Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.a (trivial) |
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: | yes |
Analytic conductor: | \(18.8926051182\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.198062 | −0.114351 | −0.0571757 | − | 0.998364i | \(-0.518210\pi\) | ||||
−0.0571757 | + | 0.998364i | \(0.518210\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.890084 | 0.398058 | 0.199029 | − | 0.979994i | \(-0.436221\pi\) | ||||
0.199029 | + | 0.979994i | \(0.436221\pi\) | |||||||
\(6\) | −0.198062 | −0.0808586 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.96077 | −0.986924 | ||||||||
\(10\) | 0.890084 | 0.281469 | ||||||||
\(11\) | 0.664874 | 0.200467 | 0.100234 | − | 0.994964i | \(-0.468041\pi\) | ||||
0.100234 | + | 0.994964i | \(0.468041\pi\) | |||||||
\(12\) | −0.198062 | −0.0571757 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −0.176292 | −0.0455184 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.44504 | −0.593010 | −0.296505 | − | 0.955031i | \(-0.595821\pi\) | ||||
−0.296505 | + | 0.955031i | \(0.595821\pi\) | |||||||
\(18\) | −2.96077 | −0.697860 | ||||||||
\(19\) | −8.63102 | −1.98009 | −0.990046 | − | 0.140743i | \(-0.955051\pi\) | ||||
−0.990046 | + | 0.140743i | \(0.955051\pi\) | |||||||
\(20\) | 0.890084 | 0.199029 | ||||||||
\(21\) | 0.198062 | 0.0432207 | ||||||||
\(22\) | 0.664874 | 0.141752 | ||||||||
\(23\) | −7.60388 | −1.58552 | −0.792759 | − | 0.609535i | \(-0.791356\pi\) | ||||
−0.792759 | + | 0.609535i | \(0.791356\pi\) | |||||||
\(24\) | −0.198062 | −0.0404293 | ||||||||
\(25\) | −4.20775 | −0.841550 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.18060 | 0.227207 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 3.60388 | 0.669223 | 0.334611 | − | 0.942356i | \(-0.391395\pi\) | ||||
0.334611 | + | 0.942356i | \(0.391395\pi\) | |||||||
\(30\) | −0.176292 | −0.0321864 | ||||||||
\(31\) | −1.50604 | −0.270493 | −0.135246 | − | 0.990812i | \(-0.543183\pi\) | ||||
−0.135246 | + | 0.990812i | \(0.543183\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.131687 | −0.0229237 | ||||||||
\(34\) | −2.44504 | −0.419321 | ||||||||
\(35\) | −0.890084 | −0.150452 | ||||||||
\(36\) | −2.96077 | −0.493462 | ||||||||
\(37\) | −5.60388 | −0.921271 | −0.460636 | − | 0.887589i | \(-0.652379\pi\) | ||||
−0.460636 | + | 0.887589i | \(0.652379\pi\) | |||||||
\(38\) | −8.63102 | −1.40014 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.890084 | 0.140735 | ||||||||
\(41\) | 7.83877 | 1.22421 | 0.612105 | − | 0.790776i | \(-0.290323\pi\) | ||||
0.612105 | + | 0.790776i | \(0.290323\pi\) | |||||||
\(42\) | 0.198062 | 0.0305617 | ||||||||
\(43\) | 7.46681 | 1.13868 | 0.569339 | − | 0.822103i | \(-0.307199\pi\) | ||||
0.569339 | + | 0.822103i | \(0.307199\pi\) | |||||||
\(44\) | 0.664874 | 0.100234 | ||||||||
\(45\) | −2.63533 | −0.392852 | ||||||||
\(46\) | −7.60388 | −1.12113 | ||||||||
\(47\) | −1.20775 | −0.176169 | −0.0880843 | − | 0.996113i | \(-0.528074\pi\) | ||||
−0.0880843 | + | 0.996113i | \(0.528074\pi\) | |||||||
\(48\) | −0.198062 | −0.0285878 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.20775 | −0.595066 | ||||||||
\(51\) | 0.484271 | 0.0678114 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89008 | −0.671705 | −0.335852 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335852 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(54\) | 1.18060 | 0.160660 | ||||||||
\(55\) | 0.591794 | 0.0797975 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.70948 | 0.226426 | ||||||||
\(58\) | 3.60388 | 0.473212 | ||||||||
\(59\) | −12.8334 | −1.67077 | −0.835383 | − | 0.549668i | \(-0.814754\pi\) | ||||
−0.835383 | + | 0.549668i | \(0.814754\pi\) | |||||||
\(60\) | −0.176292 | −0.0227592 | ||||||||
\(61\) | 7.70171 | 0.986103 | 0.493051 | − | 0.870000i | \(-0.335881\pi\) | ||||
0.493051 | + | 0.870000i | \(0.335881\pi\) | |||||||
\(62\) | −1.50604 | −0.191267 | ||||||||
\(63\) | 2.96077 | 0.373022 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.131687 | −0.0162095 | ||||||||
\(67\) | 6.07606 | 0.742309 | 0.371155 | − | 0.928571i | \(-0.378962\pi\) | ||||
0.371155 | + | 0.928571i | \(0.378962\pi\) | |||||||
\(68\) | −2.44504 | −0.296505 | ||||||||
\(69\) | 1.50604 | 0.181306 | ||||||||
\(70\) | −0.890084 | −0.106385 | ||||||||
\(71\) | −6.27413 | −0.744602 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(72\) | −2.96077 | −0.348930 | ||||||||
\(73\) | 3.67994 | 0.430704 | 0.215352 | − | 0.976536i | \(-0.430910\pi\) | ||||
0.215352 | + | 0.976536i | \(0.430910\pi\) | |||||||
\(74\) | −5.60388 | −0.651437 | ||||||||
\(75\) | 0.833397 | 0.0962324 | ||||||||
\(76\) | −8.63102 | −0.990046 | ||||||||
\(77\) | −0.664874 | −0.0757695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.37196 | 0.491884 | 0.245942 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245942 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(80\) | 0.890084 | 0.0995144 | ||||||||
\(81\) | 8.64848 | 0.960942 | ||||||||
\(82\) | 7.83877 | 0.865648 | ||||||||
\(83\) | −2.92931 | −0.321534 | −0.160767 | − | 0.986992i | \(-0.551397\pi\) | ||||
−0.160767 | + | 0.986992i | \(0.551397\pi\) | |||||||
\(84\) | 0.198062 | 0.0216104 | ||||||||
\(85\) | −2.17629 | −0.236052 | ||||||||
\(86\) | 7.46681 | 0.805167 | ||||||||
\(87\) | −0.713792 | −0.0765265 | ||||||||
\(88\) | 0.664874 | 0.0708758 | ||||||||
\(89\) | −12.5157 | −1.32666 | −0.663332 | − | 0.748325i | \(-0.730858\pi\) | ||||
−0.663332 | + | 0.748325i | \(0.730858\pi\) | |||||||
\(90\) | −2.63533 | −0.277789 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.60388 | −0.792759 | ||||||||
\(93\) | 0.298290 | 0.0309312 | ||||||||
\(94\) | −1.20775 | −0.124570 | ||||||||
\(95\) | −7.68233 | −0.788191 | ||||||||
\(96\) | −0.198062 | −0.0202146 | ||||||||
\(97\) | −10.4450 | −1.06053 | −0.530267 | − | 0.847831i | \(-0.677908\pi\) | ||||
−0.530267 | + | 0.847831i | \(0.677908\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −1.96854 | −0.197846 | ||||||||
\(100\) | −4.20775 | −0.420775 | ||||||||
\(101\) | −8.98792 | −0.894331 | −0.447166 | − | 0.894451i | \(-0.647567\pi\) | ||||
−0.447166 | + | 0.894451i | \(0.647567\pi\) | |||||||
\(102\) | 0.484271 | 0.0479499 | ||||||||
\(103\) | −8.27413 | −0.815274 | −0.407637 | − | 0.913144i | \(-0.633647\pi\) | ||||
−0.407637 | + | 0.913144i | \(0.633647\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.176292 | 0.0172043 | ||||||||
\(106\) | −4.89008 | −0.474967 | ||||||||
\(107\) | 14.5090 | 1.40264 | 0.701320 | − | 0.712846i | \(-0.252594\pi\) | ||||
0.701320 | + | 0.712846i | \(0.252594\pi\) | |||||||
\(108\) | 1.18060 | 0.113604 | ||||||||
\(109\) | 12.8659 | 1.23233 | 0.616166 | − | 0.787616i | \(-0.288685\pi\) | ||||
0.616166 | + | 0.787616i | \(0.288685\pi\) | |||||||
\(110\) | 0.591794 | 0.0564253 | ||||||||
\(111\) | 1.10992 | 0.105349 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −1.99761 | −0.187919 | −0.0939595 | − | 0.995576i | \(-0.529952\pi\) | ||||
−0.0939595 | + | 0.995576i | \(0.529952\pi\) | |||||||
\(114\) | 1.70948 | 0.160107 | ||||||||
\(115\) | −6.76809 | −0.631127 | ||||||||
\(116\) | 3.60388 | 0.334611 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.8334 | −1.18141 | ||||||||
\(119\) | 2.44504 | 0.224137 | ||||||||
\(120\) | −0.176292 | −0.0160932 | ||||||||
\(121\) | −10.5579 | −0.959813 | ||||||||
\(122\) | 7.70171 | 0.697280 | ||||||||
\(123\) | −1.55257 | −0.139990 | ||||||||
\(124\) | −1.50604 | −0.135246 | ||||||||
\(125\) | −8.19567 | −0.733043 | ||||||||
\(126\) | 2.96077 | 0.263766 | ||||||||
\(127\) | 5.78017 | 0.512907 | 0.256453 | − | 0.966557i | \(-0.417446\pi\) | ||||
0.256453 | + | 0.966557i | \(0.417446\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.47889 | −0.130209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.05861 | 0.179861 | 0.0899306 | − | 0.995948i | \(-0.471335\pi\) | ||||
0.0899306 | + | 0.995948i | \(0.471335\pi\) | |||||||
\(132\) | −0.131687 | −0.0114618 | ||||||||
\(133\) | 8.63102 | 0.748405 | ||||||||
\(134\) | 6.07606 | 0.524892 | ||||||||
\(135\) | 1.05084 | 0.0904416 | ||||||||
\(136\) | −2.44504 | −0.209661 | ||||||||
\(137\) | 6.24160 | 0.533256 | 0.266628 | − | 0.963800i | \(-0.414090\pi\) | ||||
0.266628 | + | 0.963800i | \(0.414090\pi\) | |||||||
\(138\) | 1.50604 | 0.128203 | ||||||||
\(139\) | −7.55496 | −0.640803 | −0.320402 | − | 0.947282i | \(-0.603818\pi\) | ||||
−0.320402 | + | 0.947282i | \(0.603818\pi\) | |||||||
\(140\) | −0.890084 | −0.0752258 | ||||||||
\(141\) | 0.239210 | 0.0201451 | ||||||||
\(142\) | −6.27413 | −0.526513 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.96077 | −0.246731 | ||||||||
\(145\) | 3.20775 | 0.266389 | ||||||||
\(146\) | 3.67994 | 0.304554 | ||||||||
\(147\) | −0.198062 | −0.0163359 | ||||||||
\(148\) | −5.60388 | −0.460636 | ||||||||
\(149\) | −16.8901 | −1.38369 | −0.691845 | − | 0.722046i | \(-0.743202\pi\) | ||||
−0.691845 | + | 0.722046i | \(0.743202\pi\) | |||||||
\(150\) | 0.833397 | 0.0680466 | ||||||||
\(151\) | −11.5254 | −0.937925 | −0.468963 | − | 0.883218i | \(-0.655372\pi\) | ||||
−0.468963 | + | 0.883218i | \(0.655372\pi\) | |||||||
\(152\) | −8.63102 | −0.700068 | ||||||||
\(153\) | 7.23921 | 0.585255 | ||||||||
\(154\) | −0.664874 | −0.0535771 | ||||||||
\(155\) | −1.34050 | −0.107672 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7017 | 0.933898 | 0.466949 | − | 0.884284i | \(-0.345353\pi\) | ||||
0.466949 | + | 0.884284i | \(0.345353\pi\) | |||||||
\(158\) | 4.37196 | 0.347815 | ||||||||
\(159\) | 0.968541 | 0.0768103 | ||||||||
\(160\) | 0.890084 | 0.0703673 | ||||||||
\(161\) | 7.60388 | 0.599269 | ||||||||
\(162\) | 8.64848 | 0.679489 | ||||||||
\(163\) | −20.5187 | −1.60715 | −0.803575 | − | 0.595204i | \(-0.797071\pi\) | ||||
−0.803575 | + | 0.595204i | \(0.797071\pi\) | |||||||
\(164\) | 7.83877 | 0.612105 | ||||||||
\(165\) | −0.117212 | −0.00912494 | ||||||||
\(166\) | −2.92931 | −0.227359 | ||||||||
\(167\) | 6.46980 | 0.500648 | 0.250324 | − | 0.968162i | \(-0.419463\pi\) | ||||
0.250324 | + | 0.968162i | \(0.419463\pi\) | |||||||
\(168\) | 0.198062 | 0.0152808 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.17629 | −0.166914 | ||||||||
\(171\) | 25.5545 | 1.95420 | ||||||||
\(172\) | 7.46681 | 0.569339 | ||||||||
\(173\) | 24.5133 | 1.86371 | 0.931857 | − | 0.362825i | \(-0.118188\pi\) | ||||
0.931857 | + | 0.362825i | \(0.118188\pi\) | |||||||
\(174\) | −0.713792 | −0.0541124 | ||||||||
\(175\) | 4.20775 | 0.318076 | ||||||||
\(176\) | 0.664874 | 0.0501168 | ||||||||
\(177\) | 2.54181 | 0.191054 | ||||||||
\(178\) | −12.5157 | −0.938094 | ||||||||
\(179\) | 3.67696 | 0.274829 | 0.137414 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137414 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(180\) | −2.63533 | −0.196426 | ||||||||
\(181\) | 13.7995 | 1.02571 | 0.512856 | − | 0.858475i | \(-0.328587\pi\) | ||||
0.512856 | + | 0.858475i | \(0.328587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.52542 | −0.112762 | ||||||||
\(184\) | −7.60388 | −0.560565 | ||||||||
\(185\) | −4.98792 | −0.366719 | ||||||||
\(186\) | 0.298290 | 0.0218717 | ||||||||
\(187\) | −1.62565 | −0.118879 | ||||||||
\(188\) | −1.20775 | −0.0880843 | ||||||||
\(189\) | −1.18060 | −0.0858763 | ||||||||
\(190\) | −7.68233 | −0.557335 | ||||||||
\(191\) | 20.0737 | 1.45248 | 0.726240 | − | 0.687441i | \(-0.241266\pi\) | ||||
0.726240 | + | 0.687441i | \(0.241266\pi\) | |||||||
\(192\) | −0.198062 | −0.0142939 | ||||||||
\(193\) | 3.74094 | 0.269279 | 0.134639 | − | 0.990895i | \(-0.457012\pi\) | ||||
0.134639 | + | 0.990895i | \(0.457012\pi\) | |||||||
\(194\) | −10.4450 | −0.749910 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.0978347 | 0.00697043 | 0.00348522 | − | 0.999994i | \(-0.498891\pi\) | ||||
0.00348522 | + | 0.999994i | \(0.498891\pi\) | |||||||
\(198\) | −1.96854 | −0.139898 | ||||||||
\(199\) | −20.4892 | −1.45244 | −0.726219 | − | 0.687463i | \(-0.758724\pi\) | ||||
−0.726219 | + | 0.687463i | \(0.758724\pi\) | |||||||
\(200\) | −4.20775 | −0.297533 | ||||||||
\(201\) | −1.20344 | −0.0848840 | ||||||||
\(202\) | −8.98792 | −0.632388 | ||||||||
\(203\) | −3.60388 | −0.252942 | ||||||||
\(204\) | 0.484271 | 0.0339057 | ||||||||
\(205\) | 6.97716 | 0.487306 | ||||||||
\(206\) | −8.27413 | −0.576486 | ||||||||
\(207\) | 22.5133 | 1.56479 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.73855 | −0.396944 | ||||||||
\(210\) | 0.176292 | 0.0121653 | ||||||||
\(211\) | 22.1903 | 1.52764 | 0.763821 | − | 0.645428i | \(-0.223321\pi\) | ||||
0.763821 | + | 0.645428i | \(0.223321\pi\) | |||||||
\(212\) | −4.89008 | −0.335852 | ||||||||
\(213\) | 1.24267 | 0.0851462 | ||||||||
\(214\) | 14.5090 | 0.991817 | ||||||||
\(215\) | 6.64609 | 0.453259 | ||||||||
\(216\) | 1.18060 | 0.0803299 | ||||||||
\(217\) | 1.50604 | 0.102237 | ||||||||
\(218\) | 12.8659 | 0.871390 | ||||||||
\(219\) | −0.728857 | −0.0492516 | ||||||||
\(220\) | 0.591794 | 0.0398987 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.10992 | 0.0744927 | ||||||||
\(223\) | −22.3478 | −1.49652 | −0.748260 | − | 0.663406i | \(-0.769110\pi\) | ||||
−0.748260 | + | 0.663406i | \(0.769110\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 12.4582 | 0.830546 | ||||||||
\(226\) | −1.99761 | −0.132879 | ||||||||
\(227\) | −2.61356 | −0.173468 | −0.0867342 | − | 0.996231i | \(-0.527643\pi\) | ||||
−0.0867342 | + | 0.996231i | \(0.527643\pi\) | |||||||
\(228\) | 1.70948 | 0.113213 | ||||||||
\(229\) | −16.0978 | −1.06377 | −0.531887 | − | 0.846815i | \(-0.678517\pi\) | ||||
−0.531887 | + | 0.846815i | \(0.678517\pi\) | |||||||
\(230\) | −6.76809 | −0.446274 | ||||||||
\(231\) | 0.131687 | 0.00866434 | ||||||||
\(232\) | 3.60388 | 0.236606 | ||||||||
\(233\) | −1.80194 | −0.118049 | −0.0590244 | − | 0.998257i | \(-0.518799\pi\) | ||||
−0.0590244 | + | 0.998257i | \(0.518799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.07500 | −0.0701252 | ||||||||
\(236\) | −12.8334 | −0.835383 | ||||||||
\(237\) | −0.865921 | −0.0562476 | ||||||||
\(238\) | 2.44504 | 0.158489 | ||||||||
\(239\) | −3.94571 | −0.255226 | −0.127613 | − | 0.991824i | \(-0.540732\pi\) | ||||
−0.127613 | + | 0.991824i | \(0.540732\pi\) | |||||||
\(240\) | −0.176292 | −0.0113796 | ||||||||
\(241\) | −2.79225 | −0.179865 | −0.0899323 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899323 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(242\) | −10.5579 | −0.678690 | ||||||||
\(243\) | −5.25475 | −0.337092 | ||||||||
\(244\) | 7.70171 | 0.493051 | ||||||||
\(245\) | 0.890084 | 0.0568654 | ||||||||
\(246\) | −1.55257 | −0.0989879 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.50604 | −0.0956337 | ||||||||
\(249\) | 0.580186 | 0.0367678 | ||||||||
\(250\) | −8.19567 | −0.518340 | ||||||||
\(251\) | −10.6649 | −0.673161 | −0.336580 | − | 0.941655i | \(-0.609270\pi\) | ||||
−0.336580 | + | 0.941655i | \(0.609270\pi\) | |||||||
\(252\) | 2.96077 | 0.186511 | ||||||||
\(253\) | −5.05562 | −0.317844 | ||||||||
\(254\) | 5.78017 | 0.362680 | ||||||||
\(255\) | 0.431041 | 0.0269929 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.4620 | −1.58828 | −0.794139 | − | 0.607736i | \(-0.792078\pi\) | ||||
−0.794139 | + | 0.607736i | \(0.792078\pi\) | |||||||
\(258\) | −1.47889 | −0.0920719 | ||||||||
\(259\) | 5.60388 | 0.348208 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.6703 | −0.660472 | ||||||||
\(262\) | 2.05861 | 0.127181 | ||||||||
\(263\) | 4.81163 | 0.296698 | 0.148349 | − | 0.988935i | \(-0.452604\pi\) | ||||
0.148349 | + | 0.988935i | \(0.452604\pi\) | |||||||
\(264\) | −0.131687 | −0.00810475 | ||||||||
\(265\) | −4.35258 | −0.267377 | ||||||||
\(266\) | 8.63102 | 0.529202 | ||||||||
\(267\) | 2.47889 | 0.151706 | ||||||||
\(268\) | 6.07606 | 0.371155 | ||||||||
\(269\) | 24.5133 | 1.49460 | 0.747302 | − | 0.664484i | \(-0.231349\pi\) | ||||
0.747302 | + | 0.664484i | \(0.231349\pi\) | |||||||
\(270\) | 1.05084 | 0.0639519 | ||||||||
\(271\) | 22.5241 | 1.36824 | 0.684121 | − | 0.729369i | \(-0.260186\pi\) | ||||
0.684121 | + | 0.729369i | \(0.260186\pi\) | |||||||
\(272\) | −2.44504 | −0.148252 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.24160 | 0.377069 | ||||||||
\(275\) | −2.79763 | −0.168703 | ||||||||
\(276\) | 1.50604 | 0.0906530 | ||||||||
\(277\) | 6.45042 | 0.387568 | 0.193784 | − | 0.981044i | \(-0.437924\pi\) | ||||
0.193784 | + | 0.981044i | \(0.437924\pi\) | |||||||
\(278\) | −7.55496 | −0.453116 | ||||||||
\(279\) | 4.45904 | 0.266956 | ||||||||
\(280\) | −0.890084 | −0.0531927 | ||||||||
\(281\) | −30.6165 | −1.82643 | −0.913215 | − | 0.407478i | \(-0.866408\pi\) | ||||
−0.913215 | + | 0.407478i | \(0.866408\pi\) | |||||||
\(282\) | 0.239210 | 0.0142447 | ||||||||
\(283\) | −16.9922 | −1.01008 | −0.505042 | − | 0.863095i | \(-0.668523\pi\) | ||||
−0.505042 | + | 0.863095i | \(0.668523\pi\) | |||||||
\(284\) | −6.27413 | −0.372301 | ||||||||
\(285\) | 1.52158 | 0.0901306 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.83877 | −0.462708 | ||||||||
\(288\) | −2.96077 | −0.174465 | ||||||||
\(289\) | −11.0218 | −0.648339 | ||||||||
\(290\) | 3.20775 | 0.188366 | ||||||||
\(291\) | 2.06877 | 0.121273 | ||||||||
\(292\) | 3.67994 | 0.215352 | ||||||||
\(293\) | 24.8116 | 1.44951 | 0.724755 | − | 0.689006i | \(-0.241953\pi\) | ||||
0.724755 | + | 0.689006i | \(0.241953\pi\) | |||||||
\(294\) | −0.198062 | −0.0115512 | ||||||||
\(295\) | −11.4228 | −0.665061 | ||||||||
\(296\) | −5.60388 | −0.325719 | ||||||||
\(297\) | 0.784953 | 0.0455476 | ||||||||
\(298\) | −16.8901 | −0.978416 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.833397 | 0.0481162 | ||||||||
\(301\) | −7.46681 | −0.430380 | ||||||||
\(302\) | −11.5254 | −0.663213 | ||||||||
\(303\) | 1.78017 | 0.102268 | ||||||||
\(304\) | −8.63102 | −0.495023 | ||||||||
\(305\) | 6.85517 | 0.392526 | ||||||||
\(306\) | 7.23921 | 0.413838 | ||||||||
\(307\) | −14.4209 | −0.823043 | −0.411522 | − | 0.911400i | \(-0.635002\pi\) | ||||
−0.411522 | + | 0.911400i | \(0.635002\pi\) | |||||||
\(308\) | −0.664874 | −0.0378847 | ||||||||
\(309\) | 1.63879 | 0.0932276 | ||||||||
\(310\) | −1.34050 | −0.0761354 | ||||||||
\(311\) | −22.1521 | −1.25613 | −0.628066 | − | 0.778160i | \(-0.716153\pi\) | ||||
−0.628066 | + | 0.778160i | \(0.716153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5550 | 1.44445 | 0.722226 | − | 0.691657i | \(-0.243119\pi\) | ||||
0.722226 | + | 0.691657i | \(0.243119\pi\) | |||||||
\(314\) | 11.7017 | 0.660366 | ||||||||
\(315\) | 2.63533 | 0.148484 | ||||||||
\(316\) | 4.37196 | 0.245942 | ||||||||
\(317\) | 13.3297 | 0.748673 | 0.374337 | − | 0.927293i | \(-0.377870\pi\) | ||||
0.374337 | + | 0.927293i | \(0.377870\pi\) | |||||||
\(318\) | 0.968541 | 0.0543131 | ||||||||
\(319\) | 2.39612 | 0.134157 | ||||||||
\(320\) | 0.890084 | 0.0497572 | ||||||||
\(321\) | −2.87369 | −0.160394 | ||||||||
\(322\) | 7.60388 | 0.423747 | ||||||||
\(323\) | 21.1032 | 1.17421 | ||||||||
\(324\) | 8.64848 | 0.480471 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.5187 | −1.13643 | ||||||||
\(327\) | −2.54825 | −0.140919 | ||||||||
\(328\) | 7.83877 | 0.432824 | ||||||||
\(329\) | 1.20775 | 0.0665855 | ||||||||
\(330\) | −0.117212 | −0.00645231 | ||||||||
\(331\) | 18.9638 | 1.04234 | 0.521171 | − | 0.853452i | \(-0.325495\pi\) | ||||
0.521171 | + | 0.853452i | \(0.325495\pi\) | |||||||
\(332\) | −2.92931 | −0.160767 | ||||||||
\(333\) | 16.5918 | 0.909225 | ||||||||
\(334\) | 6.46980 | 0.354011 | ||||||||
\(335\) | 5.40821 | 0.295482 | ||||||||
\(336\) | 0.198062 | 0.0108052 | ||||||||
\(337\) | 29.8823 | 1.62779 | 0.813897 | − | 0.581010i | \(-0.197342\pi\) | ||||
0.813897 | + | 0.581010i | \(0.197342\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.395651 | 0.0214888 | ||||||||
\(340\) | −2.17629 | −0.118026 | ||||||||
\(341\) | −1.00133 | −0.0542249 | ||||||||
\(342\) | 25.5545 | 1.38183 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.46681 | 0.402584 | ||||||||
\(345\) | 1.34050 | 0.0721702 | ||||||||
\(346\) | 24.5133 | 1.31785 | ||||||||
\(347\) | −5.78017 | −0.310296 | −0.155148 | − | 0.987891i | \(-0.549585\pi\) | ||||
−0.155148 | + | 0.987891i | \(0.549585\pi\) | |||||||
\(348\) | −0.713792 | −0.0382633 | ||||||||
\(349\) | 7.12929 | 0.381622 | 0.190811 | − | 0.981627i | \(-0.438888\pi\) | ||||
0.190811 | + | 0.981627i | \(0.438888\pi\) | |||||||
\(350\) | 4.20775 | 0.224914 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.664874 | 0.0354379 | ||||||||
\(353\) | −7.09113 | −0.377423 | −0.188711 | − | 0.982033i | \(-0.560431\pi\) | ||||
−0.188711 | + | 0.982033i | \(0.560431\pi\) | |||||||
\(354\) | 2.54181 | 0.135096 | ||||||||
\(355\) | −5.58450 | −0.296394 | ||||||||
\(356\) | −12.5157 | −0.663332 | ||||||||
\(357\) | −0.484271 | −0.0256303 | ||||||||
\(358\) | 3.67696 | 0.194333 | ||||||||
\(359\) | 25.9081 | 1.36738 | 0.683689 | − | 0.729773i | \(-0.260374\pi\) | ||||
0.683689 | + | 0.729773i | \(0.260374\pi\) | |||||||
\(360\) | −2.63533 | −0.138894 | ||||||||
\(361\) | 55.4946 | 2.92077 | ||||||||
\(362\) | 13.7995 | 0.725288 | ||||||||
\(363\) | 2.09113 | 0.109756 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.27545 | 0.171445 | ||||||||
\(366\) | −1.52542 | −0.0797349 | ||||||||
\(367\) | −30.4698 | −1.59051 | −0.795255 | − | 0.606275i | \(-0.792663\pi\) | ||||
−0.795255 | + | 0.606275i | \(0.792663\pi\) | |||||||
\(368\) | −7.60388 | −0.396379 | ||||||||
\(369\) | −23.2088 | −1.20820 | ||||||||
\(370\) | −4.98792 | −0.259310 | ||||||||
\(371\) | 4.89008 | 0.253880 | ||||||||
\(372\) | 0.298290 | 0.0154656 | ||||||||
\(373\) | −7.42758 | −0.384586 | −0.192293 | − | 0.981338i | \(-0.561592\pi\) | ||||
−0.192293 | + | 0.981338i | \(0.561592\pi\) | |||||||
\(374\) | −1.62565 | −0.0840601 | ||||||||
\(375\) | 1.62325 | 0.0838244 | ||||||||
\(376\) | −1.20775 | −0.0622850 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.18060 | −0.0607237 | ||||||||
\(379\) | −27.5472 | −1.41500 | −0.707502 | − | 0.706711i | \(-0.750178\pi\) | ||||
−0.707502 | + | 0.706711i | \(0.750178\pi\) | |||||||
\(380\) | −7.68233 | −0.394095 | ||||||||
\(381\) | −1.14483 | −0.0586516 | ||||||||
\(382\) | 20.0737 | 1.02706 | ||||||||
\(383\) | −30.8853 | −1.57817 | −0.789083 | − | 0.614287i | \(-0.789444\pi\) | ||||
−0.789083 | + | 0.614287i | \(0.789444\pi\) | |||||||
\(384\) | −0.198062 | −0.0101073 | ||||||||
\(385\) | −0.591794 | −0.0301606 | ||||||||
\(386\) | 3.74094 | 0.190409 | ||||||||
\(387\) | −22.1075 | −1.12379 | ||||||||
\(388\) | −10.4450 | −0.530267 | ||||||||
\(389\) | 32.0301 | 1.62399 | 0.811996 | − | 0.583663i | \(-0.198381\pi\) | ||||
0.811996 | + | 0.583663i | \(0.198381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5918 | 0.940227 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −0.407732 | −0.0205674 | ||||||||
\(394\) | 0.0978347 | 0.00492884 | ||||||||
\(395\) | 3.89141 | 0.195798 | ||||||||
\(396\) | −1.96854 | −0.0989229 | ||||||||
\(397\) | −7.06638 | −0.354651 | −0.177326 | − | 0.984152i | \(-0.556745\pi\) | ||||
−0.177326 | + | 0.984152i | \(0.556745\pi\) | |||||||
\(398\) | −20.4892 | −1.02703 | ||||||||
\(399\) | −1.70948 | −0.0855810 | ||||||||
\(400\) | −4.20775 | −0.210388 | ||||||||
\(401\) | −22.6058 | −1.12888 | −0.564440 | − | 0.825474i | \(-0.690908\pi\) | ||||
−0.564440 | + | 0.825474i | \(0.690908\pi\) | |||||||
\(402\) | −1.20344 | −0.0600221 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.98792 | −0.447166 | ||||||||
\(405\) | 7.69787 | 0.382510 | ||||||||
\(406\) | −3.60388 | −0.178857 | ||||||||
\(407\) | −3.72587 | −0.184685 | ||||||||
\(408\) | 0.484271 | 0.0239750 | ||||||||
\(409\) | −14.8006 | −0.731843 | −0.365922 | − | 0.930646i | \(-0.619246\pi\) | ||||
−0.365922 | + | 0.930646i | \(0.619246\pi\) | |||||||
\(410\) | 6.97716 | 0.344578 | ||||||||
\(411\) | −1.23623 | −0.0609785 | ||||||||
\(412\) | −8.27413 | −0.407637 | ||||||||
\(413\) | 12.8334 | 0.631490 | ||||||||
\(414\) | 22.5133 | 1.10647 | ||||||||
\(415\) | −2.60733 | −0.127989 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.49635 | 0.0732767 | ||||||||
\(418\) | −5.73855 | −0.280681 | ||||||||
\(419\) | −4.79225 | −0.234117 | −0.117058 | − | 0.993125i | \(-0.537346\pi\) | ||||
−0.117058 | + | 0.993125i | \(0.537346\pi\) | |||||||
\(420\) | 0.176292 | 0.00860217 | ||||||||
\(421\) | 7.78017 | 0.379182 | 0.189591 | − | 0.981863i | \(-0.439284\pi\) | ||||
0.189591 | + | 0.981863i | \(0.439284\pi\) | |||||||
\(422\) | 22.1903 | 1.08021 | ||||||||
\(423\) | 3.57587 | 0.173865 | ||||||||
\(424\) | −4.89008 | −0.237483 | ||||||||
\(425\) | 10.2881 | 0.499047 | ||||||||
\(426\) | 1.24267 | 0.0602074 | ||||||||
\(427\) | −7.70171 | −0.372712 | ||||||||
\(428\) | 14.5090 | 0.701320 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.64609 | 0.320503 | ||||||||
\(431\) | −9.46250 | −0.455793 | −0.227896 | − | 0.973685i | \(-0.573185\pi\) | ||||
−0.227896 | + | 0.973685i | \(0.573185\pi\) | |||||||
\(432\) | 1.18060 | 0.0568018 | ||||||||
\(433\) | −10.5351 | −0.506285 | −0.253142 | − | 0.967429i | \(-0.581464\pi\) | ||||
−0.253142 | + | 0.967429i | \(0.581464\pi\) | |||||||
\(434\) | 1.50604 | 0.0722923 | ||||||||
\(435\) | −0.635334 | −0.0304620 | ||||||||
\(436\) | 12.8659 | 0.616166 | ||||||||
\(437\) | 65.6292 | 3.13947 | ||||||||
\(438\) | −0.728857 | −0.0348261 | ||||||||
\(439\) | −2.08708 | −0.0996109 | −0.0498055 | − | 0.998759i | \(-0.515860\pi\) | ||||
−0.0498055 | + | 0.998759i | \(0.515860\pi\) | |||||||
\(440\) | 0.591794 | 0.0282127 | ||||||||
\(441\) | −2.96077 | −0.140989 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6635 | 0.839220 | 0.419610 | − | 0.907704i | \(-0.362167\pi\) | ||||
0.419610 | + | 0.907704i | \(0.362167\pi\) | |||||||
\(444\) | 1.10992 | 0.0526743 | ||||||||
\(445\) | −11.1400 | −0.528089 | ||||||||
\(446\) | −22.3478 | −1.05820 | ||||||||
\(447\) | 3.34529 | 0.158227 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 29.9124 | 1.41166 | 0.705828 | − | 0.708383i | \(-0.250575\pi\) | ||||
0.705828 | + | 0.708383i | \(0.250575\pi\) | |||||||
\(450\) | 12.4582 | 0.587285 | ||||||||
\(451\) | 5.21180 | 0.245414 | ||||||||
\(452\) | −1.99761 | −0.0939595 | ||||||||
\(453\) | 2.28275 | 0.107253 | ||||||||
\(454\) | −2.61356 | −0.122661 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.70948 | 0.0800537 | ||||||||
\(457\) | 37.5120 | 1.75474 | 0.877369 | − | 0.479816i | \(-0.159297\pi\) | ||||
0.877369 | + | 0.479816i | \(0.159297\pi\) | |||||||
\(458\) | −16.0978 | −0.752202 | ||||||||
\(459\) | −2.88663 | −0.134736 | ||||||||
\(460\) | −6.76809 | −0.315564 | ||||||||
\(461\) | 36.9288 | 1.71995 | 0.859974 | − | 0.510338i | \(-0.170480\pi\) | ||||
0.859974 | + | 0.510338i | \(0.170480\pi\) | |||||||
\(462\) | 0.131687 | 0.00612661 | ||||||||
\(463\) | −23.8237 | −1.10718 | −0.553591 | − | 0.832789i | \(-0.686743\pi\) | ||||
−0.553591 | + | 0.832789i | \(0.686743\pi\) | |||||||
\(464\) | 3.60388 | 0.167306 | ||||||||
\(465\) | 0.265503 | 0.0123124 | ||||||||
\(466\) | −1.80194 | −0.0834732 | ||||||||
\(467\) | −19.4010 | −0.897772 | −0.448886 | − | 0.893589i | \(-0.648179\pi\) | ||||
−0.448886 | + | 0.893589i | \(0.648179\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.07606 | −0.280567 | ||||||||
\(470\) | −1.07500 | −0.0495860 | ||||||||
\(471\) | −2.31767 | −0.106792 | ||||||||
\(472\) | −12.8334 | −0.590705 | ||||||||
\(473\) | 4.96449 | 0.228268 | ||||||||
\(474\) | −0.865921 | −0.0397730 | ||||||||
\(475\) | 36.3172 | 1.66635 | ||||||||
\(476\) | 2.44504 | 0.112068 | ||||||||
\(477\) | 14.4784 | 0.662921 | ||||||||
\(478\) | −3.94571 | −0.180472 | ||||||||
\(479\) | 20.7224 | 0.946831 | 0.473416 | − | 0.880839i | \(-0.343021\pi\) | ||||
0.473416 | + | 0.880839i | \(0.343021\pi\) | |||||||
\(480\) | −0.176292 | −0.00804659 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.79225 | −0.127183 | ||||||||
\(483\) | −1.50604 | −0.0685272 | ||||||||
\(484\) | −10.5579 | −0.479906 | ||||||||
\(485\) | −9.29696 | −0.422153 | ||||||||
\(486\) | −5.25475 | −0.238360 | ||||||||
\(487\) | 31.9758 | 1.44896 | 0.724482 | − | 0.689294i | \(-0.242079\pi\) | ||||
0.724482 | + | 0.689294i | \(0.242079\pi\) | |||||||
\(488\) | 7.70171 | 0.348640 | ||||||||
\(489\) | 4.06398 | 0.183780 | ||||||||
\(490\) | 0.890084 | 0.0402099 | ||||||||
\(491\) | −9.24027 | −0.417008 | −0.208504 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208504 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(492\) | −1.55257 | −0.0699950 | ||||||||
\(493\) | −8.81163 | −0.396856 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.75217 | −0.0787540 | ||||||||
\(496\) | −1.50604 | −0.0676232 | ||||||||
\(497\) | 6.27413 | 0.281433 | ||||||||
\(498\) | 0.580186 | 0.0259988 | ||||||||
\(499\) | 9.94630 | 0.445257 | 0.222629 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222629 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(500\) | −8.19567 | −0.366521 | ||||||||
\(501\) | −1.28142 | −0.0572497 | ||||||||
\(502\) | −10.6649 | −0.475997 | ||||||||
\(503\) | 21.2379 | 0.946950 | 0.473475 | − | 0.880807i | \(-0.342999\pi\) | ||||
0.473475 | + | 0.880807i | \(0.342999\pi\) | |||||||
\(504\) | 2.96077 | 0.131883 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | −5.05562 | −0.224750 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.78017 | 0.256453 | ||||||||
\(509\) | −8.29350 | −0.367603 | −0.183802 | − | 0.982963i | \(-0.558840\pi\) | ||||
−0.183802 | + | 0.982963i | \(0.558840\pi\) | |||||||
\(510\) | 0.431041 | 0.0190868 | ||||||||
\(511\) | −3.67994 | −0.162791 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.1898 | −0.449891 | ||||||||
\(514\) | −25.4620 | −1.12308 | ||||||||
\(515\) | −7.36467 | −0.324526 | ||||||||
\(516\) | −1.47889 | −0.0651047 | ||||||||
\(517\) | −0.803003 | −0.0353160 | ||||||||
\(518\) | 5.60388 | 0.246220 | ||||||||
\(519\) | −4.85517 | −0.213118 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.33214 | 0.321227 | 0.160613 | − | 0.987017i | \(-0.448653\pi\) | ||||
0.160613 | + | 0.987017i | \(0.448653\pi\) | |||||||
\(522\) | −10.6703 | −0.467024 | ||||||||
\(523\) | −36.5816 | −1.59960 | −0.799802 | − | 0.600265i | \(-0.795062\pi\) | ||||
−0.799802 | + | 0.600265i | \(0.795062\pi\) | |||||||
\(524\) | 2.05861 | 0.0899306 | ||||||||
\(525\) | −0.833397 | −0.0363724 | ||||||||
\(526\) | 4.81163 | 0.209797 | ||||||||
\(527\) | 3.68233 | 0.160405 | ||||||||
\(528\) | −0.131687 | −0.00573092 | ||||||||
\(529\) | 34.8189 | 1.51387 | ||||||||
\(530\) | −4.35258 | −0.189064 | ||||||||
\(531\) | 37.9968 | 1.64892 | ||||||||
\(532\) | 8.63102 | 0.374202 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.47889 | 0.107272 | ||||||||
\(535\) | 12.9142 | 0.558332 | ||||||||
\(536\) | 6.07606 | 0.262446 | ||||||||
\(537\) | −0.728266 | −0.0314270 | ||||||||
\(538\) | 24.5133 | 1.05684 | ||||||||
\(539\) | 0.664874 | 0.0286382 | ||||||||
\(540\) | 1.05084 | 0.0452208 | ||||||||
\(541\) | 19.7125 | 0.847505 | 0.423753 | − | 0.905778i | \(-0.360713\pi\) | ||||
0.423753 | + | 0.905778i | \(0.360713\pi\) | |||||||
\(542\) | 22.5241 | 0.967493 | ||||||||
\(543\) | −2.73317 | −0.117292 | ||||||||
\(544\) | −2.44504 | −0.104830 | ||||||||
\(545\) | 11.4517 | 0.490539 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.66786 | 0.114069 | 0.0570347 | − | 0.998372i | \(-0.481835\pi\) | ||||
0.0570347 | + | 0.998372i | \(0.481835\pi\) | |||||||
\(548\) | 6.24160 | 0.266628 | ||||||||
\(549\) | −22.8030 | −0.973208 | ||||||||
\(550\) | −2.79763 | −0.119291 | ||||||||
\(551\) | −31.1051 | −1.32512 | ||||||||
\(552\) | 1.50604 | 0.0641014 | ||||||||
\(553\) | −4.37196 | −0.185915 | ||||||||
\(554\) | 6.45042 | 0.274052 | ||||||||
\(555\) | 0.987918 | 0.0419348 | ||||||||
\(556\) | −7.55496 | −0.320402 | ||||||||
\(557\) | 16.1655 | 0.684956 | 0.342478 | − | 0.939526i | \(-0.388734\pi\) | ||||
0.342478 | + | 0.939526i | \(0.388734\pi\) | |||||||
\(558\) | 4.45904 | 0.188766 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.890084 | −0.0376129 | ||||||||
\(561\) | 0.321979 | 0.0135940 | ||||||||
\(562\) | −30.6165 | −1.29148 | ||||||||
\(563\) | −34.5241 | −1.45502 | −0.727508 | − | 0.686099i | \(-0.759322\pi\) | ||||
−0.727508 | + | 0.686099i | \(0.759322\pi\) | |||||||
\(564\) | 0.239210 | 0.0100726 | ||||||||
\(565\) | −1.77804 | −0.0748026 | ||||||||
\(566\) | −16.9922 | −0.714237 | ||||||||
\(567\) | −8.64848 | −0.363202 | ||||||||
\(568\) | −6.27413 | −0.263257 | ||||||||
\(569\) | 3.66919 | 0.153820 | 0.0769101 | − | 0.997038i | \(-0.475495\pi\) | ||||
0.0769101 | + | 0.997038i | \(0.475495\pi\) | |||||||
\(570\) | 1.52158 | 0.0637320 | ||||||||
\(571\) | 8.29590 | 0.347172 | 0.173586 | − | 0.984819i | \(-0.444464\pi\) | ||||
0.173586 | + | 0.984819i | \(0.444464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.97584 | −0.166093 | ||||||||
\(574\) | −7.83877 | −0.327184 | ||||||||
\(575\) | 31.9952 | 1.33429 | ||||||||
\(576\) | −2.96077 | −0.123365 | ||||||||
\(577\) | −15.0949 | −0.628407 | −0.314203 | − | 0.949356i | \(-0.601737\pi\) | ||||
−0.314203 | + | 0.949356i | \(0.601737\pi\) | |||||||
\(578\) | −11.0218 | −0.458445 | ||||||||
\(579\) | −0.740939 | −0.0307924 | ||||||||
\(580\) | 3.20775 | 0.133195 | ||||||||
\(581\) | 2.92931 | 0.121528 | ||||||||
\(582\) | 2.06877 | 0.0857532 | ||||||||
\(583\) | −3.25129 | −0.134655 | ||||||||
\(584\) | 3.67994 | 0.152277 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.8116 | 1.02496 | ||||||||
\(587\) | −19.0465 | −0.786134 | −0.393067 | − | 0.919510i | \(-0.628586\pi\) | ||||
−0.393067 | + | 0.919510i | \(0.628586\pi\) | |||||||
\(588\) | −0.198062 | −0.00816795 | ||||||||
\(589\) | 12.9987 | 0.535601 | ||||||||
\(590\) | −11.4228 | −0.470269 | ||||||||
\(591\) | −0.0193774 | −0.000797078 0 | ||||||||
\(592\) | −5.60388 | −0.230318 | ||||||||
\(593\) | 23.6770 | 0.972296 | 0.486148 | − | 0.873876i | \(-0.338402\pi\) | ||||
0.486148 | + | 0.873876i | \(0.338402\pi\) | |||||||
\(594\) | 0.784953 | 0.0322070 | ||||||||
\(595\) | 2.17629 | 0.0892193 | ||||||||
\(596\) | −16.8901 | −0.691845 | ||||||||
\(597\) | 4.05813 | 0.166088 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.41896 | −0.221413 | −0.110706 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110706 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(600\) | 0.833397 | 0.0340233 | ||||||||
\(601\) | −43.9861 | −1.79423 | −0.897116 | − | 0.441796i | \(-0.854342\pi\) | ||||
−0.897116 | + | 0.441796i | \(0.854342\pi\) | |||||||
\(602\) | −7.46681 | −0.304325 | ||||||||
\(603\) | −17.9898 | −0.732603 | ||||||||
\(604\) | −11.5254 | −0.468963 | ||||||||
\(605\) | −9.39745 | −0.382061 | ||||||||
\(606\) | 1.78017 | 0.0723144 | ||||||||
\(607\) | −35.6426 | −1.44669 | −0.723345 | − | 0.690487i | \(-0.757396\pi\) | ||||
−0.723345 | + | 0.690487i | \(0.757396\pi\) | |||||||
\(608\) | −8.63102 | −0.350034 | ||||||||
\(609\) | 0.713792 | 0.0289243 | ||||||||
\(610\) | 6.85517 | 0.277558 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.23921 | 0.292628 | ||||||||
\(613\) | −18.7573 | −0.757602 | −0.378801 | − | 0.925478i | \(-0.623663\pi\) | ||||
−0.378801 | + | 0.925478i | \(0.623663\pi\) | |||||||
\(614\) | −14.4209 | −0.581979 | ||||||||
\(615\) | −1.38191 | −0.0557241 | ||||||||
\(616\) | −0.664874 | −0.0267886 | ||||||||
\(617\) | 35.2247 | 1.41809 | 0.709047 | − | 0.705161i | \(-0.249125\pi\) | ||||
0.709047 | + | 0.705161i | \(0.249125\pi\) | |||||||
\(618\) | 1.63879 | 0.0659219 | ||||||||
\(619\) | 44.5870 | 1.79210 | 0.896052 | − | 0.443950i | \(-0.146423\pi\) | ||||
0.896052 | + | 0.443950i | \(0.146423\pi\) | |||||||
\(620\) | −1.34050 | −0.0538359 | ||||||||
\(621\) | −8.97716 | −0.360241 | ||||||||
\(622\) | −22.1521 | −0.888219 | ||||||||
\(623\) | 12.5157 | 0.501432 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.7439 | 0.549757 | ||||||||
\(626\) | 25.5550 | 1.02138 | ||||||||
\(627\) | 1.13659 | 0.0453910 | ||||||||
\(628\) | 11.7017 | 0.466949 | ||||||||
\(629\) | 13.7017 | 0.546323 | ||||||||
\(630\) | 2.63533 | 0.104994 | ||||||||
\(631\) | −22.9745 | −0.914601 | −0.457300 | − | 0.889312i | \(-0.651184\pi\) | ||||
−0.457300 | + | 0.889312i | \(0.651184\pi\) | |||||||
\(632\) | 4.37196 | 0.173907 | ||||||||
\(633\) | −4.39506 | −0.174688 | ||||||||
\(634\) | 13.3297 | 0.529392 | ||||||||
\(635\) | 5.14483 | 0.204166 | ||||||||
\(636\) | 0.968541 | 0.0384052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.39612 | 0.0948635 | ||||||||
\(639\) | 18.5763 | 0.734865 | ||||||||
\(640\) | 0.890084 | 0.0351836 | ||||||||
\(641\) | 9.32544 | 0.368333 | 0.184166 | − | 0.982895i | \(-0.441041\pi\) | ||||
0.184166 | + | 0.982895i | \(0.441041\pi\) | |||||||
\(642\) | −2.87369 | −0.113416 | ||||||||
\(643\) | 19.5948 | 0.772743 | 0.386371 | − | 0.922343i | \(-0.373728\pi\) | ||||
0.386371 | + | 0.922343i | \(0.373728\pi\) | |||||||
\(644\) | 7.60388 | 0.299635 | ||||||||
\(645\) | −1.31634 | −0.0518308 | ||||||||
\(646\) | 21.1032 | 0.830295 | ||||||||
\(647\) | −46.5569 | −1.83034 | −0.915170 | − | 0.403068i | \(-0.867944\pi\) | ||||
−0.915170 | + | 0.403068i | \(0.867944\pi\) | |||||||
\(648\) | 8.64848 | 0.339744 | ||||||||
\(649\) | −8.53260 | −0.334934 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.298290 | −0.0116909 | ||||||||
\(652\) | −20.5187 | −0.803575 | ||||||||
\(653\) | −13.3357 | −0.521867 | −0.260933 | − | 0.965357i | \(-0.584030\pi\) | ||||
−0.260933 | + | 0.965357i | \(0.584030\pi\) | |||||||
\(654\) | −2.54825 | −0.0996446 | ||||||||
\(655\) | 1.83233 | 0.0715951 | ||||||||
\(656\) | 7.83877 | 0.306053 | ||||||||
\(657\) | −10.8955 | −0.425072 | ||||||||
\(658\) | 1.20775 | 0.0470830 | ||||||||
\(659\) | −16.6872 | −0.650042 | −0.325021 | − | 0.945707i | \(-0.605371\pi\) | ||||
−0.325021 | + | 0.945707i | \(0.605371\pi\) | |||||||
\(660\) | −0.117212 | −0.00456247 | ||||||||
\(661\) | −47.5943 | −1.85120 | −0.925602 | − | 0.378498i | \(-0.876441\pi\) | ||||
−0.925602 | + | 0.378498i | \(0.876441\pi\) | |||||||
\(662\) | 18.9638 | 0.737047 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.92931 | −0.113679 | ||||||||
\(665\) | 7.68233 | 0.297908 | ||||||||
\(666\) | 16.5918 | 0.642919 | ||||||||
\(667\) | −27.4034 | −1.06106 | ||||||||
\(668\) | 6.46980 | 0.250324 | ||||||||
\(669\) | 4.42626 | 0.171129 | ||||||||
\(670\) | 5.40821 | 0.208937 | ||||||||
\(671\) | 5.12067 | 0.197681 | ||||||||
\(672\) | 0.198062 | 0.00764042 | ||||||||
\(673\) | 43.2683 | 1.66787 | 0.833935 | − | 0.551863i | \(-0.186083\pi\) | ||||
0.833935 | + | 0.551863i | \(0.186083\pi\) | |||||||
\(674\) | 29.8823 | 1.15102 | ||||||||
\(675\) | −4.96769 | −0.191206 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.9772 | −0.729352 | −0.364676 | − | 0.931135i | \(-0.618820\pi\) | ||||
−0.364676 | + | 0.931135i | \(0.618820\pi\) | |||||||
\(678\) | 0.395651 | 0.0151949 | ||||||||
\(679\) | 10.4450 | 0.400844 | ||||||||
\(680\) | −2.17629 | −0.0834570 | ||||||||
\(681\) | 0.517648 | 0.0198363 | ||||||||
\(682\) | −1.00133 | −0.0383428 | ||||||||
\(683\) | 26.2435 | 1.00418 | 0.502090 | − | 0.864815i | \(-0.332565\pi\) | ||||
0.502090 | + | 0.864815i | \(0.332565\pi\) | |||||||
\(684\) | 25.5545 | 0.977100 | ||||||||
\(685\) | 5.55555 | 0.212267 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 3.18837 | 0.121644 | ||||||||
\(688\) | 7.46681 | 0.284670 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.34050 | 0.0510321 | ||||||||
\(691\) | −16.1129 | −0.612964 | −0.306482 | − | 0.951877i | \(-0.599152\pi\) | ||||
−0.306482 | + | 0.951877i | \(0.599152\pi\) | |||||||
\(692\) | 24.5133 | 0.931857 | ||||||||
\(693\) | 1.96854 | 0.0747787 | ||||||||
\(694\) | −5.78017 | −0.219412 | ||||||||
\(695\) | −6.72455 | −0.255077 | ||||||||
\(696\) | −0.713792 | −0.0270562 | ||||||||
\(697\) | −19.1661 | −0.725969 | ||||||||
\(698\) | 7.12929 | 0.269848 | ||||||||
\(699\) | 0.356896 | 0.0134990 | ||||||||
\(700\) | 4.20775 | 0.159038 | ||||||||
\(701\) | −27.9409 | −1.05531 | −0.527657 | − | 0.849458i | \(-0.676929\pi\) | ||||
−0.527657 | + | 0.849458i | \(0.676929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.3672 | 1.82420 | ||||||||
\(704\) | 0.664874 | 0.0250584 | ||||||||
\(705\) | 0.212917 | 0.00801891 | ||||||||
\(706\) | −7.09113 | −0.266878 | ||||||||
\(707\) | 8.98792 | 0.338025 | ||||||||
\(708\) | 2.54181 | 0.0955271 | ||||||||
\(709\) | −37.6823 | −1.41519 | −0.707595 | − | 0.706618i | \(-0.750220\pi\) | ||||
−0.707595 | + | 0.706618i | \(0.750220\pi\) | |||||||
\(710\) | −5.58450 | −0.209582 | ||||||||
\(711\) | −12.9444 | −0.485452 | ||||||||
\(712\) | −12.5157 | −0.469047 | ||||||||
\(713\) | 11.4517 | 0.428871 | ||||||||
\(714\) | −0.484271 | −0.0181234 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.67696 | 0.137414 | ||||||||
\(717\) | 0.781495 | 0.0291855 | ||||||||
\(718\) | 25.9081 | 0.966883 | ||||||||
\(719\) | 9.53020 | 0.355417 | 0.177708 | − | 0.984083i | \(-0.443132\pi\) | ||||
0.177708 | + | 0.984083i | \(0.443132\pi\) | |||||||
\(720\) | −2.63533 | −0.0982131 | ||||||||
\(721\) | 8.27413 | 0.308145 | ||||||||
\(722\) | 55.4946 | 2.06529 | ||||||||
\(723\) | 0.553039 | 0.0205677 | ||||||||
\(724\) | 13.7995 | 0.512856 | ||||||||
\(725\) | −15.1642 | −0.563185 | ||||||||
\(726\) | 2.09113 | 0.0776091 | ||||||||
\(727\) | 1.32975 | 0.0493177 | 0.0246588 | − | 0.999696i | \(-0.492150\pi\) | ||||
0.0246588 | + | 0.999696i | \(0.492150\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.9047 | −0.922395 | ||||||||
\(730\) | 3.27545 | 0.121230 | ||||||||
\(731\) | −18.2567 | −0.675247 | ||||||||
\(732\) | −1.52542 | −0.0563811 | ||||||||
\(733\) | 32.9590 | 1.21737 | 0.608684 | − | 0.793413i | \(-0.291698\pi\) | ||||
0.608684 | + | 0.793413i | \(0.291698\pi\) | |||||||
\(734\) | −30.4698 | −1.12466 | ||||||||
\(735\) | −0.176292 | −0.00650263 | ||||||||
\(736\) | −7.60388 | −0.280283 | ||||||||
\(737\) | 4.03982 | 0.148809 | ||||||||
\(738\) | −23.2088 | −0.854328 | ||||||||
\(739\) | 10.0277 | 0.368876 | 0.184438 | − | 0.982844i | \(-0.440953\pi\) | ||||
0.184438 | + | 0.982844i | \(0.440953\pi\) | |||||||
\(740\) | −4.98792 | −0.183360 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.89008 | 0.179521 | ||||||||
\(743\) | 8.52888 | 0.312894 | 0.156447 | − | 0.987686i | \(-0.449996\pi\) | ||||
0.156447 | + | 0.987686i | \(0.449996\pi\) | |||||||
\(744\) | 0.298290 | 0.0109358 | ||||||||
\(745\) | −15.0336 | −0.550788 | ||||||||
\(746\) | −7.42758 | −0.271943 | ||||||||
\(747\) | 8.67302 | 0.317329 | ||||||||
\(748\) | −1.62565 | −0.0594395 | ||||||||
\(749\) | −14.5090 | −0.530148 | ||||||||
\(750\) | 1.62325 | 0.0592728 | ||||||||
\(751\) | 3.05084 | 0.111327 | 0.0556633 | − | 0.998450i | \(-0.482273\pi\) | ||||
0.0556633 | + | 0.998450i | \(0.482273\pi\) | |||||||
\(752\) | −1.20775 | −0.0440421 | ||||||||
\(753\) | 2.11231 | 0.0769768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.2586 | −0.373348 | ||||||||
\(756\) | −1.18060 | −0.0429381 | ||||||||
\(757\) | −45.5206 | −1.65448 | −0.827238 | − | 0.561852i | \(-0.810089\pi\) | ||||
−0.827238 | + | 0.561852i | \(0.810089\pi\) | |||||||
\(758\) | −27.5472 | −1.00056 | ||||||||
\(759\) | 1.00133 | 0.0363459 | ||||||||
\(760\) | −7.68233 | −0.278667 | ||||||||
\(761\) | 36.9101 | 1.33799 | 0.668994 | − | 0.743268i | \(-0.266725\pi\) | ||||
0.668994 | + | 0.743268i | \(0.266725\pi\) | |||||||
\(762\) | −1.14483 | −0.0414729 | ||||||||
\(763\) | −12.8659 | −0.465778 | ||||||||
\(764\) | 20.0737 | 0.726240 | ||||||||
\(765\) | 6.44350 | 0.232965 | ||||||||
\(766\) | −30.8853 | −1.11593 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.198062 | −0.00714696 | ||||||||
\(769\) | −45.6528 | −1.64628 | −0.823141 | − | 0.567837i | \(-0.807780\pi\) | ||||
−0.823141 | + | 0.567837i | \(0.807780\pi\) | |||||||
\(770\) | −0.591794 | −0.0213268 | ||||||||
\(771\) | 5.04307 | 0.181622 | ||||||||
\(772\) | 3.74094 | 0.134639 | ||||||||
\(773\) | −22.7380 | −0.817827 | −0.408914 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408914 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(774\) | −22.1075 | −0.794639 | ||||||||
\(775\) | 6.33704 | 0.227633 | ||||||||
\(776\) | −10.4450 | −0.374955 | ||||||||
\(777\) | −1.10992 | −0.0398180 | ||||||||
\(778\) | 32.0301 | 1.14834 | ||||||||
\(779\) | −67.6566 | −2.42405 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.17151 | −0.149268 | ||||||||
\(782\) | 18.5918 | 0.664841 | ||||||||
\(783\) | 4.25475 | 0.152052 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.4155 | 0.371745 | ||||||||
\(786\) | −0.407732 | −0.0145433 | ||||||||
\(787\) | 8.72779 | 0.311112 | 0.155556 | − | 0.987827i | \(-0.450283\pi\) | ||||
0.155556 | + | 0.987827i | \(0.450283\pi\) | |||||||
\(788\) | 0.0978347 | 0.00348522 | ||||||||
\(789\) | −0.953002 | −0.0339278 | ||||||||
\(790\) | 3.89141 | 0.138450 | ||||||||
\(791\) | 1.99761 | 0.0710267 | ||||||||
\(792\) | −1.96854 | −0.0699491 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −7.06638 | −0.250776 | ||||||||
\(795\) | 0.862083 | 0.0305749 | ||||||||
\(796\) | −20.4892 | −0.726219 | ||||||||
\(797\) | 52.6956 | 1.86657 | 0.933287 | − | 0.359132i | \(-0.116927\pi\) | ||||
0.933287 | + | 0.359132i | \(0.116927\pi\) | |||||||
\(798\) | −1.70948 | −0.0605149 | ||||||||
\(799\) | 2.95300 | 0.104470 | ||||||||
\(800\) | −4.20775 | −0.148766 | ||||||||
\(801\) | 37.0562 | 1.30932 | ||||||||
\(802\) | −22.6058 | −0.798238 | ||||||||
\(803\) | 2.44670 | 0.0863421 | ||||||||
\(804\) | −1.20344 | −0.0424420 | ||||||||
\(805\) | 6.76809 | 0.238544 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.85517 | −0.170910 | ||||||||
\(808\) | −8.98792 | −0.316194 | ||||||||
\(809\) | −1.09006 | −0.0383246 | −0.0191623 | − | 0.999816i | \(-0.506100\pi\) | ||||
−0.0191623 | + | 0.999816i | \(0.506100\pi\) | |||||||
\(810\) | 7.69787 | 0.270476 | ||||||||
\(811\) | −34.2747 | −1.20355 | −0.601774 | − | 0.798666i | \(-0.705539\pi\) | ||||
−0.601774 | + | 0.798666i | \(0.705539\pi\) | |||||||
\(812\) | −3.60388 | −0.126471 | ||||||||
\(813\) | −4.46117 | −0.156460 | ||||||||
\(814\) | −3.72587 | −0.130592 | ||||||||
\(815\) | −18.2634 | −0.639738 | ||||||||
\(816\) | 0.484271 | 0.0169529 | ||||||||
\(817\) | −64.4462 | −2.25469 | ||||||||
\(818\) | −14.8006 | −0.517491 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.97716 | 0.243653 | ||||||||
\(821\) | −31.4034 | −1.09599 | −0.547993 | − | 0.836483i | \(-0.684608\pi\) | ||||
−0.547993 | + | 0.836483i | \(0.684608\pi\) | |||||||
\(822\) | −1.23623 | −0.0431183 | ||||||||
\(823\) | −30.1715 | −1.05171 | −0.525856 | − | 0.850573i | \(-0.676255\pi\) | ||||
−0.525856 | + | 0.850573i | \(0.676255\pi\) | |||||||
\(824\) | −8.27413 | −0.288243 | ||||||||
\(825\) | 0.554104 | 0.0192914 | ||||||||
\(826\) | 12.8334 | 0.446531 | ||||||||
\(827\) | −28.2040 | −0.980750 | −0.490375 | − | 0.871511i | \(-0.663140\pi\) | ||||
−0.490375 | + | 0.871511i | \(0.663140\pi\) | |||||||
\(828\) | 22.5133 | 0.782393 | ||||||||
\(829\) | −34.2452 | −1.18938 | −0.594692 | − | 0.803954i | \(-0.702726\pi\) | ||||
−0.594692 | + | 0.803954i | \(0.702726\pi\) | |||||||
\(830\) | −2.60733 | −0.0905019 | ||||||||
\(831\) | −1.27758 | −0.0443189 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.44504 | −0.0847157 | ||||||||
\(834\) | 1.49635 | 0.0518144 | ||||||||
\(835\) | 5.75866 | 0.199287 | ||||||||
\(836\) | −5.73855 | −0.198472 | ||||||||
\(837\) | −1.77804 | −0.0614580 | ||||||||
\(838\) | −4.79225 | −0.165545 | ||||||||
\(839\) | −22.4590 | −0.775372 | −0.387686 | − | 0.921791i | \(-0.626726\pi\) | ||||
−0.387686 | + | 0.921791i | \(0.626726\pi\) | |||||||
\(840\) | 0.176292 | 0.00608265 | ||||||||
\(841\) | −16.0121 | −0.552141 | ||||||||
\(842\) | 7.78017 | 0.268122 | ||||||||
\(843\) | 6.06398 | 0.208855 | ||||||||
\(844\) | 22.1903 | 0.763821 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.57587 | 0.122941 | ||||||||
\(847\) | 10.5579 | 0.362775 | ||||||||
\(848\) | −4.89008 | −0.167926 | ||||||||
\(849\) | 3.36552 | 0.115504 | ||||||||
\(850\) | 10.2881 | 0.352880 | ||||||||
\(851\) | 42.6112 | 1.46069 | ||||||||
\(852\) | 1.24267 | 0.0425731 | ||||||||
\(853\) | −22.9288 | −0.785068 | −0.392534 | − | 0.919737i | \(-0.628402\pi\) | ||||
−0.392534 | + | 0.919737i | \(0.628402\pi\) | |||||||
\(854\) | −7.70171 | −0.263547 | ||||||||
\(855\) | 22.7456 | 0.777884 | ||||||||
\(856\) | 14.5090 | 0.495908 | ||||||||
\(857\) | −3.95971 | −0.135261 | −0.0676305 | − | 0.997710i | \(-0.521544\pi\) | ||||
−0.0676305 | + | 0.997710i | \(0.521544\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.00969 | 0.102689 | 0.0513446 | − | 0.998681i | \(-0.483649\pi\) | ||||
0.0513446 | + | 0.998681i | \(0.483649\pi\) | |||||||
\(860\) | 6.64609 | 0.226630 | ||||||||
\(861\) | 1.55257 | 0.0529113 | ||||||||
\(862\) | −9.46250 | −0.322294 | ||||||||
\(863\) | −20.0978 | −0.684138 | −0.342069 | − | 0.939675i | \(-0.611128\pi\) | ||||
−0.342069 | + | 0.939675i | \(0.611128\pi\) | |||||||
\(864\) | 1.18060 | 0.0401650 | ||||||||
\(865\) | 21.8189 | 0.741866 | ||||||||
\(866\) | −10.5351 | −0.357998 | ||||||||
\(867\) | 2.18300 | 0.0741385 | ||||||||
\(868\) | 1.50604 | 0.0511184 | ||||||||
\(869\) | 2.90681 | 0.0986066 | ||||||||
\(870\) | −0.635334 | −0.0215399 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.8659 | 0.435695 | ||||||||
\(873\) | 30.9254 | 1.04667 | ||||||||
\(874\) | 65.6292 | 2.21994 | ||||||||
\(875\) | 8.19567 | 0.277064 | ||||||||
\(876\) | −0.728857 | −0.0246258 | ||||||||
\(877\) | −34.7633 | −1.17387 | −0.586937 | − | 0.809633i | \(-0.699666\pi\) | ||||
−0.586937 | + | 0.809633i | \(0.699666\pi\) | |||||||
\(878\) | −2.08708 | −0.0704356 | ||||||||
\(879\) | −4.91425 | −0.165753 | ||||||||
\(880\) | 0.591794 | 0.0199494 | ||||||||
\(881\) | 39.5415 | 1.33219 | 0.666094 | − | 0.745868i | \(-0.267965\pi\) | ||||
0.666094 | + | 0.745868i | \(0.267965\pi\) | |||||||
\(882\) | −2.96077 | −0.0996944 | ||||||||
\(883\) | 32.4704 | 1.09272 | 0.546358 | − | 0.837552i | \(-0.316014\pi\) | ||||
0.546358 | + | 0.837552i | \(0.316014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.26243 | 0.0760506 | ||||||||
\(886\) | 17.6635 | 0.593418 | ||||||||
\(887\) | 19.0422 | 0.639375 | 0.319687 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319687 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(888\) | 1.10992 | 0.0372464 | ||||||||
\(889\) | −5.78017 | −0.193861 | ||||||||
\(890\) | −11.1400 | −0.373415 | ||||||||
\(891\) | 5.75015 | 0.192637 | ||||||||
\(892\) | −22.3478 | −0.748260 | ||||||||
\(893\) | 10.4241 | 0.348830 | ||||||||
\(894\) | 3.34529 | 0.111883 | ||||||||
\(895\) | 3.27280 | 0.109398 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29.9124 | 0.998191 | ||||||||
\(899\) | −5.42758 | −0.181020 | ||||||||
\(900\) | 12.4582 | 0.415273 | ||||||||
\(901\) | 11.9565 | 0.398327 | ||||||||
\(902\) | 5.21180 | 0.173534 | ||||||||
\(903\) | 1.47889 | 0.0492145 | ||||||||
\(904\) | −1.99761 | −0.0664394 | ||||||||
\(905\) | 12.2828 | 0.408292 | ||||||||
\(906\) | 2.28275 | 0.0758393 | ||||||||
\(907\) | −13.8369 | −0.459445 | −0.229723 | − | 0.973256i | \(-0.573782\pi\) | ||||
−0.229723 | + | 0.973256i | \(0.573782\pi\) | |||||||
\(908\) | −2.61356 | −0.0867342 | ||||||||
\(909\) | 26.6112 | 0.882637 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.3564 | −1.66838 | −0.834191 | − | 0.551475i | \(-0.814065\pi\) | ||||
−0.834191 | + | 0.551475i | \(0.814065\pi\) | |||||||
\(912\) | 1.70948 | 0.0566065 | ||||||||
\(913\) | −1.94762 | −0.0644570 | ||||||||
\(914\) | 37.5120 | 1.24079 | ||||||||
\(915\) | −1.35775 | −0.0448858 | ||||||||
\(916\) | −16.0978 | −0.531887 | ||||||||
\(917\) | −2.05861 | −0.0679812 | ||||||||
\(918\) | −2.88663 | −0.0952729 | ||||||||
\(919\) | −45.4965 | −1.50079 | −0.750395 | − | 0.660990i | \(-0.770137\pi\) | ||||
−0.750395 | + | 0.660990i | \(0.770137\pi\) | |||||||
\(920\) | −6.76809 | −0.223137 | ||||||||
\(921\) | 2.85623 | 0.0941160 | ||||||||
\(922\) | 36.9288 | 1.21619 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.131687 | 0.00433217 | ||||||||
\(925\) | 23.5797 | 0.775296 | ||||||||
\(926\) | −23.8237 | −0.782896 | ||||||||
\(927\) | 24.4978 | 0.804613 | ||||||||
\(928\) | 3.60388 | 0.118303 | ||||||||
\(929\) | −29.8931 | −0.980760 | −0.490380 | − | 0.871509i | \(-0.663142\pi\) | ||||
−0.490380 | + | 0.871509i | \(0.663142\pi\) | |||||||
\(930\) | 0.265503 | 0.00870618 | ||||||||
\(931\) | −8.63102 | −0.282870 | ||||||||
\(932\) | −1.80194 | −0.0590244 | ||||||||
\(933\) | 4.38750 | 0.143640 | ||||||||
\(934\) | −19.4010 | −0.634821 | ||||||||
\(935\) | −1.44696 | −0.0473207 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4077 | 0.764697 | 0.382349 | − | 0.924018i | \(-0.375115\pi\) | ||||
0.382349 | + | 0.924018i | \(0.375115\pi\) | |||||||
\(938\) | −6.07606 | −0.198391 | ||||||||
\(939\) | −5.06147 | −0.165175 | ||||||||
\(940\) | −1.07500 | −0.0350626 | ||||||||
\(941\) | −28.0650 | −0.914894 | −0.457447 | − | 0.889237i | \(-0.651236\pi\) | ||||
−0.457447 | + | 0.889237i | \(0.651236\pi\) | |||||||
\(942\) | −2.31767 | −0.0755137 | ||||||||
\(943\) | −59.6051 | −1.94101 | ||||||||
\(944\) | −12.8334 | −0.417691 | ||||||||
\(945\) | −1.05084 | −0.0341837 | ||||||||
\(946\) | 4.96449 | 0.161410 | ||||||||
\(947\) | 0.972853 | 0.0316135 | 0.0158067 | − | 0.999875i | \(-0.494968\pi\) | ||||
0.0158067 | + | 0.999875i | \(0.494968\pi\) | |||||||
\(948\) | −0.865921 | −0.0281238 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 36.3172 | 1.17829 | ||||||||
\(951\) | −2.64012 | −0.0856118 | ||||||||
\(952\) | 2.44504 | 0.0792443 | ||||||||
\(953\) | 52.5719 | 1.70297 | 0.851486 | − | 0.524377i | \(-0.175702\pi\) | ||||
0.851486 | + | 0.524377i | \(0.175702\pi\) | |||||||
\(954\) | 14.4784 | 0.468756 | ||||||||
\(955\) | 17.8672 | 0.578171 | ||||||||
\(956\) | −3.94571 | −0.127613 | ||||||||
\(957\) | −0.474582 | −0.0153411 | ||||||||
\(958\) | 20.7224 | 0.669511 | ||||||||
\(959\) | −6.24160 | −0.201552 | ||||||||
\(960\) | −0.176292 | −0.00568980 | ||||||||
\(961\) | −28.7318 | −0.926834 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.9579 | −1.38430 | ||||||||
\(964\) | −2.79225 | −0.0899323 | ||||||||
\(965\) | 3.32975 | 0.107188 | ||||||||
\(966\) | −1.50604 | −0.0484561 | ||||||||
\(967\) | 6.74392 | 0.216870 | 0.108435 | − | 0.994104i | \(-0.465416\pi\) | ||||
0.108435 | + | 0.994104i | \(0.465416\pi\) | |||||||
\(968\) | −10.5579 | −0.339345 | ||||||||
\(969\) | −4.17975 | −0.134273 | ||||||||
\(970\) | −9.29696 | −0.298507 | ||||||||
\(971\) | 42.0586 | 1.34972 | 0.674862 | − | 0.737944i | \(-0.264203\pi\) | ||||
0.674862 | + | 0.737944i | \(0.264203\pi\) | |||||||
\(972\) | −5.25475 | −0.168546 | ||||||||
\(973\) | 7.55496 | 0.242201 | ||||||||
\(974\) | 31.9758 | 1.02457 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.70171 | 0.246526 | ||||||||
\(977\) | −24.8461 | −0.794896 | −0.397448 | − | 0.917625i | \(-0.630104\pi\) | ||||
−0.397448 | + | 0.917625i | \(0.630104\pi\) | |||||||
\(978\) | 4.06398 | 0.129952 | ||||||||
\(979\) | −8.32139 | −0.265953 | ||||||||
\(980\) | 0.890084 | 0.0284327 | ||||||||
\(981\) | −38.0930 | −1.21622 | ||||||||
\(982\) | −9.24027 | −0.294869 | ||||||||
\(983\) | 19.8888 | 0.634353 | 0.317176 | − | 0.948367i | \(-0.397265\pi\) | ||||
0.317176 | + | 0.948367i | \(0.397265\pi\) | |||||||
\(984\) | −1.55257 | −0.0494940 | ||||||||
\(985\) | 0.0870811 | 0.00277463 | ||||||||
\(986\) | −8.81163 | −0.280619 | ||||||||
\(987\) | −0.239210 | −0.00761413 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.7767 | −1.80539 | ||||||||
\(990\) | −1.75217 | −0.0556875 | ||||||||
\(991\) | 36.3564 | 1.15490 | 0.577450 | − | 0.816426i | \(-0.304048\pi\) | ||||
0.577450 | + | 0.816426i | \(0.304048\pi\) | |||||||
\(992\) | −1.50604 | −0.0478168 | ||||||||
\(993\) | −3.75600 | −0.119193 | ||||||||
\(994\) | 6.27413 | 0.199003 | ||||||||
\(995\) | −18.2371 | −0.578154 | ||||||||
\(996\) | 0.580186 | 0.0183839 | ||||||||
\(997\) | −30.0000 | −0.950110 | −0.475055 | − | 0.879956i | \(-0.657572\pi\) | ||||
−0.475055 | + | 0.879956i | \(0.657572\pi\) | |||||||
\(998\) | 9.94630 | 0.314845 | ||||||||
\(999\) | −6.61596 | −0.209320 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 2366.2.a.z.1.3 | yes | 3 | |
13.5 | odd | 4 | 2366.2.d.m.337.3 | 6 | |||
13.8 | odd | 4 | 2366.2.d.m.337.6 | 6 | |||
13.12 | even | 2 | 2366.2.a.u.1.3 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2366.2.a.u.1.3 | ✓ | 3 | 13.12 | even | 2 | ||
2366.2.a.z.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
2366.2.d.m.337.3 | 6 | 13.5 | odd | 4 | |||
2366.2.d.m.337.6 | 6 | 13.8 | odd | 4 |