Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68479 | −1.89843 | −0.949216 | − | 0.314624i | \(-0.898122\pi\) | ||||
−0.949216 | + | 0.314624i | \(0.898122\pi\) | |||||||
\(3\) | 0.238039 | 0.137432 | 0.0687159 | − | 0.997636i | \(-0.478110\pi\) | ||||
0.0687159 | + | 0.997636i | \(0.478110\pi\) | |||||||
\(4\) | 5.20809 | 2.60405 | ||||||||
\(5\) | −3.86690 | −1.72933 | −0.864666 | − | 0.502347i | \(-0.832470\pi\) | ||||
−0.864666 | + | 0.502347i | \(0.832470\pi\) | |||||||
\(6\) | −0.639084 | −0.260905 | ||||||||
\(7\) | 2.11314 | 0.798693 | 0.399346 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399346 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(8\) | −8.61305 | −3.04517 | ||||||||
\(9\) | −2.94334 | −0.981113 | ||||||||
\(10\) | 10.3818 | 3.28302 | ||||||||
\(11\) | −3.07520 | −0.927208 | −0.463604 | − | 0.886042i | \(-0.653444\pi\) | ||||
−0.463604 | + | 0.886042i | \(0.653444\pi\) | |||||||
\(12\) | 1.23973 | 0.357879 | ||||||||
\(13\) | −2.57965 | −0.715467 | −0.357733 | − | 0.933824i | \(-0.616450\pi\) | ||||
−0.357733 | + | 0.933824i | \(0.616450\pi\) | |||||||
\(14\) | −5.67334 | −1.51626 | ||||||||
\(15\) | −0.920473 | −0.237665 | ||||||||
\(16\) | 12.7080 | 3.17701 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 7.90224 | 1.86258 | ||||||||
\(19\) | 3.49754 | 0.802390 | 0.401195 | − | 0.915993i | \(-0.368595\pi\) | ||||
0.401195 | + | 0.915993i | \(0.368595\pi\) | |||||||
\(20\) | −20.1392 | −4.50326 | ||||||||
\(21\) | 0.503010 | 0.109766 | ||||||||
\(22\) | 8.25627 | 1.76024 | ||||||||
\(23\) | −4.35397 | −0.907866 | −0.453933 | − | 0.891036i | \(-0.649980\pi\) | ||||
−0.453933 | + | 0.891036i | \(0.649980\pi\) | |||||||
\(24\) | −2.05024 | −0.418504 | ||||||||
\(25\) | 9.95295 | 1.99059 | ||||||||
\(26\) | 6.92582 | 1.35827 | ||||||||
\(27\) | −1.41474 | −0.272268 | ||||||||
\(28\) | 11.0054 | 2.07983 | ||||||||
\(29\) | 2.16159 | 0.401397 | 0.200699 | − | 0.979653i | \(-0.435679\pi\) | ||||
0.200699 | + | 0.979653i | \(0.435679\pi\) | |||||||
\(30\) | 2.47128 | 0.451191 | ||||||||
\(31\) | −0.560311 | −0.100635 | −0.0503174 | − | 0.998733i | \(-0.516023\pi\) | ||||
−0.0503174 | + | 0.998733i | \(0.516023\pi\) | |||||||
\(32\) | −16.8923 | −2.98617 | ||||||||
\(33\) | −0.732017 | −0.127428 | ||||||||
\(34\) | −2.68479 | −0.460438 | ||||||||
\(35\) | −8.17132 | −1.38121 | ||||||||
\(36\) | −15.3292 | −2.55486 | ||||||||
\(37\) | −2.70142 | −0.444110 | −0.222055 | − | 0.975034i | \(-0.571276\pi\) | ||||
−0.222055 | + | 0.975034i | \(0.571276\pi\) | |||||||
\(38\) | −9.39015 | −1.52328 | ||||||||
\(39\) | −0.614057 | −0.0983278 | ||||||||
\(40\) | 33.3059 | 5.26612 | ||||||||
\(41\) | −5.50111 | −0.859129 | −0.429565 | − | 0.903036i | \(-0.641333\pi\) | ||||
−0.429565 | + | 0.903036i | \(0.641333\pi\) | |||||||
\(42\) | −1.35048 | −0.208383 | ||||||||
\(43\) | 11.4089 | 1.73983 | 0.869917 | − | 0.493197i | \(-0.164172\pi\) | ||||
0.869917 | + | 0.493197i | \(0.164172\pi\) | |||||||
\(44\) | −16.0159 | −2.41449 | ||||||||
\(45\) | 11.3816 | 1.69667 | ||||||||
\(46\) | 11.6895 | 1.72352 | ||||||||
\(47\) | −1.32999 | −0.194000 | −0.0969998 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0969998 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(48\) | 3.02501 | 0.436622 | ||||||||
\(49\) | −2.53463 | −0.362090 | ||||||||
\(50\) | −26.7216 | −3.77900 | ||||||||
\(51\) | 0.238039 | 0.0333321 | ||||||||
\(52\) | −13.4351 | −1.86311 | ||||||||
\(53\) | 13.2443 | 1.81925 | 0.909624 | − | 0.415433i | \(-0.136370\pi\) | ||||
0.909624 | + | 0.415433i | \(0.136370\pi\) | |||||||
\(54\) | 3.79829 | 0.516882 | ||||||||
\(55\) | 11.8915 | 1.60345 | ||||||||
\(56\) | −18.2006 | −2.43216 | ||||||||
\(57\) | 0.832549 | 0.110274 | ||||||||
\(58\) | −5.80342 | −0.762026 | ||||||||
\(59\) | 9.14063 | 1.19001 | 0.595004 | − | 0.803723i | \(-0.297150\pi\) | ||||
0.595004 | + | 0.803723i | \(0.297150\pi\) | |||||||
\(60\) | −4.79391 | −0.618891 | ||||||||
\(61\) | −0.467478 | −0.0598544 | −0.0299272 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299272 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(62\) | 1.50432 | 0.191048 | ||||||||
\(63\) | −6.21969 | −0.783608 | ||||||||
\(64\) | 19.9362 | 2.49203 | ||||||||
\(65\) | 9.97526 | 1.23728 | ||||||||
\(66\) | 1.96531 | 0.241913 | ||||||||
\(67\) | −15.2370 | −1.86150 | −0.930751 | − | 0.365655i | \(-0.880845\pi\) | ||||
−0.930751 | + | 0.365655i | \(0.880845\pi\) | |||||||
\(68\) | 5.20809 | 0.631574 | ||||||||
\(69\) | −1.03641 | −0.124770 | ||||||||
\(70\) | 21.9383 | 2.62213 | ||||||||
\(71\) | 10.1439 | 1.20386 | 0.601930 | − | 0.798549i | \(-0.294399\pi\) | ||||
0.601930 | + | 0.798549i | \(0.294399\pi\) | |||||||
\(72\) | 25.3511 | 2.98766 | ||||||||
\(73\) | 12.4447 | 1.45654 | 0.728269 | − | 0.685292i | \(-0.240325\pi\) | ||||
0.728269 | + | 0.685292i | \(0.240325\pi\) | |||||||
\(74\) | 7.25274 | 0.843113 | ||||||||
\(75\) | 2.36919 | 0.273570 | ||||||||
\(76\) | 18.2155 | 2.08946 | ||||||||
\(77\) | −6.49834 | −0.740555 | ||||||||
\(78\) | 1.64861 | 0.186669 | ||||||||
\(79\) | −0.828583 | −0.0932229 | −0.0466115 | − | 0.998913i | \(-0.514842\pi\) | ||||
−0.0466115 | + | 0.998913i | \(0.514842\pi\) | |||||||
\(80\) | −49.1408 | −5.49411 | ||||||||
\(81\) | 8.49325 | 0.943694 | ||||||||
\(82\) | 14.7693 | 1.63100 | ||||||||
\(83\) | 2.00151 | 0.219695 | 0.109847 | − | 0.993948i | \(-0.464964\pi\) | ||||
0.109847 | + | 0.993948i | \(0.464964\pi\) | |||||||
\(84\) | 2.61972 | 0.285835 | ||||||||
\(85\) | −3.86690 | −0.419425 | ||||||||
\(86\) | −30.6304 | −3.30296 | ||||||||
\(87\) | 0.514543 | 0.0551647 | ||||||||
\(88\) | 26.4869 | 2.82351 | ||||||||
\(89\) | 0.0494759 | 0.00524443 | 0.00262222 | − | 0.999997i | \(-0.499165\pi\) | ||||
0.00262222 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(90\) | −30.5572 | −3.22101 | ||||||||
\(91\) | −5.45117 | −0.571438 | ||||||||
\(92\) | −22.6759 | −2.36413 | ||||||||
\(93\) | −0.133376 | −0.0138304 | ||||||||
\(94\) | 3.57075 | 0.368295 | ||||||||
\(95\) | −13.5246 | −1.38760 | ||||||||
\(96\) | −4.02103 | −0.410395 | ||||||||
\(97\) | 12.1077 | 1.22935 | 0.614674 | − | 0.788782i | \(-0.289288\pi\) | ||||
0.614674 | + | 0.788782i | \(0.289288\pi\) | |||||||
\(98\) | 6.80494 | 0.687403 | ||||||||
\(99\) | 9.05136 | 0.909696 | ||||||||
\(100\) | 51.8359 | 5.18359 | ||||||||
\(101\) | 9.42112 | 0.937437 | 0.468718 | − | 0.883348i | \(-0.344716\pi\) | ||||
0.468718 | + | 0.883348i | \(0.344716\pi\) | |||||||
\(102\) | −0.639084 | −0.0632787 | ||||||||
\(103\) | −10.5738 | −1.04187 | −0.520936 | − | 0.853596i | \(-0.674417\pi\) | ||||
−0.520936 | + | 0.853596i | \(0.674417\pi\) | |||||||
\(104\) | 22.2187 | 2.17872 | ||||||||
\(105\) | −1.94509 | −0.189821 | ||||||||
\(106\) | −35.5582 | −3.45372 | ||||||||
\(107\) | −15.3531 | −1.48424 | −0.742121 | − | 0.670266i | \(-0.766180\pi\) | ||||
−0.742121 | + | 0.670266i | \(0.766180\pi\) | |||||||
\(108\) | −7.36812 | −0.708998 | ||||||||
\(109\) | −5.61058 | −0.537396 | −0.268698 | − | 0.963224i | \(-0.586593\pi\) | ||||
−0.268698 | + | 0.963224i | \(0.586593\pi\) | |||||||
\(110\) | −31.9262 | −3.04404 | ||||||||
\(111\) | −0.643042 | −0.0610349 | ||||||||
\(112\) | 26.8539 | 2.53746 | ||||||||
\(113\) | −6.10517 | −0.574326 | −0.287163 | − | 0.957882i | \(-0.592712\pi\) | ||||
−0.287163 | + | 0.957882i | \(0.592712\pi\) | |||||||
\(114\) | −2.23522 | −0.209347 | ||||||||
\(115\) | 16.8364 | 1.57000 | ||||||||
\(116\) | 11.2578 | 1.04526 | ||||||||
\(117\) | 7.59278 | 0.701953 | ||||||||
\(118\) | −24.5407 | −2.25915 | ||||||||
\(119\) | 2.11314 | 0.193712 | ||||||||
\(120\) | 7.92809 | 0.723732 | ||||||||
\(121\) | −1.54313 | −0.140285 | ||||||||
\(122\) | 1.25508 | 0.113630 | ||||||||
\(123\) | −1.30948 | −0.118072 | ||||||||
\(124\) | −2.91815 | −0.262058 | ||||||||
\(125\) | −19.1526 | −1.71306 | ||||||||
\(126\) | 16.6986 | 1.48763 | ||||||||
\(127\) | 20.8117 | 1.84674 | 0.923371 | − | 0.383908i | \(-0.125422\pi\) | ||||
0.923371 | + | 0.383908i | \(0.125422\pi\) | |||||||
\(128\) | −19.7399 | −1.74478 | ||||||||
\(129\) | 2.71575 | 0.239109 | ||||||||
\(130\) | −26.7815 | −2.34889 | ||||||||
\(131\) | 16.8451 | 1.47176 | 0.735881 | − | 0.677111i | \(-0.236768\pi\) | ||||
0.735881 | + | 0.677111i | \(0.236768\pi\) | |||||||
\(132\) | −3.81241 | −0.331828 | ||||||||
\(133\) | 7.39079 | 0.640863 | ||||||||
\(134\) | 40.9082 | 3.53393 | ||||||||
\(135\) | 5.47068 | 0.470841 | ||||||||
\(136\) | −8.61305 | −0.738563 | ||||||||
\(137\) | 18.5637 | 1.58600 | 0.793000 | − | 0.609221i | \(-0.208518\pi\) | ||||
0.793000 | + | 0.609221i | \(0.208518\pi\) | |||||||
\(138\) | 2.78256 | 0.236867 | ||||||||
\(139\) | −12.9589 | −1.09916 | −0.549579 | − | 0.835442i | \(-0.685212\pi\) | ||||
−0.549579 | + | 0.835442i | \(0.685212\pi\) | |||||||
\(140\) | −42.5570 | −3.59672 | ||||||||
\(141\) | −0.316590 | −0.0266617 | ||||||||
\(142\) | −27.2343 | −2.28545 | ||||||||
\(143\) | 7.93295 | 0.663387 | ||||||||
\(144\) | −37.4041 | −3.11701 | ||||||||
\(145\) | −8.35866 | −0.694149 | ||||||||
\(146\) | −33.4113 | −2.76514 | ||||||||
\(147\) | −0.603339 | −0.0497626 | ||||||||
\(148\) | −14.0692 | −1.15648 | ||||||||
\(149\) | −8.90355 | −0.729407 | −0.364703 | − | 0.931124i | \(-0.618830\pi\) | ||||
−0.364703 | + | 0.931124i | \(0.618830\pi\) | |||||||
\(150\) | −6.36077 | −0.519355 | ||||||||
\(151\) | −15.2701 | −1.24266 | −0.621331 | − | 0.783548i | \(-0.713408\pi\) | ||||
−0.621331 | + | 0.783548i | \(0.713408\pi\) | |||||||
\(152\) | −30.1245 | −2.44342 | ||||||||
\(153\) | −2.94334 | −0.237955 | ||||||||
\(154\) | 17.4467 | 1.40589 | ||||||||
\(155\) | 2.16667 | 0.174031 | ||||||||
\(156\) | −3.19807 | −0.256050 | ||||||||
\(157\) | 6.45498 | 0.515164 | 0.257582 | − | 0.966256i | \(-0.417074\pi\) | ||||
0.257582 | + | 0.966256i | \(0.417074\pi\) | |||||||
\(158\) | 2.22457 | 0.176977 | ||||||||
\(159\) | 3.15266 | 0.250022 | ||||||||
\(160\) | 65.3210 | 5.16408 | ||||||||
\(161\) | −9.20057 | −0.725107 | ||||||||
\(162\) | −22.8026 | −1.79154 | ||||||||
\(163\) | −6.09688 | −0.477545 | −0.238772 | − | 0.971076i | \(-0.576745\pi\) | ||||
−0.238772 | + | 0.971076i | \(0.576745\pi\) | |||||||
\(164\) | −28.6503 | −2.23721 | ||||||||
\(165\) | 2.83064 | 0.220365 | ||||||||
\(166\) | −5.37364 | −0.417076 | ||||||||
\(167\) | −16.3957 | −1.26874 | −0.634370 | − | 0.773029i | \(-0.718740\pi\) | ||||
−0.634370 | + | 0.773029i | \(0.718740\pi\) | |||||||
\(168\) | −4.33245 | −0.334256 | ||||||||
\(169\) | −6.34540 | −0.488108 | ||||||||
\(170\) | 10.3818 | 0.796249 | ||||||||
\(171\) | −10.2944 | −0.787235 | ||||||||
\(172\) | 59.4184 | 4.53061 | ||||||||
\(173\) | 2.77710 | 0.211139 | 0.105570 | − | 0.994412i | \(-0.466333\pi\) | ||||
0.105570 | + | 0.994412i | \(0.466333\pi\) | |||||||
\(174\) | −1.38144 | −0.104727 | ||||||||
\(175\) | 21.0320 | 1.58987 | ||||||||
\(176\) | −39.0798 | −2.94575 | ||||||||
\(177\) | 2.17582 | 0.163545 | ||||||||
\(178\) | −0.132832 | −0.00995620 | ||||||||
\(179\) | −5.18285 | −0.387384 | −0.193692 | − | 0.981062i | \(-0.562046\pi\) | ||||
−0.193692 | + | 0.981062i | \(0.562046\pi\) | |||||||
\(180\) | 59.2765 | 4.41821 | ||||||||
\(181\) | −4.53301 | −0.336936 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(182\) | 14.6352 | 1.08484 | ||||||||
\(183\) | −0.111278 | −0.00822590 | ||||||||
\(184\) | 37.5010 | 2.76461 | ||||||||
\(185\) | 10.4461 | 0.768014 | ||||||||
\(186\) | 0.358086 | 0.0262561 | ||||||||
\(187\) | −3.07520 | −0.224881 | ||||||||
\(188\) | −6.92673 | −0.505184 | ||||||||
\(189\) | −2.98956 | −0.217458 | ||||||||
\(190\) | 36.3108 | 2.63426 | ||||||||
\(191\) | −3.88509 | −0.281115 | −0.140558 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140558 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(192\) | 4.74560 | 0.342484 | ||||||||
\(193\) | −4.72928 | −0.340421 | −0.170211 | − | 0.985408i | \(-0.554445\pi\) | ||||
−0.170211 | + | 0.985408i | \(0.554445\pi\) | |||||||
\(194\) | −32.5065 | −2.33383 | ||||||||
\(195\) | 2.37450 | 0.170041 | ||||||||
\(196\) | −13.2006 | −0.942898 | ||||||||
\(197\) | 7.03345 | 0.501113 | 0.250556 | − | 0.968102i | \(-0.419386\pi\) | ||||
0.250556 | + | 0.968102i | \(0.419386\pi\) | |||||||
\(198\) | −24.3010 | −1.72700 | ||||||||
\(199\) | 22.7510 | 1.61277 | 0.806386 | − | 0.591389i | \(-0.201420\pi\) | ||||
0.806386 | + | 0.591389i | \(0.201420\pi\) | |||||||
\(200\) | −85.7253 | −6.06169 | ||||||||
\(201\) | −3.62701 | −0.255829 | ||||||||
\(202\) | −25.2937 | −1.77966 | ||||||||
\(203\) | 4.56775 | 0.320593 | ||||||||
\(204\) | 1.23973 | 0.0867983 | ||||||||
\(205\) | 21.2723 | 1.48572 | ||||||||
\(206\) | 28.3886 | 1.97792 | ||||||||
\(207\) | 12.8152 | 0.890719 | ||||||||
\(208\) | −32.7823 | −2.27305 | ||||||||
\(209\) | −10.7556 | −0.743983 | ||||||||
\(210\) | 5.22216 | 0.360363 | ||||||||
\(211\) | 1.66136 | 0.114373 | 0.0571864 | − | 0.998364i | \(-0.481787\pi\) | ||||
0.0571864 | + | 0.998364i | \(0.481787\pi\) | |||||||
\(212\) | 68.9777 | 4.73741 | ||||||||
\(213\) | 2.41464 | 0.165449 | ||||||||
\(214\) | 41.2199 | 2.81773 | ||||||||
\(215\) | −44.1170 | −3.00875 | ||||||||
\(216\) | 12.1853 | 0.829103 | ||||||||
\(217\) | −1.18402 | −0.0803763 | ||||||||
\(218\) | 15.0632 | 1.02021 | ||||||||
\(219\) | 2.96231 | 0.200175 | ||||||||
\(220\) | 61.9321 | 4.17546 | ||||||||
\(221\) | −2.57965 | −0.173526 | ||||||||
\(222\) | 1.72643 | 0.115871 | ||||||||
\(223\) | 0.425240 | 0.0284762 | 0.0142381 | − | 0.999899i | \(-0.495468\pi\) | ||||
0.0142381 | + | 0.999899i | \(0.495468\pi\) | |||||||
\(224\) | −35.6959 | −2.38503 | ||||||||
\(225\) | −29.2949 | −1.95299 | ||||||||
\(226\) | 16.3911 | 1.09032 | ||||||||
\(227\) | 15.9773 | 1.06045 | 0.530226 | − | 0.847856i | \(-0.322107\pi\) | ||||
0.530226 | + | 0.847856i | \(0.322107\pi\) | |||||||
\(228\) | 4.33599 | 0.287158 | ||||||||
\(229\) | −6.01238 | −0.397309 | −0.198655 | − | 0.980070i | \(-0.563657\pi\) | ||||
−0.198655 | + | 0.980070i | \(0.563657\pi\) | |||||||
\(230\) | −45.2022 | −2.98054 | ||||||||
\(231\) | −1.54686 | −0.101776 | ||||||||
\(232\) | −18.6179 | −1.22233 | ||||||||
\(233\) | −13.6603 | −0.894914 | −0.447457 | − | 0.894305i | \(-0.647670\pi\) | ||||
−0.447457 | + | 0.894305i | \(0.647670\pi\) | |||||||
\(234\) | −20.3850 | −1.33261 | ||||||||
\(235\) | 5.14296 | 0.335490 | ||||||||
\(236\) | 47.6052 | 3.09884 | ||||||||
\(237\) | −0.197235 | −0.0128118 | ||||||||
\(238\) | −5.67334 | −0.367748 | ||||||||
\(239\) | −3.46888 | −0.224383 | −0.112192 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112192 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(240\) | −11.6974 | −0.755065 | ||||||||
\(241\) | −19.2299 | −1.23871 | −0.619354 | − | 0.785112i | \(-0.712605\pi\) | ||||
−0.619354 | + | 0.785112i | \(0.712605\pi\) | |||||||
\(242\) | 4.14298 | 0.266321 | ||||||||
\(243\) | 6.26596 | 0.401961 | ||||||||
\(244\) | −2.43467 | −0.155864 | ||||||||
\(245\) | 9.80116 | 0.626173 | ||||||||
\(246\) | 3.51567 | 0.224151 | ||||||||
\(247\) | −9.02242 | −0.574083 | ||||||||
\(248\) | 4.82599 | 0.306450 | ||||||||
\(249\) | 0.476438 | 0.0301930 | ||||||||
\(250\) | 51.4206 | 3.25212 | ||||||||
\(251\) | 16.4286 | 1.03697 | 0.518483 | − | 0.855088i | \(-0.326497\pi\) | ||||
0.518483 | + | 0.855088i | \(0.326497\pi\) | |||||||
\(252\) | −32.3927 | −2.04055 | ||||||||
\(253\) | 13.3894 | 0.841781 | ||||||||
\(254\) | −55.8751 | −3.50592 | ||||||||
\(255\) | −0.920473 | −0.0576423 | ||||||||
\(256\) | 13.1251 | 0.820319 | ||||||||
\(257\) | 2.35761 | 0.147064 | 0.0735320 | − | 0.997293i | \(-0.476573\pi\) | ||||
0.0735320 | + | 0.997293i | \(0.476573\pi\) | |||||||
\(258\) | −7.29122 | −0.453932 | ||||||||
\(259\) | −5.70848 | −0.354708 | ||||||||
\(260\) | 51.9521 | 3.22193 | ||||||||
\(261\) | −6.36229 | −0.393816 | ||||||||
\(262\) | −45.2255 | −2.79404 | ||||||||
\(263\) | 9.43281 | 0.581652 | 0.290826 | − | 0.956776i | \(-0.406070\pi\) | ||||
0.290826 | + | 0.956776i | \(0.406070\pi\) | |||||||
\(264\) | 6.30491 | 0.388040 | ||||||||
\(265\) | −51.2145 | −3.14608 | ||||||||
\(266\) | −19.8427 | −1.21664 | ||||||||
\(267\) | 0.0117772 | 0.000720752 0 | ||||||||
\(268\) | −79.3559 | −4.84744 | ||||||||
\(269\) | 12.1294 | 0.739540 | 0.369770 | − | 0.929123i | \(-0.379436\pi\) | ||||
0.369770 | + | 0.929123i | \(0.379436\pi\) | |||||||
\(270\) | −14.6876 | −0.893861 | ||||||||
\(271\) | −15.1624 | −0.921050 | −0.460525 | − | 0.887647i | \(-0.652339\pi\) | ||||
−0.460525 | + | 0.887647i | \(0.652339\pi\) | |||||||
\(272\) | 12.7080 | 0.770539 | ||||||||
\(273\) | −1.29759 | −0.0785337 | ||||||||
\(274\) | −49.8395 | −3.01091 | ||||||||
\(275\) | −30.6073 | −1.84569 | ||||||||
\(276\) | −5.39775 | −0.324906 | ||||||||
\(277\) | −23.9052 | −1.43633 | −0.718163 | − | 0.695875i | \(-0.755017\pi\) | ||||
−0.718163 | + | 0.695875i | \(0.755017\pi\) | |||||||
\(278\) | 34.7919 | 2.08668 | ||||||||
\(279\) | 1.64918 | 0.0987340 | ||||||||
\(280\) | 70.3800 | 4.20601 | ||||||||
\(281\) | 4.51360 | 0.269259 | 0.134630 | − | 0.990896i | \(-0.457016\pi\) | ||||
0.134630 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(282\) | 0.849978 | 0.0506154 | ||||||||
\(283\) | −5.44959 | −0.323945 | −0.161972 | − | 0.986795i | \(-0.551786\pi\) | ||||
−0.161972 | + | 0.986795i | \(0.551786\pi\) | |||||||
\(284\) | 52.8304 | 3.13491 | ||||||||
\(285\) | −3.21939 | −0.190700 | ||||||||
\(286\) | −21.2983 | −1.25939 | ||||||||
\(287\) | −11.6246 | −0.686181 | ||||||||
\(288\) | 49.7198 | 2.92977 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 22.4413 | 1.31780 | ||||||||
\(291\) | 2.88209 | 0.168951 | ||||||||
\(292\) | 64.8130 | 3.79289 | ||||||||
\(293\) | −29.9248 | −1.74822 | −0.874112 | − | 0.485724i | \(-0.838556\pi\) | ||||
−0.874112 | + | 0.485724i | \(0.838556\pi\) | |||||||
\(294\) | 1.61984 | 0.0944710 | ||||||||
\(295\) | −35.3459 | −2.05792 | ||||||||
\(296\) | 23.2675 | 1.35239 | ||||||||
\(297\) | 4.35063 | 0.252449 | ||||||||
\(298\) | 23.9041 | 1.38473 | ||||||||
\(299\) | 11.2317 | 0.649548 | ||||||||
\(300\) | 12.3389 | 0.712389 | ||||||||
\(301\) | 24.1086 | 1.38959 | ||||||||
\(302\) | 40.9970 | 2.35911 | ||||||||
\(303\) | 2.24259 | 0.128834 | ||||||||
\(304\) | 44.4469 | 2.54920 | ||||||||
\(305\) | 1.80769 | 0.103508 | ||||||||
\(306\) | 7.90224 | 0.451741 | ||||||||
\(307\) | 5.85617 | 0.334229 | 0.167115 | − | 0.985937i | \(-0.446555\pi\) | ||||
0.167115 | + | 0.985937i | \(0.446555\pi\) | |||||||
\(308\) | −33.8440 | −1.92844 | ||||||||
\(309\) | −2.51699 | −0.143186 | ||||||||
\(310\) | −5.81704 | −0.330386 | ||||||||
\(311\) | 2.45023 | 0.138940 | 0.0694698 | − | 0.997584i | \(-0.477869\pi\) | ||||
0.0694698 | + | 0.997584i | \(0.477869\pi\) | |||||||
\(312\) | 5.28891 | 0.299425 | ||||||||
\(313\) | 11.9936 | 0.677920 | 0.338960 | − | 0.940801i | \(-0.389925\pi\) | ||||
0.338960 | + | 0.940801i | \(0.389925\pi\) | |||||||
\(314\) | −17.3303 | −0.978004 | ||||||||
\(315\) | 24.0510 | 1.35512 | ||||||||
\(316\) | −4.31534 | −0.242757 | ||||||||
\(317\) | −6.38654 | −0.358704 | −0.179352 | − | 0.983785i | \(-0.557400\pi\) | ||||
−0.179352 | + | 0.983785i | \(0.557400\pi\) | |||||||
\(318\) | −8.46423 | −0.474651 | ||||||||
\(319\) | −6.64733 | −0.372179 | ||||||||
\(320\) | −77.0915 | −4.30955 | ||||||||
\(321\) | −3.65464 | −0.203982 | ||||||||
\(322\) | 24.7016 | 1.37657 | ||||||||
\(323\) | 3.49754 | 0.194608 | ||||||||
\(324\) | 44.2336 | 2.45742 | ||||||||
\(325\) | −25.6751 | −1.42420 | ||||||||
\(326\) | 16.3688 | 0.906586 | ||||||||
\(327\) | −1.33554 | −0.0738553 | ||||||||
\(328\) | 47.3814 | 2.61620 | ||||||||
\(329\) | −2.81047 | −0.154946 | ||||||||
\(330\) | −7.59967 | −0.418348 | ||||||||
\(331\) | 8.78069 | 0.482630 | 0.241315 | − | 0.970447i | \(-0.422421\pi\) | ||||
0.241315 | + | 0.970447i | \(0.422421\pi\) | |||||||
\(332\) | 10.4241 | 0.572095 | ||||||||
\(333\) | 7.95118 | 0.435722 | ||||||||
\(334\) | 44.0191 | 2.40862 | ||||||||
\(335\) | 58.9202 | 3.21915 | ||||||||
\(336\) | 6.39228 | 0.348727 | ||||||||
\(337\) | −2.57617 | −0.140333 | −0.0701664 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701664 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(338\) | 17.0361 | 0.926639 | ||||||||
\(339\) | −1.45327 | −0.0789307 | ||||||||
\(340\) | −20.1392 | −1.09220 | ||||||||
\(341\) | 1.72307 | 0.0933094 | ||||||||
\(342\) | 27.6384 | 1.49451 | ||||||||
\(343\) | −20.1480 | −1.08789 | ||||||||
\(344\) | −98.2651 | −5.29810 | ||||||||
\(345\) | 4.00772 | 0.215768 | ||||||||
\(346\) | −7.45593 | −0.400833 | ||||||||
\(347\) | 31.3116 | 1.68090 | 0.840448 | − | 0.541892i | \(-0.182292\pi\) | ||||
0.840448 | + | 0.541892i | \(0.182292\pi\) | |||||||
\(348\) | 2.67979 | 0.143652 | ||||||||
\(349\) | −17.6009 | −0.942154 | −0.471077 | − | 0.882092i | \(-0.656135\pi\) | ||||
−0.471077 | + | 0.882092i | \(0.656135\pi\) | |||||||
\(350\) | −56.4665 | −3.01826 | ||||||||
\(351\) | 3.64955 | 0.194798 | ||||||||
\(352\) | 51.9473 | 2.76880 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | −5.84163 | −0.310479 | ||||||||
\(355\) | −39.2255 | −2.08187 | ||||||||
\(356\) | 0.257675 | 0.0136567 | ||||||||
\(357\) | 0.503010 | 0.0266221 | ||||||||
\(358\) | 13.9149 | 0.735423 | ||||||||
\(359\) | 26.7136 | 1.40989 | 0.704946 | − | 0.709261i | \(-0.250971\pi\) | ||||
0.704946 | + | 0.709261i | \(0.250971\pi\) | |||||||
\(360\) | −98.0304 | −5.16665 | ||||||||
\(361\) | −6.76724 | −0.356171 | ||||||||
\(362\) | 12.1702 | 0.639651 | ||||||||
\(363\) | −0.367325 | −0.0192796 | ||||||||
\(364\) | −28.3902 | −1.48805 | ||||||||
\(365\) | −48.1223 | −2.51884 | ||||||||
\(366\) | 0.298758 | 0.0156163 | ||||||||
\(367\) | −9.79026 | −0.511048 | −0.255524 | − | 0.966803i | \(-0.582248\pi\) | ||||
−0.255524 | + | 0.966803i | \(0.582248\pi\) | |||||||
\(368\) | −55.3305 | −2.88430 | ||||||||
\(369\) | 16.1916 | 0.842903 | ||||||||
\(370\) | −28.0456 | −1.45802 | ||||||||
\(371\) | 27.9871 | 1.45302 | ||||||||
\(372\) | −0.694633 | −0.0360150 | ||||||||
\(373\) | 6.60861 | 0.342181 | 0.171091 | − | 0.985255i | \(-0.445271\pi\) | ||||
0.171091 | + | 0.985255i | \(0.445271\pi\) | |||||||
\(374\) | 8.25627 | 0.426922 | ||||||||
\(375\) | −4.55905 | −0.235429 | ||||||||
\(376\) | 11.4553 | 0.590762 | ||||||||
\(377\) | −5.57615 | −0.287186 | ||||||||
\(378\) | 8.02633 | 0.412830 | ||||||||
\(379\) | 9.12903 | 0.468927 | 0.234463 | − | 0.972125i | \(-0.424667\pi\) | ||||
0.234463 | + | 0.972125i | \(0.424667\pi\) | |||||||
\(380\) | −70.4376 | −3.61337 | ||||||||
\(381\) | 4.95400 | 0.253801 | ||||||||
\(382\) | 10.4306 | 0.533678 | ||||||||
\(383\) | −16.5312 | −0.844704 | −0.422352 | − | 0.906432i | \(-0.638795\pi\) | ||||
−0.422352 | + | 0.906432i | \(0.638795\pi\) | |||||||
\(384\) | −4.69887 | −0.239788 | ||||||||
\(385\) | 25.1285 | 1.28067 | ||||||||
\(386\) | 12.6971 | 0.646267 | ||||||||
\(387\) | −33.5801 | −1.70697 | ||||||||
\(388\) | 63.0578 | 3.20128 | ||||||||
\(389\) | 33.0435 | 1.67537 | 0.837685 | − | 0.546154i | \(-0.183909\pi\) | ||||
0.837685 | + | 0.546154i | \(0.183909\pi\) | |||||||
\(390\) | −6.37503 | −0.322812 | ||||||||
\(391\) | −4.35397 | −0.220190 | ||||||||
\(392\) | 21.8309 | 1.10263 | ||||||||
\(393\) | 4.00978 | 0.202267 | ||||||||
\(394\) | −18.8833 | −0.951328 | ||||||||
\(395\) | 3.20405 | 0.161213 | ||||||||
\(396\) | 47.1403 | 2.36889 | ||||||||
\(397\) | 10.5817 | 0.531082 | 0.265541 | − | 0.964100i | \(-0.414449\pi\) | ||||
0.265541 | + | 0.964100i | \(0.414449\pi\) | |||||||
\(398\) | −61.0815 | −3.06174 | ||||||||
\(399\) | 1.75930 | 0.0880749 | ||||||||
\(400\) | 126.483 | 6.32413 | ||||||||
\(401\) | −17.3473 | −0.866283 | −0.433141 | − | 0.901326i | \(-0.642595\pi\) | ||||
−0.433141 | + | 0.901326i | \(0.642595\pi\) | |||||||
\(402\) | 9.73775 | 0.485675 | ||||||||
\(403\) | 1.44541 | 0.0720008 | ||||||||
\(404\) | 49.0661 | 2.44113 | ||||||||
\(405\) | −32.8426 | −1.63196 | ||||||||
\(406\) | −12.2634 | −0.608625 | ||||||||
\(407\) | 8.30740 | 0.411783 | ||||||||
\(408\) | −2.05024 | −0.101502 | ||||||||
\(409\) | 21.0245 | 1.03959 | 0.519796 | − | 0.854290i | \(-0.326008\pi\) | ||||
0.519796 | + | 0.854290i | \(0.326008\pi\) | |||||||
\(410\) | −57.1116 | −2.82054 | ||||||||
\(411\) | 4.41887 | 0.217967 | ||||||||
\(412\) | −55.0696 | −2.71308 | ||||||||
\(413\) | 19.3155 | 0.950451 | ||||||||
\(414\) | −34.4062 | −1.69097 | ||||||||
\(415\) | −7.73966 | −0.379925 | ||||||||
\(416\) | 43.5763 | 2.13650 | ||||||||
\(417\) | −3.08472 | −0.151059 | ||||||||
\(418\) | 28.8766 | 1.41240 | ||||||||
\(419\) | −24.7279 | −1.20804 | −0.604019 | − | 0.796970i | \(-0.706435\pi\) | ||||
−0.604019 | + | 0.796970i | \(0.706435\pi\) | |||||||
\(420\) | −10.1302 | −0.494304 | ||||||||
\(421\) | 27.1444 | 1.32294 | 0.661469 | − | 0.749972i | \(-0.269933\pi\) | ||||
0.661469 | + | 0.749972i | \(0.269933\pi\) | |||||||
\(422\) | −4.46041 | −0.217129 | ||||||||
\(423\) | 3.91462 | 0.190335 | ||||||||
\(424\) | −114.074 | −5.53993 | ||||||||
\(425\) | 9.95295 | 0.482789 | ||||||||
\(426\) | −6.48281 | −0.314093 | ||||||||
\(427\) | −0.987848 | −0.0478053 | ||||||||
\(428\) | −79.9604 | −3.86503 | ||||||||
\(429\) | 1.88835 | 0.0911704 | ||||||||
\(430\) | 118.445 | 5.71191 | ||||||||
\(431\) | −38.2489 | −1.84239 | −0.921193 | − | 0.389105i | \(-0.872784\pi\) | ||||
−0.921193 | + | 0.389105i | \(0.872784\pi\) | |||||||
\(432\) | −17.9786 | −0.864998 | ||||||||
\(433\) | 11.3162 | 0.543819 | 0.271910 | − | 0.962323i | \(-0.412345\pi\) | ||||
0.271910 | + | 0.962323i | \(0.412345\pi\) | |||||||
\(434\) | 3.17883 | 0.152589 | ||||||||
\(435\) | −1.98969 | −0.0953982 | ||||||||
\(436\) | −29.2204 | −1.39940 | ||||||||
\(437\) | −15.2282 | −0.728463 | ||||||||
\(438\) | −7.95319 | −0.380018 | ||||||||
\(439\) | −29.0056 | −1.38436 | −0.692181 | − | 0.721724i | \(-0.743350\pi\) | ||||
−0.692181 | + | 0.721724i | \(0.743350\pi\) | |||||||
\(440\) | −102.422 | −4.88279 | ||||||||
\(441\) | 7.46026 | 0.355251 | ||||||||
\(442\) | 6.92582 | 0.329428 | ||||||||
\(443\) | 13.7757 | 0.654503 | 0.327251 | − | 0.944937i | \(-0.393878\pi\) | ||||
0.327251 | + | 0.944937i | \(0.393878\pi\) | |||||||
\(444\) | −3.34902 | −0.158938 | ||||||||
\(445\) | −0.191318 | −0.00906937 | ||||||||
\(446\) | −1.14168 | −0.0540602 | ||||||||
\(447\) | −2.11939 | −0.100244 | ||||||||
\(448\) | 42.1281 | 1.99037 | ||||||||
\(449\) | −29.7719 | −1.40502 | −0.702512 | − | 0.711672i | \(-0.747938\pi\) | ||||
−0.702512 | + | 0.711672i | \(0.747938\pi\) | |||||||
\(450\) | 78.6506 | 3.70762 | ||||||||
\(451\) | 16.9170 | 0.796592 | ||||||||
\(452\) | −31.7963 | −1.49557 | ||||||||
\(453\) | −3.63487 | −0.170781 | ||||||||
\(454\) | −42.8957 | −2.01320 | ||||||||
\(455\) | 21.0792 | 0.988206 | ||||||||
\(456\) | −7.17079 | −0.335803 | ||||||||
\(457\) | 41.3342 | 1.93353 | 0.966767 | − | 0.255659i | \(-0.0822923\pi\) | ||||
0.966767 | + | 0.255659i | \(0.0822923\pi\) | |||||||
\(458\) | 16.1420 | 0.754265 | ||||||||
\(459\) | −1.41474 | −0.0660346 | ||||||||
\(460\) | 87.6855 | 4.08836 | ||||||||
\(461\) | −19.0366 | −0.886621 | −0.443310 | − | 0.896368i | \(-0.646196\pi\) | ||||
−0.443310 | + | 0.896368i | \(0.646196\pi\) | |||||||
\(462\) | 4.15299 | 0.193214 | ||||||||
\(463\) | −4.23576 | −0.196852 | −0.0984262 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984262 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(464\) | 27.4696 | 1.27524 | ||||||||
\(465\) | 0.515751 | 0.0239174 | ||||||||
\(466\) | 36.6750 | 1.69893 | ||||||||
\(467\) | 15.9953 | 0.740173 | 0.370087 | − | 0.928997i | \(-0.379328\pi\) | ||||
0.370087 | + | 0.928997i | \(0.379328\pi\) | |||||||
\(468\) | 39.5439 | 1.82792 | ||||||||
\(469\) | −32.1981 | −1.48677 | ||||||||
\(470\) | −13.8078 | −0.636904 | ||||||||
\(471\) | 1.53654 | 0.0707999 | ||||||||
\(472\) | −78.7287 | −3.62378 | ||||||||
\(473\) | −35.0846 | −1.61319 | ||||||||
\(474\) | 0.529534 | 0.0243223 | ||||||||
\(475\) | 34.8108 | 1.59723 | ||||||||
\(476\) | 11.0054 | 0.504434 | ||||||||
\(477\) | −38.9825 | −1.78489 | ||||||||
\(478\) | 9.31322 | 0.425977 | ||||||||
\(479\) | −2.05775 | −0.0940211 | −0.0470105 | − | 0.998894i | \(-0.514969\pi\) | ||||
−0.0470105 | + | 0.998894i | \(0.514969\pi\) | |||||||
\(480\) | 15.5489 | 0.709708 | ||||||||
\(481\) | 6.96871 | 0.317746 | ||||||||
\(482\) | 51.6283 | 2.35160 | ||||||||
\(483\) | −2.19009 | −0.0996527 | ||||||||
\(484\) | −8.03678 | −0.365308 | ||||||||
\(485\) | −46.8192 | −2.12595 | ||||||||
\(486\) | −16.8228 | −0.763097 | ||||||||
\(487\) | 31.0243 | 1.40584 | 0.702922 | − | 0.711267i | \(-0.251878\pi\) | ||||
0.702922 | + | 0.711267i | \(0.251878\pi\) | |||||||
\(488\) | 4.02641 | 0.182267 | ||||||||
\(489\) | −1.45129 | −0.0656298 | ||||||||
\(490\) | −26.3140 | −1.18875 | ||||||||
\(491\) | 26.5417 | 1.19781 | 0.598906 | − | 0.800820i | \(-0.295602\pi\) | ||||
0.598906 | + | 0.800820i | \(0.295602\pi\) | |||||||
\(492\) | −6.81988 | −0.307464 | ||||||||
\(493\) | 2.16159 | 0.0973532 | ||||||||
\(494\) | 24.2233 | 1.08986 | ||||||||
\(495\) | −35.0007 | −1.57317 | ||||||||
\(496\) | −7.12045 | −0.319718 | ||||||||
\(497\) | 21.4355 | 0.961515 | ||||||||
\(498\) | −1.27914 | −0.0573194 | ||||||||
\(499\) | −24.5262 | −1.09794 | −0.548971 | − | 0.835842i | \(-0.684980\pi\) | ||||
−0.548971 | + | 0.835842i | \(0.684980\pi\) | |||||||
\(500\) | −99.7483 | −4.46088 | ||||||||
\(501\) | −3.90282 | −0.174365 | ||||||||
\(502\) | −44.1074 | −1.96861 | ||||||||
\(503\) | −14.8128 | −0.660469 | −0.330234 | − | 0.943899i | \(-0.607128\pi\) | ||||
−0.330234 | + | 0.943899i | \(0.607128\pi\) | |||||||
\(504\) | 53.5706 | 2.38622 | ||||||||
\(505\) | −36.4306 | −1.62114 | ||||||||
\(506\) | −35.9476 | −1.59807 | ||||||||
\(507\) | −1.51045 | −0.0670815 | ||||||||
\(508\) | 108.389 | 4.80900 | ||||||||
\(509\) | 15.0841 | 0.668592 | 0.334296 | − | 0.942468i | \(-0.391501\pi\) | ||||
0.334296 | + | 0.942468i | \(0.391501\pi\) | |||||||
\(510\) | 2.47128 | 0.109430 | ||||||||
\(511\) | 26.2974 | 1.16333 | ||||||||
\(512\) | 4.24173 | 0.187460 | ||||||||
\(513\) | −4.94812 | −0.218465 | ||||||||
\(514\) | −6.32970 | −0.279191 | ||||||||
\(515\) | 40.8881 | 1.80174 | ||||||||
\(516\) | 14.1439 | 0.622650 | ||||||||
\(517\) | 4.09000 | 0.179878 | ||||||||
\(518\) | 15.3261 | 0.673389 | ||||||||
\(519\) | 0.661058 | 0.0290172 | ||||||||
\(520\) | −85.9175 | −3.76773 | ||||||||
\(521\) | −20.6022 | −0.902600 | −0.451300 | − | 0.892372i | \(-0.649040\pi\) | ||||
−0.451300 | + | 0.892372i | \(0.649040\pi\) | |||||||
\(522\) | 17.0814 | 0.747633 | ||||||||
\(523\) | 22.2634 | 0.973511 | 0.486756 | − | 0.873538i | \(-0.338180\pi\) | ||||
0.486756 | + | 0.873538i | \(0.338180\pi\) | |||||||
\(524\) | 87.7308 | 3.83254 | ||||||||
\(525\) | 5.00643 | 0.218499 | ||||||||
\(526\) | −25.3251 | −1.10423 | ||||||||
\(527\) | −0.560311 | −0.0244075 | ||||||||
\(528\) | −9.30251 | −0.404840 | ||||||||
\(529\) | −4.04291 | −0.175779 | ||||||||
\(530\) | 137.500 | 5.97263 | ||||||||
\(531\) | −26.9040 | −1.16753 | ||||||||
\(532\) | 38.4919 | 1.66884 | ||||||||
\(533\) | 14.1910 | 0.614678 | ||||||||
\(534\) | −0.0316192 | −0.00136830 | ||||||||
\(535\) | 59.3690 | 2.56675 | ||||||||
\(536\) | 131.237 | 5.66860 | ||||||||
\(537\) | −1.23372 | −0.0532389 | ||||||||
\(538\) | −32.5648 | −1.40397 | ||||||||
\(539\) | 7.79449 | 0.335732 | ||||||||
\(540\) | 28.4918 | 1.22609 | ||||||||
\(541\) | 6.46705 | 0.278040 | 0.139020 | − | 0.990290i | \(-0.455605\pi\) | ||||
0.139020 | + | 0.990290i | \(0.455605\pi\) | |||||||
\(542\) | 40.7078 | 1.74855 | ||||||||
\(543\) | −1.07903 | −0.0463057 | ||||||||
\(544\) | −16.8923 | −0.724253 | ||||||||
\(545\) | 21.6956 | 0.929336 | ||||||||
\(546\) | 3.48376 | 0.149091 | ||||||||
\(547\) | 4.88597 | 0.208909 | 0.104454 | − | 0.994530i | \(-0.466690\pi\) | ||||
0.104454 | + | 0.994530i | \(0.466690\pi\) | |||||||
\(548\) | 96.6813 | 4.13002 | ||||||||
\(549\) | 1.37595 | 0.0587239 | ||||||||
\(550\) | 82.1742 | 3.50392 | ||||||||
\(551\) | 7.56024 | 0.322077 | ||||||||
\(552\) | 8.92670 | 0.379945 | ||||||||
\(553\) | −1.75091 | −0.0744565 | ||||||||
\(554\) | 64.1805 | 2.72677 | ||||||||
\(555\) | 2.48658 | 0.105550 | ||||||||
\(556\) | −67.4911 | −2.86226 | ||||||||
\(557\) | −17.4437 | −0.739112 | −0.369556 | − | 0.929208i | \(-0.620490\pi\) | ||||
−0.369556 | + | 0.929208i | \(0.620490\pi\) | |||||||
\(558\) | −4.42771 | −0.187440 | ||||||||
\(559\) | −29.4309 | −1.24479 | ||||||||
\(560\) | −103.842 | −4.38811 | ||||||||
\(561\) | −0.732017 | −0.0309058 | ||||||||
\(562\) | −12.1181 | −0.511170 | ||||||||
\(563\) | −3.53010 | −0.148776 | −0.0743881 | − | 0.997229i | \(-0.523700\pi\) | ||||
−0.0743881 | + | 0.997229i | \(0.523700\pi\) | |||||||
\(564\) | −1.64883 | −0.0694283 | ||||||||
\(565\) | 23.6081 | 0.993201 | ||||||||
\(566\) | 14.6310 | 0.614987 | ||||||||
\(567\) | 17.9474 | 0.753722 | ||||||||
\(568\) | −87.3700 | −3.66597 | ||||||||
\(569\) | −42.0708 | −1.76370 | −0.881849 | − | 0.471532i | \(-0.843701\pi\) | ||||
−0.881849 | + | 0.471532i | \(0.843701\pi\) | |||||||
\(570\) | 8.64338 | 0.362031 | ||||||||
\(571\) | 18.6763 | 0.781579 | 0.390790 | − | 0.920480i | \(-0.372202\pi\) | ||||
0.390790 | + | 0.920480i | \(0.372202\pi\) | |||||||
\(572\) | 41.3155 | 1.72749 | ||||||||
\(573\) | −0.924802 | −0.0386341 | ||||||||
\(574\) | 31.2097 | 1.30267 | ||||||||
\(575\) | −43.3349 | −1.80719 | ||||||||
\(576\) | −58.6791 | −2.44496 | ||||||||
\(577\) | −40.5092 | −1.68642 | −0.843210 | − | 0.537584i | \(-0.819337\pi\) | ||||
−0.843210 | + | 0.537584i | \(0.819337\pi\) | |||||||
\(578\) | −2.68479 | −0.111673 | ||||||||
\(579\) | −1.12575 | −0.0467847 | ||||||||
\(580\) | −43.5327 | −1.80760 | ||||||||
\(581\) | 4.22949 | 0.175469 | ||||||||
\(582\) | −7.73781 | −0.320743 | ||||||||
\(583\) | −40.7290 | −1.68682 | ||||||||
\(584\) | −107.187 | −4.43541 | ||||||||
\(585\) | −29.3606 | −1.21391 | ||||||||
\(586\) | 80.3417 | 3.31889 | ||||||||
\(587\) | −38.2597 | −1.57915 | −0.789574 | − | 0.613655i | \(-0.789698\pi\) | ||||
−0.789574 | + | 0.613655i | \(0.789698\pi\) | |||||||
\(588\) | −3.14225 | −0.129584 | ||||||||
\(589\) | −1.95971 | −0.0807483 | ||||||||
\(590\) | 94.8964 | 3.90682 | ||||||||
\(591\) | 1.67423 | 0.0688688 | ||||||||
\(592\) | −34.3297 | −1.41094 | ||||||||
\(593\) | 27.5094 | 1.12968 | 0.564838 | − | 0.825202i | \(-0.308939\pi\) | ||||
0.564838 | + | 0.825202i | \(0.308939\pi\) | |||||||
\(594\) | −11.6805 | −0.479257 | ||||||||
\(595\) | −8.17132 | −0.334991 | ||||||||
\(596\) | −46.3705 | −1.89941 | ||||||||
\(597\) | 5.41561 | 0.221646 | ||||||||
\(598\) | −30.1548 | −1.23312 | ||||||||
\(599\) | 8.53509 | 0.348734 | 0.174367 | − | 0.984681i | \(-0.444212\pi\) | ||||
0.174367 | + | 0.984681i | \(0.444212\pi\) | |||||||
\(600\) | −20.4059 | −0.833069 | ||||||||
\(601\) | 18.6374 | 0.760237 | 0.380118 | − | 0.924938i | \(-0.375883\pi\) | ||||
0.380118 | + | 0.924938i | \(0.375883\pi\) | |||||||
\(602\) | −64.7264 | −2.63805 | ||||||||
\(603\) | 44.8478 | 1.82634 | ||||||||
\(604\) | −79.5280 | −3.23595 | ||||||||
\(605\) | 5.96714 | 0.242599 | ||||||||
\(606\) | −6.02089 | −0.244582 | ||||||||
\(607\) | −21.3329 | −0.865874 | −0.432937 | − | 0.901424i | \(-0.642523\pi\) | ||||
−0.432937 | + | 0.901424i | \(0.642523\pi\) | |||||||
\(608\) | −59.0815 | −2.39607 | ||||||||
\(609\) | 1.08730 | 0.0440597 | ||||||||
\(610\) | −4.85327 | −0.196503 | ||||||||
\(611\) | 3.43092 | 0.138800 | ||||||||
\(612\) | −15.3292 | −0.619645 | ||||||||
\(613\) | −25.1706 | −1.01663 | −0.508316 | − | 0.861171i | \(-0.669732\pi\) | ||||
−0.508316 | + | 0.861171i | \(0.669732\pi\) | |||||||
\(614\) | −15.7226 | −0.634512 | ||||||||
\(615\) | 5.06363 | 0.204185 | ||||||||
\(616\) | 55.9706 | 2.25512 | ||||||||
\(617\) | −27.8906 | −1.12283 | −0.561416 | − | 0.827534i | \(-0.689743\pi\) | ||||
−0.561416 | + | 0.827534i | \(0.689743\pi\) | |||||||
\(618\) | 6.75758 | 0.271830 | ||||||||
\(619\) | −5.71695 | −0.229784 | −0.114892 | − | 0.993378i | \(-0.536652\pi\) | ||||
−0.114892 | + | 0.993378i | \(0.536652\pi\) | |||||||
\(620\) | 11.2842 | 0.453185 | ||||||||
\(621\) | 6.15976 | 0.247183 | ||||||||
\(622\) | −6.57834 | −0.263768 | ||||||||
\(623\) | 0.104550 | 0.00418869 | ||||||||
\(624\) | −7.80347 | −0.312389 | ||||||||
\(625\) | 24.2964 | 0.971856 | ||||||||
\(626\) | −32.2004 | −1.28699 | ||||||||
\(627\) | −2.56026 | −0.102247 | ||||||||
\(628\) | 33.6182 | 1.34151 | ||||||||
\(629\) | −2.70142 | −0.107713 | ||||||||
\(630\) | −64.5717 | −2.57260 | ||||||||
\(631\) | −20.9831 | −0.835324 | −0.417662 | − | 0.908602i | \(-0.637150\pi\) | ||||
−0.417662 | + | 0.908602i | \(0.637150\pi\) | |||||||
\(632\) | 7.13663 | 0.283880 | ||||||||
\(633\) | 0.395469 | 0.0157185 | ||||||||
\(634\) | 17.1465 | 0.680975 | ||||||||
\(635\) | −80.4770 | −3.19363 | ||||||||
\(636\) | 16.4194 | 0.651070 | ||||||||
\(637\) | 6.53845 | 0.259063 | ||||||||
\(638\) | 17.8467 | 0.706557 | ||||||||
\(639\) | −29.8569 | −1.18112 | ||||||||
\(640\) | 76.3325 | 3.01731 | ||||||||
\(641\) | −31.6807 | −1.25131 | −0.625655 | − | 0.780100i | \(-0.715168\pi\) | ||||
−0.625655 | + | 0.780100i | \(0.715168\pi\) | |||||||
\(642\) | 9.81193 | 0.387246 | ||||||||
\(643\) | −6.19284 | −0.244222 | −0.122111 | − | 0.992516i | \(-0.538966\pi\) | ||||
−0.122111 | + | 0.992516i | \(0.538966\pi\) | |||||||
\(644\) | −47.9174 | −1.88821 | ||||||||
\(645\) | −10.5015 | −0.413498 | ||||||||
\(646\) | −9.39015 | −0.369450 | ||||||||
\(647\) | 33.9993 | 1.33665 | 0.668326 | − | 0.743869i | \(-0.267011\pi\) | ||||
0.668326 | + | 0.743869i | \(0.267011\pi\) | |||||||
\(648\) | −73.1528 | −2.87371 | ||||||||
\(649\) | −28.1093 | −1.10339 | ||||||||
\(650\) | 68.9323 | 2.70375 | ||||||||
\(651\) | −0.281842 | −0.0110463 | ||||||||
\(652\) | −31.7531 | −1.24355 | ||||||||
\(653\) | 0.879346 | 0.0344115 | 0.0172057 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172057 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(654\) | 3.58563 | 0.140209 | ||||||||
\(655\) | −65.1383 | −2.54516 | ||||||||
\(656\) | −69.9084 | −2.72946 | ||||||||
\(657\) | −36.6288 | −1.42903 | ||||||||
\(658\) | 7.54551 | 0.294155 | ||||||||
\(659\) | −38.8054 | −1.51165 | −0.755823 | − | 0.654776i | \(-0.772763\pi\) | ||||
−0.755823 | + | 0.654776i | \(0.772763\pi\) | |||||||
\(660\) | 14.7422 | 0.573841 | ||||||||
\(661\) | −37.4692 | −1.45738 | −0.728692 | − | 0.684842i | \(-0.759871\pi\) | ||||
−0.728692 | + | 0.684842i | \(0.759871\pi\) | |||||||
\(662\) | −23.5743 | −0.916241 | ||||||||
\(663\) | −0.614057 | −0.0238480 | ||||||||
\(664\) | −17.2392 | −0.669009 | ||||||||
\(665\) | −28.5795 | −1.10827 | ||||||||
\(666\) | −21.3472 | −0.827189 | ||||||||
\(667\) | −9.41151 | −0.364415 | ||||||||
\(668\) | −85.3905 | −3.30386 | ||||||||
\(669\) | 0.101224 | 0.00391353 | ||||||||
\(670\) | −158.188 | −6.11135 | ||||||||
\(671\) | 1.43759 | 0.0554975 | ||||||||
\(672\) | −8.49701 | −0.327779 | ||||||||
\(673\) | 24.7502 | 0.954050 | 0.477025 | − | 0.878890i | \(-0.341715\pi\) | ||||
0.477025 | + | 0.878890i | \(0.341715\pi\) | |||||||
\(674\) | 6.91647 | 0.266413 | ||||||||
\(675\) | −14.0809 | −0.541973 | ||||||||
\(676\) | −33.0474 | −1.27106 | ||||||||
\(677\) | −30.6194 | −1.17680 | −0.588399 | − | 0.808571i | \(-0.700242\pi\) | ||||
−0.588399 | + | 0.808571i | \(0.700242\pi\) | |||||||
\(678\) | 3.90172 | 0.149845 | ||||||||
\(679\) | 25.5852 | 0.981871 | ||||||||
\(680\) | 33.3059 | 1.27722 | ||||||||
\(681\) | 3.80322 | 0.145740 | ||||||||
\(682\) | −4.62608 | −0.177142 | ||||||||
\(683\) | −30.1332 | −1.15301 | −0.576507 | − | 0.817092i | \(-0.695585\pi\) | ||||
−0.576507 | + | 0.817092i | \(0.695585\pi\) | |||||||
\(684\) | −53.6144 | −2.05000 | ||||||||
\(685\) | −71.7839 | −2.74272 | ||||||||
\(686\) | 54.0932 | 2.06529 | ||||||||
\(687\) | −1.43118 | −0.0546029 | ||||||||
\(688\) | 144.984 | 5.52748 | ||||||||
\(689\) | −34.1657 | −1.30161 | ||||||||
\(690\) | −10.7599 | −0.409621 | ||||||||
\(691\) | 4.13707 | 0.157381 | 0.0786907 | − | 0.996899i | \(-0.474926\pi\) | ||||
0.0786907 | + | 0.996899i | \(0.474926\pi\) | |||||||
\(692\) | 14.4634 | 0.549816 | ||||||||
\(693\) | 19.1268 | 0.726568 | ||||||||
\(694\) | −84.0651 | −3.19107 | ||||||||
\(695\) | 50.1108 | 1.90081 | ||||||||
\(696\) | −4.43178 | −0.167986 | ||||||||
\(697\) | −5.50111 | −0.208369 | ||||||||
\(698\) | 47.2547 | 1.78862 | ||||||||
\(699\) | −3.25168 | −0.122990 | ||||||||
\(700\) | 109.537 | 4.14009 | ||||||||
\(701\) | −30.3432 | −1.14605 | −0.573023 | − | 0.819539i | \(-0.694229\pi\) | ||||
−0.573023 | + | 0.819539i | \(0.694229\pi\) | |||||||
\(702\) | −9.79827 | −0.369812 | ||||||||
\(703\) | −9.44830 | −0.356350 | ||||||||
\(704\) | −61.3080 | −2.31063 | ||||||||
\(705\) | 1.22422 | 0.0461069 | ||||||||
\(706\) | −2.68479 | −0.101043 | ||||||||
\(707\) | 19.9082 | 0.748724 | ||||||||
\(708\) | 11.3319 | 0.425879 | ||||||||
\(709\) | −25.7956 | −0.968773 | −0.484386 | − | 0.874854i | \(-0.660957\pi\) | ||||
−0.484386 | + | 0.874854i | \(0.660957\pi\) | |||||||
\(710\) | 105.312 | 3.95230 | ||||||||
\(711\) | 2.43880 | 0.0914622 | ||||||||
\(712\) | −0.426139 | −0.0159702 | ||||||||
\(713\) | 2.43958 | 0.0913629 | ||||||||
\(714\) | −1.35048 | −0.0505403 | ||||||||
\(715\) | −30.6760 | −1.14722 | ||||||||
\(716\) | −26.9928 | −1.00877 | ||||||||
\(717\) | −0.825728 | −0.0308374 | ||||||||
\(718\) | −71.7205 | −2.67659 | ||||||||
\(719\) | −32.4973 | −1.21195 | −0.605973 | − | 0.795485i | \(-0.707216\pi\) | ||||
−0.605973 | + | 0.795485i | \(0.707216\pi\) | |||||||
\(720\) | 144.638 | 5.39034 | ||||||||
\(721\) | −22.3441 | −0.832136 | ||||||||
\(722\) | 18.1686 | 0.676166 | ||||||||
\(723\) | −4.57746 | −0.170238 | ||||||||
\(724\) | −23.6084 | −0.877397 | ||||||||
\(725\) | 21.5142 | 0.799017 | ||||||||
\(726\) | 0.986191 | 0.0366010 | ||||||||
\(727\) | −22.6400 | −0.839673 | −0.419836 | − | 0.907600i | \(-0.637913\pi\) | ||||
−0.419836 | + | 0.907600i | \(0.637913\pi\) | |||||||
\(728\) | 46.9512 | 1.74013 | ||||||||
\(729\) | −23.9882 | −0.888452 | ||||||||
\(730\) | 129.198 | 4.78184 | ||||||||
\(731\) | 11.4089 | 0.421972 | ||||||||
\(732\) | −0.579546 | −0.0214206 | ||||||||
\(733\) | 47.9061 | 1.76945 | 0.884726 | − | 0.466112i | \(-0.154346\pi\) | ||||
0.884726 | + | 0.466112i | \(0.154346\pi\) | |||||||
\(734\) | 26.2848 | 0.970190 | ||||||||
\(735\) | 2.33306 | 0.0860561 | ||||||||
\(736\) | 73.5488 | 2.71104 | ||||||||
\(737\) | 46.8570 | 1.72600 | ||||||||
\(738\) | −43.4711 | −1.60019 | ||||||||
\(739\) | −27.8097 | −1.02300 | −0.511499 | − | 0.859284i | \(-0.670910\pi\) | ||||
−0.511499 | + | 0.859284i | \(0.670910\pi\) | |||||||
\(740\) | 54.4044 | 1.99994 | ||||||||
\(741\) | −2.14769 | −0.0788973 | ||||||||
\(742\) | −75.1396 | −2.75846 | ||||||||
\(743\) | −34.4759 | −1.26480 | −0.632399 | − | 0.774643i | \(-0.717930\pi\) | ||||
−0.632399 | + | 0.774643i | \(0.717930\pi\) | |||||||
\(744\) | 1.14877 | 0.0421160 | ||||||||
\(745\) | 34.4292 | 1.26139 | ||||||||
\(746\) | −17.7427 | −0.649608 | ||||||||
\(747\) | −5.89113 | −0.215545 | ||||||||
\(748\) | −16.0159 | −0.585601 | ||||||||
\(749\) | −32.4433 | −1.18545 | ||||||||
\(750\) | 12.2401 | 0.446945 | ||||||||
\(751\) | 19.0952 | 0.696794 | 0.348397 | − | 0.937347i | \(-0.386726\pi\) | ||||
0.348397 | + | 0.937347i | \(0.386726\pi\) | |||||||
\(752\) | −16.9016 | −0.616339 | ||||||||
\(753\) | 3.91065 | 0.142512 | ||||||||
\(754\) | 14.9708 | 0.545204 | ||||||||
\(755\) | 59.0479 | 2.14897 | ||||||||
\(756\) | −15.5699 | −0.566272 | ||||||||
\(757\) | −37.4154 | −1.35988 | −0.679942 | − | 0.733266i | \(-0.737995\pi\) | ||||
−0.679942 | + | 0.733266i | \(0.737995\pi\) | |||||||
\(758\) | −24.5095 | −0.890226 | ||||||||
\(759\) | 3.18718 | 0.115687 | ||||||||
\(760\) | 116.488 | 4.22548 | ||||||||
\(761\) | −43.6149 | −1.58104 | −0.790519 | − | 0.612437i | \(-0.790189\pi\) | ||||
−0.790519 | + | 0.612437i | \(0.790189\pi\) | |||||||
\(762\) | −13.3004 | −0.481824 | ||||||||
\(763\) | −11.8560 | −0.429214 | ||||||||
\(764\) | −20.2339 | −0.732037 | ||||||||
\(765\) | 11.3816 | 0.411503 | ||||||||
\(766\) | 44.3827 | 1.60361 | ||||||||
\(767\) | −23.5796 | −0.851411 | ||||||||
\(768\) | 3.12429 | 0.112738 | ||||||||
\(769\) | 21.4223 | 0.772507 | 0.386254 | − | 0.922393i | \(-0.373769\pi\) | ||||
0.386254 | + | 0.922393i | \(0.373769\pi\) | |||||||
\(770\) | −67.4646 | −2.43126 | ||||||||
\(771\) | 0.561204 | 0.0202113 | ||||||||
\(772\) | −24.6305 | −0.886473 | ||||||||
\(773\) | 43.3763 | 1.56014 | 0.780068 | − | 0.625695i | \(-0.215185\pi\) | ||||
0.780068 | + | 0.625695i | \(0.215185\pi\) | |||||||
\(774\) | 90.1556 | 3.24057 | ||||||||
\(775\) | −5.57674 | −0.200322 | ||||||||
\(776\) | −104.284 | −3.74358 | ||||||||
\(777\) | −1.35884 | −0.0487481 | ||||||||
\(778\) | −88.7147 | −3.18058 | ||||||||
\(779\) | −19.2403 | −0.689357 | ||||||||
\(780\) | 12.3666 | 0.442796 | ||||||||
\(781\) | −31.1946 | −1.11623 | ||||||||
\(782\) | 11.6895 | 0.418016 | ||||||||
\(783\) | −3.05810 | −0.109288 | ||||||||
\(784\) | −32.2102 | −1.15036 | ||||||||
\(785\) | −24.9608 | −0.890889 | ||||||||
\(786\) | −10.7654 | −0.383990 | ||||||||
\(787\) | 30.3016 | 1.08013 | 0.540067 | − | 0.841622i | \(-0.318399\pi\) | ||||
0.540067 | + | 0.841622i | \(0.318399\pi\) | |||||||
\(788\) | 36.6309 | 1.30492 | ||||||||
\(789\) | 2.24537 | 0.0799374 | ||||||||
\(790\) | −8.60220 | −0.306053 | ||||||||
\(791\) | −12.9011 | −0.458710 | ||||||||
\(792\) | −77.9598 | −2.77018 | ||||||||
\(793\) | 1.20593 | 0.0428238 | ||||||||
\(794\) | −28.4097 | −1.00822 | ||||||||
\(795\) | −12.1910 | −0.432372 | ||||||||
\(796\) | 118.489 | 4.19973 | ||||||||
\(797\) | 25.9160 | 0.917992 | 0.458996 | − | 0.888438i | \(-0.348209\pi\) | ||||
0.458996 | + | 0.888438i | \(0.348209\pi\) | |||||||
\(798\) | −4.72334 | −0.167204 | ||||||||
\(799\) | −1.32999 | −0.0470518 | ||||||||
\(800\) | −168.128 | −5.94424 | ||||||||
\(801\) | −0.145624 | −0.00514538 | ||||||||
\(802\) | 46.5738 | 1.64458 | ||||||||
\(803\) | −38.2699 | −1.35051 | ||||||||
\(804\) | −18.8898 | −0.666192 | ||||||||
\(805\) | 35.5777 | 1.25395 | ||||||||
\(806\) | −3.88061 | −0.136689 | ||||||||
\(807\) | 2.88726 | 0.101636 | ||||||||
\(808\) | −81.1446 | −2.85466 | ||||||||
\(809\) | −17.3893 | −0.611375 | −0.305687 | − | 0.952132i | \(-0.598886\pi\) | ||||
−0.305687 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(810\) | 88.1754 | 3.09817 | ||||||||
\(811\) | −21.9774 | −0.771731 | −0.385865 | − | 0.922555i | \(-0.626097\pi\) | ||||
−0.385865 | + | 0.922555i | \(0.626097\pi\) | |||||||
\(812\) | 23.7893 | 0.834840 | ||||||||
\(813\) | −3.60924 | −0.126581 | ||||||||
\(814\) | −22.3036 | −0.781742 | ||||||||
\(815\) | 23.5761 | 0.825833 | ||||||||
\(816\) | 3.02501 | 0.105896 | ||||||||
\(817\) | 39.9029 | 1.39603 | ||||||||
\(818\) | −56.4462 | −1.97360 | ||||||||
\(819\) | 16.0446 | 0.560645 | ||||||||
\(820\) | 110.788 | 3.86888 | ||||||||
\(821\) | −50.0768 | −1.74769 | −0.873845 | − | 0.486204i | \(-0.838381\pi\) | ||||
−0.873845 | + | 0.486204i | \(0.838381\pi\) | |||||||
\(822\) | −11.8637 | −0.413795 | ||||||||
\(823\) | 18.9823 | 0.661682 | 0.330841 | − | 0.943687i | \(-0.392668\pi\) | ||||
0.330841 | + | 0.943687i | \(0.392668\pi\) | |||||||
\(824\) | 91.0731 | 3.17268 | ||||||||
\(825\) | −7.28573 | −0.253657 | ||||||||
\(826\) | −51.8579 | −1.80437 | ||||||||
\(827\) | 3.61530 | 0.125716 | 0.0628581 | − | 0.998022i | \(-0.479978\pi\) | ||||
0.0628581 | + | 0.998022i | \(0.479978\pi\) | |||||||
\(828\) | 66.7428 | 2.31947 | ||||||||
\(829\) | −12.6041 | −0.437760 | −0.218880 | − | 0.975752i | \(-0.570240\pi\) | ||||
−0.218880 | + | 0.975752i | \(0.570240\pi\) | |||||||
\(830\) | 20.7794 | 0.721262 | ||||||||
\(831\) | −5.69037 | −0.197397 | ||||||||
\(832\) | −51.4285 | −1.78296 | ||||||||
\(833\) | −2.53463 | −0.0878196 | ||||||||
\(834\) | 8.28182 | 0.286776 | ||||||||
\(835\) | 63.4007 | 2.19407 | ||||||||
\(836\) | −56.0163 | −1.93737 | ||||||||
\(837\) | 0.792697 | 0.0273996 | ||||||||
\(838\) | 66.3893 | 2.29338 | ||||||||
\(839\) | −7.50110 | −0.258967 | −0.129483 | − | 0.991582i | \(-0.541332\pi\) | ||||
−0.129483 | + | 0.991582i | \(0.541332\pi\) | |||||||
\(840\) | 16.7532 | 0.578040 | ||||||||
\(841\) | −24.3275 | −0.838880 | ||||||||
\(842\) | −72.8771 | −2.51151 | ||||||||
\(843\) | 1.07441 | 0.0370048 | ||||||||
\(844\) | 8.65253 | 0.297832 | ||||||||
\(845\) | 24.5370 | 0.844100 | ||||||||
\(846\) | −10.5099 | −0.361339 | ||||||||
\(847\) | −3.26086 | −0.112044 | ||||||||
\(848\) | 168.310 | 5.77977 | ||||||||
\(849\) | −1.29721 | −0.0445203 | ||||||||
\(850\) | −26.7216 | −0.916542 | ||||||||
\(851\) | 11.7619 | 0.403193 | ||||||||
\(852\) | 12.5757 | 0.430836 | ||||||||
\(853\) | −42.5662 | −1.45744 | −0.728719 | − | 0.684813i | \(-0.759884\pi\) | ||||
−0.728719 | + | 0.684813i | \(0.759884\pi\) | |||||||
\(854\) | 2.65216 | 0.0907552 | ||||||||
\(855\) | 39.8076 | 1.36139 | ||||||||
\(856\) | 132.237 | 4.51977 | ||||||||
\(857\) | −37.7156 | −1.28834 | −0.644170 | − | 0.764882i | \(-0.722797\pi\) | ||||
−0.644170 | + | 0.764882i | \(0.722797\pi\) | |||||||
\(858\) | −5.06982 | −0.173081 | ||||||||
\(859\) | −50.6473 | −1.72806 | −0.864032 | − | 0.503436i | \(-0.832069\pi\) | ||||
−0.864032 | + | 0.503436i | \(0.832069\pi\) | |||||||
\(860\) | −229.765 | −7.83493 | ||||||||
\(861\) | −2.76711 | −0.0943030 | ||||||||
\(862\) | 102.690 | 3.49765 | ||||||||
\(863\) | 43.4209 | 1.47806 | 0.739032 | − | 0.673670i | \(-0.235283\pi\) | ||||
0.739032 | + | 0.673670i | \(0.235283\pi\) | |||||||
\(864\) | 23.8983 | 0.813038 | ||||||||
\(865\) | −10.7388 | −0.365130 | ||||||||
\(866\) | −30.3815 | −1.03240 | ||||||||
\(867\) | 0.238039 | 0.00808422 | ||||||||
\(868\) | −6.16647 | −0.209304 | ||||||||
\(869\) | 2.54806 | 0.0864371 | ||||||||
\(870\) | 5.34189 | 0.181107 | ||||||||
\(871\) | 39.3063 | 1.33184 | ||||||||
\(872\) | 48.3242 | 1.63646 | ||||||||
\(873\) | −35.6369 | −1.20613 | ||||||||
\(874\) | 40.8845 | 1.38294 | ||||||||
\(875\) | −40.4721 | −1.36821 | ||||||||
\(876\) | 15.4280 | 0.521264 | ||||||||
\(877\) | −13.9419 | −0.470784 | −0.235392 | − | 0.971901i | \(-0.575637\pi\) | ||||
−0.235392 | + | 0.971901i | \(0.575637\pi\) | |||||||
\(878\) | 77.8739 | 2.62812 | ||||||||
\(879\) | −7.12326 | −0.240262 | ||||||||
\(880\) | 151.118 | 5.09418 | ||||||||
\(881\) | 5.95846 | 0.200746 | 0.100373 | − | 0.994950i | \(-0.467996\pi\) | ||||
0.100373 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(882\) | −20.0292 | −0.674419 | ||||||||
\(883\) | −16.8840 | −0.568191 | −0.284096 | − | 0.958796i | \(-0.591693\pi\) | ||||
−0.284096 | + | 0.958796i | \(0.591693\pi\) | |||||||
\(884\) | −13.4351 | −0.451870 | ||||||||
\(885\) | −8.41370 | −0.282824 | ||||||||
\(886\) | −36.9848 | −1.24253 | ||||||||
\(887\) | −48.0762 | −1.61424 | −0.807120 | − | 0.590388i | \(-0.798975\pi\) | ||||
−0.807120 | + | 0.590388i | \(0.798975\pi\) | |||||||
\(888\) | 5.53856 | 0.185862 | ||||||||
\(889\) | 43.9782 | 1.47498 | ||||||||
\(890\) | 0.513650 | 0.0172176 | ||||||||
\(891\) | −26.1185 | −0.875001 | ||||||||
\(892\) | 2.21469 | 0.0741534 | ||||||||
\(893\) | −4.65170 | −0.155663 | ||||||||
\(894\) | 5.69011 | 0.190306 | ||||||||
\(895\) | 20.0416 | 0.669916 | ||||||||
\(896\) | −41.7133 | −1.39354 | ||||||||
\(897\) | 2.67359 | 0.0892685 | ||||||||
\(898\) | 79.9313 | 2.66734 | ||||||||
\(899\) | −1.21116 | −0.0403945 | ||||||||
\(900\) | −152.570 | −5.08568 | ||||||||
\(901\) | 13.2443 | 0.441232 | ||||||||
\(902\) | −45.4187 | −1.51228 | ||||||||
\(903\) | 5.73877 | 0.190974 | ||||||||
\(904\) | 52.5842 | 1.74892 | ||||||||
\(905\) | 17.5287 | 0.582674 | ||||||||
\(906\) | 9.75887 | 0.324217 | ||||||||
\(907\) | 15.1734 | 0.503823 | 0.251911 | − | 0.967750i | \(-0.418941\pi\) | ||||
0.251911 | + | 0.967750i | \(0.418941\pi\) | |||||||
\(908\) | 83.2114 | 2.76147 | ||||||||
\(909\) | −27.7295 | −0.919731 | ||||||||
\(910\) | −56.5931 | −1.87604 | ||||||||
\(911\) | −1.95489 | −0.0647684 | −0.0323842 | − | 0.999475i | \(-0.510310\pi\) | ||||
−0.0323842 | + | 0.999475i | \(0.510310\pi\) | |||||||
\(912\) | 10.5801 | 0.350341 | ||||||||
\(913\) | −6.15506 | −0.203703 | ||||||||
\(914\) | −110.974 | −3.67068 | ||||||||
\(915\) | 0.430301 | 0.0142253 | ||||||||
\(916\) | −31.3130 | −1.03461 | ||||||||
\(917\) | 35.5961 | 1.17549 | ||||||||
\(918\) | 3.79829 | 0.125362 | ||||||||
\(919\) | 6.19568 | 0.204377 | 0.102188 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102188 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(920\) | −145.013 | −4.78093 | ||||||||
\(921\) | 1.39400 | 0.0459337 | ||||||||
\(922\) | 51.1091 | 1.68319 | ||||||||
\(923\) | −26.1677 | −0.861322 | ||||||||
\(924\) | −8.05618 | −0.265029 | ||||||||
\(925\) | −26.8871 | −0.884041 | ||||||||
\(926\) | 11.3721 | 0.373711 | ||||||||
\(927\) | 31.1224 | 1.02219 | ||||||||
\(928\) | −36.5143 | −1.19864 | ||||||||
\(929\) | 10.1993 | 0.334628 | 0.167314 | − | 0.985904i | \(-0.446491\pi\) | ||||
0.167314 | + | 0.985904i | \(0.446491\pi\) | |||||||
\(930\) | −1.38468 | −0.0454055 | ||||||||
\(931\) | −8.86495 | −0.290537 | ||||||||
\(932\) | −71.1440 | −2.33040 | ||||||||
\(933\) | 0.583249 | 0.0190947 | ||||||||
\(934\) | −42.9440 | −1.40517 | ||||||||
\(935\) | 11.8915 | 0.388894 | ||||||||
\(936\) | −65.3971 | −2.13757 | ||||||||
\(937\) | 38.0288 | 1.24235 | 0.621174 | − | 0.783673i | \(-0.286656\pi\) | ||||
0.621174 | + | 0.783673i | \(0.286656\pi\) | |||||||
\(938\) | 86.4450 | 2.82253 | ||||||||
\(939\) | 2.85495 | 0.0931677 | ||||||||
\(940\) | 26.7850 | 0.873631 | ||||||||
\(941\) | −21.3884 | −0.697242 | −0.348621 | − | 0.937264i | \(-0.613350\pi\) | ||||
−0.348621 | + | 0.937264i | \(0.613350\pi\) | |||||||
\(942\) | −4.12528 | −0.134409 | ||||||||
\(943\) | 23.9517 | 0.779975 | ||||||||
\(944\) | 116.160 | 3.78067 | ||||||||
\(945\) | 11.5603 | 0.376058 | ||||||||
\(946\) | 94.1946 | 3.06253 | ||||||||
\(947\) | 52.7187 | 1.71313 | 0.856563 | − | 0.516042i | \(-0.172595\pi\) | ||||
0.856563 | + | 0.516042i | \(0.172595\pi\) | |||||||
\(948\) | −1.02722 | −0.0333625 | ||||||||
\(949\) | −32.1029 | −1.04210 | ||||||||
\(950\) | −93.4596 | −3.03223 | ||||||||
\(951\) | −1.52024 | −0.0492973 | ||||||||
\(952\) | −18.2006 | −0.589885 | ||||||||
\(953\) | −34.0793 | −1.10394 | −0.551968 | − | 0.833865i | \(-0.686123\pi\) | ||||
−0.551968 | + | 0.833865i | \(0.686123\pi\) | |||||||
\(954\) | 104.660 | 3.38849 | ||||||||
\(955\) | 15.0233 | 0.486141 | ||||||||
\(956\) | −18.0663 | −0.584305 | ||||||||
\(957\) | −1.58232 | −0.0511492 | ||||||||
\(958\) | 5.52463 | 0.178493 | ||||||||
\(959\) | 39.2277 | 1.26673 | ||||||||
\(960\) | −18.3508 | −0.592269 | ||||||||
\(961\) | −30.6861 | −0.989873 | ||||||||
\(962\) | −18.7095 | −0.603219 | ||||||||
\(963\) | 45.1894 | 1.45621 | ||||||||
\(964\) | −100.151 | −3.22565 | ||||||||
\(965\) | 18.2877 | 0.588701 | ||||||||
\(966\) | 5.87994 | 0.189184 | ||||||||
\(967\) | 53.4542 | 1.71897 | 0.859485 | − | 0.511161i | \(-0.170784\pi\) | ||||
0.859485 | + | 0.511161i | \(0.170784\pi\) | |||||||
\(968\) | 13.2911 | 0.427192 | ||||||||
\(969\) | 0.832549 | 0.0267453 | ||||||||
\(970\) | 125.700 | 4.03597 | ||||||||
\(971\) | 10.6313 | 0.341174 | 0.170587 | − | 0.985343i | \(-0.445434\pi\) | ||||
0.170587 | + | 0.985343i | \(0.445434\pi\) | |||||||
\(972\) | 32.6337 | 1.04673 | ||||||||
\(973\) | −27.3840 | −0.877890 | ||||||||
\(974\) | −83.2936 | −2.66890 | ||||||||
\(975\) | −6.11168 | −0.195730 | ||||||||
\(976\) | −5.94073 | −0.190158 | ||||||||
\(977\) | 33.5430 | 1.07314 | 0.536568 | − | 0.843857i | \(-0.319721\pi\) | ||||
0.536568 | + | 0.843857i | \(0.319721\pi\) | |||||||
\(978\) | 3.89642 | 0.124594 | ||||||||
\(979\) | −0.152148 | −0.00486268 | ||||||||
\(980\) | 51.0453 | 1.63058 | ||||||||
\(981\) | 16.5138 | 0.527246 | ||||||||
\(982\) | −71.2590 | −2.27396 | ||||||||
\(983\) | −9.52847 | −0.303911 | −0.151956 | − | 0.988387i | \(-0.548557\pi\) | ||||
−0.151956 | + | 0.988387i | \(0.548557\pi\) | |||||||
\(984\) | 11.2786 | 0.359549 | ||||||||
\(985\) | −27.1977 | −0.866590 | ||||||||
\(986\) | −5.80342 | −0.184818 | ||||||||
\(987\) | −0.669000 | −0.0212945 | ||||||||
\(988\) | −46.9896 | −1.49494 | ||||||||
\(989\) | −49.6739 | −1.57954 | ||||||||
\(990\) | 93.9696 | 2.98655 | ||||||||
\(991\) | 51.5442 | 1.63735 | 0.818677 | − | 0.574254i | \(-0.194708\pi\) | ||||
0.818677 | + | 0.574254i | \(0.194708\pi\) | |||||||
\(992\) | 9.46495 | 0.300512 | ||||||||
\(993\) | 2.09014 | 0.0663287 | ||||||||
\(994\) | −57.5499 | −1.82537 | ||||||||
\(995\) | −87.9757 | −2.78902 | ||||||||
\(996\) | 2.48133 | 0.0786241 | ||||||||
\(997\) | 32.0275 | 1.01432 | 0.507160 | − | 0.861852i | \(-0.330695\pi\) | ||||
0.507160 | + | 0.861852i | \(0.330695\pi\) | |||||||
\(998\) | 65.8475 | 2.08437 | ||||||||
\(999\) | 3.82182 | 0.120917 |
(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 | 6001.2.a.b.1.6 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.6 | ✓ | 114 | 1.1 | even | 1 | trivial |