Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,4,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.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: | \(10.3253342510\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58579 | −0.914214 | −0.457107 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457107 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(3\) | −6.65685 | −1.28111 | −0.640556 | − | 0.767911i | \(-0.721296\pi\) | ||||
−0.640556 | + | 0.767911i | \(0.721296\pi\) | |||||||
\(4\) | −1.31371 | −0.164214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 17.2132 | 1.17121 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 24.0833 | 1.06434 | ||||||||
\(9\) | 17.3137 | 0.641248 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 38.2548 | 1.04857 | 0.524285 | − | 0.851543i | \(-0.324333\pi\) | ||||
0.524285 | + | 0.851543i | \(0.324333\pi\) | |||||||
\(12\) | 8.74517 | 0.210376 | ||||||||
\(13\) | −19.3431 | −0.412679 | −0.206339 | − | 0.978480i | \(-0.566155\pi\) | ||||
−0.206339 | + | 0.978480i | \(0.566155\pi\) | |||||||
\(14\) | −18.1005 | −0.345540 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −51.7645 | −0.808820 | ||||||||
\(17\) | 87.2254 | 1.24443 | 0.622214 | − | 0.782847i | \(-0.286233\pi\) | ||||
0.622214 | + | 0.782847i | \(0.286233\pi\) | |||||||
\(18\) | −44.7696 | −0.586238 | ||||||||
\(19\) | −44.2254 | −0.534000 | −0.267000 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.267000 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.5980 | −0.484215 | ||||||||
\(22\) | −98.9188 | −0.958617 | ||||||||
\(23\) | −218.167 | −1.97786 | −0.988932 | − | 0.148371i | \(-0.952597\pi\) | ||||
−0.988932 | + | 0.148371i | \(0.952597\pi\) | |||||||
\(24\) | −160.319 | −1.36354 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 50.0172 | 0.377276 | ||||||||
\(27\) | 64.4802 | 0.459601 | ||||||||
\(28\) | −9.19596 | −0.0620669 | ||||||||
\(29\) | −46.9411 | −0.300578 | −0.150289 | − | 0.988642i | \(-0.548020\pi\) | ||||
−0.150289 | + | 0.988642i | \(0.548020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 194.558 | 1.12722 | 0.563609 | − | 0.826042i | \(-0.309413\pi\) | ||||
0.563609 | + | 0.826042i | \(0.309413\pi\) | |||||||
\(32\) | −58.8141 | −0.324905 | ||||||||
\(33\) | −254.657 | −1.34334 | ||||||||
\(34\) | −225.546 | −1.13767 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.7452 | −0.105302 | ||||||||
\(37\) | −366.853 | −1.63001 | −0.815003 | − | 0.579457i | \(-0.803265\pi\) | ||||
−0.815003 | + | 0.579457i | \(0.803265\pi\) | |||||||
\(38\) | 114.357 | 0.488190 | ||||||||
\(39\) | 128.765 | 0.528688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −339.362 | −1.29267 | −0.646336 | − | 0.763053i | \(-0.723699\pi\) | ||||
−0.646336 | + | 0.763053i | \(0.723699\pi\) | |||||||
\(42\) | 120.492 | 0.442676 | ||||||||
\(43\) | 226.167 | 0.802095 | 0.401047 | − | 0.916057i | \(-0.368646\pi\) | ||||
0.401047 | + | 0.916057i | \(0.368646\pi\) | |||||||
\(44\) | −50.2557 | −0.172189 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 564.132 | 1.80819 | ||||||||
\(47\) | −11.6762 | −0.0362372 | −0.0181186 | − | 0.999836i | \(-0.505768\pi\) | ||||
−0.0181186 | + | 0.999836i | \(0.505768\pi\) | |||||||
\(48\) | 344.589 | 1.03619 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −580.647 | −1.59425 | ||||||||
\(52\) | 25.4113 | 0.0677674 | ||||||||
\(53\) | 209.019 | 0.541717 | 0.270859 | − | 0.962619i | \(-0.412692\pi\) | ||||
0.270859 | + | 0.962619i | \(0.412692\pi\) | |||||||
\(54\) | −166.732 | −0.420173 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 168.583 | 0.402283 | ||||||||
\(57\) | 294.402 | 0.684114 | ||||||||
\(58\) | 121.380 | 0.274792 | ||||||||
\(59\) | −616.000 | −1.35926 | −0.679630 | − | 0.733555i | \(-0.737860\pi\) | ||||
−0.679630 | + | 0.733555i | \(0.737860\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 320.735 | 0.673212 | 0.336606 | − | 0.941646i | \(-0.390721\pi\) | ||||
0.336606 | + | 0.941646i | \(0.390721\pi\) | |||||||
\(62\) | −503.087 | −1.03052 | ||||||||
\(63\) | 121.196 | 0.242369 | ||||||||
\(64\) | 566.197 | 1.10585 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 658.488 | 1.22810 | ||||||||
\(67\) | −14.5097 | −0.0264573 | −0.0132286 | − | 0.999912i | \(-0.504211\pi\) | ||||
−0.0132286 | + | 0.999912i | \(0.504211\pi\) | |||||||
\(68\) | −114.589 | −0.204352 | ||||||||
\(69\) | 1452.30 | 2.53387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −952.000 | −1.59129 | −0.795645 | − | 0.605763i | \(-0.792868\pi\) | ||||
−0.795645 | + | 0.605763i | \(0.792868\pi\) | |||||||
\(72\) | 416.971 | 0.682506 | ||||||||
\(73\) | −824.489 | −1.32191 | −0.660953 | − | 0.750427i | \(-0.729848\pi\) | ||||
−0.660953 | + | 0.750427i | \(0.729848\pi\) | |||||||
\(74\) | 948.603 | 1.49017 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 58.0993 | 0.0876901 | ||||||||
\(77\) | 267.784 | 0.396322 | ||||||||
\(78\) | −332.958 | −0.483334 | ||||||||
\(79\) | 156.275 | 0.222561 | 0.111280 | − | 0.993789i | \(-0.464505\pi\) | ||||
0.111280 | + | 0.993789i | \(0.464505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −896.706 | −1.23005 | ||||||||
\(82\) | 877.519 | 1.18178 | ||||||||
\(83\) | 1036.53 | 1.37077 | 0.685384 | − | 0.728182i | \(-0.259634\pi\) | ||||
0.685384 | + | 0.728182i | \(0.259634\pi\) | |||||||
\(84\) | 61.2162 | 0.0795147 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −584.818 | −0.733286 | ||||||||
\(87\) | 312.480 | 0.385074 | ||||||||
\(88\) | 921.301 | 1.11603 | ||||||||
\(89\) | −170.225 | −0.202740 | −0.101370 | − | 0.994849i | \(-0.532323\pi\) | ||||
−0.101370 | + | 0.994849i | \(0.532323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −135.402 | −0.155978 | ||||||||
\(92\) | 286.607 | 0.324792 | ||||||||
\(93\) | −1295.15 | −1.44409 | ||||||||
\(94\) | 30.1921 | 0.0331285 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 391.517 | 0.416240 | ||||||||
\(97\) | −1059.87 | −1.10942 | −0.554710 | − | 0.832044i | \(-0.687171\pi\) | ||||
−0.554710 | + | 0.832044i | \(0.687171\pi\) | |||||||
\(98\) | −126.704 | −0.130602 | ||||||||
\(99\) | 662.333 | 0.672394 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −241.833 | −0.238251 | −0.119125 | − | 0.992879i | \(-0.538009\pi\) | ||||
−0.119125 | + | 0.992879i | \(0.538009\pi\) | |||||||
\(102\) | 1501.43 | 1.45749 | ||||||||
\(103\) | 1679.58 | 1.60673 | 0.803367 | − | 0.595484i | \(-0.203040\pi\) | ||||
0.803367 | + | 0.595484i | \(0.203040\pi\) | |||||||
\(104\) | −465.846 | −0.439230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −540.479 | −0.495245 | ||||||||
\(107\) | −1506.88 | −1.36146 | −0.680728 | − | 0.732537i | \(-0.738336\pi\) | ||||
−0.680728 | + | 0.732537i | \(0.738336\pi\) | |||||||
\(108\) | −84.7082 | −0.0754727 | ||||||||
\(109\) | −1252.41 | −1.10054 | −0.550271 | − | 0.834986i | \(-0.685476\pi\) | ||||
−0.550271 | + | 0.834986i | \(0.685476\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2442.09 | 2.08822 | ||||||||
\(112\) | −362.352 | −0.305705 | ||||||||
\(113\) | −1370.20 | −1.14069 | −0.570345 | − | 0.821405i | \(-0.693190\pi\) | ||||
−0.570345 | + | 0.821405i | \(0.693190\pi\) | |||||||
\(114\) | −761.261 | −0.625426 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 61.6670 | 0.0493589 | ||||||||
\(117\) | −334.902 | −0.264630 | ||||||||
\(118\) | 1592.84 | 1.24265 | ||||||||
\(119\) | 610.578 | 0.470349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 132.432 | 0.0994984 | ||||||||
\(122\) | −829.352 | −0.615459 | ||||||||
\(123\) | 2259.09 | 1.65606 | ||||||||
\(124\) | −255.593 | −0.185104 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −313.387 | −0.221577 | ||||||||
\(127\) | −1213.49 | −0.847873 | −0.423936 | − | 0.905692i | \(-0.639352\pi\) | ||||
−0.423936 | + | 0.905692i | \(0.639352\pi\) | |||||||
\(128\) | −993.551 | −0.686081 | ||||||||
\(129\) | −1505.56 | −1.02757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1982.42 | −1.32217 | −0.661087 | − | 0.750309i | \(-0.729904\pi\) | ||||
−0.661087 | + | 0.750309i | \(0.729904\pi\) | |||||||
\(132\) | 334.545 | 0.220594 | ||||||||
\(133\) | −309.578 | −0.201833 | ||||||||
\(134\) | 37.5189 | 0.0241876 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2100.67 | 1.32449 | ||||||||
\(137\) | −2210.95 | −1.37879 | −0.689394 | − | 0.724386i | \(-0.742123\pi\) | ||||
−0.689394 | + | 0.724386i | \(0.742123\pi\) | |||||||
\(138\) | −3755.34 | −2.31649 | ||||||||
\(139\) | 528.039 | 0.322213 | 0.161107 | − | 0.986937i | \(-0.448494\pi\) | ||||
0.161107 | + | 0.986937i | \(0.448494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.7267 | 0.0464239 | ||||||||
\(142\) | 2461.67 | 1.45478 | ||||||||
\(143\) | −739.969 | −0.432722 | ||||||||
\(144\) | −896.235 | −0.518655 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2131.95 | 1.20851 | ||||||||
\(147\) | −326.186 | −0.183016 | ||||||||
\(148\) | 481.938 | 0.267669 | ||||||||
\(149\) | −328.372 | −0.180545 | −0.0902727 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902727 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1029.43 | 0.554793 | 0.277396 | − | 0.960756i | \(-0.410528\pi\) | ||||
0.277396 | + | 0.960756i | \(0.410528\pi\) | |||||||
\(152\) | −1065.09 | −0.568358 | ||||||||
\(153\) | 1510.20 | 0.797987 | ||||||||
\(154\) | −692.432 | −0.362323 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −169.159 | −0.0868177 | ||||||||
\(157\) | −525.098 | −0.266926 | −0.133463 | − | 0.991054i | \(-0.542610\pi\) | ||||
−0.133463 | + | 0.991054i | \(0.542610\pi\) | |||||||
\(158\) | −404.094 | −0.203468 | ||||||||
\(159\) | −1391.41 | −0.694001 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1527.17 | −0.747562 | ||||||||
\(162\) | 2318.69 | 1.12453 | ||||||||
\(163\) | −1002.63 | −0.481790 | −0.240895 | − | 0.970551i | \(-0.577441\pi\) | ||||
−0.240895 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(164\) | 445.823 | 0.212274 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2680.24 | −1.25317 | ||||||||
\(167\) | 359.422 | 0.166544 | 0.0832722 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832722 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(168\) | −1122.23 | −0.515369 | ||||||||
\(169\) | −1822.84 | −0.829696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −765.706 | −0.342427 | ||||||||
\(172\) | −297.117 | −0.131715 | ||||||||
\(173\) | −3293.65 | −1.44747 | −0.723733 | − | 0.690080i | \(-0.757575\pi\) | ||||
−0.723733 | + | 0.690080i | \(0.757575\pi\) | |||||||
\(174\) | −808.007 | −0.352039 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1980.24 | −0.848104 | ||||||||
\(177\) | 4100.62 | 1.74137 | ||||||||
\(178\) | 440.167 | 0.185348 | ||||||||
\(179\) | 2978.82 | 1.24384 | 0.621921 | − | 0.783080i | \(-0.286353\pi\) | ||||
0.621921 | + | 0.783080i | \(0.286353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1462.31 | 0.600514 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(182\) | 350.121 | 0.142597 | ||||||||
\(183\) | −2135.09 | −0.862460 | ||||||||
\(184\) | −5254.16 | −2.10512 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3348.97 | 1.32021 | ||||||||
\(187\) | 3336.79 | 1.30487 | ||||||||
\(188\) | 15.3391 | 0.00595064 | ||||||||
\(189\) | 451.362 | 0.173713 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −374.923 | −0.142034 | −0.0710169 | − | 0.997475i | \(-0.522624\pi\) | ||||
−0.0710169 | + | 0.997475i | \(0.522624\pi\) | |||||||
\(192\) | −3769.09 | −1.41672 | ||||||||
\(193\) | −733.028 | −0.273391 | −0.136696 | − | 0.990613i | \(-0.543648\pi\) | ||||
−0.136696 | + | 0.990613i | \(0.543648\pi\) | |||||||
\(194\) | 2740.61 | 1.01425 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −64.3717 | −0.0234591 | ||||||||
\(197\) | 2093.24 | 0.757043 | 0.378521 | − | 0.925593i | \(-0.376433\pi\) | ||||
0.378521 | + | 0.925593i | \(0.376433\pi\) | |||||||
\(198\) | −1712.65 | −0.614711 | ||||||||
\(199\) | 2865.04 | 1.02059 | 0.510295 | − | 0.860000i | \(-0.329536\pi\) | ||||
0.510295 | + | 0.860000i | \(0.329536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 96.5887 | 0.0338948 | ||||||||
\(202\) | 625.330 | 0.217812 | ||||||||
\(203\) | −328.588 | −0.113608 | ||||||||
\(204\) | 762.801 | 0.261798 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4343.03 | −1.46890 | ||||||||
\(207\) | −3777.27 | −1.26830 | ||||||||
\(208\) | 1001.29 | 0.333783 | ||||||||
\(209\) | −1691.84 | −0.559936 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5643.65 | 1.84135 | 0.920674 | − | 0.390331i | \(-0.127640\pi\) | ||||
0.920674 | + | 0.390331i | \(0.127640\pi\) | |||||||
\(212\) | −274.590 | −0.0889573 | ||||||||
\(213\) | 6337.33 | 2.03862 | ||||||||
\(214\) | 3896.47 | 1.24466 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1552.89 | 0.489172 | ||||||||
\(217\) | 1361.91 | 0.426048 | ||||||||
\(218\) | 3238.46 | 1.00613 | ||||||||
\(219\) | 5488.51 | 1.69351 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1687.21 | −0.513549 | ||||||||
\(222\) | −6314.71 | −1.90908 | ||||||||
\(223\) | 6369.16 | 1.91260 | 0.956302 | − | 0.292381i | \(-0.0944477\pi\) | ||||
0.956302 | + | 0.292381i | \(0.0944477\pi\) | |||||||
\(224\) | −411.699 | −0.122803 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3543.05 | 1.04283 | ||||||||
\(227\) | 1015.67 | 0.296972 | 0.148486 | − | 0.988914i | \(-0.452560\pi\) | ||||
0.148486 | + | 0.988914i | \(0.452560\pi\) | |||||||
\(228\) | −386.758 | −0.112341 | ||||||||
\(229\) | 4108.35 | 1.18554 | 0.592768 | − | 0.805373i | \(-0.298035\pi\) | ||||
0.592768 | + | 0.805373i | \(0.298035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1782.60 | −0.507733 | ||||||||
\(232\) | −1130.50 | −0.319917 | ||||||||
\(233\) | −608.431 | −0.171071 | −0.0855357 | − | 0.996335i | \(-0.527260\pi\) | ||||
−0.0855357 | + | 0.996335i | \(0.527260\pi\) | |||||||
\(234\) | 865.984 | 0.241928 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 809.244 | 0.223209 | ||||||||
\(237\) | −1040.30 | −0.285126 | ||||||||
\(238\) | −1578.82 | −0.430000 | ||||||||
\(239\) | −5054.44 | −1.36797 | −0.683985 | − | 0.729496i | \(-0.739755\pi\) | ||||
−0.683985 | + | 0.729496i | \(0.739755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.86782 | 0.00130109 | 0.000650547 | − | 1.00000i | \(-0.499793\pi\) | ||||
0.000650547 | 1.00000i | \(0.499793\pi\) | ||||||||
\(242\) | −342.442 | −0.0909628 | ||||||||
\(243\) | 4228.27 | 1.11623 | ||||||||
\(244\) | −421.352 | −0.110551 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5841.52 | −1.51399 | ||||||||
\(247\) | 855.458 | 0.220370 | ||||||||
\(248\) | 4685.60 | 1.19974 | ||||||||
\(249\) | −6900.02 | −1.75611 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −547.921 | −0.137787 | −0.0688934 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688934 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(252\) | −159.216 | −0.0398003 | ||||||||
\(253\) | −8345.92 | −2.07393 | ||||||||
\(254\) | 3137.83 | 0.775137 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1960.46 | −0.478629 | ||||||||
\(257\) | 1774.61 | 0.430729 | 0.215364 | − | 0.976534i | \(-0.430906\pi\) | ||||
0.215364 | + | 0.976534i | \(0.430906\pi\) | |||||||
\(258\) | 3893.05 | 0.939421 | ||||||||
\(259\) | −2567.97 | −0.616084 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −812.725 | −0.192745 | ||||||||
\(262\) | 5126.11 | 1.20875 | ||||||||
\(263\) | 1199.09 | 0.281138 | 0.140569 | − | 0.990071i | \(-0.455107\pi\) | ||||
0.140569 | + | 0.990071i | \(0.455107\pi\) | |||||||
\(264\) | −6132.97 | −1.42977 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 800.502 | 0.184519 | ||||||||
\(267\) | 1133.17 | 0.259733 | ||||||||
\(268\) | 19.0615 | 0.00434464 | ||||||||
\(269\) | 3250.29 | 0.736706 | 0.368353 | − | 0.929686i | \(-0.379922\pi\) | ||||
0.368353 | + | 0.929686i | \(0.379922\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −896.143 | −0.200874 | −0.100437 | − | 0.994943i | \(-0.532024\pi\) | ||||
−0.100437 | + | 0.994943i | \(0.532024\pi\) | |||||||
\(272\) | −4515.18 | −1.00652 | ||||||||
\(273\) | 901.352 | 0.199825 | ||||||||
\(274\) | 5717.04 | 1.26051 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1907.90 | −0.416095 | ||||||||
\(277\) | 386.562 | 0.0838492 | 0.0419246 | − | 0.999121i | \(-0.486651\pi\) | ||||
0.0419246 | + | 0.999121i | \(0.486651\pi\) | |||||||
\(278\) | −1365.40 | −0.294572 | ||||||||
\(279\) | 3368.53 | 0.722826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3335.10 | −0.708025 | −0.354013 | − | 0.935241i | \(-0.615183\pi\) | ||||
−0.354013 | + | 0.935241i | \(0.615183\pi\) | |||||||
\(282\) | −200.985 | −0.0424414 | ||||||||
\(283\) | −5412.26 | −1.13684 | −0.568419 | − | 0.822739i | \(-0.692445\pi\) | ||||
−0.568419 | + | 0.822739i | \(0.692445\pi\) | |||||||
\(284\) | 1250.65 | 0.261311 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1913.40 | 0.395601 | ||||||||
\(287\) | −2375.54 | −0.488584 | ||||||||
\(288\) | −1018.29 | −0.208345 | ||||||||
\(289\) | 2695.27 | 0.548600 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7055.42 | 1.42129 | ||||||||
\(292\) | 1083.14 | 0.217075 | ||||||||
\(293\) | −282.211 | −0.0562695 | −0.0281347 | − | 0.999604i | \(-0.508957\pi\) | ||||
−0.0281347 | + | 0.999604i | \(0.508957\pi\) | |||||||
\(294\) | 843.447 | 0.167316 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8835.01 | −1.73488 | ||||||||
\(297\) | 2466.68 | 0.481924 | ||||||||
\(298\) | 849.099 | 0.165057 | ||||||||
\(299\) | 4220.03 | 0.816222 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1583.17 | 0.303163 | ||||||||
\(302\) | −2661.88 | −0.507199 | ||||||||
\(303\) | 1609.85 | 0.305226 | ||||||||
\(304\) | 2289.31 | 0.431910 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3905.04 | −0.729531 | ||||||||
\(307\) | −1919.67 | −0.356878 | −0.178439 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178439 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(308\) | −351.790 | −0.0650815 | ||||||||
\(309\) | −11180.7 | −2.05841 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1213.31 | 0.221223 | 0.110612 | − | 0.993864i | \(-0.464719\pi\) | ||||
0.110612 | + | 0.993864i | \(0.464719\pi\) | |||||||
\(312\) | 3101.07 | 0.562703 | ||||||||
\(313\) | 1434.00 | 0.258960 | 0.129480 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129480 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(314\) | 1357.79 | 0.244028 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −205.300 | −0.0365475 | ||||||||
\(317\) | −6496.95 | −1.15112 | −0.575560 | − | 0.817760i | \(-0.695216\pi\) | ||||
−0.575560 | + | 0.817760i | \(0.695216\pi\) | |||||||
\(318\) | 3597.89 | 0.634465 | ||||||||
\(319\) | −1795.72 | −0.315176 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10031.1 | 1.74418 | ||||||||
\(322\) | 3948.92 | 0.683432 | ||||||||
\(323\) | −3857.58 | −0.664524 | ||||||||
\(324\) | 1178.01 | 0.201991 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2592.58 | 0.440459 | ||||||||
\(327\) | 8337.11 | 1.40992 | ||||||||
\(328\) | −8172.96 | −1.37584 | ||||||||
\(329\) | −81.7333 | −0.0136964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9683.88 | −1.60808 | −0.804039 | − | 0.594576i | \(-0.797320\pi\) | ||||
−0.804039 | + | 0.594576i | \(0.797320\pi\) | |||||||
\(332\) | −1361.70 | −0.225099 | ||||||||
\(333\) | −6351.58 | −1.04524 | ||||||||
\(334\) | −929.389 | −0.152257 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2412.12 | 0.391643 | ||||||||
\(337\) | −29.1319 | −0.00470895 | −0.00235447 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235447 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(338\) | 4713.48 | 0.758520 | ||||||||
\(339\) | 9121.24 | 1.46135 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7442.80 | 1.18197 | ||||||||
\(342\) | 1979.95 | 0.313051 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 5446.83 | 0.853701 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8516.68 | 1.32329 | ||||||||
\(347\) | 7848.58 | 1.21422 | 0.607110 | − | 0.794618i | \(-0.292329\pi\) | ||||
0.607110 | + | 0.794618i | \(0.292329\pi\) | |||||||
\(348\) | −410.508 | −0.0632343 | ||||||||
\(349\) | −10269.6 | −1.57513 | −0.787567 | − | 0.616229i | \(-0.788659\pi\) | ||||
−0.787567 | + | 0.616229i | \(0.788659\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1247.25 | −0.189668 | ||||||||
\(352\) | −2249.93 | −0.340686 | ||||||||
\(353\) | −2799.93 | −0.422168 | −0.211084 | − | 0.977468i | \(-0.567699\pi\) | ||||
−0.211084 | + | 0.977468i | \(0.567699\pi\) | |||||||
\(354\) | −10603.3 | −1.59198 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 223.627 | 0.0332927 | ||||||||
\(357\) | −4064.53 | −0.602570 | ||||||||
\(358\) | −7702.60 | −1.13714 | ||||||||
\(359\) | −3163.29 | −0.465048 | −0.232524 | − | 0.972591i | \(-0.574698\pi\) | ||||
−0.232524 | + | 0.972591i | \(0.574698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4903.11 | −0.714844 | ||||||||
\(362\) | −3781.23 | −0.548998 | ||||||||
\(363\) | −881.583 | −0.127469 | ||||||||
\(364\) | 177.879 | 0.0256137 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5520.88 | 0.788472 | ||||||||
\(367\) | −3182.85 | −0.452706 | −0.226353 | − | 0.974045i | \(-0.572680\pi\) | ||||
−0.226353 | + | 0.974045i | \(0.572680\pi\) | |||||||
\(368\) | 11293.3 | 1.59974 | ||||||||
\(369\) | −5875.62 | −0.828923 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1463.14 | 0.204750 | ||||||||
\(372\) | 1701.45 | 0.237139 | ||||||||
\(373\) | 2615.14 | 0.363021 | 0.181510 | − | 0.983389i | \(-0.441901\pi\) | ||||
0.181510 | + | 0.983389i | \(0.441901\pi\) | |||||||
\(374\) | −8628.23 | −1.19293 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −281.201 | −0.0385687 | ||||||||
\(377\) | 907.989 | 0.124042 | ||||||||
\(378\) | −1167.12 | −0.158811 | ||||||||
\(379\) | −672.434 | −0.0911362 | −0.0455681 | − | 0.998961i | \(-0.514510\pi\) | ||||
−0.0455681 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8078.03 | 1.08622 | ||||||||
\(382\) | 969.470 | 0.129849 | ||||||||
\(383\) | −1169.86 | −0.156075 | −0.0780377 | − | 0.996950i | \(-0.524865\pi\) | ||||
−0.0780377 | + | 0.996950i | \(0.524865\pi\) | |||||||
\(384\) | 6613.92 | 0.878946 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1895.45 | 0.249938 | ||||||||
\(387\) | 3915.78 | 0.514342 | ||||||||
\(388\) | 1392.36 | 0.182182 | ||||||||
\(389\) | −1122.22 | −0.146269 | −0.0731347 | − | 0.997322i | \(-0.523300\pi\) | ||||
−0.0731347 | + | 0.997322i | \(0.523300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19029.7 | −2.46131 | ||||||||
\(392\) | 1180.08 | 0.152049 | ||||||||
\(393\) | 13196.7 | 1.69385 | ||||||||
\(394\) | −5412.68 | −0.692099 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −870.113 | −0.110416 | ||||||||
\(397\) | 1985.93 | 0.251060 | 0.125530 | − | 0.992090i | \(-0.459937\pi\) | ||||
0.125530 | + | 0.992090i | \(0.459937\pi\) | |||||||
\(398\) | −7408.38 | −0.933037 | ||||||||
\(399\) | 2060.81 | 0.258571 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4172.38 | −0.519597 | −0.259799 | − | 0.965663i | \(-0.583656\pi\) | ||||
−0.259799 | + | 0.965663i | \(0.583656\pi\) | |||||||
\(402\) | −249.758 | −0.0309870 | ||||||||
\(403\) | −3763.37 | −0.465178 | ||||||||
\(404\) | 317.699 | 0.0391240 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 849.658 | 0.103862 | ||||||||
\(407\) | −14033.9 | −1.70918 | ||||||||
\(408\) | −13983.9 | −1.69682 | ||||||||
\(409\) | −11700.8 | −1.41459 | −0.707295 | − | 0.706919i | \(-0.750085\pi\) | ||||
−0.707295 | + | 0.706919i | \(0.750085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14718.0 | 1.76638 | ||||||||
\(412\) | −2206.47 | −0.263848 | ||||||||
\(413\) | −4312.00 | −0.513752 | ||||||||
\(414\) | 9767.22 | 1.15950 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1137.65 | 0.134082 | ||||||||
\(417\) | −3515.08 | −0.412791 | ||||||||
\(418\) | 4374.72 | 0.511901 | ||||||||
\(419\) | 2733.20 | 0.318677 | 0.159339 | − | 0.987224i | \(-0.449064\pi\) | ||||
0.159339 | + | 0.987224i | \(0.449064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13549.4 | 1.56854 | 0.784272 | − | 0.620417i | \(-0.213037\pi\) | ||||
0.784272 | + | 0.620417i | \(0.213037\pi\) | |||||||
\(422\) | −14593.3 | −1.68339 | ||||||||
\(423\) | −202.158 | −0.0232370 | ||||||||
\(424\) | 5033.87 | 0.576571 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16387.0 | −1.86374 | ||||||||
\(427\) | 2245.15 | 0.254450 | ||||||||
\(428\) | 1979.60 | 0.223569 | ||||||||
\(429\) | 4925.86 | 0.554366 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6429.25 | −0.718530 | −0.359265 | − | 0.933236i | \(-0.616973\pi\) | ||||
−0.359265 | + | 0.933236i | \(0.616973\pi\) | |||||||
\(432\) | −3337.79 | −0.371735 | ||||||||
\(433\) | −8022.03 | −0.890333 | −0.445166 | − | 0.895448i | \(-0.646855\pi\) | ||||
−0.445166 | + | 0.895448i | \(0.646855\pi\) | |||||||
\(434\) | −3521.61 | −0.389499 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1645.30 | 0.180724 | ||||||||
\(437\) | 9648.50 | 1.05618 | ||||||||
\(438\) | −14192.1 | −1.54823 | ||||||||
\(439\) | −5569.88 | −0.605549 | −0.302774 | − | 0.953062i | \(-0.597913\pi\) | ||||
−0.302774 | + | 0.953062i | \(0.597913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 848.372 | 0.0916069 | ||||||||
\(442\) | 4362.77 | 0.469493 | ||||||||
\(443\) | 5486.21 | 0.588392 | 0.294196 | − | 0.955745i | \(-0.404948\pi\) | ||||
0.294196 | + | 0.955745i | \(0.404948\pi\) | |||||||
\(444\) | −3208.19 | −0.342914 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16469.3 | −1.74853 | ||||||||
\(447\) | 2185.92 | 0.231299 | ||||||||
\(448\) | 3963.38 | 0.417973 | ||||||||
\(449\) | −7232.67 | −0.760203 | −0.380101 | − | 0.924945i | \(-0.624111\pi\) | ||||
−0.380101 | + | 0.924945i | \(0.624111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12982.3 | −1.35546 | ||||||||
\(452\) | 1800.05 | 0.187317 | ||||||||
\(453\) | −6852.76 | −0.710752 | ||||||||
\(454\) | −2626.32 | −0.271496 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7090.16 | 0.728130 | ||||||||
\(457\) | 2900.51 | 0.296893 | 0.148446 | − | 0.988920i | \(-0.452573\pi\) | ||||
0.148446 | + | 0.988920i | \(0.452573\pi\) | |||||||
\(458\) | −10623.3 | −1.08383 | ||||||||
\(459\) | 5624.31 | 0.571940 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6073.57 | 0.613611 | 0.306805 | − | 0.951772i | \(-0.400740\pi\) | ||||
0.306805 | + | 0.951772i | \(0.400740\pi\) | |||||||
\(462\) | 4609.42 | 0.464176 | ||||||||
\(463\) | 18922.8 | 1.89939 | 0.949693 | − | 0.313183i | \(-0.101395\pi\) | ||||
0.949693 | + | 0.313183i | \(0.101395\pi\) | |||||||
\(464\) | 2429.88 | 0.243113 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1573.27 | 0.156396 | ||||||||
\(467\) | 6776.71 | 0.671496 | 0.335748 | − | 0.941952i | \(-0.391011\pi\) | ||||
0.335748 | + | 0.941952i | \(0.391011\pi\) | |||||||
\(468\) | 439.963 | 0.0434558 | ||||||||
\(469\) | −101.568 | −0.00999991 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3495.50 | 0.341962 | ||||||||
\(472\) | −14835.3 | −1.44672 | ||||||||
\(473\) | 8651.96 | 0.841052 | ||||||||
\(474\) | 2689.99 | 0.260666 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −802.121 | −0.0772377 | ||||||||
\(477\) | 3618.90 | 0.347375 | ||||||||
\(478\) | 13069.7 | 1.25062 | ||||||||
\(479\) | 2397.32 | 0.228677 | 0.114338 | − | 0.993442i | \(-0.463525\pi\) | ||||
0.114338 | + | 0.993442i | \(0.463525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7096.09 | 0.672669 | ||||||||
\(482\) | −12.5871 | −0.00118948 | ||||||||
\(483\) | 10166.1 | 0.957711 | ||||||||
\(484\) | −173.977 | −0.0163390 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10933.4 | −1.02047 | ||||||||
\(487\) | −5586.17 | −0.519781 | −0.259890 | − | 0.965638i | \(-0.583686\pi\) | ||||
−0.259890 | + | 0.965638i | \(0.583686\pi\) | |||||||
\(488\) | 7724.35 | 0.716526 | ||||||||
\(489\) | 6674.33 | 0.617227 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 537.392 | 0.0493934 | 0.0246967 | − | 0.999695i | \(-0.492138\pi\) | ||||
0.0246967 | + | 0.999695i | \(0.492138\pi\) | |||||||
\(492\) | −2967.78 | −0.271947 | ||||||||
\(493\) | −4094.46 | −0.374047 | ||||||||
\(494\) | −2212.03 | −0.201466 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10071.2 | −0.911716 | ||||||||
\(497\) | −6664.00 | −0.601451 | ||||||||
\(498\) | 17842.0 | 1.60546 | ||||||||
\(499\) | 598.965 | 0.0537342 | 0.0268671 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268671 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2392.62 | −0.213362 | ||||||||
\(502\) | 1416.81 | 0.125966 | ||||||||
\(503\) | −4426.76 | −0.392405 | −0.196202 | − | 0.980563i | \(-0.562861\pi\) | ||||
−0.196202 | + | 0.980563i | \(0.562861\pi\) | |||||||
\(504\) | 2918.79 | 0.257963 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 21580.8 | 1.89601 | ||||||||
\(507\) | 12134.4 | 1.06293 | ||||||||
\(508\) | 1594.17 | 0.139232 | ||||||||
\(509\) | 17727.7 | 1.54374 | 0.771872 | − | 0.635779i | \(-0.219321\pi\) | ||||
0.771872 | + | 0.635779i | \(0.219321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5771.43 | −0.499634 | ||||||||
\(512\) | 13017.7 | 1.12365 | ||||||||
\(513\) | −2851.66 | −0.245427 | ||||||||
\(514\) | −4588.77 | −0.393778 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1977.86 | 0.168741 | ||||||||
\(517\) | −446.671 | −0.0379972 | ||||||||
\(518\) | 6640.22 | 0.563233 | ||||||||
\(519\) | 21925.4 | 1.85437 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8662.79 | 0.728453 | 0.364226 | − | 0.931310i | \(-0.381333\pi\) | ||||
0.364226 | + | 0.931310i | \(0.381333\pi\) | |||||||
\(522\) | 2101.53 | 0.176210 | ||||||||
\(523\) | 7770.40 | 0.649667 | 0.324833 | − | 0.945771i | \(-0.394692\pi\) | ||||
0.324833 | + | 0.945771i | \(0.394692\pi\) | |||||||
\(524\) | 2604.32 | 0.217119 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3100.60 | −0.257020 | ||||||||
\(527\) | 16970.4 | 1.40274 | ||||||||
\(528\) | 13182.2 | 1.08652 | ||||||||
\(529\) | 35429.6 | 2.91194 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10665.2 | −0.871624 | ||||||||
\(532\) | 406.695 | 0.0331437 | ||||||||
\(533\) | 6564.34 | 0.533458 | ||||||||
\(534\) | −2930.12 | −0.237451 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −349.440 | −0.0281595 | ||||||||
\(537\) | −19829.6 | −1.59350 | ||||||||
\(538\) | −8404.56 | −0.673506 | ||||||||
\(539\) | 1874.49 | 0.149796 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21641.0 | 1.71981 | 0.859906 | − | 0.510453i | \(-0.170522\pi\) | ||||
0.859906 | + | 0.510453i | \(0.170522\pi\) | |||||||
\(542\) | 2317.23 | 0.183642 | ||||||||
\(543\) | −9734.41 | −0.769325 | ||||||||
\(544\) | −5130.09 | −0.404321 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2330.70 | −0.182683 | ||||||||
\(547\) | −7489.29 | −0.585409 | −0.292705 | − | 0.956203i | \(-0.594555\pi\) | ||||
−0.292705 | + | 0.956203i | \(0.594555\pi\) | |||||||
\(548\) | 2904.54 | 0.226416 | ||||||||
\(549\) | 5553.11 | 0.431696 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2075.99 | 0.160508 | ||||||||
\(552\) | 34976.2 | 2.69689 | ||||||||
\(553\) | 1093.93 | 0.0841201 | ||||||||
\(554\) | −999.566 | −0.0766561 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −693.689 | −0.0529118 | ||||||||
\(557\) | −25297.9 | −1.92443 | −0.962214 | − | 0.272295i | \(-0.912217\pi\) | ||||
−0.962214 | + | 0.272295i | \(0.912217\pi\) | |||||||
\(558\) | −8710.29 | −0.660817 | ||||||||
\(559\) | −4374.77 | −0.331007 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22212.5 | −1.67168 | ||||||||
\(562\) | 8623.85 | 0.647286 | ||||||||
\(563\) | −15661.3 | −1.17237 | −0.586186 | − | 0.810177i | \(-0.699371\pi\) | ||||
−0.586186 | + | 0.810177i | \(0.699371\pi\) | |||||||
\(564\) | −102.110 | −0.00762343 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13994.9 | 1.03931 | ||||||||
\(567\) | −6276.94 | −0.464915 | ||||||||
\(568\) | −22927.3 | −1.69367 | ||||||||
\(569\) | −9982.75 | −0.735498 | −0.367749 | − | 0.929925i | \(-0.619871\pi\) | ||||
−0.367749 | + | 0.929925i | \(0.619871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11583.6 | −0.848966 | −0.424483 | − | 0.905436i | \(-0.639544\pi\) | ||||
−0.424483 | + | 0.905436i | \(0.639544\pi\) | |||||||
\(572\) | 972.103 | 0.0710589 | ||||||||
\(573\) | 2495.81 | 0.181961 | ||||||||
\(574\) | 6142.63 | 0.446670 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9802.97 | 0.709127 | ||||||||
\(577\) | 595.378 | 0.0429565 | 0.0214783 | − | 0.999769i | \(-0.493163\pi\) | ||||
0.0214783 | + | 0.999769i | \(0.493163\pi\) | |||||||
\(578\) | −6969.39 | −0.501537 | ||||||||
\(579\) | 4879.66 | 0.350245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7255.70 | 0.518102 | ||||||||
\(582\) | −18243.8 | −1.29936 | ||||||||
\(583\) | 7996.00 | 0.568028 | ||||||||
\(584\) | −19856.4 | −1.40696 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 729.738 | 0.0514423 | ||||||||
\(587\) | 15750.3 | 1.10747 | 0.553736 | − | 0.832693i | \(-0.313202\pi\) | ||||
0.553736 | + | 0.832693i | \(0.313202\pi\) | |||||||
\(588\) | 428.513 | 0.0300537 | ||||||||
\(589\) | −8604.42 | −0.601934 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13934.4 | −0.969856 | ||||||||
\(592\) | 18990.0 | 1.31838 | ||||||||
\(593\) | 417.878 | 0.0289379 | 0.0144690 | − | 0.999895i | \(-0.495394\pi\) | ||||
0.0144690 | + | 0.999895i | \(0.495394\pi\) | |||||||
\(594\) | −6378.31 | −0.440581 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 431.385 | 0.0296480 | ||||||||
\(597\) | −19072.2 | −1.30749 | ||||||||
\(598\) | −10912.1 | −0.746201 | ||||||||
\(599\) | −19997.3 | −1.36406 | −0.682028 | − | 0.731326i | \(-0.738902\pi\) | ||||
−0.682028 | + | 0.731326i | \(0.738902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15992.6 | −1.08545 | −0.542723 | − | 0.839912i | \(-0.682607\pi\) | ||||
−0.542723 | + | 0.839912i | \(0.682607\pi\) | |||||||
\(602\) | −4093.73 | −0.277156 | ||||||||
\(603\) | −251.216 | −0.0169657 | ||||||||
\(604\) | −1352.37 | −0.0911045 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4162.73 | −0.279042 | ||||||||
\(607\) | −14159.2 | −0.946793 | −0.473396 | − | 0.880850i | \(-0.656972\pi\) | ||||
−0.473396 | + | 0.880850i | \(0.656972\pi\) | |||||||
\(608\) | 2601.08 | 0.173499 | ||||||||
\(609\) | 2187.36 | 0.145544 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 225.854 | 0.0149543 | ||||||||
\(612\) | −1983.96 | −0.131040 | ||||||||
\(613\) | 4629.41 | 0.305025 | 0.152512 | − | 0.988302i | \(-0.451264\pi\) | ||||
0.152512 | + | 0.988302i | \(0.451264\pi\) | |||||||
\(614\) | 4963.87 | 0.326263 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6449.11 | 0.421821 | ||||||||
\(617\) | 23165.3 | 1.51151 | 0.755753 | − | 0.654857i | \(-0.227271\pi\) | ||||
0.755753 | + | 0.654857i | \(0.227271\pi\) | |||||||
\(618\) | 28910.9 | 1.88182 | ||||||||
\(619\) | 12370.6 | 0.803258 | 0.401629 | − | 0.915803i | \(-0.368444\pi\) | ||||
0.401629 | + | 0.915803i | \(0.368444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14067.4 | −0.909028 | ||||||||
\(622\) | −3137.36 | −0.202245 | ||||||||
\(623\) | −1191.58 | −0.0766285 | ||||||||
\(624\) | −6665.43 | −0.427613 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3708.02 | −0.236745 | ||||||||
\(627\) | 11262.3 | 0.717341 | ||||||||
\(628\) | 689.826 | 0.0438329 | ||||||||
\(629\) | −31998.9 | −2.02842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13980.2 | 0.882002 | 0.441001 | − | 0.897507i | \(-0.354623\pi\) | ||||
0.441001 | + | 0.897507i | \(0.354623\pi\) | |||||||
\(632\) | 3763.61 | 0.236880 | ||||||||
\(633\) | −37568.9 | −2.35897 | ||||||||
\(634\) | 16799.7 | 1.05237 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1827.91 | 0.113964 | ||||||||
\(637\) | −947.814 | −0.0589541 | ||||||||
\(638\) | 4643.36 | 0.288139 | ||||||||
\(639\) | −16482.7 | −1.02041 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16060.9 | −0.989655 | −0.494828 | − | 0.868991i | \(-0.664769\pi\) | ||||
−0.494828 | + | 0.868991i | \(0.664769\pi\) | |||||||
\(642\) | −25938.3 | −1.59455 | ||||||||
\(643\) | 4502.17 | 0.276125 | 0.138063 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138063 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(644\) | 2006.25 | 0.122760 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9974.87 | 0.607517 | ||||||||
\(647\) | −29414.8 | −1.78735 | −0.893675 | − | 0.448715i | \(-0.851882\pi\) | ||||
−0.893675 | + | 0.448715i | \(0.851882\pi\) | |||||||
\(648\) | −21595.6 | −1.30919 | ||||||||
\(649\) | −23565.0 | −1.42528 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9066.03 | −0.545815 | ||||||||
\(652\) | 1317.16 | 0.0791164 | ||||||||
\(653\) | −13013.6 | −0.779882 | −0.389941 | − | 0.920840i | \(-0.627505\pi\) | ||||
−0.389941 | + | 0.920840i | \(0.627505\pi\) | |||||||
\(654\) | −21558.0 | −1.28897 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17566.9 | 1.04554 | ||||||||
\(657\) | −14275.0 | −0.847671 | ||||||||
\(658\) | 211.345 | 0.0125214 | ||||||||
\(659\) | 23474.2 | 1.38759 | 0.693797 | − | 0.720171i | \(-0.255937\pi\) | ||||
0.693797 | + | 0.720171i | \(0.255937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9266.36 | −0.545264 | −0.272632 | − | 0.962118i | \(-0.587894\pi\) | ||||
−0.272632 | + | 0.962118i | \(0.587894\pi\) | |||||||
\(662\) | 25040.4 | 1.47013 | ||||||||
\(663\) | 11231.5 | 0.657914 | ||||||||
\(664\) | 24963.0 | 1.45896 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16423.8 | 0.955572 | ||||||||
\(667\) | 10241.0 | 0.594501 | ||||||||
\(668\) | −472.176 | −0.0273489 | ||||||||
\(669\) | −42398.6 | −2.45026 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12269.7 | 0.705909 | ||||||||
\(672\) | 2740.62 | 0.157324 | ||||||||
\(673\) | 25067.2 | 1.43576 | 0.717882 | − | 0.696164i | \(-0.245112\pi\) | ||||
0.717882 | + | 0.696164i | \(0.245112\pi\) | |||||||
\(674\) | 75.3288 | 0.00430498 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2394.68 | 0.136247 | ||||||||
\(677\) | 22409.6 | 1.27219 | 0.636093 | − | 0.771613i | \(-0.280550\pi\) | ||||
0.636093 | + | 0.771613i | \(0.280550\pi\) | |||||||
\(678\) | −23585.6 | −1.33599 | ||||||||
\(679\) | −7419.11 | −0.419322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6761.20 | −0.380455 | ||||||||
\(682\) | −19245.5 | −1.08057 | ||||||||
\(683\) | 8757.53 | 0.490626 | 0.245313 | − | 0.969444i | \(-0.421109\pi\) | ||||
0.245313 | + | 0.969444i | \(0.421109\pi\) | |||||||
\(684\) | 1005.91 | 0.0562311 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −886.925 | −0.0493629 | ||||||||
\(687\) | −27348.7 | −1.51880 | ||||||||
\(688\) | −11707.4 | −0.648750 | ||||||||
\(689\) | −4043.09 | −0.223555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8468.42 | 0.466214 | 0.233107 | − | 0.972451i | \(-0.425111\pi\) | ||||
0.233107 | + | 0.972451i | \(0.425111\pi\) | |||||||
\(692\) | 4326.90 | 0.237694 | ||||||||
\(693\) | 4636.33 | 0.254141 | ||||||||
\(694\) | −20294.8 | −1.11006 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7525.54 | 0.409849 | ||||||||
\(697\) | −29601.0 | −1.60864 | ||||||||
\(698\) | 26555.1 | 1.44001 | ||||||||
\(699\) | 4050.23 | 0.219162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15996.9 | 0.861906 | 0.430953 | − | 0.902374i | \(-0.358177\pi\) | ||||
0.430953 | + | 0.902374i | \(0.358177\pi\) | |||||||
\(702\) | 3225.12 | 0.173397 | ||||||||
\(703\) | 16224.2 | 0.870423 | ||||||||
\(704\) | 21659.8 | 1.15956 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7240.03 | 0.385952 | ||||||||
\(707\) | −1692.83 | −0.0900503 | ||||||||
\(708\) | −5387.02 | −0.285956 | ||||||||
\(709\) | 19903.0 | 1.05426 | 0.527131 | − | 0.849784i | \(-0.323268\pi\) | ||||
0.527131 | + | 0.849784i | \(0.323268\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2705.70 | 0.142717 | ||||||||
\(712\) | −4099.58 | −0.215784 | ||||||||
\(713\) | −42446.1 | −2.22948 | ||||||||
\(714\) | 10510.0 | 0.550878 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3913.30 | −0.204256 | ||||||||
\(717\) | 33646.7 | 1.75252 | ||||||||
\(718\) | 8179.59 | 0.425153 | ||||||||
\(719\) | −11073.1 | −0.574347 | −0.287174 | − | 0.957879i | \(-0.592716\pi\) | ||||
−0.287174 | + | 0.957879i | \(0.592716\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11757.0 | 0.607288 | ||||||||
\(722\) | 12678.4 | 0.653520 | ||||||||
\(723\) | −32.4043 | −0.00166685 | ||||||||
\(724\) | −1921.06 | −0.0986125 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2279.58 | 0.116533 | ||||||||
\(727\) | −31652.7 | −1.61476 | −0.807382 | − | 0.590029i | \(-0.799116\pi\) | ||||
−0.807382 | + | 0.590029i | \(0.799116\pi\) | |||||||
\(728\) | −3260.92 | −0.166013 | ||||||||
\(729\) | −3935.94 | −0.199967 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19727.5 | 0.998149 | ||||||||
\(732\) | 2804.88 | 0.141628 | ||||||||
\(733\) | −16958.3 | −0.854528 | −0.427264 | − | 0.904127i | \(-0.640523\pi\) | ||||
−0.427264 | + | 0.904127i | \(0.640523\pi\) | |||||||
\(734\) | 8230.16 | 0.413870 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12831.3 | 0.642618 | ||||||||
\(737\) | −555.065 | −0.0277423 | ||||||||
\(738\) | 15193.1 | 0.757813 | ||||||||
\(739\) | −11616.6 | −0.578245 | −0.289123 | − | 0.957292i | \(-0.593364\pi\) | ||||
−0.289123 | + | 0.957292i | \(0.593364\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5694.66 | −0.282319 | ||||||||
\(742\) | −3783.36 | −0.187185 | ||||||||
\(743\) | −15928.0 | −0.786464 | −0.393232 | − | 0.919439i | \(-0.628643\pi\) | ||||
−0.393232 | + | 0.919439i | \(0.628643\pi\) | |||||||
\(744\) | −31191.4 | −1.53700 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6762.19 | −0.331879 | ||||||||
\(747\) | 17946.1 | 0.879003 | ||||||||
\(748\) | −4383.57 | −0.214277 | ||||||||
\(749\) | −10548.2 | −0.514582 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25571.9 | 1.24252 | 0.621260 | − | 0.783604i | \(-0.286621\pi\) | ||||
0.621260 | + | 0.783604i | \(0.286621\pi\) | |||||||
\(752\) | 604.412 | 0.0293094 | ||||||||
\(753\) | 3647.43 | 0.176520 | ||||||||
\(754\) | −2347.87 | −0.113401 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −592.958 | −0.0285260 | ||||||||
\(757\) | −6202.41 | −0.297794 | −0.148897 | − | 0.988853i | \(-0.547572\pi\) | ||||
−0.148897 | + | 0.988853i | \(0.547572\pi\) | |||||||
\(758\) | 1738.77 | 0.0833179 | ||||||||
\(759\) | 55557.6 | 2.65693 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29199.1 | −1.39089 | −0.695444 | − | 0.718580i | \(-0.744792\pi\) | ||||
−0.695444 | + | 0.718580i | \(0.744792\pi\) | |||||||
\(762\) | −20888.1 | −0.993037 | ||||||||
\(763\) | −8766.87 | −0.415966 | ||||||||
\(764\) | 492.539 | 0.0233239 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3025.00 | 0.142686 | ||||||||
\(767\) | 11915.4 | 0.560938 | ||||||||
\(768\) | 13050.5 | 0.613177 | ||||||||
\(769\) | 21838.2 | 1.02407 | 0.512033 | − | 0.858966i | \(-0.328892\pi\) | ||||
0.512033 | + | 0.858966i | \(0.328892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11813.3 | −0.551812 | ||||||||
\(772\) | 962.985 | 0.0448945 | ||||||||
\(773\) | 25544.8 | 1.18859 | 0.594296 | − | 0.804246i | \(-0.297431\pi\) | ||||
0.594296 | + | 0.804246i | \(0.297431\pi\) | |||||||
\(774\) | −10125.4 | −0.470218 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25525.2 | −1.18080 | ||||||||
\(777\) | 17094.6 | 0.789273 | ||||||||
\(778\) | 2901.82 | 0.133721 | ||||||||
\(779\) | 15008.4 | 0.690286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36418.6 | −1.66858 | ||||||||
\(782\) | 49206.6 | 2.25016 | ||||||||
\(783\) | −3026.77 | −0.138146 | ||||||||
\(784\) | −2536.46 | −0.115546 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −34123.8 | −1.54854 | ||||||||
\(787\) | 37223.2 | 1.68598 | 0.842989 | − | 0.537931i | \(-0.180794\pi\) | ||||
0.842989 | + | 0.537931i | \(0.180794\pi\) | |||||||
\(788\) | −2749.91 | −0.124317 | ||||||||
\(789\) | −7982.19 | −0.360169 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9591.42 | −0.431140 | ||||||||
\(792\) | 15951.1 | 0.715655 | ||||||||
\(793\) | −6204.03 | −0.277820 | ||||||||
\(794\) | −5135.18 | −0.229522 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3763.83 | −0.167595 | ||||||||
\(797\) | 40384.6 | 1.79485 | 0.897425 | − | 0.441168i | \(-0.145436\pi\) | ||||
0.897425 | + | 0.441168i | \(0.145436\pi\) | |||||||
\(798\) | −5328.83 | −0.236389 | ||||||||
\(799\) | −1018.46 | −0.0450945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2947.23 | −0.130007 | ||||||||
\(802\) | 10788.9 | 0.475023 | ||||||||
\(803\) | −31540.7 | −1.38611 | ||||||||
\(804\) | −126.889 | −0.00556598 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9731.28 | 0.425272 | ||||||||
\(807\) | −21636.7 | −0.943803 | ||||||||
\(808\) | −5824.14 | −0.253580 | ||||||||
\(809\) | −1955.76 | −0.0849948 | −0.0424974 | − | 0.999097i | \(-0.513531\pi\) | ||||
−0.0424974 | + | 0.999097i | \(0.513531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34301.8 | −1.48520 | −0.742600 | − | 0.669735i | \(-0.766408\pi\) | ||||
−0.742600 | + | 0.669735i | \(0.766408\pi\) | |||||||
\(812\) | 431.669 | 0.0186559 | ||||||||
\(813\) | 5965.49 | 0.257342 | ||||||||
\(814\) | 36288.7 | 1.56255 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 30056.9 | 1.28946 | ||||||||
\(817\) | −10002.3 | −0.428319 | ||||||||
\(818\) | 30255.8 | 1.29324 | ||||||||
\(819\) | −2344.31 | −0.100021 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13665.6 | −0.580918 | −0.290459 | − | 0.956887i | \(-0.593808\pi\) | ||||
−0.290459 | + | 0.956887i | \(0.593808\pi\) | |||||||
\(822\) | −38057.5 | −1.61485 | ||||||||
\(823\) | 21519.5 | 0.911449 | 0.455724 | − | 0.890121i | \(-0.349380\pi\) | ||||
0.455724 | + | 0.890121i | \(0.349380\pi\) | |||||||
\(824\) | 40449.7 | 1.71011 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11149.9 | 0.469679 | ||||||||
\(827\) | −35220.6 | −1.48094 | −0.740471 | − | 0.672088i | \(-0.765398\pi\) | ||||
−0.740471 | + | 0.672088i | \(0.765398\pi\) | |||||||
\(828\) | 4962.23 | 0.208272 | ||||||||
\(829\) | 31365.5 | 1.31408 | 0.657039 | − | 0.753857i | \(-0.271809\pi\) | ||||
0.657039 | + | 0.753857i | \(0.271809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2573.28 | −0.107420 | ||||||||
\(832\) | −10952.0 | −0.456362 | ||||||||
\(833\) | 4274.04 | 0.177775 | ||||||||
\(834\) | 9089.24 | 0.377380 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2222.58 | 0.0919491 | ||||||||
\(837\) | 12545.2 | 0.518070 | ||||||||
\(838\) | −7067.48 | −0.291339 | ||||||||
\(839\) | −28287.1 | −1.16398 | −0.581990 | − | 0.813196i | \(-0.697726\pi\) | ||||
−0.581990 | + | 0.813196i | \(0.697726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22185.5 | −0.909653 | ||||||||
\(842\) | −35035.8 | −1.43398 | ||||||||
\(843\) | 22201.2 | 0.907060 | ||||||||
\(844\) | −7414.11 | −0.302374 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 522.738 | 0.0212436 | ||||||||
\(847\) | 927.026 | 0.0376068 | ||||||||
\(848\) | −10819.8 | −0.438152 | ||||||||
\(849\) | 36028.6 | 1.45642 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 80035.0 | 3.22393 | ||||||||
\(852\) | −8325.40 | −0.334769 | ||||||||
\(853\) | −9405.41 | −0.377533 | −0.188766 | − | 0.982022i | \(-0.560449\pi\) | ||||
−0.188766 | + | 0.982022i | \(0.560449\pi\) | |||||||
\(854\) | −5805.47 | −0.232622 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −36290.6 | −1.44905 | ||||||||
\(857\) | 27966.9 | 1.11474 | 0.557369 | − | 0.830265i | \(-0.311811\pi\) | ||||
0.557369 | + | 0.830265i | \(0.311811\pi\) | |||||||
\(858\) | −12737.2 | −0.506809 | ||||||||
\(859\) | 6281.11 | 0.249486 | 0.124743 | − | 0.992189i | \(-0.460189\pi\) | ||||
0.124743 | + | 0.992189i | \(0.460189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15813.6 | 0.625931 | ||||||||
\(862\) | 16624.7 | 0.656890 | ||||||||
\(863\) | 4757.13 | 0.187642 | 0.0938208 | − | 0.995589i | \(-0.470092\pi\) | ||||
0.0938208 | + | 0.995589i | \(0.470092\pi\) | |||||||
\(864\) | −3792.35 | −0.149327 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20743.3 | 0.813954 | ||||||||
\(867\) | −17942.0 | −0.702818 | ||||||||
\(868\) | −1789.15 | −0.0699629 | ||||||||
\(869\) | 5978.28 | 0.233371 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 280.663 | 0.0109184 | ||||||||
\(872\) | −30162.1 | −1.17135 | ||||||||
\(873\) | −18350.3 | −0.711414 | ||||||||
\(874\) | −24949.0 | −0.965574 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7210.30 | −0.278097 | ||||||||
\(877\) | 30240.5 | 1.16437 | 0.582184 | − | 0.813057i | \(-0.302198\pi\) | ||||
0.582184 | + | 0.813057i | \(0.302198\pi\) | |||||||
\(878\) | 14402.5 | 0.553601 | ||||||||
\(879\) | 1878.64 | 0.0720875 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44875.5 | 1.71611 | 0.858056 | − | 0.513556i | \(-0.171672\pi\) | ||||
0.858056 | + | 0.513556i | \(0.171672\pi\) | |||||||
\(882\) | −2193.71 | −0.0837483 | ||||||||
\(883\) | −4892.13 | −0.186448 | −0.0932238 | − | 0.995645i | \(-0.529717\pi\) | ||||
−0.0932238 | + | 0.995645i | \(0.529717\pi\) | |||||||
\(884\) | 2216.51 | 0.0843317 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14186.2 | −0.537916 | ||||||||
\(887\) | −1761.40 | −0.0666765 | −0.0333382 | − | 0.999444i | \(-0.510614\pi\) | ||||
−0.0333382 | + | 0.999444i | \(0.510614\pi\) | |||||||
\(888\) | 58813.4 | 2.22258 | ||||||||
\(889\) | −8494.43 | −0.320466 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34303.3 | −1.28979 | ||||||||
\(892\) | −8367.22 | −0.314075 | ||||||||
\(893\) | 516.384 | 0.0193507 | ||||||||
\(894\) | −5652.33 | −0.211457 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6954.86 | −0.259314 | ||||||||
\(897\) | −28092.1 | −1.04567 | ||||||||
\(898\) | 18702.2 | 0.694988 | ||||||||
\(899\) | −9132.79 | −0.338816 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18231.8 | 0.674128 | ||||||||
\(902\) | 33569.3 | 1.23918 | ||||||||
\(903\) | −10538.9 | −0.388386 | ||||||||
\(904\) | −32999.0 | −1.21408 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17719.8 | 0.649779 | ||||||||
\(907\) | −23689.1 | −0.867238 | −0.433619 | − | 0.901096i | \(-0.642764\pi\) | ||||
−0.433619 | + | 0.901096i | \(0.642764\pi\) | |||||||
\(908\) | −1334.30 | −0.0487669 | ||||||||
\(909\) | −4187.03 | −0.152778 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13877.3 | −0.504692 | −0.252346 | − | 0.967637i | \(-0.581202\pi\) | ||||
−0.252346 | + | 0.967637i | \(0.581202\pi\) | |||||||
\(912\) | −15239.6 | −0.553325 | ||||||||
\(913\) | 39652.2 | 1.43735 | ||||||||
\(914\) | −7500.09 | −0.271423 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5397.18 | −0.194681 | ||||||||
\(917\) | −13876.9 | −0.499735 | ||||||||
\(918\) | −14543.3 | −0.522875 | ||||||||
\(919\) | 14331.6 | 0.514426 | 0.257213 | − | 0.966355i | \(-0.417196\pi\) | ||||
0.257213 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12779.0 | 0.457201 | ||||||||
\(922\) | −15705.0 | −0.560971 | ||||||||
\(923\) | 18414.7 | 0.656692 | ||||||||
\(924\) | 2341.81 | 0.0833767 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −48930.2 | −1.73644 | ||||||||
\(927\) | 29079.7 | 1.03032 | ||||||||
\(928\) | 2760.80 | 0.0976592 | ||||||||
\(929\) | 16668.4 | 0.588668 | 0.294334 | − | 0.955703i | \(-0.404902\pi\) | ||||
0.294334 | + | 0.955703i | \(0.404902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2167.04 | −0.0762857 | ||||||||
\(932\) | 799.300 | 0.0280922 | ||||||||
\(933\) | −8076.82 | −0.283412 | ||||||||
\(934\) | −17523.1 | −0.613891 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8065.52 | −0.281656 | ||||||||
\(937\) | −30384.9 | −1.05937 | −0.529685 | − | 0.848194i | \(-0.677690\pi\) | ||||
−0.529685 | + | 0.848194i | \(0.677690\pi\) | |||||||
\(938\) | 262.632 | 0.00914206 | ||||||||
\(939\) | −9545.94 | −0.331757 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1196.35 | −0.0414452 | −0.0207226 | − | 0.999785i | \(-0.506597\pi\) | ||||
−0.0207226 | + | 0.999785i | \(0.506597\pi\) | |||||||
\(942\) | −9038.63 | −0.312627 | ||||||||
\(943\) | 74037.5 | 2.55673 | ||||||||
\(944\) | 31886.9 | 1.09940 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22372.1 | −0.768901 | ||||||||
\(947\) | −1788.41 | −0.0613681 | −0.0306840 | − | 0.999529i | \(-0.509769\pi\) | ||||
−0.0306840 | + | 0.999529i | \(0.509769\pi\) | |||||||
\(948\) | 1366.65 | 0.0468215 | ||||||||
\(949\) | 15948.2 | 0.545523 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43249.2 | 1.47471 | ||||||||
\(952\) | 14704.7 | 0.500612 | ||||||||
\(953\) | −8578.60 | −0.291593 | −0.145796 | − | 0.989315i | \(-0.546574\pi\) | ||||
−0.145796 | + | 0.989315i | \(0.546574\pi\) | |||||||
\(954\) | −9357.70 | −0.317575 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6640.06 | 0.224639 | ||||||||
\(957\) | 11953.9 | 0.403776 | ||||||||
\(958\) | −6198.95 | −0.209059 | ||||||||
\(959\) | −15476.6 | −0.521133 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8061.99 | 0.270618 | ||||||||
\(962\) | −18349.0 | −0.614963 | ||||||||
\(963\) | −26089.7 | −0.873031 | ||||||||
\(964\) | −6.39489 | −0.000213657 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −26287.4 | −0.875552 | ||||||||
\(967\) | 55459.3 | 1.84431 | 0.922156 | − | 0.386818i | \(-0.126426\pi\) | ||||
0.922156 | + | 0.386818i | \(0.126426\pi\) | |||||||
\(968\) | 3189.40 | 0.105900 | ||||||||
\(969\) | 25679.3 | 0.851330 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22047.3 | 0.728662 | 0.364331 | − | 0.931270i | \(-0.381298\pi\) | ||||
0.364331 | + | 0.931270i | \(0.381298\pi\) | |||||||
\(972\) | −5554.72 | −0.183300 | ||||||||
\(973\) | 3696.27 | 0.121785 | ||||||||
\(974\) | 14444.6 | 0.475191 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16602.7 | −0.544507 | ||||||||
\(977\) | −14402.3 | −0.471617 | −0.235809 | − | 0.971800i | \(-0.575774\pi\) | ||||
−0.235809 | + | 0.971800i | \(0.575774\pi\) | |||||||
\(978\) | −17258.4 | −0.564277 | ||||||||
\(979\) | −6511.94 | −0.212587 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21683.9 | −0.705721 | ||||||||
\(982\) | −1389.58 | −0.0451561 | ||||||||
\(983\) | −7817.11 | −0.253639 | −0.126819 | − | 0.991926i | \(-0.540477\pi\) | ||||
−0.126819 | + | 0.991926i | \(0.540477\pi\) | |||||||
\(984\) | 54406.2 | 1.76261 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10587.4 | 0.341959 | ||||||||
\(987\) | 544.087 | 0.0175466 | ||||||||
\(988\) | −1123.82 | −0.0361878 | ||||||||
\(989\) | −49342.0 | −1.58643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24501.6 | 0.785386 | 0.392693 | − | 0.919670i | \(-0.371543\pi\) | ||||
0.392693 | + | 0.919670i | \(0.371543\pi\) | |||||||
\(992\) | −11442.8 | −0.366239 | ||||||||
\(993\) | 64464.2 | 2.06013 | ||||||||
\(994\) | 17231.7 | 0.549855 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9064.61 | 0.288377 | ||||||||
\(997\) | 50696.0 | 1.61039 | 0.805195 | − | 0.593010i | \(-0.202060\pi\) | ||||
0.805195 | + | 0.593010i | \(0.202060\pi\) | |||||||
\(998\) | −1548.80 | −0.0491245 | ||||||||
\(999\) | −23654.8 | −0.749152 |
(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 | 175.4.a.c.1.2 | 2 | ||
3.2 | odd | 2 | 1575.4.a.z.1.1 | 2 | |||
5.2 | odd | 4 | 175.4.b.c.99.2 | 4 | |||
5.3 | odd | 4 | 175.4.b.c.99.3 | 4 | |||
5.4 | even | 2 | 35.4.a.b.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 1225.4.a.m.1.2 | 2 | |||
15.14 | odd | 2 | 315.4.a.f.1.2 | 2 | |||
20.19 | odd | 2 | 560.4.a.r.1.1 | 2 | |||
35.4 | even | 6 | 245.4.e.h.226.2 | 4 | |||
35.9 | even | 6 | 245.4.e.h.116.2 | 4 | |||
35.19 | odd | 6 | 245.4.e.i.116.2 | 4 | |||
35.24 | odd | 6 | 245.4.e.i.226.2 | 4 | |||
35.34 | odd | 2 | 245.4.a.k.1.1 | 2 | |||
40.19 | odd | 2 | 2240.4.a.bo.1.2 | 2 | |||
40.29 | even | 2 | 2240.4.a.bn.1.1 | 2 | |||
105.104 | even | 2 | 2205.4.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.a.b.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
175.4.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
175.4.b.c.99.2 | 4 | 5.2 | odd | 4 | |||
175.4.b.c.99.3 | 4 | 5.3 | odd | 4 | |||
245.4.a.k.1.1 | 2 | 35.34 | odd | 2 | |||
245.4.e.h.116.2 | 4 | 35.9 | even | 6 | |||
245.4.e.h.226.2 | 4 | 35.4 | even | 6 | |||
245.4.e.i.116.2 | 4 | 35.19 | odd | 6 | |||
245.4.e.i.226.2 | 4 | 35.24 | odd | 6 | |||
315.4.a.f.1.2 | 2 | 15.14 | odd | 2 | |||
560.4.a.r.1.1 | 2 | 20.19 | odd | 2 | |||
1225.4.a.m.1.2 | 2 | 7.6 | odd | 2 | |||
1575.4.a.z.1.1 | 2 | 3.2 | odd | 2 | |||
2205.4.a.u.1.2 | 2 | 105.104 | even | 2 | |||
2240.4.a.bn.1.1 | 2 | 40.29 | even | 2 | |||
2240.4.a.bo.1.2 | 2 | 40.19 | odd | 2 |