Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.32011 | 0.762164 | 0.381082 | − | 0.924541i | \(-0.375552\pi\) | ||||
0.381082 | + | 0.924541i | \(0.375552\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.16506 | 0.968244 | 0.484122 | − | 0.875000i | \(-0.339139\pi\) | ||||
0.484122 | + | 0.875000i | \(0.339139\pi\) | |||||||
\(6\) | −1.32011 | −0.538931 | ||||||||
\(7\) | −2.98980 | −1.13004 | −0.565019 | − | 0.825078i | \(-0.691131\pi\) | ||||
−0.565019 | + | 0.825078i | \(0.691131\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.25732 | −0.419106 | ||||||||
\(10\) | −2.16506 | −0.684652 | ||||||||
\(11\) | 2.12624 | 0.641085 | 0.320543 | − | 0.947234i | \(-0.396135\pi\) | ||||
0.320543 | + | 0.947234i | \(0.396135\pi\) | |||||||
\(12\) | 1.32011 | 0.381082 | ||||||||
\(13\) | 2.25829 | 0.626337 | 0.313169 | − | 0.949698i | \(-0.398609\pi\) | ||||
0.313169 | + | 0.949698i | \(0.398609\pi\) | |||||||
\(14\) | 2.98980 | 0.799057 | ||||||||
\(15\) | 2.85811 | 0.737961 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.94651 | 0.472099 | 0.236050 | − | 0.971741i | \(-0.424147\pi\) | ||||
0.236050 | + | 0.971741i | \(0.424147\pi\) | |||||||
\(18\) | 1.25732 | 0.296353 | ||||||||
\(19\) | −4.50586 | −1.03372 | −0.516858 | − | 0.856071i | \(-0.672898\pi\) | ||||
−0.516858 | + | 0.856071i | \(0.672898\pi\) | |||||||
\(20\) | 2.16506 | 0.484122 | ||||||||
\(21\) | −3.94685 | −0.861274 | ||||||||
\(22\) | −2.12624 | −0.453316 | ||||||||
\(23\) | −2.25316 | −0.469815 | −0.234908 | − | 0.972018i | \(-0.575479\pi\) | ||||
−0.234908 | + | 0.972018i | \(0.575479\pi\) | |||||||
\(24\) | −1.32011 | −0.269466 | ||||||||
\(25\) | −0.312513 | −0.0625027 | ||||||||
\(26\) | −2.25829 | −0.442887 | ||||||||
\(27\) | −5.62011 | −1.08159 | ||||||||
\(28\) | −2.98980 | −0.565019 | ||||||||
\(29\) | −3.38241 | −0.628099 | −0.314049 | − | 0.949407i | \(-0.601686\pi\) | ||||
−0.314049 | + | 0.949407i | \(0.601686\pi\) | |||||||
\(30\) | −2.85811 | −0.521817 | ||||||||
\(31\) | −6.92035 | −1.24293 | −0.621466 | − | 0.783441i | \(-0.713463\pi\) | ||||
−0.621466 | + | 0.783441i | \(0.713463\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.80686 | 0.488612 | ||||||||
\(34\) | −1.94651 | −0.333824 | ||||||||
\(35\) | −6.47309 | −1.09415 | ||||||||
\(36\) | −1.25732 | −0.209553 | ||||||||
\(37\) | −2.51819 | −0.413988 | −0.206994 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206994 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(38\) | 4.50586 | 0.730947 | ||||||||
\(39\) | 2.98119 | 0.477372 | ||||||||
\(40\) | −2.16506 | −0.342326 | ||||||||
\(41\) | −2.47696 | −0.386836 | −0.193418 | − | 0.981116i | \(-0.561957\pi\) | ||||
−0.193418 | + | 0.981116i | \(0.561957\pi\) | |||||||
\(42\) | 3.94685 | 0.609012 | ||||||||
\(43\) | −5.35666 | −0.816884 | −0.408442 | − | 0.912784i | \(-0.633928\pi\) | ||||
−0.408442 | + | 0.912784i | \(0.633928\pi\) | |||||||
\(44\) | 2.12624 | 0.320543 | ||||||||
\(45\) | −2.72217 | −0.405797 | ||||||||
\(46\) | 2.25316 | 0.332210 | ||||||||
\(47\) | 2.67325 | 0.389934 | 0.194967 | − | 0.980810i | \(-0.437540\pi\) | ||||
0.194967 | + | 0.980810i | \(0.437540\pi\) | |||||||
\(48\) | 1.32011 | 0.190541 | ||||||||
\(49\) | 1.93889 | 0.276985 | ||||||||
\(50\) | 0.312513 | 0.0441961 | ||||||||
\(51\) | 2.56961 | 0.359817 | ||||||||
\(52\) | 2.25829 | 0.313169 | ||||||||
\(53\) | −7.74916 | −1.06443 | −0.532214 | − | 0.846610i | \(-0.678640\pi\) | ||||
−0.532214 | + | 0.846610i | \(0.678640\pi\) | |||||||
\(54\) | 5.62011 | 0.764801 | ||||||||
\(55\) | 4.60343 | 0.620727 | ||||||||
\(56\) | 2.98980 | 0.399529 | ||||||||
\(57\) | −5.94822 | −0.787861 | ||||||||
\(58\) | 3.38241 | 0.444133 | ||||||||
\(59\) | 8.45119 | 1.10025 | 0.550126 | − | 0.835082i | \(-0.314580\pi\) | ||||
0.550126 | + | 0.835082i | \(0.314580\pi\) | |||||||
\(60\) | 2.85811 | 0.368980 | ||||||||
\(61\) | −7.65002 | −0.979484 | −0.489742 | − | 0.871867i | \(-0.662909\pi\) | ||||
−0.489742 | + | 0.871867i | \(0.662909\pi\) | |||||||
\(62\) | 6.92035 | 0.878886 | ||||||||
\(63\) | 3.75913 | 0.473606 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.88934 | 0.606448 | ||||||||
\(66\) | −2.80686 | −0.345501 | ||||||||
\(67\) | 0.113844 | 0.0139083 | 0.00695413 | − | 0.999976i | \(-0.497786\pi\) | ||||
0.00695413 | + | 0.999976i | \(0.497786\pi\) | |||||||
\(68\) | 1.94651 | 0.236050 | ||||||||
\(69\) | −2.97441 | −0.358076 | ||||||||
\(70\) | 6.47309 | 0.773683 | ||||||||
\(71\) | 5.80999 | 0.689519 | 0.344759 | − | 0.938691i | \(-0.387960\pi\) | ||||
0.344759 | + | 0.938691i | \(0.387960\pi\) | |||||||
\(72\) | 1.25732 | 0.148176 | ||||||||
\(73\) | −3.14947 | −0.368617 | −0.184309 | − | 0.982868i | \(-0.559005\pi\) | ||||
−0.184309 | + | 0.982868i | \(0.559005\pi\) | |||||||
\(74\) | 2.51819 | 0.292734 | ||||||||
\(75\) | −0.412551 | −0.0476373 | ||||||||
\(76\) | −4.50586 | −0.516858 | ||||||||
\(77\) | −6.35702 | −0.724450 | ||||||||
\(78\) | −2.98119 | −0.337553 | ||||||||
\(79\) | 13.9186 | 1.56597 | 0.782984 | − | 0.622041i | \(-0.213696\pi\) | ||||
0.782984 | + | 0.622041i | \(0.213696\pi\) | |||||||
\(80\) | 2.16506 | 0.242061 | ||||||||
\(81\) | −3.64719 | −0.405243 | ||||||||
\(82\) | 2.47696 | 0.273535 | ||||||||
\(83\) | 8.08512 | 0.887457 | 0.443728 | − | 0.896161i | \(-0.353655\pi\) | ||||
0.443728 | + | 0.896161i | \(0.353655\pi\) | |||||||
\(84\) | −3.94685 | −0.430637 | ||||||||
\(85\) | 4.21432 | 0.457107 | ||||||||
\(86\) | 5.35666 | 0.577624 | ||||||||
\(87\) | −4.46515 | −0.478714 | ||||||||
\(88\) | −2.12624 | −0.226658 | ||||||||
\(89\) | −9.85193 | −1.04430 | −0.522151 | − | 0.852853i | \(-0.674870\pi\) | ||||
−0.522151 | + | 0.852853i | \(0.674870\pi\) | |||||||
\(90\) | 2.72217 | 0.286942 | ||||||||
\(91\) | −6.75184 | −0.707785 | ||||||||
\(92\) | −2.25316 | −0.234908 | ||||||||
\(93\) | −9.13560 | −0.947318 | ||||||||
\(94\) | −2.67325 | −0.275725 | ||||||||
\(95\) | −9.75547 | −1.00089 | ||||||||
\(96\) | −1.32011 | −0.134733 | ||||||||
\(97\) | −15.6858 | −1.59265 | −0.796325 | − | 0.604869i | \(-0.793225\pi\) | ||||
−0.796325 | + | 0.604869i | \(0.793225\pi\) | |||||||
\(98\) | −1.93889 | −0.195858 | ||||||||
\(99\) | −2.67336 | −0.268683 | ||||||||
\(100\) | −0.312513 | −0.0312513 | ||||||||
\(101\) | −1.42458 | −0.141751 | −0.0708753 | − | 0.997485i | \(-0.522579\pi\) | ||||
−0.0708753 | + | 0.997485i | \(0.522579\pi\) | |||||||
\(102\) | −2.56961 | −0.254429 | ||||||||
\(103\) | −2.09945 | −0.206865 | −0.103433 | − | 0.994636i | \(-0.532983\pi\) | ||||
−0.103433 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(104\) | −2.25829 | −0.221444 | ||||||||
\(105\) | −8.54517 | −0.833923 | ||||||||
\(106\) | 7.74916 | 0.752665 | ||||||||
\(107\) | 13.0021 | 1.25696 | 0.628481 | − | 0.777825i | \(-0.283677\pi\) | ||||
0.628481 | + | 0.777825i | \(0.283677\pi\) | |||||||
\(108\) | −5.62011 | −0.540796 | ||||||||
\(109\) | −0.917102 | −0.0878425 | −0.0439212 | − | 0.999035i | \(-0.513985\pi\) | ||||
−0.0439212 | + | 0.999035i | \(0.513985\pi\) | |||||||
\(110\) | −4.60343 | −0.438920 | ||||||||
\(111\) | −3.32428 | −0.315527 | ||||||||
\(112\) | −2.98980 | −0.282509 | ||||||||
\(113\) | 17.1610 | 1.61437 | 0.807187 | − | 0.590296i | \(-0.200989\pi\) | ||||
0.807187 | + | 0.590296i | \(0.200989\pi\) | |||||||
\(114\) | 5.94822 | 0.557102 | ||||||||
\(115\) | −4.87822 | −0.454896 | ||||||||
\(116\) | −3.38241 | −0.314049 | ||||||||
\(117\) | −2.83939 | −0.262502 | ||||||||
\(118\) | −8.45119 | −0.777995 | ||||||||
\(119\) | −5.81969 | −0.533490 | ||||||||
\(120\) | −2.85811 | −0.260909 | ||||||||
\(121\) | −6.47911 | −0.589010 | ||||||||
\(122\) | 7.65002 | 0.692600 | ||||||||
\(123\) | −3.26985 | −0.294833 | ||||||||
\(124\) | −6.92035 | −0.621466 | ||||||||
\(125\) | −11.5019 | −1.02876 | ||||||||
\(126\) | −3.75913 | −0.334890 | ||||||||
\(127\) | −4.05230 | −0.359584 | −0.179792 | − | 0.983705i | \(-0.557542\pi\) | ||||
−0.179792 | + | 0.983705i | \(0.557542\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.07137 | −0.622599 | ||||||||
\(130\) | −4.88934 | −0.428823 | ||||||||
\(131\) | −16.2720 | −1.42169 | −0.710844 | − | 0.703349i | \(-0.751687\pi\) | ||||
−0.710844 | + | 0.703349i | \(0.751687\pi\) | |||||||
\(132\) | 2.80686 | 0.244306 | ||||||||
\(133\) | 13.4716 | 1.16814 | ||||||||
\(134\) | −0.113844 | −0.00983462 | ||||||||
\(135\) | −12.1679 | −1.04724 | ||||||||
\(136\) | −1.94651 | −0.166912 | ||||||||
\(137\) | 2.45826 | 0.210023 | 0.105012 | − | 0.994471i | \(-0.466512\pi\) | ||||
0.105012 | + | 0.994471i | \(0.466512\pi\) | |||||||
\(138\) | 2.97441 | 0.253198 | ||||||||
\(139\) | 16.3074 | 1.38318 | 0.691588 | − | 0.722293i | \(-0.256912\pi\) | ||||
0.691588 | + | 0.722293i | \(0.256912\pi\) | |||||||
\(140\) | −6.47309 | −0.547076 | ||||||||
\(141\) | 3.52897 | 0.297193 | ||||||||
\(142\) | −5.80999 | −0.487564 | ||||||||
\(143\) | 4.80167 | 0.401536 | ||||||||
\(144\) | −1.25732 | −0.104777 | ||||||||
\(145\) | −7.32313 | −0.608153 | ||||||||
\(146\) | 3.14947 | 0.260652 | ||||||||
\(147\) | 2.55955 | 0.211108 | ||||||||
\(148\) | −2.51819 | −0.206994 | ||||||||
\(149\) | −16.1736 | −1.32499 | −0.662497 | − | 0.749065i | \(-0.730503\pi\) | ||||
−0.662497 | + | 0.749065i | \(0.730503\pi\) | |||||||
\(150\) | 0.412551 | 0.0336846 | ||||||||
\(151\) | 14.1346 | 1.15026 | 0.575130 | − | 0.818062i | \(-0.304951\pi\) | ||||
0.575130 | + | 0.818062i | \(0.304951\pi\) | |||||||
\(152\) | 4.50586 | 0.365474 | ||||||||
\(153\) | −2.44739 | −0.197860 | ||||||||
\(154\) | 6.35702 | 0.512264 | ||||||||
\(155\) | −14.9830 | −1.20346 | ||||||||
\(156\) | 2.98119 | 0.238686 | ||||||||
\(157\) | −21.3423 | −1.70330 | −0.851651 | − | 0.524109i | \(-0.824398\pi\) | ||||
−0.851651 | + | 0.524109i | \(0.824398\pi\) | |||||||
\(158\) | −13.9186 | −1.10731 | ||||||||
\(159\) | −10.2297 | −0.811269 | ||||||||
\(160\) | −2.16506 | −0.171163 | ||||||||
\(161\) | 6.73648 | 0.530909 | ||||||||
\(162\) | 3.64719 | 0.286550 | ||||||||
\(163\) | −13.4852 | −1.05624 | −0.528120 | − | 0.849170i | \(-0.677103\pi\) | ||||
−0.528120 | + | 0.849170i | \(0.677103\pi\) | |||||||
\(164\) | −2.47696 | −0.193418 | ||||||||
\(165\) | 6.07702 | 0.473096 | ||||||||
\(166\) | −8.08512 | −0.627527 | ||||||||
\(167\) | −4.72981 | −0.366004 | −0.183002 | − | 0.983113i | \(-0.558581\pi\) | ||||
−0.183002 | + | 0.983113i | \(0.558581\pi\) | |||||||
\(168\) | 3.94685 | 0.304506 | ||||||||
\(169\) | −7.90012 | −0.607701 | ||||||||
\(170\) | −4.21432 | −0.323224 | ||||||||
\(171\) | 5.66531 | 0.433237 | ||||||||
\(172\) | −5.35666 | −0.408442 | ||||||||
\(173\) | −0.678924 | −0.0516176 | −0.0258088 | − | 0.999667i | \(-0.508216\pi\) | ||||
−0.0258088 | + | 0.999667i | \(0.508216\pi\) | |||||||
\(174\) | 4.46515 | 0.338502 | ||||||||
\(175\) | 0.934352 | 0.0706304 | ||||||||
\(176\) | 2.12624 | 0.160271 | ||||||||
\(177\) | 11.1565 | 0.838572 | ||||||||
\(178\) | 9.85193 | 0.738434 | ||||||||
\(179\) | 4.62412 | 0.345623 | 0.172811 | − | 0.984955i | \(-0.444715\pi\) | ||||
0.172811 | + | 0.984955i | \(0.444715\pi\) | |||||||
\(180\) | −2.72217 | −0.202899 | ||||||||
\(181\) | −20.9925 | −1.56036 | −0.780181 | − | 0.625554i | \(-0.784873\pi\) | ||||
−0.780181 | + | 0.625554i | \(0.784873\pi\) | |||||||
\(182\) | 6.75184 | 0.500479 | ||||||||
\(183\) | −10.0988 | −0.746527 | ||||||||
\(184\) | 2.25316 | 0.166105 | ||||||||
\(185\) | −5.45204 | −0.400842 | ||||||||
\(186\) | 9.13560 | 0.669855 | ||||||||
\(187\) | 4.13875 | 0.302656 | ||||||||
\(188\) | 2.67325 | 0.194967 | ||||||||
\(189\) | 16.8030 | 1.22224 | ||||||||
\(190\) | 9.75547 | 0.707736 | ||||||||
\(191\) | 17.6068 | 1.27398 | 0.636992 | − | 0.770871i | \(-0.280179\pi\) | ||||
0.636992 | + | 0.770871i | \(0.280179\pi\) | |||||||
\(192\) | 1.32011 | 0.0952705 | ||||||||
\(193\) | 2.55233 | 0.183721 | 0.0918603 | − | 0.995772i | \(-0.470719\pi\) | ||||
0.0918603 | + | 0.995772i | \(0.470719\pi\) | |||||||
\(194\) | 15.6858 | 1.12617 | ||||||||
\(195\) | 6.45445 | 0.462212 | ||||||||
\(196\) | 1.93889 | 0.138492 | ||||||||
\(197\) | −12.9771 | −0.924577 | −0.462289 | − | 0.886729i | \(-0.652972\pi\) | ||||
−0.462289 | + | 0.886729i | \(0.652972\pi\) | |||||||
\(198\) | 2.67336 | 0.189987 | ||||||||
\(199\) | 16.5052 | 1.17002 | 0.585012 | − | 0.811025i | \(-0.301090\pi\) | ||||
0.585012 | + | 0.811025i | \(0.301090\pi\) | |||||||
\(200\) | 0.312513 | 0.0220980 | ||||||||
\(201\) | 0.150286 | 0.0106004 | ||||||||
\(202\) | 1.42458 | 0.100233 | ||||||||
\(203\) | 10.1127 | 0.709775 | ||||||||
\(204\) | 2.56961 | 0.179908 | ||||||||
\(205\) | −5.36277 | −0.374552 | ||||||||
\(206\) | 2.09945 | 0.146276 | ||||||||
\(207\) | 2.83294 | 0.196903 | ||||||||
\(208\) | 2.25829 | 0.156584 | ||||||||
\(209\) | −9.58054 | −0.662700 | ||||||||
\(210\) | 8.54517 | 0.589673 | ||||||||
\(211\) | −11.7135 | −0.806388 | −0.403194 | − | 0.915114i | \(-0.632100\pi\) | ||||
−0.403194 | + | 0.915114i | \(0.632100\pi\) | |||||||
\(212\) | −7.74916 | −0.532214 | ||||||||
\(213\) | 7.66980 | 0.525526 | ||||||||
\(214\) | −13.0021 | −0.888807 | ||||||||
\(215\) | −11.5975 | −0.790943 | ||||||||
\(216\) | 5.62011 | 0.382400 | ||||||||
\(217\) | 20.6905 | 1.40456 | ||||||||
\(218\) | 0.917102 | 0.0621140 | ||||||||
\(219\) | −4.15763 | −0.280947 | ||||||||
\(220\) | 4.60343 | 0.310364 | ||||||||
\(221\) | 4.39580 | 0.295693 | ||||||||
\(222\) | 3.32428 | 0.223111 | ||||||||
\(223\) | 0.245128 | 0.0164150 | 0.00820751 | − | 0.999966i | \(-0.497387\pi\) | ||||
0.00820751 | + | 0.999966i | \(0.497387\pi\) | |||||||
\(224\) | 2.98980 | 0.199764 | ||||||||
\(225\) | 0.392929 | 0.0261953 | ||||||||
\(226\) | −17.1610 | −1.14153 | ||||||||
\(227\) | −18.4937 | −1.22747 | −0.613735 | − | 0.789512i | \(-0.710334\pi\) | ||||
−0.613735 | + | 0.789512i | \(0.710334\pi\) | |||||||
\(228\) | −5.94822 | −0.393930 | ||||||||
\(229\) | 17.8858 | 1.18193 | 0.590964 | − | 0.806698i | \(-0.298748\pi\) | ||||
0.590964 | + | 0.806698i | \(0.298748\pi\) | |||||||
\(230\) | 4.87822 | 0.321660 | ||||||||
\(231\) | −8.39195 | −0.552150 | ||||||||
\(232\) | 3.38241 | 0.222066 | ||||||||
\(233\) | 22.0406 | 1.44393 | 0.721963 | − | 0.691932i | \(-0.243240\pi\) | ||||
0.721963 | + | 0.691932i | \(0.243240\pi\) | |||||||
\(234\) | 2.83939 | 0.185617 | ||||||||
\(235\) | 5.78775 | 0.377551 | ||||||||
\(236\) | 8.45119 | 0.550126 | ||||||||
\(237\) | 18.3741 | 1.19352 | ||||||||
\(238\) | 5.81969 | 0.377234 | ||||||||
\(239\) | 12.0738 | 0.780987 | 0.390493 | − | 0.920606i | \(-0.372304\pi\) | ||||
0.390493 | + | 0.920606i | \(0.372304\pi\) | |||||||
\(240\) | 2.85811 | 0.184490 | ||||||||
\(241\) | −0.147118 | −0.00947672 | −0.00473836 | − | 0.999989i | \(-0.501508\pi\) | ||||
−0.00473836 | + | 0.999989i | \(0.501508\pi\) | |||||||
\(242\) | 6.47911 | 0.416493 | ||||||||
\(243\) | 12.0457 | 0.772730 | ||||||||
\(244\) | −7.65002 | −0.489742 | ||||||||
\(245\) | 4.19782 | 0.268189 | ||||||||
\(246\) | 3.26985 | 0.208478 | ||||||||
\(247\) | −10.1756 | −0.647455 | ||||||||
\(248\) | 6.92035 | 0.439443 | ||||||||
\(249\) | 10.6732 | 0.676388 | ||||||||
\(250\) | 11.5019 | 0.727445 | ||||||||
\(251\) | −25.4806 | −1.60832 | −0.804160 | − | 0.594413i | \(-0.797385\pi\) | ||||
−0.804160 | + | 0.594413i | \(0.797385\pi\) | |||||||
\(252\) | 3.75913 | 0.236803 | ||||||||
\(253\) | −4.79075 | −0.301192 | ||||||||
\(254\) | 4.05230 | 0.254264 | ||||||||
\(255\) | 5.56335 | 0.348391 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.7969 | 1.35965 | 0.679827 | − | 0.733372i | \(-0.262055\pi\) | ||||
0.679827 | + | 0.733372i | \(0.262055\pi\) | |||||||
\(258\) | 7.07137 | 0.440244 | ||||||||
\(259\) | 7.52889 | 0.467822 | ||||||||
\(260\) | 4.88934 | 0.303224 | ||||||||
\(261\) | 4.25278 | 0.263240 | ||||||||
\(262\) | 16.2720 | 1.00529 | ||||||||
\(263\) | −18.4250 | −1.13613 | −0.568067 | − | 0.822983i | \(-0.692308\pi\) | ||||
−0.568067 | + | 0.822983i | \(0.692308\pi\) | |||||||
\(264\) | −2.80686 | −0.172750 | ||||||||
\(265\) | −16.7774 | −1.03063 | ||||||||
\(266\) | −13.4716 | −0.825998 | ||||||||
\(267\) | −13.0056 | −0.795930 | ||||||||
\(268\) | 0.113844 | 0.00695413 | ||||||||
\(269\) | 17.1292 | 1.04439 | 0.522194 | − | 0.852827i | \(-0.325114\pi\) | ||||
0.522194 | + | 0.852827i | \(0.325114\pi\) | |||||||
\(270\) | 12.1679 | 0.740514 | ||||||||
\(271\) | 9.28318 | 0.563913 | 0.281957 | − | 0.959427i | \(-0.409017\pi\) | ||||
0.281957 | + | 0.959427i | \(0.409017\pi\) | |||||||
\(272\) | 1.94651 | 0.118025 | ||||||||
\(273\) | −8.91314 | −0.539448 | ||||||||
\(274\) | −2.45826 | −0.148509 | ||||||||
\(275\) | −0.664478 | −0.0400695 | ||||||||
\(276\) | −2.97441 | −0.179038 | ||||||||
\(277\) | 2.86014 | 0.171849 | 0.0859244 | − | 0.996302i | \(-0.472616\pi\) | ||||
0.0859244 | + | 0.996302i | \(0.472616\pi\) | |||||||
\(278\) | −16.3074 | −0.978052 | ||||||||
\(279\) | 8.70109 | 0.520921 | ||||||||
\(280\) | 6.47309 | 0.386841 | ||||||||
\(281\) | 22.8730 | 1.36449 | 0.682244 | − | 0.731124i | \(-0.261004\pi\) | ||||
0.682244 | + | 0.731124i | \(0.261004\pi\) | |||||||
\(282\) | −3.52897 | −0.210147 | ||||||||
\(283\) | −18.7531 | −1.11475 | −0.557377 | − | 0.830260i | \(-0.688192\pi\) | ||||
−0.557377 | + | 0.830260i | \(0.688192\pi\) | |||||||
\(284\) | 5.80999 | 0.344759 | ||||||||
\(285\) | −12.8783 | −0.762842 | ||||||||
\(286\) | −4.80167 | −0.283929 | ||||||||
\(287\) | 7.40561 | 0.437140 | ||||||||
\(288\) | 1.25732 | 0.0740882 | ||||||||
\(289\) | −13.2111 | −0.777122 | ||||||||
\(290\) | 7.32313 | 0.430029 | ||||||||
\(291\) | −20.7069 | −1.21386 | ||||||||
\(292\) | −3.14947 | −0.184309 | ||||||||
\(293\) | −16.6418 | −0.972224 | −0.486112 | − | 0.873897i | \(-0.661585\pi\) | ||||
−0.486112 | + | 0.873897i | \(0.661585\pi\) | |||||||
\(294\) | −2.55955 | −0.149276 | ||||||||
\(295\) | 18.2973 | 1.06531 | ||||||||
\(296\) | 2.51819 | 0.146367 | ||||||||
\(297\) | −11.9497 | −0.693392 | ||||||||
\(298\) | 16.1736 | 0.936912 | ||||||||
\(299\) | −5.08828 | −0.294263 | ||||||||
\(300\) | −0.412551 | −0.0238186 | ||||||||
\(301\) | 16.0153 | 0.923109 | ||||||||
\(302\) | −14.1346 | −0.813357 | ||||||||
\(303\) | −1.88059 | −0.108037 | ||||||||
\(304\) | −4.50586 | −0.258429 | ||||||||
\(305\) | −16.5627 | −0.948380 | ||||||||
\(306\) | 2.44739 | 0.139908 | ||||||||
\(307\) | 14.4535 | 0.824904 | 0.412452 | − | 0.910979i | \(-0.364672\pi\) | ||||
0.412452 | + | 0.910979i | \(0.364672\pi\) | |||||||
\(308\) | −6.35702 | −0.362225 | ||||||||
\(309\) | −2.77150 | −0.157665 | ||||||||
\(310\) | 14.9830 | 0.850976 | ||||||||
\(311\) | −21.4694 | −1.21742 | −0.608709 | − | 0.793394i | \(-0.708312\pi\) | ||||
−0.608709 | + | 0.793394i | \(0.708312\pi\) | |||||||
\(312\) | −2.98119 | −0.168776 | ||||||||
\(313\) | −2.02552 | −0.114489 | −0.0572446 | − | 0.998360i | \(-0.518232\pi\) | ||||
−0.0572446 | + | 0.998360i | \(0.518232\pi\) | |||||||
\(314\) | 21.3423 | 1.20442 | ||||||||
\(315\) | 8.13875 | 0.458566 | ||||||||
\(316\) | 13.9186 | 0.782984 | ||||||||
\(317\) | 28.9400 | 1.62543 | 0.812715 | − | 0.582661i | \(-0.197989\pi\) | ||||
0.812715 | + | 0.582661i | \(0.197989\pi\) | |||||||
\(318\) | 10.2297 | 0.573654 | ||||||||
\(319\) | −7.19182 | −0.402665 | ||||||||
\(320\) | 2.16506 | 0.121031 | ||||||||
\(321\) | 17.1642 | 0.958011 | ||||||||
\(322\) | −6.73648 | −0.375409 | ||||||||
\(323\) | −8.77073 | −0.488016 | ||||||||
\(324\) | −3.64719 | −0.202622 | ||||||||
\(325\) | −0.705746 | −0.0391478 | ||||||||
\(326\) | 13.4852 | 0.746874 | ||||||||
\(327\) | −1.21067 | −0.0669504 | ||||||||
\(328\) | 2.47696 | 0.136767 | ||||||||
\(329\) | −7.99248 | −0.440640 | ||||||||
\(330\) | −6.07702 | −0.334529 | ||||||||
\(331\) | 0.897068 | 0.0493073 | 0.0246537 | − | 0.999696i | \(-0.492152\pi\) | ||||
0.0246537 | + | 0.999696i | \(0.492152\pi\) | |||||||
\(332\) | 8.08512 | 0.443728 | ||||||||
\(333\) | 3.16617 | 0.173505 | ||||||||
\(334\) | 4.72981 | 0.258804 | ||||||||
\(335\) | 0.246479 | 0.0134666 | ||||||||
\(336\) | −3.94685 | −0.215318 | ||||||||
\(337\) | 6.59167 | 0.359071 | 0.179536 | − | 0.983751i | \(-0.442540\pi\) | ||||
0.179536 | + | 0.983751i | \(0.442540\pi\) | |||||||
\(338\) | 7.90012 | 0.429710 | ||||||||
\(339\) | 22.6544 | 1.23042 | ||||||||
\(340\) | 4.21432 | 0.228554 | ||||||||
\(341\) | −14.7143 | −0.796825 | ||||||||
\(342\) | −5.66531 | −0.306345 | ||||||||
\(343\) | 15.1317 | 0.817034 | ||||||||
\(344\) | 5.35666 | 0.288812 | ||||||||
\(345\) | −6.43977 | −0.346705 | ||||||||
\(346\) | 0.678924 | 0.0364992 | ||||||||
\(347\) | −10.9168 | −0.586043 | −0.293022 | − | 0.956106i | \(-0.594661\pi\) | ||||
−0.293022 | + | 0.956106i | \(0.594661\pi\) | |||||||
\(348\) | −4.46515 | −0.239357 | ||||||||
\(349\) | −21.5336 | −1.15267 | −0.576334 | − | 0.817214i | \(-0.695517\pi\) | ||||
−0.576334 | + | 0.817214i | \(0.695517\pi\) | |||||||
\(350\) | −0.934352 | −0.0499432 | ||||||||
\(351\) | −12.6919 | −0.677441 | ||||||||
\(352\) | −2.12624 | −0.113329 | ||||||||
\(353\) | −28.6488 | −1.52482 | −0.762411 | − | 0.647094i | \(-0.775984\pi\) | ||||
−0.762411 | + | 0.647094i | \(0.775984\pi\) | |||||||
\(354\) | −11.1565 | −0.592960 | ||||||||
\(355\) | 12.5790 | 0.667623 | ||||||||
\(356\) | −9.85193 | −0.522151 | ||||||||
\(357\) | −7.68260 | −0.406606 | ||||||||
\(358\) | −4.62412 | −0.244392 | ||||||||
\(359\) | −34.1295 | −1.80129 | −0.900644 | − | 0.434558i | \(-0.856904\pi\) | ||||
−0.900644 | + | 0.434558i | \(0.856904\pi\) | |||||||
\(360\) | 2.72217 | 0.143471 | ||||||||
\(361\) | 1.30280 | 0.0685685 | ||||||||
\(362\) | 20.9925 | 1.10334 | ||||||||
\(363\) | −8.55311 | −0.448922 | ||||||||
\(364\) | −6.75184 | −0.353892 | ||||||||
\(365\) | −6.81879 | −0.356912 | ||||||||
\(366\) | 10.0988 | 0.527875 | ||||||||
\(367\) | 7.10430 | 0.370842 | 0.185421 | − | 0.982659i | \(-0.440635\pi\) | ||||
0.185421 | + | 0.982659i | \(0.440635\pi\) | |||||||
\(368\) | −2.25316 | −0.117454 | ||||||||
\(369\) | 3.11433 | 0.162126 | ||||||||
\(370\) | 5.45204 | 0.283438 | ||||||||
\(371\) | 23.1684 | 1.20284 | ||||||||
\(372\) | −9.13560 | −0.473659 | ||||||||
\(373\) | −30.3597 | −1.57197 | −0.785983 | − | 0.618249i | \(-0.787842\pi\) | ||||
−0.785983 | + | 0.618249i | \(0.787842\pi\) | |||||||
\(374\) | −4.13875 | −0.214010 | ||||||||
\(375\) | −15.1837 | −0.784085 | ||||||||
\(376\) | −2.67325 | −0.137862 | ||||||||
\(377\) | −7.63848 | −0.393402 | ||||||||
\(378\) | −16.8030 | −0.864253 | ||||||||
\(379\) | 6.33979 | 0.325653 | 0.162827 | − | 0.986655i | \(-0.447939\pi\) | ||||
0.162827 | + | 0.986655i | \(0.447939\pi\) | |||||||
\(380\) | −9.75547 | −0.500445 | ||||||||
\(381\) | −5.34947 | −0.274062 | ||||||||
\(382\) | −17.6068 | −0.900842 | ||||||||
\(383\) | 13.3979 | 0.684600 | 0.342300 | − | 0.939591i | \(-0.388794\pi\) | ||||
0.342300 | + | 0.939591i | \(0.388794\pi\) | |||||||
\(384\) | −1.32011 | −0.0673664 | ||||||||
\(385\) | −13.7633 | −0.701445 | ||||||||
\(386\) | −2.55233 | −0.129910 | ||||||||
\(387\) | 6.73504 | 0.342361 | ||||||||
\(388\) | −15.6858 | −0.796325 | ||||||||
\(389\) | −16.0931 | −0.815953 | −0.407976 | − | 0.912993i | \(-0.633765\pi\) | ||||
−0.407976 | + | 0.912993i | \(0.633765\pi\) | |||||||
\(390\) | −6.45445 | −0.326834 | ||||||||
\(391\) | −4.38580 | −0.221799 | ||||||||
\(392\) | −1.93889 | −0.0979289 | ||||||||
\(393\) | −21.4807 | −1.08356 | ||||||||
\(394\) | 12.9771 | 0.653775 | ||||||||
\(395\) | 30.1347 | 1.51624 | ||||||||
\(396\) | −2.67336 | −0.134341 | ||||||||
\(397\) | 4.16939 | 0.209256 | 0.104628 | − | 0.994511i | \(-0.466635\pi\) | ||||
0.104628 | + | 0.994511i | \(0.466635\pi\) | |||||||
\(398\) | −16.5052 | −0.827332 | ||||||||
\(399\) | 17.7840 | 0.890312 | ||||||||
\(400\) | −0.312513 | −0.0156257 | ||||||||
\(401\) | −30.2228 | −1.50925 | −0.754627 | − | 0.656154i | \(-0.772182\pi\) | ||||
−0.754627 | + | 0.656154i | \(0.772182\pi\) | |||||||
\(402\) | −0.150286 | −0.00749559 | ||||||||
\(403\) | −15.6282 | −0.778495 | ||||||||
\(404\) | −1.42458 | −0.0708753 | ||||||||
\(405\) | −7.89639 | −0.392375 | ||||||||
\(406\) | −10.1127 | −0.501887 | ||||||||
\(407\) | −5.35428 | −0.265402 | ||||||||
\(408\) | −2.56961 | −0.127214 | ||||||||
\(409\) | 11.3240 | 0.559936 | 0.279968 | − | 0.960009i | \(-0.409676\pi\) | ||||
0.279968 | + | 0.960009i | \(0.409676\pi\) | |||||||
\(410\) | 5.36277 | 0.264848 | ||||||||
\(411\) | 3.24516 | 0.160072 | ||||||||
\(412\) | −2.09945 | −0.103433 | ||||||||
\(413\) | −25.2674 | −1.24333 | ||||||||
\(414\) | −2.83294 | −0.139231 | ||||||||
\(415\) | 17.5048 | 0.859275 | ||||||||
\(416\) | −2.25829 | −0.110722 | ||||||||
\(417\) | 21.5275 | 1.05421 | ||||||||
\(418\) | 9.58054 | 0.468599 | ||||||||
\(419\) | −24.0175 | −1.17333 | −0.586665 | − | 0.809829i | \(-0.699560\pi\) | ||||
−0.586665 | + | 0.809829i | \(0.699560\pi\) | |||||||
\(420\) | −8.54517 | −0.416962 | ||||||||
\(421\) | 3.70463 | 0.180553 | 0.0902763 | − | 0.995917i | \(-0.471225\pi\) | ||||
0.0902763 | + | 0.995917i | \(0.471225\pi\) | |||||||
\(422\) | 11.7135 | 0.570203 | ||||||||
\(423\) | −3.36113 | −0.163424 | ||||||||
\(424\) | 7.74916 | 0.376332 | ||||||||
\(425\) | −0.608312 | −0.0295075 | ||||||||
\(426\) | −7.66980 | −0.371603 | ||||||||
\(427\) | 22.8720 | 1.10685 | ||||||||
\(428\) | 13.0021 | 0.628481 | ||||||||
\(429\) | 6.33871 | 0.306036 | ||||||||
\(430\) | 11.5975 | 0.559281 | ||||||||
\(431\) | −7.26122 | −0.349761 | −0.174880 | − | 0.984590i | \(-0.555954\pi\) | ||||
−0.174880 | + | 0.984590i | \(0.555954\pi\) | |||||||
\(432\) | −5.62011 | −0.270398 | ||||||||
\(433\) | 19.3649 | 0.930617 | 0.465309 | − | 0.885148i | \(-0.345943\pi\) | ||||
0.465309 | + | 0.885148i | \(0.345943\pi\) | |||||||
\(434\) | −20.6905 | −0.993174 | ||||||||
\(435\) | −9.66731 | −0.463512 | ||||||||
\(436\) | −0.917102 | −0.0439212 | ||||||||
\(437\) | 10.1524 | 0.485656 | ||||||||
\(438\) | 4.15763 | 0.198659 | ||||||||
\(439\) | 7.22422 | 0.344793 | 0.172397 | − | 0.985028i | \(-0.444849\pi\) | ||||
0.172397 | + | 0.985028i | \(0.444849\pi\) | |||||||
\(440\) | −4.60343 | −0.219460 | ||||||||
\(441\) | −2.43781 | −0.116086 | ||||||||
\(442\) | −4.39580 | −0.209087 | ||||||||
\(443\) | 25.4666 | 1.20995 | 0.604977 | − | 0.796243i | \(-0.293182\pi\) | ||||
0.604977 | + | 0.796243i | \(0.293182\pi\) | |||||||
\(444\) | −3.32428 | −0.157763 | ||||||||
\(445\) | −21.3300 | −1.01114 | ||||||||
\(446\) | −0.245128 | −0.0116072 | ||||||||
\(447\) | −21.3509 | −1.00986 | ||||||||
\(448\) | −2.98980 | −0.141255 | ||||||||
\(449\) | 9.85257 | 0.464971 | 0.232486 | − | 0.972600i | \(-0.425314\pi\) | ||||
0.232486 | + | 0.972600i | \(0.425314\pi\) | |||||||
\(450\) | −0.392929 | −0.0185229 | ||||||||
\(451\) | −5.26661 | −0.247995 | ||||||||
\(452\) | 17.1610 | 0.807187 | ||||||||
\(453\) | 18.6592 | 0.876687 | ||||||||
\(454\) | 18.4937 | 0.867953 | ||||||||
\(455\) | −14.6181 | −0.685309 | ||||||||
\(456\) | 5.94822 | 0.278551 | ||||||||
\(457\) | −15.4524 | −0.722835 | −0.361417 | − | 0.932404i | \(-0.617707\pi\) | ||||
−0.361417 | + | 0.932404i | \(0.617707\pi\) | |||||||
\(458\) | −17.8858 | −0.835749 | ||||||||
\(459\) | −10.9396 | −0.510618 | ||||||||
\(460\) | −4.87822 | −0.227448 | ||||||||
\(461\) | 4.28239 | 0.199451 | 0.0997254 | − | 0.995015i | \(-0.468204\pi\) | ||||
0.0997254 | + | 0.995015i | \(0.468204\pi\) | |||||||
\(462\) | 8.39195 | 0.390429 | ||||||||
\(463\) | 15.4021 | 0.715798 | 0.357899 | − | 0.933760i | \(-0.383493\pi\) | ||||
0.357899 | + | 0.933760i | \(0.383493\pi\) | |||||||
\(464\) | −3.38241 | −0.157025 | ||||||||
\(465\) | −19.7791 | −0.917235 | ||||||||
\(466\) | −22.0406 | −1.02101 | ||||||||
\(467\) | 1.92711 | 0.0891762 | 0.0445881 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445881 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(468\) | −2.83939 | −0.131251 | ||||||||
\(469\) | −0.340370 | −0.0157168 | ||||||||
\(470\) | −5.78775 | −0.266969 | ||||||||
\(471\) | −28.1741 | −1.29820 | ||||||||
\(472\) | −8.45119 | −0.388998 | ||||||||
\(473\) | −11.3895 | −0.523692 | ||||||||
\(474\) | −18.3741 | −0.843949 | ||||||||
\(475\) | 1.40814 | 0.0646100 | ||||||||
\(476\) | −5.81969 | −0.266745 | ||||||||
\(477\) | 9.74316 | 0.446109 | ||||||||
\(478\) | −12.0738 | −0.552241 | ||||||||
\(479\) | 14.1139 | 0.644881 | 0.322441 | − | 0.946590i | \(-0.395497\pi\) | ||||
0.322441 | + | 0.946590i | \(0.395497\pi\) | |||||||
\(480\) | −2.85811 | −0.130454 | ||||||||
\(481\) | −5.68681 | −0.259296 | ||||||||
\(482\) | 0.147118 | 0.00670105 | ||||||||
\(483\) | 8.89287 | 0.404640 | ||||||||
\(484\) | −6.47911 | −0.294505 | ||||||||
\(485\) | −33.9607 | −1.54207 | ||||||||
\(486\) | −12.0457 | −0.546402 | ||||||||
\(487\) | −20.0385 | −0.908031 | −0.454016 | − | 0.890994i | \(-0.650009\pi\) | ||||
−0.454016 | + | 0.890994i | \(0.650009\pi\) | |||||||
\(488\) | 7.65002 | 0.346300 | ||||||||
\(489\) | −17.8019 | −0.805028 | ||||||||
\(490\) | −4.19782 | −0.189638 | ||||||||
\(491\) | 16.3461 | 0.737690 | 0.368845 | − | 0.929491i | \(-0.379753\pi\) | ||||
0.368845 | + | 0.929491i | \(0.379753\pi\) | |||||||
\(492\) | −3.26985 | −0.147416 | ||||||||
\(493\) | −6.58392 | −0.296525 | ||||||||
\(494\) | 10.1756 | 0.457820 | ||||||||
\(495\) | −5.78799 | −0.260151 | ||||||||
\(496\) | −6.92035 | −0.310733 | ||||||||
\(497\) | −17.3707 | −0.779182 | ||||||||
\(498\) | −10.6732 | −0.478278 | ||||||||
\(499\) | 21.2430 | 0.950966 | 0.475483 | − | 0.879725i | \(-0.342273\pi\) | ||||
0.475483 | + | 0.879725i | \(0.342273\pi\) | |||||||
\(500\) | −11.5019 | −0.514381 | ||||||||
\(501\) | −6.24386 | −0.278955 | ||||||||
\(502\) | 25.4806 | 1.13725 | ||||||||
\(503\) | −29.4391 | −1.31262 | −0.656312 | − | 0.754490i | \(-0.727885\pi\) | ||||
−0.656312 | + | 0.754490i | \(0.727885\pi\) | |||||||
\(504\) | −3.75913 | −0.167445 | ||||||||
\(505\) | −3.08429 | −0.137249 | ||||||||
\(506\) | 4.79075 | 0.212975 | ||||||||
\(507\) | −10.4290 | −0.463168 | ||||||||
\(508\) | −4.05230 | −0.179792 | ||||||||
\(509\) | −18.0171 | −0.798593 | −0.399297 | − | 0.916822i | \(-0.630746\pi\) | ||||
−0.399297 | + | 0.916822i | \(0.630746\pi\) | |||||||
\(510\) | −5.56335 | −0.246349 | ||||||||
\(511\) | 9.41628 | 0.416552 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 25.3235 | 1.11806 | ||||||||
\(514\) | −21.7969 | −0.961421 | ||||||||
\(515\) | −4.54544 | −0.200296 | ||||||||
\(516\) | −7.07137 | −0.311300 | ||||||||
\(517\) | 5.68397 | 0.249981 | ||||||||
\(518\) | −7.52889 | −0.330800 | ||||||||
\(519\) | −0.896251 | −0.0393411 | ||||||||
\(520\) | −4.88934 | −0.214412 | ||||||||
\(521\) | 5.93413 | 0.259979 | 0.129990 | − | 0.991515i | \(-0.458506\pi\) | ||||
0.129990 | + | 0.991515i | \(0.458506\pi\) | |||||||
\(522\) | −4.25278 | −0.186139 | ||||||||
\(523\) | 30.2412 | 1.32236 | 0.661178 | − | 0.750229i | \(-0.270057\pi\) | ||||
0.661178 | + | 0.750229i | \(0.270057\pi\) | |||||||
\(524\) | −16.2720 | −0.710844 | ||||||||
\(525\) | 1.23344 | 0.0538319 | ||||||||
\(526\) | 18.4250 | 0.803368 | ||||||||
\(527\) | −13.4706 | −0.586787 | ||||||||
\(528\) | 2.80686 | 0.122153 | ||||||||
\(529\) | −17.9233 | −0.779273 | ||||||||
\(530\) | 16.7774 | 0.728763 | ||||||||
\(531\) | −10.6258 | −0.461123 | ||||||||
\(532\) | 13.4716 | 0.584069 | ||||||||
\(533\) | −5.59370 | −0.242290 | ||||||||
\(534\) | 13.0056 | 0.562807 | ||||||||
\(535\) | 28.1504 | 1.21705 | ||||||||
\(536\) | −0.113844 | −0.00491731 | ||||||||
\(537\) | 6.10433 | 0.263421 | ||||||||
\(538\) | −17.1292 | −0.738494 | ||||||||
\(539\) | 4.12255 | 0.177571 | ||||||||
\(540\) | −12.1679 | −0.523622 | ||||||||
\(541\) | −23.9300 | −1.02883 | −0.514416 | − | 0.857541i | \(-0.671991\pi\) | ||||
−0.514416 | + | 0.857541i | \(0.671991\pi\) | |||||||
\(542\) | −9.28318 | −0.398747 | ||||||||
\(543\) | −27.7124 | −1.18925 | ||||||||
\(544\) | −1.94651 | −0.0834561 | ||||||||
\(545\) | −1.98558 | −0.0850530 | ||||||||
\(546\) | 8.91314 | 0.381447 | ||||||||
\(547\) | 9.37236 | 0.400733 | 0.200367 | − | 0.979721i | \(-0.435787\pi\) | ||||
0.200367 | + | 0.979721i | \(0.435787\pi\) | |||||||
\(548\) | 2.45826 | 0.105012 | ||||||||
\(549\) | 9.61851 | 0.410508 | ||||||||
\(550\) | 0.664478 | 0.0283334 | ||||||||
\(551\) | 15.2407 | 0.649276 | ||||||||
\(552\) | 2.97441 | 0.126599 | ||||||||
\(553\) | −41.6139 | −1.76960 | ||||||||
\(554\) | −2.86014 | −0.121516 | ||||||||
\(555\) | −7.19727 | −0.305507 | ||||||||
\(556\) | 16.3074 | 0.691588 | ||||||||
\(557\) | 30.0225 | 1.27209 | 0.636047 | − | 0.771650i | \(-0.280568\pi\) | ||||
0.636047 | + | 0.771650i | \(0.280568\pi\) | |||||||
\(558\) | −8.70109 | −0.368347 | ||||||||
\(559\) | −12.0969 | −0.511645 | ||||||||
\(560\) | −6.47309 | −0.273538 | ||||||||
\(561\) | 5.46359 | 0.230673 | ||||||||
\(562\) | −22.8730 | −0.964839 | ||||||||
\(563\) | −14.3485 | −0.604716 | −0.302358 | − | 0.953194i | \(-0.597774\pi\) | ||||
−0.302358 | + | 0.953194i | \(0.597774\pi\) | |||||||
\(564\) | 3.52897 | 0.148597 | ||||||||
\(565\) | 37.1547 | 1.56311 | ||||||||
\(566\) | 18.7531 | 0.788250 | ||||||||
\(567\) | 10.9044 | 0.457940 | ||||||||
\(568\) | −5.80999 | −0.243782 | ||||||||
\(569\) | 4.37504 | 0.183411 | 0.0917056 | − | 0.995786i | \(-0.470768\pi\) | ||||
0.0917056 | + | 0.995786i | \(0.470768\pi\) | |||||||
\(570\) | 12.8783 | 0.539411 | ||||||||
\(571\) | 44.4888 | 1.86180 | 0.930898 | − | 0.365279i | \(-0.119026\pi\) | ||||
0.930898 | + | 0.365279i | \(0.119026\pi\) | |||||||
\(572\) | 4.80167 | 0.200768 | ||||||||
\(573\) | 23.2428 | 0.970984 | ||||||||
\(574\) | −7.40561 | −0.309104 | ||||||||
\(575\) | 0.704141 | 0.0293647 | ||||||||
\(576\) | −1.25732 | −0.0523883 | ||||||||
\(577\) | −6.51332 | −0.271153 | −0.135576 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(578\) | 13.2111 | 0.549509 | ||||||||
\(579\) | 3.36935 | 0.140025 | ||||||||
\(580\) | −7.32313 | −0.304077 | ||||||||
\(581\) | −24.1729 | −1.00286 | ||||||||
\(582\) | 20.7069 | 0.858329 | ||||||||
\(583\) | −16.4766 | −0.682389 | ||||||||
\(584\) | 3.14947 | 0.130326 | ||||||||
\(585\) | −6.14746 | −0.254166 | ||||||||
\(586\) | 16.6418 | 0.687466 | ||||||||
\(587\) | 13.7882 | 0.569099 | 0.284550 | − | 0.958661i | \(-0.408156\pi\) | ||||
0.284550 | + | 0.958661i | \(0.408156\pi\) | |||||||
\(588\) | 2.55955 | 0.105554 | ||||||||
\(589\) | 31.1822 | 1.28484 | ||||||||
\(590\) | −18.2973 | −0.753290 | ||||||||
\(591\) | −17.1311 | −0.704679 | ||||||||
\(592\) | −2.51819 | −0.103497 | ||||||||
\(593\) | 20.8586 | 0.856560 | 0.428280 | − | 0.903646i | \(-0.359120\pi\) | ||||
0.428280 | + | 0.903646i | \(0.359120\pi\) | |||||||
\(594\) | 11.9497 | 0.490302 | ||||||||
\(595\) | −12.6000 | −0.516548 | ||||||||
\(596\) | −16.1736 | −0.662497 | ||||||||
\(597\) | 21.7886 | 0.891750 | ||||||||
\(598\) | 5.08828 | 0.208075 | ||||||||
\(599\) | 3.66284 | 0.149660 | 0.0748298 | − | 0.997196i | \(-0.476159\pi\) | ||||
0.0748298 | + | 0.997196i | \(0.476159\pi\) | |||||||
\(600\) | 0.412551 | 0.0168423 | ||||||||
\(601\) | −12.8882 | −0.525721 | −0.262860 | − | 0.964834i | \(-0.584666\pi\) | ||||
−0.262860 | + | 0.964834i | \(0.584666\pi\) | |||||||
\(602\) | −16.0153 | −0.652737 | ||||||||
\(603\) | −0.143138 | −0.00582904 | ||||||||
\(604\) | 14.1346 | 0.575130 | ||||||||
\(605\) | −14.0277 | −0.570306 | ||||||||
\(606\) | 1.88059 | 0.0763938 | ||||||||
\(607\) | 38.2100 | 1.55090 | 0.775448 | − | 0.631411i | \(-0.217524\pi\) | ||||
0.775448 | + | 0.631411i | \(0.217524\pi\) | |||||||
\(608\) | 4.50586 | 0.182737 | ||||||||
\(609\) | 13.3499 | 0.540965 | ||||||||
\(610\) | 16.5627 | 0.670606 | ||||||||
\(611\) | 6.03698 | 0.244230 | ||||||||
\(612\) | −2.44739 | −0.0989299 | ||||||||
\(613\) | 44.6251 | 1.80239 | 0.901195 | − | 0.433413i | \(-0.142691\pi\) | ||||
0.901195 | + | 0.433413i | \(0.142691\pi\) | |||||||
\(614\) | −14.4535 | −0.583295 | ||||||||
\(615\) | −7.07943 | −0.285470 | ||||||||
\(616\) | 6.35702 | 0.256132 | ||||||||
\(617\) | −17.5453 | −0.706347 | −0.353174 | − | 0.935558i | \(-0.614898\pi\) | ||||
−0.353174 | + | 0.935558i | \(0.614898\pi\) | |||||||
\(618\) | 2.77150 | 0.111486 | ||||||||
\(619\) | 38.3689 | 1.54218 | 0.771089 | − | 0.636727i | \(-0.219712\pi\) | ||||
0.771089 | + | 0.636727i | \(0.219712\pi\) | |||||||
\(620\) | −14.9830 | −0.601731 | ||||||||
\(621\) | 12.6630 | 0.508148 | ||||||||
\(622\) | 21.4694 | 0.860844 | ||||||||
\(623\) | 29.4553 | 1.18010 | ||||||||
\(624\) | 2.98119 | 0.119343 | ||||||||
\(625\) | −23.3398 | −0.933591 | ||||||||
\(626\) | 2.02552 | 0.0809561 | ||||||||
\(627\) | −12.6473 | −0.505086 | ||||||||
\(628\) | −21.3423 | −0.851651 | ||||||||
\(629\) | −4.90170 | −0.195443 | ||||||||
\(630\) | −8.13875 | −0.324255 | ||||||||
\(631\) | −13.2877 | −0.528976 | −0.264488 | − | 0.964389i | \(-0.585203\pi\) | ||||
−0.264488 | + | 0.964389i | \(0.585203\pi\) | |||||||
\(632\) | −13.9186 | −0.553654 | ||||||||
\(633\) | −15.4630 | −0.614600 | ||||||||
\(634\) | −28.9400 | −1.14935 | ||||||||
\(635\) | −8.77348 | −0.348165 | ||||||||
\(636\) | −10.2297 | −0.405634 | ||||||||
\(637\) | 4.37859 | 0.173486 | ||||||||
\(638\) | 7.19182 | 0.284727 | ||||||||
\(639\) | −7.30501 | −0.288982 | ||||||||
\(640\) | −2.16506 | −0.0855815 | ||||||||
\(641\) | −33.1174 | −1.30806 | −0.654030 | − | 0.756469i | \(-0.726923\pi\) | ||||
−0.654030 | + | 0.756469i | \(0.726923\pi\) | |||||||
\(642\) | −17.1642 | −0.677416 | ||||||||
\(643\) | 28.5513 | 1.12595 | 0.562977 | − | 0.826473i | \(-0.309656\pi\) | ||||
0.562977 | + | 0.826473i | \(0.309656\pi\) | |||||||
\(644\) | 6.73648 | 0.265455 | ||||||||
\(645\) | −15.3099 | −0.602828 | ||||||||
\(646\) | 8.77073 | 0.345080 | ||||||||
\(647\) | −1.08764 | −0.0427594 | −0.0213797 | − | 0.999771i | \(-0.506806\pi\) | ||||
−0.0213797 | + | 0.999771i | \(0.506806\pi\) | |||||||
\(648\) | 3.64719 | 0.143275 | ||||||||
\(649\) | 17.9693 | 0.705355 | ||||||||
\(650\) | 0.705746 | 0.0276817 | ||||||||
\(651\) | 27.3136 | 1.07050 | ||||||||
\(652\) | −13.4852 | −0.528120 | ||||||||
\(653\) | 21.8427 | 0.854771 | 0.427385 | − | 0.904070i | \(-0.359435\pi\) | ||||
0.427385 | + | 0.904070i | \(0.359435\pi\) | |||||||
\(654\) | 1.21067 | 0.0473410 | ||||||||
\(655\) | −35.2298 | −1.37654 | ||||||||
\(656\) | −2.47696 | −0.0967091 | ||||||||
\(657\) | 3.95989 | 0.154490 | ||||||||
\(658\) | 7.99248 | 0.311579 | ||||||||
\(659\) | 18.8299 | 0.733507 | 0.366753 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366753 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(660\) | 6.07702 | 0.236548 | ||||||||
\(661\) | −42.8016 | −1.66479 | −0.832395 | − | 0.554183i | \(-0.813031\pi\) | ||||
−0.832395 | + | 0.554183i | \(0.813031\pi\) | |||||||
\(662\) | −0.897068 | −0.0348656 | ||||||||
\(663\) | 5.80292 | 0.225367 | ||||||||
\(664\) | −8.08512 | −0.313763 | ||||||||
\(665\) | 29.1669 | 1.13104 | ||||||||
\(666\) | −3.16617 | −0.122687 | ||||||||
\(667\) | 7.62111 | 0.295090 | ||||||||
\(668\) | −4.72981 | −0.183002 | ||||||||
\(669\) | 0.323596 | 0.0125109 | ||||||||
\(670\) | −0.246479 | −0.00952231 | ||||||||
\(671\) | −16.2658 | −0.627933 | ||||||||
\(672\) | 3.94685 | 0.152253 | ||||||||
\(673\) | 4.63281 | 0.178582 | 0.0892908 | − | 0.996006i | \(-0.471540\pi\) | ||||
0.0892908 | + | 0.996006i | \(0.471540\pi\) | |||||||
\(674\) | −6.59167 | −0.253902 | ||||||||
\(675\) | 1.75636 | 0.0676024 | ||||||||
\(676\) | −7.90012 | −0.303851 | ||||||||
\(677\) | 28.1674 | 1.08256 | 0.541280 | − | 0.840843i | \(-0.317940\pi\) | ||||
0.541280 | + | 0.840843i | \(0.317940\pi\) | |||||||
\(678\) | −22.6544 | −0.870037 | ||||||||
\(679\) | 46.8973 | 1.79975 | ||||||||
\(680\) | −4.21432 | −0.161612 | ||||||||
\(681\) | −24.4137 | −0.935533 | ||||||||
\(682\) | 14.7143 | 0.563440 | ||||||||
\(683\) | −22.0673 | −0.844381 | −0.422190 | − | 0.906507i | \(-0.638739\pi\) | ||||
−0.422190 | + | 0.906507i | \(0.638739\pi\) | |||||||
\(684\) | 5.66531 | 0.216618 | ||||||||
\(685\) | 5.32228 | 0.203354 | ||||||||
\(686\) | −15.1317 | −0.577730 | ||||||||
\(687\) | 23.6112 | 0.900823 | ||||||||
\(688\) | −5.35666 | −0.204221 | ||||||||
\(689\) | −17.4999 | −0.666691 | ||||||||
\(690\) | 6.43977 | 0.245158 | ||||||||
\(691\) | −29.2271 | −1.11185 | −0.555926 | − | 0.831232i | \(-0.687636\pi\) | ||||
−0.555926 | + | 0.831232i | \(0.687636\pi\) | |||||||
\(692\) | −0.678924 | −0.0258088 | ||||||||
\(693\) | 7.99281 | 0.303622 | ||||||||
\(694\) | 10.9168 | 0.414395 | ||||||||
\(695\) | 35.3065 | 1.33925 | ||||||||
\(696\) | 4.46515 | 0.169251 | ||||||||
\(697\) | −4.82144 | −0.182625 | ||||||||
\(698\) | 21.5336 | 0.815059 | ||||||||
\(699\) | 29.0959 | 1.10051 | ||||||||
\(700\) | 0.934352 | 0.0353152 | ||||||||
\(701\) | −12.5663 | −0.474622 | −0.237311 | − | 0.971434i | \(-0.576266\pi\) | ||||
−0.237311 | + | 0.971434i | \(0.576266\pi\) | |||||||
\(702\) | 12.6919 | 0.479023 | ||||||||
\(703\) | 11.3466 | 0.427946 | ||||||||
\(704\) | 2.12624 | 0.0801356 | ||||||||
\(705\) | 7.64044 | 0.287756 | ||||||||
\(706\) | 28.6488 | 1.07821 | ||||||||
\(707\) | 4.25919 | 0.160183 | ||||||||
\(708\) | 11.1565 | 0.419286 | ||||||||
\(709\) | 42.0306 | 1.57849 | 0.789247 | − | 0.614076i | \(-0.210471\pi\) | ||||
0.789247 | + | 0.614076i | \(0.210471\pi\) | |||||||
\(710\) | −12.5790 | −0.472081 | ||||||||
\(711\) | −17.5002 | −0.656308 | ||||||||
\(712\) | 9.85193 | 0.369217 | ||||||||
\(713\) | 15.5926 | 0.583949 | ||||||||
\(714\) | 7.68260 | 0.287514 | ||||||||
\(715\) | 10.3959 | 0.388785 | ||||||||
\(716\) | 4.62412 | 0.172811 | ||||||||
\(717\) | 15.9386 | 0.595240 | ||||||||
\(718\) | 34.1295 | 1.27370 | ||||||||
\(719\) | −51.4835 | −1.92001 | −0.960006 | − | 0.279980i | \(-0.909672\pi\) | ||||
−0.960006 | + | 0.279980i | \(0.909672\pi\) | |||||||
\(720\) | −2.72217 | −0.101449 | ||||||||
\(721\) | 6.27694 | 0.233766 | ||||||||
\(722\) | −1.30280 | −0.0484852 | ||||||||
\(723\) | −0.194212 | −0.00722281 | ||||||||
\(724\) | −20.9925 | −0.780181 | ||||||||
\(725\) | 1.05705 | 0.0392578 | ||||||||
\(726\) | 8.55311 | 0.317436 | ||||||||
\(727\) | −17.0735 | −0.633220 | −0.316610 | − | 0.948556i | \(-0.602545\pi\) | ||||
−0.316610 | + | 0.948556i | \(0.602545\pi\) | |||||||
\(728\) | 6.75184 | 0.250240 | ||||||||
\(729\) | 26.8431 | 0.994190 | ||||||||
\(730\) | 6.81879 | 0.252375 | ||||||||
\(731\) | −10.4268 | −0.385650 | ||||||||
\(732\) | −10.0988 | −0.373264 | ||||||||
\(733\) | 38.9649 | 1.43920 | 0.719601 | − | 0.694387i | \(-0.244325\pi\) | ||||
0.719601 | + | 0.694387i | \(0.244325\pi\) | |||||||
\(734\) | −7.10430 | −0.262225 | ||||||||
\(735\) | 5.54157 | 0.204404 | ||||||||
\(736\) | 2.25316 | 0.0830524 | ||||||||
\(737\) | 0.242059 | 0.00891637 | ||||||||
\(738\) | −3.11433 | −0.114640 | ||||||||
\(739\) | 36.0084 | 1.32459 | 0.662295 | − | 0.749243i | \(-0.269583\pi\) | ||||
0.662295 | + | 0.749243i | \(0.269583\pi\) | |||||||
\(740\) | −5.45204 | −0.200421 | ||||||||
\(741\) | −13.4328 | −0.493467 | ||||||||
\(742\) | −23.1684 | −0.850539 | ||||||||
\(743\) | 20.1384 | 0.738807 | 0.369404 | − | 0.929269i | \(-0.379562\pi\) | ||||
0.369404 | + | 0.929269i | \(0.379562\pi\) | |||||||
\(744\) | 9.13560 | 0.334927 | ||||||||
\(745\) | −35.0168 | −1.28292 | ||||||||
\(746\) | 30.3597 | 1.11155 | ||||||||
\(747\) | −10.1656 | −0.371939 | ||||||||
\(748\) | 4.13875 | 0.151328 | ||||||||
\(749\) | −38.8737 | −1.42041 | ||||||||
\(750\) | 15.1837 | 0.554432 | ||||||||
\(751\) | −4.64736 | −0.169585 | −0.0847924 | − | 0.996399i | \(-0.527023\pi\) | ||||
−0.0847924 | + | 0.996399i | \(0.527023\pi\) | |||||||
\(752\) | 2.67325 | 0.0974834 | ||||||||
\(753\) | −33.6371 | −1.22580 | ||||||||
\(754\) | 7.63848 | 0.278177 | ||||||||
\(755\) | 30.6024 | 1.11373 | ||||||||
\(756\) | 16.8030 | 0.611119 | ||||||||
\(757\) | 15.3542 | 0.558056 | 0.279028 | − | 0.960283i | \(-0.409988\pi\) | ||||
0.279028 | + | 0.960283i | \(0.409988\pi\) | |||||||
\(758\) | −6.33979 | −0.230272 | ||||||||
\(759\) | −6.32430 | −0.229557 | ||||||||
\(760\) | 9.75547 | 0.353868 | ||||||||
\(761\) | −16.6942 | −0.605166 | −0.302583 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302583 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(762\) | 5.34947 | 0.193791 | ||||||||
\(763\) | 2.74195 | 0.0992653 | ||||||||
\(764\) | 17.6068 | 0.636992 | ||||||||
\(765\) | −5.29875 | −0.191577 | ||||||||
\(766\) | −13.3979 | −0.484085 | ||||||||
\(767\) | 19.0853 | 0.689129 | ||||||||
\(768\) | 1.32011 | 0.0476352 | ||||||||
\(769\) | 7.45227 | 0.268736 | 0.134368 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134368 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(770\) | 13.7633 | 0.495996 | ||||||||
\(771\) | 28.7742 | 1.03628 | ||||||||
\(772\) | 2.55233 | 0.0918603 | ||||||||
\(773\) | 15.6868 | 0.564215 | 0.282108 | − | 0.959383i | \(-0.408966\pi\) | ||||
0.282108 | + | 0.959383i | \(0.408966\pi\) | |||||||
\(774\) | −6.73504 | −0.242086 | ||||||||
\(775\) | 2.16270 | 0.0776866 | ||||||||
\(776\) | 15.6858 | 0.563087 | ||||||||
\(777\) | 9.93893 | 0.356557 | ||||||||
\(778\) | 16.0931 | 0.576966 | ||||||||
\(779\) | 11.1608 | 0.399879 | ||||||||
\(780\) | 6.45445 | 0.231106 | ||||||||
\(781\) | 12.3534 | 0.442040 | ||||||||
\(782\) | 4.38580 | 0.156836 | ||||||||
\(783\) | 19.0096 | 0.679346 | ||||||||
\(784\) | 1.93889 | 0.0692462 | ||||||||
\(785\) | −46.2074 | −1.64921 | ||||||||
\(786\) | 21.4807 | 0.766192 | ||||||||
\(787\) | −41.3291 | −1.47322 | −0.736611 | − | 0.676317i | \(-0.763575\pi\) | ||||
−0.736611 | + | 0.676317i | \(0.763575\pi\) | |||||||
\(788\) | −12.9771 | −0.462289 | ||||||||
\(789\) | −24.3229 | −0.865920 | ||||||||
\(790\) | −30.1347 | −1.07214 | ||||||||
\(791\) | −51.3080 | −1.82430 | ||||||||
\(792\) | 2.67336 | 0.0949937 | ||||||||
\(793\) | −17.2760 | −0.613488 | ||||||||
\(794\) | −4.16939 | −0.147966 | ||||||||
\(795\) | −22.1479 | −0.785506 | ||||||||
\(796\) | 16.5052 | 0.585012 | ||||||||
\(797\) | −50.3649 | −1.78402 | −0.892008 | − | 0.452021i | \(-0.850703\pi\) | ||||
−0.892008 | + | 0.452021i | \(0.850703\pi\) | |||||||
\(798\) | −17.7840 | −0.629546 | ||||||||
\(799\) | 5.20352 | 0.184087 | ||||||||
\(800\) | 0.312513 | 0.0110490 | ||||||||
\(801\) | 12.3870 | 0.437674 | ||||||||
\(802\) | 30.2228 | 1.06720 | ||||||||
\(803\) | −6.69652 | −0.236315 | ||||||||
\(804\) | 0.150286 | 0.00530018 | ||||||||
\(805\) | 14.5849 | 0.514050 | ||||||||
\(806\) | 15.6282 | 0.550479 | ||||||||
\(807\) | 22.6124 | 0.795994 | ||||||||
\(808\) | 1.42458 | 0.0501164 | ||||||||
\(809\) | 55.1186 | 1.93787 | 0.968933 | − | 0.247324i | \(-0.0795512\pi\) | ||||
0.968933 | + | 0.247324i | \(0.0795512\pi\) | |||||||
\(810\) | 7.89639 | 0.277451 | ||||||||
\(811\) | 2.90379 | 0.101966 | 0.0509830 | − | 0.998700i | \(-0.483765\pi\) | ||||
0.0509830 | + | 0.998700i | \(0.483765\pi\) | |||||||
\(812\) | 10.1127 | 0.354888 | ||||||||
\(813\) | 12.2548 | 0.429794 | ||||||||
\(814\) | 5.35428 | 0.187667 | ||||||||
\(815\) | −29.1962 | −1.02270 | ||||||||
\(816\) | 2.56961 | 0.0899542 | ||||||||
\(817\) | 24.1364 | 0.844426 | ||||||||
\(818\) | −11.3240 | −0.395935 | ||||||||
\(819\) | 8.48921 | 0.296637 | ||||||||
\(820\) | −5.36277 | −0.187276 | ||||||||
\(821\) | 4.44201 | 0.155027 | 0.0775136 | − | 0.996991i | \(-0.475302\pi\) | ||||
0.0775136 | + | 0.996991i | \(0.475302\pi\) | |||||||
\(822\) | −3.24516 | −0.113188 | ||||||||
\(823\) | 0.174912 | 0.00609705 | 0.00304852 | − | 0.999995i | \(-0.499030\pi\) | ||||
0.00304852 | + | 0.999995i | \(0.499030\pi\) | |||||||
\(824\) | 2.09945 | 0.0731379 | ||||||||
\(825\) | −0.877182 | −0.0305395 | ||||||||
\(826\) | 25.2674 | 0.879164 | ||||||||
\(827\) | −6.21409 | −0.216085 | −0.108043 | − | 0.994146i | \(-0.534458\pi\) | ||||
−0.108043 | + | 0.994146i | \(0.534458\pi\) | |||||||
\(828\) | 2.83294 | 0.0984513 | ||||||||
\(829\) | −15.7564 | −0.547244 | −0.273622 | − | 0.961837i | \(-0.588222\pi\) | ||||
−0.273622 | + | 0.961837i | \(0.588222\pi\) | |||||||
\(830\) | −17.5048 | −0.607599 | ||||||||
\(831\) | 3.77568 | 0.130977 | ||||||||
\(832\) | 2.25829 | 0.0782922 | ||||||||
\(833\) | 3.77409 | 0.130764 | ||||||||
\(834\) | −21.5275 | −0.745436 | ||||||||
\(835\) | −10.2403 | −0.354381 | ||||||||
\(836\) | −9.58054 | −0.331350 | ||||||||
\(837\) | 38.8932 | 1.34434 | ||||||||
\(838\) | 24.0175 | 0.829670 | ||||||||
\(839\) | −48.2103 | −1.66440 | −0.832202 | − | 0.554472i | \(-0.812920\pi\) | ||||
−0.832202 | + | 0.554472i | \(0.812920\pi\) | |||||||
\(840\) | 8.54517 | 0.294836 | ||||||||
\(841\) | −17.5593 | −0.605492 | ||||||||
\(842\) | −3.70463 | −0.127670 | ||||||||
\(843\) | 30.1948 | 1.03996 | ||||||||
\(844\) | −11.7135 | −0.403194 | ||||||||
\(845\) | −17.1042 | −0.588404 | ||||||||
\(846\) | 3.36113 | 0.115558 | ||||||||
\(847\) | 19.3712 | 0.665603 | ||||||||
\(848\) | −7.74916 | −0.266107 | ||||||||
\(849\) | −24.7560 | −0.849624 | ||||||||
\(850\) | 0.608312 | 0.0208649 | ||||||||
\(851\) | 5.67388 | 0.194498 | ||||||||
\(852\) | 7.66980 | 0.262763 | ||||||||
\(853\) | 49.3341 | 1.68917 | 0.844583 | − | 0.535424i | \(-0.179848\pi\) | ||||
0.844583 | + | 0.535424i | \(0.179848\pi\) | |||||||
\(854\) | −22.8720 | −0.782664 | ||||||||
\(855\) | 12.2657 | 0.419479 | ||||||||
\(856\) | −13.0021 | −0.444403 | ||||||||
\(857\) | 35.4657 | 1.21148 | 0.605742 | − | 0.795661i | \(-0.292876\pi\) | ||||
0.605742 | + | 0.795661i | \(0.292876\pi\) | |||||||
\(858\) | −6.33871 | −0.216400 | ||||||||
\(859\) | −23.7784 | −0.811309 | −0.405655 | − | 0.914026i | \(-0.632956\pi\) | ||||
−0.405655 | + | 0.914026i | \(0.632956\pi\) | |||||||
\(860\) | −11.5975 | −0.395471 | ||||||||
\(861\) | 9.77620 | 0.333172 | ||||||||
\(862\) | 7.26122 | 0.247318 | ||||||||
\(863\) | −18.7622 | −0.638673 | −0.319336 | − | 0.947641i | \(-0.603460\pi\) | ||||
−0.319336 | + | 0.947641i | \(0.603460\pi\) | |||||||
\(864\) | 5.62011 | 0.191200 | ||||||||
\(865\) | −1.46991 | −0.0499785 | ||||||||
\(866\) | −19.3649 | −0.658046 | ||||||||
\(867\) | −17.4400 | −0.592295 | ||||||||
\(868\) | 20.6905 | 0.702280 | ||||||||
\(869\) | 29.5943 | 1.00392 | ||||||||
\(870\) | 9.66731 | 0.327753 | ||||||||
\(871\) | 0.257093 | 0.00871126 | ||||||||
\(872\) | 0.917102 | 0.0310570 | ||||||||
\(873\) | 19.7220 | 0.667490 | ||||||||
\(874\) | −10.1524 | −0.343410 | ||||||||
\(875\) | 34.3884 | 1.16254 | ||||||||
\(876\) | −4.15763 | −0.140473 | ||||||||
\(877\) | 31.2812 | 1.05629 | 0.528146 | − | 0.849154i | \(-0.322887\pi\) | ||||
0.528146 | + | 0.849154i | \(0.322887\pi\) | |||||||
\(878\) | −7.22422 | −0.243806 | ||||||||
\(879\) | −21.9689 | −0.740994 | ||||||||
\(880\) | 4.60343 | 0.155182 | ||||||||
\(881\) | 41.1348 | 1.38587 | 0.692934 | − | 0.721001i | \(-0.256318\pi\) | ||||
0.692934 | + | 0.721001i | \(0.256318\pi\) | |||||||
\(882\) | 2.43781 | 0.0820853 | ||||||||
\(883\) | −9.90735 | −0.333409 | −0.166704 | − | 0.986007i | \(-0.553313\pi\) | ||||
−0.166704 | + | 0.986007i | \(0.553313\pi\) | |||||||
\(884\) | 4.39580 | 0.147847 | ||||||||
\(885\) | 24.1544 | 0.811943 | ||||||||
\(886\) | −25.4666 | −0.855567 | ||||||||
\(887\) | −10.1703 | −0.341484 | −0.170742 | − | 0.985316i | \(-0.554616\pi\) | ||||
−0.170742 | + | 0.985316i | \(0.554616\pi\) | |||||||
\(888\) | 3.32428 | 0.111556 | ||||||||
\(889\) | 12.1156 | 0.406343 | ||||||||
\(890\) | 21.3300 | 0.714984 | ||||||||
\(891\) | −7.75480 | −0.259795 | ||||||||
\(892\) | 0.245128 | 0.00820751 | ||||||||
\(893\) | −12.0453 | −0.403081 | ||||||||
\(894\) | 21.3509 | 0.714080 | ||||||||
\(895\) | 10.0115 | 0.334647 | ||||||||
\(896\) | 2.98980 | 0.0998822 | ||||||||
\(897\) | −6.71707 | −0.224277 | ||||||||
\(898\) | −9.85257 | −0.328784 | ||||||||
\(899\) | 23.4075 | 0.780684 | ||||||||
\(900\) | 0.392929 | 0.0130976 | ||||||||
\(901\) | −15.0838 | −0.502516 | ||||||||
\(902\) | 5.26661 | 0.175359 | ||||||||
\(903\) | 21.1420 | 0.703560 | ||||||||
\(904\) | −17.1610 | −0.570767 | ||||||||
\(905\) | −45.4501 | −1.51081 | ||||||||
\(906\) | −18.6592 | −0.619911 | ||||||||
\(907\) | 18.2885 | 0.607258 | 0.303629 | − | 0.952790i | \(-0.401802\pi\) | ||||
0.303629 | + | 0.952790i | \(0.401802\pi\) | |||||||
\(908\) | −18.4937 | −0.613735 | ||||||||
\(909\) | 1.79115 | 0.0594086 | ||||||||
\(910\) | 14.6181 | 0.484586 | ||||||||
\(911\) | −31.1506 | −1.03207 | −0.516033 | − | 0.856569i | \(-0.672592\pi\) | ||||
−0.516033 | + | 0.856569i | \(0.672592\pi\) | |||||||
\(912\) | −5.94822 | −0.196965 | ||||||||
\(913\) | 17.1909 | 0.568935 | ||||||||
\(914\) | 15.4524 | 0.511121 | ||||||||
\(915\) | −21.8646 | −0.722821 | ||||||||
\(916\) | 17.8858 | 0.590964 | ||||||||
\(917\) | 48.6499 | 1.60656 | ||||||||
\(918\) | 10.9396 | 0.361062 | ||||||||
\(919\) | −24.3536 | −0.803353 | −0.401676 | − | 0.915782i | \(-0.631572\pi\) | ||||
−0.401676 | + | 0.915782i | \(0.631572\pi\) | |||||||
\(920\) | 4.87822 | 0.160830 | ||||||||
\(921\) | 19.0801 | 0.628712 | ||||||||
\(922\) | −4.28239 | −0.141033 | ||||||||
\(923\) | 13.1207 | 0.431872 | ||||||||
\(924\) | −8.39195 | −0.276075 | ||||||||
\(925\) | 0.786969 | 0.0258754 | ||||||||
\(926\) | −15.4021 | −0.506145 | ||||||||
\(927\) | 2.63968 | 0.0866986 | ||||||||
\(928\) | 3.38241 | 0.111033 | ||||||||
\(929\) | −41.4128 | −1.35871 | −0.679355 | − | 0.733810i | \(-0.737740\pi\) | ||||
−0.679355 | + | 0.733810i | \(0.737740\pi\) | |||||||
\(930\) | 19.7791 | 0.648583 | ||||||||
\(931\) | −8.73639 | −0.286324 | ||||||||
\(932\) | 22.0406 | 0.721963 | ||||||||
\(933\) | −28.3419 | −0.927872 | ||||||||
\(934\) | −1.92711 | −0.0630571 | ||||||||
\(935\) | 8.96065 | 0.293045 | ||||||||
\(936\) | 2.83939 | 0.0928085 | ||||||||
\(937\) | 20.8122 | 0.679904 | 0.339952 | − | 0.940443i | \(-0.389589\pi\) | ||||
0.339952 | + | 0.940443i | \(0.389589\pi\) | |||||||
\(938\) | 0.340370 | 0.0111135 | ||||||||
\(939\) | −2.67390 | −0.0872596 | ||||||||
\(940\) | 5.78775 | 0.188776 | ||||||||
\(941\) | −30.2940 | −0.987555 | −0.493778 | − | 0.869588i | \(-0.664384\pi\) | ||||
−0.493778 | + | 0.869588i | \(0.664384\pi\) | |||||||
\(942\) | 28.1741 | 0.917963 | ||||||||
\(943\) | 5.58098 | 0.181742 | ||||||||
\(944\) | 8.45119 | 0.275063 | ||||||||
\(945\) | 36.3795 | 1.18343 | ||||||||
\(946\) | 11.3895 | 0.370306 | ||||||||
\(947\) | 53.3704 | 1.73431 | 0.867153 | − | 0.498042i | \(-0.165947\pi\) | ||||
0.867153 | + | 0.498042i | \(0.165947\pi\) | |||||||
\(948\) | 18.3741 | 0.596762 | ||||||||
\(949\) | −7.11242 | −0.230879 | ||||||||
\(950\) | −1.40814 | −0.0456862 | ||||||||
\(951\) | 38.2038 | 1.23884 | ||||||||
\(952\) | 5.81969 | 0.188617 | ||||||||
\(953\) | 37.1666 | 1.20395 | 0.601973 | − | 0.798517i | \(-0.294382\pi\) | ||||
0.601973 | + | 0.798517i | \(0.294382\pi\) | |||||||
\(954\) | −9.74316 | −0.315447 | ||||||||
\(955\) | 38.1198 | 1.23353 | ||||||||
\(956\) | 12.0738 | 0.390493 | ||||||||
\(957\) | −9.49397 | −0.306896 | ||||||||
\(958\) | −14.1139 | −0.456000 | ||||||||
\(959\) | −7.34970 | −0.237334 | ||||||||
\(960\) | 2.85811 | 0.0922451 | ||||||||
\(961\) | 16.8913 | 0.544880 | ||||||||
\(962\) | 5.68681 | 0.183350 | ||||||||
\(963\) | −16.3478 | −0.526801 | ||||||||
\(964\) | −0.147118 | −0.00473836 | ||||||||
\(965\) | 5.52595 | 0.177886 | ||||||||
\(966\) | −8.89287 | −0.286123 | ||||||||
\(967\) | 23.8872 | 0.768161 | 0.384080 | − | 0.923300i | \(-0.374519\pi\) | ||||
0.384080 | + | 0.923300i | \(0.374519\pi\) | |||||||
\(968\) | 6.47911 | 0.208246 | ||||||||
\(969\) | −11.5783 | −0.371948 | ||||||||
\(970\) | 33.9607 | 1.09041 | ||||||||
\(971\) | −48.1383 | −1.54483 | −0.772417 | − | 0.635116i | \(-0.780952\pi\) | ||||
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(972\) | 12.0457 | 0.386365 | ||||||||
\(973\) | −48.7558 | −1.56304 | ||||||||
\(974\) | 20.0385 | 0.642075 | ||||||||
\(975\) | −0.931660 | −0.0298370 | ||||||||
\(976\) | −7.65002 | −0.244871 | ||||||||
\(977\) | 13.3321 | 0.426531 | 0.213266 | − | 0.976994i | \(-0.431590\pi\) | ||||
0.213266 | + | 0.976994i | \(0.431590\pi\) | |||||||
\(978\) | 17.8019 | 0.569240 | ||||||||
\(979\) | −20.9476 | −0.669487 | ||||||||
\(980\) | 4.19782 | 0.134095 | ||||||||
\(981\) | 1.15309 | 0.0368153 | ||||||||
\(982\) | −16.3461 | −0.521626 | ||||||||
\(983\) | −46.9158 | −1.49638 | −0.748192 | − | 0.663483i | \(-0.769078\pi\) | ||||
−0.748192 | + | 0.663483i | \(0.769078\pi\) | |||||||
\(984\) | 3.26985 | 0.104239 | ||||||||
\(985\) | −28.0961 | −0.895217 | ||||||||
\(986\) | 6.58392 | 0.209675 | ||||||||
\(987\) | −10.5509 | −0.335840 | ||||||||
\(988\) | −10.1756 | −0.323727 | ||||||||
\(989\) | 12.0694 | 0.383785 | ||||||||
\(990\) | 5.78799 | 0.183954 | ||||||||
\(991\) | 5.15628 | 0.163795 | 0.0818973 | − | 0.996641i | \(-0.473902\pi\) | ||||
0.0818973 | + | 0.996641i | \(0.473902\pi\) | |||||||
\(992\) | 6.92035 | 0.219721 | ||||||||
\(993\) | 1.18423 | 0.0375803 | ||||||||
\(994\) | 17.3707 | 0.550965 | ||||||||
\(995\) | 35.7348 | 1.13287 | ||||||||
\(996\) | 10.6732 | 0.338194 | ||||||||
\(997\) | 4.46240 | 0.141326 | 0.0706628 | − | 0.997500i | \(-0.477489\pi\) | ||||
0.0706628 | + | 0.997500i | \(0.477489\pi\) | |||||||
\(998\) | −21.2430 | −0.672434 | ||||||||
\(999\) | 14.1525 | 0.447766 |
(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 | 4006.2.a.g.1.26 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.g.1.26 | ✓ | 40 | 1.1 | even | 1 | trivial |