Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{29}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.19258\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.7703 | −1.90394 | −0.951972 | − | 0.306186i | \(-0.900947\pi\) | ||||
−0.951972 | + | 0.306186i | \(0.900947\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 84.0000 | 2.62500 | ||||||||
\(5\) | 41.6148 | 0.744429 | 0.372214 | − | 0.928147i | \(-0.378599\pi\) | ||||
0.372214 | + | 0.928147i | \(0.378599\pi\) | |||||||
\(6\) | 96.9330 | 1.09924 | ||||||||
\(7\) | 0.236813 | 0.00182667 | 0.000913335 | − | 1.00000i | \(-0.499709\pi\) | ||||
0.000913335 | 1.00000i | \(0.499709\pi\) | ||||||||
\(8\) | −560.057 | −3.09391 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −448.205 | −1.41735 | ||||||||
\(11\) | −421.598 | −1.05055 | −0.525275 | − | 0.850933i | \(-0.676037\pi\) | ||||
−0.525275 | + | 0.850933i | \(0.676037\pi\) | |||||||
\(12\) | −756.000 | −1.51554 | ||||||||
\(13\) | 254.502 | 0.417670 | 0.208835 | − | 0.977951i | \(-0.433033\pi\) | ||||
0.208835 | + | 0.977951i | \(0.433033\pi\) | |||||||
\(14\) | −2.55055 | −0.00347788 | ||||||||
\(15\) | −374.534 | −0.429796 | ||||||||
\(16\) | 3344.00 | 3.26562 | ||||||||
\(17\) | −975.007 | −0.818249 | −0.409125 | − | 0.912479i | \(-0.634166\pi\) | ||||
−0.409125 | + | 0.912479i | \(0.634166\pi\) | |||||||
\(18\) | −872.397 | −0.634648 | ||||||||
\(19\) | 2039.79 | 1.29629 | 0.648143 | − | 0.761519i | \(-0.275546\pi\) | ||||
0.648143 | + | 0.761519i | \(0.275546\pi\) | |||||||
\(20\) | 3495.65 | 1.95413 | ||||||||
\(21\) | −2.13132 | −0.00105463 | ||||||||
\(22\) | 4540.75 | 2.00019 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 5040.51 | 1.78627 | ||||||||
\(25\) | −1393.21 | −0.445826 | ||||||||
\(26\) | −2741.07 | −0.795220 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 19.8923 | 0.00479501 | ||||||||
\(29\) | 2671.55 | 0.589885 | 0.294943 | − | 0.955515i | \(-0.404699\pi\) | ||||
0.294943 | + | 0.955515i | \(0.404699\pi\) | |||||||
\(30\) | 4033.85 | 0.818308 | ||||||||
\(31\) | 9039.14 | 1.68936 | 0.844681 | − | 0.535270i | \(-0.179790\pi\) | ||||
0.844681 | + | 0.535270i | \(0.179790\pi\) | |||||||
\(32\) | −18094.2 | −3.12366 | ||||||||
\(33\) | 3794.38 | 0.606535 | ||||||||
\(34\) | 10501.1 | 1.55790 | ||||||||
\(35\) | 9.85493 | 0.00135983 | ||||||||
\(36\) | 6804.00 | 0.875000 | ||||||||
\(37\) | −12665.3 | −1.52094 | −0.760471 | − | 0.649372i | \(-0.775032\pi\) | ||||
−0.760471 | + | 0.649372i | \(0.775032\pi\) | |||||||
\(38\) | −21969.2 | −2.46805 | ||||||||
\(39\) | −2290.52 | −0.241142 | ||||||||
\(40\) | −23306.7 | −2.30319 | ||||||||
\(41\) | 10146.4 | 0.942658 | 0.471329 | − | 0.881957i | \(-0.343774\pi\) | ||||
0.471329 | + | 0.881957i | \(0.343774\pi\) | |||||||
\(42\) | 22.9550 | 0.00200795 | ||||||||
\(43\) | 19523.2 | 1.61020 | 0.805102 | − | 0.593137i | \(-0.202111\pi\) | ||||
0.805102 | + | 0.593137i | \(0.202111\pi\) | |||||||
\(44\) | −35414.2 | −2.75769 | ||||||||
\(45\) | 3370.80 | 0.248143 | ||||||||
\(46\) | −5697.50 | −0.397000 | ||||||||
\(47\) | 27679.7 | 1.82775 | 0.913875 | − | 0.405995i | \(-0.133075\pi\) | ||||
0.913875 | + | 0.405995i | \(0.133075\pi\) | |||||||
\(48\) | −30096.0 | −1.88541 | ||||||||
\(49\) | −16806.9 | −0.999997 | ||||||||
\(50\) | 15005.3 | 0.848827 | ||||||||
\(51\) | 8775.06 | 0.472416 | ||||||||
\(52\) | 21378.2 | 1.09638 | ||||||||
\(53\) | 10852.8 | 0.530703 | 0.265351 | − | 0.964152i | \(-0.414512\pi\) | ||||
0.265351 | + | 0.964152i | \(0.414512\pi\) | |||||||
\(54\) | 7851.57 | 0.366414 | ||||||||
\(55\) | −17544.7 | −0.782059 | ||||||||
\(56\) | −132.629 | −0.00565155 | ||||||||
\(57\) | −18358.1 | −0.748411 | ||||||||
\(58\) | −28773.4 | −1.12311 | ||||||||
\(59\) | 11907.7 | 0.445345 | 0.222672 | − | 0.974893i | \(-0.428522\pi\) | ||||
0.222672 | + | 0.974893i | \(0.428522\pi\) | |||||||
\(60\) | −31460.8 | −1.12821 | ||||||||
\(61\) | 39861.9 | 1.37162 | 0.685809 | − | 0.727782i | \(-0.259449\pi\) | ||||
0.685809 | + | 0.727782i | \(0.259449\pi\) | |||||||
\(62\) | −97354.5 | −3.21645 | ||||||||
\(63\) | 19.1818 | 0.000608890 0 | ||||||||
\(64\) | 87872.0 | 2.68164 | ||||||||
\(65\) | 10591.1 | 0.310925 | ||||||||
\(66\) | −40866.7 | −1.15481 | ||||||||
\(67\) | −28550.5 | −0.777009 | −0.388504 | − | 0.921447i | \(-0.627008\pi\) | ||||
−0.388504 | + | 0.921447i | \(0.627008\pi\) | |||||||
\(68\) | −81900.6 | −2.14790 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | −106.141 | −0.00258903 | ||||||||
\(71\) | 52179.8 | 1.22845 | 0.614223 | − | 0.789132i | \(-0.289469\pi\) | ||||
0.614223 | + | 0.789132i | \(0.289469\pi\) | |||||||
\(72\) | −45364.6 | −1.03130 | ||||||||
\(73\) | 56918.0 | 1.25009 | 0.625047 | − | 0.780587i | \(-0.285080\pi\) | ||||
0.625047 | + | 0.780587i | \(0.285080\pi\) | |||||||
\(74\) | 136410. | 2.89579 | ||||||||
\(75\) | 12538.8 | 0.257398 | ||||||||
\(76\) | 171342. | 3.40275 | ||||||||
\(77\) | −99.8398 | −0.00191901 | ||||||||
\(78\) | 24669.7 | 0.459120 | ||||||||
\(79\) | 23178.3 | 0.417844 | 0.208922 | − | 0.977932i | \(-0.433004\pi\) | ||||
0.208922 | + | 0.977932i | \(0.433004\pi\) | |||||||
\(80\) | 139160. | 2.43103 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −109281. | −1.79477 | ||||||||
\(83\) | −18344.6 | −0.292289 | −0.146144 | − | 0.989263i | \(-0.546686\pi\) | ||||
−0.146144 | + | 0.989263i | \(0.546686\pi\) | |||||||
\(84\) | −179.031 | −0.00276840 | ||||||||
\(85\) | −40574.8 | −0.609128 | ||||||||
\(86\) | −210272. | −3.06574 | ||||||||
\(87\) | −24043.9 | −0.340571 | ||||||||
\(88\) | 236119. | 3.25030 | ||||||||
\(89\) | 47362.4 | 0.633810 | 0.316905 | − | 0.948457i | \(-0.397356\pi\) | ||||
0.316905 | + | 0.948457i | \(0.397356\pi\) | |||||||
\(90\) | −36304.6 | −0.472450 | ||||||||
\(91\) | 60.2694 | 0.000762945 0 | ||||||||
\(92\) | 44436.0 | 0.547350 | ||||||||
\(93\) | −81352.3 | −0.975354 | ||||||||
\(94\) | −298120. | −3.47993 | ||||||||
\(95\) | 84885.4 | 0.964992 | ||||||||
\(96\) | 162847. | 1.80344 | ||||||||
\(97\) | −140379. | −1.51486 | −0.757432 | − | 0.652915i | \(-0.773546\pi\) | ||||
−0.757432 | + | 0.652915i | \(0.773546\pi\) | |||||||
\(98\) | 181016. | 1.90394 | ||||||||
\(99\) | −34149.4 | −0.350183 | ||||||||
\(100\) | −117029. | −1.17029 | ||||||||
\(101\) | 87080.3 | 0.849408 | 0.424704 | − | 0.905332i | \(-0.360378\pi\) | ||||
0.424704 | + | 0.905332i | \(0.360378\pi\) | |||||||
\(102\) | −94510.3 | −0.899454 | ||||||||
\(103\) | 17988.9 | 0.167075 | 0.0835375 | − | 0.996505i | \(-0.473378\pi\) | ||||
0.0835375 | + | 0.996505i | \(0.473378\pi\) | |||||||
\(104\) | −142536. | −1.29223 | ||||||||
\(105\) | −88.6944 | −0.000785096 0 | ||||||||
\(106\) | −116888. | −1.01043 | ||||||||
\(107\) | −127485. | −1.07646 | −0.538231 | − | 0.842797i | \(-0.680907\pi\) | ||||
−0.538231 | + | 0.842797i | \(0.680907\pi\) | |||||||
\(108\) | −61236.0 | −0.505181 | ||||||||
\(109\) | −136418. | −1.09978 | −0.549890 | − | 0.835237i | \(-0.685330\pi\) | ||||
−0.549890 | + | 0.835237i | \(0.685330\pi\) | |||||||
\(110\) | 188962. | 1.48900 | ||||||||
\(111\) | 113988. | 0.878116 | ||||||||
\(112\) | 791.902 | 0.00596522 | ||||||||
\(113\) | −104012. | −0.766279 | −0.383139 | − | 0.923691i | \(-0.625157\pi\) | ||||
−0.383139 | + | 0.923691i | \(0.625157\pi\) | |||||||
\(114\) | 197723. | 1.42493 | ||||||||
\(115\) | 22014.2 | 0.155224 | ||||||||
\(116\) | 224410. | 1.54845 | ||||||||
\(117\) | 20614.7 | 0.139223 | ||||||||
\(118\) | −128249. | −0.847912 | ||||||||
\(119\) | −230.894 | −0.00149467 | ||||||||
\(120\) | 209760. | 1.32975 | ||||||||
\(121\) | 16693.7 | 0.103655 | ||||||||
\(122\) | −429325. | −2.61148 | ||||||||
\(123\) | −91318.0 | −0.544244 | ||||||||
\(124\) | 759288. | 4.43458 | ||||||||
\(125\) | −188024. | −1.07631 | ||||||||
\(126\) | −206.595 | −0.00115929 | ||||||||
\(127\) | 203763. | 1.12103 | 0.560513 | − | 0.828145i | \(-0.310604\pi\) | ||||
0.560513 | + | 0.828145i | \(0.310604\pi\) | |||||||
\(128\) | −367397. | −1.98203 | ||||||||
\(129\) | −175709. | −0.929651 | ||||||||
\(130\) | −114069. | −0.591984 | ||||||||
\(131\) | 60674.1 | 0.308905 | 0.154453 | − | 0.988000i | \(-0.450639\pi\) | ||||
0.154453 | + | 0.988000i | \(0.450639\pi\) | |||||||
\(132\) | 318728. | 1.59215 | ||||||||
\(133\) | 483.048 | 0.00236789 | ||||||||
\(134\) | 307498. | 1.47938 | ||||||||
\(135\) | −30337.2 | −0.143265 | ||||||||
\(136\) | 546060. | 2.53159 | ||||||||
\(137\) | 94446.5 | 0.429917 | 0.214958 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214958 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(138\) | 51277.5 | 0.229208 | ||||||||
\(139\) | 403508. | 1.77139 | 0.885697 | − | 0.464263i | \(-0.153681\pi\) | ||||
0.885697 | + | 0.464263i | \(0.153681\pi\) | |||||||
\(140\) | 827.814 | 0.00356954 | ||||||||
\(141\) | −249117. | −1.05525 | ||||||||
\(142\) | −561993. | −2.33889 | ||||||||
\(143\) | −107298. | −0.438783 | ||||||||
\(144\) | 270864. | 1.08854 | ||||||||
\(145\) | 111176. | 0.439128 | ||||||||
\(146\) | −613026. | −2.38011 | ||||||||
\(147\) | 151262. | 0.577348 | ||||||||
\(148\) | −1.06389e6 | −3.99247 | ||||||||
\(149\) | 384528. | 1.41893 | 0.709467 | − | 0.704738i | \(-0.248936\pi\) | ||||
0.709467 | + | 0.704738i | \(0.248936\pi\) | |||||||
\(150\) | −135048. | −0.490070 | ||||||||
\(151\) | −442508. | −1.57935 | −0.789675 | − | 0.613525i | \(-0.789751\pi\) | ||||
−0.789675 | + | 0.613525i | \(0.789751\pi\) | |||||||
\(152\) | −1.14240e6 | −4.01059 | ||||||||
\(153\) | −78975.6 | −0.272750 | ||||||||
\(154\) | 1075.31 | 0.00365368 | ||||||||
\(155\) | 376162. | 1.25761 | ||||||||
\(156\) | −192404. | −0.632997 | ||||||||
\(157\) | 240724. | 0.779416 | 0.389708 | − | 0.920938i | \(-0.372576\pi\) | ||||
0.389708 | + | 0.920938i | \(0.372576\pi\) | |||||||
\(158\) | −249638. | −0.795552 | ||||||||
\(159\) | −97675.1 | −0.306402 | ||||||||
\(160\) | −752985. | −2.32534 | ||||||||
\(161\) | 125.274 | 0.000380887 0 | ||||||||
\(162\) | −70664.1 | −0.211549 | ||||||||
\(163\) | −178188. | −0.525301 | −0.262651 | − | 0.964891i | \(-0.584597\pi\) | ||||
−0.262651 | + | 0.964891i | \(0.584597\pi\) | |||||||
\(164\) | 852301. | 2.47448 | ||||||||
\(165\) | 157903. | 0.451522 | ||||||||
\(166\) | 197577. | 0.556502 | ||||||||
\(167\) | 25525.2 | 0.0708236 | 0.0354118 | − | 0.999373i | \(-0.488726\pi\) | ||||
0.0354118 | + | 0.999373i | \(0.488726\pi\) | |||||||
\(168\) | 1193.66 | 0.00326292 | ||||||||
\(169\) | −306522. | −0.825552 | ||||||||
\(170\) | 437004. | 1.15975 | ||||||||
\(171\) | 165223. | 0.432095 | ||||||||
\(172\) | 1.63995e6 | 4.22678 | ||||||||
\(173\) | 701865. | 1.78295 | 0.891474 | − | 0.453072i | \(-0.149672\pi\) | ||||
0.891474 | + | 0.453072i | \(0.149672\pi\) | |||||||
\(174\) | 258961. | 0.648427 | ||||||||
\(175\) | −329.929 | −0.000814377 0 | ||||||||
\(176\) | −1.40982e6 | −3.43070 | ||||||||
\(177\) | −107169. | −0.257120 | ||||||||
\(178\) | −510109. | −1.20674 | ||||||||
\(179\) | −292917. | −0.683302 | −0.341651 | − | 0.939827i | \(-0.610986\pi\) | ||||
−0.341651 | + | 0.939827i | \(0.610986\pi\) | |||||||
\(180\) | 283147. | 0.651375 | ||||||||
\(181\) | −38932.7 | −0.0883321 | −0.0441660 | − | 0.999024i | \(-0.514063\pi\) | ||||
−0.0441660 | + | 0.999024i | \(0.514063\pi\) | |||||||
\(182\) | −649.121 | −0.00145260 | ||||||||
\(183\) | −358757. | −0.791904 | ||||||||
\(184\) | −296270. | −0.645124 | ||||||||
\(185\) | −527066. | −1.13223 | ||||||||
\(186\) | 876191. | 1.85702 | ||||||||
\(187\) | 411061. | 0.859611 | ||||||||
\(188\) | 2.32510e6 | 4.79784 | ||||||||
\(189\) | −172.637 | −0.000351543 0 | ||||||||
\(190\) | −914243. | −1.83729 | ||||||||
\(191\) | 37244.8 | 0.0738724 | 0.0369362 | − | 0.999318i | \(-0.488240\pi\) | ||||
0.0369362 | + | 0.999318i | \(0.488240\pi\) | |||||||
\(192\) | −790848. | −1.54825 | ||||||||
\(193\) | −42454.3 | −0.0820406 | −0.0410203 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410203 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(194\) | 1.51193e6 | 2.88421 | ||||||||
\(195\) | −95319.6 | −0.179513 | ||||||||
\(196\) | −1.41178e6 | −2.62499 | ||||||||
\(197\) | 87335.1 | 0.160333 | 0.0801666 | − | 0.996781i | \(-0.474455\pi\) | ||||
0.0801666 | + | 0.996781i | \(0.474455\pi\) | |||||||
\(198\) | 367801. | 0.666729 | ||||||||
\(199\) | 1.08779e6 | 1.94721 | 0.973604 | − | 0.228245i | \(-0.0732989\pi\) | ||||
0.973604 | + | 0.228245i | \(0.0732989\pi\) | |||||||
\(200\) | 780275. | 1.37934 | ||||||||
\(201\) | 256954. | 0.448606 | ||||||||
\(202\) | −937883. | −1.61722 | ||||||||
\(203\) | 632.657 | 0.00107753 | ||||||||
\(204\) | 737105. | 1.24009 | ||||||||
\(205\) | 422243. | 0.701742 | ||||||||
\(206\) | −193746. | −0.318101 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | 851055. | 1.36395 | ||||||||
\(209\) | −859969. | −1.36181 | ||||||||
\(210\) | 955.267 | 0.00149478 | ||||||||
\(211\) | −1.02777e6 | −1.58923 | −0.794617 | − | 0.607111i | \(-0.792328\pi\) | ||||
−0.794617 | + | 0.607111i | \(0.792328\pi\) | |||||||
\(212\) | 911634. | 1.39310 | ||||||||
\(213\) | −469618. | −0.709244 | ||||||||
\(214\) | 1.37305e6 | 2.04952 | ||||||||
\(215\) | 812456. | 1.19868 | ||||||||
\(216\) | 408282. | 0.595423 | ||||||||
\(217\) | 2140.58 | 0.00308591 | ||||||||
\(218\) | 1.46927e6 | 2.09392 | ||||||||
\(219\) | −512262. | −0.721742 | ||||||||
\(220\) | −1.47376e6 | −2.05291 | ||||||||
\(221\) | −248141. | −0.341758 | ||||||||
\(222\) | −1.22769e6 | −1.67188 | ||||||||
\(223\) | −209627. | −0.282284 | −0.141142 | − | 0.989989i | \(-0.545077\pi\) | ||||
−0.141142 | + | 0.989989i | \(0.545077\pi\) | |||||||
\(224\) | −4284.93 | −0.00570589 | ||||||||
\(225\) | −112850. | −0.148609 | ||||||||
\(226\) | 1.12024e6 | 1.45895 | ||||||||
\(227\) | −347103. | −0.447088 | −0.223544 | − | 0.974694i | \(-0.571763\pi\) | ||||
−0.223544 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(228\) | −1.54208e6 | −1.96458 | ||||||||
\(229\) | −474094. | −0.597414 | −0.298707 | − | 0.954345i | \(-0.596555\pi\) | ||||
−0.298707 | + | 0.954345i | \(0.596555\pi\) | |||||||
\(230\) | −237101. | −0.295538 | ||||||||
\(231\) | 898.558 | 0.00110794 | ||||||||
\(232\) | −1.49622e6 | −1.82505 | ||||||||
\(233\) | 67426.2 | 0.0813652 | 0.0406826 | − | 0.999172i | \(-0.487047\pi\) | ||||
0.0406826 | + | 0.999172i | \(0.487047\pi\) | |||||||
\(234\) | −222027. | −0.265073 | ||||||||
\(235\) | 1.15189e6 | 1.36063 | ||||||||
\(236\) | 1.00024e6 | 1.16903 | ||||||||
\(237\) | −208605. | −0.241243 | ||||||||
\(238\) | 2486.81 | 0.00284577 | ||||||||
\(239\) | −631686. | −0.715331 | −0.357665 | − | 0.933850i | \(-0.616427\pi\) | ||||
−0.357665 | + | 0.933850i | \(0.616427\pi\) | |||||||
\(240\) | −1.25244e6 | −1.40355 | ||||||||
\(241\) | −582036. | −0.645516 | −0.322758 | − | 0.946482i | \(-0.604610\pi\) | ||||
−0.322758 | + | 0.946482i | \(0.604610\pi\) | |||||||
\(242\) | −179797. | −0.197353 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 3.34840e6 | 3.60050 | ||||||||
\(245\) | −699418. | −0.744426 | ||||||||
\(246\) | 983525. | 1.03621 | ||||||||
\(247\) | 519130. | 0.541419 | ||||||||
\(248\) | −5.06243e6 | −5.22673 | ||||||||
\(249\) | 165101. | 0.168753 | ||||||||
\(250\) | 2.02508e6 | 2.04924 | ||||||||
\(251\) | −1.28835e6 | −1.29077 | −0.645386 | − | 0.763856i | \(-0.723304\pi\) | ||||
−0.645386 | + | 0.763856i | \(0.723304\pi\) | |||||||
\(252\) | 1611.27 | 0.00159834 | ||||||||
\(253\) | −223025. | −0.219055 | ||||||||
\(254\) | −2.19459e6 | −2.13437 | ||||||||
\(255\) | 365173. | 0.351680 | ||||||||
\(256\) | 1.14509e6 | 1.09204 | ||||||||
\(257\) | −204908. | −0.193520 | −0.0967601 | − | 0.995308i | \(-0.530848\pi\) | ||||
−0.0967601 | + | 0.995308i | \(0.530848\pi\) | |||||||
\(258\) | 1.89245e6 | 1.77000 | ||||||||
\(259\) | −2999.32 | −0.00277826 | ||||||||
\(260\) | 889650. | 0.816179 | ||||||||
\(261\) | 216395. | 0.196628 | ||||||||
\(262\) | −653480. | −0.588138 | ||||||||
\(263\) | 418862. | 0.373407 | 0.186703 | − | 0.982416i | \(-0.440220\pi\) | ||||
0.186703 | + | 0.982416i | \(0.440220\pi\) | |||||||
\(264\) | −2.12507e6 | −1.87656 | ||||||||
\(265\) | 451637. | 0.395071 | ||||||||
\(266\) | −5202.58 | −0.00450832 | ||||||||
\(267\) | −426262. | −0.365930 | ||||||||
\(268\) | −2.39824e6 | −2.03965 | ||||||||
\(269\) | −1.48662e6 | −1.25262 | −0.626308 | − | 0.779576i | \(-0.715435\pi\) | ||||
−0.626308 | + | 0.779576i | \(0.715435\pi\) | |||||||
\(270\) | 326742. | 0.272769 | ||||||||
\(271\) | −658640. | −0.544785 | −0.272392 | − | 0.962186i | \(-0.587815\pi\) | ||||
−0.272392 | + | 0.962186i | \(0.587815\pi\) | |||||||
\(272\) | −3.26042e6 | −2.67209 | ||||||||
\(273\) | −542.425 | −0.000440487 0 | ||||||||
\(274\) | −1.01722e6 | −0.818537 | ||||||||
\(275\) | 587372. | 0.468362 | ||||||||
\(276\) | −399924. | −0.316013 | ||||||||
\(277\) | 236526. | 0.185216 | 0.0926082 | − | 0.995703i | \(-0.470480\pi\) | ||||
0.0926082 | + | 0.995703i | \(0.470480\pi\) | |||||||
\(278\) | −4.34592e6 | −3.37263 | ||||||||
\(279\) | 732170. | 0.563121 | ||||||||
\(280\) | −5519.32 | −0.00420718 | ||||||||
\(281\) | −1.66253e6 | −1.25604 | −0.628020 | − | 0.778197i | \(-0.716134\pi\) | ||||
−0.628020 | + | 0.778197i | \(0.716134\pi\) | |||||||
\(282\) | 2.68308e6 | 2.00914 | ||||||||
\(283\) | 966812. | 0.717589 | 0.358795 | − | 0.933417i | \(-0.383188\pi\) | ||||
0.358795 | + | 0.933417i | \(0.383188\pi\) | |||||||
\(284\) | 4.38310e6 | 3.22467 | ||||||||
\(285\) | −763968. | −0.557139 | ||||||||
\(286\) | 1.15563e6 | 0.835418 | ||||||||
\(287\) | 2402.81 | 0.00172193 | ||||||||
\(288\) | −1.46563e6 | −1.04122 | ||||||||
\(289\) | −469218. | −0.330469 | ||||||||
\(290\) | −1.19740e6 | −0.836074 | ||||||||
\(291\) | 1.26341e6 | 0.874607 | ||||||||
\(292\) | 4.78111e6 | 3.28150 | ||||||||
\(293\) | −82436.0 | −0.0560981 | −0.0280490 | − | 0.999607i | \(-0.508929\pi\) | ||||
−0.0280490 | + | 0.999607i | \(0.508929\pi\) | |||||||
\(294\) | −1.62915e6 | −1.09924 | ||||||||
\(295\) | 495535. | 0.331528 | ||||||||
\(296\) | 7.09332e6 | 4.70565 | ||||||||
\(297\) | 307345. | 0.202178 | ||||||||
\(298\) | −4.14149e6 | −2.70157 | ||||||||
\(299\) | 134632. | 0.0870902 | ||||||||
\(300\) | 1.05326e6 | 0.675669 | ||||||||
\(301\) | 4623.35 | 0.00294131 | ||||||||
\(302\) | 4.76595e6 | 3.00699 | ||||||||
\(303\) | −783722. | −0.490406 | ||||||||
\(304\) | 6.82105e6 | 4.23318 | ||||||||
\(305\) | 1.65884e6 | 1.02107 | ||||||||
\(306\) | 850593. | 0.519300 | ||||||||
\(307\) | 471104. | 0.285280 | 0.142640 | − | 0.989775i | \(-0.454441\pi\) | ||||
0.142640 | + | 0.989775i | \(0.454441\pi\) | |||||||
\(308\) | −8386.54 | −0.00503740 | ||||||||
\(309\) | −161900. | −0.0964608 | ||||||||
\(310\) | −4.05139e6 | −2.39442 | ||||||||
\(311\) | 974141. | 0.571112 | 0.285556 | − | 0.958362i | \(-0.407822\pi\) | ||||
0.285556 | + | 0.958362i | \(0.407822\pi\) | |||||||
\(312\) | 1.28282e6 | 0.746071 | ||||||||
\(313\) | 203897. | 0.117639 | 0.0588194 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588194 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(314\) | −2.59267e6 | −1.48396 | ||||||||
\(315\) | 798.249 | 0.000453275 0 | ||||||||
\(316\) | 1.94698e6 | 1.09684 | ||||||||
\(317\) | −1.11600e6 | −0.623757 | −0.311879 | − | 0.950122i | \(-0.600958\pi\) | ||||
−0.311879 | + | 0.950122i | \(0.600958\pi\) | |||||||
\(318\) | 1.05199e6 | 0.583371 | ||||||||
\(319\) | −1.12632e6 | −0.619704 | ||||||||
\(320\) | 3.65678e6 | 1.99629 | ||||||||
\(321\) | 1.14736e6 | 0.621496 | ||||||||
\(322\) | −1349.24 | −0.000725187 0 | ||||||||
\(323\) | −1.98881e6 | −1.06068 | ||||||||
\(324\) | 551124. | 0.291667 | ||||||||
\(325\) | −354574. | −0.186208 | ||||||||
\(326\) | 1.91914e6 | 1.00014 | ||||||||
\(327\) | 1.22776e6 | 0.634958 | ||||||||
\(328\) | −5.68259e6 | −2.91650 | ||||||||
\(329\) | 6554.91 | 0.00333870 | ||||||||
\(330\) | −1.70066e6 | −0.859673 | ||||||||
\(331\) | 2.08998e6 | 1.04851 | 0.524254 | − | 0.851562i | \(-0.324344\pi\) | ||||
0.524254 | + | 0.851562i | \(0.324344\pi\) | |||||||
\(332\) | −1.54094e6 | −0.767258 | ||||||||
\(333\) | −1.02589e6 | −0.506981 | ||||||||
\(334\) | −274915. | −0.134844 | ||||||||
\(335\) | −1.18812e6 | −0.578428 | ||||||||
\(336\) | −7127.12 | −0.00344402 | ||||||||
\(337\) | 901699. | 0.432501 | 0.216250 | − | 0.976338i | \(-0.430617\pi\) | ||||
0.216250 | + | 0.976338i | \(0.430617\pi\) | |||||||
\(338\) | 3.30134e6 | 1.57180 | ||||||||
\(339\) | 936107. | 0.442411 | ||||||||
\(340\) | −3.40828e6 | −1.59896 | ||||||||
\(341\) | −3.81088e6 | −1.77476 | ||||||||
\(342\) | −1.77950e6 | −0.822685 | ||||||||
\(343\) | −7960.21 | −0.00365333 | ||||||||
\(344\) | −1.09341e7 | −4.98182 | ||||||||
\(345\) | −198128. | −0.0896187 | ||||||||
\(346\) | −7.55932e6 | −3.39463 | ||||||||
\(347\) | −1.53207e6 | −0.683053 | −0.341526 | − | 0.939872i | \(-0.610944\pi\) | ||||
−0.341526 | + | 0.939872i | \(0.610944\pi\) | |||||||
\(348\) | −2.01969e6 | −0.893998 | ||||||||
\(349\) | 1.28353e6 | 0.564084 | 0.282042 | − | 0.959402i | \(-0.408988\pi\) | ||||
0.282042 | + | 0.959402i | \(0.408988\pi\) | |||||||
\(350\) | 3553.44 | 0.00155053 | ||||||||
\(351\) | −185532. | −0.0803806 | ||||||||
\(352\) | 7.62846e6 | 3.28156 | ||||||||
\(353\) | −4.45978e6 | −1.90492 | −0.952460 | − | 0.304663i | \(-0.901456\pi\) | ||||
−0.952460 | + | 0.304663i | \(0.901456\pi\) | |||||||
\(354\) | 1.15425e6 | 0.489542 | ||||||||
\(355\) | 2.17145e6 | 0.914491 | ||||||||
\(356\) | 3.97844e6 | 1.66375 | ||||||||
\(357\) | 2078.05 | 0.000862949 0 | ||||||||
\(358\) | 3.15482e6 | 1.30097 | ||||||||
\(359\) | 4.67506e6 | 1.91448 | 0.957240 | − | 0.289296i | \(-0.0934213\pi\) | ||||
0.957240 | + | 0.289296i | \(0.0934213\pi\) | |||||||
\(360\) | −1.88784e6 | −0.767731 | ||||||||
\(361\) | 1.68463e6 | 0.680356 | ||||||||
\(362\) | 419318. | 0.168179 | ||||||||
\(363\) | −150243. | −0.0598451 | ||||||||
\(364\) | 5062.63 | 0.00200273 | ||||||||
\(365\) | 2.36863e6 | 0.930606 | ||||||||
\(366\) | 3.86393e6 | 1.50774 | ||||||||
\(367\) | 2.43229e6 | 0.942650 | 0.471325 | − | 0.881960i | \(-0.343776\pi\) | ||||
0.471325 | + | 0.881960i | \(0.343776\pi\) | |||||||
\(368\) | 1.76898e6 | 0.680930 | ||||||||
\(369\) | 821862. | 0.314219 | ||||||||
\(370\) | 5.67668e6 | 2.15571 | ||||||||
\(371\) | 2570.08 | 0.000969419 0 | ||||||||
\(372\) | −6.83359e6 | −2.56030 | ||||||||
\(373\) | 1.37458e6 | 0.511561 | 0.255780 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255780 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(374\) | −4.42726e6 | −1.63665 | ||||||||
\(375\) | 1.69222e6 | 0.621410 | ||||||||
\(376\) | −1.55022e7 | −5.65489 | ||||||||
\(377\) | 679914. | 0.246377 | ||||||||
\(378\) | 1859.35 | 0.000669318 0 | ||||||||
\(379\) | 2.01997e6 | 0.722350 | 0.361175 | − | 0.932498i | \(-0.382376\pi\) | ||||
0.361175 | + | 0.932498i | \(0.382376\pi\) | |||||||
\(380\) | 7.13037e6 | 2.53310 | ||||||||
\(381\) | −1.83387e6 | −0.647225 | ||||||||
\(382\) | −401139. | −0.140649 | ||||||||
\(383\) | 2.00834e6 | 0.699584 | 0.349792 | − | 0.936827i | \(-0.386252\pi\) | ||||
0.349792 | + | 0.936827i | \(0.386252\pi\) | |||||||
\(384\) | 3.30658e6 | 1.14433 | ||||||||
\(385\) | −4154.82 | −0.00142857 | ||||||||
\(386\) | 457247. | 0.156201 | ||||||||
\(387\) | 1.58138e6 | 0.536734 | ||||||||
\(388\) | −1.17919e7 | −3.97652 | ||||||||
\(389\) | 3.25055e6 | 1.08914 | 0.544569 | − | 0.838716i | \(-0.316693\pi\) | ||||
0.544569 | + | 0.838716i | \(0.316693\pi\) | |||||||
\(390\) | 1.02662e6 | 0.341782 | ||||||||
\(391\) | −515779. | −0.170617 | ||||||||
\(392\) | 9.41285e6 | 3.09390 | ||||||||
\(393\) | −546067. | −0.178346 | ||||||||
\(394\) | −940628. | −0.305265 | ||||||||
\(395\) | 964563. | 0.311055 | ||||||||
\(396\) | −2.86855e6 | −0.919231 | ||||||||
\(397\) | 5.43707e6 | 1.73137 | 0.865683 | − | 0.500592i | \(-0.166884\pi\) | ||||
0.865683 | + | 0.500592i | \(0.166884\pi\) | |||||||
\(398\) | −1.17159e7 | −3.70737 | ||||||||
\(399\) | −4347.43 | −0.00136710 | ||||||||
\(400\) | −4.65888e6 | −1.45590 | ||||||||
\(401\) | 3.27208e6 | 1.01616 | 0.508081 | − | 0.861309i | \(-0.330355\pi\) | ||||
0.508081 | + | 0.861309i | \(0.330355\pi\) | |||||||
\(402\) | −2.76748e6 | −0.854121 | ||||||||
\(403\) | 2.30048e6 | 0.705596 | ||||||||
\(404\) | 7.31474e6 | 2.22970 | ||||||||
\(405\) | 273035. | 0.0827143 | ||||||||
\(406\) | −6813.92 | −0.00205155 | ||||||||
\(407\) | 5.33968e6 | 1.59783 | ||||||||
\(408\) | −4.91454e6 | −1.46161 | ||||||||
\(409\) | −1.56299e6 | −0.462007 | −0.231003 | − | 0.972953i | \(-0.574201\pi\) | ||||
−0.231003 | + | 0.972953i | \(0.574201\pi\) | |||||||
\(410\) | −4.54769e6 | −1.33608 | ||||||||
\(411\) | −850019. | −0.248213 | ||||||||
\(412\) | 1.51107e6 | 0.438572 | ||||||||
\(413\) | 2819.89 | 0.000813498 0 | ||||||||
\(414\) | −461498. | −0.132333 | ||||||||
\(415\) | −763406. | −0.217588 | ||||||||
\(416\) | −4.60500e6 | −1.30466 | ||||||||
\(417\) | −3.63157e6 | −1.02272 | ||||||||
\(418\) | 9.26215e6 | 2.59281 | ||||||||
\(419\) | −4.76111e6 | −1.32487 | −0.662434 | − | 0.749120i | \(-0.730477\pi\) | ||||
−0.662434 | + | 0.749120i | \(0.730477\pi\) | |||||||
\(420\) | −7450.33 | −0.00206088 | ||||||||
\(421\) | −4.56989e6 | −1.25661 | −0.628305 | − | 0.777967i | \(-0.716251\pi\) | ||||
−0.628305 | + | 0.777967i | \(0.716251\pi\) | |||||||
\(422\) | 1.10694e7 | 3.02581 | ||||||||
\(423\) | 2.24206e6 | 0.609250 | ||||||||
\(424\) | −6.07818e6 | −1.64195 | ||||||||
\(425\) | 1.35839e6 | 0.364796 | ||||||||
\(426\) | 5.05794e6 | 1.35036 | ||||||||
\(427\) | 9439.80 | 0.00250549 | ||||||||
\(428\) | −1.07087e7 | −2.82571 | ||||||||
\(429\) | 965678. | 0.253331 | ||||||||
\(430\) | −8.75042e6 | −2.28222 | ||||||||
\(431\) | −3.28891e6 | −0.852824 | −0.426412 | − | 0.904529i | \(-0.640223\pi\) | ||||
−0.426412 | + | 0.904529i | \(0.640223\pi\) | |||||||
\(432\) | −2.43778e6 | −0.628470 | ||||||||
\(433\) | 2.11805e6 | 0.542895 | 0.271447 | − | 0.962453i | \(-0.412498\pi\) | ||||
0.271447 | + | 0.962453i | \(0.412498\pi\) | |||||||
\(434\) | −23054.8 | −0.00587540 | ||||||||
\(435\) | −1.00058e6 | −0.253531 | ||||||||
\(436\) | −1.14591e7 | −2.88692 | ||||||||
\(437\) | 1.07905e6 | 0.270294 | ||||||||
\(438\) | 5.51723e6 | 1.37416 | ||||||||
\(439\) | 758443. | 0.187829 | 0.0939143 | − | 0.995580i | \(-0.470062\pi\) | ||||
0.0939143 | + | 0.995580i | \(0.470062\pi\) | |||||||
\(440\) | 9.82605e6 | 2.41962 | ||||||||
\(441\) | −1.36136e6 | −0.333332 | ||||||||
\(442\) | 2.67257e6 | 0.650688 | ||||||||
\(443\) | 650377. | 0.157455 | 0.0787274 | − | 0.996896i | \(-0.474914\pi\) | ||||
0.0787274 | + | 0.996896i | \(0.474914\pi\) | |||||||
\(444\) | 9.57500e6 | 2.30506 | ||||||||
\(445\) | 1.97098e6 | 0.471826 | ||||||||
\(446\) | 2.25776e6 | 0.537452 | ||||||||
\(447\) | −3.46075e6 | −0.819222 | ||||||||
\(448\) | 20809.2 | 0.00489847 | ||||||||
\(449\) | −7.58111e6 | −1.77467 | −0.887333 | − | 0.461129i | \(-0.847445\pi\) | ||||
−0.887333 | + | 0.461129i | \(0.847445\pi\) | |||||||
\(450\) | 1.21543e6 | 0.282942 | ||||||||
\(451\) | −4.27772e6 | −0.990309 | ||||||||
\(452\) | −8.73699e6 | −2.01148 | ||||||||
\(453\) | 3.98257e6 | 0.911838 | ||||||||
\(454\) | 3.73841e6 | 0.851231 | ||||||||
\(455\) | 2508.10 | 0.000567958 0 | ||||||||
\(456\) | 1.02816e7 | 2.31551 | ||||||||
\(457\) | −8.04537e6 | −1.80200 | −0.901002 | − | 0.433815i | \(-0.857167\pi\) | ||||
−0.901002 | + | 0.433815i | \(0.857167\pi\) | |||||||
\(458\) | 5.10614e6 | 1.13744 | ||||||||
\(459\) | 710780. | 0.157472 | ||||||||
\(460\) | 1.84920e6 | 0.407463 | ||||||||
\(461\) | 5.63578e6 | 1.23510 | 0.617550 | − | 0.786532i | \(-0.288125\pi\) | ||||
0.617550 | + | 0.786532i | \(0.288125\pi\) | |||||||
\(462\) | −9677.77 | −0.00210945 | ||||||||
\(463\) | 1.39156e6 | 0.301682 | 0.150841 | − | 0.988558i | \(-0.451802\pi\) | ||||
0.150841 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(464\) | 8.93365e6 | 1.92634 | ||||||||
\(465\) | −3.38546e6 | −0.726082 | ||||||||
\(466\) | −726202. | −0.154915 | ||||||||
\(467\) | 4.05063e6 | 0.859469 | 0.429734 | − | 0.902955i | \(-0.358607\pi\) | ||||
0.429734 | + | 0.902955i | \(0.358607\pi\) | |||||||
\(468\) | 1.73163e6 | 0.365461 | ||||||||
\(469\) | −6761.12 | −0.00141934 | ||||||||
\(470\) | −1.24062e7 | −2.59056 | ||||||||
\(471\) | −2.16651e6 | −0.449996 | ||||||||
\(472\) | −6.66897e6 | −1.37786 | ||||||||
\(473\) | −8.23095e6 | −1.69160 | ||||||||
\(474\) | 2.24675e6 | 0.459312 | ||||||||
\(475\) | −2.84184e6 | −0.577917 | ||||||||
\(476\) | −19395.1 | −0.00392351 | ||||||||
\(477\) | 879076. | 0.176901 | ||||||||
\(478\) | 6.80347e6 | 1.36195 | ||||||||
\(479\) | 6.55529e6 | 1.30543 | 0.652714 | − | 0.757605i | \(-0.273630\pi\) | ||||
0.652714 | + | 0.757605i | \(0.273630\pi\) | |||||||
\(480\) | 6.77687e6 | 1.34254 | ||||||||
\(481\) | −3.22336e6 | −0.635252 | ||||||||
\(482\) | 6.26872e6 | 1.22903 | ||||||||
\(483\) | −1127.47 | −0.000219905 0 | ||||||||
\(484\) | 1.40227e6 | 0.272094 | ||||||||
\(485\) | −5.84186e6 | −1.12771 | ||||||||
\(486\) | 635977. | 0.122138 | ||||||||
\(487\) | −1.98924e6 | −0.380071 | −0.190035 | − | 0.981777i | \(-0.560860\pi\) | ||||
−0.190035 | + | 0.981777i | \(0.560860\pi\) | |||||||
\(488\) | −2.23249e7 | −4.24366 | ||||||||
\(489\) | 1.60369e6 | 0.303283 | ||||||||
\(490\) | 7.53296e6 | 1.41735 | ||||||||
\(491\) | 7.99205e6 | 1.49608 | 0.748040 | − | 0.663654i | \(-0.230995\pi\) | ||||
0.748040 | + | 0.663654i | \(0.230995\pi\) | |||||||
\(492\) | −7.67071e6 | −1.42864 | ||||||||
\(493\) | −2.60478e6 | −0.482673 | ||||||||
\(494\) | −5.59120e6 | −1.03083 | ||||||||
\(495\) | −1.42112e6 | −0.260686 | ||||||||
\(496\) | 3.02269e7 | 5.51682 | ||||||||
\(497\) | 12356.8 | 0.00224397 | ||||||||
\(498\) | −1.77819e6 | −0.321296 | ||||||||
\(499\) | −1.00308e7 | −1.80338 | −0.901688 | − | 0.432387i | \(-0.857671\pi\) | ||||
−0.901688 | + | 0.432387i | \(0.857671\pi\) | |||||||
\(500\) | −1.57940e7 | −2.82533 | ||||||||
\(501\) | −229727. | −0.0408900 | ||||||||
\(502\) | 1.38760e7 | 2.45756 | ||||||||
\(503\) | −4.82601e6 | −0.850488 | −0.425244 | − | 0.905079i | \(-0.639812\pi\) | ||||
−0.425244 | + | 0.905079i | \(0.639812\pi\) | |||||||
\(504\) | −10742.9 | −0.00188385 | ||||||||
\(505\) | 3.62383e6 | 0.632324 | ||||||||
\(506\) | 2.40206e6 | 0.417068 | ||||||||
\(507\) | 2.75869e6 | 0.476633 | ||||||||
\(508\) | 1.71161e7 | 2.94270 | ||||||||
\(509\) | 138289. | 0.0236589 | 0.0118294 | − | 0.999930i | \(-0.496234\pi\) | ||||
0.0118294 | + | 0.999930i | \(0.496234\pi\) | |||||||
\(510\) | −3.93303e6 | −0.669579 | ||||||||
\(511\) | 13478.9 | 0.00228351 | ||||||||
\(512\) | −576256. | −0.0971494 | ||||||||
\(513\) | −1.48700e6 | −0.249470 | ||||||||
\(514\) | 2.20693e6 | 0.368451 | ||||||||
\(515\) | 748605. | 0.124375 | ||||||||
\(516\) | −1.47596e7 | −2.44033 | ||||||||
\(517\) | −1.16697e7 | −1.92014 | ||||||||
\(518\) | 32303.6 | 0.00528965 | ||||||||
\(519\) | −6.31679e6 | −1.02939 | ||||||||
\(520\) | −5.93160e6 | −0.961975 | ||||||||
\(521\) | 4.62831e6 | 0.747012 | 0.373506 | − | 0.927628i | \(-0.378155\pi\) | ||||
0.373506 | + | 0.927628i | \(0.378155\pi\) | |||||||
\(522\) | −2.33065e6 | −0.374369 | ||||||||
\(523\) | −1.54914e6 | −0.247649 | −0.123825 | − | 0.992304i | \(-0.539516\pi\) | ||||
−0.123825 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(524\) | 5.09662e6 | 0.810876 | ||||||||
\(525\) | 2969.36 | 0.000470181 0 | ||||||||
\(526\) | −4.51129e6 | −0.710945 | ||||||||
\(527\) | −8.81323e6 | −1.38232 | ||||||||
\(528\) | 1.26884e7 | 1.98072 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −4.86428e6 | −0.752192 | ||||||||
\(531\) | 964521. | 0.148448 | ||||||||
\(532\) | 40576.0 | 0.00621570 | ||||||||
\(533\) | 2.58229e6 | 0.393720 | ||||||||
\(534\) | 4.59098e6 | 0.696710 | ||||||||
\(535\) | −5.30526e6 | −0.801349 | ||||||||
\(536\) | 1.59899e7 | 2.40399 | ||||||||
\(537\) | 2.63626e6 | 0.394505 | ||||||||
\(538\) | 1.60113e7 | 2.38491 | ||||||||
\(539\) | 7.08577e6 | 1.05055 | ||||||||
\(540\) | −2.54833e6 | −0.376072 | ||||||||
\(541\) | −6.52702e6 | −0.958787 | −0.479393 | − | 0.877600i | \(-0.659143\pi\) | ||||
−0.479393 | + | 0.877600i | \(0.659143\pi\) | |||||||
\(542\) | 7.09377e6 | 1.03724 | ||||||||
\(543\) | 350395. | 0.0509985 | ||||||||
\(544\) | 1.76419e7 | 2.55593 | ||||||||
\(545\) | −5.67701e6 | −0.818707 | ||||||||
\(546\) | 5842.09 | 0.000838662 0 | ||||||||
\(547\) | 1.06849e7 | 1.52686 | 0.763432 | − | 0.645888i | \(-0.223513\pi\) | ||||
0.763432 | + | 0.645888i | \(0.223513\pi\) | |||||||
\(548\) | 7.93351e6 | 1.12853 | ||||||||
\(549\) | 3.22881e6 | 0.457206 | ||||||||
\(550\) | −6.32619e6 | −0.891735 | ||||||||
\(551\) | 5.44938e6 | 0.764660 | ||||||||
\(552\) | 2.66643e6 | 0.372463 | ||||||||
\(553\) | 5488.93 | 0.000763264 0 | ||||||||
\(554\) | −2.54746e6 | −0.352642 | ||||||||
\(555\) | 4.74360e6 | 0.653695 | ||||||||
\(556\) | 3.38947e7 | 4.64991 | ||||||||
\(557\) | −3.07804e6 | −0.420374 | −0.210187 | − | 0.977661i | \(-0.567407\pi\) | ||||
−0.210187 | + | 0.977661i | \(0.567407\pi\) | |||||||
\(558\) | −7.88572e6 | −1.07215 | ||||||||
\(559\) | 4.96871e6 | 0.672533 | ||||||||
\(560\) | 32954.9 | 0.00444068 | ||||||||
\(561\) | −3.69955e6 | −0.496297 | ||||||||
\(562\) | 1.79060e7 | 2.39143 | ||||||||
\(563\) | 1.10366e7 | 1.46745 | 0.733724 | − | 0.679448i | \(-0.237781\pi\) | ||||
0.733724 | + | 0.679448i | \(0.237781\pi\) | |||||||
\(564\) | −2.09259e7 | −2.77004 | ||||||||
\(565\) | −4.32844e6 | −0.570440 | ||||||||
\(566\) | −1.04129e7 | −1.36625 | ||||||||
\(567\) | 1553.73 | 0.000202963 0 | ||||||||
\(568\) | −2.92237e7 | −3.80070 | ||||||||
\(569\) | −9.26308e6 | −1.19943 | −0.599715 | − | 0.800214i | \(-0.704719\pi\) | ||||
−0.599715 | + | 0.800214i | \(0.704719\pi\) | |||||||
\(570\) | 8.22819e6 | 1.06076 | ||||||||
\(571\) | −1.31913e7 | −1.69315 | −0.846576 | − | 0.532267i | \(-0.821340\pi\) | ||||
−0.846576 | + | 0.532267i | \(0.821340\pi\) | |||||||
\(572\) | −9.01300e6 | −1.15181 | ||||||||
\(573\) | −335203. | −0.0426503 | ||||||||
\(574\) | −25879.0 | −0.00327845 | ||||||||
\(575\) | −737006. | −0.0929611 | ||||||||
\(576\) | 7.11763e6 | 0.893880 | ||||||||
\(577\) | −1.29741e6 | −0.162232 | −0.0811160 | − | 0.996705i | \(-0.525848\pi\) | ||||
−0.0811160 | + | 0.996705i | \(0.525848\pi\) | |||||||
\(578\) | 5.05363e6 | 0.629193 | ||||||||
\(579\) | 382089. | 0.0473661 | ||||||||
\(580\) | 9.33878e6 | 1.15271 | ||||||||
\(581\) | −4344.23 | −0.000533916 0 | ||||||||
\(582\) | −1.36074e7 | −1.66520 | ||||||||
\(583\) | −4.57551e6 | −0.557530 | ||||||||
\(584\) | −3.18773e7 | −3.86767 | ||||||||
\(585\) | 857876. | 0.103642 | ||||||||
\(586\) | 887863. | 0.106808 | ||||||||
\(587\) | 4.51203e6 | 0.540477 | 0.270238 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270238 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(588\) | 1.27060e7 | 1.51554 | ||||||||
\(589\) | 1.84379e7 | 2.18990 | ||||||||
\(590\) | −5.33708e6 | −0.631210 | ||||||||
\(591\) | −786016. | −0.0925684 | ||||||||
\(592\) | −4.23529e7 | −4.96683 | ||||||||
\(593\) | 9.27288e6 | 1.08287 | 0.541437 | − | 0.840741i | \(-0.317880\pi\) | ||||
0.541437 | + | 0.840741i | \(0.317880\pi\) | |||||||
\(594\) | −3.31020e6 | −0.384936 | ||||||||
\(595\) | −9608.63 | −0.00111268 | ||||||||
\(596\) | 3.23004e7 | 3.72470 | ||||||||
\(597\) | −9.79011e6 | −1.12422 | ||||||||
\(598\) | −1.45003e6 | −0.165815 | ||||||||
\(599\) | −6.32225e6 | −0.719954 | −0.359977 | − | 0.932961i | \(-0.617215\pi\) | ||||
−0.359977 | + | 0.932961i | \(0.617215\pi\) | |||||||
\(600\) | −7.02247e6 | −0.796365 | ||||||||
\(601\) | 3.18785e6 | 0.360008 | 0.180004 | − | 0.983666i | \(-0.442389\pi\) | ||||
0.180004 | + | 0.983666i | \(0.442389\pi\) | |||||||
\(602\) | −49795.0 | −0.00560009 | ||||||||
\(603\) | −2.31259e6 | −0.259003 | ||||||||
\(604\) | −3.71706e7 | −4.14579 | ||||||||
\(605\) | 694706. | 0.0771636 | ||||||||
\(606\) | 8.44095e6 | 0.933705 | ||||||||
\(607\) | −5.70410e6 | −0.628369 | −0.314185 | − | 0.949362i | \(-0.601731\pi\) | ||||
−0.314185 | + | 0.949362i | \(0.601731\pi\) | |||||||
\(608\) | −3.69082e7 | −4.04915 | ||||||||
\(609\) | −5693.91 | −0.000622110 0 | ||||||||
\(610\) | −1.78663e7 | −1.94406 | ||||||||
\(611\) | 7.04455e6 | 0.763396 | ||||||||
\(612\) | −6.63395e6 | −0.715968 | ||||||||
\(613\) | 1.17835e7 | 1.26655 | 0.633276 | − | 0.773926i | \(-0.281710\pi\) | ||||
0.633276 | + | 0.773926i | \(0.281710\pi\) | |||||||
\(614\) | −5.07394e6 | −0.543156 | ||||||||
\(615\) | −3.80018e6 | −0.405151 | ||||||||
\(616\) | 55916.0 | 0.00593723 | ||||||||
\(617\) | 1.41628e6 | 0.149774 | 0.0748868 | − | 0.997192i | \(-0.476140\pi\) | ||||
0.0748868 | + | 0.997192i | \(0.476140\pi\) | |||||||
\(618\) | 1.74372e6 | 0.183656 | ||||||||
\(619\) | −4.37752e6 | −0.459200 | −0.229600 | − | 0.973285i | \(-0.573742\pi\) | ||||
−0.229600 | + | 0.973285i | \(0.573742\pi\) | |||||||
\(620\) | 3.15976e7 | 3.30123 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | −1.04918e7 | −1.08736 | ||||||||
\(623\) | 11216.0 | 0.00115776 | ||||||||
\(624\) | −7.65950e6 | −0.787479 | ||||||||
\(625\) | −3.47084e6 | −0.355414 | ||||||||
\(626\) | −2.19604e6 | −0.223978 | ||||||||
\(627\) | 7.73972e6 | 0.786243 | ||||||||
\(628\) | 2.02208e7 | 2.04597 | ||||||||
\(629\) | 1.23488e7 | 1.24451 | ||||||||
\(630\) | −8597.41 | −0.000863011 0 | ||||||||
\(631\) | −1.61975e7 | −1.61948 | −0.809739 | − | 0.586790i | \(-0.800391\pi\) | ||||
−0.809739 | + | 0.586790i | \(0.800391\pi\) | |||||||
\(632\) | −1.29812e7 | −1.29277 | ||||||||
\(633\) | 9.24989e6 | 0.917545 | ||||||||
\(634\) | 1.20197e7 | 1.18760 | ||||||||
\(635\) | 8.47956e6 | 0.834525 | ||||||||
\(636\) | −8.20471e6 | −0.804304 | ||||||||
\(637\) | −4.27740e6 | −0.417668 | ||||||||
\(638\) | 1.21308e7 | 1.17988 | ||||||||
\(639\) | 4.22656e6 | 0.409482 | ||||||||
\(640\) | −1.52892e7 | −1.47548 | ||||||||
\(641\) | −1.56439e7 | −1.50383 | −0.751915 | − | 0.659260i | \(-0.770870\pi\) | ||||
−0.751915 | + | 0.659260i | \(0.770870\pi\) | |||||||
\(642\) | −1.23575e7 | −1.18329 | ||||||||
\(643\) | −1.57570e7 | −1.50295 | −0.751476 | − | 0.659760i | \(-0.770658\pi\) | ||||
−0.751476 | + | 0.659760i | \(0.770658\pi\) | |||||||
\(644\) | 10523.0 | 0.000999829 0 | ||||||||
\(645\) | −7.31211e6 | −0.692059 | ||||||||
\(646\) | 2.14201e7 | 2.01948 | ||||||||
\(647\) | −660291. | −0.0620119 | −0.0310059 | − | 0.999519i | \(-0.509871\pi\) | ||||
−0.0310059 | + | 0.999519i | \(0.509871\pi\) | |||||||
\(648\) | −3.67453e6 | −0.343768 | ||||||||
\(649\) | −5.02024e6 | −0.467857 | ||||||||
\(650\) | 3.81888e6 | 0.354529 | ||||||||
\(651\) | −19265.3 | −0.00178165 | ||||||||
\(652\) | −1.49678e7 | −1.37892 | ||||||||
\(653\) | 1.24310e7 | 1.14084 | 0.570419 | − | 0.821354i | \(-0.306781\pi\) | ||||
0.570419 | + | 0.821354i | \(0.306781\pi\) | |||||||
\(654\) | −1.32234e7 | −1.20892 | ||||||||
\(655\) | 2.52494e6 | 0.229958 | ||||||||
\(656\) | 3.39297e7 | 3.07837 | ||||||||
\(657\) | 4.61036e6 | 0.416698 | ||||||||
\(658\) | −70598.6 | −0.00635669 | ||||||||
\(659\) | −13723.9 | −0.00123101 | −0.000615507 | − | 1.00000i | \(-0.500196\pi\) | ||||
−0.000615507 | 1.00000i | \(0.500196\pi\) | ||||||||
\(660\) | 1.32638e7 | 1.18525 | ||||||||
\(661\) | 6.54194e6 | 0.582375 | 0.291187 | − | 0.956666i | \(-0.405950\pi\) | ||||
0.291187 | + | 0.956666i | \(0.405950\pi\) | |||||||
\(662\) | −2.25098e7 | −1.99630 | ||||||||
\(663\) | 2.23327e6 | 0.197314 | ||||||||
\(664\) | 1.02740e7 | 0.904315 | ||||||||
\(665\) | 20101.9 | 0.00176272 | ||||||||
\(666\) | 1.10492e7 | 0.965262 | ||||||||
\(667\) | 1.41325e6 | 0.123000 | ||||||||
\(668\) | 2.14412e6 | 0.185912 | ||||||||
\(669\) | 1.88665e6 | 0.162977 | ||||||||
\(670\) | 1.27965e7 | 1.10129 | ||||||||
\(671\) | −1.68057e7 | −1.44095 | ||||||||
\(672\) | 38564.4 | 0.00329430 | ||||||||
\(673\) | 1.54266e7 | 1.31290 | 0.656451 | − | 0.754369i | \(-0.272057\pi\) | ||||
0.656451 | + | 0.754369i | \(0.272057\pi\) | |||||||
\(674\) | −9.71159e6 | −0.823456 | ||||||||
\(675\) | 1.01565e6 | 0.0857992 | ||||||||
\(676\) | −2.57478e7 | −2.16707 | ||||||||
\(677\) | 5.30462e6 | 0.444818 | 0.222409 | − | 0.974953i | \(-0.428608\pi\) | ||||
0.222409 | + | 0.974953i | \(0.428608\pi\) | |||||||
\(678\) | −1.00822e7 | −0.842326 | ||||||||
\(679\) | −33243.6 | −0.00276716 | ||||||||
\(680\) | 2.27242e7 | 1.88459 | ||||||||
\(681\) | 3.12392e6 | 0.258127 | ||||||||
\(682\) | 4.10444e7 | 3.37904 | ||||||||
\(683\) | 1.52230e7 | 1.24867 | 0.624337 | − | 0.781155i | \(-0.285369\pi\) | ||||
0.624337 | + | 0.781155i | \(0.285369\pi\) | |||||||
\(684\) | 1.38787e7 | 1.13425 | ||||||||
\(685\) | 3.93038e6 | 0.320043 | ||||||||
\(686\) | 85734.1 | 0.00695574 | ||||||||
\(687\) | 4.26684e6 | 0.344917 | ||||||||
\(688\) | 6.52857e7 | 5.25832 | ||||||||
\(689\) | 2.76206e6 | 0.221659 | ||||||||
\(690\) | 2.13391e6 | 0.170629 | ||||||||
\(691\) | 1.04711e7 | 0.834248 | 0.417124 | − | 0.908850i | \(-0.363038\pi\) | ||||
0.417124 | + | 0.908850i | \(0.363038\pi\) | |||||||
\(692\) | 5.89567e7 | 4.68024 | ||||||||
\(693\) | −8087.02 | −0.000639669 0 | ||||||||
\(694\) | 1.65009e7 | 1.30049 | ||||||||
\(695\) | 1.67919e7 | 1.31868 | ||||||||
\(696\) | 1.34660e7 | 1.05369 | ||||||||
\(697\) | −9.89286e6 | −0.771329 | ||||||||
\(698\) | −1.38241e7 | −1.07398 | ||||||||
\(699\) | −606836. | −0.0469762 | ||||||||
\(700\) | −27714.0 | −0.00213774 | ||||||||
\(701\) | −2.28874e7 | −1.75914 | −0.879572 | − | 0.475765i | \(-0.842171\pi\) | ||||
−0.879572 | + | 0.475765i | \(0.842171\pi\) | |||||||
\(702\) | 1.99824e6 | 0.153040 | ||||||||
\(703\) | −2.58346e7 | −1.97158 | ||||||||
\(704\) | −3.70466e7 | −2.81720 | ||||||||
\(705\) | −1.03670e7 | −0.785560 | ||||||||
\(706\) | 4.80333e7 | 3.62686 | ||||||||
\(707\) | 20621.7 | 0.00155159 | ||||||||
\(708\) | −9.00219e6 | −0.674940 | ||||||||
\(709\) | 1.85127e7 | 1.38310 | 0.691550 | − | 0.722329i | \(-0.256928\pi\) | ||||
0.691550 | + | 0.722329i | \(0.256928\pi\) | |||||||
\(710\) | −2.33873e7 | −1.74114 | ||||||||
\(711\) | 1.87745e6 | 0.139281 | ||||||||
\(712\) | −2.65257e7 | −1.96095 | ||||||||
\(713\) | 4.78170e6 | 0.352256 | ||||||||
\(714\) | −22381.3 | −0.00164301 | ||||||||
\(715\) | −4.46517e6 | −0.326643 | ||||||||
\(716\) | −2.46051e7 | −1.79367 | ||||||||
\(717\) | 5.68518e6 | 0.412996 | ||||||||
\(718\) | −5.03519e7 | −3.64506 | ||||||||
\(719\) | 1.25679e7 | 0.906652 | 0.453326 | − | 0.891345i | \(-0.350237\pi\) | ||||
0.453326 | + | 0.891345i | \(0.350237\pi\) | |||||||
\(720\) | 1.12720e7 | 0.810342 | ||||||||
\(721\) | 4260.00 | 0.000305191 0 | ||||||||
\(722\) | −1.81440e7 | −1.29536 | ||||||||
\(723\) | 5.23832e6 | 0.372689 | ||||||||
\(724\) | −3.27035e6 | −0.231872 | ||||||||
\(725\) | −3.72201e6 | −0.262986 | ||||||||
\(726\) | 1.61817e6 | 0.113942 | ||||||||
\(727\) | 3.64050e6 | 0.255462 | 0.127731 | − | 0.991809i | \(-0.459231\pi\) | ||||
0.127731 | + | 0.991809i | \(0.459231\pi\) | |||||||
\(728\) | −33754.3 | −0.00236048 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.55110e7 | −1.77182 | ||||||||
\(731\) | −1.90353e7 | −1.31755 | ||||||||
\(732\) | −3.01356e7 | −2.07875 | ||||||||
\(733\) | −4.38735e6 | −0.301608 | −0.150804 | − | 0.988564i | \(-0.548186\pi\) | ||||
−0.150804 | + | 0.988564i | \(0.548186\pi\) | |||||||
\(734\) | −2.61966e7 | −1.79475 | ||||||||
\(735\) | 6.29476e6 | 0.429795 | ||||||||
\(736\) | −9.57181e6 | −0.651327 | ||||||||
\(737\) | 1.20368e7 | 0.816287 | ||||||||
\(738\) | −8.85173e6 | −0.598256 | ||||||||
\(739\) | 1.95857e7 | 1.31925 | 0.659625 | − | 0.751595i | \(-0.270715\pi\) | ||||
0.659625 | + | 0.751595i | \(0.270715\pi\) | |||||||
\(740\) | −4.42736e7 | −2.97211 | ||||||||
\(741\) | −4.67217e6 | −0.312589 | ||||||||
\(742\) | −27680.6 | −0.00184572 | ||||||||
\(743\) | −2.94833e7 | −1.95931 | −0.979657 | − | 0.200678i | \(-0.935685\pi\) | ||||
−0.979657 | + | 0.200678i | \(0.935685\pi\) | |||||||
\(744\) | 4.55619e7 | 3.01766 | ||||||||
\(745\) | 1.60021e7 | 1.05630 | ||||||||
\(746\) | −1.48047e7 | −0.973983 | ||||||||
\(747\) | −1.48591e6 | −0.0974296 | ||||||||
\(748\) | 3.45291e7 | 2.25648 | ||||||||
\(749\) | −30190.0 | −0.00196634 | ||||||||
\(750\) | −1.82258e7 | −1.18313 | ||||||||
\(751\) | 1.27147e7 | 0.822634 | 0.411317 | − | 0.911492i | \(-0.365069\pi\) | ||||
0.411317 | + | 0.911492i | \(0.365069\pi\) | |||||||
\(752\) | 9.25609e7 | 5.96875 | ||||||||
\(753\) | 1.15952e7 | 0.745228 | ||||||||
\(754\) | −7.32290e6 | −0.469089 | ||||||||
\(755\) | −1.84149e7 | −1.17571 | ||||||||
\(756\) | −14501.5 | −0.000922800 0 | ||||||||
\(757\) | 1.63980e7 | 1.04004 | 0.520022 | − | 0.854153i | \(-0.325924\pi\) | ||||
0.520022 | + | 0.854153i | \(0.325924\pi\) | |||||||
\(758\) | −2.17558e7 | −1.37531 | ||||||||
\(759\) | 2.00723e6 | 0.126471 | ||||||||
\(760\) | −4.75407e7 | −2.98560 | ||||||||
\(761\) | 8.50863e6 | 0.532596 | 0.266298 | − | 0.963891i | \(-0.414199\pi\) | ||||
0.266298 | + | 0.963891i | \(0.414199\pi\) | |||||||
\(762\) | 1.97513e7 | 1.23228 | ||||||||
\(763\) | −32305.5 | −0.00200893 | ||||||||
\(764\) | 3.12856e6 | 0.193915 | ||||||||
\(765\) | −3.28656e6 | −0.203043 | ||||||||
\(766\) | −2.16305e7 | −1.33197 | ||||||||
\(767\) | 3.03053e6 | 0.186007 | ||||||||
\(768\) | −1.03058e7 | −0.630490 | ||||||||
\(769\) | 1.70141e7 | 1.03751 | 0.518755 | − | 0.854923i | \(-0.326396\pi\) | ||||
0.518755 | + | 0.854923i | \(0.326396\pi\) | |||||||
\(770\) | 44748.7 | 0.00271991 | ||||||||
\(771\) | 1.84417e6 | 0.111729 | ||||||||
\(772\) | −3.56616e6 | −0.215356 | ||||||||
\(773\) | 3.63916e6 | 0.219055 | 0.109527 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109527 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(774\) | −1.70320e7 | −1.02191 | ||||||||
\(775\) | −1.25934e7 | −0.753161 | ||||||||
\(776\) | 7.86204e7 | 4.68685 | ||||||||
\(777\) | 26993.8 | 0.00160403 | ||||||||
\(778\) | −3.50095e7 | −2.07366 | ||||||||
\(779\) | 2.06966e7 | 1.22195 | ||||||||
\(780\) | −8.00685e6 | −0.471221 | ||||||||
\(781\) | −2.19989e7 | −1.29054 | ||||||||
\(782\) | 5.55511e6 | 0.324845 | ||||||||
\(783\) | −1.94756e6 | −0.113524 | ||||||||
\(784\) | −5.62024e7 | −3.26561 | ||||||||
\(785\) | 1.00177e7 | 0.580220 | ||||||||
\(786\) | 5.88132e6 | 0.339561 | ||||||||
\(787\) | −5.30127e6 | −0.305101 | −0.152550 | − | 0.988296i | \(-0.548749\pi\) | ||||
−0.152550 | + | 0.988296i | \(0.548749\pi\) | |||||||
\(788\) | 7.33615e6 | 0.420875 | ||||||||
\(789\) | −3.76976e6 | −0.215586 | ||||||||
\(790\) | −1.03887e7 | −0.592232 | ||||||||
\(791\) | −24631.3 | −0.00139974 | ||||||||
\(792\) | 1.91256e7 | 1.08343 | ||||||||
\(793\) | 1.01449e7 | 0.572883 | ||||||||
\(794\) | −5.85591e7 | −3.29642 | ||||||||
\(795\) | −4.06473e6 | −0.228094 | ||||||||
\(796\) | 9.13743e7 | 5.11142 | ||||||||
\(797\) | 1.41955e7 | 0.791598 | 0.395799 | − | 0.918337i | \(-0.370468\pi\) | ||||
0.395799 | + | 0.918337i | \(0.370468\pi\) | |||||||
\(798\) | 46823.2 | 0.00260288 | ||||||||
\(799\) | −2.69879e7 | −1.49555 | ||||||||
\(800\) | 2.52089e7 | 1.39261 | ||||||||
\(801\) | 3.83636e6 | 0.211270 | ||||||||
\(802\) | −3.52414e7 | −1.93472 | ||||||||
\(803\) | −2.39965e7 | −1.31329 | ||||||||
\(804\) | 2.15841e7 | 1.17759 | ||||||||
\(805\) | 5213.26 | 0.000283543 0 | ||||||||
\(806\) | −2.47769e7 | −1.34341 | ||||||||
\(807\) | 1.33795e7 | 0.723198 | ||||||||
\(808\) | −4.87699e7 | −2.62799 | ||||||||
\(809\) | −1.58542e7 | −0.851675 | −0.425838 | − | 0.904800i | \(-0.640021\pi\) | ||||
−0.425838 | + | 0.904800i | \(0.640021\pi\) | |||||||
\(810\) | −2.94068e6 | −0.157483 | ||||||||
\(811\) | −1.40129e7 | −0.748127 | −0.374063 | − | 0.927403i | \(-0.622036\pi\) | ||||
−0.374063 | + | 0.927403i | \(0.622036\pi\) | |||||||
\(812\) | 53143.1 | 0.00282851 | ||||||||
\(813\) | 5.92776e6 | 0.314532 | ||||||||
\(814\) | −5.75101e7 | −3.04217 | ||||||||
\(815\) | −7.41524e6 | −0.391049 | ||||||||
\(816\) | 2.93438e7 | 1.54273 | ||||||||
\(817\) | 3.98232e7 | 2.08728 | ||||||||
\(818\) | 1.68339e7 | 0.879634 | ||||||||
\(819\) | 4881.82 | 0.000254315 0 | ||||||||
\(820\) | 3.54684e7 | 1.84207 | ||||||||
\(821\) | 1.16279e7 | 0.602065 | 0.301033 | − | 0.953614i | \(-0.402669\pi\) | ||||
0.301033 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(822\) | 9.15498e6 | 0.472583 | ||||||||
\(823\) | −2.76237e7 | −1.42161 | −0.710807 | − | 0.703387i | \(-0.751670\pi\) | ||||
−0.710807 | + | 0.703387i | \(0.751670\pi\) | |||||||
\(824\) | −1.00748e7 | −0.516914 | ||||||||
\(825\) | −5.28635e6 | −0.270409 | ||||||||
\(826\) | −30371.1 | −0.00154885 | ||||||||
\(827\) | −2.78146e7 | −1.41420 | −0.707098 | − | 0.707116i | \(-0.749996\pi\) | ||||
−0.707098 | + | 0.707116i | \(0.749996\pi\) | |||||||
\(828\) | 3.59932e6 | 0.182450 | ||||||||
\(829\) | −1.23659e7 | −0.624943 | −0.312471 | − | 0.949927i | \(-0.601157\pi\) | ||||
−0.312471 | + | 0.949927i | \(0.601157\pi\) | |||||||
\(830\) | 8.22214e6 | 0.414276 | ||||||||
\(831\) | −2.12873e6 | −0.106935 | ||||||||
\(832\) | 2.23636e7 | 1.12004 | ||||||||
\(833\) | 1.63869e7 | 0.818246 | ||||||||
\(834\) | 3.91132e7 | 1.94719 | ||||||||
\(835\) | 1.06223e6 | 0.0527231 | ||||||||
\(836\) | −7.22374e7 | −3.57476 | ||||||||
\(837\) | −6.58953e6 | −0.325118 | ||||||||
\(838\) | 5.12787e7 | 2.52247 | ||||||||
\(839\) | −3.49502e7 | −1.71413 | −0.857067 | − | 0.515205i | \(-0.827716\pi\) | ||||
−0.857067 | + | 0.515205i | \(0.827716\pi\) | |||||||
\(840\) | 49673.9 | 0.00242901 | ||||||||
\(841\) | −1.33740e7 | −0.652035 | ||||||||
\(842\) | 4.92192e7 | 2.39251 | ||||||||
\(843\) | 1.49628e7 | 0.725175 | ||||||||
\(844\) | −8.63323e7 | −4.17174 | ||||||||
\(845\) | −1.27558e7 | −0.614565 | ||||||||
\(846\) | −2.41477e7 | −1.15998 | ||||||||
\(847\) | 3953.28 | 0.000189343 0 | ||||||||
\(848\) | 3.62917e7 | 1.73308 | ||||||||
\(849\) | −8.70131e6 | −0.414300 | ||||||||
\(850\) | −1.46303e7 | −0.694552 | ||||||||
\(851\) | −6.69997e6 | −0.317138 | ||||||||
\(852\) | −3.94479e7 | −1.86177 | ||||||||
\(853\) | −9.99950e6 | −0.470550 | −0.235275 | − | 0.971929i | \(-0.575599\pi\) | ||||
−0.235275 | + | 0.971929i | \(0.575599\pi\) | |||||||
\(854\) | −101670. | −0.00477032 | ||||||||
\(855\) | 6.87571e6 | 0.321664 | ||||||||
\(856\) | 7.13987e7 | 3.33047 | ||||||||
\(857\) | 9.71240e6 | 0.451725 | 0.225863 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225863 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(858\) | −1.04007e7 | −0.482329 | ||||||||
\(859\) | 3.69393e7 | 1.70807 | 0.854035 | − | 0.520216i | \(-0.174149\pi\) | ||||
0.854035 | + | 0.520216i | \(0.174149\pi\) | |||||||
\(860\) | 6.82463e7 | 3.14654 | ||||||||
\(861\) | −21625.3 | −0.000994155 0 | ||||||||
\(862\) | 3.54227e7 | 1.62373 | ||||||||
\(863\) | −3.31284e7 | −1.51416 | −0.757082 | − | 0.653319i | \(-0.773376\pi\) | ||||
−0.757082 | + | 0.653319i | \(0.773376\pi\) | |||||||
\(864\) | 1.31906e7 | 0.601148 | ||||||||
\(865\) | 2.92080e7 | 1.32728 | ||||||||
\(866\) | −2.28121e7 | −1.03364 | ||||||||
\(867\) | 4.22296e6 | 0.190796 | ||||||||
\(868\) | 179809. | 0.00810051 | ||||||||
\(869\) | −9.77194e6 | −0.438966 | ||||||||
\(870\) | 1.07766e7 | 0.482708 | ||||||||
\(871\) | −7.26615e6 | −0.324533 | ||||||||
\(872\) | 7.64019e7 | 3.40262 | ||||||||
\(873\) | −1.13707e7 | −0.504954 | ||||||||
\(874\) | −1.16217e7 | −0.514625 | ||||||||
\(875\) | −44526.6 | −0.00196607 | ||||||||
\(876\) | −4.30300e7 | −1.89457 | ||||||||
\(877\) | 1.38007e7 | 0.605902 | 0.302951 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302951 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(878\) | −8.16869e6 | −0.357615 | ||||||||
\(879\) | 741924. | 0.0323882 | ||||||||
\(880\) | −5.86696e7 | −2.55391 | ||||||||
\(881\) | −7.74868e6 | −0.336347 | −0.168174 | − | 0.985757i | \(-0.553787\pi\) | ||||
−0.168174 | + | 0.985757i | \(0.553787\pi\) | |||||||
\(882\) | 1.46623e7 | 0.634646 | ||||||||
\(883\) | 3.79838e7 | 1.63944 | 0.819722 | − | 0.572761i | \(-0.194128\pi\) | ||||
0.819722 | + | 0.572761i | \(0.194128\pi\) | |||||||
\(884\) | −2.08439e7 | −0.897115 | ||||||||
\(885\) | −4.45982e6 | −0.191408 | ||||||||
\(886\) | −7.00477e6 | −0.299785 | ||||||||
\(887\) | −1.51721e7 | −0.647495 | −0.323747 | − | 0.946144i | \(-0.604943\pi\) | ||||
−0.323747 | + | 0.946144i | \(0.604943\pi\) | |||||||
\(888\) | −6.38398e7 | −2.71681 | ||||||||
\(889\) | 48253.7 | 0.00204775 | ||||||||
\(890\) | −2.12281e7 | −0.898330 | ||||||||
\(891\) | −2.76610e6 | −0.116728 | ||||||||
\(892\) | −1.76087e7 | −0.740995 | ||||||||
\(893\) | 5.64607e7 | 2.36929 | ||||||||
\(894\) | 3.72734e7 | 1.55975 | ||||||||
\(895\) | −1.21897e7 | −0.508670 | ||||||||
\(896\) | −87004.5 | −0.00362052 | ||||||||
\(897\) | −1.21168e6 | −0.0502815 | ||||||||
\(898\) | 8.16510e7 | 3.37886 | ||||||||
\(899\) | 2.41485e7 | 0.996530 | ||||||||
\(900\) | −9.47937e6 | −0.390098 | ||||||||
\(901\) | −1.05815e7 | −0.434247 | ||||||||
\(902\) | 4.60724e7 | 1.88549 | ||||||||
\(903\) | −41610.2 | −0.00169817 | ||||||||
\(904\) | 5.82526e7 | 2.37080 | ||||||||
\(905\) | −1.62018e6 | −0.0657569 | ||||||||
\(906\) | −4.28936e7 | −1.73609 | ||||||||
\(907\) | 8.48315e6 | 0.342404 | 0.171202 | − | 0.985236i | \(-0.445235\pi\) | ||||
0.171202 | + | 0.985236i | \(0.445235\pi\) | |||||||
\(908\) | −2.91566e7 | −1.17361 | ||||||||
\(909\) | 7.05350e6 | 0.283136 | ||||||||
\(910\) | −27013.1 | −0.00108136 | ||||||||
\(911\) | 2.96302e7 | 1.18288 | 0.591438 | − | 0.806351i | \(-0.298561\pi\) | ||||
0.591438 | + | 0.806351i | \(0.298561\pi\) | |||||||
\(912\) | −6.13894e7 | −2.44403 | ||||||||
\(913\) | 7.73403e6 | 0.307064 | ||||||||
\(914\) | 8.66513e7 | 3.43091 | ||||||||
\(915\) | −1.49296e7 | −0.589516 | ||||||||
\(916\) | −3.98239e7 | −1.56821 | ||||||||
\(917\) | 14368.4 | 0.000564268 0 | ||||||||
\(918\) | −7.65534e6 | −0.299818 | ||||||||
\(919\) | −1.27080e7 | −0.496352 | −0.248176 | − | 0.968715i | \(-0.579831\pi\) | ||||
−0.248176 | + | 0.968715i | \(0.579831\pi\) | |||||||
\(920\) | −1.23292e7 | −0.480249 | ||||||||
\(921\) | −4.23993e6 | −0.164706 | ||||||||
\(922\) | −6.06992e7 | −2.35156 | ||||||||
\(923\) | 1.32799e7 | 0.513085 | ||||||||
\(924\) | 75478.9 | 0.00290834 | ||||||||
\(925\) | 1.76454e7 | 0.678075 | ||||||||
\(926\) | −1.49875e7 | −0.574385 | ||||||||
\(927\) | 1.45710e6 | 0.0556916 | ||||||||
\(928\) | −4.83394e7 | −1.84260 | ||||||||
\(929\) | −4.50533e7 | −1.71272 | −0.856362 | − | 0.516376i | \(-0.827281\pi\) | ||||
−0.856362 | + | 0.516376i | \(0.827281\pi\) | |||||||
\(930\) | 3.64625e7 | 1.38242 | ||||||||
\(931\) | −3.42826e7 | −1.29628 | ||||||||
\(932\) | 5.66380e6 | 0.213584 | ||||||||
\(933\) | −8.76727e6 | −0.329731 | ||||||||
\(934\) | −4.36266e7 | −1.63638 | ||||||||
\(935\) | 1.71062e7 | 0.639919 | ||||||||
\(936\) | −1.15454e7 | −0.430744 | ||||||||
\(937\) | −2.49632e7 | −0.928864 | −0.464432 | − | 0.885609i | \(-0.653741\pi\) | ||||
−0.464432 | + | 0.885609i | \(0.653741\pi\) | |||||||
\(938\) | 72819.4 | 0.00270234 | ||||||||
\(939\) | −1.83508e6 | −0.0679188 | ||||||||
\(940\) | 9.67585e7 | 3.57165 | ||||||||
\(941\) | −3.36141e7 | −1.23751 | −0.618754 | − | 0.785585i | \(-0.712362\pi\) | ||||
−0.618754 | + | 0.785585i | \(0.712362\pi\) | |||||||
\(942\) | 2.33340e7 | 0.856767 | ||||||||
\(943\) | 5.36747e6 | 0.196558 | ||||||||
\(944\) | 3.98192e7 | 1.45433 | ||||||||
\(945\) | −7184.24 | −0.000261699 0 | ||||||||
\(946\) | 8.86501e7 | 3.22071 | ||||||||
\(947\) | −5.33926e6 | −0.193467 | −0.0967333 | − | 0.995310i | \(-0.530839\pi\) | ||||
−0.0967333 | + | 0.995310i | \(0.530839\pi\) | |||||||
\(948\) | −1.75228e7 | −0.633262 | ||||||||
\(949\) | 1.44858e7 | 0.522127 | ||||||||
\(950\) | 3.06076e7 | 1.10032 | ||||||||
\(951\) | 1.00440e7 | 0.360126 | ||||||||
\(952\) | 129314. | 0.00462438 | ||||||||
\(953\) | −3.69391e7 | −1.31751 | −0.658755 | − | 0.752358i | \(-0.728916\pi\) | ||||
−0.658755 | + | 0.752358i | \(0.728916\pi\) | |||||||
\(954\) | −9.46793e6 | −0.336809 | ||||||||
\(955\) | 1.54994e6 | 0.0549928 | ||||||||
\(956\) | −5.30617e7 | −1.87774 | ||||||||
\(957\) | 1.01369e7 | 0.357786 | ||||||||
\(958\) | −7.06026e7 | −2.48546 | ||||||||
\(959\) | 22366.2 | 0.000785317 0 | ||||||||
\(960\) | −3.29110e7 | −1.15256 | ||||||||
\(961\) | 5.30769e7 | 1.85395 | ||||||||
\(962\) | 3.47166e7 | 1.20948 | ||||||||
\(963\) | −1.03263e7 | −0.358821 | ||||||||
\(964\) | −4.88910e7 | −1.69448 | ||||||||
\(965\) | −1.76673e6 | −0.0610734 | ||||||||
\(966\) | 12143.2 | 0.000418687 0 | ||||||||
\(967\) | −4.47688e7 | −1.53960 | −0.769802 | − | 0.638283i | \(-0.779645\pi\) | ||||
−0.769802 | + | 0.638283i | \(0.779645\pi\) | |||||||
\(968\) | −9.34943e6 | −0.320698 | ||||||||
\(969\) | 1.78993e7 | 0.612386 | ||||||||
\(970\) | 6.29187e7 | 2.14709 | ||||||||
\(971\) | −4.07416e7 | −1.38672 | −0.693361 | − | 0.720590i | \(-0.743871\pi\) | ||||
−0.693361 | + | 0.720590i | \(0.743871\pi\) | |||||||
\(972\) | −4.96012e6 | −0.168394 | ||||||||
\(973\) | 95555.9 | 0.00323575 | ||||||||
\(974\) | 2.14247e7 | 0.723633 | ||||||||
\(975\) | 3.19116e6 | 0.107507 | ||||||||
\(976\) | 1.33298e8 | 4.47919 | ||||||||
\(977\) | 1.07576e7 | 0.360561 | 0.180281 | − | 0.983615i | \(-0.442299\pi\) | ||||
0.180281 | + | 0.983615i | \(0.442299\pi\) | |||||||
\(978\) | −1.72722e7 | −0.577433 | ||||||||
\(979\) | −1.99679e7 | −0.665849 | ||||||||
\(980\) | −5.87511e7 | −1.95412 | ||||||||
\(981\) | −1.10499e7 | −0.366593 | ||||||||
\(982\) | −8.60770e7 | −2.84845 | ||||||||
\(983\) | −2.44766e7 | −0.807917 | −0.403958 | − | 0.914777i | \(-0.632366\pi\) | ||||
−0.403958 | + | 0.914777i | \(0.632366\pi\) | |||||||
\(984\) | 5.11433e7 | 1.68384 | ||||||||
\(985\) | 3.63444e6 | 0.119357 | ||||||||
\(986\) | 2.80543e7 | 0.918982 | ||||||||
\(987\) | −58994.2 | −0.00192760 | ||||||||
\(988\) | 4.36069e7 | 1.42123 | ||||||||
\(989\) | 1.03278e7 | 0.335751 | ||||||||
\(990\) | 1.53060e7 | 0.496332 | ||||||||
\(991\) | −2.09086e6 | −0.0676301 | −0.0338151 | − | 0.999428i | \(-0.510766\pi\) | ||||
−0.0338151 | + | 0.999428i | \(0.510766\pi\) | |||||||
\(992\) | −1.63556e8 | −5.27699 | ||||||||
\(993\) | −1.88098e7 | −0.605357 | ||||||||
\(994\) | −133087. | −0.00427239 | ||||||||
\(995\) | 4.52682e7 | 1.44956 | ||||||||
\(996\) | 1.38685e7 | 0.442977 | ||||||||
\(997\) | 1.49624e7 | 0.476721 | 0.238360 | − | 0.971177i | \(-0.423390\pi\) | ||||
0.238360 | + | 0.971177i | \(0.423390\pi\) | |||||||
\(998\) | 1.08036e8 | 3.43353 | ||||||||
\(999\) | 9.23304e6 | 0.292705 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 69.6.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 207.6.a.a.1.2 | 2 | |||
4.3 | odd | 2 | 1104.6.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
207.6.a.a.1.2 | 2 | 3.2 | odd | 2 | |||
1104.6.a.h.1.1 | 2 | 4.3 | odd | 2 |