Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.63651 | −1.52219 | −0.761096 | − | 0.648640i | \(-0.775338\pi\) | ||||
−0.761096 | + | 0.648640i | \(0.775338\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.63651 | −1.07635 | ||||||||
\(7\) | 2.17132 | 0.820682 | 0.410341 | − | 0.911932i | \(-0.365410\pi\) | ||||
0.410341 | + | 0.911932i | \(0.365410\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.95120 | 1.31707 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.77623 | −0.535555 | −0.267777 | − | 0.963481i | \(-0.586289\pi\) | ||||
−0.267777 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(12\) | −2.63651 | −0.761096 | ||||||||
\(13\) | 0.900529 | 0.249762 | 0.124881 | − | 0.992172i | \(-0.460145\pi\) | ||||
0.124881 | + | 0.992172i | \(0.460145\pi\) | |||||||
\(14\) | 2.17132 | 0.580310 | ||||||||
\(15\) | 2.63651 | 0.680745 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.23605 | −1.26993 | −0.634965 | − | 0.772541i | \(-0.718985\pi\) | ||||
−0.634965 | + | 0.772541i | \(0.718985\pi\) | |||||||
\(18\) | 3.95120 | 0.931306 | ||||||||
\(19\) | 1.04540 | 0.239831 | 0.119916 | − | 0.992784i | \(-0.461738\pi\) | ||||
0.119916 | + | 0.992784i | \(0.461738\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.72472 | −1.24924 | ||||||||
\(22\) | −1.77623 | −0.378694 | ||||||||
\(23\) | 2.25167 | 0.469506 | 0.234753 | − | 0.972055i | \(-0.424572\pi\) | ||||
0.234753 | + | 0.972055i | \(0.424572\pi\) | |||||||
\(24\) | −2.63651 | −0.538176 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.900529 | 0.176608 | ||||||||
\(27\) | −2.50784 | −0.482635 | ||||||||
\(28\) | 2.17132 | 0.410341 | ||||||||
\(29\) | 4.06145 | 0.754192 | 0.377096 | − | 0.926174i | \(-0.376923\pi\) | ||||
0.377096 | + | 0.926174i | \(0.376923\pi\) | |||||||
\(30\) | 2.63651 | 0.481359 | ||||||||
\(31\) | −7.25058 | −1.30224 | −0.651122 | − | 0.758973i | \(-0.725701\pi\) | ||||
−0.651122 | + | 0.758973i | \(0.725701\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.68306 | 0.815216 | ||||||||
\(34\) | −5.23605 | −0.897976 | ||||||||
\(35\) | −2.17132 | −0.367020 | ||||||||
\(36\) | 3.95120 | 0.658533 | ||||||||
\(37\) | −1.44375 | −0.237351 | −0.118676 | − | 0.992933i | \(-0.537865\pi\) | ||||
−0.118676 | + | 0.992933i | \(0.537865\pi\) | |||||||
\(38\) | 1.04540 | 0.169586 | ||||||||
\(39\) | −2.37426 | −0.380185 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 0.883837 | 0.138032 | 0.0690161 | − | 0.997616i | \(-0.478014\pi\) | ||||
0.0690161 | + | 0.997616i | \(0.478014\pi\) | |||||||
\(42\) | −5.72472 | −0.883343 | ||||||||
\(43\) | 3.92508 | 0.598569 | 0.299284 | − | 0.954164i | \(-0.403252\pi\) | ||||
0.299284 | + | 0.954164i | \(0.403252\pi\) | |||||||
\(44\) | −1.77623 | −0.267777 | ||||||||
\(45\) | −3.95120 | −0.589010 | ||||||||
\(46\) | 2.25167 | 0.331991 | ||||||||
\(47\) | −8.40218 | −1.22558 | −0.612792 | − | 0.790244i | \(-0.709954\pi\) | ||||
−0.612792 | + | 0.790244i | \(0.709954\pi\) | |||||||
\(48\) | −2.63651 | −0.380548 | ||||||||
\(49\) | −2.28536 | −0.326480 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 13.8049 | 1.93308 | ||||||||
\(52\) | 0.900529 | 0.124881 | ||||||||
\(53\) | 2.00171 | 0.274956 | 0.137478 | − | 0.990505i | \(-0.456100\pi\) | ||||
0.137478 | + | 0.990505i | \(0.456100\pi\) | |||||||
\(54\) | −2.50784 | −0.341274 | ||||||||
\(55\) | 1.77623 | 0.239507 | ||||||||
\(56\) | 2.17132 | 0.290155 | ||||||||
\(57\) | −2.75621 | −0.365069 | ||||||||
\(58\) | 4.06145 | 0.533294 | ||||||||
\(59\) | 1.78596 | 0.232512 | 0.116256 | − | 0.993219i | \(-0.462911\pi\) | ||||
0.116256 | + | 0.993219i | \(0.462911\pi\) | |||||||
\(60\) | 2.63651 | 0.340372 | ||||||||
\(61\) | −13.2270 | −1.69355 | −0.846774 | − | 0.531953i | \(-0.821458\pi\) | ||||
−0.846774 | + | 0.531953i | \(0.821458\pi\) | |||||||
\(62\) | −7.25058 | −0.920825 | ||||||||
\(63\) | 8.57932 | 1.08089 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.900529 | −0.111697 | ||||||||
\(66\) | 4.68306 | 0.576445 | ||||||||
\(67\) | −0.937044 | −0.114478 | −0.0572391 | − | 0.998360i | \(-0.518230\pi\) | ||||
−0.0572391 | + | 0.998360i | \(0.518230\pi\) | |||||||
\(68\) | −5.23605 | −0.634965 | ||||||||
\(69\) | −5.93657 | −0.714679 | ||||||||
\(70\) | −2.17132 | −0.259523 | ||||||||
\(71\) | 14.4146 | 1.71069 | 0.855347 | − | 0.518056i | \(-0.173344\pi\) | ||||
0.855347 | + | 0.518056i | \(0.173344\pi\) | |||||||
\(72\) | 3.95120 | 0.465653 | ||||||||
\(73\) | 12.9522 | 1.51594 | 0.757969 | − | 0.652290i | \(-0.226192\pi\) | ||||
0.757969 | + | 0.652290i | \(0.226192\pi\) | |||||||
\(74\) | −1.44375 | −0.167833 | ||||||||
\(75\) | −2.63651 | −0.304438 | ||||||||
\(76\) | 1.04540 | 0.119916 | ||||||||
\(77\) | −3.85677 | −0.439520 | ||||||||
\(78\) | −2.37426 | −0.268831 | ||||||||
\(79\) | 3.52563 | 0.396665 | 0.198332 | − | 0.980135i | \(-0.436447\pi\) | ||||
0.198332 | + | 0.980135i | \(0.436447\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −5.24163 | −0.582403 | ||||||||
\(82\) | 0.883837 | 0.0976035 | ||||||||
\(83\) | −17.5229 | −1.92339 | −0.961693 | − | 0.274128i | \(-0.911611\pi\) | ||||
−0.961693 | + | 0.274128i | \(0.911611\pi\) | |||||||
\(84\) | −5.72472 | −0.624618 | ||||||||
\(85\) | 5.23605 | 0.567930 | ||||||||
\(86\) | 3.92508 | 0.423252 | ||||||||
\(87\) | −10.7081 | −1.14802 | ||||||||
\(88\) | −1.77623 | −0.189347 | ||||||||
\(89\) | −2.64012 | −0.279852 | −0.139926 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139926 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(90\) | −3.95120 | −0.416493 | ||||||||
\(91\) | 1.95534 | 0.204975 | ||||||||
\(92\) | 2.25167 | 0.234753 | ||||||||
\(93\) | 19.1163 | 1.98226 | ||||||||
\(94\) | −8.40218 | −0.866618 | ||||||||
\(95\) | −1.04540 | −0.107256 | ||||||||
\(96\) | −2.63651 | −0.269088 | ||||||||
\(97\) | 1.63106 | 0.165609 | 0.0828045 | − | 0.996566i | \(-0.473612\pi\) | ||||
0.0828045 | + | 0.996566i | \(0.473612\pi\) | |||||||
\(98\) | −2.28536 | −0.230856 | ||||||||
\(99\) | −7.01825 | −0.705361 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.1673 | 1.31020 | 0.655099 | − | 0.755543i | \(-0.272627\pi\) | ||||
0.655099 | + | 0.755543i | \(0.272627\pi\) | |||||||
\(102\) | 13.8049 | 1.36689 | ||||||||
\(103\) | −2.58917 | −0.255119 | −0.127559 | − | 0.991831i | \(-0.540714\pi\) | ||||
−0.127559 | + | 0.991831i | \(0.540714\pi\) | |||||||
\(104\) | 0.900529 | 0.0883041 | ||||||||
\(105\) | 5.72472 | 0.558675 | ||||||||
\(106\) | 2.00171 | 0.194423 | ||||||||
\(107\) | 2.64733 | 0.255927 | 0.127963 | − | 0.991779i | \(-0.459156\pi\) | ||||
0.127963 | + | 0.991779i | \(0.459156\pi\) | |||||||
\(108\) | −2.50784 | −0.241317 | ||||||||
\(109\) | 10.9027 | 1.04429 | 0.522143 | − | 0.852858i | \(-0.325133\pi\) | ||||
0.522143 | + | 0.852858i | \(0.325133\pi\) | |||||||
\(110\) | 1.77623 | 0.169357 | ||||||||
\(111\) | 3.80647 | 0.361294 | ||||||||
\(112\) | 2.17132 | 0.205171 | ||||||||
\(113\) | −10.5787 | −0.995160 | −0.497580 | − | 0.867418i | \(-0.665778\pi\) | ||||
−0.497580 | + | 0.867418i | \(0.665778\pi\) | |||||||
\(114\) | −2.75621 | −0.258143 | ||||||||
\(115\) | −2.25167 | −0.209970 | ||||||||
\(116\) | 4.06145 | 0.377096 | ||||||||
\(117\) | 3.55817 | 0.328953 | ||||||||
\(118\) | 1.78596 | 0.164411 | ||||||||
\(119\) | −11.3692 | −1.04221 | ||||||||
\(120\) | 2.63651 | 0.240680 | ||||||||
\(121\) | −7.84499 | −0.713181 | ||||||||
\(122\) | −13.2270 | −1.19752 | ||||||||
\(123\) | −2.33025 | −0.210111 | ||||||||
\(124\) | −7.25058 | −0.651122 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 8.57932 | 0.764307 | ||||||||
\(127\) | 8.06671 | 0.715805 | 0.357902 | − | 0.933759i | \(-0.383492\pi\) | ||||
0.357902 | + | 0.933759i | \(0.383492\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.3485 | −0.911136 | ||||||||
\(130\) | −0.900529 | −0.0789816 | ||||||||
\(131\) | 1.41270 | 0.123428 | 0.0617140 | − | 0.998094i | \(-0.480343\pi\) | ||||
0.0617140 | + | 0.998094i | \(0.480343\pi\) | |||||||
\(132\) | 4.68306 | 0.407608 | ||||||||
\(133\) | 2.26990 | 0.196825 | ||||||||
\(134\) | −0.937044 | −0.0809483 | ||||||||
\(135\) | 2.50784 | 0.215841 | ||||||||
\(136\) | −5.23605 | −0.448988 | ||||||||
\(137\) | −3.87128 | −0.330746 | −0.165373 | − | 0.986231i | \(-0.552883\pi\) | ||||
−0.165373 | + | 0.986231i | \(0.552883\pi\) | |||||||
\(138\) | −5.93657 | −0.505354 | ||||||||
\(139\) | −9.98899 | −0.847255 | −0.423628 | − | 0.905836i | \(-0.639243\pi\) | ||||
−0.423628 | + | 0.905836i | \(0.639243\pi\) | |||||||
\(140\) | −2.17132 | −0.183510 | ||||||||
\(141\) | 22.1524 | 1.86557 | ||||||||
\(142\) | 14.4146 | 1.20964 | ||||||||
\(143\) | −1.59955 | −0.133761 | ||||||||
\(144\) | 3.95120 | 0.329266 | ||||||||
\(145\) | −4.06145 | −0.337285 | ||||||||
\(146\) | 12.9522 | 1.07193 | ||||||||
\(147\) | 6.02539 | 0.496965 | ||||||||
\(148\) | −1.44375 | −0.118676 | ||||||||
\(149\) | 2.81037 | 0.230235 | 0.115117 | − | 0.993352i | \(-0.463276\pi\) | ||||
0.115117 | + | 0.993352i | \(0.463276\pi\) | |||||||
\(150\) | −2.63651 | −0.215270 | ||||||||
\(151\) | −11.2886 | −0.918650 | −0.459325 | − | 0.888268i | \(-0.651909\pi\) | ||||
−0.459325 | + | 0.888268i | \(0.651909\pi\) | |||||||
\(152\) | 1.04540 | 0.0847932 | ||||||||
\(153\) | −20.6887 | −1.67258 | ||||||||
\(154\) | −3.85677 | −0.310788 | ||||||||
\(155\) | 7.25058 | 0.582381 | ||||||||
\(156\) | −2.37426 | −0.190093 | ||||||||
\(157\) | −10.6219 | −0.847719 | −0.423859 | − | 0.905728i | \(-0.639325\pi\) | ||||
−0.423859 | + | 0.905728i | \(0.639325\pi\) | |||||||
\(158\) | 3.52563 | 0.280484 | ||||||||
\(159\) | −5.27753 | −0.418536 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.88911 | 0.385316 | ||||||||
\(162\) | −5.24163 | −0.411821 | ||||||||
\(163\) | −16.8717 | −1.32149 | −0.660746 | − | 0.750610i | \(-0.729760\pi\) | ||||
−0.660746 | + | 0.750610i | \(0.729760\pi\) | |||||||
\(164\) | 0.883837 | 0.0690161 | ||||||||
\(165\) | −4.68306 | −0.364576 | ||||||||
\(166\) | −17.5229 | −1.36004 | ||||||||
\(167\) | −7.27037 | −0.562598 | −0.281299 | − | 0.959620i | \(-0.590765\pi\) | ||||
−0.281299 | + | 0.959620i | \(0.590765\pi\) | |||||||
\(168\) | −5.72472 | −0.441671 | ||||||||
\(169\) | −12.1890 | −0.937619 | ||||||||
\(170\) | 5.23605 | 0.401587 | ||||||||
\(171\) | 4.13058 | 0.315874 | ||||||||
\(172\) | 3.92508 | 0.299284 | ||||||||
\(173\) | −15.6152 | −1.18720 | −0.593601 | − | 0.804760i | \(-0.702294\pi\) | ||||
−0.593601 | + | 0.804760i | \(0.702294\pi\) | |||||||
\(174\) | −10.7081 | −0.811776 | ||||||||
\(175\) | 2.17132 | 0.164136 | ||||||||
\(176\) | −1.77623 | −0.133889 | ||||||||
\(177\) | −4.70871 | −0.353928 | ||||||||
\(178\) | −2.64012 | −0.197885 | ||||||||
\(179\) | 20.0642 | 1.49967 | 0.749836 | − | 0.661624i | \(-0.230133\pi\) | ||||
0.749836 | + | 0.661624i | \(0.230133\pi\) | |||||||
\(180\) | −3.95120 | −0.294505 | ||||||||
\(181\) | 18.1864 | 1.35178 | 0.675892 | − | 0.737001i | \(-0.263759\pi\) | ||||
0.675892 | + | 0.737001i | \(0.263759\pi\) | |||||||
\(182\) | 1.95534 | 0.144939 | ||||||||
\(183\) | 34.8732 | 2.57790 | ||||||||
\(184\) | 2.25167 | 0.165996 | ||||||||
\(185\) | 1.44375 | 0.106147 | ||||||||
\(186\) | 19.1163 | 1.40167 | ||||||||
\(187\) | 9.30046 | 0.680117 | ||||||||
\(188\) | −8.40218 | −0.612792 | ||||||||
\(189\) | −5.44534 | −0.396090 | ||||||||
\(190\) | −1.04540 | −0.0758413 | ||||||||
\(191\) | −12.7274 | −0.920922 | −0.460461 | − | 0.887680i | \(-0.652316\pi\) | ||||
−0.460461 | + | 0.887680i | \(0.652316\pi\) | |||||||
\(192\) | −2.63651 | −0.190274 | ||||||||
\(193\) | 2.05041 | 0.147591 | 0.0737957 | − | 0.997273i | \(-0.476489\pi\) | ||||
0.0737957 | + | 0.997273i | \(0.476489\pi\) | |||||||
\(194\) | 1.63106 | 0.117103 | ||||||||
\(195\) | 2.37426 | 0.170024 | ||||||||
\(196\) | −2.28536 | −0.163240 | ||||||||
\(197\) | −17.8327 | −1.27053 | −0.635265 | − | 0.772295i | \(-0.719109\pi\) | ||||
−0.635265 | + | 0.772295i | \(0.719109\pi\) | |||||||
\(198\) | −7.01825 | −0.498765 | ||||||||
\(199\) | −6.63145 | −0.470091 | −0.235046 | − | 0.971984i | \(-0.575524\pi\) | ||||
−0.235046 | + | 0.971984i | \(0.575524\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 2.47053 | 0.174258 | ||||||||
\(202\) | 13.1673 | 0.926449 | ||||||||
\(203\) | 8.81871 | 0.618952 | ||||||||
\(204\) | 13.8049 | 0.966538 | ||||||||
\(205\) | −0.883837 | −0.0617299 | ||||||||
\(206\) | −2.58917 | −0.180396 | ||||||||
\(207\) | 8.89681 | 0.618371 | ||||||||
\(208\) | 0.900529 | 0.0624404 | ||||||||
\(209\) | −1.85688 | −0.128443 | ||||||||
\(210\) | 5.72472 | 0.395043 | ||||||||
\(211\) | 19.2458 | 1.32493 | 0.662467 | − | 0.749092i | \(-0.269510\pi\) | ||||
0.662467 | + | 0.749092i | \(0.269510\pi\) | |||||||
\(212\) | 2.00171 | 0.137478 | ||||||||
\(213\) | −38.0042 | −2.60400 | ||||||||
\(214\) | 2.64733 | 0.180968 | ||||||||
\(215\) | −3.92508 | −0.267688 | ||||||||
\(216\) | −2.50784 | −0.170637 | ||||||||
\(217\) | −15.7434 | −1.06873 | ||||||||
\(218\) | 10.9027 | 0.738421 | ||||||||
\(219\) | −34.1486 | −2.30755 | ||||||||
\(220\) | 1.77623 | 0.119754 | ||||||||
\(221\) | −4.71522 | −0.317180 | ||||||||
\(222\) | 3.80647 | 0.255474 | ||||||||
\(223\) | 8.59672 | 0.575679 | 0.287839 | − | 0.957679i | \(-0.407063\pi\) | ||||
0.287839 | + | 0.957679i | \(0.407063\pi\) | |||||||
\(224\) | 2.17132 | 0.145078 | ||||||||
\(225\) | 3.95120 | 0.263413 | ||||||||
\(226\) | −10.5787 | −0.703685 | ||||||||
\(227\) | −3.91770 | −0.260027 | −0.130014 | − | 0.991512i | \(-0.541502\pi\) | ||||
−0.130014 | + | 0.991512i | \(0.541502\pi\) | |||||||
\(228\) | −2.75621 | −0.182535 | ||||||||
\(229\) | 1.14916 | 0.0759389 | 0.0379695 | − | 0.999279i | \(-0.487911\pi\) | ||||
0.0379695 | + | 0.999279i | \(0.487911\pi\) | |||||||
\(230\) | −2.25167 | −0.148471 | ||||||||
\(231\) | 10.1684 | 0.669034 | ||||||||
\(232\) | 4.06145 | 0.266647 | ||||||||
\(233\) | −24.9501 | −1.63453 | −0.817267 | − | 0.576259i | \(-0.804512\pi\) | ||||
−0.817267 | + | 0.576259i | \(0.804512\pi\) | |||||||
\(234\) | 3.55817 | 0.232605 | ||||||||
\(235\) | 8.40218 | 0.548098 | ||||||||
\(236\) | 1.78596 | 0.116256 | ||||||||
\(237\) | −9.29537 | −0.603799 | ||||||||
\(238\) | −11.3692 | −0.736953 | ||||||||
\(239\) | −23.5053 | −1.52043 | −0.760217 | − | 0.649669i | \(-0.774908\pi\) | ||||
−0.760217 | + | 0.649669i | \(0.774908\pi\) | |||||||
\(240\) | 2.63651 | 0.170186 | ||||||||
\(241\) | −22.9813 | −1.48036 | −0.740179 | − | 0.672410i | \(-0.765259\pi\) | ||||
−0.740179 | + | 0.672410i | \(0.765259\pi\) | |||||||
\(242\) | −7.84499 | −0.504295 | ||||||||
\(243\) | 21.3432 | 1.36916 | ||||||||
\(244\) | −13.2270 | −0.846774 | ||||||||
\(245\) | 2.28536 | 0.146006 | ||||||||
\(246\) | −2.33025 | −0.148571 | ||||||||
\(247\) | 0.941413 | 0.0599007 | ||||||||
\(248\) | −7.25058 | −0.460413 | ||||||||
\(249\) | 46.1993 | 2.92776 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −2.85163 | −0.179993 | −0.0899967 | − | 0.995942i | \(-0.528686\pi\) | ||||
−0.0899967 | + | 0.995942i | \(0.528686\pi\) | |||||||
\(252\) | 8.57932 | 0.540446 | ||||||||
\(253\) | −3.99950 | −0.251446 | ||||||||
\(254\) | 8.06671 | 0.506150 | ||||||||
\(255\) | −13.8049 | −0.864498 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.55082 | −0.221494 | −0.110747 | − | 0.993849i | \(-0.535324\pi\) | ||||
−0.110747 | + | 0.993849i | \(0.535324\pi\) | |||||||
\(258\) | −10.3485 | −0.644271 | ||||||||
\(259\) | −3.13485 | −0.194790 | ||||||||
\(260\) | −0.900529 | −0.0558484 | ||||||||
\(261\) | 16.0476 | 0.993320 | ||||||||
\(262\) | 1.41270 | 0.0872768 | ||||||||
\(263\) | −9.96034 | −0.614181 | −0.307090 | − | 0.951680i | \(-0.599355\pi\) | ||||
−0.307090 | + | 0.951680i | \(0.599355\pi\) | |||||||
\(264\) | 4.68306 | 0.288223 | ||||||||
\(265\) | −2.00171 | −0.122964 | ||||||||
\(266\) | 2.26990 | 0.139177 | ||||||||
\(267\) | 6.96070 | 0.425988 | ||||||||
\(268\) | −0.937044 | −0.0572391 | ||||||||
\(269\) | −29.9561 | −1.82645 | −0.913227 | − | 0.407451i | \(-0.866418\pi\) | ||||
−0.913227 | + | 0.407451i | \(0.866418\pi\) | |||||||
\(270\) | 2.50784 | 0.152623 | ||||||||
\(271\) | 26.1179 | 1.58655 | 0.793276 | − | 0.608863i | \(-0.208374\pi\) | ||||
0.793276 | + | 0.608863i | \(0.208374\pi\) | |||||||
\(272\) | −5.23605 | −0.317482 | ||||||||
\(273\) | −5.15527 | −0.312011 | ||||||||
\(274\) | −3.87128 | −0.233873 | ||||||||
\(275\) | −1.77623 | −0.107111 | ||||||||
\(276\) | −5.93657 | −0.357339 | ||||||||
\(277\) | −31.1705 | −1.87285 | −0.936427 | − | 0.350861i | \(-0.885889\pi\) | ||||
−0.936427 | + | 0.350861i | \(0.885889\pi\) | |||||||
\(278\) | −9.98899 | −0.599100 | ||||||||
\(279\) | −28.6485 | −1.71514 | ||||||||
\(280\) | −2.17132 | −0.129761 | ||||||||
\(281\) | −13.8505 | −0.826250 | −0.413125 | − | 0.910674i | \(-0.635563\pi\) | ||||
−0.413125 | + | 0.910674i | \(0.635563\pi\) | |||||||
\(282\) | 22.1524 | 1.31916 | ||||||||
\(283\) | −17.4713 | −1.03856 | −0.519280 | − | 0.854604i | \(-0.673800\pi\) | ||||
−0.519280 | + | 0.854604i | \(0.673800\pi\) | |||||||
\(284\) | 14.4146 | 0.855347 | ||||||||
\(285\) | 2.75621 | 0.163264 | ||||||||
\(286\) | −1.59955 | −0.0945833 | ||||||||
\(287\) | 1.91910 | 0.113281 | ||||||||
\(288\) | 3.95120 | 0.232827 | ||||||||
\(289\) | 10.4163 | 0.612721 | ||||||||
\(290\) | −4.06145 | −0.238496 | ||||||||
\(291\) | −4.30031 | −0.252089 | ||||||||
\(292\) | 12.9522 | 0.757969 | ||||||||
\(293\) | −18.2160 | −1.06419 | −0.532096 | − | 0.846684i | \(-0.678596\pi\) | ||||
−0.532096 | + | 0.846684i | \(0.678596\pi\) | |||||||
\(294\) | 6.02539 | 0.351408 | ||||||||
\(295\) | −1.78596 | −0.103983 | ||||||||
\(296\) | −1.44375 | −0.0839164 | ||||||||
\(297\) | 4.45452 | 0.258477 | ||||||||
\(298\) | 2.81037 | 0.162801 | ||||||||
\(299\) | 2.02770 | 0.117265 | ||||||||
\(300\) | −2.63651 | −0.152219 | ||||||||
\(301\) | 8.52261 | 0.491235 | ||||||||
\(302\) | −11.2886 | −0.649584 | ||||||||
\(303\) | −34.7158 | −1.99437 | ||||||||
\(304\) | 1.04540 | 0.0599578 | ||||||||
\(305\) | 13.2270 | 0.757377 | ||||||||
\(306\) | −20.6887 | −1.18269 | ||||||||
\(307\) | 9.98595 | 0.569929 | 0.284964 | − | 0.958538i | \(-0.408018\pi\) | ||||
0.284964 | + | 0.958538i | \(0.408018\pi\) | |||||||
\(308\) | −3.85677 | −0.219760 | ||||||||
\(309\) | 6.82638 | 0.388339 | ||||||||
\(310\) | 7.25058 | 0.411806 | ||||||||
\(311\) | 0.172246 | 0.00976720 | 0.00488360 | − | 0.999988i | \(-0.498445\pi\) | ||||
0.00488360 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(312\) | −2.37426 | −0.134416 | ||||||||
\(313\) | −27.8800 | −1.57587 | −0.787935 | − | 0.615758i | \(-0.788850\pi\) | ||||
−0.787935 | + | 0.615758i | \(0.788850\pi\) | |||||||
\(314\) | −10.6219 | −0.599428 | ||||||||
\(315\) | −8.57932 | −0.483390 | ||||||||
\(316\) | 3.52563 | 0.198332 | ||||||||
\(317\) | −30.3430 | −1.70423 | −0.852115 | − | 0.523354i | \(-0.824680\pi\) | ||||
−0.852115 | + | 0.523354i | \(0.824680\pi\) | |||||||
\(318\) | −5.27753 | −0.295949 | ||||||||
\(319\) | −7.21408 | −0.403911 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −6.97971 | −0.389569 | ||||||||
\(322\) | 4.88911 | 0.272459 | ||||||||
\(323\) | −5.47377 | −0.304569 | ||||||||
\(324\) | −5.24163 | −0.291202 | ||||||||
\(325\) | 0.900529 | 0.0499523 | ||||||||
\(326\) | −16.8717 | −0.934436 | ||||||||
\(327\) | −28.7450 | −1.58960 | ||||||||
\(328\) | 0.883837 | 0.0488018 | ||||||||
\(329\) | −18.2438 | −1.00581 | ||||||||
\(330\) | −4.68306 | −0.257794 | ||||||||
\(331\) | 27.0931 | 1.48917 | 0.744587 | − | 0.667526i | \(-0.232647\pi\) | ||||
0.744587 | + | 0.667526i | \(0.232647\pi\) | |||||||
\(332\) | −17.5229 | −0.961693 | ||||||||
\(333\) | −5.70455 | −0.312607 | ||||||||
\(334\) | −7.27037 | −0.397817 | ||||||||
\(335\) | 0.937044 | 0.0511962 | ||||||||
\(336\) | −5.72472 | −0.312309 | ||||||||
\(337\) | 24.6657 | 1.34363 | 0.671814 | − | 0.740720i | \(-0.265516\pi\) | ||||
0.671814 | + | 0.740720i | \(0.265516\pi\) | |||||||
\(338\) | −12.1890 | −0.662997 | ||||||||
\(339\) | 27.8909 | 1.51482 | ||||||||
\(340\) | 5.23605 | 0.283965 | ||||||||
\(341\) | 12.8787 | 0.697422 | ||||||||
\(342\) | 4.13058 | 0.223356 | ||||||||
\(343\) | −20.1615 | −1.08862 | ||||||||
\(344\) | 3.92508 | 0.211626 | ||||||||
\(345\) | 5.93657 | 0.319614 | ||||||||
\(346\) | −15.6152 | −0.839478 | ||||||||
\(347\) | 25.1247 | 1.34876 | 0.674382 | − | 0.738383i | \(-0.264410\pi\) | ||||
0.674382 | + | 0.738383i | \(0.264410\pi\) | |||||||
\(348\) | −10.7081 | −0.574012 | ||||||||
\(349\) | 23.8129 | 1.27467 | 0.637337 | − | 0.770585i | \(-0.280036\pi\) | ||||
0.637337 | + | 0.770585i | \(0.280036\pi\) | |||||||
\(350\) | 2.17132 | 0.116062 | ||||||||
\(351\) | −2.25839 | −0.120544 | ||||||||
\(352\) | −1.77623 | −0.0946736 | ||||||||
\(353\) | 12.0812 | 0.643016 | 0.321508 | − | 0.946907i | \(-0.395810\pi\) | ||||
0.321508 | + | 0.946907i | \(0.395810\pi\) | |||||||
\(354\) | −4.70871 | −0.250265 | ||||||||
\(355\) | −14.4146 | −0.765046 | ||||||||
\(356\) | −2.64012 | −0.139926 | ||||||||
\(357\) | 29.9749 | 1.58644 | ||||||||
\(358\) | 20.0642 | 1.06043 | ||||||||
\(359\) | −24.6600 | −1.30150 | −0.650752 | − | 0.759290i | \(-0.725546\pi\) | ||||
−0.650752 | + | 0.759290i | \(0.725546\pi\) | |||||||
\(360\) | −3.95120 | −0.208246 | ||||||||
\(361\) | −17.9071 | −0.942481 | ||||||||
\(362\) | 18.1864 | 0.955855 | ||||||||
\(363\) | 20.6834 | 1.08560 | ||||||||
\(364\) | 1.95534 | 0.102488 | ||||||||
\(365\) | −12.9522 | −0.677948 | ||||||||
\(366\) | 34.8732 | 1.82285 | ||||||||
\(367\) | 7.31637 | 0.381911 | 0.190956 | − | 0.981599i | \(-0.438841\pi\) | ||||
0.190956 | + | 0.981599i | \(0.438841\pi\) | |||||||
\(368\) | 2.25167 | 0.117377 | ||||||||
\(369\) | 3.49222 | 0.181798 | ||||||||
\(370\) | 1.44375 | 0.0750571 | ||||||||
\(371\) | 4.34636 | 0.225652 | ||||||||
\(372\) | 19.1163 | 0.991132 | ||||||||
\(373\) | −13.8046 | −0.714776 | −0.357388 | − | 0.933956i | \(-0.616333\pi\) | ||||
−0.357388 | + | 0.933956i | \(0.616333\pi\) | |||||||
\(374\) | 9.30046 | 0.480915 | ||||||||
\(375\) | 2.63651 | 0.136149 | ||||||||
\(376\) | −8.40218 | −0.433309 | ||||||||
\(377\) | 3.65745 | 0.188368 | ||||||||
\(378\) | −5.44534 | −0.280078 | ||||||||
\(379\) | 19.7863 | 1.01636 | 0.508178 | − | 0.861252i | \(-0.330319\pi\) | ||||
0.508178 | + | 0.861252i | \(0.330319\pi\) | |||||||
\(380\) | −1.04540 | −0.0536279 | ||||||||
\(381\) | −21.2680 | −1.08959 | ||||||||
\(382\) | −12.7274 | −0.651190 | ||||||||
\(383\) | −29.8608 | −1.52582 | −0.762908 | − | 0.646507i | \(-0.776229\pi\) | ||||
−0.762908 | + | 0.646507i | \(0.776229\pi\) | |||||||
\(384\) | −2.63651 | −0.134544 | ||||||||
\(385\) | 3.85677 | 0.196559 | ||||||||
\(386\) | 2.05041 | 0.104363 | ||||||||
\(387\) | 15.5088 | 0.788355 | ||||||||
\(388\) | 1.63106 | 0.0828045 | ||||||||
\(389\) | −18.9990 | −0.963289 | −0.481644 | − | 0.876367i | \(-0.659960\pi\) | ||||
−0.481644 | + | 0.876367i | \(0.659960\pi\) | |||||||
\(390\) | 2.37426 | 0.120225 | ||||||||
\(391\) | −11.7899 | −0.596240 | ||||||||
\(392\) | −2.28536 | −0.115428 | ||||||||
\(393\) | −3.72460 | −0.187881 | ||||||||
\(394\) | −17.8327 | −0.898400 | ||||||||
\(395\) | −3.52563 | −0.177394 | ||||||||
\(396\) | −7.01825 | −0.352680 | ||||||||
\(397\) | 6.87745 | 0.345169 | 0.172585 | − | 0.984995i | \(-0.444788\pi\) | ||||
0.172585 | + | 0.984995i | \(0.444788\pi\) | |||||||
\(398\) | −6.63145 | −0.332405 | ||||||||
\(399\) | −5.98462 | −0.299606 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −8.89445 | −0.444168 | −0.222084 | − | 0.975028i | \(-0.571286\pi\) | ||||
−0.222084 | + | 0.975028i | \(0.571286\pi\) | |||||||
\(402\) | 2.47053 | 0.123219 | ||||||||
\(403\) | −6.52936 | −0.325251 | ||||||||
\(404\) | 13.1673 | 0.655099 | ||||||||
\(405\) | 5.24163 | 0.260459 | ||||||||
\(406\) | 8.81871 | 0.437665 | ||||||||
\(407\) | 2.56444 | 0.127115 | ||||||||
\(408\) | 13.8049 | 0.683445 | ||||||||
\(409\) | −10.7251 | −0.530323 | −0.265162 | − | 0.964204i | \(-0.585425\pi\) | ||||
−0.265162 | + | 0.964204i | \(0.585425\pi\) | |||||||
\(410\) | −0.883837 | −0.0436496 | ||||||||
\(411\) | 10.2067 | 0.503459 | ||||||||
\(412\) | −2.58917 | −0.127559 | ||||||||
\(413\) | 3.87790 | 0.190819 | ||||||||
\(414\) | 8.89681 | 0.437254 | ||||||||
\(415\) | 17.5229 | 0.860165 | ||||||||
\(416\) | 0.900529 | 0.0441521 | ||||||||
\(417\) | 26.3361 | 1.28968 | ||||||||
\(418\) | −1.85688 | −0.0908227 | ||||||||
\(419\) | −24.4326 | −1.19361 | −0.596805 | − | 0.802386i | \(-0.703563\pi\) | ||||
−0.596805 | + | 0.802386i | \(0.703563\pi\) | |||||||
\(420\) | 5.72472 | 0.279338 | ||||||||
\(421\) | 31.6170 | 1.54092 | 0.770459 | − | 0.637489i | \(-0.220027\pi\) | ||||
0.770459 | + | 0.637489i | \(0.220027\pi\) | |||||||
\(422\) | 19.2458 | 0.936869 | ||||||||
\(423\) | −33.1987 | −1.61417 | ||||||||
\(424\) | 2.00171 | 0.0972116 | ||||||||
\(425\) | −5.23605 | −0.253986 | ||||||||
\(426\) | −38.0042 | −1.84131 | ||||||||
\(427\) | −28.7201 | −1.38986 | ||||||||
\(428\) | 2.64733 | 0.127963 | ||||||||
\(429\) | 4.21723 | 0.203610 | ||||||||
\(430\) | −3.92508 | −0.189284 | ||||||||
\(431\) | −38.0324 | −1.83196 | −0.915979 | − | 0.401226i | \(-0.868584\pi\) | ||||
−0.915979 | + | 0.401226i | \(0.868584\pi\) | |||||||
\(432\) | −2.50784 | −0.120659 | ||||||||
\(433\) | 28.5182 | 1.37050 | 0.685248 | − | 0.728310i | \(-0.259694\pi\) | ||||
0.685248 | + | 0.728310i | \(0.259694\pi\) | |||||||
\(434\) | −15.7434 | −0.755705 | ||||||||
\(435\) | 10.7081 | 0.513412 | ||||||||
\(436\) | 10.9027 | 0.522143 | ||||||||
\(437\) | 2.35390 | 0.112602 | ||||||||
\(438\) | −34.1486 | −1.63168 | ||||||||
\(439\) | −2.50649 | −0.119628 | −0.0598141 | − | 0.998210i | \(-0.519051\pi\) | ||||
−0.0598141 | + | 0.998210i | \(0.519051\pi\) | |||||||
\(440\) | 1.77623 | 0.0846786 | ||||||||
\(441\) | −9.02992 | −0.429996 | ||||||||
\(442\) | −4.71522 | −0.224280 | ||||||||
\(443\) | −35.3204 | −1.67812 | −0.839061 | − | 0.544038i | \(-0.816895\pi\) | ||||
−0.839061 | + | 0.544038i | \(0.816895\pi\) | |||||||
\(444\) | 3.80647 | 0.180647 | ||||||||
\(445\) | 2.64012 | 0.125154 | ||||||||
\(446\) | 8.59672 | 0.407066 | ||||||||
\(447\) | −7.40958 | −0.350461 | ||||||||
\(448\) | 2.17132 | 0.102585 | ||||||||
\(449\) | −24.4328 | −1.15306 | −0.576528 | − | 0.817077i | \(-0.695593\pi\) | ||||
−0.576528 | + | 0.817077i | \(0.695593\pi\) | |||||||
\(450\) | 3.95120 | 0.186261 | ||||||||
\(451\) | −1.56990 | −0.0739238 | ||||||||
\(452\) | −10.5787 | −0.497580 | ||||||||
\(453\) | 29.7624 | 1.39836 | ||||||||
\(454\) | −3.91770 | −0.183867 | ||||||||
\(455\) | −1.95534 | −0.0916676 | ||||||||
\(456\) | −2.75621 | −0.129071 | ||||||||
\(457\) | −20.9258 | −0.978865 | −0.489433 | − | 0.872041i | \(-0.662796\pi\) | ||||
−0.489433 | + | 0.872041i | \(0.662796\pi\) | |||||||
\(458\) | 1.14916 | 0.0536969 | ||||||||
\(459\) | 13.1312 | 0.612912 | ||||||||
\(460\) | −2.25167 | −0.104985 | ||||||||
\(461\) | 8.09838 | 0.377179 | 0.188590 | − | 0.982056i | \(-0.439608\pi\) | ||||
0.188590 | + | 0.982056i | \(0.439608\pi\) | |||||||
\(462\) | 10.1684 | 0.473078 | ||||||||
\(463\) | −33.1924 | −1.54258 | −0.771291 | − | 0.636483i | \(-0.780389\pi\) | ||||
−0.771291 | + | 0.636483i | \(0.780389\pi\) | |||||||
\(464\) | 4.06145 | 0.188548 | ||||||||
\(465\) | −19.1163 | −0.886495 | ||||||||
\(466\) | −24.9501 | −1.15579 | ||||||||
\(467\) | 0.450355 | 0.0208399 | 0.0104200 | − | 0.999946i | \(-0.496683\pi\) | ||||
0.0104200 | + | 0.999946i | \(0.496683\pi\) | |||||||
\(468\) | 3.55817 | 0.164476 | ||||||||
\(469\) | −2.03462 | −0.0939502 | ||||||||
\(470\) | 8.40218 | 0.387564 | ||||||||
\(471\) | 28.0047 | 1.29039 | ||||||||
\(472\) | 1.78596 | 0.0822055 | ||||||||
\(473\) | −6.97186 | −0.320566 | ||||||||
\(474\) | −9.29537 | −0.426951 | ||||||||
\(475\) | 1.04540 | 0.0479663 | ||||||||
\(476\) | −11.3692 | −0.521104 | ||||||||
\(477\) | 7.90915 | 0.362135 | ||||||||
\(478\) | −23.5053 | −1.07511 | ||||||||
\(479\) | 20.8688 | 0.953518 | 0.476759 | − | 0.879034i | \(-0.341811\pi\) | ||||
0.476759 | + | 0.879034i | \(0.341811\pi\) | |||||||
\(480\) | 2.63651 | 0.120340 | ||||||||
\(481\) | −1.30014 | −0.0592813 | ||||||||
\(482\) | −22.9813 | −1.04677 | ||||||||
\(483\) | −12.8902 | −0.586524 | ||||||||
\(484\) | −7.84499 | −0.356591 | ||||||||
\(485\) | −1.63106 | −0.0740626 | ||||||||
\(486\) | 21.3432 | 0.968145 | ||||||||
\(487\) | 30.3844 | 1.37685 | 0.688425 | − | 0.725308i | \(-0.258302\pi\) | ||||
0.688425 | + | 0.725308i | \(0.258302\pi\) | |||||||
\(488\) | −13.2270 | −0.598759 | ||||||||
\(489\) | 44.4824 | 2.01156 | ||||||||
\(490\) | 2.28536 | 0.103242 | ||||||||
\(491\) | 25.3306 | 1.14316 | 0.571578 | − | 0.820548i | \(-0.306331\pi\) | ||||
0.571578 | + | 0.820548i | \(0.306331\pi\) | |||||||
\(492\) | −2.33025 | −0.105056 | ||||||||
\(493\) | −21.2660 | −0.957771 | ||||||||
\(494\) | 0.941413 | 0.0423562 | ||||||||
\(495\) | 7.01825 | 0.315447 | ||||||||
\(496\) | −7.25058 | −0.325561 | ||||||||
\(497\) | 31.2987 | 1.40394 | ||||||||
\(498\) | 46.1993 | 2.07024 | ||||||||
\(499\) | 0.774573 | 0.0346747 | 0.0173373 | − | 0.999850i | \(-0.494481\pi\) | ||||
0.0173373 | + | 0.999850i | \(0.494481\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 19.1684 | 0.856381 | ||||||||
\(502\) | −2.85163 | −0.127275 | ||||||||
\(503\) | 21.7716 | 0.970749 | 0.485375 | − | 0.874306i | \(-0.338683\pi\) | ||||
0.485375 | + | 0.874306i | \(0.338683\pi\) | |||||||
\(504\) | 8.57932 | 0.382153 | ||||||||
\(505\) | −13.1673 | −0.585938 | ||||||||
\(506\) | −3.99950 | −0.177799 | ||||||||
\(507\) | 32.1366 | 1.42724 | ||||||||
\(508\) | 8.06671 | 0.357902 | ||||||||
\(509\) | −10.5944 | −0.469590 | −0.234795 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234795 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(510\) | −13.8049 | −0.611292 | ||||||||
\(511\) | 28.1234 | 1.24410 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.62170 | −0.115751 | ||||||||
\(514\) | −3.55082 | −0.156620 | ||||||||
\(515\) | 2.58917 | 0.114093 | ||||||||
\(516\) | −10.3485 | −0.455568 | ||||||||
\(517\) | 14.9242 | 0.656367 | ||||||||
\(518\) | −3.13485 | −0.137737 | ||||||||
\(519\) | 41.1697 | 1.80715 | ||||||||
\(520\) | −0.900529 | −0.0394908 | ||||||||
\(521\) | −2.62266 | −0.114901 | −0.0574504 | − | 0.998348i | \(-0.518297\pi\) | ||||
−0.0574504 | + | 0.998348i | \(0.518297\pi\) | |||||||
\(522\) | 16.0476 | 0.702384 | ||||||||
\(523\) | 29.2273 | 1.27802 | 0.639009 | − | 0.769199i | \(-0.279345\pi\) | ||||
0.639009 | + | 0.769199i | \(0.279345\pi\) | |||||||
\(524\) | 1.41270 | 0.0617140 | ||||||||
\(525\) | −5.72472 | −0.249847 | ||||||||
\(526\) | −9.96034 | −0.434292 | ||||||||
\(527\) | 37.9645 | 1.65376 | ||||||||
\(528\) | 4.68306 | 0.203804 | ||||||||
\(529\) | −17.9300 | −0.779564 | ||||||||
\(530\) | −2.00171 | −0.0869487 | ||||||||
\(531\) | 7.05669 | 0.306234 | ||||||||
\(532\) | 2.26990 | 0.0984127 | ||||||||
\(533\) | 0.795921 | 0.0344752 | ||||||||
\(534\) | 6.96070 | 0.301219 | ||||||||
\(535\) | −2.64733 | −0.114454 | ||||||||
\(536\) | −0.937044 | −0.0404742 | ||||||||
\(537\) | −52.8996 | −2.28279 | ||||||||
\(538\) | −29.9561 | −1.29150 | ||||||||
\(539\) | 4.05934 | 0.174848 | ||||||||
\(540\) | 2.50784 | 0.107920 | ||||||||
\(541\) | 6.36416 | 0.273616 | 0.136808 | − | 0.990598i | \(-0.456316\pi\) | ||||
0.136808 | + | 0.990598i | \(0.456316\pi\) | |||||||
\(542\) | 26.1179 | 1.12186 | ||||||||
\(543\) | −47.9486 | −2.05767 | ||||||||
\(544\) | −5.23605 | −0.224494 | ||||||||
\(545\) | −10.9027 | −0.467018 | ||||||||
\(546\) | −5.15527 | −0.220625 | ||||||||
\(547\) | −23.9127 | −1.02243 | −0.511216 | − | 0.859452i | \(-0.670805\pi\) | ||||
−0.511216 | + | 0.859452i | \(0.670805\pi\) | |||||||
\(548\) | −3.87128 | −0.165373 | ||||||||
\(549\) | −52.2626 | −2.23051 | ||||||||
\(550\) | −1.77623 | −0.0757389 | ||||||||
\(551\) | 4.24584 | 0.180879 | ||||||||
\(552\) | −5.93657 | −0.252677 | ||||||||
\(553\) | 7.65528 | 0.325536 | ||||||||
\(554\) | −31.1705 | −1.32431 | ||||||||
\(555\) | −3.80647 | −0.161576 | ||||||||
\(556\) | −9.98899 | −0.423628 | ||||||||
\(557\) | 25.9381 | 1.09903 | 0.549516 | − | 0.835483i | \(-0.314812\pi\) | ||||
0.549516 | + | 0.835483i | \(0.314812\pi\) | |||||||
\(558\) | −28.6485 | −1.21279 | ||||||||
\(559\) | 3.53465 | 0.149500 | ||||||||
\(560\) | −2.17132 | −0.0917551 | ||||||||
\(561\) | −24.5208 | −1.03527 | ||||||||
\(562\) | −13.8505 | −0.584247 | ||||||||
\(563\) | −11.0540 | −0.465869 | −0.232934 | − | 0.972492i | \(-0.574833\pi\) | ||||
−0.232934 | + | 0.972492i | \(0.574833\pi\) | |||||||
\(564\) | 22.1524 | 0.932786 | ||||||||
\(565\) | 10.5787 | 0.445049 | ||||||||
\(566\) | −17.4713 | −0.734373 | ||||||||
\(567\) | −11.3813 | −0.477968 | ||||||||
\(568\) | 14.4146 | 0.604822 | ||||||||
\(569\) | −0.786619 | −0.0329768 | −0.0164884 | − | 0.999864i | \(-0.505249\pi\) | ||||
−0.0164884 | + | 0.999864i | \(0.505249\pi\) | |||||||
\(570\) | 2.75621 | 0.115445 | ||||||||
\(571\) | 27.4530 | 1.14887 | 0.574435 | − | 0.818550i | \(-0.305222\pi\) | ||||
0.574435 | + | 0.818550i | \(0.305222\pi\) | |||||||
\(572\) | −1.59955 | −0.0668805 | ||||||||
\(573\) | 33.5559 | 1.40182 | ||||||||
\(574\) | 1.91910 | 0.0801015 | ||||||||
\(575\) | 2.25167 | 0.0939013 | ||||||||
\(576\) | 3.95120 | 0.164633 | ||||||||
\(577\) | 0.759900 | 0.0316350 | 0.0158175 | − | 0.999875i | \(-0.494965\pi\) | ||||
0.0158175 | + | 0.999875i | \(0.494965\pi\) | |||||||
\(578\) | 10.4163 | 0.433259 | ||||||||
\(579\) | −5.40592 | −0.224662 | ||||||||
\(580\) | −4.06145 | −0.168642 | ||||||||
\(581\) | −38.0478 | −1.57849 | ||||||||
\(582\) | −4.30031 | −0.178254 | ||||||||
\(583\) | −3.55550 | −0.147254 | ||||||||
\(584\) | 12.9522 | 0.535965 | ||||||||
\(585\) | −3.55817 | −0.147112 | ||||||||
\(586\) | −18.2160 | −0.752498 | ||||||||
\(587\) | −20.6196 | −0.851063 | −0.425531 | − | 0.904944i | \(-0.639913\pi\) | ||||
−0.425531 | + | 0.904944i | \(0.639913\pi\) | |||||||
\(588\) | 6.02539 | 0.248483 | ||||||||
\(589\) | −7.57976 | −0.312319 | ||||||||
\(590\) | −1.78596 | −0.0735269 | ||||||||
\(591\) | 47.0162 | 1.93399 | ||||||||
\(592\) | −1.44375 | −0.0593378 | ||||||||
\(593\) | −46.5255 | −1.91057 | −0.955286 | − | 0.295682i | \(-0.904453\pi\) | ||||
−0.955286 | + | 0.295682i | \(0.904453\pi\) | |||||||
\(594\) | 4.45452 | 0.182771 | ||||||||
\(595\) | 11.3692 | 0.466090 | ||||||||
\(596\) | 2.81037 | 0.115117 | ||||||||
\(597\) | 17.4839 | 0.715569 | ||||||||
\(598\) | 2.02770 | 0.0829187 | ||||||||
\(599\) | 2.85734 | 0.116748 | 0.0583740 | − | 0.998295i | \(-0.481408\pi\) | ||||
0.0583740 | + | 0.998295i | \(0.481408\pi\) | |||||||
\(600\) | −2.63651 | −0.107635 | ||||||||
\(601\) | 1.00000 | 0.0407909 | ||||||||
\(602\) | 8.52261 | 0.347356 | ||||||||
\(603\) | −3.70245 | −0.150775 | ||||||||
\(604\) | −11.2886 | −0.459325 | ||||||||
\(605\) | 7.84499 | 0.318944 | ||||||||
\(606\) | −34.7158 | −1.41023 | ||||||||
\(607\) | −4.60050 | −0.186728 | −0.0933642 | − | 0.995632i | \(-0.529762\pi\) | ||||
−0.0933642 | + | 0.995632i | \(0.529762\pi\) | |||||||
\(608\) | 1.04540 | 0.0423966 | ||||||||
\(609\) | −23.2506 | −0.942163 | ||||||||
\(610\) | 13.2270 | 0.535547 | ||||||||
\(611\) | −7.56640 | −0.306104 | ||||||||
\(612\) | −20.6887 | −0.836291 | ||||||||
\(613\) | 8.65659 | 0.349636 | 0.174818 | − | 0.984601i | \(-0.444066\pi\) | ||||
0.174818 | + | 0.984601i | \(0.444066\pi\) | |||||||
\(614\) | 9.98595 | 0.403000 | ||||||||
\(615\) | 2.33025 | 0.0939647 | ||||||||
\(616\) | −3.85677 | −0.155394 | ||||||||
\(617\) | 31.2527 | 1.25819 | 0.629093 | − | 0.777330i | \(-0.283426\pi\) | ||||
0.629093 | + | 0.777330i | \(0.283426\pi\) | |||||||
\(618\) | 6.82638 | 0.274597 | ||||||||
\(619\) | −6.63931 | −0.266856 | −0.133428 | − | 0.991058i | \(-0.542599\pi\) | ||||
−0.133428 | + | 0.991058i | \(0.542599\pi\) | |||||||
\(620\) | 7.25058 | 0.291190 | ||||||||
\(621\) | −5.64685 | −0.226600 | ||||||||
\(622\) | 0.172246 | 0.00690645 | ||||||||
\(623\) | −5.73254 | −0.229670 | ||||||||
\(624\) | −2.37426 | −0.0950463 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −27.8800 | −1.11431 | ||||||||
\(627\) | 4.89568 | 0.195514 | ||||||||
\(628\) | −10.6219 | −0.423859 | ||||||||
\(629\) | 7.55956 | 0.301420 | ||||||||
\(630\) | −8.57932 | −0.341808 | ||||||||
\(631\) | 23.2236 | 0.924519 | 0.462259 | − | 0.886745i | \(-0.347039\pi\) | ||||
0.462259 | + | 0.886745i | \(0.347039\pi\) | |||||||
\(632\) | 3.52563 | 0.140242 | ||||||||
\(633\) | −50.7417 | −2.01680 | ||||||||
\(634\) | −30.3430 | −1.20507 | ||||||||
\(635\) | −8.06671 | −0.320118 | ||||||||
\(636\) | −5.27753 | −0.209268 | ||||||||
\(637\) | −2.05803 | −0.0815423 | ||||||||
\(638\) | −7.21408 | −0.285608 | ||||||||
\(639\) | 56.9548 | 2.25310 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 2.38410 | 0.0941663 | 0.0470831 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470831 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(642\) | −6.97971 | −0.275467 | ||||||||
\(643\) | 30.8278 | 1.21573 | 0.607864 | − | 0.794041i | \(-0.292026\pi\) | ||||
0.607864 | + | 0.794041i | \(0.292026\pi\) | |||||||
\(644\) | 4.88911 | 0.192658 | ||||||||
\(645\) | 10.3485 | 0.407472 | ||||||||
\(646\) | −5.47377 | −0.215363 | ||||||||
\(647\) | 14.0342 | 0.551742 | 0.275871 | − | 0.961195i | \(-0.411034\pi\) | ||||
0.275871 | + | 0.961195i | \(0.411034\pi\) | |||||||
\(648\) | −5.24163 | −0.205911 | ||||||||
\(649\) | −3.17228 | −0.124523 | ||||||||
\(650\) | 0.900529 | 0.0353216 | ||||||||
\(651\) | 41.5075 | 1.62681 | ||||||||
\(652\) | −16.8717 | −0.660746 | ||||||||
\(653\) | 3.78451 | 0.148099 | 0.0740497 | − | 0.997255i | \(-0.476408\pi\) | ||||
0.0740497 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(654\) | −28.7450 | −1.12402 | ||||||||
\(655\) | −1.41270 | −0.0551987 | ||||||||
\(656\) | 0.883837 | 0.0345081 | ||||||||
\(657\) | 51.1766 | 1.99659 | ||||||||
\(658\) | −18.2438 | −0.711218 | ||||||||
\(659\) | 35.2237 | 1.37212 | 0.686061 | − | 0.727544i | \(-0.259338\pi\) | ||||
0.686061 | + | 0.727544i | \(0.259338\pi\) | |||||||
\(660\) | −4.68306 | −0.182288 | ||||||||
\(661\) | 27.7448 | 1.07915 | 0.539575 | − | 0.841938i | \(-0.318585\pi\) | ||||
0.539575 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(662\) | 27.0931 | 1.05300 | ||||||||
\(663\) | 12.4317 | 0.482808 | ||||||||
\(664\) | −17.5229 | −0.680020 | ||||||||
\(665\) | −2.26990 | −0.0880230 | ||||||||
\(666\) | −5.70455 | −0.221047 | ||||||||
\(667\) | 9.14506 | 0.354098 | ||||||||
\(668\) | −7.27037 | −0.281299 | ||||||||
\(669\) | −22.6654 | −0.876293 | ||||||||
\(670\) | 0.937044 | 0.0362012 | ||||||||
\(671\) | 23.4943 | 0.906987 | ||||||||
\(672\) | −5.72472 | −0.220836 | ||||||||
\(673\) | 37.6678 | 1.45199 | 0.725994 | − | 0.687702i | \(-0.241380\pi\) | ||||
0.725994 | + | 0.687702i | \(0.241380\pi\) | |||||||
\(674\) | 24.6657 | 0.950088 | ||||||||
\(675\) | −2.50784 | −0.0965270 | ||||||||
\(676\) | −12.1890 | −0.468810 | ||||||||
\(677\) | −22.2553 | −0.855341 | −0.427671 | − | 0.903935i | \(-0.640666\pi\) | ||||
−0.427671 | + | 0.903935i | \(0.640666\pi\) | |||||||
\(678\) | 27.8909 | 1.07114 | ||||||||
\(679\) | 3.54156 | 0.135912 | ||||||||
\(680\) | 5.23605 | 0.200794 | ||||||||
\(681\) | 10.3291 | 0.395811 | ||||||||
\(682\) | 12.8787 | 0.493152 | ||||||||
\(683\) | −23.4223 | −0.896228 | −0.448114 | − | 0.893976i | \(-0.647904\pi\) | ||||
−0.448114 | + | 0.893976i | \(0.647904\pi\) | |||||||
\(684\) | 4.13058 | 0.157937 | ||||||||
\(685\) | 3.87128 | 0.147914 | ||||||||
\(686\) | −20.1615 | −0.769770 | ||||||||
\(687\) | −3.02979 | −0.115594 | ||||||||
\(688\) | 3.92508 | 0.149642 | ||||||||
\(689\) | 1.80260 | 0.0686735 | ||||||||
\(690\) | 5.93657 | 0.226001 | ||||||||
\(691\) | 4.84037 | 0.184136 | 0.0920681 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920681 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(692\) | −15.6152 | −0.593601 | ||||||||
\(693\) | −15.2389 | −0.578877 | ||||||||
\(694\) | 25.1247 | 0.953720 | ||||||||
\(695\) | 9.98899 | 0.378904 | ||||||||
\(696\) | −10.7081 | −0.405888 | ||||||||
\(697\) | −4.62782 | −0.175291 | ||||||||
\(698\) | 23.8129 | 0.901331 | ||||||||
\(699\) | 65.7812 | 2.48807 | ||||||||
\(700\) | 2.17132 | 0.0820682 | ||||||||
\(701\) | 4.91616 | 0.185681 | 0.0928404 | − | 0.995681i | \(-0.470405\pi\) | ||||
0.0928404 | + | 0.995681i | \(0.470405\pi\) | |||||||
\(702\) | −2.25839 | −0.0852373 | ||||||||
\(703\) | −1.50930 | −0.0569243 | ||||||||
\(704\) | −1.77623 | −0.0669443 | ||||||||
\(705\) | −22.1524 | −0.834309 | ||||||||
\(706\) | 12.0812 | 0.454681 | ||||||||
\(707\) | 28.5905 | 1.07526 | ||||||||
\(708\) | −4.70871 | −0.176964 | ||||||||
\(709\) | 27.7789 | 1.04326 | 0.521629 | − | 0.853173i | \(-0.325325\pi\) | ||||
0.521629 | + | 0.853173i | \(0.325325\pi\) | |||||||
\(710\) | −14.4146 | −0.540969 | ||||||||
\(711\) | 13.9305 | 0.522433 | ||||||||
\(712\) | −2.64012 | −0.0989426 | ||||||||
\(713\) | −16.3260 | −0.611412 | ||||||||
\(714\) | 29.9749 | 1.12178 | ||||||||
\(715\) | 1.59955 | 0.0598198 | ||||||||
\(716\) | 20.0642 | 0.749836 | ||||||||
\(717\) | 61.9721 | 2.31439 | ||||||||
\(718\) | −24.6600 | −0.920303 | ||||||||
\(719\) | 30.6066 | 1.14143 | 0.570716 | − | 0.821147i | \(-0.306666\pi\) | ||||
0.570716 | + | 0.821147i | \(0.306666\pi\) | |||||||
\(720\) | −3.95120 | −0.147252 | ||||||||
\(721\) | −5.62193 | −0.209371 | ||||||||
\(722\) | −17.9071 | −0.666435 | ||||||||
\(723\) | 60.5906 | 2.25339 | ||||||||
\(724\) | 18.1864 | 0.675892 | ||||||||
\(725\) | 4.06145 | 0.150838 | ||||||||
\(726\) | 20.6834 | 0.767634 | ||||||||
\(727\) | −18.2848 | −0.678147 | −0.339074 | − | 0.940760i | \(-0.610114\pi\) | ||||
−0.339074 | + | 0.940760i | \(0.610114\pi\) | |||||||
\(728\) | 1.95534 | 0.0724696 | ||||||||
\(729\) | −40.5466 | −1.50173 | ||||||||
\(730\) | −12.9522 | −0.479382 | ||||||||
\(731\) | −20.5519 | −0.760140 | ||||||||
\(732\) | 34.8732 | 1.28895 | ||||||||
\(733\) | 20.8955 | 0.771791 | 0.385896 | − | 0.922542i | \(-0.373892\pi\) | ||||
0.385896 | + | 0.922542i | \(0.373892\pi\) | |||||||
\(734\) | 7.31637 | 0.270052 | ||||||||
\(735\) | −6.02539 | −0.222250 | ||||||||
\(736\) | 2.25167 | 0.0829978 | ||||||||
\(737\) | 1.66441 | 0.0613093 | ||||||||
\(738\) | 3.49222 | 0.128550 | ||||||||
\(739\) | −15.9178 | −0.585546 | −0.292773 | − | 0.956182i | \(-0.594578\pi\) | ||||
−0.292773 | + | 0.956182i | \(0.594578\pi\) | |||||||
\(740\) | 1.44375 | 0.0530734 | ||||||||
\(741\) | −2.48205 | −0.0911803 | ||||||||
\(742\) | 4.34636 | 0.159560 | ||||||||
\(743\) | 19.6056 | 0.719258 | 0.359629 | − | 0.933095i | \(-0.382903\pi\) | ||||
0.359629 | + | 0.933095i | \(0.382903\pi\) | |||||||
\(744\) | 19.1163 | 0.700836 | ||||||||
\(745\) | −2.81037 | −0.102964 | ||||||||
\(746\) | −13.8046 | −0.505423 | ||||||||
\(747\) | −69.2364 | −2.53323 | ||||||||
\(748\) | 9.30046 | 0.340058 | ||||||||
\(749\) | 5.74820 | 0.210035 | ||||||||
\(750\) | 2.63651 | 0.0962718 | ||||||||
\(751\) | 47.6108 | 1.73734 | 0.868672 | − | 0.495387i | \(-0.164974\pi\) | ||||
0.868672 | + | 0.495387i | \(0.164974\pi\) | |||||||
\(752\) | −8.40218 | −0.306396 | ||||||||
\(753\) | 7.51836 | 0.273984 | ||||||||
\(754\) | 3.65745 | 0.133196 | ||||||||
\(755\) | 11.2886 | 0.410833 | ||||||||
\(756\) | −5.44534 | −0.198045 | ||||||||
\(757\) | 9.83741 | 0.357547 | 0.178773 | − | 0.983890i | \(-0.442787\pi\) | ||||
0.178773 | + | 0.983890i | \(0.442787\pi\) | |||||||
\(758\) | 19.7863 | 0.718672 | ||||||||
\(759\) | 10.5447 | 0.382749 | ||||||||
\(760\) | −1.04540 | −0.0379207 | ||||||||
\(761\) | −31.8608 | −1.15495 | −0.577477 | − | 0.816407i | \(-0.695963\pi\) | ||||
−0.577477 | + | 0.816407i | \(0.695963\pi\) | |||||||
\(762\) | −21.2680 | −0.770458 | ||||||||
\(763\) | 23.6732 | 0.857026 | ||||||||
\(764\) | −12.7274 | −0.460461 | ||||||||
\(765\) | 20.6887 | 0.748001 | ||||||||
\(766\) | −29.8608 | −1.07891 | ||||||||
\(767\) | 1.60831 | 0.0580727 | ||||||||
\(768\) | −2.63651 | −0.0951369 | ||||||||
\(769\) | −23.7125 | −0.855093 | −0.427546 | − | 0.903993i | \(-0.640622\pi\) | ||||
−0.427546 | + | 0.903993i | \(0.640622\pi\) | |||||||
\(770\) | 3.85677 | 0.138989 | ||||||||
\(771\) | 9.36177 | 0.337156 | ||||||||
\(772\) | 2.05041 | 0.0737957 | ||||||||
\(773\) | −16.9672 | −0.610269 | −0.305135 | − | 0.952309i | \(-0.598701\pi\) | ||||
−0.305135 | + | 0.952309i | \(0.598701\pi\) | |||||||
\(774\) | 15.5088 | 0.557451 | ||||||||
\(775\) | −7.25058 | −0.260449 | ||||||||
\(776\) | 1.63106 | 0.0585516 | ||||||||
\(777\) | 8.26507 | 0.296508 | ||||||||
\(778\) | −18.9990 | −0.681148 | ||||||||
\(779\) | 0.923964 | 0.0331044 | ||||||||
\(780\) | 2.37426 | 0.0850120 | ||||||||
\(781\) | −25.6036 | −0.916170 | ||||||||
\(782\) | −11.7899 | −0.421606 | ||||||||
\(783\) | −10.1855 | −0.363999 | ||||||||
\(784\) | −2.28536 | −0.0816201 | ||||||||
\(785\) | 10.6219 | 0.379111 | ||||||||
\(786\) | −3.72460 | −0.132852 | ||||||||
\(787\) | 21.8966 | 0.780528 | 0.390264 | − | 0.920703i | \(-0.372384\pi\) | ||||
0.390264 | + | 0.920703i | \(0.372384\pi\) | |||||||
\(788\) | −17.8327 | −0.635265 | ||||||||
\(789\) | 26.2606 | 0.934901 | ||||||||
\(790\) | −3.52563 | −0.125436 | ||||||||
\(791\) | −22.9698 | −0.816711 | ||||||||
\(792\) | −7.01825 | −0.249383 | ||||||||
\(793\) | −11.9113 | −0.422983 | ||||||||
\(794\) | 6.87745 | 0.244071 | ||||||||
\(795\) | 5.27753 | 0.187175 | ||||||||
\(796\) | −6.63145 | −0.235046 | ||||||||
\(797\) | −12.2229 | −0.432956 | −0.216478 | − | 0.976287i | \(-0.569457\pi\) | ||||
−0.216478 | + | 0.976287i | \(0.569457\pi\) | |||||||
\(798\) | −5.98462 | −0.211853 | ||||||||
\(799\) | 43.9943 | 1.55640 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −10.4316 | −0.368583 | ||||||||
\(802\) | −8.89445 | −0.314074 | ||||||||
\(803\) | −23.0061 | −0.811868 | ||||||||
\(804\) | 2.47053 | 0.0871288 | ||||||||
\(805\) | −4.88911 | −0.172318 | ||||||||
\(806\) | −6.52936 | −0.229987 | ||||||||
\(807\) | 78.9796 | 2.78021 | ||||||||
\(808\) | 13.1673 | 0.463225 | ||||||||
\(809\) | −24.7125 | −0.868846 | −0.434423 | − | 0.900709i | \(-0.643048\pi\) | ||||
−0.434423 | + | 0.900709i | \(0.643048\pi\) | |||||||
\(810\) | 5.24163 | 0.184172 | ||||||||
\(811\) | 48.0885 | 1.68862 | 0.844309 | − | 0.535857i | \(-0.180011\pi\) | ||||
0.844309 | + | 0.535857i | \(0.180011\pi\) | |||||||
\(812\) | 8.81871 | 0.309476 | ||||||||
\(813\) | −68.8603 | −2.41503 | ||||||||
\(814\) | 2.56444 | 0.0898836 | ||||||||
\(815\) | 16.8717 | 0.590989 | ||||||||
\(816\) | 13.8049 | 0.483269 | ||||||||
\(817\) | 4.10328 | 0.143556 | ||||||||
\(818\) | −10.7251 | −0.374995 | ||||||||
\(819\) | 7.72592 | 0.269966 | ||||||||
\(820\) | −0.883837 | −0.0308649 | ||||||||
\(821\) | 8.96380 | 0.312839 | 0.156419 | − | 0.987691i | \(-0.450005\pi\) | ||||
0.156419 | + | 0.987691i | \(0.450005\pi\) | |||||||
\(822\) | 10.2067 | 0.355999 | ||||||||
\(823\) | 23.8389 | 0.830973 | 0.415486 | − | 0.909599i | \(-0.363611\pi\) | ||||
0.415486 | + | 0.909599i | \(0.363611\pi\) | |||||||
\(824\) | −2.58917 | −0.0901981 | ||||||||
\(825\) | 4.68306 | 0.163043 | ||||||||
\(826\) | 3.87790 | 0.134929 | ||||||||
\(827\) | 1.26283 | 0.0439128 | 0.0219564 | − | 0.999759i | \(-0.493011\pi\) | ||||
0.0219564 | + | 0.999759i | \(0.493011\pi\) | |||||||
\(828\) | 8.89681 | 0.309185 | ||||||||
\(829\) | −8.90497 | −0.309282 | −0.154641 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154641 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(830\) | 17.5229 | 0.608228 | ||||||||
\(831\) | 82.1815 | 2.85084 | ||||||||
\(832\) | 0.900529 | 0.0312202 | ||||||||
\(833\) | 11.9663 | 0.414607 | ||||||||
\(834\) | 26.3361 | 0.911944 | ||||||||
\(835\) | 7.27037 | 0.251601 | ||||||||
\(836\) | −1.85688 | −0.0642214 | ||||||||
\(837\) | 18.1833 | 0.628508 | ||||||||
\(838\) | −24.4326 | −0.844009 | ||||||||
\(839\) | 12.5029 | 0.431649 | 0.215824 | − | 0.976432i | \(-0.430756\pi\) | ||||
0.215824 | + | 0.976432i | \(0.430756\pi\) | |||||||
\(840\) | 5.72472 | 0.197521 | ||||||||
\(841\) | −12.5046 | −0.431195 | ||||||||
\(842\) | 31.6170 | 1.08959 | ||||||||
\(843\) | 36.5170 | 1.25771 | ||||||||
\(844\) | 19.2458 | 0.662467 | ||||||||
\(845\) | 12.1890 | 0.419316 | ||||||||
\(846\) | −33.1987 | −1.14139 | ||||||||
\(847\) | −17.0340 | −0.585295 | ||||||||
\(848\) | 2.00171 | 0.0687390 | ||||||||
\(849\) | 46.0632 | 1.58089 | ||||||||
\(850\) | −5.23605 | −0.179595 | ||||||||
\(851\) | −3.25086 | −0.111438 | ||||||||
\(852\) | −38.0042 | −1.30200 | ||||||||
\(853\) | −40.3463 | −1.38143 | −0.690716 | − | 0.723126i | \(-0.742705\pi\) | ||||
−0.690716 | + | 0.723126i | \(0.742705\pi\) | |||||||
\(854\) | −28.7201 | −0.982783 | ||||||||
\(855\) | −4.13058 | −0.141263 | ||||||||
\(856\) | 2.64733 | 0.0904838 | ||||||||
\(857\) | 17.1256 | 0.584999 | 0.292500 | − | 0.956266i | \(-0.405513\pi\) | ||||
0.292500 | + | 0.956266i | \(0.405513\pi\) | |||||||
\(858\) | 4.21723 | 0.143974 | ||||||||
\(859\) | −4.28665 | −0.146259 | −0.0731293 | − | 0.997322i | \(-0.523299\pi\) | ||||
−0.0731293 | + | 0.997322i | \(0.523299\pi\) | |||||||
\(860\) | −3.92508 | −0.133844 | ||||||||
\(861\) | −5.05972 | −0.172435 | ||||||||
\(862\) | −38.0324 | −1.29539 | ||||||||
\(863\) | 23.5022 | 0.800025 | 0.400013 | − | 0.916510i | \(-0.369006\pi\) | ||||
0.400013 | + | 0.916510i | \(0.369006\pi\) | |||||||
\(864\) | −2.50784 | −0.0853186 | ||||||||
\(865\) | 15.6152 | 0.530933 | ||||||||
\(866\) | 28.5182 | 0.969087 | ||||||||
\(867\) | −27.4626 | −0.932679 | ||||||||
\(868\) | −15.7434 | −0.534364 | ||||||||
\(869\) | −6.26234 | −0.212435 | ||||||||
\(870\) | 10.7081 | 0.363037 | ||||||||
\(871\) | −0.843835 | −0.0285923 | ||||||||
\(872\) | 10.9027 | 0.369211 | ||||||||
\(873\) | 6.44464 | 0.218118 | ||||||||
\(874\) | 2.35390 | 0.0796219 | ||||||||
\(875\) | −2.17132 | −0.0734041 | ||||||||
\(876\) | −34.1486 | −1.15377 | ||||||||
\(877\) | −40.4065 | −1.36443 | −0.682215 | − | 0.731152i | \(-0.738983\pi\) | ||||
−0.682215 | + | 0.731152i | \(0.738983\pi\) | |||||||
\(878\) | −2.50649 | −0.0845899 | ||||||||
\(879\) | 48.0268 | 1.61990 | ||||||||
\(880\) | 1.77623 | 0.0598768 | ||||||||
\(881\) | −23.8372 | −0.803094 | −0.401547 | − | 0.915838i | \(-0.631527\pi\) | ||||
−0.401547 | + | 0.915838i | \(0.631527\pi\) | |||||||
\(882\) | −9.02992 | −0.304053 | ||||||||
\(883\) | 16.9901 | 0.571763 | 0.285881 | − | 0.958265i | \(-0.407714\pi\) | ||||
0.285881 | + | 0.958265i | \(0.407714\pi\) | |||||||
\(884\) | −4.71522 | −0.158590 | ||||||||
\(885\) | 4.70871 | 0.158282 | ||||||||
\(886\) | −35.3204 | −1.18661 | ||||||||
\(887\) | 30.9578 | 1.03946 | 0.519730 | − | 0.854331i | \(-0.326033\pi\) | ||||
0.519730 | + | 0.854331i | \(0.326033\pi\) | |||||||
\(888\) | 3.80647 | 0.127737 | ||||||||
\(889\) | 17.5154 | 0.587448 | ||||||||
\(890\) | 2.64012 | 0.0884969 | ||||||||
\(891\) | 9.31036 | 0.311909 | ||||||||
\(892\) | 8.59672 | 0.287839 | ||||||||
\(893\) | −8.78364 | −0.293933 | ||||||||
\(894\) | −7.40958 | −0.247814 | ||||||||
\(895\) | −20.0642 | −0.670673 | ||||||||
\(896\) | 2.17132 | 0.0725388 | ||||||||
\(897\) | −5.34605 | −0.178499 | ||||||||
\(898\) | −24.4328 | −0.815334 | ||||||||
\(899\) | −29.4479 | −0.982141 | ||||||||
\(900\) | 3.95120 | 0.131707 | ||||||||
\(901\) | −10.4811 | −0.349175 | ||||||||
\(902\) | −1.56990 | −0.0522720 | ||||||||
\(903\) | −22.4700 | −0.747753 | ||||||||
\(904\) | −10.5787 | −0.351842 | ||||||||
\(905\) | −18.1864 | −0.604536 | ||||||||
\(906\) | 29.7624 | 0.988791 | ||||||||
\(907\) | −33.2719 | −1.10478 | −0.552388 | − | 0.833587i | \(-0.686283\pi\) | ||||
−0.552388 | + | 0.833587i | \(0.686283\pi\) | |||||||
\(908\) | −3.91770 | −0.130014 | ||||||||
\(909\) | 52.0267 | 1.72562 | ||||||||
\(910\) | −1.95534 | −0.0648188 | ||||||||
\(911\) | 29.7923 | 0.987064 | 0.493532 | − | 0.869728i | \(-0.335706\pi\) | ||||
0.493532 | + | 0.869728i | \(0.335706\pi\) | |||||||
\(912\) | −2.75621 | −0.0912673 | ||||||||
\(913\) | 31.1247 | 1.03008 | ||||||||
\(914\) | −20.9258 | −0.692162 | ||||||||
\(915\) | −34.8732 | −1.15287 | ||||||||
\(916\) | 1.14916 | 0.0379695 | ||||||||
\(917\) | 3.06742 | 0.101295 | ||||||||
\(918\) | 13.1312 | 0.433394 | ||||||||
\(919\) | 24.9119 | 0.821769 | 0.410885 | − | 0.911687i | \(-0.365220\pi\) | ||||
0.410885 | + | 0.911687i | \(0.365220\pi\) | |||||||
\(920\) | −2.25167 | −0.0742355 | ||||||||
\(921\) | −26.3281 | −0.867540 | ||||||||
\(922\) | 8.09838 | 0.266706 | ||||||||
\(923\) | 12.9807 | 0.427266 | ||||||||
\(924\) | 10.1684 | 0.334517 | ||||||||
\(925\) | −1.44375 | −0.0474703 | ||||||||
\(926\) | −33.1924 | −1.09077 | ||||||||
\(927\) | −10.2303 | −0.336008 | ||||||||
\(928\) | 4.06145 | 0.133324 | ||||||||
\(929\) | 21.3235 | 0.699603 | 0.349801 | − | 0.936824i | \(-0.386249\pi\) | ||||
0.349801 | + | 0.936824i | \(0.386249\pi\) | |||||||
\(930\) | −19.1163 | −0.626847 | ||||||||
\(931\) | −2.38912 | −0.0783002 | ||||||||
\(932\) | −24.9501 | −0.817267 | ||||||||
\(933\) | −0.454130 | −0.0148675 | ||||||||
\(934\) | 0.450355 | 0.0147361 | ||||||||
\(935\) | −9.30046 | −0.304157 | ||||||||
\(936\) | 3.55817 | 0.116302 | ||||||||
\(937\) | −10.3958 | −0.339616 | −0.169808 | − | 0.985477i | \(-0.554315\pi\) | ||||
−0.169808 | + | 0.985477i | \(0.554315\pi\) | |||||||
\(938\) | −2.03462 | −0.0664329 | ||||||||
\(939\) | 73.5060 | 2.39878 | ||||||||
\(940\) | 8.40218 | 0.274049 | ||||||||
\(941\) | 31.5844 | 1.02962 | 0.514811 | − | 0.857304i | \(-0.327862\pi\) | ||||
0.514811 | + | 0.857304i | \(0.327862\pi\) | |||||||
\(942\) | 28.0047 | 0.912443 | ||||||||
\(943\) | 1.99011 | 0.0648070 | ||||||||
\(944\) | 1.78596 | 0.0581281 | ||||||||
\(945\) | 5.44534 | 0.177137 | ||||||||
\(946\) | −6.97186 | −0.226675 | ||||||||
\(947\) | −33.6642 | −1.09394 | −0.546970 | − | 0.837152i | \(-0.684219\pi\) | ||||
−0.546970 | + | 0.837152i | \(0.684219\pi\) | |||||||
\(948\) | −9.29537 | −0.301900 | ||||||||
\(949\) | 11.6638 | 0.378623 | ||||||||
\(950\) | 1.04540 | 0.0339173 | ||||||||
\(951\) | 79.9996 | 2.59416 | ||||||||
\(952\) | −11.3692 | −0.368477 | ||||||||
\(953\) | −10.7582 | −0.348491 | −0.174246 | − | 0.984702i | \(-0.555749\pi\) | ||||
−0.174246 | + | 0.984702i | \(0.555749\pi\) | |||||||
\(954\) | 7.90915 | 0.256068 | ||||||||
\(955\) | 12.7274 | 0.411849 | ||||||||
\(956\) | −23.5053 | −0.760217 | ||||||||
\(957\) | 19.0200 | 0.614830 | ||||||||
\(958\) | 20.8688 | 0.674239 | ||||||||
\(959\) | −8.40580 | −0.271437 | ||||||||
\(960\) | 2.63651 | 0.0850931 | ||||||||
\(961\) | 21.5710 | 0.695838 | ||||||||
\(962\) | −1.30014 | −0.0419182 | ||||||||
\(963\) | 10.4601 | 0.337072 | ||||||||
\(964\) | −22.9813 | −0.740179 | ||||||||
\(965\) | −2.05041 | −0.0660049 | ||||||||
\(966\) | −12.8902 | −0.414735 | ||||||||
\(967\) | −22.0062 | −0.707673 | −0.353837 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353837 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(968\) | −7.84499 | −0.252148 | ||||||||
\(969\) | 14.4317 | 0.463612 | ||||||||
\(970\) | −1.63106 | −0.0523702 | ||||||||
\(971\) | −7.05416 | −0.226379 | −0.113189 | − | 0.993573i | \(-0.536107\pi\) | ||||
−0.113189 | + | 0.993573i | \(0.536107\pi\) | |||||||
\(972\) | 21.3432 | 0.684582 | ||||||||
\(973\) | −21.6893 | −0.695327 | ||||||||
\(974\) | 30.3844 | 0.973580 | ||||||||
\(975\) | −2.37426 | −0.0760370 | ||||||||
\(976\) | −13.2270 | −0.423387 | ||||||||
\(977\) | −18.2423 | −0.583624 | −0.291812 | − | 0.956476i | \(-0.594258\pi\) | ||||
−0.291812 | + | 0.956476i | \(0.594258\pi\) | |||||||
\(978\) | 44.4824 | 1.42239 | ||||||||
\(979\) | 4.68947 | 0.149876 | ||||||||
\(980\) | 2.28536 | 0.0730032 | ||||||||
\(981\) | 43.0785 | 1.37539 | ||||||||
\(982\) | 25.3306 | 0.808333 | ||||||||
\(983\) | −39.7802 | −1.26879 | −0.634396 | − | 0.773008i | \(-0.718751\pi\) | ||||
−0.634396 | + | 0.773008i | \(0.718751\pi\) | |||||||
\(984\) | −2.33025 | −0.0742856 | ||||||||
\(985\) | 17.8327 | 0.568198 | ||||||||
\(986\) | −21.2660 | −0.677246 | ||||||||
\(987\) | 48.1001 | 1.53104 | ||||||||
\(988\) | 0.941413 | 0.0299503 | ||||||||
\(989\) | 8.83800 | 0.281032 | ||||||||
\(990\) | 7.01825 | 0.223055 | ||||||||
\(991\) | −49.8743 | −1.58431 | −0.792155 | − | 0.610320i | \(-0.791041\pi\) | ||||
−0.792155 | + | 0.610320i | \(0.791041\pi\) | |||||||
\(992\) | −7.25058 | −0.230206 | ||||||||
\(993\) | −71.4314 | −2.26681 | ||||||||
\(994\) | 31.2987 | 0.992733 | ||||||||
\(995\) | 6.63145 | 0.210231 | ||||||||
\(996\) | 46.1993 | 1.46388 | ||||||||
\(997\) | 42.5584 | 1.34784 | 0.673919 | − | 0.738805i | \(-0.264610\pi\) | ||||
0.673919 | + | 0.738805i | \(0.264610\pi\) | |||||||
\(998\) | 0.774573 | 0.0245187 | ||||||||
\(999\) | 3.62071 | 0.114554 |
(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 | 6010.2.a.f.1.3 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.f.1.3 | ✓ | 22 | 1.1 | even | 1 | trivial |