LMFDB - Embedded newform 16.9.f.a.3.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.10
Character	$\chi$	$=$	16.3
Dual form			16.9.f.a.11.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.41380 + 15.0563i) q^{2} +(63.2572 - 63.2572i) q^{3} +(-197.381 + 163.023i) q^{4} +(825.937 - 825.937i) q^{5} +(1294.88 + 609.955i) q^{6} +711.293 q^{7} +(-3523.10 - 2089.25i) q^{8} -1441.95i q^{9} +O(q^{10})$	\(q+(5.41380 + 15.0563i) q^{2} +(63.2572 - 63.2572i) q^{3} +(-197.381 + 163.023i) q^{4} +(825.937 - 825.937i) q^{5} +(1294.88 + 609.955i) q^{6} +711.293 q^{7} +(-3523.10 - 2089.25i) q^{8} -1441.95i q^{9} +(16907.0 + 7964.05i) q^{10} +(7260.95 + 7260.95i) q^{11} +(-2173.41 + 22798.2i) q^{12} +(14756.3 + 14756.3i) q^{13} +(3850.80 + 10709.4i) q^{14} -104493. i q^{15} +(12382.9 - 64355.5i) q^{16} -118889. q^{17} +(21710.4 - 7806.44i) q^{18} +(41957.1 - 41957.1i) q^{19} +(-28377.8 + 297671. i) q^{20} +(44994.4 - 44994.4i) q^{21} +(-70013.3 + 148632. i) q^{22} -255590. q^{23} +(-355022. + 90701.5i) q^{24} -973717. i q^{25} +(-142287. + 302063. i) q^{26} +(323817. + 323817. i) q^{27} +(-140396. + 115957. i) q^{28} +(-351087. - 351087. i) q^{29} +(1.57327e6 - 565704. i) q^{30} +1.79146e6i q^{31} +(1.03599e6 - 161968. i) q^{32} +918614. q^{33} +(-643643. - 1.79003e6i) q^{34} +(587483. - 587483. i) q^{35} +(235071. + 284614. i) q^{36} +(-1.67070e6 + 1.67070e6i) q^{37} +(858864. + 404569. i) q^{38} +1.86689e6 q^{39} +(-4.63545e6 + 1.18427e6i) q^{40} -812050. i q^{41} +(921039. + 433857. i) q^{42} +(1.19628e6 + 1.19628e6i) q^{43} +(-2.61688e6 - 249474. i) q^{44} +(-1.19096e6 - 1.19096e6i) q^{45} +(-1.38371e6 - 3.84823e6i) q^{46} +4.04123e6i q^{47} +(-3.28764e6 - 4.85426e6i) q^{48} -5.25886e6 q^{49} +(1.46605e7 - 5.27151e6i) q^{50} +(-7.52061e6 + 7.52061e6i) q^{51} +(-5.31825e6 - 507003. i) q^{52} +(3.74615e6 - 3.74615e6i) q^{53} +(-3.12239e6 + 6.62855e6i) q^{54} +1.19942e7 q^{55} +(-2.50596e6 - 1.48607e6i) q^{56} -5.30817e6i q^{57} +(3.38534e6 - 7.18677e6i) q^{58} +(-6.43117e6 - 6.43117e6i) q^{59} +(1.70348e7 + 2.06250e7i) q^{60} +(-5.59614e6 - 5.59614e6i) q^{61} +(-2.69726e7 + 9.69860e6i) q^{62} -1.02565e6i q^{63} +(8.04729e6 + 1.47213e7i) q^{64} +2.43756e7 q^{65} +(4.97320e6 + 1.38309e7i) q^{66} +(9.83142e6 - 9.83142e6i) q^{67} +(2.34666e7 - 1.93817e7i) q^{68} +(-1.61679e7 + 1.61679e7i) q^{69} +(1.20258e7 + 5.66478e6i) q^{70} +1.65908e7 q^{71} +(-3.01260e6 + 5.08014e6i) q^{72} -2.55375e7i q^{73} +(-3.41993e7 - 1.61096e7i) q^{74} +(-6.15946e7 - 6.15946e7i) q^{75} +(-1.44157e6 + 1.51215e7i) q^{76} +(5.16466e6 + 5.16466e6i) q^{77} +(1.01070e7 + 2.81084e7i) q^{78} +4.22360e7i q^{79} +(-4.29261e7 - 6.33810e7i) q^{80} +5.04281e7 q^{81} +(1.22264e7 - 4.39628e6i) q^{82} +(1.67996e7 - 1.67996e7i) q^{83} +(-1.54593e6 + 1.62162e7i) q^{84} +(-9.81950e7 + 9.81950e7i) q^{85} +(-1.15351e7 + 2.44879e7i) q^{86} -4.44175e7 q^{87} +(-1.04111e7 - 4.07510e7i) q^{88} +1.07047e7i q^{89} +(1.14838e7 - 2.43790e7i) q^{90} +(1.04961e7 + 1.04961e7i) q^{91} +(5.04487e7 - 4.16671e7i) q^{92} +(1.13323e8 + 1.13323e8i) q^{93} +(-6.08457e7 + 2.18784e7i) q^{94} -6.93078e7i q^{95} +(5.52883e7 - 7.57796e7i) q^{96} +9.36470e6 q^{97} +(-2.84704e7 - 7.91788e7i) q^{98} +(1.04699e7 - 1.04699e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	5.41380	+	15.0563i	0.338363	+	0.941016i
$2$	5.41380	+	15.0563i	0.338363	+	0.941016i
$3$	63.2572	−	63.2572i	0.780953	−	0.780953i	−0.199038	−	0.979992i	$-0.563782\pi$
$3$	63.2572	−	63.2572i	0.780953	−	0.780953i	0.979992	+	0.199038i	$0.0637818\pi$
$4$	−197.381	+	163.023i	−0.771021	+	0.636809i
$5$	825.937	−	825.937i	1.32150	−	1.32150i	0.408935	−	0.912564i	$-0.365900\pi$
$5$	825.937	−	825.937i	1.32150	−	1.32150i	0.912564	−	0.408935i	$-0.134100\pi$
$6$	1294.88	+	609.955i	0.999135	+	0.470644i
$7$	711.293			0.296249			0.148124	−	0.988969i	$-0.452676\pi$
$7$	711.293			0.296249			0.148124	+	0.988969i	$0.452676\pi$
$8$	−3523.10	−	2089.25i	−0.860132	−	0.510071i
$9$		−	1441.95i		−	0.219776i
$10$	16907.0	+	7964.05i	1.69070	+	0.796405i
$11$	7260.95	+	7260.95i	0.495932	+	0.495932i	0.910169	−	0.414237i	$-0.135951\pi$
$11$	7260.95	+	7260.95i	0.495932	+	0.495932i	−0.414237	+	0.910169i	$0.635951\pi$
$12$	−2173.41	+	22798.2i	−0.104813	+	1.09945i
$13$	14756.3	+	14756.3i	0.516661	+	0.516661i	0.916559	−	0.399899i	$-0.130955\pi$
$13$	14756.3	+	14756.3i	0.516661	+	0.516661i	−0.399899	+	0.916559i	$0.630955\pi$
$14$	3850.80	+	10709.4i	0.100240	+	0.278775i
$15$		−	104493.i		−	2.06406i
$16$	12382.9	−	64355.5i	0.188948	−	0.981987i
$17$	−118889.			−1.42347			−0.711733	−	0.702450i	$-0.752089\pi$
$17$	−118889.			−1.42347			−0.711733	+	0.702450i	$0.752089\pi$
$18$	21710.4	−	7806.44i	0.206813	−	0.0743640i
$19$	41957.1	−	41957.1i	0.321952	−	0.321952i	−0.527564	−	0.849515i	$-0.676894\pi$
$19$	41957.1	−	41957.1i	0.321952	−	0.321952i	0.849515	+	0.527564i	$0.176894\pi$
$20$	−28377.8	+	297671.i	−0.177361	+	1.86045i
$21$	44994.4	−	44994.4i	0.231356	−	0.231356i
$22$	−70013.3	+	148632.i	−0.298875	+	0.634485i
$23$	−255590.			−0.913340			−0.456670	−	0.889636i	$-0.650958\pi$
$23$	−255590.			−0.913340			−0.456670	+	0.889636i	$0.650958\pi$
$24$	−355022.	+	90701.5i	−1.07006	+	0.273382i
$25$		−	973717.i		−	2.49272i
$26$	−142287.	+	302063.i	−0.311367	+	0.661004i
$27$	323817.	+	323817.i	0.609318	+	0.609318i
$28$	−140396.	+	115957.i	−0.228414	+	0.188654i
$29$	−351087.	−	351087.i	−0.496389	−	0.496389i	0.413923	−	0.910312i	$-0.364158\pi$
$29$	−351087.	−	351087.i	−0.496389	−	0.496389i	−0.910312	+	0.413923i	$0.864158\pi$
$30$	1.57327e6	−	565704.i	1.94231	−	0.698400i
$31$			1.79146e6i			1.93981i	0.243478	+	0.969906i	$0.421711\pi$
$31$			1.79146e6i			1.93981i	−0.243478	+	0.969906i	$0.578289\pi$
$32$	1.03599e6	−	161968.i	0.987998	−	0.154465i
$33$	918614.			0.774600
$34$	−643643.	−	1.79003e6i	−0.481648	−	1.33950i
$35$	587483.	−	587483.i	0.391492	−	0.391492i
$36$	235071.	+	284614.i	0.139955	+	0.169452i
$37$	−1.67070e6	+	1.67070e6i	−0.891438	+	0.891438i	−0.994659	−	0.103220i	$-0.967085\pi$
$37$	−1.67070e6	+	1.67070e6i	−0.891438	+	0.891438i	0.103220	+	0.994659i	$0.467085\pi$
$38$	858864.	+	404569.i	0.411898	+	0.194025i
$39$	1.86689e6			0.806976
$40$	−4.63545e6	+	1.18427e6i	−1.81072	+	0.462606i
$41$		−	812050.i		−	0.287374i	−0.989623	−	0.143687i	$-0.954104\pi$
$41$		−	812050.i		−	0.287374i	0.989623	−	0.143687i	$-0.0458958\pi$
$42$	921039.	+	433857.i	0.295993	+	0.139428i
$43$	1.19628e6	+	1.19628e6i	0.349912	+	0.349912i	0.860077	−	0.510165i	$-0.170416\pi$
$43$	1.19628e6	+	1.19628e6i	0.349912	+	0.349912i	−0.510165	+	0.860077i	$0.670416\pi$
$44$	−2.61688e6	−	249474.i	−0.698189	−	0.0665601i
$45$	−1.19096e6	−	1.19096e6i	−0.290434	−	0.290434i
$46$	−1.38371e6	−	3.84823e6i	−0.309040	−	0.859467i
$47$			4.04123e6i			0.828175i	0.910237	+	0.414087i	$0.135899\pi$
$47$			4.04123e6i			0.828175i	−0.910237	+	0.414087i	$0.864101\pi$
$48$	−3.28764e6	−	4.85426e6i	−0.619327	−	0.914446i
$49$	−5.25886e6			−0.912237
$50$	1.46605e7	−	5.27151e6i	2.34569	−	0.843442i
$51$	−7.52061e6	+	7.52061e6i	−1.11166	+	1.11166i
$52$	−5.31825e6	−	507003.i	−0.727371	−	0.0693421i
$53$	3.74615e6	−	3.74615e6i	0.474768	−	0.474768i	−0.428686	−	0.903454i	$-0.641023\pi$
$53$	3.74615e6	−	3.74615e6i	0.474768	−	0.474768i	0.903454	+	0.428686i	$0.141023\pi$
$54$	−3.12239e6	+	6.62855e6i	−0.367208	+	0.779549i
$55$	1.19942e7			1.31075
$56$	−2.50596e6	−	1.48607e6i	−0.254813	−	0.151108i
$57$		−	5.30817e6i		−	0.502859i
$58$	3.38534e6	−	7.18677e6i	0.299151	−	0.635070i
$59$	−6.43117e6	−	6.43117e6i	−0.530741	−	0.530741i	0.390052	−	0.920793i	$-0.372457\pi$
$59$	−6.43117e6	−	6.43117e6i	−0.530741	−	0.530741i	−0.920793	+	0.390052i	$0.872457\pi$
$60$	1.70348e7	+	2.06250e7i	1.31441	+	1.59143i
$61$	−5.59614e6	−	5.59614e6i	−0.404175	−	0.404175i	0.475527	−	0.879701i	$-0.342258\pi$
$61$	−5.59614e6	−	5.59614e6i	−0.404175	−	0.404175i	−0.879701	+	0.475527i	$0.842258\pi$
$62$	−2.69726e7	+	9.69860e6i	−1.82539	+	0.656360i
$63$		−	1.02565e6i		−	0.0651084i
$64$	8.04729e6	+	1.47213e7i	0.479656	+	0.877457i
$65$	2.43756e7			1.36553
$66$	4.97320e6	+	1.38309e7i	0.262096	+	0.728911i
$67$	9.83142e6	−	9.83142e6i	0.487884	−	0.487884i	−0.419754	−	0.907638i	$-0.637884\pi$
$67$	9.83142e6	−	9.83142e6i	0.487884	−	0.487884i	0.907638	+	0.419754i	$0.137884\pi$
$68$	2.34666e7	−	1.93817e7i	1.09752	−	0.906477i
$69$	−1.61679e7	+	1.61679e7i	−0.713276	+	0.713276i
$70$	1.20258e7	+	5.66478e6i	0.500867	+	0.235934i
$71$	1.65908e7			0.652882			0.326441	−	0.945218i	$-0.394151\pi$
$71$	1.65908e7			0.652882			0.326441	+	0.945218i	$0.394151\pi$
$72$	−3.01260e6	+	5.08014e6i	−0.112101	+	0.189037i
$73$		−	2.55375e7i		−	0.899265i	−0.893214	−	0.449632i	$-0.851555\pi$
$73$		−	2.55375e7i		−	0.899265i	0.893214	−	0.449632i	$-0.148445\pi$
$74$	−3.41993e7	−	1.61096e7i	−1.14049	−	0.537228i
$75$	−6.15946e7	−	6.15946e7i	−1.94669	−	1.94669i
$76$	−1.44157e6	+	1.51215e7i	−0.0432098	+	0.453253i
$77$	5.16466e6	+	5.16466e6i	0.146919	+	0.146919i
$78$	1.01070e7	+	2.81084e7i	0.273050	+	0.759377i
$79$			4.22360e7i			1.08436i	0.840262	+	0.542181i	$0.182401\pi$
$79$			4.22360e7i			1.08436i	−0.840262	+	0.542181i	$0.817599\pi$
$80$	−4.29261e7	−	6.33810e7i	−1.04800	−	1.54739i
$81$	5.04281e7			1.17147
$82$	1.22264e7	−	4.39628e6i	0.270423	−	0.0972366i
$83$	1.67996e7	−	1.67996e7i	0.353987	−	0.353987i	−0.507604	−	0.861591i	$-0.669469\pi$
$83$	1.67996e7	−	1.67996e7i	0.353987	−	0.353987i	0.861591	+	0.507604i	$0.169469\pi$
$84$	−1.54593e6	+	1.62162e7i	−0.0310508	+	0.325711i
$85$	−9.81950e7	+	9.81950e7i	−1.88111	+	1.88111i
$86$	−1.15351e7	+	2.44879e7i	−0.210876	+	0.447670i
$87$	−4.44175e7			−0.775314
$88$	−1.04111e7	−	4.07510e7i	−0.173607	−	0.679528i
$89$			1.07047e7i			0.170614i	0.996355	+	0.0853071i	$0.0271871\pi$
$89$			1.07047e7i			0.170614i	−0.996355	+	0.0853071i	$0.972813\pi$
$90$	1.14838e7	−	2.43790e7i	0.175031	−	0.371575i
$91$	1.04961e7	+	1.04961e7i	0.153060	+	0.153060i
$92$	5.04487e7	−	4.16671e7i	0.704205	−	0.581623i
$93$	1.13323e8	+	1.13323e8i	1.51490	+	1.51490i
$94$	−6.08457e7	+	2.18784e7i	−0.779325	+	0.280223i
$95$		−	6.93078e7i		−	0.850917i
$96$	5.52883e7	−	7.57796e7i	0.650951	−	0.892210i
$97$	9.36470e6			0.105781			0.0528904	−	0.998600i	$-0.483157\pi$
$97$	9.36470e6			0.105781			0.0528904	+	0.998600i	$0.483157\pi$
$98$	−2.84704e7	−	7.91788e7i	−0.308667	−	0.858429i
$99$	1.04699e7	−	1.04699e7i	0.108994	−	0.108994i
$100$	1.58738e8	+	1.92194e8i	1.58738	+	1.92194i
$101$	3.01117e7	−	3.01117e7i	0.289367	−	0.289367i	−0.547463	−	0.836830i	$-0.684406\pi$
$101$	3.01117e7	−	3.01117e7i	0.289367	−	0.289367i	0.836830	+	0.547463i	$0.184406\pi$
$102$	−1.53947e8	−	7.25171e7i	−1.42223	−	0.669946i
$103$	1.44220e8			1.28138			0.640688	−	0.767801i	$-0.278649\pi$
$103$	1.44220e8			1.28138			0.640688	+	0.767801i	$0.278649\pi$
$104$	−2.11584e7	−	8.28178e7i	−0.180863	−	0.707930i
$105$		−	7.43251e7i		−	0.611474i
$106$	7.66839e7	+	3.61220e7i	0.607408	+	0.286120i
$107$	−2.88568e7	−	2.88568e7i	−0.220147	−	0.220147i	0.588413	−	0.808560i	$-0.299753\pi$
$107$	−2.88568e7	−	2.88568e7i	−0.220147	−	0.220147i	−0.808560	+	0.588413i	$0.799753\pi$
$108$	−1.16705e8	−	1.11258e7i	−0.857817	−	0.0817779i
$109$	−2.84239e7	−	2.84239e7i	−0.201362	−	0.201362i	0.599221	−	0.800584i	$-0.295477\pi$
$109$	−2.84239e7	−	2.84239e7i	−0.201362	−	0.201362i	−0.800584	+	0.599221i	$0.795477\pi$
$110$	6.49340e7	+	1.80587e8i	0.443508	+	1.23343i
$111$			2.11368e8i			1.39234i
$112$	8.80787e6	−	4.57756e7i	0.0559756	−	0.290913i
$113$	−1.76723e7			−0.108388			−0.0541938	−	0.998530i	$-0.517259\pi$
$113$	−1.76723e7			−0.108388			−0.0541938	+	0.998530i	$0.517259\pi$
$114$	7.99212e7	−	2.87374e7i	0.473198	−	0.170149i
$115$	−2.11101e8	+	2.11101e8i	−1.20698	+	1.20698i
$116$	1.26533e8	+	1.20627e7i	0.698832	+	0.0666215i
$117$	2.12779e7	−	2.12779e7i	0.113550	−	0.113550i
$118$	6.20123e7	−	1.31646e8i	0.319852	−	0.679018i
$119$	−8.45652e7			−0.421700
$120$	−2.18312e8	+	3.68139e8i	−1.05282	+	1.77536i
$121$		−	1.08916e8i		−	0.508102i
$122$	5.39605e7	−	1.14553e8i	0.243577	−	0.517093i
$123$	−5.13680e7	−	5.13680e7i	−0.224426	−	0.224426i
$124$	−2.92049e8	−	3.53601e8i	−1.23529	−	1.49564i
$125$	−4.81597e8	−	4.81597e8i	−1.97262	−	1.97262i
$126$	1.54425e7	−	5.55267e6i	0.0612680	−	0.0220303i
$127$		−	1.20985e8i		−	0.465070i	−0.972588	−	0.232535i	$-0.925298\pi$
$127$		−	1.20985e8i		−	0.465070i	0.972588	−	0.232535i	$-0.0747020\pi$
$128$	−1.78081e8	+	2.00860e8i	−0.663403	+	0.748262i
$129$	1.51347e8			0.546530
$130$	1.31965e8	+	3.67005e8i	0.462045	+	1.28499i
$131$	4.06743e8	−	4.06743e8i	1.38113	−	1.38113i	0.538512	−	0.842618i	$-0.318987\pi$
$131$	4.06743e8	−	4.06743e8i	1.38113	−	1.38113i	0.842618	−	0.538512i	$-0.181013\pi$
$132$	−1.81317e8	+	1.49755e8i	−0.597233	+	0.493272i
$133$	2.98438e7	−	2.98438e7i	0.0953778	−	0.0953778i
$134$	2.01250e8	+	9.47990e7i	0.624189	+	0.294025i
$135$	5.34904e8			1.61043
$136$	4.18859e8	+	2.48390e8i	1.22437	+	0.726069i
$137$			1.98115e8i			0.562388i	0.959651	+	0.281194i	$0.0907305\pi$
$137$			1.98115e8i			0.562388i	−0.959651	+	0.281194i	$0.909270\pi$
$138$	−3.30958e8	−	1.55898e8i	−0.912550	−	0.429858i
$139$	−1.44823e8	−	1.44823e8i	−0.387953	−	0.387953i	0.486004	−	0.873957i	$-0.338454\pi$
$139$	−1.44823e8	−	1.44823e8i	−0.387953	−	0.387953i	−0.873957	+	0.486004i	$0.838454\pi$
$140$	−2.01849e7	+	2.11732e8i	−0.0525430	+	0.551155i
$141$	2.55637e8	+	2.55637e8i	0.646766	+	0.646766i
$142$	8.98195e7	+	2.49796e8i	0.220911	+	0.614372i
$143$			2.14290e8i			0.512457i
$144$	−9.27975e7	−	1.78555e7i	−0.215817	−	0.0415262i
$145$	−5.79951e8			−1.31196
$146$	3.84500e8	−	1.38255e8i	0.846222	−	0.304278i
$147$	−3.32661e8	+	3.32661e8i	−0.712414	+	0.712414i
$148$	5.74024e7	−	6.02128e8i	0.119642	−	1.25499i
$149$	2.40746e8	−	2.40746e8i	0.488442	−	0.488442i	−0.419372	−	0.907814i	$-0.637750\pi$
$149$	2.40746e8	−	2.40746e8i	0.488442	−	0.488442i	0.907814	+	0.419372i	$0.137750\pi$
$150$	5.93923e8	−	1.26085e9i	1.17318	−	2.49056i
$151$	−8.21152e8			−1.57949			−0.789743	−	0.613438i	$-0.789786\pi$
$151$	−8.21152e8			−1.57949			−0.789743	+	0.613438i	$0.789786\pi$
$152$	−2.35478e8	+	6.01603e7i	−0.441139	+	0.112703i
$153$			1.71433e8i			0.312844i
$154$	−4.98000e7	+	1.05721e8i	−0.0885414	+	0.187965i
$155$	1.47963e9	+	1.47963e9i	2.56346	+	2.56346i
$156$	−3.68490e8	+	3.04346e8i	−0.622195	+	0.513890i
$157$	1.19224e8	+	1.19224e8i	0.196230	+	0.196230i	0.798382	−	0.602152i	$-0.205690\pi$
$157$	1.19224e8	+	1.19224e8i	0.196230	+	0.196230i	−0.602152	+	0.798382i	$0.705690\pi$
$158$	−6.35916e8	+	2.28657e8i	−1.02040	+	0.366908i
$159$		−	4.73942e8i		−	0.741543i
$160$	7.21888e8	−	9.89438e8i	1.10151	−	1.50976i
$161$	−1.81799e8			−0.270576
$162$	2.73008e8	+	7.59259e8i	0.396383	+	1.10238i
$163$	−3.70685e8	+	3.70685e8i	−0.525115	+	0.525115i	−0.919112	−	0.393997i	$-0.871092\pi$
$163$	−3.70685e8	+	3.70685e8i	−0.525115	+	0.525115i	0.393997	+	0.919112i	$0.371092\pi$
$164$	1.32383e8	+	1.60284e8i	0.183002	+	0.221571i
$165$	7.58717e8	−	7.58717e8i	1.02363	−	1.02363i
$166$	3.43889e8	+	1.61990e8i	0.452883	+	0.213331i
$167$	−8.64584e8			−1.11158			−0.555791	−	0.831322i	$-0.687584\pi$
$167$	−8.64584e8			−1.11158			−0.555791	+	0.831322i	$0.687584\pi$
$168$	−2.52525e8	+	6.45154e7i	−0.317005	+	0.0809890i
$169$		−	3.80231e8i		−	0.466124i
$170$	−2.01006e9	−	9.46841e8i	−2.40665	−	1.13366i
$171$	−6.05000e7	−	6.05000e7i	−0.0707573	−	0.0707573i
$172$	−4.31145e8	−	4.11021e7i	−0.492617	−	0.0469624i
$173$	5.49235e8	+	5.49235e8i	0.613160	+	0.613160i	0.943768	−	0.330608i	$-0.107254\pi$
$173$	5.49235e8	+	5.49235e8i	0.613160	+	0.613160i	−0.330608	+	0.943768i	$0.607254\pi$
$174$	−2.40468e8	−	6.68762e8i	−0.262337	−	0.729583i
$175$		−	6.92599e8i		−	0.738464i
$176$	5.57193e8	−	3.77370e8i	0.580705	−	0.393294i
$177$	−8.13636e8			−0.828967
$178$	−1.61173e8	+	5.79533e7i	−0.160551	+	0.0577295i
$179$	6.73780e8	−	6.73780e8i	0.656305	−	0.656305i	−0.298199	−	0.954504i	$-0.596386\pi$
$179$	6.73780e8	−	6.73780e8i	0.656305	−	0.656305i	0.954504	+	0.298199i	$0.0963858\pi$
$180$	4.29228e8	+	4.09194e7i	0.408882	+	0.0389797i
$181$	−8.36901e8	+	8.36901e8i	−0.779758	+	0.779758i	−0.979790	−	0.200031i	$-0.935896\pi$
$181$	−8.36901e8	+	8.36901e8i	−0.779758	+	0.779758i	0.200031	+	0.979790i	$0.435896\pi$
$182$	−1.01208e8	+	2.14856e8i	−0.0922421	+	0.195822i
$183$	−7.07992e8			−0.631283
$184$	9.00470e8	+	5.33991e8i	0.785593	+	0.465868i
$185$			2.75978e9i			2.35607i
$186$	−1.09271e9	+	2.31972e9i	−0.912961	+	1.93813i
$187$	−8.63249e8	−	8.63249e8i	−0.705943	−	0.705943i
$188$	−6.58814e8	−	7.97664e8i	−0.527389	−	0.638540i
$189$	2.30329e8	+	2.30329e8i	0.180510	+	0.180510i
$190$	1.04351e9	−	3.75219e8i	0.800727	−	0.287919i
$191$		−	1.31843e9i		−	0.990659i	−0.868705	−	0.495330i	$-0.835047\pi$
$191$		−	1.31843e9i		−	0.990659i	0.868705	−	0.495330i	$-0.164953\pi$
$192$	1.44028e9	+	4.22178e8i	1.05984	+	0.310664i
$193$	1.39864e9			1.00804			0.504020	−	0.863692i	$-0.331854\pi$
$193$	1.39864e9			1.00804			0.504020	+	0.863692i	$0.331854\pi$
$194$	5.06986e7	+	1.40997e8i	0.0357923	+	0.0995414i
$195$	1.54193e9	−	1.54193e9i	1.06642	−	1.06642i
$196$	1.03800e9	−	8.57316e8i	0.703354	−	0.580921i
$197$	3.99448e8	−	3.99448e8i	0.265213	−	0.265213i	−0.561955	−	0.827168i	$-0.689951\pi$
$197$	3.99448e8	−	3.99448e8i	0.265213	−	0.265213i	0.827168	+	0.561955i	$0.189951\pi$
$198$	2.14320e8	+	1.00956e8i	0.139445	+	0.0656856i
$199$	−1.43253e8			−0.0913465			−0.0456733	−	0.998956i	$-0.514543\pi$
$199$	−1.43253e8			−0.0913465			−0.0456733	+	0.998956i	$0.514543\pi$
$200$	−2.03434e9	+	3.43051e9i	−1.27146	+	2.14407i
$201$		−	1.24382e9i		−	0.762030i
$202$	6.16388e8	+	2.90350e8i	0.370210	+	0.174388i
$203$	−2.49726e8	−	2.49726e8i	−0.147055	−	0.147055i
$204$	2.58395e8	−	2.71046e9i	0.149198	−	1.56503i
$205$	−6.70702e8	−	6.70702e8i	−0.379764	−	0.379764i
$206$	7.80779e8	+	2.17141e9i	0.433570	+	1.20579i
$207$			3.68548e8i			0.200730i
$208$	1.13238e9	−	7.66926e8i	0.604976	−	0.409732i
$209$	6.09296e8			0.319333
$210$	1.11906e9	−	4.02381e8i	0.575407	−	0.206900i
$211$	−1.32452e9	+	1.32452e9i	−0.668236	+	0.668236i	−0.957307	−	0.289072i	$-0.906653\pi$
$211$	−1.32452e9	+	1.32452e9i	−0.668236	+	0.668236i	0.289072	+	0.957307i	$0.406653\pi$
$212$	−1.28711e8	+	1.35013e9i	−0.0637196	+	0.668393i
$213$	1.04949e9	−	1.04949e9i	0.509870	−	0.509870i
$214$	2.78251e8	−	5.90701e8i	0.132673	−	0.281652i
$215$	1.97610e9			0.924816
$216$	−4.64306e8	−	1.81737e9i	−0.213299	−	0.834890i
$217$			1.27425e9i			0.574667i
$218$	2.74076e8	−	5.81840e8i	0.121352	−	0.257619i
$219$	−1.61543e9	−	1.61543e9i	−0.702284	−	0.702284i
$220$	−2.36743e9	+	1.95533e9i	−1.01061	+	0.834696i
$221$	−1.75437e9	−	1.75437e9i	−0.735449	−	0.735449i
$222$	−3.18240e9	+	1.14430e9i	−1.31022	+	0.471117i
$223$			7.03530e8i			0.284488i	0.989832	+	0.142244i	$0.0454317\pi$
$223$			7.03530e8i			0.284488i	−0.989832	+	0.142244i	$0.954568\pi$
$224$	7.36894e8	−	1.15207e8i	0.292693	−	0.0457600i
$225$	−1.40405e9			−0.547840
$226$	−9.56744e7	−	2.66079e8i	−0.0366743	−	0.101994i
$227$	−2.75213e9	+	2.75213e9i	−1.03649	+	1.03649i	−0.0371836	+	0.999308i	$0.511839\pi$
$227$	−2.75213e9	+	2.75213e9i	−1.03649	+	1.03649i	−0.999308	+	0.0371836i	$0.988161\pi$
$228$	8.65356e8	+	1.04774e9i	0.320225	+	0.387715i
$229$	1.02302e9	−	1.02302e9i	0.372000	−	0.372000i	−0.496205	−	0.868205i	$-0.665274\pi$
$229$	1.02302e9	−	1.02302e9i	0.372000	−	0.372000i	0.868205	+	0.496205i	$0.165274\pi$
$230$	−4.32125e9	−	2.03553e9i	−1.54418	−	0.727389i
$231$	6.53404e8			0.229474
$232$	5.03407e8	+	1.97042e9i	0.173767	+	0.680154i
$233$		−	1.62416e9i		−	0.551067i	−0.961291	−	0.275534i	$-0.911145\pi$
$233$		−	1.62416e9i		−	0.551067i	0.961291	−	0.275534i	$-0.0888546\pi$
$234$	4.35560e8	+	2.05171e8i	0.145273	+	0.0684311i
$235$	3.33780e9	+	3.33780e9i	1.09443	+	1.09443i
$236$	2.31783e9	+	2.20964e8i	0.747193	+	0.0712318i
$237$	2.67173e9	+	2.67173e9i	0.846836	+	0.846836i
$238$	−4.57819e8	−	1.27323e9i	−0.142688	−	0.396827i
$239$		−	1.53122e9i		−	0.469294i	−0.972081	−	0.234647i	$-0.924607\pi$
$239$		−	1.53122e9i		−	0.469294i	0.972081	−	0.234647i	$-0.0753935\pi$
$240$	−6.72469e9	−	1.29392e9i	−2.02688	−	0.389999i
$241$	−3.00266e9			−0.890097			−0.445049	−	0.895506i	$-0.646814\pi$
$241$	−3.00266e9			−0.890097			−0.445049	+	0.895506i	$0.646814\pi$
$242$	1.63987e9	−	5.89651e8i	0.478132	−	0.171923i
$243$	1.06538e9	−	1.06538e9i	0.305549	−	0.305549i
$244$	2.01687e9	+	1.92274e8i	0.569010	+	0.0542452i
$245$	−4.34349e9	+	4.34349e9i	−1.20552	+	1.20552i
$246$	4.95314e8	−	1.05151e9i	0.135251	−	0.287125i
$247$	1.23827e9			0.332680
$248$	3.74280e9	−	6.31149e9i	0.989442	−	1.66850i
$249$		−	2.12540e9i		−	0.552895i
$250$	4.64378e9	−	9.85832e9i	1.18881	−	2.52373i
$251$	−1.06233e9	−	1.06233e9i	−0.267649	−	0.267649i	0.560503	−	0.828152i	$-0.310608\pi$
$251$	−1.06233e9	−	1.06233e9i	−0.267649	−	0.267649i	−0.828152	+	0.560503i	$0.810608\pi$
$252$	1.67205e8	+	2.02444e8i	0.0414616	+	0.0502000i
$253$	−1.85583e9	−	1.85583e9i	−0.452955	−	0.452955i
$254$	1.82159e9	−	6.54991e8i	0.437638	−	0.157362i
$255$			1.24231e10i			2.93812i
$256$	−3.98830e9	−	1.59381e9i	−0.928597	−	0.371089i
$257$	6.61182e9			1.51561			0.757807	−	0.652479i	$-0.226271\pi$
$257$	6.61182e9			1.51561			0.757807	+	0.652479i	$0.226271\pi$
$258$	8.19361e8	+	2.27871e9i	0.184925	+	0.514293i
$259$	−1.18836e9	+	1.18836e9i	−0.264088	+	0.264088i
$260$	−4.81129e9	+	3.97379e9i	−1.05285	+	0.869584i
$261$	−5.06250e8	+	5.06250e8i	−0.109095	+	0.109095i
$262$	8.32604e9	+	3.92199e9i	1.76699	+	0.832342i
$263$	3.03317e9			0.633978			0.316989	−	0.948429i	$-0.397328\pi$
$263$	3.03317e9			0.633978			0.316989	+	0.948429i	$0.397328\pi$
$264$	−3.23637e9	−	1.91922e9i	−0.666259	−	0.395101i
$265$		−	6.18816e9i		−	1.25481i
$266$	6.10904e8	+	2.87767e8i	0.122024	+	0.0574797i
$267$	6.77151e8	+	6.77151e8i	0.133242	+	0.133242i
$268$	−3.37791e8	+	3.54329e9i	−0.0654800	+	0.686859i
$269$	1.70695e9	+	1.70695e9i	0.325996	+	0.325996i	0.851062	−	0.525066i	$-0.175959\pi$
$269$	1.70695e9	+	1.70695e9i	0.325996	+	0.325996i	−0.525066	+	0.851062i	$0.675959\pi$
$270$	2.89587e9	+	8.05365e9i	0.544908	+	1.51544i
$271$		−	8.48734e8i		−	0.157360i	−0.996900	−	0.0786801i	$-0.974929\pi$
$271$		−	8.48734e8i		−	0.157360i	0.996900	−	0.0786801i	$-0.0250706\pi$
$272$	−1.47219e9	+	7.65118e9i	−0.268961	+	1.39783i
$273$	1.32791e9			0.239066
$274$	−2.98288e9	+	1.07256e9i	−0.529216	+	0.190291i
$275$	7.07011e9	−	7.07011e9i	1.23622	−	1.23622i
$276$	5.55502e8	−	5.82699e9i	0.0957303	−	1.00417i
$277$	−5.61086e9	+	5.61086e9i	−0.953038	+	0.953038i	−0.998946	−	0.0459074i	$-0.985382\pi$
$277$	−5.61086e9	+	5.61086e9i	−0.953038	+	0.953038i	0.0459074	+	0.998946i	$0.485382\pi$
$278$	1.39645e9	−	2.96454e9i	0.233801	−	0.496339i
$279$	2.58319e9			0.426324
$280$	−3.29716e9	+	8.42364e8i	−0.536424	+	0.137046i
$281$		−	8.61526e9i		−	1.38179i	−0.722954	−	0.690896i	$-0.757216\pi$
$281$		−	8.61526e9i		−	1.38179i	0.722954	−	0.690896i	$-0.242784\pi$
$282$	−2.46497e9	+	5.23290e9i	−0.389775	+	0.827458i
$283$	−7.48124e9	−	7.48124e9i	−1.16635	−	1.16635i	−0.983059	−	0.183287i	$-0.941326\pi$
$283$	−7.48124e9	−	7.48124e9i	−1.16635	−	1.16635i	−0.183287	−	0.983059i	$-0.558674\pi$
$284$	−3.27472e9	+	2.70469e9i	−0.503386	+	0.415761i
$285$	−4.38422e9	−	4.38422e9i	−0.664527	−	0.664527i
$286$	−3.22640e9	+	1.16012e9i	−0.482231	+	0.173396i
$287$		−	5.77606e8i		−	0.0851342i
$288$	−2.33550e8	−	1.49385e9i	−0.0339477	−	0.217138i
$289$	7.15892e9			1.02626
$290$	−3.13974e9	−	8.73189e9i	−0.443917	−	1.23457i
$291$	5.92385e8	−	5.92385e8i	0.0826099	−	0.0826099i
$292$	4.16321e9	+	5.04064e9i	0.572660	+	0.693352i
$293$	−5.12966e9	+	5.12966e9i	−0.696014	+	0.696014i	−0.963548	−	0.267534i	$-0.913791\pi$
$293$	−5.12966e9	+	5.12966e9i	−0.696014	+	0.696014i	0.267534	+	0.963548i	$0.413791\pi$
$294$	−6.80959e9	−	3.20767e9i	−0.911447	−	0.429339i
$295$	−1.06235e10			−1.40275
$296$	9.37655e9	−	2.39554e9i	1.22145	−	0.312058i
$297$			4.70243e9i			0.604361i
$298$	4.92807e9	+	2.32138e9i	0.624902	+	0.294361i
$299$	−3.77157e9	−	3.77157e9i	−0.471887	−	0.471887i
$300$	2.21990e10	+	2.11629e9i	2.74062	+	0.261270i
$301$	8.50906e8	+	8.50906e8i	0.103661	+	0.103661i
$302$	−4.44555e9	−	1.23635e10i	−0.534439	−	1.48632i
$303$		−	3.80956e9i		−	0.451965i
$304$	−2.18062e9	−	3.21972e9i	−0.255320	−	0.376985i
$305$	−9.24411e9			−1.06823
$306$	−2.58113e9	+	9.28102e8i	−0.294391	+	0.105855i
$307$	−7.08093e9	+	7.08093e9i	−0.797144	+	0.797144i	−0.982644	−	0.185500i	$-0.940609\pi$
$307$	−7.08093e9	+	7.08093e9i	−0.797144	+	0.797144i	0.185500	+	0.982644i	$0.440609\pi$
$308$	−1.86137e9	−	1.77449e8i	−0.206838	−	0.0197184i
$309$	9.12295e9	−	9.12295e9i	1.00069	−	1.00069i
$310$	−1.42673e10	+	3.02881e10i	−1.54488	+	3.27963i
$311$	1.35991e10			1.45368			0.726841	−	0.686806i	$-0.240988\pi$
$311$	1.35991e10			1.45368			0.726841	+	0.686806i	$0.240988\pi$
$312$	−6.57725e9	−	3.90040e9i	−0.694106	−	0.411615i
$313$			7.86426e9i			0.819371i	0.912227	+	0.409686i	$0.134362\pi$
$313$			7.86426e9i			0.819371i	−0.912227	+	0.409686i	$0.865638\pi$
$314$	−1.14961e9	+	2.44052e9i	−0.118258	+	0.251052i
$315$	−8.47122e8	−	8.47122e8i	−0.0860407	−	0.0860407i
$316$	−6.88545e9	−	8.33660e9i	−0.690532	−	0.836067i
$317$	5.07951e9	+	5.07951e9i	0.503019	+	0.503019i	0.912375	−	0.409356i	$-0.134246\pi$
$317$	5.07951e9	+	5.07951e9i	0.503019	+	0.503019i	−0.409356	+	0.912375i	$0.634246\pi$
$318$	7.13579e9	−	2.56583e9i	0.697804	−	0.250911i
$319$		−	5.09844e9i		−	0.492351i
$320$	1.88054e10	+	5.51230e9i	1.79342	+	0.525694i
$321$	−3.65081e9			−0.343850
$322$	−9.84227e8	−	2.73722e9i	−0.0915528	−	0.254616i
$323$	−4.98825e9	+	4.98825e9i	−0.458287	+	0.458287i
$324$	−9.95358e9	+	8.22096e9i	−0.903232	+	0.746006i
$325$	1.43685e10	−	1.43685e10i	1.28789	−	1.28789i
$326$	−7.58793e9	−	3.57431e9i	−0.671820	−	0.316462i
$327$	−3.59604e9			−0.314509
$328$	−1.69658e9	+	2.86094e9i	−0.146581	+	0.247180i
$329$			2.87450e9i			0.245346i
$330$	1.55310e10	+	7.31589e9i	1.30961	+	0.616895i
$331$	8.90807e9	+	8.90807e9i	0.742116	+	0.742116i	0.972985	−	0.230869i	$-0.0741570\pi$
$331$	8.90807e9	+	8.90807e9i	0.742116	+	0.742116i	−0.230869	+	0.972985i	$0.574157\pi$
$332$	−5.77207e8	+	6.05466e9i	−0.0475093	+	0.498354i
$333$	2.40907e9	+	2.40907e9i	0.195917	+	0.195917i
$334$	−4.68069e9	−	1.30174e10i	−0.376118	−	1.04602i
$335$		−	1.62403e10i		−	1.28948i
$336$	−2.33848e9	−	3.45280e9i	−0.183475	−	0.270903i
$337$	1.86003e10			1.44211			0.721057	−	0.692875i	$-0.243656\pi$
$337$	1.86003e10			1.44211			0.721057	+	0.692875i	$0.243656\pi$
$338$	5.72486e9	−	2.05850e9i	0.438630	−	0.157719i
$339$	−1.11790e9	+	1.11790e9i	−0.0846456	+	0.0846456i
$340$	3.37381e9	−	3.53899e10i	0.252468	−	2.64828i
$341$	−1.30077e10	+	1.30077e10i	−0.962016	+	0.962016i
$342$	5.83369e8	−	1.23844e9i	0.0426421	−	0.0905254i
$343$	−7.84106e9			−0.566498
$344$	−1.71529e9	−	6.71394e9i	−0.122491	−	0.479451i
$345$			2.67073e10i			1.88519i
$346$	−5.29597e9	+	1.12429e10i	−0.369523	+	0.784464i
$347$	−1.51935e9	−	1.51935e9i	−0.104795	−	0.104795i	0.652765	−	0.757560i	$-0.273609\pi$
$347$	−1.51935e9	−	1.51935e9i	−0.104795	−	0.104795i	−0.757560	+	0.652765i	$0.773609\pi$
$348$	8.76720e9	−	7.24109e9i	0.597784	−	0.493727i
$349$	1.37290e10	+	1.37290e10i	0.925419	+	0.925419i	0.997406	−	0.0719864i	$-0.0229338\pi$
$349$	1.37290e10	+	1.37290e10i	0.925419	+	0.925419i	−0.0719864	+	0.997406i	$0.522934\pi$
$350$	1.04279e10	−	3.74959e9i	0.694906	−	0.249869i
$351$			9.55670e9i			0.629622i
$352$	8.69832e9	+	6.34623e9i	0.566584	+	0.413376i
$353$	−2.41669e10			−1.55641			−0.778203	−	0.628013i	$-0.783868\pi$
$353$	−2.41669e10			−1.55641			−0.778203	+	0.628013i	$0.783868\pi$
$354$	−4.40487e9	−	1.22503e10i	−0.280492	−	0.780071i
$355$	1.37030e10	−	1.37030e10i	0.862783	−	0.862783i
$356$	−1.74512e9	−	2.11291e9i	−0.108649	−	0.131547i
$357$	−5.34936e9	+	5.34936e9i	−0.329328	+	0.329328i
$358$	1.37923e10	+	6.49689e9i	0.839663	+	0.395524i
$359$	1.59198e10			0.958429			0.479215	−	0.877698i	$-0.340922\pi$
$359$	1.59198e10			0.958429			0.479215	+	0.877698i	$0.340922\pi$
$360$	1.70766e9	+	6.68409e9i	0.101670	+	0.397953i
$361$			1.34628e10i			0.792694i
$362$	−1.71314e10	−	8.06978e9i	−0.997606	−	0.469924i
$363$	−6.88974e9	−	6.88974e9i	−0.396804	−	0.396804i
$364$	−3.78284e9	−	3.60628e8i	−0.215483	−	0.0205425i
$365$	−2.10924e10	−	2.10924e10i	−1.18838	−	1.18838i
$366$	−3.83293e9	−	1.06597e10i	−0.213603	−	0.594048i
$367$			4.39761e9i			0.242411i	0.992627	+	0.121206i	$0.0386760\pi$
$367$			4.39761e9i			0.242411i	−0.992627	+	0.121206i	$0.961324\pi$
$368$	−3.16494e9	+	1.64486e10i	−0.172574	+	0.896888i
$369$	−1.17094e9			−0.0631579
$370$	−4.15520e10	+	1.49409e10i	−2.21710	+	0.797206i
$371$	2.66461e9	−	2.66461e9i	0.140649	−	0.140649i
$372$	−4.08420e10	−	3.89357e9i	−2.13273	−	0.203318i
$373$	1.47536e10	−	1.47536e10i	0.762188	−	0.762188i	−0.214529	−	0.976718i	$-0.568822\pi$
$373$	1.47536e10	−	1.47536e10i	0.762188	−	0.762188i	0.976718	+	0.214529i	$0.0688218\pi$
$374$	8.32383e9	−	1.76708e10i	0.425439	−	0.903168i
$375$	−6.09290e10			−3.08105
$376$	8.44314e9	−	1.42377e10i	0.422428	−	0.712340i
$377$		−	1.03615e10i		−	0.512930i
$378$	−2.22093e9	+	4.71484e9i	−0.108785	+	0.230940i
$379$	1.79016e10	+	1.79016e10i	0.867633	+	0.867633i	0.992210	−	0.124577i	$-0.0397573\pi$
$379$	1.79016e10	+	1.79016e10i	0.867633	+	0.867633i	−0.124577	+	0.992210i	$0.539757\pi$
$380$	1.12988e10	+	1.36801e10i	0.541872	+	0.656075i
$381$	−7.65320e9	−	7.65320e9i	−0.363198	−	0.363198i
$382$	1.98506e10	−	7.13773e9i	0.932226	−	0.335202i
$383$			9.56706e8i			0.0444614i	0.999753	+	0.0222307i	$0.00707684\pi$
$383$			9.56706e8i			0.0444614i	−0.999753	+	0.0222307i	$0.992923\pi$
$384$	1.44095e9	+	2.39708e10i	0.0662709	+	1.10244i
$385$	8.53137e9			0.388307
$386$	7.57198e9	+	2.10583e10i	0.341083	+	0.948582i
$387$	1.72498e9	−	1.72498e9i	0.0769023	−	0.0769023i
$388$	−1.84842e9	+	1.52666e9i	−0.0815593	+	0.0673622i
$389$	−1.65877e9	+	1.65877e9i	−0.0724414	+	0.0724414i	−0.742399	−	0.669958i	$-0.766312\pi$
$389$	−1.65877e9	+	1.65877e9i	−0.0724414	+	0.0724414i	0.669958	+	0.742399i	$0.266312\pi$
$390$	3.15635e10	+	1.48680e10i	1.36435	+	0.642679i
$391$	3.03869e10			1.30011
$392$	1.85275e10	+	1.09871e10i	0.784644	+	0.465305i
$393$		−	5.14588e10i		−	2.15720i
$394$	8.17672e9	+	3.85165e9i	0.339308	+	0.159831i
$395$	3.48843e10	+	3.48843e10i	1.43298	+	1.43298i
$396$	−3.59729e8	+	3.77341e9i	−0.0146283	+	0.153445i
$397$	1.40825e9	+	1.40825e9i	0.0566915	+	0.0566915i	0.734884	−	0.678193i	$-0.237237\pi$
$397$	1.40825e9	+	1.40825e9i	0.0566915	+	0.0566915i	−0.678193	+	0.734884i	$0.737237\pi$
$398$	−7.75545e8	−	2.15686e9i	−0.0309083	−	0.0859585i
$399$		−	3.77567e9i		−	0.148971i
$400$	−6.26641e10	−	1.20574e10i	−2.44782	−	0.470994i
$401$	−2.11826e10			−0.819220			−0.409610	−	0.912261i	$-0.634335\pi$
$401$	−2.11826e10			−0.819220			−0.409610	+	0.912261i	$0.634335\pi$
$402$	1.87272e10	−	6.73378e9i	0.717082	−	0.257843i
$403$	−2.64354e10	+	2.64354e10i	−1.00222	+	1.00222i
$404$	−1.03459e9	+	1.08524e10i	−0.0388366	+	0.407380i
$405$	4.16504e10	−	4.16504e10i	1.54810	−	1.54810i
$406$	2.40797e9	−	5.11190e9i	0.0886230	−	0.188139i
$407$	−2.42617e10			−0.884186
$408$	4.22083e10	−	1.07834e10i	1.52320	−	0.389150i
$409$		−	5.54086e10i		−	1.98008i	−0.140770	−	0.990042i	$-0.544958\pi$
$409$		−	5.54086e10i		−	1.98008i	0.140770	−	0.990042i	$-0.455042\pi$
$410$	6.46721e9	−	1.37293e10i	0.228866	−	0.485862i
$411$	1.25322e10	+	1.25322e10i	0.439199	+	0.439199i
$412$	−2.84664e10	+	2.35112e10i	−0.987968	+	0.815992i
$413$	−4.57445e9	−	4.57445e9i	−0.157231	−	0.157231i
$414$	−5.54896e9	+	1.99525e9i	−0.188890	+	0.0679197i
$415$		−	2.77509e10i		−	0.935587i
$416$	1.76775e10	+	1.28974e10i	0.590266	+	0.430654i
$417$	−1.83222e10			−0.605947
$418$	3.29861e9	+	9.17371e9i	0.108050	+	0.300497i
$419$	4.04560e10	−	4.04560e10i	1.31258	−	1.31258i	0.393076	−	0.919506i	$-0.371411\pi$
$419$	4.04560e10	−	4.04560e10i	1.31258	−	1.31258i	0.919506	−	0.393076i	$-0.128589\pi$
$420$	1.21167e10	+	1.46704e10i	0.389393	+	0.471460i
$421$	1.25322e9	−	1.25322e9i	0.0398931	−	0.0398931i	−0.686879	−	0.726772i	$-0.741020\pi$
$421$	1.25322e9	−	1.25322e9i	0.0398931	−	0.0398931i	0.726772	+	0.686879i	$0.241020\pi$
$422$	−2.71131e10	−	1.27716e10i	−0.854926	−	0.402714i
$423$	5.82725e9			0.182013
$424$	−2.10247e10	+	5.37142e9i	−0.650529	+	0.166198i
$425$			1.15765e11i			3.54830i
$426$	2.14831e10	+	1.01197e10i	0.652317	+	0.307275i
$427$	−3.98050e9	−	3.98050e9i	−0.119736	−	0.119736i
$428$	1.04001e10	+	9.91472e8i	0.309930	+	0.0295465i
$429$	1.35554e10	+	1.35554e10i	0.400205	+	0.400205i
$430$	1.06982e10	+	2.97527e10i	0.312923	+	0.870267i
$431$			2.03047e10i			0.588421i	0.955741	+	0.294211i	$0.0950568\pi$
$431$			2.03047e10i			0.588421i	−0.955741	+	0.294211i	$0.904943\pi$
$432$	2.48492e10	−	1.68296e10i	0.713472	−	0.483213i
$433$	−5.03335e10			−1.43188			−0.715938	−	0.698164i	$-0.754001\pi$
$433$	−5.03335e10			−1.43188			−0.715938	+	0.698164i	$0.754001\pi$
$434$	−1.91855e10	+	6.89855e9i	−0.540771	+	0.194446i
$435$	−3.66861e10	+	3.66861e10i	−1.02458	+	1.02458i
$436$	1.02441e10	+	9.76599e8i	0.283484	+	0.0270253i
$437$	−1.07238e10	+	1.07238e10i	−0.294051	+	0.294051i
$438$	1.55767e10	−	3.30680e10i	0.423233	−	0.898487i
$439$	2.46971e10			0.664949			0.332475	−	0.943112i	$-0.392116\pi$
$439$	2.46971e10			0.664949			0.332475	+	0.943112i	$0.392116\pi$
$440$	−4.22567e10	−	2.50588e10i	−1.12742	−	0.668574i
$441$			7.58302e9i			0.200488i
$442$	1.69164e10	−	3.59121e10i	0.443221	−	0.940918i
$443$	−1.29110e10	−	1.29110e10i	−0.335232	−	0.335232i	0.519337	−	0.854569i	$-0.326179\pi$
$443$	−1.29110e10	−	1.29110e10i	−0.335232	−	0.335232i	−0.854569	+	0.519337i	$0.826179\pi$
$444$	−3.44578e10	−	4.17200e10i	−0.886657	−	1.07353i
$445$	8.84142e9	+	8.84142e9i	0.225466	+	0.225466i
$446$	−1.05925e10	+	3.80878e9i	−0.267707	+	0.0962600i
$447$		−	3.04578e10i		−	0.762901i
$448$	5.72398e9	+	1.04712e10i	0.142097	+	0.259946i
$449$	4.67334e9			0.114985			0.0574926	−	0.998346i	$-0.481689\pi$
$449$	4.67334e9			0.114985			0.0574926	+	0.998346i	$0.481689\pi$
$450$	−7.60127e9	−	2.11398e10i	−0.185368	−	0.515526i
$451$	5.89625e9	−	5.89625e9i	0.142518	−	0.142518i
$452$	3.48819e9	−	2.88100e9i	0.0835691	−	0.0690222i
$453$	−5.19438e10	+	5.19438e10i	−1.23350	+	1.23350i
$454$	−5.63363e10	−	2.65373e10i	−1.32607	−	0.624645i
$455$	1.73382e10			0.404537
$456$	−1.10901e10	+	1.87012e10i	−0.256493	+	0.432525i
$457$		−	3.70398e10i		−	0.849189i	−0.905384	−	0.424595i	$-0.860417\pi$
$457$		−	3.70398e10i		−	0.849189i	0.905384	−	0.424595i	$-0.139583\pi$
$458$	2.09413e10	+	9.86443e9i	0.475929	+	0.224187i
$459$	−3.84984e10	−	3.84984e10i	−0.867344	−	0.867344i
$460$	7.25308e9	−	7.60818e10i	0.161991	−	1.69922i
$461$	−3.56181e10	−	3.56181e10i	−0.788618	−	0.788618i	0.192649	−	0.981268i	$-0.438292\pi$
$461$	−3.56181e10	−	3.56181e10i	−0.788618	−	0.788618i	−0.981268	+	0.192649i	$0.938292\pi$
$462$	3.53740e9	+	9.83782e9i	0.0776456	+	0.215939i
$463$			3.26693e10i			0.710911i	0.934693	+	0.355456i	$0.115674\pi$
$463$			3.26693e10i			0.710911i	−0.934693	+	0.355456i	$0.884326\pi$
$464$	−2.69418e10	+	1.82469e10i	−0.581240	+	0.393656i
$465$	1.87195e11			4.00388
$466$	2.44537e10	−	8.79288e9i	0.518563	−	0.186461i
$467$	−1.76988e9	+	1.76988e9i	−0.0372114	+	0.0372114i	−0.725468	−	0.688256i	$-0.758376\pi$
$467$	−1.76988e9	+	1.76988e9i	−0.0372114	+	0.0372114i	0.688256	+	0.725468i	$0.258376\pi$
$468$	−7.31073e8	+	7.66866e9i	−0.0152397	+	0.159859i
$469$	6.99302e9	−	6.99302e9i	0.144535	−	0.144535i
$470$	−3.21845e10	+	6.83249e10i	−0.659563	+	1.40019i
$471$	1.50835e10			0.306492
$472$	9.22136e9	+	3.60940e10i	0.185792	+	0.727222i
$473$			1.73722e10i			0.347065i
$474$	−2.57620e10	+	5.46905e10i	−0.510349	+	1.08342i
$475$	−4.08543e10	−	4.08543e10i	−0.802534	−	0.802534i
$476$	1.66916e10	−	1.37861e10i	0.325140	−	0.268543i
$477$	−5.40176e9	−	5.40176e9i	−0.104343	−	0.104343i
$478$	2.30544e10	−	8.28971e9i	0.441613	−	0.158792i
$479$			1.02745e11i			1.95172i	0.218390	+	0.975861i	$0.429919\pi$
$479$			1.02745e11i			1.95172i	−0.218390	+	0.975861i	$0.570081\pi$
$480$	−1.69245e10	−	1.08254e11i	−0.318824	−	2.03928i
$481$	−4.93068e10			−0.921142
$482$	−1.62558e10	−	4.52088e10i	−0.301176	−	0.837596i
$483$	−1.15001e10	+	1.15001e10i	−0.211307	+	0.211307i
$484$	1.77559e10	+	2.14980e10i	0.323564	+	0.391758i
$485$	7.73465e9	−	7.73465e9i	0.139789	−	0.139789i
$486$	2.18084e10	+	1.02729e10i	0.390912	+	0.184140i
$487$	6.35055e10			1.12900			0.564502	−	0.825432i	$-0.309068\pi$
$487$	6.35055e10			1.12900			0.564502	+	0.825432i	$0.309068\pi$
$488$	8.02404e9	+	3.14075e10i	0.141486	+	0.553802i
$489$			4.68970e10i			0.820180i
$490$	−8.89114e10	−	4.18819e10i	−1.54232	−	0.726510i
$491$	−1.83353e10	−	1.83353e10i	−0.315473	−	0.315473i	0.531552	−	0.847026i	$-0.321609\pi$
$491$	−1.83353e10	−	1.83353e10i	−0.315473	−	0.315473i	−0.847026	+	0.531552i	$0.821609\pi$
$492$	1.85133e10	+	1.76492e9i	0.315953	+	0.0301206i
$493$	4.17405e10	+	4.17405e10i	0.706594	+	0.706594i
$494$	6.70373e9	+	1.86436e10i	0.112566	+	0.313057i
$495$		−	1.72950e10i		−	0.288071i
$496$	1.15290e11	+	2.21834e10i	1.90487	+	0.366524i
$497$	1.18009e10			0.193416
$498$	3.20005e10	−	1.15065e10i	0.520283	−	0.187079i
$499$	−2.60198e10	+	2.60198e10i	−0.419664	+	0.419664i	−0.885088	−	0.465424i	$-0.845902\pi$
$499$	−2.60198e10	+	2.60198e10i	−0.419664	+	0.419664i	0.465424	+	0.885088i	$0.345902\pi$
$500$	1.73570e11	+	1.65469e10i	2.77712	+	0.264750i
$501$	−5.46912e10	+	5.46912e10i	−0.868093	+	0.868093i
$502$	1.02435e10	−	2.17460e10i	0.161300	−	0.342425i
$503$	−9.54221e10			−1.49065			−0.745327	−	0.666699i	$-0.767707\pi$
$503$	−9.54221e10			−1.49065			−0.745327	+	0.666699i	$0.767707\pi$
$504$	−2.14284e9	+	3.61347e9i	−0.0332099	+	0.0560019i
$505$		−	4.97407e10i		−	0.764797i
$506$	1.78947e10	−	3.79888e10i	0.272975	−	0.579501i
$507$	−2.40524e10	−	2.40524e10i	−0.364021	−	0.364021i
$508$	1.97234e10	+	2.38803e10i	0.296161	+	0.358579i
$509$	5.50853e10	+	5.50853e10i	0.820662	+	0.820662i	0.986203	−	0.165541i	$-0.0529370\pi$
$509$	5.50853e10	+	5.50853e10i	0.820662	+	0.820662i	−0.165541	+	0.986203i	$0.552937\pi$
$510$	−1.87045e11	+	6.72562e10i	−2.76481	+	0.994149i
$511$		−	1.81647e10i		−	0.266406i
$512$	2.40503e9	−	6.86774e10i	0.0349977	−	0.999387i
$513$	2.71728e10			0.392342
$514$	3.57951e10	+	9.95492e10i	0.512827	+	1.42622i
$515$	1.19117e11	−	1.19117e11i	1.69334	−	1.69334i
$516$	−2.98730e10	+	2.46730e10i	−0.421386	+	0.348035i
$517$	−2.93431e10	+	2.93431e10i	−0.410719	+	0.410719i
$518$	−2.43257e10	−	1.14587e10i	−0.337868	−	0.159153i
$519$	6.94862e10			0.957699
$520$	−8.58778e10	−	5.09267e10i	−1.17454	−	0.696518i
$521$		−	1.11708e11i		−	1.51612i	−0.652183	−	0.758061i	$-0.726147\pi$
$521$		−	1.11708e11i		−	1.51612i	0.652183	−	0.758061i	$-0.273853\pi$
$522$	−1.03630e10	−	4.88149e9i	−0.139573	−	0.0657462i
$523$	−2.23681e10	−	2.23681e10i	−0.298966	−	0.298966i	0.541643	−	0.840609i	$-0.317803\pi$
$523$	−2.23681e10	−	2.23681e10i	−0.298966	−	0.298966i	−0.840609	+	0.541643i	$0.817803\pi$
$524$	−1.39750e10	+	1.46592e11i	−0.185364	+	1.94440i
$525$	−4.38119e10	−	4.38119e10i	−0.576706	−	0.576706i
$526$	1.64210e10	+	4.56682e10i	0.214515	+	0.596583i
$527$		−	2.12985e11i		−	2.76126i
$528$	1.13751e10	−	5.91179e10i	0.146359	−	0.760647i
$529$	−1.29847e10			−0.165810
$530$	9.31705e10	−	3.35015e10i	1.18080	−	0.424581i
$531$	−9.27344e9	+	9.27344e9i	−0.116644	+	0.116644i
$532$	−1.02538e9	+	1.07558e10i	−0.0128009	+	0.134276i
$533$	1.19829e10	−	1.19829e10i	0.148475	−	0.148475i
$534$	−6.52939e9	+	1.38613e10i	−0.0802986	+	0.170467i
$535$	−4.76678e10			−0.581849
$536$	−5.51774e10	+	1.40968e10i	−0.668501	+	0.170790i
$537$		−	8.52428e10i		−	1.02509i
$538$	−1.64592e10	+	3.49414e10i	−0.196462	+	0.417072i
$539$	−3.81843e10	−	3.81843e10i	−0.452408	−	0.452408i
$540$	−1.05580e11	+	8.72018e10i	−1.24167	+	1.02553i
$541$	8.19903e10	+	8.19903e10i	0.957136	+	0.957136i	0.999118	−	0.0419826i	$-0.0133674\pi$
$541$	8.19903e10	+	8.19903e10i	0.957136	+	0.957136i	−0.0419826	+	0.999118i	$0.513367\pi$
$542$	1.27788e10	−	4.59488e9i	0.148078	−	0.0532448i
$543$			1.05880e11i			1.21791i
$544$	−1.23168e11	+	1.92563e10i	−1.40638	+	0.219875i
$545$	−4.69528e10			−0.532200
$546$	7.18903e9	+	1.99933e10i	0.0808909	+	0.224964i
$547$	−9.62511e10	+	9.62511e10i	−1.07512	+	1.07512i	−0.0781787	+	0.996939i	$0.524910\pi$
$547$	−9.62511e10	+	9.62511e10i	−1.07512	+	1.07512i	−0.996939	+	0.0781787i	$0.975090\pi$
$548$	−3.22974e10	−	3.91043e10i	−0.358134	−	0.433613i
$549$	−8.06936e9	+	8.06936e9i	−0.0888280	+	0.0888280i
$550$	1.44726e11	+	6.81732e10i	1.58159	+	0.745011i
$551$	−2.94611e10			−0.319627
$552$	9.07400e10	−	2.31824e10i	0.977333	−	0.249691i
$553$			3.00422e10i			0.321241i
$554$	−1.14855e11	−	5.41024e10i	−1.21930	−	0.574351i
$555$	1.74576e11	+	1.74576e11i	1.83998	+	1.83998i
$556$	5.21950e10	+	4.97588e9i	0.546173	+	0.0520680i
$557$	−7.70516e10	−	7.70516e10i	−0.800499	−	0.800499i	0.182674	−	0.983174i	$-0.441525\pi$
$557$	−7.70516e10	−	7.70516e10i	−0.800499	−	0.800499i	−0.983174	+	0.182674i	$0.941525\pi$
$558$	1.39849e10	+	3.88932e10i	0.144252	+	0.401178i
$559$			3.53054e10i			0.361571i
$560$	−3.05330e10	−	4.50825e10i	−0.310469	−	0.458412i
$561$	−1.09213e11			−1.10262
$562$	1.29713e11	−	4.66413e10i	1.30029	−	0.467547i
$563$	9.19267e9	−	9.19267e9i	0.0914973	−	0.0914973i	−0.659877	−	0.751374i	$-0.729391\pi$
$563$	9.19267e9	−	9.19267e9i	0.0914973	−	0.0914973i	0.751374	+	0.659877i	$0.229391\pi$
$564$	−9.21327e10	−	8.78325e9i	−0.910537	−	0.0868038i
$565$	−1.45962e10	+	1.45962e10i	−0.143234	+	0.143234i
$566$	7.21375e10	−	1.53141e11i	0.702903	−	1.49220i
$567$	3.58692e10			0.347048
$568$	−5.84512e10	−	3.46624e10i	−0.561565	−	0.333016i
$569$			5.83930e10i			0.557072i	0.960426	+	0.278536i	$0.0898492\pi$
$569$			5.83930e10i			0.557072i	−0.960426	+	0.278536i	$0.910151\pi$
$570$	4.22746e10	−	8.97451e10i	0.400479	−	0.850181i
$571$	−1.31281e11	−	1.31281e11i	−1.23497	−	1.23497i	−0.962032	−	0.272937i	$-0.912005\pi$
$571$	−1.31281e11	−	1.31281e11i	−1.23497	−	1.23497i	−0.272937	−	0.962032i	$-0.587995\pi$
$572$	−3.49342e10	−	4.22969e10i	−0.326338	−	0.395116i
$573$	−8.34004e10	−	8.34004e10i	−0.773659	−	0.773659i
$574$	8.69658e9	−	3.12704e9i	0.0801126	−	0.0288062i
$575$			2.48872e11i			2.27670i
$576$	2.12274e10	−	1.16038e10i	0.192844	−	0.105417i
$577$	1.27989e11			1.15470			0.577351	−	0.816496i	$-0.304086\pi$
$577$	1.27989e11			1.15470			0.577351	+	0.816496i	$0.304086\pi$
$578$	3.87570e10	+	1.07786e11i	0.347247	+	0.965723i
$579$	8.84743e10	−	8.84743e10i	0.787232	−	0.787232i
$580$	1.14472e11	−	9.45454e10i	1.01155	−	0.835465i
$581$	1.19495e10	−	1.19495e10i	0.104868	−	0.104868i
$582$	1.21262e10	+	5.71204e9i	0.105689	+	0.0497851i
$583$	5.44012e10			0.470906
$584$	−5.33543e10	+	8.99713e10i	−0.458689	+	0.773487i
$585$		−	3.51484e10i		−	0.300111i
$586$	−1.05004e11	−	4.94625e10i	−0.890466	−	0.419455i
$587$	1.21533e11	+	1.21533e11i	1.02363	+	1.02363i	0.999714	+	0.0239143i	$0.00761287\pi$
$587$	1.21533e11	+	1.21533e11i	1.02363	+	1.02363i	0.0239143	+	0.999714i	$0.492387\pi$
$588$	1.14297e10	−	1.19893e11i	0.0956146	−	1.00296i
$589$	7.51643e10	+	7.51643e10i	0.624526	+	0.624526i
$590$	−5.75134e10	−	1.59950e11i	−0.474637	−	1.32001i
$591$		−	5.05359e10i		−	0.414238i
$592$	8.68306e10	+	1.28207e11i	0.706946	+	1.04382i
$593$	1.56584e11			1.26628			0.633140	−	0.774037i	$-0.281766\pi$
$593$	1.56584e11			1.26628			0.633140	+	0.774037i	$0.281766\pi$
$594$	−7.08010e10	+	2.54580e10i	−0.568714	+	0.204493i
$595$	−6.98455e10	+	6.98455e10i	−0.557276	+	0.557276i
$596$	−8.27161e9	+	8.67658e10i	−0.0655549	+	0.687644i
$597$	−9.06180e9	+	9.06180e9i	−0.0713374	+	0.0713374i
$598$	3.63672e10	−	7.72043e10i	0.284384	−	0.603722i
$599$	1.58577e11			1.23178			0.615889	−	0.787833i	$-0.288797\pi$
$599$	1.58577e11			1.23178			0.615889	+	0.787833i	$0.288797\pi$
$600$	8.83176e10	+	3.45691e11i	0.681463	+	2.66737i
$601$			3.46213e10i			0.265366i	0.991159	+	0.132683i	$0.0423592\pi$
$601$			3.46213e10i			0.265366i	−0.991159	+	0.132683i	$0.957641\pi$
$602$	−8.20481e9	+	1.74181e10i	−0.0624716	+	0.132622i
$603$	−1.41764e10	−	1.41764e10i	−0.107225	−	0.107225i
$604$	1.62080e11	−	1.33867e11i	1.21782	−	1.00583i
$605$	−8.99579e10	−	8.99579e10i	−0.671456	−	0.671456i
$606$	5.73577e10	−	2.06242e10i	0.425306	−	0.152928i
$607$			3.73080e10i			0.274820i	0.990514	+	0.137410i	$0.0438777\pi$
$607$			3.73080e10i			0.274820i	−0.990514	+	0.137410i	$0.956122\pi$
$608$	3.66715e10	−	5.02629e10i	0.268358	−	0.367818i
$609$	−3.15939e10			−0.229686
$610$	−5.00458e10	−	1.39182e11i	−0.361450	−	1.00522i
$611$	−5.96337e10	+	5.96337e10i	−0.427885	+	0.427885i
$612$	−2.79475e10	−	3.38376e10i	−0.199222	−	0.241209i
$613$	6.93834e10	−	6.93834e10i	0.491376	−	0.491376i	−0.417364	−	0.908740i	$-0.637046\pi$
$613$	6.93834e10	−	6.93834e10i	0.491376	−	0.491376i	0.908740	+	0.417364i	$0.137046\pi$
$614$	−1.44947e11	−	6.82775e10i	−1.01985	−	0.480401i
$615$	−8.48535e10			−0.593156
$616$	−7.40537e9	−	2.89859e10i	−0.0514308	−	0.201309i
$617$			1.14765e11i			0.791896i	0.918273	+	0.395948i	$0.129584\pi$
$617$			1.14765e11i			0.791896i	−0.918273	+	0.395948i	$0.870416\pi$
$618$	1.86747e11	+	8.79676e10i	1.28027	+	0.603072i
$619$	1.45781e11	+	1.45781e11i	0.992977	+	0.992977i	0.999976	−	0.00699815i	$-0.00222760\pi$
$619$	1.45781e11	+	1.45781e11i	0.992977	+	0.992977i	−0.00699815	+	0.999976i	$0.502228\pi$
$620$	−5.33266e11	−	5.08376e10i	−3.60892	−	0.344047i
$621$	−8.27643e10	−	8.27643e10i	−0.556515	−	0.556515i
$622$	7.36229e10	+	2.04752e11i	0.491872	+	1.36794i
$623$			7.61420e9i			0.0505443i
$624$	2.31175e10	−	1.20145e11i	0.152476	−	0.792440i
$625$	−4.15179e11			−2.72092
$626$	−1.18406e11	+	4.25756e10i	−0.771041	+	0.277245i
$627$	3.85424e10	−	3.85424e10i	0.249384	−	0.249384i
$628$	−4.29688e10	−	4.09633e9i	−0.276258	−	0.0263364i
$629$	1.98628e11	−	1.98628e11i	1.26893	−	1.26893i
$630$	8.16833e9	−	1.73406e10i	0.0518527	−	0.110079i
$631$	−2.05382e11			−1.29552			−0.647760	−	0.761845i	$-0.724294\pi$
$631$	−2.05382e11			−1.29552			−0.647760	+	0.761845i	$0.724294\pi$
$632$	8.82416e10	−	1.48802e11i	0.553102	−	0.932695i
$633$			1.67571e11i			1.04372i
$634$	−4.89789e10	+	1.03978e11i	−0.303146	+	0.643552i
$635$	−9.99262e10	−	9.99262e10i	−0.614589	−	0.614589i
$636$	7.72635e10	+	9.35473e10i	0.472222	+	0.571746i
$637$	−7.76016e10	−	7.76016e10i	−0.471317	−	0.471317i
$638$	7.67635e10	−	2.76020e10i	0.463310	−	0.166593i
$639$		−	2.39232e10i		−	0.143488i
$640$	1.88141e10	+	3.12981e11i	0.112141	+	1.86551i
$641$	9.05695e10			0.536475			0.268238	−	0.963353i	$-0.413559\pi$
$641$	9.05695e10			0.536475			0.268238	+	0.963353i	$0.413559\pi$
$642$	−1.97647e10	−	5.49675e10i	−0.116346	−	0.323568i
$643$	−1.51562e11	+	1.51562e11i	−0.886638	+	0.886638i	−0.994199	−	0.107561i	$-0.965696\pi$
$643$	−1.51562e11	+	1.51562e11i	−0.886638	+	0.886638i	0.107561	+	0.994199i	$0.465696\pi$
$644$	3.58839e10	−	2.96375e10i	0.208620	−	0.172305i
$645$	1.25003e11	−	1.25003e11i	0.722238	−	0.722238i
$646$	−1.02110e11	−	4.80989e10i	−0.586323	−	0.276188i
$647$	6.02989e10			0.344106			0.172053	−	0.985088i	$-0.444960\pi$
$647$	6.02989e10			0.344106			0.172053	+	0.985088i	$0.444960\pi$
$648$	−1.77664e11	−	1.05357e11i	−1.00762	−	0.597535i
$649$		−	9.33928e10i		−	0.526423i
$650$	2.94124e11	+	1.38548e11i	1.64770	+	0.776150i
$651$	8.06056e10	+	8.06056e10i	0.448788	+	0.448788i
$652$	1.27361e10	−	1.33596e11i	0.0704767	−	0.739272i
$653$	2.14138e11	+	2.14138e11i	1.17772	+	1.17772i	0.980325	+	0.197392i	$0.0632473\pi$
$653$	2.14138e11	+	2.14138e11i	1.17772	+	1.17772i	0.197392	+	0.980325i	$0.436753\pi$
$654$	−1.94683e10	−	5.41429e10i	−0.106418	−	0.295958i
$655$		−	6.71887e11i		−	3.65032i
$656$	−5.22599e10	−	1.00555e10i	−0.282197	−	0.0542987i
$657$	−3.68239e10			−0.197637
$658$	−4.32792e10	+	1.55620e10i	−0.230874	+	0.0830159i
$659$	3.45226e9	−	3.45226e9i	0.0183047	−	0.0183047i	−0.697895	−	0.716200i	$-0.745880\pi$
$659$	3.45226e9	−	3.45226e9i	0.0183047	−	0.0183047i	0.716200	+	0.697895i	$0.245880\pi$
$660$	−2.60682e10	+	2.73445e11i	−0.137384	+	1.44110i
$661$	−6.86767e10	+	6.86767e10i	−0.359752	+	0.359752i	−0.863722	−	0.503969i	$-0.831873\pi$
$661$	−6.86767e10	+	6.86767e10i	−0.359752	+	0.359752i	0.503969	+	0.863722i	$0.331873\pi$
$662$	−8.58956e10	+	1.82349e11i	−0.447238	+	0.949447i
$663$	−2.21953e11			−1.14870
$664$	−9.42854e10	+	2.40882e10i	−0.485034	+	0.123917i
$665$		−	4.92981e10i		−	0.252083i
$666$	−2.32293e10	+	4.93137e10i	−0.118070	+	0.250652i
$667$	8.97343e10	+	8.97343e10i	0.453372	+	0.453372i
$668$	1.70653e11	−	1.40947e11i	0.857053	−	0.707865i
$669$	4.45034e10	+	4.45034e10i	0.222172	+	0.222172i
$670$	2.44517e11	−	8.79215e10i	1.21342	−	0.436311i
$671$		−	8.12665e10i		−	0.400887i
$672$	3.93262e10	−	5.39015e10i	0.192843	−	0.264316i
$673$	−2.98364e11			−1.45441			−0.727204	−	0.686421i	$-0.759181\pi$
$673$	−2.98364e11			−1.45441			−0.727204	+	0.686421i	$0.759181\pi$
$674$	1.00698e11	+	2.80050e11i	0.487958	+	1.35705i
$675$	3.15306e11	−	3.15306e11i	1.51886	−	1.51886i
$676$	6.19865e10	+	7.50506e10i	0.296832	+	0.359391i
$677$	−6.44040e10	+	6.44040e10i	−0.306590	+	0.306590i	−0.843585	−	0.536995i	$-0.819559\pi$
$677$	−6.44040e10	+	6.44040e10i	−0.306590	+	0.306590i	0.536995	+	0.843585i	$0.319559\pi$
$678$	−2.28835e10	−	1.07793e10i	−0.108294	−	0.0510120i
$679$	6.66105e9			0.0313374
$680$	5.51105e11	−	1.40797e11i	2.57750	−	0.658504i
$681$			3.48185e11i			1.61890i
$682$	−2.66268e11	−	1.25426e11i	−1.23078	−	0.579762i
$683$	−7.54224e10	−	7.54224e10i	−0.346591	−	0.346591i	0.512247	−	0.858838i	$-0.328813\pi$
$683$	−7.54224e10	−	7.54224e10i	−0.346591	−	0.346591i	−0.858838	+	0.512247i	$0.828813\pi$
$684$	2.18045e10	+	2.07868e9i	0.0996143	+	0.00949649i
$685$	1.63631e11	+	1.63631e11i	0.743195	+	0.743195i
$686$	−4.24500e10	−	1.18057e11i	−0.191682	−	0.533083i
$687$		−	1.29427e11i		−	0.581029i
$688$	9.18006e10	−	6.21738e10i	0.409724	−	0.277494i
$689$	1.10559e11			0.490588
$690$	−4.02112e11	+	1.44588e11i	−1.77399	+	0.637877i
$691$	7.05831e10	−	7.05831e10i	0.309591	−	0.309591i	−0.535160	−	0.844751i	$-0.679749\pi$
$691$	7.05831e10	−	7.05831e10i	0.309591	−	0.309591i	0.844751	+	0.535160i	$0.179749\pi$
$692$	−1.97947e11	−	1.88708e10i	−0.863226	−	0.0822935i
$693$	7.44719e9	−	7.44719e9i	0.0322894	−	0.0322894i
$694$	1.46503e10	−	3.11013e10i	0.0631551	−	0.134073i
$695$	−2.39230e11			−1.02536
$696$	1.56488e11	+	9.27994e10i	0.666873	+	0.395465i
$697$			9.65441e10i			0.409067i
$698$	−1.32382e11	+	2.81034e11i	−0.557707	+	1.18396i
$699$	−1.02740e11	−	1.02740e11i	−0.430358	−	0.430358i
$700$	1.12910e11	+	1.36706e11i	0.470261	+	0.569372i
$701$	5.51129e10	+	5.51129e10i	0.228235	+	0.228235i	0.811955	−	0.583720i	$-0.198404\pi$
$701$	5.51129e10	+	5.51129e10i	0.228235	+	0.228235i	−0.583720	+	0.811955i	$0.698404\pi$
$702$	−1.43888e11	+	5.17381e10i	−0.592484	+	0.213040i
$703$			1.40195e11i			0.574000i
$704$	−4.84595e10	+	1.65321e11i	−0.197283	+	0.673036i
$705$	4.22280e11			1.70940
$706$	−1.30835e11	−	3.63863e11i	−0.526629	−	1.46460i
$707$	2.14182e10	−	2.14182e10i	0.0857247	−	0.0857247i
$708$	1.60597e11	−	1.32642e11i	0.639151	−	0.527894i
$709$	1.10097e11	−	1.10097e11i	0.435702	−	0.435702i	−0.454860	−	0.890563i	$-0.650311\pi$
$709$	1.10097e11	−	1.10097e11i	0.435702	−	0.435702i	0.890563	+	0.454860i	$0.150311\pi$
$710$	2.80501e11	+	1.32130e11i	1.10383	+	0.519959i
$711$	6.09023e10			0.238317
$712$	2.23648e10	−	3.77138e10i	0.0870254	−	0.146751i
$713$		−	4.57879e11i		−	1.77171i
$714$	−1.09502e11	−	5.15809e10i	−0.421335	−	0.198471i
$715$	1.76990e11	+	1.76990e11i	0.677212	+	0.677212i
$716$	−2.31499e10	+	2.42833e11i	−0.0880841	+	0.923966i
$717$	−9.68606e10	−	9.68606e10i	−0.366497	−	0.366497i
$718$	8.61867e10	+	2.39693e11i	0.324297	+	0.901897i
$719$			3.12657e11i			1.16991i	0.811066	+	0.584955i	$0.198888\pi$
$719$			3.12657e11i			1.16991i	−0.811066	+	0.584955i	$0.801112\pi$
$720$	−9.13924e10	+	6.18973e10i	−0.340079	+	0.230325i
$721$	1.02583e11			0.379606
$722$	−2.02699e11	+	7.28848e10i	−0.745938	+	0.268218i
$723$	−1.89940e11	+	1.89940e11i	−0.695124	+	0.695124i
$724$	2.87545e10	−	3.01623e11i	0.104653	−	1.09777i
$725$	−3.41859e11	+	3.41859e11i	−1.23736	+	1.23736i
$726$	6.64339e10	−	1.41033e11i	0.239135	−	0.507663i
$727$	8.53468e10			0.305527			0.152764	−	0.988263i	$-0.451183\pi$
$727$	8.53468e10			0.305527			0.152764	+	0.988263i	$0.451183\pi$
$728$	−1.50498e10	−	5.89078e10i	−0.0535805	−	0.209723i
$729$			1.96073e11i			0.694236i
$730$	2.03382e11	−	4.31762e11i	0.716179	−	1.52038i
$731$	−1.42225e11	−	1.42225e11i	−0.498088	−	0.498088i
$732$	1.39745e11	−	1.15419e11i	0.486733	−	0.402007i
$733$	−1.23829e11	−	1.23829e11i	−0.428950	−	0.428950i	0.459321	−	0.888271i	$-0.348093\pi$
$733$	−1.23829e11	−	1.23829e11i	−0.428950	−	0.428950i	−0.888271	+	0.459321i	$0.848093\pi$
$734$	−6.62116e10	+	2.38078e10i	−0.228113	+	0.0820229i
$735$			5.49514e11i			1.88291i
$736$	−2.64789e11	+	4.13974e10i	−0.902378	+	0.141079i
$737$	1.42771e11			0.483915
$738$	−6.33922e9	−	1.76299e10i	−0.0213703	−	0.0594326i
$739$	2.77559e11	−	2.77559e11i	0.930632	−	0.930632i	−0.0671130	−	0.997745i	$-0.521379\pi$
$739$	2.77559e11	−	2.77559e11i	0.930632	−	0.930632i	0.997745	+	0.0671130i	$0.0213788\pi$
$740$	−4.49909e11	−	5.44730e11i	−1.50037	−	1.81658i
$741$	7.83293e10	−	7.83293e10i	0.259807	−	0.259807i
$742$	5.45447e10	+	2.56934e10i	0.179944	+	0.0847628i
$743$	−3.49650e11			−1.14730			−0.573652	−	0.819099i	$-0.694474\pi$
$743$	−3.49650e11			−1.14730			−0.573652	+	0.819099i	$0.694474\pi$
$744$	−1.62488e11	−	6.36007e11i	−0.530309	−	2.07573i
$745$		−	3.97681e11i		−	1.29095i
$746$	3.02007e11	+	1.42261e11i	0.975127	+	0.459335i
$747$	−2.42242e10	−	2.42242e10i	−0.0777979	−	0.0777979i
$748$	3.11119e11	+	2.96598e10i	0.993848	+	0.0947461i
$749$	−2.05257e10	−	2.05257e10i	−0.0652184	−	0.0652184i
$750$	−3.29858e11	−	9.17362e11i	−1.04251	−	2.89932i
$751$			5.36727e10i			0.168730i	0.996435	+	0.0843652i	$0.0268862\pi$
$751$			5.36727e10i			0.168730i	−0.996435	+	0.0843652i	$0.973114\pi$
$752$	2.60075e11	+	5.00421e10i	0.813257	+	0.156482i
$753$	−1.34401e11			−0.418043
$754$	1.56006e11	−	5.60952e10i	0.482675	−	0.173556i
$755$	−6.78219e11	+	6.78219e11i	−2.08729	+	2.08729i
$756$	−8.30116e10	−	7.91370e9i	−0.254127	−	0.0242266i
$757$	−3.60941e11	+	3.60941e11i	−1.09914	+	1.09914i	−0.104629	+	0.994511i	$0.533365\pi$
$757$	−3.60941e11	+	3.60941e11i	−1.09914	+	1.09914i	−0.994511	+	0.104629i	$0.966635\pi$
$758$	−1.72616e11	+	3.66448e11i	−0.522882	+	1.11003i
$759$	−2.34789e11			−0.707473
$760$	−1.44801e11	+	2.44178e11i	−0.434028	+	0.731902i
$761$			3.69488e11i			1.10170i	0.834606	+	0.550848i	$0.185695\pi$
$761$			3.69488e11i			1.10170i	−0.834606	+	0.550848i	$0.814305\pi$
$762$	7.37956e10	−	1.56661e11i	0.218882	−	0.464667i
$763$	−2.02178e10	−	2.02178e10i	−0.0596534	−	0.0596534i
$764$	2.14935e11	+	2.60234e11i	0.630861	+	0.763820i
$765$	1.41592e11	+	1.41592e11i	0.413423	+	0.413423i
$766$	−1.44044e10	+	5.17942e9i	−0.0418389	+	0.0150441i
$767$		−	1.89801e11i		−	0.548425i
$768$	−3.53109e11	+	1.51468e11i	−1.01499	+	0.435388i
$769$	−4.47090e11			−1.27847			−0.639234	−	0.769012i	$-0.720748\pi$
$769$	−4.47090e11			−1.27847			−0.639234	+	0.769012i	$0.720748\pi$
$770$	4.61871e10	+	1.28450e11i	0.131389	+	0.365403i
$771$	4.18245e11	−	4.18245e11i	1.18362	−	1.18362i
$772$	−2.76066e11	+	2.28011e11i	−0.777221	+	0.641929i
$773$	2.60286e11	−	2.60286e11i	0.729008	−	0.729008i	−0.241414	−	0.970422i	$-0.577611\pi$
$773$	2.60286e11	−	2.60286e11i	0.729008	−	0.729008i	0.970422	+	0.241414i	$0.0776113\pi$
$774$	3.53104e10	+	1.66330e10i	0.0983871	+	0.0463454i
$775$	1.74437e12			4.83540
$776$	−3.29928e10	−	1.95652e10i	−0.0909855	−	0.0539557i
$777$			1.50344e11i			0.412480i
$778$	−3.39550e10	−	1.59946e10i	−0.0926800	−	0.0436570i
$779$	−3.40712e10	−	3.40712e10i	−0.0925205	−	0.0925205i
$780$	−5.29782e10	+	5.55720e11i	−0.143126	+	1.50133i
$781$	1.20465e11	+	1.20465e11i	0.323785	+	0.323785i
$782$	1.64509e11	+	4.57513e11i	0.439908	+	1.22342i
$783$		−	2.27376e11i		−	0.604918i
$784$	−6.51199e10	+	3.38437e11i	−0.172365	+	0.895805i
$785$	1.96943e11			0.518634
$786$	7.74777e11	−	2.78588e11i	2.02996	−	0.729915i
$787$	−2.65634e11	+	2.65634e11i	−0.692444	+	0.692444i	−0.962769	−	0.270325i	$-0.912869\pi$
$787$	−2.65634e11	+	2.65634e11i	−0.692444	+	0.692444i	0.270325	+	0.962769i	$0.412869\pi$
$788$	−1.37243e10	+	1.43963e11i	−0.0355948	+	0.373375i
$789$	1.91870e11	−	1.91870e11i	0.495107	−	0.495107i
$790$	−3.36370e11	+	7.14083e11i	−0.863592	+	1.83333i
$791$	−1.25702e10			−0.0321097
$792$	−5.87609e10	+	1.50123e10i	−0.149344	+	0.0381547i
$793$		−	1.65157e11i		−	0.417642i
$794$	−1.35790e10	+	2.88270e10i	−0.0341653	+	0.0725299i
$795$	−3.91446e11	−	3.91446e11i	−0.979948	−	0.979948i
$796$	2.82755e10	−	2.33536e10i	0.0704301	−	0.0581703i
$797$	−5.06547e11	−	5.06547e11i	−1.25541	−	1.25541i	−0.953260	−	0.302153i	$-0.902295\pi$
$797$	−5.06547e11	−	5.06547e11i	−1.25541	−	1.25541i	−0.302153	−	0.953260i	$-0.597705\pi$
$798$	5.68474e10	−	2.04407e10i	0.140184	−	0.0504063i
$799$		−	4.80459e11i		−	1.17888i
$800$	−1.57711e11	−	1.00876e12i	−0.385037	−	2.46280i
$801$	1.54357e10			0.0374969
$802$	−1.14678e11	−	3.18930e11i	−0.277194	−	0.770899i
$803$	1.85427e11	−	1.85427e11i	0.445974	−	0.445974i
$804$	2.02771e11	+	2.45506e11i	0.485268	+	0.587541i
$805$	−1.50155e11	+	1.50155e11i	−0.357566	+	0.357566i
$806$	−5.41133e11	−	2.54902e11i	−1.28222	−	0.603994i
$807$	2.15954e11			0.509175
$808$	−1.68997e11	+	4.31757e10i	−0.396492	+	0.101296i
$809$		−	2.68101e11i		−	0.625900i	−0.949770	−	0.312950i	$-0.898683\pi$
$809$		−	2.68101e11i		−	0.625900i	0.949770	−	0.312950i	$-0.101317\pi$
$810$	8.52587e11	+	4.01612e11i	1.98061	+	0.932968i
$811$	9.80222e10	+	9.80222e10i	0.226590	+	0.226590i	0.811267	−	0.584676i	$-0.198779\pi$
$811$	9.80222e10	+	9.80222e10i	0.226590	+	0.226590i	−0.584676	+	0.811267i	$0.698779\pi$
$812$	9.00023e10	+	8.58015e9i	0.207028	+	0.0197365i
$813$	−5.36886e10	−	5.36886e10i	−0.122891	−	0.122891i
$814$	−1.31348e11	−	3.65290e11i	−0.299176	−	0.832033i
$815$			6.12324e11i			1.38788i
$816$	3.90866e11	+	5.77119e11i	0.881591	+	1.30168i
$817$	1.00385e11			0.225310
$818$	8.34245e11	−	2.99971e11i	1.86329	−	0.669987i
$819$	1.51348e10	−	1.51348e10i	0.0336390	−	0.0336390i
$820$	2.41724e11	+	2.30442e10i	0.534644	+	0.0509689i
$821$	1.18093e11	−	1.18093e11i	0.259927	−	0.259927i	−0.565097	−	0.825024i	$-0.691161\pi$
$821$	1.18093e11	−	1.18093e11i	0.259927	−	0.259927i	0.825024	+	0.565097i	$0.191161\pi$
$822$	−1.20841e11	+	2.56536e11i	−0.264685	+	0.561902i
$823$	−4.07270e11			−0.887735			−0.443867	−	0.896092i	$-0.646394\pi$
$823$	−4.07270e11			−0.887735			−0.443867	+	0.896092i	$0.646394\pi$
$824$	−5.08102e11	−	3.01312e11i	−1.10215	−	0.653592i
$825$		−	8.94471e11i		−	1.93086i
$826$	4.41089e10	−	9.36393e10i	0.0947559	−	0.201158i
$827$	5.41240e11	+	5.41240e11i	1.15709	+	1.15709i	0.985098	+	0.171994i	$0.0550211\pi$
$827$	5.41240e11	+	5.41240e11i	1.15709	+	1.15709i	0.171994	+	0.985098i	$0.444979\pi$
$828$	−6.00819e10	−	7.27446e10i	−0.127827	−	0.154767i
$829$	−2.43383e10	−	2.43383e10i	−0.0515313	−	0.0515313i	0.680872	−	0.732403i	$-0.261601\pi$
$829$	−2.43383e10	−	2.43383e10i	−0.0515313	−	0.0515313i	−0.732403	+	0.680872i	$0.761601\pi$
$830$	4.17824e11	−	1.50238e11i	0.880402	−	0.316568i
$831$			7.09855e11i			1.48856i
$832$	−9.84838e10	+	3.35981e11i	−0.205528	+	0.701167i
$833$	6.25223e11			1.29854
$834$	−9.91930e10	−	2.75864e11i	−0.205030	−	0.570206i
$835$	−7.14091e11	+	7.14091e11i	−1.46895	+	1.46895i
$836$	−1.20264e11	+	9.93294e10i	−0.246212	+	0.203354i
$837$	−5.80104e11	+	5.80104e11i	−1.18196	+	1.18196i
$838$	8.28136e11	+	3.90094e11i	1.67929	+	0.791031i
$839$	−5.43171e9			−0.0109620			−0.00548098	−	0.999985i	$-0.501745\pi$
$839$	−5.43171e9			−0.0109620			−0.00548098	+	0.999985i	$0.501745\pi$
$840$	−1.55284e11	+	2.61855e11i	−0.311895	+	0.525949i
$841$		−	2.53723e11i		−	0.507195i
$842$	2.56534e10	+	1.20841e10i	0.0510384	+	0.0240417i
$843$	−5.44977e11	−	5.44977e11i	−1.07912	−	1.07912i
$844$	4.55084e10	−	4.77364e11i	0.0896853	−	0.940763i
$845$	−3.14047e11	−	3.14047e11i	−0.615982	−	0.615982i
$846$	3.15476e10	+	8.77366e10i	0.0615864	+	0.171277i
$847$		−	7.74714e10i		−	0.150525i
$848$	−1.94697e11	−	2.87473e11i	−0.376510	−	0.555922i
$849$	−9.46485e11			−1.82172
$850$	−1.74298e12	+	6.26727e11i	−3.33900	+	1.20061i
$851$	4.27014e11	−	4.27014e11i	0.814186	−	0.814186i
$852$	−3.60587e10	+	3.78241e11i	−0.0684308	+	0.717811i
$853$	4.79752e11	−	4.79752e11i	0.906193	−	0.906193i	−0.0897700	−	0.995963i	$-0.528613\pi$
$853$	4.79752e11	−	4.79752e11i	0.906193	−	0.906193i	0.995963	+	0.0897700i	$0.0286132\pi$
$854$	3.83817e10	−	8.14810e10i	0.0721595	−	0.153188i
$855$	−9.99384e10			−0.187011
$856$	4.13764e10	+	1.61955e11i	0.0770652	+	0.301647i
$857$		−	5.98952e10i		−	0.111037i	−0.998458	−	0.0555186i	$-0.982319\pi$
$857$		−	5.98952e10i		−	0.111037i	0.998458	−	0.0555186i	$-0.0176812\pi$
$858$	−1.30707e11	+	2.77480e11i	−0.241185	+	0.512014i
$859$	−4.21512e11	−	4.21512e11i	−0.774171	−	0.774171i	0.204662	−	0.978833i	$-0.434391\pi$
$859$	−4.21512e11	−	4.21512e11i	−0.774171	−	0.774171i	−0.978833	+	0.204662i	$0.934391\pi$
$860$	−3.90046e11	+	3.22150e11i	−0.713053	+	0.588932i
$861$	−3.65377e10	−	3.65377e10i	−0.0664858	−	0.0664858i
$862$	−3.05713e11	+	1.09926e11i	−0.553714	+	0.199100i
$863$			5.67028e11i			1.02226i	0.859503	+	0.511130i	$0.170773\pi$
$863$			5.67028e11i			1.02226i	−0.859503	+	0.511130i	$0.829227\pi$
$864$	3.87919e11	+	2.83023e11i	0.696124	+	0.507887i
$865$	9.07267e11			1.62058
$866$	−2.72496e11	−	7.57834e11i	−0.484493	−	1.34742i
$867$	4.52853e11	−	4.52853e11i	0.801458	−	0.801458i
$868$	−2.07733e11	−	2.51514e11i	−0.365953	−	0.443081i
$869$	−3.06673e11	+	3.06673e11i	−0.537770	+	0.537770i
$870$	−7.50966e11	−	3.53744e11i	−1.31082	−	0.617464i
$871$	2.90152e11			0.504141
$872$	4.07558e10	+	1.59525e11i	0.0704893	+	0.275907i
$873$		−	1.35034e10i		−	0.0232481i
$874$	−2.19517e11	−	1.03404e11i	−0.376203	−	0.177211i
$875$	−3.42557e11	−	3.42557e11i	−0.584387	−	0.584387i
$876$	5.82210e11	+	5.55035e10i	0.988696	+	0.0942550i
$877$	6.49456e11	+	6.49456e11i	1.09787	+	1.09787i	0.994659	+	0.103211i	$0.0329118\pi$
$877$	6.49456e11	+	6.49456e11i	1.09787	+	1.09787i	0.103211	+	0.994659i	$0.467088\pi$
$878$	1.33705e11	+	3.71846e11i	0.224994	+	0.625728i
$879$			6.48976e11i			1.08711i
$880$	1.48522e11	−	7.71890e11i	0.247663	−	1.28714i
$881$	5.28454e11			0.877209			0.438605	−	0.898680i	$-0.355473\pi$
$881$	5.28454e11			0.877209			0.438605	+	0.898680i	$0.355473\pi$
$882$	−1.14172e11	+	4.10530e10i	−0.188662	+	0.0678376i
$883$	7.77177e10	−	7.77177e10i	0.127843	−	0.127843i	−0.640290	−	0.768133i	$-0.721186\pi$
$883$	7.77177e10	−	7.77177e10i	0.127843	−	0.127843i	0.768133	+	0.640290i	$0.221186\pi$
$884$	6.32284e11	+	6.02772e10i	1.03539	+	0.0987062i
$885$	−6.72012e11	+	6.72012e11i	−1.09548	+	1.09548i
$886$	1.24494e11	−	2.64289e11i	0.202029	−	0.428889i
$887$	−8.64218e11			−1.39614			−0.698070	−	0.716030i	$-0.745957\pi$
$887$	−8.64218e11			−1.39614			−0.698070	+	0.716030i	$0.745957\pi$
$888$	4.41600e11	−	7.44670e11i	0.710194	−	1.19760i
$889$		−	8.60561e10i		−	0.137776i
$890$	−8.52530e10	+	1.80984e11i	−0.135878	+	0.288457i
$891$	3.66156e11	+	3.66156e11i	0.580972	+	0.580972i
$892$	−1.14692e11	−	1.38864e11i	−0.181164	−	0.219346i
$893$	1.69558e11	+	1.69558e11i	0.266632	+	0.266632i
$894$	4.58580e11	−	1.64892e11i	0.717902	−	0.258137i
$895$		−	1.11300e12i		−	1.73461i
$896$	−1.26668e11	+	1.42870e11i	−0.196532	+	0.221672i
$897$	−4.77159e11			−0.737043
$898$	2.53005e10	+	7.03630e10i	0.0389067	+	0.108203i
$899$	6.28957e11	−	6.28957e11i	0.962902	−	0.962902i
$900$	2.77134e11	−	2.28893e11i	0.422396	−	0.348869i
$901$	−4.45377e11	+	4.45377e11i	−0.675816	+	0.675816i
$902$	1.20697e11	+	5.68543e10i	0.182334	+	0.0858889i
$903$	1.07652e11			0.161909
$904$	6.22614e10	+	3.69219e10i	0.0932277	+	0.0552853i
$905$			1.38246e12i			2.06090i
$906$	−1.06329e12	−	5.00865e11i	−1.57812	−	0.743375i
$907$	6.55826e11	+	6.55826e11i	0.969080	+	0.969080i	0.999536	−	0.0304564i	$-0.00969608\pi$
$907$	6.55826e11	+	6.55826e11i	0.969080	+	0.969080i	−0.0304564	+	0.999536i	$0.509696\pi$
$908$	9.45586e10	−	9.91881e11i	0.139110	−	1.45921i
$909$	−4.34196e10	−	4.34196e10i	−0.0635960	−	0.0635960i
$910$	9.38656e10	+	2.61048e11i	0.136880	+	0.380676i
$911$		−	1.35588e12i		−	1.96855i	−0.176645	−	0.984275i	$-0.556525\pi$
$911$		−	1.35588e12i		−	1.96855i	0.176645	−	0.984275i	$-0.443475\pi$
$912$	−3.41610e11	−	6.57305e10i	−0.493801	−	0.0950141i
$913$	2.43962e11			0.351107
$914$	5.57681e11	−	2.00526e11i	0.799100	−	0.287334i
$915$	−5.84757e11	+	5.84757e11i	−0.834240	+	0.834240i
$916$	−3.51493e10	+	3.68702e11i	−0.0499269	+	0.523713i
$917$	2.89313e11	−	2.89313e11i	0.409158	−	0.409158i
$918$	3.71218e11	−	7.88064e11i	0.522708	−	1.10966i
$919$	1.06790e11			0.149717			0.0748583	−	0.997194i	$-0.476150\pi$
$919$	1.06790e11			0.149717			0.0748583	+	0.997194i	$0.476150\pi$
$920$	1.18477e12	−	3.02688e11i	1.65380	−	0.422517i
$921$			8.95840e11i			1.24506i
$922$	3.43446e11	−	7.29104e11i	0.475263	−	1.00894i
$923$	2.44820e11	+	2.44820e11i	0.337318	+	0.337318i
$924$	−1.28970e11	+	1.06520e11i	−0.176930	+	0.146131i
$925$	1.62679e12	+	1.62679e12i	2.22210	+	2.22210i
$926$	−4.91877e11	+	1.76865e11i	−0.668979	+	0.240546i
$927$		−	2.07958e11i		−	0.281616i
$928$	−4.20588e11	−	3.06858e11i	−0.567107	−	0.413757i
$929$	−5.56675e11			−0.747376			−0.373688	−	0.927554i	$-0.621907\pi$
$929$	−5.56675e11			−0.747376			−0.373688	+	0.927554i	$0.621907\pi$
$930$	1.01343e12	+	2.81845e12i	1.35476	+	3.76772i
$931$	−2.20646e11	+	2.20646e11i	−0.293696	+	0.293696i
$932$	2.64775e11	+	3.20579e11i	0.350925	+	0.424885i
$933$	8.60242e11	−	8.60242e11i	1.13526	−	1.13526i
$934$	−3.62296e10	−	1.70660e10i	−0.0476075	−	0.0224256i
$935$	−1.42598e12			−1.86581
$936$	−1.19419e11	+	3.05094e10i	−0.155586	+	0.0397494i
$937$		−	7.65073e10i		−	0.0992532i	−0.998768	−	0.0496266i	$-0.984197\pi$
$937$		−	7.65073e10i		−	0.0992532i	0.998768	−	0.0496266i	$-0.0158031\pi$
$938$	1.43148e11	+	6.74299e10i	0.184915	+	0.0871046i
$939$	4.97471e11	+	4.97471e11i	0.639891	+	0.639891i
$940$	−1.20296e12	−	1.14681e11i	−1.54077	−	0.146886i
$941$	−7.57947e11	−	7.57947e11i	−0.966675	−	0.966675i	0.0327876	−	0.999462i	$-0.489561\pi$
$941$	−7.57947e11	−	7.57947e11i	−0.966675	−	0.966675i	−0.999462	+	0.0327876i	$0.989561\pi$
$942$	8.16593e10	+	2.27102e11i	0.103706	+	0.288414i
$943$			2.07552e11i			0.262470i
$944$	−4.93518e11	+	3.34245e11i	−0.621463	+	0.420898i
$945$	3.80474e11			0.477087
$946$	−2.61561e11	+	9.40499e10i	−0.326594	+	0.117434i
$947$	−2.65488e11	+	2.65488e11i	−0.330099	+	0.330099i	−0.852624	−	0.522525i	$-0.824990\pi$
$947$	−2.65488e11	+	2.65488e11i	−0.330099	+	0.330099i	0.522525	+	0.852624i	$0.324990\pi$
$948$	−9.62905e11	−	9.17962e10i	−1.19220	−	0.113656i
$949$	3.76841e11	−	3.76841e11i	0.464615	−	0.464615i
$950$	3.93936e11	−	8.36290e11i	0.483650	−	1.02675i
$951$	6.42631e11			0.785669
$952$	2.97932e11	+	1.76678e11i	0.362718	+	0.215097i
$953$			7.23870e10i			0.0877585i	0.999037	+	0.0438793i	$0.0139717\pi$
$953$			7.23870e10i			0.0877585i	−0.999037	+	0.0438793i	$0.986028\pi$
$954$	5.20862e10	−	1.10574e11i	0.0628824	−	0.133494i
$955$	−1.08894e12	−	1.08894e12i	−1.30915	−	1.30915i
$956$	2.49624e11	+	3.02234e11i	0.298851	+	0.361836i
$957$	−3.22513e11	−	3.22513e11i	−0.384503	−	0.384503i
$958$	−1.54695e12	+	5.56241e11i	−1.83660	+	0.660390i
$959$			1.40918e11i			0.166607i
$960$	1.53827e12	−	8.40884e11i	1.81112	−	0.990037i
$961$	−2.35643e12			−2.76287
$962$	−2.66937e11	−	7.42376e11i	−0.311680	−	0.866809i
$963$	−4.16101e10	+	4.16101e10i	−0.0483831	+	0.0483831i
$964$	5.92669e11	−	4.89503e11i	0.686284	−	0.566822i
$965$	1.15519e12	−	1.15519e12i	1.33212	−	1.33212i
$966$	−2.35408e11	−	1.10889e11i	−0.270342	−	0.127345i
$967$	3.30322e11			0.377773			0.188887	−	0.981999i	$-0.439512\pi$
$967$	3.30322e11			0.377773			0.188887	+	0.981999i	$0.439512\pi$
$968$	−2.27553e11	+	3.83723e11i	−0.259168	+	0.437035i
$969$			6.31085e11i			0.715802i
$970$	1.58329e11	+	7.45809e10i	0.178843	+	0.0842444i
$971$	1.91912e11	+	1.91912e11i	0.215886	+	0.215886i	0.806762	−	0.590876i	$-0.201218\pi$
$971$	1.91912e11	+	1.91912e11i	0.215886	+	0.215886i	−0.590876	+	0.806762i	$0.701218\pi$
$972$	−3.66047e10	+	3.83969e11i	−0.0410083	+	0.430161i
$973$	−1.03012e11	−	1.03012e11i	−0.114931	−	0.114931i
$974$	3.43806e11	+	9.56155e11i	0.382013	+	1.06241i
$975$		−	1.81782e12i		−	2.01156i
$976$	−4.29439e11	+	2.90846e11i	−0.473262	+	0.320526i
$977$	−2.31450e11			−0.254026			−0.127013	−	0.991901i	$-0.540539\pi$
$977$	−2.31450e11			−0.254026			−0.127013	+	0.991901i	$0.540539\pi$
$978$	−7.06092e11	+	2.53891e11i	−0.771802	+	0.277518i
$979$	−7.77264e10	+	7.77264e10i	−0.0846131	+	0.0846131i
$980$	1.49235e11	−	1.56541e12i	0.161795	−	1.69717i
$981$	−4.09859e10	+	4.09859e10i	−0.0442547	+	0.0442547i
$982$	1.76797e11	−	3.75325e11i	0.190121	−	0.403610i
$983$	1.12443e11			0.120425			0.0602126	−	0.998186i	$-0.480822\pi$
$983$	1.12443e11			0.120425			0.0602126	+	0.998186i	$0.480822\pi$
$984$	7.36542e10	+	2.88295e11i	0.0785628	+	0.307509i
$985$		−	6.59837e11i		−	0.700957i
$986$	−4.02480e11	+	8.54430e11i	−0.425831	+	0.904001i
$987$	1.81833e11	+	1.81833e11i	0.191604	+	0.191604i
$988$	−2.44411e11	+	2.01866e11i	−0.256503	+	0.211853i
$989$	−3.05757e11	−	3.05757e11i	−0.319589	−	0.319589i
$990$	2.60398e11	−	9.36317e10i	0.271079	−	0.0974725i
$991$			1.67009e11i			0.173159i	0.996245	+	0.0865795i	$0.0275937\pi$
$991$			1.67009e11i			0.173159i	−0.996245	+	0.0865795i	$0.972406\pi$
$992$	2.90159e11	+	1.85593e12i	0.299633	+	1.91653i
$993$	1.12700e12			1.15912
$994$	6.38880e10	+	1.77678e11i	0.0654446	+	0.182007i
$995$	−1.18318e11	+	1.18318e11i	−0.120714	+	0.120714i
$996$	3.46489e11	+	4.19514e11i	0.352088	+	0.426294i
$997$	−9.51539e10	+	9.51539e10i	−0.0963044	+	0.0963044i	−0.753618	−	0.657313i	$-0.771693\pi$
$997$	−9.51539e10	+	9.51539e10i	−0.0963044	+	0.0963044i	0.657313	+	0.753618i	$0.271693\pi$
$998$	−5.32627e11	−	2.50895e11i	−0.536910	−	0.252912i
$999$	−1.08200e12			−1.08634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.3.10	✓	30
4.3	odd	2		64.9.f.a.47.4		30
8.3	odd	2		128.9.f.a.95.12		30
8.5	even	2		128.9.f.b.95.4		30
16.3	odd	4		128.9.f.b.31.4		30
16.5	even	4		64.9.f.a.15.4		30
16.11	odd	4	inner	16.9.f.a.11.10	yes	30
16.13	even	4		128.9.f.a.31.12		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.10	✓	30	1.1	even	1	trivial
16.9.f.a.11.10	yes	30	16.11	odd	4	inner
64.9.f.a.15.4		30	16.5	even	4
64.9.f.a.47.4		30	4.3	odd	2
128.9.f.a.31.12		30	16.13	even	4
128.9.f.a.95.12		30	8.3	odd	2
128.9.f.b.31.4		30	16.3	odd	4
128.9.f.b.95.4		30	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(5.41380 + 15.0563i) q^{2} +(63.2572 - 63.2572i) q^{3} +(-197.381 + 163.023i) q^{4} +(825.937 - 825.937i) q^{5} +(1294.88 + 609.955i) q^{6} +711.293 q^{7} +(-3523.10 - 2089.25i) q^{8} -1441.95i q^{9} +O(q^{10})\)	\(q+(5.41380 + 15.0563i) q^{2} +(63.2572 - 63.2572i) q^{3} +(-197.381 + 163.023i) q^{4} +(825.937 - 825.937i) q^{5} +(1294.88 + 609.955i) q^{6} +711.293 q^{7} +(-3523.10 - 2089.25i) q^{8} -1441.95i q^{9} +(16907.0 + 7964.05i) q^{10} +(7260.95 + 7260.95i) q^{11} +(-2173.41 + 22798.2i) q^{12} +(14756.3 + 14756.3i) q^{13} +(3850.80 + 10709.4i) q^{14} -104493. i q^{15} +(12382.9 - 64355.5i) q^{16} -118889. q^{17} +(21710.4 - 7806.44i) q^{18} +(41957.1 - 41957.1i) q^{19} +(-28377.8 + 297671. i) q^{20} +(44994.4 - 44994.4i) q^{21} +(-70013.3 + 148632. i) q^{22} -255590. q^{23} +(-355022. + 90701.5i) q^{24} -973717. i q^{25} +(-142287. + 302063. i) q^{26} +(323817. + 323817. i) q^{27} +(-140396. + 115957. i) q^{28} +(-351087. - 351087. i) q^{29} +(1.57327e6 - 565704. i) q^{30} +1.79146e6i q^{31} +(1.03599e6 - 161968. i) q^{32} +918614. q^{33} +(-643643. - 1.79003e6i) q^{34} +(587483. - 587483. i) q^{35} +(235071. + 284614. i) q^{36} +(-1.67070e6 + 1.67070e6i) q^{37} +(858864. + 404569. i) q^{38} +1.86689e6 q^{39} +(-4.63545e6 + 1.18427e6i) q^{40} -812050. i q^{41} +(921039. + 433857. i) q^{42} +(1.19628e6 + 1.19628e6i) q^{43} +(-2.61688e6 - 249474. i) q^{44} +(-1.19096e6 - 1.19096e6i) q^{45} +(-1.38371e6 - 3.84823e6i) q^{46} +4.04123e6i q^{47} +(-3.28764e6 - 4.85426e6i) q^{48} -5.25886e6 q^{49} +(1.46605e7 - 5.27151e6i) q^{50} +(-7.52061e6 + 7.52061e6i) q^{51} +(-5.31825e6 - 507003. i) q^{52} +(3.74615e6 - 3.74615e6i) q^{53} +(-3.12239e6 + 6.62855e6i) q^{54} +1.19942e7 q^{55} +(-2.50596e6 - 1.48607e6i) q^{56} -5.30817e6i q^{57} +(3.38534e6 - 7.18677e6i) q^{58} +(-6.43117e6 - 6.43117e6i) q^{59} +(1.70348e7 + 2.06250e7i) q^{60} +(-5.59614e6 - 5.59614e6i) q^{61} +(-2.69726e7 + 9.69860e6i) q^{62} -1.02565e6i q^{63} +(8.04729e6 + 1.47213e7i) q^{64} +2.43756e7 q^{65} +(4.97320e6 + 1.38309e7i) q^{66} +(9.83142e6 - 9.83142e6i) q^{67} +(2.34666e7 - 1.93817e7i) q^{68} +(-1.61679e7 + 1.61679e7i) q^{69} +(1.20258e7 + 5.66478e6i) q^{70} +1.65908e7 q^{71} +(-3.01260e6 + 5.08014e6i) q^{72} -2.55375e7i q^{73} +(-3.41993e7 - 1.61096e7i) q^{74} +(-6.15946e7 - 6.15946e7i) q^{75} +(-1.44157e6 + 1.51215e7i) q^{76} +(5.16466e6 + 5.16466e6i) q^{77} +(1.01070e7 + 2.81084e7i) q^{78} +4.22360e7i q^{79} +(-4.29261e7 - 6.33810e7i) q^{80} +5.04281e7 q^{81} +(1.22264e7 - 4.39628e6i) q^{82} +(1.67996e7 - 1.67996e7i) q^{83} +(-1.54593e6 + 1.62162e7i) q^{84} +(-9.81950e7 + 9.81950e7i) q^{85} +(-1.15351e7 + 2.44879e7i) q^{86} -4.44175e7 q^{87} +(-1.04111e7 - 4.07510e7i) q^{88} +1.07047e7i q^{89} +(1.14838e7 - 2.43790e7i) q^{90} +(1.04961e7 + 1.04961e7i) q^{91} +(5.04487e7 - 4.16671e7i) q^{92} +(1.13323e8 + 1.13323e8i) q^{93} +(-6.08457e7 + 2.18784e7i) q^{94} -6.93078e7i q^{95} +(5.52883e7 - 7.57796e7i) q^{96} +9.36470e6 q^{97} +(-2.84704e7 - 7.91788e7i) q^{98} +(1.04699e7 - 1.04699e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

L-functions

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