Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,6,Mod(1,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, 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("74.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(11.8684026662\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 870x^{3} - 2235x^{2} + 121361x + 481504 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(28.3792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | −24.3792 | −1.56393 | −0.781963 | − | 0.623324i | \(-0.785782\pi\) | ||||
−0.781963 | + | 0.623324i | \(0.785782\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 44.9778 | 0.804588 | 0.402294 | − | 0.915511i | \(-0.368213\pi\) | ||||
0.402294 | + | 0.915511i | \(0.368213\pi\) | |||||||
\(6\) | −97.5168 | −1.10586 | ||||||||
\(7\) | −145.948 | −1.12578 | −0.562890 | − | 0.826532i | \(-0.690311\pi\) | ||||
−0.562890 | + | 0.826532i | \(0.690311\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 351.346 | 1.44587 | ||||||||
\(10\) | 179.911 | 0.568930 | ||||||||
\(11\) | 419.587 | 1.04554 | 0.522770 | − | 0.852474i | \(-0.324899\pi\) | ||||
0.522770 | + | 0.852474i | \(0.324899\pi\) | |||||||
\(12\) | −390.067 | −0.781963 | ||||||||
\(13\) | 373.322 | 0.612668 | 0.306334 | − | 0.951924i | \(-0.400898\pi\) | ||||
0.306334 | + | 0.951924i | \(0.400898\pi\) | |||||||
\(14\) | −583.793 | −0.796047 | ||||||||
\(15\) | −1096.52 | −1.25832 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1931.97 | 1.62135 | 0.810676 | − | 0.585496i | \(-0.199100\pi\) | ||||
0.810676 | + | 0.585496i | \(0.199100\pi\) | |||||||
\(18\) | 1405.38 | 1.02238 | ||||||||
\(19\) | 1577.61 | 1.00257 | 0.501287 | − | 0.865281i | \(-0.332860\pi\) | ||||
0.501287 | + | 0.865281i | \(0.332860\pi\) | |||||||
\(20\) | 719.645 | 0.402294 | ||||||||
\(21\) | 3558.10 | 1.76064 | ||||||||
\(22\) | 1678.35 | 0.739309 | ||||||||
\(23\) | 1370.65 | 0.540265 | 0.270133 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(24\) | −1560.27 | −0.552932 | ||||||||
\(25\) | −1101.99 | −0.352638 | ||||||||
\(26\) | 1493.29 | 0.433222 | ||||||||
\(27\) | −2641.38 | −0.697303 | ||||||||
\(28\) | −2335.17 | −0.562890 | ||||||||
\(29\) | 5141.18 | 1.13519 | 0.567594 | − | 0.823309i | \(-0.307874\pi\) | ||||
0.567594 | + | 0.823309i | \(0.307874\pi\) | |||||||
\(30\) | −4386.10 | −0.889764 | ||||||||
\(31\) | −10547.9 | −1.97134 | −0.985671 | − | 0.168681i | \(-0.946049\pi\) | ||||
−0.985671 | + | 0.168681i | \(0.946049\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −10229.2 | −1.63515 | ||||||||
\(34\) | 7727.86 | 1.14647 | ||||||||
\(35\) | −6564.43 | −0.905789 | ||||||||
\(36\) | 5621.53 | 0.722933 | ||||||||
\(37\) | −1369.00 | −0.164399 | ||||||||
\(38\) | 6310.46 | 0.708928 | ||||||||
\(39\) | −9101.29 | −0.958168 | ||||||||
\(40\) | 2878.58 | 0.284465 | ||||||||
\(41\) | 3806.91 | 0.353682 | 0.176841 | − | 0.984239i | \(-0.443412\pi\) | ||||
0.176841 | + | 0.984239i | \(0.443412\pi\) | |||||||
\(42\) | 14232.4 | 1.24496 | ||||||||
\(43\) | −5509.91 | −0.454437 | −0.227219 | − | 0.973844i | \(-0.572963\pi\) | ||||
−0.227219 | + | 0.973844i | \(0.572963\pi\) | |||||||
\(44\) | 6713.40 | 0.522770 | ||||||||
\(45\) | 15802.8 | 1.16333 | ||||||||
\(46\) | 5482.60 | 0.382025 | ||||||||
\(47\) | 7069.09 | 0.466787 | 0.233393 | − | 0.972382i | \(-0.425017\pi\) | ||||
0.233393 | + | 0.972382i | \(0.425017\pi\) | |||||||
\(48\) | −6241.08 | −0.390982 | ||||||||
\(49\) | 4493.87 | 0.267381 | ||||||||
\(50\) | −4407.98 | −0.249353 | ||||||||
\(51\) | −47099.8 | −2.53567 | ||||||||
\(52\) | 5973.15 | 0.306334 | ||||||||
\(53\) | 8514.77 | 0.416374 | 0.208187 | − | 0.978089i | \(-0.433244\pi\) | ||||
0.208187 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(54\) | −10565.5 | −0.493067 | ||||||||
\(55\) | 18872.1 | 0.841229 | ||||||||
\(56\) | −9340.68 | −0.398023 | ||||||||
\(57\) | −38461.0 | −1.56795 | ||||||||
\(58\) | 20564.7 | 0.802699 | ||||||||
\(59\) | 29846.0 | 1.11624 | 0.558119 | − | 0.829761i | \(-0.311523\pi\) | ||||
0.558119 | + | 0.829761i | \(0.311523\pi\) | |||||||
\(60\) | −17544.4 | −0.629158 | ||||||||
\(61\) | 35774.7 | 1.23098 | 0.615491 | − | 0.788144i | \(-0.288958\pi\) | ||||
0.615491 | + | 0.788144i | \(0.288958\pi\) | |||||||
\(62\) | −42191.6 | −1.39395 | ||||||||
\(63\) | −51278.2 | −1.62773 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 16791.2 | 0.492945 | ||||||||
\(66\) | −40916.8 | −1.15622 | ||||||||
\(67\) | −62617.1 | −1.70414 | −0.852071 | − | 0.523426i | \(-0.824654\pi\) | ||||
−0.852071 | + | 0.523426i | \(0.824654\pi\) | |||||||
\(68\) | 30911.4 | 0.810676 | ||||||||
\(69\) | −33415.4 | −0.844935 | ||||||||
\(70\) | −26257.7 | −0.640490 | ||||||||
\(71\) | 21558.4 | 0.507541 | 0.253770 | − | 0.967265i | \(-0.418329\pi\) | ||||
0.253770 | + | 0.967265i | \(0.418329\pi\) | |||||||
\(72\) | 22486.1 | 0.511191 | ||||||||
\(73\) | −26703.8 | −0.586498 | −0.293249 | − | 0.956036i | \(-0.594737\pi\) | ||||
−0.293249 | + | 0.956036i | \(0.594737\pi\) | |||||||
\(74\) | −5476.00 | −0.116248 | ||||||||
\(75\) | 26865.7 | 0.551500 | ||||||||
\(76\) | 25241.8 | 0.501287 | ||||||||
\(77\) | −61238.0 | −1.17705 | ||||||||
\(78\) | −36405.2 | −0.677527 | ||||||||
\(79\) | 107249. | 1.93342 | 0.966711 | − | 0.255870i | \(-0.0823620\pi\) | ||||
0.966711 | + | 0.255870i | \(0.0823620\pi\) | |||||||
\(80\) | 11514.3 | 0.201147 | ||||||||
\(81\) | −20982.3 | −0.355336 | ||||||||
\(82\) | 15227.7 | 0.250091 | ||||||||
\(83\) | −57311.6 | −0.913161 | −0.456580 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456580 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(84\) | 56929.6 | 0.880319 | ||||||||
\(85\) | 86895.6 | 1.30452 | ||||||||
\(86\) | −22039.7 | −0.321335 | ||||||||
\(87\) | −125338. | −1.77535 | ||||||||
\(88\) | 26853.6 | 0.369654 | ||||||||
\(89\) | 47134.6 | 0.630761 | 0.315381 | − | 0.948965i | \(-0.397868\pi\) | ||||
0.315381 | + | 0.948965i | \(0.397868\pi\) | |||||||
\(90\) | 63211.1 | 0.822596 | ||||||||
\(91\) | −54485.7 | −0.689730 | ||||||||
\(92\) | 21930.4 | 0.270133 | ||||||||
\(93\) | 257149. | 3.08303 | ||||||||
\(94\) | 28276.3 | 0.330068 | ||||||||
\(95\) | 70957.7 | 0.806660 | ||||||||
\(96\) | −24964.3 | −0.276466 | ||||||||
\(97\) | 40076.6 | 0.432475 | 0.216238 | − | 0.976341i | \(-0.430621\pi\) | ||||
0.216238 | + | 0.976341i | \(0.430621\pi\) | |||||||
\(98\) | 17975.5 | 0.189067 | ||||||||
\(99\) | 147420. | 1.51171 | ||||||||
\(100\) | −17631.9 | −0.176319 | ||||||||
\(101\) | 91615.6 | 0.893647 | 0.446823 | − | 0.894622i | \(-0.352555\pi\) | ||||
0.446823 | + | 0.894622i | \(0.352555\pi\) | |||||||
\(102\) | −188399. | −1.79299 | ||||||||
\(103\) | −34348.8 | −0.319020 | −0.159510 | − | 0.987196i | \(-0.550991\pi\) | ||||
−0.159510 | + | 0.987196i | \(0.550991\pi\) | |||||||
\(104\) | 23892.6 | 0.216611 | ||||||||
\(105\) | 160036. | 1.41659 | ||||||||
\(106\) | 34059.1 | 0.294421 | ||||||||
\(107\) | −22234.1 | −0.187741 | −0.0938705 | − | 0.995584i | \(-0.529924\pi\) | ||||
−0.0938705 | + | 0.995584i | \(0.529924\pi\) | |||||||
\(108\) | −42262.1 | −0.348651 | ||||||||
\(109\) | −231071. | −1.86285 | −0.931427 | − | 0.363927i | \(-0.881436\pi\) | ||||
−0.931427 | + | 0.363927i | \(0.881436\pi\) | |||||||
\(110\) | 75488.5 | 0.594839 | ||||||||
\(111\) | 33375.1 | 0.257108 | ||||||||
\(112\) | −37362.7 | −0.281445 | ||||||||
\(113\) | 20790.5 | 0.153169 | 0.0765843 | − | 0.997063i | \(-0.475599\pi\) | ||||
0.0765843 | + | 0.997063i | \(0.475599\pi\) | |||||||
\(114\) | −153844. | −1.10871 | ||||||||
\(115\) | 61648.9 | 0.434691 | ||||||||
\(116\) | 82258.8 | 0.567594 | ||||||||
\(117\) | 131165. | 0.885836 | ||||||||
\(118\) | 119384. | 0.789299 | ||||||||
\(119\) | −281967. | −1.82528 | ||||||||
\(120\) | −70177.5 | −0.444882 | ||||||||
\(121\) | 15002.6 | 0.0931545 | ||||||||
\(122\) | 143099. | 0.870436 | ||||||||
\(123\) | −92809.5 | −0.553133 | ||||||||
\(124\) | −168766. | −0.985671 | ||||||||
\(125\) | −190121. | −1.08832 | ||||||||
\(126\) | −205113. | −1.15098 | ||||||||
\(127\) | −83413.4 | −0.458909 | −0.229455 | − | 0.973319i | \(-0.573694\pi\) | ||||
−0.229455 | + | 0.973319i | \(0.573694\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 134327. | 0.710706 | ||||||||
\(130\) | 67164.9 | 0.348565 | ||||||||
\(131\) | 346823. | 1.76575 | 0.882877 | − | 0.469604i | \(-0.155603\pi\) | ||||
0.882877 | + | 0.469604i | \(0.155603\pi\) | |||||||
\(132\) | −163667. | −0.817574 | ||||||||
\(133\) | −230250. | −1.12868 | ||||||||
\(134\) | −250468. | −1.20501 | ||||||||
\(135\) | −118803. | −0.561041 | ||||||||
\(136\) | 123646. | 0.573234 | ||||||||
\(137\) | −169756. | −0.772723 | −0.386362 | − | 0.922347i | \(-0.626268\pi\) | ||||
−0.386362 | + | 0.922347i | \(0.626268\pi\) | |||||||
\(138\) | −133661. | −0.597460 | ||||||||
\(139\) | 201516. | 0.884654 | 0.442327 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442327 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(140\) | −105031. | −0.452895 | ||||||||
\(141\) | −172339. | −0.730020 | ||||||||
\(142\) | 86233.6 | 0.358885 | ||||||||
\(143\) | 156641. | 0.640569 | ||||||||
\(144\) | 89944.5 | 0.361467 | ||||||||
\(145\) | 231239. | 0.913358 | ||||||||
\(146\) | −106815. | −0.414717 | ||||||||
\(147\) | −109557. | −0.418164 | ||||||||
\(148\) | −21904.0 | −0.0821995 | ||||||||
\(149\) | −92365.5 | −0.340835 | −0.170417 | − | 0.985372i | \(-0.554512\pi\) | ||||
−0.170417 | + | 0.985372i | \(0.554512\pi\) | |||||||
\(150\) | 107463. | 0.389970 | ||||||||
\(151\) | 540948. | 1.93069 | 0.965346 | − | 0.260975i | \(-0.0840440\pi\) | ||||
0.965346 | + | 0.260975i | \(0.0840440\pi\) | |||||||
\(152\) | 100967. | 0.354464 | ||||||||
\(153\) | 678788. | 2.34426 | ||||||||
\(154\) | −244952. | −0.832299 | ||||||||
\(155\) | −474422. | −1.58612 | ||||||||
\(156\) | −145621. | −0.479084 | ||||||||
\(157\) | −179937. | −0.582603 | −0.291301 | − | 0.956631i | \(-0.594088\pi\) | ||||
−0.291301 | + | 0.956631i | \(0.594088\pi\) | |||||||
\(158\) | 428997. | 1.36714 | ||||||||
\(159\) | −207583. | −0.651178 | ||||||||
\(160\) | 46057.3 | 0.142232 | ||||||||
\(161\) | −200044. | −0.608220 | ||||||||
\(162\) | −83929.1 | −0.251261 | ||||||||
\(163\) | −538231. | −1.58672 | −0.793359 | − | 0.608754i | \(-0.791670\pi\) | ||||
−0.793359 | + | 0.608754i | \(0.791670\pi\) | |||||||
\(164\) | 60910.6 | 0.176841 | ||||||||
\(165\) | −460088. | −1.31562 | ||||||||
\(166\) | −229246. | −0.645702 | ||||||||
\(167\) | −211189. | −0.585977 | −0.292988 | − | 0.956116i | \(-0.594650\pi\) | ||||
−0.292988 | + | 0.956116i | \(0.594650\pi\) | |||||||
\(168\) | 227718. | 0.622479 | ||||||||
\(169\) | −231924. | −0.624638 | ||||||||
\(170\) | 347583. | 0.922435 | ||||||||
\(171\) | 554288. | 1.44959 | ||||||||
\(172\) | −88158.6 | −0.227219 | ||||||||
\(173\) | 246945. | 0.627315 | 0.313657 | − | 0.949536i | \(-0.398446\pi\) | ||||
0.313657 | + | 0.949536i | \(0.398446\pi\) | |||||||
\(174\) | −501351. | −1.25536 | ||||||||
\(175\) | 160834. | 0.396993 | ||||||||
\(176\) | 107414. | 0.261385 | ||||||||
\(177\) | −727622. | −1.74571 | ||||||||
\(178\) | 188538. | 0.446015 | ||||||||
\(179\) | −307183. | −0.716579 | −0.358289 | − | 0.933611i | \(-0.616640\pi\) | ||||
−0.358289 | + | 0.933611i | \(0.616640\pi\) | |||||||
\(180\) | 252844. | 0.581663 | ||||||||
\(181\) | 480322. | 1.08977 | 0.544886 | − | 0.838510i | \(-0.316573\pi\) | ||||
0.544886 | + | 0.838510i | \(0.316573\pi\) | |||||||
\(182\) | −217943. | −0.487712 | ||||||||
\(183\) | −872159. | −1.92517 | ||||||||
\(184\) | 87721.6 | 0.191013 | ||||||||
\(185\) | −61574.7 | −0.132273 | ||||||||
\(186\) | 1.02860e6 | 2.18003 | ||||||||
\(187\) | 810628. | 1.69519 | ||||||||
\(188\) | 113105. | 0.233393 | ||||||||
\(189\) | 385504. | 0.785009 | ||||||||
\(190\) | 283831. | 0.570395 | ||||||||
\(191\) | −644592. | −1.27850 | −0.639252 | − | 0.768998i | \(-0.720756\pi\) | ||||
−0.639252 | + | 0.768998i | \(0.720756\pi\) | |||||||
\(192\) | −99857.2 | −0.195491 | ||||||||
\(193\) | 214964. | 0.415405 | 0.207703 | − | 0.978192i | \(-0.433401\pi\) | ||||
0.207703 | + | 0.978192i | \(0.433401\pi\) | |||||||
\(194\) | 160306. | 0.305806 | ||||||||
\(195\) | −409357. | −0.770930 | ||||||||
\(196\) | 71901.9 | 0.133690 | ||||||||
\(197\) | 18456.5 | 0.0338832 | 0.0169416 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169416 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(198\) | 589681. | 1.06894 | ||||||||
\(199\) | −476731. | −0.853377 | −0.426689 | − | 0.904399i | \(-0.640320\pi\) | ||||
−0.426689 | + | 0.904399i | \(0.640320\pi\) | |||||||
\(200\) | −70527.6 | −0.124676 | ||||||||
\(201\) | 1.52655e6 | 2.66515 | ||||||||
\(202\) | 366462. | 0.631904 | ||||||||
\(203\) | −750345. | −1.27797 | ||||||||
\(204\) | −753596. | −1.26784 | ||||||||
\(205\) | 171227. | 0.284569 | ||||||||
\(206\) | −137395. | −0.225581 | ||||||||
\(207\) | 481572. | 0.781152 | ||||||||
\(208\) | 95570.5 | 0.153167 | ||||||||
\(209\) | 661947. | 1.04823 | ||||||||
\(210\) | 640143. | 1.00168 | ||||||||
\(211\) | 321403. | 0.496986 | 0.248493 | − | 0.968634i | \(-0.420065\pi\) | ||||
0.248493 | + | 0.968634i | \(0.420065\pi\) | |||||||
\(212\) | 136236. | 0.208187 | ||||||||
\(213\) | −525577. | −0.793756 | ||||||||
\(214\) | −88936.2 | −0.132753 | ||||||||
\(215\) | −247824. | −0.365635 | ||||||||
\(216\) | −169048. | −0.246534 | ||||||||
\(217\) | 1.53945e6 | 2.21930 | ||||||||
\(218\) | −924284. | −1.31724 | ||||||||
\(219\) | 651019. | 0.917240 | ||||||||
\(220\) | 301954. | 0.420615 | ||||||||
\(221\) | 721245. | 0.993350 | ||||||||
\(222\) | 133501. | 0.181803 | ||||||||
\(223\) | −319949. | −0.430843 | −0.215421 | − | 0.976521i | \(-0.569112\pi\) | ||||
−0.215421 | + | 0.976521i | \(0.569112\pi\) | |||||||
\(224\) | −149451. | −0.199012 | ||||||||
\(225\) | −387181. | −0.509868 | ||||||||
\(226\) | 83162.2 | 0.108307 | ||||||||
\(227\) | −1.29834e6 | −1.67234 | −0.836170 | − | 0.548471i | \(-0.815210\pi\) | ||||
−0.836170 | + | 0.548471i | \(0.815210\pi\) | |||||||
\(228\) | −615376. | −0.783977 | ||||||||
\(229\) | −1.08171e6 | −1.36308 | −0.681541 | − | 0.731780i | \(-0.738690\pi\) | ||||
−0.681541 | + | 0.731780i | \(0.738690\pi\) | |||||||
\(230\) | 246596. | 0.307373 | ||||||||
\(231\) | 1.49293e6 | 1.84082 | ||||||||
\(232\) | 329035. | 0.401349 | ||||||||
\(233\) | −1.37325e6 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(234\) | 524660. | 0.626381 | ||||||||
\(235\) | 317952. | 0.375571 | ||||||||
\(236\) | 477536. | 0.558119 | ||||||||
\(237\) | −2.61465e6 | −3.02373 | ||||||||
\(238\) | −1.12787e6 | −1.29067 | ||||||||
\(239\) | −1.31403e6 | −1.48802 | −0.744012 | − | 0.668166i | \(-0.767080\pi\) | ||||
−0.744012 | + | 0.668166i | \(0.767080\pi\) | |||||||
\(240\) | −280710. | −0.314579 | ||||||||
\(241\) | 1.40950e6 | 1.56322 | 0.781612 | − | 0.623765i | \(-0.214398\pi\) | ||||
0.781612 | + | 0.623765i | \(0.214398\pi\) | |||||||
\(242\) | 60010.5 | 0.0658702 | ||||||||
\(243\) | 1.15339e6 | 1.25302 | ||||||||
\(244\) | 572396. | 0.615491 | ||||||||
\(245\) | 202125. | 0.215131 | ||||||||
\(246\) | −371238. | −0.391124 | ||||||||
\(247\) | 588958. | 0.614246 | ||||||||
\(248\) | −675066. | −0.696974 | ||||||||
\(249\) | 1.39721e6 | 1.42812 | ||||||||
\(250\) | −760484. | −0.769556 | ||||||||
\(251\) | −935529. | −0.937288 | −0.468644 | − | 0.883387i | \(-0.655257\pi\) | ||||
−0.468644 | + | 0.883387i | \(0.655257\pi\) | |||||||
\(252\) | −820452. | −0.813864 | ||||||||
\(253\) | 575108. | 0.564869 | ||||||||
\(254\) | −333654. | −0.324498 | ||||||||
\(255\) | −2.11845e6 | −2.04017 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 252017. | 0.238011 | 0.119005 | − | 0.992894i | \(-0.462029\pi\) | ||||
0.119005 | + | 0.992894i | \(0.462029\pi\) | |||||||
\(258\) | 537309. | 0.502545 | ||||||||
\(259\) | 199803. | 0.185077 | ||||||||
\(260\) | 268660. | 0.246473 | ||||||||
\(261\) | 1.80633e6 | 1.64133 | ||||||||
\(262\) | 1.38729e6 | 1.24858 | ||||||||
\(263\) | 1.87392e6 | 1.67056 | 0.835281 | − | 0.549823i | \(-0.185305\pi\) | ||||
0.835281 | + | 0.549823i | \(0.185305\pi\) | |||||||
\(264\) | −654669. | −0.578112 | ||||||||
\(265\) | 382976. | 0.335009 | ||||||||
\(266\) | −921000. | −0.798097 | ||||||||
\(267\) | −1.14910e6 | −0.986464 | ||||||||
\(268\) | −1.00187e6 | −0.852071 | ||||||||
\(269\) | 212512. | 0.179062 | 0.0895309 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895309 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(270\) | −475214. | −0.396716 | ||||||||
\(271\) | 1.24620e6 | 1.03078 | 0.515389 | − | 0.856956i | \(-0.327647\pi\) | ||||
0.515389 | + | 0.856956i | \(0.327647\pi\) | |||||||
\(272\) | 494583. | 0.405338 | ||||||||
\(273\) | 1.32832e6 | 1.07869 | ||||||||
\(274\) | −679025. | −0.546398 | ||||||||
\(275\) | −462383. | −0.368697 | ||||||||
\(276\) | −534646. | −0.422468 | ||||||||
\(277\) | −2.40327e6 | −1.88193 | −0.940963 | − | 0.338508i | \(-0.890078\pi\) | ||||
−0.940963 | + | 0.338508i | \(0.890078\pi\) | |||||||
\(278\) | 806065. | 0.625545 | ||||||||
\(279\) | −3.70596e6 | −2.85030 | ||||||||
\(280\) | −420124. | −0.320245 | ||||||||
\(281\) | −1.01520e6 | −0.766980 | −0.383490 | − | 0.923545i | \(-0.625278\pi\) | ||||
−0.383490 | + | 0.923545i | \(0.625278\pi\) | |||||||
\(282\) | −689355. | −0.516202 | ||||||||
\(283\) | 449107. | 0.333337 | 0.166668 | − | 0.986013i | \(-0.446699\pi\) | ||||
0.166668 | + | 0.986013i | \(0.446699\pi\) | |||||||
\(284\) | 344935. | 0.253770 | ||||||||
\(285\) | −1.72989e6 | −1.26156 | ||||||||
\(286\) | 626565. | 0.452951 | ||||||||
\(287\) | −555612. | −0.398169 | ||||||||
\(288\) | 359778. | 0.255596 | ||||||||
\(289\) | 2.31263e6 | 1.62878 | ||||||||
\(290\) | 924956. | 0.645842 | ||||||||
\(291\) | −977035. | −0.676360 | ||||||||
\(292\) | −427262. | −0.293249 | ||||||||
\(293\) | 1.50375e6 | 1.02331 | 0.511654 | − | 0.859191i | \(-0.329033\pi\) | ||||
0.511654 | + | 0.859191i | \(0.329033\pi\) | |||||||
\(294\) | −438228. | −0.295687 | ||||||||
\(295\) | 1.34241e6 | 0.898111 | ||||||||
\(296\) | −87616.0 | −0.0581238 | ||||||||
\(297\) | −1.10829e6 | −0.729058 | ||||||||
\(298\) | −369462. | −0.241007 | ||||||||
\(299\) | 511694. | 0.331003 | ||||||||
\(300\) | 429852. | 0.275750 | ||||||||
\(301\) | 804162. | 0.511596 | ||||||||
\(302\) | 2.16379e6 | 1.36520 | ||||||||
\(303\) | −2.23351e6 | −1.39760 | ||||||||
\(304\) | 403869. | 0.250644 | ||||||||
\(305\) | 1.60907e6 | 0.990434 | ||||||||
\(306\) | 2.71515e6 | 1.65764 | ||||||||
\(307\) | −1.58527e6 | −0.959970 | −0.479985 | − | 0.877277i | \(-0.659358\pi\) | ||||
−0.479985 | + | 0.877277i | \(0.659358\pi\) | |||||||
\(308\) | −979808. | −0.588524 | ||||||||
\(309\) | 837395. | 0.498924 | ||||||||
\(310\) | −1.89769e6 | −1.12155 | ||||||||
\(311\) | 2.13422e6 | 1.25124 | 0.625618 | − | 0.780130i | \(-0.284847\pi\) | ||||
0.625618 | + | 0.780130i | \(0.284847\pi\) | |||||||
\(312\) | −582483. | −0.338764 | ||||||||
\(313\) | 508004. | 0.293093 | 0.146547 | − | 0.989204i | \(-0.453184\pi\) | ||||
0.146547 | + | 0.989204i | \(0.453184\pi\) | |||||||
\(314\) | −719750. | −0.411962 | ||||||||
\(315\) | −2.30638e6 | −1.30965 | ||||||||
\(316\) | 1.71599e6 | 0.966711 | ||||||||
\(317\) | −2.67588e6 | −1.49561 | −0.747805 | − | 0.663919i | \(-0.768892\pi\) | ||||
−0.747805 | + | 0.663919i | \(0.768892\pi\) | |||||||
\(318\) | −830333. | −0.460452 | ||||||||
\(319\) | 2.15717e6 | 1.18688 | ||||||||
\(320\) | 184229. | 0.100573 | ||||||||
\(321\) | 542049. | 0.293613 | ||||||||
\(322\) | −800176. | −0.430076 | ||||||||
\(323\) | 3.04790e6 | 1.62553 | ||||||||
\(324\) | −335716. | −0.177668 | ||||||||
\(325\) | −411399. | −0.216050 | ||||||||
\(326\) | −2.15292e6 | −1.12198 | ||||||||
\(327\) | 5.63332e6 | 2.91337 | ||||||||
\(328\) | 243642. | 0.125046 | ||||||||
\(329\) | −1.03172e6 | −0.525499 | ||||||||
\(330\) | −1.84035e6 | −0.930284 | ||||||||
\(331\) | −3.23173e6 | −1.62131 | −0.810654 | − | 0.585525i | \(-0.800888\pi\) | ||||
−0.810654 | + | 0.585525i | \(0.800888\pi\) | |||||||
\(332\) | −916986. | −0.456580 | ||||||||
\(333\) | −480992. | −0.237699 | ||||||||
\(334\) | −844757. | −0.414348 | ||||||||
\(335\) | −2.81638e6 | −1.37113 | ||||||||
\(336\) | 910874. | 0.440159 | ||||||||
\(337\) | 3.56562e6 | 1.71025 | 0.855127 | − | 0.518419i | \(-0.173479\pi\) | ||||
0.855127 | + | 0.518419i | \(0.173479\pi\) | |||||||
\(338\) | −927695. | −0.441686 | ||||||||
\(339\) | −506857. | −0.239544 | ||||||||
\(340\) | 1.39033e6 | 0.652260 | ||||||||
\(341\) | −4.42577e6 | −2.06112 | ||||||||
\(342\) | 2.21715e6 | 1.02501 | ||||||||
\(343\) | 1.79708e6 | 0.824768 | ||||||||
\(344\) | −352635. | −0.160668 | ||||||||
\(345\) | −1.50295e6 | −0.679825 | ||||||||
\(346\) | 987781. | 0.443579 | ||||||||
\(347\) | 2.38403e6 | 1.06289 | 0.531444 | − | 0.847093i | \(-0.321649\pi\) | ||||
0.531444 | + | 0.847093i | \(0.321649\pi\) | |||||||
\(348\) | −2.00540e6 | −0.887675 | ||||||||
\(349\) | −1.22091e6 | −0.536563 | −0.268281 | − | 0.963341i | \(-0.586456\pi\) | ||||
−0.268281 | + | 0.963341i | \(0.586456\pi\) | |||||||
\(350\) | 643336. | 0.280716 | ||||||||
\(351\) | −986085. | −0.427215 | ||||||||
\(352\) | 429658. | 0.184827 | ||||||||
\(353\) | −1.43335e6 | −0.612232 | −0.306116 | − | 0.951994i | \(-0.599030\pi\) | ||||
−0.306116 | + | 0.951994i | \(0.599030\pi\) | |||||||
\(354\) | −2.91049e6 | −1.23441 | ||||||||
\(355\) | 969650. | 0.408361 | ||||||||
\(356\) | 754154. | 0.315381 | ||||||||
\(357\) | 6.87413e6 | 2.85461 | ||||||||
\(358\) | −1.22873e6 | −0.506698 | ||||||||
\(359\) | 1.56017e6 | 0.638906 | 0.319453 | − | 0.947602i | \(-0.396501\pi\) | ||||
0.319453 | + | 0.947602i | \(0.396501\pi\) | |||||||
\(360\) | 1.01138e6 | 0.411298 | ||||||||
\(361\) | 12767.9 | 0.00515646 | ||||||||
\(362\) | 1.92129e6 | 0.770585 | ||||||||
\(363\) | −365752. | −0.145687 | ||||||||
\(364\) | −871771. | −0.344865 | ||||||||
\(365\) | −1.20108e6 | −0.471889 | ||||||||
\(366\) | −3.48864e6 | −1.36130 | ||||||||
\(367\) | 1.72338e6 | 0.667907 | 0.333953 | − | 0.942590i | \(-0.391617\pi\) | ||||
0.333953 | + | 0.942590i | \(0.391617\pi\) | |||||||
\(368\) | 350886. | 0.135066 | ||||||||
\(369\) | 1.33754e6 | 0.511378 | ||||||||
\(370\) | −246299. | −0.0935315 | ||||||||
\(371\) | −1.24272e6 | −0.468745 | ||||||||
\(372\) | 4.11439e6 | 1.54152 | ||||||||
\(373\) | 2.06259e6 | 0.767612 | 0.383806 | − | 0.923414i | \(-0.374613\pi\) | ||||
0.383806 | + | 0.923414i | \(0.374613\pi\) | |||||||
\(374\) | 3.24251e6 | 1.19868 | ||||||||
\(375\) | 4.63500e6 | 1.70205 | ||||||||
\(376\) | 452422. | 0.165034 | ||||||||
\(377\) | 1.91931e6 | 0.695493 | ||||||||
\(378\) | 1.54202e6 | 0.555085 | ||||||||
\(379\) | −2.51548e6 | −0.899546 | −0.449773 | − | 0.893143i | \(-0.648495\pi\) | ||||
−0.449773 | + | 0.893143i | \(0.648495\pi\) | |||||||
\(380\) | 1.13532e6 | 0.403330 | ||||||||
\(381\) | 2.03355e6 | 0.717700 | ||||||||
\(382\) | −2.57837e6 | −0.904038 | ||||||||
\(383\) | 5.45752e6 | 1.90107 | 0.950536 | − | 0.310615i | \(-0.100535\pi\) | ||||
0.950536 | + | 0.310615i | \(0.100535\pi\) | |||||||
\(384\) | −399429. | −0.138233 | ||||||||
\(385\) | −2.75435e6 | −0.947039 | ||||||||
\(386\) | 859855. | 0.293736 | ||||||||
\(387\) | −1.93588e6 | −0.657055 | ||||||||
\(388\) | 641225. | 0.216238 | ||||||||
\(389\) | 1.22639e6 | 0.410917 | 0.205459 | − | 0.978666i | \(-0.434131\pi\) | ||||
0.205459 | + | 0.978666i | \(0.434131\pi\) | |||||||
\(390\) | −1.63743e6 | −0.545130 | ||||||||
\(391\) | 2.64805e6 | 0.875960 | ||||||||
\(392\) | 287608. | 0.0945334 | ||||||||
\(393\) | −8.45528e6 | −2.76151 | ||||||||
\(394\) | 73826.1 | 0.0239590 | ||||||||
\(395\) | 4.82384e6 | 1.55561 | ||||||||
\(396\) | 2.35872e6 | 0.755856 | ||||||||
\(397\) | −3.62294e6 | −1.15368 | −0.576840 | − | 0.816857i | \(-0.695714\pi\) | ||||
−0.576840 | + | 0.816857i | \(0.695714\pi\) | |||||||
\(398\) | −1.90693e6 | −0.603429 | ||||||||
\(399\) | 5.61331e6 | 1.76517 | ||||||||
\(400\) | −282111. | −0.0881595 | ||||||||
\(401\) | −887350. | −0.275571 | −0.137786 | − | 0.990462i | \(-0.543999\pi\) | ||||
−0.137786 | + | 0.990462i | \(0.543999\pi\) | |||||||
\(402\) | 6.10622e6 | 1.88455 | ||||||||
\(403\) | −3.93776e6 | −1.20778 | ||||||||
\(404\) | 1.46585e6 | 0.446823 | ||||||||
\(405\) | −943737. | −0.285899 | ||||||||
\(406\) | −3.00138e6 | −0.903662 | ||||||||
\(407\) | −574415. | −0.171886 | ||||||||
\(408\) | −3.01439e6 | −0.896496 | ||||||||
\(409\) | −5.25309e6 | −1.55277 | −0.776384 | − | 0.630261i | \(-0.782948\pi\) | ||||
−0.776384 | + | 0.630261i | \(0.782948\pi\) | |||||||
\(410\) | 684907. | 0.201220 | ||||||||
\(411\) | 4.13852e6 | 1.20848 | ||||||||
\(412\) | −549580. | −0.159510 | ||||||||
\(413\) | −4.35597e6 | −1.25664 | ||||||||
\(414\) | 1.92629e6 | 0.552358 | ||||||||
\(415\) | −2.57775e6 | −0.734718 | ||||||||
\(416\) | 382282. | 0.108305 | ||||||||
\(417\) | −4.91281e6 | −1.38353 | ||||||||
\(418\) | 2.64779e6 | 0.741212 | ||||||||
\(419\) | −5.44336e6 | −1.51472 | −0.757359 | − | 0.652999i | \(-0.773511\pi\) | ||||
−0.757359 | + | 0.652999i | \(0.773511\pi\) | |||||||
\(420\) | 2.56057e6 | 0.708294 | ||||||||
\(421\) | −2.17294e6 | −0.597507 | −0.298753 | − | 0.954330i | \(-0.596571\pi\) | ||||
−0.298753 | + | 0.954330i | \(0.596571\pi\) | |||||||
\(422\) | 1.28561e6 | 0.351422 | ||||||||
\(423\) | 2.48369e6 | 0.674912 | ||||||||
\(424\) | 544945. | 0.147210 | ||||||||
\(425\) | −2.12901e6 | −0.571750 | ||||||||
\(426\) | −2.10231e6 | −0.561270 | ||||||||
\(427\) | −5.22126e6 | −1.38582 | ||||||||
\(428\) | −355745. | −0.0938705 | ||||||||
\(429\) | −3.81879e6 | −1.00180 | ||||||||
\(430\) | −991296. | −0.258543 | ||||||||
\(431\) | −1.98969e6 | −0.515932 | −0.257966 | − | 0.966154i | \(-0.583052\pi\) | ||||
−0.257966 | + | 0.966154i | \(0.583052\pi\) | |||||||
\(432\) | −676193. | −0.174326 | ||||||||
\(433\) | −2.42522e6 | −0.621630 | −0.310815 | − | 0.950470i | \(-0.600602\pi\) | ||||
−0.310815 | + | 0.950470i | \(0.600602\pi\) | |||||||
\(434\) | 6.15779e6 | 1.56928 | ||||||||
\(435\) | −5.63742e6 | −1.42843 | ||||||||
\(436\) | −3.69713e6 | −0.931427 | ||||||||
\(437\) | 2.16236e6 | 0.541656 | ||||||||
\(438\) | 2.60407e6 | 0.648587 | ||||||||
\(439\) | −40746.7 | −0.0100909 | −0.00504547 | − | 0.999987i | \(-0.501606\pi\) | ||||
−0.00504547 | + | 0.999987i | \(0.501606\pi\) | |||||||
\(440\) | 1.20782e6 | 0.297419 | ||||||||
\(441\) | 1.57890e6 | 0.386597 | ||||||||
\(442\) | 2.88498e6 | 0.702405 | ||||||||
\(443\) | 3.59743e6 | 0.870930 | 0.435465 | − | 0.900206i | \(-0.356584\pi\) | ||||
0.435465 | + | 0.900206i | \(0.356584\pi\) | |||||||
\(444\) | 534002. | 0.128554 | ||||||||
\(445\) | 2.12001e6 | 0.507503 | ||||||||
\(446\) | −1.27980e6 | −0.304652 | ||||||||
\(447\) | 2.25180e6 | 0.533041 | ||||||||
\(448\) | −597804. | −0.140723 | ||||||||
\(449\) | −1.33796e6 | −0.313204 | −0.156602 | − | 0.987662i | \(-0.550054\pi\) | ||||
−0.156602 | + | 0.987662i | \(0.550054\pi\) | |||||||
\(450\) | −1.54872e6 | −0.360531 | ||||||||
\(451\) | 1.59733e6 | 0.369789 | ||||||||
\(452\) | 332649. | 0.0765843 | ||||||||
\(453\) | −1.31879e7 | −3.01946 | ||||||||
\(454\) | −5.19337e6 | −1.18252 | ||||||||
\(455\) | −2.45065e6 | −0.554948 | ||||||||
\(456\) | −2.46150e6 | −0.554355 | ||||||||
\(457\) | −7.80585e6 | −1.74835 | −0.874177 | − | 0.485607i | \(-0.838599\pi\) | ||||
−0.874177 | + | 0.485607i | \(0.838599\pi\) | |||||||
\(458\) | −4.32684e6 | −0.963845 | ||||||||
\(459\) | −5.10305e6 | −1.13057 | ||||||||
\(460\) | 986382. | 0.217345 | ||||||||
\(461\) | −7.78534e6 | −1.70618 | −0.853091 | − | 0.521762i | \(-0.825275\pi\) | ||||
−0.853091 | + | 0.521762i | \(0.825275\pi\) | |||||||
\(462\) | 5.97174e6 | 1.30165 | ||||||||
\(463\) | −3.89653e6 | −0.844746 | −0.422373 | − | 0.906422i | \(-0.638803\pi\) | ||||
−0.422373 | + | 0.906422i | \(0.638803\pi\) | |||||||
\(464\) | 1.31614e6 | 0.283797 | ||||||||
\(465\) | 1.15660e7 | 2.48057 | ||||||||
\(466\) | −5.49300e6 | −1.17178 | ||||||||
\(467\) | 2.89728e6 | 0.614750 | 0.307375 | − | 0.951588i | \(-0.400549\pi\) | ||||
0.307375 | + | 0.951588i | \(0.400549\pi\) | |||||||
\(468\) | 2.09864e6 | 0.442918 | ||||||||
\(469\) | 9.13885e6 | 1.91849 | ||||||||
\(470\) | 1.27181e6 | 0.265569 | ||||||||
\(471\) | 4.38673e6 | 0.911148 | ||||||||
\(472\) | 1.91015e6 | 0.394650 | ||||||||
\(473\) | −2.31189e6 | −0.475132 | ||||||||
\(474\) | −1.04586e7 | −2.13810 | ||||||||
\(475\) | −1.73852e6 | −0.353546 | ||||||||
\(476\) | −4.51147e6 | −0.912642 | ||||||||
\(477\) | 2.99163e6 | 0.602021 | ||||||||
\(478\) | −5.25611e6 | −1.05219 | ||||||||
\(479\) | 591289. | 0.117750 | 0.0588751 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588751 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(480\) | −1.12284e6 | −0.222441 | ||||||||
\(481\) | −511078. | −0.100722 | ||||||||
\(482\) | 5.63799e6 | 1.10537 | ||||||||
\(483\) | 4.87691e6 | 0.951211 | ||||||||
\(484\) | 240042. | 0.0465772 | ||||||||
\(485\) | 1.80256e6 | 0.347964 | ||||||||
\(486\) | 4.61354e6 | 0.886021 | ||||||||
\(487\) | 522072. | 0.0997488 | 0.0498744 | − | 0.998755i | \(-0.484118\pi\) | ||||
0.0498744 | + | 0.998755i | \(0.484118\pi\) | |||||||
\(488\) | 2.28958e6 | 0.435218 | ||||||||
\(489\) | 1.31216e7 | 2.48151 | ||||||||
\(490\) | 808498. | 0.152121 | ||||||||
\(491\) | 1.97110e6 | 0.368981 | 0.184491 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184491 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(492\) | −1.48495e6 | −0.276567 | ||||||||
\(493\) | 9.93258e6 | 1.84054 | ||||||||
\(494\) | 2.35583e6 | 0.434337 | ||||||||
\(495\) | 6.63064e6 | 1.21631 | ||||||||
\(496\) | −2.70026e6 | −0.492835 | ||||||||
\(497\) | −3.14641e6 | −0.571379 | ||||||||
\(498\) | 5.58884e6 | 1.00983 | ||||||||
\(499\) | 3.81878e6 | 0.686553 | 0.343276 | − | 0.939234i | \(-0.388463\pi\) | ||||
0.343276 | + | 0.939234i | \(0.388463\pi\) | |||||||
\(500\) | −3.04194e6 | −0.544158 | ||||||||
\(501\) | 5.14862e6 | 0.916425 | ||||||||
\(502\) | −3.74212e6 | −0.662763 | ||||||||
\(503\) | 5.51646e6 | 0.972167 | 0.486083 | − | 0.873912i | \(-0.338425\pi\) | ||||
0.486083 | + | 0.873912i | \(0.338425\pi\) | |||||||
\(504\) | −3.28181e6 | −0.575489 | ||||||||
\(505\) | 4.12067e6 | 0.719017 | ||||||||
\(506\) | 2.30043e6 | 0.399423 | ||||||||
\(507\) | 5.65411e6 | 0.976888 | ||||||||
\(508\) | −1.33461e6 | −0.229455 | ||||||||
\(509\) | 5.41413e6 | 0.926263 | 0.463132 | − | 0.886289i | \(-0.346726\pi\) | ||||
0.463132 | + | 0.886289i | \(0.346726\pi\) | |||||||
\(510\) | −8.47378e6 | −1.44262 | ||||||||
\(511\) | 3.89738e6 | 0.660268 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −4.16708e6 | −0.699098 | ||||||||
\(514\) | 1.00807e6 | 0.168299 | ||||||||
\(515\) | −1.54493e6 | −0.256680 | ||||||||
\(516\) | 2.14924e6 | 0.355353 | ||||||||
\(517\) | 2.96610e6 | 0.488045 | ||||||||
\(518\) | 799212. | 0.130869 | ||||||||
\(519\) | −6.02033e6 | −0.981075 | ||||||||
\(520\) | 1.07464e6 | 0.174283 | ||||||||
\(521\) | −786128. | −0.126882 | −0.0634408 | − | 0.997986i | \(-0.520207\pi\) | ||||
−0.0634408 | + | 0.997986i | \(0.520207\pi\) | |||||||
\(522\) | 7.22532e6 | 1.16060 | ||||||||
\(523\) | −3.43138e6 | −0.548549 | −0.274274 | − | 0.961651i | \(-0.588438\pi\) | ||||
−0.274274 | + | 0.961651i | \(0.588438\pi\) | |||||||
\(524\) | 5.54918e6 | 0.882877 | ||||||||
\(525\) | −3.92101e6 | −0.620868 | ||||||||
\(526\) | 7.49570e6 | 1.18127 | ||||||||
\(527\) | −2.03782e7 | −3.19624 | ||||||||
\(528\) | −2.61868e6 | −0.408787 | ||||||||
\(529\) | −4.55766e6 | −0.708113 | ||||||||
\(530\) | 1.53190e6 | 0.236887 | ||||||||
\(531\) | 1.04863e7 | 1.61393 | ||||||||
\(532\) | −3.68400e6 | −0.564339 | ||||||||
\(533\) | 1.42121e6 | 0.216690 | ||||||||
\(534\) | −4.59642e6 | −0.697535 | ||||||||
\(535\) | −1.00004e6 | −0.151054 | ||||||||
\(536\) | −4.00749e6 | −0.602505 | ||||||||
\(537\) | 7.48887e6 | 1.12068 | ||||||||
\(538\) | 850048. | 0.126616 | ||||||||
\(539\) | 1.88557e6 | 0.279557 | ||||||||
\(540\) | −1.90086e6 | −0.280521 | ||||||||
\(541\) | −5.88057e6 | −0.863826 | −0.431913 | − | 0.901915i | \(-0.642161\pi\) | ||||
−0.431913 | + | 0.901915i | \(0.642161\pi\) | |||||||
\(542\) | 4.98481e6 | 0.728870 | ||||||||
\(543\) | −1.17099e7 | −1.70432 | ||||||||
\(544\) | 1.97833e6 | 0.286617 | ||||||||
\(545\) | −1.03931e7 | −1.49883 | ||||||||
\(546\) | 5.31327e6 | 0.762747 | ||||||||
\(547\) | 1.26599e7 | 1.80910 | 0.904549 | − | 0.426370i | \(-0.140208\pi\) | ||||
0.904549 | + | 0.426370i | \(0.140208\pi\) | |||||||
\(548\) | −2.71610e6 | −0.386362 | ||||||||
\(549\) | 1.25693e7 | 1.77984 | ||||||||
\(550\) | −1.84953e6 | −0.260708 | ||||||||
\(551\) | 8.11079e6 | 1.13811 | ||||||||
\(552\) | −2.13858e6 | −0.298730 | ||||||||
\(553\) | −1.56528e7 | −2.17661 | ||||||||
\(554\) | −9.61307e6 | −1.33072 | ||||||||
\(555\) | 1.50114e6 | 0.206866 | ||||||||
\(556\) | 3.22426e6 | 0.442327 | ||||||||
\(557\) | 5.97765e6 | 0.816381 | 0.408190 | − | 0.912897i | \(-0.366160\pi\) | ||||
0.408190 | + | 0.912897i | \(0.366160\pi\) | |||||||
\(558\) | −1.48238e7 | −2.01546 | ||||||||
\(559\) | −2.05697e6 | −0.278419 | ||||||||
\(560\) | −1.68049e6 | −0.226447 | ||||||||
\(561\) | −1.97625e7 | −2.65115 | ||||||||
\(562\) | −4.06078e6 | −0.542337 | ||||||||
\(563\) | 9.55818e6 | 1.27088 | 0.635440 | − | 0.772151i | \(-0.280819\pi\) | ||||
0.635440 | + | 0.772151i | \(0.280819\pi\) | |||||||
\(564\) | −2.75742e6 | −0.365010 | ||||||||
\(565\) | 935114. | 0.123238 | ||||||||
\(566\) | 1.79643e6 | 0.235705 | ||||||||
\(567\) | 3.06232e6 | 0.400031 | ||||||||
\(568\) | 1.37974e6 | 0.179443 | ||||||||
\(569\) | 1.32282e7 | 1.71285 | 0.856426 | − | 0.516270i | \(-0.172680\pi\) | ||||
0.856426 | + | 0.516270i | \(0.172680\pi\) | |||||||
\(570\) | −6.91957e6 | −0.892055 | ||||||||
\(571\) | 1.05447e7 | 1.35346 | 0.676730 | − | 0.736232i | \(-0.263397\pi\) | ||||
0.676730 | + | 0.736232i | \(0.263397\pi\) | |||||||
\(572\) | 2.50626e6 | 0.320285 | ||||||||
\(573\) | 1.57146e7 | 1.99949 | ||||||||
\(574\) | −2.22245e6 | −0.281548 | ||||||||
\(575\) | −1.51045e6 | −0.190518 | ||||||||
\(576\) | 1.43911e6 | 0.180733 | ||||||||
\(577\) | −1.37791e7 | −1.72298 | −0.861491 | − | 0.507772i | \(-0.830469\pi\) | ||||
−0.861491 | + | 0.507772i | \(0.830469\pi\) | |||||||
\(578\) | 9.25053e6 | 1.15172 | ||||||||
\(579\) | −5.24065e6 | −0.649663 | ||||||||
\(580\) | 3.69982e6 | 0.456679 | ||||||||
\(581\) | 8.36452e6 | 1.02802 | ||||||||
\(582\) | −3.90814e6 | −0.478258 | ||||||||
\(583\) | 3.57269e6 | 0.435336 | ||||||||
\(584\) | −1.70905e6 | −0.207358 | ||||||||
\(585\) | 5.89952e6 | 0.712733 | ||||||||
\(586\) | 6.01500e6 | 0.723588 | ||||||||
\(587\) | −1.39841e7 | −1.67509 | −0.837547 | − | 0.546365i | \(-0.816011\pi\) | ||||
−0.837547 | + | 0.546365i | \(0.816011\pi\) | |||||||
\(588\) | −1.75291e6 | −0.209082 | ||||||||
\(589\) | −1.66405e7 | −1.97642 | ||||||||
\(590\) | 5.36964e6 | 0.635061 | ||||||||
\(591\) | −449955. | −0.0529908 | ||||||||
\(592\) | −350464. | −0.0410997 | ||||||||
\(593\) | 4.24514e6 | 0.495742 | 0.247871 | − | 0.968793i | \(-0.420269\pi\) | ||||
0.247871 | + | 0.968793i | \(0.420269\pi\) | |||||||
\(594\) | −4.43316e6 | −0.515522 | ||||||||
\(595\) | −1.26823e7 | −1.46860 | ||||||||
\(596\) | −1.47785e6 | −0.170417 | ||||||||
\(597\) | 1.16223e7 | 1.33462 | ||||||||
\(598\) | 2.04678e6 | 0.234055 | ||||||||
\(599\) | 1.20353e7 | 1.37054 | 0.685268 | − | 0.728291i | \(-0.259685\pi\) | ||||
0.685268 | + | 0.728291i | \(0.259685\pi\) | |||||||
\(600\) | 1.71941e6 | 0.194985 | ||||||||
\(601\) | 9.83468e6 | 1.11064 | 0.555321 | − | 0.831636i | \(-0.312595\pi\) | ||||
0.555321 | + | 0.831636i | \(0.312595\pi\) | |||||||
\(602\) | 3.21665e6 | 0.361753 | ||||||||
\(603\) | −2.20002e7 | −2.46396 | ||||||||
\(604\) | 8.65516e6 | 0.965346 | ||||||||
\(605\) | 674786. | 0.0749510 | ||||||||
\(606\) | −8.93406e6 | −0.988251 | ||||||||
\(607\) | −2.24274e6 | −0.247062 | −0.123531 | − | 0.992341i | \(-0.539422\pi\) | ||||
−0.123531 | + | 0.992341i | \(0.539422\pi\) | |||||||
\(608\) | 1.61548e6 | 0.177232 | ||||||||
\(609\) | 1.82928e7 | 1.99865 | ||||||||
\(610\) | 6.43628e6 | 0.700342 | ||||||||
\(611\) | 2.63905e6 | 0.285985 | ||||||||
\(612\) | 1.08606e7 | 1.17213 | ||||||||
\(613\) | 1.47635e6 | 0.158686 | 0.0793430 | − | 0.996847i | \(-0.474718\pi\) | ||||
0.0793430 | + | 0.996847i | \(0.474718\pi\) | |||||||
\(614\) | −6.34108e6 | −0.678801 | ||||||||
\(615\) | −4.17437e6 | −0.445044 | ||||||||
\(616\) | −3.91923e6 | −0.416149 | ||||||||
\(617\) | 2.92711e6 | 0.309547 | 0.154773 | − | 0.987950i | \(-0.450535\pi\) | ||||
0.154773 | + | 0.987950i | \(0.450535\pi\) | |||||||
\(618\) | 3.34958e6 | 0.352792 | ||||||||
\(619\) | −4.45422e6 | −0.467245 | −0.233623 | − | 0.972327i | \(-0.575058\pi\) | ||||
−0.233623 | + | 0.972327i | \(0.575058\pi\) | |||||||
\(620\) | −7.59075e6 | −0.793059 | ||||||||
\(621\) | −3.62041e6 | −0.376728 | ||||||||
\(622\) | 8.53689e6 | 0.884757 | ||||||||
\(623\) | −6.87921e6 | −0.710098 | ||||||||
\(624\) | −2.32993e6 | −0.239542 | ||||||||
\(625\) | −5.10750e6 | −0.523008 | ||||||||
\(626\) | 2.03201e6 | 0.207248 | ||||||||
\(627\) | −1.61377e7 | −1.63936 | ||||||||
\(628\) | −2.87900e6 | −0.291301 | ||||||||
\(629\) | −2.64486e6 | −0.266548 | ||||||||
\(630\) | −9.22554e6 | −0.926063 | ||||||||
\(631\) | 4.76316e6 | 0.476235 | 0.238118 | − | 0.971236i | \(-0.423470\pi\) | ||||
0.238118 | + | 0.971236i | \(0.423470\pi\) | |||||||
\(632\) | 6.86395e6 | 0.683568 | ||||||||
\(633\) | −7.83556e6 | −0.777250 | ||||||||
\(634\) | −1.07035e7 | −1.05756 | ||||||||
\(635\) | −3.75175e6 | −0.369233 | ||||||||
\(636\) | −3.32133e6 | −0.325589 | ||||||||
\(637\) | 1.67766e6 | 0.163816 | ||||||||
\(638\) | 8.62869e6 | 0.839254 | ||||||||
\(639\) | 7.57445e6 | 0.733836 | ||||||||
\(640\) | 736917. | 0.0711162 | ||||||||
\(641\) | −1.96386e6 | −0.188784 | −0.0943921 | − | 0.995535i | \(-0.530091\pi\) | ||||
−0.0943921 | + | 0.995535i | \(0.530091\pi\) | |||||||
\(642\) | 2.16819e6 | 0.207616 | ||||||||
\(643\) | −3.04689e6 | −0.290622 | −0.145311 | − | 0.989386i | \(-0.546418\pi\) | ||||
−0.145311 | + | 0.989386i | \(0.546418\pi\) | |||||||
\(644\) | −3.20070e6 | −0.304110 | ||||||||
\(645\) | 6.04175e6 | 0.571826 | ||||||||
\(646\) | 1.21916e7 | 1.14942 | ||||||||
\(647\) | 687296. | 0.0645480 | 0.0322740 | − | 0.999479i | \(-0.489725\pi\) | ||||
0.0322740 | + | 0.999479i | \(0.489725\pi\) | |||||||
\(648\) | −1.34286e6 | −0.125630 | ||||||||
\(649\) | 1.25230e7 | 1.16707 | ||||||||
\(650\) | −1.64560e6 | −0.152771 | ||||||||
\(651\) | −3.75305e7 | −3.47082 | ||||||||
\(652\) | −8.61170e6 | −0.793359 | ||||||||
\(653\) | −6.72763e6 | −0.617418 | −0.308709 | − | 0.951157i | \(-0.599897\pi\) | ||||
−0.308709 | + | 0.951157i | \(0.599897\pi\) | |||||||
\(654\) | 2.25333e7 | 2.06006 | ||||||||
\(655\) | 1.55994e7 | 1.42070 | ||||||||
\(656\) | 974570. | 0.0884206 | ||||||||
\(657\) | −9.38228e6 | −0.847998 | ||||||||
\(658\) | −4.12688e6 | −0.371584 | ||||||||
\(659\) | −1.31090e7 | −1.17586 | −0.587931 | − | 0.808911i | \(-0.700057\pi\) | ||||
−0.587931 | + | 0.808911i | \(0.700057\pi\) | |||||||
\(660\) | −7.36140e6 | −0.657810 | ||||||||
\(661\) | 3.19740e6 | 0.284638 | 0.142319 | − | 0.989821i | \(-0.454544\pi\) | ||||
0.142319 | + | 0.989821i | \(0.454544\pi\) | |||||||
\(662\) | −1.29269e7 | −1.14644 | ||||||||
\(663\) | −1.75834e7 | −1.55353 | ||||||||
\(664\) | −3.66794e6 | −0.322851 | ||||||||
\(665\) | −1.03561e7 | −0.908121 | ||||||||
\(666\) | −1.92397e6 | −0.168079 | ||||||||
\(667\) | 7.04676e6 | 0.613302 | ||||||||
\(668\) | −3.37903e6 | −0.292988 | ||||||||
\(669\) | 7.80010e6 | 0.673806 | ||||||||
\(670\) | −1.12655e7 | −0.969537 | ||||||||
\(671\) | 1.50106e7 | 1.28704 | ||||||||
\(672\) | 3.64349e6 | 0.311240 | ||||||||
\(673\) | −2.22874e7 | −1.89680 | −0.948398 | − | 0.317081i | \(-0.897297\pi\) | ||||
−0.948398 | + | 0.317081i | \(0.897297\pi\) | |||||||
\(674\) | 1.42625e7 | 1.20933 | ||||||||
\(675\) | 2.91078e6 | 0.245895 | ||||||||
\(676\) | −3.71078e6 | −0.312319 | ||||||||
\(677\) | −7.64388e6 | −0.640976 | −0.320488 | − | 0.947252i | \(-0.603847\pi\) | ||||
−0.320488 | + | 0.947252i | \(0.603847\pi\) | |||||||
\(678\) | −2.02743e6 | −0.169383 | ||||||||
\(679\) | −5.84910e6 | −0.486872 | ||||||||
\(680\) | 5.56132e6 | 0.461217 | ||||||||
\(681\) | 3.16525e7 | 2.61542 | ||||||||
\(682\) | −1.77031e7 | −1.45743 | ||||||||
\(683\) | 1.99971e6 | 0.164027 | 0.0820133 | − | 0.996631i | \(-0.473865\pi\) | ||||
0.0820133 | + | 0.996631i | \(0.473865\pi\) | |||||||
\(684\) | 8.86860e6 | 0.724795 | ||||||||
\(685\) | −7.63526e6 | −0.621724 | ||||||||
\(686\) | 7.18832e6 | 0.583199 | ||||||||
\(687\) | 2.63712e7 | 2.13176 | ||||||||
\(688\) | −1.41054e6 | −0.113609 | ||||||||
\(689\) | 3.17875e6 | 0.255099 | ||||||||
\(690\) | −6.01180e6 | −0.480709 | ||||||||
\(691\) | 1.26728e6 | 0.100967 | 0.0504833 | − | 0.998725i | \(-0.483924\pi\) | ||||
0.0504833 | + | 0.998725i | \(0.483924\pi\) | |||||||
\(692\) | 3.95113e6 | 0.313657 | ||||||||
\(693\) | −2.15157e7 | −1.70185 | ||||||||
\(694\) | 9.53612e6 | 0.751576 | ||||||||
\(695\) | 9.06377e6 | 0.711782 | ||||||||
\(696\) | −8.02162e6 | −0.627681 | ||||||||
\(697\) | 7.35483e6 | 0.573443 | ||||||||
\(698\) | −4.88364e6 | −0.379407 | ||||||||
\(699\) | 3.34788e7 | 2.59165 | ||||||||
\(700\) | 2.57334e6 | 0.198497 | ||||||||
\(701\) | −6.80193e6 | −0.522802 | −0.261401 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261401 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(702\) | −3.94434e6 | −0.302087 | ||||||||
\(703\) | −2.15975e6 | −0.164822 | ||||||||
\(704\) | 1.71863e6 | 0.130693 | ||||||||
\(705\) | −7.75142e6 | −0.587366 | ||||||||
\(706\) | −5.73341e6 | −0.432914 | ||||||||
\(707\) | −1.33711e7 | −1.00605 | ||||||||
\(708\) | −1.16420e7 | −0.872857 | ||||||||
\(709\) | −7.37523e6 | −0.551011 | −0.275505 | − | 0.961300i | \(-0.588845\pi\) | ||||
−0.275505 | + | 0.961300i | \(0.588845\pi\) | |||||||
\(710\) | 3.87860e6 | 0.288755 | ||||||||
\(711\) | 3.76816e7 | 2.79547 | ||||||||
\(712\) | 3.01661e6 | 0.223008 | ||||||||
\(713\) | −1.44575e7 | −1.06505 | ||||||||
\(714\) | 2.74965e7 | 2.01852 | ||||||||
\(715\) | 7.04538e6 | 0.515394 | ||||||||
\(716\) | −4.91492e6 | −0.358289 | ||||||||
\(717\) | 3.20350e7 | 2.32716 | ||||||||
\(718\) | 6.24069e6 | 0.451775 | ||||||||
\(719\) | −1.30200e7 | −0.939264 | −0.469632 | − | 0.882862i | \(-0.655613\pi\) | ||||
−0.469632 | + | 0.882862i | \(0.655613\pi\) | |||||||
\(720\) | 4.04551e6 | 0.290832 | ||||||||
\(721\) | 5.01314e6 | 0.359146 | ||||||||
\(722\) | 51071.6 | 0.00364617 | ||||||||
\(723\) | −3.43624e7 | −2.44477 | ||||||||
\(724\) | 7.68515e6 | 0.544886 | ||||||||
\(725\) | −5.66555e6 | −0.400310 | ||||||||
\(726\) | −1.46301e6 | −0.103016 | ||||||||
\(727\) | 1.90995e7 | 1.34025 | 0.670125 | − | 0.742248i | \(-0.266241\pi\) | ||||
0.670125 | + | 0.742248i | \(0.266241\pi\) | |||||||
\(728\) | −3.48708e6 | −0.243856 | ||||||||
\(729\) | −2.30199e7 | −1.60430 | ||||||||
\(730\) | −4.80432e6 | −0.333676 | ||||||||
\(731\) | −1.06450e7 | −0.736802 | ||||||||
\(732\) | −1.39546e7 | −0.962583 | ||||||||
\(733\) | −4.61791e6 | −0.317458 | −0.158729 | − | 0.987322i | \(-0.550740\pi\) | ||||
−0.158729 | + | 0.987322i | \(0.550740\pi\) | |||||||
\(734\) | 6.89352e6 | 0.472281 | ||||||||
\(735\) | −4.92764e6 | −0.336450 | ||||||||
\(736\) | 1.40355e6 | 0.0955063 | ||||||||
\(737\) | −2.62733e7 | −1.78175 | ||||||||
\(738\) | 5.35017e6 | 0.361599 | ||||||||
\(739\) | 1.88679e6 | 0.127090 | 0.0635450 | − | 0.997979i | \(-0.479759\pi\) | ||||
0.0635450 | + | 0.997979i | \(0.479759\pi\) | |||||||
\(740\) | −985195. | −0.0661367 | ||||||||
\(741\) | −1.43583e7 | −0.960635 | ||||||||
\(742\) | −4.97086e6 | −0.331453 | ||||||||
\(743\) | −4.80888e6 | −0.319574 | −0.159787 | − | 0.987151i | \(-0.551081\pi\) | ||||
−0.159787 | + | 0.987151i | \(0.551081\pi\) | |||||||
\(744\) | 1.64576e7 | 1.09002 | ||||||||
\(745\) | −4.15440e6 | −0.274232 | ||||||||
\(746\) | 8.25038e6 | 0.542784 | ||||||||
\(747\) | −2.01362e7 | −1.32031 | ||||||||
\(748\) | 1.29701e7 | 0.847594 | ||||||||
\(749\) | 3.24502e6 | 0.211355 | ||||||||
\(750\) | 1.85400e7 | 1.20353 | ||||||||
\(751\) | −3.06925e6 | −0.198579 | −0.0992894 | − | 0.995059i | \(-0.531657\pi\) | ||||
−0.0992894 | + | 0.995059i | \(0.531657\pi\) | |||||||
\(752\) | 1.80969e6 | 0.116697 | ||||||||
\(753\) | 2.28075e7 | 1.46585 | ||||||||
\(754\) | 7.67726e6 | 0.491788 | ||||||||
\(755\) | 2.43307e7 | 1.55341 | ||||||||
\(756\) | 6.16807e6 | 0.392505 | ||||||||
\(757\) | 3.63729e6 | 0.230695 | 0.115348 | − | 0.993325i | \(-0.463202\pi\) | ||||
0.115348 | + | 0.993325i | \(0.463202\pi\) | |||||||
\(758\) | −1.00619e7 | −0.636075 | ||||||||
\(759\) | −1.40207e7 | −0.883414 | ||||||||
\(760\) | 4.54129e6 | 0.285197 | ||||||||
\(761\) | 2.89664e7 | 1.81315 | 0.906574 | − | 0.422046i | \(-0.138688\pi\) | ||||
0.906574 | + | 0.422046i | \(0.138688\pi\) | |||||||
\(762\) | 8.13421e6 | 0.507491 | ||||||||
\(763\) | 3.37244e7 | 2.09716 | ||||||||
\(764\) | −1.03135e7 | −0.639252 | ||||||||
\(765\) | 3.05304e7 | 1.88616 | ||||||||
\(766\) | 2.18301e7 | 1.34426 | ||||||||
\(767\) | 1.11422e7 | 0.683883 | ||||||||
\(768\) | −1.59772e6 | −0.0977454 | ||||||||
\(769\) | 2.17703e6 | 0.132754 | 0.0663770 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663770 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(770\) | −1.10174e7 | −0.669658 | ||||||||
\(771\) | −6.14397e6 | −0.372232 | ||||||||
\(772\) | 3.43942e6 | 0.207703 | ||||||||
\(773\) | 6.60733e6 | 0.397720 | 0.198860 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198860 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(774\) | −7.74354e6 | −0.464608 | ||||||||
\(775\) | 1.16237e7 | 0.695170 | ||||||||
\(776\) | 2.56490e6 | 0.152903 | ||||||||
\(777\) | −4.87104e6 | −0.289447 | ||||||||
\(778\) | 4.90556e6 | 0.290562 | ||||||||
\(779\) | 6.00584e6 | 0.354593 | ||||||||
\(780\) | −6.54970e6 | −0.385465 | ||||||||
\(781\) | 9.04564e6 | 0.530654 | ||||||||
\(782\) | 1.05922e7 | 0.619397 | ||||||||
\(783\) | −1.35798e7 | −0.791569 | ||||||||
\(784\) | 1.15043e6 | 0.0668452 | ||||||||
\(785\) | −8.09320e6 | −0.468755 | ||||||||
\(786\) | −3.38211e7 | −1.95268 | ||||||||
\(787\) | −2.32249e7 | −1.33665 | −0.668323 | − | 0.743871i | \(-0.732988\pi\) | ||||
−0.668323 | + | 0.743871i | \(0.732988\pi\) | |||||||
\(788\) | 295304. | 0.0169416 | ||||||||
\(789\) | −4.56848e7 | −2.61264 | ||||||||
\(790\) | 1.92954e7 | 1.09998 | ||||||||
\(791\) | −3.03434e6 | −0.172434 | ||||||||
\(792\) | 9.43489e6 | 0.534471 | ||||||||
\(793\) | 1.33555e7 | 0.754184 | ||||||||
\(794\) | −1.44918e7 | −0.815775 | ||||||||
\(795\) | −9.33665e6 | −0.523930 | ||||||||
\(796\) | −7.62770e6 | −0.426689 | ||||||||
\(797\) | 5.59531e6 | 0.312017 | 0.156009 | − | 0.987756i | \(-0.450137\pi\) | ||||
0.156009 | + | 0.987756i | \(0.450137\pi\) | |||||||
\(798\) | 2.24532e7 | 1.24816 | ||||||||
\(799\) | 1.36572e7 | 0.756825 | ||||||||
\(800\) | −1.12844e6 | −0.0623382 | ||||||||
\(801\) | 1.65605e7 | 0.911996 | ||||||||
\(802\) | −3.54940e6 | −0.194858 | ||||||||
\(803\) | −1.12046e7 | −0.613207 | ||||||||
\(804\) | 2.44249e7 | 1.33258 | ||||||||
\(805\) | −8.99754e6 | −0.489366 | ||||||||
\(806\) | −1.57511e7 | −0.854028 | ||||||||
\(807\) | −5.18087e6 | −0.280039 | ||||||||
\(808\) | 5.86340e6 | 0.315952 | ||||||||
\(809\) | −2.24334e7 | −1.20510 | −0.602550 | − | 0.798081i | \(-0.705849\pi\) | ||||
−0.602550 | + | 0.798081i | \(0.705849\pi\) | |||||||
\(810\) | −3.77495e6 | −0.202161 | ||||||||
\(811\) | 6.24934e6 | 0.333643 | 0.166821 | − | 0.985987i | \(-0.446650\pi\) | ||||
0.166821 | + | 0.985987i | \(0.446650\pi\) | |||||||
\(812\) | −1.20055e7 | −0.638986 | ||||||||
\(813\) | −3.03814e7 | −1.61206 | ||||||||
\(814\) | −2.29766e6 | −0.121542 | ||||||||
\(815\) | −2.42085e7 | −1.27665 | ||||||||
\(816\) | −1.20575e7 | −0.633919 | ||||||||
\(817\) | −8.69252e6 | −0.455607 | ||||||||
\(818\) | −2.10123e7 | −1.09797 | ||||||||
\(819\) | −1.91433e7 | −0.997257 | ||||||||
\(820\) | 2.73963e6 | 0.142284 | ||||||||
\(821\) | 3.21770e7 | 1.66605 | 0.833024 | − | 0.553237i | \(-0.186608\pi\) | ||||
0.833024 | + | 0.553237i | \(0.186608\pi\) | |||||||
\(822\) | 1.65541e7 | 0.854526 | ||||||||
\(823\) | −1.60157e7 | −0.824227 | −0.412114 | − | 0.911132i | \(-0.635209\pi\) | ||||
−0.412114 | + | 0.911132i | \(0.635209\pi\) | |||||||
\(824\) | −2.19832e6 | −0.112791 | ||||||||
\(825\) | 1.12725e7 | 0.576616 | ||||||||
\(826\) | −1.74239e7 | −0.888577 | ||||||||
\(827\) | −1.11834e7 | −0.568602 | −0.284301 | − | 0.958735i | \(-0.591762\pi\) | ||||
−0.284301 | + | 0.958735i | \(0.591762\pi\) | |||||||
\(828\) | 7.70515e6 | 0.390576 | ||||||||
\(829\) | −1.20543e7 | −0.609193 | −0.304597 | − | 0.952481i | \(-0.598522\pi\) | ||||
−0.304597 | + | 0.952481i | \(0.598522\pi\) | |||||||
\(830\) | −1.03110e7 | −0.519524 | ||||||||
\(831\) | 5.85898e7 | 2.94320 | ||||||||
\(832\) | 1.52913e6 | 0.0765835 | ||||||||
\(833\) | 8.68200e6 | 0.433518 | ||||||||
\(834\) | −1.96512e7 | −0.978306 | ||||||||
\(835\) | −9.49883e6 | −0.471470 | ||||||||
\(836\) | 1.05912e7 | 0.524116 | ||||||||
\(837\) | 2.78610e7 | 1.37462 | ||||||||
\(838\) | −2.17734e7 | −1.07107 | ||||||||
\(839\) | 1.09546e7 | 0.537270 | 0.268635 | − | 0.963242i | \(-0.413427\pi\) | ||||
0.268635 | + | 0.963242i | \(0.413427\pi\) | |||||||
\(840\) | 1.02423e7 | 0.500839 | ||||||||
\(841\) | 5.92055e6 | 0.288650 | ||||||||
\(842\) | −8.69177e6 | −0.422501 | ||||||||
\(843\) | 2.47497e7 | 1.19950 | ||||||||
\(844\) | 5.14246e6 | 0.248493 | ||||||||
\(845\) | −1.04314e7 | −0.502576 | ||||||||
\(846\) | 9.93477e6 | 0.477235 | ||||||||
\(847\) | −2.18961e6 | −0.104871 | ||||||||
\(848\) | 2.17978e6 | 0.104093 | ||||||||
\(849\) | −1.09489e7 | −0.521314 | ||||||||
\(850\) | −8.51606e6 | −0.404288 | ||||||||
\(851\) | −1.87642e6 | −0.0888191 | ||||||||
\(852\) | −8.40923e6 | −0.396878 | ||||||||
\(853\) | 2.61056e7 | 1.22846 | 0.614231 | − | 0.789126i | \(-0.289466\pi\) | ||||
0.614231 | + | 0.789126i | \(0.289466\pi\) | |||||||
\(854\) | −2.08850e7 | −0.979919 | ||||||||
\(855\) | 2.49307e7 | 1.16632 | ||||||||
\(856\) | −1.42298e6 | −0.0663765 | ||||||||
\(857\) | 3.72343e7 | 1.73177 | 0.865887 | − | 0.500239i | \(-0.166755\pi\) | ||||
0.865887 | + | 0.500239i | \(0.166755\pi\) | |||||||
\(858\) | −1.52752e7 | −0.708382 | ||||||||
\(859\) | 5.97467e6 | 0.276268 | 0.138134 | − | 0.990414i | \(-0.455889\pi\) | ||||
0.138134 | + | 0.990414i | \(0.455889\pi\) | |||||||
\(860\) | −3.96518e6 | −0.182817 | ||||||||
\(861\) | 1.35454e7 | 0.622706 | ||||||||
\(862\) | −7.95877e6 | −0.364819 | ||||||||
\(863\) | −2.75432e7 | −1.25889 | −0.629443 | − | 0.777046i | \(-0.716717\pi\) | ||||
−0.629443 | + | 0.777046i | \(0.716717\pi\) | |||||||
\(864\) | −2.70477e6 | −0.123267 | ||||||||
\(865\) | 1.11071e7 | 0.504730 | ||||||||
\(866\) | −9.70089e6 | −0.439559 | ||||||||
\(867\) | −5.63802e7 | −2.54729 | ||||||||
\(868\) | 2.46312e7 | 1.10965 | ||||||||
\(869\) | 4.50005e7 | 2.02147 | ||||||||
\(870\) | −2.25497e7 | −1.01005 | ||||||||
\(871\) | −2.33763e7 | −1.04407 | ||||||||
\(872\) | −1.47885e7 | −0.658619 | ||||||||
\(873\) | 1.40807e7 | 0.625301 | ||||||||
\(874\) | 8.64943e6 | 0.383009 | ||||||||
\(875\) | 2.77478e7 | 1.22520 | ||||||||
\(876\) | 1.04163e7 | 0.458620 | ||||||||
\(877\) | 2.75263e7 | 1.20851 | 0.604254 | − | 0.796792i | \(-0.293471\pi\) | ||||
0.604254 | + | 0.796792i | \(0.293471\pi\) | |||||||
\(878\) | −162987. | −0.00713537 | ||||||||
\(879\) | −3.66602e7 | −1.60038 | ||||||||
\(880\) | 4.83127e6 | 0.210307 | ||||||||
\(881\) | 8.47736e6 | 0.367977 | 0.183989 | − | 0.982928i | \(-0.441099\pi\) | ||||
0.183989 | + | 0.982928i | \(0.441099\pi\) | |||||||
\(882\) | 6.31561e6 | 0.273365 | ||||||||
\(883\) | −1.14175e7 | −0.492799 | −0.246399 | − | 0.969168i | \(-0.579247\pi\) | ||||
−0.246399 | + | 0.969168i | \(0.579247\pi\) | |||||||
\(884\) | 1.15399e7 | 0.496675 | ||||||||
\(885\) | −3.27269e7 | −1.40458 | ||||||||
\(886\) | 1.43897e7 | 0.615840 | ||||||||
\(887\) | 1.59521e7 | 0.680782 | 0.340391 | − | 0.940284i | \(-0.389441\pi\) | ||||
0.340391 | + | 0.940284i | \(0.389441\pi\) | |||||||
\(888\) | 2.13601e6 | 0.0909014 | ||||||||
\(889\) | 1.21740e7 | 0.516631 | ||||||||
\(890\) | 8.48005e6 | 0.358859 | ||||||||
\(891\) | −8.80389e6 | −0.371519 | ||||||||
\(892\) | −5.11919e6 | −0.215421 | ||||||||
\(893\) | 1.11523e7 | 0.467989 | ||||||||
\(894\) | 9.00719e6 | 0.376917 | ||||||||
\(895\) | −1.38164e7 | −0.576551 | ||||||||
\(896\) | −2.39121e6 | −0.0995058 | ||||||||
\(897\) | −1.24747e7 | −0.517665 | ||||||||
\(898\) | −5.35183e6 | −0.221468 | ||||||||
\(899\) | −5.42286e7 | −2.23784 | ||||||||
\(900\) | −6.19489e6 | −0.254934 | ||||||||
\(901\) | 1.64502e7 | 0.675088 | ||||||||
\(902\) | 6.38933e6 | 0.261480 | ||||||||
\(903\) | −1.96048e7 | −0.800099 | ||||||||
\(904\) | 1.33059e6 | 0.0541533 | ||||||||
\(905\) | 2.16038e7 | 0.876818 | ||||||||
\(906\) | −5.27515e7 | −2.13508 | ||||||||
\(907\) | 4.89568e7 | 1.97604 | 0.988018 | − | 0.154336i | \(-0.0493238\pi\) | ||||
0.988018 | + | 0.154336i | \(0.0493238\pi\) | |||||||
\(908\) | −2.07735e7 | −0.836170 | ||||||||
\(909\) | 3.21887e7 | 1.29209 | ||||||||
\(910\) | −9.80259e6 | −0.392408 | ||||||||
\(911\) | −2.39778e7 | −0.957225 | −0.478613 | − | 0.878026i | \(-0.658860\pi\) | ||||
−0.478613 | + | 0.878026i | \(0.658860\pi\) | |||||||
\(912\) | −9.84601e6 | −0.391988 | ||||||||
\(913\) | −2.40472e7 | −0.954747 | ||||||||
\(914\) | −3.12234e7 | −1.23627 | ||||||||
\(915\) | −3.92278e7 | −1.54897 | ||||||||
\(916\) | −1.73074e7 | −0.681541 | ||||||||
\(917\) | −5.06182e7 | −1.98785 | ||||||||
\(918\) | −2.04122e7 | −0.799435 | ||||||||
\(919\) | −3.64828e7 | −1.42495 | −0.712474 | − | 0.701699i | \(-0.752425\pi\) | ||||
−0.712474 | + | 0.701699i | \(0.752425\pi\) | |||||||
\(920\) | 3.94553e6 | 0.153686 | ||||||||
\(921\) | 3.86476e7 | 1.50132 | ||||||||
\(922\) | −3.11414e7 | −1.20645 | ||||||||
\(923\) | 8.04823e6 | 0.310954 | ||||||||
\(924\) | 2.38869e7 | 0.920409 | ||||||||
\(925\) | 1.50863e6 | 0.0579734 | ||||||||
\(926\) | −1.55861e7 | −0.597325 | ||||||||
\(927\) | −1.20683e7 | −0.461260 | ||||||||
\(928\) | 5.26457e6 | 0.200675 | ||||||||
\(929\) | 6.67014e6 | 0.253569 | 0.126784 | − | 0.991930i | \(-0.459534\pi\) | ||||
0.126784 | + | 0.991930i | \(0.459534\pi\) | |||||||
\(930\) | 4.62641e7 | 1.75403 | ||||||||
\(931\) | 7.08959e6 | 0.268069 | ||||||||
\(932\) | −2.19720e7 | −0.828572 | ||||||||
\(933\) | −5.20307e7 | −1.95684 | ||||||||
\(934\) | 1.15891e7 | 0.434694 | ||||||||
\(935\) | 3.64603e7 | 1.36393 | ||||||||
\(936\) | 8.39456e6 | 0.313190 | ||||||||
\(937\) | −3.29325e7 | −1.22539 | −0.612697 | − | 0.790318i | \(-0.709915\pi\) | ||||
−0.612697 | + | 0.790318i | \(0.709915\pi\) | |||||||
\(938\) | 3.65554e7 | 1.35658 | ||||||||
\(939\) | −1.23847e7 | −0.458376 | ||||||||
\(940\) | 5.08724e6 | 0.187786 | ||||||||
\(941\) | 4.00487e7 | 1.47440 | 0.737198 | − | 0.675677i | \(-0.236148\pi\) | ||||
0.737198 | + | 0.675677i | \(0.236148\pi\) | |||||||
\(942\) | 1.75469e7 | 0.644279 | ||||||||
\(943\) | 5.21795e6 | 0.191082 | ||||||||
\(944\) | 7.64058e6 | 0.279059 | ||||||||
\(945\) | 1.73392e7 | 0.631609 | ||||||||
\(946\) | −9.24756e6 | −0.335969 | ||||||||
\(947\) | 6.91973e6 | 0.250735 | 0.125367 | − | 0.992110i | \(-0.459989\pi\) | ||||
0.125367 | + | 0.992110i | \(0.459989\pi\) | |||||||
\(948\) | −4.18344e7 | −1.51187 | ||||||||
\(949\) | −9.96914e6 | −0.359329 | ||||||||
\(950\) | −6.95409e6 | −0.249995 | ||||||||
\(951\) | 6.52358e7 | 2.33902 | ||||||||
\(952\) | −1.80459e7 | −0.645336 | ||||||||
\(953\) | 2.39076e7 | 0.852715 | 0.426357 | − | 0.904555i | \(-0.359797\pi\) | ||||
0.426357 | + | 0.904555i | \(0.359797\pi\) | |||||||
\(954\) | 1.19665e7 | 0.425693 | ||||||||
\(955\) | −2.89924e7 | −1.02867 | ||||||||
\(956\) | −2.10245e7 | −0.744012 | ||||||||
\(957\) | −5.25902e7 | −1.85620 | ||||||||
\(958\) | 2.36516e6 | 0.0832619 | ||||||||
\(959\) | 2.47756e7 | 0.869917 | ||||||||
\(960\) | −4.49136e6 | −0.157290 | ||||||||
\(961\) | 8.26291e7 | 2.88619 | ||||||||
\(962\) | −2.04431e6 | −0.0712212 | ||||||||
\(963\) | −7.81184e6 | −0.271449 | ||||||||
\(964\) | 2.25519e7 | 0.781612 | ||||||||
\(965\) | 9.66861e6 | 0.334230 | ||||||||
\(966\) | 1.95076e7 | 0.672608 | ||||||||
\(967\) | −1.85809e7 | −0.638998 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(968\) | 960168. | 0.0329351 | ||||||||
\(969\) | −7.43053e7 | −2.54220 | ||||||||
\(970\) | 7.21023e6 | 0.246048 | ||||||||
\(971\) | −4.82454e7 | −1.64213 | −0.821065 | − | 0.570834i | \(-0.806620\pi\) | ||||
−0.821065 | + | 0.570834i | \(0.806620\pi\) | |||||||
\(972\) | 1.84542e7 | 0.626511 | ||||||||
\(973\) | −2.94109e7 | −0.995926 | ||||||||
\(974\) | 2.08829e6 | 0.0705330 | ||||||||
\(975\) | 1.00296e7 | 0.337887 | ||||||||
\(976\) | 9.15833e6 | 0.307746 | ||||||||
\(977\) | −1.99798e7 | −0.669662 | −0.334831 | − | 0.942278i | \(-0.608679\pi\) | ||||
−0.334831 | + | 0.942278i | \(0.608679\pi\) | |||||||
\(978\) | 5.24866e7 | 1.75469 | ||||||||
\(979\) | 1.97771e7 | 0.659486 | ||||||||
\(980\) | 3.23399e6 | 0.107566 | ||||||||
\(981\) | −8.11857e7 | −2.69344 | ||||||||
\(982\) | 7.88439e6 | 0.260909 | ||||||||
\(983\) | 2.38930e7 | 0.788653 | 0.394327 | − | 0.918970i | \(-0.370978\pi\) | ||||
0.394327 | + | 0.918970i | \(0.370978\pi\) | |||||||
\(984\) | −5.93981e6 | −0.195562 | ||||||||
\(985\) | 830134. | 0.0272620 | ||||||||
\(986\) | 3.97303e7 | 1.30146 | ||||||||
\(987\) | 2.51525e7 | 0.821843 | ||||||||
\(988\) | 9.42333e6 | 0.307123 | ||||||||
\(989\) | −7.55217e6 | −0.245517 | ||||||||
\(990\) | 2.65226e7 | 0.860058 | ||||||||
\(991\) | −1.94203e6 | −0.0628163 | −0.0314082 | − | 0.999507i | \(-0.509999\pi\) | ||||
−0.0314082 | + | 0.999507i | \(0.509999\pi\) | |||||||
\(992\) | −1.08011e7 | −0.348487 | ||||||||
\(993\) | 7.87871e7 | 2.53561 | ||||||||
\(994\) | −1.25856e7 | −0.404026 | ||||||||
\(995\) | −2.14423e7 | −0.686617 | ||||||||
\(996\) | 2.23554e7 | 0.714058 | ||||||||
\(997\) | −1.18559e7 | −0.377744 | −0.188872 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188872 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(998\) | 1.52751e7 | 0.485466 | ||||||||
\(999\) | 3.61605e6 | 0.114636 |
(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 | 74.6.a.e.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 666.6.a.l.1.3 | 5 | |||
4.3 | odd | 2 | 592.6.a.e.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.6.a.e.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
592.6.a.e.1.5 | 5 | 4.3 | odd | 2 | |||
666.6.a.l.1.3 | 5 | 3.2 | odd | 2 |