Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8085,2,Mod(1,8085)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8085, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8085.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8085.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: | \(64.5590500342\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1155) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8085.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.732051 | −0.517638 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.46410 | −0.732051 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.732051 | −0.298858 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.53590 | 0.896575 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.732051 | −0.231495 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.46410 | −0.422650 | ||||||||
\(13\) | 4.19615 | 1.16380 | 0.581902 | − | 0.813259i | \(-0.302309\pi\) | ||||
0.581902 | + | 0.813259i | \(0.302309\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.07180 | 0.267949 | ||||||||
\(17\) | 6.46410 | 1.56777 | 0.783887 | − | 0.620903i | \(-0.213234\pi\) | ||||
0.783887 | + | 0.620903i | \(0.213234\pi\) | |||||||
\(18\) | −0.732051 | −0.172546 | ||||||||
\(19\) | 1.53590 | 0.352359 | 0.176180 | − | 0.984358i | \(-0.443626\pi\) | ||||
0.176180 | + | 0.984358i | \(0.443626\pi\) | |||||||
\(20\) | −1.46410 | −0.327383 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.732051 | 0.156074 | ||||||||
\(23\) | 8.46410 | 1.76489 | 0.882444 | − | 0.470418i | \(-0.155897\pi\) | ||||
0.882444 | + | 0.470418i | \(0.155897\pi\) | |||||||
\(24\) | 2.53590 | 0.517638 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.07180 | −0.602429 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.73205 | 1.06442 | 0.532208 | − | 0.846614i | \(-0.321363\pi\) | ||||
0.532208 | + | 0.846614i | \(0.321363\pi\) | |||||||
\(30\) | −0.732051 | −0.133654 | ||||||||
\(31\) | 5.26795 | 0.946152 | 0.473076 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473076 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(32\) | −5.85641 | −1.03528 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −4.73205 | −0.811540 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.46410 | −0.244017 | ||||||||
\(37\) | −4.19615 | −0.689843 | −0.344922 | − | 0.938631i | \(-0.612095\pi\) | ||||
−0.344922 | + | 0.938631i | \(0.612095\pi\) | |||||||
\(38\) | −1.12436 | −0.182395 | ||||||||
\(39\) | 4.19615 | 0.671922 | ||||||||
\(40\) | 2.53590 | 0.400961 | ||||||||
\(41\) | 7.66025 | 1.19633 | 0.598165 | − | 0.801373i | \(-0.295897\pi\) | ||||
0.598165 | + | 0.801373i | \(0.295897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73205 | 0.264135 | 0.132068 | − | 0.991241i | \(-0.457838\pi\) | ||||
0.132068 | + | 0.991241i | \(0.457838\pi\) | |||||||
\(44\) | 1.46410 | 0.220722 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −6.19615 | −0.913573 | ||||||||
\(47\) | −1.26795 | −0.184949 | −0.0924747 | − | 0.995715i | \(-0.529478\pi\) | ||||
−0.0924747 | + | 0.995715i | \(0.529478\pi\) | |||||||
\(48\) | 1.07180 | 0.154701 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.732051 | −0.103528 | ||||||||
\(51\) | 6.46410 | 0.905155 | ||||||||
\(52\) | −6.14359 | −0.851963 | ||||||||
\(53\) | 4.46410 | 0.613192 | 0.306596 | − | 0.951840i | \(-0.400810\pi\) | ||||
0.306596 | + | 0.951840i | \(0.400810\pi\) | |||||||
\(54\) | −0.732051 | −0.0996195 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.53590 | 0.203435 | ||||||||
\(58\) | −4.19615 | −0.550982 | ||||||||
\(59\) | −13.7321 | −1.78776 | −0.893880 | − | 0.448306i | \(-0.852028\pi\) | ||||
−0.893880 | + | 0.448306i | \(0.852028\pi\) | |||||||
\(60\) | −1.46410 | −0.189015 | ||||||||
\(61\) | −11.3923 | −1.45864 | −0.729318 | − | 0.684175i | \(-0.760162\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(62\) | −3.85641 | −0.489764 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.14359 | 0.267949 | ||||||||
\(65\) | 4.19615 | 0.520469 | ||||||||
\(66\) | 0.732051 | 0.0901092 | ||||||||
\(67\) | 4.92820 | 0.602076 | 0.301038 | − | 0.953612i | \(-0.402667\pi\) | ||||
0.301038 | + | 0.953612i | \(0.402667\pi\) | |||||||
\(68\) | −9.46410 | −1.14769 | ||||||||
\(69\) | 8.46410 | 1.01896 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.66025 | 0.909105 | 0.454552 | − | 0.890720i | \(-0.349799\pi\) | ||||
0.454552 | + | 0.890720i | \(0.349799\pi\) | |||||||
\(72\) | 2.53590 | 0.298858 | ||||||||
\(73\) | −8.39230 | −0.982245 | −0.491122 | − | 0.871091i | \(-0.663413\pi\) | ||||
−0.491122 | + | 0.871091i | \(0.663413\pi\) | |||||||
\(74\) | 3.07180 | 0.357089 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.24871 | −0.257945 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.07180 | −0.347812 | ||||||||
\(79\) | 3.66025 | 0.411811 | 0.205905 | − | 0.978572i | \(-0.433986\pi\) | ||||
0.205905 | + | 0.978572i | \(0.433986\pi\) | |||||||
\(80\) | 1.07180 | 0.119831 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.60770 | −0.619266 | ||||||||
\(83\) | −2.46410 | −0.270470 | −0.135235 | − | 0.990814i | \(-0.543179\pi\) | ||||
−0.135235 | + | 0.990814i | \(0.543179\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.46410 | 0.701130 | ||||||||
\(86\) | −1.26795 | −0.136726 | ||||||||
\(87\) | 5.73205 | 0.614540 | ||||||||
\(88\) | −2.53590 | −0.270328 | ||||||||
\(89\) | −14.6603 | −1.55398 | −0.776992 | − | 0.629511i | \(-0.783255\pi\) | ||||
−0.776992 | + | 0.629511i | \(0.783255\pi\) | |||||||
\(90\) | −0.732051 | −0.0771649 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.3923 | −1.29199 | ||||||||
\(93\) | 5.26795 | 0.546261 | ||||||||
\(94\) | 0.928203 | 0.0957369 | ||||||||
\(95\) | 1.53590 | 0.157580 | ||||||||
\(96\) | −5.85641 | −0.597717 | ||||||||
\(97\) | 2.26795 | 0.230275 | 0.115138 | − | 0.993350i | \(-0.463269\pi\) | ||||
0.115138 | + | 0.993350i | \(0.463269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −1.46410 | −0.146410 | ||||||||
\(101\) | −16.9282 | −1.68442 | −0.842210 | − | 0.539150i | \(-0.818745\pi\) | ||||
−0.842210 | + | 0.539150i | \(0.818745\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | 14.2679 | 1.40586 | 0.702931 | − | 0.711258i | \(-0.251874\pi\) | ||||
0.702931 | + | 0.711258i | \(0.251874\pi\) | |||||||
\(104\) | 10.6410 | 1.04344 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.26795 | −0.317411 | ||||||||
\(107\) | 5.26795 | 0.509272 | 0.254636 | − | 0.967037i | \(-0.418044\pi\) | ||||
0.254636 | + | 0.967037i | \(0.418044\pi\) | |||||||
\(108\) | −1.46410 | −0.140883 | ||||||||
\(109\) | −5.26795 | −0.504578 | −0.252289 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252289 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(110\) | 0.732051 | 0.0697983 | ||||||||
\(111\) | −4.19615 | −0.398281 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.8564 | 1.02128 | 0.510642 | − | 0.859793i | \(-0.329408\pi\) | ||||
0.510642 | + | 0.859793i | \(0.329408\pi\) | |||||||
\(114\) | −1.12436 | −0.105306 | ||||||||
\(115\) | 8.46410 | 0.789282 | ||||||||
\(116\) | −8.39230 | −0.779206 | ||||||||
\(117\) | 4.19615 | 0.387934 | ||||||||
\(118\) | 10.0526 | 0.925413 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.53590 | 0.231495 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.33975 | 0.755045 | ||||||||
\(123\) | 7.66025 | 0.690702 | ||||||||
\(124\) | −7.71281 | −0.692631 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.1244 | −1.96322 | −0.981610 | − | 0.190900i | \(-0.938859\pi\) | ||||
−0.981610 | + | 0.190900i | \(0.938859\pi\) | |||||||
\(128\) | 10.1436 | 0.896575 | ||||||||
\(129\) | 1.73205 | 0.152499 | ||||||||
\(130\) | −3.07180 | −0.269414 | ||||||||
\(131\) | −16.1962 | −1.41506 | −0.707532 | − | 0.706681i | \(-0.750192\pi\) | ||||
−0.707532 | + | 0.706681i | \(0.750192\pi\) | |||||||
\(132\) | 1.46410 | 0.127434 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.60770 | −0.311657 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 16.3923 | 1.40563 | ||||||||
\(137\) | −6.53590 | −0.558399 | −0.279200 | − | 0.960233i | \(-0.590069\pi\) | ||||
−0.279200 | + | 0.960233i | \(0.590069\pi\) | |||||||
\(138\) | −6.19615 | −0.527452 | ||||||||
\(139\) | −11.4641 | −0.972372 | −0.486186 | − | 0.873855i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873855i | \(0.661612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.26795 | −0.106781 | ||||||||
\(142\) | −5.60770 | −0.470587 | ||||||||
\(143\) | −4.19615 | −0.350900 | ||||||||
\(144\) | 1.07180 | 0.0893164 | ||||||||
\(145\) | 5.73205 | 0.476021 | ||||||||
\(146\) | 6.14359 | 0.508447 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.14359 | 0.505000 | ||||||||
\(149\) | 15.4641 | 1.26687 | 0.633434 | − | 0.773796i | \(-0.281645\pi\) | ||||
0.633434 | + | 0.773796i | \(0.281645\pi\) | |||||||
\(150\) | −0.732051 | −0.0597717 | ||||||||
\(151\) | −11.8564 | −0.964861 | −0.482430 | − | 0.875934i | \(-0.660246\pi\) | ||||
−0.482430 | + | 0.875934i | \(0.660246\pi\) | |||||||
\(152\) | 3.89488 | 0.315917 | ||||||||
\(153\) | 6.46410 | 0.522592 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.26795 | 0.423132 | ||||||||
\(156\) | −6.14359 | −0.491881 | ||||||||
\(157\) | 14.1244 | 1.12725 | 0.563623 | − | 0.826032i | \(-0.309407\pi\) | ||||
0.563623 | + | 0.826032i | \(0.309407\pi\) | |||||||
\(158\) | −2.67949 | −0.213169 | ||||||||
\(159\) | 4.46410 | 0.354026 | ||||||||
\(160\) | −5.85641 | −0.462990 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.732051 | −0.0575153 | ||||||||
\(163\) | 19.1244 | 1.49794 | 0.748968 | − | 0.662607i | \(-0.230550\pi\) | ||||
0.748968 | + | 0.662607i | \(0.230550\pi\) | |||||||
\(164\) | −11.2154 | −0.875775 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 1.80385 | 0.140006 | ||||||||
\(167\) | 10.3923 | 0.804181 | 0.402090 | − | 0.915600i | \(-0.368284\pi\) | ||||
0.402090 | + | 0.915600i | \(0.368284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.60770 | 0.354438 | ||||||||
\(170\) | −4.73205 | −0.362932 | ||||||||
\(171\) | 1.53590 | 0.117453 | ||||||||
\(172\) | −2.53590 | −0.193360 | ||||||||
\(173\) | 25.4641 | 1.93600 | 0.968000 | − | 0.250951i | \(-0.0807432\pi\) | ||||
0.968000 | + | 0.250951i | \(0.0807432\pi\) | |||||||
\(174\) | −4.19615 | −0.318109 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.07180 | −0.0807897 | ||||||||
\(177\) | −13.7321 | −1.03216 | ||||||||
\(178\) | 10.7321 | 0.804401 | ||||||||
\(179\) | −20.0526 | −1.49880 | −0.749399 | − | 0.662118i | \(-0.769658\pi\) | ||||
−0.749399 | + | 0.662118i | \(0.769658\pi\) | |||||||
\(180\) | −1.46410 | −0.109128 | ||||||||
\(181\) | −7.07180 | −0.525643 | −0.262821 | − | 0.964845i | \(-0.584653\pi\) | ||||
−0.262821 | + | 0.964845i | \(0.584653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3923 | −0.842143 | ||||||||
\(184\) | 21.4641 | 1.58235 | ||||||||
\(185\) | −4.19615 | −0.308507 | ||||||||
\(186\) | −3.85641 | −0.282765 | ||||||||
\(187\) | −6.46410 | −0.472702 | ||||||||
\(188\) | 1.85641 | 0.135392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.12436 | −0.0815693 | ||||||||
\(191\) | −1.07180 | −0.0775525 | −0.0387762 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387762 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(192\) | 2.14359 | 0.154701 | ||||||||
\(193\) | −7.46410 | −0.537278 | −0.268639 | − | 0.963241i | \(-0.586574\pi\) | ||||
−0.268639 | + | 0.963241i | \(0.586574\pi\) | |||||||
\(194\) | −1.66025 | −0.119199 | ||||||||
\(195\) | 4.19615 | 0.300493 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.46410 | 0.389301 | 0.194651 | − | 0.980873i | \(-0.437643\pi\) | ||||
0.194651 | + | 0.980873i | \(0.437643\pi\) | |||||||
\(198\) | 0.732051 | 0.0520246 | ||||||||
\(199\) | 14.9282 | 1.05823 | 0.529116 | − | 0.848549i | \(-0.322524\pi\) | ||||
0.529116 | + | 0.848549i | \(0.322524\pi\) | |||||||
\(200\) | 2.53590 | 0.179315 | ||||||||
\(201\) | 4.92820 | 0.347609 | ||||||||
\(202\) | 12.3923 | 0.871920 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.46410 | −0.662620 | ||||||||
\(205\) | 7.66025 | 0.535015 | ||||||||
\(206\) | −10.4449 | −0.727728 | ||||||||
\(207\) | 8.46410 | 0.588296 | ||||||||
\(208\) | 4.49742 | 0.311840 | ||||||||
\(209\) | −1.53590 | −0.106240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.53590 | 0.312264 | 0.156132 | − | 0.987736i | \(-0.450097\pi\) | ||||
0.156132 | + | 0.987736i | \(0.450097\pi\) | |||||||
\(212\) | −6.53590 | −0.448887 | ||||||||
\(213\) | 7.66025 | 0.524872 | ||||||||
\(214\) | −3.85641 | −0.263619 | ||||||||
\(215\) | 1.73205 | 0.118125 | ||||||||
\(216\) | 2.53590 | 0.172546 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.85641 | 0.261189 | ||||||||
\(219\) | −8.39230 | −0.567099 | ||||||||
\(220\) | 1.46410 | 0.0987097 | ||||||||
\(221\) | 27.1244 | 1.82458 | ||||||||
\(222\) | 3.07180 | 0.206166 | ||||||||
\(223\) | −0.803848 | −0.0538296 | −0.0269148 | − | 0.999638i | \(-0.508568\pi\) | ||||
−0.0269148 | + | 0.999638i | \(0.508568\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.94744 | −0.528656 | ||||||||
\(227\) | 5.39230 | 0.357900 | 0.178950 | − | 0.983858i | \(-0.442730\pi\) | ||||
0.178950 | + | 0.983858i | \(0.442730\pi\) | |||||||
\(228\) | −2.24871 | −0.148925 | ||||||||
\(229\) | −28.1962 | −1.86325 | −0.931627 | − | 0.363416i | \(-0.881610\pi\) | ||||
−0.931627 | + | 0.363416i | \(0.881610\pi\) | |||||||
\(230\) | −6.19615 | −0.408562 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.5359 | 0.954328 | ||||||||
\(233\) | −10.1962 | −0.667972 | −0.333986 | − | 0.942578i | \(-0.608394\pi\) | ||||
−0.333986 | + | 0.942578i | \(0.608394\pi\) | |||||||
\(234\) | −3.07180 | −0.200810 | ||||||||
\(235\) | −1.26795 | −0.0827119 | ||||||||
\(236\) | 20.1051 | 1.30873 | ||||||||
\(237\) | 3.66025 | 0.237759 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.1244 | 1.17237 | 0.586184 | − | 0.810178i | \(-0.300630\pi\) | ||||
0.586184 | + | 0.810178i | \(0.300630\pi\) | |||||||
\(240\) | 1.07180 | 0.0691842 | ||||||||
\(241\) | −26.9282 | −1.73460 | −0.867299 | − | 0.497788i | \(-0.834146\pi\) | ||||
−0.867299 | + | 0.497788i | \(0.834146\pi\) | |||||||
\(242\) | −0.732051 | −0.0470580 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 16.6795 | 1.06780 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.60770 | −0.357534 | ||||||||
\(247\) | 6.44486 | 0.410077 | ||||||||
\(248\) | 13.3590 | 0.848296 | ||||||||
\(249\) | −2.46410 | −0.156156 | ||||||||
\(250\) | −0.732051 | −0.0462990 | ||||||||
\(251\) | 6.92820 | 0.437304 | 0.218652 | − | 0.975803i | \(-0.429834\pi\) | ||||
0.218652 | + | 0.975803i | \(0.429834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.46410 | −0.532134 | ||||||||
\(254\) | 16.1962 | 1.01624 | ||||||||
\(255\) | 6.46410 | 0.404798 | ||||||||
\(256\) | −11.7128 | −0.732051 | ||||||||
\(257\) | −13.8038 | −0.861060 | −0.430530 | − | 0.902576i | \(-0.641673\pi\) | ||||
−0.430530 | + | 0.902576i | \(0.641673\pi\) | |||||||
\(258\) | −1.26795 | −0.0789391 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.14359 | −0.381009 | ||||||||
\(261\) | 5.73205 | 0.354805 | ||||||||
\(262\) | 11.8564 | 0.732491 | ||||||||
\(263\) | 11.3205 | 0.698052 | 0.349026 | − | 0.937113i | \(-0.386512\pi\) | ||||
0.349026 | + | 0.937113i | \(0.386512\pi\) | |||||||
\(264\) | −2.53590 | −0.156074 | ||||||||
\(265\) | 4.46410 | 0.274228 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.6603 | −0.897193 | ||||||||
\(268\) | −7.21539 | −0.440750 | ||||||||
\(269\) | −7.58846 | −0.462676 | −0.231338 | − | 0.972873i | \(-0.574310\pi\) | ||||
−0.231338 | + | 0.972873i | \(0.574310\pi\) | |||||||
\(270\) | −0.732051 | −0.0445512 | ||||||||
\(271\) | 17.9282 | 1.08906 | 0.544530 | − | 0.838741i | \(-0.316708\pi\) | ||||
0.544530 | + | 0.838741i | \(0.316708\pi\) | |||||||
\(272\) | 6.92820 | 0.420084 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.78461 | 0.289049 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −12.3923 | −0.745929 | ||||||||
\(277\) | −9.07180 | −0.545071 | −0.272536 | − | 0.962146i | \(-0.587862\pi\) | ||||
−0.272536 | + | 0.962146i | \(0.587862\pi\) | |||||||
\(278\) | 8.39230 | 0.503337 | ||||||||
\(279\) | 5.26795 | 0.315384 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0718 | 1.01842 | 0.509209 | − | 0.860643i | \(-0.329938\pi\) | ||||
0.509209 | + | 0.860643i | \(0.329938\pi\) | |||||||
\(282\) | 0.928203 | 0.0552737 | ||||||||
\(283\) | 0.196152 | 0.0116601 | 0.00583003 | − | 0.999983i | \(-0.498144\pi\) | ||||
0.00583003 | + | 0.999983i | \(0.498144\pi\) | |||||||
\(284\) | −11.2154 | −0.665511 | ||||||||
\(285\) | 1.53590 | 0.0909788 | ||||||||
\(286\) | 3.07180 | 0.181639 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.85641 | −0.345092 | ||||||||
\(289\) | 24.7846 | 1.45792 | ||||||||
\(290\) | −4.19615 | −0.246407 | ||||||||
\(291\) | 2.26795 | 0.132950 | ||||||||
\(292\) | 12.2872 | 0.719053 | ||||||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7321 | −0.799511 | ||||||||
\(296\) | −10.6410 | −0.618497 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −11.3205 | −0.655779 | ||||||||
\(299\) | 35.5167 | 2.05398 | ||||||||
\(300\) | −1.46410 | −0.0845299 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.67949 | 0.499449 | ||||||||
\(303\) | −16.9282 | −0.972500 | ||||||||
\(304\) | 1.64617 | 0.0944144 | ||||||||
\(305\) | −11.3923 | −0.652321 | ||||||||
\(306\) | −4.73205 | −0.270513 | ||||||||
\(307\) | 10.3923 | 0.593120 | 0.296560 | − | 0.955014i | \(-0.404160\pi\) | ||||
0.296560 | + | 0.955014i | \(0.404160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.2679 | 0.811675 | ||||||||
\(310\) | −3.85641 | −0.219029 | ||||||||
\(311\) | −7.32051 | −0.415108 | −0.207554 | − | 0.978224i | \(-0.566550\pi\) | ||||
−0.207554 | + | 0.978224i | \(0.566550\pi\) | |||||||
\(312\) | 10.6410 | 0.602429 | ||||||||
\(313\) | −1.73205 | −0.0979013 | −0.0489506 | − | 0.998801i | \(-0.515588\pi\) | ||||
−0.0489506 | + | 0.998801i | \(0.515588\pi\) | |||||||
\(314\) | −10.3397 | −0.583506 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.35898 | −0.301466 | ||||||||
\(317\) | 18.9282 | 1.06311 | 0.531557 | − | 0.847023i | \(-0.321607\pi\) | ||||
0.531557 | + | 0.847023i | \(0.321607\pi\) | |||||||
\(318\) | −3.26795 | −0.183257 | ||||||||
\(319\) | −5.73205 | −0.320933 | ||||||||
\(320\) | 2.14359 | 0.119831 | ||||||||
\(321\) | 5.26795 | 0.294028 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.92820 | 0.552420 | ||||||||
\(324\) | −1.46410 | −0.0813390 | ||||||||
\(325\) | 4.19615 | 0.232761 | ||||||||
\(326\) | −14.0000 | −0.775388 | ||||||||
\(327\) | −5.26795 | −0.291318 | ||||||||
\(328\) | 19.4256 | 1.07260 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.732051 | 0.0402981 | ||||||||
\(331\) | 8.32051 | 0.457336 | 0.228668 | − | 0.973504i | \(-0.426563\pi\) | ||||
0.228668 | + | 0.973504i | \(0.426563\pi\) | |||||||
\(332\) | 3.60770 | 0.197998 | ||||||||
\(333\) | −4.19615 | −0.229948 | ||||||||
\(334\) | −7.60770 | −0.416275 | ||||||||
\(335\) | 4.92820 | 0.269257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6603 | −0.580701 | −0.290351 | − | 0.956920i | \(-0.593772\pi\) | ||||
−0.290351 | + | 0.956920i | \(0.593772\pi\) | |||||||
\(338\) | −3.37307 | −0.183471 | ||||||||
\(339\) | 10.8564 | 0.589639 | ||||||||
\(340\) | −9.46410 | −0.513263 | ||||||||
\(341\) | −5.26795 | −0.285275 | ||||||||
\(342\) | −1.12436 | −0.0607982 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.39230 | 0.236817 | ||||||||
\(345\) | 8.46410 | 0.455692 | ||||||||
\(346\) | −18.6410 | −1.00215 | ||||||||
\(347\) | −1.46410 | −0.0785971 | −0.0392985 | − | 0.999228i | \(-0.512512\pi\) | ||||
−0.0392985 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(348\) | −8.39230 | −0.449875 | ||||||||
\(349\) | 15.0000 | 0.802932 | 0.401466 | − | 0.915874i | \(-0.368501\pi\) | ||||
0.401466 | + | 0.915874i | \(0.368501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.19615 | 0.223974 | ||||||||
\(352\) | 5.85641 | 0.312148 | ||||||||
\(353\) | −15.4641 | −0.823071 | −0.411536 | − | 0.911394i | \(-0.635007\pi\) | ||||
−0.411536 | + | 0.911394i | \(0.635007\pi\) | |||||||
\(354\) | 10.0526 | 0.534287 | ||||||||
\(355\) | 7.66025 | 0.406564 | ||||||||
\(356\) | 21.4641 | 1.13760 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.6795 | 0.775835 | ||||||||
\(359\) | −34.5167 | −1.82172 | −0.910860 | − | 0.412716i | \(-0.864580\pi\) | ||||
−0.910860 | + | 0.412716i | \(0.864580\pi\) | |||||||
\(360\) | 2.53590 | 0.133654 | ||||||||
\(361\) | −16.6410 | −0.875843 | ||||||||
\(362\) | 5.17691 | 0.272093 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.39230 | −0.439273 | ||||||||
\(366\) | 8.33975 | 0.435926 | ||||||||
\(367\) | −16.8038 | −0.877154 | −0.438577 | − | 0.898694i | \(-0.644517\pi\) | ||||
−0.438577 | + | 0.898694i | \(0.644517\pi\) | |||||||
\(368\) | 9.07180 | 0.472900 | ||||||||
\(369\) | 7.66025 | 0.398777 | ||||||||
\(370\) | 3.07180 | 0.159695 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.71281 | −0.399891 | ||||||||
\(373\) | 29.1962 | 1.51172 | 0.755860 | − | 0.654734i | \(-0.227219\pi\) | ||||
0.755860 | + | 0.654734i | \(0.227219\pi\) | |||||||
\(374\) | 4.73205 | 0.244689 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −3.21539 | −0.165821 | ||||||||
\(377\) | 24.0526 | 1.23877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8564 | 1.07132 | 0.535661 | − | 0.844433i | \(-0.320063\pi\) | ||||
0.535661 | + | 0.844433i | \(0.320063\pi\) | |||||||
\(380\) | −2.24871 | −0.115356 | ||||||||
\(381\) | −22.1244 | −1.13347 | ||||||||
\(382\) | 0.784610 | 0.0401441 | ||||||||
\(383\) | −32.7321 | −1.67253 | −0.836265 | − | 0.548326i | \(-0.815265\pi\) | ||||
−0.836265 | + | 0.548326i | \(0.815265\pi\) | |||||||
\(384\) | 10.1436 | 0.517638 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.46410 | 0.278115 | ||||||||
\(387\) | 1.73205 | 0.0880451 | ||||||||
\(388\) | −3.32051 | −0.168573 | ||||||||
\(389\) | −15.5167 | −0.786726 | −0.393363 | − | 0.919383i | \(-0.628688\pi\) | ||||
−0.393363 | + | 0.919383i | \(0.628688\pi\) | |||||||
\(390\) | −3.07180 | −0.155546 | ||||||||
\(391\) | 54.7128 | 2.76695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.1962 | −0.816988 | ||||||||
\(394\) | −4.00000 | −0.201517 | ||||||||
\(395\) | 3.66025 | 0.184167 | ||||||||
\(396\) | 1.46410 | 0.0735739 | ||||||||
\(397\) | −37.8564 | −1.89996 | −0.949979 | − | 0.312313i | \(-0.898896\pi\) | ||||
−0.949979 | + | 0.312313i | \(0.898896\pi\) | |||||||
\(398\) | −10.9282 | −0.547781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.07180 | 0.0535898 | ||||||||
\(401\) | −33.1244 | −1.65415 | −0.827076 | − | 0.562091i | \(-0.809997\pi\) | ||||
−0.827076 | + | 0.562091i | \(0.809997\pi\) | |||||||
\(402\) | −3.60770 | −0.179935 | ||||||||
\(403\) | 22.1051 | 1.10113 | ||||||||
\(404\) | 24.7846 | 1.23308 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.19615 | 0.207996 | ||||||||
\(408\) | 16.3923 | 0.811540 | ||||||||
\(409\) | 9.07180 | 0.448571 | 0.224286 | − | 0.974523i | \(-0.427995\pi\) | ||||
0.224286 | + | 0.974523i | \(0.427995\pi\) | |||||||
\(410\) | −5.60770 | −0.276944 | ||||||||
\(411\) | −6.53590 | −0.322392 | ||||||||
\(412\) | −20.8897 | −1.02916 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.19615 | −0.304524 | ||||||||
\(415\) | −2.46410 | −0.120958 | ||||||||
\(416\) | −24.5744 | −1.20486 | ||||||||
\(417\) | −11.4641 | −0.561399 | ||||||||
\(418\) | 1.12436 | 0.0549940 | ||||||||
\(419\) | −29.7321 | −1.45251 | −0.726253 | − | 0.687428i | \(-0.758740\pi\) | ||||
−0.726253 | + | 0.687428i | \(0.758740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.7128 | 1.20443 | 0.602214 | − | 0.798334i | \(-0.294285\pi\) | ||||
0.602214 | + | 0.798334i | \(0.294285\pi\) | |||||||
\(422\) | −3.32051 | −0.161640 | ||||||||
\(423\) | −1.26795 | −0.0616498 | ||||||||
\(424\) | 11.3205 | 0.549772 | ||||||||
\(425\) | 6.46410 | 0.313555 | ||||||||
\(426\) | −5.60770 | −0.271694 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.71281 | −0.372813 | ||||||||
\(429\) | −4.19615 | −0.202592 | ||||||||
\(430\) | −1.26795 | −0.0611459 | ||||||||
\(431\) | −24.3923 | −1.17494 | −0.587468 | − | 0.809247i | \(-0.699875\pi\) | ||||
−0.587468 | + | 0.809247i | \(0.699875\pi\) | |||||||
\(432\) | 1.07180 | 0.0515668 | ||||||||
\(433\) | −9.32051 | −0.447915 | −0.223958 | − | 0.974599i | \(-0.571898\pi\) | ||||
−0.223958 | + | 0.974599i | \(0.571898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.73205 | 0.274831 | ||||||||
\(436\) | 7.71281 | 0.369377 | ||||||||
\(437\) | 13.0000 | 0.621874 | ||||||||
\(438\) | 6.14359 | 0.293552 | ||||||||
\(439\) | 26.7128 | 1.27493 | 0.637467 | − | 0.770478i | \(-0.279982\pi\) | ||||
0.637467 | + | 0.770478i | \(0.279982\pi\) | |||||||
\(440\) | −2.53590 | −0.120894 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.8564 | −0.944473 | ||||||||
\(443\) | −23.4641 | −1.11481 | −0.557407 | − | 0.830240i | \(-0.688204\pi\) | ||||
−0.557407 | + | 0.830240i | \(0.688204\pi\) | |||||||
\(444\) | 6.14359 | 0.291562 | ||||||||
\(445\) | −14.6603 | −0.694963 | ||||||||
\(446\) | 0.588457 | 0.0278643 | ||||||||
\(447\) | 15.4641 | 0.731427 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0526 | 0.757567 | 0.378784 | − | 0.925485i | \(-0.376342\pi\) | ||||
0.378784 | + | 0.925485i | \(0.376342\pi\) | |||||||
\(450\) | −0.732051 | −0.0345092 | ||||||||
\(451\) | −7.66025 | −0.360707 | ||||||||
\(452\) | −15.8949 | −0.747632 | ||||||||
\(453\) | −11.8564 | −0.557063 | ||||||||
\(454\) | −3.94744 | −0.185263 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.89488 | 0.182395 | ||||||||
\(457\) | −2.66025 | −0.124441 | −0.0622207 | − | 0.998062i | \(-0.519818\pi\) | ||||
−0.0622207 | + | 0.998062i | \(0.519818\pi\) | |||||||
\(458\) | 20.6410 | 0.964491 | ||||||||
\(459\) | 6.46410 | 0.301718 | ||||||||
\(460\) | −12.3923 | −0.577794 | ||||||||
\(461\) | −29.3205 | −1.36559 | −0.682796 | − | 0.730609i | \(-0.739236\pi\) | ||||
−0.682796 | + | 0.730609i | \(0.739236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5359 | 0.582593 | 0.291296 | − | 0.956633i | \(-0.405913\pi\) | ||||
0.291296 | + | 0.956633i | \(0.405913\pi\) | |||||||
\(464\) | 6.14359 | 0.285209 | ||||||||
\(465\) | 5.26795 | 0.244295 | ||||||||
\(466\) | 7.46410 | 0.345768 | ||||||||
\(467\) | 27.3205 | 1.26424 | 0.632121 | − | 0.774870i | \(-0.282184\pi\) | ||||
0.632121 | + | 0.774870i | \(0.282184\pi\) | |||||||
\(468\) | −6.14359 | −0.283988 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.928203 | 0.0428148 | ||||||||
\(471\) | 14.1244 | 0.650816 | ||||||||
\(472\) | −34.8231 | −1.60286 | ||||||||
\(473\) | −1.73205 | −0.0796398 | ||||||||
\(474\) | −2.67949 | −0.123073 | ||||||||
\(475\) | 1.53590 | 0.0704719 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.46410 | 0.204397 | ||||||||
\(478\) | −13.2679 | −0.606862 | ||||||||
\(479\) | 6.73205 | 0.307595 | 0.153798 | − | 0.988102i | \(-0.450850\pi\) | ||||
0.153798 | + | 0.988102i | \(0.450850\pi\) | |||||||
\(480\) | −5.85641 | −0.267307 | ||||||||
\(481\) | −17.6077 | −0.802842 | ||||||||
\(482\) | 19.7128 | 0.897894 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46410 | −0.0665501 | ||||||||
\(485\) | 2.26795 | 0.102982 | ||||||||
\(486\) | −0.732051 | −0.0332065 | ||||||||
\(487\) | 0.535898 | 0.0242839 | 0.0121419 | − | 0.999926i | \(-0.496135\pi\) | ||||
0.0121419 | + | 0.999926i | \(0.496135\pi\) | |||||||
\(488\) | −28.8897 | −1.30778 | ||||||||
\(489\) | 19.1244 | 0.864833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.33975 | 0.150721 | 0.0753603 | − | 0.997156i | \(-0.475989\pi\) | ||||
0.0753603 | + | 0.997156i | \(0.475989\pi\) | |||||||
\(492\) | −11.2154 | −0.505629 | ||||||||
\(493\) | 37.0526 | 1.66876 | ||||||||
\(494\) | −4.71797 | −0.212271 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 5.64617 | 0.253521 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.80385 | 0.0808323 | ||||||||
\(499\) | 29.3923 | 1.31578 | 0.657890 | − | 0.753114i | \(-0.271449\pi\) | ||||
0.657890 | + | 0.753114i | \(0.271449\pi\) | |||||||
\(500\) | −1.46410 | −0.0654766 | ||||||||
\(501\) | 10.3923 | 0.464294 | ||||||||
\(502\) | −5.07180 | −0.226365 | ||||||||
\(503\) | 23.0000 | 1.02552 | 0.512760 | − | 0.858532i | \(-0.328623\pi\) | ||||
0.512760 | + | 0.858532i | \(0.328623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9282 | −0.753295 | ||||||||
\(506\) | 6.19615 | 0.275453 | ||||||||
\(507\) | 4.60770 | 0.204635 | ||||||||
\(508\) | 32.3923 | 1.43718 | ||||||||
\(509\) | 17.1962 | 0.762206 | 0.381103 | − | 0.924533i | \(-0.375544\pi\) | ||||
0.381103 | + | 0.924533i | \(0.375544\pi\) | |||||||
\(510\) | −4.73205 | −0.209539 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.7128 | −0.517638 | ||||||||
\(513\) | 1.53590 | 0.0678116 | ||||||||
\(514\) | 10.1051 | 0.445718 | ||||||||
\(515\) | 14.2679 | 0.628721 | ||||||||
\(516\) | −2.53590 | −0.111637 | ||||||||
\(517\) | 1.26795 | 0.0557643 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.4641 | 1.11775 | ||||||||
\(520\) | 10.6410 | 0.466639 | ||||||||
\(521\) | 9.05256 | 0.396600 | 0.198300 | − | 0.980141i | \(-0.436458\pi\) | ||||
0.198300 | + | 0.980141i | \(0.436458\pi\) | |||||||
\(522\) | −4.19615 | −0.183661 | ||||||||
\(523\) | 27.3205 | 1.19464 | 0.597321 | − | 0.802002i | \(-0.296232\pi\) | ||||
0.597321 | + | 0.802002i | \(0.296232\pi\) | |||||||
\(524\) | 23.7128 | 1.03590 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.28719 | −0.361339 | ||||||||
\(527\) | 34.0526 | 1.48335 | ||||||||
\(528\) | −1.07180 | −0.0466440 | ||||||||
\(529\) | 48.6410 | 2.11483 | ||||||||
\(530\) | −3.26795 | −0.141951 | ||||||||
\(531\) | −13.7321 | −0.595920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.1436 | 1.39229 | ||||||||
\(534\) | 10.7321 | 0.464421 | ||||||||
\(535\) | 5.26795 | 0.227753 | ||||||||
\(536\) | 12.4974 | 0.539806 | ||||||||
\(537\) | −20.0526 | −0.865332 | ||||||||
\(538\) | 5.55514 | 0.239499 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.46410 | −0.0630049 | ||||||||
\(541\) | −34.0526 | −1.46403 | −0.732017 | − | 0.681286i | \(-0.761421\pi\) | ||||
−0.732017 | + | 0.681286i | \(0.761421\pi\) | |||||||
\(542\) | −13.1244 | −0.563739 | ||||||||
\(543\) | −7.07180 | −0.303480 | ||||||||
\(544\) | −37.8564 | −1.62308 | ||||||||
\(545\) | −5.26795 | −0.225654 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.5885 | 1.00857 | 0.504285 | − | 0.863537i | \(-0.331756\pi\) | ||||
0.504285 | + | 0.863537i | \(0.331756\pi\) | |||||||
\(548\) | 9.56922 | 0.408777 | ||||||||
\(549\) | −11.3923 | −0.486212 | ||||||||
\(550\) | 0.732051 | 0.0312148 | ||||||||
\(551\) | 8.80385 | 0.375057 | ||||||||
\(552\) | 21.4641 | 0.913573 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.64102 | 0.282150 | ||||||||
\(555\) | −4.19615 | −0.178117 | ||||||||
\(556\) | 16.7846 | 0.711826 | ||||||||
\(557\) | 8.53590 | 0.361678 | 0.180839 | − | 0.983513i | \(-0.442119\pi\) | ||||
0.180839 | + | 0.983513i | \(0.442119\pi\) | |||||||
\(558\) | −3.85641 | −0.163255 | ||||||||
\(559\) | 7.26795 | 0.307401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.46410 | −0.272915 | ||||||||
\(562\) | −12.4974 | −0.527172 | ||||||||
\(563\) | 24.9282 | 1.05060 | 0.525299 | − | 0.850918i | \(-0.323953\pi\) | ||||
0.525299 | + | 0.850918i | \(0.323953\pi\) | |||||||
\(564\) | 1.85641 | 0.0781688 | ||||||||
\(565\) | 10.8564 | 0.456732 | ||||||||
\(566\) | −0.143594 | −0.00603569 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.4256 | 0.815081 | ||||||||
\(569\) | −4.66025 | −0.195368 | −0.0976840 | − | 0.995217i | \(-0.531143\pi\) | ||||
−0.0976840 | + | 0.995217i | \(0.531143\pi\) | |||||||
\(570\) | −1.12436 | −0.0470941 | ||||||||
\(571\) | 17.1244 | 0.716632 | 0.358316 | − | 0.933600i | \(-0.383351\pi\) | ||||
0.358316 | + | 0.933600i | \(0.383351\pi\) | |||||||
\(572\) | 6.14359 | 0.256877 | ||||||||
\(573\) | −1.07180 | −0.0447750 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.46410 | 0.352977 | ||||||||
\(576\) | 2.14359 | 0.0893164 | ||||||||
\(577\) | 7.07180 | 0.294403 | 0.147201 | − | 0.989107i | \(-0.452973\pi\) | ||||
0.147201 | + | 0.989107i | \(0.452973\pi\) | |||||||
\(578\) | −18.1436 | −0.754674 | ||||||||
\(579\) | −7.46410 | −0.310197 | ||||||||
\(580\) | −8.39230 | −0.348471 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.66025 | −0.0688197 | ||||||||
\(583\) | −4.46410 | −0.184884 | ||||||||
\(584\) | −21.2820 | −0.880657 | ||||||||
\(585\) | 4.19615 | 0.173490 | ||||||||
\(586\) | 6.58846 | 0.272167 | ||||||||
\(587\) | 18.5885 | 0.767228 | 0.383614 | − | 0.923494i | \(-0.374679\pi\) | ||||
0.383614 | + | 0.923494i | \(0.374679\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.09103 | 0.333385 | ||||||||
\(590\) | 10.0526 | 0.413857 | ||||||||
\(591\) | 5.46410 | 0.224763 | ||||||||
\(592\) | −4.49742 | −0.184843 | ||||||||
\(593\) | −16.0000 | −0.657041 | −0.328521 | − | 0.944497i | \(-0.606550\pi\) | ||||
−0.328521 | + | 0.944497i | \(0.606550\pi\) | |||||||
\(594\) | 0.732051 | 0.0300364 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.6410 | −0.927412 | ||||||||
\(597\) | 14.9282 | 0.610971 | ||||||||
\(598\) | −26.0000 | −1.06322 | ||||||||
\(599\) | 28.2487 | 1.15421 | 0.577106 | − | 0.816670i | \(-0.304182\pi\) | ||||
0.577106 | + | 0.816670i | \(0.304182\pi\) | |||||||
\(600\) | 2.53590 | 0.103528 | ||||||||
\(601\) | −17.7846 | −0.725449 | −0.362725 | − | 0.931896i | \(-0.618153\pi\) | ||||
−0.362725 | + | 0.931896i | \(0.618153\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.92820 | 0.200692 | ||||||||
\(604\) | 17.3590 | 0.706327 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 12.3923 | 0.503403 | ||||||||
\(607\) | −23.1769 | −0.940722 | −0.470361 | − | 0.882474i | \(-0.655876\pi\) | ||||
−0.470361 | + | 0.882474i | \(0.655876\pi\) | |||||||
\(608\) | −8.99485 | −0.364789 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.33975 | 0.337666 | ||||||||
\(611\) | −5.32051 | −0.215245 | ||||||||
\(612\) | −9.46410 | −0.382564 | ||||||||
\(613\) | 34.7846 | 1.40494 | 0.702469 | − | 0.711715i | \(-0.252081\pi\) | ||||
0.702469 | + | 0.711715i | \(0.252081\pi\) | |||||||
\(614\) | −7.60770 | −0.307022 | ||||||||
\(615\) | 7.66025 | 0.308891 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.6410 | −1.87770 | −0.938848 | − | 0.344331i | \(-0.888106\pi\) | ||||
−0.938848 | + | 0.344331i | \(0.888106\pi\) | |||||||
\(618\) | −10.4449 | −0.420154 | ||||||||
\(619\) | 24.9282 | 1.00195 | 0.500975 | − | 0.865462i | \(-0.332975\pi\) | ||||
0.500975 | + | 0.865462i | \(0.332975\pi\) | |||||||
\(620\) | −7.71281 | −0.309754 | ||||||||
\(621\) | 8.46410 | 0.339653 | ||||||||
\(622\) | 5.35898 | 0.214876 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.49742 | 0.180041 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.26795 | 0.0506774 | ||||||||
\(627\) | −1.53590 | −0.0613379 | ||||||||
\(628\) | −20.6795 | −0.825202 | ||||||||
\(629\) | −27.1244 | −1.08152 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.7128 | −0.665327 | −0.332663 | − | 0.943046i | \(-0.607947\pi\) | ||||
−0.332663 | + | 0.943046i | \(0.607947\pi\) | |||||||
\(632\) | 9.28203 | 0.369219 | ||||||||
\(633\) | 4.53590 | 0.180286 | ||||||||
\(634\) | −13.8564 | −0.550308 | ||||||||
\(635\) | −22.1244 | −0.877978 | ||||||||
\(636\) | −6.53590 | −0.259165 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.19615 | 0.166127 | ||||||||
\(639\) | 7.66025 | 0.303035 | ||||||||
\(640\) | 10.1436 | 0.400961 | ||||||||
\(641\) | −28.6410 | −1.13125 | −0.565626 | − | 0.824662i | \(-0.691365\pi\) | ||||
−0.565626 | + | 0.824662i | \(0.691365\pi\) | |||||||
\(642\) | −3.85641 | −0.152200 | ||||||||
\(643\) | 6.80385 | 0.268318 | 0.134159 | − | 0.990960i | \(-0.457167\pi\) | ||||
0.134159 | + | 0.990960i | \(0.457167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.73205 | 0.0681994 | ||||||||
\(646\) | −7.26795 | −0.285954 | ||||||||
\(647\) | −44.1051 | −1.73395 | −0.866976 | − | 0.498351i | \(-0.833939\pi\) | ||||
−0.866976 | + | 0.498351i | \(0.833939\pi\) | |||||||
\(648\) | 2.53590 | 0.0996195 | ||||||||
\(649\) | 13.7321 | 0.539030 | ||||||||
\(650\) | −3.07180 | −0.120486 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −28.0000 | −1.09656 | ||||||||
\(653\) | −29.5359 | −1.15583 | −0.577915 | − | 0.816097i | \(-0.696133\pi\) | ||||
−0.577915 | + | 0.816097i | \(0.696133\pi\) | |||||||
\(654\) | 3.85641 | 0.150797 | ||||||||
\(655\) | −16.1962 | −0.632836 | ||||||||
\(656\) | 8.21024 | 0.320556 | ||||||||
\(657\) | −8.39230 | −0.327415 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.1244 | −1.17348 | −0.586739 | − | 0.809776i | \(-0.699589\pi\) | ||||
−0.586739 | + | 0.809776i | \(0.699589\pi\) | |||||||
\(660\) | 1.46410 | 0.0569901 | ||||||||
\(661\) | 2.73205 | 0.106264 | 0.0531322 | − | 0.998587i | \(-0.483080\pi\) | ||||
0.0531322 | + | 0.998587i | \(0.483080\pi\) | |||||||
\(662\) | −6.09103 | −0.236735 | ||||||||
\(663\) | 27.1244 | 1.05342 | ||||||||
\(664\) | −6.24871 | −0.242497 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.07180 | 0.119030 | ||||||||
\(667\) | 48.5167 | 1.87857 | ||||||||
\(668\) | −15.2154 | −0.588701 | ||||||||
\(669\) | −0.803848 | −0.0310785 | ||||||||
\(670\) | −3.60770 | −0.139377 | ||||||||
\(671\) | 11.3923 | 0.439795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5885 | −0.677985 | −0.338993 | − | 0.940789i | \(-0.610086\pi\) | ||||
−0.338993 | + | 0.940789i | \(0.610086\pi\) | |||||||
\(674\) | 7.80385 | 0.300593 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −6.74613 | −0.259467 | ||||||||
\(677\) | 39.2487 | 1.50845 | 0.754225 | − | 0.656616i | \(-0.228013\pi\) | ||||
0.754225 | + | 0.656616i | \(0.228013\pi\) | |||||||
\(678\) | −7.94744 | −0.305220 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.3923 | 0.628616 | ||||||||
\(681\) | 5.39230 | 0.206634 | ||||||||
\(682\) | 3.85641 | 0.147669 | ||||||||
\(683\) | −46.9282 | −1.79566 | −0.897829 | − | 0.440344i | \(-0.854856\pi\) | ||||
−0.897829 | + | 0.440344i | \(0.854856\pi\) | |||||||
\(684\) | −2.24871 | −0.0859816 | ||||||||
\(685\) | −6.53590 | −0.249724 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.1962 | −1.07575 | ||||||||
\(688\) | 1.85641 | 0.0707748 | ||||||||
\(689\) | 18.7321 | 0.713634 | ||||||||
\(690\) | −6.19615 | −0.235883 | ||||||||
\(691\) | 26.0000 | 0.989087 | 0.494543 | − | 0.869153i | \(-0.335335\pi\) | ||||
0.494543 | + | 0.869153i | \(0.335335\pi\) | |||||||
\(692\) | −37.2820 | −1.41725 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.07180 | 0.0406848 | ||||||||
\(695\) | −11.4641 | −0.434858 | ||||||||
\(696\) | 14.5359 | 0.550982 | ||||||||
\(697\) | 49.5167 | 1.87558 | ||||||||
\(698\) | −10.9808 | −0.415628 | ||||||||
\(699\) | −10.1962 | −0.385654 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.1962 | 1.25380 | 0.626901 | − | 0.779099i | \(-0.284323\pi\) | ||||
0.626901 | + | 0.779099i | \(0.284323\pi\) | |||||||
\(702\) | −3.07180 | −0.115937 | ||||||||
\(703\) | −6.44486 | −0.243073 | ||||||||
\(704\) | −2.14359 | −0.0807897 | ||||||||
\(705\) | −1.26795 | −0.0477537 | ||||||||
\(706\) | 11.3205 | 0.426053 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20.1051 | 0.755597 | ||||||||
\(709\) | 36.4641 | 1.36944 | 0.684719 | − | 0.728807i | \(-0.259925\pi\) | ||||
0.684719 | + | 0.728807i | \(0.259925\pi\) | |||||||
\(710\) | −5.60770 | −0.210453 | ||||||||
\(711\) | 3.66025 | 0.137270 | ||||||||
\(712\) | −37.1769 | −1.39326 | ||||||||
\(713\) | 44.5885 | 1.66985 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.19615 | −0.156927 | ||||||||
\(716\) | 29.3590 | 1.09720 | ||||||||
\(717\) | 18.1244 | 0.676866 | ||||||||
\(718\) | 25.2679 | 0.942991 | ||||||||
\(719\) | −32.6603 | −1.21802 | −0.609011 | − | 0.793162i | \(-0.708433\pi\) | ||||
−0.609011 | + | 0.793162i | \(0.708433\pi\) | |||||||
\(720\) | 1.07180 | 0.0399435 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.1821 | 0.453370 | ||||||||
\(723\) | −26.9282 | −1.00147 | ||||||||
\(724\) | 10.3538 | 0.384797 | ||||||||
\(725\) | 5.73205 | 0.212883 | ||||||||
\(726\) | −0.732051 | −0.0271690 | ||||||||
\(727\) | −42.9090 | −1.59141 | −0.795703 | − | 0.605687i | \(-0.792898\pi\) | ||||
−0.795703 | + | 0.605687i | \(0.792898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.14359 | 0.227385 | ||||||||
\(731\) | 11.1962 | 0.414105 | ||||||||
\(732\) | 16.6795 | 0.616492 | ||||||||
\(733\) | −51.1769 | −1.89026 | −0.945131 | − | 0.326691i | \(-0.894066\pi\) | ||||
−0.945131 | + | 0.326691i | \(0.894066\pi\) | |||||||
\(734\) | 12.3013 | 0.454048 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −49.5692 | −1.82715 | ||||||||
\(737\) | −4.92820 | −0.181533 | ||||||||
\(738\) | −5.60770 | −0.206422 | ||||||||
\(739\) | 8.53590 | 0.313998 | 0.156999 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.156999 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(740\) | 6.14359 | 0.225843 | ||||||||
\(741\) | 6.44486 | 0.236758 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.1769 | 0.703533 | 0.351766 | − | 0.936088i | \(-0.385581\pi\) | ||||
0.351766 | + | 0.936088i | \(0.385581\pi\) | |||||||
\(744\) | 13.3590 | 0.489764 | ||||||||
\(745\) | 15.4641 | 0.566561 | ||||||||
\(746\) | −21.3731 | −0.782524 | ||||||||
\(747\) | −2.46410 | −0.0901568 | ||||||||
\(748\) | 9.46410 | 0.346042 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.732051 | −0.0267307 | ||||||||
\(751\) | 16.3205 | 0.595544 | 0.297772 | − | 0.954637i | \(-0.403757\pi\) | ||||
0.297772 | + | 0.954637i | \(0.403757\pi\) | |||||||
\(752\) | −1.35898 | −0.0495570 | ||||||||
\(753\) | 6.92820 | 0.252478 | ||||||||
\(754\) | −17.6077 | −0.641234 | ||||||||
\(755\) | −11.8564 | −0.431499 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.53590 | 0.310243 | 0.155121 | − | 0.987895i | \(-0.450423\pi\) | ||||
0.155121 | + | 0.987895i | \(0.450423\pi\) | |||||||
\(758\) | −15.2679 | −0.554557 | ||||||||
\(759\) | −8.46410 | −0.307227 | ||||||||
\(760\) | 3.89488 | 0.141282 | ||||||||
\(761\) | 11.0718 | 0.401352 | 0.200676 | − | 0.979658i | \(-0.435686\pi\) | ||||
0.200676 | + | 0.979658i | \(0.435686\pi\) | |||||||
\(762\) | 16.1962 | 0.586725 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.56922 | 0.0567724 | ||||||||
\(765\) | 6.46410 | 0.233710 | ||||||||
\(766\) | 23.9615 | 0.865765 | ||||||||
\(767\) | −57.6218 | −2.08060 | ||||||||
\(768\) | −11.7128 | −0.422650 | ||||||||
\(769\) | 23.7846 | 0.857695 | 0.428847 | − | 0.903377i | \(-0.358920\pi\) | ||||
0.428847 | + | 0.903377i | \(0.358920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.8038 | −0.497133 | ||||||||
\(772\) | 10.9282 | 0.393315 | ||||||||
\(773\) | −36.2487 | −1.30378 | −0.651888 | − | 0.758315i | \(-0.726023\pi\) | ||||
−0.651888 | + | 0.758315i | \(0.726023\pi\) | |||||||
\(774\) | −1.26795 | −0.0455755 | ||||||||
\(775\) | 5.26795 | 0.189230 | ||||||||
\(776\) | 5.75129 | 0.206459 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.3590 | 0.407239 | ||||||||
\(779\) | 11.7654 | 0.421538 | ||||||||
\(780\) | −6.14359 | −0.219976 | ||||||||
\(781\) | −7.66025 | −0.274105 | ||||||||
\(782\) | −40.0526 | −1.43228 | ||||||||
\(783\) | 5.73205 | 0.204847 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.1244 | 0.504120 | ||||||||
\(786\) | 11.8564 | 0.422904 | ||||||||
\(787\) | 42.6410 | 1.51999 | 0.759994 | − | 0.649930i | \(-0.225202\pi\) | ||||
0.759994 | + | 0.649930i | \(0.225202\pi\) | |||||||
\(788\) | −8.00000 | −0.284988 | ||||||||
\(789\) | 11.3205 | 0.403021 | ||||||||
\(790\) | −2.67949 | −0.0953320 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.53590 | −0.0901092 | ||||||||
\(793\) | −47.8038 | −1.69756 | ||||||||
\(794\) | 27.7128 | 0.983491 | ||||||||
\(795\) | 4.46410 | 0.158325 | ||||||||
\(796\) | −21.8564 | −0.774680 | ||||||||
\(797\) | 11.1769 | 0.395907 | 0.197953 | − | 0.980211i | \(-0.436571\pi\) | ||||
0.197953 | + | 0.980211i | \(0.436571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.19615 | −0.289959 | ||||||||
\(800\) | −5.85641 | −0.207055 | ||||||||
\(801\) | −14.6603 | −0.517995 | ||||||||
\(802\) | 24.2487 | 0.856252 | ||||||||
\(803\) | 8.39230 | 0.296158 | ||||||||
\(804\) | −7.21539 | −0.254467 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.1821 | −0.569989 | ||||||||
\(807\) | −7.58846 | −0.267126 | ||||||||
\(808\) | −42.9282 | −1.51021 | ||||||||
\(809\) | 8.53590 | 0.300106 | 0.150053 | − | 0.988678i | \(-0.452056\pi\) | ||||
0.150053 | + | 0.988678i | \(0.452056\pi\) | |||||||
\(810\) | −0.732051 | −0.0257216 | ||||||||
\(811\) | −4.78461 | −0.168010 | −0.0840052 | − | 0.996465i | \(-0.526771\pi\) | ||||
−0.0840052 | + | 0.996465i | \(0.526771\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.9282 | 0.628770 | ||||||||
\(814\) | −3.07180 | −0.107666 | ||||||||
\(815\) | 19.1244 | 0.669897 | ||||||||
\(816\) | 6.92820 | 0.242536 | ||||||||
\(817\) | 2.66025 | 0.0930705 | ||||||||
\(818\) | −6.64102 | −0.232198 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.2154 | −0.391658 | ||||||||
\(821\) | −9.98076 | −0.348331 | −0.174165 | − | 0.984716i | \(-0.555723\pi\) | ||||
−0.174165 | + | 0.984716i | \(0.555723\pi\) | |||||||
\(822\) | 4.78461 | 0.166882 | ||||||||
\(823\) | 18.4449 | 0.642948 | 0.321474 | − | 0.946918i | \(-0.395822\pi\) | ||||
0.321474 | + | 0.946918i | \(0.395822\pi\) | |||||||
\(824\) | 36.1821 | 1.26046 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.4641 | 0.468193 | 0.234096 | − | 0.972213i | \(-0.424787\pi\) | ||||
0.234096 | + | 0.972213i | \(0.424787\pi\) | |||||||
\(828\) | −12.3923 | −0.430662 | ||||||||
\(829\) | 35.1769 | 1.22174 | 0.610872 | − | 0.791729i | \(-0.290819\pi\) | ||||
0.610872 | + | 0.791729i | \(0.290819\pi\) | |||||||
\(830\) | 1.80385 | 0.0626125 | ||||||||
\(831\) | −9.07180 | −0.314697 | ||||||||
\(832\) | 8.99485 | 0.311840 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 8.39230 | 0.290602 | ||||||||
\(835\) | 10.3923 | 0.359641 | ||||||||
\(836\) | 2.24871 | 0.0777733 | ||||||||
\(837\) | 5.26795 | 0.182087 | ||||||||
\(838\) | 21.7654 | 0.751872 | ||||||||
\(839\) | −15.3397 | −0.529587 | −0.264793 | − | 0.964305i | \(-0.585304\pi\) | ||||
−0.264793 | + | 0.964305i | \(0.585304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.85641 | 0.132980 | ||||||||
\(842\) | −18.0910 | −0.623458 | ||||||||
\(843\) | 17.0718 | 0.587984 | ||||||||
\(844\) | −6.64102 | −0.228593 | ||||||||
\(845\) | 4.60770 | 0.158510 | ||||||||
\(846\) | 0.928203 | 0.0319123 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.78461 | 0.164304 | ||||||||
\(849\) | 0.196152 | 0.00673193 | ||||||||
\(850\) | −4.73205 | −0.162308 | ||||||||
\(851\) | −35.5167 | −1.21750 | ||||||||
\(852\) | −11.2154 | −0.384233 | ||||||||
\(853\) | −10.8756 | −0.372375 | −0.186187 | − | 0.982514i | \(-0.559613\pi\) | ||||
−0.186187 | + | 0.982514i | \(0.559613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.53590 | 0.0525266 | ||||||||
\(856\) | 13.3590 | 0.456601 | ||||||||
\(857\) | −49.7128 | −1.69816 | −0.849079 | − | 0.528266i | \(-0.822842\pi\) | ||||
−0.849079 | + | 0.528266i | \(0.822842\pi\) | |||||||
\(858\) | 3.07180 | 0.104869 | ||||||||
\(859\) | 48.5885 | 1.65782 | 0.828908 | − | 0.559384i | \(-0.188962\pi\) | ||||
0.828908 | + | 0.559384i | \(0.188962\pi\) | |||||||
\(860\) | −2.53590 | −0.0864734 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.8564 | 0.608192 | ||||||||
\(863\) | −25.5359 | −0.869252 | −0.434626 | − | 0.900611i | \(-0.643119\pi\) | ||||
−0.434626 | + | 0.900611i | \(0.643119\pi\) | |||||||
\(864\) | −5.85641 | −0.199239 | ||||||||
\(865\) | 25.4641 | 0.865805 | ||||||||
\(866\) | 6.82309 | 0.231858 | ||||||||
\(867\) | 24.7846 | 0.841729 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.66025 | −0.124166 | ||||||||
\(870\) | −4.19615 | −0.142263 | ||||||||
\(871\) | 20.6795 | 0.700698 | ||||||||
\(872\) | −13.3590 | −0.452392 | ||||||||
\(873\) | 2.26795 | 0.0767585 | ||||||||
\(874\) | −9.51666 | −0.321906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.2872 | 0.415146 | ||||||||
\(877\) | 18.3731 | 0.620414 | 0.310207 | − | 0.950669i | \(-0.399602\pi\) | ||||
0.310207 | + | 0.950669i | \(0.399602\pi\) | |||||||
\(878\) | −19.5551 | −0.659954 | ||||||||
\(879\) | −9.00000 | −0.303562 | ||||||||
\(880\) | −1.07180 | −0.0361303 | ||||||||
\(881\) | −16.9090 | −0.569678 | −0.284839 | − | 0.958575i | \(-0.591940\pi\) | ||||
−0.284839 | + | 0.958575i | \(0.591940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.1769 | −1.25110 | −0.625551 | − | 0.780183i | \(-0.715126\pi\) | ||||
−0.625551 | + | 0.780183i | \(0.715126\pi\) | |||||||
\(884\) | −39.7128 | −1.33569 | ||||||||
\(885\) | −13.7321 | −0.461598 | ||||||||
\(886\) | 17.1769 | 0.577070 | ||||||||
\(887\) | 21.3923 | 0.718283 | 0.359142 | − | 0.933283i | \(-0.383069\pi\) | ||||
0.359142 | + | 0.933283i | \(0.383069\pi\) | |||||||
\(888\) | −10.6410 | −0.357089 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.7321 | 0.359739 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 1.17691 | 0.0394060 | ||||||||
\(893\) | −1.94744 | −0.0651686 | ||||||||
\(894\) | −11.3205 | −0.378614 | ||||||||
\(895\) | −20.0526 | −0.670283 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.5167 | 1.18587 | ||||||||
\(898\) | −11.7513 | −0.392146 | ||||||||
\(899\) | 30.1962 | 1.00710 | ||||||||
\(900\) | −1.46410 | −0.0488034 | ||||||||
\(901\) | 28.8564 | 0.961346 | ||||||||
\(902\) | 5.60770 | 0.186716 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.5307 | 0.915659 | ||||||||
\(905\) | −7.07180 | −0.235074 | ||||||||
\(906\) | 8.67949 | 0.288357 | ||||||||
\(907\) | 18.3397 | 0.608961 | 0.304481 | − | 0.952519i | \(-0.401517\pi\) | ||||
0.304481 | + | 0.952519i | \(0.401517\pi\) | |||||||
\(908\) | −7.89488 | −0.262001 | ||||||||
\(909\) | −16.9282 | −0.561473 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.6077 | 1.04721 | 0.523605 | − | 0.851961i | \(-0.324587\pi\) | ||||
0.523605 | + | 0.851961i | \(0.324587\pi\) | |||||||
\(912\) | 1.64617 | 0.0545102 | ||||||||
\(913\) | 2.46410 | 0.0815499 | ||||||||
\(914\) | 1.94744 | 0.0644156 | ||||||||
\(915\) | −11.3923 | −0.376618 | ||||||||
\(916\) | 41.2820 | 1.36400 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.73205 | −0.156181 | ||||||||
\(919\) | −46.4974 | −1.53381 | −0.766904 | − | 0.641762i | \(-0.778204\pi\) | ||||
−0.766904 | + | 0.641762i | \(0.778204\pi\) | |||||||
\(920\) | 21.4641 | 0.707650 | ||||||||
\(921\) | 10.3923 | 0.342438 | ||||||||
\(922\) | 21.4641 | 0.706883 | ||||||||
\(923\) | 32.1436 | 1.05802 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.19615 | −0.137969 | ||||||||
\(926\) | −9.17691 | −0.301572 | ||||||||
\(927\) | 14.2679 | 0.468621 | ||||||||
\(928\) | −33.5692 | −1.10196 | ||||||||
\(929\) | 15.7128 | 0.515521 | 0.257760 | − | 0.966209i | \(-0.417016\pi\) | ||||
0.257760 | + | 0.966209i | \(0.417016\pi\) | |||||||
\(930\) | −3.85641 | −0.126457 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.9282 | 0.488990 | ||||||||
\(933\) | −7.32051 | −0.239663 | ||||||||
\(934\) | −20.0000 | −0.654420 | ||||||||
\(935\) | −6.46410 | −0.211399 | ||||||||
\(936\) | 10.6410 | 0.347812 | ||||||||
\(937\) | −26.9808 | −0.881423 | −0.440712 | − | 0.897649i | \(-0.645274\pi\) | ||||
−0.440712 | + | 0.897649i | \(0.645274\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.73205 | −0.0565233 | ||||||||
\(940\) | 1.85641 | 0.0605493 | ||||||||
\(941\) | −26.8372 | −0.874867 | −0.437433 | − | 0.899251i | \(-0.644112\pi\) | ||||
−0.437433 | + | 0.899251i | \(0.644112\pi\) | |||||||
\(942\) | −10.3397 | −0.336887 | ||||||||
\(943\) | 64.8372 | 2.11139 | ||||||||
\(944\) | −14.7180 | −0.479029 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.26795 | 0.0412246 | ||||||||
\(947\) | −12.7128 | −0.413111 | −0.206555 | − | 0.978435i | \(-0.566225\pi\) | ||||
−0.206555 | + | 0.978435i | \(0.566225\pi\) | |||||||
\(948\) | −5.35898 | −0.174052 | ||||||||
\(949\) | −35.2154 | −1.14314 | ||||||||
\(950\) | −1.12436 | −0.0364789 | ||||||||
\(951\) | 18.9282 | 0.613789 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.92820 | 0.289213 | 0.144606 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144606 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(954\) | −3.26795 | −0.105804 | ||||||||
\(955\) | −1.07180 | −0.0346825 | ||||||||
\(956\) | −26.5359 | −0.858232 | ||||||||
\(957\) | −5.73205 | −0.185291 | ||||||||
\(958\) | −4.92820 | −0.159223 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.14359 | 0.0691842 | ||||||||
\(961\) | −3.24871 | −0.104797 | ||||||||
\(962\) | 12.8897 | 0.415581 | ||||||||
\(963\) | 5.26795 | 0.169757 | ||||||||
\(964\) | 39.4256 | 1.26981 | ||||||||
\(965\) | −7.46410 | −0.240278 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.5167 | 0.981350 | 0.490675 | − | 0.871343i | \(-0.336750\pi\) | ||||
0.490675 | + | 0.871343i | \(0.336750\pi\) | |||||||
\(968\) | 2.53590 | 0.0815069 | ||||||||
\(969\) | 9.92820 | 0.318940 | ||||||||
\(970\) | −1.66025 | −0.0533075 | ||||||||
\(971\) | −42.6603 | −1.36903 | −0.684516 | − | 0.728998i | \(-0.739987\pi\) | ||||
−0.684516 | + | 0.728998i | \(0.739987\pi\) | |||||||
\(972\) | −1.46410 | −0.0469611 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.392305 | −0.0125703 | ||||||||
\(975\) | 4.19615 | 0.134384 | ||||||||
\(976\) | −12.2102 | −0.390840 | ||||||||
\(977\) | 11.3923 | 0.364472 | 0.182236 | − | 0.983255i | \(-0.441666\pi\) | ||||
0.182236 | + | 0.983255i | \(0.441666\pi\) | |||||||
\(978\) | −14.0000 | −0.447671 | ||||||||
\(979\) | 14.6603 | 0.468544 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.26795 | −0.168193 | ||||||||
\(982\) | −2.44486 | −0.0780187 | ||||||||
\(983\) | −10.6795 | −0.340623 | −0.170311 | − | 0.985390i | \(-0.554477\pi\) | ||||
−0.170311 | + | 0.985390i | \(0.554477\pi\) | |||||||
\(984\) | 19.4256 | 0.619266 | ||||||||
\(985\) | 5.46410 | 0.174101 | ||||||||
\(986\) | −27.1244 | −0.863815 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.43594 | −0.300197 | ||||||||
\(989\) | 14.6603 | 0.466169 | ||||||||
\(990\) | 0.732051 | 0.0232661 | ||||||||
\(991\) | −30.5692 | −0.971063 | −0.485532 | − | 0.874219i | \(-0.661374\pi\) | ||||
−0.485532 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(992\) | −30.8513 | −0.979528 | ||||||||
\(993\) | 8.32051 | 0.264043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.9282 | 0.473256 | ||||||||
\(996\) | 3.60770 | 0.114314 | ||||||||
\(997\) | 29.7128 | 0.941014 | 0.470507 | − | 0.882396i | \(-0.344071\pi\) | ||||
0.470507 | + | 0.882396i | \(0.344071\pi\) | |||||||
\(998\) | −21.5167 | −0.681098 | ||||||||
\(999\) | −4.19615 | −0.132760 |
(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 | 8085.2.a.bh.1.1 | 2 | ||
7.6 | odd | 2 | 1155.2.a.r.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 3465.2.a.v.1.2 | 2 | |||
35.34 | odd | 2 | 5775.2.a.bc.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.r.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
3465.2.a.v.1.2 | 2 | 21.20 | even | 2 | |||
5775.2.a.bc.1.2 | 2 | 35.34 | odd | 2 | |||
8085.2.a.bh.1.1 | 2 | 1.1 | even | 1 | trivial |