Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(151\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62707 | −1.85762 | −0.928809 | − | 0.370559i | \(-0.879166\pi\) | ||||
−0.928809 | + | 0.370559i | \(0.879166\pi\) | |||||||
\(3\) | −2.08646 | −1.20462 | −0.602308 | − | 0.798264i | \(-0.705752\pi\) | ||||
−0.602308 | + | 0.798264i | \(0.705752\pi\) | |||||||
\(4\) | 4.90149 | 2.45075 | ||||||||
\(5\) | 1.65471 | 0.740009 | 0.370004 | − | 0.929030i | \(-0.379356\pi\) | ||||
0.370004 | + | 0.929030i | \(0.379356\pi\) | |||||||
\(6\) | 5.48127 | 2.23772 | ||||||||
\(7\) | −3.37709 | −1.27642 | −0.638211 | − | 0.769862i | \(-0.720325\pi\) | ||||
−0.638211 | + | 0.769862i | \(0.720325\pi\) | |||||||
\(8\) | −7.62241 | −2.69493 | ||||||||
\(9\) | 1.35330 | 0.451101 | ||||||||
\(10\) | −4.34704 | −1.37465 | ||||||||
\(11\) | 3.75982 | 1.13363 | 0.566815 | − | 0.823845i | \(-0.308175\pi\) | ||||
0.566815 | + | 0.823845i | \(0.308175\pi\) | |||||||
\(12\) | −10.2267 | −2.95221 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 8.87186 | 2.37110 | ||||||||
\(15\) | −3.45248 | −0.891427 | ||||||||
\(16\) | 10.2216 | 2.55541 | ||||||||
\(17\) | 6.62891 | 1.60775 | 0.803873 | − | 0.594800i | \(-0.202769\pi\) | ||||
0.803873 | + | 0.594800i | \(0.202769\pi\) | |||||||
\(18\) | −3.55522 | −0.837973 | ||||||||
\(19\) | −1.81610 | −0.416642 | −0.208321 | − | 0.978060i | \(-0.566800\pi\) | ||||
−0.208321 | + | 0.978060i | \(0.566800\pi\) | |||||||
\(20\) | 8.11054 | 1.81357 | ||||||||
\(21\) | 7.04616 | 1.53760 | ||||||||
\(22\) | −9.87732 | −2.10585 | ||||||||
\(23\) | 5.15156 | 1.07417 | 0.537087 | − | 0.843527i | \(-0.319525\pi\) | ||||
0.537087 | + | 0.843527i | \(0.319525\pi\) | |||||||
\(24\) | 15.9038 | 3.24636 | ||||||||
\(25\) | −2.26194 | −0.452387 | ||||||||
\(26\) | 2.62707 | 0.515211 | ||||||||
\(27\) | 3.43576 | 0.661213 | ||||||||
\(28\) | −16.5528 | −3.12818 | ||||||||
\(29\) | 0.517013 | 0.0960070 | 0.0480035 | − | 0.998847i | \(-0.484714\pi\) | ||||
0.0480035 | + | 0.998847i | \(0.484714\pi\) | |||||||
\(30\) | 9.06990 | 1.65593 | ||||||||
\(31\) | 3.41712 | 0.613733 | 0.306866 | − | 0.951753i | \(-0.400720\pi\) | ||||
0.306866 | + | 0.951753i | \(0.400720\pi\) | |||||||
\(32\) | −11.6081 | −2.05204 | ||||||||
\(33\) | −7.84471 | −1.36559 | ||||||||
\(34\) | −17.4146 | −2.98658 | ||||||||
\(35\) | −5.58811 | −0.944563 | ||||||||
\(36\) | 6.63320 | 1.10553 | ||||||||
\(37\) | −10.8938 | −1.79093 | −0.895463 | − | 0.445137i | \(-0.853155\pi\) | ||||
−0.895463 | + | 0.445137i | \(0.853155\pi\) | |||||||
\(38\) | 4.77102 | 0.773962 | ||||||||
\(39\) | 2.08646 | 0.334101 | ||||||||
\(40\) | −12.6129 | −1.99427 | ||||||||
\(41\) | 0.624662 | 0.0975558 | 0.0487779 | − | 0.998810i | \(-0.484467\pi\) | ||||
0.0487779 | + | 0.998810i | \(0.484467\pi\) | |||||||
\(42\) | −18.5107 | −2.85627 | ||||||||
\(43\) | −6.66643 | −1.01662 | −0.508311 | − | 0.861174i | \(-0.669730\pi\) | ||||
−0.508311 | + | 0.861174i | \(0.669730\pi\) | |||||||
\(44\) | 18.4287 | 2.77824 | ||||||||
\(45\) | 2.23932 | 0.333819 | ||||||||
\(46\) | −13.5335 | −1.99541 | ||||||||
\(47\) | −4.43666 | −0.647153 | −0.323577 | − | 0.946202i | \(-0.604885\pi\) | ||||
−0.323577 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(48\) | −21.3270 | −3.07829 | ||||||||
\(49\) | 4.40476 | 0.629252 | ||||||||
\(50\) | 5.94226 | 0.840362 | ||||||||
\(51\) | −13.8309 | −1.93672 | ||||||||
\(52\) | −4.90149 | −0.679714 | ||||||||
\(53\) | 1.03442 | 0.142088 | 0.0710441 | − | 0.997473i | \(-0.477367\pi\) | ||||
0.0710441 | + | 0.997473i | \(0.477367\pi\) | |||||||
\(54\) | −9.02598 | −1.22828 | ||||||||
\(55\) | 6.22142 | 0.838896 | ||||||||
\(56\) | 25.7416 | 3.43987 | ||||||||
\(57\) | 3.78922 | 0.501894 | ||||||||
\(58\) | −1.35823 | −0.178344 | ||||||||
\(59\) | 0.884692 | 0.115177 | 0.0575886 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575886 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(60\) | −16.9223 | −2.18466 | ||||||||
\(61\) | −1.60178 | −0.205086 | −0.102543 | − | 0.994729i | \(-0.532698\pi\) | ||||
−0.102543 | + | 0.994729i | \(0.532698\pi\) | |||||||
\(62\) | −8.97700 | −1.14008 | ||||||||
\(63\) | −4.57023 | −0.575795 | ||||||||
\(64\) | 10.0520 | 1.25650 | ||||||||
\(65\) | −1.65471 | −0.205241 | ||||||||
\(66\) | 20.6086 | 2.53674 | ||||||||
\(67\) | 2.73694 | 0.334370 | 0.167185 | − | 0.985926i | \(-0.446532\pi\) | ||||
0.167185 | + | 0.985926i | \(0.446532\pi\) | |||||||
\(68\) | 32.4915 | 3.94018 | ||||||||
\(69\) | −10.7485 | −1.29397 | ||||||||
\(70\) | 14.6803 | 1.75464 | ||||||||
\(71\) | 3.28850 | 0.390273 | 0.195136 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195136 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(72\) | −10.3154 | −1.21569 | ||||||||
\(73\) | −9.02450 | −1.05624 | −0.528119 | − | 0.849170i | \(-0.677103\pi\) | ||||
−0.528119 | + | 0.849170i | \(0.677103\pi\) | |||||||
\(74\) | 28.6187 | 3.32686 | ||||||||
\(75\) | 4.71943 | 0.544953 | ||||||||
\(76\) | −8.90160 | −1.02108 | ||||||||
\(77\) | −12.6973 | −1.44699 | ||||||||
\(78\) | −5.48127 | −0.620631 | ||||||||
\(79\) | 8.74165 | 0.983513 | 0.491756 | − | 0.870733i | \(-0.336355\pi\) | ||||
0.491756 | + | 0.870733i | \(0.336355\pi\) | |||||||
\(80\) | 16.9138 | 1.89102 | ||||||||
\(81\) | −11.2285 | −1.24761 | ||||||||
\(82\) | −1.64103 | −0.181221 | ||||||||
\(83\) | −3.30673 | −0.362961 | −0.181481 | − | 0.983395i | \(-0.558089\pi\) | ||||
−0.181481 | + | 0.983395i | \(0.558089\pi\) | |||||||
\(84\) | 34.5367 | 3.76826 | ||||||||
\(85\) | 10.9689 | 1.18975 | ||||||||
\(86\) | 17.5132 | 1.88849 | ||||||||
\(87\) | −1.07873 | −0.115652 | ||||||||
\(88\) | −28.6589 | −3.05505 | ||||||||
\(89\) | −0.585740 | −0.0620883 | −0.0310441 | − | 0.999518i | \(-0.509883\pi\) | ||||
−0.0310441 | + | 0.999518i | \(0.509883\pi\) | |||||||
\(90\) | −5.88286 | −0.620108 | ||||||||
\(91\) | 3.37709 | 0.354016 | ||||||||
\(92\) | 25.2503 | 2.63253 | ||||||||
\(93\) | −7.12967 | −0.739312 | ||||||||
\(94\) | 11.6554 | 1.20216 | ||||||||
\(95\) | −3.00512 | −0.308319 | ||||||||
\(96\) | 24.2198 | 2.47192 | ||||||||
\(97\) | −0.605988 | −0.0615288 | −0.0307644 | − | 0.999527i | \(-0.509794\pi\) | ||||
−0.0307644 | + | 0.999527i | \(0.509794\pi\) | |||||||
\(98\) | −11.5716 | −1.16891 | ||||||||
\(99\) | 5.08818 | 0.511382 | ||||||||
\(100\) | −11.0869 | −1.10869 | ||||||||
\(101\) | 15.1065 | 1.50315 | 0.751577 | − | 0.659645i | \(-0.229294\pi\) | ||||
0.751577 | + | 0.659645i | \(0.229294\pi\) | |||||||
\(102\) | 36.3348 | 3.59768 | ||||||||
\(103\) | −7.29579 | −0.718875 | −0.359438 | − | 0.933169i | \(-0.617031\pi\) | ||||
−0.359438 | + | 0.933169i | \(0.617031\pi\) | |||||||
\(104\) | 7.62241 | 0.747439 | ||||||||
\(105\) | 11.6594 | 1.13784 | ||||||||
\(106\) | −2.71749 | −0.263946 | ||||||||
\(107\) | −10.8313 | −1.04710 | −0.523551 | − | 0.851994i | \(-0.675393\pi\) | ||||
−0.523551 | + | 0.851994i | \(0.675393\pi\) | |||||||
\(108\) | 16.8404 | 1.62046 | ||||||||
\(109\) | 1.90864 | 0.182814 | 0.0914071 | − | 0.995814i | \(-0.470864\pi\) | ||||
0.0914071 | + | 0.995814i | \(0.470864\pi\) | |||||||
\(110\) | −16.3441 | −1.55835 | ||||||||
\(111\) | 22.7294 | 2.15738 | ||||||||
\(112\) | −34.5194 | −3.26178 | ||||||||
\(113\) | 1.39133 | 0.130886 | 0.0654428 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654428 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(114\) | −9.95454 | −0.932328 | ||||||||
\(115\) | 8.52433 | 0.794898 | ||||||||
\(116\) | 2.53414 | 0.235289 | ||||||||
\(117\) | −1.35330 | −0.125113 | ||||||||
\(118\) | −2.32415 | −0.213955 | ||||||||
\(119\) | −22.3865 | −2.05216 | ||||||||
\(120\) | 26.3162 | 2.40233 | ||||||||
\(121\) | 3.13628 | 0.285117 | ||||||||
\(122\) | 4.20798 | 0.380972 | ||||||||
\(123\) | −1.30333 | −0.117517 | ||||||||
\(124\) | 16.7490 | 1.50410 | ||||||||
\(125\) | −12.0164 | −1.07478 | ||||||||
\(126\) | 12.0063 | 1.06961 | ||||||||
\(127\) | 11.9762 | 1.06272 | 0.531358 | − | 0.847148i | \(-0.321682\pi\) | ||||
0.531358 | + | 0.847148i | \(0.321682\pi\) | |||||||
\(128\) | −3.19110 | −0.282056 | ||||||||
\(129\) | 13.9092 | 1.22464 | ||||||||
\(130\) | 4.34704 | 0.381260 | ||||||||
\(131\) | −1.33810 | −0.116911 | −0.0584553 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584553 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(132\) | −38.4508 | −3.34671 | ||||||||
\(133\) | 6.13314 | 0.531811 | ||||||||
\(134\) | −7.19012 | −0.621132 | ||||||||
\(135\) | 5.68519 | 0.489303 | ||||||||
\(136\) | −50.5283 | −4.33277 | ||||||||
\(137\) | −12.9635 | −1.10755 | −0.553775 | − | 0.832666i | \(-0.686813\pi\) | ||||
−0.553775 | + | 0.832666i | \(0.686813\pi\) | |||||||
\(138\) | 28.2371 | 2.40370 | ||||||||
\(139\) | 1.21252 | 0.102845 | 0.0514224 | − | 0.998677i | \(-0.483625\pi\) | ||||
0.0514224 | + | 0.998677i | \(0.483625\pi\) | |||||||
\(140\) | −27.3901 | −2.31488 | ||||||||
\(141\) | 9.25690 | 0.779571 | ||||||||
\(142\) | −8.63911 | −0.724978 | ||||||||
\(143\) | −3.75982 | −0.314412 | ||||||||
\(144\) | 13.8330 | 1.15275 | ||||||||
\(145\) | 0.855507 | 0.0710460 | ||||||||
\(146\) | 23.7080 | 1.96209 | ||||||||
\(147\) | −9.19035 | −0.758007 | ||||||||
\(148\) | −53.3957 | −4.38910 | ||||||||
\(149\) | 6.02220 | 0.493358 | 0.246679 | − | 0.969097i | \(-0.420661\pi\) | ||||
0.246679 | + | 0.969097i | \(0.420661\pi\) | |||||||
\(150\) | −12.3983 | −1.01231 | ||||||||
\(151\) | −9.13308 | −0.743239 | −0.371620 | − | 0.928385i | \(-0.621197\pi\) | ||||
−0.371620 | + | 0.928385i | \(0.621197\pi\) | |||||||
\(152\) | 13.8431 | 1.12282 | ||||||||
\(153\) | 8.97092 | 0.725256 | ||||||||
\(154\) | 33.3566 | 2.68795 | ||||||||
\(155\) | 5.65434 | 0.454167 | ||||||||
\(156\) | 10.2267 | 0.818795 | ||||||||
\(157\) | −3.82902 | −0.305589 | −0.152795 | − | 0.988258i | \(-0.548827\pi\) | ||||
−0.152795 | + | 0.988258i | \(0.548827\pi\) | |||||||
\(158\) | −22.9649 | −1.82699 | ||||||||
\(159\) | −2.15827 | −0.171162 | ||||||||
\(160\) | −19.2080 | −1.51853 | ||||||||
\(161\) | −17.3973 | −1.37110 | ||||||||
\(162\) | 29.4980 | 2.31758 | ||||||||
\(163\) | −8.16075 | −0.639199 | −0.319600 | − | 0.947553i | \(-0.603548\pi\) | ||||
−0.319600 | + | 0.947553i | \(0.603548\pi\) | |||||||
\(164\) | 3.06177 | 0.239084 | ||||||||
\(165\) | −12.9807 | −1.01055 | ||||||||
\(166\) | 8.68702 | 0.674243 | ||||||||
\(167\) | −9.77275 | −0.756238 | −0.378119 | − | 0.925757i | \(-0.623429\pi\) | ||||
−0.378119 | + | 0.925757i | \(0.623429\pi\) | |||||||
\(168\) | −53.7088 | −4.14372 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −28.8161 | −2.21010 | ||||||||
\(171\) | −2.45774 | −0.187948 | ||||||||
\(172\) | −32.6755 | −2.49148 | ||||||||
\(173\) | 2.73054 | 0.207599 | 0.103799 | − | 0.994598i | \(-0.466900\pi\) | ||||
0.103799 | + | 0.994598i | \(0.466900\pi\) | |||||||
\(174\) | 2.83389 | 0.214836 | ||||||||
\(175\) | 7.63877 | 0.577437 | ||||||||
\(176\) | 38.4315 | 2.89689 | ||||||||
\(177\) | −1.84587 | −0.138744 | ||||||||
\(178\) | 1.53878 | 0.115336 | ||||||||
\(179\) | 8.99387 | 0.672233 | 0.336117 | − | 0.941820i | \(-0.390886\pi\) | ||||
0.336117 | + | 0.941820i | \(0.390886\pi\) | |||||||
\(180\) | 10.9760 | 0.818105 | ||||||||
\(181\) | −8.12912 | −0.604233 | −0.302116 | − | 0.953271i | \(-0.597693\pi\) | ||||
−0.302116 | + | 0.953271i | \(0.597693\pi\) | |||||||
\(182\) | −8.87186 | −0.657626 | ||||||||
\(183\) | 3.34204 | 0.247051 | ||||||||
\(184\) | −39.2673 | −2.89482 | ||||||||
\(185\) | −18.0260 | −1.32530 | ||||||||
\(186\) | 18.7301 | 1.37336 | ||||||||
\(187\) | 24.9235 | 1.82259 | ||||||||
\(188\) | −21.7462 | −1.58601 | ||||||||
\(189\) | −11.6029 | −0.843986 | ||||||||
\(190\) | 7.89466 | 0.572739 | ||||||||
\(191\) | −23.7447 | −1.71811 | −0.859053 | − | 0.511886i | \(-0.828947\pi\) | ||||
−0.859053 | + | 0.511886i | \(0.828947\pi\) | |||||||
\(192\) | −20.9730 | −1.51360 | ||||||||
\(193\) | 6.53531 | 0.470422 | 0.235211 | − | 0.971944i | \(-0.424422\pi\) | ||||
0.235211 | + | 0.971944i | \(0.424422\pi\) | |||||||
\(194\) | 1.59197 | 0.114297 | ||||||||
\(195\) | 3.45248 | 0.247237 | ||||||||
\(196\) | 21.5899 | 1.54214 | ||||||||
\(197\) | −1.38546 | −0.0987102 | −0.0493551 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493551 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(198\) | −13.3670 | −0.949952 | ||||||||
\(199\) | 18.9068 | 1.34027 | 0.670134 | − | 0.742240i | \(-0.266237\pi\) | ||||
0.670134 | + | 0.742240i | \(0.266237\pi\) | |||||||
\(200\) | 17.2414 | 1.21915 | ||||||||
\(201\) | −5.71050 | −0.402788 | ||||||||
\(202\) | −39.6858 | −2.79229 | ||||||||
\(203\) | −1.74600 | −0.122545 | ||||||||
\(204\) | −67.7922 | −4.74640 | ||||||||
\(205\) | 1.03363 | 0.0721922 | ||||||||
\(206\) | 19.1665 | 1.33540 | ||||||||
\(207\) | 6.97162 | 0.484561 | ||||||||
\(208\) | −10.2216 | −0.708742 | ||||||||
\(209\) | −6.82822 | −0.472318 | ||||||||
\(210\) | −30.6299 | −2.11367 | ||||||||
\(211\) | 22.7008 | 1.56279 | 0.781395 | − | 0.624036i | \(-0.214508\pi\) | ||||
0.781395 | + | 0.624036i | \(0.214508\pi\) | |||||||
\(212\) | 5.07019 | 0.348222 | ||||||||
\(213\) | −6.86131 | −0.470129 | ||||||||
\(214\) | 28.4546 | 1.94511 | ||||||||
\(215\) | −11.0310 | −0.752309 | ||||||||
\(216\) | −26.1888 | −1.78192 | ||||||||
\(217\) | −11.5399 | −0.783381 | ||||||||
\(218\) | −5.01412 | −0.339599 | ||||||||
\(219\) | 18.8292 | 1.27236 | ||||||||
\(220\) | 30.4942 | 2.05592 | ||||||||
\(221\) | −6.62891 | −0.445909 | ||||||||
\(222\) | −59.7117 | −4.00759 | ||||||||
\(223\) | 25.8965 | 1.73415 | 0.867077 | − | 0.498173i | \(-0.165996\pi\) | ||||
0.867077 | + | 0.498173i | \(0.165996\pi\) | |||||||
\(224\) | 39.2016 | 2.61927 | ||||||||
\(225\) | −3.06108 | −0.204072 | ||||||||
\(226\) | −3.65513 | −0.243136 | ||||||||
\(227\) | −4.63673 | −0.307750 | −0.153875 | − | 0.988090i | \(-0.549175\pi\) | ||||
−0.153875 | + | 0.988090i | \(0.549175\pi\) | |||||||
\(228\) | 18.5728 | 1.23001 | ||||||||
\(229\) | −26.8828 | −1.77646 | −0.888232 | − | 0.459395i | \(-0.848066\pi\) | ||||
−0.888232 | + | 0.459395i | \(0.848066\pi\) | |||||||
\(230\) | −22.3940 | −1.47662 | ||||||||
\(231\) | 26.4923 | 1.74307 | ||||||||
\(232\) | −3.94089 | −0.258732 | ||||||||
\(233\) | −27.6598 | −1.81205 | −0.906027 | − | 0.423219i | \(-0.860900\pi\) | ||||
−0.906027 | + | 0.423219i | \(0.860900\pi\) | |||||||
\(234\) | 3.55522 | 0.232412 | ||||||||
\(235\) | −7.34138 | −0.478899 | ||||||||
\(236\) | 4.33631 | 0.282270 | ||||||||
\(237\) | −18.2391 | −1.18476 | ||||||||
\(238\) | 58.8108 | 3.81213 | ||||||||
\(239\) | −5.79091 | −0.374583 | −0.187292 | − | 0.982304i | \(-0.559971\pi\) | ||||
−0.187292 | + | 0.982304i | \(0.559971\pi\) | |||||||
\(240\) | −35.2900 | −2.27796 | ||||||||
\(241\) | 17.3411 | 1.11704 | 0.558520 | − | 0.829491i | \(-0.311369\pi\) | ||||
0.558520 | + | 0.829491i | \(0.311369\pi\) | |||||||
\(242\) | −8.23923 | −0.529638 | ||||||||
\(243\) | 13.1205 | 0.841677 | ||||||||
\(244\) | −7.85109 | −0.502615 | ||||||||
\(245\) | 7.28860 | 0.465652 | ||||||||
\(246\) | 3.42394 | 0.218302 | ||||||||
\(247\) | 1.81610 | 0.115556 | ||||||||
\(248\) | −26.0467 | −1.65397 | ||||||||
\(249\) | 6.89936 | 0.437229 | ||||||||
\(250\) | 31.5679 | 1.99653 | ||||||||
\(251\) | 11.4533 | 0.722925 | 0.361463 | − | 0.932387i | \(-0.382277\pi\) | ||||
0.361463 | + | 0.932387i | \(0.382277\pi\) | |||||||
\(252\) | −22.4009 | −1.41113 | ||||||||
\(253\) | 19.3690 | 1.21772 | ||||||||
\(254\) | −31.4623 | −1.97412 | ||||||||
\(255\) | −22.8862 | −1.43319 | ||||||||
\(256\) | −11.7208 | −0.732547 | ||||||||
\(257\) | −1.62503 | −0.101367 | −0.0506834 | − | 0.998715i | \(-0.516140\pi\) | ||||
−0.0506834 | + | 0.998715i | \(0.516140\pi\) | |||||||
\(258\) | −36.5405 | −2.27491 | ||||||||
\(259\) | 36.7893 | 2.28598 | ||||||||
\(260\) | −8.11054 | −0.502995 | ||||||||
\(261\) | 0.699676 | 0.0433088 | ||||||||
\(262\) | 3.51529 | 0.217175 | ||||||||
\(263\) | 19.5544 | 1.20578 | 0.602888 | − | 0.797826i | \(-0.294017\pi\) | ||||
0.602888 | + | 0.797826i | \(0.294017\pi\) | |||||||
\(264\) | 59.7957 | 3.68017 | ||||||||
\(265\) | 1.71166 | 0.105147 | ||||||||
\(266\) | −16.1122 | −0.987902 | ||||||||
\(267\) | 1.22212 | 0.0747925 | ||||||||
\(268\) | 13.4151 | 0.819456 | ||||||||
\(269\) | 13.5396 | 0.825525 | 0.412763 | − | 0.910839i | \(-0.364564\pi\) | ||||
0.412763 | + | 0.910839i | \(0.364564\pi\) | |||||||
\(270\) | −14.9354 | −0.908939 | ||||||||
\(271\) | −11.4778 | −0.697225 | −0.348613 | − | 0.937267i | \(-0.613347\pi\) | ||||
−0.348613 | + | 0.937267i | \(0.613347\pi\) | |||||||
\(272\) | 67.7582 | 4.10845 | ||||||||
\(273\) | −7.04616 | −0.426453 | ||||||||
\(274\) | 34.0561 | 2.05740 | ||||||||
\(275\) | −8.50448 | −0.512840 | ||||||||
\(276\) | −52.6837 | −3.17119 | ||||||||
\(277\) | −18.0658 | −1.08547 | −0.542735 | − | 0.839904i | \(-0.682611\pi\) | ||||
−0.542735 | + | 0.839904i | \(0.682611\pi\) | |||||||
\(278\) | −3.18538 | −0.191046 | ||||||||
\(279\) | 4.62440 | 0.276855 | ||||||||
\(280\) | 42.5949 | 2.54553 | ||||||||
\(281\) | 5.66773 | 0.338109 | 0.169054 | − | 0.985607i | \(-0.445929\pi\) | ||||
0.169054 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(282\) | −24.3185 | −1.44815 | ||||||||
\(283\) | 8.40234 | 0.499467 | 0.249734 | − | 0.968315i | \(-0.419657\pi\) | ||||
0.249734 | + | 0.968315i | \(0.419657\pi\) | |||||||
\(284\) | 16.1185 | 0.956459 | ||||||||
\(285\) | 6.27006 | 0.371406 | ||||||||
\(286\) | 9.87732 | 0.584058 | ||||||||
\(287\) | −2.10954 | −0.124522 | ||||||||
\(288\) | −15.7093 | −0.925677 | ||||||||
\(289\) | 26.9425 | 1.58485 | ||||||||
\(290\) | −2.24748 | −0.131976 | ||||||||
\(291\) | 1.26437 | 0.0741186 | ||||||||
\(292\) | −44.2335 | −2.58857 | ||||||||
\(293\) | 22.5963 | 1.32009 | 0.660045 | − | 0.751226i | \(-0.270537\pi\) | ||||
0.660045 | + | 0.751226i | \(0.270537\pi\) | |||||||
\(294\) | 24.1437 | 1.40809 | ||||||||
\(295\) | 1.46391 | 0.0852321 | ||||||||
\(296\) | 83.0369 | 4.82642 | ||||||||
\(297\) | 12.9179 | 0.749571 | ||||||||
\(298\) | −15.8207 | −0.916471 | ||||||||
\(299\) | −5.15156 | −0.297922 | ||||||||
\(300\) | 23.1322 | 1.33554 | ||||||||
\(301\) | 22.5132 | 1.29764 | ||||||||
\(302\) | 23.9932 | 1.38066 | ||||||||
\(303\) | −31.5191 | −1.81072 | ||||||||
\(304\) | −18.5635 | −1.06469 | ||||||||
\(305\) | −2.65048 | −0.151766 | ||||||||
\(306\) | −23.5672 | −1.34725 | ||||||||
\(307\) | −0.759501 | −0.0433470 | −0.0216735 | − | 0.999765i | \(-0.506899\pi\) | ||||
−0.0216735 | + | 0.999765i | \(0.506899\pi\) | |||||||
\(308\) | −62.2356 | −3.54620 | ||||||||
\(309\) | 15.2223 | 0.865969 | ||||||||
\(310\) | −14.8543 | −0.843670 | ||||||||
\(311\) | −3.87253 | −0.219591 | −0.109796 | − | 0.993954i | \(-0.535020\pi\) | ||||
−0.109796 | + | 0.993954i | \(0.535020\pi\) | |||||||
\(312\) | −15.9038 | −0.900378 | ||||||||
\(313\) | −9.19425 | −0.519690 | −0.259845 | − | 0.965650i | \(-0.583671\pi\) | ||||
−0.259845 | + | 0.965650i | \(0.583671\pi\) | |||||||
\(314\) | 10.0591 | 0.567668 | ||||||||
\(315\) | −7.56241 | −0.426093 | ||||||||
\(316\) | 42.8471 | 2.41034 | ||||||||
\(317\) | 29.2747 | 1.64423 | 0.822116 | − | 0.569320i | \(-0.192793\pi\) | ||||
0.822116 | + | 0.569320i | \(0.192793\pi\) | |||||||
\(318\) | 5.66992 | 0.317953 | ||||||||
\(319\) | 1.94388 | 0.108836 | ||||||||
\(320\) | 16.6331 | 0.929820 | ||||||||
\(321\) | 22.5990 | 1.26136 | ||||||||
\(322\) | 45.7039 | 2.54698 | ||||||||
\(323\) | −12.0388 | −0.669855 | ||||||||
\(324\) | −55.0363 | −3.05757 | ||||||||
\(325\) | 2.26194 | 0.125470 | ||||||||
\(326\) | 21.4389 | 1.18739 | ||||||||
\(327\) | −3.98229 | −0.220221 | ||||||||
\(328\) | −4.76143 | −0.262906 | ||||||||
\(329\) | 14.9830 | 0.826040 | ||||||||
\(330\) | 34.1013 | 1.87721 | ||||||||
\(331\) | −24.0559 | −1.32223 | −0.661116 | − | 0.750284i | \(-0.729917\pi\) | ||||
−0.661116 | + | 0.750284i | \(0.729917\pi\) | |||||||
\(332\) | −16.2079 | −0.889525 | ||||||||
\(333\) | −14.7426 | −0.807888 | ||||||||
\(334\) | 25.6737 | 1.40480 | ||||||||
\(335\) | 4.52884 | 0.247437 | ||||||||
\(336\) | 72.0232 | 3.92919 | ||||||||
\(337\) | −14.6077 | −0.795733 | −0.397866 | − | 0.917443i | \(-0.630249\pi\) | ||||
−0.397866 | + | 0.917443i | \(0.630249\pi\) | |||||||
\(338\) | −2.62707 | −0.142894 | ||||||||
\(339\) | −2.90296 | −0.157667 | ||||||||
\(340\) | 53.7641 | 2.91577 | ||||||||
\(341\) | 12.8478 | 0.695746 | ||||||||
\(342\) | 6.45664 | 0.349135 | ||||||||
\(343\) | 8.76436 | 0.473231 | ||||||||
\(344\) | 50.8143 | 2.73972 | ||||||||
\(345\) | −17.7857 | −0.957548 | ||||||||
\(346\) | −7.17331 | −0.385639 | ||||||||
\(347\) | 6.43170 | 0.345272 | 0.172636 | − | 0.984986i | \(-0.444772\pi\) | ||||
0.172636 | + | 0.984986i | \(0.444772\pi\) | |||||||
\(348\) | −5.28736 | −0.283433 | ||||||||
\(349\) | −7.31729 | −0.391685 | −0.195843 | − | 0.980635i | \(-0.562744\pi\) | ||||
−0.195843 | + | 0.980635i | \(0.562744\pi\) | |||||||
\(350\) | −20.0676 | −1.07266 | ||||||||
\(351\) | −3.43576 | −0.183387 | ||||||||
\(352\) | −43.6444 | −2.32625 | ||||||||
\(353\) | 6.80465 | 0.362175 | 0.181087 | − | 0.983467i | \(-0.442038\pi\) | ||||
0.181087 | + | 0.983467i | \(0.442038\pi\) | |||||||
\(354\) | 4.84923 | 0.257734 | ||||||||
\(355\) | 5.44151 | 0.288805 | ||||||||
\(356\) | −2.87100 | −0.152163 | ||||||||
\(357\) | 46.7084 | 2.47207 | ||||||||
\(358\) | −23.6275 | −1.24875 | ||||||||
\(359\) | −31.0689 | −1.63975 | −0.819876 | − | 0.572542i | \(-0.805958\pi\) | ||||
−0.819876 | + | 0.572542i | \(0.805958\pi\) | |||||||
\(360\) | −17.0691 | −0.899618 | ||||||||
\(361\) | −15.7018 | −0.826409 | ||||||||
\(362\) | 21.3558 | 1.12243 | ||||||||
\(363\) | −6.54372 | −0.343456 | ||||||||
\(364\) | 16.5528 | 0.867602 | ||||||||
\(365\) | −14.9329 | −0.781626 | ||||||||
\(366\) | −8.77976 | −0.458926 | ||||||||
\(367\) | −13.5108 | −0.705260 | −0.352630 | − | 0.935763i | \(-0.614713\pi\) | ||||
−0.352630 | + | 0.935763i | \(0.614713\pi\) | |||||||
\(368\) | 52.6573 | 2.74495 | ||||||||
\(369\) | 0.845357 | 0.0440075 | ||||||||
\(370\) | 47.3556 | 2.46190 | ||||||||
\(371\) | −3.49333 | −0.181364 | ||||||||
\(372\) | −34.9460 | −1.81187 | ||||||||
\(373\) | 22.6497 | 1.17276 | 0.586379 | − | 0.810037i | \(-0.300553\pi\) | ||||
0.586379 | + | 0.810037i | \(0.300553\pi\) | |||||||
\(374\) | −65.4759 | −3.38568 | ||||||||
\(375\) | 25.0717 | 1.29470 | ||||||||
\(376\) | 33.8181 | 1.74403 | ||||||||
\(377\) | −0.517013 | −0.0266275 | ||||||||
\(378\) | 30.4816 | 1.56780 | ||||||||
\(379\) | 24.6538 | 1.26638 | 0.633191 | − | 0.773996i | \(-0.281745\pi\) | ||||
0.633191 | + | 0.773996i | \(0.281745\pi\) | |||||||
\(380\) | −14.7296 | −0.755611 | ||||||||
\(381\) | −24.9878 | −1.28016 | ||||||||
\(382\) | 62.3790 | 3.19159 | ||||||||
\(383\) | 10.6370 | 0.543526 | 0.271763 | − | 0.962364i | \(-0.412393\pi\) | ||||
0.271763 | + | 0.962364i | \(0.412393\pi\) | |||||||
\(384\) | 6.65808 | 0.339769 | ||||||||
\(385\) | −21.0103 | −1.07078 | ||||||||
\(386\) | −17.1687 | −0.873864 | ||||||||
\(387\) | −9.02171 | −0.458599 | ||||||||
\(388\) | −2.97025 | −0.150791 | ||||||||
\(389\) | 25.0086 | 1.26799 | 0.633994 | − | 0.773338i | \(-0.281414\pi\) | ||||
0.633994 | + | 0.773338i | \(0.281414\pi\) | |||||||
\(390\) | −9.06990 | −0.459272 | ||||||||
\(391\) | 34.1492 | 1.72700 | ||||||||
\(392\) | −33.5749 | −1.69579 | ||||||||
\(393\) | 2.79190 | 0.140833 | ||||||||
\(394\) | 3.63971 | 0.183366 | ||||||||
\(395\) | 14.4649 | 0.727808 | ||||||||
\(396\) | 24.9397 | 1.25327 | ||||||||
\(397\) | −13.4520 | −0.675139 | −0.337569 | − | 0.941301i | \(-0.609605\pi\) | ||||
−0.337569 | + | 0.941301i | \(0.609605\pi\) | |||||||
\(398\) | −49.6695 | −2.48971 | ||||||||
\(399\) | −12.7965 | −0.640628 | ||||||||
\(400\) | −23.1207 | −1.15603 | ||||||||
\(401\) | −20.6387 | −1.03065 | −0.515324 | − | 0.856995i | \(-0.672328\pi\) | ||||
−0.515324 | + | 0.856995i | \(0.672328\pi\) | |||||||
\(402\) | 15.0019 | 0.748226 | ||||||||
\(403\) | −3.41712 | −0.170219 | ||||||||
\(404\) | 74.0444 | 3.68385 | ||||||||
\(405\) | −18.5799 | −0.923241 | ||||||||
\(406\) | 4.58687 | 0.227642 | ||||||||
\(407\) | −40.9587 | −2.03025 | ||||||||
\(408\) | 105.425 | 5.21932 | ||||||||
\(409\) | 21.0978 | 1.04322 | 0.521610 | − | 0.853184i | \(-0.325332\pi\) | ||||
0.521610 | + | 0.853184i | \(0.325332\pi\) | |||||||
\(410\) | −2.71543 | −0.134105 | ||||||||
\(411\) | 27.0479 | 1.33417 | ||||||||
\(412\) | −35.7602 | −1.76178 | ||||||||
\(413\) | −2.98769 | −0.147015 | ||||||||
\(414\) | −18.3149 | −0.900129 | ||||||||
\(415\) | −5.47169 | −0.268594 | ||||||||
\(416\) | 11.6081 | 0.569133 | ||||||||
\(417\) | −2.52987 | −0.123888 | ||||||||
\(418\) | 17.9382 | 0.877387 | ||||||||
\(419\) | 25.4740 | 1.24449 | 0.622244 | − | 0.782823i | \(-0.286221\pi\) | ||||
0.622244 | + | 0.782823i | \(0.286221\pi\) | |||||||
\(420\) | 57.1482 | 2.78855 | ||||||||
\(421\) | −20.7905 | −1.01327 | −0.506635 | − | 0.862161i | \(-0.669111\pi\) | ||||
−0.506635 | + | 0.862161i | \(0.669111\pi\) | |||||||
\(422\) | −59.6367 | −2.90307 | ||||||||
\(423\) | −6.00414 | −0.291931 | ||||||||
\(424\) | −7.88476 | −0.382918 | ||||||||
\(425\) | −14.9942 | −0.727324 | ||||||||
\(426\) | 18.0251 | 0.873320 | ||||||||
\(427\) | 5.40935 | 0.261777 | ||||||||
\(428\) | −53.0895 | −2.56618 | ||||||||
\(429\) | 7.84471 | 0.378746 | ||||||||
\(430\) | 28.9792 | 1.39750 | ||||||||
\(431\) | 40.8120 | 1.96585 | 0.982923 | − | 0.184018i | \(-0.0589105\pi\) | ||||
0.982923 | + | 0.184018i | \(0.0589105\pi\) | |||||||
\(432\) | 35.1191 | 1.68967 | ||||||||
\(433\) | −8.84111 | −0.424877 | −0.212438 | − | 0.977174i | \(-0.568140\pi\) | ||||
−0.212438 | + | 0.977174i | \(0.568140\pi\) | |||||||
\(434\) | 30.3162 | 1.45522 | ||||||||
\(435\) | −1.78498 | −0.0855832 | ||||||||
\(436\) | 9.35516 | 0.448031 | ||||||||
\(437\) | −9.35575 | −0.447546 | ||||||||
\(438\) | −49.4657 | −2.36356 | ||||||||
\(439\) | −34.2338 | −1.63389 | −0.816945 | − | 0.576716i | \(-0.804334\pi\) | ||||
−0.816945 | + | 0.576716i | \(0.804334\pi\) | |||||||
\(440\) | −47.4222 | −2.26077 | ||||||||
\(441\) | 5.96098 | 0.283856 | ||||||||
\(442\) | 17.4146 | 0.828328 | ||||||||
\(443\) | 0.0486450 | 0.00231120 | 0.00115560 | − | 0.999999i | \(-0.499632\pi\) | ||||
0.00115560 | + | 0.999999i | \(0.499632\pi\) | |||||||
\(444\) | 111.408 | 5.28718 | ||||||||
\(445\) | −0.969229 | −0.0459459 | ||||||||
\(446\) | −68.0318 | −3.22140 | ||||||||
\(447\) | −12.5651 | −0.594307 | ||||||||
\(448\) | −33.9465 | −1.60382 | ||||||||
\(449\) | −1.90081 | −0.0897046 | −0.0448523 | − | 0.998994i | \(-0.514282\pi\) | ||||
−0.0448523 | + | 0.998994i | \(0.514282\pi\) | |||||||
\(450\) | 8.04168 | 0.379088 | ||||||||
\(451\) | 2.34862 | 0.110592 | ||||||||
\(452\) | 6.81961 | 0.320767 | ||||||||
\(453\) | 19.0558 | 0.895319 | ||||||||
\(454\) | 12.1810 | 0.571683 | ||||||||
\(455\) | 5.58811 | 0.261975 | ||||||||
\(456\) | −28.8830 | −1.35257 | ||||||||
\(457\) | −12.8247 | −0.599913 | −0.299956 | − | 0.953953i | \(-0.596972\pi\) | ||||
−0.299956 | + | 0.953953i | \(0.596972\pi\) | |||||||
\(458\) | 70.6229 | 3.29999 | ||||||||
\(459\) | 22.7754 | 1.06306 | ||||||||
\(460\) | 41.7819 | 1.94809 | ||||||||
\(461\) | −36.9887 | −1.72273 | −0.861367 | − | 0.507983i | \(-0.830391\pi\) | ||||
−0.861367 | + | 0.507983i | \(0.830391\pi\) | |||||||
\(462\) | −69.5972 | −3.23795 | ||||||||
\(463\) | 6.57372 | 0.305507 | 0.152753 | − | 0.988264i | \(-0.451186\pi\) | ||||
0.152753 | + | 0.988264i | \(0.451186\pi\) | |||||||
\(464\) | 5.28472 | 0.245337 | ||||||||
\(465\) | −11.7975 | −0.547098 | ||||||||
\(466\) | 72.6642 | 3.36611 | ||||||||
\(467\) | 30.1017 | 1.39294 | 0.696470 | − | 0.717586i | \(-0.254753\pi\) | ||||
0.696470 | + | 0.717586i | \(0.254753\pi\) | |||||||
\(468\) | −6.63320 | −0.306620 | ||||||||
\(469\) | −9.24290 | −0.426797 | ||||||||
\(470\) | 19.2863 | 0.889611 | ||||||||
\(471\) | 7.98909 | 0.368118 | ||||||||
\(472\) | −6.74349 | −0.310394 | ||||||||
\(473\) | −25.0646 | −1.15247 | ||||||||
\(474\) | 47.9153 | 2.20082 | ||||||||
\(475\) | 4.10790 | 0.188484 | ||||||||
\(476\) | −109.727 | −5.02933 | ||||||||
\(477\) | 1.39988 | 0.0640961 | ||||||||
\(478\) | 15.2131 | 0.695832 | ||||||||
\(479\) | 32.2322 | 1.47273 | 0.736363 | − | 0.676587i | \(-0.236542\pi\) | ||||
0.736363 | + | 0.676587i | \(0.236542\pi\) | |||||||
\(480\) | 40.0767 | 1.82924 | ||||||||
\(481\) | 10.8938 | 0.496713 | ||||||||
\(482\) | −45.5563 | −2.07503 | ||||||||
\(483\) | 36.2987 | 1.65165 | ||||||||
\(484\) | 15.3725 | 0.698748 | ||||||||
\(485\) | −1.00274 | −0.0455319 | ||||||||
\(486\) | −34.4683 | −1.56352 | ||||||||
\(487\) | 30.5388 | 1.38385 | 0.691923 | − | 0.721971i | \(-0.256764\pi\) | ||||
0.691923 | + | 0.721971i | \(0.256764\pi\) | |||||||
\(488\) | 12.2094 | 0.552694 | ||||||||
\(489\) | 17.0271 | 0.769990 | ||||||||
\(490\) | −19.1477 | −0.865003 | ||||||||
\(491\) | −16.8384 | −0.759904 | −0.379952 | − | 0.925006i | \(-0.624060\pi\) | ||||
−0.379952 | + | 0.925006i | \(0.624060\pi\) | |||||||
\(492\) | −6.38826 | −0.288005 | ||||||||
\(493\) | 3.42723 | 0.154355 | ||||||||
\(494\) | −4.77102 | −0.214658 | ||||||||
\(495\) | 8.41947 | 0.378427 | ||||||||
\(496\) | 34.9285 | 1.56834 | ||||||||
\(497\) | −11.1056 | −0.498153 | ||||||||
\(498\) | −18.1251 | −0.812205 | ||||||||
\(499\) | −27.7556 | −1.24251 | −0.621255 | − | 0.783608i | \(-0.713377\pi\) | ||||
−0.621255 | + | 0.783608i | \(0.713377\pi\) | |||||||
\(500\) | −58.8982 | −2.63401 | ||||||||
\(501\) | 20.3904 | 0.910977 | ||||||||
\(502\) | −30.0886 | −1.34292 | ||||||||
\(503\) | −35.7069 | −1.59209 | −0.796045 | − | 0.605238i | \(-0.793078\pi\) | ||||
−0.796045 | + | 0.605238i | \(0.793078\pi\) | |||||||
\(504\) | 34.8362 | 1.55173 | ||||||||
\(505\) | 24.9969 | 1.11235 | ||||||||
\(506\) | −50.8836 | −2.26205 | ||||||||
\(507\) | −2.08646 | −0.0926628 | ||||||||
\(508\) | 58.7012 | 2.60444 | ||||||||
\(509\) | −20.8992 | −0.926339 | −0.463170 | − | 0.886270i | \(-0.653288\pi\) | ||||
−0.463170 | + | 0.886270i | \(0.653288\pi\) | |||||||
\(510\) | 60.1236 | 2.66232 | ||||||||
\(511\) | 30.4766 | 1.34821 | ||||||||
\(512\) | 37.1734 | 1.64285 | ||||||||
\(513\) | −6.23969 | −0.275489 | ||||||||
\(514\) | 4.26908 | 0.188301 | ||||||||
\(515\) | −12.0724 | −0.531974 | ||||||||
\(516\) | 68.1760 | 3.00128 | ||||||||
\(517\) | −16.6811 | −0.733632 | ||||||||
\(518\) | −96.6480 | −4.24647 | ||||||||
\(519\) | −5.69715 | −0.250077 | ||||||||
\(520\) | 12.6129 | 0.553112 | ||||||||
\(521\) | −11.1389 | −0.488004 | −0.244002 | − | 0.969775i | \(-0.578460\pi\) | ||||
−0.244002 | + | 0.969775i | \(0.578460\pi\) | |||||||
\(522\) | −1.83810 | −0.0804513 | ||||||||
\(523\) | −1.61469 | −0.0706053 | −0.0353027 | − | 0.999377i | \(-0.511240\pi\) | ||||
−0.0353027 | + | 0.999377i | \(0.511240\pi\) | |||||||
\(524\) | −6.55870 | −0.286518 | ||||||||
\(525\) | −15.9380 | −0.695590 | ||||||||
\(526\) | −51.3707 | −2.23987 | ||||||||
\(527\) | 22.6518 | 0.986727 | ||||||||
\(528\) | −80.1857 | −3.48964 | ||||||||
\(529\) | 3.53855 | 0.153850 | ||||||||
\(530\) | −4.49665 | −0.195322 | ||||||||
\(531\) | 1.19726 | 0.0519565 | ||||||||
\(532\) | 30.0616 | 1.30333 | ||||||||
\(533\) | −0.624662 | −0.0270571 | ||||||||
\(534\) | −3.21059 | −0.138936 | ||||||||
\(535\) | −17.9227 | −0.774864 | ||||||||
\(536\) | −20.8621 | −0.901104 | ||||||||
\(537\) | −18.7653 | −0.809783 | ||||||||
\(538\) | −35.5695 | −1.53351 | ||||||||
\(539\) | 16.5611 | 0.713339 | ||||||||
\(540\) | 27.8659 | 1.19916 | ||||||||
\(541\) | −1.46182 | −0.0628483 | −0.0314242 | − | 0.999506i | \(-0.510004\pi\) | ||||
−0.0314242 | + | 0.999506i | \(0.510004\pi\) | |||||||
\(542\) | 30.1529 | 1.29518 | ||||||||
\(543\) | 16.9611 | 0.727869 | ||||||||
\(544\) | −76.9490 | −3.29916 | ||||||||
\(545\) | 3.15824 | 0.135284 | ||||||||
\(546\) | 18.5107 | 0.792187 | ||||||||
\(547\) | 40.2961 | 1.72294 | 0.861468 | − | 0.507811i | \(-0.169545\pi\) | ||||
0.861468 | + | 0.507811i | \(0.169545\pi\) | |||||||
\(548\) | −63.5407 | −2.71432 | ||||||||
\(549\) | −2.16769 | −0.0925147 | ||||||||
\(550\) | 22.3419 | 0.952660 | ||||||||
\(551\) | −0.938949 | −0.0400006 | ||||||||
\(552\) | 81.9296 | 3.48715 | ||||||||
\(553\) | −29.5214 | −1.25538 | ||||||||
\(554\) | 47.4602 | 2.01639 | ||||||||
\(555\) | 37.6105 | 1.59648 | ||||||||
\(556\) | 5.94316 | 0.252046 | ||||||||
\(557\) | −23.2093 | −0.983411 | −0.491706 | − | 0.870762i | \(-0.663626\pi\) | ||||
−0.491706 | + | 0.870762i | \(0.663626\pi\) | |||||||
\(558\) | −12.1486 | −0.514292 | ||||||||
\(559\) | 6.66643 | 0.281960 | ||||||||
\(560\) | −57.1196 | −2.41374 | ||||||||
\(561\) | −52.0019 | −2.19552 | ||||||||
\(562\) | −14.8895 | −0.628077 | ||||||||
\(563\) | −21.5878 | −0.909817 | −0.454909 | − | 0.890538i | \(-0.650328\pi\) | ||||
−0.454909 | + | 0.890538i | \(0.650328\pi\) | |||||||
\(564\) | 45.3726 | 1.91053 | ||||||||
\(565\) | 2.30225 | 0.0968566 | ||||||||
\(566\) | −22.0735 | −0.927819 | ||||||||
\(567\) | 37.9196 | 1.59247 | ||||||||
\(568\) | −25.0663 | −1.05176 | ||||||||
\(569\) | 30.9138 | 1.29597 | 0.647987 | − | 0.761651i | \(-0.275611\pi\) | ||||
0.647987 | + | 0.761651i | \(0.275611\pi\) | |||||||
\(570\) | −16.4719 | −0.689931 | ||||||||
\(571\) | −11.9781 | −0.501267 | −0.250634 | − | 0.968082i | \(-0.580639\pi\) | ||||
−0.250634 | + | 0.968082i | \(0.580639\pi\) | |||||||
\(572\) | −18.4287 | −0.770545 | ||||||||
\(573\) | 49.5423 | 2.06966 | ||||||||
\(574\) | 5.54191 | 0.231315 | ||||||||
\(575\) | −11.6525 | −0.485942 | ||||||||
\(576\) | 13.6034 | 0.566808 | ||||||||
\(577\) | −38.9687 | −1.62229 | −0.811144 | − | 0.584846i | \(-0.801155\pi\) | ||||
−0.811144 | + | 0.584846i | \(0.801155\pi\) | |||||||
\(578\) | −70.7797 | −2.94405 | ||||||||
\(579\) | −13.6356 | −0.566678 | ||||||||
\(580\) | 4.19326 | 0.174116 | ||||||||
\(581\) | 11.1672 | 0.463292 | ||||||||
\(582\) | −3.32158 | −0.137684 | ||||||||
\(583\) | 3.88923 | 0.161075 | ||||||||
\(584\) | 68.7885 | 2.84649 | ||||||||
\(585\) | −2.23932 | −0.0925846 | ||||||||
\(586\) | −59.3620 | −2.45222 | ||||||||
\(587\) | 44.1506 | 1.82229 | 0.911144 | − | 0.412087i | \(-0.135200\pi\) | ||||
0.911144 | + | 0.412087i | \(0.135200\pi\) | |||||||
\(588\) | −45.0464 | −1.85768 | ||||||||
\(589\) | −6.20583 | −0.255707 | ||||||||
\(590\) | −3.84579 | −0.158329 | ||||||||
\(591\) | 2.89071 | 0.118908 | ||||||||
\(592\) | −111.352 | −4.57654 | ||||||||
\(593\) | 17.0372 | 0.699635 | 0.349818 | − | 0.936818i | \(-0.386244\pi\) | ||||
0.349818 | + | 0.936818i | \(0.386244\pi\) | |||||||
\(594\) | −33.9361 | −1.39242 | ||||||||
\(595\) | −37.0431 | −1.51862 | ||||||||
\(596\) | 29.5178 | 1.20909 | ||||||||
\(597\) | −39.4482 | −1.61451 | ||||||||
\(598\) | 13.5335 | 0.553426 | ||||||||
\(599\) | 14.1582 | 0.578489 | 0.289245 | − | 0.957255i | \(-0.406596\pi\) | ||||
0.289245 | + | 0.957255i | \(0.406596\pi\) | |||||||
\(600\) | −35.9735 | −1.46861 | ||||||||
\(601\) | 38.8754 | 1.58576 | 0.792881 | − | 0.609377i | \(-0.208580\pi\) | ||||
0.792881 | + | 0.609377i | \(0.208580\pi\) | |||||||
\(602\) | −59.1437 | −2.41052 | ||||||||
\(603\) | 3.70391 | 0.150835 | ||||||||
\(604\) | −44.7657 | −1.82149 | ||||||||
\(605\) | 5.18964 | 0.210989 | ||||||||
\(606\) | 82.8028 | 3.36363 | ||||||||
\(607\) | −6.39023 | −0.259371 | −0.129686 | − | 0.991555i | \(-0.541397\pi\) | ||||
−0.129686 | + | 0.991555i | \(0.541397\pi\) | |||||||
\(608\) | 21.0815 | 0.854966 | ||||||||
\(609\) | 3.64296 | 0.147620 | ||||||||
\(610\) | 6.96298 | 0.281923 | ||||||||
\(611\) | 4.43666 | 0.179488 | ||||||||
\(612\) | 43.9709 | 1.77742 | ||||||||
\(613\) | −18.1835 | −0.734424 | −0.367212 | − | 0.930137i | \(-0.619688\pi\) | ||||
−0.367212 | + | 0.930137i | \(0.619688\pi\) | |||||||
\(614\) | 1.99526 | 0.0805221 | ||||||||
\(615\) | −2.15663 | −0.0869639 | ||||||||
\(616\) | 96.7839 | 3.89954 | ||||||||
\(617\) | −21.3145 | −0.858091 | −0.429045 | − | 0.903283i | \(-0.641150\pi\) | ||||
−0.429045 | + | 0.903283i | \(0.641150\pi\) | |||||||
\(618\) | −39.9902 | −1.60864 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 27.7147 | 1.11305 | ||||||||
\(621\) | 17.6995 | 0.710258 | ||||||||
\(622\) | 10.1734 | 0.407916 | ||||||||
\(623\) | 1.97810 | 0.0792508 | ||||||||
\(624\) | 21.3270 | 0.853763 | ||||||||
\(625\) | −8.57397 | −0.342959 | ||||||||
\(626\) | 24.1539 | 0.965385 | ||||||||
\(627\) | 14.2468 | 0.568962 | ||||||||
\(628\) | −18.7679 | −0.748921 | ||||||||
\(629\) | −72.2139 | −2.87935 | ||||||||
\(630\) | 19.8670 | 0.791519 | ||||||||
\(631\) | −24.9335 | −0.992588 | −0.496294 | − | 0.868155i | \(-0.665306\pi\) | ||||
−0.496294 | + | 0.868155i | \(0.665306\pi\) | |||||||
\(632\) | −66.6325 | −2.65050 | ||||||||
\(633\) | −47.3643 | −1.88256 | ||||||||
\(634\) | −76.9067 | −3.05436 | ||||||||
\(635\) | 19.8171 | 0.786419 | ||||||||
\(636\) | −10.5787 | −0.419474 | ||||||||
\(637\) | −4.40476 | −0.174523 | ||||||||
\(638\) | −5.10670 | −0.202176 | ||||||||
\(639\) | 4.45033 | 0.176052 | ||||||||
\(640\) | −5.28034 | −0.208724 | ||||||||
\(641\) | −34.9738 | −1.38138 | −0.690690 | − | 0.723151i | \(-0.742693\pi\) | ||||
−0.690690 | + | 0.723151i | \(0.742693\pi\) | |||||||
\(642\) | −59.3693 | −2.34312 | ||||||||
\(643\) | 35.1186 | 1.38494 | 0.692471 | − | 0.721446i | \(-0.256522\pi\) | ||||
0.692471 | + | 0.721446i | \(0.256522\pi\) | |||||||
\(644\) | −85.2727 | −3.36021 | ||||||||
\(645\) | 23.0157 | 0.906244 | ||||||||
\(646\) | 31.6267 | 1.24434 | ||||||||
\(647\) | −44.5409 | −1.75108 | −0.875542 | − | 0.483142i | \(-0.839495\pi\) | ||||
−0.875542 | + | 0.483142i | \(0.839495\pi\) | |||||||
\(648\) | 85.5881 | 3.36222 | ||||||||
\(649\) | 3.32629 | 0.130568 | ||||||||
\(650\) | −5.94226 | −0.233075 | ||||||||
\(651\) | 24.0776 | 0.943674 | ||||||||
\(652\) | −39.9998 | −1.56651 | ||||||||
\(653\) | 8.66687 | 0.339161 | 0.169580 | − | 0.985516i | \(-0.445759\pi\) | ||||
0.169580 | + | 0.985516i | \(0.445759\pi\) | |||||||
\(654\) | 10.4617 | 0.409087 | ||||||||
\(655\) | −2.21417 | −0.0865149 | ||||||||
\(656\) | 6.38506 | 0.249295 | ||||||||
\(657\) | −12.2129 | −0.476470 | ||||||||
\(658\) | −39.3614 | −1.53447 | ||||||||
\(659\) | 26.5626 | 1.03473 | 0.517367 | − | 0.855764i | \(-0.326912\pi\) | ||||
0.517367 | + | 0.855764i | \(0.326912\pi\) | |||||||
\(660\) | −63.6249 | −2.47660 | ||||||||
\(661\) | −27.4564 | −1.06793 | −0.533965 | − | 0.845506i | \(-0.679299\pi\) | ||||
−0.533965 | + | 0.845506i | \(0.679299\pi\) | |||||||
\(662\) | 63.1965 | 2.45620 | ||||||||
\(663\) | 13.8309 | 0.537149 | ||||||||
\(664\) | 25.2053 | 0.978155 | ||||||||
\(665\) | 10.1486 | 0.393545 | ||||||||
\(666\) | 38.7298 | 1.50075 | ||||||||
\(667\) | 2.66342 | 0.103128 | ||||||||
\(668\) | −47.9010 | −1.85335 | ||||||||
\(669\) | −54.0318 | −2.08899 | ||||||||
\(670\) | −11.8976 | −0.459643 | ||||||||
\(671\) | −6.02240 | −0.232492 | ||||||||
\(672\) | −81.7925 | −3.15521 | ||||||||
\(673\) | 1.88361 | 0.0726079 | 0.0363039 | − | 0.999341i | \(-0.488442\pi\) | ||||
0.0363039 | + | 0.999341i | \(0.488442\pi\) | |||||||
\(674\) | 38.3755 | 1.47817 | ||||||||
\(675\) | −7.77147 | −0.299124 | ||||||||
\(676\) | 4.90149 | 0.188519 | ||||||||
\(677\) | −1.75643 | −0.0675052 | −0.0337526 | − | 0.999430i | \(-0.510746\pi\) | ||||
−0.0337526 | + | 0.999430i | \(0.510746\pi\) | |||||||
\(678\) | 7.62627 | 0.292885 | ||||||||
\(679\) | 2.04648 | 0.0785367 | ||||||||
\(680\) | −83.6097 | −3.20628 | ||||||||
\(681\) | 9.67433 | 0.370721 | ||||||||
\(682\) | −33.7520 | −1.29243 | ||||||||
\(683\) | −21.4990 | −0.822635 | −0.411318 | − | 0.911492i | \(-0.634931\pi\) | ||||
−0.411318 | + | 0.911492i | \(0.634931\pi\) | |||||||
\(684\) | −12.0466 | −0.460612 | ||||||||
\(685\) | −21.4509 | −0.819597 | ||||||||
\(686\) | −23.0246 | −0.879082 | ||||||||
\(687\) | 56.0898 | 2.13996 | ||||||||
\(688\) | −68.1418 | −2.59788 | ||||||||
\(689\) | −1.03442 | −0.0394082 | ||||||||
\(690\) | 46.7241 | 1.77876 | ||||||||
\(691\) | 37.6199 | 1.43113 | 0.715564 | − | 0.698547i | \(-0.246170\pi\) | ||||
0.715564 | + | 0.698547i | \(0.246170\pi\) | |||||||
\(692\) | 13.3837 | 0.508772 | ||||||||
\(693\) | −17.1833 | −0.652738 | ||||||||
\(694\) | −16.8965 | −0.641383 | ||||||||
\(695\) | 2.00637 | 0.0761060 | ||||||||
\(696\) | 8.22250 | 0.311673 | ||||||||
\(697\) | 4.14083 | 0.156845 | ||||||||
\(698\) | 19.2230 | 0.727602 | ||||||||
\(699\) | 57.7110 | 2.18283 | ||||||||
\(700\) | 37.4413 | 1.41515 | ||||||||
\(701\) | −14.4320 | −0.545088 | −0.272544 | − | 0.962143i | \(-0.587865\pi\) | ||||
−0.272544 | + | 0.962143i | \(0.587865\pi\) | |||||||
\(702\) | 9.02598 | 0.340664 | ||||||||
\(703\) | 19.7842 | 0.746175 | ||||||||
\(704\) | 37.7937 | 1.42440 | ||||||||
\(705\) | 15.3175 | 0.576890 | ||||||||
\(706\) | −17.8763 | −0.672783 | ||||||||
\(707\) | −51.0161 | −1.91866 | ||||||||
\(708\) | −9.04753 | −0.340027 | ||||||||
\(709\) | −34.7602 | −1.30545 | −0.652723 | − | 0.757596i | \(-0.726374\pi\) | ||||
−0.652723 | + | 0.757596i | \(0.726374\pi\) | |||||||
\(710\) | −14.2952 | −0.536490 | ||||||||
\(711\) | 11.8301 | 0.443664 | ||||||||
\(712\) | 4.46475 | 0.167324 | ||||||||
\(713\) | 17.6035 | 0.659256 | ||||||||
\(714\) | −122.706 | −4.59216 | ||||||||
\(715\) | −6.22142 | −0.232668 | ||||||||
\(716\) | 44.0834 | 1.64747 | ||||||||
\(717\) | 12.0825 | 0.451229 | ||||||||
\(718\) | 81.6200 | 3.04603 | ||||||||
\(719\) | −32.7986 | −1.22318 | −0.611590 | − | 0.791175i | \(-0.709470\pi\) | ||||
−0.611590 | + | 0.791175i | \(0.709470\pi\) | |||||||
\(720\) | 22.8895 | 0.853042 | ||||||||
\(721\) | 24.6386 | 0.917588 | ||||||||
\(722\) | 41.2496 | 1.53515 | ||||||||
\(723\) | −36.1815 | −1.34560 | ||||||||
\(724\) | −39.8448 | −1.48082 | ||||||||
\(725\) | −1.16945 | −0.0434323 | ||||||||
\(726\) | 17.1908 | 0.638011 | ||||||||
\(727\) | 21.6122 | 0.801552 | 0.400776 | − | 0.916176i | \(-0.368741\pi\) | ||||
0.400776 | + | 0.916176i | \(0.368741\pi\) | |||||||
\(728\) | −25.7416 | −0.954048 | ||||||||
\(729\) | 6.31018 | 0.233710 | ||||||||
\(730\) | 39.2298 | 1.45196 | ||||||||
\(731\) | −44.1912 | −1.63447 | ||||||||
\(732\) | 16.3810 | 0.605458 | ||||||||
\(733\) | 2.48808 | 0.0918993 | 0.0459497 | − | 0.998944i | \(-0.485369\pi\) | ||||
0.0459497 | + | 0.998944i | \(0.485369\pi\) | |||||||
\(734\) | 35.4939 | 1.31010 | ||||||||
\(735\) | −15.2074 | −0.560932 | ||||||||
\(736\) | −59.7997 | −2.20425 | ||||||||
\(737\) | 10.2904 | 0.379052 | ||||||||
\(738\) | −2.22081 | −0.0817492 | ||||||||
\(739\) | 43.0241 | 1.58267 | 0.791334 | − | 0.611384i | \(-0.209387\pi\) | ||||
0.791334 | + | 0.611384i | \(0.209387\pi\) | |||||||
\(740\) | −88.3544 | −3.24797 | ||||||||
\(741\) | −3.78922 | −0.139200 | ||||||||
\(742\) | 9.17721 | 0.336906 | ||||||||
\(743\) | 2.48717 | 0.0912455 | 0.0456227 | − | 0.998959i | \(-0.485473\pi\) | ||||
0.0456227 | + | 0.998959i | \(0.485473\pi\) | |||||||
\(744\) | 54.3453 | 1.99240 | ||||||||
\(745\) | 9.96500 | 0.365089 | ||||||||
\(746\) | −59.5024 | −2.17854 | ||||||||
\(747\) | −4.47501 | −0.163732 | ||||||||
\(748\) | 122.163 | 4.46670 | ||||||||
\(749\) | 36.5783 | 1.33654 | ||||||||
\(750\) | −65.8651 | −2.40505 | ||||||||
\(751\) | −35.5407 | −1.29690 | −0.648448 | − | 0.761259i | \(-0.724582\pi\) | ||||
−0.648448 | + | 0.761259i | \(0.724582\pi\) | |||||||
\(752\) | −45.3499 | −1.65374 | ||||||||
\(753\) | −23.8968 | −0.870848 | ||||||||
\(754\) | 1.35823 | 0.0494638 | ||||||||
\(755\) | −15.1126 | −0.550004 | ||||||||
\(756\) | −56.8715 | −2.06840 | ||||||||
\(757\) | −24.7209 | −0.898495 | −0.449248 | − | 0.893407i | \(-0.648308\pi\) | ||||
−0.449248 | + | 0.893407i | \(0.648308\pi\) | |||||||
\(758\) | −64.7673 | −2.35245 | ||||||||
\(759\) | −40.4125 | −1.46688 | ||||||||
\(760\) | 22.9063 | 0.830898 | ||||||||
\(761\) | −3.23611 | −0.117309 | −0.0586544 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586544 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(762\) | 65.6447 | 2.37806 | ||||||||
\(763\) | −6.44564 | −0.233348 | ||||||||
\(764\) | −116.384 | −4.21064 | ||||||||
\(765\) | 14.8443 | 0.536696 | ||||||||
\(766\) | −27.9442 | −1.00966 | ||||||||
\(767\) | −0.884692 | −0.0319444 | ||||||||
\(768\) | 24.4549 | 0.882438 | ||||||||
\(769\) | 37.7883 | 1.36268 | 0.681340 | − | 0.731967i | \(-0.261398\pi\) | ||||
0.681340 | + | 0.731967i | \(0.261398\pi\) | |||||||
\(770\) | 55.1955 | 1.98911 | ||||||||
\(771\) | 3.39056 | 0.122108 | ||||||||
\(772\) | 32.0328 | 1.15288 | ||||||||
\(773\) | −26.7897 | −0.963557 | −0.481779 | − | 0.876293i | \(-0.660009\pi\) | ||||
−0.481779 | + | 0.876293i | \(0.660009\pi\) | |||||||
\(774\) | 23.7006 | 0.851902 | ||||||||
\(775\) | −7.72930 | −0.277645 | ||||||||
\(776\) | 4.61910 | 0.165816 | ||||||||
\(777\) | −76.7593 | −2.75372 | ||||||||
\(778\) | −65.6994 | −2.35544 | ||||||||
\(779\) | −1.13445 | −0.0406459 | ||||||||
\(780\) | 16.9223 | 0.605916 | ||||||||
\(781\) | 12.3642 | 0.442425 | ||||||||
\(782\) | −89.7123 | −3.20811 | ||||||||
\(783\) | 1.77633 | 0.0634810 | ||||||||
\(784\) | 45.0238 | 1.60799 | ||||||||
\(785\) | −6.33592 | −0.226139 | ||||||||
\(786\) | −7.33450 | −0.261613 | ||||||||
\(787\) | −36.3767 | −1.29669 | −0.648345 | − | 0.761347i | \(-0.724538\pi\) | ||||
−0.648345 | + | 0.761347i | \(0.724538\pi\) | |||||||
\(788\) | −6.79084 | −0.241914 | ||||||||
\(789\) | −40.7994 | −1.45250 | ||||||||
\(790\) | −38.0003 | −1.35199 | ||||||||
\(791\) | −4.69867 | −0.167065 | ||||||||
\(792\) | −38.7842 | −1.37814 | ||||||||
\(793\) | 1.60178 | 0.0568808 | ||||||||
\(794\) | 35.3395 | 1.25415 | ||||||||
\(795\) | −3.57131 | −0.126661 | ||||||||
\(796\) | 92.6715 | 3.28465 | ||||||||
\(797\) | −27.3149 | −0.967542 | −0.483771 | − | 0.875195i | \(-0.660733\pi\) | ||||
−0.483771 | + | 0.875195i | \(0.660733\pi\) | |||||||
\(798\) | 33.6174 | 1.19004 | ||||||||
\(799\) | −29.4102 | −1.04046 | ||||||||
\(800\) | 26.2567 | 0.928316 | ||||||||
\(801\) | −0.792683 | −0.0280081 | ||||||||
\(802\) | 54.2193 | 1.91455 | ||||||||
\(803\) | −33.9306 | −1.19738 | ||||||||
\(804\) | −27.9900 | −0.987130 | ||||||||
\(805\) | −28.7875 | −1.01463 | ||||||||
\(806\) | 8.97700 | 0.316202 | ||||||||
\(807\) | −28.2498 | −0.994441 | ||||||||
\(808\) | −115.148 | −4.05090 | ||||||||
\(809\) | 4.73446 | 0.166455 | 0.0832273 | − | 0.996531i | \(-0.473477\pi\) | ||||
0.0832273 | + | 0.996531i | \(0.473477\pi\) | |||||||
\(810\) | 48.8106 | 1.71503 | ||||||||
\(811\) | −12.6856 | −0.445451 | −0.222725 | − | 0.974881i | \(-0.571495\pi\) | ||||
−0.222725 | + | 0.974881i | \(0.571495\pi\) | |||||||
\(812\) | −8.55801 | −0.300327 | ||||||||
\(813\) | 23.9479 | 0.839889 | ||||||||
\(814\) | 107.601 | 3.77142 | ||||||||
\(815\) | −13.5037 | −0.473013 | ||||||||
\(816\) | −141.375 | −4.94910 | ||||||||
\(817\) | 12.1069 | 0.423568 | ||||||||
\(818\) | −55.4254 | −1.93790 | ||||||||
\(819\) | 4.57023 | 0.159697 | ||||||||
\(820\) | 5.06635 | 0.176925 | ||||||||
\(821\) | 29.6546 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(822\) | −71.0566 | −2.47838 | ||||||||
\(823\) | 49.1076 | 1.71178 | 0.855892 | − | 0.517155i | \(-0.173009\pi\) | ||||
0.855892 | + | 0.517155i | \(0.173009\pi\) | |||||||
\(824\) | 55.6115 | 1.93732 | ||||||||
\(825\) | 17.7442 | 0.617775 | ||||||||
\(826\) | 7.84886 | 0.273097 | ||||||||
\(827\) | 10.5392 | 0.366484 | 0.183242 | − | 0.983068i | \(-0.441341\pi\) | ||||
0.183242 | + | 0.983068i | \(0.441341\pi\) | |||||||
\(828\) | 34.1713 | 1.18754 | ||||||||
\(829\) | −13.2329 | −0.459599 | −0.229799 | − | 0.973238i | \(-0.573807\pi\) | ||||
−0.229799 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(830\) | 14.3745 | 0.498946 | ||||||||
\(831\) | 37.6936 | 1.30758 | ||||||||
\(832\) | −10.0520 | −0.348490 | ||||||||
\(833\) | 29.1988 | 1.01168 | ||||||||
\(834\) | 6.64615 | 0.230137 | ||||||||
\(835\) | −16.1711 | −0.559623 | ||||||||
\(836\) | −33.4685 | −1.15753 | ||||||||
\(837\) | 11.7404 | 0.405808 | ||||||||
\(838\) | −66.9220 | −2.31178 | ||||||||
\(839\) | −2.75841 | −0.0952309 | −0.0476155 | − | 0.998866i | \(-0.515162\pi\) | ||||
−0.0476155 | + | 0.998866i | \(0.515162\pi\) | |||||||
\(840\) | −88.8724 | −3.06639 | ||||||||
\(841\) | −28.7327 | −0.990783 | ||||||||
\(842\) | 54.6182 | 1.88227 | ||||||||
\(843\) | −11.8255 | −0.407291 | ||||||||
\(844\) | 111.268 | 3.83000 | ||||||||
\(845\) | 1.65471 | 0.0569237 | ||||||||
\(846\) | 15.7733 | 0.542297 | ||||||||
\(847\) | −10.5915 | −0.363929 | ||||||||
\(848\) | 10.5734 | 0.363093 | ||||||||
\(849\) | −17.5311 | −0.601667 | ||||||||
\(850\) | 39.3907 | 1.35109 | ||||||||
\(851\) | −56.1199 | −1.92377 | ||||||||
\(852\) | −33.6306 | −1.15217 | ||||||||
\(853\) | −40.7699 | −1.39594 | −0.697968 | − | 0.716129i | \(-0.745912\pi\) | ||||
−0.697968 | + | 0.716129i | \(0.745912\pi\) | |||||||
\(854\) | −14.2107 | −0.486281 | ||||||||
\(855\) | −4.06684 | −0.139083 | ||||||||
\(856\) | 82.5607 | 2.82187 | ||||||||
\(857\) | −38.8404 | −1.32676 | −0.663381 | − | 0.748282i | \(-0.730879\pi\) | ||||
−0.663381 | + | 0.748282i | \(0.730879\pi\) | |||||||
\(858\) | −20.6086 | −0.703566 | ||||||||
\(859\) | −14.1524 | −0.482874 | −0.241437 | − | 0.970416i | \(-0.577619\pi\) | ||||
−0.241437 | + | 0.970416i | \(0.577619\pi\) | |||||||
\(860\) | −54.0684 | −1.84372 | ||||||||
\(861\) | 4.40147 | 0.150002 | ||||||||
\(862\) | −107.216 | −3.65179 | ||||||||
\(863\) | −41.6433 | −1.41755 | −0.708777 | − | 0.705433i | \(-0.750753\pi\) | ||||
−0.708777 | + | 0.705433i | \(0.750753\pi\) | |||||||
\(864\) | −39.8826 | −1.35683 | ||||||||
\(865\) | 4.51825 | 0.153625 | ||||||||
\(866\) | 23.2262 | 0.789258 | ||||||||
\(867\) | −56.2143 | −1.90914 | ||||||||
\(868\) | −56.5629 | −1.91987 | ||||||||
\(869\) | 32.8671 | 1.11494 | ||||||||
\(870\) | 4.68926 | 0.158981 | ||||||||
\(871\) | −2.73694 | −0.0927376 | ||||||||
\(872\) | −14.5484 | −0.492672 | ||||||||
\(873\) | −0.820086 | −0.0277557 | ||||||||
\(874\) | 24.5782 | 0.831370 | ||||||||
\(875\) | 40.5805 | 1.37187 | ||||||||
\(876\) | 92.2913 | 3.11824 | ||||||||
\(877\) | −8.89547 | −0.300379 | −0.150189 | − | 0.988657i | \(-0.547988\pi\) | ||||
−0.150189 | + | 0.988657i | \(0.547988\pi\) | |||||||
\(878\) | 89.9345 | 3.03514 | ||||||||
\(879\) | −47.1462 | −1.59020 | ||||||||
\(880\) | 63.5930 | 2.14372 | ||||||||
\(881\) | 19.2090 | 0.647168 | 0.323584 | − | 0.946200i | \(-0.395112\pi\) | ||||
0.323584 | + | 0.946200i | \(0.395112\pi\) | |||||||
\(882\) | −15.6599 | −0.527296 | ||||||||
\(883\) | −26.1960 | −0.881567 | −0.440783 | − | 0.897613i | \(-0.645299\pi\) | ||||
−0.440783 | + | 0.897613i | \(0.645299\pi\) | |||||||
\(884\) | −32.4915 | −1.09281 | ||||||||
\(885\) | −3.05438 | −0.102672 | ||||||||
\(886\) | −0.127794 | −0.00429332 | ||||||||
\(887\) | −16.2576 | −0.545876 | −0.272938 | − | 0.962032i | \(-0.587995\pi\) | ||||
−0.272938 | + | 0.962032i | \(0.587995\pi\) | |||||||
\(888\) | −173.253 | −5.81398 | ||||||||
\(889\) | −40.4447 | −1.35647 | ||||||||
\(890\) | 2.54623 | 0.0853499 | ||||||||
\(891\) | −42.2171 | −1.41433 | ||||||||
\(892\) | 126.931 | 4.24997 | ||||||||
\(893\) | 8.05742 | 0.269631 | ||||||||
\(894\) | 33.0093 | 1.10400 | ||||||||
\(895\) | 14.8822 | 0.497459 | ||||||||
\(896\) | 10.7766 | 0.360022 | ||||||||
\(897\) | 10.7485 | 0.358882 | ||||||||
\(898\) | 4.99355 | 0.166637 | ||||||||
\(899\) | 1.76670 | 0.0589226 | ||||||||
\(900\) | −15.0039 | −0.500129 | ||||||||
\(901\) | 6.85706 | 0.228442 | ||||||||
\(902\) | −6.16999 | −0.205438 | ||||||||
\(903\) | −46.9728 | −1.56316 | ||||||||
\(904\) | −10.6053 | −0.352728 | ||||||||
\(905\) | −13.4513 | −0.447137 | ||||||||
\(906\) | −50.0608 | −1.66316 | ||||||||
\(907\) | −22.1068 | −0.734043 | −0.367022 | − | 0.930212i | \(-0.619623\pi\) | ||||
−0.367022 | + | 0.930212i | \(0.619623\pi\) | |||||||
\(908\) | −22.7269 | −0.754218 | ||||||||
\(909\) | 20.4437 | 0.678074 | ||||||||
\(910\) | −14.6803 | −0.486649 | ||||||||
\(911\) | −4.77016 | −0.158043 | −0.0790213 | − | 0.996873i | \(-0.525180\pi\) | ||||
−0.0790213 | + | 0.996873i | \(0.525180\pi\) | |||||||
\(912\) | 38.7320 | 1.28254 | ||||||||
\(913\) | −12.4327 | −0.411464 | ||||||||
\(914\) | 33.6913 | 1.11441 | ||||||||
\(915\) | 5.53010 | 0.182820 | ||||||||
\(916\) | −131.766 | −4.35366 | ||||||||
\(917\) | 4.51890 | 0.149227 | ||||||||
\(918\) | −59.8324 | −1.97476 | ||||||||
\(919\) | −32.1812 | −1.06156 | −0.530781 | − | 0.847509i | \(-0.678101\pi\) | ||||
−0.530781 | + | 0.847509i | \(0.678101\pi\) | |||||||
\(920\) | −64.9760 | −2.14220 | ||||||||
\(921\) | 1.58467 | 0.0522165 | ||||||||
\(922\) | 97.1718 | 3.20018 | ||||||||
\(923\) | −3.28850 | −0.108242 | ||||||||
\(924\) | 129.852 | 4.27181 | ||||||||
\(925\) | 24.6410 | 0.810192 | ||||||||
\(926\) | −17.2696 | −0.567515 | ||||||||
\(927\) | −9.87341 | −0.324285 | ||||||||
\(928\) | −6.00154 | −0.197010 | ||||||||
\(929\) | −38.1206 | −1.25070 | −0.625348 | − | 0.780346i | \(-0.715043\pi\) | ||||
−0.625348 | + | 0.780346i | \(0.715043\pi\) | |||||||
\(930\) | 30.9929 | 1.01630 | ||||||||
\(931\) | −7.99950 | −0.262173 | ||||||||
\(932\) | −135.574 | −4.44088 | ||||||||
\(933\) | 8.07987 | 0.264523 | ||||||||
\(934\) | −79.0792 | −2.58755 | ||||||||
\(935\) | 41.2412 | 1.34873 | ||||||||
\(936\) | 10.3154 | 0.337171 | ||||||||
\(937\) | 0.514006 | 0.0167918 | 0.00839592 | − | 0.999965i | \(-0.497327\pi\) | ||||
0.00839592 | + | 0.999965i | \(0.497327\pi\) | |||||||
\(938\) | 24.2817 | 0.792826 | ||||||||
\(939\) | 19.1834 | 0.626027 | ||||||||
\(940\) | −35.9837 | −1.17366 | ||||||||
\(941\) | −34.1679 | −1.11384 | −0.556921 | − | 0.830565i | \(-0.688017\pi\) | ||||
−0.556921 | + | 0.830565i | \(0.688017\pi\) | |||||||
\(942\) | −20.9879 | −0.683822 | ||||||||
\(943\) | 3.21798 | 0.104792 | ||||||||
\(944\) | 9.04299 | 0.294324 | ||||||||
\(945\) | −19.1994 | −0.624557 | ||||||||
\(946\) | 65.8465 | 2.14085 | ||||||||
\(947\) | −24.7445 | −0.804087 | −0.402043 | − | 0.915621i | \(-0.631700\pi\) | ||||
−0.402043 | + | 0.915621i | \(0.631700\pi\) | |||||||
\(948\) | −89.3987 | −2.90353 | ||||||||
\(949\) | 9.02450 | 0.292948 | ||||||||
\(950\) | −10.7917 | −0.350130 | ||||||||
\(951\) | −61.0805 | −1.98067 | ||||||||
\(952\) | 170.639 | 5.53044 | ||||||||
\(953\) | −35.4480 | −1.14827 | −0.574136 | − | 0.818760i | \(-0.694662\pi\) | ||||
−0.574136 | + | 0.818760i | \(0.694662\pi\) | |||||||
\(954\) | −3.67758 | −0.119066 | ||||||||
\(955\) | −39.2906 | −1.27141 | ||||||||
\(956\) | −28.3841 | −0.918008 | ||||||||
\(957\) | −4.05582 | −0.131106 | ||||||||
\(958\) | −84.6762 | −2.73576 | ||||||||
\(959\) | 43.7791 | 1.41370 | ||||||||
\(960\) | −34.7043 | −1.12008 | ||||||||
\(961\) | −19.3233 | −0.623332 | ||||||||
\(962\) | −28.6187 | −0.922704 | ||||||||
\(963\) | −14.6580 | −0.472349 | ||||||||
\(964\) | 84.9974 | 2.73758 | ||||||||
\(965\) | 10.8140 | 0.348116 | ||||||||
\(966\) | −95.3592 | −3.06813 | ||||||||
\(967\) | −31.1278 | −1.00100 | −0.500502 | − | 0.865736i | \(-0.666851\pi\) | ||||
−0.500502 | + | 0.865736i | \(0.666851\pi\) | |||||||
\(968\) | −23.9061 | −0.768370 | ||||||||
\(969\) | 25.1184 | 0.806919 | ||||||||
\(970\) | 2.63425 | 0.0845808 | ||||||||
\(971\) | −13.3557 | −0.428605 | −0.214303 | − | 0.976767i | \(-0.568748\pi\) | ||||
−0.214303 | + | 0.976767i | \(0.568748\pi\) | |||||||
\(972\) | 64.3098 | 2.06274 | ||||||||
\(973\) | −4.09480 | −0.131273 | ||||||||
\(974\) | −80.2276 | −2.57066 | ||||||||
\(975\) | −4.71943 | −0.151143 | ||||||||
\(976\) | −16.3728 | −0.524079 | ||||||||
\(977\) | 30.8552 | 0.987145 | 0.493572 | − | 0.869705i | \(-0.335691\pi\) | ||||
0.493572 | + | 0.869705i | \(0.335691\pi\) | |||||||
\(978\) | −44.7312 | −1.43035 | ||||||||
\(979\) | −2.20228 | −0.0703851 | ||||||||
\(980\) | 35.7250 | 1.14119 | ||||||||
\(981\) | 2.58296 | 0.0824677 | ||||||||
\(982\) | 44.2355 | 1.41161 | ||||||||
\(983\) | 8.65416 | 0.276025 | 0.138012 | − | 0.990430i | \(-0.455929\pi\) | ||||
0.138012 | + | 0.990430i | \(0.455929\pi\) | |||||||
\(984\) | 9.93453 | 0.316701 | ||||||||
\(985\) | −2.29254 | −0.0730464 | ||||||||
\(986\) | −9.00358 | −0.286732 | ||||||||
\(987\) | −31.2614 | −0.995062 | ||||||||
\(988\) | 8.90160 | 0.283198 | ||||||||
\(989\) | −34.3425 | −1.09203 | ||||||||
\(990\) | −22.1185 | −0.702973 | ||||||||
\(991\) | 18.1441 | 0.576367 | 0.288184 | − | 0.957575i | \(-0.406949\pi\) | ||||
0.288184 | + | 0.957575i | \(0.406949\pi\) | |||||||
\(992\) | −39.6662 | −1.25940 | ||||||||
\(993\) | 50.1916 | 1.59278 | ||||||||
\(994\) | 29.1751 | 0.925377 | ||||||||
\(995\) | 31.2853 | 0.991810 | ||||||||
\(996\) | 33.8171 | 1.07154 | ||||||||
\(997\) | 39.7778 | 1.25977 | 0.629887 | − | 0.776686i | \(-0.283101\pi\) | ||||
0.629887 | + | 0.776686i | \(0.283101\pi\) | |||||||
\(998\) | 72.9158 | 2.30811 | ||||||||
\(999\) | −37.4284 | −1.18418 |
(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 | 8047.2.a.c.1.10 | ✓ | 151 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.c.1.10 | ✓ | 151 | 1.1 | even | 1 | trivial |