Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.71096 | −1.91694 | −0.958471 | − | 0.285191i | \(-0.907943\pi\) | ||||
−0.958471 | + | 0.285191i | \(0.907943\pi\) | |||||||
\(3\) | 3.20670 | 1.85139 | 0.925695 | − | 0.378272i | \(-0.123481\pi\) | ||||
0.925695 | + | 0.378272i | \(0.123481\pi\) | |||||||
\(4\) | 5.34933 | 2.67466 | ||||||||
\(5\) | 3.06653 | 1.37140 | 0.685698 | − | 0.727886i | \(-0.259497\pi\) | ||||
0.685698 | + | 0.727886i | \(0.259497\pi\) | |||||||
\(6\) | −8.69325 | −3.54900 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.07991 | −3.21023 | ||||||||
\(9\) | 7.28293 | 2.42764 | ||||||||
\(10\) | −8.31326 | −2.62888 | ||||||||
\(11\) | −0.601902 | −0.181480 | −0.0907401 | − | 0.995875i | \(-0.528923\pi\) | ||||
−0.0907401 | + | 0.995875i | \(0.528923\pi\) | |||||||
\(12\) | 17.1537 | 4.95184 | ||||||||
\(13\) | −1.91242 | −0.530411 | −0.265206 | − | 0.964192i | \(-0.585440\pi\) | ||||
−0.265206 | + | 0.964192i | \(0.585440\pi\) | |||||||
\(14\) | −2.71096 | −0.724536 | ||||||||
\(15\) | 9.83345 | 2.53899 | ||||||||
\(16\) | 13.9166 | 3.47916 | ||||||||
\(17\) | 2.21291 | 0.536710 | 0.268355 | − | 0.963320i | \(-0.413520\pi\) | ||||
0.268355 | + | 0.963320i | \(0.413520\pi\) | |||||||
\(18\) | −19.7438 | −4.65365 | ||||||||
\(19\) | −1.88875 | −0.433308 | −0.216654 | − | 0.976248i | \(-0.569514\pi\) | ||||
−0.216654 | + | 0.976248i | \(0.569514\pi\) | |||||||
\(20\) | 16.4039 | 3.66802 | ||||||||
\(21\) | 3.20670 | 0.699759 | ||||||||
\(22\) | 1.63173 | 0.347887 | ||||||||
\(23\) | 0.548445 | 0.114359 | 0.0571793 | − | 0.998364i | \(-0.481789\pi\) | ||||
0.0571793 | + | 0.998364i | \(0.481789\pi\) | |||||||
\(24\) | −29.1165 | −5.94339 | ||||||||
\(25\) | 4.40363 | 0.880725 | ||||||||
\(26\) | 5.18452 | 1.01677 | ||||||||
\(27\) | 13.7341 | 2.64312 | ||||||||
\(28\) | 5.34933 | 1.01093 | ||||||||
\(29\) | −4.40627 | −0.818223 | −0.409112 | − | 0.912484i | \(-0.634161\pi\) | ||||
−0.409112 | + | 0.912484i | \(0.634161\pi\) | |||||||
\(30\) | −26.6581 | −4.86709 | ||||||||
\(31\) | −0.578064 | −0.103823 | −0.0519117 | − | 0.998652i | \(-0.516531\pi\) | ||||
−0.0519117 | + | 0.998652i | \(0.516531\pi\) | |||||||
\(32\) | −19.5677 | −3.45912 | ||||||||
\(33\) | −1.93012 | −0.335991 | ||||||||
\(34\) | −5.99912 | −1.02884 | ||||||||
\(35\) | 3.06653 | 0.518339 | ||||||||
\(36\) | 38.9588 | 6.49313 | ||||||||
\(37\) | 2.37183 | 0.389926 | 0.194963 | − | 0.980811i | \(-0.437541\pi\) | ||||
0.194963 | + | 0.980811i | \(0.437541\pi\) | |||||||
\(38\) | 5.12032 | 0.830626 | ||||||||
\(39\) | −6.13257 | −0.981998 | ||||||||
\(40\) | −27.8438 | −4.40250 | ||||||||
\(41\) | 12.1364 | 1.89539 | 0.947696 | − | 0.319174i | \(-0.103406\pi\) | ||||
0.947696 | + | 0.319174i | \(0.103406\pi\) | |||||||
\(42\) | −8.69325 | −1.34140 | ||||||||
\(43\) | 9.96651 | 1.51988 | 0.759940 | − | 0.649994i | \(-0.225229\pi\) | ||||
0.759940 | + | 0.649994i | \(0.225229\pi\) | |||||||
\(44\) | −3.21977 | −0.485398 | ||||||||
\(45\) | 22.3333 | 3.32926 | ||||||||
\(46\) | −1.48681 | −0.219219 | ||||||||
\(47\) | −2.52239 | −0.367928 | −0.183964 | − | 0.982933i | \(-0.558893\pi\) | ||||
−0.183964 | + | 0.982933i | \(0.558893\pi\) | |||||||
\(48\) | 44.6265 | 6.44128 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.9381 | −1.68830 | ||||||||
\(51\) | 7.09614 | 0.993659 | ||||||||
\(52\) | −10.2302 | −1.41867 | ||||||||
\(53\) | 1.66466 | 0.228658 | 0.114329 | − | 0.993443i | \(-0.463528\pi\) | ||||
0.114329 | + | 0.993443i | \(0.463528\pi\) | |||||||
\(54\) | −37.2326 | −5.06671 | ||||||||
\(55\) | −1.84575 | −0.248881 | ||||||||
\(56\) | −9.07991 | −1.21335 | ||||||||
\(57\) | −6.05664 | −0.802222 | ||||||||
\(58\) | 11.9452 | 1.56849 | ||||||||
\(59\) | 10.0741 | 1.31153 | 0.655765 | − | 0.754965i | \(-0.272346\pi\) | ||||
0.655765 | + | 0.754965i | \(0.272346\pi\) | |||||||
\(60\) | 52.6024 | 6.79094 | ||||||||
\(61\) | −4.42119 | −0.566075 | −0.283038 | − | 0.959109i | \(-0.591342\pi\) | ||||
−0.283038 | + | 0.959109i | \(0.591342\pi\) | |||||||
\(62\) | 1.56711 | 0.199023 | ||||||||
\(63\) | 7.28293 | 0.917563 | ||||||||
\(64\) | 25.2141 | 3.15176 | ||||||||
\(65\) | −5.86452 | −0.727404 | ||||||||
\(66\) | 5.23248 | 0.644074 | ||||||||
\(67\) | 4.37369 | 0.534331 | 0.267166 | − | 0.963651i | \(-0.413913\pi\) | ||||
0.267166 | + | 0.963651i | \(0.413913\pi\) | |||||||
\(68\) | 11.8376 | 1.43552 | ||||||||
\(69\) | 1.75870 | 0.211722 | ||||||||
\(70\) | −8.31326 | −0.993625 | ||||||||
\(71\) | −6.11918 | −0.726213 | −0.363106 | − | 0.931748i | \(-0.618284\pi\) | ||||
−0.363106 | + | 0.931748i | \(0.618284\pi\) | |||||||
\(72\) | −66.1283 | −7.79329 | ||||||||
\(73\) | −12.4692 | −1.45941 | −0.729707 | − | 0.683760i | \(-0.760344\pi\) | ||||
−0.729707 | + | 0.683760i | \(0.760344\pi\) | |||||||
\(74\) | −6.42994 | −0.747465 | ||||||||
\(75\) | 14.1211 | 1.63057 | ||||||||
\(76\) | −10.1035 | −1.15895 | ||||||||
\(77\) | −0.601902 | −0.0685931 | ||||||||
\(78\) | 16.6252 | 1.88243 | ||||||||
\(79\) | −9.20628 | −1.03579 | −0.517894 | − | 0.855445i | \(-0.673284\pi\) | ||||
−0.517894 | + | 0.855445i | \(0.673284\pi\) | |||||||
\(80\) | 42.6759 | 4.77131 | ||||||||
\(81\) | 22.1923 | 2.46581 | ||||||||
\(82\) | −32.9014 | −3.63335 | ||||||||
\(83\) | 4.25325 | 0.466854 | 0.233427 | − | 0.972374i | \(-0.425006\pi\) | ||||
0.233427 | + | 0.972374i | \(0.425006\pi\) | |||||||
\(84\) | 17.1537 | 1.87162 | ||||||||
\(85\) | 6.78597 | 0.736041 | ||||||||
\(86\) | −27.0189 | −2.91352 | ||||||||
\(87\) | −14.1296 | −1.51485 | ||||||||
\(88\) | 5.46521 | 0.582593 | ||||||||
\(89\) | 15.0841 | 1.59891 | 0.799457 | − | 0.600724i | \(-0.205121\pi\) | ||||
0.799457 | + | 0.600724i | \(0.205121\pi\) | |||||||
\(90\) | −60.5449 | −6.38199 | ||||||||
\(91\) | −1.91242 | −0.200477 | ||||||||
\(92\) | 2.93381 | 0.305871 | ||||||||
\(93\) | −1.85368 | −0.192218 | ||||||||
\(94\) | 6.83811 | 0.705297 | ||||||||
\(95\) | −5.79190 | −0.594237 | ||||||||
\(96\) | −62.7478 | −6.40417 | ||||||||
\(97\) | −2.26710 | −0.230189 | −0.115095 | − | 0.993355i | \(-0.536717\pi\) | ||||
−0.115095 | + | 0.993355i | \(0.536717\pi\) | |||||||
\(98\) | −2.71096 | −0.273849 | ||||||||
\(99\) | −4.38361 | −0.440569 | ||||||||
\(100\) | 23.5564 | 2.35564 | ||||||||
\(101\) | −12.3078 | −1.22467 | −0.612334 | − | 0.790600i | \(-0.709769\pi\) | ||||
−0.612334 | + | 0.790600i | \(0.709769\pi\) | |||||||
\(102\) | −19.2374 | −1.90479 | ||||||||
\(103\) | −9.85490 | −0.971032 | −0.485516 | − | 0.874228i | \(-0.661368\pi\) | ||||
−0.485516 | + | 0.874228i | \(0.661368\pi\) | |||||||
\(104\) | 17.3646 | 1.70274 | ||||||||
\(105\) | 9.83345 | 0.959647 | ||||||||
\(106\) | −4.51283 | −0.438325 | ||||||||
\(107\) | 5.13480 | 0.496400 | 0.248200 | − | 0.968709i | \(-0.420161\pi\) | ||||
0.248200 | + | 0.968709i | \(0.420161\pi\) | |||||||
\(108\) | 73.4680 | 7.06946 | ||||||||
\(109\) | 11.8051 | 1.13072 | 0.565362 | − | 0.824843i | \(-0.308736\pi\) | ||||
0.565362 | + | 0.824843i | \(0.308736\pi\) | |||||||
\(110\) | 5.00377 | 0.477090 | ||||||||
\(111\) | 7.60574 | 0.721905 | ||||||||
\(112\) | 13.9166 | 1.31500 | ||||||||
\(113\) | −0.284477 | −0.0267613 | −0.0133807 | − | 0.999910i | \(-0.504259\pi\) | ||||
−0.0133807 | + | 0.999910i | \(0.504259\pi\) | |||||||
\(114\) | 16.4193 | 1.53781 | ||||||||
\(115\) | 1.68182 | 0.156831 | ||||||||
\(116\) | −23.5706 | −2.18847 | ||||||||
\(117\) | −13.9281 | −1.28765 | ||||||||
\(118\) | −27.3104 | −2.51413 | ||||||||
\(119\) | 2.21291 | 0.202857 | ||||||||
\(120\) | −89.2868 | −8.15074 | ||||||||
\(121\) | −10.6377 | −0.967065 | ||||||||
\(122\) | 11.9857 | 1.08513 | ||||||||
\(123\) | 38.9179 | 3.50911 | ||||||||
\(124\) | −3.09226 | −0.277693 | ||||||||
\(125\) | −1.82880 | −0.163573 | ||||||||
\(126\) | −19.7438 | −1.75891 | ||||||||
\(127\) | −13.3238 | −1.18230 | −0.591148 | − | 0.806563i | \(-0.701325\pi\) | ||||
−0.591148 | + | 0.806563i | \(0.701325\pi\) | |||||||
\(128\) | −29.2191 | −2.58262 | ||||||||
\(129\) | 31.9596 | 2.81389 | ||||||||
\(130\) | 15.8985 | 1.39439 | ||||||||
\(131\) | −13.1087 | −1.14531 | −0.572657 | − | 0.819795i | \(-0.694087\pi\) | ||||
−0.572657 | + | 0.819795i | \(0.694087\pi\) | |||||||
\(132\) | −10.3248 | −0.898662 | ||||||||
\(133\) | −1.88875 | −0.163775 | ||||||||
\(134\) | −11.8569 | −1.02428 | ||||||||
\(135\) | 42.1160 | 3.62477 | ||||||||
\(136\) | −20.0930 | −1.72296 | ||||||||
\(137\) | 6.14328 | 0.524856 | 0.262428 | − | 0.964952i | \(-0.415477\pi\) | ||||
0.262428 | + | 0.964952i | \(0.415477\pi\) | |||||||
\(138\) | −4.76777 | −0.405859 | ||||||||
\(139\) | 17.2355 | 1.46190 | 0.730949 | − | 0.682432i | \(-0.239078\pi\) | ||||
0.730949 | + | 0.682432i | \(0.239078\pi\) | |||||||
\(140\) | 16.4039 | 1.38638 | ||||||||
\(141\) | −8.08855 | −0.681179 | ||||||||
\(142\) | 16.5889 | 1.39211 | ||||||||
\(143\) | 1.15109 | 0.0962591 | ||||||||
\(144\) | 101.354 | 8.44616 | ||||||||
\(145\) | −13.5120 | −1.12211 | ||||||||
\(146\) | 33.8037 | 2.79761 | ||||||||
\(147\) | 3.20670 | 0.264484 | ||||||||
\(148\) | 12.6877 | 1.04292 | ||||||||
\(149\) | 1.86756 | 0.152996 | 0.0764982 | − | 0.997070i | \(-0.475626\pi\) | ||||
0.0764982 | + | 0.997070i | \(0.475626\pi\) | |||||||
\(150\) | −38.2818 | −3.12570 | ||||||||
\(151\) | −1.07693 | −0.0876396 | −0.0438198 | − | 0.999039i | \(-0.513953\pi\) | ||||
−0.0438198 | + | 0.999039i | \(0.513953\pi\) | |||||||
\(152\) | 17.1496 | 1.39102 | ||||||||
\(153\) | 16.1165 | 1.30294 | ||||||||
\(154\) | 1.63173 | 0.131489 | ||||||||
\(155\) | −1.77265 | −0.142383 | ||||||||
\(156\) | −32.8051 | −2.62651 | ||||||||
\(157\) | 15.8541 | 1.26530 | 0.632649 | − | 0.774439i | \(-0.281968\pi\) | ||||
0.632649 | + | 0.774439i | \(0.281968\pi\) | |||||||
\(158\) | 24.9579 | 1.98554 | ||||||||
\(159\) | 5.33806 | 0.423336 | ||||||||
\(160\) | −60.0051 | −4.74382 | ||||||||
\(161\) | 0.548445 | 0.0432235 | ||||||||
\(162\) | −60.1624 | −4.72681 | ||||||||
\(163\) | 18.3107 | 1.43421 | 0.717103 | − | 0.696967i | \(-0.245468\pi\) | ||||
0.717103 | + | 0.696967i | \(0.245468\pi\) | |||||||
\(164\) | 64.9217 | 5.06954 | ||||||||
\(165\) | −5.91877 | −0.460776 | ||||||||
\(166\) | −11.5304 | −0.894933 | ||||||||
\(167\) | 4.09051 | 0.316533 | 0.158267 | − | 0.987396i | \(-0.449409\pi\) | ||||
0.158267 | + | 0.987396i | \(0.449409\pi\) | |||||||
\(168\) | −29.1165 | −2.24639 | ||||||||
\(169\) | −9.34263 | −0.718664 | ||||||||
\(170\) | −18.3965 | −1.41095 | ||||||||
\(171\) | −13.7556 | −1.05192 | ||||||||
\(172\) | 53.3141 | 4.06517 | ||||||||
\(173\) | −17.9424 | −1.36414 | −0.682069 | − | 0.731288i | \(-0.738920\pi\) | ||||
−0.682069 | + | 0.731288i | \(0.738920\pi\) | |||||||
\(174\) | 38.3048 | 2.90388 | ||||||||
\(175\) | 4.40363 | 0.332883 | ||||||||
\(176\) | −8.37645 | −0.631399 | ||||||||
\(177\) | 32.3045 | 2.42815 | ||||||||
\(178\) | −40.8925 | −3.06502 | ||||||||
\(179\) | 12.7114 | 0.950092 | 0.475046 | − | 0.879961i | \(-0.342431\pi\) | ||||
0.475046 | + | 0.879961i | \(0.342431\pi\) | |||||||
\(180\) | 119.468 | 8.90465 | ||||||||
\(181\) | −7.53782 | −0.560282 | −0.280141 | − | 0.959959i | \(-0.590381\pi\) | ||||
−0.280141 | + | 0.959959i | \(0.590381\pi\) | |||||||
\(182\) | 5.18452 | 0.384302 | ||||||||
\(183\) | −14.1774 | −1.04803 | ||||||||
\(184\) | −4.97983 | −0.367118 | ||||||||
\(185\) | 7.27329 | 0.534743 | ||||||||
\(186\) | 5.02526 | 0.368470 | ||||||||
\(187\) | −1.33195 | −0.0974022 | ||||||||
\(188\) | −13.4931 | −0.984084 | ||||||||
\(189\) | 13.7341 | 0.999006 | ||||||||
\(190\) | 15.7016 | 1.13912 | ||||||||
\(191\) | 19.7380 | 1.42819 | 0.714095 | − | 0.700049i | \(-0.246839\pi\) | ||||
0.714095 | + | 0.700049i | \(0.246839\pi\) | |||||||
\(192\) | 80.8540 | 5.83514 | ||||||||
\(193\) | 7.44244 | 0.535719 | 0.267859 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267859 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(194\) | 6.14602 | 0.441259 | ||||||||
\(195\) | −18.8057 | −1.34671 | ||||||||
\(196\) | 5.34933 | 0.382095 | ||||||||
\(197\) | −7.04214 | −0.501731 | −0.250866 | − | 0.968022i | \(-0.580715\pi\) | ||||
−0.250866 | + | 0.968022i | \(0.580715\pi\) | |||||||
\(198\) | 11.8838 | 0.844545 | ||||||||
\(199\) | −23.2970 | −1.65148 | −0.825741 | − | 0.564049i | \(-0.809243\pi\) | ||||
−0.825741 | + | 0.564049i | \(0.809243\pi\) | |||||||
\(200\) | −39.9845 | −2.82733 | ||||||||
\(201\) | 14.0251 | 0.989255 | ||||||||
\(202\) | 33.3659 | 2.34761 | ||||||||
\(203\) | −4.40627 | −0.309259 | ||||||||
\(204\) | 37.9596 | 2.65770 | ||||||||
\(205\) | 37.2168 | 2.59933 | ||||||||
\(206\) | 26.7163 | 1.86141 | ||||||||
\(207\) | 3.99428 | 0.277622 | ||||||||
\(208\) | −26.6145 | −1.84539 | ||||||||
\(209\) | 1.13684 | 0.0786369 | ||||||||
\(210\) | −26.6581 | −1.83959 | ||||||||
\(211\) | −28.1411 | −1.93732 | −0.968658 | − | 0.248399i | \(-0.920095\pi\) | ||||
−0.968658 | + | 0.248399i | \(0.920095\pi\) | |||||||
\(212\) | 8.90480 | 0.611584 | ||||||||
\(213\) | −19.6224 | −1.34450 | ||||||||
\(214\) | −13.9203 | −0.951569 | ||||||||
\(215\) | 30.5626 | 2.08436 | ||||||||
\(216\) | −124.704 | −8.48503 | ||||||||
\(217\) | −0.578064 | −0.0392416 | ||||||||
\(218\) | −32.0032 | −2.16753 | ||||||||
\(219\) | −39.9851 | −2.70194 | ||||||||
\(220\) | −9.87353 | −0.665673 | ||||||||
\(221\) | −4.23203 | −0.284677 | ||||||||
\(222\) | −20.6189 | −1.38385 | ||||||||
\(223\) | 6.51775 | 0.436461 | 0.218230 | − | 0.975897i | \(-0.429972\pi\) | ||||
0.218230 | + | 0.975897i | \(0.429972\pi\) | |||||||
\(224\) | −19.5677 | −1.30742 | ||||||||
\(225\) | 32.0713 | 2.13809 | ||||||||
\(226\) | 0.771207 | 0.0512999 | ||||||||
\(227\) | −1.43071 | −0.0949593 | −0.0474796 | − | 0.998872i | \(-0.515119\pi\) | ||||
−0.0474796 | + | 0.998872i | \(0.515119\pi\) | |||||||
\(228\) | −32.3990 | −2.14567 | ||||||||
\(229\) | −1.22533 | −0.0809721 | −0.0404861 | − | 0.999180i | \(-0.512891\pi\) | ||||
−0.0404861 | + | 0.999180i | \(0.512891\pi\) | |||||||
\(230\) | −4.55936 | −0.300636 | ||||||||
\(231\) | −1.93012 | −0.126992 | ||||||||
\(232\) | 40.0085 | 2.62669 | ||||||||
\(233\) | 28.8004 | 1.88677 | 0.943387 | − | 0.331693i | \(-0.107620\pi\) | ||||
0.943387 | + | 0.331693i | \(0.107620\pi\) | |||||||
\(234\) | 37.7585 | 2.46835 | ||||||||
\(235\) | −7.73499 | −0.504575 | ||||||||
\(236\) | 53.8894 | 3.50790 | ||||||||
\(237\) | −29.5218 | −1.91765 | ||||||||
\(238\) | −5.99912 | −0.388865 | ||||||||
\(239\) | 9.63367 | 0.623150 | 0.311575 | − | 0.950222i | \(-0.399143\pi\) | ||||
0.311575 | + | 0.950222i | \(0.399143\pi\) | |||||||
\(240\) | 136.849 | 8.83355 | ||||||||
\(241\) | 29.5302 | 1.90221 | 0.951103 | − | 0.308873i | \(-0.0999517\pi\) | ||||
0.951103 | + | 0.308873i | \(0.0999517\pi\) | |||||||
\(242\) | 28.8385 | 1.85381 | ||||||||
\(243\) | 29.9617 | 1.92204 | ||||||||
\(244\) | −23.6504 | −1.51406 | ||||||||
\(245\) | 3.06653 | 0.195914 | ||||||||
\(246\) | −105.505 | −6.72675 | ||||||||
\(247\) | 3.61209 | 0.229832 | ||||||||
\(248\) | 5.24877 | 0.333297 | ||||||||
\(249\) | 13.6389 | 0.864329 | ||||||||
\(250\) | 4.95780 | 0.313559 | ||||||||
\(251\) | 17.5915 | 1.11036 | 0.555182 | − | 0.831729i | \(-0.312649\pi\) | ||||
0.555182 | + | 0.831729i | \(0.312649\pi\) | |||||||
\(252\) | 38.9588 | 2.45417 | ||||||||
\(253\) | −0.330110 | −0.0207538 | ||||||||
\(254\) | 36.1204 | 2.26639 | ||||||||
\(255\) | 21.7606 | 1.36270 | ||||||||
\(256\) | 28.7837 | 1.79898 | ||||||||
\(257\) | −15.1458 | −0.944767 | −0.472383 | − | 0.881393i | \(-0.656606\pi\) | ||||
−0.472383 | + | 0.881393i | \(0.656606\pi\) | |||||||
\(258\) | −86.6414 | −5.39406 | ||||||||
\(259\) | 2.37183 | 0.147378 | ||||||||
\(260\) | −31.3712 | −1.94556 | ||||||||
\(261\) | −32.0905 | −1.98635 | ||||||||
\(262\) | 35.5373 | 2.19550 | ||||||||
\(263\) | −17.4901 | −1.07848 | −0.539242 | − | 0.842151i | \(-0.681289\pi\) | ||||
−0.539242 | + | 0.842151i | \(0.681289\pi\) | |||||||
\(264\) | 17.5253 | 1.07861 | ||||||||
\(265\) | 5.10473 | 0.313581 | ||||||||
\(266\) | 5.12032 | 0.313947 | ||||||||
\(267\) | 48.3703 | 2.96021 | ||||||||
\(268\) | 23.3963 | 1.42916 | ||||||||
\(269\) | 22.2887 | 1.35897 | 0.679483 | − | 0.733692i | \(-0.262204\pi\) | ||||
0.679483 | + | 0.733692i | \(0.262204\pi\) | |||||||
\(270\) | −114.175 | −6.94846 | ||||||||
\(271\) | −1.39582 | −0.0847901 | −0.0423951 | − | 0.999101i | \(-0.513499\pi\) | ||||
−0.0423951 | + | 0.999101i | \(0.513499\pi\) | |||||||
\(272\) | 30.7963 | 1.86730 | ||||||||
\(273\) | −6.13257 | −0.371160 | ||||||||
\(274\) | −16.6542 | −1.00612 | ||||||||
\(275\) | −2.65055 | −0.159834 | ||||||||
\(276\) | 9.40785 | 0.566286 | ||||||||
\(277\) | −8.76458 | −0.526612 | −0.263306 | − | 0.964712i | \(-0.584813\pi\) | ||||
−0.263306 | + | 0.964712i | \(0.584813\pi\) | |||||||
\(278\) | −46.7249 | −2.80237 | ||||||||
\(279\) | −4.21000 | −0.252046 | ||||||||
\(280\) | −27.8438 | −1.66399 | ||||||||
\(281\) | 9.67768 | 0.577322 | 0.288661 | − | 0.957431i | \(-0.406790\pi\) | ||||
0.288661 | + | 0.957431i | \(0.406790\pi\) | |||||||
\(282\) | 21.9278 | 1.30578 | ||||||||
\(283\) | 13.2583 | 0.788127 | 0.394063 | − | 0.919083i | \(-0.371069\pi\) | ||||
0.394063 | + | 0.919083i | \(0.371069\pi\) | |||||||
\(284\) | −32.7335 | −1.94237 | ||||||||
\(285\) | −18.5729 | −1.10016 | ||||||||
\(286\) | −3.12057 | −0.184523 | ||||||||
\(287\) | 12.1364 | 0.716391 | ||||||||
\(288\) | −142.510 | −8.39750 | ||||||||
\(289\) | −12.1030 | −0.711943 | ||||||||
\(290\) | 36.6304 | 2.15101 | ||||||||
\(291\) | −7.26991 | −0.426170 | ||||||||
\(292\) | −66.7020 | −3.90344 | ||||||||
\(293\) | 7.82011 | 0.456856 | 0.228428 | − | 0.973561i | \(-0.426642\pi\) | ||||
0.228428 | + | 0.973561i | \(0.426642\pi\) | |||||||
\(294\) | −8.69325 | −0.507001 | ||||||||
\(295\) | 30.8924 | 1.79863 | ||||||||
\(296\) | −21.5360 | −1.25175 | ||||||||
\(297\) | −8.26656 | −0.479674 | ||||||||
\(298\) | −5.06289 | −0.293285 | ||||||||
\(299\) | −1.04886 | −0.0606571 | ||||||||
\(300\) | 75.5385 | 4.36121 | ||||||||
\(301\) | 9.96651 | 0.574460 | ||||||||
\(302\) | 2.91953 | 0.168000 | ||||||||
\(303\) | −39.4673 | −2.26734 | ||||||||
\(304\) | −26.2850 | −1.50755 | ||||||||
\(305\) | −13.5577 | −0.776313 | ||||||||
\(306\) | −43.6912 | −2.49766 | ||||||||
\(307\) | 26.5077 | 1.51287 | 0.756437 | − | 0.654066i | \(-0.226938\pi\) | ||||
0.756437 | + | 0.654066i | \(0.226938\pi\) | |||||||
\(308\) | −3.21977 | −0.183463 | ||||||||
\(309\) | −31.6017 | −1.79776 | ||||||||
\(310\) | 4.80560 | 0.272940 | ||||||||
\(311\) | 9.58095 | 0.543286 | 0.271643 | − | 0.962398i | \(-0.412433\pi\) | ||||
0.271643 | + | 0.962398i | \(0.412433\pi\) | |||||||
\(312\) | 55.6832 | 3.15244 | ||||||||
\(313\) | −9.00853 | −0.509192 | −0.254596 | − | 0.967047i | \(-0.581943\pi\) | ||||
−0.254596 | + | 0.967047i | \(0.581943\pi\) | |||||||
\(314\) | −42.9800 | −2.42550 | ||||||||
\(315\) | 22.3333 | 1.25834 | ||||||||
\(316\) | −49.2474 | −2.77038 | ||||||||
\(317\) | 11.6484 | 0.654238 | 0.327119 | − | 0.944983i | \(-0.393922\pi\) | ||||
0.327119 | + | 0.944983i | \(0.393922\pi\) | |||||||
\(318\) | −14.4713 | −0.811509 | ||||||||
\(319\) | 2.65214 | 0.148491 | ||||||||
\(320\) | 77.3199 | 4.32231 | ||||||||
\(321\) | 16.4658 | 0.919029 | ||||||||
\(322\) | −1.48681 | −0.0828569 | ||||||||
\(323\) | −4.17963 | −0.232561 | ||||||||
\(324\) | 118.714 | 6.59520 | ||||||||
\(325\) | −8.42161 | −0.467147 | ||||||||
\(326\) | −49.6397 | −2.74929 | ||||||||
\(327\) | 37.8555 | 2.09341 | ||||||||
\(328\) | −110.198 | −6.08465 | ||||||||
\(329\) | −2.52239 | −0.139064 | ||||||||
\(330\) | 16.0456 | 0.883280 | ||||||||
\(331\) | −29.9465 | −1.64601 | −0.823005 | − | 0.568034i | \(-0.807704\pi\) | ||||
−0.823005 | + | 0.568034i | \(0.807704\pi\) | |||||||
\(332\) | 22.7520 | 1.24868 | ||||||||
\(333\) | 17.2738 | 0.946601 | ||||||||
\(334\) | −11.0892 | −0.606775 | ||||||||
\(335\) | 13.4121 | 0.732779 | ||||||||
\(336\) | 44.6265 | 2.43458 | ||||||||
\(337\) | −21.9141 | −1.19374 | −0.596869 | − | 0.802338i | \(-0.703589\pi\) | ||||
−0.596869 | + | 0.802338i | \(0.703589\pi\) | |||||||
\(338\) | 25.3275 | 1.37764 | ||||||||
\(339\) | −0.912232 | −0.0495457 | ||||||||
\(340\) | 36.3003 | 1.96866 | ||||||||
\(341\) | 0.347938 | 0.0188419 | ||||||||
\(342\) | 37.2910 | 2.01646 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −90.4950 | −4.87916 | ||||||||
\(345\) | 5.39311 | 0.290355 | ||||||||
\(346\) | 48.6413 | 2.61497 | ||||||||
\(347\) | −21.8573 | −1.17336 | −0.586679 | − | 0.809819i | \(-0.699565\pi\) | ||||
−0.586679 | + | 0.809819i | \(0.699565\pi\) | |||||||
\(348\) | −75.5837 | −4.05171 | ||||||||
\(349\) | −26.1942 | −1.40214 | −0.701071 | − | 0.713092i | \(-0.747294\pi\) | ||||
−0.701071 | + | 0.713092i | \(0.747294\pi\) | |||||||
\(350\) | −11.9381 | −0.638117 | ||||||||
\(351\) | −26.2654 | −1.40194 | ||||||||
\(352\) | 11.7778 | 0.627761 | ||||||||
\(353\) | −29.4961 | −1.56992 | −0.784959 | − | 0.619548i | \(-0.787316\pi\) | ||||
−0.784959 | + | 0.619548i | \(0.787316\pi\) | |||||||
\(354\) | −87.5763 | −4.65463 | ||||||||
\(355\) | −18.7647 | −0.995925 | ||||||||
\(356\) | 80.6899 | 4.27656 | ||||||||
\(357\) | 7.09614 | 0.375568 | ||||||||
\(358\) | −34.4601 | −1.82127 | ||||||||
\(359\) | 13.2883 | 0.701329 | 0.350664 | − | 0.936501i | \(-0.385956\pi\) | ||||
0.350664 | + | 0.936501i | \(0.385956\pi\) | |||||||
\(360\) | −202.785 | −10.6877 | ||||||||
\(361\) | −15.4326 | −0.812244 | ||||||||
\(362\) | 20.4348 | 1.07403 | ||||||||
\(363\) | −34.1120 | −1.79041 | ||||||||
\(364\) | −10.2302 | −0.536207 | ||||||||
\(365\) | −38.2373 | −2.00143 | ||||||||
\(366\) | 38.4345 | 2.00900 | ||||||||
\(367\) | −30.8137 | −1.60846 | −0.804231 | − | 0.594317i | \(-0.797423\pi\) | ||||
−0.804231 | + | 0.594317i | \(0.797423\pi\) | |||||||
\(368\) | 7.63251 | 0.397872 | ||||||||
\(369\) | 88.3887 | 4.60133 | ||||||||
\(370\) | −19.7176 | −1.02507 | ||||||||
\(371\) | 1.66466 | 0.0864247 | ||||||||
\(372\) | −9.91594 | −0.514117 | ||||||||
\(373\) | −12.9802 | −0.672088 | −0.336044 | − | 0.941846i | \(-0.609089\pi\) | ||||
−0.336044 | + | 0.941846i | \(0.609089\pi\) | |||||||
\(374\) | 3.61088 | 0.186714 | ||||||||
\(375\) | −5.86440 | −0.302836 | ||||||||
\(376\) | 22.9031 | 1.18114 | ||||||||
\(377\) | 8.42665 | 0.433995 | ||||||||
\(378\) | −37.2326 | −1.91504 | ||||||||
\(379\) | 1.72719 | 0.0887198 | 0.0443599 | − | 0.999016i | \(-0.485875\pi\) | ||||
0.0443599 | + | 0.999016i | \(0.485875\pi\) | |||||||
\(380\) | −30.9828 | −1.58938 | ||||||||
\(381\) | −42.7255 | −2.18889 | ||||||||
\(382\) | −53.5089 | −2.73775 | ||||||||
\(383\) | −1.19820 | −0.0612251 | −0.0306125 | − | 0.999531i | \(-0.509746\pi\) | ||||
−0.0306125 | + | 0.999531i | \(0.509746\pi\) | |||||||
\(384\) | −93.6968 | −4.78144 | ||||||||
\(385\) | −1.84575 | −0.0940682 | ||||||||
\(386\) | −20.1762 | −1.02694 | ||||||||
\(387\) | 72.5854 | 3.68972 | ||||||||
\(388\) | −12.1275 | −0.615678 | ||||||||
\(389\) | 18.8931 | 0.957916 | 0.478958 | − | 0.877838i | \(-0.341015\pi\) | ||||
0.478958 | + | 0.877838i | \(0.341015\pi\) | |||||||
\(390\) | 50.9817 | 2.58156 | ||||||||
\(391\) | 1.21366 | 0.0613774 | ||||||||
\(392\) | −9.07991 | −0.458605 | ||||||||
\(393\) | −42.0358 | −2.12042 | ||||||||
\(394\) | 19.0910 | 0.961790 | ||||||||
\(395\) | −28.2314 | −1.42047 | ||||||||
\(396\) | −23.4493 | −1.17837 | ||||||||
\(397\) | −15.8486 | −0.795420 | −0.397710 | − | 0.917511i | \(-0.630195\pi\) | ||||
−0.397710 | + | 0.917511i | \(0.630195\pi\) | |||||||
\(398\) | 63.1574 | 3.16579 | ||||||||
\(399\) | −6.05664 | −0.303211 | ||||||||
\(400\) | 61.2837 | 3.06419 | ||||||||
\(401\) | −36.6445 | −1.82994 | −0.914970 | − | 0.403522i | \(-0.867786\pi\) | ||||
−0.914970 | + | 0.403522i | \(0.867786\pi\) | |||||||
\(402\) | −38.0216 | −1.89634 | ||||||||
\(403\) | 1.10550 | 0.0550691 | ||||||||
\(404\) | −65.8382 | −3.27557 | ||||||||
\(405\) | 68.0533 | 3.38160 | ||||||||
\(406\) | 11.9452 | 0.592832 | ||||||||
\(407\) | −1.42761 | −0.0707638 | ||||||||
\(408\) | −64.4323 | −3.18987 | ||||||||
\(409\) | 12.0856 | 0.597597 | 0.298798 | − | 0.954316i | \(-0.403414\pi\) | ||||
0.298798 | + | 0.954316i | \(0.403414\pi\) | |||||||
\(410\) | −100.893 | −4.98277 | ||||||||
\(411\) | 19.6996 | 0.971712 | ||||||||
\(412\) | −52.7171 | −2.59718 | ||||||||
\(413\) | 10.0741 | 0.495712 | ||||||||
\(414\) | −10.8284 | −0.532185 | ||||||||
\(415\) | 13.0427 | 0.640242 | ||||||||
\(416\) | 37.4218 | 1.83475 | ||||||||
\(417\) | 55.2692 | 2.70654 | ||||||||
\(418\) | −3.08193 | −0.150742 | ||||||||
\(419\) | −38.1018 | −1.86139 | −0.930697 | − | 0.365791i | \(-0.880798\pi\) | ||||
−0.930697 | + | 0.365791i | \(0.880798\pi\) | |||||||
\(420\) | 52.6024 | 2.56673 | ||||||||
\(421\) | −24.5812 | −1.19801 | −0.599007 | − | 0.800744i | \(-0.704438\pi\) | ||||
−0.599007 | + | 0.800744i | \(0.704438\pi\) | |||||||
\(422\) | 76.2896 | 3.71372 | ||||||||
\(423\) | −18.3704 | −0.893198 | ||||||||
\(424\) | −15.1149 | −0.734046 | ||||||||
\(425\) | 9.74484 | 0.472694 | ||||||||
\(426\) | 53.1955 | 2.57733 | ||||||||
\(427\) | −4.42119 | −0.213956 | ||||||||
\(428\) | 27.4677 | 1.32770 | ||||||||
\(429\) | 3.69121 | 0.178213 | ||||||||
\(430\) | −82.8542 | −3.99559 | ||||||||
\(431\) | 41.3162 | 1.99013 | 0.995066 | − | 0.0992107i | \(-0.0316318\pi\) | ||||
0.995066 | + | 0.0992107i | \(0.0316318\pi\) | |||||||
\(432\) | 191.132 | 9.19585 | ||||||||
\(433\) | 25.7438 | 1.23717 | 0.618584 | − | 0.785719i | \(-0.287707\pi\) | ||||
0.618584 | + | 0.785719i | \(0.287707\pi\) | |||||||
\(434\) | 1.56711 | 0.0752238 | ||||||||
\(435\) | −43.3288 | −2.07746 | ||||||||
\(436\) | 63.1494 | 3.02431 | ||||||||
\(437\) | −1.03587 | −0.0495525 | ||||||||
\(438\) | 108.398 | 5.17947 | ||||||||
\(439\) | −3.01761 | −0.144023 | −0.0720113 | − | 0.997404i | \(-0.522942\pi\) | ||||
−0.0720113 | + | 0.997404i | \(0.522942\pi\) | |||||||
\(440\) | 16.7593 | 0.798966 | ||||||||
\(441\) | 7.28293 | 0.346806 | ||||||||
\(442\) | 11.4729 | 0.545709 | ||||||||
\(443\) | −26.9062 | −1.27835 | −0.639177 | − | 0.769060i | \(-0.720725\pi\) | ||||
−0.639177 | + | 0.769060i | \(0.720725\pi\) | |||||||
\(444\) | 40.6856 | 1.93085 | ||||||||
\(445\) | 46.2560 | 2.19274 | ||||||||
\(446\) | −17.6694 | −0.836670 | ||||||||
\(447\) | 5.98871 | 0.283256 | ||||||||
\(448\) | 25.2141 | 1.19125 | ||||||||
\(449\) | 36.7009 | 1.73202 | 0.866012 | − | 0.500023i | \(-0.166675\pi\) | ||||
0.866012 | + | 0.500023i | \(0.166675\pi\) | |||||||
\(450\) | −86.9441 | −4.09859 | ||||||||
\(451\) | −7.30494 | −0.343976 | ||||||||
\(452\) | −1.52176 | −0.0715776 | ||||||||
\(453\) | −3.45340 | −0.162255 | ||||||||
\(454\) | 3.87859 | 0.182031 | ||||||||
\(455\) | −5.86452 | −0.274933 | ||||||||
\(456\) | 54.9938 | 2.57532 | ||||||||
\(457\) | 4.66643 | 0.218286 | 0.109143 | − | 0.994026i | \(-0.465189\pi\) | ||||
0.109143 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(458\) | 3.32183 | 0.155219 | ||||||||
\(459\) | 30.3923 | 1.41859 | ||||||||
\(460\) | 8.99663 | 0.419470 | ||||||||
\(461\) | −9.94352 | −0.463116 | −0.231558 | − | 0.972821i | \(-0.574382\pi\) | ||||
−0.231558 | + | 0.972821i | \(0.574382\pi\) | |||||||
\(462\) | 5.23248 | 0.243437 | ||||||||
\(463\) | −1.46888 | −0.0682645 | −0.0341322 | − | 0.999417i | \(-0.510867\pi\) | ||||
−0.0341322 | + | 0.999417i | \(0.510867\pi\) | |||||||
\(464\) | −61.3205 | −2.84673 | ||||||||
\(465\) | −5.68437 | −0.263606 | ||||||||
\(466\) | −78.0768 | −3.61684 | ||||||||
\(467\) | −29.1967 | −1.35106 | −0.675531 | − | 0.737332i | \(-0.736085\pi\) | ||||
−0.675531 | + | 0.737332i | \(0.736085\pi\) | |||||||
\(468\) | −74.5057 | −3.44403 | ||||||||
\(469\) | 4.37369 | 0.201958 | ||||||||
\(470\) | 20.9693 | 0.967241 | ||||||||
\(471\) | 50.8395 | 2.34256 | ||||||||
\(472\) | −91.4715 | −4.21032 | ||||||||
\(473\) | −5.99886 | −0.275828 | ||||||||
\(474\) | 80.0325 | 3.67601 | ||||||||
\(475\) | −8.31734 | −0.381626 | ||||||||
\(476\) | 11.8376 | 0.542575 | ||||||||
\(477\) | 12.1236 | 0.555101 | ||||||||
\(478\) | −26.1165 | −1.19454 | ||||||||
\(479\) | −36.8990 | −1.68596 | −0.842980 | − | 0.537945i | \(-0.819201\pi\) | ||||
−0.842980 | + | 0.537945i | \(0.819201\pi\) | |||||||
\(480\) | −192.418 | −8.78265 | ||||||||
\(481\) | −4.53594 | −0.206821 | ||||||||
\(482\) | −80.0553 | −3.64642 | ||||||||
\(483\) | 1.75870 | 0.0800235 | ||||||||
\(484\) | −56.9046 | −2.58657 | ||||||||
\(485\) | −6.95213 | −0.315680 | ||||||||
\(486\) | −81.2251 | −3.68445 | ||||||||
\(487\) | 4.33836 | 0.196590 | 0.0982949 | − | 0.995157i | \(-0.468661\pi\) | ||||
0.0982949 | + | 0.995157i | \(0.468661\pi\) | |||||||
\(488\) | 40.1440 | 1.81723 | ||||||||
\(489\) | 58.7170 | 2.65527 | ||||||||
\(490\) | −8.31326 | −0.375555 | ||||||||
\(491\) | −17.5659 | −0.792739 | −0.396370 | − | 0.918091i | \(-0.629730\pi\) | ||||
−0.396370 | + | 0.918091i | \(0.629730\pi\) | |||||||
\(492\) | 208.185 | 9.38568 | ||||||||
\(493\) | −9.75068 | −0.439148 | ||||||||
\(494\) | −9.79224 | −0.440574 | ||||||||
\(495\) | −13.4425 | −0.604194 | ||||||||
\(496\) | −8.04472 | −0.361218 | ||||||||
\(497\) | −6.11918 | −0.274483 | ||||||||
\(498\) | −36.9745 | −1.65687 | ||||||||
\(499\) | −35.8314 | −1.60403 | −0.802017 | − | 0.597301i | \(-0.796240\pi\) | ||||
−0.802017 | + | 0.597301i | \(0.796240\pi\) | |||||||
\(500\) | −9.78283 | −0.437502 | ||||||||
\(501\) | 13.1170 | 0.586026 | ||||||||
\(502\) | −47.6898 | −2.12850 | ||||||||
\(503\) | 24.9407 | 1.11205 | 0.556026 | − | 0.831165i | \(-0.312326\pi\) | ||||
0.556026 | + | 0.831165i | \(0.312326\pi\) | |||||||
\(504\) | −66.1283 | −2.94559 | ||||||||
\(505\) | −37.7421 | −1.67950 | ||||||||
\(506\) | 0.894916 | 0.0397839 | ||||||||
\(507\) | −29.9590 | −1.33053 | ||||||||
\(508\) | −71.2734 | −3.16225 | ||||||||
\(509\) | −7.26986 | −0.322231 | −0.161116 | − | 0.986936i | \(-0.551509\pi\) | ||||
−0.161116 | + | 0.986936i | \(0.551509\pi\) | |||||||
\(510\) | −58.9921 | −2.61221 | ||||||||
\(511\) | −12.4692 | −0.551607 | ||||||||
\(512\) | −19.5933 | −0.865911 | ||||||||
\(513\) | −25.9402 | −1.14529 | ||||||||
\(514\) | 41.0596 | 1.81106 | ||||||||
\(515\) | −30.2204 | −1.33167 | ||||||||
\(516\) | 170.962 | 7.52620 | ||||||||
\(517\) | 1.51823 | 0.0667717 | ||||||||
\(518\) | −6.42994 | −0.282515 | ||||||||
\(519\) | −57.5360 | −2.52555 | ||||||||
\(520\) | 53.2492 | 2.33513 | ||||||||
\(521\) | 17.4924 | 0.766356 | 0.383178 | − | 0.923675i | \(-0.374830\pi\) | ||||
0.383178 | + | 0.923675i | \(0.374830\pi\) | |||||||
\(522\) | 86.9963 | 3.80772 | ||||||||
\(523\) | 39.4369 | 1.72446 | 0.862228 | − | 0.506521i | \(-0.169069\pi\) | ||||
0.862228 | + | 0.506521i | \(0.169069\pi\) | |||||||
\(524\) | −70.1229 | −3.06333 | ||||||||
\(525\) | 14.1211 | 0.616296 | ||||||||
\(526\) | 47.4149 | 2.06739 | ||||||||
\(527\) | −1.27920 | −0.0557230 | ||||||||
\(528\) | −26.8608 | −1.16897 | ||||||||
\(529\) | −22.6992 | −0.986922 | ||||||||
\(530\) | −13.8387 | −0.601116 | ||||||||
\(531\) | 73.3686 | 3.18393 | ||||||||
\(532\) | −10.1035 | −0.438043 | ||||||||
\(533\) | −23.2100 | −1.00534 | ||||||||
\(534\) | −131.130 | −5.67455 | ||||||||
\(535\) | 15.7460 | 0.680760 | ||||||||
\(536\) | −39.7127 | −1.71533 | ||||||||
\(537\) | 40.7615 | 1.75899 | ||||||||
\(538\) | −60.4238 | −2.60506 | ||||||||
\(539\) | −0.601902 | −0.0259257 | ||||||||
\(540\) | 225.292 | 9.69503 | ||||||||
\(541\) | −29.3765 | −1.26300 | −0.631498 | − | 0.775377i | \(-0.717560\pi\) | ||||
−0.631498 | + | 0.775377i | \(0.717560\pi\) | |||||||
\(542\) | 3.78402 | 0.162538 | ||||||||
\(543\) | −24.1715 | −1.03730 | ||||||||
\(544\) | −43.3016 | −1.85654 | ||||||||
\(545\) | 36.2008 | 1.55067 | ||||||||
\(546\) | 16.6252 | 0.711492 | ||||||||
\(547\) | 23.3507 | 0.998402 | 0.499201 | − | 0.866486i | \(-0.333627\pi\) | ||||
0.499201 | + | 0.866486i | \(0.333627\pi\) | |||||||
\(548\) | 32.8624 | 1.40381 | ||||||||
\(549\) | −32.1992 | −1.37423 | ||||||||
\(550\) | 7.18555 | 0.306393 | ||||||||
\(551\) | 8.32232 | 0.354543 | ||||||||
\(552\) | −15.9688 | −0.679678 | ||||||||
\(553\) | −9.20628 | −0.391491 | ||||||||
\(554\) | 23.7605 | 1.00949 | ||||||||
\(555\) | 23.3233 | 0.990017 | ||||||||
\(556\) | 92.1985 | 3.91009 | ||||||||
\(557\) | −18.7893 | −0.796127 | −0.398063 | − | 0.917358i | \(-0.630318\pi\) | ||||
−0.398063 | + | 0.917358i | \(0.630318\pi\) | |||||||
\(558\) | 11.4132 | 0.483158 | ||||||||
\(559\) | −19.0602 | −0.806161 | ||||||||
\(560\) | 42.6759 | 1.80338 | ||||||||
\(561\) | −4.27118 | −0.180329 | ||||||||
\(562\) | −26.2359 | −1.10669 | ||||||||
\(563\) | 36.2316 | 1.52698 | 0.763489 | − | 0.645820i | \(-0.223485\pi\) | ||||
0.763489 | + | 0.645820i | \(0.223485\pi\) | |||||||
\(564\) | −43.2683 | −1.82192 | ||||||||
\(565\) | −0.872358 | −0.0367004 | ||||||||
\(566\) | −35.9429 | −1.51079 | ||||||||
\(567\) | 22.1923 | 0.931987 | ||||||||
\(568\) | 55.5616 | 2.33131 | ||||||||
\(569\) | 6.51409 | 0.273085 | 0.136542 | − | 0.990634i | \(-0.456401\pi\) | ||||
0.136542 | + | 0.990634i | \(0.456401\pi\) | |||||||
\(570\) | 50.3505 | 2.10895 | ||||||||
\(571\) | −39.6208 | −1.65808 | −0.829040 | − | 0.559190i | \(-0.811112\pi\) | ||||
−0.829040 | + | 0.559190i | \(0.811112\pi\) | |||||||
\(572\) | 6.15757 | 0.257461 | ||||||||
\(573\) | 63.2937 | 2.64413 | ||||||||
\(574\) | −32.9014 | −1.37328 | ||||||||
\(575\) | 2.41515 | 0.100719 | ||||||||
\(576\) | 183.632 | 7.65135 | ||||||||
\(577\) | 34.5277 | 1.43741 | 0.718703 | − | 0.695317i | \(-0.244736\pi\) | ||||
0.718703 | + | 0.695317i | \(0.244736\pi\) | |||||||
\(578\) | 32.8109 | 1.36475 | ||||||||
\(579\) | 23.8657 | 0.991824 | ||||||||
\(580\) | −72.2799 | −3.00126 | ||||||||
\(581\) | 4.25325 | 0.176454 | ||||||||
\(582\) | 19.7085 | 0.816942 | ||||||||
\(583\) | −1.00196 | −0.0414970 | ||||||||
\(584\) | 113.220 | 4.68506 | ||||||||
\(585\) | −42.7108 | −1.76588 | ||||||||
\(586\) | −21.2000 | −0.875765 | ||||||||
\(587\) | −5.02385 | −0.207356 | −0.103678 | − | 0.994611i | \(-0.533061\pi\) | ||||
−0.103678 | + | 0.994611i | \(0.533061\pi\) | |||||||
\(588\) | 17.1537 | 0.707406 | ||||||||
\(589\) | 1.09182 | 0.0449875 | ||||||||
\(590\) | −83.7483 | −3.44786 | ||||||||
\(591\) | −22.5820 | −0.928900 | ||||||||
\(592\) | 33.0079 | 1.35662 | ||||||||
\(593\) | −8.08190 | −0.331884 | −0.165942 | − | 0.986136i | \(-0.553066\pi\) | ||||
−0.165942 | + | 0.986136i | \(0.553066\pi\) | |||||||
\(594\) | 22.4103 | 0.919508 | ||||||||
\(595\) | 6.78597 | 0.278197 | ||||||||
\(596\) | 9.99019 | 0.409214 | ||||||||
\(597\) | −74.7066 | −3.05754 | ||||||||
\(598\) | 2.84342 | 0.116276 | ||||||||
\(599\) | 8.53728 | 0.348824 | 0.174412 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174412 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(600\) | −128.218 | −5.23449 | ||||||||
\(601\) | −43.3785 | −1.76945 | −0.884724 | − | 0.466115i | \(-0.845653\pi\) | ||||
−0.884724 | + | 0.466115i | \(0.845653\pi\) | |||||||
\(602\) | −27.0189 | −1.10121 | ||||||||
\(603\) | 31.8533 | 1.29717 | ||||||||
\(604\) | −5.76087 | −0.234406 | ||||||||
\(605\) | −32.6209 | −1.32623 | ||||||||
\(606\) | 106.994 | 4.34635 | ||||||||
\(607\) | 13.8624 | 0.562659 | 0.281329 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281329 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(608\) | 36.9585 | 1.49886 | ||||||||
\(609\) | −14.1296 | −0.572559 | ||||||||
\(610\) | 36.7545 | 1.48815 | ||||||||
\(611\) | 4.82388 | 0.195153 | ||||||||
\(612\) | 86.2123 | 3.48492 | ||||||||
\(613\) | −11.5877 | −0.468021 | −0.234011 | − | 0.972234i | \(-0.575185\pi\) | ||||
−0.234011 | + | 0.972234i | \(0.575185\pi\) | |||||||
\(614\) | −71.8614 | −2.90009 | ||||||||
\(615\) | 119.343 | 4.81238 | ||||||||
\(616\) | 5.46521 | 0.220200 | ||||||||
\(617\) | 8.24646 | 0.331990 | 0.165995 | − | 0.986127i | \(-0.446916\pi\) | ||||
0.165995 | + | 0.986127i | \(0.446916\pi\) | |||||||
\(618\) | 85.6711 | 3.44620 | ||||||||
\(619\) | −19.0552 | −0.765892 | −0.382946 | − | 0.923771i | \(-0.625091\pi\) | ||||
−0.382946 | + | 0.923771i | \(0.625091\pi\) | |||||||
\(620\) | −9.48250 | −0.380827 | ||||||||
\(621\) | 7.53238 | 0.302264 | ||||||||
\(622\) | −25.9736 | −1.04145 | ||||||||
\(623\) | 15.0841 | 0.604333 | ||||||||
\(624\) | −85.3449 | −3.41653 | ||||||||
\(625\) | −27.6262 | −1.10505 | ||||||||
\(626\) | 24.4218 | 0.976092 | ||||||||
\(627\) | 3.64550 | 0.145587 | ||||||||
\(628\) | 84.8090 | 3.38425 | ||||||||
\(629\) | 5.24864 | 0.209277 | ||||||||
\(630\) | −60.5449 | −2.41217 | ||||||||
\(631\) | 26.4779 | 1.05407 | 0.527034 | − | 0.849844i | \(-0.323304\pi\) | ||||
0.527034 | + | 0.849844i | \(0.323304\pi\) | |||||||
\(632\) | 83.5921 | 3.32512 | ||||||||
\(633\) | −90.2402 | −3.58673 | ||||||||
\(634\) | −31.5783 | −1.25414 | ||||||||
\(635\) | −40.8579 | −1.62140 | ||||||||
\(636\) | 28.5550 | 1.13228 | ||||||||
\(637\) | −1.91242 | −0.0757730 | ||||||||
\(638\) | −7.18986 | −0.284649 | ||||||||
\(639\) | −44.5655 | −1.76299 | ||||||||
\(640\) | −89.6012 | −3.54180 | ||||||||
\(641\) | −8.68284 | −0.342952 | −0.171476 | − | 0.985188i | \(-0.554854\pi\) | ||||
−0.171476 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(642\) | −44.6381 | −1.76173 | ||||||||
\(643\) | −0.267433 | −0.0105465 | −0.00527327 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527327 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(644\) | 2.93381 | 0.115608 | ||||||||
\(645\) | 98.0053 | 3.85895 | ||||||||
\(646\) | 11.3308 | 0.445805 | ||||||||
\(647\) | 30.0226 | 1.18031 | 0.590154 | − | 0.807291i | \(-0.299067\pi\) | ||||
0.590154 | + | 0.807291i | \(0.299067\pi\) | |||||||
\(648\) | −201.504 | −7.91581 | ||||||||
\(649\) | −6.06359 | −0.238017 | ||||||||
\(650\) | 22.8307 | 0.895493 | ||||||||
\(651\) | −1.85368 | −0.0726514 | ||||||||
\(652\) | 97.9500 | 3.83602 | ||||||||
\(653\) | −0.661776 | −0.0258973 | −0.0129487 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129487 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(654\) | −102.625 | −4.01295 | ||||||||
\(655\) | −40.1984 | −1.57068 | ||||||||
\(656\) | 168.898 | 6.59437 | ||||||||
\(657\) | −90.8126 | −3.54294 | ||||||||
\(658\) | 6.83811 | 0.266577 | ||||||||
\(659\) | −6.77978 | −0.264103 | −0.132051 | − | 0.991243i | \(-0.542156\pi\) | ||||
−0.132051 | + | 0.991243i | \(0.542156\pi\) | |||||||
\(660\) | −31.6615 | −1.23242 | ||||||||
\(661\) | −11.1445 | −0.433471 | −0.216735 | − | 0.976230i | \(-0.569541\pi\) | ||||
−0.216735 | + | 0.976230i | \(0.569541\pi\) | |||||||
\(662\) | 81.1840 | 3.15531 | ||||||||
\(663\) | −13.5708 | −0.527048 | ||||||||
\(664\) | −38.6191 | −1.49871 | ||||||||
\(665\) | −5.79190 | −0.224600 | ||||||||
\(666\) | −46.8288 | −1.81458 | ||||||||
\(667\) | −2.41659 | −0.0935709 | ||||||||
\(668\) | 21.8815 | 0.846620 | ||||||||
\(669\) | 20.9005 | 0.808059 | ||||||||
\(670\) | −36.3596 | −1.40470 | ||||||||
\(671\) | 2.66112 | 0.102731 | ||||||||
\(672\) | −62.7478 | −2.42055 | ||||||||
\(673\) | 16.4967 | 0.635900 | 0.317950 | − | 0.948108i | \(-0.397006\pi\) | ||||
0.317950 | + | 0.948108i | \(0.397006\pi\) | |||||||
\(674\) | 59.4084 | 2.28833 | ||||||||
\(675\) | 60.4797 | 2.32787 | ||||||||
\(676\) | −49.9768 | −1.92218 | ||||||||
\(677\) | 9.29907 | 0.357392 | 0.178696 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178696 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(678\) | 2.47303 | 0.0949761 | ||||||||
\(679\) | −2.26710 | −0.0870033 | ||||||||
\(680\) | −61.6159 | −2.36286 | ||||||||
\(681\) | −4.58784 | −0.175807 | ||||||||
\(682\) | −0.943247 | −0.0361188 | ||||||||
\(683\) | 34.2106 | 1.30903 | 0.654517 | − | 0.756047i | \(-0.272872\pi\) | ||||
0.654517 | + | 0.756047i | \(0.272872\pi\) | |||||||
\(684\) | −73.5832 | −2.81353 | ||||||||
\(685\) | 18.8386 | 0.719784 | ||||||||
\(686\) | −2.71096 | −0.103505 | ||||||||
\(687\) | −3.92927 | −0.149911 | ||||||||
\(688\) | 138.700 | 5.28790 | ||||||||
\(689\) | −3.18353 | −0.121283 | ||||||||
\(690\) | −14.6205 | −0.556594 | ||||||||
\(691\) | −33.5702 | −1.27707 | −0.638535 | − | 0.769592i | \(-0.720459\pi\) | ||||
−0.638535 | + | 0.769592i | \(0.720459\pi\) | |||||||
\(692\) | −95.9799 | −3.64861 | ||||||||
\(693\) | −4.38361 | −0.166519 | ||||||||
\(694\) | 59.2542 | 2.24926 | ||||||||
\(695\) | 52.8533 | 2.00484 | ||||||||
\(696\) | 128.295 | 4.86302 | ||||||||
\(697\) | 26.8568 | 1.01728 | ||||||||
\(698\) | 71.0115 | 2.68782 | ||||||||
\(699\) | 92.3541 | 3.49315 | ||||||||
\(700\) | 23.5564 | 0.890350 | ||||||||
\(701\) | −17.6438 | −0.666397 | −0.333199 | − | 0.942857i | \(-0.608128\pi\) | ||||
−0.333199 | + | 0.942857i | \(0.608128\pi\) | |||||||
\(702\) | 71.2045 | 2.68744 | ||||||||
\(703\) | −4.47978 | −0.168958 | ||||||||
\(704\) | −15.1764 | −0.571982 | ||||||||
\(705\) | −24.8038 | −0.934165 | ||||||||
\(706\) | 79.9628 | 3.00944 | ||||||||
\(707\) | −12.3078 | −0.462881 | ||||||||
\(708\) | 172.807 | 6.49449 | ||||||||
\(709\) | −6.24030 | −0.234359 | −0.117180 | − | 0.993111i | \(-0.537385\pi\) | ||||
−0.117180 | + | 0.993111i | \(0.537385\pi\) | |||||||
\(710\) | 50.8703 | 1.90913 | ||||||||
\(711\) | −67.0487 | −2.51452 | ||||||||
\(712\) | −136.962 | −5.13288 | ||||||||
\(713\) | −0.317036 | −0.0118731 | ||||||||
\(714\) | −19.2374 | −0.719941 | ||||||||
\(715\) | 3.52986 | 0.132009 | ||||||||
\(716\) | 67.9972 | 2.54118 | ||||||||
\(717\) | 30.8923 | 1.15369 | ||||||||
\(718\) | −36.0241 | −1.34441 | ||||||||
\(719\) | 15.2834 | 0.569974 | 0.284987 | − | 0.958531i | \(-0.408011\pi\) | ||||
0.284987 | + | 0.958531i | \(0.408011\pi\) | |||||||
\(720\) | 310.805 | 11.5830 | ||||||||
\(721\) | −9.85490 | −0.367016 | ||||||||
\(722\) | 41.8373 | 1.55702 | ||||||||
\(723\) | 94.6945 | 3.52173 | ||||||||
\(724\) | −40.3223 | −1.49857 | ||||||||
\(725\) | −19.4036 | −0.720630 | ||||||||
\(726\) | 92.4763 | 3.43212 | ||||||||
\(727\) | 34.8340 | 1.29192 | 0.645961 | − | 0.763370i | \(-0.276457\pi\) | ||||
0.645961 | + | 0.763370i | \(0.276457\pi\) | |||||||
\(728\) | 17.3646 | 0.643576 | ||||||||
\(729\) | 29.5015 | 1.09265 | ||||||||
\(730\) | 103.660 | 3.83663 | ||||||||
\(731\) | 22.0550 | 0.815734 | ||||||||
\(732\) | −75.8397 | −2.80312 | ||||||||
\(733\) | −11.1026 | −0.410084 | −0.205042 | − | 0.978753i | \(-0.565733\pi\) | ||||
−0.205042 | + | 0.978753i | \(0.565733\pi\) | |||||||
\(734\) | 83.5348 | 3.08333 | ||||||||
\(735\) | 9.83345 | 0.362712 | ||||||||
\(736\) | −10.7318 | −0.395580 | ||||||||
\(737\) | −2.63253 | −0.0969705 | ||||||||
\(738\) | −239.619 | −8.82049 | ||||||||
\(739\) | −5.17889 | −0.190509 | −0.0952543 | − | 0.995453i | \(-0.530366\pi\) | ||||
−0.0952543 | + | 0.995453i | \(0.530366\pi\) | |||||||
\(740\) | 38.9072 | 1.43026 | ||||||||
\(741\) | 11.5829 | 0.425508 | ||||||||
\(742\) | −4.51283 | −0.165671 | ||||||||
\(743\) | 31.7879 | 1.16618 | 0.583092 | − | 0.812406i | \(-0.301843\pi\) | ||||
0.583092 | + | 0.812406i | \(0.301843\pi\) | |||||||
\(744\) | 16.8312 | 0.617063 | ||||||||
\(745\) | 5.72693 | 0.209819 | ||||||||
\(746\) | 35.1888 | 1.28835 | ||||||||
\(747\) | 30.9761 | 1.13336 | ||||||||
\(748\) | −7.12506 | −0.260518 | ||||||||
\(749\) | 5.13480 | 0.187622 | ||||||||
\(750\) | 15.8982 | 0.580520 | ||||||||
\(751\) | −37.4767 | −1.36755 | −0.683773 | − | 0.729695i | \(-0.739662\pi\) | ||||
−0.683773 | + | 0.729695i | \(0.739662\pi\) | |||||||
\(752\) | −35.1032 | −1.28008 | ||||||||
\(753\) | 56.4106 | 2.05572 | ||||||||
\(754\) | −22.8444 | −0.831942 | ||||||||
\(755\) | −3.30245 | −0.120188 | ||||||||
\(756\) | 73.4680 | 2.67201 | ||||||||
\(757\) | 28.3676 | 1.03104 | 0.515519 | − | 0.856878i | \(-0.327599\pi\) | ||||
0.515519 | + | 0.856878i | \(0.327599\pi\) | |||||||
\(758\) | −4.68235 | −0.170071 | ||||||||
\(759\) | −1.05856 | −0.0384234 | ||||||||
\(760\) | 52.5899 | 1.90764 | ||||||||
\(761\) | 13.4009 | 0.485784 | 0.242892 | − | 0.970053i | \(-0.421904\pi\) | ||||
0.242892 | + | 0.970053i | \(0.421904\pi\) | |||||||
\(762\) | 115.827 | 4.19598 | ||||||||
\(763\) | 11.8051 | 0.427374 | ||||||||
\(764\) | 105.585 | 3.81993 | ||||||||
\(765\) | 49.4217 | 1.78685 | ||||||||
\(766\) | 3.24827 | 0.117365 | ||||||||
\(767\) | −19.2659 | −0.695650 | ||||||||
\(768\) | 92.3006 | 3.33061 | ||||||||
\(769\) | −33.4525 | −1.20633 | −0.603163 | − | 0.797618i | \(-0.706093\pi\) | ||||
−0.603163 | + | 0.797618i | \(0.706093\pi\) | |||||||
\(770\) | 5.00377 | 0.180323 | ||||||||
\(771\) | −48.5679 | −1.74913 | ||||||||
\(772\) | 39.8120 | 1.43287 | ||||||||
\(773\) | −20.4101 | −0.734101 | −0.367050 | − | 0.930201i | \(-0.619632\pi\) | ||||
−0.367050 | + | 0.930201i | \(0.619632\pi\) | |||||||
\(774\) | −196.776 | −7.07298 | ||||||||
\(775\) | −2.54558 | −0.0914399 | ||||||||
\(776\) | 20.5850 | 0.738960 | ||||||||
\(777\) | 7.60574 | 0.272854 | ||||||||
\(778\) | −51.2184 | −1.83627 | ||||||||
\(779\) | −22.9226 | −0.821289 | ||||||||
\(780\) | −100.598 | −3.60199 | ||||||||
\(781\) | 3.68314 | 0.131793 | ||||||||
\(782\) | −3.29019 | −0.117657 | ||||||||
\(783\) | −60.5160 | −2.16266 | ||||||||
\(784\) | 13.9166 | 0.497023 | ||||||||
\(785\) | 48.6172 | 1.73522 | ||||||||
\(786\) | 113.957 | 4.06473 | ||||||||
\(787\) | 30.8722 | 1.10048 | 0.550238 | − | 0.835008i | \(-0.314537\pi\) | ||||
0.550238 | + | 0.835008i | \(0.314537\pi\) | |||||||
\(788\) | −37.6707 | −1.34196 | ||||||||
\(789\) | −56.0854 | −1.99669 | ||||||||
\(790\) | 76.5342 | 2.72297 | ||||||||
\(791\) | −0.284477 | −0.0101148 | ||||||||
\(792\) | 39.8027 | 1.41433 | ||||||||
\(793\) | 8.45519 | 0.300253 | ||||||||
\(794\) | 42.9651 | 1.52477 | ||||||||
\(795\) | 16.3693 | 0.580560 | ||||||||
\(796\) | −124.623 | −4.41716 | ||||||||
\(797\) | 14.9883 | 0.530911 | 0.265456 | − | 0.964123i | \(-0.414478\pi\) | ||||
0.265456 | + | 0.964123i | \(0.414478\pi\) | |||||||
\(798\) | 16.4193 | 0.581239 | ||||||||
\(799\) | −5.58182 | −0.197471 | ||||||||
\(800\) | −86.1689 | −3.04653 | ||||||||
\(801\) | 109.857 | 3.88159 | ||||||||
\(802\) | 99.3420 | 3.50789 | ||||||||
\(803\) | 7.50526 | 0.264855 | ||||||||
\(804\) | 75.0249 | 2.64592 | ||||||||
\(805\) | 1.68182 | 0.0592765 | ||||||||
\(806\) | −2.99698 | −0.105564 | ||||||||
\(807\) | 71.4731 | 2.51597 | ||||||||
\(808\) | 111.753 | 3.93147 | ||||||||
\(809\) | −23.7519 | −0.835072 | −0.417536 | − | 0.908660i | \(-0.637106\pi\) | ||||
−0.417536 | + | 0.908660i | \(0.637106\pi\) | |||||||
\(810\) | −184.490 | −6.48232 | ||||||||
\(811\) | 35.7034 | 1.25372 | 0.626858 | − | 0.779134i | \(-0.284341\pi\) | ||||
0.626858 | + | 0.779134i | \(0.284341\pi\) | |||||||
\(812\) | −23.5706 | −0.827165 | ||||||||
\(813\) | −4.47598 | −0.156980 | ||||||||
\(814\) | 3.87019 | 0.135650 | ||||||||
\(815\) | 56.1504 | 1.96686 | ||||||||
\(816\) | 98.7545 | 3.45710 | ||||||||
\(817\) | −18.8242 | −0.658576 | ||||||||
\(818\) | −32.7638 | −1.14556 | ||||||||
\(819\) | −13.9281 | −0.486686 | ||||||||
\(820\) | 199.085 | 6.95234 | ||||||||
\(821\) | 0.845604 | 0.0295118 | 0.0147559 | − | 0.999891i | \(-0.495303\pi\) | ||||
0.0147559 | + | 0.999891i | \(0.495303\pi\) | |||||||
\(822\) | −53.4050 | −1.86271 | ||||||||
\(823\) | 49.7219 | 1.73320 | 0.866599 | − | 0.499005i | \(-0.166301\pi\) | ||||
0.866599 | + | 0.499005i | \(0.166301\pi\) | |||||||
\(824\) | 89.4816 | 3.11724 | ||||||||
\(825\) | −8.49952 | −0.295915 | ||||||||
\(826\) | −27.3104 | −0.950251 | ||||||||
\(827\) | −46.3319 | −1.61112 | −0.805559 | − | 0.592516i | \(-0.798135\pi\) | ||||
−0.805559 | + | 0.592516i | \(0.798135\pi\) | |||||||
\(828\) | 21.3667 | 0.742545 | ||||||||
\(829\) | −45.0333 | −1.56407 | −0.782035 | − | 0.623235i | \(-0.785818\pi\) | ||||
−0.782035 | + | 0.623235i | \(0.785818\pi\) | |||||||
\(830\) | −35.3584 | −1.22731 | ||||||||
\(831\) | −28.1054 | −0.974965 | ||||||||
\(832\) | −48.2201 | −1.67173 | ||||||||
\(833\) | 2.21291 | 0.0766728 | ||||||||
\(834\) | −149.833 | −5.18828 | ||||||||
\(835\) | 12.5437 | 0.434092 | ||||||||
\(836\) | 6.08133 | 0.210327 | ||||||||
\(837\) | −7.93917 | −0.274418 | ||||||||
\(838\) | 103.293 | 3.56818 | ||||||||
\(839\) | −26.6191 | −0.918994 | −0.459497 | − | 0.888179i | \(-0.651970\pi\) | ||||
−0.459497 | + | 0.888179i | \(0.651970\pi\) | |||||||
\(840\) | −89.2868 | −3.08069 | ||||||||
\(841\) | −9.58482 | −0.330511 | ||||||||
\(842\) | 66.6387 | 2.29652 | ||||||||
\(843\) | 31.0334 | 1.06885 | ||||||||
\(844\) | −150.536 | −5.18167 | ||||||||
\(845\) | −28.6495 | −0.985572 | ||||||||
\(846\) | 49.8014 | 1.71221 | ||||||||
\(847\) | −10.6377 | −0.365516 | ||||||||
\(848\) | 23.1665 | 0.795539 | ||||||||
\(849\) | 42.5155 | 1.45913 | ||||||||
\(850\) | −26.4179 | −0.906126 | ||||||||
\(851\) | 1.30082 | 0.0445914 | ||||||||
\(852\) | −104.966 | −3.59609 | ||||||||
\(853\) | −14.5421 | −0.497911 | −0.248956 | − | 0.968515i | \(-0.580087\pi\) | ||||
−0.248956 | + | 0.968515i | \(0.580087\pi\) | |||||||
\(854\) | 11.9857 | 0.410142 | ||||||||
\(855\) | −42.1820 | −1.44259 | ||||||||
\(856\) | −46.6235 | −1.59356 | ||||||||
\(857\) | 3.56813 | 0.121885 | 0.0609425 | − | 0.998141i | \(-0.480589\pi\) | ||||
0.0609425 | + | 0.998141i | \(0.480589\pi\) | |||||||
\(858\) | −10.0067 | −0.341624 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 163.490 | 5.57495 | ||||||||
\(861\) | 38.9179 | 1.32632 | ||||||||
\(862\) | −112.007 | −3.81497 | ||||||||
\(863\) | −8.63542 | −0.293953 | −0.146977 | − | 0.989140i | \(-0.546954\pi\) | ||||
−0.146977 | + | 0.989140i | \(0.546954\pi\) | |||||||
\(864\) | −268.744 | −9.14287 | ||||||||
\(865\) | −55.0211 | −1.87077 | ||||||||
\(866\) | −69.7905 | −2.37158 | ||||||||
\(867\) | −38.8108 | −1.31808 | ||||||||
\(868\) | −3.09226 | −0.104958 | ||||||||
\(869\) | 5.54128 | 0.187975 | ||||||||
\(870\) | 117.463 | 3.98236 | ||||||||
\(871\) | −8.36435 | −0.283415 | ||||||||
\(872\) | −107.189 | −3.62989 | ||||||||
\(873\) | −16.5111 | −0.558817 | ||||||||
\(874\) | 2.80821 | 0.0949893 | ||||||||
\(875\) | −1.82880 | −0.0618246 | ||||||||
\(876\) | −213.893 | −7.22679 | ||||||||
\(877\) | 4.42770 | 0.149513 | 0.0747564 | − | 0.997202i | \(-0.476182\pi\) | ||||
0.0747564 | + | 0.997202i | \(0.476182\pi\) | |||||||
\(878\) | 8.18063 | 0.276083 | ||||||||
\(879\) | 25.0767 | 0.845817 | ||||||||
\(880\) | −25.6867 | −0.865898 | ||||||||
\(881\) | 33.2611 | 1.12060 | 0.560298 | − | 0.828291i | \(-0.310687\pi\) | ||||
0.560298 | + | 0.828291i | \(0.310687\pi\) | |||||||
\(882\) | −19.7438 | −0.664807 | ||||||||
\(883\) | −26.5866 | −0.894712 | −0.447356 | − | 0.894356i | \(-0.647634\pi\) | ||||
−0.447356 | + | 0.894356i | \(0.647634\pi\) | |||||||
\(884\) | −22.6385 | −0.761415 | ||||||||
\(885\) | 99.0628 | 3.32996 | ||||||||
\(886\) | 72.9419 | 2.45053 | ||||||||
\(887\) | −27.1995 | −0.913272 | −0.456636 | − | 0.889654i | \(-0.650946\pi\) | ||||
−0.456636 | + | 0.889654i | \(0.650946\pi\) | |||||||
\(888\) | −69.0594 | −2.31748 | ||||||||
\(889\) | −13.3238 | −0.446866 | ||||||||
\(890\) | −125.398 | −4.20336 | ||||||||
\(891\) | −13.3576 | −0.447495 | ||||||||
\(892\) | 34.8656 | 1.16739 | ||||||||
\(893\) | 4.76415 | 0.159426 | ||||||||
\(894\) | −16.2352 | −0.542985 | ||||||||
\(895\) | 38.9798 | 1.30295 | ||||||||
\(896\) | −29.2191 | −0.976140 | ||||||||
\(897\) | −3.36338 | −0.112300 | ||||||||
\(898\) | −99.4949 | −3.32019 | ||||||||
\(899\) | 2.54711 | 0.0849507 | ||||||||
\(900\) | 171.560 | 5.71866 | ||||||||
\(901\) | 3.68374 | 0.122723 | ||||||||
\(902\) | 19.8034 | 0.659382 | ||||||||
\(903\) | 31.9596 | 1.06355 | ||||||||
\(904\) | 2.58302 | 0.0859101 | ||||||||
\(905\) | −23.1150 | −0.768368 | ||||||||
\(906\) | 9.36205 | 0.311033 | ||||||||
\(907\) | −37.5501 | −1.24683 | −0.623415 | − | 0.781892i | \(-0.714255\pi\) | ||||
−0.623415 | + | 0.781892i | \(0.714255\pi\) | |||||||
\(908\) | −7.65331 | −0.253984 | ||||||||
\(909\) | −89.6365 | −2.97305 | ||||||||
\(910\) | 15.8985 | 0.527030 | ||||||||
\(911\) | −23.6806 | −0.784574 | −0.392287 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392287 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(912\) | −84.2882 | −2.79106 | ||||||||
\(913\) | −2.56004 | −0.0847248 | ||||||||
\(914\) | −12.6505 | −0.418442 | ||||||||
\(915\) | −43.4756 | −1.43726 | ||||||||
\(916\) | −6.55469 | −0.216573 | ||||||||
\(917\) | −13.1087 | −0.432888 | ||||||||
\(918\) | −82.3923 | −2.71935 | ||||||||
\(919\) | 22.2342 | 0.733440 | 0.366720 | − | 0.930331i | \(-0.380481\pi\) | ||||
0.366720 | + | 0.930331i | \(0.380481\pi\) | |||||||
\(920\) | −15.2708 | −0.503463 | ||||||||
\(921\) | 85.0023 | 2.80092 | ||||||||
\(922\) | 26.9565 | 0.887766 | ||||||||
\(923\) | 11.7025 | 0.385191 | ||||||||
\(924\) | −10.3248 | −0.339662 | ||||||||
\(925\) | 10.4446 | 0.343418 | ||||||||
\(926\) | 3.98207 | 0.130859 | ||||||||
\(927\) | −71.7725 | −2.35732 | ||||||||
\(928\) | 86.2206 | 2.83033 | ||||||||
\(929\) | −37.0580 | −1.21583 | −0.607917 | − | 0.794001i | \(-0.707995\pi\) | ||||
−0.607917 | + | 0.794001i | \(0.707995\pi\) | |||||||
\(930\) | 15.4101 | 0.505318 | ||||||||
\(931\) | −1.88875 | −0.0619012 | ||||||||
\(932\) | 154.063 | 5.04649 | ||||||||
\(933\) | 30.7232 | 1.00583 | ||||||||
\(934\) | 79.1512 | 2.58991 | ||||||||
\(935\) | −4.08448 | −0.133577 | ||||||||
\(936\) | 126.465 | 4.13365 | ||||||||
\(937\) | −35.5139 | −1.16019 | −0.580095 | − | 0.814549i | \(-0.696984\pi\) | ||||
−0.580095 | + | 0.814549i | \(0.696984\pi\) | |||||||
\(938\) | −11.8569 | −0.387142 | ||||||||
\(939\) | −28.8877 | −0.942713 | ||||||||
\(940\) | −41.3770 | −1.34957 | ||||||||
\(941\) | 9.05383 | 0.295146 | 0.147573 | − | 0.989051i | \(-0.452854\pi\) | ||||
0.147573 | + | 0.989051i | \(0.452854\pi\) | |||||||
\(942\) | −137.824 | −4.49055 | ||||||||
\(943\) | 6.65616 | 0.216754 | ||||||||
\(944\) | 140.197 | 4.56303 | ||||||||
\(945\) | 42.1160 | 1.37003 | ||||||||
\(946\) | 16.2627 | 0.528746 | ||||||||
\(947\) | 16.0623 | 0.521955 | 0.260977 | − | 0.965345i | \(-0.415955\pi\) | ||||
0.260977 | + | 0.965345i | \(0.415955\pi\) | |||||||
\(948\) | −157.922 | −5.12906 | ||||||||
\(949\) | 23.8465 | 0.774090 | ||||||||
\(950\) | 22.5480 | 0.731554 | ||||||||
\(951\) | 37.3528 | 1.21125 | ||||||||
\(952\) | −20.0930 | −0.651219 | ||||||||
\(953\) | −0.642797 | −0.0208222 | −0.0104111 | − | 0.999946i | \(-0.503314\pi\) | ||||
−0.0104111 | + | 0.999946i | \(0.503314\pi\) | |||||||
\(954\) | −32.8666 | −1.06410 | ||||||||
\(955\) | 60.5271 | 1.95861 | ||||||||
\(956\) | 51.5336 | 1.66672 | ||||||||
\(957\) | 8.50462 | 0.274915 | ||||||||
\(958\) | 100.032 | 3.23189 | ||||||||
\(959\) | 6.14328 | 0.198377 | ||||||||
\(960\) | 247.942 | 8.00228 | ||||||||
\(961\) | −30.6658 | −0.989221 | ||||||||
\(962\) | 12.2968 | 0.396464 | ||||||||
\(963\) | 37.3964 | 1.20508 | ||||||||
\(964\) | 157.967 | 5.08776 | ||||||||
\(965\) | 22.8225 | 0.734682 | ||||||||
\(966\) | −4.76777 | −0.153400 | ||||||||
\(967\) | −48.4275 | −1.55732 | −0.778661 | − | 0.627445i | \(-0.784101\pi\) | ||||
−0.778661 | + | 0.627445i | \(0.784101\pi\) | |||||||
\(968\) | 96.5894 | 3.10450 | ||||||||
\(969\) | −13.4028 | −0.430560 | ||||||||
\(970\) | 18.8470 | 0.605140 | ||||||||
\(971\) | 44.9491 | 1.44249 | 0.721243 | − | 0.692683i | \(-0.243571\pi\) | ||||
0.721243 | + | 0.692683i | \(0.243571\pi\) | |||||||
\(972\) | 160.275 | 5.14082 | ||||||||
\(973\) | 17.2355 | 0.552546 | ||||||||
\(974\) | −11.7611 | −0.376851 | ||||||||
\(975\) | −27.0056 | −0.864870 | ||||||||
\(976\) | −61.5281 | −1.96947 | ||||||||
\(977\) | −9.18954 | −0.293999 | −0.147000 | − | 0.989137i | \(-0.546962\pi\) | ||||
−0.147000 | + | 0.989137i | \(0.546962\pi\) | |||||||
\(978\) | −159.180 | −5.09000 | ||||||||
\(979\) | −9.07916 | −0.290171 | ||||||||
\(980\) | 16.4039 | 0.524003 | ||||||||
\(981\) | 85.9758 | 2.74500 | ||||||||
\(982\) | 47.6206 | 1.51963 | ||||||||
\(983\) | −12.3371 | −0.393493 | −0.196746 | − | 0.980454i | \(-0.563038\pi\) | ||||
−0.196746 | + | 0.980454i | \(0.563038\pi\) | |||||||
\(984\) | −353.371 | −11.2651 | ||||||||
\(985\) | −21.5949 | −0.688072 | ||||||||
\(986\) | 26.4337 | 0.841822 | ||||||||
\(987\) | −8.08855 | −0.257461 | ||||||||
\(988\) | 19.3222 | 0.614722 | ||||||||
\(989\) | 5.46608 | 0.173811 | ||||||||
\(990\) | 36.4421 | 1.15821 | ||||||||
\(991\) | 11.9780 | 0.380493 | 0.190246 | − | 0.981736i | \(-0.439071\pi\) | ||||
0.190246 | + | 0.981736i | \(0.439071\pi\) | |||||||
\(992\) | 11.3114 | 0.359137 | ||||||||
\(993\) | −96.0296 | −3.04741 | ||||||||
\(994\) | 16.5889 | 0.526167 | ||||||||
\(995\) | −71.4411 | −2.26484 | ||||||||
\(996\) | 72.9589 | 2.31179 | ||||||||
\(997\) | 17.8541 | 0.565445 | 0.282722 | − | 0.959202i | \(-0.408762\pi\) | ||||
0.282722 | + | 0.959202i | \(0.408762\pi\) | |||||||
\(998\) | 97.1377 | 3.07484 | ||||||||
\(999\) | 32.5748 | 1.03062 |
(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 | 6013.2.a.e.1.1 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.1 | ✓ | 109 | 1.1 | even | 1 | trivial |