Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0000972201\) |
Analytic rank: | \(0\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21148 | −0.856643 | −0.428322 | − | 0.903626i | \(-0.640895\pi\) | ||||
−0.428322 | + | 0.903626i | \(0.640895\pi\) | |||||||
\(3\) | 1.67937 | 0.969585 | 0.484793 | − | 0.874629i | \(-0.338895\pi\) | ||||
0.484793 | + | 0.874629i | \(0.338895\pi\) | |||||||
\(4\) | −0.532324 | −0.266162 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.03452 | −0.830589 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.06785 | 1.08465 | ||||||||
\(9\) | −0.179714 | −0.0599047 | ||||||||
\(10\) | 1.21148 | 0.383103 | ||||||||
\(11\) | −5.20420 | −1.56912 | −0.784562 | − | 0.620050i | \(-0.787112\pi\) | ||||
−0.784562 | + | 0.620050i | \(0.787112\pi\) | |||||||
\(12\) | −0.893970 | −0.258067 | ||||||||
\(13\) | 4.41019 | 1.22317 | 0.611583 | − | 0.791180i | \(-0.290533\pi\) | ||||
0.611583 | + | 0.791180i | \(0.290533\pi\) | |||||||
\(14\) | 1.21148 | 0.323781 | ||||||||
\(15\) | −1.67937 | −0.433612 | ||||||||
\(16\) | −2.65198 | −0.662996 | ||||||||
\(17\) | −0.830757 | −0.201488 | −0.100744 | − | 0.994912i | \(-0.532122\pi\) | ||||
−0.100744 | + | 0.994912i | \(0.532122\pi\) | |||||||
\(18\) | 0.217720 | 0.0513170 | ||||||||
\(19\) | −7.19999 | −1.65179 | −0.825896 | − | 0.563823i | \(-0.809330\pi\) | ||||
−0.825896 | + | 0.563823i | \(0.809330\pi\) | |||||||
\(20\) | 0.532324 | 0.119031 | ||||||||
\(21\) | −1.67937 | −0.366469 | ||||||||
\(22\) | 6.30476 | 1.34418 | ||||||||
\(23\) | −1.03249 | −0.215289 | −0.107644 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107644 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(24\) | 5.15206 | 1.05166 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.34284 | −1.04782 | ||||||||
\(27\) | −5.33992 | −1.02767 | ||||||||
\(28\) | 0.532324 | 0.100600 | ||||||||
\(29\) | −6.71927 | −1.24774 | −0.623868 | − | 0.781529i | \(-0.714440\pi\) | ||||
−0.623868 | + | 0.781529i | \(0.714440\pi\) | |||||||
\(30\) | 2.03452 | 0.371451 | ||||||||
\(31\) | 0.399125 | 0.0716849 | 0.0358424 | − | 0.999357i | \(-0.488589\pi\) | ||||
0.0358424 | + | 0.999357i | \(0.488589\pi\) | |||||||
\(32\) | −2.92289 | −0.516699 | ||||||||
\(33\) | −8.73977 | −1.52140 | ||||||||
\(34\) | 1.00644 | 0.172604 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0.0956662 | 0.0159444 | ||||||||
\(37\) | 6.46999 | 1.06366 | 0.531830 | − | 0.846851i | \(-0.321505\pi\) | ||||
0.531830 | + | 0.846851i | \(0.321505\pi\) | |||||||
\(38\) | 8.72262 | 1.41500 | ||||||||
\(39\) | 7.40634 | 1.18596 | ||||||||
\(40\) | −3.06785 | −0.485070 | ||||||||
\(41\) | 6.34004 | 0.990148 | 0.495074 | − | 0.868851i | \(-0.335141\pi\) | ||||
0.495074 | + | 0.868851i | \(0.335141\pi\) | |||||||
\(42\) | 2.03452 | 0.313933 | ||||||||
\(43\) | −1.63582 | −0.249461 | −0.124730 | − | 0.992191i | \(-0.539807\pi\) | ||||
−0.124730 | + | 0.992191i | \(0.539807\pi\) | |||||||
\(44\) | 2.77032 | 0.417641 | ||||||||
\(45\) | 0.179714 | 0.0267902 | ||||||||
\(46\) | 1.25084 | 0.184426 | ||||||||
\(47\) | −5.69334 | −0.830459 | −0.415229 | − | 0.909717i | \(-0.636299\pi\) | ||||
−0.415229 | + | 0.909717i | \(0.636299\pi\) | |||||||
\(48\) | −4.45366 | −0.642831 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.21148 | −0.171329 | ||||||||
\(51\) | −1.39515 | −0.195360 | ||||||||
\(52\) | −2.34765 | −0.325561 | ||||||||
\(53\) | −10.3766 | −1.42533 | −0.712665 | − | 0.701504i | \(-0.752512\pi\) | ||||
−0.712665 | + | 0.701504i | \(0.752512\pi\) | |||||||
\(54\) | 6.46919 | 0.880345 | ||||||||
\(55\) | 5.20420 | 0.701734 | ||||||||
\(56\) | −3.06785 | −0.409959 | ||||||||
\(57\) | −12.0915 | −1.60155 | ||||||||
\(58\) | 8.14024 | 1.06887 | ||||||||
\(59\) | −14.5415 | −1.89315 | −0.946574 | − | 0.322487i | \(-0.895481\pi\) | ||||
−0.946574 | + | 0.322487i | \(0.895481\pi\) | |||||||
\(60\) | 0.893970 | 0.115411 | ||||||||
\(61\) | 8.62838 | 1.10475 | 0.552375 | − | 0.833596i | \(-0.313722\pi\) | ||||
0.552375 | + | 0.833596i | \(0.313722\pi\) | |||||||
\(62\) | −0.483530 | −0.0614084 | ||||||||
\(63\) | 0.179714 | 0.0226419 | ||||||||
\(64\) | 8.84498 | 1.10562 | ||||||||
\(65\) | −4.41019 | −0.547017 | ||||||||
\(66\) | 10.5880 | 1.30330 | ||||||||
\(67\) | −2.55982 | −0.312732 | −0.156366 | − | 0.987699i | \(-0.549978\pi\) | ||||
−0.156366 | + | 0.987699i | \(0.549978\pi\) | |||||||
\(68\) | 0.442232 | 0.0536285 | ||||||||
\(69\) | −1.73393 | −0.208741 | ||||||||
\(70\) | −1.21148 | −0.144799 | ||||||||
\(71\) | 15.5322 | 1.84334 | 0.921668 | − | 0.387981i | \(-0.126827\pi\) | ||||
0.921668 | + | 0.387981i | \(0.126827\pi\) | |||||||
\(72\) | −0.551337 | −0.0649756 | ||||||||
\(73\) | 6.22453 | 0.728527 | 0.364263 | − | 0.931296i | \(-0.381321\pi\) | ||||
0.364263 | + | 0.931296i | \(0.381321\pi\) | |||||||
\(74\) | −7.83824 | −0.911177 | ||||||||
\(75\) | 1.67937 | 0.193917 | ||||||||
\(76\) | 3.83273 | 0.439644 | ||||||||
\(77\) | 5.20420 | 0.593073 | ||||||||
\(78\) | −8.97261 | −1.01595 | ||||||||
\(79\) | 8.09991 | 0.911311 | 0.455655 | − | 0.890156i | \(-0.349405\pi\) | ||||
0.455655 | + | 0.890156i | \(0.349405\pi\) | |||||||
\(80\) | 2.65198 | 0.296501 | ||||||||
\(81\) | −8.42856 | −0.936507 | ||||||||
\(82\) | −7.68081 | −0.848204 | ||||||||
\(83\) | 11.9391 | 1.31048 | 0.655242 | − | 0.755419i | \(-0.272567\pi\) | ||||
0.655242 | + | 0.755419i | \(0.272567\pi\) | |||||||
\(84\) | 0.893970 | 0.0975401 | ||||||||
\(85\) | 0.830757 | 0.0901083 | ||||||||
\(86\) | 1.98176 | 0.213699 | ||||||||
\(87\) | −11.2841 | −1.20979 | ||||||||
\(88\) | −15.9657 | −1.70195 | ||||||||
\(89\) | −5.80329 | −0.615147 | −0.307574 | − | 0.951524i | \(-0.599517\pi\) | ||||
−0.307574 | + | 0.951524i | \(0.599517\pi\) | |||||||
\(90\) | −0.217720 | −0.0229497 | ||||||||
\(91\) | −4.41019 | −0.462313 | ||||||||
\(92\) | 0.549619 | 0.0573017 | ||||||||
\(93\) | 0.670278 | 0.0695046 | ||||||||
\(94\) | 6.89735 | 0.711407 | ||||||||
\(95\) | 7.19999 | 0.738703 | ||||||||
\(96\) | −4.90861 | −0.500983 | ||||||||
\(97\) | −8.15777 | −0.828296 | −0.414148 | − | 0.910210i | \(-0.635920\pi\) | ||||
−0.414148 | + | 0.910210i | \(0.635920\pi\) | |||||||
\(98\) | −1.21148 | −0.122378 | ||||||||
\(99\) | 0.935268 | 0.0939980 | ||||||||
\(100\) | −0.532324 | −0.0532324 | ||||||||
\(101\) | 9.42696 | 0.938017 | 0.469009 | − | 0.883194i | \(-0.344611\pi\) | ||||
0.469009 | + | 0.883194i | \(0.344611\pi\) | |||||||
\(102\) | 1.69019 | 0.167354 | ||||||||
\(103\) | −0.699690 | −0.0689425 | −0.0344713 | − | 0.999406i | \(-0.510975\pi\) | ||||
−0.0344713 | + | 0.999406i | \(0.510975\pi\) | |||||||
\(104\) | 13.5298 | 1.32671 | ||||||||
\(105\) | 1.67937 | 0.163890 | ||||||||
\(106\) | 12.5710 | 1.22100 | ||||||||
\(107\) | −7.12220 | −0.688529 | −0.344264 | − | 0.938873i | \(-0.611872\pi\) | ||||
−0.344264 | + | 0.938873i | \(0.611872\pi\) | |||||||
\(108\) | 2.84257 | 0.273526 | ||||||||
\(109\) | −5.44814 | −0.521837 | −0.260919 | − | 0.965361i | \(-0.584025\pi\) | ||||
−0.260919 | + | 0.965361i | \(0.584025\pi\) | |||||||
\(110\) | −6.30476 | −0.601136 | ||||||||
\(111\) | 10.8655 | 1.03131 | ||||||||
\(112\) | 2.65198 | 0.250589 | ||||||||
\(113\) | −1.58231 | −0.148851 | −0.0744255 | − | 0.997227i | \(-0.523712\pi\) | ||||
−0.0744255 | + | 0.997227i | \(0.523712\pi\) | |||||||
\(114\) | 14.6485 | 1.37196 | ||||||||
\(115\) | 1.03249 | 0.0962801 | ||||||||
\(116\) | 3.57683 | 0.332100 | ||||||||
\(117\) | −0.792574 | −0.0732735 | ||||||||
\(118\) | 17.6167 | 1.62175 | ||||||||
\(119\) | 0.830757 | 0.0761554 | ||||||||
\(120\) | −5.15206 | −0.470317 | ||||||||
\(121\) | 16.0837 | 1.46215 | ||||||||
\(122\) | −10.4531 | −0.946377 | ||||||||
\(123\) | 10.6473 | 0.960033 | ||||||||
\(124\) | −0.212464 | −0.0190798 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.217720 | −0.0193960 | ||||||||
\(127\) | −5.30748 | −0.470963 | −0.235482 | − | 0.971879i | \(-0.575667\pi\) | ||||
−0.235482 | + | 0.971879i | \(0.575667\pi\) | |||||||
\(128\) | −4.86970 | −0.430425 | ||||||||
\(129\) | −2.74715 | −0.241873 | ||||||||
\(130\) | 5.34284 | 0.468598 | ||||||||
\(131\) | 9.34518 | 0.816492 | 0.408246 | − | 0.912872i | \(-0.366141\pi\) | ||||
0.408246 | + | 0.912872i | \(0.366141\pi\) | |||||||
\(132\) | 4.65239 | 0.404939 | ||||||||
\(133\) | 7.19999 | 0.624318 | ||||||||
\(134\) | 3.10117 | 0.267900 | ||||||||
\(135\) | 5.33992 | 0.459587 | ||||||||
\(136\) | −2.54864 | −0.218544 | ||||||||
\(137\) | −12.7964 | −1.09327 | −0.546637 | − | 0.837370i | \(-0.684092\pi\) | ||||
−0.546637 | + | 0.837370i | \(0.684092\pi\) | |||||||
\(138\) | 2.10062 | 0.178816 | ||||||||
\(139\) | 1.58170 | 0.134158 | 0.0670790 | − | 0.997748i | \(-0.478632\pi\) | ||||
0.0670790 | + | 0.997748i | \(0.478632\pi\) | |||||||
\(140\) | −0.532324 | −0.0449896 | ||||||||
\(141\) | −9.56122 | −0.805200 | ||||||||
\(142\) | −18.8169 | −1.57908 | ||||||||
\(143\) | −22.9515 | −1.91930 | ||||||||
\(144\) | 0.476599 | 0.0397166 | ||||||||
\(145\) | 6.71927 | 0.558005 | ||||||||
\(146\) | −7.54088 | −0.624087 | ||||||||
\(147\) | 1.67937 | 0.138512 | ||||||||
\(148\) | −3.44413 | −0.283106 | ||||||||
\(149\) | 1.46551 | 0.120059 | 0.0600296 | − | 0.998197i | \(-0.480880\pi\) | ||||
0.0600296 | + | 0.998197i | \(0.480880\pi\) | |||||||
\(150\) | −2.03452 | −0.166118 | ||||||||
\(151\) | 10.8842 | 0.885748 | 0.442874 | − | 0.896584i | \(-0.353959\pi\) | ||||
0.442874 | + | 0.896584i | \(0.353959\pi\) | |||||||
\(152\) | −22.0885 | −1.79161 | ||||||||
\(153\) | 0.149299 | 0.0120701 | ||||||||
\(154\) | −6.30476 | −0.508052 | ||||||||
\(155\) | −0.399125 | −0.0320585 | ||||||||
\(156\) | −3.94258 | −0.315659 | ||||||||
\(157\) | −3.90830 | −0.311917 | −0.155958 | − | 0.987764i | \(-0.549847\pi\) | ||||
−0.155958 | + | 0.987764i | \(0.549847\pi\) | |||||||
\(158\) | −9.81285 | −0.780668 | ||||||||
\(159\) | −17.4261 | −1.38198 | ||||||||
\(160\) | 2.92289 | 0.231075 | ||||||||
\(161\) | 1.03249 | 0.0813715 | ||||||||
\(162\) | 10.2110 | 0.802252 | ||||||||
\(163\) | 8.96770 | 0.702405 | 0.351202 | − | 0.936300i | \(-0.385773\pi\) | ||||
0.351202 | + | 0.936300i | \(0.385773\pi\) | |||||||
\(164\) | −3.37496 | −0.263540 | ||||||||
\(165\) | 8.73977 | 0.680391 | ||||||||
\(166\) | −14.4639 | −1.12262 | ||||||||
\(167\) | 3.62653 | 0.280630 | 0.140315 | − | 0.990107i | \(-0.455189\pi\) | ||||
0.140315 | + | 0.990107i | \(0.455189\pi\) | |||||||
\(168\) | −5.15206 | −0.397490 | ||||||||
\(169\) | 6.44977 | 0.496136 | ||||||||
\(170\) | −1.00644 | −0.0771906 | ||||||||
\(171\) | 1.29394 | 0.0989501 | ||||||||
\(172\) | 0.870788 | 0.0663970 | ||||||||
\(173\) | 7.05442 | 0.536338 | 0.268169 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268169 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(174\) | 13.6705 | 1.03636 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 13.8014 | 1.04032 | ||||||||
\(177\) | −24.4206 | −1.83557 | ||||||||
\(178\) | 7.03055 | 0.526962 | ||||||||
\(179\) | 3.13166 | 0.234071 | 0.117036 | − | 0.993128i | \(-0.462661\pi\) | ||||
0.117036 | + | 0.993128i | \(0.462661\pi\) | |||||||
\(180\) | −0.0956662 | −0.00713054 | ||||||||
\(181\) | 22.4452 | 1.66834 | 0.834168 | − | 0.551510i | \(-0.185948\pi\) | ||||
0.834168 | + | 0.551510i | \(0.185948\pi\) | |||||||
\(182\) | 5.34284 | 0.396038 | ||||||||
\(183\) | 14.4902 | 1.07115 | ||||||||
\(184\) | −3.16752 | −0.233513 | ||||||||
\(185\) | −6.46999 | −0.475683 | ||||||||
\(186\) | −0.812026 | −0.0595407 | ||||||||
\(187\) | 4.32342 | 0.316160 | ||||||||
\(188\) | 3.03070 | 0.221037 | ||||||||
\(189\) | 5.33992 | 0.388422 | ||||||||
\(190\) | −8.72262 | −0.632805 | ||||||||
\(191\) | −25.4447 | −1.84112 | −0.920558 | − | 0.390606i | \(-0.872266\pi\) | ||||
−0.920558 | + | 0.390606i | \(0.872266\pi\) | |||||||
\(192\) | 14.8540 | 1.07199 | ||||||||
\(193\) | −16.0136 | −1.15268 | −0.576341 | − | 0.817210i | \(-0.695520\pi\) | ||||
−0.576341 | + | 0.817210i | \(0.695520\pi\) | |||||||
\(194\) | 9.88295 | 0.709554 | ||||||||
\(195\) | −7.40634 | −0.530379 | ||||||||
\(196\) | −0.532324 | −0.0380232 | ||||||||
\(197\) | 24.7300 | 1.76194 | 0.880971 | − | 0.473170i | \(-0.156890\pi\) | ||||
0.880971 | + | 0.473170i | \(0.156890\pi\) | |||||||
\(198\) | −1.13306 | −0.0805228 | ||||||||
\(199\) | −1.74351 | −0.123594 | −0.0617972 | − | 0.998089i | \(-0.519683\pi\) | ||||
−0.0617972 | + | 0.998089i | \(0.519683\pi\) | |||||||
\(200\) | 3.06785 | 0.216930 | ||||||||
\(201\) | −4.29889 | −0.303221 | ||||||||
\(202\) | −11.4205 | −0.803546 | ||||||||
\(203\) | 6.71927 | 0.471600 | ||||||||
\(204\) | 0.742672 | 0.0519974 | ||||||||
\(205\) | −6.34004 | −0.442808 | ||||||||
\(206\) | 0.847658 | 0.0590592 | ||||||||
\(207\) | 0.185553 | 0.0128968 | ||||||||
\(208\) | −11.6957 | −0.810954 | ||||||||
\(209\) | 37.4702 | 2.59187 | ||||||||
\(210\) | −2.03452 | −0.140395 | ||||||||
\(211\) | −10.5180 | −0.724088 | −0.362044 | − | 0.932161i | \(-0.617921\pi\) | ||||
−0.362044 | + | 0.932161i | \(0.617921\pi\) | |||||||
\(212\) | 5.52370 | 0.379369 | ||||||||
\(213\) | 26.0843 | 1.78727 | ||||||||
\(214\) | 8.62838 | 0.589824 | ||||||||
\(215\) | 1.63582 | 0.111562 | ||||||||
\(216\) | −16.3821 | −1.11466 | ||||||||
\(217\) | −0.399125 | −0.0270943 | ||||||||
\(218\) | 6.60029 | 0.447028 | ||||||||
\(219\) | 10.4533 | 0.706368 | ||||||||
\(220\) | −2.77032 | −0.186775 | ||||||||
\(221\) | −3.66380 | −0.246454 | ||||||||
\(222\) | −13.1633 | −0.883464 | ||||||||
\(223\) | 4.06215 | 0.272021 | 0.136011 | − | 0.990707i | \(-0.456572\pi\) | ||||
0.136011 | + | 0.990707i | \(0.456572\pi\) | |||||||
\(224\) | 2.92289 | 0.195294 | ||||||||
\(225\) | −0.179714 | −0.0119809 | ||||||||
\(226\) | 1.91693 | 0.127512 | ||||||||
\(227\) | −13.3462 | −0.885820 | −0.442910 | − | 0.896566i | \(-0.646054\pi\) | ||||
−0.442910 | + | 0.896566i | \(0.646054\pi\) | |||||||
\(228\) | 6.43657 | 0.426273 | ||||||||
\(229\) | 1.00000 | 0.0660819 | ||||||||
\(230\) | −1.25084 | −0.0824777 | ||||||||
\(231\) | 8.73977 | 0.575035 | ||||||||
\(232\) | −20.6137 | −1.35336 | ||||||||
\(233\) | 15.2104 | 0.996465 | 0.498232 | − | 0.867044i | \(-0.333983\pi\) | ||||
0.498232 | + | 0.867044i | \(0.333983\pi\) | |||||||
\(234\) | 0.960185 | 0.0627692 | ||||||||
\(235\) | 5.69334 | 0.371392 | ||||||||
\(236\) | 7.74082 | 0.503884 | ||||||||
\(237\) | 13.6027 | 0.883593 | ||||||||
\(238\) | −1.00644 | −0.0652380 | ||||||||
\(239\) | −12.8861 | −0.833536 | −0.416768 | − | 0.909013i | \(-0.636837\pi\) | ||||
−0.416768 | + | 0.909013i | \(0.636837\pi\) | |||||||
\(240\) | 4.45366 | 0.287483 | ||||||||
\(241\) | 6.39447 | 0.411904 | 0.205952 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205952 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(242\) | −19.4850 | −1.25254 | ||||||||
\(243\) | 1.86508 | 0.119645 | ||||||||
\(244\) | −4.59310 | −0.294043 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −12.8989 | −0.822406 | ||||||||
\(247\) | −31.7533 | −2.02042 | ||||||||
\(248\) | 1.22446 | 0.0777530 | ||||||||
\(249\) | 20.0501 | 1.27062 | ||||||||
\(250\) | 1.21148 | 0.0766205 | ||||||||
\(251\) | −9.03909 | −0.570542 | −0.285271 | − | 0.958447i | \(-0.592084\pi\) | ||||
−0.285271 | + | 0.958447i | \(0.592084\pi\) | |||||||
\(252\) | −0.0956662 | −0.00602641 | ||||||||
\(253\) | 5.37327 | 0.337815 | ||||||||
\(254\) | 6.42989 | 0.403447 | ||||||||
\(255\) | 1.39515 | 0.0873676 | ||||||||
\(256\) | −11.7904 | −0.736901 | ||||||||
\(257\) | −17.6408 | −1.10040 | −0.550200 | − | 0.835033i | \(-0.685449\pi\) | ||||
−0.550200 | + | 0.835033i | \(0.685449\pi\) | |||||||
\(258\) | 3.32811 | 0.207199 | ||||||||
\(259\) | −6.46999 | −0.402026 | ||||||||
\(260\) | 2.34765 | 0.145595 | ||||||||
\(261\) | 1.20755 | 0.0747453 | ||||||||
\(262\) | −11.3215 | −0.699442 | ||||||||
\(263\) | 18.1765 | 1.12081 | 0.560405 | − | 0.828219i | \(-0.310646\pi\) | ||||
0.560405 | + | 0.828219i | \(0.310646\pi\) | |||||||
\(264\) | −26.8123 | −1.65019 | ||||||||
\(265\) | 10.3766 | 0.637427 | ||||||||
\(266\) | −8.72262 | −0.534818 | ||||||||
\(267\) | −9.74587 | −0.596438 | ||||||||
\(268\) | 1.36266 | 0.0832375 | ||||||||
\(269\) | −5.15450 | −0.314276 | −0.157138 | − | 0.987577i | \(-0.550227\pi\) | ||||
−0.157138 | + | 0.987577i | \(0.550227\pi\) | |||||||
\(270\) | −6.46919 | −0.393702 | ||||||||
\(271\) | 16.4518 | 0.999374 | 0.499687 | − | 0.866206i | \(-0.333448\pi\) | ||||
0.499687 | + | 0.866206i | \(0.333448\pi\) | |||||||
\(272\) | 2.20315 | 0.133586 | ||||||||
\(273\) | −7.40634 | −0.448252 | ||||||||
\(274\) | 15.5026 | 0.936546 | ||||||||
\(275\) | −5.20420 | −0.313825 | ||||||||
\(276\) | 0.923014 | 0.0555589 | ||||||||
\(277\) | 29.5923 | 1.77803 | 0.889015 | − | 0.457877i | \(-0.151390\pi\) | ||||
0.889015 | + | 0.457877i | \(0.151390\pi\) | |||||||
\(278\) | −1.91619 | −0.114926 | ||||||||
\(279\) | −0.0717284 | −0.00429427 | ||||||||
\(280\) | 3.06785 | 0.183339 | ||||||||
\(281\) | 6.48794 | 0.387038 | 0.193519 | − | 0.981097i | \(-0.438010\pi\) | ||||
0.193519 | + | 0.981097i | \(0.438010\pi\) | |||||||
\(282\) | 11.5832 | 0.689770 | ||||||||
\(283\) | −20.9612 | −1.24601 | −0.623007 | − | 0.782217i | \(-0.714089\pi\) | ||||
−0.623007 | + | 0.782217i | \(0.714089\pi\) | |||||||
\(284\) | −8.26818 | −0.490626 | ||||||||
\(285\) | 12.0915 | 0.716236 | ||||||||
\(286\) | 27.8052 | 1.64416 | ||||||||
\(287\) | −6.34004 | −0.374241 | ||||||||
\(288\) | 0.525285 | 0.0309527 | ||||||||
\(289\) | −16.3098 | −0.959403 | ||||||||
\(290\) | −8.14024 | −0.478011 | ||||||||
\(291\) | −13.6999 | −0.803104 | ||||||||
\(292\) | −3.31347 | −0.193906 | ||||||||
\(293\) | −9.48074 | −0.553871 | −0.276935 | − | 0.960889i | \(-0.589319\pi\) | ||||
−0.276935 | + | 0.960889i | \(0.589319\pi\) | |||||||
\(294\) | −2.03452 | −0.118656 | ||||||||
\(295\) | 14.5415 | 0.846641 | ||||||||
\(296\) | 19.8490 | 1.15370 | ||||||||
\(297\) | 27.7900 | 1.61254 | ||||||||
\(298\) | −1.77543 | −0.102848 | ||||||||
\(299\) | −4.55347 | −0.263334 | ||||||||
\(300\) | −0.893970 | −0.0516134 | ||||||||
\(301\) | 1.63582 | 0.0942872 | ||||||||
\(302\) | −13.1860 | −0.758770 | ||||||||
\(303\) | 15.8314 | 0.909487 | ||||||||
\(304\) | 19.0942 | 1.09513 | ||||||||
\(305\) | −8.62838 | −0.494059 | ||||||||
\(306\) | −0.180872 | −0.0103398 | ||||||||
\(307\) | −14.2468 | −0.813109 | −0.406554 | − | 0.913627i | \(-0.633270\pi\) | ||||
−0.406554 | + | 0.913627i | \(0.633270\pi\) | |||||||
\(308\) | −2.77032 | −0.157854 | ||||||||
\(309\) | −1.17504 | −0.0668457 | ||||||||
\(310\) | 0.483530 | 0.0274627 | ||||||||
\(311\) | 3.14087 | 0.178102 | 0.0890512 | − | 0.996027i | \(-0.471617\pi\) | ||||
0.0890512 | + | 0.996027i | \(0.471617\pi\) | |||||||
\(312\) | 22.7216 | 1.28636 | ||||||||
\(313\) | 29.6973 | 1.67859 | 0.839295 | − | 0.543677i | \(-0.182968\pi\) | ||||
0.839295 | + | 0.543677i | \(0.182968\pi\) | |||||||
\(314\) | 4.73482 | 0.267201 | ||||||||
\(315\) | −0.179714 | −0.0101257 | ||||||||
\(316\) | −4.31178 | −0.242556 | ||||||||
\(317\) | 26.3993 | 1.48273 | 0.741367 | − | 0.671100i | \(-0.234178\pi\) | ||||
0.741367 | + | 0.671100i | \(0.234178\pi\) | |||||||
\(318\) | 21.1113 | 1.18386 | ||||||||
\(319\) | 34.9684 | 1.95785 | ||||||||
\(320\) | −8.84498 | −0.494449 | ||||||||
\(321\) | −11.9608 | −0.667587 | ||||||||
\(322\) | −1.25084 | −0.0697064 | ||||||||
\(323\) | 5.98144 | 0.332816 | ||||||||
\(324\) | 4.48673 | 0.249263 | ||||||||
\(325\) | 4.41019 | 0.244633 | ||||||||
\(326\) | −10.8642 | −0.601710 | ||||||||
\(327\) | −9.14944 | −0.505965 | ||||||||
\(328\) | 19.4503 | 1.07396 | ||||||||
\(329\) | 5.69334 | 0.313884 | ||||||||
\(330\) | −10.5880 | −0.582852 | ||||||||
\(331\) | 17.4298 | 0.958029 | 0.479015 | − | 0.877807i | \(-0.340994\pi\) | ||||
0.479015 | + | 0.877807i | \(0.340994\pi\) | |||||||
\(332\) | −6.35546 | −0.348801 | ||||||||
\(333\) | −1.16275 | −0.0637183 | ||||||||
\(334\) | −4.39346 | −0.240399 | ||||||||
\(335\) | 2.55982 | 0.139858 | ||||||||
\(336\) | 4.45366 | 0.242967 | ||||||||
\(337\) | 16.5637 | 0.902282 | 0.451141 | − | 0.892453i | \(-0.351017\pi\) | ||||
0.451141 | + | 0.892453i | \(0.351017\pi\) | |||||||
\(338\) | −7.81375 | −0.425012 | ||||||||
\(339\) | −2.65728 | −0.144324 | ||||||||
\(340\) | −0.442232 | −0.0239834 | ||||||||
\(341\) | −2.07712 | −0.112483 | ||||||||
\(342\) | −1.56758 | −0.0847650 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −5.01846 | −0.270577 | ||||||||
\(345\) | 1.73393 | 0.0933517 | ||||||||
\(346\) | −8.54627 | −0.459450 | ||||||||
\(347\) | 23.3487 | 1.25342 | 0.626712 | − | 0.779251i | \(-0.284400\pi\) | ||||
0.626712 | + | 0.779251i | \(0.284400\pi\) | |||||||
\(348\) | 6.00682 | 0.321999 | ||||||||
\(349\) | 24.2150 | 1.29620 | 0.648101 | − | 0.761555i | \(-0.275564\pi\) | ||||
0.648101 | + | 0.761555i | \(0.275564\pi\) | |||||||
\(350\) | 1.21148 | 0.0647562 | ||||||||
\(351\) | −23.5501 | −1.25701 | ||||||||
\(352\) | 15.2113 | 0.810764 | ||||||||
\(353\) | 6.44993 | 0.343295 | 0.171647 | − | 0.985158i | \(-0.445091\pi\) | ||||
0.171647 | + | 0.985158i | \(0.445091\pi\) | |||||||
\(354\) | 29.5850 | 1.57243 | ||||||||
\(355\) | −15.5322 | −0.824365 | ||||||||
\(356\) | 3.08923 | 0.163729 | ||||||||
\(357\) | 1.39515 | 0.0738391 | ||||||||
\(358\) | −3.79394 | −0.200516 | ||||||||
\(359\) | 32.5794 | 1.71948 | 0.859739 | − | 0.510734i | \(-0.170626\pi\) | ||||
0.859739 | + | 0.510734i | \(0.170626\pi\) | |||||||
\(360\) | 0.551337 | 0.0290580 | ||||||||
\(361\) | 32.8399 | 1.72841 | ||||||||
\(362\) | −27.1918 | −1.42917 | ||||||||
\(363\) | 27.0104 | 1.41768 | ||||||||
\(364\) | 2.34765 | 0.123050 | ||||||||
\(365\) | −6.22453 | −0.325807 | ||||||||
\(366\) | −17.5546 | −0.917593 | ||||||||
\(367\) | −3.67511 | −0.191839 | −0.0959197 | − | 0.995389i | \(-0.530579\pi\) | ||||
−0.0959197 | + | 0.995389i | \(0.530579\pi\) | |||||||
\(368\) | 2.73814 | 0.142736 | ||||||||
\(369\) | −1.13940 | −0.0593146 | ||||||||
\(370\) | 7.83824 | 0.407491 | ||||||||
\(371\) | 10.3766 | 0.538724 | ||||||||
\(372\) | −0.356805 | −0.0184995 | ||||||||
\(373\) | 0.818134 | 0.0423614 | 0.0211807 | − | 0.999776i | \(-0.493257\pi\) | ||||
0.0211807 | + | 0.999776i | \(0.493257\pi\) | |||||||
\(374\) | −5.23773 | −0.270836 | ||||||||
\(375\) | −1.67937 | −0.0867223 | ||||||||
\(376\) | −17.4663 | −0.900757 | ||||||||
\(377\) | −29.6332 | −1.52619 | ||||||||
\(378\) | −6.46919 | −0.332739 | ||||||||
\(379\) | 7.86409 | 0.403951 | 0.201976 | − | 0.979391i | \(-0.435264\pi\) | ||||
0.201976 | + | 0.979391i | \(0.435264\pi\) | |||||||
\(380\) | −3.83273 | −0.196615 | ||||||||
\(381\) | −8.91323 | −0.456639 | ||||||||
\(382\) | 30.8257 | 1.57718 | ||||||||
\(383\) | −16.6110 | −0.848784 | −0.424392 | − | 0.905479i | \(-0.639512\pi\) | ||||
−0.424392 | + | 0.905479i | \(0.639512\pi\) | |||||||
\(384\) | −8.17804 | −0.417334 | ||||||||
\(385\) | −5.20420 | −0.265230 | ||||||||
\(386\) | 19.4001 | 0.987437 | ||||||||
\(387\) | 0.293981 | 0.0149439 | ||||||||
\(388\) | 4.34258 | 0.220461 | ||||||||
\(389\) | 16.1772 | 0.820219 | 0.410110 | − | 0.912036i | \(-0.365490\pi\) | ||||
0.410110 | + | 0.912036i | \(0.365490\pi\) | |||||||
\(390\) | 8.97261 | 0.454346 | ||||||||
\(391\) | 0.857747 | 0.0433781 | ||||||||
\(392\) | 3.06785 | 0.154950 | ||||||||
\(393\) | 15.6940 | 0.791658 | ||||||||
\(394\) | −29.9599 | −1.50936 | ||||||||
\(395\) | −8.09991 | −0.407551 | ||||||||
\(396\) | −0.497866 | −0.0250187 | ||||||||
\(397\) | 1.58954 | 0.0797767 | 0.0398884 | − | 0.999204i | \(-0.487300\pi\) | ||||
0.0398884 | + | 0.999204i | \(0.487300\pi\) | |||||||
\(398\) | 2.11223 | 0.105876 | ||||||||
\(399\) | 12.0915 | 0.605330 | ||||||||
\(400\) | −2.65198 | −0.132599 | ||||||||
\(401\) | 0.780173 | 0.0389600 | 0.0194800 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194800 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(402\) | 5.20801 | 0.259752 | ||||||||
\(403\) | 1.76022 | 0.0876826 | ||||||||
\(404\) | −5.01820 | −0.249665 | ||||||||
\(405\) | 8.42856 | 0.418819 | ||||||||
\(406\) | −8.14024 | −0.403993 | ||||||||
\(407\) | −33.6711 | −1.66901 | ||||||||
\(408\) | −4.28011 | −0.211897 | ||||||||
\(409\) | −31.1049 | −1.53804 | −0.769018 | − | 0.639227i | \(-0.779254\pi\) | ||||
−0.769018 | + | 0.639227i | \(0.779254\pi\) | |||||||
\(410\) | 7.68081 | 0.379328 | ||||||||
\(411\) | −21.4900 | −1.06002 | ||||||||
\(412\) | 0.372462 | 0.0183499 | ||||||||
\(413\) | 14.5415 | 0.715543 | ||||||||
\(414\) | −0.224793 | −0.0110480 | ||||||||
\(415\) | −11.9391 | −0.586066 | ||||||||
\(416\) | −12.8905 | −0.632008 | ||||||||
\(417\) | 2.65626 | 0.130078 | ||||||||
\(418\) | −45.3942 | −2.22030 | ||||||||
\(419\) | −11.7006 | −0.571611 | −0.285806 | − | 0.958288i | \(-0.592261\pi\) | ||||
−0.285806 | + | 0.958288i | \(0.592261\pi\) | |||||||
\(420\) | −0.893970 | −0.0436213 | ||||||||
\(421\) | −31.0490 | −1.51323 | −0.756617 | − | 0.653858i | \(-0.773149\pi\) | ||||
−0.756617 | + | 0.653858i | \(0.773149\pi\) | |||||||
\(422\) | 12.7423 | 0.620285 | ||||||||
\(423\) | 1.02317 | 0.0497484 | ||||||||
\(424\) | −31.8338 | −1.54598 | ||||||||
\(425\) | −0.830757 | −0.0402976 | ||||||||
\(426\) | −31.6006 | −1.53105 | ||||||||
\(427\) | −8.62838 | −0.417556 | ||||||||
\(428\) | 3.79132 | 0.183260 | ||||||||
\(429\) | −38.5441 | −1.86092 | ||||||||
\(430\) | −1.98176 | −0.0955690 | ||||||||
\(431\) | 7.44759 | 0.358738 | 0.179369 | − | 0.983782i | \(-0.442594\pi\) | ||||
0.179369 | + | 0.983782i | \(0.442594\pi\) | |||||||
\(432\) | 14.1614 | 0.681339 | ||||||||
\(433\) | 18.3812 | 0.883344 | 0.441672 | − | 0.897177i | \(-0.354385\pi\) | ||||
0.441672 | + | 0.897177i | \(0.354385\pi\) | |||||||
\(434\) | 0.483530 | 0.0232102 | ||||||||
\(435\) | 11.2841 | 0.541033 | ||||||||
\(436\) | 2.90018 | 0.138893 | ||||||||
\(437\) | 7.43391 | 0.355612 | ||||||||
\(438\) | −12.6639 | −0.605106 | ||||||||
\(439\) | 9.57580 | 0.457028 | 0.228514 | − | 0.973541i | \(-0.426613\pi\) | ||||
0.228514 | + | 0.973541i | \(0.426613\pi\) | |||||||
\(440\) | 15.9657 | 0.761135 | ||||||||
\(441\) | −0.179714 | −0.00855782 | ||||||||
\(442\) | 4.43860 | 0.211123 | ||||||||
\(443\) | −10.9484 | −0.520174 | −0.260087 | − | 0.965585i | \(-0.583751\pi\) | ||||
−0.260087 | + | 0.965585i | \(0.583751\pi\) | |||||||
\(444\) | −5.78397 | −0.274495 | ||||||||
\(445\) | 5.80329 | 0.275102 | ||||||||
\(446\) | −4.92119 | −0.233025 | ||||||||
\(447\) | 2.46113 | 0.116408 | ||||||||
\(448\) | −8.84498 | −0.417886 | ||||||||
\(449\) | 27.2355 | 1.28532 | 0.642661 | − | 0.766150i | \(-0.277830\pi\) | ||||
0.642661 | + | 0.766150i | \(0.277830\pi\) | |||||||
\(450\) | 0.217720 | 0.0102634 | ||||||||
\(451\) | −32.9948 | −1.55367 | ||||||||
\(452\) | 0.842301 | 0.0396185 | ||||||||
\(453\) | 18.2787 | 0.858808 | ||||||||
\(454\) | 16.1686 | 0.758832 | ||||||||
\(455\) | 4.41019 | 0.206753 | ||||||||
\(456\) | −37.0948 | −1.73712 | ||||||||
\(457\) | −0.651536 | −0.0304776 | −0.0152388 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152388 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(458\) | −1.21148 | −0.0566086 | ||||||||
\(459\) | 4.43618 | 0.207063 | ||||||||
\(460\) | −0.549619 | −0.0256261 | ||||||||
\(461\) | 14.3290 | 0.667369 | 0.333684 | − | 0.942685i | \(-0.391708\pi\) | ||||
0.333684 | + | 0.942685i | \(0.391708\pi\) | |||||||
\(462\) | −10.5880 | −0.492600 | ||||||||
\(463\) | −8.87000 | −0.412224 | −0.206112 | − | 0.978528i | \(-0.566081\pi\) | ||||
−0.206112 | + | 0.978528i | \(0.566081\pi\) | |||||||
\(464\) | 17.8194 | 0.827244 | ||||||||
\(465\) | −0.670278 | −0.0310834 | ||||||||
\(466\) | −18.4270 | −0.853615 | ||||||||
\(467\) | 14.8062 | 0.685150 | 0.342575 | − | 0.939491i | \(-0.388701\pi\) | ||||
0.342575 | + | 0.939491i | \(0.388701\pi\) | |||||||
\(468\) | 0.421906 | 0.0195026 | ||||||||
\(469\) | 2.55982 | 0.118202 | ||||||||
\(470\) | −6.89735 | −0.318151 | ||||||||
\(471\) | −6.56349 | −0.302430 | ||||||||
\(472\) | −44.6113 | −2.05340 | ||||||||
\(473\) | 8.51314 | 0.391435 | ||||||||
\(474\) | −16.4794 | −0.756924 | ||||||||
\(475\) | −7.19999 | −0.330358 | ||||||||
\(476\) | −0.442232 | −0.0202697 | ||||||||
\(477\) | 1.86482 | 0.0853841 | ||||||||
\(478\) | 15.6113 | 0.714043 | ||||||||
\(479\) | 21.2236 | 0.969730 | 0.484865 | − | 0.874589i | \(-0.338869\pi\) | ||||
0.484865 | + | 0.874589i | \(0.338869\pi\) | |||||||
\(480\) | 4.90861 | 0.224047 | ||||||||
\(481\) | 28.5339 | 1.30103 | ||||||||
\(482\) | −7.74675 | −0.352855 | ||||||||
\(483\) | 1.73393 | 0.0788966 | ||||||||
\(484\) | −8.56172 | −0.389169 | ||||||||
\(485\) | 8.15777 | 0.370425 | ||||||||
\(486\) | −2.25950 | −0.102493 | ||||||||
\(487\) | 31.8562 | 1.44354 | 0.721770 | − | 0.692132i | \(-0.243329\pi\) | ||||
0.721770 | + | 0.692132i | \(0.243329\pi\) | |||||||
\(488\) | 26.4706 | 1.19827 | ||||||||
\(489\) | 15.0601 | 0.681041 | ||||||||
\(490\) | 1.21148 | 0.0547289 | ||||||||
\(491\) | −18.6585 | −0.842046 | −0.421023 | − | 0.907050i | \(-0.638329\pi\) | ||||
−0.421023 | + | 0.907050i | \(0.638329\pi\) | |||||||
\(492\) | −5.66781 | −0.255524 | ||||||||
\(493\) | 5.58208 | 0.251404 | ||||||||
\(494\) | 38.4684 | 1.73078 | ||||||||
\(495\) | −0.935268 | −0.0420372 | ||||||||
\(496\) | −1.05847 | −0.0475268 | ||||||||
\(497\) | −15.5322 | −0.696715 | ||||||||
\(498\) | −24.2903 | −1.08847 | ||||||||
\(499\) | −12.6494 | −0.566264 | −0.283132 | − | 0.959081i | \(-0.591373\pi\) | ||||
−0.283132 | + | 0.959081i | \(0.591373\pi\) | |||||||
\(500\) | 0.532324 | 0.0238063 | ||||||||
\(501\) | 6.09029 | 0.272094 | ||||||||
\(502\) | 10.9506 | 0.488751 | ||||||||
\(503\) | 29.5547 | 1.31778 | 0.658889 | − | 0.752240i | \(-0.271027\pi\) | ||||
0.658889 | + | 0.752240i | \(0.271027\pi\) | |||||||
\(504\) | 0.551337 | 0.0245585 | ||||||||
\(505\) | −9.42696 | −0.419494 | ||||||||
\(506\) | −6.50960 | −0.289387 | ||||||||
\(507\) | 10.8316 | 0.481046 | ||||||||
\(508\) | 2.82530 | 0.125353 | ||||||||
\(509\) | −16.4136 | −0.727520 | −0.363760 | − | 0.931493i | \(-0.618507\pi\) | ||||
−0.363760 | + | 0.931493i | \(0.618507\pi\) | |||||||
\(510\) | −1.69019 | −0.0748429 | ||||||||
\(511\) | −6.22453 | −0.275357 | ||||||||
\(512\) | 24.0232 | 1.06169 | ||||||||
\(513\) | 38.4474 | 1.69749 | ||||||||
\(514\) | 21.3714 | 0.942651 | ||||||||
\(515\) | 0.699690 | 0.0308320 | ||||||||
\(516\) | 1.46238 | 0.0643775 | ||||||||
\(517\) | 29.6292 | 1.30309 | ||||||||
\(518\) | 7.83824 | 0.344392 | ||||||||
\(519\) | 11.8470 | 0.520025 | ||||||||
\(520\) | −13.5298 | −0.593321 | ||||||||
\(521\) | −12.0011 | −0.525776 | −0.262888 | − | 0.964826i | \(-0.584675\pi\) | ||||
−0.262888 | + | 0.964826i | \(0.584675\pi\) | |||||||
\(522\) | −1.46292 | −0.0640301 | ||||||||
\(523\) | −37.2948 | −1.63079 | −0.815393 | − | 0.578907i | \(-0.803479\pi\) | ||||
−0.815393 | + | 0.578907i | \(0.803479\pi\) | |||||||
\(524\) | −4.97466 | −0.217319 | ||||||||
\(525\) | −1.67937 | −0.0732937 | ||||||||
\(526\) | −22.0204 | −0.960134 | ||||||||
\(527\) | −0.331576 | −0.0144437 | ||||||||
\(528\) | 23.1777 | 1.00868 | ||||||||
\(529\) | −21.9340 | −0.953651 | ||||||||
\(530\) | −12.5710 | −0.546048 | ||||||||
\(531\) | 2.61332 | 0.113409 | ||||||||
\(532\) | −3.83273 | −0.166170 | ||||||||
\(533\) | 27.9608 | 1.21112 | ||||||||
\(534\) | 11.8069 | 0.510934 | ||||||||
\(535\) | 7.12220 | 0.307919 | ||||||||
\(536\) | −7.85316 | −0.339205 | ||||||||
\(537\) | 5.25922 | 0.226952 | ||||||||
\(538\) | 6.24456 | 0.269222 | ||||||||
\(539\) | −5.20420 | −0.224161 | ||||||||
\(540\) | −2.84257 | −0.122325 | ||||||||
\(541\) | 16.4106 | 0.705549 | 0.352774 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352774 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(542\) | −19.9309 | −0.856107 | ||||||||
\(543\) | 37.6938 | 1.61759 | ||||||||
\(544\) | 2.42821 | 0.104109 | ||||||||
\(545\) | 5.44814 | 0.233373 | ||||||||
\(546\) | 8.97261 | 0.383992 | ||||||||
\(547\) | −3.72065 | −0.159084 | −0.0795418 | − | 0.996832i | \(-0.525346\pi\) | ||||
−0.0795418 | + | 0.996832i | \(0.525346\pi\) | |||||||
\(548\) | 6.81186 | 0.290988 | ||||||||
\(549\) | −1.55064 | −0.0661798 | ||||||||
\(550\) | 6.30476 | 0.268836 | ||||||||
\(551\) | 48.3787 | 2.06100 | ||||||||
\(552\) | −5.31944 | −0.226411 | ||||||||
\(553\) | −8.09991 | −0.344443 | ||||||||
\(554\) | −35.8504 | −1.52314 | ||||||||
\(555\) | −10.8655 | −0.461215 | ||||||||
\(556\) | −0.841977 | −0.0357078 | ||||||||
\(557\) | −18.5330 | −0.785268 | −0.392634 | − | 0.919695i | \(-0.628436\pi\) | ||||
−0.392634 | + | 0.919695i | \(0.628436\pi\) | |||||||
\(558\) | 0.0868972 | 0.00367865 | ||||||||
\(559\) | −7.21429 | −0.305132 | ||||||||
\(560\) | −2.65198 | −0.112067 | ||||||||
\(561\) | 7.26063 | 0.306544 | ||||||||
\(562\) | −7.85999 | −0.331554 | ||||||||
\(563\) | −22.1107 | −0.931857 | −0.465928 | − | 0.884822i | \(-0.654280\pi\) | ||||
−0.465928 | + | 0.884822i | \(0.654280\pi\) | |||||||
\(564\) | 5.08967 | 0.214314 | ||||||||
\(565\) | 1.58231 | 0.0665682 | ||||||||
\(566\) | 25.3940 | 1.06739 | ||||||||
\(567\) | 8.42856 | 0.353966 | ||||||||
\(568\) | 47.6505 | 1.99937 | ||||||||
\(569\) | 0.831052 | 0.0348395 | 0.0174198 | − | 0.999848i | \(-0.494455\pi\) | ||||
0.0174198 | + | 0.999848i | \(0.494455\pi\) | |||||||
\(570\) | −14.6485 | −0.613559 | ||||||||
\(571\) | 23.5897 | 0.987200 | 0.493600 | − | 0.869689i | \(-0.335681\pi\) | ||||
0.493600 | + | 0.869689i | \(0.335681\pi\) | |||||||
\(572\) | 12.2176 | 0.510845 | ||||||||
\(573\) | −42.7311 | −1.78512 | ||||||||
\(574\) | 7.68081 | 0.320591 | ||||||||
\(575\) | −1.03249 | −0.0430578 | ||||||||
\(576\) | −1.58957 | −0.0662320 | ||||||||
\(577\) | 46.7857 | 1.94771 | 0.973857 | − | 0.227163i | \(-0.0729450\pi\) | ||||
0.973857 | + | 0.227163i | \(0.0729450\pi\) | |||||||
\(578\) | 19.7590 | 0.821866 | ||||||||
\(579\) | −26.8927 | −1.11762 | ||||||||
\(580\) | −3.57683 | −0.148520 | ||||||||
\(581\) | −11.9391 | −0.495316 | ||||||||
\(582\) | 16.5971 | 0.687973 | ||||||||
\(583\) | 54.0017 | 2.23652 | ||||||||
\(584\) | 19.0959 | 0.790196 | ||||||||
\(585\) | 0.792574 | 0.0327689 | ||||||||
\(586\) | 11.4857 | 0.474469 | ||||||||
\(587\) | −22.4244 | −0.925552 | −0.462776 | − | 0.886475i | \(-0.653147\pi\) | ||||
−0.462776 | + | 0.886475i | \(0.653147\pi\) | |||||||
\(588\) | −0.893970 | −0.0368667 | ||||||||
\(589\) | −2.87369 | −0.118408 | ||||||||
\(590\) | −17.6167 | −0.725270 | ||||||||
\(591\) | 41.5309 | 1.70835 | ||||||||
\(592\) | −17.1583 | −0.705202 | ||||||||
\(593\) | 18.9139 | 0.776700 | 0.388350 | − | 0.921512i | \(-0.373045\pi\) | ||||
0.388350 | + | 0.921512i | \(0.373045\pi\) | |||||||
\(594\) | −33.6669 | −1.38137 | ||||||||
\(595\) | −0.830757 | −0.0340577 | ||||||||
\(596\) | −0.780126 | −0.0319552 | ||||||||
\(597\) | −2.92801 | −0.119835 | ||||||||
\(598\) | 5.51642 | 0.225583 | ||||||||
\(599\) | 27.9809 | 1.14327 | 0.571635 | − | 0.820508i | \(-0.306309\pi\) | ||||
0.571635 | + | 0.820508i | \(0.306309\pi\) | |||||||
\(600\) | 5.15206 | 0.210332 | ||||||||
\(601\) | −23.5211 | −0.959444 | −0.479722 | − | 0.877420i | \(-0.659263\pi\) | ||||
−0.479722 | + | 0.877420i | \(0.659263\pi\) | |||||||
\(602\) | −1.98176 | −0.0807705 | ||||||||
\(603\) | 0.460037 | 0.0187341 | ||||||||
\(604\) | −5.79395 | −0.235752 | ||||||||
\(605\) | −16.0837 | −0.653894 | ||||||||
\(606\) | −19.1793 | −0.779106 | ||||||||
\(607\) | 24.4743 | 0.993383 | 0.496691 | − | 0.867927i | \(-0.334548\pi\) | ||||
0.496691 | + | 0.867927i | \(0.334548\pi\) | |||||||
\(608\) | 21.0448 | 0.853478 | ||||||||
\(609\) | 11.2841 | 0.457256 | ||||||||
\(610\) | 10.4531 | 0.423233 | ||||||||
\(611\) | −25.1087 | −1.01579 | ||||||||
\(612\) | −0.0794754 | −0.00321260 | ||||||||
\(613\) | −28.3221 | −1.14392 | −0.571959 | − | 0.820283i | \(-0.693816\pi\) | ||||
−0.571959 | + | 0.820283i | \(0.693816\pi\) | |||||||
\(614\) | 17.2597 | 0.696544 | ||||||||
\(615\) | −10.6473 | −0.429340 | ||||||||
\(616\) | 15.9657 | 0.643277 | ||||||||
\(617\) | 4.95914 | 0.199647 | 0.0998237 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998237 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(618\) | 1.42353 | 0.0572629 | ||||||||
\(619\) | −18.2756 | −0.734557 | −0.367278 | − | 0.930111i | \(-0.619710\pi\) | ||||
−0.367278 | + | 0.930111i | \(0.619710\pi\) | |||||||
\(620\) | 0.212464 | 0.00853275 | ||||||||
\(621\) | 5.51341 | 0.221245 | ||||||||
\(622\) | −3.80509 | −0.152570 | ||||||||
\(623\) | 5.80329 | 0.232504 | ||||||||
\(624\) | −19.6415 | −0.786289 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −35.9776 | −1.43795 | ||||||||
\(627\) | 62.9263 | 2.51303 | ||||||||
\(628\) | 2.08048 | 0.0830204 | ||||||||
\(629\) | −5.37499 | −0.214315 | ||||||||
\(630\) | 0.217720 | 0.00867416 | ||||||||
\(631\) | 37.5771 | 1.49592 | 0.747960 | − | 0.663744i | \(-0.231034\pi\) | ||||
0.747960 | + | 0.663744i | \(0.231034\pi\) | |||||||
\(632\) | 24.8493 | 0.988453 | ||||||||
\(633\) | −17.6636 | −0.702065 | ||||||||
\(634\) | −31.9822 | −1.27017 | ||||||||
\(635\) | 5.30748 | 0.210621 | ||||||||
\(636\) | 9.27633 | 0.367831 | ||||||||
\(637\) | 4.41019 | 0.174738 | ||||||||
\(638\) | −42.3634 | −1.67718 | ||||||||
\(639\) | −2.79136 | −0.110425 | ||||||||
\(640\) | 4.86970 | 0.192492 | ||||||||
\(641\) | 39.1973 | 1.54820 | 0.774100 | − | 0.633063i | \(-0.218203\pi\) | ||||
0.774100 | + | 0.633063i | \(0.218203\pi\) | |||||||
\(642\) | 14.4902 | 0.571884 | ||||||||
\(643\) | 11.1838 | 0.441044 | 0.220522 | − | 0.975382i | \(-0.429224\pi\) | ||||
0.220522 | + | 0.975382i | \(0.429224\pi\) | |||||||
\(644\) | −0.549619 | −0.0216580 | ||||||||
\(645\) | 2.74715 | 0.108169 | ||||||||
\(646\) | −7.24638 | −0.285105 | ||||||||
\(647\) | 8.01306 | 0.315026 | 0.157513 | − | 0.987517i | \(-0.449652\pi\) | ||||
0.157513 | + | 0.987517i | \(0.449652\pi\) | |||||||
\(648\) | −25.8576 | −1.01578 | ||||||||
\(649\) | 75.6770 | 2.97058 | ||||||||
\(650\) | −5.34284 | −0.209563 | ||||||||
\(651\) | −0.670278 | −0.0262703 | ||||||||
\(652\) | −4.77373 | −0.186954 | ||||||||
\(653\) | −31.1546 | −1.21917 | −0.609586 | − | 0.792720i | \(-0.708664\pi\) | ||||
−0.609586 | + | 0.792720i | \(0.708664\pi\) | |||||||
\(654\) | 11.0843 | 0.433432 | ||||||||
\(655\) | −9.34518 | −0.365146 | ||||||||
\(656\) | −16.8137 | −0.656464 | ||||||||
\(657\) | −1.11864 | −0.0436422 | ||||||||
\(658\) | −6.89735 | −0.268887 | ||||||||
\(659\) | −5.48445 | −0.213644 | −0.106822 | − | 0.994278i | \(-0.534067\pi\) | ||||
−0.106822 | + | 0.994278i | \(0.534067\pi\) | |||||||
\(660\) | −4.65239 | −0.181094 | ||||||||
\(661\) | 40.0157 | 1.55643 | 0.778215 | − | 0.627998i | \(-0.216125\pi\) | ||||
0.778215 | + | 0.627998i | \(0.216125\pi\) | |||||||
\(662\) | −21.1158 | −0.820690 | ||||||||
\(663\) | −6.15287 | −0.238958 | ||||||||
\(664\) | 36.6273 | 1.42141 | ||||||||
\(665\) | −7.19999 | −0.279204 | ||||||||
\(666\) | 1.40864 | 0.0545838 | ||||||||
\(667\) | 6.93757 | 0.268624 | ||||||||
\(668\) | −1.93049 | −0.0746930 | ||||||||
\(669\) | 6.82185 | 0.263748 | ||||||||
\(670\) | −3.10117 | −0.119809 | ||||||||
\(671\) | −44.9038 | −1.73349 | ||||||||
\(672\) | 4.90861 | 0.189354 | ||||||||
\(673\) | −30.4785 | −1.17486 | −0.587431 | − | 0.809274i | \(-0.699861\pi\) | ||||
−0.587431 | + | 0.809274i | \(0.699861\pi\) | |||||||
\(674\) | −20.0665 | −0.772933 | ||||||||
\(675\) | −5.33992 | −0.205534 | ||||||||
\(676\) | −3.43337 | −0.132053 | ||||||||
\(677\) | 14.6811 | 0.564241 | 0.282121 | − | 0.959379i | \(-0.408962\pi\) | ||||
0.282121 | + | 0.959379i | \(0.408962\pi\) | |||||||
\(678\) | 3.21923 | 0.123634 | ||||||||
\(679\) | 8.15777 | 0.313067 | ||||||||
\(680\) | 2.54864 | 0.0977359 | ||||||||
\(681\) | −22.4133 | −0.858878 | ||||||||
\(682\) | 2.51639 | 0.0963574 | ||||||||
\(683\) | 13.7959 | 0.527886 | 0.263943 | − | 0.964538i | \(-0.414977\pi\) | ||||
0.263943 | + | 0.964538i | \(0.414977\pi\) | |||||||
\(684\) | −0.688796 | −0.0263368 | ||||||||
\(685\) | 12.7964 | 0.488927 | ||||||||
\(686\) | 1.21148 | 0.0462544 | ||||||||
\(687\) | 1.67937 | 0.0640720 | ||||||||
\(688\) | 4.33817 | 0.165391 | ||||||||
\(689\) | −45.7626 | −1.74342 | ||||||||
\(690\) | −2.10062 | −0.0799691 | ||||||||
\(691\) | 33.3779 | 1.26975 | 0.634877 | − | 0.772614i | \(-0.281051\pi\) | ||||
0.634877 | + | 0.772614i | \(0.281051\pi\) | |||||||
\(692\) | −3.75524 | −0.142753 | ||||||||
\(693\) | −0.935268 | −0.0355279 | ||||||||
\(694\) | −28.2864 | −1.07374 | ||||||||
\(695\) | −1.58170 | −0.0599973 | ||||||||
\(696\) | −34.6181 | −1.31219 | ||||||||
\(697\) | −5.26703 | −0.199503 | ||||||||
\(698\) | −29.3360 | −1.11038 | ||||||||
\(699\) | 25.5439 | 0.966157 | ||||||||
\(700\) | 0.532324 | 0.0201200 | ||||||||
\(701\) | −5.55442 | −0.209787 | −0.104894 | − | 0.994483i | \(-0.533450\pi\) | ||||
−0.104894 | + | 0.994483i | \(0.533450\pi\) | |||||||
\(702\) | 28.5303 | 1.07681 | ||||||||
\(703\) | −46.5839 | −1.75694 | ||||||||
\(704\) | −46.0310 | −1.73486 | ||||||||
\(705\) | 9.56122 | 0.360097 | ||||||||
\(706\) | −7.81393 | −0.294081 | ||||||||
\(707\) | −9.42696 | −0.354537 | ||||||||
\(708\) | 12.9997 | 0.488559 | ||||||||
\(709\) | 31.4048 | 1.17943 | 0.589717 | − | 0.807610i | \(-0.299239\pi\) | ||||
0.589717 | + | 0.807610i | \(0.299239\pi\) | |||||||
\(710\) | 18.8169 | 0.706186 | ||||||||
\(711\) | −1.45567 | −0.0545918 | ||||||||
\(712\) | −17.8036 | −0.667219 | ||||||||
\(713\) | −0.412092 | −0.0154330 | ||||||||
\(714\) | −1.69019 | −0.0632538 | ||||||||
\(715\) | 22.9515 | 0.858337 | ||||||||
\(716\) | −1.66706 | −0.0623010 | ||||||||
\(717\) | −21.6406 | −0.808184 | ||||||||
\(718\) | −39.4692 | −1.47298 | ||||||||
\(719\) | −36.5380 | −1.36264 | −0.681318 | − | 0.731987i | \(-0.738593\pi\) | ||||
−0.681318 | + | 0.731987i | \(0.738593\pi\) | |||||||
\(720\) | −0.476599 | −0.0177618 | ||||||||
\(721\) | 0.699690 | 0.0260578 | ||||||||
\(722\) | −39.7847 | −1.48063 | ||||||||
\(723\) | 10.7387 | 0.399376 | ||||||||
\(724\) | −11.9481 | −0.444048 | ||||||||
\(725\) | −6.71927 | −0.249547 | ||||||||
\(726\) | −32.7225 | −1.21445 | ||||||||
\(727\) | 31.0389 | 1.15117 | 0.575585 | − | 0.817742i | \(-0.304774\pi\) | ||||
0.575585 | + | 0.817742i | \(0.304774\pi\) | |||||||
\(728\) | −13.5298 | −0.501448 | ||||||||
\(729\) | 28.4178 | 1.05251 | ||||||||
\(730\) | 7.54088 | 0.279100 | ||||||||
\(731\) | 1.35897 | 0.0502634 | ||||||||
\(732\) | −7.71351 | −0.285099 | ||||||||
\(733\) | 1.66939 | 0.0616602 | 0.0308301 | − | 0.999525i | \(-0.490185\pi\) | ||||
0.0308301 | + | 0.999525i | \(0.490185\pi\) | |||||||
\(734\) | 4.45231 | 0.164338 | ||||||||
\(735\) | −1.67937 | −0.0619445 | ||||||||
\(736\) | 3.01785 | 0.111239 | ||||||||
\(737\) | 13.3218 | 0.490716 | ||||||||
\(738\) | 1.38035 | 0.0508114 | ||||||||
\(739\) | −40.7099 | −1.49754 | −0.748769 | − | 0.662831i | \(-0.769355\pi\) | ||||
−0.748769 | + | 0.662831i | \(0.769355\pi\) | |||||||
\(740\) | 3.44413 | 0.126609 | ||||||||
\(741\) | −53.3256 | −1.95896 | ||||||||
\(742\) | −12.5710 | −0.461495 | ||||||||
\(743\) | 2.42226 | 0.0888639 | 0.0444320 | − | 0.999012i | \(-0.485852\pi\) | ||||
0.0444320 | + | 0.999012i | \(0.485852\pi\) | |||||||
\(744\) | 2.05631 | 0.0753881 | ||||||||
\(745\) | −1.46551 | −0.0536921 | ||||||||
\(746\) | −0.991150 | −0.0362886 | ||||||||
\(747\) | −2.14562 | −0.0785042 | ||||||||
\(748\) | −2.30146 | −0.0841498 | ||||||||
\(749\) | 7.12220 | 0.260239 | ||||||||
\(750\) | 2.03452 | 0.0742901 | ||||||||
\(751\) | −28.5100 | −1.04034 | −0.520172 | − | 0.854061i | \(-0.674132\pi\) | ||||
−0.520172 | + | 0.854061i | \(0.674132\pi\) | |||||||
\(752\) | 15.0986 | 0.550590 | ||||||||
\(753\) | −15.1800 | −0.553189 | ||||||||
\(754\) | 35.9000 | 1.30740 | ||||||||
\(755\) | −10.8842 | −0.396118 | ||||||||
\(756\) | −2.84257 | −0.103383 | ||||||||
\(757\) | 26.2780 | 0.955089 | 0.477544 | − | 0.878608i | \(-0.341527\pi\) | ||||
0.477544 | + | 0.878608i | \(0.341527\pi\) | |||||||
\(758\) | −9.52717 | −0.346042 | ||||||||
\(759\) | 9.02372 | 0.327540 | ||||||||
\(760\) | 22.0885 | 0.801234 | ||||||||
\(761\) | −44.1265 | −1.59958 | −0.799792 | − | 0.600277i | \(-0.795057\pi\) | ||||
−0.799792 | + | 0.600277i | \(0.795057\pi\) | |||||||
\(762\) | 10.7982 | 0.391177 | ||||||||
\(763\) | 5.44814 | 0.197236 | ||||||||
\(764\) | 13.5448 | 0.490035 | ||||||||
\(765\) | −0.149299 | −0.00539791 | ||||||||
\(766\) | 20.1239 | 0.727105 | ||||||||
\(767\) | −64.1310 | −2.31563 | ||||||||
\(768\) | −19.8005 | −0.714488 | ||||||||
\(769\) | 50.7840 | 1.83132 | 0.915659 | − | 0.401956i | \(-0.131670\pi\) | ||||
0.915659 | + | 0.401956i | \(0.131670\pi\) | |||||||
\(770\) | 6.30476 | 0.227208 | ||||||||
\(771\) | −29.6254 | −1.06693 | ||||||||
\(772\) | 8.52441 | 0.306800 | ||||||||
\(773\) | −33.1988 | −1.19408 | −0.597038 | − | 0.802213i | \(-0.703656\pi\) | ||||
−0.597038 | + | 0.802213i | \(0.703656\pi\) | |||||||
\(774\) | −0.356151 | −0.0128016 | ||||||||
\(775\) | 0.399125 | 0.0143370 | ||||||||
\(776\) | −25.0268 | −0.898411 | ||||||||
\(777\) | −10.8655 | −0.389798 | ||||||||
\(778\) | −19.5984 | −0.702635 | ||||||||
\(779\) | −45.6482 | −1.63552 | ||||||||
\(780\) | 3.94258 | 0.141167 | ||||||||
\(781\) | −80.8327 | −2.89242 | ||||||||
\(782\) | −1.03914 | −0.0371596 | ||||||||
\(783\) | 35.8803 | 1.28226 | ||||||||
\(784\) | −2.65198 | −0.0947137 | ||||||||
\(785\) | 3.90830 | 0.139493 | ||||||||
\(786\) | −19.0129 | −0.678169 | ||||||||
\(787\) | −45.7887 | −1.63219 | −0.816096 | − | 0.577916i | \(-0.803866\pi\) | ||||
−0.816096 | + | 0.577916i | \(0.803866\pi\) | |||||||
\(788\) | −13.1644 | −0.468962 | ||||||||
\(789\) | 30.5250 | 1.08672 | ||||||||
\(790\) | 9.81285 | 0.349126 | ||||||||
\(791\) | 1.58231 | 0.0562604 | ||||||||
\(792\) | 2.86926 | 0.101955 | ||||||||
\(793\) | 38.0528 | 1.35129 | ||||||||
\(794\) | −1.92569 | −0.0683402 | ||||||||
\(795\) | 17.4261 | 0.618040 | ||||||||
\(796\) | 0.928115 | 0.0328962 | ||||||||
\(797\) | 19.1935 | 0.679868 | 0.339934 | − | 0.940449i | \(-0.389595\pi\) | ||||
0.339934 | + | 0.940449i | \(0.389595\pi\) | |||||||
\(798\) | −14.6485 | −0.518552 | ||||||||
\(799\) | 4.72978 | 0.167328 | ||||||||
\(800\) | −2.92289 | −0.103340 | ||||||||
\(801\) | 1.04293 | 0.0368503 | ||||||||
\(802\) | −0.945161 | −0.0333748 | ||||||||
\(803\) | −32.3937 | −1.14315 | ||||||||
\(804\) | 2.28840 | 0.0807058 | ||||||||
\(805\) | −1.03249 | −0.0363905 | ||||||||
\(806\) | −2.13246 | −0.0751127 | ||||||||
\(807\) | −8.65632 | −0.304717 | ||||||||
\(808\) | 28.9205 | 1.01742 | ||||||||
\(809\) | −3.73090 | −0.131171 | −0.0655857 | − | 0.997847i | \(-0.520892\pi\) | ||||
−0.0655857 | + | 0.997847i | \(0.520892\pi\) | |||||||
\(810\) | −10.2110 | −0.358778 | ||||||||
\(811\) | −50.0738 | −1.75833 | −0.879165 | − | 0.476518i | \(-0.841899\pi\) | ||||
−0.879165 | + | 0.476518i | \(0.841899\pi\) | |||||||
\(812\) | −3.57683 | −0.125522 | ||||||||
\(813\) | 27.6286 | 0.968978 | ||||||||
\(814\) | 40.7917 | 1.42975 | ||||||||
\(815\) | −8.96770 | −0.314125 | ||||||||
\(816\) | 3.69991 | 0.129523 | ||||||||
\(817\) | 11.7779 | 0.412057 | ||||||||
\(818\) | 37.6828 | 1.31755 | ||||||||
\(819\) | 0.792574 | 0.0276948 | ||||||||
\(820\) | 3.37496 | 0.117859 | ||||||||
\(821\) | 41.5748 | 1.45097 | 0.725485 | − | 0.688238i | \(-0.241615\pi\) | ||||
0.725485 | + | 0.688238i | \(0.241615\pi\) | |||||||
\(822\) | 26.0346 | 0.908061 | ||||||||
\(823\) | −32.8745 | −1.14593 | −0.572967 | − | 0.819578i | \(-0.694208\pi\) | ||||
−0.572967 | + | 0.819578i | \(0.694208\pi\) | |||||||
\(824\) | −2.14655 | −0.0747785 | ||||||||
\(825\) | −8.73977 | −0.304280 | ||||||||
\(826\) | −17.6167 | −0.612965 | ||||||||
\(827\) | 15.5065 | 0.539214 | 0.269607 | − | 0.962970i | \(-0.413106\pi\) | ||||
0.269607 | + | 0.962970i | \(0.413106\pi\) | |||||||
\(828\) | −0.0987743 | −0.00343265 | ||||||||
\(829\) | 43.5863 | 1.51382 | 0.756908 | − | 0.653522i | \(-0.226709\pi\) | ||||
0.756908 | + | 0.653522i | \(0.226709\pi\) | |||||||
\(830\) | 14.4639 | 0.502049 | ||||||||
\(831\) | 49.6965 | 1.72395 | ||||||||
\(832\) | 39.0080 | 1.35236 | ||||||||
\(833\) | −0.830757 | −0.0287840 | ||||||||
\(834\) | −3.21800 | −0.111430 | ||||||||
\(835\) | −3.62653 | −0.125501 | ||||||||
\(836\) | −19.9463 | −0.689857 | ||||||||
\(837\) | −2.13129 | −0.0736683 | ||||||||
\(838\) | 14.1750 | 0.489667 | ||||||||
\(839\) | −8.93743 | −0.308554 | −0.154277 | − | 0.988028i | \(-0.549305\pi\) | ||||
−0.154277 | + | 0.988028i | \(0.549305\pi\) | |||||||
\(840\) | 5.15206 | 0.177763 | ||||||||
\(841\) | 16.1486 | 0.556847 | ||||||||
\(842\) | 37.6151 | 1.29630 | ||||||||
\(843\) | 10.8957 | 0.375267 | ||||||||
\(844\) | 5.59898 | 0.192725 | ||||||||
\(845\) | −6.44977 | −0.221879 | ||||||||
\(846\) | −1.23955 | −0.0426167 | ||||||||
\(847\) | −16.0837 | −0.552641 | ||||||||
\(848\) | 27.5185 | 0.944988 | ||||||||
\(849\) | −35.2016 | −1.20812 | ||||||||
\(850\) | 1.00644 | 0.0345207 | ||||||||
\(851\) | −6.68019 | −0.228994 | ||||||||
\(852\) | −13.8853 | −0.475704 | ||||||||
\(853\) | −20.3463 | −0.696646 | −0.348323 | − | 0.937375i | \(-0.613249\pi\) | ||||
−0.348323 | + | 0.937375i | \(0.613249\pi\) | |||||||
\(854\) | 10.4531 | 0.357697 | ||||||||
\(855\) | −1.29394 | −0.0442518 | ||||||||
\(856\) | −21.8498 | −0.746812 | ||||||||
\(857\) | −24.2576 | −0.828622 | −0.414311 | − | 0.910135i | \(-0.635977\pi\) | ||||
−0.414311 | + | 0.910135i | \(0.635977\pi\) | |||||||
\(858\) | 46.6952 | 1.59415 | ||||||||
\(859\) | −58.1446 | −1.98387 | −0.991933 | − | 0.126761i | \(-0.959542\pi\) | ||||
−0.991933 | + | 0.126761i | \(0.959542\pi\) | |||||||
\(860\) | −0.870788 | −0.0296936 | ||||||||
\(861\) | −10.6473 | −0.362858 | ||||||||
\(862\) | −9.02258 | −0.307310 | ||||||||
\(863\) | −12.4828 | −0.424920 | −0.212460 | − | 0.977170i | \(-0.568148\pi\) | ||||
−0.212460 | + | 0.977170i | \(0.568148\pi\) | |||||||
\(864\) | 15.6080 | 0.530995 | ||||||||
\(865\) | −7.05442 | −0.239858 | ||||||||
\(866\) | −22.2684 | −0.756711 | ||||||||
\(867\) | −27.3903 | −0.930222 | ||||||||
\(868\) | 0.212464 | 0.00721149 | ||||||||
\(869\) | −42.1535 | −1.42996 | ||||||||
\(870\) | −13.6705 | −0.463472 | ||||||||
\(871\) | −11.2893 | −0.382524 | ||||||||
\(872\) | −16.7141 | −0.566010 | ||||||||
\(873\) | 1.46607 | 0.0496189 | ||||||||
\(874\) | −9.00601 | −0.304633 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −5.56454 | −0.188009 | ||||||||
\(877\) | 28.4690 | 0.961330 | 0.480665 | − | 0.876904i | \(-0.340395\pi\) | ||||
0.480665 | + | 0.876904i | \(0.340395\pi\) | |||||||
\(878\) | −11.6009 | −0.391510 | ||||||||
\(879\) | −15.9217 | −0.537025 | ||||||||
\(880\) | −13.8014 | −0.465246 | ||||||||
\(881\) | 19.1957 | 0.646719 | 0.323360 | − | 0.946276i | \(-0.395188\pi\) | ||||
0.323360 | + | 0.946276i | \(0.395188\pi\) | |||||||
\(882\) | 0.217720 | 0.00733100 | ||||||||
\(883\) | 2.63445 | 0.0886561 | 0.0443281 | − | 0.999017i | \(-0.485885\pi\) | ||||
0.0443281 | + | 0.999017i | \(0.485885\pi\) | |||||||
\(884\) | 1.95033 | 0.0655966 | ||||||||
\(885\) | 24.4206 | 0.820891 | ||||||||
\(886\) | 13.2637 | 0.445603 | ||||||||
\(887\) | −21.7274 | −0.729533 | −0.364767 | − | 0.931099i | \(-0.618851\pi\) | ||||
−0.364767 | + | 0.931099i | \(0.618851\pi\) | |||||||
\(888\) | 33.3338 | 1.11861 | ||||||||
\(889\) | 5.30748 | 0.178007 | ||||||||
\(890\) | −7.03055 | −0.235665 | ||||||||
\(891\) | 43.8639 | 1.46950 | ||||||||
\(892\) | −2.16238 | −0.0724018 | ||||||||
\(893\) | 40.9920 | 1.37174 | ||||||||
\(894\) | −2.98161 | −0.0997198 | ||||||||
\(895\) | −3.13166 | −0.104680 | ||||||||
\(896\) | 4.86970 | 0.162685 | ||||||||
\(897\) | −7.64697 | −0.255325 | ||||||||
\(898\) | −32.9952 | −1.10106 | ||||||||
\(899\) | −2.68182 | −0.0894439 | ||||||||
\(900\) | 0.0956662 | 0.00318887 | ||||||||
\(901\) | 8.62040 | 0.287187 | ||||||||
\(902\) | 39.9725 | 1.33094 | ||||||||
\(903\) | 2.74715 | 0.0914195 | ||||||||
\(904\) | −4.85428 | −0.161451 | ||||||||
\(905\) | −22.4452 | −0.746103 | ||||||||
\(906\) | −22.1442 | −0.735692 | ||||||||
\(907\) | −24.4192 | −0.810826 | −0.405413 | − | 0.914134i | \(-0.632872\pi\) | ||||
−0.405413 | + | 0.914134i | \(0.632872\pi\) | |||||||
\(908\) | 7.10452 | 0.235772 | ||||||||
\(909\) | −1.69416 | −0.0561917 | ||||||||
\(910\) | −5.34284 | −0.177113 | ||||||||
\(911\) | 33.0116 | 1.09372 | 0.546862 | − | 0.837223i | \(-0.315822\pi\) | ||||
0.546862 | + | 0.837223i | \(0.315822\pi\) | |||||||
\(912\) | 32.0663 | 1.06182 | ||||||||
\(913\) | −62.1333 | −2.05631 | ||||||||
\(914\) | 0.789321 | 0.0261084 | ||||||||
\(915\) | −14.4902 | −0.479033 | ||||||||
\(916\) | −0.532324 | −0.0175885 | ||||||||
\(917\) | −9.34518 | −0.308605 | ||||||||
\(918\) | −5.37432 | −0.177379 | ||||||||
\(919\) | 42.2800 | 1.39469 | 0.697344 | − | 0.716736i | \(-0.254365\pi\) | ||||
0.697344 | + | 0.716736i | \(0.254365\pi\) | |||||||
\(920\) | 3.16752 | 0.104430 | ||||||||
\(921\) | −23.9257 | −0.788378 | ||||||||
\(922\) | −17.3593 | −0.571697 | ||||||||
\(923\) | 68.5000 | 2.25471 | ||||||||
\(924\) | −4.65239 | −0.153053 | ||||||||
\(925\) | 6.46999 | 0.212732 | ||||||||
\(926\) | 10.7458 | 0.353129 | ||||||||
\(927\) | 0.125744 | 0.00412998 | ||||||||
\(928\) | 19.6397 | 0.644704 | ||||||||
\(929\) | 7.20203 | 0.236291 | 0.118145 | − | 0.992996i | \(-0.462305\pi\) | ||||
0.118145 | + | 0.992996i | \(0.462305\pi\) | |||||||
\(930\) | 0.812026 | 0.0266274 | ||||||||
\(931\) | −7.19999 | −0.235970 | ||||||||
\(932\) | −8.09685 | −0.265221 | ||||||||
\(933\) | 5.27469 | 0.172685 | ||||||||
\(934\) | −17.9374 | −0.586929 | ||||||||
\(935\) | −4.32342 | −0.141391 | ||||||||
\(936\) | −2.43150 | −0.0794760 | ||||||||
\(937\) | 41.1492 | 1.34428 | 0.672142 | − | 0.740422i | \(-0.265374\pi\) | ||||
0.672142 | + | 0.740422i | \(0.265374\pi\) | |||||||
\(938\) | −3.10117 | −0.101257 | ||||||||
\(939\) | 49.8727 | 1.62754 | ||||||||
\(940\) | −3.03070 | −0.0988506 | ||||||||
\(941\) | −26.8462 | −0.875161 | −0.437580 | − | 0.899179i | \(-0.644164\pi\) | ||||
−0.437580 | + | 0.899179i | \(0.644164\pi\) | |||||||
\(942\) | 7.95151 | 0.259074 | ||||||||
\(943\) | −6.54602 | −0.213168 | ||||||||
\(944\) | 38.5639 | 1.25515 | ||||||||
\(945\) | −5.33992 | −0.173708 | ||||||||
\(946\) | −10.3135 | −0.335320 | ||||||||
\(947\) | −40.7037 | −1.32269 | −0.661347 | − | 0.750080i | \(-0.730015\pi\) | ||||
−0.661347 | + | 0.750080i | \(0.730015\pi\) | |||||||
\(948\) | −7.24107 | −0.235179 | ||||||||
\(949\) | 27.4514 | 0.891109 | ||||||||
\(950\) | 8.72262 | 0.282999 | ||||||||
\(951\) | 44.3342 | 1.43764 | ||||||||
\(952\) | 2.54864 | 0.0826019 | ||||||||
\(953\) | −40.7762 | −1.32087 | −0.660435 | − | 0.750883i | \(-0.729628\pi\) | ||||
−0.660435 | + | 0.750883i | \(0.729628\pi\) | |||||||
\(954\) | −2.25918 | −0.0731437 | ||||||||
\(955\) | 25.4447 | 0.823372 | ||||||||
\(956\) | 6.85961 | 0.221856 | ||||||||
\(957\) | 58.7249 | 1.89831 | ||||||||
\(958\) | −25.7119 | −0.830713 | ||||||||
\(959\) | 12.7964 | 0.413219 | ||||||||
\(960\) | −14.8540 | −0.479411 | ||||||||
\(961\) | −30.8407 | −0.994861 | ||||||||
\(962\) | −34.5681 | −1.11452 | ||||||||
\(963\) | 1.27996 | 0.0412461 | ||||||||
\(964\) | −3.40393 | −0.109633 | ||||||||
\(965\) | 16.0136 | 0.515495 | ||||||||
\(966\) | −2.10062 | −0.0675863 | ||||||||
\(967\) | 25.7602 | 0.828393 | 0.414197 | − | 0.910187i | \(-0.364063\pi\) | ||||
0.414197 | + | 0.910187i | \(0.364063\pi\) | |||||||
\(968\) | 49.3423 | 1.58592 | ||||||||
\(969\) | 10.0451 | 0.322694 | ||||||||
\(970\) | −9.88295 | −0.317322 | ||||||||
\(971\) | 3.89442 | 0.124978 | 0.0624890 | − | 0.998046i | \(-0.480096\pi\) | ||||
0.0624890 | + | 0.998046i | \(0.480096\pi\) | |||||||
\(972\) | −0.992827 | −0.0318449 | ||||||||
\(973\) | −1.58170 | −0.0507069 | ||||||||
\(974\) | −38.5930 | −1.23660 | ||||||||
\(975\) | 7.40634 | 0.237193 | ||||||||
\(976\) | −22.8823 | −0.732445 | ||||||||
\(977\) | −41.5162 | −1.32822 | −0.664111 | − | 0.747634i | \(-0.731190\pi\) | ||||
−0.664111 | + | 0.747634i | \(0.731190\pi\) | |||||||
\(978\) | −18.2450 | −0.583409 | ||||||||
\(979\) | 30.2015 | 0.965243 | ||||||||
\(980\) | 0.532324 | 0.0170045 | ||||||||
\(981\) | 0.979108 | 0.0312605 | ||||||||
\(982\) | 22.6043 | 0.721333 | ||||||||
\(983\) | −53.0915 | −1.69336 | −0.846679 | − | 0.532105i | \(-0.821401\pi\) | ||||
−0.846679 | + | 0.532105i | \(0.821401\pi\) | |||||||
\(984\) | 32.6643 | 1.04130 | ||||||||
\(985\) | −24.7300 | −0.787965 | ||||||||
\(986\) | −6.76256 | −0.215364 | ||||||||
\(987\) | 9.56122 | 0.304337 | ||||||||
\(988\) | 16.9031 | 0.537758 | ||||||||
\(989\) | 1.68897 | 0.0537061 | ||||||||
\(990\) | 1.13306 | 0.0360109 | ||||||||
\(991\) | −6.81162 | −0.216378 | −0.108189 | − | 0.994130i | \(-0.534505\pi\) | ||||
−0.108189 | + | 0.994130i | \(0.534505\pi\) | |||||||
\(992\) | −1.16660 | −0.0370395 | ||||||||
\(993\) | 29.2711 | 0.928891 | ||||||||
\(994\) | 18.8169 | 0.596836 | ||||||||
\(995\) | 1.74351 | 0.0552731 | ||||||||
\(996\) | −10.6732 | −0.338192 | ||||||||
\(997\) | 41.2097 | 1.30512 | 0.652561 | − | 0.757736i | \(-0.273694\pi\) | ||||
0.652561 | + | 0.757736i | \(0.273694\pi\) | |||||||
\(998\) | 15.3244 | 0.485086 | ||||||||
\(999\) | −34.5492 | −1.09309 |
(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 | 8015.2.a.l.1.20 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.l.1.20 | ✓ | 62 | 1.1 | even | 1 | trivial |