Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.576096652.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 8x^{4} + 11x^{3} + 16x^{2} - 6x - 4 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.13326\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | −2.13326 | −1.23164 | −0.615819 | − | 0.787888i | \(-0.711175\pi\) | ||||
−0.615819 | + | 0.787888i | \(0.711175\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.368439 | 0.164771 | 0.0823856 | − | 0.996601i | \(-0.473746\pi\) | ||||
0.0823856 | + | 0.996601i | \(0.473746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.29504 | −1.62337 | −0.811686 | − | 0.584094i | \(-0.801450\pi\) | ||||
−0.811686 | + | 0.584094i | \(0.801450\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.55080 | 0.516932 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.29504 | 1.19123 | 0.595615 | − | 0.803270i | \(-0.296908\pi\) | ||||
0.595615 | + | 0.803270i | \(0.296908\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.785977 | −0.202938 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.76482 | 0.428032 | 0.214016 | − | 0.976830i | \(-0.431346\pi\) | ||||
0.214016 | + | 0.976830i | \(0.431346\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.16244 | 1.99941 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.34414 | 0.488787 | 0.244393 | − | 0.969676i | \(-0.421411\pi\) | ||||
0.244393 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.86425 | −0.972850 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.09153 | 0.594964 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.93765 | −0.359813 | −0.179906 | − | 0.983684i | \(-0.557579\pi\) | ||||
−0.179906 | + | 0.983684i | \(0.557579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.63918 | 1.19243 | 0.596216 | − | 0.802824i | \(-0.296670\pi\) | ||||
0.596216 | + | 0.802824i | \(0.296670\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.13326 | 0.371353 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.58246 | −0.267485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.57932 | −0.424037 | −0.212019 | − | 0.977266i | \(-0.568004\pi\) | ||||
−0.212019 | + | 0.977266i | \(0.568004\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.16244 | −1.46716 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.79334 | 0.592420 | 0.296210 | − | 0.955123i | \(-0.404277\pi\) | ||||
0.296210 | + | 0.955123i | \(0.404277\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7240 | 1.78789 | 0.893946 | − | 0.448174i | \(-0.147925\pi\) | ||||
0.893946 | + | 0.448174i | \(0.147925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.571375 | 0.0851756 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.32356 | −1.21412 | −0.607058 | − | 0.794657i | \(-0.707650\pi\) | ||||
−0.607058 | + | 0.794657i | \(0.707650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.4474 | 1.63534 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.76482 | −0.527180 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.31345 | 1.00458 | 0.502290 | − | 0.864699i | \(-0.332491\pi\) | ||||
0.502290 | + | 0.864699i | \(0.332491\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.368439 | −0.0496804 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.13326 | 0.282557 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.635940 | 0.0827924 | 0.0413962 | − | 0.999143i | \(-0.486819\pi\) | ||||
0.0413962 | + | 0.999143i | \(0.486819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2466 | −1.43998 | −0.719990 | − | 0.693985i | \(-0.755853\pi\) | ||||
−0.719990 | + | 0.693985i | \(0.755853\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.66074 | −0.839174 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.58246 | 0.196280 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.63536 | −0.688469 | −0.344234 | − | 0.938884i | \(-0.611862\pi\) | ||||
−0.344234 | + | 0.938884i | \(0.611862\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.00066 | −0.602008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.65279 | 0.314829 | 0.157414 | − | 0.987533i | \(-0.449684\pi\) | ||||
0.157414 | + | 0.987533i | \(0.449684\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.519535 | 0.0608069 | 0.0304035 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304035 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.3767 | 1.19820 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.29504 | 0.489465 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.02123 | 0.339915 | 0.169958 | − | 0.985451i | \(-0.445637\pi\) | ||||
0.169958 | + | 0.985451i | \(0.445637\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2474 | −1.24971 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0641 | −1.32420 | −0.662102 | − | 0.749413i | \(-0.730336\pi\) | ||||
−0.662102 | + | 0.749413i | \(0.730336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.650229 | 0.0705273 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.13351 | 0.443159 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.05192 | 0.429502 | 0.214751 | − | 0.976669i | \(-0.431106\pi\) | ||||
0.214751 | + | 0.976669i | \(0.431106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.4474 | −1.93381 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.1631 | −1.46864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.368439 | −0.0378011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.4338 | −1.87167 | −0.935836 | − | 0.352436i | \(-0.885354\pi\) | ||||
−0.935836 | + | 0.352436i | \(0.885354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.55080 | −0.155861 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.98008 | 0.694544 | 0.347272 | − | 0.937764i | \(-0.387108\pi\) | ||||
0.347272 | + | 0.937764i | \(0.387108\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.96899 | −0.588142 | −0.294071 | − | 0.955784i | \(-0.595010\pi\) | ||||
−0.294071 | + | 0.955784i | \(0.595010\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.37580 | 0.329445 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.57658 | −0.635782 | −0.317891 | − | 0.948127i | \(-0.602975\pi\) | ||||
−0.317891 | + | 0.948127i | \(0.602975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.78605 | −0.841551 | −0.420776 | − | 0.907165i | \(-0.638242\pi\) | ||||
−0.420776 | + | 0.907165i | \(0.638242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.50236 | 0.522260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.9008 | 1.68396 | 0.841982 | − | 0.539505i | \(-0.181389\pi\) | ||||
0.841982 | + | 0.539505i | \(0.181389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.863673 | 0.0805379 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.66074 | 0.615785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.57997 | −0.694855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.09218 | −0.729647 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.63438 | −0.325069 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5097 | 0.932587 | 0.466293 | − | 0.884630i | \(-0.345589\pi\) | ||||
0.466293 | + | 0.884630i | \(0.345589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.0103 | −2.20204 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0578 | −1.31560 | −0.657802 | − | 0.753191i | \(-0.728514\pi\) | ||||
−0.657802 | + | 0.753191i | \(0.728514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.29504 | 0.372427 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.13904 | 0.0980330 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1409 | −0.951829 | −0.475915 | − | 0.879491i | \(-0.657883\pi\) | ||||
−0.475915 | + | 0.879491i | \(0.657883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.78283 | −0.151218 | −0.0756090 | − | 0.997138i | \(-0.524090\pi\) | ||||
−0.0756090 | + | 0.997138i | \(0.524090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.7563 | 1.49535 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.29504 | −0.359169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.713907 | −0.0592868 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −24.4202 | −2.01415 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0249 | −1.39474 | −0.697368 | − | 0.716713i | \(-0.745646\pi\) | ||||
−0.697368 | + | 0.716713i | \(0.745646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8398 | 0.963508 | 0.481754 | − | 0.876306i | \(-0.340000\pi\) | ||||
0.481754 | + | 0.876306i | \(0.340000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.73688 | 0.221264 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.44614 | 0.196478 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7949 | 1.26057 | 0.630285 | − | 0.776363i | \(-0.282938\pi\) | ||||
0.630285 | + | 0.776363i | \(0.282938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.6015 | −1.23728 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.0682 | −0.793483 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4299 | 1.28689 | 0.643443 | − | 0.765494i | \(-0.277505\pi\) | ||||
0.643443 | + | 0.765494i | \(0.277505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.785977 | 0.0611882 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.92808 | 0.768258 | 0.384129 | − | 0.923279i | \(-0.374502\pi\) | ||||
0.384129 | + | 0.923279i | \(0.374502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.44737 | 0.419029 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.55080 | −0.118592 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8140 | −1.12629 | −0.563145 | − | 0.826358i | \(-0.690409\pi\) | ||||
−0.563145 | + | 0.826358i | \(0.690409\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.8922 | 1.57930 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.35663 | −0.101970 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.6413 | −0.870109 | −0.435054 | − | 0.900404i | \(-0.643271\pi\) | ||||
−0.435054 | + | 0.900404i | \(0.643271\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.35395 | −0.174968 | −0.0874840 | − | 0.996166i | \(-0.527883\pi\) | ||||
−0.0874840 | + | 0.996166i | \(0.527883\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.9919 | 1.77353 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.950323 | −0.0698691 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.76482 | −0.129056 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.2782 | −0.965849 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.4735 | −1.26434 | −0.632171 | − | 0.774829i | \(-0.717836\pi\) | ||||
−0.632171 | + | 0.774829i | \(0.717836\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.12828 | 0.0812152 | 0.0406076 | − | 0.999175i | \(-0.487071\pi\) | ||||
0.0406076 | + | 0.999175i | \(0.487071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.37580 | −0.241746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −27.0948 | −1.93043 | −0.965213 | − | 0.261464i | \(-0.915795\pi\) | ||||
−0.965213 | + | 0.261464i | \(0.915795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.84021 | −0.697554 | −0.348777 | − | 0.937206i | \(-0.613403\pi\) | ||||
−0.348777 | + | 0.937206i | \(0.613403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0217 | 0.847945 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.32229 | 0.584110 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.39762 | 0.0976138 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.63528 | 0.252670 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.1342 | −1.59263 | −0.796314 | − | 0.604884i | \(-0.793219\pi\) | ||||
−0.796314 | + | 0.604884i | \(0.793219\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.65910 | −0.387755 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.31958 | 0.294593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.5155 | −1.93576 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.10830 | −0.0748921 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.57997 | 0.509884 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2571 | −0.686864 | −0.343432 | − | 0.939178i | \(-0.611590\pi\) | ||||
−0.343432 | + | 0.939178i | \(0.611590\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.54347 | −0.502898 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.44257 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.80092 | −0.515499 | −0.257750 | − | 0.966212i | \(-0.582981\pi\) | ||||
−0.257750 | + | 0.966212i | \(0.582981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.16244 | −0.602844 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.284355 | −0.0186287 | −0.00931436 | − | 0.999957i | \(-0.502965\pi\) | ||||
−0.00931436 | + | 0.999957i | \(0.502965\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.06673 | −0.200051 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.44508 | −0.418653 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.3450 | 0.863214 | 0.431607 | − | 0.902062i | \(-0.357947\pi\) | ||||
0.431607 | + | 0.902062i | \(0.357947\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.3523 | 1.63309 | 0.816544 | − | 0.577283i | \(-0.195887\pi\) | ||||
0.816544 | + | 0.577283i | \(0.195887\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.7191 | 0.944230 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.21766 | 0.269457 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.29504 | −0.273287 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 25.7358 | 1.63094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.4410 | −0.722149 | −0.361074 | − | 0.932537i | \(-0.617590\pi\) | ||||
−0.361074 | + | 0.932537i | \(0.617590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.34414 | −0.147375 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.38711 | −0.0868641 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.77306 | 0.422492 | 0.211246 | − | 0.977433i | \(-0.432248\pi\) | ||||
0.211246 | + | 0.977433i | \(0.432248\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0783 | 0.688371 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00491 | −0.185999 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7941 | 1.09723 | 0.548616 | − | 0.836074i | \(-0.315155\pi\) | ||||
0.548616 | + | 0.836074i | \(0.315155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.69457 | 0.165526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.64379 | −0.528992 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.2225 | −0.928131 | −0.464065 | − | 0.885801i | \(-0.653610\pi\) | ||||
−0.464065 | + | 0.885801i | \(0.653610\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8640 | −0.842181 | −0.421090 | − | 0.907019i | \(-0.638352\pi\) | ||||
−0.421090 | + | 0.907019i | \(0.638352\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39.3530 | 2.38175 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.86425 | 0.293325 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.9664 | −0.959331 | −0.479665 | − | 0.877451i | \(-0.659242\pi\) | ||||
−0.479665 | + | 0.877451i | \(0.659242\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.2960 | 0.616407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.50948 | −0.388323 | −0.194161 | − | 0.980970i | \(-0.562199\pi\) | ||||
−0.194161 | + | 0.980970i | \(0.562199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.6521 | 1.28709 | 0.643543 | − | 0.765410i | \(-0.277464\pi\) | ||||
0.643543 | + | 0.765410i | \(0.277464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.785977 | 0.0465573 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.2926 | −0.961719 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8854 | −0.816789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 39.3242 | 2.30522 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.27143 | −0.0742777 | −0.0371389 | − | 0.999310i | \(-0.511824\pi\) | ||||
−0.0371389 | + | 0.999310i | \(0.511824\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.234306 | 0.0136418 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.09153 | −0.179389 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0682 | 0.582257 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −50.3550 | −2.90242 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.8903 | −0.855427 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.14369 | −0.237267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.1122 | −1.14786 | −0.573932 | − | 0.818903i | \(-0.694583\pi\) | ||||
−0.573932 | + | 0.818903i | \(0.694583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.7334 | 0.724378 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.2293 | −0.693458 | −0.346729 | − | 0.937965i | \(-0.612708\pi\) | ||||
−0.346729 | + | 0.937965i | \(0.612708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.6832 | −1.45170 | −0.725850 | − | 0.687853i | \(-0.758554\pi\) | ||||
−0.725850 | + | 0.687853i | \(0.758554\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.45408 | −0.138272 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.1568 | 0.570464 | 0.285232 | − | 0.958459i | \(-0.407929\pi\) | ||||
0.285232 | + | 0.958459i | \(0.407929\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.93765 | 0.108488 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0295 | 0.783053 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.76482 | −0.0981972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.8922 | −1.15889 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.7429 | 1.03649 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 35.7500 | 1.97096 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.9975 | −1.26405 | −0.632027 | − | 0.774946i | \(-0.717777\pi\) | ||||
−0.632027 | + | 0.774946i | \(0.717777\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.07629 | −0.113440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.9446 | −0.868560 | −0.434280 | − | 0.900778i | \(-0.642997\pi\) | ||||
−0.434280 | + | 0.900778i | \(0.642997\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −38.1870 | −2.07404 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.63918 | −0.359532 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1016 | −1.03139 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.84244 | −0.0991936 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.7552 | 0.792102 | 0.396051 | − | 0.918229i | \(-0.370380\pi\) | ||||
0.396051 | + | 0.918229i | \(0.370380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.0348 | 1.87537 | 0.937684 | − | 0.347489i | \(-0.112966\pi\) | ||||
0.937684 | + | 0.347489i | \(0.112966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.2782 | 0.708739 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.53960 | −0.188394 | −0.0941971 | − | 0.995554i | \(-0.530028\pi\) | ||||
−0.0941971 | + | 0.995554i | \(0.530028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.977394 | 0.0518747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.1701 | 0.855810 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0685 | 0.848065 | 0.424032 | − | 0.905647i | \(-0.360614\pi\) | ||||
0.424032 | + | 0.905647i | \(0.360614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.13326 | −0.111967 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.191417 | 0.0100192 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.31930 | 0.173266 | 0.0866331 | − | 0.996240i | \(-0.472389\pi\) | ||||
0.0866331 | + | 0.996240i | \(0.472389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.88270 | 0.306241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.4116 | −1.63081 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.75685 | 0.246301 | 0.123150 | − | 0.992388i | \(-0.460700\pi\) | ||||
0.123150 | + | 0.992388i | \(0.460700\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.75308 | 0.400367 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.32229 | −0.428620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9302 | −0.766912 | −0.383456 | − | 0.923559i | \(-0.625266\pi\) | ||||
−0.383456 | + | 0.923559i | \(0.625266\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.4200 | −1.14861 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.5424 | 1.66284 | 0.831421 | − | 0.555643i | \(-0.187528\pi\) | ||||
0.831421 | + | 0.555643i | \(0.187528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.58246 | 0.0806497 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.1815 | 0.924220 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.4819 | −1.34268 | −0.671342 | − | 0.741148i | \(-0.734282\pi\) | ||||
−0.671342 | + | 0.741148i | \(0.734282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.13698 | 0.209216 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.1221 | 1.62035 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.11314 | 0.0560082 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7685 | 0.941964 | 0.470982 | − | 0.882143i | \(-0.343900\pi\) | ||||
0.470982 | + | 0.882143i | \(0.343900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.16244 | −0.458696 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.76842 | 0.288061 | 0.144031 | − | 0.989573i | \(-0.453994\pi\) | ||||
0.144031 | + | 0.989573i | \(0.453994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.5155 | 1.42046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.14399 | −0.205917 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.57932 | 0.127852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.9722 | −0.591986 | −0.295993 | − | 0.955190i | \(-0.595650\pi\) | ||||
−0.295993 | + | 0.955190i | \(0.595650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.7664 | 1.17231 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.73139 | −0.134403 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.44488 | −0.218191 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.80325 | 0.186246 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.8202 | −1.74993 | −0.874965 | − | 0.484187i | \(-0.839115\pi\) | ||||
−0.874965 | + | 0.484187i | \(0.839115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.5248 | −0.854104 | −0.427052 | − | 0.904227i | \(-0.640448\pi\) | ||||
−0.427052 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.9082 | −0.627616 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.58453 | −0.416411 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.3046 | 2.33762 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.16244 | 0.442367 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2381 | 0.493153 | 0.246577 | − | 0.969123i | \(-0.420694\pi\) | ||||
0.246577 | + | 0.969123i | \(0.420694\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.0289 | −1.29893 | −0.649463 | − | 0.760393i | \(-0.725006\pi\) | ||||
−0.649463 | + | 0.760393i | \(0.725006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.52295 | 0.0730199 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.34414 | −0.112135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.5862 | −1.69844 | −0.849218 | − | 0.528042i | \(-0.822926\pi\) | ||||
−0.849218 | + | 0.528042i | \(0.822926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.7526 | 0.845360 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.3060 | −1.91500 | −0.957499 | − | 0.288438i | \(-0.906864\pi\) | ||||
−0.957499 | + | 0.288438i | \(0.906864\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.49289 | 0.0707696 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 36.3186 | 1.71781 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.72627 | −0.223047 | −0.111523 | − | 0.993762i | \(-0.535573\pi\) | ||||
−0.111523 | + | 0.993762i | \(0.535573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.79334 | −0.178621 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −25.2573 | −1.18669 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.79674 | −0.318636 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.557936 | −0.0260992 | −0.0130496 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130496 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.45599 | 0.254664 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.88592 | 0.180985 | 0.0904926 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904926 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3618 | 0.899821 | 0.449911 | − | 0.893074i | \(-0.351456\pi\) | ||||
0.449911 | + | 0.893074i | \(0.351456\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.21824 | −0.241990 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.62076 | 0.167549 | 0.0837745 | − | 0.996485i | \(-0.473302\pi\) | ||||
0.0837745 | + | 0.996485i | \(0.473302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.2041 | 1.11764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.6946 | −1.55257 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.7240 | −0.539070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.86425 | 0.223187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3417 | 0.519300 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.9363 | 1.59628 | 0.798139 | − | 0.602473i | \(-0.205818\pi\) | ||||
0.798139 | + | 0.602473i | \(0.205818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0783 | −0.505126 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.4780 | 0.977284 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.79175 | −0.308398 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9504 | 1.13061 | 0.565306 | − | 0.824881i | \(-0.308758\pi\) | ||||
0.565306 | + | 0.824881i | \(0.308758\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.0492 | −1.58498 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.3947 | 1.46195 | 0.730976 | − | 0.682403i | \(-0.239065\pi\) | ||||
0.730976 | + | 0.682403i | \(0.239065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.41961 | −0.154011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.571375 | −0.0256814 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.3939 | −0.511084 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.67702 | 0.254138 | 0.127069 | − | 0.991894i | \(-0.459443\pi\) | ||||
0.127069 | + | 0.991894i | \(0.459443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1792 | −0.946216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.9667 | 0.801095 | 0.400547 | − | 0.916276i | \(-0.368820\pi\) | ||||
0.400547 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.57174 | 0.114441 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.6207 | −0.516092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.9900 | −0.886040 | −0.443020 | − | 0.896512i | \(-0.646093\pi\) | ||||
−0.443020 | + | 0.896512i | \(0.646093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.23142 | −0.0987123 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.09153 | −0.136494 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.19921 | −0.0969089 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.32356 | 0.366070 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.6022 | 1.38718 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.2081 | 1.71774 | 0.858870 | − | 0.512194i | \(-0.171167\pi\) | ||||
0.858870 | + | 0.512194i | \(0.171167\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6782 | 0.685559 | 0.342779 | − | 0.939416i | \(-0.388632\pi\) | ||||
0.342779 | + | 0.939416i | \(0.388632\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −44.5684 | −1.94512 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.7170 | 0.510399 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5050 | −0.761088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.986215 | 0.0427981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.2926 | 0.705709 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.42307 | −0.104758 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.8338 | 1.07166 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.4474 | −0.493073 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.6920 | −1.31955 | −0.659775 | − | 0.751463i | \(-0.729349\pi\) | ||||
−0.659775 | + | 0.751463i | \(0.729349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.02159 | 0.215497 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.23713 | −0.138663 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0271 | −1.19835 | −0.599176 | − | 0.800617i | \(-0.704505\pi\) | ||||
−0.599176 | + | 0.800617i | \(0.704505\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.4412 | −0.744372 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.93765 | 0.0825467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9763 | −0.551809 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.02729 | 0.0860535 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.1122 | 1.74198 | 0.870989 | − | 0.491302i | \(-0.163479\pi\) | ||||
0.870989 | + | 0.491302i | \(0.163479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 50.3550 | 2.12979 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.76482 | 0.158951 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.1179 | −0.679287 | −0.339643 | − | 0.940554i | \(-0.610306\pi\) | ||||
−0.339643 | + | 0.940554i | \(0.610306\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.59536 | 0.277469 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 48.3081 | 2.02875 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.59832 | −0.402383 | −0.201191 | − | 0.979552i | \(-0.564481\pi\) | ||||
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.1814 | −0.844564 | −0.422282 | − | 0.906464i | \(-0.638771\pi\) | ||||
−0.422282 | + | 0.906464i | \(0.638771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.2756 | 1.55721 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.4025 | −0.475516 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.6942 | 1.36108 | 0.680539 | − | 0.732712i | \(-0.261746\pi\) | ||||
0.680539 | + | 0.732712i | \(0.261746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.40691 | −0.100028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 51.8157 | 2.14968 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.31345 | −0.302892 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.45408 | 0.101464 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 43.4049 | 1.79151 | 0.895755 | − | 0.444547i | \(-0.146635\pi\) | ||||
0.895755 | + | 0.444547i | \(0.146635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.63918 | −0.273563 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 57.8003 | 2.37759 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.471672 | −0.0193693 | −0.00968463 | − | 0.999953i | \(-0.503083\pi\) | ||||
−0.00968463 | + | 0.999953i | \(0.503083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.79276 | −0.114492 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.9917 | 0.859134 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.2715 | 0.746555 | 0.373277 | − | 0.927720i | \(-0.378234\pi\) | ||||
0.373277 | + | 0.927720i | \(0.378234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50378 | −0.346876 | −0.173438 | − | 0.984845i | \(-0.555488\pi\) | ||||
−0.173438 | + | 0.984845i | \(0.555488\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.73930 | −0.355892 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.368439 | 0.0149792 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.4070 | −1.23418 | −0.617092 | − | 0.786891i | \(-0.711689\pi\) | ||||
−0.617092 | + | 0.786891i | \(0.711689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.7536 | −0.719413 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.7500 | −1.44629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.8580 | 0.478942 | 0.239471 | − | 0.970904i | \(-0.423026\pi\) | ||||
0.239471 | + | 0.970904i | \(0.423026\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.98148 | −0.120225 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 43.1793 | 1.73833 | 0.869167 | − | 0.494519i | \(-0.164656\pi\) | ||||
0.869167 | + | 0.494519i | \(0.164656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.3194 | −1.37941 | −0.689706 | − | 0.724090i | \(-0.742260\pi\) | ||||
−0.689706 | + | 0.724090i | \(0.742260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.24696 | 0.290811 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.4031 | −0.697242 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.9822 | 0.919289 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.13326 | −0.0851942 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.55203 | −0.181501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.90779 | 0.115757 | 0.0578787 | − | 0.998324i | \(-0.481566\pi\) | ||||
0.0578787 | + | 0.998324i | \(0.481566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49.3514 | 1.96154 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.87220 | 0.153663 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 49.1669 | 1.94806 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.11395 | 0.162745 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.5767 | −0.852227 | −0.426113 | − | 0.904670i | \(-0.640118\pi\) | ||||
−0.426113 | + | 0.904670i | \(0.640118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3190 | 0.722432 | 0.361216 | − | 0.932482i | \(-0.382362\pi\) | ||||
0.361216 | + | 0.932482i | \(0.382362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.21479 | −0.362832 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.74136 | 0.265030 | 0.132515 | − | 0.991181i | \(-0.457695\pi\) | ||||
0.132515 | + | 0.991181i | \(0.457695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.635940 | −0.0249628 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 60.8311 | 2.38416 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.1161 | −0.748071 | −0.374036 | − | 0.927414i | \(-0.622026\pi\) | ||||
−0.374036 | + | 0.927414i | \(0.622026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.54788 | −0.216774 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.805693 | 0.0314331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.91788 | −0.347391 | −0.173696 | − | 0.984799i | \(-0.555571\pi\) | ||||
−0.173696 | + | 0.984799i | \(0.555571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.2681 | 0.399383 | 0.199691 | − | 0.979859i | \(-0.436006\pi\) | ||||
0.199691 | + | 0.979859i | \(0.436006\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.1701 | −0.627993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.58246 | 0.0613653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.54212 | −0.175872 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.8810 | 0.845968 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.2466 | 0.434170 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2347 | −0.625800 | −0.312900 | − | 0.949786i | \(-0.601301\pi\) | ||||
−0.312900 | + | 0.949786i | \(0.601301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0380 | −0.578811 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.1769 | 1.19822 | 0.599112 | − | 0.800665i | \(-0.295520\pi\) | ||||
0.599112 | + | 0.800665i | \(0.295520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 79.1741 | 3.03842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.1435 | 0.771899 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9358 | 1.10720 | 0.553599 | − | 0.832783i | \(-0.313254\pi\) | ||||
0.553599 | + | 0.832783i | \(0.313254\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.10474 | −0.156834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.6414 | 0.634909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.4116 | 1.19669 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.96767 | −0.265063 | −0.132531 | − | 0.991179i | \(-0.542311\pi\) | ||||
−0.132531 | + | 0.991179i | \(0.542311\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.66074 | 0.253020 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.656866 | −0.0249163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.69457 | 0.253575 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.606603 | 0.0229438 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6325 | −1.11920 | −0.559601 | − | 0.828762i | \(-0.689046\pi\) | ||||
−0.559601 | + | 0.828762i | \(0.689046\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.57932 | 0.0972808 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.54213 | 0.246391 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.9797 | −1.12750 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.9959 | 1.35185 | 0.675927 | − | 0.736968i | \(-0.263743\pi\) | ||||
0.675927 | + | 0.736968i | \(0.263743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.68532 | 0.175713 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.5632 | 0.582845 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.58246 | −0.0591807 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.4683 | −1.06317 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.9296 | −1.48912 | −0.744562 | − | 0.667553i | \(-0.767342\pi\) | ||||
−0.744562 | + | 0.667553i | \(0.767342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.6371 | 0.954774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54.0831 | −2.01137 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.42523 | 0.350044 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3904 | 1.12712 | 0.563559 | − | 0.826076i | \(-0.309432\pi\) | ||||
0.563559 | + | 0.826076i | \(0.309432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.34261 | 0.0867634 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.6907 | 0.765275 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.38711 | −0.198977 | −0.0994887 | − | 0.995039i | \(-0.531721\pi\) | ||||
−0.0994887 | + | 0.995039i | \(0.531721\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.99737 | −0.331873 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.63536 | 0.207581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.1257 | 0.850692 | 0.425346 | − | 0.905031i | \(-0.360152\pi\) | ||||
0.425346 | + | 0.905031i | \(0.360152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.16244 | 0.336591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.424027 | −0.0155560 | −0.00777802 | − | 0.999970i | \(-0.502476\pi\) | ||||
−0.00777802 | + | 0.999970i | \(0.502476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.27265 | −0.229812 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.7089 | −0.684525 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.2467 | 1.03211 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6179 | −0.496923 | −0.248462 | − | 0.968642i | \(-0.579925\pi\) | ||||
−0.248462 | + | 0.968642i | \(0.579925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.4066 | 0.889426 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.36224 | 0.158758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.3559 | 0.594465 | 0.297232 | − | 0.954805i | \(-0.403936\pi\) | ||||
0.297232 | + | 0.954805i | \(0.403936\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.00066 | 0.181512 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.0288 | 1.63229 | 0.816146 | − | 0.577845i | \(-0.196106\pi\) | ||||
0.816146 | + | 0.577845i | \(0.196106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 37.7365 | 1.36615 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00837 | 0.0364578 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.73139 | 0.0986248 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.44528 | −0.124240 | −0.0621200 | − | 0.998069i | \(-0.519786\pi\) | ||||
−0.0621200 | + | 0.998069i | \(0.519786\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.4487 | −0.520357 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.0468702 | 0.00168580 | 0.000842901 | − | 1.00000i | \(-0.499732\pi\) | ||||
0.000842901 | 1.00000i | \(0.499732\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.2946 | −1.16006 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.6328 | −0.847823 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.79334 | −0.135911 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.65279 | −0.0949244 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.99030 | −0.214076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.81947 | 0.207706 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8161 | −0.706368 | −0.353184 | − | 0.935554i | \(-0.614901\pi\) | ||||
−0.353184 | + | 0.935554i | \(0.614901\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.9595 | −1.35139 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −76.8846 | −2.73370 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.3046 | −1.71535 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.74821 | −0.203868 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.71688 | −0.237924 | −0.118962 | − | 0.992899i | \(-0.537957\pi\) | ||||
−0.118962 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6896 | −0.519680 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.28370 | 0.222024 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.519535 | −0.0183340 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.70951 | −0.130743 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.4735 | 1.14312 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.18834 | −0.323045 | −0.161522 | − | 0.986869i | \(-0.551640\pi\) | ||||
−0.161522 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.2974 | −1.23946 | −0.619730 | − | 0.784815i | \(-0.712758\pi\) | ||||
−0.619730 | + | 0.784815i | \(0.712758\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.5756 | 1.03726 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.05341 | 0.212042 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.7240 | −0.410171 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −28.6081 | −0.999649 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.4473 | 1.72572 | 0.862861 | − | 0.505441i | \(-0.168670\pi\) | ||||
0.862861 | + | 0.505441i | \(0.168670\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.8595 | −1.38941 | −0.694707 | − | 0.719292i | \(-0.744466\pi\) | ||||
−0.694707 | + | 0.719292i | \(0.744466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.3767 | −0.361271 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.30898 | −0.149838 | −0.0749190 | − | 0.997190i | \(-0.523870\pi\) | ||||
−0.0749190 | + | 0.997190i | \(0.523870\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.92252 | −0.101503 | −0.0507516 | − | 0.998711i | \(-0.516162\pi\) | ||||
−0.0507516 | + | 0.998711i | \(0.516162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.0606 | 1.18155 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.2026 | 0.699977 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.65790 | 0.126587 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.5252 | 0.709454 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.3066 | −1.59868 | −0.799341 | − | 0.600878i | \(-0.794818\pi\) | ||||
−0.799341 | + | 0.600878i | \(0.794818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.2455 | −0.870535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.8864 | 0.478273 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.00703 | 0.0690438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.29504 | −0.147579 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −46.1896 | −1.58522 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.04628 | −0.207264 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 55.6663 | 1.90598 | 0.952988 | − | 0.303007i | \(-0.0979906\pi\) | ||||
0.952988 | + | 0.303007i | \(0.0979906\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.571375 | −0.0195406 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.4470 | 1.27916 | 0.639582 | − | 0.768723i | \(-0.279107\pi\) | ||||
0.639582 | + | 0.768723i | \(0.279107\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.88100 | −0.337135 | −0.168568 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168568 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.7562 | 1.18449 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.5374 | −0.562941 | −0.281470 | − | 0.959570i | \(-0.590822\pi\) | ||||
−0.281470 | + | 0.959570i | \(0.590822\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.45808 | −0.185580 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.6212 | 1.00599 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.02123 | −0.102488 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.2041 | −0.820125 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.5871 | −0.967528 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.6098 | 0.527708 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.6237 | 0.392506 | 0.196253 | − | 0.980553i | \(-0.437123\pi\) | ||||
0.196253 | + | 0.980553i | \(0.437123\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.71229 | 0.0914833 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3316 | −0.348079 | −0.174040 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174040 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.4388 | −0.620515 | −0.310258 | − | 0.950653i | \(-0.600415\pi\) | ||||
−0.310258 | + | 0.950653i | \(0.600415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.499835 | −0.0168018 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.4700 | 1.32527 | 0.662636 | − | 0.748941i | \(-0.269437\pi\) | ||||
0.662636 | + | 0.748941i | \(0.269437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.1397 | −1.51394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.2474 | 0.376803 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.32356 | 0.278537 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.28910 | −0.143369 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.4780 | −0.717130 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.8644 | −0.429052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.9069 | 0.429992 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 107.420 | 3.57473 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.867289 | −0.0288297 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.8936 | −1.45746 | −0.728731 | − | 0.684800i | \(-0.759890\pi\) | ||||
−0.728731 | + | 0.684800i | \(0.759890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.8247 | 0.359032 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.7253 | −1.15050 | −0.575251 | − | 0.817977i | \(-0.695096\pi\) | ||||
−0.575251 | + | 0.817977i | \(0.695096\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0641 | 0.399263 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.83957 | 0.292227 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 64.6737 | 2.13572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.18965 | 0.303139 | 0.151569 | − | 0.988447i | \(-0.451567\pi\) | ||||
0.151569 | + | 0.988447i | \(0.451567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.9046 | 1.41375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3939 | 0.375033 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5465 | 0.412525 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.25670 | −0.304030 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.5639 | −0.805917 | −0.402958 | − | 0.915218i | \(-0.632018\pi\) | ||||
−0.402958 | + | 0.915218i | \(0.632018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.4474 | −0.375172 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 26.0882 | 0.854090 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.650229 | −0.0212648 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.1667 | −1.08351 | −0.541754 | − | 0.840537i | \(-0.682240\pi\) | ||||
−0.541754 | + | 0.840537i | \(0.682240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.7890 | 1.78797 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0332 | 0.913855 | 0.456927 | − | 0.889504i | \(-0.348950\pi\) | ||||
0.456927 | + | 0.889504i | \(0.348950\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.89212 | 0.289567 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.89222 | −0.159144 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.1601 | −0.850089 | −0.425044 | − | 0.905173i | \(-0.639742\pi\) | ||||
−0.425044 | + | 0.905173i | \(0.639742\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.23142 | 0.0724350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.6671 | −0.702605 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.6523 | −0.733779 | −0.366890 | − | 0.930264i | \(-0.619577\pi\) | ||||
−0.366890 | + | 0.930264i | \(0.619577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.43794 | −0.208327 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.13351 | −0.133618 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.8505 | 1.54517 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0787 | 0.421893 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.1989 | −0.328656 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.415702 | 0.0133819 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0751 | −0.709888 | −0.354944 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354944 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.76482 | 0.120943 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50.8293 | −1.63119 | −0.815595 | − | 0.578623i | \(-0.803590\pi\) | ||||
−0.815595 | + | 0.578623i | \(0.803590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.65734 | 0.245483 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 44.5684 | 1.42733 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.5689 | −0.913999 | −0.456999 | − | 0.889467i | \(-0.651076\pi\) | ||||
−0.456999 | + | 0.889467i | \(0.651076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.05192 | −0.129500 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6254 | −0.435025 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.1620 | −0.356012 | −0.178006 | − | 0.984029i | \(-0.556965\pi\) | ||||
−0.178006 | + | 0.984029i | \(0.556965\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.98280 | −0.318079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −76.2641 | −2.42751 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.4827 | 0.873898 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.53878 | 0.239477 | 0.119739 | − | 0.992805i | \(-0.461794\pi\) | ||||
0.119739 | + | 0.992805i | \(0.461794\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.0596 | 1.55686 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.62552 | −0.114937 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.6859 | −0.655129 | −0.327565 | − | 0.944829i | \(-0.606228\pi\) | ||||
−0.327565 | + | 0.944829i | \(0.606228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.97403 | −0.252287 |
(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 | 3344.2.a.v.1.2 | 6 | ||
4.3 | odd | 2 | 1672.2.a.j.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1672.2.a.j.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.v.1.2 | 6 | 1.1 | even | 1 | trivial |