Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, 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("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.08419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08419 | −0.766635 | −0.383317 | − | 0.923617i | \(-0.625218\pi\) | ||||
−0.383317 | + | 0.923617i | \(0.625218\pi\) | |||||||
\(3\) | 1.50990 | 0.871740 | 0.435870 | − | 0.900010i | \(-0.356441\pi\) | ||||
0.435870 | + | 0.900010i | \(0.356441\pi\) | |||||||
\(4\) | −0.824542 | −0.412271 | ||||||||
\(5\) | 0.786014 | 0.351516 | 0.175758 | − | 0.984433i | \(-0.443762\pi\) | ||||
0.175758 | + | 0.984433i | \(0.443762\pi\) | |||||||
\(6\) | −1.63701 | −0.668306 | ||||||||
\(7\) | −4.63453 | −1.75169 | −0.875845 | − | 0.482593i | \(-0.839695\pi\) | ||||
−0.875845 | + | 0.482593i | \(0.839695\pi\) | |||||||
\(8\) | 3.06233 | 1.08270 | ||||||||
\(9\) | −0.720207 | −0.240069 | ||||||||
\(10\) | −0.852185 | −0.269485 | ||||||||
\(11\) | 4.80440 | 1.44858 | 0.724290 | − | 0.689496i | \(-0.242168\pi\) | ||||
0.724290 | + | 0.689496i | \(0.242168\pi\) | |||||||
\(12\) | −1.24497 | −0.359393 | ||||||||
\(13\) | −3.44502 | −0.955477 | −0.477738 | − | 0.878502i | \(-0.658543\pi\) | ||||
−0.477738 | + | 0.878502i | \(0.658543\pi\) | |||||||
\(14\) | 5.02469 | 1.34291 | ||||||||
\(15\) | 1.18680 | 0.306431 | ||||||||
\(16\) | −1.67105 | −0.417761 | ||||||||
\(17\) | −1.46070 | −0.354272 | −0.177136 | − | 0.984186i | \(-0.556683\pi\) | ||||
−0.177136 | + | 0.984186i | \(0.556683\pi\) | |||||||
\(18\) | 0.780838 | 0.184045 | ||||||||
\(19\) | −1.81007 | −0.415259 | −0.207630 | − | 0.978208i | \(-0.566575\pi\) | ||||
−0.207630 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(20\) | −0.648102 | −0.144920 | ||||||||
\(21\) | −6.99768 | −1.52702 | ||||||||
\(22\) | −5.20885 | −1.11053 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 4.62380 | 0.943830 | ||||||||
\(25\) | −4.38218 | −0.876436 | ||||||||
\(26\) | 3.73504 | 0.732502 | ||||||||
\(27\) | −5.61713 | −1.08102 | ||||||||
\(28\) | 3.82137 | 0.722171 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.28671 | −0.234921 | ||||||||
\(31\) | −4.86699 | −0.874137 | −0.437069 | − | 0.899428i | \(-0.643983\pi\) | ||||
−0.437069 | + | 0.899428i | \(0.643983\pi\) | |||||||
\(32\) | −4.31293 | −0.762426 | ||||||||
\(33\) | 7.25415 | 1.26279 | ||||||||
\(34\) | 1.58367 | 0.271598 | ||||||||
\(35\) | −3.64281 | −0.615747 | ||||||||
\(36\) | 0.593841 | 0.0989735 | ||||||||
\(37\) | −10.3517 | −1.70182 | −0.850908 | − | 0.525315i | \(-0.823947\pi\) | ||||
−0.850908 | + | 0.525315i | \(0.823947\pi\) | |||||||
\(38\) | 1.96245 | 0.318352 | ||||||||
\(39\) | −5.20163 | −0.832928 | ||||||||
\(40\) | 2.40703 | 0.380585 | ||||||||
\(41\) | 9.91091 | 1.54782 | 0.773912 | − | 0.633293i | \(-0.218297\pi\) | ||||
0.773912 | + | 0.633293i | \(0.218297\pi\) | |||||||
\(42\) | 7.58678 | 1.17067 | ||||||||
\(43\) | −6.59023 | −1.00500 | −0.502500 | − | 0.864577i | \(-0.667586\pi\) | ||||
−0.502500 | + | 0.864577i | \(0.667586\pi\) | |||||||
\(44\) | −3.96143 | −0.597208 | ||||||||
\(45\) | −0.566093 | −0.0843881 | ||||||||
\(46\) | 1.08419 | 0.159854 | ||||||||
\(47\) | 2.49788 | 0.364353 | 0.182177 | − | 0.983266i | \(-0.441686\pi\) | ||||
0.182177 | + | 0.983266i | \(0.441686\pi\) | |||||||
\(48\) | −2.52311 | −0.364179 | ||||||||
\(49\) | 14.4789 | 2.06842 | ||||||||
\(50\) | 4.75110 | 0.671907 | ||||||||
\(51\) | −2.20551 | −0.308834 | ||||||||
\(52\) | 2.84056 | 0.393915 | ||||||||
\(53\) | 1.06830 | 0.146742 | 0.0733709 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733709 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(54\) | 6.09001 | 0.828746 | ||||||||
\(55\) | 3.77632 | 0.509199 | ||||||||
\(56\) | −14.1925 | −1.89655 | ||||||||
\(57\) | −2.73303 | −0.361998 | ||||||||
\(58\) | 1.08419 | 0.142361 | ||||||||
\(59\) | −8.50982 | −1.10788 | −0.553942 | − | 0.832555i | \(-0.686877\pi\) | ||||
−0.553942 | + | 0.832555i | \(0.686877\pi\) | |||||||
\(60\) | −0.978568 | −0.126333 | ||||||||
\(61\) | 5.33862 | 0.683540 | 0.341770 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341770 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(62\) | 5.27672 | 0.670144 | ||||||||
\(63\) | 3.33782 | 0.420526 | ||||||||
\(64\) | 8.01811 | 1.00226 | ||||||||
\(65\) | −2.70783 | −0.335866 | ||||||||
\(66\) | −7.86484 | −0.968095 | ||||||||
\(67\) | −2.04102 | −0.249350 | −0.124675 | − | 0.992198i | \(-0.539789\pi\) | ||||
−0.124675 | + | 0.992198i | \(0.539789\pi\) | |||||||
\(68\) | 1.20441 | 0.146056 | ||||||||
\(69\) | −1.50990 | −0.181770 | ||||||||
\(70\) | 3.94948 | 0.472053 | ||||||||
\(71\) | −7.02707 | −0.833959 | −0.416980 | − | 0.908916i | \(-0.636911\pi\) | ||||
−0.416980 | + | 0.908916i | \(0.636911\pi\) | |||||||
\(72\) | −2.20551 | −0.259922 | ||||||||
\(73\) | −6.41672 | −0.751020 | −0.375510 | − | 0.926818i | \(-0.622532\pi\) | ||||
−0.375510 | + | 0.926818i | \(0.622532\pi\) | |||||||
\(74\) | 11.2232 | 1.30467 | ||||||||
\(75\) | −6.61665 | −0.764025 | ||||||||
\(76\) | 1.49248 | 0.171199 | ||||||||
\(77\) | −22.2661 | −2.53746 | ||||||||
\(78\) | 5.63953 | 0.638551 | ||||||||
\(79\) | −4.87925 | −0.548958 | −0.274479 | − | 0.961593i | \(-0.588505\pi\) | ||||
−0.274479 | + | 0.961593i | \(0.588505\pi\) | |||||||
\(80\) | −1.31347 | −0.146850 | ||||||||
\(81\) | −6.32068 | −0.702298 | ||||||||
\(82\) | −10.7453 | −1.18662 | ||||||||
\(83\) | 1.67762 | 0.184143 | 0.0920715 | − | 0.995752i | \(-0.470651\pi\) | ||||
0.0920715 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(84\) | 5.76988 | 0.629545 | ||||||||
\(85\) | −1.14813 | −0.124532 | ||||||||
\(86\) | 7.14503 | 0.770468 | ||||||||
\(87\) | −1.50990 | −0.161878 | ||||||||
\(88\) | 14.7126 | 1.56837 | ||||||||
\(89\) | 14.1259 | 1.49735 | 0.748673 | − | 0.662940i | \(-0.230692\pi\) | ||||
0.748673 | + | 0.662940i | \(0.230692\pi\) | |||||||
\(90\) | 0.613749 | 0.0646949 | ||||||||
\(91\) | 15.9661 | 1.67370 | ||||||||
\(92\) | 0.824542 | 0.0859645 | ||||||||
\(93\) | −7.34866 | −0.762021 | ||||||||
\(94\) | −2.70816 | −0.279326 | ||||||||
\(95\) | −1.42274 | −0.145970 | ||||||||
\(96\) | −6.51209 | −0.664637 | ||||||||
\(97\) | −8.39649 | −0.852535 | −0.426267 | − | 0.904597i | \(-0.640172\pi\) | ||||
−0.426267 | + | 0.904597i | \(0.640172\pi\) | |||||||
\(98\) | −15.6978 | −1.58572 | ||||||||
\(99\) | −3.46016 | −0.347759 | ||||||||
\(100\) | 3.61329 | 0.361329 | ||||||||
\(101\) | −3.68109 | −0.366283 | −0.183141 | − | 0.983087i | \(-0.558627\pi\) | ||||
−0.183141 | + | 0.983087i | \(0.558627\pi\) | |||||||
\(102\) | 2.39118 | 0.236763 | ||||||||
\(103\) | 12.6337 | 1.24483 | 0.622417 | − | 0.782686i | \(-0.286151\pi\) | ||||
0.622417 | + | 0.782686i | \(0.286151\pi\) | |||||||
\(104\) | −10.5498 | −1.03449 | ||||||||
\(105\) | −5.50027 | −0.536772 | ||||||||
\(106\) | −1.15823 | −0.112497 | ||||||||
\(107\) | 17.1297 | 1.65599 | 0.827997 | − | 0.560732i | \(-0.189480\pi\) | ||||
0.827997 | + | 0.560732i | \(0.189480\pi\) | |||||||
\(108\) | 4.63156 | 0.445672 | ||||||||
\(109\) | −4.21849 | −0.404058 | −0.202029 | − | 0.979380i | \(-0.564754\pi\) | ||||
−0.202029 | + | 0.979380i | \(0.564754\pi\) | |||||||
\(110\) | −4.09423 | −0.390370 | ||||||||
\(111\) | −15.6301 | −1.48354 | ||||||||
\(112\) | 7.74452 | 0.731788 | ||||||||
\(113\) | −12.4166 | −1.16806 | −0.584028 | − | 0.811734i | \(-0.698524\pi\) | ||||
−0.584028 | + | 0.811734i | \(0.698524\pi\) | |||||||
\(114\) | 2.96311 | 0.277520 | ||||||||
\(115\) | −0.786014 | −0.0732962 | ||||||||
\(116\) | 0.824542 | 0.0765568 | ||||||||
\(117\) | 2.48113 | 0.229380 | ||||||||
\(118\) | 9.22622 | 0.849343 | ||||||||
\(119\) | 6.76968 | 0.620575 | ||||||||
\(120\) | 3.63437 | 0.331771 | ||||||||
\(121\) | 12.0822 | 1.09838 | ||||||||
\(122\) | −5.78805 | −0.524026 | ||||||||
\(123\) | 14.9645 | 1.34930 | ||||||||
\(124\) | 4.01304 | 0.360382 | ||||||||
\(125\) | −7.37453 | −0.659598 | ||||||||
\(126\) | −3.61882 | −0.322390 | ||||||||
\(127\) | −1.77286 | −0.157316 | −0.0786578 | − | 0.996902i | \(-0.525063\pi\) | ||||
−0.0786578 | + | 0.996902i | \(0.525063\pi\) | |||||||
\(128\) | −0.0672536 | −0.00594443 | ||||||||
\(129\) | −9.95058 | −0.876099 | ||||||||
\(130\) | 2.93579 | 0.257486 | ||||||||
\(131\) | 5.37219 | 0.469370 | 0.234685 | − | 0.972071i | \(-0.424594\pi\) | ||||
0.234685 | + | 0.972071i | \(0.424594\pi\) | |||||||
\(132\) | −5.98135 | −0.520610 | ||||||||
\(133\) | 8.38885 | 0.727405 | ||||||||
\(134\) | 2.21284 | 0.191160 | ||||||||
\(135\) | −4.41515 | −0.379995 | ||||||||
\(136\) | −4.47315 | −0.383569 | ||||||||
\(137\) | −15.7630 | −1.34672 | −0.673361 | − | 0.739314i | \(-0.735150\pi\) | ||||
−0.673361 | + | 0.739314i | \(0.735150\pi\) | |||||||
\(138\) | 1.63701 | 0.139352 | ||||||||
\(139\) | 16.2070 | 1.37466 | 0.687329 | − | 0.726346i | \(-0.258783\pi\) | ||||
0.687329 | + | 0.726346i | \(0.258783\pi\) | |||||||
\(140\) | 3.00365 | 0.253855 | ||||||||
\(141\) | 3.77154 | 0.317621 | ||||||||
\(142\) | 7.61864 | 0.639342 | ||||||||
\(143\) | −16.5512 | −1.38408 | ||||||||
\(144\) | 1.20350 | 0.100292 | ||||||||
\(145\) | −0.786014 | −0.0652749 | ||||||||
\(146\) | 6.95691 | 0.575758 | ||||||||
\(147\) | 21.8617 | 1.80312 | ||||||||
\(148\) | 8.53544 | 0.701609 | ||||||||
\(149\) | −0.767900 | −0.0629088 | −0.0314544 | − | 0.999505i | \(-0.510014\pi\) | ||||
−0.0314544 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(150\) | 7.17367 | 0.585728 | ||||||||
\(151\) | 3.51621 | 0.286145 | 0.143073 | − | 0.989712i | \(-0.454302\pi\) | ||||
0.143073 | + | 0.989712i | \(0.454302\pi\) | |||||||
\(152\) | −5.54304 | −0.449600 | ||||||||
\(153\) | 1.05201 | 0.0850498 | ||||||||
\(154\) | 24.1406 | 1.94531 | ||||||||
\(155\) | −3.82552 | −0.307273 | ||||||||
\(156\) | 4.28896 | 0.343392 | ||||||||
\(157\) | 13.6276 | 1.08760 | 0.543799 | − | 0.839216i | \(-0.316986\pi\) | ||||
0.543799 | + | 0.839216i | \(0.316986\pi\) | |||||||
\(158\) | 5.29001 | 0.420851 | ||||||||
\(159\) | 1.61302 | 0.127921 | ||||||||
\(160\) | −3.39002 | −0.268005 | ||||||||
\(161\) | 4.63453 | 0.365252 | ||||||||
\(162\) | 6.85279 | 0.538406 | ||||||||
\(163\) | 24.1685 | 1.89302 | 0.946510 | − | 0.322675i | \(-0.104582\pi\) | ||||
0.946510 | + | 0.322675i | \(0.104582\pi\) | |||||||
\(164\) | −8.17196 | −0.638123 | ||||||||
\(165\) | 5.70186 | 0.443889 | ||||||||
\(166\) | −1.81885 | −0.141170 | ||||||||
\(167\) | 3.00489 | 0.232526 | 0.116263 | − | 0.993218i | \(-0.462909\pi\) | ||||
0.116263 | + | 0.993218i | \(0.462909\pi\) | |||||||
\(168\) | −21.4292 | −1.65330 | ||||||||
\(169\) | −1.13183 | −0.0870639 | ||||||||
\(170\) | 1.24479 | 0.0954709 | ||||||||
\(171\) | 1.30363 | 0.0996909 | ||||||||
\(172\) | 5.43392 | 0.414333 | ||||||||
\(173\) | −3.14834 | −0.239364 | −0.119682 | − | 0.992812i | \(-0.538187\pi\) | ||||
−0.119682 | + | 0.992812i | \(0.538187\pi\) | |||||||
\(174\) | 1.63701 | 0.124101 | ||||||||
\(175\) | 20.3094 | 1.53524 | ||||||||
\(176\) | −8.02836 | −0.605161 | ||||||||
\(177\) | −12.8490 | −0.965787 | ||||||||
\(178\) | −15.3151 | −1.14792 | ||||||||
\(179\) | 24.8759 | 1.85931 | 0.929656 | − | 0.368430i | \(-0.120104\pi\) | ||||
0.929656 | + | 0.368430i | \(0.120104\pi\) | |||||||
\(180\) | 0.466767 | 0.0347908 | ||||||||
\(181\) | −1.14502 | −0.0851086 | −0.0425543 | − | 0.999094i | \(-0.513550\pi\) | ||||
−0.0425543 | + | 0.999094i | \(0.513550\pi\) | |||||||
\(182\) | −17.3102 | −1.28312 | ||||||||
\(183\) | 8.06077 | 0.595869 | ||||||||
\(184\) | −3.06233 | −0.225758 | ||||||||
\(185\) | −8.13661 | −0.598216 | ||||||||
\(186\) | 7.96731 | 0.584192 | ||||||||
\(187\) | −7.01779 | −0.513192 | ||||||||
\(188\) | −2.05961 | −0.150212 | ||||||||
\(189\) | 26.0328 | 1.89361 | ||||||||
\(190\) | 1.54252 | 0.111906 | ||||||||
\(191\) | −12.7023 | −0.919109 | −0.459555 | − | 0.888150i | \(-0.651991\pi\) | ||||
−0.459555 | + | 0.888150i | \(0.651991\pi\) | |||||||
\(192\) | 12.1065 | 0.873713 | ||||||||
\(193\) | 15.7139 | 1.13111 | 0.565555 | − | 0.824711i | \(-0.308662\pi\) | ||||
0.565555 | + | 0.824711i | \(0.308662\pi\) | |||||||
\(194\) | 9.10335 | 0.653583 | ||||||||
\(195\) | −4.08856 | −0.292788 | ||||||||
\(196\) | −11.9385 | −0.852748 | ||||||||
\(197\) | 5.69145 | 0.405499 | 0.202749 | − | 0.979231i | \(-0.435012\pi\) | ||||
0.202749 | + | 0.979231i | \(0.435012\pi\) | |||||||
\(198\) | 3.75145 | 0.266604 | ||||||||
\(199\) | −26.0226 | −1.84469 | −0.922347 | − | 0.386363i | \(-0.873731\pi\) | ||||
−0.922347 | + | 0.386363i | \(0.873731\pi\) | |||||||
\(200\) | −13.4197 | −0.948914 | ||||||||
\(201\) | −3.08173 | −0.217368 | ||||||||
\(202\) | 3.99099 | 0.280805 | ||||||||
\(203\) | 4.63453 | 0.325281 | ||||||||
\(204\) | 1.81854 | 0.127323 | ||||||||
\(205\) | 7.79012 | 0.544085 | ||||||||
\(206\) | −13.6973 | −0.954333 | ||||||||
\(207\) | 0.720207 | 0.0500578 | ||||||||
\(208\) | 5.75679 | 0.399161 | ||||||||
\(209\) | −8.69631 | −0.601536 | ||||||||
\(210\) | 5.96331 | 0.411508 | ||||||||
\(211\) | 5.97054 | 0.411029 | 0.205514 | − | 0.978654i | \(-0.434113\pi\) | ||||
0.205514 | + | 0.978654i | \(0.434113\pi\) | |||||||
\(212\) | −0.880855 | −0.0604974 | ||||||||
\(213\) | −10.6102 | −0.726996 | ||||||||
\(214\) | −18.5718 | −1.26954 | ||||||||
\(215\) | −5.18001 | −0.353274 | ||||||||
\(216\) | −17.2015 | −1.17041 | ||||||||
\(217\) | 22.5562 | 1.53122 | ||||||||
\(218\) | 4.57363 | 0.309765 | ||||||||
\(219\) | −9.68860 | −0.654695 | ||||||||
\(220\) | −3.11374 | −0.209928 | ||||||||
\(221\) | 5.03215 | 0.338499 | ||||||||
\(222\) | 16.9459 | 1.13733 | ||||||||
\(223\) | −1.94599 | −0.130313 | −0.0651565 | − | 0.997875i | \(-0.520755\pi\) | ||||
−0.0651565 | + | 0.997875i | \(0.520755\pi\) | |||||||
\(224\) | 19.9884 | 1.33553 | ||||||||
\(225\) | 3.15608 | 0.210405 | ||||||||
\(226\) | 13.4619 | 0.895472 | ||||||||
\(227\) | 14.1896 | 0.941794 | 0.470897 | − | 0.882188i | \(-0.343930\pi\) | ||||
0.470897 | + | 0.882188i | \(0.343930\pi\) | |||||||
\(228\) | 2.25350 | 0.149241 | ||||||||
\(229\) | −17.1122 | −1.13081 | −0.565405 | − | 0.824814i | \(-0.691280\pi\) | ||||
−0.565405 | + | 0.824814i | \(0.691280\pi\) | |||||||
\(230\) | 0.852185 | 0.0561914 | ||||||||
\(231\) | −33.6196 | −2.21201 | ||||||||
\(232\) | −3.06233 | −0.201052 | ||||||||
\(233\) | 9.79924 | 0.641970 | 0.320985 | − | 0.947084i | \(-0.395986\pi\) | ||||
0.320985 | + | 0.947084i | \(0.395986\pi\) | |||||||
\(234\) | −2.69000 | −0.175851 | ||||||||
\(235\) | 1.96337 | 0.128076 | ||||||||
\(236\) | 7.01671 | 0.456749 | ||||||||
\(237\) | −7.36717 | −0.478549 | ||||||||
\(238\) | −7.33958 | −0.475755 | ||||||||
\(239\) | 13.8667 | 0.896964 | 0.448482 | − | 0.893792i | \(-0.351965\pi\) | ||||
0.448482 | + | 0.893792i | \(0.351965\pi\) | |||||||
\(240\) | −1.98320 | −0.128015 | ||||||||
\(241\) | −11.2309 | −0.723443 | −0.361722 | − | 0.932286i | \(-0.617811\pi\) | ||||
−0.361722 | + | 0.932286i | \(0.617811\pi\) | |||||||
\(242\) | −13.0994 | −0.842059 | ||||||||
\(243\) | 7.30782 | 0.468797 | ||||||||
\(244\) | −4.40192 | −0.281804 | ||||||||
\(245\) | 11.3806 | 0.727082 | ||||||||
\(246\) | −16.2243 | −1.03442 | ||||||||
\(247\) | 6.23574 | 0.396771 | ||||||||
\(248\) | −14.9043 | −0.946425 | ||||||||
\(249\) | 2.53304 | 0.160525 | ||||||||
\(250\) | 7.99535 | 0.505671 | ||||||||
\(251\) | −7.20786 | −0.454956 | −0.227478 | − | 0.973783i | \(-0.573048\pi\) | ||||
−0.227478 | + | 0.973783i | \(0.573048\pi\) | |||||||
\(252\) | −2.75218 | −0.173371 | ||||||||
\(253\) | −4.80440 | −0.302050 | ||||||||
\(254\) | 1.92210 | 0.120604 | ||||||||
\(255\) | −1.73356 | −0.108560 | ||||||||
\(256\) | −15.9633 | −0.997706 | ||||||||
\(257\) | −22.1065 | −1.37897 | −0.689483 | − | 0.724302i | \(-0.742162\pi\) | ||||
−0.689483 | + | 0.724302i | \(0.742162\pi\) | |||||||
\(258\) | 10.7883 | 0.671648 | ||||||||
\(259\) | 47.9755 | 2.98105 | ||||||||
\(260\) | 2.23272 | 0.138468 | ||||||||
\(261\) | 0.720207 | 0.0445797 | ||||||||
\(262\) | −5.82444 | −0.359835 | ||||||||
\(263\) | 8.38486 | 0.517033 | 0.258516 | − | 0.966007i | \(-0.416766\pi\) | ||||
0.258516 | + | 0.966007i | \(0.416766\pi\) | |||||||
\(264\) | 22.2146 | 1.36721 | ||||||||
\(265\) | 0.839696 | 0.0515821 | ||||||||
\(266\) | −9.09506 | −0.557654 | ||||||||
\(267\) | 21.3287 | 1.30530 | ||||||||
\(268\) | 1.68291 | 0.102800 | ||||||||
\(269\) | 5.76591 | 0.351554 | 0.175777 | − | 0.984430i | \(-0.443756\pi\) | ||||
0.175777 | + | 0.984430i | \(0.443756\pi\) | |||||||
\(270\) | 4.78684 | 0.291318 | ||||||||
\(271\) | −20.2643 | −1.23097 | −0.615484 | − | 0.788149i | \(-0.711039\pi\) | ||||
−0.615484 | + | 0.788149i | \(0.711039\pi\) | |||||||
\(272\) | 2.44090 | 0.148001 | ||||||||
\(273\) | 24.1071 | 1.45903 | ||||||||
\(274\) | 17.0900 | 1.03244 | ||||||||
\(275\) | −21.0537 | −1.26959 | ||||||||
\(276\) | 1.24497 | 0.0749387 | ||||||||
\(277\) | −27.1992 | −1.63424 | −0.817120 | − | 0.576468i | \(-0.804431\pi\) | ||||
−0.817120 | + | 0.576468i | \(0.804431\pi\) | |||||||
\(278\) | −17.5714 | −1.05386 | ||||||||
\(279\) | 3.50524 | 0.209853 | ||||||||
\(280\) | −11.1555 | −0.666667 | ||||||||
\(281\) | 6.82835 | 0.407345 | 0.203673 | − | 0.979039i | \(-0.434712\pi\) | ||||
0.203673 | + | 0.979039i | \(0.434712\pi\) | |||||||
\(282\) | −4.08905 | −0.243500 | ||||||||
\(283\) | −27.8034 | −1.65274 | −0.826369 | − | 0.563128i | \(-0.809598\pi\) | ||||
−0.826369 | + | 0.563128i | \(0.809598\pi\) | |||||||
\(284\) | 5.79411 | 0.343817 | ||||||||
\(285\) | −2.14820 | −0.127248 | ||||||||
\(286\) | 17.9446 | 1.06109 | ||||||||
\(287\) | −45.9325 | −2.71131 | ||||||||
\(288\) | 3.10620 | 0.183035 | ||||||||
\(289\) | −14.8663 | −0.874491 | ||||||||
\(290\) | 0.852185 | 0.0500420 | ||||||||
\(291\) | −12.6778 | −0.743189 | ||||||||
\(292\) | 5.29086 | 0.309624 | ||||||||
\(293\) | −0.0118298 | −0.000691103 0 | −0.000345552 | − | 1.00000i | \(-0.500110\pi\) | ||||
−0.000345552 | 1.00000i | \(0.500110\pi\) | ||||||||
\(294\) | −23.7021 | −1.38234 | ||||||||
\(295\) | −6.68884 | −0.389439 | ||||||||
\(296\) | −31.7004 | −1.84255 | ||||||||
\(297\) | −26.9869 | −1.56594 | ||||||||
\(298\) | 0.832545 | 0.0482281 | ||||||||
\(299\) | 3.44502 | 0.199231 | ||||||||
\(300\) | 5.45571 | 0.314985 | ||||||||
\(301\) | 30.5426 | 1.76045 | ||||||||
\(302\) | −3.81223 | −0.219369 | ||||||||
\(303\) | −5.55808 | −0.319303 | ||||||||
\(304\) | 3.02472 | 0.173479 | ||||||||
\(305\) | 4.19623 | 0.240275 | ||||||||
\(306\) | −1.14057 | −0.0652021 | ||||||||
\(307\) | −0.487792 | −0.0278398 | −0.0139199 | − | 0.999903i | \(-0.504431\pi\) | ||||
−0.0139199 | + | 0.999903i | \(0.504431\pi\) | |||||||
\(308\) | 18.3594 | 1.04612 | ||||||||
\(309\) | 19.0756 | 1.08517 | ||||||||
\(310\) | 4.14758 | 0.235567 | ||||||||
\(311\) | 33.4115 | 1.89459 | 0.947297 | − | 0.320356i | \(-0.103802\pi\) | ||||
0.947297 | + | 0.320356i | \(0.103802\pi\) | |||||||
\(312\) | −15.9291 | −0.901808 | ||||||||
\(313\) | 19.5869 | 1.10712 | 0.553559 | − | 0.832810i | \(-0.313270\pi\) | ||||
0.553559 | + | 0.832810i | \(0.313270\pi\) | |||||||
\(314\) | −14.7748 | −0.833790 | ||||||||
\(315\) | 2.62358 | 0.147822 | ||||||||
\(316\) | 4.02315 | 0.226320 | ||||||||
\(317\) | −11.5304 | −0.647613 | −0.323807 | − | 0.946123i | \(-0.604963\pi\) | ||||
−0.323807 | + | 0.946123i | \(0.604963\pi\) | |||||||
\(318\) | −1.74881 | −0.0980684 | ||||||||
\(319\) | −4.80440 | −0.268994 | ||||||||
\(320\) | 6.30235 | 0.352312 | ||||||||
\(321\) | 25.8642 | 1.44360 | ||||||||
\(322\) | −5.02469 | −0.280015 | ||||||||
\(323\) | 2.64398 | 0.147115 | ||||||||
\(324\) | 5.21167 | 0.289537 | ||||||||
\(325\) | 15.0967 | 0.837415 | ||||||||
\(326\) | −26.2031 | −1.45125 | ||||||||
\(327\) | −6.36949 | −0.352234 | ||||||||
\(328\) | 30.3505 | 1.67582 | ||||||||
\(329\) | −11.5765 | −0.638234 | ||||||||
\(330\) | −6.18188 | −0.340301 | ||||||||
\(331\) | −31.3361 | −1.72239 | −0.861193 | − | 0.508278i | \(-0.830282\pi\) | ||||
−0.861193 | + | 0.508278i | \(0.830282\pi\) | |||||||
\(332\) | −1.38327 | −0.0759169 | ||||||||
\(333\) | 7.45539 | 0.408553 | ||||||||
\(334\) | −3.25786 | −0.178262 | ||||||||
\(335\) | −1.60427 | −0.0876506 | ||||||||
\(336\) | 11.6934 | 0.637929 | ||||||||
\(337\) | −13.3519 | −0.727323 | −0.363661 | − | 0.931531i | \(-0.618473\pi\) | ||||
−0.363661 | + | 0.931531i | \(0.618473\pi\) | |||||||
\(338\) | 1.22711 | 0.0667462 | ||||||||
\(339\) | −18.7478 | −1.01824 | ||||||||
\(340\) | 0.946684 | 0.0513411 | ||||||||
\(341\) | −23.3829 | −1.26626 | ||||||||
\(342\) | −1.41337 | −0.0764265 | ||||||||
\(343\) | −34.6613 | −1.87153 | ||||||||
\(344\) | −20.1814 | −1.08811 | ||||||||
\(345\) | −1.18680 | −0.0638952 | ||||||||
\(346\) | 3.41338 | 0.183505 | ||||||||
\(347\) | 8.66047 | 0.464919 | 0.232459 | − | 0.972606i | \(-0.425323\pi\) | ||||
0.232459 | + | 0.972606i | \(0.425323\pi\) | |||||||
\(348\) | 1.24497 | 0.0667377 | ||||||||
\(349\) | −13.0354 | −0.697767 | −0.348883 | − | 0.937166i | \(-0.613439\pi\) | ||||
−0.348883 | + | 0.937166i | \(0.613439\pi\) | |||||||
\(350\) | −22.0191 | −1.17697 | ||||||||
\(351\) | 19.3511 | 1.03289 | ||||||||
\(352\) | −20.7210 | −1.10443 | ||||||||
\(353\) | −18.8898 | −1.00540 | −0.502702 | − | 0.864460i | \(-0.667661\pi\) | ||||
−0.502702 | + | 0.864460i | \(0.667661\pi\) | |||||||
\(354\) | 13.9307 | 0.740406 | ||||||||
\(355\) | −5.52337 | −0.293150 | ||||||||
\(356\) | −11.6474 | −0.617312 | ||||||||
\(357\) | 10.2215 | 0.540980 | ||||||||
\(358\) | −26.9701 | −1.42541 | ||||||||
\(359\) | 26.9376 | 1.42171 | 0.710856 | − | 0.703337i | \(-0.248308\pi\) | ||||
0.710856 | + | 0.703337i | \(0.248308\pi\) | |||||||
\(360\) | −1.73356 | −0.0913667 | ||||||||
\(361\) | −15.7236 | −0.827560 | ||||||||
\(362\) | 1.24141 | 0.0652472 | ||||||||
\(363\) | 18.2429 | 0.957505 | ||||||||
\(364\) | −13.1647 | −0.690018 | ||||||||
\(365\) | −5.04363 | −0.263996 | ||||||||
\(366\) | −8.73937 | −0.456814 | ||||||||
\(367\) | −33.8885 | −1.76897 | −0.884483 | − | 0.466572i | \(-0.845489\pi\) | ||||
−0.884483 | + | 0.466572i | \(0.845489\pi\) | |||||||
\(368\) | 1.67105 | 0.0871093 | ||||||||
\(369\) | −7.13791 | −0.371584 | ||||||||
\(370\) | 8.82160 | 0.458613 | ||||||||
\(371\) | −4.95105 | −0.257046 | ||||||||
\(372\) | 6.05928 | 0.314159 | ||||||||
\(373\) | −23.7038 | −1.22734 | −0.613668 | − | 0.789564i | \(-0.710307\pi\) | ||||
−0.613668 | + | 0.789564i | \(0.710307\pi\) | |||||||
\(374\) | 7.60859 | 0.393431 | ||||||||
\(375\) | −11.1348 | −0.574998 | ||||||||
\(376\) | 7.64932 | 0.394484 | ||||||||
\(377\) | 3.44502 | 0.177428 | ||||||||
\(378\) | −28.2244 | −1.45171 | ||||||||
\(379\) | −4.50732 | −0.231525 | −0.115763 | − | 0.993277i | \(-0.536931\pi\) | ||||
−0.115763 | + | 0.993277i | \(0.536931\pi\) | |||||||
\(380\) | 1.17311 | 0.0601794 | ||||||||
\(381\) | −2.67683 | −0.137138 | ||||||||
\(382\) | 13.7717 | 0.704621 | ||||||||
\(383\) | 14.3548 | 0.733496 | 0.366748 | − | 0.930320i | \(-0.380471\pi\) | ||||
0.366748 | + | 0.930320i | \(0.380471\pi\) | |||||||
\(384\) | −0.101546 | −0.00518200 | ||||||||
\(385\) | −17.5015 | −0.891959 | ||||||||
\(386\) | −17.0367 | −0.867148 | ||||||||
\(387\) | 4.74633 | 0.241269 | ||||||||
\(388\) | 6.92326 | 0.351475 | ||||||||
\(389\) | −34.9730 | −1.77320 | −0.886601 | − | 0.462534i | \(-0.846940\pi\) | ||||
−0.886601 | + | 0.462534i | \(0.846940\pi\) | |||||||
\(390\) | 4.43275 | 0.224461 | ||||||||
\(391\) | 1.46070 | 0.0738709 | ||||||||
\(392\) | 44.3392 | 2.23947 | ||||||||
\(393\) | 8.11145 | 0.409169 | ||||||||
\(394\) | −6.17058 | −0.310870 | ||||||||
\(395\) | −3.83516 | −0.192968 | ||||||||
\(396\) | 2.85305 | 0.143371 | ||||||||
\(397\) | 17.6680 | 0.886733 | 0.443366 | − | 0.896341i | \(-0.353784\pi\) | ||||
0.443366 | + | 0.896341i | \(0.353784\pi\) | |||||||
\(398\) | 28.2133 | 1.41421 | ||||||||
\(399\) | 12.6663 | 0.634108 | ||||||||
\(400\) | 7.32283 | 0.366141 | ||||||||
\(401\) | −21.8754 | −1.09241 | −0.546203 | − | 0.837653i | \(-0.683927\pi\) | ||||
−0.546203 | + | 0.837653i | \(0.683927\pi\) | |||||||
\(402\) | 3.34117 | 0.166642 | ||||||||
\(403\) | 16.7669 | 0.835218 | ||||||||
\(404\) | 3.03522 | 0.151008 | ||||||||
\(405\) | −4.96814 | −0.246869 | ||||||||
\(406\) | −5.02469 | −0.249371 | ||||||||
\(407\) | −49.7338 | −2.46522 | ||||||||
\(408\) | −6.75400 | −0.334373 | ||||||||
\(409\) | 9.81435 | 0.485288 | 0.242644 | − | 0.970115i | \(-0.421985\pi\) | ||||
0.242644 | + | 0.970115i | \(0.421985\pi\) | |||||||
\(410\) | −8.44593 | −0.417115 | ||||||||
\(411\) | −23.8005 | −1.17399 | ||||||||
\(412\) | −10.4170 | −0.513209 | ||||||||
\(413\) | 39.4391 | 1.94067 | ||||||||
\(414\) | −0.780838 | −0.0383761 | ||||||||
\(415\) | 1.31864 | 0.0647293 | ||||||||
\(416\) | 14.8581 | 0.728480 | ||||||||
\(417\) | 24.4709 | 1.19834 | ||||||||
\(418\) | 9.42841 | 0.461159 | ||||||||
\(419\) | 0.696845 | 0.0340431 | 0.0170216 | − | 0.999855i | \(-0.494582\pi\) | ||||
0.0170216 | + | 0.999855i | \(0.494582\pi\) | |||||||
\(420\) | 4.53521 | 0.221295 | ||||||||
\(421\) | 3.13846 | 0.152959 | 0.0764795 | − | 0.997071i | \(-0.475632\pi\) | ||||
0.0764795 | + | 0.997071i | \(0.475632\pi\) | |||||||
\(422\) | −6.47317 | −0.315109 | ||||||||
\(423\) | −1.79899 | −0.0874699 | ||||||||
\(424\) | 3.27147 | 0.158877 | ||||||||
\(425\) | 6.40106 | 0.310497 | ||||||||
\(426\) | 11.5034 | 0.557340 | ||||||||
\(427\) | −24.7420 | −1.19735 | ||||||||
\(428\) | −14.1242 | −0.682719 | ||||||||
\(429\) | −24.9907 | −1.20656 | ||||||||
\(430\) | 5.61609 | 0.270832 | ||||||||
\(431\) | 37.0873 | 1.78643 | 0.893217 | − | 0.449626i | \(-0.148443\pi\) | ||||
0.893217 | + | 0.449626i | \(0.148443\pi\) | |||||||
\(432\) | 9.38649 | 0.451608 | ||||||||
\(433\) | −20.1836 | −0.969960 | −0.484980 | − | 0.874525i | \(-0.661173\pi\) | ||||
−0.484980 | + | 0.874525i | \(0.661173\pi\) | |||||||
\(434\) | −24.4551 | −1.17388 | ||||||||
\(435\) | −1.18680 | −0.0569028 | ||||||||
\(436\) | 3.47832 | 0.166582 | ||||||||
\(437\) | 1.81007 | 0.0865875 | ||||||||
\(438\) | 10.5042 | 0.501912 | ||||||||
\(439\) | −28.5330 | −1.36181 | −0.680904 | − | 0.732373i | \(-0.738413\pi\) | ||||
−0.680904 | + | 0.732373i | \(0.738413\pi\) | |||||||
\(440\) | 11.5643 | 0.551308 | ||||||||
\(441\) | −10.4278 | −0.496562 | ||||||||
\(442\) | −5.45578 | −0.259505 | ||||||||
\(443\) | −29.2659 | −1.39046 | −0.695231 | − | 0.718786i | \(-0.744698\pi\) | ||||
−0.695231 | + | 0.718786i | \(0.744698\pi\) | |||||||
\(444\) | 12.8877 | 0.611621 | ||||||||
\(445\) | 11.1032 | 0.526341 | ||||||||
\(446\) | 2.10981 | 0.0999025 | ||||||||
\(447\) | −1.15945 | −0.0548401 | ||||||||
\(448\) | −37.1602 | −1.75565 | ||||||||
\(449\) | 4.20481 | 0.198437 | 0.0992185 | − | 0.995066i | \(-0.468366\pi\) | ||||
0.0992185 | + | 0.995066i | \(0.468366\pi\) | |||||||
\(450\) | −3.42177 | −0.161304 | ||||||||
\(451\) | 47.6159 | 2.24215 | ||||||||
\(452\) | 10.2380 | 0.481556 | ||||||||
\(453\) | 5.30912 | 0.249444 | ||||||||
\(454\) | −15.3841 | −0.722012 | ||||||||
\(455\) | 12.5496 | 0.588332 | ||||||||
\(456\) | −8.36942 | −0.391934 | ||||||||
\(457\) | 20.6073 | 0.963968 | 0.481984 | − | 0.876180i | \(-0.339916\pi\) | ||||
0.481984 | + | 0.876180i | \(0.339916\pi\) | |||||||
\(458\) | 18.5529 | 0.866918 | ||||||||
\(459\) | 8.20496 | 0.382975 | ||||||||
\(460\) | 0.648102 | 0.0302179 | ||||||||
\(461\) | 21.3498 | 0.994359 | 0.497179 | − | 0.867648i | \(-0.334369\pi\) | ||||
0.497179 | + | 0.867648i | \(0.334369\pi\) | |||||||
\(462\) | 36.4499 | 1.69580 | ||||||||
\(463\) | −11.0632 | −0.514148 | −0.257074 | − | 0.966392i | \(-0.582758\pi\) | ||||
−0.257074 | + | 0.966392i | \(0.582758\pi\) | |||||||
\(464\) | 1.67105 | 0.0775764 | ||||||||
\(465\) | −5.77615 | −0.267863 | ||||||||
\(466\) | −10.6242 | −0.492156 | ||||||||
\(467\) | 28.8402 | 1.33457 | 0.667283 | − | 0.744804i | \(-0.267457\pi\) | ||||
0.667283 | + | 0.744804i | \(0.267457\pi\) | |||||||
\(468\) | −2.04579 | −0.0945669 | ||||||||
\(469\) | 9.45917 | 0.436784 | ||||||||
\(470\) | −2.12866 | −0.0981875 | ||||||||
\(471\) | 20.5762 | 0.948102 | ||||||||
\(472\) | −26.0599 | −1.19950 | ||||||||
\(473\) | −31.6621 | −1.45582 | ||||||||
\(474\) | 7.98738 | 0.366872 | ||||||||
\(475\) | 7.93207 | 0.363948 | ||||||||
\(476\) | −5.58188 | −0.255845 | ||||||||
\(477\) | −0.769394 | −0.0352281 | ||||||||
\(478\) | −15.0341 | −0.687644 | ||||||||
\(479\) | −38.2372 | −1.74710 | −0.873550 | − | 0.486734i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486734i | \(0.838188\pi\) | |||||||
\(480\) | −5.11859 | −0.233631 | ||||||||
\(481\) | 35.6620 | 1.62605 | ||||||||
\(482\) | 12.1763 | 0.554617 | ||||||||
\(483\) | 6.99768 | 0.318405 | ||||||||
\(484\) | −9.96229 | −0.452832 | ||||||||
\(485\) | −6.59976 | −0.299680 | ||||||||
\(486\) | −7.92303 | −0.359396 | ||||||||
\(487\) | 35.5068 | 1.60897 | 0.804484 | − | 0.593975i | \(-0.202442\pi\) | ||||
0.804484 | + | 0.593975i | \(0.202442\pi\) | |||||||
\(488\) | 16.3486 | 0.740066 | ||||||||
\(489\) | 36.4919 | 1.65022 | ||||||||
\(490\) | −12.3387 | −0.557406 | ||||||||
\(491\) | 35.3266 | 1.59427 | 0.797135 | − | 0.603802i | \(-0.206348\pi\) | ||||
0.797135 | + | 0.603802i | \(0.206348\pi\) | |||||||
\(492\) | −12.3388 | −0.556278 | ||||||||
\(493\) | 1.46070 | 0.0657867 | ||||||||
\(494\) | −6.76070 | −0.304178 | ||||||||
\(495\) | −2.71973 | −0.122243 | ||||||||
\(496\) | 8.13297 | 0.365181 | ||||||||
\(497\) | 32.5672 | 1.46084 | ||||||||
\(498\) | −2.74629 | −0.123064 | ||||||||
\(499\) | 22.0133 | 0.985449 | 0.492724 | − | 0.870185i | \(-0.336001\pi\) | ||||
0.492724 | + | 0.870185i | \(0.336001\pi\) | |||||||
\(500\) | 6.08061 | 0.271933 | ||||||||
\(501\) | 4.53708 | 0.202702 | ||||||||
\(502\) | 7.81466 | 0.348785 | ||||||||
\(503\) | −6.03824 | −0.269232 | −0.134616 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134616 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(504\) | 10.2215 | 0.455302 | ||||||||
\(505\) | −2.89339 | −0.128754 | ||||||||
\(506\) | 5.20885 | 0.231562 | ||||||||
\(507\) | −1.70895 | −0.0758971 | ||||||||
\(508\) | 1.46179 | 0.0648566 | ||||||||
\(509\) | −10.2485 | −0.454258 | −0.227129 | − | 0.973865i | \(-0.572934\pi\) | ||||
−0.227129 | + | 0.973865i | \(0.572934\pi\) | |||||||
\(510\) | 1.87950 | 0.0832259 | ||||||||
\(511\) | 29.7385 | 1.31555 | ||||||||
\(512\) | 17.4417 | 0.770821 | ||||||||
\(513\) | 10.1674 | 0.448903 | ||||||||
\(514\) | 23.9675 | 1.05716 | ||||||||
\(515\) | 9.93026 | 0.437579 | ||||||||
\(516\) | 8.20467 | 0.361190 | ||||||||
\(517\) | 12.0008 | 0.527795 | ||||||||
\(518\) | −52.0143 | −2.28538 | ||||||||
\(519\) | −4.75367 | −0.208663 | ||||||||
\(520\) | −8.29228 | −0.363640 | ||||||||
\(521\) | −4.07192 | −0.178394 | −0.0891971 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891971 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(522\) | −0.780838 | −0.0341763 | ||||||||
\(523\) | 11.8406 | 0.517755 | 0.258878 | − | 0.965910i | \(-0.416647\pi\) | ||||
0.258878 | + | 0.965910i | \(0.416647\pi\) | |||||||
\(524\) | −4.42959 | −0.193508 | ||||||||
\(525\) | 30.6651 | 1.33833 | ||||||||
\(526\) | −9.09075 | −0.396375 | ||||||||
\(527\) | 7.10923 | 0.309683 | ||||||||
\(528\) | −12.1220 | −0.527543 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.910386 | −0.0395446 | ||||||||
\(531\) | 6.12883 | 0.265969 | ||||||||
\(532\) | −6.91696 | −0.299888 | ||||||||
\(533\) | −34.1433 | −1.47891 | ||||||||
\(534\) | −23.1243 | −1.00069 | ||||||||
\(535\) | 13.4642 | 0.582109 | ||||||||
\(536\) | −6.25027 | −0.269970 | ||||||||
\(537\) | 37.5601 | 1.62084 | ||||||||
\(538\) | −6.25131 | −0.269513 | ||||||||
\(539\) | 69.5624 | 2.99626 | ||||||||
\(540\) | 3.64047 | 0.156661 | ||||||||
\(541\) | 23.8471 | 1.02527 | 0.512634 | − | 0.858607i | \(-0.328670\pi\) | ||||
0.512634 | + | 0.858607i | \(0.328670\pi\) | |||||||
\(542\) | 21.9702 | 0.943703 | ||||||||
\(543\) | −1.72886 | −0.0741926 | ||||||||
\(544\) | 6.29991 | 0.270106 | ||||||||
\(545\) | −3.31579 | −0.142033 | ||||||||
\(546\) | −26.1366 | −1.11854 | ||||||||
\(547\) | 1.89606 | 0.0810697 | 0.0405349 | − | 0.999178i | \(-0.487094\pi\) | ||||
0.0405349 | + | 0.999178i | \(0.487094\pi\) | |||||||
\(548\) | 12.9972 | 0.555214 | ||||||||
\(549\) | −3.84491 | −0.164097 | ||||||||
\(550\) | 22.8261 | 0.973310 | ||||||||
\(551\) | 1.81007 | 0.0771117 | ||||||||
\(552\) | −4.62380 | −0.196802 | ||||||||
\(553\) | 22.6130 | 0.961604 | ||||||||
\(554\) | 29.4889 | 1.25287 | ||||||||
\(555\) | −12.2855 | −0.521489 | ||||||||
\(556\) | −13.3633 | −0.566732 | ||||||||
\(557\) | −37.6779 | −1.59646 | −0.798231 | − | 0.602351i | \(-0.794231\pi\) | ||||
−0.798231 | + | 0.602351i | \(0.794231\pi\) | |||||||
\(558\) | −3.80033 | −0.160881 | ||||||||
\(559\) | 22.7035 | 0.960255 | ||||||||
\(560\) | 6.08730 | 0.257235 | ||||||||
\(561\) | −10.5962 | −0.447370 | ||||||||
\(562\) | −7.40319 | −0.312285 | ||||||||
\(563\) | −21.4129 | −0.902444 | −0.451222 | − | 0.892412i | \(-0.649012\pi\) | ||||
−0.451222 | + | 0.892412i | \(0.649012\pi\) | |||||||
\(564\) | −3.10980 | −0.130946 | ||||||||
\(565\) | −9.75962 | −0.410590 | ||||||||
\(566\) | 30.1440 | 1.26705 | ||||||||
\(567\) | 29.2934 | 1.23021 | ||||||||
\(568\) | −21.5192 | −0.902925 | ||||||||
\(569\) | 7.76547 | 0.325545 | 0.162773 | − | 0.986664i | \(-0.447956\pi\) | ||||
0.162773 | + | 0.986664i | \(0.447956\pi\) | |||||||
\(570\) | 2.32904 | 0.0975529 | ||||||||
\(571\) | −28.3747 | −1.18744 | −0.593721 | − | 0.804671i | \(-0.702342\pi\) | ||||
−0.593721 | + | 0.804671i | \(0.702342\pi\) | |||||||
\(572\) | 13.6472 | 0.570618 | ||||||||
\(573\) | −19.1792 | −0.801224 | ||||||||
\(574\) | 49.7993 | 2.07858 | ||||||||
\(575\) | 4.38218 | 0.182750 | ||||||||
\(576\) | −5.77470 | −0.240612 | ||||||||
\(577\) | −3.14685 | −0.131005 | −0.0655026 | − | 0.997852i | \(-0.520865\pi\) | ||||
−0.0655026 | + | 0.997852i | \(0.520865\pi\) | |||||||
\(578\) | 16.1179 | 0.670415 | ||||||||
\(579\) | 23.7264 | 0.986033 | ||||||||
\(580\) | 0.648102 | 0.0269110 | ||||||||
\(581\) | −7.77500 | −0.322561 | ||||||||
\(582\) | 13.7451 | 0.569754 | ||||||||
\(583\) | 5.13252 | 0.212567 | ||||||||
\(584\) | −19.6501 | −0.813127 | ||||||||
\(585\) | 1.95020 | 0.0806309 | ||||||||
\(586\) | 0.0128257 | 0.000529824 0 | ||||||||
\(587\) | 27.8440 | 1.14924 | 0.574622 | − | 0.818419i | \(-0.305149\pi\) | ||||
0.574622 | + | 0.818419i | \(0.305149\pi\) | |||||||
\(588\) | −18.0259 | −0.743375 | ||||||||
\(589\) | 8.80961 | 0.362994 | ||||||||
\(590\) | 7.25194 | 0.298558 | ||||||||
\(591\) | 8.59351 | 0.353490 | ||||||||
\(592\) | 17.2982 | 0.710953 | ||||||||
\(593\) | 2.77521 | 0.113964 | 0.0569820 | − | 0.998375i | \(-0.481852\pi\) | ||||
0.0569820 | + | 0.998375i | \(0.481852\pi\) | |||||||
\(594\) | 29.2588 | 1.20050 | ||||||||
\(595\) | 5.32106 | 0.218142 | ||||||||
\(596\) | 0.633166 | 0.0259355 | ||||||||
\(597\) | −39.2915 | −1.60809 | ||||||||
\(598\) | −3.73504 | −0.152737 | ||||||||
\(599\) | −23.8140 | −0.973012 | −0.486506 | − | 0.873677i | \(-0.661729\pi\) | ||||
−0.486506 | + | 0.873677i | \(0.661729\pi\) | |||||||
\(600\) | −20.2623 | −0.827207 | ||||||||
\(601\) | 20.9662 | 0.855231 | 0.427616 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427616 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(602\) | −33.1139 | −1.34962 | ||||||||
\(603\) | 1.46996 | 0.0598612 | ||||||||
\(604\) | −2.89926 | −0.117969 | ||||||||
\(605\) | 9.49679 | 0.386099 | ||||||||
\(606\) | 6.02599 | 0.244789 | ||||||||
\(607\) | −2.59519 | −0.105336 | −0.0526678 | − | 0.998612i | \(-0.516772\pi\) | ||||
−0.0526678 | + | 0.998612i | \(0.516772\pi\) | |||||||
\(608\) | 7.80672 | 0.316604 | ||||||||
\(609\) | 6.99768 | 0.283560 | ||||||||
\(610\) | −4.54949 | −0.184204 | ||||||||
\(611\) | −8.60525 | −0.348131 | ||||||||
\(612\) | −0.867425 | −0.0350636 | ||||||||
\(613\) | −35.4865 | −1.43329 | −0.716644 | − | 0.697439i | \(-0.754323\pi\) | ||||
−0.716644 | + | 0.697439i | \(0.754323\pi\) | |||||||
\(614\) | 0.528857 | 0.0213429 | ||||||||
\(615\) | 11.7623 | 0.474301 | ||||||||
\(616\) | −68.1862 | −2.74730 | ||||||||
\(617\) | −15.1294 | −0.609085 | −0.304543 | − | 0.952499i | \(-0.598504\pi\) | ||||
−0.304543 | + | 0.952499i | \(0.598504\pi\) | |||||||
\(618\) | −20.6815 | −0.831931 | ||||||||
\(619\) | −28.5271 | −1.14660 | −0.573301 | − | 0.819345i | \(-0.694338\pi\) | ||||
−0.573301 | + | 0.819345i | \(0.694338\pi\) | |||||||
\(620\) | 3.15431 | 0.126680 | ||||||||
\(621\) | 5.61713 | 0.225408 | ||||||||
\(622\) | −36.2243 | −1.45246 | ||||||||
\(623\) | −65.4671 | −2.62288 | ||||||||
\(624\) | 8.69217 | 0.347965 | ||||||||
\(625\) | 16.1144 | 0.644577 | ||||||||
\(626\) | −21.2358 | −0.848754 | ||||||||
\(627\) | −13.1305 | −0.524383 | ||||||||
\(628\) | −11.2365 | −0.448385 | ||||||||
\(629\) | 15.1208 | 0.602906 | ||||||||
\(630\) | −2.84444 | −0.113325 | ||||||||
\(631\) | 19.9685 | 0.794935 | 0.397467 | − | 0.917616i | \(-0.369889\pi\) | ||||
0.397467 | + | 0.917616i | \(0.369889\pi\) | |||||||
\(632\) | −14.9419 | −0.594355 | ||||||||
\(633\) | 9.01491 | 0.358310 | ||||||||
\(634\) | 12.5011 | 0.496483 | ||||||||
\(635\) | −1.39349 | −0.0552990 | ||||||||
\(636\) | −1.33000 | −0.0527380 | ||||||||
\(637\) | −49.8801 | −1.97632 | ||||||||
\(638\) | 5.20885 | 0.206221 | ||||||||
\(639\) | 5.06094 | 0.200208 | ||||||||
\(640\) | −0.0528623 | −0.00208956 | ||||||||
\(641\) | −22.0041 | −0.869111 | −0.434556 | − | 0.900645i | \(-0.643095\pi\) | ||||
−0.434556 | + | 0.900645i | \(0.643095\pi\) | |||||||
\(642\) | −28.0415 | −1.10671 | ||||||||
\(643\) | −43.6608 | −1.72181 | −0.860907 | − | 0.508763i | \(-0.830103\pi\) | ||||
−0.860907 | + | 0.508763i | \(0.830103\pi\) | |||||||
\(644\) | −3.82137 | −0.150583 | ||||||||
\(645\) | −7.82129 | −0.307963 | ||||||||
\(646\) | −2.86656 | −0.112783 | ||||||||
\(647\) | −39.8183 | −1.56542 | −0.782709 | − | 0.622388i | \(-0.786162\pi\) | ||||
−0.782709 | + | 0.622388i | \(0.786162\pi\) | |||||||
\(648\) | −19.3560 | −0.760375 | ||||||||
\(649\) | −40.8845 | −1.60486 | ||||||||
\(650\) | −16.3676 | −0.641991 | ||||||||
\(651\) | 34.0576 | 1.33482 | ||||||||
\(652\) | −19.9279 | −0.780437 | ||||||||
\(653\) | −15.2538 | −0.596927 | −0.298463 | − | 0.954421i | \(-0.596474\pi\) | ||||
−0.298463 | + | 0.954421i | \(0.596474\pi\) | |||||||
\(654\) | 6.90571 | 0.270035 | ||||||||
\(655\) | 4.22261 | 0.164991 | ||||||||
\(656\) | −16.5616 | −0.646621 | ||||||||
\(657\) | 4.62137 | 0.180297 | ||||||||
\(658\) | 12.5511 | 0.489292 | ||||||||
\(659\) | 2.69443 | 0.104960 | 0.0524801 | − | 0.998622i | \(-0.483287\pi\) | ||||
0.0524801 | + | 0.998622i | \(0.483287\pi\) | |||||||
\(660\) | −4.70143 | −0.183003 | ||||||||
\(661\) | 19.4470 | 0.756402 | 0.378201 | − | 0.925723i | \(-0.376543\pi\) | ||||
0.378201 | + | 0.925723i | \(0.376543\pi\) | |||||||
\(662\) | 33.9741 | 1.32044 | ||||||||
\(663\) | 7.59804 | 0.295083 | ||||||||
\(664\) | 5.13743 | 0.199371 | ||||||||
\(665\) | 6.59375 | 0.255695 | ||||||||
\(666\) | −8.08303 | −0.313211 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −2.47766 | −0.0958635 | ||||||||
\(669\) | −2.93825 | −0.113599 | ||||||||
\(670\) | 1.73933 | 0.0671960 | ||||||||
\(671\) | 25.6488 | 0.990162 | ||||||||
\(672\) | 30.1805 | 1.16424 | ||||||||
\(673\) | −35.7115 | −1.37658 | −0.688289 | − | 0.725436i | \(-0.741638\pi\) | ||||
−0.688289 | + | 0.725436i | \(0.741638\pi\) | |||||||
\(674\) | 14.4759 | 0.557591 | ||||||||
\(675\) | 24.6153 | 0.947443 | ||||||||
\(676\) | 0.933242 | 0.0358939 | ||||||||
\(677\) | −21.0987 | −0.810890 | −0.405445 | − | 0.914119i | \(-0.632883\pi\) | ||||
−0.405445 | + | 0.914119i | \(0.632883\pi\) | |||||||
\(678\) | 20.3261 | 0.780619 | ||||||||
\(679\) | 38.9138 | 1.49338 | ||||||||
\(680\) | −3.51596 | −0.134831 | ||||||||
\(681\) | 21.4248 | 0.821000 | ||||||||
\(682\) | 25.3515 | 0.970757 | ||||||||
\(683\) | 37.5417 | 1.43649 | 0.718247 | − | 0.695788i | \(-0.244945\pi\) | ||||
0.718247 | + | 0.695788i | \(0.244945\pi\) | |||||||
\(684\) | −1.07490 | −0.0410997 | ||||||||
\(685\) | −12.3899 | −0.473394 | ||||||||
\(686\) | 37.5792 | 1.43478 | ||||||||
\(687\) | −25.8378 | −0.985772 | ||||||||
\(688\) | 11.0126 | 0.419850 | ||||||||
\(689\) | −3.68030 | −0.140208 | ||||||||
\(690\) | 1.28671 | 0.0489843 | ||||||||
\(691\) | −16.6961 | −0.635148 | −0.317574 | − | 0.948234i | \(-0.602868\pi\) | ||||
−0.317574 | + | 0.948234i | \(0.602868\pi\) | |||||||
\(692\) | 2.59594 | 0.0986828 | ||||||||
\(693\) | 16.0362 | 0.609166 | ||||||||
\(694\) | −9.38956 | −0.356423 | ||||||||
\(695\) | 12.7389 | 0.483214 | ||||||||
\(696\) | −4.62380 | −0.175265 | ||||||||
\(697\) | −14.4769 | −0.548351 | ||||||||
\(698\) | 14.1327 | 0.534932 | ||||||||
\(699\) | 14.7959 | 0.559631 | ||||||||
\(700\) | −16.7459 | −0.632937 | ||||||||
\(701\) | −13.1653 | −0.497248 | −0.248624 | − | 0.968600i | \(-0.579978\pi\) | ||||
−0.248624 | + | 0.968600i | \(0.579978\pi\) | |||||||
\(702\) | −20.9802 | −0.791848 | ||||||||
\(703\) | 18.7374 | 0.706695 | ||||||||
\(704\) | 38.5222 | 1.45186 | ||||||||
\(705\) | 2.96449 | 0.111649 | ||||||||
\(706\) | 20.4801 | 0.770778 | ||||||||
\(707\) | 17.0602 | 0.641613 | ||||||||
\(708\) | 10.5945 | 0.398166 | ||||||||
\(709\) | 38.7350 | 1.45472 | 0.727362 | − | 0.686254i | \(-0.240746\pi\) | ||||
0.727362 | + | 0.686254i | \(0.240746\pi\) | |||||||
\(710\) | 5.98836 | 0.224739 | ||||||||
\(711\) | 3.51407 | 0.131788 | ||||||||
\(712\) | 43.2582 | 1.62117 | ||||||||
\(713\) | 4.86699 | 0.182270 | ||||||||
\(714\) | −11.0820 | −0.414734 | ||||||||
\(715\) | −13.0095 | −0.486528 | ||||||||
\(716\) | −20.5112 | −0.766540 | ||||||||
\(717\) | 20.9373 | 0.781920 | ||||||||
\(718\) | −29.2054 | −1.08993 | ||||||||
\(719\) | 23.8247 | 0.888510 | 0.444255 | − | 0.895900i | \(-0.353468\pi\) | ||||
0.444255 | + | 0.895900i | \(0.353468\pi\) | |||||||
\(720\) | 0.945967 | 0.0352541 | ||||||||
\(721\) | −58.5513 | −2.18056 | ||||||||
\(722\) | 17.0473 | 0.634436 | ||||||||
\(723\) | −16.9575 | −0.630654 | ||||||||
\(724\) | 0.944117 | 0.0350878 | ||||||||
\(725\) | 4.38218 | 0.162750 | ||||||||
\(726\) | −19.7787 | −0.734056 | ||||||||
\(727\) | −31.4321 | −1.16575 | −0.582877 | − | 0.812561i | \(-0.698073\pi\) | ||||
−0.582877 | + | 0.812561i | \(0.698073\pi\) | |||||||
\(728\) | 48.8933 | 1.81211 | ||||||||
\(729\) | 29.9961 | 1.11097 | ||||||||
\(730\) | 5.46823 | 0.202388 | ||||||||
\(731\) | 9.62636 | 0.356044 | ||||||||
\(732\) | −6.64645 | −0.245660 | ||||||||
\(733\) | −38.3457 | −1.41633 | −0.708165 | − | 0.706047i | \(-0.750477\pi\) | ||||
−0.708165 | + | 0.706047i | \(0.750477\pi\) | |||||||
\(734\) | 36.7414 | 1.35615 | ||||||||
\(735\) | 17.1836 | 0.633826 | ||||||||
\(736\) | 4.31293 | 0.158977 | ||||||||
\(737\) | −9.80586 | −0.361203 | ||||||||
\(738\) | 7.73881 | 0.284870 | ||||||||
\(739\) | 34.3034 | 1.26187 | 0.630935 | − | 0.775836i | \(-0.282672\pi\) | ||||
0.630935 | + | 0.775836i | \(0.282672\pi\) | |||||||
\(740\) | 6.70898 | 0.246627 | ||||||||
\(741\) | 9.41533 | 0.345881 | ||||||||
\(742\) | 5.36786 | 0.197060 | ||||||||
\(743\) | 10.8086 | 0.396529 | 0.198264 | − | 0.980149i | \(-0.436470\pi\) | ||||
0.198264 | + | 0.980149i | \(0.436470\pi\) | |||||||
\(744\) | −22.5040 | −0.825037 | ||||||||
\(745\) | −0.603580 | −0.0221135 | ||||||||
\(746\) | 25.6993 | 0.940919 | ||||||||
\(747\) | −1.20824 | −0.0442070 | ||||||||
\(748\) | 5.78647 | 0.211574 | ||||||||
\(749\) | −79.3884 | −2.90079 | ||||||||
\(750\) | 12.0722 | 0.440813 | ||||||||
\(751\) | −24.6782 | −0.900521 | −0.450260 | − | 0.892897i | \(-0.648669\pi\) | ||||
−0.450260 | + | 0.892897i | \(0.648669\pi\) | |||||||
\(752\) | −4.17407 | −0.152213 | ||||||||
\(753\) | −10.8831 | −0.396604 | ||||||||
\(754\) | −3.73504 | −0.136022 | ||||||||
\(755\) | 2.76379 | 0.100585 | ||||||||
\(756\) | −21.4651 | −0.780680 | ||||||||
\(757\) | 32.4734 | 1.18027 | 0.590134 | − | 0.807306i | \(-0.299075\pi\) | ||||
0.590134 | + | 0.807306i | \(0.299075\pi\) | |||||||
\(758\) | 4.88677 | 0.177495 | ||||||||
\(759\) | −7.25415 | −0.263309 | ||||||||
\(760\) | −4.35690 | −0.158042 | ||||||||
\(761\) | 17.9063 | 0.649104 | 0.324552 | − | 0.945868i | \(-0.394786\pi\) | ||||
0.324552 | + | 0.945868i | \(0.394786\pi\) | |||||||
\(762\) | 2.90218 | 0.105135 | ||||||||
\(763\) | 19.5507 | 0.707785 | ||||||||
\(764\) | 10.4736 | 0.378922 | ||||||||
\(765\) | 0.826893 | 0.0298964 | ||||||||
\(766\) | −15.5633 | −0.562324 | ||||||||
\(767\) | 29.3165 | 1.05856 | ||||||||
\(768\) | −24.1030 | −0.869741 | ||||||||
\(769\) | 18.7697 | 0.676852 | 0.338426 | − | 0.940993i | \(-0.390106\pi\) | ||||
0.338426 | + | 0.940993i | \(0.390106\pi\) | |||||||
\(770\) | 18.9749 | 0.683807 | ||||||||
\(771\) | −33.3786 | −1.20210 | ||||||||
\(772\) | −12.9567 | −0.466324 | ||||||||
\(773\) | −44.3825 | −1.59633 | −0.798163 | − | 0.602441i | \(-0.794195\pi\) | ||||
−0.798163 | + | 0.602441i | \(0.794195\pi\) | |||||||
\(774\) | −5.14590 | −0.184966 | ||||||||
\(775\) | 21.3280 | 0.766126 | ||||||||
\(776\) | −25.7128 | −0.923036 | ||||||||
\(777\) | 72.4381 | 2.59870 | ||||||||
\(778\) | 37.9172 | 1.35940 | ||||||||
\(779\) | −17.9395 | −0.642748 | ||||||||
\(780\) | 3.37119 | 0.120708 | ||||||||
\(781\) | −33.7608 | −1.20806 | ||||||||
\(782\) | −1.58367 | −0.0566320 | ||||||||
\(783\) | 5.61713 | 0.200740 | ||||||||
\(784\) | −24.1949 | −0.864104 | ||||||||
\(785\) | 10.7114 | 0.382308 | ||||||||
\(786\) | −8.79432 | −0.313683 | ||||||||
\(787\) | −29.9582 | −1.06790 | −0.533948 | − | 0.845517i | \(-0.679292\pi\) | ||||
−0.533948 | + | 0.845517i | \(0.679292\pi\) | |||||||
\(788\) | −4.69284 | −0.167175 | ||||||||
\(789\) | 12.6603 | 0.450718 | ||||||||
\(790\) | 4.15802 | 0.147936 | ||||||||
\(791\) | 57.5452 | 2.04607 | ||||||||
\(792\) | −10.5961 | −0.376517 | ||||||||
\(793\) | −18.3917 | −0.653107 | ||||||||
\(794\) | −19.1554 | −0.679800 | ||||||||
\(795\) | 1.26786 | 0.0449662 | ||||||||
\(796\) | 21.4567 | 0.760514 | ||||||||
\(797\) | 3.16027 | 0.111942 | 0.0559712 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559712 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(798\) | −13.7326 | −0.486130 | ||||||||
\(799\) | −3.64866 | −0.129080 | ||||||||
\(800\) | 18.9000 | 0.668218 | ||||||||
\(801\) | −10.1736 | −0.359466 | ||||||||
\(802\) | 23.7170 | 0.837476 | ||||||||
\(803\) | −30.8285 | −1.08791 | ||||||||
\(804\) | 2.54102 | 0.0896147 | ||||||||
\(805\) | 3.64281 | 0.128392 | ||||||||
\(806\) | −18.1784 | −0.640307 | ||||||||
\(807\) | 8.70594 | 0.306464 | ||||||||
\(808\) | −11.2727 | −0.396573 | ||||||||
\(809\) | −45.7986 | −1.61019 | −0.805096 | − | 0.593145i | \(-0.797886\pi\) | ||||
−0.805096 | + | 0.593145i | \(0.797886\pi\) | |||||||
\(810\) | 5.38639 | 0.189258 | ||||||||
\(811\) | 16.1790 | 0.568120 | 0.284060 | − | 0.958806i | \(-0.408318\pi\) | ||||
0.284060 | + | 0.958806i | \(0.408318\pi\) | |||||||
\(812\) | −3.82137 | −0.134104 | ||||||||
\(813\) | −30.5970 | −1.07308 | ||||||||
\(814\) | 53.9207 | 1.88992 | ||||||||
\(815\) | 18.9967 | 0.665427 | ||||||||
\(816\) | 3.68551 | 0.129019 | ||||||||
\(817\) | 11.9288 | 0.417336 | ||||||||
\(818\) | −10.6406 | −0.372039 | ||||||||
\(819\) | −11.4989 | −0.401803 | ||||||||
\(820\) | −6.42328 | −0.224311 | ||||||||
\(821\) | −5.87948 | −0.205195 | −0.102598 | − | 0.994723i | \(-0.532715\pi\) | ||||
−0.102598 | + | 0.994723i | \(0.532715\pi\) | |||||||
\(822\) | 25.8041 | 0.900023 | ||||||||
\(823\) | −38.8583 | −1.35452 | −0.677258 | − | 0.735745i | \(-0.736832\pi\) | ||||
−0.677258 | + | 0.735745i | \(0.736832\pi\) | |||||||
\(824\) | 38.6885 | 1.34778 | ||||||||
\(825\) | −31.7890 | −1.10675 | ||||||||
\(826\) | −42.7592 | −1.48778 | ||||||||
\(827\) | 22.6489 | 0.787581 | 0.393791 | − | 0.919200i | \(-0.371164\pi\) | ||||
0.393791 | + | 0.919200i | \(0.371164\pi\) | |||||||
\(828\) | −0.593841 | −0.0206374 | ||||||||
\(829\) | −2.01054 | −0.0698290 | −0.0349145 | − | 0.999390i | \(-0.511116\pi\) | ||||
−0.0349145 | + | 0.999390i | \(0.511116\pi\) | |||||||
\(830\) | −1.42965 | −0.0496237 | ||||||||
\(831\) | −41.0680 | −1.42463 | ||||||||
\(832\) | −27.6226 | −0.957640 | ||||||||
\(833\) | −21.1494 | −0.732783 | ||||||||
\(834\) | −26.5310 | −0.918692 | ||||||||
\(835\) | 2.36189 | 0.0817365 | ||||||||
\(836\) | 7.17047 | 0.247996 | ||||||||
\(837\) | 27.3385 | 0.944958 | ||||||||
\(838\) | −0.755510 | −0.0260986 | ||||||||
\(839\) | 7.17708 | 0.247780 | 0.123890 | − | 0.992296i | \(-0.460463\pi\) | ||||
0.123890 | + | 0.992296i | \(0.460463\pi\) | |||||||
\(840\) | −16.8436 | −0.581161 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −3.40267 | −0.117264 | ||||||||
\(843\) | 10.3101 | 0.355099 | ||||||||
\(844\) | −4.92296 | −0.169455 | ||||||||
\(845\) | −0.889635 | −0.0306044 | ||||||||
\(846\) | 1.95044 | 0.0670574 | ||||||||
\(847\) | −55.9954 | −1.92403 | ||||||||
\(848\) | −1.78517 | −0.0613030 | ||||||||
\(849\) | −41.9803 | −1.44076 | ||||||||
\(850\) | −6.93994 | −0.238038 | ||||||||
\(851\) | 10.3517 | 0.354853 | ||||||||
\(852\) | 8.74852 | 0.299719 | ||||||||
\(853\) | 17.2084 | 0.589204 | 0.294602 | − | 0.955620i | \(-0.404813\pi\) | ||||
0.294602 | + | 0.955620i | \(0.404813\pi\) | |||||||
\(854\) | 26.8249 | 0.917930 | ||||||||
\(855\) | 1.02467 | 0.0350429 | ||||||||
\(856\) | 52.4569 | 1.79294 | ||||||||
\(857\) | −35.4590 | −1.21126 | −0.605629 | − | 0.795747i | \(-0.707078\pi\) | ||||
−0.605629 | + | 0.795747i | \(0.707078\pi\) | |||||||
\(858\) | 27.0945 | 0.924992 | ||||||||
\(859\) | 53.2336 | 1.81631 | 0.908153 | − | 0.418638i | \(-0.137492\pi\) | ||||
0.908153 | + | 0.418638i | \(0.137492\pi\) | |||||||
\(860\) | 4.27114 | 0.145645 | ||||||||
\(861\) | −69.3533 | −2.36356 | ||||||||
\(862\) | −40.2095 | −1.36954 | ||||||||
\(863\) | −24.5153 | −0.834509 | −0.417255 | − | 0.908790i | \(-0.637008\pi\) | ||||
−0.417255 | + | 0.908790i | \(0.637008\pi\) | |||||||
\(864\) | 24.2263 | 0.824196 | ||||||||
\(865\) | −2.47464 | −0.0841402 | ||||||||
\(866\) | 21.8827 | 0.743605 | ||||||||
\(867\) | −22.4467 | −0.762329 | ||||||||
\(868\) | −18.5986 | −0.631277 | ||||||||
\(869\) | −23.4418 | −0.795210 | ||||||||
\(870\) | 1.28671 | 0.0436236 | ||||||||
\(871\) | 7.03135 | 0.238248 | ||||||||
\(872\) | −12.9184 | −0.437472 | ||||||||
\(873\) | 6.04721 | 0.204667 | ||||||||
\(874\) | −1.96245 | −0.0663810 | ||||||||
\(875\) | 34.1775 | 1.15541 | ||||||||
\(876\) | 7.98866 | 0.269912 | ||||||||
\(877\) | 32.3744 | 1.09320 | 0.546602 | − | 0.837392i | \(-0.315921\pi\) | ||||
0.546602 | + | 0.837392i | \(0.315921\pi\) | |||||||
\(878\) | 30.9351 | 1.04401 | ||||||||
\(879\) | −0.0178618 | −0.000602463 0 | ||||||||
\(880\) | −6.31041 | −0.212724 | ||||||||
\(881\) | 8.70671 | 0.293337 | 0.146668 | − | 0.989186i | \(-0.453145\pi\) | ||||
0.146668 | + | 0.989186i | \(0.453145\pi\) | |||||||
\(882\) | 11.3057 | 0.380682 | ||||||||
\(883\) | 21.8907 | 0.736681 | 0.368341 | − | 0.929691i | \(-0.379926\pi\) | ||||
0.368341 | + | 0.929691i | \(0.379926\pi\) | |||||||
\(884\) | −4.14922 | −0.139553 | ||||||||
\(885\) | −10.0995 | −0.339490 | ||||||||
\(886\) | 31.7296 | 1.06598 | ||||||||
\(887\) | −38.4846 | −1.29219 | −0.646093 | − | 0.763259i | \(-0.723598\pi\) | ||||
−0.646093 | + | 0.763259i | \(0.723598\pi\) | |||||||
\(888\) | −47.8644 | −1.60622 | ||||||||
\(889\) | 8.21636 | 0.275568 | ||||||||
\(890\) | −12.0379 | −0.403511 | ||||||||
\(891\) | −30.3671 | −1.01733 | ||||||||
\(892\) | 1.60455 | 0.0537243 | ||||||||
\(893\) | −4.52134 | −0.151301 | ||||||||
\(894\) | 1.25706 | 0.0420423 | ||||||||
\(895\) | 19.5528 | 0.653578 | ||||||||
\(896\) | 0.311689 | 0.0104128 | ||||||||
\(897\) | 5.20163 | 0.173677 | ||||||||
\(898\) | −4.55879 | −0.152129 | ||||||||
\(899\) | 4.86699 | 0.162323 | ||||||||
\(900\) | −2.60232 | −0.0867440 | ||||||||
\(901\) | −1.56046 | −0.0519866 | ||||||||
\(902\) | −51.6245 | −1.71891 | ||||||||
\(903\) | 46.1163 | 1.53465 | ||||||||
\(904\) | −38.0237 | −1.26465 | ||||||||
\(905\) | −0.900002 | −0.0299171 | ||||||||
\(906\) | −5.75607 | −0.191233 | ||||||||
\(907\) | −2.29646 | −0.0762528 | −0.0381264 | − | 0.999273i | \(-0.512139\pi\) | ||||
−0.0381264 | + | 0.999273i | \(0.512139\pi\) | |||||||
\(908\) | −11.6999 | −0.388274 | ||||||||
\(909\) | 2.65115 | 0.0879331 | ||||||||
\(910\) | −13.6060 | −0.451036 | ||||||||
\(911\) | 51.4864 | 1.70582 | 0.852910 | − | 0.522059i | \(-0.174836\pi\) | ||||
0.852910 | + | 0.522059i | \(0.174836\pi\) | |||||||
\(912\) | 4.56701 | 0.151229 | ||||||||
\(913\) | 8.05997 | 0.266746 | ||||||||
\(914\) | −22.3421 | −0.739011 | ||||||||
\(915\) | 6.33588 | 0.209458 | ||||||||
\(916\) | 14.1098 | 0.466200 | ||||||||
\(917\) | −24.8976 | −0.822190 | ||||||||
\(918\) | −8.89570 | −0.293602 | ||||||||
\(919\) | 35.4694 | 1.17003 | 0.585014 | − | 0.811023i | \(-0.301089\pi\) | ||||
0.585014 | + | 0.811023i | \(0.301089\pi\) | |||||||
\(920\) | −2.40703 | −0.0793575 | ||||||||
\(921\) | −0.736517 | −0.0242690 | ||||||||
\(922\) | −23.1471 | −0.762310 | ||||||||
\(923\) | 24.2084 | 0.796829 | ||||||||
\(924\) | 27.7208 | 0.911947 | ||||||||
\(925\) | 45.3632 | 1.49153 | ||||||||
\(926\) | 11.9945 | 0.394164 | ||||||||
\(927\) | −9.09887 | −0.298846 | ||||||||
\(928\) | 4.31293 | 0.141579 | ||||||||
\(929\) | −31.5925 | −1.03652 | −0.518258 | − | 0.855224i | \(-0.673419\pi\) | ||||
−0.518258 | + | 0.855224i | \(0.673419\pi\) | |||||||
\(930\) | 6.26242 | 0.205353 | ||||||||
\(931\) | −26.2079 | −0.858929 | ||||||||
\(932\) | −8.07989 | −0.264666 | ||||||||
\(933\) | 50.4480 | 1.65159 | ||||||||
\(934\) | −31.2681 | −1.02312 | ||||||||
\(935\) | −5.51608 | −0.180395 | ||||||||
\(936\) | 7.59802 | 0.248349 | ||||||||
\(937\) | −31.3788 | −1.02510 | −0.512550 | − | 0.858657i | \(-0.671299\pi\) | ||||
−0.512550 | + | 0.858657i | \(0.671299\pi\) | |||||||
\(938\) | −10.2555 | −0.334854 | ||||||||
\(939\) | 29.5742 | 0.965118 | ||||||||
\(940\) | −1.61888 | −0.0528020 | ||||||||
\(941\) | −23.7309 | −0.773606 | −0.386803 | − | 0.922162i | \(-0.626421\pi\) | ||||
−0.386803 | + | 0.922162i | \(0.626421\pi\) | |||||||
\(942\) | −22.3084 | −0.726848 | ||||||||
\(943\) | −9.91091 | −0.322744 | ||||||||
\(944\) | 14.2203 | 0.462831 | ||||||||
\(945\) | 20.4621 | 0.665634 | ||||||||
\(946\) | 34.3275 | 1.11608 | ||||||||
\(947\) | −36.6882 | −1.19221 | −0.596103 | − | 0.802908i | \(-0.703285\pi\) | ||||
−0.596103 | + | 0.802908i | \(0.703285\pi\) | |||||||
\(948\) | 6.07454 | 0.197292 | ||||||||
\(949\) | 22.1057 | 0.717583 | ||||||||
\(950\) | −8.59983 | −0.279015 | ||||||||
\(951\) | −17.4098 | −0.564551 | ||||||||
\(952\) | 20.7310 | 0.671894 | ||||||||
\(953\) | 22.0458 | 0.714133 | 0.357067 | − | 0.934079i | \(-0.383777\pi\) | ||||
0.357067 | + | 0.934079i | \(0.383777\pi\) | |||||||
\(954\) | 0.834166 | 0.0270071 | ||||||||
\(955\) | −9.98422 | −0.323082 | ||||||||
\(956\) | −11.4337 | −0.369792 | ||||||||
\(957\) | −7.25415 | −0.234493 | ||||||||
\(958\) | 41.4562 | 1.33939 | ||||||||
\(959\) | 73.0540 | 2.35904 | ||||||||
\(960\) | 9.51590 | 0.307124 | ||||||||
\(961\) | −7.31240 | −0.235884 | ||||||||
\(962\) | −38.6642 | −1.24658 | ||||||||
\(963\) | −12.3370 | −0.397553 | ||||||||
\(964\) | 9.26031 | 0.298255 | ||||||||
\(965\) | 12.3513 | 0.397603 | ||||||||
\(966\) | −7.58678 | −0.244101 | ||||||||
\(967\) | 35.0782 | 1.12804 | 0.564019 | − | 0.825762i | \(-0.309254\pi\) | ||||
0.564019 | + | 0.825762i | \(0.309254\pi\) | |||||||
\(968\) | 36.9997 | 1.18922 | ||||||||
\(969\) | 3.99214 | 0.128246 | ||||||||
\(970\) | 7.15536 | 0.229745 | ||||||||
\(971\) | 33.0765 | 1.06147 | 0.530737 | − | 0.847537i | \(-0.321915\pi\) | ||||
0.530737 | + | 0.847537i | \(0.321915\pi\) | |||||||
\(972\) | −6.02560 | −0.193271 | ||||||||
\(973\) | −75.1118 | −2.40797 | ||||||||
\(974\) | −38.4960 | −1.23349 | ||||||||
\(975\) | 22.7945 | 0.730008 | ||||||||
\(976\) | −8.92108 | −0.285557 | ||||||||
\(977\) | 47.8887 | 1.53209 | 0.766047 | − | 0.642785i | \(-0.222221\pi\) | ||||
0.766047 | + | 0.642785i | \(0.222221\pi\) | |||||||
\(978\) | −39.5640 | −1.26512 | ||||||||
\(979\) | 67.8665 | 2.16902 | ||||||||
\(980\) | −9.38381 | −0.299755 | ||||||||
\(981\) | 3.03819 | 0.0970018 | ||||||||
\(982\) | −38.3006 | −1.22222 | ||||||||
\(983\) | 36.4581 | 1.16283 | 0.581416 | − | 0.813606i | \(-0.302499\pi\) | ||||
0.581416 | + | 0.813606i | \(0.302499\pi\) | |||||||
\(984\) | 45.8261 | 1.46088 | ||||||||
\(985\) | 4.47356 | 0.142539 | ||||||||
\(986\) | −1.58367 | −0.0504344 | ||||||||
\(987\) | −17.4794 | −0.556374 | ||||||||
\(988\) | −5.14163 | −0.163577 | ||||||||
\(989\) | 6.59023 | 0.209557 | ||||||||
\(990\) | 2.94869 | 0.0937157 | ||||||||
\(991\) | −29.1548 | −0.926134 | −0.463067 | − | 0.886323i | \(-0.653251\pi\) | ||||
−0.463067 | + | 0.886323i | \(0.653251\pi\) | |||||||
\(992\) | 20.9910 | 0.666465 | ||||||||
\(993\) | −47.3143 | −1.50147 | ||||||||
\(994\) | −35.3089 | −1.11993 | ||||||||
\(995\) | −20.4541 | −0.648440 | ||||||||
\(996\) | −2.08860 | −0.0661798 | ||||||||
\(997\) | 38.3967 | 1.21604 | 0.608018 | − | 0.793923i | \(-0.291965\pi\) | ||||
0.608018 | + | 0.793923i | \(0.291965\pi\) | |||||||
\(998\) | −23.8665 | −0.755479 | ||||||||
\(999\) | 58.1471 | 1.83969 |
(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 | 667.2.a.b.1.5 | ✓ | 12 | |
3.2 | odd | 2 | 6003.2.a.n.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.b.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
6003.2.a.n.1.8 | 12 | 3.2 | odd | 2 |