Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3179,2,Mod(1,3179)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3179, 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("3179.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3179 = 11 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3179.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: | \(25.3844428026\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 187) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 3179.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40039 | −1.69733 | −0.848665 | − | 0.528931i | \(-0.822593\pi\) | ||||
−0.848665 | + | 0.528931i | \(0.822593\pi\) | |||||||
\(3\) | 1.98044 | 1.14341 | 0.571703 | − | 0.820461i | \(-0.306283\pi\) | ||||
0.571703 | + | 0.820461i | \(0.306283\pi\) | |||||||
\(4\) | 3.76185 | 1.88093 | ||||||||
\(5\) | 1.54647 | 0.691601 | 0.345800 | − | 0.938308i | \(-0.387607\pi\) | ||||
0.345800 | + | 0.938308i | \(0.387607\pi\) | |||||||
\(6\) | −4.75381 | −1.94074 | ||||||||
\(7\) | 3.54271 | 1.33902 | 0.669509 | − | 0.742804i | \(-0.266504\pi\) | ||||
0.669509 | + | 0.742804i | \(0.266504\pi\) | |||||||
\(8\) | −4.22913 | −1.49522 | ||||||||
\(9\) | 0.922127 | 0.307376 | ||||||||
\(10\) | −3.71212 | −1.17387 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 7.45011 | 2.15066 | ||||||||
\(13\) | 4.25413 | 1.17988 | 0.589941 | − | 0.807446i | \(-0.299151\pi\) | ||||
0.589941 | + | 0.807446i | \(0.299151\pi\) | |||||||
\(14\) | −8.50387 | −2.27276 | ||||||||
\(15\) | 3.06268 | 0.790780 | ||||||||
\(16\) | 2.62783 | 0.656958 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −2.21346 | −0.521718 | ||||||||
\(19\) | −5.26313 | −1.20744 | −0.603722 | − | 0.797195i | \(-0.706316\pi\) | ||||
−0.603722 | + | 0.797195i | \(0.706316\pi\) | |||||||
\(20\) | 5.81758 | 1.30085 | ||||||||
\(21\) | 7.01611 | 1.53104 | ||||||||
\(22\) | 2.40039 | 0.511764 | ||||||||
\(23\) | 2.07684 | 0.433050 | 0.216525 | − | 0.976277i | \(-0.430528\pi\) | ||||
0.216525 | + | 0.976277i | \(0.430528\pi\) | |||||||
\(24\) | −8.37552 | −1.70965 | ||||||||
\(25\) | −2.60844 | −0.521689 | ||||||||
\(26\) | −10.2115 | −2.00265 | ||||||||
\(27\) | −4.11510 | −0.791950 | ||||||||
\(28\) | 13.3272 | 2.51860 | ||||||||
\(29\) | 4.52834 | 0.840892 | 0.420446 | − | 0.907318i | \(-0.361874\pi\) | ||||
0.420446 | + | 0.907318i | \(0.361874\pi\) | |||||||
\(30\) | −7.35161 | −1.34221 | ||||||||
\(31\) | 4.96669 | 0.892044 | 0.446022 | − | 0.895022i | \(-0.352840\pi\) | ||||
0.446022 | + | 0.895022i | \(0.352840\pi\) | |||||||
\(32\) | 2.15044 | 0.380148 | ||||||||
\(33\) | −1.98044 | −0.344750 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.47868 | 0.926066 | ||||||||
\(36\) | 3.46891 | 0.578151 | ||||||||
\(37\) | −3.82293 | −0.628486 | −0.314243 | − | 0.949343i | \(-0.601751\pi\) | ||||
−0.314243 | + | 0.949343i | \(0.601751\pi\) | |||||||
\(38\) | 12.6335 | 2.04943 | ||||||||
\(39\) | 8.42503 | 1.34908 | ||||||||
\(40\) | −6.54020 | −1.03410 | ||||||||
\(41\) | −4.88476 | −0.762871 | −0.381436 | − | 0.924395i | \(-0.624570\pi\) | ||||
−0.381436 | + | 0.924395i | \(0.624570\pi\) | |||||||
\(42\) | −16.8414 | −2.59868 | ||||||||
\(43\) | 8.31739 | 1.26839 | 0.634195 | − | 0.773173i | \(-0.281332\pi\) | ||||
0.634195 | + | 0.773173i | \(0.281332\pi\) | |||||||
\(44\) | −3.76185 | −0.567121 | ||||||||
\(45\) | 1.42604 | 0.212581 | ||||||||
\(46\) | −4.98521 | −0.735029 | ||||||||
\(47\) | −0.821811 | −0.119873 | −0.0599367 | − | 0.998202i | \(-0.519090\pi\) | ||||
−0.0599367 | + | 0.998202i | \(0.519090\pi\) | |||||||
\(48\) | 5.20425 | 0.751169 | ||||||||
\(49\) | 5.55079 | 0.792970 | ||||||||
\(50\) | 6.26127 | 0.885477 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.0034 | 2.21927 | ||||||||
\(53\) | 2.23371 | 0.306824 | 0.153412 | − | 0.988162i | \(-0.450974\pi\) | ||||
0.153412 | + | 0.988162i | \(0.450974\pi\) | |||||||
\(54\) | 9.87782 | 1.34420 | ||||||||
\(55\) | −1.54647 | −0.208525 | ||||||||
\(56\) | −14.9826 | −2.00213 | ||||||||
\(57\) | −10.4233 | −1.38060 | ||||||||
\(58\) | −10.8698 | −1.42727 | ||||||||
\(59\) | 1.81700 | 0.236553 | 0.118276 | − | 0.992981i | \(-0.462263\pi\) | ||||
0.118276 | + | 0.992981i | \(0.462263\pi\) | |||||||
\(60\) | 11.5213 | 1.48740 | ||||||||
\(61\) | 11.2904 | 1.44558 | 0.722791 | − | 0.691067i | \(-0.242859\pi\) | ||||
0.722791 | + | 0.691067i | \(0.242859\pi\) | |||||||
\(62\) | −11.9220 | −1.51409 | ||||||||
\(63\) | 3.26683 | 0.411582 | ||||||||
\(64\) | −10.4176 | −1.30219 | ||||||||
\(65\) | 6.57886 | 0.816008 | ||||||||
\(66\) | 4.75381 | 0.585154 | ||||||||
\(67\) | 15.5881 | 1.90439 | 0.952194 | − | 0.305493i | \(-0.0988211\pi\) | ||||
0.952194 | + | 0.305493i | \(0.0988211\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.11304 | 0.495152 | ||||||||
\(70\) | −13.1509 | −1.57184 | ||||||||
\(71\) | −14.5263 | −1.72395 | −0.861976 | − | 0.506949i | \(-0.830773\pi\) | ||||
−0.861976 | + | 0.506949i | \(0.830773\pi\) | |||||||
\(72\) | −3.89979 | −0.459595 | ||||||||
\(73\) | 14.6099 | 1.70996 | 0.854979 | − | 0.518662i | \(-0.173570\pi\) | ||||
0.854979 | + | 0.518662i | \(0.173570\pi\) | |||||||
\(74\) | 9.17651 | 1.06675 | ||||||||
\(75\) | −5.16585 | −0.596502 | ||||||||
\(76\) | −19.7991 | −2.27111 | ||||||||
\(77\) | −3.54271 | −0.403729 | ||||||||
\(78\) | −20.2233 | −2.28984 | ||||||||
\(79\) | −1.80220 | −0.202763 | −0.101382 | − | 0.994848i | \(-0.532326\pi\) | ||||
−0.101382 | + | 0.994848i | \(0.532326\pi\) | |||||||
\(80\) | 4.06385 | 0.454353 | ||||||||
\(81\) | −10.9161 | −1.21290 | ||||||||
\(82\) | 11.7253 | 1.29484 | ||||||||
\(83\) | 16.7121 | 1.83439 | 0.917196 | − | 0.398436i | \(-0.130447\pi\) | ||||
0.917196 | + | 0.398436i | \(0.130447\pi\) | |||||||
\(84\) | 26.3936 | 2.87978 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.9649 | −2.15288 | ||||||||
\(87\) | 8.96809 | 0.961480 | ||||||||
\(88\) | 4.22913 | 0.450827 | ||||||||
\(89\) | −1.75856 | −0.186407 | −0.0932036 | − | 0.995647i | \(-0.529711\pi\) | ||||
−0.0932036 | + | 0.995647i | \(0.529711\pi\) | |||||||
\(90\) | −3.42304 | −0.360820 | ||||||||
\(91\) | 15.0711 | 1.57988 | ||||||||
\(92\) | 7.81275 | 0.814536 | ||||||||
\(93\) | 9.83622 | 1.01997 | ||||||||
\(94\) | 1.97266 | 0.203465 | ||||||||
\(95\) | −8.13925 | −0.835069 | ||||||||
\(96\) | 4.25881 | 0.434663 | ||||||||
\(97\) | 10.4058 | 1.05655 | 0.528273 | − | 0.849075i | \(-0.322840\pi\) | ||||
0.528273 | + | 0.849075i | \(0.322840\pi\) | |||||||
\(98\) | −13.3240 | −1.34593 | ||||||||
\(99\) | −0.922127 | −0.0926772 | ||||||||
\(100\) | −9.81258 | −0.981258 | ||||||||
\(101\) | 8.53318 | 0.849083 | 0.424542 | − | 0.905408i | \(-0.360435\pi\) | ||||
0.424542 | + | 0.905408i | \(0.360435\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.63774 | 0.949634 | 0.474817 | − | 0.880084i | \(-0.342514\pi\) | ||||
0.474817 | + | 0.880084i | \(0.342514\pi\) | |||||||
\(104\) | −17.9912 | −1.76419 | ||||||||
\(105\) | 10.8502 | 1.05887 | ||||||||
\(106\) | −5.36177 | −0.520781 | ||||||||
\(107\) | −7.06136 | −0.682647 | −0.341323 | − | 0.939946i | \(-0.610875\pi\) | ||||
−0.341323 | + | 0.939946i | \(0.610875\pi\) | |||||||
\(108\) | −15.4804 | −1.48960 | ||||||||
\(109\) | 7.56923 | 0.725001 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(110\) | 3.71212 | 0.353936 | ||||||||
\(111\) | −7.57107 | −0.718615 | ||||||||
\(112\) | 9.30965 | 0.879679 | ||||||||
\(113\) | 2.46444 | 0.231835 | 0.115917 | − | 0.993259i | \(-0.463019\pi\) | ||||
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(114\) | 25.0199 | 2.34333 | ||||||||
\(115\) | 3.21176 | 0.299498 | ||||||||
\(116\) | 17.0350 | 1.58166 | ||||||||
\(117\) | 3.92285 | 0.362667 | ||||||||
\(118\) | −4.36149 | −0.401508 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12.9525 | −1.18239 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −27.1012 | −2.45363 | ||||||||
\(123\) | −9.67396 | −0.872271 | ||||||||
\(124\) | 18.6840 | 1.67787 | ||||||||
\(125\) | −11.7662 | −1.05240 | ||||||||
\(126\) | −7.84165 | −0.698589 | ||||||||
\(127\) | 21.3507 | 1.89457 | 0.947286 | − | 0.320390i | \(-0.103814\pi\) | ||||
0.947286 | + | 0.320390i | \(0.103814\pi\) | |||||||
\(128\) | 20.7053 | 1.83010 | ||||||||
\(129\) | 16.4721 | 1.45028 | ||||||||
\(130\) | −15.7918 | −1.38503 | ||||||||
\(131\) | −8.61944 | −0.753084 | −0.376542 | − | 0.926400i | \(-0.622887\pi\) | ||||
−0.376542 | + | 0.926400i | \(0.622887\pi\) | |||||||
\(132\) | −7.45011 | −0.648449 | ||||||||
\(133\) | −18.6457 | −1.61679 | ||||||||
\(134\) | −37.4174 | −3.23237 | ||||||||
\(135\) | −6.36385 | −0.547713 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.53363 | −0.729077 | −0.364538 | − | 0.931188i | \(-0.618773\pi\) | ||||
−0.364538 | + | 0.931188i | \(0.618773\pi\) | |||||||
\(138\) | −9.87289 | −0.840436 | ||||||||
\(139\) | −18.6190 | −1.57924 | −0.789621 | − | 0.613595i | \(-0.789723\pi\) | ||||
−0.789621 | + | 0.613595i | \(0.789723\pi\) | |||||||
\(140\) | 20.6100 | 1.74186 | ||||||||
\(141\) | −1.62754 | −0.137064 | ||||||||
\(142\) | 34.8687 | 2.92611 | ||||||||
\(143\) | −4.25413 | −0.355748 | ||||||||
\(144\) | 2.42319 | 0.201933 | ||||||||
\(145\) | 7.00292 | 0.581561 | ||||||||
\(146\) | −35.0694 | −2.90236 | ||||||||
\(147\) | 10.9930 | 0.906687 | ||||||||
\(148\) | −14.3813 | −1.18214 | ||||||||
\(149\) | −2.39421 | −0.196141 | −0.0980705 | − | 0.995179i | \(-0.531267\pi\) | ||||
−0.0980705 | + | 0.995179i | \(0.531267\pi\) | |||||||
\(150\) | 12.4000 | 1.01246 | ||||||||
\(151\) | 1.07037 | 0.0871054 | 0.0435527 | − | 0.999051i | \(-0.486132\pi\) | ||||
0.0435527 | + | 0.999051i | \(0.486132\pi\) | |||||||
\(152\) | 22.2584 | 1.80540 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.50387 | 0.685261 | ||||||||
\(155\) | 7.68082 | 0.616938 | ||||||||
\(156\) | 31.6937 | 2.53753 | ||||||||
\(157\) | −5.83648 | −0.465802 | −0.232901 | − | 0.972500i | \(-0.574822\pi\) | ||||
−0.232901 | + | 0.972500i | \(0.574822\pi\) | |||||||
\(158\) | 4.32597 | 0.344156 | ||||||||
\(159\) | 4.42372 | 0.350824 | ||||||||
\(160\) | 3.32559 | 0.262911 | ||||||||
\(161\) | 7.35763 | 0.579862 | ||||||||
\(162\) | 26.2028 | 2.05868 | ||||||||
\(163\) | 7.03397 | 0.550943 | 0.275472 | − | 0.961309i | \(-0.411166\pi\) | ||||
0.275472 | + | 0.961309i | \(0.411166\pi\) | |||||||
\(164\) | −18.3758 | −1.43491 | ||||||||
\(165\) | −3.06268 | −0.238429 | ||||||||
\(166\) | −40.1155 | −3.11357 | ||||||||
\(167\) | 5.17611 | 0.400539 | 0.200270 | − | 0.979741i | \(-0.435818\pi\) | ||||
0.200270 | + | 0.979741i | \(0.435818\pi\) | |||||||
\(168\) | −29.6720 | −2.28925 | ||||||||
\(169\) | 5.09760 | 0.392123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85327 | −0.371139 | ||||||||
\(172\) | 31.2888 | 2.38575 | ||||||||
\(173\) | −17.9115 | −1.36179 | −0.680894 | − | 0.732382i | \(-0.738409\pi\) | ||||
−0.680894 | + | 0.732382i | \(0.738409\pi\) | |||||||
\(174\) | −21.5269 | −1.63195 | ||||||||
\(175\) | −9.24096 | −0.698551 | ||||||||
\(176\) | −2.62783 | −0.198080 | ||||||||
\(177\) | 3.59845 | 0.270476 | ||||||||
\(178\) | 4.22123 | 0.316394 | ||||||||
\(179\) | −21.7082 | −1.62255 | −0.811274 | − | 0.584666i | \(-0.801226\pi\) | ||||
−0.811274 | + | 0.584666i | \(0.801226\pi\) | |||||||
\(180\) | 5.36454 | 0.399849 | ||||||||
\(181\) | 3.10555 | 0.230834 | 0.115417 | − | 0.993317i | \(-0.463180\pi\) | ||||
0.115417 | + | 0.993317i | \(0.463180\pi\) | |||||||
\(182\) | −36.1766 | −2.68158 | ||||||||
\(183\) | 22.3598 | 1.65289 | ||||||||
\(184\) | −8.78321 | −0.647507 | ||||||||
\(185\) | −5.91204 | −0.434661 | ||||||||
\(186\) | −23.6107 | −1.73122 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.09153 | −0.225473 | ||||||||
\(189\) | −14.5786 | −1.06044 | ||||||||
\(190\) | 19.5373 | 1.41739 | ||||||||
\(191\) | 10.8201 | 0.782911 | 0.391456 | − | 0.920197i | \(-0.371972\pi\) | ||||
0.391456 | + | 0.920197i | \(0.371972\pi\) | |||||||
\(192\) | −20.6313 | −1.48894 | ||||||||
\(193\) | 6.73996 | 0.485153 | 0.242576 | − | 0.970132i | \(-0.422008\pi\) | ||||
0.242576 | + | 0.970132i | \(0.422008\pi\) | |||||||
\(194\) | −24.9779 | −1.79331 | ||||||||
\(195\) | 13.0290 | 0.933027 | ||||||||
\(196\) | 20.8813 | 1.49152 | ||||||||
\(197\) | −4.98840 | −0.355408 | −0.177704 | − | 0.984084i | \(-0.556867\pi\) | ||||
−0.177704 | + | 0.984084i | \(0.556867\pi\) | |||||||
\(198\) | 2.21346 | 0.157304 | ||||||||
\(199\) | −14.2143 | −1.00763 | −0.503813 | − | 0.863813i | \(-0.668070\pi\) | ||||
−0.503813 | + | 0.863813i | \(0.668070\pi\) | |||||||
\(200\) | 11.0314 | 0.780041 | ||||||||
\(201\) | 30.8712 | 2.17749 | ||||||||
\(202\) | −20.4829 | −1.44117 | ||||||||
\(203\) | 16.0426 | 1.12597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.55412 | −0.527602 | ||||||||
\(206\) | −23.1343 | −1.61184 | ||||||||
\(207\) | 1.91511 | 0.133109 | ||||||||
\(208\) | 11.1791 | 0.775134 | ||||||||
\(209\) | 5.26313 | 0.364058 | ||||||||
\(210\) | −26.0446 | −1.79725 | ||||||||
\(211\) | −6.83146 | −0.470297 | −0.235148 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235148 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(212\) | 8.40289 | 0.577113 | ||||||||
\(213\) | −28.7684 | −1.97118 | ||||||||
\(214\) | 16.9500 | 1.15868 | ||||||||
\(215\) | 12.8626 | 0.877219 | ||||||||
\(216\) | 17.4033 | 1.18414 | ||||||||
\(217\) | 17.5956 | 1.19446 | ||||||||
\(218\) | −18.1691 | −1.23056 | ||||||||
\(219\) | 28.9340 | 1.95518 | ||||||||
\(220\) | −5.81758 | −0.392221 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 18.1735 | 1.21973 | ||||||||
\(223\) | −12.2401 | −0.819660 | −0.409830 | − | 0.912162i | \(-0.634412\pi\) | ||||
−0.409830 | + | 0.912162i | \(0.634412\pi\) | |||||||
\(224\) | 7.61840 | 0.509025 | ||||||||
\(225\) | −2.40532 | −0.160354 | ||||||||
\(226\) | −5.91560 | −0.393500 | ||||||||
\(227\) | −20.8281 | −1.38241 | −0.691206 | − | 0.722658i | \(-0.742920\pi\) | ||||
−0.691206 | + | 0.722658i | \(0.742920\pi\) | |||||||
\(228\) | −39.2109 | −2.59680 | ||||||||
\(229\) | −22.1240 | −1.46199 | −0.730996 | − | 0.682381i | \(-0.760944\pi\) | ||||
−0.730996 | + | 0.682381i | \(0.760944\pi\) | |||||||
\(230\) | −7.70946 | −0.508347 | ||||||||
\(231\) | −7.01611 | −0.461626 | ||||||||
\(232\) | −19.1509 | −1.25732 | ||||||||
\(233\) | 18.6226 | 1.22001 | 0.610005 | − | 0.792398i | \(-0.291168\pi\) | ||||
0.610005 | + | 0.792398i | \(0.291168\pi\) | |||||||
\(234\) | −9.41634 | −0.615566 | ||||||||
\(235\) | −1.27090 | −0.0829045 | ||||||||
\(236\) | 6.83528 | 0.444939 | ||||||||
\(237\) | −3.56914 | −0.231841 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8188 | −1.54071 | −0.770354 | − | 0.637617i | \(-0.779920\pi\) | ||||
−0.770354 | + | 0.637617i | \(0.779920\pi\) | |||||||
\(240\) | 8.04820 | 0.519509 | ||||||||
\(241\) | −2.73729 | −0.176325 | −0.0881623 | − | 0.996106i | \(-0.528099\pi\) | ||||
−0.0881623 | + | 0.996106i | \(0.528099\pi\) | |||||||
\(242\) | −2.40039 | −0.154303 | ||||||||
\(243\) | −9.27328 | −0.594881 | ||||||||
\(244\) | 42.4726 | 2.71903 | ||||||||
\(245\) | 8.58411 | 0.548419 | ||||||||
\(246\) | 23.2212 | 1.48053 | ||||||||
\(247\) | −22.3900 | −1.42464 | ||||||||
\(248\) | −21.0048 | −1.33380 | ||||||||
\(249\) | 33.0973 | 2.09745 | ||||||||
\(250\) | 28.2434 | 1.78627 | ||||||||
\(251\) | −10.1022 | −0.637645 | −0.318823 | − | 0.947814i | \(-0.603287\pi\) | ||||
−0.318823 | + | 0.947814i | \(0.603287\pi\) | |||||||
\(252\) | 12.2893 | 0.774155 | ||||||||
\(253\) | −2.07684 | −0.130570 | ||||||||
\(254\) | −51.2500 | −3.21571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.8655 | −1.80410 | ||||||||
\(257\) | 3.10755 | 0.193844 | 0.0969219 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969219 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(258\) | −39.5393 | −2.46161 | ||||||||
\(259\) | −13.5435 | −0.841555 | ||||||||
\(260\) | 24.7487 | 1.53485 | ||||||||
\(261\) | 4.17570 | 0.258470 | ||||||||
\(262\) | 20.6900 | 1.27823 | ||||||||
\(263\) | −11.9401 | −0.736260 | −0.368130 | − | 0.929774i | \(-0.620002\pi\) | ||||
−0.368130 | + | 0.929774i | \(0.620002\pi\) | |||||||
\(264\) | 8.37552 | 0.515477 | ||||||||
\(265\) | 3.45436 | 0.212199 | ||||||||
\(266\) | 44.7570 | 2.74423 | ||||||||
\(267\) | −3.48272 | −0.213139 | ||||||||
\(268\) | 58.6401 | 3.58202 | ||||||||
\(269\) | −15.7794 | −0.962089 | −0.481044 | − | 0.876696i | \(-0.659742\pi\) | ||||
−0.481044 | + | 0.876696i | \(0.659742\pi\) | |||||||
\(270\) | 15.2757 | 0.929650 | ||||||||
\(271\) | −29.2332 | −1.77579 | −0.887896 | − | 0.460044i | \(-0.847834\pi\) | ||||
−0.887896 | + | 0.460044i | \(0.847834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 29.8474 | 1.80645 | ||||||||
\(274\) | 20.4840 | 1.23748 | ||||||||
\(275\) | 2.60844 | 0.157295 | ||||||||
\(276\) | 15.4727 | 0.931345 | ||||||||
\(277\) | 19.0156 | 1.14254 | 0.571269 | − | 0.820763i | \(-0.306451\pi\) | ||||
0.571269 | + | 0.820763i | \(0.306451\pi\) | |||||||
\(278\) | 44.6927 | 2.68049 | ||||||||
\(279\) | 4.57992 | 0.274193 | ||||||||
\(280\) | −23.1700 | −1.38467 | ||||||||
\(281\) | 29.6991 | 1.77170 | 0.885850 | − | 0.463973i | \(-0.153576\pi\) | ||||
0.885850 | + | 0.463973i | \(0.153576\pi\) | |||||||
\(282\) | 3.90673 | 0.232643 | ||||||||
\(283\) | 23.7863 | 1.41395 | 0.706975 | − | 0.707238i | \(-0.250059\pi\) | ||||
0.706975 | + | 0.707238i | \(0.250059\pi\) | |||||||
\(284\) | −54.6457 | −3.24263 | ||||||||
\(285\) | −16.1193 | −0.954822 | ||||||||
\(286\) | 10.2115 | 0.603822 | ||||||||
\(287\) | −17.3053 | −1.02150 | ||||||||
\(288\) | 1.98298 | 0.116848 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −16.8097 | −0.987101 | ||||||||
\(291\) | 20.6080 | 1.20806 | ||||||||
\(292\) | 54.9603 | 3.21631 | ||||||||
\(293\) | 7.51115 | 0.438806 | 0.219403 | − | 0.975634i | \(-0.429589\pi\) | ||||
0.219403 | + | 0.975634i | \(0.429589\pi\) | |||||||
\(294\) | −26.3874 | −1.53895 | ||||||||
\(295\) | 2.80992 | 0.163600 | ||||||||
\(296\) | 16.1677 | 0.939727 | ||||||||
\(297\) | 4.11510 | 0.238782 | ||||||||
\(298\) | 5.74702 | 0.332916 | ||||||||
\(299\) | 8.83513 | 0.510949 | ||||||||
\(300\) | −19.4332 | −1.12198 | ||||||||
\(301\) | 29.4661 | 1.69840 | ||||||||
\(302\) | −2.56930 | −0.147847 | ||||||||
\(303\) | 16.8994 | 0.970846 | ||||||||
\(304\) | −13.8306 | −0.793240 | ||||||||
\(305\) | 17.4601 | 0.999765 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.6058 | −0.776525 | −0.388263 | − | 0.921549i | \(-0.626925\pi\) | ||||
−0.388263 | + | 0.921549i | \(0.626925\pi\) | |||||||
\(308\) | −13.3272 | −0.759385 | ||||||||
\(309\) | 19.0869 | 1.08582 | ||||||||
\(310\) | −18.4369 | −1.04715 | ||||||||
\(311\) | 15.6446 | 0.887121 | 0.443561 | − | 0.896244i | \(-0.353715\pi\) | ||||
0.443561 | + | 0.896244i | \(0.353715\pi\) | |||||||
\(312\) | −35.6305 | −2.01718 | ||||||||
\(313\) | 2.93041 | 0.165636 | 0.0828182 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828182 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(314\) | 14.0098 | 0.790620 | ||||||||
\(315\) | 5.05204 | 0.284650 | ||||||||
\(316\) | −6.77961 | −0.381383 | ||||||||
\(317\) | −8.89700 | −0.499705 | −0.249853 | − | 0.968284i | \(-0.580382\pi\) | ||||
−0.249853 | + | 0.968284i | \(0.580382\pi\) | |||||||
\(318\) | −10.6186 | −0.595463 | ||||||||
\(319\) | −4.52834 | −0.253538 | ||||||||
\(320\) | −16.1104 | −0.900599 | ||||||||
\(321\) | −13.9846 | −0.780542 | ||||||||
\(322\) | −17.6612 | −0.984217 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −41.0646 | −2.28137 | ||||||||
\(325\) | −11.0967 | −0.615531 | ||||||||
\(326\) | −16.8842 | −0.935132 | ||||||||
\(327\) | 14.9904 | 0.828969 | ||||||||
\(328\) | 20.6583 | 1.14066 | ||||||||
\(329\) | −2.91144 | −0.160513 | ||||||||
\(330\) | 7.35161 | 0.404693 | ||||||||
\(331\) | 4.00205 | 0.219972 | 0.109986 | − | 0.993933i | \(-0.464919\pi\) | ||||
0.109986 | + | 0.993933i | \(0.464919\pi\) | |||||||
\(332\) | 62.8685 | 3.45036 | ||||||||
\(333\) | −3.52523 | −0.193181 | ||||||||
\(334\) | −12.4247 | −0.679847 | ||||||||
\(335\) | 24.1065 | 1.31708 | ||||||||
\(336\) | 18.4372 | 1.00583 | ||||||||
\(337\) | −29.3932 | −1.60115 | −0.800575 | − | 0.599232i | \(-0.795473\pi\) | ||||
−0.800575 | + | 0.599232i | \(0.795473\pi\) | |||||||
\(338\) | −12.2362 | −0.665563 | ||||||||
\(339\) | 4.88066 | 0.265081 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.96669 | −0.268962 | ||||||||
\(342\) | 11.6497 | 0.629945 | ||||||||
\(343\) | −5.13412 | −0.277216 | ||||||||
\(344\) | −35.1753 | −1.89653 | ||||||||
\(345\) | 6.36068 | 0.342447 | ||||||||
\(346\) | 42.9946 | 2.31140 | ||||||||
\(347\) | −2.77849 | −0.149157 | −0.0745785 | − | 0.997215i | \(-0.523761\pi\) | ||||
−0.0745785 | + | 0.997215i | \(0.523761\pi\) | |||||||
\(348\) | 33.7366 | 1.80847 | ||||||||
\(349\) | −21.4935 | −1.15052 | −0.575261 | − | 0.817970i | \(-0.695100\pi\) | ||||
−0.575261 | + | 0.817970i | \(0.695100\pi\) | |||||||
\(350\) | 22.1819 | 1.18567 | ||||||||
\(351\) | −17.5061 | −0.934409 | ||||||||
\(352\) | −2.15044 | −0.114619 | ||||||||
\(353\) | 7.63990 | 0.406631 | 0.203316 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203316 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(354\) | −8.63766 | −0.459087 | ||||||||
\(355\) | −22.4644 | −1.19229 | ||||||||
\(356\) | −6.61545 | −0.350618 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 52.1081 | 2.75400 | ||||||||
\(359\) | −6.70242 | −0.353740 | −0.176870 | − | 0.984234i | \(-0.556597\pi\) | ||||
−0.176870 | + | 0.984234i | \(0.556597\pi\) | |||||||
\(360\) | −6.03089 | −0.317856 | ||||||||
\(361\) | 8.70052 | 0.457922 | ||||||||
\(362\) | −7.45452 | −0.391801 | ||||||||
\(363\) | 1.98044 | 0.103946 | ||||||||
\(364\) | 56.6954 | 2.97165 | ||||||||
\(365\) | 22.5937 | 1.18261 | ||||||||
\(366\) | −53.6722 | −2.80549 | ||||||||
\(367\) | 37.6850 | 1.96714 | 0.983570 | − | 0.180528i | \(-0.0577806\pi\) | ||||
0.983570 | + | 0.180528i | \(0.0577806\pi\) | |||||||
\(368\) | 5.45758 | 0.284496 | ||||||||
\(369\) | −4.50437 | −0.234488 | ||||||||
\(370\) | 14.1912 | 0.737764 | ||||||||
\(371\) | 7.91338 | 0.410842 | ||||||||
\(372\) | 37.0024 | 1.91849 | ||||||||
\(373\) | −6.79786 | −0.351980 | −0.175990 | − | 0.984392i | \(-0.556313\pi\) | ||||
−0.175990 | + | 0.984392i | \(0.556313\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.3022 | −1.20332 | ||||||||
\(376\) | 3.47554 | 0.179237 | ||||||||
\(377\) | 19.2641 | 0.992154 | ||||||||
\(378\) | 34.9942 | 1.79991 | ||||||||
\(379\) | 24.4279 | 1.25477 | 0.627387 | − | 0.778707i | \(-0.284124\pi\) | ||||
0.627387 | + | 0.778707i | \(0.284124\pi\) | |||||||
\(380\) | −30.6187 | −1.57070 | ||||||||
\(381\) | 42.2838 | 2.16626 | ||||||||
\(382\) | −25.9723 | −1.32886 | ||||||||
\(383\) | 6.27522 | 0.320649 | 0.160324 | − | 0.987064i | \(-0.448746\pi\) | ||||
0.160324 | + | 0.987064i | \(0.448746\pi\) | |||||||
\(384\) | 41.0055 | 2.09255 | ||||||||
\(385\) | −5.47868 | −0.279219 | ||||||||
\(386\) | −16.1785 | −0.823464 | ||||||||
\(387\) | 7.66969 | 0.389872 | ||||||||
\(388\) | 39.1450 | 1.98728 | ||||||||
\(389\) | −17.9748 | −0.911361 | −0.455680 | − | 0.890143i | \(-0.650604\pi\) | ||||
−0.455680 | + | 0.890143i | \(0.650604\pi\) | |||||||
\(390\) | −31.2747 | −1.58365 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −23.4750 | −1.18567 | ||||||||
\(393\) | −17.0702 | −0.861080 | ||||||||
\(394\) | 11.9741 | 0.603245 | ||||||||
\(395\) | −2.78704 | −0.140231 | ||||||||
\(396\) | −3.46891 | −0.174319 | ||||||||
\(397\) | 10.9351 | 0.548818 | 0.274409 | − | 0.961613i | \(-0.411518\pi\) | ||||
0.274409 | + | 0.961613i | \(0.411518\pi\) | |||||||
\(398\) | 34.1199 | 1.71027 | ||||||||
\(399\) | −36.9267 | −1.84865 | ||||||||
\(400\) | −6.85455 | −0.342728 | ||||||||
\(401\) | −29.5780 | −1.47705 | −0.738527 | − | 0.674224i | \(-0.764478\pi\) | ||||
−0.738527 | + | 0.674224i | \(0.764478\pi\) | |||||||
\(402\) | −74.1029 | −3.69591 | ||||||||
\(403\) | 21.1289 | 1.05251 | ||||||||
\(404\) | 32.1006 | 1.59706 | ||||||||
\(405\) | −16.8813 | −0.838839 | ||||||||
\(406\) | −38.5084 | −1.91114 | ||||||||
\(407\) | 3.82293 | 0.189496 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.7932 | 1.47318 | 0.736590 | − | 0.676340i | \(-0.236435\pi\) | ||||
0.736590 | + | 0.676340i | \(0.236435\pi\) | |||||||
\(410\) | 18.1328 | 0.895515 | ||||||||
\(411\) | −16.9003 | −0.833630 | ||||||||
\(412\) | 36.2557 | 1.78619 | ||||||||
\(413\) | 6.43709 | 0.316749 | ||||||||
\(414\) | −4.59699 | −0.225930 | ||||||||
\(415\) | 25.8447 | 1.26867 | ||||||||
\(416\) | 9.14826 | 0.448530 | ||||||||
\(417\) | −36.8737 | −1.80571 | ||||||||
\(418\) | −12.6335 | −0.617927 | ||||||||
\(419\) | 19.0060 | 0.928506 | 0.464253 | − | 0.885703i | \(-0.346323\pi\) | ||||
0.464253 | + | 0.885703i | \(0.346323\pi\) | |||||||
\(420\) | 40.8168 | 1.99165 | ||||||||
\(421\) | −16.8146 | −0.819493 | −0.409747 | − | 0.912199i | \(-0.634383\pi\) | ||||
−0.409747 | + | 0.912199i | \(0.634383\pi\) | |||||||
\(422\) | 16.3981 | 0.798248 | ||||||||
\(423\) | −0.757814 | −0.0368462 | ||||||||
\(424\) | −9.44664 | −0.458770 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 69.0552 | 3.34573 | ||||||||
\(427\) | 39.9984 | 1.93566 | ||||||||
\(428\) | −26.5638 | −1.28401 | ||||||||
\(429\) | −8.42503 | −0.406764 | ||||||||
\(430\) | −30.8751 | −1.48893 | ||||||||
\(431\) | 18.6198 | 0.896886 | 0.448443 | − | 0.893811i | \(-0.351979\pi\) | ||||
0.448443 | + | 0.893811i | \(0.351979\pi\) | |||||||
\(432\) | −10.8138 | −0.520278 | ||||||||
\(433\) | −24.4907 | −1.17695 | −0.588473 | − | 0.808517i | \(-0.700271\pi\) | ||||
−0.588473 | + | 0.808517i | \(0.700271\pi\) | |||||||
\(434\) | −42.2361 | −2.02740 | ||||||||
\(435\) | 13.8688 | 0.664960 | ||||||||
\(436\) | 28.4743 | 1.36367 | ||||||||
\(437\) | −10.9307 | −0.522884 | ||||||||
\(438\) | −69.4527 | −3.31858 | ||||||||
\(439\) | 3.42155 | 0.163302 | 0.0816508 | − | 0.996661i | \(-0.473981\pi\) | ||||
0.0816508 | + | 0.996661i | \(0.473981\pi\) | |||||||
\(440\) | 6.54020 | 0.311792 | ||||||||
\(441\) | 5.11853 | 0.243740 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.33855 | 0.0635962 | 0.0317981 | − | 0.999494i | \(-0.489877\pi\) | ||||
0.0317981 | + | 0.999494i | \(0.489877\pi\) | |||||||
\(444\) | −28.4813 | −1.35166 | ||||||||
\(445\) | −2.71955 | −0.128919 | ||||||||
\(446\) | 29.3811 | 1.39123 | ||||||||
\(447\) | −4.74157 | −0.224269 | ||||||||
\(448\) | −36.9064 | −1.74366 | ||||||||
\(449\) | 35.7885 | 1.68896 | 0.844481 | − | 0.535585i | \(-0.179909\pi\) | ||||
0.844481 | + | 0.535585i | \(0.179909\pi\) | |||||||
\(450\) | 5.77369 | 0.272174 | ||||||||
\(451\) | 4.88476 | 0.230014 | ||||||||
\(452\) | 9.27086 | 0.436064 | ||||||||
\(453\) | 2.11980 | 0.0995967 | ||||||||
\(454\) | 49.9955 | 2.34641 | ||||||||
\(455\) | 23.3070 | 1.09265 | ||||||||
\(456\) | 44.0814 | 2.06430 | ||||||||
\(457\) | −17.3901 | −0.813472 | −0.406736 | − | 0.913546i | \(-0.633333\pi\) | ||||
−0.406736 | + | 0.913546i | \(0.633333\pi\) | |||||||
\(458\) | 53.1061 | 2.48148 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0822 | 0.563334 | ||||||||
\(461\) | 33.1530 | 1.54409 | 0.772044 | − | 0.635569i | \(-0.219234\pi\) | ||||
0.772044 | + | 0.635569i | \(0.219234\pi\) | |||||||
\(462\) | 16.8414 | 0.783532 | ||||||||
\(463\) | 11.4076 | 0.530158 | 0.265079 | − | 0.964227i | \(-0.414602\pi\) | ||||
0.265079 | + | 0.964227i | \(0.414602\pi\) | |||||||
\(464\) | 11.8997 | 0.552431 | ||||||||
\(465\) | 15.2114 | 0.705411 | ||||||||
\(466\) | −44.7015 | −2.07076 | ||||||||
\(467\) | −5.75869 | −0.266481 | −0.133240 | − | 0.991084i | \(-0.542538\pi\) | ||||
−0.133240 | + | 0.991084i | \(0.542538\pi\) | |||||||
\(468\) | 14.7572 | 0.682150 | ||||||||
\(469\) | 55.2241 | 2.55001 | ||||||||
\(470\) | 3.05066 | 0.140716 | ||||||||
\(471\) | −11.5588 | −0.532601 | ||||||||
\(472\) | −7.68431 | −0.353699 | ||||||||
\(473\) | −8.31739 | −0.382434 | ||||||||
\(474\) | 8.56732 | 0.393510 | ||||||||
\(475\) | 13.7286 | 0.629910 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.05976 | 0.0943101 | ||||||||
\(478\) | 57.1742 | 2.61509 | ||||||||
\(479\) | 7.06735 | 0.322915 | 0.161458 | − | 0.986880i | \(-0.448380\pi\) | ||||
0.161458 | + | 0.986880i | \(0.448380\pi\) | |||||||
\(480\) | 6.58611 | 0.300613 | ||||||||
\(481\) | −16.2632 | −0.741540 | ||||||||
\(482\) | 6.57056 | 0.299281 | ||||||||
\(483\) | 14.5713 | 0.663018 | ||||||||
\(484\) | 3.76185 | 0.170993 | ||||||||
\(485\) | 16.0922 | 0.730708 | ||||||||
\(486\) | 22.2594 | 1.00971 | ||||||||
\(487\) | −16.0859 | −0.728920 | −0.364460 | − | 0.931219i | \(-0.618746\pi\) | ||||
−0.364460 | + | 0.931219i | \(0.618746\pi\) | |||||||
\(488\) | −47.7483 | −2.16147 | ||||||||
\(489\) | 13.9303 | 0.629951 | ||||||||
\(490\) | −20.6052 | −0.930847 | ||||||||
\(491\) | 36.0180 | 1.62547 | 0.812734 | − | 0.582634i | \(-0.197978\pi\) | ||||
0.812734 | + | 0.582634i | \(0.197978\pi\) | |||||||
\(492\) | −36.3920 | −1.64068 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 53.7447 | 2.41809 | ||||||||
\(495\) | −1.42604 | −0.0640956 | ||||||||
\(496\) | 13.0516 | 0.586036 | ||||||||
\(497\) | −51.4624 | −2.30840 | ||||||||
\(498\) | −79.4462 | −3.56007 | ||||||||
\(499\) | −25.2752 | −1.13147 | −0.565736 | − | 0.824587i | \(-0.691408\pi\) | ||||
−0.565736 | + | 0.824587i | \(0.691408\pi\) | |||||||
\(500\) | −44.2627 | −1.97949 | ||||||||
\(501\) | 10.2510 | 0.457979 | ||||||||
\(502\) | 24.2492 | 1.08229 | ||||||||
\(503\) | 5.61582 | 0.250397 | 0.125198 | − | 0.992132i | \(-0.460043\pi\) | ||||
0.125198 | + | 0.992132i | \(0.460043\pi\) | |||||||
\(504\) | −13.8158 | −0.615406 | ||||||||
\(505\) | 13.1963 | 0.587226 | ||||||||
\(506\) | 4.98521 | 0.221620 | ||||||||
\(507\) | 10.0955 | 0.448356 | ||||||||
\(508\) | 80.3183 | 3.56355 | ||||||||
\(509\) | −40.7415 | −1.80584 | −0.902918 | − | 0.429813i | \(-0.858579\pi\) | ||||
−0.902918 | + | 0.429813i | \(0.858579\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.7586 | 2.28967 | ||||||||
\(512\) | 27.8779 | 1.23204 | ||||||||
\(513\) | 21.6583 | 0.956236 | ||||||||
\(514\) | −7.45932 | −0.329017 | ||||||||
\(515\) | 14.9044 | 0.656768 | ||||||||
\(516\) | 61.9655 | 2.72788 | ||||||||
\(517\) | 0.821811 | 0.0361432 | ||||||||
\(518\) | 32.5097 | 1.42840 | ||||||||
\(519\) | −35.4726 | −1.55708 | ||||||||
\(520\) | −27.8229 | −1.22011 | ||||||||
\(521\) | 6.02738 | 0.264064 | 0.132032 | − | 0.991245i | \(-0.457850\pi\) | ||||
0.132032 | + | 0.991245i | \(0.457850\pi\) | |||||||
\(522\) | −10.0233 | −0.438708 | ||||||||
\(523\) | 9.87471 | 0.431791 | 0.215895 | − | 0.976416i | \(-0.430733\pi\) | ||||
0.215895 | + | 0.976416i | \(0.430733\pi\) | |||||||
\(524\) | −32.4251 | −1.41650 | ||||||||
\(525\) | −18.3011 | −0.798727 | ||||||||
\(526\) | 28.6609 | 1.24968 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5.20425 | −0.226486 | ||||||||
\(529\) | −18.6867 | −0.812467 | ||||||||
\(530\) | −8.29179 | −0.360172 | ||||||||
\(531\) | 1.67550 | 0.0727106 | ||||||||
\(532\) | −70.1425 | −3.04106 | ||||||||
\(533\) | −20.7804 | −0.900099 | ||||||||
\(534\) | 8.35987 | 0.361767 | ||||||||
\(535\) | −10.9201 | −0.472119 | ||||||||
\(536\) | −65.9240 | −2.84748 | ||||||||
\(537\) | −42.9917 | −1.85523 | ||||||||
\(538\) | 37.8767 | 1.63298 | ||||||||
\(539\) | −5.55079 | −0.239090 | ||||||||
\(540\) | −23.9399 | −1.03021 | ||||||||
\(541\) | −19.7963 | −0.851110 | −0.425555 | − | 0.904932i | \(-0.639921\pi\) | ||||
−0.425555 | + | 0.904932i | \(0.639921\pi\) | |||||||
\(542\) | 70.1710 | 3.01410 | ||||||||
\(543\) | 6.15034 | 0.263936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.7056 | 0.501411 | ||||||||
\(546\) | −71.6454 | −3.06614 | ||||||||
\(547\) | −3.14858 | −0.134624 | −0.0673119 | − | 0.997732i | \(-0.521442\pi\) | ||||
−0.0673119 | + | 0.997732i | \(0.521442\pi\) | |||||||
\(548\) | −32.1023 | −1.37134 | ||||||||
\(549\) | 10.4111 | 0.444336 | ||||||||
\(550\) | −6.26127 | −0.266981 | ||||||||
\(551\) | −23.8332 | −1.01533 | ||||||||
\(552\) | −17.3946 | −0.740362 | ||||||||
\(553\) | −6.38467 | −0.271504 | ||||||||
\(554\) | −45.6449 | −1.93926 | ||||||||
\(555\) | −11.7084 | −0.496994 | ||||||||
\(556\) | −70.0419 | −2.97044 | ||||||||
\(557\) | 4.35315 | 0.184449 | 0.0922245 | − | 0.995738i | \(-0.470602\pi\) | ||||
0.0922245 | + | 0.995738i | \(0.470602\pi\) | |||||||
\(558\) | −10.9936 | −0.465395 | ||||||||
\(559\) | 35.3832 | 1.49655 | ||||||||
\(560\) | 14.3971 | 0.608386 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −71.2893 | −3.00716 | ||||||||
\(563\) | −17.3001 | −0.729112 | −0.364556 | − | 0.931181i | \(-0.618779\pi\) | ||||
−0.364556 | + | 0.931181i | \(0.618779\pi\) | |||||||
\(564\) | −6.12258 | −0.257807 | ||||||||
\(565\) | 3.81117 | 0.160337 | ||||||||
\(566\) | −57.0964 | −2.39994 | ||||||||
\(567\) | −38.6724 | −1.62409 | ||||||||
\(568\) | 61.4335 | 2.57769 | ||||||||
\(569\) | 29.5341 | 1.23813 | 0.619067 | − | 0.785338i | \(-0.287511\pi\) | ||||
0.619067 | + | 0.785338i | \(0.287511\pi\) | |||||||
\(570\) | 38.6924 | 1.62065 | ||||||||
\(571\) | −13.8263 | −0.578614 | −0.289307 | − | 0.957236i | \(-0.593425\pi\) | ||||
−0.289307 | + | 0.957236i | \(0.593425\pi\) | |||||||
\(572\) | −16.0034 | −0.669136 | ||||||||
\(573\) | 21.4284 | 0.895185 | ||||||||
\(574\) | 41.5394 | 1.73382 | ||||||||
\(575\) | −5.41731 | −0.225917 | ||||||||
\(576\) | −9.60631 | −0.400263 | ||||||||
\(577\) | −9.31419 | −0.387755 | −0.193878 | − | 0.981026i | \(-0.562106\pi\) | ||||
−0.193878 | + | 0.981026i | \(0.562106\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.3481 | 0.554726 | ||||||||
\(580\) | 26.3440 | 1.09387 | ||||||||
\(581\) | 59.2061 | 2.45628 | ||||||||
\(582\) | −49.4671 | −2.05048 | ||||||||
\(583\) | −2.23371 | −0.0925108 | ||||||||
\(584\) | −61.7871 | −2.55677 | ||||||||
\(585\) | 6.06655 | 0.250821 | ||||||||
\(586\) | −18.0297 | −0.744799 | ||||||||
\(587\) | 7.12868 | 0.294232 | 0.147116 | − | 0.989119i | \(-0.453001\pi\) | ||||
0.147116 | + | 0.989119i | \(0.453001\pi\) | |||||||
\(588\) | 41.3540 | 1.70541 | ||||||||
\(589\) | −26.1403 | −1.07709 | ||||||||
\(590\) | −6.74490 | −0.277683 | ||||||||
\(591\) | −9.87920 | −0.406376 | ||||||||
\(592\) | −10.0460 | −0.412889 | ||||||||
\(593\) | −17.0526 | −0.700268 | −0.350134 | − | 0.936700i | \(-0.613864\pi\) | ||||
−0.350134 | + | 0.936700i | \(0.613864\pi\) | |||||||
\(594\) | −9.87782 | −0.405292 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.00665 | −0.368927 | ||||||||
\(597\) | −28.1506 | −1.15213 | ||||||||
\(598\) | −21.2077 | −0.867248 | ||||||||
\(599\) | −9.66080 | −0.394730 | −0.197365 | − | 0.980330i | \(-0.563238\pi\) | ||||
−0.197365 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(600\) | 21.8471 | 0.891902 | ||||||||
\(601\) | −16.7076 | −0.681519 | −0.340759 | − | 0.940151i | \(-0.610684\pi\) | ||||
−0.340759 | + | 0.940151i | \(0.610684\pi\) | |||||||
\(602\) | −70.7300 | −2.88274 | ||||||||
\(603\) | 14.3742 | 0.585363 | ||||||||
\(604\) | 4.02657 | 0.163839 | ||||||||
\(605\) | 1.54647 | 0.0628728 | ||||||||
\(606\) | −40.5651 | −1.64785 | ||||||||
\(607\) | −29.7638 | −1.20808 | −0.604038 | − | 0.796955i | \(-0.706443\pi\) | ||||
−0.604038 | + | 0.796955i | \(0.706443\pi\) | |||||||
\(608\) | −11.3181 | −0.459008 | ||||||||
\(609\) | 31.7713 | 1.28744 | ||||||||
\(610\) | −41.9111 | −1.69693 | ||||||||
\(611\) | −3.49609 | −0.141437 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.7618 | −1.24246 | −0.621229 | − | 0.783629i | \(-0.713366\pi\) | ||||
−0.621229 | + | 0.783629i | \(0.713366\pi\) | |||||||
\(614\) | 32.6592 | 1.31802 | ||||||||
\(615\) | −14.9604 | −0.603263 | ||||||||
\(616\) | 14.9826 | 0.603665 | ||||||||
\(617\) | 4.28739 | 0.172604 | 0.0863019 | − | 0.996269i | \(-0.472495\pi\) | ||||
0.0863019 | + | 0.996269i | \(0.472495\pi\) | |||||||
\(618\) | −45.8160 | −1.84299 | ||||||||
\(619\) | 15.3564 | 0.617227 | 0.308613 | − | 0.951188i | \(-0.400135\pi\) | ||||
0.308613 | + | 0.951188i | \(0.400135\pi\) | |||||||
\(620\) | 28.8941 | 1.16042 | ||||||||
\(621\) | −8.54638 | −0.342954 | ||||||||
\(622\) | −37.5530 | −1.50574 | ||||||||
\(623\) | −6.23007 | −0.249603 | ||||||||
\(624\) | 22.1396 | 0.886292 | ||||||||
\(625\) | −5.15381 | −0.206152 | ||||||||
\(626\) | −7.03411 | −0.281139 | ||||||||
\(627\) | 10.4233 | 0.416266 | ||||||||
\(628\) | −21.9560 | −0.876140 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −12.1268 | −0.483145 | ||||||||
\(631\) | −10.3768 | −0.413094 | −0.206547 | − | 0.978437i | \(-0.566223\pi\) | ||||
−0.206547 | + | 0.978437i | \(0.566223\pi\) | |||||||
\(632\) | 7.62173 | 0.303176 | ||||||||
\(633\) | −13.5293 | −0.537740 | ||||||||
\(634\) | 21.3562 | 0.848164 | ||||||||
\(635\) | 33.0182 | 1.31029 | ||||||||
\(636\) | 16.6414 | 0.659874 | ||||||||
\(637\) | 23.6138 | 0.935612 | ||||||||
\(638\) | 10.8698 | 0.430338 | ||||||||
\(639\) | −13.3951 | −0.529901 | ||||||||
\(640\) | 32.0200 | 1.26570 | ||||||||
\(641\) | −1.48379 | −0.0586063 | −0.0293032 | − | 0.999571i | \(-0.509329\pi\) | ||||
−0.0293032 | + | 0.999571i | \(0.509329\pi\) | |||||||
\(642\) | 33.5683 | 1.32484 | ||||||||
\(643\) | −7.02830 | −0.277169 | −0.138585 | − | 0.990351i | \(-0.544255\pi\) | ||||
−0.138585 | + | 0.990351i | \(0.544255\pi\) | |||||||
\(644\) | 27.6783 | 1.09068 | ||||||||
\(645\) | 25.4735 | 1.00302 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.1964 | −0.911946 | −0.455973 | − | 0.889994i | \(-0.650709\pi\) | ||||
−0.455973 | + | 0.889994i | \(0.650709\pi\) | |||||||
\(648\) | 46.1654 | 1.81355 | ||||||||
\(649\) | −1.81700 | −0.0713234 | ||||||||
\(650\) | 26.6362 | 1.04476 | ||||||||
\(651\) | 34.8469 | 1.36576 | ||||||||
\(652\) | 26.4608 | 1.03628 | ||||||||
\(653\) | −15.0865 | −0.590382 | −0.295191 | − | 0.955438i | \(-0.595383\pi\) | ||||
−0.295191 | + | 0.955438i | \(0.595383\pi\) | |||||||
\(654\) | −35.9827 | −1.40703 | ||||||||
\(655\) | −13.3297 | −0.520833 | ||||||||
\(656\) | −12.8363 | −0.501175 | ||||||||
\(657\) | 13.4722 | 0.525600 | ||||||||
\(658\) | 6.98857 | 0.272443 | ||||||||
\(659\) | −21.6863 | −0.844779 | −0.422390 | − | 0.906414i | \(-0.638809\pi\) | ||||
−0.422390 | + | 0.906414i | \(0.638809\pi\) | |||||||
\(660\) | −11.5213 | −0.448468 | ||||||||
\(661\) | 21.1802 | 0.823815 | 0.411907 | − | 0.911226i | \(-0.364863\pi\) | ||||
0.411907 | + | 0.911226i | \(0.364863\pi\) | |||||||
\(662\) | −9.60646 | −0.373366 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −70.6776 | −2.74282 | ||||||||
\(665\) | −28.8350 | −1.11817 | ||||||||
\(666\) | 8.46191 | 0.327892 | ||||||||
\(667\) | 9.40462 | 0.364148 | ||||||||
\(668\) | 19.4718 | 0.753385 | ||||||||
\(669\) | −24.2408 | −0.937204 | ||||||||
\(670\) | −57.8648 | −2.23551 | ||||||||
\(671\) | −11.2904 | −0.435859 | ||||||||
\(672\) | 15.0877 | 0.582022 | ||||||||
\(673\) | −2.31538 | −0.0892514 | −0.0446257 | − | 0.999004i | \(-0.514210\pi\) | ||||
−0.0446257 | + | 0.999004i | \(0.514210\pi\) | |||||||
\(674\) | 70.5550 | 2.71768 | ||||||||
\(675\) | 10.7340 | 0.413152 | ||||||||
\(676\) | 19.1764 | 0.737555 | ||||||||
\(677\) | −1.66733 | −0.0640809 | −0.0320404 | − | 0.999487i | \(-0.510201\pi\) | ||||
−0.0320404 | + | 0.999487i | \(0.510201\pi\) | |||||||
\(678\) | −11.7155 | −0.449930 | ||||||||
\(679\) | 36.8646 | 1.41473 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.2488 | −1.58066 | ||||||||
\(682\) | 11.9220 | 0.456516 | ||||||||
\(683\) | 19.0953 | 0.730662 | 0.365331 | − | 0.930878i | \(-0.380956\pi\) | ||||
0.365331 | + | 0.930878i | \(0.380956\pi\) | |||||||
\(684\) | −18.2573 | −0.698085 | ||||||||
\(685\) | −13.1970 | −0.504230 | ||||||||
\(686\) | 12.3239 | 0.470527 | ||||||||
\(687\) | −43.8151 | −1.67165 | ||||||||
\(688\) | 21.8567 | 0.833279 | ||||||||
\(689\) | 9.50249 | 0.362016 | ||||||||
\(690\) | −15.2681 | −0.581246 | ||||||||
\(691\) | 25.5219 | 0.970898 | 0.485449 | − | 0.874265i | \(-0.338656\pi\) | ||||
0.485449 | + | 0.874265i | \(0.338656\pi\) | |||||||
\(692\) | −67.3806 | −2.56142 | ||||||||
\(693\) | −3.26683 | −0.124097 | ||||||||
\(694\) | 6.66945 | 0.253169 | ||||||||
\(695\) | −28.7936 | −1.09220 | ||||||||
\(696\) | −37.9272 | −1.43763 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 51.5928 | 1.95281 | ||||||||
\(699\) | 36.8809 | 1.39496 | ||||||||
\(700\) | −34.7631 | −1.31392 | ||||||||
\(701\) | −28.3803 | −1.07191 | −0.535955 | − | 0.844247i | \(-0.680048\pi\) | ||||
−0.535955 | + | 0.844247i | \(0.680048\pi\) | |||||||
\(702\) | 42.0215 | 1.58600 | ||||||||
\(703\) | 20.1206 | 0.758862 | ||||||||
\(704\) | 10.4176 | 0.392626 | ||||||||
\(705\) | −2.51694 | −0.0947935 | ||||||||
\(706\) | −18.3387 | −0.690187 | ||||||||
\(707\) | 30.2306 | 1.13694 | ||||||||
\(708\) | 13.5368 | 0.508745 | ||||||||
\(709\) | 10.8901 | 0.408985 | 0.204492 | − | 0.978868i | \(-0.434446\pi\) | ||||
0.204492 | + | 0.978868i | \(0.434446\pi\) | |||||||
\(710\) | 53.9232 | 2.02370 | ||||||||
\(711\) | −1.66186 | −0.0623245 | ||||||||
\(712\) | 7.43718 | 0.278720 | ||||||||
\(713\) | 10.3150 | 0.386300 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.57886 | −0.246036 | ||||||||
\(716\) | −81.6631 | −3.05189 | ||||||||
\(717\) | −47.1715 | −1.76165 | ||||||||
\(718\) | 16.0884 | 0.600413 | ||||||||
\(719\) | −19.2995 | −0.719750 | −0.359875 | − | 0.933001i | \(-0.617181\pi\) | ||||
−0.359875 | + | 0.933001i | \(0.617181\pi\) | |||||||
\(720\) | 3.74739 | 0.139657 | ||||||||
\(721\) | 34.1437 | 1.27158 | ||||||||
\(722\) | −20.8846 | −0.777244 | ||||||||
\(723\) | −5.42104 | −0.201610 | ||||||||
\(724\) | 11.6826 | 0.434181 | ||||||||
\(725\) | −11.8119 | −0.438684 | ||||||||
\(726\) | −4.75381 | −0.176430 | ||||||||
\(727\) | −18.6357 | −0.691158 | −0.345579 | − | 0.938390i | \(-0.612318\pi\) | ||||
−0.345579 | + | 0.938390i | \(0.612318\pi\) | |||||||
\(728\) | −63.7378 | −2.36228 | ||||||||
\(729\) | 14.3831 | 0.532706 | ||||||||
\(730\) | −54.2336 | −2.00728 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 84.1144 | 3.10896 | ||||||||
\(733\) | 2.28825 | 0.0845185 | 0.0422592 | − | 0.999107i | \(-0.486544\pi\) | ||||
0.0422592 | + | 0.999107i | \(0.486544\pi\) | |||||||
\(734\) | −90.4585 | −3.33888 | ||||||||
\(735\) | 17.0003 | 0.627065 | ||||||||
\(736\) | 4.46612 | 0.164623 | ||||||||
\(737\) | −15.5881 | −0.574195 | ||||||||
\(738\) | 10.8122 | 0.398003 | ||||||||
\(739\) | −2.89271 | −0.106410 | −0.0532050 | − | 0.998584i | \(-0.516944\pi\) | ||||
−0.0532050 | + | 0.998584i | \(0.516944\pi\) | |||||||
\(740\) | −22.2402 | −0.817566 | ||||||||
\(741\) | −44.3420 | −1.62894 | ||||||||
\(742\) | −18.9952 | −0.697335 | ||||||||
\(743\) | −25.5858 | −0.938654 | −0.469327 | − | 0.883025i | \(-0.655503\pi\) | ||||
−0.469327 | + | 0.883025i | \(0.655503\pi\) | |||||||
\(744\) | −41.5986 | −1.52508 | ||||||||
\(745\) | −3.70256 | −0.135651 | ||||||||
\(746\) | 16.3175 | 0.597426 | ||||||||
\(747\) | 15.4107 | 0.563847 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.0163 | −0.914077 | ||||||||
\(750\) | 55.9343 | 2.04243 | ||||||||
\(751\) | −9.88931 | −0.360866 | −0.180433 | − | 0.983587i | \(-0.557750\pi\) | ||||
−0.180433 | + | 0.983587i | \(0.557750\pi\) | |||||||
\(752\) | −2.15958 | −0.0787518 | ||||||||
\(753\) | −20.0068 | −0.729087 | ||||||||
\(754\) | −46.2414 | −1.68401 | ||||||||
\(755\) | 1.65529 | 0.0602421 | ||||||||
\(756\) | −54.8425 | −1.99460 | ||||||||
\(757\) | 28.8410 | 1.04824 | 0.524121 | − | 0.851644i | \(-0.324394\pi\) | ||||
0.524121 | + | 0.851644i | \(0.324394\pi\) | |||||||
\(758\) | −58.6363 | −2.12977 | ||||||||
\(759\) | −4.11304 | −0.149294 | ||||||||
\(760\) | 34.4219 | 1.24861 | ||||||||
\(761\) | −33.6168 | −1.21861 | −0.609304 | − | 0.792936i | \(-0.708551\pi\) | ||||
−0.609304 | + | 0.792936i | \(0.708551\pi\) | |||||||
\(762\) | −101.497 | −3.67686 | ||||||||
\(763\) | 26.8156 | 0.970789 | ||||||||
\(764\) | 40.7034 | 1.47260 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.0630 | −0.544247 | ||||||||
\(767\) | 7.72974 | 0.279105 | ||||||||
\(768\) | −57.1663 | −2.06281 | ||||||||
\(769\) | 6.70627 | 0.241834 | 0.120917 | − | 0.992663i | \(-0.461416\pi\) | ||||
0.120917 | + | 0.992663i | \(0.461416\pi\) | |||||||
\(770\) | 13.1509 | 0.473927 | ||||||||
\(771\) | 6.15431 | 0.221642 | ||||||||
\(772\) | 25.3547 | 0.912537 | ||||||||
\(773\) | 16.8964 | 0.607722 | 0.303861 | − | 0.952716i | \(-0.401724\pi\) | ||||
0.303861 | + | 0.952716i | \(0.401724\pi\) | |||||||
\(774\) | −18.4102 | −0.661741 | ||||||||
\(775\) | −12.9553 | −0.465369 | ||||||||
\(776\) | −44.0073 | −1.57977 | ||||||||
\(777\) | −26.8221 | −0.962238 | ||||||||
\(778\) | 43.1466 | 1.54688 | ||||||||
\(779\) | 25.7091 | 0.921125 | ||||||||
\(780\) | 49.0133 | 1.75496 | ||||||||
\(781\) | 14.5263 | 0.519791 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.6346 | −0.665944 | ||||||||
\(784\) | 14.5866 | 0.520948 | ||||||||
\(785\) | −9.02592 | −0.322149 | ||||||||
\(786\) | 40.9752 | 1.46154 | ||||||||
\(787\) | 38.5837 | 1.37536 | 0.687681 | − | 0.726013i | \(-0.258629\pi\) | ||||
0.687681 | + | 0.726013i | \(0.258629\pi\) | |||||||
\(788\) | −18.7656 | −0.668497 | ||||||||
\(789\) | −23.6467 | −0.841843 | ||||||||
\(790\) | 6.68997 | 0.238019 | ||||||||
\(791\) | 8.73079 | 0.310431 | ||||||||
\(792\) | 3.89979 | 0.138573 | ||||||||
\(793\) | 48.0306 | 1.70562 | ||||||||
\(794\) | −26.2485 | −0.931525 | ||||||||
\(795\) | 6.84113 | 0.242630 | ||||||||
\(796\) | −53.4722 | −1.89527 | ||||||||
\(797\) | −22.3104 | −0.790275 | −0.395138 | − | 0.918622i | \(-0.629303\pi\) | ||||
−0.395138 | + | 0.918622i | \(0.629303\pi\) | |||||||
\(798\) | 88.6383 | 3.13776 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.60931 | −0.198319 | ||||||||
\(801\) | −1.62162 | −0.0572970 | ||||||||
\(802\) | 70.9986 | 2.50705 | ||||||||
\(803\) | −14.6099 | −0.515572 | ||||||||
\(804\) | 116.133 | 4.09570 | ||||||||
\(805\) | 11.3783 | 0.401033 | ||||||||
\(806\) | −50.7176 | −1.78645 | ||||||||
\(807\) | −31.2502 | −1.10006 | ||||||||
\(808\) | −36.0879 | −1.26957 | ||||||||
\(809\) | −26.9861 | −0.948779 | −0.474390 | − | 0.880315i | \(-0.657331\pi\) | ||||
−0.474390 | + | 0.880315i | \(0.657331\pi\) | |||||||
\(810\) | 40.5217 | 1.42379 | ||||||||
\(811\) | −45.4115 | −1.59461 | −0.797306 | − | 0.603575i | \(-0.793742\pi\) | ||||
−0.797306 | + | 0.603575i | \(0.793742\pi\) | |||||||
\(812\) | 60.3499 | 2.11787 | ||||||||
\(813\) | −57.8945 | −2.03045 | ||||||||
\(814\) | −9.17651 | −0.321637 | ||||||||
\(815\) | 10.8778 | 0.381033 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.7755 | −1.53151 | ||||||||
\(818\) | −71.5152 | −2.50047 | ||||||||
\(819\) | 13.8975 | 0.485618 | ||||||||
\(820\) | −28.4175 | −0.992381 | ||||||||
\(821\) | 5.14534 | 0.179574 | 0.0897868 | − | 0.995961i | \(-0.471381\pi\) | ||||
0.0897868 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(822\) | 40.5672 | 1.41495 | ||||||||
\(823\) | −24.7390 | −0.862348 | −0.431174 | − | 0.902269i | \(-0.641900\pi\) | ||||
−0.431174 | + | 0.902269i | \(0.641900\pi\) | |||||||
\(824\) | −40.7592 | −1.41991 | ||||||||
\(825\) | 5.16585 | 0.179852 | ||||||||
\(826\) | −15.4515 | −0.537627 | ||||||||
\(827\) | −32.5824 | −1.13300 | −0.566500 | − | 0.824061i | \(-0.691703\pi\) | ||||
−0.566500 | + | 0.824061i | \(0.691703\pi\) | |||||||
\(828\) | 7.20435 | 0.250368 | ||||||||
\(829\) | −5.51888 | −0.191679 | −0.0958393 | − | 0.995397i | \(-0.530553\pi\) | ||||
−0.0958393 | + | 0.995397i | \(0.530553\pi\) | |||||||
\(830\) | −62.0373 | −2.15334 | ||||||||
\(831\) | 37.6592 | 1.30638 | ||||||||
\(832\) | −44.3176 | −1.53644 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 88.5111 | 3.06489 | ||||||||
\(835\) | 8.00468 | 0.277013 | ||||||||
\(836\) | 19.7991 | 0.684767 | ||||||||
\(837\) | −20.4384 | −0.706455 | ||||||||
\(838\) | −45.6218 | −1.57598 | ||||||||
\(839\) | 13.1816 | 0.455079 | 0.227540 | − | 0.973769i | \(-0.426932\pi\) | ||||
0.227540 | + | 0.973769i | \(0.426932\pi\) | |||||||
\(840\) | −45.8868 | −1.58324 | ||||||||
\(841\) | −8.49414 | −0.292901 | ||||||||
\(842\) | 40.3615 | 1.39095 | ||||||||
\(843\) | 58.8171 | 2.02577 | ||||||||
\(844\) | −25.6989 | −0.884594 | ||||||||
\(845\) | 7.88327 | 0.271193 | ||||||||
\(846\) | 1.81905 | 0.0625401 | ||||||||
\(847\) | 3.54271 | 0.121729 | ||||||||
\(848\) | 5.86981 | 0.201570 | ||||||||
\(849\) | 47.1073 | 1.61672 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.93961 | −0.272166 | ||||||||
\(852\) | −108.222 | −3.70764 | ||||||||
\(853\) | 11.2378 | 0.384776 | 0.192388 | − | 0.981319i | \(-0.438377\pi\) | ||||
0.192388 | + | 0.981319i | \(0.438377\pi\) | |||||||
\(854\) | −96.0117 | −3.28545 | ||||||||
\(855\) | −7.50542 | −0.256680 | ||||||||
\(856\) | 29.8634 | 1.02071 | ||||||||
\(857\) | −45.2264 | −1.54490 | −0.772452 | − | 0.635073i | \(-0.780970\pi\) | ||||
−0.772452 | + | 0.635073i | \(0.780970\pi\) | |||||||
\(858\) | 20.2233 | 0.690413 | ||||||||
\(859\) | 4.39071 | 0.149809 | 0.0749045 | − | 0.997191i | \(-0.476135\pi\) | ||||
0.0749045 | + | 0.997191i | \(0.476135\pi\) | |||||||
\(860\) | 48.3871 | 1.64998 | ||||||||
\(861\) | −34.2720 | −1.16799 | ||||||||
\(862\) | −44.6948 | −1.52231 | ||||||||
\(863\) | −3.89363 | −0.132541 | −0.0662704 | − | 0.997802i | \(-0.521110\pi\) | ||||
−0.0662704 | + | 0.997802i | \(0.521110\pi\) | |||||||
\(864\) | −8.84928 | −0.301059 | ||||||||
\(865\) | −27.6996 | −0.941814 | ||||||||
\(866\) | 58.7870 | 1.99766 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 66.1919 | 2.24670 | ||||||||
\(869\) | 1.80220 | 0.0611354 | ||||||||
\(870\) | −33.2906 | −1.12866 | ||||||||
\(871\) | 66.3138 | 2.24696 | ||||||||
\(872\) | −32.0112 | −1.08404 | ||||||||
\(873\) | 9.59544 | 0.324756 | ||||||||
\(874\) | 26.2378 | 0.887507 | ||||||||
\(875\) | −41.6842 | −1.40918 | ||||||||
\(876\) | 108.845 | 3.67754 | ||||||||
\(877\) | 15.9496 | 0.538580 | 0.269290 | − | 0.963059i | \(-0.413211\pi\) | ||||
0.269290 | + | 0.963059i | \(0.413211\pi\) | |||||||
\(878\) | −8.21304 | −0.277177 | ||||||||
\(879\) | 14.8754 | 0.501733 | ||||||||
\(880\) | −4.06385 | −0.136992 | ||||||||
\(881\) | 29.1600 | 0.982424 | 0.491212 | − | 0.871040i | \(-0.336554\pi\) | ||||
0.491212 | + | 0.871040i | \(0.336554\pi\) | |||||||
\(882\) | −12.2865 | −0.413707 | ||||||||
\(883\) | −43.6727 | −1.46970 | −0.734852 | − | 0.678228i | \(-0.762748\pi\) | ||||
−0.734852 | + | 0.678228i | \(0.762748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.56487 | 0.187061 | ||||||||
\(886\) | −3.21303 | −0.107944 | ||||||||
\(887\) | 15.9946 | 0.537046 | 0.268523 | − | 0.963273i | \(-0.413464\pi\) | ||||
0.268523 | + | 0.963273i | \(0.413464\pi\) | |||||||
\(888\) | 32.0190 | 1.07449 | ||||||||
\(889\) | 75.6395 | 2.53687 | ||||||||
\(890\) | 6.52798 | 0.218818 | ||||||||
\(891\) | 10.9161 | 0.365702 | ||||||||
\(892\) | −46.0456 | −1.54172 | ||||||||
\(893\) | 4.32530 | 0.144740 | ||||||||
\(894\) | 11.3816 | 0.380658 | ||||||||
\(895\) | −33.5710 | −1.12216 | ||||||||
\(896\) | 73.3528 | 2.45054 | ||||||||
\(897\) | 17.4974 | 0.584221 | ||||||||
\(898\) | −85.9061 | −2.86673 | ||||||||
\(899\) | 22.4909 | 0.750113 | ||||||||
\(900\) | −9.04844 | −0.301615 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −11.7253 | −0.390410 | ||||||||
\(903\) | 58.3557 | 1.94196 | ||||||||
\(904\) | −10.4224 | −0.346645 | ||||||||
\(905\) | 4.80263 | 0.159645 | ||||||||
\(906\) | −5.08833 | −0.169048 | ||||||||
\(907\) | −35.8315 | −1.18976 | −0.594882 | − | 0.803813i | \(-0.702801\pi\) | ||||
−0.594882 | + | 0.803813i | \(0.702801\pi\) | |||||||
\(908\) | −78.3524 | −2.60021 | ||||||||
\(909\) | 7.86867 | 0.260987 | ||||||||
\(910\) | −55.9458 | −1.85459 | ||||||||
\(911\) | 7.34288 | 0.243281 | 0.121640 | − | 0.992574i | \(-0.461185\pi\) | ||||
0.121640 | + | 0.992574i | \(0.461185\pi\) | |||||||
\(912\) | −27.3907 | −0.906995 | ||||||||
\(913\) | −16.7121 | −0.553090 | ||||||||
\(914\) | 41.7428 | 1.38073 | ||||||||
\(915\) | 34.5787 | 1.14314 | ||||||||
\(916\) | −83.2271 | −2.74990 | ||||||||
\(917\) | −30.5362 | −1.00839 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.79334 | −0.158118 | −0.0790589 | − | 0.996870i | \(-0.525192\pi\) | ||||
−0.0790589 | + | 0.996870i | \(0.525192\pi\) | |||||||
\(920\) | −13.5829 | −0.447816 | ||||||||
\(921\) | −26.9455 | −0.887883 | ||||||||
\(922\) | −79.5799 | −2.62083 | ||||||||
\(923\) | −61.7967 | −2.03406 | ||||||||
\(924\) | −26.3936 | −0.868285 | ||||||||
\(925\) | 9.97190 | 0.327874 | ||||||||
\(926\) | −27.3828 | −0.899853 | ||||||||
\(927\) | 8.88721 | 0.291894 | ||||||||
\(928\) | 9.73794 | 0.319663 | ||||||||
\(929\) | 22.6314 | 0.742513 | 0.371256 | − | 0.928530i | \(-0.378927\pi\) | ||||
0.371256 | + | 0.928530i | \(0.378927\pi\) | |||||||
\(930\) | −36.5132 | −1.19731 | ||||||||
\(931\) | −29.2145 | −0.957468 | ||||||||
\(932\) | 70.0556 | 2.29475 | ||||||||
\(933\) | 30.9830 | 1.01434 | ||||||||
\(934\) | 13.8231 | 0.452305 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.5902 | −0.542268 | ||||||||
\(937\) | −11.0630 | −0.361412 | −0.180706 | − | 0.983537i | \(-0.557838\pi\) | ||||
−0.180706 | + | 0.983537i | \(0.557838\pi\) | |||||||
\(938\) | −132.559 | −4.32821 | ||||||||
\(939\) | 5.80348 | 0.189389 | ||||||||
\(940\) | −4.78095 | −0.155937 | ||||||||
\(941\) | 23.6759 | 0.771814 | 0.385907 | − | 0.922538i | \(-0.373889\pi\) | ||||
0.385907 | + | 0.922538i | \(0.373889\pi\) | |||||||
\(942\) | 27.7455 | 0.903999 | ||||||||
\(943\) | −10.1448 | −0.330362 | ||||||||
\(944\) | 4.77476 | 0.155405 | ||||||||
\(945\) | −22.5453 | −0.733398 | ||||||||
\(946\) | 19.9649 | 0.649116 | ||||||||
\(947\) | −18.1918 | −0.591154 | −0.295577 | − | 0.955319i | \(-0.595512\pi\) | ||||
−0.295577 | + | 0.955319i | \(0.595512\pi\) | |||||||
\(948\) | −13.4266 | −0.436075 | ||||||||
\(949\) | 62.1524 | 2.01755 | ||||||||
\(950\) | −32.9539 | −1.06916 | ||||||||
\(951\) | −17.6199 | −0.571366 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.5803 | 0.861020 | 0.430510 | − | 0.902586i | \(-0.358334\pi\) | ||||
0.430510 | + | 0.902586i | \(0.358334\pi\) | |||||||
\(954\) | −4.94423 | −0.160075 | ||||||||
\(955\) | 16.7328 | 0.541462 | ||||||||
\(956\) | −89.6027 | −2.89796 | ||||||||
\(957\) | −8.96809 | −0.289897 | ||||||||
\(958\) | −16.9644 | −0.548094 | ||||||||
\(959\) | −30.2322 | −0.976247 | ||||||||
\(960\) | −31.9056 | −1.02975 | ||||||||
\(961\) | −6.33196 | −0.204257 | ||||||||
\(962\) | 39.0381 | 1.25864 | ||||||||
\(963\) | −6.51146 | −0.209829 | ||||||||
\(964\) | −10.2973 | −0.331654 | ||||||||
\(965\) | 10.4231 | 0.335532 | ||||||||
\(966\) | −34.9768 | −1.12536 | ||||||||
\(967\) | −29.8071 | −0.958533 | −0.479266 | − | 0.877670i | \(-0.659097\pi\) | ||||
−0.479266 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(968\) | −4.22913 | −0.135929 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −38.6274 | −1.24025 | ||||||||
\(971\) | 10.6586 | 0.342052 | 0.171026 | − | 0.985266i | \(-0.445292\pi\) | ||||
0.171026 | + | 0.985266i | \(0.445292\pi\) | |||||||
\(972\) | −34.8847 | −1.11893 | ||||||||
\(973\) | −65.9616 | −2.11463 | ||||||||
\(974\) | 38.6123 | 1.23722 | ||||||||
\(975\) | −21.9762 | −0.703802 | ||||||||
\(976\) | 29.6692 | 0.949686 | ||||||||
\(977\) | −7.35465 | −0.235296 | −0.117648 | − | 0.993055i | \(-0.537535\pi\) | ||||
−0.117648 | + | 0.993055i | \(0.537535\pi\) | |||||||
\(978\) | −33.4382 | −1.06923 | ||||||||
\(979\) | 1.75856 | 0.0562039 | ||||||||
\(980\) | 32.2922 | 1.03154 | ||||||||
\(981\) | 6.97979 | 0.222847 | ||||||||
\(982\) | −86.4571 | −2.75896 | ||||||||
\(983\) | 21.6516 | 0.690577 | 0.345289 | − | 0.938497i | \(-0.387781\pi\) | ||||
0.345289 | + | 0.938497i | \(0.387781\pi\) | |||||||
\(984\) | 40.9124 | 1.30424 | ||||||||
\(985\) | −7.71438 | −0.245801 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.76592 | −0.183531 | ||||||||
\(988\) | −84.2280 | −2.67965 | ||||||||
\(989\) | 17.2739 | 0.549277 | ||||||||
\(990\) | 3.42304 | 0.108791 | ||||||||
\(991\) | −43.7032 | −1.38828 | −0.694138 | − | 0.719842i | \(-0.744214\pi\) | ||||
−0.694138 | + | 0.719842i | \(0.744214\pi\) | |||||||
\(992\) | 10.6806 | 0.339109 | ||||||||
\(993\) | 7.92580 | 0.251518 | ||||||||
\(994\) | 123.530 | 3.91812 | ||||||||
\(995\) | −21.9820 | −0.696875 | ||||||||
\(996\) | 124.507 | 3.94516 | ||||||||
\(997\) | −40.8062 | −1.29234 | −0.646172 | − | 0.763192i | \(-0.723631\pi\) | ||||
−0.646172 | + | 0.763192i | \(0.723631\pi\) | |||||||
\(998\) | 60.6701 | 1.92048 | ||||||||
\(999\) | 15.7317 | 0.497730 |
(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 | 3179.2.a.bi.1.3 | 28 | ||
17.11 | odd | 16 | 187.2.h.a.155.2 | yes | 56 | ||
17.14 | odd | 16 | 187.2.h.a.111.2 | ✓ | 56 | ||
17.16 | even | 2 | 3179.2.a.bh.1.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.h.a.111.2 | ✓ | 56 | 17.14 | odd | 16 | ||
187.2.h.a.155.2 | yes | 56 | 17.11 | odd | 16 | ||
3179.2.a.bh.1.3 | 28 | 17.16 | even | 2 | |||
3179.2.a.bi.1.3 | 28 | 1.1 | even | 1 | trivial |