Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57358 | −1.81979 | −0.909896 | − | 0.414836i | \(-0.863839\pi\) | ||||
−0.909896 | + | 0.414836i | \(0.863839\pi\) | |||||||
\(3\) | −2.79713 | −1.61493 | −0.807463 | − | 0.589918i | \(-0.799160\pi\) | ||||
−0.807463 | + | 0.589918i | \(0.799160\pi\) | |||||||
\(4\) | 4.62329 | 2.31164 | ||||||||
\(5\) | 0.767586 | 0.343275 | 0.171637 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171637 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(6\) | 7.19864 | 2.93883 | ||||||||
\(7\) | −3.79460 | −1.43422 | −0.717112 | − | 0.696958i | \(-0.754537\pi\) | ||||
−0.717112 | + | 0.696958i | \(0.754537\pi\) | |||||||
\(8\) | −6.75123 | −2.38692 | ||||||||
\(9\) | 4.82396 | 1.60799 | ||||||||
\(10\) | −1.97544 | −0.624689 | ||||||||
\(11\) | −3.35791 | −1.01245 | −0.506223 | − | 0.862402i | \(-0.668959\pi\) | ||||
−0.506223 | + | 0.862402i | \(0.668959\pi\) | |||||||
\(12\) | −12.9320 | −3.73314 | ||||||||
\(13\) | −5.51722 | −1.53020 | −0.765100 | − | 0.643911i | \(-0.777311\pi\) | ||||
−0.765100 | + | 0.643911i | \(0.777311\pi\) | |||||||
\(14\) | 9.76569 | 2.60999 | ||||||||
\(15\) | −2.14704 | −0.554364 | ||||||||
\(16\) | 8.12822 | 2.03206 | ||||||||
\(17\) | 1.14705 | 0.278201 | 0.139101 | − | 0.990278i | \(-0.455579\pi\) | ||||
0.139101 | + | 0.990278i | \(0.455579\pi\) | |||||||
\(18\) | −12.4148 | −2.92620 | ||||||||
\(19\) | −0.276498 | −0.0634330 | −0.0317165 | − | 0.999497i | \(-0.510097\pi\) | ||||
−0.0317165 | + | 0.999497i | \(0.510097\pi\) | |||||||
\(20\) | 3.54877 | 0.793529 | ||||||||
\(21\) | 10.6140 | 2.31617 | ||||||||
\(22\) | 8.64182 | 1.84244 | ||||||||
\(23\) | −5.90396 | −1.23106 | −0.615530 | − | 0.788113i | \(-0.711058\pi\) | ||||
−0.615530 | + | 0.788113i | \(0.711058\pi\) | |||||||
\(24\) | 18.8841 | 3.85470 | ||||||||
\(25\) | −4.41081 | −0.882162 | ||||||||
\(26\) | 14.1990 | 2.78465 | ||||||||
\(27\) | −5.10186 | −0.981854 | ||||||||
\(28\) | −17.5435 | −3.31542 | ||||||||
\(29\) | 4.65044 | 0.863565 | 0.431782 | − | 0.901978i | \(-0.357885\pi\) | ||||
0.431782 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(30\) | 5.52557 | 1.00883 | ||||||||
\(31\) | 8.20608 | 1.47385 | 0.736927 | − | 0.675972i | \(-0.236276\pi\) | ||||
0.736927 | + | 0.675972i | \(0.236276\pi\) | |||||||
\(32\) | −7.41613 | −1.31100 | ||||||||
\(33\) | 9.39251 | 1.63503 | ||||||||
\(34\) | −2.95203 | −0.506269 | ||||||||
\(35\) | −2.91268 | −0.492333 | ||||||||
\(36\) | 22.3026 | 3.71709 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0.711589 | 0.115435 | ||||||||
\(39\) | 15.4324 | 2.47116 | ||||||||
\(40\) | −5.18215 | −0.819370 | ||||||||
\(41\) | 3.88860 | 0.607297 | 0.303648 | − | 0.952784i | \(-0.401795\pi\) | ||||
0.303648 | + | 0.952784i | \(0.401795\pi\) | |||||||
\(42\) | −27.3160 | −4.21494 | ||||||||
\(43\) | −0.0399814 | −0.00609710 | −0.00304855 | − | 0.999995i | \(-0.500970\pi\) | ||||
−0.00304855 | + | 0.999995i | \(0.500970\pi\) | |||||||
\(44\) | −15.5246 | −2.34042 | ||||||||
\(45\) | 3.70280 | 0.551981 | ||||||||
\(46\) | 15.1943 | 2.24027 | ||||||||
\(47\) | 5.73139 | 0.836009 | 0.418005 | − | 0.908445i | \(-0.362730\pi\) | ||||
0.418005 | + | 0.908445i | \(0.362730\pi\) | |||||||
\(48\) | −22.7357 | −3.28162 | ||||||||
\(49\) | 7.39901 | 1.05700 | ||||||||
\(50\) | 11.3516 | 1.60535 | ||||||||
\(51\) | −3.20846 | −0.449275 | ||||||||
\(52\) | −25.5077 | −3.53728 | ||||||||
\(53\) | 0.502954 | 0.0690860 | 0.0345430 | − | 0.999403i | \(-0.489002\pi\) | ||||
0.0345430 | + | 0.999403i | \(0.489002\pi\) | |||||||
\(54\) | 13.1300 | 1.78677 | ||||||||
\(55\) | −2.57748 | −0.347548 | ||||||||
\(56\) | 25.6182 | 3.42338 | ||||||||
\(57\) | 0.773402 | 0.102440 | ||||||||
\(58\) | −11.9683 | −1.57151 | ||||||||
\(59\) | −8.19480 | −1.06687 | −0.533436 | − | 0.845840i | \(-0.679100\pi\) | ||||
−0.533436 | + | 0.845840i | \(0.679100\pi\) | |||||||
\(60\) | −9.92639 | −1.28149 | ||||||||
\(61\) | 8.28663 | 1.06099 | 0.530497 | − | 0.847687i | \(-0.322005\pi\) | ||||
0.530497 | + | 0.847687i | \(0.322005\pi\) | |||||||
\(62\) | −21.1190 | −2.68211 | ||||||||
\(63\) | −18.3050 | −2.30621 | ||||||||
\(64\) | 2.82952 | 0.353690 | ||||||||
\(65\) | −4.23494 | −0.525279 | ||||||||
\(66\) | −24.1723 | −2.97541 | ||||||||
\(67\) | −1.33314 | −0.162868 | −0.0814342 | − | 0.996679i | \(-0.525950\pi\) | ||||
−0.0814342 | + | 0.996679i | \(0.525950\pi\) | |||||||
\(68\) | 5.30316 | 0.643103 | ||||||||
\(69\) | 16.5142 | 1.98807 | ||||||||
\(70\) | 7.49601 | 0.895945 | ||||||||
\(71\) | −11.6076 | −1.37757 | −0.688787 | − | 0.724964i | \(-0.741856\pi\) | ||||
−0.688787 | + | 0.724964i | \(0.741856\pi\) | |||||||
\(72\) | −32.5677 | −3.83814 | ||||||||
\(73\) | 4.79490 | 0.561201 | 0.280601 | − | 0.959825i | \(-0.409466\pi\) | ||||
0.280601 | + | 0.959825i | \(0.409466\pi\) | |||||||
\(74\) | −2.57358 | −0.299172 | ||||||||
\(75\) | 12.3376 | 1.42463 | ||||||||
\(76\) | −1.27833 | −0.146635 | ||||||||
\(77\) | 12.7419 | 1.45208 | ||||||||
\(78\) | −39.7164 | −4.49700 | ||||||||
\(79\) | −1.36951 | −0.154082 | −0.0770410 | − | 0.997028i | \(-0.524547\pi\) | ||||
−0.0770410 | + | 0.997028i | \(0.524547\pi\) | |||||||
\(80\) | 6.23911 | 0.697554 | ||||||||
\(81\) | −0.201290 | −0.0223656 | ||||||||
\(82\) | −10.0076 | −1.10515 | ||||||||
\(83\) | 8.55030 | 0.938518 | 0.469259 | − | 0.883061i | \(-0.344521\pi\) | ||||
0.469259 | + | 0.883061i | \(0.344521\pi\) | |||||||
\(84\) | 49.0716 | 5.35416 | ||||||||
\(85\) | 0.880462 | 0.0954995 | ||||||||
\(86\) | 0.102895 | 0.0110955 | ||||||||
\(87\) | −13.0079 | −1.39459 | ||||||||
\(88\) | 22.6700 | 2.41663 | ||||||||
\(89\) | −9.22223 | −0.977554 | −0.488777 | − | 0.872409i | \(-0.662557\pi\) | ||||
−0.488777 | + | 0.872409i | \(0.662557\pi\) | |||||||
\(90\) | −9.52944 | −1.00449 | ||||||||
\(91\) | 20.9356 | 2.19465 | ||||||||
\(92\) | −27.2957 | −2.84577 | ||||||||
\(93\) | −22.9535 | −2.38017 | ||||||||
\(94\) | −14.7502 | −1.52136 | ||||||||
\(95\) | −0.212236 | −0.0217750 | ||||||||
\(96\) | 20.7439 | 2.11717 | ||||||||
\(97\) | 9.14002 | 0.928028 | 0.464014 | − | 0.885828i | \(-0.346409\pi\) | ||||
0.464014 | + | 0.885828i | \(0.346409\pi\) | |||||||
\(98\) | −19.0419 | −1.92352 | ||||||||
\(99\) | −16.1984 | −1.62800 | ||||||||
\(100\) | −20.3925 | −2.03925 | ||||||||
\(101\) | 13.2634 | 1.31975 | 0.659877 | − | 0.751374i | \(-0.270608\pi\) | ||||
0.659877 | + | 0.751374i | \(0.270608\pi\) | |||||||
\(102\) | 8.25722 | 0.817587 | ||||||||
\(103\) | 12.2364 | 1.20569 | 0.602843 | − | 0.797860i | \(-0.294034\pi\) | ||||
0.602843 | + | 0.797860i | \(0.294034\pi\) | |||||||
\(104\) | 37.2480 | 3.65247 | ||||||||
\(105\) | 8.14717 | 0.795082 | ||||||||
\(106\) | −1.29439 | −0.125722 | ||||||||
\(107\) | 2.66166 | 0.257313 | 0.128656 | − | 0.991689i | \(-0.458934\pi\) | ||||
0.128656 | + | 0.991689i | \(0.458934\pi\) | |||||||
\(108\) | −23.5874 | −2.26970 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 6.63334 | 0.632464 | ||||||||
\(111\) | −2.79713 | −0.265492 | ||||||||
\(112\) | −30.8434 | −2.91442 | ||||||||
\(113\) | 1.33424 | 0.125515 | 0.0627574 | − | 0.998029i | \(-0.480011\pi\) | ||||
0.0627574 | + | 0.998029i | \(0.480011\pi\) | |||||||
\(114\) | −1.99041 | −0.186419 | ||||||||
\(115\) | −4.53179 | −0.422592 | ||||||||
\(116\) | 21.5003 | 1.99625 | ||||||||
\(117\) | −26.6148 | −2.46054 | ||||||||
\(118\) | 21.0899 | 1.94149 | ||||||||
\(119\) | −4.35261 | −0.399003 | ||||||||
\(120\) | 14.4952 | 1.32322 | ||||||||
\(121\) | 0.275534 | 0.0250486 | ||||||||
\(122\) | −21.3263 | −1.93079 | ||||||||
\(123\) | −10.8769 | −0.980739 | ||||||||
\(124\) | 37.9391 | 3.40703 | ||||||||
\(125\) | −7.22361 | −0.646099 | ||||||||
\(126\) | 47.1093 | 4.19683 | ||||||||
\(127\) | 6.44128 | 0.571571 | 0.285786 | − | 0.958294i | \(-0.407745\pi\) | ||||
0.285786 | + | 0.958294i | \(0.407745\pi\) | |||||||
\(128\) | 7.55027 | 0.667356 | ||||||||
\(129\) | 0.111833 | 0.00984637 | ||||||||
\(130\) | 10.8989 | 0.955899 | ||||||||
\(131\) | −14.3757 | −1.25601 | −0.628004 | − | 0.778210i | \(-0.716128\pi\) | ||||
−0.628004 | + | 0.778210i | \(0.716128\pi\) | |||||||
\(132\) | 43.4243 | 3.77960 | ||||||||
\(133\) | 1.04920 | 0.0909772 | ||||||||
\(134\) | 3.43092 | 0.296387 | ||||||||
\(135\) | −3.91612 | −0.337046 | ||||||||
\(136\) | −7.74402 | −0.664045 | ||||||||
\(137\) | −6.62586 | −0.566086 | −0.283043 | − | 0.959107i | \(-0.591344\pi\) | ||||
−0.283043 | + | 0.959107i | \(0.591344\pi\) | |||||||
\(138\) | −42.5004 | −3.61788 | ||||||||
\(139\) | −12.7350 | −1.08017 | −0.540085 | − | 0.841611i | \(-0.681608\pi\) | ||||
−0.540085 | + | 0.841611i | \(0.681608\pi\) | |||||||
\(140\) | −13.4662 | −1.13810 | ||||||||
\(141\) | −16.0315 | −1.35009 | ||||||||
\(142\) | 29.8731 | 2.50690 | ||||||||
\(143\) | 18.5263 | 1.54925 | ||||||||
\(144\) | 39.2102 | 3.26752 | ||||||||
\(145\) | 3.56961 | 0.296440 | ||||||||
\(146\) | −12.3400 | −1.02127 | ||||||||
\(147\) | −20.6960 | −1.70698 | ||||||||
\(148\) | 4.62329 | 0.380032 | ||||||||
\(149\) | 19.1438 | 1.56832 | 0.784161 | − | 0.620558i | \(-0.213094\pi\) | ||||
0.784161 | + | 0.620558i | \(0.213094\pi\) | |||||||
\(150\) | −31.7518 | −2.59253 | ||||||||
\(151\) | 10.8135 | 0.879986 | 0.439993 | − | 0.898001i | \(-0.354981\pi\) | ||||
0.439993 | + | 0.898001i | \(0.354981\pi\) | |||||||
\(152\) | 1.86670 | 0.151410 | ||||||||
\(153\) | 5.53334 | 0.447344 | ||||||||
\(154\) | −32.7923 | −2.64248 | ||||||||
\(155\) | 6.29887 | 0.505937 | ||||||||
\(156\) | 71.3484 | 5.71245 | ||||||||
\(157\) | 5.47855 | 0.437236 | 0.218618 | − | 0.975811i | \(-0.429845\pi\) | ||||
0.218618 | + | 0.975811i | \(0.429845\pi\) | |||||||
\(158\) | 3.52454 | 0.280397 | ||||||||
\(159\) | −1.40683 | −0.111569 | ||||||||
\(160\) | −5.69252 | −0.450033 | ||||||||
\(161\) | 22.4032 | 1.76562 | ||||||||
\(162\) | 0.518036 | 0.0407008 | ||||||||
\(163\) | 2.88406 | 0.225897 | 0.112949 | − | 0.993601i | \(-0.463970\pi\) | ||||
0.112949 | + | 0.993601i | \(0.463970\pi\) | |||||||
\(164\) | 17.9781 | 1.40385 | ||||||||
\(165\) | 7.20956 | 0.561264 | ||||||||
\(166\) | −22.0048 | −1.70791 | ||||||||
\(167\) | −21.6857 | −1.67809 | −0.839046 | − | 0.544061i | \(-0.816886\pi\) | ||||
−0.839046 | + | 0.544061i | \(0.816886\pi\) | |||||||
\(168\) | −71.6576 | −5.52851 | ||||||||
\(169\) | 17.4397 | 1.34151 | ||||||||
\(170\) | −2.26594 | −0.173789 | ||||||||
\(171\) | −1.33382 | −0.101999 | ||||||||
\(172\) | −0.184845 | −0.0140943 | ||||||||
\(173\) | −5.33883 | −0.405903 | −0.202952 | − | 0.979189i | \(-0.565053\pi\) | ||||
−0.202952 | + | 0.979189i | \(0.565053\pi\) | |||||||
\(174\) | 33.4768 | 2.53787 | ||||||||
\(175\) | 16.7373 | 1.26522 | ||||||||
\(176\) | −27.2938 | −2.05735 | ||||||||
\(177\) | 22.9220 | 1.72292 | ||||||||
\(178\) | 23.7341 | 1.77895 | ||||||||
\(179\) | 7.27425 | 0.543703 | 0.271852 | − | 0.962339i | \(-0.412364\pi\) | ||||
0.271852 | + | 0.962339i | \(0.412364\pi\) | |||||||
\(180\) | 17.1191 | 1.27598 | ||||||||
\(181\) | 20.8989 | 1.55340 | 0.776700 | − | 0.629871i | \(-0.216892\pi\) | ||||
0.776700 | + | 0.629871i | \(0.216892\pi\) | |||||||
\(182\) | −53.8794 | −3.99381 | ||||||||
\(183\) | −23.1788 | −1.71343 | ||||||||
\(184\) | 39.8590 | 2.93844 | ||||||||
\(185\) | 0.767586 | 0.0564340 | ||||||||
\(186\) | 59.0725 | 4.33141 | ||||||||
\(187\) | −3.85170 | −0.281664 | ||||||||
\(188\) | 26.4979 | 1.93256 | ||||||||
\(189\) | 19.3595 | 1.40820 | ||||||||
\(190\) | 0.546206 | 0.0396259 | ||||||||
\(191\) | 15.0179 | 1.08665 | 0.543327 | − | 0.839521i | \(-0.317164\pi\) | ||||
0.543327 | + | 0.839521i | \(0.317164\pi\) | |||||||
\(192\) | −7.91455 | −0.571184 | ||||||||
\(193\) | 25.7071 | 1.85043 | 0.925217 | − | 0.379438i | \(-0.123883\pi\) | ||||
0.925217 | + | 0.379438i | \(0.123883\pi\) | |||||||
\(194\) | −23.5225 | −1.68882 | ||||||||
\(195\) | 11.8457 | 0.848287 | ||||||||
\(196\) | 34.2077 | 2.44341 | ||||||||
\(197\) | 23.5858 | 1.68042 | 0.840210 | − | 0.542262i | \(-0.182432\pi\) | ||||
0.840210 | + | 0.542262i | \(0.182432\pi\) | |||||||
\(198\) | 41.6878 | 2.96262 | ||||||||
\(199\) | −7.33314 | −0.519833 | −0.259916 | − | 0.965631i | \(-0.583695\pi\) | ||||
−0.259916 | + | 0.965631i | \(0.583695\pi\) | |||||||
\(200\) | 29.7784 | 2.10565 | ||||||||
\(201\) | 3.72896 | 0.263020 | ||||||||
\(202\) | −34.1343 | −2.40168 | ||||||||
\(203\) | −17.6466 | −1.23855 | ||||||||
\(204\) | −14.8336 | −1.03856 | ||||||||
\(205\) | 2.98483 | 0.208470 | ||||||||
\(206\) | −31.4912 | −2.19410 | ||||||||
\(207\) | −28.4805 | −1.97953 | ||||||||
\(208\) | −44.8452 | −3.10945 | ||||||||
\(209\) | 0.928455 | 0.0642226 | ||||||||
\(210\) | −20.9673 | −1.44688 | ||||||||
\(211\) | −5.23824 | −0.360615 | −0.180308 | − | 0.983610i | \(-0.557709\pi\) | ||||
−0.180308 | + | 0.983610i | \(0.557709\pi\) | |||||||
\(212\) | 2.32530 | 0.159702 | ||||||||
\(213\) | 32.4681 | 2.22468 | ||||||||
\(214\) | −6.84999 | −0.468256 | ||||||||
\(215\) | −0.0306891 | −0.00209298 | ||||||||
\(216\) | 34.4438 | 2.34361 | ||||||||
\(217\) | −31.1388 | −2.11384 | ||||||||
\(218\) | −2.57358 | −0.174305 | ||||||||
\(219\) | −13.4120 | −0.906298 | ||||||||
\(220\) | −11.9164 | −0.803406 | ||||||||
\(221\) | −6.32854 | −0.425704 | ||||||||
\(222\) | 7.19864 | 0.483141 | ||||||||
\(223\) | 7.11102 | 0.476189 | 0.238095 | − | 0.971242i | \(-0.423477\pi\) | ||||
0.238095 | + | 0.971242i | \(0.423477\pi\) | |||||||
\(224\) | 28.1413 | 1.88027 | ||||||||
\(225\) | −21.2776 | −1.41851 | ||||||||
\(226\) | −3.43377 | −0.228411 | ||||||||
\(227\) | 5.16276 | 0.342665 | 0.171332 | − | 0.985213i | \(-0.445193\pi\) | ||||
0.171332 | + | 0.985213i | \(0.445193\pi\) | |||||||
\(228\) | 3.57566 | 0.236804 | ||||||||
\(229\) | 16.8898 | 1.11611 | 0.558054 | − | 0.829805i | \(-0.311548\pi\) | ||||
0.558054 | + | 0.829805i | \(0.311548\pi\) | |||||||
\(230\) | 11.6629 | 0.769030 | ||||||||
\(231\) | −35.6409 | −2.34500 | ||||||||
\(232\) | −31.3962 | −2.06126 | ||||||||
\(233\) | −16.2147 | −1.06226 | −0.531130 | − | 0.847291i | \(-0.678232\pi\) | ||||
−0.531130 | + | 0.847291i | \(0.678232\pi\) | |||||||
\(234\) | 68.4953 | 4.47768 | ||||||||
\(235\) | 4.39933 | 0.286981 | ||||||||
\(236\) | −37.8869 | −2.46623 | ||||||||
\(237\) | 3.83071 | 0.248831 | ||||||||
\(238\) | 11.2018 | 0.726103 | ||||||||
\(239\) | −23.4314 | −1.51565 | −0.757825 | − | 0.652458i | \(-0.773738\pi\) | ||||
−0.757825 | + | 0.652458i | \(0.773738\pi\) | |||||||
\(240\) | −17.4516 | −1.12650 | ||||||||
\(241\) | 18.4882 | 1.19093 | 0.595466 | − | 0.803380i | \(-0.296967\pi\) | ||||
0.595466 | + | 0.803380i | \(0.296967\pi\) | |||||||
\(242\) | −0.709108 | −0.0455832 | ||||||||
\(243\) | 15.8686 | 1.01797 | ||||||||
\(244\) | 38.3115 | 2.45264 | ||||||||
\(245\) | 5.67937 | 0.362842 | ||||||||
\(246\) | 27.9926 | 1.78474 | ||||||||
\(247\) | 1.52550 | 0.0970652 | ||||||||
\(248\) | −55.4011 | −3.51797 | ||||||||
\(249\) | −23.9163 | −1.51564 | ||||||||
\(250\) | 18.5905 | 1.17577 | ||||||||
\(251\) | 22.9496 | 1.44857 | 0.724284 | − | 0.689502i | \(-0.242171\pi\) | ||||
0.724284 | + | 0.689502i | \(0.242171\pi\) | |||||||
\(252\) | −84.6293 | −5.33115 | ||||||||
\(253\) | 19.8249 | 1.24638 | ||||||||
\(254\) | −16.5771 | −1.04014 | ||||||||
\(255\) | −2.46277 | −0.154225 | ||||||||
\(256\) | −25.0902 | −1.56814 | ||||||||
\(257\) | −25.2387 | −1.57434 | −0.787172 | − | 0.616734i | \(-0.788456\pi\) | ||||
−0.787172 | + | 0.616734i | \(0.788456\pi\) | |||||||
\(258\) | −0.287811 | −0.0179183 | ||||||||
\(259\) | −3.79460 | −0.235785 | ||||||||
\(260\) | −19.5793 | −1.21426 | ||||||||
\(261\) | 22.4335 | 1.38860 | ||||||||
\(262\) | 36.9968 | 2.28567 | ||||||||
\(263\) | −14.0847 | −0.868502 | −0.434251 | − | 0.900792i | \(-0.642987\pi\) | ||||
−0.434251 | + | 0.900792i | \(0.642987\pi\) | |||||||
\(264\) | −63.4110 | −3.90268 | ||||||||
\(265\) | 0.386060 | 0.0237155 | ||||||||
\(266\) | −2.70020 | −0.165560 | ||||||||
\(267\) | 25.7958 | 1.57868 | ||||||||
\(268\) | −6.16347 | −0.376494 | ||||||||
\(269\) | −20.5744 | −1.25444 | −0.627221 | − | 0.778841i | \(-0.715808\pi\) | ||||
−0.627221 | + | 0.778841i | \(0.715808\pi\) | |||||||
\(270\) | 10.0784 | 0.613353 | ||||||||
\(271\) | −5.67560 | −0.344768 | −0.172384 | − | 0.985030i | \(-0.555147\pi\) | ||||
−0.172384 | + | 0.985030i | \(0.555147\pi\) | |||||||
\(272\) | 9.32351 | 0.565321 | ||||||||
\(273\) | −58.5598 | −3.54420 | ||||||||
\(274\) | 17.0522 | 1.03016 | ||||||||
\(275\) | 14.8111 | 0.893142 | ||||||||
\(276\) | 76.3497 | 4.59571 | ||||||||
\(277\) | −11.9693 | −0.719165 | −0.359583 | − | 0.933113i | \(-0.617081\pi\) | ||||
−0.359583 | + | 0.933113i | \(0.617081\pi\) | |||||||
\(278\) | 32.7745 | 1.96568 | ||||||||
\(279\) | 39.5858 | 2.36994 | ||||||||
\(280\) | 19.6642 | 1.17516 | ||||||||
\(281\) | −0.290839 | −0.0173500 | −0.00867500 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867500 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(282\) | 41.2582 | 2.45689 | ||||||||
\(283\) | 22.7986 | 1.35523 | 0.677617 | − | 0.735415i | \(-0.263013\pi\) | ||||
0.677617 | + | 0.735415i | \(0.263013\pi\) | |||||||
\(284\) | −53.6655 | −3.18446 | ||||||||
\(285\) | 0.593653 | 0.0351650 | ||||||||
\(286\) | −47.6788 | −2.81931 | ||||||||
\(287\) | −14.7557 | −0.871000 | ||||||||
\(288\) | −35.7751 | −2.10807 | ||||||||
\(289\) | −15.6843 | −0.922604 | ||||||||
\(290\) | −9.18666 | −0.539459 | ||||||||
\(291\) | −25.5659 | −1.49870 | ||||||||
\(292\) | 22.1682 | 1.29730 | ||||||||
\(293\) | −19.2419 | −1.12412 | −0.562062 | − | 0.827095i | \(-0.689992\pi\) | ||||
−0.562062 | + | 0.827095i | \(0.689992\pi\) | |||||||
\(294\) | 53.2627 | 3.10635 | ||||||||
\(295\) | −6.29022 | −0.366231 | ||||||||
\(296\) | −6.75123 | −0.392407 | ||||||||
\(297\) | 17.1316 | 0.994075 | ||||||||
\(298\) | −49.2680 | −2.85402 | ||||||||
\(299\) | 32.5734 | 1.88377 | ||||||||
\(300\) | 57.0404 | 3.29323 | ||||||||
\(301\) | 0.151713 | 0.00874461 | ||||||||
\(302\) | −27.8292 | −1.60139 | ||||||||
\(303\) | −37.0994 | −2.13130 | ||||||||
\(304\) | −2.24744 | −0.128899 | ||||||||
\(305\) | 6.36070 | 0.364213 | ||||||||
\(306\) | −14.2405 | −0.814073 | ||||||||
\(307\) | −32.1616 | −1.83556 | −0.917781 | − | 0.397087i | \(-0.870021\pi\) | ||||
−0.917781 | + | 0.397087i | \(0.870021\pi\) | |||||||
\(308\) | 58.9096 | 3.35668 | ||||||||
\(309\) | −34.2268 | −1.94709 | ||||||||
\(310\) | −16.2106 | −0.920701 | ||||||||
\(311\) | −15.6063 | −0.884953 | −0.442477 | − | 0.896780i | \(-0.645900\pi\) | ||||
−0.442477 | + | 0.896780i | \(0.645900\pi\) | |||||||
\(312\) | −104.188 | −5.89846 | ||||||||
\(313\) | 23.1099 | 1.30625 | 0.653125 | − | 0.757250i | \(-0.273458\pi\) | ||||
0.653125 | + | 0.757250i | \(0.273458\pi\) | |||||||
\(314\) | −14.0995 | −0.795679 | ||||||||
\(315\) | −14.0507 | −0.791665 | ||||||||
\(316\) | −6.33164 | −0.356183 | ||||||||
\(317\) | −14.6109 | −0.820628 | −0.410314 | − | 0.911944i | \(-0.634581\pi\) | ||||
−0.410314 | + | 0.911944i | \(0.634581\pi\) | |||||||
\(318\) | 3.62058 | 0.203032 | ||||||||
\(319\) | −15.6157 | −0.874313 | ||||||||
\(320\) | 2.17190 | 0.121413 | ||||||||
\(321\) | −7.44503 | −0.415541 | ||||||||
\(322\) | −57.6562 | −3.21306 | ||||||||
\(323\) | −0.317158 | −0.0176472 | ||||||||
\(324\) | −0.930624 | −0.0517013 | ||||||||
\(325\) | 24.3354 | 1.34989 | ||||||||
\(326\) | −7.42236 | −0.411086 | ||||||||
\(327\) | −2.79713 | −0.154682 | ||||||||
\(328\) | −26.2528 | −1.44957 | ||||||||
\(329\) | −21.7483 | −1.19903 | ||||||||
\(330\) | −18.5544 | −1.02138 | ||||||||
\(331\) | −18.8464 | −1.03589 | −0.517946 | − | 0.855413i | \(-0.673303\pi\) | ||||
−0.517946 | + | 0.855413i | \(0.673303\pi\) | |||||||
\(332\) | 39.5305 | 2.16952 | ||||||||
\(333\) | 4.82396 | 0.264351 | ||||||||
\(334\) | 55.8098 | 3.05378 | ||||||||
\(335\) | −1.02330 | −0.0559086 | ||||||||
\(336\) | 86.2731 | 4.70658 | ||||||||
\(337\) | 6.09462 | 0.331995 | 0.165998 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165998 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(338\) | −44.8823 | −2.44128 | ||||||||
\(339\) | −3.73205 | −0.202697 | ||||||||
\(340\) | 4.07063 | 0.220761 | ||||||||
\(341\) | −27.5552 | −1.49220 | ||||||||
\(342\) | 3.43268 | 0.185618 | ||||||||
\(343\) | −1.51407 | −0.0817520 | ||||||||
\(344\) | 0.269923 | 0.0145533 | ||||||||
\(345\) | 12.6760 | 0.682455 | ||||||||
\(346\) | 13.7399 | 0.738660 | ||||||||
\(347\) | 4.15108 | 0.222842 | 0.111421 | − | 0.993773i | \(-0.464460\pi\) | ||||
0.111421 | + | 0.993773i | \(0.464460\pi\) | |||||||
\(348\) | −60.1393 | −3.22380 | ||||||||
\(349\) | 1.11621 | 0.0597494 | 0.0298747 | − | 0.999554i | \(-0.490489\pi\) | ||||
0.0298747 | + | 0.999554i | \(0.490489\pi\) | |||||||
\(350\) | −43.0746 | −2.30244 | ||||||||
\(351\) | 28.1481 | 1.50243 | ||||||||
\(352\) | 24.9027 | 1.32732 | ||||||||
\(353\) | −24.3085 | −1.29381 | −0.646905 | − | 0.762570i | \(-0.723937\pi\) | ||||
−0.646905 | + | 0.762570i | \(0.723937\pi\) | |||||||
\(354\) | −58.9914 | −3.13536 | ||||||||
\(355\) | −8.90986 | −0.472886 | ||||||||
\(356\) | −42.6370 | −2.25976 | ||||||||
\(357\) | 12.1748 | 0.644361 | ||||||||
\(358\) | −18.7208 | −0.989427 | ||||||||
\(359\) | 21.0044 | 1.10857 | 0.554285 | − | 0.832327i | \(-0.312992\pi\) | ||||
0.554285 | + | 0.832327i | \(0.312992\pi\) | |||||||
\(360\) | −24.9985 | −1.31754 | ||||||||
\(361\) | −18.9235 | −0.995976 | ||||||||
\(362\) | −53.7848 | −2.82687 | ||||||||
\(363\) | −0.770707 | −0.0404516 | ||||||||
\(364\) | 96.7915 | 5.07325 | ||||||||
\(365\) | 3.68050 | 0.192646 | ||||||||
\(366\) | 59.6524 | 3.11808 | ||||||||
\(367\) | 7.53376 | 0.393259 | 0.196629 | − | 0.980478i | \(-0.437000\pi\) | ||||
0.196629 | + | 0.980478i | \(0.437000\pi\) | |||||||
\(368\) | −47.9887 | −2.50158 | ||||||||
\(369\) | 18.7584 | 0.976525 | ||||||||
\(370\) | −1.97544 | −0.102698 | ||||||||
\(371\) | −1.90851 | −0.0990849 | ||||||||
\(372\) | −106.121 | −5.50210 | ||||||||
\(373\) | 3.67283 | 0.190172 | 0.0950861 | − | 0.995469i | \(-0.469687\pi\) | ||||
0.0950861 | + | 0.995469i | \(0.469687\pi\) | |||||||
\(374\) | 9.91263 | 0.512570 | ||||||||
\(375\) | 20.2054 | 1.04340 | ||||||||
\(376\) | −38.6939 | −1.99549 | ||||||||
\(377\) | −25.6575 | −1.32143 | ||||||||
\(378\) | −49.8232 | −2.56263 | ||||||||
\(379\) | −7.97831 | −0.409818 | −0.204909 | − | 0.978781i | \(-0.565690\pi\) | ||||
−0.204909 | + | 0.978781i | \(0.565690\pi\) | |||||||
\(380\) | −0.981229 | −0.0503360 | ||||||||
\(381\) | −18.0171 | −0.923046 | ||||||||
\(382\) | −38.6496 | −1.97749 | ||||||||
\(383\) | 15.5308 | 0.793589 | 0.396795 | − | 0.917907i | \(-0.370123\pi\) | ||||
0.396795 | + | 0.917907i | \(0.370123\pi\) | |||||||
\(384\) | −21.1191 | −1.07773 | ||||||||
\(385\) | 9.78052 | 0.498461 | ||||||||
\(386\) | −66.1590 | −3.36741 | ||||||||
\(387\) | −0.192868 | −0.00980406 | ||||||||
\(388\) | 42.2569 | 2.14527 | ||||||||
\(389\) | 23.1812 | 1.17533 | 0.587667 | − | 0.809103i | \(-0.300047\pi\) | ||||
0.587667 | + | 0.809103i | \(0.300047\pi\) | |||||||
\(390\) | −30.4858 | −1.54371 | ||||||||
\(391\) | −6.77215 | −0.342483 | ||||||||
\(392\) | −49.9524 | −2.52298 | ||||||||
\(393\) | 40.2107 | 2.02836 | ||||||||
\(394\) | −60.6999 | −3.05801 | ||||||||
\(395\) | −1.05122 | −0.0528925 | ||||||||
\(396\) | −74.8899 | −3.76336 | ||||||||
\(397\) | 32.1465 | 1.61339 | 0.806694 | − | 0.590969i | \(-0.201255\pi\) | ||||
0.806694 | + | 0.590969i | \(0.201255\pi\) | |||||||
\(398\) | 18.8724 | 0.945987 | ||||||||
\(399\) | −2.93475 | −0.146921 | ||||||||
\(400\) | −35.8521 | −1.79260 | ||||||||
\(401\) | −24.8193 | −1.23942 | −0.619709 | − | 0.784832i | \(-0.712749\pi\) | ||||
−0.619709 | + | 0.784832i | \(0.712749\pi\) | |||||||
\(402\) | −9.59676 | −0.478643 | ||||||||
\(403\) | −45.2747 | −2.25529 | ||||||||
\(404\) | 61.3203 | 3.05080 | ||||||||
\(405\) | −0.154508 | −0.00767755 | ||||||||
\(406\) | 45.4148 | 2.25390 | ||||||||
\(407\) | −3.35791 | −0.166445 | ||||||||
\(408\) | 21.6611 | 1.07238 | ||||||||
\(409\) | 21.2342 | 1.04996 | 0.524981 | − | 0.851114i | \(-0.324072\pi\) | ||||
0.524981 | + | 0.851114i | \(0.324072\pi\) | |||||||
\(410\) | −7.68169 | −0.379372 | ||||||||
\(411\) | 18.5334 | 0.914187 | ||||||||
\(412\) | 56.5723 | 2.78712 | ||||||||
\(413\) | 31.0960 | 1.53013 | ||||||||
\(414\) | 73.2966 | 3.60233 | ||||||||
\(415\) | 6.56309 | 0.322170 | ||||||||
\(416\) | 40.9164 | 2.00609 | ||||||||
\(417\) | 35.6215 | 1.74439 | ||||||||
\(418\) | −2.38945 | −0.116872 | ||||||||
\(419\) | −18.0652 | −0.882541 | −0.441271 | − | 0.897374i | \(-0.645472\pi\) | ||||
−0.441271 | + | 0.897374i | \(0.645472\pi\) | |||||||
\(420\) | 37.6667 | 1.83795 | ||||||||
\(421\) | 2.97743 | 0.145111 | 0.0725556 | − | 0.997364i | \(-0.476885\pi\) | ||||
0.0725556 | + | 0.997364i | \(0.476885\pi\) | |||||||
\(422\) | 13.4810 | 0.656245 | ||||||||
\(423\) | 27.6480 | 1.34429 | ||||||||
\(424\) | −3.39556 | −0.164903 | ||||||||
\(425\) | −5.05944 | −0.245419 | ||||||||
\(426\) | −83.5591 | −4.04845 | ||||||||
\(427\) | −31.4445 | −1.52170 | ||||||||
\(428\) | 12.3056 | 0.594815 | ||||||||
\(429\) | −51.8205 | −2.50192 | ||||||||
\(430\) | 0.0789808 | 0.00380879 | ||||||||
\(431\) | 10.9728 | 0.528542 | 0.264271 | − | 0.964448i | \(-0.414869\pi\) | ||||
0.264271 | + | 0.964448i | \(0.414869\pi\) | |||||||
\(432\) | −41.4691 | −1.99518 | ||||||||
\(433\) | 5.18439 | 0.249146 | 0.124573 | − | 0.992210i | \(-0.460244\pi\) | ||||
0.124573 | + | 0.992210i | \(0.460244\pi\) | |||||||
\(434\) | 80.1380 | 3.84675 | ||||||||
\(435\) | −9.98468 | −0.478729 | ||||||||
\(436\) | 4.62329 | 0.221415 | ||||||||
\(437\) | 1.63243 | 0.0780899 | ||||||||
\(438\) | 34.5168 | 1.64927 | ||||||||
\(439\) | −21.7006 | −1.03571 | −0.517855 | − | 0.855468i | \(-0.673269\pi\) | ||||
−0.517855 | + | 0.855468i | \(0.673269\pi\) | |||||||
\(440\) | 17.4012 | 0.829568 | ||||||||
\(441\) | 35.6925 | 1.69964 | ||||||||
\(442\) | 16.2870 | 0.774693 | ||||||||
\(443\) | 10.0546 | 0.477708 | 0.238854 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238854 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(444\) | −12.9320 | −0.613724 | ||||||||
\(445\) | −7.07885 | −0.335570 | ||||||||
\(446\) | −18.3008 | −0.866566 | ||||||||
\(447\) | −53.5478 | −2.53272 | ||||||||
\(448\) | −10.7369 | −0.507271 | ||||||||
\(449\) | −27.5531 | −1.30031 | −0.650157 | − | 0.759800i | \(-0.725297\pi\) | ||||
−0.650157 | + | 0.759800i | \(0.725297\pi\) | |||||||
\(450\) | 54.7594 | 2.58139 | ||||||||
\(451\) | −13.0575 | −0.614856 | ||||||||
\(452\) | 6.16858 | 0.290146 | ||||||||
\(453\) | −30.2467 | −1.42111 | ||||||||
\(454\) | −13.2868 | −0.623578 | ||||||||
\(455\) | 16.0699 | 0.753369 | ||||||||
\(456\) | −5.22142 | −0.244515 | ||||||||
\(457\) | −6.43745 | −0.301131 | −0.150566 | − | 0.988600i | \(-0.548109\pi\) | ||||
−0.150566 | + | 0.988600i | \(0.548109\pi\) | |||||||
\(458\) | −43.4671 | −2.03108 | ||||||||
\(459\) | −5.85211 | −0.273153 | ||||||||
\(460\) | −20.9518 | −0.976883 | ||||||||
\(461\) | 22.8235 | 1.06300 | 0.531498 | − | 0.847060i | \(-0.321629\pi\) | ||||
0.531498 | + | 0.847060i | \(0.321629\pi\) | |||||||
\(462\) | 91.7244 | 4.26741 | ||||||||
\(463\) | −5.67923 | −0.263936 | −0.131968 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131968 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(464\) | 37.7998 | 1.75481 | ||||||||
\(465\) | −17.6188 | −0.817051 | ||||||||
\(466\) | 41.7297 | 1.93309 | ||||||||
\(467\) | −26.7411 | −1.23743 | −0.618716 | − | 0.785615i | \(-0.712347\pi\) | ||||
−0.618716 | + | 0.785615i | \(0.712347\pi\) | |||||||
\(468\) | −123.048 | −5.68790 | ||||||||
\(469\) | 5.05872 | 0.233590 | ||||||||
\(470\) | −11.3220 | −0.522246 | ||||||||
\(471\) | −15.3242 | −0.706104 | ||||||||
\(472\) | 55.3250 | 2.54654 | ||||||||
\(473\) | 0.134254 | 0.00617299 | ||||||||
\(474\) | −9.85861 | −0.452821 | ||||||||
\(475\) | 1.21958 | 0.0559582 | ||||||||
\(476\) | −20.1234 | −0.922354 | ||||||||
\(477\) | 2.42623 | 0.111089 | ||||||||
\(478\) | 60.3024 | 2.75817 | ||||||||
\(479\) | −34.5141 | −1.57699 | −0.788494 | − | 0.615043i | \(-0.789139\pi\) | ||||
−0.788494 | + | 0.615043i | \(0.789139\pi\) | |||||||
\(480\) | 15.9227 | 0.726770 | ||||||||
\(481\) | −5.51722 | −0.251563 | ||||||||
\(482\) | −47.5809 | −2.16725 | ||||||||
\(483\) | −62.6647 | −2.85134 | ||||||||
\(484\) | 1.27387 | 0.0579034 | ||||||||
\(485\) | 7.01575 | 0.318569 | ||||||||
\(486\) | −40.8391 | −1.85250 | ||||||||
\(487\) | −12.9759 | −0.587993 | −0.293997 | − | 0.955806i | \(-0.594985\pi\) | ||||
−0.293997 | + | 0.955806i | \(0.594985\pi\) | |||||||
\(488\) | −55.9449 | −2.53251 | ||||||||
\(489\) | −8.06711 | −0.364807 | ||||||||
\(490\) | −14.6163 | −0.660297 | ||||||||
\(491\) | −10.4326 | −0.470814 | −0.235407 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235407 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(492\) | −50.2872 | −2.26712 | ||||||||
\(493\) | 5.33430 | 0.240245 | ||||||||
\(494\) | −3.92599 | −0.176639 | ||||||||
\(495\) | −12.4337 | −0.558852 | ||||||||
\(496\) | 66.7008 | 2.99495 | ||||||||
\(497\) | 44.0464 | 1.97575 | ||||||||
\(498\) | 61.5505 | 2.75814 | ||||||||
\(499\) | 11.8480 | 0.530391 | 0.265195 | − | 0.964195i | \(-0.414564\pi\) | ||||
0.265195 | + | 0.964195i | \(0.414564\pi\) | |||||||
\(500\) | −33.3968 | −1.49355 | ||||||||
\(501\) | 60.6579 | 2.70999 | ||||||||
\(502\) | −59.0626 | −2.63609 | ||||||||
\(503\) | 7.03071 | 0.313484 | 0.156742 | − | 0.987640i | \(-0.449901\pi\) | ||||
0.156742 | + | 0.987640i | \(0.449901\pi\) | |||||||
\(504\) | 123.581 | 5.50475 | ||||||||
\(505\) | 10.1808 | 0.453038 | ||||||||
\(506\) | −51.0210 | −2.26816 | ||||||||
\(507\) | −48.7811 | −2.16645 | ||||||||
\(508\) | 29.7799 | 1.32127 | ||||||||
\(509\) | 14.6601 | 0.649795 | 0.324898 | − | 0.945749i | \(-0.394670\pi\) | ||||
0.324898 | + | 0.945749i | \(0.394670\pi\) | |||||||
\(510\) | 6.33813 | 0.280657 | ||||||||
\(511\) | −18.1948 | −0.804888 | ||||||||
\(512\) | 49.4711 | 2.18633 | ||||||||
\(513\) | 1.41065 | 0.0622819 | ||||||||
\(514\) | 64.9536 | 2.86498 | ||||||||
\(515\) | 9.39248 | 0.413882 | ||||||||
\(516\) | 0.517037 | 0.0227613 | ||||||||
\(517\) | −19.2455 | −0.846415 | ||||||||
\(518\) | 9.76569 | 0.429080 | ||||||||
\(519\) | 14.9334 | 0.655504 | ||||||||
\(520\) | 28.5910 | 1.25380 | ||||||||
\(521\) | 10.8376 | 0.474803 | 0.237402 | − | 0.971412i | \(-0.423704\pi\) | ||||
0.237402 | + | 0.971412i | \(0.423704\pi\) | |||||||
\(522\) | −57.7344 | −2.52696 | ||||||||
\(523\) | −42.1034 | −1.84105 | −0.920526 | − | 0.390682i | \(-0.872239\pi\) | ||||
−0.920526 | + | 0.390682i | \(0.872239\pi\) | |||||||
\(524\) | −66.4628 | −2.90344 | ||||||||
\(525\) | −46.8164 | −2.04324 | ||||||||
\(526\) | 36.2481 | 1.58049 | ||||||||
\(527\) | 9.41281 | 0.410028 | ||||||||
\(528\) | 76.3445 | 3.32247 | ||||||||
\(529\) | 11.8567 | 0.515509 | ||||||||
\(530\) | −0.993555 | −0.0431573 | ||||||||
\(531\) | −39.5314 | −1.71552 | ||||||||
\(532\) | 4.85076 | 0.210307 | ||||||||
\(533\) | −21.4542 | −0.929286 | ||||||||
\(534\) | −66.3874 | −2.87287 | ||||||||
\(535\) | 2.04306 | 0.0883290 | ||||||||
\(536\) | 9.00031 | 0.388754 | ||||||||
\(537\) | −20.3471 | −0.878040 | ||||||||
\(538\) | 52.9497 | 2.28283 | ||||||||
\(539\) | −24.8452 | −1.07016 | ||||||||
\(540\) | −18.1053 | −0.779130 | ||||||||
\(541\) | −40.1221 | −1.72498 | −0.862492 | − | 0.506070i | \(-0.831098\pi\) | ||||
−0.862492 | + | 0.506070i | \(0.831098\pi\) | |||||||
\(542\) | 14.6066 | 0.627406 | ||||||||
\(543\) | −58.4569 | −2.50863 | ||||||||
\(544\) | −8.50670 | −0.364722 | ||||||||
\(545\) | 0.767586 | 0.0328798 | ||||||||
\(546\) | 150.708 | 6.44971 | ||||||||
\(547\) | 15.6923 | 0.670956 | 0.335478 | − | 0.942048i | \(-0.391102\pi\) | ||||
0.335478 | + | 0.942048i | \(0.391102\pi\) | |||||||
\(548\) | −30.6333 | −1.30859 | ||||||||
\(549\) | 39.9744 | 1.70606 | ||||||||
\(550\) | −38.1175 | −1.62533 | ||||||||
\(551\) | −1.28584 | −0.0547785 | ||||||||
\(552\) | −111.491 | −4.74537 | ||||||||
\(553\) | 5.19675 | 0.220988 | ||||||||
\(554\) | 30.8039 | 1.30873 | ||||||||
\(555\) | −2.14704 | −0.0911368 | ||||||||
\(556\) | −58.8776 | −2.49697 | ||||||||
\(557\) | 6.60905 | 0.280035 | 0.140017 | − | 0.990149i | \(-0.455284\pi\) | ||||
0.140017 | + | 0.990149i | \(0.455284\pi\) | |||||||
\(558\) | −101.877 | −4.31280 | ||||||||
\(559\) | 0.220586 | 0.00932979 | ||||||||
\(560\) | −23.6749 | −1.00045 | ||||||||
\(561\) | 10.7737 | 0.454867 | ||||||||
\(562\) | 0.748496 | 0.0315734 | ||||||||
\(563\) | 31.5226 | 1.32852 | 0.664259 | − | 0.747503i | \(-0.268747\pi\) | ||||
0.664259 | + | 0.747503i | \(0.268747\pi\) | |||||||
\(564\) | −74.1181 | −3.12094 | ||||||||
\(565\) | 1.02414 | 0.0430861 | ||||||||
\(566\) | −58.6738 | −2.46624 | ||||||||
\(567\) | 0.763817 | 0.0320773 | ||||||||
\(568\) | 78.3658 | 3.28816 | ||||||||
\(569\) | −24.2340 | −1.01594 | −0.507970 | − | 0.861375i | \(-0.669604\pi\) | ||||
−0.507970 | + | 0.861375i | \(0.669604\pi\) | |||||||
\(570\) | −1.52781 | −0.0639929 | ||||||||
\(571\) | −34.7542 | −1.45442 | −0.727210 | − | 0.686415i | \(-0.759183\pi\) | ||||
−0.727210 | + | 0.686415i | \(0.759183\pi\) | |||||||
\(572\) | 85.6524 | 3.58131 | ||||||||
\(573\) | −42.0070 | −1.75487 | ||||||||
\(574\) | 37.9748 | 1.58504 | ||||||||
\(575\) | 26.0412 | 1.08599 | ||||||||
\(576\) | 13.6495 | 0.568729 | ||||||||
\(577\) | 33.3451 | 1.38817 | 0.694087 | − | 0.719891i | \(-0.255808\pi\) | ||||
0.694087 | + | 0.719891i | \(0.255808\pi\) | |||||||
\(578\) | 40.3646 | 1.67895 | ||||||||
\(579\) | −71.9061 | −2.98831 | ||||||||
\(580\) | 16.5033 | 0.685264 | ||||||||
\(581\) | −32.4450 | −1.34605 | ||||||||
\(582\) | 65.7957 | 2.72732 | ||||||||
\(583\) | −1.68887 | −0.0699459 | ||||||||
\(584\) | −32.3715 | −1.33954 | ||||||||
\(585\) | −20.4292 | −0.844642 | ||||||||
\(586\) | 49.5205 | 2.04567 | ||||||||
\(587\) | −12.4789 | −0.515060 | −0.257530 | − | 0.966270i | \(-0.582909\pi\) | ||||
−0.257530 | + | 0.966270i | \(0.582909\pi\) | |||||||
\(588\) | −95.6836 | −3.94593 | ||||||||
\(589\) | −2.26896 | −0.0934911 | ||||||||
\(590\) | 16.1883 | 0.666464 | ||||||||
\(591\) | −65.9727 | −2.71375 | ||||||||
\(592\) | 8.12822 | 0.334068 | ||||||||
\(593\) | −8.27400 | −0.339772 | −0.169886 | − | 0.985464i | \(-0.554340\pi\) | ||||
−0.169886 | + | 0.985464i | \(0.554340\pi\) | |||||||
\(594\) | −44.0894 | −1.80901 | ||||||||
\(595\) | −3.34100 | −0.136968 | ||||||||
\(596\) | 88.5073 | 3.62540 | ||||||||
\(597\) | 20.5118 | 0.839491 | ||||||||
\(598\) | −83.8301 | −3.42807 | ||||||||
\(599\) | 3.22235 | 0.131662 | 0.0658309 | − | 0.997831i | \(-0.479030\pi\) | ||||
0.0658309 | + | 0.997831i | \(0.479030\pi\) | |||||||
\(600\) | −83.2942 | −3.40047 | ||||||||
\(601\) | −36.4396 | −1.48640 | −0.743200 | − | 0.669069i | \(-0.766693\pi\) | ||||
−0.743200 | + | 0.669069i | \(0.766693\pi\) | |||||||
\(602\) | −0.390446 | −0.0159134 | ||||||||
\(603\) | −6.43099 | −0.261890 | ||||||||
\(604\) | 49.9937 | 2.03422 | ||||||||
\(605\) | 0.211496 | 0.00859855 | ||||||||
\(606\) | 95.4781 | 3.87853 | ||||||||
\(607\) | 39.1463 | 1.58890 | 0.794449 | − | 0.607331i | \(-0.207760\pi\) | ||||
0.794449 | + | 0.607331i | \(0.207760\pi\) | |||||||
\(608\) | 2.05055 | 0.0831606 | ||||||||
\(609\) | 49.3598 | 2.00016 | ||||||||
\(610\) | −16.3697 | −0.662791 | ||||||||
\(611\) | −31.6213 | −1.27926 | ||||||||
\(612\) | 25.5822 | 1.03410 | ||||||||
\(613\) | 26.5512 | 1.07239 | 0.536196 | − | 0.844093i | \(-0.319861\pi\) | ||||
0.536196 | + | 0.844093i | \(0.319861\pi\) | |||||||
\(614\) | 82.7704 | 3.34034 | ||||||||
\(615\) | −8.34898 | −0.336663 | ||||||||
\(616\) | −86.0236 | −3.46599 | ||||||||
\(617\) | 23.5946 | 0.949883 | 0.474941 | − | 0.880017i | \(-0.342469\pi\) | ||||
0.474941 | + | 0.880017i | \(0.342469\pi\) | |||||||
\(618\) | 88.0852 | 3.54331 | ||||||||
\(619\) | 31.1957 | 1.25386 | 0.626930 | − | 0.779076i | \(-0.284311\pi\) | ||||
0.626930 | + | 0.779076i | \(0.284311\pi\) | |||||||
\(620\) | 29.1215 | 1.16955 | ||||||||
\(621\) | 30.1212 | 1.20872 | ||||||||
\(622\) | 40.1640 | 1.61043 | ||||||||
\(623\) | 34.9947 | 1.40203 | ||||||||
\(624\) | 125.438 | 5.02154 | ||||||||
\(625\) | 16.5093 | 0.660373 | ||||||||
\(626\) | −59.4751 | −2.37710 | ||||||||
\(627\) | −2.59701 | −0.103715 | ||||||||
\(628\) | 25.3289 | 1.01073 | ||||||||
\(629\) | 1.14705 | 0.0457360 | ||||||||
\(630\) | 36.1605 | 1.44067 | ||||||||
\(631\) | 20.2848 | 0.807523 | 0.403762 | − | 0.914864i | \(-0.367703\pi\) | ||||
0.403762 | + | 0.914864i | \(0.367703\pi\) | |||||||
\(632\) | 9.24588 | 0.367782 | ||||||||
\(633\) | 14.6521 | 0.582367 | ||||||||
\(634\) | 37.6022 | 1.49337 | ||||||||
\(635\) | 4.94424 | 0.196206 | ||||||||
\(636\) | −6.50418 | −0.257908 | ||||||||
\(637\) | −40.8219 | −1.61742 | ||||||||
\(638\) | 40.1883 | 1.59107 | ||||||||
\(639\) | −55.9948 | −2.21512 | ||||||||
\(640\) | 5.79548 | 0.229087 | ||||||||
\(641\) | −17.5595 | −0.693560 | −0.346780 | − | 0.937946i | \(-0.612725\pi\) | ||||
−0.346780 | + | 0.937946i | \(0.612725\pi\) | |||||||
\(642\) | 19.1603 | 0.756198 | ||||||||
\(643\) | 8.88187 | 0.350267 | 0.175133 | − | 0.984545i | \(-0.443964\pi\) | ||||
0.175133 | + | 0.984545i | \(0.443964\pi\) | |||||||
\(644\) | 103.576 | 4.08148 | ||||||||
\(645\) | 0.0858416 | 0.00338001 | ||||||||
\(646\) | 0.816230 | 0.0321142 | ||||||||
\(647\) | 16.0580 | 0.631304 | 0.315652 | − | 0.948875i | \(-0.397777\pi\) | ||||
0.315652 | + | 0.948875i | \(0.397777\pi\) | |||||||
\(648\) | 1.35896 | 0.0533849 | ||||||||
\(649\) | 27.5174 | 1.08015 | ||||||||
\(650\) | −62.6290 | −2.45651 | ||||||||
\(651\) | 87.0994 | 3.41369 | ||||||||
\(652\) | 13.3339 | 0.522194 | ||||||||
\(653\) | −43.0734 | −1.68559 | −0.842796 | − | 0.538234i | \(-0.819092\pi\) | ||||
−0.842796 | + | 0.538234i | \(0.819092\pi\) | |||||||
\(654\) | 7.19864 | 0.281489 | ||||||||
\(655\) | −11.0346 | −0.431156 | ||||||||
\(656\) | 31.6074 | 1.23406 | ||||||||
\(657\) | 23.1304 | 0.902404 | ||||||||
\(658\) | 55.9710 | 2.18198 | ||||||||
\(659\) | 35.6114 | 1.38722 | 0.693611 | − | 0.720350i | \(-0.256019\pi\) | ||||
0.693611 | + | 0.720350i | \(0.256019\pi\) | |||||||
\(660\) | 33.3319 | 1.29744 | ||||||||
\(661\) | −19.1643 | −0.745404 | −0.372702 | − | 0.927951i | \(-0.621569\pi\) | ||||
−0.372702 | + | 0.927951i | \(0.621569\pi\) | |||||||
\(662\) | 48.5027 | 1.88511 | ||||||||
\(663\) | 17.7018 | 0.687480 | ||||||||
\(664\) | −57.7251 | −2.24017 | ||||||||
\(665\) | 0.805352 | 0.0312302 | ||||||||
\(666\) | −12.4148 | −0.481065 | ||||||||
\(667\) | −27.4560 | −1.06310 | ||||||||
\(668\) | −100.259 | −3.87915 | ||||||||
\(669\) | −19.8905 | −0.769011 | ||||||||
\(670\) | 2.63353 | 0.101742 | ||||||||
\(671\) | −27.8257 | −1.07420 | ||||||||
\(672\) | −78.7149 | −3.03649 | ||||||||
\(673\) | 25.3342 | 0.976560 | 0.488280 | − | 0.872687i | \(-0.337624\pi\) | ||||
0.488280 | + | 0.872687i | \(0.337624\pi\) | |||||||
\(674\) | −15.6850 | −0.604162 | ||||||||
\(675\) | 22.5033 | 0.866154 | ||||||||
\(676\) | 80.6287 | 3.10110 | ||||||||
\(677\) | 25.4550 | 0.978317 | 0.489158 | − | 0.872195i | \(-0.337304\pi\) | ||||
0.489158 | + | 0.872195i | \(0.337304\pi\) | |||||||
\(678\) | 9.60471 | 0.368867 | ||||||||
\(679\) | −34.6827 | −1.33100 | ||||||||
\(680\) | −5.94420 | −0.227950 | ||||||||
\(681\) | −14.4409 | −0.553378 | ||||||||
\(682\) | 70.9155 | 2.71549 | ||||||||
\(683\) | −24.2521 | −0.927980 | −0.463990 | − | 0.885841i | \(-0.653583\pi\) | ||||
−0.463990 | + | 0.885841i | \(0.653583\pi\) | |||||||
\(684\) | −6.16662 | −0.235786 | ||||||||
\(685\) | −5.08592 | −0.194323 | ||||||||
\(686\) | 3.89657 | 0.148772 | ||||||||
\(687\) | −47.2430 | −1.80243 | ||||||||
\(688\) | −0.324977 | −0.0123896 | ||||||||
\(689\) | −2.77491 | −0.105715 | ||||||||
\(690\) | −32.6227 | −1.24193 | ||||||||
\(691\) | 34.0736 | 1.29622 | 0.648111 | − | 0.761546i | \(-0.275559\pi\) | ||||
0.648111 | + | 0.761546i | \(0.275559\pi\) | |||||||
\(692\) | −24.6829 | −0.938304 | ||||||||
\(693\) | 61.4665 | 2.33492 | ||||||||
\(694\) | −10.6831 | −0.405525 | ||||||||
\(695\) | −9.77521 | −0.370795 | ||||||||
\(696\) | 87.8193 | 3.32878 | ||||||||
\(697\) | 4.46043 | 0.168951 | ||||||||
\(698\) | −2.87265 | −0.108732 | ||||||||
\(699\) | 45.3546 | 1.71547 | ||||||||
\(700\) | 77.3813 | 2.92474 | ||||||||
\(701\) | 17.0263 | 0.643074 | 0.321537 | − | 0.946897i | \(-0.395801\pi\) | ||||
0.321537 | + | 0.946897i | \(0.395801\pi\) | |||||||
\(702\) | −72.4412 | −2.73412 | ||||||||
\(703\) | −0.276498 | −0.0104283 | ||||||||
\(704\) | −9.50127 | −0.358093 | ||||||||
\(705\) | −12.3055 | −0.463453 | ||||||||
\(706\) | 62.5597 | 2.35447 | ||||||||
\(707\) | −50.3292 | −1.89282 | ||||||||
\(708\) | 105.975 | 3.98278 | ||||||||
\(709\) | −16.6910 | −0.626844 | −0.313422 | − | 0.949614i | \(-0.601475\pi\) | ||||
−0.313422 | + | 0.949614i | \(0.601475\pi\) | |||||||
\(710\) | 22.9302 | 0.860555 | ||||||||
\(711\) | −6.60647 | −0.247762 | ||||||||
\(712\) | 62.2614 | 2.33334 | ||||||||
\(713\) | −48.4483 | −1.81440 | ||||||||
\(714\) | −31.3329 | −1.17260 | ||||||||
\(715\) | 14.2205 | 0.531817 | ||||||||
\(716\) | 33.6310 | 1.25685 | ||||||||
\(717\) | 65.5407 | 2.44766 | ||||||||
\(718\) | −54.0564 | −2.01737 | ||||||||
\(719\) | −22.3267 | −0.832644 | −0.416322 | − | 0.909217i | \(-0.636681\pi\) | ||||
−0.416322 | + | 0.909217i | \(0.636681\pi\) | |||||||
\(720\) | 30.0972 | 1.12166 | ||||||||
\(721\) | −46.4322 | −1.72923 | ||||||||
\(722\) | 48.7012 | 1.81247 | ||||||||
\(723\) | −51.7141 | −1.92327 | ||||||||
\(724\) | 96.6215 | 3.59091 | ||||||||
\(725\) | −20.5122 | −0.761804 | ||||||||
\(726\) | 1.98347 | 0.0736135 | ||||||||
\(727\) | 31.8223 | 1.18022 | 0.590112 | − | 0.807321i | \(-0.299084\pi\) | ||||
0.590112 | + | 0.807321i | \(0.299084\pi\) | |||||||
\(728\) | −141.341 | −5.23846 | ||||||||
\(729\) | −43.7828 | −1.62158 | ||||||||
\(730\) | −9.47205 | −0.350576 | ||||||||
\(731\) | −0.0458608 | −0.00169622 | ||||||||
\(732\) | −107.162 | −3.96083 | ||||||||
\(733\) | 9.69282 | 0.358012 | 0.179006 | − | 0.983848i | \(-0.442712\pi\) | ||||
0.179006 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(734\) | −19.3887 | −0.715649 | ||||||||
\(735\) | −15.8860 | −0.585963 | ||||||||
\(736\) | 43.7845 | 1.61392 | ||||||||
\(737\) | 4.47654 | 0.164896 | ||||||||
\(738\) | −48.2762 | −1.77707 | ||||||||
\(739\) | 44.9298 | 1.65277 | 0.826384 | − | 0.563107i | \(-0.190394\pi\) | ||||
0.826384 | + | 0.563107i | \(0.190394\pi\) | |||||||
\(740\) | 3.54877 | 0.130455 | ||||||||
\(741\) | −4.26703 | −0.156753 | ||||||||
\(742\) | 4.91169 | 0.180314 | ||||||||
\(743\) | −17.8303 | −0.654128 | −0.327064 | − | 0.945002i | \(-0.606059\pi\) | ||||
−0.327064 | + | 0.945002i | \(0.606059\pi\) | |||||||
\(744\) | 154.964 | 5.68127 | ||||||||
\(745\) | 14.6945 | 0.538365 | ||||||||
\(746\) | −9.45232 | −0.346074 | ||||||||
\(747\) | 41.2463 | 1.50912 | ||||||||
\(748\) | −17.8075 | −0.651107 | ||||||||
\(749\) | −10.1000 | −0.369044 | ||||||||
\(750\) | −52.0001 | −1.89878 | ||||||||
\(751\) | 14.2598 | 0.520348 | 0.260174 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260174 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(752\) | 46.5860 | 1.69882 | ||||||||
\(753\) | −64.1932 | −2.33933 | ||||||||
\(754\) | 66.0314 | 2.40472 | ||||||||
\(755\) | 8.30025 | 0.302077 | ||||||||
\(756\) | 89.5047 | 3.25525 | ||||||||
\(757\) | −42.2575 | −1.53587 | −0.767937 | − | 0.640526i | \(-0.778716\pi\) | ||||
−0.767937 | + | 0.640526i | \(0.778716\pi\) | |||||||
\(758\) | 20.5328 | 0.745784 | ||||||||
\(759\) | −55.4530 | −2.01282 | ||||||||
\(760\) | 1.43285 | 0.0519751 | ||||||||
\(761\) | −5.79752 | −0.210160 | −0.105080 | − | 0.994464i | \(-0.533510\pi\) | ||||
−0.105080 | + | 0.994464i | \(0.533510\pi\) | |||||||
\(762\) | 46.3684 | 1.67975 | ||||||||
\(763\) | −3.79460 | −0.137374 | ||||||||
\(764\) | 69.4319 | 2.51196 | ||||||||
\(765\) | 4.24731 | 0.153562 | ||||||||
\(766\) | −39.9698 | −1.44417 | ||||||||
\(767\) | 45.2125 | 1.63253 | ||||||||
\(768\) | 70.1808 | 2.53243 | ||||||||
\(769\) | −41.7493 | −1.50552 | −0.752759 | − | 0.658296i | \(-0.771278\pi\) | ||||
−0.752759 | + | 0.658296i | \(0.771278\pi\) | |||||||
\(770\) | −25.1709 | −0.907096 | ||||||||
\(771\) | 70.5959 | 2.54245 | ||||||||
\(772\) | 118.851 | 4.27755 | ||||||||
\(773\) | 9.73903 | 0.350289 | 0.175144 | − | 0.984543i | \(-0.443961\pi\) | ||||
0.175144 | + | 0.984543i | \(0.443961\pi\) | |||||||
\(774\) | 0.496362 | 0.0178413 | ||||||||
\(775\) | −36.1955 | −1.30018 | ||||||||
\(776\) | −61.7064 | −2.21513 | ||||||||
\(777\) | 10.6140 | 0.380776 | ||||||||
\(778\) | −59.6585 | −2.13886 | ||||||||
\(779\) | −1.07519 | −0.0385227 | ||||||||
\(780\) | 54.7660 | 1.96094 | ||||||||
\(781\) | 38.9774 | 1.39472 | ||||||||
\(782\) | 17.4286 | 0.623247 | ||||||||
\(783\) | −23.7259 | −0.847894 | ||||||||
\(784\) | 60.1408 | 2.14788 | ||||||||
\(785\) | 4.20526 | 0.150092 | ||||||||
\(786\) | −103.485 | −3.69119 | ||||||||
\(787\) | −15.3198 | −0.546091 | −0.273045 | − | 0.962001i | \(-0.588031\pi\) | ||||
−0.273045 | + | 0.962001i | \(0.588031\pi\) | |||||||
\(788\) | 109.044 | 3.88453 | ||||||||
\(789\) | 39.3969 | 1.40257 | ||||||||
\(790\) | 2.70539 | 0.0962533 | ||||||||
\(791\) | −5.06291 | −0.180016 | ||||||||
\(792\) | 109.359 | 3.88591 | ||||||||
\(793\) | −45.7191 | −1.62353 | ||||||||
\(794\) | −82.7315 | −2.93603 | ||||||||
\(795\) | −1.07986 | −0.0382988 | ||||||||
\(796\) | −33.9032 | −1.20167 | ||||||||
\(797\) | −40.0378 | −1.41821 | −0.709105 | − | 0.705103i | \(-0.750901\pi\) | ||||
−0.709105 | + | 0.705103i | \(0.750901\pi\) | |||||||
\(798\) | 7.55281 | 0.267367 | ||||||||
\(799\) | 6.57421 | 0.232579 | ||||||||
\(800\) | 32.7112 | 1.15651 | ||||||||
\(801\) | −44.4877 | −1.57189 | ||||||||
\(802\) | 63.8744 | 2.25548 | ||||||||
\(803\) | −16.1008 | −0.568186 | ||||||||
\(804\) | 17.2401 | 0.608010 | ||||||||
\(805\) | 17.1964 | 0.606092 | ||||||||
\(806\) | 116.518 | 4.10417 | ||||||||
\(807\) | 57.5493 | 2.02583 | ||||||||
\(808\) | −89.5440 | −3.15015 | ||||||||
\(809\) | 30.5895 | 1.07547 | 0.537735 | − | 0.843114i | \(-0.319280\pi\) | ||||
0.537735 | + | 0.843114i | \(0.319280\pi\) | |||||||
\(810\) | 0.397637 | 0.0139715 | ||||||||
\(811\) | −46.7273 | −1.64082 | −0.820409 | − | 0.571776i | \(-0.806254\pi\) | ||||
−0.820409 | + | 0.571776i | \(0.806254\pi\) | |||||||
\(812\) | −81.5852 | −2.86308 | ||||||||
\(813\) | 15.8754 | 0.556775 | ||||||||
\(814\) | 8.64182 | 0.302896 | ||||||||
\(815\) | 2.21377 | 0.0775449 | ||||||||
\(816\) | −26.0791 | −0.912951 | ||||||||
\(817\) | 0.0110548 | 0.000386758 0 | ||||||||
\(818\) | −54.6477 | −1.91071 | ||||||||
\(819\) | 100.993 | 3.52897 | ||||||||
\(820\) | 13.7997 | 0.481908 | ||||||||
\(821\) | 17.3017 | 0.603832 | 0.301916 | − | 0.953335i | \(-0.402374\pi\) | ||||
0.301916 | + | 0.953335i | \(0.402374\pi\) | |||||||
\(822\) | −47.6972 | −1.66363 | ||||||||
\(823\) | −22.5515 | −0.786097 | −0.393049 | − | 0.919518i | \(-0.628580\pi\) | ||||
−0.393049 | + | 0.919518i | \(0.628580\pi\) | |||||||
\(824\) | −82.6106 | −2.87788 | ||||||||
\(825\) | −41.4286 | −1.44236 | ||||||||
\(826\) | −80.0279 | −2.78453 | ||||||||
\(827\) | −30.5809 | −1.06340 | −0.531701 | − | 0.846932i | \(-0.678447\pi\) | ||||
−0.531701 | + | 0.846932i | \(0.678447\pi\) | |||||||
\(828\) | −131.673 | −4.57597 | ||||||||
\(829\) | −4.08466 | −0.141866 | −0.0709331 | − | 0.997481i | \(-0.522598\pi\) | ||||
−0.0709331 | + | 0.997481i | \(0.522598\pi\) | |||||||
\(830\) | −16.8906 | −0.586282 | ||||||||
\(831\) | 33.4797 | 1.16140 | ||||||||
\(832\) | −15.6111 | −0.541217 | ||||||||
\(833\) | 8.48706 | 0.294059 | ||||||||
\(834\) | −91.6747 | −3.17443 | ||||||||
\(835\) | −16.6457 | −0.576047 | ||||||||
\(836\) | 4.29251 | 0.148460 | ||||||||
\(837\) | −41.8663 | −1.44711 | ||||||||
\(838\) | 46.4921 | 1.60604 | ||||||||
\(839\) | −34.6580 | −1.19653 | −0.598263 | − | 0.801300i | \(-0.704142\pi\) | ||||
−0.598263 | + | 0.801300i | \(0.704142\pi\) | |||||||
\(840\) | −55.0034 | −1.89780 | ||||||||
\(841\) | −7.37343 | −0.254256 | ||||||||
\(842\) | −7.66265 | −0.264072 | ||||||||
\(843\) | 0.813516 | 0.0280190 | ||||||||
\(844\) | −24.2179 | −0.833615 | ||||||||
\(845\) | 13.3864 | 0.460508 | ||||||||
\(846\) | −71.1542 | −2.44633 | ||||||||
\(847\) | −1.04554 | −0.0359253 | ||||||||
\(848\) | 4.08812 | 0.140387 | ||||||||
\(849\) | −63.7706 | −2.18860 | ||||||||
\(850\) | 13.0208 | 0.446611 | ||||||||
\(851\) | −5.90396 | −0.202385 | ||||||||
\(852\) | 150.110 | 5.14267 | ||||||||
\(853\) | 6.82471 | 0.233674 | 0.116837 | − | 0.993151i | \(-0.462725\pi\) | ||||
0.116837 | + | 0.993151i | \(0.462725\pi\) | |||||||
\(854\) | 80.9247 | 2.76919 | ||||||||
\(855\) | −1.02382 | −0.0350138 | ||||||||
\(856\) | −17.9695 | −0.614185 | ||||||||
\(857\) | −21.9574 | −0.750052 | −0.375026 | − | 0.927014i | \(-0.622366\pi\) | ||||
−0.375026 | + | 0.927014i | \(0.622366\pi\) | |||||||
\(858\) | 133.364 | 4.55297 | ||||||||
\(859\) | 0.141623 | 0.00483210 | 0.00241605 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241605 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(860\) | −0.141885 | −0.00483823 | ||||||||
\(861\) | 41.2736 | 1.40660 | ||||||||
\(862\) | −28.2394 | −0.961837 | ||||||||
\(863\) | −31.2078 | −1.06232 | −0.531162 | − | 0.847270i | \(-0.678245\pi\) | ||||
−0.531162 | + | 0.847270i | \(0.678245\pi\) | |||||||
\(864\) | 37.8361 | 1.28721 | ||||||||
\(865\) | −4.09801 | −0.139336 | ||||||||
\(866\) | −13.3424 | −0.453394 | ||||||||
\(867\) | 43.8710 | 1.48994 | ||||||||
\(868\) | −143.964 | −4.88644 | ||||||||
\(869\) | 4.59869 | 0.156000 | ||||||||
\(870\) | 25.6963 | 0.871187 | ||||||||
\(871\) | 7.35520 | 0.249221 | ||||||||
\(872\) | −6.75123 | −0.228626 | ||||||||
\(873\) | 44.0911 | 1.49226 | ||||||||
\(874\) | −4.20119 | −0.142107 | ||||||||
\(875\) | 27.4107 | 0.926651 | ||||||||
\(876\) | −62.0075 | −2.09504 | ||||||||
\(877\) | −44.2548 | −1.49438 | −0.747189 | − | 0.664612i | \(-0.768597\pi\) | ||||
−0.747189 | + | 0.664612i | \(0.768597\pi\) | |||||||
\(878\) | 55.8480 | 1.88478 | ||||||||
\(879\) | 53.8222 | 1.81538 | ||||||||
\(880\) | −20.9503 | −0.706236 | ||||||||
\(881\) | 30.2757 | 1.02001 | 0.510007 | − | 0.860170i | \(-0.329643\pi\) | ||||
0.510007 | + | 0.860170i | \(0.329643\pi\) | |||||||
\(882\) | −91.8574 | −3.09300 | ||||||||
\(883\) | −20.2487 | −0.681424 | −0.340712 | − | 0.940168i | \(-0.610668\pi\) | ||||
−0.340712 | + | 0.940168i | \(0.610668\pi\) | |||||||
\(884\) | −29.2587 | −0.984076 | ||||||||
\(885\) | 17.5946 | 0.591435 | ||||||||
\(886\) | −25.8763 | −0.869330 | ||||||||
\(887\) | −37.7946 | −1.26902 | −0.634509 | − | 0.772916i | \(-0.718798\pi\) | ||||
−0.634509 | + | 0.772916i | \(0.718798\pi\) | |||||||
\(888\) | 18.8841 | 0.633709 | ||||||||
\(889\) | −24.4421 | −0.819762 | ||||||||
\(890\) | 18.2180 | 0.610667 | ||||||||
\(891\) | 0.675915 | 0.0226440 | ||||||||
\(892\) | 32.8763 | 1.10078 | ||||||||
\(893\) | −1.58472 | −0.0530306 | ||||||||
\(894\) | 137.809 | 4.60903 | ||||||||
\(895\) | 5.58361 | 0.186640 | ||||||||
\(896\) | −28.6503 | −0.957139 | ||||||||
\(897\) | −91.1122 | −3.04215 | ||||||||
\(898\) | 70.9101 | 2.36630 | ||||||||
\(899\) | 38.1618 | 1.27277 | ||||||||
\(900\) | −98.3724 | −3.27908 | ||||||||
\(901\) | 0.576915 | 0.0192198 | ||||||||
\(902\) | 33.6046 | 1.11891 | ||||||||
\(903\) | −0.424363 | −0.0141219 | ||||||||
\(904\) | −9.00777 | −0.299594 | ||||||||
\(905\) | 16.0417 | 0.533243 | ||||||||
\(906\) | 77.8421 | 2.58613 | ||||||||
\(907\) | −23.9684 | −0.795859 | −0.397929 | − | 0.917416i | \(-0.630271\pi\) | ||||
−0.397929 | + | 0.917416i | \(0.630271\pi\) | |||||||
\(908\) | 23.8689 | 0.792119 | ||||||||
\(909\) | 63.9819 | 2.12215 | ||||||||
\(910\) | −41.3571 | −1.37097 | ||||||||
\(911\) | 22.9683 | 0.760974 | 0.380487 | − | 0.924786i | \(-0.375756\pi\) | ||||
0.380487 | + | 0.924786i | \(0.375756\pi\) | |||||||
\(912\) | 6.28639 | 0.208163 | ||||||||
\(913\) | −28.7111 | −0.950199 | ||||||||
\(914\) | 16.5673 | 0.547996 | ||||||||
\(915\) | −17.7917 | −0.588177 | ||||||||
\(916\) | 78.0863 | 2.58004 | ||||||||
\(917\) | 54.5499 | 1.80140 | ||||||||
\(918\) | 15.0608 | 0.497082 | ||||||||
\(919\) | −3.41070 | −0.112509 | −0.0562543 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562543 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(920\) | 30.5952 | 1.00869 | ||||||||
\(921\) | 89.9604 | 2.96430 | ||||||||
\(922\) | −58.7380 | −1.93443 | ||||||||
\(923\) | 64.0418 | 2.10796 | ||||||||
\(924\) | −164.778 | −5.42080 | ||||||||
\(925\) | −4.41081 | −0.145027 | ||||||||
\(926\) | 14.6159 | 0.480309 | ||||||||
\(927\) | 59.0278 | 1.93873 | ||||||||
\(928\) | −34.4883 | −1.13213 | ||||||||
\(929\) | −19.4744 | −0.638933 | −0.319467 | − | 0.947598i | \(-0.603504\pi\) | ||||
−0.319467 | + | 0.947598i | \(0.603504\pi\) | |||||||
\(930\) | 45.3433 | 1.48686 | ||||||||
\(931\) | −2.04581 | −0.0670488 | ||||||||
\(932\) | −74.9652 | −2.45557 | ||||||||
\(933\) | 43.6530 | 1.42913 | ||||||||
\(934\) | 68.8203 | 2.25187 | ||||||||
\(935\) | −2.95651 | −0.0966882 | ||||||||
\(936\) | 179.683 | 5.87312 | ||||||||
\(937\) | −2.62172 | −0.0856478 | −0.0428239 | − | 0.999083i | \(-0.513635\pi\) | ||||
−0.0428239 | + | 0.999083i | \(0.513635\pi\) | |||||||
\(938\) | −13.0190 | −0.425085 | ||||||||
\(939\) | −64.6415 | −2.10950 | ||||||||
\(940\) | 20.3394 | 0.663398 | ||||||||
\(941\) | 45.9973 | 1.49947 | 0.749735 | − | 0.661738i | \(-0.230181\pi\) | ||||
0.749735 | + | 0.661738i | \(0.230181\pi\) | |||||||
\(942\) | 39.4381 | 1.28496 | ||||||||
\(943\) | −22.9581 | −0.747619 | ||||||||
\(944\) | −66.6092 | −2.16794 | ||||||||
\(945\) | 14.8601 | 0.483399 | ||||||||
\(946\) | −0.345512 | −0.0112336 | ||||||||
\(947\) | 19.8395 | 0.644697 | 0.322348 | − | 0.946621i | \(-0.395528\pi\) | ||||
0.322348 | + | 0.946621i | \(0.395528\pi\) | |||||||
\(948\) | 17.7105 | 0.575209 | ||||||||
\(949\) | −26.4545 | −0.858750 | ||||||||
\(950\) | −3.13868 | −0.101832 | ||||||||
\(951\) | 40.8686 | 1.32525 | ||||||||
\(952\) | 29.3855 | 0.952389 | ||||||||
\(953\) | 33.6483 | 1.08998 | 0.544988 | − | 0.838444i | \(-0.316534\pi\) | ||||
0.544988 | + | 0.838444i | \(0.316534\pi\) | |||||||
\(954\) | −6.24408 | −0.202160 | ||||||||
\(955\) | 11.5275 | 0.373021 | ||||||||
\(956\) | −108.330 | −3.50364 | ||||||||
\(957\) | 43.6793 | 1.41195 | ||||||||
\(958\) | 88.8245 | 2.86979 | ||||||||
\(959\) | 25.1425 | 0.811894 | ||||||||
\(960\) | −6.07510 | −0.196073 | ||||||||
\(961\) | 36.3397 | 1.17225 | ||||||||
\(962\) | 14.1990 | 0.457793 | ||||||||
\(963\) | 12.8398 | 0.413755 | ||||||||
\(964\) | 85.4765 | 2.75301 | ||||||||
\(965\) | 19.7324 | 0.635208 | ||||||||
\(966\) | 161.272 | 5.18885 | ||||||||
\(967\) | −33.3040 | −1.07098 | −0.535492 | − | 0.844540i | \(-0.679874\pi\) | ||||
−0.535492 | + | 0.844540i | \(0.679874\pi\) | |||||||
\(968\) | −1.86020 | −0.0597890 | ||||||||
\(969\) | 0.887134 | 0.0284988 | ||||||||
\(970\) | −18.0556 | −0.579729 | ||||||||
\(971\) | 5.80116 | 0.186168 | 0.0930840 | − | 0.995658i | \(-0.470327\pi\) | ||||
0.0930840 | + | 0.995658i | \(0.470327\pi\) | |||||||
\(972\) | 73.3652 | 2.35319 | ||||||||
\(973\) | 48.3243 | 1.54921 | ||||||||
\(974\) | 33.3944 | 1.07003 | ||||||||
\(975\) | −68.0694 | −2.17997 | ||||||||
\(976\) | 67.3556 | 2.15600 | ||||||||
\(977\) | 17.6175 | 0.563632 | 0.281816 | − | 0.959468i | \(-0.409063\pi\) | ||||
0.281816 | + | 0.959468i | \(0.409063\pi\) | |||||||
\(978\) | 20.7613 | 0.663874 | ||||||||
\(979\) | 30.9674 | 0.989722 | ||||||||
\(980\) | 26.2574 | 0.838761 | ||||||||
\(981\) | 4.82396 | 0.154017 | ||||||||
\(982\) | 26.8490 | 0.856785 | ||||||||
\(983\) | −47.7074 | −1.52163 | −0.760814 | − | 0.648970i | \(-0.775200\pi\) | ||||
−0.760814 | + | 0.648970i | \(0.775200\pi\) | |||||||
\(984\) | 73.4326 | 2.34095 | ||||||||
\(985\) | 18.1041 | 0.576846 | ||||||||
\(986\) | −13.7282 | −0.437196 | ||||||||
\(987\) | 60.8330 | 1.93634 | ||||||||
\(988\) | 7.05283 | 0.224380 | ||||||||
\(989\) | 0.236048 | 0.00750590 | ||||||||
\(990\) | 31.9990 | 1.01699 | ||||||||
\(991\) | 15.9733 | 0.507409 | 0.253704 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253704 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(992\) | −60.8573 | −1.93222 | ||||||||
\(993\) | 52.7160 | 1.67289 | ||||||||
\(994\) | −113.357 | −3.59545 | ||||||||
\(995\) | −5.62882 | −0.178445 | ||||||||
\(996\) | −110.572 | −3.50361 | ||||||||
\(997\) | 44.3315 | 1.40399 | 0.701997 | − | 0.712180i | \(-0.252292\pi\) | ||||
0.701997 | + | 0.712180i | \(0.252292\pi\) | |||||||
\(998\) | −30.4918 | −0.965201 | ||||||||
\(999\) | −5.10186 | −0.161416 |
(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 | 4033.2.a.c.1.5 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.5 | ✓ | 77 | 1.1 | even | 1 | trivial |