Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.28561300.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.23039\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97462 | −1.39627 | −0.698135 | − | 0.715966i | \(-0.745986\pi\) | ||||
−0.698135 | + | 0.715966i | \(0.745986\pi\) | |||||||
\(3\) | −0.571492 | −0.329951 | −0.164976 | − | 0.986298i | \(-0.552755\pi\) | ||||
−0.164976 | + | 0.986298i | \(0.552755\pi\) | |||||||
\(4\) | 1.89914 | 0.949569 | ||||||||
\(5\) | −1.23039 | −0.550246 | −0.275123 | − | 0.961409i | \(-0.588719\pi\) | ||||
−0.275123 | + | 0.961409i | \(0.588719\pi\) | |||||||
\(6\) | 1.12848 | 0.460701 | ||||||||
\(7\) | 2.55803 | 0.966845 | 0.483423 | − | 0.875387i | \(-0.339393\pi\) | ||||
0.483423 | + | 0.875387i | \(0.339393\pi\) | |||||||
\(8\) | 0.199164 | 0.0704150 | ||||||||
\(9\) | −2.67340 | −0.891132 | ||||||||
\(10\) | 2.42955 | 0.768291 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.08534 | −0.313312 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −5.05115 | −1.34998 | ||||||||
\(15\) | 0.703156 | 0.181554 | ||||||||
\(16\) | −4.19155 | −1.04789 | ||||||||
\(17\) | 5.97567 | 1.44931 | 0.724656 | − | 0.689111i | \(-0.241999\pi\) | ||||
0.724656 | + | 0.689111i | \(0.241999\pi\) | |||||||
\(18\) | 5.27895 | 1.24426 | ||||||||
\(19\) | 5.32116 | 1.22076 | 0.610378 | − | 0.792110i | \(-0.291017\pi\) | ||||
0.610378 | + | 0.792110i | \(0.291017\pi\) | |||||||
\(20\) | −2.33667 | −0.522496 | ||||||||
\(21\) | −1.46190 | −0.319012 | ||||||||
\(22\) | −1.97462 | −0.420991 | ||||||||
\(23\) | −3.26161 | −0.680093 | −0.340046 | − | 0.940409i | \(-0.610443\pi\) | ||||
−0.340046 | + | 0.940409i | \(0.610443\pi\) | |||||||
\(24\) | −0.113821 | −0.0232335 | ||||||||
\(25\) | −3.48615 | −0.697230 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.24230 | 0.623981 | ||||||||
\(28\) | 4.85806 | 0.918087 | ||||||||
\(29\) | −2.86469 | −0.531959 | −0.265979 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265979 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(30\) | −1.38847 | −0.253499 | ||||||||
\(31\) | −2.90456 | −0.521675 | −0.260838 | − | 0.965383i | \(-0.583999\pi\) | ||||
−0.260838 | + | 0.965383i | \(0.583999\pi\) | |||||||
\(32\) | 7.87841 | 1.39272 | ||||||||
\(33\) | −0.571492 | −0.0994841 | ||||||||
\(34\) | −11.7997 | −2.02363 | ||||||||
\(35\) | −3.14737 | −0.532002 | ||||||||
\(36\) | −5.07715 | −0.846192 | ||||||||
\(37\) | 9.62343 | 1.58208 | 0.791041 | − | 0.611764i | \(-0.209540\pi\) | ||||
0.791041 | + | 0.611764i | \(0.209540\pi\) | |||||||
\(38\) | −10.5073 | −1.70451 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.245048 | −0.0387455 | ||||||||
\(41\) | 3.47319 | 0.542421 | 0.271211 | − | 0.962520i | \(-0.412576\pi\) | ||||
0.271211 | + | 0.962520i | \(0.412576\pi\) | |||||||
\(42\) | 2.88669 | 0.445427 | ||||||||
\(43\) | 4.53626 | 0.691773 | 0.345886 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345886 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(44\) | 1.89914 | 0.286306 | ||||||||
\(45\) | 3.28931 | 0.490341 | ||||||||
\(46\) | 6.44045 | 0.949593 | ||||||||
\(47\) | −0.858478 | −0.125222 | −0.0626109 | − | 0.998038i | \(-0.519943\pi\) | ||||
−0.0626109 | + | 0.998038i | \(0.519943\pi\) | |||||||
\(48\) | 2.39544 | 0.345752 | ||||||||
\(49\) | −0.456470 | −0.0652100 | ||||||||
\(50\) | 6.88383 | 0.973521 | ||||||||
\(51\) | −3.41505 | −0.478202 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.7446 | −1.88796 | −0.943980 | − | 0.330003i | \(-0.892950\pi\) | ||||
−0.943980 | + | 0.330003i | \(0.892950\pi\) | |||||||
\(54\) | −6.40233 | −0.871246 | ||||||||
\(55\) | −1.23039 | −0.165905 | ||||||||
\(56\) | 0.509467 | 0.0680804 | ||||||||
\(57\) | −3.04100 | −0.402790 | ||||||||
\(58\) | 5.65668 | 0.742758 | ||||||||
\(59\) | −8.76048 | −1.14052 | −0.570259 | − | 0.821465i | \(-0.693157\pi\) | ||||
−0.570259 | + | 0.821465i | \(0.693157\pi\) | |||||||
\(60\) | 1.33539 | 0.172398 | ||||||||
\(61\) | 2.76304 | 0.353771 | 0.176886 | − | 0.984231i | \(-0.443398\pi\) | ||||
0.176886 | + | 0.984231i | \(0.443398\pi\) | |||||||
\(62\) | 5.73542 | 0.728399 | ||||||||
\(63\) | −6.83863 | −0.861587 | ||||||||
\(64\) | −7.17379 | −0.896723 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.12848 | 0.138907 | ||||||||
\(67\) | −3.64984 | −0.445899 | −0.222950 | − | 0.974830i | \(-0.571569\pi\) | ||||
−0.222950 | + | 0.974830i | \(0.571569\pi\) | |||||||
\(68\) | 11.3486 | 1.37622 | ||||||||
\(69\) | 1.86398 | 0.224397 | ||||||||
\(70\) | 6.21487 | 0.742819 | ||||||||
\(71\) | 7.31017 | 0.867558 | 0.433779 | − | 0.901019i | \(-0.357180\pi\) | ||||
0.433779 | + | 0.901019i | \(0.357180\pi\) | |||||||
\(72\) | −0.532443 | −0.0627491 | ||||||||
\(73\) | 5.63352 | 0.659353 | 0.329677 | − | 0.944094i | \(-0.393060\pi\) | ||||
0.329677 | + | 0.944094i | \(0.393060\pi\) | |||||||
\(74\) | −19.0026 | −2.20901 | ||||||||
\(75\) | 1.99231 | 0.230052 | ||||||||
\(76\) | 10.1056 | 1.15919 | ||||||||
\(77\) | 2.55803 | 0.291515 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.57221 | 0.851940 | 0.425970 | − | 0.904737i | \(-0.359933\pi\) | ||||
0.425970 | + | 0.904737i | \(0.359933\pi\) | |||||||
\(80\) | 5.15723 | 0.576595 | ||||||||
\(81\) | 6.16724 | 0.685249 | ||||||||
\(82\) | −6.85824 | −0.757366 | ||||||||
\(83\) | 0.707087 | 0.0776129 | 0.0388065 | − | 0.999247i | \(-0.487644\pi\) | ||||
0.0388065 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(84\) | −2.77634 | −0.302924 | ||||||||
\(85\) | −7.35238 | −0.797477 | ||||||||
\(86\) | −8.95740 | −0.965902 | ||||||||
\(87\) | 1.63715 | 0.175520 | ||||||||
\(88\) | 0.199164 | 0.0212309 | ||||||||
\(89\) | −12.1474 | −1.28762 | −0.643812 | − | 0.765183i | \(-0.722648\pi\) | ||||
−0.643812 | + | 0.765183i | \(0.722648\pi\) | |||||||
\(90\) | −6.49515 | −0.684649 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.19425 | −0.645795 | ||||||||
\(93\) | 1.65994 | 0.172127 | ||||||||
\(94\) | 1.69517 | 0.174844 | ||||||||
\(95\) | −6.54708 | −0.671716 | ||||||||
\(96\) | −4.50245 | −0.459529 | ||||||||
\(97\) | −3.45779 | −0.351086 | −0.175543 | − | 0.984472i | \(-0.556168\pi\) | ||||
−0.175543 | + | 0.984472i | \(0.556168\pi\) | |||||||
\(98\) | 0.901356 | 0.0910507 | ||||||||
\(99\) | −2.67340 | −0.268686 | ||||||||
\(100\) | −6.62068 | −0.662068 | ||||||||
\(101\) | −17.7093 | −1.76214 | −0.881071 | − | 0.472984i | \(-0.843177\pi\) | ||||
−0.881071 | + | 0.472984i | \(0.843177\pi\) | |||||||
\(102\) | 6.74343 | 0.667699 | ||||||||
\(103\) | 15.6365 | 1.54071 | 0.770355 | − | 0.637616i | \(-0.220079\pi\) | ||||
0.770355 | + | 0.637616i | \(0.220079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.79870 | 0.175535 | ||||||||
\(106\) | 27.1403 | 2.63610 | ||||||||
\(107\) | 4.15886 | 0.402053 | 0.201026 | − | 0.979586i | \(-0.435572\pi\) | ||||
0.201026 | + | 0.979586i | \(0.435572\pi\) | |||||||
\(108\) | 6.15758 | 0.592514 | ||||||||
\(109\) | 4.52071 | 0.433006 | 0.216503 | − | 0.976282i | \(-0.430535\pi\) | ||||
0.216503 | + | 0.976282i | \(0.430535\pi\) | |||||||
\(110\) | 2.42955 | 0.231649 | ||||||||
\(111\) | −5.49971 | −0.522010 | ||||||||
\(112\) | −10.7221 | −1.01315 | ||||||||
\(113\) | −6.36127 | −0.598418 | −0.299209 | − | 0.954188i | \(-0.596723\pi\) | ||||
−0.299209 | + | 0.954188i | \(0.596723\pi\) | |||||||
\(114\) | 6.00483 | 0.562404 | ||||||||
\(115\) | 4.01304 | 0.374218 | ||||||||
\(116\) | −5.44043 | −0.505132 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 17.2987 | 1.59247 | ||||||||
\(119\) | 15.2859 | 1.40126 | ||||||||
\(120\) | 0.140043 | 0.0127841 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.45597 | −0.493960 | ||||||||
\(123\) | −1.98490 | −0.178973 | ||||||||
\(124\) | −5.51617 | −0.495367 | ||||||||
\(125\) | 10.4412 | 0.933893 | ||||||||
\(126\) | 13.5037 | 1.20301 | ||||||||
\(127\) | 21.7096 | 1.92642 | 0.963210 | − | 0.268750i | \(-0.0866106\pi\) | ||||
0.963210 | + | 0.268750i | \(0.0866106\pi\) | |||||||
\(128\) | −1.59128 | −0.140651 | ||||||||
\(129\) | −2.59244 | −0.228251 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7296 | 1.11219 | 0.556097 | − | 0.831118i | \(-0.312298\pi\) | ||||
0.556097 | + | 0.831118i | \(0.312298\pi\) | |||||||
\(132\) | −1.08534 | −0.0944670 | ||||||||
\(133\) | 13.6117 | 1.18028 | ||||||||
\(134\) | 7.20707 | 0.622596 | ||||||||
\(135\) | −3.98929 | −0.343343 | ||||||||
\(136\) | 1.19014 | 0.102053 | ||||||||
\(137\) | 9.57974 | 0.818452 | 0.409226 | − | 0.912433i | \(-0.365799\pi\) | ||||
0.409226 | + | 0.912433i | \(0.365799\pi\) | |||||||
\(138\) | −3.68067 | −0.313319 | ||||||||
\(139\) | 8.55587 | 0.725700 | 0.362850 | − | 0.931848i | \(-0.381804\pi\) | ||||
0.362850 | + | 0.931848i | \(0.381804\pi\) | |||||||
\(140\) | −5.97729 | −0.505173 | ||||||||
\(141\) | 0.490614 | 0.0413171 | ||||||||
\(142\) | −14.4348 | −1.21135 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 11.2057 | 0.933806 | ||||||||
\(145\) | 3.52467 | 0.292708 | ||||||||
\(146\) | −11.1241 | −0.920635 | ||||||||
\(147\) | 0.260869 | 0.0215161 | ||||||||
\(148\) | 18.2762 | 1.50230 | ||||||||
\(149\) | 6.92454 | 0.567281 | 0.283640 | − | 0.958931i | \(-0.408458\pi\) | ||||
0.283640 | + | 0.958931i | \(0.408458\pi\) | |||||||
\(150\) | −3.93406 | −0.321214 | ||||||||
\(151\) | 8.53083 | 0.694229 | 0.347115 | − | 0.937823i | \(-0.387161\pi\) | ||||
0.347115 | + | 0.937823i | \(0.387161\pi\) | |||||||
\(152\) | 1.05978 | 0.0859596 | ||||||||
\(153\) | −15.9753 | −1.29153 | ||||||||
\(154\) | −5.05115 | −0.407033 | ||||||||
\(155\) | 3.57374 | 0.287049 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8805 | −1.26740 | −0.633701 | − | 0.773578i | \(-0.718465\pi\) | ||||
−0.633701 | + | 0.773578i | \(0.718465\pi\) | |||||||
\(158\) | −14.9523 | −1.18954 | ||||||||
\(159\) | 7.85491 | 0.622935 | ||||||||
\(160\) | −9.69348 | −0.766337 | ||||||||
\(161\) | −8.34330 | −0.657544 | ||||||||
\(162\) | −12.1780 | −0.956792 | ||||||||
\(163\) | 23.4750 | 1.83871 | 0.919353 | − | 0.393435i | \(-0.128713\pi\) | ||||
0.919353 | + | 0.393435i | \(0.128713\pi\) | |||||||
\(164\) | 6.59607 | 0.515066 | ||||||||
\(165\) | 0.703156 | 0.0547407 | ||||||||
\(166\) | −1.39623 | −0.108369 | ||||||||
\(167\) | −7.74766 | −0.599532 | −0.299766 | − | 0.954013i | \(-0.596909\pi\) | ||||
−0.299766 | + | 0.954013i | \(0.596909\pi\) | |||||||
\(168\) | −0.291157 | −0.0224632 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 14.5182 | 1.11349 | ||||||||
\(171\) | −14.2256 | −1.08786 | ||||||||
\(172\) | 8.61498 | 0.656886 | ||||||||
\(173\) | 11.5028 | 0.874545 | 0.437273 | − | 0.899329i | \(-0.355944\pi\) | ||||
0.437273 | + | 0.899329i | \(0.355944\pi\) | |||||||
\(174\) | −3.23275 | −0.245074 | ||||||||
\(175\) | −8.91768 | −0.674113 | ||||||||
\(176\) | −4.19155 | −0.315950 | ||||||||
\(177\) | 5.00655 | 0.376315 | ||||||||
\(178\) | 23.9866 | 1.79787 | ||||||||
\(179\) | 15.7027 | 1.17367 | 0.586836 | − | 0.809706i | \(-0.300373\pi\) | ||||
0.586836 | + | 0.809706i | \(0.300373\pi\) | |||||||
\(180\) | 6.24686 | 0.465613 | ||||||||
\(181\) | 16.7002 | 1.24132 | 0.620659 | − | 0.784081i | \(-0.286865\pi\) | ||||
0.620659 | + | 0.784081i | \(0.286865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57906 | −0.116727 | ||||||||
\(184\) | −0.649594 | −0.0478887 | ||||||||
\(185\) | −11.8405 | −0.870533 | ||||||||
\(186\) | −3.27775 | −0.240336 | ||||||||
\(187\) | 5.97567 | 0.436984 | ||||||||
\(188\) | −1.63037 | −0.118907 | ||||||||
\(189\) | 8.29392 | 0.603294 | ||||||||
\(190\) | 12.9280 | 0.937897 | ||||||||
\(191\) | −6.83739 | −0.494736 | −0.247368 | − | 0.968922i | \(-0.579566\pi\) | ||||
−0.247368 | + | 0.968922i | \(0.579566\pi\) | |||||||
\(192\) | 4.09976 | 0.295875 | ||||||||
\(193\) | −11.0834 | −0.797804 | −0.398902 | − | 0.916994i | \(-0.630609\pi\) | ||||
−0.398902 | + | 0.916994i | \(0.630609\pi\) | |||||||
\(194\) | 6.82784 | 0.490210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.866900 | −0.0619214 | ||||||||
\(197\) | 26.0214 | 1.85395 | 0.926975 | − | 0.375123i | \(-0.122400\pi\) | ||||
0.926975 | + | 0.375123i | \(0.122400\pi\) | |||||||
\(198\) | 5.27895 | 0.375159 | ||||||||
\(199\) | 5.57241 | 0.395018 | 0.197509 | − | 0.980301i | \(-0.436715\pi\) | ||||
0.197509 | + | 0.980301i | \(0.436715\pi\) | |||||||
\(200\) | −0.694314 | −0.0490954 | ||||||||
\(201\) | 2.08586 | 0.147125 | ||||||||
\(202\) | 34.9692 | 2.46043 | ||||||||
\(203\) | −7.32796 | −0.514322 | ||||||||
\(204\) | −6.48565 | −0.454086 | ||||||||
\(205\) | −4.27337 | −0.298465 | ||||||||
\(206\) | −30.8762 | −2.15125 | ||||||||
\(207\) | 8.71957 | 0.606052 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.32116 | 0.368072 | ||||||||
\(210\) | −3.55175 | −0.245094 | ||||||||
\(211\) | −6.08881 | −0.419171 | −0.209585 | − | 0.977790i | \(-0.567211\pi\) | ||||
−0.209585 | + | 0.977790i | \(0.567211\pi\) | |||||||
\(212\) | −26.1028 | −1.79275 | ||||||||
\(213\) | −4.17771 | −0.286252 | ||||||||
\(214\) | −8.21219 | −0.561374 | ||||||||
\(215\) | −5.58135 | −0.380645 | ||||||||
\(216\) | 0.645749 | 0.0439376 | ||||||||
\(217\) | −7.42997 | −0.504379 | ||||||||
\(218\) | −8.92671 | −0.604593 | ||||||||
\(219\) | −3.21951 | −0.217554 | ||||||||
\(220\) | −2.33667 | −0.157539 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.8599 | 0.728866 | ||||||||
\(223\) | 9.78336 | 0.655143 | 0.327571 | − | 0.944826i | \(-0.393770\pi\) | ||||
0.327571 | + | 0.944826i | \(0.393770\pi\) | |||||||
\(224\) | 20.1532 | 1.34654 | ||||||||
\(225\) | 9.31986 | 0.621324 | ||||||||
\(226\) | 12.5611 | 0.835553 | ||||||||
\(227\) | −12.5722 | −0.834446 | −0.417223 | − | 0.908804i | \(-0.636997\pi\) | ||||
−0.417223 | + | 0.908804i | \(0.636997\pi\) | |||||||
\(228\) | −5.77528 | −0.382477 | ||||||||
\(229\) | 13.6835 | 0.904230 | 0.452115 | − | 0.891960i | \(-0.350670\pi\) | ||||
0.452115 | + | 0.891960i | \(0.350670\pi\) | |||||||
\(230\) | −7.92424 | −0.522509 | ||||||||
\(231\) | −1.46190 | −0.0961857 | ||||||||
\(232\) | −0.570541 | −0.0374579 | ||||||||
\(233\) | −15.9817 | −1.04700 | −0.523499 | − | 0.852026i | \(-0.675374\pi\) | ||||
−0.523499 | + | 0.852026i | \(0.675374\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.05626 | 0.0689028 | ||||||||
\(236\) | −16.6374 | −1.08300 | ||||||||
\(237\) | −4.32746 | −0.281099 | ||||||||
\(238\) | −30.1840 | −1.95654 | ||||||||
\(239\) | 16.8419 | 1.08941 | 0.544707 | − | 0.838627i | \(-0.316641\pi\) | ||||
0.544707 | + | 0.838627i | \(0.316641\pi\) | |||||||
\(240\) | −2.94732 | −0.190248 | ||||||||
\(241\) | 9.06598 | 0.583991 | 0.291996 | − | 0.956420i | \(-0.405681\pi\) | ||||
0.291996 | + | 0.956420i | \(0.405681\pi\) | |||||||
\(242\) | −1.97462 | −0.126934 | ||||||||
\(243\) | −13.2514 | −0.850080 | ||||||||
\(244\) | 5.24740 | 0.335930 | ||||||||
\(245\) | 0.561634 | 0.0358815 | ||||||||
\(246\) | 3.91943 | 0.249894 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.578484 | −0.0367338 | ||||||||
\(249\) | −0.404095 | −0.0256085 | ||||||||
\(250\) | −20.6175 | −1.30397 | ||||||||
\(251\) | 6.35232 | 0.400955 | 0.200477 | − | 0.979698i | \(-0.435751\pi\) | ||||
0.200477 | + | 0.979698i | \(0.435751\pi\) | |||||||
\(252\) | −12.9875 | −0.818136 | ||||||||
\(253\) | −3.26161 | −0.205056 | ||||||||
\(254\) | −42.8684 | −2.68980 | ||||||||
\(255\) | 4.20183 | 0.263129 | ||||||||
\(256\) | 17.4898 | 1.09311 | ||||||||
\(257\) | 24.2690 | 1.51386 | 0.756928 | − | 0.653498i | \(-0.226699\pi\) | ||||
0.756928 | + | 0.653498i | \(0.226699\pi\) | |||||||
\(258\) | 5.11909 | 0.318700 | ||||||||
\(259\) | 24.6170 | 1.52963 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.65844 | 0.474046 | ||||||||
\(262\) | −25.1362 | −1.55292 | ||||||||
\(263\) | −7.83939 | −0.483398 | −0.241699 | − | 0.970351i | \(-0.577705\pi\) | ||||
−0.241699 | + | 0.970351i | \(0.577705\pi\) | |||||||
\(264\) | −0.113821 | −0.00700517 | ||||||||
\(265\) | 16.9111 | 1.03884 | ||||||||
\(266\) | −26.8780 | −1.64799 | ||||||||
\(267\) | 6.94216 | 0.424853 | ||||||||
\(268\) | −6.93156 | −0.423412 | ||||||||
\(269\) | 0.246971 | 0.0150581 | 0.00752905 | − | 0.999972i | \(-0.497603\pi\) | ||||
0.00752905 | + | 0.999972i | \(0.497603\pi\) | |||||||
\(270\) | 7.87734 | 0.479399 | ||||||||
\(271\) | 17.6629 | 1.07295 | 0.536473 | − | 0.843917i | \(-0.319756\pi\) | ||||
0.536473 | + | 0.843917i | \(0.319756\pi\) | |||||||
\(272\) | −25.0473 | −1.51872 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.9164 | −1.14278 | ||||||||
\(275\) | −3.48615 | −0.210223 | ||||||||
\(276\) | 3.53997 | 0.213081 | ||||||||
\(277\) | 10.7868 | 0.648114 | 0.324057 | − | 0.946038i | \(-0.394953\pi\) | ||||
0.324057 | + | 0.946038i | \(0.394953\pi\) | |||||||
\(278\) | −16.8946 | −1.01327 | ||||||||
\(279\) | 7.76505 | 0.464882 | ||||||||
\(280\) | −0.626841 | −0.0374609 | ||||||||
\(281\) | 25.4436 | 1.51784 | 0.758919 | − | 0.651185i | \(-0.225728\pi\) | ||||
0.758919 | + | 0.651185i | \(0.225728\pi\) | |||||||
\(282\) | −0.968777 | −0.0576898 | ||||||||
\(283\) | −31.0858 | −1.84786 | −0.923928 | − | 0.382566i | \(-0.875040\pi\) | ||||
−0.923928 | + | 0.382566i | \(0.875040\pi\) | |||||||
\(284\) | 13.8830 | 0.823806 | ||||||||
\(285\) | 3.74161 | 0.221634 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.88453 | 0.524437 | ||||||||
\(288\) | −21.0621 | −1.24110 | ||||||||
\(289\) | 18.7086 | 1.10051 | ||||||||
\(290\) | −6.95990 | −0.408699 | ||||||||
\(291\) | 1.97610 | 0.115841 | ||||||||
\(292\) | 10.6988 | 0.626102 | ||||||||
\(293\) | 11.3869 | 0.665232 | 0.332616 | − | 0.943062i | \(-0.392069\pi\) | ||||
0.332616 | + | 0.943062i | \(0.392069\pi\) | |||||||
\(294\) | −0.515118 | −0.0300423 | ||||||||
\(295\) | 10.7788 | 0.627565 | ||||||||
\(296\) | 1.91664 | 0.111402 | ||||||||
\(297\) | 3.24230 | 0.188137 | ||||||||
\(298\) | −13.6734 | −0.792077 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.78367 | 0.218450 | ||||||||
\(301\) | 11.6039 | 0.668837 | ||||||||
\(302\) | −16.8452 | −0.969331 | ||||||||
\(303\) | 10.1207 | 0.581421 | ||||||||
\(304\) | −22.3039 | −1.27922 | ||||||||
\(305\) | −3.39961 | −0.194661 | ||||||||
\(306\) | 31.5453 | 1.80332 | ||||||||
\(307\) | 20.2057 | 1.15320 | 0.576600 | − | 0.817027i | \(-0.304379\pi\) | ||||
0.576600 | + | 0.817027i | \(0.304379\pi\) | |||||||
\(308\) | 4.85806 | 0.276814 | ||||||||
\(309\) | −8.93613 | −0.508359 | ||||||||
\(310\) | −7.05679 | −0.400798 | ||||||||
\(311\) | 12.1332 | 0.688011 | 0.344005 | − | 0.938968i | \(-0.388216\pi\) | ||||
0.344005 | + | 0.938968i | \(0.388216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.4422 | 1.09894 | 0.549468 | − | 0.835514i | \(-0.314830\pi\) | ||||
0.549468 | + | 0.835514i | \(0.314830\pi\) | |||||||
\(314\) | 31.3580 | 1.76963 | ||||||||
\(315\) | 8.41416 | 0.474084 | ||||||||
\(316\) | 14.3807 | 0.808976 | ||||||||
\(317\) | −5.36260 | −0.301193 | −0.150597 | − | 0.988595i | \(-0.548120\pi\) | ||||
−0.150597 | + | 0.988595i | \(0.548120\pi\) | |||||||
\(318\) | −15.5105 | −0.869785 | ||||||||
\(319\) | −2.86469 | −0.160392 | ||||||||
\(320\) | 8.82653 | 0.493418 | ||||||||
\(321\) | −2.37676 | −0.132658 | ||||||||
\(322\) | 16.4749 | 0.918109 | ||||||||
\(323\) | 31.7974 | 1.76926 | ||||||||
\(324\) | 11.7124 | 0.650691 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −46.3543 | −2.56733 | ||||||||
\(327\) | −2.58355 | −0.142871 | ||||||||
\(328\) | 0.691733 | 0.0381946 | ||||||||
\(329\) | −2.19601 | −0.121070 | ||||||||
\(330\) | −1.38847 | −0.0764327 | ||||||||
\(331\) | −15.9251 | −0.875322 | −0.437661 | − | 0.899140i | \(-0.644193\pi\) | ||||
−0.437661 | + | 0.899140i | \(0.644193\pi\) | |||||||
\(332\) | 1.34286 | 0.0736988 | ||||||||
\(333\) | −25.7272 | −1.40984 | ||||||||
\(334\) | 15.2987 | 0.837108 | ||||||||
\(335\) | 4.49072 | 0.245354 | ||||||||
\(336\) | 6.12761 | 0.334289 | ||||||||
\(337\) | 7.71234 | 0.420118 | 0.210059 | − | 0.977689i | \(-0.432634\pi\) | ||||
0.210059 | + | 0.977689i | \(0.432634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.63542 | 0.197449 | ||||||||
\(340\) | −13.9632 | −0.757260 | ||||||||
\(341\) | −2.90456 | −0.157291 | ||||||||
\(342\) | 28.0901 | 1.51894 | ||||||||
\(343\) | −19.0739 | −1.02989 | ||||||||
\(344\) | 0.903458 | 0.0487112 | ||||||||
\(345\) | −2.29342 | −0.123474 | ||||||||
\(346\) | −22.7138 | −1.22110 | ||||||||
\(347\) | −24.3767 | −1.30861 | −0.654305 | − | 0.756231i | \(-0.727039\pi\) | ||||
−0.654305 | + | 0.756231i | \(0.727039\pi\) | |||||||
\(348\) | 3.10917 | 0.166669 | ||||||||
\(349\) | −20.5401 | −1.09949 | −0.549743 | − | 0.835334i | \(-0.685274\pi\) | ||||
−0.549743 | + | 0.835334i | \(0.685274\pi\) | |||||||
\(350\) | 17.6091 | 0.941244 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.87841 | 0.419920 | ||||||||
\(353\) | −11.4487 | −0.609355 | −0.304678 | − | 0.952456i | \(-0.598549\pi\) | ||||
−0.304678 | + | 0.952456i | \(0.598549\pi\) | |||||||
\(354\) | −9.88605 | −0.525438 | ||||||||
\(355\) | −8.99434 | −0.477370 | ||||||||
\(356\) | −23.0696 | −1.22269 | ||||||||
\(357\) | −8.73580 | −0.462348 | ||||||||
\(358\) | −31.0068 | −1.63876 | ||||||||
\(359\) | 12.2180 | 0.644841 | 0.322421 | − | 0.946596i | \(-0.395503\pi\) | ||||
0.322421 | + | 0.946596i | \(0.395503\pi\) | |||||||
\(360\) | 0.655111 | 0.0345274 | ||||||||
\(361\) | 9.31470 | 0.490247 | ||||||||
\(362\) | −32.9766 | −1.73321 | ||||||||
\(363\) | −0.571492 | −0.0299956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.93140 | −0.362806 | ||||||||
\(366\) | 3.11804 | 0.162983 | ||||||||
\(367\) | −36.1839 | −1.88878 | −0.944391 | − | 0.328823i | \(-0.893348\pi\) | ||||
−0.944391 | + | 0.328823i | \(0.893348\pi\) | |||||||
\(368\) | 13.6712 | 0.712660 | ||||||||
\(369\) | −9.28521 | −0.483369 | ||||||||
\(370\) | 23.3806 | 1.21550 | ||||||||
\(371\) | −35.1590 | −1.82537 | ||||||||
\(372\) | 3.15245 | 0.163447 | ||||||||
\(373\) | 12.9241 | 0.669186 | 0.334593 | − | 0.942363i | \(-0.391401\pi\) | ||||
0.334593 | + | 0.942363i | \(0.391401\pi\) | |||||||
\(374\) | −11.7997 | −0.610148 | ||||||||
\(375\) | −5.96709 | −0.308139 | ||||||||
\(376\) | −0.170978 | −0.00881750 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −16.3774 | −0.842361 | ||||||||
\(379\) | −35.3528 | −1.81595 | −0.907975 | − | 0.419024i | \(-0.862372\pi\) | ||||
−0.907975 | + | 0.419024i | \(0.862372\pi\) | |||||||
\(380\) | −12.4338 | −0.637841 | ||||||||
\(381\) | −12.4069 | −0.635625 | ||||||||
\(382\) | 13.5013 | 0.690786 | ||||||||
\(383\) | −1.52246 | −0.0777941 | −0.0388970 | − | 0.999243i | \(-0.512384\pi\) | ||||
−0.0388970 | + | 0.999243i | \(0.512384\pi\) | |||||||
\(384\) | 0.909406 | 0.0464079 | ||||||||
\(385\) | −3.14737 | −0.160405 | ||||||||
\(386\) | 21.8856 | 1.11395 | ||||||||
\(387\) | −12.1272 | −0.616461 | ||||||||
\(388\) | −6.56683 | −0.333380 | ||||||||
\(389\) | 33.3803 | 1.69245 | 0.846225 | − | 0.532826i | \(-0.178870\pi\) | ||||
0.846225 | + | 0.532826i | \(0.178870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.4903 | −0.985666 | ||||||||
\(392\) | −0.0909122 | −0.00459176 | ||||||||
\(393\) | −7.27489 | −0.366970 | ||||||||
\(394\) | −51.3825 | −2.58861 | ||||||||
\(395\) | −9.31674 | −0.468776 | ||||||||
\(396\) | −5.07715 | −0.255136 | ||||||||
\(397\) | −26.4193 | −1.32595 | −0.662974 | − | 0.748642i | \(-0.730706\pi\) | ||||
−0.662974 | + | 0.748642i | \(0.730706\pi\) | |||||||
\(398\) | −11.0034 | −0.551551 | ||||||||
\(399\) | −7.77898 | −0.389436 | ||||||||
\(400\) | 14.6124 | 0.730618 | ||||||||
\(401\) | −15.8033 | −0.789179 | −0.394589 | − | 0.918858i | \(-0.629113\pi\) | ||||
−0.394589 | + | 0.918858i | \(0.629113\pi\) | |||||||
\(402\) | −4.11878 | −0.205426 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −33.6324 | −1.67328 | ||||||||
\(405\) | −7.58809 | −0.377055 | ||||||||
\(406\) | 14.4700 | 0.718132 | ||||||||
\(407\) | 9.62343 | 0.477015 | ||||||||
\(408\) | −0.680153 | −0.0336726 | ||||||||
\(409\) | 32.1554 | 1.58998 | 0.794992 | − | 0.606620i | \(-0.207475\pi\) | ||||
0.794992 | + | 0.606620i | \(0.207475\pi\) | |||||||
\(410\) | 8.43829 | 0.416737 | ||||||||
\(411\) | −5.47475 | −0.270049 | ||||||||
\(412\) | 29.6959 | 1.46301 | ||||||||
\(413\) | −22.4096 | −1.10270 | ||||||||
\(414\) | −17.2179 | −0.846213 | ||||||||
\(415\) | −0.869991 | −0.0427062 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.88962 | −0.239445 | ||||||||
\(418\) | −10.5073 | −0.513928 | ||||||||
\(419\) | 6.35735 | 0.310577 | 0.155288 | − | 0.987869i | \(-0.450369\pi\) | ||||
0.155288 | + | 0.987869i | \(0.450369\pi\) | |||||||
\(420\) | 3.41597 | 0.166682 | ||||||||
\(421\) | 4.90563 | 0.239086 | 0.119543 | − | 0.992829i | \(-0.461857\pi\) | ||||
0.119543 | + | 0.992829i | \(0.461857\pi\) | |||||||
\(422\) | 12.0231 | 0.585275 | ||||||||
\(423\) | 2.29505 | 0.111589 | ||||||||
\(424\) | −2.73742 | −0.132941 | ||||||||
\(425\) | −20.8321 | −1.01050 | ||||||||
\(426\) | 8.24940 | 0.399685 | ||||||||
\(427\) | 7.06795 | 0.342042 | ||||||||
\(428\) | 7.89826 | 0.381777 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0211 | 0.531483 | ||||||||
\(431\) | −15.9218 | −0.766928 | −0.383464 | − | 0.923556i | \(-0.625269\pi\) | ||||
−0.383464 | + | 0.923556i | \(0.625269\pi\) | |||||||
\(432\) | −13.5903 | −0.653862 | ||||||||
\(433\) | −25.1376 | −1.20804 | −0.604019 | − | 0.796970i | \(-0.706435\pi\) | ||||
−0.604019 | + | 0.796970i | \(0.706435\pi\) | |||||||
\(434\) | 14.6714 | 0.704249 | ||||||||
\(435\) | −2.01432 | −0.0965794 | ||||||||
\(436\) | 8.58546 | 0.411169 | ||||||||
\(437\) | −17.3555 | −0.830228 | ||||||||
\(438\) | 6.35733 | 0.303765 | ||||||||
\(439\) | 11.5138 | 0.549523 | 0.274761 | − | 0.961512i | \(-0.411401\pi\) | ||||
0.274761 | + | 0.961512i | \(0.411401\pi\) | |||||||
\(440\) | −0.245048 | −0.0116822 | ||||||||
\(441\) | 1.22033 | 0.0581107 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.8533 | −1.56091 | −0.780453 | − | 0.625214i | \(-0.785012\pi\) | ||||
−0.780453 | + | 0.625214i | \(0.785012\pi\) | |||||||
\(444\) | −10.4447 | −0.495684 | ||||||||
\(445\) | 14.9460 | 0.708510 | ||||||||
\(446\) | −19.3185 | −0.914756 | ||||||||
\(447\) | −3.95732 | −0.187175 | ||||||||
\(448\) | −18.3508 | −0.866993 | ||||||||
\(449\) | 9.56841 | 0.451561 | 0.225781 | − | 0.974178i | \(-0.427507\pi\) | ||||
0.225781 | + | 0.974178i | \(0.427507\pi\) | |||||||
\(450\) | −18.4032 | −0.867536 | ||||||||
\(451\) | 3.47319 | 0.163546 | ||||||||
\(452\) | −12.0809 | −0.568239 | ||||||||
\(453\) | −4.87531 | −0.229062 | ||||||||
\(454\) | 24.8253 | 1.16511 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.605657 | −0.0283625 | ||||||||
\(457\) | −20.9620 | −0.980561 | −0.490281 | − | 0.871565i | \(-0.663106\pi\) | ||||
−0.490281 | + | 0.871565i | \(0.663106\pi\) | |||||||
\(458\) | −27.0197 | −1.26255 | ||||||||
\(459\) | 19.3749 | 0.904344 | ||||||||
\(460\) | 7.62132 | 0.355346 | ||||||||
\(461\) | 6.45806 | 0.300782 | 0.150391 | − | 0.988627i | \(-0.451947\pi\) | ||||
0.150391 | + | 0.988627i | \(0.451947\pi\) | |||||||
\(462\) | 2.88669 | 0.134301 | ||||||||
\(463\) | −4.97086 | −0.231015 | −0.115508 | − | 0.993307i | \(-0.536849\pi\) | ||||
−0.115508 | + | 0.993307i | \(0.536849\pi\) | |||||||
\(464\) | 12.0075 | 0.557433 | ||||||||
\(465\) | −2.04236 | −0.0947123 | ||||||||
\(466\) | 31.5579 | 1.46189 | ||||||||
\(467\) | −9.95319 | −0.460579 | −0.230289 | − | 0.973122i | \(-0.573967\pi\) | ||||
−0.230289 | + | 0.973122i | \(0.573967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.33642 | −0.431116 | ||||||||
\(470\) | −2.08572 | −0.0962069 | ||||||||
\(471\) | 9.07558 | 0.418181 | ||||||||
\(472\) | −1.74477 | −0.0803095 | ||||||||
\(473\) | 4.53626 | 0.208577 | ||||||||
\(474\) | 8.54510 | 0.392489 | ||||||||
\(475\) | −18.5503 | −0.851148 | ||||||||
\(476\) | 29.0301 | 1.33059 | ||||||||
\(477\) | 36.7446 | 1.68242 | ||||||||
\(478\) | −33.2565 | −1.52111 | ||||||||
\(479\) | 15.8258 | 0.723097 | 0.361549 | − | 0.932353i | \(-0.382248\pi\) | ||||
0.361549 | + | 0.932353i | \(0.382248\pi\) | |||||||
\(480\) | 5.53975 | 0.252854 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.9019 | −0.815409 | ||||||||
\(483\) | 4.76813 | 0.216958 | ||||||||
\(484\) | 1.89914 | 0.0863245 | ||||||||
\(485\) | 4.25442 | 0.193183 | ||||||||
\(486\) | 26.1666 | 1.18694 | ||||||||
\(487\) | −20.8272 | −0.943771 | −0.471885 | − | 0.881660i | \(-0.656426\pi\) | ||||
−0.471885 | + | 0.881660i | \(0.656426\pi\) | |||||||
\(488\) | 0.550298 | 0.0249108 | ||||||||
\(489\) | −13.4158 | −0.606683 | ||||||||
\(490\) | −1.10902 | −0.0501003 | ||||||||
\(491\) | 26.3130 | 1.18749 | 0.593744 | − | 0.804654i | \(-0.297649\pi\) | ||||
0.593744 | + | 0.804654i | \(0.297649\pi\) | |||||||
\(492\) | −3.76960 | −0.169947 | ||||||||
\(493\) | −17.1184 | −0.770974 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.28931 | 0.147844 | ||||||||
\(496\) | 12.1746 | 0.546657 | ||||||||
\(497\) | 18.6997 | 0.838795 | ||||||||
\(498\) | 0.797936 | 0.0357563 | ||||||||
\(499\) | 30.9638 | 1.38613 | 0.693064 | − | 0.720876i | \(-0.256260\pi\) | ||||
0.693064 | + | 0.720876i | \(0.256260\pi\) | |||||||
\(500\) | 19.8294 | 0.886796 | ||||||||
\(501\) | 4.42773 | 0.197816 | ||||||||
\(502\) | −12.5434 | −0.559841 | ||||||||
\(503\) | −32.4429 | −1.44656 | −0.723279 | − | 0.690556i | \(-0.757366\pi\) | ||||
−0.723279 | + | 0.690556i | \(0.757366\pi\) | |||||||
\(504\) | −1.36201 | −0.0606686 | ||||||||
\(505\) | 21.7893 | 0.969611 | ||||||||
\(506\) | 6.44045 | 0.286313 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 41.2296 | 1.82927 | ||||||||
\(509\) | 17.9485 | 0.795551 | 0.397776 | − | 0.917483i | \(-0.369782\pi\) | ||||
0.397776 | + | 0.917483i | \(0.369782\pi\) | |||||||
\(510\) | −8.29703 | −0.367399 | ||||||||
\(511\) | 14.4107 | 0.637493 | ||||||||
\(512\) | −31.3531 | −1.38563 | ||||||||
\(513\) | 17.2528 | 0.761730 | ||||||||
\(514\) | −47.9221 | −2.11375 | ||||||||
\(515\) | −19.2389 | −0.847768 | ||||||||
\(516\) | −4.92340 | −0.216740 | ||||||||
\(517\) | −0.858478 | −0.0377558 | ||||||||
\(518\) | −48.6094 | −2.13577 | ||||||||
\(519\) | −6.57379 | −0.288557 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0093 | −1.05187 | −0.525934 | − | 0.850525i | \(-0.676284\pi\) | ||||
−0.525934 | + | 0.850525i | \(0.676284\pi\) | |||||||
\(522\) | −15.1225 | −0.661895 | ||||||||
\(523\) | −26.5869 | −1.16256 | −0.581281 | − | 0.813703i | \(-0.697448\pi\) | ||||
−0.581281 | + | 0.813703i | \(0.697448\pi\) | |||||||
\(524\) | 24.1753 | 1.05610 | ||||||||
\(525\) | 5.09639 | 0.222425 | ||||||||
\(526\) | 15.4798 | 0.674953 | ||||||||
\(527\) | −17.3567 | −0.756070 | ||||||||
\(528\) | 2.39544 | 0.104248 | ||||||||
\(529\) | −12.3619 | −0.537474 | ||||||||
\(530\) | −33.3931 | −1.45050 | ||||||||
\(531\) | 23.4202 | 1.01635 | ||||||||
\(532\) | 25.8505 | 1.12076 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −13.7082 | −0.593210 | ||||||||
\(535\) | −5.11701 | −0.221228 | ||||||||
\(536\) | −0.726916 | −0.0313980 | ||||||||
\(537\) | −8.97395 | −0.387254 | ||||||||
\(538\) | −0.487675 | −0.0210252 | ||||||||
\(539\) | −0.456470 | −0.0196616 | ||||||||
\(540\) | −7.57621 | −0.326028 | ||||||||
\(541\) | 7.65866 | 0.329271 | 0.164636 | − | 0.986354i | \(-0.447355\pi\) | ||||
0.164636 | + | 0.986354i | \(0.447355\pi\) | |||||||
\(542\) | −34.8776 | −1.49812 | ||||||||
\(543\) | −9.54405 | −0.409574 | ||||||||
\(544\) | 47.0787 | 2.01848 | ||||||||
\(545\) | −5.56222 | −0.238260 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.5681 | 1.39251 | 0.696255 | − | 0.717794i | \(-0.254848\pi\) | ||||
0.696255 | + | 0.717794i | \(0.254848\pi\) | |||||||
\(548\) | 18.1933 | 0.777177 | ||||||||
\(549\) | −7.38671 | −0.315257 | ||||||||
\(550\) | 6.88383 | 0.293528 | ||||||||
\(551\) | −15.2434 | −0.649392 | ||||||||
\(552\) | 0.371238 | 0.0158009 | ||||||||
\(553\) | 19.3699 | 0.823694 | ||||||||
\(554\) | −21.2998 | −0.904941 | ||||||||
\(555\) | 6.76677 | 0.287234 | ||||||||
\(556\) | 16.2488 | 0.689102 | ||||||||
\(557\) | 42.0379 | 1.78120 | 0.890601 | − | 0.454786i | \(-0.150284\pi\) | ||||
0.890601 | + | 0.454786i | \(0.150284\pi\) | |||||||
\(558\) | −15.3331 | −0.649100 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 13.1924 | 0.557479 | ||||||||
\(561\) | −3.41505 | −0.144183 | ||||||||
\(562\) | −50.2415 | −2.11931 | ||||||||
\(563\) | −6.16552 | −0.259846 | −0.129923 | − | 0.991524i | \(-0.541473\pi\) | ||||
−0.129923 | + | 0.991524i | \(0.541473\pi\) | |||||||
\(564\) | 0.931743 | 0.0392335 | ||||||||
\(565\) | 7.82682 | 0.329277 | ||||||||
\(566\) | 61.3827 | 2.58011 | ||||||||
\(567\) | 15.7760 | 0.662530 | ||||||||
\(568\) | 1.45592 | 0.0610891 | ||||||||
\(569\) | 2.68172 | 0.112424 | 0.0562119 | − | 0.998419i | \(-0.482098\pi\) | ||||
0.0562119 | + | 0.998419i | \(0.482098\pi\) | |||||||
\(570\) | −7.38826 | −0.309460 | ||||||||
\(571\) | −21.1358 | −0.884505 | −0.442253 | − | 0.896891i | \(-0.645821\pi\) | ||||
−0.442253 | + | 0.896891i | \(0.645821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.90752 | 0.163239 | ||||||||
\(574\) | −17.5436 | −0.732256 | ||||||||
\(575\) | 11.3705 | 0.474181 | ||||||||
\(576\) | 19.1784 | 0.799099 | ||||||||
\(577\) | −8.09962 | −0.337192 | −0.168596 | − | 0.985685i | \(-0.553923\pi\) | ||||
−0.168596 | + | 0.985685i | \(0.553923\pi\) | |||||||
\(578\) | −36.9424 | −1.53660 | ||||||||
\(579\) | 6.33411 | 0.263236 | ||||||||
\(580\) | 6.69384 | 0.277946 | ||||||||
\(581\) | 1.80875 | 0.0750397 | ||||||||
\(582\) | −3.90206 | −0.161746 | ||||||||
\(583\) | −13.7446 | −0.569241 | ||||||||
\(584\) | 1.12199 | 0.0464284 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.4849 | −0.928843 | ||||||||
\(587\) | −13.0544 | −0.538813 | −0.269406 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269406 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(588\) | 0.495427 | 0.0204310 | ||||||||
\(589\) | −15.4556 | −0.636839 | ||||||||
\(590\) | −21.2840 | −0.876250 | ||||||||
\(591\) | −14.8710 | −0.611713 | ||||||||
\(592\) | −40.3371 | −1.65784 | ||||||||
\(593\) | 0.674849 | 0.0277127 | 0.0138564 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138564 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(594\) | −6.40233 | −0.262691 | ||||||||
\(595\) | −18.8076 | −0.771037 | ||||||||
\(596\) | 13.1507 | 0.538672 | ||||||||
\(597\) | −3.18459 | −0.130337 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.2030 | −1.47922 | −0.739608 | − | 0.673038i | \(-0.764989\pi\) | ||||
−0.739608 | + | 0.673038i | \(0.764989\pi\) | |||||||
\(600\) | 0.396795 | 0.0161991 | ||||||||
\(601\) | −33.0688 | −1.34890 | −0.674451 | − | 0.738319i | \(-0.735620\pi\) | ||||
−0.674451 | + | 0.738319i | \(0.735620\pi\) | |||||||
\(602\) | −22.9133 | −0.933877 | ||||||||
\(603\) | 9.75748 | 0.397355 | ||||||||
\(604\) | 16.2012 | 0.659219 | ||||||||
\(605\) | −1.23039 | −0.0500223 | ||||||||
\(606\) | −19.9846 | −0.811821 | ||||||||
\(607\) | 18.8366 | 0.764554 | 0.382277 | − | 0.924048i | \(-0.375140\pi\) | ||||
0.382277 | + | 0.924048i | \(0.375140\pi\) | |||||||
\(608\) | 41.9222 | 1.70017 | ||||||||
\(609\) | 4.18787 | 0.169701 | ||||||||
\(610\) | 6.71295 | 0.271799 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −30.3394 | −1.22640 | ||||||||
\(613\) | 36.5545 | 1.47642 | 0.738211 | − | 0.674570i | \(-0.235671\pi\) | ||||
0.738211 | + | 0.674570i | \(0.235671\pi\) | |||||||
\(614\) | −39.8986 | −1.61018 | ||||||||
\(615\) | 2.44220 | 0.0984789 | ||||||||
\(616\) | 0.509467 | 0.0205270 | ||||||||
\(617\) | −2.77177 | −0.111587 | −0.0557936 | − | 0.998442i | \(-0.517769\pi\) | ||||
−0.0557936 | + | 0.998442i | \(0.517769\pi\) | |||||||
\(618\) | 17.6455 | 0.709806 | ||||||||
\(619\) | 38.3647 | 1.54201 | 0.771004 | − | 0.636830i | \(-0.219755\pi\) | ||||
0.771004 | + | 0.636830i | \(0.219755\pi\) | |||||||
\(620\) | 6.78702 | 0.272573 | ||||||||
\(621\) | −10.5751 | −0.424365 | ||||||||
\(622\) | −23.9585 | −0.960649 | ||||||||
\(623\) | −31.0735 | −1.24493 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.58398 | 0.183359 | ||||||||
\(626\) | −38.3910 | −1.53441 | ||||||||
\(627\) | −3.04100 | −0.121446 | ||||||||
\(628\) | −30.1593 | −1.20349 | ||||||||
\(629\) | 57.5064 | 2.29293 | ||||||||
\(630\) | −16.6148 | −0.661950 | ||||||||
\(631\) | 14.0166 | 0.557994 | 0.278997 | − | 0.960292i | \(-0.409998\pi\) | ||||
0.278997 | + | 0.960292i | \(0.409998\pi\) | |||||||
\(632\) | 1.50811 | 0.0599893 | ||||||||
\(633\) | 3.47971 | 0.138306 | ||||||||
\(634\) | 10.5891 | 0.420547 | ||||||||
\(635\) | −26.7113 | −1.06000 | ||||||||
\(636\) | 14.9176 | 0.591520 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.65668 | 0.223950 | ||||||||
\(639\) | −19.5430 | −0.773109 | ||||||||
\(640\) | 1.95789 | 0.0773925 | ||||||||
\(641\) | 7.86006 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(642\) | 4.69321 | 0.185226 | ||||||||
\(643\) | −24.1774 | −0.953463 | −0.476731 | − | 0.879049i | \(-0.658179\pi\) | ||||
−0.476731 | + | 0.879049i | \(0.658179\pi\) | |||||||
\(644\) | −15.8451 | −0.624384 | ||||||||
\(645\) | 3.18970 | 0.125594 | ||||||||
\(646\) | −62.7880 | −2.47036 | ||||||||
\(647\) | 17.1838 | 0.675565 | 0.337782 | − | 0.941224i | \(-0.390323\pi\) | ||||
0.337782 | + | 0.941224i | \(0.390323\pi\) | |||||||
\(648\) | 1.22829 | 0.0482518 | ||||||||
\(649\) | −8.76048 | −0.343879 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.24617 | 0.166421 | ||||||||
\(652\) | 44.5823 | 1.74598 | ||||||||
\(653\) | 25.7432 | 1.00741 | 0.503705 | − | 0.863876i | \(-0.331970\pi\) | ||||
0.503705 | + | 0.863876i | \(0.331970\pi\) | |||||||
\(654\) | 5.10155 | 0.199486 | ||||||||
\(655\) | −15.6624 | −0.611979 | ||||||||
\(656\) | −14.5581 | −0.568396 | ||||||||
\(657\) | −15.0606 | −0.587571 | ||||||||
\(658\) | 4.33630 | 0.169047 | ||||||||
\(659\) | 13.2942 | 0.517869 | 0.258934 | − | 0.965895i | \(-0.416629\pi\) | ||||
0.258934 | + | 0.965895i | \(0.416629\pi\) | |||||||
\(660\) | 1.33539 | 0.0519800 | ||||||||
\(661\) | −8.72799 | −0.339480 | −0.169740 | − | 0.985489i | \(-0.554293\pi\) | ||||
−0.169740 | + | 0.985489i | \(0.554293\pi\) | |||||||
\(662\) | 31.4461 | 1.22219 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.140826 | 0.00546511 | ||||||||
\(665\) | −16.7476 | −0.649446 | ||||||||
\(666\) | 50.8016 | 1.96852 | ||||||||
\(667\) | 9.34349 | 0.361781 | ||||||||
\(668\) | −14.7139 | −0.569297 | ||||||||
\(669\) | −5.59112 | −0.216165 | ||||||||
\(670\) | −8.86748 | −0.342581 | ||||||||
\(671\) | 2.76304 | 0.106666 | ||||||||
\(672\) | −11.5174 | −0.444294 | ||||||||
\(673\) | −10.7132 | −0.412965 | −0.206483 | − | 0.978450i | \(-0.566202\pi\) | ||||
−0.206483 | + | 0.978450i | \(0.566202\pi\) | |||||||
\(674\) | −15.2290 | −0.586598 | ||||||||
\(675\) | −11.3032 | −0.435059 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.57693 | −0.175906 | −0.0879528 | − | 0.996125i | \(-0.528032\pi\) | ||||
−0.0879528 | + | 0.996125i | \(0.528032\pi\) | |||||||
\(678\) | −7.17858 | −0.275692 | ||||||||
\(679\) | −8.84515 | −0.339446 | ||||||||
\(680\) | −1.46433 | −0.0561544 | ||||||||
\(681\) | 7.18491 | 0.275326 | ||||||||
\(682\) | 5.73542 | 0.219621 | ||||||||
\(683\) | 38.0713 | 1.45676 | 0.728379 | − | 0.685174i | \(-0.240274\pi\) | ||||
0.728379 | + | 0.685174i | \(0.240274\pi\) | |||||||
\(684\) | −27.0163 | −1.03299 | ||||||||
\(685\) | −11.7868 | −0.450350 | ||||||||
\(686\) | 37.6638 | 1.43801 | ||||||||
\(687\) | −7.82001 | −0.298352 | ||||||||
\(688\) | −19.0140 | −0.724900 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.52864 | 0.172403 | ||||||||
\(691\) | 33.4726 | 1.27336 | 0.636679 | − | 0.771129i | \(-0.280308\pi\) | ||||
0.636679 | + | 0.771129i | \(0.280308\pi\) | |||||||
\(692\) | 21.8455 | 0.830441 | ||||||||
\(693\) | −6.83863 | −0.259778 | ||||||||
\(694\) | 48.1348 | 1.82717 | ||||||||
\(695\) | −10.5270 | −0.399313 | ||||||||
\(696\) | 0.326060 | 0.0123593 | ||||||||
\(697\) | 20.7546 | 0.786137 | ||||||||
\(698\) | 40.5590 | 1.53518 | ||||||||
\(699\) | 9.13344 | 0.345459 | ||||||||
\(700\) | −16.9359 | −0.640117 | ||||||||
\(701\) | 9.43568 | 0.356381 | 0.178190 | − | 0.983996i | \(-0.442976\pi\) | ||||
0.178190 | + | 0.983996i | \(0.442976\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.2077 | 1.93134 | ||||||||
\(704\) | −7.17379 | −0.270372 | ||||||||
\(705\) | −0.603644 | −0.0227346 | ||||||||
\(706\) | 22.6070 | 0.850825 | ||||||||
\(707\) | −45.3010 | −1.70372 | ||||||||
\(708\) | 9.50813 | 0.357337 | ||||||||
\(709\) | 15.7263 | 0.590613 | 0.295307 | − | 0.955403i | \(-0.404578\pi\) | ||||
0.295307 | + | 0.955403i | \(0.404578\pi\) | |||||||
\(710\) | 17.7604 | 0.666537 | ||||||||
\(711\) | −20.2435 | −0.759191 | ||||||||
\(712\) | −2.41933 | −0.0906681 | ||||||||
\(713\) | 9.47355 | 0.354787 | ||||||||
\(714\) | 17.2499 | 0.645562 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.8215 | 1.11448 | ||||||||
\(717\) | −9.62503 | −0.359453 | ||||||||
\(718\) | −24.1260 | −0.900373 | ||||||||
\(719\) | −50.6347 | −1.88836 | −0.944178 | − | 0.329436i | \(-0.893141\pi\) | ||||
−0.944178 | + | 0.329436i | \(0.893141\pi\) | |||||||
\(720\) | −13.7873 | −0.513823 | ||||||||
\(721\) | 39.9986 | 1.48963 | ||||||||
\(722\) | −18.3930 | −0.684517 | ||||||||
\(723\) | −5.18114 | −0.192689 | ||||||||
\(724\) | 31.7160 | 1.17872 | ||||||||
\(725\) | 9.98672 | 0.370898 | ||||||||
\(726\) | 1.12848 | 0.0418819 | ||||||||
\(727\) | −38.4164 | −1.42478 | −0.712392 | − | 0.701782i | \(-0.752388\pi\) | ||||
−0.712392 | + | 0.701782i | \(0.752388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.9286 | −0.404764 | ||||||||
\(730\) | 13.6869 | 0.506575 | ||||||||
\(731\) | 27.1072 | 1.00259 | ||||||||
\(732\) | −2.99885 | −0.110841 | ||||||||
\(733\) | 10.8611 | 0.401165 | 0.200582 | − | 0.979677i | \(-0.435717\pi\) | ||||
0.200582 | + | 0.979677i | \(0.435717\pi\) | |||||||
\(734\) | 71.4495 | 2.63725 | ||||||||
\(735\) | −0.320970 | −0.0118391 | ||||||||
\(736\) | −25.6963 | −0.947178 | ||||||||
\(737\) | −3.64984 | −0.134444 | ||||||||
\(738\) | 18.3348 | 0.674913 | ||||||||
\(739\) | 42.5093 | 1.56373 | 0.781866 | − | 0.623447i | \(-0.214268\pi\) | ||||
0.781866 | + | 0.623447i | \(0.214268\pi\) | |||||||
\(740\) | −22.4868 | −0.826632 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 69.4258 | 2.54870 | ||||||||
\(743\) | 25.6654 | 0.941574 | 0.470787 | − | 0.882247i | \(-0.343970\pi\) | ||||
0.470787 | + | 0.882247i | \(0.343970\pi\) | |||||||
\(744\) | 0.330599 | 0.0121203 | ||||||||
\(745\) | −8.51986 | −0.312144 | ||||||||
\(746\) | −25.5203 | −0.934364 | ||||||||
\(747\) | −1.89032 | −0.0691634 | ||||||||
\(748\) | 11.3486 | 0.414947 | ||||||||
\(749\) | 10.6385 | 0.388723 | ||||||||
\(750\) | 11.7828 | 0.430246 | ||||||||
\(751\) | −37.6242 | −1.37293 | −0.686464 | − | 0.727164i | \(-0.740838\pi\) | ||||
−0.686464 | + | 0.727164i | \(0.740838\pi\) | |||||||
\(752\) | 3.59835 | 0.131218 | ||||||||
\(753\) | −3.63030 | −0.132296 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.4962 | −0.381997 | ||||||||
\(756\) | 15.7513 | 0.572869 | ||||||||
\(757\) | 17.2379 | 0.626521 | 0.313260 | − | 0.949667i | \(-0.398579\pi\) | ||||
0.313260 | + | 0.949667i | \(0.398579\pi\) | |||||||
\(758\) | 69.8084 | 2.53556 | ||||||||
\(759\) | 1.86398 | 0.0676584 | ||||||||
\(760\) | −1.30394 | −0.0472989 | ||||||||
\(761\) | 8.83215 | 0.320165 | 0.160083 | − | 0.987104i | \(-0.448824\pi\) | ||||
0.160083 | + | 0.987104i | \(0.448824\pi\) | |||||||
\(762\) | 24.4990 | 0.887504 | ||||||||
\(763\) | 11.5641 | 0.418650 | ||||||||
\(764\) | −12.9852 | −0.469787 | ||||||||
\(765\) | 19.6558 | 0.710658 | ||||||||
\(766\) | 3.00629 | 0.108622 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9.99526 | −0.360673 | ||||||||
\(769\) | −13.5004 | −0.486837 | −0.243419 | − | 0.969921i | \(-0.578269\pi\) | ||||
−0.243419 | + | 0.969921i | \(0.578269\pi\) | |||||||
\(770\) | 6.21487 | 0.223968 | ||||||||
\(771\) | −13.8695 | −0.499499 | ||||||||
\(772\) | −21.0490 | −0.757570 | ||||||||
\(773\) | 10.4625 | 0.376309 | 0.188155 | − | 0.982139i | \(-0.439749\pi\) | ||||
0.188155 | + | 0.982139i | \(0.439749\pi\) | |||||||
\(774\) | 23.9467 | 0.860746 | ||||||||
\(775\) | 10.1257 | 0.363728 | ||||||||
\(776\) | −0.688667 | −0.0247217 | ||||||||
\(777\) | −14.0684 | −0.504703 | ||||||||
\(778\) | −65.9136 | −2.36312 | ||||||||
\(779\) | 18.4814 | 0.662164 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.31017 | 0.261579 | ||||||||
\(782\) | 38.4860 | 1.37626 | ||||||||
\(783\) | −9.28818 | −0.331932 | ||||||||
\(784\) | 1.91332 | 0.0683327 | ||||||||
\(785\) | 19.5391 | 0.697382 | ||||||||
\(786\) | 14.3652 | 0.512388 | ||||||||
\(787\) | 43.1408 | 1.53781 | 0.768903 | − | 0.639366i | \(-0.220803\pi\) | ||||
0.768903 | + | 0.639366i | \(0.220803\pi\) | |||||||
\(788\) | 49.4183 | 1.76045 | ||||||||
\(789\) | 4.48015 | 0.159498 | ||||||||
\(790\) | 18.3971 | 0.654538 | ||||||||
\(791\) | −16.2723 | −0.578578 | ||||||||
\(792\) | −0.532443 | −0.0189196 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 52.1682 | 1.85138 | ||||||||
\(795\) | −9.66457 | −0.342767 | ||||||||
\(796\) | 10.5828 | 0.375097 | ||||||||
\(797\) | 25.8798 | 0.916710 | 0.458355 | − | 0.888769i | \(-0.348439\pi\) | ||||
0.458355 | + | 0.888769i | \(0.348439\pi\) | |||||||
\(798\) | 15.3606 | 0.543758 | ||||||||
\(799\) | −5.12998 | −0.181486 | ||||||||
\(800\) | −27.4653 | −0.971045 | ||||||||
\(801\) | 32.4749 | 1.14744 | ||||||||
\(802\) | 31.2055 | 1.10191 | ||||||||
\(803\) | 5.63352 | 0.198803 | ||||||||
\(804\) | 3.96133 | 0.139705 | ||||||||
\(805\) | 10.2655 | 0.361811 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.141142 | −0.00496844 | ||||||||
\(808\) | −3.52705 | −0.124081 | ||||||||
\(809\) | 18.8775 | 0.663696 | 0.331848 | − | 0.943333i | \(-0.392328\pi\) | ||||
0.331848 | + | 0.943333i | \(0.392328\pi\) | |||||||
\(810\) | 14.9836 | 0.526471 | ||||||||
\(811\) | −24.3009 | −0.853320 | −0.426660 | − | 0.904412i | \(-0.640310\pi\) | ||||
−0.426660 | + | 0.904412i | \(0.640310\pi\) | |||||||
\(812\) | −13.9168 | −0.488384 | ||||||||
\(813\) | −10.0942 | −0.354020 | ||||||||
\(814\) | −19.0026 | −0.666042 | ||||||||
\(815\) | −28.8833 | −1.01174 | ||||||||
\(816\) | 14.3143 | 0.501102 | ||||||||
\(817\) | 24.1381 | 0.844486 | ||||||||
\(818\) | −63.4949 | −2.22005 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.11571 | −0.283413 | ||||||||
\(821\) | 38.7547 | 1.35255 | 0.676274 | − | 0.736650i | \(-0.263594\pi\) | ||||
0.676274 | + | 0.736650i | \(0.263594\pi\) | |||||||
\(822\) | 10.8106 | 0.377062 | ||||||||
\(823\) | 20.1615 | 0.702784 | 0.351392 | − | 0.936228i | \(-0.385708\pi\) | ||||
0.351392 | + | 0.936228i | \(0.385708\pi\) | |||||||
\(824\) | 3.11422 | 0.108489 | ||||||||
\(825\) | 1.99231 | 0.0693633 | ||||||||
\(826\) | 44.2505 | 1.53967 | ||||||||
\(827\) | −46.3998 | −1.61348 | −0.806740 | − | 0.590906i | \(-0.798770\pi\) | ||||
−0.806740 | + | 0.590906i | \(0.798770\pi\) | |||||||
\(828\) | 16.5597 | 0.575489 | ||||||||
\(829\) | −6.74133 | −0.234136 | −0.117068 | − | 0.993124i | \(-0.537350\pi\) | ||||
−0.117068 | + | 0.993124i | \(0.537350\pi\) | |||||||
\(830\) | 1.71790 | 0.0596293 | ||||||||
\(831\) | −6.16455 | −0.213846 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.72771 | −0.0945096 | ||||||||
\(834\) | 9.65515 | 0.334331 | ||||||||
\(835\) | 9.53262 | 0.329890 | ||||||||
\(836\) | 10.1056 | 0.349510 | ||||||||
\(837\) | −9.41748 | −0.325516 | ||||||||
\(838\) | −12.5534 | −0.433649 | ||||||||
\(839\) | −10.1387 | −0.350028 | −0.175014 | − | 0.984566i | \(-0.555997\pi\) | ||||
−0.175014 | + | 0.984566i | \(0.555997\pi\) | |||||||
\(840\) | 0.358235 | 0.0123603 | ||||||||
\(841\) | −20.7936 | −0.717020 | ||||||||
\(842\) | −9.68677 | −0.333828 | ||||||||
\(843\) | −14.5408 | −0.500812 | ||||||||
\(844\) | −11.5635 | −0.398032 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.53186 | −0.155809 | ||||||||
\(847\) | 2.55803 | 0.0878950 | ||||||||
\(848\) | 57.6110 | 1.97837 | ||||||||
\(849\) | 17.7653 | 0.609703 | ||||||||
\(850\) | 41.1355 | 1.41094 | ||||||||
\(851\) | −31.3879 | −1.07596 | ||||||||
\(852\) | −7.93405 | −0.271816 | ||||||||
\(853\) | −13.8261 | −0.473395 | −0.236698 | − | 0.971583i | \(-0.576065\pi\) | ||||
−0.236698 | + | 0.971583i | \(0.576065\pi\) | |||||||
\(854\) | −13.9565 | −0.477583 | ||||||||
\(855\) | 17.5029 | 0.598588 | ||||||||
\(856\) | 0.828295 | 0.0283105 | ||||||||
\(857\) | 21.5044 | 0.734576 | 0.367288 | − | 0.930107i | \(-0.380286\pi\) | ||||
0.367288 | + | 0.930107i | \(0.380286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.6851 | 0.978724 | 0.489362 | − | 0.872081i | \(-0.337230\pi\) | ||||
0.489362 | + | 0.872081i | \(0.337230\pi\) | |||||||
\(860\) | −10.5998 | −0.361449 | ||||||||
\(861\) | −5.07744 | −0.173039 | ||||||||
\(862\) | 31.4396 | 1.07084 | ||||||||
\(863\) | −22.3203 | −0.759791 | −0.379895 | − | 0.925029i | \(-0.624040\pi\) | ||||
−0.379895 | + | 0.925029i | \(0.624040\pi\) | |||||||
\(864\) | 25.5442 | 0.869031 | ||||||||
\(865\) | −14.1529 | −0.481215 | ||||||||
\(866\) | 49.6373 | 1.68675 | ||||||||
\(867\) | −10.6918 | −0.363113 | ||||||||
\(868\) | −14.1105 | −0.478943 | ||||||||
\(869\) | 7.57221 | 0.256869 | ||||||||
\(870\) | 3.97753 | 0.134851 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.900362 | 0.0304901 | ||||||||
\(873\) | 9.24405 | 0.312864 | ||||||||
\(874\) | 34.2706 | 1.15922 | ||||||||
\(875\) | 26.7090 | 0.902930 | ||||||||
\(876\) | −6.11430 | −0.206583 | ||||||||
\(877\) | −0.127784 | −0.00431496 | −0.00215748 | − | 0.999998i | \(-0.500687\pi\) | ||||
−0.00215748 | + | 0.999998i | \(0.500687\pi\) | |||||||
\(878\) | −22.7354 | −0.767282 | ||||||||
\(879\) | −6.50755 | −0.219494 | ||||||||
\(880\) | 5.15723 | 0.173850 | ||||||||
\(881\) | −34.7183 | −1.16969 | −0.584844 | − | 0.811146i | \(-0.698844\pi\) | ||||
−0.584844 | + | 0.811146i | \(0.698844\pi\) | |||||||
\(882\) | −2.40968 | −0.0811382 | ||||||||
\(883\) | 12.4010 | 0.417328 | 0.208664 | − | 0.977987i | \(-0.433089\pi\) | ||||
0.208664 | + | 0.977987i | \(0.433089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.15999 | −0.207066 | ||||||||
\(886\) | 64.8729 | 2.17945 | ||||||||
\(887\) | 24.5776 | 0.825234 | 0.412617 | − | 0.910905i | \(-0.364615\pi\) | ||||
0.412617 | + | 0.910905i | \(0.364615\pi\) | |||||||
\(888\) | −1.09534 | −0.0367573 | ||||||||
\(889\) | 55.5340 | 1.86255 | ||||||||
\(890\) | −29.5128 | −0.989271 | ||||||||
\(891\) | 6.16724 | 0.206610 | ||||||||
\(892\) | 18.5800 | 0.622103 | ||||||||
\(893\) | −4.56809 | −0.152865 | ||||||||
\(894\) | 7.81422 | 0.261347 | ||||||||
\(895\) | −19.3203 | −0.645807 | ||||||||
\(896\) | −4.07055 | −0.135988 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.8940 | −0.630501 | ||||||||
\(899\) | 8.32066 | 0.277510 | ||||||||
\(900\) | 17.6997 | 0.589990 | ||||||||
\(901\) | −82.1329 | −2.73624 | ||||||||
\(902\) | −6.85824 | −0.228355 | ||||||||
\(903\) | −6.63154 | −0.220684 | ||||||||
\(904\) | −1.26693 | −0.0421376 | ||||||||
\(905\) | −20.5477 | −0.683029 | ||||||||
\(906\) | 9.62689 | 0.319832 | ||||||||
\(907\) | 17.2563 | 0.572987 | 0.286494 | − | 0.958082i | \(-0.407510\pi\) | ||||
0.286494 | + | 0.958082i | \(0.407510\pi\) | |||||||
\(908\) | −23.8763 | −0.792364 | ||||||||
\(909\) | 47.3440 | 1.57030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.76841 | 0.224247 | 0.112124 | − | 0.993694i | \(-0.464235\pi\) | ||||
0.112124 | + | 0.993694i | \(0.464235\pi\) | |||||||
\(912\) | 12.7465 | 0.422079 | ||||||||
\(913\) | 0.707087 | 0.0234012 | ||||||||
\(914\) | 41.3921 | 1.36913 | ||||||||
\(915\) | 1.94285 | 0.0642287 | ||||||||
\(916\) | 25.9868 | 0.858629 | ||||||||
\(917\) | 32.5628 | 1.07532 | ||||||||
\(918\) | −38.2582 | −1.26271 | ||||||||
\(919\) | −4.80101 | −0.158371 | −0.0791853 | − | 0.996860i | \(-0.525232\pi\) | ||||
−0.0791853 | + | 0.996860i | \(0.525232\pi\) | |||||||
\(920\) | 0.799252 | 0.0263505 | ||||||||
\(921\) | −11.5474 | −0.380500 | ||||||||
\(922\) | −12.7522 | −0.419973 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.77634 | −0.0913350 | ||||||||
\(925\) | −33.5487 | −1.10307 | ||||||||
\(926\) | 9.81557 | 0.322560 | ||||||||
\(927\) | −41.8025 | −1.37298 | ||||||||
\(928\) | −22.5692 | −0.740869 | ||||||||
\(929\) | −46.0294 | −1.51018 | −0.755088 | − | 0.655624i | \(-0.772406\pi\) | ||||
−0.755088 | + | 0.655624i | \(0.772406\pi\) | |||||||
\(930\) | 4.03290 | 0.132244 | ||||||||
\(931\) | −2.42895 | −0.0796055 | ||||||||
\(932\) | −30.3515 | −0.994198 | ||||||||
\(933\) | −6.93403 | −0.227010 | ||||||||
\(934\) | 19.6538 | 0.643092 | ||||||||
\(935\) | −7.35238 | −0.240448 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2841 | 1.54470 | 0.772352 | − | 0.635195i | \(-0.219080\pi\) | ||||
0.772352 | + | 0.635195i | \(0.219080\pi\) | |||||||
\(938\) | 18.4359 | 0.601954 | ||||||||
\(939\) | −11.1111 | −0.362596 | ||||||||
\(940\) | 2.00598 | 0.0654280 | ||||||||
\(941\) | −23.6968 | −0.772494 | −0.386247 | − | 0.922395i | \(-0.626229\pi\) | ||||
−0.386247 | + | 0.922395i | \(0.626229\pi\) | |||||||
\(942\) | −17.9209 | −0.583893 | ||||||||
\(943\) | −11.3282 | −0.368897 | ||||||||
\(944\) | 36.7200 | 1.19513 | ||||||||
\(945\) | −10.2047 | −0.331960 | ||||||||
\(946\) | −8.95740 | −0.291230 | ||||||||
\(947\) | 25.5082 | 0.828904 | 0.414452 | − | 0.910071i | \(-0.363973\pi\) | ||||
0.414452 | + | 0.910071i | \(0.363973\pi\) | |||||||
\(948\) | −8.21844 | −0.266923 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 36.6299 | 1.18843 | ||||||||
\(951\) | 3.06468 | 0.0993792 | ||||||||
\(952\) | 3.04441 | 0.0986697 | ||||||||
\(953\) | −10.7323 | −0.347655 | −0.173827 | − | 0.984776i | \(-0.555613\pi\) | ||||
−0.173827 | + | 0.984776i | \(0.555613\pi\) | |||||||
\(954\) | −72.5568 | −2.34911 | ||||||||
\(955\) | 8.41264 | 0.272227 | ||||||||
\(956\) | 31.9851 | 1.03447 | ||||||||
\(957\) | 1.63715 | 0.0529214 | ||||||||
\(958\) | −31.2499 | −1.00964 | ||||||||
\(959\) | 24.5053 | 0.791317 | ||||||||
\(960\) | −5.04429 | −0.162804 | ||||||||
\(961\) | −22.5635 | −0.727855 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.1183 | −0.358282 | ||||||||
\(964\) | 17.2176 | 0.554540 | ||||||||
\(965\) | 13.6369 | 0.438988 | ||||||||
\(966\) | −9.41527 | −0.302931 | ||||||||
\(967\) | 18.6494 | 0.599724 | 0.299862 | − | 0.953983i | \(-0.403059\pi\) | ||||
0.299862 | + | 0.953983i | \(0.403059\pi\) | |||||||
\(968\) | 0.199164 | 0.00640136 | ||||||||
\(969\) | −18.1720 | −0.583769 | ||||||||
\(970\) | −8.40088 | −0.269736 | ||||||||
\(971\) | 29.4517 | 0.945151 | 0.472575 | − | 0.881290i | \(-0.343324\pi\) | ||||
0.472575 | + | 0.881290i | \(0.343324\pi\) | |||||||
\(972\) | −25.1663 | −0.807210 | ||||||||
\(973\) | 21.8862 | 0.701639 | ||||||||
\(974\) | 41.1259 | 1.31776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.5814 | −0.370713 | ||||||||
\(977\) | −1.04992 | −0.0335898 | −0.0167949 | − | 0.999859i | \(-0.505346\pi\) | ||||
−0.0167949 | + | 0.999859i | \(0.505346\pi\) | |||||||
\(978\) | 26.4911 | 0.847093 | ||||||||
\(979\) | −12.1474 | −0.388233 | ||||||||
\(980\) | 1.06662 | 0.0340720 | ||||||||
\(981\) | −12.0857 | −0.385865 | ||||||||
\(982\) | −51.9582 | −1.65805 | ||||||||
\(983\) | −4.58788 | −0.146330 | −0.0731652 | − | 0.997320i | \(-0.523310\pi\) | ||||
−0.0731652 | + | 0.997320i | \(0.523310\pi\) | |||||||
\(984\) | −0.395320 | −0.0126024 | ||||||||
\(985\) | −32.0164 | −1.02013 | ||||||||
\(986\) | 33.8024 | 1.07649 | ||||||||
\(987\) | 1.25501 | 0.0399473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.7955 | −0.470470 | ||||||||
\(990\) | −6.49515 | −0.206429 | ||||||||
\(991\) | −20.1109 | −0.638845 | −0.319423 | − | 0.947612i | \(-0.603489\pi\) | ||||
−0.319423 | + | 0.947612i | \(0.603489\pi\) | |||||||
\(992\) | −22.8833 | −0.726547 | ||||||||
\(993\) | 9.10107 | 0.288814 | ||||||||
\(994\) | −36.9248 | −1.17118 | ||||||||
\(995\) | −6.85622 | −0.217357 | ||||||||
\(996\) | −0.767432 | −0.0243170 | ||||||||
\(997\) | 4.50022 | 0.142523 | 0.0712617 | − | 0.997458i | \(-0.477297\pi\) | ||||
0.0712617 | + | 0.997458i | \(0.477297\pi\) | |||||||
\(998\) | −61.1418 | −1.93541 | ||||||||
\(999\) | 31.2021 | 0.987189 |
(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 | 1859.2.a.l.1.2 | 6 | ||
13.4 | even | 6 | 143.2.e.c.133.2 | yes | 12 | ||
13.10 | even | 6 | 143.2.e.c.100.2 | ✓ | 12 | ||
13.12 | even | 2 | 1859.2.a.k.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.2.e.c.100.2 | ✓ | 12 | 13.10 | even | 6 | ||
143.2.e.c.133.2 | yes | 12 | 13.4 | even | 6 | ||
1859.2.a.k.1.5 | 6 | 13.12 | even | 2 | |||
1859.2.a.l.1.2 | 6 | 1.1 | even | 1 | trivial |