Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, 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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(1\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.49383 | −1.76340 | −0.881702 | − | 0.471807i | \(-0.843602\pi\) | ||||
−0.881702 | + | 0.471807i | \(0.843602\pi\) | |||||||
\(3\) | −0.270355 | −0.156090 | −0.0780449 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780449 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(4\) | 4.21918 | 2.10959 | ||||||||
\(5\) | −2.99495 | −1.33938 | −0.669692 | − | 0.742639i | \(-0.733574\pi\) | ||||
−0.669692 | + | 0.742639i | \(0.733574\pi\) | |||||||
\(6\) | 0.674220 | 0.275249 | ||||||||
\(7\) | −3.80387 | −1.43773 | −0.718865 | − | 0.695150i | \(-0.755338\pi\) | ||||
−0.718865 | + | 0.695150i | \(0.755338\pi\) | |||||||
\(8\) | −5.53426 | −1.95666 | ||||||||
\(9\) | −2.92691 | −0.975636 | ||||||||
\(10\) | 7.46890 | 2.36187 | ||||||||
\(11\) | −5.91933 | −1.78475 | −0.892373 | − | 0.451299i | \(-0.850961\pi\) | ||||
−0.892373 | + | 0.451299i | \(0.850961\pi\) | |||||||
\(12\) | −1.14068 | −0.329286 | ||||||||
\(13\) | −0.710532 | −0.197066 | −0.0985331 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985331 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(14\) | 9.48621 | 2.53530 | ||||||||
\(15\) | 0.809702 | 0.209064 | ||||||||
\(16\) | 5.36314 | 1.34078 | ||||||||
\(17\) | −1.35009 | −0.327446 | −0.163723 | − | 0.986506i | \(-0.552350\pi\) | ||||
−0.163723 | + | 0.986506i | \(0.552350\pi\) | |||||||
\(18\) | 7.29921 | 1.72044 | ||||||||
\(19\) | −5.05928 | −1.16068 | −0.580339 | − | 0.814375i | \(-0.697080\pi\) | ||||
−0.580339 | + | 0.814375i | \(0.697080\pi\) | |||||||
\(20\) | −12.6363 | −2.82555 | ||||||||
\(21\) | 1.02840 | 0.224415 | ||||||||
\(22\) | 14.7618 | 3.14723 | ||||||||
\(23\) | 6.13130 | 1.27847 | 0.639233 | − | 0.769013i | \(-0.279252\pi\) | ||||
0.639233 | + | 0.769013i | \(0.279252\pi\) | |||||||
\(24\) | 1.49622 | 0.305414 | ||||||||
\(25\) | 3.96974 | 0.793948 | ||||||||
\(26\) | 1.77195 | 0.347507 | ||||||||
\(27\) | 1.60237 | 0.308377 | ||||||||
\(28\) | −16.0492 | −3.03302 | ||||||||
\(29\) | −0.793559 | −0.147360 | −0.0736801 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736801 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(30\) | −2.01926 | −0.368664 | ||||||||
\(31\) | 1.55429 | 0.279158 | 0.139579 | − | 0.990211i | \(-0.455425\pi\) | ||||
0.139579 | + | 0.990211i | \(0.455425\pi\) | |||||||
\(32\) | −2.30622 | −0.407686 | ||||||||
\(33\) | 1.60032 | 0.278581 | ||||||||
\(34\) | 3.36690 | 0.577419 | ||||||||
\(35\) | 11.3924 | 1.92567 | ||||||||
\(36\) | −12.3492 | −2.05819 | ||||||||
\(37\) | −11.1363 | −1.83080 | −0.915399 | − | 0.402548i | \(-0.868125\pi\) | ||||
−0.915399 | + | 0.402548i | \(0.868125\pi\) | |||||||
\(38\) | 12.6170 | 2.04674 | ||||||||
\(39\) | 0.192096 | 0.0307600 | ||||||||
\(40\) | 16.5748 | 2.62071 | ||||||||
\(41\) | 7.91233 | 1.23570 | 0.617849 | − | 0.786297i | \(-0.288004\pi\) | ||||
0.617849 | + | 0.786297i | \(0.288004\pi\) | |||||||
\(42\) | −2.56465 | −0.395734 | ||||||||
\(43\) | −11.5314 | −1.75852 | −0.879262 | − | 0.476339i | \(-0.841963\pi\) | ||||
−0.879262 | + | 0.476339i | \(0.841963\pi\) | |||||||
\(44\) | −24.9747 | −3.76508 | ||||||||
\(45\) | 8.76595 | 1.30675 | ||||||||
\(46\) | −15.2904 | −2.25445 | ||||||||
\(47\) | −3.68696 | −0.537798 | −0.268899 | − | 0.963168i | \(-0.586660\pi\) | ||||
−0.268899 | + | 0.963168i | \(0.586660\pi\) | |||||||
\(48\) | −1.44995 | −0.209283 | ||||||||
\(49\) | 7.46946 | 1.06707 | ||||||||
\(50\) | −9.89985 | −1.40005 | ||||||||
\(51\) | 0.365005 | 0.0511109 | ||||||||
\(52\) | −2.99786 | −0.415729 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | −3.99604 | −0.543792 | ||||||||
\(55\) | 17.7281 | 2.39046 | ||||||||
\(56\) | 21.0516 | 2.81314 | ||||||||
\(57\) | 1.36780 | 0.181170 | ||||||||
\(58\) | 1.97900 | 0.259855 | ||||||||
\(59\) | 1.22514 | 0.159499 | 0.0797496 | − | 0.996815i | \(-0.474588\pi\) | ||||
0.0797496 | + | 0.996815i | \(0.474588\pi\) | |||||||
\(60\) | 3.41628 | 0.441040 | ||||||||
\(61\) | 1.94993 | 0.249663 | 0.124831 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124831 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(62\) | −3.87613 | −0.492269 | ||||||||
\(63\) | 11.1336 | 1.40270 | ||||||||
\(64\) | −4.97495 | −0.621869 | ||||||||
\(65\) | 2.12801 | 0.263947 | ||||||||
\(66\) | −3.99093 | −0.491250 | ||||||||
\(67\) | 6.11454 | 0.747009 | 0.373505 | − | 0.927628i | \(-0.378156\pi\) | ||||
0.373505 | + | 0.927628i | \(0.378156\pi\) | |||||||
\(68\) | −5.69629 | −0.690776 | ||||||||
\(69\) | −1.65763 | −0.199555 | ||||||||
\(70\) | −28.4108 | −3.39573 | ||||||||
\(71\) | −13.2576 | −1.57339 | −0.786694 | − | 0.617343i | \(-0.788209\pi\) | ||||
−0.786694 | + | 0.617343i | \(0.788209\pi\) | |||||||
\(72\) | 16.1983 | 1.90898 | ||||||||
\(73\) | 5.38563 | 0.630340 | 0.315170 | − | 0.949035i | \(-0.397938\pi\) | ||||
0.315170 | + | 0.949035i | \(0.397938\pi\) | |||||||
\(74\) | 27.7720 | 3.22843 | ||||||||
\(75\) | −1.07324 | −0.123927 | ||||||||
\(76\) | −21.3460 | −2.44856 | ||||||||
\(77\) | 22.5164 | 2.56598 | ||||||||
\(78\) | −0.479055 | −0.0542423 | ||||||||
\(79\) | 10.0480 | 1.13049 | 0.565247 | − | 0.824922i | \(-0.308781\pi\) | ||||
0.565247 | + | 0.824922i | \(0.308781\pi\) | |||||||
\(80\) | −16.0623 | −1.79582 | ||||||||
\(81\) | 8.34751 | 0.927502 | ||||||||
\(82\) | −19.7320 | −2.17903 | ||||||||
\(83\) | 13.3540 | 1.46579 | 0.732895 | − | 0.680342i | \(-0.238169\pi\) | ||||
0.732895 | + | 0.680342i | \(0.238169\pi\) | |||||||
\(84\) | 4.33900 | 0.473424 | ||||||||
\(85\) | 4.04346 | 0.438575 | ||||||||
\(86\) | 28.7574 | 3.10099 | ||||||||
\(87\) | 0.214543 | 0.0230014 | ||||||||
\(88\) | 32.7591 | 3.49213 | ||||||||
\(89\) | 7.27485 | 0.771132 | 0.385566 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385566 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(90\) | −21.8608 | −2.30433 | ||||||||
\(91\) | 2.70278 | 0.283328 | ||||||||
\(92\) | 25.8691 | 2.69704 | ||||||||
\(93\) | −0.420210 | −0.0435738 | ||||||||
\(94\) | 9.19464 | 0.948355 | ||||||||
\(95\) | 15.1523 | 1.55459 | ||||||||
\(96\) | 0.623500 | 0.0636357 | ||||||||
\(97\) | −12.8467 | −1.30438 | −0.652190 | − | 0.758056i | \(-0.726150\pi\) | ||||
−0.652190 | + | 0.758056i | \(0.726150\pi\) | |||||||
\(98\) | −18.6276 | −1.88167 | ||||||||
\(99\) | 17.3253 | 1.74126 | ||||||||
\(100\) | 16.7491 | 1.67491 | ||||||||
\(101\) | −12.7204 | −1.26573 | −0.632863 | − | 0.774264i | \(-0.718120\pi\) | ||||
−0.632863 | + | 0.774264i | \(0.718120\pi\) | |||||||
\(102\) | −0.910260 | −0.0901292 | ||||||||
\(103\) | 6.80892 | 0.670903 | 0.335451 | − | 0.942058i | \(-0.391111\pi\) | ||||
0.335451 | + | 0.942058i | \(0.391111\pi\) | |||||||
\(104\) | 3.93227 | 0.385591 | ||||||||
\(105\) | −3.08000 | −0.300578 | ||||||||
\(106\) | 2.49383 | 0.242222 | ||||||||
\(107\) | 7.22091 | 0.698071 | 0.349036 | − | 0.937109i | \(-0.386509\pi\) | ||||
0.349036 | + | 0.937109i | \(0.386509\pi\) | |||||||
\(108\) | 6.76070 | 0.650549 | ||||||||
\(109\) | −17.5619 | −1.68212 | −0.841061 | − | 0.540941i | \(-0.818068\pi\) | ||||
−0.841061 | + | 0.540941i | \(0.818068\pi\) | |||||||
\(110\) | −44.2109 | −4.21534 | ||||||||
\(111\) | 3.01076 | 0.285769 | ||||||||
\(112\) | −20.4007 | −1.92768 | ||||||||
\(113\) | −0.715990 | −0.0673547 | −0.0336773 | − | 0.999433i | \(-0.510722\pi\) | ||||
−0.0336773 | + | 0.999433i | \(0.510722\pi\) | |||||||
\(114\) | −3.41107 | −0.319476 | ||||||||
\(115\) | −18.3630 | −1.71236 | ||||||||
\(116\) | −3.34817 | −0.310870 | ||||||||
\(117\) | 2.07966 | 0.192265 | ||||||||
\(118\) | −3.05528 | −0.281261 | ||||||||
\(119\) | 5.13558 | 0.470778 | ||||||||
\(120\) | −4.48110 | −0.409067 | ||||||||
\(121\) | 24.0385 | 2.18532 | ||||||||
\(122\) | −4.86279 | −0.440256 | ||||||||
\(123\) | −2.13914 | −0.192880 | ||||||||
\(124\) | 6.55782 | 0.588910 | ||||||||
\(125\) | 3.08558 | 0.275983 | ||||||||
\(126\) | −27.7653 | −2.47353 | ||||||||
\(127\) | 5.75524 | 0.510695 | 0.255348 | − | 0.966849i | \(-0.417810\pi\) | ||||
0.255348 | + | 0.966849i | \(0.417810\pi\) | |||||||
\(128\) | 17.0191 | 1.50429 | ||||||||
\(129\) | 3.11758 | 0.274488 | ||||||||
\(130\) | −5.30689 | −0.465445 | ||||||||
\(131\) | 4.95580 | 0.432991 | 0.216495 | − | 0.976284i | \(-0.430537\pi\) | ||||
0.216495 | + | 0.976284i | \(0.430537\pi\) | |||||||
\(132\) | 6.75206 | 0.587691 | ||||||||
\(133\) | 19.2449 | 1.66874 | ||||||||
\(134\) | −15.2486 | −1.31728 | ||||||||
\(135\) | −4.79903 | −0.413035 | ||||||||
\(136\) | 7.47177 | 0.640699 | ||||||||
\(137\) | 21.0949 | 1.80226 | 0.901128 | − | 0.433553i | \(-0.142740\pi\) | ||||
0.901128 | + | 0.433553i | \(0.142740\pi\) | |||||||
\(138\) | 4.13385 | 0.351897 | ||||||||
\(139\) | −12.6542 | −1.07331 | −0.536657 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536657 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(140\) | 48.0667 | 4.06238 | ||||||||
\(141\) | 0.996790 | 0.0839448 | ||||||||
\(142\) | 33.0622 | 2.77452 | ||||||||
\(143\) | 4.20587 | 0.351713 | ||||||||
\(144\) | −15.6974 | −1.30812 | ||||||||
\(145\) | 2.37667 | 0.197372 | ||||||||
\(146\) | −13.4308 | −1.11154 | ||||||||
\(147\) | −2.01941 | −0.166558 | ||||||||
\(148\) | −46.9861 | −3.86224 | ||||||||
\(149\) | 20.6126 | 1.68865 | 0.844326 | − | 0.535831i | \(-0.180001\pi\) | ||||
0.844326 | + | 0.535831i | \(0.180001\pi\) | |||||||
\(150\) | 2.67648 | 0.218534 | ||||||||
\(151\) | −1.00000 | −0.0813788 | ||||||||
\(152\) | 27.9994 | 2.27105 | ||||||||
\(153\) | 3.95160 | 0.319468 | ||||||||
\(154\) | −56.1520 | −4.52486 | ||||||||
\(155\) | −4.65502 | −0.373900 | ||||||||
\(156\) | 0.810489 | 0.0648911 | ||||||||
\(157\) | 3.26944 | 0.260929 | 0.130465 | − | 0.991453i | \(-0.458353\pi\) | ||||
0.130465 | + | 0.991453i | \(0.458353\pi\) | |||||||
\(158\) | −25.0581 | −1.99352 | ||||||||
\(159\) | 0.270355 | 0.0214406 | ||||||||
\(160\) | 6.90702 | 0.546048 | ||||||||
\(161\) | −23.3227 | −1.83809 | ||||||||
\(162\) | −20.8173 | −1.63556 | ||||||||
\(163\) | −4.61933 | −0.361813 | −0.180907 | − | 0.983500i | \(-0.557903\pi\) | ||||
−0.180907 | + | 0.983500i | \(0.557903\pi\) | |||||||
\(164\) | 33.3836 | 2.60682 | ||||||||
\(165\) | −4.79289 | −0.373126 | ||||||||
\(166\) | −33.3025 | −2.58478 | ||||||||
\(167\) | 13.8528 | 1.07196 | 0.535981 | − | 0.844230i | \(-0.319942\pi\) | ||||
0.535981 | + | 0.844230i | \(0.319942\pi\) | |||||||
\(168\) | −5.69143 | −0.439103 | ||||||||
\(169\) | −12.4951 | −0.961165 | ||||||||
\(170\) | −10.0837 | −0.773385 | ||||||||
\(171\) | 14.8081 | 1.13240 | ||||||||
\(172\) | −48.6531 | −3.70977 | ||||||||
\(173\) | −7.01099 | −0.533036 | −0.266518 | − | 0.963830i | \(-0.585873\pi\) | ||||
−0.266518 | + | 0.963830i | \(0.585873\pi\) | |||||||
\(174\) | −0.535033 | −0.0405608 | ||||||||
\(175\) | −15.1004 | −1.14148 | ||||||||
\(176\) | −31.7462 | −2.39296 | ||||||||
\(177\) | −0.331222 | −0.0248962 | ||||||||
\(178\) | −18.1422 | −1.35982 | ||||||||
\(179\) | 18.7287 | 1.39985 | 0.699923 | − | 0.714218i | \(-0.253218\pi\) | ||||
0.699923 | + | 0.714218i | \(0.253218\pi\) | |||||||
\(180\) | 36.9851 | 2.75671 | ||||||||
\(181\) | 23.8184 | 1.77041 | 0.885205 | − | 0.465201i | \(-0.154018\pi\) | ||||
0.885205 | + | 0.465201i | \(0.154018\pi\) | |||||||
\(182\) | −6.74026 | −0.499621 | ||||||||
\(183\) | −0.527174 | −0.0389698 | ||||||||
\(184\) | −33.9322 | −2.50152 | ||||||||
\(185\) | 33.3527 | 2.45214 | ||||||||
\(186\) | 1.04793 | 0.0768381 | ||||||||
\(187\) | 7.99164 | 0.584407 | ||||||||
\(188\) | −15.5560 | −1.13453 | ||||||||
\(189\) | −6.09522 | −0.443362 | ||||||||
\(190\) | −37.7873 | −2.74138 | ||||||||
\(191\) | −2.16339 | −0.156537 | −0.0782687 | − | 0.996932i | \(-0.524939\pi\) | ||||
−0.0782687 | + | 0.996932i | \(0.524939\pi\) | |||||||
\(192\) | 1.34501 | 0.0970674 | ||||||||
\(193\) | −9.37160 | −0.674582 | −0.337291 | − | 0.941400i | \(-0.609511\pi\) | ||||
−0.337291 | + | 0.941400i | \(0.609511\pi\) | |||||||
\(194\) | 32.0373 | 2.30015 | ||||||||
\(195\) | −0.575319 | −0.0411995 | ||||||||
\(196\) | 31.5150 | 2.25107 | ||||||||
\(197\) | −16.5235 | −1.17725 | −0.588627 | − | 0.808405i | \(-0.700331\pi\) | ||||
−0.588627 | + | 0.808405i | \(0.700331\pi\) | |||||||
\(198\) | −43.2064 | −3.07055 | ||||||||
\(199\) | −0.932005 | −0.0660681 | −0.0330341 | − | 0.999454i | \(-0.510517\pi\) | ||||
−0.0330341 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(200\) | −21.9696 | −1.55348 | ||||||||
\(201\) | −1.65310 | −0.116601 | ||||||||
\(202\) | 31.7225 | 2.23198 | ||||||||
\(203\) | 3.01860 | 0.211864 | ||||||||
\(204\) | 1.54002 | 0.107823 | ||||||||
\(205\) | −23.6970 | −1.65507 | ||||||||
\(206\) | −16.9803 | −1.18307 | ||||||||
\(207\) | −17.9458 | −1.24732 | ||||||||
\(208\) | −3.81068 | −0.264223 | ||||||||
\(209\) | 29.9476 | 2.07152 | ||||||||
\(210\) | 7.68100 | 0.530040 | ||||||||
\(211\) | 12.3506 | 0.850250 | 0.425125 | − | 0.905135i | \(-0.360230\pi\) | ||||
0.425125 | + | 0.905135i | \(0.360230\pi\) | |||||||
\(212\) | −4.21918 | −0.289775 | ||||||||
\(213\) | 3.58427 | 0.245590 | ||||||||
\(214\) | −18.0077 | −1.23098 | ||||||||
\(215\) | 34.5360 | 2.35534 | ||||||||
\(216\) | −8.86795 | −0.603387 | ||||||||
\(217\) | −5.91232 | −0.401354 | ||||||||
\(218\) | 43.7963 | 2.96626 | ||||||||
\(219\) | −1.45603 | −0.0983897 | ||||||||
\(220\) | 74.7981 | 5.04289 | ||||||||
\(221\) | 0.959284 | 0.0645284 | ||||||||
\(222\) | −7.50833 | −0.503926 | ||||||||
\(223\) | −26.4463 | −1.77097 | −0.885487 | − | 0.464665i | \(-0.846175\pi\) | ||||
−0.885487 | + | 0.464665i | \(0.846175\pi\) | |||||||
\(224\) | 8.77258 | 0.586142 | ||||||||
\(225\) | −11.6191 | −0.774604 | ||||||||
\(226\) | 1.78556 | 0.118773 | ||||||||
\(227\) | −27.5481 | −1.82843 | −0.914217 | − | 0.405225i | \(-0.867193\pi\) | ||||
−0.914217 | + | 0.405225i | \(0.867193\pi\) | |||||||
\(228\) | 5.77102 | 0.382195 | ||||||||
\(229\) | 17.4888 | 1.15570 | 0.577848 | − | 0.816145i | \(-0.303893\pi\) | ||||
0.577848 | + | 0.816145i | \(0.303893\pi\) | |||||||
\(230\) | 45.7941 | 3.01957 | ||||||||
\(231\) | −6.08743 | −0.400524 | ||||||||
\(232\) | 4.39176 | 0.288333 | ||||||||
\(233\) | 15.6435 | 1.02484 | 0.512421 | − | 0.858734i | \(-0.328749\pi\) | ||||
0.512421 | + | 0.858734i | \(0.328749\pi\) | |||||||
\(234\) | −5.18632 | −0.339040 | ||||||||
\(235\) | 11.0423 | 0.720318 | ||||||||
\(236\) | 5.16908 | 0.336478 | ||||||||
\(237\) | −2.71654 | −0.176458 | ||||||||
\(238\) | −12.8073 | −0.830172 | ||||||||
\(239\) | 3.08331 | 0.199443 | 0.0997213 | − | 0.995015i | \(-0.468205\pi\) | ||||
0.0997213 | + | 0.995015i | \(0.468205\pi\) | |||||||
\(240\) | 4.34254 | 0.280310 | ||||||||
\(241\) | −13.8297 | −0.890847 | −0.445423 | − | 0.895320i | \(-0.646947\pi\) | ||||
−0.445423 | + | 0.895320i | \(0.646947\pi\) | |||||||
\(242\) | −59.9478 | −3.85359 | ||||||||
\(243\) | −7.06391 | −0.453150 | ||||||||
\(244\) | 8.22711 | 0.526687 | ||||||||
\(245\) | −22.3707 | −1.42921 | ||||||||
\(246\) | 5.33465 | 0.340125 | ||||||||
\(247\) | 3.59478 | 0.228731 | ||||||||
\(248\) | −8.60184 | −0.546217 | ||||||||
\(249\) | −3.61032 | −0.228795 | ||||||||
\(250\) | −7.69491 | −0.486669 | ||||||||
\(251\) | −12.5883 | −0.794567 | −0.397283 | − | 0.917696i | \(-0.630047\pi\) | ||||
−0.397283 | + | 0.917696i | \(0.630047\pi\) | |||||||
\(252\) | 46.9747 | 2.95913 | ||||||||
\(253\) | −36.2932 | −2.28173 | ||||||||
\(254\) | −14.3526 | −0.900562 | ||||||||
\(255\) | −1.09317 | −0.0684571 | ||||||||
\(256\) | −32.4929 | −2.03080 | ||||||||
\(257\) | −9.11094 | −0.568325 | −0.284162 | − | 0.958776i | \(-0.591715\pi\) | ||||
−0.284162 | + | 0.958776i | \(0.591715\pi\) | |||||||
\(258\) | −7.77471 | −0.484032 | ||||||||
\(259\) | 42.3611 | 2.63219 | ||||||||
\(260\) | 8.97846 | 0.556821 | ||||||||
\(261\) | 2.32267 | 0.143770 | ||||||||
\(262\) | −12.3589 | −0.763537 | ||||||||
\(263\) | −17.4088 | −1.07347 | −0.536737 | − | 0.843750i | \(-0.680343\pi\) | ||||
−0.536737 | + | 0.843750i | \(0.680343\pi\) | |||||||
\(264\) | −8.85661 | −0.545087 | ||||||||
\(265\) | 2.99495 | 0.183978 | ||||||||
\(266\) | −47.9934 | −2.94267 | ||||||||
\(267\) | −1.96679 | −0.120366 | ||||||||
\(268\) | 25.7983 | 1.57588 | ||||||||
\(269\) | −12.0663 | −0.735695 | −0.367848 | − | 0.929886i | \(-0.619905\pi\) | ||||
−0.367848 | + | 0.929886i | \(0.619905\pi\) | |||||||
\(270\) | 11.9680 | 0.728347 | ||||||||
\(271\) | 17.1722 | 1.04314 | 0.521569 | − | 0.853209i | \(-0.325347\pi\) | ||||
0.521569 | + | 0.853209i | \(0.325347\pi\) | |||||||
\(272\) | −7.24073 | −0.439034 | ||||||||
\(273\) | −0.730710 | −0.0442246 | ||||||||
\(274\) | −52.6070 | −3.17810 | ||||||||
\(275\) | −23.4982 | −1.41699 | ||||||||
\(276\) | −6.99385 | −0.420980 | ||||||||
\(277\) | 26.6336 | 1.60026 | 0.800129 | − | 0.599828i | \(-0.204765\pi\) | ||||
0.800129 | + | 0.599828i | \(0.204765\pi\) | |||||||
\(278\) | 31.5574 | 1.89268 | ||||||||
\(279\) | −4.54926 | −0.272357 | ||||||||
\(280\) | −63.0487 | −3.76788 | ||||||||
\(281\) | 1.20934 | 0.0721429 | 0.0360714 | − | 0.999349i | \(-0.488516\pi\) | ||||
0.0360714 | + | 0.999349i | \(0.488516\pi\) | |||||||
\(282\) | −2.48582 | −0.148029 | ||||||||
\(283\) | −9.16240 | −0.544648 | −0.272324 | − | 0.962206i | \(-0.587792\pi\) | ||||
−0.272324 | + | 0.962206i | \(0.587792\pi\) | |||||||
\(284\) | −55.9363 | −3.31921 | ||||||||
\(285\) | −4.09651 | −0.242656 | ||||||||
\(286\) | −10.4887 | −0.620212 | ||||||||
\(287\) | −30.0975 | −1.77660 | ||||||||
\(288\) | 6.75010 | 0.397753 | ||||||||
\(289\) | −15.1772 | −0.892779 | ||||||||
\(290\) | −5.92701 | −0.348046 | ||||||||
\(291\) | 3.47316 | 0.203600 | ||||||||
\(292\) | 22.7229 | 1.32976 | ||||||||
\(293\) | −13.2386 | −0.773408 | −0.386704 | − | 0.922204i | \(-0.626387\pi\) | ||||
−0.386704 | + | 0.922204i | \(0.626387\pi\) | |||||||
\(294\) | 5.03606 | 0.293709 | ||||||||
\(295\) | −3.66923 | −0.213631 | ||||||||
\(296\) | 61.6312 | 3.58224 | ||||||||
\(297\) | −9.48497 | −0.550374 | ||||||||
\(298\) | −51.4043 | −2.97777 | ||||||||
\(299\) | −4.35649 | −0.251942 | ||||||||
\(300\) | −4.52820 | −0.261436 | ||||||||
\(301\) | 43.8640 | 2.52828 | ||||||||
\(302\) | 2.49383 | 0.143504 | ||||||||
\(303\) | 3.43903 | 0.197567 | ||||||||
\(304\) | −27.1336 | −1.55622 | ||||||||
\(305\) | −5.83995 | −0.334394 | ||||||||
\(306\) | −9.85461 | −0.563350 | ||||||||
\(307\) | −12.3148 | −0.702843 | −0.351421 | − | 0.936217i | \(-0.614302\pi\) | ||||
−0.351421 | + | 0.936217i | \(0.614302\pi\) | |||||||
\(308\) | 95.0008 | 5.41317 | ||||||||
\(309\) | −1.84083 | −0.104721 | ||||||||
\(310\) | 11.6088 | 0.659337 | ||||||||
\(311\) | 17.8033 | 1.00953 | 0.504765 | − | 0.863257i | \(-0.331579\pi\) | ||||
0.504765 | + | 0.863257i | \(0.331579\pi\) | |||||||
\(312\) | −1.06311 | −0.0601868 | ||||||||
\(313\) | 4.60176 | 0.260107 | 0.130054 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130054 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(314\) | −8.15342 | −0.460124 | ||||||||
\(315\) | −33.3446 | −1.87875 | ||||||||
\(316\) | 42.3945 | 2.38488 | ||||||||
\(317\) | −26.0244 | −1.46168 | −0.730839 | − | 0.682550i | \(-0.760871\pi\) | ||||
−0.730839 | + | 0.682550i | \(0.760871\pi\) | |||||||
\(318\) | −0.674220 | −0.0378084 | ||||||||
\(319\) | 4.69734 | 0.263000 | ||||||||
\(320\) | 14.8997 | 0.832921 | ||||||||
\(321\) | −1.95221 | −0.108962 | ||||||||
\(322\) | 58.1629 | 3.24129 | ||||||||
\(323\) | 6.83050 | 0.380059 | ||||||||
\(324\) | 35.2197 | 1.95665 | ||||||||
\(325\) | −2.82063 | −0.156460 | ||||||||
\(326\) | 11.5198 | 0.638023 | ||||||||
\(327\) | 4.74795 | 0.262562 | ||||||||
\(328\) | −43.7889 | −2.41784 | ||||||||
\(329\) | 14.0247 | 0.773208 | ||||||||
\(330\) | 11.9527 | 0.657972 | ||||||||
\(331\) | −34.8481 | −1.91542 | −0.957712 | − | 0.287727i | \(-0.907100\pi\) | ||||
−0.957712 | + | 0.287727i | \(0.907100\pi\) | |||||||
\(332\) | 56.3429 | 3.09222 | ||||||||
\(333\) | 32.5949 | 1.78619 | ||||||||
\(334\) | −34.5465 | −1.89030 | ||||||||
\(335\) | −18.3127 | −1.00053 | ||||||||
\(336\) | 5.51544 | 0.300892 | ||||||||
\(337\) | −19.4476 | −1.05938 | −0.529688 | − | 0.848193i | \(-0.677691\pi\) | ||||
−0.529688 | + | 0.848193i | \(0.677691\pi\) | |||||||
\(338\) | 31.1608 | 1.69492 | ||||||||
\(339\) | 0.193572 | 0.0105134 | ||||||||
\(340\) | 17.0601 | 0.925214 | ||||||||
\(341\) | −9.20034 | −0.498227 | ||||||||
\(342\) | −36.9287 | −1.99688 | ||||||||
\(343\) | −1.78578 | −0.0964231 | ||||||||
\(344\) | 63.8178 | 3.44083 | ||||||||
\(345\) | 4.96453 | 0.267281 | ||||||||
\(346\) | 17.4842 | 0.939957 | ||||||||
\(347\) | −1.99030 | −0.106845 | −0.0534224 | − | 0.998572i | \(-0.517013\pi\) | ||||
−0.0534224 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(348\) | 0.905196 | 0.0485236 | ||||||||
\(349\) | −28.4979 | −1.52546 | −0.762728 | − | 0.646719i | \(-0.776141\pi\) | ||||
−0.762728 | + | 0.646719i | \(0.776141\pi\) | |||||||
\(350\) | 37.6578 | 2.01289 | ||||||||
\(351\) | −1.13854 | −0.0607706 | ||||||||
\(352\) | 13.6513 | 0.727616 | ||||||||
\(353\) | −12.3755 | −0.658681 | −0.329340 | − | 0.944211i | \(-0.606826\pi\) | ||||
−0.329340 | + | 0.944211i | \(0.606826\pi\) | |||||||
\(354\) | 0.826012 | 0.0439021 | ||||||||
\(355\) | 39.7059 | 2.10737 | ||||||||
\(356\) | 30.6939 | 1.62677 | ||||||||
\(357\) | −1.38843 | −0.0734837 | ||||||||
\(358\) | −46.7061 | −2.46849 | ||||||||
\(359\) | 18.6661 | 0.985160 | 0.492580 | − | 0.870267i | \(-0.336054\pi\) | ||||
0.492580 | + | 0.870267i | \(0.336054\pi\) | |||||||
\(360\) | −48.5131 | −2.55686 | ||||||||
\(361\) | 6.59633 | 0.347175 | ||||||||
\(362\) | −59.3991 | −3.12195 | ||||||||
\(363\) | −6.49893 | −0.341106 | ||||||||
\(364\) | 11.4035 | 0.597706 | ||||||||
\(365\) | −16.1297 | −0.844267 | ||||||||
\(366\) | 1.31468 | 0.0687195 | ||||||||
\(367\) | 20.6907 | 1.08004 | 0.540022 | − | 0.841651i | \(-0.318416\pi\) | ||||
0.540022 | + | 0.841651i | \(0.318416\pi\) | |||||||
\(368\) | 32.8830 | 1.71415 | ||||||||
\(369\) | −23.1587 | −1.20559 | ||||||||
\(370\) | −83.1760 | −4.32411 | ||||||||
\(371\) | 3.80387 | 0.197487 | ||||||||
\(372\) | −1.77294 | −0.0919229 | ||||||||
\(373\) | 31.1248 | 1.61158 | 0.805791 | − | 0.592200i | \(-0.201741\pi\) | ||||
0.805791 | + | 0.592200i | \(0.201741\pi\) | |||||||
\(374\) | −19.9298 | −1.03055 | ||||||||
\(375\) | −0.834204 | −0.0430781 | ||||||||
\(376\) | 20.4046 | 1.05229 | ||||||||
\(377\) | 0.563849 | 0.0290397 | ||||||||
\(378\) | 15.2004 | 0.781826 | ||||||||
\(379\) | 25.2642 | 1.29774 | 0.648868 | − | 0.760901i | \(-0.275243\pi\) | ||||
0.648868 | + | 0.760901i | \(0.275243\pi\) | |||||||
\(380\) | 63.9303 | 3.27956 | ||||||||
\(381\) | −1.55596 | −0.0797143 | ||||||||
\(382\) | 5.39512 | 0.276039 | ||||||||
\(383\) | 33.1576 | 1.69427 | 0.847136 | − | 0.531376i | \(-0.178325\pi\) | ||||
0.847136 | + | 0.531376i | \(0.178325\pi\) | |||||||
\(384\) | −4.60121 | −0.234805 | ||||||||
\(385\) | −67.4355 | −3.43683 | ||||||||
\(386\) | 23.3712 | 1.18956 | ||||||||
\(387\) | 33.7514 | 1.71568 | ||||||||
\(388\) | −54.2024 | −2.75171 | ||||||||
\(389\) | −2.79210 | −0.141565 | −0.0707827 | − | 0.997492i | \(-0.522550\pi\) | ||||
−0.0707827 | + | 0.997492i | \(0.522550\pi\) | |||||||
\(390\) | 1.43475 | 0.0726513 | ||||||||
\(391\) | −8.27783 | −0.418628 | ||||||||
\(392\) | −41.3380 | −2.08788 | ||||||||
\(393\) | −1.33983 | −0.0675854 | ||||||||
\(394\) | 41.2069 | 2.07597 | ||||||||
\(395\) | −30.0934 | −1.51416 | ||||||||
\(396\) | 73.0988 | 3.67335 | ||||||||
\(397\) | −25.0948 | −1.25947 | −0.629735 | − | 0.776810i | \(-0.716837\pi\) | ||||
−0.629735 | + | 0.776810i | \(0.716837\pi\) | |||||||
\(398\) | 2.32426 | 0.116505 | ||||||||
\(399\) | −5.20296 | −0.260474 | ||||||||
\(400\) | 21.2903 | 1.06451 | ||||||||
\(401\) | 18.6521 | 0.931442 | 0.465721 | − | 0.884932i | \(-0.345795\pi\) | ||||
0.465721 | + | 0.884932i | \(0.345795\pi\) | |||||||
\(402\) | 4.12254 | 0.205614 | ||||||||
\(403\) | −1.10437 | −0.0550127 | ||||||||
\(404\) | −53.6696 | −2.67016 | ||||||||
\(405\) | −25.0004 | −1.24228 | ||||||||
\(406\) | −7.52787 | −0.373602 | ||||||||
\(407\) | 65.9195 | 3.26751 | ||||||||
\(408\) | −2.02003 | −0.100007 | ||||||||
\(409\) | 16.0222 | 0.792248 | 0.396124 | − | 0.918197i | \(-0.370355\pi\) | ||||
0.396124 | + | 0.918197i | \(0.370355\pi\) | |||||||
\(410\) | 59.0964 | 2.91856 | ||||||||
\(411\) | −5.70311 | −0.281314 | ||||||||
\(412\) | 28.7281 | 1.41533 | ||||||||
\(413\) | −4.66027 | −0.229317 | ||||||||
\(414\) | 44.7537 | 2.19952 | ||||||||
\(415\) | −39.9945 | −1.96325 | ||||||||
\(416\) | 1.63864 | 0.0803411 | ||||||||
\(417\) | 3.42113 | 0.167533 | ||||||||
\(418\) | −74.6841 | −3.65292 | ||||||||
\(419\) | 32.2329 | 1.57468 | 0.787340 | − | 0.616520i | \(-0.211458\pi\) | ||||
0.787340 | + | 0.616520i | \(0.211458\pi\) | |||||||
\(420\) | −12.9951 | −0.634096 | ||||||||
\(421\) | −3.91209 | −0.190663 | −0.0953317 | − | 0.995446i | \(-0.530391\pi\) | ||||
−0.0953317 | + | 0.995446i | \(0.530391\pi\) | |||||||
\(422\) | −30.8003 | −1.49933 | ||||||||
\(423\) | 10.7914 | 0.524695 | ||||||||
\(424\) | 5.53426 | 0.268767 | ||||||||
\(425\) | −5.35952 | −0.259975 | ||||||||
\(426\) | −8.93855 | −0.433074 | ||||||||
\(427\) | −7.41729 | −0.358948 | ||||||||
\(428\) | 30.4663 | 1.47265 | ||||||||
\(429\) | −1.13708 | −0.0548988 | ||||||||
\(430\) | −86.1269 | −4.15341 | ||||||||
\(431\) | 18.8524 | 0.908090 | 0.454045 | − | 0.890979i | \(-0.349981\pi\) | ||||
0.454045 | + | 0.890979i | \(0.349981\pi\) | |||||||
\(432\) | 8.59374 | 0.413467 | ||||||||
\(433\) | −27.0571 | −1.30028 | −0.650140 | − | 0.759815i | \(-0.725290\pi\) | ||||
−0.650140 | + | 0.759815i | \(0.725290\pi\) | |||||||
\(434\) | 14.7443 | 0.707749 | ||||||||
\(435\) | −0.642546 | −0.0308077 | ||||||||
\(436\) | −74.0967 | −3.54859 | ||||||||
\(437\) | −31.0200 | −1.48389 | ||||||||
\(438\) | 3.63110 | 0.173501 | ||||||||
\(439\) | 18.9505 | 0.904458 | 0.452229 | − | 0.891902i | \(-0.350629\pi\) | ||||
0.452229 | + | 0.891902i | \(0.350629\pi\) | |||||||
\(440\) | −98.1120 | −4.67731 | ||||||||
\(441\) | −21.8624 | −1.04107 | ||||||||
\(442\) | −2.39229 | −0.113790 | ||||||||
\(443\) | −34.4655 | −1.63750 | −0.818752 | − | 0.574148i | \(-0.805333\pi\) | ||||
−0.818752 | + | 0.574148i | \(0.805333\pi\) | |||||||
\(444\) | 12.7030 | 0.602856 | ||||||||
\(445\) | −21.7878 | −1.03284 | ||||||||
\(446\) | 65.9525 | 3.12294 | ||||||||
\(447\) | −5.57273 | −0.263581 | ||||||||
\(448\) | 18.9241 | 0.894079 | ||||||||
\(449\) | 5.47937 | 0.258588 | 0.129294 | − | 0.991606i | \(-0.458729\pi\) | ||||
0.129294 | + | 0.991606i | \(0.458729\pi\) | |||||||
\(450\) | 28.9759 | 1.36594 | ||||||||
\(451\) | −46.8357 | −2.20541 | ||||||||
\(452\) | −3.02089 | −0.142091 | ||||||||
\(453\) | 0.270355 | 0.0127024 | ||||||||
\(454\) | 68.7003 | 3.22427 | ||||||||
\(455\) | −8.09468 | −0.379485 | ||||||||
\(456\) | −7.56979 | −0.354488 | ||||||||
\(457\) | 3.31085 | 0.154875 | 0.0774374 | − | 0.996997i | \(-0.475326\pi\) | ||||
0.0774374 | + | 0.996997i | \(0.475326\pi\) | |||||||
\(458\) | −43.6142 | −2.03796 | ||||||||
\(459\) | −2.16335 | −0.100977 | ||||||||
\(460\) | −77.4767 | −3.61237 | ||||||||
\(461\) | 3.79258 | 0.176638 | 0.0883189 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883189 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(462\) | 15.1810 | 0.706285 | ||||||||
\(463\) | −20.1484 | −0.936376 | −0.468188 | − | 0.883629i | \(-0.655093\pi\) | ||||
−0.468188 | + | 0.883629i | \(0.655093\pi\) | |||||||
\(464\) | −4.25596 | −0.197578 | ||||||||
\(465\) | 1.25851 | 0.0583620 | ||||||||
\(466\) | −39.0123 | −1.80721 | ||||||||
\(467\) | 27.3475 | 1.26549 | 0.632746 | − | 0.774359i | \(-0.281928\pi\) | ||||
0.632746 | + | 0.774359i | \(0.281928\pi\) | |||||||
\(468\) | 8.77447 | 0.405600 | ||||||||
\(469\) | −23.2589 | −1.07400 | ||||||||
\(470\) | −27.5375 | −1.27021 | ||||||||
\(471\) | −0.883910 | −0.0407284 | ||||||||
\(472\) | −6.78023 | −0.312085 | ||||||||
\(473\) | 68.2582 | 3.13852 | ||||||||
\(474\) | 6.77459 | 0.311167 | ||||||||
\(475\) | −20.0840 | −0.921518 | ||||||||
\(476\) | 21.6680 | 0.993149 | ||||||||
\(477\) | 2.92691 | 0.134014 | ||||||||
\(478\) | −7.68924 | −0.351698 | ||||||||
\(479\) | 30.7768 | 1.40623 | 0.703114 | − | 0.711078i | \(-0.251793\pi\) | ||||
0.703114 | + | 0.711078i | \(0.251793\pi\) | |||||||
\(480\) | −1.86735 | −0.0852325 | ||||||||
\(481\) | 7.91271 | 0.360788 | ||||||||
\(482\) | 34.4888 | 1.57092 | ||||||||
\(483\) | 6.30542 | 0.286907 | ||||||||
\(484\) | 101.423 | 4.61012 | ||||||||
\(485\) | 38.4751 | 1.74706 | ||||||||
\(486\) | 17.6162 | 0.799087 | ||||||||
\(487\) | −3.29348 | −0.149242 | −0.0746209 | − | 0.997212i | \(-0.523775\pi\) | ||||
−0.0746209 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(488\) | −10.7914 | −0.488505 | ||||||||
\(489\) | 1.24886 | 0.0564754 | ||||||||
\(490\) | 55.7887 | 2.52028 | ||||||||
\(491\) | −7.82130 | −0.352970 | −0.176485 | − | 0.984303i | \(-0.556473\pi\) | ||||
−0.176485 | + | 0.984303i | \(0.556473\pi\) | |||||||
\(492\) | −9.02543 | −0.406898 | ||||||||
\(493\) | 1.07138 | 0.0482524 | ||||||||
\(494\) | −8.96477 | −0.403344 | ||||||||
\(495\) | −51.8886 | −2.33222 | ||||||||
\(496\) | 8.33586 | 0.374291 | ||||||||
\(497\) | 50.4303 | 2.26211 | ||||||||
\(498\) | 9.00353 | 0.403458 | ||||||||
\(499\) | 26.3426 | 1.17926 | 0.589629 | − | 0.807674i | \(-0.299274\pi\) | ||||
0.589629 | + | 0.807674i | \(0.299274\pi\) | |||||||
\(500\) | 13.0186 | 0.582211 | ||||||||
\(501\) | −3.74518 | −0.167322 | ||||||||
\(502\) | 31.3931 | 1.40114 | ||||||||
\(503\) | 39.4518 | 1.75907 | 0.879534 | − | 0.475836i | \(-0.157854\pi\) | ||||
0.879534 | + | 0.475836i | \(0.157854\pi\) | |||||||
\(504\) | −61.6162 | −2.74460 | ||||||||
\(505\) | 38.0969 | 1.69529 | ||||||||
\(506\) | 90.5091 | 4.02362 | ||||||||
\(507\) | 3.37813 | 0.150028 | ||||||||
\(508\) | 24.2824 | 1.07736 | ||||||||
\(509\) | −13.5318 | −0.599788 | −0.299894 | − | 0.953973i | \(-0.596951\pi\) | ||||
−0.299894 | + | 0.953973i | \(0.596951\pi\) | |||||||
\(510\) | 2.72619 | 0.120718 | ||||||||
\(511\) | −20.4863 | −0.906258 | ||||||||
\(512\) | 46.9934 | 2.07684 | ||||||||
\(513\) | −8.10685 | −0.357926 | ||||||||
\(514\) | 22.7211 | 1.00219 | ||||||||
\(515\) | −20.3924 | −0.898596 | ||||||||
\(516\) | 13.1536 | 0.579057 | ||||||||
\(517\) | 21.8243 | 0.959833 | ||||||||
\(518\) | −105.641 | −4.64162 | ||||||||
\(519\) | 1.89546 | 0.0832014 | ||||||||
\(520\) | −11.7770 | −0.516454 | ||||||||
\(521\) | 30.1322 | 1.32012 | 0.660058 | − | 0.751215i | \(-0.270532\pi\) | ||||
0.660058 | + | 0.751215i | \(0.270532\pi\) | |||||||
\(522\) | −5.79235 | −0.253524 | ||||||||
\(523\) | 20.9590 | 0.916472 | 0.458236 | − | 0.888831i | \(-0.348482\pi\) | ||||
0.458236 | + | 0.888831i | \(0.348482\pi\) | |||||||
\(524\) | 20.9094 | 0.913433 | ||||||||
\(525\) | 4.08247 | 0.178174 | ||||||||
\(526\) | 43.4146 | 1.89297 | ||||||||
\(527\) | −2.09843 | −0.0914092 | ||||||||
\(528\) | 8.58275 | 0.373516 | ||||||||
\(529\) | 14.5929 | 0.634473 | ||||||||
\(530\) | −7.46890 | −0.324428 | ||||||||
\(531\) | −3.58586 | −0.155613 | ||||||||
\(532\) | 81.1976 | 3.52036 | ||||||||
\(533\) | −5.62196 | −0.243514 | ||||||||
\(534\) | 4.90485 | 0.212254 | ||||||||
\(535\) | −21.6263 | −0.934985 | ||||||||
\(536\) | −33.8394 | −1.46164 | ||||||||
\(537\) | −5.06340 | −0.218502 | ||||||||
\(538\) | 30.0913 | 1.29733 | ||||||||
\(539\) | −44.2142 | −1.90444 | ||||||||
\(540\) | −20.2480 | −0.871334 | ||||||||
\(541\) | 11.7712 | 0.506082 | 0.253041 | − | 0.967456i | \(-0.418569\pi\) | ||||
0.253041 | + | 0.967456i | \(0.418569\pi\) | |||||||
\(542\) | −42.8245 | −1.83947 | ||||||||
\(543\) | −6.43944 | −0.276343 | ||||||||
\(544\) | 3.11361 | 0.133495 | ||||||||
\(545\) | 52.5969 | 2.25301 | ||||||||
\(546\) | 1.82227 | 0.0779858 | ||||||||
\(547\) | −38.8657 | −1.66178 | −0.830888 | − | 0.556440i | \(-0.812167\pi\) | ||||
−0.830888 | + | 0.556440i | \(0.812167\pi\) | |||||||
\(548\) | 89.0031 | 3.80202 | ||||||||
\(549\) | −5.70726 | −0.243580 | ||||||||
\(550\) | 58.6005 | 2.49873 | ||||||||
\(551\) | 4.01484 | 0.171038 | ||||||||
\(552\) | 9.17377 | 0.390461 | ||||||||
\(553\) | −38.2215 | −1.62534 | ||||||||
\(554\) | −66.4196 | −2.82190 | ||||||||
\(555\) | −9.01709 | −0.382754 | ||||||||
\(556\) | −53.3903 | −2.26425 | ||||||||
\(557\) | −9.30813 | −0.394398 | −0.197199 | − | 0.980363i | \(-0.563185\pi\) | ||||
−0.197199 | + | 0.980363i | \(0.563185\pi\) | |||||||
\(558\) | 11.3451 | 0.480275 | ||||||||
\(559\) | 8.19344 | 0.346545 | ||||||||
\(560\) | 61.0991 | 2.58191 | ||||||||
\(561\) | −2.16059 | −0.0912200 | ||||||||
\(562\) | −3.01587 | −0.127217 | ||||||||
\(563\) | −46.8765 | −1.97561 | −0.987804 | − | 0.155705i | \(-0.950235\pi\) | ||||
−0.987804 | + | 0.155705i | \(0.950235\pi\) | |||||||
\(564\) | 4.20564 | 0.177089 | ||||||||
\(565\) | 2.14436 | 0.0902137 | ||||||||
\(566\) | 22.8495 | 0.960435 | ||||||||
\(567\) | −31.7529 | −1.33350 | ||||||||
\(568\) | 73.3711 | 3.07858 | ||||||||
\(569\) | 4.50586 | 0.188895 | 0.0944477 | − | 0.995530i | \(-0.469891\pi\) | ||||
0.0944477 | + | 0.995530i | \(0.469891\pi\) | |||||||
\(570\) | 10.2160 | 0.427901 | ||||||||
\(571\) | 19.3350 | 0.809144 | 0.404572 | − | 0.914506i | \(-0.367421\pi\) | ||||
0.404572 | + | 0.914506i | \(0.367421\pi\) | |||||||
\(572\) | 17.7454 | 0.741971 | ||||||||
\(573\) | 0.584884 | 0.0244339 | ||||||||
\(574\) | 75.0580 | 3.13286 | ||||||||
\(575\) | 24.3397 | 1.01503 | ||||||||
\(576\) | 14.5612 | 0.606718 | ||||||||
\(577\) | 11.9494 | 0.497461 | 0.248731 | − | 0.968573i | \(-0.419987\pi\) | ||||
0.248731 | + | 0.968573i | \(0.419987\pi\) | |||||||
\(578\) | 37.8495 | 1.57433 | ||||||||
\(579\) | 2.53366 | 0.105295 | ||||||||
\(580\) | 10.0276 | 0.416374 | ||||||||
\(581\) | −50.7969 | −2.10741 | ||||||||
\(582\) | −8.66147 | −0.359030 | ||||||||
\(583\) | 5.91933 | 0.245154 | ||||||||
\(584\) | −29.8055 | −1.23336 | ||||||||
\(585\) | −6.22849 | −0.257516 | ||||||||
\(586\) | 33.0148 | 1.36383 | ||||||||
\(587\) | −44.6268 | −1.84195 | −0.920973 | − | 0.389626i | \(-0.872604\pi\) | ||||
−0.920973 | + | 0.389626i | \(0.872604\pi\) | |||||||
\(588\) | −8.52026 | −0.351370 | ||||||||
\(589\) | −7.86358 | −0.324013 | ||||||||
\(590\) | 9.15042 | 0.376717 | ||||||||
\(591\) | 4.46723 | 0.183757 | ||||||||
\(592\) | −59.7255 | −2.45470 | ||||||||
\(593\) | 33.5780 | 1.37888 | 0.689442 | − | 0.724341i | \(-0.257856\pi\) | ||||
0.689442 | + | 0.724341i | \(0.257856\pi\) | |||||||
\(594\) | 23.6539 | 0.970531 | ||||||||
\(595\) | −15.3808 | −0.630552 | ||||||||
\(596\) | 86.9684 | 3.56236 | ||||||||
\(597\) | 0.251973 | 0.0103126 | ||||||||
\(598\) | 10.8643 | 0.444276 | ||||||||
\(599\) | −7.11680 | −0.290784 | −0.145392 | − | 0.989374i | \(-0.546444\pi\) | ||||
−0.145392 | + | 0.989374i | \(0.546444\pi\) | |||||||
\(600\) | 5.93960 | 0.242483 | ||||||||
\(601\) | −8.78356 | −0.358289 | −0.179144 | − | 0.983823i | \(-0.557333\pi\) | ||||
−0.179144 | + | 0.983823i | \(0.557333\pi\) | |||||||
\(602\) | −109.389 | −4.45838 | ||||||||
\(603\) | −17.8967 | −0.728809 | ||||||||
\(604\) | −4.21918 | −0.171676 | ||||||||
\(605\) | −71.9941 | −2.92698 | ||||||||
\(606\) | −8.57634 | −0.348390 | ||||||||
\(607\) | 19.7804 | 0.802862 | 0.401431 | − | 0.915889i | \(-0.368513\pi\) | ||||
0.401431 | + | 0.915889i | \(0.368513\pi\) | |||||||
\(608\) | 11.6678 | 0.473193 | ||||||||
\(609\) | −0.816094 | −0.0330698 | ||||||||
\(610\) | 14.5638 | 0.589672 | ||||||||
\(611\) | 2.61970 | 0.105982 | ||||||||
\(612\) | 16.6725 | 0.673946 | ||||||||
\(613\) | −37.0598 | −1.49683 | −0.748415 | − | 0.663231i | \(-0.769185\pi\) | ||||
−0.748415 | + | 0.663231i | \(0.769185\pi\) | |||||||
\(614\) | 30.7110 | 1.23940 | ||||||||
\(615\) | 6.40663 | 0.258340 | ||||||||
\(616\) | −124.612 | −5.02074 | ||||||||
\(617\) | 0.629611 | 0.0253472 | 0.0126736 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126736 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(618\) | 4.59071 | 0.184666 | ||||||||
\(619\) | −13.4695 | −0.541385 | −0.270692 | − | 0.962666i | \(-0.587253\pi\) | ||||
−0.270692 | + | 0.962666i | \(0.587253\pi\) | |||||||
\(620\) | −19.6404 | −0.788776 | ||||||||
\(621\) | 9.82463 | 0.394249 | ||||||||
\(622\) | −44.3983 | −1.78021 | ||||||||
\(623\) | −27.6726 | −1.10868 | ||||||||
\(624\) | 1.03024 | 0.0412425 | ||||||||
\(625\) | −29.0899 | −1.16359 | ||||||||
\(626\) | −11.4760 | −0.458674 | ||||||||
\(627\) | −8.09649 | −0.323343 | ||||||||
\(628\) | 13.7944 | 0.550455 | ||||||||
\(629\) | 15.0350 | 0.599487 | ||||||||
\(630\) | 83.1557 | 3.31300 | ||||||||
\(631\) | −17.0508 | −0.678781 | −0.339390 | − | 0.940646i | \(-0.610221\pi\) | ||||
−0.339390 | + | 0.940646i | \(0.610221\pi\) | |||||||
\(632\) | −55.6085 | −2.21199 | ||||||||
\(633\) | −3.33905 | −0.132715 | ||||||||
\(634\) | 64.9005 | 2.57753 | ||||||||
\(635\) | −17.2367 | −0.684017 | ||||||||
\(636\) | 1.14068 | 0.0452309 | ||||||||
\(637\) | −5.30729 | −0.210283 | ||||||||
\(638\) | −11.7144 | −0.463776 | ||||||||
\(639\) | 38.8038 | 1.53505 | ||||||||
\(640\) | −50.9715 | −2.01482 | ||||||||
\(641\) | −25.8251 | −1.02003 | −0.510015 | − | 0.860165i | \(-0.670360\pi\) | ||||
−0.510015 | + | 0.860165i | \(0.670360\pi\) | |||||||
\(642\) | 4.86848 | 0.192144 | ||||||||
\(643\) | −9.98445 | −0.393748 | −0.196874 | − | 0.980429i | \(-0.563079\pi\) | ||||
−0.196874 | + | 0.980429i | \(0.563079\pi\) | |||||||
\(644\) | −98.4028 | −3.87761 | ||||||||
\(645\) | −9.33700 | −0.367644 | ||||||||
\(646\) | −17.0341 | −0.670197 | ||||||||
\(647\) | −28.3035 | −1.11273 | −0.556363 | − | 0.830939i | \(-0.687804\pi\) | ||||
−0.556363 | + | 0.830939i | \(0.687804\pi\) | |||||||
\(648\) | −46.1973 | −1.81480 | ||||||||
\(649\) | −7.25199 | −0.284666 | ||||||||
\(650\) | 7.03416 | 0.275903 | ||||||||
\(651\) | 1.59843 | 0.0626473 | ||||||||
\(652\) | −19.4898 | −0.763279 | ||||||||
\(653\) | 6.16685 | 0.241327 | 0.120664 | − | 0.992693i | \(-0.461498\pi\) | ||||
0.120664 | + | 0.992693i | \(0.461498\pi\) | |||||||
\(654\) | −11.8406 | −0.463003 | ||||||||
\(655\) | −14.8424 | −0.579940 | ||||||||
\(656\) | 42.4349 | 1.65680 | ||||||||
\(657\) | −15.7632 | −0.614982 | ||||||||
\(658\) | −34.9753 | −1.36348 | ||||||||
\(659\) | 7.71567 | 0.300560 | 0.150280 | − | 0.988643i | \(-0.451983\pi\) | ||||
0.150280 | + | 0.988643i | \(0.451983\pi\) | |||||||
\(660\) | −20.2221 | −0.787144 | ||||||||
\(661\) | 6.20728 | 0.241435 | 0.120718 | − | 0.992687i | \(-0.461480\pi\) | ||||
0.120718 | + | 0.992687i | \(0.461480\pi\) | |||||||
\(662\) | 86.9052 | 3.37767 | ||||||||
\(663\) | −0.259348 | −0.0100722 | ||||||||
\(664\) | −73.9044 | −2.86805 | ||||||||
\(665\) | −57.6375 | −2.23509 | ||||||||
\(666\) | −81.2862 | −3.14978 | ||||||||
\(667\) | −4.86555 | −0.188395 | ||||||||
\(668\) | 58.4475 | 2.26140 | ||||||||
\(669\) | 7.14989 | 0.276431 | ||||||||
\(670\) | 45.6688 | 1.76434 | ||||||||
\(671\) | −11.5423 | −0.445585 | ||||||||
\(672\) | −2.37171 | −0.0914909 | ||||||||
\(673\) | 1.45038 | 0.0559082 | 0.0279541 | − | 0.999609i | \(-0.491101\pi\) | ||||
0.0279541 | + | 0.999609i | \(0.491101\pi\) | |||||||
\(674\) | 48.4989 | 1.86811 | ||||||||
\(675\) | 6.36100 | 0.244835 | ||||||||
\(676\) | −52.7193 | −2.02767 | ||||||||
\(677\) | 7.96736 | 0.306210 | 0.153105 | − | 0.988210i | \(-0.451073\pi\) | ||||
0.153105 | + | 0.988210i | \(0.451073\pi\) | |||||||
\(678\) | −0.482735 | −0.0185393 | ||||||||
\(679\) | 48.8671 | 1.87535 | ||||||||
\(680\) | −22.3776 | −0.858141 | ||||||||
\(681\) | 7.44779 | 0.285400 | ||||||||
\(682\) | 22.9441 | 0.878574 | ||||||||
\(683\) | −12.7448 | −0.487667 | −0.243833 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243833 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(684\) | 62.4779 | 2.38890 | ||||||||
\(685\) | −63.1781 | −2.41391 | ||||||||
\(686\) | 4.45343 | 0.170033 | ||||||||
\(687\) | −4.72821 | −0.180392 | ||||||||
\(688\) | −61.8445 | −2.35780 | ||||||||
\(689\) | 0.710532 | 0.0270691 | ||||||||
\(690\) | −12.3807 | −0.471325 | ||||||||
\(691\) | 10.4885 | 0.399002 | 0.199501 | − | 0.979898i | \(-0.436068\pi\) | ||||
0.199501 | + | 0.979898i | \(0.436068\pi\) | |||||||
\(692\) | −29.5806 | −1.12449 | ||||||||
\(693\) | −65.9034 | −2.50346 | ||||||||
\(694\) | 4.96346 | 0.188411 | ||||||||
\(695\) | 37.8987 | 1.43758 | ||||||||
\(696\) | −1.18734 | −0.0450059 | ||||||||
\(697\) | −10.6824 | −0.404624 | ||||||||
\(698\) | 71.0689 | 2.69000 | ||||||||
\(699\) | −4.22932 | −0.159967 | ||||||||
\(700\) | −63.7113 | −2.40806 | ||||||||
\(701\) | −8.51378 | −0.321561 | −0.160781 | − | 0.986990i | \(-0.551401\pi\) | ||||
−0.160781 | + | 0.986990i | \(0.551401\pi\) | |||||||
\(702\) | 2.83932 | 0.107163 | ||||||||
\(703\) | 56.3417 | 2.12497 | ||||||||
\(704\) | 29.4484 | 1.10988 | ||||||||
\(705\) | −2.98534 | −0.112434 | ||||||||
\(706\) | 30.8624 | 1.16152 | ||||||||
\(707\) | 48.3867 | 1.81977 | ||||||||
\(708\) | −1.39749 | −0.0525208 | ||||||||
\(709\) | 12.5248 | 0.470378 | 0.235189 | − | 0.971950i | \(-0.424429\pi\) | ||||
0.235189 | + | 0.971950i | \(0.424429\pi\) | |||||||
\(710\) | −99.0197 | −3.71614 | ||||||||
\(711\) | −29.4097 | −1.10295 | ||||||||
\(712\) | −40.2609 | −1.50884 | ||||||||
\(713\) | 9.52981 | 0.356894 | ||||||||
\(714\) | 3.46251 | 0.129581 | ||||||||
\(715\) | −12.5964 | −0.471078 | ||||||||
\(716\) | 79.0197 | 2.95310 | ||||||||
\(717\) | −0.833589 | −0.0311310 | ||||||||
\(718\) | −46.5501 | −1.73723 | ||||||||
\(719\) | 15.4011 | 0.574366 | 0.287183 | − | 0.957876i | \(-0.407281\pi\) | ||||
0.287183 | + | 0.957876i | \(0.407281\pi\) | |||||||
\(720\) | 47.0130 | 1.75207 | ||||||||
\(721\) | −25.9003 | −0.964577 | ||||||||
\(722\) | −16.4501 | −0.612210 | ||||||||
\(723\) | 3.73892 | 0.139052 | ||||||||
\(724\) | 100.494 | 3.73484 | ||||||||
\(725\) | −3.15022 | −0.116996 | ||||||||
\(726\) | 16.2072 | 0.601507 | ||||||||
\(727\) | 28.9939 | 1.07532 | 0.537662 | − | 0.843161i | \(-0.319308\pi\) | ||||
0.537662 | + | 0.843161i | \(0.319308\pi\) | |||||||
\(728\) | −14.9579 | −0.554375 | ||||||||
\(729\) | −23.1328 | −0.856769 | ||||||||
\(730\) | 40.2247 | 1.48878 | ||||||||
\(731\) | 15.5685 | 0.575821 | ||||||||
\(732\) | −2.22424 | −0.0822104 | ||||||||
\(733\) | 12.5287 | 0.462758 | 0.231379 | − | 0.972864i | \(-0.425676\pi\) | ||||
0.231379 | + | 0.972864i | \(0.425676\pi\) | |||||||
\(734\) | −51.5990 | −1.90455 | ||||||||
\(735\) | 6.04804 | 0.223085 | ||||||||
\(736\) | −14.1401 | −0.521213 | ||||||||
\(737\) | −36.1940 | −1.33322 | ||||||||
\(738\) | 57.7537 | 2.12594 | ||||||||
\(739\) | 34.7636 | 1.27880 | 0.639400 | − | 0.768874i | \(-0.279183\pi\) | ||||
0.639400 | + | 0.768874i | \(0.279183\pi\) | |||||||
\(740\) | 140.721 | 5.17301 | ||||||||
\(741\) | −0.971869 | −0.0357025 | ||||||||
\(742\) | −9.48621 | −0.348250 | ||||||||
\(743\) | −17.8328 | −0.654223 | −0.327112 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327112 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(744\) | 2.32555 | 0.0852589 | ||||||||
\(745\) | −61.7338 | −2.26175 | ||||||||
\(746\) | −77.6199 | −2.84187 | ||||||||
\(747\) | −39.0859 | −1.43008 | ||||||||
\(748\) | 33.7182 | 1.23286 | ||||||||
\(749\) | −27.4674 | −1.00364 | ||||||||
\(750\) | 2.08036 | 0.0759641 | ||||||||
\(751\) | −32.8177 | −1.19753 | −0.598767 | − | 0.800923i | \(-0.704343\pi\) | ||||
−0.598767 | + | 0.800923i | \(0.704343\pi\) | |||||||
\(752\) | −19.7737 | −0.721071 | ||||||||
\(753\) | 3.40332 | 0.124024 | ||||||||
\(754\) | −1.40614 | −0.0512087 | ||||||||
\(755\) | 2.99495 | 0.108997 | ||||||||
\(756\) | −25.7169 | −0.935313 | ||||||||
\(757\) | 19.2850 | 0.700925 | 0.350463 | − | 0.936577i | \(-0.386024\pi\) | ||||
0.350463 | + | 0.936577i | \(0.386024\pi\) | |||||||
\(758\) | −63.0047 | −2.28843 | ||||||||
\(759\) | 9.81207 | 0.356156 | ||||||||
\(760\) | −83.8568 | −3.04181 | ||||||||
\(761\) | −9.65993 | −0.350172 | −0.175086 | − | 0.984553i | \(-0.556020\pi\) | ||||
−0.175086 | + | 0.984553i | \(0.556020\pi\) | |||||||
\(762\) | 3.88030 | 0.140569 | ||||||||
\(763\) | 66.8031 | 2.41844 | ||||||||
\(764\) | −9.12774 | −0.330230 | ||||||||
\(765\) | −11.8348 | −0.427890 | ||||||||
\(766\) | −82.6893 | −2.98769 | ||||||||
\(767\) | −0.870499 | −0.0314319 | ||||||||
\(768\) | 8.78463 | 0.316988 | ||||||||
\(769\) | 5.82885 | 0.210194 | 0.105097 | − | 0.994462i | \(-0.466485\pi\) | ||||
0.105097 | + | 0.994462i | \(0.466485\pi\) | |||||||
\(770\) | 168.173 | 6.06052 | ||||||||
\(771\) | 2.46319 | 0.0887097 | ||||||||
\(772\) | −39.5405 | −1.42309 | ||||||||
\(773\) | 8.60045 | 0.309337 | 0.154668 | − | 0.987966i | \(-0.450569\pi\) | ||||
0.154668 | + | 0.987966i | \(0.450569\pi\) | |||||||
\(774\) | −84.1701 | −3.02543 | ||||||||
\(775\) | 6.17012 | 0.221637 | ||||||||
\(776\) | 71.0967 | 2.55222 | ||||||||
\(777\) | −11.4526 | −0.410858 | ||||||||
\(778\) | 6.96303 | 0.249637 | ||||||||
\(779\) | −40.0307 | −1.43425 | ||||||||
\(780\) | −2.42738 | −0.0869140 | ||||||||
\(781\) | 78.4761 | 2.80810 | ||||||||
\(782\) | 20.6435 | 0.738210 | ||||||||
\(783\) | −1.27158 | −0.0454424 | ||||||||
\(784\) | 40.0598 | 1.43071 | ||||||||
\(785\) | −9.79181 | −0.349485 | ||||||||
\(786\) | 3.34130 | 0.119180 | ||||||||
\(787\) | 21.7986 | 0.777037 | 0.388518 | − | 0.921441i | \(-0.372987\pi\) | ||||
0.388518 | + | 0.921441i | \(0.372987\pi\) | |||||||
\(788\) | −69.7159 | −2.48352 | ||||||||
\(789\) | 4.70657 | 0.167558 | ||||||||
\(790\) | 75.0478 | 2.67008 | ||||||||
\(791\) | 2.72354 | 0.0968378 | ||||||||
\(792\) | −95.8829 | −3.40705 | ||||||||
\(793\) | −1.38549 | −0.0492001 | ||||||||
\(794\) | 62.5821 | 2.22095 | ||||||||
\(795\) | −0.809702 | −0.0287172 | ||||||||
\(796\) | −3.93230 | −0.139377 | ||||||||
\(797\) | −45.0899 | −1.59717 | −0.798584 | − | 0.601883i | \(-0.794417\pi\) | ||||
−0.798584 | + | 0.601883i | \(0.794417\pi\) | |||||||
\(798\) | 12.9753 | 0.459320 | ||||||||
\(799\) | 4.97774 | 0.176100 | ||||||||
\(800\) | −9.15510 | −0.323682 | ||||||||
\(801\) | −21.2928 | −0.752344 | ||||||||
\(802\) | −46.5152 | −1.64251 | ||||||||
\(803\) | −31.8793 | −1.12500 | ||||||||
\(804\) | −6.97472 | −0.245980 | ||||||||
\(805\) | 69.8504 | 2.46190 | ||||||||
\(806\) | 2.75411 | 0.0970095 | ||||||||
\(807\) | 3.26219 | 0.114835 | ||||||||
\(808\) | 70.3979 | 2.47659 | ||||||||
\(809\) | 10.5838 | 0.372107 | 0.186054 | − | 0.982540i | \(-0.440430\pi\) | ||||
0.186054 | + | 0.982540i | \(0.440430\pi\) | |||||||
\(810\) | 62.3467 | 2.19064 | ||||||||
\(811\) | 49.0823 | 1.72351 | 0.861756 | − | 0.507323i | \(-0.169365\pi\) | ||||
0.861756 | + | 0.507323i | \(0.169365\pi\) | |||||||
\(812\) | 12.7360 | 0.446946 | ||||||||
\(813\) | −4.64260 | −0.162823 | ||||||||
\(814\) | −164.392 | −5.76193 | ||||||||
\(815\) | 13.8347 | 0.484607 | ||||||||
\(816\) | 1.95757 | 0.0685287 | ||||||||
\(817\) | 58.3406 | 2.04108 | ||||||||
\(818\) | −39.9567 | −1.39705 | ||||||||
\(819\) | −7.91077 | −0.276425 | ||||||||
\(820\) | −99.9821 | −3.49153 | ||||||||
\(821\) | −45.1254 | −1.57489 | −0.787443 | − | 0.616387i | \(-0.788596\pi\) | ||||
−0.787443 | + | 0.616387i | \(0.788596\pi\) | |||||||
\(822\) | 14.2226 | 0.496070 | ||||||||
\(823\) | −24.2784 | −0.846291 | −0.423146 | − | 0.906062i | \(-0.639074\pi\) | ||||
−0.423146 | + | 0.906062i | \(0.639074\pi\) | |||||||
\(824\) | −37.6823 | −1.31273 | ||||||||
\(825\) | 6.35287 | 0.221178 | ||||||||
\(826\) | 11.6219 | 0.404378 | ||||||||
\(827\) | −40.3463 | −1.40298 | −0.701489 | − | 0.712680i | \(-0.747481\pi\) | ||||
−0.701489 | + | 0.712680i | \(0.747481\pi\) | |||||||
\(828\) | −75.7164 | −2.63133 | ||||||||
\(829\) | 55.2221 | 1.91794 | 0.958971 | − | 0.283504i | \(-0.0914969\pi\) | ||||
0.958971 | + | 0.283504i | \(0.0914969\pi\) | |||||||
\(830\) | 99.7395 | 3.46201 | ||||||||
\(831\) | −7.20054 | −0.249784 | ||||||||
\(832\) | 3.53486 | 0.122549 | ||||||||
\(833\) | −10.0845 | −0.349406 | ||||||||
\(834\) | −8.53171 | −0.295429 | ||||||||
\(835\) | −41.4885 | −1.43577 | ||||||||
\(836\) | 126.354 | 4.37005 | ||||||||
\(837\) | 2.49055 | 0.0860859 | ||||||||
\(838\) | −80.3833 | −2.77679 | ||||||||
\(839\) | −18.1392 | −0.626233 | −0.313117 | − | 0.949715i | \(-0.601373\pi\) | ||||
−0.313117 | + | 0.949715i | \(0.601373\pi\) | |||||||
\(840\) | 17.0455 | 0.588127 | ||||||||
\(841\) | −28.3703 | −0.978285 | ||||||||
\(842\) | 9.75607 | 0.336217 | ||||||||
\(843\) | −0.326950 | −0.0112608 | ||||||||
\(844\) | 52.1094 | 1.79368 | ||||||||
\(845\) | 37.4224 | 1.28737 | ||||||||
\(846\) | −26.9119 | −0.925249 | ||||||||
\(847\) | −91.4394 | −3.14189 | ||||||||
\(848\) | −5.36314 | −0.184171 | ||||||||
\(849\) | 2.47711 | 0.0850140 | ||||||||
\(850\) | 13.3657 | 0.458440 | ||||||||
\(851\) | −68.2801 | −2.34061 | ||||||||
\(852\) | 15.1227 | 0.518094 | ||||||||
\(853\) | −1.67034 | −0.0571914 | −0.0285957 | − | 0.999591i | \(-0.509104\pi\) | ||||
−0.0285957 | + | 0.999591i | \(0.509104\pi\) | |||||||
\(854\) | 18.4974 | 0.632970 | ||||||||
\(855\) | −44.3494 | −1.51672 | ||||||||
\(856\) | −39.9624 | −1.36589 | ||||||||
\(857\) | 9.03369 | 0.308585 | 0.154292 | − | 0.988025i | \(-0.450690\pi\) | ||||
0.154292 | + | 0.988025i | \(0.450690\pi\) | |||||||
\(858\) | 2.83569 | 0.0968087 | ||||||||
\(859\) | −36.1729 | −1.23420 | −0.617101 | − | 0.786884i | \(-0.711693\pi\) | ||||
−0.617101 | + | 0.786884i | \(0.711693\pi\) | |||||||
\(860\) | 145.714 | 4.96880 | ||||||||
\(861\) | 8.13703 | 0.277309 | ||||||||
\(862\) | −47.0147 | −1.60133 | ||||||||
\(863\) | −40.4673 | −1.37752 | −0.688761 | − | 0.724989i | \(-0.741845\pi\) | ||||
−0.688761 | + | 0.724989i | \(0.741845\pi\) | |||||||
\(864\) | −3.69542 | −0.125721 | ||||||||
\(865\) | 20.9976 | 0.713939 | ||||||||
\(866\) | 67.4757 | 2.29292 | ||||||||
\(867\) | 4.10325 | 0.139354 | ||||||||
\(868\) | −24.9451 | −0.846693 | ||||||||
\(869\) | −59.4777 | −2.01764 | ||||||||
\(870\) | 1.60240 | 0.0543264 | ||||||||
\(871\) | −4.34457 | −0.147210 | ||||||||
\(872\) | 97.1919 | 3.29133 | ||||||||
\(873\) | 37.6010 | 1.27260 | ||||||||
\(874\) | 77.3585 | 2.61669 | ||||||||
\(875\) | −11.7372 | −0.396789 | ||||||||
\(876\) | −6.14327 | −0.207562 | ||||||||
\(877\) | −38.4110 | −1.29705 | −0.648524 | − | 0.761194i | \(-0.724614\pi\) | ||||
−0.648524 | + | 0.761194i | \(0.724614\pi\) | |||||||
\(878\) | −47.2593 | −1.59492 | ||||||||
\(879\) | 3.57913 | 0.120721 | ||||||||
\(880\) | 95.0783 | 3.20509 | ||||||||
\(881\) | −7.06338 | −0.237971 | −0.118986 | − | 0.992896i | \(-0.537964\pi\) | ||||
−0.118986 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(882\) | 54.5212 | 1.83582 | ||||||||
\(883\) | 7.98840 | 0.268831 | 0.134416 | − | 0.990925i | \(-0.457084\pi\) | ||||
0.134416 | + | 0.990925i | \(0.457084\pi\) | |||||||
\(884\) | 4.04740 | 0.136129 | ||||||||
\(885\) | 0.991995 | 0.0333456 | ||||||||
\(886\) | 85.9509 | 2.88758 | ||||||||
\(887\) | 29.8603 | 1.00261 | 0.501305 | − | 0.865270i | \(-0.332853\pi\) | ||||
0.501305 | + | 0.865270i | \(0.332853\pi\) | |||||||
\(888\) | −16.6623 | −0.559152 | ||||||||
\(889\) | −21.8922 | −0.734242 | ||||||||
\(890\) | 54.3351 | 1.82132 | ||||||||
\(891\) | −49.4117 | −1.65535 | ||||||||
\(892\) | −111.582 | −3.73603 | ||||||||
\(893\) | 18.6534 | 0.624211 | ||||||||
\(894\) | 13.8974 | 0.464800 | ||||||||
\(895\) | −56.0915 | −1.87493 | ||||||||
\(896\) | −64.7386 | −2.16277 | ||||||||
\(897\) | 1.17780 | 0.0393256 | ||||||||
\(898\) | −13.6646 | −0.455994 | ||||||||
\(899\) | −1.23342 | −0.0411368 | ||||||||
\(900\) | −49.0229 | −1.63410 | ||||||||
\(901\) | 1.35009 | 0.0449781 | ||||||||
\(902\) | 116.800 | 3.88902 | ||||||||
\(903\) | −11.8589 | −0.394639 | ||||||||
\(904\) | 3.96248 | 0.131790 | ||||||||
\(905\) | −71.3351 | −2.37126 | ||||||||
\(906\) | −0.674220 | −0.0223995 | ||||||||
\(907\) | 30.3325 | 1.00717 | 0.503587 | − | 0.863944i | \(-0.332013\pi\) | ||||
0.503587 | + | 0.863944i | \(0.332013\pi\) | |||||||
\(908\) | −116.231 | −3.85725 | ||||||||
\(909\) | 37.2314 | 1.23489 | ||||||||
\(910\) | 20.1868 | 0.669184 | ||||||||
\(911\) | −20.5698 | −0.681507 | −0.340753 | − | 0.940153i | \(-0.610682\pi\) | ||||
−0.340753 | + | 0.940153i | \(0.610682\pi\) | |||||||
\(912\) | 7.33572 | 0.242910 | ||||||||
\(913\) | −79.0466 | −2.61606 | ||||||||
\(914\) | −8.25669 | −0.273107 | ||||||||
\(915\) | 1.57886 | 0.0521956 | ||||||||
\(916\) | 73.7886 | 2.43804 | ||||||||
\(917\) | −18.8513 | −0.622523 | ||||||||
\(918\) | 5.39503 | 0.178062 | ||||||||
\(919\) | −10.0515 | −0.331569 | −0.165784 | − | 0.986162i | \(-0.553016\pi\) | ||||
−0.165784 | + | 0.986162i | \(0.553016\pi\) | |||||||
\(920\) | 101.625 | 3.35049 | ||||||||
\(921\) | 3.32937 | 0.109707 | ||||||||
\(922\) | −9.45804 | −0.311484 | ||||||||
\(923\) | 9.41995 | 0.310062 | ||||||||
\(924\) | −25.6840 | −0.844941 | ||||||||
\(925\) | −44.2082 | −1.45356 | ||||||||
\(926\) | 50.2467 | 1.65121 | ||||||||
\(927\) | −19.9291 | −0.654557 | ||||||||
\(928\) | 1.83012 | 0.0600767 | ||||||||
\(929\) | 38.7601 | 1.27168 | 0.635839 | − | 0.771822i | \(-0.280654\pi\) | ||||
0.635839 | + | 0.771822i | \(0.280654\pi\) | |||||||
\(930\) | −3.13851 | −0.102916 | ||||||||
\(931\) | −37.7901 | −1.23852 | ||||||||
\(932\) | 66.0029 | 2.16200 | ||||||||
\(933\) | −4.81321 | −0.157577 | ||||||||
\(934\) | −68.2000 | −2.23157 | ||||||||
\(935\) | −23.9346 | −0.782745 | ||||||||
\(936\) | −11.5094 | −0.376196 | ||||||||
\(937\) | 28.0589 | 0.916645 | 0.458323 | − | 0.888786i | \(-0.348450\pi\) | ||||
0.458323 | + | 0.888786i | \(0.348450\pi\) | |||||||
\(938\) | 58.0038 | 1.89389 | ||||||||
\(939\) | −1.24411 | −0.0406001 | ||||||||
\(940\) | 46.5893 | 1.51958 | ||||||||
\(941\) | −0.0441714 | −0.00143995 | −0.000719974 | − | 1.00000i | \(-0.500229\pi\) | ||||
−0.000719974 | 1.00000i | \(0.500229\pi\) | ||||||||
\(942\) | 2.20432 | 0.0718207 | ||||||||
\(943\) | 48.5129 | 1.57980 | ||||||||
\(944\) | 6.57058 | 0.213854 | ||||||||
\(945\) | 18.2549 | 0.593832 | ||||||||
\(946\) | −170.224 | −5.53447 | ||||||||
\(947\) | 28.2800 | 0.918975 | 0.459488 | − | 0.888184i | \(-0.348033\pi\) | ||||
0.459488 | + | 0.888184i | \(0.348033\pi\) | |||||||
\(948\) | −11.4616 | −0.372255 | ||||||||
\(949\) | −3.82666 | −0.124219 | ||||||||
\(950\) | 50.0861 | 1.62501 | ||||||||
\(951\) | 7.03585 | 0.228153 | ||||||||
\(952\) | −28.4217 | −0.921151 | ||||||||
\(953\) | −26.8106 | −0.868481 | −0.434240 | − | 0.900797i | \(-0.642983\pi\) | ||||
−0.434240 | + | 0.900797i | \(0.642983\pi\) | |||||||
\(954\) | −7.29921 | −0.236321 | ||||||||
\(955\) | 6.47925 | 0.209664 | ||||||||
\(956\) | 13.0090 | 0.420742 | ||||||||
\(957\) | −1.26995 | −0.0410517 | ||||||||
\(958\) | −76.7520 | −2.47975 | ||||||||
\(959\) | −80.2422 | −2.59116 | ||||||||
\(960\) | −4.02823 | −0.130010 | ||||||||
\(961\) | −28.5842 | −0.922071 | ||||||||
\(962\) | −19.7329 | −0.636215 | ||||||||
\(963\) | −21.1349 | −0.681064 | ||||||||
\(964\) | −58.3498 | −1.87932 | ||||||||
\(965\) | 28.0675 | 0.903525 | ||||||||
\(966\) | −15.7246 | −0.505932 | ||||||||
\(967\) | −28.5787 | −0.919028 | −0.459514 | − | 0.888171i | \(-0.651976\pi\) | ||||
−0.459514 | + | 0.888171i | \(0.651976\pi\) | |||||||
\(968\) | −133.035 | −4.27591 | ||||||||
\(969\) | −1.84666 | −0.0593234 | ||||||||
\(970\) | −95.9503 | −3.08078 | ||||||||
\(971\) | −6.40099 | −0.205417 | −0.102709 | − | 0.994711i | \(-0.532751\pi\) | ||||
−0.102709 | + | 0.994711i | \(0.532751\pi\) | |||||||
\(972\) | −29.8039 | −0.955962 | ||||||||
\(973\) | 48.1349 | 1.54313 | ||||||||
\(974\) | 8.21337 | 0.263173 | ||||||||
\(975\) | 0.762572 | 0.0244219 | ||||||||
\(976\) | 10.4577 | 0.334744 | ||||||||
\(977\) | 15.9966 | 0.511775 | 0.255887 | − | 0.966707i | \(-0.417632\pi\) | ||||
0.255887 | + | 0.966707i | \(0.417632\pi\) | |||||||
\(978\) | −3.11444 | −0.0995889 | ||||||||
\(979\) | −43.0622 | −1.37627 | ||||||||
\(980\) | −94.3860 | −3.01505 | ||||||||
\(981\) | 51.4020 | 1.64114 | ||||||||
\(982\) | 19.5050 | 0.622429 | ||||||||
\(983\) | 46.7269 | 1.49036 | 0.745178 | − | 0.666866i | \(-0.232364\pi\) | ||||
0.745178 | + | 0.666866i | \(0.232364\pi\) | |||||||
\(984\) | 11.8386 | 0.377400 | ||||||||
\(985\) | 49.4872 | 1.57679 | ||||||||
\(986\) | −2.67183 | −0.0850885 | ||||||||
\(987\) | −3.79166 | −0.120690 | ||||||||
\(988\) | 15.1670 | 0.482528 | ||||||||
\(989\) | −70.7026 | −2.24821 | ||||||||
\(990\) | 129.401 | 4.11264 | ||||||||
\(991\) | −11.5653 | −0.367383 | −0.183691 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183691 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(992\) | −3.58453 | −0.113809 | ||||||||
\(993\) | 9.42138 | 0.298978 | ||||||||
\(994\) | −125.764 | −3.98901 | ||||||||
\(995\) | 2.79131 | 0.0884905 | ||||||||
\(996\) | −15.2326 | −0.482664 | ||||||||
\(997\) | 8.85376 | 0.280401 | 0.140201 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140201 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(998\) | −65.6940 | −2.07951 | ||||||||
\(999\) | −17.8445 | −0.564575 |
(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 | 8003.2.a.b.1.11 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.b.1.11 | ✓ | 153 | 1.1 | even | 1 | trivial |