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: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 39x^{2} - 30x + 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(6.56547\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.56547 | 1.33740 | 0.668699 | − | 0.743533i | \(-0.266851\pi\) | ||||
0.668699 | + | 0.743533i | \(0.266851\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 25.2363 | 0.788635 | ||||||||
\(5\) | 40.1532 | 0.718283 | 0.359141 | − | 0.933283i | \(-0.383070\pi\) | ||||
0.359141 | + | 0.933283i | \(0.383070\pi\) | |||||||
\(6\) | −68.0892 | −0.772147 | ||||||||
\(7\) | 194.921 | 1.50354 | 0.751769 | − | 0.659426i | \(-0.229201\pi\) | ||||
0.751769 | + | 0.659426i | \(0.229201\pi\) | |||||||
\(8\) | −51.1704 | −0.282679 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 303.778 | 0.960630 | ||||||||
\(11\) | −39.1915 | −0.0976585 | −0.0488292 | − | 0.998807i | \(-0.515549\pi\) | ||||
−0.0488292 | + | 0.998807i | \(0.515549\pi\) | |||||||
\(12\) | −227.127 | −0.455319 | ||||||||
\(13\) | 705.021 | 1.15703 | 0.578514 | − | 0.815673i | \(-0.303633\pi\) | ||||
0.578514 | + | 0.815673i | \(0.303633\pi\) | |||||||
\(14\) | 1474.67 | 2.01083 | ||||||||
\(15\) | −361.379 | −0.414701 | ||||||||
\(16\) | −1194.69 | −1.16669 | ||||||||
\(17\) | 1222.51 | 1.02596 | 0.512979 | − | 0.858401i | \(-0.328542\pi\) | ||||
0.512979 | + | 0.858401i | \(0.328542\pi\) | |||||||
\(18\) | 612.803 | 0.445800 | ||||||||
\(19\) | 1891.46 | 1.20202 | 0.601011 | − | 0.799241i | \(-0.294765\pi\) | ||||
0.601011 | + | 0.799241i | \(0.294765\pi\) | |||||||
\(20\) | 1013.32 | 0.566463 | ||||||||
\(21\) | −1754.29 | −0.868068 | ||||||||
\(22\) | −296.502 | −0.130608 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 460.534 | 0.163205 | ||||||||
\(25\) | −1512.72 | −0.484070 | ||||||||
\(26\) | 5333.81 | 1.54741 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4919.10 | 1.18574 | ||||||||
\(29\) | −8579.39 | −1.89436 | −0.947178 | − | 0.320709i | \(-0.896079\pi\) | ||||
−0.947178 | + | 0.320709i | \(0.896079\pi\) | |||||||
\(30\) | −2734.00 | −0.554620 | ||||||||
\(31\) | −9582.72 | −1.79095 | −0.895477 | − | 0.445107i | \(-0.853165\pi\) | ||||
−0.895477 | + | 0.445107i | \(0.853165\pi\) | |||||||
\(32\) | −7400.94 | −1.27765 | ||||||||
\(33\) | 352.723 | 0.0563832 | ||||||||
\(34\) | 9248.86 | 1.37212 | ||||||||
\(35\) | 7826.73 | 1.07997 | ||||||||
\(36\) | 2044.14 | 0.262878 | ||||||||
\(37\) | −8144.49 | −0.978046 | −0.489023 | − | 0.872271i | \(-0.662647\pi\) | ||||
−0.489023 | + | 0.872271i | \(0.662647\pi\) | |||||||
\(38\) | 14309.8 | 1.60758 | ||||||||
\(39\) | −6345.19 | −0.668010 | ||||||||
\(40\) | −2054.66 | −0.203044 | ||||||||
\(41\) | 4834.24 | 0.449127 | 0.224563 | − | 0.974459i | \(-0.427904\pi\) | ||||
0.224563 | + | 0.974459i | \(0.427904\pi\) | |||||||
\(42\) | −13272.0 | −1.16095 | ||||||||
\(43\) | 10631.5 | 0.876843 | 0.438422 | − | 0.898769i | \(-0.355538\pi\) | ||||
0.438422 | + | 0.898769i | \(0.355538\pi\) | |||||||
\(44\) | −989.049 | −0.0770169 | ||||||||
\(45\) | 3252.41 | 0.239428 | ||||||||
\(46\) | 4002.13 | 0.278867 | ||||||||
\(47\) | 222.835 | 0.0147142 | 0.00735712 | − | 0.999973i | \(-0.497658\pi\) | ||||
0.00735712 | + | 0.999973i | \(0.497658\pi\) | |||||||
\(48\) | 10752.2 | 0.673589 | ||||||||
\(49\) | 21187.4 | 1.26063 | ||||||||
\(50\) | −11444.4 | −0.647394 | ||||||||
\(51\) | −11002.6 | −0.592338 | ||||||||
\(52\) | 17792.1 | 0.912472 | ||||||||
\(53\) | 6577.44 | 0.321638 | 0.160819 | − | 0.986984i | \(-0.448586\pi\) | ||||
0.160819 | + | 0.986984i | \(0.448586\pi\) | |||||||
\(54\) | −5515.23 | −0.257382 | ||||||||
\(55\) | −1573.66 | −0.0701464 | ||||||||
\(56\) | −9974.21 | −0.425019 | ||||||||
\(57\) | −17023.1 | −0.693988 | ||||||||
\(58\) | −64907.1 | −2.53351 | ||||||||
\(59\) | −30780.8 | −1.15120 | −0.575600 | − | 0.817732i | \(-0.695231\pi\) | ||||
−0.575600 | + | 0.817732i | \(0.695231\pi\) | |||||||
\(60\) | −9119.88 | −0.327048 | ||||||||
\(61\) | −8695.20 | −0.299196 | −0.149598 | − | 0.988747i | \(-0.547798\pi\) | ||||
−0.149598 | + | 0.988747i | \(0.547798\pi\) | |||||||
\(62\) | −72497.8 | −2.39522 | ||||||||
\(63\) | 15788.6 | 0.501179 | ||||||||
\(64\) | −17761.5 | −0.542038 | ||||||||
\(65\) | 28308.9 | 0.831073 | ||||||||
\(66\) | 2668.52 | 0.0754067 | ||||||||
\(67\) | 48398.0 | 1.31716 | 0.658582 | − | 0.752509i | \(-0.271156\pi\) | ||||
0.658582 | + | 0.752509i | \(0.271156\pi\) | |||||||
\(68\) | 30851.6 | 0.809107 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | 59212.8 | 1.44434 | ||||||||
\(71\) | −60285.7 | −1.41928 | −0.709640 | − | 0.704564i | \(-0.751142\pi\) | ||||
−0.709640 | + | 0.704564i | \(0.751142\pi\) | |||||||
\(72\) | −4144.80 | −0.0942264 | ||||||||
\(73\) | 30638.2 | 0.672908 | 0.336454 | − | 0.941700i | \(-0.390772\pi\) | ||||
0.336454 | + | 0.941700i | \(0.390772\pi\) | |||||||
\(74\) | −61616.8 | −1.30804 | ||||||||
\(75\) | 13614.5 | 0.279478 | ||||||||
\(76\) | 47733.4 | 0.947957 | ||||||||
\(77\) | −7639.26 | −0.146833 | ||||||||
\(78\) | −48004.3 | −0.893396 | ||||||||
\(79\) | 50285.3 | 0.906512 | 0.453256 | − | 0.891380i | \(-0.350262\pi\) | ||||
0.453256 | + | 0.891380i | \(0.350262\pi\) | |||||||
\(80\) | −47970.7 | −0.838013 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 36573.3 | 0.600661 | ||||||||
\(83\) | −35671.7 | −0.568366 | −0.284183 | − | 0.958770i | \(-0.591722\pi\) | ||||
−0.284183 | + | 0.958770i | \(0.591722\pi\) | |||||||
\(84\) | −44271.9 | −0.684589 | ||||||||
\(85\) | 49087.7 | 0.736929 | ||||||||
\(86\) | 80432.0 | 1.17269 | ||||||||
\(87\) | 77214.5 | 1.09371 | ||||||||
\(88\) | 2005.44 | 0.0276060 | ||||||||
\(89\) | −77619.2 | −1.03871 | −0.519355 | − | 0.854559i | \(-0.673828\pi\) | ||||
−0.519355 | + | 0.854559i | \(0.673828\pi\) | |||||||
\(90\) | 24606.0 | 0.320210 | ||||||||
\(91\) | 137424. | 1.73963 | ||||||||
\(92\) | 13350.0 | 0.164442 | ||||||||
\(93\) | 86244.5 | 1.03401 | ||||||||
\(94\) | 1685.85 | 0.0196788 | ||||||||
\(95\) | 75948.1 | 0.863392 | ||||||||
\(96\) | 66608.5 | 0.737652 | ||||||||
\(97\) | −83069.4 | −0.896421 | −0.448210 | − | 0.893928i | \(-0.647938\pi\) | ||||
−0.448210 | + | 0.893928i | \(0.647938\pi\) | |||||||
\(98\) | 160292. | 1.68596 | ||||||||
\(99\) | −3174.51 | −0.0325528 | ||||||||
\(100\) | −38175.4 | −0.381754 | ||||||||
\(101\) | 30834.9 | 0.300773 | 0.150387 | − | 0.988627i | \(-0.451948\pi\) | ||||
0.150387 | + | 0.988627i | \(0.451948\pi\) | |||||||
\(102\) | −83239.7 | −0.792191 | ||||||||
\(103\) | 141687. | 1.31594 | 0.657970 | − | 0.753044i | \(-0.271415\pi\) | ||||
0.657970 | + | 0.753044i | \(0.271415\pi\) | |||||||
\(104\) | −36076.2 | −0.327068 | ||||||||
\(105\) | −70440.5 | −0.623518 | ||||||||
\(106\) | 49761.4 | 0.430158 | ||||||||
\(107\) | 132757. | 1.12098 | 0.560488 | − | 0.828162i | \(-0.310614\pi\) | ||||
0.560488 | + | 0.828162i | \(0.310614\pi\) | |||||||
\(108\) | −18397.3 | −0.151773 | ||||||||
\(109\) | −113030. | −0.911232 | −0.455616 | − | 0.890176i | \(-0.650581\pi\) | ||||
−0.455616 | + | 0.890176i | \(0.650581\pi\) | |||||||
\(110\) | −11905.5 | −0.0938137 | ||||||||
\(111\) | 73300.4 | 0.564675 | ||||||||
\(112\) | −232871. | −1.75416 | ||||||||
\(113\) | 46155.5 | 0.340038 | 0.170019 | − | 0.985441i | \(-0.445617\pi\) | ||||
0.170019 | + | 0.985441i | \(0.445617\pi\) | |||||||
\(114\) | −128788. | −0.928138 | ||||||||
\(115\) | 21241.1 | 0.149772 | ||||||||
\(116\) | −216512. | −1.49396 | ||||||||
\(117\) | 57106.7 | 0.385676 | ||||||||
\(118\) | −232872. | −1.53961 | ||||||||
\(119\) | 238293. | 1.54257 | ||||||||
\(120\) | 18491.9 | 0.117227 | ||||||||
\(121\) | −159515. | −0.990463 | ||||||||
\(122\) | −65783.3 | −0.400144 | ||||||||
\(123\) | −43508.2 | −0.259303 | ||||||||
\(124\) | −241833. | −1.41241 | ||||||||
\(125\) | −186219. | −1.06598 | ||||||||
\(126\) | 119448. | 0.670277 | ||||||||
\(127\) | −223792. | −1.23122 | −0.615609 | − | 0.788051i | \(-0.711090\pi\) | ||||
−0.615609 | + | 0.788051i | \(0.711090\pi\) | |||||||
\(128\) | 102456. | 0.552730 | ||||||||
\(129\) | −95683.2 | −0.506246 | ||||||||
\(130\) | 214170. | 1.11148 | ||||||||
\(131\) | −249499. | −1.27025 | −0.635127 | − | 0.772407i | \(-0.719052\pi\) | ||||
−0.635127 | + | 0.772407i | \(0.719052\pi\) | |||||||
\(132\) | 8901.44 | 0.0444657 | ||||||||
\(133\) | 368685. | 1.80729 | ||||||||
\(134\) | 366153. | 1.76157 | ||||||||
\(135\) | −29271.7 | −0.138234 | ||||||||
\(136\) | −62556.3 | −0.290017 | ||||||||
\(137\) | −25829.5 | −0.117575 | −0.0587875 | − | 0.998271i | \(-0.518723\pi\) | ||||
−0.0587875 | + | 0.998271i | \(0.518723\pi\) | |||||||
\(138\) | −36019.2 | −0.161004 | ||||||||
\(139\) | 79301.9 | 0.348134 | 0.174067 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174067 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(140\) | 197518. | 0.851699 | ||||||||
\(141\) | −2005.51 | −0.00849527 | ||||||||
\(142\) | −456089. | −1.89814 | ||||||||
\(143\) | −27630.8 | −0.112994 | ||||||||
\(144\) | −96769.9 | −0.388897 | ||||||||
\(145\) | −344490. | −1.36068 | ||||||||
\(146\) | 231792. | 0.899947 | ||||||||
\(147\) | −190686. | −0.727823 | ||||||||
\(148\) | −205537. | −0.771321 | ||||||||
\(149\) | −338110. | −1.24765 | −0.623825 | − | 0.781564i | \(-0.714422\pi\) | ||||
−0.623825 | + | 0.781564i | \(0.714422\pi\) | |||||||
\(150\) | 103000. | 0.373773 | ||||||||
\(151\) | 494788. | 1.76594 | 0.882971 | − | 0.469427i | \(-0.155539\pi\) | ||||
0.882971 | + | 0.469427i | \(0.155539\pi\) | |||||||
\(152\) | −96786.6 | −0.339787 | ||||||||
\(153\) | 99023.3 | 0.341986 | ||||||||
\(154\) | −57794.6 | −0.196375 | ||||||||
\(155\) | −384777. | −1.28641 | ||||||||
\(156\) | −160129. | −0.526816 | ||||||||
\(157\) | 195963. | 0.634490 | 0.317245 | − | 0.948344i | \(-0.397242\pi\) | ||||
0.317245 | + | 0.948344i | \(0.397242\pi\) | |||||||
\(158\) | 380432. | 1.21237 | ||||||||
\(159\) | −59197.0 | −0.185698 | ||||||||
\(160\) | −297172. | −0.917714 | ||||||||
\(161\) | 103113. | 0.313509 | ||||||||
\(162\) | 49637.0 | 0.148600 | ||||||||
\(163\) | 223223. | 0.658067 | 0.329034 | − | 0.944318i | \(-0.393277\pi\) | ||||
0.329034 | + | 0.944318i | \(0.393277\pi\) | |||||||
\(164\) | 121999. | 0.354197 | ||||||||
\(165\) | 14163.0 | 0.0404991 | ||||||||
\(166\) | −269873. | −0.760132 | ||||||||
\(167\) | −232525. | −0.645176 | −0.322588 | − | 0.946539i | \(-0.604553\pi\) | ||||
−0.322588 | + | 0.946539i | \(0.604553\pi\) | |||||||
\(168\) | 89767.9 | 0.245385 | ||||||||
\(169\) | 125762. | 0.338713 | ||||||||
\(170\) | 371372. | 0.985567 | ||||||||
\(171\) | 153208. | 0.400674 | ||||||||
\(172\) | 268299. | 0.691509 | ||||||||
\(173\) | 129688. | 0.329445 | 0.164723 | − | 0.986340i | \(-0.447327\pi\) | ||||
0.164723 | + | 0.986340i | \(0.447327\pi\) | |||||||
\(174\) | 584164. | 1.46272 | ||||||||
\(175\) | −294861. | −0.727817 | ||||||||
\(176\) | 46821.7 | 0.113937 | ||||||||
\(177\) | 277028. | 0.664645 | ||||||||
\(178\) | −587225. | −1.38917 | ||||||||
\(179\) | 722275. | 1.68489 | 0.842443 | − | 0.538786i | \(-0.181117\pi\) | ||||
0.842443 | + | 0.538786i | \(0.181117\pi\) | |||||||
\(180\) | 82078.9 | 0.188821 | ||||||||
\(181\) | −126793. | −0.287672 | −0.143836 | − | 0.989602i | \(-0.545944\pi\) | ||||
−0.143836 | + | 0.989602i | \(0.545944\pi\) | |||||||
\(182\) | 1.03967e6 | 2.32659 | ||||||||
\(183\) | 78256.8 | 0.172741 | ||||||||
\(184\) | −27069.1 | −0.0589427 | ||||||||
\(185\) | −327027. | −0.702514 | ||||||||
\(186\) | 652480. | 1.38288 | ||||||||
\(187\) | −47912.0 | −0.100194 | ||||||||
\(188\) | 5623.53 | 0.0116042 | ||||||||
\(189\) | −142098. | −0.289356 | ||||||||
\(190\) | 574583. | 1.15470 | ||||||||
\(191\) | −582441. | −1.15523 | −0.577615 | − | 0.816310i | \(-0.696016\pi\) | ||||
−0.577615 | + | 0.816310i | \(0.696016\pi\) | |||||||
\(192\) | 159853. | 0.312946 | ||||||||
\(193\) | −441777. | −0.853709 | −0.426855 | − | 0.904320i | \(-0.640378\pi\) | ||||
−0.426855 | + | 0.904320i | \(0.640378\pi\) | |||||||
\(194\) | −628459. | −1.19887 | ||||||||
\(195\) | −254780. | −0.479820 | ||||||||
\(196\) | 534691. | 0.994175 | ||||||||
\(197\) | −149838. | −0.275078 | −0.137539 | − | 0.990496i | \(-0.543919\pi\) | ||||
−0.137539 | + | 0.990496i | \(0.543919\pi\) | |||||||
\(198\) | −24016.7 | −0.0435361 | ||||||||
\(199\) | −48644.4 | −0.0870764 | −0.0435382 | − | 0.999052i | \(-0.513863\pi\) | ||||
−0.0435382 | + | 0.999052i | \(0.513863\pi\) | |||||||
\(200\) | 77406.4 | 0.136836 | ||||||||
\(201\) | −435582. | −0.760465 | ||||||||
\(202\) | 233280. | 0.402254 | ||||||||
\(203\) | −1.67231e6 | −2.84824 | ||||||||
\(204\) | −277665. | −0.467138 | ||||||||
\(205\) | 194111. | 0.322600 | ||||||||
\(206\) | 1.07193e6 | 1.75994 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | −842282. | −1.34989 | ||||||||
\(209\) | −74129.0 | −0.117388 | ||||||||
\(210\) | −532916. | −0.833893 | ||||||||
\(211\) | 921315. | 1.42463 | 0.712315 | − | 0.701860i | \(-0.247647\pi\) | ||||
0.712315 | + | 0.701860i | \(0.247647\pi\) | |||||||
\(212\) | 165990. | 0.253655 | ||||||||
\(213\) | 542571. | 0.819422 | ||||||||
\(214\) | 1.00437e6 | 1.49919 | ||||||||
\(215\) | 426888. | 0.629822 | ||||||||
\(216\) | 37303.2 | 0.0544016 | ||||||||
\(217\) | −1.86788e6 | −2.69277 | ||||||||
\(218\) | −855128. | −1.21868 | ||||||||
\(219\) | −275744. | −0.388504 | ||||||||
\(220\) | −39713.5 | −0.0553199 | ||||||||
\(221\) | 861895. | 1.18706 | ||||||||
\(222\) | 554552. | 0.755196 | ||||||||
\(223\) | 998446. | 1.34450 | 0.672252 | − | 0.740322i | \(-0.265327\pi\) | ||||
0.672252 | + | 0.740322i | \(0.265327\pi\) | |||||||
\(224\) | −1.44260e6 | −1.92100 | ||||||||
\(225\) | −122530. | −0.161357 | ||||||||
\(226\) | 349188. | 0.454766 | ||||||||
\(227\) | −376703. | −0.485215 | −0.242608 | − | 0.970125i | \(-0.578003\pi\) | ||||
−0.242608 | + | 0.970125i | \(0.578003\pi\) | |||||||
\(228\) | −429601. | −0.547303 | ||||||||
\(229\) | 814218. | 1.02601 | 0.513005 | − | 0.858385i | \(-0.328532\pi\) | ||||
0.513005 | + | 0.858385i | \(0.328532\pi\) | |||||||
\(230\) | 160699. | 0.200305 | ||||||||
\(231\) | 68753.3 | 0.0847742 | ||||||||
\(232\) | 439011. | 0.535495 | ||||||||
\(233\) | 255689. | 0.308547 | 0.154274 | − | 0.988028i | \(-0.450696\pi\) | ||||
0.154274 | + | 0.988028i | \(0.450696\pi\) | |||||||
\(234\) | 432039. | 0.515802 | ||||||||
\(235\) | 8947.53 | 0.0105690 | ||||||||
\(236\) | −776795. | −0.907876 | ||||||||
\(237\) | −452568. | −0.523375 | ||||||||
\(238\) | 1.80280e6 | 2.06303 | ||||||||
\(239\) | −1.27483e6 | −1.44364 | −0.721818 | − | 0.692083i | \(-0.756693\pi\) | ||||
−0.721818 | + | 0.692083i | \(0.756693\pi\) | |||||||
\(240\) | 431736. | 0.483827 | ||||||||
\(241\) | −1.47036e6 | −1.63073 | −0.815365 | − | 0.578948i | \(-0.803464\pi\) | ||||
−0.815365 | + | 0.578948i | \(0.803464\pi\) | |||||||
\(242\) | −1.20681e6 | −1.32464 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −219435. | −0.235956 | ||||||||
\(245\) | 850741. | 0.905487 | ||||||||
\(246\) | −329160. | −0.346792 | ||||||||
\(247\) | 1.33352e6 | 1.39077 | ||||||||
\(248\) | 490352. | 0.506266 | ||||||||
\(249\) | 321045. | 0.328146 | ||||||||
\(250\) | −1.40884e6 | −1.42564 | ||||||||
\(251\) | 1.25961e6 | 1.26197 | 0.630987 | − | 0.775793i | \(-0.282650\pi\) | ||||
0.630987 | + | 0.775793i | \(0.282650\pi\) | |||||||
\(252\) | 398447. | 0.395248 | ||||||||
\(253\) | −20732.3 | −0.0203632 | ||||||||
\(254\) | −1.69309e6 | −1.64663 | ||||||||
\(255\) | −441789. | −0.425466 | ||||||||
\(256\) | 1.34350e6 | 1.28126 | ||||||||
\(257\) | 400710. | 0.378440 | 0.189220 | − | 0.981935i | \(-0.439404\pi\) | ||||
0.189220 | + | 0.981935i | \(0.439404\pi\) | |||||||
\(258\) | −723888. | −0.677052 | ||||||||
\(259\) | −1.58753e6 | −1.47053 | ||||||||
\(260\) | 714412. | 0.655413 | ||||||||
\(261\) | −694931. | −0.631452 | ||||||||
\(262\) | −1.88758e6 | −1.69884 | ||||||||
\(263\) | 1.10828e6 | 0.988009 | 0.494004 | − | 0.869459i | \(-0.335533\pi\) | ||||
0.494004 | + | 0.869459i | \(0.335533\pi\) | |||||||
\(264\) | −18049.0 | −0.0159383 | ||||||||
\(265\) | 264105. | 0.231027 | ||||||||
\(266\) | 2.78928e6 | 2.41706 | ||||||||
\(267\) | 698573. | 0.599699 | ||||||||
\(268\) | 1.22139e6 | 1.03876 | ||||||||
\(269\) | −1.22073e6 | −1.02858 | −0.514289 | − | 0.857617i | \(-0.671944\pi\) | ||||
−0.514289 | + | 0.857617i | \(0.671944\pi\) | |||||||
\(270\) | −221454. | −0.184873 | ||||||||
\(271\) | −606547. | −0.501697 | −0.250848 | − | 0.968026i | \(-0.580710\pi\) | ||||
−0.250848 | + | 0.968026i | \(0.580710\pi\) | |||||||
\(272\) | −1.46052e6 | −1.19698 | ||||||||
\(273\) | −1.23681e6 | −1.00438 | ||||||||
\(274\) | −195413. | −0.157245 | ||||||||
\(275\) | 59285.7 | 0.0472735 | ||||||||
\(276\) | −120150. | −0.0949405 | ||||||||
\(277\) | 1.73194e6 | 1.35623 | 0.678116 | − | 0.734955i | \(-0.262797\pi\) | ||||
0.678116 | + | 0.734955i | \(0.262797\pi\) | |||||||
\(278\) | 599956. | 0.465594 | ||||||||
\(279\) | −776200. | −0.596985 | ||||||||
\(280\) | −400497. | −0.305284 | ||||||||
\(281\) | −1.03139e6 | −0.779212 | −0.389606 | − | 0.920982i | \(-0.627389\pi\) | ||||
−0.389606 | + | 0.920982i | \(0.627389\pi\) | |||||||
\(282\) | −15172.6 | −0.0113616 | ||||||||
\(283\) | 1.83231e6 | 1.35998 | 0.679990 | − | 0.733221i | \(-0.261984\pi\) | ||||
0.679990 | + | 0.733221i | \(0.261984\pi\) | |||||||
\(284\) | −1.52139e6 | −1.11929 | ||||||||
\(285\) | −683533. | −0.498480 | ||||||||
\(286\) | −209040. | −0.151117 | ||||||||
\(287\) | 942298. | 0.675279 | ||||||||
\(288\) | −599476. | −0.425883 | ||||||||
\(289\) | 74672.5 | 0.0525915 | ||||||||
\(290\) | −2.60623e6 | −1.81978 | ||||||||
\(291\) | 747625. | 0.517549 | ||||||||
\(292\) | 773195. | 0.530679 | ||||||||
\(293\) | −277123. | −0.188584 | −0.0942919 | − | 0.995545i | \(-0.530059\pi\) | ||||
−0.0942919 | + | 0.995545i | \(0.530059\pi\) | |||||||
\(294\) | −1.44263e6 | −0.973390 | ||||||||
\(295\) | −1.23595e6 | −0.826887 | ||||||||
\(296\) | 416757. | 0.276473 | ||||||||
\(297\) | 28570.6 | 0.0187944 | ||||||||
\(298\) | −2.55796e6 | −1.66860 | ||||||||
\(299\) | 372956. | 0.241257 | ||||||||
\(300\) | 343579. | 0.220406 | ||||||||
\(301\) | 2.07230e6 | 1.31837 | ||||||||
\(302\) | 3.74330e6 | 2.36177 | ||||||||
\(303\) | −277514. | −0.173651 | ||||||||
\(304\) | −2.25971e6 | −1.40239 | ||||||||
\(305\) | −349141. | −0.214907 | ||||||||
\(306\) | 749157. | 0.457372 | ||||||||
\(307\) | 1.98065e6 | 1.19939 | 0.599696 | − | 0.800228i | \(-0.295288\pi\) | ||||
0.599696 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(308\) | −192787. | −0.115798 | ||||||||
\(309\) | −1.27518e6 | −0.759758 | ||||||||
\(310\) | −2.91102e6 | −1.72045 | ||||||||
\(311\) | 2.56169e6 | 1.50185 | 0.750925 | − | 0.660388i | \(-0.229608\pi\) | ||||
0.750925 | + | 0.660388i | \(0.229608\pi\) | |||||||
\(312\) | 324686. | 0.188833 | ||||||||
\(313\) | 2.46321e6 | 1.42115 | 0.710576 | − | 0.703621i | \(-0.248435\pi\) | ||||
0.710576 | + | 0.703621i | \(0.248435\pi\) | |||||||
\(314\) | 1.48255e6 | 0.848566 | ||||||||
\(315\) | 633965. | 0.359989 | ||||||||
\(316\) | 1.26902e6 | 0.714907 | ||||||||
\(317\) | −3.04669e6 | −1.70287 | −0.851433 | − | 0.524464i | \(-0.824266\pi\) | ||||
−0.851433 | + | 0.524464i | \(0.824266\pi\) | |||||||
\(318\) | −447853. | −0.248352 | ||||||||
\(319\) | 336239. | 0.185000 | ||||||||
\(320\) | −713181. | −0.389336 | ||||||||
\(321\) | −1.19481e6 | −0.647196 | ||||||||
\(322\) | 780101. | 0.419287 | ||||||||
\(323\) | 2.31232e6 | 1.23323 | ||||||||
\(324\) | 165575. | 0.0876261 | ||||||||
\(325\) | −1.06650e6 | −0.560082 | ||||||||
\(326\) | 1.68879e6 | 0.880098 | ||||||||
\(327\) | 1.01727e6 | 0.526100 | ||||||||
\(328\) | −247370. | −0.126959 | ||||||||
\(329\) | 43435.2 | 0.0221234 | ||||||||
\(330\) | 107150. | 0.0541634 | ||||||||
\(331\) | −2.59437e6 | −1.30155 | −0.650776 | − | 0.759270i | \(-0.725556\pi\) | ||||
−0.650776 | + | 0.759270i | \(0.725556\pi\) | |||||||
\(332\) | −900222. | −0.448234 | ||||||||
\(333\) | −659703. | −0.326015 | ||||||||
\(334\) | −1.75916e6 | −0.862857 | ||||||||
\(335\) | 1.94333e6 | 0.946097 | ||||||||
\(336\) | 2.09584e6 | 1.01277 | ||||||||
\(337\) | 2.23509e6 | 1.07206 | 0.536032 | − | 0.844198i | \(-0.319923\pi\) | ||||
0.536032 | + | 0.844198i | \(0.319923\pi\) | |||||||
\(338\) | 951445. | 0.452994 | ||||||||
\(339\) | −415400. | −0.196321 | ||||||||
\(340\) | 1.23879e6 | 0.581168 | ||||||||
\(341\) | 375561. | 0.174902 | ||||||||
\(342\) | 1.15909e6 | 0.535861 | ||||||||
\(343\) | 853826. | 0.391863 | ||||||||
\(344\) | −544017. | −0.247865 | ||||||||
\(345\) | −191170. | −0.0864711 | ||||||||
\(346\) | 981148. | 0.440600 | ||||||||
\(347\) | 1.61546e6 | 0.720230 | 0.360115 | − | 0.932908i | \(-0.382737\pi\) | ||||
0.360115 | + | 0.932908i | \(0.382737\pi\) | |||||||
\(348\) | 1.94861e6 | 0.862535 | ||||||||
\(349\) | −2.56381e6 | −1.12674 | −0.563369 | − | 0.826205i | \(-0.690495\pi\) | ||||
−0.563369 | + | 0.826205i | \(0.690495\pi\) | |||||||
\(350\) | −2.23076e6 | −0.973382 | ||||||||
\(351\) | −513960. | −0.222670 | ||||||||
\(352\) | 290054. | 0.124773 | ||||||||
\(353\) | −1.64946e6 | −0.704541 | −0.352271 | − | 0.935898i | \(-0.614590\pi\) | ||||
−0.352271 | + | 0.935898i | \(0.614590\pi\) | |||||||
\(354\) | 2.09584e6 | 0.888896 | ||||||||
\(355\) | −2.42066e6 | −1.01944 | ||||||||
\(356\) | −1.95882e6 | −0.819162 | ||||||||
\(357\) | −2.14464e6 | −0.890602 | ||||||||
\(358\) | 5.46435e6 | 2.25336 | ||||||||
\(359\) | 1.30522e6 | 0.534500 | 0.267250 | − | 0.963627i | \(-0.413885\pi\) | ||||
0.267250 | + | 0.963627i | \(0.413885\pi\) | |||||||
\(360\) | −166427. | −0.0676812 | ||||||||
\(361\) | 1.10151e6 | 0.444857 | ||||||||
\(362\) | −959247. | −0.384732 | ||||||||
\(363\) | 1.43564e6 | 0.571844 | ||||||||
\(364\) | 3.46807e6 | 1.37194 | ||||||||
\(365\) | 1.23022e6 | 0.483338 | ||||||||
\(366\) | 592050. | 0.231023 | ||||||||
\(367\) | 5.04859e6 | 1.95661 | 0.978306 | − | 0.207164i | \(-0.0664233\pi\) | ||||
0.978306 | + | 0.207164i | \(0.0664233\pi\) | |||||||
\(368\) | −631991. | −0.243272 | ||||||||
\(369\) | 391574. | 0.149709 | ||||||||
\(370\) | −2.47412e6 | −0.939541 | ||||||||
\(371\) | 1.28208e6 | 0.483595 | ||||||||
\(372\) | 2.17649e6 | 0.815455 | ||||||||
\(373\) | 512860. | 0.190865 | 0.0954326 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954326 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(374\) | −362476. | −0.133999 | ||||||||
\(375\) | 1.67597e6 | 0.615445 | ||||||||
\(376\) | −11402.5 | −0.00415941 | ||||||||
\(377\) | −6.04865e6 | −2.19182 | ||||||||
\(378\) | −1.07504e6 | −0.386984 | ||||||||
\(379\) | 1.34067e6 | 0.479429 | 0.239714 | − | 0.970843i | \(-0.422946\pi\) | ||||
0.239714 | + | 0.970843i | \(0.422946\pi\) | |||||||
\(380\) | 1.91665e6 | 0.680901 | ||||||||
\(381\) | 2.01413e6 | 0.710844 | ||||||||
\(382\) | −4.40644e6 | −1.54500 | ||||||||
\(383\) | −5.32498e6 | −1.85490 | −0.927451 | − | 0.373944i | \(-0.878005\pi\) | ||||
−0.927451 | + | 0.373944i | \(0.878005\pi\) | |||||||
\(384\) | −922105. | −0.319119 | ||||||||
\(385\) | −306741. | −0.105468 | ||||||||
\(386\) | −3.34225e6 | −1.14175 | ||||||||
\(387\) | 861149. | 0.292281 | ||||||||
\(388\) | −2.09637e6 | −0.706949 | ||||||||
\(389\) | 4.22472e6 | 1.41554 | 0.707772 | − | 0.706441i | \(-0.249700\pi\) | ||||
0.707772 | + | 0.706441i | \(0.249700\pi\) | |||||||
\(390\) | −1.92753e6 | −0.641711 | ||||||||
\(391\) | 646708. | 0.213927 | ||||||||
\(392\) | −1.08417e6 | −0.356353 | ||||||||
\(393\) | 2.24549e6 | 0.733382 | ||||||||
\(394\) | −1.13359e6 | −0.367889 | ||||||||
\(395\) | 2.01912e6 | 0.651132 | ||||||||
\(396\) | −80113.0 | −0.0256723 | ||||||||
\(397\) | −451747. | −0.143853 | −0.0719266 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719266 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(398\) | −368018. | −0.116456 | ||||||||
\(399\) | −3.31817e6 | −1.04344 | ||||||||
\(400\) | 1.80723e6 | 0.564759 | ||||||||
\(401\) | 1.72721e6 | 0.536395 | 0.268197 | − | 0.963364i | \(-0.413572\pi\) | ||||
0.268197 | + | 0.963364i | \(0.413572\pi\) | |||||||
\(402\) | −3.29538e6 | −1.01705 | ||||||||
\(403\) | −6.75602e6 | −2.07218 | ||||||||
\(404\) | 778159. | 0.237200 | ||||||||
\(405\) | 263445. | 0.0798092 | ||||||||
\(406\) | −1.26518e7 | −3.80923 | ||||||||
\(407\) | 319194. | 0.0955145 | ||||||||
\(408\) | 563007. | 0.167442 | ||||||||
\(409\) | −1.57103e6 | −0.464384 | −0.232192 | − | 0.972670i | \(-0.574590\pi\) | ||||
−0.232192 | + | 0.972670i | \(0.574590\pi\) | |||||||
\(410\) | 1.46854e6 | 0.431445 | ||||||||
\(411\) | 232466. | 0.0678820 | ||||||||
\(412\) | 3.57565e6 | 1.03780 | ||||||||
\(413\) | −5.99985e6 | −1.73087 | ||||||||
\(414\) | 324173. | 0.0929556 | ||||||||
\(415\) | −1.43233e6 | −0.408248 | ||||||||
\(416\) | −5.21782e6 | −1.47828 | ||||||||
\(417\) | −713717. | −0.200995 | ||||||||
\(418\) | −560821. | −0.156994 | ||||||||
\(419\) | −1.93316e6 | −0.537938 | −0.268969 | − | 0.963149i | \(-0.586683\pi\) | ||||
−0.268969 | + | 0.963149i | \(0.586683\pi\) | |||||||
\(420\) | −1.77766e6 | −0.491729 | ||||||||
\(421\) | −188965. | −0.0519610 | −0.0259805 | − | 0.999662i | \(-0.508271\pi\) | ||||
−0.0259805 | + | 0.999662i | \(0.508271\pi\) | |||||||
\(422\) | 6.97018e6 | 1.90530 | ||||||||
\(423\) | 18049.6 | 0.00490475 | ||||||||
\(424\) | −336570. | −0.0909204 | ||||||||
\(425\) | −1.84931e6 | −0.496636 | ||||||||
\(426\) | 4.10480e6 | 1.09589 | ||||||||
\(427\) | −1.69488e6 | −0.449852 | ||||||||
\(428\) | 3.35029e6 | 0.884041 | ||||||||
\(429\) | 248677. | 0.0652369 | ||||||||
\(430\) | 3.22961e6 | 0.842323 | ||||||||
\(431\) | −3.11533e6 | −0.807812 | −0.403906 | − | 0.914800i | \(-0.632348\pi\) | ||||
−0.403906 | + | 0.914800i | \(0.632348\pi\) | |||||||
\(432\) | 870929. | 0.224530 | ||||||||
\(433\) | −2.18147e6 | −0.559151 | −0.279576 | − | 0.960124i | \(-0.590194\pi\) | ||||
−0.279576 | + | 0.960124i | \(0.590194\pi\) | |||||||
\(434\) | −1.41314e7 | −3.60130 | ||||||||
\(435\) | 3.10041e6 | 0.785591 | ||||||||
\(436\) | −2.85247e6 | −0.718629 | ||||||||
\(437\) | 1.00058e6 | 0.250639 | ||||||||
\(438\) | −2.08613e6 | −0.519584 | ||||||||
\(439\) | −3.03543e6 | −0.751725 | −0.375863 | − | 0.926675i | \(-0.622654\pi\) | ||||
−0.375863 | + | 0.926675i | \(0.622654\pi\) | |||||||
\(440\) | 80525.1 | 0.0198289 | ||||||||
\(441\) | 1.71618e6 | 0.420209 | ||||||||
\(442\) | 6.52064e6 | 1.58758 | ||||||||
\(443\) | −3.62547e6 | −0.877719 | −0.438859 | − | 0.898556i | \(-0.644617\pi\) | ||||
−0.438859 | + | 0.898556i | \(0.644617\pi\) | |||||||
\(444\) | 1.84983e6 | 0.445323 | ||||||||
\(445\) | −3.11666e6 | −0.746087 | ||||||||
\(446\) | 7.55371e6 | 1.79814 | ||||||||
\(447\) | 3.04299e6 | 0.720331 | ||||||||
\(448\) | −3.46209e6 | −0.814974 | ||||||||
\(449\) | 6.84914e6 | 1.60332 | 0.801660 | − | 0.597781i | \(-0.203951\pi\) | ||||
0.801660 | + | 0.597781i | \(0.203951\pi\) | |||||||
\(450\) | −926998. | −0.215798 | ||||||||
\(451\) | −189461. | −0.0438610 | ||||||||
\(452\) | 1.16480e6 | 0.268166 | ||||||||
\(453\) | −4.45309e6 | −1.01957 | ||||||||
\(454\) | −2.84993e6 | −0.648926 | ||||||||
\(455\) | 5.51801e6 | 1.24955 | ||||||||
\(456\) | 871080. | 0.196176 | ||||||||
\(457\) | 4.07502e6 | 0.912725 | 0.456362 | − | 0.889794i | \(-0.349152\pi\) | ||||
0.456362 | + | 0.889794i | \(0.349152\pi\) | |||||||
\(458\) | 6.15994e6 | 1.37219 | ||||||||
\(459\) | −891209. | −0.197446 | ||||||||
\(460\) | 536046. | 0.118116 | ||||||||
\(461\) | 1.10815e6 | 0.242854 | 0.121427 | − | 0.992600i | \(-0.461253\pi\) | ||||
0.121427 | + | 0.992600i | \(0.461253\pi\) | |||||||
\(462\) | 520151. | 0.113377 | ||||||||
\(463\) | 3.77893e6 | 0.819251 | 0.409625 | − | 0.912254i | \(-0.365659\pi\) | ||||
0.409625 | + | 0.912254i | \(0.365659\pi\) | |||||||
\(464\) | 1.02497e7 | 2.21013 | ||||||||
\(465\) | 3.46299e6 | 0.742710 | ||||||||
\(466\) | 1.93440e6 | 0.412650 | ||||||||
\(467\) | 8.40396e6 | 1.78317 | 0.891583 | − | 0.452857i | \(-0.149595\pi\) | ||||
0.891583 | + | 0.452857i | \(0.149595\pi\) | |||||||
\(468\) | 1.44116e6 | 0.304157 | ||||||||
\(469\) | 9.43380e6 | 1.98041 | ||||||||
\(470\) | 67692.3 | 0.0141350 | ||||||||
\(471\) | −1.76367e6 | −0.366323 | ||||||||
\(472\) | 1.57507e6 | 0.325420 | ||||||||
\(473\) | −416663. | −0.0856312 | ||||||||
\(474\) | −3.42389e6 | −0.699961 | ||||||||
\(475\) | −2.86124e6 | −0.581863 | ||||||||
\(476\) | 6.01365e6 | 1.21652 | ||||||||
\(477\) | 532773. | 0.107213 | ||||||||
\(478\) | −9.64470e6 | −1.93072 | ||||||||
\(479\) | 6.44233e6 | 1.28293 | 0.641467 | − | 0.767151i | \(-0.278326\pi\) | ||||
0.641467 | + | 0.767151i | \(0.278326\pi\) | |||||||
\(480\) | 2.67454e6 | 0.529843 | ||||||||
\(481\) | −5.74203e6 | −1.13163 | ||||||||
\(482\) | −1.11240e7 | −2.18094 | ||||||||
\(483\) | −928021. | −0.181005 | ||||||||
\(484\) | −4.02557e6 | −0.781114 | ||||||||
\(485\) | −3.33551e6 | −0.643884 | ||||||||
\(486\) | −446733. | −0.0857942 | ||||||||
\(487\) | −2.57622e6 | −0.492221 | −0.246111 | − | 0.969242i | \(-0.579153\pi\) | ||||
−0.246111 | + | 0.969242i | \(0.579153\pi\) | |||||||
\(488\) | 444937. | 0.0845764 | ||||||||
\(489\) | −2.00901e6 | −0.379935 | ||||||||
\(490\) | 6.43625e6 | 1.21100 | ||||||||
\(491\) | −443058. | −0.0829386 | −0.0414693 | − | 0.999140i | \(-0.513204\pi\) | ||||
−0.0414693 | + | 0.999140i | \(0.513204\pi\) | |||||||
\(492\) | −1.09799e6 | −0.204496 | ||||||||
\(493\) | −1.04884e7 | −1.94353 | ||||||||
\(494\) | 1.00887e7 | 1.86002 | ||||||||
\(495\) | −127467. | −0.0233821 | ||||||||
\(496\) | 1.14484e7 | 2.08949 | ||||||||
\(497\) | −1.17510e7 | −2.13394 | ||||||||
\(498\) | 2.42886e6 | 0.438863 | ||||||||
\(499\) | 6.36169e6 | 1.14372 | 0.571862 | − | 0.820350i | \(-0.306221\pi\) | ||||
0.571862 | + | 0.820350i | \(0.306221\pi\) | |||||||
\(500\) | −4.69949e6 | −0.840671 | ||||||||
\(501\) | 2.09272e6 | 0.372492 | ||||||||
\(502\) | 9.52952e6 | 1.68776 | ||||||||
\(503\) | 4.69139e6 | 0.826763 | 0.413382 | − | 0.910558i | \(-0.364348\pi\) | ||||
0.413382 | + | 0.910558i | \(0.364348\pi\) | |||||||
\(504\) | −807911. | −0.141673 | ||||||||
\(505\) | 1.23812e6 | 0.216040 | ||||||||
\(506\) | −156850. | −0.0272337 | ||||||||
\(507\) | −1.13185e6 | −0.195556 | ||||||||
\(508\) | −5.64769e6 | −0.970982 | ||||||||
\(509\) | 3.35385e6 | 0.573785 | 0.286893 | − | 0.957963i | \(-0.407378\pi\) | ||||
0.286893 | + | 0.957963i | \(0.407378\pi\) | |||||||
\(510\) | −3.34234e6 | −0.569018 | ||||||||
\(511\) | 5.97204e6 | 1.01174 | ||||||||
\(512\) | 6.88558e6 | 1.16082 | ||||||||
\(513\) | −1.37887e6 | −0.231329 | ||||||||
\(514\) | 3.03156e6 | 0.506125 | ||||||||
\(515\) | 5.68918e6 | 0.945217 | ||||||||
\(516\) | −2.41469e6 | −0.399243 | ||||||||
\(517\) | −8733.22 | −0.00143697 | ||||||||
\(518\) | −1.20104e7 | −1.96668 | ||||||||
\(519\) | −1.16719e6 | −0.190205 | ||||||||
\(520\) | −1.44858e6 | −0.234927 | ||||||||
\(521\) | 3.64554e6 | 0.588393 | 0.294196 | − | 0.955745i | \(-0.404948\pi\) | ||||
0.294196 | + | 0.955745i | \(0.404948\pi\) | |||||||
\(522\) | −5.25748e6 | −0.844503 | ||||||||
\(523\) | −9.63934e6 | −1.54097 | −0.770483 | − | 0.637461i | \(-0.779985\pi\) | ||||
−0.770483 | + | 0.637461i | \(0.779985\pi\) | |||||||
\(524\) | −6.29644e6 | −1.00177 | ||||||||
\(525\) | 2.65375e6 | 0.420206 | ||||||||
\(526\) | 8.38467e6 | 1.32136 | ||||||||
\(527\) | −1.17150e7 | −1.83745 | ||||||||
\(528\) | −421395. | −0.0657816 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 1.99808e6 | 0.308975 | ||||||||
\(531\) | −2.49325e6 | −0.383733 | ||||||||
\(532\) | 9.30426e6 | 1.42529 | ||||||||
\(533\) | 3.40824e6 | 0.519652 | ||||||||
\(534\) | 5.28503e6 | 0.802037 | ||||||||
\(535\) | 5.33060e6 | 0.805178 | ||||||||
\(536\) | −2.47654e6 | −0.372335 | ||||||||
\(537\) | −6.50048e6 | −0.972769 | ||||||||
\(538\) | −9.23537e6 | −1.37562 | ||||||||
\(539\) | −830364. | −0.123111 | ||||||||
\(540\) | −738710. | −0.109016 | ||||||||
\(541\) | 1.04511e7 | 1.53521 | 0.767604 | − | 0.640925i | \(-0.221449\pi\) | ||||
0.767604 | + | 0.640925i | \(0.221449\pi\) | |||||||
\(542\) | −4.58881e6 | −0.670969 | ||||||||
\(543\) | 1.14113e6 | 0.166088 | ||||||||
\(544\) | −9.04772e6 | −1.31082 | ||||||||
\(545\) | −4.53854e6 | −0.654522 | ||||||||
\(546\) | −9.35707e6 | −1.34325 | ||||||||
\(547\) | −6.35425e6 | −0.908021 | −0.454011 | − | 0.890996i | \(-0.650007\pi\) | ||||
−0.454011 | + | 0.890996i | \(0.650007\pi\) | |||||||
\(548\) | −651843. | −0.0927238 | ||||||||
\(549\) | −704312. | −0.0997319 | ||||||||
\(550\) | 448524. | 0.0632235 | ||||||||
\(551\) | −1.62276e7 | −2.27706 | ||||||||
\(552\) | 243622. | 0.0340306 | ||||||||
\(553\) | 9.80169e6 | 1.36298 | ||||||||
\(554\) | 1.31030e7 | 1.81382 | ||||||||
\(555\) | 2.94325e6 | 0.405596 | ||||||||
\(556\) | 2.00129e6 | 0.274551 | ||||||||
\(557\) | −283483. | −0.0387159 | −0.0193580 | − | 0.999813i | \(-0.506162\pi\) | ||||
−0.0193580 | + | 0.999813i | \(0.506162\pi\) | |||||||
\(558\) | −5.87232e6 | −0.798407 | ||||||||
\(559\) | 7.49541e6 | 1.01453 | ||||||||
\(560\) | −9.35051e6 | −1.25999 | ||||||||
\(561\) | 431208. | 0.0578468 | ||||||||
\(562\) | −7.80292e6 | −1.04212 | ||||||||
\(563\) | 1.05154e7 | 1.39815 | 0.699076 | − | 0.715047i | \(-0.253595\pi\) | ||||
0.699076 | + | 0.715047i | \(0.253595\pi\) | |||||||
\(564\) | −50611.7 | −0.00669967 | ||||||||
\(565\) | 1.85329e6 | 0.244243 | ||||||||
\(566\) | 1.38623e7 | 1.81884 | ||||||||
\(567\) | 1.27888e6 | 0.167060 | ||||||||
\(568\) | 3.08484e6 | 0.401201 | ||||||||
\(569\) | 6.83667e6 | 0.885246 | 0.442623 | − | 0.896708i | \(-0.354048\pi\) | ||||
0.442623 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(570\) | −5.17125e6 | −0.666666 | ||||||||
\(571\) | 3.11227e6 | 0.399473 | 0.199736 | − | 0.979850i | \(-0.435991\pi\) | ||||
0.199736 | + | 0.979850i | \(0.435991\pi\) | |||||||
\(572\) | −697300. | −0.0891107 | ||||||||
\(573\) | 5.24197e6 | 0.666972 | ||||||||
\(574\) | 7.12892e6 | 0.903117 | ||||||||
\(575\) | −800228. | −0.100936 | ||||||||
\(576\) | −1.43868e6 | −0.180679 | ||||||||
\(577\) | −1.10234e7 | −1.37841 | −0.689203 | − | 0.724569i | \(-0.742039\pi\) | ||||
−0.689203 | + | 0.724569i | \(0.742039\pi\) | |||||||
\(578\) | 564932. | 0.0703358 | ||||||||
\(579\) | 3.97599e6 | 0.492889 | ||||||||
\(580\) | −8.69367e6 | −1.07308 | ||||||||
\(581\) | −6.95317e6 | −0.854560 | ||||||||
\(582\) | 5.65613e6 | 0.692169 | ||||||||
\(583\) | −257780. | −0.0314107 | ||||||||
\(584\) | −1.56777e6 | −0.190217 | ||||||||
\(585\) | 2.29302e6 | 0.277024 | ||||||||
\(586\) | −2.09657e6 | −0.252212 | ||||||||
\(587\) | −2.79249e6 | −0.334500 | −0.167250 | − | 0.985915i | \(-0.553489\pi\) | ||||
−0.167250 | + | 0.985915i | \(0.553489\pi\) | |||||||
\(588\) | −4.81222e6 | −0.573987 | ||||||||
\(589\) | −1.81253e7 | −2.15277 | ||||||||
\(590\) | −9.35054e6 | −1.10588 | ||||||||
\(591\) | 1.34854e6 | 0.158816 | ||||||||
\(592\) | 9.73014e6 | 1.14108 | ||||||||
\(593\) | −1.65811e7 | −1.93632 | −0.968161 | − | 0.250328i | \(-0.919462\pi\) | ||||
−0.968161 | + | 0.250328i | \(0.919462\pi\) | |||||||
\(594\) | 216150. | 0.0251356 | ||||||||
\(595\) | 9.56825e6 | 1.10800 | ||||||||
\(596\) | −8.53266e6 | −0.983940 | ||||||||
\(597\) | 437800. | 0.0502736 | ||||||||
\(598\) | 2.82159e6 | 0.322657 | ||||||||
\(599\) | 6.89907e6 | 0.785640 | 0.392820 | − | 0.919615i | \(-0.371500\pi\) | ||||
0.392820 | + | 0.919615i | \(0.371500\pi\) | |||||||
\(600\) | −696658. | −0.0790026 | ||||||||
\(601\) | −807441. | −0.0911853 | −0.0455927 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455927 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(602\) | 1.56779e7 | 1.76318 | ||||||||
\(603\) | 3.92023e6 | 0.439055 | ||||||||
\(604\) | 1.24866e7 | 1.39268 | ||||||||
\(605\) | −6.40504e6 | −0.711432 | ||||||||
\(606\) | −2.09952e6 | −0.232241 | ||||||||
\(607\) | −1.46288e6 | −0.161153 | −0.0805765 | − | 0.996748i | \(-0.525676\pi\) | ||||
−0.0805765 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(608\) | −1.39986e7 | −1.53576 | ||||||||
\(609\) | 1.50508e7 | 1.64443 | ||||||||
\(610\) | −2.64141e6 | −0.287416 | ||||||||
\(611\) | 157103. | 0.0170248 | ||||||||
\(612\) | 2.49898e6 | 0.269702 | ||||||||
\(613\) | −1.41124e7 | −1.51687 | −0.758435 | − | 0.651749i | \(-0.774036\pi\) | ||||
−0.758435 | + | 0.651749i | \(0.774036\pi\) | |||||||
\(614\) | 1.49845e7 | 1.60406 | ||||||||
\(615\) | −1.74699e6 | −0.186253 | ||||||||
\(616\) | 390904. | 0.0415067 | ||||||||
\(617\) | −1.32361e7 | −1.39974 | −0.699871 | − | 0.714269i | \(-0.746759\pi\) | ||||
−0.699871 | + | 0.714269i | \(0.746759\pi\) | |||||||
\(618\) | −9.64734e6 | −1.01610 | ||||||||
\(619\) | 3.89949e6 | 0.409055 | 0.204527 | − | 0.978861i | \(-0.434434\pi\) | ||||
0.204527 | + | 0.978861i | \(0.434434\pi\) | |||||||
\(620\) | −9.71036e6 | −1.01451 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | 1.93804e7 | 2.00857 | ||||||||
\(623\) | −1.51296e7 | −1.56174 | ||||||||
\(624\) | 7.58054e6 | 0.779361 | ||||||||
\(625\) | −2.75007e6 | −0.281607 | ||||||||
\(626\) | 1.86353e7 | 1.90065 | ||||||||
\(627\) | 667161. | 0.0677738 | ||||||||
\(628\) | 4.94538e6 | 0.500381 | ||||||||
\(629\) | −9.95671e6 | −1.00344 | ||||||||
\(630\) | 4.79624e6 | 0.481448 | ||||||||
\(631\) | −7.32659e6 | −0.732535 | −0.366268 | − | 0.930510i | \(-0.619365\pi\) | ||||
−0.366268 | + | 0.930510i | \(0.619365\pi\) | |||||||
\(632\) | −2.57312e6 | −0.256252 | ||||||||
\(633\) | −8.29184e6 | −0.822511 | ||||||||
\(634\) | −2.30497e7 | −2.27741 | ||||||||
\(635\) | −8.98597e6 | −0.884363 | ||||||||
\(636\) | −1.49391e6 | −0.146448 | ||||||||
\(637\) | 1.49375e7 | 1.45858 | ||||||||
\(638\) | 2.54381e6 | 0.247419 | ||||||||
\(639\) | −4.88314e6 | −0.473093 | ||||||||
\(640\) | 4.11394e6 | 0.397016 | ||||||||
\(641\) | 4.68243e6 | 0.450118 | 0.225059 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225059 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(642\) | −9.03929e6 | −0.865559 | ||||||||
\(643\) | 5.15232e6 | 0.491445 | 0.245723 | − | 0.969340i | \(-0.420975\pi\) | ||||
0.245723 | + | 0.969340i | \(0.420975\pi\) | |||||||
\(644\) | 2.60220e6 | 0.247244 | ||||||||
\(645\) | −3.84199e6 | −0.363628 | ||||||||
\(646\) | 1.74938e7 | 1.64931 | ||||||||
\(647\) | −5.60768e6 | −0.526650 | −0.263325 | − | 0.964707i | \(-0.584819\pi\) | ||||
−0.263325 | + | 0.964707i | \(0.584819\pi\) | |||||||
\(648\) | −335729. | −0.0314088 | ||||||||
\(649\) | 1.20635e6 | 0.112424 | ||||||||
\(650\) | −8.06856e6 | −0.749053 | ||||||||
\(651\) | 1.68109e7 | 1.55467 | ||||||||
\(652\) | 5.63333e6 | 0.518975 | ||||||||
\(653\) | 7.57877e6 | 0.695530 | 0.347765 | − | 0.937582i | \(-0.386941\pi\) | ||||
0.347765 | + | 0.937582i | \(0.386941\pi\) | |||||||
\(654\) | 7.69615e6 | 0.703605 | ||||||||
\(655\) | −1.00182e7 | −0.912402 | ||||||||
\(656\) | −5.77542e6 | −0.523992 | ||||||||
\(657\) | 2.48169e6 | 0.224303 | ||||||||
\(658\) | 328608. | 0.0295878 | ||||||||
\(659\) | 1.64530e7 | 1.47581 | 0.737905 | − | 0.674904i | \(-0.235815\pi\) | ||||
0.737905 | + | 0.674904i | \(0.235815\pi\) | |||||||
\(660\) | 357422. | 0.0319390 | ||||||||
\(661\) | 1.72074e6 | 0.153184 | 0.0765918 | − | 0.997063i | \(-0.475596\pi\) | ||||
0.0765918 | + | 0.997063i | \(0.475596\pi\) | |||||||
\(662\) | −1.96276e7 | −1.74069 | ||||||||
\(663\) | −7.75705e6 | −0.685351 | ||||||||
\(664\) | 1.82533e6 | 0.160665 | ||||||||
\(665\) | 1.48039e7 | 1.29814 | ||||||||
\(666\) | −4.99096e6 | −0.436012 | ||||||||
\(667\) | −4.53850e6 | −0.395000 | ||||||||
\(668\) | −5.86807e6 | −0.508808 | ||||||||
\(669\) | −8.98601e6 | −0.776250 | ||||||||
\(670\) | 1.47022e7 | 1.26531 | ||||||||
\(671\) | 340778. | 0.0292190 | ||||||||
\(672\) | 1.29834e7 | 1.10909 | ||||||||
\(673\) | 8.54705e6 | 0.727408 | 0.363704 | − | 0.931514i | \(-0.381512\pi\) | ||||
0.363704 | + | 0.931514i | \(0.381512\pi\) | |||||||
\(674\) | 1.69095e7 | 1.43378 | ||||||||
\(675\) | 1.10277e6 | 0.0931593 | ||||||||
\(676\) | 3.17376e6 | 0.267121 | ||||||||
\(677\) | −8.31269e6 | −0.697060 | −0.348530 | − | 0.937298i | \(-0.613319\pi\) | ||||
−0.348530 | + | 0.937298i | \(0.613319\pi\) | |||||||
\(678\) | −3.14269e6 | −0.262559 | ||||||||
\(679\) | −1.61920e7 | −1.34780 | ||||||||
\(680\) | −2.51184e6 | −0.208314 | ||||||||
\(681\) | 3.39033e6 | 0.280139 | ||||||||
\(682\) | 2.84129e6 | 0.233914 | ||||||||
\(683\) | −1.80054e6 | −0.147690 | −0.0738451 | − | 0.997270i | \(-0.523527\pi\) | ||||
−0.0738451 | + | 0.997270i | \(0.523527\pi\) | |||||||
\(684\) | 3.86641e6 | 0.315986 | ||||||||
\(685\) | −1.03714e6 | −0.0844522 | ||||||||
\(686\) | 6.45960e6 | 0.524077 | ||||||||
\(687\) | −7.32796e6 | −0.592368 | ||||||||
\(688\) | −1.27013e7 | −1.02300 | ||||||||
\(689\) | 4.63723e6 | 0.372144 | ||||||||
\(690\) | −1.44629e6 | −0.115646 | ||||||||
\(691\) | −1.38259e7 | −1.10153 | −0.550766 | − | 0.834660i | \(-0.685664\pi\) | ||||
−0.550766 | + | 0.834660i | \(0.685664\pi\) | |||||||
\(692\) | 3.27284e6 | 0.259812 | ||||||||
\(693\) | −618780. | −0.0489444 | ||||||||
\(694\) | 1.22217e7 | 0.963235 | ||||||||
\(695\) | 3.18423e6 | 0.250059 | ||||||||
\(696\) | −3.95110e6 | −0.309168 | ||||||||
\(697\) | 5.90991e6 | 0.460786 | ||||||||
\(698\) | −1.93965e7 | −1.50690 | ||||||||
\(699\) | −2.30120e6 | −0.178140 | ||||||||
\(700\) | −7.44121e6 | −0.573982 | ||||||||
\(701\) | 2.42009e7 | 1.86010 | 0.930051 | − | 0.367430i | \(-0.119762\pi\) | ||||
0.930051 | + | 0.367430i | \(0.119762\pi\) | |||||||
\(702\) | −3.88835e6 | −0.297799 | ||||||||
\(703\) | −1.54049e7 | −1.17563 | ||||||||
\(704\) | 696099. | 0.0529346 | ||||||||
\(705\) | −80527.8 | −0.00610201 | ||||||||
\(706\) | −1.24790e7 | −0.942252 | ||||||||
\(707\) | 6.01038e6 | 0.452224 | ||||||||
\(708\) | 6.99116e6 | 0.524162 | ||||||||
\(709\) | −1.13875e7 | −0.850768 | −0.425384 | − | 0.905013i | \(-0.639861\pi\) | ||||
−0.425384 | + | 0.905013i | \(0.639861\pi\) | |||||||
\(710\) | −1.83135e7 | −1.36340 | ||||||||
\(711\) | 4.07311e6 | 0.302171 | ||||||||
\(712\) | 3.97181e6 | 0.293622 | ||||||||
\(713\) | −5.06926e6 | −0.373440 | ||||||||
\(714\) | −1.62252e7 | −1.19109 | ||||||||
\(715\) | −1.10947e6 | −0.0811613 | ||||||||
\(716\) | 1.82276e7 | 1.32876 | ||||||||
\(717\) | 1.14735e7 | 0.833484 | ||||||||
\(718\) | 9.87459e6 | 0.714839 | ||||||||
\(719\) | −1.24869e7 | −0.900807 | −0.450403 | − | 0.892825i | \(-0.648720\pi\) | ||||
−0.450403 | + | 0.892825i | \(0.648720\pi\) | |||||||
\(720\) | −3.88563e6 | −0.279338 | ||||||||
\(721\) | 2.76178e7 | 1.97857 | ||||||||
\(722\) | 8.33344e6 | 0.594951 | ||||||||
\(723\) | 1.32333e7 | 0.941502 | ||||||||
\(724\) | −3.19978e6 | −0.226868 | ||||||||
\(725\) | 1.29782e7 | 0.917000 | ||||||||
\(726\) | 1.08613e7 | 0.764783 | ||||||||
\(727\) | −1.69620e7 | −1.19026 | −0.595128 | − | 0.803631i | \(-0.702899\pi\) | ||||
−0.595128 | + | 0.803631i | \(0.702899\pi\) | |||||||
\(728\) | −7.03203e6 | −0.491759 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 9.30721e6 | 0.646416 | ||||||||
\(731\) | 1.29971e7 | 0.899605 | ||||||||
\(732\) | 1.97491e6 | 0.136229 | ||||||||
\(733\) | 1.73348e7 | 1.19168 | 0.595839 | − | 0.803104i | \(-0.296820\pi\) | ||||
0.595839 | + | 0.803104i | \(0.296820\pi\) | |||||||
\(734\) | 3.81949e7 | 2.61677 | ||||||||
\(735\) | −7.65667e6 | −0.522783 | ||||||||
\(736\) | −3.91510e6 | −0.266408 | ||||||||
\(737\) | −1.89679e6 | −0.128632 | ||||||||
\(738\) | 2.96244e6 | 0.200220 | ||||||||
\(739\) | 2.67348e6 | 0.180080 | 0.0900400 | − | 0.995938i | \(-0.471301\pi\) | ||||
0.0900400 | + | 0.995938i | \(0.471301\pi\) | |||||||
\(740\) | −8.25297e6 | −0.554027 | ||||||||
\(741\) | −1.20017e7 | −0.802963 | ||||||||
\(742\) | 9.69957e6 | 0.646759 | ||||||||
\(743\) | 1.67454e7 | 1.11281 | 0.556407 | − | 0.830910i | \(-0.312180\pi\) | ||||
0.556407 | + | 0.830910i | \(0.312180\pi\) | |||||||
\(744\) | −4.41316e6 | −0.292293 | ||||||||
\(745\) | −1.35762e7 | −0.896165 | ||||||||
\(746\) | 3.88002e6 | 0.255263 | ||||||||
\(747\) | −2.88941e6 | −0.189455 | ||||||||
\(748\) | −1.20912e6 | −0.0790162 | ||||||||
\(749\) | 2.58771e7 | 1.68543 | ||||||||
\(750\) | 1.26795e7 | 0.823095 | ||||||||
\(751\) | −2.86431e7 | −1.85319 | −0.926595 | − | 0.376062i | \(-0.877278\pi\) | ||||
−0.926595 | + | 0.376062i | \(0.877278\pi\) | |||||||
\(752\) | −266218. | −0.0171670 | ||||||||
\(753\) | −1.13365e7 | −0.728601 | ||||||||
\(754\) | −4.57609e7 | −2.93134 | ||||||||
\(755\) | 1.98673e7 | 1.26845 | ||||||||
\(756\) | −3.58602e6 | −0.228196 | ||||||||
\(757\) | 2.69646e7 | 1.71023 | 0.855113 | − | 0.518441i | \(-0.173487\pi\) | ||||
0.855113 | + | 0.518441i | \(0.173487\pi\) | |||||||
\(758\) | 1.01428e7 | 0.641188 | ||||||||
\(759\) | 186591. | 0.0117567 | ||||||||
\(760\) | −3.88630e6 | −0.244063 | ||||||||
\(761\) | 4.94085e6 | 0.309272 | 0.154636 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154636 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(762\) | 1.52378e7 | 0.950682 | ||||||||
\(763\) | −2.20320e7 | −1.37007 | ||||||||
\(764\) | −1.46987e7 | −0.911054 | ||||||||
\(765\) | 3.97610e6 | 0.245643 | ||||||||
\(766\) | −4.02860e7 | −2.48074 | ||||||||
\(767\) | −2.17011e7 | −1.33197 | ||||||||
\(768\) | −1.20915e7 | −0.739734 | ||||||||
\(769\) | 3.74373e6 | 0.228291 | 0.114145 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114145 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(770\) | −2.32064e6 | −0.141053 | ||||||||
\(771\) | −3.60639e6 | −0.218492 | ||||||||
\(772\) | −1.11488e7 | −0.673265 | ||||||||
\(773\) | 2.17718e7 | 1.31053 | 0.655264 | − | 0.755400i | \(-0.272557\pi\) | ||||
0.655264 | + | 0.755400i | \(0.272557\pi\) | |||||||
\(774\) | 6.51500e6 | 0.390896 | ||||||||
\(775\) | 1.44960e7 | 0.866947 | ||||||||
\(776\) | 4.25070e6 | 0.253400 | ||||||||
\(777\) | 1.42878e7 | 0.849011 | ||||||||
\(778\) | 3.19620e7 | 1.89315 | ||||||||
\(779\) | 9.14376e6 | 0.539860 | ||||||||
\(780\) | −6.42971e6 | −0.378403 | ||||||||
\(781\) | 2.36268e6 | 0.138605 | ||||||||
\(782\) | 4.89265e6 | 0.286106 | ||||||||
\(783\) | 6.25438e6 | 0.364569 | ||||||||
\(784\) | −2.53123e7 | −1.47076 | ||||||||
\(785\) | 7.86855e6 | 0.455743 | ||||||||
\(786\) | 1.69882e7 | 0.980824 | ||||||||
\(787\) | −2.13696e7 | −1.22987 | −0.614936 | − | 0.788577i | \(-0.710818\pi\) | ||||
−0.614936 | + | 0.788577i | \(0.710818\pi\) | |||||||
\(788\) | −3.78135e6 | −0.216936 | ||||||||
\(789\) | −9.97454e6 | −0.570427 | ||||||||
\(790\) | 1.52756e7 | 0.870823 | ||||||||
\(791\) | 8.99670e6 | 0.511260 | ||||||||
\(792\) | 162441. | 0.00920201 | ||||||||
\(793\) | −6.13030e6 | −0.346178 | ||||||||
\(794\) | −3.41768e6 | −0.192389 | ||||||||
\(795\) | −2.37695e6 | −0.133384 | ||||||||
\(796\) | −1.22761e6 | −0.0686715 | ||||||||
\(797\) | 2.80148e7 | 1.56222 | 0.781108 | − | 0.624396i | \(-0.214655\pi\) | ||||
0.781108 | + | 0.624396i | \(0.214655\pi\) | |||||||
\(798\) | −2.51035e7 | −1.39549 | ||||||||
\(799\) | 272417. | 0.0150962 | ||||||||
\(800\) | 1.11955e7 | 0.618472 | ||||||||
\(801\) | −6.28715e6 | −0.346236 | ||||||||
\(802\) | 1.30672e7 | 0.717374 | ||||||||
\(803\) | −1.20076e6 | −0.0657152 | ||||||||
\(804\) | −1.09925e7 | −0.599730 | ||||||||
\(805\) | 4.14034e6 | 0.225188 | ||||||||
\(806\) | −5.11124e7 | −2.77134 | ||||||||
\(807\) | 1.09865e7 | 0.593850 | ||||||||
\(808\) | −1.57783e6 | −0.0850223 | ||||||||
\(809\) | −3.12241e7 | −1.67733 | −0.838665 | − | 0.544648i | \(-0.816663\pi\) | ||||
−0.838665 | + | 0.544648i | \(0.816663\pi\) | |||||||
\(810\) | 1.99309e6 | 0.106737 | ||||||||
\(811\) | 1.30079e7 | 0.694471 | 0.347235 | − | 0.937778i | \(-0.387120\pi\) | ||||
0.347235 | + | 0.937778i | \(0.387120\pi\) | |||||||
\(812\) | −4.22029e7 | −2.24622 | ||||||||
\(813\) | 5.45892e6 | 0.289655 | ||||||||
\(814\) | 2.41486e6 | 0.127741 | ||||||||
\(815\) | 8.96313e6 | 0.472678 | ||||||||
\(816\) | 1.31447e7 | 0.691074 | ||||||||
\(817\) | 2.01090e7 | 1.05399 | ||||||||
\(818\) | −1.18856e7 | −0.621066 | ||||||||
\(819\) | 1.11313e7 | 0.579878 | ||||||||
\(820\) | 4.89863e6 | 0.254414 | ||||||||
\(821\) | 9.48385e6 | 0.491051 | 0.245526 | − | 0.969390i | \(-0.421039\pi\) | ||||
0.245526 | + | 0.969390i | \(0.421039\pi\) | |||||||
\(822\) | 1.75871e6 | 0.0907853 | ||||||||
\(823\) | −1.57317e7 | −0.809610 | −0.404805 | − | 0.914403i | \(-0.632661\pi\) | ||||
−0.404805 | + | 0.914403i | \(0.632661\pi\) | |||||||
\(824\) | −7.25017e6 | −0.371989 | ||||||||
\(825\) | −533571. | −0.0272934 | ||||||||
\(826\) | −4.53916e7 | −2.31487 | ||||||||
\(827\) | −1.68809e7 | −0.858284 | −0.429142 | − | 0.903237i | \(-0.641184\pi\) | ||||
−0.429142 | + | 0.903237i | \(0.641184\pi\) | |||||||
\(828\) | 1.08135e6 | 0.0548139 | ||||||||
\(829\) | 2.04228e7 | 1.03212 | 0.516059 | − | 0.856553i | \(-0.327399\pi\) | ||||
0.516059 | + | 0.856553i | \(0.327399\pi\) | |||||||
\(830\) | −1.08363e7 | −0.545990 | ||||||||
\(831\) | −1.55875e7 | −0.783021 | ||||||||
\(832\) | −1.25222e7 | −0.627152 | ||||||||
\(833\) | 2.59018e7 | 1.29335 | ||||||||
\(834\) | −5.39961e6 | −0.268811 | ||||||||
\(835\) | −9.33662e6 | −0.463419 | ||||||||
\(836\) | −1.87074e6 | −0.0925760 | ||||||||
\(837\) | 6.98580e6 | 0.344669 | ||||||||
\(838\) | −1.46252e7 | −0.719437 | ||||||||
\(839\) | −3.17685e7 | −1.55809 | −0.779044 | − | 0.626970i | \(-0.784295\pi\) | ||||
−0.779044 | + | 0.626970i | \(0.784295\pi\) | |||||||
\(840\) | 3.60447e6 | 0.176256 | ||||||||
\(841\) | 5.30948e7 | 2.58858 | ||||||||
\(842\) | −1.42961e6 | −0.0694925 | ||||||||
\(843\) | 9.28248e6 | 0.449878 | ||||||||
\(844\) | 2.32506e7 | 1.12351 | ||||||||
\(845\) | 5.04973e6 | 0.243291 | ||||||||
\(846\) | 136554. | 0.00655960 | ||||||||
\(847\) | −3.10929e7 | −1.48920 | ||||||||
\(848\) | −7.85800e6 | −0.375252 | ||||||||
\(849\) | −1.64908e7 | −0.785185 | ||||||||
\(850\) | −1.39909e7 | −0.664200 | ||||||||
\(851\) | −4.30843e6 | −0.203937 | ||||||||
\(852\) | 1.36925e7 | 0.646225 | ||||||||
\(853\) | −1.26754e7 | −0.596471 | −0.298236 | − | 0.954492i | \(-0.596398\pi\) | ||||
−0.298236 | + | 0.954492i | \(0.596398\pi\) | |||||||
\(854\) | −1.28226e7 | −0.601631 | ||||||||
\(855\) | 6.15180e6 | 0.287797 | ||||||||
\(856\) | −6.79321e6 | −0.316877 | ||||||||
\(857\) | −1.77408e7 | −0.825126 | −0.412563 | − | 0.910929i | \(-0.635366\pi\) | ||||
−0.412563 | + | 0.910929i | \(0.635366\pi\) | |||||||
\(858\) | 1.88136e6 | 0.0872477 | ||||||||
\(859\) | 3.98531e6 | 0.184280 | 0.0921401 | − | 0.995746i | \(-0.470629\pi\) | ||||
0.0921401 | + | 0.995746i | \(0.470629\pi\) | |||||||
\(860\) | 1.07731e7 | 0.496699 | ||||||||
\(861\) | −8.48068e6 | −0.389873 | ||||||||
\(862\) | −2.35689e7 | −1.08037 | ||||||||
\(863\) | 3.42751e7 | 1.56658 | 0.783289 | − | 0.621658i | \(-0.213541\pi\) | ||||
0.783289 | + | 0.621658i | \(0.213541\pi\) | |||||||
\(864\) | 5.39529e6 | 0.245884 | ||||||||
\(865\) | 5.20738e6 | 0.236635 | ||||||||
\(866\) | −1.65038e7 | −0.747808 | ||||||||
\(867\) | −672052. | −0.0303637 | ||||||||
\(868\) | −4.71383e7 | −2.12361 | ||||||||
\(869\) | −1.97076e6 | −0.0885286 | ||||||||
\(870\) | 2.34561e7 | 1.05065 | ||||||||
\(871\) | 3.41216e7 | 1.52400 | ||||||||
\(872\) | 5.78381e6 | 0.257586 | ||||||||
\(873\) | −6.72862e6 | −0.298807 | ||||||||
\(874\) | 7.56986e6 | 0.335204 | ||||||||
\(875\) | −3.62981e7 | −1.60274 | ||||||||
\(876\) | −6.95875e6 | −0.306388 | ||||||||
\(877\) | −3.57889e7 | −1.57126 | −0.785632 | − | 0.618694i | \(-0.787662\pi\) | ||||
−0.785632 | + | 0.618694i | \(0.787662\pi\) | |||||||
\(878\) | −2.29645e7 | −1.00536 | ||||||||
\(879\) | 2.49411e6 | 0.108879 | ||||||||
\(880\) | 1.88004e6 | 0.0818391 | ||||||||
\(881\) | 5.76071e6 | 0.250055 | 0.125028 | − | 0.992153i | \(-0.460098\pi\) | ||||
0.125028 | + | 0.992153i | \(0.460098\pi\) | |||||||
\(882\) | 1.29837e7 | 0.561987 | ||||||||
\(883\) | −4.41397e7 | −1.90514 | −0.952572 | − | 0.304312i | \(-0.901573\pi\) | ||||
−0.952572 | + | 0.304312i | \(0.901573\pi\) | |||||||
\(884\) | 2.17511e7 | 0.936159 | ||||||||
\(885\) | 1.11236e7 | 0.477403 | ||||||||
\(886\) | −2.74284e7 | −1.17386 | ||||||||
\(887\) | −9.63127e6 | −0.411031 | −0.205515 | − | 0.978654i | \(-0.565887\pi\) | ||||
−0.205515 | + | 0.978654i | \(0.565887\pi\) | |||||||
\(888\) | −3.75081e6 | −0.159622 | ||||||||
\(889\) | −4.36218e7 | −1.85118 | ||||||||
\(890\) | −2.35790e7 | −0.997816 | ||||||||
\(891\) | −257135. | −0.0108509 | ||||||||
\(892\) | 2.51971e7 | 1.06032 | ||||||||
\(893\) | 421482. | 0.0176869 | ||||||||
\(894\) | 2.30217e7 | 0.963369 | ||||||||
\(895\) | 2.90017e7 | 1.21022 | ||||||||
\(896\) | 1.99709e7 | 0.831050 | ||||||||
\(897\) | −3.35660e6 | −0.139290 | ||||||||
\(898\) | 5.18169e7 | 2.14428 | ||||||||
\(899\) | 8.22139e7 | 3.39270 | ||||||||
\(900\) | −3.09221e6 | −0.127251 | ||||||||
\(901\) | 8.04098e6 | 0.329987 | ||||||||
\(902\) | −1.43336e6 | −0.0586597 | ||||||||
\(903\) | −1.86507e7 | −0.761160 | ||||||||
\(904\) | −2.36180e6 | −0.0961217 | ||||||||
\(905\) | −5.09114e6 | −0.206630 | ||||||||
\(906\) | −3.36897e7 | −1.36357 | ||||||||
\(907\) | 1.72941e7 | 0.698037 | 0.349019 | − | 0.937116i | \(-0.386515\pi\) | ||||
0.349019 | + | 0.937116i | \(0.386515\pi\) | |||||||
\(908\) | −9.50659e6 | −0.382658 | ||||||||
\(909\) | 2.49763e6 | 0.100258 | ||||||||
\(910\) | 4.17463e7 | 1.67115 | ||||||||
\(911\) | −3.64206e7 | −1.45396 | −0.726978 | − | 0.686660i | \(-0.759076\pi\) | ||||
−0.726978 | + | 0.686660i | \(0.759076\pi\) | |||||||
\(912\) | 2.03373e7 | 0.809669 | ||||||||
\(913\) | 1.39803e6 | 0.0555058 | ||||||||
\(914\) | 3.08295e7 | 1.22068 | ||||||||
\(915\) | 3.14227e6 | 0.124077 | ||||||||
\(916\) | 2.05479e7 | 0.809148 | ||||||||
\(917\) | −4.86327e7 | −1.90988 | ||||||||
\(918\) | −6.74242e6 | −0.264064 | ||||||||
\(919\) | 3.59707e7 | 1.40495 | 0.702474 | − | 0.711710i | \(-0.252079\pi\) | ||||
0.702474 | + | 0.711710i | \(0.252079\pi\) | |||||||
\(920\) | −1.08691e6 | −0.0423375 | ||||||||
\(921\) | −1.78258e7 | −0.692469 | ||||||||
\(922\) | 8.38366e6 | 0.324793 | ||||||||
\(923\) | −4.25027e7 | −1.64215 | ||||||||
\(924\) | 1.73508e6 | 0.0668559 | ||||||||
\(925\) | 1.23203e7 | 0.473443 | ||||||||
\(926\) | 2.85894e7 | 1.09566 | ||||||||
\(927\) | 1.14766e7 | 0.438647 | ||||||||
\(928\) | 6.34956e7 | 2.42032 | ||||||||
\(929\) | −1.66420e7 | −0.632654 | −0.316327 | − | 0.948650i | \(-0.602450\pi\) | ||||
−0.316327 | + | 0.948650i | \(0.602450\pi\) | |||||||
\(930\) | 2.61992e7 | 0.993300 | ||||||||
\(931\) | 4.00750e7 | 1.51530 | ||||||||
\(932\) | 6.45264e6 | 0.243331 | ||||||||
\(933\) | −2.30552e7 | −0.867093 | ||||||||
\(934\) | 6.35799e7 | 2.38480 | ||||||||
\(935\) | −1.92382e6 | −0.0719673 | ||||||||
\(936\) | −2.92217e6 | −0.109023 | ||||||||
\(937\) | 1.14846e7 | 0.427332 | 0.213666 | − | 0.976907i | \(-0.431460\pi\) | ||||
0.213666 | + | 0.976907i | \(0.431460\pi\) | |||||||
\(938\) | 7.13711e7 | 2.64859 | ||||||||
\(939\) | −2.21689e7 | −0.820502 | ||||||||
\(940\) | 225803. | 0.00833508 | ||||||||
\(941\) | 4.50411e7 | 1.65819 | 0.829095 | − | 0.559107i | \(-0.188856\pi\) | ||||
0.829095 | + | 0.559107i | \(0.188856\pi\) | |||||||
\(942\) | −1.33430e7 | −0.489920 | ||||||||
\(943\) | 2.55731e6 | 0.0936494 | ||||||||
\(944\) | 3.67736e7 | 1.34309 | ||||||||
\(945\) | −5.70568e6 | −0.207839 | ||||||||
\(946\) | −3.15225e6 | −0.114523 | ||||||||
\(947\) | 3.18096e7 | 1.15261 | 0.576307 | − | 0.817234i | \(-0.304493\pi\) | ||||
0.576307 | + | 0.817234i | \(0.304493\pi\) | |||||||
\(948\) | −1.14211e7 | −0.412752 | ||||||||
\(949\) | 2.16006e7 | 0.778573 | ||||||||
\(950\) | −2.16466e7 | −0.778182 | ||||||||
\(951\) | 2.74202e7 | 0.983150 | ||||||||
\(952\) | −1.21936e7 | −0.436052 | ||||||||
\(953\) | −3.14562e7 | −1.12195 | −0.560975 | − | 0.827833i | \(-0.689574\pi\) | ||||
−0.560975 | + | 0.827833i | \(0.689574\pi\) | |||||||
\(954\) | 4.03068e6 | 0.143386 | ||||||||
\(955\) | −2.33869e7 | −0.829781 | ||||||||
\(956\) | −3.21720e7 | −1.13850 | ||||||||
\(957\) | −3.02615e6 | −0.106810 | ||||||||
\(958\) | 4.87393e7 | 1.71579 | ||||||||
\(959\) | −5.03473e6 | −0.176779 | ||||||||
\(960\) | 6.41863e6 | 0.224783 | ||||||||
\(961\) | 6.31993e7 | 2.20752 | ||||||||
\(962\) | −4.34412e7 | −1.51344 | ||||||||
\(963\) | 1.07533e7 | 0.373659 | ||||||||
\(964\) | −3.71065e7 | −1.28605 | ||||||||
\(965\) | −1.77388e7 | −0.613205 | ||||||||
\(966\) | −7.02091e6 | −0.242075 | ||||||||
\(967\) | −1.39347e7 | −0.479216 | −0.239608 | − | 0.970870i | \(-0.577019\pi\) | ||||
−0.239608 | + | 0.970870i | \(0.577019\pi\) | |||||||
\(968\) | 8.16245e6 | 0.279983 | ||||||||
\(969\) | −2.08109e7 | −0.712003 | ||||||||
\(970\) | −2.52347e7 | −0.861129 | ||||||||
\(971\) | −6.17798e6 | −0.210280 | −0.105140 | − | 0.994457i | \(-0.533529\pi\) | ||||
−0.105140 | + | 0.994457i | \(0.533529\pi\) | |||||||
\(972\) | −1.49018e6 | −0.0505910 | ||||||||
\(973\) | 1.54576e7 | 0.523433 | ||||||||
\(974\) | −1.94903e7 | −0.658296 | ||||||||
\(975\) | 9.59848e6 | 0.323363 | ||||||||
\(976\) | 1.03881e7 | 0.349068 | ||||||||
\(977\) | −2.28927e7 | −0.767293 | −0.383646 | − | 0.923480i | \(-0.625332\pi\) | ||||
−0.383646 | + | 0.923480i | \(0.625332\pi\) | |||||||
\(978\) | −1.51991e7 | −0.508125 | ||||||||
\(979\) | 3.04201e6 | 0.101439 | ||||||||
\(980\) | 2.14696e7 | 0.714099 | ||||||||
\(981\) | −9.15546e6 | −0.303744 | ||||||||
\(982\) | −3.35194e6 | −0.110922 | ||||||||
\(983\) | −3.76941e7 | −1.24420 | −0.622100 | − | 0.782938i | \(-0.713720\pi\) | ||||
−0.622100 | + | 0.782938i | \(0.713720\pi\) | |||||||
\(984\) | 2.22633e6 | 0.0732997 | ||||||||
\(985\) | −6.01647e6 | −0.197584 | ||||||||
\(986\) | −7.93496e7 | −2.59928 | ||||||||
\(987\) | −390917. | −0.0127730 | ||||||||
\(988\) | 3.36531e7 | 1.09681 | ||||||||
\(989\) | 5.62405e6 | 0.182835 | ||||||||
\(990\) | −964346. | −0.0312712 | ||||||||
\(991\) | −2.55042e7 | −0.824951 | −0.412475 | − | 0.910969i | \(-0.635336\pi\) | ||||
−0.412475 | + | 0.910969i | \(0.635336\pi\) | |||||||
\(992\) | 7.09211e7 | 2.28821 | ||||||||
\(993\) | 2.33493e7 | 0.751451 | ||||||||
\(994\) | −8.89016e7 | −2.85393 | ||||||||
\(995\) | −1.95323e6 | −0.0625455 | ||||||||
\(996\) | 8.10200e6 | 0.258788 | ||||||||
\(997\) | −2.40517e7 | −0.766315 | −0.383157 | − | 0.923683i | \(-0.625163\pi\) | ||||
−0.383157 | + | 0.923683i | \(0.625163\pi\) | |||||||
\(998\) | 4.81292e7 | 1.52961 | ||||||||
\(999\) | 5.93733e6 | 0.188225 |
(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.c.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 207.6.a.d.1.1 | 4 | |||
4.3 | odd | 2 | 1104.6.a.n.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.c.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
207.6.a.d.1.1 | 4 | 3.2 | odd | 2 | |||
1104.6.a.n.1.4 | 4 | 4.3 | odd | 2 |