Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6022,2,Mod(1,6022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6022 = 2 \cdot 3011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6022.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: | \(48.0859120972\) |
Analytic rank: | \(1\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6022.1 |
$q$-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 | ||||||||
\(3\) | −1.92077 | −1.10896 | −0.554478 | − | 0.832199i | \(-0.687082\pi\) | ||||
−0.554478 | + | 0.832199i | \(0.687082\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.09656 | 1.38482 | 0.692412 | − | 0.721502i | \(-0.256548\pi\) | ||||
0.692412 | + | 0.721502i | \(0.256548\pi\) | |||||||
\(6\) | −1.92077 | −0.784150 | ||||||||
\(7\) | −3.07737 | −1.16313 | −0.581567 | − | 0.813498i | \(-0.697560\pi\) | ||||
−0.581567 | + | 0.813498i | \(0.697560\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.689347 | 0.229782 | ||||||||
\(10\) | 3.09656 | 0.979219 | ||||||||
\(11\) | −0.0868382 | −0.0261827 | −0.0130914 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130914 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(12\) | −1.92077 | −0.554478 | ||||||||
\(13\) | 1.23108 | 0.341440 | 0.170720 | − | 0.985320i | \(-0.445391\pi\) | ||||
0.170720 | + | 0.985320i | \(0.445391\pi\) | |||||||
\(14\) | −3.07737 | −0.822461 | ||||||||
\(15\) | −5.94777 | −1.53571 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.46364 | 1.32513 | 0.662564 | − | 0.749005i | \(-0.269468\pi\) | ||||
0.662564 | + | 0.749005i | \(0.269468\pi\) | |||||||
\(18\) | 0.689347 | 0.162481 | ||||||||
\(19\) | −3.74953 | −0.860201 | −0.430101 | − | 0.902781i | \(-0.641522\pi\) | ||||
−0.430101 | + | 0.902781i | \(0.641522\pi\) | |||||||
\(20\) | 3.09656 | 0.692412 | ||||||||
\(21\) | 5.91090 | 1.28986 | ||||||||
\(22\) | −0.0868382 | −0.0185140 | ||||||||
\(23\) | −6.57027 | −1.37000 | −0.684998 | − | 0.728545i | \(-0.740197\pi\) | ||||
−0.684998 | + | 0.728545i | \(0.740197\pi\) | |||||||
\(24\) | −1.92077 | −0.392075 | ||||||||
\(25\) | 4.58869 | 0.917739 | ||||||||
\(26\) | 1.23108 | 0.241435 | ||||||||
\(27\) | 4.43823 | 0.854137 | ||||||||
\(28\) | −3.07737 | −0.581567 | ||||||||
\(29\) | −7.64556 | −1.41974 | −0.709872 | − | 0.704331i | \(-0.751247\pi\) | ||||
−0.709872 | + | 0.704331i | \(0.751247\pi\) | |||||||
\(30\) | −5.94777 | −1.08591 | ||||||||
\(31\) | −0.596870 | −0.107201 | −0.0536005 | − | 0.998562i | \(-0.517070\pi\) | ||||
−0.0536005 | + | 0.998562i | \(0.517070\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.166796 | 0.0290355 | ||||||||
\(34\) | 5.46364 | 0.937007 | ||||||||
\(35\) | −9.52925 | −1.61074 | ||||||||
\(36\) | 0.689347 | 0.114891 | ||||||||
\(37\) | −0.702711 | −0.115525 | −0.0577625 | − | 0.998330i | \(-0.518397\pi\) | ||||
−0.0577625 | + | 0.998330i | \(0.518397\pi\) | |||||||
\(38\) | −3.74953 | −0.608254 | ||||||||
\(39\) | −2.36462 | −0.378642 | ||||||||
\(40\) | 3.09656 | 0.489609 | ||||||||
\(41\) | 4.85857 | 0.758782 | 0.379391 | − | 0.925237i | \(-0.376134\pi\) | ||||
0.379391 | + | 0.925237i | \(0.376134\pi\) | |||||||
\(42\) | 5.91090 | 0.912072 | ||||||||
\(43\) | −6.26112 | −0.954812 | −0.477406 | − | 0.878683i | \(-0.658423\pi\) | ||||
−0.477406 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(44\) | −0.0868382 | −0.0130914 | ||||||||
\(45\) | 2.13460 | 0.318208 | ||||||||
\(46\) | −6.57027 | −0.968734 | ||||||||
\(47\) | −5.40358 | −0.788193 | −0.394097 | − | 0.919069i | \(-0.628942\pi\) | ||||
−0.394097 | + | 0.919069i | \(0.628942\pi\) | |||||||
\(48\) | −1.92077 | −0.277239 | ||||||||
\(49\) | 2.47018 | 0.352883 | ||||||||
\(50\) | 4.58869 | 0.648939 | ||||||||
\(51\) | −10.4944 | −1.46951 | ||||||||
\(52\) | 1.23108 | 0.170720 | ||||||||
\(53\) | 13.4051 | 1.84134 | 0.920668 | − | 0.390346i | \(-0.127645\pi\) | ||||
0.920668 | + | 0.390346i | \(0.127645\pi\) | |||||||
\(54\) | 4.43823 | 0.603966 | ||||||||
\(55\) | −0.268900 | −0.0362585 | ||||||||
\(56\) | −3.07737 | −0.411230 | ||||||||
\(57\) | 7.20198 | 0.953925 | ||||||||
\(58\) | −7.64556 | −1.00391 | ||||||||
\(59\) | −5.15049 | −0.670536 | −0.335268 | − | 0.942123i | \(-0.608827\pi\) | ||||
−0.335268 | + | 0.942123i | \(0.608827\pi\) | |||||||
\(60\) | −5.94777 | −0.767854 | ||||||||
\(61\) | −4.14673 | −0.530934 | −0.265467 | − | 0.964120i | \(-0.585526\pi\) | ||||
−0.265467 | + | 0.964120i | \(0.585526\pi\) | |||||||
\(62\) | −0.596870 | −0.0758025 | ||||||||
\(63\) | −2.12137 | −0.267268 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.81212 | 0.472835 | ||||||||
\(66\) | 0.166796 | 0.0205312 | ||||||||
\(67\) | −8.70756 | −1.06380 | −0.531899 | − | 0.846808i | \(-0.678521\pi\) | ||||
−0.531899 | + | 0.846808i | \(0.678521\pi\) | |||||||
\(68\) | 5.46364 | 0.662564 | ||||||||
\(69\) | 12.6200 | 1.51927 | ||||||||
\(70\) | −9.52925 | −1.13896 | ||||||||
\(71\) | −1.88332 | −0.223509 | −0.111754 | − | 0.993736i | \(-0.535647\pi\) | ||||
−0.111754 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(72\) | 0.689347 | 0.0812403 | ||||||||
\(73\) | 11.3462 | 1.32797 | 0.663987 | − | 0.747744i | \(-0.268863\pi\) | ||||
0.663987 | + | 0.747744i | \(0.268863\pi\) | |||||||
\(74\) | −0.702711 | −0.0816885 | ||||||||
\(75\) | −8.81381 | −1.01773 | ||||||||
\(76\) | −3.74953 | −0.430101 | ||||||||
\(77\) | 0.267233 | 0.0304540 | ||||||||
\(78\) | −2.36462 | −0.267740 | ||||||||
\(79\) | −7.21356 | −0.811589 | −0.405794 | − | 0.913964i | \(-0.633005\pi\) | ||||
−0.405794 | + | 0.913964i | \(0.633005\pi\) | |||||||
\(80\) | 3.09656 | 0.346206 | ||||||||
\(81\) | −10.5928 | −1.17698 | ||||||||
\(82\) | 4.85857 | 0.536540 | ||||||||
\(83\) | 2.30311 | 0.252799 | 0.126400 | − | 0.991979i | \(-0.459658\pi\) | ||||
0.126400 | + | 0.991979i | \(0.459658\pi\) | |||||||
\(84\) | 5.91090 | 0.644932 | ||||||||
\(85\) | 16.9185 | 1.83507 | ||||||||
\(86\) | −6.26112 | −0.675154 | ||||||||
\(87\) | 14.6853 | 1.57443 | ||||||||
\(88\) | −0.0868382 | −0.00925699 | ||||||||
\(89\) | −6.30610 | −0.668446 | −0.334223 | − | 0.942494i | \(-0.608474\pi\) | ||||
−0.334223 | + | 0.942494i | \(0.608474\pi\) | |||||||
\(90\) | 2.13460 | 0.225007 | ||||||||
\(91\) | −3.78848 | −0.397141 | ||||||||
\(92\) | −6.57027 | −0.684998 | ||||||||
\(93\) | 1.14645 | 0.118881 | ||||||||
\(94\) | −5.40358 | −0.557337 | ||||||||
\(95\) | −11.6107 | −1.19123 | ||||||||
\(96\) | −1.92077 | −0.196037 | ||||||||
\(97\) | 7.66801 | 0.778568 | 0.389284 | − | 0.921118i | \(-0.372722\pi\) | ||||
0.389284 | + | 0.921118i | \(0.372722\pi\) | |||||||
\(98\) | 2.47018 | 0.249526 | ||||||||
\(99\) | −0.0598616 | −0.00601632 | ||||||||
\(100\) | 4.58869 | 0.458869 | ||||||||
\(101\) | 5.85604 | 0.582698 | 0.291349 | − | 0.956617i | \(-0.405896\pi\) | ||||
0.291349 | + | 0.956617i | \(0.405896\pi\) | |||||||
\(102\) | −10.4944 | −1.03910 | ||||||||
\(103\) | −19.4504 | −1.91650 | −0.958251 | − | 0.285930i | \(-0.907698\pi\) | ||||
−0.958251 | + | 0.285930i | \(0.907698\pi\) | |||||||
\(104\) | 1.23108 | 0.120717 | ||||||||
\(105\) | 18.3035 | 1.78624 | ||||||||
\(106\) | 13.4051 | 1.30202 | ||||||||
\(107\) | 18.2950 | 1.76865 | 0.884325 | − | 0.466873i | \(-0.154619\pi\) | ||||
0.884325 | + | 0.466873i | \(0.154619\pi\) | |||||||
\(108\) | 4.43823 | 0.427069 | ||||||||
\(109\) | −20.1991 | −1.93472 | −0.967361 | − | 0.253401i | \(-0.918451\pi\) | ||||
−0.967361 | + | 0.253401i | \(0.918451\pi\) | |||||||
\(110\) | −0.268900 | −0.0256386 | ||||||||
\(111\) | 1.34974 | 0.128112 | ||||||||
\(112\) | −3.07737 | −0.290784 | ||||||||
\(113\) | −15.4086 | −1.44952 | −0.724760 | − | 0.689002i | \(-0.758049\pi\) | ||||
−0.724760 | + | 0.689002i | \(0.758049\pi\) | |||||||
\(114\) | 7.20198 | 0.674527 | ||||||||
\(115\) | −20.3453 | −1.89720 | ||||||||
\(116\) | −7.64556 | −0.709872 | ||||||||
\(117\) | 0.848641 | 0.0784569 | ||||||||
\(118\) | −5.15049 | −0.474141 | ||||||||
\(119\) | −16.8136 | −1.54130 | ||||||||
\(120\) | −5.94777 | −0.542955 | ||||||||
\(121\) | −10.9925 | −0.999314 | ||||||||
\(122\) | −4.14673 | −0.375427 | ||||||||
\(123\) | −9.33219 | −0.841455 | ||||||||
\(124\) | −0.596870 | −0.0536005 | ||||||||
\(125\) | −1.27364 | −0.113917 | ||||||||
\(126\) | −2.12137 | −0.188987 | ||||||||
\(127\) | 19.7872 | 1.75583 | 0.877914 | − | 0.478819i | \(-0.158935\pi\) | ||||
0.877914 | + | 0.478819i | \(0.158935\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.0262 | 1.05884 | ||||||||
\(130\) | 3.81212 | 0.334345 | ||||||||
\(131\) | −4.76810 | −0.416591 | −0.208296 | − | 0.978066i | \(-0.566792\pi\) | ||||
−0.208296 | + | 0.978066i | \(0.566792\pi\) | |||||||
\(132\) | 0.166796 | 0.0145177 | ||||||||
\(133\) | 11.5387 | 1.00053 | ||||||||
\(134\) | −8.70756 | −0.752218 | ||||||||
\(135\) | 13.7432 | 1.18283 | ||||||||
\(136\) | 5.46364 | 0.468504 | ||||||||
\(137\) | −15.3109 | −1.30810 | −0.654049 | − | 0.756453i | \(-0.726931\pi\) | ||||
−0.654049 | + | 0.756453i | \(0.726931\pi\) | |||||||
\(138\) | 12.6200 | 1.07428 | ||||||||
\(139\) | 18.4532 | 1.56518 | 0.782589 | − | 0.622539i | \(-0.213899\pi\) | ||||
0.782589 | + | 0.622539i | \(0.213899\pi\) | |||||||
\(140\) | −9.52925 | −0.805369 | ||||||||
\(141\) | 10.3790 | 0.874071 | ||||||||
\(142\) | −1.88332 | −0.158045 | ||||||||
\(143\) | −0.106905 | −0.00893983 | ||||||||
\(144\) | 0.689347 | 0.0574456 | ||||||||
\(145\) | −23.6749 | −1.96610 | ||||||||
\(146\) | 11.3462 | 0.939019 | ||||||||
\(147\) | −4.74464 | −0.391332 | ||||||||
\(148\) | −0.702711 | −0.0577625 | ||||||||
\(149\) | −2.12820 | −0.174349 | −0.0871745 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871745 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(150\) | −8.81381 | −0.719645 | ||||||||
\(151\) | −4.69400 | −0.381992 | −0.190996 | − | 0.981591i | \(-0.561172\pi\) | ||||
−0.190996 | + | 0.981591i | \(0.561172\pi\) | |||||||
\(152\) | −3.74953 | −0.304127 | ||||||||
\(153\) | 3.76634 | 0.304491 | ||||||||
\(154\) | 0.267233 | 0.0215343 | ||||||||
\(155\) | −1.84824 | −0.148455 | ||||||||
\(156\) | −2.36462 | −0.189321 | ||||||||
\(157\) | −4.24205 | −0.338552 | −0.169276 | − | 0.985569i | \(-0.554143\pi\) | ||||
−0.169276 | + | 0.985569i | \(0.554143\pi\) | |||||||
\(158\) | −7.21356 | −0.573880 | ||||||||
\(159\) | −25.7481 | −2.04196 | ||||||||
\(160\) | 3.09656 | 0.244805 | ||||||||
\(161\) | 20.2191 | 1.59349 | ||||||||
\(162\) | −10.5928 | −0.832252 | ||||||||
\(163\) | 0.946145 | 0.0741078 | 0.0370539 | − | 0.999313i | \(-0.488203\pi\) | ||||
0.0370539 | + | 0.999313i | \(0.488203\pi\) | |||||||
\(164\) | 4.85857 | 0.379391 | ||||||||
\(165\) | 0.516494 | 0.0402090 | ||||||||
\(166\) | 2.30311 | 0.178756 | ||||||||
\(167\) | 16.2744 | 1.25935 | 0.629674 | − | 0.776860i | \(-0.283189\pi\) | ||||
0.629674 | + | 0.776860i | \(0.283189\pi\) | |||||||
\(168\) | 5.91090 | 0.456036 | ||||||||
\(169\) | −11.4844 | −0.883419 | ||||||||
\(170\) | 16.9185 | 1.29759 | ||||||||
\(171\) | −2.58473 | −0.197659 | ||||||||
\(172\) | −6.26112 | −0.477406 | ||||||||
\(173\) | −21.7471 | −1.65340 | −0.826700 | − | 0.562643i | \(-0.809785\pi\) | ||||
−0.826700 | + | 0.562643i | \(0.809785\pi\) | |||||||
\(174\) | 14.6853 | 1.11329 | ||||||||
\(175\) | −14.1211 | −1.06745 | ||||||||
\(176\) | −0.0868382 | −0.00654568 | ||||||||
\(177\) | 9.89288 | 0.743595 | ||||||||
\(178\) | −6.30610 | −0.472663 | ||||||||
\(179\) | −8.96135 | −0.669803 | −0.334901 | − | 0.942253i | \(-0.608703\pi\) | ||||
−0.334901 | + | 0.942253i | \(0.608703\pi\) | |||||||
\(180\) | 2.13460 | 0.159104 | ||||||||
\(181\) | 7.93227 | 0.589601 | 0.294800 | − | 0.955559i | \(-0.404747\pi\) | ||||
0.294800 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(182\) | −3.78848 | −0.280821 | ||||||||
\(183\) | 7.96489 | 0.588782 | ||||||||
\(184\) | −6.57027 | −0.484367 | ||||||||
\(185\) | −2.17599 | −0.159982 | ||||||||
\(186\) | 1.14645 | 0.0840616 | ||||||||
\(187\) | −0.474453 | −0.0346955 | ||||||||
\(188\) | −5.40358 | −0.394097 | ||||||||
\(189\) | −13.6580 | −0.993477 | ||||||||
\(190\) | −11.6107 | −0.842325 | ||||||||
\(191\) | −10.8672 | −0.786322 | −0.393161 | − | 0.919470i | \(-0.628619\pi\) | ||||
−0.393161 | + | 0.919470i | \(0.628619\pi\) | |||||||
\(192\) | −1.92077 | −0.138619 | ||||||||
\(193\) | −13.4725 | −0.969775 | −0.484888 | − | 0.874576i | \(-0.661139\pi\) | ||||
−0.484888 | + | 0.874576i | \(0.661139\pi\) | |||||||
\(194\) | 7.66801 | 0.550531 | ||||||||
\(195\) | −7.32219 | −0.524353 | ||||||||
\(196\) | 2.47018 | 0.176442 | ||||||||
\(197\) | −22.3555 | −1.59276 | −0.796381 | − | 0.604796i | \(-0.793255\pi\) | ||||
−0.796381 | + | 0.604796i | \(0.793255\pi\) | |||||||
\(198\) | −0.0598616 | −0.00425418 | ||||||||
\(199\) | −15.6192 | −1.10721 | −0.553607 | − | 0.832778i | \(-0.686749\pi\) | ||||
−0.553607 | + | 0.832778i | \(0.686749\pi\) | |||||||
\(200\) | 4.58869 | 0.324470 | ||||||||
\(201\) | 16.7252 | 1.17970 | ||||||||
\(202\) | 5.85604 | 0.412030 | ||||||||
\(203\) | 23.5282 | 1.65135 | ||||||||
\(204\) | −10.4944 | −0.734754 | ||||||||
\(205\) | 15.0449 | 1.05078 | ||||||||
\(206\) | −19.4504 | −1.35517 | ||||||||
\(207\) | −4.52920 | −0.314801 | ||||||||
\(208\) | 1.23108 | 0.0853600 | ||||||||
\(209\) | 0.325603 | 0.0225224 | ||||||||
\(210\) | 18.3035 | 1.26306 | ||||||||
\(211\) | 14.8399 | 1.02162 | 0.510812 | − | 0.859692i | \(-0.329345\pi\) | ||||
0.510812 | + | 0.859692i | \(0.329345\pi\) | |||||||
\(212\) | 13.4051 | 0.920668 | ||||||||
\(213\) | 3.61742 | 0.247861 | ||||||||
\(214\) | 18.2950 | 1.25062 | ||||||||
\(215\) | −19.3879 | −1.32225 | ||||||||
\(216\) | 4.43823 | 0.301983 | ||||||||
\(217\) | 1.83679 | 0.124689 | ||||||||
\(218\) | −20.1991 | −1.36806 | ||||||||
\(219\) | −21.7934 | −1.47266 | ||||||||
\(220\) | −0.268900 | −0.0181292 | ||||||||
\(221\) | 6.72618 | 0.452452 | ||||||||
\(222\) | 1.34974 | 0.0905889 | ||||||||
\(223\) | 19.6674 | 1.31702 | 0.658512 | − | 0.752570i | \(-0.271186\pi\) | ||||
0.658512 | + | 0.752570i | \(0.271186\pi\) | |||||||
\(224\) | −3.07737 | −0.205615 | ||||||||
\(225\) | 3.16320 | 0.210880 | ||||||||
\(226\) | −15.4086 | −1.02496 | ||||||||
\(227\) | 4.86018 | 0.322582 | 0.161291 | − | 0.986907i | \(-0.448434\pi\) | ||||
0.161291 | + | 0.986907i | \(0.448434\pi\) | |||||||
\(228\) | 7.20198 | 0.476963 | ||||||||
\(229\) | −6.78352 | −0.448267 | −0.224134 | − | 0.974558i | \(-0.571955\pi\) | ||||
−0.224134 | + | 0.974558i | \(0.571955\pi\) | |||||||
\(230\) | −20.3453 | −1.34153 | ||||||||
\(231\) | −0.513292 | −0.0337722 | ||||||||
\(232\) | −7.64556 | −0.501955 | ||||||||
\(233\) | −27.2439 | −1.78481 | −0.892405 | − | 0.451236i | \(-0.850983\pi\) | ||||
−0.892405 | + | 0.451236i | \(0.850983\pi\) | |||||||
\(234\) | 0.848641 | 0.0554774 | ||||||||
\(235\) | −16.7325 | −1.09151 | ||||||||
\(236\) | −5.15049 | −0.335268 | ||||||||
\(237\) | 13.8556 | 0.900016 | ||||||||
\(238\) | −16.8136 | −1.08987 | ||||||||
\(239\) | 12.1334 | 0.784846 | 0.392423 | − | 0.919785i | \(-0.371637\pi\) | ||||
0.392423 | + | 0.919785i | \(0.371637\pi\) | |||||||
\(240\) | −5.94777 | −0.383927 | ||||||||
\(241\) | 8.41981 | 0.542368 | 0.271184 | − | 0.962528i | \(-0.412585\pi\) | ||||
0.271184 | + | 0.962528i | \(0.412585\pi\) | |||||||
\(242\) | −10.9925 | −0.706622 | ||||||||
\(243\) | 7.03170 | 0.451084 | ||||||||
\(244\) | −4.14673 | −0.265467 | ||||||||
\(245\) | 7.64907 | 0.488681 | ||||||||
\(246\) | −9.33219 | −0.594999 | ||||||||
\(247\) | −4.61597 | −0.293707 | ||||||||
\(248\) | −0.596870 | −0.0379013 | ||||||||
\(249\) | −4.42374 | −0.280343 | ||||||||
\(250\) | −1.27364 | −0.0805518 | ||||||||
\(251\) | 18.1704 | 1.14690 | 0.573452 | − | 0.819239i | \(-0.305604\pi\) | ||||
0.573452 | + | 0.819239i | \(0.305604\pi\) | |||||||
\(252\) | −2.12137 | −0.133634 | ||||||||
\(253\) | 0.570551 | 0.0358702 | ||||||||
\(254\) | 19.7872 | 1.24156 | ||||||||
\(255\) | −32.4965 | −2.03501 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.6006 | 1.59692 | 0.798461 | − | 0.602046i | \(-0.205648\pi\) | ||||
0.798461 | + | 0.602046i | \(0.205648\pi\) | |||||||
\(258\) | 12.0262 | 0.748716 | ||||||||
\(259\) | 2.16250 | 0.134371 | ||||||||
\(260\) | 3.81212 | 0.236417 | ||||||||
\(261\) | −5.27044 | −0.326232 | ||||||||
\(262\) | −4.76810 | −0.294574 | ||||||||
\(263\) | 15.0802 | 0.929882 | 0.464941 | − | 0.885342i | \(-0.346076\pi\) | ||||
0.464941 | + | 0.885342i | \(0.346076\pi\) | |||||||
\(264\) | 0.166796 | 0.0102656 | ||||||||
\(265\) | 41.5098 | 2.54993 | ||||||||
\(266\) | 11.5387 | 0.707482 | ||||||||
\(267\) | 12.1126 | 0.741277 | ||||||||
\(268\) | −8.70756 | −0.531899 | ||||||||
\(269\) | 24.3510 | 1.48471 | 0.742355 | − | 0.670007i | \(-0.233709\pi\) | ||||
0.742355 | + | 0.670007i | \(0.233709\pi\) | |||||||
\(270\) | 13.7432 | 0.836387 | ||||||||
\(271\) | −0.982042 | −0.0596548 | −0.0298274 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298274 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(272\) | 5.46364 | 0.331282 | ||||||||
\(273\) | 7.27680 | 0.440412 | ||||||||
\(274\) | −15.3109 | −0.924964 | ||||||||
\(275\) | −0.398474 | −0.0240289 | ||||||||
\(276\) | 12.6200 | 0.759633 | ||||||||
\(277\) | −3.94284 | −0.236902 | −0.118451 | − | 0.992960i | \(-0.537793\pi\) | ||||
−0.118451 | + | 0.992960i | \(0.537793\pi\) | |||||||
\(278\) | 18.4532 | 1.10675 | ||||||||
\(279\) | −0.411450 | −0.0246329 | ||||||||
\(280\) | −9.52925 | −0.569482 | ||||||||
\(281\) | 2.11191 | 0.125986 | 0.0629930 | − | 0.998014i | \(-0.479935\pi\) | ||||
0.0629930 | + | 0.998014i | \(0.479935\pi\) | |||||||
\(282\) | 10.3790 | 0.618062 | ||||||||
\(283\) | 1.00358 | 0.0596565 | 0.0298283 | − | 0.999555i | \(-0.490504\pi\) | ||||
0.0298283 | + | 0.999555i | \(0.490504\pi\) | |||||||
\(284\) | −1.88332 | −0.111754 | ||||||||
\(285\) | 22.3014 | 1.32102 | ||||||||
\(286\) | −0.106905 | −0.00632141 | ||||||||
\(287\) | −14.9516 | −0.882566 | ||||||||
\(288\) | 0.689347 | 0.0406201 | ||||||||
\(289\) | 12.8514 | 0.755965 | ||||||||
\(290\) | −23.6749 | −1.39024 | ||||||||
\(291\) | −14.7285 | −0.863398 | ||||||||
\(292\) | 11.3462 | 0.663987 | ||||||||
\(293\) | −29.2786 | −1.71047 | −0.855236 | − | 0.518239i | \(-0.826588\pi\) | ||||
−0.855236 | + | 0.518239i | \(0.826588\pi\) | |||||||
\(294\) | −4.74464 | −0.276713 | ||||||||
\(295\) | −15.9488 | −0.928575 | ||||||||
\(296\) | −0.702711 | −0.0408443 | ||||||||
\(297\) | −0.385408 | −0.0223636 | ||||||||
\(298\) | −2.12820 | −0.123283 | ||||||||
\(299\) | −8.08853 | −0.467772 | ||||||||
\(300\) | −8.81381 | −0.508866 | ||||||||
\(301\) | 19.2678 | 1.11058 | ||||||||
\(302\) | −4.69400 | −0.270109 | ||||||||
\(303\) | −11.2481 | −0.646186 | ||||||||
\(304\) | −3.74953 | −0.215050 | ||||||||
\(305\) | −12.8406 | −0.735250 | ||||||||
\(306\) | 3.76634 | 0.215308 | ||||||||
\(307\) | −30.0391 | −1.71442 | −0.857210 | − | 0.514966i | \(-0.827804\pi\) | ||||
−0.857210 | + | 0.514966i | \(0.827804\pi\) | |||||||
\(308\) | 0.267233 | 0.0152270 | ||||||||
\(309\) | 37.3596 | 2.12531 | ||||||||
\(310\) | −1.84824 | −0.104973 | ||||||||
\(311\) | −0.838753 | −0.0475613 | −0.0237806 | − | 0.999717i | \(-0.507570\pi\) | ||||
−0.0237806 | + | 0.999717i | \(0.507570\pi\) | |||||||
\(312\) | −2.36462 | −0.133870 | ||||||||
\(313\) | −25.1099 | −1.41929 | −0.709647 | − | 0.704558i | \(-0.751145\pi\) | ||||
−0.709647 | + | 0.704558i | \(0.751145\pi\) | |||||||
\(314\) | −4.24205 | −0.239393 | ||||||||
\(315\) | −6.56896 | −0.370119 | ||||||||
\(316\) | −7.21356 | −0.405794 | ||||||||
\(317\) | −23.5696 | −1.32380 | −0.661901 | − | 0.749592i | \(-0.730250\pi\) | ||||
−0.661901 | + | 0.749592i | \(0.730250\pi\) | |||||||
\(318\) | −25.7481 | −1.44388 | ||||||||
\(319\) | 0.663927 | 0.0371727 | ||||||||
\(320\) | 3.09656 | 0.173103 | ||||||||
\(321\) | −35.1405 | −1.96135 | ||||||||
\(322\) | 20.2191 | 1.12677 | ||||||||
\(323\) | −20.4861 | −1.13988 | ||||||||
\(324\) | −10.5928 | −0.588491 | ||||||||
\(325\) | 5.64905 | 0.313353 | ||||||||
\(326\) | 0.946145 | 0.0524021 | ||||||||
\(327\) | 38.7978 | 2.14552 | ||||||||
\(328\) | 4.85857 | 0.268270 | ||||||||
\(329\) | 16.6288 | 0.916775 | ||||||||
\(330\) | 0.516494 | 0.0284321 | ||||||||
\(331\) | −31.8993 | −1.75334 | −0.876672 | − | 0.481089i | \(-0.840242\pi\) | ||||
−0.876672 | + | 0.481089i | \(0.840242\pi\) | |||||||
\(332\) | 2.30311 | 0.126400 | ||||||||
\(333\) | −0.484412 | −0.0265456 | ||||||||
\(334\) | 16.2744 | 0.890493 | ||||||||
\(335\) | −26.9635 | −1.47317 | ||||||||
\(336\) | 5.91090 | 0.322466 | ||||||||
\(337\) | −26.2190 | −1.42824 | −0.714120 | − | 0.700024i | \(-0.753173\pi\) | ||||
−0.714120 | + | 0.700024i | \(0.753173\pi\) | |||||||
\(338\) | −11.4844 | −0.624671 | ||||||||
\(339\) | 29.5963 | 1.60745 | ||||||||
\(340\) | 16.9185 | 0.917535 | ||||||||
\(341\) | 0.0518311 | 0.00280681 | ||||||||
\(342\) | −2.58473 | −0.139766 | ||||||||
\(343\) | 13.9399 | 0.752684 | ||||||||
\(344\) | −6.26112 | −0.337577 | ||||||||
\(345\) | 39.0785 | 2.10392 | ||||||||
\(346\) | −21.7471 | −1.16913 | ||||||||
\(347\) | 7.46521 | 0.400753 | 0.200377 | − | 0.979719i | \(-0.435783\pi\) | ||||
0.200377 | + | 0.979719i | \(0.435783\pi\) | |||||||
\(348\) | 14.6853 | 0.787216 | ||||||||
\(349\) | −2.51923 | −0.134851 | −0.0674256 | − | 0.997724i | \(-0.521479\pi\) | ||||
−0.0674256 | + | 0.997724i | \(0.521479\pi\) | |||||||
\(350\) | −14.1211 | −0.754804 | ||||||||
\(351\) | 5.46381 | 0.291637 | ||||||||
\(352\) | −0.0868382 | −0.00462849 | ||||||||
\(353\) | 17.3573 | 0.923833 | 0.461917 | − | 0.886923i | \(-0.347162\pi\) | ||||
0.461917 | + | 0.886923i | \(0.347162\pi\) | |||||||
\(354\) | 9.89288 | 0.525801 | ||||||||
\(355\) | −5.83181 | −0.309520 | ||||||||
\(356\) | −6.30610 | −0.334223 | ||||||||
\(357\) | 32.2951 | 1.70924 | ||||||||
\(358\) | −8.96135 | −0.473622 | ||||||||
\(359\) | 36.4948 | 1.92612 | 0.963060 | − | 0.269286i | \(-0.0867876\pi\) | ||||
0.963060 | + | 0.269286i | \(0.0867876\pi\) | |||||||
\(360\) | 2.13460 | 0.112504 | ||||||||
\(361\) | −4.94102 | −0.260054 | ||||||||
\(362\) | 7.93227 | 0.416911 | ||||||||
\(363\) | 21.1140 | 1.10820 | ||||||||
\(364\) | −3.78848 | −0.198571 | ||||||||
\(365\) | 35.1342 | 1.83901 | ||||||||
\(366\) | 7.96489 | 0.416332 | ||||||||
\(367\) | −10.9063 | −0.569304 | −0.284652 | − | 0.958631i | \(-0.591878\pi\) | ||||
−0.284652 | + | 0.958631i | \(0.591878\pi\) | |||||||
\(368\) | −6.57027 | −0.342499 | ||||||||
\(369\) | 3.34924 | 0.174355 | ||||||||
\(370\) | −2.17599 | −0.113124 | ||||||||
\(371\) | −41.2525 | −2.14172 | ||||||||
\(372\) | 1.14645 | 0.0594405 | ||||||||
\(373\) | −34.0149 | −1.76122 | −0.880611 | − | 0.473839i | \(-0.842868\pi\) | ||||
−0.880611 | + | 0.473839i | \(0.842868\pi\) | |||||||
\(374\) | −0.474453 | −0.0245334 | ||||||||
\(375\) | 2.44636 | 0.126329 | ||||||||
\(376\) | −5.40358 | −0.278668 | ||||||||
\(377\) | −9.41229 | −0.484758 | ||||||||
\(378\) | −13.6580 | −0.702494 | ||||||||
\(379\) | −31.7579 | −1.63129 | −0.815646 | − | 0.578551i | \(-0.803618\pi\) | ||||
−0.815646 | + | 0.578551i | \(0.803618\pi\) | |||||||
\(380\) | −11.6107 | −0.595614 | ||||||||
\(381\) | −38.0065 | −1.94713 | ||||||||
\(382\) | −10.8672 | −0.556014 | ||||||||
\(383\) | 16.1480 | 0.825122 | 0.412561 | − | 0.910930i | \(-0.364634\pi\) | ||||
0.412561 | + | 0.910930i | \(0.364634\pi\) | |||||||
\(384\) | −1.92077 | −0.0980187 | ||||||||
\(385\) | 0.827504 | 0.0421735 | ||||||||
\(386\) | −13.4725 | −0.685735 | ||||||||
\(387\) | −4.31608 | −0.219399 | ||||||||
\(388\) | 7.66801 | 0.389284 | ||||||||
\(389\) | 34.3674 | 1.74249 | 0.871247 | − | 0.490845i | \(-0.163312\pi\) | ||||
0.871247 | + | 0.490845i | \(0.163312\pi\) | |||||||
\(390\) | −7.32219 | −0.370773 | ||||||||
\(391\) | −35.8976 | −1.81542 | ||||||||
\(392\) | 2.47018 | 0.124763 | ||||||||
\(393\) | 9.15842 | 0.461981 | ||||||||
\(394\) | −22.3555 | −1.12625 | ||||||||
\(395\) | −22.3372 | −1.12391 | ||||||||
\(396\) | −0.0598616 | −0.00300816 | ||||||||
\(397\) | −3.64407 | −0.182891 | −0.0914453 | − | 0.995810i | \(-0.529149\pi\) | ||||
−0.0914453 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(398\) | −15.6192 | −0.782919 | ||||||||
\(399\) | −22.1631 | −1.10954 | ||||||||
\(400\) | 4.58869 | 0.229435 | ||||||||
\(401\) | 23.4469 | 1.17088 | 0.585442 | − | 0.810714i | \(-0.300921\pi\) | ||||
0.585442 | + | 0.810714i | \(0.300921\pi\) | |||||||
\(402\) | 16.7252 | 0.834177 | ||||||||
\(403\) | −0.734794 | −0.0366027 | ||||||||
\(404\) | 5.85604 | 0.291349 | ||||||||
\(405\) | −32.8014 | −1.62991 | ||||||||
\(406\) | 23.5282 | 1.16768 | ||||||||
\(407\) | 0.0610222 | 0.00302476 | ||||||||
\(408\) | −10.4944 | −0.519550 | ||||||||
\(409\) | −15.8618 | −0.784316 | −0.392158 | − | 0.919898i | \(-0.628271\pi\) | ||||
−0.392158 | + | 0.919898i | \(0.628271\pi\) | |||||||
\(410\) | 15.0449 | 0.743013 | ||||||||
\(411\) | 29.4086 | 1.45062 | ||||||||
\(412\) | −19.4504 | −0.958251 | ||||||||
\(413\) | 15.8499 | 0.779924 | ||||||||
\(414\) | −4.52920 | −0.222598 | ||||||||
\(415\) | 7.13172 | 0.350082 | ||||||||
\(416\) | 1.23108 | 0.0603587 | ||||||||
\(417\) | −35.4442 | −1.73571 | ||||||||
\(418\) | 0.325603 | 0.0159257 | ||||||||
\(419\) | −38.3568 | −1.87385 | −0.936927 | − | 0.349526i | \(-0.886343\pi\) | ||||
−0.936927 | + | 0.349526i | \(0.886343\pi\) | |||||||
\(420\) | 18.3035 | 0.893118 | ||||||||
\(421\) | 32.5351 | 1.58566 | 0.792831 | − | 0.609442i | \(-0.208606\pi\) | ||||
0.792831 | + | 0.609442i | \(0.208606\pi\) | |||||||
\(422\) | 14.8399 | 0.722397 | ||||||||
\(423\) | −3.72494 | −0.181113 | ||||||||
\(424\) | 13.4051 | 0.651011 | ||||||||
\(425\) | 25.0710 | 1.21612 | ||||||||
\(426\) | 3.61742 | 0.175264 | ||||||||
\(427\) | 12.7610 | 0.617548 | ||||||||
\(428\) | 18.2950 | 0.884325 | ||||||||
\(429\) | 0.205339 | 0.00991387 | ||||||||
\(430\) | −19.3879 | −0.934970 | ||||||||
\(431\) | −10.8875 | −0.524431 | −0.262215 | − | 0.965009i | \(-0.584453\pi\) | ||||
−0.262215 | + | 0.965009i | \(0.584453\pi\) | |||||||
\(432\) | 4.43823 | 0.213534 | ||||||||
\(433\) | −15.7157 | −0.755251 | −0.377625 | − | 0.925958i | \(-0.623259\pi\) | ||||
−0.377625 | + | 0.925958i | \(0.623259\pi\) | |||||||
\(434\) | 1.83679 | 0.0881686 | ||||||||
\(435\) | 45.4740 | 2.18031 | ||||||||
\(436\) | −20.1991 | −0.967361 | ||||||||
\(437\) | 24.6354 | 1.17847 | ||||||||
\(438\) | −21.7934 | −1.04133 | ||||||||
\(439\) | 13.7872 | 0.658025 | 0.329013 | − | 0.944326i | \(-0.393284\pi\) | ||||
0.329013 | + | 0.944326i | \(0.393284\pi\) | |||||||
\(440\) | −0.268900 | −0.0128193 | ||||||||
\(441\) | 1.70281 | 0.0810862 | ||||||||
\(442\) | 6.72618 | 0.319932 | ||||||||
\(443\) | −27.8742 | −1.32434 | −0.662172 | − | 0.749352i | \(-0.730365\pi\) | ||||
−0.662172 | + | 0.749352i | \(0.730365\pi\) | |||||||
\(444\) | 1.34974 | 0.0640561 | ||||||||
\(445\) | −19.5272 | −0.925680 | ||||||||
\(446\) | 19.6674 | 0.931277 | ||||||||
\(447\) | 4.08778 | 0.193345 | ||||||||
\(448\) | −3.07737 | −0.145392 | ||||||||
\(449\) | −14.2230 | −0.671223 | −0.335611 | − | 0.942001i | \(-0.608943\pi\) | ||||
−0.335611 | + | 0.942001i | \(0.608943\pi\) | |||||||
\(450\) | 3.16320 | 0.149115 | ||||||||
\(451\) | −0.421910 | −0.0198670 | ||||||||
\(452\) | −15.4086 | −0.724760 | ||||||||
\(453\) | 9.01608 | 0.423613 | ||||||||
\(454\) | 4.86018 | 0.228100 | ||||||||
\(455\) | −11.7313 | −0.549971 | ||||||||
\(456\) | 7.20198 | 0.337263 | ||||||||
\(457\) | −40.0549 | −1.87369 | −0.936844 | − | 0.349747i | \(-0.886268\pi\) | ||||
−0.936844 | + | 0.349747i | \(0.886268\pi\) | |||||||
\(458\) | −6.78352 | −0.316973 | ||||||||
\(459\) | 24.2489 | 1.13184 | ||||||||
\(460\) | −20.3453 | −0.948602 | ||||||||
\(461\) | 25.7487 | 1.19923 | 0.599617 | − | 0.800287i | \(-0.295320\pi\) | ||||
0.599617 | + | 0.800287i | \(0.295320\pi\) | |||||||
\(462\) | −0.513292 | −0.0238805 | ||||||||
\(463\) | −29.3136 | −1.36232 | −0.681159 | − | 0.732136i | \(-0.738524\pi\) | ||||
−0.681159 | + | 0.732136i | \(0.738524\pi\) | |||||||
\(464\) | −7.64556 | −0.354936 | ||||||||
\(465\) | 3.55005 | 0.164629 | ||||||||
\(466\) | −27.2439 | −1.26205 | ||||||||
\(467\) | −23.9427 | −1.10793 | −0.553967 | − | 0.832539i | \(-0.686887\pi\) | ||||
−0.553967 | + | 0.832539i | \(0.686887\pi\) | |||||||
\(468\) | 0.848641 | 0.0392284 | ||||||||
\(469\) | 26.7963 | 1.23734 | ||||||||
\(470\) | −16.7325 | −0.771813 | ||||||||
\(471\) | 8.14798 | 0.375439 | ||||||||
\(472\) | −5.15049 | −0.237070 | ||||||||
\(473\) | 0.543705 | 0.0249996 | ||||||||
\(474\) | 13.8556 | 0.636407 | ||||||||
\(475\) | −17.2054 | −0.789440 | ||||||||
\(476\) | −16.8136 | −0.770652 | ||||||||
\(477\) | 9.24078 | 0.423106 | ||||||||
\(478\) | 12.1334 | 0.554970 | ||||||||
\(479\) | 31.2124 | 1.42613 | 0.713065 | − | 0.701098i | \(-0.247306\pi\) | ||||
0.713065 | + | 0.701098i | \(0.247306\pi\) | |||||||
\(480\) | −5.94777 | −0.271477 | ||||||||
\(481\) | −0.865094 | −0.0394449 | ||||||||
\(482\) | 8.41981 | 0.383512 | ||||||||
\(483\) | −38.8363 | −1.76711 | ||||||||
\(484\) | −10.9925 | −0.499657 | ||||||||
\(485\) | 23.7445 | 1.07818 | ||||||||
\(486\) | 7.03170 | 0.318964 | ||||||||
\(487\) | −33.3702 | −1.51215 | −0.756074 | − | 0.654486i | \(-0.772885\pi\) | ||||
−0.756074 | + | 0.654486i | \(0.772885\pi\) | |||||||
\(488\) | −4.14673 | −0.187713 | ||||||||
\(489\) | −1.81732 | −0.0821823 | ||||||||
\(490\) | 7.64907 | 0.345550 | ||||||||
\(491\) | 3.48110 | 0.157100 | 0.0785499 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785499 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(492\) | −9.33219 | −0.420728 | ||||||||
\(493\) | −41.7726 | −1.88134 | ||||||||
\(494\) | −4.61597 | −0.207682 | ||||||||
\(495\) | −0.185365 | −0.00833155 | ||||||||
\(496\) | −0.596870 | −0.0268002 | ||||||||
\(497\) | 5.79566 | 0.259971 | ||||||||
\(498\) | −4.42374 | −0.198232 | ||||||||
\(499\) | 20.2119 | 0.904810 | 0.452405 | − | 0.891813i | \(-0.350566\pi\) | ||||
0.452405 | + | 0.891813i | \(0.350566\pi\) | |||||||
\(500\) | −1.27364 | −0.0569587 | ||||||||
\(501\) | −31.2592 | −1.39656 | ||||||||
\(502\) | 18.1704 | 0.810984 | ||||||||
\(503\) | 4.68984 | 0.209110 | 0.104555 | − | 0.994519i | \(-0.466658\pi\) | ||||
0.104555 | + | 0.994519i | \(0.466658\pi\) | |||||||
\(504\) | −2.12137 | −0.0944934 | ||||||||
\(505\) | 18.1336 | 0.806934 | ||||||||
\(506\) | 0.570551 | 0.0253641 | ||||||||
\(507\) | 22.0589 | 0.979672 | ||||||||
\(508\) | 19.7872 | 0.877914 | ||||||||
\(509\) | 22.8872 | 1.01446 | 0.507228 | − | 0.861812i | \(-0.330670\pi\) | ||||
0.507228 | + | 0.861812i | \(0.330670\pi\) | |||||||
\(510\) | −32.4965 | −1.43897 | ||||||||
\(511\) | −34.9164 | −1.54461 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −16.6413 | −0.734730 | ||||||||
\(514\) | 25.6006 | 1.12919 | ||||||||
\(515\) | −60.2292 | −2.65402 | ||||||||
\(516\) | 12.0262 | 0.529422 | ||||||||
\(517\) | 0.469237 | 0.0206370 | ||||||||
\(518\) | 2.16250 | 0.0950148 | ||||||||
\(519\) | 41.7711 | 1.83355 | ||||||||
\(520\) | 3.81212 | 0.167172 | ||||||||
\(521\) | −9.53723 | −0.417834 | −0.208917 | − | 0.977933i | \(-0.566994\pi\) | ||||
−0.208917 | + | 0.977933i | \(0.566994\pi\) | |||||||
\(522\) | −5.27044 | −0.230681 | ||||||||
\(523\) | −5.79916 | −0.253580 | −0.126790 | − | 0.991930i | \(-0.540467\pi\) | ||||
−0.126790 | + | 0.991930i | \(0.540467\pi\) | |||||||
\(524\) | −4.76810 | −0.208296 | ||||||||
\(525\) | 27.1233 | 1.18376 | ||||||||
\(526\) | 15.0802 | 0.657526 | ||||||||
\(527\) | −3.26108 | −0.142055 | ||||||||
\(528\) | 0.166796 | 0.00725887 | ||||||||
\(529\) | 20.1685 | 0.876891 | ||||||||
\(530\) | 41.5098 | 1.80307 | ||||||||
\(531\) | −3.55047 | −0.154077 | ||||||||
\(532\) | 11.5387 | 0.500265 | ||||||||
\(533\) | 5.98129 | 0.259079 | ||||||||
\(534\) | 12.1126 | 0.524162 | ||||||||
\(535\) | 56.6517 | 2.44927 | ||||||||
\(536\) | −8.70756 | −0.376109 | ||||||||
\(537\) | 17.2127 | 0.742782 | ||||||||
\(538\) | 24.3510 | 1.04985 | ||||||||
\(539\) | −0.214506 | −0.00923943 | ||||||||
\(540\) | 13.7432 | 0.591415 | ||||||||
\(541\) | −16.7935 | −0.722010 | −0.361005 | − | 0.932564i | \(-0.617566\pi\) | ||||
−0.361005 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(542\) | −0.982042 | −0.0421823 | ||||||||
\(543\) | −15.2360 | −0.653841 | ||||||||
\(544\) | 5.46364 | 0.234252 | ||||||||
\(545\) | −62.5477 | −2.67925 | ||||||||
\(546\) | 7.27680 | 0.311418 | ||||||||
\(547\) | −39.0011 | −1.66756 | −0.833782 | − | 0.552093i | \(-0.813829\pi\) | ||||
−0.833782 | + | 0.552093i | \(0.813829\pi\) | |||||||
\(548\) | −15.3109 | −0.654049 | ||||||||
\(549\) | −2.85853 | −0.121999 | ||||||||
\(550\) | −0.398474 | −0.0169910 | ||||||||
\(551\) | 28.6672 | 1.22127 | ||||||||
\(552\) | 12.6200 | 0.537141 | ||||||||
\(553\) | 22.1988 | 0.943987 | ||||||||
\(554\) | −3.94284 | −0.167515 | ||||||||
\(555\) | 4.17957 | 0.177413 | ||||||||
\(556\) | 18.4532 | 0.782589 | ||||||||
\(557\) | 33.9443 | 1.43827 | 0.719133 | − | 0.694872i | \(-0.244539\pi\) | ||||
0.719133 | + | 0.694872i | \(0.244539\pi\) | |||||||
\(558\) | −0.411450 | −0.0174181 | ||||||||
\(559\) | −7.70794 | −0.326011 | ||||||||
\(560\) | −9.52925 | −0.402684 | ||||||||
\(561\) | 0.911314 | 0.0384757 | ||||||||
\(562\) | 2.11191 | 0.0890856 | ||||||||
\(563\) | −28.8983 | −1.21792 | −0.608959 | − | 0.793202i | \(-0.708412\pi\) | ||||
−0.608959 | + | 0.793202i | \(0.708412\pi\) | |||||||
\(564\) | 10.3790 | 0.437036 | ||||||||
\(565\) | −47.7137 | −2.00733 | ||||||||
\(566\) | 1.00358 | 0.0421835 | ||||||||
\(567\) | 32.5980 | 1.36899 | ||||||||
\(568\) | −1.88332 | −0.0790223 | ||||||||
\(569\) | 39.5839 | 1.65944 | 0.829721 | − | 0.558178i | \(-0.188500\pi\) | ||||
0.829721 | + | 0.558178i | \(0.188500\pi\) | |||||||
\(570\) | 22.3014 | 0.934101 | ||||||||
\(571\) | 33.9517 | 1.42084 | 0.710418 | − | 0.703780i | \(-0.248506\pi\) | ||||
0.710418 | + | 0.703780i | \(0.248506\pi\) | |||||||
\(572\) | −0.106905 | −0.00446992 | ||||||||
\(573\) | 20.8733 | 0.871996 | ||||||||
\(574\) | −14.9516 | −0.624068 | ||||||||
\(575\) | −30.1490 | −1.25730 | ||||||||
\(576\) | 0.689347 | 0.0287228 | ||||||||
\(577\) | 4.12321 | 0.171651 | 0.0858257 | − | 0.996310i | \(-0.472647\pi\) | ||||
0.0858257 | + | 0.996310i | \(0.472647\pi\) | |||||||
\(578\) | 12.8514 | 0.534548 | ||||||||
\(579\) | 25.8776 | 1.07544 | ||||||||
\(580\) | −23.6749 | −0.983048 | ||||||||
\(581\) | −7.08751 | −0.294040 | ||||||||
\(582\) | −14.7285 | −0.610514 | ||||||||
\(583\) | −1.16408 | −0.0482112 | ||||||||
\(584\) | 11.3462 | 0.469510 | ||||||||
\(585\) | 2.62787 | 0.108649 | ||||||||
\(586\) | −29.2786 | −1.20949 | ||||||||
\(587\) | 20.5507 | 0.848217 | 0.424109 | − | 0.905611i | \(-0.360587\pi\) | ||||
0.424109 | + | 0.905611i | \(0.360587\pi\) | |||||||
\(588\) | −4.74464 | −0.195666 | ||||||||
\(589\) | 2.23798 | 0.0922144 | ||||||||
\(590\) | −15.9488 | −0.656601 | ||||||||
\(591\) | 42.9396 | 1.76630 | ||||||||
\(592\) | −0.702711 | −0.0288813 | ||||||||
\(593\) | 31.7929 | 1.30558 | 0.652789 | − | 0.757540i | \(-0.273599\pi\) | ||||
0.652789 | + | 0.757540i | \(0.273599\pi\) | |||||||
\(594\) | −0.385408 | −0.0158135 | ||||||||
\(595\) | −52.0644 | −2.13443 | ||||||||
\(596\) | −2.12820 | −0.0871745 | ||||||||
\(597\) | 30.0008 | 1.22785 | ||||||||
\(598\) | −8.08853 | −0.330765 | ||||||||
\(599\) | 23.0785 | 0.942964 | 0.471482 | − | 0.881876i | \(-0.343719\pi\) | ||||
0.471482 | + | 0.881876i | \(0.343719\pi\) | |||||||
\(600\) | −8.81381 | −0.359822 | ||||||||
\(601\) | 25.6563 | 1.04654 | 0.523271 | − | 0.852166i | \(-0.324711\pi\) | ||||
0.523271 | + | 0.852166i | \(0.324711\pi\) | |||||||
\(602\) | 19.2678 | 0.785295 | ||||||||
\(603\) | −6.00253 | −0.244442 | ||||||||
\(604\) | −4.69400 | −0.190996 | ||||||||
\(605\) | −34.0388 | −1.38388 | ||||||||
\(606\) | −11.2481 | −0.456923 | ||||||||
\(607\) | 23.0522 | 0.935660 | 0.467830 | − | 0.883818i | \(-0.345036\pi\) | ||||
0.467830 | + | 0.883818i | \(0.345036\pi\) | |||||||
\(608\) | −3.74953 | −0.152064 | ||||||||
\(609\) | −45.1921 | −1.83128 | ||||||||
\(610\) | −12.8406 | −0.519900 | ||||||||
\(611\) | −6.65224 | −0.269121 | ||||||||
\(612\) | 3.76634 | 0.152245 | ||||||||
\(613\) | 18.2475 | 0.737011 | 0.368506 | − | 0.929626i | \(-0.379870\pi\) | ||||
0.368506 | + | 0.929626i | \(0.379870\pi\) | |||||||
\(614\) | −30.0391 | −1.21228 | ||||||||
\(615\) | −28.8977 | −1.16527 | ||||||||
\(616\) | 0.267233 | 0.0107671 | ||||||||
\(617\) | 15.8961 | 0.639954 | 0.319977 | − | 0.947425i | \(-0.396325\pi\) | ||||
0.319977 | + | 0.947425i | \(0.396325\pi\) | |||||||
\(618\) | 37.3596 | 1.50282 | ||||||||
\(619\) | 6.90958 | 0.277720 | 0.138860 | − | 0.990312i | \(-0.455656\pi\) | ||||
0.138860 | + | 0.990312i | \(0.455656\pi\) | |||||||
\(620\) | −1.84824 | −0.0742273 | ||||||||
\(621\) | −29.1604 | −1.17017 | ||||||||
\(622\) | −0.838753 | −0.0336309 | ||||||||
\(623\) | 19.4062 | 0.777493 | ||||||||
\(624\) | −2.36462 | −0.0946605 | ||||||||
\(625\) | −26.8874 | −1.07549 | ||||||||
\(626\) | −25.1099 | −1.00359 | ||||||||
\(627\) | −0.625407 | −0.0249763 | ||||||||
\(628\) | −4.24205 | −0.169276 | ||||||||
\(629\) | −3.83936 | −0.153085 | ||||||||
\(630\) | −6.56896 | −0.261714 | ||||||||
\(631\) | −16.1979 | −0.644828 | −0.322414 | − | 0.946599i | \(-0.604494\pi\) | ||||
−0.322414 | + | 0.946599i | \(0.604494\pi\) | |||||||
\(632\) | −7.21356 | −0.286940 | ||||||||
\(633\) | −28.5041 | −1.13294 | ||||||||
\(634\) | −23.5696 | −0.936069 | ||||||||
\(635\) | 61.2722 | 2.43151 | ||||||||
\(636\) | −25.7481 | −1.02098 | ||||||||
\(637\) | 3.04099 | 0.120488 | ||||||||
\(638\) | 0.663927 | 0.0262851 | ||||||||
\(639\) | −1.29826 | −0.0513583 | ||||||||
\(640\) | 3.09656 | 0.122402 | ||||||||
\(641\) | −24.8644 | −0.982083 | −0.491042 | − | 0.871136i | \(-0.663384\pi\) | ||||
−0.491042 | + | 0.871136i | \(0.663384\pi\) | |||||||
\(642\) | −35.1405 | −1.38689 | ||||||||
\(643\) | −33.3717 | −1.31605 | −0.658025 | − | 0.752996i | \(-0.728608\pi\) | ||||
−0.658025 | + | 0.752996i | \(0.728608\pi\) | |||||||
\(644\) | 20.2191 | 0.796746 | ||||||||
\(645\) | 37.2397 | 1.46631 | ||||||||
\(646\) | −20.4861 | −0.806015 | ||||||||
\(647\) | 5.99364 | 0.235634 | 0.117817 | − | 0.993035i | \(-0.462410\pi\) | ||||
0.117817 | + | 0.993035i | \(0.462410\pi\) | |||||||
\(648\) | −10.5928 | −0.416126 | ||||||||
\(649\) | 0.447259 | 0.0175565 | ||||||||
\(650\) | 5.64905 | 0.221574 | ||||||||
\(651\) | −3.52804 | −0.138275 | ||||||||
\(652\) | 0.946145 | 0.0370539 | ||||||||
\(653\) | 47.7885 | 1.87011 | 0.935055 | − | 0.354503i | \(-0.115350\pi\) | ||||
0.935055 | + | 0.354503i | \(0.115350\pi\) | |||||||
\(654\) | 38.7978 | 1.51711 | ||||||||
\(655\) | −14.7647 | −0.576906 | ||||||||
\(656\) | 4.85857 | 0.189695 | ||||||||
\(657\) | 7.82147 | 0.305145 | ||||||||
\(658\) | 16.6288 | 0.648258 | ||||||||
\(659\) | −15.7904 | −0.615108 | −0.307554 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307554 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(660\) | 0.516494 | 0.0201045 | ||||||||
\(661\) | 38.9596 | 1.51535 | 0.757677 | − | 0.652629i | \(-0.226334\pi\) | ||||
0.757677 | + | 0.652629i | \(0.226334\pi\) | |||||||
\(662\) | −31.8993 | −1.23980 | ||||||||
\(663\) | −12.9194 | −0.501749 | ||||||||
\(664\) | 2.30311 | 0.0893780 | ||||||||
\(665\) | 35.7302 | 1.38556 | ||||||||
\(666\) | −0.484412 | −0.0187706 | ||||||||
\(667\) | 50.2334 | 1.94504 | ||||||||
\(668\) | 16.2744 | 0.629674 | ||||||||
\(669\) | −37.7764 | −1.46052 | ||||||||
\(670\) | −26.9635 | −1.04169 | ||||||||
\(671\) | 0.360094 | 0.0139013 | ||||||||
\(672\) | 5.91090 | 0.228018 | ||||||||
\(673\) | 38.5825 | 1.48725 | 0.743623 | − | 0.668600i | \(-0.233106\pi\) | ||||
0.743623 | + | 0.668600i | \(0.233106\pi\) | |||||||
\(674\) | −26.2190 | −1.00992 | ||||||||
\(675\) | 20.3657 | 0.783875 | ||||||||
\(676\) | −11.4844 | −0.441709 | ||||||||
\(677\) | −46.2289 | −1.77672 | −0.888361 | − | 0.459146i | \(-0.848156\pi\) | ||||
−0.888361 | + | 0.459146i | \(0.848156\pi\) | |||||||
\(678\) | 29.5963 | 1.13664 | ||||||||
\(679\) | −23.5973 | −0.905580 | ||||||||
\(680\) | 16.9185 | 0.648795 | ||||||||
\(681\) | −9.33528 | −0.357729 | ||||||||
\(682\) | 0.0518311 | 0.00198472 | ||||||||
\(683\) | −22.0882 | −0.845180 | −0.422590 | − | 0.906321i | \(-0.638879\pi\) | ||||
−0.422590 | + | 0.906321i | \(0.638879\pi\) | |||||||
\(684\) | −2.58473 | −0.0988295 | ||||||||
\(685\) | −47.4111 | −1.81148 | ||||||||
\(686\) | 13.9399 | 0.532228 | ||||||||
\(687\) | 13.0296 | 0.497109 | ||||||||
\(688\) | −6.26112 | −0.238703 | ||||||||
\(689\) | 16.5028 | 0.628706 | ||||||||
\(690\) | 39.0785 | 1.48769 | ||||||||
\(691\) | 42.5120 | 1.61723 | 0.808617 | − | 0.588336i | \(-0.200217\pi\) | ||||
0.808617 | + | 0.588336i | \(0.200217\pi\) | |||||||
\(692\) | −21.7471 | −0.826700 | ||||||||
\(693\) | 0.184216 | 0.00699779 | ||||||||
\(694\) | 7.46521 | 0.283375 | ||||||||
\(695\) | 57.1414 | 2.16750 | ||||||||
\(696\) | 14.6853 | 0.556646 | ||||||||
\(697\) | 26.5455 | 1.00548 | ||||||||
\(698\) | −2.51923 | −0.0953543 | ||||||||
\(699\) | 52.3293 | 1.97927 | ||||||||
\(700\) | −14.1211 | −0.533727 | ||||||||
\(701\) | 35.6036 | 1.34473 | 0.672364 | − | 0.740221i | \(-0.265279\pi\) | ||||
0.672364 | + | 0.740221i | \(0.265279\pi\) | |||||||
\(702\) | 5.46381 | 0.206218 | ||||||||
\(703\) | 2.63484 | 0.0993748 | ||||||||
\(704\) | −0.0868382 | −0.00327284 | ||||||||
\(705\) | 32.1393 | 1.21043 | ||||||||
\(706\) | 17.3573 | 0.653249 | ||||||||
\(707\) | −18.0212 | −0.677756 | ||||||||
\(708\) | 9.89288 | 0.371797 | ||||||||
\(709\) | −26.1287 | −0.981285 | −0.490643 | − | 0.871361i | \(-0.663238\pi\) | ||||
−0.490643 | + | 0.871361i | \(0.663238\pi\) | |||||||
\(710\) | −5.83181 | −0.218864 | ||||||||
\(711\) | −4.97264 | −0.186489 | ||||||||
\(712\) | −6.30610 | −0.236331 | ||||||||
\(713\) | 3.92160 | 0.146865 | ||||||||
\(714\) | 32.2951 | 1.20861 | ||||||||
\(715\) | −0.331037 | −0.0123801 | ||||||||
\(716\) | −8.96135 | −0.334901 | ||||||||
\(717\) | −23.3055 | −0.870359 | ||||||||
\(718\) | 36.4948 | 1.36197 | ||||||||
\(719\) | 37.2498 | 1.38918 | 0.694592 | − | 0.719404i | \(-0.255585\pi\) | ||||
0.694592 | + | 0.719404i | \(0.255585\pi\) | |||||||
\(720\) | 2.13460 | 0.0795520 | ||||||||
\(721\) | 59.8559 | 2.22915 | ||||||||
\(722\) | −4.94102 | −0.183886 | ||||||||
\(723\) | −16.1725 | −0.601462 | ||||||||
\(724\) | 7.93227 | 0.294800 | ||||||||
\(725\) | −35.0831 | −1.30295 | ||||||||
\(726\) | 21.1140 | 0.783612 | ||||||||
\(727\) | 21.5124 | 0.797852 | 0.398926 | − | 0.916983i | \(-0.369383\pi\) | ||||
0.398926 | + | 0.916983i | \(0.369383\pi\) | |||||||
\(728\) | −3.78848 | −0.140411 | ||||||||
\(729\) | 18.2723 | 0.676751 | ||||||||
\(730\) | 35.1342 | 1.30038 | ||||||||
\(731\) | −34.2085 | −1.26525 | ||||||||
\(732\) | 7.96489 | 0.294391 | ||||||||
\(733\) | −5.05277 | −0.186628 | −0.0933142 | − | 0.995637i | \(-0.529746\pi\) | ||||
−0.0933142 | + | 0.995637i | \(0.529746\pi\) | |||||||
\(734\) | −10.9063 | −0.402559 | ||||||||
\(735\) | −14.6921 | −0.541925 | ||||||||
\(736\) | −6.57027 | −0.242183 | ||||||||
\(737\) | 0.756149 | 0.0278531 | ||||||||
\(738\) | 3.34924 | 0.123287 | ||||||||
\(739\) | −7.82744 | −0.287937 | −0.143969 | − | 0.989582i | \(-0.545986\pi\) | ||||
−0.143969 | + | 0.989582i | \(0.545986\pi\) | |||||||
\(740\) | −2.17599 | −0.0799909 | ||||||||
\(741\) | 8.86621 | 0.325708 | ||||||||
\(742\) | −41.2525 | −1.51443 | ||||||||
\(743\) | −6.42215 | −0.235606 | −0.117803 | − | 0.993037i | \(-0.537585\pi\) | ||||
−0.117803 | + | 0.993037i | \(0.537585\pi\) | |||||||
\(744\) | 1.14645 | 0.0420308 | ||||||||
\(745\) | −6.59011 | −0.241443 | ||||||||
\(746\) | −34.0149 | −1.24537 | ||||||||
\(747\) | 1.58764 | 0.0580887 | ||||||||
\(748\) | −0.474453 | −0.0173477 | ||||||||
\(749\) | −56.3006 | −2.05718 | ||||||||
\(750\) | 2.44636 | 0.0893284 | ||||||||
\(751\) | 37.0950 | 1.35362 | 0.676808 | − | 0.736159i | \(-0.263363\pi\) | ||||
0.676808 | + | 0.736159i | \(0.263363\pi\) | |||||||
\(752\) | −5.40358 | −0.197048 | ||||||||
\(753\) | −34.9011 | −1.27187 | ||||||||
\(754\) | −9.41229 | −0.342775 | ||||||||
\(755\) | −14.5353 | −0.528992 | ||||||||
\(756\) | −13.6580 | −0.496738 | ||||||||
\(757\) | −15.3017 | −0.556148 | −0.278074 | − | 0.960560i | \(-0.589696\pi\) | ||||
−0.278074 | + | 0.960560i | \(0.589696\pi\) | |||||||
\(758\) | −31.7579 | −1.15350 | ||||||||
\(759\) | −1.09590 | −0.0397785 | ||||||||
\(760\) | −11.6107 | −0.421163 | ||||||||
\(761\) | −4.34317 | −0.157440 | −0.0787199 | − | 0.996897i | \(-0.525083\pi\) | ||||
−0.0787199 | + | 0.996897i | \(0.525083\pi\) | |||||||
\(762\) | −38.0065 | −1.37683 | ||||||||
\(763\) | 62.1600 | 2.25034 | ||||||||
\(764\) | −10.8672 | −0.393161 | ||||||||
\(765\) | 11.6627 | 0.421666 | ||||||||
\(766\) | 16.1480 | 0.583450 | ||||||||
\(767\) | −6.34066 | −0.228948 | ||||||||
\(768\) | −1.92077 | −0.0693097 | ||||||||
\(769\) | −18.4962 | −0.666989 | −0.333494 | − | 0.942752i | \(-0.608228\pi\) | ||||
−0.333494 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(770\) | 0.827504 | 0.0298212 | ||||||||
\(771\) | −49.1728 | −1.77092 | ||||||||
\(772\) | −13.4725 | −0.484888 | ||||||||
\(773\) | 37.0953 | 1.33423 | 0.667113 | − | 0.744956i | \(-0.267530\pi\) | ||||
0.667113 | + | 0.744956i | \(0.267530\pi\) | |||||||
\(774\) | −4.31608 | −0.155138 | ||||||||
\(775\) | −2.73885 | −0.0983825 | ||||||||
\(776\) | 7.66801 | 0.275265 | ||||||||
\(777\) | −4.15366 | −0.149012 | ||||||||
\(778\) | 34.3674 | 1.23213 | ||||||||
\(779\) | −18.2174 | −0.652705 | ||||||||
\(780\) | −7.32219 | −0.262176 | ||||||||
\(781\) | 0.163544 | 0.00585207 | ||||||||
\(782\) | −35.8976 | −1.28370 | ||||||||
\(783\) | −33.9327 | −1.21266 | ||||||||
\(784\) | 2.47018 | 0.0882208 | ||||||||
\(785\) | −13.1358 | −0.468835 | ||||||||
\(786\) | 9.15842 | 0.326670 | ||||||||
\(787\) | 16.9449 | 0.604021 | 0.302010 | − | 0.953305i | \(-0.402342\pi\) | ||||
0.302010 | + | 0.953305i | \(0.402342\pi\) | |||||||
\(788\) | −22.3555 | −0.796381 | ||||||||
\(789\) | −28.9655 | −1.03120 | ||||||||
\(790\) | −22.3372 | −0.794723 | ||||||||
\(791\) | 47.4179 | 1.68599 | ||||||||
\(792\) | −0.0598616 | −0.00212709 | ||||||||
\(793\) | −5.10495 | −0.181282 | ||||||||
\(794\) | −3.64407 | −0.129323 | ||||||||
\(795\) | −79.7307 | −2.82776 | ||||||||
\(796\) | −15.6192 | −0.553607 | ||||||||
\(797\) | 8.92472 | 0.316130 | 0.158065 | − | 0.987429i | \(-0.449474\pi\) | ||||
0.158065 | + | 0.987429i | \(0.449474\pi\) | |||||||
\(798\) | −22.1631 | −0.784566 | ||||||||
\(799\) | −29.5232 | −1.04446 | ||||||||
\(800\) | 4.58869 | 0.162235 | ||||||||
\(801\) | −4.34709 | −0.153597 | ||||||||
\(802\) | 23.4469 | 0.827940 | ||||||||
\(803\) | −0.985285 | −0.0347700 | ||||||||
\(804\) | 16.7252 | 0.589852 | ||||||||
\(805\) | 62.6098 | 2.20671 | ||||||||
\(806\) | −0.734794 | −0.0258820 | ||||||||
\(807\) | −46.7727 | −1.64648 | ||||||||
\(808\) | 5.85604 | 0.206015 | ||||||||
\(809\) | −25.8858 | −0.910095 | −0.455047 | − | 0.890467i | \(-0.650378\pi\) | ||||
−0.455047 | + | 0.890467i | \(0.650378\pi\) | |||||||
\(810\) | −32.8014 | −1.15252 | ||||||||
\(811\) | −36.4203 | −1.27889 | −0.639445 | − | 0.768837i | \(-0.720836\pi\) | ||||
−0.639445 | + | 0.768837i | \(0.720836\pi\) | |||||||
\(812\) | 23.5282 | 0.825677 | ||||||||
\(813\) | 1.88627 | 0.0661546 | ||||||||
\(814\) | 0.0610222 | 0.00213883 | ||||||||
\(815\) | 2.92980 | 0.102626 | ||||||||
\(816\) | −10.4944 | −0.367377 | ||||||||
\(817\) | 23.4763 | 0.821331 | ||||||||
\(818\) | −15.8618 | −0.554595 | ||||||||
\(819\) | −2.61158 | −0.0912559 | ||||||||
\(820\) | 15.0449 | 0.525390 | ||||||||
\(821\) | 26.7190 | 0.932499 | 0.466250 | − | 0.884653i | \(-0.345605\pi\) | ||||
0.466250 | + | 0.884653i | \(0.345605\pi\) | |||||||
\(822\) | 29.4086 | 1.02574 | ||||||||
\(823\) | −16.3123 | −0.568611 | −0.284306 | − | 0.958734i | \(-0.591763\pi\) | ||||
−0.284306 | + | 0.958734i | \(0.591763\pi\) | |||||||
\(824\) | −19.4504 | −0.677586 | ||||||||
\(825\) | 0.765376 | 0.0266470 | ||||||||
\(826\) | 15.8499 | 0.551489 | ||||||||
\(827\) | 23.9166 | 0.831663 | 0.415831 | − | 0.909442i | \(-0.363491\pi\) | ||||
0.415831 | + | 0.909442i | \(0.363491\pi\) | |||||||
\(828\) | −4.52920 | −0.157400 | ||||||||
\(829\) | −44.0013 | −1.52823 | −0.764114 | − | 0.645082i | \(-0.776823\pi\) | ||||
−0.764114 | + | 0.645082i | \(0.776823\pi\) | |||||||
\(830\) | 7.13172 | 0.247546 | ||||||||
\(831\) | 7.57328 | 0.262714 | ||||||||
\(832\) | 1.23108 | 0.0426800 | ||||||||
\(833\) | 13.4962 | 0.467615 | ||||||||
\(834\) | −35.4442 | −1.22733 | ||||||||
\(835\) | 50.3945 | 1.74397 | ||||||||
\(836\) | 0.325603 | 0.0112612 | ||||||||
\(837\) | −2.64904 | −0.0915643 | ||||||||
\(838\) | −38.3568 | −1.32501 | ||||||||
\(839\) | 23.5514 | 0.813085 | 0.406542 | − | 0.913632i | \(-0.366734\pi\) | ||||
0.406542 | + | 0.913632i | \(0.366734\pi\) | |||||||
\(840\) | 18.3035 | 0.631530 | ||||||||
\(841\) | 29.4545 | 1.01567 | ||||||||
\(842\) | 32.5351 | 1.12123 | ||||||||
\(843\) | −4.05649 | −0.139713 | ||||||||
\(844\) | 14.8399 | 0.510812 | ||||||||
\(845\) | −35.5623 | −1.22338 | ||||||||
\(846\) | −3.72494 | −0.128066 | ||||||||
\(847\) | 33.8278 | 1.16234 | ||||||||
\(848\) | 13.4051 | 0.460334 | ||||||||
\(849\) | −1.92764 | −0.0661564 | ||||||||
\(850\) | 25.0710 | 0.859928 | ||||||||
\(851\) | 4.61701 | 0.158269 | ||||||||
\(852\) | 3.61742 | 0.123931 | ||||||||
\(853\) | 29.0352 | 0.994146 | 0.497073 | − | 0.867709i | \(-0.334408\pi\) | ||||
0.497073 | + | 0.867709i | \(0.334408\pi\) | |||||||
\(854\) | 12.7610 | 0.436672 | ||||||||
\(855\) | −8.00376 | −0.273723 | ||||||||
\(856\) | 18.2950 | 0.625312 | ||||||||
\(857\) | −42.4326 | −1.44947 | −0.724735 | − | 0.689028i | \(-0.758038\pi\) | ||||
−0.724735 | + | 0.689028i | \(0.758038\pi\) | |||||||
\(858\) | 0.205339 | 0.00701017 | ||||||||
\(859\) | −10.8638 | −0.370667 | −0.185333 | − | 0.982676i | \(-0.559337\pi\) | ||||
−0.185333 | + | 0.982676i | \(0.559337\pi\) | |||||||
\(860\) | −19.3879 | −0.661123 | ||||||||
\(861\) | 28.7186 | 0.978726 | ||||||||
\(862\) | −10.8875 | −0.370828 | ||||||||
\(863\) | −46.6455 | −1.58783 | −0.793915 | − | 0.608028i | \(-0.791961\pi\) | ||||
−0.793915 | + | 0.608028i | \(0.791961\pi\) | |||||||
\(864\) | 4.43823 | 0.150992 | ||||||||
\(865\) | −67.3412 | −2.28967 | ||||||||
\(866\) | −15.7157 | −0.534043 | ||||||||
\(867\) | −24.6846 | −0.838331 | ||||||||
\(868\) | 1.83679 | 0.0623446 | ||||||||
\(869\) | 0.626413 | 0.0212496 | ||||||||
\(870\) | 45.4740 | 1.54171 | ||||||||
\(871\) | −10.7197 | −0.363223 | ||||||||
\(872\) | −20.1991 | −0.684028 | ||||||||
\(873\) | 5.28592 | 0.178901 | ||||||||
\(874\) | 24.6354 | 0.833306 | ||||||||
\(875\) | 3.91945 | 0.132501 | ||||||||
\(876\) | −21.7934 | −0.736332 | ||||||||
\(877\) | −3.68041 | −0.124279 | −0.0621393 | − | 0.998067i | \(-0.519792\pi\) | ||||
−0.0621393 | + | 0.998067i | \(0.519792\pi\) | |||||||
\(878\) | 13.7872 | 0.465294 | ||||||||
\(879\) | 56.2373 | 1.89684 | ||||||||
\(880\) | −0.268900 | −0.00906462 | ||||||||
\(881\) | 14.5066 | 0.488741 | 0.244370 | − | 0.969682i | \(-0.421419\pi\) | ||||
0.244370 | + | 0.969682i | \(0.421419\pi\) | |||||||
\(882\) | 1.70281 | 0.0573366 | ||||||||
\(883\) | −4.31157 | −0.145096 | −0.0725479 | − | 0.997365i | \(-0.523113\pi\) | ||||
−0.0725479 | + | 0.997365i | \(0.523113\pi\) | |||||||
\(884\) | 6.72618 | 0.226226 | ||||||||
\(885\) | 30.6339 | 1.02975 | ||||||||
\(886\) | −27.8742 | −0.936452 | ||||||||
\(887\) | 7.69966 | 0.258529 | 0.129265 | − | 0.991610i | \(-0.458738\pi\) | ||||
0.129265 | + | 0.991610i | \(0.458738\pi\) | |||||||
\(888\) | 1.34974 | 0.0452945 | ||||||||
\(889\) | −60.8923 | −2.04226 | ||||||||
\(890\) | −19.5272 | −0.654555 | ||||||||
\(891\) | 0.919864 | 0.0308166 | ||||||||
\(892\) | 19.6674 | 0.658512 | ||||||||
\(893\) | 20.2609 | 0.678005 | ||||||||
\(894\) | 4.08778 | 0.136716 | ||||||||
\(895\) | −27.7494 | −0.927559 | ||||||||
\(896\) | −3.07737 | −0.102808 | ||||||||
\(897\) | 15.5362 | 0.518738 | ||||||||
\(898\) | −14.2230 | −0.474626 | ||||||||
\(899\) | 4.56340 | 0.152198 | ||||||||
\(900\) | 3.16320 | 0.105440 | ||||||||
\(901\) | 73.2409 | 2.44001 | ||||||||
\(902\) | −0.421910 | −0.0140481 | ||||||||
\(903\) | −37.0089 | −1.23158 | ||||||||
\(904\) | −15.4086 | −0.512482 | ||||||||
\(905\) | 24.5627 | 0.816493 | ||||||||
\(906\) | 9.01608 | 0.299539 | ||||||||
\(907\) | 37.1909 | 1.23490 | 0.617452 | − | 0.786609i | \(-0.288165\pi\) | ||||
0.617452 | + | 0.786609i | \(0.288165\pi\) | |||||||
\(908\) | 4.86018 | 0.161291 | ||||||||
\(909\) | 4.03684 | 0.133894 | ||||||||
\(910\) | −11.7313 | −0.388888 | ||||||||
\(911\) | 24.0237 | 0.795939 | 0.397970 | − | 0.917399i | \(-0.369715\pi\) | ||||
0.397970 | + | 0.917399i | \(0.369715\pi\) | |||||||
\(912\) | 7.20198 | 0.238481 | ||||||||
\(913\) | −0.199998 | −0.00661897 | ||||||||
\(914\) | −40.0549 | −1.32490 | ||||||||
\(915\) | 24.6638 | 0.815360 | ||||||||
\(916\) | −6.78352 | −0.224134 | ||||||||
\(917\) | 14.6732 | 0.484552 | ||||||||
\(918\) | 24.2489 | 0.800333 | ||||||||
\(919\) | 8.16935 | 0.269482 | 0.134741 | − | 0.990881i | \(-0.456980\pi\) | ||||
0.134741 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(920\) | −20.3453 | −0.670763 | ||||||||
\(921\) | 57.6981 | 1.90122 | ||||||||
\(922\) | 25.7487 | 0.847987 | ||||||||
\(923\) | −2.31852 | −0.0763149 | ||||||||
\(924\) | −0.513292 | −0.0168861 | ||||||||
\(925\) | −3.22453 | −0.106022 | ||||||||
\(926\) | −29.3136 | −0.963304 | ||||||||
\(927\) | −13.4080 | −0.440378 | ||||||||
\(928\) | −7.64556 | −0.250978 | ||||||||
\(929\) | 24.8952 | 0.816786 | 0.408393 | − | 0.912806i | \(-0.366089\pi\) | ||||
0.408393 | + | 0.912806i | \(0.366089\pi\) | |||||||
\(930\) | 3.55005 | 0.116411 | ||||||||
\(931\) | −9.26202 | −0.303550 | ||||||||
\(932\) | −27.2439 | −0.892405 | ||||||||
\(933\) | 1.61105 | 0.0527434 | ||||||||
\(934\) | −23.9427 | −0.783428 | ||||||||
\(935\) | −1.46917 | −0.0480471 | ||||||||
\(936\) | 0.848641 | 0.0277387 | ||||||||
\(937\) | 36.2269 | 1.18348 | 0.591740 | − | 0.806129i | \(-0.298441\pi\) | ||||
0.591740 | + | 0.806129i | \(0.298441\pi\) | |||||||
\(938\) | 26.7963 | 0.874931 | ||||||||
\(939\) | 48.2302 | 1.57393 | ||||||||
\(940\) | −16.7325 | −0.545755 | ||||||||
\(941\) | −39.7401 | −1.29549 | −0.647744 | − | 0.761858i | \(-0.724288\pi\) | ||||
−0.647744 | + | 0.761858i | \(0.724288\pi\) | |||||||
\(942\) | 8.14798 | 0.265476 | ||||||||
\(943\) | −31.9222 | −1.03953 | ||||||||
\(944\) | −5.15049 | −0.167634 | ||||||||
\(945\) | −42.2930 | −1.37579 | ||||||||
\(946\) | 0.543705 | 0.0176774 | ||||||||
\(947\) | 38.1539 | 1.23983 | 0.619917 | − | 0.784667i | \(-0.287166\pi\) | ||||
0.619917 | + | 0.784667i | \(0.287166\pi\) | |||||||
\(948\) | 13.8556 | 0.450008 | ||||||||
\(949\) | 13.9681 | 0.453424 | ||||||||
\(950\) | −17.2054 | −0.558218 | ||||||||
\(951\) | 45.2717 | 1.46804 | ||||||||
\(952\) | −16.8136 | −0.544933 | ||||||||
\(953\) | 4.49069 | 0.145468 | 0.0727339 | − | 0.997351i | \(-0.476828\pi\) | ||||
0.0727339 | + | 0.997351i | \(0.476828\pi\) | |||||||
\(954\) | 9.24078 | 0.299181 | ||||||||
\(955\) | −33.6509 | −1.08892 | ||||||||
\(956\) | 12.1334 | 0.392423 | ||||||||
\(957\) | −1.27525 | −0.0412229 | ||||||||
\(958\) | 31.2124 | 1.00843 | ||||||||
\(959\) | 47.1172 | 1.52149 | ||||||||
\(960\) | −5.94777 | −0.191964 | ||||||||
\(961\) | −30.6437 | −0.988508 | ||||||||
\(962\) | −0.865094 | −0.0278917 | ||||||||
\(963\) | 12.6116 | 0.406404 | ||||||||
\(964\) | 8.41981 | 0.271184 | ||||||||
\(965\) | −41.7186 | −1.34297 | ||||||||
\(966\) | −38.8363 | −1.24954 | ||||||||
\(967\) | −35.7548 | −1.14980 | −0.574898 | − | 0.818225i | \(-0.694958\pi\) | ||||
−0.574898 | + | 0.818225i | \(0.694958\pi\) | |||||||
\(968\) | −10.9925 | −0.353311 | ||||||||
\(969\) | 39.3490 | 1.26407 | ||||||||
\(970\) | 23.7445 | 0.762389 | ||||||||
\(971\) | 15.2131 | 0.488213 | 0.244106 | − | 0.969748i | \(-0.421505\pi\) | ||||
0.244106 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(972\) | 7.03170 | 0.225542 | ||||||||
\(973\) | −56.7871 | −1.82051 | ||||||||
\(974\) | −33.3702 | −1.06925 | ||||||||
\(975\) | −10.8505 | −0.347494 | ||||||||
\(976\) | −4.14673 | −0.132733 | ||||||||
\(977\) | −19.3840 | −0.620150 | −0.310075 | − | 0.950712i | \(-0.600354\pi\) | ||||
−0.310075 | + | 0.950712i | \(0.600354\pi\) | |||||||
\(978\) | −1.81732 | −0.0581116 | ||||||||
\(979\) | 0.547611 | 0.0175017 | ||||||||
\(980\) | 7.64907 | 0.244341 | ||||||||
\(981\) | −13.9242 | −0.444565 | ||||||||
\(982\) | 3.48110 | 0.111086 | ||||||||
\(983\) | 6.79339 | 0.216676 | 0.108338 | − | 0.994114i | \(-0.465447\pi\) | ||||
0.108338 | + | 0.994114i | \(0.465447\pi\) | |||||||
\(984\) | −9.33219 | −0.297499 | ||||||||
\(985\) | −69.2251 | −2.20569 | ||||||||
\(986\) | −41.7726 | −1.33031 | ||||||||
\(987\) | −31.9400 | −1.01666 | ||||||||
\(988\) | −4.61597 | −0.146854 | ||||||||
\(989\) | 41.1373 | 1.30809 | ||||||||
\(990\) | −0.185365 | −0.00589129 | ||||||||
\(991\) | 7.86384 | 0.249803 | 0.124902 | − | 0.992169i | \(-0.460138\pi\) | ||||
0.124902 | + | 0.992169i | \(0.460138\pi\) | |||||||
\(992\) | −0.596870 | −0.0189506 | ||||||||
\(993\) | 61.2711 | 1.94438 | ||||||||
\(994\) | 5.79566 | 0.183827 | ||||||||
\(995\) | −48.3658 | −1.53330 | ||||||||
\(996\) | −4.42374 | −0.140171 | ||||||||
\(997\) | 20.3390 | 0.644141 | 0.322071 | − | 0.946716i | \(-0.395621\pi\) | ||||
0.322071 | + | 0.946716i | \(0.395621\pi\) | |||||||
\(998\) | 20.2119 | 0.639797 | ||||||||
\(999\) | −3.11879 | −0.0986742 |
(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 | 6022.2.a.b.1.13 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6022.2.a.b.1.13 | ✓ | 54 | 1.1 | even | 1 | trivial |