Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} + \cdots - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(2.80172\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.80172 | 1.98112 | 0.990559 | − | 0.137088i | \(-0.0437745\pi\) | ||||
0.990559 | + | 0.137088i | \(0.0437745\pi\) | |||||||
\(3\) | −1.73197 | −0.999952 | −0.499976 | − | 0.866039i | \(-0.666658\pi\) | ||||
−0.499976 | + | 0.866039i | \(0.666658\pi\) | |||||||
\(4\) | 5.84965 | 2.92483 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.85249 | −1.98102 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.7857 | 3.81331 | ||||||||
\(9\) | −0.000289796 0 | −9.65986e−5 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.96838 | 0.593488 | 0.296744 | − | 0.954957i | \(-0.404099\pi\) | ||||
0.296744 | + | 0.954957i | \(0.404099\pi\) | |||||||
\(12\) | −10.1314 | −2.92469 | ||||||||
\(13\) | 3.06234 | 0.849342 | 0.424671 | − | 0.905348i | \(-0.360390\pi\) | ||||
0.424671 | + | 0.905348i | \(0.360390\pi\) | |||||||
\(14\) | 2.80172 | 0.748792 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.5191 | 4.62979 | ||||||||
\(17\) | −5.01983 | −1.21749 | −0.608744 | − | 0.793367i | \(-0.708326\pi\) | ||||
−0.608744 | + | 0.793367i | \(0.708326\pi\) | |||||||
\(18\) | −0.000811928 0 | −0.000191373 0 | ||||||||
\(19\) | −0.164590 | −0.0377596 | −0.0188798 | − | 0.999822i | \(-0.506010\pi\) | ||||
−0.0188798 | + | 0.999822i | \(0.506010\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73197 | −0.377946 | ||||||||
\(22\) | 5.51485 | 1.17577 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −18.6804 | −3.81312 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.57984 | 1.68265 | ||||||||
\(27\) | 5.19640 | 1.00005 | ||||||||
\(28\) | 5.84965 | 1.10548 | ||||||||
\(29\) | −1.60357 | −0.297776 | −0.148888 | − | 0.988854i | \(-0.547569\pi\) | ||||
−0.148888 | + | 0.988854i | \(0.547569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84062 | −0.330585 | −0.165293 | − | 0.986245i | \(-0.552857\pi\) | ||||
−0.165293 | + | 0.986245i | \(0.552857\pi\) | |||||||
\(32\) | 30.3142 | 5.35884 | ||||||||
\(33\) | −3.40917 | −0.593460 | ||||||||
\(34\) | −14.0642 | −2.41199 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.00169521 | −0.000282534 0 | ||||||||
\(37\) | 7.42117 | 1.22003 | 0.610016 | − | 0.792389i | \(-0.291163\pi\) | ||||
0.610016 | + | 0.792389i | \(0.291163\pi\) | |||||||
\(38\) | −0.461136 | −0.0748062 | ||||||||
\(39\) | −5.30388 | −0.849301 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.05737 | 0.946002 | 0.473001 | − | 0.881062i | \(-0.343171\pi\) | ||||
0.473001 | + | 0.881062i | \(0.343171\pi\) | |||||||
\(42\) | −4.85249 | −0.748756 | ||||||||
\(43\) | 7.22063 | 1.10114 | 0.550568 | − | 0.834790i | \(-0.314411\pi\) | ||||
0.550568 | + | 0.834790i | \(0.314411\pi\) | |||||||
\(44\) | 11.5143 | 1.73585 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.80172 | 0.413092 | ||||||||
\(47\) | −4.25995 | −0.621377 | −0.310689 | − | 0.950512i | \(-0.600560\pi\) | ||||
−0.310689 | + | 0.950512i | \(0.600560\pi\) | |||||||
\(48\) | −32.0746 | −4.62956 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.69418 | 1.21743 | ||||||||
\(52\) | 17.9137 | 2.48418 | ||||||||
\(53\) | −3.65970 | −0.502699 | −0.251349 | − | 0.967896i | \(-0.580874\pi\) | ||||
−0.251349 | + | 0.967896i | \(0.580874\pi\) | |||||||
\(54\) | 14.5589 | 1.98121 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.7857 | 1.44130 | ||||||||
\(57\) | 0.285065 | 0.0377578 | ||||||||
\(58\) | −4.49276 | −0.589929 | ||||||||
\(59\) | −7.76391 | −1.01078 | −0.505388 | − | 0.862892i | \(-0.668650\pi\) | ||||
−0.505388 | + | 0.862892i | \(0.668650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.38754 | 1.20195 | 0.600975 | − | 0.799268i | \(-0.294779\pi\) | ||||
0.600975 | + | 0.799268i | \(0.294779\pi\) | |||||||
\(62\) | −5.15691 | −0.654928 | ||||||||
\(63\) | −0.000289796 0 | −3.65109e−5 0 | ||||||||
\(64\) | 47.8937 | 5.98671 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.55154 | −1.17571 | ||||||||
\(67\) | 13.6408 | 1.66649 | 0.833243 | − | 0.552906i | \(-0.186481\pi\) | ||||
0.833243 | + | 0.552906i | \(0.186481\pi\) | |||||||
\(68\) | −29.3643 | −3.56094 | ||||||||
\(69\) | −1.73197 | −0.208504 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.4953 | −1.95764 | −0.978818 | − | 0.204733i | \(-0.934367\pi\) | ||||
−0.978818 | + | 0.204733i | \(0.934367\pi\) | |||||||
\(72\) | −0.00312564 | −0.000368360 0 | ||||||||
\(73\) | −11.4879 | −1.34456 | −0.672280 | − | 0.740297i | \(-0.734685\pi\) | ||||
−0.672280 | + | 0.740297i | \(0.734685\pi\) | |||||||
\(74\) | 20.7921 | 2.41703 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.962796 | −0.110440 | ||||||||
\(77\) | 1.96838 | 0.224318 | ||||||||
\(78\) | −14.8600 | −1.68256 | ||||||||
\(79\) | −6.11051 | −0.687486 | −0.343743 | − | 0.939064i | \(-0.611695\pi\) | ||||
−0.343743 | + | 0.939064i | \(0.611695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.99913 | −0.999903 | ||||||||
\(82\) | 16.9711 | 1.87414 | ||||||||
\(83\) | −10.3687 | −1.13811 | −0.569056 | − | 0.822299i | \(-0.692691\pi\) | ||||
−0.569056 | + | 0.822299i | \(0.692691\pi\) | |||||||
\(84\) | −10.1314 | −1.10543 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20.2302 | 2.18148 | ||||||||
\(87\) | 2.77733 | 0.297761 | ||||||||
\(88\) | 21.2303 | 2.26315 | ||||||||
\(89\) | 8.46385 | 0.897166 | 0.448583 | − | 0.893741i | \(-0.351929\pi\) | ||||
0.448583 | + | 0.893741i | \(0.351929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.06234 | 0.321021 | ||||||||
\(92\) | 5.84965 | 0.609869 | ||||||||
\(93\) | 3.18789 | 0.330569 | ||||||||
\(94\) | −11.9352 | −1.23102 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −52.5032 | −5.35858 | ||||||||
\(97\) | 4.55947 | 0.462944 | 0.231472 | − | 0.972842i | \(-0.425646\pi\) | ||||
0.231472 | + | 0.972842i | \(0.425646\pi\) | |||||||
\(98\) | 2.80172 | 0.283017 | ||||||||
\(99\) | −0.000570428 0 | −5.73302e−5 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.82561 | −0.181655 | −0.0908274 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908274 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(102\) | 24.3587 | 2.41187 | ||||||||
\(103\) | 11.5393 | 1.13700 | 0.568499 | − | 0.822684i | \(-0.307524\pi\) | ||||
0.568499 | + | 0.822684i | \(0.307524\pi\) | |||||||
\(104\) | 33.0294 | 3.23880 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2535 | −0.995905 | ||||||||
\(107\) | −0.820582 | −0.0793287 | −0.0396643 | − | 0.999213i | \(-0.512629\pi\) | ||||
−0.0396643 | + | 0.999213i | \(0.512629\pi\) | |||||||
\(108\) | 30.3972 | 2.92497 | ||||||||
\(109\) | −5.41869 | −0.519017 | −0.259508 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259508 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.8532 | −1.21997 | ||||||||
\(112\) | 18.5191 | 1.74989 | ||||||||
\(113\) | −0.845882 | −0.0795739 | −0.0397869 | − | 0.999208i | \(-0.512668\pi\) | ||||
−0.0397869 | + | 0.999208i | \(0.512668\pi\) | |||||||
\(114\) | 0.798673 | 0.0748026 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.38034 | −0.870943 | ||||||||
\(117\) | −0.000887455 0 | −8.20452e−5 0 | ||||||||
\(118\) | −21.7523 | −2.00246 | ||||||||
\(119\) | −5.01983 | −0.460167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.12549 | −0.647772 | ||||||||
\(122\) | 26.3013 | 2.38121 | ||||||||
\(123\) | −10.4912 | −0.945956 | ||||||||
\(124\) | −10.7670 | −0.966904 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.000811928 0 | −7.23323e−5 0 | ||||||||
\(127\) | −1.90738 | −0.169252 | −0.0846261 | − | 0.996413i | \(-0.526970\pi\) | ||||
−0.0846261 | + | 0.996413i | \(0.526970\pi\) | |||||||
\(128\) | 73.5565 | 6.50154 | ||||||||
\(129\) | −12.5059 | −1.10108 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2089 | 1.41618 | 0.708091 | − | 0.706122i | \(-0.249557\pi\) | ||||
0.708091 | + | 0.706122i | \(0.249557\pi\) | |||||||
\(132\) | −19.9424 | −1.73577 | ||||||||
\(133\) | −0.164590 | −0.0142718 | ||||||||
\(134\) | 38.2177 | 3.30151 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −54.1422 | −4.64265 | ||||||||
\(137\) | 8.74940 | 0.747512 | 0.373756 | − | 0.927527i | \(-0.378070\pi\) | ||||
0.373756 | + | 0.927527i | \(0.378070\pi\) | |||||||
\(138\) | −4.85249 | −0.413072 | ||||||||
\(139\) | −18.7390 | −1.58942 | −0.794711 | − | 0.606988i | \(-0.792378\pi\) | ||||
−0.794711 | + | 0.606988i | \(0.792378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.37809 | 0.621347 | ||||||||
\(142\) | −46.2154 | −3.87831 | ||||||||
\(143\) | 6.02785 | 0.504074 | ||||||||
\(144\) | −0.00536677 | −0.000447231 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −32.1860 | −2.66373 | ||||||||
\(147\) | −1.73197 | −0.142850 | ||||||||
\(148\) | 43.4113 | 3.56838 | ||||||||
\(149\) | −16.8025 | −1.37651 | −0.688256 | − | 0.725468i | \(-0.741624\pi\) | ||||
−0.688256 | + | 0.725468i | \(0.741624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.8327 | 1.85810 | 0.929048 | − | 0.369960i | \(-0.120629\pi\) | ||||
0.929048 | + | 0.369960i | \(0.120629\pi\) | |||||||
\(152\) | −1.77521 | −0.143989 | ||||||||
\(153\) | 0.00145473 | 0.000117608 0 | ||||||||
\(154\) | 5.51485 | 0.444399 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −31.0259 | −2.48406 | ||||||||
\(157\) | 23.0014 | 1.83571 | 0.917854 | − | 0.396918i | \(-0.129920\pi\) | ||||
0.917854 | + | 0.396918i | \(0.129920\pi\) | |||||||
\(158\) | −17.1200 | −1.36199 | ||||||||
\(159\) | 6.33848 | 0.502674 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −25.2131 | −1.98093 | ||||||||
\(163\) | 21.8404 | 1.71067 | 0.855337 | − | 0.518073i | \(-0.173350\pi\) | ||||
0.855337 | + | 0.518073i | \(0.173350\pi\) | |||||||
\(164\) | 35.4335 | 2.76689 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −29.0502 | −2.25473 | ||||||||
\(167\) | 7.18029 | 0.555628 | 0.277814 | − | 0.960635i | \(-0.410390\pi\) | ||||
0.277814 | + | 0.960635i | \(0.410390\pi\) | |||||||
\(168\) | −18.6804 | −1.44123 | ||||||||
\(169\) | −3.62205 | −0.278619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.76976e−5 0 | 3.64752e−6 0 | ||||||||
\(172\) | 42.2382 | 3.22063 | ||||||||
\(173\) | −9.42006 | −0.716194 | −0.358097 | − | 0.933684i | \(-0.616574\pi\) | ||||
−0.358097 | + | 0.933684i | \(0.616574\pi\) | |||||||
\(174\) | 7.78132 | 0.589900 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 36.4527 | 2.74772 | ||||||||
\(177\) | 13.4468 | 1.01073 | ||||||||
\(178\) | 23.7134 | 1.77739 | ||||||||
\(179\) | −1.60900 | −0.120262 | −0.0601311 | − | 0.998190i | \(-0.519152\pi\) | ||||
−0.0601311 | + | 0.998190i | \(0.519152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.8702 | 1.92292 | 0.961459 | − | 0.274949i | \(-0.0886610\pi\) | ||||
0.961459 | + | 0.274949i | \(0.0886610\pi\) | |||||||
\(182\) | 8.57984 | 0.635980 | ||||||||
\(183\) | −16.2589 | −1.20189 | ||||||||
\(184\) | 10.7857 | 0.795130 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.93160 | 0.654896 | ||||||||
\(187\) | −9.88092 | −0.722565 | ||||||||
\(188\) | −24.9192 | −1.81742 | ||||||||
\(189\) | 5.19640 | 0.377983 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.52391 | 0.472053 | 0.236027 | − | 0.971747i | \(-0.424155\pi\) | ||||
0.236027 | + | 0.971747i | \(0.424155\pi\) | |||||||
\(192\) | −82.9503 | −5.98642 | ||||||||
\(193\) | −2.27932 | −0.164069 | −0.0820346 | − | 0.996629i | \(-0.526142\pi\) | ||||
−0.0820346 | + | 0.996629i | \(0.526142\pi\) | |||||||
\(194\) | 12.7744 | 0.917147 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.84965 | 0.417832 | ||||||||
\(197\) | −2.02369 | −0.144182 | −0.0720911 | − | 0.997398i | \(-0.522967\pi\) | ||||
−0.0720911 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(198\) | −0.00159818 | −0.000113578 0 | ||||||||
\(199\) | −23.2968 | −1.65147 | −0.825734 | − | 0.564060i | \(-0.809239\pi\) | ||||
−0.825734 | + | 0.564060i | \(0.809239\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.6254 | −1.66641 | ||||||||
\(202\) | −5.11485 | −0.359880 | ||||||||
\(203\) | −1.60357 | −0.112549 | ||||||||
\(204\) | 50.8579 | 3.56077 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 32.3299 | 2.25253 | ||||||||
\(207\) | −0.000289796 0 | −2.01422e−5 0 | ||||||||
\(208\) | 56.7120 | 3.93227 | ||||||||
\(209\) | −0.323976 | −0.0224099 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9306 | −0.959024 | −0.479512 | − | 0.877535i | \(-0.659186\pi\) | ||||
−0.479512 | + | 0.877535i | \(0.659186\pi\) | |||||||
\(212\) | −21.4080 | −1.47031 | ||||||||
\(213\) | 28.5694 | 1.95754 | ||||||||
\(214\) | −2.29904 | −0.157159 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 56.0467 | 3.81349 | ||||||||
\(217\) | −1.84062 | −0.124949 | ||||||||
\(218\) | −15.1817 | −1.02823 | ||||||||
\(219\) | 19.8967 | 1.34449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.3724 | −1.03406 | ||||||||
\(222\) | −36.0112 | −2.41691 | ||||||||
\(223\) | −3.14488 | −0.210597 | −0.105298 | − | 0.994441i | \(-0.533580\pi\) | ||||
−0.105298 | + | 0.994441i | \(0.533580\pi\) | |||||||
\(224\) | 30.3142 | 2.02545 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.36993 | −0.157645 | ||||||||
\(227\) | −16.8929 | −1.12122 | −0.560611 | − | 0.828079i | \(-0.689434\pi\) | ||||
−0.560611 | + | 0.828079i | \(0.689434\pi\) | |||||||
\(228\) | 1.66753 | 0.110435 | ||||||||
\(229\) | −4.02594 | −0.266041 | −0.133021 | − | 0.991113i | \(-0.542468\pi\) | ||||
−0.133021 | + | 0.991113i | \(0.542468\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.40917 | −0.224307 | ||||||||
\(232\) | −17.2956 | −1.13551 | ||||||||
\(233\) | −14.8042 | −0.969858 | −0.484929 | − | 0.874554i | \(-0.661154\pi\) | ||||
−0.484929 | + | 0.874554i | \(0.661154\pi\) | |||||||
\(234\) | −0.00248640 | −0.000162541 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −45.4162 | −2.95634 | ||||||||
\(237\) | 10.5832 | 0.687453 | ||||||||
\(238\) | −14.0642 | −0.911645 | ||||||||
\(239\) | −13.9903 | −0.904960 | −0.452480 | − | 0.891775i | \(-0.649461\pi\) | ||||
−0.452480 | + | 0.891775i | \(0.649461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.7603 | −1.85261 | −0.926306 | − | 0.376771i | \(-0.877034\pi\) | ||||
−0.926306 | + | 0.376771i | \(0.877034\pi\) | |||||||
\(242\) | −19.9636 | −1.28331 | ||||||||
\(243\) | −0.00301165 | −0.000193197 0 | ||||||||
\(244\) | 54.9138 | 3.51550 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −29.3933 | −1.87405 | ||||||||
\(247\) | −0.504032 | −0.0320708 | ||||||||
\(248\) | −19.8523 | −1.26062 | ||||||||
\(249\) | 17.9582 | 1.13806 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0954598 | −0.00602537 | −0.00301268 | − | 0.999995i | \(-0.500959\pi\) | ||||
−0.00301268 | + | 0.999995i | \(0.500959\pi\) | |||||||
\(252\) | −0.00169521 | −0.000106788 0 | ||||||||
\(253\) | 1.96838 | 0.123751 | ||||||||
\(254\) | −5.34394 | −0.335309 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 110.298 | 6.89360 | ||||||||
\(257\) | −12.9724 | −0.809196 | −0.404598 | − | 0.914495i | \(-0.632589\pi\) | ||||
−0.404598 | + | 0.914495i | \(0.632589\pi\) | |||||||
\(258\) | −35.0381 | −2.18137 | ||||||||
\(259\) | 7.42117 | 0.461129 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.000464709 0 | 2.87647e−5 0 | ||||||||
\(262\) | 45.4130 | 2.80562 | ||||||||
\(263\) | 5.69130 | 0.350940 | 0.175470 | − | 0.984485i | \(-0.443855\pi\) | ||||
0.175470 | + | 0.984485i | \(0.443855\pi\) | |||||||
\(264\) | −36.7701 | −2.26305 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.461136 | −0.0282741 | ||||||||
\(267\) | −14.6591 | −0.897123 | ||||||||
\(268\) | 79.7939 | 4.87419 | ||||||||
\(269\) | −22.8837 | −1.39524 | −0.697622 | − | 0.716466i | \(-0.745759\pi\) | ||||
−0.697622 | + | 0.716466i | \(0.745759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4239 | −1.17992 | −0.589959 | − | 0.807433i | \(-0.700856\pi\) | ||||
−0.589959 | + | 0.807433i | \(0.700856\pi\) | |||||||
\(272\) | −92.9629 | −5.63671 | ||||||||
\(273\) | −5.30388 | −0.321005 | ||||||||
\(274\) | 24.5134 | 1.48091 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.1314 | −0.609839 | ||||||||
\(277\) | −15.9057 | −0.955680 | −0.477840 | − | 0.878447i | \(-0.658580\pi\) | ||||
−0.477840 | + | 0.878447i | \(0.658580\pi\) | |||||||
\(278\) | −52.5015 | −3.14883 | ||||||||
\(279\) | 0.000533404 0 | 3.19341e−5 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.3213 | −0.615718 | −0.307859 | − | 0.951432i | \(-0.599612\pi\) | ||||
−0.307859 | + | 0.951432i | \(0.599612\pi\) | |||||||
\(282\) | 20.6714 | 1.23096 | ||||||||
\(283\) | 2.91321 | 0.173173 | 0.0865863 | − | 0.996244i | \(-0.472404\pi\) | ||||
0.0865863 | + | 0.996244i | \(0.472404\pi\) | |||||||
\(284\) | −96.4920 | −5.72575 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.8884 | 0.998631 | ||||||||
\(287\) | 6.05737 | 0.357555 | ||||||||
\(288\) | −0.00878493 | −0.000517657 0 | ||||||||
\(289\) | 8.19868 | 0.482275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.89686 | −0.462922 | ||||||||
\(292\) | −67.2004 | −3.93260 | ||||||||
\(293\) | 18.3822 | 1.07390 | 0.536951 | − | 0.843613i | \(-0.319576\pi\) | ||||
0.536951 | + | 0.843613i | \(0.319576\pi\) | |||||||
\(294\) | −4.85249 | −0.283003 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 80.0422 | 4.65236 | ||||||||
\(297\) | 10.2285 | 0.593517 | ||||||||
\(298\) | −47.0759 | −2.72703 | ||||||||
\(299\) | 3.06234 | 0.177100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.22063 | 0.416190 | ||||||||
\(302\) | 63.9708 | 3.68111 | ||||||||
\(303\) | 3.16189 | 0.181646 | ||||||||
\(304\) | −3.04807 | −0.174819 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.00407574 | 0.000232994 0 | ||||||||
\(307\) | −7.87997 | −0.449733 | −0.224867 | − | 0.974390i | \(-0.572195\pi\) | ||||
−0.224867 | + | 0.974390i | \(0.572195\pi\) | |||||||
\(308\) | 11.5143 | 0.656090 | ||||||||
\(309\) | −19.9856 | −1.13694 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.11384 | 0.516798 | 0.258399 | − | 0.966038i | \(-0.416805\pi\) | ||||
0.258399 | + | 0.966038i | \(0.416805\pi\) | |||||||
\(312\) | −57.2059 | −3.23865 | ||||||||
\(313\) | −2.44826 | −0.138384 | −0.0691919 | − | 0.997603i | \(-0.522042\pi\) | ||||
−0.0691919 | + | 0.997603i | \(0.522042\pi\) | |||||||
\(314\) | 64.4434 | 3.63675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −35.7444 | −2.01078 | ||||||||
\(317\) | 31.4163 | 1.76452 | 0.882258 | − | 0.470767i | \(-0.156023\pi\) | ||||
0.882258 | + | 0.470767i | \(0.156023\pi\) | |||||||
\(318\) | 17.7587 | 0.995857 | ||||||||
\(319\) | −3.15644 | −0.176726 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.42122 | 0.0793248 | ||||||||
\(322\) | 2.80172 | 0.156134 | ||||||||
\(323\) | 0.826215 | 0.0459718 | ||||||||
\(324\) | −52.6418 | −2.92454 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 61.1908 | 3.38904 | ||||||||
\(327\) | 9.38500 | 0.518992 | ||||||||
\(328\) | 65.3327 | 3.60740 | ||||||||
\(329\) | −4.25995 | −0.234859 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1021 | 0.720156 | 0.360078 | − | 0.932922i | \(-0.382750\pi\) | ||||
0.360078 | + | 0.932922i | \(0.382750\pi\) | |||||||
\(332\) | −60.6532 | −3.32878 | ||||||||
\(333\) | −0.00215062 | −0.000117853 0 | ||||||||
\(334\) | 20.1172 | 1.10076 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −32.0746 | −1.74981 | ||||||||
\(337\) | 3.40979 | 0.185743 | 0.0928716 | − | 0.995678i | \(-0.470395\pi\) | ||||
0.0928716 | + | 0.995678i | \(0.470395\pi\) | |||||||
\(338\) | −10.1480 | −0.551977 | ||||||||
\(339\) | 1.46504 | 0.0795700 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.62304 | −0.196198 | ||||||||
\(342\) | 0.000133635 0 | 7.22617e−6 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 77.8793 | 4.19897 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.3924 | −1.41886 | ||||||||
\(347\) | −28.2070 | −1.51423 | −0.757115 | − | 0.653282i | \(-0.773392\pi\) | ||||
−0.757115 | + | 0.653282i | \(0.773392\pi\) | |||||||
\(348\) | 16.2464 | 0.870901 | ||||||||
\(349\) | 12.4114 | 0.664366 | 0.332183 | − | 0.943215i | \(-0.392215\pi\) | ||||
0.332183 | + | 0.943215i | \(0.392215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.9132 | 0.849383 | ||||||||
\(352\) | 59.6698 | 3.18041 | ||||||||
\(353\) | −31.8989 | −1.69781 | −0.848904 | − | 0.528546i | \(-0.822737\pi\) | ||||
−0.848904 | + | 0.528546i | \(0.822737\pi\) | |||||||
\(354\) | 37.6743 | 2.00237 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 49.5106 | 2.62406 | ||||||||
\(357\) | 8.69418 | 0.460145 | ||||||||
\(358\) | −4.50797 | −0.238253 | ||||||||
\(359\) | −14.0257 | −0.740249 | −0.370125 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370125 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9729 | −0.998574 | ||||||||
\(362\) | 72.4812 | 3.80953 | ||||||||
\(363\) | 12.3411 | 0.647740 | ||||||||
\(364\) | 17.9137 | 0.938931 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −45.5530 | −2.38109 | ||||||||
\(367\) | −26.3734 | −1.37668 | −0.688340 | − | 0.725389i | \(-0.741660\pi\) | ||||
−0.688340 | + | 0.725389i | \(0.741660\pi\) | |||||||
\(368\) | 18.5191 | 0.965377 | ||||||||
\(369\) | −0.00175540 | −9.13825e−5 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.65970 | −0.190002 | ||||||||
\(372\) | 18.6481 | 0.966858 | ||||||||
\(373\) | −33.2683 | −1.72257 | −0.861284 | − | 0.508124i | \(-0.830339\pi\) | ||||
−0.861284 | + | 0.508124i | \(0.830339\pi\) | |||||||
\(374\) | −27.6836 | −1.43149 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −45.9464 | −2.36950 | ||||||||
\(377\) | −4.91069 | −0.252913 | ||||||||
\(378\) | 14.5589 | 0.748828 | ||||||||
\(379\) | −9.47885 | −0.486896 | −0.243448 | − | 0.969914i | \(-0.578279\pi\) | ||||
−0.243448 | + | 0.969914i | \(0.578279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.30351 | 0.169244 | ||||||||
\(382\) | 18.2782 | 0.935193 | ||||||||
\(383\) | 11.6012 | 0.592792 | 0.296396 | − | 0.955065i | \(-0.404215\pi\) | ||||
0.296396 | + | 0.955065i | \(0.404215\pi\) | |||||||
\(384\) | −127.397 | −6.50122 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.38603 | −0.325040 | ||||||||
\(387\) | −0.00209251 | −0.000106368 0 | ||||||||
\(388\) | 26.6713 | 1.35403 | ||||||||
\(389\) | 16.8170 | 0.852655 | 0.426327 | − | 0.904569i | \(-0.359807\pi\) | ||||
0.426327 | + | 0.904569i | \(0.359807\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.01983 | −0.253864 | ||||||||
\(392\) | 10.7857 | 0.544758 | ||||||||
\(393\) | −28.0733 | −1.41611 | ||||||||
\(394\) | −5.66983 | −0.285642 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.00333681 | −0.000167681 0 | ||||||||
\(397\) | 14.4914 | 0.727301 | 0.363650 | − | 0.931536i | \(-0.381530\pi\) | ||||
0.363650 | + | 0.931536i | \(0.381530\pi\) | |||||||
\(398\) | −65.2713 | −3.27175 | ||||||||
\(399\) | 0.285065 | 0.0142711 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.5629 | −1.27655 | −0.638274 | − | 0.769809i | \(-0.720351\pi\) | ||||
−0.638274 | + | 0.769809i | \(0.720351\pi\) | |||||||
\(402\) | −66.1918 | −3.30135 | ||||||||
\(403\) | −5.63661 | −0.280780 | ||||||||
\(404\) | −10.6792 | −0.531309 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.49276 | −0.222972 | ||||||||
\(407\) | 14.6077 | 0.724075 | ||||||||
\(408\) | 93.7725 | 4.64243 | ||||||||
\(409\) | −13.5625 | −0.670623 | −0.335311 | − | 0.942107i | \(-0.608842\pi\) | ||||
−0.335311 | + | 0.942107i | \(0.608842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.1537 | −0.747476 | ||||||||
\(412\) | 67.5008 | 3.32552 | ||||||||
\(413\) | −7.76391 | −0.382037 | ||||||||
\(414\) | −0.000811928 0 | −3.99041e−5 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 92.8325 | 4.55149 | ||||||||
\(417\) | 32.4554 | 1.58935 | ||||||||
\(418\) | −0.907691 | −0.0443966 | ||||||||
\(419\) | 14.9218 | 0.728977 | 0.364489 | − | 0.931208i | \(-0.381244\pi\) | ||||
0.364489 | + | 0.931208i | \(0.381244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −39.5654 | −1.92830 | −0.964150 | − | 0.265358i | \(-0.914510\pi\) | ||||
−0.964150 | + | 0.265358i | \(0.914510\pi\) | |||||||
\(422\) | −39.0298 | −1.89994 | ||||||||
\(423\) | 0.00123452 | 6.00242e−5 0 | ||||||||
\(424\) | −39.4723 | −1.91695 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 80.0435 | 3.87812 | ||||||||
\(427\) | 9.38754 | 0.454295 | ||||||||
\(428\) | −4.80012 | −0.232023 | ||||||||
\(429\) | −10.4400 | −0.504050 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2822 | −1.21780 | −0.608901 | − | 0.793246i | \(-0.708389\pi\) | ||||
−0.608901 | + | 0.793246i | \(0.708389\pi\) | |||||||
\(432\) | 96.2329 | 4.63001 | ||||||||
\(433\) | −4.49189 | −0.215866 | −0.107933 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107933 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(434\) | −5.15691 | −0.247540 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.6975 | −1.51803 | ||||||||
\(437\) | −0.164590 | −0.00787342 | ||||||||
\(438\) | 55.7451 | 2.66360 | ||||||||
\(439\) | −30.6305 | −1.46191 | −0.730956 | − | 0.682424i | \(-0.760926\pi\) | ||||
−0.730956 | + | 0.682424i | \(0.760926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.000289796 0 | −1.37998e−5 0 | ||||||||
\(442\) | −43.0693 | −2.04860 | ||||||||
\(443\) | −4.34787 | −0.206574 | −0.103287 | − | 0.994652i | \(-0.532936\pi\) | ||||
−0.103287 | + | 0.994652i | \(0.532936\pi\) | |||||||
\(444\) | −75.1869 | −3.56821 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.81107 | −0.417216 | ||||||||
\(447\) | 29.1013 | 1.37645 | ||||||||
\(448\) | 47.8937 | 2.26276 | ||||||||
\(449\) | −24.1293 | −1.13873 | −0.569367 | − | 0.822084i | \(-0.692811\pi\) | ||||
−0.569367 | + | 0.822084i | \(0.692811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9232 | 0.561441 | ||||||||
\(452\) | −4.94812 | −0.232740 | ||||||||
\(453\) | −39.5454 | −1.85801 | ||||||||
\(454\) | −47.3292 | −2.22127 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.07461 | 0.143982 | ||||||||
\(457\) | 4.02157 | 0.188121 | 0.0940607 | − | 0.995566i | \(-0.470015\pi\) | ||||
0.0940607 | + | 0.995566i | \(0.470015\pi\) | |||||||
\(458\) | −11.2796 | −0.527059 | ||||||||
\(459\) | −26.0851 | −1.21755 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.2045 | −0.754717 | −0.377358 | − | 0.926067i | \(-0.623168\pi\) | ||||
−0.377358 | + | 0.926067i | \(0.623168\pi\) | |||||||
\(462\) | −9.55154 | −0.444378 | ||||||||
\(463\) | 5.27208 | 0.245014 | 0.122507 | − | 0.992468i | \(-0.460907\pi\) | ||||
0.122507 | + | 0.992468i | \(0.460907\pi\) | |||||||
\(464\) | −29.6968 | −1.37864 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.4774 | −1.92140 | ||||||||
\(467\) | 37.3929 | 1.73034 | 0.865169 | − | 0.501481i | \(-0.167211\pi\) | ||||
0.865169 | + | 0.501481i | \(0.167211\pi\) | |||||||
\(468\) | −0.00519130 | −0.000239968 0 | ||||||||
\(469\) | 13.6408 | 0.629873 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −39.8376 | −1.83562 | ||||||||
\(472\) | −83.7390 | −3.85440 | ||||||||
\(473\) | 14.2129 | 0.653511 | ||||||||
\(474\) | 29.6512 | 1.36193 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −29.3643 | −1.34591 | ||||||||
\(477\) | 0.00106057 | 4.85600e−5 0 | ||||||||
\(478\) | −39.1971 | −1.79283 | ||||||||
\(479\) | −35.0887 | −1.60324 | −0.801622 | − | 0.597832i | \(-0.796029\pi\) | ||||
−0.801622 | + | 0.597832i | \(0.796029\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7262 | 1.03622 | ||||||||
\(482\) | −80.5784 | −3.67024 | ||||||||
\(483\) | −1.73197 | −0.0788072 | ||||||||
\(484\) | −41.6816 | −1.89462 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.00843780 | −0.000382747 0 | ||||||||
\(487\) | 8.17541 | 0.370463 | 0.185232 | − | 0.982695i | \(-0.440696\pi\) | ||||
0.185232 | + | 0.982695i | \(0.440696\pi\) | |||||||
\(488\) | 101.251 | 4.58341 | ||||||||
\(489\) | −37.8269 | −1.71059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.6565 | 1.51889 | 0.759447 | − | 0.650569i | \(-0.225469\pi\) | ||||
0.759447 | + | 0.650569i | \(0.225469\pi\) | |||||||
\(492\) | −61.3697 | −2.76676 | ||||||||
\(493\) | 8.04966 | 0.362538 | ||||||||
\(494\) | −1.41216 | −0.0635360 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −34.0867 | −1.53054 | ||||||||
\(497\) | −16.4953 | −0.739917 | ||||||||
\(498\) | 50.3140 | 2.25462 | ||||||||
\(499\) | 34.0630 | 1.52487 | 0.762436 | − | 0.647064i | \(-0.224003\pi\) | ||||
0.762436 | + | 0.647064i | \(0.224003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.4360 | −0.555601 | ||||||||
\(502\) | −0.267452 | −0.0119370 | ||||||||
\(503\) | 43.7840 | 1.95223 | 0.976116 | − | 0.217250i | \(-0.0697087\pi\) | ||||
0.976116 | + | 0.217250i | \(0.0697087\pi\) | |||||||
\(504\) | −0.00312564 | −0.000139227 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.51485 | 0.245165 | ||||||||
\(507\) | 6.27326 | 0.278605 | ||||||||
\(508\) | −11.1575 | −0.495033 | ||||||||
\(509\) | 10.5402 | 0.467186 | 0.233593 | − | 0.972335i | \(-0.424952\pi\) | ||||
0.233593 | + | 0.972335i | \(0.424952\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.4879 | −0.508196 | ||||||||
\(512\) | 161.910 | 7.15549 | ||||||||
\(513\) | −0.855277 | −0.0377614 | ||||||||
\(514\) | −36.3451 | −1.60311 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −73.1552 | −3.22048 | ||||||||
\(517\) | −8.38519 | −0.368780 | ||||||||
\(518\) | 20.7921 | 0.913550 | ||||||||
\(519\) | 16.3152 | 0.716160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9328 | 1.17995 | 0.589974 | − | 0.807423i | \(-0.299138\pi\) | ||||
0.589974 | + | 0.807423i | \(0.299138\pi\) | |||||||
\(522\) | 0.00130198 | 5.69863e−5 0 | ||||||||
\(523\) | −7.04134 | −0.307896 | −0.153948 | − | 0.988079i | \(-0.549199\pi\) | ||||
−0.153948 | + | 0.988079i | \(0.549199\pi\) | |||||||
\(524\) | 94.8167 | 4.14209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.9454 | 0.695254 | ||||||||
\(527\) | 9.23960 | 0.402483 | ||||||||
\(528\) | −63.1349 | −2.74759 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.00224995 | 9.76395e−5 0 | ||||||||
\(532\) | −0.962796 | −0.0417425 | ||||||||
\(533\) | 18.5497 | 0.803479 | ||||||||
\(534\) | −41.0708 | −1.77731 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 147.125 | 6.35483 | ||||||||
\(537\) | 2.78673 | 0.120256 | ||||||||
\(538\) | −64.1138 | −2.76414 | ||||||||
\(539\) | 1.96838 | 0.0847841 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6283 | −0.714908 | −0.357454 | − | 0.933931i | \(-0.616355\pi\) | ||||
−0.357454 | + | 0.933931i | \(0.616355\pi\) | |||||||
\(542\) | −54.4204 | −2.33756 | ||||||||
\(543\) | −44.8064 | −1.92282 | ||||||||
\(544\) | −152.172 | −6.52432 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.8600 | −0.635950 | ||||||||
\(547\) | −14.4768 | −0.618982 | −0.309491 | − | 0.950902i | \(-0.600159\pi\) | ||||
−0.309491 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(548\) | 51.1810 | 2.18634 | ||||||||
\(549\) | −0.00272047 | −0.000116107 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.263932 | 0.0112439 | ||||||||
\(552\) | −18.6804 | −0.795091 | ||||||||
\(553\) | −6.11051 | −0.259845 | ||||||||
\(554\) | −44.5633 | −1.89331 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −109.617 | −4.64879 | ||||||||
\(557\) | −36.3690 | −1.54100 | −0.770502 | − | 0.637438i | \(-0.779994\pi\) | ||||
−0.770502 | + | 0.637438i | \(0.779994\pi\) | |||||||
\(558\) | 0.00149445 | 6.32652e−5 0 | ||||||||
\(559\) | 22.1121 | 0.935240 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.1134 | 0.722530 | ||||||||
\(562\) | −28.9175 | −1.21981 | ||||||||
\(563\) | −14.1270 | −0.595383 | −0.297691 | − | 0.954662i | \(-0.596217\pi\) | ||||
−0.297691 | + | 0.954662i | \(0.596217\pi\) | |||||||
\(564\) | 43.1593 | 1.81733 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.16202 | 0.343075 | ||||||||
\(567\) | −8.99913 | −0.377928 | ||||||||
\(568\) | −177.913 | −7.46507 | ||||||||
\(569\) | −11.1036 | −0.465489 | −0.232745 | − | 0.972538i | \(-0.574771\pi\) | ||||
−0.232745 | + | 0.972538i | \(0.574771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.7756 | 1.20422 | 0.602111 | − | 0.798412i | \(-0.294326\pi\) | ||||
0.602111 | + | 0.798412i | \(0.294326\pi\) | |||||||
\(572\) | 35.2609 | 1.47433 | ||||||||
\(573\) | −11.2992 | −0.472031 | ||||||||
\(574\) | 16.9711 | 0.708359 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0138794 | −0.000578308 0 | ||||||||
\(577\) | 31.6960 | 1.31952 | 0.659761 | − | 0.751476i | \(-0.270658\pi\) | ||||
0.659761 | + | 0.751476i | \(0.270658\pi\) | |||||||
\(578\) | 22.9704 | 0.955444 | ||||||||
\(579\) | 3.94771 | 0.164061 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3687 | −0.430166 | ||||||||
\(582\) | −22.1248 | −0.917103 | ||||||||
\(583\) | −7.20368 | −0.298346 | ||||||||
\(584\) | −123.905 | −5.12722 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.5020 | 2.12753 | ||||||||
\(587\) | 2.13491 | 0.0881170 | 0.0440585 | − | 0.999029i | \(-0.485971\pi\) | ||||
0.0440585 | + | 0.999029i | \(0.485971\pi\) | |||||||
\(588\) | −10.1314 | −0.417812 | ||||||||
\(589\) | 0.302948 | 0.0124828 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.50497 | 0.144175 | ||||||||
\(592\) | 137.434 | 5.64849 | ||||||||
\(593\) | −6.65285 | −0.273200 | −0.136600 | − | 0.990626i | \(-0.543617\pi\) | ||||
−0.136600 | + | 0.990626i | \(0.543617\pi\) | |||||||
\(594\) | 28.6574 | 1.17583 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −98.2887 | −4.02606 | ||||||||
\(597\) | 40.3493 | 1.65139 | ||||||||
\(598\) | 8.57984 | 0.350856 | ||||||||
\(599\) | 2.08780 | 0.0853051 | 0.0426526 | − | 0.999090i | \(-0.486419\pi\) | ||||
0.0426526 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.7870 | −1.13345 | −0.566727 | − | 0.823906i | \(-0.691791\pi\) | ||||
−0.566727 | + | 0.823906i | \(0.691791\pi\) | |||||||
\(602\) | 20.2302 | 0.824522 | ||||||||
\(603\) | −0.00395304 | −0.000160980 0 | ||||||||
\(604\) | 133.563 | 5.43461 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.85875 | 0.359862 | ||||||||
\(607\) | 14.1069 | 0.572582 | 0.286291 | − | 0.958143i | \(-0.407578\pi\) | ||||
0.286291 | + | 0.958143i | \(0.407578\pi\) | |||||||
\(608\) | −4.98942 | −0.202348 | ||||||||
\(609\) | 2.77733 | 0.112543 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0454 | −0.527762 | ||||||||
\(612\) | 0.00850964 | 0.000343982 0 | ||||||||
\(613\) | −46.0056 | −1.85815 | −0.929075 | − | 0.369892i | \(-0.879395\pi\) | ||||
−0.929075 | + | 0.369892i | \(0.879395\pi\) | |||||||
\(614\) | −22.0775 | −0.890975 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.2303 | 0.855392 | ||||||||
\(617\) | −27.8600 | −1.12160 | −0.560801 | − | 0.827950i | \(-0.689507\pi\) | ||||
−0.560801 | + | 0.827950i | \(0.689507\pi\) | |||||||
\(618\) | −55.9942 | −2.25242 | ||||||||
\(619\) | 34.2780 | 1.37775 | 0.688876 | − | 0.724880i | \(-0.258105\pi\) | ||||
0.688876 | + | 0.724880i | \(0.258105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.19640 | 0.208524 | ||||||||
\(622\) | 25.5345 | 1.02384 | ||||||||
\(623\) | 8.46385 | 0.339097 | ||||||||
\(624\) | −98.2233 | −3.93208 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.85935 | −0.274155 | ||||||||
\(627\) | 0.561115 | 0.0224088 | ||||||||
\(628\) | 134.550 | 5.36913 | ||||||||
\(629\) | −37.2530 | −1.48537 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.9555 | −0.993461 | −0.496730 | − | 0.867905i | \(-0.665466\pi\) | ||||
−0.496730 | + | 0.867905i | \(0.665466\pi\) | |||||||
\(632\) | −65.9059 | −2.62160 | ||||||||
\(633\) | 24.1274 | 0.958977 | ||||||||
\(634\) | 88.0198 | 3.49571 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 37.0779 | 1.47024 | ||||||||
\(637\) | 3.06234 | 0.121335 | ||||||||
\(638\) | −8.84346 | −0.350116 | ||||||||
\(639\) | 0.00478028 | 0.000189105 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3721 | −0.409673 | −0.204836 | − | 0.978796i | \(-0.565666\pi\) | ||||
−0.204836 | + | 0.978796i | \(0.565666\pi\) | |||||||
\(642\) | 3.98187 | 0.157152 | ||||||||
\(643\) | −1.61996 | −0.0638849 | −0.0319424 | − | 0.999490i | \(-0.510169\pi\) | ||||
−0.0319424 | + | 0.999490i | \(0.510169\pi\) | |||||||
\(644\) | 5.84965 | 0.230509 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.31482 | 0.0910756 | ||||||||
\(647\) | 31.5338 | 1.23972 | 0.619861 | − | 0.784711i | \(-0.287189\pi\) | ||||
0.619861 | + | 0.784711i | \(0.287189\pi\) | |||||||
\(648\) | −97.0616 | −3.81294 | ||||||||
\(649\) | −15.2823 | −0.599883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.18789 | 0.124943 | ||||||||
\(652\) | 127.759 | 5.00342 | ||||||||
\(653\) | −6.21910 | −0.243372 | −0.121686 | − | 0.992569i | \(-0.538830\pi\) | ||||
−0.121686 | + | 0.992569i | \(0.538830\pi\) | |||||||
\(654\) | 26.2942 | 1.02818 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 112.177 | 4.37979 | ||||||||
\(657\) | 0.00332915 | 0.000129883 0 | ||||||||
\(658\) | −11.9352 | −0.465282 | ||||||||
\(659\) | −15.2002 | −0.592115 | −0.296057 | − | 0.955170i | \(-0.595672\pi\) | ||||
−0.296057 | + | 0.955170i | \(0.595672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0579 | 1.36359 | 0.681796 | − | 0.731542i | \(-0.261199\pi\) | ||||
0.681796 | + | 0.731542i | \(0.261199\pi\) | |||||||
\(662\) | 36.7084 | 1.42671 | ||||||||
\(663\) | 26.6246 | 1.03401 | ||||||||
\(664\) | −111.833 | −4.33997 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.00602545 | −0.000233482 0 | ||||||||
\(667\) | −1.60357 | −0.0620905 | ||||||||
\(668\) | 42.0022 | 1.62511 | ||||||||
\(669\) | 5.44682 | 0.210586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4782 | 0.713344 | ||||||||
\(672\) | −52.5032 | −2.02535 | ||||||||
\(673\) | 17.4556 | 0.672863 | 0.336431 | − | 0.941708i | \(-0.390780\pi\) | ||||
0.336431 | + | 0.941708i | \(0.390780\pi\) | |||||||
\(674\) | 9.55330 | 0.367979 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.1877 | −0.814912 | ||||||||
\(677\) | −14.2438 | −0.547432 | −0.273716 | − | 0.961811i | \(-0.588253\pi\) | ||||
−0.273716 | + | 0.961811i | \(0.588253\pi\) | |||||||
\(678\) | 4.10464 | 0.157638 | ||||||||
\(679\) | 4.55947 | 0.174976 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.2580 | 1.12117 | ||||||||
\(682\) | −10.1507 | −0.388692 | ||||||||
\(683\) | 29.5756 | 1.13168 | 0.565840 | − | 0.824515i | \(-0.308552\pi\) | ||||
0.565840 | + | 0.824515i | \(0.308552\pi\) | |||||||
\(684\) | 0.000279014 0 | 1.06684e−5 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.80172 | 0.106970 | ||||||||
\(687\) | 6.97279 | 0.266029 | ||||||||
\(688\) | 133.720 | 5.09802 | ||||||||
\(689\) | −11.2073 | −0.426963 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.420090 | 0.0159810 | 0.00799049 | − | 0.999968i | \(-0.497457\pi\) | ||||
0.00799049 | + | 0.999968i | \(0.497457\pi\) | |||||||
\(692\) | −55.1041 | −2.09474 | ||||||||
\(693\) | −0.000570428 0 | −2.16688e−5 0 | ||||||||
\(694\) | −79.0281 | −2.99987 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 29.9554 | 1.13546 | ||||||||
\(697\) | −30.4069 | −1.15174 | ||||||||
\(698\) | 34.7732 | 1.31619 | ||||||||
\(699\) | 25.6404 | 0.969811 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8846 | 0.675491 | 0.337746 | − | 0.941237i | \(-0.390336\pi\) | ||||
0.337746 | + | 0.941237i | \(0.390336\pi\) | |||||||
\(702\) | 44.5843 | 1.68273 | ||||||||
\(703\) | −1.22145 | −0.0460679 | ||||||||
\(704\) | 94.2729 | 3.55304 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −89.3720 | −3.36356 | ||||||||
\(707\) | −1.82561 | −0.0686591 | ||||||||
\(708\) | 78.6594 | 2.95620 | ||||||||
\(709\) | 37.7351 | 1.41717 | 0.708585 | − | 0.705625i | \(-0.249334\pi\) | ||||
0.708585 | + | 0.705625i | \(0.249334\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.00177080 | 6.64102e−5 0 | ||||||||
\(712\) | 91.2883 | 3.42117 | ||||||||
\(713\) | −1.84062 | −0.0689318 | ||||||||
\(714\) | 24.3587 | 0.911601 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.41208 | −0.351746 | ||||||||
\(717\) | 24.2308 | 0.904916 | ||||||||
\(718\) | −39.2962 | −1.46652 | ||||||||
\(719\) | 18.0899 | 0.674640 | 0.337320 | − | 0.941390i | \(-0.390480\pi\) | ||||
0.337320 | + | 0.941390i | \(0.390480\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5393 | 0.429745 | ||||||||
\(722\) | −53.1568 | −1.97829 | ||||||||
\(723\) | 49.8119 | 1.85252 | ||||||||
\(724\) | 151.332 | 5.62420 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 34.5764 | 1.28325 | ||||||||
\(727\) | −4.46598 | −0.165634 | −0.0828171 | − | 0.996565i | \(-0.526392\pi\) | ||||
−0.0828171 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(728\) | 33.0294 | 1.22415 | ||||||||
\(729\) | 27.0026 | 1.00010 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36.2463 | −1.34062 | ||||||||
\(732\) | −95.1090 | −3.51533 | ||||||||
\(733\) | 47.7138 | 1.76235 | 0.881174 | − | 0.472792i | \(-0.156754\pi\) | ||||
0.881174 | + | 0.472792i | \(0.156754\pi\) | |||||||
\(734\) | −73.8909 | −2.72736 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.3142 | 1.11740 | ||||||||
\(737\) | 26.8502 | 0.989041 | ||||||||
\(738\) | −0.00491815 | −0.000181039 0 | ||||||||
\(739\) | 20.8292 | 0.766214 | 0.383107 | − | 0.923704i | \(-0.374854\pi\) | ||||
0.383107 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.872967 | 0.0320692 | ||||||||
\(742\) | −10.2535 | −0.376417 | ||||||||
\(743\) | 5.83129 | 0.213929 | 0.106965 | − | 0.994263i | \(-0.465887\pi\) | ||||
0.106965 | + | 0.994263i | \(0.465887\pi\) | |||||||
\(744\) | 34.3836 | 1.26056 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −93.2086 | −3.41261 | ||||||||
\(747\) | 0.00300480 | 0.000109940 0 | ||||||||
\(748\) | −57.8000 | −2.11338 | ||||||||
\(749\) | −0.820582 | −0.0299834 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.2146 | 1.79587 | 0.897933 | − | 0.440133i | \(-0.145069\pi\) | ||||
0.897933 | + | 0.440133i | \(0.145069\pi\) | |||||||
\(752\) | −78.8906 | −2.87684 | ||||||||
\(753\) | 0.165333 | 0.00602507 | ||||||||
\(754\) | −13.7584 | −0.501051 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 30.3972 | 1.10553 | ||||||||
\(757\) | −19.7407 | −0.717489 | −0.358744 | − | 0.933436i | \(-0.616795\pi\) | ||||
−0.358744 | + | 0.933436i | \(0.616795\pi\) | |||||||
\(758\) | −26.5571 | −0.964598 | ||||||||
\(759\) | −3.40917 | −0.123745 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.8533 | 1.58968 | 0.794840 | − | 0.606819i | \(-0.207555\pi\) | ||||
0.794840 | + | 0.606819i | \(0.207555\pi\) | |||||||
\(762\) | 9.25553 | 0.335292 | ||||||||
\(763\) | −5.41869 | −0.196170 | ||||||||
\(764\) | 38.1626 | 1.38067 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.5033 | 1.17439 | ||||||||
\(767\) | −23.7758 | −0.858493 | ||||||||
\(768\) | −191.032 | −6.89326 | ||||||||
\(769\) | 16.5364 | 0.596316 | 0.298158 | − | 0.954516i | \(-0.403628\pi\) | ||||
0.298158 | + | 0.954516i | \(0.403628\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4678 | 0.809157 | ||||||||
\(772\) | −13.3332 | −0.479874 | ||||||||
\(773\) | 24.3268 | 0.874974 | 0.437487 | − | 0.899225i | \(-0.355869\pi\) | ||||
0.437487 | + | 0.899225i | \(0.355869\pi\) | |||||||
\(774\) | −0.00586263 | −0.000210728 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 49.1769 | 1.76535 | ||||||||
\(777\) | −12.8532 | −0.461107 | ||||||||
\(778\) | 47.1165 | 1.68921 | ||||||||
\(779\) | −0.996983 | −0.0357206 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.4691 | −1.16183 | ||||||||
\(782\) | −14.0642 | −0.502934 | ||||||||
\(783\) | −8.33281 | −0.297790 | ||||||||
\(784\) | 18.5191 | 0.661398 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −78.6538 | −2.80549 | ||||||||
\(787\) | 27.8243 | 0.991830 | 0.495915 | − | 0.868371i | \(-0.334833\pi\) | ||||
0.495915 | + | 0.868371i | \(0.334833\pi\) | |||||||
\(788\) | −11.8379 | −0.421708 | ||||||||
\(789\) | −9.85714 | −0.350923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.845882 | −0.0300761 | ||||||||
\(792\) | −0.00615245 | −0.000218618 0 | ||||||||
\(793\) | 28.7479 | 1.02087 | ||||||||
\(794\) | 40.6008 | 1.44087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −136.278 | −4.83026 | ||||||||
\(797\) | 10.5441 | 0.373491 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(798\) | 0.798673 | 0.0282727 | ||||||||
\(799\) | 21.3842 | 0.756519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.00245279 | −8.66650e−5 0 | ||||||||
\(802\) | −71.6201 | −2.52899 | ||||||||
\(803\) | −22.6126 | −0.797980 | ||||||||
\(804\) | −138.200 | −4.87395 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.7922 | −0.556258 | ||||||||
\(807\) | 39.6338 | 1.39518 | ||||||||
\(808\) | −19.6904 | −0.692706 | ||||||||
\(809\) | −10.8405 | −0.381132 | −0.190566 | − | 0.981674i | \(-0.561032\pi\) | ||||
−0.190566 | + | 0.981674i | \(0.561032\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.1903 | −1.06013 | −0.530063 | − | 0.847959i | \(-0.677832\pi\) | ||||
−0.530063 | + | 0.847959i | \(0.677832\pi\) | |||||||
\(812\) | −9.38034 | −0.329185 | ||||||||
\(813\) | 33.6416 | 1.17986 | ||||||||
\(814\) | 40.9266 | 1.43448 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 161.009 | 5.63643 | ||||||||
\(817\) | −1.18844 | −0.0415784 | ||||||||
\(818\) | −37.9984 | −1.32858 | ||||||||
\(819\) | −0.000887455 0 | −3.10102e−5 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.3428 | −0.744870 | −0.372435 | − | 0.928058i | \(-0.621477\pi\) | ||||
−0.372435 | + | 0.928058i | \(0.621477\pi\) | |||||||
\(822\) | −42.4564 | −1.48084 | ||||||||
\(823\) | −29.6059 | −1.03200 | −0.515998 | − | 0.856590i | \(-0.672579\pi\) | ||||
−0.515998 | + | 0.856590i | \(0.672579\pi\) | |||||||
\(824\) | 124.459 | 4.33573 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.7523 | −0.756860 | ||||||||
\(827\) | −31.4922 | −1.09509 | −0.547545 | − | 0.836776i | \(-0.684437\pi\) | ||||
−0.547545 | + | 0.836776i | \(0.684437\pi\) | |||||||
\(828\) | −0.00169521 | −5.89125e−5 0 | ||||||||
\(829\) | −27.4940 | −0.954905 | −0.477452 | − | 0.878658i | \(-0.658440\pi\) | ||||
−0.477452 | + | 0.878658i | \(0.658440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.5481 | 0.955634 | ||||||||
\(832\) | 146.667 | 5.08476 | ||||||||
\(833\) | −5.01983 | −0.173927 | ||||||||
\(834\) | 90.9309 | 3.14868 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.89515 | −0.0655450 | ||||||||
\(837\) | −9.56460 | −0.330601 | ||||||||
\(838\) | 41.8067 | 1.44419 | ||||||||
\(839\) | 35.9545 | 1.24129 | 0.620643 | − | 0.784093i | \(-0.286871\pi\) | ||||
0.620643 | + | 0.784093i | \(0.286871\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4286 | −0.911330 | ||||||||
\(842\) | −110.851 | −3.82019 | ||||||||
\(843\) | 17.8762 | 0.615688 | ||||||||
\(844\) | −81.4893 | −2.80498 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.00345877 | 0.000118915 0 | ||||||||
\(847\) | −7.12549 | −0.244835 | ||||||||
\(848\) | −67.7745 | −2.32739 | ||||||||
\(849\) | −5.04559 | −0.173164 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.42117 | 0.254394 | ||||||||
\(852\) | 167.121 | 5.72547 | ||||||||
\(853\) | −30.4795 | −1.04360 | −0.521799 | − | 0.853068i | \(-0.674739\pi\) | ||||
−0.521799 | + | 0.853068i | \(0.674739\pi\) | |||||||
\(854\) | 26.3013 | 0.900011 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.85053 | −0.302505 | ||||||||
\(857\) | 3.98363 | 0.136078 | 0.0680391 | − | 0.997683i | \(-0.478326\pi\) | ||||
0.0680391 | + | 0.997683i | \(0.478326\pi\) | |||||||
\(858\) | −29.2501 | −0.998582 | ||||||||
\(859\) | 49.8467 | 1.70075 | 0.850374 | − | 0.526179i | \(-0.176376\pi\) | ||||
0.850374 | + | 0.526179i | \(0.176376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4912 | −0.357538 | ||||||||
\(862\) | −70.8338 | −2.41261 | ||||||||
\(863\) | 12.1535 | 0.413711 | 0.206855 | − | 0.978372i | \(-0.433677\pi\) | ||||
0.206855 | + | 0.978372i | \(0.433677\pi\) | |||||||
\(864\) | 157.525 | 5.35910 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.5850 | −0.427657 | ||||||||
\(867\) | −14.1998 | −0.482252 | ||||||||
\(868\) | −10.7670 | −0.365455 | ||||||||
\(869\) | −12.0278 | −0.408015 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 41.7728 | 1.41542 | ||||||||
\(872\) | −58.4442 | −1.97917 | ||||||||
\(873\) | −0.00132132 | −4.47198e−5 0 | ||||||||
\(874\) | −0.461136 | −0.0155982 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 116.389 | 3.93241 | ||||||||
\(877\) | −56.5162 | −1.90842 | −0.954209 | − | 0.299141i | \(-0.903300\pi\) | ||||
−0.954209 | + | 0.299141i | \(0.903300\pi\) | |||||||
\(878\) | −85.8181 | −2.89622 | ||||||||
\(879\) | −31.8374 | −1.07385 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.619072 | 0.0208571 | 0.0104285 | − | 0.999946i | \(-0.496680\pi\) | ||||
0.0104285 | + | 0.999946i | \(0.496680\pi\) | |||||||
\(882\) | −0.000811928 0 | −2.73390e−5 0 | ||||||||
\(883\) | 50.2806 | 1.69208 | 0.846039 | − | 0.533121i | \(-0.178981\pi\) | ||||
0.846039 | + | 0.533121i | \(0.178981\pi\) | |||||||
\(884\) | −89.9235 | −3.02445 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.1815 | −0.409246 | ||||||||
\(887\) | 23.9620 | 0.804567 | 0.402283 | − | 0.915515i | \(-0.368217\pi\) | ||||
0.402283 | + | 0.915515i | \(0.368217\pi\) | |||||||
\(888\) | −138.630 | −4.65213 | ||||||||
\(889\) | −1.90738 | −0.0639713 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.7137 | −0.593431 | ||||||||
\(892\) | −18.3964 | −0.615958 | ||||||||
\(893\) | 0.701146 | 0.0234629 | ||||||||
\(894\) | 81.5339 | 2.72690 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 73.5565 | 2.45735 | ||||||||
\(897\) | −5.30388 | −0.177091 | ||||||||
\(898\) | −67.6037 | −2.25596 | ||||||||
\(899\) | 2.95157 | 0.0984402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.3711 | 0.612029 | ||||||||
\(902\) | 33.4055 | 1.11228 | ||||||||
\(903\) | −12.5059 | −0.416170 | ||||||||
\(904\) | −9.12340 | −0.303440 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −110.795 | −3.68093 | ||||||||
\(907\) | 27.7804 | 0.922432 | 0.461216 | − | 0.887288i | \(-0.347413\pi\) | ||||
0.461216 | + | 0.887288i | \(0.347413\pi\) | |||||||
\(908\) | −98.8176 | −3.27938 | ||||||||
\(909\) | 0.000529054 0 | 1.75476e−5 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.6697 | 0.916738 | 0.458369 | − | 0.888762i | \(-0.348434\pi\) | ||||
0.458369 | + | 0.888762i | \(0.348434\pi\) | |||||||
\(912\) | 5.27916 | 0.174810 | ||||||||
\(913\) | −20.4095 | −0.675456 | ||||||||
\(914\) | 11.2673 | 0.372690 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −23.5503 | −0.778125 | ||||||||
\(917\) | 16.2089 | 0.535266 | ||||||||
\(918\) | −73.0831 | −2.41210 | ||||||||
\(919\) | −40.1657 | −1.32495 | −0.662473 | − | 0.749086i | \(-0.730493\pi\) | ||||
−0.662473 | + | 0.749086i | \(0.730493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.6478 | 0.449712 | ||||||||
\(922\) | −45.4004 | −1.49518 | ||||||||
\(923\) | −50.5144 | −1.66270 | ||||||||
\(924\) | −19.9424 | −0.656058 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.7709 | 0.485402 | ||||||||
\(927\) | −0.00334403 | −0.000109832 0 | ||||||||
\(928\) | −48.6110 | −1.59573 | ||||||||
\(929\) | −21.6852 | −0.711469 | −0.355734 | − | 0.934587i | \(-0.615769\pi\) | ||||
−0.355734 | + | 0.934587i | \(0.615769\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.164590 | −0.00539423 | ||||||||
\(932\) | −86.5996 | −2.83667 | ||||||||
\(933\) | −15.7849 | −0.516773 | ||||||||
\(934\) | 104.765 | 3.42800 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.00957179 | −0.000312864 0 | ||||||||
\(937\) | 8.63117 | 0.281968 | 0.140984 | − | 0.990012i | \(-0.454973\pi\) | ||||
0.140984 | + | 0.990012i | \(0.454973\pi\) | |||||||
\(938\) | 38.2177 | 1.24785 | ||||||||
\(939\) | 4.24031 | 0.138377 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.0813 | −0.817626 | −0.408813 | − | 0.912618i | \(-0.634057\pi\) | ||||
−0.408813 | + | 0.912618i | \(0.634057\pi\) | |||||||
\(942\) | −111.614 | −3.63658 | ||||||||
\(943\) | 6.05737 | 0.197255 | ||||||||
\(944\) | −143.781 | −4.67967 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 39.8207 | 1.29468 | ||||||||
\(947\) | −4.94123 | −0.160568 | −0.0802842 | − | 0.996772i | \(-0.525583\pi\) | ||||
−0.0802842 | + | 0.996772i | \(0.525583\pi\) | |||||||
\(948\) | 61.9081 | 2.01068 | ||||||||
\(949\) | −35.1800 | −1.14199 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.4120 | −1.76443 | ||||||||
\(952\) | −54.1422 | −1.75476 | ||||||||
\(953\) | −7.21931 | −0.233856 | −0.116928 | − | 0.993140i | \(-0.537305\pi\) | ||||
−0.116928 | + | 0.993140i | \(0.537305\pi\) | |||||||
\(954\) | 0.00297141 | 9.62031e−5 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −81.8387 | −2.64685 | ||||||||
\(957\) | 5.46684 | 0.176718 | ||||||||
\(958\) | −98.3088 | −3.17621 | ||||||||
\(959\) | 8.74940 | 0.282533 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6121 | −0.890713 | ||||||||
\(962\) | 63.6724 | 2.05288 | ||||||||
\(963\) | 0.000237801 0 | 7.66304e−6 0 | ||||||||
\(964\) | −168.238 | −5.41857 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.85249 | −0.156126 | ||||||||
\(967\) | 26.2278 | 0.843430 | 0.421715 | − | 0.906728i | \(-0.361428\pi\) | ||||
0.421715 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(968\) | −76.8531 | −2.47015 | ||||||||
\(969\) | −1.43098 | −0.0459696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5539 | 0.820063 | 0.410032 | − | 0.912071i | \(-0.365518\pi\) | ||||
0.410032 | + | 0.912071i | \(0.365518\pi\) | |||||||
\(972\) | −0.0176171 | −0.000565069 0 | ||||||||
\(973\) | −18.7390 | −0.600745 | ||||||||
\(974\) | 22.9052 | 0.733931 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 173.849 | 5.56478 | ||||||||
\(977\) | 2.92251 | 0.0934993 | 0.0467497 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467497 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(978\) | −105.980 | −3.38888 | ||||||||
\(979\) | 16.6601 | 0.532458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.00157031 | 5.01363e−5 0 | ||||||||
\(982\) | 94.2961 | 3.00911 | ||||||||
\(983\) | 17.6138 | 0.561792 | 0.280896 | − | 0.959738i | \(-0.409368\pi\) | ||||
0.280896 | + | 0.959738i | \(0.409368\pi\) | |||||||
\(984\) | −113.154 | −3.60722 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.5529 | 0.718231 | ||||||||
\(987\) | 7.37809 | 0.234847 | ||||||||
\(988\) | −2.94841 | −0.0938015 | ||||||||
\(989\) | 7.22063 | 0.229603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.1062 | −1.05165 | −0.525827 | − | 0.850592i | \(-0.676244\pi\) | ||||
−0.525827 | + | 0.850592i | \(0.676244\pi\) | |||||||
\(992\) | −55.7969 | −1.77155 | ||||||||
\(993\) | −22.6924 | −0.720121 | ||||||||
\(994\) | −46.2154 | −1.46586 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 105.049 | 3.32862 | ||||||||
\(997\) | −16.6806 | −0.528280 | −0.264140 | − | 0.964484i | \(-0.585088\pi\) | ||||
−0.264140 | + | 0.964484i | \(0.585088\pi\) | |||||||
\(998\) | 95.4352 | 3.02095 | ||||||||
\(999\) | 38.5634 | 1.22009 |
(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 | 4025.2.a.bc.1.14 | yes | 14 | |
5.4 | even | 2 | 4025.2.a.z.1.1 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.z.1.1 | ✓ | 14 | 5.4 | even | 2 | ||
4025.2.a.bc.1.14 | yes | 14 | 1.1 | even | 1 | trivial |