Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 82x^{2} + 58x + 1168 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
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 | \(4.73688\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73688 | −0.483816 | −0.241908 | − | 0.970299i | \(-0.577773\pi\) | ||||
−0.241908 | + | 0.970299i | \(0.577773\pi\) | |||||||
\(3\) | 28.3358 | 1.81774 | 0.908871 | − | 0.417077i | \(-0.136946\pi\) | ||||
0.908871 | + | 0.417077i | \(0.136946\pi\) | |||||||
\(4\) | −24.5095 | −0.765922 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −77.5516 | −0.879453 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 154.660 | 0.854382 | ||||||||
\(9\) | 559.917 | 2.30419 | ||||||||
\(10\) | 68.4220 | 0.216369 | ||||||||
\(11\) | 63.4296 | 0.158056 | 0.0790279 | − | 0.996872i | \(-0.474818\pi\) | ||||
0.0790279 | + | 0.996872i | \(0.474818\pi\) | |||||||
\(12\) | −694.496 | −1.39225 | ||||||||
\(13\) | 868.146 | 1.42474 | 0.712368 | − | 0.701806i | \(-0.247623\pi\) | ||||
0.712368 | + | 0.701806i | \(0.247623\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −708.395 | −0.812919 | ||||||||
\(16\) | 361.019 | 0.352558 | ||||||||
\(17\) | −1189.74 | −0.998460 | −0.499230 | − | 0.866469i | \(-0.666384\pi\) | ||||
−0.499230 | + | 0.866469i | \(0.666384\pi\) | |||||||
\(18\) | −1532.43 | −1.11480 | ||||||||
\(19\) | −1532.71 | −0.974041 | −0.487020 | − | 0.873391i | \(-0.661916\pi\) | ||||
−0.487020 | + | 0.873391i | \(0.661916\pi\) | |||||||
\(20\) | 612.737 | 0.342531 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −173.599 | −0.0764699 | ||||||||
\(23\) | −2337.74 | −0.921460 | −0.460730 | − | 0.887540i | \(-0.652412\pi\) | ||||
−0.460730 | + | 0.887540i | \(0.652412\pi\) | |||||||
\(24\) | 4382.40 | 1.55305 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −2376.01 | −0.689310 | ||||||||
\(27\) | 8980.10 | 2.37067 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8169.03 | 1.80375 | 0.901874 | − | 0.432000i | \(-0.142192\pi\) | ||||
0.901874 | + | 0.432000i | \(0.142192\pi\) | |||||||
\(30\) | 1938.79 | 0.393303 | ||||||||
\(31\) | 2369.72 | 0.442887 | 0.221444 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221444 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(32\) | −5937.17 | −1.02496 | ||||||||
\(33\) | 1797.33 | 0.287305 | ||||||||
\(34\) | 3256.18 | 0.483071 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13723.3 | −1.76483 | ||||||||
\(37\) | 12841.3 | 1.54207 | 0.771035 | − | 0.636793i | \(-0.219739\pi\) | ||||
0.771035 | + | 0.636793i | \(0.219739\pi\) | |||||||
\(38\) | 4194.85 | 0.471257 | ||||||||
\(39\) | 24599.6 | 2.58980 | ||||||||
\(40\) | −3866.49 | −0.382091 | ||||||||
\(41\) | −1652.93 | −0.153566 | −0.0767830 | − | 0.997048i | \(-0.524465\pi\) | ||||
−0.0767830 | + | 0.997048i | \(0.524465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12971.1 | 1.06980 | 0.534902 | − | 0.844914i | \(-0.320348\pi\) | ||||
0.534902 | + | 0.844914i | \(0.320348\pi\) | |||||||
\(44\) | −1554.63 | −0.121058 | ||||||||
\(45\) | −13997.9 | −1.03046 | ||||||||
\(46\) | 6398.11 | 0.445817 | ||||||||
\(47\) | 6219.00 | 0.410654 | 0.205327 | − | 0.978693i | \(-0.434174\pi\) | ||||
0.205327 | + | 0.978693i | \(0.434174\pi\) | |||||||
\(48\) | 10229.8 | 0.640859 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1710.55 | −0.0967633 | ||||||||
\(51\) | −33712.3 | −1.81494 | ||||||||
\(52\) | −21277.8 | −1.09124 | ||||||||
\(53\) | 19944.4 | 0.975283 | 0.487642 | − | 0.873044i | \(-0.337857\pi\) | ||||
0.487642 | + | 0.873044i | \(0.337857\pi\) | |||||||
\(54\) | −24577.5 | −1.14697 | ||||||||
\(55\) | −1585.74 | −0.0706847 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −43430.7 | −1.77056 | ||||||||
\(58\) | −22357.7 | −0.872682 | ||||||||
\(59\) | 30708.0 | 1.14847 | 0.574237 | − | 0.818689i | \(-0.305299\pi\) | ||||
0.574237 | + | 0.818689i | \(0.305299\pi\) | |||||||
\(60\) | 17362.4 | 0.622632 | ||||||||
\(61\) | −19901.3 | −0.684790 | −0.342395 | − | 0.939556i | \(-0.611238\pi\) | ||||
−0.342395 | + | 0.939556i | \(0.611238\pi\) | |||||||
\(62\) | −6485.64 | −0.214276 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4696.70 | 0.143332 | ||||||||
\(65\) | −21703.6 | −0.637161 | ||||||||
\(66\) | −4919.07 | −0.139003 | ||||||||
\(67\) | 31668.6 | 0.861869 | 0.430935 | − | 0.902383i | \(-0.358184\pi\) | ||||
0.430935 | + | 0.902383i | \(0.358184\pi\) | |||||||
\(68\) | 29160.0 | 0.764743 | ||||||||
\(69\) | −66241.7 | −1.67498 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32747.5 | −0.770960 | −0.385480 | − | 0.922716i | \(-0.625964\pi\) | ||||
−0.385480 | + | 0.922716i | \(0.625964\pi\) | |||||||
\(72\) | 86596.6 | 1.96865 | ||||||||
\(73\) | 54441.9 | 1.19571 | 0.597856 | − | 0.801604i | \(-0.296020\pi\) | ||||
0.597856 | + | 0.801604i | \(0.296020\pi\) | |||||||
\(74\) | −35145.0 | −0.746078 | ||||||||
\(75\) | 17709.9 | 0.363548 | ||||||||
\(76\) | 37566.1 | 0.746039 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −67326.1 | −1.25299 | ||||||||
\(79\) | 47649.2 | 0.858989 | 0.429495 | − | 0.903069i | \(-0.358692\pi\) | ||||
0.429495 | + | 0.903069i | \(0.358692\pi\) | |||||||
\(80\) | −9025.48 | −0.157669 | ||||||||
\(81\) | 118398. | 2.00509 | ||||||||
\(82\) | 4523.87 | 0.0742977 | ||||||||
\(83\) | 56509.0 | 0.900372 | 0.450186 | − | 0.892935i | \(-0.351358\pi\) | ||||
0.450186 | + | 0.892935i | \(0.351358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29743.6 | 0.446525 | ||||||||
\(86\) | −35500.2 | −0.517589 | ||||||||
\(87\) | 231476. | 3.27875 | ||||||||
\(88\) | 9810.00 | 0.135040 | ||||||||
\(89\) | −2533.69 | −0.0339061 | −0.0169531 | − | 0.999856i | \(-0.505397\pi\) | ||||
−0.0169531 | + | 0.999856i | \(0.505397\pi\) | |||||||
\(90\) | 38310.6 | 0.498555 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 57296.8 | 0.705766 | ||||||||
\(93\) | 67148.0 | 0.805055 | ||||||||
\(94\) | −17020.7 | −0.198681 | ||||||||
\(95\) | 38317.9 | 0.435604 | ||||||||
\(96\) | −168235. | −1.86310 | ||||||||
\(97\) | −58075.1 | −0.626701 | −0.313350 | − | 0.949638i | \(-0.601451\pi\) | ||||
−0.313350 | + | 0.949638i | \(0.601451\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 35515.3 | 0.364190 | ||||||||
\(100\) | −15318.4 | −0.153184 | ||||||||
\(101\) | −98422.7 | −0.960045 | −0.480023 | − | 0.877256i | \(-0.659372\pi\) | ||||
−0.480023 | + | 0.877256i | \(0.659372\pi\) | |||||||
\(102\) | 92266.5 | 0.878099 | ||||||||
\(103\) | −179343. | −1.66568 | −0.832840 | − | 0.553514i | \(-0.813287\pi\) | ||||
−0.832840 | + | 0.553514i | \(0.813287\pi\) | |||||||
\(104\) | 134267. | 1.21727 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −54585.3 | −0.471858 | ||||||||
\(107\) | 159436. | 1.34626 | 0.673128 | − | 0.739526i | \(-0.264950\pi\) | ||||
0.673128 | + | 0.739526i | \(0.264950\pi\) | |||||||
\(108\) | −220098. | −1.81575 | ||||||||
\(109\) | −97547.7 | −0.786413 | −0.393207 | − | 0.919450i | \(-0.628634\pi\) | ||||
−0.393207 | + | 0.919450i | \(0.628634\pi\) | |||||||
\(110\) | 4339.98 | 0.0341984 | ||||||||
\(111\) | 363868. | 2.80308 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 140601. | 1.03584 | 0.517919 | − | 0.855430i | \(-0.326707\pi\) | ||||
0.517919 | + | 0.855430i | \(0.326707\pi\) | |||||||
\(114\) | 118864. | 0.856623 | ||||||||
\(115\) | 58443.5 | 0.412090 | ||||||||
\(116\) | −200219. | −1.38153 | ||||||||
\(117\) | 486090. | 3.28286 | ||||||||
\(118\) | −84044.0 | −0.555650 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −109560. | −0.694543 | ||||||||
\(121\) | −157028. | −0.975018 | ||||||||
\(122\) | 54467.5 | 0.331312 | ||||||||
\(123\) | −46837.1 | −0.279143 | ||||||||
\(124\) | −58080.7 | −0.339217 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 233889. | 1.28677 | 0.643385 | − | 0.765543i | \(-0.277529\pi\) | ||||
0.643385 | + | 0.765543i | \(0.277529\pi\) | |||||||
\(128\) | 177135. | 0.955609 | ||||||||
\(129\) | 367546. | 1.94463 | ||||||||
\(130\) | 59400.2 | 0.308269 | ||||||||
\(131\) | −181216. | −0.922610 | −0.461305 | − | 0.887242i | \(-0.652619\pi\) | ||||
−0.461305 | + | 0.887242i | \(0.652619\pi\) | |||||||
\(132\) | −44051.6 | −0.220053 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −86673.0 | −0.416986 | ||||||||
\(135\) | −224503. | −1.06020 | ||||||||
\(136\) | −184005. | −0.853066 | ||||||||
\(137\) | −203830. | −0.927827 | −0.463914 | − | 0.885880i | \(-0.653555\pi\) | ||||
−0.463914 | + | 0.885880i | \(0.653555\pi\) | |||||||
\(138\) | 181296. | 0.810381 | ||||||||
\(139\) | −51086.4 | −0.224269 | −0.112134 | − | 0.993693i | \(-0.535769\pi\) | ||||
−0.112134 | + | 0.993693i | \(0.535769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 176220. | 0.746463 | ||||||||
\(142\) | 89625.8 | 0.373003 | ||||||||
\(143\) | 55066.1 | 0.225188 | ||||||||
\(144\) | 202141. | 0.812359 | ||||||||
\(145\) | −204226. | −0.806660 | ||||||||
\(146\) | −149001. | −0.578505 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −314733. | −1.18110 | ||||||||
\(149\) | −307059. | −1.13307 | −0.566533 | − | 0.824039i | \(-0.691716\pi\) | ||||
−0.566533 | + | 0.824039i | \(0.691716\pi\) | |||||||
\(150\) | −48469.8 | −0.175891 | ||||||||
\(151\) | 358221. | 1.27852 | 0.639261 | − | 0.768990i | \(-0.279240\pi\) | ||||
0.639261 | + | 0.768990i | \(0.279240\pi\) | |||||||
\(152\) | −237049. | −0.832203 | ||||||||
\(153\) | −666158. | −2.30064 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −59243.0 | −0.198065 | ||||||||
\(156\) | −602924. | −1.98359 | ||||||||
\(157\) | −437769. | −1.41741 | −0.708705 | − | 0.705505i | \(-0.750720\pi\) | ||||
−0.708705 | + | 0.705505i | \(0.750720\pi\) | |||||||
\(158\) | −130410. | −0.415593 | ||||||||
\(159\) | 565140. | 1.77281 | ||||||||
\(160\) | 148429. | 0.458374 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −324042. | −0.970095 | ||||||||
\(163\) | −430265. | −1.26843 | −0.634216 | − | 0.773156i | \(-0.718677\pi\) | ||||
−0.634216 | + | 0.773156i | \(0.718677\pi\) | |||||||
\(164\) | 40512.5 | 0.117620 | ||||||||
\(165\) | −44933.2 | −0.128486 | ||||||||
\(166\) | −154658. | −0.435615 | ||||||||
\(167\) | −229736. | −0.637437 | −0.318718 | − | 0.947849i | \(-0.603252\pi\) | ||||
−0.318718 | + | 0.947849i | \(0.603252\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 382384. | 1.02987 | ||||||||
\(170\) | −81404.6 | −0.216036 | ||||||||
\(171\) | −858193. | −2.24437 | ||||||||
\(172\) | −317914. | −0.819387 | ||||||||
\(173\) | −67029.4 | −0.170275 | −0.0851374 | − | 0.996369i | \(-0.527133\pi\) | ||||
−0.0851374 | + | 0.996369i | \(0.527133\pi\) | |||||||
\(174\) | −633522. | −1.58631 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22899.3 | 0.0557238 | ||||||||
\(177\) | 870135. | 2.08763 | ||||||||
\(178\) | 6934.39 | 0.0164043 | ||||||||
\(179\) | −234462. | −0.546940 | −0.273470 | − | 0.961881i | \(-0.588171\pi\) | ||||
−0.273470 | + | 0.961881i | \(0.588171\pi\) | |||||||
\(180\) | 343082. | 0.789254 | ||||||||
\(181\) | 199344. | 0.452278 | 0.226139 | − | 0.974095i | \(-0.427390\pi\) | ||||
0.226139 | + | 0.974095i | \(0.427390\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −563920. | −1.24477 | ||||||||
\(184\) | −361554. | −0.787279 | ||||||||
\(185\) | −321032. | −0.689634 | ||||||||
\(186\) | −183776. | −0.389499 | ||||||||
\(187\) | −75464.9 | −0.157812 | ||||||||
\(188\) | −152425. | −0.314529 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −104871. | −0.210752 | ||||||||
\(191\) | 300904. | 0.596821 | 0.298410 | − | 0.954438i | \(-0.403544\pi\) | ||||
0.298410 | + | 0.954438i | \(0.403544\pi\) | |||||||
\(192\) | 133085. | 0.260541 | ||||||||
\(193\) | −173138. | −0.334579 | −0.167289 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167289 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(194\) | 158944. | 0.303208 | ||||||||
\(195\) | −614990. | −1.15819 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 100950. | 0.185329 | 0.0926644 | − | 0.995697i | \(-0.470462\pi\) | ||||
0.0926644 | + | 0.995697i | \(0.470462\pi\) | |||||||
\(198\) | −97201.1 | −0.176201 | ||||||||
\(199\) | 809079. | 1.44830 | 0.724149 | − | 0.689643i | \(-0.242233\pi\) | ||||
0.724149 | + | 0.689643i | \(0.242233\pi\) | |||||||
\(200\) | 96662.3 | 0.170876 | ||||||||
\(201\) | 897354. | 1.56666 | ||||||||
\(202\) | 269371. | 0.464486 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 826272. | 1.39010 | ||||||||
\(205\) | 41323.3 | 0.0686768 | ||||||||
\(206\) | 490840. | 0.805883 | ||||||||
\(207\) | −1.30894e6 | −2.12322 | ||||||||
\(208\) | 313417. | 0.502302 | ||||||||
\(209\) | −97219.4 | −0.153953 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 183306. | 0.283446 | 0.141723 | − | 0.989906i | \(-0.454736\pi\) | ||||
0.141723 | + | 0.989906i | \(0.454736\pi\) | |||||||
\(212\) | −488826. | −0.746991 | ||||||||
\(213\) | −927925. | −1.40141 | ||||||||
\(214\) | −436358. | −0.651340 | ||||||||
\(215\) | −324277. | −0.478431 | ||||||||
\(216\) | 1.38886e6 | 2.02546 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 266976. | 0.380480 | ||||||||
\(219\) | 1.54266e6 | 2.17350 | ||||||||
\(220\) | 38865.7 | 0.0541389 | ||||||||
\(221\) | −1.03287e6 | −1.42254 | ||||||||
\(222\) | −995862. | −1.35618 | ||||||||
\(223\) | 678874. | 0.914171 | 0.457085 | − | 0.889423i | \(-0.348893\pi\) | ||||
0.457085 | + | 0.889423i | \(0.348893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 349948. | 0.460837 | ||||||||
\(226\) | −384808. | −0.501156 | ||||||||
\(227\) | 256484. | 0.330366 | 0.165183 | − | 0.986263i | \(-0.447179\pi\) | ||||
0.165183 | + | 0.986263i | \(0.447179\pi\) | |||||||
\(228\) | 1.06446e6 | 1.35611 | ||||||||
\(229\) | −321802. | −0.405509 | −0.202754 | − | 0.979230i | \(-0.564989\pi\) | ||||
−0.202754 | + | 0.979230i | \(0.564989\pi\) | |||||||
\(230\) | −159953. | −0.199376 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.26342e6 | 1.54109 | ||||||||
\(233\) | 193589. | 0.233609 | 0.116805 | − | 0.993155i | \(-0.462735\pi\) | ||||
0.116805 | + | 0.993155i | \(0.462735\pi\) | |||||||
\(234\) | −1.33037e6 | −1.58830 | ||||||||
\(235\) | −155475. | −0.183650 | ||||||||
\(236\) | −752637. | −0.879641 | ||||||||
\(237\) | 1.35018e6 | 1.56142 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −482857. | −0.546794 | −0.273397 | − | 0.961901i | \(-0.588147\pi\) | ||||
−0.273397 | + | 0.961901i | \(0.588147\pi\) | |||||||
\(240\) | −255744. | −0.286601 | ||||||||
\(241\) | 1.06213e6 | 1.17797 | 0.588984 | − | 0.808145i | \(-0.299528\pi\) | ||||
0.588984 | + | 0.808145i | \(0.299528\pi\) | |||||||
\(242\) | 429766. | 0.471730 | ||||||||
\(243\) | 1.17275e6 | 1.27406 | ||||||||
\(244\) | 487771. | 0.524495 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 128188. | 0.135054 | ||||||||
\(247\) | −1.33062e6 | −1.38775 | ||||||||
\(248\) | 366500. | 0.378395 | ||||||||
\(249\) | 1.60123e6 | 1.63664 | ||||||||
\(250\) | 42763.7 | 0.0432738 | ||||||||
\(251\) | −1.43228e6 | −1.43497 | −0.717484 | − | 0.696575i | \(-0.754707\pi\) | ||||
−0.717484 | + | 0.696575i | \(0.754707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −148282. | −0.145642 | ||||||||
\(254\) | −640126. | −0.622560 | ||||||||
\(255\) | 842808. | 0.811667 | ||||||||
\(256\) | −635092. | −0.605671 | ||||||||
\(257\) | 491843. | 0.464508 | 0.232254 | − | 0.972655i | \(-0.425390\pi\) | ||||
0.232254 | + | 0.972655i | \(0.425390\pi\) | |||||||
\(258\) | −1.00593e6 | −0.940844 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 531945. | 0.488016 | ||||||||
\(261\) | 4.57398e6 | 4.15617 | ||||||||
\(262\) | 495966. | 0.446374 | ||||||||
\(263\) | −1.41098e6 | −1.25786 | −0.628928 | − | 0.777464i | \(-0.716506\pi\) | ||||
−0.628928 | + | 0.777464i | \(0.716506\pi\) | |||||||
\(264\) | 277974. | 0.245468 | ||||||||
\(265\) | −498609. | −0.436160 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −71794.0 | −0.0616325 | ||||||||
\(268\) | −776181. | −0.660124 | ||||||||
\(269\) | −847237. | −0.713878 | −0.356939 | − | 0.934128i | \(-0.616180\pi\) | ||||
−0.356939 | + | 0.934128i | \(0.616180\pi\) | |||||||
\(270\) | 614436. | 0.512941 | ||||||||
\(271\) | −1.14845e6 | −0.949923 | −0.474961 | − | 0.880007i | \(-0.657538\pi\) | ||||
−0.474961 | + | 0.880007i | \(0.657538\pi\) | |||||||
\(272\) | −429520. | −0.352015 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 557859. | 0.448898 | ||||||||
\(275\) | 39643.5 | 0.0316111 | ||||||||
\(276\) | 1.62355e6 | 1.28290 | ||||||||
\(277\) | 1.17885e6 | 0.923124 | 0.461562 | − | 0.887108i | \(-0.347289\pi\) | ||||
0.461562 | + | 0.887108i | \(0.347289\pi\) | |||||||
\(278\) | 139817. | 0.108505 | ||||||||
\(279\) | 1.32685e6 | 1.02049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 112265. | 0.0848164 | 0.0424082 | − | 0.999100i | \(-0.486497\pi\) | ||||
0.0424082 | + | 0.999100i | \(0.486497\pi\) | |||||||
\(282\) | −482294. | −0.361151 | ||||||||
\(283\) | −1.67112e6 | −1.24034 | −0.620172 | − | 0.784466i | \(-0.712937\pi\) | ||||
−0.620172 | + | 0.784466i | \(0.712937\pi\) | |||||||
\(284\) | 802624. | 0.590495 | ||||||||
\(285\) | 1.08577e6 | 0.791816 | ||||||||
\(286\) | −150709. | −0.108949 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.32433e6 | −2.36169 | ||||||||
\(289\) | −4368.41 | −0.00307665 | ||||||||
\(290\) | 558941. | 0.390275 | ||||||||
\(291\) | −1.64560e6 | −1.13918 | ||||||||
\(292\) | −1.33434e6 | −0.915822 | ||||||||
\(293\) | −2.28723e6 | −1.55647 | −0.778235 | − | 0.627973i | \(-0.783885\pi\) | ||||
−0.778235 | + | 0.627973i | \(0.783885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −767699. | −0.513613 | ||||||||
\(296\) | 1.98603e6 | 1.31752 | ||||||||
\(297\) | 569604. | 0.374699 | ||||||||
\(298\) | 840382. | 0.548196 | ||||||||
\(299\) | −2.02950e6 | −1.31284 | ||||||||
\(300\) | −434060. | −0.278450 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −980406. | −0.618570 | ||||||||
\(303\) | −2.78888e6 | −1.74511 | ||||||||
\(304\) | −553339. | −0.343406 | ||||||||
\(305\) | 497533. | 0.306247 | ||||||||
\(306\) | 1.82319e6 | 1.11309 | ||||||||
\(307\) | −449789. | −0.272372 | −0.136186 | − | 0.990683i | \(-0.543485\pi\) | ||||
−0.136186 | + | 0.990683i | \(0.543485\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.08183e6 | −3.02778 | ||||||||
\(310\) | 162141. | 0.0958272 | ||||||||
\(311\) | 605586. | 0.355038 | 0.177519 | − | 0.984117i | \(-0.443193\pi\) | ||||
0.177519 | + | 0.984117i | \(0.443193\pi\) | |||||||
\(312\) | 3.80456e6 | 2.21268 | ||||||||
\(313\) | 2.03261e6 | 1.17272 | 0.586359 | − | 0.810052i | \(-0.300561\pi\) | ||||
0.586359 | + | 0.810052i | \(0.300561\pi\) | |||||||
\(314\) | 1.19812e6 | 0.685766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.16786e6 | −0.657918 | ||||||||
\(317\) | −2.61940e6 | −1.46404 | −0.732021 | − | 0.681282i | \(-0.761423\pi\) | ||||
−0.732021 | + | 0.681282i | \(0.761423\pi\) | |||||||
\(318\) | −1.54672e6 | −0.857716 | ||||||||
\(319\) | 518158. | 0.285093 | ||||||||
\(320\) | −117418. | −0.0641000 | ||||||||
\(321\) | 4.51775e6 | 2.44715 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.82354e6 | 0.972541 | ||||||||
\(324\) | −2.90189e6 | −1.53574 | ||||||||
\(325\) | 542591. | 0.284947 | ||||||||
\(326\) | 1.17758e6 | 0.613688 | ||||||||
\(327\) | −2.76409e6 | −1.42950 | ||||||||
\(328\) | −255642. | −0.131204 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 122977. | 0.0621639 | ||||||||
\(331\) | 1.79427e6 | 0.900155 | 0.450078 | − | 0.892989i | \(-0.351396\pi\) | ||||
0.450078 | + | 0.892989i | \(0.351396\pi\) | |||||||
\(332\) | −1.38501e6 | −0.689615 | ||||||||
\(333\) | 7.19005e6 | 3.55322 | ||||||||
\(334\) | 628758. | 0.308402 | ||||||||
\(335\) | −791714. | −0.385440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.10766e6 | −0.531292 | −0.265646 | − | 0.964071i | \(-0.585585\pi\) | ||||
−0.265646 | + | 0.964071i | \(0.585585\pi\) | |||||||
\(338\) | −1.04654e6 | −0.498269 | ||||||||
\(339\) | 3.98404e6 | 1.88289 | ||||||||
\(340\) | −729000. | −0.342003 | ||||||||
\(341\) | 150311. | 0.0700009 | ||||||||
\(342\) | 2.34877e6 | 1.08586 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.00610e6 | 0.914022 | ||||||||
\(345\) | 1.65604e6 | 0.749072 | ||||||||
\(346\) | 183451. | 0.0823817 | ||||||||
\(347\) | −2.46825e6 | −1.10044 | −0.550218 | − | 0.835021i | \(-0.685455\pi\) | ||||
−0.550218 | + | 0.835021i | \(0.685455\pi\) | |||||||
\(348\) | −5.67336e6 | −2.51126 | ||||||||
\(349\) | −2.41856e6 | −1.06290 | −0.531451 | − | 0.847089i | \(-0.678353\pi\) | ||||
−0.531451 | + | 0.847089i | \(0.678353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.79604e6 | 3.37758 | ||||||||
\(352\) | −376593. | −0.162000 | ||||||||
\(353\) | 1.84853e6 | 0.789570 | 0.394785 | − | 0.918774i | \(-0.370819\pi\) | ||||
0.394785 | + | 0.918774i | \(0.370819\pi\) | |||||||
\(354\) | −2.38145e6 | −1.01003 | ||||||||
\(355\) | 818687. | 0.344784 | ||||||||
\(356\) | 62099.4 | 0.0259694 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 641693. | 0.264618 | ||||||||
\(359\) | −552362. | −0.226197 | −0.113099 | − | 0.993584i | \(-0.536078\pi\) | ||||
−0.113099 | + | 0.993584i | \(0.536078\pi\) | |||||||
\(360\) | −2.16491e6 | −0.880409 | ||||||||
\(361\) | −126886. | −0.0512444 | ||||||||
\(362\) | −545579. | −0.218820 | ||||||||
\(363\) | −4.44950e6 | −1.77233 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.36105e6 | −0.534739 | ||||||||
\(366\) | 1.54338e6 | 0.602241 | ||||||||
\(367\) | −4.18145e6 | −1.62055 | −0.810273 | − | 0.586053i | \(-0.800681\pi\) | ||||
−0.810273 | + | 0.586053i | \(0.800681\pi\) | |||||||
\(368\) | −843969. | −0.324868 | ||||||||
\(369\) | −925505. | −0.353845 | ||||||||
\(370\) | 878625. | 0.333656 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.64576e6 | −0.616609 | ||||||||
\(373\) | 2.29821e6 | 0.855300 | 0.427650 | − | 0.903944i | \(-0.359342\pi\) | ||||
0.427650 | + | 0.903944i | \(0.359342\pi\) | |||||||
\(374\) | 206538. | 0.0763522 | ||||||||
\(375\) | −442747. | −0.162584 | ||||||||
\(376\) | 961829. | 0.350855 | ||||||||
\(377\) | 7.09191e6 | 2.56986 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.55567e6 | 1.27152 | 0.635760 | − | 0.771886i | \(-0.280687\pi\) | ||||
0.635760 | + | 0.771886i | \(0.280687\pi\) | |||||||
\(380\) | −939151. | −0.333639 | ||||||||
\(381\) | 6.62744e6 | 2.33902 | ||||||||
\(382\) | −823536. | −0.288752 | ||||||||
\(383\) | 1.57080e6 | 0.547172 | 0.273586 | − | 0.961848i | \(-0.411790\pi\) | ||||
0.273586 | + | 0.961848i | \(0.411790\pi\) | |||||||
\(384\) | 5.01927e6 | 1.73705 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 473857. | 0.161875 | ||||||||
\(387\) | 7.26273e6 | 2.46503 | ||||||||
\(388\) | 1.42339e6 | 0.480004 | ||||||||
\(389\) | −1.33556e6 | −0.447495 | −0.223747 | − | 0.974647i | \(-0.571829\pi\) | ||||
−0.223747 | + | 0.974647i | \(0.571829\pi\) | |||||||
\(390\) | 1.68315e6 | 0.560353 | ||||||||
\(391\) | 2.78131e6 | 0.920042 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.13490e6 | −1.67707 | ||||||||
\(394\) | −276289. | −0.0896651 | ||||||||
\(395\) | −1.19123e6 | −0.384152 | ||||||||
\(396\) | −870463. | −0.278941 | ||||||||
\(397\) | 1.47124e6 | 0.468496 | 0.234248 | − | 0.972177i | \(-0.424737\pi\) | ||||
0.234248 | + | 0.972177i | \(0.424737\pi\) | |||||||
\(398\) | −2.21435e6 | −0.700710 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 225637. | 0.0705116 | ||||||||
\(401\) | 994719. | 0.308915 | 0.154458 | − | 0.987999i | \(-0.450637\pi\) | ||||
0.154458 | + | 0.987999i | \(0.450637\pi\) | |||||||
\(402\) | −2.45595e6 | −0.757974 | ||||||||
\(403\) | 2.05726e6 | 0.630997 | ||||||||
\(404\) | 2.41229e6 | 0.735320 | ||||||||
\(405\) | −2.95996e6 | −0.896703 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 814517. | 0.243733 | ||||||||
\(408\) | −5.21393e6 | −1.55065 | ||||||||
\(409\) | 995359. | 0.294220 | 0.147110 | − | 0.989120i | \(-0.453003\pi\) | ||||
0.147110 | + | 0.989120i | \(0.453003\pi\) | |||||||
\(410\) | −113097. | −0.0332270 | ||||||||
\(411\) | −5.77569e6 | −1.68655 | ||||||||
\(412\) | 4.39561e6 | 1.27578 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.58241e6 | 1.02725 | ||||||||
\(415\) | −1.41272e6 | −0.402659 | ||||||||
\(416\) | −5.15433e6 | −1.46029 | ||||||||
\(417\) | −1.44757e6 | −0.407662 | ||||||||
\(418\) | 266078. | 0.0744848 | ||||||||
\(419\) | −62520.7 | −0.0173976 | −0.00869879 | − | 0.999962i | \(-0.502769\pi\) | ||||
−0.00869879 | + | 0.999962i | \(0.502769\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.26482e6 | 0.897747 | 0.448874 | − | 0.893595i | \(-0.351825\pi\) | ||||
0.448874 | + | 0.893595i | \(0.351825\pi\) | |||||||
\(422\) | −501686. | −0.137136 | ||||||||
\(423\) | 3.48213e6 | 0.946224 | ||||||||
\(424\) | 3.08459e6 | 0.833264 | ||||||||
\(425\) | −743589. | −0.199692 | ||||||||
\(426\) | 2.53962e6 | 0.678023 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.90770e6 | −1.03113 | ||||||||
\(429\) | 1.56034e6 | 0.409333 | ||||||||
\(430\) | 887506. | 0.231473 | ||||||||
\(431\) | −2.05017e6 | −0.531615 | −0.265807 | − | 0.964026i | \(-0.585639\pi\) | ||||
−0.265807 | + | 0.964026i | \(0.585639\pi\) | |||||||
\(432\) | 3.24199e6 | 0.835800 | ||||||||
\(433\) | −627607. | −0.160867 | −0.0804337 | − | 0.996760i | \(-0.525631\pi\) | ||||
−0.0804337 | + | 0.996760i | \(0.525631\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.78690e6 | −1.46630 | ||||||||
\(436\) | 2.39085e6 | 0.602331 | ||||||||
\(437\) | 3.58309e6 | 0.897540 | ||||||||
\(438\) | −4.22206e6 | −1.05157 | ||||||||
\(439\) | −6.13266e6 | −1.51876 | −0.759378 | − | 0.650650i | \(-0.774496\pi\) | ||||
−0.759378 | + | 0.650650i | \(0.774496\pi\) | |||||||
\(440\) | −245250. | −0.0603917 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.82684e6 | 0.688249 | ||||||||
\(443\) | −2.08811e6 | −0.505526 | −0.252763 | − | 0.967528i | \(-0.581339\pi\) | ||||
−0.252763 | + | 0.967528i | \(0.581339\pi\) | |||||||
\(444\) | −8.91822e6 | −2.14694 | ||||||||
\(445\) | 63342.2 | 0.0151633 | ||||||||
\(446\) | −1.85800e6 | −0.442291 | ||||||||
\(447\) | −8.70075e6 | −2.05962 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.77740e6 | −1.58653 | −0.793263 | − | 0.608880i | \(-0.791619\pi\) | ||||
−0.793263 | + | 0.608880i | \(0.791619\pi\) | |||||||
\(450\) | −957766. | −0.222961 | ||||||||
\(451\) | −104845. | −0.0242720 | ||||||||
\(452\) | −3.44606e6 | −0.793371 | ||||||||
\(453\) | 1.01505e7 | 2.32402 | ||||||||
\(454\) | −701965. | −0.159836 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.71697e6 | −1.51273 | ||||||||
\(457\) | 3.89825e6 | 0.873131 | 0.436566 | − | 0.899672i | \(-0.356195\pi\) | ||||
0.436566 | + | 0.899672i | \(0.356195\pi\) | |||||||
\(458\) | 880733. | 0.196192 | ||||||||
\(459\) | −1.06840e7 | −2.36702 | ||||||||
\(460\) | −1.43242e6 | −0.315628 | ||||||||
\(461\) | −4.27807e6 | −0.937552 | −0.468776 | − | 0.883317i | \(-0.655305\pi\) | ||||
−0.468776 | + | 0.883317i | \(0.655305\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.18974e6 | 1.55869 | 0.779347 | − | 0.626593i | \(-0.215551\pi\) | ||||
0.779347 | + | 0.626593i | \(0.215551\pi\) | |||||||
\(464\) | 2.94918e6 | 0.635925 | ||||||||
\(465\) | −1.67870e6 | −0.360031 | ||||||||
\(466\) | −529829. | −0.113024 | ||||||||
\(467\) | 5.72641e6 | 1.21504 | 0.607519 | − | 0.794305i | \(-0.292165\pi\) | ||||
0.607519 | + | 0.794305i | \(0.292165\pi\) | |||||||
\(468\) | −1.19138e7 | −2.51441 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 425516. | 0.0888529 | ||||||||
\(471\) | −1.24045e7 | −2.57649 | ||||||||
\(472\) | 4.74928e6 | 0.981235 | ||||||||
\(473\) | 822750. | 0.169089 | ||||||||
\(474\) | −3.69527e6 | −0.755441 | ||||||||
\(475\) | −957946. | −0.194808 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.11672e7 | 2.24723 | ||||||||
\(478\) | 1.32152e6 | 0.264548 | ||||||||
\(479\) | 696853. | 0.138772 | 0.0693861 | − | 0.997590i | \(-0.477896\pi\) | ||||
0.0693861 | + | 0.997590i | \(0.477896\pi\) | |||||||
\(480\) | 4.20586e6 | 0.833205 | ||||||||
\(481\) | 1.11481e7 | 2.19704 | ||||||||
\(482\) | −2.90691e6 | −0.569920 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.84867e6 | 0.746788 | ||||||||
\(485\) | 1.45188e6 | 0.280269 | ||||||||
\(486\) | −3.20967e6 | −0.616411 | ||||||||
\(487\) | 7.51712e6 | 1.43625 | 0.718123 | − | 0.695916i | \(-0.245001\pi\) | ||||
0.718123 | + | 0.695916i | \(0.245001\pi\) | |||||||
\(488\) | −3.07793e6 | −0.585072 | ||||||||
\(489\) | −1.21919e7 | −2.30568 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −255540. | −0.0478360 | −0.0239180 | − | 0.999714i | \(-0.507614\pi\) | ||||
−0.0239180 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(492\) | 1.14795e6 | 0.213802 | ||||||||
\(493\) | −9.71905e6 | −1.80097 | ||||||||
\(494\) | 3.64174e6 | 0.671416 | ||||||||
\(495\) | −887883. | −0.162871 | ||||||||
\(496\) | 855515. | 0.156143 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.38236e6 | −0.791835 | ||||||||
\(499\) | 8.14998e6 | 1.46523 | 0.732614 | − | 0.680645i | \(-0.238300\pi\) | ||||
0.732614 | + | 0.680645i | \(0.238300\pi\) | |||||||
\(500\) | 382961. | 0.0685061 | ||||||||
\(501\) | −6.50974e6 | −1.15870 | ||||||||
\(502\) | 3.91997e6 | 0.694261 | ||||||||
\(503\) | −5.64001e6 | −0.993939 | −0.496969 | − | 0.867768i | \(-0.665554\pi\) | ||||
−0.496969 | + | 0.867768i | \(0.665554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.46057e6 | 0.429345 | ||||||||
\(506\) | 405829. | 0.0704640 | ||||||||
\(507\) | 1.08352e7 | 1.87204 | ||||||||
\(508\) | −5.73251e6 | −0.985565 | ||||||||
\(509\) | 7.79954e6 | 1.33436 | 0.667182 | − | 0.744895i | \(-0.267500\pi\) | ||||
0.667182 | + | 0.744895i | \(0.267500\pi\) | |||||||
\(510\) | −2.30666e6 | −0.392698 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.93016e6 | −0.662575 | ||||||||
\(513\) | −1.37639e7 | −2.30913 | ||||||||
\(514\) | −1.34611e6 | −0.224737 | ||||||||
\(515\) | 4.48358e6 | 0.744915 | ||||||||
\(516\) | −9.00836e6 | −1.48943 | ||||||||
\(517\) | 394469. | 0.0649062 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.89933e6 | −0.309516 | ||||||||
\(520\) | −3.35668e6 | −0.544379 | ||||||||
\(521\) | −6.04835e6 | −0.976208 | −0.488104 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488104 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(522\) | −1.25184e7 | −2.01082 | ||||||||
\(523\) | 7.64614e6 | 1.22233 | 0.611165 | − | 0.791503i | \(-0.290701\pi\) | ||||
0.611165 | + | 0.791503i | \(0.290701\pi\) | |||||||
\(524\) | 4.44151e6 | 0.706647 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.86167e6 | 0.608571 | ||||||||
\(527\) | −2.81936e6 | −0.442205 | ||||||||
\(528\) | 648870. | 0.101291 | ||||||||
\(529\) | −971316. | −0.150911 | ||||||||
\(530\) | 1.36463e6 | 0.211021 | ||||||||
\(531\) | 1.71939e7 | 2.64630 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.43499e6 | −0.218791 | ||||||||
\(534\) | 196492. | 0.0298188 | ||||||||
\(535\) | −3.98591e6 | −0.602064 | ||||||||
\(536\) | 4.89785e6 | 0.736365 | ||||||||
\(537\) | −6.64366e6 | −0.994195 | ||||||||
\(538\) | 2.31878e6 | 0.345386 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.50245e6 | 0.812029 | ||||||||
\(541\) | −1.17724e7 | −1.72930 | −0.864651 | − | 0.502374i | \(-0.832460\pi\) | ||||
−0.864651 | + | 0.502374i | \(0.832460\pi\) | |||||||
\(542\) | 3.14316e6 | 0.459588 | ||||||||
\(543\) | 5.64856e6 | 0.822125 | ||||||||
\(544\) | 7.06371e6 | 1.02338 | ||||||||
\(545\) | 2.43869e6 | 0.351695 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 930880. | 0.133023 | 0.0665113 | − | 0.997786i | \(-0.478813\pi\) | ||||
0.0665113 | + | 0.997786i | \(0.478813\pi\) | |||||||
\(548\) | 4.99578e6 | 0.710643 | ||||||||
\(549\) | −1.11431e7 | −1.57788 | ||||||||
\(550\) | −108499. | −0.0152940 | ||||||||
\(551\) | −1.25208e7 | −1.75692 | ||||||||
\(552\) | −1.02449e7 | −1.43107 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.22638e6 | −0.446622 | ||||||||
\(555\) | −9.09670e6 | −1.25358 | ||||||||
\(556\) | 1.25210e6 | 0.171772 | ||||||||
\(557\) | −4.66844e6 | −0.637579 | −0.318790 | − | 0.947825i | \(-0.603276\pi\) | ||||
−0.318790 | + | 0.947825i | \(0.603276\pi\) | |||||||
\(558\) | −3.63142e6 | −0.493732 | ||||||||
\(559\) | 1.12608e7 | 1.52419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.13836e6 | −0.286862 | ||||||||
\(562\) | −307256. | −0.0410355 | ||||||||
\(563\) | −1.30772e6 | −0.173878 | −0.0869388 | − | 0.996214i | \(-0.527708\pi\) | ||||
−0.0869388 | + | 0.996214i | \(0.527708\pi\) | |||||||
\(564\) | −4.31907e6 | −0.571732 | ||||||||
\(565\) | −3.51502e6 | −0.463241 | ||||||||
\(566\) | 4.57366e6 | 0.600099 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.06471e6 | −0.658694 | ||||||||
\(569\) | 1.46759e7 | 1.90031 | 0.950154 | − | 0.311779i | \(-0.100925\pi\) | ||||
0.950154 | + | 0.311779i | \(0.100925\pi\) | |||||||
\(570\) | −2.97161e6 | −0.383094 | ||||||||
\(571\) | 1.12905e6 | 0.144918 | 0.0724590 | − | 0.997371i | \(-0.476915\pi\) | ||||
0.0724590 | + | 0.997371i | \(0.476915\pi\) | |||||||
\(572\) | −1.34964e6 | −0.172476 | ||||||||
\(573\) | 8.52634e6 | 1.08487 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.46109e6 | −0.184292 | ||||||||
\(576\) | 2.62977e6 | 0.330264 | ||||||||
\(577\) | −8.94245e6 | −1.11819 | −0.559097 | − | 0.829102i | \(-0.688852\pi\) | ||||
−0.559097 | + | 0.829102i | \(0.688852\pi\) | |||||||
\(578\) | 11955.8 | 0.00148854 | ||||||||
\(579\) | −4.90600e6 | −0.608178 | ||||||||
\(580\) | 5.00547e6 | 0.617839 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.50382e6 | 0.551154 | ||||||||
\(583\) | 1.26506e6 | 0.154149 | ||||||||
\(584\) | 8.41997e6 | 1.02159 | ||||||||
\(585\) | −1.21522e7 | −1.46814 | ||||||||
\(586\) | 6.25987e6 | 0.753046 | ||||||||
\(587\) | −3.97509e6 | −0.476158 | −0.238079 | − | 0.971246i | \(-0.576518\pi\) | ||||
−0.238079 | + | 0.971246i | \(0.576518\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.63211e6 | −0.431390 | ||||||||
\(590\) | 2.10110e6 | 0.248494 | ||||||||
\(591\) | 2.86051e6 | 0.336880 | ||||||||
\(592\) | 4.63595e6 | 0.543669 | ||||||||
\(593\) | 3.27487e6 | 0.382434 | 0.191217 | − | 0.981548i | \(-0.438757\pi\) | ||||
0.191217 | + | 0.981548i | \(0.438757\pi\) | |||||||
\(594\) | −1.55894e6 | −0.181285 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.52585e6 | 0.867841 | ||||||||
\(597\) | 2.29259e7 | 2.63263 | ||||||||
\(598\) | 5.55449e6 | 0.635172 | ||||||||
\(599\) | −4.45624e6 | −0.507460 | −0.253730 | − | 0.967275i | \(-0.581657\pi\) | ||||
−0.253730 | + | 0.967275i | \(0.581657\pi\) | |||||||
\(600\) | 2.73900e6 | 0.310609 | ||||||||
\(601\) | 8.18581e6 | 0.924433 | 0.462216 | − | 0.886767i | \(-0.347054\pi\) | ||||
0.462216 | + | 0.886767i | \(0.347054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.77318e7 | 1.98591 | ||||||||
\(604\) | −8.77981e6 | −0.979248 | ||||||||
\(605\) | 3.92569e6 | 0.436041 | ||||||||
\(606\) | 7.63284e6 | 0.844315 | ||||||||
\(607\) | 6.82736e6 | 0.752109 | 0.376055 | − | 0.926598i | \(-0.377281\pi\) | ||||
0.376055 | + | 0.926598i | \(0.377281\pi\) | |||||||
\(608\) | 9.09999e6 | 0.998348 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.36169e6 | −0.148167 | ||||||||
\(611\) | 5.39900e6 | 0.585073 | ||||||||
\(612\) | 1.63272e7 | 1.76211 | ||||||||
\(613\) | 6.39746e6 | 0.687632 | 0.343816 | − | 0.939037i | \(-0.388280\pi\) | ||||
0.343816 | + | 0.939037i | \(0.388280\pi\) | |||||||
\(614\) | 1.23102e6 | 0.131778 | ||||||||
\(615\) | 1.17093e6 | 0.124837 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.68341e7 | −1.78024 | −0.890118 | − | 0.455730i | \(-0.849378\pi\) | ||||
−0.890118 | + | 0.455730i | \(0.849378\pi\) | |||||||
\(618\) | 1.39083e7 | 1.46489 | ||||||||
\(619\) | 8.82274e6 | 0.925501 | 0.462751 | − | 0.886488i | \(-0.346863\pi\) | ||||
0.462751 | + | 0.886488i | \(0.346863\pi\) | |||||||
\(620\) | 1.45202e6 | 0.151702 | ||||||||
\(621\) | −2.09931e7 | −2.18448 | ||||||||
\(622\) | −1.65742e6 | −0.171773 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.88093e6 | 0.913055 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −5.56301e6 | −0.567380 | ||||||||
\(627\) | −2.75479e6 | −0.279846 | ||||||||
\(628\) | 1.07295e7 | 1.08563 | ||||||||
\(629\) | −1.52778e7 | −1.53970 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −375030. | −0.0374966 | −0.0187483 | − | 0.999824i | \(-0.505968\pi\) | ||||
−0.0187483 | + | 0.999824i | \(0.505968\pi\) | |||||||
\(632\) | 7.36940e6 | 0.733905 | ||||||||
\(633\) | 5.19412e6 | 0.515232 | ||||||||
\(634\) | 7.16898e6 | 0.708328 | ||||||||
\(635\) | −5.84723e6 | −0.575461 | ||||||||
\(636\) | −1.38513e7 | −1.35784 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.41814e6 | −0.137932 | ||||||||
\(639\) | −1.83359e7 | −1.77644 | ||||||||
\(640\) | −4.42838e6 | −0.427361 | ||||||||
\(641\) | 3.25010e6 | 0.312430 | 0.156215 | − | 0.987723i | \(-0.450071\pi\) | ||||
0.156215 | + | 0.987723i | \(0.450071\pi\) | |||||||
\(642\) | −1.23645e7 | −1.18397 | ||||||||
\(643\) | −2.71365e6 | −0.258837 | −0.129418 | − | 0.991590i | \(-0.541311\pi\) | ||||
−0.129418 | + | 0.991590i | \(0.541311\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.18864e6 | −0.869665 | ||||||||
\(646\) | −4.99080e6 | −0.470531 | ||||||||
\(647\) | −1.67261e7 | −1.57085 | −0.785426 | − | 0.618956i | \(-0.787556\pi\) | ||||
−0.785426 | + | 0.618956i | \(0.787556\pi\) | |||||||
\(648\) | 1.83115e7 | 1.71311 | ||||||||
\(649\) | 1.94779e6 | 0.181523 | ||||||||
\(650\) | −1.48501e6 | −0.137862 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.05456e7 | 0.971519 | ||||||||
\(653\) | −1.17470e7 | −1.07806 | −0.539031 | − | 0.842286i | \(-0.681209\pi\) | ||||
−0.539031 | + | 0.842286i | \(0.681209\pi\) | |||||||
\(654\) | 7.56499e6 | 0.691614 | ||||||||
\(655\) | 4.53040e6 | 0.412604 | ||||||||
\(656\) | −596740. | −0.0541409 | ||||||||
\(657\) | 3.04830e7 | 2.75514 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.16720e6 | −0.822286 | −0.411143 | − | 0.911571i | \(-0.634870\pi\) | ||||
−0.411143 | + | 0.911571i | \(0.634870\pi\) | |||||||
\(660\) | 1.10129e6 | 0.0984106 | ||||||||
\(661\) | −9.54925e6 | −0.850092 | −0.425046 | − | 0.905172i | \(-0.639742\pi\) | ||||
−0.425046 | + | 0.905172i | \(0.639742\pi\) | |||||||
\(662\) | −4.91069e6 | −0.435510 | ||||||||
\(663\) | −2.92672e7 | −2.58581 | ||||||||
\(664\) | 8.73965e6 | 0.769262 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.96783e7 | −1.71910 | ||||||||
\(667\) | −1.90971e7 | −1.66208 | ||||||||
\(668\) | 5.63070e6 | 0.488227 | ||||||||
\(669\) | 1.92364e7 | 1.66173 | ||||||||
\(670\) | 2.16683e6 | 0.186482 | ||||||||
\(671\) | −1.26233e6 | −0.108235 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.70373e6 | 0.315211 | 0.157606 | − | 0.987502i | \(-0.449623\pi\) | ||||
0.157606 | + | 0.987502i | \(0.449623\pi\) | |||||||
\(674\) | 3.03154e6 | 0.257048 | ||||||||
\(675\) | 5.61256e6 | 0.474135 | ||||||||
\(676\) | −9.37204e6 | −0.788801 | ||||||||
\(677\) | −1.93998e7 | −1.62677 | −0.813386 | − | 0.581724i | \(-0.802378\pi\) | ||||
−0.813386 | + | 0.581724i | \(0.802378\pi\) | |||||||
\(678\) | −1.09038e7 | −0.910972 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.60013e6 | 0.381503 | ||||||||
\(681\) | 7.26767e6 | 0.600520 | ||||||||
\(682\) | −411382. | −0.0338676 | ||||||||
\(683\) | 290718. | 0.0238463 | 0.0119231 | − | 0.999929i | \(-0.496205\pi\) | ||||
0.0119231 | + | 0.999929i | \(0.496205\pi\) | |||||||
\(684\) | 2.10339e7 | 1.71901 | ||||||||
\(685\) | 5.09576e6 | 0.414937 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.11852e6 | −0.737110 | ||||||||
\(688\) | 4.68281e6 | 0.377168 | ||||||||
\(689\) | 1.73146e7 | 1.38952 | ||||||||
\(690\) | −4.53239e6 | −0.362413 | ||||||||
\(691\) | 2.05452e7 | 1.63688 | 0.818438 | − | 0.574594i | \(-0.194840\pi\) | ||||
0.818438 | + | 0.574594i | \(0.194840\pi\) | |||||||
\(692\) | 1.64286e6 | 0.130417 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.75529e6 | 0.532409 | ||||||||
\(695\) | 1.27716e6 | 0.100296 | ||||||||
\(696\) | 3.58000e7 | 2.80130 | ||||||||
\(697\) | 1.96656e6 | 0.153330 | ||||||||
\(698\) | 6.61930e6 | 0.514249 | ||||||||
\(699\) | 5.48549e6 | 0.424642 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.57106e7 | −1.20753 | −0.603764 | − | 0.797163i | \(-0.706333\pi\) | ||||
−0.603764 | + | 0.797163i | \(0.706333\pi\) | |||||||
\(702\) | −2.13368e7 | −1.63413 | ||||||||
\(703\) | −1.96820e7 | −1.50204 | ||||||||
\(704\) | 297910. | 0.0226545 | ||||||||
\(705\) | −4.40551e6 | −0.333829 | ||||||||
\(706\) | −5.05921e6 | −0.382007 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.13266e7 | −1.59896 | ||||||||
\(709\) | −6.48343e6 | −0.484383 | −0.242192 | − | 0.970228i | \(-0.577866\pi\) | ||||
−0.242192 | + | 0.970228i | \(0.577866\pi\) | |||||||
\(710\) | −2.24065e6 | −0.166812 | ||||||||
\(711\) | 2.66796e7 | 1.97927 | ||||||||
\(712\) | −391859. | −0.0289688 | ||||||||
\(713\) | −5.53979e6 | −0.408103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.37665e6 | −0.100707 | ||||||||
\(716\) | 5.74654e6 | 0.418913 | ||||||||
\(717\) | −1.36821e7 | −0.993930 | ||||||||
\(718\) | 1.51175e6 | 0.109438 | ||||||||
\(719\) | 4.83478e6 | 0.348782 | 0.174391 | − | 0.984676i | \(-0.444204\pi\) | ||||
0.174391 | + | 0.984676i | \(0.444204\pi\) | |||||||
\(720\) | −5.05352e6 | −0.363298 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 347272. | 0.0247929 | ||||||||
\(723\) | 3.00962e7 | 2.14124 | ||||||||
\(724\) | −4.88581e6 | −0.346410 | ||||||||
\(725\) | 5.10565e6 | 0.360749 | ||||||||
\(726\) | 1.21778e7 | 0.857483 | ||||||||
\(727\) | −8.57824e6 | −0.601953 | −0.300976 | − | 0.953632i | \(-0.597313\pi\) | ||||
−0.300976 | + | 0.953632i | \(0.597313\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.45997e6 | 0.310823 | ||||||||
\(730\) | 3.72502e6 | 0.258715 | ||||||||
\(731\) | −1.54322e7 | −1.06816 | ||||||||
\(732\) | 1.38214e7 | 0.953397 | ||||||||
\(733\) | −863417. | −0.0593555 | −0.0296777 | − | 0.999560i | \(-0.509448\pi\) | ||||
−0.0296777 | + | 0.999560i | \(0.509448\pi\) | |||||||
\(734\) | 1.14441e7 | 0.784047 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.38796e7 | 0.944455 | ||||||||
\(737\) | 2.00872e6 | 0.136223 | ||||||||
\(738\) | 2.53299e6 | 0.171196 | ||||||||
\(739\) | 1.26850e7 | 0.854436 | 0.427218 | − | 0.904149i | \(-0.359494\pi\) | ||||
0.427218 | + | 0.904149i | \(0.359494\pi\) | |||||||
\(740\) | 7.86833e6 | 0.528206 | ||||||||
\(741\) | −3.77042e7 | −2.52257 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.16786e7 | 0.776104 | 0.388052 | − | 0.921637i | \(-0.373148\pi\) | ||||
0.388052 | + | 0.921637i | \(0.373148\pi\) | |||||||
\(744\) | 1.03851e7 | 0.687824 | ||||||||
\(745\) | 7.67646e6 | 0.506723 | ||||||||
\(746\) | −6.28993e6 | −0.413808 | ||||||||
\(747\) | 3.16403e7 | 2.07463 | ||||||||
\(748\) | 1.84961e6 | 0.120872 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.21174e6 | 0.0786607 | ||||||||
\(751\) | −6.46655e6 | −0.418382 | −0.209191 | − | 0.977875i | \(-0.567083\pi\) | ||||
−0.209191 | + | 0.977875i | \(0.567083\pi\) | |||||||
\(752\) | 2.24518e6 | 0.144779 | ||||||||
\(753\) | −4.05847e7 | −2.60840 | ||||||||
\(754\) | −1.94097e7 | −1.24334 | ||||||||
\(755\) | −8.95551e6 | −0.571772 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.00203e6 | 0.190404 | 0.0952018 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952018 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(758\) | −9.73144e6 | −0.615183 | ||||||||
\(759\) | −4.20169e6 | −0.264740 | ||||||||
\(760\) | 5.92622e6 | 0.372172 | ||||||||
\(761\) | 2.83373e7 | 1.77377 | 0.886885 | − | 0.461989i | \(-0.152864\pi\) | ||||
0.886885 | + | 0.461989i | \(0.152864\pi\) | |||||||
\(762\) | −1.81385e7 | −1.13165 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.37499e6 | −0.457118 | ||||||||
\(765\) | 1.66539e7 | 1.02888 | ||||||||
\(766\) | −4.29909e6 | −0.264731 | ||||||||
\(767\) | 2.66590e7 | 1.63627 | ||||||||
\(768\) | −1.79958e7 | −1.10095 | ||||||||
\(769\) | 4.74192e6 | 0.289160 | 0.144580 | − | 0.989493i | \(-0.453817\pi\) | ||||
0.144580 | + | 0.989493i | \(0.453817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39368e7 | 0.844356 | ||||||||
\(772\) | 4.24352e6 | 0.256261 | ||||||||
\(773\) | 1.37810e7 | 0.829530 | 0.414765 | − | 0.909928i | \(-0.363864\pi\) | ||||
0.414765 | + | 0.909928i | \(0.363864\pi\) | |||||||
\(774\) | −1.98772e7 | −1.19262 | ||||||||
\(775\) | 1.48108e6 | 0.0885774 | ||||||||
\(776\) | −8.98187e6 | −0.535442 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.65525e6 | 0.216505 | ||||||||
\(779\) | 2.53347e6 | 0.149580 | ||||||||
\(780\) | 1.50731e7 | 0.887086 | ||||||||
\(781\) | −2.07716e6 | −0.121855 | ||||||||
\(782\) | −7.61211e6 | −0.445131 | ||||||||
\(783\) | 7.33588e7 | 4.27610 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.09442e7 | 0.633885 | ||||||||
\(786\) | 1.40536e7 | 0.811392 | ||||||||
\(787\) | −1.22505e7 | −0.705046 | −0.352523 | − | 0.935803i | \(-0.614676\pi\) | ||||
−0.352523 | + | 0.935803i | \(0.614676\pi\) | |||||||
\(788\) | −2.47424e6 | −0.141947 | ||||||||
\(789\) | −3.99812e7 | −2.28646 | ||||||||
\(790\) | 3.26025e6 | 0.185859 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.49279e6 | 0.311157 | ||||||||
\(793\) | −1.72772e7 | −0.975644 | ||||||||
\(794\) | −4.02659e6 | −0.226666 | ||||||||
\(795\) | −1.41285e7 | −0.792826 | ||||||||
\(796\) | −1.98301e7 | −1.10928 | ||||||||
\(797\) | 1.42979e7 | 0.797310 | 0.398655 | − | 0.917101i | \(-0.369477\pi\) | ||||
0.398655 | + | 0.917101i | \(0.369477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.39902e6 | −0.410022 | ||||||||
\(800\) | −3.71073e6 | −0.204991 | ||||||||
\(801\) | −1.41865e6 | −0.0781260 | ||||||||
\(802\) | −2.72242e6 | −0.149458 | ||||||||
\(803\) | 3.45323e6 | 0.188989 | ||||||||
\(804\) | −2.19937e7 | −1.19994 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.63048e6 | −0.305287 | ||||||||
\(807\) | −2.40071e7 | −1.29765 | ||||||||
\(808\) | −1.52220e7 | −0.820245 | ||||||||
\(809\) | 3.38944e7 | 1.82078 | 0.910389 | − | 0.413753i | \(-0.135782\pi\) | ||||
0.910389 | + | 0.413753i | \(0.135782\pi\) | |||||||
\(810\) | 8.10106e6 | 0.433839 | ||||||||
\(811\) | 1.94505e7 | 1.03843 | 0.519216 | − | 0.854643i | \(-0.326224\pi\) | ||||
0.519216 | + | 0.854643i | \(0.326224\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.25422e7 | −1.72671 | ||||||||
\(814\) | −2.22923e6 | −0.117922 | ||||||||
\(815\) | 1.07566e7 | 0.567260 | ||||||||
\(816\) | −1.21708e7 | −0.639873 | ||||||||
\(817\) | −1.98809e7 | −1.04203 | ||||||||
\(818\) | −2.72418e6 | −0.142348 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.01281e6 | −0.0526011 | ||||||||
\(821\) | 5.51562e6 | 0.285586 | 0.142793 | − | 0.989753i | \(-0.454392\pi\) | ||||
0.142793 | + | 0.989753i | \(0.454392\pi\) | |||||||
\(822\) | 1.58074e7 | 0.815981 | ||||||||
\(823\) | −2.72639e7 | −1.40310 | −0.701549 | − | 0.712621i | \(-0.747508\pi\) | ||||
−0.701549 | + | 0.712621i | \(0.747508\pi\) | |||||||
\(824\) | −2.77371e7 | −1.42313 | ||||||||
\(825\) | 1.12333e6 | 0.0574609 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.97531e6 | −0.303806 | −0.151903 | − | 0.988395i | \(-0.548540\pi\) | ||||
−0.151903 | + | 0.988395i | \(0.548540\pi\) | |||||||
\(828\) | 3.20815e7 | 1.62622 | ||||||||
\(829\) | −6.28083e6 | −0.317418 | −0.158709 | − | 0.987325i | \(-0.550733\pi\) | ||||
−0.158709 | + | 0.987325i | \(0.550733\pi\) | |||||||
\(830\) | 3.86645e6 | 0.194813 | ||||||||
\(831\) | 3.34037e7 | 1.67800 | ||||||||
\(832\) | 4.07742e6 | 0.204210 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.96183e6 | 0.197234 | ||||||||
\(835\) | 5.74339e6 | 0.285070 | ||||||||
\(836\) | 2.38280e6 | 0.117916 | ||||||||
\(837\) | 2.12803e7 | 1.04994 | ||||||||
\(838\) | 171112. | 0.00841724 | ||||||||
\(839\) | 1.22748e7 | 0.602019 | 0.301010 | − | 0.953621i | \(-0.402676\pi\) | ||||
0.301010 | + | 0.953621i | \(0.402676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.62220e7 | 2.25350 | ||||||||
\(842\) | −8.93542e6 | −0.434345 | ||||||||
\(843\) | 3.18113e6 | 0.154174 | ||||||||
\(844\) | −4.49274e6 | −0.217098 | ||||||||
\(845\) | −9.55960e6 | −0.460572 | ||||||||
\(846\) | −9.53016e6 | −0.457798 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.20030e6 | 0.343844 | ||||||||
\(849\) | −4.73526e7 | −2.25463 | ||||||||
\(850\) | 2.03511e6 | 0.0966143 | ||||||||
\(851\) | −3.00196e7 | −1.42096 | ||||||||
\(852\) | 2.27430e7 | 1.07337 | ||||||||
\(853\) | −6.63619e6 | −0.312281 | −0.156141 | − | 0.987735i | \(-0.549905\pi\) | ||||
−0.156141 | + | 0.987735i | \(0.549905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.14548e7 | 1.00371 | ||||||||
\(856\) | 2.46583e7 | 1.15022 | ||||||||
\(857\) | 3.01234e7 | 1.40105 | 0.700523 | − | 0.713630i | \(-0.252950\pi\) | ||||
0.700523 | + | 0.713630i | \(0.252950\pi\) | |||||||
\(858\) | −4.27047e6 | −0.198042 | ||||||||
\(859\) | 4.11124e7 | 1.90103 | 0.950517 | − | 0.310672i | \(-0.100554\pi\) | ||||
0.950517 | + | 0.310672i | \(0.100554\pi\) | |||||||
\(860\) | 7.94786e6 | 0.366441 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.61107e6 | 0.257204 | ||||||||
\(863\) | −3.41903e6 | −0.156270 | −0.0781351 | − | 0.996943i | \(-0.524897\pi\) | ||||
−0.0781351 | + | 0.996943i | \(0.524897\pi\) | |||||||
\(864\) | −5.33164e7 | −2.42983 | ||||||||
\(865\) | 1.67574e6 | 0.0761492 | ||||||||
\(866\) | 1.71768e6 | 0.0778303 | ||||||||
\(867\) | −123782. | −0.00559256 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.02237e6 | 0.135768 | ||||||||
\(870\) | 1.58380e7 | 0.709420 | ||||||||
\(871\) | 2.74929e7 | 1.22794 | ||||||||
\(872\) | −1.50867e7 | −0.671897 | ||||||||
\(873\) | −3.25172e7 | −1.44404 | ||||||||
\(874\) | −9.80647e6 | −0.434244 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.78097e7 | −1.66473 | ||||||||
\(877\) | −2.94070e7 | −1.29108 | −0.645538 | − | 0.763728i | \(-0.723367\pi\) | ||||
−0.645538 | + | 0.763728i | \(0.723367\pi\) | |||||||
\(878\) | 1.67844e7 | 0.734798 | ||||||||
\(879\) | −6.48105e7 | −2.82926 | ||||||||
\(880\) | −572483. | −0.0249204 | ||||||||
\(881\) | −3.32494e7 | −1.44326 | −0.721628 | − | 0.692281i | \(-0.756606\pi\) | ||||
−0.721628 | + | 0.692281i | \(0.756606\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.53523e7 | 1.09425 | 0.547124 | − | 0.837051i | \(-0.315722\pi\) | ||||
0.547124 | + | 0.837051i | \(0.315722\pi\) | |||||||
\(884\) | 2.53151e7 | 1.08956 | ||||||||
\(885\) | −2.17534e7 | −0.933616 | ||||||||
\(886\) | 5.71490e6 | 0.244582 | ||||||||
\(887\) | −1.95997e6 | −0.0836450 | −0.0418225 | − | 0.999125i | \(-0.513316\pi\) | ||||
−0.0418225 | + | 0.999125i | \(0.513316\pi\) | |||||||
\(888\) | 5.62757e7 | 2.39490 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −173360. | −0.00733624 | ||||||||
\(891\) | 7.50997e6 | 0.316916 | ||||||||
\(892\) | −1.66389e7 | −0.700183 | ||||||||
\(893\) | −9.53196e6 | −0.399994 | ||||||||
\(894\) | 2.38129e7 | 0.996480 | ||||||||
\(895\) | 5.86154e6 | 0.244599 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.75075e7 | −2.38640 | ||||||||
\(898\) | 1.85489e7 | 0.767587 | ||||||||
\(899\) | 1.93583e7 | 0.798857 | ||||||||
\(900\) | −8.57706e6 | −0.352965 | ||||||||
\(901\) | −2.37287e7 | −0.973782 | ||||||||
\(902\) | 286947. | 0.0117432 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.17453e7 | 0.885002 | ||||||||
\(905\) | −4.98359e6 | −0.202265 | ||||||||
\(906\) | −2.77806e7 | −1.12440 | ||||||||
\(907\) | −8.69678e6 | −0.351027 | −0.175513 | − | 0.984477i | \(-0.556159\pi\) | ||||
−0.175513 | + | 0.984477i | \(0.556159\pi\) | |||||||
\(908\) | −6.28629e6 | −0.253034 | ||||||||
\(909\) | −5.51086e7 | −2.21212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.87563e7 | −1.54720 | −0.773600 | − | 0.633674i | \(-0.781546\pi\) | ||||
−0.773600 | + | 0.633674i | \(0.781546\pi\) | |||||||
\(912\) | −1.56793e7 | −0.624223 | ||||||||
\(913\) | 3.58434e6 | 0.142309 | ||||||||
\(914\) | −1.06690e7 | −0.422435 | ||||||||
\(915\) | 1.40980e7 | 0.556679 | ||||||||
\(916\) | 7.88721e6 | 0.310588 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.92409e7 | 1.14521 | ||||||||
\(919\) | −1.97989e7 | −0.773309 | −0.386655 | − | 0.922225i | \(-0.626369\pi\) | ||||
−0.386655 | + | 0.922225i | \(0.626369\pi\) | |||||||
\(920\) | 9.03885e6 | 0.352082 | ||||||||
\(921\) | −1.27451e7 | −0.495103 | ||||||||
\(922\) | 1.17085e7 | 0.453603 | ||||||||
\(923\) | −2.84296e7 | −1.09841 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.02580e6 | 0.308414 | ||||||||
\(926\) | −1.96774e7 | −0.754121 | ||||||||
\(927\) | −1.00417e8 | −3.83804 | ||||||||
\(928\) | −4.85010e7 | −1.84876 | ||||||||
\(929\) | −4.20864e7 | −1.59993 | −0.799967 | − | 0.600044i | \(-0.795150\pi\) | ||||
−0.799967 | + | 0.600044i | \(0.795150\pi\) | |||||||
\(930\) | 4.59439e6 | 0.174189 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.74476e6 | −0.178927 | ||||||||
\(933\) | 1.71598e7 | 0.645368 | ||||||||
\(934\) | −1.56725e7 | −0.587856 | ||||||||
\(935\) | 1.88662e6 | 0.0705758 | ||||||||
\(936\) | 7.51785e7 | 2.80481 | ||||||||
\(937\) | −2.14089e7 | −0.796608 | −0.398304 | − | 0.917254i | \(-0.630401\pi\) | ||||
−0.398304 | + | 0.917254i | \(0.630401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.75956e7 | 2.13170 | ||||||||
\(940\) | 3.81062e6 | 0.140662 | ||||||||
\(941\) | 2.30140e7 | 0.847264 | 0.423632 | − | 0.905834i | \(-0.360755\pi\) | ||||
0.423632 | + | 0.905834i | \(0.360755\pi\) | |||||||
\(942\) | 3.39497e7 | 1.24655 | ||||||||
\(943\) | 3.86412e6 | 0.141505 | ||||||||
\(944\) | 1.10862e7 | 0.404904 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.25177e6 | −0.0818079 | ||||||||
\(947\) | −1.69350e7 | −0.613636 | −0.306818 | − | 0.951768i | \(-0.599264\pi\) | ||||
−0.306818 | + | 0.951768i | \(0.599264\pi\) | |||||||
\(948\) | −3.30922e7 | −1.19593 | ||||||||
\(949\) | 4.72635e7 | 1.70357 | ||||||||
\(950\) | 2.62178e6 | 0.0942514 | ||||||||
\(951\) | −7.42228e7 | −2.66125 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.73067e7 | 0.973952 | 0.486976 | − | 0.873415i | \(-0.338100\pi\) | ||||
0.486976 | + | 0.873415i | \(0.338100\pi\) | |||||||
\(954\) | −3.05633e7 | −1.08725 | ||||||||
\(955\) | −7.52259e6 | −0.266906 | ||||||||
\(956\) | 1.18346e7 | 0.418801 | ||||||||
\(957\) | 1.46824e7 | 0.518225 | ||||||||
\(958\) | −1.90720e6 | −0.0671402 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.32712e6 | −0.116517 | ||||||||
\(961\) | −2.30136e7 | −0.803851 | ||||||||
\(962\) | −3.05110e7 | −1.06296 | ||||||||
\(963\) | 8.92711e7 | 3.10202 | ||||||||
\(964\) | −2.60322e7 | −0.902232 | ||||||||
\(965\) | 4.32844e6 | 0.149628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.08494e7 | −0.373111 | −0.186555 | − | 0.982444i | \(-0.559732\pi\) | ||||
−0.186555 | + | 0.982444i | \(0.559732\pi\) | |||||||
\(968\) | −2.42858e7 | −0.833038 | ||||||||
\(969\) | 5.16713e7 | 1.76783 | ||||||||
\(970\) | −3.97361e6 | −0.135599 | ||||||||
\(971\) | −5.42053e7 | −1.84499 | −0.922495 | − | 0.386010i | \(-0.873853\pi\) | ||||
−0.922495 | + | 0.386010i | \(0.873853\pi\) | |||||||
\(972\) | −2.87435e7 | −0.975830 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.05734e7 | −0.694879 | ||||||||
\(975\) | 1.53748e7 | 0.517960 | ||||||||
\(976\) | −7.18476e6 | −0.241428 | ||||||||
\(977\) | −4.07229e7 | −1.36490 | −0.682452 | − | 0.730930i | \(-0.739086\pi\) | ||||
−0.682452 | + | 0.730930i | \(0.739086\pi\) | |||||||
\(978\) | 3.33678e7 | 1.11553 | ||||||||
\(979\) | −160711. | −0.00535905 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.46187e7 | −1.81204 | ||||||||
\(982\) | 699382. | 0.0231438 | ||||||||
\(983\) | −1.40230e7 | −0.462869 | −0.231434 | − | 0.972851i | \(-0.574342\pi\) | ||||
−0.231434 | + | 0.972851i | \(0.574342\pi\) | |||||||
\(984\) | −7.24381e6 | −0.238495 | ||||||||
\(985\) | −2.52376e6 | −0.0828815 | ||||||||
\(986\) | 2.65999e7 | 0.871339 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.26128e7 | 1.06291 | ||||||||
\(989\) | −3.03230e7 | −0.985783 | ||||||||
\(990\) | 2.43003e6 | 0.0787995 | ||||||||
\(991\) | 3.52354e7 | 1.13971 | 0.569855 | − | 0.821745i | \(-0.306999\pi\) | ||||
0.569855 | + | 0.821745i | \(0.306999\pi\) | |||||||
\(992\) | −1.40695e7 | −0.453939 | ||||||||
\(993\) | 5.08420e7 | 1.63625 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.02270e7 | −0.647699 | ||||||||
\(996\) | −3.92453e7 | −1.25354 | ||||||||
\(997\) | 1.29377e7 | 0.412210 | 0.206105 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206105 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(998\) | −2.23055e7 | −0.708901 | ||||||||
\(999\) | 1.15316e8 | 3.65574 |
(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 | 245.6.a.e.1.2 | 4 | ||
7.6 | odd | 2 | 35.6.a.d.1.2 | ✓ | 4 | ||
21.20 | even | 2 | 315.6.a.l.1.3 | 4 | |||
28.27 | even | 2 | 560.6.a.v.1.4 | 4 | |||
35.13 | even | 4 | 175.6.b.f.99.5 | 8 | |||
35.27 | even | 4 | 175.6.b.f.99.4 | 8 | |||
35.34 | odd | 2 | 175.6.a.f.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.d.1.2 | ✓ | 4 | 7.6 | odd | 2 | ||
175.6.a.f.1.3 | 4 | 35.34 | odd | 2 | |||
175.6.b.f.99.4 | 8 | 35.27 | even | 4 | |||
175.6.b.f.99.5 | 8 | 35.13 | even | 4 | |||
245.6.a.e.1.2 | 4 | 1.1 | even | 1 | trivial | ||
315.6.a.l.1.3 | 4 | 21.20 | even | 2 | |||
560.6.a.v.1.4 | 4 | 28.27 | even | 2 |