Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 7 x^{14} - 7 x^{13} + 133 x^{12} - 99 x^{11} - 941 x^{10} + 1290 x^{9} + 3031 x^{8} - 5452 x^{7} - 4098 x^{6} + 9986 x^{5} + 850 x^{4} - 7216 x^{3} + 1688 x^{2} + \cdots - 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.09866\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.86623 | −1.65482 | −0.827408 | − | 0.561601i | \(-0.810186\pi\) | ||||
−0.827408 | + | 0.561601i | \(0.810186\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.86623 | 1.17013 | ||||||||
\(7\) | 0.981408 | 0.370937 | 0.185469 | − | 0.982650i | \(-0.440620\pi\) | ||||
0.185469 | + | 0.982650i | \(0.440620\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.21525 | 1.73842 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.23699 | 0.975989 | 0.487995 | − | 0.872847i | \(-0.337729\pi\) | ||||
0.487995 | + | 0.872847i | \(0.337729\pi\) | |||||||
\(12\) | −2.86623 | −0.827408 | ||||||||
\(13\) | −5.40206 | −1.49826 | −0.749130 | − | 0.662423i | \(-0.769528\pi\) | ||||
−0.749130 | + | 0.662423i | \(0.769528\pi\) | |||||||
\(14\) | −0.981408 | −0.262292 | ||||||||
\(15\) | 2.86623 | 0.740056 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.01470 | −0.731173 | −0.365587 | − | 0.930777i | \(-0.619132\pi\) | ||||
−0.365587 | + | 0.930777i | \(0.619132\pi\) | |||||||
\(18\) | −5.21525 | −1.22925 | ||||||||
\(19\) | 4.93600 | 1.13240 | 0.566198 | − | 0.824269i | \(-0.308414\pi\) | ||||
0.566198 | + | 0.824269i | \(0.308414\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.81294 | −0.613833 | ||||||||
\(22\) | −3.23699 | −0.690128 | ||||||||
\(23\) | 1.30284 | 0.271660 | 0.135830 | − | 0.990732i | \(-0.456630\pi\) | ||||
0.135830 | + | 0.990732i | \(0.456630\pi\) | |||||||
\(24\) | 2.86623 | 0.585066 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.40206 | 1.05943 | ||||||||
\(27\) | −6.34940 | −1.22194 | ||||||||
\(28\) | 0.981408 | 0.185469 | ||||||||
\(29\) | −4.83903 | −0.898586 | −0.449293 | − | 0.893385i | \(-0.648324\pi\) | ||||
−0.449293 | + | 0.893385i | \(0.648324\pi\) | |||||||
\(30\) | −2.86623 | −0.523299 | ||||||||
\(31\) | −1.22857 | −0.220658 | −0.110329 | − | 0.993895i | \(-0.535190\pi\) | ||||
−0.110329 | + | 0.993895i | \(0.535190\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −9.27794 | −1.61508 | ||||||||
\(34\) | 3.01470 | 0.517017 | ||||||||
\(35\) | −0.981408 | −0.165888 | ||||||||
\(36\) | 5.21525 | 0.869208 | ||||||||
\(37\) | −1.55379 | −0.255442 | −0.127721 | − | 0.991810i | \(-0.540766\pi\) | ||||
−0.127721 | + | 0.991810i | \(0.540766\pi\) | |||||||
\(38\) | −4.93600 | −0.800724 | ||||||||
\(39\) | 15.4835 | 2.47935 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 3.26728 | 0.510263 | 0.255131 | − | 0.966906i | \(-0.417881\pi\) | ||||
0.255131 | + | 0.966906i | \(0.417881\pi\) | |||||||
\(42\) | 2.81294 | 0.434046 | ||||||||
\(43\) | −8.01745 | −1.22265 | −0.611325 | − | 0.791380i | \(-0.709363\pi\) | ||||
−0.611325 | + | 0.791380i | \(0.709363\pi\) | |||||||
\(44\) | 3.23699 | 0.487995 | ||||||||
\(45\) | −5.21525 | −0.777443 | ||||||||
\(46\) | −1.30284 | −0.192093 | ||||||||
\(47\) | 11.0348 | 1.60959 | 0.804795 | − | 0.593553i | \(-0.202275\pi\) | ||||
0.804795 | + | 0.593553i | \(0.202275\pi\) | |||||||
\(48\) | −2.86623 | −0.413704 | ||||||||
\(49\) | −6.03684 | −0.862405 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 8.64082 | 1.20996 | ||||||||
\(52\) | −5.40206 | −0.749130 | ||||||||
\(53\) | −3.38794 | −0.465370 | −0.232685 | − | 0.972552i | \(-0.574751\pi\) | ||||
−0.232685 | + | 0.972552i | \(0.574751\pi\) | |||||||
\(54\) | 6.34940 | 0.864044 | ||||||||
\(55\) | −3.23699 | −0.436476 | ||||||||
\(56\) | −0.981408 | −0.131146 | ||||||||
\(57\) | −14.1477 | −1.87391 | ||||||||
\(58\) | 4.83903 | 0.635396 | ||||||||
\(59\) | −12.6162 | −1.64248 | −0.821242 | − | 0.570580i | \(-0.806718\pi\) | ||||
−0.821242 | + | 0.570580i | \(0.806718\pi\) | |||||||
\(60\) | 2.86623 | 0.370028 | ||||||||
\(61\) | 15.0176 | 1.92281 | 0.961406 | − | 0.275133i | \(-0.0887218\pi\) | ||||
0.961406 | + | 0.275133i | \(0.0887218\pi\) | |||||||
\(62\) | 1.22857 | 0.156029 | ||||||||
\(63\) | 5.11829 | 0.644844 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.40206 | 0.670043 | ||||||||
\(66\) | 9.27794 | 1.14204 | ||||||||
\(67\) | −4.93266 | −0.602620 | −0.301310 | − | 0.953526i | \(-0.597424\pi\) | ||||
−0.301310 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(68\) | −3.01470 | −0.365587 | ||||||||
\(69\) | −3.73423 | −0.449548 | ||||||||
\(70\) | 0.981408 | 0.117301 | ||||||||
\(71\) | −0.116467 | −0.0138221 | −0.00691103 | − | 0.999976i | \(-0.502200\pi\) | ||||
−0.00691103 | + | 0.999976i | \(0.502200\pi\) | |||||||
\(72\) | −5.21525 | −0.614623 | ||||||||
\(73\) | 4.74753 | 0.555657 | 0.277828 | − | 0.960631i | \(-0.410385\pi\) | ||||
0.277828 | + | 0.960631i | \(0.410385\pi\) | |||||||
\(74\) | 1.55379 | 0.180625 | ||||||||
\(75\) | −2.86623 | −0.330963 | ||||||||
\(76\) | 4.93600 | 0.566198 | ||||||||
\(77\) | 3.17681 | 0.362031 | ||||||||
\(78\) | −15.4835 | −1.75316 | ||||||||
\(79\) | −0.914963 | −0.102941 | −0.0514707 | − | 0.998675i | \(-0.516391\pi\) | ||||
−0.0514707 | + | 0.998675i | \(0.516391\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 2.55308 | 0.283675 | ||||||||
\(82\) | −3.26728 | −0.360810 | ||||||||
\(83\) | 7.48174 | 0.821227 | 0.410614 | − | 0.911809i | \(-0.365315\pi\) | ||||
0.410614 | + | 0.911809i | \(0.365315\pi\) | |||||||
\(84\) | −2.81294 | −0.306917 | ||||||||
\(85\) | 3.01470 | 0.326991 | ||||||||
\(86\) | 8.01745 | 0.864544 | ||||||||
\(87\) | 13.8698 | 1.48699 | ||||||||
\(88\) | −3.23699 | −0.345064 | ||||||||
\(89\) | 16.9966 | 1.80164 | 0.900820 | − | 0.434194i | \(-0.142967\pi\) | ||||
0.900820 | + | 0.434194i | \(0.142967\pi\) | |||||||
\(90\) | 5.21525 | 0.549736 | ||||||||
\(91\) | −5.30162 | −0.555761 | ||||||||
\(92\) | 1.30284 | 0.135830 | ||||||||
\(93\) | 3.52136 | 0.365148 | ||||||||
\(94\) | −11.0348 | −1.13815 | ||||||||
\(95\) | −4.93600 | −0.506423 | ||||||||
\(96\) | 2.86623 | 0.292533 | ||||||||
\(97\) | 10.3353 | 1.04939 | 0.524696 | − | 0.851289i | \(-0.324179\pi\) | ||||
0.524696 | + | 0.851289i | \(0.324179\pi\) | |||||||
\(98\) | 6.03684 | 0.609813 | ||||||||
\(99\) | 16.8817 | 1.69668 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 11.1862 | 1.11307 | 0.556535 | − | 0.830824i | \(-0.312131\pi\) | ||||
0.556535 | + | 0.830824i | \(0.312131\pi\) | |||||||
\(102\) | −8.64082 | −0.855569 | ||||||||
\(103\) | −1.10982 | −0.109354 | −0.0546769 | − | 0.998504i | \(-0.517413\pi\) | ||||
−0.0546769 | + | 0.998504i | \(0.517413\pi\) | |||||||
\(104\) | 5.40206 | 0.529715 | ||||||||
\(105\) | 2.81294 | 0.274515 | ||||||||
\(106\) | 3.38794 | 0.329066 | ||||||||
\(107\) | 16.0511 | 1.55171 | 0.775857 | − | 0.630909i | \(-0.217318\pi\) | ||||
0.775857 | + | 0.630909i | \(0.217318\pi\) | |||||||
\(108\) | −6.34940 | −0.610972 | ||||||||
\(109\) | −15.0220 | −1.43884 | −0.719422 | − | 0.694573i | \(-0.755593\pi\) | ||||
−0.719422 | + | 0.694573i | \(0.755593\pi\) | |||||||
\(110\) | 3.23699 | 0.308635 | ||||||||
\(111\) | 4.45352 | 0.422710 | ||||||||
\(112\) | 0.981408 | 0.0927344 | ||||||||
\(113\) | −8.26597 | −0.777597 | −0.388798 | − | 0.921323i | \(-0.627110\pi\) | ||||
−0.388798 | + | 0.921323i | \(0.627110\pi\) | |||||||
\(114\) | 14.1477 | 1.32505 | ||||||||
\(115\) | −1.30284 | −0.121490 | ||||||||
\(116\) | −4.83903 | −0.449293 | ||||||||
\(117\) | −28.1731 | −2.60460 | ||||||||
\(118\) | 12.6162 | 1.16141 | ||||||||
\(119\) | −2.95866 | −0.271219 | ||||||||
\(120\) | −2.86623 | −0.261649 | ||||||||
\(121\) | −0.521900 | −0.0474455 | ||||||||
\(122\) | −15.0176 | −1.35963 | ||||||||
\(123\) | −9.36475 | −0.844391 | ||||||||
\(124\) | −1.22857 | −0.110329 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.11829 | −0.455973 | ||||||||
\(127\) | 11.8238 | 1.04919 | 0.524595 | − | 0.851352i | \(-0.324217\pi\) | ||||
0.524595 | + | 0.851352i | \(0.324217\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.9798 | 2.02326 | ||||||||
\(130\) | −5.40206 | −0.473792 | ||||||||
\(131\) | −5.74416 | −0.501870 | −0.250935 | − | 0.968004i | \(-0.580738\pi\) | ||||
−0.250935 | + | 0.968004i | \(0.580738\pi\) | |||||||
\(132\) | −9.27794 | −0.807541 | ||||||||
\(133\) | 4.84423 | 0.420048 | ||||||||
\(134\) | 4.93266 | 0.426117 | ||||||||
\(135\) | 6.34940 | 0.546470 | ||||||||
\(136\) | 3.01470 | 0.258509 | ||||||||
\(137\) | 13.5128 | 1.15447 | 0.577236 | − | 0.816577i | \(-0.304131\pi\) | ||||
0.577236 | + | 0.816577i | \(0.304131\pi\) | |||||||
\(138\) | 3.73423 | 0.317878 | ||||||||
\(139\) | 1.06732 | 0.0905289 | 0.0452644 | − | 0.998975i | \(-0.485587\pi\) | ||||
0.0452644 | + | 0.998975i | \(0.485587\pi\) | |||||||
\(140\) | −0.981408 | −0.0829441 | ||||||||
\(141\) | −31.6282 | −2.66358 | ||||||||
\(142\) | 0.116467 | 0.00977367 | ||||||||
\(143\) | −17.4864 | −1.46229 | ||||||||
\(144\) | 5.21525 | 0.434604 | ||||||||
\(145\) | 4.83903 | 0.401860 | ||||||||
\(146\) | −4.74753 | −0.392909 | ||||||||
\(147\) | 17.3029 | 1.42712 | ||||||||
\(148\) | −1.55379 | −0.127721 | ||||||||
\(149\) | 13.3247 | 1.09160 | 0.545799 | − | 0.837916i | \(-0.316226\pi\) | ||||
0.545799 | + | 0.837916i | \(0.316226\pi\) | |||||||
\(150\) | 2.86623 | 0.234026 | ||||||||
\(151\) | −18.5077 | −1.50614 | −0.753069 | − | 0.657942i | \(-0.771427\pi\) | ||||
−0.753069 | + | 0.657942i | \(0.771427\pi\) | |||||||
\(152\) | −4.93600 | −0.400362 | ||||||||
\(153\) | −15.7224 | −1.27108 | ||||||||
\(154\) | −3.17681 | −0.255995 | ||||||||
\(155\) | 1.22857 | 0.0986812 | ||||||||
\(156\) | 15.4835 | 1.23967 | ||||||||
\(157\) | −1.35261 | −0.107950 | −0.0539749 | − | 0.998542i | \(-0.517189\pi\) | ||||
−0.0539749 | + | 0.998542i | \(0.517189\pi\) | |||||||
\(158\) | 0.914963 | 0.0727905 | ||||||||
\(159\) | 9.71061 | 0.770102 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.27862 | 0.100769 | ||||||||
\(162\) | −2.55308 | −0.200589 | ||||||||
\(163\) | −3.44154 | −0.269562 | −0.134781 | − | 0.990875i | \(-0.543033\pi\) | ||||
−0.134781 | + | 0.990875i | \(0.543033\pi\) | |||||||
\(164\) | 3.26728 | 0.255131 | ||||||||
\(165\) | 9.27794 | 0.722287 | ||||||||
\(166\) | −7.48174 | −0.580695 | ||||||||
\(167\) | 0.681978 | 0.0527730 | 0.0263865 | − | 0.999652i | \(-0.491600\pi\) | ||||
0.0263865 | + | 0.999652i | \(0.491600\pi\) | |||||||
\(168\) | 2.81294 | 0.217023 | ||||||||
\(169\) | 16.1822 | 1.24479 | ||||||||
\(170\) | −3.01470 | −0.231217 | ||||||||
\(171\) | 25.7425 | 1.96857 | ||||||||
\(172\) | −8.01745 | −0.611325 | ||||||||
\(173\) | 2.33733 | 0.177704 | 0.0888520 | − | 0.996045i | \(-0.471680\pi\) | ||||
0.0888520 | + | 0.996045i | \(0.471680\pi\) | |||||||
\(174\) | −13.8698 | −1.05146 | ||||||||
\(175\) | 0.981408 | 0.0741875 | ||||||||
\(176\) | 3.23699 | 0.243997 | ||||||||
\(177\) | 36.1607 | 2.71801 | ||||||||
\(178\) | −16.9966 | −1.27395 | ||||||||
\(179\) | −12.0967 | −0.904151 | −0.452075 | − | 0.891980i | \(-0.649316\pi\) | ||||
−0.452075 | + | 0.891980i | \(0.649316\pi\) | |||||||
\(180\) | −5.21525 | −0.388722 | ||||||||
\(181\) | −5.64646 | −0.419698 | −0.209849 | − | 0.977734i | \(-0.567297\pi\) | ||||
−0.209849 | + | 0.977734i | \(0.567297\pi\) | |||||||
\(182\) | 5.30162 | 0.392982 | ||||||||
\(183\) | −43.0440 | −3.18190 | ||||||||
\(184\) | −1.30284 | −0.0960465 | ||||||||
\(185\) | 1.55379 | 0.114237 | ||||||||
\(186\) | −3.52136 | −0.258199 | ||||||||
\(187\) | −9.75856 | −0.713617 | ||||||||
\(188\) | 11.0348 | 0.804795 | ||||||||
\(189\) | −6.23136 | −0.453265 | ||||||||
\(190\) | 4.93600 | 0.358095 | ||||||||
\(191\) | −2.53824 | −0.183661 | −0.0918303 | − | 0.995775i | \(-0.529272\pi\) | ||||
−0.0918303 | + | 0.995775i | \(0.529272\pi\) | |||||||
\(192\) | −2.86623 | −0.206852 | ||||||||
\(193\) | −5.15005 | −0.370709 | −0.185354 | − | 0.982672i | \(-0.559343\pi\) | ||||
−0.185354 | + | 0.982672i | \(0.559343\pi\) | |||||||
\(194\) | −10.3353 | −0.742033 | ||||||||
\(195\) | −15.4835 | −1.10880 | ||||||||
\(196\) | −6.03684 | −0.431203 | ||||||||
\(197\) | −8.93316 | −0.636461 | −0.318230 | − | 0.948013i | \(-0.603089\pi\) | ||||
−0.318230 | + | 0.948013i | \(0.603089\pi\) | |||||||
\(198\) | −16.8817 | −1.19973 | ||||||||
\(199\) | −8.47376 | −0.600689 | −0.300344 | − | 0.953831i | \(-0.597102\pi\) | ||||
−0.300344 | + | 0.953831i | \(0.597102\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 14.1381 | 0.997225 | ||||||||
\(202\) | −11.1862 | −0.787059 | ||||||||
\(203\) | −4.74907 | −0.333319 | ||||||||
\(204\) | 8.64082 | 0.604978 | ||||||||
\(205\) | −3.26728 | −0.228196 | ||||||||
\(206\) | 1.10982 | 0.0773248 | ||||||||
\(207\) | 6.79462 | 0.472259 | ||||||||
\(208\) | −5.40206 | −0.374565 | ||||||||
\(209\) | 15.9778 | 1.10521 | ||||||||
\(210\) | −2.81294 | −0.194111 | ||||||||
\(211\) | 0.757364 | 0.0521391 | 0.0260696 | − | 0.999660i | \(-0.491701\pi\) | ||||
0.0260696 | + | 0.999660i | \(0.491701\pi\) | |||||||
\(212\) | −3.38794 | −0.232685 | ||||||||
\(213\) | 0.333820 | 0.0228730 | ||||||||
\(214\) | −16.0511 | −1.09723 | ||||||||
\(215\) | 8.01745 | 0.546786 | ||||||||
\(216\) | 6.34940 | 0.432022 | ||||||||
\(217\) | −1.20573 | −0.0818503 | ||||||||
\(218\) | 15.0220 | 1.01742 | ||||||||
\(219\) | −13.6075 | −0.919510 | ||||||||
\(220\) | −3.23699 | −0.218238 | ||||||||
\(221\) | 16.2856 | 1.09549 | ||||||||
\(222\) | −4.45352 | −0.298901 | ||||||||
\(223\) | 17.5519 | 1.17537 | 0.587683 | − | 0.809092i | \(-0.300040\pi\) | ||||
0.587683 | + | 0.809092i | \(0.300040\pi\) | |||||||
\(224\) | −0.981408 | −0.0655731 | ||||||||
\(225\) | 5.21525 | 0.347683 | ||||||||
\(226\) | 8.26597 | 0.549844 | ||||||||
\(227\) | −25.8206 | −1.71377 | −0.856887 | − | 0.515504i | \(-0.827605\pi\) | ||||
−0.856887 | + | 0.515504i | \(0.827605\pi\) | |||||||
\(228\) | −14.1477 | −0.936953 | ||||||||
\(229\) | −18.8698 | −1.24695 | −0.623477 | − | 0.781842i | \(-0.714281\pi\) | ||||
−0.623477 | + | 0.781842i | \(0.714281\pi\) | |||||||
\(230\) | 1.30284 | 0.0859066 | ||||||||
\(231\) | −9.10545 | −0.599095 | ||||||||
\(232\) | 4.83903 | 0.317698 | ||||||||
\(233\) | −20.3884 | −1.33569 | −0.667845 | − | 0.744300i | \(-0.732783\pi\) | ||||
−0.667845 | + | 0.744300i | \(0.732783\pi\) | |||||||
\(234\) | 28.1731 | 1.84173 | ||||||||
\(235\) | −11.0348 | −0.719831 | ||||||||
\(236\) | −12.6162 | −0.821242 | ||||||||
\(237\) | 2.62249 | 0.170349 | ||||||||
\(238\) | 2.95866 | 0.191781 | ||||||||
\(239\) | −15.4040 | −0.996400 | −0.498200 | − | 0.867062i | \(-0.666005\pi\) | ||||
−0.498200 | + | 0.867062i | \(0.666005\pi\) | |||||||
\(240\) | 2.86623 | 0.185014 | ||||||||
\(241\) | −6.89885 | −0.444394 | −0.222197 | − | 0.975002i | \(-0.571323\pi\) | ||||
−0.222197 | + | 0.975002i | \(0.571323\pi\) | |||||||
\(242\) | 0.521900 | 0.0335490 | ||||||||
\(243\) | 11.7305 | 0.752513 | ||||||||
\(244\) | 15.0176 | 0.961406 | ||||||||
\(245\) | 6.03684 | 0.385679 | ||||||||
\(246\) | 9.36475 | 0.597074 | ||||||||
\(247\) | −26.6645 | −1.69662 | ||||||||
\(248\) | 1.22857 | 0.0780143 | ||||||||
\(249\) | −21.4443 | −1.35898 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −11.2393 | −0.709419 | −0.354710 | − | 0.934976i | \(-0.615420\pi\) | ||||
−0.354710 | + | 0.934976i | \(0.615420\pi\) | |||||||
\(252\) | 5.11829 | 0.322422 | ||||||||
\(253\) | 4.21727 | 0.265138 | ||||||||
\(254\) | −11.8238 | −0.741890 | ||||||||
\(255\) | −8.64082 | −0.541109 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.32977 | −0.332462 | −0.166231 | − | 0.986087i | \(-0.553160\pi\) | ||||
−0.166231 | + | 0.986087i | \(0.553160\pi\) | |||||||
\(258\) | −22.9798 | −1.43066 | ||||||||
\(259\) | −1.52491 | −0.0947530 | ||||||||
\(260\) | 5.40206 | 0.335021 | ||||||||
\(261\) | −25.2368 | −1.56212 | ||||||||
\(262\) | 5.74416 | 0.354876 | ||||||||
\(263\) | −23.1323 | −1.42640 | −0.713200 | − | 0.700961i | \(-0.752755\pi\) | ||||
−0.713200 | + | 0.700961i | \(0.752755\pi\) | |||||||
\(264\) | 9.27794 | 0.571018 | ||||||||
\(265\) | 3.38794 | 0.208120 | ||||||||
\(266\) | −4.84423 | −0.297019 | ||||||||
\(267\) | −48.7162 | −2.98138 | ||||||||
\(268\) | −4.93266 | −0.301310 | ||||||||
\(269\) | 18.7660 | 1.14418 | 0.572090 | − | 0.820191i | \(-0.306133\pi\) | ||||
0.572090 | + | 0.820191i | \(0.306133\pi\) | |||||||
\(270\) | −6.34940 | −0.386412 | ||||||||
\(271\) | −2.18592 | −0.132785 | −0.0663925 | − | 0.997794i | \(-0.521149\pi\) | ||||
−0.0663925 | + | 0.997794i | \(0.521149\pi\) | |||||||
\(272\) | −3.01470 | −0.182793 | ||||||||
\(273\) | 15.1956 | 0.919682 | ||||||||
\(274\) | −13.5128 | −0.816336 | ||||||||
\(275\) | 3.23699 | 0.195198 | ||||||||
\(276\) | −3.73423 | −0.224774 | ||||||||
\(277\) | 1.10562 | 0.0664304 | 0.0332152 | − | 0.999448i | \(-0.489425\pi\) | ||||
0.0332152 | + | 0.999448i | \(0.489425\pi\) | |||||||
\(278\) | −1.06732 | −0.0640136 | ||||||||
\(279\) | −6.40730 | −0.383595 | ||||||||
\(280\) | 0.981408 | 0.0586504 | ||||||||
\(281\) | 23.5114 | 1.40257 | 0.701285 | − | 0.712881i | \(-0.252610\pi\) | ||||
0.701285 | + | 0.712881i | \(0.252610\pi\) | |||||||
\(282\) | 31.6282 | 1.88343 | ||||||||
\(283\) | −16.7860 | −0.997821 | −0.498911 | − | 0.866653i | \(-0.666266\pi\) | ||||
−0.498911 | + | 0.866653i | \(0.666266\pi\) | |||||||
\(284\) | −0.116467 | −0.00691103 | ||||||||
\(285\) | 14.1477 | 0.838036 | ||||||||
\(286\) | 17.4864 | 1.03399 | ||||||||
\(287\) | 3.20653 | 0.189276 | ||||||||
\(288\) | −5.21525 | −0.307312 | ||||||||
\(289\) | −7.91156 | −0.465386 | ||||||||
\(290\) | −4.83903 | −0.284158 | ||||||||
\(291\) | −29.6234 | −1.73655 | ||||||||
\(292\) | 4.74753 | 0.277828 | ||||||||
\(293\) | −10.9849 | −0.641742 | −0.320871 | − | 0.947123i | \(-0.603976\pi\) | ||||
−0.320871 | + | 0.947123i | \(0.603976\pi\) | |||||||
\(294\) | −17.3029 | −1.00913 | ||||||||
\(295\) | 12.6162 | 0.734541 | ||||||||
\(296\) | 1.55379 | 0.0903124 | ||||||||
\(297\) | −20.5530 | −1.19260 | ||||||||
\(298\) | −13.3247 | −0.771877 | ||||||||
\(299\) | −7.03800 | −0.407018 | ||||||||
\(300\) | −2.86623 | −0.165482 | ||||||||
\(301\) | −7.86840 | −0.453527 | ||||||||
\(302\) | 18.5077 | 1.06500 | ||||||||
\(303\) | −32.0622 | −1.84193 | ||||||||
\(304\) | 4.93600 | 0.283099 | ||||||||
\(305\) | −15.0176 | −0.859908 | ||||||||
\(306\) | 15.7224 | 0.898792 | ||||||||
\(307\) | −16.5978 | −0.947287 | −0.473644 | − | 0.880717i | \(-0.657061\pi\) | ||||
−0.473644 | + | 0.880717i | \(0.657061\pi\) | |||||||
\(308\) | 3.17681 | 0.181015 | ||||||||
\(309\) | 3.18099 | 0.180960 | ||||||||
\(310\) | −1.22857 | −0.0697781 | ||||||||
\(311\) | −22.9342 | −1.30048 | −0.650239 | − | 0.759730i | \(-0.725331\pi\) | ||||
−0.650239 | + | 0.759730i | \(0.725331\pi\) | |||||||
\(312\) | −15.4835 | −0.876581 | ||||||||
\(313\) | −24.0683 | −1.36042 | −0.680209 | − | 0.733018i | \(-0.738111\pi\) | ||||
−0.680209 | + | 0.733018i | \(0.738111\pi\) | |||||||
\(314\) | 1.35261 | 0.0763320 | ||||||||
\(315\) | −5.11829 | −0.288383 | ||||||||
\(316\) | −0.914963 | −0.0514707 | ||||||||
\(317\) | −10.9487 | −0.614941 | −0.307471 | − | 0.951558i | \(-0.599483\pi\) | ||||
−0.307471 | + | 0.951558i | \(0.599483\pi\) | |||||||
\(318\) | −9.71061 | −0.544544 | ||||||||
\(319\) | −15.6639 | −0.877010 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −46.0060 | −2.56780 | ||||||||
\(322\) | −1.27862 | −0.0712545 | ||||||||
\(323\) | −14.8806 | −0.827977 | ||||||||
\(324\) | 2.55308 | 0.141838 | ||||||||
\(325\) | −5.40206 | −0.299652 | ||||||||
\(326\) | 3.44154 | 0.190609 | ||||||||
\(327\) | 43.0564 | 2.38102 | ||||||||
\(328\) | −3.26728 | −0.180405 | ||||||||
\(329\) | 10.8296 | 0.597057 | ||||||||
\(330\) | −9.27794 | −0.510734 | ||||||||
\(331\) | 12.5841 | 0.691683 | 0.345841 | − | 0.938293i | \(-0.387594\pi\) | ||||
0.345841 | + | 0.938293i | \(0.387594\pi\) | |||||||
\(332\) | 7.48174 | 0.410614 | ||||||||
\(333\) | −8.10342 | −0.444065 | ||||||||
\(334\) | −0.681978 | −0.0373162 | ||||||||
\(335\) | 4.93266 | 0.269500 | ||||||||
\(336\) | −2.81294 | −0.153458 | ||||||||
\(337\) | 13.0258 | 0.709560 | 0.354780 | − | 0.934950i | \(-0.384556\pi\) | ||||
0.354780 | + | 0.934950i | \(0.384556\pi\) | |||||||
\(338\) | −16.1822 | −0.880196 | ||||||||
\(339\) | 23.6921 | 1.28678 | ||||||||
\(340\) | 3.01470 | 0.163495 | ||||||||
\(341\) | −3.97687 | −0.215360 | ||||||||
\(342\) | −25.7425 | −1.39199 | ||||||||
\(343\) | −12.7945 | −0.690836 | ||||||||
\(344\) | 8.01745 | 0.432272 | ||||||||
\(345\) | 3.73423 | 0.201044 | ||||||||
\(346\) | −2.33733 | −0.125656 | ||||||||
\(347\) | −11.7323 | −0.629821 | −0.314911 | − | 0.949121i | \(-0.601975\pi\) | ||||
−0.314911 | + | 0.949121i | \(0.601975\pi\) | |||||||
\(348\) | 13.8698 | 0.743497 | ||||||||
\(349\) | −25.2634 | −1.35232 | −0.676159 | − | 0.736756i | \(-0.736357\pi\) | ||||
−0.676159 | + | 0.736756i | \(0.736357\pi\) | |||||||
\(350\) | −0.981408 | −0.0524585 | ||||||||
\(351\) | 34.2998 | 1.83079 | ||||||||
\(352\) | −3.23699 | −0.172532 | ||||||||
\(353\) | 29.8560 | 1.58907 | 0.794537 | − | 0.607215i | \(-0.207713\pi\) | ||||
0.794537 | + | 0.607215i | \(0.207713\pi\) | |||||||
\(354\) | −36.1607 | −1.92192 | ||||||||
\(355\) | 0.116467 | 0.00618141 | ||||||||
\(356\) | 16.9966 | 0.900820 | ||||||||
\(357\) | 8.48017 | 0.448818 | ||||||||
\(358\) | 12.0967 | 0.639331 | ||||||||
\(359\) | 32.6092 | 1.72105 | 0.860525 | − | 0.509409i | \(-0.170136\pi\) | ||||
0.860525 | + | 0.509409i | \(0.170136\pi\) | |||||||
\(360\) | 5.21525 | 0.274868 | ||||||||
\(361\) | 5.36407 | 0.282319 | ||||||||
\(362\) | 5.64646 | 0.296772 | ||||||||
\(363\) | 1.49588 | 0.0785135 | ||||||||
\(364\) | −5.30162 | −0.277881 | ||||||||
\(365\) | −4.74753 | −0.248497 | ||||||||
\(366\) | 43.0440 | 2.24994 | ||||||||
\(367\) | 15.6372 | 0.816257 | 0.408129 | − | 0.912924i | \(-0.366182\pi\) | ||||
0.408129 | + | 0.912924i | \(0.366182\pi\) | |||||||
\(368\) | 1.30284 | 0.0679151 | ||||||||
\(369\) | 17.0397 | 0.887049 | ||||||||
\(370\) | −1.55379 | −0.0807779 | ||||||||
\(371\) | −3.32496 | −0.172623 | ||||||||
\(372\) | 3.52136 | 0.182574 | ||||||||
\(373\) | 18.8479 | 0.975909 | 0.487955 | − | 0.872869i | \(-0.337743\pi\) | ||||
0.487955 | + | 0.872869i | \(0.337743\pi\) | |||||||
\(374\) | 9.75856 | 0.504603 | ||||||||
\(375\) | 2.86623 | 0.148011 | ||||||||
\(376\) | −11.0348 | −0.569076 | ||||||||
\(377\) | 26.1407 | 1.34632 | ||||||||
\(378\) | 6.23136 | 0.320506 | ||||||||
\(379\) | −32.5777 | −1.67341 | −0.836703 | − | 0.547658i | \(-0.815520\pi\) | ||||
−0.836703 | + | 0.547658i | \(0.815520\pi\) | |||||||
\(380\) | −4.93600 | −0.253211 | ||||||||
\(381\) | −33.8896 | −1.73622 | ||||||||
\(382\) | 2.53824 | 0.129868 | ||||||||
\(383\) | 0.283228 | 0.0144723 | 0.00723613 | − | 0.999974i | \(-0.497697\pi\) | ||||
0.00723613 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(384\) | 2.86623 | 0.146266 | ||||||||
\(385\) | −3.17681 | −0.161905 | ||||||||
\(386\) | 5.15005 | 0.262131 | ||||||||
\(387\) | −41.8130 | −2.12548 | ||||||||
\(388\) | 10.3353 | 0.524696 | ||||||||
\(389\) | 28.7129 | 1.45580 | 0.727900 | − | 0.685683i | \(-0.240496\pi\) | ||||
0.727900 | + | 0.685683i | \(0.240496\pi\) | |||||||
\(390\) | 15.4835 | 0.784038 | ||||||||
\(391\) | −3.92767 | −0.198631 | ||||||||
\(392\) | 6.03684 | 0.304906 | ||||||||
\(393\) | 16.4641 | 0.830503 | ||||||||
\(394\) | 8.93316 | 0.450046 | ||||||||
\(395\) | 0.914963 | 0.0460368 | ||||||||
\(396\) | 16.8817 | 0.848338 | ||||||||
\(397\) | 12.1688 | 0.610733 | 0.305367 | − | 0.952235i | \(-0.401221\pi\) | ||||
0.305367 | + | 0.952235i | \(0.401221\pi\) | |||||||
\(398\) | 8.47376 | 0.424751 | ||||||||
\(399\) | −13.8847 | −0.695102 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −14.1381 | −0.705145 | ||||||||
\(403\) | 6.63681 | 0.330603 | ||||||||
\(404\) | 11.1862 | 0.556535 | ||||||||
\(405\) | −2.55308 | −0.126863 | ||||||||
\(406\) | 4.74907 | 0.235692 | ||||||||
\(407\) | −5.02961 | −0.249309 | ||||||||
\(408\) | −8.64082 | −0.427784 | ||||||||
\(409\) | −8.12653 | −0.401831 | −0.200916 | − | 0.979609i | \(-0.564392\pi\) | ||||
−0.200916 | + | 0.979609i | \(0.564392\pi\) | |||||||
\(410\) | 3.26728 | 0.161359 | ||||||||
\(411\) | −38.7306 | −1.91044 | ||||||||
\(412\) | −1.10982 | −0.0546769 | ||||||||
\(413\) | −12.3816 | −0.609259 | ||||||||
\(414\) | −6.79462 | −0.333937 | ||||||||
\(415\) | −7.48174 | −0.367264 | ||||||||
\(416\) | 5.40206 | 0.264858 | ||||||||
\(417\) | −3.05918 | −0.149809 | ||||||||
\(418\) | −15.9778 | −0.781498 | ||||||||
\(419\) | 31.2448 | 1.52641 | 0.763205 | − | 0.646156i | \(-0.223625\pi\) | ||||
0.763205 | + | 0.646156i | \(0.223625\pi\) | |||||||
\(420\) | 2.81294 | 0.137257 | ||||||||
\(421\) | −1.26922 | −0.0618578 | −0.0309289 | − | 0.999522i | \(-0.509847\pi\) | ||||
−0.0309289 | + | 0.999522i | \(0.509847\pi\) | |||||||
\(422\) | −0.757364 | −0.0368679 | ||||||||
\(423\) | 57.5492 | 2.79814 | ||||||||
\(424\) | 3.38794 | 0.164533 | ||||||||
\(425\) | −3.01470 | −0.146235 | ||||||||
\(426\) | −0.333820 | −0.0161736 | ||||||||
\(427\) | 14.7384 | 0.713243 | ||||||||
\(428\) | 16.0511 | 0.775857 | ||||||||
\(429\) | 50.1200 | 2.41981 | ||||||||
\(430\) | −8.01745 | −0.386636 | ||||||||
\(431\) | −11.9607 | −0.576129 | −0.288064 | − | 0.957611i | \(-0.593012\pi\) | ||||
−0.288064 | + | 0.957611i | \(0.593012\pi\) | |||||||
\(432\) | −6.34940 | −0.305486 | ||||||||
\(433\) | −40.3389 | −1.93856 | −0.969281 | − | 0.245956i | \(-0.920898\pi\) | ||||
−0.969281 | + | 0.245956i | \(0.920898\pi\) | |||||||
\(434\) | 1.20573 | 0.0578769 | ||||||||
\(435\) | −13.8698 | −0.665004 | ||||||||
\(436\) | −15.0220 | −0.719422 | ||||||||
\(437\) | 6.43080 | 0.307627 | ||||||||
\(438\) | 13.6075 | 0.650191 | ||||||||
\(439\) | −35.8412 | −1.71061 | −0.855303 | − | 0.518129i | \(-0.826629\pi\) | ||||
−0.855303 | + | 0.518129i | \(0.826629\pi\) | |||||||
\(440\) | 3.23699 | 0.154317 | ||||||||
\(441\) | −31.4836 | −1.49922 | ||||||||
\(442\) | −16.2856 | −0.774627 | ||||||||
\(443\) | −25.8381 | −1.22761 | −0.613803 | − | 0.789460i | \(-0.710361\pi\) | ||||
−0.613803 | + | 0.789460i | \(0.710361\pi\) | |||||||
\(444\) | 4.45352 | 0.211355 | ||||||||
\(445\) | −16.9966 | −0.805717 | ||||||||
\(446\) | −17.5519 | −0.831109 | ||||||||
\(447\) | −38.1915 | −1.80640 | ||||||||
\(448\) | 0.981408 | 0.0463672 | ||||||||
\(449\) | −10.2434 | −0.483417 | −0.241709 | − | 0.970349i | \(-0.577708\pi\) | ||||
−0.241709 | + | 0.970349i | \(0.577708\pi\) | |||||||
\(450\) | −5.21525 | −0.245849 | ||||||||
\(451\) | 10.5761 | 0.498011 | ||||||||
\(452\) | −8.26597 | −0.388798 | ||||||||
\(453\) | 53.0473 | 2.49238 | ||||||||
\(454\) | 25.8206 | 1.21182 | ||||||||
\(455\) | 5.30162 | 0.248544 | ||||||||
\(456\) | 14.1477 | 0.662526 | ||||||||
\(457\) | −23.6779 | −1.10760 | −0.553802 | − | 0.832648i | \(-0.686824\pi\) | ||||
−0.553802 | + | 0.832648i | \(0.686824\pi\) | |||||||
\(458\) | 18.8698 | 0.881730 | ||||||||
\(459\) | 19.1416 | 0.893452 | ||||||||
\(460\) | −1.30284 | −0.0607451 | ||||||||
\(461\) | 0.150219 | 0.00699642 | 0.00349821 | − | 0.999994i | \(-0.498886\pi\) | ||||
0.00349821 | + | 0.999994i | \(0.498886\pi\) | |||||||
\(462\) | 9.10545 | 0.423624 | ||||||||
\(463\) | 28.3404 | 1.31709 | 0.658544 | − | 0.752542i | \(-0.271173\pi\) | ||||
0.658544 | + | 0.752542i | \(0.271173\pi\) | |||||||
\(464\) | −4.83903 | −0.224646 | ||||||||
\(465\) | −3.52136 | −0.163299 | ||||||||
\(466\) | 20.3884 | 0.944476 | ||||||||
\(467\) | −6.79712 | −0.314533 | −0.157267 | − | 0.987556i | \(-0.550268\pi\) | ||||
−0.157267 | + | 0.987556i | \(0.550268\pi\) | |||||||
\(468\) | −28.1731 | −1.30230 | ||||||||
\(469\) | −4.84095 | −0.223534 | ||||||||
\(470\) | 11.0348 | 0.508997 | ||||||||
\(471\) | 3.87688 | 0.178637 | ||||||||
\(472\) | 12.6162 | 0.580706 | ||||||||
\(473\) | −25.9524 | −1.19329 | ||||||||
\(474\) | −2.62249 | −0.120455 | ||||||||
\(475\) | 4.93600 | 0.226479 | ||||||||
\(476\) | −2.95866 | −0.135610 | ||||||||
\(477\) | −17.6690 | −0.809007 | ||||||||
\(478\) | 15.4040 | 0.704561 | ||||||||
\(479\) | 37.2822 | 1.70347 | 0.851735 | − | 0.523974i | \(-0.175551\pi\) | ||||
0.851735 | + | 0.523974i | \(0.175551\pi\) | |||||||
\(480\) | −2.86623 | −0.130825 | ||||||||
\(481\) | 8.39368 | 0.382719 | ||||||||
\(482\) | 6.89885 | 0.314234 | ||||||||
\(483\) | −3.66480 | −0.166754 | ||||||||
\(484\) | −0.521900 | −0.0237227 | ||||||||
\(485\) | −10.3353 | −0.469303 | ||||||||
\(486\) | −11.7305 | −0.532107 | ||||||||
\(487\) | −1.95947 | −0.0887922 | −0.0443961 | − | 0.999014i | \(-0.514136\pi\) | ||||
−0.0443961 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(488\) | −15.0176 | −0.679817 | ||||||||
\(489\) | 9.86422 | 0.446076 | ||||||||
\(490\) | −6.03684 | −0.272717 | ||||||||
\(491\) | −26.0586 | −1.17601 | −0.588004 | − | 0.808858i | \(-0.700086\pi\) | ||||
−0.588004 | + | 0.808858i | \(0.700086\pi\) | |||||||
\(492\) | −9.36475 | −0.422195 | ||||||||
\(493\) | 14.5882 | 0.657022 | ||||||||
\(494\) | 26.6645 | 1.19969 | ||||||||
\(495\) | −16.8817 | −0.758776 | ||||||||
\(496\) | −1.22857 | −0.0551645 | ||||||||
\(497\) | −0.114301 | −0.00512712 | ||||||||
\(498\) | 21.4443 | 0.960944 | ||||||||
\(499\) | −2.70819 | −0.121235 | −0.0606176 | − | 0.998161i | \(-0.519307\pi\) | ||||
−0.0606176 | + | 0.998161i | \(0.519307\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −1.95470 | −0.0873297 | ||||||||
\(502\) | 11.2393 | 0.501635 | ||||||||
\(503\) | 29.7184 | 1.32508 | 0.662540 | − | 0.749027i | \(-0.269479\pi\) | ||||
0.662540 | + | 0.749027i | \(0.269479\pi\) | |||||||
\(504\) | −5.11829 | −0.227987 | ||||||||
\(505\) | −11.1862 | −0.497780 | ||||||||
\(506\) | −4.21727 | −0.187481 | ||||||||
\(507\) | −46.3819 | −2.05989 | ||||||||
\(508\) | 11.8238 | 0.524595 | ||||||||
\(509\) | −6.03921 | −0.267683 | −0.133842 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133842 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(510\) | 8.64082 | 0.382622 | ||||||||
\(511\) | 4.65927 | 0.206114 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −31.3406 | −1.38372 | ||||||||
\(514\) | 5.32977 | 0.235086 | ||||||||
\(515\) | 1.10982 | 0.0489045 | ||||||||
\(516\) | 22.9798 | 1.01163 | ||||||||
\(517\) | 35.7195 | 1.57094 | ||||||||
\(518\) | 1.52491 | 0.0670005 | ||||||||
\(519\) | −6.69932 | −0.294067 | ||||||||
\(520\) | −5.40206 | −0.236896 | ||||||||
\(521\) | −24.3339 | −1.06609 | −0.533044 | − | 0.846088i | \(-0.678952\pi\) | ||||
−0.533044 | + | 0.846088i | \(0.678952\pi\) | |||||||
\(522\) | 25.2368 | 1.10458 | ||||||||
\(523\) | −33.3422 | −1.45795 | −0.728977 | − | 0.684538i | \(-0.760004\pi\) | ||||
−0.728977 | + | 0.684538i | \(0.760004\pi\) | |||||||
\(524\) | −5.74416 | −0.250935 | ||||||||
\(525\) | −2.81294 | −0.122767 | ||||||||
\(526\) | 23.1323 | 1.00862 | ||||||||
\(527\) | 3.70378 | 0.161339 | ||||||||
\(528\) | −9.27794 | −0.403771 | ||||||||
\(529\) | −21.3026 | −0.926201 | ||||||||
\(530\) | −3.38794 | −0.147163 | ||||||||
\(531\) | −65.7964 | −2.85532 | ||||||||
\(532\) | 4.84423 | 0.210024 | ||||||||
\(533\) | −17.6500 | −0.764506 | ||||||||
\(534\) | 48.7162 | 2.10815 | ||||||||
\(535\) | −16.0511 | −0.693948 | ||||||||
\(536\) | 4.93266 | 0.213058 | ||||||||
\(537\) | 34.6719 | 1.49620 | ||||||||
\(538\) | −18.7660 | −0.809058 | ||||||||
\(539\) | −19.5412 | −0.841698 | ||||||||
\(540\) | 6.34940 | 0.273235 | ||||||||
\(541\) | 6.10904 | 0.262648 | 0.131324 | − | 0.991339i | \(-0.458077\pi\) | ||||
0.131324 | + | 0.991339i | \(0.458077\pi\) | |||||||
\(542\) | 2.18592 | 0.0938932 | ||||||||
\(543\) | 16.1840 | 0.694524 | ||||||||
\(544\) | 3.01470 | 0.129254 | ||||||||
\(545\) | 15.0220 | 0.643471 | ||||||||
\(546\) | −15.1956 | −0.650314 | ||||||||
\(547\) | −43.0814 | −1.84203 | −0.921014 | − | 0.389529i | \(-0.872638\pi\) | ||||
−0.921014 | + | 0.389529i | \(0.872638\pi\) | |||||||
\(548\) | 13.5128 | 0.577236 | ||||||||
\(549\) | 78.3208 | 3.34265 | ||||||||
\(550\) | −3.23699 | −0.138026 | ||||||||
\(551\) | −23.8854 | −1.01755 | ||||||||
\(552\) | 3.73423 | 0.158939 | ||||||||
\(553\) | −0.897952 | −0.0381848 | ||||||||
\(554\) | −1.10562 | −0.0469734 | ||||||||
\(555\) | −4.45352 | −0.189042 | ||||||||
\(556\) | 1.06732 | 0.0452644 | ||||||||
\(557\) | −4.45115 | −0.188601 | −0.0943007 | − | 0.995544i | \(-0.530062\pi\) | ||||
−0.0943007 | + | 0.995544i | \(0.530062\pi\) | |||||||
\(558\) | 6.40730 | 0.271243 | ||||||||
\(559\) | 43.3107 | 1.83185 | ||||||||
\(560\) | −0.981408 | −0.0414721 | ||||||||
\(561\) | 27.9702 | 1.18090 | ||||||||
\(562\) | −23.5114 | −0.991767 | ||||||||
\(563\) | −10.2067 | −0.430162 | −0.215081 | − | 0.976596i | \(-0.569002\pi\) | ||||
−0.215081 | + | 0.976596i | \(0.569002\pi\) | |||||||
\(564\) | −31.6282 | −1.33179 | ||||||||
\(565\) | 8.26597 | 0.347752 | ||||||||
\(566\) | 16.7860 | 0.705566 | ||||||||
\(567\) | 2.50561 | 0.105226 | ||||||||
\(568\) | 0.116467 | 0.00488684 | ||||||||
\(569\) | 11.7620 | 0.493089 | 0.246544 | − | 0.969132i | \(-0.420705\pi\) | ||||
0.246544 | + | 0.969132i | \(0.420705\pi\) | |||||||
\(570\) | −14.1477 | −0.592581 | ||||||||
\(571\) | −37.3525 | −1.56315 | −0.781577 | − | 0.623809i | \(-0.785585\pi\) | ||||
−0.781577 | + | 0.623809i | \(0.785585\pi\) | |||||||
\(572\) | −17.4864 | −0.731143 | ||||||||
\(573\) | 7.27517 | 0.303924 | ||||||||
\(574\) | −3.20653 | −0.133838 | ||||||||
\(575\) | 1.30284 | 0.0543321 | ||||||||
\(576\) | 5.21525 | 0.217302 | ||||||||
\(577\) | 26.4195 | 1.09986 | 0.549930 | − | 0.835211i | \(-0.314654\pi\) | ||||
0.549930 | + | 0.835211i | \(0.314654\pi\) | |||||||
\(578\) | 7.91156 | 0.329078 | ||||||||
\(579\) | 14.7612 | 0.613455 | ||||||||
\(580\) | 4.83903 | 0.200930 | ||||||||
\(581\) | 7.34264 | 0.304624 | ||||||||
\(582\) | 29.6234 | 1.22793 | ||||||||
\(583\) | −10.9667 | −0.454196 | ||||||||
\(584\) | −4.74753 | −0.196454 | ||||||||
\(585\) | 28.1731 | 1.16481 | ||||||||
\(586\) | 10.9849 | 0.453780 | ||||||||
\(587\) | 45.8820 | 1.89375 | 0.946877 | − | 0.321595i | \(-0.104219\pi\) | ||||
0.946877 | + | 0.321595i | \(0.104219\pi\) | |||||||
\(588\) | 17.3029 | 0.713561 | ||||||||
\(589\) | −6.06422 | −0.249872 | ||||||||
\(590\) | −12.6162 | −0.519399 | ||||||||
\(591\) | 25.6044 | 1.05323 | ||||||||
\(592\) | −1.55379 | −0.0638605 | ||||||||
\(593\) | 28.1648 | 1.15659 | 0.578296 | − | 0.815827i | \(-0.303718\pi\) | ||||
0.578296 | + | 0.815827i | \(0.303718\pi\) | |||||||
\(594\) | 20.5530 | 0.843298 | ||||||||
\(595\) | 2.95866 | 0.121293 | ||||||||
\(596\) | 13.3247 | 0.545799 | ||||||||
\(597\) | 24.2877 | 0.994029 | ||||||||
\(598\) | 7.03800 | 0.287805 | ||||||||
\(599\) | −15.8266 | −0.646657 | −0.323329 | − | 0.946287i | \(-0.604802\pi\) | ||||
−0.323329 | + | 0.946287i | \(0.604802\pi\) | |||||||
\(600\) | 2.86623 | 0.117013 | ||||||||
\(601\) | 41.2359 | 1.68205 | 0.841024 | − | 0.540998i | \(-0.181953\pi\) | ||||
0.841024 | + | 0.540998i | \(0.181953\pi\) | |||||||
\(602\) | 7.86840 | 0.320692 | ||||||||
\(603\) | −25.7250 | −1.04760 | ||||||||
\(604\) | −18.5077 | −0.753069 | ||||||||
\(605\) | 0.521900 | 0.0212183 | ||||||||
\(606\) | 32.0622 | 1.30244 | ||||||||
\(607\) | −11.9281 | −0.484146 | −0.242073 | − | 0.970258i | \(-0.577827\pi\) | ||||
−0.242073 | + | 0.970258i | \(0.577827\pi\) | |||||||
\(608\) | −4.93600 | −0.200181 | ||||||||
\(609\) | 13.6119 | 0.551582 | ||||||||
\(610\) | 15.0176 | 0.608047 | ||||||||
\(611\) | −59.6106 | −2.41159 | ||||||||
\(612\) | −15.7224 | −0.635542 | ||||||||
\(613\) | 0.285543 | 0.0115330 | 0.00576648 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576648 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(614\) | 16.5978 | 0.669833 | ||||||||
\(615\) | 9.36475 | 0.377623 | ||||||||
\(616\) | −3.17681 | −0.127997 | ||||||||
\(617\) | −44.6205 | −1.79635 | −0.898177 | − | 0.439635i | \(-0.855108\pi\) | ||||
−0.898177 | + | 0.439635i | \(0.855108\pi\) | |||||||
\(618\) | −3.18099 | −0.127958 | ||||||||
\(619\) | −4.94927 | −0.198928 | −0.0994639 | − | 0.995041i | \(-0.531713\pi\) | ||||
−0.0994639 | + | 0.995041i | \(0.531713\pi\) | |||||||
\(620\) | 1.22857 | 0.0493406 | ||||||||
\(621\) | −8.27224 | −0.331954 | ||||||||
\(622\) | 22.9342 | 0.919577 | ||||||||
\(623\) | 16.6806 | 0.668295 | ||||||||
\(624\) | 15.4835 | 0.619837 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.0683 | 0.961961 | ||||||||
\(627\) | −45.7959 | −1.82891 | ||||||||
\(628\) | −1.35261 | −0.0539749 | ||||||||
\(629\) | 4.68423 | 0.186772 | ||||||||
\(630\) | 5.11829 | 0.203918 | ||||||||
\(631\) | −21.2275 | −0.845054 | −0.422527 | − | 0.906350i | \(-0.638857\pi\) | ||||
−0.422527 | + | 0.906350i | \(0.638857\pi\) | |||||||
\(632\) | 0.914963 | 0.0363953 | ||||||||
\(633\) | −2.17078 | −0.0862806 | ||||||||
\(634\) | 10.9487 | 0.434829 | ||||||||
\(635\) | −11.8238 | −0.469212 | ||||||||
\(636\) | 9.71061 | 0.385051 | ||||||||
\(637\) | 32.6113 | 1.29211 | ||||||||
\(638\) | 15.6639 | 0.620139 | ||||||||
\(639\) | −0.607403 | −0.0240285 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 6.25157 | 0.246922 | 0.123461 | − | 0.992349i | \(-0.460601\pi\) | ||||
0.123461 | + | 0.992349i | \(0.460601\pi\) | |||||||
\(642\) | 46.0060 | 1.81571 | ||||||||
\(643\) | −7.27224 | −0.286789 | −0.143395 | − | 0.989666i | \(-0.545802\pi\) | ||||
−0.143395 | + | 0.989666i | \(0.545802\pi\) | |||||||
\(644\) | 1.27862 | 0.0503845 | ||||||||
\(645\) | −22.9798 | −0.904830 | ||||||||
\(646\) | 14.8806 | 0.585468 | ||||||||
\(647\) | −24.6580 | −0.969406 | −0.484703 | − | 0.874679i | \(-0.661072\pi\) | ||||
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(648\) | −2.55308 | −0.100294 | ||||||||
\(649\) | −40.8384 | −1.60305 | ||||||||
\(650\) | 5.40206 | 0.211886 | ||||||||
\(651\) | 3.45589 | 0.135447 | ||||||||
\(652\) | −3.44154 | −0.134781 | ||||||||
\(653\) | −14.9540 | −0.585196 | −0.292598 | − | 0.956236i | \(-0.594520\pi\) | ||||
−0.292598 | + | 0.956236i | \(0.594520\pi\) | |||||||
\(654\) | −43.0564 | −1.68364 | ||||||||
\(655\) | 5.74416 | 0.224443 | ||||||||
\(656\) | 3.26728 | 0.127566 | ||||||||
\(657\) | 24.7596 | 0.965963 | ||||||||
\(658\) | −10.8296 | −0.422183 | ||||||||
\(659\) | −40.4956 | −1.57749 | −0.788743 | − | 0.614723i | \(-0.789268\pi\) | ||||
−0.788743 | + | 0.614723i | \(0.789268\pi\) | |||||||
\(660\) | 9.27794 | 0.361143 | ||||||||
\(661\) | −2.19717 | −0.0854600 | −0.0427300 | − | 0.999087i | \(-0.513606\pi\) | ||||
−0.0427300 | + | 0.999087i | \(0.513606\pi\) | |||||||
\(662\) | −12.5841 | −0.489094 | ||||||||
\(663\) | −46.6782 | −1.81283 | ||||||||
\(664\) | −7.48174 | −0.290348 | ||||||||
\(665\) | −4.84423 | −0.187851 | ||||||||
\(666\) | 8.10342 | 0.314001 | ||||||||
\(667\) | −6.30447 | −0.244110 | ||||||||
\(668\) | 0.681978 | 0.0263865 | ||||||||
\(669\) | −50.3078 | −1.94501 | ||||||||
\(670\) | −4.93266 | −0.190565 | ||||||||
\(671\) | 48.6120 | 1.87664 | ||||||||
\(672\) | 2.81294 | 0.108511 | ||||||||
\(673\) | −10.2059 | −0.393410 | −0.196705 | − | 0.980463i | \(-0.563024\pi\) | ||||
−0.196705 | + | 0.980463i | \(0.563024\pi\) | |||||||
\(674\) | −13.0258 | −0.501735 | ||||||||
\(675\) | −6.34940 | −0.244389 | ||||||||
\(676\) | 16.1822 | 0.622393 | ||||||||
\(677\) | 41.6339 | 1.60012 | 0.800061 | − | 0.599919i | \(-0.204800\pi\) | ||||
0.800061 | + | 0.599919i | \(0.204800\pi\) | |||||||
\(678\) | −23.6921 | −0.909891 | ||||||||
\(679\) | 10.1432 | 0.389259 | ||||||||
\(680\) | −3.01470 | −0.115609 | ||||||||
\(681\) | 74.0077 | 2.83598 | ||||||||
\(682\) | 3.97687 | 0.152282 | ||||||||
\(683\) | 15.5843 | 0.596317 | 0.298158 | − | 0.954516i | \(-0.403628\pi\) | ||||
0.298158 | + | 0.954516i | \(0.403628\pi\) | |||||||
\(684\) | 25.7425 | 0.984287 | ||||||||
\(685\) | −13.5128 | −0.516296 | ||||||||
\(686\) | 12.7945 | 0.488495 | ||||||||
\(687\) | 54.0852 | 2.06348 | ||||||||
\(688\) | −8.01745 | −0.305663 | ||||||||
\(689\) | 18.3019 | 0.697246 | ||||||||
\(690\) | −3.73423 | −0.142160 | ||||||||
\(691\) | 8.82809 | 0.335836 | 0.167918 | − | 0.985801i | \(-0.446296\pi\) | ||||
0.167918 | + | 0.985801i | \(0.446296\pi\) | |||||||
\(692\) | 2.33733 | 0.0888520 | ||||||||
\(693\) | 16.5678 | 0.629360 | ||||||||
\(694\) | 11.7323 | 0.445351 | ||||||||
\(695\) | −1.06732 | −0.0404857 | ||||||||
\(696\) | −13.8698 | −0.525732 | ||||||||
\(697\) | −9.84987 | −0.373090 | ||||||||
\(698\) | 25.2634 | 0.956233 | ||||||||
\(699\) | 58.4378 | 2.21032 | ||||||||
\(700\) | 0.981408 | 0.0370937 | ||||||||
\(701\) | −1.55139 | −0.0585950 | −0.0292975 | − | 0.999571i | \(-0.509327\pi\) | ||||
−0.0292975 | + | 0.999571i | \(0.509327\pi\) | |||||||
\(702\) | −34.2998 | −1.29456 | ||||||||
\(703\) | −7.66952 | −0.289261 | ||||||||
\(704\) | 3.23699 | 0.121999 | ||||||||
\(705\) | 31.6282 | 1.19119 | ||||||||
\(706\) | −29.8560 | −1.12365 | ||||||||
\(707\) | 10.9782 | 0.412879 | ||||||||
\(708\) | 36.1607 | 1.35900 | ||||||||
\(709\) | −51.6685 | −1.94045 | −0.970226 | − | 0.242202i | \(-0.922130\pi\) | ||||
−0.970226 | + | 0.242202i | \(0.922130\pi\) | |||||||
\(710\) | −0.116467 | −0.00437092 | ||||||||
\(711\) | −4.77176 | −0.178955 | ||||||||
\(712\) | −16.9966 | −0.636976 | ||||||||
\(713\) | −1.60063 | −0.0599440 | ||||||||
\(714\) | −8.48017 | −0.317363 | ||||||||
\(715\) | 17.4864 | 0.653954 | ||||||||
\(716\) | −12.0967 | −0.452075 | ||||||||
\(717\) | 44.1512 | 1.64886 | ||||||||
\(718\) | −32.6092 | −1.21697 | ||||||||
\(719\) | 32.1417 | 1.19868 | 0.599341 | − | 0.800494i | \(-0.295429\pi\) | ||||
0.599341 | + | 0.800494i | \(0.295429\pi\) | |||||||
\(720\) | −5.21525 | −0.194361 | ||||||||
\(721\) | −1.08919 | −0.0405634 | ||||||||
\(722\) | −5.36407 | −0.199630 | ||||||||
\(723\) | 19.7736 | 0.735390 | ||||||||
\(724\) | −5.64646 | −0.209849 | ||||||||
\(725\) | −4.83903 | −0.179717 | ||||||||
\(726\) | −1.49588 | −0.0555174 | ||||||||
\(727\) | −15.1473 | −0.561784 | −0.280892 | − | 0.959739i | \(-0.590630\pi\) | ||||
−0.280892 | + | 0.959739i | \(0.590630\pi\) | |||||||
\(728\) | 5.30162 | 0.196491 | ||||||||
\(729\) | −41.2815 | −1.52895 | ||||||||
\(730\) | 4.74753 | 0.175714 | ||||||||
\(731\) | 24.1703 | 0.893969 | ||||||||
\(732\) | −43.0440 | −1.59095 | ||||||||
\(733\) | −12.2881 | −0.453870 | −0.226935 | − | 0.973910i | \(-0.572870\pi\) | ||||
−0.226935 | + | 0.973910i | \(0.572870\pi\) | |||||||
\(734\) | −15.6372 | −0.577181 | ||||||||
\(735\) | −17.3029 | −0.638229 | ||||||||
\(736\) | −1.30284 | −0.0480232 | ||||||||
\(737\) | −15.9670 | −0.588150 | ||||||||
\(738\) | −17.0397 | −0.627238 | ||||||||
\(739\) | 37.5098 | 1.37982 | 0.689911 | − | 0.723894i | \(-0.257650\pi\) | ||||
0.689911 | + | 0.723894i | \(0.257650\pi\) | |||||||
\(740\) | 1.55379 | 0.0571186 | ||||||||
\(741\) | 76.4266 | 2.80760 | ||||||||
\(742\) | 3.32496 | 0.122063 | ||||||||
\(743\) | −42.9813 | −1.57683 | −0.788416 | − | 0.615142i | \(-0.789099\pi\) | ||||
−0.788416 | + | 0.615142i | \(0.789099\pi\) | |||||||
\(744\) | −3.52136 | −0.129099 | ||||||||
\(745\) | −13.3247 | −0.488178 | ||||||||
\(746\) | −18.8479 | −0.690072 | ||||||||
\(747\) | 39.0191 | 1.42764 | ||||||||
\(748\) | −9.75856 | −0.356808 | ||||||||
\(749\) | 15.7526 | 0.575589 | ||||||||
\(750\) | −2.86623 | −0.104660 | ||||||||
\(751\) | −13.1162 | −0.478617 | −0.239309 | − | 0.970944i | \(-0.576921\pi\) | ||||
−0.239309 | + | 0.970944i | \(0.576921\pi\) | |||||||
\(752\) | 11.0348 | 0.402398 | ||||||||
\(753\) | 32.2144 | 1.17396 | ||||||||
\(754\) | −26.1407 | −0.951989 | ||||||||
\(755\) | 18.5077 | 0.673565 | ||||||||
\(756\) | −6.23136 | −0.226632 | ||||||||
\(757\) | −21.2470 | −0.772234 | −0.386117 | − | 0.922450i | \(-0.626184\pi\) | ||||
−0.386117 | + | 0.922450i | \(0.626184\pi\) | |||||||
\(758\) | 32.5777 | 1.18328 | ||||||||
\(759\) | −12.0877 | −0.438754 | ||||||||
\(760\) | 4.93600 | 0.179047 | ||||||||
\(761\) | −4.30816 | −0.156171 | −0.0780854 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780854 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(762\) | 33.8896 | 1.22769 | ||||||||
\(763\) | −14.7427 | −0.533721 | ||||||||
\(764\) | −2.53824 | −0.0918303 | ||||||||
\(765\) | 15.7224 | 0.568446 | ||||||||
\(766\) | −0.283228 | −0.0102334 | ||||||||
\(767\) | 68.1532 | 2.46087 | ||||||||
\(768\) | −2.86623 | −0.103426 | ||||||||
\(769\) | 40.7149 | 1.46822 | 0.734109 | − | 0.679032i | \(-0.237600\pi\) | ||||
0.734109 | + | 0.679032i | \(0.237600\pi\) | |||||||
\(770\) | 3.17681 | 0.114484 | ||||||||
\(771\) | 15.2763 | 0.550164 | ||||||||
\(772\) | −5.15005 | −0.185354 | ||||||||
\(773\) | 19.5182 | 0.702020 | 0.351010 | − | 0.936372i | \(-0.385838\pi\) | ||||
0.351010 | + | 0.936372i | \(0.385838\pi\) | |||||||
\(774\) | 41.8130 | 1.50294 | ||||||||
\(775\) | −1.22857 | −0.0441316 | ||||||||
\(776\) | −10.3353 | −0.371016 | ||||||||
\(777\) | 4.37072 | 0.156799 | ||||||||
\(778\) | −28.7129 | −1.02941 | ||||||||
\(779\) | 16.1273 | 0.577819 | ||||||||
\(780\) | −15.4835 | −0.554399 | ||||||||
\(781\) | −0.377002 | −0.0134902 | ||||||||
\(782\) | 3.92767 | 0.140453 | ||||||||
\(783\) | 30.7250 | 1.09802 | ||||||||
\(784\) | −6.03684 | −0.215601 | ||||||||
\(785\) | 1.35261 | 0.0482766 | ||||||||
\(786\) | −16.4641 | −0.587254 | ||||||||
\(787\) | −26.2803 | −0.936793 | −0.468396 | − | 0.883518i | \(-0.655168\pi\) | ||||
−0.468396 | + | 0.883518i | \(0.655168\pi\) | |||||||
\(788\) | −8.93316 | −0.318230 | ||||||||
\(789\) | 66.3024 | 2.36043 | ||||||||
\(790\) | −0.914963 | −0.0325529 | ||||||||
\(791\) | −8.11229 | −0.288440 | ||||||||
\(792\) | −16.8817 | −0.599865 | ||||||||
\(793\) | −81.1262 | −2.88087 | ||||||||
\(794\) | −12.1688 | −0.431854 | ||||||||
\(795\) | −9.71061 | −0.344400 | ||||||||
\(796\) | −8.47376 | −0.300344 | ||||||||
\(797\) | −32.6893 | −1.15792 | −0.578958 | − | 0.815358i | \(-0.696540\pi\) | ||||
−0.578958 | + | 0.815358i | \(0.696540\pi\) | |||||||
\(798\) | 13.8847 | 0.491511 | ||||||||
\(799\) | −33.2666 | −1.17689 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 88.6417 | 3.13200 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | 15.3677 | 0.542315 | ||||||||
\(804\) | 14.1381 | 0.498612 | ||||||||
\(805\) | −1.27862 | −0.0450653 | ||||||||
\(806\) | −6.63681 | −0.233772 | ||||||||
\(807\) | −53.7875 | −1.89341 | ||||||||
\(808\) | −11.1862 | −0.393530 | ||||||||
\(809\) | 37.1799 | 1.30718 | 0.653588 | − | 0.756851i | \(-0.273263\pi\) | ||||
0.653588 | + | 0.756851i | \(0.273263\pi\) | |||||||
\(810\) | 2.55308 | 0.0897060 | ||||||||
\(811\) | −12.4269 | −0.436368 | −0.218184 | − | 0.975908i | \(-0.570013\pi\) | ||||
−0.218184 | + | 0.975908i | \(0.570013\pi\) | |||||||
\(812\) | −4.74907 | −0.166660 | ||||||||
\(813\) | 6.26534 | 0.219735 | ||||||||
\(814\) | 5.02961 | 0.176288 | ||||||||
\(815\) | 3.44154 | 0.120552 | ||||||||
\(816\) | 8.64082 | 0.302489 | ||||||||
\(817\) | −39.5741 | −1.38452 | ||||||||
\(818\) | 8.12653 | 0.284138 | ||||||||
\(819\) | −27.6493 | −0.966144 | ||||||||
\(820\) | −3.26728 | −0.114098 | ||||||||
\(821\) | 12.0558 | 0.420750 | 0.210375 | − | 0.977621i | \(-0.432532\pi\) | ||||
0.210375 | + | 0.977621i | \(0.432532\pi\) | |||||||
\(822\) | 38.7306 | 1.35089 | ||||||||
\(823\) | 40.1242 | 1.39864 | 0.699321 | − | 0.714808i | \(-0.253486\pi\) | ||||
0.699321 | + | 0.714808i | \(0.253486\pi\) | |||||||
\(824\) | 1.10982 | 0.0386624 | ||||||||
\(825\) | −9.27794 | −0.323016 | ||||||||
\(826\) | 12.3816 | 0.430811 | ||||||||
\(827\) | 14.4220 | 0.501502 | 0.250751 | − | 0.968052i | \(-0.419323\pi\) | ||||
0.250751 | + | 0.968052i | \(0.419323\pi\) | |||||||
\(828\) | 6.79462 | 0.236129 | ||||||||
\(829\) | −3.22843 | −0.112128 | −0.0560641 | − | 0.998427i | \(-0.517855\pi\) | ||||
−0.0560641 | + | 0.998427i | \(0.517855\pi\) | |||||||
\(830\) | 7.48174 | 0.259695 | ||||||||
\(831\) | −3.16896 | −0.109930 | ||||||||
\(832\) | −5.40206 | −0.187283 | ||||||||
\(833\) | 18.1993 | 0.630568 | ||||||||
\(834\) | 3.05918 | 0.105931 | ||||||||
\(835\) | −0.681978 | −0.0236008 | ||||||||
\(836\) | 15.9778 | 0.552603 | ||||||||
\(837\) | 7.80069 | 0.269631 | ||||||||
\(838\) | −31.2448 | −1.07934 | ||||||||
\(839\) | −8.87424 | −0.306373 | −0.153186 | − | 0.988197i | \(-0.548953\pi\) | ||||
−0.153186 | + | 0.988197i | \(0.548953\pi\) | |||||||
\(840\) | −2.81294 | −0.0970556 | ||||||||
\(841\) | −5.58378 | −0.192544 | ||||||||
\(842\) | 1.26922 | 0.0437401 | ||||||||
\(843\) | −67.3888 | −2.32100 | ||||||||
\(844\) | 0.757364 | 0.0260696 | ||||||||
\(845\) | −16.1822 | −0.556685 | ||||||||
\(846\) | −57.5492 | −1.97858 | ||||||||
\(847\) | −0.512197 | −0.0175993 | ||||||||
\(848\) | −3.38794 | −0.116342 | ||||||||
\(849\) | 48.1123 | 1.65121 | ||||||||
\(850\) | 3.01470 | 0.103403 | ||||||||
\(851\) | −2.02434 | −0.0693935 | ||||||||
\(852\) | 0.333820 | 0.0114365 | ||||||||
\(853\) | −48.4722 | −1.65966 | −0.829828 | − | 0.558019i | \(-0.811562\pi\) | ||||
−0.829828 | + | 0.558019i | \(0.811562\pi\) | |||||||
\(854\) | −14.7384 | −0.504339 | ||||||||
\(855\) | −25.7425 | −0.880373 | ||||||||
\(856\) | −16.0511 | −0.548614 | ||||||||
\(857\) | −15.2432 | −0.520698 | −0.260349 | − | 0.965515i | \(-0.583838\pi\) | ||||
−0.260349 | + | 0.965515i | \(0.583838\pi\) | |||||||
\(858\) | −50.1200 | −1.71107 | ||||||||
\(859\) | 0.988211 | 0.0337173 | 0.0168587 | − | 0.999858i | \(-0.494633\pi\) | ||||
0.0168587 | + | 0.999858i | \(0.494633\pi\) | |||||||
\(860\) | 8.01745 | 0.273393 | ||||||||
\(861\) | −9.19064 | −0.313216 | ||||||||
\(862\) | 11.9607 | 0.407384 | ||||||||
\(863\) | 21.0637 | 0.717016 | 0.358508 | − | 0.933527i | \(-0.383286\pi\) | ||||
0.358508 | + | 0.933527i | \(0.383286\pi\) | |||||||
\(864\) | 6.34940 | 0.216011 | ||||||||
\(865\) | −2.33733 | −0.0794716 | ||||||||
\(866\) | 40.3389 | 1.37077 | ||||||||
\(867\) | 22.6763 | 0.770128 | ||||||||
\(868\) | −1.20573 | −0.0409251 | ||||||||
\(869\) | −2.96172 | −0.100470 | ||||||||
\(870\) | 13.8698 | 0.470229 | ||||||||
\(871\) | 26.6465 | 0.902882 | ||||||||
\(872\) | 15.0220 | 0.508708 | ||||||||
\(873\) | 53.9013 | 1.82428 | ||||||||
\(874\) | −6.43080 | −0.217525 | ||||||||
\(875\) | −0.981408 | −0.0331777 | ||||||||
\(876\) | −13.6075 | −0.459755 | ||||||||
\(877\) | 0.602518 | 0.0203456 | 0.0101728 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101728 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(878\) | 35.8412 | 1.20958 | ||||||||
\(879\) | 31.4851 | 1.06197 | ||||||||
\(880\) | −3.23699 | −0.109119 | ||||||||
\(881\) | −31.8197 | −1.07203 | −0.536017 | − | 0.844207i | \(-0.680072\pi\) | ||||
−0.536017 | + | 0.844207i | \(0.680072\pi\) | |||||||
\(882\) | 31.4836 | 1.06011 | ||||||||
\(883\) | 3.26342 | 0.109823 | 0.0549115 | − | 0.998491i | \(-0.482512\pi\) | ||||
0.0549115 | + | 0.998491i | \(0.482512\pi\) | |||||||
\(884\) | 16.2856 | 0.547744 | ||||||||
\(885\) | −36.1607 | −1.21553 | ||||||||
\(886\) | 25.8381 | 0.868048 | ||||||||
\(887\) | −22.7994 | −0.765528 | −0.382764 | − | 0.923846i | \(-0.625028\pi\) | ||||
−0.382764 | + | 0.923846i | \(0.625028\pi\) | |||||||
\(888\) | −4.45352 | −0.149450 | ||||||||
\(889\) | 11.6040 | 0.389184 | ||||||||
\(890\) | 16.9966 | 0.569728 | ||||||||
\(891\) | 8.26428 | 0.276864 | ||||||||
\(892\) | 17.5519 | 0.587683 | ||||||||
\(893\) | 54.4677 | 1.82269 | ||||||||
\(894\) | 38.1915 | 1.27731 | ||||||||
\(895\) | 12.0967 | 0.404349 | ||||||||
\(896\) | −0.981408 | −0.0327866 | ||||||||
\(897\) | 20.1725 | 0.673540 | ||||||||
\(898\) | 10.2434 | 0.341828 | ||||||||
\(899\) | 5.94509 | 0.198280 | ||||||||
\(900\) | 5.21525 | 0.173842 | ||||||||
\(901\) | 10.2136 | 0.340266 | ||||||||
\(902\) | −10.5761 | −0.352147 | ||||||||
\(903\) | 22.5526 | 0.750504 | ||||||||
\(904\) | 8.26597 | 0.274922 | ||||||||
\(905\) | 5.64646 | 0.187695 | ||||||||
\(906\) | −53.0473 | −1.76238 | ||||||||
\(907\) | −25.4084 | −0.843671 | −0.421835 | − | 0.906672i | \(-0.638614\pi\) | ||||
−0.421835 | + | 0.906672i | \(0.638614\pi\) | |||||||
\(908\) | −25.8206 | −0.856887 | ||||||||
\(909\) | 58.3389 | 1.93498 | ||||||||
\(910\) | −5.30162 | −0.175747 | ||||||||
\(911\) | 3.34150 | 0.110709 | 0.0553544 | − | 0.998467i | \(-0.482371\pi\) | ||||
0.0553544 | + | 0.998467i | \(0.482371\pi\) | |||||||
\(912\) | −14.1477 | −0.468477 | ||||||||
\(913\) | 24.2183 | 0.801509 | ||||||||
\(914\) | 23.6779 | 0.783194 | ||||||||
\(915\) | 43.0440 | 1.42299 | ||||||||
\(916\) | −18.8698 | −0.623477 | ||||||||
\(917\) | −5.63737 | −0.186162 | ||||||||
\(918\) | −19.1416 | −0.631766 | ||||||||
\(919\) | 44.5860 | 1.47076 | 0.735379 | − | 0.677656i | \(-0.237004\pi\) | ||||
0.735379 | + | 0.677656i | \(0.237004\pi\) | |||||||
\(920\) | 1.30284 | 0.0429533 | ||||||||
\(921\) | 47.5731 | 1.56759 | ||||||||
\(922\) | −0.150219 | −0.00494722 | ||||||||
\(923\) | 0.629160 | 0.0207091 | ||||||||
\(924\) | −9.10545 | −0.299547 | ||||||||
\(925\) | −1.55379 | −0.0510884 | ||||||||
\(926\) | −28.3404 | −0.931322 | ||||||||
\(927\) | −5.78798 | −0.190102 | ||||||||
\(928\) | 4.83903 | 0.158849 | ||||||||
\(929\) | 6.30033 | 0.206707 | 0.103354 | − | 0.994645i | \(-0.467043\pi\) | ||||
0.103354 | + | 0.994645i | \(0.467043\pi\) | |||||||
\(930\) | 3.52136 | 0.115470 | ||||||||
\(931\) | −29.7978 | −0.976584 | ||||||||
\(932\) | −20.3884 | −0.667845 | ||||||||
\(933\) | 65.7345 | 2.15205 | ||||||||
\(934\) | 6.79712 | 0.222408 | ||||||||
\(935\) | 9.75856 | 0.319139 | ||||||||
\(936\) | 28.1731 | 0.920866 | ||||||||
\(937\) | −9.79260 | −0.319910 | −0.159955 | − | 0.987124i | \(-0.551135\pi\) | ||||
−0.159955 | + | 0.987124i | \(0.551135\pi\) | |||||||
\(938\) | 4.84095 | 0.158063 | ||||||||
\(939\) | 68.9851 | 2.25124 | ||||||||
\(940\) | −11.0348 | −0.359915 | ||||||||
\(941\) | 9.26615 | 0.302068 | 0.151034 | − | 0.988529i | \(-0.451740\pi\) | ||||
0.151034 | + | 0.988529i | \(0.451740\pi\) | |||||||
\(942\) | −3.87688 | −0.126315 | ||||||||
\(943\) | 4.25673 | 0.138618 | ||||||||
\(944\) | −12.6162 | −0.410621 | ||||||||
\(945\) | 6.23136 | 0.202706 | ||||||||
\(946\) | 25.9524 | 0.843786 | ||||||||
\(947\) | 42.2598 | 1.37326 | 0.686630 | − | 0.727007i | \(-0.259089\pi\) | ||||
0.686630 | + | 0.727007i | \(0.259089\pi\) | |||||||
\(948\) | 2.62249 | 0.0851745 | ||||||||
\(949\) | −25.6464 | −0.832519 | ||||||||
\(950\) | −4.93600 | −0.160145 | ||||||||
\(951\) | 31.3815 | 1.01761 | ||||||||
\(952\) | 2.95866 | 0.0958906 | ||||||||
\(953\) | −56.9411 | −1.84450 | −0.922251 | − | 0.386591i | \(-0.873653\pi\) | ||||
−0.922251 | + | 0.386591i | \(0.873653\pi\) | |||||||
\(954\) | 17.6690 | 0.572054 | ||||||||
\(955\) | 2.53824 | 0.0821355 | ||||||||
\(956\) | −15.4040 | −0.498200 | ||||||||
\(957\) | 44.8962 | 1.45129 | ||||||||
\(958\) | −37.2822 | −1.20453 | ||||||||
\(959\) | 13.2615 | 0.428237 | ||||||||
\(960\) | 2.86623 | 0.0925070 | ||||||||
\(961\) | −29.4906 | −0.951310 | ||||||||
\(962\) | −8.39368 | −0.270623 | ||||||||
\(963\) | 83.7103 | 2.69753 | ||||||||
\(964\) | −6.89885 | −0.222197 | ||||||||
\(965\) | 5.15005 | 0.165786 | ||||||||
\(966\) | 3.66480 | 0.117913 | ||||||||
\(967\) | 15.1523 | 0.487265 | 0.243633 | − | 0.969868i | \(-0.421661\pi\) | ||||
0.243633 | + | 0.969868i | \(0.421661\pi\) | |||||||
\(968\) | 0.521900 | 0.0167745 | ||||||||
\(969\) | 42.6511 | 1.37015 | ||||||||
\(970\) | 10.3353 | 0.331847 | ||||||||
\(971\) | 18.5151 | 0.594178 | 0.297089 | − | 0.954850i | \(-0.403984\pi\) | ||||
0.297089 | + | 0.954850i | \(0.403984\pi\) | |||||||
\(972\) | 11.7305 | 0.376257 | ||||||||
\(973\) | 1.04748 | 0.0335805 | ||||||||
\(974\) | 1.95947 | 0.0627856 | ||||||||
\(975\) | 15.4835 | 0.495869 | ||||||||
\(976\) | 15.0176 | 0.480703 | ||||||||
\(977\) | −2.34607 | −0.0750575 | −0.0375288 | − | 0.999296i | \(-0.511949\pi\) | ||||
−0.0375288 | + | 0.999296i | \(0.511949\pi\) | |||||||
\(978\) | −9.86422 | −0.315423 | ||||||||
\(979\) | 55.0179 | 1.75838 | ||||||||
\(980\) | 6.03684 | 0.192840 | ||||||||
\(981\) | −78.3434 | −2.50131 | ||||||||
\(982\) | 26.0586 | 0.831563 | ||||||||
\(983\) | 51.5565 | 1.64440 | 0.822198 | − | 0.569202i | \(-0.192748\pi\) | ||||
0.822198 | + | 0.569202i | \(0.192748\pi\) | |||||||
\(984\) | 9.36475 | 0.298537 | ||||||||
\(985\) | 8.93316 | 0.284634 | ||||||||
\(986\) | −14.5882 | −0.464584 | ||||||||
\(987\) | −31.0402 | −0.988020 | ||||||||
\(988\) | −26.6645 | −0.848312 | ||||||||
\(989\) | −10.4454 | −0.332146 | ||||||||
\(990\) | 16.8817 | 0.536536 | ||||||||
\(991\) | −45.4156 | −1.44268 | −0.721338 | − | 0.692584i | \(-0.756472\pi\) | ||||
−0.721338 | + | 0.692584i | \(0.756472\pi\) | |||||||
\(992\) | 1.22857 | 0.0390072 | ||||||||
\(993\) | −36.0688 | −1.14461 | ||||||||
\(994\) | 0.114301 | 0.00362542 | ||||||||
\(995\) | 8.47376 | 0.268636 | ||||||||
\(996\) | −21.4443 | −0.679490 | ||||||||
\(997\) | 10.7484 | 0.340405 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(998\) | 2.70819 | 0.0857262 | ||||||||
\(999\) | 9.86566 | 0.312136 |
(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 | 4010.2.a.k.1.3 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.k.1.3 | ✓ | 15 | 1.1 | even | 1 | trivial |