LMFDB - Embedded newform 43.9.b.b.42.15

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			42.15
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} +O(q^{10})$	\(q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} -3661.61 q^{10} +24815.2 q^{11} +25337.9i q^{12} +8701.41 q^{13} -14301.5 q^{14} -71305.8 q^{15} +40224.6 q^{16} +10140.4 q^{17} -38333.6i q^{18} -186604. i q^{19} +138060. i q^{20} -278506. q^{21} +145774. i q^{22} -387538. q^{23} -320878. q^{24} +2096.22 q^{25} +51115.2i q^{26} +4052.57i q^{27} +539236. i q^{28} -1.03599e6i q^{29} -418876. i q^{30} +146035. q^{31} +954363. i q^{32} +2.83878e6i q^{33} +59568.6i q^{34} -1.51752e6 q^{35} -1.44536e6 q^{36} -2.77780e6i q^{37} +1.09618e6 q^{38} +995411. i q^{39} -1.74839e6 q^{40} +89036.0 q^{41} -1.63604e6i q^{42} +(-3.30170e6 - 887103. i) q^{43} +5.49637e6 q^{44} -4.06753e6i q^{45} -2.27654e6i q^{46} +867696. q^{47} +4.60155e6i q^{48} -162308. q^{49} +12314.0i q^{50} +1.16003e6i q^{51} +1.92729e6 q^{52} +1.05861e7 q^{53} -23806.3 q^{54} +1.54678e7i q^{55} -6.82886e6 q^{56} +2.13468e7 q^{57} +6.08576e6 q^{58} +1.99430e7 q^{59} -1.57936e7 q^{60} -9.32889e6i q^{61} +857860. i q^{62} -1.58869e7i q^{63} +4.69121e6 q^{64} +5.42377e6i q^{65} -1.66760e7 q^{66} -1.83542e7 q^{67} +2.24602e6 q^{68} -4.43330e7i q^{69} -8.91443e6i q^{70} +8.73139e6i q^{71} -1.83040e7i q^{72} +3.39275e7i q^{73} +1.63178e7 q^{74} +239800. i q^{75} -4.13312e7i q^{76} +6.04143e7i q^{77} -5.84741e6 q^{78} +2.74337e7 q^{79} +2.50728e7i q^{80} -4.32779e7 q^{81} +523029. i q^{82} -6.16851e7 q^{83} -6.16868e7 q^{84} +6.32074e6i q^{85} +(5.21116e6 - 1.93954e7i) q^{86} +1.18513e8 q^{87} +6.96057e7i q^{88} +9.46713e6i q^{89} +2.38941e7 q^{90} +2.11841e7i q^{91} -8.58366e7 q^{92} +1.67059e7i q^{93} +5.09716e6i q^{94} +1.16314e8 q^{95} -1.09176e8 q^{96} -1.54639e8 q^{97} -953454. i q^{98} -1.61934e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			5.87436i			0.367148i	0.983006	+	0.183574i	$0.0587666\pi$
$2$			5.87436i			0.367148i	−0.983006	+	0.183574i	$0.941233\pi$
$3$			114.397i			1.41230i	0.708061	+	0.706152i	$0.249570\pi$
$3$			114.397i			1.41230i	−0.708061	+	0.706152i	$0.750430\pi$
$4$	221.492			0.865203
$5$			623.321i			0.997313i	0.866800	+	0.498657i	$0.166173\pi$
$5$			623.321i			0.997313i	−0.866800	+	0.498657i	$0.833827\pi$
$6$	−672.007			−0.518524
$7$			2434.57i			1.01398i	0.861952	+	0.506990i	$0.169242\pi$
$7$			2434.57i			1.01398i	−0.861952	+	0.506990i	$0.830758\pi$
$8$			2804.96i			0.684805i
$9$	−6525.57			−0.994601
$10$	−3661.61			−0.366161
$11$	24815.2			1.69491			0.847457	−	0.530864i	$-0.178133\pi$
$11$	24815.2			1.69491			0.847457	+	0.530864i	$0.178133\pi$
$12$			25337.9i			1.22193i
$13$	8701.41			0.304660			0.152330	−	0.988330i	$-0.451322\pi$
$13$	8701.41			0.304660			0.152330	+	0.988330i	$0.451322\pi$
$14$	−14301.5			−0.372280
$15$	−71305.8			−1.40851
$16$	40224.6			0.613778
$17$	10140.4			0.121412			0.0607059	−	0.998156i	$-0.480665\pi$
$17$	10140.4			0.121412			0.0607059	+	0.998156i	$0.480665\pi$
$18$		−	38333.6i		−	0.365165i
$19$		−	186604.i		−	1.43188i	−0.698163	−	0.715938i	$-0.745999\pi$
$19$		−	186604.i		−	1.43188i	0.698163	−	0.715938i	$-0.254001\pi$
$20$			138060.i			0.862878i
$21$	−278506.			−1.43205
$22$			145774.i			0.622284i
$23$	−387538.			−1.38485			−0.692426	−	0.721489i	$-0.743458\pi$
$23$	−387538.			−1.38485			−0.692426	+	0.721489i	$0.743458\pi$
$24$	−320878.			−0.967152
$25$	2096.22			0.00536632
$26$			51115.2i			0.111855i
$27$			4052.57i			0.00762562i
$28$			539236.i			0.877298i
$29$		−	1.03599e6i		−	1.46474i	−0.680905	−	0.732372i	$-0.738413\pi$
$29$		−	1.03599e6i		−	1.46474i	0.680905	−	0.732372i	$-0.261587\pi$
$30$		−	418876.i		−	0.517131i
$31$	146035.			0.158128			0.0790640	−	0.996870i	$-0.474807\pi$
$31$	146035.			0.158128			0.0790640	+	0.996870i	$0.474807\pi$
$32$			954363.i			0.910152i
$33$			2.83878e6i			2.39373i
$34$			59568.6i			0.0445761i
$35$	−1.51752e6			−1.01126
$36$	−1.44536e6			−0.860531
$37$		−	2.77780e6i		−	1.48216i	−0.671418	−	0.741079i	$-0.734314\pi$
$37$		−	2.77780e6i		−	1.48216i	0.671418	−	0.741079i	$-0.265686\pi$
$38$	1.09618e6			0.525710
$39$			995411.i			0.430273i
$40$	−1.74839e6			−0.682965
$41$	89036.0			0.0315087			0.0157543	−	0.999876i	$-0.494985\pi$
$41$	89036.0			0.0315087			0.0157543	+	0.999876i	$0.494985\pi$
$42$		−	1.63604e6i		−	0.525773i
$43$	−3.30170e6	−	887103.i	−0.965749	−	0.259478i
$43$	−3.30170e6	−	887103.i	−0.965749	−	0.259478i
$44$	5.49637e6			1.46644
$45$		−	4.06753e6i		−	0.991928i
$46$		−	2.27654e6i		−	0.508445i
$47$	867696.			0.177818			0.0889090	−	0.996040i	$-0.471662\pi$
$47$	867696.			0.177818			0.0889090	+	0.996040i	$0.471662\pi$
$48$			4.60155e6i			0.866841i
$49$	−162308.			−0.0281550
$50$			12314.0i			0.00197023i
$51$			1.16003e6i			0.171470i
$52$	1.92729e6			0.263593
$53$	1.05861e7			1.34164			0.670818	−	0.741622i	$-0.265943\pi$
$53$	1.05861e7			1.34164			0.670818	+	0.741622i	$0.265943\pi$
$54$	−23806.3			−0.00279973
$55$			1.54678e7i			1.69036i
$56$	−6.82886e6			−0.694378
$57$	2.13468e7			2.02224
$58$	6.08576e6			0.537777
$59$	1.99430e7			1.64582			0.822911	−	0.568171i	$-0.192349\pi$
$59$	1.99430e7			1.64582			0.822911	+	0.568171i	$0.192349\pi$
$60$	−1.57936e7			−1.21865
$61$		−	9.32889e6i		−	0.673769i	−0.941546	−	0.336884i	$-0.890627\pi$
$61$		−	9.32889e6i		−	0.673769i	0.941546	−	0.336884i	$-0.109373\pi$
$62$			857860.i			0.0580563i
$63$		−	1.58869e7i		−	1.00850i
$64$	4.69121e6			0.279618
$65$			5.42377e6i			0.303842i
$66$	−1.66760e7			−0.878853
$67$	−1.83542e7			−0.910830			−0.455415	−	0.890279i	$-0.650509\pi$
$67$	−1.83542e7			−0.910830			−0.455415	+	0.890279i	$0.650509\pi$
$68$	2.24602e6			0.105046
$69$		−	4.43330e7i		−	1.95583i
$70$		−	8.91443e6i		−	0.371280i
$71$			8.73139e6i			0.343598i	0.985132	+	0.171799i	$0.0549579\pi$
$71$			8.73139e6i			0.343598i	−0.985132	+	0.171799i	$0.945042\pi$
$72$		−	1.83040e7i		−	0.681107i
$73$			3.39275e7i			1.19470i	0.801980	+	0.597351i	$0.203780\pi$
$73$			3.39275e7i			1.19470i	−0.801980	+	0.597351i	$0.796220\pi$
$74$	1.63178e7			0.544171
$75$			239800.i			0.00757888i
$76$		−	4.13312e7i		−	1.23886i
$77$			6.04143e7i			1.71861i
$78$	−5.84741e6			−0.157974
$79$	2.74337e7			0.704331			0.352165	−	0.935938i	$-0.385445\pi$
$79$	2.74337e7			0.704331			0.352165	+	0.935938i	$0.385445\pi$
$80$			2.50728e7i			0.612129i
$81$	−4.32779e7			−1.00537
$82$			523029.i			0.0115683i
$83$	−6.16851e7			−1.29977			−0.649887	−	0.760031i	$-0.725184\pi$
$83$	−6.16851e7			−1.29977			−0.649887	+	0.760031i	$0.725184\pi$
$84$	−6.16868e7			−1.23901
$85$			6.32074e6i			0.121086i
$86$	5.21116e6	−	1.93954e7i	0.0952666	−	0.354572i
$87$	1.18513e8			2.06866
$88$			6.96057e7i			1.16068i
$89$			9.46713e6i			0.150889i	0.997150	+	0.0754446i	$0.0240376\pi$
$89$			9.46713e6i			0.150889i	−0.997150	+	0.0754446i	$0.975962\pi$
$90$	2.38941e7			0.364184
$91$			2.11841e7i			0.308920i
$92$	−8.58366e7			−1.19818
$93$			1.67059e7i			0.223325i
$94$			5.09716e6i			0.0652855i
$95$	1.16314e8			1.42803
$96$	−1.09176e8			−1.28541
$97$	−1.54639e8			−1.74675			−0.873377	−	0.487044i	$-0.838075\pi$
$97$	−1.54639e8			−1.74675			−0.873377	+	0.487044i	$0.838075\pi$
$98$		−	953454.i		−	0.0103370i
$99$	−1.61934e8			−1.68576
$100$	464296.			0.00464296
$101$	8.21423e7			0.789372			0.394686	−	0.918816i	$-0.370853\pi$
$101$	8.21423e7			0.789372			0.394686	+	0.918816i	$0.370853\pi$
$102$	−6.81444e6			−0.0629549
$103$	1.77239e7			0.157475			0.0787373	−	0.996895i	$-0.474911\pi$
$103$	1.77239e7			0.157475			0.0787373	+	0.996895i	$0.474911\pi$
$104$			2.44071e7i			0.208633i
$105$		−	1.73599e8i		−	1.42820i
$106$			6.21869e7i			0.492578i
$107$	8.41719e7			0.642143			0.321072	−	0.947055i	$-0.395957\pi$
$107$	8.41719e7			0.642143			0.321072	+	0.947055i	$0.395957\pi$
$108$			897611.i			0.00659771i
$109$	−7.25493e7			−0.513958			−0.256979	−	0.966417i	$-0.582727\pi$
$109$	−7.25493e7			−0.513958			−0.256979	+	0.966417i	$0.582727\pi$
$110$	−9.08638e7			−0.620612
$111$	3.17771e8			2.09326
$112$			9.79293e7i			0.622359i
$113$		−	2.18133e8i		−	1.33785i	−0.743331	−	0.668924i	$-0.766755\pi$
$113$		−	2.18133e8i		−	1.33785i	0.743331	−	0.668924i	$-0.233245\pi$
$114$			1.25399e8i			0.742462i
$115$		−	2.41561e8i		−	1.38113i
$116$		−	2.29462e8i		−	1.26730i
$117$	−5.67817e7			−0.303015
$118$			1.17152e8i			0.604260i
$119$			2.46876e7i			0.123109i
$120$		−	2.00010e8i		−	0.964553i
$121$	4.01437e8			1.87273
$122$	5.48013e7			0.247373
$123$			1.01854e7i			0.0444998i
$124$	3.23455e7			0.136813
$125$			2.44791e8i			1.00267i
$126$	9.33256e7			0.370270
$127$	−1.63395e8			−0.628093			−0.314047	−	0.949408i	$-0.601685\pi$
$127$	−1.63395e8			−0.628093			−0.314047	+	0.949408i	$0.601685\pi$
$128$			2.71875e8i			1.01281i
$129$	1.01482e8	−	3.77704e8i	0.366461	−	1.36393i
$130$	−3.18612e7			−0.111555
$131$			1.37699e8i			0.467567i	0.972289	+	0.233784i	$0.0751108\pi$
$131$			1.37699e8i			0.467567i	−0.972289	+	0.233784i	$0.924889\pi$
$132$			6.28766e8i			2.07106i
$133$	4.54299e8			1.45189
$134$		−	1.07819e8i		−	0.334409i
$135$	−2.52605e6			−0.00760513
$136$			2.84435e7i			0.0831434i
$137$			2.58691e8i			0.734345i	0.930153	+	0.367172i	$0.119674\pi$
$137$			2.58691e8i			0.734345i	−0.930153	+	0.367172i	$0.880326\pi$
$138$	2.60428e8			0.718078
$139$	−4.65272e8			−1.24637			−0.623185	−	0.782074i	$-0.714162\pi$
$139$	−4.65272e8			−1.24637			−0.623185	+	0.782074i	$0.714162\pi$
$140$	−3.36117e8			−0.874941
$141$			9.92614e7i			0.251133i
$142$	−5.12914e7			−0.126151
$143$	2.15927e8			0.516373
$144$	−2.62488e8			−0.610464
$145$	6.45751e8			1.46081
$146$	−1.99302e8			−0.438632
$147$		−	1.85674e7i		−	0.0397633i
$148$		−	6.15261e8i		−	1.28237i
$149$		−	6.44932e8i		−	1.30849i	−0.756285	−	0.654243i	$-0.772988\pi$
$149$		−	6.44932e8i		−	1.30849i	0.756285	−	0.654243i	$-0.227012\pi$
$150$	−1.40867e6			−0.00278257
$151$		−	1.88178e8i		−	0.361961i	−0.983487	−	0.180980i	$-0.942073\pi$
$151$		−	1.88178e8i		−	0.361961i	0.983487	−	0.180980i	$-0.0579271\pi$
$152$	5.23416e8			0.980556
$153$	−6.61722e7			−0.120756
$154$	−3.54896e8			−0.630983
$155$			9.10264e7i			0.157703i
$156$			2.20475e8i			0.372273i
$157$		−	7.61809e8i		−	1.25386i	−0.779077	−	0.626928i	$-0.784312\pi$
$157$		−	7.61809e8i		−	1.25386i	0.779077	−	0.626928i	$-0.215688\pi$
$158$			1.61156e8i			0.258593i
$159$			1.21102e9i			1.89480i
$160$	−5.94875e8			−0.907707
$161$		−	9.43487e8i		−	1.40421i
$162$		−	2.54230e8i		−	0.369119i
$163$			3.05982e8i			0.433456i	0.976232	+	0.216728i	$0.0695385\pi$
$163$			3.05982e8i			0.433456i	−0.976232	+	0.216728i	$0.930462\pi$
$164$	1.97207e7			0.0272614
$165$	−1.76947e9			−2.38730
$166$		−	3.62361e8i		−	0.477209i
$167$	4.61955e8			0.593928			0.296964	−	0.954889i	$-0.404026\pi$
$167$	4.61955e8			0.593928			0.296964	+	0.954889i	$0.404026\pi$
$168$		−	7.81198e8i		−	0.980673i
$169$	−7.40016e8			−0.907182
$170$	−3.71303e7			−0.0444563
$171$			1.21770e9i			1.42415i
$172$	−7.31301e8	−	1.96486e8i	−0.835569	−	0.224501i
$173$	−4.46260e8			−0.498199			−0.249100	−	0.968478i	$-0.580135\pi$
$173$	−4.46260e8			−0.498199			−0.249100	+	0.968478i	$0.580135\pi$
$174$			6.96190e8i			0.759505i
$175$			5.10338e6i			0.00544134i
$176$	9.98182e8			1.04030
$177$			2.28141e9i			2.32440i
$178$	−5.56133e7			−0.0553986
$179$			1.17123e9i			1.14085i	0.821350	+	0.570425i	$0.193221\pi$
$179$			1.17123e9i			1.14085i	−0.821350	+	0.570425i	$0.806779\pi$
$180$		−	9.00924e8i		−	0.858219i
$181$	−1.36206e9			−1.26906			−0.634530	−	0.772898i	$-0.718806\pi$
$181$	−1.36206e9			−1.26906			−0.634530	+	0.772898i	$0.718806\pi$
$182$	−1.24443e8			−0.113419
$183$	1.06719e9			0.951566
$184$		−	1.08703e9i		−	0.948353i
$185$	1.73146e9			1.47818
$186$	−9.81362e7			−0.0819932
$187$	2.51637e8			0.205783
$188$	1.92188e8			0.153849
$189$	−9.86624e6			−0.00773223
$190$			6.83270e8i			0.524298i
$191$			1.08502e9i			0.815274i	0.913144	+	0.407637i	$0.133647\pi$
$191$			1.08502e9i			0.815274i	−0.913144	+	0.407637i	$0.866353\pi$
$192$			5.36659e8i			0.394905i
$193$	−1.56571e9			−1.12845			−0.564223	−	0.825622i	$-0.690824\pi$
$193$	−1.56571e9			−1.12845			−0.564223	+	0.825622i	$0.690824\pi$
$194$		−	9.08405e8i		−	0.641317i
$195$	−6.20460e8			−0.429117
$196$	−3.59498e7			−0.0243597
$197$	−5.30678e8			−0.352343			−0.176172	−	0.984359i	$-0.556371\pi$
$197$	−5.30678e8			−0.352343			−0.176172	+	0.984359i	$0.556371\pi$
$198$		−	9.51257e8i		−	0.618924i
$199$		−	3.44705e8i		−	0.219804i	−0.993942	−	0.109902i	$-0.964946\pi$
$199$		−	3.44705e8i		−	0.219804i	0.993942	−	0.109902i	$-0.0350537\pi$
$200$			5.87981e6i			0.00367488i
$201$		−	2.09966e9i		−	1.28637i
$202$			4.82534e8i			0.289816i
$203$	2.52218e9			1.48522
$204$			2.56937e8i			0.148357i
$205$			5.54980e7i			0.0314240i
$206$			1.04117e8i			0.0578164i
$207$	2.52891e9			1.37737
$208$	3.50010e8			0.186994
$209$		−	4.63061e9i		−	2.42691i
$210$	1.01978e9			0.524360
$211$		−	5.11802e8i		−	0.258209i	−0.991631	−	0.129105i	$-0.958790\pi$
$211$		−	5.11802e8i		−	0.258209i	0.991631	−	0.129105i	$-0.0412103\pi$
$212$	2.34475e9			1.16079
$213$	−9.98841e8			−0.485264
$214$			4.94456e8i			0.235761i
$215$	5.52950e8	−	2.05802e9i	0.258781	−	0.963154i
$216$	−1.13673e7			−0.00522206
$217$			3.55531e8i			0.160339i
$218$		−	4.26181e8i		−	0.188698i
$219$	−3.88118e9			−1.68728
$220$			3.42600e9i			1.46250i
$221$	8.82361e7			0.0369894
$222$			1.86670e9i			0.768534i
$223$			3.42233e9i			1.38389i	0.721949	+	0.691947i	$0.243247\pi$
$223$			3.42233e9i			1.38389i	−0.721949	+	0.691947i	$0.756753\pi$
$224$	−2.32346e9			−0.922876
$225$	−1.36790e7			−0.00533735
$226$	1.28139e9			0.491188
$227$		−	6.00502e8i		−	0.226158i	−0.993586	−	0.113079i	$-0.963929\pi$
$227$		−	6.00502e8i		−	0.226158i	0.993586	−	0.113079i	$-0.0360713\pi$
$228$	4.72815e9			1.74965
$229$	2.23823e9			0.813883			0.406942	−	0.913454i	$-0.366595\pi$
$229$	2.23823e9			0.813883			0.406942	+	0.913454i	$0.366595\pi$
$230$	1.41901e9			0.507079
$231$	−6.91119e9			−2.42720
$232$	2.90590e9			1.00306
$233$		−	2.27230e9i		−	0.770978i	−0.922712	−	0.385489i	$-0.874033\pi$
$233$		−	2.27230e9i		−	0.770978i	0.922712	−	0.385489i	$-0.125967\pi$
$234$		−	3.33556e8i		−	0.111251i
$235$			5.40853e8i			0.177340i
$236$	4.41722e9			1.42397
$237$			3.13833e9i			0.994729i
$238$	−1.45024e8			−0.0451992
$239$	3.04573e9			0.933468			0.466734	−	0.884398i	$-0.345431\pi$
$239$	3.04573e9			0.933468			0.466734	+	0.884398i	$0.345431\pi$
$240$	−2.86824e9			−0.864512
$241$			3.05625e9i			0.905984i	0.891515	+	0.452992i	$0.149643\pi$
$241$			3.05625e9i			0.905984i	−0.891515	+	0.452992i	$0.850357\pi$
$242$			2.35819e9i			0.687569i
$243$		−	4.92425e9i		−	1.41226i
$244$		−	2.06627e9i		−	0.582946i
$245$		−	1.01170e8i		−	0.0280793i
$246$	−5.98328e7			−0.0163380
$247$		−	1.62371e9i		−	0.436236i
$248$			4.09621e8i			0.108287i
$249$		−	7.05657e9i		−	1.83568i
$250$	−1.43799e9			−0.368126
$251$	−2.03301e9			−0.512206			−0.256103	−	0.966650i	$-0.582439\pi$
$251$	−2.03301e9			−0.512206			−0.256103	+	0.966650i	$0.582439\pi$
$252$		−	3.51883e9i		−	0.872561i
$253$	−9.61685e9			−2.34720
$254$		−	9.59842e8i		−	0.230603i
$255$	−7.23071e8			−0.171010
$256$	−3.96142e8			−0.0922339
$257$			7.06887e9i			1.62038i	0.586166	+	0.810191i	$0.300637\pi$
$257$			7.06887e9i			1.62038i	−0.586166	+	0.810191i	$0.699363\pi$
$258$	2.21877e9	+	5.96139e8i	0.500764	+	0.134545i
$259$	6.76274e9			1.50288
$260$			1.20132e9i			0.262885i
$261$			6.76040e9i			1.45684i
$262$	−8.08891e8			−0.171666
$263$		−	5.55283e9i		−	1.16062i	−0.814394	−	0.580312i	$-0.802931\pi$
$263$		−	5.55283e9i		−	1.16062i	0.814394	−	0.580312i	$-0.197069\pi$
$264$	−7.96266e9			−1.63924
$265$			6.59856e9i			1.33803i
$266$			2.66872e9i			0.533060i
$267$	−1.08301e9			−0.213101
$268$	−4.06532e9			−0.788052
$269$	9.84458e9			1.88013			0.940066	−	0.340993i	$-0.110763\pi$
$269$	9.84458e9			1.88013			0.940066	+	0.340993i	$0.110763\pi$
$270$		−	1.48389e7i		−	0.00279221i
$271$	−3.61617e9			−0.670457			−0.335229	−	0.942137i	$-0.608814\pi$
$271$	−3.61617e9			−0.670457			−0.335229	+	0.942137i	$0.608814\pi$
$272$	4.07895e8			0.0745199
$273$	−2.42339e9			−0.436288
$274$	−1.51965e9			−0.269613
$275$	5.20182e7			0.00909545
$276$		−	9.81941e9i		−	1.69219i
$277$			3.11399e9i			0.528931i	0.964395	+	0.264465i	$0.0851955\pi$
$277$			3.11399e9i			0.528931i	−0.964395	+	0.264465i	$0.914805\pi$
$278$		−	2.73317e9i		−	0.457602i
$279$	−9.52959e8			−0.157274
$280$		−	4.25657e9i		−	0.692513i
$281$	−9.27076e9			−1.48693			−0.743464	−	0.668776i	$-0.766819\pi$
$281$	−9.27076e9			−1.48693			−0.743464	+	0.668776i	$0.766819\pi$
$282$	−5.83097e8			−0.0922029
$283$	−4.58820e9			−0.715314			−0.357657	−	0.933853i	$-0.616424\pi$
$283$	−4.58820e9			−0.715314			−0.357657	+	0.933853i	$0.616424\pi$
$284$			1.93393e9i			0.297282i
$285$			1.33059e10i			2.01681i
$286$			1.26844e9i			0.189585i
$287$			2.16764e8i			0.0319491i
$288$		−	6.22777e9i		−	0.905238i
$289$	−6.87293e9			−0.985259
$290$			3.79338e9i			0.536333i
$291$		−	1.76902e10i		−	2.46695i
$292$			7.51465e9i			1.03366i
$293$	4.17635e9			0.566665			0.283332	−	0.959022i	$-0.408560\pi$
$293$	4.17635e9			0.566665			0.283332	+	0.959022i	$0.408560\pi$
$294$	1.09072e8			0.0145990
$295$			1.24309e10i			1.64140i
$296$	7.79163e9			1.01499
$297$			1.00565e8i			0.0129248i
$298$	3.78856e9			0.480407
$299$	−3.37213e9			−0.421909
$300$			5.31138e7i			0.00655726i
$301$	2.15971e9	−	8.03821e9i	0.263105	−	0.979250i
$302$	1.10543e9			0.132893
$303$			9.39680e9i			1.11483i
$304$		−	7.50605e9i		−	0.878855i
$305$	5.81489e9			0.671958
$306$		−	3.88719e8i		−	0.0443354i
$307$	1.21829e10			1.37151			0.685755	−	0.727833i	$-0.259472\pi$
$307$	1.21829e10			1.37151			0.685755	+	0.727833i	$0.259472\pi$
$308$			1.33813e10i			1.48694i
$309$			2.02755e9i			0.222402i
$310$	−5.34722e8			−0.0579004
$311$	4.50189e9			0.481230			0.240615	−	0.970621i	$-0.422651\pi$
$311$	4.50189e9			0.481230			0.240615	+	0.970621i	$0.422651\pi$
$312$	−2.79209e9			−0.294653
$313$		−	4.06436e9i		−	0.423462i	−0.977328	−	0.211731i	$-0.932090\pi$
$313$		−	4.06436e9i		−	0.423462i	0.977328	−	0.211731i	$-0.0679101\pi$
$314$	4.47514e9			0.460350
$315$	9.90266e9			1.00580
$316$	6.07635e9			0.609389
$317$	1.19109e9			0.117953			0.0589763	−	0.998259i	$-0.481216\pi$
$317$	1.19109e9			0.117953			0.0589763	+	0.998259i	$0.481216\pi$
$318$	−7.11396e9			−0.695670
$319$		−	2.57082e10i		−	2.48262i
$320$			2.92413e9i			0.278867i
$321$			9.62897e9i			0.906901i
$322$	5.54239e9			0.515553
$323$		−	1.89224e9i		−	0.173847i
$324$	−9.58570e9			−0.869849
$325$	1.82401e7			0.00163491
$326$	−1.79745e9			−0.159142
$327$		−	8.29939e9i		−	0.725864i
$328$			2.49742e8i			0.0215773i
$329$			2.11246e9i			0.180304i
$330$		−	1.03945e10i		−	0.876492i
$331$		−	2.05943e10i		−	1.71567i	−0.513923	−	0.857836i	$-0.671808\pi$
$331$		−	2.05943e10i		−	1.71567i	0.513923	−	0.857836i	$-0.328192\pi$
$332$	−1.36628e10			−1.12457
$333$			1.81268e10i			1.47416i
$334$			2.71369e9i			0.218059i
$335$		−	1.14406e10i		−	0.908383i
$336$	−1.12028e10			−0.878959
$337$	−1.99136e10			−1.54394			−0.771969	−	0.635660i	$-0.780728\pi$
$337$	−1.99136e10			−1.54394			−0.771969	+	0.635660i	$0.780728\pi$
$338$		−	4.34712e9i		−	0.333070i
$339$	2.49536e10			1.88945
$340$			1.39999e9i			0.104764i
$341$	3.62388e9			0.268013
$342$	−7.15319e9			−0.522872
$343$			1.36396e10i			0.985431i
$344$	2.48829e9	−	9.26115e9i	0.177692	−	0.661350i
$345$	2.76337e10			1.95058
$346$		−	2.62149e9i		−	0.182913i
$347$		−	2.86452e10i		−	1.97576i	−0.155233	−	0.987878i	$-0.549613\pi$
$347$		−	2.86452e10i		−	1.97576i	0.155233	−	0.987878i	$-0.450387\pi$
$348$	2.62497e10			1.78981
$349$			1.74936e10i			1.17917i	0.807706	+	0.589585i	$0.200709\pi$
$349$			1.74936e10i			1.17917i	−0.807706	+	0.589585i	$0.799291\pi$
$350$	−2.99791e7			−0.00199778
$351$			3.52630e7i			0.00232323i
$352$			2.36828e10i			1.54263i
$353$	2.64209e10			1.70156			0.850782	−	0.525519i	$-0.176129\pi$
$353$	2.64209e10			1.70156			0.850782	+	0.525519i	$0.176129\pi$
$354$	−1.34018e10			−0.853398
$355$	−5.44246e9			−0.342674
$356$			2.09689e9i			0.130550i
$357$	−2.82417e9			−0.173867
$358$	−6.88020e9			−0.418860
$359$	5.08982e9			0.306425			0.153213	−	0.988193i	$-0.451038\pi$
$359$	5.08982e9			0.306425			0.153213	+	0.988193i	$0.451038\pi$
$360$	1.14092e10			0.679277
$361$	−1.78373e10			−1.05027
$362$		−	8.00124e9i		−	0.465933i
$363$			4.59230e10i			2.64487i
$364$			4.69212e9i			0.267278i
$365$	−2.11477e10			−1.19149
$366$			6.26908e9i			0.349365i
$367$	2.73675e10			1.50859			0.754294	−	0.656537i	$-0.227979\pi$
$367$	2.73675e10			1.50859			0.754294	+	0.656537i	$0.227979\pi$
$368$	−1.55886e10			−0.849992
$369$	−5.81011e8			−0.0313385
$370$			1.01712e10i			0.542709i
$371$			2.57727e10i			1.36039i
$372$			3.70021e9i			0.193221i
$373$		−	2.95512e10i		−	1.52665i	−0.646013	−	0.763326i	$-0.723565\pi$
$373$		−	2.95512e10i		−	1.52665i	0.646013	−	0.763326i	$-0.276435\pi$
$374$			1.47821e9i			0.0755526i
$375$	−2.80033e10			−1.41607
$376$			2.43385e9i			0.121771i
$377$		−	9.01453e9i		−	0.446250i
$378$		−	5.79579e7i		−	0.00283887i
$379$	3.25095e10			1.57563			0.787815	−	0.615912i	$-0.211212\pi$
$379$	3.25095e10			1.57563			0.787815	+	0.615912i	$0.211212\pi$
$380$	2.57626e10			1.23554
$381$		−	1.86918e10i		−	0.887058i
$382$	−6.37379e9			−0.299326
$383$		−	9.61425e9i		−	0.446807i	−0.974726	−	0.223404i	$-0.928283\pi$
$383$		−	9.61425e9i		−	0.446807i	0.974726	−	0.223404i	$-0.0717168\pi$
$384$	−3.11016e10			−1.43040
$385$	−3.76575e10			−1.71399
$386$		−	9.19753e9i		−	0.414307i
$387$	2.15455e10	+	5.78886e9i	0.960535	+	0.258077i
$388$	−3.42513e10			−1.51130
$389$		−	1.61948e10i		−	0.707259i	−0.935386	−	0.353629i	$-0.884947\pi$
$389$		−	1.61948e10i		−	0.707259i	0.935386	−	0.353629i	$-0.115053\pi$
$390$		−	3.64481e9i		−	0.157549i
$391$	−3.92981e9			−0.168137
$392$		−	4.55267e8i		−	0.0192806i
$393$	−1.57522e10			−0.660347
$394$		−	3.11739e9i		−	0.129362i
$395$			1.71000e10i			0.702439i
$396$	−3.58670e10			−1.45853
$397$	−8.23528e9			−0.331525			−0.165762	−	0.986166i	$-0.553009\pi$
$397$	−8.23528e9			−0.331525			−0.165762	+	0.986166i	$0.553009\pi$
$398$	2.02492e9			0.0807005
$399$			5.19702e10i			2.05051i
$400$	8.43195e7			0.00329373
$401$	−2.90216e10			−1.12239			−0.561194	−	0.827684i	$-0.689658\pi$
$401$	−2.90216e10			−1.12239			−0.561194	+	0.827684i	$0.689658\pi$
$402$	1.23342e10			0.472287
$403$	1.27071e9			0.0481754
$404$	1.81939e10			0.682967
$405$		−	2.69760e10i		−	1.00267i
$406$			1.48162e10i			0.545295i
$407$		−	6.89318e10i		−	2.51213i
$408$	−3.25384e9			−0.117424
$409$		−	3.99243e10i		−	1.42674i	−0.700788	−	0.713369i	$-0.747168\pi$
$409$		−	3.99243e10i		−	1.42674i	0.700788	−	0.713369i	$-0.252832\pi$
$410$	−3.26015e8			−0.0115373
$411$	−2.95934e10			−1.03712
$412$	3.92570e9			0.136247
$413$			4.85526e10i			1.66883i
$414$			1.48557e10i			0.505700i
$415$		−	3.84496e10i		−	1.29628i
$416$			8.30431e9i			0.277287i
$417$		−	5.32255e10i		−	1.76025i
$418$	2.72019e10			0.891033
$419$			2.61104e10i			0.847144i	0.905863	+	0.423572i	$0.139224\pi$
$419$			2.61104e10i			0.847144i	−0.905863	+	0.423572i	$0.860776\pi$
$420$		−	3.84507e10i		−	1.23568i
$421$			1.77984e10i			0.566569i	0.959036	+	0.283284i	$0.0914240\pi$
$421$			1.77984e10i			0.566569i	−0.959036	+	0.283284i	$0.908576\pi$
$422$	3.00651e9			0.0948009
$423$	−5.66221e9			−0.176858
$424$			2.96937e10i			0.918758i
$425$	2.12566e7			0.000651535
$426$		−	5.86756e9i		−	0.178164i
$427$	2.27118e10			0.683188
$428$	1.86434e10			0.555584
$429$			2.47014e10i			0.729276i
$430$	1.20896e10	+	3.24823e9i	0.353620	+	0.0950107i
$431$	7.12863e9			0.206584			0.103292	−	0.994651i	$-0.467062\pi$
$431$	7.12863e9			0.206584			0.103292	+	0.994651i	$0.467062\pi$
$432$			1.63013e8i			0.00468044i
$433$		−	2.26003e10i		−	0.642928i	−0.946922	−	0.321464i	$-0.895825\pi$
$433$		−	2.26003e10i		−	0.642928i	0.946922	−	0.321464i	$-0.104175\pi$
$434$	−2.08852e9			−0.0588680
$435$			7.38718e10i			2.06311i
$436$	−1.60691e10			−0.444678
$437$			7.23160e10i			1.98294i
$438$		−	2.27995e10i		−	0.619482i
$439$	5.85076e10			1.57527			0.787633	−	0.616144i	$-0.211306\pi$
$439$	5.85076e10			1.57527			0.787633	+	0.616144i	$0.211306\pi$
$440$	−4.33867e10			−1.15757
$441$	1.05915e9			0.0280029
$442$			5.18331e8i			0.0135806i
$443$	−3.14896e10			−0.817621			−0.408810	−	0.912619i	$-0.634056\pi$
$443$	−3.14896e10			−0.817621			−0.408810	+	0.912619i	$0.634056\pi$
$444$	7.03837e10			1.81109
$445$	−5.90106e9			−0.150484
$446$	−2.01040e10			−0.508093
$447$	7.37780e10			1.84798
$448$			1.14211e10i			0.283527i
$449$			7.24862e10i			1.78349i	0.452540	+	0.891744i	$0.350518\pi$
$449$			7.24862e10i			1.78349i	−0.452540	+	0.891744i	$0.649482\pi$
$450$		−	8.03556e7i		−	0.00195959i
$451$	2.20945e9			0.0534045
$452$		−	4.83146e10i		−	1.15751i
$453$	2.15269e10			0.511199
$454$	3.52757e9			0.0830332
$455$	−1.32045e10			−0.308090
$456$			5.98770e10i			1.38484i
$457$		−	3.18344e10i		−	0.729846i	−0.931038	−	0.364923i	$-0.881095\pi$
$457$		−	3.18344e10i		−	0.729846i	0.931038	−	0.364923i	$-0.118905\pi$
$458$			1.31482e10i			0.298815i
$459$			4.10948e7i			0.000925841i
$460$		−	5.35037e10i		−	1.19496i
$461$	2.31271e10			0.512055			0.256028	−	0.966669i	$-0.417586\pi$
$461$	2.31271e10			0.512055			0.256028	+	0.966669i	$0.417586\pi$
$462$		−	4.05988e10i		−	0.891139i
$463$		−	3.12379e10i		−	0.679764i	−0.940468	−	0.339882i	$-0.889613\pi$
$463$		−	3.12379e10i		−	0.679764i	0.940468	−	0.339882i	$-0.110387\pi$
$464$		−	4.16721e10i		−	0.899028i
$465$	−1.04131e10			−0.222725
$466$	1.33483e10			0.283063
$467$			8.61020e9i			0.181028i	0.995895	+	0.0905140i	$0.0288510\pi$
$467$			8.61020e9i			0.181028i	−0.995895	+	0.0905140i	$0.971149\pi$
$468$	−1.25767e10			−0.262170
$469$		−	4.46846e10i		−	0.923563i
$470$	−3.17716e9			−0.0651101
$471$	8.71484e10			1.77083
$472$			5.59394e10i			1.12707i
$473$	−8.19325e10	−	2.20137e10i	−1.63686	−	0.439792i
$474$	−1.84357e10			−0.365212
$475$		−	3.91162e8i		−	0.00768391i
$476$			5.46809e9i			0.106514i
$477$	−6.90807e10			−1.33439
$478$			1.78917e10i			0.342721i
$479$	−4.39993e10			−0.835803			−0.417902	−	0.908492i	$-0.637234\pi$
$479$	−4.39993e10			−0.835803			−0.417902	+	0.908492i	$0.637234\pi$
$480$		−	6.80516e10i		−	1.28196i
$481$		−	2.41708e10i		−	0.451555i
$482$	−1.79535e10			−0.332630
$483$	1.07932e11			1.98317
$484$	8.89150e10			1.62029
$485$		−	9.63897e10i		−	1.74206i
$486$	2.89268e10			0.518509
$487$	−8.06027e9			−0.143296			−0.0716479	−	0.997430i	$-0.522826\pi$
$487$	−8.06027e9			−0.143296			−0.0716479	+	0.997430i	$0.522826\pi$
$488$	2.61672e10			0.461400
$489$	−3.50033e10			−0.612171
$490$	5.94308e8			0.0103093
$491$			9.23725e10i			1.58934i	0.607042	+	0.794670i	$0.292356\pi$
$491$			9.23725e10i			1.58934i	−0.607042	+	0.794670i	$0.707644\pi$
$492$			2.25599e9i			0.0385013i
$493$		−	1.05053e10i		−	0.177837i
$494$	9.53828e9			0.160163
$495$		−	1.00937e11i		−	1.68123i
$496$	5.87418e9			0.0970555
$497$	−2.12571e10			−0.348401
$498$	4.14528e10			0.673964
$499$			9.81123e10i			1.58242i	0.611546	+	0.791209i	$0.290548\pi$
$499$			9.81123e10i			1.58242i	−0.611546	+	0.791209i	$0.709452\pi$
$500$			5.42193e10i			0.867508i
$501$			5.28461e10i			0.838807i
$502$		−	1.19426e10i		−	0.188055i
$503$		−	9.29511e9i		−	0.145205i	−0.997361	−	0.0726027i	$-0.976869\pi$
$503$		−	9.29511e9i		−	0.145205i	0.997361	−	0.0726027i	$-0.0231305\pi$
$504$	4.45622e10			0.690629
$505$			5.12010e10i			0.787251i
$506$		−	5.64929e10i		−	0.861770i
$507$		−	8.46553e10i		−	1.28122i
$508$	−3.61907e10			−0.543428
$509$	−9.44904e10			−1.40772			−0.703860	−	0.710339i	$-0.748542\pi$
$509$	−9.44904e10			−1.40772			−0.703860	+	0.710339i	$0.748542\pi$
$510$		−	4.24758e9i		−	0.0627858i
$511$	−8.25986e10			−1.21140
$512$			6.72729e10i			0.978950i
$513$	7.56224e8			0.0109190
$514$	−4.15251e10			−0.594919
$515$			1.10477e10i			0.157051i
$516$	2.24773e10	−	8.36583e10i	0.317063	−	1.18008i
$517$	2.15321e10			0.301386
$518$			3.97268e10i			0.551778i
$519$		−	5.10506e10i		−	0.703609i
$520$	−1.52135e10			−0.208072
$521$			9.40814e10i			1.27689i	0.769668	+	0.638444i	$0.220422\pi$
$521$			9.40814e10i			1.27689i	−0.769668	+	0.638444i	$0.779578\pi$
$522$	−3.97131e10			−0.534874
$523$			4.56576e7i			0.000610248i	1.00000		0.000305124i	$9.71239e-5\pi$
$523$			4.56576e7i			0.000610248i	−1.00000		0.000305124i	$0.999903\pi$
$524$			3.04991e10i			0.404541i
$525$	−5.83810e8			−0.00768483
$526$	3.26193e10			0.426120
$527$	1.48085e9			0.0191986
$528$			1.14189e11i			1.46922i
$529$	7.18749e10			0.917813
$530$	−3.87624e10			−0.491255
$531$	−1.30140e11			−1.63694
$532$	1.00623e11			1.25618
$533$	7.74738e8			0.00959944
$534$		−	6.36198e9i		−	0.0782397i
$535$			5.24661e10i			0.640418i
$536$		−	5.14829e10i		−	0.623741i
$537$	−1.33984e11			−1.61123
$538$			5.78306e10i			0.690286i
$539$	−4.02770e9			−0.0477202
$540$	−5.59500e8			−0.00657998
$541$	−9.37761e10			−1.09472			−0.547360	−	0.836897i	$-0.684367\pi$
$541$	−9.37761e10			−1.09472			−0.547360	+	0.836897i	$0.684367\pi$
$542$		−	2.12427e10i		−	0.246157i
$543$		−	1.55815e11i		−	1.79230i
$544$			9.67766e9i			0.110503i
$545$		−	4.52215e10i		−	0.512577i
$546$		−	1.42359e10i		−	0.160182i
$547$	8.48538e10			0.947811			0.473906	−	0.880576i	$-0.342844\pi$
$547$	8.48538e10			0.947811			0.473906	+	0.880576i	$0.342844\pi$
$548$			5.72981e10i			0.635357i
$549$			6.08764e10i			0.670131i
$550$			3.05574e8i			0.00333937i
$551$	−1.93319e11			−2.09733
$552$	1.24352e11			1.33936
$553$			6.67893e10i			0.714177i
$554$	−1.82927e10			−0.194196
$555$			1.98073e11i			2.08763i
$556$	−1.03054e11			−1.07836
$557$	4.81386e10			0.500118			0.250059	−	0.968231i	$-0.419550\pi$
$557$	4.81386e10			0.500118			0.250059	+	0.968231i	$0.419550\pi$
$558$		−	5.59803e9i		−	0.0577429i
$559$	−2.87295e10	−	7.71904e9i	−0.294226	−	0.0790526i
$560$	−6.10414e10			−0.620687
$561$			2.87864e10i			0.290627i
$562$		−	5.44598e10i		−	0.545922i
$563$	5.17901e10			0.515482			0.257741	−	0.966214i	$-0.417022\pi$
$563$	5.17901e10			0.515482			0.257741	+	0.966214i	$0.417022\pi$
$564$			2.19856e10i			0.217281i
$565$	1.35967e11			1.33425
$566$		−	2.69528e10i		−	0.262626i
$567$		−	1.05363e11i		−	1.01943i
$568$	−2.44912e10			−0.235297
$569$	−2.44189e10			−0.232958			−0.116479	−	0.993193i	$-0.537161\pi$
$569$	−2.44189e10			−0.232958			−0.116479	+	0.993193i	$0.537161\pi$
$570$	−7.81637e10			−0.740467
$571$			1.70378e11i			1.60277i	0.598152	+	0.801383i	$0.295902\pi$
$571$			1.70378e11i			1.60277i	−0.598152	+	0.801383i	$0.704098\pi$
$572$	4.78262e10			0.446767
$573$	−1.24122e11			−1.15141
$574$	−1.27335e9			−0.0117301
$575$	−8.12365e8			−0.00743156
$576$	−3.06129e10			−0.278108
$577$		−	1.12467e11i		−	1.01466i	−0.861751	−	0.507332i	$-0.830632\pi$
$577$		−	1.12467e11i		−	1.01466i	0.861751	−	0.507332i	$-0.169368\pi$
$578$		−	4.03741e10i		−	0.361736i
$579$		−	1.79111e11i		−	1.59371i
$580$	1.43029e11			1.26390
$581$		−	1.50176e11i		−	1.31795i
$582$	1.03918e11			0.905734
$583$	2.62698e11			2.27396
$584$	−9.51652e10			−0.818138
$585$		−	3.53932e10i		−	0.302201i
$586$			2.45334e10i			0.208050i
$587$		−	2.80170e10i		−	0.235977i	−0.993015	−	0.117988i	$-0.962355\pi$
$587$		−	2.80170e10i		−	0.235977i	0.993015	−	0.117988i	$-0.0376446\pi$
$588$		−	4.11254e9i		−	0.0344033i
$589$		−	2.72506e10i		−	0.226420i
$590$	−7.30236e10			−0.602636
$591$		−	6.07077e10i		−	0.497616i
$592$		−	1.11736e11i		−	0.909716i
$593$			9.56213e10i			0.773278i	0.922231	+	0.386639i	$0.126364\pi$
$593$			9.56213e10i			0.773278i	−0.922231	+	0.386639i	$0.873636\pi$
$594$	−5.90758e8			−0.00474530
$595$	−1.53883e10			−0.122778
$596$		−	1.42847e11i		−	1.13210i
$597$	3.94331e10			0.310430
$598$		−	1.98091e10i		−	0.154903i
$599$	1.13123e11			0.878707			0.439353	−	0.898314i	$-0.355208\pi$
$599$	1.13123e11			0.878707			0.439353	+	0.898314i	$0.355208\pi$
$600$	−6.72630e8			−0.00519005
$601$		−	8.52889e10i		−	0.653724i	−0.945072	−	0.326862i	$-0.894009\pi$
$601$		−	8.52889e10i		−	0.653724i	0.945072	−	0.326862i	$-0.105991\pi$
$602$	4.72194e10	+	1.26869e10i	0.359529	+	0.0965985i
$603$	1.19772e11			0.905912
$604$		−	4.16799e10i		−	0.313169i
$605$			2.50224e11i			1.86770i
$606$	−5.52002e10			−0.409308
$607$			7.30935e9i			0.0538423i	0.999638	+	0.0269212i	$0.00857031\pi$
$607$			7.30935e9i			0.0538423i	−0.999638	+	0.0269212i	$0.991430\pi$
$608$	1.78088e11			1.30323
$609$			2.88528e11i			2.09758i
$610$			3.41588e10i			0.246708i
$611$	7.55017e9			0.0541741
$612$	−1.46566e10			−0.104479
$613$	−1.49080e11			−1.05579			−0.527895	−	0.849310i	$-0.677019\pi$
$613$	−1.49080e11			−1.05579			−0.527895	+	0.849310i	$0.677019\pi$
$614$			7.15670e10i			0.503547i
$615$	−6.34878e9			−0.0443802
$616$	−1.69460e11			−1.17691
$617$	3.12248e10			0.215456			0.107728	−	0.994180i	$-0.465642\pi$
$617$	3.12248e10			0.215456			0.107728	+	0.994180i	$0.465642\pi$
$618$	−1.19106e10			−0.0816543
$619$	−1.39975e11			−0.953429			−0.476715	−	0.879058i	$-0.658173\pi$
$619$	−1.39975e11			−0.953429			−0.476715	+	0.879058i	$0.658173\pi$
$620$			2.01616e10i			0.136445i
$621$		−	1.57053e9i		−	0.0105604i
$622$			2.64457e10i			0.176683i
$623$	−2.30483e10			−0.152999
$624$			4.00400e10i			0.264092i
$625$	−1.51765e11			−0.994605
$626$	2.38755e10			0.155473
$627$	5.29726e11			3.42753
$628$		−	1.68735e11i		−	1.08484i
$629$		−	2.81681e10i		−	0.179951i
$630$			5.81718e10i			0.369275i
$631$			1.57640e11i			0.994375i	0.867643	+	0.497188i	$0.165634\pi$
$631$			1.57640e11i			0.994375i	−0.867643	+	0.497188i	$0.834366\pi$
$632$			7.69506e10i			0.482329i
$633$	5.85483e10			0.364670
$634$			6.99689e9i			0.0433060i
$635$		−	1.01848e11i		−	0.626406i
$636$			2.68231e11i			1.63938i
$637$	−1.41231e9			−0.00857770
$638$	1.51019e11			0.911486
$639$		−	5.69774e10i		−	0.341742i
$640$	−1.69465e11			−1.01009
$641$		−	6.49048e10i		−	0.384454i	−0.981350	−	0.192227i	$-0.938429\pi$
$641$		−	6.49048e10i		−	0.384454i	0.981350	−	0.192227i	$-0.0615711\pi$
$642$	−5.65641e10			−0.332967
$643$	7.92194e10			0.463434			0.231717	−	0.972783i	$-0.425566\pi$
$643$	7.92194e10			0.463434			0.231717	+	0.972783i	$0.425566\pi$
$644$		−	2.08975e11i		−	1.21493i
$645$	2.35430e11	+	6.32555e10i	1.36027	+	0.365477i
$646$	1.11157e10			0.0638274
$647$		−	9.19245e10i		−	0.524583i	−0.964989	−	0.262291i	$-0.915522\pi$
$647$		−	9.19245e10i		−	0.524583i	0.964989	−	0.262291i	$-0.0844782\pi$
$648$		−	1.21393e11i		−	0.688482i
$649$	4.94891e11			2.78953
$650$			1.07149e8i			0.000600252i
$651$	−4.06715e10			−0.226447
$652$			6.77725e10i			0.375027i
$653$		−	2.05884e11i		−	1.13232i	−0.824295	−	0.566161i	$-0.808428\pi$
$653$		−	2.05884e11i		−	1.13232i	0.824295	−	0.566161i	$-0.191572\pi$
$654$	4.87536e10			0.266499
$655$	−8.58304e10			−0.466311
$656$	3.58143e9			0.0193393
$657$		−	2.21396e11i		−	1.18825i
$658$	−1.24094e10			−0.0661982
$659$	−3.07836e11			−1.63222			−0.816108	−	0.577899i	$-0.803873\pi$
$659$	−3.07836e11			−1.63222			−0.816108	+	0.577899i	$0.803873\pi$
$660$	−3.91923e11			−2.06550
$661$	1.12652e11			0.590108			0.295054	−	0.955481i	$-0.404662\pi$
$661$	1.12652e11			0.590108			0.295054	+	0.955481i	$0.404662\pi$
$662$	1.20978e11			0.629905
$663$			1.00939e10i			0.0522402i
$664$		−	1.73024e11i		−	0.890092i
$665$			2.83174e11i			1.44799i
$666$	−1.06483e11			−0.541233
$667$			4.01484e11i			2.02845i
$668$	1.02319e11			0.513868
$669$	−3.91503e11			−1.95448
$670$	6.72061e10			0.333511
$671$		−	2.31499e11i		−	1.14198i
$672$		−	2.65796e11i		−	1.30338i
$673$		−	8.41903e10i		−	0.410395i	−0.978721	−	0.205197i	$-0.934216\pi$
$673$		−	8.41903e10i		−	0.410395i	0.978721	−	0.205197i	$-0.0657836\pi$
$674$		−	1.16980e11i		−	0.566853i
$675$			8.49507e6i			4.09216e-5i
$676$	−1.63908e11			−0.784896
$677$			2.00105e11i			0.952583i	0.879287	+	0.476292i	$0.158019\pi$
$677$			2.00105e11i			0.952583i	−0.879287	+	0.476292i	$0.841981\pi$
$678$			1.46587e11i			0.693706i
$679$		−	3.76479e11i		−	1.77117i
$680$	−1.77294e10			−0.0829200
$681$	6.86954e10			0.319403
$682$			2.12880e10i			0.0984005i
$683$	1.23376e10			0.0566955			0.0283478	−	0.999598i	$-0.490975\pi$
$683$	1.23376e10			0.0566955			0.0283478	+	0.999598i	$0.490975\pi$
$684$			2.69710e11i			1.23217i
$685$	−1.61248e11			−0.732372
$686$	−8.01242e10			−0.361799
$687$			2.56046e11i			1.14945i
$688$	−1.32810e11	−	3.56833e10i	−0.592756	−	0.159262i
$689$	9.21144e10			0.408743
$690$			1.62330e11i			0.716149i
$691$			7.88294e9i			0.0345761i	0.999851	+	0.0172880i	$0.00550323\pi$
$691$			7.88294e9i			0.0345761i	−0.999851	+	0.0172880i	$0.994497\pi$
$692$	−9.88429e10			−0.431043
$693$		−	3.94238e11i		−	1.70933i
$694$	1.68272e11			0.725394
$695$		−	2.90013e11i		−	1.24302i
$696$			3.32425e11i			1.41663i
$697$	9.02863e8			0.00382552
$698$	−1.02764e11			−0.432930
$699$	2.59943e11			1.08885
$700$			1.13036e9i			0.00470786i
$701$	−2.09607e11			−0.868026			−0.434013	−	0.900907i	$-0.642903\pi$
$701$	−2.09607e11			−0.868026			−0.434013	+	0.900907i	$0.642903\pi$
$702$	−2.07148e8			−0.000852967
$703$	−5.18348e11			−2.12227
$704$	1.16414e11			0.473928
$705$	−6.18717e10			−0.250458
$706$			1.55206e11i			0.624725i
$707$			1.99981e11i			0.800407i
$708$			5.05314e11i			2.01108i
$709$	2.55986e11			1.01305			0.506525	−	0.862225i	$-0.330930\pi$
$709$	2.55986e11			1.01305			0.506525	+	0.862225i	$0.330930\pi$
$710$		−	3.19710e10i		−	0.125812i
$711$	−1.79021e11			−0.700528
$712$	−2.65549e10			−0.103330
$713$	−5.65940e10			−0.218984
$714$		−	1.65902e10i		−	0.0638350i
$715$			1.34592e11i			0.514986i
$716$			2.59417e11i			0.987066i
$717$			3.48421e11i			1.31834i
$718$			2.98994e10i			0.112503i
$719$	1.70885e11			0.639425			0.319712	−	0.947515i	$-0.396414\pi$
$719$	1.70885e11			0.639425			0.319712	+	0.947515i	$0.396414\pi$
$720$		−	1.63614e11i		−	0.608824i
$721$			4.31500e10i			0.159676i
$722$		−	1.04783e11i		−	0.385605i
$723$	−3.49624e11			−1.27952
$724$	−3.01685e11			−1.09799
$725$		−	2.17165e9i		−	0.00786029i
$726$	−2.69768e11			−0.971056
$727$		−	6.84993e10i		−	0.245216i	−0.992455	−	0.122608i	$-0.960874\pi$
$727$		−	6.84993e10i		−	0.245216i	0.992455	−	0.122608i	$-0.0391257\pi$
$728$	−5.94207e10			−0.211550
$729$	2.79371e11			0.989172
$730$		−	1.24229e11i		−	0.437454i
$731$	−3.34807e10	−	8.99561e9i	−0.117253	−	0.0315037i
$732$	2.36375e11			0.823297
$733$		−	3.03637e11i		−	1.05181i	−0.850542	−	0.525907i	$-0.823726\pi$
$733$		−	3.03637e11i		−	1.05181i	0.850542	−	0.525907i	$-0.176274\pi$
$734$			1.60767e11i			0.553874i
$735$	1.15735e10			0.0396565
$736$		−	3.69852e11i		−	1.26043i
$737$	−4.55465e11			−1.54378
$738$		−	3.41307e9i		−	0.0115059i
$739$		−	2.59994e11i		−	0.871738i	−0.900010	−	0.435869i	$-0.856441\pi$
$739$		−	2.59994e11i		−	0.871738i	0.900010	−	0.435869i	$-0.143559\pi$
$740$	3.83505e11			1.27892
$741$	1.85747e11			0.616098
$742$	−1.51398e11			−0.499464
$743$		−	3.83121e11i		−	1.25713i	−0.777757	−	0.628565i	$-0.783643\pi$
$743$		−	3.83121e11i		−	1.25713i	0.777757	−	0.628565i	$-0.216357\pi$
$744$	−4.68593e10			−0.152934
$745$	4.01999e11			1.30497
$746$	1.73595e11			0.560507
$747$	4.02531e11			1.29276
$748$	5.57356e10			0.178044
$749$			2.04922e11i			0.651120i
$750$		−	1.64501e11i		−	0.519906i
$751$			5.66675e11i			1.78145i	0.454541	+	0.890726i	$0.349803\pi$
$751$			5.66675e11i			1.78145i	−0.454541	+	0.890726i	$0.650197\pi$
$752$	3.49027e10			0.109141
$753$		−	2.32569e11i		−	0.723390i
$754$	5.29546e10			0.163840
$755$	1.17295e11			0.360988
$756$	−2.18529e9			−0.00668994
$757$		−	3.67371e11i		−	1.11872i	−0.828925	−	0.559360i	$-0.811047\pi$
$757$		−	3.67371e11i		−	1.11872i	0.828925	−	0.559360i	$-0.188953\pi$
$758$			1.90973e11i			0.578489i
$759$		−	1.10013e12i		−	3.31496i
$760$			3.26256e11i			0.977922i
$761$			4.84998e11i			1.44611i	0.690790	+	0.723055i	$0.257263\pi$
$761$			4.84998e11i			1.44611i	−0.690790	+	0.723055i	$0.742737\pi$
$762$	1.09803e11			0.325681
$763$		−	1.76626e11i		−	0.521143i
$764$			2.40323e11i			0.705377i
$765$		−	4.12465e10i		−	0.120432i
$766$	5.64776e10			0.164044
$767$	1.73532e11			0.501417
$768$		−	4.53172e10i		−	0.130262i
$769$	−3.76649e11			−1.07704			−0.538519	−	0.842613i	$-0.681016\pi$
$769$	−3.76649e11			−1.07704			−0.538519	+	0.842613i	$0.681016\pi$
$770$		−	2.21214e11i		−	0.629288i
$771$	−8.08654e11			−2.28847
$772$	−3.46791e11			−0.976335
$773$		−	1.40564e11i		−	0.393693i	−0.980434	−	0.196846i	$-0.936930\pi$
$773$		−	1.40564e11i		−	0.393693i	0.980434	−	0.196846i	$-0.0630700\pi$
$774$	−3.40058e10	+	1.26566e11i	−0.0947523	+	0.352658i
$775$	3.06121e8			0.000848566
$776$		−	4.33756e11i		−	1.19619i
$777$			7.73634e11i			2.12252i
$778$	9.51343e10			0.259668
$779$		−	1.66144e10i		−	0.0451165i
$780$	−1.37427e11			−0.371273
$781$			2.16672e11i			0.582368i
$782$		−	2.30851e10i		−	0.0617312i
$783$	4.19840e9			0.0111696
$784$	−6.52876e9			−0.0172809
$785$	4.74852e11			1.25049
$786$		−	9.25344e10i		−	0.242445i
$787$	6.67009e11			1.73873			0.869367	−	0.494168i	$-0.164527\pi$
$787$	6.67009e11			1.73873			0.869367	+	0.494168i	$0.164527\pi$
$788$	−1.17541e11			−0.304848
$789$	6.35225e11			1.63915
$790$	−1.00452e11			−0.257899
$791$	5.31058e11			1.35655
$792$		−	4.54217e11i		−	1.15442i
$793$		−	8.11745e10i		−	0.205271i
$794$		−	4.83770e10i		−	0.121719i
$795$	−7.54853e11			−1.88970
$796$		−	7.63494e10i		−	0.190175i
$797$	4.73408e11			1.17328			0.586640	−	0.809848i	$-0.300450\pi$
$797$	4.73408e11			1.17328			0.586640	+	0.809848i	$0.300450\pi$
$798$	−3.05292e11			−0.752842
$799$	8.79881e9			0.0215892
$800$			2.00056e9i			0.00488417i
$801$		−	6.17785e10i		−	0.150075i
$802$		−	1.70483e11i		−	0.412082i
$803$			8.41918e11i			2.02492i
$804$		−	4.65058e11i		−	1.11297i
$805$	5.88095e11			1.40044
$806$			7.46459e9i			0.0176875i
$807$			1.12619e12i			2.65532i
$808$			2.30406e11i			0.540566i
$809$	−1.04627e11			−0.244260			−0.122130	−	0.992514i	$-0.538972\pi$
$809$	−1.04627e11			−0.244260			−0.122130	+	0.992514i	$0.538972\pi$
$810$	1.58467e11			0.368128
$811$		−	5.04643e10i		−	0.116654i	−0.998298	−	0.0583272i	$-0.981423\pi$
$811$		−	5.04643e10i		−	0.116654i	0.998298	−	0.0583272i	$-0.0185767\pi$
$812$	5.58641e11			1.28502
$813$		−	4.13677e11i		−	0.946889i
$814$	4.04930e11			0.922323
$815$	−1.90725e11			−0.432291
$816$			4.66617e10i			0.105245i
$817$	−1.65537e11	+	6.16110e11i	−0.371540	+	1.38283i
$818$	2.34530e11			0.523824
$819$		−	1.38239e11i		−	0.307252i
$820$			1.22923e10i			0.0271881i
$821$	−7.92306e10			−0.174389			−0.0871947	−	0.996191i	$-0.527790\pi$
$821$	−7.92306e10			−0.174389			−0.0871947	+	0.996191i	$0.527790\pi$
$822$		−	1.73842e11i		−	0.380775i
$823$	−6.78651e11			−1.47927			−0.739634	−	0.673009i	$-0.765002\pi$
$823$	−6.78651e11			−1.47927			−0.739634	+	0.673009i	$0.765002\pi$
$824$			4.97148e10i			0.107839i
$825$			5.95070e9i			0.0128455i
$826$	−2.85215e11			−0.612707
$827$	2.25852e11			0.482838			0.241419	−	0.970421i	$-0.422387\pi$
$827$	2.25852e11			0.482838			0.241419	+	0.970421i	$0.422387\pi$
$828$	5.60133e11			1.19171
$829$		−	2.68034e10i		−	0.0567507i	−0.999597	−	0.0283753i	$-0.990967\pi$
$829$		−	2.68034e10i		−	0.0567507i	0.999597	−	0.0283753i	$-0.00903337\pi$
$830$	2.25867e11			0.475927
$831$	−3.56230e11			−0.747010
$832$	4.08201e10			0.0851886
$833$	−1.64587e9			−0.00341834
$834$	3.12666e11			0.646273
$835$			2.87946e11i			0.592332i
$836$		−	1.02564e12i		−	2.09977i
$837$			5.91815e8i			0.00120582i
$838$	−1.53382e11			−0.311027
$839$			7.97781e11i			1.61004i	0.593250	+	0.805019i	$0.297845\pi$
$839$			7.97781e11i			1.61004i	−0.593250	+	0.805019i	$0.702155\pi$
$840$	4.86937e11			0.978038
$841$	−5.73020e11			−1.14548
$842$	−1.04554e11			−0.208014
$843$		−	1.06054e12i		−	2.09999i
$844$		−	1.13360e11i		−	0.223403i
$845$		−	4.61267e11i		−	0.904745i
$846$		−	3.32619e10i		−	0.0649330i
$847$			9.77324e11i			1.89891i
$848$	4.25823e11			0.823466
$849$		−	5.24874e11i		−	1.01024i
$850$			1.24869e8i			0.000239210i
$851$			1.07650e12i			2.05257i
$852$	−2.21235e11			−0.419852
$853$	−7.47205e11			−1.41138			−0.705690	−	0.708521i	$-0.749363\pi$
$853$	−7.47205e11			−1.41138			−0.705690	+	0.708521i	$0.749363\pi$
$854$			1.33417e11i			0.250831i
$855$	−7.59015e11			−1.42032
$856$			2.36099e11i			0.439743i
$857$	−7.52101e10			−0.139429			−0.0697145	−	0.997567i	$-0.522209\pi$
$857$	−7.52101e10			−0.139429			−0.0697145	+	0.997567i	$0.522209\pi$
$858$	−1.45105e11			−0.267752
$859$		−	4.14782e11i		−	0.761811i	−0.924614	−	0.380906i	$-0.875612\pi$
$859$		−	4.14782e11i		−	0.761811i	0.924614	−	0.380906i	$-0.124388\pi$
$860$	1.22474e11	−	4.55835e11i	0.223898	−	0.833324i
$861$	−2.47970e10			−0.0451219
$862$			4.18761e10i			0.0758469i
$863$		−	3.46104e11i		−	0.623969i	−0.950087	−	0.311985i	$-0.899006\pi$
$863$		−	3.46104e11i		−	0.623969i	0.950087	−	0.311985i	$-0.100994\pi$
$864$	−3.86762e9			−0.00694047
$865$		−	2.78163e11i		−	0.496861i
$866$	1.32762e11			0.236050
$867$		−	7.86239e11i		−	1.39148i
$868$			7.87472e10i			0.138725i
$869$	6.80775e11			1.19378
$870$	−4.33949e11			−0.757464
$871$	−1.59708e11			−0.277494
$872$		−	2.03498e11i		−	0.351961i
$873$	1.00911e12			1.73732
$874$	−4.24811e11			−0.728031
$875$	−5.95960e11			−1.01668
$876$	−8.59651e11			−1.45984
$877$	7.51681e11			1.27068			0.635339	−	0.772233i	$-0.280860\pi$
$877$	7.51681e11			1.27068			0.635339	+	0.772233i	$0.280860\pi$
$878$			3.43695e11i			0.578356i
$879$			4.77760e11i			0.800302i
$880$			6.22188e11i			1.03751i
$881$	−3.84486e11			−0.638229			−0.319114	−	0.947716i	$-0.603385\pi$
$881$	−3.84486e11			−0.638229			−0.319114	+	0.947716i	$0.603385\pi$
$882$			6.22184e9i			0.0102812i
$883$	6.62262e11			1.08940			0.544700	−	0.838631i	$-0.316644\pi$
$883$	6.62262e11			1.08940			0.544700	+	0.838631i	$0.316644\pi$
$884$	1.95436e10			0.0320033
$885$	−1.42205e12			−2.31815
$886$		−	1.84981e11i		−	0.300188i
$887$		−	1.19235e12i		−	1.92623i	−0.269093	−	0.963114i	$-0.586724\pi$
$887$		−	1.19235e12i		−	1.92623i	0.269093	−	0.963114i	$-0.413276\pi$
$888$			8.91335e11i			1.43347i
$889$		−	3.97796e11i		−	0.636874i
$890$		−	3.46650e10i		−	0.0552498i
$891$	−1.07395e12			−1.70402
$892$			7.58018e11i			1.19735i
$893$		−	1.61915e11i		−	0.254614i
$894$			4.33399e11i			0.678481i
$895$	−7.30049e11			−1.13778
$896$	−6.61897e11			−1.02697
$897$		−	3.85760e11i		−	0.595864i
$898$	−4.25810e11			−0.654803
$899$		−	1.51290e11i		−	0.231617i
$900$	−3.02980e9			−0.00461789
$901$	1.07348e11			0.162890
$902$			1.29791e10i			0.0196073i
$903$	9.19544e11	+	2.47063e11i	1.38300	+	0.371584i
$904$	6.11853e11			0.916165
$905$		−	8.49001e11i		−	1.26565i
$906$			1.26457e11i			0.187685i
$907$	4.17537e11			0.616972			0.308486	−	0.951229i	$-0.400178\pi$
$907$	4.17537e11			0.616972			0.308486	+	0.951229i	$0.400178\pi$
$908$		−	1.33006e11i		−	0.195672i
$909$	−5.36026e11			−0.785110
$910$		−	7.75681e10i		−	0.113114i
$911$			4.38304e11i			0.636359i	0.948030	+	0.318180i	$0.103071\pi$
$911$			4.38304e11i			0.636359i	−0.948030	+	0.318180i	$0.896929\pi$
$912$	8.58666e11			1.24121
$913$	−1.53073e12			−2.20301
$914$	1.87007e11			0.267961
$915$			6.65204e11i			0.949009i
$916$	4.95749e11			0.704174
$917$	−3.35236e11			−0.474104
$918$	−2.41406e8			−0.000339920
$919$	8.43969e10			0.118322			0.0591608	−	0.998248i	$-0.481158\pi$
$919$	8.43969e10			0.118322			0.0591608	+	0.998248i	$0.481158\pi$
$920$	6.77568e11			0.945805
$921$			1.39369e12i			1.93699i
$922$			1.35857e11i			0.188000i
$923$			7.59754e10i			0.104681i
$924$	−1.53077e12			−2.10002
$925$		−	5.82289e9i		−	0.00795374i
$926$	1.83503e11			0.249574
$927$	−1.15659e11			−0.156624
$928$	9.88707e11			1.33314
$929$			1.50574e11i			0.202156i	0.994879	+	0.101078i	$0.0322291\pi$
$929$			1.50574e11i			0.202156i	−0.994879	+	0.101078i	$0.967771\pi$
$930$		−	6.11704e10i		−	0.0817729i
$931$			3.02872e10i			0.0403144i
$932$		−	5.03296e11i		−	0.667052i
$933$			5.15000e11i			0.679643i
$934$	−5.05794e10			−0.0664640
$935$			1.56851e11i			0.205230i
$936$		−	1.59270e11i		−	0.207506i
$937$		−	8.63682e11i		−	1.12046i	−0.828338	−	0.560229i	$-0.810713\pi$
$937$		−	8.63682e11i		−	1.12046i	0.828338	−	0.560229i	$-0.189287\pi$
$938$	2.62494e11			0.339084
$939$	4.64949e11			0.598057
$940$			1.19794e11i			0.153435i
$941$	3.86913e11			0.493463			0.246732	−	0.969084i	$-0.420643\pi$
$941$	3.86913e11			0.493463			0.246732	+	0.969084i	$0.420643\pi$
$942$			5.11941e11i			0.650154i
$943$	−3.45048e10			−0.0436348
$944$	8.02199e11			1.01017
$945$		−	6.14983e9i		−	0.00771145i
$946$	1.29316e11	−	4.81301e11i	0.161469	−	0.600970i
$947$	−1.23084e11			−0.153039			−0.0765193	−	0.997068i	$-0.524381\pi$
$947$	−1.23084e11			−0.153039			−0.0765193	+	0.997068i	$0.524381\pi$
$948$			6.95114e11i			0.860642i
$949$			2.95217e11i			0.363979i
$950$	2.29783e9			0.00282113
$951$			1.36257e11i			0.166585i
$952$	−6.92476e10			−0.0843057
$953$		−	4.55382e10i		−	0.0552083i	−0.999619	−	0.0276041i	$-0.991212\pi$
$953$		−	4.55382e10i		−	0.0552083i	0.999619	−	0.0276041i	$-0.00878779\pi$
$954$		−	4.05805e11i		−	0.489919i
$955$	−6.76315e11			−0.813084
$956$	6.74604e11			0.807639
$957$	2.94093e12			3.50621
$958$		−	2.58468e11i		−	0.306863i
$959$	−6.29801e11			−0.744611
$960$	−3.34510e11			−0.393844
$961$	−8.31565e11			−0.974996
$962$	1.41988e11			0.165787
$963$	−5.49270e11			−0.638676
$964$			6.76934e11i			0.783860i
$965$		−	9.75937e11i		−	1.12542i
$966$			6.34030e11i			0.728117i
$967$	1.08233e12			1.23781			0.618904	−	0.785466i	$-0.287577\pi$
$967$	1.08233e12			1.23781			0.618904	+	0.785466i	$0.287577\pi$
$968$			1.12601e12i			1.28246i
$969$	2.16466e11			0.245524
$970$	5.66228e11			0.639594
$971$	−1.17929e12			−1.32661			−0.663303	−	0.748351i	$-0.730846\pi$
$971$	−1.17929e12			−1.32661			−0.663303	+	0.748351i	$0.730846\pi$
$972$		−	1.09068e12i		−	1.22189i
$973$		−	1.13273e12i		−	1.26379i
$974$		−	4.73489e10i		−	0.0526107i
$975$			2.08660e9i			0.00230898i
$976$		−	3.75251e11i		−	0.413544i
$977$	−1.42702e12			−1.56621			−0.783106	−	0.621888i	$-0.786366\pi$
$977$	−1.42702e12			−1.56621			−0.783106	+	0.621888i	$0.786366\pi$
$978$		−	2.05622e11i		−	0.224757i
$979$			2.34929e11i			0.255744i
$980$		−	2.24083e10i		−	0.0242943i
$981$	4.73426e11			0.511183
$982$	−5.42630e11			−0.583522
$983$			9.86220e11i			1.05623i	0.849172	+	0.528117i	$0.177102\pi$
$983$			9.86220e11i			1.05623i	−0.849172	+	0.528117i	$0.822898\pi$
$984$	−2.85697e10			−0.0304737
$985$		−	3.30783e11i		−	0.351397i
$986$	6.17122e10			0.0652925
$987$	−2.41658e11			−0.254644
$988$		−	3.59639e11i		−	0.377433i
$989$	1.27954e12	+	3.43786e11i	1.33742	+	0.359338i
$990$	5.92938e11			0.617261
$991$			9.77300e11i			1.01329i	0.862155	+	0.506644i	$0.169114\pi$
$991$			9.77300e11i			1.01329i	−0.862155	+	0.506644i	$0.830886\pi$
$992$			1.39370e11i			0.143921i
$993$	2.35591e12			2.42305
$994$		−	1.24872e11i		−	0.127915i
$995$	2.14862e11			0.219213
$996$		−	1.56297e12i		−	1.58823i
$997$		−	1.05101e12i		−	1.06372i	−0.846833	−	0.531858i	$-0.821494\pi$
$997$		−	1.05101e12i		−	1.06372i	0.846833	−	0.531858i	$-0.178506\pi$
$998$	−5.76347e11			−0.580981
$999$	1.12572e10			0.0113024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.15	yes	28
43.42	odd	2	inner	43.9.b.b.42.14	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.14	✓	28	43.42	odd	2	inner
43.9.b.b.42.15	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)

\(f(q)\)	\(=\)	\(q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} +O(q^{10})\)	\(q+5.87436i q^{2} +114.397i q^{3} +221.492 q^{4} +623.321i q^{5} -672.007 q^{6} +2434.57i q^{7} +2804.96i q^{8} -6525.57 q^{9} -3661.61 q^{10} +24815.2 q^{11} +25337.9i q^{12} +8701.41 q^{13} -14301.5 q^{14} -71305.8 q^{15} +40224.6 q^{16} +10140.4 q^{17} -38333.6i q^{18} -186604. i q^{19} +138060. i q^{20} -278506. q^{21} +145774. i q^{22} -387538. q^{23} -320878. q^{24} +2096.22 q^{25} +51115.2i q^{26} +4052.57i q^{27} +539236. i q^{28} -1.03599e6i q^{29} -418876. i q^{30} +146035. q^{31} +954363. i q^{32} +2.83878e6i q^{33} +59568.6i q^{34} -1.51752e6 q^{35} -1.44536e6 q^{36} -2.77780e6i q^{37} +1.09618e6 q^{38} +995411. i q^{39} -1.74839e6 q^{40} +89036.0 q^{41} -1.63604e6i q^{42} +(-3.30170e6 - 887103. i) q^{43} +5.49637e6 q^{44} -4.06753e6i q^{45} -2.27654e6i q^{46} +867696. q^{47} +4.60155e6i q^{48} -162308. q^{49} +12314.0i q^{50} +1.16003e6i q^{51} +1.92729e6 q^{52} +1.05861e7 q^{53} -23806.3 q^{54} +1.54678e7i q^{55} -6.82886e6 q^{56} +2.13468e7 q^{57} +6.08576e6 q^{58} +1.99430e7 q^{59} -1.57936e7 q^{60} -9.32889e6i q^{61} +857860. i q^{62} -1.58869e7i q^{63} +4.69121e6 q^{64} +5.42377e6i q^{65} -1.66760e7 q^{66} -1.83542e7 q^{67} +2.24602e6 q^{68} -4.43330e7i q^{69} -8.91443e6i q^{70} +8.73139e6i q^{71} -1.83040e7i q^{72} +3.39275e7i q^{73} +1.63178e7 q^{74} +239800. i q^{75} -4.13312e7i q^{76} +6.04143e7i q^{77} -5.84741e6 q^{78} +2.74337e7 q^{79} +2.50728e7i q^{80} -4.32779e7 q^{81} +523029. i q^{82} -6.16851e7 q^{83} -6.16868e7 q^{84} +6.32074e6i q^{85} +(5.21116e6 - 1.93954e7i) q^{86} +1.18513e8 q^{87} +6.96057e7i q^{88} +9.46713e6i q^{89} +2.38941e7 q^{90} +2.11841e7i q^{91} -8.58366e7 q^{92} +1.67059e7i q^{93} +5.09716e6i q^{94} +1.16314e8 q^{95} -1.09176e8 q^{96} -1.54639e8 q^{97} -953454. i q^{98} -1.61934e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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