Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.901374 | −0.637368 | −0.318684 | − | 0.947861i | \(-0.603241\pi\) | ||||
−0.318684 | + | 0.947861i | \(0.603241\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.18752 | −0.593762 | ||||||||
\(5\) | 1.97657 | 0.883948 | 0.441974 | − | 0.897028i | \(-0.354278\pi\) | ||||
0.441974 | + | 0.897028i | \(0.354278\pi\) | |||||||
\(6\) | 0.901374 | 0.367985 | ||||||||
\(7\) | 4.00403 | 1.51338 | 0.756691 | − | 0.653772i | \(-0.226815\pi\) | ||||
0.756691 | + | 0.653772i | \(0.226815\pi\) | |||||||
\(8\) | 2.87315 | 1.01581 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.78163 | −0.563400 | ||||||||
\(11\) | −4.85826 | −1.46482 | −0.732410 | − | 0.680864i | \(-0.761605\pi\) | ||||
−0.732410 | + | 0.680864i | \(0.761605\pi\) | |||||||
\(12\) | 1.18752 | 0.342809 | ||||||||
\(13\) | −5.58466 | −1.54891 | −0.774453 | − | 0.632631i | \(-0.781975\pi\) | ||||
−0.774453 | + | 0.632631i | \(0.781975\pi\) | |||||||
\(14\) | −3.60913 | −0.964582 | ||||||||
\(15\) | −1.97657 | −0.510348 | ||||||||
\(16\) | −0.214739 | −0.0536847 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.901374 | −0.212456 | ||||||||
\(19\) | 4.03916 | 0.926646 | 0.463323 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463323 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(20\) | −2.34722 | −0.524855 | ||||||||
\(21\) | −4.00403 | −0.873752 | ||||||||
\(22\) | 4.37911 | 0.933630 | ||||||||
\(23\) | −0.727073 | −0.151605 | −0.0758026 | − | 0.997123i | \(-0.524152\pi\) | ||||
−0.0758026 | + | 0.997123i | \(0.524152\pi\) | |||||||
\(24\) | −2.87315 | −0.586480 | ||||||||
\(25\) | −1.09318 | −0.218635 | ||||||||
\(26\) | 5.03387 | 0.987223 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.75489 | −0.898589 | ||||||||
\(29\) | 6.57485 | 1.22092 | 0.610460 | − | 0.792047i | \(-0.290985\pi\) | ||||
0.610460 | + | 0.792047i | \(0.290985\pi\) | |||||||
\(30\) | 1.78163 | 0.325279 | ||||||||
\(31\) | −2.80931 | −0.504567 | −0.252283 | − | 0.967653i | \(-0.581182\pi\) | ||||
−0.252283 | + | 0.967653i | \(0.581182\pi\) | |||||||
\(32\) | −5.55275 | −0.981596 | ||||||||
\(33\) | 4.85826 | 0.845715 | ||||||||
\(34\) | 0.901374 | 0.154584 | ||||||||
\(35\) | 7.91425 | 1.33775 | ||||||||
\(36\) | −1.18752 | −0.197921 | ||||||||
\(37\) | 1.01262 | 0.166474 | 0.0832371 | − | 0.996530i | \(-0.473474\pi\) | ||||
0.0832371 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(38\) | −3.64079 | −0.590615 | ||||||||
\(39\) | 5.58466 | 0.894261 | ||||||||
\(40\) | 5.67898 | 0.897926 | ||||||||
\(41\) | 3.57212 | 0.557871 | 0.278935 | − | 0.960310i | \(-0.410018\pi\) | ||||
0.278935 | + | 0.960310i | \(0.410018\pi\) | |||||||
\(42\) | 3.60913 | 0.556902 | ||||||||
\(43\) | 2.80186 | 0.427280 | 0.213640 | − | 0.976912i | \(-0.431468\pi\) | ||||
0.213640 | + | 0.976912i | \(0.431468\pi\) | |||||||
\(44\) | 5.76930 | 0.869755 | ||||||||
\(45\) | 1.97657 | 0.294649 | ||||||||
\(46\) | 0.655365 | 0.0966283 | ||||||||
\(47\) | 9.68563 | 1.41279 | 0.706397 | − | 0.707815i | \(-0.250319\pi\) | ||||
0.706397 | + | 0.707815i | \(0.250319\pi\) | |||||||
\(48\) | 0.214739 | 0.0309949 | ||||||||
\(49\) | 9.03230 | 1.29033 | ||||||||
\(50\) | 0.985361 | 0.139351 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 6.63192 | 0.919682 | ||||||||
\(53\) | −13.7314 | −1.88615 | −0.943076 | − | 0.332579i | \(-0.892081\pi\) | ||||
−0.943076 | + | 0.332579i | \(0.892081\pi\) | |||||||
\(54\) | 0.901374 | 0.122662 | ||||||||
\(55\) | −9.60269 | −1.29483 | ||||||||
\(56\) | 11.5042 | 1.53731 | ||||||||
\(57\) | −4.03916 | −0.534999 | ||||||||
\(58\) | −5.92640 | −0.778175 | ||||||||
\(59\) | −4.64387 | −0.604581 | −0.302290 | − | 0.953216i | \(-0.597751\pi\) | ||||
−0.302290 | + | 0.953216i | \(0.597751\pi\) | |||||||
\(60\) | 2.34722 | 0.303025 | ||||||||
\(61\) | 14.4603 | 1.85146 | 0.925728 | − | 0.378190i | \(-0.123454\pi\) | ||||
0.925728 | + | 0.378190i | \(0.123454\pi\) | |||||||
\(62\) | 2.53224 | 0.321595 | ||||||||
\(63\) | 4.00403 | 0.504461 | ||||||||
\(64\) | 5.43458 | 0.679323 | ||||||||
\(65\) | −11.0385 | −1.36915 | ||||||||
\(66\) | −4.37911 | −0.539031 | ||||||||
\(67\) | −14.3176 | −1.74917 | −0.874584 | − | 0.484874i | \(-0.838866\pi\) | ||||
−0.874584 | + | 0.484874i | \(0.838866\pi\) | |||||||
\(68\) | 1.18752 | 0.144008 | ||||||||
\(69\) | 0.727073 | 0.0875293 | ||||||||
\(70\) | −7.13370 | −0.852641 | ||||||||
\(71\) | 5.65707 | 0.671371 | 0.335685 | − | 0.941974i | \(-0.391032\pi\) | ||||
0.335685 | + | 0.941974i | \(0.391032\pi\) | |||||||
\(72\) | 2.87315 | 0.338604 | ||||||||
\(73\) | −7.35379 | −0.860696 | −0.430348 | − | 0.902663i | \(-0.641609\pi\) | ||||
−0.430348 | + | 0.902663i | \(0.641609\pi\) | |||||||
\(74\) | −0.912753 | −0.106105 | ||||||||
\(75\) | 1.09318 | 0.126229 | ||||||||
\(76\) | −4.79660 | −0.550207 | ||||||||
\(77\) | −19.4526 | −2.21683 | ||||||||
\(78\) | −5.03387 | −0.569974 | ||||||||
\(79\) | −7.48554 | −0.842189 | −0.421095 | − | 0.907017i | \(-0.638354\pi\) | ||||
−0.421095 | + | 0.907017i | \(0.638354\pi\) | |||||||
\(80\) | −0.424446 | −0.0474545 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.21981 | −0.355569 | ||||||||
\(83\) | −14.8209 | −1.62681 | −0.813405 | − | 0.581698i | \(-0.802388\pi\) | ||||
−0.813405 | + | 0.581698i | \(0.802388\pi\) | |||||||
\(84\) | 4.75489 | 0.518801 | ||||||||
\(85\) | −1.97657 | −0.214389 | ||||||||
\(86\) | −2.52553 | −0.272335 | ||||||||
\(87\) | −6.57485 | −0.704898 | ||||||||
\(88\) | −13.9585 | −1.48798 | ||||||||
\(89\) | 0.976320 | 0.103490 | 0.0517448 | − | 0.998660i | \(-0.483522\pi\) | ||||
0.0517448 | + | 0.998660i | \(0.483522\pi\) | |||||||
\(90\) | −1.78163 | −0.187800 | ||||||||
\(91\) | −22.3612 | −2.34409 | ||||||||
\(92\) | 0.863416 | 0.0900174 | ||||||||
\(93\) | 2.80931 | 0.291312 | ||||||||
\(94\) | −8.73038 | −0.900470 | ||||||||
\(95\) | 7.98367 | 0.819107 | ||||||||
\(96\) | 5.55275 | 0.566725 | ||||||||
\(97\) | −4.48034 | −0.454910 | −0.227455 | − | 0.973789i | \(-0.573040\pi\) | ||||
−0.227455 | + | 0.973789i | \(0.573040\pi\) | |||||||
\(98\) | −8.14148 | −0.822414 | ||||||||
\(99\) | −4.85826 | −0.488274 | ||||||||
\(100\) | 1.29817 | 0.129817 | ||||||||
\(101\) | 15.4458 | 1.53692 | 0.768458 | − | 0.639900i | \(-0.221024\pi\) | ||||
0.768458 | + | 0.639900i | \(0.221024\pi\) | |||||||
\(102\) | −0.901374 | −0.0892494 | ||||||||
\(103\) | −16.2499 | −1.60115 | −0.800576 | − | 0.599231i | \(-0.795473\pi\) | ||||
−0.800576 | + | 0.599231i | \(0.795473\pi\) | |||||||
\(104\) | −16.0456 | −1.57340 | ||||||||
\(105\) | −7.91425 | −0.772352 | ||||||||
\(106\) | 12.3771 | 1.20217 | ||||||||
\(107\) | 3.01898 | 0.291856 | 0.145928 | − | 0.989295i | \(-0.453383\pi\) | ||||
0.145928 | + | 0.989295i | \(0.453383\pi\) | |||||||
\(108\) | 1.18752 | 0.114270 | ||||||||
\(109\) | −0.176188 | −0.0168758 | −0.00843789 | − | 0.999964i | \(-0.502686\pi\) | ||||
−0.00843789 | + | 0.999964i | \(0.502686\pi\) | |||||||
\(110\) | 8.65562 | 0.825281 | ||||||||
\(111\) | −1.01262 | −0.0961139 | ||||||||
\(112\) | −0.859821 | −0.0812454 | ||||||||
\(113\) | −4.38115 | −0.412144 | −0.206072 | − | 0.978537i | \(-0.566068\pi\) | ||||
−0.206072 | + | 0.978537i | \(0.566068\pi\) | |||||||
\(114\) | 3.64079 | 0.340991 | ||||||||
\(115\) | −1.43711 | −0.134011 | ||||||||
\(116\) | −7.80779 | −0.724936 | ||||||||
\(117\) | −5.58466 | −0.516302 | ||||||||
\(118\) | 4.18587 | 0.385340 | ||||||||
\(119\) | −4.00403 | −0.367049 | ||||||||
\(120\) | −5.67898 | −0.518418 | ||||||||
\(121\) | 12.6027 | 1.14570 | ||||||||
\(122\) | −13.0342 | −1.18006 | ||||||||
\(123\) | −3.57212 | −0.322087 | ||||||||
\(124\) | 3.33612 | 0.299593 | ||||||||
\(125\) | −12.0436 | −1.07721 | ||||||||
\(126\) | −3.60913 | −0.321527 | ||||||||
\(127\) | 1.50887 | 0.133891 | 0.0669455 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669455 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(128\) | 6.20690 | 0.548618 | ||||||||
\(129\) | −2.80186 | −0.246690 | ||||||||
\(130\) | 9.94979 | 0.872654 | ||||||||
\(131\) | 20.3494 | 1.77794 | 0.888969 | − | 0.457967i | \(-0.151422\pi\) | ||||
0.888969 | + | 0.457967i | \(0.151422\pi\) | |||||||
\(132\) | −5.76930 | −0.502153 | ||||||||
\(133\) | 16.1729 | 1.40237 | ||||||||
\(134\) | 12.9055 | 1.11486 | ||||||||
\(135\) | −1.97657 | −0.170116 | ||||||||
\(136\) | −2.87315 | −0.246371 | ||||||||
\(137\) | −7.54344 | −0.644480 | −0.322240 | − | 0.946658i | \(-0.604436\pi\) | ||||
−0.322240 | + | 0.946658i | \(0.604436\pi\) | |||||||
\(138\) | −0.655365 | −0.0557884 | ||||||||
\(139\) | −7.69508 | −0.652689 | −0.326344 | − | 0.945251i | \(-0.605817\pi\) | ||||
−0.326344 | + | 0.945251i | \(0.605817\pi\) | |||||||
\(140\) | −9.39836 | −0.794307 | ||||||||
\(141\) | −9.68563 | −0.815677 | ||||||||
\(142\) | −5.09914 | −0.427910 | ||||||||
\(143\) | 27.1317 | 2.26887 | ||||||||
\(144\) | −0.214739 | −0.0178949 | ||||||||
\(145\) | 12.9956 | 1.07923 | ||||||||
\(146\) | 6.62852 | 0.548580 | ||||||||
\(147\) | −9.03230 | −0.744971 | ||||||||
\(148\) | −1.20251 | −0.0988461 | ||||||||
\(149\) | −13.8089 | −1.13127 | −0.565633 | − | 0.824657i | \(-0.691368\pi\) | ||||
−0.565633 | + | 0.824657i | \(0.691368\pi\) | |||||||
\(150\) | −0.985361 | −0.0804544 | ||||||||
\(151\) | 4.58302 | 0.372961 | 0.186480 | − | 0.982459i | \(-0.440292\pi\) | ||||
0.186480 | + | 0.982459i | \(0.440292\pi\) | |||||||
\(152\) | 11.6051 | 0.941299 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 17.5341 | 1.41294 | ||||||||
\(155\) | −5.55279 | −0.446011 | ||||||||
\(156\) | −6.63192 | −0.530978 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 6.74728 | 0.536785 | ||||||||
\(159\) | 13.7314 | 1.08897 | ||||||||
\(160\) | −10.9754 | −0.867680 | ||||||||
\(161\) | −2.91122 | −0.229437 | ||||||||
\(162\) | −0.901374 | −0.0708187 | ||||||||
\(163\) | 10.3001 | 0.806762 | 0.403381 | − | 0.915032i | \(-0.367835\pi\) | ||||
0.403381 | + | 0.915032i | \(0.367835\pi\) | |||||||
\(164\) | −4.24197 | −0.331243 | ||||||||
\(165\) | 9.60269 | 0.747568 | ||||||||
\(166\) | 13.3592 | 1.03688 | ||||||||
\(167\) | 16.0730 | 1.24377 | 0.621883 | − | 0.783110i | \(-0.286368\pi\) | ||||
0.621883 | + | 0.783110i | \(0.286368\pi\) | |||||||
\(168\) | −11.5042 | −0.887569 | ||||||||
\(169\) | 18.1884 | 1.39911 | ||||||||
\(170\) | 1.78163 | 0.136645 | ||||||||
\(171\) | 4.03916 | 0.308882 | ||||||||
\(172\) | −3.32728 | −0.253703 | ||||||||
\(173\) | −22.1149 | −1.68136 | −0.840681 | − | 0.541530i | \(-0.817845\pi\) | ||||
−0.840681 | + | 0.541530i | \(0.817845\pi\) | |||||||
\(174\) | 5.92640 | 0.449280 | ||||||||
\(175\) | −4.37711 | −0.330879 | ||||||||
\(176\) | 1.04326 | 0.0786384 | ||||||||
\(177\) | 4.64387 | 0.349055 | ||||||||
\(178\) | −0.880030 | −0.0659610 | ||||||||
\(179\) | 18.7067 | 1.39820 | 0.699102 | − | 0.715022i | \(-0.253583\pi\) | ||||
0.699102 | + | 0.715022i | \(0.253583\pi\) | |||||||
\(180\) | −2.34722 | −0.174952 | ||||||||
\(181\) | −2.45583 | −0.182541 | −0.0912704 | − | 0.995826i | \(-0.529093\pi\) | ||||
−0.0912704 | + | 0.995826i | \(0.529093\pi\) | |||||||
\(182\) | 20.1558 | 1.49405 | ||||||||
\(183\) | −14.4603 | −1.06894 | ||||||||
\(184\) | −2.08899 | −0.154002 | ||||||||
\(185\) | 2.00152 | 0.147155 | ||||||||
\(186\) | −2.53224 | −0.185673 | ||||||||
\(187\) | 4.85826 | 0.355271 | ||||||||
\(188\) | −11.5019 | −0.838864 | ||||||||
\(189\) | −4.00403 | −0.291251 | ||||||||
\(190\) | −7.19628 | −0.522073 | ||||||||
\(191\) | −13.6758 | −0.989547 | −0.494773 | − | 0.869022i | \(-0.664749\pi\) | ||||
−0.494773 | + | 0.869022i | \(0.664749\pi\) | |||||||
\(192\) | −5.43458 | −0.392207 | ||||||||
\(193\) | −14.0366 | −1.01038 | −0.505189 | − | 0.863009i | \(-0.668577\pi\) | ||||
−0.505189 | + | 0.863009i | \(0.668577\pi\) | |||||||
\(194\) | 4.03846 | 0.289945 | ||||||||
\(195\) | 11.0385 | 0.790481 | ||||||||
\(196\) | −10.7261 | −0.766148 | ||||||||
\(197\) | 1.95214 | 0.139084 | 0.0695421 | − | 0.997579i | \(-0.477846\pi\) | ||||
0.0695421 | + | 0.997579i | \(0.477846\pi\) | |||||||
\(198\) | 4.37911 | 0.311210 | ||||||||
\(199\) | −6.99554 | −0.495901 | −0.247950 | − | 0.968773i | \(-0.579757\pi\) | ||||
−0.247950 | + | 0.968773i | \(0.579757\pi\) | |||||||
\(200\) | −3.14086 | −0.222092 | ||||||||
\(201\) | 14.3176 | 1.00988 | ||||||||
\(202\) | −13.9225 | −0.979581 | ||||||||
\(203\) | 26.3259 | 1.84772 | ||||||||
\(204\) | −1.18752 | −0.0831433 | ||||||||
\(205\) | 7.06053 | 0.493129 | ||||||||
\(206\) | 14.6473 | 1.02052 | ||||||||
\(207\) | −0.727073 | −0.0505350 | ||||||||
\(208\) | 1.19924 | 0.0831525 | ||||||||
\(209\) | −19.6233 | −1.35737 | ||||||||
\(210\) | 7.13370 | 0.492272 | ||||||||
\(211\) | 16.7151 | 1.15071 | 0.575357 | − | 0.817902i | \(-0.304863\pi\) | ||||
0.575357 | + | 0.817902i | \(0.304863\pi\) | |||||||
\(212\) | 16.3064 | 1.11992 | ||||||||
\(213\) | −5.65707 | −0.387616 | ||||||||
\(214\) | −2.72123 | −0.186020 | ||||||||
\(215\) | 5.53807 | 0.377693 | ||||||||
\(216\) | −2.87315 | −0.195493 | ||||||||
\(217\) | −11.2486 | −0.763603 | ||||||||
\(218\) | 0.158812 | 0.0107561 | ||||||||
\(219\) | 7.35379 | 0.496923 | ||||||||
\(220\) | 11.4034 | 0.768818 | ||||||||
\(221\) | 5.58466 | 0.375665 | ||||||||
\(222\) | 0.912753 | 0.0612599 | ||||||||
\(223\) | 6.45163 | 0.432033 | 0.216017 | − | 0.976390i | \(-0.430693\pi\) | ||||
0.216017 | + | 0.976390i | \(0.430693\pi\) | |||||||
\(224\) | −22.2334 | −1.48553 | ||||||||
\(225\) | −1.09318 | −0.0728784 | ||||||||
\(226\) | 3.94906 | 0.262687 | ||||||||
\(227\) | 24.3973 | 1.61931 | 0.809653 | − | 0.586908i | \(-0.199655\pi\) | ||||
0.809653 | + | 0.586908i | \(0.199655\pi\) | |||||||
\(228\) | 4.79660 | 0.317662 | ||||||||
\(229\) | −15.6536 | −1.03442 | −0.517208 | − | 0.855860i | \(-0.673029\pi\) | ||||
−0.517208 | + | 0.855860i | \(0.673029\pi\) | |||||||
\(230\) | 1.29537 | 0.0854144 | ||||||||
\(231\) | 19.4526 | 1.27989 | ||||||||
\(232\) | 18.8906 | 1.24023 | ||||||||
\(233\) | −26.1415 | −1.71259 | −0.856293 | − | 0.516491i | \(-0.827238\pi\) | ||||
−0.856293 | + | 0.516491i | \(0.827238\pi\) | |||||||
\(234\) | 5.03387 | 0.329074 | ||||||||
\(235\) | 19.1443 | 1.24884 | ||||||||
\(236\) | 5.51471 | 0.358977 | ||||||||
\(237\) | 7.48554 | 0.486238 | ||||||||
\(238\) | 3.60913 | 0.233945 | ||||||||
\(239\) | −25.4998 | −1.64944 | −0.824722 | − | 0.565539i | \(-0.808668\pi\) | ||||
−0.824722 | + | 0.565539i | \(0.808668\pi\) | |||||||
\(240\) | 0.424446 | 0.0273979 | ||||||||
\(241\) | −7.65946 | −0.493389 | −0.246694 | − | 0.969093i | \(-0.579344\pi\) | ||||
−0.246694 | + | 0.969093i | \(0.579344\pi\) | |||||||
\(242\) | −11.3597 | −0.730232 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −17.1720 | −1.09932 | ||||||||
\(245\) | 17.8530 | 1.14058 | ||||||||
\(246\) | 3.21981 | 0.205288 | ||||||||
\(247\) | −22.5573 | −1.43529 | ||||||||
\(248\) | −8.07158 | −0.512546 | ||||||||
\(249\) | 14.8209 | 0.939239 | ||||||||
\(250\) | 10.8558 | 0.686580 | ||||||||
\(251\) | −7.36609 | −0.464944 | −0.232472 | − | 0.972603i | \(-0.574681\pi\) | ||||
−0.232472 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(252\) | −4.75489 | −0.299530 | ||||||||
\(253\) | 3.53231 | 0.222074 | ||||||||
\(254\) | −1.36006 | −0.0853378 | ||||||||
\(255\) | 1.97657 | 0.123778 | ||||||||
\(256\) | −16.4639 | −1.02899 | ||||||||
\(257\) | 3.39521 | 0.211787 | 0.105894 | − | 0.994377i | \(-0.466230\pi\) | ||||
0.105894 | + | 0.994377i | \(0.466230\pi\) | |||||||
\(258\) | 2.52553 | 0.157232 | ||||||||
\(259\) | 4.05458 | 0.251939 | ||||||||
\(260\) | 13.1084 | 0.812951 | ||||||||
\(261\) | 6.57485 | 0.406973 | ||||||||
\(262\) | −18.3425 | −1.13320 | ||||||||
\(263\) | −18.2555 | −1.12568 | −0.562841 | − | 0.826565i | \(-0.690292\pi\) | ||||
−0.562841 | + | 0.826565i | \(0.690292\pi\) | |||||||
\(264\) | 13.9585 | 0.859088 | ||||||||
\(265\) | −27.1410 | −1.66726 | ||||||||
\(266\) | −14.5779 | −0.893826 | ||||||||
\(267\) | −0.976320 | −0.0597498 | ||||||||
\(268\) | 17.0024 | 1.03859 | ||||||||
\(269\) | 19.0312 | 1.16035 | 0.580176 | − | 0.814491i | \(-0.302984\pi\) | ||||
0.580176 | + | 0.814491i | \(0.302984\pi\) | |||||||
\(270\) | 1.78163 | 0.108426 | ||||||||
\(271\) | −12.1192 | −0.736190 | −0.368095 | − | 0.929788i | \(-0.619990\pi\) | ||||
−0.368095 | + | 0.929788i | \(0.619990\pi\) | |||||||
\(272\) | 0.214739 | 0.0130204 | ||||||||
\(273\) | 22.3612 | 1.35336 | ||||||||
\(274\) | 6.79947 | 0.410771 | ||||||||
\(275\) | 5.31093 | 0.320261 | ||||||||
\(276\) | −0.863416 | −0.0519716 | ||||||||
\(277\) | 32.6006 | 1.95878 | 0.979389 | − | 0.201983i | \(-0.0647387\pi\) | ||||
0.979389 | + | 0.201983i | \(0.0647387\pi\) | |||||||
\(278\) | 6.93615 | 0.416003 | ||||||||
\(279\) | −2.80931 | −0.168189 | ||||||||
\(280\) | 22.7389 | 1.35891 | ||||||||
\(281\) | 10.6437 | 0.634950 | 0.317475 | − | 0.948267i | \(-0.397165\pi\) | ||||
0.317475 | + | 0.948267i | \(0.397165\pi\) | |||||||
\(282\) | 8.73038 | 0.519887 | ||||||||
\(283\) | −18.9562 | −1.12683 | −0.563416 | − | 0.826174i | \(-0.690513\pi\) | ||||
−0.563416 | + | 0.826174i | \(0.690513\pi\) | |||||||
\(284\) | −6.71791 | −0.398634 | ||||||||
\(285\) | −7.98367 | −0.472912 | ||||||||
\(286\) | −24.4559 | −1.44610 | ||||||||
\(287\) | 14.3029 | 0.844272 | ||||||||
\(288\) | −5.55275 | −0.327199 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −11.7139 | −0.687867 | ||||||||
\(291\) | 4.48034 | 0.262642 | ||||||||
\(292\) | 8.73281 | 0.511049 | ||||||||
\(293\) | −13.5918 | −0.794039 | −0.397019 | − | 0.917810i | \(-0.629955\pi\) | ||||
−0.397019 | + | 0.917810i | \(0.629955\pi\) | |||||||
\(294\) | 8.14148 | 0.474821 | ||||||||
\(295\) | −9.17893 | −0.534418 | ||||||||
\(296\) | 2.90942 | 0.169107 | ||||||||
\(297\) | 4.85826 | 0.281905 | ||||||||
\(298\) | 12.4470 | 0.721033 | ||||||||
\(299\) | 4.06045 | 0.234822 | ||||||||
\(300\) | −1.29817 | −0.0749500 | ||||||||
\(301\) | 11.2188 | 0.646638 | ||||||||
\(302\) | −4.13101 | −0.237713 | ||||||||
\(303\) | −15.4458 | −0.887339 | ||||||||
\(304\) | −0.867363 | −0.0497467 | ||||||||
\(305\) | 28.5818 | 1.63659 | ||||||||
\(306\) | 0.901374 | 0.0515282 | ||||||||
\(307\) | −33.0191 | −1.88450 | −0.942249 | − | 0.334914i | \(-0.891293\pi\) | ||||
−0.942249 | + | 0.334914i | \(0.891293\pi\) | |||||||
\(308\) | 23.1005 | 1.31627 | ||||||||
\(309\) | 16.2499 | 0.924426 | ||||||||
\(310\) | 5.00515 | 0.284273 | ||||||||
\(311\) | −0.148991 | −0.00844852 | −0.00422426 | − | 0.999991i | \(-0.501345\pi\) | ||||
−0.00422426 | + | 0.999991i | \(0.501345\pi\) | |||||||
\(312\) | 16.0456 | 0.908402 | ||||||||
\(313\) | −11.2746 | −0.637276 | −0.318638 | − | 0.947876i | \(-0.603225\pi\) | ||||
−0.318638 | + | 0.947876i | \(0.603225\pi\) | |||||||
\(314\) | 0.901374 | 0.0508675 | ||||||||
\(315\) | 7.91425 | 0.445917 | ||||||||
\(316\) | 8.88926 | 0.500060 | ||||||||
\(317\) | 22.7598 | 1.27832 | 0.639159 | − | 0.769075i | \(-0.279283\pi\) | ||||
0.639159 | + | 0.769075i | \(0.279283\pi\) | |||||||
\(318\) | −12.3771 | −0.694075 | ||||||||
\(319\) | −31.9423 | −1.78843 | ||||||||
\(320\) | 10.7418 | 0.600486 | ||||||||
\(321\) | −3.01898 | −0.168503 | ||||||||
\(322\) | 2.62410 | 0.146236 | ||||||||
\(323\) | −4.03916 | −0.224745 | ||||||||
\(324\) | −1.18752 | −0.0659736 | ||||||||
\(325\) | 6.10501 | 0.338645 | ||||||||
\(326\) | −9.28420 | −0.514204 | ||||||||
\(327\) | 0.176188 | 0.00974324 | ||||||||
\(328\) | 10.2632 | 0.566692 | ||||||||
\(329\) | 38.7816 | 2.13810 | ||||||||
\(330\) | −8.65562 | −0.476476 | ||||||||
\(331\) | 9.42962 | 0.518299 | 0.259149 | − | 0.965837i | \(-0.416558\pi\) | ||||
0.259149 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(332\) | 17.6002 | 0.965937 | ||||||||
\(333\) | 1.01262 | 0.0554914 | ||||||||
\(334\) | −14.4878 | −0.792737 | ||||||||
\(335\) | −28.2996 | −1.54617 | ||||||||
\(336\) | 0.859821 | 0.0469071 | ||||||||
\(337\) | 0.114336 | 0.00622826 | 0.00311413 | − | 0.999995i | \(-0.499009\pi\) | ||||
0.00311413 | + | 0.999995i | \(0.499009\pi\) | |||||||
\(338\) | −16.3946 | −0.891748 | ||||||||
\(339\) | 4.38115 | 0.237951 | ||||||||
\(340\) | 2.34722 | 0.127296 | ||||||||
\(341\) | 13.6484 | 0.739100 | ||||||||
\(342\) | −3.64079 | −0.196872 | ||||||||
\(343\) | 8.13738 | 0.439377 | ||||||||
\(344\) | 8.05018 | 0.434036 | ||||||||
\(345\) | 1.43711 | 0.0773714 | ||||||||
\(346\) | 19.9338 | 1.07165 | ||||||||
\(347\) | −17.2859 | −0.927956 | −0.463978 | − | 0.885847i | \(-0.653578\pi\) | ||||
−0.463978 | + | 0.885847i | \(0.653578\pi\) | |||||||
\(348\) | 7.80779 | 0.418542 | ||||||||
\(349\) | −12.7291 | −0.681374 | −0.340687 | − | 0.940177i | \(-0.610660\pi\) | ||||
−0.340687 | + | 0.940177i | \(0.610660\pi\) | |||||||
\(350\) | 3.94542 | 0.210891 | ||||||||
\(351\) | 5.58466 | 0.298087 | ||||||||
\(352\) | 26.9767 | 1.43786 | ||||||||
\(353\) | −36.3196 | −1.93310 | −0.966550 | − | 0.256480i | \(-0.917437\pi\) | ||||
−0.966550 | + | 0.256480i | \(0.917437\pi\) | |||||||
\(354\) | −4.18587 | −0.222476 | ||||||||
\(355\) | 11.1816 | 0.593457 | ||||||||
\(356\) | −1.15940 | −0.0614483 | ||||||||
\(357\) | 4.00403 | 0.211916 | ||||||||
\(358\) | −16.8617 | −0.891171 | ||||||||
\(359\) | −12.9981 | −0.686012 | −0.343006 | − | 0.939333i | \(-0.611445\pi\) | ||||
−0.343006 | + | 0.939333i | \(0.611445\pi\) | |||||||
\(360\) | 5.67898 | 0.299309 | ||||||||
\(361\) | −2.68521 | −0.141327 | ||||||||
\(362\) | 2.21363 | 0.116346 | ||||||||
\(363\) | −12.6027 | −0.661470 | ||||||||
\(364\) | 26.5544 | 1.39183 | ||||||||
\(365\) | −14.5353 | −0.760811 | ||||||||
\(366\) | 13.0342 | 0.681307 | ||||||||
\(367\) | 1.00888 | 0.0526633 | 0.0263316 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263316 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(368\) | 0.156131 | 0.00813887 | ||||||||
\(369\) | 3.57212 | 0.185957 | ||||||||
\(370\) | −1.80412 | −0.0937916 | ||||||||
\(371\) | −54.9810 | −2.85447 | ||||||||
\(372\) | −3.33612 | −0.172970 | ||||||||
\(373\) | 34.6154 | 1.79232 | 0.896160 | − | 0.443732i | \(-0.146346\pi\) | ||||
0.896160 | + | 0.443732i | \(0.146346\pi\) | |||||||
\(374\) | −4.37911 | −0.226438 | ||||||||
\(375\) | 12.0436 | 0.621928 | ||||||||
\(376\) | 27.8283 | 1.43514 | ||||||||
\(377\) | −36.7183 | −1.89109 | ||||||||
\(378\) | 3.60913 | 0.185634 | ||||||||
\(379\) | −16.2918 | −0.836852 | −0.418426 | − | 0.908251i | \(-0.637418\pi\) | ||||
−0.418426 | + | 0.908251i | \(0.637418\pi\) | |||||||
\(380\) | −9.48080 | −0.486355 | ||||||||
\(381\) | −1.50887 | −0.0773020 | ||||||||
\(382\) | 12.3270 | 0.630705 | ||||||||
\(383\) | −0.0693234 | −0.00354226 | −0.00177113 | − | 0.999998i | \(-0.500564\pi\) | ||||
−0.00177113 | + | 0.999998i | \(0.500564\pi\) | |||||||
\(384\) | −6.20690 | −0.316744 | ||||||||
\(385\) | −38.4495 | −1.95957 | ||||||||
\(386\) | 12.6522 | 0.643982 | ||||||||
\(387\) | 2.80186 | 0.142427 | ||||||||
\(388\) | 5.32051 | 0.270108 | ||||||||
\(389\) | −10.4815 | −0.531435 | −0.265718 | − | 0.964051i | \(-0.585609\pi\) | ||||
−0.265718 | + | 0.964051i | \(0.585609\pi\) | |||||||
\(390\) | −9.94979 | −0.503827 | ||||||||
\(391\) | 0.727073 | 0.0367696 | ||||||||
\(392\) | 25.9512 | 1.31073 | ||||||||
\(393\) | −20.3494 | −1.02649 | ||||||||
\(394\) | −1.75961 | −0.0886478 | ||||||||
\(395\) | −14.7957 | −0.744452 | ||||||||
\(396\) | 5.76930 | 0.289918 | ||||||||
\(397\) | 13.4453 | 0.674803 | 0.337401 | − | 0.941361i | \(-0.390452\pi\) | ||||
0.337401 | + | 0.941361i | \(0.390452\pi\) | |||||||
\(398\) | 6.30560 | 0.316071 | ||||||||
\(399\) | −16.1729 | −0.809659 | ||||||||
\(400\) | 0.234747 | 0.0117374 | ||||||||
\(401\) | 20.3625 | 1.01685 | 0.508427 | − | 0.861105i | \(-0.330227\pi\) | ||||
0.508427 | + | 0.861105i | \(0.330227\pi\) | |||||||
\(402\) | −12.9055 | −0.643667 | ||||||||
\(403\) | 15.6890 | 0.781527 | ||||||||
\(404\) | −18.3423 | −0.912562 | ||||||||
\(405\) | 1.97657 | 0.0982165 | ||||||||
\(406\) | −23.7295 | −1.17768 | ||||||||
\(407\) | −4.91959 | −0.243855 | ||||||||
\(408\) | 2.87315 | 0.142242 | ||||||||
\(409\) | −8.39804 | −0.415257 | −0.207628 | − | 0.978208i | \(-0.566574\pi\) | ||||
−0.207628 | + | 0.978208i | \(0.566574\pi\) | |||||||
\(410\) | −6.36419 | −0.314305 | ||||||||
\(411\) | 7.54344 | 0.372091 | ||||||||
\(412\) | 19.2972 | 0.950704 | ||||||||
\(413\) | −18.5942 | −0.914962 | ||||||||
\(414\) | 0.655365 | 0.0322094 | ||||||||
\(415\) | −29.2946 | −1.43802 | ||||||||
\(416\) | 31.0102 | 1.52040 | ||||||||
\(417\) | 7.69508 | 0.376830 | ||||||||
\(418\) | 17.6879 | 0.865144 | ||||||||
\(419\) | −17.6752 | −0.863488 | −0.431744 | − | 0.901996i | \(-0.642102\pi\) | ||||
−0.431744 | + | 0.901996i | \(0.642102\pi\) | |||||||
\(420\) | 9.39836 | 0.458593 | ||||||||
\(421\) | 32.2777 | 1.57312 | 0.786561 | − | 0.617513i | \(-0.211860\pi\) | ||||
0.786561 | + | 0.617513i | \(0.211860\pi\) | |||||||
\(422\) | −15.0666 | −0.733429 | ||||||||
\(423\) | 9.68563 | 0.470932 | ||||||||
\(424\) | −39.4524 | −1.91598 | ||||||||
\(425\) | 1.09318 | 0.0530268 | ||||||||
\(426\) | 5.09914 | 0.247054 | ||||||||
\(427\) | 57.8997 | 2.80196 | ||||||||
\(428\) | −3.58511 | −0.173293 | ||||||||
\(429\) | −27.1317 | −1.30993 | ||||||||
\(430\) | −4.99188 | −0.240730 | ||||||||
\(431\) | 17.4216 | 0.839167 | 0.419583 | − | 0.907717i | \(-0.362176\pi\) | ||||
0.419583 | + | 0.907717i | \(0.362176\pi\) | |||||||
\(432\) | 0.214739 | 0.0103316 | ||||||||
\(433\) | 6.40846 | 0.307971 | 0.153986 | − | 0.988073i | \(-0.450789\pi\) | ||||
0.153986 | + | 0.988073i | \(0.450789\pi\) | |||||||
\(434\) | 10.1392 | 0.486696 | ||||||||
\(435\) | −12.9956 | −0.623094 | ||||||||
\(436\) | 0.209228 | 0.0100202 | ||||||||
\(437\) | −2.93676 | −0.140484 | ||||||||
\(438\) | −6.62852 | −0.316723 | ||||||||
\(439\) | −12.0771 | −0.576408 | −0.288204 | − | 0.957569i | \(-0.593058\pi\) | ||||
−0.288204 | + | 0.957569i | \(0.593058\pi\) | |||||||
\(440\) | −27.5900 | −1.31530 | ||||||||
\(441\) | 9.03230 | 0.430109 | ||||||||
\(442\) | −5.03387 | −0.239437 | ||||||||
\(443\) | 25.8910 | 1.23012 | 0.615059 | − | 0.788481i | \(-0.289132\pi\) | ||||
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(444\) | 1.20251 | 0.0570688 | ||||||||
\(445\) | 1.92976 | 0.0914796 | ||||||||
\(446\) | −5.81533 | −0.275364 | ||||||||
\(447\) | 13.8089 | 0.653137 | ||||||||
\(448\) | 21.7603 | 1.02808 | ||||||||
\(449\) | 15.9342 | 0.751979 | 0.375990 | − | 0.926624i | \(-0.377303\pi\) | ||||
0.375990 | + | 0.926624i | \(0.377303\pi\) | |||||||
\(450\) | 0.985361 | 0.0464503 | ||||||||
\(451\) | −17.3543 | −0.817181 | ||||||||
\(452\) | 5.20272 | 0.244715 | ||||||||
\(453\) | −4.58302 | −0.215329 | ||||||||
\(454\) | −21.9911 | −1.03209 | ||||||||
\(455\) | −44.1984 | −2.07205 | ||||||||
\(456\) | −11.6051 | −0.543459 | ||||||||
\(457\) | −20.6003 | −0.963641 | −0.481820 | − | 0.876270i | \(-0.660024\pi\) | ||||
−0.481820 | + | 0.876270i | \(0.660024\pi\) | |||||||
\(458\) | 14.1097 | 0.659304 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 1.70660 | 0.0795707 | ||||||||
\(461\) | 29.0359 | 1.35233 | 0.676167 | − | 0.736748i | \(-0.263640\pi\) | ||||
0.676167 | + | 0.736748i | \(0.263640\pi\) | |||||||
\(462\) | −17.5341 | −0.815761 | ||||||||
\(463\) | −25.5814 | −1.18887 | −0.594434 | − | 0.804145i | \(-0.702624\pi\) | ||||
−0.594434 | + | 0.804145i | \(0.702624\pi\) | |||||||
\(464\) | −1.41187 | −0.0655446 | ||||||||
\(465\) | 5.55279 | 0.257505 | ||||||||
\(466\) | 23.5633 | 1.09155 | ||||||||
\(467\) | 40.0020 | 1.85107 | 0.925537 | − | 0.378658i | \(-0.123614\pi\) | ||||
0.925537 | + | 0.378658i | \(0.123614\pi\) | |||||||
\(468\) | 6.63192 | 0.306561 | ||||||||
\(469\) | −57.3280 | −2.64716 | ||||||||
\(470\) | −17.2562 | −0.795969 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −13.3426 | −0.614141 | ||||||||
\(473\) | −13.6122 | −0.625888 | ||||||||
\(474\) | −6.74728 | −0.309913 | ||||||||
\(475\) | −4.41551 | −0.202597 | ||||||||
\(476\) | 4.75489 | 0.217940 | ||||||||
\(477\) | −13.7314 | −0.628717 | ||||||||
\(478\) | 22.9848 | 1.05130 | ||||||||
\(479\) | −31.0140 | −1.41707 | −0.708534 | − | 0.705677i | \(-0.750643\pi\) | ||||
−0.708534 | + | 0.705677i | \(0.750643\pi\) | |||||||
\(480\) | 10.9754 | 0.500955 | ||||||||
\(481\) | −5.65516 | −0.257853 | ||||||||
\(482\) | 6.90404 | 0.314470 | ||||||||
\(483\) | 2.91122 | 0.132465 | ||||||||
\(484\) | −14.9660 | −0.680273 | ||||||||
\(485\) | −8.85570 | −0.402117 | ||||||||
\(486\) | 0.901374 | 0.0408872 | ||||||||
\(487\) | −22.8004 | −1.03319 | −0.516593 | − | 0.856231i | \(-0.672800\pi\) | ||||
−0.516593 | + | 0.856231i | \(0.672800\pi\) | |||||||
\(488\) | 41.5467 | 1.88073 | ||||||||
\(489\) | −10.3001 | −0.465784 | ||||||||
\(490\) | −16.0922 | −0.726971 | ||||||||
\(491\) | −16.6588 | −0.751801 | −0.375900 | − | 0.926660i | \(-0.622667\pi\) | ||||
−0.375900 | + | 0.926660i | \(0.622667\pi\) | |||||||
\(492\) | 4.24197 | 0.191243 | ||||||||
\(493\) | −6.57485 | −0.296116 | ||||||||
\(494\) | 20.3326 | 0.914807 | ||||||||
\(495\) | −9.60269 | −0.431609 | ||||||||
\(496\) | 0.603267 | 0.0270875 | ||||||||
\(497\) | 22.6511 | 1.01604 | ||||||||
\(498\) | −13.3592 | −0.598641 | ||||||||
\(499\) | 10.1046 | 0.452344 | 0.226172 | − | 0.974087i | \(-0.427379\pi\) | ||||
0.226172 | + | 0.974087i | \(0.427379\pi\) | |||||||
\(500\) | 14.3020 | 0.639607 | ||||||||
\(501\) | −16.0730 | −0.718089 | ||||||||
\(502\) | 6.63961 | 0.296340 | ||||||||
\(503\) | −11.3078 | −0.504189 | −0.252095 | − | 0.967703i | \(-0.581119\pi\) | ||||
−0.252095 | + | 0.967703i | \(0.581119\pi\) | |||||||
\(504\) | 11.5042 | 0.512438 | ||||||||
\(505\) | 30.5297 | 1.35855 | ||||||||
\(506\) | −3.18393 | −0.141543 | ||||||||
\(507\) | −18.1884 | −0.807777 | ||||||||
\(508\) | −1.79182 | −0.0794994 | ||||||||
\(509\) | −13.7871 | −0.611104 | −0.305552 | − | 0.952175i | \(-0.598841\pi\) | ||||
−0.305552 | + | 0.952175i | \(0.598841\pi\) | |||||||
\(510\) | −1.78163 | −0.0788918 | ||||||||
\(511\) | −29.4448 | −1.30256 | ||||||||
\(512\) | 2.42634 | 0.107230 | ||||||||
\(513\) | −4.03916 | −0.178333 | ||||||||
\(514\) | −3.06035 | −0.134986 | ||||||||
\(515\) | −32.1191 | −1.41534 | ||||||||
\(516\) | 3.32728 | 0.146475 | ||||||||
\(517\) | −47.0553 | −2.06949 | ||||||||
\(518\) | −3.65469 | −0.160578 | ||||||||
\(519\) | 22.1149 | 0.970735 | ||||||||
\(520\) | −31.7152 | −1.39080 | ||||||||
\(521\) | −22.8461 | −1.00091 | −0.500453 | − | 0.865764i | \(-0.666833\pi\) | ||||
−0.500453 | + | 0.865764i | \(0.666833\pi\) | |||||||
\(522\) | −5.92640 | −0.259392 | ||||||||
\(523\) | −34.4478 | −1.50630 | −0.753150 | − | 0.657849i | \(-0.771466\pi\) | ||||
−0.753150 | + | 0.657849i | \(0.771466\pi\) | |||||||
\(524\) | −24.1654 | −1.05567 | ||||||||
\(525\) | 4.37711 | 0.191033 | ||||||||
\(526\) | 16.4550 | 0.717474 | ||||||||
\(527\) | 2.80931 | 0.122375 | ||||||||
\(528\) | −1.04326 | −0.0454019 | ||||||||
\(529\) | −22.4714 | −0.977016 | ||||||||
\(530\) | 24.4642 | 1.06266 | ||||||||
\(531\) | −4.64387 | −0.201527 | ||||||||
\(532\) | −19.2057 | −0.832674 | ||||||||
\(533\) | −19.9491 | −0.864090 | ||||||||
\(534\) | 0.880030 | 0.0380826 | ||||||||
\(535\) | 5.96722 | 0.257985 | ||||||||
\(536\) | −41.1365 | −1.77683 | ||||||||
\(537\) | −18.7067 | −0.807254 | ||||||||
\(538\) | −17.1542 | −0.739571 | ||||||||
\(539\) | −43.8812 | −1.89010 | ||||||||
\(540\) | 2.34722 | 0.101008 | ||||||||
\(541\) | −12.9680 | −0.557539 | −0.278770 | − | 0.960358i | \(-0.589927\pi\) | ||||
−0.278770 | + | 0.960358i | \(0.589927\pi\) | |||||||
\(542\) | 10.9240 | 0.469224 | ||||||||
\(543\) | 2.45583 | 0.105390 | ||||||||
\(544\) | 5.55275 | 0.238072 | ||||||||
\(545\) | −0.348248 | −0.0149173 | ||||||||
\(546\) | −20.1558 | −0.862588 | ||||||||
\(547\) | −14.2555 | −0.609523 | −0.304762 | − | 0.952429i | \(-0.598577\pi\) | ||||
−0.304762 | + | 0.952429i | \(0.598577\pi\) | |||||||
\(548\) | 8.95802 | 0.382668 | ||||||||
\(549\) | 14.4603 | 0.617152 | ||||||||
\(550\) | −4.78714 | −0.204124 | ||||||||
\(551\) | 26.5569 | 1.13136 | ||||||||
\(552\) | 2.08899 | 0.0889134 | ||||||||
\(553\) | −29.9724 | −1.27455 | ||||||||
\(554\) | −29.3853 | −1.24846 | ||||||||
\(555\) | −2.00152 | −0.0849598 | ||||||||
\(556\) | 9.13810 | 0.387542 | ||||||||
\(557\) | 4.41660 | 0.187137 | 0.0935686 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935686 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(558\) | 2.53224 | 0.107198 | ||||||||
\(559\) | −15.6474 | −0.661816 | ||||||||
\(560\) | −1.69950 | −0.0718168 | ||||||||
\(561\) | −4.85826 | −0.205116 | ||||||||
\(562\) | −9.59396 | −0.404697 | ||||||||
\(563\) | 10.0813 | 0.424877 | 0.212439 | − | 0.977174i | \(-0.431859\pi\) | ||||
0.212439 | + | 0.977174i | \(0.431859\pi\) | |||||||
\(564\) | 11.5019 | 0.484318 | ||||||||
\(565\) | −8.65965 | −0.364314 | ||||||||
\(566\) | 17.0867 | 0.718206 | ||||||||
\(567\) | 4.00403 | 0.168154 | ||||||||
\(568\) | 16.2536 | 0.681987 | ||||||||
\(569\) | 0.218235 | 0.00914890 | 0.00457445 | − | 0.999990i | \(-0.498544\pi\) | ||||
0.00457445 | + | 0.999990i | \(0.498544\pi\) | |||||||
\(570\) | 7.19628 | 0.301419 | ||||||||
\(571\) | 9.67997 | 0.405094 | 0.202547 | − | 0.979273i | \(-0.435078\pi\) | ||||
0.202547 | + | 0.979273i | \(0.435078\pi\) | |||||||
\(572\) | −32.2196 | −1.34717 | ||||||||
\(573\) | 13.6758 | 0.571315 | ||||||||
\(574\) | −12.8923 | −0.538112 | ||||||||
\(575\) | 0.794818 | 0.0331462 | ||||||||
\(576\) | 5.43458 | 0.226441 | ||||||||
\(577\) | −9.41424 | −0.391920 | −0.195960 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195960 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(578\) | −0.901374 | −0.0374922 | ||||||||
\(579\) | 14.0366 | 0.583342 | ||||||||
\(580\) | −15.4326 | −0.640806 | ||||||||
\(581\) | −59.3435 | −2.46199 | ||||||||
\(582\) | −4.03846 | −0.167400 | ||||||||
\(583\) | 66.7106 | 2.76287 | ||||||||
\(584\) | −21.1286 | −0.874307 | ||||||||
\(585\) | −11.0385 | −0.456384 | ||||||||
\(586\) | 12.2513 | 0.506095 | ||||||||
\(587\) | 30.7666 | 1.26988 | 0.634938 | − | 0.772563i | \(-0.281026\pi\) | ||||
0.634938 | + | 0.772563i | \(0.281026\pi\) | |||||||
\(588\) | 10.7261 | 0.442336 | ||||||||
\(589\) | −11.3472 | −0.467555 | ||||||||
\(590\) | 8.27366 | 0.340621 | ||||||||
\(591\) | −1.95214 | −0.0803003 | ||||||||
\(592\) | −0.217449 | −0.00893711 | ||||||||
\(593\) | −19.2426 | −0.790198 | −0.395099 | − | 0.918639i | \(-0.629290\pi\) | ||||
−0.395099 | + | 0.918639i | \(0.629290\pi\) | |||||||
\(594\) | −4.37911 | −0.179677 | ||||||||
\(595\) | −7.91425 | −0.324453 | ||||||||
\(596\) | 16.3984 | 0.671703 | ||||||||
\(597\) | 6.99554 | 0.286308 | ||||||||
\(598\) | −3.65999 | −0.149668 | ||||||||
\(599\) | 27.2999 | 1.11544 | 0.557721 | − | 0.830028i | \(-0.311676\pi\) | ||||
0.557721 | + | 0.830028i | \(0.311676\pi\) | |||||||
\(600\) | 3.14086 | 0.128225 | ||||||||
\(601\) | −46.6198 | −1.90166 | −0.950830 | − | 0.309714i | \(-0.899767\pi\) | ||||
−0.950830 | + | 0.309714i | \(0.899767\pi\) | |||||||
\(602\) | −10.1123 | −0.412146 | ||||||||
\(603\) | −14.3176 | −0.583056 | ||||||||
\(604\) | −5.44244 | −0.221450 | ||||||||
\(605\) | 24.9101 | 1.01274 | ||||||||
\(606\) | 13.9225 | 0.565561 | ||||||||
\(607\) | −8.35444 | −0.339096 | −0.169548 | − | 0.985522i | \(-0.554231\pi\) | ||||
−0.169548 | + | 0.985522i | \(0.554231\pi\) | |||||||
\(608\) | −22.4284 | −0.909592 | ||||||||
\(609\) | −26.3259 | −1.06678 | ||||||||
\(610\) | −25.7629 | −1.04311 | ||||||||
\(611\) | −54.0910 | −2.18829 | ||||||||
\(612\) | 1.18752 | 0.0480028 | ||||||||
\(613\) | −41.5278 | −1.67729 | −0.838646 | − | 0.544677i | \(-0.816652\pi\) | ||||
−0.838646 | + | 0.544677i | \(0.816652\pi\) | |||||||
\(614\) | 29.7625 | 1.20112 | ||||||||
\(615\) | −7.06053 | −0.284708 | ||||||||
\(616\) | −55.8904 | −2.25189 | ||||||||
\(617\) | −17.6664 | −0.711223 | −0.355611 | − | 0.934634i | \(-0.615727\pi\) | ||||
−0.355611 | + | 0.934634i | \(0.615727\pi\) | |||||||
\(618\) | −14.6473 | −0.589199 | ||||||||
\(619\) | 12.6051 | 0.506643 | 0.253322 | − | 0.967382i | \(-0.418477\pi\) | ||||
0.253322 | + | 0.967382i | \(0.418477\pi\) | |||||||
\(620\) | 6.59408 | 0.264824 | ||||||||
\(621\) | 0.727073 | 0.0291764 | ||||||||
\(622\) | 0.134297 | 0.00538482 | ||||||||
\(623\) | 3.90922 | 0.156620 | ||||||||
\(624\) | −1.19924 | −0.0480081 | ||||||||
\(625\) | −18.3391 | −0.733564 | ||||||||
\(626\) | 10.1626 | 0.406179 | ||||||||
\(627\) | 19.6233 | 0.783678 | ||||||||
\(628\) | 1.18752 | 0.0473874 | ||||||||
\(629\) | −1.01262 | −0.0403759 | ||||||||
\(630\) | −7.13370 | −0.284214 | ||||||||
\(631\) | −35.3696 | −1.40804 | −0.704021 | − | 0.710180i | \(-0.748614\pi\) | ||||
−0.704021 | + | 0.710180i | \(0.748614\pi\) | |||||||
\(632\) | −21.5071 | −0.855507 | ||||||||
\(633\) | −16.7151 | −0.664366 | ||||||||
\(634\) | −20.5151 | −0.814759 | ||||||||
\(635\) | 2.98239 | 0.118353 | ||||||||
\(636\) | −16.3064 | −0.646589 | ||||||||
\(637\) | −50.4423 | −1.99860 | ||||||||
\(638\) | 28.7920 | 1.13989 | ||||||||
\(639\) | 5.65707 | 0.223790 | ||||||||
\(640\) | 12.2684 | 0.484950 | ||||||||
\(641\) | −29.4882 | −1.16471 | −0.582356 | − | 0.812934i | \(-0.697869\pi\) | ||||
−0.582356 | + | 0.812934i | \(0.697869\pi\) | |||||||
\(642\) | 2.72123 | 0.107398 | ||||||||
\(643\) | −2.17328 | −0.0857057 | −0.0428528 | − | 0.999081i | \(-0.513645\pi\) | ||||
−0.0428528 | + | 0.999081i | \(0.513645\pi\) | |||||||
\(644\) | 3.45715 | 0.136231 | ||||||||
\(645\) | −5.53807 | −0.218061 | ||||||||
\(646\) | 3.64079 | 0.143245 | ||||||||
\(647\) | −36.4755 | −1.43400 | −0.717000 | − | 0.697073i | \(-0.754485\pi\) | ||||
−0.717000 | + | 0.697073i | \(0.754485\pi\) | |||||||
\(648\) | 2.87315 | 0.112868 | ||||||||
\(649\) | 22.5611 | 0.885602 | ||||||||
\(650\) | −5.50290 | −0.215842 | ||||||||
\(651\) | 11.2486 | 0.440866 | ||||||||
\(652\) | −12.2316 | −0.479025 | ||||||||
\(653\) | 36.1841 | 1.41599 | 0.707996 | − | 0.706217i | \(-0.249600\pi\) | ||||
0.707996 | + | 0.706217i | \(0.249600\pi\) | |||||||
\(654\) | −0.158812 | −0.00621003 | ||||||||
\(655\) | 40.2221 | 1.57161 | ||||||||
\(656\) | −0.767071 | −0.0299491 | ||||||||
\(657\) | −7.35379 | −0.286899 | ||||||||
\(658\) | −34.9568 | −1.36276 | ||||||||
\(659\) | 37.6293 | 1.46583 | 0.732914 | − | 0.680321i | \(-0.238160\pi\) | ||||
0.732914 | + | 0.680321i | \(0.238160\pi\) | |||||||
\(660\) | −11.4034 | −0.443877 | ||||||||
\(661\) | 25.3661 | 0.986625 | 0.493313 | − | 0.869852i | \(-0.335786\pi\) | ||||
0.493313 | + | 0.869852i | \(0.335786\pi\) | |||||||
\(662\) | −8.49962 | −0.330347 | ||||||||
\(663\) | −5.58466 | −0.216890 | ||||||||
\(664\) | −42.5828 | −1.65253 | ||||||||
\(665\) | 31.9669 | 1.23962 | ||||||||
\(666\) | −0.912753 | −0.0353684 | ||||||||
\(667\) | −4.78040 | −0.185098 | ||||||||
\(668\) | −19.0871 | −0.738501 | ||||||||
\(669\) | −6.45163 | −0.249434 | ||||||||
\(670\) | 25.5086 | 0.985482 | ||||||||
\(671\) | −70.2520 | −2.71205 | ||||||||
\(672\) | 22.2334 | 0.857672 | ||||||||
\(673\) | −30.9145 | −1.19167 | −0.595834 | − | 0.803108i | \(-0.703178\pi\) | ||||
−0.595834 | + | 0.803108i | \(0.703178\pi\) | |||||||
\(674\) | −0.103059 | −0.00396969 | ||||||||
\(675\) | 1.09318 | 0.0420764 | ||||||||
\(676\) | −21.5992 | −0.830738 | ||||||||
\(677\) | 25.9296 | 0.996557 | 0.498279 | − | 0.867017i | \(-0.333966\pi\) | ||||
0.498279 | + | 0.867017i | \(0.333966\pi\) | |||||||
\(678\) | −3.94906 | −0.151663 | ||||||||
\(679\) | −17.9394 | −0.688452 | ||||||||
\(680\) | −5.67898 | −0.217779 | ||||||||
\(681\) | −24.3973 | −0.934907 | ||||||||
\(682\) | −12.3023 | −0.471079 | ||||||||
\(683\) | 33.1170 | 1.26719 | 0.633593 | − | 0.773667i | \(-0.281579\pi\) | ||||
0.633593 | + | 0.773667i | \(0.281579\pi\) | |||||||
\(684\) | −4.79660 | −0.183402 | ||||||||
\(685\) | −14.9101 | −0.569687 | ||||||||
\(686\) | −7.33483 | −0.280045 | ||||||||
\(687\) | 15.6536 | 0.597221 | ||||||||
\(688\) | −0.601668 | −0.0229384 | ||||||||
\(689\) | 76.6851 | 2.92147 | ||||||||
\(690\) | −1.29537 | −0.0493140 | ||||||||
\(691\) | 32.8021 | 1.24785 | 0.623926 | − | 0.781484i | \(-0.285537\pi\) | ||||
0.623926 | + | 0.781484i | \(0.285537\pi\) | |||||||
\(692\) | 26.2619 | 0.998329 | ||||||||
\(693\) | −19.4526 | −0.738945 | ||||||||
\(694\) | 15.5811 | 0.591450 | ||||||||
\(695\) | −15.2099 | −0.576943 | ||||||||
\(696\) | −18.8906 | −0.716045 | ||||||||
\(697\) | −3.57212 | −0.135304 | ||||||||
\(698\) | 11.4737 | 0.434286 | ||||||||
\(699\) | 26.1415 | 0.988762 | ||||||||
\(700\) | 5.19793 | 0.196463 | ||||||||
\(701\) | 12.0851 | 0.456450 | 0.228225 | − | 0.973608i | \(-0.426708\pi\) | ||||
0.228225 | + | 0.973608i | \(0.426708\pi\) | |||||||
\(702\) | −5.03387 | −0.189991 | ||||||||
\(703\) | 4.09014 | 0.154263 | ||||||||
\(704\) | −26.4026 | −0.995086 | ||||||||
\(705\) | −19.1443 | −0.721017 | ||||||||
\(706\) | 32.7376 | 1.23210 | ||||||||
\(707\) | 61.8456 | 2.32594 | ||||||||
\(708\) | −5.51471 | −0.207256 | ||||||||
\(709\) | −47.9036 | −1.79906 | −0.899528 | − | 0.436863i | \(-0.856089\pi\) | ||||
−0.899528 | + | 0.436863i | \(0.856089\pi\) | |||||||
\(710\) | −10.0788 | −0.378251 | ||||||||
\(711\) | −7.48554 | −0.280730 | ||||||||
\(712\) | 2.80512 | 0.105126 | ||||||||
\(713\) | 2.04257 | 0.0764949 | ||||||||
\(714\) | −3.60913 | −0.135068 | ||||||||
\(715\) | 53.6277 | 2.00556 | ||||||||
\(716\) | −22.2147 | −0.830201 | ||||||||
\(717\) | 25.4998 | 0.952306 | ||||||||
\(718\) | 11.7161 | 0.437242 | ||||||||
\(719\) | −36.8186 | −1.37310 | −0.686551 | − | 0.727082i | \(-0.740876\pi\) | ||||
−0.686551 | + | 0.727082i | \(0.740876\pi\) | |||||||
\(720\) | −0.424446 | −0.0158182 | ||||||||
\(721\) | −65.0653 | −2.42316 | ||||||||
\(722\) | 2.42038 | 0.0900773 | ||||||||
\(723\) | 7.65946 | 0.284858 | ||||||||
\(724\) | 2.91636 | 0.108386 | ||||||||
\(725\) | −7.18747 | −0.266936 | ||||||||
\(726\) | 11.3597 | 0.421600 | ||||||||
\(727\) | 13.9091 | 0.515860 | 0.257930 | − | 0.966164i | \(-0.416960\pi\) | ||||
0.257930 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(728\) | −64.2471 | −2.38115 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.1017 | 0.484917 | ||||||||
\(731\) | −2.80186 | −0.103631 | ||||||||
\(732\) | 17.1720 | 0.634695 | ||||||||
\(733\) | −25.3253 | −0.935412 | −0.467706 | − | 0.883884i | \(-0.654919\pi\) | ||||
−0.467706 | + | 0.883884i | \(0.654919\pi\) | |||||||
\(734\) | −0.909382 | −0.0335659 | ||||||||
\(735\) | −17.8530 | −0.658516 | ||||||||
\(736\) | 4.03725 | 0.148815 | ||||||||
\(737\) | 69.5584 | 2.56222 | ||||||||
\(738\) | −3.21981 | −0.118523 | ||||||||
\(739\) | −25.0658 | −0.922061 | −0.461030 | − | 0.887384i | \(-0.652520\pi\) | ||||
−0.461030 | + | 0.887384i | \(0.652520\pi\) | |||||||
\(740\) | −2.37685 | −0.0873748 | ||||||||
\(741\) | 22.5573 | 0.828664 | ||||||||
\(742\) | 49.5584 | 1.81935 | ||||||||
\(743\) | 28.7396 | 1.05435 | 0.527176 | − | 0.849756i | \(-0.323251\pi\) | ||||
0.527176 | + | 0.849756i | \(0.323251\pi\) | |||||||
\(744\) | 8.07158 | 0.295918 | ||||||||
\(745\) | −27.2942 | −0.999981 | ||||||||
\(746\) | −31.2015 | −1.14237 | ||||||||
\(747\) | −14.8209 | −0.542270 | ||||||||
\(748\) | −5.76930 | −0.210947 | ||||||||
\(749\) | 12.0881 | 0.441689 | ||||||||
\(750\) | −10.8558 | −0.396397 | ||||||||
\(751\) | −31.2776 | −1.14133 | −0.570667 | − | 0.821182i | \(-0.693315\pi\) | ||||
−0.570667 | + | 0.821182i | \(0.693315\pi\) | |||||||
\(752\) | −2.07988 | −0.0758454 | ||||||||
\(753\) | 7.36609 | 0.268435 | ||||||||
\(754\) | 33.0970 | 1.20532 | ||||||||
\(755\) | 9.05865 | 0.329678 | ||||||||
\(756\) | 4.75489 | 0.172934 | ||||||||
\(757\) | −38.7372 | −1.40793 | −0.703964 | − | 0.710236i | \(-0.748588\pi\) | ||||
−0.703964 | + | 0.710236i | \(0.748588\pi\) | |||||||
\(758\) | 14.6850 | 0.533383 | ||||||||
\(759\) | −3.53231 | −0.128215 | ||||||||
\(760\) | 22.9383 | 0.832060 | ||||||||
\(761\) | 21.3683 | 0.774601 | 0.387300 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387300 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(762\) | 1.36006 | 0.0492698 | ||||||||
\(763\) | −0.705464 | −0.0255395 | ||||||||
\(764\) | 16.2403 | 0.587555 | ||||||||
\(765\) | −1.97657 | −0.0714630 | ||||||||
\(766\) | 0.0624864 | 0.00225772 | ||||||||
\(767\) | 25.9345 | 0.936439 | ||||||||
\(768\) | 16.4639 | 0.594090 | ||||||||
\(769\) | 37.8457 | 1.36475 | 0.682376 | − | 0.731001i | \(-0.260947\pi\) | ||||
0.682376 | + | 0.731001i | \(0.260947\pi\) | |||||||
\(770\) | 34.6574 | 1.24897 | ||||||||
\(771\) | −3.39521 | −0.122275 | ||||||||
\(772\) | 16.6688 | 0.599924 | ||||||||
\(773\) | 21.6879 | 0.780060 | 0.390030 | − | 0.920802i | \(-0.372465\pi\) | ||||
0.390030 | + | 0.920802i | \(0.372465\pi\) | |||||||
\(774\) | −2.52553 | −0.0907782 | ||||||||
\(775\) | 3.07107 | 0.110316 | ||||||||
\(776\) | −12.8727 | −0.462103 | ||||||||
\(777\) | −4.05458 | −0.145457 | ||||||||
\(778\) | 9.44779 | 0.338720 | ||||||||
\(779\) | 14.4283 | 0.516949 | ||||||||
\(780\) | −13.1084 | −0.469358 | ||||||||
\(781\) | −27.4835 | −0.983437 | ||||||||
\(782\) | −0.655365 | −0.0234358 | ||||||||
\(783\) | −6.57485 | −0.234966 | ||||||||
\(784\) | −1.93958 | −0.0692708 | ||||||||
\(785\) | −1.97657 | −0.0705468 | ||||||||
\(786\) | 18.3425 | 0.654254 | ||||||||
\(787\) | −31.9571 | −1.13915 | −0.569573 | − | 0.821941i | \(-0.692892\pi\) | ||||
−0.569573 | + | 0.821941i | \(0.692892\pi\) | |||||||
\(788\) | −2.31821 | −0.0825829 | ||||||||
\(789\) | 18.2555 | 0.649913 | ||||||||
\(790\) | 13.3365 | 0.474490 | ||||||||
\(791\) | −17.5423 | −0.623732 | ||||||||
\(792\) | −13.9585 | −0.495995 | ||||||||
\(793\) | −80.7560 | −2.86773 | ||||||||
\(794\) | −12.1193 | −0.430098 | ||||||||
\(795\) | 27.1410 | 0.962593 | ||||||||
\(796\) | 8.30737 | 0.294447 | ||||||||
\(797\) | −10.4559 | −0.370368 | −0.185184 | − | 0.982704i | \(-0.559288\pi\) | ||||
−0.185184 | + | 0.982704i | \(0.559288\pi\) | |||||||
\(798\) | 14.5779 | 0.516051 | ||||||||
\(799\) | −9.68563 | −0.342653 | ||||||||
\(800\) | 6.07013 | 0.214611 | ||||||||
\(801\) | 0.976320 | 0.0344966 | ||||||||
\(802\) | −18.3542 | −0.648110 | ||||||||
\(803\) | 35.7266 | 1.26077 | ||||||||
\(804\) | −17.0024 | −0.599630 | ||||||||
\(805\) | −5.75424 | −0.202810 | ||||||||
\(806\) | −14.1417 | −0.498120 | ||||||||
\(807\) | −19.0312 | −0.669929 | ||||||||
\(808\) | 44.3782 | 1.56122 | ||||||||
\(809\) | 4.86640 | 0.171094 | 0.0855468 | − | 0.996334i | \(-0.472736\pi\) | ||||
0.0855468 | + | 0.996334i | \(0.472736\pi\) | |||||||
\(810\) | −1.78163 | −0.0626001 | ||||||||
\(811\) | 26.6349 | 0.935278 | 0.467639 | − | 0.883920i | \(-0.345105\pi\) | ||||
0.467639 | + | 0.883920i | \(0.345105\pi\) | |||||||
\(812\) | −31.2627 | −1.09711 | ||||||||
\(813\) | 12.1192 | 0.425039 | ||||||||
\(814\) | 4.43439 | 0.155425 | ||||||||
\(815\) | 20.3588 | 0.713136 | ||||||||
\(816\) | −0.214739 | −0.00751736 | ||||||||
\(817\) | 11.3172 | 0.395937 | ||||||||
\(818\) | 7.56978 | 0.264671 | ||||||||
\(819\) | −22.3612 | −0.781363 | ||||||||
\(820\) | −8.38455 | −0.292801 | ||||||||
\(821\) | −33.4488 | −1.16737 | −0.583686 | − | 0.811980i | \(-0.698390\pi\) | ||||
−0.583686 | + | 0.811980i | \(0.698390\pi\) | |||||||
\(822\) | −6.79947 | −0.237159 | ||||||||
\(823\) | 12.5234 | 0.436538 | 0.218269 | − | 0.975889i | \(-0.429959\pi\) | ||||
0.218269 | + | 0.975889i | \(0.429959\pi\) | |||||||
\(824\) | −46.6885 | −1.62647 | ||||||||
\(825\) | −5.31093 | −0.184903 | ||||||||
\(826\) | 16.7604 | 0.583168 | ||||||||
\(827\) | −17.6604 | −0.614113 | −0.307057 | − | 0.951691i | \(-0.599344\pi\) | ||||
−0.307057 | + | 0.951691i | \(0.599344\pi\) | |||||||
\(828\) | 0.863416 | 0.0300058 | ||||||||
\(829\) | −13.7180 | −0.476446 | −0.238223 | − | 0.971210i | \(-0.576565\pi\) | ||||
−0.238223 | + | 0.971210i | \(0.576565\pi\) | |||||||
\(830\) | 26.4054 | 0.916545 | ||||||||
\(831\) | −32.6006 | −1.13090 | ||||||||
\(832\) | −30.3503 | −1.05221 | ||||||||
\(833\) | −9.03230 | −0.312950 | ||||||||
\(834\) | −6.93615 | −0.240179 | ||||||||
\(835\) | 31.7694 | 1.09943 | ||||||||
\(836\) | 23.3031 | 0.805955 | ||||||||
\(837\) | 2.80931 | 0.0971039 | ||||||||
\(838\) | 15.9319 | 0.550360 | ||||||||
\(839\) | −15.2862 | −0.527737 | −0.263869 | − | 0.964559i | \(-0.584999\pi\) | ||||
−0.263869 | + | 0.964559i | \(0.584999\pi\) | |||||||
\(840\) | −22.7389 | −0.784565 | ||||||||
\(841\) | 14.2287 | 0.490644 | ||||||||
\(842\) | −29.0943 | −1.00266 | ||||||||
\(843\) | −10.6437 | −0.366589 | ||||||||
\(844\) | −19.8496 | −0.683251 | ||||||||
\(845\) | 35.9507 | 1.23674 | ||||||||
\(846\) | −8.73038 | −0.300157 | ||||||||
\(847\) | 50.4616 | 1.73388 | ||||||||
\(848\) | 2.94866 | 0.101257 | ||||||||
\(849\) | 18.9562 | 0.650576 | ||||||||
\(850\) | −0.985361 | −0.0337976 | ||||||||
\(851\) | −0.736251 | −0.0252383 | ||||||||
\(852\) | 6.71791 | 0.230152 | ||||||||
\(853\) | −30.1917 | −1.03375 | −0.516873 | − | 0.856062i | \(-0.672904\pi\) | ||||
−0.516873 | + | 0.856062i | \(0.672904\pi\) | |||||||
\(854\) | −52.1893 | −1.78588 | ||||||||
\(855\) | 7.98367 | 0.273036 | ||||||||
\(856\) | 8.67399 | 0.296471 | ||||||||
\(857\) | −34.8504 | −1.19047 | −0.595234 | − | 0.803553i | \(-0.702941\pi\) | ||||
−0.595234 | + | 0.803553i | \(0.702941\pi\) | |||||||
\(858\) | 24.4559 | 0.834909 | ||||||||
\(859\) | −30.8469 | −1.05248 | −0.526242 | − | 0.850335i | \(-0.676399\pi\) | ||||
−0.526242 | + | 0.850335i | \(0.676399\pi\) | |||||||
\(860\) | −6.57659 | −0.224260 | ||||||||
\(861\) | −14.3029 | −0.487441 | ||||||||
\(862\) | −15.7033 | −0.534858 | ||||||||
\(863\) | 42.6497 | 1.45181 | 0.725906 | − | 0.687794i | \(-0.241421\pi\) | ||||
0.725906 | + | 0.687794i | \(0.241421\pi\) | |||||||
\(864\) | 5.55275 | 0.188908 | ||||||||
\(865\) | −43.7116 | −1.48624 | ||||||||
\(866\) | −5.77642 | −0.196291 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 13.3580 | 0.453398 | ||||||||
\(869\) | 36.3667 | 1.23366 | ||||||||
\(870\) | 11.7139 | 0.397140 | ||||||||
\(871\) | 79.9587 | 2.70930 | ||||||||
\(872\) | −0.506216 | −0.0171426 | ||||||||
\(873\) | −4.48034 | −0.151637 | ||||||||
\(874\) | 2.64712 | 0.0895402 | ||||||||
\(875\) | −48.2229 | −1.63023 | ||||||||
\(876\) | −8.73281 | −0.295054 | ||||||||
\(877\) | 18.3259 | 0.618823 | 0.309411 | − | 0.950928i | \(-0.399868\pi\) | ||||
0.309411 | + | 0.950928i | \(0.399868\pi\) | |||||||
\(878\) | 10.8860 | 0.367384 | ||||||||
\(879\) | 13.5918 | 0.458439 | ||||||||
\(880\) | 2.06207 | 0.0695123 | ||||||||
\(881\) | 41.7070 | 1.40515 | 0.702573 | − | 0.711612i | \(-0.252035\pi\) | ||||
0.702573 | + | 0.711612i | \(0.252035\pi\) | |||||||
\(882\) | −8.14148 | −0.274138 | ||||||||
\(883\) | −49.1414 | −1.65374 | −0.826870 | − | 0.562393i | \(-0.809881\pi\) | ||||
−0.826870 | + | 0.562393i | \(0.809881\pi\) | |||||||
\(884\) | −6.63192 | −0.223056 | ||||||||
\(885\) | 9.17893 | 0.308547 | ||||||||
\(886\) | −23.3375 | −0.784038 | ||||||||
\(887\) | 28.3542 | 0.952040 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(888\) | −2.90942 | −0.0976338 | ||||||||
\(889\) | 6.04159 | 0.202628 | ||||||||
\(890\) | −1.73944 | −0.0583061 | ||||||||
\(891\) | −4.85826 | −0.162758 | ||||||||
\(892\) | −7.66146 | −0.256525 | ||||||||
\(893\) | 39.1218 | 1.30916 | ||||||||
\(894\) | −12.4470 | −0.416289 | ||||||||
\(895\) | 36.9751 | 1.23594 | ||||||||
\(896\) | 24.8526 | 0.830268 | ||||||||
\(897\) | −4.06045 | −0.135575 | ||||||||
\(898\) | −14.3626 | −0.479288 | ||||||||
\(899\) | −18.4708 | −0.616035 | ||||||||
\(900\) | 1.29817 | 0.0432724 | ||||||||
\(901\) | 13.7314 | 0.457459 | ||||||||
\(902\) | 15.6427 | 0.520845 | ||||||||
\(903\) | −11.2188 | −0.373337 | ||||||||
\(904\) | −12.5877 | −0.418661 | ||||||||
\(905\) | −4.85412 | −0.161357 | ||||||||
\(906\) | 4.13101 | 0.137244 | ||||||||
\(907\) | −24.9896 | −0.829765 | −0.414882 | − | 0.909875i | \(-0.636177\pi\) | ||||
−0.414882 | + | 0.909875i | \(0.636177\pi\) | |||||||
\(908\) | −28.9724 | −0.961483 | ||||||||
\(909\) | 15.4458 | 0.512305 | ||||||||
\(910\) | 39.8393 | 1.32066 | ||||||||
\(911\) | 33.8947 | 1.12298 | 0.561490 | − | 0.827483i | \(-0.310228\pi\) | ||||
0.561490 | + | 0.827483i | \(0.310228\pi\) | |||||||
\(912\) | 0.867363 | 0.0287213 | ||||||||
\(913\) | 72.0040 | 2.38298 | ||||||||
\(914\) | 18.5686 | 0.614194 | ||||||||
\(915\) | −28.5818 | −0.944886 | ||||||||
\(916\) | 18.5890 | 0.614197 | ||||||||
\(917\) | 81.4798 | 2.69070 | ||||||||
\(918\) | −0.901374 | −0.0297498 | ||||||||
\(919\) | 3.06773 | 0.101195 | 0.0505975 | − | 0.998719i | \(-0.483887\pi\) | ||||
0.0505975 | + | 0.998719i | \(0.483887\pi\) | |||||||
\(920\) | −4.12903 | −0.136130 | ||||||||
\(921\) | 33.0191 | 1.08802 | ||||||||
\(922\) | −26.1722 | −0.861935 | ||||||||
\(923\) | −31.5928 | −1.03989 | ||||||||
\(924\) | −23.1005 | −0.759950 | ||||||||
\(925\) | −1.10697 | −0.0363971 | ||||||||
\(926\) | 23.0584 | 0.757746 | ||||||||
\(927\) | −16.2499 | −0.533718 | ||||||||
\(928\) | −36.5085 | −1.19845 | ||||||||
\(929\) | 28.3020 | 0.928560 | 0.464280 | − | 0.885688i | \(-0.346313\pi\) | ||||
0.464280 | + | 0.885688i | \(0.346313\pi\) | |||||||
\(930\) | −5.00515 | −0.164125 | ||||||||
\(931\) | 36.4829 | 1.19568 | ||||||||
\(932\) | 31.0436 | 1.01687 | ||||||||
\(933\) | 0.148991 | 0.00487776 | ||||||||
\(934\) | −36.0568 | −1.17981 | ||||||||
\(935\) | 9.60269 | 0.314041 | ||||||||
\(936\) | −16.0456 | −0.524466 | ||||||||
\(937\) | −41.6790 | −1.36159 | −0.680797 | − | 0.732472i | \(-0.738366\pi\) | ||||
−0.680797 | + | 0.732472i | \(0.738366\pi\) | |||||||
\(938\) | 51.6740 | 1.68722 | ||||||||
\(939\) | 11.2746 | 0.367931 | ||||||||
\(940\) | −22.7343 | −0.741512 | ||||||||
\(941\) | −36.9478 | −1.20446 | −0.602231 | − | 0.798322i | \(-0.705721\pi\) | ||||
−0.602231 | + | 0.798322i | \(0.705721\pi\) | |||||||
\(942\) | −0.901374 | −0.0293684 | ||||||||
\(943\) | −2.59719 | −0.0845761 | ||||||||
\(944\) | 0.997219 | 0.0324567 | ||||||||
\(945\) | −7.91425 | −0.257451 | ||||||||
\(946\) | 12.2697 | 0.398921 | ||||||||
\(947\) | 34.3275 | 1.11549 | 0.557746 | − | 0.830011i | \(-0.311666\pi\) | ||||
0.557746 | + | 0.830011i | \(0.311666\pi\) | |||||||
\(948\) | −8.88926 | −0.288710 | ||||||||
\(949\) | 41.0684 | 1.33314 | ||||||||
\(950\) | 3.98003 | 0.129129 | ||||||||
\(951\) | −22.7598 | −0.738037 | ||||||||
\(952\) | −11.5042 | −0.372853 | ||||||||
\(953\) | −24.5438 | −0.795051 | −0.397525 | − | 0.917591i | \(-0.630131\pi\) | ||||
−0.397525 | + | 0.917591i | \(0.630131\pi\) | |||||||
\(954\) | 12.3771 | 0.400724 | ||||||||
\(955\) | −27.0312 | −0.874708 | ||||||||
\(956\) | 30.2816 | 0.979377 | ||||||||
\(957\) | 31.9423 | 1.03255 | ||||||||
\(958\) | 27.9553 | 0.903194 | ||||||||
\(959\) | −30.2042 | −0.975345 | ||||||||
\(960\) | −10.7418 | −0.346691 | ||||||||
\(961\) | −23.1078 | −0.745412 | ||||||||
\(962\) | 5.09741 | 0.164347 | ||||||||
\(963\) | 3.01898 | 0.0972852 | ||||||||
\(964\) | 9.09579 | 0.292956 | ||||||||
\(965\) | −27.7443 | −0.893121 | ||||||||
\(966\) | −2.62410 | −0.0844291 | ||||||||
\(967\) | −3.74119 | −0.120309 | −0.0601543 | − | 0.998189i | \(-0.519159\pi\) | ||||
−0.0601543 | + | 0.998189i | \(0.519159\pi\) | |||||||
\(968\) | 36.2095 | 1.16382 | ||||||||
\(969\) | 4.03916 | 0.129756 | ||||||||
\(970\) | 7.98230 | 0.256296 | ||||||||
\(971\) | −8.28895 | −0.266005 | −0.133003 | − | 0.991116i | \(-0.542462\pi\) | ||||
−0.133003 | + | 0.991116i | \(0.542462\pi\) | |||||||
\(972\) | 1.18752 | 0.0380899 | ||||||||
\(973\) | −30.8114 | −0.987768 | ||||||||
\(974\) | 20.5517 | 0.658520 | ||||||||
\(975\) | −6.10501 | −0.195517 | ||||||||
\(976\) | −3.10519 | −0.0993948 | ||||||||
\(977\) | 37.4629 | 1.19854 | 0.599272 | − | 0.800545i | \(-0.295457\pi\) | ||||
0.599272 | + | 0.800545i | \(0.295457\pi\) | |||||||
\(978\) | 9.28420 | 0.296876 | ||||||||
\(979\) | −4.74322 | −0.151594 | ||||||||
\(980\) | −21.2008 | −0.677235 | ||||||||
\(981\) | −0.176188 | −0.00562526 | ||||||||
\(982\) | 15.0158 | 0.479174 | ||||||||
\(983\) | 27.2958 | 0.870601 | 0.435301 | − | 0.900285i | \(-0.356642\pi\) | ||||
0.435301 | + | 0.900285i | \(0.356642\pi\) | |||||||
\(984\) | −10.2632 | −0.327180 | ||||||||
\(985\) | 3.85854 | 0.122943 | ||||||||
\(986\) | 5.92640 | 0.188735 | ||||||||
\(987\) | −38.7816 | −1.23443 | ||||||||
\(988\) | 26.7874 | 0.852219 | ||||||||
\(989\) | −2.03716 | −0.0647778 | ||||||||
\(990\) | 8.65562 | 0.275094 | ||||||||
\(991\) | 58.7636 | 1.86669 | 0.933343 | − | 0.358986i | \(-0.116877\pi\) | ||||
0.933343 | + | 0.358986i | \(0.116877\pi\) | |||||||
\(992\) | 15.5994 | 0.495281 | ||||||||
\(993\) | −9.42962 | −0.299240 | ||||||||
\(994\) | −20.4171 | −0.647592 | ||||||||
\(995\) | −13.8272 | −0.438351 | ||||||||
\(996\) | −17.6002 | −0.557684 | ||||||||
\(997\) | −0.968736 | −0.0306802 | −0.0153401 | − | 0.999882i | \(-0.504883\pi\) | ||||
−0.0153401 | + | 0.999882i | \(0.504883\pi\) | |||||||
\(998\) | −9.10804 | −0.288310 | ||||||||
\(999\) | −1.01262 | −0.0320380 |
(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 | 8007.2.a.f.1.18 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.18 | ✓ | 48 | 1.1 | even | 1 | trivial |