Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9016,2,Mod(1,9016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("9016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9016 = 2^{3} \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9016.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: | \(71.9931224624\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 4x^{10} - 14x^{9} + 63x^{8} + 51x^{7} - 305x^{6} + 16x^{5} + 429x^{4} - 234x^{3} - 42x^{2} + 39x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1288) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.69483\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9016.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.69483 | 1.55586 | 0.777930 | − | 0.628351i | \(-0.216270\pi\) | ||||
0.777930 | + | 0.628351i | \(0.216270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.987745 | −0.441733 | −0.220866 | − | 0.975304i | \(-0.570888\pi\) | ||||
−0.220866 | + | 0.975304i | \(0.570888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.26210 | 1.42070 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.37013 | 0.714620 | 0.357310 | − | 0.933986i | \(-0.383694\pi\) | ||||
0.357310 | + | 0.933986i | \(0.383694\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.07929 | 1.13139 | 0.565696 | − | 0.824614i | \(-0.308607\pi\) | ||||
0.565696 | + | 0.824614i | \(0.308607\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.66180 | −0.687275 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.58866 | −1.84052 | −0.920260 | − | 0.391307i | \(-0.872023\pi\) | ||||
−0.920260 | + | 0.391307i | \(0.872023\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.98174 | −0.454641 | −0.227321 | − | 0.973820i | \(-0.572997\pi\) | ||||
−0.227321 | + | 0.973820i | \(0.572997\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.02436 | −0.804872 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.40115 | 0.654552 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.65576 | −1.79303 | −0.896515 | − | 0.443013i | \(-0.853909\pi\) | ||||
−0.896515 | + | 0.443013i | \(0.853909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.17029 | −1.10822 | −0.554108 | − | 0.832445i | \(-0.686941\pi\) | ||||
−0.554108 | + | 0.832445i | \(0.686941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.38709 | 1.11185 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0640261 | 0.0105258 | 0.00526292 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526292 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.9930 | 1.76029 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2783 | −1.76137 | −0.880685 | − | 0.473702i | \(-0.842918\pi\) | ||||
−0.880685 | + | 0.473702i | \(0.842918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.61229 | −0.855866 | −0.427933 | − | 0.903810i | \(-0.640758\pi\) | ||||
−0.427933 | + | 0.903810i | \(0.640758\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.20987 | −0.627571 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3526 | −1.65595 | −0.827975 | − | 0.560765i | \(-0.810507\pi\) | ||||
−0.827975 | + | 0.560765i | \(0.810507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.4501 | −2.86359 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.57754 | −1.04086 | −0.520428 | − | 0.853906i | \(-0.674228\pi\) | ||||
−0.520428 | + | 0.853906i | \(0.674228\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.34108 | −0.315671 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.34044 | −0.707359 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.78879 | −0.623447 | −0.311723 | − | 0.950173i | \(-0.600906\pi\) | ||||
−0.311723 | + | 0.950173i | \(0.600906\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.53051 | −1.22026 | −0.610129 | − | 0.792302i | \(-0.708882\pi\) | ||||
−0.610129 | + | 0.792302i | \(0.708882\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.02930 | −0.499773 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.8562 | 1.32630 | 0.663148 | − | 0.748488i | \(-0.269220\pi\) | ||||
0.663148 | + | 0.748488i | \(0.269220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.69483 | 0.324419 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.82290 | 0.928408 | 0.464204 | − | 0.885728i | \(-0.346340\pi\) | ||||
0.464204 | + | 0.885728i | \(0.346340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.95332 | 0.813825 | 0.406912 | − | 0.913467i | \(-0.366605\pi\) | ||||
0.406912 | + | 0.913467i | \(0.366605\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.8450 | −1.25227 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.96992 | 0.334142 | 0.167071 | − | 0.985945i | \(-0.446569\pi\) | ||||
0.167071 | + | 0.985945i | \(0.446569\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.62078 | −0.402309 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8626 | 1.74115 | 0.870575 | − | 0.492036i | \(-0.163747\pi\) | ||||
0.870575 | + | 0.492036i | \(0.163747\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.49566 | 0.813018 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −26.0206 | −2.78970 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.81027 | 0.509887 | 0.254944 | − | 0.966956i | \(-0.417943\pi\) | ||||
0.254944 | + | 0.966956i | \(0.417943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.6279 | −1.72423 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.95745 | 0.200830 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.63923 | −0.267973 | −0.133987 | − | 0.990983i | \(-0.542778\pi\) | ||||
−0.133987 | + | 0.990983i | \(0.542778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.1017 | 1.01526 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4154 | 1.03637 | 0.518186 | − | 0.855268i | \(-0.326608\pi\) | ||||
0.518186 | + | 0.855268i | \(0.326608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.81381 | 0.375786 | 0.187893 | − | 0.982189i | \(-0.439834\pi\) | ||||
0.187893 | + | 0.982189i | \(0.439834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.3838 | −1.29386 | −0.646931 | − | 0.762548i | \(-0.723948\pi\) | ||||
−0.646931 | + | 0.762548i | \(0.723948\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.1577 | 1.26028 | 0.630142 | − | 0.776480i | \(-0.282997\pi\) | ||||
0.630142 | + | 0.776480i | \(0.282997\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.172540 | 0.0163767 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7207 | 1.00852 | 0.504259 | − | 0.863552i | \(-0.331766\pi\) | ||||
0.504259 | + | 0.863552i | \(0.331766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.987745 | −0.0921077 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.3864 | 1.60737 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.38250 | −0.489318 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −30.3930 | −2.74045 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.91376 | 0.797271 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.10959 | 0.0984604 | 0.0492302 | − | 0.998787i | \(-0.484323\pi\) | ||||
0.0492302 | + | 0.998787i | \(0.484323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.1242 | −1.33161 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3702 | −1.60501 | −0.802504 | − | 0.596647i | \(-0.796499\pi\) | ||||
−0.802504 | + | 0.596647i | \(0.796499\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.35947 | −0.289137 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.0068 | −1.36755 | −0.683776 | − | 0.729692i | \(-0.739663\pi\) | ||||
−0.683776 | + | 0.729692i | \(0.739663\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.19528 | −0.355839 | −0.177920 | − | 0.984045i | \(-0.556937\pi\) | ||||
−0.177920 | + | 0.984045i | \(0.556937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.5934 | −2.57643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.66845 | 0.808516 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.53743 | 0.792040 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.21653 | −0.755048 | −0.377524 | − | 0.926000i | \(-0.623224\pi\) | ||||
−0.377524 | + | 0.926000i | \(0.623224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.6426 | 1.76125 | 0.880625 | − | 0.473813i | \(-0.157123\pi\) | ||||
0.880625 | + | 0.473813i | \(0.157123\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32.3437 | −2.61483 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.09467 | 0.489535 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.50023 | −0.518774 | −0.259387 | − | 0.965773i | \(-0.583521\pi\) | ||||
−0.259387 | + | 0.965773i | \(0.583521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.4202 | −1.61943 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7470 | 1.23340 | 0.616701 | − | 0.787198i | \(-0.288469\pi\) | ||||
0.616701 | + | 0.787198i | \(0.288469\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.30881 | −0.491140 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.2107 | 1.79610 | 0.898049 | − | 0.439896i | \(-0.144985\pi\) | ||||
0.898049 | + | 0.439896i | \(0.144985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.64065 | 0.280050 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.44636 | −0.645910 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.68879 | −0.204425 | −0.102213 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102213 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.9050 | −0.969996 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.5089 | 1.38342 | 0.691709 | − | 0.722176i | \(-0.256858\pi\) | ||||
0.691709 | + | 0.722176i | \(0.256858\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.9626 | 1.85545 | 0.927726 | − | 0.373262i | \(-0.121761\pi\) | ||||
0.927726 | + | 0.373262i | \(0.121761\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.6831 | −1.89855 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0632415 | −0.00464961 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.9861 | −1.31527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5132 | −0.977781 | −0.488890 | − | 0.872345i | \(-0.662598\pi\) | ||||
−0.488890 | + | 0.872345i | \(0.662598\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.02075 | 0.361402 | 0.180701 | − | 0.983538i | \(-0.442163\pi\) | ||||
0.180701 | + | 0.983538i | \(0.442163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.8583 | −0.777578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.03479 | 0.144973 | 0.0724865 | − | 0.997369i | \(-0.476907\pi\) | ||||
0.0724865 | + | 0.997369i | \(0.476907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.77058 | 0.621730 | 0.310865 | − | 0.950454i | \(-0.399381\pi\) | ||||
0.310865 | + | 0.950454i | \(0.399381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 29.2556 | 2.06353 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1401 | 0.778055 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.26210 | 0.296237 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.69697 | −0.324896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.6551 | −1.28427 | −0.642136 | − | 0.766590i | \(-0.721952\pi\) | ||||
−0.642136 | + | 0.766590i | \(0.721952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.0814 | 1.44447 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.54351 | 0.378064 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.7380 | 1.26620 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.9564 | −2.08235 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65726 | 0.378838 | 0.189419 | − | 0.981896i | \(-0.439340\pi\) | ||||
0.189419 | + | 0.981896i | \(0.439340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −17.1522 | −1.14348 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5286 | 0.765180 | 0.382590 | − | 0.923918i | \(-0.375032\pi\) | ||||
0.382590 | + | 0.923918i | \(0.375032\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3831 | −0.950460 | −0.475230 | − | 0.879862i | \(-0.657635\pi\) | ||||
−0.475230 | + | 0.879862i | \(0.657635\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.10030 | −0.334132 | −0.167066 | − | 0.985946i | \(-0.553429\pi\) | ||||
−0.167066 | + | 0.985946i | \(0.553429\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.2135 | 0.731488 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.00343 | 0.519879 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.8025 | 1.41029 | 0.705143 | − | 0.709065i | \(-0.250883\pi\) | ||||
0.705143 | + | 0.709065i | \(0.250883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7370 | 0.884879 | 0.442440 | − | 0.896798i | \(-0.354113\pi\) | ||||
0.442440 | + | 0.896798i | \(0.354113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.9609 | −1.28049 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.08409 | −0.514378 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 42.7471 | 2.70898 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.89434 | −0.245809 | −0.122904 | − | 0.992419i | \(-0.539221\pi\) | ||||
−0.122904 | + | 0.992419i | \(0.539221\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.37013 | 0.149009 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.1995 | 1.26494 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.3661 | −1.08327 | −0.541634 | − | 0.840614i | \(-0.682194\pi\) | ||||
−0.541634 | + | 0.840614i | \(0.682194\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −41.1539 | −2.54736 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.78239 | 0.233232 | 0.116616 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116616 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.48468 | 0.459780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9628 | 0.793313 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.05445 | 0.369147 | 0.184573 | − | 0.982819i | \(-0.440910\pi\) | ||||
0.184573 | + | 0.982819i | \(0.440910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.35742 | −0.203948 | −0.101974 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101974 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.53825 | −0.575178 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.95480 | 0.417874 | 0.208937 | − | 0.977929i | \(-0.433000\pi\) | ||||
0.208937 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.2984 | −1.57444 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9204 | 0.711109 | 0.355555 | − | 0.934656i | \(-0.384292\pi\) | ||||
0.355555 | + | 0.934656i | \(0.384292\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.2946 | −0.790280 | −0.395140 | − | 0.918621i | \(-0.629304\pi\) | ||||
−0.395140 | + | 0.918621i | \(0.629304\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.27499 | 0.312464 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.5878 | 2.38752 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.11228 | −0.416929 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.09325 | −0.414392 | −0.207196 | − | 0.978299i | \(-0.566434\pi\) | ||||
−0.207196 | + | 0.978299i | \(0.566434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.73010 | 0.275397 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.06117 | 0.467756 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.07929 | 0.235912 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.0677 | 1.61245 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.41371 | 0.539028 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.71310 | −0.383137 | −0.191569 | − | 0.981479i | \(-0.561357\pi\) | ||||
−0.191569 | + | 0.981479i | \(0.561357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.2776 | 0.584671 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.29794 | 0.187009 | 0.0935044 | − | 0.995619i | \(-0.470193\pi\) | ||||
0.0935044 | + | 0.995619i | \(0.470193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.19958 | −0.519991 | −0.259996 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259996 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.6963 | −1.72407 | −0.862037 | − | 0.506845i | \(-0.830812\pi\) | ||||
−0.862037 | + | 0.506845i | \(0.830812\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.8854 | −1.28134 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −36.0671 | −2.01307 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0387 | 0.836777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.4166 | −0.910626 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 35.4579 | 1.96082 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.84446 | −0.211310 | −0.105655 | − | 0.994403i | \(-0.533694\pi\) | ||||
−0.105655 | + | 0.994403i | \(0.533694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.272886 | 0.0149541 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.7232 | −0.585869 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1802 | −0.826916 | −0.413458 | − | 0.910523i | \(-0.635679\pi\) | ||||
−0.413458 | + | 0.910523i | \(0.635679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.8904 | 1.56911 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.6244 | −0.791954 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.66180 | −0.143307 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.87353 | −0.261625 | −0.130813 | − | 0.991407i | \(-0.541759\pi\) | ||||
−0.130813 | + | 0.991407i | \(0.541759\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.4939 | −0.722313 | −0.361157 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361157 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8743 | 0.740556 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −28.5154 | −1.51772 | −0.758860 | − | 0.651254i | \(-0.774243\pi\) | ||||
−0.758860 | + | 0.651254i | \(0.774243\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.72703 | −0.410108 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.6781 | 0.827458 | 0.413729 | − | 0.910400i | \(-0.364226\pi\) | ||||
0.413729 | + | 0.910400i | \(0.364226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0727 | −0.793301 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.5049 | −0.761310 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.86811 | −0.359493 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.96664 | −0.154857 | −0.0774286 | − | 0.996998i | \(-0.524671\pi\) | ||||
−0.0774286 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.0692 | −2.50238 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.276321 | 0.0143074 | 0.00715368 | − | 0.999974i | \(-0.497723\pi\) | ||||
0.00715368 | + | 0.999974i | \(0.497723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.0211 | 1.24044 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.3887 | −2.02862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.76290 | 0.141921 | 0.0709603 | − | 0.997479i | \(-0.477394\pi\) | ||||
0.0709603 | + | 0.997479i | \(0.477394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.99016 | 0.153191 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.8062 | 0.705465 | 0.352732 | − | 0.935724i | \(-0.385253\pi\) | ||||
0.352732 | + | 0.935724i | \(0.385253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −23.9202 | −1.21593 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.8648 | −0.956484 | −0.478242 | − | 0.878228i | \(-0.658726\pi\) | ||||
−0.478242 | + | 0.878228i | \(0.658726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.58866 | −0.383775 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −49.5044 | −2.49717 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.93352 | −0.147602 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.4233 | −1.32615 | −0.663075 | − | 0.748553i | \(-0.730749\pi\) | ||||
−0.663075 | + | 0.748553i | \(0.730749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.33152 | −0.416056 | −0.208028 | − | 0.978123i | \(-0.566705\pi\) | ||||
−0.208028 | + | 0.978123i | \(0.566705\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.1704 | −1.25383 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.57641 | 0.177713 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.151750 | 0.00752197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.33363 | −0.362625 | −0.181312 | − | 0.983426i | \(-0.558035\pi\) | ||||
−0.181312 | + | 0.983426i | \(0.558035\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.1356 | −2.12772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.6682 | −0.769123 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3056 | −0.553636 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.3626 | −0.555098 | −0.277549 | − | 0.960711i | \(-0.589522\pi\) | ||||
−0.277549 | + | 0.960711i | \(0.589522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3418 | 0.601500 | 0.300750 | − | 0.953703i | \(-0.402763\pi\) | ||||
0.300750 | + | 0.953703i | \(0.402763\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −48.3860 | −2.35261 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.5395 | 1.48138 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 26.0548 | 1.25794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.06925 | 0.340514 | 0.170257 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170257 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.71716 | −0.0825213 | −0.0412606 | − | 0.999148i | \(-0.513137\pi\) | ||||
−0.0412606 | + | 0.999148i | \(0.513137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 25.7017 | 1.23230 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.98174 | −0.0947993 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.0074 | 1.00263 | 0.501314 | − | 0.865266i | \(-0.332850\pi\) | ||||
0.501314 | + | 0.865266i | \(0.332850\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.13482 | 0.101428 | 0.0507141 | − | 0.998713i | \(-0.483850\pi\) | ||||
0.0507141 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.75132 | −0.225234 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.8370 | −1.17475 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.98723 | −0.424133 | −0.212067 | − | 0.977255i | \(-0.568019\pi\) | ||||
−0.212067 | + | 0.977255i | \(0.568019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.7310 | −1.25871 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 58.3231 | 2.74026 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.1059 | 1.50185 | 0.750925 | − | 0.660387i | \(-0.229608\pi\) | ||||
0.750925 | + | 0.660387i | \(0.229608\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.8102 | −1.20472 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.1388 | −0.937956 | −0.468978 | − | 0.883210i | \(-0.655378\pi\) | ||||
−0.468978 | + | 0.883210i | \(0.655378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.8725 | −0.691186 | −0.345593 | − | 0.938385i | \(-0.612322\pi\) | ||||
−0.345593 | + | 0.938385i | \(0.612322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.4241 | 0.761649 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.8511 | −1.52017 | −0.760084 | − | 0.649825i | \(-0.774842\pi\) | ||||
−0.760084 | + | 0.649825i | \(0.774842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.5170 | −0.807141 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.3018 | −0.611619 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.97522 | 0.365928 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.2963 | −1.47874 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.7914 | 1.08706 | 0.543528 | − | 0.839391i | \(-0.317088\pi\) | ||||
0.543528 | + | 0.839391i | \(0.317088\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.261182 | 0.0119089 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.60689 | 0.118373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.4468 | 0.835904 | 0.417952 | − | 0.908469i | \(-0.362748\pi\) | ||||
0.417952 | + | 0.908469i | \(0.362748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.4355 | 1.91900 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.0803 | 1.13186 | 0.565930 | − | 0.824453i | \(-0.308517\pi\) | ||||
0.565930 | + | 0.824453i | \(0.308517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 73.2743 | 3.30011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.97793 | −0.448475 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.4790 | −0.872000 | −0.436000 | − | 0.899947i | \(-0.643605\pi\) | ||||
−0.436000 | + | 0.899947i | \(0.643605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 62.5489 | 2.79448 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.49658 | 0.245080 | 0.122540 | − | 0.992464i | \(-0.460896\pi\) | ||||
0.122540 | + | 0.992464i | \(0.460896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2878 | −0.457799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.81092 | 0.435718 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.0812 | 1.02306 | 0.511529 | − | 0.859266i | \(-0.329079\pi\) | ||||
0.511529 | + | 0.859266i | \(0.329079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.74019 | −0.297587 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.76707 | −0.165997 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.9072 | −1.18338 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.24584 | −0.318057 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.36861 | 0.410446 | 0.205223 | − | 0.978715i | \(-0.434208\pi\) | ||||
0.205223 | + | 0.978715i | \(0.434208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.5537 | −0.548933 | −0.274467 | − | 0.961597i | \(-0.588501\pi\) | ||||
−0.274467 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.8242 | 2.03969 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.4103 | −0.885732 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −46.0074 | −1.99280 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2198 | 0.571541 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 49.8782 | 2.15240 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.25060 | 0.225741 | 0.112870 | − | 0.993610i | \(-0.463995\pi\) | ||||
0.112870 | + | 0.993610i | \(0.463995\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 67.2698 | 2.88682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9965 | −0.556709 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.598591 | 0.0255939 | 0.0127969 | − | 0.999918i | \(-0.495926\pi\) | ||||
0.0127969 | + | 0.999918i | \(0.495926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.6200 | −1.73362 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.1352 | 0.815186 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.170425 | −0.00723414 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.0121 | 1.39877 | 0.699384 | − | 0.714746i | \(-0.253458\pi\) | ||||
0.699384 | + | 0.714746i | \(0.253458\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.8942 | −0.968320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.4694 | −2.04638 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.7182 | −1.67392 | −0.836961 | − | 0.547262i | \(-0.815670\pi\) | ||||
−0.836961 | + | 0.547262i | \(0.815670\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.5893 | −0.445496 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.11738 | −0.172610 | −0.0863048 | − | 0.996269i | \(-0.527506\pi\) | ||||
−0.0863048 | + | 0.996269i | \(0.527506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.6733 | 1.61843 | 0.809215 | − | 0.587513i | \(-0.199893\pi\) | ||||
0.809215 | + | 0.587513i | \(0.199893\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36.4158 | −1.52129 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.02436 | −0.167827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.4095 | −1.55738 | −0.778688 | − | 0.627411i | \(-0.784115\pi\) | ||||
−0.778688 | + | 0.627411i | \(0.784115\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.5301 | 0.562290 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.9597 | −0.743817 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.1733 | −0.710029 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.7805 | −1.06408 | −0.532038 | − | 0.846721i | \(-0.678573\pi\) | ||||
−0.532038 | + | 0.846721i | \(0.678573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2279 | 0.503841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.48342 | 0.225558 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.6506 | −1.25867 | −0.629334 | − | 0.777135i | \(-0.716672\pi\) | ||||
−0.629334 | + | 0.777135i | \(0.716672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.6352 | 0.967325 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.93269 | −0.160686 | −0.0803428 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803428 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4423 | 1.11940 | 0.559698 | − | 0.828697i | \(-0.310917\pi\) | ||||
0.559698 | + | 0.828697i | \(0.310917\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.2703 | 1.88427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.31653 | 0.216148 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.0293 | −1.54356 | −0.771781 | − | 0.635888i | \(-0.780634\pi\) | ||||
−0.771781 | + | 0.635888i | \(0.780634\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.3107 | −1.87353 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.7113 | 0.473013 | 0.236506 | − | 0.971630i | \(-0.423998\pi\) | ||||
0.236506 | + | 0.971630i | \(0.423998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30.0206 | 1.21055 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.0965 | 1.41293 | 0.706466 | − | 0.707747i | \(-0.250288\pi\) | ||||
0.706466 | + | 0.707747i | \(0.250288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.5605 | −0.705815 | −0.352908 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352908 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.40115 | 0.136484 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.3173 | 0.452691 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.6575 | −0.505493 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.485873 | −0.0193730 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.36226 | −0.0542307 | −0.0271154 | − | 0.999632i | \(-0.508632\pi\) | ||||
−0.0271154 | + | 0.999632i | \(0.508632\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.2724 | −1.99815 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.09599 | −0.0434932 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.3420 | 1.31899 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.6027 | 0.576771 | 0.288385 | − | 0.957514i | \(-0.406882\pi\) | ||||
0.288385 | + | 0.957514i | \(0.406882\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3215 | 0.722529 | 0.361265 | − | 0.932463i | \(-0.382345\pi\) | ||||
0.361265 | + | 0.932463i | \(0.382345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.9388 | 0.588215 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.2648 | −1.77954 | −0.889772 | − | 0.456405i | \(-0.849137\pi\) | ||||
−0.889772 | + | 0.456405i | \(0.849137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.3500 | −0.445528 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.93885 | 0.271538 | 0.135769 | − | 0.990741i | \(-0.456649\pi\) | ||||
0.135769 | + | 0.990741i | \(0.456649\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1450 | 0.708985 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.6358 | 1.15620 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8233 | 1.43443 | 0.717215 | − | 0.696852i | \(-0.245416\pi\) | ||||
0.717215 | + | 0.696852i | \(0.245416\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.6351 | −1.65831 | −0.829157 | − | 0.559015i | \(-0.811179\pi\) | ||||
−0.829157 | + | 0.559015i | \(0.811179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −83.4222 | −3.23985 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.65576 | −0.373873 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.2453 | 0.589419 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.5885 | −0.872020 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.5976 | −1.14090 | −0.570452 | − | 0.821331i | \(-0.693232\pi\) | ||||
−0.570452 | + | 0.821331i | \(0.693232\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.6875 | −0.526831 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.1886 | 1.00651 | 0.503255 | − | 0.864138i | \(-0.332136\pi\) | ||||
0.503255 | + | 0.864138i | \(0.332136\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 31.0676 | 1.19051 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.94336 | −0.0743606 | −0.0371803 | − | 0.999309i | \(-0.511838\pi\) | ||||
−0.0371803 | + | 0.999309i | \(0.511838\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.8106 | 0.604093 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.7599 | −1.47878 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.9110 | −1.17762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.7475 | −1.01752 | −0.508761 | − | 0.860908i | \(-0.669896\pi\) | ||||
−0.508761 | + | 0.860908i | \(0.669896\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.14387 | 0.157186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 85.5870 | 3.24184 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.7444 | −0.519862 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.10164 | 0.0793779 | 0.0396890 | − | 0.999212i | \(-0.487363\pi\) | ||||
0.0396890 | + | 0.999212i | \(0.487363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.126883 | −0.00478548 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.2184 | 1.13809 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.3222 | 1.92745 | 0.963723 | − | 0.266906i | \(-0.0860012\pi\) | ||||
0.963723 | + | 0.266906i | \(0.0860012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.6581 | 0.474716 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.17029 | −0.231079 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.54996 | −0.357148 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 58.7540 | 2.19421 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.4316 | −1.73161 | −0.865804 | − | 0.500384i | \(-0.833192\pi\) | ||||
−0.865804 | + | 0.500384i | \(0.833192\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 37.0189 | 1.37675 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.8583 | 1.44316 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.0942 | 1.07904 | 0.539521 | − | 0.841972i | \(-0.318605\pi\) | ||||
0.539521 | + | 0.841972i | \(0.318605\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.9287 | −1.58995 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.5897 | 1.57524 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8319 | 1.69284 | 0.846420 | − | 0.532516i | \(-0.178753\pi\) | ||||
0.846420 | + | 0.532516i | \(0.178753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.7306 | 0.947798 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.0618 | −0.958700 | −0.479350 | − | 0.877624i | \(-0.659128\pi\) | ||||
−0.479350 | + | 0.877624i | \(0.659128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.7852 | −0.800300 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.87154 | 0.105347 | 0.0526733 | − | 0.998612i | \(-0.483226\pi\) | ||||
0.0526733 | + | 0.998612i | \(0.483226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.10358 | 0.333529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67.6082 | 2.47365 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.21840 | 0.299894 | 0.149947 | − | 0.988694i | \(-0.452090\pi\) | ||||
0.149947 | + | 0.988694i | \(0.452090\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.4946 | −0.382444 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.3774 | −0.778002 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.8844 | 0.395602 | 0.197801 | − | 0.980242i | \(-0.436620\pi\) | ||||
0.197801 | + | 0.980242i | \(0.436620\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.38709 | 0.231837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.5739 | −0.890804 | −0.445402 | − | 0.895331i | \(-0.646939\pi\) | ||||
−0.445402 | + | 0.895331i | \(0.646939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.9473 | 1.15506 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.5349 | −0.705363 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6181 | −1.75321 | −0.876607 | − | 0.481206i | \(-0.840199\pi\) | ||||
−0.876607 | + | 0.481206i | \(0.840199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46.7987 | −1.68541 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.9021 | 1.47115 | 0.735573 | − | 0.677445i | \(-0.236913\pi\) | ||||
0.735573 | + | 0.677445i | \(0.236913\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.8315 | 0.891972 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.3506 | 0.800792 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.5413 | 0.663459 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.8407 | −1.17363 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.42056 | 0.229160 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.7819 | −0.491272 | −0.245636 | − | 0.969362i | \(-0.578997\pi\) | ||||
−0.245636 | + | 0.969362i | \(0.578997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.1929 | 0.362877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.8778 | −1.38059 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 20.1699 | 0.715354 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8832 | 0.704299 | 0.352150 | − | 0.935944i | \(-0.385451\pi\) | ||||
0.352150 | + | 0.935944i | \(0.385451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 86.1512 | 3.04781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.5019 | 0.724398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.4803 | 0.581576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3157 | 0.574340 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 52.9515 | 1.86167 | 0.930837 | − | 0.365435i | \(-0.119080\pi\) | ||||
0.930837 | + | 0.365435i | \(0.119080\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0859 | −0.740427 | −0.370213 | − | 0.928947i | \(-0.620715\pi\) | ||||
−0.370213 | + | 0.928947i | \(0.620715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.04766 | −0.317315 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.5540 | −0.544834 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1221 | 0.389112 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0104 | −0.419164 | −0.209582 | − | 0.977791i | \(-0.567210\pi\) | ||||
−0.209582 | + | 0.977791i | \(0.567210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.52381 | −0.297121 | −0.148561 | − | 0.988903i | \(-0.547464\pi\) | ||||
−0.148561 | + | 0.988903i | \(0.547464\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.7039 | −0.894896 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.3301 | −1.43719 | −0.718594 | − | 0.695430i | \(-0.755214\pi\) | ||||
−0.718594 | + | 0.695430i | \(0.755214\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.50736 | −0.260741 | −0.130371 | − | 0.991465i | \(-0.541617\pi\) | ||||
−0.130371 | + | 0.991465i | \(0.541617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7420 | 0.650153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.9262 | −0.793395 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.9861 | −0.725386 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −56.2893 | −1.94332 | −0.971662 | − | 0.236374i | \(-0.924041\pi\) | ||||
−0.971662 | + | 0.236374i | \(0.924041\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.2338 | 2.21496 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.1233 | 1.10639 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.59603 | −0.123707 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −35.8266 | −1.22956 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0640261 | 0.00219479 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.83615 | 0.0971081 | 0.0485540 | − | 0.998821i | \(-0.484539\pi\) | ||||
0.0485540 | + | 0.998821i | \(0.484539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.34285 | 0.285320 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.25343 | 0.213613 | 0.106806 | − | 0.994280i | \(-0.465937\pi\) | ||||
0.106806 | + | 0.994280i | \(0.465937\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.9497 | 1.67014 | 0.835071 | − | 0.550142i | \(-0.185426\pi\) | ||||
0.835071 | + | 0.550142i | \(0.185426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.7758 | −1.21782 | −0.608911 | − | 0.793238i | \(-0.708394\pi\) | ||||
−0.608911 | + | 0.793238i | \(0.708394\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.65584 | 0.0903013 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 109.377 | 3.71464 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.03909 | 0.238785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.2857 | 1.50056 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.2487 | −0.380710 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1606 | 0.376867 | 0.188434 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188434 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.1151 | −0.644737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.96039 | −0.0660473 | −0.0330237 | − | 0.999455i | \(-0.510514\pi\) | ||||
−0.0330237 | + | 0.999455i | \(0.510514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.79898 | −0.127846 | −0.0639229 | − | 0.997955i | \(-0.520361\pi\) | ||||
−0.0639229 | + | 0.997955i | \(0.520361\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.7468 | 0.428479 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23.2012 | 0.779021 | 0.389511 | − | 0.921022i | \(-0.372644\pi\) | ||||
0.389511 | + | 0.921022i | \(0.372644\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.58171 | −0.287498 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.4979 | 0.752863 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.2820 | −0.611101 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.9930 | 0.367046 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.5788 | 1.98706 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 57.5034 | 1.91572 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.6566 | −0.819614 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7518 | −0.888279 | −0.444139 | − | 0.895958i | \(-0.646490\pi\) | ||||
−0.444139 | + | 0.895958i | \(0.646490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.3915 | 1.47237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0286 | 0.531050 | 0.265525 | − | 0.964104i | \(-0.414455\pi\) | ||||
0.265525 | + | 0.964104i | \(0.414455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.5964 | 1.24426 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.3684 | 0.838652 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.1809 | −0.632719 | −0.316360 | − | 0.948639i | \(-0.602461\pi\) | ||||
−0.316360 | + | 0.948639i | \(0.602461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.0907 | −0.596108 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.9119 | 1.05039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.257664 | −0.00847195 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.2549 | 0.533880 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.9710 | −0.688036 | −0.344018 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344018 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.88737 | 0.290959 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.7657 | 0.580999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.6522 | 1.49139 | 0.745697 | − | 0.666285i | \(-0.232117\pi\) | ||||
0.745697 | + | 0.666285i | \(0.232117\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.7913 | −0.809034 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.160121 | −0.00521980 | −0.00260990 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00260990 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.2783 | −0.367271 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.31824 | −0.172820 | −0.0864099 | − | 0.996260i | \(-0.527539\pi\) | ||||
−0.0864099 | + | 0.996260i | \(0.527539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.3646 | 0.920755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82.7212 | −2.68242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.05836 | 0.0990699 | 0.0495349 | − | 0.998772i | \(-0.484226\pi\) | ||||
0.0495349 | + | 0.998772i | \(0.484226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3476 | 0.431918 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −61.6722 | −1.99358 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.07243 | 0.228143 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −57.0432 | −1.83819 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.95922 | −0.159643 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.96793 | −0.127600 | −0.0638001 | − | 0.997963i | \(-0.520322\pi\) | ||||
−0.0638001 | + | 0.997963i | \(0.520322\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.5268 | 1.30191 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.3548 | −1.35923 | −0.679615 | − | 0.733569i | \(-0.737853\pi\) | ||||
−0.679615 | + | 0.733569i | \(0.737853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −44.2398 | −1.41681 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.77393 | 0.312696 | 0.156348 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156348 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.4009 | 0.364376 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 56.0797 | 1.79049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.20960 | −0.134265 | −0.0671326 | − | 0.997744i | \(-0.521385\pi\) | ||||
−0.0671326 | + | 0.997744i | \(0.521385\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.00986 | −0.0640394 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.61229 | −0.178460 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.1486 | 1.30713 | 0.653564 | − | 0.756871i | \(-0.273273\pi\) | ||||
0.653564 | + | 0.756871i | \(0.273273\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.3602 | −0.328770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.66310 | −0.274639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.6805 | 1.03500 | 0.517501 | − | 0.855682i | \(-0.326862\pi\) | ||||
0.517501 | + | 0.855682i | \(0.326862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.217763 | 0.00688971 |
(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 | 9016.2.a.bl.1.11 | 11 | ||
7.3 | odd | 6 | 1288.2.q.a.737.11 | ✓ | 22 | ||
7.5 | odd | 6 | 1288.2.q.a.921.11 | yes | 22 | ||
7.6 | odd | 2 | 9016.2.a.bq.1.1 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1288.2.q.a.737.11 | ✓ | 22 | 7.3 | odd | 6 | ||
1288.2.q.a.921.11 | yes | 22 | 7.5 | odd | 6 | ||
9016.2.a.bl.1.11 | 11 | 1.1 | even | 1 | trivial | ||
9016.2.a.bq.1.1 | 11 | 7.6 | odd | 2 |