Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.08589 | 1.47495 | 0.737474 | − | 0.675375i | \(-0.236018\pi\) | ||||
0.737474 | + | 0.675375i | \(0.236018\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 2.35095 | 1.17547 | ||||||||
\(5\) | 0.140268 | 0.0627299 | 0.0313649 | − | 0.999508i | \(-0.490015\pi\) | ||||
0.0313649 | + | 0.999508i | \(0.490015\pi\) | |||||||
\(6\) | −2.08589 | −0.851562 | ||||||||
\(7\) | 1.76887 | 0.668569 | 0.334285 | − | 0.942472i | \(-0.391505\pi\) | ||||
0.334285 | + | 0.942472i | \(0.391505\pi\) | |||||||
\(8\) | 0.732041 | 0.258816 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.292585 | 0.0925234 | ||||||||
\(11\) | −2.44783 | −0.738048 | −0.369024 | − | 0.929420i | \(-0.620308\pi\) | ||||
−0.369024 | + | 0.929420i | \(0.620308\pi\) | |||||||
\(12\) | −2.35095 | −0.678660 | ||||||||
\(13\) | 1.47150 | 0.408120 | 0.204060 | − | 0.978958i | \(-0.434586\pi\) | ||||
0.204060 | + | 0.978958i | \(0.434586\pi\) | |||||||
\(14\) | 3.68967 | 0.986105 | ||||||||
\(15\) | −0.140268 | −0.0362171 | ||||||||
\(16\) | −3.17494 | −0.793734 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 2.08589 | 0.491650 | ||||||||
\(19\) | −5.38878 | −1.23627 | −0.618135 | − | 0.786072i | \(-0.712112\pi\) | ||||
−0.618135 | + | 0.786072i | \(0.712112\pi\) | |||||||
\(20\) | 0.329763 | 0.0737374 | ||||||||
\(21\) | −1.76887 | −0.385999 | ||||||||
\(22\) | −5.10591 | −1.08858 | ||||||||
\(23\) | −7.77124 | −1.62042 | −0.810208 | − | 0.586143i | \(-0.800646\pi\) | ||||
−0.810208 | + | 0.586143i | \(0.800646\pi\) | |||||||
\(24\) | −0.732041 | −0.149427 | ||||||||
\(25\) | −4.98032 | −0.996065 | ||||||||
\(26\) | 3.06938 | 0.601956 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.15852 | 0.785886 | ||||||||
\(29\) | −5.37989 | −0.999020 | −0.499510 | − | 0.866308i | \(-0.666487\pi\) | ||||
−0.499510 | + | 0.866308i | \(0.666487\pi\) | |||||||
\(30\) | −0.292585 | −0.0534184 | ||||||||
\(31\) | 2.36220 | 0.424264 | 0.212132 | − | 0.977241i | \(-0.431959\pi\) | ||||
0.212132 | + | 0.977241i | \(0.431959\pi\) | |||||||
\(32\) | −8.08666 | −1.42953 | ||||||||
\(33\) | 2.44783 | 0.426112 | ||||||||
\(34\) | −2.08589 | −0.357728 | ||||||||
\(35\) | 0.248116 | 0.0419393 | ||||||||
\(36\) | 2.35095 | 0.391825 | ||||||||
\(37\) | 1.32119 | 0.217202 | 0.108601 | − | 0.994085i | \(-0.465363\pi\) | ||||
0.108601 | + | 0.994085i | \(0.465363\pi\) | |||||||
\(38\) | −11.2404 | −1.82344 | ||||||||
\(39\) | −1.47150 | −0.235628 | ||||||||
\(40\) | 0.102682 | 0.0162355 | ||||||||
\(41\) | 3.53576 | 0.552194 | 0.276097 | − | 0.961130i | \(-0.410959\pi\) | ||||
0.276097 | + | 0.961130i | \(0.410959\pi\) | |||||||
\(42\) | −3.68967 | −0.569328 | ||||||||
\(43\) | −4.67768 | −0.713340 | −0.356670 | − | 0.934230i | \(-0.616088\pi\) | ||||
−0.356670 | + | 0.934230i | \(0.616088\pi\) | |||||||
\(44\) | −5.75472 | −0.867557 | ||||||||
\(45\) | 0.140268 | 0.0209100 | ||||||||
\(46\) | −16.2100 | −2.39003 | ||||||||
\(47\) | 11.1381 | 1.62466 | 0.812328 | − | 0.583201i | \(-0.198200\pi\) | ||||
0.812328 | + | 0.583201i | \(0.198200\pi\) | |||||||
\(48\) | 3.17494 | 0.458263 | ||||||||
\(49\) | −3.87111 | −0.553015 | ||||||||
\(50\) | −10.3884 | −1.46914 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 3.45941 | 0.479734 | ||||||||
\(53\) | −0.209911 | −0.0288334 | −0.0144167 | − | 0.999896i | \(-0.504589\pi\) | ||||
−0.0144167 | + | 0.999896i | \(0.504589\pi\) | |||||||
\(54\) | −2.08589 | −0.283854 | ||||||||
\(55\) | −0.343353 | −0.0462977 | ||||||||
\(56\) | 1.29488 | 0.173036 | ||||||||
\(57\) | 5.38878 | 0.713761 | ||||||||
\(58\) | −11.2219 | −1.47350 | ||||||||
\(59\) | 9.96744 | 1.29765 | 0.648825 | − | 0.760938i | \(-0.275261\pi\) | ||||
0.648825 | + | 0.760938i | \(0.275261\pi\) | |||||||
\(60\) | −0.329763 | −0.0425723 | ||||||||
\(61\) | 1.71172 | 0.219163 | 0.109581 | − | 0.993978i | \(-0.465049\pi\) | ||||
0.109581 | + | 0.993978i | \(0.465049\pi\) | |||||||
\(62\) | 4.92729 | 0.625767 | ||||||||
\(63\) | 1.76887 | 0.222856 | ||||||||
\(64\) | −10.5180 | −1.31475 | ||||||||
\(65\) | 0.206404 | 0.0256013 | ||||||||
\(66\) | 5.10591 | 0.628494 | ||||||||
\(67\) | −9.81778 | −1.19943 | −0.599716 | − | 0.800213i | \(-0.704720\pi\) | ||||
−0.599716 | + | 0.800213i | \(0.704720\pi\) | |||||||
\(68\) | −2.35095 | −0.285094 | ||||||||
\(69\) | 7.77124 | 0.935548 | ||||||||
\(70\) | 0.517543 | 0.0618583 | ||||||||
\(71\) | 3.49626 | 0.414929 | 0.207465 | − | 0.978243i | \(-0.433479\pi\) | ||||
0.207465 | + | 0.978243i | \(0.433479\pi\) | |||||||
\(72\) | 0.732041 | 0.0862719 | ||||||||
\(73\) | 5.72483 | 0.670040 | 0.335020 | − | 0.942211i | \(-0.391257\pi\) | ||||
0.335020 | + | 0.942211i | \(0.391257\pi\) | |||||||
\(74\) | 2.75585 | 0.320361 | ||||||||
\(75\) | 4.98032 | 0.575078 | ||||||||
\(76\) | −12.6687 | −1.45320 | ||||||||
\(77\) | −4.32989 | −0.493436 | ||||||||
\(78\) | −3.06938 | −0.347539 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | −0.445343 | −0.0497909 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.37522 | 0.814457 | ||||||||
\(83\) | −17.4586 | −1.91633 | −0.958165 | − | 0.286217i | \(-0.907602\pi\) | ||||
−0.958165 | + | 0.286217i | \(0.907602\pi\) | |||||||
\(84\) | −4.15852 | −0.453731 | ||||||||
\(85\) | −0.140268 | −0.0152142 | ||||||||
\(86\) | −9.75714 | −1.05214 | ||||||||
\(87\) | 5.37989 | 0.576785 | ||||||||
\(88\) | −1.79191 | −0.191018 | ||||||||
\(89\) | 5.07693 | 0.538154 | 0.269077 | − | 0.963119i | \(-0.413281\pi\) | ||||
0.269077 | + | 0.963119i | \(0.413281\pi\) | |||||||
\(90\) | 0.292585 | 0.0308411 | ||||||||
\(91\) | 2.60288 | 0.272856 | ||||||||
\(92\) | −18.2698 | −1.90476 | ||||||||
\(93\) | −2.36220 | −0.244949 | ||||||||
\(94\) | 23.2328 | 2.39628 | ||||||||
\(95\) | −0.755874 | −0.0775511 | ||||||||
\(96\) | 8.08666 | 0.825342 | ||||||||
\(97\) | −9.54399 | −0.969045 | −0.484523 | − | 0.874779i | \(-0.661007\pi\) | ||||
−0.484523 | + | 0.874779i | \(0.661007\pi\) | |||||||
\(98\) | −8.07472 | −0.815669 | ||||||||
\(99\) | −2.44783 | −0.246016 | ||||||||
\(100\) | −11.7085 | −1.17085 | ||||||||
\(101\) | −2.06114 | −0.205091 | −0.102545 | − | 0.994728i | \(-0.532699\pi\) | ||||
−0.102545 | + | 0.994728i | \(0.532699\pi\) | |||||||
\(102\) | 2.08589 | 0.206534 | ||||||||
\(103\) | −5.73622 | −0.565207 | −0.282603 | − | 0.959237i | \(-0.591198\pi\) | ||||
−0.282603 | + | 0.959237i | \(0.591198\pi\) | |||||||
\(104\) | 1.07720 | 0.105628 | ||||||||
\(105\) | −0.248116 | −0.0242136 | ||||||||
\(106\) | −0.437851 | −0.0425278 | ||||||||
\(107\) | −12.4941 | −1.20785 | −0.603925 | − | 0.797041i | \(-0.706398\pi\) | ||||
−0.603925 | + | 0.797041i | \(0.706398\pi\) | |||||||
\(108\) | −2.35095 | −0.226220 | ||||||||
\(109\) | −6.84570 | −0.655699 | −0.327850 | − | 0.944730i | \(-0.606324\pi\) | ||||
−0.327850 | + | 0.944730i | \(0.606324\pi\) | |||||||
\(110\) | −0.716197 | −0.0682867 | ||||||||
\(111\) | −1.32119 | −0.125401 | ||||||||
\(112\) | −5.61604 | −0.530666 | ||||||||
\(113\) | 14.0784 | 1.32439 | 0.662194 | − | 0.749332i | \(-0.269625\pi\) | ||||
0.662194 | + | 0.749332i | \(0.269625\pi\) | |||||||
\(114\) | 11.2404 | 1.05276 | ||||||||
\(115\) | −1.09006 | −0.101648 | ||||||||
\(116\) | −12.6478 | −1.17432 | ||||||||
\(117\) | 1.47150 | 0.136040 | ||||||||
\(118\) | 20.7910 | 1.91397 | ||||||||
\(119\) | −1.76887 | −0.162152 | ||||||||
\(120\) | −0.102682 | −0.00937355 | ||||||||
\(121\) | −5.00813 | −0.455285 | ||||||||
\(122\) | 3.57046 | 0.323254 | ||||||||
\(123\) | −3.53576 | −0.318809 | ||||||||
\(124\) | 5.55341 | 0.498711 | ||||||||
\(125\) | −1.39992 | −0.125213 | ||||||||
\(126\) | 3.68967 | 0.328702 | ||||||||
\(127\) | 19.6610 | 1.74463 | 0.872316 | − | 0.488943i | \(-0.162617\pi\) | ||||
0.872316 | + | 0.488943i | \(0.162617\pi\) | |||||||
\(128\) | −5.76617 | −0.509662 | ||||||||
\(129\) | 4.67768 | 0.411847 | ||||||||
\(130\) | 0.430537 | 0.0377606 | ||||||||
\(131\) | 8.36193 | 0.730586 | 0.365293 | − | 0.930893i | \(-0.380969\pi\) | ||||
0.365293 | + | 0.930893i | \(0.380969\pi\) | |||||||
\(132\) | 5.75472 | 0.500884 | ||||||||
\(133\) | −9.53203 | −0.826532 | ||||||||
\(134\) | −20.4788 | −1.76910 | ||||||||
\(135\) | −0.140268 | −0.0120724 | ||||||||
\(136\) | −0.732041 | −0.0627720 | ||||||||
\(137\) | 15.8738 | 1.35619 | 0.678093 | − | 0.734976i | \(-0.262806\pi\) | ||||
0.678093 | + | 0.734976i | \(0.262806\pi\) | |||||||
\(138\) | 16.2100 | 1.37988 | ||||||||
\(139\) | −18.7464 | −1.59005 | −0.795026 | − | 0.606575i | \(-0.792543\pi\) | ||||
−0.795026 | + | 0.606575i | \(0.792543\pi\) | |||||||
\(140\) | 0.583308 | 0.0492985 | ||||||||
\(141\) | −11.1381 | −0.937996 | ||||||||
\(142\) | 7.29282 | 0.611999 | ||||||||
\(143\) | −3.60197 | −0.301212 | ||||||||
\(144\) | −3.17494 | −0.264578 | ||||||||
\(145\) | −0.754628 | −0.0626684 | ||||||||
\(146\) | 11.9414 | 0.988275 | ||||||||
\(147\) | 3.87111 | 0.319284 | ||||||||
\(148\) | 3.10604 | 0.255315 | ||||||||
\(149\) | −10.7818 | −0.883277 | −0.441638 | − | 0.897193i | \(-0.645603\pi\) | ||||
−0.441638 | + | 0.897193i | \(0.645603\pi\) | |||||||
\(150\) | 10.3884 | 0.848211 | ||||||||
\(151\) | −18.4500 | −1.50144 | −0.750720 | − | 0.660621i | \(-0.770293\pi\) | ||||
−0.750720 | + | 0.660621i | \(0.770293\pi\) | |||||||
\(152\) | −3.94481 | −0.319966 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −9.03168 | −0.727793 | ||||||||
\(155\) | 0.331342 | 0.0266140 | ||||||||
\(156\) | −3.45941 | −0.276975 | ||||||||
\(157\) | −15.5799 | −1.24341 | −0.621706 | − | 0.783251i | \(-0.713560\pi\) | ||||
−0.621706 | + | 0.783251i | \(0.713560\pi\) | |||||||
\(158\) | −2.08589 | −0.165945 | ||||||||
\(159\) | 0.209911 | 0.0166470 | ||||||||
\(160\) | −1.13430 | −0.0896745 | ||||||||
\(161\) | −13.7463 | −1.08336 | ||||||||
\(162\) | 2.08589 | 0.163883 | ||||||||
\(163\) | −14.5802 | −1.14201 | −0.571006 | − | 0.820946i | \(-0.693447\pi\) | ||||
−0.571006 | + | 0.820946i | \(0.693447\pi\) | |||||||
\(164\) | 8.31240 | 0.649089 | ||||||||
\(165\) | 0.343353 | 0.0267300 | ||||||||
\(166\) | −36.4168 | −2.82649 | ||||||||
\(167\) | 7.87714 | 0.609551 | 0.304776 | − | 0.952424i | \(-0.401419\pi\) | ||||
0.304776 | + | 0.952424i | \(0.401419\pi\) | |||||||
\(168\) | −1.29488 | −0.0999025 | ||||||||
\(169\) | −10.8347 | −0.833438 | ||||||||
\(170\) | −0.292585 | −0.0224402 | ||||||||
\(171\) | −5.38878 | −0.412090 | ||||||||
\(172\) | −10.9970 | −0.838513 | ||||||||
\(173\) | 2.59830 | 0.197545 | 0.0987726 | − | 0.995110i | \(-0.468508\pi\) | ||||
0.0987726 | + | 0.995110i | \(0.468508\pi\) | |||||||
\(174\) | 11.2219 | 0.850728 | ||||||||
\(175\) | −8.80953 | −0.665938 | ||||||||
\(176\) | 7.77171 | 0.585814 | ||||||||
\(177\) | −9.96744 | −0.749198 | ||||||||
\(178\) | 10.5899 | 0.793749 | ||||||||
\(179\) | 6.06085 | 0.453009 | 0.226504 | − | 0.974010i | \(-0.427270\pi\) | ||||
0.226504 | + | 0.974010i | \(0.427270\pi\) | |||||||
\(180\) | 0.329763 | 0.0245791 | ||||||||
\(181\) | 1.82586 | 0.135715 | 0.0678574 | − | 0.997695i | \(-0.478384\pi\) | ||||
0.0678574 | + | 0.997695i | \(0.478384\pi\) | |||||||
\(182\) | 5.42933 | 0.402449 | ||||||||
\(183\) | −1.71172 | −0.126534 | ||||||||
\(184\) | −5.68887 | −0.419389 | ||||||||
\(185\) | 0.185320 | 0.0136250 | ||||||||
\(186\) | −4.92729 | −0.361287 | ||||||||
\(187\) | 2.44783 | 0.179003 | ||||||||
\(188\) | 26.1851 | 1.90974 | ||||||||
\(189\) | −1.76887 | −0.128666 | ||||||||
\(190\) | −1.57667 | −0.114384 | ||||||||
\(191\) | −3.46885 | −0.250997 | −0.125499 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125499 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(192\) | 10.5180 | 0.759074 | ||||||||
\(193\) | 26.3873 | 1.89940 | 0.949699 | − | 0.313165i | \(-0.101389\pi\) | ||||
0.949699 | + | 0.313165i | \(0.101389\pi\) | |||||||
\(194\) | −19.9077 | −1.42929 | ||||||||
\(195\) | −0.206404 | −0.0147809 | ||||||||
\(196\) | −9.10078 | −0.650055 | ||||||||
\(197\) | 18.7104 | 1.33306 | 0.666531 | − | 0.745477i | \(-0.267778\pi\) | ||||
0.666531 | + | 0.745477i | \(0.267778\pi\) | |||||||
\(198\) | −5.10591 | −0.362861 | ||||||||
\(199\) | −26.0633 | −1.84758 | −0.923790 | − | 0.382899i | \(-0.874926\pi\) | ||||
−0.923790 | + | 0.382899i | \(0.874926\pi\) | |||||||
\(200\) | −3.64580 | −0.257797 | ||||||||
\(201\) | 9.81778 | 0.692493 | ||||||||
\(202\) | −4.29931 | −0.302498 | ||||||||
\(203\) | −9.51631 | −0.667914 | ||||||||
\(204\) | 2.35095 | 0.164599 | ||||||||
\(205\) | 0.495955 | 0.0346390 | ||||||||
\(206\) | −11.9651 | −0.833651 | ||||||||
\(207\) | −7.77124 | −0.540139 | ||||||||
\(208\) | −4.67191 | −0.323939 | ||||||||
\(209\) | 13.1908 | 0.912427 | ||||||||
\(210\) | −0.517543 | −0.0357139 | ||||||||
\(211\) | 20.8950 | 1.43847 | 0.719235 | − | 0.694767i | \(-0.244493\pi\) | ||||
0.719235 | + | 0.694767i | \(0.244493\pi\) | |||||||
\(212\) | −0.493489 | −0.0338930 | ||||||||
\(213\) | −3.49626 | −0.239560 | ||||||||
\(214\) | −26.0614 | −1.78152 | ||||||||
\(215\) | −0.656130 | −0.0447477 | ||||||||
\(216\) | −0.732041 | −0.0498091 | ||||||||
\(217\) | 4.17842 | 0.283649 | ||||||||
\(218\) | −14.2794 | −0.967123 | ||||||||
\(219\) | −5.72483 | −0.386848 | ||||||||
\(220\) | −0.807205 | −0.0544217 | ||||||||
\(221\) | −1.47150 | −0.0989836 | ||||||||
\(222\) | −2.75585 | −0.184961 | ||||||||
\(223\) | −6.89174 | −0.461505 | −0.230753 | − | 0.973012i | \(-0.574119\pi\) | ||||
−0.230753 | + | 0.973012i | \(0.574119\pi\) | |||||||
\(224\) | −14.3042 | −0.955742 | ||||||||
\(225\) | −4.98032 | −0.332022 | ||||||||
\(226\) | 29.3661 | 1.95341 | ||||||||
\(227\) | −16.4113 | −1.08925 | −0.544627 | − | 0.838679i | \(-0.683329\pi\) | ||||
−0.544627 | + | 0.838679i | \(0.683329\pi\) | |||||||
\(228\) | 12.6687 | 0.839008 | ||||||||
\(229\) | −15.9846 | −1.05629 | −0.528146 | − | 0.849153i | \(-0.677113\pi\) | ||||
−0.528146 | + | 0.849153i | \(0.677113\pi\) | |||||||
\(230\) | −2.27375 | −0.149926 | ||||||||
\(231\) | 4.32989 | 0.284886 | ||||||||
\(232\) | −3.93830 | −0.258562 | ||||||||
\(233\) | 6.04582 | 0.396075 | 0.198037 | − | 0.980194i | \(-0.436543\pi\) | ||||
0.198037 | + | 0.980194i | \(0.436543\pi\) | |||||||
\(234\) | 3.06938 | 0.200652 | ||||||||
\(235\) | 1.56232 | 0.101914 | ||||||||
\(236\) | 23.4329 | 1.52535 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | −3.68967 | −0.239166 | ||||||||
\(239\) | −10.6450 | −0.688568 | −0.344284 | − | 0.938866i | \(-0.611878\pi\) | ||||
−0.344284 | + | 0.938866i | \(0.611878\pi\) | |||||||
\(240\) | 0.445343 | 0.0287468 | ||||||||
\(241\) | 2.95261 | 0.190195 | 0.0950973 | − | 0.995468i | \(-0.469684\pi\) | ||||
0.0950973 | + | 0.995468i | \(0.469684\pi\) | |||||||
\(242\) | −10.4464 | −0.671521 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.02416 | 0.257620 | ||||||||
\(245\) | −0.542994 | −0.0346906 | ||||||||
\(246\) | −7.37522 | −0.470227 | ||||||||
\(247\) | −7.92957 | −0.504546 | ||||||||
\(248\) | 1.72923 | 0.109806 | ||||||||
\(249\) | 17.4586 | 1.10639 | ||||||||
\(250\) | −2.92009 | −0.184683 | ||||||||
\(251\) | 15.6584 | 0.988349 | 0.494174 | − | 0.869363i | \(-0.335470\pi\) | ||||
0.494174 | + | 0.869363i | \(0.335470\pi\) | |||||||
\(252\) | 4.15852 | 0.261962 | ||||||||
\(253\) | 19.0227 | 1.19595 | ||||||||
\(254\) | 41.0107 | 2.57324 | ||||||||
\(255\) | 0.140268 | 0.00878394 | ||||||||
\(256\) | 9.00846 | 0.563029 | ||||||||
\(257\) | −22.2563 | −1.38831 | −0.694155 | − | 0.719825i | \(-0.744222\pi\) | ||||
−0.694155 | + | 0.719825i | \(0.744222\pi\) | |||||||
\(258\) | 9.75714 | 0.607453 | ||||||||
\(259\) | 2.33700 | 0.145214 | ||||||||
\(260\) | 0.485246 | 0.0300937 | ||||||||
\(261\) | −5.37989 | −0.333007 | ||||||||
\(262\) | 17.4421 | 1.07758 | ||||||||
\(263\) | 3.39626 | 0.209422 | 0.104711 | − | 0.994503i | \(-0.466608\pi\) | ||||
0.104711 | + | 0.994503i | \(0.466608\pi\) | |||||||
\(264\) | 1.79191 | 0.110285 | ||||||||
\(265\) | −0.0294438 | −0.00180872 | ||||||||
\(266\) | −19.8828 | −1.21909 | ||||||||
\(267\) | −5.07693 | −0.310703 | ||||||||
\(268\) | −23.0811 | −1.40990 | ||||||||
\(269\) | 20.1378 | 1.22783 | 0.613913 | − | 0.789374i | \(-0.289594\pi\) | ||||
0.613913 | + | 0.789374i | \(0.289594\pi\) | |||||||
\(270\) | −0.292585 | −0.0178061 | ||||||||
\(271\) | 27.4628 | 1.66825 | 0.834125 | − | 0.551576i | \(-0.185973\pi\) | ||||
0.834125 | + | 0.551576i | \(0.185973\pi\) | |||||||
\(272\) | 3.17494 | 0.192509 | ||||||||
\(273\) | −2.60288 | −0.157534 | ||||||||
\(274\) | 33.1110 | 2.00031 | ||||||||
\(275\) | 12.1910 | 0.735144 | ||||||||
\(276\) | 18.2698 | 1.09971 | ||||||||
\(277\) | −22.0555 | −1.32519 | −0.662593 | − | 0.748980i | \(-0.730544\pi\) | ||||
−0.662593 | + | 0.748980i | \(0.730544\pi\) | |||||||
\(278\) | −39.1031 | −2.34525 | ||||||||
\(279\) | 2.36220 | 0.141421 | ||||||||
\(280\) | 0.181631 | 0.0108545 | ||||||||
\(281\) | 18.0037 | 1.07401 | 0.537004 | − | 0.843579i | \(-0.319556\pi\) | ||||
0.537004 | + | 0.843579i | \(0.319556\pi\) | |||||||
\(282\) | −23.2328 | −1.38350 | ||||||||
\(283\) | 19.1507 | 1.13839 | 0.569196 | − | 0.822202i | \(-0.307255\pi\) | ||||
0.569196 | + | 0.822202i | \(0.307255\pi\) | |||||||
\(284\) | 8.21952 | 0.487739 | ||||||||
\(285\) | 0.755874 | 0.0447741 | ||||||||
\(286\) | −7.51333 | −0.444273 | ||||||||
\(287\) | 6.25430 | 0.369180 | ||||||||
\(288\) | −8.08666 | −0.476511 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.57407 | −0.0924327 | ||||||||
\(291\) | 9.54399 | 0.559479 | ||||||||
\(292\) | 13.4588 | 0.787615 | ||||||||
\(293\) | −9.45058 | −0.552109 | −0.276054 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276054 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(294\) | 8.07472 | 0.470927 | ||||||||
\(295\) | 1.39811 | 0.0814014 | ||||||||
\(296\) | 0.967162 | 0.0562151 | ||||||||
\(297\) | 2.44783 | 0.142037 | ||||||||
\(298\) | −22.4896 | −1.30279 | ||||||||
\(299\) | −11.4354 | −0.661324 | ||||||||
\(300\) | 11.7085 | 0.675990 | ||||||||
\(301\) | −8.27420 | −0.476917 | ||||||||
\(302\) | −38.4847 | −2.21455 | ||||||||
\(303\) | 2.06114 | 0.118409 | ||||||||
\(304\) | 17.1090 | 0.981270 | ||||||||
\(305\) | 0.240100 | 0.0137481 | ||||||||
\(306\) | −2.08589 | −0.119243 | ||||||||
\(307\) | −1.88031 | −0.107315 | −0.0536574 | − | 0.998559i | \(-0.517088\pi\) | ||||
−0.0536574 | + | 0.998559i | \(0.517088\pi\) | |||||||
\(308\) | −10.1793 | −0.580022 | ||||||||
\(309\) | 5.73622 | 0.326322 | ||||||||
\(310\) | 0.691143 | 0.0392543 | ||||||||
\(311\) | 20.9805 | 1.18969 | 0.594847 | − | 0.803839i | \(-0.297213\pi\) | ||||
0.594847 | + | 0.803839i | \(0.297213\pi\) | |||||||
\(312\) | −1.07720 | −0.0609842 | ||||||||
\(313\) | 33.9738 | 1.92031 | 0.960157 | − | 0.279460i | \(-0.0901555\pi\) | ||||
0.960157 | + | 0.279460i | \(0.0901555\pi\) | |||||||
\(314\) | −32.4980 | −1.83397 | ||||||||
\(315\) | 0.248116 | 0.0139798 | ||||||||
\(316\) | −2.35095 | −0.132251 | ||||||||
\(317\) | 18.0211 | 1.01217 | 0.506083 | − | 0.862485i | \(-0.331093\pi\) | ||||
0.506083 | + | 0.862485i | \(0.331093\pi\) | |||||||
\(318\) | 0.437851 | 0.0245535 | ||||||||
\(319\) | 13.1691 | 0.737325 | ||||||||
\(320\) | −1.47535 | −0.0824744 | ||||||||
\(321\) | 12.4941 | 0.697353 | ||||||||
\(322\) | −28.6733 | −1.59790 | ||||||||
\(323\) | 5.38878 | 0.299840 | ||||||||
\(324\) | 2.35095 | 0.130608 | ||||||||
\(325\) | −7.32853 | −0.406514 | ||||||||
\(326\) | −30.4128 | −1.68441 | ||||||||
\(327\) | 6.84570 | 0.378568 | ||||||||
\(328\) | 2.58832 | 0.142916 | ||||||||
\(329\) | 19.7018 | 1.08619 | ||||||||
\(330\) | 0.716197 | 0.0394254 | ||||||||
\(331\) | 18.2450 | 1.00284 | 0.501418 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501418 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(332\) | −41.0443 | −2.25260 | ||||||||
\(333\) | 1.32119 | 0.0724005 | ||||||||
\(334\) | 16.4309 | 0.899057 | ||||||||
\(335\) | −1.37712 | −0.0752403 | ||||||||
\(336\) | 5.61604 | 0.306380 | ||||||||
\(337\) | 18.9468 | 1.03210 | 0.516049 | − | 0.856559i | \(-0.327402\pi\) | ||||
0.516049 | + | 0.856559i | \(0.327402\pi\) | |||||||
\(338\) | −22.6000 | −1.22928 | ||||||||
\(339\) | −14.0784 | −0.764636 | ||||||||
\(340\) | −0.329763 | −0.0178839 | ||||||||
\(341\) | −5.78226 | −0.313127 | ||||||||
\(342\) | −11.2404 | −0.607812 | ||||||||
\(343\) | −19.2295 | −1.03830 | ||||||||
\(344\) | −3.42426 | −0.184624 | ||||||||
\(345\) | 1.09006 | 0.0586868 | ||||||||
\(346\) | 5.41978 | 0.291369 | ||||||||
\(347\) | 28.8043 | 1.54630 | 0.773149 | − | 0.634225i | \(-0.218681\pi\) | ||||
0.773149 | + | 0.634225i | \(0.218681\pi\) | |||||||
\(348\) | 12.6478 | 0.677996 | ||||||||
\(349\) | 26.0275 | 1.39322 | 0.696609 | − | 0.717451i | \(-0.254691\pi\) | ||||
0.696609 | + | 0.717451i | \(0.254691\pi\) | |||||||
\(350\) | −18.3757 | −0.982225 | ||||||||
\(351\) | −1.47150 | −0.0785427 | ||||||||
\(352\) | 19.7948 | 1.05506 | ||||||||
\(353\) | −29.6973 | −1.58063 | −0.790315 | − | 0.612701i | \(-0.790083\pi\) | ||||
−0.790315 | + | 0.612701i | \(0.790083\pi\) | |||||||
\(354\) | −20.7910 | −1.10503 | ||||||||
\(355\) | 0.490414 | 0.0260285 | ||||||||
\(356\) | 11.9356 | 0.632586 | ||||||||
\(357\) | 1.76887 | 0.0936184 | ||||||||
\(358\) | 12.6423 | 0.668165 | ||||||||
\(359\) | −24.1413 | −1.27413 | −0.637064 | − | 0.770811i | \(-0.719852\pi\) | ||||
−0.637064 | + | 0.770811i | \(0.719852\pi\) | |||||||
\(360\) | 0.102682 | 0.00541182 | ||||||||
\(361\) | 10.0389 | 0.528364 | ||||||||
\(362\) | 3.80854 | 0.200172 | ||||||||
\(363\) | 5.00813 | 0.262859 | ||||||||
\(364\) | 6.11924 | 0.320736 | ||||||||
\(365\) | 0.803011 | 0.0420315 | ||||||||
\(366\) | −3.57046 | −0.186631 | ||||||||
\(367\) | −11.1079 | −0.579828 | −0.289914 | − | 0.957053i | \(-0.593627\pi\) | ||||
−0.289914 | + | 0.957053i | \(0.593627\pi\) | |||||||
\(368\) | 24.6732 | 1.28618 | ||||||||
\(369\) | 3.53576 | 0.184065 | ||||||||
\(370\) | 0.386558 | 0.0200962 | ||||||||
\(371\) | −0.371304 | −0.0192771 | ||||||||
\(372\) | −5.55341 | −0.287931 | ||||||||
\(373\) | −33.2434 | −1.72128 | −0.860639 | − | 0.509216i | \(-0.829936\pi\) | ||||
−0.860639 | + | 0.509216i | \(0.829936\pi\) | |||||||
\(374\) | 5.10591 | 0.264020 | ||||||||
\(375\) | 1.39992 | 0.0722917 | ||||||||
\(376\) | 8.15353 | 0.420486 | ||||||||
\(377\) | −7.91649 | −0.407720 | ||||||||
\(378\) | −3.68967 | −0.189776 | ||||||||
\(379\) | −23.2407 | −1.19379 | −0.596897 | − | 0.802318i | \(-0.703600\pi\) | ||||
−0.596897 | + | 0.802318i | \(0.703600\pi\) | |||||||
\(380\) | −1.77702 | −0.0911593 | ||||||||
\(381\) | −19.6610 | −1.00726 | ||||||||
\(382\) | −7.23565 | −0.370208 | ||||||||
\(383\) | −23.6303 | −1.20745 | −0.603725 | − | 0.797193i | \(-0.706317\pi\) | ||||
−0.603725 | + | 0.797193i | \(0.706317\pi\) | |||||||
\(384\) | 5.76617 | 0.294253 | ||||||||
\(385\) | −0.607346 | −0.0309532 | ||||||||
\(386\) | 55.0410 | 2.80151 | ||||||||
\(387\) | −4.67768 | −0.237780 | ||||||||
\(388\) | −22.4374 | −1.13909 | ||||||||
\(389\) | 14.2837 | 0.724212 | 0.362106 | − | 0.932137i | \(-0.382058\pi\) | ||||
0.362106 | + | 0.932137i | \(0.382058\pi\) | |||||||
\(390\) | −0.430537 | −0.0218011 | ||||||||
\(391\) | 7.77124 | 0.393009 | ||||||||
\(392\) | −2.83381 | −0.143129 | ||||||||
\(393\) | −8.36193 | −0.421804 | ||||||||
\(394\) | 39.0279 | 1.96620 | ||||||||
\(395\) | −0.140268 | −0.00705766 | ||||||||
\(396\) | −5.75472 | −0.289186 | ||||||||
\(397\) | 31.1662 | 1.56419 | 0.782093 | − | 0.623162i | \(-0.214152\pi\) | ||||
0.782093 | + | 0.623162i | \(0.214152\pi\) | |||||||
\(398\) | −54.3653 | −2.72509 | ||||||||
\(399\) | 9.53203 | 0.477199 | ||||||||
\(400\) | 15.8122 | 0.790611 | ||||||||
\(401\) | 6.19151 | 0.309189 | 0.154595 | − | 0.987978i | \(-0.450593\pi\) | ||||
0.154595 | + | 0.987978i | \(0.450593\pi\) | |||||||
\(402\) | 20.4788 | 1.02139 | ||||||||
\(403\) | 3.47597 | 0.173150 | ||||||||
\(404\) | −4.84563 | −0.241079 | ||||||||
\(405\) | 0.140268 | 0.00696999 | ||||||||
\(406\) | −19.8500 | −0.985139 | ||||||||
\(407\) | −3.23404 | −0.160305 | ||||||||
\(408\) | 0.732041 | 0.0362414 | ||||||||
\(409\) | −26.6687 | −1.31868 | −0.659342 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659342 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(410\) | 1.03451 | 0.0510908 | ||||||||
\(411\) | −15.8738 | −0.782995 | ||||||||
\(412\) | −13.4856 | −0.664386 | ||||||||
\(413\) | 17.6311 | 0.867568 | ||||||||
\(414\) | −16.2100 | −0.796677 | ||||||||
\(415\) | −2.44889 | −0.120211 | ||||||||
\(416\) | −11.8995 | −0.583421 | ||||||||
\(417\) | 18.7464 | 0.918017 | ||||||||
\(418\) | 27.5146 | 1.34578 | ||||||||
\(419\) | −4.41752 | −0.215810 | −0.107905 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107905 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(420\) | −0.583308 | −0.0284625 | ||||||||
\(421\) | 0.965972 | 0.0470786 | 0.0235393 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235393 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(422\) | 43.5847 | 2.12167 | ||||||||
\(423\) | 11.1381 | 0.541552 | ||||||||
\(424\) | −0.153663 | −0.00746254 | ||||||||
\(425\) | 4.98032 | 0.241581 | ||||||||
\(426\) | −7.29282 | −0.353338 | ||||||||
\(427\) | 3.02780 | 0.146526 | ||||||||
\(428\) | −29.3730 | −1.41980 | ||||||||
\(429\) | 3.60197 | 0.173905 | ||||||||
\(430\) | −1.36862 | −0.0660006 | ||||||||
\(431\) | 15.1526 | 0.729877 | 0.364939 | − | 0.931032i | \(-0.381090\pi\) | ||||
0.364939 | + | 0.931032i | \(0.381090\pi\) | |||||||
\(432\) | 3.17494 | 0.152754 | ||||||||
\(433\) | −5.53821 | −0.266149 | −0.133075 | − | 0.991106i | \(-0.542485\pi\) | ||||
−0.133075 | + | 0.991106i | \(0.542485\pi\) | |||||||
\(434\) | 8.71573 | 0.418368 | ||||||||
\(435\) | 0.754628 | 0.0361816 | ||||||||
\(436\) | −16.0939 | −0.770758 | ||||||||
\(437\) | 41.8775 | 2.00327 | ||||||||
\(438\) | −11.9414 | −0.570581 | ||||||||
\(439\) | −12.1857 | −0.581592 | −0.290796 | − | 0.956785i | \(-0.593920\pi\) | ||||
−0.290796 | + | 0.956785i | \(0.593920\pi\) | |||||||
\(440\) | −0.251348 | −0.0119826 | ||||||||
\(441\) | −3.87111 | −0.184338 | ||||||||
\(442\) | −3.06938 | −0.145996 | ||||||||
\(443\) | 5.77436 | 0.274348 | 0.137174 | − | 0.990547i | \(-0.456198\pi\) | ||||
0.137174 | + | 0.990547i | \(0.456198\pi\) | |||||||
\(444\) | −3.10604 | −0.147406 | ||||||||
\(445\) | 0.712132 | 0.0337583 | ||||||||
\(446\) | −14.3754 | −0.680697 | ||||||||
\(447\) | 10.7818 | 0.509960 | ||||||||
\(448\) | −18.6050 | −0.879004 | ||||||||
\(449\) | −3.28196 | −0.154885 | −0.0774426 | − | 0.996997i | \(-0.524675\pi\) | ||||
−0.0774426 | + | 0.996997i | \(0.524675\pi\) | |||||||
\(450\) | −10.3884 | −0.489715 | ||||||||
\(451\) | −8.65495 | −0.407546 | ||||||||
\(452\) | 33.0977 | 1.55679 | ||||||||
\(453\) | 18.4500 | 0.866857 | ||||||||
\(454\) | −34.2321 | −1.60659 | ||||||||
\(455\) | 0.365102 | 0.0171162 | ||||||||
\(456\) | 3.94481 | 0.184732 | ||||||||
\(457\) | 34.4508 | 1.61154 | 0.805770 | − | 0.592229i | \(-0.201752\pi\) | ||||
0.805770 | + | 0.592229i | \(0.201752\pi\) | |||||||
\(458\) | −33.3422 | −1.55798 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −2.56267 | −0.119485 | ||||||||
\(461\) | 21.9961 | 1.02446 | 0.512231 | − | 0.858848i | \(-0.328819\pi\) | ||||
0.512231 | + | 0.858848i | \(0.328819\pi\) | |||||||
\(462\) | 9.03168 | 0.420192 | ||||||||
\(463\) | 1.56414 | 0.0726920 | 0.0363460 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363460 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(464\) | 17.0808 | 0.792957 | ||||||||
\(465\) | −0.331342 | −0.0153656 | ||||||||
\(466\) | 12.6109 | 0.584190 | ||||||||
\(467\) | −11.7478 | −0.543622 | −0.271811 | − | 0.962351i | \(-0.587623\pi\) | ||||
−0.271811 | + | 0.962351i | \(0.587623\pi\) | |||||||
\(468\) | 3.45941 | 0.159911 | ||||||||
\(469\) | −17.3664 | −0.801904 | ||||||||
\(470\) | 3.25883 | 0.150319 | ||||||||
\(471\) | 15.5799 | 0.717884 | ||||||||
\(472\) | 7.29657 | 0.335852 | ||||||||
\(473\) | 11.4502 | 0.526479 | ||||||||
\(474\) | 2.08589 | 0.0958082 | ||||||||
\(475\) | 26.8379 | 1.23141 | ||||||||
\(476\) | −4.15852 | −0.190605 | ||||||||
\(477\) | −0.209911 | −0.00961114 | ||||||||
\(478\) | −22.2043 | −1.01560 | ||||||||
\(479\) | −34.6987 | −1.58542 | −0.792711 | − | 0.609597i | \(-0.791331\pi\) | ||||
−0.792711 | + | 0.609597i | \(0.791331\pi\) | |||||||
\(480\) | 1.13430 | 0.0517736 | ||||||||
\(481\) | 1.94412 | 0.0886442 | ||||||||
\(482\) | 6.15884 | 0.280527 | ||||||||
\(483\) | 13.7463 | 0.625478 | ||||||||
\(484\) | −11.7739 | −0.535175 | ||||||||
\(485\) | −1.33872 | −0.0607881 | ||||||||
\(486\) | −2.08589 | −0.0946180 | ||||||||
\(487\) | −18.5027 | −0.838435 | −0.419218 | − | 0.907886i | \(-0.637696\pi\) | ||||
−0.419218 | + | 0.907886i | \(0.637696\pi\) | |||||||
\(488\) | 1.25305 | 0.0567228 | ||||||||
\(489\) | 14.5802 | 0.659341 | ||||||||
\(490\) | −1.13263 | −0.0511668 | ||||||||
\(491\) | −24.0229 | −1.08414 | −0.542069 | − | 0.840334i | \(-0.682359\pi\) | ||||
−0.542069 | + | 0.840334i | \(0.682359\pi\) | |||||||
\(492\) | −8.31240 | −0.374752 | ||||||||
\(493\) | 5.37989 | 0.242298 | ||||||||
\(494\) | −16.5402 | −0.744180 | ||||||||
\(495\) | −0.343353 | −0.0154326 | ||||||||
\(496\) | −7.49984 | −0.336753 | ||||||||
\(497\) | 6.18441 | 0.277409 | ||||||||
\(498\) | 36.4168 | 1.63187 | ||||||||
\(499\) | −2.78339 | −0.124602 | −0.0623008 | − | 0.998057i | \(-0.519844\pi\) | ||||
−0.0623008 | + | 0.998057i | \(0.519844\pi\) | |||||||
\(500\) | −3.29115 | −0.147185 | ||||||||
\(501\) | −7.87714 | −0.351925 | ||||||||
\(502\) | 32.6617 | 1.45776 | ||||||||
\(503\) | −1.15409 | −0.0514585 | −0.0257292 | − | 0.999669i | \(-0.508191\pi\) | ||||
−0.0257292 | + | 0.999669i | \(0.508191\pi\) | |||||||
\(504\) | 1.29488 | 0.0576787 | ||||||||
\(505\) | −0.289112 | −0.0128653 | ||||||||
\(506\) | 39.6793 | 1.76396 | ||||||||
\(507\) | 10.8347 | 0.481186 | ||||||||
\(508\) | 46.2220 | 2.05077 | ||||||||
\(509\) | 4.25435 | 0.188571 | 0.0942853 | − | 0.995545i | \(-0.469943\pi\) | ||||
0.0942853 | + | 0.995545i | \(0.469943\pi\) | |||||||
\(510\) | 0.292585 | 0.0129559 | ||||||||
\(511\) | 10.1265 | 0.447968 | ||||||||
\(512\) | 30.3230 | 1.34010 | ||||||||
\(513\) | 5.38878 | 0.237920 | ||||||||
\(514\) | −46.4243 | −2.04769 | ||||||||
\(515\) | −0.804610 | −0.0354553 | ||||||||
\(516\) | 10.9970 | 0.484116 | ||||||||
\(517\) | −27.2641 | −1.19908 | ||||||||
\(518\) | 4.87473 | 0.214184 | ||||||||
\(519\) | −2.59830 | −0.114053 | ||||||||
\(520\) | 0.151096 | 0.00662602 | ||||||||
\(521\) | −32.4163 | −1.42018 | −0.710091 | − | 0.704110i | \(-0.751346\pi\) | ||||
−0.710091 | + | 0.704110i | \(0.751346\pi\) | |||||||
\(522\) | −11.2219 | −0.491168 | ||||||||
\(523\) | 2.15610 | 0.0942796 | 0.0471398 | − | 0.998888i | \(-0.484989\pi\) | ||||
0.0471398 | + | 0.998888i | \(0.484989\pi\) | |||||||
\(524\) | 19.6585 | 0.858785 | ||||||||
\(525\) | 8.80953 | 0.384480 | ||||||||
\(526\) | 7.08423 | 0.308887 | ||||||||
\(527\) | −2.36220 | −0.102899 | ||||||||
\(528\) | −7.77171 | −0.338220 | ||||||||
\(529\) | 37.3922 | 1.62575 | ||||||||
\(530\) | −0.0614166 | −0.00266777 | ||||||||
\(531\) | 9.96744 | 0.432550 | ||||||||
\(532\) | −22.4093 | −0.971567 | ||||||||
\(533\) | 5.20287 | 0.225361 | ||||||||
\(534\) | −10.5899 | −0.458271 | ||||||||
\(535\) | −1.75253 | −0.0757683 | ||||||||
\(536\) | −7.18702 | −0.310432 | ||||||||
\(537\) | −6.06085 | −0.261545 | ||||||||
\(538\) | 42.0054 | 1.81098 | ||||||||
\(539\) | 9.47581 | 0.408152 | ||||||||
\(540\) | −0.329763 | −0.0141908 | ||||||||
\(541\) | 32.6923 | 1.40555 | 0.702777 | − | 0.711411i | \(-0.251943\pi\) | ||||
0.702777 | + | 0.711411i | \(0.251943\pi\) | |||||||
\(542\) | 57.2846 | 2.46058 | ||||||||
\(543\) | −1.82586 | −0.0783550 | ||||||||
\(544\) | 8.08666 | 0.346713 | ||||||||
\(545\) | −0.960235 | −0.0411319 | ||||||||
\(546\) | −5.42933 | −0.232354 | ||||||||
\(547\) | −28.1774 | −1.20478 | −0.602389 | − | 0.798203i | \(-0.705784\pi\) | ||||
−0.602389 | + | 0.798203i | \(0.705784\pi\) | |||||||
\(548\) | 37.3184 | 1.59416 | ||||||||
\(549\) | 1.71172 | 0.0730543 | ||||||||
\(550\) | 25.4291 | 1.08430 | ||||||||
\(551\) | 28.9910 | 1.23506 | ||||||||
\(552\) | 5.68887 | 0.242134 | ||||||||
\(553\) | −1.76887 | −0.0752199 | ||||||||
\(554\) | −46.0054 | −1.95458 | ||||||||
\(555\) | −0.185320 | −0.00786641 | ||||||||
\(556\) | −44.0719 | −1.86907 | ||||||||
\(557\) | −9.44003 | −0.399987 | −0.199993 | − | 0.979797i | \(-0.564092\pi\) | ||||
−0.199993 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(558\) | 4.92729 | 0.208589 | ||||||||
\(559\) | −6.88319 | −0.291128 | ||||||||
\(560\) | −0.787753 | −0.0332886 | ||||||||
\(561\) | −2.44783 | −0.103347 | ||||||||
\(562\) | 37.5537 | 1.58411 | ||||||||
\(563\) | −41.1339 | −1.73359 | −0.866794 | − | 0.498667i | \(-0.833823\pi\) | ||||
−0.866794 | + | 0.498667i | \(0.833823\pi\) | |||||||
\(564\) | −26.1851 | −1.10259 | ||||||||
\(565\) | 1.97476 | 0.0830787 | ||||||||
\(566\) | 39.9463 | 1.67907 | ||||||||
\(567\) | 1.76887 | 0.0742855 | ||||||||
\(568\) | 2.55940 | 0.107390 | ||||||||
\(569\) | −17.4857 | −0.733037 | −0.366519 | − | 0.930411i | \(-0.619450\pi\) | ||||
−0.366519 | + | 0.930411i | \(0.619450\pi\) | |||||||
\(570\) | 1.57667 | 0.0660396 | ||||||||
\(571\) | 26.7210 | 1.11824 | 0.559120 | − | 0.829087i | \(-0.311139\pi\) | ||||
0.559120 | + | 0.829087i | \(0.311139\pi\) | |||||||
\(572\) | −8.46805 | −0.354067 | ||||||||
\(573\) | 3.46885 | 0.144913 | ||||||||
\(574\) | 13.0458 | 0.544521 | ||||||||
\(575\) | 38.7033 | 1.61404 | ||||||||
\(576\) | −10.5180 | −0.438251 | ||||||||
\(577\) | 36.1461 | 1.50478 | 0.752390 | − | 0.658717i | \(-0.228901\pi\) | ||||
0.752390 | + | 0.658717i | \(0.228901\pi\) | |||||||
\(578\) | 2.08589 | 0.0867617 | ||||||||
\(579\) | −26.3873 | −1.09662 | ||||||||
\(580\) | −1.77409 | −0.0736651 | ||||||||
\(581\) | −30.8819 | −1.28120 | ||||||||
\(582\) | 19.9077 | 0.825202 | ||||||||
\(583\) | 0.513825 | 0.0212805 | ||||||||
\(584\) | 4.19081 | 0.173417 | ||||||||
\(585\) | 0.206404 | 0.00853377 | ||||||||
\(586\) | −19.7129 | −0.814332 | ||||||||
\(587\) | 18.3268 | 0.756428 | 0.378214 | − | 0.925718i | \(-0.376538\pi\) | ||||
0.378214 | + | 0.925718i | \(0.376538\pi\) | |||||||
\(588\) | 9.10078 | 0.375310 | ||||||||
\(589\) | −12.7294 | −0.524504 | ||||||||
\(590\) | 2.91632 | 0.120063 | ||||||||
\(591\) | −18.7104 | −0.769644 | ||||||||
\(592\) | −4.19468 | −0.172400 | ||||||||
\(593\) | −35.0087 | −1.43763 | −0.718817 | − | 0.695200i | \(-0.755316\pi\) | ||||
−0.718817 | + | 0.695200i | \(0.755316\pi\) | |||||||
\(594\) | 5.10591 | 0.209498 | ||||||||
\(595\) | −0.248116 | −0.0101718 | ||||||||
\(596\) | −25.3474 | −1.03827 | ||||||||
\(597\) | 26.0633 | 1.06670 | ||||||||
\(598\) | −23.8529 | −0.975419 | ||||||||
\(599\) | 17.8087 | 0.727644 | 0.363822 | − | 0.931468i | \(-0.381472\pi\) | ||||
0.363822 | + | 0.931468i | \(0.381472\pi\) | |||||||
\(600\) | 3.64580 | 0.148839 | ||||||||
\(601\) | −46.4446 | −1.89451 | −0.947257 | − | 0.320475i | \(-0.896157\pi\) | ||||
−0.947257 | + | 0.320475i | \(0.896157\pi\) | |||||||
\(602\) | −17.2591 | −0.703428 | ||||||||
\(603\) | −9.81778 | −0.399811 | ||||||||
\(604\) | −43.3750 | −1.76490 | ||||||||
\(605\) | −0.702482 | −0.0285599 | ||||||||
\(606\) | 4.29931 | 0.174648 | ||||||||
\(607\) | 24.2122 | 0.982741 | 0.491371 | − | 0.870951i | \(-0.336496\pi\) | ||||
0.491371 | + | 0.870951i | \(0.336496\pi\) | |||||||
\(608\) | 43.5772 | 1.76729 | ||||||||
\(609\) | 9.51631 | 0.385620 | ||||||||
\(610\) | 0.500822 | 0.0202777 | ||||||||
\(611\) | 16.3897 | 0.663054 | ||||||||
\(612\) | −2.35095 | −0.0950315 | ||||||||
\(613\) | −42.9836 | −1.73609 | −0.868045 | − | 0.496485i | \(-0.834624\pi\) | ||||
−0.868045 | + | 0.496485i | \(0.834624\pi\) | |||||||
\(614\) | −3.92212 | −0.158284 | ||||||||
\(615\) | −0.495955 | −0.0199989 | ||||||||
\(616\) | −3.16965 | −0.127709 | ||||||||
\(617\) | −32.1545 | −1.29449 | −0.647247 | − | 0.762281i | \(-0.724080\pi\) | ||||
−0.647247 | + | 0.762281i | \(0.724080\pi\) | |||||||
\(618\) | 11.9651 | 0.481309 | ||||||||
\(619\) | 4.57705 | 0.183967 | 0.0919836 | − | 0.995761i | \(-0.470679\pi\) | ||||
0.0919836 | + | 0.995761i | \(0.470679\pi\) | |||||||
\(620\) | 0.778967 | 0.0312841 | ||||||||
\(621\) | 7.77124 | 0.311849 | ||||||||
\(622\) | 43.7631 | 1.75474 | ||||||||
\(623\) | 8.98042 | 0.359793 | ||||||||
\(624\) | 4.67191 | 0.187026 | ||||||||
\(625\) | 24.7053 | 0.988210 | ||||||||
\(626\) | 70.8658 | 2.83237 | ||||||||
\(627\) | −13.1908 | −0.526790 | ||||||||
\(628\) | −36.6276 | −1.46160 | ||||||||
\(629\) | −1.32119 | −0.0526791 | ||||||||
\(630\) | 0.517543 | 0.0206194 | ||||||||
\(631\) | −12.3671 | −0.492327 | −0.246163 | − | 0.969228i | \(-0.579170\pi\) | ||||
−0.246163 | + | 0.969228i | \(0.579170\pi\) | |||||||
\(632\) | −0.732041 | −0.0291190 | ||||||||
\(633\) | −20.8950 | −0.830501 | ||||||||
\(634\) | 37.5901 | 1.49289 | ||||||||
\(635\) | 2.75781 | 0.109440 | ||||||||
\(636\) | 0.493489 | 0.0195681 | ||||||||
\(637\) | −5.69632 | −0.225697 | ||||||||
\(638\) | 27.4692 | 1.08752 | ||||||||
\(639\) | 3.49626 | 0.138310 | ||||||||
\(640\) | −0.808810 | −0.0319710 | ||||||||
\(641\) | 25.4989 | 1.00715 | 0.503573 | − | 0.863953i | \(-0.332019\pi\) | ||||
0.503573 | + | 0.863953i | \(0.332019\pi\) | |||||||
\(642\) | 26.0614 | 1.02856 | ||||||||
\(643\) | −40.1968 | −1.58521 | −0.792604 | − | 0.609737i | \(-0.791275\pi\) | ||||
−0.792604 | + | 0.609737i | \(0.791275\pi\) | |||||||
\(644\) | −32.3168 | −1.27346 | ||||||||
\(645\) | 0.656130 | 0.0258351 | ||||||||
\(646\) | 11.2404 | 0.442248 | ||||||||
\(647\) | −34.0661 | −1.33928 | −0.669638 | − | 0.742688i | \(-0.733551\pi\) | ||||
−0.669638 | + | 0.742688i | \(0.733551\pi\) | |||||||
\(648\) | 0.732041 | 0.0287573 | ||||||||
\(649\) | −24.3986 | −0.957728 | ||||||||
\(650\) | −15.2865 | −0.599587 | ||||||||
\(651\) | −4.17842 | −0.163765 | ||||||||
\(652\) | −34.2774 | −1.34241 | ||||||||
\(653\) | 3.99738 | 0.156429 | 0.0782147 | − | 0.996937i | \(-0.475078\pi\) | ||||
0.0782147 | + | 0.996937i | \(0.475078\pi\) | |||||||
\(654\) | 14.2794 | 0.558369 | ||||||||
\(655\) | 1.17291 | 0.0458295 | ||||||||
\(656\) | −11.2258 | −0.438295 | ||||||||
\(657\) | 5.72483 | 0.223347 | ||||||||
\(658\) | 41.0958 | 1.60208 | ||||||||
\(659\) | 34.3326 | 1.33741 | 0.668704 | − | 0.743528i | \(-0.266849\pi\) | ||||
0.668704 | + | 0.743528i | \(0.266849\pi\) | |||||||
\(660\) | 0.807205 | 0.0314204 | ||||||||
\(661\) | 12.3659 | 0.480976 | 0.240488 | − | 0.970652i | \(-0.422693\pi\) | ||||
0.240488 | + | 0.970652i | \(0.422693\pi\) | |||||||
\(662\) | 38.0571 | 1.47913 | ||||||||
\(663\) | 1.47150 | 0.0571482 | ||||||||
\(664\) | −12.7804 | −0.495976 | ||||||||
\(665\) | −1.33704 | −0.0518483 | ||||||||
\(666\) | 2.75585 | 0.106787 | ||||||||
\(667\) | 41.8084 | 1.61883 | ||||||||
\(668\) | 18.5187 | 0.716512 | ||||||||
\(669\) | 6.89174 | 0.266450 | ||||||||
\(670\) | −2.87253 | −0.110976 | ||||||||
\(671\) | −4.18999 | −0.161753 | ||||||||
\(672\) | 14.3042 | 0.551798 | ||||||||
\(673\) | −23.5698 | −0.908548 | −0.454274 | − | 0.890862i | \(-0.650101\pi\) | ||||
−0.454274 | + | 0.890862i | \(0.650101\pi\) | |||||||
\(674\) | 39.5210 | 1.52229 | ||||||||
\(675\) | 4.98032 | 0.191693 | ||||||||
\(676\) | −25.4718 | −0.979685 | ||||||||
\(677\) | 0.0626834 | 0.00240912 | 0.00120456 | − | 0.999999i | \(-0.499617\pi\) | ||||
0.00120456 | + | 0.999999i | \(0.499617\pi\) | |||||||
\(678\) | −29.3661 | −1.12780 | ||||||||
\(679\) | −16.8821 | −0.647874 | ||||||||
\(680\) | −0.102682 | −0.00393768 | ||||||||
\(681\) | 16.4113 | 0.628881 | ||||||||
\(682\) | −12.0612 | −0.461846 | ||||||||
\(683\) | −0.157880 | −0.00604111 | −0.00302056 | − | 0.999995i | \(-0.500961\pi\) | ||||
−0.00302056 | + | 0.999995i | \(0.500961\pi\) | |||||||
\(684\) | −12.6687 | −0.484401 | ||||||||
\(685\) | 2.22658 | 0.0850734 | ||||||||
\(686\) | −40.1108 | −1.53144 | ||||||||
\(687\) | 15.9846 | 0.609851 | ||||||||
\(688\) | 14.8514 | 0.566202 | ||||||||
\(689\) | −0.308883 | −0.0117675 | ||||||||
\(690\) | 2.27375 | 0.0865600 | ||||||||
\(691\) | 6.15612 | 0.234190 | 0.117095 | − | 0.993121i | \(-0.462642\pi\) | ||||
0.117095 | + | 0.993121i | \(0.462642\pi\) | |||||||
\(692\) | 6.10847 | 0.232209 | ||||||||
\(693\) | −4.32989 | −0.164479 | ||||||||
\(694\) | 60.0828 | 2.28071 | ||||||||
\(695\) | −2.62953 | −0.0997438 | ||||||||
\(696\) | 3.93830 | 0.149281 | ||||||||
\(697\) | −3.53576 | −0.133927 | ||||||||
\(698\) | 54.2905 | 2.05492 | ||||||||
\(699\) | −6.04582 | −0.228674 | ||||||||
\(700\) | −20.7108 | −0.782793 | ||||||||
\(701\) | −33.1235 | −1.25106 | −0.625529 | − | 0.780201i | \(-0.715117\pi\) | ||||
−0.625529 | + | 0.780201i | \(0.715117\pi\) | |||||||
\(702\) | −3.06938 | −0.115846 | ||||||||
\(703\) | −7.11957 | −0.268520 | ||||||||
\(704\) | 25.7464 | 0.970352 | ||||||||
\(705\) | −1.56232 | −0.0588404 | ||||||||
\(706\) | −61.9454 | −2.33135 | ||||||||
\(707\) | −3.64588 | −0.137117 | ||||||||
\(708\) | −23.4329 | −0.880663 | ||||||||
\(709\) | 5.19852 | 0.195235 | 0.0976173 | − | 0.995224i | \(-0.468878\pi\) | ||||
0.0976173 | + | 0.995224i | \(0.468878\pi\) | |||||||
\(710\) | 1.02295 | 0.0383906 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 3.71652 | 0.139283 | ||||||||
\(713\) | −18.3572 | −0.687483 | ||||||||
\(714\) | 3.68967 | 0.138082 | ||||||||
\(715\) | −0.505243 | −0.0188950 | ||||||||
\(716\) | 14.2487 | 0.532500 | ||||||||
\(717\) | 10.6450 | 0.397545 | ||||||||
\(718\) | −50.3562 | −1.87928 | ||||||||
\(719\) | 12.3466 | 0.460449 | 0.230225 | − | 0.973137i | \(-0.426054\pi\) | ||||
0.230225 | + | 0.973137i | \(0.426054\pi\) | |||||||
\(720\) | −0.445343 | −0.0165970 | ||||||||
\(721\) | −10.1466 | −0.377880 | ||||||||
\(722\) | 20.9401 | 0.779310 | ||||||||
\(723\) | −2.95261 | −0.109809 | ||||||||
\(724\) | 4.29249 | 0.159529 | ||||||||
\(725\) | 26.7936 | 0.995089 | ||||||||
\(726\) | 10.4464 | 0.387703 | ||||||||
\(727\) | −35.7172 | −1.32468 | −0.662339 | − | 0.749204i | \(-0.730436\pi\) | ||||
−0.662339 | + | 0.749204i | \(0.730436\pi\) | |||||||
\(728\) | 1.90542 | 0.0706195 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.67500 | 0.0619944 | ||||||||
\(731\) | 4.67768 | 0.173010 | ||||||||
\(732\) | −4.02416 | −0.148737 | ||||||||
\(733\) | −35.9278 | −1.32702 | −0.663512 | − | 0.748165i | \(-0.730935\pi\) | ||||
−0.663512 | + | 0.748165i | \(0.730935\pi\) | |||||||
\(734\) | −23.1699 | −0.855216 | ||||||||
\(735\) | 0.542994 | 0.0200286 | ||||||||
\(736\) | 62.8434 | 2.31644 | ||||||||
\(737\) | 24.0323 | 0.885240 | ||||||||
\(738\) | 7.37522 | 0.271486 | ||||||||
\(739\) | 45.9551 | 1.69048 | 0.845242 | − | 0.534383i | \(-0.179456\pi\) | ||||
0.845242 | + | 0.534383i | \(0.179456\pi\) | |||||||
\(740\) | 0.435679 | 0.0160159 | ||||||||
\(741\) | 7.92957 | 0.291300 | ||||||||
\(742\) | −0.774500 | −0.0284328 | ||||||||
\(743\) | −19.6847 | −0.722163 | −0.361081 | − | 0.932534i | \(-0.617592\pi\) | ||||
−0.361081 | + | 0.932534i | \(0.617592\pi\) | |||||||
\(744\) | −1.72923 | −0.0633965 | ||||||||
\(745\) | −1.51234 | −0.0554078 | ||||||||
\(746\) | −69.3422 | −2.53880 | ||||||||
\(747\) | −17.4586 | −0.638777 | ||||||||
\(748\) | 5.75472 | 0.210413 | ||||||||
\(749\) | −22.1004 | −0.807532 | ||||||||
\(750\) | 2.92009 | 0.106627 | ||||||||
\(751\) | 20.0946 | 0.733263 | 0.366632 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366632 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(752\) | −35.3627 | −1.28955 | ||||||||
\(753\) | −15.6584 | −0.570623 | ||||||||
\(754\) | −16.5129 | −0.601366 | ||||||||
\(755\) | −2.58795 | −0.0941851 | ||||||||
\(756\) | −4.15852 | −0.151244 | ||||||||
\(757\) | −14.5966 | −0.530523 | −0.265262 | − | 0.964176i | \(-0.585458\pi\) | ||||
−0.265262 | + | 0.964176i | \(0.585458\pi\) | |||||||
\(758\) | −48.4776 | −1.76079 | ||||||||
\(759\) | −19.0227 | −0.690479 | ||||||||
\(760\) | −0.553331 | −0.0200714 | ||||||||
\(761\) | −8.77877 | −0.318230 | −0.159115 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159115 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(762\) | −41.0107 | −1.48566 | ||||||||
\(763\) | −12.1091 | −0.438380 | ||||||||
\(764\) | −8.15509 | −0.295041 | ||||||||
\(765\) | −0.140268 | −0.00507141 | ||||||||
\(766\) | −49.2902 | −1.78093 | ||||||||
\(767\) | 14.6670 | 0.529596 | ||||||||
\(768\) | −9.00846 | −0.325065 | ||||||||
\(769\) | 31.1511 | 1.12334 | 0.561669 | − | 0.827362i | \(-0.310159\pi\) | ||||
0.561669 | + | 0.827362i | \(0.310159\pi\) | |||||||
\(770\) | −1.26686 | −0.0456544 | ||||||||
\(771\) | 22.2563 | 0.801541 | ||||||||
\(772\) | 62.0351 | 2.23269 | ||||||||
\(773\) | 6.06133 | 0.218011 | 0.109005 | − | 0.994041i | \(-0.465233\pi\) | ||||
0.109005 | + | 0.994041i | \(0.465233\pi\) | |||||||
\(774\) | −9.75714 | −0.350713 | ||||||||
\(775\) | −11.7645 | −0.422594 | ||||||||
\(776\) | −6.98659 | −0.250804 | ||||||||
\(777\) | −2.33700 | −0.0838395 | ||||||||
\(778\) | 29.7942 | 1.06818 | ||||||||
\(779\) | −19.0534 | −0.682660 | ||||||||
\(780\) | −0.485246 | −0.0173746 | ||||||||
\(781\) | −8.55824 | −0.306238 | ||||||||
\(782\) | 16.2100 | 0.579668 | ||||||||
\(783\) | 5.37989 | 0.192262 | ||||||||
\(784\) | 12.2905 | 0.438947 | ||||||||
\(785\) | −2.18537 | −0.0779991 | ||||||||
\(786\) | −17.4421 | −0.622139 | ||||||||
\(787\) | 2.88069 | 0.102686 | 0.0513428 | − | 0.998681i | \(-0.483650\pi\) | ||||
0.0513428 | + | 0.998681i | \(0.483650\pi\) | |||||||
\(788\) | 43.9872 | 1.56698 | ||||||||
\(789\) | −3.39626 | −0.120910 | ||||||||
\(790\) | −0.292585 | −0.0104097 | ||||||||
\(791\) | 24.9029 | 0.885445 | ||||||||
\(792\) | −1.79191 | −0.0636728 | ||||||||
\(793\) | 2.51879 | 0.0894447 | ||||||||
\(794\) | 65.0093 | 2.30709 | ||||||||
\(795\) | 0.0294438 | 0.00104426 | ||||||||
\(796\) | −61.2735 | −2.17178 | ||||||||
\(797\) | 15.3069 | 0.542198 | 0.271099 | − | 0.962551i | \(-0.412613\pi\) | ||||
0.271099 | + | 0.962551i | \(0.412613\pi\) | |||||||
\(798\) | 19.8828 | 0.703843 | ||||||||
\(799\) | −11.1381 | −0.394037 | ||||||||
\(800\) | 40.2742 | 1.42391 | ||||||||
\(801\) | 5.07693 | 0.179385 | ||||||||
\(802\) | 12.9148 | 0.456039 | ||||||||
\(803\) | −14.0134 | −0.494522 | ||||||||
\(804\) | 23.0811 | 0.814008 | ||||||||
\(805\) | −1.92817 | −0.0679590 | ||||||||
\(806\) | 7.25050 | 0.255388 | ||||||||
\(807\) | −20.1378 | −0.708886 | ||||||||
\(808\) | −1.50884 | −0.0530807 | ||||||||
\(809\) | −46.3098 | −1.62817 | −0.814084 | − | 0.580747i | \(-0.802760\pi\) | ||||
−0.814084 | + | 0.580747i | \(0.802760\pi\) | |||||||
\(810\) | 0.292585 | 0.0102804 | ||||||||
\(811\) | −16.4120 | −0.576305 | −0.288152 | − | 0.957585i | \(-0.593041\pi\) | ||||
−0.288152 | + | 0.957585i | \(0.593041\pi\) | |||||||
\(812\) | −22.3724 | −0.785116 | ||||||||
\(813\) | −27.4628 | −0.963164 | ||||||||
\(814\) | −6.74585 | −0.236442 | ||||||||
\(815\) | −2.04514 | −0.0716382 | ||||||||
\(816\) | −3.17494 | −0.111145 | ||||||||
\(817\) | 25.2070 | 0.881881 | ||||||||
\(818\) | −55.6281 | −1.94499 | ||||||||
\(819\) | 2.60288 | 0.0909521 | ||||||||
\(820\) | 1.16597 | 0.0407173 | ||||||||
\(821\) | −19.4459 | −0.678668 | −0.339334 | − | 0.940666i | \(-0.610202\pi\) | ||||
−0.339334 | + | 0.940666i | \(0.610202\pi\) | |||||||
\(822\) | −33.1110 | −1.15488 | ||||||||
\(823\) | 12.9908 | 0.452832 | 0.226416 | − | 0.974031i | \(-0.427299\pi\) | ||||
0.226416 | + | 0.974031i | \(0.427299\pi\) | |||||||
\(824\) | −4.19915 | −0.146284 | ||||||||
\(825\) | −12.1910 | −0.424436 | ||||||||
\(826\) | 36.7765 | 1.27962 | ||||||||
\(827\) | 49.0775 | 1.70659 | 0.853296 | − | 0.521427i | \(-0.174600\pi\) | ||||
0.853296 | + | 0.521427i | \(0.174600\pi\) | |||||||
\(828\) | −18.2698 | −0.634919 | ||||||||
\(829\) | 29.5132 | 1.02504 | 0.512518 | − | 0.858677i | \(-0.328713\pi\) | ||||
0.512518 | + | 0.858677i | \(0.328713\pi\) | |||||||
\(830\) | −5.10811 | −0.177305 | ||||||||
\(831\) | 22.0555 | 0.765096 | ||||||||
\(832\) | −15.4773 | −0.536577 | ||||||||
\(833\) | 3.87111 | 0.134126 | ||||||||
\(834\) | 39.1031 | 1.35403 | ||||||||
\(835\) | 1.10491 | 0.0382371 | ||||||||
\(836\) | 31.0109 | 1.07253 | ||||||||
\(837\) | −2.36220 | −0.0816496 | ||||||||
\(838\) | −9.21446 | −0.318308 | ||||||||
\(839\) | 26.6810 | 0.921132 | 0.460566 | − | 0.887626i | \(-0.347647\pi\) | ||||
0.460566 | + | 0.887626i | \(0.347647\pi\) | |||||||
\(840\) | −0.181631 | −0.00626687 | ||||||||
\(841\) | −0.0567871 | −0.00195818 | ||||||||
\(842\) | 2.01491 | 0.0694385 | ||||||||
\(843\) | −18.0037 | −0.620079 | ||||||||
\(844\) | 49.1230 | 1.69088 | ||||||||
\(845\) | −1.51976 | −0.0522815 | ||||||||
\(846\) | 23.2328 | 0.798762 | ||||||||
\(847\) | −8.85872 | −0.304389 | ||||||||
\(848\) | 0.666453 | 0.0228861 | ||||||||
\(849\) | −19.1507 | −0.657251 | ||||||||
\(850\) | 10.3884 | 0.356320 | ||||||||
\(851\) | −10.2672 | −0.351957 | ||||||||
\(852\) | −8.21952 | −0.281596 | ||||||||
\(853\) | 7.72389 | 0.264461 | 0.132230 | − | 0.991219i | \(-0.457786\pi\) | ||||
0.132230 | + | 0.991219i | \(0.457786\pi\) | |||||||
\(854\) | 6.31567 | 0.216118 | ||||||||
\(855\) | −0.755874 | −0.0258504 | ||||||||
\(856\) | −9.14620 | −0.312611 | ||||||||
\(857\) | 17.4470 | 0.595977 | 0.297989 | − | 0.954569i | \(-0.403684\pi\) | ||||
0.297989 | + | 0.954569i | \(0.403684\pi\) | |||||||
\(858\) | 7.51333 | 0.256501 | ||||||||
\(859\) | −49.0330 | −1.67299 | −0.836493 | − | 0.547978i | \(-0.815398\pi\) | ||||
−0.836493 | + | 0.547978i | \(0.815398\pi\) | |||||||
\(860\) | −1.54253 | −0.0525998 | ||||||||
\(861\) | −6.25430 | −0.213146 | ||||||||
\(862\) | 31.6068 | 1.07653 | ||||||||
\(863\) | −12.9665 | −0.441385 | −0.220693 | − | 0.975343i | \(-0.570832\pi\) | ||||
−0.220693 | + | 0.975343i | \(0.570832\pi\) | |||||||
\(864\) | 8.08666 | 0.275114 | ||||||||
\(865\) | 0.364459 | 0.0123920 | ||||||||
\(866\) | −11.5521 | −0.392557 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 9.82324 | 0.333423 | ||||||||
\(869\) | 2.44783 | 0.0830369 | ||||||||
\(870\) | 1.57407 | 0.0533661 | ||||||||
\(871\) | −14.4468 | −0.489512 | ||||||||
\(872\) | −5.01133 | −0.169705 | ||||||||
\(873\) | −9.54399 | −0.323015 | ||||||||
\(874\) | 87.3520 | 2.95472 | ||||||||
\(875\) | −2.47628 | −0.0837135 | ||||||||
\(876\) | −13.4588 | −0.454730 | ||||||||
\(877\) | 27.5641 | 0.930774 | 0.465387 | − | 0.885107i | \(-0.345915\pi\) | ||||
0.465387 | + | 0.885107i | \(0.345915\pi\) | |||||||
\(878\) | −25.4181 | −0.857818 | ||||||||
\(879\) | 9.45058 | 0.318760 | ||||||||
\(880\) | 1.09012 | 0.0367481 | ||||||||
\(881\) | 23.7321 | 0.799553 | 0.399777 | − | 0.916613i | \(-0.369088\pi\) | ||||
0.399777 | + | 0.916613i | \(0.369088\pi\) | |||||||
\(882\) | −8.07472 | −0.271890 | ||||||||
\(883\) | 29.4934 | 0.992532 | 0.496266 | − | 0.868170i | \(-0.334704\pi\) | ||||
0.496266 | + | 0.868170i | \(0.334704\pi\) | |||||||
\(884\) | −3.45941 | −0.116353 | ||||||||
\(885\) | −1.39811 | −0.0469971 | ||||||||
\(886\) | 12.0447 | 0.404649 | ||||||||
\(887\) | −5.65133 | −0.189753 | −0.0948766 | − | 0.995489i | \(-0.530246\pi\) | ||||
−0.0948766 | + | 0.995489i | \(0.530246\pi\) | |||||||
\(888\) | −0.967162 | −0.0324558 | ||||||||
\(889\) | 34.7777 | 1.16641 | ||||||||
\(890\) | 1.48543 | 0.0497918 | ||||||||
\(891\) | −2.44783 | −0.0820054 | ||||||||
\(892\) | −16.2021 | −0.542488 | ||||||||
\(893\) | −60.0206 | −2.00851 | ||||||||
\(894\) | 22.4896 | 0.752165 | ||||||||
\(895\) | 0.850144 | 0.0284172 | ||||||||
\(896\) | −10.1996 | −0.340744 | ||||||||
\(897\) | 11.4354 | 0.381815 | ||||||||
\(898\) | −6.84582 | −0.228448 | ||||||||
\(899\) | −12.7084 | −0.423848 | ||||||||
\(900\) | −11.7085 | −0.390283 | ||||||||
\(901\) | 0.209911 | 0.00699313 | ||||||||
\(902\) | −18.0533 | −0.601109 | ||||||||
\(903\) | 8.27420 | 0.275348 | ||||||||
\(904\) | 10.3060 | 0.342773 | ||||||||
\(905\) | 0.256110 | 0.00851337 | ||||||||
\(906\) | 38.4847 | 1.27857 | ||||||||
\(907\) | −16.8237 | −0.558623 | −0.279312 | − | 0.960201i | \(-0.590106\pi\) | ||||
−0.279312 | + | 0.960201i | \(0.590106\pi\) | |||||||
\(908\) | −38.5820 | −1.28039 | ||||||||
\(909\) | −2.06114 | −0.0683636 | ||||||||
\(910\) | 0.761563 | 0.0252456 | ||||||||
\(911\) | 36.0202 | 1.19340 | 0.596701 | − | 0.802464i | \(-0.296478\pi\) | ||||
0.596701 | + | 0.802464i | \(0.296478\pi\) | |||||||
\(912\) | −17.1090 | −0.566537 | ||||||||
\(913\) | 42.7357 | 1.41434 | ||||||||
\(914\) | 71.8606 | 2.37694 | ||||||||
\(915\) | −0.240100 | −0.00793745 | ||||||||
\(916\) | −37.5790 | −1.24165 | ||||||||
\(917\) | 14.7912 | 0.488447 | ||||||||
\(918\) | 2.08589 | 0.0688447 | ||||||||
\(919\) | −53.8788 | −1.77730 | −0.888649 | − | 0.458588i | \(-0.848355\pi\) | ||||
−0.888649 | + | 0.458588i | \(0.848355\pi\) | |||||||
\(920\) | −0.797968 | −0.0263082 | ||||||||
\(921\) | 1.88031 | 0.0619582 | ||||||||
\(922\) | 45.8816 | 1.51103 | ||||||||
\(923\) | 5.14473 | 0.169341 | ||||||||
\(924\) | 10.1793 | 0.334876 | ||||||||
\(925\) | −6.57993 | −0.216347 | ||||||||
\(926\) | 3.26264 | 0.107217 | ||||||||
\(927\) | −5.73622 | −0.188402 | ||||||||
\(928\) | 43.5054 | 1.42813 | ||||||||
\(929\) | 34.6314 | 1.13622 | 0.568110 | − | 0.822953i | \(-0.307675\pi\) | ||||
0.568110 | + | 0.822953i | \(0.307675\pi\) | |||||||
\(930\) | −0.691143 | −0.0226635 | ||||||||
\(931\) | 20.8605 | 0.683676 | ||||||||
\(932\) | 14.2134 | 0.465576 | ||||||||
\(933\) | −20.9805 | −0.686870 | ||||||||
\(934\) | −24.5046 | −0.801815 | ||||||||
\(935\) | 0.343353 | 0.0112288 | ||||||||
\(936\) | 1.07720 | 0.0352093 | ||||||||
\(937\) | 15.5029 | 0.506459 | 0.253229 | − | 0.967406i | \(-0.418507\pi\) | ||||
0.253229 | + | 0.967406i | \(0.418507\pi\) | |||||||
\(938\) | −36.2244 | −1.18277 | ||||||||
\(939\) | −33.9738 | −1.10869 | ||||||||
\(940\) | 3.67293 | 0.119798 | ||||||||
\(941\) | 34.0338 | 1.10947 | 0.554736 | − | 0.832027i | \(-0.312819\pi\) | ||||
0.554736 | + | 0.832027i | \(0.312819\pi\) | |||||||
\(942\) | 32.4980 | 1.05884 | ||||||||
\(943\) | −27.4773 | −0.894783 | ||||||||
\(944\) | −31.6460 | −1.02999 | ||||||||
\(945\) | −0.248116 | −0.00807121 | ||||||||
\(946\) | 23.8838 | 0.776530 | ||||||||
\(947\) | −1.96102 | −0.0637246 | −0.0318623 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318623 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(948\) | 2.35095 | 0.0763553 | ||||||||
\(949\) | 8.42406 | 0.273457 | ||||||||
\(950\) | 55.9809 | 1.81626 | ||||||||
\(951\) | −18.0211 | −0.584375 | ||||||||
\(952\) | −1.29488 | −0.0419674 | ||||||||
\(953\) | 33.3348 | 1.07982 | 0.539910 | − | 0.841723i | \(-0.318458\pi\) | ||||
0.539910 | + | 0.841723i | \(0.318458\pi\) | |||||||
\(954\) | −0.437851 | −0.0141759 | ||||||||
\(955\) | −0.486570 | −0.0157450 | ||||||||
\(956\) | −25.0258 | −0.809393 | ||||||||
\(957\) | −13.1691 | −0.425695 | ||||||||
\(958\) | −72.3777 | −2.33842 | ||||||||
\(959\) | 28.0786 | 0.906705 | ||||||||
\(960\) | 1.47535 | 0.0476166 | ||||||||
\(961\) | −25.4200 | −0.820000 | ||||||||
\(962\) | 4.05523 | 0.130746 | ||||||||
\(963\) | −12.4941 | −0.402617 | ||||||||
\(964\) | 6.94144 | 0.223569 | ||||||||
\(965\) | 3.70130 | 0.119149 | ||||||||
\(966\) | 28.6733 | 0.922548 | ||||||||
\(967\) | −47.6659 | −1.53283 | −0.766416 | − | 0.642345i | \(-0.777962\pi\) | ||||
−0.766416 | + | 0.642345i | \(0.777962\pi\) | |||||||
\(968\) | −3.66616 | −0.117835 | ||||||||
\(969\) | −5.38878 | −0.173112 | ||||||||
\(970\) | −2.79242 | −0.0896593 | ||||||||
\(971\) | −39.3174 | −1.26176 | −0.630878 | − | 0.775882i | \(-0.717305\pi\) | ||||
−0.630878 | + | 0.775882i | \(0.717305\pi\) | |||||||
\(972\) | −2.35095 | −0.0754067 | ||||||||
\(973\) | −33.1600 | −1.06306 | ||||||||
\(974\) | −38.5946 | −1.23665 | ||||||||
\(975\) | 7.32853 | 0.234701 | ||||||||
\(976\) | −5.43460 | −0.173957 | ||||||||
\(977\) | 53.4361 | 1.70957 | 0.854786 | − | 0.518981i | \(-0.173689\pi\) | ||||
0.854786 | + | 0.518981i | \(0.173689\pi\) | |||||||
\(978\) | 30.4128 | 0.972494 | ||||||||
\(979\) | −12.4275 | −0.397183 | ||||||||
\(980\) | −1.27655 | −0.0407779 | ||||||||
\(981\) | −6.84570 | −0.218566 | ||||||||
\(982\) | −50.1092 | −1.59905 | ||||||||
\(983\) | 53.0299 | 1.69139 | 0.845696 | − | 0.533665i | \(-0.179186\pi\) | ||||
0.845696 | + | 0.533665i | \(0.179186\pi\) | |||||||
\(984\) | −2.58832 | −0.0825128 | ||||||||
\(985\) | 2.62448 | 0.0836228 | ||||||||
\(986\) | 11.2219 | 0.357377 | ||||||||
\(987\) | −19.7018 | −0.627115 | ||||||||
\(988\) | −18.6420 | −0.593081 | ||||||||
\(989\) | 36.3514 | 1.15591 | ||||||||
\(990\) | −0.716197 | −0.0227622 | ||||||||
\(991\) | 10.4399 | 0.331633 | 0.165816 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165816 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(992\) | −19.1023 | −0.606499 | ||||||||
\(993\) | −18.2450 | −0.578988 | ||||||||
\(994\) | 12.9000 | 0.409164 | ||||||||
\(995\) | −3.65586 | −0.115898 | ||||||||
\(996\) | 41.0443 | 1.30054 | ||||||||
\(997\) | −10.1949 | −0.322875 | −0.161437 | − | 0.986883i | \(-0.551613\pi\) | ||||
−0.161437 | + | 0.986883i | \(0.551613\pi\) | |||||||
\(998\) | −5.80585 | −0.183781 | ||||||||
\(999\) | −1.32119 | −0.0418004 |
(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 | 4029.2.a.g.1.19 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.g.1.19 | ✓ | 22 | 1.1 | even | 1 | trivial |