LMFDB - Embedded newform 43.9.b.b.42.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	43.b (of order $2$, degree $1$, 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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.28
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+31.2764i q^{2} +113.679i q^{3} -722.216 q^{4} -959.913i q^{5} -3555.47 q^{6} +3354.89i q^{7} -14581.6i q^{8} -6361.87 q^{9} +O(q^{10})$	\(q+31.2764i q^{2} +113.679i q^{3} -722.216 q^{4} -959.913i q^{5} -3555.47 q^{6} +3354.89i q^{7} -14581.6i q^{8} -6361.87 q^{9} +30022.7 q^{10} +5045.72 q^{11} -82100.6i q^{12} -13469.7 q^{13} -104929. q^{14} +109122. q^{15} +271172. q^{16} -93670.1 q^{17} -198977. i q^{18} -74948.1i q^{19} +693264. i q^{20} -381380. q^{21} +157812. i q^{22} -309529. q^{23} +1.65762e6 q^{24} -530808. q^{25} -421285. i q^{26} +22636.4i q^{27} -2.42295e6i q^{28} -568675. i q^{29} +3.41294e6i q^{30} +953857. q^{31} +4.74843e6i q^{32} +573591. i q^{33} -2.92967e6i q^{34} +3.22040e6 q^{35} +4.59465e6 q^{36} +3565.48i q^{37} +2.34411e6 q^{38} -1.53122e6i q^{39} -1.39970e7 q^{40} -264952. q^{41} -1.19282e7i q^{42} +(3.41591e6 - 140476. i) q^{43} -3.64410e6 q^{44} +6.10685e6i q^{45} -9.68097e6i q^{46} -8.56154e6 q^{47} +3.08266e7i q^{48} -5.49048e6 q^{49} -1.66018e7i q^{50} -1.06483e7i q^{51} +9.72805e6 q^{52} -381997. q^{53} -707985. q^{54} -4.84345e6i q^{55} +4.89195e7 q^{56} +8.52001e6 q^{57} +1.77861e7 q^{58} -9.85667e6 q^{59} -7.88095e7 q^{60} +1.09708e7i q^{61} +2.98332e7i q^{62} -2.13434e7i q^{63} -7.90937e7 q^{64} +1.29298e7i q^{65} -1.79399e7 q^{66} -1.57820e6 q^{67} +6.76500e7 q^{68} -3.51869e7i q^{69} +1.00723e8i q^{70} -4.72551e7i q^{71} +9.27661e7i q^{72} -1.85106e7i q^{73} -111516. q^{74} -6.03417e7i q^{75} +5.41287e7i q^{76} +1.69278e7i q^{77} +4.78912e7 q^{78} +2.99604e7 q^{79} -2.60302e8i q^{80} -4.43135e7 q^{81} -8.28675e6i q^{82} -5.39305e7 q^{83} +2.75438e8 q^{84} +8.99151e7i q^{85} +(4.39360e6 + 1.06838e8i) q^{86} +6.46463e7 q^{87} -7.35745e7i q^{88} -1.45976e7i q^{89} -1.91000e8 q^{90} -4.51894e7i q^{91} +2.23547e8 q^{92} +1.08433e8i q^{93} -2.67774e8i q^{94} -7.19437e7 q^{95} -5.39795e8 q^{96} +3.45903e7 q^{97} -1.71723e8i q^{98} -3.21002e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$			31.2764i			1.95478i	0.211450	+	0.977389i	$0.432181\pi$
$2$			31.2764i			1.95478i	−0.211450	+	0.977389i	$0.567819\pi$
$3$			113.679i			1.40344i	0.712452	+	0.701721i	$0.247585\pi$
$3$			113.679i			1.40344i	−0.712452	+	0.701721i	$0.752415\pi$
$4$	−722.216			−2.82116
$5$		−	959.913i		−	1.53586i	−0.640533	−	0.767931i	$-0.721287\pi$
$5$		−	959.913i		−	1.53586i	0.640533	−	0.767931i	$-0.278713\pi$
$6$	−3555.47			−2.74342
$7$			3354.89i			1.39729i	0.715469	+	0.698644i	$0.246213\pi$
$7$			3354.89i			1.39729i	−0.715469	+	0.698644i	$0.753787\pi$
$8$		−	14581.6i		−	3.55995i
$9$	−6361.87			−0.969650
$10$	30022.7			3.00227
$11$	5045.72			0.344629			0.172315	−	0.985042i	$-0.444875\pi$
$11$	5045.72			0.344629			0.172315	+	0.985042i	$0.444875\pi$
$12$		−	82100.6i		−	3.95933i
$13$	−13469.7			−0.471613			−0.235806	−	0.971800i	$-0.575773\pi$
$13$	−13469.7			−0.471613			−0.235806	+	0.971800i	$0.575773\pi$
$14$	−104929.			−2.73139
$15$	109122.			2.15549
$16$	271172.			4.13776
$17$	−93670.1			−1.12152			−0.560758	−	0.827980i	$-0.689490\pi$
$17$	−93670.1			−1.12152			−0.560758	+	0.827980i	$0.689490\pi$
$18$		−	198977.i		−	1.89545i
$19$		−	74948.1i		−	0.575104i	−0.957765	−	0.287552i	$-0.907159\pi$
$19$		−	74948.1i		−	0.575104i	0.957765	−	0.287552i	$-0.0928414\pi$
$20$			693264.i			4.33290i
$21$	−381380.			−1.96101
$22$			157812.i			0.673673i
$23$	−309529.			−1.10609			−0.553045	−	0.833152i	$-0.686534\pi$
$23$	−309529.			−1.10609			−0.553045	+	0.833152i	$0.686534\pi$
$24$	1.65762e6			4.99619
$25$	−530808.			−1.35887
$26$		−	421285.i		−	0.921898i
$27$			22636.4i			0.0425943i
$28$		−	2.42295e6i		−	3.94197i
$29$		−	568675.i		−	0.804029i	−0.915633	−	0.402015i	$-0.868310\pi$
$29$		−	568675.i		−	0.804029i	0.915633	−	0.402015i	$-0.131690\pi$
$30$			3.41294e6i			4.21351i
$31$	953857.			1.03285			0.516424	−	0.856333i	$-0.327263\pi$
$31$	953857.			1.03285			0.516424	+	0.856333i	$0.327263\pi$
$32$			4.74843e6i			4.52845i
$33$			573591.i			0.483667i
$34$		−	2.92967e6i		−	2.19231i
$35$	3.22040e6			2.14604
$36$	4.59465e6			2.73553
$37$			3565.48i			0.00190244i	1.00000		0.000951221i	$0.000302783\pi$
$37$			3565.48i			0.00190244i	−1.00000		0.000951221i	$0.999697\pi$
$38$	2.34411e6			1.12420
$39$		−	1.53122e6i		−	0.661881i
$40$	−1.39970e7			−5.46759
$41$	−264952.			−0.0937630			−0.0468815	−	0.998900i	$-0.514928\pi$
$41$	−264952.			−0.0937630			−0.0468815	+	0.998900i	$0.514928\pi$
$42$		−	1.19282e7i		−	3.83334i
$43$	3.41591e6	−	140476.i	0.999155	−	0.0410893i
$43$	3.41591e6	−	140476.i	0.999155	−	0.0410893i
$44$	−3.64410e6			−0.972252
$45$			6.10685e6i			1.48925i
$46$		−	9.68097e6i		−	2.16216i
$47$	−8.56154e6			−1.75453			−0.877264	−	0.480008i	$-0.840634\pi$
$47$	−8.56154e6			−1.75453			−0.877264	+	0.480008i	$0.840634\pi$
$48$			3.08266e7i			5.80711i
$49$	−5.49048e6			−0.952414
$50$		−	1.66018e7i		−	2.65629i
$51$		−	1.06483e7i		−	1.57398i
$52$	9.72805e6			1.33049
$53$	−381997.			−0.0484123			−0.0242062	−	0.999707i	$-0.507706\pi$
$53$	−381997.			−0.0484123			−0.0242062	+	0.999707i	$0.507706\pi$
$54$	−707985.			−0.0832624
$55$		−	4.84345e6i		−	0.529302i
$56$	4.89195e7			4.97428
$57$	8.52001e6			0.807125
$58$	1.77861e7			1.57170
$59$	−9.85667e6			−0.813433			−0.406717	−	0.913554i	$-0.633326\pi$
$59$	−9.85667e6			−0.813433			−0.406717	+	0.913554i	$0.633326\pi$
$60$	−7.88095e7			−6.08098
$61$			1.09708e7i			0.792354i	0.918174	+	0.396177i	$0.129663\pi$
$61$			1.09708e7i			0.792354i	−0.918174	+	0.396177i	$0.870337\pi$
$62$			2.98332e7i			2.01899i
$63$		−	2.13434e7i		−	1.35488i
$64$	−7.90937e7			−4.71435
$65$			1.29298e7i			0.724332i
$66$	−1.79399e7			−0.945462
$67$	−1.57820e6			−0.0783181			−0.0391590	−	0.999233i	$-0.512468\pi$
$67$	−1.57820e6			−0.0783181			−0.0391590	+	0.999233i	$0.512468\pi$
$68$	6.76500e7			3.16397
$69$		−	3.51869e7i		−	1.55233i
$70$			1.00723e8i			4.19503i
$71$		−	4.72551e7i		−	1.85958i	−0.368086	−	0.929792i	$-0.619987\pi$
$71$		−	4.72551e7i		−	1.85958i	0.368086	−	0.929792i	$-0.380013\pi$
$72$			9.27661e7i			3.45191i
$73$		−	1.85106e7i		−	0.651823i	−0.945400	−	0.325911i	$-0.894329\pi$
$73$		−	1.85106e7i		−	0.651823i	0.945400	−	0.325911i	$-0.105671\pi$
$74$	−111516.			−0.00371885
$75$		−	6.03417e7i		−	1.90709i
$76$			5.41287e7i			1.62246i
$77$			1.69278e7i			0.481546i
$78$	4.78912e7			1.29383
$79$	2.99604e7			0.769200			0.384600	−	0.923083i	$-0.374339\pi$
$79$	2.99604e7			0.769200			0.384600	+	0.923083i	$0.374339\pi$
$80$		−	2.60302e8i		−	6.35503i
$81$	−4.43135e7			−1.02943
$82$		−	8.28675e6i		−	0.183286i
$83$	−5.39305e7			−1.13638			−0.568188	−	0.822899i	$-0.692355\pi$
$83$	−5.39305e7			−1.13638			−0.568188	+	0.822899i	$0.692355\pi$
$84$	2.75438e8			5.53232
$85$			8.99151e7i			1.72249i
$86$	4.39360e6	+	1.06838e8i	0.0803205	+	1.95313i
$87$	6.46463e7			1.12841
$88$		−	7.35745e7i		−	1.22686i
$89$		−	1.45976e7i		−	0.232659i	−0.993211	−	0.116330i	$-0.962887\pi$
$89$		−	1.45976e7i		−	0.232659i	0.993211	−	0.116330i	$-0.0371129\pi$
$90$	−1.91000e8			−2.91115
$91$		−	4.51894e7i		−	0.658979i
$92$	2.23547e8			3.12045
$93$			1.08433e8i			1.44954i
$94$		−	2.67774e8i		−	3.42971i
$95$	−7.19437e7			−0.883280
$96$	−5.39795e8			−6.35542
$97$	3.45903e7			0.390721			0.195361	−	0.980731i	$-0.437412\pi$
$97$	3.45903e7			0.390721			0.195361	+	0.980731i	$0.437412\pi$
$98$		−	1.71723e8i		−	1.86176i
$99$	−3.21002e7			−0.334170
$100$	3.83358e8			3.83358
$101$	−1.49089e8			−1.43271			−0.716356	−	0.697735i	$-0.754192\pi$
$101$	−1.49089e8			−1.43271			−0.716356	+	0.697735i	$0.754192\pi$
$102$	3.33041e8			3.07678
$103$	2.09069e7			0.185755			0.0928776	−	0.995678i	$-0.470393\pi$
$103$	2.09069e7			0.185755			0.0928776	+	0.995678i	$0.470393\pi$
$104$			1.96410e8i			1.67892i
$105$			3.66091e8i			3.01184i
$106$		−	1.19475e7i		−	0.0946354i
$107$	−2.05062e8			−1.56441			−0.782203	−	0.623024i	$-0.785904\pi$
$107$	−2.05062e8			−1.56441			−0.782203	+	0.623024i	$0.785904\pi$
$108$		−	1.63483e7i		−	0.120165i
$109$	−1.27916e7			−0.0906193			−0.0453096	−	0.998973i	$-0.514427\pi$
$109$	−1.27916e7			−0.0906193			−0.0453096	+	0.998973i	$0.514427\pi$
$110$	1.51486e8			1.03467
$111$	−405320.			−0.00266997
$112$			9.09753e8i			5.78165i
$113$		−	3.28021e7i		−	0.201182i	−0.994928	−	0.100591i	$-0.967927\pi$
$113$		−	3.28021e7i		−	0.201182i	0.994928	−	0.100591i	$-0.0320733\pi$
$114$			2.66476e8i			1.57775i
$115$			2.97121e8i			1.69880i
$116$			4.10706e8i			2.26829i
$117$	8.56927e7			0.457299
$118$		−	3.08281e8i		−	1.59008i
$119$		−	3.14253e8i		−	1.56708i
$120$		−	1.59117e9i		−	7.67345i
$121$	−1.88900e8			−0.881231
$122$	−3.43128e8			−1.54888
$123$		−	3.01194e7i		−	0.131591i
$124$	−6.88890e8			−2.91382
$125$			1.34564e8i			0.551173i
$126$	6.67545e8			2.64849
$127$	−3.31370e7			−0.127379			−0.0636895	−	0.997970i	$-0.520287\pi$
$127$	−3.31370e7			−0.127379			−0.0636895	+	0.997970i	$0.520287\pi$
$128$		−	1.25817e9i		−	4.68706i
$129$	1.59692e7	+	3.88317e8i	0.0576665	+	1.40226i
$130$	−4.04397e8			−1.41591
$131$			2.70330e8i			0.917930i	0.888454	+	0.458965i	$0.151780\pi$
$131$			2.70330e8i			0.917930i	−0.888454	+	0.458965i	$0.848220\pi$
$132$		−	4.14256e8i		−	1.36450i
$133$	2.51443e8			0.803586
$134$		−	4.93604e7i		−	0.153094i
$135$	2.17289e7			0.0654189
$136$			1.36586e9i			3.99254i
$137$		−	1.27305e8i		−	0.361378i	−0.983540	−	0.180689i	$-0.942167\pi$
$137$		−	1.27305e8i		−	0.361378i	0.983540	−	0.180689i	$-0.0578328\pi$
$138$	1.10052e9			3.03447
$139$	−2.00149e8			−0.536159			−0.268080	−	0.963397i	$-0.586389\pi$
$139$	−2.00149e8			−0.536159			−0.268080	+	0.963397i	$0.586389\pi$
$140$	−2.32582e9			−6.05431
$141$		−	9.73265e8i		−	2.46238i
$142$	1.47797e9			3.63507
$143$	−6.79644e7			−0.162531
$144$	−1.72516e9			−4.01218
$145$	−5.45878e8			−1.23488
$146$	5.78947e8			1.27417
$147$		−	6.24151e8i		−	1.33666i
$148$		−	2.57505e6i		−	0.00536709i
$149$			7.17341e8i			1.45539i	0.685899	+	0.727697i	$0.259409\pi$
$149$			7.17341e8i			1.45539i	−0.685899	+	0.727697i	$0.740591\pi$
$150$	1.88727e9			3.72795
$151$			3.89398e8i			0.749007i	0.927226	+	0.374503i	$0.122187\pi$
$151$			3.89398e8i			0.749007i	−0.927226	+	0.374503i	$0.877813\pi$
$152$	−1.09286e9			−2.04734
$153$	5.95917e8			1.08748
$154$	−5.29442e8			−0.941316
$155$		−	9.15620e8i		−	1.58631i
$156$			1.10587e9i			1.86727i
$157$			8.94542e8i			1.47232i	0.676808	+	0.736160i	$0.263363\pi$
$157$			8.94542e8i			1.47232i	−0.676808	+	0.736160i	$0.736637\pi$
$158$			9.37055e8i			1.50362i
$159$		−	4.34249e7i		−	0.0679439i
$160$	4.55808e9			6.95507
$161$		−	1.03844e9i		−	1.54553i
$162$		−	1.38597e9i		−	2.01230i
$163$			8.43950e8i			1.19555i	0.801665	+	0.597773i	$0.203948\pi$
$163$			8.43950e8i			1.19555i	−0.801665	+	0.597773i	$0.796052\pi$
$164$	1.91352e8			0.264520
$165$	5.50598e8			0.742845
$166$		−	1.68675e9i		−	2.22136i
$167$	1.21430e9			1.56120			0.780602	−	0.625028i	$-0.214913\pi$
$167$	1.21430e9			1.56120			0.780602	+	0.625028i	$0.214913\pi$
$168$			5.56112e9i			6.98112i
$169$	−6.34297e8			−0.777581
$170$	−2.81223e9			−3.36709
$171$			4.76810e8i			0.557650i
$172$	−2.46703e9	+	1.01454e8i	−2.81877	+	0.115919i
$173$	−6.89077e8			−0.769278			−0.384639	−	0.923067i	$-0.625674\pi$
$173$	−6.89077e8			−0.769278			−0.384639	+	0.923067i	$0.625674\pi$
$174$			2.02190e9i			2.20579i
$175$		−	1.78080e9i		−	1.89873i
$176$	1.36826e9			1.42599
$177$		−	1.12049e9i		−	1.14161i
$178$	4.56560e8			0.454797
$179$		−	1.17356e9i		−	1.14312i	−0.820560	−	0.571560i	$-0.806338\pi$
$179$		−	1.17356e9i		−	1.14312i	0.820560	−	0.571560i	$-0.193662\pi$
$180$		−	4.41046e9i		−	4.20140i
$181$	−1.12673e9			−1.04980			−0.524901	−	0.851164i	$-0.675898\pi$
$181$	−1.12673e9			−1.04980			−0.524901	+	0.851164i	$0.675898\pi$
$182$	1.41336e9			1.28816
$183$	−1.24715e9			−1.11202
$184$			4.51342e9i			3.93763i
$185$	3.42255e6			0.00292189
$186$	−3.39141e9			−2.83353
$187$	−4.72633e8			−0.386507
$188$	6.18328e9			4.94980
$189$	−7.59425e7			−0.0595165
$190$		−	2.25014e9i		−	1.72662i
$191$			5.17933e8i			0.389171i	0.980886	+	0.194585i	$0.0623362\pi$
$191$			5.17933e8i			0.389171i	−0.980886	+	0.194585i	$0.937664\pi$
$192$		−	8.99128e9i		−	6.61632i
$193$	−8.56057e8			−0.616983			−0.308492	−	0.951227i	$-0.599824\pi$
$193$	−8.56057e8			−0.616983			−0.308492	+	0.951227i	$0.599824\pi$
$194$			1.08186e9i			0.763773i
$195$	−1.46984e9			−1.01656
$196$	3.96531e9			2.68691
$197$	1.73863e9			1.15437			0.577183	−	0.816615i	$-0.304152\pi$
$197$	1.73863e9			1.15437			0.577183	+	0.816615i	$0.304152\pi$
$198$		−	1.00398e9i		−	0.653227i
$199$		−	6.62621e8i		−	0.422526i	−0.977429	−	0.211263i	$-0.932242\pi$
$199$		−	6.62621e8i		−	0.422526i	0.977429	−	0.211263i	$-0.0677576\pi$
$200$			7.74002e9i			4.83751i
$201$		−	1.79408e8i		−	0.109915i
$202$		−	4.66296e9i		−	2.80063i
$203$	1.90784e9			1.12346
$204$			7.69037e9i			4.44045i
$205$			2.54331e8i			0.144007i
$206$			6.53894e8i			0.363110i
$207$	1.96919e9			1.07252
$208$	−3.65262e9			−1.95142
$209$		−	3.78167e8i		−	0.198198i
$210$	−1.14500e10			−5.88748
$211$		−	5.32912e8i		−	0.268859i	−0.990923	−	0.134430i	$-0.957080\pi$
$211$		−	5.32912e8i		−	0.268859i	0.990923	−	0.134430i	$-0.0429203\pi$
$212$	2.75884e8			0.136579
$213$	5.37191e9			2.60982
$214$		−	6.41360e9i		−	3.05806i
$215$	−1.34845e8	−	3.27898e9i	−0.0631075	−	1.53456i
$216$	3.30074e8			0.151634
$217$			3.20008e9i			1.44319i
$218$		−	4.00077e8i		−	0.177140i
$219$	2.10427e9			0.914796
$220$			3.49801e9i			1.49324i
$221$	1.26171e9			0.528921
$222$		−	1.26770e7i		−	0.00521919i
$223$			3.32528e8i			0.134465i	0.997737	+	0.0672325i	$0.0214169\pi$
$223$			3.32528e8i			0.134465i	−0.997737	+	0.0672325i	$0.978583\pi$
$224$	−1.59304e10			−6.32755
$225$	3.37694e9			1.31763
$226$	1.02593e9			0.393265
$227$			4.20770e9i			1.58468i	0.610079	+	0.792340i	$0.291138\pi$
$227$			4.20770e9i			1.58468i	−0.610079	+	0.792340i	$0.708862\pi$
$228$	−6.15329e9			−2.27703
$229$	7.65732e8			0.278442			0.139221	−	0.990261i	$-0.455540\pi$
$229$	7.65732e8			0.278442			0.139221	+	0.990261i	$0.455540\pi$
$230$	−9.29289e9			−3.32078
$231$	−1.92433e9			−0.675822
$232$	−8.29217e9			−2.86231
$233$		−	1.30824e9i		−	0.443878i	−0.975061	−	0.221939i	$-0.928761\pi$
$233$		−	1.30824e9i		−	0.443878i	0.975061	−	0.221939i	$-0.0712386\pi$
$234$			2.68016e9i			0.893918i
$235$			8.21833e9i			2.69471i
$236$	7.11864e9			2.29482
$237$			3.40586e9i			1.07953i
$238$	9.82870e9			3.06329
$239$	−4.43573e9			−1.35948			−0.679741	−	0.733452i	$-0.737908\pi$
$239$	−4.43573e9			−1.35948			−0.679741	+	0.733452i	$0.737908\pi$
$240$	2.95908e10			8.91891
$241$			9.19495e8i			0.272572i	0.990670	+	0.136286i	$0.0435166\pi$
$241$			9.19495e8i			0.272572i	−0.990670	+	0.136286i	$0.956483\pi$
$242$		−	5.90811e9i		−	1.72261i
$243$		−	4.88899e9i		−	1.40215i
$244$		−	7.92329e9i		−	2.23535i
$245$			5.27038e9i			1.46278i
$246$	9.42028e8			0.257231
$247$			1.00953e9i			0.271226i
$248$		−	1.39087e10i		−	3.67689i
$249$		−	6.13076e9i		−	1.59484i
$250$	−4.20868e9			−1.07742
$251$	4.86683e9			1.22617			0.613086	−	0.790016i	$-0.289928\pi$
$251$	4.86683e9			1.22617			0.613086	+	0.790016i	$0.289928\pi$
$252$			1.54145e10i			3.82233i
$253$	−1.56180e9			−0.381191
$254$		−	1.03641e9i		−	0.248998i
$255$	−1.02214e10			−2.41742
$256$	1.91032e10			4.44781
$257$			9.95226e8i			0.228134i	0.993473	+	0.114067i	$0.0363878\pi$
$257$			9.95226e8i			0.228134i	−0.993473	+	0.114067i	$0.963612\pi$
$258$	−1.21452e10	+	4.99459e8i	−2.74110	+	0.112725i
$259$	−1.19618e7			−0.00265826
$260$		−	9.33808e9i		−	2.04345i
$261$			3.61784e9i			0.779627i
$262$	−8.45497e9			−1.79435
$263$			4.32574e9i			0.904145i	0.891981	+	0.452072i	$0.149315\pi$
$263$			4.32574e9i			0.904145i	−0.891981	+	0.452072i	$0.850685\pi$
$264$	8.36386e9			1.72183
$265$			3.66684e8i			0.0743546i
$266$			7.86423e9i			1.57083i
$267$	1.65943e9			0.326524
$268$	1.13980e9			0.220947
$269$	−4.97219e9			−0.949595			−0.474797	−	0.880095i	$-0.657479\pi$
$269$	−4.97219e9			−0.949595			−0.474797	+	0.880095i	$0.657479\pi$
$270$			6.79604e8i			0.127879i
$271$	6.79997e9			1.26075			0.630377	−	0.776290i	$-0.282901\pi$
$271$	6.79997e9			1.26075			0.630377	+	0.776290i	$0.282901\pi$
$272$	−2.54007e10			−4.64056
$273$	5.13708e9			0.924839
$274$	3.98164e9			0.706414
$275$	−2.67831e9			−0.468306
$276$			2.54125e10i			4.37937i
$277$		−	8.34803e9i		−	1.41796i	−0.705227	−	0.708982i	$-0.749155\pi$
$277$		−	8.34803e9i		−	1.41796i	0.705227	−	0.708982i	$-0.250845\pi$
$278$		−	6.25994e9i		−	1.04807i
$279$	−6.06832e9			−1.00150
$280$		−	4.69585e10i		−	7.63980i
$281$	−6.24432e9			−1.00152			−0.500760	−	0.865586i	$-0.666946\pi$
$281$	−6.24432e9			−1.00152			−0.500760	+	0.865586i	$0.666946\pi$
$282$	3.04403e10			4.81340
$283$	4.82638e9			0.752447			0.376224	−	0.926529i	$-0.377222\pi$
$283$	4.82638e9			0.752447			0.376224	+	0.926529i	$0.377222\pi$
$284$			3.41284e10i			5.24617i
$285$		−	8.17847e9i		−	1.23963i
$286$		−	2.12569e9i		−	0.317713i
$287$		−	8.88883e8i		−	0.131014i
$288$		−	3.02089e10i		−	4.39101i
$289$	1.79832e9			0.257796
$290$		−	1.70731e10i		−	2.41391i
$291$			3.93218e9i			0.548355i
$292$			1.33687e10i			1.83889i
$293$	8.17623e9			1.10939			0.554693	−	0.832055i	$-0.312836\pi$
$293$	8.17623e9			1.10939			0.554693	+	0.832055i	$0.312836\pi$
$294$	1.95212e10			2.61287
$295$			9.46154e9i			1.24932i
$296$	5.19903e7			0.00677261
$297$			1.14217e8i			0.0146792i
$298$	−2.24359e10			−2.84497
$299$	4.16928e9			0.521646
$300$			4.35797e10i			5.38021i
$301$	4.71282e8	+	1.14600e10i	0.0574137	+	1.39611i
$302$	−1.21790e10			−1.46414
$303$		−	1.69482e10i		−	2.01073i
$304$		−	2.03239e10i		−	2.37964i
$305$	1.05310e10			1.21695
$306$			1.86382e10i			2.12578i
$307$	−5.25589e9			−0.591688			−0.295844	−	0.955236i	$-0.595601\pi$
$307$	−5.25589e9			−0.591688			−0.295844	+	0.955236i	$0.595601\pi$
$308$		−	1.22255e10i		−	1.35852i
$309$			2.37667e9i			0.260697i
$310$	2.86373e10			3.10088
$311$	1.34118e10			1.43366			0.716831	−	0.697247i	$-0.245592\pi$
$311$	1.34118e10			1.43366			0.716831	+	0.697247i	$0.245592\pi$
$312$	−2.23276e10			−2.35627
$313$		−	2.87909e9i		−	0.299970i	−0.988688	−	0.149985i	$-0.952078\pi$
$313$		−	2.87909e9i		−	0.299970i	0.988688	−	0.149985i	$-0.0479225\pi$
$314$	−2.79781e10			−2.87806
$315$	−2.04878e10			−2.08091
$316$	−2.16379e10			−2.17003
$317$	−1.72017e10			−1.70347			−0.851736	−	0.523972i	$-0.824450\pi$
$317$	−1.72017e10			−1.70347			−0.851736	+	0.523972i	$0.824450\pi$
$318$	1.35818e9			0.132815
$319$		−	2.86937e9i		−	0.277092i
$320$			7.59231e10i			7.24059i
$321$		−	2.33112e10i		−	2.19555i
$322$	3.24786e10			3.02116
$323$			7.02040e9i			0.644988i
$324$	3.20039e10			2.90418
$325$	7.14984e9			0.640860
$326$	−2.63958e10			−2.33703
$327$		−	1.45414e9i		−	0.127179i
$328$			3.86341e9i			0.333792i
$329$		−	2.87230e10i		−	2.45158i
$330$			1.72207e10i			1.45210i
$331$		−	6.13133e9i		−	0.510790i	−0.966837	−	0.255395i	$-0.917794\pi$
$331$		−	6.13133e9i		−	0.510790i	0.966837	−	0.255395i	$-0.0822056\pi$
$332$	3.89495e10			3.20589
$333$		−	2.26832e7i		−	0.00184470i
$334$			3.79790e10i			3.05181i
$335$			1.51493e9i			0.120286i
$336$	−1.03420e11			−8.11421
$337$	8.98842e9			0.696890			0.348445	−	0.937329i	$-0.386710\pi$
$337$	8.98842e9			0.696890			0.348445	+	0.937329i	$0.386710\pi$
$338$		−	1.98386e10i		−	1.52000i
$339$	3.72891e9			0.282347
$340$		−	6.49381e10i		−	4.85942i
$341$	4.81289e9			0.355949
$342$	−1.49129e10			−1.09008
$343$			9.20331e8i			0.0664918i
$344$	−2.04837e9	−	4.98094e10i	−0.146276	−	3.55695i
$345$	−3.37764e10			−2.38417
$346$		−	2.15519e10i		−	1.50377i
$347$			2.09994e10i			1.44840i	0.689589	+	0.724201i	$0.257791\pi$
$347$			2.09994e10i			1.44840i	−0.689589	+	0.724201i	$0.742209\pi$
$348$	−4.66885e10			−3.18342
$349$			1.43451e10i			0.966944i	0.875360	+	0.483472i	$0.160625\pi$
$349$			1.43451e10i			0.966944i	−0.875360	+	0.483472i	$0.839375\pi$
$350$	5.56972e10			3.71160
$351$		−	3.04906e8i		−	0.0200880i
$352$			2.39592e10i			1.56064i
$353$	2.42506e10			1.56179			0.780895	−	0.624662i	$-0.214763\pi$
$353$	2.42506e10			1.56179			0.780895	+	0.624662i	$0.214763\pi$
$354$	3.50451e10			2.23159
$355$	−4.53608e10			−2.85606
$356$			1.05426e10i			0.656368i
$357$	3.57239e10			2.19931
$358$	3.67047e10			2.23455
$359$	−1.62715e10			−0.979601			−0.489801	−	0.871835i	$-0.662930\pi$
$359$	−1.62715e10			−0.979601			−0.489801	+	0.871835i	$0.662930\pi$
$360$	8.90474e10			5.30165
$361$	1.13663e10			0.669256
$362$		−	3.52402e10i		−	2.05213i
$363$		−	2.14739e10i		−	1.23676i
$364$			3.26365e10i			1.85908i
$365$	−1.77686e10			−1.00111
$366$		−	3.90064e10i		−	2.17376i
$367$	−1.48349e10			−0.817750			−0.408875	−	0.912590i	$-0.634079\pi$
$367$	−1.48349e10			−0.817750			−0.408875	+	0.912590i	$0.634079\pi$
$368$	−8.39358e10			−4.57674
$369$	1.68559e9			0.0909173
$370$			1.07045e8i			0.00571164i
$371$		−	1.28156e9i		−	0.0676460i
$372$		−	7.83122e10i		−	4.08938i
$373$			8.79867e9i			0.454550i	0.973831	+	0.227275i	$0.0729816\pi$
$373$			8.79867e9i			0.454550i	−0.973831	+	0.227275i	$0.927018\pi$
$374$		−	1.47823e10i		−	0.755535i
$375$	−1.52970e10			−0.773540
$376$			1.24841e11i			6.24604i
$377$			7.65989e9i			0.379190i
$378$		−	2.37521e9i		−	0.116342i
$379$	−2.14636e10			−1.04027			−0.520136	−	0.854084i	$-0.674119\pi$
$379$	−2.14636e10			−1.04027			−0.520136	+	0.854084i	$0.674119\pi$
$380$	5.19589e10			2.49187
$381$		−	3.76697e9i		−	0.178769i
$382$	−1.61991e10			−0.760743
$383$			2.03358e10i			0.945075i	0.881310	+	0.472538i	$0.156662\pi$
$383$			2.03358e10i			0.945075i	−0.881310	+	0.472538i	$0.843338\pi$
$384$	1.43028e11			6.57802
$385$	1.62492e10			0.739588
$386$		−	2.67744e10i		−	1.20606i
$387$	−2.17316e10	+	8.93693e8i	−0.968831	+	0.0398423i
$388$	−2.49816e10			−1.10229
$389$			1.22806e10i			0.536318i	0.963375	+	0.268159i	$0.0864153\pi$
$389$			1.22806e10i			0.536318i	−0.963375	+	0.268159i	$0.913585\pi$
$390$		−	4.59714e10i		−	1.98714i
$391$	2.89936e10			1.24050
$392$			8.00598e10i			3.39055i
$393$	−3.07308e10			−1.28826
$394$			5.43783e10i			2.25653i
$395$		−	2.87594e10i		−	1.18138i
$396$	2.31833e10			0.942745
$397$	2.41690e10			0.972964			0.486482	−	0.873691i	$-0.338280\pi$
$397$	2.41690e10			0.972964			0.486482	+	0.873691i	$0.338280\pi$
$398$	2.07244e10			0.825944
$399$			2.85837e10i			1.12779i
$400$	−1.43941e11			−5.62268
$401$	−2.06970e10			−0.800441			−0.400220	−	0.916419i	$-0.631066\pi$
$401$	−2.06970e10			−0.800441			−0.400220	+	0.916419i	$0.631066\pi$
$402$	5.61123e9			0.214859
$403$	−1.28482e10			−0.487104
$404$	1.07674e11			4.04191
$405$			4.25371e10i			1.58106i
$406$			5.96704e10i			2.19612i
$407$			1.79904e7i			0.000655637i
$408$	−1.55269e11			−5.60330
$409$		−	1.95719e9i		−	0.0699422i	−0.999388	−	0.0349711i	$-0.988866\pi$
$409$		−	1.95719e9i		−	0.0699422i	0.999388	−	0.0349711i	$-0.0111339\pi$
$410$	−7.95456e9			−0.281501
$411$	1.44718e10			0.507174
$412$	−1.50993e10			−0.524044
$413$		−	3.30680e10i		−	1.13660i
$414$			6.15891e10i			2.09654i
$415$			5.17686e10i			1.74532i
$416$		−	6.39600e10i		−	2.13568i
$417$		−	2.27527e10i		−	0.752469i
$418$	1.18277e10			0.387432
$419$		−	2.78733e10i		−	0.904341i	−0.891931	−	0.452171i	$-0.850650\pi$
$419$		−	2.78733e10i		−	0.904341i	0.891931	−	0.452171i	$-0.149350\pi$
$420$		−	2.64397e11i		−	8.49688i
$421$			2.18730e10i			0.696274i	0.937444	+	0.348137i	$0.113186\pi$
$421$			2.18730e10i			0.696274i	−0.937444	+	0.348137i	$0.886814\pi$
$422$	1.66676e10			0.525560
$423$	5.44674e10			1.70128
$424$			5.57011e9i			0.172346i
$425$	4.97208e10			1.52399
$426$			1.68014e11i			5.10161i
$427$	−3.68058e10			−1.10715
$428$	1.48099e11			4.41343
$429$		−	7.72612e9i		−	0.228104i
$430$	1.02555e11	−	4.21747e9i	2.99973	−	0.123361i
$431$	1.78281e10			0.516649			0.258324	−	0.966058i	$-0.416830\pi$
$431$	1.78281e10			0.516649			0.258324	+	0.966058i	$0.416830\pi$
$432$			6.13836e9i			0.176245i
$433$		−	9.84525e9i		−	0.280076i	−0.990146	−	0.140038i	$-0.955278\pi$
$433$		−	9.84525e9i		−	0.280076i	0.990146	−	0.140038i	$-0.0447224\pi$
$434$	−1.00087e11			−2.82111
$435$		−	6.20548e10i		−	1.73308i
$436$	9.23833e9			0.255651
$437$			2.31986e10i			0.636116i
$438$			6.58140e10i			1.78822i
$439$	4.30569e10			1.15927			0.579635	−	0.814877i	$-0.303195\pi$
$439$	4.30569e10			1.15927			0.579635	+	0.814877i	$0.303195\pi$
$440$	−7.06251e10			−1.88429
$441$	3.49297e10			0.923508
$442$			3.94618e10i			1.03392i
$443$	9.46657e9			0.245798			0.122899	−	0.992419i	$-0.460781\pi$
$443$	9.46657e9			0.245798			0.122899	+	0.992419i	$0.460781\pi$
$444$	2.92728e8			0.00753240
$445$	−1.40124e10			−0.357332
$446$	−1.04003e10			−0.262849
$447$	−8.15465e10			−2.04256
$448$		−	2.65351e11i		−	6.58731i
$449$			2.05489e10i			0.505596i	0.967519	+	0.252798i	$0.0813508\pi$
$449$			2.05489e10i			0.505596i	−0.967519	+	0.252798i	$0.918649\pi$
$450$			1.05619e11i			2.57567i
$451$	−1.33687e9			−0.0323135
$452$			2.36902e10i			0.567564i
$453$	−4.42663e10			−1.05119
$454$	−1.31602e11			−3.09770
$455$	−4.33779e10			−1.01210
$456$		−	1.24235e11i		−	2.87333i
$457$		−	2.06983e10i		−	0.474538i	−0.971444	−	0.237269i	$-0.923748\pi$
$457$		−	2.06983e10i		−	0.474538i	0.971444	−	0.237269i	$-0.0762522\pi$
$458$			2.39494e10i			0.544293i
$459$		−	2.12035e9i		−	0.0477702i
$460$		−	2.14586e11i		−	4.79258i
$461$	3.94084e10			0.872541			0.436270	−	0.899816i	$-0.356299\pi$
$461$	3.94084e10			0.872541			0.436270	+	0.899816i	$0.356299\pi$
$462$		−	6.01863e10i		−	1.32108i
$463$			3.51471e10i			0.764832i	0.923990	+	0.382416i	$0.124908\pi$
$463$			3.51471e10i			0.764832i	−0.923990	+	0.382416i	$0.875092\pi$
$464$		−	1.54209e11i		−	3.32688i
$465$	1.04087e11			2.22630
$466$	4.09171e10			0.867683
$467$		−	4.16099e9i		−	0.0874840i	−0.999043	−	0.0437420i	$-0.986072\pi$
$467$		−	4.16099e9i		−	0.0874840i	0.999043	−	0.0437420i	$-0.0139280\pi$
$468$	−6.18886e10			−1.29011
$469$		−	5.29468e9i		−	0.109433i
$470$	−2.57040e11			−5.26756
$471$	−1.01690e11			−2.06632
$472$			1.43726e11i			2.89579i
$473$	1.72357e10	−	7.08803e8i	0.344338	−	0.0141606i
$474$	−1.06523e11			−2.11024
$475$			3.97831e10i			0.781491i
$476$			2.26958e11i			4.42098i
$477$	2.43021e9			0.0469430
$478$		−	1.38734e11i		−	2.65748i
$479$	−9.43016e10			−1.79134			−0.895668	−	0.444723i	$-0.853302\pi$
$479$	−9.43016e10			−1.79134			−0.895668	+	0.444723i	$0.853302\pi$
$480$			5.18157e11i			9.76104i
$481$		−	4.80261e7i		−	0.000897216i
$482$	−2.87585e10			−0.532818
$483$	1.18048e11			2.16906
$484$	1.36426e11			2.48609
$485$		−	3.32037e10i		−	0.600093i
$486$	1.52910e11			2.74089
$487$	1.36814e10			0.243228			0.121614	−	0.992577i	$-0.461193\pi$
$487$	1.36814e10			0.243228			0.121614	+	0.992577i	$0.461193\pi$
$488$	1.59972e11			2.82074
$489$	−9.59393e10			−1.67788
$490$	−1.64839e11			−2.85940
$491$		−	9.15932e10i		−	1.57593i	−0.615720	−	0.787965i	$-0.711135\pi$
$491$		−	9.15932e10i		−	1.57593i	0.615720	−	0.787965i	$-0.288865\pi$
$492$			2.17527e10i			0.371238i
$493$			5.32678e10i			0.901731i
$494$	−3.15745e10			−0.530187
$495$			3.08134e10i			0.513238i
$496$	2.58660e11			4.27368
$497$	1.58536e11			2.59837
$498$	1.91748e11			3.11755
$499$		−	5.23882e10i		−	0.844951i	−0.906374	−	0.422475i	$-0.861161\pi$
$499$		−	5.23882e10i		−	0.844951i	0.906374	−	0.422475i	$-0.138839\pi$
$500$		−	9.71841e10i		−	1.55495i
$501$			1.38040e11i			2.19106i
$502$			1.52217e11i			2.39689i
$503$			1.09470e11i			1.71010i	0.518543	+	0.855052i	$0.326475\pi$
$503$			1.09470e11i			1.71010i	−0.518543	+	0.855052i	$0.673525\pi$
$504$	−3.11220e11			−4.82331
$505$			1.43112e11i			2.20045i
$506$		−	4.88474e10i		−	0.745143i
$507$		−	7.21061e10i		−	1.09129i
$508$	2.39321e10			0.359356
$509$	−2.73186e10			−0.406993			−0.203496	−	0.979076i	$-0.565231\pi$
$509$	−2.73186e10			−0.406993			−0.203496	+	0.979076i	$0.565231\pi$
$510$		−	3.19690e11i		−	4.72551i
$511$	6.21011e10			0.910784
$512$			2.75387e11i			4.00741i
$513$	1.69655e9			0.0244961
$514$	−3.11271e10			−0.445950
$515$		−	2.00688e10i		−	0.285294i
$516$	−1.15332e10	−	2.80449e11i	−0.162686	−	3.95598i
$517$	−4.31991e10			−0.604662
$518$		−	3.74123e8i		−	0.00519631i
$519$		−	7.83334e10i		−	1.07964i
$520$	1.88536e11			2.57859
$521$		−	1.39505e11i		−	1.89339i	−0.322132	−	0.946695i	$-0.604399\pi$
$521$		−	1.39505e11i		−	1.89339i	0.322132	−	0.946695i	$-0.395601\pi$
$522$	−1.13153e11			−1.52400
$523$		−	8.40035e10i		−	1.12277i	−0.827555	−	0.561385i	$-0.810269\pi$
$523$		−	8.40035e10i		−	1.12277i	0.827555	−	0.561385i	$-0.189731\pi$
$524$		−	1.95237e11i		−	2.58962i
$525$	2.02440e11			2.66476
$526$	−1.35294e11			−1.76740
$527$	−8.93478e10			−1.15835
$528$			1.55542e11i			2.00130i
$529$	1.74974e10			0.223434
$530$	−1.14686e10			−0.145347
$531$	6.27069e10			0.788746
$532$	−1.81596e11			−2.26704
$533$	3.56883e9			0.0442198
$534$			5.19012e10i			0.638282i
$535$			1.96841e11i			2.40271i
$536$			2.30126e10i			0.278809i
$537$	1.33409e11			1.60430
$538$		−	1.55512e11i		−	1.85625i
$539$	−2.77034e10			−0.328230
$540$	−1.56930e10			−0.184557
$541$	−1.49875e11			−1.74960			−0.874801	−	0.484483i	$-0.839008\pi$
$541$	−1.49875e11			−1.74960			−0.874801	+	0.484483i	$0.839008\pi$
$542$			2.12679e11i			2.46449i
$543$		−	1.28086e11i		−	1.47334i
$544$		−	4.44785e11i		−	5.07873i
$545$			1.22789e10i			0.139179i
$546$			1.60670e11i			1.80785i
$547$	1.07146e11			1.19681			0.598406	−	0.801193i	$-0.295801\pi$
$547$	1.07146e11			1.19681			0.598406	+	0.801193i	$0.295801\pi$
$548$			9.19414e10i			1.01950i
$549$		−	6.97949e10i		−	0.768306i
$550$		−	8.37679e10i		−	0.915434i
$551$	−4.26211e10			−0.462400
$552$	−5.13081e11			−5.52623
$553$			1.00514e11i			1.07479i
$554$	2.61097e11			2.77180
$555$			3.89072e8i			0.00410070i
$556$	1.44551e11			1.51259
$557$	3.95668e10			0.411065			0.205532	−	0.978650i	$-0.434107\pi$
$557$	3.95668e10			0.411065			0.205532	+	0.978650i	$0.434107\pi$
$558$		−	1.89795e11i		−	1.95771i
$559$	−4.60114e10	+	1.89218e9i	−0.471214	+	0.0193783i
$560$	8.73284e11			8.87980
$561$		−	5.37283e10i		−	0.542440i
$562$		−	1.95300e11i		−	1.95775i
$563$	−3.42250e10			−0.340652			−0.170326	−	0.985388i	$-0.554482\pi$
$563$	−3.42250e10			−0.340652			−0.170326	+	0.985388i	$0.554482\pi$
$564$			7.02908e11i			6.94675i
$565$	−3.14872e10			−0.308987
$566$			1.50952e11i			1.47087i
$567$		−	1.48667e11i		−	1.43841i
$568$	−6.89054e11			−6.62003
$569$	−8.05501e10			−0.768453			−0.384226	−	0.923239i	$-0.625532\pi$
$569$	−8.05501e10			−0.768453			−0.384226	+	0.923239i	$0.625532\pi$
$570$	2.55794e11			2.42320
$571$		−	1.76714e11i		−	1.66237i	−0.555999	−	0.831183i	$-0.687664\pi$
$571$		−	1.76714e11i		−	1.66237i	0.555999	−	0.831183i	$-0.312336\pi$
$572$	4.90850e10			0.458527
$573$	−5.88781e10			−0.546179
$574$	2.78011e10			0.256103
$575$	1.64301e11			1.50303
$576$	5.03184e11			4.57127
$577$			1.37822e10i			0.124342i	0.998066	+	0.0621708i	$0.0198023\pi$
$577$			1.37822e10i			0.124342i	−0.998066	+	0.0621708i	$0.980198\pi$
$578$			5.62452e10i			0.503935i
$579$		−	9.73155e10i		−	0.865900i
$580$	3.94242e11			3.48378
$581$		−	1.80931e11i		−	1.58784i
$582$	−1.22985e11			−1.07191
$583$	−1.92745e9			−0.0166843
$584$	−2.69914e11			−2.32046
$585$		−	8.22576e10i		−	0.702348i
$586$			2.55723e11i			2.16860i
$587$		−	1.82554e11i		−	1.53759i	−0.639498	−	0.768793i	$-0.720858\pi$
$587$		−	1.82554e11i		−	1.53759i	0.639498	−	0.768793i	$-0.279142\pi$
$588$			4.50772e11i			3.77092i
$589$		−	7.14898e10i		−	0.593995i
$590$	−2.95923e11			−2.44214
$591$			1.97646e11i			1.62009i
$592$			9.66861e8i			0.00787185i
$593$			1.43538e11i			1.16078i	0.814340	+	0.580388i	$0.197099\pi$
$593$			1.43538e11i			1.16078i	−0.814340	+	0.580388i	$0.802901\pi$
$594$	−3.57229e9			−0.0286946
$595$	−3.01655e11			−2.40682
$596$		−	5.18075e11i		−	4.10589i
$597$	7.53260e10			0.592990
$598$			1.30400e11i			1.01970i
$599$	−2.27622e11			−1.76810			−0.884050	−	0.467392i	$-0.845194\pi$
$599$	−2.27622e11			−1.76810			−0.884050	+	0.467392i	$0.845194\pi$
$600$	−8.79876e11			−6.78917
$601$		−	3.77861e10i		−	0.289624i	−0.989459	−	0.144812i	$-0.953742\pi$
$601$		−	3.77861e10i		−	0.289624i	0.989459	−	0.144812i	$-0.0462578\pi$
$602$	−3.58428e11	+	1.47400e10i	−2.72908	+	0.112231i
$603$	1.00403e10			0.0759411
$604$		−	2.81229e11i		−	2.11306i
$605$			1.81327e11i			1.35345i
$606$	5.30080e11			3.93053
$607$			2.22698e11i			1.64044i	0.572047	+	0.820221i	$0.306150\pi$
$607$			2.22698e11i			1.64044i	−0.572047	+	0.820221i	$0.693850\pi$
$608$	3.55886e11			2.60433
$609$			2.16881e11i			1.57671i
$610$			3.29373e11i			2.37886i
$611$	1.15322e11			0.827458
$612$	−4.30381e11			−3.06794
$613$	2.51319e11			1.77985			0.889926	−	0.456105i	$-0.150756\pi$
$613$	2.51319e11			1.77985			0.889926	+	0.456105i	$0.150756\pi$
$614$		−	1.64386e11i		−	1.15662i
$615$	−2.89120e10			−0.202105
$616$	2.46834e11			1.71428
$617$	−9.10397e10			−0.628189			−0.314094	−	0.949392i	$-0.601701\pi$
$617$	−9.10397e10			−0.628189			−0.314094	+	0.949392i	$0.601701\pi$
$618$	−7.43339e10			−0.509604
$619$	−1.28665e11			−0.876391			−0.438195	−	0.898880i	$-0.644382\pi$
$619$	−1.28665e11			−0.876391			−0.438195	+	0.898880i	$0.644382\pi$
$620$			6.61275e11i			4.47523i
$621$		−	7.00661e9i		−	0.0471131i
$622$			4.19474e11i			2.80249i
$623$	4.89732e10			0.325092
$624$		−	4.15225e11i		−	2.73871i
$625$	−7.81775e10			−0.512344
$626$	9.00476e10			0.586374
$627$	4.29896e10			0.278159
$628$		−	6.46052e11i		−	4.15364i
$629$		−	3.33979e8i		−	0.00213362i
$630$		−	6.40785e11i		−	4.06771i
$631$		−	1.01164e11i		−	0.638131i	−0.947733	−	0.319066i	$-0.896631\pi$
$631$		−	1.01164e11i		−	0.638131i	0.947733	−	0.319066i	$-0.103369\pi$
$632$		−	4.36870e11i		−	2.73832i
$633$	6.05808e10			0.377329
$634$		−	5.38009e11i		−	3.32991i
$635$			3.18086e10i			0.195637i
$636$			3.13622e10i			0.191680i
$637$	7.39552e10			0.449170
$638$	8.97437e10			0.541653
$639$			3.00631e11i			1.80315i
$640$	−1.20774e12			−7.19867
$641$		−	6.04868e10i		−	0.358285i	−0.983823	−	0.179142i	$-0.942668\pi$
$641$		−	6.04868e10i		−	0.358285i	0.983823	−	0.179142i	$-0.0573323\pi$
$642$	7.29090e11			4.29182
$643$	−9.88166e10			−0.578077			−0.289039	−	0.957317i	$-0.593336\pi$
$643$	−9.88166e10			−0.578077			−0.289039	+	0.957317i	$0.593336\pi$
$644$			7.49975e11i			4.36017i
$645$	3.72751e11	−	1.53290e10i	2.15367	−	0.0885678i
$646$	−2.19573e11			−1.26081
$647$			6.03495e10i			0.344395i	0.985062	+	0.172197i	$0.0550867\pi$
$647$			6.03495e10i			0.344395i	−0.985062	+	0.172197i	$0.944913\pi$
$648$			6.46161e11i			3.66472i
$649$	−4.97339e10			−0.280333
$650$			2.23622e11i			1.25274i
$651$	−3.63782e11			−2.02543
$652$		−	6.09514e11i		−	3.37282i
$653$		−	7.86810e10i		−	0.432730i	−0.976313	−	0.216365i	$-0.930580\pi$
$653$		−	7.86810e10i		−	0.432730i	0.976313	−	0.216365i	$-0.0694202\pi$
$654$	4.54803e10			0.248606
$655$	2.59494e11			1.40981
$656$	−7.18476e10			−0.387969
$657$			1.17762e11i			0.632040i
$658$	8.98353e11			4.79230
$659$	8.07210e10			0.428001			0.214001	−	0.976834i	$-0.431351\pi$
$659$	8.07210e10			0.428001			0.214001	+	0.976834i	$0.431351\pi$
$660$	−3.97650e11			−2.09568
$661$	−2.27444e10			−0.119143			−0.0595716	−	0.998224i	$-0.518973\pi$
$661$	−2.27444e10			−0.119143			−0.0595716	+	0.998224i	$0.518973\pi$
$662$	1.91766e11			0.998481
$663$			1.43430e11i			0.742310i
$664$			7.86391e11i			4.04545i
$665$		−	2.41363e11i		−	1.23420i
$666$	7.09448e8			0.00360599
$667$			1.76021e11i			0.889328i
$668$	−8.76986e11			−4.40440
$669$	−3.78014e10			−0.188714
$670$	−4.73817e10			−0.235132
$671$			5.53556e10i			0.273068i
$672$		−	1.81095e12i		−	8.88035i
$673$		−	9.31399e10i		−	0.454020i	−0.973892	−	0.227010i	$-0.927105\pi$
$673$		−	9.31399e10i		−	0.454020i	0.973892	−	0.227010i	$-0.0728951\pi$
$674$			2.81126e11i			1.36226i
$675$		−	1.20156e10i		−	0.0578801i
$676$	4.58099e11			2.19368
$677$		−	1.19826e11i		−	0.570420i	−0.958465	−	0.285210i	$-0.907937\pi$
$677$		−	1.19826e11i		−	0.570420i	0.958465	−	0.285210i	$-0.0920634\pi$
$678$			1.16627e11i			0.551925i
$679$			1.16046e11i			0.545950i
$680$	1.31110e12			6.13199
$681$	−4.78327e11			−2.22401
$682$			1.50530e11i			0.695802i
$683$	2.38715e11			1.09697			0.548487	−	0.836159i	$-0.315204\pi$
$683$	2.38715e11			1.09697			0.548487	+	0.836159i	$0.315204\pi$
$684$		−	3.44360e11i		−	1.57322i
$685$	−1.22201e11			−0.555027
$686$	−2.87847e10			−0.129977
$687$			8.70476e10i			0.390778i
$688$	9.26301e11	−	3.80933e10i	4.13427	−	0.170018i
$689$	5.14539e9			0.0228319
$690$		−	1.05641e12i		−	4.66052i
$691$			3.43316e11i			1.50585i	0.658107	+	0.752924i	$0.271357\pi$
$691$			3.43316e11i			1.50585i	−0.658107	+	0.752924i	$0.728643\pi$
$692$	4.97662e11			2.17025
$693$		−	1.07693e11i		−	0.466931i
$694$	−6.56787e11			−2.83130
$695$			1.92126e11i			0.823466i
$696$		−	9.42644e11i		−	4.01708i
$697$	2.48180e10			0.105157
$698$	−4.48663e11			−1.89016
$699$	1.48719e11			0.622957
$700$			1.28612e12i			5.35662i
$701$	−1.30956e11			−0.542319			−0.271159	−	0.962534i	$-0.587407\pi$
$701$	−1.30956e11			−0.542319			−0.271159	+	0.962534i	$0.587407\pi$
$702$	9.53636e9			0.0392676
$703$	2.67226e8			0.00109410
$704$	−3.99084e11			−1.62470
$705$	−9.34250e11			−3.78187
$706$			7.58471e11i			3.05295i
$707$		−	5.00176e11i		−	2.00191i
$708$			8.09239e11i			3.22065i
$709$	1.43918e11			0.569549			0.284775	−	0.958594i	$-0.408081\pi$
$709$	1.43918e11			0.569549			0.284775	+	0.958594i	$0.408081\pi$
$710$		−	1.41873e12i		−	5.58297i
$711$	−1.90604e11			−0.745855
$712$	−2.12855e11			−0.828256
$713$	−2.95247e11			−1.14242
$714$			1.11732e12i			4.29915i
$715$			6.52399e10i			0.249626i
$716$			8.47562e11i			3.22492i
$717$		−	5.04248e11i		−	1.90795i
$718$		−	5.08914e11i		−	1.91490i
$719$	5.08125e11			1.90132			0.950660	−	0.310234i	$-0.100407\pi$
$719$	5.08125e11			1.90132			0.950660	+	0.310234i	$0.100407\pi$
$720$			1.65601e12i			6.16215i
$721$			7.01404e10i			0.259554i
$722$			3.55499e11i			1.30825i
$723$	−1.04527e11			−0.382539
$724$	8.13745e11			2.96165
$725$			3.01857e11i			1.09257i
$726$	6.71627e11			2.41758
$727$			1.86214e11i			0.666613i	0.942819	+	0.333306i	$0.108164\pi$
$727$			1.86214e11i			0.666613i	−0.942819	+	0.333306i	$0.891836\pi$
$728$	−6.58933e11			−2.34593
$729$	2.65034e11			0.938407
$730$		−	5.55738e11i		−	1.95695i
$731$	−3.19969e11	+	1.31584e10i	−1.12057	+	0.0460823i
$732$	9.00711e11			3.13719
$733$		−	2.14404e11i		−	0.742705i	−0.928492	−	0.371352i	$-0.878894\pi$
$733$		−	2.14404e11i		−	0.742705i	0.928492	−	0.371352i	$-0.121106\pi$
$734$		−	4.63983e11i		−	1.59852i
$735$	−5.99131e11			−2.05292
$736$		−	1.46978e12i		−	5.00887i
$737$	−7.96313e9			−0.0269907
$738$			5.27192e10i			0.177723i
$739$			5.48486e11i			1.83902i	0.393061	+	0.919512i	$0.371416\pi$
$739$			5.48486e11i			1.83902i	−0.393061	+	0.919512i	$0.628584\pi$
$740$	−2.47182e9			−0.00824310
$741$	−1.14762e11			−0.380650
$742$	4.00825e10			0.132233
$743$			5.34775e11i			1.75475i	0.479805	+	0.877375i	$0.340708\pi$
$743$			5.34775e11i			1.75475i	−0.479805	+	0.877375i	$0.659292\pi$
$744$	1.58113e12			5.16030
$745$	6.88585e11			2.23528
$746$	−2.75191e11			−0.888544
$747$	3.43099e11			1.10189
$748$	3.41343e11			1.09040
$749$		−	6.87959e11i		−	2.18592i
$750$		−	4.78437e11i		−	1.51210i
$751$		−	3.06199e11i		−	0.962596i	−0.876557	−	0.481298i	$-0.840165\pi$
$751$		−	3.06199e11i		−	0.962596i	0.876557	−	0.481298i	$-0.159835\pi$
$752$	−2.32165e12			−7.25982
$753$			5.53256e11i			1.72086i
$754$	−2.39574e11			−0.741233
$755$	3.73788e11			1.15037
$756$	5.48468e10			0.167905
$757$		−	3.81892e11i		−	1.16294i	−0.813568	−	0.581470i	$-0.802478\pi$
$757$		−	3.81892e11i		−	1.16294i	0.813568	−	0.581470i	$-0.197522\pi$
$758$		−	6.71306e11i		−	2.03350i
$759$		−	1.77543e11i		−	0.534979i
$760$			1.04905e12i			3.14443i
$761$			4.86988e10i			0.145204i	0.997361	+	0.0726022i	$0.0231304\pi$
$761$			4.86988e10i			0.145204i	−0.997361	+	0.0726022i	$0.976870\pi$
$762$	1.17818e11			0.349454
$763$		−	4.29146e10i		−	0.126621i
$764$		−	3.74060e11i		−	1.09791i
$765$		−	5.72029e11i		−	1.67021i
$766$	−6.36032e11			−1.84741
$767$	1.32767e11			0.383626
$768$			2.17163e12i			6.24224i
$769$	1.78411e11			0.510172			0.255086	−	0.966918i	$-0.417896\pi$
$769$	1.78411e11			0.510172			0.255086	+	0.966918i	$0.417896\pi$
$770$			5.08218e11i			1.44573i
$771$	−1.13136e11			−0.320172
$772$	6.18258e11			1.74061
$773$			2.72750e11i			0.763917i	0.924180	+	0.381958i	$0.124750\pi$
$773$			2.72750e11i			0.763917i	−0.924180	+	0.381958i	$0.875250\pi$
$774$	−2.79515e10	−	6.79688e11i	−0.0778828	−	1.89385i
$775$	−5.06315e11			−1.40350
$776$		−	5.04380e11i		−	1.39095i
$777$		−	1.35980e9i		−	0.00373071i
$778$	−3.84095e11			−1.04838
$779$			1.98576e10i			0.0539234i
$780$	1.06154e12			2.86787
$781$		−	2.38436e11i		−	0.640867i
$782$			9.06817e11i			2.42489i
$783$	1.28727e10			0.0342471
$784$	−1.48887e12			−3.94086
$785$	8.58683e11			2.26128
$786$		−	9.61151e11i		−	2.51826i
$787$	−5.48896e11			−1.43084			−0.715420	−	0.698695i	$-0.753764\pi$
$787$	−5.48896e11			−1.43084			−0.715420	+	0.698695i	$0.753764\pi$
$788$	−1.25567e12			−3.25665
$789$	−4.91746e11			−1.26891
$790$	8.99492e11			2.30934
$791$	1.10047e11			0.281109
$792$			4.68071e11i			1.18963i
$793$		−	1.47774e11i		−	0.373684i
$794$			7.55921e11i			1.90193i
$795$	−4.16842e10			−0.104352
$796$			4.78556e11i			1.19201i
$797$	−4.72648e11			−1.17140			−0.585699	−	0.810528i	$-0.699180\pi$
$797$	−4.72648e11			−1.17140			−0.585699	+	0.810528i	$0.699180\pi$
$798$	−8.93996e11			−2.20457
$799$	8.01960e11			1.96773
$800$		−	2.52050e12i		−	6.15357i
$801$			9.28679e10i			0.225598i
$802$		−	6.47327e11i		−	1.56468i
$803$		−	9.33993e10i		−	0.224637i
$804$			1.29571e11i			0.310087i
$805$	−9.96808e11			−2.37371
$806$		−	4.01846e11i		−	0.952180i
$807$		−	5.65232e11i		−	1.33270i
$808$			2.17395e12i			5.10039i
$809$	1.26552e11			0.295443			0.147721	−	0.989029i	$-0.452806\pi$
$809$	1.26552e11			0.295443			0.147721	+	0.989029i	$0.452806\pi$
$810$	−1.33041e12			−3.09062
$811$		−	2.53327e11i		−	0.585595i	−0.956174	−	0.292797i	$-0.905414\pi$
$811$		−	2.53327e11i		−	0.585595i	0.956174	−	0.292797i	$-0.0945862\pi$
$812$	−1.37787e12			−3.16946
$813$			7.73013e11i			1.76939i
$814$	−5.62676e8			−0.00128162
$815$	8.10119e11			1.83619
$816$		−	2.88753e12i		−	6.51276i
$817$	−1.05284e10	−	2.56016e11i	−0.0236306	−	0.574618i
$818$	6.12139e10			0.136721
$819$			2.87490e11i			0.638979i
$820$		−	1.83682e11i		−	0.406266i
$821$	4.14699e11			0.912769			0.456384	−	0.889783i	$-0.349144\pi$
$821$	4.14699e11			0.912769			0.456384	+	0.889783i	$0.349144\pi$
$822$			4.52628e11i			0.991412i
$823$	−2.10060e11			−0.457872			−0.228936	−	0.973441i	$-0.573525\pi$
$823$	−2.10060e11			−0.457872			−0.228936	+	0.973441i	$0.573525\pi$
$824$		−	3.04856e11i		−	0.661280i
$825$		−	3.04467e11i		−	0.657240i
$826$	1.03425e12			2.22180
$827$	8.01048e11			1.71252			0.856261	−	0.516543i	$-0.172781\pi$
$827$	8.01048e11			1.71252			0.856261	+	0.516543i	$0.172781\pi$
$828$	−1.42218e12			−3.02575
$829$			4.05691e10i			0.0858969i	0.999077	+	0.0429485i	$0.0136751\pi$
$829$			4.05691e10i			0.0858969i	−0.999077	+	0.0429485i	$0.986325\pi$
$830$	−1.61914e12			−3.41170
$831$	9.48995e11			1.99003
$832$	1.06537e12			2.22335
$833$	5.14293e11			1.06815
$834$	7.11623e11			1.47091
$835$		−	1.16562e12i		−	2.39779i
$836$			2.73118e11i			0.559146i
$837$			2.15918e10i			0.0439934i
$838$	8.71778e11			1.76779
$839$		−	4.87908e11i		−	0.984669i	−0.870406	−	0.492334i	$-0.836144\pi$
$839$		−	4.87908e11i		−	0.984669i	0.870406	−	0.492334i	$-0.163856\pi$
$840$	5.33819e12			10.7220
$841$	1.76856e11			0.353537
$842$	−6.84110e11			−1.36106
$843$		−	7.09846e11i		−	1.40558i
$844$			3.84877e11i			0.758494i
$845$			6.08870e11i			1.19426i
$846$			1.70355e12i			3.32562i
$847$		−	6.33737e11i		−	1.23133i
$848$	−1.03587e11			−0.200319
$849$			5.48657e11i			1.05602i
$850$			1.55509e12i			2.97907i
$851$		−	1.10362e9i		−	0.00210427i
$852$	−3.87968e12			−7.36270
$853$	−9.56233e11			−1.80621			−0.903104	−	0.429423i	$-0.858717\pi$
$853$	−9.56233e11			−1.80621			−0.903104	+	0.429423i	$0.858717\pi$
$854$		−	1.15116e12i		−	2.16423i
$855$	4.57697e11			0.856472
$856$			2.99012e12i			5.56921i
$857$	6.85492e11			1.27081			0.635403	−	0.772181i	$-0.280834\pi$
$857$	6.85492e11			1.27081			0.635403	+	0.772181i	$0.280834\pi$
$858$	2.41645e11			0.445892
$859$			3.77688e11i			0.693681i	0.937924	+	0.346841i	$0.112746\pi$
$859$			3.77688e11i			0.693681i	−0.937924	+	0.346841i	$0.887254\pi$
$860$	9.73872e10	+	2.36813e12i	0.178036	+	4.32924i
$861$	1.01047e11			0.183870
$862$			5.57599e11i			1.00993i
$863$		−	2.63832e11i		−	0.475647i	−0.971308	−	0.237824i	$-0.923566\pi$
$863$		−	2.63832e11i		−	0.475647i	0.971308	−	0.237824i	$-0.0764340\pi$
$864$	−1.07487e11			−0.192886
$865$			6.61454e11i			1.18150i
$866$	3.07924e11			0.547486
$867$			2.04431e11i			0.361802i
$868$		−	2.31115e12i		−	4.07145i
$869$	1.51172e11			0.265089
$870$	1.94085e12			3.38778
$871$	2.12579e10			0.0369358
$872$			1.86522e11i			0.322600i
$873$	−2.20059e11			−0.378863
$874$	−7.25571e11			−1.24347
$875$	−4.51446e11			−0.770148
$876$	−1.51973e12			−2.58078
$877$	−7.94644e11			−1.34330			−0.671652	−	0.740867i	$-0.734415\pi$
$877$	−7.94644e11			−1.34330			−0.671652	+	0.740867i	$0.734415\pi$
$878$			1.34667e12i			2.26611i
$879$			9.29464e11i			1.55696i
$880$		−	1.31341e12i		−	2.19013i
$881$	3.46286e10			0.0574820			0.0287410	−	0.999587i	$-0.490850\pi$
$881$	3.46286e10			0.0574820			0.0287410	+	0.999587i	$0.490850\pi$
$882$			1.09248e12i			1.80525i
$883$	4.25295e11			0.699596			0.349798	−	0.936825i	$-0.386250\pi$
$883$	4.25295e11			0.699596			0.349798	+	0.936825i	$0.386250\pi$
$884$	−9.11227e11			−1.49217
$885$	−1.07558e12			−1.75335
$886$			2.96081e11i			0.480480i
$887$		−	1.13313e12i		−	1.83056i	−0.402821	−	0.915279i	$-0.631970\pi$
$887$		−	1.13313e12i		−	1.83056i	0.402821	−	0.915279i	$-0.368030\pi$
$888$			5.91020e9i			0.00950496i
$889$		−	1.11171e11i		−	0.177985i
$890$		−	4.38258e11i		−	0.698505i
$891$	−2.23593e11			−0.354771
$892$		−	2.40157e11i		−	0.379347i
$893$			6.41671e11i			1.00904i
$894$		−	2.55048e12i		−	3.99275i
$895$	−1.12651e12			−1.75567
$896$	4.22103e12			6.54917
$897$			4.73958e11i			0.732100i
$898$	−6.42697e11			−0.988328
$899$		−	5.42434e11i		−	0.830440i
$900$	−2.43888e12			−3.71723
$901$	3.57817e10			0.0542952
$902$		−	4.18126e10i		−	0.0631656i
$903$	−1.30276e12	+	5.35748e10i	−1.95936	+	0.0805767i
$904$	−4.78306e11			−0.716197
$905$			1.08157e12i			1.61235i
$906$		−	1.38449e12i		−	2.05484i
$907$	1.06396e12			1.57216			0.786082	−	0.618122i	$-0.212106\pi$
$907$	1.06396e12			1.57216			0.786082	+	0.618122i	$0.212106\pi$
$908$		−	3.03887e12i		−	4.47063i
$909$	9.48483e11			1.38923
$910$		−	1.35671e12i		−	1.97843i
$911$		−	1.02928e12i		−	1.49438i	−0.664612	−	0.747189i	$-0.731403\pi$
$911$		−	1.02928e12i		−	1.49438i	0.664612	−	0.747189i	$-0.268597\pi$
$912$	2.31039e12			3.33969
$913$	−2.72118e11			−0.391628
$914$	6.47370e11			0.927616
$915$			1.19715e12i			1.70791i
$916$	−5.53024e11			−0.785529
$917$	−9.06928e11			−1.28261
$918$	6.63170e10			0.0933800
$919$	9.78879e11			1.37236			0.686178	−	0.727433i	$-0.259287\pi$
$919$	9.78879e11			1.37236			0.686178	+	0.727433i	$0.259287\pi$
$920$	4.33249e12			6.04765
$921$		−	5.97484e11i		−	0.830401i
$922$			1.23256e12i			1.70562i
$923$			6.36514e11i			0.877003i
$924$	1.38978e12			1.90660
$925$		−	1.89259e9i		−	0.00258517i
$926$	−1.09928e12			−1.49508
$927$	−1.33007e11			−0.180118
$928$	2.70031e12			3.64101
$929$			1.02731e12i			1.37923i	0.724176	+	0.689615i	$0.242220\pi$
$929$			1.02731e12i			1.37923i	−0.724176	+	0.689615i	$0.757780\pi$
$930$			3.25546e12i			4.35191i
$931$			4.11501e11i			0.547737i
$932$			9.44832e11i			1.25225i
$933$			1.52464e12i			2.01206i
$934$	1.30141e11			0.171012
$935$			4.53686e11i			0.593621i
$936$		−	1.24953e12i		−	1.62796i
$937$			2.93934e11i			0.381322i	0.981656	+	0.190661i	$0.0610632\pi$
$937$			2.93934e11i			0.381322i	−0.981656	+	0.190661i	$0.938937\pi$
$938$	1.65599e11			0.213917
$939$	3.27291e11			0.420990
$940$		−	5.93541e12i		−	7.60220i
$941$	1.10210e12			1.40561			0.702804	−	0.711383i	$-0.251931\pi$
$941$	1.10210e12			1.40561			0.702804	+	0.711383i	$0.251931\pi$
$942$		−	3.18052e12i		−	4.03919i
$943$	8.20103e10			0.103710
$944$	−2.67286e12			−3.36579
$945$			7.28982e10i			0.0914091i
$946$	2.21688e10	+	5.39072e11i	0.0276808	+	0.673104i
$947$	−8.17388e11			−1.01631			−0.508157	−	0.861264i	$-0.669673\pi$
$947$	−8.17388e11			−1.01631			−0.508157	+	0.861264i	$0.669673\pi$
$948$		−	2.45977e12i		−	3.04552i
$949$			2.49333e11i			0.307408i
$950$	−1.24427e12			−1.52764
$951$		−	1.95547e12i		−	2.39072i
$952$	−4.58230e12			−5.57873
$953$			9.57039e11i			1.16027i	0.814521	+	0.580134i	$0.197000\pi$
$953$			9.57039e11i			1.16027i	−0.814521	+	0.580134i	$0.803000\pi$
$954$			7.60085e10i			0.0917632i
$955$	4.97171e11			0.597713
$956$	3.20355e12			3.83531
$957$	3.26187e11			0.388882
$958$		−	2.94942e12i		−	3.50166i
$959$	4.27093e11			0.504950
$960$	−8.63085e12			−10.1618
$961$	5.69514e10			0.0667745
$962$	1.50209e9			0.00175386
$963$	1.30458e12			1.51693
$964$		−	6.64074e11i		−	0.768968i
$965$			8.21740e11i			0.947600i
$966$			3.69213e12i			4.24002i
$967$	2.25768e11			0.258201			0.129100	−	0.991632i	$-0.458791\pi$
$967$	2.25768e11			0.258201			0.129100	+	0.991632i	$0.458791\pi$
$968$			2.75445e12i			3.13714i
$969$	−7.98070e11			−0.905203
$970$	1.03849e12			1.17305
$971$	9.42089e11			1.05978			0.529889	−	0.848067i	$-0.322234\pi$
$971$	9.42089e11			1.05978			0.529889	+	0.848067i	$0.322234\pi$
$972$			3.53091e12i			3.95568i
$973$		−	6.71477e11i		−	0.749169i
$974$			4.27904e11i			0.475457i
$975$			8.12786e11i			0.899410i
$976$			2.97498e12i			3.27857i
$977$	−1.32854e12			−1.45813			−0.729064	−	0.684446i	$-0.760044\pi$
$977$	−1.32854e12			−1.45813			−0.729064	+	0.684446i	$0.760044\pi$
$978$		−	3.00064e12i		−	3.27988i
$979$		−	7.36552e10i		−	0.0801812i
$980$		−	3.80635e12i		−	4.12672i
$981$	8.13789e10			0.0878690
$982$	2.86471e12			3.08059
$983$			1.19093e12i			1.27548i	0.770253	+	0.637738i	$0.220130\pi$
$983$			1.19093e12i			1.27548i	−0.770253	+	0.637738i	$0.779870\pi$
$984$	−4.39188e11			−0.468458
$985$		−	1.66894e12i		−	1.77295i
$986$	−1.66603e12			−1.76268
$987$	3.26520e12			3.44065
$988$		−	7.29099e11i		−	0.765172i
$989$	−1.05733e12	+	4.34815e10i	−1.10516	+	0.0454485i
$990$	−9.63734e11			−1.00327
$991$			1.64001e12i			1.70040i	0.526457	+	0.850202i	$0.323520\pi$
$991$			1.64001e12i			1.70040i	−0.526457	+	0.850202i	$0.676480\pi$
$992$			4.52932e12i			4.67720i
$993$	6.97002e11			0.716865
$994$			4.95843e12i			5.07924i
$995$	−6.36059e11			−0.648941
$996$			4.42773e12i			4.49929i
$997$		−	9.66217e11i		−	0.977899i	−0.872312	−	0.488949i	$-0.837380\pi$
$997$		−	9.66217e11i		−	0.977899i	0.872312	−	0.488949i	$-0.162620\pi$
$998$	1.63852e12			1.65169
$999$	−8.07096e7			−8.10332e−5

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.28	yes	28
43.42	odd	2	inner	43.9.b.b.42.1	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.1	✓	28	43.42	odd	2	inner
43.9.b.b.42.28	yes	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+31.2764i q^{2} +113.679i q^{3} -722.216 q^{4} -959.913i q^{5} -3555.47 q^{6} +3354.89i q^{7} -14581.6i q^{8} -6361.87 q^{9} +O(q^{10})\)	\(q+31.2764i q^{2} +113.679i q^{3} -722.216 q^{4} -959.913i q^{5} -3555.47 q^{6} +3354.89i q^{7} -14581.6i q^{8} -6361.87 q^{9} +30022.7 q^{10} +5045.72 q^{11} -82100.6i q^{12} -13469.7 q^{13} -104929. q^{14} +109122. q^{15} +271172. q^{16} -93670.1 q^{17} -198977. i q^{18} -74948.1i q^{19} +693264. i q^{20} -381380. q^{21} +157812. i q^{22} -309529. q^{23} +1.65762e6 q^{24} -530808. q^{25} -421285. i q^{26} +22636.4i q^{27} -2.42295e6i q^{28} -568675. i q^{29} +3.41294e6i q^{30} +953857. q^{31} +4.74843e6i q^{32} +573591. i q^{33} -2.92967e6i q^{34} +3.22040e6 q^{35} +4.59465e6 q^{36} +3565.48i q^{37} +2.34411e6 q^{38} -1.53122e6i q^{39} -1.39970e7 q^{40} -264952. q^{41} -1.19282e7i q^{42} +(3.41591e6 - 140476. i) q^{43} -3.64410e6 q^{44} +6.10685e6i q^{45} -9.68097e6i q^{46} -8.56154e6 q^{47} +3.08266e7i q^{48} -5.49048e6 q^{49} -1.66018e7i q^{50} -1.06483e7i q^{51} +9.72805e6 q^{52} -381997. q^{53} -707985. q^{54} -4.84345e6i q^{55} +4.89195e7 q^{56} +8.52001e6 q^{57} +1.77861e7 q^{58} -9.85667e6 q^{59} -7.88095e7 q^{60} +1.09708e7i q^{61} +2.98332e7i q^{62} -2.13434e7i q^{63} -7.90937e7 q^{64} +1.29298e7i q^{65} -1.79399e7 q^{66} -1.57820e6 q^{67} +6.76500e7 q^{68} -3.51869e7i q^{69} +1.00723e8i q^{70} -4.72551e7i q^{71} +9.27661e7i q^{72} -1.85106e7i q^{73} -111516. q^{74} -6.03417e7i q^{75} +5.41287e7i q^{76} +1.69278e7i q^{77} +4.78912e7 q^{78} +2.99604e7 q^{79} -2.60302e8i q^{80} -4.43135e7 q^{81} -8.28675e6i q^{82} -5.39305e7 q^{83} +2.75438e8 q^{84} +8.99151e7i q^{85} +(4.39360e6 + 1.06838e8i) q^{86} +6.46463e7 q^{87} -7.35745e7i q^{88} -1.45976e7i q^{89} -1.91000e8 q^{90} -4.51894e7i q^{91} +2.23547e8 q^{92} +1.08433e8i q^{93} -2.67774e8i q^{94} -7.19437e7 q^{95} -5.39795e8 q^{96} +3.45903e7 q^{97} -1.71723e8i q^{98} -3.21002e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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