Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6031,2,Mod(1,6031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6031 = 37 \cdot 163 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6031.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: | \(48.1577774590\) |
Analytic rank: | \(0\) |
Dimension: | \(133\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.27893 | −1.61145 | −0.805724 | − | 0.592291i | \(-0.798224\pi\) | ||||
−0.805724 | + | 0.592291i | \(0.798224\pi\) | |||||||
\(3\) | 2.16909 | 1.25232 | 0.626162 | − | 0.779693i | \(-0.284625\pi\) | ||||
0.626162 | + | 0.779693i | \(0.284625\pi\) | |||||||
\(4\) | 3.19353 | 1.59677 | ||||||||
\(5\) | 2.05388 | 0.918523 | 0.459261 | − | 0.888301i | \(-0.348114\pi\) | ||||
0.459261 | + | 0.888301i | \(0.348114\pi\) | |||||||
\(6\) | −4.94321 | −2.01806 | ||||||||
\(7\) | −4.20533 | −1.58946 | −0.794732 | − | 0.606960i | \(-0.792389\pi\) | ||||
−0.794732 | + | 0.606960i | \(0.792389\pi\) | |||||||
\(8\) | −2.71998 | −0.961657 | ||||||||
\(9\) | 1.70495 | 0.568317 | ||||||||
\(10\) | −4.68065 | −1.48015 | ||||||||
\(11\) | 4.59267 | 1.38474 | 0.692372 | − | 0.721541i | \(-0.256566\pi\) | ||||
0.692372 | + | 0.721541i | \(0.256566\pi\) | |||||||
\(12\) | 6.92706 | 1.99967 | ||||||||
\(13\) | −5.82463 | −1.61546 | −0.807731 | − | 0.589551i | \(-0.799305\pi\) | ||||
−0.807731 | + | 0.589551i | \(0.799305\pi\) | |||||||
\(14\) | 9.58365 | 2.56134 | ||||||||
\(15\) | 4.45505 | 1.15029 | ||||||||
\(16\) | −0.188418 | −0.0471046 | ||||||||
\(17\) | 0.108379 | 0.0262857 | 0.0131428 | − | 0.999914i | \(-0.495816\pi\) | ||||
0.0131428 | + | 0.999914i | \(0.495816\pi\) | |||||||
\(18\) | −3.88547 | −0.915814 | ||||||||
\(19\) | 7.39501 | 1.69653 | 0.848266 | − | 0.529571i | \(-0.177647\pi\) | ||||
0.848266 | + | 0.529571i | \(0.177647\pi\) | |||||||
\(20\) | 6.55913 | 1.46667 | ||||||||
\(21\) | −9.12173 | −1.99053 | ||||||||
\(22\) | −10.4664 | −2.23144 | ||||||||
\(23\) | −6.46256 | −1.34754 | −0.673768 | − | 0.738943i | \(-0.735325\pi\) | ||||
−0.673768 | + | 0.738943i | \(0.735325\pi\) | |||||||
\(24\) | −5.89988 | −1.20431 | ||||||||
\(25\) | −0.781579 | −0.156316 | ||||||||
\(26\) | 13.2739 | 2.60323 | ||||||||
\(27\) | −2.80908 | −0.540607 | ||||||||
\(28\) | −13.4298 | −2.53800 | ||||||||
\(29\) | −2.52187 | −0.468299 | −0.234150 | − | 0.972201i | \(-0.575231\pi\) | ||||
−0.234150 | + | 0.972201i | \(0.575231\pi\) | |||||||
\(30\) | −10.1528 | −1.85363 | ||||||||
\(31\) | 6.98897 | 1.25526 | 0.627628 | − | 0.778514i | \(-0.284026\pi\) | ||||
0.627628 | + | 0.778514i | \(0.284026\pi\) | |||||||
\(32\) | 5.86935 | 1.03756 | ||||||||
\(33\) | 9.96192 | 1.73415 | ||||||||
\(34\) | −0.246987 | −0.0423580 | ||||||||
\(35\) | −8.63724 | −1.45996 | ||||||||
\(36\) | 5.44482 | 0.907470 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −16.8527 | −2.73387 | ||||||||
\(39\) | −12.6341 | −2.02308 | ||||||||
\(40\) | −5.58651 | −0.883304 | ||||||||
\(41\) | 3.22113 | 0.503056 | 0.251528 | − | 0.967850i | \(-0.419067\pi\) | ||||
0.251528 | + | 0.967850i | \(0.419067\pi\) | |||||||
\(42\) | 20.7878 | 3.20763 | ||||||||
\(43\) | 8.71497 | 1.32902 | 0.664510 | − | 0.747279i | \(-0.268640\pi\) | ||||
0.664510 | + | 0.747279i | \(0.268640\pi\) | |||||||
\(44\) | 14.6668 | 2.21111 | ||||||||
\(45\) | 3.50177 | 0.522012 | ||||||||
\(46\) | 14.7277 | 2.17149 | ||||||||
\(47\) | −1.83441 | −0.267576 | −0.133788 | − | 0.991010i | \(-0.542714\pi\) | ||||
−0.133788 | + | 0.991010i | \(0.542714\pi\) | |||||||
\(48\) | −0.408696 | −0.0589902 | ||||||||
\(49\) | 10.6848 | 1.52640 | ||||||||
\(50\) | 1.78116 | 0.251895 | ||||||||
\(51\) | 0.235083 | 0.0329182 | ||||||||
\(52\) | −18.6011 | −2.57951 | ||||||||
\(53\) | −6.34346 | −0.871341 | −0.435671 | − | 0.900106i | \(-0.643489\pi\) | ||||
−0.435671 | + | 0.900106i | \(0.643489\pi\) | |||||||
\(54\) | 6.40169 | 0.871160 | ||||||||
\(55\) | 9.43280 | 1.27192 | ||||||||
\(56\) | 11.4384 | 1.52852 | ||||||||
\(57\) | 16.0404 | 2.12461 | ||||||||
\(58\) | 5.74717 | 0.754640 | ||||||||
\(59\) | 3.43767 | 0.447546 | 0.223773 | − | 0.974641i | \(-0.428163\pi\) | ||||
0.223773 | + | 0.974641i | \(0.428163\pi\) | |||||||
\(60\) | 14.2273 | 1.83674 | ||||||||
\(61\) | −7.08449 | −0.907076 | −0.453538 | − | 0.891237i | \(-0.649838\pi\) | ||||
−0.453538 | + | 0.891237i | \(0.649838\pi\) | |||||||
\(62\) | −15.9274 | −2.02278 | ||||||||
\(63\) | −7.16988 | −0.903320 | ||||||||
\(64\) | −12.9990 | −1.62488 | ||||||||
\(65\) | −11.9631 | −1.48384 | ||||||||
\(66\) | −22.7025 | −2.79449 | ||||||||
\(67\) | 14.7522 | 1.80227 | 0.901134 | − | 0.433541i | \(-0.142736\pi\) | ||||
0.901134 | + | 0.433541i | \(0.142736\pi\) | |||||||
\(68\) | 0.346110 | 0.0419721 | ||||||||
\(69\) | −14.0179 | −1.68755 | ||||||||
\(70\) | 19.6837 | 2.35265 | ||||||||
\(71\) | 8.21120 | 0.974490 | 0.487245 | − | 0.873265i | \(-0.338002\pi\) | ||||
0.487245 | + | 0.873265i | \(0.338002\pi\) | |||||||
\(72\) | −4.63743 | −0.546527 | ||||||||
\(73\) | 10.5250 | 1.23186 | 0.615928 | − | 0.787802i | \(-0.288781\pi\) | ||||
0.615928 | + | 0.787802i | \(0.288781\pi\) | |||||||
\(74\) | 2.27893 | 0.264920 | ||||||||
\(75\) | −1.69531 | −0.195758 | ||||||||
\(76\) | 23.6162 | 2.70896 | ||||||||
\(77\) | −19.3137 | −2.20100 | ||||||||
\(78\) | 28.7924 | 3.26009 | ||||||||
\(79\) | 13.3156 | 1.49812 | 0.749059 | − | 0.662503i | \(-0.230506\pi\) | ||||
0.749059 | + | 0.662503i | \(0.230506\pi\) | |||||||
\(80\) | −0.386988 | −0.0432666 | ||||||||
\(81\) | −11.2080 | −1.24533 | ||||||||
\(82\) | −7.34073 | −0.810649 | ||||||||
\(83\) | 16.1527 | 1.77299 | 0.886494 | − | 0.462739i | \(-0.153133\pi\) | ||||
0.886494 | + | 0.462739i | \(0.153133\pi\) | |||||||
\(84\) | −29.1305 | −3.17840 | ||||||||
\(85\) | 0.222597 | 0.0241440 | ||||||||
\(86\) | −19.8608 | −2.14165 | ||||||||
\(87\) | −5.47016 | −0.586463 | ||||||||
\(88\) | −12.4920 | −1.33165 | ||||||||
\(89\) | −6.53385 | −0.692587 | −0.346293 | − | 0.938126i | \(-0.612560\pi\) | ||||
−0.346293 | + | 0.938126i | \(0.612560\pi\) | |||||||
\(90\) | −7.98029 | −0.841196 | ||||||||
\(91\) | 24.4945 | 2.56772 | ||||||||
\(92\) | −20.6384 | −2.15170 | ||||||||
\(93\) | 15.1597 | 1.57199 | ||||||||
\(94\) | 4.18050 | 0.431185 | ||||||||
\(95\) | 15.1885 | 1.55830 | ||||||||
\(96\) | 12.7311 | 1.29937 | ||||||||
\(97\) | −15.9586 | −1.62035 | −0.810174 | − | 0.586190i | \(-0.800627\pi\) | ||||
−0.810174 | + | 0.586190i | \(0.800627\pi\) | |||||||
\(98\) | −24.3499 | −2.45971 | ||||||||
\(99\) | 7.83029 | 0.786973 | ||||||||
\(100\) | −2.49600 | −0.249600 | ||||||||
\(101\) | −3.23571 | −0.321965 | −0.160983 | − | 0.986957i | \(-0.551466\pi\) | ||||
−0.160983 | + | 0.986957i | \(0.551466\pi\) | |||||||
\(102\) | −0.535738 | −0.0530460 | ||||||||
\(103\) | −15.5334 | −1.53055 | −0.765274 | − | 0.643704i | \(-0.777397\pi\) | ||||
−0.765274 | + | 0.643704i | \(0.777397\pi\) | |||||||
\(104\) | 15.8429 | 1.55352 | ||||||||
\(105\) | −18.7349 | −1.82834 | ||||||||
\(106\) | 14.4563 | 1.40412 | ||||||||
\(107\) | −7.79363 | −0.753438 | −0.376719 | − | 0.926328i | \(-0.622948\pi\) | ||||
−0.376719 | + | 0.926328i | \(0.622948\pi\) | |||||||
\(108\) | −8.97087 | −0.863223 | ||||||||
\(109\) | 8.37928 | 0.802590 | 0.401295 | − | 0.915949i | \(-0.368560\pi\) | ||||
0.401295 | + | 0.915949i | \(0.368560\pi\) | |||||||
\(110\) | −21.4967 | −2.04963 | ||||||||
\(111\) | −2.16909 | −0.205881 | ||||||||
\(112\) | 0.792360 | 0.0748710 | ||||||||
\(113\) | 8.71776 | 0.820098 | 0.410049 | − | 0.912064i | \(-0.365512\pi\) | ||||
0.410049 | + | 0.912064i | \(0.365512\pi\) | |||||||
\(114\) | −36.5551 | −3.42370 | ||||||||
\(115\) | −13.2733 | −1.23774 | ||||||||
\(116\) | −8.05367 | −0.747765 | ||||||||
\(117\) | −9.93071 | −0.918095 | ||||||||
\(118\) | −7.83421 | −0.721197 | ||||||||
\(119\) | −0.455767 | −0.0417801 | ||||||||
\(120\) | −12.1176 | −1.10618 | ||||||||
\(121\) | 10.0927 | 0.917514 | ||||||||
\(122\) | 16.1451 | 1.46171 | ||||||||
\(123\) | 6.98692 | 0.629989 | ||||||||
\(124\) | 22.3195 | 2.00435 | ||||||||
\(125\) | −11.8747 | −1.06210 | ||||||||
\(126\) | 16.3397 | 1.45565 | ||||||||
\(127\) | 19.2005 | 1.70377 | 0.851887 | − | 0.523726i | \(-0.175459\pi\) | ||||
0.851887 | + | 0.523726i | \(0.175459\pi\) | |||||||
\(128\) | 17.8852 | 1.58084 | ||||||||
\(129\) | 18.9036 | 1.66437 | ||||||||
\(130\) | 27.2631 | 2.39113 | ||||||||
\(131\) | 4.08012 | 0.356482 | 0.178241 | − | 0.983987i | \(-0.442959\pi\) | ||||
0.178241 | + | 0.983987i | \(0.442959\pi\) | |||||||
\(132\) | 31.8137 | 2.76903 | ||||||||
\(133\) | −31.0984 | −2.69658 | ||||||||
\(134\) | −33.6193 | −2.90426 | ||||||||
\(135\) | −5.76950 | −0.496560 | ||||||||
\(136\) | −0.294787 | −0.0252778 | ||||||||
\(137\) | −2.97414 | −0.254098 | −0.127049 | − | 0.991896i | \(-0.540551\pi\) | ||||
−0.127049 | + | 0.991896i | \(0.540551\pi\) | |||||||
\(138\) | 31.9458 | 2.71941 | ||||||||
\(139\) | 1.02746 | 0.0871476 | 0.0435738 | − | 0.999050i | \(-0.486126\pi\) | ||||
0.0435738 | + | 0.999050i | \(0.486126\pi\) | |||||||
\(140\) | −27.5833 | −2.33121 | ||||||||
\(141\) | −3.97900 | −0.335092 | ||||||||
\(142\) | −18.7128 | −1.57034 | ||||||||
\(143\) | −26.7506 | −2.23700 | ||||||||
\(144\) | −0.321244 | −0.0267703 | ||||||||
\(145\) | −5.17962 | −0.430144 | ||||||||
\(146\) | −23.9857 | −1.98507 | ||||||||
\(147\) | 23.1762 | 1.91154 | ||||||||
\(148\) | −3.19353 | −0.262507 | ||||||||
\(149\) | 20.8668 | 1.70948 | 0.854738 | − | 0.519060i | \(-0.173718\pi\) | ||||
0.854738 | + | 0.519060i | \(0.173718\pi\) | |||||||
\(150\) | 3.86351 | 0.315454 | ||||||||
\(151\) | −4.60859 | −0.375042 | −0.187521 | − | 0.982261i | \(-0.560045\pi\) | ||||
−0.187521 | + | 0.982261i | \(0.560045\pi\) | |||||||
\(152\) | −20.1143 | −1.63148 | ||||||||
\(153\) | 0.184780 | 0.0149386 | ||||||||
\(154\) | 44.0146 | 3.54680 | ||||||||
\(155\) | 14.3545 | 1.15298 | ||||||||
\(156\) | −40.3476 | −3.23039 | ||||||||
\(157\) | −2.45217 | −0.195704 | −0.0978522 | − | 0.995201i | \(-0.531197\pi\) | ||||
−0.0978522 | + | 0.995201i | \(0.531197\pi\) | |||||||
\(158\) | −30.3453 | −2.41414 | ||||||||
\(159\) | −13.7595 | −1.09120 | ||||||||
\(160\) | 12.0549 | 0.953026 | ||||||||
\(161\) | 27.1772 | 2.14186 | ||||||||
\(162\) | 25.5423 | 2.00679 | ||||||||
\(163\) | 1.00000 | 0.0783260 | ||||||||
\(164\) | 10.2868 | 0.803262 | ||||||||
\(165\) | 20.4606 | 1.59285 | ||||||||
\(166\) | −36.8109 | −2.85708 | ||||||||
\(167\) | 18.8280 | 1.45696 | 0.728478 | − | 0.685069i | \(-0.240228\pi\) | ||||
0.728478 | + | 0.685069i | \(0.240228\pi\) | |||||||
\(168\) | 24.8109 | 1.91420 | ||||||||
\(169\) | 20.9263 | 1.60972 | ||||||||
\(170\) | −0.507282 | −0.0389068 | ||||||||
\(171\) | 12.6081 | 0.964168 | ||||||||
\(172\) | 27.8315 | 2.12213 | ||||||||
\(173\) | 13.0528 | 0.992385 | 0.496193 | − | 0.868212i | \(-0.334731\pi\) | ||||
0.496193 | + | 0.868212i | \(0.334731\pi\) | |||||||
\(174\) | 12.4661 | 0.945055 | ||||||||
\(175\) | 3.28679 | 0.248458 | ||||||||
\(176\) | −0.865343 | −0.0652277 | ||||||||
\(177\) | 7.45661 | 0.560473 | ||||||||
\(178\) | 14.8902 | 1.11607 | ||||||||
\(179\) | 19.7553 | 1.47658 | 0.738291 | − | 0.674482i | \(-0.235633\pi\) | ||||
0.738291 | + | 0.674482i | \(0.235633\pi\) | |||||||
\(180\) | 11.1830 | 0.833532 | ||||||||
\(181\) | −2.40263 | −0.178586 | −0.0892930 | − | 0.996005i | \(-0.528461\pi\) | ||||
−0.0892930 | + | 0.996005i | \(0.528461\pi\) | |||||||
\(182\) | −55.8212 | −4.13775 | ||||||||
\(183\) | −15.3669 | −1.13595 | ||||||||
\(184\) | 17.5780 | 1.29587 | ||||||||
\(185\) | −2.05388 | −0.151004 | ||||||||
\(186\) | −34.5479 | −2.53318 | ||||||||
\(187\) | 0.497747 | 0.0363989 | ||||||||
\(188\) | −5.85825 | −0.427257 | ||||||||
\(189\) | 11.8131 | 0.859275 | ||||||||
\(190\) | −34.6135 | −2.51112 | ||||||||
\(191\) | −8.02052 | −0.580344 | −0.290172 | − | 0.956974i | \(-0.593713\pi\) | ||||
−0.290172 | + | 0.956974i | \(0.593713\pi\) | |||||||
\(192\) | −28.1960 | −2.03487 | ||||||||
\(193\) | 18.4999 | 1.33165 | 0.665825 | − | 0.746108i | \(-0.268080\pi\) | ||||
0.665825 | + | 0.746108i | \(0.268080\pi\) | |||||||
\(194\) | 36.3685 | 2.61111 | ||||||||
\(195\) | −25.9490 | −1.85825 | ||||||||
\(196\) | 34.1222 | 2.43730 | ||||||||
\(197\) | −8.83344 | −0.629356 | −0.314678 | − | 0.949198i | \(-0.601897\pi\) | ||||
−0.314678 | + | 0.949198i | \(0.601897\pi\) | |||||||
\(198\) | −17.8447 | −1.26817 | ||||||||
\(199\) | 7.49780 | 0.531505 | 0.265752 | − | 0.964041i | \(-0.414380\pi\) | ||||
0.265752 | + | 0.964041i | \(0.414380\pi\) | |||||||
\(200\) | 2.12588 | 0.150322 | ||||||||
\(201\) | 31.9989 | 2.25702 | ||||||||
\(202\) | 7.37396 | 0.518830 | ||||||||
\(203\) | 10.6053 | 0.744345 | ||||||||
\(204\) | 0.750745 | 0.0525626 | ||||||||
\(205\) | 6.61581 | 0.462068 | ||||||||
\(206\) | 35.3995 | 2.46640 | ||||||||
\(207\) | −11.0184 | −0.765828 | ||||||||
\(208\) | 1.09747 | 0.0760956 | ||||||||
\(209\) | 33.9629 | 2.34926 | ||||||||
\(210\) | 42.6957 | 2.94628 | ||||||||
\(211\) | −3.69343 | −0.254266 | −0.127133 | − | 0.991886i | \(-0.540578\pi\) | ||||
−0.127133 | + | 0.991886i | \(0.540578\pi\) | |||||||
\(212\) | −20.2580 | −1.39133 | ||||||||
\(213\) | 17.8108 | 1.22038 | ||||||||
\(214\) | 17.7611 | 1.21413 | ||||||||
\(215\) | 17.8995 | 1.22074 | ||||||||
\(216\) | 7.64063 | 0.519879 | ||||||||
\(217\) | −29.3909 | −1.99518 | ||||||||
\(218\) | −19.0958 | −1.29333 | ||||||||
\(219\) | 22.8296 | 1.54268 | ||||||||
\(220\) | 30.1239 | 2.03096 | ||||||||
\(221\) | −0.631265 | −0.0424635 | ||||||||
\(222\) | 4.94321 | 0.331766 | ||||||||
\(223\) | 14.1857 | 0.949945 | 0.474973 | − | 0.880001i | \(-0.342458\pi\) | ||||
0.474973 | + | 0.880001i | \(0.342458\pi\) | |||||||
\(224\) | −24.6825 | −1.64917 | ||||||||
\(225\) | −1.33255 | −0.0888369 | ||||||||
\(226\) | −19.8672 | −1.32154 | ||||||||
\(227\) | 23.2879 | 1.54567 | 0.772837 | − | 0.634605i | \(-0.218837\pi\) | ||||
0.772837 | + | 0.634605i | \(0.218837\pi\) | |||||||
\(228\) | 51.2256 | 3.39250 | ||||||||
\(229\) | 19.5275 | 1.29041 | 0.645207 | − | 0.764008i | \(-0.276771\pi\) | ||||
0.645207 | + | 0.764008i | \(0.276771\pi\) | |||||||
\(230\) | 30.2490 | 1.99456 | ||||||||
\(231\) | −41.8931 | −2.75637 | ||||||||
\(232\) | 6.85943 | 0.450344 | ||||||||
\(233\) | −9.33242 | −0.611387 | −0.305694 | − | 0.952130i | \(-0.598888\pi\) | ||||
−0.305694 | + | 0.952130i | \(0.598888\pi\) | |||||||
\(234\) | 22.6314 | 1.47946 | ||||||||
\(235\) | −3.76766 | −0.245775 | ||||||||
\(236\) | 10.9783 | 0.714626 | ||||||||
\(237\) | 28.8827 | 1.87613 | ||||||||
\(238\) | 1.03866 | 0.0673265 | ||||||||
\(239\) | 10.8003 | 0.698615 | 0.349307 | − | 0.937008i | \(-0.386417\pi\) | ||||
0.349307 | + | 0.937008i | \(0.386417\pi\) | |||||||
\(240\) | −0.839413 | −0.0541838 | ||||||||
\(241\) | 18.4174 | 1.18637 | 0.593184 | − | 0.805067i | \(-0.297871\pi\) | ||||
0.593184 | + | 0.805067i | \(0.297871\pi\) | |||||||
\(242\) | −23.0005 | −1.47853 | ||||||||
\(243\) | −15.8839 | −1.01895 | ||||||||
\(244\) | −22.6245 | −1.44839 | ||||||||
\(245\) | 21.9452 | 1.40203 | ||||||||
\(246\) | −15.9227 | −1.01520 | ||||||||
\(247\) | −43.0732 | −2.74068 | ||||||||
\(248\) | −19.0098 | −1.20713 | ||||||||
\(249\) | 35.0367 | 2.22036 | ||||||||
\(250\) | 27.0616 | 1.71152 | ||||||||
\(251\) | −14.3379 | −0.904998 | −0.452499 | − | 0.891765i | \(-0.649467\pi\) | ||||
−0.452499 | + | 0.891765i | \(0.649467\pi\) | |||||||
\(252\) | −22.8972 | −1.44239 | ||||||||
\(253\) | −29.6804 | −1.86599 | ||||||||
\(254\) | −43.7567 | −2.74554 | ||||||||
\(255\) | 0.482832 | 0.0302361 | ||||||||
\(256\) | −14.7611 | −0.922566 | ||||||||
\(257\) | 13.2502 | 0.826525 | 0.413262 | − | 0.910612i | \(-0.364389\pi\) | ||||
0.413262 | + | 0.910612i | \(0.364389\pi\) | |||||||
\(258\) | −43.0799 | −2.68204 | ||||||||
\(259\) | 4.20533 | 0.261306 | ||||||||
\(260\) | −38.2045 | −2.36934 | ||||||||
\(261\) | −4.29967 | −0.266143 | ||||||||
\(262\) | −9.29832 | −0.574452 | ||||||||
\(263\) | 0.765699 | 0.0472150 | 0.0236075 | − | 0.999721i | \(-0.492485\pi\) | ||||
0.0236075 | + | 0.999721i | \(0.492485\pi\) | |||||||
\(264\) | −27.0962 | −1.66766 | ||||||||
\(265\) | −13.0287 | −0.800347 | ||||||||
\(266\) | 70.8712 | 4.34539 | ||||||||
\(267\) | −14.1725 | −0.867343 | ||||||||
\(268\) | 47.1116 | 2.87780 | ||||||||
\(269\) | −13.2097 | −0.805412 | −0.402706 | − | 0.915329i | \(-0.631930\pi\) | ||||
−0.402706 | + | 0.915329i | \(0.631930\pi\) | |||||||
\(270\) | 13.1483 | 0.800181 | ||||||||
\(271\) | −3.24964 | −0.197401 | −0.0987006 | − | 0.995117i | \(-0.531469\pi\) | ||||
−0.0987006 | + | 0.995117i | \(0.531469\pi\) | |||||||
\(272\) | −0.0204205 | −0.00123817 | ||||||||
\(273\) | 53.1307 | 3.21562 | ||||||||
\(274\) | 6.77787 | 0.409466 | ||||||||
\(275\) | −3.58954 | −0.216457 | ||||||||
\(276\) | −44.7665 | −2.69463 | ||||||||
\(277\) | 3.24333 | 0.194873 | 0.0974365 | − | 0.995242i | \(-0.468936\pi\) | ||||
0.0974365 | + | 0.995242i | \(0.468936\pi\) | |||||||
\(278\) | −2.34150 | −0.140434 | ||||||||
\(279\) | 11.9158 | 0.713383 | ||||||||
\(280\) | 23.4931 | 1.40398 | ||||||||
\(281\) | −12.0682 | −0.719927 | −0.359963 | − | 0.932966i | \(-0.617211\pi\) | ||||
−0.359963 | + | 0.932966i | \(0.617211\pi\) | |||||||
\(282\) | 9.06787 | 0.539984 | ||||||||
\(283\) | −26.7246 | −1.58861 | −0.794306 | − | 0.607518i | \(-0.792165\pi\) | ||||
−0.794306 | + | 0.607518i | \(0.792165\pi\) | |||||||
\(284\) | 26.2227 | 1.55603 | ||||||||
\(285\) | 32.9451 | 1.95150 | ||||||||
\(286\) | 60.9629 | 3.60481 | ||||||||
\(287\) | −13.5459 | −0.799589 | ||||||||
\(288\) | 10.0070 | 0.589666 | ||||||||
\(289\) | −16.9883 | −0.999309 | ||||||||
\(290\) | 11.8040 | 0.693154 | ||||||||
\(291\) | −34.6156 | −2.02920 | ||||||||
\(292\) | 33.6119 | 1.96699 | ||||||||
\(293\) | −29.3029 | −1.71189 | −0.855947 | − | 0.517063i | \(-0.827025\pi\) | ||||
−0.855947 | + | 0.517063i | \(0.827025\pi\) | |||||||
\(294\) | −52.8171 | −3.08035 | ||||||||
\(295\) | 7.06055 | 0.411081 | ||||||||
\(296\) | 2.71998 | 0.158096 | ||||||||
\(297\) | −12.9012 | −0.748602 | ||||||||
\(298\) | −47.5540 | −2.75473 | ||||||||
\(299\) | 37.6420 | 2.17689 | ||||||||
\(300\) | −5.41404 | −0.312580 | ||||||||
\(301\) | −36.6493 | −2.11243 | ||||||||
\(302\) | 10.5027 | 0.604360 | ||||||||
\(303\) | −7.01855 | −0.403205 | ||||||||
\(304\) | −1.39335 | −0.0799143 | ||||||||
\(305\) | −14.5507 | −0.833170 | ||||||||
\(306\) | −0.421102 | −0.0240728 | ||||||||
\(307\) | −11.0948 | −0.633211 | −0.316606 | − | 0.948557i | \(-0.602543\pi\) | ||||
−0.316606 | + | 0.948557i | \(0.602543\pi\) | |||||||
\(308\) | −61.6789 | −3.51448 | ||||||||
\(309\) | −33.6933 | −1.91674 | ||||||||
\(310\) | −32.7129 | −1.85797 | ||||||||
\(311\) | 14.6518 | 0.830827 | 0.415413 | − | 0.909633i | \(-0.363637\pi\) | ||||
0.415413 | + | 0.909633i | \(0.363637\pi\) | |||||||
\(312\) | 34.3646 | 1.94551 | ||||||||
\(313\) | 19.2674 | 1.08906 | 0.544529 | − | 0.838742i | \(-0.316708\pi\) | ||||
0.544529 | + | 0.838742i | \(0.316708\pi\) | |||||||
\(314\) | 5.58833 | 0.315367 | ||||||||
\(315\) | −14.7261 | −0.829720 | ||||||||
\(316\) | 42.5237 | 2.39215 | ||||||||
\(317\) | −14.9657 | −0.840555 | −0.420277 | − | 0.907396i | \(-0.638067\pi\) | ||||
−0.420277 | + | 0.907396i | \(0.638067\pi\) | |||||||
\(318\) | 31.3570 | 1.75842 | ||||||||
\(319\) | −11.5821 | −0.648474 | ||||||||
\(320\) | −26.6984 | −1.49249 | ||||||||
\(321\) | −16.9051 | −0.943550 | ||||||||
\(322\) | −61.9349 | −3.45150 | ||||||||
\(323\) | 0.801460 | 0.0445944 | ||||||||
\(324\) | −35.7931 | −1.98850 | ||||||||
\(325\) | 4.55241 | 0.252522 | ||||||||
\(326\) | −2.27893 | −0.126218 | ||||||||
\(327\) | 18.1754 | 1.00510 | ||||||||
\(328\) | −8.76140 | −0.483767 | ||||||||
\(329\) | 7.71430 | 0.425303 | ||||||||
\(330\) | −46.6283 | −2.56680 | ||||||||
\(331\) | 0.991384 | 0.0544914 | 0.0272457 | − | 0.999629i | \(-0.491326\pi\) | ||||
0.0272457 | + | 0.999629i | \(0.491326\pi\) | |||||||
\(332\) | 51.5841 | 2.83105 | ||||||||
\(333\) | −1.70495 | −0.0934308 | ||||||||
\(334\) | −42.9078 | −2.34781 | ||||||||
\(335\) | 30.2992 | 1.65542 | ||||||||
\(336\) | 1.71870 | 0.0937628 | ||||||||
\(337\) | −0.879684 | −0.0479194 | −0.0239597 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239597 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(338\) | −47.6897 | −2.59398 | ||||||||
\(339\) | 18.9096 | 1.02703 | ||||||||
\(340\) | 0.710869 | 0.0385523 | ||||||||
\(341\) | 32.0980 | 1.73821 | ||||||||
\(342\) | −28.7331 | −1.55371 | ||||||||
\(343\) | −15.4957 | −0.836688 | ||||||||
\(344\) | −23.7045 | −1.27806 | ||||||||
\(345\) | −28.7910 | −1.55006 | ||||||||
\(346\) | −29.7464 | −1.59918 | ||||||||
\(347\) | 22.1730 | 1.19031 | 0.595156 | − | 0.803610i | \(-0.297090\pi\) | ||||
0.595156 | + | 0.803610i | \(0.297090\pi\) | |||||||
\(348\) | −17.4691 | −0.936444 | ||||||||
\(349\) | −14.3541 | −0.768358 | −0.384179 | − | 0.923259i | \(-0.625516\pi\) | ||||
−0.384179 | + | 0.923259i | \(0.625516\pi\) | |||||||
\(350\) | −7.49038 | −0.400378 | ||||||||
\(351\) | 16.3618 | 0.873330 | ||||||||
\(352\) | 26.9560 | 1.43676 | ||||||||
\(353\) | −1.41109 | −0.0751046 | −0.0375523 | − | 0.999295i | \(-0.511956\pi\) | ||||
−0.0375523 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(354\) | −16.9931 | −0.903173 | ||||||||
\(355\) | 16.8648 | 0.895091 | ||||||||
\(356\) | −20.8661 | −1.10590 | ||||||||
\(357\) | −0.988600 | −0.0523223 | ||||||||
\(358\) | −45.0210 | −2.37944 | ||||||||
\(359\) | −0.422995 | −0.0223248 | −0.0111624 | − | 0.999938i | \(-0.503553\pi\) | ||||
−0.0111624 | + | 0.999938i | \(0.503553\pi\) | |||||||
\(360\) | −9.52473 | −0.501997 | ||||||||
\(361\) | 35.6861 | 1.87822 | ||||||||
\(362\) | 5.47543 | 0.287782 | ||||||||
\(363\) | 21.8919 | 1.14903 | ||||||||
\(364\) | 78.2239 | 4.10005 | ||||||||
\(365\) | 21.6170 | 1.13149 | ||||||||
\(366\) | 35.0201 | 1.83053 | ||||||||
\(367\) | 9.63825 | 0.503113 | 0.251556 | − | 0.967843i | \(-0.419058\pi\) | ||||
0.251556 | + | 0.967843i | \(0.419058\pi\) | |||||||
\(368\) | 1.21766 | 0.0634751 | ||||||||
\(369\) | 5.49187 | 0.285895 | ||||||||
\(370\) | 4.68065 | 0.243336 | ||||||||
\(371\) | 26.6763 | 1.38497 | ||||||||
\(372\) | 48.4130 | 2.51010 | ||||||||
\(373\) | −29.3435 | −1.51935 | −0.759674 | − | 0.650304i | \(-0.774641\pi\) | ||||
−0.759674 | + | 0.650304i | \(0.774641\pi\) | |||||||
\(374\) | −1.13433 | −0.0586549 | ||||||||
\(375\) | −25.7572 | −1.33010 | ||||||||
\(376\) | 4.98956 | 0.257317 | ||||||||
\(377\) | 14.6890 | 0.756520 | ||||||||
\(378\) | −26.9212 | −1.38468 | ||||||||
\(379\) | 3.41769 | 0.175555 | 0.0877774 | − | 0.996140i | \(-0.472024\pi\) | ||||
0.0877774 | + | 0.996140i | \(0.472024\pi\) | |||||||
\(380\) | 48.5048 | 2.48824 | ||||||||
\(381\) | 41.6477 | 2.13368 | ||||||||
\(382\) | 18.2782 | 0.935195 | ||||||||
\(383\) | 17.5086 | 0.894649 | 0.447324 | − | 0.894372i | \(-0.352377\pi\) | ||||
0.447324 | + | 0.894372i | \(0.352377\pi\) | |||||||
\(384\) | 38.7945 | 1.97973 | ||||||||
\(385\) | −39.6680 | −2.02167 | ||||||||
\(386\) | −42.1599 | −2.14588 | ||||||||
\(387\) | 14.8586 | 0.755305 | ||||||||
\(388\) | −50.9642 | −2.58732 | ||||||||
\(389\) | −21.4604 | −1.08809 | −0.544043 | − | 0.839058i | \(-0.683107\pi\) | ||||
−0.544043 | + | 0.839058i | \(0.683107\pi\) | |||||||
\(390\) | 59.1361 | 2.99447 | ||||||||
\(391\) | −0.700403 | −0.0354209 | ||||||||
\(392\) | −29.0624 | −1.46787 | ||||||||
\(393\) | 8.85016 | 0.446431 | ||||||||
\(394\) | 20.1308 | 1.01418 | ||||||||
\(395\) | 27.3486 | 1.37606 | ||||||||
\(396\) | 25.0063 | 1.25661 | ||||||||
\(397\) | 21.1800 | 1.06300 | 0.531498 | − | 0.847060i | \(-0.321629\pi\) | ||||
0.531498 | + | 0.847060i | \(0.321629\pi\) | |||||||
\(398\) | −17.0870 | −0.856493 | ||||||||
\(399\) | −67.4553 | −3.37699 | ||||||||
\(400\) | 0.147264 | 0.00736318 | ||||||||
\(401\) | 23.5552 | 1.17629 | 0.588145 | − | 0.808756i | \(-0.299858\pi\) | ||||
0.588145 | + | 0.808756i | \(0.299858\pi\) | |||||||
\(402\) | −72.9232 | −3.63708 | ||||||||
\(403\) | −40.7081 | −2.02782 | ||||||||
\(404\) | −10.3333 | −0.514103 | ||||||||
\(405\) | −23.0199 | −1.14387 | ||||||||
\(406\) | −24.1687 | −1.19947 | ||||||||
\(407\) | −4.59267 | −0.227650 | ||||||||
\(408\) | −0.639420 | −0.0316560 | ||||||||
\(409\) | −4.62663 | −0.228772 | −0.114386 | − | 0.993436i | \(-0.536490\pi\) | ||||
−0.114386 | + | 0.993436i | \(0.536490\pi\) | |||||||
\(410\) | −15.0770 | −0.744599 | ||||||||
\(411\) | −6.45118 | −0.318213 | ||||||||
\(412\) | −49.6063 | −2.44393 | ||||||||
\(413\) | −14.4565 | −0.711358 | ||||||||
\(414\) | 25.1101 | 1.23409 | ||||||||
\(415\) | 33.1757 | 1.62853 | ||||||||
\(416\) | −34.1868 | −1.67615 | ||||||||
\(417\) | 2.22864 | 0.109137 | ||||||||
\(418\) | −77.3990 | −3.78571 | ||||||||
\(419\) | −20.9541 | −1.02368 | −0.511838 | − | 0.859082i | \(-0.671035\pi\) | ||||
−0.511838 | + | 0.859082i | \(0.671035\pi\) | |||||||
\(420\) | −59.8306 | −2.91944 | ||||||||
\(421\) | −11.8492 | −0.577493 | −0.288746 | − | 0.957406i | \(-0.593238\pi\) | ||||
−0.288746 | + | 0.957406i | \(0.593238\pi\) | |||||||
\(422\) | 8.41708 | 0.409737 | ||||||||
\(423\) | −3.12758 | −0.152068 | ||||||||
\(424\) | 17.2541 | 0.837932 | ||||||||
\(425\) | −0.0847064 | −0.00410886 | ||||||||
\(426\) | −40.5897 | −1.96658 | ||||||||
\(427\) | 29.7926 | 1.44176 | ||||||||
\(428\) | −24.8892 | −1.20306 | ||||||||
\(429\) | −58.0245 | −2.80145 | ||||||||
\(430\) | −40.7917 | −1.96715 | ||||||||
\(431\) | 23.6766 | 1.14046 | 0.570230 | − | 0.821485i | \(-0.306854\pi\) | ||||
0.570230 | + | 0.821485i | \(0.306854\pi\) | |||||||
\(432\) | 0.529281 | 0.0254651 | ||||||||
\(433\) | −37.2537 | −1.79030 | −0.895149 | − | 0.445766i | \(-0.852931\pi\) | ||||
−0.895149 | + | 0.445766i | \(0.852931\pi\) | |||||||
\(434\) | 66.9798 | 3.21513 | ||||||||
\(435\) | −11.2351 | −0.538680 | ||||||||
\(436\) | 26.7595 | 1.28155 | ||||||||
\(437\) | −47.7907 | −2.28614 | ||||||||
\(438\) | −52.0272 | −2.48596 | ||||||||
\(439\) | 30.6492 | 1.46281 | 0.731403 | − | 0.681946i | \(-0.238866\pi\) | ||||
0.731403 | + | 0.681946i | \(0.238866\pi\) | |||||||
\(440\) | −25.6570 | −1.22315 | ||||||||
\(441\) | 18.2170 | 0.867477 | ||||||||
\(442\) | 1.43861 | 0.0684277 | ||||||||
\(443\) | −4.11907 | −0.195703 | −0.0978514 | − | 0.995201i | \(-0.531197\pi\) | ||||
−0.0978514 | + | 0.995201i | \(0.531197\pi\) | |||||||
\(444\) | −6.92706 | −0.328744 | ||||||||
\(445\) | −13.4197 | −0.636157 | ||||||||
\(446\) | −32.3283 | −1.53079 | ||||||||
\(447\) | 45.2620 | 2.14082 | ||||||||
\(448\) | 54.6651 | 2.58268 | ||||||||
\(449\) | −5.74593 | −0.271167 | −0.135584 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135584 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(450\) | 3.03680 | 0.143156 | ||||||||
\(451\) | 14.7936 | 0.696603 | ||||||||
\(452\) | 27.8404 | 1.30950 | ||||||||
\(453\) | −9.99645 | −0.469674 | ||||||||
\(454\) | −53.0716 | −2.49077 | ||||||||
\(455\) | 50.3087 | 2.35851 | ||||||||
\(456\) | −43.6296 | −2.04315 | ||||||||
\(457\) | −7.10168 | −0.332203 | −0.166101 | − | 0.986109i | \(-0.553118\pi\) | ||||
−0.166101 | + | 0.986109i | \(0.553118\pi\) | |||||||
\(458\) | −44.5019 | −2.07944 | ||||||||
\(459\) | −0.304444 | −0.0142102 | ||||||||
\(460\) | −42.3888 | −1.97639 | ||||||||
\(461\) | 30.0886 | 1.40137 | 0.700684 | − | 0.713472i | \(-0.252878\pi\) | ||||
0.700684 | + | 0.713472i | \(0.252878\pi\) | |||||||
\(462\) | 95.4716 | 4.44174 | ||||||||
\(463\) | −23.9992 | −1.11534 | −0.557668 | − | 0.830064i | \(-0.688304\pi\) | ||||
−0.557668 | + | 0.830064i | \(0.688304\pi\) | |||||||
\(464\) | 0.475166 | 0.0220590 | ||||||||
\(465\) | 31.1362 | 1.44391 | ||||||||
\(466\) | 21.2680 | 0.985219 | ||||||||
\(467\) | 1.22602 | 0.0567334 | 0.0283667 | − | 0.999598i | \(-0.490969\pi\) | ||||
0.0283667 | + | 0.999598i | \(0.490969\pi\) | |||||||
\(468\) | −31.7141 | −1.46598 | ||||||||
\(469\) | −62.0378 | −2.86464 | ||||||||
\(470\) | 8.58624 | 0.396054 | ||||||||
\(471\) | −5.31897 | −0.245085 | ||||||||
\(472\) | −9.35037 | −0.430386 | ||||||||
\(473\) | 40.0250 | 1.84035 | ||||||||
\(474\) | −65.8217 | −3.02329 | ||||||||
\(475\) | −5.77978 | −0.265195 | ||||||||
\(476\) | −1.45551 | −0.0667131 | ||||||||
\(477\) | −10.8153 | −0.495198 | ||||||||
\(478\) | −24.6132 | −1.12578 | ||||||||
\(479\) | −9.69163 | −0.442822 | −0.221411 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221411 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(480\) | 26.1482 | 1.19350 | ||||||||
\(481\) | 5.82463 | 0.265580 | ||||||||
\(482\) | −41.9719 | −1.91177 | ||||||||
\(483\) | 58.9497 | 2.68231 | ||||||||
\(484\) | 32.2312 | 1.46505 | ||||||||
\(485\) | −32.7770 | −1.48833 | ||||||||
\(486\) | 36.1984 | 1.64199 | ||||||||
\(487\) | −17.9547 | −0.813604 | −0.406802 | − | 0.913516i | \(-0.633356\pi\) | ||||
−0.406802 | + | 0.913516i | \(0.633356\pi\) | |||||||
\(488\) | 19.2697 | 0.872296 | ||||||||
\(489\) | 2.16909 | 0.0980896 | ||||||||
\(490\) | −50.0117 | −2.25930 | ||||||||
\(491\) | −13.1073 | −0.591523 | −0.295762 | − | 0.955262i | \(-0.595573\pi\) | ||||
−0.295762 | + | 0.955262i | \(0.595573\pi\) | |||||||
\(492\) | 22.3129 | 1.00595 | ||||||||
\(493\) | −0.273317 | −0.0123096 | ||||||||
\(494\) | 98.1609 | 4.41647 | ||||||||
\(495\) | 16.0825 | 0.722853 | ||||||||
\(496\) | −1.31685 | −0.0591282 | ||||||||
\(497\) | −34.5308 | −1.54892 | ||||||||
\(498\) | −79.8462 | −3.57799 | ||||||||
\(499\) | 8.33773 | 0.373248 | 0.186624 | − | 0.982431i | \(-0.440245\pi\) | ||||
0.186624 | + | 0.982431i | \(0.440245\pi\) | |||||||
\(500\) | −37.9221 | −1.69593 | ||||||||
\(501\) | 40.8397 | 1.82458 | ||||||||
\(502\) | 32.6750 | 1.45836 | ||||||||
\(503\) | 7.30103 | 0.325537 | 0.162769 | − | 0.986664i | \(-0.447958\pi\) | ||||
0.162769 | + | 0.986664i | \(0.447958\pi\) | |||||||
\(504\) | 19.5019 | 0.868684 | ||||||||
\(505\) | −6.64576 | −0.295732 | ||||||||
\(506\) | 67.6397 | 3.00695 | ||||||||
\(507\) | 45.3911 | 2.01589 | ||||||||
\(508\) | 61.3176 | 2.72053 | ||||||||
\(509\) | −3.14249 | −0.139289 | −0.0696443 | − | 0.997572i | \(-0.522186\pi\) | ||||
−0.0696443 | + | 0.997572i | \(0.522186\pi\) | |||||||
\(510\) | −1.10034 | −0.0487239 | ||||||||
\(511\) | −44.2610 | −1.95799 | ||||||||
\(512\) | −2.13088 | −0.0941724 | ||||||||
\(513\) | −20.7731 | −0.917157 | ||||||||
\(514\) | −30.1963 | −1.33190 | ||||||||
\(515\) | −31.9037 | −1.40584 | ||||||||
\(516\) | 60.3691 | 2.65760 | ||||||||
\(517\) | −8.42485 | −0.370524 | ||||||||
\(518\) | −9.58365 | −0.421082 | ||||||||
\(519\) | 28.3127 | 1.24279 | ||||||||
\(520\) | 32.5393 | 1.42694 | ||||||||
\(521\) | 29.7982 | 1.30548 | 0.652742 | − | 0.757580i | \(-0.273619\pi\) | ||||
0.652742 | + | 0.757580i | \(0.273619\pi\) | |||||||
\(522\) | 9.79865 | 0.428875 | ||||||||
\(523\) | −11.6955 | −0.511407 | −0.255704 | − | 0.966755i | \(-0.582307\pi\) | ||||
−0.255704 | + | 0.966755i | \(0.582307\pi\) | |||||||
\(524\) | 13.0300 | 0.569218 | ||||||||
\(525\) | 7.12935 | 0.311150 | ||||||||
\(526\) | −1.74498 | −0.0760846 | ||||||||
\(527\) | 0.757454 | 0.0329952 | ||||||||
\(528\) | −1.87701 | −0.0816863 | ||||||||
\(529\) | 18.7647 | 0.815855 | ||||||||
\(530\) | 29.6915 | 1.28972 | ||||||||
\(531\) | 5.86105 | 0.254348 | ||||||||
\(532\) | −99.3138 | −4.30580 | ||||||||
\(533\) | −18.7619 | −0.812667 | ||||||||
\(534\) | 32.2982 | 1.39768 | ||||||||
\(535\) | −16.0072 | −0.692050 | ||||||||
\(536\) | −40.1257 | −1.73316 | ||||||||
\(537\) | 42.8511 | 1.84916 | ||||||||
\(538\) | 30.1041 | 1.29788 | ||||||||
\(539\) | 49.0717 | 2.11367 | ||||||||
\(540\) | −18.4251 | −0.792890 | ||||||||
\(541\) | 1.79676 | 0.0772486 | 0.0386243 | − | 0.999254i | \(-0.487702\pi\) | ||||
0.0386243 | + | 0.999254i | \(0.487702\pi\) | |||||||
\(542\) | 7.40570 | 0.318102 | ||||||||
\(543\) | −5.21152 | −0.223648 | ||||||||
\(544\) | 0.636112 | 0.0272731 | ||||||||
\(545\) | 17.2100 | 0.737197 | ||||||||
\(546\) | −121.081 | −5.18180 | ||||||||
\(547\) | −39.0950 | −1.67158 | −0.835792 | − | 0.549047i | \(-0.814991\pi\) | ||||
−0.835792 | + | 0.549047i | \(0.814991\pi\) | |||||||
\(548\) | −9.49801 | −0.405735 | ||||||||
\(549\) | −12.0787 | −0.515507 | ||||||||
\(550\) | 8.18031 | 0.348810 | ||||||||
\(551\) | −18.6492 | −0.794485 | ||||||||
\(552\) | 38.1283 | 1.62285 | ||||||||
\(553\) | −55.9963 | −2.38121 | ||||||||
\(554\) | −7.39134 | −0.314028 | ||||||||
\(555\) | −4.45505 | −0.189106 | ||||||||
\(556\) | 3.28121 | 0.139154 | ||||||||
\(557\) | −2.13218 | −0.0903434 | −0.0451717 | − | 0.998979i | \(-0.514383\pi\) | ||||
−0.0451717 | + | 0.998979i | \(0.514383\pi\) | |||||||
\(558\) | −27.1554 | −1.14958 | ||||||||
\(559\) | −50.7615 | −2.14698 | ||||||||
\(560\) | 1.62741 | 0.0687707 | ||||||||
\(561\) | 1.07966 | 0.0455832 | ||||||||
\(562\) | 27.5025 | 1.16012 | ||||||||
\(563\) | −0.583463 | −0.0245900 | −0.0122950 | − | 0.999924i | \(-0.503914\pi\) | ||||
−0.0122950 | + | 0.999924i | \(0.503914\pi\) | |||||||
\(564\) | −12.7071 | −0.535064 | ||||||||
\(565\) | 17.9052 | 0.753278 | ||||||||
\(566\) | 60.9035 | 2.55997 | ||||||||
\(567\) | 47.1333 | 1.97941 | ||||||||
\(568\) | −22.3343 | −0.937125 | ||||||||
\(569\) | 24.5130 | 1.02764 | 0.513820 | − | 0.857898i | \(-0.328230\pi\) | ||||
0.513820 | + | 0.857898i | \(0.328230\pi\) | |||||||
\(570\) | −75.0797 | −3.14474 | ||||||||
\(571\) | −11.4186 | −0.477855 | −0.238928 | − | 0.971037i | \(-0.576796\pi\) | ||||
−0.238928 | + | 0.971037i | \(0.576796\pi\) | |||||||
\(572\) | −85.4290 | −3.57196 | ||||||||
\(573\) | −17.3972 | −0.726780 | ||||||||
\(574\) | 30.8702 | 1.28850 | ||||||||
\(575\) | 5.05100 | 0.210641 | ||||||||
\(576\) | −22.1627 | −0.923445 | ||||||||
\(577\) | 42.1839 | 1.75614 | 0.878068 | − | 0.478535i | \(-0.158832\pi\) | ||||
0.878068 | + | 0.478535i | \(0.158832\pi\) | |||||||
\(578\) | 38.7151 | 1.61033 | ||||||||
\(579\) | 40.1279 | 1.66766 | ||||||||
\(580\) | −16.5413 | −0.686839 | ||||||||
\(581\) | −67.9274 | −2.81810 | ||||||||
\(582\) | 78.8865 | 3.26995 | ||||||||
\(583\) | −29.1334 | −1.20658 | ||||||||
\(584\) | −28.6277 | −1.18462 | ||||||||
\(585\) | −20.3965 | −0.843291 | ||||||||
\(586\) | 66.7794 | 2.75863 | ||||||||
\(587\) | −29.9323 | −1.23544 | −0.617719 | − | 0.786399i | \(-0.711943\pi\) | ||||
−0.617719 | + | 0.786399i | \(0.711943\pi\) | |||||||
\(588\) | 74.0141 | 3.05229 | ||||||||
\(589\) | 51.6835 | 2.12958 | ||||||||
\(590\) | −16.0905 | −0.662436 | ||||||||
\(591\) | −19.1605 | −0.788159 | ||||||||
\(592\) | 0.188418 | 0.00774394 | ||||||||
\(593\) | −14.4682 | −0.594137 | −0.297069 | − | 0.954856i | \(-0.596009\pi\) | ||||
−0.297069 | + | 0.954856i | \(0.596009\pi\) | |||||||
\(594\) | 29.4009 | 1.20633 | ||||||||
\(595\) | −0.936091 | −0.0383760 | ||||||||
\(596\) | 66.6388 | 2.72963 | ||||||||
\(597\) | 16.2634 | 0.665617 | ||||||||
\(598\) | −85.7836 | −3.50795 | ||||||||
\(599\) | 42.9934 | 1.75666 | 0.878331 | − | 0.478053i | \(-0.158657\pi\) | ||||
0.878331 | + | 0.478053i | \(0.158657\pi\) | |||||||
\(600\) | 4.61122 | 0.188252 | ||||||||
\(601\) | −23.9128 | −0.975422 | −0.487711 | − | 0.873005i | \(-0.662168\pi\) | ||||
−0.487711 | + | 0.873005i | \(0.662168\pi\) | |||||||
\(602\) | 83.5213 | 3.40407 | ||||||||
\(603\) | 25.1518 | 1.02426 | ||||||||
\(604\) | −14.7177 | −0.598854 | ||||||||
\(605\) | 20.7291 | 0.842757 | ||||||||
\(606\) | 15.9948 | 0.649744 | ||||||||
\(607\) | 37.8974 | 1.53821 | 0.769104 | − | 0.639123i | \(-0.220703\pi\) | ||||
0.769104 | + | 0.639123i | \(0.220703\pi\) | |||||||
\(608\) | 43.4039 | 1.76026 | ||||||||
\(609\) | 23.0038 | 0.932162 | ||||||||
\(610\) | 33.1600 | 1.34261 | ||||||||
\(611\) | 10.6848 | 0.432259 | ||||||||
\(612\) | 0.590102 | 0.0238534 | ||||||||
\(613\) | 31.1097 | 1.25651 | 0.628255 | − | 0.778008i | \(-0.283770\pi\) | ||||
0.628255 | + | 0.778008i | \(0.283770\pi\) | |||||||
\(614\) | 25.2842 | 1.02039 | ||||||||
\(615\) | 14.3503 | 0.578660 | ||||||||
\(616\) | 52.5328 | 2.11661 | ||||||||
\(617\) | 24.6801 | 0.993583 | 0.496792 | − | 0.867870i | \(-0.334511\pi\) | ||||
0.496792 | + | 0.867870i | \(0.334511\pi\) | |||||||
\(618\) | 76.7847 | 3.08873 | ||||||||
\(619\) | −11.3523 | −0.456287 | −0.228144 | − | 0.973627i | \(-0.573266\pi\) | ||||
−0.228144 | + | 0.973627i | \(0.573266\pi\) | |||||||
\(620\) | 45.8415 | 1.84104 | ||||||||
\(621\) | 18.1538 | 0.728488 | ||||||||
\(622\) | −33.3904 | −1.33883 | ||||||||
\(623\) | 27.4770 | 1.10084 | ||||||||
\(624\) | 2.38050 | 0.0952964 | ||||||||
\(625\) | −20.4812 | −0.819250 | ||||||||
\(626\) | −43.9091 | −1.75496 | ||||||||
\(627\) | 73.6685 | 2.94204 | ||||||||
\(628\) | −7.83108 | −0.312494 | ||||||||
\(629\) | −0.108379 | −0.00432134 | ||||||||
\(630\) | 33.5597 | 1.33705 | ||||||||
\(631\) | −17.0749 | −0.679741 | −0.339870 | − | 0.940472i | \(-0.610383\pi\) | ||||
−0.339870 | + | 0.940472i | \(0.610383\pi\) | |||||||
\(632\) | −36.2181 | −1.44068 | ||||||||
\(633\) | −8.01139 | −0.318424 | ||||||||
\(634\) | 34.1057 | 1.35451 | ||||||||
\(635\) | 39.4356 | 1.56495 | ||||||||
\(636\) | −43.9415 | −1.74239 | ||||||||
\(637\) | −62.2349 | −2.46584 | ||||||||
\(638\) | 26.3949 | 1.04498 | ||||||||
\(639\) | 13.9997 | 0.553819 | ||||||||
\(640\) | 36.7340 | 1.45204 | ||||||||
\(641\) | −9.00725 | −0.355765 | −0.177882 | − | 0.984052i | \(-0.556925\pi\) | ||||
−0.177882 | + | 0.984052i | \(0.556925\pi\) | |||||||
\(642\) | 38.5255 | 1.52048 | ||||||||
\(643\) | 40.7261 | 1.60608 | 0.803041 | − | 0.595924i | \(-0.203214\pi\) | ||||
0.803041 | + | 0.595924i | \(0.203214\pi\) | |||||||
\(644\) | 86.7912 | 3.42005 | ||||||||
\(645\) | 38.8256 | 1.52876 | ||||||||
\(646\) | −1.82647 | −0.0718616 | ||||||||
\(647\) | 20.6018 | 0.809942 | 0.404971 | − | 0.914330i | \(-0.367282\pi\) | ||||
0.404971 | + | 0.914330i | \(0.367282\pi\) | |||||||
\(648\) | 30.4855 | 1.19758 | ||||||||
\(649\) | 15.7881 | 0.619736 | ||||||||
\(650\) | −10.3746 | −0.406926 | ||||||||
\(651\) | −63.7515 | −2.49862 | ||||||||
\(652\) | 3.19353 | 0.125068 | ||||||||
\(653\) | 3.23934 | 0.126765 | 0.0633826 | − | 0.997989i | \(-0.479811\pi\) | ||||
0.0633826 | + | 0.997989i | \(0.479811\pi\) | |||||||
\(654\) | −41.4205 | −1.61967 | ||||||||
\(655\) | 8.38008 | 0.327437 | ||||||||
\(656\) | −0.606919 | −0.0236962 | ||||||||
\(657\) | 17.9446 | 0.700085 | ||||||||
\(658\) | −17.5804 | −0.685354 | ||||||||
\(659\) | −35.1331 | −1.36859 | −0.684295 | − | 0.729205i | \(-0.739890\pi\) | ||||
−0.684295 | + | 0.729205i | \(0.739890\pi\) | |||||||
\(660\) | 65.3415 | 2.54342 | ||||||||
\(661\) | −13.4660 | −0.523766 | −0.261883 | − | 0.965100i | \(-0.584343\pi\) | ||||
−0.261883 | + | 0.965100i | \(0.584343\pi\) | |||||||
\(662\) | −2.25930 | −0.0878100 | ||||||||
\(663\) | −1.36927 | −0.0531781 | ||||||||
\(664\) | −43.9350 | −1.70501 | ||||||||
\(665\) | −63.8724 | −2.47687 | ||||||||
\(666\) | 3.88547 | 0.150559 | ||||||||
\(667\) | 16.2977 | 0.631051 | ||||||||
\(668\) | 60.1279 | 2.32642 | ||||||||
\(669\) | 30.7701 | 1.18964 | ||||||||
\(670\) | −69.0499 | −2.66763 | ||||||||
\(671\) | −32.5368 | −1.25607 | ||||||||
\(672\) | −53.5386 | −2.06530 | ||||||||
\(673\) | 13.4884 | 0.519938 | 0.259969 | − | 0.965617i | \(-0.416288\pi\) | ||||
0.259969 | + | 0.965617i | \(0.416288\pi\) | |||||||
\(674\) | 2.00474 | 0.0772197 | ||||||||
\(675\) | 2.19551 | 0.0845054 | ||||||||
\(676\) | 66.8289 | 2.57034 | ||||||||
\(677\) | 24.5875 | 0.944975 | 0.472488 | − | 0.881337i | \(-0.343356\pi\) | ||||
0.472488 | + | 0.881337i | \(0.343356\pi\) | |||||||
\(678\) | −43.0937 | −1.65500 | ||||||||
\(679\) | 67.1110 | 2.57548 | ||||||||
\(680\) | −0.605458 | −0.0232182 | ||||||||
\(681\) | 50.5136 | 1.93569 | ||||||||
\(682\) | −73.1492 | −2.80103 | ||||||||
\(683\) | −33.8075 | −1.29361 | −0.646805 | − | 0.762656i | \(-0.723895\pi\) | ||||
−0.646805 | + | 0.762656i | \(0.723895\pi\) | |||||||
\(684\) | 40.2645 | 1.53955 | ||||||||
\(685\) | −6.10853 | −0.233395 | ||||||||
\(686\) | 35.3136 | 1.34828 | ||||||||
\(687\) | 42.3569 | 1.61602 | ||||||||
\(688\) | −1.64206 | −0.0626029 | ||||||||
\(689\) | 36.9483 | 1.40762 | ||||||||
\(690\) | 65.6128 | 2.49784 | ||||||||
\(691\) | 7.97835 | 0.303511 | 0.151755 | − | 0.988418i | \(-0.451507\pi\) | ||||
0.151755 | + | 0.988418i | \(0.451507\pi\) | |||||||
\(692\) | 41.6845 | 1.58461 | ||||||||
\(693\) | −32.9289 | −1.25087 | ||||||||
\(694\) | −50.5309 | −1.91813 | ||||||||
\(695\) | 2.11027 | 0.0800471 | ||||||||
\(696\) | 14.8787 | 0.563976 | ||||||||
\(697\) | 0.349101 | 0.0132232 | ||||||||
\(698\) | 32.7121 | 1.23817 | ||||||||
\(699\) | −20.2429 | −0.765656 | ||||||||
\(700\) | 10.4965 | 0.396730 | ||||||||
\(701\) | −4.98654 | −0.188339 | −0.0941696 | − | 0.995556i | \(-0.530020\pi\) | ||||
−0.0941696 | + | 0.995556i | \(0.530020\pi\) | |||||||
\(702\) | −37.2875 | −1.40733 | ||||||||
\(703\) | −7.39501 | −0.278908 | ||||||||
\(704\) | −59.7002 | −2.25004 | ||||||||
\(705\) | −8.17239 | −0.307790 | ||||||||
\(706\) | 3.21577 | 0.121027 | ||||||||
\(707\) | 13.6072 | 0.511752 | ||||||||
\(708\) | 23.8129 | 0.894944 | ||||||||
\(709\) | −35.1957 | −1.32180 | −0.660902 | − | 0.750472i | \(-0.729826\pi\) | ||||
−0.660902 | + | 0.750472i | \(0.729826\pi\) | |||||||
\(710\) | −38.4338 | −1.44239 | ||||||||
\(711\) | 22.7024 | 0.851407 | ||||||||
\(712\) | 17.7719 | 0.666031 | ||||||||
\(713\) | −45.1666 | −1.69150 | ||||||||
\(714\) | 2.25295 | 0.0843147 | ||||||||
\(715\) | −54.9426 | −2.05474 | ||||||||
\(716\) | 63.0892 | 2.35776 | ||||||||
\(717\) | 23.4269 | 0.874893 | ||||||||
\(718\) | 0.963977 | 0.0359753 | ||||||||
\(719\) | 2.52041 | 0.0939953 | 0.0469976 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469976 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(720\) | −0.659796 | −0.0245892 | ||||||||
\(721\) | 65.3229 | 2.43275 | ||||||||
\(722\) | −81.3263 | −3.02665 | ||||||||
\(723\) | 39.9489 | 1.48572 | ||||||||
\(724\) | −7.67287 | −0.285160 | ||||||||
\(725\) | 1.97104 | 0.0732026 | ||||||||
\(726\) | −49.8901 | −1.85159 | ||||||||
\(727\) | 39.7612 | 1.47466 | 0.737330 | − | 0.675532i | \(-0.236086\pi\) | ||||
0.737330 | + | 0.675532i | \(0.236086\pi\) | |||||||
\(728\) | −66.6244 | −2.46927 | ||||||||
\(729\) | −0.829673 | −0.0307286 | ||||||||
\(730\) | −49.2638 | −1.82333 | ||||||||
\(731\) | 0.944516 | 0.0349342 | ||||||||
\(732\) | −49.0747 | −1.81385 | ||||||||
\(733\) | 16.5173 | 0.610081 | 0.305041 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305041 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(734\) | −21.9649 | −0.810740 | ||||||||
\(735\) | 47.6012 | 1.75580 | ||||||||
\(736\) | −37.9310 | −1.39816 | ||||||||
\(737\) | 67.7520 | 2.49568 | ||||||||
\(738\) | −12.5156 | −0.460706 | ||||||||
\(739\) | 34.4225 | 1.26625 | 0.633127 | − | 0.774048i | \(-0.281771\pi\) | ||||
0.633127 | + | 0.774048i | \(0.281771\pi\) | |||||||
\(740\) | −6.55913 | −0.241118 | ||||||||
\(741\) | −93.4296 | −3.43222 | ||||||||
\(742\) | −60.7935 | −2.23180 | ||||||||
\(743\) | −24.4142 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(744\) | −41.2340 | −1.51171 | ||||||||
\(745\) | 42.8579 | 1.57019 | ||||||||
\(746\) | 66.8718 | 2.44835 | ||||||||
\(747\) | 27.5396 | 1.00762 | ||||||||
\(748\) | 1.58957 | 0.0581205 | ||||||||
\(749\) | 32.7748 | 1.19756 | ||||||||
\(750\) | 58.6990 | 2.14338 | ||||||||
\(751\) | 4.19723 | 0.153159 | 0.0765795 | − | 0.997063i | \(-0.475600\pi\) | ||||
0.0765795 | + | 0.997063i | \(0.475600\pi\) | |||||||
\(752\) | 0.345636 | 0.0126041 | ||||||||
\(753\) | −31.1001 | −1.13335 | ||||||||
\(754\) | −33.4751 | −1.21909 | ||||||||
\(755\) | −9.46549 | −0.344484 | ||||||||
\(756\) | 37.7255 | 1.37206 | ||||||||
\(757\) | 22.2342 | 0.808116 | 0.404058 | − | 0.914733i | \(-0.367599\pi\) | ||||
0.404058 | + | 0.914733i | \(0.367599\pi\) | |||||||
\(758\) | −7.78868 | −0.282898 | ||||||||
\(759\) | −64.3795 | −2.33683 | ||||||||
\(760\) | −41.3123 | −1.49855 | ||||||||
\(761\) | −3.63986 | −0.131945 | −0.0659724 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659724 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(762\) | −94.9123 | −3.43831 | ||||||||
\(763\) | −35.2376 | −1.27569 | ||||||||
\(764\) | −25.6138 | −0.926674 | ||||||||
\(765\) | 0.379516 | 0.0137214 | ||||||||
\(766\) | −39.9010 | −1.44168 | ||||||||
\(767\) | −20.0231 | −0.722993 | ||||||||
\(768\) | −32.0181 | −1.15535 | ||||||||
\(769\) | −29.4726 | −1.06281 | −0.531404 | − | 0.847119i | \(-0.678335\pi\) | ||||
−0.531404 | + | 0.847119i | \(0.678335\pi\) | |||||||
\(770\) | 90.4007 | 3.25781 | ||||||||
\(771\) | 28.7409 | 1.03508 | ||||||||
\(772\) | 59.0799 | 2.12633 | ||||||||
\(773\) | 7.67941 | 0.276209 | 0.138105 | − | 0.990418i | \(-0.455899\pi\) | ||||
0.138105 | + | 0.990418i | \(0.455899\pi\) | |||||||
\(774\) | −33.8617 | −1.21714 | ||||||||
\(775\) | −5.46243 | −0.196216 | ||||||||
\(776\) | 43.4070 | 1.55822 | ||||||||
\(777\) | 9.12173 | 0.327240 | ||||||||
\(778\) | 48.9068 | 1.75339 | ||||||||
\(779\) | 23.8203 | 0.853450 | ||||||||
\(780\) | −82.8690 | −2.96719 | ||||||||
\(781\) | 37.7113 | 1.34942 | ||||||||
\(782\) | 1.59617 | 0.0570789 | ||||||||
\(783\) | 7.08412 | 0.253166 | ||||||||
\(784\) | −2.01321 | −0.0719002 | ||||||||
\(785\) | −5.03646 | −0.179759 | ||||||||
\(786\) | −20.1689 | −0.719401 | ||||||||
\(787\) | −42.3843 | −1.51084 | −0.755419 | − | 0.655242i | \(-0.772566\pi\) | ||||
−0.755419 | + | 0.655242i | \(0.772566\pi\) | |||||||
\(788\) | −28.2099 | −1.00493 | ||||||||
\(789\) | 1.66087 | 0.0591286 | ||||||||
\(790\) | −62.3256 | −2.21744 | ||||||||
\(791\) | −36.6610 | −1.30352 | ||||||||
\(792\) | −21.2982 | −0.756799 | ||||||||
\(793\) | 41.2645 | 1.46535 | ||||||||
\(794\) | −48.2679 | −1.71296 | ||||||||
\(795\) | −28.2604 | −1.00229 | ||||||||
\(796\) | 23.9445 | 0.848689 | ||||||||
\(797\) | 27.4066 | 0.970793 | 0.485397 | − | 0.874294i | \(-0.338675\pi\) | ||||
0.485397 | + | 0.874294i | \(0.338675\pi\) | |||||||
\(798\) | 153.726 | 5.44184 | ||||||||
\(799\) | −0.198811 | −0.00703342 | ||||||||
\(800\) | −4.58736 | −0.162188 | ||||||||
\(801\) | −11.1399 | −0.393609 | ||||||||
\(802\) | −53.6807 | −1.89553 | ||||||||
\(803\) | 48.3378 | 1.70580 | ||||||||
\(804\) | 102.189 | 3.60394 | ||||||||
\(805\) | 55.8186 | 1.96735 | ||||||||
\(806\) | 92.7711 | 3.26772 | ||||||||
\(807\) | −28.6531 | −1.00864 | ||||||||
\(808\) | 8.80106 | 0.309620 | ||||||||
\(809\) | −22.8533 | −0.803479 | −0.401740 | − | 0.915754i | \(-0.631594\pi\) | ||||
−0.401740 | + | 0.915754i | \(0.631594\pi\) | |||||||
\(810\) | 52.4607 | 1.84328 | ||||||||
\(811\) | 44.3589 | 1.55765 | 0.778827 | − | 0.627239i | \(-0.215815\pi\) | ||||
0.778827 | + | 0.627239i | \(0.215815\pi\) | |||||||
\(812\) | 33.8683 | 1.18854 | ||||||||
\(813\) | −7.04875 | −0.247210 | ||||||||
\(814\) | 10.4664 | 0.366847 | ||||||||
\(815\) | 2.05388 | 0.0719443 | ||||||||
\(816\) | −0.0442939 | −0.00155060 | ||||||||
\(817\) | 64.4473 | 2.25472 | ||||||||
\(818\) | 10.5438 | 0.368655 | ||||||||
\(819\) | 41.7619 | 1.45928 | ||||||||
\(820\) | 21.1278 | 0.737815 | ||||||||
\(821\) | −32.2162 | −1.12435 | −0.562177 | − | 0.827017i | \(-0.690036\pi\) | ||||
−0.562177 | + | 0.827017i | \(0.690036\pi\) | |||||||
\(822\) | 14.7018 | 0.512784 | ||||||||
\(823\) | 4.50826 | 0.157148 | 0.0785740 | − | 0.996908i | \(-0.474963\pi\) | ||||
0.0785740 | + | 0.996908i | \(0.474963\pi\) | |||||||
\(824\) | 42.2504 | 1.47186 | ||||||||
\(825\) | −7.78603 | −0.271075 | ||||||||
\(826\) | 32.9454 | 1.14632 | ||||||||
\(827\) | 23.3468 | 0.811849 | 0.405924 | − | 0.913907i | \(-0.366950\pi\) | ||||
0.405924 | + | 0.913907i | \(0.366950\pi\) | |||||||
\(828\) | −35.1875 | −1.22285 | ||||||||
\(829\) | −31.7389 | −1.10234 | −0.551168 | − | 0.834394i | \(-0.685818\pi\) | ||||
−0.551168 | + | 0.834394i | \(0.685818\pi\) | |||||||
\(830\) | −75.6052 | −2.62429 | ||||||||
\(831\) | 7.03508 | 0.244044 | ||||||||
\(832\) | 75.7144 | 2.62493 | ||||||||
\(833\) | 1.15800 | 0.0401223 | ||||||||
\(834\) | −5.07893 | −0.175869 | ||||||||
\(835\) | 38.6705 | 1.33825 | ||||||||
\(836\) | 108.461 | 3.75122 | ||||||||
\(837\) | −19.6325 | −0.678600 | ||||||||
\(838\) | 47.7530 | 1.64960 | ||||||||
\(839\) | 35.2819 | 1.21807 | 0.609033 | − | 0.793145i | \(-0.291558\pi\) | ||||
0.609033 | + | 0.793145i | \(0.291558\pi\) | |||||||
\(840\) | 50.9586 | 1.75824 | ||||||||
\(841\) | −22.6402 | −0.780696 | ||||||||
\(842\) | 27.0034 | 0.930600 | ||||||||
\(843\) | −26.1769 | −0.901582 | ||||||||
\(844\) | −11.7951 | −0.406004 | ||||||||
\(845\) | 42.9801 | 1.47856 | ||||||||
\(846\) | 7.12755 | 0.245050 | ||||||||
\(847\) | −42.4429 | −1.45836 | ||||||||
\(848\) | 1.19522 | 0.0410441 | ||||||||
\(849\) | −57.9681 | −1.98946 | ||||||||
\(850\) | 0.193040 | 0.00662122 | ||||||||
\(851\) | 6.46256 | 0.221534 | ||||||||
\(852\) | 56.8794 | 1.94866 | ||||||||
\(853\) | 27.8440 | 0.953361 | 0.476681 | − | 0.879077i | \(-0.341840\pi\) | ||||
0.476681 | + | 0.879077i | \(0.341840\pi\) | |||||||
\(854\) | −67.8953 | −2.32333 | ||||||||
\(855\) | 25.8956 | 0.885610 | ||||||||
\(856\) | 21.1985 | 0.724550 | ||||||||
\(857\) | 15.7519 | 0.538075 | 0.269038 | − | 0.963130i | \(-0.413294\pi\) | ||||
0.269038 | + | 0.963130i | \(0.413294\pi\) | |||||||
\(858\) | 132.234 | 4.51439 | ||||||||
\(859\) | −39.2892 | −1.34053 | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(860\) | 57.1626 | 1.94923 | ||||||||
\(861\) | −29.3823 | −1.00135 | ||||||||
\(862\) | −53.9573 | −1.83779 | ||||||||
\(863\) | −12.8863 | −0.438654 | −0.219327 | − | 0.975651i | \(-0.570386\pi\) | ||||
−0.219327 | + | 0.975651i | \(0.570386\pi\) | |||||||
\(864\) | −16.4874 | −0.560914 | ||||||||
\(865\) | 26.8089 | 0.911529 | ||||||||
\(866\) | 84.8987 | 2.88497 | ||||||||
\(867\) | −36.8491 | −1.25146 | ||||||||
\(868\) | −93.8607 | −3.18584 | ||||||||
\(869\) | 61.1541 | 2.07451 | ||||||||
\(870\) | 25.6039 | 0.868054 | ||||||||
\(871\) | −85.9261 | −2.91150 | ||||||||
\(872\) | −22.7915 | −0.771816 | ||||||||
\(873\) | −27.2086 | −0.920871 | ||||||||
\(874\) | 108.912 | 3.68399 | ||||||||
\(875\) | 49.9369 | 1.68817 | ||||||||
\(876\) | 72.9072 | 2.46331 | ||||||||
\(877\) | 15.1718 | 0.512316 | 0.256158 | − | 0.966635i | \(-0.417543\pi\) | ||||
0.256158 | + | 0.966635i | \(0.417543\pi\) | |||||||
\(878\) | −69.8474 | −2.35724 | ||||||||
\(879\) | −63.5607 | −2.14385 | ||||||||
\(880\) | −1.77731 | −0.0599131 | ||||||||
\(881\) | −46.8022 | −1.57681 | −0.788404 | − | 0.615158i | \(-0.789092\pi\) | ||||
−0.788404 | + | 0.615158i | \(0.789092\pi\) | |||||||
\(882\) | −41.5154 | −1.39790 | ||||||||
\(883\) | 7.68630 | 0.258665 | 0.129332 | − | 0.991601i | \(-0.458717\pi\) | ||||
0.129332 | + | 0.991601i | \(0.458717\pi\) | |||||||
\(884\) | −2.01597 | −0.0678042 | ||||||||
\(885\) | 15.3150 | 0.514807 | ||||||||
\(886\) | 9.38708 | 0.315365 | ||||||||
\(887\) | 14.4641 | 0.485657 | 0.242829 | − | 0.970069i | \(-0.421925\pi\) | ||||
0.242829 | + | 0.970069i | \(0.421925\pi\) | |||||||
\(888\) | 5.89988 | 0.197987 | ||||||||
\(889\) | −80.7446 | −2.70809 | ||||||||
\(890\) | 30.5827 | 1.02513 | ||||||||
\(891\) | −51.4747 | −1.72447 | ||||||||
\(892\) | 45.3025 | 1.51684 | ||||||||
\(893\) | −13.5655 | −0.453951 | ||||||||
\(894\) | −103.149 | −3.44982 | ||||||||
\(895\) | 40.5750 | 1.35627 | ||||||||
\(896\) | −75.2130 | −2.51269 | ||||||||
\(897\) | 81.6489 | 2.72618 | ||||||||
\(898\) | 13.0946 | 0.436972 | ||||||||
\(899\) | −17.6253 | −0.587835 | ||||||||
\(900\) | −4.25555 | −0.141852 | ||||||||
\(901\) | −0.687495 | −0.0229038 | ||||||||
\(902\) | −33.7136 | −1.12254 | ||||||||
\(903\) | −79.4956 | −2.64545 | ||||||||
\(904\) | −23.7121 | −0.788653 | ||||||||
\(905\) | −4.93471 | −0.164035 | ||||||||
\(906\) | 22.7812 | 0.756855 | ||||||||
\(907\) | −16.7664 | −0.556719 | −0.278360 | − | 0.960477i | \(-0.589791\pi\) | ||||
−0.278360 | + | 0.960477i | \(0.589791\pi\) | |||||||
\(908\) | 74.3707 | 2.46808 | ||||||||
\(909\) | −5.51673 | −0.182978 | ||||||||
\(910\) | −114.650 | −3.80061 | ||||||||
\(911\) | −19.3773 | −0.642000 | −0.321000 | − | 0.947079i | \(-0.604019\pi\) | ||||
−0.321000 | + | 0.947079i | \(0.604019\pi\) | |||||||
\(912\) | −3.02231 | −0.100079 | ||||||||
\(913\) | 74.1841 | 2.45513 | ||||||||
\(914\) | 16.1842 | 0.535327 | ||||||||
\(915\) | −31.5618 | −1.04340 | ||||||||
\(916\) | 62.3617 | 2.06049 | ||||||||
\(917\) | −17.1583 | −0.566615 | ||||||||
\(918\) | 0.693806 | 0.0228990 | ||||||||
\(919\) | −43.4662 | −1.43382 | −0.716909 | − | 0.697166i | \(-0.754444\pi\) | ||||
−0.716909 | + | 0.697166i | \(0.754444\pi\) | |||||||
\(920\) | 36.1031 | 1.19029 | ||||||||
\(921\) | −24.0655 | −0.792986 | ||||||||
\(922\) | −68.5699 | −2.25823 | ||||||||
\(923\) | −47.8272 | −1.57425 | ||||||||
\(924\) | −133.787 | −4.40127 | ||||||||
\(925\) | 0.781579 | 0.0256981 | ||||||||
\(926\) | 54.6925 | 1.79731 | ||||||||
\(927\) | −26.4837 | −0.869837 | ||||||||
\(928\) | −14.8017 | −0.485891 | ||||||||
\(929\) | 1.64859 | 0.0540886 | 0.0270443 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270443 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(930\) | −70.9573 | −2.32678 | ||||||||
\(931\) | 79.0140 | 2.58958 | ||||||||
\(932\) | −29.8034 | −0.976243 | ||||||||
\(933\) | 31.7810 | 1.04046 | ||||||||
\(934\) | −2.79401 | −0.0914229 | ||||||||
\(935\) | 1.02231 | 0.0334332 | ||||||||
\(936\) | 27.0113 | 0.882893 | ||||||||
\(937\) | −39.1738 | −1.27975 | −0.639876 | − | 0.768478i | \(-0.721014\pi\) | ||||
−0.639876 | + | 0.768478i | \(0.721014\pi\) | |||||||
\(938\) | 141.380 | 4.61622 | ||||||||
\(939\) | 41.7928 | 1.36385 | ||||||||
\(940\) | −12.0321 | −0.392445 | ||||||||
\(941\) | 9.62466 | 0.313755 | 0.156878 | − | 0.987618i | \(-0.449857\pi\) | ||||
0.156878 | + | 0.987618i | \(0.449857\pi\) | |||||||
\(942\) | 12.1216 | 0.394943 | ||||||||
\(943\) | −20.8167 | −0.677886 | ||||||||
\(944\) | −0.647719 | −0.0210815 | ||||||||
\(945\) | 24.2627 | 0.789264 | ||||||||
\(946\) | −91.2143 | −2.96563 | ||||||||
\(947\) | −0.374898 | −0.0121825 | −0.00609127 | − | 0.999981i | \(-0.501939\pi\) | ||||
−0.00609127 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(948\) | 92.2377 | 2.99574 | ||||||||
\(949\) | −61.3041 | −1.99002 | ||||||||
\(950\) | 13.1717 | 0.427347 | ||||||||
\(951\) | −32.4618 | −1.05265 | ||||||||
\(952\) | 1.23968 | 0.0401782 | ||||||||
\(953\) | −53.8917 | −1.74572 | −0.872862 | − | 0.487967i | \(-0.837739\pi\) | ||||
−0.872862 | + | 0.487967i | \(0.837739\pi\) | |||||||
\(954\) | 24.6473 | 0.797986 | ||||||||
\(955\) | −16.4732 | −0.533060 | ||||||||
\(956\) | 34.4912 | 1.11552 | ||||||||
\(957\) | −25.1227 | −0.812101 | ||||||||
\(958\) | 22.0866 | 0.713585 | ||||||||
\(959\) | 12.5072 | 0.403880 | ||||||||
\(960\) | −57.9112 | −1.86908 | ||||||||
\(961\) | 17.8456 | 0.575666 | ||||||||
\(962\) | −13.2739 | −0.427969 | ||||||||
\(963\) | −13.2878 | −0.428192 | ||||||||
\(964\) | 58.8165 | 1.89435 | ||||||||
\(965\) | 37.9965 | 1.22315 | ||||||||
\(966\) | −134.342 | −4.32240 | ||||||||
\(967\) | 26.1449 | 0.840762 | 0.420381 | − | 0.907348i | \(-0.361896\pi\) | ||||
0.420381 | + | 0.907348i | \(0.361896\pi\) | |||||||
\(968\) | −27.4518 | −0.882334 | ||||||||
\(969\) | 1.73844 | 0.0558467 | ||||||||
\(970\) | 74.6965 | 2.39836 | ||||||||
\(971\) | 15.9611 | 0.512215 | 0.256108 | − | 0.966648i | \(-0.417560\pi\) | ||||
0.256108 | + | 0.966648i | \(0.417560\pi\) | |||||||
\(972\) | −50.7258 | −1.62703 | ||||||||
\(973\) | −4.32079 | −0.138518 | ||||||||
\(974\) | 40.9175 | 1.31108 | ||||||||
\(975\) | 9.87458 | 0.316240 | ||||||||
\(976\) | 1.33485 | 0.0427274 | ||||||||
\(977\) | 55.6769 | 1.78126 | 0.890631 | − | 0.454728i | \(-0.150263\pi\) | ||||
0.890631 | + | 0.454728i | \(0.150263\pi\) | |||||||
\(978\) | −4.94321 | −0.158066 | ||||||||
\(979\) | −30.0078 | −0.959055 | ||||||||
\(980\) | 70.0828 | 2.23871 | ||||||||
\(981\) | 14.2863 | 0.456126 | ||||||||
\(982\) | 29.8706 | 0.953209 | ||||||||
\(983\) | 11.9908 | 0.382446 | 0.191223 | − | 0.981547i | \(-0.438755\pi\) | ||||
0.191223 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(984\) | −19.0043 | −0.605834 | ||||||||
\(985\) | −18.1428 | −0.578078 | ||||||||
\(986\) | 0.622870 | 0.0198362 | ||||||||
\(987\) | 16.7330 | 0.532617 | ||||||||
\(988\) | −137.556 | −4.37623 | ||||||||
\(989\) | −56.3210 | −1.79090 | ||||||||
\(990\) | −36.6509 | −1.16484 | ||||||||
\(991\) | 56.7964 | 1.80420 | 0.902098 | − | 0.431532i | \(-0.142027\pi\) | ||||
0.902098 | + | 0.431532i | \(0.142027\pi\) | |||||||
\(992\) | 41.0207 | 1.30241 | ||||||||
\(993\) | 2.15040 | 0.0682409 | ||||||||
\(994\) | 78.6933 | 2.49600 | ||||||||
\(995\) | 15.3996 | 0.488199 | ||||||||
\(996\) | 111.891 | 3.54539 | ||||||||
\(997\) | −3.68949 | −0.116847 | −0.0584236 | − | 0.998292i | \(-0.518607\pi\) | ||||
−0.0584236 | + | 0.998292i | \(0.518607\pi\) | |||||||
\(998\) | −19.0011 | −0.601470 | ||||||||
\(999\) | 2.80908 | 0.0888752 |
(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 | 6031.2.a.d.1.16 | ✓ | 133 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6031.2.a.d.1.16 | ✓ | 133 | 1.1 | even | 1 | trivial |