Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(28,29)]
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([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(4.65113077458\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 278x^{10} + 28285x^{8} + 1260472x^{6} + 22944832x^{4} + 140087936x^{2} + 966400 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{14}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.9 | ||
Root | \(4.44887i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.6.b.a.28.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.44887i | 0.786457i | 0.919441 | + | 0.393229i | \(0.128642\pi\) | ||||
−0.919441 | + | 0.393229i | \(0.871358\pi\) | |||||||
\(3\) | 21.5070i | 1.37968i | 0.723963 | + | 0.689839i | \(0.242319\pi\) | ||||
−0.723963 | + | 0.689839i | \(0.757681\pi\) | |||||||
\(4\) | 12.2075 | 0.381485 | ||||||||
\(5\) | 90.0922 | 1.61162 | 0.805809 | − | 0.592175i | \(-0.201731\pi\) | ||||
0.805809 | + | 0.592175i | \(0.201731\pi\) | |||||||
\(6\) | −95.6821 | −1.08506 | ||||||||
\(7\) | −211.678 | −1.63279 | −0.816394 | − | 0.577495i | \(-0.804030\pi\) | ||||
−0.816394 | + | 0.577495i | \(0.804030\pi\) | |||||||
\(8\) | 196.674i | 1.08648i | ||||||||
\(9\) | −219.553 | −0.903510 | ||||||||
\(10\) | 400.809i | 1.26747i | ||||||||
\(11\) | − | 593.900i | − | 1.47990i | −0.672663 | − | 0.739949i | \(-0.734850\pi\) | ||
0.672663 | − | 0.739949i | \(-0.265150\pi\) | |||||||
\(12\) | 262.548i | 0.526326i | ||||||||
\(13\) | 445.466 | 0.731065 | 0.365532 | − | 0.930799i | \(-0.380887\pi\) | ||||
0.365532 | + | 0.930799i | \(0.380887\pi\) | |||||||
\(14\) | − | 941.727i | − | 1.28412i | ||||||
\(15\) | 1937.62i | 2.22351i | ||||||||
\(16\) | −484.336 | −0.472985 | ||||||||
\(17\) | − | 368.642i | − | 0.309373i | −0.987964 | − | 0.154687i | \(-0.950563\pi\) | ||
0.987964 | − | 0.154687i | \(-0.0494368\pi\) | |||||||
\(18\) | − | 976.764i | − | 0.710572i | ||||||
\(19\) | 761.926i | 0.484205i | 0.970251 | + | 0.242102i | \(0.0778370\pi\) | ||||
−0.970251 | + | 0.242102i | \(0.922163\pi\) | |||||||
\(20\) | 1099.80 | 0.614808 | ||||||||
\(21\) | − | 4552.56i | − | 2.25272i | ||||||
\(22\) | 2642.19 | 1.16388 | ||||||||
\(23\) | 728.987 | 0.287343 | 0.143671 | − | 0.989625i | \(-0.454109\pi\) | ||||
0.143671 | + | 0.989625i | \(0.454109\pi\) | |||||||
\(24\) | −4229.87 | −1.49899 | ||||||||
\(25\) | 4991.60 | 1.59731 | ||||||||
\(26\) | 1981.82i | 0.574951i | ||||||||
\(27\) | 504.276i | 0.133125i | ||||||||
\(28\) | −2584.06 | −0.622884 | ||||||||
\(29\) | 2787.76 | + | 3569.25i | 0.615547 | + | 0.788100i | ||||
\(30\) | −8620.22 | −1.74870 | ||||||||
\(31\) | − | 9222.49i | − | 1.72363i | −0.507223 | − | 0.861815i | \(-0.669328\pi\) | ||
0.507223 | − | 0.861815i | \(-0.330672\pi\) | |||||||
\(32\) | 4138.81i | 0.714497i | ||||||||
\(33\) | 12773.0 | 2.04178 | ||||||||
\(34\) | 1640.04 | 0.243309 | ||||||||
\(35\) | −19070.5 | −2.63143 | ||||||||
\(36\) | −2680.20 | −0.344675 | ||||||||
\(37\) | − | 3392.70i | − | 0.407418i | −0.979031 | − | 0.203709i | \(-0.934700\pi\) | ||
0.979031 | − | 0.203709i | \(-0.0652997\pi\) | |||||||
\(38\) | −3389.71 | −0.380806 | ||||||||
\(39\) | 9580.65i | 1.00863i | ||||||||
\(40\) | 17718.8i | 1.75099i | ||||||||
\(41\) | 1763.84i | 0.163870i | 0.996638 | + | 0.0819351i | \(0.0261100\pi\) | ||||
−0.996638 | + | 0.0819351i | \(0.973890\pi\) | |||||||
\(42\) | 20253.8 | 1.77167 | ||||||||
\(43\) | 5296.04i | 0.436797i | 0.975860 | + | 0.218399i | \(0.0700833\pi\) | ||||
−0.975860 | + | 0.218399i | \(0.929917\pi\) | |||||||
\(44\) | − | 7250.04i | − | 0.564559i | ||||||
\(45\) | −19780.0 | −1.45611 | ||||||||
\(46\) | 3243.17i | 0.225983i | ||||||||
\(47\) | − | 12459.7i | − | 0.822741i | −0.911468 | − | 0.411371i | \(-0.865050\pi\) | ||
0.911468 | − | 0.411371i | \(-0.134950\pi\) | |||||||
\(48\) | − | 10416.6i | − | 0.652566i | ||||||
\(49\) | 28000.4 | 1.66600 | ||||||||
\(50\) | 22207.0i | 1.25622i | ||||||||
\(51\) | 7928.41 | 0.426836 | ||||||||
\(52\) | 5438.03 | 0.278890 | ||||||||
\(53\) | −14753.2 | −0.721432 | −0.360716 | − | 0.932676i | \(-0.617468\pi\) | ||||
−0.360716 | + | 0.932676i | \(0.617468\pi\) | |||||||
\(54\) | −2243.46 | −0.104697 | ||||||||
\(55\) | − | 53505.8i | − | 2.38503i | ||||||
\(56\) | − | 41631.4i | − | 1.77399i | ||||||
\(57\) | −16386.8 | −0.668046 | ||||||||
\(58\) | −15879.1 | + | 12402.4i | −0.619807 | + | 0.484101i | ||||
\(59\) | −34598.5 | −1.29398 | −0.646989 | − | 0.762499i | \(-0.723972\pi\) | ||||
−0.646989 | + | 0.762499i | \(0.723972\pi\) | |||||||
\(60\) | 23653.5i | 0.848237i | ||||||||
\(61\) | − | 9455.51i | − | 0.325357i | −0.986679 | − | 0.162679i | \(-0.947987\pi\) | ||
0.986679 | − | 0.162679i | \(-0.0520133\pi\) | |||||||
\(62\) | 41029.7 | 1.35556 | ||||||||
\(63\) | 46474.5 | 1.47524 | ||||||||
\(64\) | −33911.8 | −1.03491 | ||||||||
\(65\) | 40133.0 | 1.17820 | ||||||||
\(66\) | 56825.6i | 1.60577i | ||||||||
\(67\) | 41093.0 | 1.11836 | 0.559179 | − | 0.829047i | \(-0.311116\pi\) | ||||
0.559179 | + | 0.829047i | \(0.311116\pi\) | |||||||
\(68\) | − | 4500.21i | − | 0.118021i | ||||||
\(69\) | 15678.4i | 0.396440i | ||||||||
\(70\) | − | 84842.3i | − | 2.06951i | ||||||
\(71\) | −23404.1 | −0.550992 | −0.275496 | − | 0.961302i | \(-0.588842\pi\) | ||||
−0.275496 | + | 0.961302i | \(0.588842\pi\) | |||||||
\(72\) | − | 43180.3i | − | 0.981645i | ||||||
\(73\) | 25457.6i | 0.559127i | 0.960127 | + | 0.279563i | \(0.0901897\pi\) | ||||
−0.960127 | + | 0.279563i | \(0.909810\pi\) | |||||||
\(74\) | 15093.7 | 0.320417 | ||||||||
\(75\) | 107355.i | 2.20378i | ||||||||
\(76\) | 9301.22i | 0.184717i | ||||||||
\(77\) | 125715.i | 2.41636i | ||||||||
\(78\) | −42623.1 | −0.793248 | ||||||||
\(79\) | − | 45401.0i | − | 0.818460i | −0.912431 | − | 0.409230i | \(-0.865797\pi\) | ||
0.912431 | − | 0.409230i | \(-0.134203\pi\) | |||||||
\(80\) | −43634.9 | −0.762270 | ||||||||
\(81\) | −64196.9 | −1.08718 | ||||||||
\(82\) | −7847.11 | −0.128877 | ||||||||
\(83\) | −53492.2 | −0.852306 | −0.426153 | − | 0.904651i | \(-0.640131\pi\) | ||||
−0.426153 | + | 0.904651i | \(0.640131\pi\) | |||||||
\(84\) | − | 55575.5i | − | 0.859379i | ||||||
\(85\) | − | 33211.8i | − | 0.498592i | ||||||
\(86\) | −23561.4 | −0.343523 | ||||||||
\(87\) | −76763.9 | + | 59956.6i | −1.08732 | + | 0.849256i | ||||
\(88\) | 116805. | 1.60788 | ||||||||
\(89\) | − | 112498.i | − | 1.50547i | −0.658326 | − | 0.752733i | \(-0.728735\pi\) | ||
0.658326 | − | 0.752733i | \(-0.271265\pi\) | |||||||
\(90\) | − | 87998.8i | − | 1.14517i | ||||||
\(91\) | −94295.2 | −1.19367 | ||||||||
\(92\) | 8899.12 | 0.109617 | ||||||||
\(93\) | 198349. | 2.37805 | ||||||||
\(94\) | 55431.7 | 0.647051 | ||||||||
\(95\) | 68643.6i | 0.780353i | ||||||||
\(96\) | −89013.5 | −0.985775 | ||||||||
\(97\) | − | 724.916i | − | 0.00782273i | −0.999992 | − | 0.00391137i | \(-0.998755\pi\) | ||
0.999992 | − | 0.00391137i | \(-0.00124503\pi\) | |||||||
\(98\) | 124570.i | 1.31024i | ||||||||
\(99\) | 130393.i | 1.33710i | ||||||||
\(100\) | 60935.1 | 0.609351 | ||||||||
\(101\) | 55652.7i | 0.542854i | 0.962459 | + | 0.271427i | \(0.0874955\pi\) | ||||
−0.962459 | + | 0.271427i | \(0.912505\pi\) | |||||||
\(102\) | 35272.5i | 0.335688i | ||||||||
\(103\) | 86986.8 | 0.807905 | 0.403953 | − | 0.914780i | \(-0.367636\pi\) | ||||
0.403953 | + | 0.914780i | \(0.367636\pi\) | |||||||
\(104\) | 87611.4i | 0.794287i | ||||||||
\(105\) | − | 410150.i | − | 3.63053i | ||||||
\(106\) | − | 65635.0i | − | 0.567376i | ||||||
\(107\) | −67319.9 | −0.568439 | −0.284220 | − | 0.958759i | \(-0.591734\pi\) | ||||
−0.284220 | + | 0.958759i | \(0.591734\pi\) | |||||||
\(108\) | 6155.96i | 0.0507851i | ||||||||
\(109\) | −107618. | −0.867595 | −0.433797 | − | 0.901010i | \(-0.642827\pi\) | ||||
−0.433797 | + | 0.901010i | \(0.642827\pi\) | |||||||
\(110\) | 238040. | 1.87572 | ||||||||
\(111\) | 72966.9 | 0.562106 | ||||||||
\(112\) | 102523. | 0.772284 | ||||||||
\(113\) | − | 140630.i | − | 1.03605i | −0.855365 | − | 0.518027i | \(-0.826667\pi\) | ||
0.855365 | − | 0.518027i | \(-0.173333\pi\) | |||||||
\(114\) | − | 72902.7i | − | 0.525390i | ||||||
\(115\) | 65676.0 | 0.463087 | ||||||||
\(116\) | 34031.7 | + | 43571.6i | 0.234822 | + | 0.300648i | ||||
\(117\) | −97803.3 | −0.660525 | ||||||||
\(118\) | − | 153924.i | − | 1.01766i | ||||||
\(119\) | 78033.4i | 0.505141i | ||||||||
\(120\) | −381078. | −2.41580 | ||||||||
\(121\) | −191666. | −1.19010 | ||||||||
\(122\) | 42066.4 | 0.255879 | ||||||||
\(123\) | −37935.0 | −0.226088 | ||||||||
\(124\) | − | 112584.i | − | 0.657539i | ||||||
\(125\) | 168167. | 0.962642 | ||||||||
\(126\) | 206759.i | 1.16021i | ||||||||
\(127\) | 210012.i | 1.15541i | 0.816247 | + | 0.577703i | \(0.196051\pi\) | ||||
−0.816247 | + | 0.577703i | \(0.803949\pi\) | |||||||
\(128\) | − | 18427.5i | − | 0.0994125i | ||||||
\(129\) | −113902. | −0.602640 | ||||||||
\(130\) | 178547.i | 0.926602i | ||||||||
\(131\) | 92160.7i | 0.469210i | 0.972091 | + | 0.234605i | \(0.0753797\pi\) | ||||
−0.972091 | + | 0.234605i | \(0.924620\pi\) | |||||||
\(132\) | 155927. | 0.778909 | ||||||||
\(133\) | − | 161283.i | − | 0.790604i | ||||||
\(134\) | 182818.i | 0.879541i | ||||||||
\(135\) | 45431.3i | 0.214546i | ||||||||
\(136\) | 72502.3 | 0.336128 | ||||||||
\(137\) | − | 102506.i | − | 0.466602i | −0.972405 | − | 0.233301i | \(-0.925047\pi\) | ||
0.972405 | − | 0.233301i | \(-0.0749528\pi\) | |||||||
\(138\) | −69751.0 | −0.311783 | ||||||||
\(139\) | −199342. | −0.875106 | −0.437553 | − | 0.899193i | \(-0.644155\pi\) | ||||
−0.437553 | + | 0.899193i | \(0.644155\pi\) | |||||||
\(140\) | −232803. | −1.00385 | ||||||||
\(141\) | 267972. | 1.13512 | ||||||||
\(142\) | − | 104122.i | − | 0.433332i | ||||||
\(143\) | − | 264562.i | − | 1.08190i | ||||||
\(144\) | 106337. | 0.427346 | ||||||||
\(145\) | 251156. | + | 321561.i | 0.992026 | + | 1.27012i | ||||
\(146\) | −113258. | −0.439729 | ||||||||
\(147\) | 602207.i | 2.29854i | ||||||||
\(148\) | − | 41416.4i | − | 0.155424i | ||||||
\(149\) | −9725.12 | −0.0358863 | −0.0179432 | − | 0.999839i | \(-0.505712\pi\) | ||||
−0.0179432 | + | 0.999839i | \(0.505712\pi\) | |||||||
\(150\) | −477607. | −1.73318 | ||||||||
\(151\) | 483239. | 1.72472 | 0.862362 | − | 0.506292i | \(-0.168984\pi\) | ||||
0.862362 | + | 0.506292i | \(0.168984\pi\) | |||||||
\(152\) | −149851. | −0.526078 | ||||||||
\(153\) | 80936.5i | 0.279522i | ||||||||
\(154\) | −559292. | −1.90036 | ||||||||
\(155\) | − | 830874.i | − | 2.77783i | ||||||
\(156\) | 116956.i | 0.384779i | ||||||||
\(157\) | − | 84963.6i | − | 0.275096i | −0.990495 | − | 0.137548i | \(-0.956078\pi\) | ||
0.990495 | − | 0.137548i | \(-0.0439221\pi\) | |||||||
\(158\) | 201983. | 0.643684 | ||||||||
\(159\) | − | 317297.i | − | 0.995344i | ||||||
\(160\) | 372874.i | 1.15150i | ||||||||
\(161\) | −154310. | −0.469170 | ||||||||
\(162\) | − | 285604.i | − | 0.855020i | ||||||
\(163\) | 531836.i | 1.56786i | 0.620846 | + | 0.783932i | \(0.286789\pi\) | ||||
−0.620846 | + | 0.783932i | \(0.713211\pi\) | |||||||
\(164\) | 21532.1i | 0.0625140i | ||||||||
\(165\) | 1.15075e6 | 3.29057 | ||||||||
\(166\) | − | 237980.i | − | 0.670302i | ||||||
\(167\) | −505065. | −1.40138 | −0.700690 | − | 0.713466i | \(-0.747124\pi\) | ||||
−0.700690 | + | 0.713466i | \(0.747124\pi\) | |||||||
\(168\) | 895369. | 2.44753 | ||||||||
\(169\) | −172853. | −0.465544 | ||||||||
\(170\) | 147755. | 0.392121 | ||||||||
\(171\) | − | 167283.i | − | 0.437484i | ||||||
\(172\) | 64651.5i | 0.166632i | ||||||||
\(173\) | −187852. | −0.477201 | −0.238601 | − | 0.971118i | \(-0.576689\pi\) | ||||
−0.238601 | + | 0.971118i | \(0.576689\pi\) | |||||||
\(174\) | −266739. | − | 341513.i | −0.667904 | − | 0.855134i | ||||
\(175\) | −1.05661e6 | −2.60808 | ||||||||
\(176\) | 287647.i | 0.699969i | ||||||||
\(177\) | − | 744111.i | − | 1.78527i | ||||||
\(178\) | 500491. | 1.18398 | ||||||||
\(179\) | 834374. | 1.94638 | 0.973191 | − | 0.229999i | \(-0.0738724\pi\) | ||||
0.973191 | + | 0.229999i | \(0.0738724\pi\) | |||||||
\(180\) | −241465. | −0.555485 | ||||||||
\(181\) | 84063.7 | 0.190727 | 0.0953635 | − | 0.995443i | \(-0.469599\pi\) | ||||
0.0953635 | + | 0.995443i | \(0.469599\pi\) | |||||||
\(182\) | − | 419507.i | − | 0.938774i | ||||||
\(183\) | 203360. | 0.448888 | ||||||||
\(184\) | 143373.i | 0.312192i | ||||||||
\(185\) | − | 305655.i | − | 0.656603i | ||||||
\(186\) | 882428.i | 1.87024i | ||||||||
\(187\) | −218937. | −0.457841 | ||||||||
\(188\) | − | 152102.i | − | 0.313863i | ||||||
\(189\) | − | 106744.i | − | 0.217365i | ||||||
\(190\) | −305387. | −0.613714 | ||||||||
\(191\) | 454281.i | 0.901034i | 0.892768 | + | 0.450517i | \(0.148760\pi\) | ||||
−0.892768 | + | 0.450517i | \(0.851240\pi\) | |||||||
\(192\) | − | 729342.i | − | 1.42784i | ||||||
\(193\) | − | 461063.i | − | 0.890979i | −0.895287 | − | 0.445489i | \(-0.853030\pi\) | ||
0.895287 | − | 0.445489i | \(-0.146970\pi\) | |||||||
\(194\) | 3225.06 | 0.00615225 | ||||||||
\(195\) | 863142.i | 1.62553i | ||||||||
\(196\) | 341816. | 0.635553 | ||||||||
\(197\) | −401536. | −0.737154 | −0.368577 | − | 0.929597i | \(-0.620155\pi\) | ||||
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(198\) | −580100. | −1.05157 | ||||||||
\(199\) | 107914. | 0.193173 | 0.0965863 | − | 0.995325i | \(-0.469208\pi\) | ||||
0.0965863 | + | 0.995325i | \(0.469208\pi\) | |||||||
\(200\) | 981717.i | 1.73545i | ||||||||
\(201\) | 883789.i | 1.54297i | ||||||||
\(202\) | −247592. | −0.426931 | ||||||||
\(203\) | −590107. | − | 755530.i | −1.00506 | − | 1.28680i | ||||
\(204\) | 96786.2 | 0.162831 | ||||||||
\(205\) | 158908.i | 0.264096i | ||||||||
\(206\) | 386994.i | 0.635383i | ||||||||
\(207\) | −160051. | −0.259617 | ||||||||
\(208\) | −215755. | −0.345782 | ||||||||
\(209\) | 452508. | 0.716573 | ||||||||
\(210\) | 1.82471e6 | 2.85526 | ||||||||
\(211\) | − | 296058.i | − | 0.457794i | −0.973451 | − | 0.228897i | \(-0.926488\pi\) | ||
0.973451 | − | 0.228897i | \(-0.0735120\pi\) | |||||||
\(212\) | −180099. | −0.275215 | ||||||||
\(213\) | − | 503352.i | − | 0.760192i | ||||||
\(214\) | − | 299498.i | − | 0.447053i | ||||||
\(215\) | 477132.i | 0.703951i | ||||||||
\(216\) | −99177.8 | −0.144637 | ||||||||
\(217\) | 1.95220e6i | 2.81432i | ||||||||
\(218\) | − | 478777.i | − | 0.682326i | ||||||
\(219\) | −547518. | −0.771415 | ||||||||
\(220\) | − | 653172.i | − | 0.909853i | ||||||
\(221\) | − | 164218.i | − | 0.226172i | ||||||
\(222\) | 324620.i | 0.442072i | ||||||||
\(223\) | 857377. | 1.15454 | 0.577271 | − | 0.816552i | \(-0.304118\pi\) | ||||
0.577271 | + | 0.816552i | \(0.304118\pi\) | |||||||
\(224\) | − | 876093.i | − | 1.16662i | ||||||
\(225\) | −1.09592e6 | −1.44319 | ||||||||
\(226\) | 625646. | 0.814812 | ||||||||
\(227\) | −265585. | −0.342089 | −0.171045 | − | 0.985263i | \(-0.554714\pi\) | ||||
−0.171045 | + | 0.985263i | \(0.554714\pi\) | |||||||
\(228\) | −200042. | −0.254849 | ||||||||
\(229\) | 1.13602e6i | 1.43152i | 0.698349 | + | 0.715758i | \(0.253919\pi\) | ||||
−0.698349 | + | 0.715758i | \(0.746081\pi\) | |||||||
\(230\) | 292184.i | 0.364198i | ||||||||
\(231\) | −2.70377e6 | −3.33380 | ||||||||
\(232\) | −701977. | + | 548280.i | −0.856254 | + | 0.668779i | ||||
\(233\) | −341111. | −0.411629 | −0.205814 | − | 0.978591i | \(-0.565984\pi\) | ||||
−0.205814 | + | 0.978591i | \(0.565984\pi\) | |||||||
\(234\) | − | 435115.i | − | 0.519475i | ||||||
\(235\) | − | 1.12252e6i | − | 1.32594i | ||||||
\(236\) | −422361. | −0.493633 | ||||||||
\(237\) | 976441. | 1.12921 | ||||||||
\(238\) | −347161. | −0.397272 | ||||||||
\(239\) | 1.46515e6 | 1.65916 | 0.829578 | − | 0.558391i | \(-0.188581\pi\) | ||||
0.829578 | + | 0.558391i | \(0.188581\pi\) | |||||||
\(240\) | − | 938458.i | − | 1.05169i | ||||||
\(241\) | 31493.9 | 0.0349288 | 0.0174644 | − | 0.999847i | \(-0.494441\pi\) | ||||
0.0174644 | + | 0.999847i | \(0.494441\pi\) | |||||||
\(242\) | − | 852700.i | − | 0.935961i | ||||||
\(243\) | − | 1.25815e6i | − | 1.36683i | ||||||
\(244\) | − | 115428.i | − | 0.124119i | ||||||
\(245\) | 2.52262e6 | 2.68495 | ||||||||
\(246\) | − | 168768.i | − | 0.177809i | ||||||
\(247\) | 339412.i | 0.353985i | ||||||||
\(248\) | 1.81382e6 | 1.87269 | ||||||||
\(249\) | − | 1.15046e6i | − | 1.17591i | ||||||
\(250\) | 748152.i | 0.757076i | ||||||||
\(251\) | 974972.i | 0.976805i | 0.872618 | + | 0.488402i | \(0.162420\pi\) | ||||
−0.872618 | + | 0.488402i | \(0.837580\pi\) | |||||||
\(252\) | 567338. | 0.562782 | ||||||||
\(253\) | − | 432945.i | − | 0.425238i | ||||||
\(254\) | −934317. | −0.908678 | ||||||||
\(255\) | 714288. | 0.687896 | ||||||||
\(256\) | −1.00320e6 | −0.956722 | ||||||||
\(257\) | −127188. | −0.120119 | −0.0600596 | − | 0.998195i | \(-0.519129\pi\) | ||||
−0.0600596 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(258\) | − | 506736.i | − | 0.473950i | ||||||
\(259\) | 718158.i | 0.665228i | ||||||||
\(260\) | 489924. | 0.449465 | ||||||||
\(261\) | −612062. | − | 783639.i | −0.556153 | − | 0.712057i | ||||
\(262\) | −410011. | −0.369014 | ||||||||
\(263\) | 644306.i | 0.574385i | 0.957873 | + | 0.287192i | \(0.0927219\pi\) | ||||
−0.957873 | + | 0.287192i | \(0.907278\pi\) | |||||||
\(264\) | 2.51212e6i | 2.21835i | ||||||||
\(265\) | −1.32914e6 | −1.16267 | ||||||||
\(266\) | 717527. | 0.621776 | ||||||||
\(267\) | 2.41951e6 | 2.07706 | ||||||||
\(268\) | 501643. | 0.426637 | ||||||||
\(269\) | 2.20790e6i | 1.86037i | 0.367095 | + | 0.930183i | \(0.380352\pi\) | ||||
−0.367095 | + | 0.930183i | \(0.619648\pi\) | |||||||
\(270\) | −202118. | −0.168731 | ||||||||
\(271\) | 1.15746e6i | 0.957374i | 0.877986 | + | 0.478687i | \(0.158887\pi\) | ||||
−0.877986 | + | 0.478687i | \(0.841113\pi\) | |||||||
\(272\) | 178547.i | 0.146329i | ||||||||
\(273\) | − | 2.02801e6i | − | 1.64689i | ||||||
\(274\) | 456035. | 0.366963 | ||||||||
\(275\) | − | 2.96451e6i | − | 2.36386i | ||||||
\(276\) | 191394.i | 0.151236i | ||||||||
\(277\) | −699513. | −0.547768 | −0.273884 | − | 0.961763i | \(-0.588308\pi\) | ||||
−0.273884 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(278\) | − | 886846.i | − | 0.688234i | ||||||
\(279\) | 2.02483e6i | 1.55732i | ||||||||
\(280\) | − | 3.75067e6i | − | 2.85900i | ||||||
\(281\) | −2.48281e6 | −1.87576 | −0.937881 | − | 0.346956i | \(-0.887215\pi\) | ||||
−0.937881 | + | 0.346956i | \(0.887215\pi\) | |||||||
\(282\) | 1.19217e6i | 0.892722i | ||||||||
\(283\) | 169883. | 0.126091 | 0.0630456 | − | 0.998011i | \(-0.479919\pi\) | ||||
0.0630456 | + | 0.998011i | \(0.479919\pi\) | |||||||
\(284\) | −285705. | −0.210195 | ||||||||
\(285\) | −1.47632e6 | −1.07664 | ||||||||
\(286\) | 1.17700e6 | 0.850869 | ||||||||
\(287\) | − | 373366.i | − | 0.267565i | ||||||
\(288\) | − | 908688.i | − | 0.645555i | ||||||
\(289\) | 1.28396e6 | 0.904288 | ||||||||
\(290\) | −1.43059e6 | + | 1.11736e6i | −0.998893 | + | 0.780187i | ||||
\(291\) | 15590.8 | 0.0107929 | ||||||||
\(292\) | 310774.i | 0.213298i | ||||||||
\(293\) | 1.09182e6i | 0.742985i | 0.928436 | + | 0.371493i | \(0.121154\pi\) | ||||
−0.928436 | + | 0.371493i | \(0.878846\pi\) | |||||||
\(294\) | −2.67914e6 | −1.80770 | ||||||||
\(295\) | −3.11705e6 | −2.08540 | ||||||||
\(296\) | 667254. | 0.442651 | ||||||||
\(297\) | 299490. | 0.197011 | ||||||||
\(298\) | − | 43265.8i | − | 0.0282231i | ||||||
\(299\) | 324739. | 0.210066 | ||||||||
\(300\) | 1.31053e6i | 0.840708i | ||||||||
\(301\) | − | 1.12105e6i | − | 0.713198i | ||||||
\(302\) | 2.14987e6i | 1.35642i | ||||||||
\(303\) | −1.19692e6 | −0.748963 | ||||||||
\(304\) | − | 369028.i | − | 0.229021i | ||||||
\(305\) | − | 851867.i | − | 0.524351i | ||||||
\(306\) | −360076. | −0.219832 | ||||||||
\(307\) | 2.17551e6i | 1.31739i | 0.752410 | + | 0.658696i | \(0.228891\pi\) | ||||
−0.752410 | + | 0.658696i | \(0.771109\pi\) | |||||||
\(308\) | 1.53467e6i | 0.921805i | ||||||||
\(309\) | 1.87083e6i | 1.11465i | ||||||||
\(310\) | 3.69646e6 | 2.18465 | ||||||||
\(311\) | 891275.i | 0.522529i | 0.965267 | + | 0.261265i | \(0.0841395\pi\) | ||||
−0.965267 | + | 0.261265i | \(0.915860\pi\) | |||||||
\(312\) | −1.88426e6 | −1.09586 | ||||||||
\(313\) | 1.33851e6 | 0.772252 | 0.386126 | − | 0.922446i | \(-0.373813\pi\) | ||||
0.386126 | + | 0.922446i | \(0.373813\pi\) | |||||||
\(314\) | 377992. | 0.216351 | ||||||||
\(315\) | 4.18699e6 | 2.37753 | ||||||||
\(316\) | − | 554233.i | − | 0.312230i | ||||||
\(317\) | − | 1.37267e6i | − | 0.767219i | −0.923495 | − | 0.383610i | \(-0.874681\pi\) | ||
0.923495 | − | 0.383610i | \(-0.125319\pi\) | |||||||
\(318\) | 1.41161e6 | 0.782795 | ||||||||
\(319\) | 2.11978e6 | − | 1.65565e6i | 1.16631 | − | 0.910946i | ||||
\(320\) | −3.05519e6 | −1.66787 | ||||||||
\(321\) | − | 1.44785e6i | − | 0.784263i | ||||||
\(322\) | − | 686507.i | − | 0.368982i | ||||||
\(323\) | 280878. | 0.149800 | ||||||||
\(324\) | −783684. | −0.414742 | ||||||||
\(325\) | 2.22359e6 | 1.16774 | ||||||||
\(326\) | −2.36607e6 | −1.23306 | ||||||||
\(327\) | − | 2.31454e6i | − | 1.19700i | ||||||
\(328\) | −346901. | −0.178041 | ||||||||
\(329\) | 2.63744e6i | 1.34336i | ||||||||
\(330\) | 5.11955e6i | 2.58790i | ||||||||
\(331\) | − | 3.39178e6i | − | 1.70160i | −0.525488 | − | 0.850801i | \(-0.676117\pi\) | ||
0.525488 | − | 0.850801i | \(-0.323883\pi\) | |||||||
\(332\) | −653007. | −0.325142 | ||||||||
\(333\) | 744876.i | 0.368107i | ||||||||
\(334\) | − | 2.24697e6i | − | 1.10213i | ||||||
\(335\) | 3.70216e6 | 1.80237 | ||||||||
\(336\) | 2.20497e6i | 1.06550i | ||||||||
\(337\) | − | 3.55335e6i | − | 1.70437i | −0.523243 | − | 0.852184i | \(-0.675278\pi\) | ||
0.523243 | − | 0.852184i | \(-0.324722\pi\) | |||||||
\(338\) | − | 769002.i | − | 0.366130i | ||||||
\(339\) | 3.02454e6 | 1.42942 | ||||||||
\(340\) | − | 405434.i | − | 0.190205i | ||||||
\(341\) | −5.47724e6 | −2.55080 | ||||||||
\(342\) | 744222. | 0.344062 | ||||||||
\(343\) | −2.36940e6 | −1.08743 | ||||||||
\(344\) | −1.04159e6 | −0.474571 | ||||||||
\(345\) | 1.41250e6i | 0.638910i | ||||||||
\(346\) | − | 835732.i | − | 0.375298i | ||||||
\(347\) | 657758. | 0.293253 | 0.146626 | − | 0.989192i | \(-0.453158\pi\) | ||||
0.146626 | + | 0.989192i | \(0.453158\pi\) | |||||||
\(348\) | −937097. | + | 731921.i | −0.414798 | + | 0.323978i | ||||
\(349\) | −2.16941e6 | −0.953408 | −0.476704 | − | 0.879064i | \(-0.658169\pi\) | ||||
−0.476704 | + | 0.879064i | \(0.658169\pi\) | |||||||
\(350\) | − | 4.70073e6i | − | 2.05114i | ||||||
\(351\) | 224638.i | 0.0973228i | ||||||||
\(352\) | 2.45804e6 | 1.05738 | ||||||||
\(353\) | 420369. | 0.179554 | 0.0897768 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897768 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(354\) | 3.31046e6 | 1.40404 | ||||||||
\(355\) | −2.10852e6 | −0.887989 | ||||||||
\(356\) | − | 1.37332e6i | − | 0.574312i | ||||||
\(357\) | −1.67827e6 | −0.696932 | ||||||||
\(358\) | 3.71202e6i | 1.53075i | ||||||||
\(359\) | − | 4.02963e6i | − | 1.65017i | −0.565006 | − | 0.825087i | \(-0.691126\pi\) | ||
0.565006 | − | 0.825087i | \(-0.308874\pi\) | |||||||
\(360\) | − | 3.89021e6i | − | 1.58204i | ||||||
\(361\) | 1.89557e6 | 0.765546 | ||||||||
\(362\) | 373989.i | 0.149999i | ||||||||
\(363\) | − | 4.12218e6i | − | 1.64195i | ||||||
\(364\) | −1.15111e6 | −0.455369 | ||||||||
\(365\) | 2.29353e6i | 0.901099i | ||||||||
\(366\) | 904723.i | 0.353031i | ||||||||
\(367\) | 4.42973e6i | 1.71677i | 0.513006 | + | 0.858385i | \(0.328532\pi\) | ||||
−0.513006 | + | 0.858385i | \(0.671468\pi\) | |||||||
\(368\) | −353075. | −0.135909 | ||||||||
\(369\) | − | 387257.i | − | 0.148058i | ||||||
\(370\) | 1.35982e6 | 0.516390 | ||||||||
\(371\) | 3.12292e6 | 1.17795 | ||||||||
\(372\) | 2.42134e6 | 0.907191 | ||||||||
\(373\) | −185657. | −0.0690939 | −0.0345470 | − | 0.999403i | \(-0.510999\pi\) | ||||
−0.0345470 | + | 0.999403i | \(0.510999\pi\) | |||||||
\(374\) | − | 974022.i | − | 0.360072i | ||||||
\(375\) | 3.61677e6i | 1.32813i | ||||||||
\(376\) | 2.45050e6 | 0.893891 | ||||||||
\(377\) | 1.24185e6 | + | 1.58998e6i | 0.450005 | + | 0.576153i | ||||
\(378\) | 474890. | 0.170948 | ||||||||
\(379\) | − | 2.45032e6i | − | 0.876245i | −0.898915 | − | 0.438123i | \(-0.855644\pi\) | ||
0.898915 | − | 0.438123i | \(-0.144356\pi\) | |||||||
\(380\) | 837968.i | 0.297693i | ||||||||
\(381\) | −4.51674e6 | −1.59409 | ||||||||
\(382\) | −2.02104e6 | −0.708625 | ||||||||
\(383\) | −3.91750e6 | −1.36462 | −0.682310 | − | 0.731063i | \(-0.739025\pi\) | ||||
−0.682310 | + | 0.731063i | \(0.739025\pi\) | |||||||
\(384\) | 396320. | 0.137157 | ||||||||
\(385\) | 1.13260e7i | 3.89425i | ||||||||
\(386\) | 2.05121e6 | 0.700717 | ||||||||
\(387\) | − | 1.16276e6i | − | 0.394651i | ||||||
\(388\) | − | 8849.43i | − | 0.00298425i | ||||||
\(389\) | − | 571898.i | − | 0.191622i | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) | ||
0.995400 | − | 0.0958109i | \(-0.0305444\pi\) | |||||||
\(390\) | −3.84001e6 | −1.27841 | ||||||||
\(391\) | − | 268735.i | − | 0.0888962i | ||||||
\(392\) | 5.50695e6i | 1.81007i | ||||||||
\(393\) | −1.98210e6 | −0.647359 | ||||||||
\(394\) | − | 1.78638e6i | − | 0.579740i | ||||||
\(395\) | − | 4.09028e6i | − | 1.31905i | ||||||
\(396\) | 1.59177e6i | 0.510084i | ||||||||
\(397\) | 1.49161e6 | 0.474984 | 0.237492 | − | 0.971389i | \(-0.423675\pi\) | ||||
0.237492 | + | 0.971389i | \(0.423675\pi\) | |||||||
\(398\) | 480096.i | 0.151922i | ||||||||
\(399\) | 3.46872e6 | 1.09078 | ||||||||
\(400\) | −2.41761e6 | −0.755505 | ||||||||
\(401\) | 1.92589e6 | 0.598096 | 0.299048 | − | 0.954238i | \(-0.403331\pi\) | ||||
0.299048 | + | 0.954238i | \(0.403331\pi\) | |||||||
\(402\) | −3.93187e6 | −1.21348 | ||||||||
\(403\) | − | 4.10830e6i | − | 1.26009i | ||||||
\(404\) | 679381.i | 0.207090i | ||||||||
\(405\) | −5.78364e6 | −1.75212 | ||||||||
\(406\) | 3.36126e6 | − | 2.62531e6i | 1.01201 | − | 0.790435i | ||||
\(407\) | −2.01492e6 | −0.602938 | ||||||||
\(408\) | 1.55931e6i | 0.463748i | ||||||||
\(409\) | 2.15032e6i | 0.635615i | 0.948155 | + | 0.317808i | \(0.102947\pi\) | ||||
−0.948155 | + | 0.317808i | \(0.897053\pi\) | |||||||
\(410\) | −706963. | −0.207700 | ||||||||
\(411\) | 2.20460e6 | 0.643761 | ||||||||
\(412\) | 1.06189e6 | 0.308204 | ||||||||
\(413\) | 7.32373e6 | 2.11279 | ||||||||
\(414\) | − | 712048.i | − | 0.204178i | ||||||
\(415\) | −4.81923e6 | −1.37359 | ||||||||
\(416\) | 1.84370e6i | 0.522344i | ||||||||
\(417\) | − | 4.28725e6i | − | 1.20736i | ||||||
\(418\) | 2.01315e6i | 0.563554i | ||||||||
\(419\) | −4.31814e6 | −1.20161 | −0.600803 | − | 0.799397i | \(-0.705152\pi\) | ||||
−0.600803 | + | 0.799397i | \(0.705152\pi\) | |||||||
\(420\) | − | 5.00692e6i | − | 1.38499i | ||||||
\(421\) | 3.57350e6i | 0.982627i | 0.870983 | + | 0.491314i | \(0.163483\pi\) | ||||
−0.870983 | + | 0.491314i | \(0.836517\pi\) | |||||||
\(422\) | 1.31712e6 | 0.360036 | ||||||||
\(423\) | 2.73557e6i | 0.743355i | ||||||||
\(424\) | − | 2.90156e6i | − | 0.783821i | ||||||
\(425\) | − | 1.84012e6i | − | 0.494166i | ||||||
\(426\) | 2.23935e6 | 0.597858 | ||||||||
\(427\) | 2.00152e6i | 0.531239i | ||||||||
\(428\) | −821809. | −0.216851 | ||||||||
\(429\) | 5.68995e6 | 1.49268 | ||||||||
\(430\) | −2.12270e6 | −0.553627 | ||||||||
\(431\) | 3.79128e6 | 0.983088 | 0.491544 | − | 0.870853i | \(-0.336433\pi\) | ||||
0.491544 | + | 0.870853i | \(0.336433\pi\) | |||||||
\(432\) | − | 244239.i | − | 0.0629659i | ||||||
\(433\) | − | 2.38236e6i | − | 0.610644i | −0.952249 | − | 0.305322i | \(-0.901236\pi\) | ||
0.952249 | − | 0.305322i | \(-0.0987641\pi\) | |||||||
\(434\) | −8.68507e6 | −2.21334 | ||||||||
\(435\) | −6.91583e6 | + | 5.40162e6i | −1.75235 | + | 1.36868i | ||||
\(436\) | −1.31374e6 | −0.330974 | ||||||||
\(437\) | 555434.i | 0.139133i | ||||||||
\(438\) | − | 2.43584e6i | − | 0.606685i | ||||||
\(439\) | 7.23282e6 | 1.79121 | 0.895605 | − | 0.444851i | \(-0.146743\pi\) | ||||
0.895605 | + | 0.444851i | \(0.146743\pi\) | |||||||
\(440\) | 1.05232e7 | 2.59129 | ||||||||
\(441\) | −6.14758e6 | −1.50525 | ||||||||
\(442\) | 730583. | 0.177875 | ||||||||
\(443\) | 2.05198e6i | 0.496780i | 0.968660 | + | 0.248390i | \(0.0799015\pi\) | ||||
−0.968660 | + | 0.248390i | \(0.920099\pi\) | |||||||
\(444\) | 890744. | 0.214435 | ||||||||
\(445\) | − | 1.01352e7i | − | 2.42624i | ||||||
\(446\) | 3.81436e6i | 0.907998i | ||||||||
\(447\) | − | 209159.i | − | 0.0495116i | ||||||
\(448\) | 7.17837e6 | 1.68978 | ||||||||
\(449\) | 3.05219e6i | 0.714489i | 0.934011 | + | 0.357245i | \(0.116284\pi\) | ||||
−0.934011 | + | 0.357245i | \(0.883716\pi\) | |||||||
\(450\) | − | 4.87562e6i | − | 1.13501i | ||||||
\(451\) | 1.04755e6 | 0.242511 | ||||||||
\(452\) | − | 1.71674e6i | − | 0.395239i | ||||||
\(453\) | 1.03930e7i | 2.37956i | ||||||||
\(454\) | − | 1.18156e6i | − | 0.269039i | ||||||
\(455\) | −8.49526e6 | −1.92375 | ||||||||
\(456\) | − | 3.22285e6i | − | 0.725818i | ||||||
\(457\) | 2.06974e6 | 0.463581 | 0.231790 | − | 0.972766i | \(-0.425542\pi\) | ||||
0.231790 | + | 0.972766i | \(0.425542\pi\) | |||||||
\(458\) | −5.05400e6 | −1.12583 | ||||||||
\(459\) | 185897. | 0.0411853 | ||||||||
\(460\) | 801741. | 0.176661 | ||||||||
\(461\) | − | 3.36651e6i | − | 0.737781i | −0.929473 | − | 0.368890i | \(-0.879738\pi\) | ||
0.929473 | − | 0.368890i | \(-0.120262\pi\) | |||||||
\(462\) | − | 1.20287e7i | − | 2.62189i | ||||||
\(463\) | −81095.6 | −0.0175811 | −0.00879053 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879053 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(464\) | −1.35022e6 | − | 1.72871e6i | −0.291144 | − | 0.372759i | ||||
\(465\) | 1.78697e7 | 3.83251 | ||||||||
\(466\) | − | 1.51756e6i | − | 0.323729i | ||||||
\(467\) | 1.95508e6i | 0.414833i | 0.978253 | + | 0.207416i | \(0.0665055\pi\) | ||||
−0.978253 | + | 0.207416i | \(0.933495\pi\) | |||||||
\(468\) | −1.19394e6 | −0.251980 | ||||||||
\(469\) | −8.69847e6 | −1.82604 | ||||||||
\(470\) | 4.99396e6 | 1.04280 | ||||||||
\(471\) | 1.82732e6 | 0.379543 | ||||||||
\(472\) | − | 6.80461e6i | − | 1.40588i | ||||||
\(473\) | 3.14532e6 | 0.646416 | ||||||||
\(474\) | 4.34406e6i | 0.888077i | ||||||||
\(475\) | 3.80323e6i | 0.773427i | ||||||||
\(476\) | 952593.i | 0.192704i | ||||||||
\(477\) | 3.23910e6 | 0.651821 | ||||||||
\(478\) | 6.51827e6i | 1.30486i | ||||||||
\(479\) | − | 5.02666e6i | − | 1.00102i | −0.865732 | − | 0.500508i | \(-0.833147\pi\) | ||
0.865732 | − | 0.500508i | \(-0.166853\pi\) | |||||||
\(480\) | −8.01942e6 | −1.58869 | ||||||||
\(481\) | − | 1.51133e6i | − | 0.297849i | ||||||
\(482\) | 140112.i | 0.0274700i | ||||||||
\(483\) | − | 3.31876e6i | − | 0.647303i | ||||||
\(484\) | −2.33977e6 | −0.454004 | ||||||||
\(485\) | − | 65309.3i | − | 0.0126073i | ||||||
\(486\) | 5.59733e6 | 1.07496 | ||||||||
\(487\) | −7.01534e6 | −1.34038 | −0.670188 | − | 0.742192i | \(-0.733786\pi\) | ||||
−0.670188 | + | 0.742192i | \(0.733786\pi\) | |||||||
\(488\) | 1.85965e6 | 0.353494 | ||||||||
\(489\) | −1.14382e7 | −2.16315 | ||||||||
\(490\) | 1.12228e7i | 2.11160i | ||||||||
\(491\) | 6.04666e6i | 1.13191i | 0.824436 | + | 0.565954i | \(0.191492\pi\) | ||||
−0.824436 | + | 0.565954i | \(0.808508\pi\) | |||||||
\(492\) | −463092. | −0.0862491 | ||||||||
\(493\) | 1.31578e6 | − | 1.02769e6i | 0.243817 | − | 0.190434i | ||||
\(494\) | −1.51000e6 | −0.278394 | ||||||||
\(495\) | 1.17474e7i | 2.15490i | ||||||||
\(496\) | 4.46679e6i | 0.815250i | ||||||||
\(497\) | 4.95412e6 | 0.899654 | ||||||||
\(498\) | 5.11825e6 | 0.924801 | ||||||||
\(499\) | −5.31655e6 | −0.955825 | −0.477912 | − | 0.878408i | \(-0.658606\pi\) | ||||
−0.477912 | + | 0.878408i | \(0.658606\pi\) | |||||||
\(500\) | 2.05290e6 | 0.367233 | ||||||||
\(501\) | − | 1.08625e7i | − | 1.93345i | ||||||
\(502\) | −4.33753e6 | −0.768215 | ||||||||
\(503\) | − | 667123.i | − | 0.117567i | −0.998271 | − | 0.0587835i | \(-0.981278\pi\) | ||
0.998271 | − | 0.0587835i | \(-0.0187222\pi\) | |||||||
\(504\) | 9.14030e6i | 1.60282i | ||||||||
\(505\) | 5.01387e6i | 0.874873i | ||||||||
\(506\) | 1.92612e6 | 0.334431 | ||||||||
\(507\) | − | 3.71756e6i | − | 0.642301i | ||||||
\(508\) | 2.56372e6i | 0.440770i | ||||||||
\(509\) | 852016. | 0.145765 | 0.0728825 | − | 0.997341i | \(-0.476780\pi\) | ||||
0.0728825 | + | 0.997341i | \(0.476780\pi\) | |||||||
\(510\) | 3.17778e6i | 0.541001i | ||||||||
\(511\) | − | 5.38881e6i | − | 0.912936i | ||||||
\(512\) | − | 5.05277e6i | − | 0.851834i | ||||||
\(513\) | −384221. | −0.0644596 | ||||||||
\(514\) | − | 565842.i | − | 0.0944686i | ||||||
\(515\) | 7.83684e6 | 1.30204 | ||||||||
\(516\) | −1.39046e6 | −0.229898 | ||||||||
\(517\) | −7.39982e6 | −1.21757 | ||||||||
\(518\) | −3.19499e6 | −0.523173 | ||||||||
\(519\) | − | 4.04015e6i | − | 0.658384i | ||||||
\(520\) | 7.89310e6i | 1.28009i | ||||||||
\(521\) | 8.30897e6 | 1.34107 | 0.670537 | − | 0.741876i | \(-0.266064\pi\) | ||||
0.670537 | + | 0.741876i | \(0.266064\pi\) | |||||||
\(522\) | 3.48631e6 | − | 2.72299e6i | 0.560002 | − | 0.437390i | ||||
\(523\) | −5.37728e6 | −0.859625 | −0.429812 | − | 0.902918i | \(-0.641420\pi\) | ||||
−0.429812 | + | 0.902918i | \(0.641420\pi\) | |||||||
\(524\) | 1.12505e6i | 0.178997i | ||||||||
\(525\) | − | 2.27246e7i | − | 3.59830i | ||||||
\(526\) | −2.86644e6 | −0.451729 | ||||||||
\(527\) | −3.39980e6 | −0.533245 | ||||||||
\(528\) | −6.18644e6 | −0.965731 | ||||||||
\(529\) | −5.90492e6 | −0.917434 | ||||||||
\(530\) | − | 5.91320e6i | − | 0.914393i | ||||||
\(531\) | 7.59620e6 | 1.16912 | ||||||||
\(532\) | − | 1.96886e6i | − | 0.301603i | ||||||
\(533\) | 785731.i | 0.119800i | ||||||||
\(534\) | 1.07641e7i | 1.63352i | ||||||||
\(535\) | −6.06500e6 | −0.916107 | ||||||||
\(536\) | 8.08191e6i | 1.21507i | ||||||||
\(537\) | 1.79449e7i | 2.68538i | ||||||||
\(538\) | −9.82267e6 | −1.46310 | ||||||||
\(539\) | − | 1.66295e7i | − | 2.46551i | ||||||
\(540\) | 554604.i | 0.0818461i | ||||||||
\(541\) | 7.17375e6i | 1.05379i | 0.849931 | + | 0.526894i | \(0.176643\pi\) | ||||
−0.849931 | + | 0.526894i | \(0.823357\pi\) | |||||||
\(542\) | −5.14938e6 | −0.752934 | ||||||||
\(543\) | 1.80796e6i | 0.263142i | ||||||||
\(544\) | 1.52574e6 | 0.221046 | ||||||||
\(545\) | −9.69550e6 | −1.39823 | ||||||||
\(546\) | 9.02236e6 | 1.29521 | ||||||||
\(547\) | 8.04876e6 | 1.15017 | 0.575083 | − | 0.818095i | \(-0.304970\pi\) | ||||
0.575083 | + | 0.818095i | \(0.304970\pi\) | |||||||
\(548\) | − | 1.25134e6i | − | 0.178002i | ||||||
\(549\) | 2.07598e6i | 0.293963i | ||||||||
\(550\) | 1.31888e7 | 1.85908 | ||||||||
\(551\) | −2.71950e6 | + | 2.12407e6i | −0.381602 | + | 0.298051i | ||||
\(552\) | −3.08352e6 | −0.430724 | ||||||||
\(553\) | 9.61038e6i | 1.33637i | ||||||||
\(554\) | − | 3.11205e6i | − | 0.430796i | ||||||
\(555\) | 6.57374e6 | 0.905900 | ||||||||
\(556\) | −2.43347e6 | −0.333840 | ||||||||
\(557\) | 1.01144e6 | 0.138134 | 0.0690669 | − | 0.997612i | \(-0.477998\pi\) | ||||
0.0690669 | + | 0.997612i | \(0.477998\pi\) | |||||||
\(558\) | −9.00819e6 | −1.22476 | ||||||||
\(559\) | 2.35920e6i | 0.319327i | ||||||||
\(560\) | 9.23654e6 | 1.24463 | ||||||||
\(561\) | − | 4.70868e6i | − | 0.631673i | ||||||
\(562\) | − | 1.10457e7i | − | 1.47521i | ||||||
\(563\) | 1.26692e6i | 0.168453i | 0.996447 | + | 0.0842266i | \(0.0268419\pi\) | ||||
−0.996447 | + | 0.0842266i | \(0.973158\pi\) | |||||||
\(564\) | 3.27127e6 | 0.433030 | ||||||||
\(565\) | − | 1.26697e7i | − | 1.66972i | ||||||
\(566\) | 755789.i | 0.0991653i | ||||||||
\(567\) | 1.35890e7 | 1.77513 | ||||||||
\(568\) | − | 4.60296e6i | − | 0.598641i | ||||||
\(569\) | − | 8.25094e6i | − | 1.06837i | −0.845367 | − | 0.534187i | \(-0.820618\pi\) | ||
0.845367 | − | 0.534187i | \(-0.179382\pi\) | |||||||
\(570\) | − | 6.56797e6i | − | 0.846728i | ||||||
\(571\) | 1.12215e7 | 1.44032 | 0.720160 | − | 0.693808i | \(-0.244068\pi\) | ||||
0.720160 | + | 0.693808i | \(0.244068\pi\) | |||||||
\(572\) | − | 3.22965e6i | − | 0.412729i | ||||||
\(573\) | −9.77025e6 | −1.24314 | ||||||||
\(574\) | 1.66106e6 | 0.210429 | ||||||||
\(575\) | 3.63881e6 | 0.458976 | ||||||||
\(576\) | 7.44544e6 | 0.935048 | ||||||||
\(577\) | 7.06718e6i | 0.883703i | 0.897088 | + | 0.441852i | \(0.145678\pi\) | ||||
−0.897088 | + | 0.441852i | \(0.854322\pi\) | |||||||
\(578\) | 5.71218e6i | 0.711184i | ||||||||
\(579\) | 9.91611e6 | 1.22926 | ||||||||
\(580\) | 3.06599e6 | + | 3.92546e6i | 0.378443 | + | 0.484530i | ||||
\(581\) | 1.13231e7 | 1.39164 | ||||||||
\(582\) | 69361.5i | 0.00848812i | ||||||||
\(583\) | 8.76191e6i | 1.06765i | ||||||||
\(584\) | −5.00684e6 | −0.607480 | ||||||||
\(585\) | −8.81132e6 | −1.06451 | ||||||||
\(586\) | −4.85735e6 | −0.584326 | ||||||||
\(587\) | −9.89439e6 | −1.18521 | −0.592603 | − | 0.805495i | \(-0.701900\pi\) | ||||
−0.592603 | + | 0.805495i | \(0.701900\pi\) | |||||||
\(588\) | 7.35145e6i | 0.876858i | ||||||||
\(589\) | 7.02686e6 | 0.834589 | ||||||||
\(590\) | − | 1.38674e7i | − | 1.64008i | ||||||
\(591\) | − | 8.63584e6i | − | 1.01704i | ||||||
\(592\) | 1.64321e6i | 0.192703i | ||||||||
\(593\) | 3.83383e6 | 0.447709 | 0.223854 | − | 0.974623i | \(-0.428136\pi\) | ||||
0.223854 | + | 0.974623i | \(0.428136\pi\) | |||||||
\(594\) | 1.33239e6i | 0.154941i | ||||||||
\(595\) | 7.03020e6i | 0.814095i | ||||||||
\(596\) | −118720. | −0.0136901 | ||||||||
\(597\) | 2.32091e6i | 0.266516i | ||||||||
\(598\) | 1.44472e6i | 0.165208i | ||||||||
\(599\) | 1.47715e7i | 1.68212i | 0.540938 | + | 0.841062i | \(0.318069\pi\) | ||||
−0.540938 | + | 0.841062i | \(0.681931\pi\) | |||||||
\(600\) | −2.11138e7 | −2.39436 | ||||||||
\(601\) | − | 1.70212e7i | − | 1.92223i | −0.276155 | − | 0.961113i | \(-0.589060\pi\) | ||
0.276155 | − | 0.961113i | \(-0.410940\pi\) | |||||||
\(602\) | 4.98743e6 | 0.560900 | ||||||||
\(603\) | −9.02209e6 | −1.01045 | ||||||||
\(604\) | 5.89915e6 | 0.657956 | ||||||||
\(605\) | −1.72676e7 | −1.91798 | ||||||||
\(606\) | − | 5.32497e6i | − | 0.589027i | ||||||
\(607\) | − | 1.99520e6i | − | 0.219794i | −0.993943 | − | 0.109897i | \(-0.964948\pi\) | ||
0.993943 | − | 0.109897i | \(-0.0350520\pi\) | |||||||
\(608\) | −3.15347e6 | −0.345963 | ||||||||
\(609\) | 1.62492e7 | − | 1.26915e7i | 1.77537 | − | 1.38666i | ||||
\(610\) | 3.78985e6 | 0.412380 | ||||||||
\(611\) | − | 5.55037e6i | − | 0.601477i | ||||||
\(612\) | 988034.i | 0.106633i | ||||||||
\(613\) | 8.31000e6 | 0.893202 | 0.446601 | − | 0.894733i | \(-0.352634\pi\) | ||||
0.446601 | + | 0.894733i | \(0.352634\pi\) | |||||||
\(614\) | −9.67856e6 | −1.03607 | ||||||||
\(615\) | −3.41765e6 | −0.364368 | ||||||||
\(616\) | −2.47249e7 | −2.62532 | ||||||||
\(617\) | − | 3.70169e6i | − | 0.391460i | −0.980658 | − | 0.195730i | \(-0.937292\pi\) | ||
0.980658 | − | 0.195730i | \(-0.0627076\pi\) | |||||||
\(618\) | −8.32309e6 | −0.876624 | ||||||||
\(619\) | − | 1.29198e7i | − | 1.35528i | −0.735395 | − | 0.677639i | \(-0.763003\pi\) | ||
0.735395 | − | 0.677639i | \(-0.236997\pi\) | |||||||
\(620\) | − | 1.01429e7i | − | 1.05970i | ||||||
\(621\) | 367611.i | 0.0382524i | ||||||||
\(622\) | −3.96517e6 | −0.410947 | ||||||||
\(623\) | 2.38134e7i | 2.45811i | ||||||||
\(624\) | − | 4.64026e6i | − | 0.477068i | ||||||
\(625\) | −448271. | −0.0459029 | ||||||||
\(626\) | 5.95484e6i | 0.607344i | ||||||||
\(627\) | 9.73211e6i | 0.988640i | ||||||||
\(628\) | − | 1.03719e6i | − | 0.104945i | ||||||
\(629\) | −1.25069e6 | −0.126044 | ||||||||
\(630\) | 1.86274e7i | 1.86982i | ||||||||
\(631\) | 1.52718e6 | 0.152692 | 0.0763459 | − | 0.997081i | \(-0.475675\pi\) | ||||
0.0763459 | + | 0.997081i | \(0.475675\pi\) | |||||||
\(632\) | 8.92918e6 | 0.889240 | ||||||||
\(633\) | 6.36733e6 | 0.631609 | ||||||||
\(634\) | 6.10686e6 | 0.603385 | ||||||||
\(635\) | 1.89204e7i | 1.86207i | ||||||||
\(636\) | − | 3.87341e6i | − | 0.379709i | ||||||
\(637\) | 1.24732e7 | 1.21795 | ||||||||
\(638\) | 7.36580e6 | + | 9.43062e6i | 0.716420 | + | 0.917251i | ||||
\(639\) | 5.13843e6 | 0.497827 | ||||||||
\(640\) | − | 1.66017e6i | − | 0.160215i | ||||||
\(641\) | − | 9.43372e6i | − | 0.906855i | −0.891293 | − | 0.453427i | \(-0.850201\pi\) | ||
0.891293 | − | 0.453427i | \(-0.149799\pi\) | |||||||
\(642\) | 6.44131e6 | 0.616789 | ||||||||
\(643\) | 1.37293e7 | 1.30954 | 0.654772 | − | 0.755826i | \(-0.272765\pi\) | ||||
0.654772 | + | 0.755826i | \(0.272765\pi\) | |||||||
\(644\) | −1.88374e6 | −0.178981 | ||||||||
\(645\) | −1.02617e7 | −0.971225 | ||||||||
\(646\) | 1.24959e6i | 0.117811i | ||||||||
\(647\) | −1.73477e7 | −1.62922 | −0.814611 | − | 0.580007i | \(-0.803050\pi\) | ||||
−0.814611 | + | 0.580007i | \(0.803050\pi\) | |||||||
\(648\) | − | 1.26258e7i | − | 1.18120i | ||||||
\(649\) | 2.05480e7i | 1.91496i | ||||||||
\(650\) | 9.89247e6i | 0.918378i | ||||||||
\(651\) | −4.19860e7 | −3.88286 | ||||||||
\(652\) | 6.49239e6i | 0.598117i | ||||||||
\(653\) | − | 6.34963e6i | − | 0.582728i | −0.956612 | − | 0.291364i | \(-0.905891\pi\) | ||
0.956612 | − | 0.291364i | \(-0.0941090\pi\) | |||||||
\(654\) | 1.02971e7 | 0.941390 | ||||||||
\(655\) | 8.30296e6i | 0.756188i | ||||||||
\(656\) | − | 854292.i | − | 0.0775081i | ||||||
\(657\) | − | 5.58929e6i | − | 0.505177i | ||||||
\(658\) | −1.17336e7 | −1.05650 | ||||||||
\(659\) | − | 4.42658e6i | − | 0.397058i | −0.980095 | − | 0.198529i | \(-0.936384\pi\) | ||
0.980095 | − | 0.198529i | \(-0.0636165\pi\) | |||||||
\(660\) | 1.40478e7 | 1.25530 | ||||||||
\(661\) | 1.51522e7 | 1.34887 | 0.674437 | − | 0.738332i | \(-0.264386\pi\) | ||||
0.674437 | + | 0.738332i | \(0.264386\pi\) | |||||||
\(662\) | 1.50896e7 | 1.33824 | ||||||||
\(663\) | 3.53183e6 | 0.312044 | ||||||||
\(664\) | − | 1.05205e7i | − | 0.926012i | ||||||
\(665\) | − | 1.45303e7i | − | 1.27415i | ||||||
\(666\) | −3.31386e6 | −0.289500 | ||||||||
\(667\) | 2.03224e6 | + | 2.60193e6i | 0.176873 | + | 0.226455i | ||||
\(668\) | −6.16559e6 | −0.534605 | ||||||||
\(669\) | 1.84397e7i | 1.59290i | ||||||||
\(670\) | 1.64704e7i | 1.41748i | ||||||||
\(671\) | −5.61563e6 | −0.481495 | ||||||||
\(672\) | 1.88422e7 | 1.60956 | ||||||||
\(673\) | −1.21002e7 | −1.02980 | −0.514901 | − | 0.857249i | \(-0.672171\pi\) | ||||
−0.514901 | + | 0.857249i | \(0.672171\pi\) | |||||||
\(674\) | 1.58084e7 | 1.34041 | ||||||||
\(675\) | 2.51715e6i | 0.212642i | ||||||||
\(676\) | −2.11011e6 | −0.177598 | ||||||||
\(677\) | 1.94913e7i | 1.63444i | 0.576326 | + | 0.817220i | \(0.304486\pi\) | ||||
−0.576326 | + | 0.817220i | \(0.695514\pi\) | |||||||
\(678\) | 1.34558e7i | 1.12418i | ||||||||
\(679\) | 153449.i | 0.0127729i | ||||||||
\(680\) | 6.53189e6 | 0.541709 | ||||||||
\(681\) | − | 5.71196e6i | − | 0.471973i | ||||||
\(682\) | − | 2.43675e7i | − | 2.00609i | ||||||
\(683\) | −1.58984e6 | −0.130407 | −0.0652034 | − | 0.997872i | \(-0.520770\pi\) | ||||
−0.0652034 | + | 0.997872i | \(0.520770\pi\) | |||||||
\(684\) | − | 2.04211e6i | − | 0.166893i | ||||||
\(685\) | − | 9.23497e6i | − | 0.751985i | ||||||
\(686\) | − | 1.05412e7i | − | 0.855221i | ||||||
\(687\) | −2.44324e7 | −1.97503 | ||||||||
\(688\) | − | 2.56506e6i | − | 0.206598i | ||||||
\(689\) | −6.57203e6 | −0.527414 | ||||||||
\(690\) | −6.28402e6 | −0.502476 | ||||||||
\(691\) | −478964. | −0.0381599 | −0.0190800 | − | 0.999818i | \(-0.506074\pi\) | ||||
−0.0190800 | + | 0.999818i | \(0.506074\pi\) | |||||||
\(692\) | −2.29321e6 | −0.182045 | ||||||||
\(693\) | − | 2.76012e7i | − | 2.18321i | ||||||
\(694\) | 2.92628e6i | 0.230631i | ||||||||
\(695\) | −1.79591e7 | −1.41034 | ||||||||
\(696\) | −1.17919e7 | − | 1.50974e7i | −0.922699 | − | 1.18136i | ||||
\(697\) | 650227. | 0.0506971 | ||||||||
\(698\) | − | 9.65145e6i | − | 0.749815i | ||||||
\(699\) | − | 7.33629e6i | − | 0.567915i | ||||||
\(700\) | −1.28986e7 | −0.994941 | ||||||||
\(701\) | 4.60638e6 | 0.354050 | 0.177025 | − | 0.984206i | \(-0.443353\pi\) | ||||
0.177025 | + | 0.984206i | \(0.443353\pi\) | |||||||
\(702\) | −999385. | −0.0765403 | ||||||||
\(703\) | 2.58498e6 | 0.197274 | ||||||||
\(704\) | 2.01402e7i | 1.53155i | ||||||||
\(705\) | 2.41421e7 | 1.82938 | ||||||||
\(706\) | 1.87017e6i | 0.141211i | ||||||||
\(707\) | − | 1.17804e7i | − | 0.886365i | ||||||
\(708\) | − | 9.08375e6i | − | 0.681055i | ||||||
\(709\) | 9.47025e6 | 0.707531 | 0.353766 | − | 0.935334i | \(-0.384901\pi\) | ||||
0.353766 | + | 0.935334i | \(0.384901\pi\) | |||||||
\(710\) | − | 9.38056e6i | − | 0.698366i | ||||||
\(711\) | 9.96792e6i | 0.739487i | ||||||||
\(712\) | 2.21254e7 | 1.63566 | ||||||||
\(713\) | − | 6.72307e6i | − | 0.495272i | ||||||
\(714\) | − | 7.46640e6i | − | 0.548107i | ||||||
\(715\) | − | 2.38350e7i | − | 1.74361i | ||||||
\(716\) | 1.01856e7 | 0.742515 | ||||||||
\(717\) | 3.15110e7i | 2.28910i | ||||||||
\(718\) | 1.79273e7 | 1.29779 | ||||||||
\(719\) | −1.63490e7 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700759\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700759\pi\) | |||||||
\(720\) | 9.58017e6 | 0.688719 | ||||||||
\(721\) | −1.84132e7 | −1.31914 | ||||||||
\(722\) | 8.43314e6i | 0.602069i | ||||||||
\(723\) | 677341.i | 0.0481905i | ||||||||
\(724\) | 1.02621e6 | 0.0727594 | ||||||||
\(725\) | 1.39154e7 | + | 1.78163e7i | 0.983221 | + | 1.25884i | ||||
\(726\) | 1.83391e7 | 1.29132 | ||||||||
\(727\) | − | 1.79177e7i | − | 1.25732i | −0.777679 | − | 0.628661i | \(-0.783603\pi\) | ||
0.777679 | − | 0.628661i | \(-0.216397\pi\) | |||||||
\(728\) | − | 1.85454e7i | − | 1.29690i | ||||||
\(729\) | 1.14592e7 | 0.798609 | ||||||||
\(730\) | −1.02036e7 | −0.708676 | ||||||||
\(731\) | 1.95234e6 | 0.135133 | ||||||||
\(732\) | 2.48252e6 | 0.171244 | ||||||||
\(733\) | − | 1.78468e7i | − | 1.22687i | −0.789744 | − | 0.613436i | \(-0.789787\pi\) | ||
0.789744 | − | 0.613436i | \(-0.210213\pi\) | |||||||
\(734\) | −1.97073e7 | −1.35017 | ||||||||
\(735\) | 5.42541e7i | 3.70437i | ||||||||
\(736\) | 3.01714e6i | 0.205305i | ||||||||
\(737\) | − | 2.44051e7i | − | 1.65506i | ||||||
\(738\) | 1.72286e6 | 0.116442 | ||||||||
\(739\) | − | 2.55426e7i | − | 1.72050i | −0.509876 | − | 0.860248i | \(-0.670309\pi\) | ||
0.509876 | − | 0.860248i | \(-0.329691\pi\) | |||||||
\(740\) | − | 3.73129e6i | − | 0.250484i | ||||||
\(741\) | −7.29975e6 | −0.488385 | ||||||||
\(742\) | 1.38935e7i | 0.926404i | ||||||||
\(743\) | 1.50256e7i | 0.998528i | 0.866450 | + | 0.499264i | \(0.166396\pi\) | ||||
−0.866450 | + | 0.499264i | \(0.833604\pi\) | |||||||
\(744\) | 3.90099e7i | 2.58370i | ||||||||
\(745\) | −876157. | −0.0578351 | ||||||||
\(746\) | − | 825966.i | − | 0.0543394i | ||||||
\(747\) | 1.17444e7 | 0.770067 | ||||||||
\(748\) | −2.67267e6 | −0.174659 | ||||||||
\(749\) | 1.42501e7 | 0.928141 | ||||||||
\(750\) | −1.60905e7 | −1.04452 | ||||||||
\(751\) | − | 2.09579e6i | − | 0.135597i | −0.997699 | − | 0.0677983i | \(-0.978403\pi\) | ||
0.997699 | − | 0.0677983i | \(-0.0215974\pi\) | |||||||
\(752\) | 6.03469e6i | 0.389144i | ||||||||
\(753\) | −2.09688e7 | −1.34768 | ||||||||
\(754\) | −7.07361e6 | + | 5.52485e6i | −0.453119 | + | 0.353910i | ||||
\(755\) | 4.35361e7 | 2.77960 | ||||||||
\(756\) | − | 1.30308e6i | − | 0.0829213i | ||||||
\(757\) | 2.93991e7i | 1.86464i | 0.361639 | + | 0.932318i | \(0.382217\pi\) | ||||
−0.361639 | + | 0.932318i | \(0.617783\pi\) | |||||||
\(758\) | 1.09012e7 | 0.689129 | ||||||||
\(759\) | 9.31138e6 | 0.586691 | ||||||||
\(760\) | −1.35004e7 | −0.847837 | ||||||||
\(761\) | −9.58603e6 | −0.600036 | −0.300018 | − | 0.953934i | \(-0.596993\pi\) | ||||
−0.300018 | + | 0.953934i | \(0.596993\pi\) | |||||||
\(762\) | − | 2.00944e7i | − | 1.25368i | ||||||
\(763\) | 2.27802e7 | 1.41660 | ||||||||
\(764\) | 5.54564e6i | 0.343731i | ||||||||
\(765\) | 7.29175e6i | 0.450483i | ||||||||
\(766\) | − | 1.74285e7i | − | 1.07322i | ||||||
\(767\) | −1.54124e7 | −0.945982 | ||||||||
\(768\) | − | 2.15758e7i | − | 1.31997i | ||||||
\(769\) | 1.57832e7i | 0.962453i | 0.876596 | + | 0.481226i | \(0.159808\pi\) | ||||
−0.876596 | + | 0.481226i | \(0.840192\pi\) | |||||||
\(770\) | −5.03879e7 | −3.06266 | ||||||||
\(771\) | − | 2.73543e6i | − | 0.165726i | ||||||
\(772\) | − | 5.62844e6i | − | 0.339895i | ||||||
\(773\) | 1.49255e7i | 0.898423i | 0.893425 | + | 0.449212i | \(0.148295\pi\) | ||||
−0.893425 | + | 0.449212i | \(0.851705\pi\) | |||||||
\(774\) | 5.17298e6 | 0.310376 | ||||||||
\(775\) | − | 4.60350e7i | − | 2.75318i | ||||||
\(776\) | 142572. | 0.00849923 | ||||||||
\(777\) | −1.54455e7 | −0.917800 | ||||||||
\(778\) | 2.54430e6 | 0.150702 | ||||||||
\(779\) | −1.34392e6 | −0.0793467 | ||||||||
\(780\) | 1.05368e7i | 0.620116i | ||||||||
\(781\) | 1.38997e7i | 0.815412i | ||||||||
\(782\) | 1.19557e6 | 0.0699130 | ||||||||
\(783\) | −1.79988e6 | + | 1.40580e6i | −0.104916 | + | 0.0819445i | ||||
\(784\) | −1.35616e7 | −0.787991 | ||||||||
\(785\) | − | 7.65456e6i | − | 0.443349i | ||||||
\(786\) | − | 8.81813e6i | − | 0.509120i | ||||||
\(787\) | 3.13562e7 | 1.80462 | 0.902312 | − | 0.431083i | \(-0.141868\pi\) | ||||
0.902312 | + | 0.431083i | \(0.141868\pi\) | |||||||
\(788\) | −4.90175e6 | −0.281213 | ||||||||
\(789\) | −1.38571e7 | −0.792466 | ||||||||
\(790\) | 1.81971e7 | 1.03737 | ||||||||
\(791\) | 2.97682e7i | 1.69166i | ||||||||
\(792\) | −2.56448e7 | −1.45273 | ||||||||
\(793\) | − | 4.21210e6i | − | 0.237857i | ||||||
\(794\) | 6.63599e6i | 0.373555i | ||||||||
\(795\) | − | 2.85860e7i | − | 1.60411i | ||||||
\(796\) | 1.31736e6 | 0.0736924 | ||||||||
\(797\) | − | 2.64771e6i | − | 0.147647i | −0.997271 | − | 0.0738235i | \(-0.976480\pi\) | ||
0.997271 | − | 0.0738235i | \(-0.0235202\pi\) | |||||||
\(798\) | 1.54319e7i | 0.857851i | ||||||||
\(799\) | −4.59318e6 | −0.254534 | ||||||||
\(800\) | 2.06593e7i | 1.14128i | ||||||||
\(801\) | 2.46993e7i | 1.36020i | ||||||||
\(802\) | 8.56805e6i | 0.470377i | ||||||||
\(803\) | 1.51193e7 | 0.827451 | ||||||||
\(804\) | 1.07889e7i | 0.588621i | ||||||||
\(805\) | −1.39021e7 | −0.756123 | ||||||||
\(806\) | 1.82773e7 | 0.991003 | ||||||||
\(807\) | −4.74854e7 | −2.56671 | ||||||||
\(808\) | −1.09454e7 | −0.589799 | ||||||||
\(809\) | − | 9.80290e6i | − | 0.526603i | −0.964714 | − | 0.263301i | \(-0.915189\pi\) | ||
0.964714 | − | 0.263301i | \(-0.0848114\pi\) | |||||||
\(810\) | − | 2.57307e7i | − | 1.37797i | ||||||
\(811\) | −6.02035e6 | −0.321417 | −0.160709 | − | 0.987002i | \(-0.551378\pi\) | ||||
−0.160709 | + | 0.987002i | \(0.551378\pi\) | |||||||
\(812\) | −7.20375e6 | − | 9.22314e6i | −0.383414 | − | 0.490895i | ||||
\(813\) | −2.48935e7 | −1.32087 | ||||||||
\(814\) | − | 8.96414e6i | − | 0.474185i | ||||||
\(815\) | 4.79143e7i | 2.52680i | ||||||||
\(816\) | −3.84001e6 | −0.201887 | ||||||||
\(817\) | −4.03519e6 | −0.211499 | ||||||||
\(818\) | −9.56650e6 | −0.499884 | ||||||||
\(819\) | 2.07028e7 | 1.07850 | ||||||||
\(820\) | 1.93988e6i | 0.100749i | ||||||||
\(821\) | 3.70550e7 | 1.91862 | 0.959309 | − | 0.282359i | \(-0.0911171\pi\) | ||||
0.959309 | + | 0.282359i | \(0.0911171\pi\) | |||||||
\(822\) | 9.80797e6i | 0.506290i | ||||||||
\(823\) | − | 2.15600e7i | − | 1.10956i | −0.831998 | − | 0.554779i | \(-0.812803\pi\) | ||
0.831998 | − | 0.554779i | \(-0.187197\pi\) | |||||||
\(824\) | 1.71080e7i | 0.877772i | ||||||||
\(825\) | 6.37580e7 | 3.26137 | ||||||||
\(826\) | 3.25823e7i | 1.66162i | ||||||||
\(827\) | − | 1.21823e7i | − | 0.619391i | −0.950836 | − | 0.309696i | \(-0.899773\pi\) | ||
0.950836 | − | 0.309696i | \(-0.100227\pi\) | |||||||
\(828\) | −1.95383e6 | −0.0990400 | ||||||||
\(829\) | − | 1.49741e6i | − | 0.0756756i | −0.999284 | − | 0.0378378i | \(-0.987953\pi\) | ||
0.999284 | − | 0.0378378i | \(-0.0120470\pi\) | |||||||
\(830\) | − | 2.14402e7i | − | 1.08027i | ||||||
\(831\) | − | 1.50445e7i | − | 0.755743i | ||||||
\(832\) | −1.51065e7 | −0.756583 | ||||||||
\(833\) | − | 1.03221e7i | − | 0.515416i | ||||||
\(834\) | 1.90734e7 | 0.949541 | ||||||||
\(835\) | −4.55024e7 | −2.25849 | ||||||||
\(836\) | 5.52400e6 | 0.273362 | ||||||||
\(837\) | 4.65068e6 | 0.229458 | ||||||||
\(838\) | − | 1.92109e7i | − | 0.945012i | ||||||
\(839\) | − | 2.46412e7i | − | 1.20853i | −0.796785 | − | 0.604263i | \(-0.793468\pi\) | ||
0.796785 | − | 0.604263i | \(-0.206532\pi\) | |||||||
\(840\) | 8.06658e7 | 3.94449 | ||||||||
\(841\) | −4.96789e6 | + | 1.99004e7i | −0.242204 | + | 0.970225i | ||||
\(842\) | −1.58981e7 | −0.772794 | ||||||||
\(843\) | − | 5.33979e7i | − | 2.58795i | ||||||
\(844\) | − | 3.61413e6i | − | 0.174642i | ||||||
\(845\) | −1.55727e7 | −0.750279 | ||||||||
\(846\) | −1.21702e7 | −0.584617 | ||||||||
\(847\) | 4.05715e7 | 1.94318 | ||||||||
\(848\) | 7.14549e6 | 0.341226 | ||||||||
\(849\) | 3.65369e6i | 0.173965i | ||||||||
\(850\) | 8.18645e6 | 0.388641 | ||||||||
\(851\) | − | 2.47323e6i | − | 0.117069i | ||||||
\(852\) | − | 6.14468e6i | − | 0.290002i | ||||||
\(853\) | 2.54111e7i | 1.19578i | 0.801578 | + | 0.597890i | \(0.203994\pi\) | ||||
−0.801578 | + | 0.597890i | \(0.796006\pi\) | |||||||
\(854\) | −8.90451e6 | −0.417797 | ||||||||
\(855\) | − | 1.50709e7i | − | 0.705057i | ||||||
\(856\) | − | 1.32401e7i | − | 0.617597i | ||||||
\(857\) | −1.32471e7 | −0.616127 | −0.308063 | − | 0.951366i | \(-0.599681\pi\) | ||||
−0.308063 | + | 0.951366i | \(0.599681\pi\) | |||||||
\(858\) | 2.53139e7i | 1.17393i | ||||||||
\(859\) | − | 8.05724e6i | − | 0.372566i | −0.982496 | − | 0.186283i | \(-0.940356\pi\) | ||
0.982496 | − | 0.186283i | \(-0.0596441\pi\) | |||||||
\(860\) | 5.82459e6i | 0.268547i | ||||||||
\(861\) | 8.03000e6 | 0.369154 | ||||||||
\(862\) | 1.68669e7i | 0.773157i | ||||||||
\(863\) | 2.46723e7 | 1.12767 | 0.563836 | − | 0.825887i | \(-0.309325\pi\) | ||||
0.563836 | + | 0.825887i | \(0.309325\pi\) | |||||||
\(864\) | −2.08710e6 | −0.0951172 | ||||||||
\(865\) | −1.69240e7 | −0.769066 | ||||||||
\(866\) | 1.05988e7 | 0.480246 | ||||||||
\(867\) | 2.76142e7i | 1.24763i | ||||||||
\(868\) | 2.38315e7i | 1.07362i | ||||||||
\(869\) | −2.69637e7 | −1.21124 | ||||||||
\(870\) | −2.40311e7 | − | 3.07677e7i | −1.07641 | − | 1.37815i | ||||
\(871\) | 1.83055e7 | 0.817592 | ||||||||
\(872\) | − | 2.11655e7i | − | 0.942623i | ||||||
\(873\) | 159158.i | 0.00706792i | ||||||||
\(874\) | −2.47106e6 | −0.109422 | ||||||||
\(875\) | −3.55971e7 | −1.57179 | ||||||||
\(876\) | −6.68383e6 | −0.294283 | ||||||||
\(877\) | −4.30471e6 | −0.188993 | −0.0944963 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944963 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(878\) | 3.21779e7i | 1.40871i | ||||||||
\(879\) | −2.34817e7 | −1.02508 | ||||||||
\(880\) | 2.59148e7i | 1.12808i | ||||||||
\(881\) | 7.17894e6i | 0.311617i | 0.987787 | + | 0.155808i | \(0.0497982\pi\) | ||||
−0.987787 | + | 0.155808i | \(0.950202\pi\) | |||||||
\(882\) | − | 2.73498e7i | − | 1.18381i | ||||||
\(883\) | −2.27258e6 | −0.0980884 | −0.0490442 | − | 0.998797i | \(-0.515618\pi\) | ||||
−0.0490442 | + | 0.998797i | \(0.515618\pi\) | |||||||
\(884\) | − | 2.00469e6i | − | 0.0862812i | ||||||
\(885\) | − | 6.70386e7i | − | 2.87718i | ||||||
\(886\) | −9.12901e6 | −0.390696 | ||||||||
\(887\) | − | 3.19149e7i | − | 1.36202i | −0.732273 | − | 0.681012i | \(-0.761540\pi\) | ||
0.732273 | − | 0.681012i | \(-0.238460\pi\) | |||||||
\(888\) | 1.43507e7i | 0.610716i | ||||||||
\(889\) | − | 4.44548e7i | − | 1.88653i | ||||||
\(890\) | 4.50903e7 | 1.90813 | ||||||||
\(891\) | 3.81265e7i | 1.60891i | ||||||||
\(892\) | 1.04664e7 | 0.440440 | ||||||||
\(893\) | 9.49338e6 | 0.398375 | ||||||||
\(894\) | 930520. | 0.0389388 | ||||||||
\(895\) | 7.51706e7 | 3.13682 | ||||||||
\(896\) | 3.90068e6i | 0.162320i | ||||||||
\(897\) | 6.98417e6i | 0.289824i | ||||||||
\(898\) | −1.35788e7 | −0.561915 | ||||||||
\(899\) | 3.29173e7 | − | 2.57101e7i | 1.35839 | − | 1.06097i | ||||
\(900\) | −1.33785e7 | −0.550555 | ||||||||
\(901\) | 5.43864e6i | 0.223192i | ||||||||
\(902\) | 4.66040e6i | 0.190725i | ||||||||
\(903\) | 2.41105e7 | 0.983983 | ||||||||
\(904\) | 2.76582e7 | 1.12565 | ||||||||
\(905\) | 7.57348e6 | 0.307379 | ||||||||
\(906\) | −4.62373e7 | −1.87142 | ||||||||
\(907\) | 2.84496e7i | 1.14831i | 0.818748 | + | 0.574153i | \(0.194669\pi\) | ||||
−0.818748 | + | 0.574153i | \(0.805331\pi\) | |||||||
\(908\) | −3.24214e6 | −0.130502 | ||||||||
\(909\) | − | 1.22187e7i | − | 0.490474i | ||||||
\(910\) | − | 3.77943e7i | − | 1.51295i | ||||||
\(911\) | 1.64758e7i | 0.657734i | 0.944376 | + | 0.328867i | \(0.106667\pi\) | ||||
−0.944376 | + | 0.328867i | \(0.893333\pi\) | |||||||
\(912\) | 7.93671e6 | 0.315976 | ||||||||
\(913\) | 3.17690e7i | 1.26133i | ||||||||
\(914\) | 9.20802e6i | 0.364587i | ||||||||
\(915\) | 1.83211e7 | 0.723436 | ||||||||
\(916\) | 1.38679e7i | 0.546101i | ||||||||
\(917\) | − | 1.95084e7i | − | 0.766121i | ||||||
\(918\) | 827034.i | 0.0323904i | ||||||||
\(919\) | −2.11310e7 | −0.825336 | −0.412668 | − | 0.910881i | \(-0.635403\pi\) | ||||
−0.412668 | + | 0.910881i | \(0.635403\pi\) | |||||||
\(920\) | 1.29167e7i | 0.503134i | ||||||||
\(921\) | −4.67887e7 | −1.81757 | ||||||||
\(922\) | 1.49772e7 | 0.580233 | ||||||||
\(923\) | −1.04257e7 | −0.402811 | ||||||||
\(924\) | −3.30063e7 | −1.27179 | ||||||||
\(925\) | − | 1.69350e7i | − | 0.650775i | ||||||
\(926\) | − | 360784.i | − | 0.0138268i | ||||||
\(927\) | −1.90982e7 | −0.729951 | ||||||||
\(928\) | −1.47724e7 | + | 1.15380e7i | −0.563095 | + | 0.439806i | ||||
\(929\) | −1.53237e7 | −0.582538 | −0.291269 | − | 0.956641i | \(-0.594077\pi\) | ||||
−0.291269 | + | 0.956641i | \(0.594077\pi\) | |||||||
\(930\) | 7.94999e7i | 3.01411i | ||||||||
\(931\) | 2.13343e7i | 0.806684i | ||||||||
\(932\) | −4.16412e6 | −0.157030 | ||||||||
\(933\) | −1.91687e7 | −0.720922 | ||||||||
\(934\) | −8.69792e6 | −0.326248 | ||||||||
\(935\) | −1.97245e7 | −0.737865 | ||||||||
\(936\) | − | 1.92353e7i | − | 0.717646i | ||||||
\(937\) | −2.82423e7 | −1.05087 | −0.525437 | − | 0.850832i | \(-0.676098\pi\) | ||||
−0.525437 | + | 0.850832i | \(0.676098\pi\) | |||||||
\(938\) | − | 3.86984e7i | − | 1.43610i | ||||||
\(939\) | 2.87873e7i | 1.06546i | ||||||||
\(940\) | − | 1.37032e7i | − | 0.505828i | ||||||
\(941\) | −1.91232e7 | −0.704022 | −0.352011 | − | 0.935996i | \(-0.614502\pi\) | ||||
−0.352011 | + | 0.935996i | \(0.614502\pi\) | |||||||
\(942\) | 8.12950e6i | 0.298495i | ||||||||
\(943\) | 1.28582e6i | 0.0470869i | ||||||||
\(944\) | 1.67573e7 | 0.612032 | ||||||||
\(945\) | − | 9.61680e6i | − | 0.350309i | ||||||
\(946\) | 1.39931e7i | 0.508378i | ||||||||
\(947\) | 916050.i | 0.0331928i | 0.999862 | + | 0.0165964i | \(0.00528305\pi\) | ||||
−0.999862 | + | 0.0165964i | \(0.994717\pi\) | |||||||
\(948\) | 1.19199e7 | 0.430777 | ||||||||
\(949\) | 1.13405e7i | 0.408758i | ||||||||
\(950\) | −1.69201e7 | −0.608267 | ||||||||
\(951\) | 2.95222e7 | 1.05852 | ||||||||
\(952\) | −1.53471e7 | −0.548825 | ||||||||
\(953\) | 7.31338e6 | 0.260847 | 0.130423 | − | 0.991458i | \(-0.458366\pi\) | ||||
0.130423 | + | 0.991458i | \(0.458366\pi\) | |||||||
\(954\) | 1.44104e7i | 0.512630i | ||||||||
\(955\) | 4.09272e7i | 1.45212i | ||||||||
\(956\) | 1.78858e7 | 0.632943 | ||||||||
\(957\) | 3.56082e7 | + | 4.55901e7i | 1.25681 | + | 1.60913i | ||||
\(958\) | 2.23630e7 | 0.787257 | ||||||||
\(959\) | 2.16982e7i | 0.761863i | ||||||||
\(960\) | − | 6.57081e7i | − | 2.30113i | ||||||
\(961\) | −5.64252e7 | −1.97090 | ||||||||
\(962\) | 6.72372e6 | 0.234246 | ||||||||
\(963\) | 1.47803e7 | 0.513591 | ||||||||
\(964\) | 384462. | 0.0133248 | ||||||||
\(965\) | − | 4.15382e7i | − | 1.43592i | ||||||
\(966\) | 1.47647e7 | 0.509076 | ||||||||
\(967\) | − | 5.71496e6i | − | 0.196538i | −0.995160 | − | 0.0982692i | \(-0.968669\pi\) | ||
0.995160 | − | 0.0982692i | \(-0.0313306\pi\) | |||||||
\(968\) | − | 3.76957e7i | − | 1.29302i | ||||||
\(969\) | 6.04086e6i | 0.206676i | ||||||||
\(970\) | 290553. | 0.00991507 | ||||||||
\(971\) | − | 3.76567e7i | − | 1.28172i | −0.767657 | − | 0.640861i | \(-0.778578\pi\) | ||
0.767657 | − | 0.640861i | \(-0.221422\pi\) | |||||||
\(972\) | − | 1.53588e7i | − | 0.521426i | ||||||
\(973\) | 4.21962e7 | 1.42886 | ||||||||
\(974\) | − | 3.12104e7i | − | 1.05415i | ||||||
\(975\) | 4.78228e7i | 1.61110i | ||||||||
\(976\) | 4.57964e6i | 0.153889i | ||||||||
\(977\) | −1.50840e7 | −0.505567 | −0.252784 | − | 0.967523i | \(-0.581346\pi\) | ||||
−0.252784 | + | 0.967523i | \(0.581346\pi\) | |||||||
\(978\) | − | 5.08872e7i | − | 1.70122i | ||||||
\(979\) | −6.68127e7 | −2.22793 | ||||||||
\(980\) | 3.07949e7 | 1.02427 | ||||||||
\(981\) | 2.36278e7 | 0.783881 | ||||||||
\(982\) | −2.69008e7 | −0.890198 | ||||||||
\(983\) | 4.82887e7i | 1.59390i | 0.604043 | + | 0.796951i | \(0.293555\pi\) | ||||
−0.604043 | + | 0.796951i | \(0.706445\pi\) | |||||||
\(984\) | − | 7.46082e6i | − | 0.245640i | ||||||
\(985\) | −3.61752e7 | −1.18801 | ||||||||
\(986\) | 4.57206e6 | + | 5.85372e6i | 0.149768 | + | 0.191752i | ||||
\(987\) | −5.67236e7 | −1.85341 | ||||||||
\(988\) | 4.14338e6i | 0.135040i | ||||||||
\(989\) | 3.86074e6i | 0.125511i | ||||||||
\(990\) | −5.22625e7 | −1.69474 | ||||||||
\(991\) | 4.54332e7 | 1.46957 | 0.734783 | − | 0.678303i | \(-0.237284\pi\) | ||||
0.734783 | + | 0.678303i | \(0.237284\pi\) | |||||||
\(992\) | 3.81701e7 | 1.23153 | ||||||||
\(993\) | 7.29472e7 | 2.34766 | ||||||||
\(994\) | 2.20403e7i | 0.707539i | ||||||||
\(995\) | 9.72222e6 | 0.311321 | ||||||||
\(996\) | − | 1.40443e7i | − | 0.448591i | ||||||
\(997\) | 6.29767e6i | 0.200651i | 0.994955 | + | 0.100326i | \(0.0319884\pi\) | ||||
−0.994955 | + | 0.100326i | \(0.968012\pi\) | |||||||
\(998\) | − | 2.36527e7i | − | 0.751715i | ||||||
\(999\) | 1.71085e6 | 0.0542375 |
(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.b.a.28.9 | yes | 12 | |
3.2 | odd | 2 | 261.6.c.b.28.4 | 12 | |||
4.3 | odd | 2 | 464.6.e.c.289.3 | 12 | |||
29.12 | odd | 4 | 841.6.a.d.1.4 | 12 | |||
29.17 | odd | 4 | 841.6.a.d.1.9 | 12 | |||
29.28 | even | 2 | inner | 29.6.b.a.28.4 | ✓ | 12 | |
87.86 | odd | 2 | 261.6.c.b.28.9 | 12 | |||
116.115 | odd | 2 | 464.6.e.c.289.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.b.a.28.4 | ✓ | 12 | 29.28 | even | 2 | inner | |
29.6.b.a.28.9 | yes | 12 | 1.1 | even | 1 | trivial | |
261.6.c.b.28.4 | 12 | 3.2 | odd | 2 | |||
261.6.c.b.28.9 | 12 | 87.86 | odd | 2 | |||
464.6.e.c.289.3 | 12 | 4.3 | odd | 2 | |||
464.6.e.c.289.10 | 12 | 116.115 | odd | 2 | |||
841.6.a.d.1.4 | 12 | 29.12 | odd | 4 | |||
841.6.a.d.1.9 | 12 | 29.17 | odd | 4 |