Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(11.0664835671\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5333.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 11x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.49331\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29009 | −0.228058 | −0.114029 | − | 0.993477i | \(-0.536376\pi\) | ||||
−0.114029 | + | 0.993477i | \(0.536376\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −30.3357 | −0.947990 | ||||||||
\(5\) | 59.1123 | 1.05743 | 0.528716 | − | 0.848799i | \(-0.322674\pi\) | ||||
0.528716 | + | 0.848799i | \(0.322674\pi\) | |||||||
\(6\) | −11.6108 | −0.131669 | ||||||||
\(7\) | −213.331 | −1.64554 | −0.822772 | − | 0.568371i | \(-0.807574\pi\) | ||||
−0.822772 | + | 0.568371i | \(0.807574\pi\) | |||||||
\(8\) | 80.4187 | 0.444255 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −76.2602 | −0.241156 | ||||||||
\(11\) | 126.528 | 0.315287 | 0.157643 | − | 0.987496i | \(-0.449610\pi\) | ||||
0.157643 | + | 0.987496i | \(0.449610\pi\) | |||||||
\(12\) | −273.021 | −0.547322 | ||||||||
\(13\) | −884.825 | −1.45211 | −0.726054 | − | 0.687638i | \(-0.758648\pi\) | ||||
−0.726054 | + | 0.687638i | \(0.758648\pi\) | |||||||
\(14\) | 275.217 | 0.375280 | ||||||||
\(15\) | 532.011 | 0.610509 | ||||||||
\(16\) | 866.994 | 0.846674 | ||||||||
\(17\) | −1179.98 | −0.990264 | −0.495132 | − | 0.868818i | \(-0.664880\pi\) | ||||
−0.495132 | + | 0.868818i | \(0.664880\pi\) | |||||||
\(18\) | −104.497 | −0.0760194 | ||||||||
\(19\) | −1866.19 | −1.18596 | −0.592981 | − | 0.805216i | \(-0.702049\pi\) | ||||
−0.592981 | + | 0.805216i | \(0.702049\pi\) | |||||||
\(20\) | −1793.21 | −1.00244 | ||||||||
\(21\) | −1919.98 | −0.950056 | ||||||||
\(22\) | −163.233 | −0.0719037 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 723.768 | 0.256491 | ||||||||
\(25\) | 369.263 | 0.118164 | ||||||||
\(26\) | 1141.50 | 0.331165 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 6471.55 | 1.55996 | ||||||||
\(29\) | −6786.62 | −1.49851 | −0.749253 | − | 0.662284i | \(-0.769587\pi\) | ||||
−0.749253 | + | 0.662284i | \(0.769587\pi\) | |||||||
\(30\) | −686.342 | −0.139232 | ||||||||
\(31\) | −5146.34 | −0.961820 | −0.480910 | − | 0.876770i | \(-0.659694\pi\) | ||||
−0.480910 | + | 0.876770i | \(0.659694\pi\) | |||||||
\(32\) | −3691.90 | −0.637345 | ||||||||
\(33\) | 1138.75 | 0.182031 | ||||||||
\(34\) | 1522.28 | 0.225838 | ||||||||
\(35\) | −12610.5 | −1.74005 | ||||||||
\(36\) | −2457.19 | −0.315997 | ||||||||
\(37\) | 5137.07 | 0.616895 | 0.308448 | − | 0.951241i | \(-0.400191\pi\) | ||||
0.308448 | + | 0.951241i | \(0.400191\pi\) | |||||||
\(38\) | 2407.55 | 0.270468 | ||||||||
\(39\) | −7963.42 | −0.838375 | ||||||||
\(40\) | 4753.73 | 0.469769 | ||||||||
\(41\) | 12482.7 | 1.15971 | 0.579855 | − | 0.814720i | \(-0.303109\pi\) | ||||
0.579855 | + | 0.814720i | \(0.303109\pi\) | |||||||
\(42\) | 2476.95 | 0.216668 | ||||||||
\(43\) | 4198.66 | 0.346290 | 0.173145 | − | 0.984896i | \(-0.444607\pi\) | ||||
0.173145 | + | 0.984896i | \(0.444607\pi\) | |||||||
\(44\) | −3838.32 | −0.298889 | ||||||||
\(45\) | 4788.10 | 0.352478 | ||||||||
\(46\) | −682.458 | −0.0475534 | ||||||||
\(47\) | 23006.9 | 1.51919 | 0.759596 | − | 0.650395i | \(-0.225397\pi\) | ||||
0.759596 | + | 0.650395i | \(0.225397\pi\) | |||||||
\(48\) | 7802.94 | 0.488827 | ||||||||
\(49\) | 28703.3 | 1.70782 | ||||||||
\(50\) | −476.382 | −0.0269483 | ||||||||
\(51\) | −10619.8 | −0.571729 | ||||||||
\(52\) | 26841.8 | 1.37658 | ||||||||
\(53\) | 25175.4 | 1.23108 | 0.615541 | − | 0.788105i | \(-0.288938\pi\) | ||||
0.615541 | + | 0.788105i | \(0.288938\pi\) | |||||||
\(54\) | −940.476 | −0.0438898 | ||||||||
\(55\) | 7479.38 | 0.333395 | ||||||||
\(56\) | −17155.8 | −0.731041 | ||||||||
\(57\) | −16795.7 | −0.684716 | ||||||||
\(58\) | 8755.36 | 0.341746 | ||||||||
\(59\) | −37118.1 | −1.38821 | −0.694107 | − | 0.719872i | \(-0.744200\pi\) | ||||
−0.694107 | + | 0.719872i | \(0.744200\pi\) | |||||||
\(60\) | −16138.9 | −0.578756 | ||||||||
\(61\) | 26410.4 | 0.908761 | 0.454381 | − | 0.890808i | \(-0.349861\pi\) | ||||
0.454381 | + | 0.890808i | \(0.349861\pi\) | |||||||
\(62\) | 6639.24 | 0.219351 | ||||||||
\(63\) | −17279.8 | −0.548515 | ||||||||
\(64\) | −22980.9 | −0.701322 | ||||||||
\(65\) | −52304.0 | −1.53551 | ||||||||
\(66\) | −1469.10 | −0.0415136 | ||||||||
\(67\) | −54398.5 | −1.48047 | −0.740236 | − | 0.672347i | \(-0.765286\pi\) | ||||
−0.740236 | + | 0.672347i | \(0.765286\pi\) | |||||||
\(68\) | 35795.4 | 0.938760 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 16268.7 | 0.396833 | ||||||||
\(71\) | 35684.7 | 0.840110 | 0.420055 | − | 0.907499i | \(-0.362011\pi\) | ||||
0.420055 | + | 0.907499i | \(0.362011\pi\) | |||||||
\(72\) | 6513.91 | 0.148085 | ||||||||
\(73\) | 33937.4 | 0.745369 | 0.372684 | − | 0.927958i | \(-0.378437\pi\) | ||||
0.372684 | + | 0.927958i | \(0.378437\pi\) | |||||||
\(74\) | −6627.29 | −0.140688 | ||||||||
\(75\) | 3323.36 | 0.0682220 | ||||||||
\(76\) | 56612.0 | 1.12428 | ||||||||
\(77\) | −26992.5 | −0.518819 | ||||||||
\(78\) | 10273.5 | 0.191198 | ||||||||
\(79\) | −76625.8 | −1.38136 | −0.690681 | − | 0.723160i | \(-0.742689\pi\) | ||||
−0.690681 | + | 0.723160i | \(0.742689\pi\) | |||||||
\(80\) | 51250.0 | 0.895300 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −16103.8 | −0.264481 | ||||||||
\(83\) | −96627.2 | −1.53959 | −0.769794 | − | 0.638293i | \(-0.779641\pi\) | ||||
−0.769794 | + | 0.638293i | \(0.779641\pi\) | |||||||
\(84\) | 58244.0 | 0.900643 | ||||||||
\(85\) | −69751.1 | −1.04714 | ||||||||
\(86\) | −5416.65 | −0.0789741 | ||||||||
\(87\) | −61079.6 | −0.865163 | ||||||||
\(88\) | 10175.2 | 0.140068 | ||||||||
\(89\) | 30080.8 | 0.402545 | 0.201273 | − | 0.979535i | \(-0.435492\pi\) | ||||
0.201273 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(90\) | −6177.08 | −0.0803854 | ||||||||
\(91\) | 188761. | 2.38951 | ||||||||
\(92\) | −16047.6 | −0.197669 | ||||||||
\(93\) | −46317.0 | −0.555307 | ||||||||
\(94\) | −29680.9 | −0.346464 | ||||||||
\(95\) | −110315. | −1.25408 | ||||||||
\(96\) | −33227.1 | −0.367972 | ||||||||
\(97\) | −14637.2 | −0.157953 | −0.0789766 | − | 0.996876i | \(-0.525165\pi\) | ||||
−0.0789766 | + | 0.996876i | \(0.525165\pi\) | |||||||
\(98\) | −37029.9 | −0.389482 | ||||||||
\(99\) | 10248.8 | 0.105096 | ||||||||
\(100\) | −11201.8 | −0.112018 | ||||||||
\(101\) | −37693.7 | −0.367676 | −0.183838 | − | 0.982957i | \(-0.558852\pi\) | ||||
−0.183838 | + | 0.982957i | \(0.558852\pi\) | |||||||
\(102\) | 13700.5 | 0.130388 | ||||||||
\(103\) | 125252. | 1.16330 | 0.581649 | − | 0.813440i | \(-0.302408\pi\) | ||||
0.581649 | + | 0.813440i | \(0.302408\pi\) | |||||||
\(104\) | −71156.5 | −0.645106 | ||||||||
\(105\) | −113495. | −1.00462 | ||||||||
\(106\) | −32478.6 | −0.280758 | ||||||||
\(107\) | 28002.7 | 0.236451 | 0.118225 | − | 0.992987i | \(-0.462279\pi\) | ||||
0.118225 | + | 0.992987i | \(0.462279\pi\) | |||||||
\(108\) | −22114.7 | −0.182441 | ||||||||
\(109\) | −64151.4 | −0.517178 | −0.258589 | − | 0.965987i | \(-0.583257\pi\) | ||||
−0.258589 | + | 0.965987i | \(0.583257\pi\) | |||||||
\(110\) | −9649.08 | −0.0760333 | ||||||||
\(111\) | 46233.6 | 0.356165 | ||||||||
\(112\) | −184957. | −1.39324 | ||||||||
\(113\) | −25226.7 | −0.185851 | −0.0929253 | − | 0.995673i | \(-0.529622\pi\) | ||||
−0.0929253 | + | 0.995673i | \(0.529622\pi\) | |||||||
\(114\) | 21668.0 | 0.156155 | ||||||||
\(115\) | 31270.4 | 0.220490 | ||||||||
\(116\) | 205877. | 1.42057 | ||||||||
\(117\) | −71670.8 | −0.484036 | ||||||||
\(118\) | 47885.8 | 0.316593 | ||||||||
\(119\) | 251726. | 1.62952 | ||||||||
\(120\) | 42783.6 | 0.271222 | ||||||||
\(121\) | −145042. | −0.900594 | ||||||||
\(122\) | −34071.8 | −0.207250 | ||||||||
\(123\) | 112344. | 0.669559 | ||||||||
\(124\) | 156118. | 0.911796 | ||||||||
\(125\) | −162898. | −0.932482 | ||||||||
\(126\) | 22292.6 | 0.125093 | ||||||||
\(127\) | 35783.9 | 0.196870 | 0.0984348 | − | 0.995144i | \(-0.468616\pi\) | ||||
0.0984348 | + | 0.995144i | \(0.468616\pi\) | |||||||
\(128\) | 147788. | 0.797288 | ||||||||
\(129\) | 37787.9 | 0.199930 | ||||||||
\(130\) | 67477.0 | 0.350185 | ||||||||
\(131\) | 78119.6 | 0.397724 | 0.198862 | − | 0.980028i | \(-0.436275\pi\) | ||||
0.198862 | + | 0.980028i | \(0.436275\pi\) | |||||||
\(132\) | −34544.9 | −0.172563 | ||||||||
\(133\) | 398116. | 1.95155 | ||||||||
\(134\) | 70179.1 | 0.337634 | ||||||||
\(135\) | 43092.9 | 0.203503 | ||||||||
\(136\) | −94892.2 | −0.439930 | ||||||||
\(137\) | −92816.7 | −0.422498 | −0.211249 | − | 0.977432i | \(-0.567753\pi\) | ||||
−0.211249 | + | 0.977432i | \(0.567753\pi\) | |||||||
\(138\) | −6142.12 | −0.0274550 | ||||||||
\(139\) | −417118. | −1.83114 | −0.915570 | − | 0.402159i | \(-0.868260\pi\) | ||||
−0.915570 | + | 0.402159i | \(0.868260\pi\) | |||||||
\(140\) | 382548. | 1.64955 | ||||||||
\(141\) | 207062. | 0.877106 | ||||||||
\(142\) | −46036.5 | −0.191594 | ||||||||
\(143\) | −111955. | −0.457831 | ||||||||
\(144\) | 70226.5 | 0.282225 | ||||||||
\(145\) | −401173. | −1.58457 | ||||||||
\(146\) | −43782.3 | −0.169987 | ||||||||
\(147\) | 258330. | 0.986009 | ||||||||
\(148\) | −155836. | −0.584810 | ||||||||
\(149\) | 445936. | 1.64553 | 0.822766 | − | 0.568380i | \(-0.192430\pi\) | ||||
0.822766 | + | 0.568380i | \(0.192430\pi\) | |||||||
\(150\) | −4287.44 | −0.0155586 | ||||||||
\(151\) | −260458. | −0.929597 | −0.464799 | − | 0.885416i | \(-0.653873\pi\) | ||||
−0.464799 | + | 0.885416i | \(0.653873\pi\) | |||||||
\(152\) | −150076. | −0.526869 | ||||||||
\(153\) | −95578.1 | −0.330088 | ||||||||
\(154\) | 34822.7 | 0.118321 | ||||||||
\(155\) | −304212. | −1.01706 | ||||||||
\(156\) | 241576. | 0.794771 | ||||||||
\(157\) | 46067.4 | 0.149157 | 0.0745787 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745787 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(158\) | 98854.3 | 0.315031 | ||||||||
\(159\) | 226579. | 0.710765 | ||||||||
\(160\) | −218237. | −0.673950 | ||||||||
\(161\) | −112852. | −0.343120 | ||||||||
\(162\) | −8464.29 | −0.0253398 | ||||||||
\(163\) | 188377. | 0.555341 | 0.277671 | − | 0.960676i | \(-0.410438\pi\) | ||||
0.277671 | + | 0.960676i | \(0.410438\pi\) | |||||||
\(164\) | −378671. | −1.09939 | ||||||||
\(165\) | 67314.4 | 0.192485 | ||||||||
\(166\) | 124658. | 0.351115 | ||||||||
\(167\) | 203214. | 0.563849 | 0.281924 | − | 0.959437i | \(-0.409027\pi\) | ||||
0.281924 | + | 0.959437i | \(0.409027\pi\) | |||||||
\(168\) | −154403. | −0.422067 | ||||||||
\(169\) | 411622. | 1.10862 | ||||||||
\(170\) | 89985.3 | 0.238808 | ||||||||
\(171\) | −151161. | −0.395321 | ||||||||
\(172\) | −127369. | −0.328279 | ||||||||
\(173\) | 158051. | 0.401497 | 0.200749 | − | 0.979643i | \(-0.435663\pi\) | ||||
0.200749 | + | 0.979643i | \(0.435663\pi\) | |||||||
\(174\) | 78798.2 | 0.197307 | ||||||||
\(175\) | −78775.3 | −0.194444 | ||||||||
\(176\) | 109699. | 0.266945 | ||||||||
\(177\) | −334063. | −0.801485 | ||||||||
\(178\) | −38807.0 | −0.0918037 | ||||||||
\(179\) | 166444. | 0.388271 | 0.194136 | − | 0.980975i | \(-0.437810\pi\) | ||||
0.194136 | + | 0.980975i | \(0.437810\pi\) | |||||||
\(180\) | −145250. | −0.334145 | ||||||||
\(181\) | 185620. | 0.421141 | 0.210571 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210571 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(182\) | −243519. | −0.544947 | ||||||||
\(183\) | 237693. | 0.524673 | ||||||||
\(184\) | 42541.5 | 0.0926335 | ||||||||
\(185\) | 303664. | 0.652325 | ||||||||
\(186\) | 59753.2 | 0.126642 | ||||||||
\(187\) | −149300. | −0.312217 | ||||||||
\(188\) | −697928. | −1.44018 | ||||||||
\(189\) | −155519. | −0.316685 | ||||||||
\(190\) | 142316. | 0.286002 | ||||||||
\(191\) | −769733. | −1.52671 | −0.763356 | − | 0.645978i | \(-0.776450\pi\) | ||||
−0.763356 | + | 0.645978i | \(0.776450\pi\) | |||||||
\(192\) | −206828. | −0.404908 | ||||||||
\(193\) | −384145. | −0.742338 | −0.371169 | − | 0.928565i | \(-0.621043\pi\) | ||||
−0.371169 | + | 0.928565i | \(0.621043\pi\) | |||||||
\(194\) | 18883.3 | 0.0360225 | ||||||||
\(195\) | −470736. | −0.886525 | ||||||||
\(196\) | −870734. | −1.61899 | ||||||||
\(197\) | 266048. | 0.488421 | 0.244211 | − | 0.969722i | \(-0.421471\pi\) | ||||
0.244211 | + | 0.969722i | \(0.421471\pi\) | |||||||
\(198\) | −13221.9 | −0.0239679 | ||||||||
\(199\) | −706070. | −1.26391 | −0.631953 | − | 0.775007i | \(-0.717746\pi\) | ||||
−0.631953 | + | 0.775007i | \(0.717746\pi\) | |||||||
\(200\) | 29695.6 | 0.0524949 | ||||||||
\(201\) | −489587. | −0.854751 | ||||||||
\(202\) | 48628.3 | 0.0838515 | ||||||||
\(203\) | 1.44780e6 | 2.46586 | ||||||||
\(204\) | 322158. | 0.541994 | ||||||||
\(205\) | 737882. | 1.22631 | ||||||||
\(206\) | −161586. | −0.265300 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | −767138. | −1.22946 | ||||||||
\(209\) | −236125. | −0.373918 | ||||||||
\(210\) | 146418. | 0.229112 | ||||||||
\(211\) | −290636. | −0.449410 | −0.224705 | − | 0.974427i | \(-0.572142\pi\) | ||||
−0.224705 | + | 0.974427i | \(0.572142\pi\) | |||||||
\(212\) | −763712. | −1.16705 | ||||||||
\(213\) | 321162. | 0.485038 | ||||||||
\(214\) | −36126.1 | −0.0539245 | ||||||||
\(215\) | 248192. | 0.366178 | ||||||||
\(216\) | 58625.2 | 0.0854969 | ||||||||
\(217\) | 1.09788e6 | 1.58272 | ||||||||
\(218\) | 82761.1 | 0.117947 | ||||||||
\(219\) | 305436. | 0.430339 | ||||||||
\(220\) | −226892. | −0.316055 | ||||||||
\(221\) | 1.04407e6 | 1.43797 | ||||||||
\(222\) | −59645.6 | −0.0812262 | ||||||||
\(223\) | −574915. | −0.774179 | −0.387089 | − | 0.922042i | \(-0.626519\pi\) | ||||
−0.387089 | + | 0.922042i | \(0.626519\pi\) | |||||||
\(224\) | 787598. | 1.04878 | ||||||||
\(225\) | 29910.3 | 0.0393880 | ||||||||
\(226\) | 32544.7 | 0.0423847 | ||||||||
\(227\) | −1.37363e6 | −1.76931 | −0.884655 | − | 0.466246i | \(-0.845606\pi\) | ||||
−0.884655 | + | 0.466246i | \(0.845606\pi\) | |||||||
\(228\) | 509508. | 0.649103 | ||||||||
\(229\) | 870725. | 1.09722 | 0.548608 | − | 0.836080i | \(-0.315158\pi\) | ||||
0.548608 | + | 0.836080i | \(0.315158\pi\) | |||||||
\(230\) | −40341.7 | −0.0502845 | ||||||||
\(231\) | −242932. | −0.299540 | ||||||||
\(232\) | −545771. | −0.665718 | ||||||||
\(233\) | −1.61732e6 | −1.95166 | −0.975832 | − | 0.218522i | \(-0.929876\pi\) | ||||
−0.975832 | + | 0.218522i | \(0.929876\pi\) | |||||||
\(234\) | 92461.9 | 0.110388 | ||||||||
\(235\) | 1.35999e6 | 1.60644 | ||||||||
\(236\) | 1.12600e6 | 1.31601 | ||||||||
\(237\) | −689633. | −0.797530 | ||||||||
\(238\) | −324750. | −0.371626 | ||||||||
\(239\) | −1.65281e6 | −1.87167 | −0.935833 | − | 0.352444i | \(-0.885351\pi\) | ||||
−0.935833 | + | 0.352444i | \(0.885351\pi\) | |||||||
\(240\) | 461250. | 0.516902 | ||||||||
\(241\) | 928466. | 1.02973 | 0.514865 | − | 0.857271i | \(-0.327842\pi\) | ||||
0.514865 | + | 0.857271i | \(0.327842\pi\) | |||||||
\(242\) | 187117. | 0.205388 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −801176. | −0.861496 | ||||||||
\(245\) | 1.69672e6 | 1.80590 | ||||||||
\(246\) | −144935. | −0.152698 | ||||||||
\(247\) | 1.65125e6 | 1.72215 | ||||||||
\(248\) | −413862. | −0.427293 | ||||||||
\(249\) | −869645. | −0.888881 | ||||||||
\(250\) | 210153. | 0.212660 | ||||||||
\(251\) | −909693. | −0.911403 | −0.455702 | − | 0.890133i | \(-0.650612\pi\) | ||||
−0.455702 | + | 0.890133i | \(0.650612\pi\) | |||||||
\(252\) | 524196. | 0.519986 | ||||||||
\(253\) | 66933.5 | 0.0657419 | ||||||||
\(254\) | −46164.5 | −0.0448977 | ||||||||
\(255\) | −627760. | −0.604565 | ||||||||
\(256\) | 544729. | 0.519494 | ||||||||
\(257\) | 52666.7 | 0.0497397 | 0.0248699 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248699 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(258\) | −48749.9 | −0.0455957 | ||||||||
\(259\) | −1.09590e6 | −1.01513 | ||||||||
\(260\) | 1.58668e6 | 1.45564 | ||||||||
\(261\) | −549716. | −0.499502 | ||||||||
\(262\) | −100781. | −0.0907042 | ||||||||
\(263\) | 464764. | 0.414327 | 0.207164 | − | 0.978306i | \(-0.433577\pi\) | ||||
0.207164 | + | 0.978306i | \(0.433577\pi\) | |||||||
\(264\) | 91577.1 | 0.0808681 | ||||||||
\(265\) | 1.48818e6 | 1.30179 | ||||||||
\(266\) | −513606. | −0.445068 | ||||||||
\(267\) | 270727. | 0.232410 | ||||||||
\(268\) | 1.65022e6 | 1.40347 | ||||||||
\(269\) | 968420. | 0.815987 | 0.407993 | − | 0.912985i | \(-0.366229\pi\) | ||||
0.407993 | + | 0.912985i | \(0.366229\pi\) | |||||||
\(270\) | −55593.7 | −0.0464105 | ||||||||
\(271\) | 2.29262e6 | 1.89630 | 0.948152 | − | 0.317817i | \(-0.102950\pi\) | ||||
0.948152 | + | 0.317817i | \(0.102950\pi\) | |||||||
\(272\) | −1.02303e6 | −0.838431 | ||||||||
\(273\) | 1.69885e6 | 1.37958 | ||||||||
\(274\) | 119742. | 0.0963541 | ||||||||
\(275\) | 46722.2 | 0.0372556 | ||||||||
\(276\) | −144428. | −0.114125 | ||||||||
\(277\) | 290954. | 0.227837 | 0.113919 | − | 0.993490i | \(-0.463660\pi\) | ||||
0.113919 | + | 0.993490i | \(0.463660\pi\) | |||||||
\(278\) | 538120. | 0.417606 | ||||||||
\(279\) | −416853. | −0.320607 | ||||||||
\(280\) | −1.01412e6 | −0.773027 | ||||||||
\(281\) | −391978. | −0.296139 | −0.148070 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148070 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(282\) | −267128. | −0.200031 | ||||||||
\(283\) | 732768. | 0.543877 | 0.271938 | − | 0.962315i | \(-0.412335\pi\) | ||||
0.271938 | + | 0.962315i | \(0.412335\pi\) | |||||||
\(284\) | −1.08252e6 | −0.796415 | ||||||||
\(285\) | −992831. | −0.724041 | ||||||||
\(286\) | 144433. | 0.104412 | ||||||||
\(287\) | −2.66295e6 | −1.90835 | ||||||||
\(288\) | −299044. | −0.212448 | ||||||||
\(289\) | −27511.7 | −0.0193764 | ||||||||
\(290\) | 517549. | 0.361374 | ||||||||
\(291\) | −131735. | −0.0911944 | ||||||||
\(292\) | −1.02951e6 | −0.706602 | ||||||||
\(293\) | 1.62587e6 | 1.10641 | 0.553207 | − | 0.833044i | \(-0.313404\pi\) | ||||
0.553207 | + | 0.833044i | \(0.313404\pi\) | |||||||
\(294\) | −333269. | −0.224867 | ||||||||
\(295\) | −2.19414e6 | −1.46794 | ||||||||
\(296\) | 413117. | 0.274059 | ||||||||
\(297\) | 92239.1 | 0.0606770 | ||||||||
\(298\) | −575298. | −0.375277 | ||||||||
\(299\) | −468072. | −0.302785 | ||||||||
\(300\) | −100816. | −0.0646738 | ||||||||
\(301\) | −895706. | −0.569835 | ||||||||
\(302\) | 336014. | 0.212002 | ||||||||
\(303\) | −339243. | −0.212278 | ||||||||
\(304\) | −1.61797e6 | −1.00412 | ||||||||
\(305\) | 1.56118e6 | 0.960954 | ||||||||
\(306\) | 123304. | 0.0752793 | ||||||||
\(307\) | 1.24581e6 | 0.754406 | 0.377203 | − | 0.926131i | \(-0.376886\pi\) | ||||
0.377203 | + | 0.926131i | \(0.376886\pi\) | |||||||
\(308\) | 818834. | 0.491835 | ||||||||
\(309\) | 1.12727e6 | 0.671631 | ||||||||
\(310\) | 392461. | 0.231949 | ||||||||
\(311\) | −3.26852e6 | −1.91624 | −0.958119 | − | 0.286369i | \(-0.907552\pi\) | ||||
−0.958119 | + | 0.286369i | \(0.907552\pi\) | |||||||
\(312\) | −640408. | −0.372452 | ||||||||
\(313\) | 1.70161e6 | 0.981744 | 0.490872 | − | 0.871232i | \(-0.336678\pi\) | ||||
0.490872 | + | 0.871232i | \(0.336678\pi\) | |||||||
\(314\) | −59431.2 | −0.0340166 | ||||||||
\(315\) | −1.02145e6 | −0.580018 | ||||||||
\(316\) | 2.32450e6 | 1.30952 | ||||||||
\(317\) | −908317. | −0.507679 | −0.253840 | − | 0.967246i | \(-0.581694\pi\) | ||||
−0.253840 | + | 0.967246i | \(0.581694\pi\) | |||||||
\(318\) | −292307. | −0.162096 | ||||||||
\(319\) | −858699. | −0.472459 | ||||||||
\(320\) | −1.35845e6 | −0.741601 | ||||||||
\(321\) | 252025. | 0.136515 | ||||||||
\(322\) | 145590. | 0.0782512 | ||||||||
\(323\) | 2.20206e6 | 1.17442 | ||||||||
\(324\) | −199032. | −0.105332 | ||||||||
\(325\) | −326733. | −0.171587 | ||||||||
\(326\) | −243024. | −0.126650 | ||||||||
\(327\) | −577362. | −0.298593 | ||||||||
\(328\) | 1.00384e6 | 0.515206 | ||||||||
\(329\) | −4.90809e6 | −2.49990 | ||||||||
\(330\) | −86841.7 | −0.0438979 | ||||||||
\(331\) | −2.14345e6 | −1.07533 | −0.537666 | − | 0.843158i | \(-0.680694\pi\) | ||||
−0.537666 | + | 0.843158i | \(0.680694\pi\) | |||||||
\(332\) | 2.93125e6 | 1.45951 | ||||||||
\(333\) | 416103. | 0.205632 | ||||||||
\(334\) | −262165. | −0.128590 | ||||||||
\(335\) | −3.21562e6 | −1.56550 | ||||||||
\(336\) | −1.66461e6 | −0.804387 | ||||||||
\(337\) | 817498. | 0.392114 | 0.196057 | − | 0.980593i | \(-0.437186\pi\) | ||||
0.196057 | + | 0.980593i | \(0.437186\pi\) | |||||||
\(338\) | −531030. | −0.252829 | ||||||||
\(339\) | −227040. | −0.107301 | ||||||||
\(340\) | 2.11595e6 | 0.992676 | ||||||||
\(341\) | −651157. | −0.303249 | ||||||||
\(342\) | 195012. | 0.0901561 | ||||||||
\(343\) | −2.53785e6 | −1.16475 | ||||||||
\(344\) | 337651. | 0.153841 | ||||||||
\(345\) | 281434. | 0.127300 | ||||||||
\(346\) | −203900. | −0.0915647 | ||||||||
\(347\) | 3.20207e6 | 1.42760 | 0.713801 | − | 0.700349i | \(-0.246972\pi\) | ||||
0.713801 | + | 0.700349i | \(0.246972\pi\) | |||||||
\(348\) | 1.85289e6 | 0.820165 | ||||||||
\(349\) | −3.23916e6 | −1.42354 | −0.711768 | − | 0.702415i | \(-0.752105\pi\) | ||||
−0.711768 | + | 0.702415i | \(0.752105\pi\) | |||||||
\(350\) | 101627. | 0.0443446 | ||||||||
\(351\) | −645037. | −0.279458 | ||||||||
\(352\) | −467130. | −0.200947 | ||||||||
\(353\) | −1.72676e6 | −0.737555 | −0.368777 | − | 0.929518i | \(-0.620224\pi\) | ||||
−0.368777 | + | 0.929518i | \(0.620224\pi\) | |||||||
\(354\) | 430972. | 0.182785 | ||||||||
\(355\) | 2.10940e6 | 0.888360 | ||||||||
\(356\) | −912522. | −0.381609 | ||||||||
\(357\) | 2.26554e6 | 0.940806 | ||||||||
\(358\) | −214728. | −0.0885484 | ||||||||
\(359\) | 3.12338e6 | 1.27905 | 0.639527 | − | 0.768769i | \(-0.279130\pi\) | ||||
0.639527 | + | 0.768769i | \(0.279130\pi\) | |||||||
\(360\) | 385052. | 0.156590 | ||||||||
\(361\) | 1.00655e6 | 0.406507 | ||||||||
\(362\) | −239466. | −0.0960446 | ||||||||
\(363\) | −1.30537e6 | −0.519958 | ||||||||
\(364\) | −5.72619e6 | −2.26523 | ||||||||
\(365\) | 2.00612e6 | 0.788177 | ||||||||
\(366\) | −306646. | −0.119656 | ||||||||
\(367\) | 1.17031e6 | 0.453560 | 0.226780 | − | 0.973946i | \(-0.427180\pi\) | ||||
0.226780 | + | 0.973946i | \(0.427180\pi\) | |||||||
\(368\) | 458640. | 0.176544 | ||||||||
\(369\) | 1.01110e6 | 0.386570 | ||||||||
\(370\) | −391754. | −0.148768 | ||||||||
\(371\) | −5.37070e6 | −2.02580 | ||||||||
\(372\) | 1.40506e6 | 0.526425 | ||||||||
\(373\) | −692891. | −0.257865 | −0.128933 | − | 0.991653i | \(-0.541155\pi\) | ||||
−0.128933 | + | 0.991653i | \(0.541155\pi\) | |||||||
\(374\) | 192611. | 0.0712037 | ||||||||
\(375\) | −1.46608e6 | −0.538369 | ||||||||
\(376\) | 1.85018e6 | 0.674908 | ||||||||
\(377\) | 6.00497e6 | 2.17599 | ||||||||
\(378\) | 200633. | 0.0722226 | ||||||||
\(379\) | 2.12163e6 | 0.758702 | 0.379351 | − | 0.925253i | \(-0.376147\pi\) | ||||
0.379351 | + | 0.925253i | \(0.376147\pi\) | |||||||
\(380\) | 3.34646e6 | 1.18885 | ||||||||
\(381\) | 322055. | 0.113663 | ||||||||
\(382\) | 993026. | 0.348179 | ||||||||
\(383\) | −287079. | −0.100001 | −0.0500005 | − | 0.998749i | \(-0.515922\pi\) | ||||
−0.0500005 | + | 0.998749i | \(0.515922\pi\) | |||||||
\(384\) | 1.33009e6 | 0.460314 | ||||||||
\(385\) | −1.59559e6 | −0.548616 | ||||||||
\(386\) | 495582. | 0.169296 | ||||||||
\(387\) | 340091. | 0.115430 | ||||||||
\(388\) | 444029. | 0.149738 | ||||||||
\(389\) | 679811. | 0.227779 | 0.113890 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113890 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(390\) | 607293. | 0.202179 | ||||||||
\(391\) | −624208. | −0.206484 | ||||||||
\(392\) | 2.30828e6 | 0.758706 | ||||||||
\(393\) | 703076. | 0.229626 | ||||||||
\(394\) | −343226. | −0.111388 | ||||||||
\(395\) | −4.52953e6 | −1.46070 | ||||||||
\(396\) | −310904. | −0.0996295 | ||||||||
\(397\) | −5.39917e6 | −1.71930 | −0.859648 | − | 0.510886i | \(-0.829317\pi\) | ||||
−0.859648 | + | 0.510886i | \(0.829317\pi\) | |||||||
\(398\) | 910894. | 0.288244 | ||||||||
\(399\) | 3.58304e6 | 1.12673 | ||||||||
\(400\) | 320148. | 0.100046 | ||||||||
\(401\) | −2.17808e6 | −0.676416 | −0.338208 | − | 0.941071i | \(-0.609821\pi\) | ||||
−0.338208 | + | 0.941071i | \(0.609821\pi\) | |||||||
\(402\) | 631612. | 0.194933 | ||||||||
\(403\) | 4.55361e6 | 1.39667 | ||||||||
\(404\) | 1.14346e6 | 0.348553 | ||||||||
\(405\) | 387836. | 0.117493 | ||||||||
\(406\) | −1.86779e6 | −0.562359 | ||||||||
\(407\) | 649985. | 0.194499 | ||||||||
\(408\) | −854030. | −0.253993 | ||||||||
\(409\) | −356567. | −0.105398 | −0.0526991 | − | 0.998610i | \(-0.516782\pi\) | ||||
−0.0526991 | + | 0.998610i | \(0.516782\pi\) | |||||||
\(410\) | −951934. | −0.279671 | ||||||||
\(411\) | −835350. | −0.243929 | ||||||||
\(412\) | −3.79960e6 | −1.10279 | ||||||||
\(413\) | 7.91847e6 | 2.28437 | ||||||||
\(414\) | −55279.1 | −0.0158511 | ||||||||
\(415\) | −5.71186e6 | −1.62801 | ||||||||
\(416\) | 3.26668e6 | 0.925495 | ||||||||
\(417\) | −3.75406e6 | −1.05721 | ||||||||
\(418\) | 304623. | 0.0852751 | ||||||||
\(419\) | 3.82634e6 | 1.06475 | 0.532376 | − | 0.846508i | \(-0.321299\pi\) | ||||
0.532376 | + | 0.846508i | \(0.321299\pi\) | |||||||
\(420\) | 3.44293e6 | 0.952369 | ||||||||
\(421\) | −3.00814e6 | −0.827167 | −0.413584 | − | 0.910466i | \(-0.635723\pi\) | ||||
−0.413584 | + | 0.910466i | \(0.635723\pi\) | |||||||
\(422\) | 374947. | 0.102492 | ||||||||
\(423\) | 1.86356e6 | 0.506397 | ||||||||
\(424\) | 2.02457e6 | 0.546914 | ||||||||
\(425\) | −435721. | −0.117014 | ||||||||
\(426\) | −414329. | −0.110617 | ||||||||
\(427\) | −5.63416e6 | −1.49541 | ||||||||
\(428\) | −849481. | −0.224153 | ||||||||
\(429\) | −1.00760e6 | −0.264329 | ||||||||
\(430\) | −320191. | −0.0835098 | ||||||||
\(431\) | 577809. | 0.149827 | 0.0749136 | − | 0.997190i | \(-0.476132\pi\) | ||||
0.0749136 | + | 0.997190i | \(0.476132\pi\) | |||||||
\(432\) | 632038. | 0.162942 | ||||||||
\(433\) | 7.21909e6 | 1.85039 | 0.925194 | − | 0.379494i | \(-0.123902\pi\) | ||||
0.925194 | + | 0.379494i | \(0.123902\pi\) | |||||||
\(434\) | −1.41636e6 | −0.360952 | ||||||||
\(435\) | −3.61055e6 | −0.914852 | ||||||||
\(436\) | 1.94607e6 | 0.490279 | ||||||||
\(437\) | −987212. | −0.247290 | ||||||||
\(438\) | −394041. | −0.0981422 | ||||||||
\(439\) | −760935. | −0.188446 | −0.0942229 | − | 0.995551i | \(-0.530037\pi\) | ||||
−0.0942229 | + | 0.995551i | \(0.530037\pi\) | |||||||
\(440\) | 601482. | 0.148112 | ||||||||
\(441\) | 2.32497e6 | 0.569273 | ||||||||
\(442\) | −1.34695e6 | −0.327941 | ||||||||
\(443\) | −6.96892e6 | −1.68716 | −0.843580 | − | 0.537003i | \(-0.819556\pi\) | ||||
−0.843580 | + | 0.537003i | \(0.819556\pi\) | |||||||
\(444\) | −1.40253e6 | −0.337640 | ||||||||
\(445\) | 1.77815e6 | 0.425665 | ||||||||
\(446\) | 741692. | 0.176558 | ||||||||
\(447\) | 4.01342e6 | 0.950049 | ||||||||
\(448\) | 4.90255e6 | 1.15406 | ||||||||
\(449\) | 5.48897e6 | 1.28492 | 0.642458 | − | 0.766321i | \(-0.277915\pi\) | ||||
0.642458 | + | 0.766321i | \(0.277915\pi\) | |||||||
\(450\) | −38587.0 | −0.00898275 | ||||||||
\(451\) | 1.57942e6 | 0.365641 | ||||||||
\(452\) | 765268. | 0.176184 | ||||||||
\(453\) | −2.34412e6 | −0.536703 | ||||||||
\(454\) | 1.77210e6 | 0.403506 | ||||||||
\(455\) | 1.11581e7 | 2.52675 | ||||||||
\(456\) | −1.35069e6 | −0.304188 | ||||||||
\(457\) | −2.49968e6 | −0.559879 | −0.279940 | − | 0.960018i | \(-0.590314\pi\) | ||||
−0.279940 | + | 0.960018i | \(0.590314\pi\) | |||||||
\(458\) | −1.12331e6 | −0.250229 | ||||||||
\(459\) | −860203. | −0.190576 | ||||||||
\(460\) | −948608. | −0.209022 | ||||||||
\(461\) | −8.10339e6 | −1.77588 | −0.887942 | − | 0.459956i | \(-0.847865\pi\) | ||||
−0.887942 | + | 0.459956i | \(0.847865\pi\) | |||||||
\(462\) | 313405. | 0.0683125 | ||||||||
\(463\) | −4.71421e6 | −1.02201 | −0.511007 | − | 0.859577i | \(-0.670727\pi\) | ||||
−0.511007 | + | 0.859577i | \(0.670727\pi\) | |||||||
\(464\) | −5.88396e6 | −1.26875 | ||||||||
\(465\) | −2.73791e6 | −0.587200 | ||||||||
\(466\) | 2.08649e6 | 0.445093 | ||||||||
\(467\) | −1.03346e6 | −0.219281 | −0.109641 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109641 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(468\) | 2.17418e6 | 0.458861 | ||||||||
\(469\) | 1.16049e7 | 2.43618 | ||||||||
\(470\) | −1.75451e6 | −0.366362 | ||||||||
\(471\) | 414607. | 0.0861161 | ||||||||
\(472\) | −2.98499e6 | −0.616720 | ||||||||
\(473\) | 531249. | 0.109181 | ||||||||
\(474\) | 889689. | 0.181883 | ||||||||
\(475\) | −689113. | −0.140138 | ||||||||
\(476\) | −7.63628e6 | −1.54477 | ||||||||
\(477\) | 2.03921e6 | 0.410360 | ||||||||
\(478\) | 2.13228e6 | 0.426849 | ||||||||
\(479\) | 1.13020e6 | 0.225069 | 0.112534 | − | 0.993648i | \(-0.464103\pi\) | ||||
0.112534 | + | 0.993648i | \(0.464103\pi\) | |||||||
\(480\) | −1.96413e6 | −0.389105 | ||||||||
\(481\) | −4.54541e6 | −0.895798 | ||||||||
\(482\) | −1.19781e6 | −0.234838 | ||||||||
\(483\) | −1.01567e6 | −0.198100 | ||||||||
\(484\) | 4.39993e6 | 0.853754 | ||||||||
\(485\) | −865238. | −0.167025 | ||||||||
\(486\) | −76178.6 | −0.0146299 | ||||||||
\(487\) | −793366. | −0.151583 | −0.0757916 | − | 0.997124i | \(-0.524148\pi\) | ||||
−0.0757916 | + | 0.997124i | \(0.524148\pi\) | |||||||
\(488\) | 2.12389e6 | 0.403721 | ||||||||
\(489\) | 1.69540e6 | 0.320626 | ||||||||
\(490\) | −2.18892e6 | −0.411851 | ||||||||
\(491\) | −3.66618e6 | −0.686294 | −0.343147 | − | 0.939282i | \(-0.611493\pi\) | ||||
−0.343147 | + | 0.939282i | \(0.611493\pi\) | |||||||
\(492\) | −3.40804e6 | −0.634735 | ||||||||
\(493\) | 8.00805e6 | 1.48392 | ||||||||
\(494\) | −2.13026e6 | −0.392749 | ||||||||
\(495\) | 605829. | 0.111132 | ||||||||
\(496\) | −4.46184e6 | −0.814348 | ||||||||
\(497\) | −7.61267e6 | −1.38244 | ||||||||
\(498\) | 1.12192e6 | 0.202717 | ||||||||
\(499\) | −5.08658e6 | −0.914480 | −0.457240 | − | 0.889343i | \(-0.651162\pi\) | ||||
−0.457240 | + | 0.889343i | \(0.651162\pi\) | |||||||
\(500\) | 4.94162e6 | 0.883983 | ||||||||
\(501\) | 1.82893e6 | 0.325538 | ||||||||
\(502\) | 1.17359e6 | 0.207853 | ||||||||
\(503\) | 6.49233e6 | 1.14414 | 0.572072 | − | 0.820203i | \(-0.306140\pi\) | ||||
0.572072 | + | 0.820203i | \(0.306140\pi\) | |||||||
\(504\) | −1.38962e6 | −0.243680 | ||||||||
\(505\) | −2.22816e6 | −0.388793 | ||||||||
\(506\) | −86350.3 | −0.0149930 | ||||||||
\(507\) | 3.70460e6 | 0.640061 | ||||||||
\(508\) | −1.08553e6 | −0.186630 | ||||||||
\(509\) | −5.58035e6 | −0.954700 | −0.477350 | − | 0.878713i | \(-0.658403\pi\) | ||||
−0.477350 | + | 0.878713i | \(0.658403\pi\) | |||||||
\(510\) | 809868. | 0.137876 | ||||||||
\(511\) | −7.23991e6 | −1.22654 | ||||||||
\(512\) | −5.43197e6 | −0.915762 | ||||||||
\(513\) | −1.36045e6 | −0.228239 | ||||||||
\(514\) | −67944.9 | −0.0113435 | ||||||||
\(515\) | 7.40393e6 | 1.23011 | ||||||||
\(516\) | −1.14632e6 | −0.189532 | ||||||||
\(517\) | 2.91102e6 | 0.478981 | ||||||||
\(518\) | 1.41381e6 | 0.231508 | ||||||||
\(519\) | 1.42246e6 | 0.231804 | ||||||||
\(520\) | −4.20622e6 | −0.682156 | ||||||||
\(521\) | −4.02579e6 | −0.649766 | −0.324883 | − | 0.945754i | \(-0.605325\pi\) | ||||
−0.324883 | + | 0.945754i | \(0.605325\pi\) | |||||||
\(522\) | 709184. | 0.113915 | ||||||||
\(523\) | −9.41059e6 | −1.50440 | −0.752198 | − | 0.658937i | \(-0.771007\pi\) | ||||
−0.752198 | + | 0.658937i | \(0.771007\pi\) | |||||||
\(524\) | −2.36981e6 | −0.377038 | ||||||||
\(525\) | −708978. | −0.112262 | ||||||||
\(526\) | −599588. | −0.0944906 | ||||||||
\(527\) | 6.07256e6 | 0.952457 | ||||||||
\(528\) | 987293. | 0.154121 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −1.91988e6 | −0.296883 | ||||||||
\(531\) | −3.00657e6 | −0.462738 | ||||||||
\(532\) | −1.20771e7 | −1.85005 | ||||||||
\(533\) | −1.10450e7 | −1.68402 | ||||||||
\(534\) | −349263. | −0.0530029 | ||||||||
\(535\) | 1.65531e6 | 0.250031 | ||||||||
\(536\) | −4.37466e6 | −0.657707 | ||||||||
\(537\) | 1.49800e6 | 0.224169 | ||||||||
\(538\) | −1.24935e6 | −0.186092 | ||||||||
\(539\) | 3.63178e6 | 0.538453 | ||||||||
\(540\) | −1.30725e6 | −0.192919 | ||||||||
\(541\) | −2.68147e6 | −0.393894 | −0.196947 | − | 0.980414i | \(-0.563103\pi\) | ||||
−0.196947 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(542\) | −2.95768e6 | −0.432467 | ||||||||
\(543\) | 1.67058e6 | 0.243146 | ||||||||
\(544\) | 4.35636e6 | 0.631141 | ||||||||
\(545\) | −3.79214e6 | −0.546881 | ||||||||
\(546\) | −2.19167e6 | −0.314625 | ||||||||
\(547\) | 8.74676e6 | 1.24991 | 0.624955 | − | 0.780660i | \(-0.285117\pi\) | ||||
0.624955 | + | 0.780660i | \(0.285117\pi\) | |||||||
\(548\) | 2.81566e6 | 0.400524 | ||||||||
\(549\) | 2.13924e6 | 0.302920 | ||||||||
\(550\) | −60275.8 | −0.00849643 | ||||||||
\(551\) | 1.26651e7 | 1.77717 | ||||||||
\(552\) | 382873. | 0.0534820 | ||||||||
\(553\) | 1.63467e7 | 2.27309 | ||||||||
\(554\) | −375357. | −0.0519601 | ||||||||
\(555\) | 2.73298e6 | 0.376620 | ||||||||
\(556\) | 1.26535e7 | 1.73590 | ||||||||
\(557\) | 2.07905e6 | 0.283940 | 0.141970 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141970 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(558\) | 537779. | 0.0731170 | ||||||||
\(559\) | −3.71508e6 | −0.502850 | ||||||||
\(560\) | −1.09332e7 | −1.47326 | ||||||||
\(561\) | −1.34370e6 | −0.180259 | ||||||||
\(562\) | 505687. | 0.0675369 | ||||||||
\(563\) | 8.52157e6 | 1.13305 | 0.566524 | − | 0.824045i | \(-0.308288\pi\) | ||||
0.566524 | + | 0.824045i | \(0.308288\pi\) | |||||||
\(564\) | −6.28135e6 | −0.831487 | ||||||||
\(565\) | −1.49121e6 | −0.196524 | ||||||||
\(566\) | −945338. | −0.124035 | ||||||||
\(567\) | −1.39967e6 | −0.182838 | ||||||||
\(568\) | 2.86972e6 | 0.373223 | ||||||||
\(569\) | 6.58526e6 | 0.852692 | 0.426346 | − | 0.904560i | \(-0.359801\pi\) | ||||
0.426346 | + | 0.904560i | \(0.359801\pi\) | |||||||
\(570\) | 1.28084e6 | 0.165123 | ||||||||
\(571\) | −6.31614e6 | −0.810702 | −0.405351 | − | 0.914161i | \(-0.632851\pi\) | ||||
−0.405351 | + | 0.914161i | \(0.632851\pi\) | |||||||
\(572\) | 3.39624e6 | 0.434019 | ||||||||
\(573\) | −6.92760e6 | −0.881447 | ||||||||
\(574\) | 3.43545e6 | 0.435216 | ||||||||
\(575\) | 195340. | 0.0246389 | ||||||||
\(576\) | −1.86145e6 | −0.233774 | ||||||||
\(577\) | 4.48677e6 | 0.561040 | 0.280520 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280520 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(578\) | 35492.6 | 0.00441894 | ||||||||
\(579\) | −3.45730e6 | −0.428589 | ||||||||
\(580\) | 1.21698e7 | 1.50216 | ||||||||
\(581\) | 2.06136e7 | 2.53346 | ||||||||
\(582\) | 169950. | 0.0207976 | ||||||||
\(583\) | 3.18540e6 | 0.388144 | ||||||||
\(584\) | 2.72920e6 | 0.331134 | ||||||||
\(585\) | −4.23663e6 | −0.511836 | ||||||||
\(586\) | −2.09752e6 | −0.252326 | ||||||||
\(587\) | −7.42328e6 | −0.889203 | −0.444601 | − | 0.895729i | \(-0.646655\pi\) | ||||
−0.444601 | + | 0.895729i | \(0.646655\pi\) | |||||||
\(588\) | −7.83660e6 | −0.934726 | ||||||||
\(589\) | 9.60402e6 | 1.14068 | ||||||||
\(590\) | 2.83064e6 | 0.334776 | ||||||||
\(591\) | 2.39443e6 | 0.281990 | ||||||||
\(592\) | 4.45381e6 | 0.522309 | ||||||||
\(593\) | 7.02182e6 | 0.819998 | 0.409999 | − | 0.912086i | \(-0.365529\pi\) | ||||
0.409999 | + | 0.912086i | \(0.365529\pi\) | |||||||
\(594\) | −118997. | −0.0138379 | ||||||||
\(595\) | 1.48801e7 | 1.72311 | ||||||||
\(596\) | −1.35278e7 | −1.55995 | ||||||||
\(597\) | −6.35463e6 | −0.729717 | ||||||||
\(598\) | 603856. | 0.0690527 | ||||||||
\(599\) | 5.02165e6 | 0.571846 | 0.285923 | − | 0.958253i | \(-0.407700\pi\) | ||||
0.285923 | + | 0.958253i | \(0.407700\pi\) | |||||||
\(600\) | 267261. | 0.0303080 | ||||||||
\(601\) | 4.66921e6 | 0.527300 | 0.263650 | − | 0.964618i | \(-0.415074\pi\) | ||||
0.263650 | + | 0.964618i | \(0.415074\pi\) | |||||||
\(602\) | 1.15554e6 | 0.129955 | ||||||||
\(603\) | −4.40628e6 | −0.493491 | ||||||||
\(604\) | 7.90116e6 | 0.881248 | ||||||||
\(605\) | −8.57374e6 | −0.952318 | ||||||||
\(606\) | 437655. | 0.0484117 | ||||||||
\(607\) | −1.48942e7 | −1.64076 | −0.820380 | − | 0.571819i | \(-0.806238\pi\) | ||||
−0.820380 | + | 0.571819i | \(0.806238\pi\) | |||||||
\(608\) | 6.88977e6 | 0.755868 | ||||||||
\(609\) | 1.30302e7 | 1.42366 | ||||||||
\(610\) | −2.01406e6 | −0.219153 | ||||||||
\(611\) | −2.03570e7 | −2.20603 | ||||||||
\(612\) | 2.89943e6 | 0.312920 | ||||||||
\(613\) | 1.09408e7 | 1.17598 | 0.587989 | − | 0.808869i | \(-0.299920\pi\) | ||||
0.587989 | + | 0.808869i | \(0.299920\pi\) | |||||||
\(614\) | −1.60721e6 | −0.172048 | ||||||||
\(615\) | 6.64093e6 | 0.708013 | ||||||||
\(616\) | −2.17070e6 | −0.230488 | ||||||||
\(617\) | −6.42199e6 | −0.679136 | −0.339568 | − | 0.940582i | \(-0.610281\pi\) | ||||
−0.339568 | + | 0.940582i | \(0.610281\pi\) | |||||||
\(618\) | −1.45428e6 | −0.153171 | ||||||||
\(619\) | −3.05345e6 | −0.320305 | −0.160152 | − | 0.987092i | \(-0.551199\pi\) | ||||
−0.160152 | + | 0.987092i | \(0.551199\pi\) | |||||||
\(620\) | 9.22847e6 | 0.964163 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | 4.21668e6 | 0.437014 | ||||||||
\(623\) | −6.41719e6 | −0.662406 | ||||||||
\(624\) | −6.90424e6 | −0.709830 | ||||||||
\(625\) | −1.07832e7 | −1.10420 | ||||||||
\(626\) | −2.19523e6 | −0.223895 | ||||||||
\(627\) | −2.12513e6 | −0.215882 | ||||||||
\(628\) | −1.39749e6 | −0.141400 | ||||||||
\(629\) | −6.06162e6 | −0.610889 | ||||||||
\(630\) | 1.31777e6 | 0.132278 | ||||||||
\(631\) | 1.05012e7 | 1.04994 | 0.524971 | − | 0.851120i | \(-0.324076\pi\) | ||||
0.524971 | + | 0.851120i | \(0.324076\pi\) | |||||||
\(632\) | −6.16215e6 | −0.613677 | ||||||||
\(633\) | −2.61572e6 | −0.259467 | ||||||||
\(634\) | 1.17181e6 | 0.115780 | ||||||||
\(635\) | 2.11527e6 | 0.208176 | ||||||||
\(636\) | −6.87341e6 | −0.673798 | ||||||||
\(637\) | −2.53974e7 | −2.47994 | ||||||||
\(638\) | 1.10780e6 | 0.107748 | ||||||||
\(639\) | 2.89046e6 | 0.280037 | ||||||||
\(640\) | 8.73610e6 | 0.843078 | ||||||||
\(641\) | −1.57928e7 | −1.51815 | −0.759073 | − | 0.651006i | \(-0.774347\pi\) | ||||
−0.759073 | + | 0.651006i | \(0.774347\pi\) | |||||||
\(642\) | −325135. | −0.0311333 | ||||||||
\(643\) | 551159. | 0.0525714 | 0.0262857 | − | 0.999654i | \(-0.491632\pi\) | ||||
0.0262857 | + | 0.999654i | \(0.491632\pi\) | |||||||
\(644\) | 3.42345e6 | 0.325274 | ||||||||
\(645\) | 2.23373e6 | 0.211413 | ||||||||
\(646\) | −2.84085e6 | −0.267835 | ||||||||
\(647\) | 1.12498e7 | 1.05653 | 0.528267 | − | 0.849078i | \(-0.322842\pi\) | ||||
0.528267 | + | 0.849078i | \(0.322842\pi\) | |||||||
\(648\) | 527627. | 0.0493616 | ||||||||
\(649\) | −4.69649e6 | −0.437685 | ||||||||
\(650\) | 421515. | 0.0391318 | ||||||||
\(651\) | 9.88088e6 | 0.913783 | ||||||||
\(652\) | −5.71456e6 | −0.526458 | ||||||||
\(653\) | −2.56046e6 | −0.234982 | −0.117491 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117491 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(654\) | 744850. | 0.0680965 | ||||||||
\(655\) | 4.61783e6 | 0.420566 | ||||||||
\(656\) | 1.08224e7 | 0.981895 | ||||||||
\(657\) | 2.74893e6 | 0.248456 | ||||||||
\(658\) | 6.33188e6 | 0.570122 | ||||||||
\(659\) | −734143. | −0.0658518 | −0.0329259 | − | 0.999458i | \(-0.510483\pi\) | ||||
−0.0329259 | + | 0.999458i | \(0.510483\pi\) | |||||||
\(660\) | −2.04203e6 | −0.182474 | ||||||||
\(661\) | 1.92354e7 | 1.71237 | 0.856185 | − | 0.516670i | \(-0.172828\pi\) | ||||
0.856185 | + | 0.516670i | \(0.172828\pi\) | |||||||
\(662\) | 2.76524e6 | 0.245238 | ||||||||
\(663\) | 9.39666e6 | 0.830213 | ||||||||
\(664\) | −7.77064e6 | −0.683969 | ||||||||
\(665\) | 2.35336e7 | 2.06364 | ||||||||
\(666\) | −536810. | −0.0468960 | ||||||||
\(667\) | −3.59012e6 | −0.312460 | ||||||||
\(668\) | −6.16464e6 | −0.534523 | ||||||||
\(669\) | −5.17423e6 | −0.446972 | ||||||||
\(670\) | 4.14845e6 | 0.357025 | ||||||||
\(671\) | 3.34166e6 | 0.286520 | ||||||||
\(672\) | 7.08838e6 | 0.605514 | ||||||||
\(673\) | 1.20397e7 | 1.02465 | 0.512326 | − | 0.858791i | \(-0.328784\pi\) | ||||
0.512326 | + | 0.858791i | \(0.328784\pi\) | |||||||
\(674\) | −1.05465e6 | −0.0894247 | ||||||||
\(675\) | 269192. | 0.0227407 | ||||||||
\(676\) | −1.24868e7 | −1.05096 | ||||||||
\(677\) | 99259.2 | 0.00832337 | 0.00416168 | − | 0.999991i | \(-0.498675\pi\) | ||||
0.00416168 | + | 0.999991i | \(0.498675\pi\) | |||||||
\(678\) | 292902. | 0.0244708 | ||||||||
\(679\) | 3.12257e6 | 0.259919 | ||||||||
\(680\) | −5.60929e6 | −0.465196 | ||||||||
\(681\) | −1.23626e7 | −1.02151 | ||||||||
\(682\) | 840052. | 0.0691585 | ||||||||
\(683\) | 9.22059e6 | 0.756323 | 0.378161 | − | 0.925740i | \(-0.376556\pi\) | ||||
0.378161 | + | 0.925740i | \(0.376556\pi\) | |||||||
\(684\) | 4.58557e6 | 0.374760 | ||||||||
\(685\) | −5.48661e6 | −0.446763 | ||||||||
\(686\) | 3.27406e6 | 0.265630 | ||||||||
\(687\) | 7.83652e6 | 0.633478 | ||||||||
\(688\) | 3.64021e6 | 0.293194 | ||||||||
\(689\) | −2.22758e7 | −1.78766 | ||||||||
\(690\) | −363075. | −0.0290318 | ||||||||
\(691\) | −1.77887e7 | −1.41726 | −0.708629 | − | 0.705581i | \(-0.750686\pi\) | ||||
−0.708629 | + | 0.705581i | \(0.750686\pi\) | |||||||
\(692\) | −4.79459e6 | −0.380615 | ||||||||
\(693\) | −2.18639e6 | −0.172940 | ||||||||
\(694\) | −4.13096e6 | −0.325576 | ||||||||
\(695\) | −2.46568e7 | −1.93631 | ||||||||
\(696\) | −4.91194e6 | −0.384353 | ||||||||
\(697\) | −1.47293e7 | −1.14842 | ||||||||
\(698\) | 4.17881e6 | 0.324649 | ||||||||
\(699\) | −1.45558e7 | −1.12679 | ||||||||
\(700\) | 2.38970e6 | 0.184331 | ||||||||
\(701\) | 1.60390e7 | 1.23277 | 0.616384 | − | 0.787446i | \(-0.288597\pi\) | ||||
0.616384 | + | 0.787446i | \(0.288597\pi\) | |||||||
\(702\) | 832157. | 0.0637327 | ||||||||
\(703\) | −9.58673e6 | −0.731614 | ||||||||
\(704\) | −2.90774e6 | −0.221118 | ||||||||
\(705\) | 1.22399e7 | 0.927480 | ||||||||
\(706\) | 2.22767e6 | 0.168205 | ||||||||
\(707\) | 8.04125e6 | 0.605028 | ||||||||
\(708\) | 1.01340e7 | 0.759800 | ||||||||
\(709\) | −1.64673e7 | −1.23029 | −0.615145 | − | 0.788414i | \(-0.710903\pi\) | ||||
−0.615145 | + | 0.788414i | \(0.710903\pi\) | |||||||
\(710\) | −2.72132e6 | −0.202598 | ||||||||
\(711\) | −6.20669e6 | −0.460454 | ||||||||
\(712\) | 2.41906e6 | 0.178833 | ||||||||
\(713\) | −2.72241e6 | −0.200553 | ||||||||
\(714\) | −2.92275e6 | −0.214558 | ||||||||
\(715\) | −6.61794e6 | −0.484125 | ||||||||
\(716\) | −5.04919e6 | −0.368077 | ||||||||
\(717\) | −1.48753e7 | −1.08061 | ||||||||
\(718\) | −4.02945e6 | −0.291698 | ||||||||
\(719\) | 5.48538e6 | 0.395717 | 0.197859 | − | 0.980231i | \(-0.436601\pi\) | ||||
0.197859 | + | 0.980231i | \(0.436601\pi\) | |||||||
\(720\) | 4.15125e6 | 0.298433 | ||||||||
\(721\) | −2.67202e7 | −1.91426 | ||||||||
\(722\) | −1.29854e6 | −0.0927071 | ||||||||
\(723\) | 8.35619e6 | 0.594515 | ||||||||
\(724\) | −5.63090e6 | −0.399237 | ||||||||
\(725\) | −2.50604e6 | −0.177070 | ||||||||
\(726\) | 1.68405e6 | 0.118581 | ||||||||
\(727\) | −2.75484e7 | −1.93313 | −0.966563 | − | 0.256431i | \(-0.917453\pi\) | ||||
−0.966563 | + | 0.256431i | \(0.917453\pi\) | |||||||
\(728\) | 1.51799e7 | 1.06155 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.58807e6 | −0.179750 | ||||||||
\(731\) | −4.95432e6 | −0.342918 | ||||||||
\(732\) | −7.21058e6 | −0.497385 | ||||||||
\(733\) | 1.51233e7 | 1.03965 | 0.519825 | − | 0.854273i | \(-0.325997\pi\) | ||||
0.519825 | + | 0.854273i | \(0.325997\pi\) | |||||||
\(734\) | −1.50980e6 | −0.103438 | ||||||||
\(735\) | 1.52705e7 | 1.04264 | ||||||||
\(736\) | −1.95301e6 | −0.132896 | ||||||||
\(737\) | −6.88295e6 | −0.466773 | ||||||||
\(738\) | −1.30441e6 | −0.0881604 | ||||||||
\(739\) | −1.56004e7 | −1.05081 | −0.525405 | − | 0.850852i | \(-0.676086\pi\) | ||||
−0.525405 | + | 0.850852i | \(0.676086\pi\) | |||||||
\(740\) | −9.21185e6 | −0.618397 | ||||||||
\(741\) | 1.48612e7 | 0.994281 | ||||||||
\(742\) | 6.92870e6 | 0.462000 | ||||||||
\(743\) | 1.77279e6 | 0.117811 | 0.0589053 | − | 0.998264i | \(-0.481239\pi\) | ||||
0.0589053 | + | 0.998264i | \(0.481239\pi\) | |||||||
\(744\) | −3.72476e6 | −0.246698 | ||||||||
\(745\) | 2.63603e7 | 1.74004 | ||||||||
\(746\) | 893892. | 0.0588082 | ||||||||
\(747\) | −7.82681e6 | −0.513196 | ||||||||
\(748\) | 4.52913e6 | 0.295979 | ||||||||
\(749\) | −5.97386e6 | −0.389090 | ||||||||
\(750\) | 1.89138e6 | 0.122779 | ||||||||
\(751\) | 5.07089e6 | 0.328083 | 0.164042 | − | 0.986453i | \(-0.447547\pi\) | ||||
0.164042 | + | 0.986453i | \(0.447547\pi\) | |||||||
\(752\) | 1.99468e7 | 1.28626 | ||||||||
\(753\) | −8.18724e6 | −0.526199 | ||||||||
\(754\) | −7.74696e6 | −0.496253 | ||||||||
\(755\) | −1.53962e7 | −0.982987 | ||||||||
\(756\) | 4.71776e6 | 0.300214 | ||||||||
\(757\) | −733561. | −0.0465261 | −0.0232631 | − | 0.999729i | \(-0.507406\pi\) | ||||
−0.0232631 | + | 0.999729i | \(0.507406\pi\) | |||||||
\(758\) | −2.73709e6 | −0.173028 | ||||||||
\(759\) | 602401. | 0.0379561 | ||||||||
\(760\) | −8.87135e6 | −0.557129 | ||||||||
\(761\) | 2.90077e6 | 0.181573 | 0.0907866 | − | 0.995870i | \(-0.471062\pi\) | ||||
0.0907866 | + | 0.995870i | \(0.471062\pi\) | |||||||
\(762\) | −415481. | −0.0259217 | ||||||||
\(763\) | 1.36855e7 | 0.851039 | ||||||||
\(764\) | 2.33504e7 | 1.44731 | ||||||||
\(765\) | −5.64984e6 | −0.349046 | ||||||||
\(766\) | 370358. | 0.0228060 | ||||||||
\(767\) | 3.28431e7 | 2.01584 | ||||||||
\(768\) | 4.90256e6 | 0.299930 | ||||||||
\(769\) | −6.02882e6 | −0.367635 | −0.183817 | − | 0.982960i | \(-0.558846\pi\) | ||||
−0.183817 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(770\) | 2.05845e6 | 0.125116 | ||||||||
\(771\) | 474001. | 0.0287173 | ||||||||
\(772\) | 1.16533e7 | 0.703729 | ||||||||
\(773\) | 1.48827e7 | 0.895844 | 0.447922 | − | 0.894073i | \(-0.352164\pi\) | ||||
0.447922 | + | 0.894073i | \(0.352164\pi\) | |||||||
\(774\) | −438749. | −0.0263247 | ||||||||
\(775\) | −1.90035e6 | −0.113653 | ||||||||
\(776\) | −1.17710e6 | −0.0701715 | ||||||||
\(777\) | −9.86309e6 | −0.586085 | ||||||||
\(778\) | −877019. | −0.0519469 | ||||||||
\(779\) | −2.32951e7 | −1.37537 | ||||||||
\(780\) | 1.42801e7 | 0.840417 | ||||||||
\(781\) | 4.51512e6 | 0.264876 | ||||||||
\(782\) | 805285. | 0.0470904 | ||||||||
\(783\) | −4.94745e6 | −0.288388 | ||||||||
\(784\) | 2.48856e7 | 1.44596 | ||||||||
\(785\) | 2.72315e6 | 0.157724 | ||||||||
\(786\) | −907033. | −0.0523681 | ||||||||
\(787\) | 2.19846e7 | 1.26526 | 0.632631 | − | 0.774453i | \(-0.281975\pi\) | ||||
0.632631 | + | 0.774453i | \(0.281975\pi\) | |||||||
\(788\) | −8.07075e6 | −0.463018 | ||||||||
\(789\) | 4.18288e6 | 0.239212 | ||||||||
\(790\) | 5.84350e6 | 0.333124 | ||||||||
\(791\) | 5.38164e6 | 0.305825 | ||||||||
\(792\) | 824194. | 0.0466892 | ||||||||
\(793\) | −2.33685e7 | −1.31962 | ||||||||
\(794\) | 6.96542e6 | 0.392099 | ||||||||
\(795\) | 1.33936e7 | 0.751586 | ||||||||
\(796\) | 2.14191e7 | 1.19817 | ||||||||
\(797\) | −2.92578e6 | −0.163153 | −0.0815765 | − | 0.996667i | \(-0.525995\pi\) | ||||
−0.0815765 | + | 0.996667i | \(0.525995\pi\) | |||||||
\(798\) | −4.62245e6 | −0.256960 | ||||||||
\(799\) | −2.71476e7 | −1.50440 | ||||||||
\(800\) | −1.36328e6 | −0.0753113 | ||||||||
\(801\) | 2.43655e6 | 0.134182 | ||||||||
\(802\) | 2.80993e6 | 0.154262 | ||||||||
\(803\) | 4.29404e6 | 0.235005 | ||||||||
\(804\) | 1.48519e7 | 0.810295 | ||||||||
\(805\) | −6.67096e6 | −0.362826 | ||||||||
\(806\) | −5.87457e6 | −0.318521 | ||||||||
\(807\) | 8.71578e6 | 0.471110 | ||||||||
\(808\) | −3.03128e6 | −0.163342 | ||||||||
\(809\) | −2.36363e6 | −0.126972 | −0.0634860 | − | 0.997983i | \(-0.520222\pi\) | ||||
−0.0634860 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(810\) | −500343. | −0.0267951 | ||||||||
\(811\) | −1.40226e7 | −0.748648 | −0.374324 | − | 0.927298i | \(-0.622125\pi\) | ||||
−0.374324 | + | 0.927298i | \(0.622125\pi\) | |||||||
\(812\) | −4.39200e7 | −2.33761 | ||||||||
\(813\) | 2.06335e7 | 1.09483 | ||||||||
\(814\) | −838540. | −0.0443570 | ||||||||
\(815\) | 1.11354e7 | 0.587236 | ||||||||
\(816\) | −9.20729e6 | −0.484068 | ||||||||
\(817\) | −7.83548e6 | −0.410686 | ||||||||
\(818\) | 460004. | 0.0240369 | ||||||||
\(819\) | 1.52896e7 | 0.796503 | ||||||||
\(820\) | −2.23841e7 | −1.16253 | ||||||||
\(821\) | 3.57170e7 | 1.84934 | 0.924670 | − | 0.380769i | \(-0.124341\pi\) | ||||
0.924670 | + | 0.380769i | \(0.124341\pi\) | |||||||
\(822\) | 1.07768e6 | 0.0556300 | ||||||||
\(823\) | −1.15100e7 | −0.592344 | −0.296172 | − | 0.955135i | \(-0.595710\pi\) | ||||
−0.296172 | + | 0.955135i | \(0.595710\pi\) | |||||||
\(824\) | 1.00726e7 | 0.516801 | ||||||||
\(825\) | 420499. | 0.0215095 | ||||||||
\(826\) | −1.02155e7 | −0.520968 | ||||||||
\(827\) | −1.24864e7 | −0.634854 | −0.317427 | − | 0.948283i | \(-0.602819\pi\) | ||||
−0.317427 | + | 0.948283i | \(0.602819\pi\) | |||||||
\(828\) | −1.29985e6 | −0.0658898 | ||||||||
\(829\) | −1.13398e7 | −0.573087 | −0.286544 | − | 0.958067i | \(-0.592506\pi\) | ||||
−0.286544 | + | 0.958067i | \(0.592506\pi\) | |||||||
\(830\) | 7.36882e6 | 0.371281 | ||||||||
\(831\) | 2.61858e6 | 0.131542 | ||||||||
\(832\) | 2.03341e7 | 1.01840 | ||||||||
\(833\) | −3.38692e7 | −1.69119 | ||||||||
\(834\) | 4.84308e6 | 0.241105 | ||||||||
\(835\) | 1.20125e7 | 0.596232 | ||||||||
\(836\) | 7.16302e6 | 0.354471 | ||||||||
\(837\) | −3.75168e6 | −0.185102 | ||||||||
\(838\) | −4.93633e6 | −0.242825 | ||||||||
\(839\) | 2.91430e7 | 1.42932 | 0.714659 | − | 0.699473i | \(-0.246582\pi\) | ||||
0.714659 | + | 0.699473i | \(0.246582\pi\) | |||||||
\(840\) | −9.12709e6 | −0.446307 | ||||||||
\(841\) | 2.55471e7 | 1.24552 | ||||||||
\(842\) | 3.88078e6 | 0.188642 | ||||||||
\(843\) | −3.52780e6 | −0.170976 | ||||||||
\(844\) | 8.81663e6 | 0.426036 | ||||||||
\(845\) | 2.43319e7 | 1.17229 | ||||||||
\(846\) | −2.40416e6 | −0.115488 | ||||||||
\(847\) | 3.09419e7 | 1.48197 | ||||||||
\(848\) | 2.18269e7 | 1.04232 | ||||||||
\(849\) | 6.59491e6 | 0.314007 | ||||||||
\(850\) | 562120. | 0.0266859 | ||||||||
\(851\) | 2.71751e6 | 0.128632 | ||||||||
\(852\) | −9.74267e6 | −0.459811 | ||||||||
\(853\) | −9.77420e6 | −0.459948 | −0.229974 | − | 0.973197i | \(-0.573864\pi\) | ||||
−0.229974 | + | 0.973197i | \(0.573864\pi\) | |||||||
\(854\) | 7.26858e6 | 0.341040 | ||||||||
\(855\) | −8.93548e6 | −0.418025 | ||||||||
\(856\) | 2.25194e6 | 0.105044 | ||||||||
\(857\) | −2.33262e7 | −1.08491 | −0.542453 | − | 0.840086i | \(-0.682504\pi\) | ||||
−0.542453 | + | 0.840086i | \(0.682504\pi\) | |||||||
\(858\) | 1.29989e6 | 0.0602823 | ||||||||
\(859\) | −1.14340e7 | −0.528708 | −0.264354 | − | 0.964426i | \(-0.585159\pi\) | ||||
−0.264354 | + | 0.964426i | \(0.585159\pi\) | |||||||
\(860\) | −7.52908e6 | −0.347133 | ||||||||
\(861\) | −2.39666e7 | −1.10179 | ||||||||
\(862\) | −745426. | −0.0341693 | ||||||||
\(863\) | −7.70458e6 | −0.352145 | −0.176073 | − | 0.984377i | \(-0.556339\pi\) | ||||
−0.176073 | + | 0.984377i | \(0.556339\pi\) | |||||||
\(864\) | −2.69139e6 | −0.122657 | ||||||||
\(865\) | 9.34277e6 | 0.424556 | ||||||||
\(866\) | −9.31329e6 | −0.421996 | ||||||||
\(867\) | −247605. | −0.0111870 | ||||||||
\(868\) | −3.33048e7 | −1.50040 | ||||||||
\(869\) | −9.69534e6 | −0.435525 | ||||||||
\(870\) | 4.65794e6 | 0.208639 | ||||||||
\(871\) | 4.81332e7 | 2.14981 | ||||||||
\(872\) | −5.15897e6 | −0.229759 | ||||||||
\(873\) | −1.18561e6 | −0.0526511 | ||||||||
\(874\) | 1.27359e6 | 0.0563965 | ||||||||
\(875\) | 3.47513e7 | 1.53444 | ||||||||
\(876\) | −9.26562e6 | −0.407957 | ||||||||
\(877\) | 1.42476e7 | 0.625520 | 0.312760 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312760 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(878\) | 981676. | 0.0429766 | ||||||||
\(879\) | 1.46328e7 | 0.638788 | ||||||||
\(880\) | 6.48457e6 | 0.282276 | ||||||||
\(881\) | −1.76114e7 | −0.764459 | −0.382230 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382230 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(882\) | −2.99942e6 | −0.129827 | ||||||||
\(883\) | −9.40461e6 | −0.405919 | −0.202959 | − | 0.979187i | \(-0.565056\pi\) | ||||
−0.202959 | + | 0.979187i | \(0.565056\pi\) | |||||||
\(884\) | −3.16726e7 | −1.36318 | ||||||||
\(885\) | −1.97472e7 | −0.847517 | ||||||||
\(886\) | 8.99054e6 | 0.384770 | ||||||||
\(887\) | 1.38034e7 | 0.589086 | 0.294543 | − | 0.955638i | \(-0.404833\pi\) | ||||
0.294543 | + | 0.955638i | \(0.404833\pi\) | |||||||
\(888\) | 3.71805e6 | 0.158228 | ||||||||
\(889\) | −7.63383e6 | −0.323958 | ||||||||
\(890\) | −2.29397e6 | −0.0970762 | ||||||||
\(891\) | 830152. | 0.0350319 | ||||||||
\(892\) | 1.74404e7 | 0.733913 | ||||||||
\(893\) | −4.29351e7 | −1.80170 | ||||||||
\(894\) | −5.17768e6 | −0.216666 | ||||||||
\(895\) | 9.83888e6 | 0.410571 | ||||||||
\(896\) | −3.15279e7 | −1.31197 | ||||||||
\(897\) | −4.21265e6 | −0.174813 | ||||||||
\(898\) | −7.08127e6 | −0.293036 | ||||||||
\(899\) | 3.49262e7 | 1.44129 | ||||||||
\(900\) | −907348. | −0.0373394 | ||||||||
\(901\) | −2.97064e7 | −1.21910 | ||||||||
\(902\) | −2.03759e6 | −0.0833874 | ||||||||
\(903\) | −8.06135e6 | −0.328994 | ||||||||
\(904\) | −2.02870e6 | −0.0825650 | ||||||||
\(905\) | 1.09724e7 | 0.445328 | ||||||||
\(906\) | 3.02413e6 | 0.122399 | ||||||||
\(907\) | 802157. | 0.0323773 | 0.0161887 | − | 0.999869i | \(-0.494847\pi\) | ||||
0.0161887 | + | 0.999869i | \(0.494847\pi\) | |||||||
\(908\) | 4.16699e7 | 1.67729 | ||||||||
\(909\) | −3.05319e6 | −0.122559 | ||||||||
\(910\) | −1.43950e7 | −0.576245 | ||||||||
\(911\) | 4.80457e6 | 0.191804 | 0.0959022 | − | 0.995391i | \(-0.469426\pi\) | ||||
0.0959022 | + | 0.995391i | \(0.469426\pi\) | |||||||
\(912\) | −1.45617e7 | −0.579731 | ||||||||
\(913\) | −1.22261e7 | −0.485412 | ||||||||
\(914\) | 3.22482e6 | 0.127685 | ||||||||
\(915\) | 1.40506e7 | 0.554807 | ||||||||
\(916\) | −2.64140e7 | −1.04015 | ||||||||
\(917\) | −1.66654e7 | −0.654473 | ||||||||
\(918\) | 1.10974e6 | 0.0434625 | ||||||||
\(919\) | 2.84366e7 | 1.11068 | 0.555339 | − | 0.831624i | \(-0.312588\pi\) | ||||
0.555339 | + | 0.831624i | \(0.312588\pi\) | |||||||
\(920\) | 2.51472e6 | 0.0979537 | ||||||||
\(921\) | 1.12123e7 | 0.435556 | ||||||||
\(922\) | 1.04541e7 | 0.405005 | ||||||||
\(923\) | −3.15747e7 | −1.21993 | ||||||||
\(924\) | 7.36951e6 | 0.283961 | ||||||||
\(925\) | 1.89693e6 | 0.0728948 | ||||||||
\(926\) | 6.08176e6 | 0.233078 | ||||||||
\(927\) | 1.01454e7 | 0.387766 | ||||||||
\(928\) | 2.50555e7 | 0.955066 | ||||||||
\(929\) | 5.06040e6 | 0.192374 | 0.0961868 | − | 0.995363i | \(-0.469335\pi\) | ||||
0.0961868 | + | 0.995363i | \(0.469335\pi\) | |||||||
\(930\) | 3.53215e6 | 0.133916 | ||||||||
\(931\) | −5.35657e7 | −2.02541 | ||||||||
\(932\) | 4.90624e7 | 1.85016 | ||||||||
\(933\) | −2.94166e7 | −1.10634 | ||||||||
\(934\) | 1.33326e6 | 0.0500089 | ||||||||
\(935\) | −8.82549e6 | −0.330149 | ||||||||
\(936\) | −5.76367e6 | −0.215035 | ||||||||
\(937\) | 1.27197e7 | 0.473291 | 0.236646 | − | 0.971596i | \(-0.423952\pi\) | ||||
0.236646 | + | 0.971596i | \(0.423952\pi\) | |||||||
\(938\) | −1.49714e7 | −0.555591 | ||||||||
\(939\) | 1.53145e7 | 0.566810 | ||||||||
\(940\) | −4.12561e7 | −1.52289 | ||||||||
\(941\) | −1.66122e7 | −0.611581 | −0.305790 | − | 0.952099i | \(-0.598921\pi\) | ||||
−0.305790 | + | 0.952099i | \(0.598921\pi\) | |||||||
\(942\) | −534881. | −0.0196395 | ||||||||
\(943\) | 6.60335e6 | 0.241816 | ||||||||
\(944\) | −3.21812e7 | −1.17536 | ||||||||
\(945\) | −9.19306e6 | −0.334873 | ||||||||
\(946\) | −685360. | −0.0248995 | ||||||||
\(947\) | 4.77751e7 | 1.73112 | 0.865558 | − | 0.500808i | \(-0.166964\pi\) | ||||
0.865558 | + | 0.500808i | \(0.166964\pi\) | |||||||
\(948\) | 2.09205e7 | 0.756050 | ||||||||
\(949\) | −3.00286e7 | −1.08236 | ||||||||
\(950\) | 889018. | 0.0319596 | ||||||||
\(951\) | −8.17485e6 | −0.293109 | ||||||||
\(952\) | 2.02435e7 | 0.723924 | ||||||||
\(953\) | −3.77139e7 | −1.34514 | −0.672572 | − | 0.740032i | \(-0.734810\pi\) | ||||
−0.672572 | + | 0.740032i | \(0.734810\pi\) | |||||||
\(954\) | −2.63076e6 | −0.0935860 | ||||||||
\(955\) | −4.55007e7 | −1.61439 | ||||||||
\(956\) | 5.01391e7 | 1.77432 | ||||||||
\(957\) | −7.72829e6 | −0.272775 | ||||||||
\(958\) | −1.45806e6 | −0.0513287 | ||||||||
\(959\) | 1.98007e7 | 0.695239 | ||||||||
\(960\) | −1.22261e7 | −0.428163 | ||||||||
\(961\) | −2.14436e6 | −0.0749014 | ||||||||
\(962\) | 5.86399e6 | 0.204294 | ||||||||
\(963\) | 2.26822e6 | 0.0788169 | ||||||||
\(964\) | −2.81656e7 | −0.976173 | ||||||||
\(965\) | −2.27077e7 | −0.784973 | ||||||||
\(966\) | 1.31031e6 | 0.0451784 | ||||||||
\(967\) | −1.36407e7 | −0.469105 | −0.234553 | − | 0.972103i | \(-0.575362\pi\) | ||||
−0.234553 | + | 0.972103i | \(0.575362\pi\) | |||||||
\(968\) | −1.16641e7 | −0.400093 | ||||||||
\(969\) | 1.98185e7 | 0.678050 | ||||||||
\(970\) | 1.11624e6 | 0.0380914 | ||||||||
\(971\) | −3.96602e7 | −1.34992 | −0.674958 | − | 0.737856i | \(-0.735838\pi\) | ||||
−0.674958 | + | 0.737856i | \(0.735838\pi\) | |||||||
\(972\) | −1.79129e6 | −0.0608136 | ||||||||
\(973\) | 8.89843e7 | 3.01322 | ||||||||
\(974\) | 1.02351e6 | 0.0345698 | ||||||||
\(975\) | −2.94059e6 | −0.0990658 | ||||||||
\(976\) | 2.28976e7 | 0.769424 | ||||||||
\(977\) | −9.70600e6 | −0.325315 | −0.162657 | − | 0.986683i | \(-0.552007\pi\) | ||||
−0.162657 | + | 0.986683i | \(0.552007\pi\) | |||||||
\(978\) | −2.18722e6 | −0.0731214 | ||||||||
\(979\) | 3.80608e6 | 0.126917 | ||||||||
\(980\) | −5.14711e7 | −1.71198 | ||||||||
\(981\) | −5.19626e6 | −0.172393 | ||||||||
\(982\) | 4.72971e6 | 0.156515 | ||||||||
\(983\) | −2.88398e7 | −0.951937 | −0.475969 | − | 0.879462i | \(-0.657902\pi\) | ||||
−0.475969 | + | 0.879462i | \(0.657902\pi\) | |||||||
\(984\) | 9.03459e6 | 0.297455 | ||||||||
\(985\) | 1.57267e7 | 0.516473 | ||||||||
\(986\) | −1.03311e7 | −0.338419 | ||||||||
\(987\) | −4.41728e7 | −1.44332 | ||||||||
\(988\) | −5.00917e7 | −1.63258 | ||||||||
\(989\) | 2.22109e6 | 0.0722064 | ||||||||
\(990\) | −781575. | −0.0253444 | ||||||||
\(991\) | 3.94595e7 | 1.27634 | 0.638172 | − | 0.769894i | \(-0.279691\pi\) | ||||
0.638172 | + | 0.769894i | \(0.279691\pi\) | |||||||
\(992\) | 1.89998e7 | 0.613012 | ||||||||
\(993\) | −1.92910e7 | −0.620844 | ||||||||
\(994\) | 9.82104e6 | 0.315276 | ||||||||
\(995\) | −4.17374e7 | −1.33650 | ||||||||
\(996\) | 2.63813e7 | 0.842650 | ||||||||
\(997\) | 3.61342e7 | 1.15128 | 0.575639 | − | 0.817704i | \(-0.304753\pi\) | ||||
0.575639 | + | 0.817704i | \(0.304753\pi\) | |||||||
\(998\) | 6.56215e6 | 0.208555 | ||||||||
\(999\) | 3.74492e6 | 0.118722 |
(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 | 69.6.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 207.6.a.c.1.2 | 3 | |||
4.3 | odd | 2 | 1104.6.a.i.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
207.6.a.c.1.2 | 3 | 3.2 | odd | 2 | |||
1104.6.a.i.1.3 | 3 | 4.3 | odd | 2 |