Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(4.65113077458\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-4.83960\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.83960 | 1.03231 | 0.516153 | − | 0.856497i | \(-0.327364\pi\) | ||||
0.516153 | + | 0.856497i | \(0.327364\pi\) | |||||||
\(3\) | 15.9679 | 1.02434 | 0.512170 | − | 0.858884i | \(-0.328842\pi\) | ||||
0.512170 | + | 0.858884i | \(0.328842\pi\) | |||||||
\(4\) | 2.10095 | 0.0656545 | ||||||||
\(5\) | 31.5616 | 0.564590 | 0.282295 | − | 0.959328i | \(-0.408904\pi\) | ||||
0.282295 | + | 0.959328i | \(0.408904\pi\) | |||||||
\(6\) | 93.2461 | 1.05743 | ||||||||
\(7\) | 106.304 | 0.819986 | 0.409993 | − | 0.912089i | \(-0.365531\pi\) | ||||
0.409993 | + | 0.912089i | \(0.365531\pi\) | |||||||
\(8\) | −174.599 | −0.964530 | ||||||||
\(9\) | 11.9736 | 0.0492742 | ||||||||
\(10\) | 184.307 | 0.582830 | ||||||||
\(11\) | −152.796 | −0.380741 | −0.190371 | − | 0.981712i | \(-0.560969\pi\) | ||||
−0.190371 | + | 0.981712i | \(0.560969\pi\) | |||||||
\(12\) | 33.5477 | 0.0672526 | ||||||||
\(13\) | 325.745 | 0.534589 | 0.267294 | − | 0.963615i | \(-0.413870\pi\) | ||||
0.267294 | + | 0.963615i | \(0.413870\pi\) | |||||||
\(14\) | 620.776 | 0.846476 | ||||||||
\(15\) | 503.972 | 0.578333 | ||||||||
\(16\) | −1086.82 | −1.06134 | ||||||||
\(17\) | −664.939 | −0.558033 | −0.279016 | − | 0.960286i | \(-0.590008\pi\) | ||||
−0.279016 | + | 0.960286i | \(0.590008\pi\) | |||||||
\(18\) | 69.9212 | 0.0508660 | ||||||||
\(19\) | −1595.33 | −1.01383 | −0.506917 | − | 0.861995i | \(-0.669215\pi\) | ||||
−0.506917 | + | 0.861995i | \(0.669215\pi\) | |||||||
\(20\) | 66.3091 | 0.0370679 | ||||||||
\(21\) | 1697.46 | 0.839945 | ||||||||
\(22\) | −892.268 | −0.393041 | ||||||||
\(23\) | 719.327 | 0.283535 | 0.141768 | − | 0.989900i | \(-0.454721\pi\) | ||||
0.141768 | + | 0.989900i | \(0.454721\pi\) | |||||||
\(24\) | −2787.97 | −0.988007 | ||||||||
\(25\) | −2128.87 | −0.681238 | ||||||||
\(26\) | 1902.22 | 0.551859 | ||||||||
\(27\) | −3689.00 | −0.973867 | ||||||||
\(28\) | 223.340 | 0.0538358 | ||||||||
\(29\) | 841.000 | 0.185695 | ||||||||
\(30\) | 2942.99 | 0.597016 | ||||||||
\(31\) | 2059.61 | 0.384929 | 0.192464 | − | 0.981304i | \(-0.438352\pi\) | ||||
0.192464 | + | 0.981304i | \(0.438352\pi\) | |||||||
\(32\) | −759.420 | −0.131101 | ||||||||
\(33\) | −2439.83 | −0.390009 | ||||||||
\(34\) | −3882.98 | −0.576060 | ||||||||
\(35\) | 3355.13 | 0.462956 | ||||||||
\(36\) | 25.1559 | 0.00323508 | ||||||||
\(37\) | 14948.4 | 1.79511 | 0.897556 | − | 0.440901i | \(-0.145341\pi\) | ||||
0.897556 | + | 0.440901i | \(0.145341\pi\) | |||||||
\(38\) | −9316.11 | −1.04659 | ||||||||
\(39\) | 5201.47 | 0.547601 | ||||||||
\(40\) | −5510.60 | −0.544564 | ||||||||
\(41\) | 14673.9 | 1.36328 | 0.681641 | − | 0.731687i | \(-0.261267\pi\) | ||||
0.681641 | + | 0.731687i | \(0.261267\pi\) | |||||||
\(42\) | 9912.48 | 0.867080 | ||||||||
\(43\) | 10298.3 | 0.849367 | 0.424683 | − | 0.905342i | \(-0.360385\pi\) | ||||
0.424683 | + | 0.905342i | \(0.360385\pi\) | |||||||
\(44\) | −321.016 | −0.0249974 | ||||||||
\(45\) | 377.906 | 0.0278197 | ||||||||
\(46\) | 4200.58 | 0.292695 | ||||||||
\(47\) | 4588.36 | 0.302979 | 0.151490 | − | 0.988459i | \(-0.451593\pi\) | ||||
0.151490 | + | 0.988459i | \(0.451593\pi\) | |||||||
\(48\) | −17354.2 | −1.08718 | ||||||||
\(49\) | −5506.36 | −0.327623 | ||||||||
\(50\) | −12431.7 | −0.703246 | ||||||||
\(51\) | −10617.7 | −0.571616 | ||||||||
\(52\) | 684.373 | 0.0350982 | ||||||||
\(53\) | 8952.75 | 0.437791 | 0.218896 | − | 0.975748i | \(-0.429755\pi\) | ||||
0.218896 | + | 0.975748i | \(0.429755\pi\) | |||||||
\(54\) | −21542.3 | −1.00533 | ||||||||
\(55\) | −4822.48 | −0.214963 | ||||||||
\(56\) | −18560.6 | −0.790901 | ||||||||
\(57\) | −25474.1 | −1.03851 | ||||||||
\(58\) | 4911.10 | 0.191694 | ||||||||
\(59\) | −13734.5 | −0.513670 | −0.256835 | − | 0.966455i | \(-0.582680\pi\) | ||||
−0.256835 | + | 0.966455i | \(0.582680\pi\) | |||||||
\(60\) | 1058.82 | 0.0379702 | ||||||||
\(61\) | −33480.9 | −1.15205 | −0.576026 | − | 0.817431i | \(-0.695397\pi\) | ||||
−0.576026 | + | 0.817431i | \(0.695397\pi\) | |||||||
\(62\) | 12027.3 | 0.397364 | ||||||||
\(63\) | 1272.85 | 0.0404042 | ||||||||
\(64\) | 30343.4 | 0.926007 | ||||||||
\(65\) | 10281.0 | 0.301824 | ||||||||
\(66\) | −14247.6 | −0.402608 | ||||||||
\(67\) | 37519.2 | 1.02110 | 0.510548 | − | 0.859849i | \(-0.329442\pi\) | ||||
0.510548 | + | 0.859849i | \(0.329442\pi\) | |||||||
\(68\) | −1397.00 | −0.0366374 | ||||||||
\(69\) | 11486.1 | 0.290437 | ||||||||
\(70\) | 19592.6 | 0.477912 | ||||||||
\(71\) | −14763.7 | −0.347576 | −0.173788 | − | 0.984783i | \(-0.555601\pi\) | ||||
−0.173788 | + | 0.984783i | \(0.555601\pi\) | |||||||
\(72\) | −2090.58 | −0.0475264 | ||||||||
\(73\) | 63298.3 | 1.39022 | 0.695112 | − | 0.718901i | \(-0.255355\pi\) | ||||
0.695112 | + | 0.718901i | \(0.255355\pi\) | |||||||
\(74\) | 87292.9 | 1.85310 | ||||||||
\(75\) | −33993.5 | −0.697820 | ||||||||
\(76\) | −3351.71 | −0.0665629 | ||||||||
\(77\) | −16242.9 | −0.312203 | ||||||||
\(78\) | 30374.5 | 0.565292 | ||||||||
\(79\) | −27148.9 | −0.489423 | −0.244711 | − | 0.969596i | \(-0.578693\pi\) | ||||
−0.244711 | + | 0.969596i | \(0.578693\pi\) | |||||||
\(80\) | −34301.6 | −0.599224 | ||||||||
\(81\) | −61815.2 | −1.04685 | ||||||||
\(82\) | 85689.7 | 1.40732 | ||||||||
\(83\) | −54499.5 | −0.868356 | −0.434178 | − | 0.900827i | \(-0.642961\pi\) | ||||
−0.434178 | + | 0.900827i | \(0.642961\pi\) | |||||||
\(84\) | 3566.27 | 0.0551462 | ||||||||
\(85\) | −20986.5 | −0.315060 | ||||||||
\(86\) | 60138.1 | 0.876806 | ||||||||
\(87\) | 13429.0 | 0.190215 | ||||||||
\(88\) | 26678.0 | 0.367237 | ||||||||
\(89\) | −139829. | −1.87120 | −0.935602 | − | 0.353057i | \(-0.885142\pi\) | ||||
−0.935602 | + | 0.353057i | \(0.885142\pi\) | |||||||
\(90\) | 2206.82 | 0.0287185 | ||||||||
\(91\) | 34628.2 | 0.438355 | ||||||||
\(92\) | 1511.27 | 0.0186154 | ||||||||
\(93\) | 32887.6 | 0.394298 | ||||||||
\(94\) | 26794.2 | 0.312767 | ||||||||
\(95\) | −50351.2 | −0.572401 | ||||||||
\(96\) | −12126.3 | −0.134292 | ||||||||
\(97\) | 89845.2 | 0.969539 | 0.484770 | − | 0.874642i | \(-0.338903\pi\) | ||||
0.484770 | + | 0.874642i | \(0.338903\pi\) | |||||||
\(98\) | −32154.9 | −0.338207 | ||||||||
\(99\) | −1829.52 | −0.0187607 | ||||||||
\(100\) | −4472.64 | −0.0447264 | ||||||||
\(101\) | −107293. | −1.04657 | −0.523285 | − | 0.852158i | \(-0.675294\pi\) | ||||
−0.523285 | + | 0.852158i | \(0.675294\pi\) | |||||||
\(102\) | −62003.0 | −0.590082 | ||||||||
\(103\) | 160302. | 1.48884 | 0.744419 | − | 0.667713i | \(-0.232727\pi\) | ||||
0.744419 | + | 0.667713i | \(0.232727\pi\) | |||||||
\(104\) | −56874.7 | −0.515627 | ||||||||
\(105\) | 53574.4 | 0.474225 | ||||||||
\(106\) | 52280.5 | 0.451934 | ||||||||
\(107\) | 79970.2 | 0.675256 | 0.337628 | − | 0.941280i | \(-0.390375\pi\) | ||||
0.337628 | + | 0.941280i | \(0.390375\pi\) | |||||||
\(108\) | −7750.40 | −0.0639388 | ||||||||
\(109\) | −97964.0 | −0.789769 | −0.394885 | − | 0.918731i | \(-0.629215\pi\) | ||||
−0.394885 | + | 0.918731i | \(0.629215\pi\) | |||||||
\(110\) | −28161.3 | −0.221907 | ||||||||
\(111\) | 238695. | 1.83881 | ||||||||
\(112\) | −115533. | −0.870287 | ||||||||
\(113\) | −237682. | −1.75105 | −0.875527 | − | 0.483170i | \(-0.839485\pi\) | ||||
−0.875527 | + | 0.483170i | \(0.839485\pi\) | |||||||
\(114\) | −148759. | −1.07206 | ||||||||
\(115\) | 22703.1 | 0.160081 | ||||||||
\(116\) | 1766.90 | 0.0121917 | ||||||||
\(117\) | 3900.36 | 0.0263414 | ||||||||
\(118\) | −80204.2 | −0.530264 | ||||||||
\(119\) | −70686.0 | −0.457579 | ||||||||
\(120\) | −87992.7 | −0.557819 | ||||||||
\(121\) | −137704. | −0.855036 | ||||||||
\(122\) | −195515. | −1.18927 | ||||||||
\(123\) | 234311. | 1.39647 | ||||||||
\(124\) | 4327.12 | 0.0252723 | ||||||||
\(125\) | −165820. | −0.949210 | ||||||||
\(126\) | 7432.94 | 0.0417094 | ||||||||
\(127\) | 194961. | 1.07260 | 0.536299 | − | 0.844028i | \(-0.319822\pi\) | ||||
0.536299 | + | 0.844028i | \(0.319822\pi\) | |||||||
\(128\) | 201495. | 1.08702 | ||||||||
\(129\) | 164442. | 0.870041 | ||||||||
\(130\) | 60037.1 | 0.311574 | ||||||||
\(131\) | 350750. | 1.78575 | 0.892873 | − | 0.450309i | \(-0.148686\pi\) | ||||
0.892873 | + | 0.450309i | \(0.148686\pi\) | |||||||
\(132\) | −5125.95 | −0.0256059 | ||||||||
\(133\) | −169591. | −0.831330 | ||||||||
\(134\) | 219097. | 1.05408 | ||||||||
\(135\) | −116431. | −0.549836 | ||||||||
\(136\) | 116097. | 0.538239 | ||||||||
\(137\) | 185712. | 0.845356 | 0.422678 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422678 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(138\) | 67074.5 | 0.299819 | ||||||||
\(139\) | −316673. | −1.39019 | −0.695095 | − | 0.718918i | \(-0.744638\pi\) | ||||
−0.695095 | + | 0.718918i | \(0.744638\pi\) | |||||||
\(140\) | 7048.95 | 0.0303952 | ||||||||
\(141\) | 73266.4 | 0.310354 | ||||||||
\(142\) | −86214.2 | −0.358804 | ||||||||
\(143\) | −49772.6 | −0.203540 | ||||||||
\(144\) | −13013.1 | −0.0522969 | ||||||||
\(145\) | 26543.3 | 0.104842 | ||||||||
\(146\) | 369637. | 1.43514 | ||||||||
\(147\) | −87925.0 | −0.335598 | ||||||||
\(148\) | 31405.8 | 0.117857 | ||||||||
\(149\) | −326686. | −1.20549 | −0.602747 | − | 0.797932i | \(-0.705927\pi\) | ||||
−0.602747 | + | 0.797932i | \(0.705927\pi\) | |||||||
\(150\) | −198509. | −0.720363 | ||||||||
\(151\) | 427072. | 1.52426 | 0.762130 | − | 0.647424i | \(-0.224154\pi\) | ||||
0.762130 | + | 0.647424i | \(0.224154\pi\) | |||||||
\(152\) | 278543. | 0.977874 | ||||||||
\(153\) | −7961.74 | −0.0274966 | ||||||||
\(154\) | −94852.0 | −0.322289 | ||||||||
\(155\) | 65004.4 | 0.217327 | ||||||||
\(156\) | 10928.0 | 0.0359525 | ||||||||
\(157\) | 48668.5 | 0.157579 | 0.0787896 | − | 0.996891i | \(-0.474894\pi\) | ||||
0.0787896 | + | 0.996891i | \(0.474894\pi\) | |||||||
\(158\) | −158539. | −0.505234 | ||||||||
\(159\) | 142957. | 0.448447 | ||||||||
\(160\) | −23968.5 | −0.0740185 | ||||||||
\(161\) | 76467.7 | 0.232495 | ||||||||
\(162\) | −360976. | −1.08067 | ||||||||
\(163\) | −149764. | −0.441509 | −0.220755 | − | 0.975329i | \(-0.570852\pi\) | ||||
−0.220755 | + | 0.975329i | \(0.570852\pi\) | |||||||
\(164\) | 30829.0 | 0.0895056 | ||||||||
\(165\) | −77004.8 | −0.220195 | ||||||||
\(166\) | −318256. | −0.896408 | ||||||||
\(167\) | 371818. | 1.03167 | 0.515833 | − | 0.856689i | \(-0.327482\pi\) | ||||
0.515833 | + | 0.856689i | \(0.327482\pi\) | |||||||
\(168\) | −296374. | −0.810152 | ||||||||
\(169\) | −265183. | −0.714215 | ||||||||
\(170\) | −122553. | −0.325238 | ||||||||
\(171\) | −19101.9 | −0.0499559 | ||||||||
\(172\) | 21636.2 | 0.0557648 | ||||||||
\(173\) | −434068. | −1.10266 | −0.551331 | − | 0.834287i | \(-0.685880\pi\) | ||||
−0.551331 | + | 0.834287i | \(0.685880\pi\) | |||||||
\(174\) | 78420.0 | 0.196360 | ||||||||
\(175\) | −226308. | −0.558606 | ||||||||
\(176\) | 166061. | 0.404098 | ||||||||
\(177\) | −219312. | −0.526173 | ||||||||
\(178\) | −816543. | −1.93165 | ||||||||
\(179\) | 341482. | 0.796590 | 0.398295 | − | 0.917257i | \(-0.369602\pi\) | ||||
0.398295 | + | 0.917257i | \(0.369602\pi\) | |||||||
\(180\) | 793.961 | 0.00182649 | ||||||||
\(181\) | 542203. | 1.23017 | 0.615086 | − | 0.788460i | \(-0.289121\pi\) | ||||
0.615086 | + | 0.788460i | \(0.289121\pi\) | |||||||
\(182\) | 202215. | 0.452517 | ||||||||
\(183\) | −534619. | −1.18009 | ||||||||
\(184\) | −125593. | −0.273478 | ||||||||
\(185\) | 471796. | 1.01350 | ||||||||
\(186\) | 192050. | 0.407036 | ||||||||
\(187\) | 101600. | 0.212466 | ||||||||
\(188\) | 9639.89 | 0.0198920 | ||||||||
\(189\) | −392158. | −0.798558 | ||||||||
\(190\) | −294031. | −0.590893 | ||||||||
\(191\) | −454420. | −0.901310 | −0.450655 | − | 0.892698i | \(-0.648810\pi\) | ||||
−0.450655 | + | 0.892698i | \(0.648810\pi\) | |||||||
\(192\) | 484520. | 0.948547 | ||||||||
\(193\) | 791182. | 1.52891 | 0.764457 | − | 0.644674i | \(-0.223007\pi\) | ||||
0.764457 | + | 0.644674i | \(0.223007\pi\) | |||||||
\(194\) | 524660. | 1.00086 | ||||||||
\(195\) | 164166. | 0.309170 | ||||||||
\(196\) | −11568.6 | −0.0215099 | ||||||||
\(197\) | −519219. | −0.953201 | −0.476601 | − | 0.879120i | \(-0.658131\pi\) | ||||
−0.476601 | + | 0.879120i | \(0.658131\pi\) | |||||||
\(198\) | −10683.7 | −0.0193668 | ||||||||
\(199\) | −301548. | −0.539789 | −0.269895 | − | 0.962890i | \(-0.586989\pi\) | ||||
−0.269895 | + | 0.962890i | \(0.586989\pi\) | |||||||
\(200\) | 371697. | 0.657074 | ||||||||
\(201\) | 599103. | 1.04595 | ||||||||
\(202\) | −626548. | −1.08038 | ||||||||
\(203\) | 89402.1 | 0.152268 | ||||||||
\(204\) | −22307.2 | −0.0375292 | ||||||||
\(205\) | 463131. | 0.769696 | ||||||||
\(206\) | 936103. | 1.53693 | ||||||||
\(207\) | 8612.96 | 0.0139710 | ||||||||
\(208\) | −354025. | −0.567383 | ||||||||
\(209\) | 243760. | 0.386009 | ||||||||
\(210\) | 312853. | 0.489545 | ||||||||
\(211\) | −473908. | −0.732804 | −0.366402 | − | 0.930457i | \(-0.619410\pi\) | ||||
−0.366402 | + | 0.930457i | \(0.619410\pi\) | |||||||
\(212\) | 18809.2 | 0.0287430 | ||||||||
\(213\) | −235745. | −0.356036 | ||||||||
\(214\) | 466994. | 0.697071 | ||||||||
\(215\) | 325031. | 0.479544 | ||||||||
\(216\) | 644095. | 0.939324 | ||||||||
\(217\) | 218945. | 0.315636 | ||||||||
\(218\) | −572071. | −0.815283 | ||||||||
\(219\) | 1.01074e6 | 1.42406 | ||||||||
\(220\) | −10131.8 | −0.0141133 | ||||||||
\(221\) | −216601. | −0.298318 | ||||||||
\(222\) | 1.39388e6 | 1.89821 | ||||||||
\(223\) | −135893. | −0.182993 | −0.0914963 | − | 0.995805i | \(-0.529165\pi\) | ||||
−0.0914963 | + | 0.995805i | \(0.529165\pi\) | |||||||
\(224\) | −80729.7 | −0.107501 | ||||||||
\(225\) | −25490.3 | −0.0335675 | ||||||||
\(226\) | −1.38797e6 | −1.80762 | ||||||||
\(227\) | −1.21029e6 | −1.55893 | −0.779464 | − | 0.626448i | \(-0.784508\pi\) | ||||
−0.779464 | + | 0.626448i | \(0.784508\pi\) | |||||||
\(228\) | −53519.7 | −0.0681831 | ||||||||
\(229\) | −577029. | −0.727125 | −0.363563 | − | 0.931570i | \(-0.618440\pi\) | ||||
−0.363563 | + | 0.931570i | \(0.618440\pi\) | |||||||
\(230\) | 132577. | 0.165253 | ||||||||
\(231\) | −259365. | −0.319802 | ||||||||
\(232\) | −146837. | −0.179109 | ||||||||
\(233\) | −966231. | −1.16598 | −0.582990 | − | 0.812479i | \(-0.698117\pi\) | ||||
−0.582990 | + | 0.812479i | \(0.698117\pi\) | |||||||
\(234\) | 22776.5 | 0.0271924 | ||||||||
\(235\) | 144816. | 0.171059 | ||||||||
\(236\) | −28855.5 | −0.0337248 | ||||||||
\(237\) | −433510. | −0.501336 | ||||||||
\(238\) | −412778. | −0.472361 | ||||||||
\(239\) | 592337. | 0.670771 | 0.335386 | − | 0.942081i | \(-0.391133\pi\) | ||||
0.335386 | + | 0.942081i | \(0.391133\pi\) | |||||||
\(240\) | −547724. | −0.613810 | ||||||||
\(241\) | 405276. | 0.449478 | 0.224739 | − | 0.974419i | \(-0.427847\pi\) | ||||
0.224739 | + | 0.974419i | \(0.427847\pi\) | |||||||
\(242\) | −804139. | −0.882658 | ||||||||
\(243\) | −90630.9 | −0.0984601 | ||||||||
\(244\) | −70341.5 | −0.0756374 | ||||||||
\(245\) | −173789. | −0.184973 | ||||||||
\(246\) | 1.36828e6 | 1.44158 | ||||||||
\(247\) | −519672. | −0.541985 | ||||||||
\(248\) | −359605. | −0.371275 | ||||||||
\(249\) | −870243. | −0.889492 | ||||||||
\(250\) | −968324. | −0.979875 | ||||||||
\(251\) | 922052. | 0.923785 | 0.461893 | − | 0.886936i | \(-0.347171\pi\) | ||||
0.461893 | + | 0.886936i | \(0.347171\pi\) | |||||||
\(252\) | 2674.19 | 0.00265272 | ||||||||
\(253\) | −109910. | −0.107954 | ||||||||
\(254\) | 1.13849e6 | 1.10725 | ||||||||
\(255\) | −335110. | −0.322729 | ||||||||
\(256\) | 205661. | 0.196133 | ||||||||
\(257\) | 461687. | 0.436028 | 0.218014 | − | 0.975946i | \(-0.430042\pi\) | ||||
0.218014 | + | 0.975946i | \(0.430042\pi\) | |||||||
\(258\) | 960279. | 0.898148 | ||||||||
\(259\) | 1.58909e6 | 1.47197 | ||||||||
\(260\) | 21599.9 | 0.0198161 | ||||||||
\(261\) | 10069.8 | 0.00914999 | ||||||||
\(262\) | 2.04824e6 | 1.84344 | ||||||||
\(263\) | −1.78425e6 | −1.59062 | −0.795311 | − | 0.606202i | \(-0.792692\pi\) | ||||
−0.795311 | + | 0.606202i | \(0.792692\pi\) | |||||||
\(264\) | 425991. | 0.376175 | ||||||||
\(265\) | 282563. | 0.247173 | ||||||||
\(266\) | −990344. | −0.858187 | ||||||||
\(267\) | −2.23277e6 | −1.91675 | ||||||||
\(268\) | 78825.9 | 0.0670396 | ||||||||
\(269\) | −1.43033e6 | −1.20519 | −0.602596 | − | 0.798046i | \(-0.705867\pi\) | ||||
−0.602596 | + | 0.798046i | \(0.705867\pi\) | |||||||
\(270\) | −679909. | −0.567599 | ||||||||
\(271\) | 418695. | 0.346318 | 0.173159 | − | 0.984894i | \(-0.444603\pi\) | ||||
0.173159 | + | 0.984894i | \(0.444603\pi\) | |||||||
\(272\) | 722667. | 0.592265 | ||||||||
\(273\) | 552939. | 0.449025 | ||||||||
\(274\) | 1.08449e6 | 0.872666 | ||||||||
\(275\) | 325282. | 0.259375 | ||||||||
\(276\) | 24131.7 | 0.0190685 | ||||||||
\(277\) | 319476. | 0.250172 | 0.125086 | − | 0.992146i | \(-0.460079\pi\) | ||||
0.125086 | + | 0.992146i | \(0.460079\pi\) | |||||||
\(278\) | −1.84925e6 | −1.43510 | ||||||||
\(279\) | 24661.0 | 0.0189671 | ||||||||
\(280\) | −585802. | −0.446535 | ||||||||
\(281\) | 421076. | 0.318123 | 0.159061 | − | 0.987269i | \(-0.449153\pi\) | ||||
0.159061 | + | 0.987269i | \(0.449153\pi\) | |||||||
\(282\) | 427847. | 0.320380 | ||||||||
\(283\) | −129444. | −0.0960759 | −0.0480380 | − | 0.998846i | \(-0.515297\pi\) | ||||
−0.0480380 | + | 0.998846i | \(0.515297\pi\) | |||||||
\(284\) | −31017.7 | −0.0228199 | ||||||||
\(285\) | −804002. | −0.586334 | ||||||||
\(286\) | −290652. | −0.210116 | ||||||||
\(287\) | 1.55990e6 | 1.11787 | ||||||||
\(288\) | −9093.02 | −0.00645991 | ||||||||
\(289\) | −977713. | −0.688600 | ||||||||
\(290\) | 155002. | 0.108229 | ||||||||
\(291\) | 1.43464e6 | 0.993139 | ||||||||
\(292\) | 132986. | 0.0912746 | ||||||||
\(293\) | 1.71643e6 | 1.16804 | 0.584020 | − | 0.811740i | \(-0.301479\pi\) | ||||
0.584020 | + | 0.811740i | \(0.301479\pi\) | |||||||
\(294\) | −513447. | −0.346439 | ||||||||
\(295\) | −433483. | −0.290013 | ||||||||
\(296\) | −2.60998e6 | −1.73144 | ||||||||
\(297\) | 563665. | 0.370792 | ||||||||
\(298\) | −1.90772e6 | −1.24444 | ||||||||
\(299\) | 234317. | 0.151575 | ||||||||
\(300\) | −71418.6 | −0.0458150 | ||||||||
\(301\) | 1.09476e6 | 0.696469 | ||||||||
\(302\) | 2.49393e6 | 1.57350 | ||||||||
\(303\) | −1.71324e6 | −1.07204 | ||||||||
\(304\) | 1.73383e6 | 1.07603 | ||||||||
\(305\) | −1.05671e6 | −0.650437 | ||||||||
\(306\) | −46493.4 | −0.0283849 | ||||||||
\(307\) | 2.88448e6 | 1.74671 | 0.873356 | − | 0.487083i | \(-0.161939\pi\) | ||||
0.873356 | + | 0.487083i | \(0.161939\pi\) | |||||||
\(308\) | −34125.4 | −0.0204975 | ||||||||
\(309\) | 2.55969e6 | 1.52508 | ||||||||
\(310\) | 379600. | 0.224348 | ||||||||
\(311\) | −2.59382e6 | −1.52069 | −0.760343 | − | 0.649522i | \(-0.774969\pi\) | ||||
−0.760343 | + | 0.649522i | \(0.774969\pi\) | |||||||
\(312\) | −908169. | −0.528178 | ||||||||
\(313\) | 1.47281e6 | 0.849742 | 0.424871 | − | 0.905254i | \(-0.360319\pi\) | ||||
0.424871 | + | 0.905254i | \(0.360319\pi\) | |||||||
\(314\) | 284205. | 0.162670 | ||||||||
\(315\) | 40173.1 | 0.0228118 | ||||||||
\(316\) | −57038.3 | −0.0321328 | ||||||||
\(317\) | 661940. | 0.369973 | 0.184987 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184987 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(318\) | 834809. | 0.462935 | ||||||||
\(319\) | −128501. | −0.0707019 | ||||||||
\(320\) | 957685. | 0.522815 | ||||||||
\(321\) | 1.27696e6 | 0.691693 | ||||||||
\(322\) | 446541. | 0.240006 | ||||||||
\(323\) | 1.06080e6 | 0.565753 | ||||||||
\(324\) | −129870. | −0.0687302 | ||||||||
\(325\) | −693469. | −0.364182 | ||||||||
\(326\) | −874564. | −0.455772 | ||||||||
\(327\) | −1.56428e6 | −0.808993 | ||||||||
\(328\) | −2.56204e6 | −1.31493 | ||||||||
\(329\) | 487763. | 0.248439 | ||||||||
\(330\) | −449677. | −0.227309 | ||||||||
\(331\) | 3.40774e6 | 1.70961 | 0.854805 | − | 0.518949i | \(-0.173677\pi\) | ||||
0.854805 | + | 0.518949i | \(0.173677\pi\) | |||||||
\(332\) | −114501. | −0.0570115 | ||||||||
\(333\) | 178987. | 0.0884527 | ||||||||
\(334\) | 2.17127e6 | 1.06499 | ||||||||
\(335\) | 1.18417e6 | 0.576501 | ||||||||
\(336\) | −1.84483e6 | −0.891471 | ||||||||
\(337\) | −2.52588e6 | −1.21154 | −0.605771 | − | 0.795639i | \(-0.707135\pi\) | ||||
−0.605771 | + | 0.795639i | \(0.707135\pi\) | |||||||
\(338\) | −1.54856e6 | −0.737288 | ||||||||
\(339\) | −3.79527e6 | −1.79368 | ||||||||
\(340\) | −44091.5 | −0.0206851 | ||||||||
\(341\) | −314700. | −0.146558 | ||||||||
\(342\) | −111548. | −0.0515698 | ||||||||
\(343\) | −2.37201e6 | −1.08863 | ||||||||
\(344\) | −1.79807e6 | −0.819240 | ||||||||
\(345\) | 362520. | 0.163978 | ||||||||
\(346\) | −2.53478e6 | −1.13828 | ||||||||
\(347\) | −2.09340e6 | −0.933317 | −0.466658 | − | 0.884438i | \(-0.654542\pi\) | ||||
−0.466658 | + | 0.884438i | \(0.654542\pi\) | |||||||
\(348\) | 28213.6 | 0.0124885 | ||||||||
\(349\) | 2.90749e6 | 1.27777 | 0.638887 | − | 0.769300i | \(-0.279395\pi\) | ||||
0.638887 | + | 0.769300i | \(0.279395\pi\) | |||||||
\(350\) | −1.32155e6 | −0.576652 | ||||||||
\(351\) | −1.20168e6 | −0.520619 | ||||||||
\(352\) | 116036. | 0.0499157 | ||||||||
\(353\) | −8176.61 | −0.00349250 | −0.00174625 | − | 0.999998i | \(-0.500556\pi\) | ||||
−0.00174625 | + | 0.999998i | \(0.500556\pi\) | |||||||
\(354\) | −1.28069e6 | −0.543171 | ||||||||
\(355\) | −465966. | −0.196238 | ||||||||
\(356\) | −293772. | −0.122853 | ||||||||
\(357\) | −1.12871e6 | −0.468717 | ||||||||
\(358\) | 1.99412e6 | 0.822324 | ||||||||
\(359\) | 457001. | 0.187146 | 0.0935732 | − | 0.995612i | \(-0.470171\pi\) | ||||
0.0935732 | + | 0.995612i | \(0.470171\pi\) | |||||||
\(360\) | −65981.9 | −0.0268330 | ||||||||
\(361\) | 68986.9 | 0.0278611 | ||||||||
\(362\) | 3.16625e6 | 1.26991 | ||||||||
\(363\) | −2.19885e6 | −0.875848 | ||||||||
\(364\) | 72752.0 | 0.0287800 | ||||||||
\(365\) | 1.99779e6 | 0.784907 | ||||||||
\(366\) | −3.12196e6 | −1.21822 | ||||||||
\(367\) | 3.50049e6 | 1.35664 | 0.678318 | − | 0.734768i | \(-0.262709\pi\) | ||||
0.678318 | + | 0.734768i | \(0.262709\pi\) | |||||||
\(368\) | −781776. | −0.300928 | ||||||||
\(369\) | 175700. | 0.0671746 | ||||||||
\(370\) | 2.75510e6 | 1.04624 | ||||||||
\(371\) | 951717. | 0.358983 | ||||||||
\(372\) | 69095.0 | 0.0258875 | ||||||||
\(373\) | −2.17554e6 | −0.809645 | −0.404822 | − | 0.914395i | \(-0.632667\pi\) | ||||
−0.404822 | + | 0.914395i | \(0.632667\pi\) | |||||||
\(374\) | 593304. | 0.219330 | ||||||||
\(375\) | −2.64780e6 | −0.972315 | ||||||||
\(376\) | −801121. | −0.292232 | ||||||||
\(377\) | 273952. | 0.0992707 | ||||||||
\(378\) | −2.29004e6 | −0.824355 | ||||||||
\(379\) | 1.97581e6 | 0.706557 | 0.353278 | − | 0.935518i | \(-0.385067\pi\) | ||||
0.353278 | + | 0.935518i | \(0.385067\pi\) | |||||||
\(380\) | −105785. | −0.0375807 | ||||||||
\(381\) | 3.11311e6 | 1.09871 | ||||||||
\(382\) | −2.65363e6 | −0.930428 | ||||||||
\(383\) | 2.77434e6 | 0.966412 | 0.483206 | − | 0.875507i | \(-0.339472\pi\) | ||||
0.483206 | + | 0.875507i | \(0.339472\pi\) | |||||||
\(384\) | 3.21745e6 | 1.11348 | ||||||||
\(385\) | −512651. | −0.176267 | ||||||||
\(386\) | 4.62019e6 | 1.57831 | ||||||||
\(387\) | 123308. | 0.0418519 | ||||||||
\(388\) | 188760. | 0.0636547 | ||||||||
\(389\) | 2.12869e6 | 0.713245 | 0.356622 | − | 0.934249i | \(-0.383928\pi\) | ||||
0.356622 | + | 0.934249i | \(0.383928\pi\) | |||||||
\(390\) | 958667. | 0.319158 | ||||||||
\(391\) | −478309. | −0.158222 | ||||||||
\(392\) | 961402. | 0.316002 | ||||||||
\(393\) | 5.60074e6 | 1.82921 | ||||||||
\(394\) | −3.03203e6 | −0.983995 | ||||||||
\(395\) | −856861. | −0.276323 | ||||||||
\(396\) | −3843.73 | −0.00123173 | ||||||||
\(397\) | 2.73423e6 | 0.870680 | 0.435340 | − | 0.900266i | \(-0.356628\pi\) | ||||
0.435340 | + | 0.900266i | \(0.356628\pi\) | |||||||
\(398\) | −1.76092e6 | −0.557228 | ||||||||
\(399\) | −2.70801e6 | −0.851566 | ||||||||
\(400\) | 2.31369e6 | 0.723028 | ||||||||
\(401\) | −1.29206e6 | −0.401257 | −0.200628 | − | 0.979667i | \(-0.564298\pi\) | ||||
−0.200628 | + | 0.979667i | \(0.564298\pi\) | |||||||
\(402\) | 3.49852e6 | 1.07974 | ||||||||
\(403\) | 670908. | 0.205779 | ||||||||
\(404\) | −225417. | −0.0687120 | ||||||||
\(405\) | −1.95098e6 | −0.591039 | ||||||||
\(406\) | 522072. | 0.157187 | ||||||||
\(407\) | −2.28406e6 | −0.683473 | ||||||||
\(408\) | 1.85383e6 | 0.551340 | ||||||||
\(409\) | −2.78691e6 | −0.823787 | −0.411894 | − | 0.911232i | \(-0.635132\pi\) | ||||
−0.411894 | + | 0.911232i | \(0.635132\pi\) | |||||||
\(410\) | 2.70450e6 | 0.794561 | ||||||||
\(411\) | 2.96544e6 | 0.865933 | ||||||||
\(412\) | 336787. | 0.0977489 | ||||||||
\(413\) | −1.46004e6 | −0.421202 | ||||||||
\(414\) | 50296.2 | 0.0144223 | ||||||||
\(415\) | −1.72009e6 | −0.490265 | ||||||||
\(416\) | −247378. | −0.0700853 | ||||||||
\(417\) | −5.05660e6 | −1.42403 | ||||||||
\(418\) | 1.42346e6 | 0.398479 | ||||||||
\(419\) | −1.51265e6 | −0.420924 | −0.210462 | − | 0.977602i | \(-0.567497\pi\) | ||||
−0.210462 | + | 0.977602i | \(0.567497\pi\) | |||||||
\(420\) | 112557. | 0.0311350 | ||||||||
\(421\) | 2.55990e6 | 0.703911 | 0.351955 | − | 0.936017i | \(-0.385517\pi\) | ||||
0.351955 | + | 0.936017i | \(0.385517\pi\) | |||||||
\(422\) | −2.76743e6 | −0.756477 | ||||||||
\(423\) | 54939.3 | 0.0149291 | ||||||||
\(424\) | −1.56314e6 | −0.422263 | ||||||||
\(425\) | 1.41557e6 | 0.380153 | ||||||||
\(426\) | −1.37666e6 | −0.367538 | ||||||||
\(427\) | −3.55917e6 | −0.944666 | ||||||||
\(428\) | 168013. | 0.0443336 | ||||||||
\(429\) | −794763. | −0.208495 | ||||||||
\(430\) | 1.89805e6 | 0.495036 | ||||||||
\(431\) | −5.38406e6 | −1.39610 | −0.698051 | − | 0.716048i | \(-0.745949\pi\) | ||||
−0.698051 | + | 0.716048i | \(0.745949\pi\) | |||||||
\(432\) | 4.00927e6 | 1.03361 | ||||||||
\(433\) | 1.90699e6 | 0.488797 | 0.244398 | − | 0.969675i | \(-0.421410\pi\) | ||||
0.244398 | + | 0.969675i | \(0.421410\pi\) | |||||||
\(434\) | 1.27855e6 | 0.325833 | ||||||||
\(435\) | 423840. | 0.107394 | ||||||||
\(436\) | −205817. | −0.0518520 | ||||||||
\(437\) | −1.14757e6 | −0.287458 | ||||||||
\(438\) | 5.90232e6 | 1.47007 | ||||||||
\(439\) | −3.84641e6 | −0.952565 | −0.476283 | − | 0.879292i | \(-0.658016\pi\) | ||||
−0.476283 | + | 0.879292i | \(0.658016\pi\) | |||||||
\(440\) | 841998. | 0.207338 | ||||||||
\(441\) | −65931.1 | −0.0161434 | ||||||||
\(442\) | −1.26486e6 | −0.307955 | ||||||||
\(443\) | 1.43911e6 | 0.348406 | 0.174203 | − | 0.984710i | \(-0.444265\pi\) | ||||
0.174203 | + | 0.984710i | \(0.444265\pi\) | |||||||
\(444\) | 501485. | 0.120726 | ||||||||
\(445\) | −4.41321e6 | −1.05646 | ||||||||
\(446\) | −793558. | −0.188904 | ||||||||
\(447\) | −5.21649e6 | −1.23484 | ||||||||
\(448\) | 3.22564e6 | 0.759313 | ||||||||
\(449\) | −5.05146e6 | −1.18250 | −0.591249 | − | 0.806489i | \(-0.701365\pi\) | ||||
−0.591249 | + | 0.806489i | \(0.701365\pi\) | |||||||
\(450\) | −148853. | −0.0346519 | ||||||||
\(451\) | −2.24211e6 | −0.519058 | ||||||||
\(452\) | −499356. | −0.114965 | ||||||||
\(453\) | 6.81945e6 | 1.56136 | ||||||||
\(454\) | −7.06763e6 | −1.60929 | ||||||||
\(455\) | 1.09292e6 | 0.247491 | ||||||||
\(456\) | 4.44774e6 | 1.00168 | ||||||||
\(457\) | −3.02849e6 | −0.678323 | −0.339161 | − | 0.940728i | \(-0.610143\pi\) | ||||
−0.339161 | + | 0.940728i | \(0.610143\pi\) | |||||||
\(458\) | −3.36962e6 | −0.750615 | ||||||||
\(459\) | 2.45296e6 | 0.543450 | ||||||||
\(460\) | 47697.9 | 0.0105101 | ||||||||
\(461\) | −3.54068e6 | −0.775951 | −0.387976 | − | 0.921670i | \(-0.626826\pi\) | ||||
−0.387976 | + | 0.921670i | \(0.626826\pi\) | |||||||
\(462\) | −1.51459e6 | −0.330133 | ||||||||
\(463\) | 3.78475e6 | 0.820512 | 0.410256 | − | 0.911970i | \(-0.365439\pi\) | ||||
0.410256 | + | 0.911970i | \(0.365439\pi\) | |||||||
\(464\) | −914012. | −0.197087 | ||||||||
\(465\) | 1.03798e6 | 0.222617 | ||||||||
\(466\) | −5.64240e6 | −1.20365 | ||||||||
\(467\) | −3.93030e6 | −0.833938 | −0.416969 | − | 0.908921i | \(-0.636908\pi\) | ||||
−0.416969 | + | 0.908921i | \(0.636908\pi\) | |||||||
\(468\) | 8194.44 | 0.00172944 | ||||||||
\(469\) | 3.98846e6 | 0.837285 | ||||||||
\(470\) | 845666. | 0.176585 | ||||||||
\(471\) | 777134. | 0.161415 | ||||||||
\(472\) | 2.39803e6 | 0.495450 | ||||||||
\(473\) | −1.57354e6 | −0.323389 | ||||||||
\(474\) | −2.53153e6 | −0.517531 | ||||||||
\(475\) | 3.39625e6 | 0.690663 | ||||||||
\(476\) | −148507. | −0.0300421 | ||||||||
\(477\) | 107197. | 0.0215718 | ||||||||
\(478\) | 3.45901e6 | 0.692441 | ||||||||
\(479\) | −3.65493e6 | −0.727848 | −0.363924 | − | 0.931429i | \(-0.618563\pi\) | ||||
−0.363924 | + | 0.931429i | \(0.618563\pi\) | |||||||
\(480\) | −382726. | −0.0758202 | ||||||||
\(481\) | 4.86938e6 | 0.959647 | ||||||||
\(482\) | 2.36665e6 | 0.463999 | ||||||||
\(483\) | 1.22103e6 | 0.238154 | ||||||||
\(484\) | −289309. | −0.0561370 | ||||||||
\(485\) | 2.83565e6 | 0.547392 | ||||||||
\(486\) | −529248. | −0.101641 | ||||||||
\(487\) | −3.90232e6 | −0.745591 | −0.372796 | − | 0.927913i | \(-0.621601\pi\) | ||||
−0.372796 | + | 0.927913i | \(0.621601\pi\) | |||||||
\(488\) | 5.84571e6 | 1.11119 | ||||||||
\(489\) | −2.39142e6 | −0.452256 | ||||||||
\(490\) | −1.01486e6 | −0.190948 | ||||||||
\(491\) | 8.22645e6 | 1.53996 | 0.769979 | − | 0.638069i | \(-0.220267\pi\) | ||||
0.769979 | + | 0.638069i | \(0.220267\pi\) | |||||||
\(492\) | 492275. | 0.0916843 | ||||||||
\(493\) | −559214. | −0.103624 | ||||||||
\(494\) | −3.03468e6 | −0.559494 | ||||||||
\(495\) | −57742.6 | −0.0105921 | ||||||||
\(496\) | −2.23841e6 | −0.408542 | ||||||||
\(497\) | −1.56945e6 | −0.285007 | ||||||||
\(498\) | −5.08187e6 | −0.918228 | ||||||||
\(499\) | 1.95126e6 | 0.350803 | 0.175401 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175401 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(500\) | −348379. | −0.0623200 | ||||||||
\(501\) | 5.93715e6 | 1.05678 | ||||||||
\(502\) | 5.38442e6 | 0.953629 | ||||||||
\(503\) | 6.74097e6 | 1.18796 | 0.593981 | − | 0.804479i | \(-0.297555\pi\) | ||||
0.593981 | + | 0.804479i | \(0.297555\pi\) | |||||||
\(504\) | −222238. | −0.0389710 | ||||||||
\(505\) | −3.38633e6 | −0.590883 | ||||||||
\(506\) | −641832. | −0.111441 | ||||||||
\(507\) | −4.23441e6 | −0.731599 | ||||||||
\(508\) | 409601. | 0.0704210 | ||||||||
\(509\) | 2.57165e6 | 0.439964 | 0.219982 | − | 0.975504i | \(-0.429400\pi\) | ||||
0.219982 | + | 0.975504i | \(0.429400\pi\) | |||||||
\(510\) | −1.95691e6 | −0.333155 | ||||||||
\(511\) | 6.72889e6 | 1.13996 | ||||||||
\(512\) | −5.24686e6 | −0.884554 | ||||||||
\(513\) | 5.88519e6 | 0.987341 | ||||||||
\(514\) | 2.69607e6 | 0.450114 | ||||||||
\(515\) | 5.05940e6 | 0.840583 | ||||||||
\(516\) | 345485. | 0.0571221 | ||||||||
\(517\) | −701083. | −0.115357 | ||||||||
\(518\) | 9.27963e6 | 1.51952 | ||||||||
\(519\) | −6.93115e6 | −1.12950 | ||||||||
\(520\) | −1.79505e6 | −0.291118 | ||||||||
\(521\) | 1.25025e6 | 0.201791 | 0.100896 | − | 0.994897i | \(-0.467829\pi\) | ||||
0.100896 | + | 0.994897i | \(0.467829\pi\) | |||||||
\(522\) | 58803.8 | 0.00944559 | ||||||||
\(523\) | −188395. | −0.0301172 | −0.0150586 | − | 0.999887i | \(-0.504793\pi\) | ||||
−0.0150586 | + | 0.999887i | \(0.504793\pi\) | |||||||
\(524\) | 736907. | 0.117242 | ||||||||
\(525\) | −3.61367e6 | −0.572202 | ||||||||
\(526\) | −1.04193e7 | −1.64201 | ||||||||
\(527\) | −1.36951e6 | −0.214803 | ||||||||
\(528\) | 2.65165e6 | 0.413934 | ||||||||
\(529\) | −5.91891e6 | −0.919608 | ||||||||
\(530\) | 1.65005e6 | 0.255158 | ||||||||
\(531\) | −164452. | −0.0253107 | ||||||||
\(532\) | −356301. | −0.0545806 | ||||||||
\(533\) | 4.77995e6 | 0.728795 | ||||||||
\(534\) | −1.30385e7 | −1.97867 | ||||||||
\(535\) | 2.52398e6 | 0.381243 | ||||||||
\(536\) | −6.55080e6 | −0.984878 | ||||||||
\(537\) | 5.45274e6 | 0.815980 | ||||||||
\(538\) | −8.35258e6 | −1.24413 | ||||||||
\(539\) | 841349. | 0.124740 | ||||||||
\(540\) | −244615. | −0.0360992 | ||||||||
\(541\) | −7.69990e6 | −1.13108 | −0.565538 | − | 0.824722i | \(-0.691331\pi\) | ||||
−0.565538 | + | 0.824722i | \(0.691331\pi\) | |||||||
\(542\) | 2.44501e6 | 0.357506 | ||||||||
\(543\) | 8.65785e6 | 1.26012 | ||||||||
\(544\) | 504968. | 0.0731588 | ||||||||
\(545\) | −3.09190e6 | −0.445896 | ||||||||
\(546\) | 3.22895e6 | 0.463531 | ||||||||
\(547\) | 1.21820e7 | 1.74081 | 0.870406 | − | 0.492334i | \(-0.163856\pi\) | ||||
0.870406 | + | 0.492334i | \(0.163856\pi\) | |||||||
\(548\) | 390172. | 0.0555015 | ||||||||
\(549\) | −400888. | −0.0567664 | ||||||||
\(550\) | 1.89952e6 | 0.267755 | ||||||||
\(551\) | −1.34167e6 | −0.188264 | ||||||||
\(552\) | −2.00546e6 | −0.280135 | ||||||||
\(553\) | −2.88605e6 | −0.401320 | ||||||||
\(554\) | 1.86561e6 | 0.258254 | ||||||||
\(555\) | 7.53359e6 | 1.03817 | ||||||||
\(556\) | −665313. | −0.0912723 | ||||||||
\(557\) | 5.21687e6 | 0.712479 | 0.356239 | − | 0.934395i | \(-0.384059\pi\) | ||||
0.356239 | + | 0.934395i | \(0.384059\pi\) | |||||||
\(558\) | 144010. | 0.0195798 | ||||||||
\(559\) | 3.35463e6 | 0.454062 | ||||||||
\(560\) | −3.64641e6 | −0.491356 | ||||||||
\(561\) | 1.62234e6 | 0.217638 | ||||||||
\(562\) | 2.45892e6 | 0.328400 | ||||||||
\(563\) | −782547. | −0.104049 | −0.0520247 | − | 0.998646i | \(-0.516567\pi\) | ||||
−0.0520247 | + | 0.998646i | \(0.516567\pi\) | |||||||
\(564\) | 153929. | 0.0203761 | ||||||||
\(565\) | −7.50160e6 | −0.988627 | ||||||||
\(566\) | −755899. | −0.0991797 | ||||||||
\(567\) | −6.57123e6 | −0.858399 | ||||||||
\(568\) | 2.57772e6 | 0.335247 | ||||||||
\(569\) | 1.01820e7 | 1.31841 | 0.659206 | − | 0.751962i | \(-0.270893\pi\) | ||||
0.659206 | + | 0.751962i | \(0.270893\pi\) | |||||||
\(570\) | −4.69505e6 | −0.605276 | ||||||||
\(571\) | −1.56900e6 | −0.201388 | −0.100694 | − | 0.994917i | \(-0.532106\pi\) | ||||
−0.100694 | + | 0.994917i | \(0.532106\pi\) | |||||||
\(572\) | −104569. | −0.0133633 | ||||||||
\(573\) | −7.25614e6 | −0.923249 | ||||||||
\(574\) | 9.10919e6 | 1.15399 | ||||||||
\(575\) | −1.53135e6 | −0.193155 | ||||||||
\(576\) | 363321. | 0.0456283 | ||||||||
\(577\) | −1.53116e7 | −1.91462 | −0.957308 | − | 0.289069i | \(-0.906654\pi\) | ||||
−0.957308 | + | 0.289069i | \(0.906654\pi\) | |||||||
\(578\) | −5.70945e6 | −0.710845 | ||||||||
\(579\) | 1.26335e7 | 1.56613 | ||||||||
\(580\) | 55766.0 | 0.00688334 | ||||||||
\(581\) | −5.79355e6 | −0.712040 | ||||||||
\(582\) | 8.37771e6 | 1.02522 | ||||||||
\(583\) | −1.36794e6 | −0.166685 | ||||||||
\(584\) | −1.10518e7 | −1.34091 | ||||||||
\(585\) | 123101. | 0.0148721 | ||||||||
\(586\) | 1.00233e7 | 1.20577 | ||||||||
\(587\) | 3.65745e6 | 0.438110 | 0.219055 | − | 0.975712i | \(-0.429703\pi\) | ||||
0.219055 | + | 0.975712i | \(0.429703\pi\) | |||||||
\(588\) | −184726. | −0.0220335 | ||||||||
\(589\) | −3.28576e6 | −0.390254 | ||||||||
\(590\) | −2.53137e6 | −0.299382 | ||||||||
\(591\) | −8.29083e6 | −0.976403 | ||||||||
\(592\) | −1.62462e7 | −1.90523 | ||||||||
\(593\) | −7.18479e6 | −0.839029 | −0.419515 | − | 0.907749i | \(-0.637800\pi\) | ||||
−0.419515 | + | 0.907749i | \(0.637800\pi\) | |||||||
\(594\) | 3.29158e6 | 0.382770 | ||||||||
\(595\) | −2.23096e6 | −0.258345 | ||||||||
\(596\) | −686350. | −0.0791462 | ||||||||
\(597\) | −4.81509e6 | −0.552928 | ||||||||
\(598\) | 1.36832e6 | 0.156471 | ||||||||
\(599\) | 2.35482e6 | 0.268158 | 0.134079 | − | 0.990971i | \(-0.457192\pi\) | ||||
0.134079 | + | 0.990971i | \(0.457192\pi\) | |||||||
\(600\) | 5.93522e6 | 0.673068 | ||||||||
\(601\) | −7.49135e6 | −0.846007 | −0.423003 | − | 0.906128i | \(-0.639024\pi\) | ||||
−0.423003 | + | 0.906128i | \(0.639024\pi\) | |||||||
\(602\) | 6.39295e6 | 0.718969 | ||||||||
\(603\) | 449241. | 0.0503137 | ||||||||
\(604\) | 897256. | 0.100075 | ||||||||
\(605\) | −4.34616e6 | −0.482745 | ||||||||
\(606\) | −1.00047e7 | −1.10668 | ||||||||
\(607\) | 248110. | 0.0273320 | 0.0136660 | − | 0.999907i | \(-0.495650\pi\) | ||||
0.0136660 | + | 0.999907i | \(0.495650\pi\) | |||||||
\(608\) | 1.21153e6 | 0.132915 | ||||||||
\(609\) | 1.42756e6 | 0.155974 | ||||||||
\(610\) | −6.17075e6 | −0.671450 | ||||||||
\(611\) | 1.49464e6 | 0.161969 | ||||||||
\(612\) | −16727.2 | −0.00180528 | ||||||||
\(613\) | −1.97712e6 | −0.212511 | −0.106256 | − | 0.994339i | \(-0.533886\pi\) | ||||
−0.106256 | + | 0.994339i | \(0.533886\pi\) | |||||||
\(614\) | 1.68442e7 | 1.80314 | ||||||||
\(615\) | 7.39522e6 | 0.788431 | ||||||||
\(616\) | 2.83599e6 | 0.301129 | ||||||||
\(617\) | 1.43605e7 | 1.51865 | 0.759323 | − | 0.650714i | \(-0.225530\pi\) | ||||
0.759323 | + | 0.650714i | \(0.225530\pi\) | |||||||
\(618\) | 1.49476e7 | 1.57435 | ||||||||
\(619\) | −3.63487e6 | −0.381297 | −0.190648 | − | 0.981658i | \(-0.561059\pi\) | ||||
−0.190648 | + | 0.981658i | \(0.561059\pi\) | |||||||
\(620\) | 136571. | 0.0142685 | ||||||||
\(621\) | −2.65360e6 | −0.276126 | ||||||||
\(622\) | −1.51469e7 | −1.56981 | ||||||||
\(623\) | −1.48644e7 | −1.53436 | ||||||||
\(624\) | −5.65304e6 | −0.581193 | ||||||||
\(625\) | 1.41917e6 | 0.145323 | ||||||||
\(626\) | 8.60065e6 | 0.877193 | ||||||||
\(627\) | 3.89234e6 | 0.395405 | ||||||||
\(628\) | 102250. | 0.0103458 | ||||||||
\(629\) | −9.93980e6 | −1.00173 | ||||||||
\(630\) | 234595. | 0.0235487 | ||||||||
\(631\) | −1.71093e6 | −0.171065 | −0.0855323 | − | 0.996335i | \(-0.527259\pi\) | ||||
−0.0855323 | + | 0.996335i | \(0.527259\pi\) | |||||||
\(632\) | 4.74015e6 | 0.472063 | ||||||||
\(633\) | −7.56731e6 | −0.750641 | ||||||||
\(634\) | 3.86547e6 | 0.381926 | ||||||||
\(635\) | 6.15326e6 | 0.605579 | ||||||||
\(636\) | 300344. | 0.0294426 | ||||||||
\(637\) | −1.79367e6 | −0.175144 | ||||||||
\(638\) | −750397. | −0.0729860 | ||||||||
\(639\) | −176775. | −0.0171265 | ||||||||
\(640\) | 6.35949e6 | 0.613723 | ||||||||
\(641\) | −7.33888e6 | −0.705480 | −0.352740 | − | 0.935721i | \(-0.614750\pi\) | ||||
−0.352740 | + | 0.935721i | \(0.614750\pi\) | |||||||
\(642\) | 7.45691e6 | 0.714038 | ||||||||
\(643\) | 1.65108e7 | 1.57485 | 0.787426 | − | 0.616409i | \(-0.211413\pi\) | ||||
0.787426 | + | 0.616409i | \(0.211413\pi\) | |||||||
\(644\) | 160654. | 0.0152643 | ||||||||
\(645\) | 5.19006e6 | 0.491217 | ||||||||
\(646\) | 6.19464e6 | 0.584030 | ||||||||
\(647\) | −4.75302e6 | −0.446384 | −0.223192 | − | 0.974774i | \(-0.571648\pi\) | ||||
−0.223192 | + | 0.974774i | \(0.571648\pi\) | |||||||
\(648\) | 1.07928e7 | 1.00971 | ||||||||
\(649\) | 2.09858e6 | 0.195575 | ||||||||
\(650\) | −4.04958e6 | −0.375947 | ||||||||
\(651\) | 3.49610e6 | 0.323319 | ||||||||
\(652\) | −314647. | −0.0289871 | ||||||||
\(653\) | 2.06957e7 | 1.89932 | 0.949658 | − | 0.313290i | \(-0.101431\pi\) | ||||
0.949658 | + | 0.313290i | \(0.101431\pi\) | |||||||
\(654\) | −9.13477e6 | −0.835128 | ||||||||
\(655\) | 1.10702e7 | 1.00821 | ||||||||
\(656\) | −1.59478e7 | −1.44691 | ||||||||
\(657\) | 757911. | 0.0685022 | ||||||||
\(658\) | 2.84834e6 | 0.256465 | ||||||||
\(659\) | 1.75250e7 | 1.57197 | 0.785987 | − | 0.618244i | \(-0.212155\pi\) | ||||
0.785987 | + | 0.618244i | \(0.212155\pi\) | |||||||
\(660\) | −161783. | −0.0144568 | ||||||||
\(661\) | 5.06876e6 | 0.451230 | 0.225615 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225615 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(662\) | 1.98999e7 | 1.76484 | ||||||||
\(663\) | −3.45866e6 | −0.305579 | ||||||||
\(664\) | 9.51554e6 | 0.837555 | ||||||||
\(665\) | −5.35256e6 | −0.469361 | ||||||||
\(666\) | 1.04521e6 | 0.0913102 | ||||||||
\(667\) | 604954. | 0.0526511 | ||||||||
\(668\) | 781170. | 0.0677336 | ||||||||
\(669\) | −2.16992e6 | −0.187447 | ||||||||
\(670\) | 6.91505e6 | 0.595125 | ||||||||
\(671\) | 5.11574e6 | 0.438634 | ||||||||
\(672\) | −1.28908e6 | −0.110118 | ||||||||
\(673\) | 1.07503e7 | 0.914922 | 0.457461 | − | 0.889230i | \(-0.348759\pi\) | ||||
0.457461 | + | 0.889230i | \(0.348759\pi\) | |||||||
\(674\) | −1.47501e7 | −1.25068 | ||||||||
\(675\) | 7.85340e6 | 0.663435 | ||||||||
\(676\) | −557135. | −0.0468914 | ||||||||
\(677\) | −6.95239e6 | −0.582992 | −0.291496 | − | 0.956572i | \(-0.594153\pi\) | ||||
−0.291496 | + | 0.956572i | \(0.594153\pi\) | |||||||
\(678\) | −2.21629e7 | −1.85162 | ||||||||
\(679\) | 9.55094e6 | 0.795009 | ||||||||
\(680\) | 3.66422e6 | 0.303885 | ||||||||
\(681\) | −1.93258e7 | −1.59687 | ||||||||
\(682\) | −1.83772e6 | −0.151293 | ||||||||
\(683\) | −1.26571e7 | −1.03821 | −0.519103 | − | 0.854711i | \(-0.673734\pi\) | ||||
−0.519103 | + | 0.854711i | \(0.673734\pi\) | |||||||
\(684\) | −40132.1 | −0.00327983 | ||||||||
\(685\) | 5.86137e6 | 0.477280 | ||||||||
\(686\) | −1.38516e7 | −1.12380 | ||||||||
\(687\) | −9.21394e6 | −0.744824 | ||||||||
\(688\) | −1.11924e7 | −0.901470 | ||||||||
\(689\) | 2.91632e6 | 0.234038 | ||||||||
\(690\) | 2.11697e6 | 0.169275 | ||||||||
\(691\) | −7.61067e6 | −0.606356 | −0.303178 | − | 0.952934i | \(-0.598048\pi\) | ||||
−0.303178 | + | 0.952934i | \(0.598048\pi\) | |||||||
\(692\) | −911952. | −0.0723947 | ||||||||
\(693\) | −194486. | −0.0153835 | ||||||||
\(694\) | −1.22246e7 | −0.963468 | ||||||||
\(695\) | −9.99470e6 | −0.784888 | ||||||||
\(696\) | −2.34468e6 | −0.183468 | ||||||||
\(697\) | −9.75724e6 | −0.760756 | ||||||||
\(698\) | 1.69786e7 | 1.31905 | ||||||||
\(699\) | −1.54287e7 | −1.19436 | ||||||||
\(700\) | −475461. | −0.0366750 | ||||||||
\(701\) | −1.63413e7 | −1.25600 | −0.628002 | − | 0.778211i | \(-0.716127\pi\) | ||||
−0.628002 | + | 0.778211i | \(0.716127\pi\) | |||||||
\(702\) | −7.01731e6 | −0.537437 | ||||||||
\(703\) | −2.38477e7 | −1.81995 | ||||||||
\(704\) | −4.63635e6 | −0.352569 | ||||||||
\(705\) | 2.31240e6 | 0.175223 | ||||||||
\(706\) | −47748.1 | −0.00360533 | ||||||||
\(707\) | −1.14057e7 | −0.858172 | ||||||||
\(708\) | −460762. | −0.0345456 | ||||||||
\(709\) | 1.11269e7 | 0.831300 | 0.415650 | − | 0.909525i | \(-0.363554\pi\) | ||||
0.415650 | + | 0.909525i | \(0.363554\pi\) | |||||||
\(710\) | −2.72105e6 | −0.202577 | ||||||||
\(711\) | −325071. | −0.0241159 | ||||||||
\(712\) | 2.44139e7 | 1.80483 | ||||||||
\(713\) | 1.48153e6 | 0.109141 | ||||||||
\(714\) | −6.59120e6 | −0.483859 | ||||||||
\(715\) | −1.57090e6 | −0.114917 | ||||||||
\(716\) | 717434. | 0.0522997 | ||||||||
\(717\) | 9.45838e6 | 0.687098 | ||||||||
\(718\) | 2.66871e6 | 0.193192 | ||||||||
\(719\) | 1.28895e7 | 0.929849 | 0.464924 | − | 0.885350i | \(-0.346081\pi\) | ||||
0.464924 | + | 0.885350i | \(0.346081\pi\) | |||||||
\(720\) | −410715. | −0.0295263 | ||||||||
\(721\) | 1.70409e7 | 1.22083 | ||||||||
\(722\) | 402856. | 0.0287612 | ||||||||
\(723\) | 6.47141e6 | 0.460419 | ||||||||
\(724\) | 1.13914e6 | 0.0807664 | ||||||||
\(725\) | −1.79038e6 | −0.126503 | ||||||||
\(726\) | −1.28404e7 | −0.904143 | ||||||||
\(727\) | −2.32214e7 | −1.62949 | −0.814745 | − | 0.579820i | \(-0.803123\pi\) | ||||
−0.814745 | + | 0.579820i | \(0.803123\pi\) | |||||||
\(728\) | −6.04603e6 | −0.422807 | ||||||||
\(729\) | 1.35739e7 | 0.945990 | ||||||||
\(730\) | 1.16663e7 | 0.810264 | ||||||||
\(731\) | −6.84776e6 | −0.473974 | ||||||||
\(732\) | −1.12321e6 | −0.0774785 | ||||||||
\(733\) | −8.72009e6 | −0.599461 | −0.299731 | − | 0.954024i | \(-0.596897\pi\) | ||||
−0.299731 | + | 0.954024i | \(0.596897\pi\) | |||||||
\(734\) | 2.04415e7 | 1.40046 | ||||||||
\(735\) | −2.77505e6 | −0.189475 | ||||||||
\(736\) | −546271. | −0.0371718 | ||||||||
\(737\) | −5.73279e6 | −0.388774 | ||||||||
\(738\) | 1.02602e6 | 0.0693447 | ||||||||
\(739\) | 2.49740e7 | 1.68220 | 0.841098 | − | 0.540882i | \(-0.181910\pi\) | ||||
0.841098 | + | 0.540882i | \(0.181910\pi\) | |||||||
\(740\) | 991217. | 0.0665410 | ||||||||
\(741\) | −8.29807e6 | −0.555177 | ||||||||
\(742\) | 5.55765e6 | 0.370580 | ||||||||
\(743\) | −288063. | −0.0191433 | −0.00957164 | − | 0.999954i | \(-0.503047\pi\) | ||||
−0.00957164 | + | 0.999954i | \(0.503047\pi\) | |||||||
\(744\) | −5.74213e6 | −0.380312 | ||||||||
\(745\) | −1.03107e7 | −0.680611 | ||||||||
\(746\) | −1.27043e7 | −0.835801 | ||||||||
\(747\) | −652558. | −0.0427875 | ||||||||
\(748\) | 213456. | 0.0139494 | ||||||||
\(749\) | 8.50119e6 | 0.553701 | ||||||||
\(750\) | −1.54621e7 | −1.00373 | ||||||||
\(751\) | 2.19870e7 | 1.42255 | 0.711274 | − | 0.702915i | \(-0.248119\pi\) | ||||
0.711274 | + | 0.702915i | \(0.248119\pi\) | |||||||
\(752\) | −4.98670e6 | −0.321565 | ||||||||
\(753\) | 1.47232e7 | 0.946271 | ||||||||
\(754\) | 1.59977e6 | 0.102478 | ||||||||
\(755\) | 1.34791e7 | 0.860582 | ||||||||
\(756\) | −823902. | −0.0524289 | ||||||||
\(757\) | −6.72062e6 | −0.426255 | −0.213128 | − | 0.977024i | \(-0.568365\pi\) | ||||
−0.213128 | + | 0.977024i | \(0.568365\pi\) | |||||||
\(758\) | 1.15379e7 | 0.729382 | ||||||||
\(759\) | −1.75504e6 | −0.110581 | ||||||||
\(760\) | 8.79124e6 | 0.552098 | ||||||||
\(761\) | −1.10936e7 | −0.694400 | −0.347200 | − | 0.937791i | \(-0.612868\pi\) | ||||
−0.347200 | + | 0.937791i | \(0.612868\pi\) | |||||||
\(762\) | 1.81793e7 | 1.13420 | ||||||||
\(763\) | −1.04140e7 | −0.647600 | ||||||||
\(764\) | −954712. | −0.0591751 | ||||||||
\(765\) | −251285. | −0.0155243 | ||||||||
\(766\) | 1.62010e7 | 0.997632 | ||||||||
\(767\) | −4.47396e6 | −0.274602 | ||||||||
\(768\) | 3.28397e6 | 0.200907 | ||||||||
\(769\) | 6.42928e6 | 0.392054 | 0.196027 | − | 0.980598i | \(-0.437196\pi\) | ||||
0.196027 | + | 0.980598i | \(0.437196\pi\) | |||||||
\(770\) | −2.99368e6 | −0.181961 | ||||||||
\(771\) | 7.37217e6 | 0.446642 | ||||||||
\(772\) | 1.66223e6 | 0.100380 | ||||||||
\(773\) | −1.38614e7 | −0.834371 | −0.417185 | − | 0.908821i | \(-0.636983\pi\) | ||||
−0.417185 | + | 0.908821i | \(0.636983\pi\) | |||||||
\(774\) | 720071. | 0.0432039 | ||||||||
\(775\) | −4.38463e6 | −0.262228 | ||||||||
\(776\) | −1.56868e7 | −0.935150 | ||||||||
\(777\) | 2.53743e7 | 1.50780 | ||||||||
\(778\) | 1.24307e7 | 0.736287 | ||||||||
\(779\) | −2.34097e7 | −1.38214 | ||||||||
\(780\) | 344905. | 0.0202984 | ||||||||
\(781\) | 2.25584e6 | 0.132337 | ||||||||
\(782\) | −2.79313e6 | −0.163333 | ||||||||
\(783\) | −3.10245e6 | −0.180843 | ||||||||
\(784\) | 5.98440e6 | 0.347721 | ||||||||
\(785\) | 1.53605e6 | 0.0889677 | ||||||||
\(786\) | 3.27061e7 | 1.88831 | ||||||||
\(787\) | 2.48798e7 | 1.43189 | 0.715945 | − | 0.698157i | \(-0.245996\pi\) | ||||
0.715945 | + | 0.698157i | \(0.245996\pi\) | |||||||
\(788\) | −1.09085e6 | −0.0625820 | ||||||||
\(789\) | −2.84907e7 | −1.62934 | ||||||||
\(790\) | −5.00372e6 | −0.285250 | ||||||||
\(791\) | −2.52666e7 | −1.43584 | ||||||||
\(792\) | 319432. | 0.0180953 | ||||||||
\(793\) | −1.09062e7 | −0.615874 | ||||||||
\(794\) | 1.59668e7 | 0.898808 | ||||||||
\(795\) | 4.51193e6 | 0.253189 | ||||||||
\(796\) | −633537. | −0.0354396 | ||||||||
\(797\) | 2.80418e7 | 1.56372 | 0.781861 | − | 0.623453i | \(-0.214271\pi\) | ||||
0.781861 | + | 0.623453i | \(0.214271\pi\) | |||||||
\(798\) | −1.58137e7 | −0.879076 | ||||||||
\(799\) | −3.05098e6 | −0.169072 | ||||||||
\(800\) | 1.61671e6 | 0.0893112 | ||||||||
\(801\) | −1.67426e6 | −0.0922021 | ||||||||
\(802\) | −7.54513e6 | −0.414220 | ||||||||
\(803\) | −9.67173e6 | −0.529316 | ||||||||
\(804\) | 1.25868e6 | 0.0686714 | ||||||||
\(805\) | 2.41344e6 | 0.131264 | ||||||||
\(806\) | 3.91783e6 | 0.212426 | ||||||||
\(807\) | −2.28394e7 | −1.23453 | ||||||||
\(808\) | 1.87332e7 | 1.00945 | ||||||||
\(809\) | 2.45320e7 | 1.31784 | 0.658919 | − | 0.752214i | \(-0.271014\pi\) | ||||
0.658919 | + | 0.752214i | \(0.271014\pi\) | |||||||
\(810\) | −1.13930e7 | −0.610133 | ||||||||
\(811\) | 2.44306e7 | 1.30431 | 0.652156 | − | 0.758084i | \(-0.273865\pi\) | ||||
0.652156 | + | 0.758084i | \(0.273865\pi\) | |||||||
\(812\) | 187829. | 0.00999706 | ||||||||
\(813\) | 6.68568e6 | 0.354748 | ||||||||
\(814\) | −1.33380e7 | −0.705553 | ||||||||
\(815\) | −4.72680e6 | −0.249272 | ||||||||
\(816\) | 1.15395e7 | 0.606681 | ||||||||
\(817\) | −1.64292e7 | −0.861118 | ||||||||
\(818\) | −1.62745e7 | −0.850400 | ||||||||
\(819\) | 414625. | 0.0215996 | ||||||||
\(820\) | 973012. | 0.0505340 | ||||||||
\(821\) | −4.22220e6 | −0.218615 | −0.109308 | − | 0.994008i | \(-0.534863\pi\) | ||||
−0.109308 | + | 0.994008i | \(0.534863\pi\) | |||||||
\(822\) | 1.73170e7 | 0.893907 | ||||||||
\(823\) | −2.11475e7 | −1.08833 | −0.544165 | − | 0.838979i | \(-0.683153\pi\) | ||||
−0.544165 | + | 0.838979i | \(0.683153\pi\) | |||||||
\(824\) | −2.79886e7 | −1.43603 | ||||||||
\(825\) | 5.19408e6 | 0.265689 | ||||||||
\(826\) | −8.52607e6 | −0.434809 | ||||||||
\(827\) | 2.31990e6 | 0.117952 | 0.0589761 | − | 0.998259i | \(-0.481216\pi\) | ||||
0.0589761 | + | 0.998259i | \(0.481216\pi\) | |||||||
\(828\) | 18095.4 | 0.000917257 0 | ||||||||
\(829\) | 2.89837e7 | 1.46476 | 0.732381 | − | 0.680895i | \(-0.238409\pi\) | ||||
0.732381 | + | 0.680895i | \(0.238409\pi\) | |||||||
\(830\) | −1.00446e7 | −0.506103 | ||||||||
\(831\) | 5.10137e6 | 0.256262 | ||||||||
\(832\) | 9.88423e6 | 0.495033 | ||||||||
\(833\) | 3.66139e6 | 0.182824 | ||||||||
\(834\) | −2.95286e7 | −1.47003 | ||||||||
\(835\) | 1.17352e7 | 0.582469 | ||||||||
\(836\) | 512127. | 0.0253432 | ||||||||
\(837\) | −7.59790e6 | −0.374869 | ||||||||
\(838\) | −8.83328e6 | −0.434522 | ||||||||
\(839\) | 3.32541e7 | 1.63095 | 0.815473 | − | 0.578795i | \(-0.196477\pi\) | ||||
0.815473 | + | 0.578795i | \(0.196477\pi\) | |||||||
\(840\) | −9.35402e6 | −0.457404 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | 1.49488e7 | 0.726651 | ||||||||
\(843\) | 6.72370e6 | 0.325866 | ||||||||
\(844\) | −995655. | −0.0481119 | ||||||||
\(845\) | −8.36958e6 | −0.403239 | ||||||||
\(846\) | 320824. | 0.0154113 | ||||||||
\(847\) | −1.46386e7 | −0.701118 | ||||||||
\(848\) | −9.73000e6 | −0.464647 | ||||||||
\(849\) | −2.06694e6 | −0.0984145 | ||||||||
\(850\) | 8.26635e6 | 0.392434 | ||||||||
\(851\) | 1.07528e7 | 0.508977 | ||||||||
\(852\) | −495288. | −0.0233754 | ||||||||
\(853\) | 1.48503e7 | 0.698816 | 0.349408 | − | 0.936971i | \(-0.386383\pi\) | ||||
0.349408 | + | 0.936971i | \(0.386383\pi\) | |||||||
\(854\) | −2.07841e7 | −0.975184 | ||||||||
\(855\) | −602886. | −0.0282046 | ||||||||
\(856\) | −1.39627e7 | −0.651305 | ||||||||
\(857\) | 2.15523e7 | 1.00240 | 0.501201 | − | 0.865331i | \(-0.332892\pi\) | ||||
0.501201 | + | 0.865331i | \(0.332892\pi\) | |||||||
\(858\) | −4.64110e6 | −0.215230 | ||||||||
\(859\) | −1.84444e7 | −0.852867 | −0.426434 | − | 0.904519i | \(-0.640230\pi\) | ||||
−0.426434 | + | 0.904519i | \(0.640230\pi\) | |||||||
\(860\) | 682872. | 0.0314843 | ||||||||
\(861\) | 2.49083e7 | 1.14508 | ||||||||
\(862\) | −3.14408e7 | −1.44120 | ||||||||
\(863\) | −2.12674e7 | −0.972046 | −0.486023 | − | 0.873946i | \(-0.661553\pi\) | ||||
−0.486023 | + | 0.873946i | \(0.661553\pi\) | |||||||
\(864\) | 2.80150e6 | 0.127675 | ||||||||
\(865\) | −1.36999e7 | −0.622552 | ||||||||
\(866\) | 1.11360e7 | 0.504587 | ||||||||
\(867\) | −1.56120e7 | −0.705361 | ||||||||
\(868\) | 459993. | 0.0207229 | ||||||||
\(869\) | 4.14824e6 | 0.186343 | ||||||||
\(870\) | 2.47506e6 | 0.110863 | ||||||||
\(871\) | 1.22217e7 | 0.545867 | ||||||||
\(872\) | 1.71044e7 | 0.761756 | ||||||||
\(873\) | 1.07577e6 | 0.0477733 | ||||||||
\(874\) | −6.70133e6 | −0.296744 | ||||||||
\(875\) | −1.76274e7 | −0.778339 | ||||||||
\(876\) | 2.12351e6 | 0.0934963 | ||||||||
\(877\) | −2.51615e7 | −1.10468 | −0.552342 | − | 0.833618i | \(-0.686266\pi\) | ||||
−0.552342 | + | 0.833618i | \(0.686266\pi\) | |||||||
\(878\) | −2.24615e7 | −0.983338 | ||||||||
\(879\) | 2.74078e7 | 1.19647 | ||||||||
\(880\) | 5.24115e6 | 0.228150 | ||||||||
\(881\) | 1.60794e7 | 0.697961 | 0.348980 | − | 0.937130i | \(-0.386528\pi\) | ||||
0.348980 | + | 0.937130i | \(0.386528\pi\) | |||||||
\(882\) | −385011. | −0.0166649 | ||||||||
\(883\) | −7.09137e6 | −0.306075 | −0.153038 | − | 0.988220i | \(-0.548906\pi\) | ||||
−0.153038 | + | 0.988220i | \(0.548906\pi\) | |||||||
\(884\) | −455067. | −0.0195859 | ||||||||
\(885\) | −6.92182e6 | −0.297072 | ||||||||
\(886\) | 8.40384e6 | 0.359661 | ||||||||
\(887\) | −1.00313e7 | −0.428103 | −0.214051 | − | 0.976822i | \(-0.568666\pi\) | ||||
−0.214051 | + | 0.976822i | \(0.568666\pi\) | |||||||
\(888\) | −4.16758e7 | −1.77358 | ||||||||
\(889\) | 2.07252e7 | 0.879516 | ||||||||
\(890\) | −2.57714e7 | −1.09059 | ||||||||
\(891\) | 9.44512e6 | 0.398578 | ||||||||
\(892\) | −285503. | −0.0120143 | ||||||||
\(893\) | −7.31996e6 | −0.307171 | ||||||||
\(894\) | −3.04622e7 | −1.27473 | ||||||||
\(895\) | 1.07777e7 | 0.449747 | ||||||||
\(896\) | 2.14198e7 | 0.891344 | ||||||||
\(897\) | 3.74156e6 | 0.155264 | ||||||||
\(898\) | −2.94985e7 | −1.22070 | ||||||||
\(899\) | 1.73213e6 | 0.0714795 | ||||||||
\(900\) | −53553.7 | −0.00220386 | ||||||||
\(901\) | −5.95304e6 | −0.244302 | ||||||||
\(902\) | −1.30930e7 | −0.535826 | ||||||||
\(903\) | 1.74810e7 | 0.713421 | ||||||||
\(904\) | 4.14989e7 | 1.68894 | ||||||||
\(905\) | 1.71128e7 | 0.694543 | ||||||||
\(906\) | 3.98228e7 | 1.61180 | ||||||||
\(907\) | −2.99381e7 | −1.20839 | −0.604193 | − | 0.796838i | \(-0.706505\pi\) | ||||
−0.604193 | + | 0.796838i | \(0.706505\pi\) | |||||||
\(908\) | −2.54276e6 | −0.102351 | ||||||||
\(909\) | −1.28469e6 | −0.0515689 | ||||||||
\(910\) | 6.38222e6 | 0.255487 | ||||||||
\(911\) | 2.83738e7 | 1.13272 | 0.566360 | − | 0.824158i | \(-0.308351\pi\) | ||||
0.566360 | + | 0.824158i | \(0.308351\pi\) | |||||||
\(912\) | 2.76857e7 | 1.10222 | ||||||||
\(913\) | 8.32731e6 | 0.330619 | ||||||||
\(914\) | −1.76852e7 | −0.700236 | ||||||||
\(915\) | −1.68734e7 | −0.666269 | ||||||||
\(916\) | −1.21231e6 | −0.0477391 | ||||||||
\(917\) | 3.72863e7 | 1.46429 | ||||||||
\(918\) | 1.43243e7 | 0.561006 | ||||||||
\(919\) | −3.91491e7 | −1.52909 | −0.764545 | − | 0.644570i | \(-0.777036\pi\) | ||||
−0.764545 | + | 0.644570i | \(0.777036\pi\) | |||||||
\(920\) | −3.96392e6 | −0.154403 | ||||||||
\(921\) | 4.60590e7 | 1.78923 | ||||||||
\(922\) | −2.06762e7 | −0.801019 | ||||||||
\(923\) | −4.80921e6 | −0.185810 | ||||||||
\(924\) | −544911. | −0.0209965 | ||||||||
\(925\) | −3.18233e7 | −1.22290 | ||||||||
\(926\) | 2.21014e7 | 0.847019 | ||||||||
\(927\) | 1.91940e6 | 0.0733613 | ||||||||
\(928\) | −638672. | −0.0243449 | ||||||||
\(929\) | 3.44851e6 | 0.131097 | 0.0655484 | − | 0.997849i | \(-0.479120\pi\) | ||||
0.0655484 | + | 0.997849i | \(0.479120\pi\) | |||||||
\(930\) | 6.06141e6 | 0.229809 | ||||||||
\(931\) | 8.78447e6 | 0.332156 | ||||||||
\(932\) | −2.03000e6 | −0.0765519 | ||||||||
\(933\) | −4.14179e7 | −1.55770 | ||||||||
\(934\) | −2.29514e7 | −0.860879 | ||||||||
\(935\) | 3.20665e6 | 0.119956 | ||||||||
\(936\) | −680997. | −0.0254071 | ||||||||
\(937\) | −3.55183e7 | −1.32161 | −0.660805 | − | 0.750558i | \(-0.729785\pi\) | ||||
−0.660805 | + | 0.750558i | \(0.729785\pi\) | |||||||
\(938\) | 2.32910e7 | 0.864334 | ||||||||
\(939\) | 2.35177e7 | 0.870425 | ||||||||
\(940\) | 304250. | 0.0112308 | ||||||||
\(941\) | −8.10962e6 | −0.298557 | −0.149278 | − | 0.988795i | \(-0.547695\pi\) | ||||
−0.149278 | + | 0.988795i | \(0.547695\pi\) | |||||||
\(942\) | 4.53815e6 | 0.166629 | ||||||||
\(943\) | 1.05553e7 | 0.386538 | ||||||||
\(944\) | 1.49269e7 | 0.545180 | ||||||||
\(945\) | −1.23771e7 | −0.450858 | ||||||||
\(946\) | −9.18886e6 | −0.333836 | ||||||||
\(947\) | 1.58835e7 | 0.575535 | 0.287767 | − | 0.957700i | \(-0.407087\pi\) | ||||
0.287767 | + | 0.957700i | \(0.407087\pi\) | |||||||
\(948\) | −910781. | −0.0329150 | ||||||||
\(949\) | 2.06191e7 | 0.743199 | ||||||||
\(950\) | 1.98328e7 | 0.712975 | ||||||||
\(951\) | 1.05698e7 | 0.378979 | ||||||||
\(952\) | 1.23417e7 | 0.441349 | ||||||||
\(953\) | −1.76043e7 | −0.627893 | −0.313946 | − | 0.949441i | \(-0.601651\pi\) | ||||
−0.313946 | + | 0.949441i | \(0.601651\pi\) | |||||||
\(954\) | 625988. | 0.0222687 | ||||||||
\(955\) | −1.43422e7 | −0.508871 | ||||||||
\(956\) | 1.24447e6 | 0.0440392 | ||||||||
\(957\) | −2.05190e6 | −0.0724229 | ||||||||
\(958\) | −2.13433e7 | −0.751361 | ||||||||
\(959\) | 1.97421e7 | 0.693180 | ||||||||
\(960\) | 1.52922e7 | 0.535541 | ||||||||
\(961\) | −2.43872e7 | −0.851830 | ||||||||
\(962\) | 2.84353e7 | 0.990649 | ||||||||
\(963\) | 957534. | 0.0332727 | ||||||||
\(964\) | 851464. | 0.0295103 | ||||||||
\(965\) | 2.49709e7 | 0.863210 | ||||||||
\(966\) | 7.13032e6 | 0.245848 | ||||||||
\(967\) | −5.37843e7 | −1.84965 | −0.924825 | − | 0.380393i | \(-0.875789\pi\) | ||||
−0.924825 | + | 0.380393i | \(0.875789\pi\) | |||||||
\(968\) | 2.40430e7 | 0.824708 | ||||||||
\(969\) | 1.69387e7 | 0.579524 | ||||||||
\(970\) | 1.65591e7 | 0.565076 | ||||||||
\(971\) | 1.22227e7 | 0.416026 | 0.208013 | − | 0.978126i | \(-0.433300\pi\) | ||||
0.208013 | + | 0.978126i | \(0.433300\pi\) | |||||||
\(972\) | −190410. | −0.00646435 | ||||||||
\(973\) | −3.36638e7 | −1.13994 | ||||||||
\(974\) | −2.27880e7 | −0.769678 | ||||||||
\(975\) | −1.10732e7 | −0.373047 | ||||||||
\(976\) | 3.63875e7 | 1.22272 | ||||||||
\(977\) | 4.33000e6 | 0.145128 | 0.0725640 | − | 0.997364i | \(-0.476882\pi\) | ||||
0.0725640 | + | 0.997364i | \(0.476882\pi\) | |||||||
\(978\) | −1.39650e7 | −0.466866 | ||||||||
\(979\) | 2.13652e7 | 0.712445 | ||||||||
\(980\) | −365122. | −0.0121443 | ||||||||
\(981\) | −1.17299e6 | −0.0389153 | ||||||||
\(982\) | 4.80392e7 | 1.58971 | ||||||||
\(983\) | 4.71098e7 | 1.55499 | 0.777494 | − | 0.628890i | \(-0.216490\pi\) | ||||
0.777494 | + | 0.628890i | \(0.216490\pi\) | |||||||
\(984\) | −4.09104e7 | −1.34693 | ||||||||
\(985\) | −1.63873e7 | −0.538168 | ||||||||
\(986\) | −3.26559e6 | −0.106972 | ||||||||
\(987\) | 7.78855e6 | 0.254486 | ||||||||
\(988\) | −1.09180e6 | −0.0355838 | ||||||||
\(989\) | 7.40786e6 | 0.240825 | ||||||||
\(990\) | −337194. | −0.0109343 | ||||||||
\(991\) | −2.09978e7 | −0.679187 | −0.339594 | − | 0.940572i | \(-0.610290\pi\) | ||||
−0.339594 | + | 0.940572i | \(0.610290\pi\) | |||||||
\(992\) | −1.56411e6 | −0.0504647 | ||||||||
\(993\) | 5.44145e7 | 1.75122 | ||||||||
\(994\) | −9.16495e6 | −0.294215 | ||||||||
\(995\) | −9.51734e6 | −0.304760 | ||||||||
\(996\) | −1.82833e6 | −0.0583992 | ||||||||
\(997\) | −4.51805e7 | −1.43951 | −0.719753 | − | 0.694231i | \(-0.755745\pi\) | ||||
−0.719753 | + | 0.694231i | \(0.755745\pi\) | |||||||
\(998\) | 1.13946e7 | 0.362136 | ||||||||
\(999\) | −5.51448e7 | −1.74820 |
(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 | 29.6.a.b.1.5 | ✓ | 7 | |
3.2 | odd | 2 | 261.6.a.e.1.3 | 7 | |||
4.3 | odd | 2 | 464.6.a.k.1.3 | 7 | |||
5.4 | even | 2 | 725.6.a.b.1.3 | 7 | |||
29.28 | even | 2 | 841.6.a.b.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.b.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial | |
261.6.a.e.1.3 | 7 | 3.2 | odd | 2 | |||
464.6.a.k.1.3 | 7 | 4.3 | odd | 2 | |||
725.6.a.b.1.3 | 7 | 5.4 | even | 2 | |||
841.6.a.b.1.3 | 7 | 29.28 | even | 2 |