Properties

Label 23.15.b.b.22.20
Level $23$
Weight $15$
Character 23.22
Analytic conductor $28.596$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [23,15,Mod(22,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 15, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.22");
 
S:= CuspForms(chi, 15);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 23.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: \(28.5956626749\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.20
Character \(\chi\) \(=\) 23.22
Dual form 23.15.b.b.22.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+137.789 q^{2} +2037.01 q^{3} +2601.83 q^{4} +58362.5i q^{5} +280678. q^{6} +1.12900e6i q^{7} -1.89903e6 q^{8} -633549. q^{9} +O(q^{10})\) \(q+137.789 q^{2} +2037.01 q^{3} +2601.83 q^{4} +58362.5i q^{5} +280678. q^{6} +1.12900e6i q^{7} -1.89903e6 q^{8} -633549. q^{9} +8.04171e6i q^{10} -7.80142e6i q^{11} +5.29996e6 q^{12} -7.61695e7 q^{13} +1.55563e8i q^{14} +1.18885e8i q^{15} -3.04294e8 q^{16} +4.29810e8i q^{17} -8.72962e7 q^{18} -8.27065e8i q^{19} +1.51849e8i q^{20} +2.29978e9i q^{21} -1.07495e9i q^{22} +(1.95836e9 + 2.78526e9i) q^{23} -3.86835e9 q^{24} +2.69734e9 q^{25} -1.04953e10 q^{26} -1.10335e10 q^{27} +2.93746e9i q^{28} +1.59943e10 q^{29} +1.63811e10i q^{30} +2.16761e10 q^{31} -1.08147e10 q^{32} -1.58916e10i q^{33} +5.92232e10i q^{34} -6.58910e10 q^{35} -1.64839e9 q^{36} +9.88060e10i q^{37} -1.13961e11i q^{38} -1.55158e11 q^{39} -1.10832e11i q^{40} +1.77934e10 q^{41} +3.16885e11i q^{42} +4.10966e11i q^{43} -2.02980e10i q^{44} -3.69755e10i q^{45} +(2.69841e11 + 3.83778e11i) q^{46} -3.61631e11 q^{47} -6.19851e11 q^{48} -5.96410e11 q^{49} +3.71664e11 q^{50} +8.75529e11i q^{51} -1.98180e11 q^{52} +1.13469e12i q^{53} -1.52030e12 q^{54} +4.55310e11 q^{55} -2.14400e12i q^{56} -1.68474e12i q^{57} +2.20383e12 q^{58} +3.54124e12 q^{59} +3.09319e11i q^{60} -5.08379e12i q^{61} +2.98673e12 q^{62} -7.15275e11i q^{63} +3.49541e12 q^{64} -4.44544e12i q^{65} -2.18969e12i q^{66} -9.73344e12i q^{67} +1.11829e12i q^{68} +(3.98920e12 + 5.67360e12i) q^{69} -9.07907e12 q^{70} -4.25884e12 q^{71} +1.20313e12 q^{72} +6.04556e12 q^{73} +1.36144e13i q^{74} +5.49451e12 q^{75} -2.15188e12i q^{76} +8.80777e12 q^{77} -2.13791e13 q^{78} +2.57109e13i q^{79} -1.77594e13i q^{80} -1.94452e13 q^{81} +2.45174e12 q^{82} -8.42299e12i q^{83} +5.98364e12i q^{84} -2.50848e13 q^{85} +5.66267e13i q^{86} +3.25805e13 q^{87} +1.48151e13i q^{88} -9.49852e11i q^{89} -5.09482e12i q^{90} -8.59951e13i q^{91} +(5.09532e12 + 7.24677e12i) q^{92} +4.41545e13 q^{93} -4.98287e13 q^{94} +4.82696e13 q^{95} -2.20297e13 q^{96} -3.57714e13i q^{97} -8.21788e13 q^{98} +4.94258e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9} - 61408584 q^{12} - 75796032 q^{13} + 61604880 q^{16} + 2078422368 q^{18} + 11061310696 q^{23} - 31030771920 q^{24} - 46421538840 q^{25} - 2664699128 q^{26} + 53616275568 q^{27} + 34752122960 q^{29} - 66504561216 q^{31} - 119385530304 q^{32} + 268767587760 q^{35} - 826304812272 q^{36} - 531040317600 q^{39} - 586388906608 q^{41} - 219014904864 q^{46} + 552854704544 q^{47} + 1314198459696 q^{48} - 2682585958584 q^{49} + 1292374320920 q^{50} - 614830645416 q^{52} - 756511540560 q^{54} - 4886166096240 q^{55} - 4069251029352 q^{58} + 17167207160144 q^{59} + 7479493046896 q^{62} + 18607147469856 q^{64} - 1866422538000 q^{69} + 10676769015360 q^{70} + 15000981757712 q^{71} + 5949703969824 q^{72} + 17535136179168 q^{73} - 79533751619520 q^{75} + 53823905395344 q^{77} + 6433358950512 q^{78} + 149774494087944 q^{81} - 27510435600840 q^{82} - 170228194057680 q^{85} - 286575506293872 q^{87} + 133024510658856 q^{92} + 66347882278032 q^{93} - 205878296932464 q^{94} - 211992774994560 q^{95} + 494703018436320 q^{96} - 537018388090408 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 137.789 1.07648 0.538239 0.842793i \(-0.319090\pi\)
0.538239 + 0.842793i \(0.319090\pi\)
\(3\) 2037.01 0.931419 0.465709 0.884938i \(-0.345799\pi\)
0.465709 + 0.884938i \(0.345799\pi\)
\(4\) 2601.83 0.158803
\(5\) 58362.5i 0.747040i 0.927622 + 0.373520i \(0.121849\pi\)
−0.927622 + 0.373520i \(0.878151\pi\)
\(6\) 280678. 1.00265
\(7\) 1.12900e6i 1.37090i 0.728119 + 0.685451i \(0.240395\pi\)
−0.728119 + 0.685451i \(0.759605\pi\)
\(8\) −1.89903e6 −0.905529
\(9\) −633549. −0.132459
\(10\) 8.04171e6i 0.804171i
\(11\) 7.80142e6i 0.400336i −0.979762 0.200168i \(-0.935851\pi\)
0.979762 0.200168i \(-0.0641488\pi\)
\(12\) 5.29996e6 0.147912
\(13\) −7.61695e7 −1.21388 −0.606942 0.794746i \(-0.707604\pi\)
−0.606942 + 0.794746i \(0.707604\pi\)
\(14\) 1.55563e8i 1.47574i
\(15\) 1.18885e8i 0.695807i
\(16\) −3.04294e8 −1.13358
\(17\) 4.29810e8i 1.04745i 0.851887 + 0.523726i \(0.175459\pi\)
−0.851887 + 0.523726i \(0.824541\pi\)
\(18\) −8.72962e7 −0.142590
\(19\) 8.27065e8i 0.925261i −0.886551 0.462631i \(-0.846906\pi\)
0.886551 0.462631i \(-0.153094\pi\)
\(20\) 1.51849e8i 0.118632i
\(21\) 2.29978e9i 1.27688i
\(22\) 1.07495e9i 0.430953i
\(23\) 1.95836e9 + 2.78526e9i 0.575172 + 0.818032i
\(24\) −3.86835e9 −0.843427
\(25\) 2.69734e9 0.441932
\(26\) −1.04953e10 −1.30672
\(27\) −1.10335e10 −1.05479
\(28\) 2.93746e9i 0.217703i
\(29\) 1.59943e10 0.927210 0.463605 0.886042i \(-0.346556\pi\)
0.463605 + 0.886042i \(0.346556\pi\)
\(30\) 1.63811e10i 0.749020i
\(31\) 2.16761e10 0.787861 0.393930 0.919140i \(-0.371115\pi\)
0.393930 + 0.919140i \(0.371115\pi\)
\(32\) −1.08147e10 −0.314749
\(33\) 1.58916e10i 0.372880i
\(34\) 5.92232e10i 1.12756i
\(35\) −6.58910e10 −1.02412
\(36\) −1.64839e9 −0.0210350
\(37\) 9.88060e10i 1.04081i 0.853920 + 0.520404i \(0.174219\pi\)
−0.853920 + 0.520404i \(0.825781\pi\)
\(38\) 1.13961e11i 0.996023i
\(39\) −1.55158e11 −1.13063
\(40\) 1.10832e11i 0.676466i
\(41\) 1.77934e10 0.0913635 0.0456818 0.998956i \(-0.485454\pi\)
0.0456818 + 0.998956i \(0.485454\pi\)
\(42\) 3.16885e11i 1.37454i
\(43\) 4.10966e11i 1.51191i 0.654621 + 0.755957i \(0.272828\pi\)
−0.654621 + 0.755957i \(0.727172\pi\)
\(44\) 2.02980e10i 0.0635746i
\(45\) 3.69755e10i 0.0989524i
\(46\) 2.69841e11 + 3.83778e11i 0.619160 + 0.880593i
\(47\) −3.61631e11 −0.713806 −0.356903 0.934141i \(-0.616167\pi\)
−0.356903 + 0.934141i \(0.616167\pi\)
\(48\) −6.19851e11 −1.05584
\(49\) −5.96410e11 −0.879372
\(50\) 3.71664e11 0.475729
\(51\) 8.75529e11i 0.975617i
\(52\) −1.98180e11 −0.192769
\(53\) 1.13469e12i 0.965932i 0.875639 + 0.482966i \(0.160441\pi\)
−0.875639 + 0.482966i \(0.839559\pi\)
\(54\) −1.52030e12 −1.13546
\(55\) 4.55310e11 0.299067
\(56\) 2.14400e12i 1.24139i
\(57\) 1.68474e12i 0.861806i
\(58\) 2.20383e12 0.998120
\(59\) 3.54124e12 1.42295 0.711477 0.702709i \(-0.248026\pi\)
0.711477 + 0.702709i \(0.248026\pi\)
\(60\) 3.09319e11i 0.110496i
\(61\) 5.08379e12i 1.61763i −0.588065 0.808814i \(-0.700110\pi\)
0.588065 0.808814i \(-0.299890\pi\)
\(62\) 2.98673e12 0.848114
\(63\) 7.15275e11i 0.181589i
\(64\) 3.49541e12 0.794765
\(65\) 4.44544e12i 0.906820i
\(66\) 2.18969e12i 0.401397i
\(67\) 9.73344e12i 1.60599i −0.595986 0.802995i \(-0.703239\pi\)
0.595986 0.802995i \(-0.296761\pi\)
\(68\) 1.11829e12i 0.166339i
\(69\) 3.98920e12 + 5.67360e12i 0.535726 + 0.761931i
\(70\) −9.07907e12 −1.10244
\(71\) −4.25884e12 −0.468255 −0.234127 0.972206i \(-0.575223\pi\)
−0.234127 + 0.972206i \(0.575223\pi\)
\(72\) 1.20313e12 0.119946
\(73\) 6.04556e12 0.547239 0.273619 0.961838i \(-0.411779\pi\)
0.273619 + 0.961838i \(0.411779\pi\)
\(74\) 1.36144e13i 1.12041i
\(75\) 5.49451e12 0.411623
\(76\) 2.15188e12i 0.146934i
\(77\) 8.80777e12 0.548821
\(78\) −2.13791e13 −1.21710
\(79\) 2.57109e13i 1.33884i 0.742885 + 0.669419i \(0.233457\pi\)
−0.742885 + 0.669419i \(0.766543\pi\)
\(80\) 1.77594e13i 0.846833i
\(81\) −1.94452e13 −0.849995
\(82\) 2.45174e12 0.0983507
\(83\) 8.42299e12i 0.310399i −0.987883 0.155199i \(-0.950398\pi\)
0.987883 0.155199i \(-0.0496020\pi\)
\(84\) 5.98364e12i 0.202773i
\(85\) −2.50848e13 −0.782489
\(86\) 5.66267e13i 1.62754i
\(87\) 3.25805e13 0.863620
\(88\) 1.48151e13i 0.362516i
\(89\) 9.49852e11i 0.0214746i −0.999942 0.0107373i \(-0.996582\pi\)
0.999942 0.0107373i \(-0.00341786\pi\)
\(90\) 5.09482e12i 0.106520i
\(91\) 8.59951e13i 1.66412i
\(92\) 5.09532e12 + 7.24677e12i 0.0913391 + 0.129906i
\(93\) 4.41545e13 0.733828
\(94\) −4.98287e13 −0.768396
\(95\) 4.82696e13 0.691207
\(96\) −2.20297e13 −0.293163
\(97\) 3.57714e13i 0.442725i −0.975192 0.221363i \(-0.928950\pi\)
0.975192 0.221363i \(-0.0710504\pi\)
\(98\) −8.21788e13 −0.946624
\(99\) 4.94258e12i 0.0530283i
\(100\) 7.01801e12 0.0701801
\(101\) −8.62056e13 −0.804055 −0.402028 0.915628i \(-0.631694\pi\)
−0.402028 + 0.915628i \(0.631694\pi\)
\(102\) 1.20638e14i 1.05023i
\(103\) 2.14857e14i 1.74698i 0.486838 + 0.873492i \(0.338150\pi\)
−0.486838 + 0.873492i \(0.661850\pi\)
\(104\) 1.44648e14 1.09921
\(105\) −1.34221e14 −0.953883
\(106\) 1.56348e14i 1.03980i
\(107\) 3.81103e13i 0.237332i −0.992934 0.118666i \(-0.962138\pi\)
0.992934 0.118666i \(-0.0378617\pi\)
\(108\) −2.87073e13 −0.167505
\(109\) 1.41808e14i 0.775738i −0.921714 0.387869i \(-0.873211\pi\)
0.921714 0.387869i \(-0.126789\pi\)
\(110\) 6.27367e13 0.321939
\(111\) 2.01269e14i 0.969429i
\(112\) 3.43547e14i 1.55403i
\(113\) 2.74981e13i 0.116884i −0.998291 0.0584418i \(-0.981387\pi\)
0.998291 0.0584418i \(-0.0186132\pi\)
\(114\) 2.32139e14i 0.927714i
\(115\) −1.62555e14 + 1.14295e14i −0.611103 + 0.429676i
\(116\) 4.16143e13 0.147244
\(117\) 4.82571e13 0.160790
\(118\) 4.87944e14 1.53178
\(119\) −4.85254e14 −1.43595
\(120\) 2.25767e14i 0.630073i
\(121\) 3.18888e14 0.839731
\(122\) 7.00490e14i 1.74134i
\(123\) 3.62454e13 0.0850977
\(124\) 5.63976e13 0.125115
\(125\) 5.13640e14i 1.07718i
\(126\) 9.85571e13i 0.195476i
\(127\) 5.77041e14 1.08288 0.541441 0.840739i \(-0.317879\pi\)
0.541441 + 0.840739i \(0.317879\pi\)
\(128\) 6.58817e14 1.17029
\(129\) 8.37144e14i 1.40823i
\(130\) 6.12533e14i 0.976171i
\(131\) −1.27284e15 −1.92254 −0.961269 0.275611i \(-0.911120\pi\)
−0.961269 + 0.275611i \(0.911120\pi\)
\(132\) 4.13472e13i 0.0592146i
\(133\) 9.33753e14 1.26844
\(134\) 1.34116e15i 1.72881i
\(135\) 6.43943e14i 0.787973i
\(136\) 8.16224e14i 0.948499i
\(137\) 5.61791e14i 0.620199i 0.950704 + 0.310099i \(0.100362\pi\)
−0.950704 + 0.310099i \(0.899638\pi\)
\(138\) 5.49669e14 + 7.81761e14i 0.576697 + 0.820201i
\(139\) −5.55761e14 −0.554350 −0.277175 0.960819i \(-0.589398\pi\)
−0.277175 + 0.960819i \(0.589398\pi\)
\(140\) −1.71437e14 −0.162633
\(141\) −7.36646e14 −0.664852
\(142\) −5.86821e14 −0.504066
\(143\) 5.94230e14i 0.485962i
\(144\) 1.92785e14 0.150154
\(145\) 9.33464e14i 0.692663i
\(146\) 8.33013e14 0.589090
\(147\) −1.21490e15 −0.819063
\(148\) 2.57076e14i 0.165284i
\(149\) 1.34502e15i 0.824946i 0.910970 + 0.412473i \(0.135335\pi\)
−0.910970 + 0.412473i \(0.864665\pi\)
\(150\) 7.57083e14 0.443103
\(151\) −1.32797e15 −0.741907 −0.370953 0.928651i \(-0.620969\pi\)
−0.370953 + 0.928651i \(0.620969\pi\)
\(152\) 1.57062e15i 0.837851i
\(153\) 2.72306e14i 0.138745i
\(154\) 1.21362e15 0.590794
\(155\) 1.26507e15i 0.588563i
\(156\) −4.03695e14 −0.179548
\(157\) 3.44722e15i 1.46613i −0.680160 0.733064i \(-0.738090\pi\)
0.680160 0.733064i \(-0.261910\pi\)
\(158\) 3.54268e15i 1.44123i
\(159\) 2.31138e15i 0.899687i
\(160\) 6.31172e14i 0.235130i
\(161\) −3.14455e15 + 2.21098e15i −1.12144 + 0.788504i
\(162\) −2.67933e15 −0.915000
\(163\) −4.32305e15 −1.41409 −0.707045 0.707168i \(-0.749972\pi\)
−0.707045 + 0.707168i \(0.749972\pi\)
\(164\) 4.62955e13 0.0145088
\(165\) 9.27472e14 0.278556
\(166\) 1.16060e15i 0.334137i
\(167\) 3.06701e15 0.846643 0.423322 0.905979i \(-0.360864\pi\)
0.423322 + 0.905979i \(0.360864\pi\)
\(168\) 4.36736e15i 1.15626i
\(169\) 1.86441e15 0.473516
\(170\) −3.45641e15 −0.842331
\(171\) 5.23986e14i 0.122560i
\(172\) 1.06926e15i 0.240097i
\(173\) 2.23477e15 0.481848 0.240924 0.970544i \(-0.422550\pi\)
0.240924 + 0.970544i \(0.422550\pi\)
\(174\) 4.48924e15 0.929668
\(175\) 3.04528e15i 0.605845i
\(176\) 2.37393e15i 0.453815i
\(177\) 7.21355e15 1.32537
\(178\) 1.30879e14i 0.0231170i
\(179\) 9.99495e14 0.169750 0.0848749 0.996392i \(-0.472951\pi\)
0.0848749 + 0.996392i \(0.472951\pi\)
\(180\) 9.62040e13i 0.0157140i
\(181\) 1.15490e14i 0.0181466i −0.999959 0.00907329i \(-0.997112\pi\)
0.999959 0.00907329i \(-0.00288816\pi\)
\(182\) 1.18492e16i 1.79138i
\(183\) 1.03557e16i 1.50669i
\(184\) −3.71899e15 5.28930e15i −0.520835 0.740752i
\(185\) −5.76656e15 −0.777526
\(186\) 6.08401e15 0.789949
\(187\) 3.35313e15 0.419333
\(188\) −9.40901e14 −0.113355
\(189\) 1.24568e16i 1.44602i
\(190\) 6.65102e15 0.744068
\(191\) 1.30175e16i 1.40376i 0.712296 + 0.701879i \(0.247655\pi\)
−0.712296 + 0.701879i \(0.752345\pi\)
\(192\) 7.12020e15 0.740259
\(193\) 4.22945e15 0.424016 0.212008 0.977268i \(-0.432000\pi\)
0.212008 + 0.977268i \(0.432000\pi\)
\(194\) 4.92891e15i 0.476584i
\(195\) 9.05541e15i 0.844629i
\(196\) −1.55176e15 −0.139647
\(197\) −4.49025e15 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(198\) 6.81034e14i 0.0570837i
\(199\) 1.93481e16i 1.56555i 0.622308 + 0.782773i \(0.286195\pi\)
−0.622308 + 0.782773i \(0.713805\pi\)
\(200\) −5.12233e15 −0.400182
\(201\) 1.98271e16i 1.49585i
\(202\) −1.18782e16 −0.865547
\(203\) 1.80575e16i 1.27111i
\(204\) 2.27798e15i 0.154931i
\(205\) 1.03847e15i 0.0682522i
\(206\) 2.96050e16i 1.88059i
\(207\) −1.24072e15 1.76460e15i −0.0761870 0.108356i
\(208\) 2.31779e16 1.37604
\(209\) −6.45228e15 −0.370415
\(210\) −1.84942e16 −1.02683
\(211\) −1.18264e16 −0.635149 −0.317574 0.948233i \(-0.602868\pi\)
−0.317574 + 0.948233i \(0.602868\pi\)
\(212\) 2.95227e15i 0.153393i
\(213\) −8.67530e15 −0.436141
\(214\) 5.25118e15i 0.255482i
\(215\) −2.39850e16 −1.12946
\(216\) 2.09530e16 0.955147
\(217\) 2.44723e16i 1.08008i
\(218\) 1.95396e16i 0.835064i
\(219\) 1.23149e16 0.509708
\(220\) 1.18464e15 0.0474928
\(221\) 3.27384e16i 1.27149i
\(222\) 2.77327e16i 1.04357i
\(223\) 2.42052e16 0.882623 0.441312 0.897354i \(-0.354513\pi\)
0.441312 + 0.897354i \(0.354513\pi\)
\(224\) 1.22097e16i 0.431490i
\(225\) −1.70890e15 −0.0585380
\(226\) 3.78894e15i 0.125822i
\(227\) 2.67934e16i 0.862673i 0.902191 + 0.431337i \(0.141958\pi\)
−0.902191 + 0.431337i \(0.858042\pi\)
\(228\) 4.38341e15i 0.136857i
\(229\) 2.01899e16i 0.611344i −0.952137 0.305672i \(-0.901119\pi\)
0.952137 0.305672i \(-0.0988811\pi\)
\(230\) −2.23982e16 + 1.57486e16i −0.657838 + 0.462537i
\(231\) 1.79415e16 0.511182
\(232\) −3.03736e16 −0.839616
\(233\) −9.46251e15 −0.253814 −0.126907 0.991915i \(-0.540505\pi\)
−0.126907 + 0.991915i \(0.540505\pi\)
\(234\) 6.64930e15 0.173087
\(235\) 2.11057e16i 0.533241i
\(236\) 9.21370e15 0.225970
\(237\) 5.23734e16i 1.24702i
\(238\) −6.68628e16 −1.54577
\(239\) 2.96264e16 0.665110 0.332555 0.943084i \(-0.392089\pi\)
0.332555 + 0.943084i \(0.392089\pi\)
\(240\) 3.61761e16i 0.788756i
\(241\) 9.61938e15i 0.203717i 0.994799 + 0.101859i \(0.0324789\pi\)
−0.994799 + 0.101859i \(0.967521\pi\)
\(242\) 4.39392e16 0.903951
\(243\) 1.31629e16 0.263093
\(244\) 1.32272e16i 0.256884i
\(245\) 3.48080e16i 0.656926i
\(246\) 4.99423e15 0.0916057
\(247\) 6.29971e16i 1.12316i
\(248\) −4.11636e16 −0.713431
\(249\) 1.71577e16i 0.289111i
\(250\) 7.07739e16i 1.15956i
\(251\) 9.84235e15i 0.156813i −0.996921 0.0784066i \(-0.975017\pi\)
0.996921 0.0784066i \(-0.0249832\pi\)
\(252\) 1.86102e15i 0.0288369i
\(253\) 2.17290e16 1.52780e16i 0.327488 0.230262i
\(254\) 7.95100e16 1.16570
\(255\) −5.10980e16 −0.728825
\(256\) 3.35090e16 0.465031
\(257\) 7.06118e15 0.0953554 0.0476777 0.998863i \(-0.484818\pi\)
0.0476777 + 0.998863i \(0.484818\pi\)
\(258\) 1.15349e17i 1.51592i
\(259\) −1.11552e17 −1.42685
\(260\) 1.15663e16i 0.144006i
\(261\) −1.01331e16 −0.122818
\(262\) −1.75384e17 −2.06957
\(263\) 1.23692e17i 1.42119i −0.703600 0.710596i \(-0.748425\pi\)
0.703600 0.710596i \(-0.251575\pi\)
\(264\) 3.01786e16i 0.337654i
\(265\) −6.62234e16 −0.721589
\(266\) 1.28661e17 1.36545
\(267\) 1.93486e15i 0.0200019i
\(268\) 2.53247e16i 0.255036i
\(269\) 1.79119e17 1.75742 0.878708 0.477360i \(-0.158406\pi\)
0.878708 + 0.477360i \(0.158406\pi\)
\(270\) 8.87283e16i 0.848235i
\(271\) 1.41141e17 1.31482 0.657411 0.753532i \(-0.271651\pi\)
0.657411 + 0.753532i \(0.271651\pi\)
\(272\) 1.30789e17i 1.18738i
\(273\) 1.75173e17i 1.54999i
\(274\) 7.74087e16i 0.667630i
\(275\) 2.10431e16i 0.176921i
\(276\) 1.03792e16 + 1.47618e16i 0.0850749 + 0.120997i
\(277\) 2.20460e17 1.76186 0.880930 0.473247i \(-0.156918\pi\)
0.880930 + 0.473247i \(0.156918\pi\)
\(278\) −7.65777e16 −0.596745
\(279\) −1.37329e16 −0.104360
\(280\) 1.25129e17 0.927369
\(281\) 1.31107e17i 0.947724i −0.880599 0.473862i \(-0.842860\pi\)
0.880599 0.473862i \(-0.157140\pi\)
\(282\) −1.01502e17 −0.715698
\(283\) 1.55980e17i 1.07291i −0.843929 0.536455i \(-0.819763\pi\)
0.843929 0.536455i \(-0.180237\pi\)
\(284\) −1.10808e16 −0.0743603
\(285\) 9.83257e16 0.643803
\(286\) 8.18784e16i 0.523127i
\(287\) 2.00887e16i 0.125250i
\(288\) 6.85164e15 0.0416914
\(289\) −1.63591e16 −0.0971574
\(290\) 1.28621e17i 0.745635i
\(291\) 7.28669e16i 0.412362i
\(292\) 1.57295e16 0.0869032
\(293\) 2.15234e17i 1.16101i 0.814256 + 0.580506i \(0.197145\pi\)
−0.814256 + 0.580506i \(0.802855\pi\)
\(294\) −1.67399e17 −0.881703
\(295\) 2.06675e17i 1.06300i
\(296\) 1.87636e17i 0.942483i
\(297\) 8.60771e16i 0.422272i
\(298\) 1.85329e17i 0.888036i
\(299\) −1.49167e17 2.12152e17i −0.698193 0.992997i
\(300\) 1.42958e16 0.0653671
\(301\) −4.63980e17 −2.07269
\(302\) −1.82980e17 −0.798646
\(303\) −1.75602e17 −0.748912
\(304\) 2.51671e17i 1.04886i
\(305\) 2.96702e17 1.20843
\(306\) 3.75208e16i 0.149356i
\(307\) −3.06657e17 −1.19312 −0.596560 0.802568i \(-0.703466\pi\)
−0.596560 + 0.802568i \(0.703466\pi\)
\(308\) 2.29163e16 0.0871546
\(309\) 4.37667e17i 1.62717i
\(310\) 1.74313e17i 0.633575i
\(311\) 2.83499e17 1.00746 0.503731 0.863861i \(-0.331960\pi\)
0.503731 + 0.863861i \(0.331960\pi\)
\(312\) 2.94650e17 1.02382
\(313\) 3.67542e17i 1.24881i 0.781101 + 0.624405i \(0.214658\pi\)
−0.781101 + 0.624405i \(0.785342\pi\)
\(314\) 4.74990e17i 1.57825i
\(315\) 4.17452e16 0.135654
\(316\) 6.68954e16i 0.212612i
\(317\) 3.77489e16 0.117352 0.0586759 0.998277i \(-0.481312\pi\)
0.0586759 + 0.998277i \(0.481312\pi\)
\(318\) 3.18483e17i 0.968492i
\(319\) 1.24778e17i 0.371196i
\(320\) 2.04001e17i 0.593721i
\(321\) 7.76311e16i 0.221055i
\(322\) −4.33284e17 + 3.04649e17i −1.20721 + 0.848807i
\(323\) 3.55481e17 0.969167
\(324\) −5.05930e16 −0.134982
\(325\) −2.05455e17 −0.536454
\(326\) −5.95669e17 −1.52224
\(327\) 2.88865e17i 0.722537i
\(328\) −3.37903e16 −0.0827323
\(329\) 4.08280e17i 0.978558i
\(330\) 1.27796e17 0.299860
\(331\) −3.16425e17 −0.726899 −0.363450 0.931614i \(-0.618401\pi\)
−0.363450 + 0.931614i \(0.618401\pi\)
\(332\) 2.19152e16i 0.0492923i
\(333\) 6.25984e16i 0.137865i
\(334\) 4.22601e17 0.911392
\(335\) 5.68067e17 1.19974
\(336\) 6.99810e17i 1.44746i
\(337\) 4.86788e16i 0.0986122i 0.998784 + 0.0493061i \(0.0157010\pi\)
−0.998784 + 0.0493061i \(0.984299\pi\)
\(338\) 2.56896e17 0.509730
\(339\) 5.60139e16i 0.108868i
\(340\) −6.52664e16 −0.124262
\(341\) 1.69104e17i 0.315409i
\(342\) 7.21996e16i 0.131933i
\(343\) 9.23664e16i 0.165369i
\(344\) 7.80439e17i 1.36908i
\(345\) −3.31126e17 + 2.32820e17i −0.569192 + 0.400209i
\(346\) 3.07927e17 0.518698
\(347\) 5.16729e17 0.853014 0.426507 0.904484i \(-0.359744\pi\)
0.426507 + 0.904484i \(0.359744\pi\)
\(348\) 8.47689e16 0.137146
\(349\) −7.79449e17 −1.23598 −0.617988 0.786188i \(-0.712052\pi\)
−0.617988 + 0.786188i \(0.712052\pi\)
\(350\) 4.19607e17i 0.652178i
\(351\) 8.40417e17 1.28040
\(352\) 8.43699e16i 0.126005i
\(353\) 4.53420e17 0.663862 0.331931 0.943304i \(-0.392300\pi\)
0.331931 + 0.943304i \(0.392300\pi\)
\(354\) 9.93948e17 1.42673
\(355\) 2.48556e17i 0.349805i
\(356\) 2.47135e15i 0.00341024i
\(357\) −9.88469e17 −1.33748
\(358\) 1.37720e17 0.182732
\(359\) 9.69024e17i 1.26088i −0.776238 0.630439i \(-0.782875\pi\)
0.776238 0.630439i \(-0.217125\pi\)
\(360\) 7.02177e16i 0.0896043i
\(361\) 1.14970e17 0.143892
\(362\) 1.59133e16i 0.0195344i
\(363\) 6.49578e17 0.782141
\(364\) 2.23745e17i 0.264267i
\(365\) 3.52834e17i 0.408809i
\(366\) 1.42691e18i 1.62192i
\(367\) 8.63965e17i 0.963460i 0.876320 + 0.481730i \(0.159991\pi\)
−0.876320 + 0.481730i \(0.840009\pi\)
\(368\) −5.95918e17 8.47538e17i −0.652006 0.927309i
\(369\) −1.12730e16 −0.0121020
\(370\) −7.94569e17 −0.836989
\(371\) −1.28106e18 −1.32420
\(372\) 1.14883e17 0.116534
\(373\) 8.42416e17i 0.838620i 0.907843 + 0.419310i \(0.137728\pi\)
−0.907843 + 0.419310i \(0.862272\pi\)
\(374\) 4.62025e17 0.451403
\(375\) 1.04629e18i 1.00331i
\(376\) 6.86748e17 0.646372
\(377\) −1.21827e18 −1.12553
\(378\) 1.71641e18i 1.55661i
\(379\) 1.62272e17i 0.144467i 0.997388 + 0.0722334i \(0.0230126\pi\)
−0.997388 + 0.0722334i \(0.976987\pi\)
\(380\) 1.25589e17 0.109766
\(381\) 1.17544e18 1.00862
\(382\) 1.79366e18i 1.51111i
\(383\) 5.04550e17i 0.417362i 0.977984 + 0.208681i \(0.0669170\pi\)
−0.977984 + 0.208681i \(0.933083\pi\)
\(384\) 1.34202e18 1.09003
\(385\) 5.14043e17i 0.409991i
\(386\) 5.82771e17 0.456444
\(387\) 2.60368e17i 0.200267i
\(388\) 9.30712e16i 0.0703061i
\(389\) 5.34673e17i 0.396681i 0.980133 + 0.198340i \(0.0635552\pi\)
−0.980133 + 0.198340i \(0.936445\pi\)
\(390\) 1.24774e18i 0.909224i
\(391\) −1.19713e18 + 8.41724e17i −0.856850 + 0.602466i
\(392\) 1.13260e18 0.796297
\(393\) −2.59279e18 −1.79069
\(394\) −6.18708e17 −0.419771
\(395\) −1.50055e18 −1.00016
\(396\) 1.28598e16i 0.00842106i
\(397\) −1.02854e18 −0.661740 −0.330870 0.943676i \(-0.607342\pi\)
−0.330870 + 0.943676i \(0.607342\pi\)
\(398\) 2.66595e18i 1.68527i
\(399\) 1.90207e18 1.18145
\(400\) −8.20784e17 −0.500967
\(401\) 2.01703e18i 1.20977i 0.796313 + 0.604884i \(0.206781\pi\)
−0.796313 + 0.604884i \(0.793219\pi\)
\(402\) 2.73196e18i 1.61025i
\(403\) −1.65106e18 −0.956372
\(404\) −2.24292e17 −0.127686
\(405\) 1.13487e18i 0.634980i
\(406\) 2.48812e18i 1.36832i
\(407\) 7.70826e17 0.416673
\(408\) 1.66266e18i 0.883450i
\(409\) 1.95903e18 1.02324 0.511621 0.859211i \(-0.329045\pi\)
0.511621 + 0.859211i \(0.329045\pi\)
\(410\) 1.43090e17i 0.0734719i
\(411\) 1.14438e18i 0.577665i
\(412\) 5.59022e17i 0.277427i
\(413\) 3.99805e18i 1.95073i
\(414\) −1.70957e17 2.43142e17i −0.0820135 0.116643i
\(415\) 4.91587e17 0.231880
\(416\) 8.23749e17 0.382069
\(417\) −1.13209e18 −0.516332
\(418\) −8.89053e17 −0.398744
\(419\) 4.15676e18i 1.83340i −0.399579 0.916699i \(-0.630844\pi\)
0.399579 0.916699i \(-0.369156\pi\)
\(420\) −3.49220e17 −0.151480
\(421\) 2.76660e18i 1.18025i −0.807314 0.590123i \(-0.799079\pi\)
0.807314 0.590123i \(-0.200921\pi\)
\(422\) −1.62955e18 −0.683723
\(423\) 2.29111e17 0.0945503
\(424\) 2.15482e18i 0.874680i
\(425\) 1.15934e18i 0.462903i
\(426\) −1.19536e18 −0.469496
\(427\) 5.73958e18 2.21761
\(428\) 9.91565e16i 0.0376890i
\(429\) 1.21045e18i 0.452634i
\(430\) −3.30487e18 −1.21584
\(431\) 3.54954e18i 1.28479i −0.766375 0.642393i \(-0.777942\pi\)
0.766375 0.642393i \(-0.222058\pi\)
\(432\) 3.35744e18 1.19570
\(433\) 9.99469e17i 0.350230i −0.984548 0.175115i \(-0.943970\pi\)
0.984548 0.175115i \(-0.0560298\pi\)
\(434\) 3.37201e18i 1.16268i
\(435\) 1.90148e18i 0.645159i
\(436\) 3.68960e17i 0.123190i
\(437\) 2.30359e18 1.61969e18i 0.756894 0.532184i
\(438\) 1.69686e18 0.548689
\(439\) 6.16885e17 0.196315 0.0981573 0.995171i \(-0.468705\pi\)
0.0981573 + 0.995171i \(0.468705\pi\)
\(440\) −8.64649e17 −0.270814
\(441\) 3.77855e17 0.116481
\(442\) 4.51100e18i 1.36873i
\(443\) −4.96476e18 −1.48276 −0.741382 0.671083i \(-0.765829\pi\)
−0.741382 + 0.671083i \(0.765829\pi\)
\(444\) 5.23668e17i 0.153948i
\(445\) 5.54357e16 0.0160424
\(446\) 3.33522e18 0.950124
\(447\) 2.73983e18i 0.768370i
\(448\) 3.94631e18i 1.08954i
\(449\) −6.59082e18 −1.79149 −0.895746 0.444566i \(-0.853358\pi\)
−0.895746 + 0.444566i \(0.853358\pi\)
\(450\) −2.35467e17 −0.0630148
\(451\) 1.38814e17i 0.0365761i
\(452\) 7.15454e16i 0.0185615i
\(453\) −2.70509e18 −0.691026
\(454\) 3.69183e18i 0.928648i
\(455\) 5.01889e18 1.24316
\(456\) 3.19938e18i 0.780390i
\(457\) 1.50674e18i 0.361930i −0.983490 0.180965i \(-0.942078\pi\)
0.983490 0.180965i \(-0.0579221\pi\)
\(458\) 2.78195e18i 0.658098i
\(459\) 4.74232e18i 1.10485i
\(460\) −4.22939e17 + 2.97376e17i −0.0970450 + 0.0682339i
\(461\) 8.19334e18 1.85163 0.925816 0.377975i \(-0.123379\pi\)
0.925816 + 0.377975i \(0.123379\pi\)
\(462\) 2.47215e18 0.550276
\(463\) −5.62016e18 −1.23220 −0.616101 0.787667i \(-0.711289\pi\)
−0.616101 + 0.787667i \(0.711289\pi\)
\(464\) −4.86696e18 −1.05107
\(465\) 2.57697e18i 0.548199i
\(466\) −1.30383e18 −0.273225
\(467\) 4.43115e18i 0.914741i −0.889276 0.457371i \(-0.848791\pi\)
0.889276 0.457371i \(-0.151209\pi\)
\(468\) 1.25557e17 0.0255340
\(469\) 1.09890e19 2.20165
\(470\) 2.90813e18i 0.574022i
\(471\) 7.02204e18i 1.36558i
\(472\) −6.72493e18 −1.28853
\(473\) 3.20612e18 0.605274
\(474\) 7.21649e18i 1.34239i
\(475\) 2.23087e18i 0.408902i
\(476\) −1.26255e18 −0.228034
\(477\) 7.18883e17i 0.127947i
\(478\) 4.08219e18 0.715976
\(479\) 7.29563e18i 1.26100i −0.776190 0.630499i \(-0.782850\pi\)
0.776190 0.630499i \(-0.217150\pi\)
\(480\) 1.28570e18i 0.219004i
\(481\) 7.52600e18i 1.26342i
\(482\) 1.32545e18i 0.219297i
\(483\) −6.40548e18 + 4.50380e18i −1.04453 + 0.734428i
\(484\) 8.29692e17 0.133352
\(485\) 2.08771e18 0.330733
\(486\) 1.81371e18 0.283213
\(487\) 3.34405e18 0.514719 0.257359 0.966316i \(-0.417148\pi\)
0.257359 + 0.966316i \(0.417148\pi\)
\(488\) 9.65428e18i 1.46481i
\(489\) −8.80611e18 −1.31711
\(490\) 4.79616e18i 0.707165i
\(491\) 1.15300e19 1.67594 0.837969 0.545718i \(-0.183743\pi\)
0.837969 + 0.545718i \(0.183743\pi\)
\(492\) 9.43045e16 0.0135138
\(493\) 6.87450e18i 0.971208i
\(494\) 8.68031e18i 1.20906i
\(495\) −2.88461e17 −0.0396142
\(496\) −6.59592e18 −0.893107
\(497\) 4.80821e18i 0.641932i
\(498\) 2.36415e18i 0.311221i
\(499\) 2.63099e18 0.341520 0.170760 0.985313i \(-0.445378\pi\)
0.170760 + 0.985313i \(0.445378\pi\)
\(500\) 1.33640e18i 0.171060i
\(501\) 6.24755e18 0.788579
\(502\) 1.35617e18i 0.168806i
\(503\) 6.37067e17i 0.0782004i −0.999235 0.0391002i \(-0.987551\pi\)
0.999235 0.0391002i \(-0.0124492\pi\)
\(504\) 1.35833e18i 0.164434i
\(505\) 5.03117e18i 0.600661i
\(506\) 2.99401e18 2.10514e18i 0.352533 0.247872i
\(507\) 3.79783e18 0.441042
\(508\) 1.50136e18 0.171965
\(509\) −1.18529e19 −1.33906 −0.669528 0.742787i \(-0.733504\pi\)
−0.669528 + 0.742787i \(0.733504\pi\)
\(510\) −7.04075e18 −0.784563
\(511\) 6.82542e18i 0.750210i
\(512\) −6.17689e18 −0.669700
\(513\) 9.12543e18i 0.975960i
\(514\) 9.72953e17 0.102648
\(515\) −1.25396e19 −1.30507
\(516\) 2.17811e18i 0.223631i
\(517\) 2.82123e18i 0.285762i
\(518\) −1.53706e19 −1.53597
\(519\) 4.55225e18 0.448802
\(520\) 8.44203e18i 0.821152i
\(521\) 8.24803e18i 0.791565i −0.918344 0.395782i \(-0.870473\pi\)
0.918344 0.395782i \(-0.129527\pi\)
\(522\) −1.39624e18 −0.132210
\(523\) 1.82691e19i 1.70689i 0.521185 + 0.853444i \(0.325490\pi\)
−0.521185 + 0.853444i \(0.674510\pi\)
\(524\) −3.31172e18 −0.305305
\(525\) 6.20328e18i 0.564295i
\(526\) 1.70435e19i 1.52988i
\(527\) 9.31662e18i 0.825247i
\(528\) 4.83572e18i 0.422692i
\(529\) −3.92249e18 + 1.09091e19i −0.338354 + 0.941019i
\(530\) −9.12486e18 −0.776775
\(531\) −2.24355e18 −0.188484
\(532\) 2.42947e18 0.201433
\(533\) −1.35532e18 −0.110905
\(534\) 2.66603e17i 0.0215316i
\(535\) 2.22421e18 0.177296
\(536\) 1.84841e19i 1.45427i
\(537\) 2.03598e18 0.158108
\(538\) 2.46806e19 1.89182
\(539\) 4.65285e18i 0.352044i
\(540\) 1.67543e18i 0.125133i
\(541\) −2.44163e19 −1.80011 −0.900053 0.435780i \(-0.856473\pi\)
−0.900053 + 0.435780i \(0.856473\pi\)
\(542\) 1.94476e19 1.41538
\(543\) 2.35255e17i 0.0169021i
\(544\) 4.64826e18i 0.329685i
\(545\) 8.27626e18 0.579507
\(546\) 2.41369e19i 1.66853i
\(547\) 2.53778e19 1.73198 0.865990 0.500061i \(-0.166689\pi\)
0.865990 + 0.500061i \(0.166689\pi\)
\(548\) 1.46168e18i 0.0984895i
\(549\) 3.22083e18i 0.214270i
\(550\) 2.89950e18i 0.190452i
\(551\) 1.32283e19i 0.857911i
\(552\) −7.57563e18 1.07744e19i −0.485115 0.689951i
\(553\) −2.90275e19 −1.83541
\(554\) 3.03770e19 1.89660
\(555\) −1.17466e19 −0.724202
\(556\) −1.44599e18 −0.0880325
\(557\) 2.07893e19i 1.24984i −0.780689 0.624920i \(-0.785132\pi\)
0.780689 0.624920i \(-0.214868\pi\)
\(558\) −1.89224e18 −0.112341
\(559\) 3.13031e19i 1.83529i
\(560\) 2.00503e19 1.16092
\(561\) 6.83037e18 0.390575
\(562\) 1.80651e19i 1.02020i
\(563\) 2.61350e19i 1.45769i −0.684681 0.728843i \(-0.740058\pi\)
0.684681 0.728843i \(-0.259942\pi\)
\(564\) −1.91663e18 −0.105581
\(565\) 1.60486e18 0.0873166
\(566\) 2.14923e19i 1.15496i
\(567\) 2.19535e19i 1.16526i
\(568\) 8.08767e18 0.424019
\(569\) 2.59722e19i 1.34500i 0.740097 + 0.672500i \(0.234780\pi\)
−0.740097 + 0.672500i \(0.765220\pi\)
\(570\) 1.35482e19 0.693039
\(571\) 1.54450e19i 0.780430i 0.920724 + 0.390215i \(0.127599\pi\)
−0.920724 + 0.390215i \(0.872401\pi\)
\(572\) 1.54609e18i 0.0771723i
\(573\) 2.65167e19i 1.30749i
\(574\) 2.76801e18i 0.134829i
\(575\) 5.28236e18 + 7.51278e18i 0.254187 + 0.361515i
\(576\) −2.21452e18 −0.105274
\(577\) −8.16943e18 −0.383673 −0.191836 0.981427i \(-0.561444\pi\)
−0.191836 + 0.981427i \(0.561444\pi\)
\(578\) −2.25411e18 −0.104588
\(579\) 8.61543e18 0.394936
\(580\) 2.42872e18i 0.109997i
\(581\) 9.50953e18 0.425526
\(582\) 1.00403e19i 0.443899i
\(583\) 8.85220e18 0.386697
\(584\) −1.14807e19 −0.495541
\(585\) 2.81640e18i 0.120117i
\(586\) 2.96568e19i 1.24980i
\(587\) 2.20336e19 0.917528 0.458764 0.888558i \(-0.348292\pi\)
0.458764 + 0.888558i \(0.348292\pi\)
\(588\) −3.16095e18 −0.130070
\(589\) 1.79276e19i 0.728977i
\(590\) 2.84776e19i 1.14430i
\(591\) −9.14670e18 −0.363205
\(592\) 3.00661e19i 1.17985i
\(593\) 1.65096e19 0.640258 0.320129 0.947374i \(-0.396274\pi\)
0.320129 + 0.947374i \(0.396274\pi\)
\(594\) 1.18605e19i 0.454566i
\(595\) 2.83207e19i 1.07272i
\(596\) 3.49952e18i 0.131004i
\(597\) 3.94122e19i 1.45818i
\(598\) −2.05536e19 2.92322e19i −0.751588 1.06894i
\(599\) −2.68291e19 −0.969656 −0.484828 0.874610i \(-0.661118\pi\)
−0.484828 + 0.874610i \(0.661118\pi\)
\(600\) −1.04343e19 −0.372737
\(601\) 7.15467e18 0.252620 0.126310 0.991991i \(-0.459687\pi\)
0.126310 + 0.991991i \(0.459687\pi\)
\(602\) −6.39313e19 −2.23120
\(603\) 6.16661e18i 0.212728i
\(604\) −3.45515e18 −0.117817
\(605\) 1.86111e19i 0.627312i
\(606\) −2.41960e19 −0.806187
\(607\) −2.88767e18 −0.0951102 −0.0475551 0.998869i \(-0.515143\pi\)
−0.0475551 + 0.998869i \(0.515143\pi\)
\(608\) 8.94445e18i 0.291225i
\(609\) 3.67833e19i 1.18394i
\(610\) 4.08824e19 1.30085
\(611\) 2.75452e19 0.866478
\(612\) 7.08494e17i 0.0220331i
\(613\) 5.05757e19i 1.55496i 0.628910 + 0.777478i \(0.283501\pi\)
−0.628910 + 0.777478i \(0.716499\pi\)
\(614\) −4.22540e19 −1.28437
\(615\) 2.11537e18i 0.0635713i
\(616\) −1.67262e19 −0.496974
\(617\) 3.52476e19i 1.03546i −0.855544 0.517730i \(-0.826777\pi\)
0.855544 0.517730i \(-0.173223\pi\)
\(618\) 6.03057e19i 1.75162i
\(619\) 2.23761e19i 0.642613i −0.946975 0.321307i \(-0.895878\pi\)
0.946975 0.321307i \(-0.104122\pi\)
\(620\) 3.29150e18i 0.0934657i
\(621\) −2.16076e19 3.07312e19i −0.606688 0.862856i
\(622\) 3.90630e19 1.08451
\(623\) 1.07238e18 0.0294396
\(624\) 4.72137e19 1.28167
\(625\) −1.35140e19 −0.362765
\(626\) 5.06432e19i 1.34431i
\(627\) −1.31434e19 −0.345012
\(628\) 8.96909e18i 0.232826i
\(629\) −4.24678e19 −1.09020
\(630\) 5.75204e18 0.146029
\(631\) 5.32087e19i 1.33591i −0.744202 0.667955i \(-0.767170\pi\)
0.744202 0.667955i \(-0.232830\pi\)
\(632\) 4.88259e19i 1.21236i
\(633\) −2.40905e19 −0.591589
\(634\) 5.20139e18 0.126326
\(635\) 3.36776e19i 0.808955i
\(636\) 6.01382e18i 0.142873i
\(637\) 4.54283e19 1.06746
\(638\) 1.71930e19i 0.399583i
\(639\) 2.69818e18 0.0620248
\(640\) 3.84502e19i 0.874257i
\(641\) 4.52785e19i 1.01832i 0.860671 + 0.509162i \(0.170045\pi\)
−0.860671 + 0.509162i \(0.829955\pi\)
\(642\) 1.06967e19i 0.237961i
\(643\) 1.88343e19i 0.414451i 0.978293 + 0.207225i \(0.0664434\pi\)
−0.978293 + 0.207225i \(0.933557\pi\)
\(644\) −8.18158e18 + 5.75260e18i −0.178089 + 0.125217i
\(645\) −4.88578e19 −1.05200
\(646\) 4.89814e19 1.04329
\(647\) 7.80559e19 1.64466 0.822329 0.569013i \(-0.192674\pi\)
0.822329 + 0.569013i \(0.192674\pi\)
\(648\) 3.69270e19 0.769695
\(649\) 2.76267e19i 0.569660i
\(650\) −2.83094e19 −0.577481
\(651\) 4.98503e19i 1.00601i
\(652\) −1.12478e19 −0.224562
\(653\) −7.58993e19 −1.49915 −0.749576 0.661918i \(-0.769743\pi\)
−0.749576 + 0.661918i \(0.769743\pi\)
\(654\) 3.98024e19i 0.777794i
\(655\) 7.42862e19i 1.43621i
\(656\) −5.41444e18 −0.103568
\(657\) −3.83016e18 −0.0724869
\(658\) 5.62565e19i 1.05340i
\(659\) 4.77947e19i 0.885487i −0.896648 0.442744i \(-0.854005\pi\)
0.896648 0.442744i \(-0.145995\pi\)
\(660\) 2.41313e18 0.0442356
\(661\) 5.44299e19i 0.987250i 0.869675 + 0.493625i \(0.164329\pi\)
−0.869675 + 0.493625i \(0.835671\pi\)
\(662\) −4.35998e19 −0.782490
\(663\) 6.66886e19i 1.18429i
\(664\) 1.59955e19i 0.281075i
\(665\) 5.44962e19i 0.947577i
\(666\) 8.62538e18i 0.148408i
\(667\) 3.13225e19 + 4.45481e19i 0.533305 + 0.758488i
\(668\) 7.97985e18 0.134450
\(669\) 4.93064e19 0.822092
\(670\) 7.82735e19 1.29149
\(671\) −3.96607e19 −0.647595
\(672\) 2.48714e19i 0.401898i
\(673\) −9.01741e19 −1.44204 −0.721018 0.692916i \(-0.756326\pi\)
−0.721018 + 0.692916i \(0.756326\pi\)
\(674\) 6.70741e18i 0.106154i
\(675\) −2.97611e19 −0.466147
\(676\) 4.85088e18 0.0751959
\(677\) 8.16439e19i 1.25257i 0.779593 + 0.626286i \(0.215426\pi\)
−0.779593 + 0.626286i \(0.784574\pi\)
\(678\) 7.71811e18i 0.117193i
\(679\) 4.03858e19 0.606933
\(680\) 4.76368e19 0.708567
\(681\) 5.45784e19i 0.803510i
\(682\) 2.33007e19i 0.339531i
\(683\) 9.14636e19 1.31918 0.659589 0.751626i \(-0.270730\pi\)
0.659589 + 0.751626i \(0.270730\pi\)
\(684\) 1.36332e18i 0.0194628i
\(685\) −3.27875e19 −0.463313
\(686\) 1.27271e19i 0.178016i
\(687\) 4.11271e19i 0.569417i
\(688\) 1.25055e20i 1.71388i
\(689\) 8.64288e19i 1.17253i
\(690\) −4.56255e19 + 3.20800e19i −0.612723 + 0.430815i
\(691\) 4.85514e18 0.0645439 0.0322720 0.999479i \(-0.489726\pi\)
0.0322720 + 0.999479i \(0.489726\pi\)
\(692\) 5.81449e18 0.0765189
\(693\) −5.58016e18 −0.0726966
\(694\) 7.11996e19 0.918250
\(695\) 3.24356e19i 0.414122i
\(696\) −6.18714e19 −0.782034
\(697\) 7.64780e18i 0.0956990i
\(698\) −1.07400e20 −1.33050
\(699\) −1.92753e19 −0.236407
\(700\) 7.92331e18i 0.0962101i
\(701\) 9.49951e19i 1.14202i 0.820942 + 0.571012i \(0.193449\pi\)
−0.820942 + 0.571012i \(0.806551\pi\)
\(702\) 1.15800e20 1.37832
\(703\) 8.17189e19 0.963020
\(704\) 2.72692e19i 0.318173i
\(705\) 4.29925e19i 0.496671i
\(706\) 6.24763e19 0.714632
\(707\) 9.73258e19i 1.10228i
\(708\) 1.87684e19 0.210472
\(709\) 3.80305e19i 0.422287i 0.977455 + 0.211144i \(0.0677188\pi\)
−0.977455 + 0.211144i \(0.932281\pi\)
\(710\) 3.42483e19i 0.376557i
\(711\) 1.62891e19i 0.177342i
\(712\) 1.80380e18i 0.0194459i
\(713\) 4.24496e19 + 6.03736e19i 0.453156 + 0.644496i
\(714\) −1.36200e20 −1.43976
\(715\) −3.46807e19 −0.363033
\(716\) 2.60052e18 0.0269568
\(717\) 6.03493e19 0.619496
\(718\) 1.33521e20i 1.35731i
\(719\) 1.16463e20 1.17243 0.586215 0.810156i \(-0.300617\pi\)
0.586215 + 0.810156i \(0.300617\pi\)
\(720\) 1.12514e19i 0.112171i
\(721\) −2.42573e20 −2.39494
\(722\) 1.58417e19 0.154896
\(723\) 1.95948e19i 0.189746i
\(724\) 3.00486e17i 0.00288173i
\(725\) 4.31419e19 0.409763
\(726\) 8.95048e19 0.841957
\(727\) 1.06408e20i 0.991363i 0.868504 + 0.495682i \(0.165082\pi\)
−0.868504 + 0.495682i \(0.834918\pi\)
\(728\) 1.63307e20i 1.50691i
\(729\) 1.19819e20 1.09504
\(730\) 4.86167e19i 0.440074i
\(731\) −1.76638e20 −1.58366
\(732\) 2.69439e19i 0.239267i
\(733\) 1.13276e20i 0.996347i −0.867077 0.498174i \(-0.834004\pi\)
0.867077 0.498174i \(-0.165996\pi\)
\(734\) 1.19045e20i 1.03714i
\(735\) 7.09043e19i 0.611873i
\(736\) −2.11791e19 3.01217e19i −0.181035 0.257475i
\(737\) −7.59346e19 −0.642935
\(738\) −1.55330e18 −0.0130275
\(739\) 1.18974e20 0.988419 0.494209 0.869343i \(-0.335458\pi\)
0.494209 + 0.869343i \(0.335458\pi\)
\(740\) −1.50036e19 −0.123473
\(741\) 1.28326e20i 1.04613i
\(742\) −1.76516e20 −1.42547
\(743\) 1.46518e20i 1.17212i −0.810269 0.586058i \(-0.800679\pi\)
0.810269 0.586058i \(-0.199321\pi\)
\(744\) −8.38508e19 −0.664503
\(745\) −7.84988e19 −0.616267
\(746\) 1.16076e20i 0.902755i
\(747\) 5.33638e18i 0.0411152i
\(748\) 8.72428e18 0.0665914
\(749\) 4.30264e19 0.325359
\(750\) 1.44167e20i 1.08004i
\(751\) 1.97365e19i 0.146484i 0.997314 + 0.0732420i \(0.0233345\pi\)
−0.997314 + 0.0732420i \(0.976665\pi\)
\(752\) 1.10042e20 0.809159
\(753\) 2.00490e19i 0.146059i
\(754\) −1.67865e20 −1.21160
\(755\) 7.75036e19i 0.554234i
\(756\) 3.24105e19i 0.229632i
\(757\) 1.51607e20i 1.06426i −0.846661 0.532132i \(-0.821391\pi\)
0.846661 0.532132i \(-0.178609\pi\)
\(758\) 2.23593e19i 0.155515i
\(759\) 4.42622e19 3.11214e19i 0.305028 0.214470i
\(760\) −9.16654e19 −0.625908
\(761\) 2.71683e20 1.83810 0.919051 0.394139i \(-0.128957\pi\)
0.919051 + 0.394139i \(0.128957\pi\)
\(762\) 1.61963e20 1.08575
\(763\) 1.60101e20 1.06346
\(764\) 3.38692e19i 0.222921i
\(765\) 1.58925e19 0.103648
\(766\) 6.95215e19i 0.449280i
\(767\) −2.69734e20 −1.72730
\(768\) 6.82583e19 0.433139
\(769\) 1.88496e20i 1.18527i 0.805471 + 0.592635i \(0.201912\pi\)
−0.805471 + 0.592635i \(0.798088\pi\)
\(770\) 7.08296e19i 0.441346i
\(771\) 1.43837e19 0.0888158
\(772\) 1.10043e19 0.0673351
\(773\) 1.32572e20i 0.803890i −0.915664 0.401945i \(-0.868334\pi\)
0.915664 0.401945i \(-0.131666\pi\)
\(774\) 3.58758e19i 0.215583i
\(775\) 5.84678e19 0.348181
\(776\) 6.79311e19i 0.400901i
\(777\) −2.27232e20 −1.32899
\(778\) 7.36721e19i 0.427018i
\(779\) 1.47163e19i 0.0845351i
\(780\) 2.35607e19i 0.134130i
\(781\) 3.32249e19i 0.187459i
\(782\) −1.64952e20 + 1.15980e20i −0.922380 + 0.648540i
\(783\) −1.76473e20 −0.978015
\(784\) 1.81484e20 0.996842
\(785\) 2.01188e20 1.09526
\(786\) −3.57259e20 −1.92764
\(787\) 1.85324e20i 0.991082i 0.868585 + 0.495541i \(0.165030\pi\)
−0.868585 + 0.495541i \(0.834970\pi\)
\(788\) −1.16829e19 −0.0619250
\(789\) 2.51963e20i 1.32372i
\(790\) −2.06760e20 −1.07665
\(791\) 3.10452e19 0.160236
\(792\) 9.38612e18i 0.0480187i
\(793\) 3.87229e20i 1.96361i
\(794\) −1.41721e20 −0.712348
\(795\) −1.34898e20 −0.672102
\(796\) 5.03403e19i 0.248613i
\(797\) 1.76047e20i 0.861825i −0.902394 0.430913i \(-0.858192\pi\)
0.902394 0.430913i \(-0.141808\pi\)
\(798\) 2.62084e20 1.27180
\(799\) 1.55433e20i 0.747678i
\(800\) −2.91709e19 −0.139097
\(801\) 6.01778e17i 0.00284452i
\(802\) 2.77925e20i 1.30229i
\(803\) 4.71640e19i 0.219079i
\(804\) 5.15868e19i 0.237545i
\(805\) −1.29038e20 1.83524e20i −0.589044 0.837762i
\(806\) −2.27498e20 −1.02951
\(807\) 3.64867e20 1.63689
\(808\) 1.63707e20 0.728096
\(809\) 1.96550e20 0.866632 0.433316 0.901242i \(-0.357343\pi\)
0.433316 + 0.901242i \(0.357343\pi\)
\(810\) 1.56372e20i 0.683542i
\(811\) −3.18086e20 −1.37847 −0.689236 0.724536i \(-0.742054\pi\)
−0.689236 + 0.724536i \(0.742054\pi\)
\(812\) 4.69824e19i 0.201857i
\(813\) 2.87505e20 1.22465
\(814\) 1.06211e20 0.448539
\(815\) 2.52304e20i 1.05638i
\(816\) 2.66419e20i 1.10594i
\(817\) 3.39896e20 1.39892
\(818\) 2.69933e20 1.10150
\(819\) 5.44821e19i 0.220428i
\(820\) 2.70192e18i 0.0108387i
\(821\) −1.05029e20 −0.417741 −0.208870 0.977943i \(-0.566979\pi\)
−0.208870 + 0.977943i \(0.566979\pi\)
\(822\) 1.57682e20i 0.621843i
\(823\) 3.47206e20 1.35765 0.678826 0.734299i \(-0.262489\pi\)
0.678826 + 0.734299i \(0.262489\pi\)
\(824\) 4.08021e20i 1.58195i
\(825\) 4.28650e19i 0.164788i
\(826\) 5.50887e20i 2.09992i
\(827\) 1.11144e20i 0.420095i 0.977691 + 0.210047i \(0.0673618\pi\)
−0.977691 + 0.210047i \(0.932638\pi\)
\(828\) −3.22814e18 4.59119e18i −0.0120987 0.0172073i
\(829\) −3.71470e20 −1.38052 −0.690259 0.723563i \(-0.742503\pi\)
−0.690259 + 0.723563i \(0.742503\pi\)
\(830\) 6.77353e19 0.249614
\(831\) 4.49080e20 1.64103
\(832\) −2.66244e20 −0.964753
\(833\) 2.56343e20i 0.921100i
\(834\) −1.55990e20 −0.555820
\(835\) 1.78999e20i 0.632476i
\(836\) −1.67877e19 −0.0588231
\(837\) −2.39164e20 −0.831031
\(838\) 5.72756e20i 1.97361i
\(839\) 4.53957e20i 1.55125i −0.631195 0.775624i \(-0.717435\pi\)
0.631195 0.775624i \(-0.282565\pi\)
\(840\) 2.54890e20 0.863769
\(841\) −4.17421e19 −0.140282
\(842\) 3.81208e20i 1.27051i
\(843\) 2.67067e20i 0.882728i
\(844\) −3.07703e19 −0.100864
\(845\) 1.08812e20i 0.353735i
\(846\) 3.15690e19 0.101781
\(847\) 3.60023e20i 1.15119i
\(848\) 3.45280e20i 1.09497i
\(849\) 3.17733e20i 0.999328i
\(850\) 1.59745e20i 0.498304i
\(851\) −2.75200e20 + 1.93498e20i −0.851416 + 0.598644i
\(852\) −2.25717e19 −0.0692606
\(853\) 1.50373e20 0.457644 0.228822 0.973468i \(-0.426513\pi\)
0.228822 + 0.973468i \(0.426513\pi\)
\(854\) 7.90851e20 2.38721
\(855\) −3.05811e19 −0.0915569
\(856\) 7.23727e19i 0.214911i
\(857\) 1.03203e20 0.303966 0.151983 0.988383i \(-0.451434\pi\)
0.151983 + 0.988383i \(0.451434\pi\)
\(858\) 1.66787e20i 0.487250i
\(859\) −5.26547e20 −1.52576 −0.762878 0.646542i \(-0.776214\pi\)
−0.762878 + 0.646542i \(0.776214\pi\)
\(860\) −6.24049e19 −0.179362
\(861\) 4.09210e19i 0.116661i
\(862\) 4.89088e20i 1.38304i
\(863\) 1.72159e20 0.482896 0.241448 0.970414i \(-0.422378\pi\)
0.241448 + 0.970414i \(0.422378\pi\)
\(864\) 1.19324e20 0.331995
\(865\) 1.30427e20i 0.359959i
\(866\) 1.37716e20i 0.377015i
\(867\) −3.33238e19 −0.0904942
\(868\) 6.36727e19i 0.171520i
\(869\) 2.00582e20 0.535985
\(870\) 2.62003e20i 0.694499i
\(871\) 7.41391e20i 1.94949i
\(872\) 2.69298e20i 0.702454i
\(873\) 2.26630e19i 0.0586431i
\(874\) 3.17409e20 2.23176e20i 0.814779 0.572884i
\(875\) −5.79897e20 −1.47671
\(876\) 3.20412e19 0.0809433
\(877\) −4.28662e20 −1.07428 −0.537141 0.843492i \(-0.680496\pi\)
−0.537141 + 0.843492i \(0.680496\pi\)
\(878\) 8.50000e19 0.211328
\(879\) 4.38434e20i 1.08139i
\(880\) −1.38548e20 −0.339018
\(881\) 2.99471e20i 0.726982i 0.931598 + 0.363491i \(0.118415\pi\)
−0.931598 + 0.363491i \(0.881585\pi\)
\(882\) 5.20643e19 0.125389
\(883\) −2.41781e20 −0.577694 −0.288847 0.957375i \(-0.593272\pi\)
−0.288847 + 0.957375i \(0.593272\pi\)
\(884\) 8.51798e19i 0.201916i
\(885\) 4.21001e20i 0.990101i
\(886\) −6.84089e20 −1.59616
\(887\) 3.50368e20 0.811071 0.405535 0.914079i \(-0.367085\pi\)
0.405535 + 0.914079i \(0.367085\pi\)
\(888\) 3.82216e20i 0.877846i
\(889\) 6.51478e20i 1.48452i
\(890\) 7.63844e18 0.0172693
\(891\) 1.51700e20i 0.340284i
\(892\) 6.29779e19 0.140163
\(893\) 2.99092e20i 0.660457i
\(894\) 3.77518e20i 0.827133i
\(895\) 5.83330e19i 0.126810i
\(896\) 7.43803e20i 1.60436i
\(897\) −3.03856e20 4.32155e20i −0.650310 0.924896i
\(898\) −9.08143e20 −1.92850
\(899\) 3.46693e20 0.730512
\(900\) −4.44626e18 −0.00929602
\(901\) −4.87702e20 −1.01177
\(902\) 1.91271e19i 0.0393733i
\(903\) −9.45132e20 −1.93054
\(904\) 5.22198e19i 0.105841i
\(905\) 6.74029e18 0.0135562
\(906\) −3.72732e20 −0.743874
\(907\) 3.62231e20i 0.717357i 0.933461 + 0.358678i \(0.116772\pi\)
−0.933461 + 0.358678i \(0.883228\pi\)
\(908\) 6.97118e19i 0.136995i
\(909\) 5.46155e19 0.106505
\(910\) 6.91548e20 1.33823
\(911\) 1.46755e20i 0.281814i 0.990023 + 0.140907i \(0.0450019\pi\)
−0.990023 + 0.140907i \(0.954998\pi\)
\(912\) 5.12657e20i 0.976930i
\(913\) −6.57113e19 −0.124264
\(914\) 2.07612e20i 0.389610i
\(915\) 6.04387e20 1.12556
\(916\) 5.25307e19i 0.0970833i
\(917\) 1.43703e21i 2.63561i
\(918\) 6.53440e20i 1.18934i
\(919\) 5.88168e20i 1.06241i −0.847243 0.531206i \(-0.821739\pi\)
0.847243 0.531206i \(-0.178261\pi\)
\(920\) 3.08696e20 2.17049e20i 0.553371 0.389084i
\(921\) −6.24664e20 −1.11129
\(922\) 1.12895e21 1.99324
\(923\) 3.24393e20 0.568408
\(924\) 4.66809e19 0.0811774
\(925\) 2.66513e20i 0.459967i
\(926\) −7.74397e20 −1.32644
\(927\) 1.36123e20i 0.231405i
\(928\) −1.72973e20 −0.291838
\(929\) 7.29333e20 1.22128 0.610641 0.791908i \(-0.290912\pi\)
0.610641 + 0.791908i \(0.290912\pi\)
\(930\) 3.55078e20i 0.590124i
\(931\) 4.93270e20i 0.813649i
\(932\) −2.46198e19 −0.0403064
\(933\) 5.77491e20 0.938369
\(934\) 6.10564e20i 0.984698i
\(935\) 1.95697e20i 0.313258i
\(936\) −9.16418e19 −0.145600
\(937\) 1.03045e21i 1.62499i −0.582965 0.812497i \(-0.698108\pi\)
0.582965 0.812497i \(-0.301892\pi\)
\(938\) 1.51417e21 2.37003
\(939\) 7.48687e20i 1.16316i
\(940\) 5.49133e19i 0.0846804i
\(941\) 8.79559e20i 1.34629i 0.739512 + 0.673144i \(0.235056\pi\)
−0.739512 + 0.673144i \(0.764944\pi\)
\(942\) 9.67560e20i 1.47001i
\(943\) 3.48460e19 + 4.95593e19i 0.0525497 + 0.0747383i
\(944\) −1.07758e21 −1.61304
\(945\) 7.27010e20 1.08023
\(946\) 4.41768e20 0.651563
\(947\) −3.32817e20 −0.487254 −0.243627 0.969869i \(-0.578337\pi\)
−0.243627 + 0.969869i \(0.578337\pi\)
\(948\) 1.36267e20i 0.198030i
\(949\) −4.60487e20 −0.664285
\(950\) 3.07390e20i 0.440174i
\(951\) 7.68950e19 0.109304
\(952\) 9.21514e20 1.30030
\(953\) 7.83606e20i 1.09761i −0.835951 0.548804i \(-0.815083\pi\)
0.835951 0.548804i \(-0.184917\pi\)
\(954\) 9.90542e19i 0.137732i
\(955\) −7.59731e20 −1.04866
\(956\) 7.70829e19 0.105622
\(957\) 2.54174e20i 0.345738i
\(958\) 1.00526e21i 1.35743i
\(959\) −6.34260e20 −0.850231
\(960\) 4.15552e20i 0.553003i
\(961\) −2.87090e20 −0.379275
\(962\) 1.03700e21i 1.36005i
\(963\) 2.41447e19i 0.0314368i
\(964\) 2.50280e19i 0.0323509i
\(965\) 2.46841e20i 0.316757i
\(966\) −8.82605e20 + 6.20574e20i −1.12442 + 0.790595i
\(967\) 1.33489e21 1.68834 0.844168 0.536079i \(-0.180095\pi\)
0.844168 + 0.536079i \(0.180095\pi\)
\(968\) −6.05578e20 −0.760401
\(969\) 7.24119e20 0.902701
\(970\) 2.87664e20 0.356027
\(971\) 7.59002e20i 0.932627i −0.884619 0.466314i \(-0.845582\pi\)
0.884619 0.466314i \(-0.154418\pi\)
\(972\) 3.42477e19 0.0417799
\(973\) 6.27452e20i 0.759960i
\(974\) 4.60773e20 0.554083
\(975\) −4.18514e20 −0.499663
\(976\) 1.54697e21i 1.83372i
\(977\) 6.28594e20i 0.739789i 0.929074 + 0.369895i \(0.120606\pi\)
−0.929074 + 0.369895i \(0.879394\pi\)
\(978\) −1.21339e21 −1.41784
\(979\) −7.41019e18 −0.00859707
\(980\) 9.05645e19i 0.104322i
\(981\) 8.98423e19i 0.102754i
\(982\) 1.58870e21 1.80411
\(983\) 7.23188e20i 0.815412i 0.913113 + 0.407706i \(0.133671\pi\)
−0.913113 + 0.407706i \(0.866329\pi\)
\(984\) −6.88313e19 −0.0770584
\(985\) 2.62062e20i 0.291307i
\(986\) 9.47231e20i 1.04548i
\(987\) 8.31671e20i 0.911447i
\(988\) 1.63908e20i 0.178361i
\(989\) −1.14465e21 + 8.04820e20i −1.23680 + 0.869611i
\(990\) −3.97468e19 −0.0426438
\(991\) 1.29131e21 1.37567 0.687836 0.725866i \(-0.258561\pi\)
0.687836 + 0.725866i \(0.258561\pi\)
\(992\) −2.34420e20 −0.247978
\(993\) −6.44561e20 −0.677047
\(994\) 6.62519e20i 0.691025i
\(995\) −1.12920e21 −1.16952
\(996\) 4.46415e19i 0.0459117i
\(997\) −3.27971e20 −0.334942 −0.167471 0.985877i \(-0.553560\pi\)
−0.167471 + 0.985877i \(0.553560\pi\)
\(998\) 3.62522e20 0.367639
\(999\) 1.09018e21i 1.09784i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 23.15.b.b.22.20 yes 24
23.22 odd 2 inner 23.15.b.b.22.19 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.15.b.b.22.19 24 23.22 odd 2 inner
23.15.b.b.22.20 yes 24 1.1 even 1 trivial