.55.6		8
21.5	even	6		126.13.c.a.55.7		8
28.19	even	6		112.13.c.c.97.5		8
28.23	odd	6		112.13.c.c.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.2	✓	8	7.5	odd	6
14.13.b.a.13.3	yes	8	7.2	even	3
98.13.d.b.19.6		16	7.6	odd	2	inner
98.13.d.b.19.7		16	1.1	even	1	trivial
98.13.d.b.31.6		16	7.4	even	3	inner
98.13.d.b.31.7		16	7.3	odd	6	inner
112.13.c.c.97.4		8	28.23	odd	6
112.13.c.c.97.5		8	28.19	even	6
126.13.c.a.55.6		8	21.2	odd	6
126.13.c.a.55.7		8	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(22.6274 - 39.1918i) q^{2} +(88.3706 - 51.0208i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-5989.93 - 3458.29i) q^{5} -4617.87i q^{6} -92681.9 q^{8} +(-260514. + 451224. i) q^{9} +O(q^{10})\)	\(q+(22.6274 - 39.1918i) q^{2} +(88.3706 - 51.0208i) q^{3} +(-1024.00 - 1773.62i) q^{4} +(-5989.93 - 3458.29i) q^{5} -4617.87i q^{6} -92681.9 q^{8} +(-260514. + 451224. i) q^{9} +(-271073. + 156504. i) q^{10} +(672699. + 1.16515e6i) q^{11} +(-180983. - 104491. i) q^{12} +5.40570e6i q^{13} -705778. q^{15} +(-2.09715e6 + 3.63237e6i) q^{16} +(3.75433e7 - 2.16756e7i) q^{17} +(1.17895e7 + 2.04201e7i) q^{18} +(-4.16802e7 - 2.40641e7i) q^{19} +1.41652e7i q^{20} +6.08857e7 q^{22} +(8.06349e7 - 1.39664e8i) q^{23} +(-8.19035e6 + 4.72870e6i) q^{24} +(-9.81508e7 - 1.70002e8i) q^{25} +(2.11859e8 + 1.22317e8i) q^{26} +1.07396e8i q^{27} -7.77122e7 q^{29} +(-1.59699e7 + 2.76607e7i) q^{30} +(1.18013e8 - 6.81348e7i) q^{31} +(9.49063e7 + 1.64382e8i) q^{32} +(1.18893e8 + 6.86432e7i) q^{33} -1.96185e9i q^{34} +1.06707e9 q^{36} +(6.77800e8 - 1.17398e9i) q^{37} +(-1.88623e9 + 1.08902e9i) q^{38} +(2.75803e8 + 4.77705e8i) q^{39} +(5.55158e8 + 3.20521e8i) q^{40} +4.10282e9i q^{41} +2.00941e9 q^{43} +(1.37769e9 - 2.38622e9i) q^{44} +(3.12093e9 - 1.80187e9i) q^{45} +(-3.64912e9 - 6.32046e9i) q^{46} +(-1.42119e10 - 8.20527e9i) q^{47} +4.27993e8i q^{48} -8.88359e9 q^{50} +(2.21181e9 - 3.83097e9i) q^{51} +(9.58765e9 - 5.53543e9i) q^{52} +(-1.38335e10 - 2.39604e10i) q^{53} +(4.20903e9 + 2.43009e9i) q^{54} -9.30554e9i q^{55} -4.91107e9 q^{57} +(-1.75843e9 + 3.04568e9i) q^{58} +(-3.29737e10 + 1.90374e10i) q^{59} +(7.22717e8 + 1.25178e9i) q^{60} +(7.24689e10 + 4.18399e10i) q^{61} -6.16686e9i q^{62} +8.58993e9 q^{64} +(1.86945e10 - 3.23798e10i) q^{65} +(5.38051e9 - 3.10644e9i) q^{66} +(-4.96015e10 - 8.59123e10i) q^{67} +(-7.68886e10 - 4.43916e10i) q^{68} -1.64562e10i q^{69} -3.72326e10 q^{71} +(2.41450e10 - 4.18203e10i) q^{72} +(6.66093e10 - 3.84569e10i) q^{73} +(-3.06737e10 - 5.31285e10i) q^{74} +(-1.73473e10 - 1.00155e10i) q^{75} +9.85665e10i q^{76} +2.49628e10 q^{78} +(1.13765e11 - 1.97046e11i) q^{79} +(2.51236e10 - 1.45051e10i) q^{80} +(-1.32969e11 - 2.30308e11i) q^{81} +(1.60797e11 + 9.28362e10i) q^{82} +1.32152e11i q^{83} -2.99842e11 q^{85} +(4.54677e10 - 7.87523e10i) q^{86} +(-6.86747e9 + 3.96493e9i) q^{87} +(-6.23470e10 - 1.07988e11i) q^{88} +(-4.39326e11 - 2.53645e11i) q^{89} -1.63086e11i q^{90} -3.30281e11 q^{92} +(6.95258e9 - 1.20422e10i) q^{93} +(-6.43159e11 + 3.71328e11i) q^{94} +(1.66441e11 + 2.88284e11i) q^{95} +(1.67738e10 + 9.68438e9i) q^{96} -2.74033e11i q^{97} -7.00990e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16384 q^{4} + 1478904 q^{9}+O(q^{10}) \) 16 * q - 16384 * q^4 + 1478904 * q^9	\( 16 q - 16384 q^{4} + 1478904 q^{9} + 213840 q^{11} + 131764608 q^{15} - 33554432 q^{16} - 32547840 q^{18} - 442675200 q^{22} - 156731760 q^{23} - 191237000 q^{25} + 617707296 q^{29} + 2203567104 q^{30} - 6057590784 q^{36} + 3243600880 q^{37} - 13521315264 q^{39} + 42012604000 q^{43} + 437944320 q^{44} - 9664610304 q^{46} + 52518979584 q^{50} + 80965832832 q^{51} - 180445637520 q^{53} - 126291924480 q^{57} + 94193264640 q^{58} - 134926958592 q^{60} + 137438953472 q^{64} + 424890168192 q^{65} - 369211259440 q^{67} + 1148116288608 q^{71} - 66657976320 q^{72} - 450517137408 q^{74} - 502001694720 q^{78} + 607826610128 q^{79} - 919051941384 q^{81} - 494404521216 q^{85} + 413092638720 q^{86} + 453299404800 q^{88} + 641973288960 q^{92} - 2292312458880 q^{93} + 1053641981376 q^{95} - 3601908512928 q^{99}+O(q^{100}) \) 16 * q - 16384 * q^4 + 1478904 * q^9 + 213840 * q^11 + 131764608 * q^15 - 33554432 * q^16 - 32547840 * q^18 - 442675200 * q^22 - 156731760 * q^23 - 191237000 * q^25 + 617707296 * q^29 + 2203567104 * q^30 - 6057590784 * q^36 + 3243600880 * q^37 - 13521315264 * q^39 + 42012604000 * q^43 + 437944320 * q^44 - 9664610304 * q^46 + 52518979584 * q^50 + 80965832832 * q^51 - 180445637520 * q^53 - 126291924480 * q^57 + 94193264640 * q^58 - 134926958592 * q^60 + 137438953472 * q^64 + 424890168192 * q^65 - 369211259440 * q^67 + 1148116288608 * q^71 - 66657976320 * q^72 - 450517137408 * q^74 - 502001694720 * q^78 + 607826610128 * q^79 - 919051941384 * q^81 - 494404521216 * q^85 + 413092638720 * q^86 + 453299404800 * q^88 + 641973288960 * q^92 - 2292312458880 * q^93 + 1053641981376 * q^95 - 3601908512928 * q^99

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