Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(1,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, 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("1960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.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: | \(15.6506787962\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.18398\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.1 |
$q$-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 | ||||||||
\(3\) | 1.18398 | 0.683571 | 0.341785 | − | 0.939778i | \(-0.388968\pi\) | ||||
0.341785 | + | 0.939778i | \(0.388968\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.59819 | −0.532731 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.230234 | 0.0694182 | 0.0347091 | − | 0.999397i | \(-0.488950\pi\) | ||||
0.0347091 | + | 0.999397i | \(0.488950\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.27259 | 0.630304 | 0.315152 | − | 0.949041i | \(-0.397945\pi\) | ||||
0.315152 | + | 0.949041i | \(0.397945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.18398 | −0.305702 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.53278 | −1.58443 | −0.792216 | − | 0.610241i | \(-0.791073\pi\) | ||||
−0.792216 | + | 0.610241i | \(0.791073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.260186 | 0.0596908 | 0.0298454 | − | 0.999555i | \(-0.490499\pi\) | ||||
0.0298454 | + | 0.999555i | \(0.490499\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.87079 | −1.84969 | −0.924843 | − | 0.380348i | \(-0.875804\pi\) | ||||
−0.924843 | + | 0.380348i | \(0.875804\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.44417 | −1.04773 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.42662 | 1.00770 | 0.503849 | − | 0.863792i | \(-0.331917\pi\) | ||||
0.503849 | + | 0.863792i | \(0.331917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.87079 | −0.874819 | −0.437409 | − | 0.899262i | \(-0.644104\pi\) | ||||
−0.437409 | + | 0.899262i | \(0.644104\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.272593 | 0.0474523 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.15403 | −0.189721 | −0.0948605 | − | 0.995491i | \(-0.530240\pi\) | ||||
−0.0948605 | + | 0.995491i | \(0.530240\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.69070 | 0.430857 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.43337 | −0.692377 | −0.346188 | − | 0.938165i | \(-0.612524\pi\) | ||||
−0.346188 | + | 0.938165i | \(0.612524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.17723 | 0.637021 | 0.318511 | − | 0.947919i | \(-0.396817\pi\) | ||||
0.318511 | + | 0.947919i | \(0.396817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.59819 | 0.238245 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.923793 | −0.134749 | −0.0673745 | − | 0.997728i | \(-0.521462\pi\) | ||||
−0.0673745 | + | 0.997728i | \(0.521462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.73467 | −1.08307 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.13487 | −0.293247 | −0.146623 | − | 0.989192i | \(-0.546841\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546841\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.230234 | −0.0310448 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.308055 | 0.0408029 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.07107 | 0.660197 | 0.330098 | − | 0.943947i | \(-0.392918\pi\) | ||||
0.330098 | + | 0.943947i | \(0.392918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.88833 | −1.13803 | −0.569017 | − | 0.822326i | \(-0.692676\pi\) | ||||
−0.569017 | + | 0.822326i | \(0.692676\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.27259 | −0.281880 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.15968 | 0.996864 | 0.498432 | − | 0.866929i | \(-0.333909\pi\) | ||||
0.498432 | + | 0.866929i | \(0.333909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.5028 | −1.26439 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.06556 | −1.07588 | −0.537942 | − | 0.842982i | \(-0.680798\pi\) | ||||
−0.537942 | + | 0.842982i | \(0.680798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00955 | −0.703365 | −0.351682 | − | 0.936119i | \(-0.614390\pi\) | ||||
−0.351682 | + | 0.936119i | \(0.614390\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.18398 | 0.136714 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.112912 | 0.0127035 | 0.00635177 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635177 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.65120 | −0.183467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.72065 | −0.957216 | −0.478608 | − | 0.878029i | \(-0.658859\pi\) | ||||
−0.478608 | + | 0.878029i | \(0.658859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.53278 | 0.708579 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.42501 | 0.688833 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.9170 | −1.68720 | −0.843601 | − | 0.536970i | \(-0.819569\pi\) | ||||
−0.843601 | + | 0.536970i | \(0.819569\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.76691 | −0.598001 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.260186 | −0.0266945 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.29565 | −0.436157 | −0.218079 | − | 0.975931i | \(-0.569979\pi\) | ||||
−0.218079 | + | 0.975931i | \(0.569979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.367959 | −0.0369812 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.38712 | −0.735046 | −0.367523 | − | 0.930014i | \(-0.619794\pi\) | ||||
−0.367523 | + | 0.930014i | \(0.619794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5806 | 1.04254 | 0.521271 | − | 0.853391i | \(-0.325458\pi\) | ||||
0.521271 | + | 0.853391i | \(0.325458\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4661 | −1.30182 | −0.650910 | − | 0.759155i | \(-0.725612\pi\) | ||||
−0.650910 | + | 0.759155i | \(0.725612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.50568 | 0.814697 | 0.407348 | − | 0.913273i | \(-0.366453\pi\) | ||||
0.407348 | + | 0.913273i | \(0.366453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.36634 | −0.129688 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.3968 | 1.73063 | 0.865313 | − | 0.501232i | \(-0.167120\pi\) | ||||
0.865313 | + | 0.501232i | \(0.167120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.87079 | 0.827205 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.63204 | −0.335782 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9470 | −0.995181 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.24902 | −0.473288 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.41032 | 0.746295 | 0.373147 | − | 0.927772i | \(-0.378279\pi\) | ||||
0.373147 | + | 0.927772i | \(0.378279\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.94575 | 0.435449 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.78217 | 0.155709 | 0.0778546 | − | 0.996965i | \(-0.475193\pi\) | ||||
0.0778546 | + | 0.996965i | \(0.475193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.44417 | 0.468559 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3137 | −0.966595 | −0.483298 | − | 0.875456i | \(-0.660561\pi\) | ||||
−0.483298 | + | 0.875456i | \(0.660561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4390 | −1.30952 | −0.654761 | − | 0.755836i | \(-0.727231\pi\) | ||||
−0.654761 | + | 0.755836i | \(0.727231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.09375 | −0.0921105 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.523229 | 0.0437546 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.42662 | −0.450656 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.2811 | 1.90726 | 0.953631 | − | 0.300978i | \(-0.0973130\pi\) | ||||
0.953631 | + | 0.300978i | \(0.0973130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.3398 | 1.81798 | 0.908992 | − | 0.416813i | \(-0.136853\pi\) | ||||
0.908992 | + | 0.416813i | \(0.136853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.4406 | 0.844076 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.87079 | 0.391231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.52603 | 0.281407 | 0.140704 | − | 0.990052i | \(-0.455063\pi\) | ||||
0.140704 | + | 0.990052i | \(0.455063\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.52764 | −0.200455 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.2522 | −1.27297 | −0.636485 | − | 0.771289i | \(-0.719612\pi\) | ||||
−0.636485 | + | 0.771289i | \(0.719612\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.272593 | −0.0212213 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.99714 | 0.309308 | 0.154654 | − | 0.987969i | \(-0.450574\pi\) | ||||
0.154654 | + | 0.987969i | \(0.450574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.83532 | −0.602717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.415828 | −0.0317991 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.6214 | −1.33973 | −0.669865 | − | 0.742483i | \(-0.733648\pi\) | ||||
−0.669865 | + | 0.742483i | \(0.733648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00404 | 0.451291 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25.2811 | 1.88960 | 0.944799 | − | 0.327650i | \(-0.106257\pi\) | ||||
0.944799 | + | 0.327650i | \(0.106257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4950 | −1.37473 | −0.687363 | − | 0.726315i | \(-0.741232\pi\) | ||||
−0.687363 | + | 0.726315i | \(0.741232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5236 | −0.777927 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.15403 | 0.0848458 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.50407 | −0.109988 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8658 | 1.43744 | 0.718719 | − | 0.695301i | \(-0.244729\pi\) | ||||
0.718719 | + | 0.695301i | \(0.244729\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4335 | −0.823002 | −0.411501 | − | 0.911409i | \(-0.634995\pi\) | ||||
−0.411501 | + | 0.911409i | \(0.634995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.69070 | −0.192685 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56273 | −0.325081 | −0.162541 | − | 0.986702i | \(-0.551969\pi\) | ||||
−0.162541 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.4429 | 1.02383 | 0.511916 | − | 0.859036i | \(-0.328936\pi\) | ||||
0.511916 | + | 0.859036i | \(0.328936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.66089 | 0.681427 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.43337 | 0.309640 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.1772 | 0.985385 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0599037 | 0.00414363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.63651 | 0.456876 | 0.228438 | − | 0.973558i | \(-0.426638\pi\) | ||||
0.228438 | + | 0.973558i | \(0.426638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.7334 | −0.735443 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.17723 | −0.284884 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.11518 | −0.480800 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.8463 | −0.998673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.3325 | 1.36156 | 0.680782 | − | 0.732486i | \(-0.261640\pi\) | ||||
0.680782 | + | 0.732486i | \(0.261640\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.59819 | −0.106546 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.9312 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.59534 | −0.171505 | −0.0857523 | − | 0.996316i | \(-0.527329\pi\) | ||||
−0.0857523 | + | 0.996316i | \(0.527329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.1638 | −0.993412 | −0.496706 | − | 0.867919i | \(-0.665457\pi\) | ||||
−0.496706 | + | 0.867919i | \(0.665457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.923793 | 0.0602616 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.133685 | 0.00868377 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5656 | 0.683431 | 0.341716 | − | 0.939803i | \(-0.388992\pi\) | ||||
0.341716 | + | 0.939803i | \(0.388992\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6762 | −1.26745 | −0.633726 | − | 0.773557i | \(-0.718475\pi\) | ||||
−0.633726 | + | 0.773557i | \(0.718475\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3775 | 0.922318 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.591297 | 0.0376233 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.3251 | −0.654325 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0498 | 1.58113 | 0.790564 | − | 0.612380i | \(-0.209788\pi\) | ||||
0.790564 | + | 0.612380i | \(0.209788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.04236 | −0.128402 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.73467 | 0.484364 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.71500 | −0.106979 | −0.0534894 | − | 0.998568i | \(-0.517034\pi\) | ||||
−0.0534894 | + | 0.998568i | \(0.517034\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.67279 | −0.536832 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.1173 | −1.36381 | −0.681906 | − | 0.731440i | \(-0.738849\pi\) | ||||
−0.681906 | + | 0.731440i | \(0.738849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.13487 | 0.131144 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.8454 | −1.15332 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 31.9261 | 1.94657 | 0.973283 | − | 0.229608i | \(-0.0737443\pi\) | ||||
0.973283 | + | 0.229608i | \(0.0737443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7767 | 1.56582 | 0.782910 | − | 0.622135i | \(-0.213734\pi\) | ||||
0.782910 | + | 0.622135i | \(0.213734\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.230234 | 0.0138836 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.01755 | −0.481728 | −0.240864 | − | 0.970559i | \(-0.577431\pi\) | ||||
−0.240864 | + | 0.970559i | \(0.577431\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.78445 | 0.466043 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.13207 | −0.186844 | −0.0934218 | − | 0.995627i | \(-0.529781\pi\) | ||||
−0.0934218 | + | 0.995627i | \(0.529781\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.17047 | −0.188465 | −0.0942325 | − | 0.995550i | \(-0.530040\pi\) | ||||
−0.0942325 | + | 0.995550i | \(0.530040\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.308055 | −0.0182476 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.6772 | 1.51042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.08596 | −0.298144 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5264 | 1.02390 | 0.511952 | − | 0.859014i | \(-0.328923\pi\) | ||||
0.511952 | + | 0.859014i | \(0.328923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.07107 | −0.295249 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.25343 | −0.0727316 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.1597 | −1.16586 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.74620 | −0.502456 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.88833 | 0.508944 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.11063 | −0.120460 | −0.0602300 | − | 0.998185i | \(-0.519183\pi\) | ||||
−0.0602300 | + | 0.998185i | \(0.519183\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.5273 | 0.712651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.8149 | −1.18031 | −0.590153 | − | 0.807291i | \(-0.700933\pi\) | ||||
−0.590153 | + | 0.807291i | \(0.700933\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.3860 | 1.20881 | 0.604405 | − | 0.796678i | \(-0.293411\pi\) | ||||
0.604405 | + | 0.796678i | \(0.293411\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.4909 | 0.870058 | 0.435029 | − | 0.900417i | \(-0.356738\pi\) | ||||
0.435029 | + | 0.900417i | \(0.356738\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.24939 | 0.0699526 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9436 | −0.889886 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.69974 | −0.0945760 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.27259 | 0.126061 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0706 | 0.556903 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.52360 | −0.468499 | −0.234250 | − | 0.972176i | \(-0.575263\pi\) | ||||
−0.234250 | + | 0.972176i | \(0.575263\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.84436 | 0.101070 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.15968 | −0.445811 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.1246 | −0.987309 | −0.493655 | − | 0.869658i | \(-0.664339\pi\) | ||||
−0.493655 | + | 0.869658i | \(0.664339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.7814 | 1.18301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.12142 | −0.0607284 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5028 | 0.565453 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.10226 | 0.220221 | 0.110110 | − | 0.993919i | \(-0.464880\pi\) | ||||
0.110110 | + | 0.993919i | \(0.464880\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.67850 | 0.464549 | 0.232275 | − | 0.972650i | \(-0.425383\pi\) | ||||
0.232275 | + | 0.972650i | \(0.425383\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3724 | −0.660388 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.1162 | −1.60292 | −0.801462 | − | 0.598045i | \(-0.795944\pi\) | ||||
−0.801462 | + | 0.598045i | \(0.795944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.06556 | 0.481150 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.2843 | 1.91501 | 0.957505 | − | 0.288416i | \(-0.0931285\pi\) | ||||
0.957505 | + | 0.288416i | \(0.0931285\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9323 | −0.996437 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.9610 | −0.680277 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00955 | 0.314554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.7115 | 0.559134 | 0.279567 | − | 0.960126i | \(-0.409809\pi\) | ||||
0.279567 | + | 0.960126i | \(0.409809\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.08539 | 0.368850 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64335 | 0.292202 | 0.146101 | − | 0.989270i | \(-0.453328\pi\) | ||||
0.146101 | + | 0.989270i | \(0.453328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.18398 | −0.0611404 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.3325 | 0.635156 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.59944 | −0.0821575 | −0.0410787 | − | 0.999156i | \(-0.513079\pi\) | ||||
−0.0410787 | + | 0.999156i | \(0.513079\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.95764 | 0.510145 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.8894 | 1.47618 | 0.738089 | − | 0.674704i | \(-0.235729\pi\) | ||||
0.738089 | + | 0.674704i | \(0.235729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.67601 | −0.339361 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.5226 | −1.19265 | −0.596323 | − | 0.802745i | \(-0.703372\pi\) | ||||
−0.596323 | + | 0.802745i | \(0.703372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.9509 | 2.93070 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.11006 | 0.106438 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.112912 | −0.00568120 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5806 | 0.832159 | 0.416079 | − | 0.909328i | \(-0.363404\pi\) | ||||
0.416079 | + | 0.909328i | \(0.363404\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.52161 | −0.0759858 | −0.0379929 | − | 0.999278i | \(-0.512096\pi\) | ||||
−0.0379929 | + | 0.999278i | \(0.512096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0693 | −0.551402 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.65120 | 0.0820488 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.265697 | −0.0131701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.42927 | 0.268460 | 0.134230 | − | 0.990950i | \(-0.457144\pi\) | ||||
0.134230 | + | 0.990950i | \(0.457144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.3952 | −0.660736 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.72065 | 0.428080 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.2795 | −0.895150 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.4199 | −0.606750 | −0.303375 | − | 0.952871i | \(-0.598114\pi\) | ||||
−0.303375 | + | 0.952871i | \(0.598114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.6804 | −1.00790 | −0.503951 | − | 0.863732i | \(-0.668121\pi\) | ||||
−0.503951 | + | 0.863732i | \(0.668121\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.47640 | 0.0717850 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.53278 | −0.316886 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.619492 | 0.0299093 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.6152 | −1.52285 | −0.761424 | − | 0.648254i | \(-0.775500\pi\) | ||||
−0.761424 | + | 0.648254i | \(0.775500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.1247 | 1.49576 | 0.747880 | − | 0.663834i | \(-0.231072\pi\) | ||||
0.747880 | + | 0.663834i | \(0.231072\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.42501 | −0.308055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.30805 | −0.110409 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.244398 | −0.0116645 | −0.00583223 | − | 0.999983i | \(-0.501856\pi\) | ||||
−0.00583223 | + | 0.999983i | \(0.501856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.45481 | −0.164143 | −0.0820716 | − | 0.996626i | \(-0.526154\pi\) | ||||
−0.0820716 | + | 0.996626i | \(0.526154\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.9170 | 0.754540 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.5643 | 1.30375 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5329 | −0.733044 | −0.366522 | − | 0.930409i | \(-0.619452\pi\) | ||||
−0.366522 | + | 0.930409i | \(0.619452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.02071 | −0.0480636 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 26.4498 | 1.24272 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5379 | −0.492943 | −0.246471 | − | 0.969150i | \(-0.579271\pi\) | ||||
−0.246471 | + | 0.969150i | \(0.579271\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.5655 | 1.66006 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.98972 | −0.278969 | −0.139485 | − | 0.990224i | \(-0.544545\pi\) | ||||
−0.139485 | + | 0.990224i | \(0.544545\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.3601 | −1.55038 | −0.775188 | − | 0.631731i | \(-0.782345\pi\) | ||||
−0.775188 | + | 0.631731i | \(0.782345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.76691 | 0.267434 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7076 | −0.911958 | −0.455979 | − | 0.889991i | \(-0.650711\pi\) | ||||
−0.455979 | + | 0.889991i | \(0.650711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.17474 | 0.192362 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.961740 | 0.0442209 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.260186 | 0.0119382 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.41193 | 0.156222 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.325600 | −0.0148771 | −0.00743853 | − | 0.999972i | \(-0.502368\pi\) | ||||
−0.00743853 | + | 0.999972i | \(0.502368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.62263 | −0.119582 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.29565 | 0.195055 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.9204 | −0.766737 | −0.383369 | − | 0.923595i | \(-0.625236\pi\) | ||||
−0.383369 | + | 0.923595i | \(0.625236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.2423 | −0.870165 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0203 | 0.677859 | 0.338929 | − | 0.940812i | \(-0.389935\pi\) | ||||
0.338929 | + | 0.940812i | \(0.389935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.4509 | −1.59663 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.367959 | 0.0165385 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.0431 | 1.83734 | 0.918670 | − | 0.395025i | \(-0.129264\pi\) | ||||
0.918670 | + | 0.395025i | \(0.129264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.73254 | 0.211434 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.29741 | −0.369963 | −0.184982 | − | 0.982742i | \(-0.559223\pi\) | ||||
−0.184982 | + | 0.982742i | \(0.559223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.38712 | 0.328722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.27686 | −0.412000 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.71266 | −0.386182 | −0.193091 | − | 0.981181i | \(-0.561851\pi\) | ||||
−0.193091 | + | 0.981181i | \(0.561851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.41650 | −0.0625398 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.5806 | −0.466239 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.212689 | −0.00935404 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8634 | −0.915800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.1056 | 1.18752 | 0.593760 | − | 0.804642i | \(-0.297643\pi\) | ||||
0.593760 | + | 0.804642i | \(0.297643\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.37186 | 0.0599870 | 0.0299935 | − | 0.999550i | \(-0.490451\pi\) | ||||
0.0299935 | + | 0.999550i | \(0.490451\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.8198 | 1.38609 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.6908 | 2.42134 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.10454 | −0.351707 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0753 | −0.436408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.4661 | 0.582191 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.9323 | 1.29167 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.56559 | 0.368263 | 0.184132 | − | 0.982902i | \(-0.441053\pi\) | ||||
0.184132 | + | 0.982902i | \(0.441053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.8977 | −0.939722 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.50568 | −0.364343 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.2056 | 1.89009 | 0.945046 | − | 0.326936i | \(-0.106016\pi\) | ||||
0.945046 | + | 0.326936i | \(0.106016\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.2053 | 0.606266 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.41193 | 0.0601503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.36634 | 0.0579981 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.3385 | −0.565171 | −0.282586 | − | 0.959242i | \(-0.591192\pi\) | ||||
−0.282586 | + | 0.959242i | \(0.591192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.49313 | 0.401517 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.78079 | −0.0751849 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.7320 | −1.25306 | −0.626528 | − | 0.779399i | \(-0.715524\pi\) | ||||
−0.626528 | + | 0.779399i | \(0.715524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.3968 | −0.773960 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.5859 | 0.988774 | 0.494387 | − | 0.869242i | \(-0.335393\pi\) | ||||
0.494387 | + | 0.869242i | \(0.335393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6434 | 1.36608 | 0.683042 | − | 0.730379i | \(-0.260657\pi\) | ||||
0.683042 | + | 0.730379i | \(0.260657\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.5207 | 0.982591 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.87079 | −0.369937 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8195 | 1.19977 | 0.599886 | − | 0.800085i | \(-0.295212\pi\) | ||||
0.599886 | + | 0.800085i | \(0.295212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.5370 | −0.562580 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.491520 | −0.0203567 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.63204 | 0.150166 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.82205 | 0.0752039 | 0.0376019 | − | 0.999293i | \(-0.488028\pi\) | ||||
0.0376019 | + | 0.999293i | \(0.488028\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.26731 | −0.0522186 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.40218 | −0.222216 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.9369 | −1.27042 | −0.635212 | − | 0.772338i | \(-0.719087\pi\) | ||||
−0.635212 | + | 0.772338i | \(0.719087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.1001 | 0.699861 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.2912 | −1.31938 | −0.659691 | − | 0.751537i | \(-0.729313\pi\) | ||||
−0.659691 | + | 0.751537i | \(0.729313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2829 | 1.03131 | 0.515655 | − | 0.856797i | \(-0.327549\pi\) | ||||
0.515655 | + | 0.856797i | \(0.327549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0407 | −0.531060 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9470 | 0.445059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.28852 | 0.377010 | 0.188505 | − | 0.982072i | \(-0.439636\pi\) | ||||
0.188505 | + | 0.982072i | \(0.439636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.09941 | −0.0849329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.0609 | 1.61805 | 0.809023 | − | 0.587777i | \(-0.199997\pi\) | ||||
0.809023 | + | 0.587777i | \(0.199997\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.24902 | 0.211661 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.9860 | 1.12667 | 0.563336 | − | 0.826228i | \(-0.309518\pi\) | ||||
0.563336 | + | 0.826228i | \(0.309518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 45.8048 | 1.84105 | 0.920525 | − | 0.390684i | \(-0.127761\pi\) | ||||
0.920525 | + | 0.390684i | \(0.127761\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.2940 | 1.93797 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0709248 | 0.00283246 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.53901 | 0.300600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5847 | 0.899082 | 0.449541 | − | 0.893260i | \(-0.351588\pi\) | ||||
0.449541 | + | 0.893260i | \(0.351588\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.85749 | 0.312307 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.41032 | −0.333753 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.4885 | 0.573157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.5125 | −1.32366 | −0.661832 | − | 0.749652i | \(-0.730221\pi\) | ||||
−0.661832 | + | 0.749652i | \(0.730221\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −46.4980 | −1.83370 | −0.916851 | − | 0.399231i | \(-0.869277\pi\) | ||||
−0.916851 | + | 0.399231i | \(0.869277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.94575 | −0.194739 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.57565 | 0.0619453 | 0.0309726 | − | 0.999520i | \(-0.490140\pi\) | ||||
0.0309726 | + | 0.999520i | \(0.490140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.16753 | 0.0458297 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1311 | 0.474727 | 0.237364 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237364 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.78217 | −0.0696352 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.60442 | 0.374704 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1682 | 1.36996 | 0.684979 | − | 0.728563i | \(-0.259811\pi\) | ||||
0.684979 | + | 0.728563i | \(0.259811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.62425 | 0.0631759 | 0.0315880 | − | 0.999501i | \(-0.489944\pi\) | ||||
0.0315880 | + | 0.999501i | \(0.489944\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.5778 | −0.682664 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.1384 | −1.86393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0733 | 0.930726 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.04640 | −0.0790003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3194 | −0.937443 | −0.468721 | − | 0.883346i | \(-0.655285\pi\) | ||||
−0.468721 | + | 0.883346i | \(0.655285\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.44417 | −0.209546 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.1553 | −0.467165 | −0.233582 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233582 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.3341 | −1.08576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.5158 | −1.24418 | −0.622091 | − | 0.782945i | \(-0.713717\pi\) | ||||
−0.622091 | + | 0.782945i | \(0.713717\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3137 | 0.432275 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.07282 | −0.117236 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.85169 | −0.184834 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.3311 | −0.773432 | −0.386716 | − | 0.922199i | \(-0.626391\pi\) | ||||
−0.386716 | + | 0.922199i | \(0.626391\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.4390 | 0.585636 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.9622 | 1.09702 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.9536 | −0.679068 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.35321 | 0.277727 | 0.138863 | − | 0.990312i | \(-0.455655\pi\) | ||||
0.138863 | + | 0.990312i | \(0.455655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.300262 | −0.0113246 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.09375 | 0.0411931 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.6638 | −0.438041 | −0.219021 | − | 0.975720i | \(-0.570286\pi\) | ||||
−0.219021 | + | 0.975720i | \(0.570286\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.180454 | −0.00676757 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.2077 | 1.61814 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.523229 | −0.0195676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.5094 | 0.467173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.68571 | 0.212041 | 0.106021 | − | 0.994364i | \(-0.466189\pi\) | ||||
0.106021 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.2962 | −0.866394 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.42662 | 0.201540 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.6873 | −0.693074 | −0.346537 | − | 0.938036i | \(-0.612643\pi\) | ||||
−0.346537 | + | 0.938036i | \(0.612643\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.9763 | 0.813936 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.2889 | −1.00932 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.83694 | −0.0678488 | −0.0339244 | − | 0.999424i | \(-0.510801\pi\) | ||||
−0.0339244 | + | 0.999424i | \(0.510801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.87864 | 0.0692005 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5634 | −0.903579 | −0.451789 | − | 0.892125i | \(-0.649214\pi\) | ||||
−0.451789 | + | 0.892125i | \(0.649214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.700083 | 0.0257182 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1926 | −0.997601 | −0.498800 | − | 0.866717i | \(-0.666226\pi\) | ||||
−0.498800 | + | 0.866717i | \(0.666226\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2811 | −0.852954 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.9373 | 0.509939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.328457 | 0.0119856 | 0.00599278 | − | 0.999982i | \(-0.498092\pi\) | ||||
0.00599278 | + | 0.999982i | \(0.498092\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.6584 | 1.08081 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.3398 | −0.813027 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.6331 | −1.76760 | −0.883801 | − | 0.467864i | \(-0.845024\pi\) | ||||
−0.883801 | + | 0.467864i | \(0.845024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.41811 | −0.0877718 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.02253 | 0.290817 | 0.145408 | − | 0.989372i | \(-0.453550\pi\) | ||||
0.145408 | + | 0.989372i | \(0.453550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4406 | −0.377482 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5245 | 0.416125 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.6370 | −1.28510 | −0.642552 | − | 0.766242i | \(-0.722124\pi\) | ||||
−0.642552 | + | 0.766242i | \(0.722124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.03053 | −0.0731276 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.5955 | −1.78383 | −0.891914 | − | 0.452206i | \(-0.850637\pi\) | ||||
−0.891914 | + | 0.452206i | \(0.850637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.87079 | −0.174964 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.15350 | −0.0413285 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.08720 | −0.0746859 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.5434 | −1.05580 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.52603 | −0.125849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.4434 | −0.764376 | −0.382188 | − | 0.924085i | \(-0.624829\pi\) | ||||
−0.382188 | + | 0.924085i | \(0.624829\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.1865 | −0.932262 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.1996 | −0.717307 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.52764 | 0.0896461 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.1429 | −1.24482 | −0.622412 | − | 0.782690i | \(-0.713847\pi\) | ||||
−0.622412 | + | 0.782690i | \(0.713847\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.03494 | 0.213501 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.4385 | 0.898825 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.38360 | −0.0488263 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.7998 | 1.33062 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.32597 | −0.0817768 | −0.0408884 | − | 0.999164i | \(-0.513019\pi\) | ||||
−0.0408884 | + | 0.999164i | \(0.513019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8045 | 0.414512 | 0.207256 | − | 0.978287i | \(-0.433547\pi\) | ||||
0.207256 | + | 0.978287i | \(0.433547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.5190 | 1.07035 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.2522 | 0.569289 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.08686 | 0.0380243 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.7790 | −1.80710 | −0.903550 | − | 0.428483i | \(-0.859048\pi\) | ||||
−0.903550 | + | 0.428483i | \(0.859048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.6259 | −1.41613 | −0.708064 | − | 0.706148i | \(-0.750431\pi\) | ||||
−0.708064 | + | 0.706148i | \(0.750431\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.272593 | 0.00949045 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6201 | 0.438846 | 0.219423 | − | 0.975630i | \(-0.429583\pi\) | ||||
0.219423 | + | 0.975630i | \(0.429583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.4905 | 1.75361 | 0.876803 | − | 0.480849i | \(-0.159672\pi\) | ||||
0.876803 | + | 0.480849i | \(0.159672\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.49261 | −0.329295 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.99714 | −0.138327 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.5174 | 0.916574 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.41032 | 0.152261 | 0.0761305 | − | 0.997098i | \(-0.475743\pi\) | ||||
0.0761305 | + | 0.997098i | \(0.475743\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.448205 | 0.0154553 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.70831 | −0.127721 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.83532 | 0.269543 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.75378 | −0.128829 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2371 | 0.350924 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.6785 | −0.708018 | −0.354009 | − | 0.935242i | \(-0.615182\pi\) | ||||
−0.354009 | + | 0.935242i | \(0.615182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.415828 | 0.0142210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.93055 | 0.202584 | 0.101292 | − | 0.994857i | \(-0.467702\pi\) | ||||
0.101292 | + | 0.994857i | \(0.467702\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3832 | −1.07078 | −0.535390 | − | 0.844605i | \(-0.679835\pi\) | ||||
−0.535390 | + | 0.844605i | \(0.679835\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.1710 | 0.890871 | 0.445435 | − | 0.895314i | \(-0.353049\pi\) | ||||
0.445435 | + | 0.895314i | \(0.353049\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.6214 | 0.599145 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.4013 | 1.03248 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0259961 | 0.000881857 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.5436 | 0.628327 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.86527 | 0.232354 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.2304 | −1.76369 | −0.881847 | − | 0.471536i | \(-0.843700\pi\) | ||||
−0.881847 | + | 0.471536i | \(0.843700\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7509 | 0.699910 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.5930 | −1.13178 | −0.565888 | − | 0.824482i | \(-0.691467\pi\) | ||||
−0.565888 | + | 0.824482i | \(0.691467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.5923 | 1.02951 | 0.514757 | − | 0.857336i | \(-0.327882\pi\) | ||||
0.514757 | + | 0.857336i | \(0.327882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.00404 | −0.201824 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.0305 | −1.64628 | −0.823141 | − | 0.567837i | \(-0.807780\pi\) | ||||
−0.823141 | + | 0.567837i | \(0.807780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.380163 | −0.0127359 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.240358 | −0.00804328 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.2811 | −0.845054 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.8686 | −0.796951 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −26.4319 | −0.881553 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9466 | 0.464629 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.4950 | 0.614796 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.9013 | −1.22529 | −0.612644 | − | 0.790359i | \(-0.709894\pi\) | ||||
−0.612644 | + | 0.790359i | \(0.709894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.8060 | 0.391582 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6118 | 1.14674 | 0.573371 | − | 0.819296i | \(-0.305636\pi\) | ||||
0.573371 | + | 0.819296i | \(0.305636\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00779 | −0.0664483 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.5236 | 0.347899 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.8170 | −1.01656 | −0.508279 | − | 0.861192i | \(-0.669718\pi\) | ||||
−0.508279 | + | 0.861192i | \(0.669718\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.49894 | −0.0823429 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.6023 | −0.678134 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.15403 | −0.0379442 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9099 | −0.555395 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.3387 | 0.568865 | 0.284433 | − | 0.958696i | \(-0.408195\pi\) | ||||
0.284433 | + | 0.958696i | \(0.408195\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.6444 | −0.806823 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.50407 | 0.0491883 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.3736 | −1.44962 | −0.724811 | − | 0.688948i | \(-0.758073\pi\) | ||||
−0.724811 | + | 0.688948i | \(0.758073\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.3206 | 0.826307 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.65934 | −0.0540929 | −0.0270465 | − | 0.999634i | \(-0.508610\pi\) | ||||
−0.0270465 | + | 0.999634i | \(0.508610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.3275 | 1.28068 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.4486 | −1.21692 | −0.608458 | − | 0.793586i | \(-0.708211\pi\) | ||||
−0.608458 | + | 0.793586i | \(0.708211\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6573 | −0.443333 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.3409 | 0.594746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.5875 | 1.21758 | 0.608789 | − | 0.793332i | \(-0.291656\pi\) | ||||
0.608789 | + | 0.793332i | \(0.291656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.8658 | −0.642842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.47926 | 0.0478176 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.27545 | −0.234692 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.5215 | 0.693519 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4335 | 0.368058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.5757 | −0.790302 | −0.395151 | − | 0.918616i | \(-0.629308\pi\) | ||||
−0.395151 | + | 0.918616i | \(0.629308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.01245 | −0.0646494 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.6354 | −1.56078 | −0.780392 | − | 0.625290i | \(-0.784981\pi\) | ||||
−0.780392 | + | 0.625290i | \(0.784981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.69070 | 0.0861714 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.33743 | 0.0747811 | 0.0373906 | − | 0.999301i | \(-0.488095\pi\) | ||||
0.0373906 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.66465 | −0.117123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5937 | −0.434014 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.7331 | −0.916442 | −0.458221 | − | 0.888838i | \(-0.651513\pi\) | ||||
−0.458221 | + | 0.888838i | \(0.651513\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.56273 | 0.145381 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.0553 | −1.17829 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.84787 | −0.249296 | −0.124648 | − | 0.992201i | \(-0.539780\pi\) | ||||
−0.124648 | + | 0.992201i | \(0.539780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0918 | −0.320253 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.4429 | −0.457871 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.4523 | −1.09112 | −0.545558 | − | 0.838073i | \(-0.683682\pi\) | ||||
−0.545558 | + | 0.838073i | \(0.683682\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.28272 | 0.198776 |
(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 | 1960.2.a.x.1.3 | ✓ | 4 | |
4.3 | odd | 2 | 3920.2.a.ce.1.2 | 4 | |||
5.4 | even | 2 | 9800.2.a.cs.1.2 | 4 | |||
7.2 | even | 3 | 1960.2.q.y.361.2 | 8 | |||
7.3 | odd | 6 | 1960.2.q.x.961.3 | 8 | |||
7.4 | even | 3 | 1960.2.q.y.961.2 | 8 | |||
7.5 | odd | 6 | 1960.2.q.x.361.3 | 8 | |||
7.6 | odd | 2 | 1960.2.a.y.1.2 | yes | 4 | ||
28.27 | even | 2 | 3920.2.a.cd.1.3 | 4 | |||
35.34 | odd | 2 | 9800.2.a.cl.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.x.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1960.2.a.y.1.2 | yes | 4 | 7.6 | odd | 2 | ||
1960.2.q.x.361.3 | 8 | 7.5 | odd | 6 | |||
1960.2.q.x.961.3 | 8 | 7.3 | odd | 6 | |||
1960.2.q.y.361.2 | 8 | 7.2 | even | 3 | |||
1960.2.q.y.961.2 | 8 | 7.4 | even | 3 | |||
3920.2.a.cd.1.3 | 4 | 28.27 | even | 2 | |||
3920.2.a.ce.1.2 | 4 | 4.3 | odd | 2 | |||
9800.2.a.cl.1.3 | 4 | 35.34 | odd | 2 | |||
9800.2.a.cs.1.2 | 4 | 5.4 | even | 2 |