Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3775,2,Mod(1,3775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3775, 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("3775.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3775 = 5^{2} \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3775.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: | \(30.1435267630\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} - 2 x^{17} - 32 x^{16} + 64 x^{15} + 417 x^{14} - 839 x^{13} - 2829 x^{12} + 5789 x^{11} + \cdots + 576 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 755) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.74545\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3775.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.74545 | −1.94133 | −0.970664 | − | 0.240440i | \(-0.922708\pi\) | ||||
−0.970664 | + | 0.240440i | \(0.922708\pi\) | |||||||
\(3\) | 2.37118 | 1.36900 | 0.684501 | − | 0.729012i | \(-0.260020\pi\) | ||||
0.684501 | + | 0.729012i | \(0.260020\pi\) | |||||||
\(4\) | 5.53751 | 2.76875 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.50997 | −2.65768 | ||||||||
\(7\) | 0.409554 | 0.154797 | 0.0773984 | − | 0.997000i | \(-0.475339\pi\) | ||||
0.0773984 | + | 0.997000i | \(0.475339\pi\) | |||||||
\(8\) | −9.71206 | −3.43373 | ||||||||
\(9\) | 2.62250 | 0.874168 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.72690 | 1.72672 | 0.863362 | − | 0.504585i | \(-0.168354\pi\) | ||||
0.863362 | + | 0.504585i | \(0.168354\pi\) | |||||||
\(12\) | 13.1304 | 3.79043 | ||||||||
\(13\) | −1.36347 | −0.378159 | −0.189080 | − | 0.981962i | \(-0.560550\pi\) | ||||
−0.189080 | + | 0.981962i | \(0.560550\pi\) | |||||||
\(14\) | −1.12441 | −0.300511 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5890 | 3.89724 | ||||||||
\(17\) | −3.94334 | −0.956399 | −0.478200 | − | 0.878251i | \(-0.658710\pi\) | ||||
−0.478200 | + | 0.878251i | \(0.658710\pi\) | |||||||
\(18\) | −7.19996 | −1.69705 | ||||||||
\(19\) | −7.09974 | −1.62879 | −0.814396 | − | 0.580310i | \(-0.802931\pi\) | ||||
−0.814396 | + | 0.580310i | \(0.802931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.971127 | 0.211917 | ||||||||
\(22\) | −15.7229 | −3.35214 | ||||||||
\(23\) | 2.57969 | 0.537903 | 0.268951 | − | 0.963154i | \(-0.413323\pi\) | ||||
0.268951 | + | 0.963154i | \(0.413323\pi\) | |||||||
\(24\) | −23.0291 | −4.70079 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.74335 | 0.734131 | ||||||||
\(27\) | −0.895110 | −0.172264 | ||||||||
\(28\) | 2.26791 | 0.428594 | ||||||||
\(29\) | 5.12396 | 0.951495 | 0.475748 | − | 0.879582i | \(-0.342178\pi\) | ||||
0.475748 | + | 0.879582i | \(0.342178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.92785 | 0.705462 | 0.352731 | − | 0.935725i | \(-0.385253\pi\) | ||||
0.352731 | + | 0.935725i | \(0.385253\pi\) | |||||||
\(32\) | −23.3747 | −4.13210 | ||||||||
\(33\) | 13.5795 | 2.36389 | ||||||||
\(34\) | 10.8262 | 1.85668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 14.5221 | 2.42036 | ||||||||
\(37\) | 2.09769 | 0.344857 | 0.172429 | − | 0.985022i | \(-0.444839\pi\) | ||||
0.172429 | + | 0.985022i | \(0.444839\pi\) | |||||||
\(38\) | 19.4920 | 3.16202 | ||||||||
\(39\) | −3.23304 | −0.517701 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.147496 | 0.0230350 | 0.0115175 | − | 0.999934i | \(-0.496334\pi\) | ||||
0.0115175 | + | 0.999934i | \(0.496334\pi\) | |||||||
\(42\) | −2.66618 | −0.411401 | ||||||||
\(43\) | −1.71111 | −0.260942 | −0.130471 | − | 0.991452i | \(-0.541649\pi\) | ||||
−0.130471 | + | 0.991452i | \(0.541649\pi\) | |||||||
\(44\) | 31.7127 | 4.78087 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.08242 | −1.04425 | ||||||||
\(47\) | 7.21140 | 1.05189 | 0.525945 | − | 0.850518i | \(-0.323712\pi\) | ||||
0.525945 | + | 0.850518i | \(0.323712\pi\) | |||||||
\(48\) | 36.9643 | 5.33534 | ||||||||
\(49\) | −6.83227 | −0.976038 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.35037 | −1.30931 | ||||||||
\(52\) | −7.55024 | −1.04703 | ||||||||
\(53\) | 11.1784 | 1.53547 | 0.767737 | − | 0.640766i | \(-0.221383\pi\) | ||||
0.767737 | + | 0.640766i | \(0.221383\pi\) | |||||||
\(54\) | 2.45748 | 0.334421 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.97761 | −0.531531 | ||||||||
\(57\) | −16.8348 | −2.22982 | ||||||||
\(58\) | −14.0676 | −1.84716 | ||||||||
\(59\) | −0.776067 | −0.101035 | −0.0505177 | − | 0.998723i | \(-0.516087\pi\) | ||||
−0.0505177 | + | 0.998723i | \(0.516087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.83711 | 0.747365 | 0.373683 | − | 0.927557i | \(-0.378095\pi\) | ||||
0.373683 | + | 0.927557i | \(0.378095\pi\) | |||||||
\(62\) | −10.7837 | −1.36953 | ||||||||
\(63\) | 1.07406 | 0.135318 | ||||||||
\(64\) | 32.9961 | 4.12451 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −37.2819 | −4.58909 | ||||||||
\(67\) | 12.6969 | 1.55117 | 0.775585 | − | 0.631243i | \(-0.217455\pi\) | ||||
0.775585 | + | 0.631243i | \(0.217455\pi\) | |||||||
\(68\) | −21.8363 | −2.64803 | ||||||||
\(69\) | 6.11692 | 0.736390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.98583 | 0.235675 | 0.117837 | − | 0.993033i | \(-0.462404\pi\) | ||||
0.117837 | + | 0.993033i | \(0.462404\pi\) | |||||||
\(72\) | −25.4699 | −3.00166 | ||||||||
\(73\) | 13.6922 | 1.60255 | 0.801274 | − | 0.598298i | \(-0.204156\pi\) | ||||
0.801274 | + | 0.598298i | \(0.204156\pi\) | |||||||
\(74\) | −5.75909 | −0.669481 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −39.3148 | −4.50972 | ||||||||
\(77\) | 2.34547 | 0.267291 | ||||||||
\(78\) | 8.87616 | 1.00503 | ||||||||
\(79\) | −14.3558 | −1.61516 | −0.807579 | − | 0.589760i | \(-0.799222\pi\) | ||||
−0.807579 | + | 0.589760i | \(0.799222\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.98998 | −1.11000 | ||||||||
\(82\) | −0.404944 | −0.0447185 | ||||||||
\(83\) | −2.08110 | −0.228430 | −0.114215 | − | 0.993456i | \(-0.536435\pi\) | ||||
−0.114215 | + | 0.993456i | \(0.536435\pi\) | |||||||
\(84\) | 5.37762 | 0.586747 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.69778 | 0.506575 | ||||||||
\(87\) | 12.1498 | 1.30260 | ||||||||
\(88\) | −55.6200 | −5.92911 | ||||||||
\(89\) | 8.84651 | 0.937728 | 0.468864 | − | 0.883270i | \(-0.344663\pi\) | ||||
0.468864 | + | 0.883270i | \(0.344663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.558415 | −0.0585378 | ||||||||
\(92\) | 14.2851 | 1.48932 | ||||||||
\(93\) | 9.31364 | 0.965780 | ||||||||
\(94\) | −19.7986 | −2.04206 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −55.4256 | −5.65685 | ||||||||
\(97\) | −10.3150 | −1.04733 | −0.523663 | − | 0.851926i | \(-0.675435\pi\) | ||||
−0.523663 | + | 0.851926i | \(0.675435\pi\) | |||||||
\(98\) | 18.7577 | 1.89481 | ||||||||
\(99\) | 15.0188 | 1.50945 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.21622 | 0.817544 | 0.408772 | − | 0.912636i | \(-0.365957\pi\) | ||||
0.408772 | + | 0.912636i | \(0.365957\pi\) | |||||||
\(102\) | 25.6710 | 2.54181 | ||||||||
\(103\) | 15.5311 | 1.53032 | 0.765161 | − | 0.643839i | \(-0.222659\pi\) | ||||
0.765161 | + | 0.643839i | \(0.222659\pi\) | |||||||
\(104\) | 13.2421 | 1.29850 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −30.6898 | −2.98086 | ||||||||
\(107\) | 17.3828 | 1.68046 | 0.840230 | − | 0.542231i | \(-0.182420\pi\) | ||||
0.840230 | + | 0.542231i | \(0.182420\pi\) | |||||||
\(108\) | −4.95668 | −0.476956 | ||||||||
\(109\) | 8.03341 | 0.769461 | 0.384730 | − | 0.923029i | \(-0.374294\pi\) | ||||
0.384730 | + | 0.923029i | \(0.374294\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.97399 | 0.472111 | ||||||||
\(112\) | 6.38453 | 0.603281 | ||||||||
\(113\) | −3.31515 | −0.311863 | −0.155932 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155932 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(114\) | 46.2190 | 4.32881 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 28.3740 | 2.63446 | ||||||||
\(117\) | −3.57571 | −0.330575 | ||||||||
\(118\) | 2.13066 | 0.196143 | ||||||||
\(119\) | −1.61501 | −0.148048 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.7973 | 1.98158 | ||||||||
\(122\) | −16.0255 | −1.45088 | ||||||||
\(123\) | 0.349740 | 0.0315350 | ||||||||
\(124\) | 21.7505 | 1.95325 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.94877 | −0.262698 | ||||||||
\(127\) | −20.8447 | −1.84967 | −0.924833 | − | 0.380374i | \(-0.875795\pi\) | ||||
−0.924833 | + | 0.380374i | \(0.875795\pi\) | |||||||
\(128\) | −43.8399 | −3.87493 | ||||||||
\(129\) | −4.05736 | −0.357231 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3616 | 1.51689 | 0.758446 | − | 0.651736i | \(-0.225959\pi\) | ||||
0.758446 | + | 0.651736i | \(0.225959\pi\) | |||||||
\(132\) | 75.1967 | 6.54503 | ||||||||
\(133\) | −2.90772 | −0.252132 | ||||||||
\(134\) | −34.8587 | −3.01133 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 38.2979 | 3.28402 | ||||||||
\(137\) | 17.4458 | 1.49050 | 0.745248 | − | 0.666788i | \(-0.232331\pi\) | ||||
0.745248 | + | 0.666788i | \(0.232331\pi\) | |||||||
\(138\) | −16.7937 | −1.42958 | ||||||||
\(139\) | 14.8163 | 1.25670 | 0.628349 | − | 0.777931i | \(-0.283731\pi\) | ||||
0.628349 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0995 | 1.44004 | ||||||||
\(142\) | −5.45200 | −0.457522 | ||||||||
\(143\) | −7.80846 | −0.652976 | ||||||||
\(144\) | 40.8822 | 3.40685 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −37.5912 | −3.11107 | ||||||||
\(147\) | −16.2005 | −1.33620 | ||||||||
\(148\) | 11.6159 | 0.954825 | ||||||||
\(149\) | 9.04142 | 0.740702 | 0.370351 | − | 0.928892i | \(-0.379237\pi\) | ||||
0.370351 | + | 0.928892i | \(0.379237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 68.9531 | 5.59283 | ||||||||
\(153\) | −10.3414 | −0.836054 | ||||||||
\(154\) | −6.43938 | −0.518900 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −17.9030 | −1.43339 | ||||||||
\(157\) | −11.1420 | −0.889227 | −0.444613 | − | 0.895723i | \(-0.646659\pi\) | ||||
−0.444613 | + | 0.895723i | \(0.646659\pi\) | |||||||
\(158\) | 39.4132 | 3.13555 | ||||||||
\(159\) | 26.5061 | 2.10207 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.05652 | 0.0832656 | ||||||||
\(162\) | 27.4270 | 2.15487 | ||||||||
\(163\) | 13.2605 | 1.03864 | 0.519321 | − | 0.854579i | \(-0.326185\pi\) | ||||
0.519321 | + | 0.854579i | \(0.326185\pi\) | |||||||
\(164\) | 0.816761 | 0.0637783 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.71355 | 0.443458 | ||||||||
\(167\) | 7.09489 | 0.549019 | 0.274509 | − | 0.961584i | \(-0.411485\pi\) | ||||
0.274509 | + | 0.961584i | \(0.411485\pi\) | |||||||
\(168\) | −9.43164 | −0.727667 | ||||||||
\(169\) | −11.1409 | −0.856996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.6191 | −1.42384 | ||||||||
\(172\) | −9.47530 | −0.722485 | ||||||||
\(173\) | 17.4978 | 1.33033 | 0.665165 | − | 0.746697i | \(-0.268361\pi\) | ||||
0.665165 | + | 0.746697i | \(0.268361\pi\) | |||||||
\(174\) | −33.3568 | −2.52877 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 89.2765 | 6.72947 | ||||||||
\(177\) | −1.84020 | −0.138318 | ||||||||
\(178\) | −24.2877 | −1.82044 | ||||||||
\(179\) | −16.3614 | −1.22291 | −0.611454 | − | 0.791280i | \(-0.709415\pi\) | ||||
−0.611454 | + | 0.791280i | \(0.709415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8496 | −0.806441 | −0.403220 | − | 0.915103i | \(-0.632109\pi\) | ||||
−0.403220 | + | 0.915103i | \(0.632109\pi\) | |||||||
\(182\) | 1.53310 | 0.113641 | ||||||||
\(183\) | 13.8408 | 1.02315 | ||||||||
\(184\) | −25.0541 | −1.84701 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −25.5702 | −1.87490 | ||||||||
\(187\) | −22.5831 | −1.65144 | ||||||||
\(188\) | 39.9332 | 2.91243 | ||||||||
\(189\) | −0.366596 | −0.0266659 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.1127 | −1.45531 | −0.727653 | − | 0.685945i | \(-0.759389\pi\) | ||||
−0.727653 | + | 0.685945i | \(0.759389\pi\) | |||||||
\(192\) | 78.2398 | 5.64647 | ||||||||
\(193\) | −22.6793 | −1.63249 | −0.816245 | − | 0.577706i | \(-0.803948\pi\) | ||||
−0.816245 | + | 0.577706i | \(0.803948\pi\) | |||||||
\(194\) | 28.3192 | 2.03320 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.8337 | −2.70241 | ||||||||
\(197\) | −10.2683 | −0.731583 | −0.365792 | − | 0.930697i | \(-0.619202\pi\) | ||||
−0.365792 | + | 0.930697i | \(0.619202\pi\) | |||||||
\(198\) | −41.2334 | −2.93033 | ||||||||
\(199\) | 2.10850 | 0.149468 | 0.0747338 | − | 0.997204i | \(-0.476189\pi\) | ||||
0.0747338 | + | 0.997204i | \(0.476189\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 30.1066 | 2.12356 | ||||||||
\(202\) | −22.5572 | −1.58712 | ||||||||
\(203\) | 2.09854 | 0.147288 | ||||||||
\(204\) | −51.7777 | −3.62517 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −42.6398 | −2.97086 | ||||||||
\(207\) | 6.76525 | 0.470218 | ||||||||
\(208\) | −21.2551 | −1.47378 | ||||||||
\(209\) | −40.6594 | −2.81247 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.57718 | −0.383949 | −0.191974 | − | 0.981400i | \(-0.561489\pi\) | ||||
−0.191974 | + | 0.981400i | \(0.561489\pi\) | |||||||
\(212\) | 61.9006 | 4.25135 | ||||||||
\(213\) | 4.70876 | 0.322639 | ||||||||
\(214\) | −47.7237 | −3.26232 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.69336 | 0.591508 | ||||||||
\(217\) | 1.60867 | 0.109203 | ||||||||
\(218\) | −22.0553 | −1.49378 | ||||||||
\(219\) | 32.4666 | 2.19389 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.37663 | 0.361671 | ||||||||
\(222\) | −13.6559 | −0.916521 | ||||||||
\(223\) | −0.748241 | −0.0501059 | −0.0250530 | − | 0.999686i | \(-0.507975\pi\) | ||||
−0.0250530 | + | 0.999686i | \(0.507975\pi\) | |||||||
\(224\) | −9.57319 | −0.639636 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.10159 | 0.605429 | ||||||||
\(227\) | 2.87119 | 0.190567 | 0.0952837 | − | 0.995450i | \(-0.469624\pi\) | ||||
0.0952837 | + | 0.995450i | \(0.469624\pi\) | |||||||
\(228\) | −93.2227 | −6.17382 | ||||||||
\(229\) | 21.0587 | 1.39160 | 0.695799 | − | 0.718236i | \(-0.255050\pi\) | ||||
0.695799 | + | 0.718236i | \(0.255050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.56154 | 0.365923 | ||||||||
\(232\) | −49.7642 | −3.26718 | ||||||||
\(233\) | −19.6997 | −1.29057 | −0.645285 | − | 0.763942i | \(-0.723261\pi\) | ||||
−0.645285 | + | 0.763942i | \(0.723261\pi\) | |||||||
\(234\) | 9.81695 | 0.641754 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.29748 | −0.279742 | ||||||||
\(237\) | −34.0403 | −2.21115 | ||||||||
\(238\) | 4.43393 | 0.287409 | ||||||||
\(239\) | 4.87975 | 0.315645 | 0.157822 | − | 0.987468i | \(-0.449553\pi\) | ||||
0.157822 | + | 0.987468i | \(0.449553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.84024 | −0.376203 | −0.188102 | − | 0.982150i | \(-0.560233\pi\) | ||||
−0.188102 | + | 0.982150i | \(0.560233\pi\) | |||||||
\(242\) | −59.8435 | −3.84689 | ||||||||
\(243\) | −21.0027 | −1.34733 | ||||||||
\(244\) | 32.3230 | 2.06927 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.960195 | −0.0612198 | ||||||||
\(247\) | 9.68029 | 0.615942 | ||||||||
\(248\) | −38.1475 | −2.42237 | ||||||||
\(249\) | −4.93466 | −0.312721 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3099 | −0.650755 | −0.325378 | − | 0.945584i | \(-0.605491\pi\) | ||||
−0.325378 | + | 0.945584i | \(0.605491\pi\) | |||||||
\(252\) | 5.94760 | 0.374664 | ||||||||
\(253\) | 14.7736 | 0.928810 | ||||||||
\(254\) | 57.2280 | 3.59081 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 54.3681 | 3.39800 | ||||||||
\(257\) | 23.6882 | 1.47763 | 0.738814 | − | 0.673909i | \(-0.235386\pi\) | ||||
0.738814 | + | 0.673909i | \(0.235386\pi\) | |||||||
\(258\) | 11.1393 | 0.693502 | ||||||||
\(259\) | 0.859115 | 0.0533828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4376 | 0.831767 | ||||||||
\(262\) | −47.6655 | −2.94478 | ||||||||
\(263\) | 5.10433 | 0.314747 | 0.157373 | − | 0.987539i | \(-0.449697\pi\) | ||||
0.157373 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(264\) | −131.885 | −8.11696 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.98302 | 0.489470 | ||||||||
\(267\) | 20.9767 | 1.28375 | ||||||||
\(268\) | 70.3091 | 4.29481 | ||||||||
\(269\) | 2.11997 | 0.129257 | 0.0646285 | − | 0.997909i | \(-0.479414\pi\) | ||||
0.0646285 | + | 0.997909i | \(0.479414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.8282 | −1.38671 | −0.693356 | − | 0.720595i | \(-0.743869\pi\) | ||||
−0.693356 | + | 0.720595i | \(0.743869\pi\) | |||||||
\(272\) | −61.4726 | −3.72732 | ||||||||
\(273\) | −1.32410 | −0.0801384 | ||||||||
\(274\) | −47.8966 | −2.89354 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 33.8725 | 2.03888 | ||||||||
\(277\) | −27.0330 | −1.62425 | −0.812127 | − | 0.583481i | \(-0.801690\pi\) | ||||
−0.812127 | + | 0.583481i | \(0.801690\pi\) | |||||||
\(278\) | −40.6773 | −2.43966 | ||||||||
\(279\) | 10.3008 | 0.616693 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.97790 | 0.416266 | 0.208133 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208133 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(282\) | −46.9460 | −2.79559 | ||||||||
\(283\) | 9.00783 | 0.535460 | 0.267730 | − | 0.963494i | \(-0.413726\pi\) | ||||
0.267730 | + | 0.963494i | \(0.413726\pi\) | |||||||
\(284\) | 10.9965 | 0.652525 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4378 | 1.26764 | ||||||||
\(287\) | 0.0604076 | 0.00356575 | ||||||||
\(288\) | −61.3002 | −3.61215 | ||||||||
\(289\) | −1.45011 | −0.0853003 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.4587 | −1.43379 | ||||||||
\(292\) | 75.8205 | 4.43706 | ||||||||
\(293\) | −28.4414 | −1.66156 | −0.830782 | − | 0.556598i | \(-0.812107\pi\) | ||||
−0.830782 | + | 0.556598i | \(0.812107\pi\) | |||||||
\(294\) | 44.4778 | 2.59400 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −20.3728 | −1.18415 | ||||||||
\(297\) | −5.12620 | −0.297452 | ||||||||
\(298\) | −24.8228 | −1.43795 | ||||||||
\(299\) | −3.51734 | −0.203413 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.700793 | −0.0403930 | ||||||||
\(302\) | −2.74545 | −0.157983 | ||||||||
\(303\) | 19.4822 | 1.11922 | ||||||||
\(304\) | −110.678 | −6.34780 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 28.3919 | 1.62305 | ||||||||
\(307\) | 8.39020 | 0.478854 | 0.239427 | − | 0.970914i | \(-0.423040\pi\) | ||||
0.239427 | + | 0.970914i | \(0.423040\pi\) | |||||||
\(308\) | 12.9881 | 0.740064 | ||||||||
\(309\) | 36.8270 | 2.09502 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.70291 | 0.493497 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(312\) | 31.3995 | 1.77765 | ||||||||
\(313\) | −16.4553 | −0.930109 | −0.465055 | − | 0.885282i | \(-0.653965\pi\) | ||||
−0.465055 | + | 0.885282i | \(0.653965\pi\) | |||||||
\(314\) | 30.5898 | 1.72628 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −79.4955 | −4.47197 | ||||||||
\(317\) | −13.2192 | −0.742466 | −0.371233 | − | 0.928540i | \(-0.621065\pi\) | ||||
−0.371233 | + | 0.928540i | \(0.621065\pi\) | |||||||
\(318\) | −72.7711 | −4.08080 | ||||||||
\(319\) | 29.3444 | 1.64297 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.2178 | 2.30055 | ||||||||
\(322\) | −2.90063 | −0.161646 | ||||||||
\(323\) | 27.9966 | 1.55777 | ||||||||
\(324\) | −55.3196 | −3.07331 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.4060 | −2.01634 | ||||||||
\(327\) | 19.0487 | 1.05339 | ||||||||
\(328\) | −1.43249 | −0.0790961 | ||||||||
\(329\) | 2.95346 | 0.162829 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.9734 | 1.20777 | 0.603883 | − | 0.797073i | \(-0.293619\pi\) | ||||
0.603883 | + | 0.797073i | \(0.293619\pi\) | |||||||
\(332\) | −11.5241 | −0.632467 | ||||||||
\(333\) | 5.50119 | 0.301463 | ||||||||
\(334\) | −19.4787 | −1.06583 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 15.1389 | 0.825893 | ||||||||
\(337\) | −8.04206 | −0.438079 | −0.219040 | − | 0.975716i | \(-0.570292\pi\) | ||||
−0.219040 | + | 0.975716i | \(0.570292\pi\) | |||||||
\(338\) | 30.5869 | 1.66371 | ||||||||
\(339\) | −7.86083 | −0.426941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.4944 | 1.21814 | ||||||||
\(342\) | 51.1178 | 2.76414 | ||||||||
\(343\) | −5.66506 | −0.305884 | ||||||||
\(344\) | 16.6184 | 0.896006 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0392 | −2.58261 | ||||||||
\(347\) | 23.5159 | 1.26240 | 0.631201 | − | 0.775620i | \(-0.282562\pi\) | ||||
0.631201 | + | 0.775620i | \(0.282562\pi\) | |||||||
\(348\) | 67.2798 | 3.60658 | ||||||||
\(349\) | 25.8680 | 1.38468 | 0.692341 | − | 0.721570i | \(-0.256579\pi\) | ||||
0.692341 | + | 0.721570i | \(0.256579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.22046 | 0.0651432 | ||||||||
\(352\) | −133.864 | −7.13499 | ||||||||
\(353\) | 30.3878 | 1.61738 | 0.808689 | − | 0.588236i | \(-0.200178\pi\) | ||||
0.808689 | + | 0.588236i | \(0.200178\pi\) | |||||||
\(354\) | 5.05217 | 0.268520 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 48.9876 | 2.59634 | ||||||||
\(357\) | −3.82948 | −0.202678 | ||||||||
\(358\) | 44.9194 | 2.37407 | ||||||||
\(359\) | −14.7748 | −0.779785 | −0.389892 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389892 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.4062 | 1.65296 | ||||||||
\(362\) | 29.7869 | 1.56557 | ||||||||
\(363\) | 51.6855 | 2.71278 | ||||||||
\(364\) | −3.09223 | −0.162077 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −37.9994 | −1.98626 | ||||||||
\(367\) | 5.94394 | 0.310271 | 0.155136 | − | 0.987893i | \(-0.450419\pi\) | ||||
0.155136 | + | 0.987893i | \(0.450419\pi\) | |||||||
\(368\) | 40.2147 | 2.09634 | ||||||||
\(369\) | 0.386809 | 0.0201365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57816 | 0.237686 | ||||||||
\(372\) | 51.5744 | 2.67401 | ||||||||
\(373\) | −29.1043 | −1.50696 | −0.753482 | − | 0.657469i | \(-0.771627\pi\) | ||||
−0.753482 | + | 0.657469i | \(0.771627\pi\) | |||||||
\(374\) | 62.0007 | 3.20598 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −70.0375 | −3.61191 | ||||||||
\(377\) | −6.98637 | −0.359817 | ||||||||
\(378\) | 1.00647 | 0.0517673 | ||||||||
\(379\) | −1.66503 | −0.0855268 | −0.0427634 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427634 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −49.4265 | −2.53220 | ||||||||
\(382\) | 55.2186 | 2.82523 | ||||||||
\(383\) | −6.99444 | −0.357399 | −0.178700 | − | 0.983904i | \(-0.557189\pi\) | ||||
−0.178700 | + | 0.983904i | \(0.557189\pi\) | |||||||
\(384\) | −103.952 | −5.30479 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 62.2649 | 3.16920 | ||||||||
\(387\) | −4.48740 | −0.228107 | ||||||||
\(388\) | −57.1192 | −2.89979 | ||||||||
\(389\) | −0.271314 | −0.0137562 | −0.00687809 | − | 0.999976i | \(-0.502189\pi\) | ||||
−0.00687809 | + | 0.999976i | \(0.502189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.1726 | −0.514450 | ||||||||
\(392\) | 66.3554 | 3.35145 | ||||||||
\(393\) | 41.1676 | 2.07663 | ||||||||
\(394\) | 28.1910 | 1.42024 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 83.1668 | 4.17929 | ||||||||
\(397\) | −7.26762 | −0.364751 | −0.182376 | − | 0.983229i | \(-0.558379\pi\) | ||||
−0.182376 | + | 0.983229i | \(0.558379\pi\) | |||||||
\(398\) | −5.78879 | −0.290166 | ||||||||
\(399\) | −6.89474 | −0.345169 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7453 | −1.03597 | −0.517986 | − | 0.855389i | \(-0.673318\pi\) | ||||
−0.517986 | + | 0.855389i | \(0.673318\pi\) | |||||||
\(402\) | −82.6563 | −4.12252 | ||||||||
\(403\) | −5.35551 | −0.266777 | ||||||||
\(404\) | 45.4974 | 2.26358 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.76143 | −0.285935 | ||||||||
\(407\) | 12.0132 | 0.595473 | ||||||||
\(408\) | 90.8113 | 4.49583 | ||||||||
\(409\) | −17.8601 | −0.883127 | −0.441564 | − | 0.897230i | \(-0.645576\pi\) | ||||
−0.441564 | + | 0.897230i | \(0.645576\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.3672 | 2.04049 | ||||||||
\(412\) | 86.0035 | 4.23709 | ||||||||
\(413\) | −0.317841 | −0.0156399 | ||||||||
\(414\) | −18.5737 | −0.912846 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 31.8707 | 1.56259 | ||||||||
\(417\) | 35.1321 | 1.72042 | ||||||||
\(418\) | 111.629 | 5.45993 | ||||||||
\(419\) | 7.42282 | 0.362629 | 0.181314 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181314 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8561 | −0.529094 | −0.264547 | − | 0.964373i | \(-0.585222\pi\) | ||||
−0.264547 | + | 0.964373i | \(0.585222\pi\) | |||||||
\(422\) | 15.3119 | 0.745370 | ||||||||
\(423\) | 18.9119 | 0.919529 | ||||||||
\(424\) | −108.565 | −5.27240 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.9277 | −0.626348 | ||||||||
\(427\) | 2.39061 | 0.115690 | ||||||||
\(428\) | 96.2574 | 4.65278 | ||||||||
\(429\) | −18.5153 | −0.893926 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1617 | 0.682147 | 0.341073 | − | 0.940037i | \(-0.389210\pi\) | ||||
0.341073 | + | 0.940037i | \(0.389210\pi\) | |||||||
\(432\) | −13.9538 | −0.671355 | ||||||||
\(433\) | 10.6625 | 0.512407 | 0.256203 | − | 0.966623i | \(-0.417528\pi\) | ||||
0.256203 | + | 0.966623i | \(0.417528\pi\) | |||||||
\(434\) | −4.41651 | −0.211999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 44.4851 | 2.13045 | ||||||||
\(437\) | −18.3151 | −0.876131 | ||||||||
\(438\) | −89.1356 | −4.25906 | ||||||||
\(439\) | −26.0303 | −1.24236 | −0.621179 | − | 0.783669i | \(-0.713346\pi\) | ||||
−0.621179 | + | 0.783669i | \(0.713346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.9176 | −0.853221 | ||||||||
\(442\) | −14.7613 | −0.702122 | ||||||||
\(443\) | −32.4476 | −1.54163 | −0.770817 | − | 0.637057i | \(-0.780152\pi\) | ||||
−0.770817 | + | 0.637057i | \(0.780152\pi\) | |||||||
\(444\) | 27.5435 | 1.30716 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.05426 | 0.0972720 | ||||||||
\(447\) | 21.4389 | 1.01402 | ||||||||
\(448\) | 13.5137 | 0.638462 | ||||||||
\(449\) | −27.7702 | −1.31056 | −0.655278 | − | 0.755388i | \(-0.727448\pi\) | ||||
−0.655278 | + | 0.755388i | \(0.727448\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.844695 | 0.0397751 | ||||||||
\(452\) | −18.3577 | −0.863472 | ||||||||
\(453\) | 2.37118 | 0.111408 | ||||||||
\(454\) | −7.88271 | −0.369954 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 163.500 | 7.65660 | ||||||||
\(457\) | 4.67961 | 0.218903 | 0.109452 | − | 0.993992i | \(-0.465091\pi\) | ||||
0.109452 | + | 0.993992i | \(0.465091\pi\) | |||||||
\(458\) | −57.8157 | −2.70155 | ||||||||
\(459\) | 3.52972 | 0.164753 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.9640 | −0.836666 | −0.418333 | − | 0.908294i | \(-0.637386\pi\) | ||||
−0.418333 | + | 0.908294i | \(0.637386\pi\) | |||||||
\(462\) | −15.2690 | −0.710376 | ||||||||
\(463\) | 34.6368 | 1.60971 | 0.804855 | − | 0.593471i | \(-0.202243\pi\) | ||||
0.804855 | + | 0.593471i | \(0.202243\pi\) | |||||||
\(464\) | 79.8773 | 3.70821 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 54.0846 | 2.50542 | ||||||||
\(467\) | −4.70383 | −0.217667 | −0.108834 | − | 0.994060i | \(-0.534712\pi\) | ||||
−0.108834 | + | 0.994060i | \(0.534712\pi\) | |||||||
\(468\) | −19.8005 | −0.915280 | ||||||||
\(469\) | 5.20006 | 0.240116 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.4197 | −1.21735 | ||||||||
\(472\) | 7.53721 | 0.346928 | ||||||||
\(473\) | −9.79937 | −0.450575 | ||||||||
\(474\) | 93.4560 | 4.29258 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.94312 | −0.409907 | ||||||||
\(477\) | 29.3154 | 1.34226 | ||||||||
\(478\) | −13.3971 | −0.612770 | ||||||||
\(479\) | 14.2102 | 0.649279 | 0.324640 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324640 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.86014 | −0.130411 | ||||||||
\(482\) | 16.0341 | 0.730334 | ||||||||
\(483\) | 2.50521 | 0.113991 | ||||||||
\(484\) | 120.703 | 5.48650 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 57.6620 | 2.61560 | ||||||||
\(487\) | 11.0703 | 0.501642 | 0.250821 | − | 0.968033i | \(-0.419299\pi\) | ||||
0.250821 | + | 0.968033i | \(0.419299\pi\) | |||||||
\(488\) | −56.6904 | −2.56625 | ||||||||
\(489\) | 31.4430 | 1.42190 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.8004 | −0.713062 | −0.356531 | − | 0.934284i | \(-0.616041\pi\) | ||||
−0.356531 | + | 0.934284i | \(0.616041\pi\) | |||||||
\(492\) | 1.93669 | 0.0873127 | ||||||||
\(493\) | −20.2055 | −0.910009 | ||||||||
\(494\) | −26.5768 | −1.19575 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 61.2311 | 2.74936 | ||||||||
\(497\) | 0.813304 | 0.0364817 | ||||||||
\(498\) | 13.5479 | 0.607095 | ||||||||
\(499\) | 4.30734 | 0.192823 | 0.0964115 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964115 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.8233 | 0.751608 | ||||||||
\(502\) | 28.3054 | 1.26333 | ||||||||
\(503\) | −23.2152 | −1.03511 | −0.517556 | − | 0.855649i | \(-0.673158\pi\) | ||||
−0.517556 | + | 0.855649i | \(0.673158\pi\) | |||||||
\(504\) | −10.4313 | −0.464647 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −40.5603 | −1.80312 | ||||||||
\(507\) | −26.4172 | −1.17323 | ||||||||
\(508\) | −115.428 | −5.12127 | ||||||||
\(509\) | −25.7517 | −1.14142 | −0.570712 | − | 0.821150i | \(-0.693333\pi\) | ||||
−0.570712 | + | 0.821150i | \(0.693333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.60768 | 0.248069 | ||||||||
\(512\) | −61.5852 | −2.72171 | ||||||||
\(513\) | 6.35504 | 0.280582 | ||||||||
\(514\) | −65.0348 | −2.86856 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −22.4677 | −0.989084 | ||||||||
\(517\) | 41.2989 | 1.81632 | ||||||||
\(518\) | −2.35866 | −0.103634 | ||||||||
\(519\) | 41.4904 | 1.82122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.0511 | −1.14132 | −0.570661 | − | 0.821186i | \(-0.693313\pi\) | ||||
−0.570661 | + | 0.821186i | \(0.693313\pi\) | |||||||
\(522\) | −36.8923 | −1.61473 | ||||||||
\(523\) | 16.2781 | 0.711790 | 0.355895 | − | 0.934526i | \(-0.384176\pi\) | ||||
0.355895 | + | 0.934526i | \(0.384176\pi\) | |||||||
\(524\) | 96.1401 | 4.19990 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0137 | −0.611026 | ||||||||
\(527\) | −15.4888 | −0.674704 | ||||||||
\(528\) | 211.691 | 9.21266 | ||||||||
\(529\) | −16.3452 | −0.710661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.03524 | −0.0883219 | ||||||||
\(532\) | −16.1015 | −0.698091 | ||||||||
\(533\) | −0.201107 | −0.00871091 | ||||||||
\(534\) | −57.5905 | −2.49218 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −123.313 | −5.32630 | ||||||||
\(537\) | −38.7958 | −1.67416 | ||||||||
\(538\) | −5.82028 | −0.250930 | ||||||||
\(539\) | −39.1277 | −1.68535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.7624 | 1.36557 | 0.682785 | − | 0.730619i | \(-0.260768\pi\) | ||||
0.682785 | + | 0.730619i | \(0.260768\pi\) | |||||||
\(542\) | 62.6737 | 2.69206 | ||||||||
\(543\) | −25.7263 | −1.10402 | ||||||||
\(544\) | 92.1742 | 3.95194 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.63527 | 0.155575 | ||||||||
\(547\) | −16.3708 | −0.699967 | −0.349983 | − | 0.936756i | \(-0.613813\pi\) | ||||
−0.349983 | + | 0.936756i | \(0.613813\pi\) | |||||||
\(548\) | 96.6063 | 4.12682 | ||||||||
\(549\) | 15.3078 | 0.653323 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.3787 | −1.54979 | ||||||||
\(552\) | −59.4079 | −2.52857 | ||||||||
\(553\) | −5.87949 | −0.250021 | ||||||||
\(554\) | 74.2178 | 3.15321 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 82.0452 | 3.47949 | ||||||||
\(557\) | 8.20755 | 0.347765 | 0.173883 | − | 0.984766i | \(-0.444369\pi\) | ||||
0.173883 | + | 0.984766i | \(0.444369\pi\) | |||||||
\(558\) | −28.2804 | −1.19720 | ||||||||
\(559\) | 2.33305 | 0.0986777 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53.5486 | −2.26082 | ||||||||
\(562\) | −19.1575 | −0.808109 | ||||||||
\(563\) | 14.6402 | 0.617010 | 0.308505 | − | 0.951223i | \(-0.400171\pi\) | ||||
0.308505 | + | 0.951223i | \(0.400171\pi\) | |||||||
\(564\) | 94.6888 | 3.98712 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24.7306 | −1.03950 | ||||||||
\(567\) | −4.09144 | −0.171824 | ||||||||
\(568\) | −19.2865 | −0.809243 | ||||||||
\(569\) | 34.6261 | 1.45160 | 0.725801 | − | 0.687905i | \(-0.241469\pi\) | ||||
0.725801 | + | 0.687905i | \(0.241469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.8854 | 0.999571 | 0.499786 | − | 0.866149i | \(-0.333412\pi\) | ||||
0.499786 | + | 0.866149i | \(0.333412\pi\) | |||||||
\(572\) | −43.2394 | −1.80793 | ||||||||
\(573\) | −47.6910 | −1.99232 | ||||||||
\(574\) | −0.165846 | −0.00692229 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 86.5324 | 3.60552 | ||||||||
\(577\) | −20.4468 | −0.851209 | −0.425605 | − | 0.904909i | \(-0.639939\pi\) | ||||
−0.425605 | + | 0.904909i | \(0.639939\pi\) | |||||||
\(578\) | 3.98120 | 0.165596 | ||||||||
\(579\) | −53.7767 | −2.23488 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.852321 | −0.0353603 | ||||||||
\(582\) | 67.1501 | 2.78346 | ||||||||
\(583\) | 64.0176 | 2.65134 | ||||||||
\(584\) | −132.979 | −5.50272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 78.0845 | 3.22564 | ||||||||
\(587\) | −6.11666 | −0.252461 | −0.126231 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126231 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(588\) | −89.7107 | −3.69961 | ||||||||
\(589\) | −27.8867 | −1.14905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3479 | −1.00154 | ||||||||
\(592\) | 32.7008 | 1.34399 | ||||||||
\(593\) | 28.3186 | 1.16290 | 0.581452 | − | 0.813581i | \(-0.302485\pi\) | ||||
0.581452 | + | 0.813581i | \(0.302485\pi\) | |||||||
\(594\) | 14.0737 | 0.577452 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 50.0669 | 2.05082 | ||||||||
\(597\) | 4.99964 | 0.204622 | ||||||||
\(598\) | 9.65668 | 0.394891 | ||||||||
\(599\) | 35.6183 | 1.45533 | 0.727663 | − | 0.685935i | \(-0.240607\pi\) | ||||
0.727663 | + | 0.685935i | \(0.240607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5191 | 1.28569 | 0.642845 | − | 0.765996i | \(-0.277754\pi\) | ||||
0.642845 | + | 0.765996i | \(0.277754\pi\) | |||||||
\(602\) | 1.92399 | 0.0784161 | ||||||||
\(603\) | 33.2976 | 1.35598 | ||||||||
\(604\) | 5.53751 | 0.225318 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −53.4873 | −2.17277 | ||||||||
\(607\) | −3.32898 | −0.135119 | −0.0675596 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675596 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(608\) | 165.954 | 6.73032 | ||||||||
\(609\) | 4.97601 | 0.201638 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.83254 | −0.397782 | ||||||||
\(612\) | −57.2657 | −2.31483 | ||||||||
\(613\) | 28.8013 | 1.16327 | 0.581636 | − | 0.813449i | \(-0.302413\pi\) | ||||
0.581636 | + | 0.813449i | \(0.302413\pi\) | |||||||
\(614\) | −23.0349 | −0.929612 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.7794 | −0.917807 | ||||||||
\(617\) | 33.0710 | 1.33139 | 0.665694 | − | 0.746225i | \(-0.268136\pi\) | ||||
0.665694 | + | 0.746225i | \(0.268136\pi\) | |||||||
\(618\) | −101.107 | −4.06711 | ||||||||
\(619\) | −4.02487 | −0.161773 | −0.0808865 | − | 0.996723i | \(-0.525775\pi\) | ||||
−0.0808865 | + | 0.996723i | \(0.525775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.30911 | −0.0926612 | ||||||||
\(622\) | −23.8934 | −0.958039 | ||||||||
\(623\) | 3.62312 | 0.145157 | ||||||||
\(624\) | −50.3998 | −2.01761 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 45.1773 | 1.80565 | ||||||||
\(627\) | −96.4110 | −3.85028 | ||||||||
\(628\) | −61.6988 | −2.46205 | ||||||||
\(629\) | −8.27188 | −0.329821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4434 | 1.37117 | 0.685585 | − | 0.727993i | \(-0.259547\pi\) | ||||
0.685585 | + | 0.727993i | \(0.259547\pi\) | |||||||
\(632\) | 139.425 | 5.54602 | ||||||||
\(633\) | −13.2245 | −0.525627 | ||||||||
\(634\) | 36.2928 | 1.44137 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 146.777 | 5.82011 | ||||||||
\(637\) | 9.31560 | 0.369098 | ||||||||
\(638\) | −80.5636 | −3.18954 | ||||||||
\(639\) | 5.20785 | 0.206019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.5044 | −0.849374 | −0.424687 | − | 0.905340i | \(-0.639616\pi\) | ||||
−0.424687 | + | 0.905340i | \(0.639616\pi\) | |||||||
\(642\) | −113.162 | −4.46613 | ||||||||
\(643\) | 2.46658 | 0.0972723 | 0.0486362 | − | 0.998817i | \(-0.484513\pi\) | ||||
0.0486362 | + | 0.998817i | \(0.484513\pi\) | |||||||
\(644\) | 5.85050 | 0.230542 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −76.8634 | −3.02415 | ||||||||
\(647\) | −4.94737 | −0.194501 | −0.0972506 | − | 0.995260i | \(-0.531005\pi\) | ||||
−0.0972506 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(648\) | 97.0233 | 3.81144 | ||||||||
\(649\) | −4.44446 | −0.174460 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.81444 | 0.149500 | ||||||||
\(652\) | 73.4300 | 2.87574 | ||||||||
\(653\) | 13.7880 | 0.539566 | 0.269783 | − | 0.962921i | \(-0.413048\pi\) | ||||
0.269783 | + | 0.962921i | \(0.413048\pi\) | |||||||
\(654\) | −52.2972 | −2.04498 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.29931 | 0.0897731 | ||||||||
\(657\) | 35.9078 | 1.40090 | ||||||||
\(658\) | −8.10857 | −0.316105 | ||||||||
\(659\) | 4.51603 | 0.175919 | 0.0879597 | − | 0.996124i | \(-0.471965\pi\) | ||||
0.0879597 | + | 0.996124i | \(0.471965\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.84653 | −0.188508 | −0.0942541 | − | 0.995548i | \(-0.530047\pi\) | ||||
−0.0942541 | + | 0.995548i | \(0.530047\pi\) | |||||||
\(662\) | −60.3268 | −2.34467 | ||||||||
\(663\) | 12.7490 | 0.495129 | ||||||||
\(664\) | 20.2117 | 0.784368 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −15.1033 | −0.585239 | ||||||||
\(667\) | 13.2182 | 0.511812 | ||||||||
\(668\) | 39.2880 | 1.52010 | ||||||||
\(669\) | −1.77422 | −0.0685952 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.4285 | 1.29049 | ||||||||
\(672\) | −22.6998 | −0.875663 | ||||||||
\(673\) | −41.1033 | −1.58442 | −0.792208 | − | 0.610252i | \(-0.791068\pi\) | ||||
−0.792208 | + | 0.610252i | \(0.791068\pi\) | |||||||
\(674\) | 22.0791 | 0.850455 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −61.6931 | −2.37281 | ||||||||
\(677\) | 4.33170 | 0.166481 | 0.0832404 | − | 0.996529i | \(-0.473473\pi\) | ||||
0.0832404 | + | 0.996529i | \(0.473473\pi\) | |||||||
\(678\) | 21.5815 | 0.828833 | ||||||||
\(679\) | −4.22453 | −0.162123 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.80811 | 0.260887 | ||||||||
\(682\) | −61.7572 | −2.36481 | ||||||||
\(683\) | −9.02009 | −0.345144 | −0.172572 | − | 0.984997i | \(-0.555208\pi\) | ||||
−0.172572 | + | 0.984997i | \(0.555208\pi\) | |||||||
\(684\) | −103.103 | −3.94226 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.5531 | 0.593822 | ||||||||
\(687\) | 49.9340 | 1.90510 | ||||||||
\(688\) | −26.6745 | −1.01696 | ||||||||
\(689\) | −15.2415 | −0.580653 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7051 | −0.559407 | −0.279704 | − | 0.960086i | \(-0.590236\pi\) | ||||
−0.279704 | + | 0.960086i | \(0.590236\pi\) | |||||||
\(692\) | 96.8939 | 3.68336 | ||||||||
\(693\) | 6.15101 | 0.233658 | ||||||||
\(694\) | −64.5619 | −2.45074 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −118.000 | −4.47278 | ||||||||
\(697\) | −0.581627 | −0.0220307 | ||||||||
\(698\) | −71.0193 | −2.68812 | ||||||||
\(699\) | −46.7116 | −1.76679 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.4801 | −0.471369 | −0.235684 | − | 0.971830i | \(-0.575733\pi\) | ||||
−0.235684 | + | 0.971830i | \(0.575733\pi\) | |||||||
\(702\) | −3.35071 | −0.126464 | ||||||||
\(703\) | −14.8930 | −0.561700 | ||||||||
\(704\) | 188.965 | 7.12190 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −83.4282 | −3.13986 | ||||||||
\(707\) | 3.36498 | 0.126553 | ||||||||
\(708\) | −10.1901 | −0.382968 | ||||||||
\(709\) | 13.7565 | 0.516635 | 0.258318 | − | 0.966060i | \(-0.416832\pi\) | ||||
0.258318 | + | 0.966060i | \(0.416832\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.6482 | −1.41192 | ||||||||
\(712\) | −85.9178 | −3.21991 | ||||||||
\(713\) | 10.1326 | 0.379470 | ||||||||
\(714\) | 10.5137 | 0.393464 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −90.6013 | −3.38593 | ||||||||
\(717\) | 11.5708 | 0.432118 | ||||||||
\(718\) | 40.5635 | 1.51382 | ||||||||
\(719\) | −13.5291 | −0.504551 | −0.252275 | − | 0.967656i | \(-0.581179\pi\) | ||||
−0.252275 | + | 0.967656i | \(0.581179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.36081 | 0.236889 | ||||||||
\(722\) | −86.2243 | −3.20894 | ||||||||
\(723\) | −13.8483 | −0.515023 | ||||||||
\(724\) | −60.0795 | −2.23284 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −141.900 | −5.26640 | ||||||||
\(727\) | −6.07544 | −0.225326 | −0.112663 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112663 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(728\) | 5.42336 | 0.201003 | ||||||||
\(729\) | −19.8314 | −0.734495 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.74749 | 0.249565 | ||||||||
\(732\) | 76.6438 | 2.83284 | ||||||||
\(733\) | −41.7228 | −1.54107 | −0.770534 | − | 0.637399i | \(-0.780010\pi\) | ||||
−0.770534 | + | 0.637399i | \(0.780010\pi\) | |||||||
\(734\) | −16.3188 | −0.602338 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −60.2994 | −2.22267 | ||||||||
\(737\) | 72.7137 | 2.67844 | ||||||||
\(738\) | −1.06197 | −0.0390915 | ||||||||
\(739\) | 38.9251 | 1.43188 | 0.715942 | − | 0.698160i | \(-0.245998\pi\) | ||||
0.715942 | + | 0.698160i | \(0.245998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.9537 | 0.843226 | ||||||||
\(742\) | −12.5691 | −0.461427 | ||||||||
\(743\) | −26.2242 | −0.962071 | −0.481036 | − | 0.876701i | \(-0.659739\pi\) | ||||
−0.481036 | + | 0.876701i | \(0.659739\pi\) | |||||||
\(744\) | −90.4546 | −3.31623 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 79.9045 | 2.92551 | ||||||||
\(747\) | −5.45769 | −0.199686 | ||||||||
\(748\) | −125.054 | −4.57242 | ||||||||
\(749\) | 7.11920 | 0.260130 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.4457 | −0.673094 | −0.336547 | − | 0.941667i | \(-0.609259\pi\) | ||||
−0.336547 | + | 0.941667i | \(0.609259\pi\) | |||||||
\(752\) | 112.418 | 4.09948 | ||||||||
\(753\) | −24.4467 | −0.890886 | ||||||||
\(754\) | 19.1808 | 0.698522 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.03003 | −0.0738313 | ||||||||
\(757\) | −36.3116 | −1.31977 | −0.659885 | − | 0.751367i | \(-0.729395\pi\) | ||||
−0.659885 | + | 0.751367i | \(0.729395\pi\) | |||||||
\(758\) | 4.57126 | 0.166036 | ||||||||
\(759\) | 35.0309 | 1.27154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1080 | 0.620165 | 0.310083 | − | 0.950710i | \(-0.399643\pi\) | ||||
0.310083 | + | 0.950710i | \(0.399643\pi\) | |||||||
\(762\) | 135.698 | 4.91582 | ||||||||
\(763\) | 3.29011 | 0.119110 | ||||||||
\(764\) | −111.374 | −4.02939 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.2029 | 0.693829 | ||||||||
\(767\) | 1.05815 | 0.0382074 | ||||||||
\(768\) | 128.917 | 4.65188 | ||||||||
\(769\) | 25.4156 | 0.916511 | 0.458256 | − | 0.888820i | \(-0.348474\pi\) | ||||
0.458256 | + | 0.888820i | \(0.348474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 56.1690 | 2.02288 | ||||||||
\(772\) | −125.587 | −4.51996 | ||||||||
\(773\) | −2.14231 | −0.0770536 | −0.0385268 | − | 0.999258i | \(-0.512266\pi\) | ||||
−0.0385268 | + | 0.999258i | \(0.512266\pi\) | |||||||
\(774\) | 12.3199 | 0.442831 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 100.180 | 3.59623 | ||||||||
\(777\) | 2.03712 | 0.0730812 | ||||||||
\(778\) | 0.744881 | 0.0267053 | ||||||||
\(779\) | −1.04718 | −0.0375192 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3726 | 0.406945 | ||||||||
\(782\) | 27.9284 | 0.998716 | ||||||||
\(783\) | −4.58650 | −0.163908 | ||||||||
\(784\) | −106.508 | −3.80386 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −113.024 | −4.03142 | ||||||||
\(787\) | 36.0836 | 1.28624 | 0.643121 | − | 0.765765i | \(-0.277639\pi\) | ||||
0.643121 | + | 0.765765i | \(0.277639\pi\) | |||||||
\(788\) | −56.8606 | −2.02557 | ||||||||
\(789\) | 12.1033 | 0.430889 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.35773 | −0.0482754 | ||||||||
\(792\) | −145.864 | −5.18304 | ||||||||
\(793\) | −7.95874 | −0.282623 | ||||||||
\(794\) | 19.9529 | 0.708102 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.6758 | 0.413839 | ||||||||
\(797\) | 19.3971 | 0.687081 | 0.343541 | − | 0.939138i | \(-0.388374\pi\) | ||||
0.343541 | + | 0.939138i | \(0.388374\pi\) | |||||||
\(798\) | 18.9292 | 0.670086 | ||||||||
\(799\) | −28.4370 | −1.00603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 23.2000 | 0.819732 | ||||||||
\(802\) | 56.9553 | 2.01116 | ||||||||
\(803\) | 78.4136 | 2.76716 | ||||||||
\(804\) | 166.716 | 5.87961 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.7033 | 0.517902 | ||||||||
\(807\) | 5.02684 | 0.176953 | ||||||||
\(808\) | −79.7964 | −2.80723 | ||||||||
\(809\) | 39.5269 | 1.38969 | 0.694846 | − | 0.719158i | \(-0.255472\pi\) | ||||
0.694846 | + | 0.719158i | \(0.255472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.5967 | 1.46066 | 0.730329 | − | 0.683095i | \(-0.239367\pi\) | ||||
0.730329 | + | 0.683095i | \(0.239367\pi\) | |||||||
\(812\) | 11.6207 | 0.407805 | ||||||||
\(813\) | −54.1298 | −1.89841 | ||||||||
\(814\) | −32.9817 | −1.15601 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −145.763 | −5.10271 | ||||||||
\(817\) | 12.1485 | 0.425020 | ||||||||
\(818\) | 49.0342 | 1.71444 | ||||||||
\(819\) | −1.46445 | −0.0511719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.9498 | −1.56876 | −0.784380 | − | 0.620280i | \(-0.787019\pi\) | ||||
−0.784380 | + | 0.620280i | \(0.787019\pi\) | |||||||
\(822\) | −113.572 | −3.96126 | ||||||||
\(823\) | −17.8689 | −0.622870 | −0.311435 | − | 0.950268i | \(-0.600810\pi\) | ||||
−0.311435 | + | 0.950268i | \(0.600810\pi\) | |||||||
\(824\) | −150.839 | −5.25472 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.872618 | 0.0303623 | ||||||||
\(827\) | −24.8985 | −0.865806 | −0.432903 | − | 0.901440i | \(-0.642511\pi\) | ||||
−0.432903 | + | 0.901440i | \(0.642511\pi\) | |||||||
\(828\) | 37.4626 | 1.30192 | ||||||||
\(829\) | 35.1635 | 1.22128 | 0.610640 | − | 0.791909i | \(-0.290912\pi\) | ||||
0.610640 | + | 0.791909i | \(0.290912\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.1001 | −2.22361 | ||||||||
\(832\) | −44.9893 | −1.55972 | ||||||||
\(833\) | 26.9419 | 0.933482 | ||||||||
\(834\) | −96.4534 | −3.33991 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −225.152 | −7.78704 | ||||||||
\(837\) | −3.51585 | −0.121526 | ||||||||
\(838\) | −20.3790 | −0.703981 | ||||||||
\(839\) | 35.9651 | 1.24165 | 0.620826 | − | 0.783948i | \(-0.286797\pi\) | ||||
0.620826 | + | 0.783948i | \(0.286797\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.74506 | −0.0946571 | ||||||||
\(842\) | 29.8049 | 1.02714 | ||||||||
\(843\) | 16.5459 | 0.569870 | ||||||||
\(844\) | −30.8837 | −1.06306 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −51.9218 | −1.78511 | ||||||||
\(847\) | 8.92718 | 0.306742 | ||||||||
\(848\) | 174.260 | 5.98411 | ||||||||
\(849\) | 21.3592 | 0.733046 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.41138 | 0.185500 | ||||||||
\(852\) | 26.0748 | 0.893308 | ||||||||
\(853\) | 20.1505 | 0.689939 | 0.344970 | − | 0.938614i | \(-0.387889\pi\) | ||||
0.344970 | + | 0.938614i | \(0.387889\pi\) | |||||||
\(854\) | −6.56331 | −0.224592 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −168.823 | −5.77025 | ||||||||
\(857\) | −32.5725 | −1.11266 | −0.556328 | − | 0.830963i | \(-0.687790\pi\) | ||||
−0.556328 | + | 0.830963i | \(0.687790\pi\) | |||||||
\(858\) | 50.8328 | 1.73540 | ||||||||
\(859\) | 11.5974 | 0.395698 | 0.197849 | − | 0.980233i | \(-0.436604\pi\) | ||||
0.197849 | + | 0.980233i | \(0.436604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.143237 | 0.00488152 | ||||||||
\(862\) | −38.8804 | −1.32427 | ||||||||
\(863\) | 3.25780 | 0.110897 | 0.0554485 | − | 0.998462i | \(-0.482341\pi\) | ||||
0.0554485 | + | 0.998462i | \(0.482341\pi\) | |||||||
\(864\) | 20.9229 | 0.711812 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.2734 | −0.994749 | ||||||||
\(867\) | −3.43847 | −0.116776 | ||||||||
\(868\) | 8.90800 | 0.302357 | ||||||||
\(869\) | −82.2143 | −2.78893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.3118 | −0.586589 | ||||||||
\(872\) | −78.0209 | −2.64212 | ||||||||
\(873\) | −27.0510 | −0.915539 | ||||||||
\(874\) | 50.2833 | 1.70086 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 179.784 | 6.07435 | ||||||||
\(877\) | 21.9443 | 0.741006 | 0.370503 | − | 0.928831i | \(-0.379185\pi\) | ||||
0.370503 | + | 0.928831i | \(0.379185\pi\) | |||||||
\(878\) | 71.4649 | 2.41182 | ||||||||
\(879\) | −67.4397 | −2.27469 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0285 | 0.843233 | 0.421616 | − | 0.906774i | \(-0.361463\pi\) | ||||
0.421616 | + | 0.906774i | \(0.361463\pi\) | |||||||
\(882\) | 49.1921 | 1.65638 | ||||||||
\(883\) | −13.6265 | −0.458568 | −0.229284 | − | 0.973360i | \(-0.573639\pi\) | ||||
−0.229284 | + | 0.973360i | \(0.573639\pi\) | |||||||
\(884\) | 29.7731 | 1.00138 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 89.0834 | 2.99282 | ||||||||
\(887\) | −43.3273 | −1.45479 | −0.727394 | − | 0.686220i | \(-0.759269\pi\) | ||||
−0.727394 | + | 0.686220i | \(0.759269\pi\) | |||||||
\(888\) | −48.3077 | −1.62110 | ||||||||
\(889\) | −8.53702 | −0.286322 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −57.2116 | −1.91666 | ||||||||
\(892\) | −4.14339 | −0.138731 | ||||||||
\(893\) | −51.1990 | −1.71331 | ||||||||
\(894\) | −58.8594 | −1.96855 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17.9548 | −0.599827 | ||||||||
\(897\) | −8.34025 | −0.278473 | ||||||||
\(898\) | 76.2417 | 2.54422 | ||||||||
\(899\) | 20.1261 | 0.671244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.0802 | −1.46853 | ||||||||
\(902\) | −2.31907 | −0.0772166 | ||||||||
\(903\) | −1.66171 | −0.0552982 | ||||||||
\(904\) | 32.1969 | 1.07085 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.50997 | −0.216279 | ||||||||
\(907\) | −38.2121 | −1.26881 | −0.634406 | − | 0.773000i | \(-0.718755\pi\) | ||||
−0.634406 | + | 0.773000i | \(0.718755\pi\) | |||||||
\(908\) | 15.8992 | 0.527634 | ||||||||
\(909\) | 21.5471 | 0.714671 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.2420 | −1.56520 | −0.782599 | − | 0.622526i | \(-0.786106\pi\) | ||||
−0.782599 | + | 0.622526i | \(0.786106\pi\) | |||||||
\(912\) | −262.437 | −8.69015 | ||||||||
\(913\) | −11.9182 | −0.394436 | ||||||||
\(914\) | −12.8477 | −0.424963 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 116.613 | 3.85300 | ||||||||
\(917\) | 7.11052 | 0.234810 | ||||||||
\(918\) | −9.69067 | −0.319840 | ||||||||
\(919\) | −20.7803 | −0.685480 | −0.342740 | − | 0.939430i | \(-0.611355\pi\) | ||||
−0.342740 | + | 0.939430i | \(0.611355\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.8947 | 0.655552 | ||||||||
\(922\) | 49.3193 | 1.62424 | ||||||||
\(923\) | −2.70762 | −0.0891225 | ||||||||
\(924\) | 30.7971 | 1.01315 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −95.0938 | −3.12498 | ||||||||
\(927\) | 40.7303 | 1.33776 | ||||||||
\(928\) | −119.771 | −3.93167 | ||||||||
\(929\) | 16.1602 | 0.530198 | 0.265099 | − | 0.964221i | \(-0.414595\pi\) | ||||
0.265099 | + | 0.964221i | \(0.414595\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.5073 | 1.58976 | ||||||||
\(932\) | −109.087 | −3.57327 | ||||||||
\(933\) | 20.6362 | 0.675598 | ||||||||
\(934\) | 12.9141 | 0.422563 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 34.7275 | 1.13510 | ||||||||
\(937\) | −1.67931 | −0.0548605 | −0.0274303 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274303 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(938\) | −14.2765 | −0.466144 | ||||||||
\(939\) | −39.0186 | −1.27332 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.66990 | 0.0544370 | 0.0272185 | − | 0.999630i | \(-0.491335\pi\) | ||||
0.0272185 | + | 0.999630i | \(0.491335\pi\) | |||||||
\(942\) | 72.5339 | 2.36328 | ||||||||
\(943\) | 0.380494 | 0.0123906 | ||||||||
\(944\) | −12.0981 | −0.393759 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.9037 | 0.874714 | ||||||||
\(947\) | −11.8324 | −0.384501 | −0.192251 | − | 0.981346i | \(-0.561579\pi\) | ||||
−0.192251 | + | 0.981346i | \(0.561579\pi\) | |||||||
\(948\) | −188.498 | −6.12214 | ||||||||
\(949\) | −18.6689 | −0.606018 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.3452 | −1.01644 | ||||||||
\(952\) | 15.6851 | 0.508356 | ||||||||
\(953\) | 5.06600 | 0.164104 | 0.0820519 | − | 0.996628i | \(-0.473853\pi\) | ||||
0.0820519 | + | 0.996628i | \(0.473853\pi\) | |||||||
\(954\) | −80.4842 | −2.60577 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 27.0216 | 0.873942 | ||||||||
\(957\) | 69.5809 | 2.24923 | ||||||||
\(958\) | −39.0133 | −1.26046 | ||||||||
\(959\) | 7.14500 | 0.230724 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5720 | −0.502323 | ||||||||
\(962\) | 7.85236 | 0.253170 | ||||||||
\(963\) | 45.5865 | 1.46900 | ||||||||
\(964\) | −32.3404 | −1.04161 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.87793 | −0.221294 | ||||||||
\(967\) | −28.1196 | −0.904265 | −0.452132 | − | 0.891951i | \(-0.649337\pi\) | ||||
−0.452132 | + | 0.891951i | \(0.649337\pi\) | |||||||
\(968\) | −211.697 | −6.80420 | ||||||||
\(969\) | 66.3851 | 2.13260 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.2285 | 1.51563 | 0.757817 | − | 0.652468i | \(-0.226266\pi\) | ||||
0.757817 | + | 0.652468i | \(0.226266\pi\) | |||||||
\(972\) | −116.303 | −3.73042 | ||||||||
\(973\) | 6.06806 | 0.194533 | ||||||||
\(974\) | −30.3929 | −0.973852 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 90.9946 | 2.91267 | ||||||||
\(977\) | −11.8376 | −0.378718 | −0.189359 | − | 0.981908i | \(-0.560641\pi\) | ||||
−0.189359 | + | 0.981908i | \(0.560641\pi\) | |||||||
\(978\) | −86.3253 | −2.76038 | ||||||||
\(979\) | 50.6630 | 1.61920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.0676 | 0.672638 | ||||||||
\(982\) | 43.3792 | 1.38429 | ||||||||
\(983\) | 4.86039 | 0.155022 | 0.0775112 | − | 0.996991i | \(-0.475303\pi\) | ||||
0.0775112 | + | 0.996991i | \(0.475303\pi\) | |||||||
\(984\) | −3.39670 | −0.108283 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 55.4732 | 1.76663 | ||||||||
\(987\) | 7.00318 | 0.222914 | ||||||||
\(988\) | 53.6047 | 1.70539 | ||||||||
\(989\) | −4.41414 | −0.140362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.7600 | −1.26302 | −0.631508 | − | 0.775369i | \(-0.717564\pi\) | ||||
−0.631508 | + | 0.775369i | \(0.717564\pi\) | |||||||
\(992\) | −91.8122 | −2.91504 | ||||||||
\(993\) | 52.1029 | 1.65343 | ||||||||
\(994\) | −2.23289 | −0.0708229 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −27.3257 | −0.865849 | ||||||||
\(997\) | −58.7462 | −1.86051 | −0.930256 | − | 0.366912i | \(-0.880415\pi\) | ||||
−0.930256 | + | 0.366912i | \(0.880415\pi\) | |||||||
\(998\) | −11.8256 | −0.374333 | ||||||||
\(999\) | −1.87766 | −0.0594065 |
(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 | 3775.2.a.r.1.1 | 18 | ||
5.4 | even | 2 | 755.2.a.k.1.18 | ✓ | 18 | ||
15.14 | odd | 2 | 6795.2.a.bi.1.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
755.2.a.k.1.18 | ✓ | 18 | 5.4 | even | 2 | ||
3775.2.a.r.1.1 | 18 | 1.1 | even | 1 | trivial | ||
6795.2.a.bi.1.1 | 18 | 15.14 | odd | 2 |