Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8673,2,Mod(1,8673)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8673, 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("8673.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8673 = 3 \cdot 7^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8673.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: | \(69.2542536731\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8673.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11491 | 1.49547 | 0.747733 | − | 0.664000i | \(-0.231142\pi\) | ||||
0.747733 | + | 0.664000i | \(0.231142\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.47283 | 1.23642 | ||||||||
\(5\) | 0.357926 | 0.160070 | 0.0800348 | − | 0.996792i | \(-0.474497\pi\) | ||||
0.0800348 | + | 0.996792i | \(0.474497\pi\) | |||||||
\(6\) | 2.11491 | 0.863407 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.756981 | 0.239378 | ||||||||
\(11\) | −4.58774 | −1.38326 | −0.691628 | − | 0.722254i | \(-0.743106\pi\) | ||||
−0.691628 | + | 0.722254i | \(0.743106\pi\) | |||||||
\(12\) | 2.47283 | 0.713846 | ||||||||
\(13\) | 2.58774 | 0.717710 | 0.358855 | − | 0.933393i | \(-0.383167\pi\) | ||||
0.358855 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.357926 | 0.0924162 | ||||||||
\(16\) | −2.83076 | −0.707690 | ||||||||
\(17\) | −2.18869 | −0.530834 | −0.265417 | − | 0.964134i | \(-0.585510\pi\) | ||||
−0.265417 | + | 0.964134i | \(0.585510\pi\) | |||||||
\(18\) | 2.11491 | 0.498488 | ||||||||
\(19\) | −0.527166 | −0.120940 | −0.0604701 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604701 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(20\) | 0.885092 | 0.197913 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.70265 | −2.06861 | ||||||||
\(23\) | −5.70265 | −1.18908 | −0.594542 | − | 0.804064i | \(-0.702667\pi\) | ||||
−0.594542 | + | 0.804064i | \(0.702667\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.87189 | −0.974378 | ||||||||
\(26\) | 5.47283 | 1.07331 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.06058 | 0.382639 | 0.191320 | − | 0.981528i | \(-0.438723\pi\) | ||||
0.191320 | + | 0.981528i | \(0.438723\pi\) | |||||||
\(30\) | 0.756981 | 0.138205 | ||||||||
\(31\) | −5.83076 | −1.04724 | −0.523618 | − | 0.851953i | \(-0.675418\pi\) | ||||
−0.523618 | + | 0.851953i | \(0.675418\pi\) | |||||||
\(32\) | −7.98680 | −1.41188 | ||||||||
\(33\) | −4.58774 | −0.798623 | ||||||||
\(34\) | −4.62887 | −0.793845 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.47283 | 0.412139 | ||||||||
\(37\) | −7.70265 | −1.26631 | −0.633154 | − | 0.774026i | \(-0.718240\pi\) | ||||
−0.633154 | + | 0.774026i | \(0.718240\pi\) | |||||||
\(38\) | −1.11491 | −0.180862 | ||||||||
\(39\) | 2.58774 | 0.414370 | ||||||||
\(40\) | 0.357926 | 0.0565931 | ||||||||
\(41\) | −2.39905 | −0.374669 | −0.187335 | − | 0.982296i | \(-0.559985\pi\) | ||||
−0.187335 | + | 0.982296i | \(0.559985\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.15604 | 1.09129 | 0.545643 | − | 0.838018i | \(-0.316286\pi\) | ||||
0.545643 | + | 0.838018i | \(0.316286\pi\) | |||||||
\(44\) | −11.3447 | −1.71028 | ||||||||
\(45\) | 0.357926 | 0.0533565 | ||||||||
\(46\) | −12.0606 | −1.77823 | ||||||||
\(47\) | −8.77643 | −1.28017 | −0.640087 | − | 0.768303i | \(-0.721102\pi\) | ||||
−0.640087 | + | 0.768303i | \(0.721102\pi\) | |||||||
\(48\) | −2.83076 | −0.408585 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −10.3036 | −1.45715 | ||||||||
\(51\) | −2.18869 | −0.306477 | ||||||||
\(52\) | 6.39905 | 0.887389 | ||||||||
\(53\) | −8.10170 | −1.11285 | −0.556427 | − | 0.830896i | \(-0.687828\pi\) | ||||
−0.556427 | + | 0.830896i | \(0.687828\pi\) | |||||||
\(54\) | 2.11491 | 0.287802 | ||||||||
\(55\) | −1.64207 | −0.221417 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.527166 | −0.0698249 | ||||||||
\(58\) | 4.35793 | 0.572224 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0.885092 | 0.114265 | ||||||||
\(61\) | −9.00624 | −1.15313 | −0.576566 | − | 0.817051i | \(-0.695607\pi\) | ||||
−0.576566 | + | 0.817051i | \(0.695607\pi\) | |||||||
\(62\) | −12.3315 | −1.56610 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.2298 | −1.40373 | ||||||||
\(65\) | 0.926221 | 0.114884 | ||||||||
\(66\) | −9.70265 | −1.19431 | ||||||||
\(67\) | 14.4791 | 1.76890 | 0.884450 | − | 0.466634i | \(-0.154534\pi\) | ||||
0.884450 | + | 0.466634i | \(0.154534\pi\) | |||||||
\(68\) | −5.41226 | −0.656333 | ||||||||
\(69\) | −5.70265 | −0.686518 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.12811 | 0.489917 | 0.244958 | − | 0.969534i | \(-0.421226\pi\) | ||||
0.244958 | + | 0.969534i | \(0.421226\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 11.2361 | 1.31508 | 0.657541 | − | 0.753419i | \(-0.271597\pi\) | ||||
0.657541 | + | 0.753419i | \(0.271597\pi\) | |||||||
\(74\) | −16.2904 | −1.89372 | ||||||||
\(75\) | −4.87189 | −0.562557 | ||||||||
\(76\) | −1.30359 | −0.149533 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.47283 | 0.619676 | ||||||||
\(79\) | −3.87189 | −0.435622 | −0.217811 | − | 0.975991i | \(-0.569892\pi\) | ||||
−0.217811 | + | 0.975991i | \(0.569892\pi\) | |||||||
\(80\) | −1.01320 | −0.113280 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.07378 | −0.560305 | ||||||||
\(83\) | 0.737534 | 0.0809549 | 0.0404775 | − | 0.999180i | \(-0.487112\pi\) | ||||
0.0404775 | + | 0.999180i | \(0.487112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.783389 | −0.0849704 | ||||||||
\(86\) | 15.1344 | 1.63198 | ||||||||
\(87\) | 2.06058 | 0.220917 | ||||||||
\(88\) | −4.58774 | −0.489055 | ||||||||
\(89\) | 8.54661 | 0.905939 | 0.452970 | − | 0.891526i | \(-0.350365\pi\) | ||||
0.452970 | + | 0.891526i | \(0.350365\pi\) | |||||||
\(90\) | 0.756981 | 0.0797928 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −14.1017 | −1.47020 | ||||||||
\(93\) | −5.83076 | −0.604622 | ||||||||
\(94\) | −18.5613 | −1.91446 | ||||||||
\(95\) | −0.188687 | −0.0193588 | ||||||||
\(96\) | −7.98680 | −0.815149 | ||||||||
\(97\) | 4.10170 | 0.416465 | 0.208232 | − | 0.978079i | \(-0.433229\pi\) | ||||
0.208232 | + | 0.978079i | \(0.433229\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.58774 | −0.461085 | ||||||||
\(100\) | −12.0474 | −1.20474 | ||||||||
\(101\) | 8.22982 | 0.818897 | 0.409449 | − | 0.912333i | \(-0.365721\pi\) | ||||
0.409449 | + | 0.912333i | \(0.365721\pi\) | |||||||
\(102\) | −4.62887 | −0.458326 | ||||||||
\(103\) | −4.79811 | −0.472772 | −0.236386 | − | 0.971659i | \(-0.575963\pi\) | ||||
−0.236386 | + | 0.971659i | \(0.575963\pi\) | |||||||
\(104\) | 2.58774 | 0.253749 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.1344 | −1.66424 | ||||||||
\(107\) | 14.0411 | 1.35741 | 0.678704 | − | 0.734412i | \(-0.262542\pi\) | ||||
0.678704 | + | 0.734412i | \(0.262542\pi\) | |||||||
\(108\) | 2.47283 | 0.237949 | ||||||||
\(109\) | −9.81131 | −0.939753 | −0.469877 | − | 0.882732i | \(-0.655702\pi\) | ||||
−0.469877 | + | 0.882732i | \(0.655702\pi\) | |||||||
\(110\) | −3.47283 | −0.331122 | ||||||||
\(111\) | −7.70265 | −0.731103 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2772 | 1.24901 | 0.624506 | − | 0.781020i | \(-0.285300\pi\) | ||||
0.624506 | + | 0.781020i | \(0.285300\pi\) | |||||||
\(114\) | −1.11491 | −0.104421 | ||||||||
\(115\) | −2.04113 | −0.190336 | ||||||||
\(116\) | 5.09546 | 0.473102 | ||||||||
\(117\) | 2.58774 | 0.239237 | ||||||||
\(118\) | −2.11491 | −0.194693 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.357926 | 0.0326741 | ||||||||
\(121\) | 10.0474 | 0.913397 | ||||||||
\(122\) | −19.0474 | −1.72447 | ||||||||
\(123\) | −2.39905 | −0.216315 | ||||||||
\(124\) | −14.4185 | −1.29482 | ||||||||
\(125\) | −3.53341 | −0.316038 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.587741 | −0.0521536 | −0.0260768 | − | 0.999660i | \(-0.508301\pi\) | ||||
−0.0260768 | + | 0.999660i | \(0.508301\pi\) | |||||||
\(128\) | −7.77643 | −0.687346 | ||||||||
\(129\) | 7.15604 | 0.630054 | ||||||||
\(130\) | 1.95887 | 0.171804 | ||||||||
\(131\) | 8.08226 | 0.706150 | 0.353075 | − | 0.935595i | \(-0.385136\pi\) | ||||
0.353075 | + | 0.935595i | \(0.385136\pi\) | |||||||
\(132\) | −11.3447 | −0.987431 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 30.6219 | 2.64533 | ||||||||
\(135\) | 0.357926 | 0.0308054 | ||||||||
\(136\) | −2.18869 | −0.187678 | ||||||||
\(137\) | 8.10170 | 0.692175 | 0.346088 | − | 0.938202i | \(-0.387510\pi\) | ||||
0.346088 | + | 0.938202i | \(0.387510\pi\) | |||||||
\(138\) | −12.0606 | −1.02666 | ||||||||
\(139\) | −4.96511 | −0.421136 | −0.210568 | − | 0.977579i | \(-0.567531\pi\) | ||||
−0.210568 | + | 0.977579i | \(0.567531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.77643 | −0.739109 | ||||||||
\(142\) | 8.73057 | 0.732653 | ||||||||
\(143\) | −11.8719 | −0.992777 | ||||||||
\(144\) | −2.83076 | −0.235897 | ||||||||
\(145\) | 0.737534 | 0.0612489 | ||||||||
\(146\) | 23.7632 | 1.96666 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.0474 | −1.56568 | ||||||||
\(149\) | −21.9325 | −1.79678 | −0.898389 | − | 0.439201i | \(-0.855262\pi\) | ||||
−0.898389 | + | 0.439201i | \(0.855262\pi\) | |||||||
\(150\) | −10.3036 | −0.841285 | ||||||||
\(151\) | 1.49228 | 0.121440 | 0.0607200 | − | 0.998155i | \(-0.480660\pi\) | ||||
0.0607200 | + | 0.998155i | \(0.480660\pi\) | |||||||
\(152\) | −0.527166 | −0.0427588 | ||||||||
\(153\) | −2.18869 | −0.176945 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.08698 | −0.167630 | ||||||||
\(156\) | 6.39905 | 0.512334 | ||||||||
\(157\) | 18.7089 | 1.49313 | 0.746566 | − | 0.665311i | \(-0.231701\pi\) | ||||
0.746566 | + | 0.665311i | \(0.231701\pi\) | |||||||
\(158\) | −8.18869 | −0.651457 | ||||||||
\(159\) | −8.10170 | −0.642507 | ||||||||
\(160\) | −2.85868 | −0.225999 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.11491 | 0.166163 | ||||||||
\(163\) | 3.34472 | 0.261979 | 0.130989 | − | 0.991384i | \(-0.458185\pi\) | ||||
0.130989 | + | 0.991384i | \(0.458185\pi\) | |||||||
\(164\) | −5.93246 | −0.463248 | ||||||||
\(165\) | −1.64207 | −0.127835 | ||||||||
\(166\) | 1.55982 | 0.121065 | ||||||||
\(167\) | −16.3991 | −1.26900 | −0.634498 | − | 0.772924i | \(-0.718793\pi\) | ||||
−0.634498 | + | 0.772924i | \(0.718793\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.30359 | −0.484892 | ||||||||
\(170\) | −1.65679 | −0.127070 | ||||||||
\(171\) | −0.527166 | −0.0403134 | ||||||||
\(172\) | 17.6957 | 1.34928 | ||||||||
\(173\) | −25.2097 | −1.91665 | −0.958327 | − | 0.285673i | \(-0.907783\pi\) | ||||
−0.958327 | + | 0.285673i | \(0.907783\pi\) | |||||||
\(174\) | 4.35793 | 0.330374 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.9868 | 0.978917 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 18.0753 | 1.35480 | ||||||||
\(179\) | −15.0738 | −1.12667 | −0.563334 | − | 0.826230i | \(-0.690481\pi\) | ||||
−0.563334 | + | 0.826230i | \(0.690481\pi\) | |||||||
\(180\) | 0.885092 | 0.0659709 | ||||||||
\(181\) | −14.7764 | −1.09832 | −0.549162 | − | 0.835716i | \(-0.685053\pi\) | ||||
−0.549162 | + | 0.835716i | \(0.685053\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.00624 | −0.665761 | ||||||||
\(184\) | −5.70265 | −0.420405 | ||||||||
\(185\) | −2.75698 | −0.202697 | ||||||||
\(186\) | −12.3315 | −0.904191 | ||||||||
\(187\) | 10.0411 | 0.734280 | ||||||||
\(188\) | −21.7026 | −1.58283 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.399055 | −0.0289505 | ||||||||
\(191\) | −19.9930 | −1.44665 | −0.723323 | − | 0.690510i | \(-0.757386\pi\) | ||||
−0.723323 | + | 0.690510i | \(0.757386\pi\) | |||||||
\(192\) | −11.2298 | −0.810442 | ||||||||
\(193\) | 5.28415 | 0.380361 | 0.190181 | − | 0.981749i | \(-0.439093\pi\) | ||||
0.190181 | + | 0.981749i | \(0.439093\pi\) | |||||||
\(194\) | 8.67472 | 0.622809 | ||||||||
\(195\) | 0.926221 | 0.0663281 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.12115 | 0.436114 | 0.218057 | − | 0.975936i | \(-0.430028\pi\) | ||||
0.218057 | + | 0.975936i | \(0.430028\pi\) | |||||||
\(198\) | −9.70265 | −0.689537 | ||||||||
\(199\) | 18.7500 | 1.32915 | 0.664577 | − | 0.747220i | \(-0.268612\pi\) | ||||
0.664577 | + | 0.747220i | \(0.268612\pi\) | |||||||
\(200\) | −4.87189 | −0.344495 | ||||||||
\(201\) | 14.4791 | 1.02128 | ||||||||
\(202\) | 17.4053 | 1.22463 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5.41226 | −0.378934 | ||||||||
\(205\) | −0.858685 | −0.0599732 | ||||||||
\(206\) | −10.1476 | −0.707014 | ||||||||
\(207\) | −5.70265 | −0.396362 | ||||||||
\(208\) | −7.32528 | −0.507916 | ||||||||
\(209\) | 2.41850 | 0.167291 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.32528 | 0.366607 | 0.183304 | − | 0.983056i | \(-0.441321\pi\) | ||||
0.183304 | + | 0.983056i | \(0.441321\pi\) | |||||||
\(212\) | −20.0342 | −1.37595 | ||||||||
\(213\) | 4.12811 | 0.282854 | ||||||||
\(214\) | 29.6957 | 2.02996 | ||||||||
\(215\) | 2.56133 | 0.174682 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.7500 | −1.40537 | ||||||||
\(219\) | 11.2361 | 0.759262 | ||||||||
\(220\) | −4.06058 | −0.273764 | ||||||||
\(221\) | −5.66376 | −0.380985 | ||||||||
\(222\) | −16.2904 | −1.09334 | ||||||||
\(223\) | 11.0279 | 0.738484 | 0.369242 | − | 0.929333i | \(-0.379617\pi\) | ||||
0.369242 | + | 0.929333i | \(0.379617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.87189 | −0.324793 | ||||||||
\(226\) | 28.0800 | 1.86786 | ||||||||
\(227\) | 11.1344 | 0.739013 | 0.369507 | − | 0.929228i | \(-0.379527\pi\) | ||||
0.369507 | + | 0.929228i | \(0.379527\pi\) | |||||||
\(228\) | −1.30359 | −0.0863326 | ||||||||
\(229\) | −25.4270 | −1.68026 | −0.840131 | − | 0.542383i | \(-0.817522\pi\) | ||||
−0.840131 | + | 0.542383i | \(0.817522\pi\) | |||||||
\(230\) | −4.31680 | −0.284641 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.06058 | 0.135283 | ||||||||
\(233\) | −10.1212 | −0.663059 | −0.331529 | − | 0.943445i | \(-0.607565\pi\) | ||||
−0.331529 | + | 0.943445i | \(0.607565\pi\) | |||||||
\(234\) | 5.47283 | 0.357770 | ||||||||
\(235\) | −3.14132 | −0.204917 | ||||||||
\(236\) | −2.47283 | −0.160968 | ||||||||
\(237\) | −3.87189 | −0.251506 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.9387 | 0.707566 | 0.353783 | − | 0.935328i | \(-0.384895\pi\) | ||||
0.353783 | + | 0.935328i | \(0.384895\pi\) | |||||||
\(240\) | −1.01320 | −0.0654020 | ||||||||
\(241\) | 10.2034 | 0.657259 | 0.328630 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328630 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(242\) | 21.2493 | 1.36595 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −22.2709 | −1.42575 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.07378 | −0.323492 | ||||||||
\(247\) | −1.36417 | −0.0868000 | ||||||||
\(248\) | −5.83076 | −0.370254 | ||||||||
\(249\) | 0.737534 | 0.0467393 | ||||||||
\(250\) | −7.47283 | −0.472624 | ||||||||
\(251\) | −12.2104 | −0.770712 | −0.385356 | − | 0.922768i | \(-0.625921\pi\) | ||||
−0.385356 | + | 0.922768i | \(0.625921\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26.1623 | 1.64481 | ||||||||
\(254\) | −1.24302 | −0.0779939 | ||||||||
\(255\) | −0.783389 | −0.0490577 | ||||||||
\(256\) | 6.01320 | 0.375825 | ||||||||
\(257\) | 9.52645 | 0.594244 | 0.297122 | − | 0.954840i | \(-0.403973\pi\) | ||||
0.297122 | + | 0.954840i | \(0.403973\pi\) | |||||||
\(258\) | 15.1344 | 0.942224 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.29039 | 0.142044 | ||||||||
\(261\) | 2.06058 | 0.127546 | ||||||||
\(262\) | 17.0932 | 1.05602 | ||||||||
\(263\) | −16.0995 | −0.992736 | −0.496368 | − | 0.868112i | \(-0.665333\pi\) | ||||
−0.496368 | + | 0.868112i | \(0.665333\pi\) | |||||||
\(264\) | −4.58774 | −0.282356 | ||||||||
\(265\) | −2.89981 | −0.178134 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.54661 | 0.523044 | ||||||||
\(268\) | 35.8044 | 2.18710 | ||||||||
\(269\) | −28.3051 | −1.72579 | −0.862897 | − | 0.505381i | \(-0.831352\pi\) | ||||
−0.862897 | + | 0.505381i | \(0.831352\pi\) | |||||||
\(270\) | 0.756981 | 0.0460684 | ||||||||
\(271\) | −1.38585 | −0.0841845 | −0.0420922 | − | 0.999114i | \(-0.513402\pi\) | ||||
−0.0420922 | + | 0.999114i | \(0.513402\pi\) | |||||||
\(272\) | 6.19565 | 0.375666 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.1344 | 1.03512 | ||||||||
\(275\) | 22.3510 | 1.34781 | ||||||||
\(276\) | −14.1017 | −0.848823 | ||||||||
\(277\) | −1.15604 | −0.0694595 | −0.0347297 | − | 0.999397i | \(-0.511057\pi\) | ||||
−0.0347297 | + | 0.999397i | \(0.511057\pi\) | |||||||
\(278\) | −10.5008 | −0.629794 | ||||||||
\(279\) | −5.83076 | −0.349078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5140 | −1.16411 | −0.582053 | − | 0.813151i | \(-0.697750\pi\) | ||||
−0.582053 | + | 0.813151i | \(0.697750\pi\) | |||||||
\(282\) | −18.5613 | −1.10531 | ||||||||
\(283\) | 2.04113 | 0.121332 | 0.0606662 | − | 0.998158i | \(-0.480677\pi\) | ||||
0.0606662 | + | 0.998158i | \(0.480677\pi\) | |||||||
\(284\) | 10.2081 | 0.605741 | ||||||||
\(285\) | −0.188687 | −0.0111768 | ||||||||
\(286\) | −25.1079 | −1.48466 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −7.98680 | −0.470626 | ||||||||
\(289\) | −12.2097 | −0.718215 | ||||||||
\(290\) | 1.55982 | 0.0915956 | ||||||||
\(291\) | 4.10170 | 0.240446 | ||||||||
\(292\) | 27.7849 | 1.62599 | ||||||||
\(293\) | 2.73057 | 0.159522 | 0.0797609 | − | 0.996814i | \(-0.474584\pi\) | ||||
0.0797609 | + | 0.996814i | \(0.474584\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.357926 | −0.0208393 | ||||||||
\(296\) | −7.70265 | −0.447707 | ||||||||
\(297\) | −4.58774 | −0.266208 | ||||||||
\(298\) | −46.3851 | −2.68702 | ||||||||
\(299\) | −14.7570 | −0.853418 | ||||||||
\(300\) | −12.0474 | −0.695555 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.15604 | 0.181609 | ||||||||
\(303\) | 8.22982 | 0.472791 | ||||||||
\(304\) | 1.49228 | 0.0855882 | ||||||||
\(305\) | −3.22357 | −0.184581 | ||||||||
\(306\) | −4.62887 | −0.264615 | ||||||||
\(307\) | 28.2423 | 1.61187 | 0.805937 | − | 0.592002i | \(-0.201662\pi\) | ||||
0.805937 | + | 0.592002i | \(0.201662\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.79811 | −0.272955 | ||||||||
\(310\) | −4.41378 | −0.250686 | ||||||||
\(311\) | −20.5272 | −1.16399 | −0.581994 | − | 0.813193i | \(-0.697727\pi\) | ||||
−0.581994 | + | 0.813193i | \(0.697727\pi\) | |||||||
\(312\) | 2.58774 | 0.146502 | ||||||||
\(313\) | 6.86565 | 0.388069 | 0.194035 | − | 0.980995i | \(-0.437843\pi\) | ||||
0.194035 | + | 0.980995i | \(0.437843\pi\) | |||||||
\(314\) | 39.5676 | 2.23293 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.57454 | −0.538610 | ||||||||
\(317\) | 28.6002 | 1.60635 | 0.803174 | − | 0.595744i | \(-0.203143\pi\) | ||||
0.803174 | + | 0.595744i | \(0.203143\pi\) | |||||||
\(318\) | −17.1344 | −0.960847 | ||||||||
\(319\) | −9.45339 | −0.529288 | ||||||||
\(320\) | −4.01945 | −0.224694 | ||||||||
\(321\) | 14.0411 | 0.783699 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.15380 | 0.0641992 | ||||||||
\(324\) | 2.47283 | 0.137380 | ||||||||
\(325\) | −12.6072 | −0.699321 | ||||||||
\(326\) | 7.07378 | 0.391780 | ||||||||
\(327\) | −9.81131 | −0.542567 | ||||||||
\(328\) | −2.39905 | −0.132466 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.47283 | −0.191173 | ||||||||
\(331\) | 21.2966 | 1.17057 | 0.585284 | − | 0.810828i | \(-0.300983\pi\) | ||||
0.585284 | + | 0.810828i | \(0.300983\pi\) | |||||||
\(332\) | 1.82380 | 0.100094 | ||||||||
\(333\) | −7.70265 | −0.422103 | ||||||||
\(334\) | −34.6825 | −1.89774 | ||||||||
\(335\) | 5.18244 | 0.283147 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.3253 | −0.616927 | −0.308464 | − | 0.951236i | \(-0.599815\pi\) | ||||
−0.308464 | + | 0.951236i | \(0.599815\pi\) | |||||||
\(338\) | −13.3315 | −0.725139 | ||||||||
\(339\) | 13.2772 | 0.721118 | ||||||||
\(340\) | −1.93719 | −0.105059 | ||||||||
\(341\) | 26.7500 | 1.44859 | ||||||||
\(342\) | −1.11491 | −0.0602873 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.15604 | 0.385828 | ||||||||
\(345\) | −2.04113 | −0.109891 | ||||||||
\(346\) | −53.3161 | −2.86629 | ||||||||
\(347\) | 2.58998 | 0.139037 | 0.0695186 | − | 0.997581i | \(-0.477854\pi\) | ||||
0.0695186 | + | 0.997581i | \(0.477854\pi\) | |||||||
\(348\) | 5.09546 | 0.273145 | ||||||||
\(349\) | 26.0319 | 1.39346 | 0.696729 | − | 0.717335i | \(-0.254638\pi\) | ||||
0.696729 | + | 0.717335i | \(0.254638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.58774 | 0.138123 | ||||||||
\(352\) | 36.6414 | 1.95299 | ||||||||
\(353\) | −13.9325 | −0.741550 | −0.370775 | − | 0.928723i | \(-0.620908\pi\) | ||||
−0.370775 | + | 0.928723i | \(0.620908\pi\) | |||||||
\(354\) | −2.11491 | −0.112406 | ||||||||
\(355\) | 1.47756 | 0.0784207 | ||||||||
\(356\) | 21.1344 | 1.12012 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.8796 | −1.68489 | ||||||||
\(359\) | −5.89134 | −0.310933 | −0.155466 | − | 0.987841i | \(-0.549688\pi\) | ||||
−0.155466 | + | 0.987841i | \(0.549688\pi\) | |||||||
\(360\) | 0.357926 | 0.0188644 | ||||||||
\(361\) | −18.7221 | −0.985373 | ||||||||
\(362\) | −31.2508 | −1.64250 | ||||||||
\(363\) | 10.0474 | 0.527350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.02168 | 0.210504 | ||||||||
\(366\) | −19.0474 | −0.995622 | ||||||||
\(367\) | 0.926221 | 0.0483483 | 0.0241742 | − | 0.999708i | \(-0.492304\pi\) | ||||
0.0241742 | + | 0.999708i | \(0.492304\pi\) | |||||||
\(368\) | 16.1428 | 0.841503 | ||||||||
\(369\) | −2.39905 | −0.124890 | ||||||||
\(370\) | −5.83076 | −0.303127 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −14.4185 | −0.747564 | ||||||||
\(373\) | 10.1498 | 0.525536 | 0.262768 | − | 0.964859i | \(-0.415365\pi\) | ||||
0.262768 | + | 0.964859i | \(0.415365\pi\) | |||||||
\(374\) | 21.2361 | 1.09809 | ||||||||
\(375\) | −3.53341 | −0.182464 | ||||||||
\(376\) | −8.77643 | −0.452610 | ||||||||
\(377\) | 5.33224 | 0.274624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0753 | −1.44213 | −0.721066 | − | 0.692867i | \(-0.756347\pi\) | ||||
−0.721066 | + | 0.692867i | \(0.756347\pi\) | |||||||
\(380\) | −0.466591 | −0.0239356 | ||||||||
\(381\) | −0.587741 | −0.0301109 | ||||||||
\(382\) | −42.2834 | −2.16341 | ||||||||
\(383\) | −34.8176 | −1.77909 | −0.889547 | − | 0.456844i | \(-0.848980\pi\) | ||||
−0.889547 | + | 0.456844i | \(0.848980\pi\) | |||||||
\(384\) | −7.77643 | −0.396839 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.1755 | 0.568817 | ||||||||
\(387\) | 7.15604 | 0.363762 | ||||||||
\(388\) | 10.1428 | 0.514924 | ||||||||
\(389\) | 1.78267 | 0.0903850 | 0.0451925 | − | 0.998978i | \(-0.485610\pi\) | ||||
0.0451925 | + | 0.998978i | \(0.485610\pi\) | |||||||
\(390\) | 1.95887 | 0.0991913 | ||||||||
\(391\) | 12.4813 | 0.631207 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.08226 | 0.407696 | ||||||||
\(394\) | 12.9457 | 0.652193 | ||||||||
\(395\) | −1.38585 | −0.0697297 | ||||||||
\(396\) | −11.3447 | −0.570094 | ||||||||
\(397\) | −0.817557 | −0.0410320 | −0.0205160 | − | 0.999790i | \(-0.506531\pi\) | ||||
−0.0205160 | + | 0.999790i | \(0.506531\pi\) | |||||||
\(398\) | 39.6546 | 1.98770 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.7911 | 0.689557 | ||||||||
\(401\) | −5.35168 | −0.267250 | −0.133625 | − | 0.991032i | \(-0.542662\pi\) | ||||
−0.133625 | + | 0.991032i | \(0.542662\pi\) | |||||||
\(402\) | 30.6219 | 1.52728 | ||||||||
\(403\) | −15.0885 | −0.751612 | ||||||||
\(404\) | 20.3510 | 1.01250 | ||||||||
\(405\) | 0.357926 | 0.0177855 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.3378 | 1.75163 | ||||||||
\(408\) | −2.18869 | −0.108356 | ||||||||
\(409\) | 38.4068 | 1.89909 | 0.949547 | − | 0.313624i | \(-0.101543\pi\) | ||||
0.949547 | + | 0.313624i | \(0.101543\pi\) | |||||||
\(410\) | −1.81604 | −0.0896878 | ||||||||
\(411\) | 8.10170 | 0.399628 | ||||||||
\(412\) | −11.8649 | −0.584543 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −12.0606 | −0.592745 | ||||||||
\(415\) | 0.263983 | 0.0129584 | ||||||||
\(416\) | −20.6678 | −1.01332 | ||||||||
\(417\) | −4.96511 | −0.243143 | ||||||||
\(418\) | 5.11491 | 0.250178 | ||||||||
\(419\) | −8.71585 | −0.425797 | −0.212899 | − | 0.977074i | \(-0.568290\pi\) | ||||
−0.212899 | + | 0.977074i | \(0.568290\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.357926 | −0.0174443 | −0.00872213 | − | 0.999962i | \(-0.502776\pi\) | ||||
−0.00872213 | + | 0.999962i | \(0.502776\pi\) | |||||||
\(422\) | 11.2625 | 0.548248 | ||||||||
\(423\) | −8.77643 | −0.426725 | ||||||||
\(424\) | −8.10170 | −0.393454 | ||||||||
\(425\) | 10.6630 | 0.517233 | ||||||||
\(426\) | 8.73057 | 0.422998 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 34.7214 | 1.67832 | ||||||||
\(429\) | −11.8719 | −0.573180 | ||||||||
\(430\) | 5.41698 | 0.261230 | ||||||||
\(431\) | −13.2361 | −0.637558 | −0.318779 | − | 0.947829i | \(-0.603273\pi\) | ||||
−0.318779 | + | 0.947829i | \(0.603273\pi\) | |||||||
\(432\) | −2.83076 | −0.136195 | ||||||||
\(433\) | 27.4031 | 1.31691 | 0.658454 | − | 0.752621i | \(-0.271211\pi\) | ||||
0.658454 | + | 0.752621i | \(0.271211\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.737534 | 0.0353621 | ||||||||
\(436\) | −24.2617 | −1.16193 | ||||||||
\(437\) | 3.00624 | 0.143808 | ||||||||
\(438\) | 23.7632 | 1.13545 | ||||||||
\(439\) | −32.5955 | −1.55570 | −0.777849 | − | 0.628451i | \(-0.783689\pi\) | ||||
−0.777849 | + | 0.628451i | \(0.783689\pi\) | |||||||
\(440\) | −1.64207 | −0.0782828 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.9783 | −0.569751 | ||||||||
\(443\) | −30.8392 | −1.46522 | −0.732608 | − | 0.680651i | \(-0.761697\pi\) | ||||
−0.732608 | + | 0.680651i | \(0.761697\pi\) | |||||||
\(444\) | −19.0474 | −0.903948 | ||||||||
\(445\) | 3.05906 | 0.145013 | ||||||||
\(446\) | 23.3230 | 1.10438 | ||||||||
\(447\) | −21.9325 | −1.03737 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.0863 | 1.65582 | 0.827912 | − | 0.560859i | \(-0.189529\pi\) | ||||
0.827912 | + | 0.560859i | \(0.189529\pi\) | |||||||
\(450\) | −10.3036 | −0.485716 | ||||||||
\(451\) | 11.0062 | 0.518264 | ||||||||
\(452\) | 32.8323 | 1.54430 | ||||||||
\(453\) | 1.49228 | 0.0701135 | ||||||||
\(454\) | 23.5481 | 1.10517 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.527166 | −0.0246868 | ||||||||
\(457\) | 10.6414 | 0.497782 | 0.248891 | − | 0.968532i | \(-0.419934\pi\) | ||||
0.248891 | + | 0.968532i | \(0.419934\pi\) | |||||||
\(458\) | −53.7757 | −2.51277 | ||||||||
\(459\) | −2.18869 | −0.102159 | ||||||||
\(460\) | −5.04737 | −0.235335 | ||||||||
\(461\) | 28.4046 | 1.32293 | 0.661467 | − | 0.749975i | \(-0.269934\pi\) | ||||
0.661467 | + | 0.749975i | \(0.269934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.58150 | −0.445290 | −0.222645 | − | 0.974900i | \(-0.571469\pi\) | ||||
−0.222645 | + | 0.974900i | \(0.571469\pi\) | |||||||
\(464\) | −5.83299 | −0.270790 | ||||||||
\(465\) | −2.08698 | −0.0967815 | ||||||||
\(466\) | −21.4053 | −0.991581 | ||||||||
\(467\) | −26.1336 | −1.20932 | −0.604660 | − | 0.796484i | \(-0.706691\pi\) | ||||
−0.604660 | + | 0.796484i | \(0.706691\pi\) | |||||||
\(468\) | 6.39905 | 0.295796 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.64359 | −0.306446 | ||||||||
\(471\) | 18.7089 | 0.862060 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −32.8300 | −1.50953 | ||||||||
\(474\) | −8.18869 | −0.376119 | ||||||||
\(475\) | 2.56829 | 0.117841 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.10170 | −0.370952 | ||||||||
\(478\) | 23.1344 | 1.05814 | ||||||||
\(479\) | 18.5397 | 0.847098 | 0.423549 | − | 0.905873i | \(-0.360784\pi\) | ||||
0.423549 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(480\) | −2.85868 | −0.130481 | ||||||||
\(481\) | −19.9325 | −0.908842 | ||||||||
\(482\) | 21.5793 | 0.982909 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24.8455 | 1.12934 | ||||||||
\(485\) | 1.46811 | 0.0666633 | ||||||||
\(486\) | 2.11491 | 0.0959342 | ||||||||
\(487\) | −21.5676 | −0.977320 | −0.488660 | − | 0.872474i | \(-0.662514\pi\) | ||||
−0.488660 | + | 0.872474i | \(0.662514\pi\) | |||||||
\(488\) | −9.00624 | −0.407693 | ||||||||
\(489\) | 3.34472 | 0.151254 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4659 | −0.517448 | −0.258724 | − | 0.965951i | \(-0.583302\pi\) | ||||
−0.258724 | + | 0.965951i | \(0.583302\pi\) | |||||||
\(492\) | −5.93246 | −0.267456 | ||||||||
\(493\) | −4.50995 | −0.203118 | ||||||||
\(494\) | −2.88509 | −0.129806 | ||||||||
\(495\) | −1.64207 | −0.0738057 | ||||||||
\(496\) | 16.5055 | 0.741118 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.55982 | 0.0698971 | ||||||||
\(499\) | −17.4681 | −0.781980 | −0.390990 | − | 0.920395i | \(-0.627867\pi\) | ||||
−0.390990 | + | 0.920395i | \(0.627867\pi\) | |||||||
\(500\) | −8.73753 | −0.390754 | ||||||||
\(501\) | −16.3991 | −0.732656 | ||||||||
\(502\) | −25.8238 | −1.15257 | ||||||||
\(503\) | −0.655277 | −0.0292174 | −0.0146087 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146087 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.94567 | 0.131080 | ||||||||
\(506\) | 55.3308 | 2.45975 | ||||||||
\(507\) | −6.30359 | −0.279952 | ||||||||
\(508\) | −1.45339 | −0.0644836 | ||||||||
\(509\) | 15.8168 | 0.701069 | 0.350535 | − | 0.936550i | \(-0.386000\pi\) | ||||
0.350535 | + | 0.936550i | \(0.386000\pi\) | |||||||
\(510\) | −1.65679 | −0.0733641 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 28.2702 | 1.24938 | ||||||||
\(513\) | −0.527166 | −0.0232750 | ||||||||
\(514\) | 20.1476 | 0.888671 | ||||||||
\(515\) | −1.71737 | −0.0756764 | ||||||||
\(516\) | 17.6957 | 0.779009 | ||||||||
\(517\) | 40.2640 | 1.77081 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.2097 | −1.10658 | ||||||||
\(520\) | 0.926221 | 0.0406175 | ||||||||
\(521\) | 12.2470 | 0.536552 | 0.268276 | − | 0.963342i | \(-0.413546\pi\) | ||||
0.268276 | + | 0.963342i | \(0.413546\pi\) | |||||||
\(522\) | 4.35793 | 0.190741 | ||||||||
\(523\) | 2.23678 | 0.0978074 | 0.0489037 | − | 0.998803i | \(-0.484427\pi\) | ||||
0.0489037 | + | 0.998803i | \(0.484427\pi\) | |||||||
\(524\) | 19.9861 | 0.873096 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −34.0489 | −1.48460 | ||||||||
\(527\) | 12.7617 | 0.555909 | ||||||||
\(528\) | 12.9868 | 0.565178 | ||||||||
\(529\) | 9.52021 | 0.413922 | ||||||||
\(530\) | −6.13284 | −0.266393 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.20813 | −0.268904 | ||||||||
\(534\) | 18.0753 | 0.782195 | ||||||||
\(535\) | 5.02569 | 0.217280 | ||||||||
\(536\) | 14.4791 | 0.625401 | ||||||||
\(537\) | −15.0738 | −0.650482 | ||||||||
\(538\) | −59.8627 | −2.58086 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.885092 | 0.0380883 | ||||||||
\(541\) | −11.0863 | −0.476636 | −0.238318 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238318 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(542\) | −2.93095 | −0.125895 | ||||||||
\(543\) | −14.7764 | −0.634117 | ||||||||
\(544\) | 17.4806 | 0.749474 | ||||||||
\(545\) | −3.51173 | −0.150426 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.1887 | 0.521151 | 0.260575 | − | 0.965454i | \(-0.416088\pi\) | ||||
0.260575 | + | 0.965454i | \(0.416088\pi\) | |||||||
\(548\) | 20.0342 | 0.855817 | ||||||||
\(549\) | −9.00624 | −0.384377 | ||||||||
\(550\) | 47.2702 | 2.01561 | ||||||||
\(551\) | −1.08627 | −0.0462765 | ||||||||
\(552\) | −5.70265 | −0.242721 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.44491 | −0.103874 | ||||||||
\(555\) | −2.75698 | −0.117027 | ||||||||
\(556\) | −12.2779 | −0.520699 | ||||||||
\(557\) | −8.56829 | −0.363050 | −0.181525 | − | 0.983386i | \(-0.558103\pi\) | ||||
−0.181525 | + | 0.983386i | \(0.558103\pi\) | |||||||
\(558\) | −12.3315 | −0.522035 | ||||||||
\(559\) | 18.5180 | 0.783227 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0411 | 0.423937 | ||||||||
\(562\) | −41.2702 | −1.74088 | ||||||||
\(563\) | −9.98055 | −0.420630 | −0.210315 | − | 0.977634i | \(-0.567449\pi\) | ||||
−0.210315 | + | 0.977634i | \(0.567449\pi\) | |||||||
\(564\) | −21.7026 | −0.913846 | ||||||||
\(565\) | 4.75226 | 0.199929 | ||||||||
\(566\) | 4.31680 | 0.181449 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.12811 | 0.173212 | ||||||||
\(569\) | 46.1428 | 1.93441 | 0.967204 | − | 0.254001i | \(-0.0817465\pi\) | ||||
0.967204 | + | 0.254001i | \(0.0817465\pi\) | |||||||
\(570\) | −0.399055 | −0.0167146 | ||||||||
\(571\) | −21.1824 | −0.886458 | −0.443229 | − | 0.896409i | \(-0.646167\pi\) | ||||
−0.443229 | + | 0.896409i | \(0.646167\pi\) | |||||||
\(572\) | −29.3572 | −1.22749 | ||||||||
\(573\) | −19.9930 | −0.835221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.7827 | 1.15862 | ||||||||
\(576\) | −11.2298 | −0.467909 | ||||||||
\(577\) | −40.8859 | −1.70210 | −0.851051 | − | 0.525083i | \(-0.824034\pi\) | ||||
−0.851051 | + | 0.525083i | \(0.824034\pi\) | |||||||
\(578\) | −25.8223 | −1.07407 | ||||||||
\(579\) | 5.28415 | 0.219602 | ||||||||
\(580\) | 1.82380 | 0.0757292 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.67472 | 0.359579 | ||||||||
\(583\) | 37.1685 | 1.53936 | ||||||||
\(584\) | 11.2361 | 0.464951 | ||||||||
\(585\) | 0.926221 | 0.0382945 | ||||||||
\(586\) | 5.77491 | 0.238559 | ||||||||
\(587\) | 4.21037 | 0.173780 | 0.0868902 | − | 0.996218i | \(-0.472307\pi\) | ||||
0.0868902 | + | 0.996218i | \(0.472307\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.07378 | 0.126653 | ||||||||
\(590\) | −0.756981 | −0.0311644 | ||||||||
\(591\) | 6.12115 | 0.251790 | ||||||||
\(592\) | 21.8044 | 0.896153 | ||||||||
\(593\) | 22.5202 | 0.924794 | 0.462397 | − | 0.886673i | \(-0.346990\pi\) | ||||
0.462397 | + | 0.886673i | \(0.346990\pi\) | |||||||
\(594\) | −9.70265 | −0.398105 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −54.2353 | −2.22157 | ||||||||
\(597\) | 18.7500 | 0.767387 | ||||||||
\(598\) | −31.2097 | −1.27626 | ||||||||
\(599\) | −16.7981 | −0.686352 | −0.343176 | − | 0.939271i | \(-0.611503\pi\) | ||||
−0.343176 | + | 0.939271i | \(0.611503\pi\) | |||||||
\(600\) | −4.87189 | −0.198894 | ||||||||
\(601\) | 17.0955 | 0.697338 | 0.348669 | − | 0.937246i | \(-0.386634\pi\) | ||||
0.348669 | + | 0.937246i | \(0.386634\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4791 | 0.589634 | ||||||||
\(604\) | 3.69016 | 0.150151 | ||||||||
\(605\) | 3.59622 | 0.146207 | ||||||||
\(606\) | 17.4053 | 0.707042 | ||||||||
\(607\) | 7.53341 | 0.305772 | 0.152886 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152886 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(608\) | 4.21037 | 0.170753 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.81756 | −0.276035 | ||||||||
\(611\) | −22.7111 | −0.918794 | ||||||||
\(612\) | −5.41226 | −0.218778 | ||||||||
\(613\) | 15.1321 | 0.611181 | 0.305590 | − | 0.952163i | \(-0.401146\pi\) | ||||
0.305590 | + | 0.952163i | \(0.401146\pi\) | |||||||
\(614\) | 59.7299 | 2.41050 | ||||||||
\(615\) | −0.858685 | −0.0346255 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8672 | 0.638788 | 0.319394 | − | 0.947622i | \(-0.396521\pi\) | ||||
0.319394 | + | 0.947622i | \(0.396521\pi\) | |||||||
\(618\) | −10.1476 | −0.408195 | ||||||||
\(619\) | −11.0210 | −0.442970 | −0.221485 | − | 0.975164i | \(-0.571090\pi\) | ||||
−0.221485 | + | 0.975164i | \(0.571090\pi\) | |||||||
\(620\) | −5.16076 | −0.207261 | ||||||||
\(621\) | −5.70265 | −0.228839 | ||||||||
\(622\) | −43.4131 | −1.74071 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.32528 | −0.293246 | ||||||||
\(625\) | 23.0947 | 0.923790 | ||||||||
\(626\) | 14.5202 | 0.580344 | ||||||||
\(627\) | 2.41850 | 0.0965857 | ||||||||
\(628\) | 46.2640 | 1.84613 | ||||||||
\(629\) | 16.8587 | 0.672200 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1560 | −0.921827 | −0.460914 | − | 0.887445i | \(-0.652478\pi\) | ||||
−0.460914 | + | 0.887445i | \(0.652478\pi\) | |||||||
\(632\) | −3.87189 | −0.154015 | ||||||||
\(633\) | 5.32528 | 0.211661 | ||||||||
\(634\) | 60.4868 | 2.40224 | ||||||||
\(635\) | −0.210368 | −0.00834821 | ||||||||
\(636\) | −20.0342 | −0.794406 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −19.9930 | −0.791532 | ||||||||
\(639\) | 4.12811 | 0.163306 | ||||||||
\(640\) | −2.78339 | −0.110023 | ||||||||
\(641\) | 39.5459 | 1.56197 | 0.780984 | − | 0.624550i | \(-0.214718\pi\) | ||||
0.780984 | + | 0.624550i | \(0.214718\pi\) | |||||||
\(642\) | 29.6957 | 1.17200 | ||||||||
\(643\) | −18.6219 | −0.734376 | −0.367188 | − | 0.930147i | \(-0.619680\pi\) | ||||
−0.367188 | + | 0.930147i | \(0.619680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.56133 | 0.100852 | ||||||||
\(646\) | 2.44018 | 0.0960077 | ||||||||
\(647\) | −7.24525 | −0.284840 | −0.142420 | − | 0.989806i | \(-0.545488\pi\) | ||||
−0.142420 | + | 0.989806i | \(0.545488\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 4.58774 | 0.180085 | ||||||||
\(650\) | −26.6630 | −1.04581 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.27094 | 0.323915 | ||||||||
\(653\) | 31.3183 | 1.22558 | 0.612790 | − | 0.790246i | \(-0.290047\pi\) | ||||
0.612790 | + | 0.790246i | \(0.290047\pi\) | |||||||
\(654\) | −20.7500 | −0.811390 | ||||||||
\(655\) | 2.89285 | 0.113033 | ||||||||
\(656\) | 6.79115 | 0.265150 | ||||||||
\(657\) | 11.2361 | 0.438360 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.13587 | 0.316929 | 0.158464 | − | 0.987365i | \(-0.449346\pi\) | ||||
0.158464 | + | 0.987365i | \(0.449346\pi\) | |||||||
\(660\) | −4.06058 | −0.158058 | ||||||||
\(661\) | 9.47979 | 0.368721 | 0.184361 | − | 0.982859i | \(-0.440979\pi\) | ||||
0.184361 | + | 0.982859i | \(0.440979\pi\) | |||||||
\(662\) | 45.0404 | 1.75055 | ||||||||
\(663\) | −5.66376 | −0.219962 | ||||||||
\(664\) | 0.737534 | 0.0286219 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.2904 | −0.631240 | ||||||||
\(667\) | −11.7507 | −0.454990 | ||||||||
\(668\) | −40.5521 | −1.56901 | ||||||||
\(669\) | 11.0279 | 0.426364 | ||||||||
\(670\) | 10.9604 | 0.423437 | ||||||||
\(671\) | 41.3183 | 1.59508 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4317 | 0.440660 | 0.220330 | − | 0.975425i | \(-0.429287\pi\) | ||||
0.220330 | + | 0.975425i | \(0.429287\pi\) | |||||||
\(674\) | −23.9519 | −0.922593 | ||||||||
\(675\) | −4.87189 | −0.187519 | ||||||||
\(676\) | −15.5877 | −0.599529 | ||||||||
\(677\) | 6.83700 | 0.262767 | 0.131384 | − | 0.991332i | \(-0.458058\pi\) | ||||
0.131384 | + | 0.991332i | \(0.458058\pi\) | |||||||
\(678\) | 28.0800 | 1.07841 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.783389 | −0.0300416 | ||||||||
\(681\) | 11.1344 | 0.426669 | ||||||||
\(682\) | 56.5738 | 2.16632 | ||||||||
\(683\) | −34.6002 | −1.32394 | −0.661970 | − | 0.749530i | \(-0.730280\pi\) | ||||
−0.661970 | + | 0.749530i | \(0.730280\pi\) | |||||||
\(684\) | −1.30359 | −0.0498442 | ||||||||
\(685\) | 2.89981 | 0.110796 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.4270 | −0.970100 | ||||||||
\(688\) | −20.2570 | −0.772292 | ||||||||
\(689\) | −20.9651 | −0.798707 | ||||||||
\(690\) | −4.31680 | −0.164338 | ||||||||
\(691\) | 42.8929 | 1.63172 | 0.815861 | − | 0.578249i | \(-0.196264\pi\) | ||||
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(692\) | −62.3393 | −2.36978 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.47756 | 0.207925 | ||||||||
\(695\) | −1.77715 | −0.0674110 | ||||||||
\(696\) | 2.06058 | 0.0781059 | ||||||||
\(697\) | 5.25078 | 0.198887 | ||||||||
\(698\) | 55.0551 | 2.08387 | ||||||||
\(699\) | −10.1212 | −0.382817 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.83228 | 0.333591 | 0.166795 | − | 0.985992i | \(-0.446658\pi\) | ||||
0.166795 | + | 0.985992i | \(0.446658\pi\) | |||||||
\(702\) | 5.47283 | 0.206559 | ||||||||
\(703\) | 4.06058 | 0.153148 | ||||||||
\(704\) | 51.5195 | 1.94171 | ||||||||
\(705\) | −3.14132 | −0.118309 | ||||||||
\(706\) | −29.4659 | −1.10896 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.47283 | −0.0929348 | ||||||||
\(709\) | 22.7981 | 0.856201 | 0.428100 | − | 0.903731i | \(-0.359183\pi\) | ||||
0.428100 | + | 0.903731i | \(0.359183\pi\) | |||||||
\(710\) | 3.12490 | 0.117276 | ||||||||
\(711\) | −3.87189 | −0.145207 | ||||||||
\(712\) | 8.54661 | 0.320298 | ||||||||
\(713\) | 33.2508 | 1.24525 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.24926 | −0.158913 | ||||||||
\(716\) | −37.2750 | −1.39303 | ||||||||
\(717\) | 10.9387 | 0.408514 | ||||||||
\(718\) | −12.4596 | −0.464989 | ||||||||
\(719\) | −21.6887 | −0.808853 | −0.404427 | − | 0.914570i | \(-0.632529\pi\) | ||||
−0.404427 | + | 0.914570i | \(0.632529\pi\) | |||||||
\(720\) | −1.01320 | −0.0377599 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −39.5955 | −1.47359 | ||||||||
\(723\) | 10.2034 | 0.379469 | ||||||||
\(724\) | −36.5397 | −1.35799 | ||||||||
\(725\) | −10.0389 | −0.372835 | ||||||||
\(726\) | 21.2493 | 0.788634 | ||||||||
\(727\) | −47.7438 | −1.77072 | −0.885359 | − | 0.464907i | \(-0.846088\pi\) | ||||
−0.885359 | + | 0.464907i | \(0.846088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.50548 | 0.314802 | ||||||||
\(731\) | −15.6623 | −0.579292 | ||||||||
\(732\) | −22.2709 | −0.823158 | ||||||||
\(733\) | −37.3983 | −1.38134 | −0.690670 | − | 0.723170i | \(-0.742684\pi\) | ||||
−0.690670 | + | 0.723170i | \(0.742684\pi\) | |||||||
\(734\) | 1.95887 | 0.0723033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.5459 | 1.67884 | ||||||||
\(737\) | −66.4263 | −2.44684 | ||||||||
\(738\) | −5.07378 | −0.186768 | ||||||||
\(739\) | −13.9450 | −0.512973 | −0.256487 | − | 0.966548i | \(-0.582565\pi\) | ||||
−0.256487 | + | 0.966548i | \(0.582565\pi\) | |||||||
\(740\) | −6.81756 | −0.250618 | ||||||||
\(741\) | −1.36417 | −0.0501140 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.4200 | 1.73967 | 0.869836 | − | 0.493341i | \(-0.164225\pi\) | ||||
0.869836 | + | 0.493341i | \(0.164225\pi\) | |||||||
\(744\) | −5.83076 | −0.213766 | ||||||||
\(745\) | −7.85021 | −0.287609 | ||||||||
\(746\) | 21.4659 | 0.785921 | ||||||||
\(747\) | 0.737534 | 0.0269850 | ||||||||
\(748\) | 24.8300 | 0.907876 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.47283 | −0.272869 | ||||||||
\(751\) | 46.8929 | 1.71114 | 0.855572 | − | 0.517683i | \(-0.173205\pi\) | ||||
0.855572 | + | 0.517683i | \(0.173205\pi\) | |||||||
\(752\) | 24.8440 | 0.905966 | ||||||||
\(753\) | −12.2104 | −0.444971 | ||||||||
\(754\) | 11.2772 | 0.410691 | ||||||||
\(755\) | 0.534127 | 0.0194389 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.7151 | −0.789250 | −0.394625 | − | 0.918842i | \(-0.629125\pi\) | ||||
−0.394625 | + | 0.918842i | \(0.629125\pi\) | |||||||
\(758\) | −59.3767 | −2.15666 | ||||||||
\(759\) | 26.1623 | 0.949631 | ||||||||
\(760\) | −0.188687 | −0.00684438 | ||||||||
\(761\) | 36.6002 | 1.32676 | 0.663379 | − | 0.748284i | \(-0.269122\pi\) | ||||
0.663379 | + | 0.748284i | \(0.269122\pi\) | |||||||
\(762\) | −1.24302 | −0.0450298 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −49.4395 | −1.78866 | ||||||||
\(765\) | −0.783389 | −0.0283235 | ||||||||
\(766\) | −73.6359 | −2.66057 | ||||||||
\(767\) | −2.58774 | −0.0934379 | ||||||||
\(768\) | 6.01320 | 0.216983 | ||||||||
\(769\) | −11.9200 | −0.429845 | −0.214923 | − | 0.976631i | \(-0.568950\pi\) | ||||
−0.214923 | + | 0.976631i | \(0.568950\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.52645 | 0.343087 | ||||||||
\(772\) | 13.0668 | 0.470285 | ||||||||
\(773\) | −20.3076 | −0.730414 | −0.365207 | − | 0.930926i | \(-0.619002\pi\) | ||||
−0.365207 | + | 0.930926i | \(0.619002\pi\) | |||||||
\(774\) | 15.1344 | 0.543993 | ||||||||
\(775\) | 28.4068 | 1.02040 | ||||||||
\(776\) | 4.10170 | 0.147243 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.77018 | 0.135168 | ||||||||
\(779\) | 1.26470 | 0.0453126 | ||||||||
\(780\) | 2.29039 | 0.0820091 | ||||||||
\(781\) | −18.9387 | −0.677680 | ||||||||
\(782\) | 26.3968 | 0.943948 | ||||||||
\(783\) | 2.06058 | 0.0736390 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.69641 | 0.239005 | ||||||||
\(786\) | 17.0932 | 0.609695 | ||||||||
\(787\) | −18.2687 | −0.651209 | −0.325605 | − | 0.945506i | \(-0.605568\pi\) | ||||
−0.325605 | + | 0.945506i | \(0.605568\pi\) | |||||||
\(788\) | 15.1366 | 0.539219 | ||||||||
\(789\) | −16.0995 | −0.573156 | ||||||||
\(790\) | −2.93095 | −0.104278 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.58774 | −0.163018 | ||||||||
\(793\) | −23.3058 | −0.827614 | ||||||||
\(794\) | −1.72906 | −0.0613619 | ||||||||
\(795\) | −2.89981 | −0.102846 | ||||||||
\(796\) | 46.3657 | 1.64339 | ||||||||
\(797\) | 21.3664 | 0.756837 | 0.378418 | − | 0.925635i | \(-0.376468\pi\) | ||||
0.378418 | + | 0.925635i | \(0.376468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.2089 | 0.679560 | ||||||||
\(800\) | 38.9108 | 1.37570 | ||||||||
\(801\) | 8.54661 | 0.301980 | ||||||||
\(802\) | −11.3183 | −0.399664 | ||||||||
\(803\) | −51.5481 | −1.81909 | ||||||||
\(804\) | 35.8044 | 1.26272 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31.9108 | −1.12401 | ||||||||
\(807\) | −28.3051 | −0.996387 | ||||||||
\(808\) | 8.22982 | 0.289524 | ||||||||
\(809\) | −23.7460 | −0.834865 | −0.417433 | − | 0.908708i | \(-0.637070\pi\) | ||||
−0.417433 | + | 0.908708i | \(0.637070\pi\) | |||||||
\(810\) | 0.756981 | 0.0265976 | ||||||||
\(811\) | −15.3664 | −0.539587 | −0.269794 | − | 0.962918i | \(-0.586956\pi\) | ||||
−0.269794 | + | 0.962918i | \(0.586956\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.38585 | −0.0486039 | ||||||||
\(814\) | 74.7361 | 2.61950 | ||||||||
\(815\) | 1.19716 | 0.0419348 | ||||||||
\(816\) | 6.19565 | 0.216891 | ||||||||
\(817\) | −3.77242 | −0.131980 | ||||||||
\(818\) | 81.2269 | 2.84003 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.12339 | −0.0741518 | ||||||||
\(821\) | −29.6009 | −1.03308 | −0.516540 | − | 0.856263i | \(-0.672780\pi\) | ||||
−0.516540 | + | 0.856263i | \(0.672780\pi\) | |||||||
\(822\) | 17.1344 | 0.597629 | ||||||||
\(823\) | −19.6546 | −0.685115 | −0.342557 | − | 0.939497i | \(-0.611293\pi\) | ||||
−0.342557 | + | 0.939497i | \(0.611293\pi\) | |||||||
\(824\) | −4.79811 | −0.167150 | ||||||||
\(825\) | 22.3510 | 0.778161 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.1296 | −0.456562 | −0.228281 | − | 0.973595i | \(-0.573310\pi\) | ||||
−0.228281 | + | 0.973595i | \(0.573310\pi\) | |||||||
\(828\) | −14.1017 | −0.490068 | ||||||||
\(829\) | 3.69569 | 0.128357 | 0.0641783 | − | 0.997938i | \(-0.479557\pi\) | ||||
0.0641783 | + | 0.997938i | \(0.479557\pi\) | |||||||
\(830\) | 0.558300 | 0.0193789 | ||||||||
\(831\) | −1.15604 | −0.0401024 | ||||||||
\(832\) | −29.0599 | −1.00747 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.5008 | −0.363612 | ||||||||
\(835\) | −5.86965 | −0.203128 | ||||||||
\(836\) | 5.98055 | 0.206842 | ||||||||
\(837\) | −5.83076 | −0.201541 | ||||||||
\(838\) | −18.4332 | −0.636765 | ||||||||
\(839\) | −20.7911 | −0.717790 | −0.358895 | − | 0.933378i | \(-0.616846\pi\) | ||||
−0.358895 | + | 0.933378i | \(0.616846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7540 | −0.853587 | ||||||||
\(842\) | −0.756981 | −0.0260873 | ||||||||
\(843\) | −19.5140 | −0.672097 | ||||||||
\(844\) | 13.1685 | 0.453279 | ||||||||
\(845\) | −2.25622 | −0.0776164 | ||||||||
\(846\) | −18.5613 | −0.638152 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 22.9340 | 0.787556 | ||||||||
\(849\) | 2.04113 | 0.0700513 | ||||||||
\(850\) | 22.5513 | 0.773505 | ||||||||
\(851\) | 43.9255 | 1.50575 | ||||||||
\(852\) | 10.2081 | 0.349725 | ||||||||
\(853\) | −17.5162 | −0.599743 | −0.299872 | − | 0.953980i | \(-0.596944\pi\) | ||||
−0.299872 | + | 0.953980i | \(0.596944\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.188687 | −0.00645295 | ||||||||
\(856\) | 14.0411 | 0.479916 | ||||||||
\(857\) | −16.0628 | −0.548695 | −0.274348 | − | 0.961631i | \(-0.588462\pi\) | ||||
−0.274348 | + | 0.961631i | \(0.588462\pi\) | |||||||
\(858\) | −25.1079 | −0.857171 | ||||||||
\(859\) | 5.39281 | 0.184000 | 0.0920002 | − | 0.995759i | \(-0.470674\pi\) | ||||
0.0920002 | + | 0.995759i | \(0.470674\pi\) | |||||||
\(860\) | 6.33375 | 0.215979 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.9930 | −0.953447 | ||||||||
\(863\) | 7.55509 | 0.257178 | 0.128589 | − | 0.991698i | \(-0.458955\pi\) | ||||
0.128589 | + | 0.991698i | \(0.458955\pi\) | |||||||
\(864\) | −7.98680 | −0.271716 | ||||||||
\(865\) | −9.02320 | −0.306798 | ||||||||
\(866\) | 57.9549 | 1.96939 | ||||||||
\(867\) | −12.2097 | −0.414661 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.7632 | 0.602576 | ||||||||
\(870\) | 1.55982 | 0.0528827 | ||||||||
\(871\) | 37.4681 | 1.26956 | ||||||||
\(872\) | −9.81131 | −0.332253 | ||||||||
\(873\) | 4.10170 | 0.138822 | ||||||||
\(874\) | 6.35793 | 0.215060 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.7849 | 0.938765 | ||||||||
\(877\) | 21.0807 | 0.711846 | 0.355923 | − | 0.934515i | \(-0.384167\pi\) | ||||
0.355923 | + | 0.934515i | \(0.384167\pi\) | |||||||
\(878\) | −68.9365 | −2.32649 | ||||||||
\(879\) | 2.73057 | 0.0921000 | ||||||||
\(880\) | 4.64832 | 0.156695 | ||||||||
\(881\) | −8.90677 | −0.300077 | −0.150038 | − | 0.988680i | \(-0.547940\pi\) | ||||
−0.150038 | + | 0.988680i | \(0.547940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.94719 | 0.267444 | 0.133722 | − | 0.991019i | \(-0.457307\pi\) | ||||
0.133722 | + | 0.991019i | \(0.457307\pi\) | |||||||
\(884\) | −14.0055 | −0.471057 | ||||||||
\(885\) | −0.357926 | −0.0120316 | ||||||||
\(886\) | −65.2221 | −2.19118 | ||||||||
\(887\) | 13.1685 | 0.442156 | 0.221078 | − | 0.975256i | \(-0.429043\pi\) | ||||
0.221078 | + | 0.975256i | \(0.429043\pi\) | |||||||
\(888\) | −7.70265 | −0.258484 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.46963 | 0.216862 | ||||||||
\(891\) | −4.58774 | −0.153695 | ||||||||
\(892\) | 27.2702 | 0.913075 | ||||||||
\(893\) | 4.62664 | 0.154824 | ||||||||
\(894\) | −46.3851 | −1.55135 | ||||||||
\(895\) | −5.39530 | −0.180345 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7570 | −0.492721 | ||||||||
\(898\) | 74.2042 | 2.47623 | ||||||||
\(899\) | −12.0147 | −0.400713 | ||||||||
\(900\) | −12.0474 | −0.401579 | ||||||||
\(901\) | 17.7321 | 0.590742 | ||||||||
\(902\) | 23.2772 | 0.775046 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.2772 | 0.441593 | ||||||||
\(905\) | −5.28887 | −0.175808 | ||||||||
\(906\) | 3.15604 | 0.104852 | ||||||||
\(907\) | −23.9497 | −0.795236 | −0.397618 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397618 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(908\) | 27.5334 | 0.913728 | ||||||||
\(909\) | 8.22982 | 0.272966 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8184 | −1.55116 | −0.775581 | − | 0.631248i | \(-0.782543\pi\) | ||||
−0.775581 | + | 0.631248i | \(0.782543\pi\) | |||||||
\(912\) | 1.49228 | 0.0494144 | ||||||||
\(913\) | −3.38362 | −0.111981 | ||||||||
\(914\) | 22.5055 | 0.744415 | ||||||||
\(915\) | −3.22357 | −0.106568 | ||||||||
\(916\) | −62.8767 | −2.07750 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.62887 | −0.152775 | ||||||||
\(919\) | 30.6506 | 1.01107 | 0.505534 | − | 0.862807i | \(-0.331295\pi\) | ||||
0.505534 | + | 0.862807i | \(0.331295\pi\) | |||||||
\(920\) | −2.04113 | −0.0672940 | ||||||||
\(921\) | 28.2423 | 0.930615 | ||||||||
\(922\) | 60.0731 | 1.97840 | ||||||||
\(923\) | 10.6825 | 0.351618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 37.5264 | 1.23386 | ||||||||
\(926\) | −20.2640 | −0.665916 | ||||||||
\(927\) | −4.79811 | −0.157591 | ||||||||
\(928\) | −16.4574 | −0.540240 | ||||||||
\(929\) | −7.52092 | −0.246753 | −0.123377 | − | 0.992360i | \(-0.539372\pi\) | ||||
−0.123377 | + | 0.992360i | \(0.539372\pi\) | |||||||
\(930\) | −4.41378 | −0.144733 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.0279 | −0.819817 | ||||||||
\(933\) | −20.5272 | −0.672029 | ||||||||
\(934\) | −55.2702 | −1.80850 | ||||||||
\(935\) | 3.59398 | 0.117536 | ||||||||
\(936\) | 2.58774 | 0.0845830 | ||||||||
\(937\) | 31.6421 | 1.03370 | 0.516851 | − | 0.856076i | \(-0.327104\pi\) | ||||
0.516851 | + | 0.856076i | \(0.327104\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.86565 | 0.224052 | ||||||||
\(940\) | −7.76795 | −0.253363 | ||||||||
\(941\) | 11.1824 | 0.364537 | 0.182269 | − | 0.983249i | \(-0.441656\pi\) | ||||
0.182269 | + | 0.983249i | \(0.441656\pi\) | |||||||
\(942\) | 39.5676 | 1.28918 | ||||||||
\(943\) | 13.6810 | 0.445514 | ||||||||
\(944\) | 2.83076 | 0.0921334 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −69.4325 | −2.25745 | ||||||||
\(947\) | −30.6149 | −0.994852 | −0.497426 | − | 0.867506i | \(-0.665721\pi\) | ||||
−0.497426 | + | 0.867506i | \(0.665721\pi\) | |||||||
\(948\) | −9.57454 | −0.310967 | ||||||||
\(949\) | 29.0760 | 0.943847 | ||||||||
\(950\) | 5.43171 | 0.176228 | ||||||||
\(951\) | 28.6002 | 0.927426 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.17548 | 0.102864 | 0.0514320 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514320 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(954\) | −17.1344 | −0.554745 | ||||||||
\(955\) | −7.15604 | −0.231564 | ||||||||
\(956\) | 27.0496 | 0.874847 | ||||||||
\(957\) | −9.45339 | −0.305585 | ||||||||
\(958\) | 39.2097 | 1.26681 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.01945 | −0.129727 | ||||||||
\(961\) | 2.99777 | 0.0967021 | ||||||||
\(962\) | −42.1553 | −1.35914 | ||||||||
\(963\) | 14.0411 | 0.452469 | ||||||||
\(964\) | 25.2313 | 0.812646 | ||||||||
\(965\) | 1.89134 | 0.0608842 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5566 | 1.30421 | 0.652106 | − | 0.758128i | \(-0.273886\pi\) | ||||
0.652106 | + | 0.758128i | \(0.273886\pi\) | |||||||
\(968\) | 10.0474 | 0.322935 | ||||||||
\(969\) | 1.15380 | 0.0370654 | ||||||||
\(970\) | 3.10491 | 0.0996927 | ||||||||
\(971\) | 4.23205 | 0.135813 | 0.0679065 | − | 0.997692i | \(-0.478368\pi\) | ||||
0.0679065 | + | 0.997692i | \(0.478368\pi\) | |||||||
\(972\) | 2.47283 | 0.0793162 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −45.6134 | −1.46155 | ||||||||
\(975\) | −12.6072 | −0.403753 | ||||||||
\(976\) | 25.4945 | 0.816060 | ||||||||
\(977\) | 26.5055 | 0.847986 | 0.423993 | − | 0.905666i | \(-0.360628\pi\) | ||||
0.423993 | + | 0.905666i | \(0.360628\pi\) | |||||||
\(978\) | 7.07378 | 0.226195 | ||||||||
\(979\) | −39.2097 | −1.25315 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.81131 | −0.313251 | ||||||||
\(982\) | −24.2493 | −0.773825 | ||||||||
\(983\) | −2.27567 | −0.0725826 | −0.0362913 | − | 0.999341i | \(-0.511554\pi\) | ||||
−0.0362913 | + | 0.999341i | \(0.511554\pi\) | |||||||
\(984\) | −2.39905 | −0.0764791 | ||||||||
\(985\) | 2.19092 | 0.0698086 | ||||||||
\(986\) | −9.53814 | −0.303756 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.37336 | −0.107321 | ||||||||
\(989\) | −40.8084 | −1.29763 | ||||||||
\(990\) | −3.47283 | −0.110374 | ||||||||
\(991\) | 43.9185 | 1.39512 | 0.697559 | − | 0.716527i | \(-0.254269\pi\) | ||||
0.697559 | + | 0.716527i | \(0.254269\pi\) | |||||||
\(992\) | 46.5691 | 1.47857 | ||||||||
\(993\) | 21.2966 | 0.675828 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.71113 | 0.212757 | ||||||||
\(996\) | 1.82380 | 0.0577893 | ||||||||
\(997\) | −2.81532 | −0.0891621 | −0.0445811 | − | 0.999006i | \(-0.514195\pi\) | ||||
−0.0445811 | + | 0.999006i | \(0.514195\pi\) | |||||||
\(998\) | −36.9434 | −1.16942 | ||||||||
\(999\) | −7.70265 | −0.243701 |
(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 | 8673.2.a.s.1.3 | 3 | ||
7.6 | odd | 2 | 177.2.a.d.1.3 | ✓ | 3 | ||
21.20 | even | 2 | 531.2.a.d.1.1 | 3 | |||
28.27 | even | 2 | 2832.2.a.t.1.2 | 3 | |||
35.34 | odd | 2 | 4425.2.a.w.1.1 | 3 | |||
84.83 | odd | 2 | 8496.2.a.bl.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.a.d.1.3 | ✓ | 3 | 7.6 | odd | 2 | ||
531.2.a.d.1.1 | 3 | 21.20 | even | 2 | |||
2832.2.a.t.1.2 | 3 | 28.27 | even | 2 | |||
4425.2.a.w.1.1 | 3 | 35.34 | odd | 2 | |||
8496.2.a.bl.1.2 | 3 | 84.83 | odd | 2 | |||
8673.2.a.s.1.3 | 3 | 1.1 | even | 1 | trivial |