Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1339,2,Mod(1,1339)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1339, 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("1339.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1339 = 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1339.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: | \(10.6919688306\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 1339.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0264721 | −0.0187186 | −0.00935930 | − | 0.999956i | \(-0.502979\pi\) | ||||
−0.00935930 | + | 0.999956i | \(0.502979\pi\) | |||||||
\(3\) | −1.87769 | −1.08408 | −0.542042 | − | 0.840352i | \(-0.682348\pi\) | ||||
−0.542042 | + | 0.840352i | \(0.682348\pi\) | |||||||
\(4\) | −1.99930 | −0.999650 | ||||||||
\(5\) | 2.52751 | 1.13034 | 0.565168 | − | 0.824976i | \(-0.308811\pi\) | ||||
0.565168 | + | 0.824976i | \(0.308811\pi\) | |||||||
\(6\) | 0.0497063 | 0.0202925 | ||||||||
\(7\) | −1.16160 | −0.439043 | −0.219522 | − | 0.975608i | \(-0.570450\pi\) | ||||
−0.219522 | + | 0.975608i | \(0.570450\pi\) | |||||||
\(8\) | 0.105870 | 0.0374307 | ||||||||
\(9\) | 0.525708 | 0.175236 | ||||||||
\(10\) | −0.0669085 | −0.0211583 | ||||||||
\(11\) | 0.665143 | 0.200548 | 0.100274 | − | 0.994960i | \(-0.468028\pi\) | ||||
0.100274 | + | 0.994960i | \(0.468028\pi\) | |||||||
\(12\) | 3.75406 | 1.08370 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.0307500 | 0.00821828 | ||||||||
\(15\) | −4.74587 | −1.22538 | ||||||||
\(16\) | 3.99580 | 0.998949 | ||||||||
\(17\) | −0.273990 | −0.0664522 | −0.0332261 | − | 0.999448i | \(-0.510578\pi\) | ||||
−0.0332261 | + | 0.999448i | \(0.510578\pi\) | |||||||
\(18\) | −0.0139166 | −0.00328017 | ||||||||
\(19\) | 6.34288 | 1.45516 | 0.727579 | − | 0.686024i | \(-0.240646\pi\) | ||||
0.727579 | + | 0.686024i | \(0.240646\pi\) | |||||||
\(20\) | −5.05325 | −1.12994 | ||||||||
\(21\) | 2.18112 | 0.475959 | ||||||||
\(22\) | −0.0176077 | −0.00375398 | ||||||||
\(23\) | −4.90600 | −1.02297 | −0.511486 | − | 0.859292i | \(-0.670905\pi\) | ||||
−0.511486 | + | 0.859292i | \(0.670905\pi\) | |||||||
\(24\) | −0.198791 | −0.0405779 | ||||||||
\(25\) | 1.38831 | 0.277661 | ||||||||
\(26\) | 0.0264721 | 0.00519161 | ||||||||
\(27\) | 4.64595 | 0.894113 | ||||||||
\(28\) | 2.32238 | 0.438889 | ||||||||
\(29\) | −1.80420 | −0.335032 | −0.167516 | − | 0.985869i | \(-0.553575\pi\) | ||||
−0.167516 | + | 0.985869i | \(0.553575\pi\) | |||||||
\(30\) | 0.125633 | 0.0229374 | ||||||||
\(31\) | −0.915299 | −0.164393 | −0.0821963 | − | 0.996616i | \(-0.526193\pi\) | ||||
−0.0821963 | + | 0.996616i | \(0.526193\pi\) | |||||||
\(32\) | −0.317517 | −0.0561296 | ||||||||
\(33\) | −1.24893 | −0.217411 | ||||||||
\(34\) | 0.00725308 | 0.00124389 | ||||||||
\(35\) | −2.93595 | −0.496267 | ||||||||
\(36\) | −1.05105 | −0.175175 | ||||||||
\(37\) | −1.13362 | −0.186366 | −0.0931829 | − | 0.995649i | \(-0.529704\pi\) | ||||
−0.0931829 | + | 0.995649i | \(0.529704\pi\) | |||||||
\(38\) | −0.167910 | −0.0272385 | ||||||||
\(39\) | 1.87769 | 0.300671 | ||||||||
\(40\) | 0.267587 | 0.0423093 | ||||||||
\(41\) | −11.7774 | −1.83931 | −0.919657 | − | 0.392723i | \(-0.871533\pi\) | ||||
−0.919657 | + | 0.392723i | \(0.871533\pi\) | |||||||
\(42\) | −0.0577388 | −0.00890929 | ||||||||
\(43\) | 1.90151 | 0.289977 | 0.144988 | − | 0.989433i | \(-0.453685\pi\) | ||||
0.144988 | + | 0.989433i | \(0.453685\pi\) | |||||||
\(44\) | −1.32982 | −0.200478 | ||||||||
\(45\) | 1.32873 | 0.198076 | ||||||||
\(46\) | 0.129872 | 0.0191486 | ||||||||
\(47\) | 8.92385 | 1.30168 | 0.650838 | − | 0.759216i | \(-0.274417\pi\) | ||||
0.650838 | + | 0.759216i | \(0.274417\pi\) | |||||||
\(48\) | −7.50285 | −1.08294 | ||||||||
\(49\) | −5.65069 | −0.807241 | ||||||||
\(50\) | −0.0367514 | −0.00519743 | ||||||||
\(51\) | 0.514467 | 0.0720397 | ||||||||
\(52\) | 1.99930 | 0.277253 | ||||||||
\(53\) | 2.31382 | 0.317828 | 0.158914 | − | 0.987292i | \(-0.449201\pi\) | ||||
0.158914 | + | 0.987292i | \(0.449201\pi\) | |||||||
\(54\) | −0.122988 | −0.0167365 | ||||||||
\(55\) | 1.68115 | 0.226687 | ||||||||
\(56\) | −0.122978 | −0.0164337 | ||||||||
\(57\) | −11.9100 | −1.57751 | ||||||||
\(58\) | 0.0477610 | 0.00627132 | ||||||||
\(59\) | 9.78985 | 1.27453 | 0.637265 | − | 0.770645i | \(-0.280066\pi\) | ||||
0.637265 | + | 0.770645i | \(0.280066\pi\) | |||||||
\(60\) | 9.48842 | 1.22495 | ||||||||
\(61\) | −12.3026 | −1.57519 | −0.787595 | − | 0.616193i | \(-0.788674\pi\) | ||||
−0.787595 | + | 0.616193i | \(0.788674\pi\) | |||||||
\(62\) | 0.0242299 | 0.00307720 | ||||||||
\(63\) | −0.610662 | −0.0769362 | ||||||||
\(64\) | −7.98319 | −0.997898 | ||||||||
\(65\) | −2.52751 | −0.313499 | ||||||||
\(66\) | 0.0330618 | 0.00406963 | ||||||||
\(67\) | −13.4446 | −1.64252 | −0.821260 | − | 0.570555i | \(-0.806728\pi\) | ||||
−0.821260 | + | 0.570555i | \(0.806728\pi\) | |||||||
\(68\) | 0.547787 | 0.0664290 | ||||||||
\(69\) | 9.21194 | 1.10899 | ||||||||
\(70\) | 0.0777209 | 0.00928942 | ||||||||
\(71\) | −11.1693 | −1.32556 | −0.662779 | − | 0.748815i | \(-0.730623\pi\) | ||||
−0.662779 | + | 0.748815i | \(0.730623\pi\) | |||||||
\(72\) | 0.0556567 | 0.00655920 | ||||||||
\(73\) | 4.99515 | 0.584638 | 0.292319 | − | 0.956321i | \(-0.405573\pi\) | ||||
0.292319 | + | 0.956321i | \(0.405573\pi\) | |||||||
\(74\) | 0.0300093 | 0.00348851 | ||||||||
\(75\) | −2.60680 | −0.301008 | ||||||||
\(76\) | −12.6813 | −1.45465 | ||||||||
\(77\) | −0.772629 | −0.0880492 | ||||||||
\(78\) | −0.0497063 | −0.00562813 | ||||||||
\(79\) | −14.1648 | −1.59366 | −0.796832 | − | 0.604201i | \(-0.793492\pi\) | ||||
−0.796832 | + | 0.604201i | \(0.793492\pi\) | |||||||
\(80\) | 10.0994 | 1.12915 | ||||||||
\(81\) | −10.3008 | −1.14453 | ||||||||
\(82\) | 0.311771 | 0.0344294 | ||||||||
\(83\) | −1.68710 | −0.185183 | −0.0925916 | − | 0.995704i | \(-0.529515\pi\) | ||||
−0.0925916 | + | 0.995704i | \(0.529515\pi\) | |||||||
\(84\) | −4.36071 | −0.475792 | ||||||||
\(85\) | −0.692511 | −0.0751134 | ||||||||
\(86\) | −0.0503369 | −0.00542797 | ||||||||
\(87\) | 3.38772 | 0.363202 | ||||||||
\(88\) | 0.0704186 | 0.00750665 | ||||||||
\(89\) | 2.04119 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(90\) | −0.0351744 | −0.00370770 | ||||||||
\(91\) | 1.16160 | 0.121769 | ||||||||
\(92\) | 9.80857 | 1.02261 | ||||||||
\(93\) | 1.71865 | 0.178215 | ||||||||
\(94\) | −0.236233 | −0.0243656 | ||||||||
\(95\) | 16.0317 | 1.64482 | ||||||||
\(96\) | 0.596197 | 0.0608491 | ||||||||
\(97\) | −19.1043 | −1.93975 | −0.969875 | − | 0.243604i | \(-0.921670\pi\) | ||||
−0.969875 | + | 0.243604i | \(0.921670\pi\) | |||||||
\(98\) | 0.149586 | 0.0151104 | ||||||||
\(99\) | 0.349671 | 0.0351432 | ||||||||
\(100\) | −2.77564 | −0.277564 | ||||||||
\(101\) | −10.8816 | −1.08275 | −0.541377 | − | 0.840780i | \(-0.682097\pi\) | ||||
−0.541377 | + | 0.840780i | \(0.682097\pi\) | |||||||
\(102\) | −0.0136190 | −0.00134848 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −0.105870 | −0.0103814 | ||||||||
\(105\) | 5.51280 | 0.537994 | ||||||||
\(106\) | −0.0612518 | −0.00594930 | ||||||||
\(107\) | 1.93815 | 0.187368 | 0.0936838 | − | 0.995602i | \(-0.470136\pi\) | ||||
0.0936838 | + | 0.995602i | \(0.470136\pi\) | |||||||
\(108\) | −9.28864 | −0.893799 | ||||||||
\(109\) | −0.415219 | −0.0397707 | −0.0198854 | − | 0.999802i | \(-0.506330\pi\) | ||||
−0.0198854 | + | 0.999802i | \(0.506330\pi\) | |||||||
\(110\) | −0.0445037 | −0.00424326 | ||||||||
\(111\) | 2.12858 | 0.202036 | ||||||||
\(112\) | −4.64151 | −0.438582 | ||||||||
\(113\) | −2.07720 | −0.195407 | −0.0977035 | − | 0.995216i | \(-0.531150\pi\) | ||||
−0.0977035 | + | 0.995216i | \(0.531150\pi\) | |||||||
\(114\) | 0.315282 | 0.0295288 | ||||||||
\(115\) | −12.4000 | −1.15630 | ||||||||
\(116\) | 3.60714 | 0.334914 | ||||||||
\(117\) | −0.525708 | −0.0486017 | ||||||||
\(118\) | −0.259158 | −0.0238574 | ||||||||
\(119\) | 0.318266 | 0.0291754 | ||||||||
\(120\) | −0.502445 | −0.0458667 | ||||||||
\(121\) | −10.5576 | −0.959780 | ||||||||
\(122\) | 0.325677 | 0.0294854 | ||||||||
\(123\) | 22.1142 | 1.99397 | ||||||||
\(124\) | 1.82996 | 0.164335 | ||||||||
\(125\) | −9.12859 | −0.816486 | ||||||||
\(126\) | 0.0161655 | 0.00144014 | ||||||||
\(127\) | 3.34549 | 0.296864 | 0.148432 | − | 0.988923i | \(-0.452577\pi\) | ||||
0.148432 | + | 0.988923i | \(0.452577\pi\) | |||||||
\(128\) | 0.846366 | 0.0748089 | ||||||||
\(129\) | −3.57043 | −0.314359 | ||||||||
\(130\) | 0.0669085 | 0.00586827 | ||||||||
\(131\) | 2.97858 | 0.260240 | 0.130120 | − | 0.991498i | \(-0.458464\pi\) | ||||
0.130120 | + | 0.991498i | \(0.458464\pi\) | |||||||
\(132\) | 2.49698 | 0.217335 | ||||||||
\(133\) | −7.36789 | −0.638877 | ||||||||
\(134\) | 0.355907 | 0.0307457 | ||||||||
\(135\) | 11.7427 | 1.01065 | ||||||||
\(136\) | −0.0290073 | −0.00248735 | ||||||||
\(137\) | −13.2508 | −1.13210 | −0.566048 | − | 0.824372i | \(-0.691528\pi\) | ||||
−0.566048 | + | 0.824372i | \(0.691528\pi\) | |||||||
\(138\) | −0.243859 | −0.0207587 | ||||||||
\(139\) | 10.6139 | 0.900262 | 0.450131 | − | 0.892962i | \(-0.351377\pi\) | ||||
0.450131 | + | 0.892962i | \(0.351377\pi\) | |||||||
\(140\) | 5.86985 | 0.496093 | ||||||||
\(141\) | −16.7562 | −1.41113 | ||||||||
\(142\) | 0.295676 | 0.0248126 | ||||||||
\(143\) | −0.665143 | −0.0556220 | ||||||||
\(144\) | 2.10062 | 0.175052 | ||||||||
\(145\) | −4.56013 | −0.378699 | ||||||||
\(146\) | −0.132232 | −0.0109436 | ||||||||
\(147\) | 10.6102 | 0.875116 | ||||||||
\(148\) | 2.26644 | 0.186300 | ||||||||
\(149\) | −17.6602 | −1.44678 | −0.723390 | − | 0.690439i | \(-0.757417\pi\) | ||||
−0.723390 | + | 0.690439i | \(0.757417\pi\) | |||||||
\(150\) | 0.0690076 | 0.00563445 | ||||||||
\(151\) | −13.8272 | −1.12524 | −0.562622 | − | 0.826714i | \(-0.690207\pi\) | ||||
−0.562622 | + | 0.826714i | \(0.690207\pi\) | |||||||
\(152\) | 0.671520 | 0.0544675 | ||||||||
\(153\) | −0.144039 | −0.0116448 | ||||||||
\(154\) | 0.0204531 | 0.00164816 | ||||||||
\(155\) | −2.31343 | −0.185819 | ||||||||
\(156\) | −3.75406 | −0.300565 | ||||||||
\(157\) | 16.3694 | 1.30642 | 0.653211 | − | 0.757176i | \(-0.273421\pi\) | ||||
0.653211 | + | 0.757176i | \(0.273421\pi\) | |||||||
\(158\) | 0.374972 | 0.0298312 | ||||||||
\(159\) | −4.34464 | −0.344552 | ||||||||
\(160\) | −0.802527 | −0.0634453 | ||||||||
\(161\) | 5.69881 | 0.449129 | ||||||||
\(162\) | 0.272683 | 0.0214240 | ||||||||
\(163\) | 15.5596 | 1.21872 | 0.609360 | − | 0.792894i | \(-0.291426\pi\) | ||||
0.609360 | + | 0.792894i | \(0.291426\pi\) | |||||||
\(164\) | 23.5465 | 1.83867 | ||||||||
\(165\) | −3.15668 | −0.245747 | ||||||||
\(166\) | 0.0446611 | 0.00346637 | ||||||||
\(167\) | −1.98668 | −0.153734 | −0.0768671 | − | 0.997041i | \(-0.524492\pi\) | ||||
−0.0768671 | + | 0.997041i | \(0.524492\pi\) | |||||||
\(168\) | 0.230915 | 0.0178155 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.0183322 | 0.00140602 | ||||||||
\(171\) | 3.33451 | 0.254996 | ||||||||
\(172\) | −3.80168 | −0.289875 | ||||||||
\(173\) | 15.6300 | 1.18833 | 0.594164 | − | 0.804344i | \(-0.297483\pi\) | ||||
0.594164 | + | 0.804344i | \(0.297483\pi\) | |||||||
\(174\) | −0.0896802 | −0.00679864 | ||||||||
\(175\) | −1.61266 | −0.121905 | ||||||||
\(176\) | 2.65777 | 0.200337 | ||||||||
\(177\) | −18.3823 | −1.38170 | ||||||||
\(178\) | −0.0540347 | −0.00405007 | ||||||||
\(179\) | 15.3182 | 1.14493 | 0.572467 | − | 0.819928i | \(-0.305986\pi\) | ||||
0.572467 | + | 0.819928i | \(0.305986\pi\) | |||||||
\(180\) | −2.65653 | −0.198006 | ||||||||
\(181\) | 2.77898 | 0.206560 | 0.103280 | − | 0.994652i | \(-0.467066\pi\) | ||||
0.103280 | + | 0.994652i | \(0.467066\pi\) | |||||||
\(182\) | −0.0307500 | −0.00227934 | ||||||||
\(183\) | 23.1005 | 1.70764 | ||||||||
\(184\) | −0.519398 | −0.0382905 | ||||||||
\(185\) | −2.86523 | −0.210656 | ||||||||
\(186\) | −0.0454962 | −0.00333594 | ||||||||
\(187\) | −0.182242 | −0.0133269 | ||||||||
\(188\) | −17.8414 | −1.30122 | ||||||||
\(189\) | −5.39672 | −0.392554 | ||||||||
\(190\) | −0.424393 | −0.0307887 | ||||||||
\(191\) | −15.2138 | −1.10083 | −0.550416 | − | 0.834890i | \(-0.685531\pi\) | ||||
−0.550416 | + | 0.834890i | \(0.685531\pi\) | |||||||
\(192\) | 14.9899 | 1.08180 | ||||||||
\(193\) | 6.89410 | 0.496248 | 0.248124 | − | 0.968728i | \(-0.420186\pi\) | ||||
0.248124 | + | 0.968728i | \(0.420186\pi\) | |||||||
\(194\) | 0.505732 | 0.0363094 | ||||||||
\(195\) | 4.74587 | 0.339859 | ||||||||
\(196\) | 11.2974 | 0.806958 | ||||||||
\(197\) | 2.21792 | 0.158020 | 0.0790101 | − | 0.996874i | \(-0.474824\pi\) | ||||
0.0790101 | + | 0.996874i | \(0.474824\pi\) | |||||||
\(198\) | −0.00925653 | −0.000657833 0 | ||||||||
\(199\) | 9.73336 | 0.689980 | 0.344990 | − | 0.938606i | \(-0.387882\pi\) | ||||
0.344990 | + | 0.938606i | \(0.387882\pi\) | |||||||
\(200\) | 0.146980 | 0.0103930 | ||||||||
\(201\) | 25.2447 | 1.78063 | ||||||||
\(202\) | 0.288058 | 0.0202677 | ||||||||
\(203\) | 2.09576 | 0.147093 | ||||||||
\(204\) | −1.02857 | −0.0720145 | ||||||||
\(205\) | −29.7674 | −2.07904 | ||||||||
\(206\) | 0.0264721 | 0.00184440 | ||||||||
\(207\) | −2.57913 | −0.179262 | ||||||||
\(208\) | −3.99580 | −0.277059 | ||||||||
\(209\) | 4.21892 | 0.291829 | ||||||||
\(210\) | −0.145935 | −0.0100705 | ||||||||
\(211\) | 14.1331 | 0.972961 | 0.486481 | − | 0.873691i | \(-0.338280\pi\) | ||||
0.486481 | + | 0.873691i | \(0.338280\pi\) | |||||||
\(212\) | −4.62602 | −0.317717 | ||||||||
\(213\) | 20.9725 | 1.43701 | ||||||||
\(214\) | −0.0513068 | −0.00350726 | ||||||||
\(215\) | 4.80608 | 0.327772 | ||||||||
\(216\) | 0.491866 | 0.0334672 | ||||||||
\(217\) | 1.06321 | 0.0721754 | ||||||||
\(218\) | 0.0109917 | 0.000744453 0 | ||||||||
\(219\) | −9.37933 | −0.633796 | ||||||||
\(220\) | −3.36113 | −0.226607 | ||||||||
\(221\) | 0.273990 | 0.0184305 | ||||||||
\(222\) | −0.0563480 | −0.00378183 | ||||||||
\(223\) | −17.5433 | −1.17479 | −0.587393 | − | 0.809302i | \(-0.699846\pi\) | ||||
−0.587393 | + | 0.809302i | \(0.699846\pi\) | |||||||
\(224\) | 0.368827 | 0.0246433 | ||||||||
\(225\) | 0.729844 | 0.0486563 | ||||||||
\(226\) | 0.0549880 | 0.00365775 | ||||||||
\(227\) | 2.38137 | 0.158057 | 0.0790284 | − | 0.996872i | \(-0.474818\pi\) | ||||
0.0790284 | + | 0.996872i | \(0.474818\pi\) | |||||||
\(228\) | 23.8116 | 1.57696 | ||||||||
\(229\) | 16.3212 | 1.07853 | 0.539267 | − | 0.842135i | \(-0.318701\pi\) | ||||
0.539267 | + | 0.842135i | \(0.318701\pi\) | |||||||
\(230\) | 0.328253 | 0.0216444 | ||||||||
\(231\) | 1.45076 | 0.0954527 | ||||||||
\(232\) | −0.191010 | −0.0125405 | ||||||||
\(233\) | 8.02615 | 0.525810 | 0.262905 | − | 0.964822i | \(-0.415319\pi\) | ||||
0.262905 | + | 0.964822i | \(0.415319\pi\) | |||||||
\(234\) | 0.0139166 | 0.000909757 0 | ||||||||
\(235\) | 22.5551 | 1.47133 | ||||||||
\(236\) | −19.5728 | −1.27408 | ||||||||
\(237\) | 26.5971 | 1.72766 | ||||||||
\(238\) | −0.00842517 | −0.000546123 0 | ||||||||
\(239\) | −11.4228 | −0.738881 | −0.369440 | − | 0.929254i | \(-0.620451\pi\) | ||||
−0.369440 | + | 0.929254i | \(0.620451\pi\) | |||||||
\(240\) | −18.9635 | −1.22409 | ||||||||
\(241\) | 19.1046 | 1.23064 | 0.615319 | − | 0.788278i | \(-0.289027\pi\) | ||||
0.615319 | + | 0.788278i | \(0.289027\pi\) | |||||||
\(242\) | 0.279482 | 0.0179658 | ||||||||
\(243\) | 5.40376 | 0.346651 | ||||||||
\(244\) | 24.5966 | 1.57464 | ||||||||
\(245\) | −14.2822 | −0.912454 | ||||||||
\(246\) | −0.585409 | −0.0373243 | ||||||||
\(247\) | −6.34288 | −0.403588 | ||||||||
\(248\) | −0.0969026 | −0.00615332 | ||||||||
\(249\) | 3.16784 | 0.200754 | ||||||||
\(250\) | 0.241653 | 0.0152835 | ||||||||
\(251\) | 1.23750 | 0.0781105 | 0.0390553 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390553 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(252\) | 1.22090 | 0.0769092 | ||||||||
\(253\) | −3.26319 | −0.205155 | ||||||||
\(254\) | −0.0885622 | −0.00555689 | ||||||||
\(255\) | 1.30032 | 0.0814292 | ||||||||
\(256\) | 15.9440 | 0.996498 | ||||||||
\(257\) | 12.2839 | 0.766249 | 0.383124 | − | 0.923697i | \(-0.374848\pi\) | ||||
0.383124 | + | 0.923697i | \(0.374848\pi\) | |||||||
\(258\) | 0.0945169 | 0.00588437 | ||||||||
\(259\) | 1.31681 | 0.0818226 | ||||||||
\(260\) | 5.05325 | 0.313389 | ||||||||
\(261\) | −0.948483 | −0.0587096 | ||||||||
\(262\) | −0.0788493 | −0.00487133 | ||||||||
\(263\) | −7.40087 | −0.456357 | −0.228179 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228179 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(264\) | −0.132224 | −0.00813783 | ||||||||
\(265\) | 5.84821 | 0.359253 | ||||||||
\(266\) | 0.195044 | 0.0119589 | ||||||||
\(267\) | −3.83272 | −0.234559 | ||||||||
\(268\) | 26.8798 | 1.64194 | ||||||||
\(269\) | −9.73367 | −0.593472 | −0.296736 | − | 0.954959i | \(-0.595898\pi\) | ||||
−0.296736 | + | 0.954959i | \(0.595898\pi\) | |||||||
\(270\) | −0.310853 | −0.0189179 | ||||||||
\(271\) | −14.0883 | −0.855801 | −0.427901 | − | 0.903826i | \(-0.640747\pi\) | ||||
−0.427901 | + | 0.903826i | \(0.640747\pi\) | |||||||
\(272\) | −1.09481 | −0.0663824 | ||||||||
\(273\) | −2.18112 | −0.132007 | ||||||||
\(274\) | 0.350778 | 0.0211913 | ||||||||
\(275\) | 0.923422 | 0.0556844 | ||||||||
\(276\) | −18.4174 | −1.10860 | ||||||||
\(277\) | 22.3287 | 1.34160 | 0.670800 | − | 0.741639i | \(-0.265951\pi\) | ||||
0.670800 | + | 0.741639i | \(0.265951\pi\) | |||||||
\(278\) | −0.280973 | −0.0168517 | ||||||||
\(279\) | −0.481180 | −0.0288075 | ||||||||
\(280\) | −0.310829 | −0.0185756 | ||||||||
\(281\) | 31.5303 | 1.88094 | 0.940469 | − | 0.339879i | \(-0.110386\pi\) | ||||
0.940469 | + | 0.339879i | \(0.110386\pi\) | |||||||
\(282\) | 0.443572 | 0.0264143 | ||||||||
\(283\) | 29.7311 | 1.76733 | 0.883665 | − | 0.468121i | \(-0.155069\pi\) | ||||
0.883665 | + | 0.468121i | \(0.155069\pi\) | |||||||
\(284\) | 22.3309 | 1.32509 | ||||||||
\(285\) | −30.1025 | −1.78312 | ||||||||
\(286\) | 0.0176077 | 0.00104117 | ||||||||
\(287\) | 13.6806 | 0.807538 | ||||||||
\(288\) | −0.166921 | −0.00983593 | ||||||||
\(289\) | −16.9249 | −0.995584 | ||||||||
\(290\) | 0.120716 | 0.00708871 | ||||||||
\(291\) | 35.8719 | 2.10285 | ||||||||
\(292\) | −9.98680 | −0.584433 | ||||||||
\(293\) | −1.75503 | −0.102530 | −0.0512649 | − | 0.998685i | \(-0.516325\pi\) | ||||
−0.0512649 | + | 0.998685i | \(0.516325\pi\) | |||||||
\(294\) | −0.280875 | −0.0163810 | ||||||||
\(295\) | 24.7440 | 1.44065 | ||||||||
\(296\) | −0.120016 | −0.00697579 | ||||||||
\(297\) | 3.09022 | 0.179313 | ||||||||
\(298\) | 0.467503 | 0.0270817 | ||||||||
\(299\) | 4.90600 | 0.283721 | ||||||||
\(300\) | 5.21178 | 0.300902 | ||||||||
\(301\) | −2.20879 | −0.127312 | ||||||||
\(302\) | 0.366036 | 0.0210630 | ||||||||
\(303\) | 20.4321 | 1.17380 | ||||||||
\(304\) | 25.3449 | 1.45363 | ||||||||
\(305\) | −31.0950 | −1.78050 | ||||||||
\(306\) | 0.00381300 | 0.000217975 0 | ||||||||
\(307\) | −25.0177 | −1.42784 | −0.713919 | − | 0.700228i | \(-0.753082\pi\) | ||||
−0.713919 | + | 0.700228i | \(0.753082\pi\) | |||||||
\(308\) | 1.54472 | 0.0880184 | ||||||||
\(309\) | 1.87769 | 0.106818 | ||||||||
\(310\) | 0.0612413 | 0.00347827 | ||||||||
\(311\) | −26.0663 | −1.47808 | −0.739041 | − | 0.673660i | \(-0.764721\pi\) | ||||
−0.739041 | + | 0.673660i | \(0.764721\pi\) | |||||||
\(312\) | 0.198791 | 0.0112543 | ||||||||
\(313\) | −18.3238 | −1.03572 | −0.517862 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517862 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(314\) | −0.433333 | −0.0244544 | ||||||||
\(315\) | −1.54345 | −0.0869638 | ||||||||
\(316\) | 28.3197 | 1.59311 | ||||||||
\(317\) | 2.91049 | 0.163469 | 0.0817346 | − | 0.996654i | \(-0.473954\pi\) | ||||
0.0817346 | + | 0.996654i | \(0.473954\pi\) | |||||||
\(318\) | 0.115012 | 0.00644953 | ||||||||
\(319\) | −1.20005 | −0.0671899 | ||||||||
\(320\) | −20.1776 | −1.12796 | ||||||||
\(321\) | −3.63923 | −0.203122 | ||||||||
\(322\) | −0.150859 | −0.00840707 | ||||||||
\(323\) | −1.73788 | −0.0966985 | ||||||||
\(324\) | 20.5943 | 1.14413 | ||||||||
\(325\) | −1.38831 | −0.0770094 | ||||||||
\(326\) | −0.411895 | −0.0228127 | ||||||||
\(327\) | 0.779651 | 0.0431148 | ||||||||
\(328\) | −1.24687 | −0.0688467 | ||||||||
\(329\) | −10.3659 | −0.571492 | ||||||||
\(330\) | 0.0835640 | 0.00460005 | ||||||||
\(331\) | −20.4831 | −1.12585 | −0.562927 | − | 0.826507i | \(-0.690325\pi\) | ||||
−0.562927 | + | 0.826507i | \(0.690325\pi\) | |||||||
\(332\) | 3.37301 | 0.185118 | ||||||||
\(333\) | −0.595952 | −0.0326580 | ||||||||
\(334\) | 0.0525917 | 0.00287769 | ||||||||
\(335\) | −33.9814 | −1.85660 | ||||||||
\(336\) | 8.71531 | 0.475459 | ||||||||
\(337\) | −20.9638 | −1.14197 | −0.570986 | − | 0.820960i | \(-0.693439\pi\) | ||||
−0.570986 | + | 0.820960i | \(0.693439\pi\) | |||||||
\(338\) | −0.0264721 | −0.00143989 | ||||||||
\(339\) | 3.90034 | 0.211837 | ||||||||
\(340\) | 1.38454 | 0.0750871 | ||||||||
\(341\) | −0.608804 | −0.0329686 | ||||||||
\(342\) | −0.0882714 | −0.00477317 | ||||||||
\(343\) | 14.6950 | 0.793457 | ||||||||
\(344\) | 0.201312 | 0.0108540 | ||||||||
\(345\) | 23.2833 | 1.25353 | ||||||||
\(346\) | −0.413759 | −0.0222438 | ||||||||
\(347\) | −18.2463 | −0.979511 | −0.489755 | − | 0.871860i | \(-0.662914\pi\) | ||||
−0.489755 | + | 0.871860i | \(0.662914\pi\) | |||||||
\(348\) | −6.77307 | −0.363075 | ||||||||
\(349\) | −34.0706 | −1.82376 | −0.911878 | − | 0.410462i | \(-0.865367\pi\) | ||||
−0.911878 | + | 0.410462i | \(0.865367\pi\) | |||||||
\(350\) | 0.0426904 | 0.00228190 | ||||||||
\(351\) | −4.64595 | −0.247982 | ||||||||
\(352\) | −0.211194 | −0.0112567 | ||||||||
\(353\) | −25.4823 | −1.35629 | −0.678144 | − | 0.734929i | \(-0.737215\pi\) | ||||
−0.678144 | + | 0.734929i | \(0.737215\pi\) | |||||||
\(354\) | 0.486618 | 0.0258634 | ||||||||
\(355\) | −28.2306 | −1.49833 | ||||||||
\(356\) | −4.08095 | −0.216290 | ||||||||
\(357\) | −0.597604 | −0.0316286 | ||||||||
\(358\) | −0.405505 | −0.0214316 | ||||||||
\(359\) | 4.20677 | 0.222025 | 0.111012 | − | 0.993819i | \(-0.464591\pi\) | ||||
0.111012 | + | 0.993819i | \(0.464591\pi\) | |||||||
\(360\) | 0.140673 | 0.00741411 | ||||||||
\(361\) | 21.2322 | 1.11748 | ||||||||
\(362\) | −0.0735656 | −0.00386652 | ||||||||
\(363\) | 19.8238 | 1.04048 | ||||||||
\(364\) | −2.32238 | −0.121726 | ||||||||
\(365\) | 12.6253 | 0.660838 | ||||||||
\(366\) | −0.611519 | −0.0319646 | ||||||||
\(367\) | 27.8945 | 1.45608 | 0.728042 | − | 0.685533i | \(-0.240431\pi\) | ||||
0.728042 | + | 0.685533i | \(0.240431\pi\) | |||||||
\(368\) | −19.6034 | −1.02190 | ||||||||
\(369\) | −6.19145 | −0.322314 | ||||||||
\(370\) | 0.0758487 | 0.00394319 | ||||||||
\(371\) | −2.68773 | −0.139540 | ||||||||
\(372\) | −3.43609 | −0.178153 | ||||||||
\(373\) | −30.9092 | −1.60042 | −0.800208 | − | 0.599723i | \(-0.795277\pi\) | ||||
−0.800208 | + | 0.599723i | \(0.795277\pi\) | |||||||
\(374\) | 0.00482434 | 0.000249460 0 | ||||||||
\(375\) | 17.1406 | 0.885139 | ||||||||
\(376\) | 0.944767 | 0.0487226 | ||||||||
\(377\) | 1.80420 | 0.0929210 | ||||||||
\(378\) | 0.142863 | 0.00734806 | ||||||||
\(379\) | −5.21292 | −0.267770 | −0.133885 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133885 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(380\) | −32.0522 | −1.64424 | ||||||||
\(381\) | −6.28178 | −0.321826 | ||||||||
\(382\) | 0.402742 | 0.0206061 | ||||||||
\(383\) | −17.0700 | −0.872235 | −0.436118 | − | 0.899890i | \(-0.643647\pi\) | ||||
−0.436118 | + | 0.899890i | \(0.643647\pi\) | |||||||
\(384\) | −1.58921 | −0.0810990 | ||||||||
\(385\) | −1.95283 | −0.0995253 | ||||||||
\(386\) | −0.182501 | −0.00928907 | ||||||||
\(387\) | 0.999637 | 0.0508144 | ||||||||
\(388\) | 38.1953 | 1.93907 | ||||||||
\(389\) | −7.66444 | −0.388603 | −0.194301 | − | 0.980942i | \(-0.562244\pi\) | ||||
−0.194301 | + | 0.980942i | \(0.562244\pi\) | |||||||
\(390\) | −0.125633 | −0.00636169 | ||||||||
\(391\) | 1.34419 | 0.0679788 | ||||||||
\(392\) | −0.598238 | −0.0302156 | ||||||||
\(393\) | −5.59284 | −0.282121 | ||||||||
\(394\) | −0.0587130 | −0.00295792 | ||||||||
\(395\) | −35.8017 | −1.80138 | ||||||||
\(396\) | −0.699097 | −0.0351309 | ||||||||
\(397\) | −17.1066 | −0.858556 | −0.429278 | − | 0.903172i | \(-0.641232\pi\) | ||||
−0.429278 | + | 0.903172i | \(0.641232\pi\) | |||||||
\(398\) | −0.257663 | −0.0129155 | ||||||||
\(399\) | 13.8346 | 0.692596 | ||||||||
\(400\) | 5.54739 | 0.277369 | ||||||||
\(401\) | −31.7593 | −1.58598 | −0.792991 | − | 0.609233i | \(-0.791477\pi\) | ||||
−0.792991 | + | 0.609233i | \(0.791477\pi\) | |||||||
\(402\) | −0.668282 | −0.0333309 | ||||||||
\(403\) | 0.915299 | 0.0455943 | ||||||||
\(404\) | 21.7555 | 1.08238 | ||||||||
\(405\) | −26.0353 | −1.29370 | ||||||||
\(406\) | −0.0554791 | −0.00275338 | ||||||||
\(407\) | −0.754018 | −0.0373753 | ||||||||
\(408\) | 0.0544665 | 0.00269650 | ||||||||
\(409\) | 9.36485 | 0.463062 | 0.231531 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231531 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(410\) | 0.788005 | 0.0389168 | ||||||||
\(411\) | 24.8809 | 1.22729 | ||||||||
\(412\) | 1.99930 | 0.0984984 | ||||||||
\(413\) | −11.3719 | −0.559574 | ||||||||
\(414\) | 0.0682749 | 0.00335553 | ||||||||
\(415\) | −4.26416 | −0.209319 | ||||||||
\(416\) | 0.317517 | 0.0155675 | ||||||||
\(417\) | −19.9297 | −0.975959 | ||||||||
\(418\) | −0.111684 | −0.00546263 | ||||||||
\(419\) | 34.2734 | 1.67437 | 0.837183 | − | 0.546922i | \(-0.184201\pi\) | ||||
0.837183 | + | 0.546922i | \(0.184201\pi\) | |||||||
\(420\) | −11.0217 | −0.537806 | ||||||||
\(421\) | −20.4077 | −0.994609 | −0.497305 | − | 0.867576i | \(-0.665677\pi\) | ||||
−0.497305 | + | 0.867576i | \(0.665677\pi\) | |||||||
\(422\) | −0.374132 | −0.0182125 | ||||||||
\(423\) | 4.69134 | 0.228101 | ||||||||
\(424\) | 0.244964 | 0.0118965 | ||||||||
\(425\) | −0.380382 | −0.0184512 | ||||||||
\(426\) | −0.555187 | −0.0268989 | ||||||||
\(427\) | 14.2907 | 0.691577 | ||||||||
\(428\) | −3.87493 | −0.187302 | ||||||||
\(429\) | 1.24893 | 0.0602989 | ||||||||
\(430\) | −0.127227 | −0.00613543 | ||||||||
\(431\) | −29.9027 | −1.44036 | −0.720182 | − | 0.693785i | \(-0.755942\pi\) | ||||
−0.720182 | + | 0.693785i | \(0.755942\pi\) | |||||||
\(432\) | 18.5642 | 0.893173 | ||||||||
\(433\) | 18.2765 | 0.878312 | 0.439156 | − | 0.898411i | \(-0.355278\pi\) | ||||
0.439156 | + | 0.898411i | \(0.355278\pi\) | |||||||
\(434\) | −0.0281454 | −0.00135102 | ||||||||
\(435\) | 8.56250 | 0.410541 | ||||||||
\(436\) | 0.830146 | 0.0397568 | ||||||||
\(437\) | −31.1182 | −1.48859 | ||||||||
\(438\) | 0.248291 | 0.0118638 | ||||||||
\(439\) | 23.9802 | 1.14451 | 0.572255 | − | 0.820076i | \(-0.306069\pi\) | ||||
0.572255 | + | 0.820076i | \(0.306069\pi\) | |||||||
\(440\) | 0.177984 | 0.00848504 | ||||||||
\(441\) | −2.97061 | −0.141458 | ||||||||
\(442\) | −0.00725308 | −0.000344994 0 | ||||||||
\(443\) | 24.8953 | 1.18281 | 0.591406 | − | 0.806374i | \(-0.298573\pi\) | ||||
0.591406 | + | 0.806374i | \(0.298573\pi\) | |||||||
\(444\) | −4.25567 | −0.201965 | ||||||||
\(445\) | 5.15913 | 0.244566 | ||||||||
\(446\) | 0.464408 | 0.0219904 | ||||||||
\(447\) | 33.1603 | 1.56843 | ||||||||
\(448\) | 9.27326 | 0.438120 | ||||||||
\(449\) | −8.50644 | −0.401444 | −0.200722 | − | 0.979648i | \(-0.564329\pi\) | ||||
−0.200722 | + | 0.979648i | \(0.564329\pi\) | |||||||
\(450\) | −0.0193205 | −0.000910778 0 | ||||||||
\(451\) | −7.83362 | −0.368871 | ||||||||
\(452\) | 4.15295 | 0.195339 | ||||||||
\(453\) | 25.9632 | 1.21986 | ||||||||
\(454\) | −0.0630398 | −0.00295860 | ||||||||
\(455\) | 2.93595 | 0.137640 | ||||||||
\(456\) | −1.26091 | −0.0590473 | ||||||||
\(457\) | −24.6845 | −1.15469 | −0.577347 | − | 0.816499i | \(-0.695912\pi\) | ||||
−0.577347 | + | 0.816499i | \(0.695912\pi\) | |||||||
\(458\) | −0.432056 | −0.0201886 | ||||||||
\(459\) | −1.27294 | −0.0594158 | ||||||||
\(460\) | 24.7912 | 1.15590 | ||||||||
\(461\) | 27.3082 | 1.27187 | 0.635935 | − | 0.771742i | \(-0.280614\pi\) | ||||
0.635935 | + | 0.771742i | \(0.280614\pi\) | |||||||
\(462\) | −0.0384046 | −0.00178674 | ||||||||
\(463\) | 12.2607 | 0.569805 | 0.284902 | − | 0.958557i | \(-0.408039\pi\) | ||||
0.284902 | + | 0.958557i | \(0.408039\pi\) | |||||||
\(464\) | −7.20922 | −0.334679 | ||||||||
\(465\) | 4.34389 | 0.201443 | ||||||||
\(466\) | −0.212469 | −0.00984244 | ||||||||
\(467\) | −1.56547 | −0.0724415 | −0.0362207 | − | 0.999344i | \(-0.511532\pi\) | ||||
−0.0362207 | + | 0.999344i | \(0.511532\pi\) | |||||||
\(468\) | 1.05105 | 0.0485847 | ||||||||
\(469\) | 15.6172 | 0.721137 | ||||||||
\(470\) | −0.597081 | −0.0275413 | ||||||||
\(471\) | −30.7367 | −1.41627 | ||||||||
\(472\) | 1.03645 | 0.0477065 | ||||||||
\(473\) | 1.26477 | 0.0581543 | ||||||||
\(474\) | −0.704080 | −0.0323395 | ||||||||
\(475\) | 8.80587 | 0.404041 | ||||||||
\(476\) | −0.636309 | −0.0291652 | ||||||||
\(477\) | 1.21640 | 0.0556949 | ||||||||
\(478\) | 0.302386 | 0.0138308 | ||||||||
\(479\) | 30.1358 | 1.37694 | 0.688469 | − | 0.725266i | \(-0.258283\pi\) | ||||
0.688469 | + | 0.725266i | \(0.258283\pi\) | |||||||
\(480\) | 1.50689 | 0.0687800 | ||||||||
\(481\) | 1.13362 | 0.0516886 | ||||||||
\(482\) | −0.505740 | −0.0230358 | ||||||||
\(483\) | −10.7006 | −0.486893 | ||||||||
\(484\) | 21.1078 | 0.959444 | ||||||||
\(485\) | −48.2864 | −2.19257 | ||||||||
\(486\) | −0.143049 | −0.00648883 | ||||||||
\(487\) | 12.0921 | 0.547943 | 0.273972 | − | 0.961738i | \(-0.411663\pi\) | ||||
0.273972 | + | 0.961738i | \(0.411663\pi\) | |||||||
\(488\) | −1.30248 | −0.0589604 | ||||||||
\(489\) | −29.2160 | −1.32119 | ||||||||
\(490\) | 0.378079 | 0.0170799 | ||||||||
\(491\) | −27.0980 | −1.22292 | −0.611459 | − | 0.791276i | \(-0.709417\pi\) | ||||
−0.611459 | + | 0.791276i | \(0.709417\pi\) | |||||||
\(492\) | −44.2129 | −1.99327 | ||||||||
\(493\) | 0.494332 | 0.0222636 | ||||||||
\(494\) | 0.167910 | 0.00755461 | ||||||||
\(495\) | 0.883797 | 0.0397237 | ||||||||
\(496\) | −3.65735 | −0.164220 | ||||||||
\(497\) | 12.9743 | 0.581977 | ||||||||
\(498\) | −0.0838595 | −0.00375783 | ||||||||
\(499\) | 18.1906 | 0.814324 | 0.407162 | − | 0.913356i | \(-0.366519\pi\) | ||||
0.407162 | + | 0.913356i | \(0.366519\pi\) | |||||||
\(500\) | 18.2508 | 0.816200 | ||||||||
\(501\) | 3.73037 | 0.166661 | ||||||||
\(502\) | −0.0327593 | −0.00146212 | ||||||||
\(503\) | −3.39831 | −0.151523 | −0.0757615 | − | 0.997126i | \(-0.524139\pi\) | ||||
−0.0757615 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(504\) | −0.0646507 | −0.00287977 | ||||||||
\(505\) | −27.5032 | −1.22388 | ||||||||
\(506\) | 0.0863836 | 0.00384022 | ||||||||
\(507\) | −1.87769 | −0.0833910 | ||||||||
\(508\) | −6.68864 | −0.296760 | ||||||||
\(509\) | −17.7501 | −0.786759 | −0.393379 | − | 0.919376i | \(-0.628694\pi\) | ||||
−0.393379 | + | 0.919376i | \(0.628694\pi\) | |||||||
\(510\) | −0.0344222 | −0.00152424 | ||||||||
\(511\) | −5.80236 | −0.256681 | ||||||||
\(512\) | −2.11480 | −0.0934619 | ||||||||
\(513\) | 29.4687 | 1.30107 | ||||||||
\(514\) | −0.325181 | −0.0143431 | ||||||||
\(515\) | −2.52751 | −0.111375 | ||||||||
\(516\) | 7.13836 | 0.314249 | ||||||||
\(517\) | 5.93563 | 0.261049 | ||||||||
\(518\) | −0.0348587 | −0.00153160 | ||||||||
\(519\) | −29.3483 | −1.28825 | ||||||||
\(520\) | −0.267587 | −0.0117345 | ||||||||
\(521\) | 18.4586 | 0.808688 | 0.404344 | − | 0.914607i | \(-0.367500\pi\) | ||||
0.404344 | + | 0.914607i | \(0.367500\pi\) | |||||||
\(522\) | 0.0251083 | 0.00109896 | ||||||||
\(523\) | 6.30900 | 0.275874 | 0.137937 | − | 0.990441i | \(-0.455953\pi\) | ||||
0.137937 | + | 0.990441i | \(0.455953\pi\) | |||||||
\(524\) | −5.95507 | −0.260149 | ||||||||
\(525\) | 3.02806 | 0.132155 | ||||||||
\(526\) | 0.195917 | 0.00854238 | ||||||||
\(527\) | 0.250782 | 0.0109243 | ||||||||
\(528\) | −4.99047 | −0.217182 | ||||||||
\(529\) | 1.06885 | 0.0464719 | ||||||||
\(530\) | −0.154814 | −0.00672471 | ||||||||
\(531\) | 5.14661 | 0.223344 | ||||||||
\(532\) | 14.7306 | 0.638653 | ||||||||
\(533\) | 11.7774 | 0.510134 | ||||||||
\(534\) | 0.101460 | 0.00439061 | ||||||||
\(535\) | 4.89868 | 0.211789 | ||||||||
\(536\) | −1.42338 | −0.0614806 | ||||||||
\(537\) | −28.7628 | −1.24120 | ||||||||
\(538\) | 0.257671 | 0.0111090 | ||||||||
\(539\) | −3.75851 | −0.161891 | ||||||||
\(540\) | −23.4771 | −1.01029 | ||||||||
\(541\) | 25.1022 | 1.07923 | 0.539614 | − | 0.841912i | \(-0.318570\pi\) | ||||
0.539614 | + | 0.841912i | \(0.318570\pi\) | |||||||
\(542\) | 0.372946 | 0.0160194 | ||||||||
\(543\) | −5.21806 | −0.223928 | ||||||||
\(544\) | 0.0869963 | 0.00372994 | ||||||||
\(545\) | −1.04947 | −0.0449543 | ||||||||
\(546\) | 0.0577388 | 0.00247099 | ||||||||
\(547\) | −23.2214 | −0.992875 | −0.496438 | − | 0.868072i | \(-0.665359\pi\) | ||||
−0.496438 | + | 0.868072i | \(0.665359\pi\) | |||||||
\(548\) | 26.4924 | 1.13170 | ||||||||
\(549\) | −6.46759 | −0.276030 | ||||||||
\(550\) | −0.0244449 | −0.00104234 | ||||||||
\(551\) | −11.4438 | −0.487524 | ||||||||
\(552\) | 0.975267 | 0.0415101 | ||||||||
\(553\) | 16.4538 | 0.699687 | ||||||||
\(554\) | −0.591087 | −0.0251129 | ||||||||
\(555\) | 5.38001 | 0.228369 | ||||||||
\(556\) | −21.2204 | −0.899947 | ||||||||
\(557\) | 15.0923 | 0.639482 | 0.319741 | − | 0.947505i | \(-0.396404\pi\) | ||||
0.319741 | + | 0.947505i | \(0.396404\pi\) | |||||||
\(558\) | 0.0127379 | 0.000539236 0 | ||||||||
\(559\) | −1.90151 | −0.0804251 | ||||||||
\(560\) | −11.7315 | −0.495745 | ||||||||
\(561\) | 0.342194 | 0.0144474 | ||||||||
\(562\) | −0.834673 | −0.0352085 | ||||||||
\(563\) | −42.9093 | −1.80841 | −0.904206 | − | 0.427096i | \(-0.859537\pi\) | ||||
−0.904206 | + | 0.427096i | \(0.859537\pi\) | |||||||
\(564\) | 33.5006 | 1.41063 | ||||||||
\(565\) | −5.25016 | −0.220876 | ||||||||
\(566\) | −0.787044 | −0.0330819 | ||||||||
\(567\) | 11.9653 | 0.502497 | ||||||||
\(568\) | −1.18250 | −0.0496165 | ||||||||
\(569\) | 13.6945 | 0.574103 | 0.287052 | − | 0.957915i | \(-0.407325\pi\) | ||||
0.287052 | + | 0.957915i | \(0.407325\pi\) | |||||||
\(570\) | 0.796877 | 0.0333775 | ||||||||
\(571\) | −13.5970 | −0.569018 | −0.284509 | − | 0.958673i | \(-0.591831\pi\) | ||||
−0.284509 | + | 0.958673i | \(0.591831\pi\) | |||||||
\(572\) | 1.32982 | 0.0556025 | ||||||||
\(573\) | 28.5668 | 1.19339 | ||||||||
\(574\) | −0.362153 | −0.0151160 | ||||||||
\(575\) | −6.81103 | −0.284040 | ||||||||
\(576\) | −4.19683 | −0.174868 | ||||||||
\(577\) | 1.50292 | 0.0625673 | 0.0312837 | − | 0.999511i | \(-0.490040\pi\) | ||||
0.0312837 | + | 0.999511i | \(0.490040\pi\) | |||||||
\(578\) | 0.448039 | 0.0186359 | ||||||||
\(579\) | −12.9450 | −0.537974 | ||||||||
\(580\) | 9.11707 | 0.378566 | ||||||||
\(581\) | 1.95973 | 0.0813034 | ||||||||
\(582\) | −0.949606 | −0.0393624 | ||||||||
\(583\) | 1.53902 | 0.0637398 | ||||||||
\(584\) | 0.528836 | 0.0218834 | ||||||||
\(585\) | −1.32873 | −0.0549363 | ||||||||
\(586\) | 0.0464593 | 0.00191922 | ||||||||
\(587\) | 37.0399 | 1.52880 | 0.764401 | − | 0.644742i | \(-0.223035\pi\) | ||||
0.764401 | + | 0.644742i | \(0.223035\pi\) | |||||||
\(588\) | −21.2130 | −0.874810 | ||||||||
\(589\) | −5.80564 | −0.239217 | ||||||||
\(590\) | −0.655025 | −0.0269669 | ||||||||
\(591\) | −4.16456 | −0.171307 | ||||||||
\(592\) | −4.52971 | −0.186170 | ||||||||
\(593\) | 26.4248 | 1.08514 | 0.542568 | − | 0.840012i | \(-0.317452\pi\) | ||||
0.542568 | + | 0.840012i | \(0.317452\pi\) | |||||||
\(594\) | −0.0818046 | −0.00335648 | ||||||||
\(595\) | 0.804420 | 0.0329780 | ||||||||
\(596\) | 35.3080 | 1.44627 | ||||||||
\(597\) | −18.2762 | −0.747995 | ||||||||
\(598\) | −0.129872 | −0.00531087 | ||||||||
\(599\) | 4.30567 | 0.175925 | 0.0879625 | − | 0.996124i | \(-0.471964\pi\) | ||||
0.0879625 | + | 0.996124i | \(0.471964\pi\) | |||||||
\(600\) | −0.275982 | −0.0112669 | ||||||||
\(601\) | 8.02478 | 0.327338 | 0.163669 | − | 0.986515i | \(-0.447667\pi\) | ||||
0.163669 | + | 0.986515i | \(0.447667\pi\) | |||||||
\(602\) | 0.0584713 | 0.00238311 | ||||||||
\(603\) | −7.06794 | −0.287829 | ||||||||
\(604\) | 27.6448 | 1.12485 | ||||||||
\(605\) | −26.6844 | −1.08488 | ||||||||
\(606\) | −0.540882 | −0.0219718 | ||||||||
\(607\) | −4.42667 | −0.179673 | −0.0898365 | − | 0.995957i | \(-0.528634\pi\) | ||||
−0.0898365 | + | 0.995957i | \(0.528634\pi\) | |||||||
\(608\) | −2.01397 | −0.0816774 | ||||||||
\(609\) | −3.93518 | −0.159461 | ||||||||
\(610\) | 0.823151 | 0.0333284 | ||||||||
\(611\) | −8.92385 | −0.361020 | ||||||||
\(612\) | 0.287976 | 0.0116407 | ||||||||
\(613\) | 10.7965 | 0.436066 | 0.218033 | − | 0.975941i | \(-0.430036\pi\) | ||||
0.218033 | + | 0.975941i | \(0.430036\pi\) | |||||||
\(614\) | 0.662272 | 0.0267271 | ||||||||
\(615\) | 55.8938 | 2.25386 | ||||||||
\(616\) | −0.0817981 | −0.00329574 | ||||||||
\(617\) | 18.1610 | 0.731133 | 0.365567 | − | 0.930785i | \(-0.380875\pi\) | ||||
0.365567 | + | 0.930785i | \(0.380875\pi\) | |||||||
\(618\) | −0.0497063 | −0.00199948 | ||||||||
\(619\) | 17.2708 | 0.694170 | 0.347085 | − | 0.937834i | \(-0.387171\pi\) | ||||
0.347085 | + | 0.937834i | \(0.387171\pi\) | |||||||
\(620\) | 4.62523 | 0.185754 | ||||||||
\(621\) | −22.7930 | −0.914652 | ||||||||
\(622\) | 0.690029 | 0.0276676 | ||||||||
\(623\) | −2.37105 | −0.0949939 | ||||||||
\(624\) | 7.50285 | 0.300355 | ||||||||
\(625\) | −30.0141 | −1.20057 | ||||||||
\(626\) | 0.485071 | 0.0193873 | ||||||||
\(627\) | −7.92182 | −0.316367 | ||||||||
\(628\) | −32.7274 | −1.30596 | ||||||||
\(629\) | 0.310600 | 0.0123844 | ||||||||
\(630\) | 0.0408585 | 0.00162784 | ||||||||
\(631\) | 12.4101 | 0.494040 | 0.247020 | − | 0.969010i | \(-0.420549\pi\) | ||||
0.247020 | + | 0.969010i | \(0.420549\pi\) | |||||||
\(632\) | −1.49963 | −0.0596519 | ||||||||
\(633\) | −26.5375 | −1.05477 | ||||||||
\(634\) | −0.0770467 | −0.00305992 | ||||||||
\(635\) | 8.45576 | 0.335557 | ||||||||
\(636\) | 8.68623 | 0.344431 | ||||||||
\(637\) | 5.65069 | 0.223888 | ||||||||
\(638\) | 0.0317679 | 0.00125770 | ||||||||
\(639\) | −5.87182 | −0.232286 | ||||||||
\(640\) | 2.13920 | 0.0845592 | ||||||||
\(641\) | 31.8180 | 1.25674 | 0.628368 | − | 0.777916i | \(-0.283723\pi\) | ||||
0.628368 | + | 0.777916i | \(0.283723\pi\) | |||||||
\(642\) | 0.0963381 | 0.00380216 | ||||||||
\(643\) | −14.1932 | −0.559725 | −0.279863 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279863 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(644\) | −11.3936 | −0.448971 | ||||||||
\(645\) | −9.02431 | −0.355332 | ||||||||
\(646\) | 0.0460055 | 0.00181006 | ||||||||
\(647\) | −5.19642 | −0.204292 | −0.102146 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102146 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(648\) | −1.09054 | −0.0428405 | ||||||||
\(649\) | 6.51165 | 0.255605 | ||||||||
\(650\) | 0.0367514 | 0.00144151 | ||||||||
\(651\) | −1.99638 | −0.0782441 | ||||||||
\(652\) | −31.1083 | −1.21829 | ||||||||
\(653\) | 8.00734 | 0.313351 | 0.156676 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156676 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(654\) | −0.0206390 | −0.000807049 0 | ||||||||
\(655\) | 7.52839 | 0.294159 | ||||||||
\(656\) | −47.0599 | −1.83738 | ||||||||
\(657\) | 2.62599 | 0.102450 | ||||||||
\(658\) | 0.274408 | 0.0106975 | ||||||||
\(659\) | −40.9699 | −1.59596 | −0.797981 | − | 0.602683i | \(-0.794098\pi\) | ||||
−0.797981 | + | 0.602683i | \(0.794098\pi\) | |||||||
\(660\) | 6.31115 | 0.245661 | ||||||||
\(661\) | 20.3039 | 0.789728 | 0.394864 | − | 0.918740i | \(-0.370792\pi\) | ||||
0.394864 | + | 0.918740i | \(0.370792\pi\) | |||||||
\(662\) | 0.542231 | 0.0210744 | ||||||||
\(663\) | −0.514467 | −0.0199802 | ||||||||
\(664\) | −0.178613 | −0.00693153 | ||||||||
\(665\) | −18.6224 | −0.722146 | ||||||||
\(666\) | 0.0157761 | 0.000611312 0 | ||||||||
\(667\) | 8.85141 | 0.342728 | ||||||||
\(668\) | 3.97197 | 0.153680 | ||||||||
\(669\) | 32.9408 | 1.27357 | ||||||||
\(670\) | 0.899558 | 0.0347530 | ||||||||
\(671\) | −8.18301 | −0.315901 | ||||||||
\(672\) | −0.692542 | −0.0267154 | ||||||||
\(673\) | 27.7916 | 1.07129 | 0.535644 | − | 0.844444i | \(-0.320069\pi\) | ||||
0.535644 | + | 0.844444i | \(0.320069\pi\) | |||||||
\(674\) | 0.554957 | 0.0213761 | ||||||||
\(675\) | 6.45000 | 0.248260 | ||||||||
\(676\) | −1.99930 | −0.0768961 | ||||||||
\(677\) | 29.4085 | 1.13026 | 0.565129 | − | 0.825002i | \(-0.308826\pi\) | ||||
0.565129 | + | 0.825002i | \(0.308826\pi\) | |||||||
\(678\) | −0.103250 | −0.00396530 | ||||||||
\(679\) | 22.1916 | 0.851634 | ||||||||
\(680\) | −0.0733161 | −0.00281154 | ||||||||
\(681\) | −4.47146 | −0.171347 | ||||||||
\(682\) | 0.0161163 | 0.000617127 0 | ||||||||
\(683\) | 12.6764 | 0.485047 | 0.242524 | − | 0.970146i | \(-0.422025\pi\) | ||||
0.242524 | + | 0.970146i | \(0.422025\pi\) | |||||||
\(684\) | −6.66668 | −0.254907 | ||||||||
\(685\) | −33.4916 | −1.27965 | ||||||||
\(686\) | −0.389008 | −0.0148524 | ||||||||
\(687\) | −30.6461 | −1.16922 | ||||||||
\(688\) | 7.59803 | 0.289672 | ||||||||
\(689\) | −2.31382 | −0.0881496 | ||||||||
\(690\) | −0.616357 | −0.0234643 | ||||||||
\(691\) | 23.9852 | 0.912439 | 0.456219 | − | 0.889867i | \(-0.349203\pi\) | ||||
0.456219 | + | 0.889867i | \(0.349203\pi\) | |||||||
\(692\) | −31.2491 | −1.18791 | ||||||||
\(693\) | −0.406177 | −0.0154294 | ||||||||
\(694\) | 0.483017 | 0.0183351 | ||||||||
\(695\) | 26.8268 | 1.01760 | ||||||||
\(696\) | 0.358658 | 0.0135949 | ||||||||
\(697\) | 3.22687 | 0.122226 | ||||||||
\(698\) | 0.901920 | 0.0341382 | ||||||||
\(699\) | −15.0706 | −0.570022 | ||||||||
\(700\) | 3.22418 | 0.121863 | ||||||||
\(701\) | −43.5421 | −1.64456 | −0.822280 | − | 0.569083i | \(-0.807298\pi\) | ||||
−0.822280 | + | 0.569083i | \(0.807298\pi\) | |||||||
\(702\) | 0.122988 | 0.00464188 | ||||||||
\(703\) | −7.19041 | −0.271192 | ||||||||
\(704\) | −5.30996 | −0.200127 | ||||||||
\(705\) | −42.3514 | −1.59505 | ||||||||
\(706\) | 0.674571 | 0.0253878 | ||||||||
\(707\) | 12.6400 | 0.475376 | ||||||||
\(708\) | 36.7517 | 1.38121 | ||||||||
\(709\) | 22.5445 | 0.846678 | 0.423339 | − | 0.905971i | \(-0.360858\pi\) | ||||
0.423339 | + | 0.905971i | \(0.360858\pi\) | |||||||
\(710\) | 0.747325 | 0.0280466 | ||||||||
\(711\) | −7.44655 | −0.279267 | ||||||||
\(712\) | 0.216101 | 0.00809872 | ||||||||
\(713\) | 4.49046 | 0.168169 | ||||||||
\(714\) | 0.0158198 | 0.000592043 0 | ||||||||
\(715\) | −1.68115 | −0.0628716 | ||||||||
\(716\) | −30.6256 | −1.14453 | ||||||||
\(717\) | 21.4485 | 0.801008 | ||||||||
\(718\) | −0.111362 | −0.00415600 | ||||||||
\(719\) | −29.6930 | −1.10736 | −0.553680 | − | 0.832729i | \(-0.686777\pi\) | ||||
−0.553680 | + | 0.832729i | \(0.686777\pi\) | |||||||
\(720\) | 5.30934 | 0.197868 | ||||||||
\(721\) | 1.16160 | 0.0432602 | ||||||||
\(722\) | −0.562061 | −0.0209177 | ||||||||
\(723\) | −35.8725 | −1.33411 | ||||||||
\(724\) | −5.55602 | −0.206488 | ||||||||
\(725\) | −2.50478 | −0.0930253 | ||||||||
\(726\) | −0.524779 | −0.0194764 | ||||||||
\(727\) | 0.0713199 | 0.00264511 | 0.00132255 | − | 0.999999i | \(-0.499579\pi\) | ||||
0.00132255 | + | 0.999999i | \(0.499579\pi\) | |||||||
\(728\) | 0.122978 | 0.00455788 | ||||||||
\(729\) | 20.7557 | 0.768730 | ||||||||
\(730\) | −0.334218 | −0.0123700 | ||||||||
\(731\) | −0.520993 | −0.0192696 | ||||||||
\(732\) | −46.1848 | −1.70704 | ||||||||
\(733\) | −25.7162 | −0.949850 | −0.474925 | − | 0.880026i | \(-0.657525\pi\) | ||||
−0.474925 | + | 0.880026i | \(0.657525\pi\) | |||||||
\(734\) | −0.738427 | −0.0272558 | ||||||||
\(735\) | 26.8174 | 0.989176 | ||||||||
\(736\) | 1.55774 | 0.0574190 | ||||||||
\(737\) | −8.94258 | −0.329404 | ||||||||
\(738\) | 0.163901 | 0.00603327 | ||||||||
\(739\) | −41.2789 | −1.51847 | −0.759234 | − | 0.650817i | \(-0.774426\pi\) | ||||
−0.759234 | + | 0.650817i | \(0.774426\pi\) | |||||||
\(740\) | 5.72846 | 0.210582 | ||||||||
\(741\) | 11.9100 | 0.437523 | ||||||||
\(742\) | 0.0711500 | 0.00261200 | ||||||||
\(743\) | 40.7379 | 1.49453 | 0.747264 | − | 0.664527i | \(-0.231367\pi\) | ||||
0.747264 | + | 0.664527i | \(0.231367\pi\) | |||||||
\(744\) | 0.181953 | 0.00667071 | ||||||||
\(745\) | −44.6363 | −1.63535 | ||||||||
\(746\) | 0.818230 | 0.0299575 | ||||||||
\(747\) | −0.886921 | −0.0324508 | ||||||||
\(748\) | 0.364357 | 0.0133222 | ||||||||
\(749\) | −2.25135 | −0.0822625 | ||||||||
\(750\) | −0.453749 | −0.0165686 | ||||||||
\(751\) | −33.6914 | −1.22942 | −0.614708 | − | 0.788755i | \(-0.710726\pi\) | ||||
−0.614708 | + | 0.788755i | \(0.710726\pi\) | |||||||
\(752\) | 35.6579 | 1.30031 | ||||||||
\(753\) | −2.32364 | −0.0846783 | ||||||||
\(754\) | −0.0477610 | −0.00173935 | ||||||||
\(755\) | −34.9485 | −1.27190 | ||||||||
\(756\) | 10.7897 | 0.392416 | ||||||||
\(757\) | 41.7799 | 1.51852 | 0.759258 | − | 0.650790i | \(-0.225562\pi\) | ||||
0.759258 | + | 0.650790i | \(0.225562\pi\) | |||||||
\(758\) | 0.137997 | 0.00501227 | ||||||||
\(759\) | 6.12725 | 0.222405 | ||||||||
\(760\) | 1.69727 | 0.0615666 | ||||||||
\(761\) | −26.3942 | −0.956791 | −0.478395 | − | 0.878145i | \(-0.658781\pi\) | ||||
−0.478395 | + | 0.878145i | \(0.658781\pi\) | |||||||
\(762\) | 0.166292 | 0.00602413 | ||||||||
\(763\) | 0.482317 | 0.0174611 | ||||||||
\(764\) | 30.4170 | 1.10045 | ||||||||
\(765\) | −0.364059 | −0.0131626 | ||||||||
\(766\) | 0.451878 | 0.0163270 | ||||||||
\(767\) | −9.78985 | −0.353491 | ||||||||
\(768\) | −29.9378 | −1.08029 | ||||||||
\(769\) | 10.0084 | 0.360911 | 0.180456 | − | 0.983583i | \(-0.442243\pi\) | ||||
0.180456 | + | 0.983583i | \(0.442243\pi\) | |||||||
\(770\) | 0.0516955 | 0.00186298 | ||||||||
\(771\) | −23.0653 | −0.830677 | ||||||||
\(772\) | −13.7834 | −0.496074 | ||||||||
\(773\) | 7.73312 | 0.278141 | 0.139071 | − | 0.990282i | \(-0.455589\pi\) | ||||
0.139071 | + | 0.990282i | \(0.455589\pi\) | |||||||
\(774\) | −0.0264625 | −0.000951175 0 | ||||||||
\(775\) | −1.27072 | −0.0456455 | ||||||||
\(776\) | −2.02257 | −0.0726061 | ||||||||
\(777\) | −2.47256 | −0.0887025 | ||||||||
\(778\) | 0.202894 | 0.00727410 | ||||||||
\(779\) | −74.7024 | −2.67649 | ||||||||
\(780\) | −9.48842 | −0.339740 | ||||||||
\(781\) | −7.42921 | −0.265838 | ||||||||
\(782\) | −0.0355836 | −0.00127247 | ||||||||
\(783\) | −8.38222 | −0.299556 | ||||||||
\(784\) | −22.5790 | −0.806393 | ||||||||
\(785\) | 41.3739 | 1.47670 | ||||||||
\(786\) | 0.148054 | 0.00528092 | ||||||||
\(787\) | −3.06461 | −0.109241 | −0.0546207 | − | 0.998507i | \(-0.517395\pi\) | ||||
−0.0546207 | + | 0.998507i | \(0.517395\pi\) | |||||||
\(788\) | −4.43428 | −0.157965 | ||||||||
\(789\) | 13.8965 | 0.494729 | ||||||||
\(790\) | 0.947746 | 0.0337193 | ||||||||
\(791\) | 2.41288 | 0.0857921 | ||||||||
\(792\) | 0.0370196 | 0.00131543 | ||||||||
\(793\) | 12.3026 | 0.436879 | ||||||||
\(794\) | 0.452848 | 0.0160710 | ||||||||
\(795\) | −10.9811 | −0.389460 | ||||||||
\(796\) | −19.4599 | −0.689738 | ||||||||
\(797\) | −36.4767 | −1.29207 | −0.646035 | − | 0.763308i | \(-0.723574\pi\) | ||||
−0.646035 | + | 0.763308i | \(0.723574\pi\) | |||||||
\(798\) | −0.366231 | −0.0129644 | ||||||||
\(799\) | −2.44504 | −0.0864994 | ||||||||
\(800\) | −0.440811 | −0.0155850 | ||||||||
\(801\) | 1.07307 | 0.0379151 | ||||||||
\(802\) | 0.840735 | 0.0296874 | ||||||||
\(803\) | 3.32249 | 0.117248 | ||||||||
\(804\) | −50.4718 | −1.78000 | ||||||||
\(805\) | 14.4038 | 0.507667 | ||||||||
\(806\) | −0.0242299 | −0.000853462 0 | ||||||||
\(807\) | 18.2768 | 0.643373 | ||||||||
\(808\) | −1.15203 | −0.0405282 | ||||||||
\(809\) | −44.0720 | −1.54949 | −0.774744 | − | 0.632275i | \(-0.782121\pi\) | ||||
−0.774744 | + | 0.632275i | \(0.782121\pi\) | |||||||
\(810\) | 0.689208 | 0.0242163 | ||||||||
\(811\) | 29.5356 | 1.03713 | 0.518567 | − | 0.855037i | \(-0.326466\pi\) | ||||
0.518567 | + | 0.855037i | \(0.326466\pi\) | |||||||
\(812\) | −4.19004 | −0.147042 | ||||||||
\(813\) | 26.4534 | 0.927760 | ||||||||
\(814\) | 0.0199604 | 0.000699613 0 | ||||||||
\(815\) | 39.3270 | 1.37756 | ||||||||
\(816\) | 2.05570 | 0.0719640 | ||||||||
\(817\) | 12.0610 | 0.421962 | ||||||||
\(818\) | −0.247907 | −0.00866788 | ||||||||
\(819\) | 0.610662 | 0.0213383 | ||||||||
\(820\) | 59.5139 | 2.07832 | ||||||||
\(821\) | −46.6122 | −1.62678 | −0.813388 | − | 0.581722i | \(-0.802379\pi\) | ||||
−0.813388 | + | 0.581722i | \(0.802379\pi\) | |||||||
\(822\) | −0.658651 | −0.0229731 | ||||||||
\(823\) | 26.3732 | 0.919311 | 0.459656 | − | 0.888097i | \(-0.347973\pi\) | ||||
0.459656 | + | 0.888097i | \(0.347973\pi\) | |||||||
\(824\) | −0.105870 | −0.00368815 | ||||||||
\(825\) | −1.73390 | −0.0603666 | ||||||||
\(826\) | 0.301038 | 0.0104744 | ||||||||
\(827\) | −10.5308 | −0.366192 | −0.183096 | − | 0.983095i | \(-0.558612\pi\) | ||||
−0.183096 | + | 0.983095i | \(0.558612\pi\) | |||||||
\(828\) | 5.15644 | 0.179199 | ||||||||
\(829\) | 11.8489 | 0.411529 | 0.205764 | − | 0.978602i | \(-0.434032\pi\) | ||||
0.205764 | + | 0.978602i | \(0.434032\pi\) | |||||||
\(830\) | 0.112881 | 0.00391817 | ||||||||
\(831\) | −41.9262 | −1.45441 | ||||||||
\(832\) | 7.98319 | 0.276767 | ||||||||
\(833\) | 1.54823 | 0.0536430 | ||||||||
\(834\) | 0.527580 | 0.0182686 | ||||||||
\(835\) | −5.02136 | −0.173771 | ||||||||
\(836\) | −8.43489 | −0.291727 | ||||||||
\(837\) | −4.25243 | −0.146985 | ||||||||
\(838\) | −0.907290 | −0.0313418 | ||||||||
\(839\) | −26.8766 | −0.927883 | −0.463941 | − | 0.885866i | \(-0.653565\pi\) | ||||
−0.463941 | + | 0.885866i | \(0.653565\pi\) | |||||||
\(840\) | 0.583639 | 0.0201375 | ||||||||
\(841\) | −25.7449 | −0.887754 | ||||||||
\(842\) | 0.540234 | 0.0186177 | ||||||||
\(843\) | −59.2040 | −2.03909 | ||||||||
\(844\) | −28.2562 | −0.972620 | ||||||||
\(845\) | 2.52751 | 0.0869490 | ||||||||
\(846\) | −0.124190 | −0.00426973 | ||||||||
\(847\) | 12.2637 | 0.421385 | ||||||||
\(848\) | 9.24556 | 0.317494 | ||||||||
\(849\) | −55.8257 | −1.91593 | ||||||||
\(850\) | 0.0100695 | 0.000345381 0 | ||||||||
\(851\) | 5.56153 | 0.190647 | ||||||||
\(852\) | −41.9304 | −1.43651 | ||||||||
\(853\) | −15.6788 | −0.536832 | −0.268416 | − | 0.963303i | \(-0.586500\pi\) | ||||
−0.268416 | + | 0.963303i | \(0.586500\pi\) | |||||||
\(854\) | −0.378306 | −0.0129454 | ||||||||
\(855\) | 8.42800 | 0.288231 | ||||||||
\(856\) | 0.205191 | 0.00701329 | ||||||||
\(857\) | −50.2928 | −1.71797 | −0.858984 | − | 0.512002i | \(-0.828904\pi\) | ||||
−0.858984 | + | 0.512002i | \(0.828904\pi\) | |||||||
\(858\) | −0.0330618 | −0.00112871 | ||||||||
\(859\) | −8.65814 | −0.295412 | −0.147706 | − | 0.989031i | \(-0.547189\pi\) | ||||
−0.147706 | + | 0.989031i | \(0.547189\pi\) | |||||||
\(860\) | −9.60878 | −0.327657 | ||||||||
\(861\) | −25.6878 | −0.875438 | ||||||||
\(862\) | 0.791589 | 0.0269616 | ||||||||
\(863\) | 24.1610 | 0.822450 | 0.411225 | − | 0.911534i | \(-0.365101\pi\) | ||||
0.411225 | + | 0.911534i | \(0.365101\pi\) | |||||||
\(864\) | −1.47517 | −0.0501862 | ||||||||
\(865\) | 39.5050 | 1.34321 | ||||||||
\(866\) | −0.483817 | −0.0164408 | ||||||||
\(867\) | 31.7797 | 1.07930 | ||||||||
\(868\) | −2.12568 | −0.0721501 | ||||||||
\(869\) | −9.42161 | −0.319606 | ||||||||
\(870\) | −0.226668 | −0.00768475 | ||||||||
\(871\) | 13.4446 | 0.455553 | ||||||||
\(872\) | −0.0439591 | −0.00148864 | ||||||||
\(873\) | −10.0433 | −0.339914 | ||||||||
\(874\) | 0.823764 | 0.0278642 | ||||||||
\(875\) | 10.6038 | 0.358473 | ||||||||
\(876\) | 18.7521 | 0.633574 | ||||||||
\(877\) | 28.7207 | 0.969830 | 0.484915 | − | 0.874561i | \(-0.338851\pi\) | ||||
0.484915 | + | 0.874561i | \(0.338851\pi\) | |||||||
\(878\) | −0.634805 | −0.0214236 | ||||||||
\(879\) | 3.29540 | 0.111151 | ||||||||
\(880\) | 6.71755 | 0.226449 | ||||||||
\(881\) | −47.6364 | −1.60491 | −0.802455 | − | 0.596712i | \(-0.796473\pi\) | ||||
−0.802455 | + | 0.596712i | \(0.796473\pi\) | |||||||
\(882\) | 0.0786384 | 0.00264789 | ||||||||
\(883\) | 56.3760 | 1.89720 | 0.948602 | − | 0.316472i | \(-0.102498\pi\) | ||||
0.948602 | + | 0.316472i | \(0.102498\pi\) | |||||||
\(884\) | −0.547787 | −0.0184241 | ||||||||
\(885\) | −46.4614 | −1.56178 | ||||||||
\(886\) | −0.659032 | −0.0221406 | ||||||||
\(887\) | −6.51770 | −0.218843 | −0.109422 | − | 0.993995i | \(-0.534900\pi\) | ||||
−0.109422 | + | 0.993995i | \(0.534900\pi\) | |||||||
\(888\) | 0.225353 | 0.00756234 | ||||||||
\(889\) | −3.88612 | −0.130336 | ||||||||
\(890\) | −0.136573 | −0.00457794 | ||||||||
\(891\) | −6.85147 | −0.229533 | ||||||||
\(892\) | 35.0743 | 1.17438 | ||||||||
\(893\) | 56.6029 | 1.89414 | ||||||||
\(894\) | −0.877824 | −0.0293588 | ||||||||
\(895\) | 38.7169 | 1.29416 | ||||||||
\(896\) | −0.983137 | −0.0328443 | ||||||||
\(897\) | −9.21194 | −0.307578 | ||||||||
\(898\) | 0.225183 | 0.00751447 | ||||||||
\(899\) | 1.65138 | 0.0550767 | ||||||||
\(900\) | −1.45918 | −0.0486392 | ||||||||
\(901\) | −0.633963 | −0.0211204 | ||||||||
\(902\) | 0.207372 | 0.00690475 | ||||||||
\(903\) | 4.14741 | 0.138017 | ||||||||
\(904\) | −0.219913 | −0.00731421 | ||||||||
\(905\) | 7.02391 | 0.233483 | ||||||||
\(906\) | −0.687301 | −0.0228340 | ||||||||
\(907\) | 37.8942 | 1.25826 | 0.629129 | − | 0.777301i | \(-0.283412\pi\) | ||||
0.629129 | + | 0.777301i | \(0.283412\pi\) | |||||||
\(908\) | −4.76106 | −0.158001 | ||||||||
\(909\) | −5.72052 | −0.189738 | ||||||||
\(910\) | −0.0777209 | −0.00257642 | ||||||||
\(911\) | −36.0556 | −1.19457 | −0.597287 | − | 0.802027i | \(-0.703755\pi\) | ||||
−0.597287 | + | 0.802027i | \(0.703755\pi\) | |||||||
\(912\) | −47.5897 | −1.57585 | ||||||||
\(913\) | −1.12216 | −0.0371381 | ||||||||
\(914\) | 0.653452 | 0.0216143 | ||||||||
\(915\) | 58.3867 | 1.93021 | ||||||||
\(916\) | −32.6309 | −1.07816 | ||||||||
\(917\) | −3.45991 | −0.114256 | ||||||||
\(918\) | 0.0336974 | 0.00111218 | ||||||||
\(919\) | 37.2801 | 1.22976 | 0.614878 | − | 0.788622i | \(-0.289205\pi\) | ||||
0.614878 | + | 0.788622i | \(0.289205\pi\) | |||||||
\(920\) | −1.31278 | −0.0432812 | ||||||||
\(921\) | 46.9755 | 1.54789 | ||||||||
\(922\) | −0.722906 | −0.0238077 | ||||||||
\(923\) | 11.1693 | 0.367644 | ||||||||
\(924\) | −2.90049 | −0.0954192 | ||||||||
\(925\) | −1.57381 | −0.0517466 | ||||||||
\(926\) | −0.324567 | −0.0106659 | ||||||||
\(927\) | −0.525708 | −0.0172665 | ||||||||
\(928\) | 0.572864 | 0.0188052 | ||||||||
\(929\) | 30.7339 | 1.00835 | 0.504173 | − | 0.863603i | \(-0.331797\pi\) | ||||
0.504173 | + | 0.863603i | \(0.331797\pi\) | |||||||
\(930\) | −0.114992 | −0.00377074 | ||||||||
\(931\) | −35.8417 | −1.17466 | ||||||||
\(932\) | −16.0467 | −0.525626 | ||||||||
\(933\) | 48.9443 | 1.60236 | ||||||||
\(934\) | 0.0414414 | 0.00135600 | ||||||||
\(935\) | −0.460619 | −0.0150639 | ||||||||
\(936\) | −0.0556567 | −0.00181919 | ||||||||
\(937\) | −15.1454 | −0.494778 | −0.247389 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247389 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(938\) | −0.413421 | −0.0134987 | ||||||||
\(939\) | 34.4064 | 1.12281 | ||||||||
\(940\) | −45.0944 | −1.47082 | ||||||||
\(941\) | −8.57099 | −0.279406 | −0.139703 | − | 0.990193i | \(-0.544615\pi\) | ||||
−0.139703 | + | 0.990193i | \(0.544615\pi\) | |||||||
\(942\) | 0.813664 | 0.0265106 | ||||||||
\(943\) | 57.7797 | 1.88157 | ||||||||
\(944\) | 39.1183 | 1.27319 | ||||||||
\(945\) | −13.6403 | −0.443718 | ||||||||
\(946\) | −0.0334812 | −0.00108857 | ||||||||
\(947\) | −19.1228 | −0.621408 | −0.310704 | − | 0.950507i | \(-0.600565\pi\) | ||||
−0.310704 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(948\) | −53.1755 | −1.72706 | ||||||||
\(949\) | −4.99515 | −0.162149 | ||||||||
\(950\) | −0.233110 | −0.00756308 | ||||||||
\(951\) | −5.46498 | −0.177214 | ||||||||
\(952\) | 0.0336948 | 0.00109205 | ||||||||
\(953\) | 9.70290 | 0.314308 | 0.157154 | − | 0.987574i | \(-0.449768\pi\) | ||||
0.157154 | + | 0.987574i | \(0.449768\pi\) | |||||||
\(954\) | −0.0322006 | −0.00104253 | ||||||||
\(955\) | −38.4530 | −1.24431 | ||||||||
\(956\) | 22.8376 | 0.738622 | ||||||||
\(957\) | 2.25332 | 0.0728395 | ||||||||
\(958\) | −0.797757 | −0.0257744 | ||||||||
\(959\) | 15.3922 | 0.497039 | ||||||||
\(960\) | 37.8872 | 1.22280 | ||||||||
\(961\) | −30.1622 | −0.972975 | ||||||||
\(962\) | −0.0300093 | −0.000967538 0 | ||||||||
\(963\) | 1.01890 | 0.0328336 | ||||||||
\(964\) | −38.1959 | −1.23021 | ||||||||
\(965\) | 17.4249 | 0.560927 | ||||||||
\(966\) | 0.283267 | 0.00911396 | ||||||||
\(967\) | 39.0287 | 1.25508 | 0.627539 | − | 0.778585i | \(-0.284062\pi\) | ||||
0.627539 | + | 0.778585i | \(0.284062\pi\) | |||||||
\(968\) | −1.11773 | −0.0359252 | ||||||||
\(969\) | 3.26320 | 0.104829 | ||||||||
\(970\) | 1.27824 | 0.0410419 | ||||||||
\(971\) | −10.2814 | −0.329947 | −0.164974 | − | 0.986298i | \(-0.552754\pi\) | ||||
−0.164974 | + | 0.986298i | \(0.552754\pi\) | |||||||
\(972\) | −10.8037 | −0.346530 | ||||||||
\(973\) | −12.3291 | −0.395254 | ||||||||
\(974\) | −0.320102 | −0.0102567 | ||||||||
\(975\) | 2.60680 | 0.0834846 | ||||||||
\(976\) | −49.1588 | −1.57354 | ||||||||
\(977\) | 35.6529 | 1.14064 | 0.570318 | − | 0.821424i | \(-0.306820\pi\) | ||||
0.570318 | + | 0.821424i | \(0.306820\pi\) | |||||||
\(978\) | 0.773410 | 0.0247309 | ||||||||
\(979\) | 1.35768 | 0.0433918 | ||||||||
\(980\) | 28.5543 | 0.912135 | ||||||||
\(981\) | −0.218284 | −0.00696927 | ||||||||
\(982\) | 0.717342 | 0.0228913 | ||||||||
\(983\) | −14.2218 | −0.453606 | −0.226803 | − | 0.973941i | \(-0.572827\pi\) | ||||
−0.226803 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(984\) | 2.34123 | 0.0746355 | ||||||||
\(985\) | 5.60581 | 0.178616 | ||||||||
\(986\) | −0.0130860 | −0.000416744 0 | ||||||||
\(987\) | 19.4640 | 0.619545 | ||||||||
\(988\) | 12.6813 | 0.403447 | ||||||||
\(989\) | −9.32879 | −0.296638 | ||||||||
\(990\) | −0.0233960 | −0.000743573 0 | ||||||||
\(991\) | −21.0208 | −0.667749 | −0.333874 | − | 0.942618i | \(-0.608356\pi\) | ||||
−0.333874 | + | 0.942618i | \(0.608356\pi\) | |||||||
\(992\) | 0.290623 | 0.00922729 | ||||||||
\(993\) | 38.4609 | 1.22052 | ||||||||
\(994\) | −0.343457 | −0.0108938 | ||||||||
\(995\) | 24.6012 | 0.779909 | ||||||||
\(996\) | −6.33347 | −0.200684 | ||||||||
\(997\) | 16.9039 | 0.535353 | 0.267676 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267676 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(998\) | −0.481544 | −0.0152430 | ||||||||
\(999\) | −5.26673 | −0.166632 |
(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 | 1339.2.a.e.1.11 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1339.2.a.e.1.11 | ✓ | 21 | 1.1 | even | 1 | trivial |