Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [755,2,Mod(1,755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(755, 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("755.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 755 = 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 755.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: | \(6.02870535261\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.74545\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 755.1 |
$q$-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 | \(-0.0772918\pi\) | ||||
0.970664 | + | 0.240440i | \(0.0772918\pi\) | |||||||
\(3\) | −2.37118 | −1.36900 | −0.684501 | − | 0.729012i | \(-0.739980\pi\) | ||||
−0.684501 | + | 0.729012i | \(0.739980\pi\) | |||||||
\(4\) | 5.53751 | 2.76875 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −6.50997 | −2.65768 | ||||||||
\(7\) | −0.409554 | −0.154797 | −0.0773984 | − | 0.997000i | \(-0.524661\pi\) | ||||
−0.0773984 | + | 0.997000i | \(0.524661\pi\) | |||||||
\(8\) | 9.71206 | 3.43373 | ||||||||
\(9\) | 2.62250 | 0.874168 | ||||||||
\(10\) | −2.74545 | −0.868188 | ||||||||
\(11\) | 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 | \(-0.439450\pi\) | ||||
0.189080 | + | 0.981962i | \(0.439450\pi\) | |||||||
\(14\) | −1.12441 | −0.300511 | ||||||||
\(15\) | 2.37118 | 0.612237 | ||||||||
\(16\) | 15.5890 | 3.89724 | ||||||||
\(17\) | 3.94334 | 0.956399 | 0.478200 | − | 0.878251i | \(-0.341290\pi\) | ||||
0.478200 | + | 0.878251i | \(0.341290\pi\) | |||||||
\(18\) | 7.19996 | 1.69705 | ||||||||
\(19\) | −7.09974 | −1.62879 | −0.814396 | − | 0.580310i | \(-0.802931\pi\) | ||||
−0.814396 | + | 0.580310i | \(0.802931\pi\) | |||||||
\(20\) | −5.53751 | −1.23822 | ||||||||
\(21\) | 0.971127 | 0.211917 | ||||||||
\(22\) | 15.7229 | 3.35214 | ||||||||
\(23\) | −2.57969 | −0.537903 | −0.268951 | − | 0.963154i | \(-0.586677\pi\) | ||||
−0.268951 | + | 0.963154i | \(0.586677\pi\) | |||||||
\(24\) | −23.0291 | −4.70079 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 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 | \(0.342178\pi\) | |||||||
\(30\) | 6.50997 | 1.18855 | ||||||||
\(31\) | 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 | ||||||||
\(35\) | 0.409554 | 0.0692272 | ||||||||
\(36\) | 14.5221 | 2.42036 | ||||||||
\(37\) | −2.09769 | −0.344857 | −0.172429 | − | 0.985022i | \(-0.555161\pi\) | ||||
−0.172429 | + | 0.985022i | \(0.555161\pi\) | |||||||
\(38\) | −19.4920 | −3.16202 | ||||||||
\(39\) | −3.23304 | −0.517701 | ||||||||
\(40\) | −9.71206 | −1.53561 | ||||||||
\(41\) | 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 | \(-0.458351\pi\) | ||||
0.130471 | + | 0.991452i | \(0.458351\pi\) | |||||||
\(44\) | 31.7127 | 4.78087 | ||||||||
\(45\) | −2.62250 | −0.390940 | ||||||||
\(46\) | −7.08242 | −1.04425 | ||||||||
\(47\) | −7.21140 | −1.05189 | −0.525945 | − | 0.850518i | \(-0.676288\pi\) | ||||
−0.525945 | + | 0.850518i | \(0.676288\pi\) | |||||||
\(48\) | −36.9643 | −5.33534 | ||||||||
\(49\) | −6.83227 | −0.976038 | ||||||||
\(50\) | 2.74545 | 0.388266 | ||||||||
\(51\) | −9.35037 | −1.30931 | ||||||||
\(52\) | 7.55024 | 1.04703 | ||||||||
\(53\) | −11.1784 | −1.53547 | −0.767737 | − | 0.640766i | \(-0.778617\pi\) | ||||
−0.767737 | + | 0.640766i | \(0.778617\pi\) | |||||||
\(54\) | 2.45748 | 0.334421 | ||||||||
\(55\) | −5.72690 | −0.772214 | ||||||||
\(56\) | −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 | \(0.516087\pi\) | |||||||
\(60\) | 13.1304 | 1.69513 | ||||||||
\(61\) | 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 | ||||||||
\(65\) | −1.36347 | −0.169118 | ||||||||
\(66\) | −37.2819 | −4.58909 | ||||||||
\(67\) | −12.6969 | −1.55117 | −0.775585 | − | 0.631243i | \(-0.782545\pi\) | ||||
−0.775585 | + | 0.631243i | \(0.782545\pi\) | |||||||
\(68\) | 21.8363 | 2.64803 | ||||||||
\(69\) | 6.11692 | 0.736390 | ||||||||
\(70\) | 1.12441 | 0.134393 | ||||||||
\(71\) | 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 | \(-0.795844\pi\) | ||||
−0.801274 | + | 0.598298i | \(0.795844\pi\) | |||||||
\(74\) | −5.75909 | −0.669481 | ||||||||
\(75\) | −2.37118 | −0.273801 | ||||||||
\(76\) | −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 | \(0.799222\pi\) | |||||||
\(80\) | −15.5890 | −1.74290 | ||||||||
\(81\) | −9.98998 | −1.11000 | ||||||||
\(82\) | 0.404944 | 0.0447185 | ||||||||
\(83\) | 2.08110 | 0.228430 | 0.114215 | − | 0.993456i | \(-0.463565\pi\) | ||||
0.114215 | + | 0.993456i | \(0.463565\pi\) | |||||||
\(84\) | 5.37762 | 0.586747 | ||||||||
\(85\) | −3.94334 | −0.427715 | ||||||||
\(86\) | 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 | \(0.344663\pi\) | |||||||
\(90\) | −7.19996 | −0.758943 | ||||||||
\(91\) | −0.558415 | −0.0585378 | ||||||||
\(92\) | −14.2851 | −1.48932 | ||||||||
\(93\) | −9.31364 | −0.965780 | ||||||||
\(94\) | −19.7986 | −2.04206 | ||||||||
\(95\) | 7.09974 | 0.728417 | ||||||||
\(96\) | −55.4256 | −5.65685 | ||||||||
\(97\) | 10.3150 | 1.04733 | 0.523663 | − | 0.851926i | \(-0.324565\pi\) | ||||
0.523663 | + | 0.851926i | \(0.324565\pi\) | |||||||
\(98\) | −18.7577 | −1.89481 | ||||||||
\(99\) | 15.0188 | 1.50945 | ||||||||
\(100\) | 5.53751 | 0.553751 | ||||||||
\(101\) | 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 | \(-0.777341\pi\) | ||||
−0.765161 | + | 0.643839i | \(0.777341\pi\) | |||||||
\(104\) | 13.2421 | 1.29850 | ||||||||
\(105\) | −0.971127 | −0.0947723 | ||||||||
\(106\) | −30.6898 | −2.98086 | ||||||||
\(107\) | −17.3828 | −1.68046 | −0.840230 | − | 0.542231i | \(-0.817580\pi\) | ||||
−0.840230 | + | 0.542231i | \(0.817580\pi\) | |||||||
\(108\) | 4.95668 | 0.476956 | ||||||||
\(109\) | 8.03341 | 0.769461 | 0.384730 | − | 0.923029i | \(-0.374294\pi\) | ||||
0.384730 | + | 0.923029i | \(0.374294\pi\) | |||||||
\(110\) | −15.7229 | −1.49912 | ||||||||
\(111\) | 4.97399 | 0.472111 | ||||||||
\(112\) | −6.38453 | −0.603281 | ||||||||
\(113\) | 3.31515 | 0.311863 | 0.155932 | − | 0.987768i | \(-0.450162\pi\) | ||||
0.155932 | + | 0.987768i | \(0.450162\pi\) | |||||||
\(114\) | 46.2190 | 4.32881 | ||||||||
\(115\) | 2.57969 | 0.240557 | ||||||||
\(116\) | 28.3740 | 2.63446 | ||||||||
\(117\) | 3.57571 | 0.330575 | ||||||||
\(118\) | −2.13066 | −0.196143 | ||||||||
\(119\) | −1.61501 | −0.148048 | ||||||||
\(120\) | 23.0291 | 2.10226 | ||||||||
\(121\) | 21.7973 | 1.98158 | ||||||||
\(122\) | 16.0255 | 1.45088 | ||||||||
\(123\) | −0.349740 | −0.0315350 | ||||||||
\(124\) | 21.7505 | 1.95325 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.94877 | −0.262698 | ||||||||
\(127\) | 20.8447 | 1.84967 | 0.924833 | − | 0.380374i | \(-0.124205\pi\) | ||||
0.924833 | + | 0.380374i | \(0.124205\pi\) | |||||||
\(128\) | 43.8399 | 3.87493 | ||||||||
\(129\) | −4.05736 | −0.357231 | ||||||||
\(130\) | −3.74335 | −0.328313 | ||||||||
\(131\) | 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 | ||||||||
\(135\) | −0.895110 | −0.0770388 | ||||||||
\(136\) | 38.2979 | 3.28402 | ||||||||
\(137\) | −17.4458 | −1.49050 | −0.745248 | − | 0.666788i | \(-0.767669\pi\) | ||||
−0.745248 | + | 0.666788i | \(0.767669\pi\) | |||||||
\(138\) | 16.7937 | 1.42958 | ||||||||
\(139\) | 14.8163 | 1.25670 | 0.628349 | − | 0.777931i | \(-0.283731\pi\) | ||||
0.628349 | + | 0.777931i | \(0.283731\pi\) | |||||||
\(140\) | 2.26791 | 0.191673 | ||||||||
\(141\) | 17.0995 | 1.44004 | ||||||||
\(142\) | 5.45200 | 0.457522 | ||||||||
\(143\) | 7.80846 | 0.652976 | ||||||||
\(144\) | 40.8822 | 3.40685 | ||||||||
\(145\) | −5.12396 | −0.425522 | ||||||||
\(146\) | −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 | \(0.379237\pi\) | |||||||
\(150\) | −6.50997 | −0.531537 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | −68.9531 | −5.59283 | ||||||||
\(153\) | 10.3414 | 0.836054 | ||||||||
\(154\) | −6.43938 | −0.518900 | ||||||||
\(155\) | −3.92785 | −0.315492 | ||||||||
\(156\) | −17.9030 | −1.43339 | ||||||||
\(157\) | 11.1420 | 0.889227 | 0.444613 | − | 0.895723i | \(-0.353341\pi\) | ||||
0.444613 | + | 0.895723i | \(0.353341\pi\) | |||||||
\(158\) | −39.4132 | −3.13555 | ||||||||
\(159\) | 26.5061 | 2.10207 | ||||||||
\(160\) | −23.3747 | −1.84793 | ||||||||
\(161\) | 1.05652 | 0.0832656 | ||||||||
\(162\) | −27.4270 | −2.15487 | ||||||||
\(163\) | −13.2605 | −1.03864 | −0.519321 | − | 0.854579i | \(-0.673815\pi\) | ||||
−0.519321 | + | 0.854579i | \(0.673815\pi\) | |||||||
\(164\) | 0.816761 | 0.0637783 | ||||||||
\(165\) | 13.5795 | 1.05716 | ||||||||
\(166\) | 5.71355 | 0.443458 | ||||||||
\(167\) | −7.09489 | −0.549019 | −0.274509 | − | 0.961584i | \(-0.588515\pi\) | ||||
−0.274509 | + | 0.961584i | \(0.588515\pi\) | |||||||
\(168\) | 9.43164 | 0.727667 | ||||||||
\(169\) | −11.1409 | −0.856996 | ||||||||
\(170\) | −10.8262 | −0.830335 | ||||||||
\(171\) | −18.6191 | −1.42384 | ||||||||
\(172\) | 9.47530 | 0.722485 | ||||||||
\(173\) | −17.4978 | −1.33033 | −0.665165 | − | 0.746697i | \(-0.731639\pi\) | ||||
−0.665165 | + | 0.746697i | \(0.731639\pi\) | |||||||
\(174\) | −33.3568 | −2.52877 | ||||||||
\(175\) | −0.409554 | −0.0309594 | ||||||||
\(176\) | 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 | \(0.709415\pi\) | |||||||
\(180\) | −14.5221 | −1.08242 | ||||||||
\(181\) | −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 | ||||||||
\(185\) | 2.09769 | 0.154225 | ||||||||
\(186\) | −25.5702 | −1.87490 | ||||||||
\(187\) | 22.5831 | 1.65144 | ||||||||
\(188\) | −39.9332 | −2.91243 | ||||||||
\(189\) | −0.366596 | −0.0266659 | ||||||||
\(190\) | 19.4920 | 1.41410 | ||||||||
\(191\) | −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 | \(-0.196052\pi\) | ||||
0.816245 | + | 0.577706i | \(0.196052\pi\) | |||||||
\(194\) | 28.3192 | 2.03320 | ||||||||
\(195\) | 3.23304 | 0.231523 | ||||||||
\(196\) | −37.8337 | −2.70241 | ||||||||
\(197\) | 10.2683 | 0.731583 | 0.365792 | − | 0.930697i | \(-0.380798\pi\) | ||||
0.365792 | + | 0.930697i | \(0.380798\pi\) | |||||||
\(198\) | 41.2334 | 2.93033 | ||||||||
\(199\) | 2.10850 | 0.149468 | 0.0747338 | − | 0.997204i | \(-0.476189\pi\) | ||||
0.0747338 | + | 0.997204i | \(0.476189\pi\) | |||||||
\(200\) | 9.71206 | 0.686746 | ||||||||
\(201\) | 30.1066 | 2.12356 | ||||||||
\(202\) | 22.5572 | 1.58712 | ||||||||
\(203\) | −2.09854 | −0.147288 | ||||||||
\(204\) | −51.7777 | −3.62517 | ||||||||
\(205\) | −0.147496 | −0.0103016 | ||||||||
\(206\) | −42.6398 | −2.97086 | ||||||||
\(207\) | −6.76525 | −0.470218 | ||||||||
\(208\) | 21.2551 | 1.47378 | ||||||||
\(209\) | −40.6594 | −2.81247 | ||||||||
\(210\) | −2.66618 | −0.183984 | ||||||||
\(211\) | −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 | ||||||||
\(215\) | −1.71111 | −0.116697 | ||||||||
\(216\) | 8.69336 | 0.591508 | ||||||||
\(217\) | −1.60867 | −0.109203 | ||||||||
\(218\) | 22.0553 | 1.49378 | ||||||||
\(219\) | 32.4666 | 2.19389 | ||||||||
\(220\) | −31.7127 | −2.13807 | ||||||||
\(221\) | 5.37663 | 0.361671 | ||||||||
\(222\) | 13.6559 | 0.916521 | ||||||||
\(223\) | 0.748241 | 0.0501059 | 0.0250530 | − | 0.999686i | \(-0.492025\pi\) | ||||
0.0250530 | + | 0.999686i | \(0.492025\pi\) | |||||||
\(224\) | −9.57319 | −0.639636 | ||||||||
\(225\) | 2.62250 | 0.174834 | ||||||||
\(226\) | 9.10159 | 0.605429 | ||||||||
\(227\) | −2.87119 | −0.190567 | −0.0952837 | − | 0.995450i | \(-0.530376\pi\) | ||||
−0.0952837 | + | 0.995450i | \(0.530376\pi\) | |||||||
\(228\) | 93.2227 | 6.17382 | ||||||||
\(229\) | 21.0587 | 1.39160 | 0.695799 | − | 0.718236i | \(-0.255050\pi\) | ||||
0.695799 | + | 0.718236i | \(0.255050\pi\) | |||||||
\(230\) | 7.08242 | 0.467001 | ||||||||
\(231\) | 5.56154 | 0.365923 | ||||||||
\(232\) | 49.7642 | 3.26718 | ||||||||
\(233\) | 19.6997 | 1.29057 | 0.645285 | − | 0.763942i | \(-0.276739\pi\) | ||||
0.645285 | + | 0.763942i | \(0.276739\pi\) | |||||||
\(234\) | 9.81695 | 0.641754 | ||||||||
\(235\) | 7.21140 | 0.470420 | ||||||||
\(236\) | −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 | \(0.449553\pi\) | |||||||
\(240\) | 36.9643 | 2.38604 | ||||||||
\(241\) | −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 | ||||||||
\(245\) | 6.83227 | 0.436497 | ||||||||
\(246\) | −0.960195 | −0.0612198 | ||||||||
\(247\) | −9.68029 | −0.615942 | ||||||||
\(248\) | 38.1475 | 2.42237 | ||||||||
\(249\) | −4.93466 | −0.312721 | ||||||||
\(250\) | −2.74545 | −0.173638 | ||||||||
\(251\) | −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 | ||||||||
\(255\) | 9.35037 | 0.585543 | ||||||||
\(256\) | 54.3681 | 3.39800 | ||||||||
\(257\) | −23.6882 | −1.47763 | −0.738814 | − | 0.673909i | \(-0.764614\pi\) | ||||
−0.738814 | + | 0.673909i | \(0.764614\pi\) | |||||||
\(258\) | −11.1393 | −0.693502 | ||||||||
\(259\) | 0.859115 | 0.0533828 | ||||||||
\(260\) | −7.55024 | −0.468246 | ||||||||
\(261\) | 13.4376 | 0.831767 | ||||||||
\(262\) | 47.6655 | 2.94478 | ||||||||
\(263\) | −5.10433 | −0.314747 | −0.157373 | − | 0.987539i | \(-0.550303\pi\) | ||||
−0.157373 | + | 0.987539i | \(0.550303\pi\) | |||||||
\(264\) | −131.885 | −8.11696 | ||||||||
\(265\) | 11.1784 | 0.686684 | ||||||||
\(266\) | 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 | \(0.479414\pi\) | |||||||
\(270\) | −2.45748 | −0.149558 | ||||||||
\(271\) | −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 | ||||||||
\(275\) | 5.72690 | 0.345345 | ||||||||
\(276\) | 33.8725 | 2.03888 | ||||||||
\(277\) | 27.0330 | 1.62425 | 0.812127 | − | 0.583481i | \(-0.198310\pi\) | ||||
0.812127 | + | 0.583481i | \(0.198310\pi\) | |||||||
\(278\) | 40.6773 | 2.43966 | ||||||||
\(279\) | 10.3008 | 0.616693 | ||||||||
\(280\) | 3.97761 | 0.237708 | ||||||||
\(281\) | 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 | \(-0.586274\pi\) | ||||
−0.267730 | + | 0.963494i | \(0.586274\pi\) | |||||||
\(284\) | 10.9965 | 0.652525 | ||||||||
\(285\) | −16.8348 | −0.997205 | ||||||||
\(286\) | 21.4378 | 1.26764 | ||||||||
\(287\) | −0.0604076 | −0.00356575 | ||||||||
\(288\) | 61.3002 | 3.61215 | ||||||||
\(289\) | −1.45011 | −0.0853003 | ||||||||
\(290\) | −14.0676 | −0.826077 | ||||||||
\(291\) | −24.4587 | −1.43379 | ||||||||
\(292\) | −75.8205 | −4.43706 | ||||||||
\(293\) | 28.4414 | 1.66156 | 0.830782 | − | 0.556598i | \(-0.187893\pi\) | ||||
0.830782 | + | 0.556598i | \(0.187893\pi\) | |||||||
\(294\) | 44.4778 | 2.59400 | ||||||||
\(295\) | 0.776067 | 0.0451844 | ||||||||
\(296\) | −20.3728 | −1.18415 | ||||||||
\(297\) | 5.12620 | 0.297452 | ||||||||
\(298\) | 24.8228 | 1.43795 | ||||||||
\(299\) | −3.51734 | −0.203413 | ||||||||
\(300\) | −13.1304 | −0.758086 | ||||||||
\(301\) | −0.700793 | −0.0403930 | ||||||||
\(302\) | 2.74545 | 0.157983 | ||||||||
\(303\) | −19.4822 | −1.11922 | ||||||||
\(304\) | −110.678 | −6.34780 | ||||||||
\(305\) | −5.83711 | −0.334232 | ||||||||
\(306\) | 28.3919 | 1.62305 | ||||||||
\(307\) | −8.39020 | −0.478854 | −0.239427 | − | 0.970914i | \(-0.576960\pi\) | ||||
−0.239427 | + | 0.970914i | \(0.576960\pi\) | |||||||
\(308\) | −12.9881 | −0.740064 | ||||||||
\(309\) | 36.8270 | 2.09502 | ||||||||
\(310\) | −10.7837 | −0.612474 | ||||||||
\(311\) | 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 | \(-0.346035\pi\) | ||||
0.465055 | + | 0.885282i | \(0.346035\pi\) | |||||||
\(314\) | 30.5898 | 1.72628 | ||||||||
\(315\) | 1.07406 | 0.0605163 | ||||||||
\(316\) | −79.4955 | −4.47197 | ||||||||
\(317\) | 13.2192 | 0.742466 | 0.371233 | − | 0.928540i | \(-0.378935\pi\) | ||||
0.371233 | + | 0.928540i | \(0.378935\pi\) | |||||||
\(318\) | 72.7711 | 4.08080 | ||||||||
\(319\) | 29.3444 | 1.64297 | ||||||||
\(320\) | −32.9961 | −1.84454 | ||||||||
\(321\) | 41.2178 | 2.30055 | ||||||||
\(322\) | 2.90063 | 0.161646 | ||||||||
\(323\) | −27.9966 | −1.55777 | ||||||||
\(324\) | −55.3196 | −3.07331 | ||||||||
\(325\) | 1.36347 | 0.0756318 | ||||||||
\(326\) | −36.4060 | −2.01634 | ||||||||
\(327\) | −19.0487 | −1.05339 | ||||||||
\(328\) | 1.43249 | 0.0790961 | ||||||||
\(329\) | 2.95346 | 0.162829 | ||||||||
\(330\) | 37.2819 | 2.05230 | ||||||||
\(331\) | 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 | ||||||||
\(335\) | 12.6969 | 0.693705 | ||||||||
\(336\) | 15.1389 | 0.825893 | ||||||||
\(337\) | 8.04206 | 0.438079 | 0.219040 | − | 0.975716i | \(-0.429708\pi\) | ||||
0.219040 | + | 0.975716i | \(0.429708\pi\) | |||||||
\(338\) | −30.5869 | −1.66371 | ||||||||
\(339\) | −7.86083 | −0.426941 | ||||||||
\(340\) | −21.8363 | −1.18424 | ||||||||
\(341\) | 22.4944 | 1.21814 | ||||||||
\(342\) | −51.1178 | −2.76414 | ||||||||
\(343\) | 5.66506 | 0.305884 | ||||||||
\(344\) | 16.6184 | 0.896006 | ||||||||
\(345\) | −6.11692 | −0.329324 | ||||||||
\(346\) | −48.0392 | −2.58261 | ||||||||
\(347\) | −23.5159 | −1.26240 | −0.631201 | − | 0.775620i | \(-0.717438\pi\) | ||||
−0.631201 | + | 0.775620i | \(0.717438\pi\) | |||||||
\(348\) | −67.2798 | −3.60658 | ||||||||
\(349\) | 25.8680 | 1.38468 | 0.692341 | − | 0.721570i | \(-0.256579\pi\) | ||||
0.692341 | + | 0.721570i | \(0.256579\pi\) | |||||||
\(350\) | −1.12441 | −0.0601023 | ||||||||
\(351\) | 1.22046 | 0.0651432 | ||||||||
\(352\) | 133.864 | 7.13499 | ||||||||
\(353\) | −30.3878 | −1.61738 | −0.808689 | − | 0.588236i | \(-0.799822\pi\) | ||||
−0.808689 | + | 0.588236i | \(0.799822\pi\) | |||||||
\(354\) | 5.05217 | 0.268520 | ||||||||
\(355\) | −1.98583 | −0.105397 | ||||||||
\(356\) | 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 | \(0.627488\pi\) | |||||||
\(360\) | −25.4699 | −1.34238 | ||||||||
\(361\) | 31.4062 | 1.65296 | ||||||||
\(362\) | −29.7869 | −1.56557 | ||||||||
\(363\) | −51.6855 | −2.71278 | ||||||||
\(364\) | −3.09223 | −0.162077 | ||||||||
\(365\) | 13.6922 | 0.716681 | ||||||||
\(366\) | −37.9994 | −1.98626 | ||||||||
\(367\) | −5.94394 | −0.310271 | −0.155136 | − | 0.987893i | \(-0.549581\pi\) | ||||
−0.155136 | + | 0.987893i | \(0.549581\pi\) | |||||||
\(368\) | −40.2147 | −2.09634 | ||||||||
\(369\) | 0.386809 | 0.0201365 | ||||||||
\(370\) | 5.75909 | 0.299401 | ||||||||
\(371\) | 4.57816 | 0.237686 | ||||||||
\(372\) | −51.5744 | −2.67401 | ||||||||
\(373\) | 29.1043 | 1.50696 | 0.753482 | − | 0.657469i | \(-0.228373\pi\) | ||||
0.753482 | + | 0.657469i | \(0.228373\pi\) | |||||||
\(374\) | 62.0007 | 3.20598 | ||||||||
\(375\) | 2.37118 | 0.122447 | ||||||||
\(376\) | −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 | \(0.513616\pi\) | |||||||
\(380\) | 39.3148 | 2.01681 | ||||||||
\(381\) | −49.4265 | −2.53220 | ||||||||
\(382\) | −55.2186 | −2.82523 | ||||||||
\(383\) | 6.99444 | 0.357399 | 0.178700 | − | 0.983904i | \(-0.442811\pi\) | ||||
0.178700 | + | 0.983904i | \(0.442811\pi\) | |||||||
\(384\) | −103.952 | −5.30479 | ||||||||
\(385\) | 2.34547 | 0.119536 | ||||||||
\(386\) | 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 | \(0.502189\pi\) | |||||||
\(390\) | 8.87616 | 0.449462 | ||||||||
\(391\) | −10.1726 | −0.514450 | ||||||||
\(392\) | −66.3554 | −3.35145 | ||||||||
\(393\) | −41.1676 | −2.07663 | ||||||||
\(394\) | 28.1910 | 1.42024 | ||||||||
\(395\) | 14.3558 | 0.722320 | ||||||||
\(396\) | 83.1668 | 4.17929 | ||||||||
\(397\) | 7.26762 | 0.364751 | 0.182376 | − | 0.983229i | \(-0.441621\pi\) | ||||
0.182376 | + | 0.983229i | \(0.441621\pi\) | |||||||
\(398\) | 5.78879 | 0.290166 | ||||||||
\(399\) | −6.89474 | −0.345169 | ||||||||
\(400\) | 15.5890 | 0.779449 | ||||||||
\(401\) | −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 | ||||||||
\(405\) | 9.98998 | 0.496406 | ||||||||
\(406\) | −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 | \(0.645576\pi\) | |||||||
\(410\) | −0.404944 | −0.0199987 | ||||||||
\(411\) | 41.3672 | 2.04049 | ||||||||
\(412\) | −86.0035 | −4.23709 | ||||||||
\(413\) | 0.317841 | 0.0156399 | ||||||||
\(414\) | −18.5737 | −0.912846 | ||||||||
\(415\) | −2.08110 | −0.102157 | ||||||||
\(416\) | 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 | \(0.441965\pi\) | |||||||
\(420\) | −5.37762 | −0.262401 | ||||||||
\(421\) | −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 | ||||||||
\(425\) | 3.94334 | 0.191280 | ||||||||
\(426\) | −12.9277 | −0.626348 | ||||||||
\(427\) | −2.39061 | −0.115690 | ||||||||
\(428\) | −96.2574 | −4.65278 | ||||||||
\(429\) | −18.5153 | −0.893926 | ||||||||
\(430\) | −4.69778 | −0.226547 | ||||||||
\(431\) | 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 | \(-0.582472\pi\) | ||||
−0.256203 | + | 0.966623i | \(0.582472\pi\) | |||||||
\(434\) | −4.41651 | −0.211999 | ||||||||
\(435\) | 12.1498 | 0.582540 | ||||||||
\(436\) | 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 | \(0.713346\pi\) | |||||||
\(440\) | −55.6200 | −2.65158 | ||||||||
\(441\) | −17.9176 | −0.853221 | ||||||||
\(442\) | 14.7613 | 0.702122 | ||||||||
\(443\) | 32.4476 | 1.54163 | 0.770817 | − | 0.637057i | \(-0.219848\pi\) | ||||
0.770817 | + | 0.637057i | \(0.219848\pi\) | |||||||
\(444\) | 27.5435 | 1.30716 | ||||||||
\(445\) | −8.84651 | −0.419365 | ||||||||
\(446\) | 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 | \(0.727448\pi\) | |||||||
\(450\) | 7.19996 | 0.339409 | ||||||||
\(451\) | 0.844695 | 0.0397751 | ||||||||
\(452\) | 18.3577 | 0.863472 | ||||||||
\(453\) | −2.37118 | −0.111408 | ||||||||
\(454\) | −7.88271 | −0.369954 | ||||||||
\(455\) | 0.558415 | 0.0261789 | ||||||||
\(456\) | 163.500 | 7.65660 | ||||||||
\(457\) | −4.67961 | −0.218903 | −0.109452 | − | 0.993992i | \(-0.534909\pi\) | ||||
−0.109452 | + | 0.993992i | \(0.534909\pi\) | |||||||
\(458\) | 57.8157 | 2.70155 | ||||||||
\(459\) | 3.52972 | 0.164753 | ||||||||
\(460\) | 14.2851 | 0.666044 | ||||||||
\(461\) | −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 | \(-0.797757\pi\) | ||||
−0.804855 | + | 0.593471i | \(0.797757\pi\) | |||||||
\(464\) | 79.8773 | 3.70821 | ||||||||
\(465\) | 9.31364 | 0.431910 | ||||||||
\(466\) | 54.0846 | 2.50542 | ||||||||
\(467\) | 4.70383 | 0.217667 | 0.108834 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108834 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(468\) | 19.8005 | 0.915280 | ||||||||
\(469\) | 5.20006 | 0.240116 | ||||||||
\(470\) | 19.7986 | 0.913239 | ||||||||
\(471\) | −26.4197 | −1.21735 | ||||||||
\(472\) | −7.53721 | −0.346928 | ||||||||
\(473\) | 9.79937 | 0.450575 | ||||||||
\(474\) | 93.4560 | 4.29258 | ||||||||
\(475\) | −7.09974 | −0.325758 | ||||||||
\(476\) | −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 | \(0.394757\pi\) | |||||||
\(480\) | 55.4256 | 2.52982 | ||||||||
\(481\) | −2.86014 | −0.130411 | ||||||||
\(482\) | −16.0341 | −0.730334 | ||||||||
\(483\) | −2.50521 | −0.113991 | ||||||||
\(484\) | 120.703 | 5.48650 | ||||||||
\(485\) | −10.3150 | −0.468378 | ||||||||
\(486\) | 57.6620 | 2.61560 | ||||||||
\(487\) | −11.0703 | −0.501642 | −0.250821 | − | 0.968033i | \(-0.580701\pi\) | ||||
−0.250821 | + | 0.968033i | \(0.580701\pi\) | |||||||
\(488\) | 56.6904 | 2.56625 | ||||||||
\(489\) | 31.4430 | 1.42190 | ||||||||
\(490\) | 18.7577 | 0.847385 | ||||||||
\(491\) | −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 | ||||||||
\(495\) | −15.0188 | −0.675045 | ||||||||
\(496\) | 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 | \(0.469264\pi\) | |||||||
\(500\) | −5.53751 | −0.247645 | ||||||||
\(501\) | 16.8233 | 0.751608 | ||||||||
\(502\) | −28.3054 | −1.26333 | ||||||||
\(503\) | 23.2152 | 1.03511 | 0.517556 | − | 0.855649i | \(-0.326842\pi\) | ||||
0.517556 | + | 0.855649i | \(0.326842\pi\) | |||||||
\(504\) | −10.4313 | −0.464647 | ||||||||
\(505\) | −8.21622 | −0.365617 | ||||||||
\(506\) | −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 | \(0.693333\pi\) | |||||||
\(510\) | 25.6710 | 1.13673 | ||||||||
\(511\) | 5.60768 | 0.248069 | ||||||||
\(512\) | 61.5852 | 2.72171 | ||||||||
\(513\) | −6.35504 | −0.280582 | ||||||||
\(514\) | −65.0348 | −2.86856 | ||||||||
\(515\) | 15.5311 | 0.684381 | ||||||||
\(516\) | −22.4677 | −0.989084 | ||||||||
\(517\) | −41.2989 | −1.81632 | ||||||||
\(518\) | 2.35866 | 0.103634 | ||||||||
\(519\) | 41.4904 | 1.82122 | ||||||||
\(520\) | −13.2421 | −0.580705 | ||||||||
\(521\) | −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 | \(-0.615824\pi\) | ||||
−0.355895 | + | 0.934526i | \(0.615824\pi\) | |||||||
\(524\) | 96.1401 | 4.19990 | ||||||||
\(525\) | 0.971127 | 0.0423835 | ||||||||
\(526\) | −14.0137 | −0.611026 | ||||||||
\(527\) | 15.4888 | 0.674704 | ||||||||
\(528\) | −211.691 | −9.21266 | ||||||||
\(529\) | −16.3452 | −0.710661 | ||||||||
\(530\) | 30.6898 | 1.33308 | ||||||||
\(531\) | −2.03524 | −0.0883219 | ||||||||
\(532\) | 16.1015 | 0.698091 | ||||||||
\(533\) | 0.201107 | 0.00871091 | ||||||||
\(534\) | −57.5905 | −2.49218 | ||||||||
\(535\) | 17.3828 | 0.751524 | ||||||||
\(536\) | −123.313 | −5.32630 | ||||||||
\(537\) | 38.7958 | 1.67416 | ||||||||
\(538\) | 5.82028 | 0.250930 | ||||||||
\(539\) | −39.1277 | −1.68535 | ||||||||
\(540\) | −4.95668 | −0.213301 | ||||||||
\(541\) | 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 | ||||||||
\(545\) | −8.03341 | −0.344113 | ||||||||
\(546\) | 3.63527 | 0.155575 | ||||||||
\(547\) | 16.3708 | 0.699967 | 0.349983 | − | 0.936756i | \(-0.386187\pi\) | ||||
0.349983 | + | 0.936756i | \(0.386187\pi\) | |||||||
\(548\) | −96.6063 | −4.12682 | ||||||||
\(549\) | 15.3078 | 0.653323 | ||||||||
\(550\) | 15.7229 | 0.670428 | ||||||||
\(551\) | −36.3787 | −1.54979 | ||||||||
\(552\) | 59.4079 | 2.52857 | ||||||||
\(553\) | 5.87949 | 0.250021 | ||||||||
\(554\) | 74.2178 | 3.15321 | ||||||||
\(555\) | −4.97399 | −0.211134 | ||||||||
\(556\) | 82.0452 | 3.47949 | ||||||||
\(557\) | −8.20755 | −0.347765 | −0.173883 | − | 0.984766i | \(-0.555631\pi\) | ||||
−0.173883 | + | 0.984766i | \(0.555631\pi\) | |||||||
\(558\) | 28.2804 | 1.19720 | ||||||||
\(559\) | 2.33305 | 0.0986777 | ||||||||
\(560\) | 6.38453 | 0.269796 | ||||||||
\(561\) | −53.5486 | −2.26082 | ||||||||
\(562\) | 19.1575 | 0.808109 | ||||||||
\(563\) | −14.6402 | −0.617010 | −0.308505 | − | 0.951223i | \(-0.599829\pi\) | ||||
−0.308505 | + | 0.951223i | \(0.599829\pi\) | |||||||
\(564\) | 94.6888 | 3.98712 | ||||||||
\(565\) | −3.31515 | −0.139469 | ||||||||
\(566\) | −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 | \(0.241469\pi\) | |||||||
\(570\) | −46.2190 | −1.93590 | ||||||||
\(571\) | 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 | ||||||||
\(575\) | −2.57969 | −0.107581 | ||||||||
\(576\) | 86.5324 | 3.60552 | ||||||||
\(577\) | 20.4468 | 0.851209 | 0.425605 | − | 0.904909i | \(-0.360061\pi\) | ||||
0.425605 | + | 0.904909i | \(0.360061\pi\) | |||||||
\(578\) | −3.98120 | −0.165596 | ||||||||
\(579\) | −53.7767 | −2.23488 | ||||||||
\(580\) | −28.3740 | −1.17816 | ||||||||
\(581\) | −0.852321 | −0.0353603 | ||||||||
\(582\) | −67.1501 | −2.78346 | ||||||||
\(583\) | −64.0176 | −2.65134 | ||||||||
\(584\) | −132.979 | −5.50272 | ||||||||
\(585\) | −3.57571 | −0.147837 | ||||||||
\(586\) | 78.0845 | 3.22564 | ||||||||
\(587\) | 6.11666 | 0.252461 | 0.126231 | − | 0.992001i | \(-0.459712\pi\) | ||||
0.126231 | + | 0.992001i | \(0.459712\pi\) | |||||||
\(588\) | 89.7107 | 3.69961 | ||||||||
\(589\) | −27.8867 | −1.14905 | ||||||||
\(590\) | 2.13066 | 0.0877177 | ||||||||
\(591\) | −24.3479 | −1.00154 | ||||||||
\(592\) | −32.7008 | −1.34399 | ||||||||
\(593\) | −28.3186 | −1.16290 | −0.581452 | − | 0.813581i | \(-0.697515\pi\) | ||||
−0.581452 | + | 0.813581i | \(0.697515\pi\) | |||||||
\(594\) | 14.0737 | 0.577452 | ||||||||
\(595\) | 1.61501 | 0.0662089 | ||||||||
\(596\) | 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 | \(0.240607\pi\) | |||||||
\(600\) | −23.0291 | −0.940158 | ||||||||
\(601\) | 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 | ||||||||
\(605\) | −21.7973 | −0.886188 | ||||||||
\(606\) | −53.4873 | −2.17277 | ||||||||
\(607\) | 3.32898 | 0.135119 | 0.0675596 | − | 0.997715i | \(-0.478479\pi\) | ||||
0.0675596 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(608\) | −165.954 | −6.73032 | ||||||||
\(609\) | 4.97601 | 0.201638 | ||||||||
\(610\) | −16.0255 | −0.648854 | ||||||||
\(611\) | −9.83254 | −0.397782 | ||||||||
\(612\) | 57.2657 | 2.31483 | ||||||||
\(613\) | −28.8013 | −1.16327 | −0.581636 | − | 0.813449i | \(-0.697587\pi\) | ||||
−0.581636 | + | 0.813449i | \(0.697587\pi\) | |||||||
\(614\) | −23.0349 | −0.929612 | ||||||||
\(615\) | 0.349740 | 0.0141029 | ||||||||
\(616\) | −22.7794 | −0.917807 | ||||||||
\(617\) | −33.0710 | −1.33139 | −0.665694 | − | 0.746225i | \(-0.731864\pi\) | ||||
−0.665694 | + | 0.746225i | \(0.731864\pi\) | |||||||
\(618\) | 101.107 | 4.06711 | ||||||||
\(619\) | −4.02487 | −0.161773 | −0.0808865 | − | 0.996723i | \(-0.525775\pi\) | ||||
−0.0808865 | + | 0.996723i | \(0.525775\pi\) | |||||||
\(620\) | −21.7505 | −0.873521 | ||||||||
\(621\) | −2.30911 | −0.0926612 | ||||||||
\(622\) | 23.8934 | 0.958039 | ||||||||
\(623\) | −3.62312 | −0.145157 | ||||||||
\(624\) | −50.3998 | −2.01761 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 45.1773 | 1.80565 | ||||||||
\(627\) | 96.4110 | 3.85028 | ||||||||
\(628\) | 61.6988 | 2.46205 | ||||||||
\(629\) | −8.27188 | −0.329821 | ||||||||
\(630\) | 2.94877 | 0.117482 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | −20.8447 | −0.827195 | ||||||||
\(636\) | 146.777 | 5.82011 | ||||||||
\(637\) | −9.31560 | −0.369098 | ||||||||
\(638\) | 80.5636 | 3.18954 | ||||||||
\(639\) | 5.20785 | 0.206019 | ||||||||
\(640\) | −43.8399 | −1.73292 | ||||||||
\(641\) | −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 | \(-0.515487\pi\) | ||||
−0.0486362 | + | 0.998817i | \(0.515487\pi\) | |||||||
\(644\) | 5.85050 | 0.230542 | ||||||||
\(645\) | 4.05736 | 0.159758 | ||||||||
\(646\) | −76.8634 | −3.02415 | ||||||||
\(647\) | 4.94737 | 0.194501 | 0.0972506 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972506 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(648\) | −97.0233 | −3.81144 | ||||||||
\(649\) | −4.44446 | −0.174460 | ||||||||
\(650\) | 3.74335 | 0.146826 | ||||||||
\(651\) | 3.81444 | 0.149500 | ||||||||
\(652\) | −73.4300 | −2.87574 | ||||||||
\(653\) | −13.7880 | −0.539566 | −0.269783 | − | 0.962921i | \(-0.586952\pi\) | ||||
−0.269783 | + | 0.962921i | \(0.586952\pi\) | |||||||
\(654\) | −52.2972 | −2.04498 | ||||||||
\(655\) | −17.3616 | −0.678375 | ||||||||
\(656\) | 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 | \(0.471965\pi\) | |||||||
\(660\) | 75.1967 | 2.92703 | ||||||||
\(661\) | −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 | ||||||||
\(665\) | −2.90772 | −0.112757 | ||||||||
\(666\) | −15.1033 | −0.585239 | ||||||||
\(667\) | −13.2182 | −0.511812 | ||||||||
\(668\) | −39.2880 | −1.52010 | ||||||||
\(669\) | −1.77422 | −0.0685952 | ||||||||
\(670\) | 34.8587 | 1.34671 | ||||||||
\(671\) | 33.4285 | 1.29049 | ||||||||
\(672\) | 22.6998 | 0.875663 | ||||||||
\(673\) | 41.1033 | 1.58442 | 0.792208 | − | 0.610252i | \(-0.208932\pi\) | ||||
0.792208 | + | 0.610252i | \(0.208932\pi\) | |||||||
\(674\) | 22.0791 | 0.850455 | ||||||||
\(675\) | 0.895110 | 0.0344528 | ||||||||
\(676\) | −61.6931 | −2.37281 | ||||||||
\(677\) | −4.33170 | −0.166481 | −0.0832404 | − | 0.996529i | \(-0.526527\pi\) | ||||
−0.0832404 | + | 0.996529i | \(0.526527\pi\) | |||||||
\(678\) | −21.5815 | −0.828833 | ||||||||
\(679\) | −4.22453 | −0.162123 | ||||||||
\(680\) | −38.2979 | −1.46866 | ||||||||
\(681\) | 6.80811 | 0.260887 | ||||||||
\(682\) | 61.7572 | 2.36481 | ||||||||
\(683\) | 9.02009 | 0.345144 | 0.172572 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172572 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(684\) | −103.103 | −3.94226 | ||||||||
\(685\) | 17.4458 | 0.666570 | ||||||||
\(686\) | 15.5531 | 0.593822 | ||||||||
\(687\) | −49.9340 | −1.90510 | ||||||||
\(688\) | 26.6745 | 1.01696 | ||||||||
\(689\) | −15.2415 | −0.580653 | ||||||||
\(690\) | −16.7937 | −0.639325 | ||||||||
\(691\) | −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 | ||||||||
\(695\) | −14.8163 | −0.562013 | ||||||||
\(696\) | −118.000 | −4.47278 | ||||||||
\(697\) | 0.581627 | 0.0220307 | ||||||||
\(698\) | 71.0193 | 2.68812 | ||||||||
\(699\) | −46.7116 | −1.76679 | ||||||||
\(700\) | −2.26791 | −0.0857189 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | −17.0995 | −0.644006 | ||||||||
\(706\) | −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 | \(0.416832\pi\) | |||||||
\(710\) | −5.45200 | −0.204610 | ||||||||
\(711\) | −37.6482 | −1.41192 | ||||||||
\(712\) | 85.9178 | 3.21991 | ||||||||
\(713\) | −10.1326 | −0.379470 | ||||||||
\(714\) | 10.5137 | 0.393464 | ||||||||
\(715\) | −7.80846 | −0.292020 | ||||||||
\(716\) | −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 | \(0.581179\pi\) | |||||||
\(720\) | −40.8822 | −1.52359 | ||||||||
\(721\) | 6.36081 | 0.236889 | ||||||||
\(722\) | 86.2243 | 3.20894 | ||||||||
\(723\) | 13.8483 | 0.515023 | ||||||||
\(724\) | −60.0795 | −2.23284 | ||||||||
\(725\) | 5.12396 | 0.190299 | ||||||||
\(726\) | −141.900 | −5.26640 | ||||||||
\(727\) | 6.07544 | 0.225326 | 0.112663 | − | 0.993633i | \(-0.464062\pi\) | ||||
0.112663 | + | 0.993633i | \(0.464062\pi\) | |||||||
\(728\) | −5.42336 | −0.201003 | ||||||||
\(729\) | −19.8314 | −0.734495 | ||||||||
\(730\) | 37.5912 | 1.39131 | ||||||||
\(731\) | 6.74749 | 0.249565 | ||||||||
\(732\) | −76.6438 | −2.83284 | ||||||||
\(733\) | 41.7228 | 1.54107 | 0.770534 | − | 0.637399i | \(-0.219990\pi\) | ||||
0.770534 | + | 0.637399i | \(0.219990\pi\) | |||||||
\(734\) | −16.3188 | −0.602338 | ||||||||
\(735\) | −16.2005 | −0.597566 | ||||||||
\(736\) | −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 | \(0.245998\pi\) | |||||||
\(740\) | 11.6159 | 0.427011 | ||||||||
\(741\) | 22.9537 | 0.843226 | ||||||||
\(742\) | 12.5691 | 0.461427 | ||||||||
\(743\) | 26.2242 | 0.962071 | 0.481036 | − | 0.876701i | \(-0.340261\pi\) | ||||
0.481036 | + | 0.876701i | \(0.340261\pi\) | |||||||
\(744\) | −90.4546 | −3.31623 | ||||||||
\(745\) | −9.04142 | −0.331252 | ||||||||
\(746\) | 79.9045 | 2.92551 | ||||||||
\(747\) | 5.45769 | 0.199686 | ||||||||
\(748\) | 125.054 | 4.57242 | ||||||||
\(749\) | 7.11920 | 0.260130 | ||||||||
\(750\) | 6.50997 | 0.237710 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | −1.00000 | −0.0363937 | ||||||||
\(756\) | −2.03003 | −0.0738313 | ||||||||
\(757\) | 36.3116 | 1.31977 | 0.659885 | − | 0.751367i | \(-0.270605\pi\) | ||||
0.659885 | + | 0.751367i | \(0.270605\pi\) | |||||||
\(758\) | −4.57126 | −0.166036 | ||||||||
\(759\) | 35.0309 | 1.27154 | ||||||||
\(760\) | 68.9531 | 2.50119 | ||||||||
\(761\) | 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 | ||||||||
\(765\) | −10.3414 | −0.373895 | ||||||||
\(766\) | 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 | \(0.348474\pi\) | |||||||
\(770\) | 6.43938 | 0.232059 | ||||||||
\(771\) | 56.1690 | 2.02288 | ||||||||
\(772\) | 125.587 | 4.51996 | ||||||||
\(773\) | 2.14231 | 0.0770536 | 0.0385268 | − | 0.999258i | \(-0.487734\pi\) | ||||
0.0385268 | + | 0.999258i | \(0.487734\pi\) | |||||||
\(774\) | 12.3199 | 0.442831 | ||||||||
\(775\) | 3.92785 | 0.141092 | ||||||||
\(776\) | 100.180 | 3.59623 | ||||||||
\(777\) | −2.03712 | −0.0730812 | ||||||||
\(778\) | −0.744881 | −0.0267053 | ||||||||
\(779\) | −1.04718 | −0.0375192 | ||||||||
\(780\) | 17.9030 | 0.641030 | ||||||||
\(781\) | 11.3726 | 0.406945 | ||||||||
\(782\) | −27.9284 | −0.998716 | ||||||||
\(783\) | 4.58650 | 0.163908 | ||||||||
\(784\) | −106.508 | −3.80386 | ||||||||
\(785\) | −11.1420 | −0.397674 | ||||||||
\(786\) | −113.024 | −4.03142 | ||||||||
\(787\) | −36.0836 | −1.28624 | −0.643121 | − | 0.765765i | \(-0.722361\pi\) | ||||
−0.643121 | + | 0.765765i | \(0.722361\pi\) | |||||||
\(788\) | 56.8606 | 2.02557 | ||||||||
\(789\) | 12.1033 | 0.430889 | ||||||||
\(790\) | 39.4132 | 1.40226 | ||||||||
\(791\) | −1.35773 | −0.0482754 | ||||||||
\(792\) | 145.864 | 5.18304 | ||||||||
\(793\) | 7.95874 | 0.282623 | ||||||||
\(794\) | 19.9529 | 0.708102 | ||||||||
\(795\) | −26.5061 | −0.940073 | ||||||||
\(796\) | 11.6758 | 0.413839 | ||||||||
\(797\) | −19.3971 | −0.687081 | −0.343541 | − | 0.939138i | \(-0.611626\pi\) | ||||
−0.343541 | + | 0.939138i | \(0.611626\pi\) | |||||||
\(798\) | −18.9292 | −0.670086 | ||||||||
\(799\) | −28.4370 | −1.00603 | ||||||||
\(800\) | 23.3747 | 0.826420 | ||||||||
\(801\) | 23.2000 | 0.819732 | ||||||||
\(802\) | −56.9553 | −2.01116 | ||||||||
\(803\) | −78.4136 | −2.76716 | ||||||||
\(804\) | 166.716 | 5.87961 | ||||||||
\(805\) | −1.05652 | −0.0372375 | ||||||||
\(806\) | 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 | \(0.255472\pi\) | |||||||
\(810\) | 27.4270 | 0.963687 | ||||||||
\(811\) | 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 | ||||||||
\(815\) | 13.2605 | 0.464494 | ||||||||
\(816\) | −145.763 | −5.10271 | ||||||||
\(817\) | −12.1485 | −0.425020 | ||||||||
\(818\) | −49.0342 | −1.71444 | ||||||||
\(819\) | −1.46445 | −0.0511719 | ||||||||
\(820\) | −0.816761 | −0.0285225 | ||||||||
\(821\) | −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 | \(-0.399190\pi\) | ||||
0.311435 | + | 0.950268i | \(0.399190\pi\) | |||||||
\(824\) | −150.839 | −5.25472 | ||||||||
\(825\) | −13.5795 | −0.472778 | ||||||||
\(826\) | 0.872618 | 0.0303623 | ||||||||
\(827\) | 24.8985 | 0.865806 | 0.432903 | − | 0.901440i | \(-0.357489\pi\) | ||||
0.432903 | + | 0.901440i | \(0.357489\pi\) | |||||||
\(828\) | −37.4626 | −1.30192 | ||||||||
\(829\) | 35.1635 | 1.22128 | 0.610640 | − | 0.791909i | \(-0.290912\pi\) | ||||
0.610640 | + | 0.791909i | \(0.290912\pi\) | |||||||
\(830\) | −5.71355 | −0.198320 | ||||||||
\(831\) | −64.1001 | −2.22361 | ||||||||
\(832\) | 44.9893 | 1.55972 | ||||||||
\(833\) | −26.9419 | −0.933482 | ||||||||
\(834\) | −96.4534 | −3.33991 | ||||||||
\(835\) | 7.09489 | 0.245529 | ||||||||
\(836\) | −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 | \(0.286797\pi\) | |||||||
\(840\) | −9.43164 | −0.325423 | ||||||||
\(841\) | −2.74506 | −0.0946571 | ||||||||
\(842\) | −29.8049 | −1.02714 | ||||||||
\(843\) | −16.5459 | −0.569870 | ||||||||
\(844\) | −30.8837 | −1.06306 | ||||||||
\(845\) | 11.1409 | 0.383260 | ||||||||
\(846\) | −51.9218 | −1.78511 | ||||||||
\(847\) | −8.92718 | −0.306742 | ||||||||
\(848\) | −174.260 | −5.98411 | ||||||||
\(849\) | 21.3592 | 0.733046 | ||||||||
\(850\) | 10.8262 | 0.371337 | ||||||||
\(851\) | 5.41138 | 0.185500 | ||||||||
\(852\) | −26.0748 | −0.893308 | ||||||||
\(853\) | −20.1505 | −0.689939 | −0.344970 | − | 0.938614i | \(-0.612111\pi\) | ||||
−0.344970 | + | 0.938614i | \(0.612111\pi\) | |||||||
\(854\) | −6.56331 | −0.224592 | ||||||||
\(855\) | 18.6191 | 0.636759 | ||||||||
\(856\) | −168.823 | −5.77025 | ||||||||
\(857\) | 32.5725 | 1.11266 | 0.556328 | − | 0.830963i | \(-0.312210\pi\) | ||||
0.556328 | + | 0.830963i | \(0.312210\pi\) | |||||||
\(858\) | −50.8328 | −1.73540 | ||||||||
\(859\) | 11.5974 | 0.395698 | 0.197849 | − | 0.980233i | \(-0.436604\pi\) | ||||
0.197849 | + | 0.980233i | \(0.436604\pi\) | |||||||
\(860\) | −9.47530 | −0.323105 | ||||||||
\(861\) | 0.143237 | 0.00488152 | ||||||||
\(862\) | 38.8804 | 1.32427 | ||||||||
\(863\) | −3.25780 | −0.110897 | −0.0554485 | − | 0.998462i | \(-0.517659\pi\) | ||||
−0.0554485 | + | 0.998462i | \(0.517659\pi\) | |||||||
\(864\) | 20.9229 | 0.711812 | ||||||||
\(865\) | 17.4978 | 0.594941 | ||||||||
\(866\) | −29.2734 | −0.994749 | ||||||||
\(867\) | 3.43847 | 0.116776 | ||||||||
\(868\) | −8.90800 | −0.302357 | ||||||||
\(869\) | −82.2143 | −2.78893 | ||||||||
\(870\) | 33.3568 | 1.13090 | ||||||||
\(871\) | −17.3118 | −0.586589 | ||||||||
\(872\) | 78.0209 | 2.64212 | ||||||||
\(873\) | 27.0510 | 0.915539 | ||||||||
\(874\) | 50.2833 | 1.70086 | ||||||||
\(875\) | 0.409554 | 0.0138454 | ||||||||
\(876\) | 179.784 | 6.07435 | ||||||||
\(877\) | −21.9443 | −0.741006 | −0.370503 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370503 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(878\) | −71.4649 | −2.41182 | ||||||||
\(879\) | −67.4397 | −2.27469 | ||||||||
\(880\) | −89.2765 | −3.00951 | ||||||||
\(881\) | 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 | \(-0.426361\pi\) | ||||
0.229284 | + | 0.973360i | \(0.426361\pi\) | |||||||
\(884\) | 29.7731 | 1.00138 | ||||||||
\(885\) | −1.84020 | −0.0618575 | ||||||||
\(886\) | 89.0834 | 2.99282 | ||||||||
\(887\) | 43.3273 | 1.45479 | 0.727394 | − | 0.686220i | \(-0.240731\pi\) | ||||
0.727394 | + | 0.686220i | \(0.240731\pi\) | |||||||
\(888\) | 48.3077 | 1.62110 | ||||||||
\(889\) | −8.53702 | −0.286322 | ||||||||
\(890\) | −24.2877 | −0.814125 | ||||||||
\(891\) | −57.2116 | −1.91666 | ||||||||
\(892\) | 4.14339 | 0.138731 | ||||||||
\(893\) | 51.1990 | 1.71331 | ||||||||
\(894\) | −58.8594 | −1.96855 | ||||||||
\(895\) | 16.3614 | 0.546901 | ||||||||
\(896\) | −17.9548 | −0.599827 | ||||||||
\(897\) | 8.34025 | 0.278473 | ||||||||
\(898\) | −76.2417 | −2.54422 | ||||||||
\(899\) | 20.1261 | 0.671244 | ||||||||
\(900\) | 14.5221 | 0.484071 | ||||||||
\(901\) | −44.0802 | −1.46853 | ||||||||
\(902\) | 2.31907 | 0.0772166 | ||||||||
\(903\) | 1.66171 | 0.0552982 | ||||||||
\(904\) | 32.1969 | 1.07085 | ||||||||
\(905\) | 10.8496 | 0.360651 | ||||||||
\(906\) | −6.50997 | −0.216279 | ||||||||
\(907\) | 38.2121 | 1.26881 | 0.634406 | − | 0.773000i | \(-0.281245\pi\) | ||||
0.634406 | + | 0.773000i | \(0.281245\pi\) | |||||||
\(908\) | −15.8992 | −0.527634 | ||||||||
\(909\) | 21.5471 | 0.714671 | ||||||||
\(910\) | 1.53310 | 0.0508219 | ||||||||
\(911\) | −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 | ||||||||
\(915\) | 13.8408 | 0.457564 | ||||||||
\(916\) | 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 | \(0.611355\pi\) | |||||||
\(920\) | 25.0541 | 0.826010 | ||||||||
\(921\) | 19.8947 | 0.655552 | ||||||||
\(922\) | −49.3193 | −1.62424 | ||||||||
\(923\) | 2.70762 | 0.0891225 | ||||||||
\(924\) | 30.7971 | 1.01315 | ||||||||
\(925\) | −2.09769 | −0.0689715 | ||||||||
\(926\) | −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 | \(0.414595\pi\) | |||||||
\(930\) | 25.5702 | 0.838479 | ||||||||
\(931\) | 48.5073 | 1.58976 | ||||||||
\(932\) | 109.087 | 3.57327 | ||||||||
\(933\) | −20.6362 | −0.675598 | ||||||||
\(934\) | 12.9141 | 0.422563 | ||||||||
\(935\) | −22.5831 | −0.738545 | ||||||||
\(936\) | 34.7275 | 1.13510 | ||||||||
\(937\) | 1.67931 | 0.0548605 | 0.0274303 | − | 0.999624i | \(-0.491268\pi\) | ||||
0.0274303 | + | 0.999624i | \(0.491268\pi\) | |||||||
\(938\) | 14.2765 | 0.466144 | ||||||||
\(939\) | −39.0186 | −1.27332 | ||||||||
\(940\) | 39.9332 | 1.30248 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | 0.366596 | 0.0119254 | ||||||||
\(946\) | 26.9037 | 0.874714 | ||||||||
\(947\) | 11.8324 | 0.384501 | 0.192251 | − | 0.981346i | \(-0.438421\pi\) | ||||
0.192251 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(948\) | 188.498 | 6.12214 | ||||||||
\(949\) | −18.6689 | −0.606018 | ||||||||
\(950\) | −19.4920 | −0.632403 | ||||||||
\(951\) | −31.3452 | −1.01644 | ||||||||
\(952\) | −15.6851 | −0.508356 | ||||||||
\(953\) | −5.06600 | −0.164104 | −0.0820519 | − | 0.996628i | \(-0.526147\pi\) | ||||
−0.0820519 | + | 0.996628i | \(0.526147\pi\) | |||||||
\(954\) | −80.4842 | −2.60577 | ||||||||
\(955\) | 20.1127 | 0.650833 | ||||||||
\(956\) | 27.0216 | 0.873942 | ||||||||
\(957\) | −69.5809 | −2.24923 | ||||||||
\(958\) | 39.0133 | 1.26046 | ||||||||
\(959\) | 7.14500 | 0.230724 | ||||||||
\(960\) | 78.2398 | 2.52518 | ||||||||
\(961\) | −15.5720 | −0.502323 | ||||||||
\(962\) | −7.85236 | −0.253170 | ||||||||
\(963\) | −45.5865 | −1.46900 | ||||||||
\(964\) | −32.3404 | −1.04161 | ||||||||
\(965\) | −22.6793 | −0.730072 | ||||||||
\(966\) | −6.87793 | −0.221294 | ||||||||
\(967\) | 28.1196 | 0.904265 | 0.452132 | − | 0.891951i | \(-0.350663\pi\) | ||||
0.452132 | + | 0.891951i | \(0.350663\pi\) | |||||||
\(968\) | 211.697 | 6.80420 | ||||||||
\(969\) | 66.3851 | 2.13260 | ||||||||
\(970\) | −28.3192 | −0.909276 | ||||||||
\(971\) | 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 | ||||||||
\(975\) | −3.23304 | −0.103540 | ||||||||
\(976\) | 90.9946 | 2.91267 | ||||||||
\(977\) | 11.8376 | 0.378718 | 0.189359 | − | 0.981908i | \(-0.439359\pi\) | ||||
0.189359 | + | 0.981908i | \(0.439359\pi\) | |||||||
\(978\) | 86.3253 | 2.76038 | ||||||||
\(979\) | 50.6630 | 1.61920 | ||||||||
\(980\) | 37.8337 | 1.20855 | ||||||||
\(981\) | 21.0676 | 0.672638 | ||||||||
\(982\) | −43.3792 | −1.38429 | ||||||||
\(983\) | −4.86039 | −0.155022 | −0.0775112 | − | 0.996991i | \(-0.524697\pi\) | ||||
−0.0775112 | + | 0.996991i | \(0.524697\pi\) | |||||||
\(984\) | −3.39670 | −0.108283 | ||||||||
\(985\) | −10.2683 | −0.327174 | ||||||||
\(986\) | 55.4732 | 1.76663 | ||||||||
\(987\) | −7.00318 | −0.222914 | ||||||||
\(988\) | −53.6047 | −1.70539 | ||||||||
\(989\) | −4.41414 | −0.140362 | ||||||||
\(990\) | −41.2334 | −1.31048 | ||||||||
\(991\) | −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 | ||||||||
\(995\) | −2.10850 | −0.0668439 | ||||||||
\(996\) | −27.3257 | −0.865849 | ||||||||
\(997\) | 58.7462 | 1.86051 | 0.930256 | − | 0.366912i | \(-0.119585\pi\) | ||||
0.930256 | + | 0.366912i | \(0.119585\pi\) | |||||||
\(998\) | 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 | 755.2.a.k.1.18 | ✓ | 18 | |
3.2 | odd | 2 | 6795.2.a.bi.1.1 | 18 | |||
5.4 | even | 2 | 3775.2.a.r.1.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
755.2.a.k.1.18 | ✓ | 18 | 1.1 | even | 1 | trivial | |
3775.2.a.r.1.1 | 18 | 5.4 | even | 2 | |||
6795.2.a.bi.1.1 | 18 | 3.2 | odd | 2 |