Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8037,2,Mod(1,8037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8037 = 3^{2} \cdot 19 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8037.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: | \(64.1757681045\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 13 x^{14} + 65 x^{13} + 47 x^{12} - 390 x^{11} + 4 x^{10} + 1115 x^{9} - 320 x^{8} - 1639 x^{7} + 618 x^{6} + 1250 x^{5} - 487 x^{4} - 456 x^{3} + 179 x^{2} + \cdots - 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 893) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(1.22346\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22346 | 0.865114 | 0.432557 | − | 0.901607i | \(-0.357611\pi\) | ||||
0.432557 | + | 0.901607i | \(0.357611\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.503155 | −0.251578 | ||||||||
\(5\) | −1.49488 | −0.668530 | −0.334265 | − | 0.942479i | \(-0.608488\pi\) | ||||
−0.334265 | + | 0.942479i | \(0.608488\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.92629 | 0.728071 | 0.364035 | − | 0.931385i | \(-0.381399\pi\) | ||||
0.364035 | + | 0.931385i | \(0.381399\pi\) | |||||||
\(8\) | −3.06250 | −1.08276 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.82892 | −0.578355 | ||||||||
\(11\) | 5.98067 | 1.80324 | 0.901620 | − | 0.432529i | \(-0.142379\pi\) | ||||
0.901620 | + | 0.432529i | \(0.142379\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.688389 | 0.190925 | 0.0954624 | − | 0.995433i | \(-0.469567\pi\) | ||||
0.0954624 | + | 0.995433i | \(0.469567\pi\) | |||||||
\(14\) | 2.35674 | 0.629864 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.74052 | −0.685131 | ||||||||
\(17\) | −1.22062 | −0.296045 | −0.148022 | − | 0.988984i | \(-0.547291\pi\) | ||||
−0.148022 | + | 0.988984i | \(0.547291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.752156 | 0.168187 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.31709 | 1.56001 | ||||||||
\(23\) | −7.14665 | −1.49018 | −0.745089 | − | 0.666965i | \(-0.767593\pi\) | ||||
−0.745089 | + | 0.666965i | \(0.767593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.76534 | −0.553068 | ||||||||
\(26\) | 0.842214 | 0.165172 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.969225 | −0.183166 | ||||||||
\(29\) | −6.31879 | −1.17337 | −0.586685 | − | 0.809816i | \(-0.699567\pi\) | ||||
−0.586685 | + | 0.809816i | \(0.699567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41339 | −0.613063 | −0.306532 | − | 0.951860i | \(-0.599169\pi\) | ||||
−0.306532 | + | 0.951860i | \(0.599169\pi\) | |||||||
\(32\) | 2.77209 | 0.490041 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.49338 | −0.256113 | ||||||||
\(35\) | −2.87958 | −0.486737 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.81678 | 0.627475 | 0.313737 | − | 0.949510i | \(-0.398419\pi\) | ||||
0.313737 | + | 0.949510i | \(0.398419\pi\) | |||||||
\(38\) | −1.22346 | −0.198471 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.57807 | 0.723856 | ||||||||
\(41\) | 11.6520 | 1.81974 | 0.909869 | − | 0.414896i | \(-0.136182\pi\) | ||||
0.909869 | + | 0.414896i | \(0.136182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.30138 | −0.960951 | −0.480475 | − | 0.877008i | \(-0.659536\pi\) | ||||
−0.480475 | + | 0.877008i | \(0.659536\pi\) | |||||||
\(44\) | −3.00920 | −0.453655 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.74361 | −1.28917 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.28939 | −0.469913 | ||||||||
\(50\) | −3.38327 | −0.478467 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.346366 | −0.0480324 | ||||||||
\(53\) | 4.61374 | 0.633746 | 0.316873 | − | 0.948468i | \(-0.397367\pi\) | ||||
0.316873 | + | 0.948468i | \(0.397367\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.94038 | −1.20552 | ||||||||
\(56\) | −5.89928 | −0.788324 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.73076 | −1.01510 | ||||||||
\(59\) | 8.93709 | 1.16351 | 0.581755 | − | 0.813364i | \(-0.302366\pi\) | ||||
0.581755 | + | 0.813364i | \(0.302366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.297368 | 0.0380740 | 0.0190370 | − | 0.999819i | \(-0.493940\pi\) | ||||
0.0190370 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(62\) | −4.17613 | −0.530370 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.87258 | 1.10907 | ||||||||
\(65\) | −1.02906 | −0.127639 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9319 | −1.82423 | −0.912113 | − | 0.409938i | \(-0.865550\pi\) | ||||
−0.912113 | + | 0.409938i | \(0.865550\pi\) | |||||||
\(68\) | 0.614163 | 0.0744782 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.52303 | −0.421083 | ||||||||
\(71\) | 8.44664 | 1.00243 | 0.501216 | − | 0.865322i | \(-0.332886\pi\) | ||||
0.501216 | + | 0.865322i | \(0.332886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.11139 | 0.364161 | 0.182081 | − | 0.983284i | \(-0.441717\pi\) | ||||
0.182081 | + | 0.983284i | \(0.441717\pi\) | |||||||
\(74\) | 4.66966 | 0.542837 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.503155 | 0.0577159 | ||||||||
\(77\) | 11.5205 | 1.31289 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6188 | −1.30722 | −0.653610 | − | 0.756831i | \(-0.726746\pi\) | ||||
−0.653610 | + | 0.756831i | \(0.726746\pi\) | |||||||
\(80\) | 4.09675 | 0.458031 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.2557 | 1.57428 | ||||||||
\(83\) | −7.52556 | −0.826037 | −0.413018 | − | 0.910723i | \(-0.635526\pi\) | ||||
−0.413018 | + | 0.910723i | \(0.635526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.82468 | 0.197915 | ||||||||
\(86\) | −7.70946 | −0.831332 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −18.3158 | −1.95247 | ||||||||
\(89\) | 7.87193 | 0.834423 | 0.417212 | − | 0.908809i | \(-0.363007\pi\) | ||||
0.417212 | + | 0.908809i | \(0.363007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.32604 | 0.139007 | ||||||||
\(92\) | 3.59587 | 0.374896 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.22346 | 0.126190 | ||||||||
\(95\) | 1.49488 | 0.153371 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4165 | 1.56531 | 0.782656 | − | 0.622455i | \(-0.213865\pi\) | ||||
0.782656 | + | 0.622455i | \(0.213865\pi\) | |||||||
\(98\) | −4.02443 | −0.406528 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.39139 | 0.139139 | ||||||||
\(101\) | −8.02244 | −0.798262 | −0.399131 | − | 0.916894i | \(-0.630688\pi\) | ||||
−0.399131 | + | 0.916894i | \(0.630688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.3108 | −1.50862 | −0.754310 | − | 0.656518i | \(-0.772028\pi\) | ||||
−0.754310 | + | 0.656518i | \(0.772028\pi\) | |||||||
\(104\) | −2.10819 | −0.206725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.64471 | 0.548262 | ||||||||
\(107\) | −1.39574 | −0.134932 | −0.0674658 | − | 0.997722i | \(-0.521491\pi\) | ||||
−0.0674658 | + | 0.997722i | \(0.521491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.40912 | −0.805448 | −0.402724 | − | 0.915322i | \(-0.631936\pi\) | ||||
−0.402724 | + | 0.915322i | \(0.631936\pi\) | |||||||
\(110\) | −10.9382 | −1.04291 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.27906 | −0.498824 | ||||||||
\(113\) | −6.96791 | −0.655486 | −0.327743 | − | 0.944767i | \(-0.606288\pi\) | ||||
−0.327743 | + | 0.944767i | \(0.606288\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6834 | 0.996229 | ||||||||
\(116\) | 3.17933 | 0.295193 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.9341 | 1.00657 | ||||||||
\(119\) | −2.35128 | −0.215542 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.7684 | 2.25167 | ||||||||
\(122\) | 0.363816 | 0.0329384 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.71747 | 0.154233 | ||||||||
\(125\) | 11.6082 | 1.03827 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.6731 | −1.92317 | −0.961586 | − | 0.274503i | \(-0.911487\pi\) | ||||
−0.961586 | + | 0.274503i | \(0.911487\pi\) | |||||||
\(128\) | 5.31103 | 0.469433 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.25901 | −0.110422 | ||||||||
\(131\) | −1.73571 | −0.151650 | −0.0758249 | − | 0.997121i | \(-0.524159\pi\) | ||||
−0.0758249 | + | 0.997121i | \(0.524159\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.92629 | −0.167031 | ||||||||
\(134\) | −18.2686 | −1.57816 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.73816 | 0.320545 | ||||||||
\(137\) | −21.5158 | −1.83822 | −0.919111 | − | 0.393998i | \(-0.871092\pi\) | ||||
−0.919111 | + | 0.393998i | \(0.871092\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −23.1810 | −1.96619 | −0.983094 | − | 0.183101i | \(-0.941387\pi\) | ||||
−0.983094 | + | 0.183101i | \(0.941387\pi\) | |||||||
\(140\) | 1.44887 | 0.122452 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3341 | 0.867218 | ||||||||
\(143\) | 4.11703 | 0.344283 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.44582 | 0.784433 | ||||||||
\(146\) | 3.80665 | 0.315041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.92043 | −0.157859 | ||||||||
\(149\) | 4.54134 | 0.372041 | 0.186020 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186020 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6606 | 1.51858 | 0.759290 | − | 0.650753i | \(-0.225547\pi\) | ||||
0.759290 | + | 0.650753i | \(0.225547\pi\) | |||||||
\(152\) | 3.06250 | 0.248402 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.0949 | 1.13580 | ||||||||
\(155\) | 5.10261 | 0.409851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.8978 | −1.58802 | −0.794009 | − | 0.607906i | \(-0.792010\pi\) | ||||
−0.794009 | + | 0.607906i | \(0.792010\pi\) | |||||||
\(158\) | −14.2151 | −1.13089 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.14394 | −0.327607 | ||||||||
\(161\) | −13.7665 | −1.08496 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.13350 | −0.323760 | −0.161880 | − | 0.986810i | \(-0.551756\pi\) | ||||
−0.161880 | + | 0.986810i | \(0.551756\pi\) | |||||||
\(164\) | −5.86277 | −0.457805 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.20719 | −0.714616 | ||||||||
\(167\) | −3.16675 | −0.245051 | −0.122525 | − | 0.992465i | \(-0.539099\pi\) | ||||
−0.122525 | + | 0.992465i | \(0.539099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5261 | −0.963548 | ||||||||
\(170\) | 2.23242 | 0.171219 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.17057 | 0.241754 | ||||||||
\(173\) | 7.56877 | 0.575443 | 0.287721 | − | 0.957714i | \(-0.407102\pi\) | ||||
0.287721 | + | 0.957714i | \(0.407102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.32685 | −0.402672 | ||||||||
\(176\) | −16.3902 | −1.23546 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.63096 | 0.721871 | ||||||||
\(179\) | 22.3928 | 1.67371 | 0.836857 | − | 0.547422i | \(-0.184391\pi\) | ||||
0.836857 | + | 0.547422i | \(0.184391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.90461 | 0.364557 | 0.182279 | − | 0.983247i | \(-0.441653\pi\) | ||||
0.182279 | + | 0.983247i | \(0.441653\pi\) | |||||||
\(182\) | 1.62235 | 0.120257 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 21.8866 | 1.61350 | ||||||||
\(185\) | −5.70562 | −0.419486 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.30015 | −0.533840 | ||||||||
\(188\) | −0.503155 | −0.0366964 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.82892 | 0.132684 | ||||||||
\(191\) | −9.22858 | −0.667757 | −0.333878 | − | 0.942616i | \(-0.608357\pi\) | ||||
−0.333878 | + | 0.942616i | \(0.608357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.6393 | −1.70159 | −0.850797 | − | 0.525495i | \(-0.823880\pi\) | ||||
−0.850797 | + | 0.525495i | \(0.823880\pi\) | |||||||
\(194\) | 18.8614 | 1.35417 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.65507 | 0.118220 | ||||||||
\(197\) | 14.1239 | 1.00629 | 0.503143 | − | 0.864203i | \(-0.332177\pi\) | ||||
0.503143 | + | 0.864203i | \(0.332177\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.02709 | 0.285473 | 0.142736 | − | 0.989761i | \(-0.454410\pi\) | ||||
0.142736 | + | 0.989761i | \(0.454410\pi\) | |||||||
\(200\) | 8.46885 | 0.598838 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.81510 | −0.690588 | ||||||||
\(203\) | −12.1718 | −0.854296 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.4183 | −1.21655 | ||||||||
\(206\) | −18.7321 | −1.30513 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.88655 | −0.130808 | ||||||||
\(209\) | −5.98067 | −0.413692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.89473 | −0.474653 | −0.237326 | − | 0.971430i | \(-0.576271\pi\) | ||||
−0.237326 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(212\) | −2.32143 | −0.159436 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.70763 | −0.116731 | ||||||||
\(215\) | 9.41979 | 0.642425 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.57520 | −0.446353 | ||||||||
\(218\) | −10.2882 | −0.696804 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.49840 | 0.303282 | ||||||||
\(221\) | −0.840264 | −0.0565223 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.9566 | 1.06853 | 0.534265 | − | 0.845317i | \(-0.320588\pi\) | ||||
0.534265 | + | 0.845317i | \(0.320588\pi\) | |||||||
\(224\) | 5.33986 | 0.356784 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.52493 | −0.567070 | ||||||||
\(227\) | −2.18124 | −0.144774 | −0.0723871 | − | 0.997377i | \(-0.523062\pi\) | ||||
−0.0723871 | + | 0.997377i | \(0.523062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0499 | 1.12669 | 0.563344 | − | 0.826222i | \(-0.309514\pi\) | ||||
0.563344 | + | 0.826222i | \(0.309514\pi\) | |||||||
\(230\) | 13.0706 | 0.861852 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.3513 | 1.27047 | ||||||||
\(233\) | −18.3157 | −1.19990 | −0.599951 | − | 0.800037i | \(-0.704813\pi\) | ||||
−0.599951 | + | 0.800037i | \(0.704813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.49488 | −0.0975151 | ||||||||
\(236\) | −4.49674 | −0.292713 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.87669 | −0.186468 | ||||||||
\(239\) | −13.2209 | −0.855188 | −0.427594 | − | 0.903971i | \(-0.640639\pi\) | ||||
−0.427594 | + | 0.903971i | \(0.640639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.44331 | −0.157388 | −0.0786938 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786938 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(242\) | 30.3031 | 1.94795 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.149622 | −0.00957857 | ||||||||
\(245\) | 4.91724 | 0.314151 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.688389 | −0.0438011 | ||||||||
\(248\) | 10.4535 | 0.663799 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 14.2022 | 0.898224 | ||||||||
\(251\) | −10.0476 | −0.634201 | −0.317101 | − | 0.948392i | \(-0.602709\pi\) | ||||
−0.317101 | + | 0.948392i | \(0.602709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.7417 | −2.68715 | ||||||||
\(254\) | −26.5160 | −1.66376 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.2473 | −0.702959 | ||||||||
\(257\) | −18.6200 | −1.16148 | −0.580740 | − | 0.814089i | \(-0.697237\pi\) | ||||
−0.580740 | + | 0.814089i | \(0.697237\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.35224 | 0.456846 | ||||||||
\(260\) | 0.517776 | 0.0321111 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.12357 | −0.131194 | ||||||||
\(263\) | 0.577076 | 0.0355840 | 0.0177920 | − | 0.999842i | \(-0.494336\pi\) | ||||
0.0177920 | + | 0.999842i | \(0.494336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.89698 | −0.423678 | ||||||||
\(266\) | −2.35674 | −0.144501 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.51308 | 0.458934 | ||||||||
\(269\) | −19.8758 | −1.21185 | −0.605924 | − | 0.795523i | \(-0.707196\pi\) | ||||
−0.605924 | + | 0.795523i | \(0.707196\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5339 | 1.06511 | 0.532555 | − | 0.846395i | \(-0.321232\pi\) | ||||
0.532555 | + | 0.846395i | \(0.321232\pi\) | |||||||
\(272\) | 3.34515 | 0.202829 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.3237 | −1.59027 | ||||||||
\(275\) | −16.5386 | −0.997313 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4987 | 1.35181 | 0.675907 | − | 0.736987i | \(-0.263752\pi\) | ||||
0.675907 | + | 0.736987i | \(0.263752\pi\) | |||||||
\(278\) | −28.3610 | −1.70098 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.81870 | 0.527018 | ||||||||
\(281\) | −22.9312 | −1.36796 | −0.683981 | − | 0.729500i | \(-0.739753\pi\) | ||||
−0.683981 | + | 0.729500i | \(0.739753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.03247 | −0.477481 | −0.238740 | − | 0.971083i | \(-0.576734\pi\) | ||||
−0.238740 | + | 0.971083i | \(0.576734\pi\) | |||||||
\(284\) | −4.24997 | −0.252189 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.03700 | 0.297844 | ||||||||
\(287\) | 22.4452 | 1.32490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.5101 | −0.912357 | ||||||||
\(290\) | 11.5565 | 0.678624 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.56551 | −0.0916148 | ||||||||
\(293\) | −11.7285 | −0.685185 | −0.342592 | − | 0.939484i | \(-0.611305\pi\) | ||||
−0.342592 | + | 0.939484i | \(0.611305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.3599 | −0.777842 | ||||||||
\(296\) | −11.6889 | −0.679403 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.55613 | 0.321858 | ||||||||
\(299\) | −4.91967 | −0.284512 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.1383 | −0.699640 | ||||||||
\(302\) | 22.8304 | 1.31374 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.74052 | 0.157180 | ||||||||
\(305\) | −0.444528 | −0.0254536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.18614 | 0.353062 | 0.176531 | − | 0.984295i | \(-0.443512\pi\) | ||||
0.176531 | + | 0.984295i | \(0.443512\pi\) | |||||||
\(308\) | −5.79661 | −0.330293 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.24281 | 0.354568 | ||||||||
\(311\) | −12.8865 | −0.730728 | −0.365364 | − | 0.930865i | \(-0.619056\pi\) | ||||
−0.365364 | + | 0.930865i | \(0.619056\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1220 | −0.572128 | −0.286064 | − | 0.958211i | \(-0.592347\pi\) | ||||
−0.286064 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(314\) | −24.3441 | −1.37382 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.84607 | 0.328867 | ||||||||
\(317\) | 16.2871 | 0.914774 | 0.457387 | − | 0.889268i | \(-0.348785\pi\) | ||||
0.457387 | + | 0.889268i | \(0.348785\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.7906 | −2.11587 | ||||||||
\(320\) | −13.2634 | −0.741448 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.8428 | −0.938610 | ||||||||
\(323\) | 1.22062 | 0.0679173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.90363 | −0.105594 | ||||||||
\(326\) | −5.05715 | −0.280090 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −35.6843 | −1.97033 | ||||||||
\(329\) | 1.92629 | 0.106200 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.44340 | 0.409126 | 0.204563 | − | 0.978853i | \(-0.434423\pi\) | ||||
0.204563 | + | 0.978853i | \(0.434423\pi\) | |||||||
\(332\) | 3.78652 | 0.207812 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.87439 | −0.211997 | ||||||||
\(335\) | 22.3214 | 1.21955 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2307 | −0.938617 | −0.469308 | − | 0.883034i | \(-0.655497\pi\) | ||||
−0.469308 | + | 0.883034i | \(0.655497\pi\) | |||||||
\(338\) | −15.3252 | −0.833579 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.918099 | −0.0497909 | ||||||||
\(341\) | −20.4144 | −1.10550 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8204 | −1.07020 | ||||||||
\(344\) | 19.2980 | 1.04048 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.26005 | 0.497824 | ||||||||
\(347\) | 4.46467 | 0.239676 | 0.119838 | − | 0.992793i | \(-0.461762\pi\) | ||||
0.119838 | + | 0.992793i | \(0.461762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8361 | −1.16886 | −0.584431 | − | 0.811443i | \(-0.698682\pi\) | ||||
−0.584431 | + | 0.811443i | \(0.698682\pi\) | |||||||
\(350\) | −6.51717 | −0.348357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.5790 | 0.883661 | ||||||||
\(353\) | −32.7096 | −1.74096 | −0.870479 | − | 0.492205i | \(-0.836191\pi\) | ||||
−0.870479 | + | 0.492205i | \(0.836191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.6267 | −0.670156 | ||||||||
\(356\) | −3.96080 | −0.209922 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.3966 | 1.44795 | ||||||||
\(359\) | −7.15938 | −0.377858 | −0.188929 | − | 0.981991i | \(-0.560502\pi\) | ||||
−0.188929 | + | 0.981991i | \(0.560502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.00058 | 0.315383 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.667204 | −0.0349710 | ||||||||
\(365\) | −4.65116 | −0.243453 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5644 | 1.28225 | 0.641124 | − | 0.767437i | \(-0.278468\pi\) | ||||
0.641124 | + | 0.767437i | \(0.278468\pi\) | |||||||
\(368\) | 19.5856 | 1.02097 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.98058 | −0.362903 | ||||||||
\(371\) | 8.88742 | 0.461412 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.26957 | −0.0657359 | −0.0328680 | − | 0.999460i | \(-0.510464\pi\) | ||||
−0.0328680 | + | 0.999460i | \(0.510464\pi\) | |||||||
\(374\) | −8.93141 | −0.461832 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.06250 | −0.157936 | ||||||||
\(377\) | −4.34978 | −0.224025 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.26839 | −0.270619 | −0.135310 | − | 0.990803i | \(-0.543203\pi\) | ||||
−0.135310 | + | 0.990803i | \(0.543203\pi\) | |||||||
\(380\) | −0.752156 | −0.0385848 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.2908 | −0.577686 | ||||||||
\(383\) | −2.29974 | −0.117511 | −0.0587556 | − | 0.998272i | \(-0.518713\pi\) | ||||
−0.0587556 | + | 0.998272i | \(0.518713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.2218 | −0.877704 | ||||||||
\(386\) | −28.9216 | −1.47207 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.75690 | −0.393797 | ||||||||
\(389\) | 11.3158 | 0.573732 | 0.286866 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286866 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.72337 | 0.441160 | ||||||||
\(392\) | 10.0738 | 0.508802 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.2800 | 0.870552 | ||||||||
\(395\) | 17.3687 | 0.873916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.8254 | −1.39652 | −0.698260 | − | 0.715845i | \(-0.746042\pi\) | ||||
−0.698260 | + | 0.715845i | \(0.746042\pi\) | |||||||
\(398\) | 4.92696 | 0.246966 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.57848 | 0.378924 | ||||||||
\(401\) | 19.4971 | 0.973638 | 0.486819 | − | 0.873503i | \(-0.338157\pi\) | ||||
0.486819 | + | 0.873503i | \(0.338157\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.34974 | −0.117049 | ||||||||
\(404\) | 4.03653 | 0.200825 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.8917 | −0.739063 | ||||||||
\(407\) | 22.8269 | 1.13149 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.7035 | 1.12262 | 0.561308 | − | 0.827607i | \(-0.310298\pi\) | ||||
0.561308 | + | 0.827607i | \(0.310298\pi\) | |||||||
\(410\) | −21.3106 | −1.05245 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.70372 | 0.379535 | ||||||||
\(413\) | 17.2155 | 0.847118 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2498 | 0.552231 | ||||||||
\(416\) | 1.90828 | 0.0935609 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.31709 | −0.357890 | ||||||||
\(419\) | −19.4931 | −0.952299 | −0.476149 | − | 0.879364i | \(-0.657968\pi\) | ||||
−0.476149 | + | 0.879364i | \(0.657968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.983589 | −0.0479372 | −0.0239686 | − | 0.999713i | \(-0.507630\pi\) | ||||
−0.0239686 | + | 0.999713i | \(0.507630\pi\) | |||||||
\(422\) | −8.43540 | −0.410629 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.1296 | −0.686193 | ||||||||
\(425\) | 3.37544 | 0.163733 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.572817 | 0.0277206 | ||||||||
\(428\) | 0.702275 | 0.0339458 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.5247 | 0.555771 | ||||||||
\(431\) | 16.4580 | 0.792755 | 0.396378 | − | 0.918088i | \(-0.370267\pi\) | ||||
0.396378 | + | 0.918088i | \(0.370267\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.9519 | 1.67968 | 0.839840 | − | 0.542834i | \(-0.182649\pi\) | ||||
0.839840 | + | 0.542834i | \(0.182649\pi\) | |||||||
\(434\) | −8.04446 | −0.386147 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.23109 | 0.202633 | ||||||||
\(437\) | 7.14665 | 0.341870 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4572 | −1.21500 | −0.607502 | − | 0.794318i | \(-0.707828\pi\) | ||||
−0.607502 | + | 0.794318i | \(0.707828\pi\) | |||||||
\(440\) | 27.3799 | 1.30529 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.02803 | −0.0488982 | ||||||||
\(443\) | −23.4363 | −1.11349 | −0.556747 | − | 0.830682i | \(-0.687951\pi\) | ||||
−0.556747 | + | 0.830682i | \(0.687951\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7676 | −0.557837 | ||||||||
\(446\) | 19.5221 | 0.924400 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.0912 | 0.807483 | ||||||||
\(449\) | −35.5270 | −1.67662 | −0.838311 | − | 0.545192i | \(-0.816457\pi\) | ||||
−0.838311 | + | 0.545192i | \(0.816457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 69.6868 | 3.28142 | ||||||||
\(452\) | 3.50594 | 0.164906 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.66866 | −0.125246 | ||||||||
\(455\) | −1.98227 | −0.0929302 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.39683 | −0.439565 | −0.219783 | − | 0.975549i | \(-0.570535\pi\) | ||||
−0.219783 | + | 0.975549i | \(0.570535\pi\) | |||||||
\(458\) | 20.8598 | 0.974714 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.37539 | −0.250629 | ||||||||
\(461\) | −9.50836 | −0.442849 | −0.221424 | − | 0.975178i | \(-0.571071\pi\) | ||||
−0.221424 | + | 0.975178i | \(0.571071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.51358 | 0.163290 | 0.0816450 | − | 0.996661i | \(-0.473983\pi\) | ||||
0.0816450 | + | 0.996661i | \(0.473983\pi\) | |||||||
\(464\) | 17.3168 | 0.803912 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.4085 | −1.03805 | ||||||||
\(467\) | −18.0939 | −0.837285 | −0.418642 | − | 0.908151i | \(-0.637494\pi\) | ||||
−0.418642 | + | 0.908151i | \(0.637494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.7633 | −1.32817 | ||||||||
\(470\) | −1.82892 | −0.0843617 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.3699 | −1.25980 | ||||||||
\(473\) | −37.6865 | −1.73282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.76534 | 0.126882 | ||||||||
\(476\) | 1.18306 | 0.0542254 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.1752 | −0.739835 | ||||||||
\(479\) | 29.4690 | 1.34647 | 0.673236 | − | 0.739428i | \(-0.264904\pi\) | ||||
0.673236 | + | 0.739428i | \(0.264904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.62743 | 0.119800 | ||||||||
\(482\) | −2.98929 | −0.136158 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.4624 | −0.566471 | ||||||||
\(485\) | −23.0458 | −1.04646 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.48046 | −0.248343 | −0.124172 | − | 0.992261i | \(-0.539627\pi\) | ||||
−0.124172 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(488\) | −0.910688 | −0.0412249 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.01603 | 0.271776 | ||||||||
\(491\) | 24.3494 | 1.09887 | 0.549436 | − | 0.835536i | \(-0.314843\pi\) | ||||
0.549436 | + | 0.835536i | \(0.314843\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.71286 | 0.347370 | ||||||||
\(494\) | −0.842214 | −0.0378930 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.35448 | 0.420029 | ||||||||
\(497\) | 16.2707 | 0.729841 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.1326 | −1.16986 | −0.584928 | − | 0.811085i | \(-0.698877\pi\) | ||||
−0.584928 | + | 0.811085i | \(0.698877\pi\) | |||||||
\(500\) | −5.84074 | −0.261206 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.2928 | −0.548657 | ||||||||
\(503\) | 44.1872 | 1.97021 | 0.985105 | − | 0.171956i | \(-0.0550086\pi\) | ||||
0.985105 | + | 0.171956i | \(0.0550086\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.9926 | 0.533662 | ||||||||
\(506\) | −52.2926 | −2.32469 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.9049 | 0.483827 | ||||||||
\(509\) | 34.7489 | 1.54022 | 0.770108 | − | 0.637914i | \(-0.220202\pi\) | ||||
0.770108 | + | 0.637914i | \(0.220202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.99346 | 0.265135 | ||||||||
\(512\) | −24.3827 | −1.07757 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.7807 | −1.00481 | ||||||||
\(515\) | 22.8878 | 1.00856 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.98067 | 0.263030 | ||||||||
\(518\) | 8.99515 | 0.395224 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.15149 | 0.138202 | ||||||||
\(521\) | −17.0091 | −0.745182 | −0.372591 | − | 0.927996i | \(-0.621530\pi\) | ||||
−0.372591 | + | 0.927996i | \(0.621530\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.7876 | −1.78352 | −0.891759 | − | 0.452511i | \(-0.850528\pi\) | ||||
−0.891759 | + | 0.452511i | \(0.850528\pi\) | |||||||
\(524\) | 0.873332 | 0.0381517 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.706027 | 0.0307842 | ||||||||
\(527\) | 4.16647 | 0.181494 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.0745 | 1.22063 | ||||||||
\(530\) | −8.43815 | −0.366530 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.969225 | 0.0420212 | ||||||||
\(533\) | 8.02111 | 0.347433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.08647 | 0.0902058 | ||||||||
\(536\) | 45.7291 | 1.97519 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.3171 | −1.04839 | ||||||||
\(539\) | −19.6728 | −0.847366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.56934 | 0.0674714 | 0.0337357 | − | 0.999431i | \(-0.489260\pi\) | ||||
0.0337357 | + | 0.999431i | \(0.489260\pi\) | |||||||
\(542\) | 21.4520 | 0.921443 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.38368 | −0.145074 | ||||||||
\(545\) | 12.5706 | 0.538466 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.70011 | −0.371990 | −0.185995 | − | 0.982551i | \(-0.559551\pi\) | ||||
−0.185995 | + | 0.982551i | \(0.559551\pi\) | |||||||
\(548\) | 10.8258 | 0.462456 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.2342 | −0.862790 | ||||||||
\(551\) | 6.31879 | 0.269189 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.3813 | −0.951749 | ||||||||
\(554\) | 27.5261 | 1.16947 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6636 | 0.494649 | ||||||||
\(557\) | 26.0422 | 1.10344 | 0.551722 | − | 0.834028i | \(-0.313971\pi\) | ||||
0.551722 | + | 0.834028i | \(0.313971\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.33780 | −0.183469 | ||||||||
\(560\) | 7.89155 | 0.333479 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.0553 | −1.18344 | ||||||||
\(563\) | 0.109118 | 0.00459876 | 0.00229938 | − | 0.999997i | \(-0.499268\pi\) | ||||
0.00229938 | + | 0.999997i | \(0.499268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4162 | 0.438212 | ||||||||
\(566\) | −9.82737 | −0.413075 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.8678 | −1.08539 | ||||||||
\(569\) | 25.2719 | 1.05945 | 0.529727 | − | 0.848168i | \(-0.322294\pi\) | ||||
0.529727 | + | 0.848168i | \(0.322294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37573 | −0.266816 | −0.133408 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133408 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(572\) | −2.07150 | −0.0866139 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 27.4607 | 1.14619 | ||||||||
\(575\) | 19.7629 | 0.824169 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.8745 | 0.660864 | 0.330432 | − | 0.943830i | \(-0.392806\pi\) | ||||
0.330432 | + | 0.943830i | \(0.392806\pi\) | |||||||
\(578\) | −18.9759 | −0.789293 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.75271 | −0.197346 | ||||||||
\(581\) | −14.4964 | −0.601413 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.5933 | 1.14280 | ||||||||
\(584\) | −9.52865 | −0.394298 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.3493 | −0.592763 | ||||||||
\(587\) | 24.3827 | 1.00638 | 0.503190 | − | 0.864176i | \(-0.332160\pi\) | ||||
0.503190 | + | 0.864176i | \(0.332160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.41339 | 0.140646 | ||||||||
\(590\) | −16.3452 | −0.672922 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.4600 | −0.429903 | ||||||||
\(593\) | −47.0711 | −1.93298 | −0.966489 | − | 0.256709i | \(-0.917362\pi\) | ||||
−0.966489 | + | 0.256709i | \(0.917362\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.51488 | 0.144096 | ||||||||
\(596\) | −2.28500 | −0.0935971 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.01900 | −0.246135 | ||||||||
\(599\) | −18.6311 | −0.761245 | −0.380623 | − | 0.924730i | \(-0.624290\pi\) | ||||
−0.380623 | + | 0.924730i | \(0.624290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0775 | 0.982141 | 0.491071 | − | 0.871120i | \(-0.336606\pi\) | ||||
0.491071 | + | 0.871120i | \(0.336606\pi\) | |||||||
\(602\) | −14.8507 | −0.605269 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.38919 | −0.382041 | ||||||||
\(605\) | −37.0258 | −1.50531 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.3991 | −0.787385 | −0.393693 | − | 0.919242i | \(-0.628803\pi\) | ||||
−0.393693 | + | 0.919242i | \(0.628803\pi\) | |||||||
\(608\) | −2.77209 | −0.112423 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.543861 | −0.0220203 | ||||||||
\(611\) | 0.688389 | 0.0278492 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.2484 | 1.94873 | 0.974367 | − | 0.224965i | \(-0.0722268\pi\) | ||||
0.974367 | + | 0.224965i | \(0.0722268\pi\) | |||||||
\(614\) | 7.56847 | 0.305439 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.2816 | −1.42154 | ||||||||
\(617\) | −10.5954 | −0.426555 | −0.213277 | − | 0.976992i | \(-0.568414\pi\) | ||||
−0.213277 | + | 0.976992i | \(0.568414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.9503 | −1.20380 | −0.601902 | − | 0.798570i | \(-0.705590\pi\) | ||||
−0.601902 | + | 0.798570i | \(0.705590\pi\) | |||||||
\(620\) | −2.56740 | −0.103109 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.7661 | −0.632163 | ||||||||
\(623\) | 15.1637 | 0.607519 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.52622 | −0.141049 | ||||||||
\(626\) | −12.3838 | −0.494956 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0117 | 0.399510 | ||||||||
\(629\) | −4.65885 | −0.185761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.2272 | 1.04409 | 0.522043 | − | 0.852919i | \(-0.325170\pi\) | ||||
0.522043 | + | 0.852919i | \(0.325170\pi\) | |||||||
\(632\) | 35.5827 | 1.41540 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.9265 | 0.791384 | ||||||||
\(635\) | 32.3986 | 1.28570 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.26438 | −0.0897180 | ||||||||
\(638\) | −46.2351 | −1.83047 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.93935 | −0.313830 | ||||||||
\(641\) | 14.4853 | 0.572135 | 0.286067 | − | 0.958210i | \(-0.407652\pi\) | ||||
0.286067 | + | 0.958210i | \(0.407652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.63994 | −0.104109 | −0.0520545 | − | 0.998644i | \(-0.516577\pi\) | ||||
−0.0520545 | + | 0.998644i | \(0.516577\pi\) | |||||||
\(644\) | 6.92671 | 0.272950 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.49338 | 0.0587562 | ||||||||
\(647\) | 8.18381 | 0.321739 | 0.160869 | − | 0.986976i | \(-0.448570\pi\) | ||||
0.160869 | + | 0.986976i | \(0.448570\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.4498 | 2.09809 | ||||||||
\(650\) | −2.32900 | −0.0913511 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.07979 | 0.0814509 | ||||||||
\(653\) | −32.2292 | −1.26123 | −0.630613 | − | 0.776098i | \(-0.717196\pi\) | ||||
−0.630613 | + | 0.776098i | \(0.717196\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.59468 | 0.101382 | ||||||||
\(656\) | −31.9326 | −1.24676 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.35674 | 0.0918751 | ||||||||
\(659\) | 3.30985 | 0.128934 | 0.0644668 | − | 0.997920i | \(-0.479465\pi\) | ||||
0.0644668 | + | 0.997920i | \(0.479465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.8264 | −0.771157 | −0.385579 | − | 0.922675i | \(-0.625998\pi\) | ||||
−0.385579 | + | 0.922675i | \(0.625998\pi\) | |||||||
\(662\) | 9.10667 | 0.353941 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.0470 | 0.894398 | ||||||||
\(665\) | 2.87958 | 0.111665 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.1581 | 1.74853 | ||||||||
\(668\) | 1.59337 | 0.0616493 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.3093 | 1.05505 | ||||||||
\(671\) | 1.77846 | 0.0686566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.12655 | 0.159067 | 0.0795333 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795333 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(674\) | −21.0810 | −0.812011 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.30258 | 0.242407 | ||||||||
\(677\) | 13.2120 | 0.507779 | 0.253890 | − | 0.967233i | \(-0.418290\pi\) | ||||
0.253890 | + | 0.967233i | \(0.418290\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.6968 | 1.13966 | ||||||||
\(680\) | −5.58810 | −0.214294 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −24.9761 | −0.956384 | ||||||||
\(683\) | 21.0203 | 0.804319 | 0.402159 | − | 0.915570i | \(-0.368260\pi\) | ||||
0.402159 | + | 0.915570i | \(0.368260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.1636 | 1.22891 | ||||||||
\(686\) | −24.2494 | −0.925846 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.2691 | 0.658377 | ||||||||
\(689\) | 3.17605 | 0.120998 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.0482 | −0.724630 | −0.362315 | − | 0.932056i | \(-0.618013\pi\) | ||||
−0.362315 | + | 0.932056i | \(0.618013\pi\) | |||||||
\(692\) | −3.80826 | −0.144768 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.46233 | 0.207347 | ||||||||
\(695\) | 34.6528 | 1.31446 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.2227 | −0.538724 | ||||||||
\(698\) | −26.7156 | −1.01120 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.68023 | 0.101303 | ||||||||
\(701\) | 44.2411 | 1.67096 | 0.835481 | − | 0.549519i | \(-0.185189\pi\) | ||||
0.835481 | + | 0.549519i | \(0.185189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.81678 | −0.143953 | ||||||||
\(704\) | 53.0640 | 1.99992 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.0188 | −1.50613 | ||||||||
\(707\) | −15.4536 | −0.581191 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.7579 | 1.26780 | 0.633902 | − | 0.773414i | \(-0.281452\pi\) | ||||
0.633902 | + | 0.773414i | \(0.281452\pi\) | |||||||
\(710\) | −15.4482 | −0.579761 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24.1078 | −0.903478 | ||||||||
\(713\) | 24.3943 | 0.913574 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.15446 | −0.230164 | ||||||||
\(716\) | −11.2670 | −0.421069 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.75919 | −0.326890 | ||||||||
\(719\) | 37.0118 | 1.38031 | 0.690153 | − | 0.723664i | \(-0.257543\pi\) | ||||
0.690153 | + | 0.723664i | \(0.257543\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.4931 | −1.09838 | ||||||||
\(722\) | 1.22346 | 0.0455323 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.46778 | −0.0917144 | ||||||||
\(725\) | 17.4736 | 0.648952 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.84394 | −0.179652 | −0.0898260 | − | 0.995957i | \(-0.528631\pi\) | ||||
−0.0898260 | + | 0.995957i | \(0.528631\pi\) | |||||||
\(728\) | −4.06100 | −0.150511 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.69049 | −0.210614 | ||||||||
\(731\) | 7.69161 | 0.284484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.7224 | 0.617655 | 0.308828 | − | 0.951118i | \(-0.400063\pi\) | ||||
0.308828 | + | 0.951118i | \(0.400063\pi\) | |||||||
\(734\) | 30.0534 | 1.10929 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.8111 | −0.730248 | ||||||||
\(737\) | −89.3030 | −3.28952 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0263 | 0.883821 | 0.441910 | − | 0.897059i | \(-0.354301\pi\) | ||||
0.441910 | + | 0.897059i | \(0.354301\pi\) | |||||||
\(740\) | 2.87081 | 0.105533 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.8734 | 0.399174 | ||||||||
\(743\) | 25.6863 | 0.942340 | 0.471170 | − | 0.882042i | \(-0.343832\pi\) | ||||
0.471170 | + | 0.882042i | \(0.343832\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.78875 | −0.248720 | ||||||||
\(746\) | −1.55327 | −0.0568691 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.67311 | 0.134302 | ||||||||
\(749\) | −2.68861 | −0.0982397 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.49816 | −0.164140 | −0.0820701 | − | 0.996627i | \(-0.526153\pi\) | ||||
−0.0820701 | + | 0.996627i | \(0.526153\pi\) | |||||||
\(752\) | −2.74052 | −0.0999367 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.32177 | −0.193807 | ||||||||
\(755\) | −27.8954 | −1.01522 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.3153 | 0.883754 | 0.441877 | − | 0.897076i | \(-0.354313\pi\) | ||||
0.441877 | + | 0.897076i | \(0.354313\pi\) | |||||||
\(758\) | −6.44565 | −0.234116 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.57807 | −0.166064 | ||||||||
\(761\) | −16.0639 | −0.582317 | −0.291158 | − | 0.956675i | \(-0.594041\pi\) | ||||
−0.291158 | + | 0.956675i | \(0.594041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.1984 | −0.586423 | ||||||||
\(764\) | 4.64341 | 0.167993 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.81363 | −0.101661 | ||||||||
\(767\) | 6.15220 | 0.222143 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.39454 | 0.338776 | 0.169388 | − | 0.985549i | \(-0.445821\pi\) | ||||
0.169388 | + | 0.985549i | \(0.445821\pi\) | |||||||
\(770\) | −21.0701 | −0.759314 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8942 | 0.428083 | ||||||||
\(773\) | 19.5949 | 0.704779 | 0.352390 | − | 0.935853i | \(-0.385369\pi\) | ||||
0.352390 | + | 0.935853i | \(0.385369\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.43918 | 0.339065 | ||||||||
\(776\) | −47.2131 | −1.69485 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8443 | 0.496343 | ||||||||
\(779\) | −11.6520 | −0.417476 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.5166 | 1.80762 | ||||||||
\(782\) | 10.6727 | 0.381653 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.01466 | 0.321952 | ||||||||
\(785\) | 29.7448 | 1.06164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0212478 | 0.000757403 0 | 0.000378701 | − | 1.00000i | \(-0.499879\pi\) | ||||
0.000378701 | 1.00000i | \(0.499879\pi\) | ||||||||
\(788\) | −7.10651 | −0.253159 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.2499 | 0.756037 | ||||||||
\(791\) | −13.4222 | −0.477240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.204705 | 0.00726927 | ||||||||
\(794\) | −34.0432 | −1.20815 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.02625 | −0.0718185 | ||||||||
\(797\) | −23.4986 | −0.832365 | −0.416182 | − | 0.909281i | \(-0.636632\pi\) | ||||
−0.416182 | + | 0.909281i | \(0.636632\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.22062 | −0.0431826 | ||||||||
\(800\) | −7.66576 | −0.271026 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.8538 | 0.842308 | ||||||||
\(803\) | 18.6082 | 0.656670 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.5793 | 0.725325 | ||||||||
\(806\) | −2.87480 | −0.101261 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.5687 | 0.864325 | ||||||||
\(809\) | 43.8069 | 1.54017 | 0.770085 | − | 0.637942i | \(-0.220214\pi\) | ||||
0.770085 | + | 0.637942i | \(0.220214\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.0957 | 1.75910 | 0.879549 | − | 0.475808i | \(-0.157844\pi\) | ||||
0.879549 | + | 0.475808i | \(0.157844\pi\) | |||||||
\(812\) | 6.12432 | 0.214922 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.9277 | 0.978866 | ||||||||
\(815\) | 6.17908 | 0.216444 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.30138 | 0.220457 | ||||||||
\(818\) | 27.7767 | 0.971191 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.76412 | 0.306057 | ||||||||
\(821\) | 13.9525 | 0.486947 | 0.243473 | − | 0.969908i | \(-0.421713\pi\) | ||||
0.243473 | + | 0.969908i | \(0.421713\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.555562 | 0.0193657 | 0.00968284 | − | 0.999953i | \(-0.496918\pi\) | ||||
0.00968284 | + | 0.999953i | \(0.496918\pi\) | |||||||
\(824\) | 46.8894 | 1.63347 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.0624 | 0.732854 | ||||||||
\(827\) | −53.0942 | −1.84627 | −0.923134 | − | 0.384479i | \(-0.874381\pi\) | ||||
−0.923134 | + | 0.384479i | \(0.874381\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.5139 | −1.78915 | −0.894575 | − | 0.446918i | \(-0.852522\pi\) | ||||
−0.894575 | + | 0.446918i | \(0.852522\pi\) | |||||||
\(830\) | 13.7636 | 0.477742 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.10778 | 0.211749 | ||||||||
\(833\) | 4.01511 | 0.139115 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73391 | 0.163824 | ||||||||
\(836\) | 3.00920 | 0.104076 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.8489 | −0.823847 | ||||||||
\(839\) | −23.7392 | −0.819568 | −0.409784 | − | 0.912183i | \(-0.634396\pi\) | ||||
−0.409784 | + | 0.912183i | \(0.634396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9271 | 0.376795 | ||||||||
\(842\) | −1.20338 | −0.0414711 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.46912 | 0.119412 | ||||||||
\(845\) | 18.7250 | 0.644161 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47.7112 | 1.63938 | ||||||||
\(848\) | −12.6441 | −0.434199 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.12970 | 0.141648 | ||||||||
\(851\) | −27.2772 | −0.935050 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.82861 | −0.131089 | −0.0655446 | − | 0.997850i | \(-0.520878\pi\) | ||||
−0.0655446 | + | 0.997850i | \(0.520878\pi\) | |||||||
\(854\) | 0.700817 | 0.0239815 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.27446 | 0.146098 | ||||||||
\(857\) | −0.182682 | −0.00624031 | −0.00312016 | − | 0.999995i | \(-0.500993\pi\) | ||||
−0.00312016 | + | 0.999995i | \(0.500993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5064 | 0.972625 | 0.486313 | − | 0.873785i | \(-0.338342\pi\) | ||||
0.486313 | + | 0.873785i | \(0.338342\pi\) | |||||||
\(860\) | −4.73962 | −0.161620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.1357 | 0.685824 | ||||||||
\(863\) | −5.32537 | −0.181278 | −0.0906389 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906389 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3144 | −0.384701 | ||||||||
\(866\) | 42.7621 | 1.45312 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.30834 | 0.112292 | ||||||||
\(869\) | −69.4884 | −2.35723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2790 | −0.348290 | ||||||||
\(872\) | 25.7529 | 0.872104 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.74361 | 0.295757 | ||||||||
\(875\) | 22.3609 | 0.755936 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.7758 | 1.30937 | 0.654684 | − | 0.755903i | \(-0.272802\pi\) | ||||
0.654684 | + | 0.755903i | \(0.272802\pi\) | |||||||
\(878\) | −31.1457 | −1.05112 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 24.5013 | 0.825939 | ||||||||
\(881\) | 50.1536 | 1.68972 | 0.844859 | − | 0.534989i | \(-0.179684\pi\) | ||||
0.844859 | + | 0.534989i | \(0.179684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.8316 | 1.40774 | 0.703872 | − | 0.710326i | \(-0.251453\pi\) | ||||
0.703872 | + | 0.710326i | \(0.251453\pi\) | |||||||
\(884\) | 0.422783 | 0.0142197 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.6733 | −0.963299 | ||||||||
\(887\) | 11.0837 | 0.372153 | 0.186076 | − | 0.982535i | \(-0.440423\pi\) | ||||
0.186076 | + | 0.982535i | \(0.440423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.7487 | −1.40021 | ||||||||
\(890\) | −14.3971 | −0.482593 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.02862 | −0.268818 | ||||||||
\(893\) | −1.00000 | −0.0334637 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −33.4745 | −1.11893 | ||||||||
\(896\) | 10.2306 | 0.341781 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −43.4657 | −1.45047 | ||||||||
\(899\) | 21.5685 | 0.719349 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.63164 | −0.187617 | ||||||||
\(902\) | 85.2587 | 2.83881 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21.3392 | 0.709732 | ||||||||
\(905\) | −7.33180 | −0.243717 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3842 | 1.60657 | 0.803286 | − | 0.595594i | \(-0.203083\pi\) | ||||
0.803286 | + | 0.595594i | \(0.203083\pi\) | |||||||
\(908\) | 1.09750 | 0.0364219 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.42522 | −0.0803952 | ||||||||
\(911\) | −16.9006 | −0.559943 | −0.279971 | − | 0.960008i | \(-0.590325\pi\) | ||||
−0.279971 | + | 0.960008i | \(0.590325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0079 | −1.48954 | ||||||||
\(914\) | −11.4966 | −0.380274 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.57874 | −0.283450 | ||||||||
\(917\) | −3.34349 | −0.110412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.7264 | 1.01357 | 0.506785 | − | 0.862073i | \(-0.330834\pi\) | ||||
0.506785 | + | 0.862073i | \(0.330834\pi\) | |||||||
\(920\) | −32.7178 | −1.07867 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.6331 | −0.383115 | ||||||||
\(923\) | 5.81457 | 0.191389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5547 | −0.347036 | ||||||||
\(926\) | 4.29871 | 0.141264 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17.5162 | −0.574999 | ||||||||
\(929\) | −8.50427 | −0.279016 | −0.139508 | − | 0.990221i | \(-0.544552\pi\) | ||||
−0.139508 | + | 0.990221i | \(0.544552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.28939 | 0.107805 | ||||||||
\(932\) | 9.21564 | 0.301868 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.1371 | −0.724347 | ||||||||
\(935\) | 10.9128 | 0.356888 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.8894 | −0.715096 | −0.357548 | − | 0.933895i | \(-0.616387\pi\) | ||||
−0.357548 | + | 0.933895i | \(0.616387\pi\) | |||||||
\(938\) | −35.1906 | −1.14902 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.752156 | 0.0245326 | ||||||||
\(941\) | −26.7202 | −0.871055 | −0.435528 | − | 0.900175i | \(-0.643438\pi\) | ||||
−0.435528 | + | 0.900175i | \(0.643438\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −83.2728 | −2.71173 | ||||||||
\(944\) | −24.4923 | −0.797157 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −46.1077 | −1.49909 | ||||||||
\(947\) | −52.6629 | −1.71131 | −0.855657 | − | 0.517544i | \(-0.826846\pi\) | ||||
−0.855657 | + | 0.517544i | \(0.826846\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.14185 | 0.0695274 | ||||||||
\(950\) | 3.38327 | 0.109768 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.20080 | 0.233379 | ||||||||
\(953\) | 40.1413 | 1.30030 | 0.650152 | − | 0.759804i | \(-0.274705\pi\) | ||||
0.650152 | + | 0.759804i | \(0.274705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.7956 | 0.446415 | ||||||||
\(956\) | 6.65216 | 0.215146 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.0540 | 1.16485 | ||||||||
\(959\) | −41.4458 | −1.33836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3488 | −0.624154 | ||||||||
\(962\) | 3.21454 | 0.103641 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.22937 | 0.0395952 | ||||||||
\(965\) | 35.3379 | 1.13757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.6891 | 0.826107 | 0.413053 | − | 0.910707i | \(-0.364462\pi\) | ||||
0.413053 | + | 0.910707i | \(0.364462\pi\) | |||||||
\(968\) | −75.8533 | −2.43802 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −28.1956 | −0.905305 | ||||||||
\(971\) | 4.88601 | 0.156800 | 0.0783998 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0783998 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.6535 | −1.43152 | ||||||||
\(974\) | −6.70510 | −0.214845 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.814943 | −0.0260857 | ||||||||
\(977\) | 8.61035 | 0.275469 | 0.137735 | − | 0.990469i | \(-0.456018\pi\) | ||||
0.137735 | + | 0.990469i | \(0.456018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.0794 | 1.50467 | ||||||||
\(980\) | −2.47413 | −0.0790333 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 29.7904 | 0.950649 | ||||||||
\(983\) | −32.6483 | −1.04132 | −0.520660 | − | 0.853764i | \(-0.674314\pi\) | ||||
−0.520660 | + | 0.853764i | \(0.674314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.1135 | −0.672732 | ||||||||
\(986\) | 9.43635 | 0.300515 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.346366 | 0.0110194 | ||||||||
\(989\) | 45.0337 | 1.43199 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4086 | 0.425938 | 0.212969 | − | 0.977059i | \(-0.431687\pi\) | ||||
0.212969 | + | 0.977059i | \(0.431687\pi\) | |||||||
\(992\) | −9.46223 | −0.300426 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.9065 | 0.631396 | ||||||||
\(995\) | −6.02001 | −0.190847 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.1372 | −0.764432 | −0.382216 | − | 0.924073i | \(-0.624839\pi\) | ||||
−0.382216 | + | 0.924073i | \(0.624839\pi\) | |||||||
\(998\) | −31.9721 | −1.01206 | ||||||||
\(999\) | 0 | 0 |
(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 | 8037.2.a.n.1.11 | 16 | ||
3.2 | odd | 2 | 893.2.a.b.1.6 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
893.2.a.b.1.6 | ✓ | 16 | 3.2 | odd | 2 | ||
8037.2.a.n.1.11 | 16 | 1.1 | even | 1 | trivial |