Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1003,2,Mod(1,1003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1003, 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("1003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1003 = 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1003.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: | \(8.00899532273\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} - 695 x^{7} + 2641 x^{6} - 151 x^{5} - 1323 x^{4} + 301 x^{3} + 179 x^{2} + \cdots - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.52760\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52760 | −1.78728 | −0.893640 | − | 0.448785i | \(-0.851857\pi\) | ||||
−0.893640 | + | 0.448785i | \(0.851857\pi\) | |||||||
\(3\) | −0.131380 | −0.0758523 | −0.0379261 | − | 0.999281i | \(-0.512075\pi\) | ||||
−0.0379261 | + | 0.999281i | \(0.512075\pi\) | |||||||
\(4\) | 4.38874 | 2.19437 | ||||||||
\(5\) | −1.05573 | −0.472136 | −0.236068 | − | 0.971737i | \(-0.575859\pi\) | ||||
−0.236068 | + | 0.971737i | \(0.575859\pi\) | |||||||
\(6\) | 0.332076 | 0.135569 | ||||||||
\(7\) | 3.96203 | 1.49751 | 0.748753 | − | 0.662850i | \(-0.230653\pi\) | ||||
0.748753 | + | 0.662850i | \(0.230653\pi\) | |||||||
\(8\) | −6.03776 | −2.13467 | ||||||||
\(9\) | −2.98274 | −0.994246 | ||||||||
\(10\) | 2.66845 | 0.843839 | ||||||||
\(11\) | −0.143171 | −0.0431676 | −0.0215838 | − | 0.999767i | \(-0.506871\pi\) | ||||
−0.0215838 | + | 0.999767i | \(0.506871\pi\) | |||||||
\(12\) | −0.576593 | −0.166448 | ||||||||
\(13\) | −0.0778021 | −0.0215784 | −0.0107892 | − | 0.999942i | \(-0.503434\pi\) | ||||
−0.0107892 | + | 0.999942i | \(0.503434\pi\) | |||||||
\(14\) | −10.0144 | −2.67646 | ||||||||
\(15\) | 0.138702 | 0.0358126 | ||||||||
\(16\) | 6.48355 | 1.62089 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 7.53916 | 1.77700 | ||||||||
\(19\) | −3.11646 | −0.714964 | −0.357482 | − | 0.933920i | \(-0.616365\pi\) | ||||
−0.357482 | + | 0.933920i | \(0.616365\pi\) | |||||||
\(20\) | −4.63331 | −1.03604 | ||||||||
\(21\) | −0.520531 | −0.113589 | ||||||||
\(22\) | 0.361878 | 0.0771526 | ||||||||
\(23\) | −4.34147 | −0.905258 | −0.452629 | − | 0.891699i | \(-0.649514\pi\) | ||||
−0.452629 | + | 0.891699i | \(0.649514\pi\) | |||||||
\(24\) | 0.793242 | 0.161920 | ||||||||
\(25\) | −3.88544 | −0.777088 | ||||||||
\(26\) | 0.196652 | 0.0385667 | ||||||||
\(27\) | 0.786013 | 0.151268 | ||||||||
\(28\) | 17.3883 | 3.28608 | ||||||||
\(29\) | −9.30274 | −1.72748 | −0.863738 | − | 0.503941i | \(-0.831883\pi\) | ||||
−0.863738 | + | 0.503941i | \(0.831883\pi\) | |||||||
\(30\) | −0.350581 | −0.0640071 | ||||||||
\(31\) | 4.72224 | 0.848140 | 0.424070 | − | 0.905630i | \(-0.360601\pi\) | ||||
0.424070 | + | 0.905630i | \(0.360601\pi\) | |||||||
\(32\) | −4.31225 | −0.762306 | ||||||||
\(33\) | 0.0188098 | 0.00327436 | ||||||||
\(34\) | −2.52760 | −0.433479 | ||||||||
\(35\) | −4.18282 | −0.707026 | ||||||||
\(36\) | −13.0905 | −2.18174 | ||||||||
\(37\) | 7.09149 | 1.16583 | 0.582917 | − | 0.812532i | \(-0.301911\pi\) | ||||
0.582917 | + | 0.812532i | \(0.301911\pi\) | |||||||
\(38\) | 7.87714 | 1.27784 | ||||||||
\(39\) | 0.0102216 | 0.00163677 | ||||||||
\(40\) | 6.37423 | 1.00785 | ||||||||
\(41\) | 6.54746 | 1.02254 | 0.511270 | − | 0.859420i | \(-0.329175\pi\) | ||||
0.511270 | + | 0.859420i | \(0.329175\pi\) | |||||||
\(42\) | 1.31569 | 0.203016 | ||||||||
\(43\) | −10.8062 | −1.64792 | −0.823962 | − | 0.566645i | \(-0.808241\pi\) | ||||
−0.823962 | + | 0.566645i | \(0.808241\pi\) | |||||||
\(44\) | −0.628339 | −0.0947257 | ||||||||
\(45\) | 3.14896 | 0.469419 | ||||||||
\(46\) | 10.9735 | 1.61795 | ||||||||
\(47\) | 1.89212 | 0.275995 | 0.137997 | − | 0.990433i | \(-0.455933\pi\) | ||||
0.137997 | + | 0.990433i | \(0.455933\pi\) | |||||||
\(48\) | −0.851808 | −0.122948 | ||||||||
\(49\) | 8.69765 | 1.24252 | ||||||||
\(50\) | 9.82082 | 1.38887 | ||||||||
\(51\) | −0.131380 | −0.0183969 | ||||||||
\(52\) | −0.341453 | −0.0473510 | ||||||||
\(53\) | −7.03133 | −0.965828 | −0.482914 | − | 0.875668i | \(-0.660422\pi\) | ||||
−0.482914 | + | 0.875668i | \(0.660422\pi\) | |||||||
\(54\) | −1.98672 | −0.270359 | ||||||||
\(55\) | 0.151149 | 0.0203810 | ||||||||
\(56\) | −23.9218 | −3.19668 | ||||||||
\(57\) | 0.409440 | 0.0542317 | ||||||||
\(58\) | 23.5136 | 3.08748 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0.608725 | 0.0785860 | ||||||||
\(61\) | 11.8426 | 1.51629 | 0.758143 | − | 0.652088i | \(-0.226107\pi\) | ||||
0.758143 | + | 0.652088i | \(0.226107\pi\) | |||||||
\(62\) | −11.9359 | −1.51586 | ||||||||
\(63\) | −11.8177 | −1.48889 | ||||||||
\(64\) | −2.06746 | −0.258433 | ||||||||
\(65\) | 0.0821378 | 0.0101879 | ||||||||
\(66\) | −0.0475435 | −0.00585220 | ||||||||
\(67\) | −15.3533 | −1.87571 | −0.937853 | − | 0.347032i | \(-0.887189\pi\) | ||||
−0.937853 | + | 0.347032i | \(0.887189\pi\) | |||||||
\(68\) | 4.38874 | 0.532213 | ||||||||
\(69\) | 0.570382 | 0.0686659 | ||||||||
\(70\) | 10.5725 | 1.26365 | ||||||||
\(71\) | −2.35610 | −0.279617 | −0.139809 | − | 0.990179i | \(-0.544649\pi\) | ||||
−0.139809 | + | 0.990179i | \(0.544649\pi\) | |||||||
\(72\) | 18.0091 | 2.12239 | ||||||||
\(73\) | 1.35256 | 0.158305 | 0.0791524 | − | 0.996863i | \(-0.474779\pi\) | ||||
0.0791524 | + | 0.996863i | \(0.474779\pi\) | |||||||
\(74\) | −17.9244 | −2.08367 | ||||||||
\(75\) | 0.510469 | 0.0589439 | ||||||||
\(76\) | −13.6773 | −1.56890 | ||||||||
\(77\) | −0.567246 | −0.0646437 | ||||||||
\(78\) | −0.0258362 | −0.00292537 | ||||||||
\(79\) | −1.77810 | −0.200052 | −0.100026 | − | 0.994985i | \(-0.531893\pi\) | ||||
−0.100026 | + | 0.994985i | \(0.531893\pi\) | |||||||
\(80\) | −6.84486 | −0.765278 | ||||||||
\(81\) | 8.84495 | 0.982772 | ||||||||
\(82\) | −16.5493 | −1.82757 | ||||||||
\(83\) | −6.22111 | −0.682856 | −0.341428 | − | 0.939908i | \(-0.610910\pi\) | ||||
−0.341428 | + | 0.939908i | \(0.610910\pi\) | |||||||
\(84\) | −2.28448 | −0.249257 | ||||||||
\(85\) | −1.05573 | −0.114510 | ||||||||
\(86\) | 27.3136 | 2.94530 | ||||||||
\(87\) | 1.22219 | 0.131033 | ||||||||
\(88\) | 0.864431 | 0.0921487 | ||||||||
\(89\) | 0.231814 | 0.0245723 | 0.0122861 | − | 0.999925i | \(-0.496089\pi\) | ||||
0.0122861 | + | 0.999925i | \(0.496089\pi\) | |||||||
\(90\) | −7.95930 | −0.838984 | ||||||||
\(91\) | −0.308254 | −0.0323138 | ||||||||
\(92\) | −19.0536 | −1.98647 | ||||||||
\(93\) | −0.620408 | −0.0643333 | ||||||||
\(94\) | −4.78253 | −0.493280 | ||||||||
\(95\) | 3.29013 | 0.337560 | ||||||||
\(96\) | 0.566544 | 0.0578227 | ||||||||
\(97\) | 2.09622 | 0.212839 | 0.106419 | − | 0.994321i | \(-0.466061\pi\) | ||||
0.106419 | + | 0.994321i | \(0.466061\pi\) | |||||||
\(98\) | −21.9841 | −2.22073 | ||||||||
\(99\) | 0.427041 | 0.0429192 | ||||||||
\(100\) | −17.0522 | −1.70522 | ||||||||
\(101\) | −11.8306 | −1.17719 | −0.588596 | − | 0.808427i | \(-0.700319\pi\) | ||||
−0.588596 | + | 0.808427i | \(0.700319\pi\) | |||||||
\(102\) | 0.332076 | 0.0328804 | ||||||||
\(103\) | 3.23062 | 0.318322 | 0.159161 | − | 0.987253i | \(-0.449121\pi\) | ||||
0.159161 | + | 0.987253i | \(0.449121\pi\) | |||||||
\(104\) | 0.469751 | 0.0460628 | ||||||||
\(105\) | 0.549539 | 0.0536295 | ||||||||
\(106\) | 17.7724 | 1.72620 | ||||||||
\(107\) | −14.1116 | −1.36422 | −0.682109 | − | 0.731251i | \(-0.738937\pi\) | ||||
−0.682109 | + | 0.731251i | \(0.738937\pi\) | |||||||
\(108\) | 3.44960 | 0.331938 | ||||||||
\(109\) | −17.3998 | −1.66660 | −0.833298 | − | 0.552824i | \(-0.813550\pi\) | ||||
−0.833298 | + | 0.552824i | \(0.813550\pi\) | |||||||
\(110\) | −0.382044 | −0.0364265 | ||||||||
\(111\) | −0.931680 | −0.0884312 | ||||||||
\(112\) | 25.6880 | 2.42729 | ||||||||
\(113\) | −15.3935 | −1.44810 | −0.724051 | − | 0.689746i | \(-0.757722\pi\) | ||||
−0.724051 | + | 0.689746i | \(0.757722\pi\) | |||||||
\(114\) | −1.03490 | −0.0969272 | ||||||||
\(115\) | 4.58341 | 0.427405 | ||||||||
\(116\) | −40.8273 | −3.79072 | ||||||||
\(117\) | 0.232063 | 0.0214543 | ||||||||
\(118\) | −2.52760 | −0.232684 | ||||||||
\(119\) | 3.96203 | 0.363198 | ||||||||
\(120\) | −0.837447 | −0.0764481 | ||||||||
\(121\) | −10.9795 | −0.998137 | ||||||||
\(122\) | −29.9332 | −2.71003 | ||||||||
\(123\) | −0.860205 | −0.0775621 | ||||||||
\(124\) | 20.7247 | 1.86113 | ||||||||
\(125\) | 9.38060 | 0.839027 | ||||||||
\(126\) | 29.8703 | 2.66106 | ||||||||
\(127\) | −8.69637 | −0.771678 | −0.385839 | − | 0.922566i | \(-0.626088\pi\) | ||||
−0.385839 | + | 0.922566i | \(0.626088\pi\) | |||||||
\(128\) | 13.8502 | 1.22420 | ||||||||
\(129\) | 1.41971 | 0.124999 | ||||||||
\(130\) | −0.207611 | −0.0182087 | ||||||||
\(131\) | 8.14459 | 0.711596 | 0.355798 | − | 0.934563i | \(-0.384209\pi\) | ||||
0.355798 | + | 0.934563i | \(0.384209\pi\) | |||||||
\(132\) | 0.0825512 | 0.00718516 | ||||||||
\(133\) | −12.3475 | −1.07066 | ||||||||
\(134\) | 38.8070 | 3.35241 | ||||||||
\(135\) | −0.829815 | −0.0714191 | ||||||||
\(136\) | −6.03776 | −0.517734 | ||||||||
\(137\) | −6.41725 | −0.548263 | −0.274131 | − | 0.961692i | \(-0.588390\pi\) | ||||
−0.274131 | + | 0.961692i | \(0.588390\pi\) | |||||||
\(138\) | −1.44169 | −0.122725 | ||||||||
\(139\) | −12.6874 | −1.07613 | −0.538067 | − | 0.842902i | \(-0.680845\pi\) | ||||
−0.538067 | + | 0.842902i | \(0.680845\pi\) | |||||||
\(140\) | −18.3573 | −1.55148 | ||||||||
\(141\) | −0.248587 | −0.0209348 | ||||||||
\(142\) | 5.95526 | 0.499754 | ||||||||
\(143\) | 0.0111390 | 0.000931489 0 | ||||||||
\(144\) | −19.3387 | −1.61156 | ||||||||
\(145\) | 9.82116 | 0.815603 | ||||||||
\(146\) | −3.41872 | −0.282935 | ||||||||
\(147\) | −1.14270 | −0.0942482 | ||||||||
\(148\) | 31.1227 | 2.55827 | ||||||||
\(149\) | −3.04529 | −0.249480 | −0.124740 | − | 0.992189i | \(-0.539810\pi\) | ||||
−0.124740 | + | 0.992189i | \(0.539810\pi\) | |||||||
\(150\) | −1.29026 | −0.105349 | ||||||||
\(151\) | 4.30708 | 0.350505 | 0.175253 | − | 0.984523i | \(-0.443926\pi\) | ||||
0.175253 | + | 0.984523i | \(0.443926\pi\) | |||||||
\(152\) | 18.8164 | 1.52621 | ||||||||
\(153\) | −2.98274 | −0.241140 | ||||||||
\(154\) | 1.43377 | 0.115536 | ||||||||
\(155\) | −4.98540 | −0.400437 | ||||||||
\(156\) | 0.0448601 | 0.00359168 | ||||||||
\(157\) | −11.3866 | −0.908748 | −0.454374 | − | 0.890811i | \(-0.650137\pi\) | ||||
−0.454374 | + | 0.890811i | \(0.650137\pi\) | |||||||
\(158\) | 4.49432 | 0.357549 | ||||||||
\(159\) | 0.923777 | 0.0732603 | ||||||||
\(160\) | 4.55256 | 0.359912 | ||||||||
\(161\) | −17.2010 | −1.35563 | ||||||||
\(162\) | −22.3565 | −1.75649 | ||||||||
\(163\) | −11.7585 | −0.920999 | −0.460500 | − | 0.887660i | \(-0.652330\pi\) | ||||
−0.460500 | + | 0.887660i | \(0.652330\pi\) | |||||||
\(164\) | 28.7351 | 2.24383 | ||||||||
\(165\) | −0.0198580 | −0.00154594 | ||||||||
\(166\) | 15.7244 | 1.22045 | ||||||||
\(167\) | −12.7938 | −0.990013 | −0.495007 | − | 0.868889i | \(-0.664834\pi\) | ||||
−0.495007 | + | 0.868889i | \(0.664834\pi\) | |||||||
\(168\) | 3.14284 | 0.242476 | ||||||||
\(169\) | −12.9939 | −0.999534 | ||||||||
\(170\) | 2.66845 | 0.204661 | ||||||||
\(171\) | 9.29558 | 0.710851 | ||||||||
\(172\) | −47.4254 | −3.61615 | ||||||||
\(173\) | 7.42598 | 0.564586 | 0.282293 | − | 0.959328i | \(-0.408905\pi\) | ||||
0.282293 | + | 0.959328i | \(0.408905\pi\) | |||||||
\(174\) | −3.08921 | −0.234193 | ||||||||
\(175\) | −15.3942 | −1.16369 | ||||||||
\(176\) | −0.928254 | −0.0699698 | ||||||||
\(177\) | −0.131380 | −0.00987513 | ||||||||
\(178\) | −0.585932 | −0.0439175 | ||||||||
\(179\) | 18.3553 | 1.37194 | 0.685969 | − | 0.727631i | \(-0.259379\pi\) | ||||
0.685969 | + | 0.727631i | \(0.259379\pi\) | |||||||
\(180\) | 13.8200 | 1.03008 | ||||||||
\(181\) | 14.3361 | 1.06560 | 0.532798 | − | 0.846242i | \(-0.321141\pi\) | ||||
0.532798 | + | 0.846242i | \(0.321141\pi\) | |||||||
\(182\) | 0.779141 | 0.0577538 | ||||||||
\(183\) | −1.55588 | −0.115014 | ||||||||
\(184\) | 26.2127 | 1.93243 | ||||||||
\(185\) | −7.48668 | −0.550432 | ||||||||
\(186\) | 1.56814 | 0.114982 | ||||||||
\(187\) | −0.143171 | −0.0104697 | ||||||||
\(188\) | 8.30404 | 0.605634 | ||||||||
\(189\) | 3.11420 | 0.226525 | ||||||||
\(190\) | −8.31612 | −0.603314 | ||||||||
\(191\) | 9.30556 | 0.673327 | 0.336663 | − | 0.941625i | \(-0.390702\pi\) | ||||
0.336663 | + | 0.941625i | \(0.390702\pi\) | |||||||
\(192\) | 0.271623 | 0.0196027 | ||||||||
\(193\) | −12.3151 | −0.886463 | −0.443231 | − | 0.896407i | \(-0.646168\pi\) | ||||
−0.443231 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(194\) | −5.29839 | −0.380402 | ||||||||
\(195\) | −0.0107913 | −0.000772779 0 | ||||||||
\(196\) | 38.1717 | 2.72655 | ||||||||
\(197\) | 8.10614 | 0.577538 | 0.288769 | − | 0.957399i | \(-0.406754\pi\) | ||||
0.288769 | + | 0.957399i | \(0.406754\pi\) | |||||||
\(198\) | −1.07939 | −0.0767087 | ||||||||
\(199\) | 25.6544 | 1.81859 | 0.909295 | − | 0.416152i | \(-0.136622\pi\) | ||||
0.909295 | + | 0.416152i | \(0.136622\pi\) | |||||||
\(200\) | 23.4594 | 1.65883 | ||||||||
\(201\) | 2.01712 | 0.142277 | ||||||||
\(202\) | 29.9031 | 2.10397 | ||||||||
\(203\) | −36.8577 | −2.58690 | ||||||||
\(204\) | −0.576593 | −0.0403696 | ||||||||
\(205\) | −6.91233 | −0.482778 | ||||||||
\(206\) | −8.16570 | −0.568931 | ||||||||
\(207\) | 12.9495 | 0.900050 | ||||||||
\(208\) | −0.504433 | −0.0349762 | ||||||||
\(209\) | 0.446186 | 0.0308633 | ||||||||
\(210\) | −1.38901 | −0.0958510 | ||||||||
\(211\) | 4.75556 | 0.327386 | 0.163693 | − | 0.986511i | \(-0.447659\pi\) | ||||
0.163693 | + | 0.986511i | \(0.447659\pi\) | |||||||
\(212\) | −30.8587 | −2.11938 | ||||||||
\(213\) | 0.309544 | 0.0212096 | ||||||||
\(214\) | 35.6683 | 2.43824 | ||||||||
\(215\) | 11.4084 | 0.778044 | ||||||||
\(216\) | −4.74576 | −0.322908 | ||||||||
\(217\) | 18.7096 | 1.27009 | ||||||||
\(218\) | 43.9796 | 2.97867 | ||||||||
\(219\) | −0.177699 | −0.0120078 | ||||||||
\(220\) | 0.663355 | 0.0447234 | ||||||||
\(221\) | −0.0778021 | −0.00523353 | ||||||||
\(222\) | 2.35491 | 0.158051 | ||||||||
\(223\) | −13.5394 | −0.906664 | −0.453332 | − | 0.891342i | \(-0.649765\pi\) | ||||
−0.453332 | + | 0.891342i | \(0.649765\pi\) | |||||||
\(224\) | −17.0853 | −1.14156 | ||||||||
\(225\) | 11.5893 | 0.772617 | ||||||||
\(226\) | 38.9086 | 2.58816 | ||||||||
\(227\) | 22.6419 | 1.50280 | 0.751398 | − | 0.659849i | \(-0.229380\pi\) | ||||
0.751398 | + | 0.659849i | \(0.229380\pi\) | |||||||
\(228\) | 1.79693 | 0.119004 | ||||||||
\(229\) | 26.3719 | 1.74270 | 0.871352 | − | 0.490658i | \(-0.163244\pi\) | ||||
0.871352 | + | 0.490658i | \(0.163244\pi\) | |||||||
\(230\) | −11.5850 | −0.763892 | ||||||||
\(231\) | 0.0745249 | 0.00490338 | ||||||||
\(232\) | 56.1678 | 3.68759 | ||||||||
\(233\) | 16.3691 | 1.07238 | 0.536189 | − | 0.844098i | \(-0.319863\pi\) | ||||
0.536189 | + | 0.844098i | \(0.319863\pi\) | |||||||
\(234\) | −0.586562 | −0.0383448 | ||||||||
\(235\) | −1.99757 | −0.130307 | ||||||||
\(236\) | 4.38874 | 0.285683 | ||||||||
\(237\) | 0.233607 | 0.0151744 | ||||||||
\(238\) | −10.0144 | −0.649137 | ||||||||
\(239\) | 7.70132 | 0.498157 | 0.249078 | − | 0.968483i | \(-0.419872\pi\) | ||||
0.249078 | + | 0.968483i | \(0.419872\pi\) | |||||||
\(240\) | 0.899278 | 0.0580481 | ||||||||
\(241\) | −16.7487 | −1.07888 | −0.539440 | − | 0.842024i | \(-0.681364\pi\) | ||||
−0.539440 | + | 0.842024i | \(0.681364\pi\) | |||||||
\(242\) | 27.7517 | 1.78395 | ||||||||
\(243\) | −3.52009 | −0.225814 | ||||||||
\(244\) | 51.9740 | 3.32729 | ||||||||
\(245\) | −9.18235 | −0.586639 | ||||||||
\(246\) | 2.17425 | 0.138625 | ||||||||
\(247\) | 0.242467 | 0.0154278 | ||||||||
\(248\) | −28.5118 | −1.81050 | ||||||||
\(249\) | 0.817330 | 0.0517962 | ||||||||
\(250\) | −23.7104 | −1.49958 | ||||||||
\(251\) | −23.6645 | −1.49369 | −0.746845 | − | 0.664998i | \(-0.768432\pi\) | ||||
−0.746845 | + | 0.664998i | \(0.768432\pi\) | |||||||
\(252\) | −51.8648 | −3.26717 | ||||||||
\(253\) | 0.621571 | 0.0390778 | ||||||||
\(254\) | 21.9809 | 1.37920 | ||||||||
\(255\) | 0.138702 | 0.00868583 | ||||||||
\(256\) | −30.8728 | −1.92955 | ||||||||
\(257\) | −7.53649 | −0.470113 | −0.235057 | − | 0.971982i | \(-0.575528\pi\) | ||||
−0.235057 | + | 0.971982i | \(0.575528\pi\) | |||||||
\(258\) | −3.58846 | −0.223408 | ||||||||
\(259\) | 28.0967 | 1.74584 | ||||||||
\(260\) | 0.360481 | 0.0223561 | ||||||||
\(261\) | 27.7477 | 1.71754 | ||||||||
\(262\) | −20.5862 | −1.27182 | ||||||||
\(263\) | −7.26470 | −0.447960 | −0.223980 | − | 0.974594i | \(-0.571905\pi\) | ||||
−0.223980 | + | 0.974594i | \(0.571905\pi\) | |||||||
\(264\) | −0.113569 | −0.00698969 | ||||||||
\(265\) | 7.42317 | 0.456002 | ||||||||
\(266\) | 31.2094 | 1.91357 | ||||||||
\(267\) | −0.0304558 | −0.00186386 | ||||||||
\(268\) | −67.3817 | −4.11599 | ||||||||
\(269\) | 4.96620 | 0.302795 | 0.151397 | − | 0.988473i | \(-0.451623\pi\) | ||||
0.151397 | + | 0.988473i | \(0.451623\pi\) | |||||||
\(270\) | 2.09744 | 0.127646 | ||||||||
\(271\) | −23.2652 | −1.41326 | −0.706631 | − | 0.707582i | \(-0.749786\pi\) | ||||
−0.706631 | + | 0.707582i | \(0.749786\pi\) | |||||||
\(272\) | 6.48355 | 0.393123 | ||||||||
\(273\) | 0.0404984 | 0.00245108 | ||||||||
\(274\) | 16.2202 | 0.979899 | ||||||||
\(275\) | 0.556281 | 0.0335450 | ||||||||
\(276\) | 2.50326 | 0.150678 | ||||||||
\(277\) | −17.5601 | −1.05508 | −0.527541 | − | 0.849529i | \(-0.676886\pi\) | ||||
−0.527541 | + | 0.849529i | \(0.676886\pi\) | |||||||
\(278\) | 32.0687 | 1.92335 | ||||||||
\(279\) | −14.0852 | −0.843260 | ||||||||
\(280\) | 25.2549 | 1.50927 | ||||||||
\(281\) | 11.4656 | 0.683979 | 0.341989 | − | 0.939704i | \(-0.388899\pi\) | ||||
0.341989 | + | 0.939704i | \(0.388899\pi\) | |||||||
\(282\) | 0.628328 | 0.0374164 | ||||||||
\(283\) | 18.6179 | 1.10672 | 0.553359 | − | 0.832943i | \(-0.313346\pi\) | ||||
0.553359 | + | 0.832943i | \(0.313346\pi\) | |||||||
\(284\) | −10.3403 | −0.613583 | ||||||||
\(285\) | −0.432257 | −0.0256047 | ||||||||
\(286\) | −0.0281548 | −0.00166483 | ||||||||
\(287\) | 25.9412 | 1.53126 | ||||||||
\(288\) | 12.8623 | 0.757920 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −24.8239 | −1.45771 | ||||||||
\(291\) | −0.275401 | −0.0161443 | ||||||||
\(292\) | 5.93602 | 0.347379 | ||||||||
\(293\) | −12.1329 | −0.708814 | −0.354407 | − | 0.935091i | \(-0.615317\pi\) | ||||
−0.354407 | + | 0.935091i | \(0.615317\pi\) | |||||||
\(294\) | 2.88828 | 0.168448 | ||||||||
\(295\) | −1.05573 | −0.0614668 | ||||||||
\(296\) | −42.8167 | −2.48867 | ||||||||
\(297\) | −0.112534 | −0.00652989 | ||||||||
\(298\) | 7.69725 | 0.445890 | ||||||||
\(299\) | 0.337775 | 0.0195340 | ||||||||
\(300\) | 2.24032 | 0.129345 | ||||||||
\(301\) | −42.8143 | −2.46778 | ||||||||
\(302\) | −10.8866 | −0.626451 | ||||||||
\(303\) | 1.55431 | 0.0892928 | ||||||||
\(304\) | −20.2057 | −1.15888 | ||||||||
\(305\) | −12.5025 | −0.715893 | ||||||||
\(306\) | 7.53916 | 0.430985 | ||||||||
\(307\) | −14.1309 | −0.806493 | −0.403246 | − | 0.915091i | \(-0.632118\pi\) | ||||
−0.403246 | + | 0.915091i | \(0.632118\pi\) | |||||||
\(308\) | −2.48950 | −0.141852 | ||||||||
\(309\) | −0.424439 | −0.0241455 | ||||||||
\(310\) | 12.6011 | 0.715693 | ||||||||
\(311\) | 24.8276 | 1.40785 | 0.703923 | − | 0.710276i | \(-0.251430\pi\) | ||||
0.703923 | + | 0.710276i | \(0.251430\pi\) | |||||||
\(312\) | −0.0617158 | −0.00349397 | ||||||||
\(313\) | 4.82660 | 0.272816 | 0.136408 | − | 0.990653i | \(-0.456444\pi\) | ||||
0.136408 | + | 0.990653i | \(0.456444\pi\) | |||||||
\(314\) | 28.7807 | 1.62419 | ||||||||
\(315\) | 12.4763 | 0.702958 | ||||||||
\(316\) | −7.80361 | −0.438988 | ||||||||
\(317\) | 8.50056 | 0.477439 | 0.238720 | − | 0.971089i | \(-0.423272\pi\) | ||||
0.238720 | + | 0.971089i | \(0.423272\pi\) | |||||||
\(318\) | −2.33493 | −0.130937 | ||||||||
\(319\) | 1.33188 | 0.0745710 | ||||||||
\(320\) | 2.18268 | 0.122015 | ||||||||
\(321\) | 1.85398 | 0.103479 | ||||||||
\(322\) | 43.4772 | 2.42289 | ||||||||
\(323\) | −3.11646 | −0.173404 | ||||||||
\(324\) | 38.8182 | 2.15657 | ||||||||
\(325\) | 0.302295 | 0.0167683 | ||||||||
\(326\) | 29.7208 | 1.64608 | ||||||||
\(327\) | 2.28598 | 0.126415 | ||||||||
\(328\) | −39.5320 | −2.18279 | ||||||||
\(329\) | 7.49665 | 0.413304 | ||||||||
\(330\) | 0.0501930 | 0.00276303 | ||||||||
\(331\) | 3.12950 | 0.172013 | 0.0860065 | − | 0.996295i | \(-0.472589\pi\) | ||||
0.0860065 | + | 0.996295i | \(0.472589\pi\) | |||||||
\(332\) | −27.3028 | −1.49844 | ||||||||
\(333\) | −21.1521 | −1.15913 | ||||||||
\(334\) | 32.3375 | 1.76943 | ||||||||
\(335\) | 16.2089 | 0.885588 | ||||||||
\(336\) | −3.37489 | −0.184115 | ||||||||
\(337\) | 8.50675 | 0.463392 | 0.231696 | − | 0.972788i | \(-0.425573\pi\) | ||||
0.231696 | + | 0.972788i | \(0.425573\pi\) | |||||||
\(338\) | 32.8434 | 1.78645 | ||||||||
\(339\) | 2.02240 | 0.109842 | ||||||||
\(340\) | −4.63331 | −0.251277 | ||||||||
\(341\) | −0.676087 | −0.0366122 | ||||||||
\(342\) | −23.4955 | −1.27049 | ||||||||
\(343\) | 6.72615 | 0.363178 | ||||||||
\(344\) | 65.2451 | 3.51778 | ||||||||
\(345\) | −0.602168 | −0.0324196 | ||||||||
\(346\) | −18.7699 | −1.00907 | ||||||||
\(347\) | 10.8779 | 0.583957 | 0.291979 | − | 0.956425i | \(-0.405686\pi\) | ||||
0.291979 | + | 0.956425i | \(0.405686\pi\) | |||||||
\(348\) | 5.36389 | 0.287535 | ||||||||
\(349\) | −20.4253 | −1.09334 | −0.546671 | − | 0.837348i | \(-0.684105\pi\) | ||||
−0.546671 | + | 0.837348i | \(0.684105\pi\) | |||||||
\(350\) | 38.9103 | 2.07985 | ||||||||
\(351\) | −0.0611534 | −0.00326413 | ||||||||
\(352\) | 0.617389 | 0.0329069 | ||||||||
\(353\) | −7.21912 | −0.384235 | −0.192117 | − | 0.981372i | \(-0.561535\pi\) | ||||
−0.192117 | + | 0.981372i | \(0.561535\pi\) | |||||||
\(354\) | 0.332076 | 0.0176496 | ||||||||
\(355\) | 2.48740 | 0.132017 | ||||||||
\(356\) | 1.01737 | 0.0539206 | ||||||||
\(357\) | −0.520531 | −0.0275494 | ||||||||
\(358\) | −46.3947 | −2.45204 | ||||||||
\(359\) | 5.86760 | 0.309680 | 0.154840 | − | 0.987940i | \(-0.450514\pi\) | ||||
0.154840 | + | 0.987940i | \(0.450514\pi\) | |||||||
\(360\) | −19.0127 | −1.00206 | ||||||||
\(361\) | −9.28770 | −0.488826 | ||||||||
\(362\) | −36.2359 | −1.90452 | ||||||||
\(363\) | 1.44249 | 0.0757110 | ||||||||
\(364\) | −1.35285 | −0.0709084 | ||||||||
\(365\) | −1.42793 | −0.0747414 | ||||||||
\(366\) | 3.93263 | 0.205562 | ||||||||
\(367\) | −10.6311 | −0.554939 | −0.277469 | − | 0.960734i | \(-0.589496\pi\) | ||||
−0.277469 | + | 0.960734i | \(0.589496\pi\) | |||||||
\(368\) | −28.1481 | −1.46732 | ||||||||
\(369\) | −19.5294 | −1.01666 | ||||||||
\(370\) | 18.9233 | 0.983776 | ||||||||
\(371\) | −27.8583 | −1.44633 | ||||||||
\(372\) | −2.72281 | −0.141171 | ||||||||
\(373\) | 24.7657 | 1.28232 | 0.641158 | − | 0.767409i | \(-0.278454\pi\) | ||||
0.641158 | + | 0.767409i | \(0.278454\pi\) | |||||||
\(374\) | 0.361878 | 0.0187123 | ||||||||
\(375\) | −1.23242 | −0.0636421 | ||||||||
\(376\) | −11.4242 | −0.589158 | ||||||||
\(377\) | 0.723773 | 0.0372762 | ||||||||
\(378\) | −7.87144 | −0.404863 | ||||||||
\(379\) | −1.70887 | −0.0877790 | −0.0438895 | − | 0.999036i | \(-0.513975\pi\) | ||||
−0.0438895 | + | 0.999036i | \(0.513975\pi\) | |||||||
\(380\) | 14.4395 | 0.740732 | ||||||||
\(381\) | 1.14253 | 0.0585336 | ||||||||
\(382\) | −23.5207 | −1.20342 | ||||||||
\(383\) | 7.89067 | 0.403194 | 0.201597 | − | 0.979469i | \(-0.435387\pi\) | ||||
0.201597 | + | 0.979469i | \(0.435387\pi\) | |||||||
\(384\) | −1.81964 | −0.0928582 | ||||||||
\(385\) | 0.598858 | 0.0305206 | ||||||||
\(386\) | 31.1277 | 1.58436 | ||||||||
\(387\) | 32.2320 | 1.63844 | ||||||||
\(388\) | 9.19975 | 0.467046 | ||||||||
\(389\) | −7.20820 | −0.365470 | −0.182735 | − | 0.983162i | \(-0.558495\pi\) | ||||
−0.182735 | + | 0.983162i | \(0.558495\pi\) | |||||||
\(390\) | 0.0272760 | 0.00138117 | ||||||||
\(391\) | −4.34147 | −0.219557 | ||||||||
\(392\) | −52.5144 | −2.65238 | ||||||||
\(393\) | −1.07004 | −0.0539762 | ||||||||
\(394\) | −20.4890 | −1.03222 | ||||||||
\(395\) | 1.87719 | 0.0944516 | ||||||||
\(396\) | 1.87417 | 0.0941807 | ||||||||
\(397\) | −16.3584 | −0.821007 | −0.410503 | − | 0.911859i | \(-0.634647\pi\) | ||||
−0.410503 | + | 0.911859i | \(0.634647\pi\) | |||||||
\(398\) | −64.8439 | −3.25033 | ||||||||
\(399\) | 1.62221 | 0.0812122 | ||||||||
\(400\) | −25.1914 | −1.25957 | ||||||||
\(401\) | −1.96622 | −0.0981884 | −0.0490942 | − | 0.998794i | \(-0.515633\pi\) | ||||
−0.0490942 | + | 0.998794i | \(0.515633\pi\) | |||||||
\(402\) | −5.09846 | −0.254288 | ||||||||
\(403\) | −0.367400 | −0.0183015 | ||||||||
\(404\) | −51.9216 | −2.58319 | ||||||||
\(405\) | −9.33786 | −0.464002 | ||||||||
\(406\) | 93.1614 | 4.62352 | ||||||||
\(407\) | −1.01529 | −0.0503263 | ||||||||
\(408\) | 0.793242 | 0.0392713 | ||||||||
\(409\) | 33.2077 | 1.64201 | 0.821006 | − | 0.570919i | \(-0.193413\pi\) | ||||
0.821006 | + | 0.570919i | \(0.193413\pi\) | |||||||
\(410\) | 17.4716 | 0.862859 | ||||||||
\(411\) | 0.843099 | 0.0415870 | ||||||||
\(412\) | 14.1783 | 0.698517 | ||||||||
\(413\) | 3.96203 | 0.194959 | ||||||||
\(414\) | −32.7310 | −1.60864 | ||||||||
\(415\) | 6.56780 | 0.322401 | ||||||||
\(416\) | 0.335502 | 0.0164494 | ||||||||
\(417\) | 1.66688 | 0.0816273 | ||||||||
\(418\) | −1.12778 | −0.0551613 | ||||||||
\(419\) | −35.0489 | −1.71225 | −0.856125 | − | 0.516770i | \(-0.827134\pi\) | ||||
−0.856125 | + | 0.516770i | \(0.827134\pi\) | |||||||
\(420\) | 2.41178 | 0.117683 | ||||||||
\(421\) | −0.801576 | −0.0390664 | −0.0195332 | − | 0.999809i | \(-0.506218\pi\) | ||||
−0.0195332 | + | 0.999809i | \(0.506218\pi\) | |||||||
\(422\) | −12.0201 | −0.585131 | ||||||||
\(423\) | −5.64372 | −0.274407 | ||||||||
\(424\) | 42.4535 | 2.06173 | ||||||||
\(425\) | −3.88544 | −0.188471 | ||||||||
\(426\) | −0.782402 | −0.0379075 | ||||||||
\(427\) | 46.9206 | 2.27065 | ||||||||
\(428\) | −61.9320 | −2.99360 | ||||||||
\(429\) | −0.00146344 | −7.06556e−5 0 | ||||||||
\(430\) | −28.8357 | −1.39058 | ||||||||
\(431\) | −0.544234 | −0.0262148 | −0.0131074 | − | 0.999914i | \(-0.504172\pi\) | ||||
−0.0131074 | + | 0.999914i | \(0.504172\pi\) | |||||||
\(432\) | 5.09615 | 0.245189 | ||||||||
\(433\) | −32.6724 | −1.57014 | −0.785068 | − | 0.619409i | \(-0.787372\pi\) | ||||
−0.785068 | + | 0.619409i | \(0.787372\pi\) | |||||||
\(434\) | −47.2904 | −2.27001 | ||||||||
\(435\) | −1.29030 | −0.0618654 | ||||||||
\(436\) | −76.3631 | −3.65713 | ||||||||
\(437\) | 13.5300 | 0.647227 | ||||||||
\(438\) | 0.449151 | 0.0214613 | ||||||||
\(439\) | 38.8081 | 1.85221 | 0.926106 | − | 0.377264i | \(-0.123135\pi\) | ||||
0.926106 | + | 0.377264i | \(0.123135\pi\) | |||||||
\(440\) | −0.912604 | −0.0435067 | ||||||||
\(441\) | −25.9428 | −1.23537 | ||||||||
\(442\) | 0.196652 | 0.00935379 | ||||||||
\(443\) | −11.1198 | −0.528316 | −0.264158 | − | 0.964479i | \(-0.585094\pi\) | ||||
−0.264158 | + | 0.964479i | \(0.585094\pi\) | |||||||
\(444\) | −4.08890 | −0.194051 | ||||||||
\(445\) | −0.244733 | −0.0116014 | ||||||||
\(446\) | 34.2221 | 1.62046 | ||||||||
\(447\) | 0.400090 | 0.0189236 | ||||||||
\(448\) | −8.19133 | −0.387004 | ||||||||
\(449\) | −22.7913 | −1.07559 | −0.537794 | − | 0.843076i | \(-0.680742\pi\) | ||||
−0.537794 | + | 0.843076i | \(0.680742\pi\) | |||||||
\(450\) | −29.2929 | −1.38088 | ||||||||
\(451\) | −0.937404 | −0.0441407 | ||||||||
\(452\) | −67.5582 | −3.17767 | ||||||||
\(453\) | −0.565864 | −0.0265866 | ||||||||
\(454\) | −57.2296 | −2.68592 | ||||||||
\(455\) | 0.325432 | 0.0152565 | ||||||||
\(456\) | −2.47210 | −0.115767 | ||||||||
\(457\) | −0.494743 | −0.0231431 | −0.0115715 | − | 0.999933i | \(-0.503683\pi\) | ||||
−0.0115715 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(458\) | −66.6575 | −3.11470 | ||||||||
\(459\) | 0.786013 | 0.0366879 | ||||||||
\(460\) | 20.1154 | 0.937884 | ||||||||
\(461\) | −3.13609 | −0.146063 | −0.0730313 | − | 0.997330i | \(-0.523267\pi\) | ||||
−0.0730313 | + | 0.997330i | \(0.523267\pi\) | |||||||
\(462\) | −0.188369 | −0.00876370 | ||||||||
\(463\) | −7.24660 | −0.336778 | −0.168389 | − | 0.985721i | \(-0.553857\pi\) | ||||
−0.168389 | + | 0.985721i | \(0.553857\pi\) | |||||||
\(464\) | −60.3148 | −2.80004 | ||||||||
\(465\) | 0.654982 | 0.0303741 | ||||||||
\(466\) | −41.3746 | −1.91664 | ||||||||
\(467\) | −32.5522 | −1.50634 | −0.753168 | − | 0.657829i | \(-0.771475\pi\) | ||||
−0.753168 | + | 0.657829i | \(0.771475\pi\) | |||||||
\(468\) | 1.01847 | 0.0470786 | ||||||||
\(469\) | −60.8303 | −2.80888 | ||||||||
\(470\) | 5.04904 | 0.232895 | ||||||||
\(471\) | 1.49597 | 0.0689306 | ||||||||
\(472\) | −6.03776 | −0.277911 | ||||||||
\(473\) | 1.54713 | 0.0711370 | ||||||||
\(474\) | −0.590463 | −0.0271209 | ||||||||
\(475\) | 12.1088 | 0.555590 | ||||||||
\(476\) | 17.3883 | 0.796991 | ||||||||
\(477\) | 20.9726 | 0.960271 | ||||||||
\(478\) | −19.4658 | −0.890346 | ||||||||
\(479\) | −8.88084 | −0.405776 | −0.202888 | − | 0.979202i | \(-0.565033\pi\) | ||||
−0.202888 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(480\) | −0.598116 | −0.0273001 | ||||||||
\(481\) | −0.551733 | −0.0251569 | ||||||||
\(482\) | 42.3340 | 1.92826 | ||||||||
\(483\) | 2.25987 | 0.102828 | ||||||||
\(484\) | −48.1862 | −2.19028 | ||||||||
\(485\) | −2.21303 | −0.100489 | ||||||||
\(486\) | 8.89736 | 0.403592 | ||||||||
\(487\) | 20.8123 | 0.943097 | 0.471548 | − | 0.881840i | \(-0.343695\pi\) | ||||
0.471548 | + | 0.881840i | \(0.343695\pi\) | |||||||
\(488\) | −71.5027 | −3.23677 | ||||||||
\(489\) | 1.54484 | 0.0698599 | ||||||||
\(490\) | 23.2093 | 1.04849 | ||||||||
\(491\) | 22.6789 | 1.02349 | 0.511743 | − | 0.859139i | \(-0.329000\pi\) | ||||
0.511743 | + | 0.859139i | \(0.329000\pi\) | |||||||
\(492\) | −3.77521 | −0.170200 | ||||||||
\(493\) | −9.30274 | −0.418975 | ||||||||
\(494\) | −0.612858 | −0.0275738 | ||||||||
\(495\) | −0.450839 | −0.0202637 | ||||||||
\(496\) | 30.6169 | 1.37474 | ||||||||
\(497\) | −9.33492 | −0.418728 | ||||||||
\(498\) | −2.06588 | −0.0925742 | ||||||||
\(499\) | 12.8234 | 0.574055 | 0.287027 | − | 0.957922i | \(-0.407333\pi\) | ||||
0.287027 | + | 0.957922i | \(0.407333\pi\) | |||||||
\(500\) | 41.1690 | 1.84113 | ||||||||
\(501\) | 1.68085 | 0.0750948 | ||||||||
\(502\) | 59.8143 | 2.66964 | ||||||||
\(503\) | 42.4655 | 1.89344 | 0.946722 | − | 0.322051i | \(-0.104372\pi\) | ||||
0.946722 | + | 0.322051i | \(0.104372\pi\) | |||||||
\(504\) | 71.3524 | 3.17829 | ||||||||
\(505\) | 12.4899 | 0.555795 | ||||||||
\(506\) | −1.57108 | −0.0698430 | ||||||||
\(507\) | 1.70715 | 0.0758170 | ||||||||
\(508\) | −38.1661 | −1.69335 | ||||||||
\(509\) | 37.9196 | 1.68076 | 0.840379 | − | 0.542000i | \(-0.182333\pi\) | ||||
0.840379 | + | 0.542000i | \(0.182333\pi\) | |||||||
\(510\) | −0.350581 | −0.0155240 | ||||||||
\(511\) | 5.35887 | 0.237062 | ||||||||
\(512\) | 50.3335 | 2.22445 | ||||||||
\(513\) | −2.44957 | −0.108151 | ||||||||
\(514\) | 19.0492 | 0.840224 | ||||||||
\(515\) | −3.41065 | −0.150291 | ||||||||
\(516\) | 6.23075 | 0.274294 | ||||||||
\(517\) | −0.270897 | −0.0119140 | ||||||||
\(518\) | −71.0170 | −3.12031 | ||||||||
\(519\) | −0.975625 | −0.0428252 | ||||||||
\(520\) | −0.495929 | −0.0217479 | ||||||||
\(521\) | −17.2911 | −0.757536 | −0.378768 | − | 0.925492i | \(-0.623652\pi\) | ||||
−0.378768 | + | 0.925492i | \(0.623652\pi\) | |||||||
\(522\) | −70.1349 | −3.06972 | ||||||||
\(523\) | 35.1954 | 1.53899 | 0.769494 | − | 0.638654i | \(-0.220508\pi\) | ||||
0.769494 | + | 0.638654i | \(0.220508\pi\) | |||||||
\(524\) | 35.7445 | 1.56150 | ||||||||
\(525\) | 2.02249 | 0.0882688 | ||||||||
\(526\) | 18.3622 | 0.800631 | ||||||||
\(527\) | 4.72224 | 0.205704 | ||||||||
\(528\) | 0.121954 | 0.00530737 | ||||||||
\(529\) | −4.15167 | −0.180507 | ||||||||
\(530\) | −18.7628 | −0.815003 | ||||||||
\(531\) | −2.98274 | −0.129440 | ||||||||
\(532\) | −54.1899 | −2.34943 | ||||||||
\(533\) | −0.509406 | −0.0220648 | ||||||||
\(534\) | 0.0769798 | 0.00333124 | ||||||||
\(535\) | 14.8980 | 0.644096 | ||||||||
\(536\) | 92.6997 | 4.00402 | ||||||||
\(537\) | −2.41152 | −0.104065 | ||||||||
\(538\) | −12.5526 | −0.541179 | ||||||||
\(539\) | −1.24525 | −0.0536367 | ||||||||
\(540\) | −3.64184 | −0.156720 | ||||||||
\(541\) | 2.03948 | 0.0876842 | 0.0438421 | − | 0.999038i | \(-0.486040\pi\) | ||||
0.0438421 | + | 0.999038i | \(0.486040\pi\) | |||||||
\(542\) | 58.8051 | 2.52590 | ||||||||
\(543\) | −1.88348 | −0.0808279 | ||||||||
\(544\) | −4.31225 | −0.184886 | ||||||||
\(545\) | 18.3694 | 0.786860 | ||||||||
\(546\) | −0.102364 | −0.00438076 | ||||||||
\(547\) | 39.3632 | 1.68305 | 0.841524 | − | 0.540220i | \(-0.181659\pi\) | ||||
0.841524 | + | 0.540220i | \(0.181659\pi\) | |||||||
\(548\) | −28.1636 | −1.20309 | ||||||||
\(549\) | −35.3233 | −1.50756 | ||||||||
\(550\) | −1.40605 | −0.0599544 | ||||||||
\(551\) | 28.9916 | 1.23508 | ||||||||
\(552\) | −3.44383 | −0.146579 | ||||||||
\(553\) | −7.04488 | −0.299579 | ||||||||
\(554\) | 44.3847 | 1.88573 | ||||||||
\(555\) | 0.983601 | 0.0417515 | ||||||||
\(556\) | −55.6818 | −2.36144 | ||||||||
\(557\) | 8.78350 | 0.372169 | 0.186084 | − | 0.982534i | \(-0.440420\pi\) | ||||
0.186084 | + | 0.982534i | \(0.440420\pi\) | |||||||
\(558\) | 35.6017 | 1.50714 | ||||||||
\(559\) | 0.840742 | 0.0355596 | ||||||||
\(560\) | −27.1195 | −1.14601 | ||||||||
\(561\) | 0.0188098 | 0.000794150 0 | ||||||||
\(562\) | −28.9803 | −1.22246 | ||||||||
\(563\) | 35.9554 | 1.51534 | 0.757670 | − | 0.652638i | \(-0.226338\pi\) | ||||
0.757670 | + | 0.652638i | \(0.226338\pi\) | |||||||
\(564\) | −1.09099 | −0.0459388 | ||||||||
\(565\) | 16.2514 | 0.683701 | ||||||||
\(566\) | −47.0585 | −1.97802 | ||||||||
\(567\) | 35.0439 | 1.47171 | ||||||||
\(568\) | 14.2256 | 0.596891 | ||||||||
\(569\) | −18.7524 | −0.786140 | −0.393070 | − | 0.919509i | \(-0.628587\pi\) | ||||
−0.393070 | + | 0.919509i | \(0.628587\pi\) | |||||||
\(570\) | 1.09257 | 0.0457628 | ||||||||
\(571\) | −29.3361 | −1.22768 | −0.613839 | − | 0.789431i | \(-0.710375\pi\) | ||||
−0.613839 | + | 0.789431i | \(0.710375\pi\) | |||||||
\(572\) | 0.0488861 | 0.00204403 | ||||||||
\(573\) | −1.22257 | −0.0510734 | ||||||||
\(574\) | −65.5688 | −2.73679 | ||||||||
\(575\) | 16.8685 | 0.703465 | ||||||||
\(576\) | 6.16670 | 0.256946 | ||||||||
\(577\) | 43.0974 | 1.79417 | 0.897084 | − | 0.441860i | \(-0.145681\pi\) | ||||
0.897084 | + | 0.441860i | \(0.145681\pi\) | |||||||
\(578\) | −2.52760 | −0.105134 | ||||||||
\(579\) | 1.61796 | 0.0672402 | ||||||||
\(580\) | 43.1025 | 1.78973 | ||||||||
\(581\) | −24.6482 | −1.02258 | ||||||||
\(582\) | 0.696103 | 0.0288544 | ||||||||
\(583\) | 1.00668 | 0.0416925 | ||||||||
\(584\) | −8.16642 | −0.337929 | ||||||||
\(585\) | −0.244996 | −0.0101293 | ||||||||
\(586\) | 30.6672 | 1.26685 | ||||||||
\(587\) | −9.58551 | −0.395636 | −0.197818 | − | 0.980239i | \(-0.563386\pi\) | ||||
−0.197818 | + | 0.980239i | \(0.563386\pi\) | |||||||
\(588\) | −5.01500 | −0.206815 | ||||||||
\(589\) | −14.7167 | −0.606389 | ||||||||
\(590\) | 2.66845 | 0.109858 | ||||||||
\(591\) | −1.06498 | −0.0438076 | ||||||||
\(592\) | 45.9780 | 1.88968 | ||||||||
\(593\) | −9.06335 | −0.372187 | −0.186094 | − | 0.982532i | \(-0.559583\pi\) | ||||
−0.186094 | + | 0.982532i | \(0.559583\pi\) | |||||||
\(594\) | 0.284440 | 0.0116707 | ||||||||
\(595\) | −4.18282 | −0.171479 | ||||||||
\(596\) | −13.3650 | −0.547450 | ||||||||
\(597\) | −3.37047 | −0.137944 | ||||||||
\(598\) | −0.853759 | −0.0349128 | ||||||||
\(599\) | 2.13607 | 0.0872775 | 0.0436387 | − | 0.999047i | \(-0.486105\pi\) | ||||
0.0436387 | + | 0.999047i | \(0.486105\pi\) | |||||||
\(600\) | −3.08209 | −0.125826 | ||||||||
\(601\) | −11.4477 | −0.466960 | −0.233480 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233480 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(602\) | 108.217 | 4.41061 | ||||||||
\(603\) | 45.7949 | 1.86491 | ||||||||
\(604\) | 18.9027 | 0.769138 | ||||||||
\(605\) | 11.5914 | 0.471256 | ||||||||
\(606\) | −3.92867 | −0.159591 | ||||||||
\(607\) | 34.0756 | 1.38309 | 0.691543 | − | 0.722335i | \(-0.256931\pi\) | ||||
0.691543 | + | 0.722335i | \(0.256931\pi\) | |||||||
\(608\) | 13.4389 | 0.545021 | ||||||||
\(609\) | 4.84237 | 0.196223 | ||||||||
\(610\) | 31.6013 | 1.27950 | ||||||||
\(611\) | −0.147211 | −0.00595553 | ||||||||
\(612\) | −13.0905 | −0.529151 | ||||||||
\(613\) | −19.8612 | −0.802186 | −0.401093 | − | 0.916037i | \(-0.631370\pi\) | ||||
−0.401093 | + | 0.916037i | \(0.631370\pi\) | |||||||
\(614\) | 35.7172 | 1.44143 | ||||||||
\(615\) | 0.908142 | 0.0366198 | ||||||||
\(616\) | 3.42490 | 0.137993 | ||||||||
\(617\) | −19.6163 | −0.789722 | −0.394861 | − | 0.918741i | \(-0.629207\pi\) | ||||
−0.394861 | + | 0.918741i | \(0.629207\pi\) | |||||||
\(618\) | 1.07281 | 0.0431547 | ||||||||
\(619\) | −16.2618 | −0.653618 | −0.326809 | − | 0.945090i | \(-0.605973\pi\) | ||||
−0.326809 | + | 0.945090i | \(0.605973\pi\) | |||||||
\(620\) | −21.8796 | −0.878707 | ||||||||
\(621\) | −3.41245 | −0.136937 | ||||||||
\(622\) | −62.7542 | −2.51621 | ||||||||
\(623\) | 0.918454 | 0.0367971 | ||||||||
\(624\) | 0.0662725 | 0.00265302 | ||||||||
\(625\) | 9.52383 | 0.380953 | ||||||||
\(626\) | −12.1997 | −0.487598 | ||||||||
\(627\) | −0.0586199 | −0.00234105 | ||||||||
\(628\) | −49.9727 | −1.99413 | ||||||||
\(629\) | 7.09149 | 0.282756 | ||||||||
\(630\) | −31.5349 | −1.25638 | ||||||||
\(631\) | 42.1213 | 1.67682 | 0.838411 | − | 0.545038i | \(-0.183485\pi\) | ||||
0.838411 | + | 0.545038i | \(0.183485\pi\) | |||||||
\(632\) | 10.7357 | 0.427045 | ||||||||
\(633\) | −0.624786 | −0.0248330 | ||||||||
\(634\) | −21.4860 | −0.853318 | ||||||||
\(635\) | 9.18100 | 0.364337 | ||||||||
\(636\) | 4.05421 | 0.160760 | ||||||||
\(637\) | −0.676696 | −0.0268117 | ||||||||
\(638\) | −3.36646 | −0.133279 | ||||||||
\(639\) | 7.02762 | 0.278008 | ||||||||
\(640\) | −14.6220 | −0.577987 | ||||||||
\(641\) | 50.0629 | 1.97736 | 0.988682 | − | 0.150024i | \(-0.0479352\pi\) | ||||
0.988682 | + | 0.150024i | \(0.0479352\pi\) | |||||||
\(642\) | −4.68611 | −0.184946 | ||||||||
\(643\) | 25.7809 | 1.01670 | 0.508349 | − | 0.861151i | \(-0.330256\pi\) | ||||
0.508349 | + | 0.861151i | \(0.330256\pi\) | |||||||
\(644\) | −75.4907 | −2.97475 | ||||||||
\(645\) | −1.49883 | −0.0590164 | ||||||||
\(646\) | 7.87714 | 0.309922 | ||||||||
\(647\) | −30.9564 | −1.21702 | −0.608510 | − | 0.793546i | \(-0.708233\pi\) | ||||
−0.608510 | + | 0.793546i | \(0.708233\pi\) | |||||||
\(648\) | −53.4037 | −2.09790 | ||||||||
\(649\) | −0.143171 | −0.00561994 | ||||||||
\(650\) | −0.764080 | −0.0299697 | ||||||||
\(651\) | −2.45807 | −0.0963395 | ||||||||
\(652\) | −51.6051 | −2.02101 | ||||||||
\(653\) | −5.83621 | −0.228389 | −0.114194 | − | 0.993458i | \(-0.536429\pi\) | ||||
−0.114194 | + | 0.993458i | \(0.536429\pi\) | |||||||
\(654\) | −5.77804 | −0.225939 | ||||||||
\(655\) | −8.59846 | −0.335970 | ||||||||
\(656\) | 42.4507 | 1.65742 | ||||||||
\(657\) | −4.03432 | −0.157394 | ||||||||
\(658\) | −18.9485 | −0.738689 | ||||||||
\(659\) | 43.9526 | 1.71215 | 0.856076 | − | 0.516851i | \(-0.172896\pi\) | ||||
0.856076 | + | 0.516851i | \(0.172896\pi\) | |||||||
\(660\) | −0.0871516 | −0.00339237 | ||||||||
\(661\) | 32.5866 | 1.26747 | 0.633735 | − | 0.773550i | \(-0.281521\pi\) | ||||
0.633735 | + | 0.773550i | \(0.281521\pi\) | |||||||
\(662\) | −7.91012 | −0.307435 | ||||||||
\(663\) | 0.0102216 | 0.000396976 0 | ||||||||
\(664\) | 37.5616 | 1.45767 | ||||||||
\(665\) | 13.0356 | 0.505498 | ||||||||
\(666\) | 53.4639 | 2.07168 | ||||||||
\(667\) | 40.3875 | 1.56381 | ||||||||
\(668\) | −56.1486 | −2.17245 | ||||||||
\(669\) | 1.77880 | 0.0687725 | ||||||||
\(670\) | −40.9696 | −1.58279 | ||||||||
\(671\) | −1.69551 | −0.0654545 | ||||||||
\(672\) | 2.24466 | 0.0865897 | ||||||||
\(673\) | −12.1877 | −0.469800 | −0.234900 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234900 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(674\) | −21.5016 | −0.828211 | ||||||||
\(675\) | −3.05400 | −0.117549 | ||||||||
\(676\) | −57.0270 | −2.19335 | ||||||||
\(677\) | −31.8860 | −1.22548 | −0.612740 | − | 0.790285i | \(-0.709933\pi\) | ||||
−0.612740 | + | 0.790285i | \(0.709933\pi\) | |||||||
\(678\) | −5.11182 | −0.196318 | ||||||||
\(679\) | 8.30527 | 0.318727 | ||||||||
\(680\) | 6.37423 | 0.244441 | ||||||||
\(681\) | −2.97470 | −0.113991 | ||||||||
\(682\) | 1.70887 | 0.0654362 | ||||||||
\(683\) | −25.1992 | −0.964219 | −0.482110 | − | 0.876111i | \(-0.660129\pi\) | ||||
−0.482110 | + | 0.876111i | \(0.660129\pi\) | |||||||
\(684\) | 40.7959 | 1.55987 | ||||||||
\(685\) | 6.77487 | 0.258854 | ||||||||
\(686\) | −17.0010 | −0.649101 | ||||||||
\(687\) | −3.46474 | −0.132188 | ||||||||
\(688\) | −70.0623 | −2.67110 | ||||||||
\(689\) | 0.547052 | 0.0208410 | ||||||||
\(690\) | 1.52204 | 0.0579430 | ||||||||
\(691\) | 29.7311 | 1.13102 | 0.565511 | − | 0.824740i | \(-0.308679\pi\) | ||||
0.565511 | + | 0.824740i | \(0.308679\pi\) | |||||||
\(692\) | 32.5907 | 1.23891 | ||||||||
\(693\) | 1.69195 | 0.0642718 | ||||||||
\(694\) | −27.4950 | −1.04369 | ||||||||
\(695\) | 13.3945 | 0.508082 | ||||||||
\(696\) | −7.37932 | −0.279713 | ||||||||
\(697\) | 6.54746 | 0.248003 | ||||||||
\(698\) | 51.6269 | 1.95411 | ||||||||
\(699\) | −2.15058 | −0.0813424 | ||||||||
\(700\) | −67.5612 | −2.55357 | ||||||||
\(701\) | 34.7676 | 1.31315 | 0.656576 | − | 0.754260i | \(-0.272004\pi\) | ||||
0.656576 | + | 0.754260i | \(0.272004\pi\) | |||||||
\(702\) | 0.154571 | 0.00583391 | ||||||||
\(703\) | −22.1003 | −0.833530 | ||||||||
\(704\) | 0.296000 | 0.0111559 | ||||||||
\(705\) | 0.262441 | 0.00988409 | ||||||||
\(706\) | 18.2470 | 0.686735 | ||||||||
\(707\) | −46.8733 | −1.76285 | ||||||||
\(708\) | −0.576593 | −0.0216697 | ||||||||
\(709\) | −16.8180 | −0.631614 | −0.315807 | − | 0.948823i | \(-0.602275\pi\) | ||||
−0.315807 | + | 0.948823i | \(0.602275\pi\) | |||||||
\(710\) | −6.28713 | −0.235952 | ||||||||
\(711\) | 5.30361 | 0.198901 | ||||||||
\(712\) | −1.39964 | −0.0524537 | ||||||||
\(713\) | −20.5015 | −0.767785 | ||||||||
\(714\) | 1.31569 | 0.0492385 | ||||||||
\(715\) | −0.0117597 | −0.000439789 0 | ||||||||
\(716\) | 80.5565 | 3.01054 | ||||||||
\(717\) | −1.01180 | −0.0377863 | ||||||||
\(718\) | −14.8309 | −0.553485 | ||||||||
\(719\) | 7.78192 | 0.290217 | 0.145108 | − | 0.989416i | \(-0.453647\pi\) | ||||
0.145108 | + | 0.989416i | \(0.453647\pi\) | |||||||
\(720\) | 20.4164 | 0.760875 | ||||||||
\(721\) | 12.7998 | 0.476689 | ||||||||
\(722\) | 23.4755 | 0.873669 | ||||||||
\(723\) | 2.20045 | 0.0818355 | ||||||||
\(724\) | 62.9175 | 2.33831 | ||||||||
\(725\) | 36.1452 | 1.34240 | ||||||||
\(726\) | −3.64602 | −0.135317 | ||||||||
\(727\) | −19.4438 | −0.721131 | −0.360565 | − | 0.932734i | \(-0.617416\pi\) | ||||
−0.360565 | + | 0.932734i | \(0.617416\pi\) | |||||||
\(728\) | 1.86116 | 0.0689793 | ||||||||
\(729\) | −26.0724 | −0.965644 | ||||||||
\(730\) | 3.60923 | 0.133584 | ||||||||
\(731\) | −10.8062 | −0.399680 | ||||||||
\(732\) | −6.82834 | −0.252383 | ||||||||
\(733\) | −29.9760 | −1.10719 | −0.553595 | − | 0.832786i | \(-0.686744\pi\) | ||||
−0.553595 | + | 0.832786i | \(0.686744\pi\) | |||||||
\(734\) | 26.8711 | 0.991831 | ||||||||
\(735\) | 1.20638 | 0.0444979 | ||||||||
\(736\) | 18.7215 | 0.690084 | ||||||||
\(737\) | 2.19815 | 0.0809698 | ||||||||
\(738\) | 49.3623 | 1.81705 | ||||||||
\(739\) | −28.4875 | −1.04793 | −0.523966 | − | 0.851739i | \(-0.675548\pi\) | ||||
−0.523966 | + | 0.851739i | \(0.675548\pi\) | |||||||
\(740\) | −32.8571 | −1.20785 | ||||||||
\(741\) | −0.0318553 | −0.00117023 | ||||||||
\(742\) | 70.4146 | 2.58500 | ||||||||
\(743\) | 12.4142 | 0.455431 | 0.227716 | − | 0.973728i | \(-0.426874\pi\) | ||||
0.227716 | + | 0.973728i | \(0.426874\pi\) | |||||||
\(744\) | 3.74588 | 0.137331 | ||||||||
\(745\) | 3.21499 | 0.117788 | ||||||||
\(746\) | −62.5975 | −2.29186 | ||||||||
\(747\) | 18.5560 | 0.678927 | ||||||||
\(748\) | −0.628339 | −0.0229744 | ||||||||
\(749\) | −55.9104 | −2.04292 | ||||||||
\(750\) | 3.11507 | 0.113746 | ||||||||
\(751\) | 0.351895 | 0.0128408 | 0.00642041 | − | 0.999979i | \(-0.497956\pi\) | ||||
0.00642041 | + | 0.999979i | \(0.497956\pi\) | |||||||
\(752\) | 12.2677 | 0.447356 | ||||||||
\(753\) | 3.10904 | 0.113300 | ||||||||
\(754\) | −1.82940 | −0.0666230 | ||||||||
\(755\) | −4.54710 | −0.165486 | ||||||||
\(756\) | 13.6674 | 0.497079 | ||||||||
\(757\) | −7.46814 | −0.271434 | −0.135717 | − | 0.990748i | \(-0.543334\pi\) | ||||
−0.135717 | + | 0.990748i | \(0.543334\pi\) | |||||||
\(758\) | 4.31934 | 0.156886 | ||||||||
\(759\) | −0.0816620 | −0.00296414 | ||||||||
\(760\) | −19.8650 | −0.720580 | ||||||||
\(761\) | 34.3692 | 1.24588 | 0.622941 | − | 0.782269i | \(-0.285938\pi\) | ||||
0.622941 | + | 0.782269i | \(0.285938\pi\) | |||||||
\(762\) | −2.88785 | −0.104616 | ||||||||
\(763\) | −68.9384 | −2.49574 | ||||||||
\(764\) | 40.8397 | 1.47753 | ||||||||
\(765\) | 3.14896 | 0.113851 | ||||||||
\(766\) | −19.9444 | −0.720621 | ||||||||
\(767\) | −0.0778021 | −0.00280927 | ||||||||
\(768\) | 4.05607 | 0.146361 | ||||||||
\(769\) | −10.1357 | −0.365504 | −0.182752 | − | 0.983159i | \(-0.558501\pi\) | ||||
−0.182752 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(770\) | −1.51367 | −0.0545489 | ||||||||
\(771\) | 0.990144 | 0.0356592 | ||||||||
\(772\) | −54.0479 | −1.94523 | ||||||||
\(773\) | 1.29325 | 0.0465151 | 0.0232575 | − | 0.999730i | \(-0.492596\pi\) | ||||
0.0232575 | + | 0.999730i | \(0.492596\pi\) | |||||||
\(774\) | −81.4694 | −2.92836 | ||||||||
\(775\) | −18.3480 | −0.659079 | ||||||||
\(776\) | −12.6565 | −0.454341 | ||||||||
\(777\) | −3.69134 | −0.132426 | ||||||||
\(778\) | 18.2194 | 0.653198 | ||||||||
\(779\) | −20.4049 | −0.731080 | ||||||||
\(780\) | −0.0473600 | −0.00169576 | ||||||||
\(781\) | 0.337324 | 0.0120704 | ||||||||
\(782\) | 10.9735 | 0.392410 | ||||||||
\(783\) | −7.31207 | −0.261312 | ||||||||
\(784\) | 56.3916 | 2.01399 | ||||||||
\(785\) | 12.0211 | 0.429052 | ||||||||
\(786\) | 2.70462 | 0.0964705 | ||||||||
\(787\) | 25.8497 | 0.921442 | 0.460721 | − | 0.887545i | \(-0.347591\pi\) | ||||
0.460721 | + | 0.887545i | \(0.347591\pi\) | |||||||
\(788\) | 35.5757 | 1.26733 | ||||||||
\(789\) | 0.954436 | 0.0339788 | ||||||||
\(790\) | −4.74477 | −0.168811 | ||||||||
\(791\) | −60.9896 | −2.16854 | ||||||||
\(792\) | −2.57837 | −0.0916185 | ||||||||
\(793\) | −0.921377 | −0.0327191 | ||||||||
\(794\) | 41.3475 | 1.46737 | ||||||||
\(795\) | −0.975257 | −0.0345888 | ||||||||
\(796\) | 112.590 | 3.99066 | ||||||||
\(797\) | 0.00206699 | 7.32164e−5 0 | 3.66082e−5 | − | 1.00000i | \(-0.499988\pi\) | ||||
3.66082e−5 | 1.00000i | \(0.499988\pi\) | ||||||||
\(798\) | −4.10030 | −0.145149 | ||||||||
\(799\) | 1.89212 | 0.0669386 | ||||||||
\(800\) | 16.7550 | 0.592379 | ||||||||
\(801\) | −0.691441 | −0.0244309 | ||||||||
\(802\) | 4.96981 | 0.175490 | ||||||||
\(803\) | −0.193647 | −0.00683364 | ||||||||
\(804\) | 8.85261 | 0.312207 | ||||||||
\(805\) | 18.1596 | 0.640041 | ||||||||
\(806\) | 0.928639 | 0.0327099 | ||||||||
\(807\) | −0.652460 | −0.0229677 | ||||||||
\(808\) | 71.4306 | 2.51292 | ||||||||
\(809\) | −24.8077 | −0.872192 | −0.436096 | − | 0.899900i | \(-0.643639\pi\) | ||||
−0.436096 | + | 0.899900i | \(0.643639\pi\) | |||||||
\(810\) | 23.6023 | 0.829301 | ||||||||
\(811\) | 6.54547 | 0.229843 | 0.114921 | − | 0.993375i | \(-0.463338\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463338\pi\) | |||||||
\(812\) | −161.759 | −5.67662 | ||||||||
\(813\) | 3.05659 | 0.107199 | ||||||||
\(814\) | 2.56625 | 0.0899471 | ||||||||
\(815\) | 12.4138 | 0.434837 | ||||||||
\(816\) | −0.851808 | −0.0298193 | ||||||||
\(817\) | 33.6769 | 1.17821 | ||||||||
\(818\) | −83.9355 | −2.93474 | ||||||||
\(819\) | 0.919441 | 0.0321279 | ||||||||
\(820\) | −30.3364 | −1.05939 | ||||||||
\(821\) | −20.2305 | −0.706048 | −0.353024 | − | 0.935614i | \(-0.614847\pi\) | ||||
−0.353024 | + | 0.935614i | \(0.614847\pi\) | |||||||
\(822\) | −2.13101 | −0.0743276 | ||||||||
\(823\) | −10.1864 | −0.355075 | −0.177537 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177537 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(824\) | −19.5057 | −0.679514 | ||||||||
\(825\) | −0.0730843 | −0.00254447 | ||||||||
\(826\) | −10.0144 | −0.348446 | ||||||||
\(827\) | −47.0412 | −1.63578 | −0.817891 | − | 0.575373i | \(-0.804857\pi\) | ||||
−0.817891 | + | 0.575373i | \(0.804857\pi\) | |||||||
\(828\) | 56.8318 | 1.97504 | ||||||||
\(829\) | −33.8762 | −1.17657 | −0.588285 | − | 0.808654i | \(-0.700197\pi\) | ||||
−0.588285 | + | 0.808654i | \(0.700197\pi\) | |||||||
\(830\) | −16.6007 | −0.576220 | ||||||||
\(831\) | 2.30704 | 0.0800304 | ||||||||
\(832\) | 0.160853 | 0.00557657 | ||||||||
\(833\) | 8.69765 | 0.301356 | ||||||||
\(834\) | −4.21319 | −0.145891 | ||||||||
\(835\) | 13.5068 | 0.467421 | ||||||||
\(836\) | 1.95819 | 0.0677255 | ||||||||
\(837\) | 3.71174 | 0.128297 | ||||||||
\(838\) | 88.5893 | 3.06027 | ||||||||
\(839\) | 41.1867 | 1.42192 | 0.710962 | − | 0.703231i | \(-0.248260\pi\) | ||||
0.710962 | + | 0.703231i | \(0.248260\pi\) | |||||||
\(840\) | −3.31799 | −0.114481 | ||||||||
\(841\) | 57.5410 | 1.98417 | ||||||||
\(842\) | 2.02606 | 0.0698226 | ||||||||
\(843\) | −1.50635 | −0.0518814 | ||||||||
\(844\) | 20.8709 | 0.718406 | ||||||||
\(845\) | 13.7181 | 0.471916 | ||||||||
\(846\) | 14.2650 | 0.490442 | ||||||||
\(847\) | −43.5011 | −1.49471 | ||||||||
\(848\) | −45.5880 | −1.56550 | ||||||||
\(849\) | −2.44602 | −0.0839472 | ||||||||
\(850\) | 9.82082 | 0.336851 | ||||||||
\(851\) | −30.7875 | −1.05538 | ||||||||
\(852\) | 1.35851 | 0.0465417 | ||||||||
\(853\) | −20.8869 | −0.715155 | −0.357578 | − | 0.933883i | \(-0.616397\pi\) | ||||
−0.357578 | + | 0.933883i | \(0.616397\pi\) | |||||||
\(854\) | −118.596 | −4.05828 | ||||||||
\(855\) | −9.81360 | −0.335618 | ||||||||
\(856\) | 85.2023 | 2.91216 | ||||||||
\(857\) | 42.8548 | 1.46389 | 0.731946 | − | 0.681362i | \(-0.238612\pi\) | ||||
0.731946 | + | 0.681362i | \(0.238612\pi\) | |||||||
\(858\) | 0.00369898 | 0.000126281 0 | ||||||||
\(859\) | −48.0358 | −1.63896 | −0.819481 | − | 0.573107i | \(-0.805738\pi\) | ||||
−0.819481 | + | 0.573107i | \(0.805738\pi\) | |||||||
\(860\) | 50.0683 | 1.70732 | ||||||||
\(861\) | −3.40816 | −0.116150 | ||||||||
\(862\) | 1.37560 | 0.0468532 | ||||||||
\(863\) | 22.7316 | 0.773792 | 0.386896 | − | 0.922123i | \(-0.373547\pi\) | ||||
0.386896 | + | 0.922123i | \(0.373547\pi\) | |||||||
\(864\) | −3.38948 | −0.115313 | ||||||||
\(865\) | −7.83981 | −0.266561 | ||||||||
\(866\) | 82.5826 | 2.80627 | ||||||||
\(867\) | −0.131380 | −0.00446190 | ||||||||
\(868\) | 82.1117 | 2.78705 | ||||||||
\(869\) | 0.254572 | 0.00863576 | ||||||||
\(870\) | 3.26137 | 0.110571 | ||||||||
\(871\) | 1.19452 | 0.0404748 | ||||||||
\(872\) | 105.056 | 3.55764 | ||||||||
\(873\) | −6.25247 | −0.211614 | ||||||||
\(874\) | −34.1983 | −1.15678 | ||||||||
\(875\) | 37.1662 | 1.25645 | ||||||||
\(876\) | −0.779874 | −0.0263495 | ||||||||
\(877\) | −47.7357 | −1.61192 | −0.805959 | − | 0.591971i | \(-0.798350\pi\) | ||||
−0.805959 | + | 0.591971i | \(0.798350\pi\) | |||||||
\(878\) | −98.0913 | −3.31042 | ||||||||
\(879\) | 1.59403 | 0.0537652 | ||||||||
\(880\) | 0.979984 | 0.0330352 | ||||||||
\(881\) | 1.96598 | 0.0662354 | 0.0331177 | − | 0.999451i | \(-0.489456\pi\) | ||||
0.0331177 | + | 0.999451i | \(0.489456\pi\) | |||||||
\(882\) | 65.5730 | 2.20796 | ||||||||
\(883\) | −47.2819 | −1.59116 | −0.795582 | − | 0.605846i | \(-0.792835\pi\) | ||||
−0.795582 | + | 0.605846i | \(0.792835\pi\) | |||||||
\(884\) | −0.341453 | −0.0114843 | ||||||||
\(885\) | 0.138702 | 0.00466240 | ||||||||
\(886\) | 28.1063 | 0.944248 | ||||||||
\(887\) | 5.05234 | 0.169641 | 0.0848205 | − | 0.996396i | \(-0.472968\pi\) | ||||
0.0848205 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(888\) | 5.62527 | 0.188772 | ||||||||
\(889\) | −34.4552 | −1.15559 | ||||||||
\(890\) | 0.618585 | 0.0207350 | ||||||||
\(891\) | −1.26634 | −0.0424239 | ||||||||
\(892\) | −59.4208 | −1.98956 | ||||||||
\(893\) | −5.89673 | −0.197326 | ||||||||
\(894\) | −1.01127 | −0.0338218 | ||||||||
\(895\) | −19.3782 | −0.647741 | ||||||||
\(896\) | 54.8749 | 1.83324 | ||||||||
\(897\) | −0.0443769 | −0.00148170 | ||||||||
\(898\) | 57.6072 | 1.92238 | ||||||||
\(899\) | −43.9298 | −1.46514 | ||||||||
\(900\) | 50.8622 | 1.69541 | ||||||||
\(901\) | −7.03133 | −0.234248 | ||||||||
\(902\) | 2.36938 | 0.0788917 | ||||||||
\(903\) | 5.62494 | 0.187186 | ||||||||
\(904\) | 92.9426 | 3.09122 | ||||||||
\(905\) | −15.1350 | −0.503106 | ||||||||
\(906\) | 1.43028 | 0.0475178 | ||||||||
\(907\) | −39.0723 | −1.29738 | −0.648688 | − | 0.761055i | \(-0.724682\pi\) | ||||
−0.648688 | + | 0.761055i | \(0.724682\pi\) | |||||||
\(908\) | 99.3694 | 3.29769 | ||||||||
\(909\) | 35.2877 | 1.17042 | ||||||||
\(910\) | −0.822561 | −0.0272676 | ||||||||
\(911\) | 1.23848 | 0.0410328 | 0.0205164 | − | 0.999790i | \(-0.493469\pi\) | ||||
0.0205164 | + | 0.999790i | \(0.493469\pi\) | |||||||
\(912\) | 2.65462 | 0.0879034 | ||||||||
\(913\) | 0.890681 | 0.0294772 | ||||||||
\(914\) | 1.25051 | 0.0413632 | ||||||||
\(915\) | 1.64258 | 0.0543021 | ||||||||
\(916\) | 115.739 | 3.82414 | ||||||||
\(917\) | 32.2691 | 1.06562 | ||||||||
\(918\) | −1.98672 | −0.0655716 | ||||||||
\(919\) | 37.5030 | 1.23711 | 0.618555 | − | 0.785742i | \(-0.287718\pi\) | ||||
0.618555 | + | 0.785742i | \(0.287718\pi\) | |||||||
\(920\) | −27.6735 | −0.912369 | ||||||||
\(921\) | 1.85652 | 0.0611743 | ||||||||
\(922\) | 7.92678 | 0.261055 | ||||||||
\(923\) | 0.183309 | 0.00603370 | ||||||||
\(924\) | 0.327070 | 0.0107598 | ||||||||
\(925\) | −27.5536 | −0.905955 | ||||||||
\(926\) | 18.3165 | 0.601917 | ||||||||
\(927\) | −9.63610 | −0.316491 | ||||||||
\(928\) | 40.1158 | 1.31687 | ||||||||
\(929\) | 4.23768 | 0.139034 | 0.0695169 | − | 0.997581i | \(-0.477854\pi\) | ||||
0.0695169 | + | 0.997581i | \(0.477854\pi\) | |||||||
\(930\) | −1.65553 | −0.0542870 | ||||||||
\(931\) | −27.1059 | −0.888359 | ||||||||
\(932\) | 71.8399 | 2.35319 | ||||||||
\(933\) | −3.26186 | −0.106788 | ||||||||
\(934\) | 82.2788 | 2.69224 | ||||||||
\(935\) | 0.151149 | 0.00494311 | ||||||||
\(936\) | −1.40114 | −0.0457978 | ||||||||
\(937\) | 4.04551 | 0.132161 | 0.0660805 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660805 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(938\) | 153.754 | 5.02025 | ||||||||
\(939\) | −0.634119 | −0.0206937 | ||||||||
\(940\) | −8.76681 | −0.285942 | ||||||||
\(941\) | 9.64397 | 0.314384 | 0.157192 | − | 0.987568i | \(-0.449756\pi\) | ||||
0.157192 | + | 0.987568i | \(0.449756\pi\) | |||||||
\(942\) | −3.78121 | −0.123198 | ||||||||
\(943\) | −28.4256 | −0.925664 | ||||||||
\(944\) | 6.48355 | 0.211021 | ||||||||
\(945\) | −3.28775 | −0.106950 | ||||||||
\(946\) | −3.91051 | −0.127142 | ||||||||
\(947\) | −0.00195680 | −6.35875e−5 0 | −3.17938e−5 | − | 1.00000i | \(-0.500010\pi\) | ||||
−3.17938e−5 | 1.00000i | \(0.500010\pi\) | ||||||||
\(948\) | 1.02524 | 0.0332982 | ||||||||
\(949\) | −0.105232 | −0.00341597 | ||||||||
\(950\) | −30.6062 | −0.992995 | ||||||||
\(951\) | −1.11680 | −0.0362149 | ||||||||
\(952\) | −23.9218 | −0.775309 | ||||||||
\(953\) | 6.59785 | 0.213725 | 0.106863 | − | 0.994274i | \(-0.465919\pi\) | ||||
0.106863 | + | 0.994274i | \(0.465919\pi\) | |||||||
\(954\) | −53.0103 | −1.71627 | ||||||||
\(955\) | −9.82414 | −0.317902 | ||||||||
\(956\) | 33.7991 | 1.09314 | ||||||||
\(957\) | −0.174983 | −0.00565638 | ||||||||
\(958\) | 22.4472 | 0.725235 | ||||||||
\(959\) | −25.4253 | −0.821026 | ||||||||
\(960\) | −0.286760 | −0.00925514 | ||||||||
\(961\) | −8.70044 | −0.280659 | ||||||||
\(962\) | 1.39456 | 0.0449623 | ||||||||
\(963\) | 42.0911 | 1.35637 | ||||||||
\(964\) | −73.5057 | −2.36746 | ||||||||
\(965\) | 13.0014 | 0.418531 | ||||||||
\(966\) | −5.71203 | −0.183782 | ||||||||
\(967\) | 19.7521 | 0.635185 | 0.317592 | − | 0.948227i | \(-0.397126\pi\) | ||||
0.317592 | + | 0.948227i | \(0.397126\pi\) | |||||||
\(968\) | 66.2916 | 2.13069 | ||||||||
\(969\) | 0.409440 | 0.0131531 | ||||||||
\(970\) | 5.59366 | 0.179601 | ||||||||
\(971\) | 1.06475 | 0.0341693 | 0.0170846 | − | 0.999854i | \(-0.494562\pi\) | ||||
0.0170846 | + | 0.999854i | \(0.494562\pi\) | |||||||
\(972\) | −15.4487 | −0.495519 | ||||||||
\(973\) | −50.2680 | −1.61152 | ||||||||
\(974\) | −52.6051 | −1.68558 | ||||||||
\(975\) | −0.0397156 | −0.00127192 | ||||||||
\(976\) | 76.7819 | 2.45773 | ||||||||
\(977\) | 54.5120 | 1.74399 | 0.871996 | − | 0.489513i | \(-0.162825\pi\) | ||||
0.871996 | + | 0.489513i | \(0.162825\pi\) | |||||||
\(978\) | −3.90472 | −0.124859 | ||||||||
\(979\) | −0.0331890 | −0.00106073 | ||||||||
\(980\) | −40.2989 | −1.28730 | ||||||||
\(981\) | 51.8990 | 1.65701 | ||||||||
\(982\) | −57.3231 | −1.82925 | ||||||||
\(983\) | 3.44716 | 0.109947 | 0.0549737 | − | 0.998488i | \(-0.482492\pi\) | ||||
0.0549737 | + | 0.998488i | \(0.482492\pi\) | |||||||
\(984\) | 5.19371 | 0.165570 | ||||||||
\(985\) | −8.55787 | −0.272677 | ||||||||
\(986\) | 23.5136 | 0.748825 | ||||||||
\(987\) | −0.984910 | −0.0313500 | ||||||||
\(988\) | 1.06412 | 0.0338543 | ||||||||
\(989\) | 46.9146 | 1.49180 | ||||||||
\(990\) | 1.13954 | 0.0362169 | ||||||||
\(991\) | −8.86662 | −0.281657 | −0.140829 | − | 0.990034i | \(-0.544977\pi\) | ||||
−0.140829 | + | 0.990034i | \(0.544977\pi\) | |||||||
\(992\) | −20.3635 | −0.646542 | ||||||||
\(993\) | −0.411154 | −0.0130476 | ||||||||
\(994\) | 23.5949 | 0.748384 | ||||||||
\(995\) | −27.0840 | −0.858621 | ||||||||
\(996\) | 3.58705 | 0.113660 | ||||||||
\(997\) | −10.9481 | −0.346729 | −0.173365 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173365 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(998\) | −32.4124 | −1.02600 | ||||||||
\(999\) | 5.57400 | 0.176354 |
(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 | 1003.2.a.h.1.2 | ✓ | 16 | |
3.2 | odd | 2 | 9027.2.a.n.1.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1003.2.a.h.1.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
9027.2.a.n.1.15 | 16 | 3.2 | odd | 2 |