Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.89955 | −1.67406 | −0.837028 | − | 0.547160i | \(-0.815709\pi\) | ||||
−0.837028 | + | 0.547160i | \(0.815709\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.35107 | −1.49865 | −0.749323 | − | 0.662205i | \(-0.769621\pi\) | ||||
−0.749323 | + | 0.662205i | \(0.769621\pi\) | |||||||
\(6\) | 2.89955 | 1.18374 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.40739 | 1.80246 | ||||||||
\(10\) | 3.35107 | 1.05970 | ||||||||
\(11\) | 5.34965 | 1.61298 | 0.806489 | − | 0.591249i | \(-0.201365\pi\) | ||||
0.806489 | + | 0.591249i | \(0.201365\pi\) | |||||||
\(12\) | −2.89955 | −0.837028 | ||||||||
\(13\) | 2.77854 | 0.770630 | 0.385315 | − | 0.922785i | \(-0.374093\pi\) | ||||
0.385315 | + | 0.922785i | \(0.374093\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 9.71661 | 2.50882 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.18328 | −0.286988 | −0.143494 | − | 0.989651i | \(-0.545834\pi\) | ||||
−0.143494 | + | 0.989651i | \(0.545834\pi\) | |||||||
\(18\) | −5.40739 | −1.27453 | ||||||||
\(19\) | −8.21463 | −1.88456 | −0.942282 | − | 0.334819i | \(-0.891325\pi\) | ||||
−0.942282 | + | 0.334819i | \(0.891325\pi\) | |||||||
\(20\) | −3.35107 | −0.749323 | ||||||||
\(21\) | 2.89955 | 0.632734 | ||||||||
\(22\) | −5.34965 | −1.14055 | ||||||||
\(23\) | 0.111080 | 0.0231618 | 0.0115809 | − | 0.999933i | \(-0.496314\pi\) | ||||
0.0115809 | + | 0.999933i | \(0.496314\pi\) | |||||||
\(24\) | 2.89955 | 0.591868 | ||||||||
\(25\) | 6.22970 | 1.24594 | ||||||||
\(26\) | −2.77854 | −0.544917 | ||||||||
\(27\) | −6.98035 | −1.34337 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −7.47496 | −1.38806 | −0.694032 | − | 0.719944i | \(-0.744168\pi\) | ||||
−0.694032 | + | 0.719944i | \(0.744168\pi\) | |||||||
\(30\) | −9.71661 | −1.77400 | ||||||||
\(31\) | −3.87355 | −0.695710 | −0.347855 | − | 0.937548i | \(-0.613090\pi\) | ||||
−0.347855 | + | 0.937548i | \(0.613090\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −15.5116 | −2.70022 | ||||||||
\(34\) | 1.18328 | 0.202931 | ||||||||
\(35\) | 3.35107 | 0.566435 | ||||||||
\(36\) | 5.40739 | 0.901232 | ||||||||
\(37\) | 1.22307 | 0.201072 | 0.100536 | − | 0.994933i | \(-0.467944\pi\) | ||||
0.100536 | + | 0.994933i | \(0.467944\pi\) | |||||||
\(38\) | 8.21463 | 1.33259 | ||||||||
\(39\) | −8.05653 | −1.29008 | ||||||||
\(40\) | 3.35107 | 0.529851 | ||||||||
\(41\) | −4.76950 | −0.744871 | −0.372435 | − | 0.928058i | \(-0.621477\pi\) | ||||
−0.372435 | + | 0.928058i | \(0.621477\pi\) | |||||||
\(42\) | −2.89955 | −0.447410 | ||||||||
\(43\) | 10.9734 | 1.67343 | 0.836716 | − | 0.547638i | \(-0.184473\pi\) | ||||
0.836716 | + | 0.547638i | \(0.184473\pi\) | |||||||
\(44\) | 5.34965 | 0.806489 | ||||||||
\(45\) | −18.1206 | −2.70126 | ||||||||
\(46\) | −0.111080 | −0.0163778 | ||||||||
\(47\) | −3.72068 | −0.542716 | −0.271358 | − | 0.962478i | \(-0.587473\pi\) | ||||
−0.271358 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(48\) | −2.89955 | −0.418514 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.22970 | −0.881013 | ||||||||
\(51\) | 3.43098 | 0.480434 | ||||||||
\(52\) | 2.77854 | 0.385315 | ||||||||
\(53\) | 3.45969 | 0.475225 | 0.237612 | − | 0.971360i | \(-0.423635\pi\) | ||||
0.237612 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(54\) | 6.98035 | 0.949905 | ||||||||
\(55\) | −17.9271 | −2.41728 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 23.8187 | 3.15487 | ||||||||
\(58\) | 7.47496 | 0.981510 | ||||||||
\(59\) | 7.41617 | 0.965503 | 0.482751 | − | 0.875758i | \(-0.339638\pi\) | ||||
0.482751 | + | 0.875758i | \(0.339638\pi\) | |||||||
\(60\) | 9.71661 | 1.25441 | ||||||||
\(61\) | −0.674429 | −0.0863518 | −0.0431759 | − | 0.999067i | \(-0.513748\pi\) | ||||
−0.0431759 | + | 0.999067i | \(0.513748\pi\) | |||||||
\(62\) | 3.87355 | 0.491941 | ||||||||
\(63\) | −5.40739 | −0.681267 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.31111 | −1.15490 | ||||||||
\(66\) | 15.5116 | 1.90934 | ||||||||
\(67\) | −8.63322 | −1.05472 | −0.527358 | − | 0.849643i | \(-0.676817\pi\) | ||||
−0.527358 | + | 0.849643i | \(0.676817\pi\) | |||||||
\(68\) | −1.18328 | −0.143494 | ||||||||
\(69\) | −0.322082 | −0.0387741 | ||||||||
\(70\) | −3.35107 | −0.400530 | ||||||||
\(71\) | −4.81812 | −0.571806 | −0.285903 | − | 0.958259i | \(-0.592293\pi\) | ||||
−0.285903 | + | 0.958259i | \(0.592293\pi\) | |||||||
\(72\) | −5.40739 | −0.637267 | ||||||||
\(73\) | 3.52593 | 0.412679 | 0.206340 | − | 0.978480i | \(-0.433845\pi\) | ||||
0.206340 | + | 0.978480i | \(0.433845\pi\) | |||||||
\(74\) | −1.22307 | −0.142179 | ||||||||
\(75\) | −18.0633 | −2.08577 | ||||||||
\(76\) | −8.21463 | −0.942282 | ||||||||
\(77\) | −5.34965 | −0.609649 | ||||||||
\(78\) | 8.05653 | 0.912222 | ||||||||
\(79\) | −1.08915 | −0.122538 | −0.0612692 | − | 0.998121i | \(-0.519515\pi\) | ||||
−0.0612692 | + | 0.998121i | \(0.519515\pi\) | |||||||
\(80\) | −3.35107 | −0.374662 | ||||||||
\(81\) | 4.01770 | 0.446411 | ||||||||
\(82\) | 4.76950 | 0.526703 | ||||||||
\(83\) | 0.907057 | 0.0995624 | 0.0497812 | − | 0.998760i | \(-0.484148\pi\) | ||||
0.0497812 | + | 0.998760i | \(0.484148\pi\) | |||||||
\(84\) | 2.89955 | 0.316367 | ||||||||
\(85\) | 3.96526 | 0.430093 | ||||||||
\(86\) | −10.9734 | −1.18329 | ||||||||
\(87\) | 21.6740 | 2.32370 | ||||||||
\(88\) | −5.34965 | −0.570274 | ||||||||
\(89\) | 0.159247 | 0.0168801 | 0.00844006 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844006 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(90\) | 18.1206 | 1.91008 | ||||||||
\(91\) | −2.77854 | −0.291271 | ||||||||
\(92\) | 0.111080 | 0.0115809 | ||||||||
\(93\) | 11.2316 | 1.16466 | ||||||||
\(94\) | 3.72068 | 0.383758 | ||||||||
\(95\) | 27.5278 | 2.82430 | ||||||||
\(96\) | 2.89955 | 0.295934 | ||||||||
\(97\) | 14.5975 | 1.48215 | 0.741076 | − | 0.671421i | \(-0.234316\pi\) | ||||
0.741076 | + | 0.671421i | \(0.234316\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 28.9276 | 2.90734 | ||||||||
\(100\) | 6.22970 | 0.622970 | ||||||||
\(101\) | 7.37963 | 0.734300 | 0.367150 | − | 0.930162i | \(-0.380334\pi\) | ||||
0.367150 | + | 0.930162i | \(0.380334\pi\) | |||||||
\(102\) | −3.43098 | −0.339718 | ||||||||
\(103\) | 5.22762 | 0.515093 | 0.257546 | − | 0.966266i | \(-0.417086\pi\) | ||||
0.257546 | + | 0.966266i | \(0.417086\pi\) | |||||||
\(104\) | −2.77854 | −0.272459 | ||||||||
\(105\) | −9.71661 | −0.948244 | ||||||||
\(106\) | −3.45969 | −0.336035 | ||||||||
\(107\) | 10.9803 | 1.06150 | 0.530751 | − | 0.847528i | \(-0.321910\pi\) | ||||
0.530751 | + | 0.847528i | \(0.321910\pi\) | |||||||
\(108\) | −6.98035 | −0.671684 | ||||||||
\(109\) | 15.2126 | 1.45711 | 0.728553 | − | 0.684989i | \(-0.240193\pi\) | ||||
0.728553 | + | 0.684989i | \(0.240193\pi\) | |||||||
\(110\) | 17.9271 | 1.70928 | ||||||||
\(111\) | −3.54636 | −0.336605 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 13.8700 | 1.30478 | 0.652391 | − | 0.757882i | \(-0.273766\pi\) | ||||
0.652391 | + | 0.757882i | \(0.273766\pi\) | |||||||
\(114\) | −23.8187 | −2.23083 | ||||||||
\(115\) | −0.372237 | −0.0347113 | ||||||||
\(116\) | −7.47496 | −0.694032 | ||||||||
\(117\) | 15.0247 | 1.38903 | ||||||||
\(118\) | −7.41617 | −0.682713 | ||||||||
\(119\) | 1.18328 | 0.108471 | ||||||||
\(120\) | −9.71661 | −0.887001 | ||||||||
\(121\) | 17.6187 | 1.60170 | ||||||||
\(122\) | 0.674429 | 0.0610599 | ||||||||
\(123\) | 13.8294 | 1.24696 | ||||||||
\(124\) | −3.87355 | −0.347855 | ||||||||
\(125\) | −4.12083 | −0.368578 | ||||||||
\(126\) | 5.40739 | 0.481729 | ||||||||
\(127\) | 8.34294 | 0.740317 | 0.370158 | − | 0.928969i | \(-0.379303\pi\) | ||||
0.370158 | + | 0.928969i | \(0.379303\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −31.8180 | −2.80142 | ||||||||
\(130\) | 9.31111 | 0.816638 | ||||||||
\(131\) | −18.0094 | −1.57349 | −0.786745 | − | 0.617279i | \(-0.788235\pi\) | ||||
−0.786745 | + | 0.617279i | \(0.788235\pi\) | |||||||
\(132\) | −15.5116 | −1.35011 | ||||||||
\(133\) | 8.21463 | 0.712299 | ||||||||
\(134\) | 8.63322 | 0.745797 | ||||||||
\(135\) | 23.3917 | 2.01323 | ||||||||
\(136\) | 1.18328 | 0.101465 | ||||||||
\(137\) | 4.30484 | 0.367787 | 0.183894 | − | 0.982946i | \(-0.441130\pi\) | ||||
0.183894 | + | 0.982946i | \(0.441130\pi\) | |||||||
\(138\) | 0.322082 | 0.0274174 | ||||||||
\(139\) | 17.2429 | 1.46252 | 0.731261 | − | 0.682098i | \(-0.238932\pi\) | ||||
0.731261 | + | 0.682098i | \(0.238932\pi\) | |||||||
\(140\) | 3.35107 | 0.283218 | ||||||||
\(141\) | 10.7883 | 0.908537 | ||||||||
\(142\) | 4.81812 | 0.404328 | ||||||||
\(143\) | 14.8642 | 1.24301 | ||||||||
\(144\) | 5.40739 | 0.450616 | ||||||||
\(145\) | 25.0491 | 2.08022 | ||||||||
\(146\) | −3.52593 | −0.291808 | ||||||||
\(147\) | −2.89955 | −0.239151 | ||||||||
\(148\) | 1.22307 | 0.100536 | ||||||||
\(149\) | −21.2617 | −1.74182 | −0.870912 | − | 0.491439i | \(-0.836471\pi\) | ||||
−0.870912 | + | 0.491439i | \(0.836471\pi\) | |||||||
\(150\) | 18.0633 | 1.47487 | ||||||||
\(151\) | −12.2728 | −0.998749 | −0.499375 | − | 0.866386i | \(-0.666437\pi\) | ||||
−0.499375 | + | 0.866386i | \(0.666437\pi\) | |||||||
\(152\) | 8.21463 | 0.666294 | ||||||||
\(153\) | −6.39846 | −0.517285 | ||||||||
\(154\) | 5.34965 | 0.431087 | ||||||||
\(155\) | 12.9806 | 1.04262 | ||||||||
\(156\) | −8.05653 | −0.645039 | ||||||||
\(157\) | −1.28169 | −0.102290 | −0.0511451 | − | 0.998691i | \(-0.516287\pi\) | ||||
−0.0511451 | + | 0.998691i | \(0.516287\pi\) | |||||||
\(158\) | 1.08915 | 0.0866478 | ||||||||
\(159\) | −10.0315 | −0.795553 | ||||||||
\(160\) | 3.35107 | 0.264926 | ||||||||
\(161\) | −0.111080 | −0.00875432 | ||||||||
\(162\) | −4.01770 | −0.315660 | ||||||||
\(163\) | 1.62246 | 0.127081 | 0.0635406 | − | 0.997979i | \(-0.479761\pi\) | ||||
0.0635406 | + | 0.997979i | \(0.479761\pi\) | |||||||
\(164\) | −4.76950 | −0.372435 | ||||||||
\(165\) | 51.9804 | 4.04667 | ||||||||
\(166\) | −0.907057 | −0.0704012 | ||||||||
\(167\) | −13.7556 | −1.06444 | −0.532222 | − | 0.846605i | \(-0.678643\pi\) | ||||
−0.532222 | + | 0.846605i | \(0.678643\pi\) | |||||||
\(168\) | −2.89955 | −0.223705 | ||||||||
\(169\) | −5.27969 | −0.406130 | ||||||||
\(170\) | −3.96526 | −0.304122 | ||||||||
\(171\) | −44.4197 | −3.39686 | ||||||||
\(172\) | 10.9734 | 0.836716 | ||||||||
\(173\) | 3.09879 | 0.235597 | 0.117798 | − | 0.993038i | \(-0.462416\pi\) | ||||
0.117798 | + | 0.993038i | \(0.462416\pi\) | |||||||
\(174\) | −21.6740 | −1.64310 | ||||||||
\(175\) | −6.22970 | −0.470921 | ||||||||
\(176\) | 5.34965 | 0.403245 | ||||||||
\(177\) | −21.5035 | −1.61631 | ||||||||
\(178\) | −0.159247 | −0.0119361 | ||||||||
\(179\) | 3.55238 | 0.265517 | 0.132759 | − | 0.991148i | \(-0.457616\pi\) | ||||
0.132759 | + | 0.991148i | \(0.457616\pi\) | |||||||
\(180\) | −18.1206 | −1.35063 | ||||||||
\(181\) | −13.5674 | −1.00845 | −0.504227 | − | 0.863571i | \(-0.668223\pi\) | ||||
−0.504227 | + | 0.863571i | \(0.668223\pi\) | |||||||
\(182\) | 2.77854 | 0.205959 | ||||||||
\(183\) | 1.95554 | 0.144558 | ||||||||
\(184\) | −0.111080 | −0.00818892 | ||||||||
\(185\) | −4.09860 | −0.301335 | ||||||||
\(186\) | −11.2316 | −0.823537 | ||||||||
\(187\) | −6.33013 | −0.462905 | ||||||||
\(188\) | −3.72068 | −0.271358 | ||||||||
\(189\) | 6.98035 | 0.507746 | ||||||||
\(190\) | −27.5278 | −1.99708 | ||||||||
\(191\) | −15.6436 | −1.13193 | −0.565965 | − | 0.824429i | \(-0.691496\pi\) | ||||
−0.565965 | + | 0.824429i | \(0.691496\pi\) | |||||||
\(192\) | −2.89955 | −0.209257 | ||||||||
\(193\) | −27.3651 | −1.96978 | −0.984890 | − | 0.173181i | \(-0.944595\pi\) | ||||
−0.984890 | + | 0.173181i | \(0.944595\pi\) | |||||||
\(194\) | −14.5975 | −1.04804 | ||||||||
\(195\) | 26.9980 | 1.93337 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −24.6276 | −1.75464 | −0.877320 | − | 0.479905i | \(-0.840671\pi\) | ||||
−0.877320 | + | 0.479905i | \(0.840671\pi\) | |||||||
\(198\) | −28.9276 | −2.05580 | ||||||||
\(199\) | 17.8996 | 1.26887 | 0.634436 | − | 0.772975i | \(-0.281232\pi\) | ||||
0.634436 | + | 0.772975i | \(0.281232\pi\) | |||||||
\(200\) | −6.22970 | −0.440507 | ||||||||
\(201\) | 25.0325 | 1.76565 | ||||||||
\(202\) | −7.37963 | −0.519229 | ||||||||
\(203\) | 7.47496 | 0.524639 | ||||||||
\(204\) | 3.43098 | 0.240217 | ||||||||
\(205\) | 15.9830 | 1.11630 | ||||||||
\(206\) | −5.22762 | −0.364226 | ||||||||
\(207\) | 0.600652 | 0.0417482 | ||||||||
\(208\) | 2.77854 | 0.192657 | ||||||||
\(209\) | −43.9453 | −3.03976 | ||||||||
\(210\) | 9.71661 | 0.670510 | ||||||||
\(211\) | 18.6795 | 1.28595 | 0.642975 | − | 0.765887i | \(-0.277700\pi\) | ||||
0.642975 | + | 0.765887i | \(0.277700\pi\) | |||||||
\(212\) | 3.45969 | 0.237612 | ||||||||
\(213\) | 13.9704 | 0.957235 | ||||||||
\(214\) | −10.9803 | −0.750595 | ||||||||
\(215\) | −36.7728 | −2.50788 | ||||||||
\(216\) | 6.98035 | 0.474953 | ||||||||
\(217\) | 3.87355 | 0.262954 | ||||||||
\(218\) | −15.2126 | −1.03033 | ||||||||
\(219\) | −10.2236 | −0.690848 | ||||||||
\(220\) | −17.9271 | −1.20864 | ||||||||
\(221\) | −3.28780 | −0.221161 | ||||||||
\(222\) | 3.54636 | 0.238016 | ||||||||
\(223\) | −20.2817 | −1.35816 | −0.679081 | − | 0.734063i | \(-0.737621\pi\) | ||||
−0.679081 | + | 0.734063i | \(0.737621\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 33.6864 | 2.24576 | ||||||||
\(226\) | −13.8700 | −0.922621 | ||||||||
\(227\) | 15.7833 | 1.04758 | 0.523788 | − | 0.851849i | \(-0.324519\pi\) | ||||
0.523788 | + | 0.851849i | \(0.324519\pi\) | |||||||
\(228\) | 23.8187 | 1.57743 | ||||||||
\(229\) | 9.01082 | 0.595452 | 0.297726 | − | 0.954651i | \(-0.403772\pi\) | ||||
0.297726 | + | 0.954651i | \(0.403772\pi\) | |||||||
\(230\) | 0.372237 | 0.0245446 | ||||||||
\(231\) | 15.5116 | 1.02059 | ||||||||
\(232\) | 7.47496 | 0.490755 | ||||||||
\(233\) | 13.8008 | 0.904121 | 0.452060 | − | 0.891987i | \(-0.350689\pi\) | ||||
0.452060 | + | 0.891987i | \(0.350689\pi\) | |||||||
\(234\) | −15.0247 | −0.982194 | ||||||||
\(235\) | 12.4683 | 0.813340 | ||||||||
\(236\) | 7.41617 | 0.482751 | ||||||||
\(237\) | 3.15803 | 0.205136 | ||||||||
\(238\) | −1.18328 | −0.0767007 | ||||||||
\(239\) | −8.98950 | −0.581482 | −0.290741 | − | 0.956802i | \(-0.593902\pi\) | ||||
−0.290741 | + | 0.956802i | \(0.593902\pi\) | |||||||
\(240\) | 9.71661 | 0.627204 | ||||||||
\(241\) | 29.0628 | 1.87210 | 0.936050 | − | 0.351867i | \(-0.114453\pi\) | ||||
0.936050 | + | 0.351867i | \(0.114453\pi\) | |||||||
\(242\) | −17.6187 | −1.13257 | ||||||||
\(243\) | 9.29152 | 0.596052 | ||||||||
\(244\) | −0.674429 | −0.0431759 | ||||||||
\(245\) | −3.35107 | −0.214092 | ||||||||
\(246\) | −13.8294 | −0.881731 | ||||||||
\(247\) | −22.8247 | −1.45230 | ||||||||
\(248\) | 3.87355 | 0.245971 | ||||||||
\(249\) | −2.63006 | −0.166673 | ||||||||
\(250\) | 4.12083 | 0.260624 | ||||||||
\(251\) | −0.476213 | −0.0300583 | −0.0150291 | − | 0.999887i | \(-0.504784\pi\) | ||||
−0.0150291 | + | 0.999887i | \(0.504784\pi\) | |||||||
\(252\) | −5.40739 | −0.340634 | ||||||||
\(253\) | 0.594238 | 0.0373594 | ||||||||
\(254\) | −8.34294 | −0.523483 | ||||||||
\(255\) | −11.4975 | −0.720000 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.69576 | −0.417670 | −0.208835 | − | 0.977951i | \(-0.566967\pi\) | ||||
−0.208835 | + | 0.977951i | \(0.566967\pi\) | |||||||
\(258\) | 31.8180 | 1.98090 | ||||||||
\(259\) | −1.22307 | −0.0759980 | ||||||||
\(260\) | −9.31111 | −0.577451 | ||||||||
\(261\) | −40.4200 | −2.50194 | ||||||||
\(262\) | 18.0094 | 1.11262 | ||||||||
\(263\) | 27.4036 | 1.68978 | 0.844888 | − | 0.534943i | \(-0.179667\pi\) | ||||
0.844888 | + | 0.534943i | \(0.179667\pi\) | |||||||
\(264\) | 15.5116 | 0.954671 | ||||||||
\(265\) | −11.5937 | −0.712194 | ||||||||
\(266\) | −8.21463 | −0.503671 | ||||||||
\(267\) | −0.461744 | −0.0282583 | ||||||||
\(268\) | −8.63322 | −0.527358 | ||||||||
\(269\) | 19.5892 | 1.19437 | 0.597187 | − | 0.802102i | \(-0.296285\pi\) | ||||
0.597187 | + | 0.802102i | \(0.296285\pi\) | |||||||
\(270\) | −23.3917 | −1.42357 | ||||||||
\(271\) | −1.99730 | −0.121327 | −0.0606636 | − | 0.998158i | \(-0.519322\pi\) | ||||
−0.0606636 | + | 0.998158i | \(0.519322\pi\) | |||||||
\(272\) | −1.18328 | −0.0717469 | ||||||||
\(273\) | 8.05653 | 0.487603 | ||||||||
\(274\) | −4.30484 | −0.260065 | ||||||||
\(275\) | 33.3267 | 2.00968 | ||||||||
\(276\) | −0.322082 | −0.0193870 | ||||||||
\(277\) | 0.800922 | 0.0481227 | 0.0240614 | − | 0.999710i | \(-0.492340\pi\) | ||||
0.0240614 | + | 0.999710i | \(0.492340\pi\) | |||||||
\(278\) | −17.2429 | −1.03416 | ||||||||
\(279\) | −20.9458 | −1.25399 | ||||||||
\(280\) | −3.35107 | −0.200265 | ||||||||
\(281\) | 9.16859 | 0.546952 | 0.273476 | − | 0.961879i | \(-0.411827\pi\) | ||||
0.273476 | + | 0.961879i | \(0.411827\pi\) | |||||||
\(282\) | −10.7883 | −0.642433 | ||||||||
\(283\) | 10.0066 | 0.594833 | 0.297417 | − | 0.954748i | \(-0.403875\pi\) | ||||
0.297417 | + | 0.954748i | \(0.403875\pi\) | |||||||
\(284\) | −4.81812 | −0.285903 | ||||||||
\(285\) | −79.8183 | −4.72803 | ||||||||
\(286\) | −14.8642 | −0.878940 | ||||||||
\(287\) | 4.76950 | 0.281535 | ||||||||
\(288\) | −5.40739 | −0.318634 | ||||||||
\(289\) | −15.5998 | −0.917638 | ||||||||
\(290\) | −25.0491 | −1.47094 | ||||||||
\(291\) | −42.3262 | −2.48121 | ||||||||
\(292\) | 3.52593 | 0.206340 | ||||||||
\(293\) | 16.0734 | 0.939018 | 0.469509 | − | 0.882928i | \(-0.344431\pi\) | ||||
0.469509 | + | 0.882928i | \(0.344431\pi\) | |||||||
\(294\) | 2.89955 | 0.169105 | ||||||||
\(295\) | −24.8521 | −1.44695 | ||||||||
\(296\) | −1.22307 | −0.0710896 | ||||||||
\(297\) | −37.3424 | −2.16683 | ||||||||
\(298\) | 21.2617 | 1.23166 | ||||||||
\(299\) | 0.308640 | 0.0178491 | ||||||||
\(300\) | −18.0633 | −1.04289 | ||||||||
\(301\) | −10.9734 | −0.632498 | ||||||||
\(302\) | 12.2728 | 0.706222 | ||||||||
\(303\) | −21.3976 | −1.22926 | ||||||||
\(304\) | −8.21463 | −0.471141 | ||||||||
\(305\) | 2.26006 | 0.129411 | ||||||||
\(306\) | 6.39846 | 0.365776 | ||||||||
\(307\) | −22.7974 | −1.30112 | −0.650559 | − | 0.759456i | \(-0.725465\pi\) | ||||
−0.650559 | + | 0.759456i | \(0.725465\pi\) | |||||||
\(308\) | −5.34965 | −0.304824 | ||||||||
\(309\) | −15.1577 | −0.862294 | ||||||||
\(310\) | −12.9806 | −0.737246 | ||||||||
\(311\) | −10.1888 | −0.577755 | −0.288877 | − | 0.957366i | \(-0.593282\pi\) | ||||
−0.288877 | + | 0.957366i | \(0.593282\pi\) | |||||||
\(312\) | 8.05653 | 0.456111 | ||||||||
\(313\) | 21.3794 | 1.20843 | 0.604217 | − | 0.796820i | \(-0.293486\pi\) | ||||
0.604217 | + | 0.796820i | \(0.293486\pi\) | |||||||
\(314\) | 1.28169 | 0.0723301 | ||||||||
\(315\) | 18.1206 | 1.02098 | ||||||||
\(316\) | −1.08915 | −0.0612692 | ||||||||
\(317\) | 6.92557 | 0.388979 | 0.194489 | − | 0.980905i | \(-0.437695\pi\) | ||||
0.194489 | + | 0.980905i | \(0.437695\pi\) | |||||||
\(318\) | 10.0315 | 0.562541 | ||||||||
\(319\) | −39.9884 | −2.23892 | ||||||||
\(320\) | −3.35107 | −0.187331 | ||||||||
\(321\) | −31.8378 | −1.77701 | ||||||||
\(322\) | 0.111080 | 0.00619024 | ||||||||
\(323\) | 9.72021 | 0.540847 | ||||||||
\(324\) | 4.01770 | 0.223206 | ||||||||
\(325\) | 17.3095 | 0.960159 | ||||||||
\(326\) | −1.62246 | −0.0898600 | ||||||||
\(327\) | −44.1098 | −2.43928 | ||||||||
\(328\) | 4.76950 | 0.263352 | ||||||||
\(329\) | 3.72068 | 0.205127 | ||||||||
\(330\) | −51.9804 | −2.86143 | ||||||||
\(331\) | −16.7005 | −0.917943 | −0.458971 | − | 0.888451i | \(-0.651782\pi\) | ||||
−0.458971 | + | 0.888451i | \(0.651782\pi\) | |||||||
\(332\) | 0.907057 | 0.0497812 | ||||||||
\(333\) | 6.61363 | 0.362424 | ||||||||
\(334\) | 13.7556 | 0.752675 | ||||||||
\(335\) | 28.9306 | 1.58065 | ||||||||
\(336\) | 2.89955 | 0.158183 | ||||||||
\(337\) | 11.0483 | 0.601841 | 0.300921 | − | 0.953649i | \(-0.402706\pi\) | ||||
0.300921 | + | 0.953649i | \(0.402706\pi\) | |||||||
\(338\) | 5.27969 | 0.287177 | ||||||||
\(339\) | −40.2168 | −2.18428 | ||||||||
\(340\) | 3.96526 | 0.215047 | ||||||||
\(341\) | −20.7221 | −1.12217 | ||||||||
\(342\) | 44.4197 | 2.40194 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −10.9734 | −0.591647 | ||||||||
\(345\) | 1.07932 | 0.0581086 | ||||||||
\(346\) | −3.09879 | −0.166592 | ||||||||
\(347\) | −20.6926 | −1.11084 | −0.555419 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555419 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(348\) | 21.6740 | 1.16185 | ||||||||
\(349\) | −6.06856 | −0.324843 | −0.162421 | − | 0.986721i | \(-0.551930\pi\) | ||||
−0.162421 | + | 0.986721i | \(0.551930\pi\) | |||||||
\(350\) | 6.22970 | 0.332992 | ||||||||
\(351\) | −19.3952 | −1.03524 | ||||||||
\(352\) | −5.34965 | −0.285137 | ||||||||
\(353\) | 2.63860 | 0.140438 | 0.0702192 | − | 0.997532i | \(-0.477630\pi\) | ||||
0.0702192 | + | 0.997532i | \(0.477630\pi\) | |||||||
\(354\) | 21.5035 | 1.14290 | ||||||||
\(355\) | 16.1459 | 0.856935 | ||||||||
\(356\) | 0.159247 | 0.00844006 | ||||||||
\(357\) | −3.43098 | −0.181587 | ||||||||
\(358\) | −3.55238 | −0.187749 | ||||||||
\(359\) | −20.8998 | −1.10305 | −0.551525 | − | 0.834158i | \(-0.685954\pi\) | ||||
−0.551525 | + | 0.834158i | \(0.685954\pi\) | |||||||
\(360\) | 18.1206 | 0.955038 | ||||||||
\(361\) | 48.4801 | 2.55159 | ||||||||
\(362\) | 13.5674 | 0.713085 | ||||||||
\(363\) | −51.0863 | −2.68134 | ||||||||
\(364\) | −2.77854 | −0.145635 | ||||||||
\(365\) | −11.8157 | −0.618460 | ||||||||
\(366\) | −1.95554 | −0.102218 | ||||||||
\(367\) | −3.30242 | −0.172385 | −0.0861924 | − | 0.996279i | \(-0.527470\pi\) | ||||
−0.0861924 | + | 0.996279i | \(0.527470\pi\) | |||||||
\(368\) | 0.111080 | 0.00579044 | ||||||||
\(369\) | −25.7906 | −1.34260 | ||||||||
\(370\) | 4.09860 | 0.213076 | ||||||||
\(371\) | −3.45969 | −0.179618 | ||||||||
\(372\) | 11.2316 | 0.582329 | ||||||||
\(373\) | 30.3078 | 1.56928 | 0.784640 | − | 0.619952i | \(-0.212848\pi\) | ||||
0.784640 | + | 0.619952i | \(0.212848\pi\) | |||||||
\(374\) | 6.33013 | 0.327323 | ||||||||
\(375\) | 11.9485 | 0.617020 | ||||||||
\(376\) | 3.72068 | 0.191879 | ||||||||
\(377\) | −20.7695 | −1.06968 | ||||||||
\(378\) | −6.98035 | −0.359030 | ||||||||
\(379\) | 18.4903 | 0.949781 | 0.474890 | − | 0.880045i | \(-0.342488\pi\) | ||||
0.474890 | + | 0.880045i | \(0.342488\pi\) | |||||||
\(380\) | 27.5278 | 1.41215 | ||||||||
\(381\) | −24.1908 | −1.23933 | ||||||||
\(382\) | 15.6436 | 0.800396 | ||||||||
\(383\) | −33.1678 | −1.69479 | −0.847397 | − | 0.530960i | \(-0.821831\pi\) | ||||
−0.847397 | + | 0.530960i | \(0.821831\pi\) | |||||||
\(384\) | 2.89955 | 0.147967 | ||||||||
\(385\) | 17.9271 | 0.913648 | ||||||||
\(386\) | 27.3651 | 1.39284 | ||||||||
\(387\) | 59.3376 | 3.01630 | ||||||||
\(388\) | 14.5975 | 0.741076 | ||||||||
\(389\) | 34.9633 | 1.77271 | 0.886355 | − | 0.463005i | \(-0.153229\pi\) | ||||
0.886355 | + | 0.463005i | \(0.153229\pi\) | |||||||
\(390\) | −26.9980 | −1.36710 | ||||||||
\(391\) | −0.131439 | −0.00664714 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 52.2192 | 2.63411 | ||||||||
\(394\) | 24.6276 | 1.24072 | ||||||||
\(395\) | 3.64981 | 0.183642 | ||||||||
\(396\) | 28.9276 | 1.45367 | ||||||||
\(397\) | 26.5591 | 1.33296 | 0.666481 | − | 0.745522i | \(-0.267800\pi\) | ||||
0.666481 | + | 0.745522i | \(0.267800\pi\) | |||||||
\(398\) | −17.8996 | −0.897228 | ||||||||
\(399\) | −23.8187 | −1.19243 | ||||||||
\(400\) | 6.22970 | 0.311485 | ||||||||
\(401\) | −25.0671 | −1.25179 | −0.625896 | − | 0.779907i | \(-0.715267\pi\) | ||||
−0.625896 | + | 0.779907i | \(0.715267\pi\) | |||||||
\(402\) | −25.0325 | −1.24851 | ||||||||
\(403\) | −10.7628 | −0.536135 | ||||||||
\(404\) | 7.37963 | 0.367150 | ||||||||
\(405\) | −13.4636 | −0.669012 | ||||||||
\(406\) | −7.47496 | −0.370976 | ||||||||
\(407\) | 6.54300 | 0.324324 | ||||||||
\(408\) | −3.43098 | −0.169859 | ||||||||
\(409\) | 3.80485 | 0.188138 | 0.0940690 | − | 0.995566i | \(-0.470013\pi\) | ||||
0.0940690 | + | 0.995566i | \(0.470013\pi\) | |||||||
\(410\) | −15.9830 | −0.789342 | ||||||||
\(411\) | −12.4821 | −0.615696 | ||||||||
\(412\) | 5.22762 | 0.257546 | ||||||||
\(413\) | −7.41617 | −0.364926 | ||||||||
\(414\) | −0.600652 | −0.0295204 | ||||||||
\(415\) | −3.03961 | −0.149209 | ||||||||
\(416\) | −2.77854 | −0.136229 | ||||||||
\(417\) | −49.9966 | −2.44834 | ||||||||
\(418\) | 43.9453 | 2.14944 | ||||||||
\(419\) | −12.5299 | −0.612126 | −0.306063 | − | 0.952011i | \(-0.599012\pi\) | ||||
−0.306063 | + | 0.952011i | \(0.599012\pi\) | |||||||
\(420\) | −9.71661 | −0.474122 | ||||||||
\(421\) | −21.5252 | −1.04907 | −0.524537 | − | 0.851388i | \(-0.675762\pi\) | ||||
−0.524537 | + | 0.851388i | \(0.675762\pi\) | |||||||
\(422\) | −18.6795 | −0.909304 | ||||||||
\(423\) | −20.1191 | −0.978226 | ||||||||
\(424\) | −3.45969 | −0.168017 | ||||||||
\(425\) | −7.37149 | −0.357570 | ||||||||
\(426\) | −13.9704 | −0.676867 | ||||||||
\(427\) | 0.674429 | 0.0326379 | ||||||||
\(428\) | 10.9803 | 0.530751 | ||||||||
\(429\) | −43.0996 | −2.08087 | ||||||||
\(430\) | 36.7728 | 1.77334 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −6.98035 | −0.335842 | ||||||||
\(433\) | 7.94016 | 0.381580 | 0.190790 | − | 0.981631i | \(-0.438895\pi\) | ||||
0.190790 | + | 0.981631i | \(0.438895\pi\) | |||||||
\(434\) | −3.87355 | −0.185936 | ||||||||
\(435\) | −72.6312 | −3.48240 | ||||||||
\(436\) | 15.2126 | 0.728553 | ||||||||
\(437\) | −0.912480 | −0.0436498 | ||||||||
\(438\) | 10.2236 | 0.488503 | ||||||||
\(439\) | 4.78946 | 0.228588 | 0.114294 | − | 0.993447i | \(-0.463539\pi\) | ||||
0.114294 | + | 0.993447i | \(0.463539\pi\) | |||||||
\(440\) | 17.9271 | 0.854639 | ||||||||
\(441\) | 5.40739 | 0.257495 | ||||||||
\(442\) | 3.28780 | 0.156385 | ||||||||
\(443\) | 36.7286 | 1.74503 | 0.872514 | − | 0.488590i | \(-0.162489\pi\) | ||||
0.872514 | + | 0.488590i | \(0.162489\pi\) | |||||||
\(444\) | −3.54636 | −0.168303 | ||||||||
\(445\) | −0.533648 | −0.0252973 | ||||||||
\(446\) | 20.2817 | 0.960365 | ||||||||
\(447\) | 61.6493 | 2.91591 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −21.2727 | −1.00392 | −0.501960 | − | 0.864891i | \(-0.667387\pi\) | ||||
−0.501960 | + | 0.864891i | \(0.667387\pi\) | |||||||
\(450\) | −33.6864 | −1.58799 | ||||||||
\(451\) | −25.5151 | −1.20146 | ||||||||
\(452\) | 13.8700 | 0.652391 | ||||||||
\(453\) | 35.5857 | 1.67196 | ||||||||
\(454\) | −15.7833 | −0.740748 | ||||||||
\(455\) | 9.31111 | 0.436512 | ||||||||
\(456\) | −23.8187 | −1.11541 | ||||||||
\(457\) | −1.75027 | −0.0818742 | −0.0409371 | − | 0.999162i | \(-0.513034\pi\) | ||||
−0.0409371 | + | 0.999162i | \(0.513034\pi\) | |||||||
\(458\) | −9.01082 | −0.421048 | ||||||||
\(459\) | 8.25971 | 0.385530 | ||||||||
\(460\) | −0.372237 | −0.0173556 | ||||||||
\(461\) | −9.45946 | −0.440571 | −0.220286 | − | 0.975435i | \(-0.570699\pi\) | ||||
−0.220286 | + | 0.975435i | \(0.570699\pi\) | |||||||
\(462\) | −15.5116 | −0.721663 | ||||||||
\(463\) | −4.01164 | −0.186437 | −0.0932183 | − | 0.995646i | \(-0.529715\pi\) | ||||
−0.0932183 | + | 0.995646i | \(0.529715\pi\) | |||||||
\(464\) | −7.47496 | −0.347016 | ||||||||
\(465\) | −37.6378 | −1.74541 | ||||||||
\(466\) | −13.8008 | −0.639310 | ||||||||
\(467\) | 8.52792 | 0.394625 | 0.197313 | − | 0.980341i | \(-0.436779\pi\) | ||||
0.197313 | + | 0.980341i | \(0.436779\pi\) | |||||||
\(468\) | 15.0247 | 0.694516 | ||||||||
\(469\) | 8.63322 | 0.398645 | ||||||||
\(470\) | −12.4683 | −0.575118 | ||||||||
\(471\) | 3.71633 | 0.171239 | ||||||||
\(472\) | −7.41617 | −0.341357 | ||||||||
\(473\) | 58.7039 | 2.69921 | ||||||||
\(474\) | −3.15803 | −0.145053 | ||||||||
\(475\) | −51.1747 | −2.34806 | ||||||||
\(476\) | 1.18328 | 0.0542356 | ||||||||
\(477\) | 18.7079 | 0.856576 | ||||||||
\(478\) | 8.98950 | 0.411170 | ||||||||
\(479\) | −24.0773 | −1.10012 | −0.550061 | − | 0.835125i | \(-0.685395\pi\) | ||||
−0.550061 | + | 0.835125i | \(0.685395\pi\) | |||||||
\(480\) | −9.71661 | −0.443501 | ||||||||
\(481\) | 3.39836 | 0.154952 | ||||||||
\(482\) | −29.0628 | −1.32377 | ||||||||
\(483\) | 0.322082 | 0.0146552 | ||||||||
\(484\) | 17.6187 | 0.800850 | ||||||||
\(485\) | −48.9173 | −2.22122 | ||||||||
\(486\) | −9.29152 | −0.421472 | ||||||||
\(487\) | −4.92742 | −0.223283 | −0.111641 | − | 0.993749i | \(-0.535611\pi\) | ||||
−0.111641 | + | 0.993749i | \(0.535611\pi\) | |||||||
\(488\) | 0.674429 | 0.0305300 | ||||||||
\(489\) | −4.70442 | −0.212741 | ||||||||
\(490\) | 3.35107 | 0.151386 | ||||||||
\(491\) | −37.0739 | −1.67312 | −0.836561 | − | 0.547874i | \(-0.815437\pi\) | ||||
−0.836561 | + | 0.547874i | \(0.815437\pi\) | |||||||
\(492\) | 13.8294 | 0.623478 | ||||||||
\(493\) | 8.84497 | 0.398358 | ||||||||
\(494\) | 22.8247 | 1.02693 | ||||||||
\(495\) | −96.9386 | −4.35707 | ||||||||
\(496\) | −3.87355 | −0.173928 | ||||||||
\(497\) | 4.81812 | 0.216122 | ||||||||
\(498\) | 2.63006 | 0.117856 | ||||||||
\(499\) | 32.5784 | 1.45841 | 0.729205 | − | 0.684295i | \(-0.239890\pi\) | ||||
0.729205 | + | 0.684295i | \(0.239890\pi\) | |||||||
\(500\) | −4.12083 | −0.184289 | ||||||||
\(501\) | 39.8852 | 1.78194 | ||||||||
\(502\) | 0.476213 | 0.0212544 | ||||||||
\(503\) | −15.6439 | −0.697526 | −0.348763 | − | 0.937211i | \(-0.613398\pi\) | ||||
−0.348763 | + | 0.937211i | \(0.613398\pi\) | |||||||
\(504\) | 5.40739 | 0.240864 | ||||||||
\(505\) | −24.7297 | −1.10046 | ||||||||
\(506\) | −0.594238 | −0.0264171 | ||||||||
\(507\) | 15.3087 | 0.679884 | ||||||||
\(508\) | 8.34294 | 0.370158 | ||||||||
\(509\) | 15.5276 | 0.688247 | 0.344124 | − | 0.938924i | \(-0.388176\pi\) | ||||
0.344124 | + | 0.938924i | \(0.388176\pi\) | |||||||
\(510\) | 11.4975 | 0.509117 | ||||||||
\(511\) | −3.52593 | −0.155978 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 57.3410 | 2.53167 | ||||||||
\(514\) | 6.69576 | 0.295337 | ||||||||
\(515\) | −17.5181 | −0.771942 | ||||||||
\(516\) | −31.8180 | −1.40071 | ||||||||
\(517\) | −19.9043 | −0.875390 | ||||||||
\(518\) | 1.22307 | 0.0537387 | ||||||||
\(519\) | −8.98510 | −0.394402 | ||||||||
\(520\) | 9.31111 | 0.408319 | ||||||||
\(521\) | −5.11431 | −0.224062 | −0.112031 | − | 0.993705i | \(-0.535736\pi\) | ||||
−0.112031 | + | 0.993705i | \(0.535736\pi\) | |||||||
\(522\) | 40.4200 | 1.76914 | ||||||||
\(523\) | −15.2652 | −0.667499 | −0.333750 | − | 0.942662i | \(-0.608314\pi\) | ||||
−0.333750 | + | 0.942662i | \(0.608314\pi\) | |||||||
\(524\) | −18.0094 | −0.786745 | ||||||||
\(525\) | 18.0633 | 0.788349 | ||||||||
\(526\) | −27.4036 | −1.19485 | ||||||||
\(527\) | 4.58350 | 0.199660 | ||||||||
\(528\) | −15.5116 | −0.675054 | ||||||||
\(529\) | −22.9877 | −0.999464 | ||||||||
\(530\) | 11.5937 | 0.503597 | ||||||||
\(531\) | 40.1021 | 1.74028 | ||||||||
\(532\) | 8.21463 | 0.356149 | ||||||||
\(533\) | −13.2523 | −0.574020 | ||||||||
\(534\) | 0.461744 | 0.0199816 | ||||||||
\(535\) | −36.7957 | −1.59082 | ||||||||
\(536\) | 8.63322 | 0.372898 | ||||||||
\(537\) | −10.3003 | −0.444491 | ||||||||
\(538\) | −19.5892 | −0.844550 | ||||||||
\(539\) | 5.34965 | 0.230426 | ||||||||
\(540\) | 23.3917 | 1.00662 | ||||||||
\(541\) | 42.2533 | 1.81661 | 0.908306 | − | 0.418307i | \(-0.137376\pi\) | ||||
0.908306 | + | 0.418307i | \(0.137376\pi\) | |||||||
\(542\) | 1.99730 | 0.0857912 | ||||||||
\(543\) | 39.3393 | 1.68821 | ||||||||
\(544\) | 1.18328 | 0.0507327 | ||||||||
\(545\) | −50.9787 | −2.18369 | ||||||||
\(546\) | −8.05653 | −0.344788 | ||||||||
\(547\) | −32.9417 | −1.40849 | −0.704243 | − | 0.709959i | \(-0.748713\pi\) | ||||
−0.704243 | + | 0.709959i | \(0.748713\pi\) | |||||||
\(548\) | 4.30484 | 0.183894 | ||||||||
\(549\) | −3.64690 | −0.155646 | ||||||||
\(550\) | −33.3267 | −1.42106 | ||||||||
\(551\) | 61.4040 | 2.61590 | ||||||||
\(552\) | 0.322082 | 0.0137087 | ||||||||
\(553\) | 1.08915 | 0.0463152 | ||||||||
\(554\) | −0.800922 | −0.0340279 | ||||||||
\(555\) | 11.8841 | 0.504452 | ||||||||
\(556\) | 17.2429 | 0.731261 | ||||||||
\(557\) | −37.7321 | −1.59876 | −0.799381 | − | 0.600825i | \(-0.794839\pi\) | ||||
−0.799381 | + | 0.600825i | \(0.794839\pi\) | |||||||
\(558\) | 20.9458 | 0.886706 | ||||||||
\(559\) | 30.4901 | 1.28960 | ||||||||
\(560\) | 3.35107 | 0.141609 | ||||||||
\(561\) | 18.3545 | 0.774929 | ||||||||
\(562\) | −9.16859 | −0.386753 | ||||||||
\(563\) | −25.5532 | −1.07694 | −0.538470 | − | 0.842645i | \(-0.680997\pi\) | ||||
−0.538470 | + | 0.842645i | \(0.680997\pi\) | |||||||
\(564\) | 10.7883 | 0.454269 | ||||||||
\(565\) | −46.4795 | −1.95541 | ||||||||
\(566\) | −10.0066 | −0.420611 | ||||||||
\(567\) | −4.01770 | −0.168728 | ||||||||
\(568\) | 4.81812 | 0.202164 | ||||||||
\(569\) | −19.8398 | −0.831728 | −0.415864 | − | 0.909427i | \(-0.636521\pi\) | ||||
−0.415864 | + | 0.909427i | \(0.636521\pi\) | |||||||
\(570\) | 79.8183 | 3.34322 | ||||||||
\(571\) | 22.0403 | 0.922358 | 0.461179 | − | 0.887307i | \(-0.347427\pi\) | ||||
0.461179 | + | 0.887307i | \(0.347427\pi\) | |||||||
\(572\) | 14.8642 | 0.621505 | ||||||||
\(573\) | 45.3594 | 1.89492 | ||||||||
\(574\) | −4.76950 | −0.199075 | ||||||||
\(575\) | 0.691994 | 0.0288582 | ||||||||
\(576\) | 5.40739 | 0.225308 | ||||||||
\(577\) | 28.1623 | 1.17241 | 0.586205 | − | 0.810162i | \(-0.300621\pi\) | ||||
0.586205 | + | 0.810162i | \(0.300621\pi\) | |||||||
\(578\) | 15.5998 | 0.648868 | ||||||||
\(579\) | 79.3464 | 3.29752 | ||||||||
\(580\) | 25.0491 | 1.04011 | ||||||||
\(581\) | −0.907057 | −0.0376310 | ||||||||
\(582\) | 42.3262 | 1.75448 | ||||||||
\(583\) | 18.5081 | 0.766528 | ||||||||
\(584\) | −3.52593 | −0.145904 | ||||||||
\(585\) | −50.3488 | −2.08167 | ||||||||
\(586\) | −16.0734 | −0.663986 | ||||||||
\(587\) | −20.0591 | −0.827926 | −0.413963 | − | 0.910294i | \(-0.635856\pi\) | ||||
−0.413963 | + | 0.910294i | \(0.635856\pi\) | |||||||
\(588\) | −2.89955 | −0.119575 | ||||||||
\(589\) | 31.8198 | 1.31111 | ||||||||
\(590\) | 24.8521 | 1.02315 | ||||||||
\(591\) | 71.4088 | 2.93737 | ||||||||
\(592\) | 1.22307 | 0.0502679 | ||||||||
\(593\) | 13.5893 | 0.558044 | 0.279022 | − | 0.960285i | \(-0.409990\pi\) | ||||
0.279022 | + | 0.960285i | \(0.409990\pi\) | |||||||
\(594\) | 37.3424 | 1.53218 | ||||||||
\(595\) | −3.96526 | −0.162560 | ||||||||
\(596\) | −21.2617 | −0.870912 | ||||||||
\(597\) | −51.9009 | −2.12416 | ||||||||
\(598\) | −0.308640 | −0.0126212 | ||||||||
\(599\) | −31.4306 | −1.28422 | −0.642110 | − | 0.766612i | \(-0.721941\pi\) | ||||
−0.642110 | + | 0.766612i | \(0.721941\pi\) | |||||||
\(600\) | 18.0633 | 0.737433 | ||||||||
\(601\) | −20.4441 | −0.833934 | −0.416967 | − | 0.908922i | \(-0.636907\pi\) | ||||
−0.416967 | + | 0.908922i | \(0.636907\pi\) | |||||||
\(602\) | 10.9734 | 0.447243 | ||||||||
\(603\) | −46.6832 | −1.90109 | ||||||||
\(604\) | −12.2728 | −0.499375 | ||||||||
\(605\) | −59.0416 | −2.40038 | ||||||||
\(606\) | 21.3976 | 0.869218 | ||||||||
\(607\) | −0.628313 | −0.0255024 | −0.0127512 | − | 0.999919i | \(-0.504059\pi\) | ||||
−0.0127512 | + | 0.999919i | \(0.504059\pi\) | |||||||
\(608\) | 8.21463 | 0.333147 | ||||||||
\(609\) | −21.6740 | −0.878275 | ||||||||
\(610\) | −2.26006 | −0.0915072 | ||||||||
\(611\) | −10.3381 | −0.418233 | ||||||||
\(612\) | −6.39846 | −0.258642 | ||||||||
\(613\) | −2.50434 | −0.101149 | −0.0505746 | − | 0.998720i | \(-0.516105\pi\) | ||||
−0.0505746 | + | 0.998720i | \(0.516105\pi\) | |||||||
\(614\) | 22.7974 | 0.920029 | ||||||||
\(615\) | −46.3434 | −1.86875 | ||||||||
\(616\) | 5.34965 | 0.215543 | ||||||||
\(617\) | −12.6270 | −0.508344 | −0.254172 | − | 0.967159i | \(-0.581803\pi\) | ||||
−0.254172 | + | 0.967159i | \(0.581803\pi\) | |||||||
\(618\) | 15.1577 | 0.609734 | ||||||||
\(619\) | −38.7800 | −1.55870 | −0.779349 | − | 0.626590i | \(-0.784450\pi\) | ||||
−0.779349 | + | 0.626590i | \(0.784450\pi\) | |||||||
\(620\) | 12.9806 | 0.521312 | ||||||||
\(621\) | −0.775376 | −0.0311148 | ||||||||
\(622\) | 10.1888 | 0.408534 | ||||||||
\(623\) | −0.159247 | −0.00638009 | ||||||||
\(624\) | −8.05653 | −0.322519 | ||||||||
\(625\) | −17.3393 | −0.693573 | ||||||||
\(626\) | −21.3794 | −0.854492 | ||||||||
\(627\) | 127.422 | 5.08873 | ||||||||
\(628\) | −1.28169 | −0.0511451 | ||||||||
\(629\) | −1.44724 | −0.0577051 | ||||||||
\(630\) | −18.1206 | −0.721941 | ||||||||
\(631\) | −19.3148 | −0.768910 | −0.384455 | − | 0.923144i | \(-0.625611\pi\) | ||||
−0.384455 | + | 0.923144i | \(0.625611\pi\) | |||||||
\(632\) | 1.08915 | 0.0433239 | ||||||||
\(633\) | −54.1622 | −2.15275 | ||||||||
\(634\) | −6.92557 | −0.275049 | ||||||||
\(635\) | −27.9578 | −1.10947 | ||||||||
\(636\) | −10.0315 | −0.397777 | ||||||||
\(637\) | 2.77854 | 0.110090 | ||||||||
\(638\) | 39.9884 | 1.58315 | ||||||||
\(639\) | −26.0535 | −1.03066 | ||||||||
\(640\) | 3.35107 | 0.132463 | ||||||||
\(641\) | −43.3826 | −1.71351 | −0.856755 | − | 0.515724i | \(-0.827523\pi\) | ||||
−0.856755 | + | 0.515724i | \(0.827523\pi\) | |||||||
\(642\) | 31.8378 | 1.25654 | ||||||||
\(643\) | 40.5360 | 1.59858 | 0.799292 | − | 0.600942i | \(-0.205208\pi\) | ||||
0.799292 | + | 0.600942i | \(0.205208\pi\) | |||||||
\(644\) | −0.111080 | −0.00437716 | ||||||||
\(645\) | 106.624 | 4.19833 | ||||||||
\(646\) | −9.72021 | −0.382437 | ||||||||
\(647\) | 41.4339 | 1.62893 | 0.814466 | − | 0.580211i | \(-0.197030\pi\) | ||||
0.814466 | + | 0.580211i | \(0.197030\pi\) | |||||||
\(648\) | −4.01770 | −0.157830 | ||||||||
\(649\) | 39.6739 | 1.55733 | ||||||||
\(650\) | −17.3095 | −0.678935 | ||||||||
\(651\) | −11.2316 | −0.440199 | ||||||||
\(652\) | 1.62246 | 0.0635406 | ||||||||
\(653\) | −37.3521 | −1.46170 | −0.730850 | − | 0.682538i | \(-0.760876\pi\) | ||||
−0.730850 | + | 0.682538i | \(0.760876\pi\) | |||||||
\(654\) | 44.1098 | 1.72483 | ||||||||
\(655\) | 60.3509 | 2.35810 | ||||||||
\(656\) | −4.76950 | −0.186218 | ||||||||
\(657\) | 19.0661 | 0.743839 | ||||||||
\(658\) | −3.72068 | −0.145047 | ||||||||
\(659\) | −17.0881 | −0.665657 | −0.332829 | − | 0.942987i | \(-0.608003\pi\) | ||||
−0.332829 | + | 0.942987i | \(0.608003\pi\) | |||||||
\(660\) | 51.9804 | 2.02333 | ||||||||
\(661\) | 8.16677 | 0.317650 | 0.158825 | − | 0.987307i | \(-0.449229\pi\) | ||||
0.158825 | + | 0.987307i | \(0.449229\pi\) | |||||||
\(662\) | 16.7005 | 0.649083 | ||||||||
\(663\) | 9.53314 | 0.370236 | ||||||||
\(664\) | −0.907057 | −0.0352006 | ||||||||
\(665\) | −27.5278 | −1.06748 | ||||||||
\(666\) | −6.61363 | −0.256273 | ||||||||
\(667\) | −0.830317 | −0.0321500 | ||||||||
\(668\) | −13.7556 | −0.532222 | ||||||||
\(669\) | 58.8078 | 2.27364 | ||||||||
\(670\) | −28.9306 | −1.11769 | ||||||||
\(671\) | −3.60796 | −0.139284 | ||||||||
\(672\) | −2.89955 | −0.111853 | ||||||||
\(673\) | −7.31793 | −0.282086 | −0.141043 | − | 0.990004i | \(-0.545046\pi\) | ||||
−0.141043 | + | 0.990004i | \(0.545046\pi\) | |||||||
\(674\) | −11.0483 | −0.425566 | ||||||||
\(675\) | −43.4855 | −1.67376 | ||||||||
\(676\) | −5.27969 | −0.203065 | ||||||||
\(677\) | 18.8622 | 0.724935 | 0.362467 | − | 0.931996i | \(-0.381934\pi\) | ||||
0.362467 | + | 0.931996i | \(0.381934\pi\) | |||||||
\(678\) | 40.2168 | 1.54452 | ||||||||
\(679\) | −14.5975 | −0.560201 | ||||||||
\(680\) | −3.96526 | −0.152061 | ||||||||
\(681\) | −45.7645 | −1.75370 | ||||||||
\(682\) | 20.7221 | 0.793491 | ||||||||
\(683\) | −23.2750 | −0.890595 | −0.445297 | − | 0.895383i | \(-0.646902\pi\) | ||||
−0.445297 | + | 0.895383i | \(0.646902\pi\) | |||||||
\(684\) | −44.4197 | −1.69843 | ||||||||
\(685\) | −14.4258 | −0.551183 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −26.1273 | −0.996820 | ||||||||
\(688\) | 10.9734 | 0.418358 | ||||||||
\(689\) | 9.61290 | 0.366222 | ||||||||
\(690\) | −1.07932 | −0.0410890 | ||||||||
\(691\) | −35.2859 | −1.34234 | −0.671169 | − | 0.741304i | \(-0.734208\pi\) | ||||
−0.671169 | + | 0.741304i | \(0.734208\pi\) | |||||||
\(692\) | 3.09879 | 0.117798 | ||||||||
\(693\) | −28.9276 | −1.09887 | ||||||||
\(694\) | 20.6926 | 0.785481 | ||||||||
\(695\) | −57.7821 | −2.19180 | ||||||||
\(696\) | −21.6740 | −0.821551 | ||||||||
\(697\) | 5.64366 | 0.213769 | ||||||||
\(698\) | 6.06856 | 0.229698 | ||||||||
\(699\) | −40.0161 | −1.51355 | ||||||||
\(700\) | −6.22970 | −0.235461 | ||||||||
\(701\) | −9.72151 | −0.367176 | −0.183588 | − | 0.983003i | \(-0.558771\pi\) | ||||
−0.183588 | + | 0.983003i | \(0.558771\pi\) | |||||||
\(702\) | 19.3952 | 0.732025 | ||||||||
\(703\) | −10.0471 | −0.378933 | ||||||||
\(704\) | 5.34965 | 0.201622 | ||||||||
\(705\) | −36.1523 | −1.36158 | ||||||||
\(706\) | −2.63860 | −0.0993049 | ||||||||
\(707\) | −7.37963 | −0.277539 | ||||||||
\(708\) | −21.5035 | −0.808153 | ||||||||
\(709\) | 32.1634 | 1.20792 | 0.603961 | − | 0.797014i | \(-0.293588\pi\) | ||||
0.603961 | + | 0.797014i | \(0.293588\pi\) | |||||||
\(710\) | −16.1459 | −0.605944 | ||||||||
\(711\) | −5.88944 | −0.220871 | ||||||||
\(712\) | −0.159247 | −0.00596803 | ||||||||
\(713\) | −0.430273 | −0.0161139 | ||||||||
\(714\) | 3.43098 | 0.128401 | ||||||||
\(715\) | −49.8111 | −1.86283 | ||||||||
\(716\) | 3.55238 | 0.132759 | ||||||||
\(717\) | 26.0655 | 0.973434 | ||||||||
\(718\) | 20.8998 | 0.779975 | ||||||||
\(719\) | −22.1291 | −0.825275 | −0.412637 | − | 0.910895i | \(-0.635392\pi\) | ||||
−0.412637 | + | 0.910895i | \(0.635392\pi\) | |||||||
\(720\) | −18.1206 | −0.675314 | ||||||||
\(721\) | −5.22762 | −0.194687 | ||||||||
\(722\) | −48.4801 | −1.80424 | ||||||||
\(723\) | −84.2691 | −3.13400 | ||||||||
\(724\) | −13.5674 | −0.504227 | ||||||||
\(725\) | −46.5668 | −1.72945 | ||||||||
\(726\) | 51.0863 | 1.89599 | ||||||||
\(727\) | 7.76586 | 0.288020 | 0.144010 | − | 0.989576i | \(-0.454000\pi\) | ||||
0.144010 | + | 0.989576i | \(0.454000\pi\) | |||||||
\(728\) | 2.77854 | 0.102980 | ||||||||
\(729\) | −38.9943 | −1.44423 | ||||||||
\(730\) | 11.8157 | 0.437317 | ||||||||
\(731\) | −12.9846 | −0.480254 | ||||||||
\(732\) | 1.95554 | 0.0722788 | ||||||||
\(733\) | 21.7272 | 0.802511 | 0.401256 | − | 0.915966i | \(-0.368574\pi\) | ||||
0.401256 | + | 0.915966i | \(0.368574\pi\) | |||||||
\(734\) | 3.30242 | 0.121894 | ||||||||
\(735\) | 9.71661 | 0.358403 | ||||||||
\(736\) | −0.111080 | −0.00409446 | ||||||||
\(737\) | −46.1847 | −1.70123 | ||||||||
\(738\) | 25.7906 | 0.949363 | ||||||||
\(739\) | 28.1868 | 1.03687 | 0.518435 | − | 0.855117i | \(-0.326515\pi\) | ||||
0.518435 | + | 0.855117i | \(0.326515\pi\) | |||||||
\(740\) | −4.09860 | −0.150668 | ||||||||
\(741\) | 66.1814 | 2.43123 | ||||||||
\(742\) | 3.45969 | 0.127009 | ||||||||
\(743\) | −2.98384 | −0.109467 | −0.0547333 | − | 0.998501i | \(-0.517431\pi\) | ||||
−0.0547333 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(744\) | −11.2316 | −0.411769 | ||||||||
\(745\) | 71.2495 | 2.61038 | ||||||||
\(746\) | −30.3078 | −1.10965 | ||||||||
\(747\) | 4.90481 | 0.179458 | ||||||||
\(748\) | −6.33013 | −0.231453 | ||||||||
\(749\) | −10.9803 | −0.401210 | ||||||||
\(750\) | −11.9485 | −0.436299 | ||||||||
\(751\) | −27.8884 | −1.01766 | −0.508831 | − | 0.860867i | \(-0.669922\pi\) | ||||
−0.508831 | + | 0.860867i | \(0.669922\pi\) | |||||||
\(752\) | −3.72068 | −0.135679 | ||||||||
\(753\) | 1.38080 | 0.0503192 | ||||||||
\(754\) | 20.7695 | 0.756381 | ||||||||
\(755\) | 41.1272 | 1.49677 | ||||||||
\(756\) | 6.98035 | 0.253873 | ||||||||
\(757\) | 21.7298 | 0.789784 | 0.394892 | − | 0.918727i | \(-0.370782\pi\) | ||||
0.394892 | + | 0.918727i | \(0.370782\pi\) | |||||||
\(758\) | −18.4903 | −0.671596 | ||||||||
\(759\) | −1.72302 | −0.0625417 | ||||||||
\(760\) | −27.5278 | −0.998540 | ||||||||
\(761\) | −29.5943 | −1.07279 | −0.536396 | − | 0.843967i | \(-0.680214\pi\) | ||||
−0.536396 | + | 0.843967i | \(0.680214\pi\) | |||||||
\(762\) | 24.1908 | 0.876340 | ||||||||
\(763\) | −15.2126 | −0.550734 | ||||||||
\(764\) | −15.6436 | −0.565965 | ||||||||
\(765\) | 21.4417 | 0.775227 | ||||||||
\(766\) | 33.1678 | 1.19840 | ||||||||
\(767\) | 20.6061 | 0.744045 | ||||||||
\(768\) | −2.89955 | −0.104628 | ||||||||
\(769\) | −23.1609 | −0.835203 | −0.417601 | − | 0.908630i | \(-0.637129\pi\) | ||||
−0.417601 | + | 0.908630i | \(0.637129\pi\) | |||||||
\(770\) | −17.9271 | −0.646046 | ||||||||
\(771\) | 19.4147 | 0.699203 | ||||||||
\(772\) | −27.3651 | −0.984890 | ||||||||
\(773\) | 12.5669 | 0.452001 | 0.226001 | − | 0.974127i | \(-0.427435\pi\) | ||||
0.226001 | + | 0.974127i | \(0.427435\pi\) | |||||||
\(774\) | −59.3376 | −2.13285 | ||||||||
\(775\) | −24.1311 | −0.866814 | ||||||||
\(776\) | −14.5975 | −0.524020 | ||||||||
\(777\) | 3.54636 | 0.127225 | ||||||||
\(778\) | −34.9633 | −1.25350 | ||||||||
\(779\) | 39.1797 | 1.40376 | ||||||||
\(780\) | 26.9980 | 0.966685 | ||||||||
\(781\) | −25.7752 | −0.922311 | ||||||||
\(782\) | 0.131439 | 0.00470024 | ||||||||
\(783\) | 52.1778 | 1.86468 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 4.29505 | 0.153297 | ||||||||
\(786\) | −52.2192 | −1.86260 | ||||||||
\(787\) | −17.1128 | −0.610007 | −0.305003 | − | 0.952351i | \(-0.598658\pi\) | ||||
−0.305003 | + | 0.952351i | \(0.598658\pi\) | |||||||
\(788\) | −24.6276 | −0.877320 | ||||||||
\(789\) | −79.4580 | −2.82878 | ||||||||
\(790\) | −3.64981 | −0.129854 | ||||||||
\(791\) | −13.8700 | −0.493161 | ||||||||
\(792\) | −28.9276 | −1.02790 | ||||||||
\(793\) | −1.87393 | −0.0665452 | ||||||||
\(794\) | −26.5591 | −0.942546 | ||||||||
\(795\) | 33.6165 | 1.19225 | ||||||||
\(796\) | 17.8996 | 0.634436 | ||||||||
\(797\) | −17.9195 | −0.634741 | −0.317371 | − | 0.948302i | \(-0.602800\pi\) | ||||
−0.317371 | + | 0.948302i | \(0.602800\pi\) | |||||||
\(798\) | 23.8187 | 0.843174 | ||||||||
\(799\) | 4.40260 | 0.155753 | ||||||||
\(800\) | −6.22970 | −0.220253 | ||||||||
\(801\) | 0.861110 | 0.0304258 | ||||||||
\(802\) | 25.0671 | 0.885150 | ||||||||
\(803\) | 18.8625 | 0.665643 | ||||||||
\(804\) | 25.0325 | 0.882827 | ||||||||
\(805\) | 0.372237 | 0.0131196 | ||||||||
\(806\) | 10.7628 | 0.379105 | ||||||||
\(807\) | −56.7998 | −1.99945 | ||||||||
\(808\) | −7.37963 | −0.259614 | ||||||||
\(809\) | 18.7742 | 0.660065 | 0.330032 | − | 0.943970i | \(-0.392940\pi\) | ||||
0.330032 | + | 0.943970i | \(0.392940\pi\) | |||||||
\(810\) | 13.4636 | 0.473063 | ||||||||
\(811\) | 24.5643 | 0.862568 | 0.431284 | − | 0.902216i | \(-0.358061\pi\) | ||||
0.431284 | + | 0.902216i | \(0.358061\pi\) | |||||||
\(812\) | 7.47496 | 0.262320 | ||||||||
\(813\) | 5.79126 | 0.203108 | ||||||||
\(814\) | −6.54300 | −0.229332 | ||||||||
\(815\) | −5.43700 | −0.190450 | ||||||||
\(816\) | 3.43098 | 0.120108 | ||||||||
\(817\) | −90.1426 | −3.15369 | ||||||||
\(818\) | −3.80485 | −0.133034 | ||||||||
\(819\) | −15.0247 | −0.525005 | ||||||||
\(820\) | 15.9830 | 0.558149 | ||||||||
\(821\) | 16.8467 | 0.587953 | 0.293977 | − | 0.955813i | \(-0.405021\pi\) | ||||
0.293977 | + | 0.955813i | \(0.405021\pi\) | |||||||
\(822\) | 12.4821 | 0.435363 | ||||||||
\(823\) | −7.56628 | −0.263744 | −0.131872 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131872 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(824\) | −5.22762 | −0.182113 | ||||||||
\(825\) | −96.6324 | −3.36431 | ||||||||
\(826\) | 7.41617 | 0.258041 | ||||||||
\(827\) | −0.204095 | −0.00709707 | −0.00354854 | − | 0.999994i | \(-0.501130\pi\) | ||||
−0.00354854 | + | 0.999994i | \(0.501130\pi\) | |||||||
\(828\) | 0.600652 | 0.0208741 | ||||||||
\(829\) | 24.8892 | 0.864439 | 0.432219 | − | 0.901769i | \(-0.357731\pi\) | ||||
0.432219 | + | 0.901769i | \(0.357731\pi\) | |||||||
\(830\) | 3.03961 | 0.105507 | ||||||||
\(831\) | −2.32231 | −0.0805602 | ||||||||
\(832\) | 2.77854 | 0.0963287 | ||||||||
\(833\) | −1.18328 | −0.0409983 | ||||||||
\(834\) | 49.9966 | 1.73124 | ||||||||
\(835\) | 46.0962 | 1.59522 | ||||||||
\(836\) | −43.9453 | −1.51988 | ||||||||
\(837\) | 27.0387 | 0.934595 | ||||||||
\(838\) | 12.5299 | 0.432839 | ||||||||
\(839\) | 32.8301 | 1.13342 | 0.566710 | − | 0.823918i | \(-0.308216\pi\) | ||||
0.566710 | + | 0.823918i | \(0.308216\pi\) | |||||||
\(840\) | 9.71661 | 0.335255 | ||||||||
\(841\) | 26.8750 | 0.926724 | ||||||||
\(842\) | 21.5252 | 0.741808 | ||||||||
\(843\) | −26.5848 | −0.915628 | ||||||||
\(844\) | 18.6795 | 0.642975 | ||||||||
\(845\) | 17.6926 | 0.608645 | ||||||||
\(846\) | 20.1191 | 0.691710 | ||||||||
\(847\) | −17.6187 | −0.605386 | ||||||||
\(848\) | 3.45969 | 0.118806 | ||||||||
\(849\) | −29.0148 | −0.995784 | ||||||||
\(850\) | 7.37149 | 0.252840 | ||||||||
\(851\) | 0.135859 | 0.00465717 | ||||||||
\(852\) | 13.9704 | 0.478617 | ||||||||
\(853\) | 7.00241 | 0.239758 | 0.119879 | − | 0.992789i | \(-0.461749\pi\) | ||||
0.119879 | + | 0.992789i | \(0.461749\pi\) | |||||||
\(854\) | −0.674429 | −0.0230785 | ||||||||
\(855\) | 148.854 | 5.09069 | ||||||||
\(856\) | −10.9803 | −0.375298 | ||||||||
\(857\) | −25.9672 | −0.887023 | −0.443511 | − | 0.896269i | \(-0.646267\pi\) | ||||
−0.443511 | + | 0.896269i | \(0.646267\pi\) | |||||||
\(858\) | 43.0996 | 1.47140 | ||||||||
\(859\) | −29.2579 | −0.998266 | −0.499133 | − | 0.866525i | \(-0.666348\pi\) | ||||
−0.499133 | + | 0.866525i | \(0.666348\pi\) | |||||||
\(860\) | −36.7728 | −1.25394 | ||||||||
\(861\) | −13.8294 | −0.471305 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −18.0305 | −0.613764 | −0.306882 | − | 0.951748i | \(-0.599286\pi\) | ||||
−0.306882 | + | 0.951748i | \(0.599286\pi\) | |||||||
\(864\) | 6.98035 | 0.237476 | ||||||||
\(865\) | −10.3843 | −0.353076 | ||||||||
\(866\) | −7.94016 | −0.269818 | ||||||||
\(867\) | 45.2325 | 1.53618 | ||||||||
\(868\) | 3.87355 | 0.131477 | ||||||||
\(869\) | −5.82654 | −0.197652 | ||||||||
\(870\) | 72.6312 | 2.46243 | ||||||||
\(871\) | −23.9878 | −0.812796 | ||||||||
\(872\) | −15.2126 | −0.515165 | ||||||||
\(873\) | 78.9344 | 2.67153 | ||||||||
\(874\) | 0.912480 | 0.0308651 | ||||||||
\(875\) | 4.12083 | 0.139309 | ||||||||
\(876\) | −10.2236 | −0.345424 | ||||||||
\(877\) | −36.5108 | −1.23288 | −0.616442 | − | 0.787401i | \(-0.711426\pi\) | ||||
−0.616442 | + | 0.787401i | \(0.711426\pi\) | |||||||
\(878\) | −4.78946 | −0.161636 | ||||||||
\(879\) | −46.6056 | −1.57197 | ||||||||
\(880\) | −17.9271 | −0.604321 | ||||||||
\(881\) | 28.2687 | 0.952398 | 0.476199 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476199 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(882\) | −5.40739 | −0.182076 | ||||||||
\(883\) | −14.6824 | −0.494103 | −0.247051 | − | 0.969002i | \(-0.579462\pi\) | ||||
−0.247051 | + | 0.969002i | \(0.579462\pi\) | |||||||
\(884\) | −3.28780 | −0.110581 | ||||||||
\(885\) | 72.0600 | 2.42227 | ||||||||
\(886\) | −36.7286 | −1.23392 | ||||||||
\(887\) | −50.4856 | −1.69514 | −0.847570 | − | 0.530684i | \(-0.821935\pi\) | ||||
−0.847570 | + | 0.530684i | \(0.821935\pi\) | |||||||
\(888\) | 3.54636 | 0.119008 | ||||||||
\(889\) | −8.34294 | −0.279813 | ||||||||
\(890\) | 0.533648 | 0.0178879 | ||||||||
\(891\) | 21.4933 | 0.720052 | ||||||||
\(892\) | −20.2817 | −0.679081 | ||||||||
\(893\) | 30.5640 | 1.02278 | ||||||||
\(894\) | −61.6493 | −2.06186 | ||||||||
\(895\) | −11.9043 | −0.397917 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −0.894918 | −0.0298804 | ||||||||
\(898\) | 21.2727 | 0.709878 | ||||||||
\(899\) | 28.9546 | 0.965691 | ||||||||
\(900\) | 33.6864 | 1.12288 | ||||||||
\(901\) | −4.09378 | −0.136384 | ||||||||
\(902\) | 25.5151 | 0.849561 | ||||||||
\(903\) | 31.8180 | 1.05884 | ||||||||
\(904\) | −13.8700 | −0.461310 | ||||||||
\(905\) | 45.4653 | 1.51132 | ||||||||
\(906\) | −35.5857 | −1.18226 | ||||||||
\(907\) | 46.3852 | 1.54020 | 0.770098 | − | 0.637926i | \(-0.220208\pi\) | ||||
0.770098 | + | 0.637926i | \(0.220208\pi\) | |||||||
\(908\) | 15.7833 | 0.523788 | ||||||||
\(909\) | 39.9045 | 1.32355 | ||||||||
\(910\) | −9.31111 | −0.308660 | ||||||||
\(911\) | 18.4009 | 0.609648 | 0.304824 | − | 0.952409i | \(-0.401402\pi\) | ||||
0.304824 | + | 0.952409i | \(0.401402\pi\) | |||||||
\(912\) | 23.8187 | 0.788717 | ||||||||
\(913\) | 4.85243 | 0.160592 | ||||||||
\(914\) | 1.75027 | 0.0578938 | ||||||||
\(915\) | −6.55316 | −0.216641 | ||||||||
\(916\) | 9.01082 | 0.297726 | ||||||||
\(917\) | 18.0094 | 0.594723 | ||||||||
\(918\) | −8.25971 | −0.272611 | ||||||||
\(919\) | 14.0594 | 0.463777 | 0.231889 | − | 0.972742i | \(-0.425509\pi\) | ||||
0.231889 | + | 0.972742i | \(0.425509\pi\) | |||||||
\(920\) | 0.372237 | 0.0122723 | ||||||||
\(921\) | 66.1023 | 2.17814 | ||||||||
\(922\) | 9.45946 | 0.311531 | ||||||||
\(923\) | −13.3874 | −0.440650 | ||||||||
\(924\) | 15.5116 | 0.510293 | ||||||||
\(925\) | 7.61937 | 0.250523 | ||||||||
\(926\) | 4.01164 | 0.131831 | ||||||||
\(927\) | 28.2678 | 0.928436 | ||||||||
\(928\) | 7.47496 | 0.245378 | ||||||||
\(929\) | −34.6751 | −1.13765 | −0.568827 | − | 0.822457i | \(-0.692603\pi\) | ||||
−0.568827 | + | 0.822457i | \(0.692603\pi\) | |||||||
\(930\) | 37.6378 | 1.23419 | ||||||||
\(931\) | −8.21463 | −0.269224 | ||||||||
\(932\) | 13.8008 | 0.452060 | ||||||||
\(933\) | 29.5430 | 0.967194 | ||||||||
\(934\) | −8.52792 | −0.279042 | ||||||||
\(935\) | 21.2127 | 0.693731 | ||||||||
\(936\) | −15.0247 | −0.491097 | ||||||||
\(937\) | 35.5973 | 1.16291 | 0.581457 | − | 0.813577i | \(-0.302483\pi\) | ||||
0.581457 | + | 0.813577i | \(0.302483\pi\) | |||||||
\(938\) | −8.63322 | −0.281885 | ||||||||
\(939\) | −61.9906 | −2.02299 | ||||||||
\(940\) | 12.4683 | 0.406670 | ||||||||
\(941\) | 40.6357 | 1.32469 | 0.662343 | − | 0.749201i | \(-0.269562\pi\) | ||||
0.662343 | + | 0.749201i | \(0.269562\pi\) | |||||||
\(942\) | −3.71633 | −0.121085 | ||||||||
\(943\) | −0.529795 | −0.0172525 | ||||||||
\(944\) | 7.41617 | 0.241376 | ||||||||
\(945\) | −23.3917 | −0.760931 | ||||||||
\(946\) | −58.7039 | −1.90863 | ||||||||
\(947\) | 12.4476 | 0.404491 | 0.202246 | − | 0.979335i | \(-0.435176\pi\) | ||||
0.202246 | + | 0.979335i | \(0.435176\pi\) | |||||||
\(948\) | 3.15803 | 0.102568 | ||||||||
\(949\) | 9.79696 | 0.318023 | ||||||||
\(950\) | 51.1747 | 1.66033 | ||||||||
\(951\) | −20.0810 | −0.651172 | ||||||||
\(952\) | −1.18328 | −0.0383504 | ||||||||
\(953\) | 3.88437 | 0.125827 | 0.0629136 | − | 0.998019i | \(-0.479961\pi\) | ||||
0.0629136 | + | 0.998019i | \(0.479961\pi\) | |||||||
\(954\) | −18.7079 | −0.605690 | ||||||||
\(955\) | 52.4229 | 1.69636 | ||||||||
\(956\) | −8.98950 | −0.290741 | ||||||||
\(957\) | 115.948 | 3.74808 | ||||||||
\(958\) | 24.0773 | 0.777903 | ||||||||
\(959\) | −4.30484 | −0.139011 | ||||||||
\(960\) | 9.71661 | 0.313602 | ||||||||
\(961\) | −15.9956 | −0.515987 | ||||||||
\(962\) | −3.39836 | −0.109567 | ||||||||
\(963\) | 59.3746 | 1.91332 | ||||||||
\(964\) | 29.0628 | 0.936050 | ||||||||
\(965\) | 91.7024 | 2.95200 | ||||||||
\(966\) | −0.322082 | −0.0103628 | ||||||||
\(967\) | −36.3245 | −1.16812 | −0.584058 | − | 0.811712i | \(-0.698536\pi\) | ||||
−0.584058 | + | 0.811712i | \(0.698536\pi\) | |||||||
\(968\) | −17.6187 | −0.566287 | ||||||||
\(969\) | −28.1842 | −0.905408 | ||||||||
\(970\) | 48.9173 | 1.57064 | ||||||||
\(971\) | −44.3366 | −1.42283 | −0.711415 | − | 0.702772i | \(-0.751945\pi\) | ||||
−0.711415 | + | 0.702772i | \(0.751945\pi\) | |||||||
\(972\) | 9.29152 | 0.298026 | ||||||||
\(973\) | −17.2429 | −0.552781 | ||||||||
\(974\) | 4.92742 | 0.157885 | ||||||||
\(975\) | −50.1898 | −1.60736 | ||||||||
\(976\) | −0.674429 | −0.0215879 | ||||||||
\(977\) | −27.6645 | −0.885064 | −0.442532 | − | 0.896753i | \(-0.645920\pi\) | ||||
−0.442532 | + | 0.896753i | \(0.645920\pi\) | |||||||
\(978\) | 4.70442 | 0.150431 | ||||||||
\(979\) | 0.851914 | 0.0272273 | ||||||||
\(980\) | −3.35107 | −0.107046 | ||||||||
\(981\) | 82.2606 | 2.62638 | ||||||||
\(982\) | 37.0739 | 1.18308 | ||||||||
\(983\) | −32.2099 | −1.02734 | −0.513668 | − | 0.857989i | \(-0.671714\pi\) | ||||
−0.513668 | + | 0.857989i | \(0.671714\pi\) | |||||||
\(984\) | −13.8294 | −0.440865 | ||||||||
\(985\) | 82.5288 | 2.62959 | ||||||||
\(986\) | −8.84497 | −0.281681 | ||||||||
\(987\) | −10.7883 | −0.343395 | ||||||||
\(988\) | −22.8247 | −0.726151 | ||||||||
\(989\) | 1.21893 | 0.0387596 | ||||||||
\(990\) | 96.9386 | 3.08091 | ||||||||
\(991\) | −0.938694 | −0.0298186 | −0.0149093 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149093 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(992\) | 3.87355 | 0.122985 | ||||||||
\(993\) | 48.4239 | 1.53669 | ||||||||
\(994\) | −4.81812 | −0.152822 | ||||||||
\(995\) | −59.9831 | −1.90159 | ||||||||
\(996\) | −2.63006 | −0.0833365 | ||||||||
\(997\) | 52.3283 | 1.65725 | 0.828627 | − | 0.559801i | \(-0.189122\pi\) | ||||
0.828627 | + | 0.559801i | \(0.189122\pi\) | |||||||
\(998\) | −32.5784 | −1.03125 | ||||||||
\(999\) | −8.53747 | −0.270114 |
(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 | 6034.2.a.o.1.4 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.o.1.4 | ✓ | 25 | 1.1 | even | 1 | trivial |