Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2601,2,Mod(1,2601)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2601.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2601 = 3^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2601.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: | \(20.7690895657\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.3418281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} - 4x^{3} + 18x^{2} + 12x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 867) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.73700\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2601.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.43915 | 1.01764 | 0.508818 | − | 0.860874i | \(-0.330083\pi\) | ||||
0.508818 | + | 0.860874i | \(0.330083\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0711653 | 0.0355827 | ||||||||
\(5\) | −2.31394 | −1.03483 | −0.517414 | − | 0.855735i | \(-0.673105\pi\) | ||||
−0.517414 | + | 0.855735i | \(0.673105\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.44173 | 1.67881 | 0.839407 | − | 0.543503i | \(-0.182902\pi\) | ||||
0.839407 | + | 0.543503i | \(0.182902\pi\) | |||||||
\(8\) | −2.77589 | −0.981426 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.33012 | −1.05308 | ||||||||
\(11\) | −4.52453 | −1.36420 | −0.682098 | − | 0.731260i | \(-0.738932\pi\) | ||||
−0.682098 | + | 0.731260i | \(0.738932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.17466 | 0.325792 | 0.162896 | − | 0.986643i | \(-0.447916\pi\) | ||||
0.162896 | + | 0.986643i | \(0.447916\pi\) | |||||||
\(14\) | 6.39233 | 1.70842 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.13727 | −1.03432 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.86615 | 1.11637 | 0.558186 | − | 0.829716i | \(-0.311498\pi\) | ||||
0.558186 | + | 0.829716i | \(0.311498\pi\) | |||||||
\(20\) | −0.164673 | −0.0368219 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.51150 | −1.38826 | ||||||||
\(23\) | −0.625397 | −0.130404 | −0.0652022 | − | 0.997872i | \(-0.520769\pi\) | ||||
−0.0652022 | + | 0.997872i | \(0.520769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.354337 | 0.0708674 | ||||||||
\(26\) | 1.69052 | 0.331538 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.316097 | 0.0597367 | ||||||||
\(29\) | −1.51032 | −0.280459 | −0.140230 | − | 0.990119i | \(-0.544784\pi\) | ||||
−0.140230 | + | 0.990119i | \(0.544784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.73592 | −1.56902 | −0.784509 | − | 0.620117i | \(-0.787085\pi\) | ||||
−0.784509 | + | 0.620117i | \(0.787085\pi\) | |||||||
\(32\) | −0.402383 | −0.0711319 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2779 | −1.73728 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.79254 | −1.44549 | −0.722743 | − | 0.691117i | \(-0.757119\pi\) | ||||
−0.722743 | + | 0.691117i | \(0.757119\pi\) | |||||||
\(38\) | 7.00315 | 1.13606 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.42326 | 1.01561 | ||||||||
\(41\) | −0.464965 | −0.0726153 | −0.0363077 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363077 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51327 | −0.230771 | −0.115385 | − | 0.993321i | \(-0.536810\pi\) | ||||
−0.115385 | + | 0.993321i | \(0.536810\pi\) | |||||||
\(44\) | −0.321990 | −0.0485418 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.900043 | −0.132704 | ||||||||
\(47\) | −6.01904 | −0.877968 | −0.438984 | − | 0.898495i | \(-0.644661\pi\) | ||||
−0.438984 | + | 0.898495i | \(0.644661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.7289 | 1.81842 | ||||||||
\(50\) | 0.509946 | 0.0721172 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0835951 | 0.0115925 | ||||||||
\(53\) | −7.12324 | −0.978452 | −0.489226 | − | 0.872157i | \(-0.662721\pi\) | ||||
−0.489226 | + | 0.872157i | \(0.662721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.4695 | 1.41171 | ||||||||
\(56\) | −12.3297 | −1.64763 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.17358 | −0.285405 | ||||||||
\(59\) | 10.4025 | 1.35429 | 0.677143 | − | 0.735852i | \(-0.263218\pi\) | ||||
0.677143 | + | 0.735852i | \(0.263218\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.55882 | −0.327624 | −0.163812 | − | 0.986492i | \(-0.552379\pi\) | ||||
−0.163812 | + | 0.986492i | \(0.552379\pi\) | |||||||
\(62\) | −12.5723 | −1.59669 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.69544 | 0.961930 | ||||||||
\(65\) | −2.71810 | −0.337138 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.71801 | −0.454227 | −0.227114 | − | 0.973868i | \(-0.572929\pi\) | ||||
−0.227114 | + | 0.973868i | \(0.572929\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −14.7915 | −1.76792 | ||||||||
\(71\) | −15.2429 | −1.80900 | −0.904500 | − | 0.426473i | \(-0.859756\pi\) | ||||
−0.904500 | + | 0.426473i | \(0.859756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.70186 | −0.316229 | −0.158114 | − | 0.987421i | \(-0.550541\pi\) | ||||
−0.158114 | + | 0.987421i | \(0.550541\pi\) | |||||||
\(74\) | −12.6538 | −1.47098 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.346301 | 0.0397235 | ||||||||
\(77\) | −20.0967 | −2.29023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6972 | −1.87858 | −0.939291 | − | 0.343120i | \(-0.888516\pi\) | ||||
−0.939291 | + | 0.343120i | \(0.888516\pi\) | |||||||
\(80\) | 9.57340 | 1.07034 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.669156 | −0.0738959 | ||||||||
\(83\) | 4.45459 | 0.488954 | 0.244477 | − | 0.969655i | \(-0.421384\pi\) | ||||
0.244477 | + | 0.969655i | \(0.421384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.17782 | −0.234841 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.5596 | 1.33886 | ||||||||
\(89\) | −1.54030 | −0.163272 | −0.0816359 | − | 0.996662i | \(-0.526014\pi\) | ||||
−0.0816359 | + | 0.996662i | \(0.526014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.21752 | 0.546944 | ||||||||
\(92\) | −0.0445066 | −0.00464013 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.66233 | −0.893451 | ||||||||
\(95\) | −11.2600 | −1.15525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.83886 | 0.389778 | 0.194889 | − | 0.980825i | \(-0.437565\pi\) | ||||
0.194889 | + | 0.980825i | \(0.437565\pi\) | |||||||
\(98\) | 18.3189 | 1.85049 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0252165 | 0.00252165 | ||||||||
\(101\) | −11.9158 | −1.18567 | −0.592833 | − | 0.805325i | \(-0.701991\pi\) | ||||
−0.592833 | + | 0.805325i | \(0.701991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.41240 | −0.139168 | −0.0695838 | − | 0.997576i | \(-0.522167\pi\) | ||||
−0.0695838 | + | 0.997576i | \(0.522167\pi\) | |||||||
\(104\) | −3.26073 | −0.319741 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.2514 | −0.995708 | ||||||||
\(107\) | 15.6540 | 1.51333 | 0.756665 | − | 0.653803i | \(-0.226828\pi\) | ||||
0.756665 | + | 0.653803i | \(0.226828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1437 | −0.971593 | −0.485796 | − | 0.874072i | \(-0.661470\pi\) | ||||
−0.485796 | + | 0.874072i | \(0.661470\pi\) | |||||||
\(110\) | 15.0672 | 1.43660 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.3766 | −1.73643 | ||||||||
\(113\) | −0.798760 | −0.0751410 | −0.0375705 | − | 0.999294i | \(-0.511962\pi\) | ||||
−0.0375705 | + | 0.999294i | \(0.511962\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.44713 | 0.134946 | ||||||||
\(116\) | −0.107482 | −0.00997949 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.9708 | 1.37817 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.47136 | 0.861033 | ||||||||
\(122\) | −3.68254 | −0.333402 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.621695 | −0.0558299 | ||||||||
\(125\) | 10.7498 | 0.961492 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.36696 | 0.298769 | 0.149385 | − | 0.988779i | \(-0.452271\pi\) | ||||
0.149385 | + | 0.988779i | \(0.452271\pi\) | |||||||
\(128\) | 11.8797 | 1.05003 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.91176 | −0.343084 | ||||||||
\(131\) | −1.43966 | −0.125783 | −0.0628916 | − | 0.998020i | \(-0.520032\pi\) | ||||
−0.0628916 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.6141 | 1.87418 | ||||||||
\(134\) | −5.35079 | −0.462238 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.86924 | −0.672315 | −0.336157 | − | 0.941806i | \(-0.609127\pi\) | ||||
−0.336157 | + | 0.941806i | \(0.609127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.82784 | −0.833586 | −0.416793 | − | 0.909001i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909001i | \(0.636846\pi\) | |||||||
\(140\) | −0.731431 | −0.0618172 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.9369 | −1.84090 | ||||||||
\(143\) | −5.31478 | −0.444444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.49480 | 0.290227 | ||||||||
\(146\) | −3.88839 | −0.321806 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.625724 | −0.0514342 | ||||||||
\(149\) | 6.30050 | 0.516157 | 0.258078 | − | 0.966124i | \(-0.416911\pi\) | ||||
0.258078 | + | 0.966124i | \(0.416911\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8279 | −0.881159 | −0.440580 | − | 0.897714i | \(-0.645227\pi\) | ||||
−0.440580 | + | 0.897714i | \(0.645227\pi\) | |||||||
\(152\) | −13.5079 | −1.09564 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −28.9223 | −2.33062 | ||||||||
\(155\) | 20.2144 | 1.62366 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8250 | 0.863933 | 0.431966 | − | 0.901890i | \(-0.357820\pi\) | ||||
0.431966 | + | 0.901890i | \(0.357820\pi\) | |||||||
\(158\) | −24.0299 | −1.91171 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.931092 | 0.0736093 | ||||||||
\(161\) | −2.77784 | −0.218925 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2781 | 0.883371 | 0.441686 | − | 0.897170i | \(-0.354381\pi\) | ||||
0.441686 | + | 0.897170i | \(0.354381\pi\) | |||||||
\(164\) | −0.0330894 | −0.00258385 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.41084 | 0.497577 | ||||||||
\(167\) | 12.3669 | 0.956980 | 0.478490 | − | 0.878093i | \(-0.341184\pi\) | ||||
0.478490 | + | 0.878093i | \(0.341184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6202 | −0.893860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.107692 | −0.00821145 | ||||||||
\(173\) | 3.19740 | 0.243094 | 0.121547 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121547 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.57387 | 0.118973 | ||||||||
\(176\) | 18.7192 | 1.41101 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.21673 | −0.166151 | ||||||||
\(179\) | 19.0135 | 1.42113 | 0.710567 | − | 0.703629i | \(-0.248438\pi\) | ||||
0.710567 | + | 0.703629i | \(0.248438\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0196 | 0.893409 | 0.446705 | − | 0.894682i | \(-0.352598\pi\) | ||||
0.446705 | + | 0.894682i | \(0.352598\pi\) | |||||||
\(182\) | 7.50881 | 0.556590 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.73603 | 0.127982 | ||||||||
\(185\) | 20.3455 | 1.49583 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.428347 | −0.0312404 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.2049 | −1.17563 | ||||||||
\(191\) | −22.3102 | −1.61431 | −0.807154 | − | 0.590341i | \(-0.798993\pi\) | ||||
−0.807154 | + | 0.590341i | \(0.798993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.49591 | 0.251641 | 0.125821 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125821 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(194\) | 5.52472 | 0.396652 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.905859 | 0.0647042 | ||||||||
\(197\) | −11.9973 | −0.854770 | −0.427385 | − | 0.904070i | \(-0.640565\pi\) | ||||
−0.427385 | + | 0.904070i | \(0.640565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.02251 | −0.285148 | −0.142574 | − | 0.989784i | \(-0.545538\pi\) | ||||
−0.142574 | + | 0.989784i | \(0.545538\pi\) | |||||||
\(200\) | −0.983601 | −0.0695511 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −17.1487 | −1.20658 | ||||||||
\(203\) | −6.70843 | −0.470839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.07590 | 0.0751443 | ||||||||
\(206\) | −2.03266 | −0.141622 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.85988 | −0.336972 | ||||||||
\(209\) | −22.0170 | −1.52295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9602 | 1.09874 | 0.549372 | − | 0.835578i | \(-0.314867\pi\) | ||||
0.549372 | + | 0.835578i | \(0.314867\pi\) | |||||||
\(212\) | −0.506928 | −0.0348159 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.5285 | 1.54002 | ||||||||
\(215\) | 3.50161 | 0.238808 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38.8026 | −2.63409 | ||||||||
\(218\) | −14.5984 | −0.988728 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.745066 | 0.0502323 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.35573 | 0.358646 | 0.179323 | − | 0.983790i | \(-0.442609\pi\) | ||||
0.179323 | + | 0.983790i | \(0.442609\pi\) | |||||||
\(224\) | −1.78728 | −0.119417 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.14954 | −0.0764662 | ||||||||
\(227\) | 1.71274 | 0.113679 | 0.0568393 | − | 0.998383i | \(-0.481898\pi\) | ||||
0.0568393 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.380619 | −0.0251520 | −0.0125760 | − | 0.999921i | \(-0.504003\pi\) | ||||
−0.0125760 | + | 0.999921i | \(0.504003\pi\) | |||||||
\(230\) | 2.08265 | 0.137326 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.19248 | 0.275250 | ||||||||
\(233\) | −8.96281 | −0.587173 | −0.293587 | − | 0.955933i | \(-0.594849\pi\) | ||||
−0.293587 | + | 0.955933i | \(0.594849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9277 | 0.908545 | ||||||||
\(236\) | 0.740295 | 0.0481891 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.70928 | 0.433987 | 0.216994 | − | 0.976173i | \(-0.430375\pi\) | ||||
0.216994 | + | 0.976173i | \(0.430375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.83991 | 0.569428 | 0.284714 | − | 0.958612i | \(-0.408101\pi\) | ||||
0.284714 | + | 0.958612i | \(0.408101\pi\) | |||||||
\(242\) | 13.6307 | 0.876218 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.182099 | −0.0116577 | ||||||||
\(245\) | −29.4540 | −1.88175 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.71607 | 0.363705 | ||||||||
\(248\) | 24.2500 | 1.53987 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.4706 | 0.978448 | ||||||||
\(251\) | 24.4193 | 1.54133 | 0.770667 | − | 0.637238i | \(-0.219923\pi\) | ||||
0.770667 | + | 0.637238i | \(0.219923\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82963 | 0.177897 | ||||||||
\(254\) | 4.84557 | 0.304038 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.70583 | 0.106614 | ||||||||
\(257\) | −25.9327 | −1.61764 | −0.808819 | − | 0.588057i | \(-0.799893\pi\) | ||||
−0.808819 | + | 0.588057i | \(0.799893\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.0541 | −2.42670 | ||||||||
\(260\) | −0.193434 | −0.0119963 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.07189 | −0.128002 | ||||||||
\(263\) | −1.74151 | −0.107386 | −0.0536932 | − | 0.998557i | \(-0.517099\pi\) | ||||
−0.0536932 | + | 0.998557i | \(0.517099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4828 | 1.01253 | ||||||||
\(266\) | 31.1061 | 1.90723 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.264594 | −0.0161626 | ||||||||
\(269\) | 31.4782 | 1.91926 | 0.959630 | − | 0.281264i | \(-0.0907536\pi\) | ||||
0.959630 | + | 0.281264i | \(0.0907536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8066 | −1.20316 | −0.601582 | − | 0.798811i | \(-0.705463\pi\) | ||||
−0.601582 | + | 0.798811i | \(0.705463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.3251 | −0.684172 | ||||||||
\(275\) | −1.60321 | −0.0966771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.33073 | 0.140040 | 0.0700201 | − | 0.997546i | \(-0.477694\pi\) | ||||
0.0700201 | + | 0.997546i | \(0.477694\pi\) | |||||||
\(278\) | −14.1438 | −0.848287 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 28.5303 | 1.70501 | ||||||||
\(281\) | −0.306147 | −0.0182632 | −0.00913161 | − | 0.999958i | \(-0.502907\pi\) | ||||
−0.00913161 | + | 0.999958i | \(0.502907\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3142 | −1.08867 | −0.544333 | − | 0.838869i | \(-0.683217\pi\) | ||||
−0.544333 | + | 0.838869i | \(0.683217\pi\) | |||||||
\(284\) | −1.08477 | −0.0643691 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.64879 | −0.452282 | ||||||||
\(287\) | −2.06525 | −0.121908 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 5.02955 | 0.295345 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.192279 | −0.0112523 | ||||||||
\(293\) | −15.2652 | −0.891801 | −0.445900 | − | 0.895083i | \(-0.647116\pi\) | ||||
−0.445900 | + | 0.895083i | \(0.647116\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.0707 | −1.40145 | ||||||||
\(296\) | 24.4071 | 1.41864 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.06739 | 0.525260 | ||||||||
\(299\) | −0.734629 | −0.0424847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.72151 | −0.387422 | ||||||||
\(302\) | −15.5830 | −0.896699 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −20.1326 | −1.15468 | ||||||||
\(305\) | 5.92097 | 0.339034 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.9884 | 1.71153 | 0.855765 | − | 0.517365i | \(-0.173087\pi\) | ||||
0.855765 | + | 0.517365i | \(0.173087\pi\) | |||||||
\(308\) | −1.43019 | −0.0814926 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.0917 | 1.65230 | ||||||||
\(311\) | 23.3246 | 1.32261 | 0.661307 | − | 0.750115i | \(-0.270002\pi\) | ||||
0.661307 | + | 0.750115i | \(0.270002\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.9568 | −1.35412 | −0.677059 | − | 0.735929i | \(-0.736746\pi\) | ||||
−0.677059 | + | 0.735929i | \(0.736746\pi\) | |||||||
\(314\) | 15.5789 | 0.879169 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.18826 | −0.0668450 | ||||||||
\(317\) | −18.7844 | −1.05504 | −0.527519 | − | 0.849543i | \(-0.676878\pi\) | ||||
−0.527519 | + | 0.849543i | \(0.676878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.83348 | 0.382602 | ||||||||
\(320\) | −17.8068 | −0.995432 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.99775 | −0.222786 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.416226 | 0.0230880 | ||||||||
\(326\) | 16.2310 | 0.898950 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.29069 | 0.0712665 | ||||||||
\(329\) | −26.7349 | −1.47395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.6869 | 1.30195 | 0.650975 | − | 0.759099i | \(-0.274360\pi\) | ||||
0.650975 | + | 0.759099i | \(0.274360\pi\) | |||||||
\(332\) | 0.317012 | 0.0173983 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.7979 | 0.973857 | ||||||||
\(335\) | 8.60327 | 0.470047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.07072 | 0.330693 | 0.165347 | − | 0.986236i | \(-0.447126\pi\) | ||||
0.165347 | + | 0.986236i | \(0.447126\pi\) | |||||||
\(338\) | −16.7232 | −0.909624 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.5259 | 2.14045 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.4464 | 1.37398 | ||||||||
\(344\) | 4.20066 | 0.226484 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.60155 | 0.247381 | ||||||||
\(347\) | −7.13506 | −0.383030 | −0.191515 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191515 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7825 | 0.844819 | 0.422410 | − | 0.906405i | \(-0.361184\pi\) | ||||
0.422410 | + | 0.906405i | \(0.361184\pi\) | |||||||
\(350\) | 2.26504 | 0.121071 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.82059 | 0.0970380 | ||||||||
\(353\) | −35.2308 | −1.87515 | −0.937573 | − | 0.347788i | \(-0.886933\pi\) | ||||
−0.937573 | + | 0.347788i | \(0.886933\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.2712 | 1.87200 | ||||||||
\(356\) | −0.109616 | −0.00580965 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 27.3633 | 1.44620 | ||||||||
\(359\) | 25.7316 | 1.35806 | 0.679030 | − | 0.734110i | \(-0.262400\pi\) | ||||
0.679030 | + | 0.734110i | \(0.262400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.67944 | 0.246287 | ||||||||
\(362\) | 17.2980 | 0.909165 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.371306 | 0.0194617 | ||||||||
\(365\) | 6.25195 | 0.327242 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.26095 | 0.431218 | 0.215609 | − | 0.976480i | \(-0.430826\pi\) | ||||
0.215609 | + | 0.976480i | \(0.430826\pi\) | |||||||
\(368\) | 2.58743 | 0.134879 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 29.2802 | 1.52221 | ||||||||
\(371\) | −31.6395 | −1.64264 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.4360 | 1.21347 | 0.606734 | − | 0.794905i | \(-0.292479\pi\) | ||||
0.606734 | + | 0.794905i | \(0.292479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.7082 | 0.861660 | ||||||||
\(377\) | −1.77411 | −0.0913714 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.0621 | 0.773687 | 0.386843 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386843 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(380\) | −0.801322 | −0.0411070 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −32.1078 | −1.64278 | ||||||||
\(383\) | 15.9980 | 0.817459 | 0.408729 | − | 0.912656i | \(-0.365972\pi\) | ||||
0.408729 | + | 0.912656i | \(0.365972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 46.5027 | 2.37000 | ||||||||
\(386\) | 5.03116 | 0.256079 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.273194 | 0.0138693 | ||||||||
\(389\) | −2.98991 | −0.151595 | −0.0757973 | − | 0.997123i | \(-0.524150\pi\) | ||||
−0.0757973 | + | 0.997123i | \(0.524150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −35.3341 | −1.78464 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.2659 | −0.869844 | ||||||||
\(395\) | 38.6364 | 1.94401 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.6527 | 0.635019 | 0.317509 | − | 0.948255i | \(-0.397153\pi\) | ||||
0.317509 | + | 0.948255i | \(0.397153\pi\) | |||||||
\(398\) | −5.78902 | −0.290177 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.46599 | −0.0732994 | ||||||||
\(401\) | 14.6689 | 0.732528 | 0.366264 | − | 0.930511i | \(-0.380637\pi\) | ||||
0.366264 | + | 0.930511i | \(0.380637\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.2617 | −0.511174 | ||||||||
\(404\) | −0.847992 | −0.0421892 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.65446 | −0.479143 | ||||||||
\(407\) | 39.7821 | 1.97193 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3219 | −0.807067 | −0.403534 | − | 0.914965i | \(-0.632218\pi\) | ||||
−0.403534 | + | 0.914965i | \(0.632218\pi\) | |||||||
\(410\) | 1.54839 | 0.0764695 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.100514 | −0.00495196 | ||||||||
\(413\) | 46.2049 | 2.27359 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.3077 | −0.505983 | ||||||||
\(416\) | −0.472663 | −0.0231742 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −31.6859 | −1.54981 | ||||||||
\(419\) | −15.7098 | −0.767473 | −0.383737 | − | 0.923443i | \(-0.625363\pi\) | ||||
−0.383737 | + | 0.923443i | \(0.625363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.1035 | 1.07726 | 0.538630 | − | 0.842542i | \(-0.318942\pi\) | ||||
0.538630 | + | 0.842542i | \(0.318942\pi\) | |||||||
\(422\) | 22.9692 | 1.11812 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.7733 | 0.960278 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3656 | −0.550019 | ||||||||
\(428\) | 1.11402 | 0.0538483 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.03936 | 0.243020 | ||||||||
\(431\) | 4.15528 | 0.200153 | 0.100076 | − | 0.994980i | \(-0.468091\pi\) | ||||
0.100076 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.0766 | −0.628420 | −0.314210 | − | 0.949354i | \(-0.601740\pi\) | ||||
−0.314210 | + | 0.949354i | \(0.601740\pi\) | |||||||
\(434\) | −55.8429 | −2.68055 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.721882 | −0.0345719 | ||||||||
\(437\) | −3.04328 | −0.145580 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.5938 | −0.553342 | −0.276671 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276671 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(440\) | −29.0622 | −1.38549 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6619 | −0.839144 | −0.419572 | − | 0.907722i | \(-0.637820\pi\) | ||||
−0.419572 | + | 0.907722i | \(0.637820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.56418 | 0.168958 | ||||||||
\(446\) | 7.70773 | 0.364971 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 34.1810 | 1.61490 | ||||||||
\(449\) | 35.1414 | 1.65843 | 0.829213 | − | 0.558932i | \(-0.188789\pi\) | ||||
0.829213 | + | 0.558932i | \(0.188789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.10375 | 0.0990616 | ||||||||
\(452\) | −0.0568440 | −0.00267372 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.46490 | 0.115683 | ||||||||
\(455\) | −12.0730 | −0.565993 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6306 | 1.15217 | 0.576086 | − | 0.817389i | \(-0.304580\pi\) | ||||
0.576086 | + | 0.817389i | \(0.304580\pi\) | |||||||
\(458\) | −0.547769 | −0.0255956 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.102986 | 0.00480174 | ||||||||
\(461\) | 1.00413 | 0.0467668 | 0.0233834 | − | 0.999727i | \(-0.492556\pi\) | ||||
0.0233834 | + | 0.999727i | \(0.492556\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4600 | −0.950856 | −0.475428 | − | 0.879755i | \(-0.657707\pi\) | ||||
−0.475428 | + | 0.879755i | \(0.657707\pi\) | |||||||
\(464\) | 6.24859 | 0.290084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8989 | −0.597528 | ||||||||
\(467\) | −35.1659 | −1.62728 | −0.813642 | − | 0.581366i | \(-0.802519\pi\) | ||||
−0.813642 | + | 0.581366i | \(0.802519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.5144 | −0.762564 | ||||||||
\(470\) | 20.0442 | 0.924568 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28.8761 | −1.32913 | ||||||||
\(473\) | 6.84682 | 0.314817 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.72426 | 0.0791144 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.65570 | 0.441641 | ||||||||
\(479\) | −3.85721 | −0.176240 | −0.0881201 | − | 0.996110i | \(-0.528086\pi\) | ||||
−0.0881201 | + | 0.996110i | \(0.528086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3282 | −0.470927 | ||||||||
\(482\) | 12.7220 | 0.579471 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.674032 | 0.0306378 | ||||||||
\(485\) | −8.88292 | −0.403353 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.3689 | −0.923003 | −0.461502 | − | 0.887139i | \(-0.652689\pi\) | ||||
−0.461502 | + | 0.887139i | \(0.652689\pi\) | |||||||
\(488\) | 7.10301 | 0.321538 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −42.3889 | −1.91494 | ||||||||
\(491\) | 6.38676 | 0.288231 | 0.144115 | − | 0.989561i | \(-0.453966\pi\) | ||||
0.144115 | + | 0.989561i | \(0.453966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8.22631 | 0.370119 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.1428 | 1.62286 | ||||||||
\(497\) | −67.7048 | −3.03698 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.64385 | −0.0735887 | −0.0367944 | − | 0.999323i | \(-0.511715\pi\) | ||||
−0.0367944 | + | 0.999323i | \(0.511715\pi\) | |||||||
\(500\) | 0.765013 | 0.0342124 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 35.1432 | 1.56852 | ||||||||
\(503\) | 26.6120 | 1.18657 | 0.593285 | − | 0.804993i | \(-0.297831\pi\) | ||||
0.593285 | + | 0.804993i | \(0.297831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.5725 | 1.22696 | ||||||||
\(506\) | 4.07227 | 0.181035 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.239611 | 0.0106310 | ||||||||
\(509\) | −14.0065 | −0.620827 | −0.310413 | − | 0.950602i | \(-0.600467\pi\) | ||||
−0.310413 | + | 0.950602i | \(0.600467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0009 | −0.530890 | ||||||||
\(512\) | −21.3044 | −0.941532 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −37.3212 | −1.64617 | ||||||||
\(515\) | 3.26821 | 0.144014 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.2333 | 1.19772 | ||||||||
\(518\) | −56.2048 | −2.46950 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.54514 | 0.330876 | ||||||||
\(521\) | 18.9615 | 0.830717 | 0.415358 | − | 0.909658i | \(-0.363656\pi\) | ||||
0.415358 | + | 0.909658i | \(0.363656\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.3838 | 0.891320 | 0.445660 | − | 0.895202i | \(-0.352969\pi\) | ||||
0.445660 | + | 0.895202i | \(0.352969\pi\) | |||||||
\(524\) | −0.102454 | −0.00447571 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.50631 | −0.109280 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6089 | −0.982995 | ||||||||
\(530\) | 23.7213 | 1.03039 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.53818 | 0.0666884 | ||||||||
\(533\) | −0.546175 | −0.0236575 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.2225 | −1.56603 | ||||||||
\(536\) | 10.3208 | 0.445790 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45.3020 | 1.95311 | ||||||||
\(539\) | −57.5924 | −2.48068 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5413 | −0.969127 | −0.484563 | − | 0.874756i | \(-0.661021\pi\) | ||||
−0.484563 | + | 0.874756i | \(0.661021\pi\) | |||||||
\(542\) | −28.5047 | −1.22438 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.4720 | 1.00543 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.30730 | 0.141410 | 0.0707049 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707049 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(548\) | −0.560018 | −0.0239228 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.30726 | −0.0983821 | ||||||||
\(551\) | −7.34945 | −0.313097 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −74.1644 | −3.15379 | ||||||||
\(554\) | 3.35428 | 0.142510 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.699401 | −0.0296612 | ||||||||
\(557\) | −34.4355 | −1.45908 | −0.729540 | − | 0.683938i | \(-0.760266\pi\) | ||||
−0.729540 | + | 0.683938i | \(0.760266\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.77757 | −0.0751833 | ||||||||
\(560\) | 42.5224 | 1.79690 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.440593 | −0.0185853 | ||||||||
\(563\) | 4.70471 | 0.198280 | 0.0991399 | − | 0.995074i | \(-0.468391\pi\) | ||||
0.0991399 | + | 0.995074i | \(0.468391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.84829 | 0.0777580 | ||||||||
\(566\) | −26.3570 | −1.10787 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42.3126 | 1.77540 | ||||||||
\(569\) | −37.2742 | −1.56262 | −0.781308 | − | 0.624145i | \(-0.785447\pi\) | ||||
−0.781308 | + | 0.624145i | \(0.785447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3123 | −0.850043 | −0.425021 | − | 0.905183i | \(-0.639733\pi\) | ||||
−0.425021 | + | 0.905183i | \(0.639733\pi\) | |||||||
\(572\) | −0.378228 | −0.0158145 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.97221 | −0.124058 | ||||||||
\(575\) | −0.221601 | −0.00924142 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.5408 | −1.39632 | −0.698161 | − | 0.715941i | \(-0.745998\pi\) | ||||
−0.698161 | + | 0.715941i | \(0.745998\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.248708 | 0.0103271 | ||||||||
\(581\) | 19.7861 | 0.820864 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.2293 | 1.33480 | ||||||||
\(584\) | 7.50007 | 0.310355 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.9689 | −0.907528 | ||||||||
\(587\) | 21.8364 | 0.901285 | 0.450642 | − | 0.892705i | \(-0.351195\pi\) | ||||
0.450642 | + | 0.892705i | \(0.351195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.5103 | −1.75161 | ||||||||
\(590\) | −34.6415 | −1.42617 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 36.3771 | 1.49509 | ||||||||
\(593\) | 24.6066 | 1.01047 | 0.505236 | − | 0.862981i | \(-0.331406\pi\) | ||||
0.505236 | + | 0.862981i | \(0.331406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.448377 | 0.0183662 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.05724 | −0.0432339 | ||||||||
\(599\) | 40.9057 | 1.67136 | 0.835681 | − | 0.549215i | \(-0.185073\pi\) | ||||
0.835681 | + | 0.549215i | \(0.185073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.8554 | 1.50336 | 0.751682 | − | 0.659525i | \(-0.229243\pi\) | ||||
0.751682 | + | 0.659525i | \(0.229243\pi\) | |||||||
\(602\) | −9.67330 | −0.394254 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.770569 | −0.0313540 | ||||||||
\(605\) | −21.9162 | −0.891020 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.2384 | −1.95794 | −0.978968 | − | 0.204015i | \(-0.934601\pi\) | ||||
−0.978968 | + | 0.204015i | \(0.934601\pi\) | |||||||
\(608\) | −1.95806 | −0.0794097 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.52119 | 0.345013 | ||||||||
\(611\) | −7.07033 | −0.286035 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.2900 | 1.06184 | 0.530922 | − | 0.847421i | \(-0.321846\pi\) | ||||
0.530922 | + | 0.847421i | \(0.321846\pi\) | |||||||
\(614\) | 43.1580 | 1.74171 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 55.7863 | 2.24769 | ||||||||
\(617\) | −3.91276 | −0.157522 | −0.0787610 | − | 0.996894i | \(-0.525096\pi\) | ||||
−0.0787610 | + | 0.996894i | \(0.525096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.50634 | −0.341899 | −0.170949 | − | 0.985280i | \(-0.554683\pi\) | ||||
−0.170949 | + | 0.985280i | \(0.554683\pi\) | |||||||
\(620\) | 1.43857 | 0.0577743 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.5676 | 1.34594 | ||||||||
\(623\) | −6.84161 | −0.274103 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.6461 | −1.06585 | ||||||||
\(626\) | −34.4775 | −1.37800 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.770368 | 0.0307410 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.26384 | −0.289169 | −0.144584 | − | 0.989492i | \(-0.546185\pi\) | ||||
−0.144584 | + | 0.989492i | \(0.546185\pi\) | |||||||
\(632\) | 46.3496 | 1.84369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.0337 | −1.07364 | ||||||||
\(635\) | −7.79096 | −0.309175 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.9522 | 0.592427 | ||||||||
\(638\) | 9.83444 | 0.389349 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.4889 | −1.08660 | ||||||||
\(641\) | 38.6207 | 1.52542 | 0.762712 | − | 0.646738i | \(-0.223867\pi\) | ||||
0.762712 | + | 0.646738i | \(0.223867\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.6378 | −1.24767 | −0.623836 | − | 0.781555i | \(-0.714427\pi\) | ||||
−0.623836 | + | 0.781555i | \(0.714427\pi\) | |||||||
\(644\) | −0.197686 | −0.00778993 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.64576 | −0.104016 | −0.0520078 | − | 0.998647i | \(-0.516562\pi\) | ||||
−0.0520078 | + | 0.998647i | \(0.516562\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.0662 | −1.84751 | ||||||||
\(650\) | 0.599013 | 0.0234952 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.802612 | 0.0314327 | ||||||||
\(653\) | 35.1366 | 1.37500 | 0.687502 | − | 0.726183i | \(-0.258707\pi\) | ||||
0.687502 | + | 0.726183i | \(0.258707\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.33128 | 0.130164 | ||||||||
\(656\) | 1.92368 | 0.0751072 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −38.4757 | −1.49994 | ||||||||
\(659\) | −23.7941 | −0.926888 | −0.463444 | − | 0.886126i | \(-0.653387\pi\) | ||||
−0.463444 | + | 0.886126i | \(0.653387\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.3068 | −1.37328 | −0.686639 | − | 0.726999i | \(-0.740914\pi\) | ||||
−0.686639 | + | 0.726999i | \(0.740914\pi\) | |||||||
\(662\) | 34.0891 | 1.32491 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.3654 | −0.479872 | ||||||||
\(665\) | −50.0139 | −1.93945 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.944550 | 0.0365731 | ||||||||
\(668\) | 0.880095 | 0.0340519 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.3814 | 0.478337 | ||||||||
\(671\) | 11.5775 | 0.446943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.3050 | −0.898341 | −0.449171 | − | 0.893446i | \(-0.648280\pi\) | ||||
−0.449171 | + | 0.893446i | \(0.648280\pi\) | |||||||
\(674\) | 8.73670 | 0.336525 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.826954 | −0.0318059 | ||||||||
\(677\) | −10.3028 | −0.395967 | −0.197984 | − | 0.980205i | \(-0.563439\pi\) | ||||
−0.197984 | + | 0.980205i | \(0.563439\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.0512 | 0.654365 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 56.8839 | 2.17820 | ||||||||
\(683\) | −27.5907 | −1.05573 | −0.527865 | − | 0.849328i | \(-0.677007\pi\) | ||||
−0.527865 | + | 0.849328i | \(0.677007\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.2090 | 0.695730 | ||||||||
\(686\) | 36.6213 | 1.39821 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.26078 | 0.238690 | ||||||||
\(689\) | −8.36738 | −0.318772 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5242 | 0.970985 | 0.485493 | − | 0.874241i | \(-0.338640\pi\) | ||||
0.485493 | + | 0.874241i | \(0.338640\pi\) | |||||||
\(692\) | 0.227544 | 0.00864992 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.2685 | −0.389785 | ||||||||
\(695\) | 22.7411 | 0.862618 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 22.7135 | 0.859718 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.112005 | 0.00423339 | ||||||||
\(701\) | 14.8327 | 0.560225 | 0.280113 | − | 0.959967i | \(-0.409628\pi\) | ||||
0.280113 | + | 0.959967i | \(0.409628\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.7859 | −1.61370 | ||||||||
\(704\) | −34.8182 | −1.31226 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −50.7026 | −1.90822 | ||||||||
\(707\) | −52.9267 | −1.99051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.69498 | −0.176324 | −0.0881618 | − | 0.996106i | \(-0.528099\pi\) | ||||
−0.0881618 | + | 0.996106i | \(0.528099\pi\) | |||||||
\(710\) | 50.7607 | 1.90502 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.27571 | 0.160239 | ||||||||
\(713\) | 5.46342 | 0.204607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.2981 | 0.459923 | ||||||||
\(716\) | 1.35310 | 0.0505678 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 37.0317 | 1.38201 | ||||||||
\(719\) | 0.412832 | 0.0153960 | 0.00769802 | − | 0.999970i | \(-0.497550\pi\) | ||||
0.00769802 | + | 0.999970i | \(0.497550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.27348 | −0.233637 | ||||||||
\(722\) | 6.73444 | 0.250630 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.855378 | 0.0317899 | ||||||||
\(725\) | −0.535162 | −0.0198754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9236 | −1.22107 | −0.610534 | − | 0.791990i | \(-0.709045\pi\) | ||||
−0.610534 | + | 0.791990i | \(0.709045\pi\) | |||||||
\(728\) | −14.4833 | −0.536785 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.99753 | 0.333013 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.5965 | 1.35172 | 0.675861 | − | 0.737029i | \(-0.263772\pi\) | ||||
0.675861 | + | 0.737029i | \(0.263772\pi\) | |||||||
\(734\) | 11.8888 | 0.438823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.251649 | 0.00927591 | ||||||||
\(737\) | 16.8222 | 0.619655 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.0262 | −1.65632 | −0.828158 | − | 0.560494i | \(-0.810611\pi\) | ||||
−0.828158 | + | 0.560494i | \(0.810611\pi\) | |||||||
\(740\) | 1.44789 | 0.0532255 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −45.5341 | −1.67161 | ||||||||
\(743\) | −19.7422 | −0.724271 | −0.362136 | − | 0.932125i | \(-0.617952\pi\) | ||||
−0.362136 | + | 0.932125i | \(0.617952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.5790 | −0.534133 | ||||||||
\(746\) | 33.7280 | 1.23487 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 69.5308 | 2.54060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2639 | 0.848913 | 0.424457 | − | 0.905448i | \(-0.360465\pi\) | ||||
0.424457 | + | 0.905448i | \(0.360465\pi\) | |||||||
\(752\) | 24.9024 | 0.908097 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.55322 | −0.0929828 | ||||||||
\(755\) | 25.0551 | 0.911847 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.82437 | −0.357073 | −0.178536 | − | 0.983933i | \(-0.557136\pi\) | ||||
−0.178536 | + | 0.983933i | \(0.557136\pi\) | |||||||
\(758\) | 21.6767 | 0.787332 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 31.2565 | 1.13379 | ||||||||
\(761\) | 38.2412 | 1.38624 | 0.693121 | − | 0.720822i | \(-0.256235\pi\) | ||||
0.693121 | + | 0.720822i | \(0.256235\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −45.0557 | −1.63112 | ||||||||
\(764\) | −1.58771 | −0.0574414 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.0236 | 0.831876 | ||||||||
\(767\) | 12.2194 | 0.441215 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.2020 | 1.59396 | 0.796982 | − | 0.604002i | \(-0.206428\pi\) | ||||
0.796982 | + | 0.604002i | \(0.206428\pi\) | |||||||
\(770\) | 66.9245 | 2.41179 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.248788 | 0.00895407 | ||||||||
\(773\) | −5.09149 | −0.183128 | −0.0915641 | − | 0.995799i | \(-0.529187\pi\) | ||||
−0.0915641 | + | 0.995799i | \(0.529187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.09546 | −0.111192 | ||||||||
\(776\) | −10.6563 | −0.382538 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.30295 | −0.154268 | ||||||||
\(779\) | −2.26259 | −0.0810657 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 68.9670 | 2.46783 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −52.6630 | −1.88082 | ||||||||
\(785\) | −25.0486 | −0.894021 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.27515 | −0.330623 | −0.165312 | − | 0.986241i | \(-0.552863\pi\) | ||||
−0.165312 | + | 0.986241i | \(0.552863\pi\) | |||||||
\(788\) | −0.853789 | −0.0304150 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 55.6038 | 1.97829 | ||||||||
\(791\) | −3.54787 | −0.126148 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.00575 | −0.106737 | ||||||||
\(794\) | 18.2091 | 0.646218 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.286263 | −0.0101463 | ||||||||
\(797\) | −24.7276 | −0.875897 | −0.437949 | − | 0.899000i | \(-0.644295\pi\) | ||||
−0.437949 | + | 0.899000i | \(0.644295\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.142579 | −0.00504094 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.1108 | 0.745447 | ||||||||
\(803\) | 12.2246 | 0.431398 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.42777 | 0.226549 | ||||||||
\(806\) | −14.7682 | −0.520189 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.0770 | 1.16364 | ||||||||
\(809\) | 29.7012 | 1.04424 | 0.522119 | − | 0.852873i | \(-0.325142\pi\) | ||||
0.522119 | + | 0.852873i | \(0.325142\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2770 | 0.992940 | 0.496470 | − | 0.868054i | \(-0.334629\pi\) | ||||
0.496470 | + | 0.868054i | \(0.334629\pi\) | |||||||
\(812\) | −0.477408 | −0.0167537 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 57.2526 | 2.00670 | ||||||||
\(815\) | −26.0970 | −0.914137 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.36378 | −0.257626 | ||||||||
\(818\) | −23.4898 | −0.821301 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0765670 | 0.00267383 | ||||||||
\(821\) | −42.8794 | −1.49650 | −0.748251 | − | 0.663415i | \(-0.769106\pi\) | ||||
−0.748251 | + | 0.663415i | \(0.769106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.1963 | 1.01772 | 0.508859 | − | 0.860850i | \(-0.330068\pi\) | ||||
0.508859 | + | 0.860850i | \(0.330068\pi\) | |||||||
\(824\) | 3.92066 | 0.136583 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 66.4960 | 2.31369 | ||||||||
\(827\) | 51.0303 | 1.77450 | 0.887249 | − | 0.461291i | \(-0.152613\pi\) | ||||
0.887249 | + | 0.461291i | \(0.152613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.2122 | −0.563072 | −0.281536 | − | 0.959551i | \(-0.590844\pi\) | ||||
−0.281536 | + | 0.959551i | \(0.590844\pi\) | |||||||
\(830\) | −14.8343 | −0.514907 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.03952 | 0.313389 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.6163 | −0.990309 | ||||||||
\(836\) | −1.56685 | −0.0541907 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22.6088 | −0.781008 | ||||||||
\(839\) | −35.7772 | −1.23517 | −0.617583 | − | 0.786506i | \(-0.711888\pi\) | ||||
−0.617583 | + | 0.786506i | \(0.711888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.7189 | −0.921343 | ||||||||
\(842\) | 31.8104 | 1.09626 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.13581 | 0.0390962 | ||||||||
\(845\) | 26.8884 | 0.924990 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.0692 | 1.44551 | ||||||||
\(848\) | 29.4707 | 1.01203 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.49883 | 0.188498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.9313 | −1.77809 | −0.889047 | − | 0.457815i | \(-0.848632\pi\) | ||||
−0.889047 | + | 0.457815i | \(0.848632\pi\) | |||||||
\(854\) | −16.3568 | −0.559720 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −43.4538 | −1.48522 | ||||||||
\(857\) | 36.4929 | 1.24657 | 0.623287 | − | 0.781994i | \(-0.285797\pi\) | ||||
0.623287 | + | 0.781994i | \(0.285797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0367 | 0.888361 | 0.444181 | − | 0.895937i | \(-0.353495\pi\) | ||||
0.444181 | + | 0.895937i | \(0.353495\pi\) | |||||||
\(860\) | 0.249193 | 0.00849743 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.98009 | 0.203683 | ||||||||
\(863\) | −37.5428 | −1.27797 | −0.638986 | − | 0.769218i | \(-0.720646\pi\) | ||||
−0.638986 | + | 0.769218i | \(0.720646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.39860 | −0.251560 | ||||||||
\(866\) | −18.8192 | −0.639502 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.76140 | −0.0937280 | ||||||||
\(869\) | 75.5470 | 2.56276 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.36740 | −0.147984 | ||||||||
\(872\) | 28.1579 | 0.953546 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.37975 | −0.148147 | ||||||||
\(875\) | 47.7477 | 1.61417 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.0738 | −1.31943 | −0.659714 | − | 0.751517i | \(-0.729323\pi\) | ||||
−0.659714 | + | 0.751517i | \(0.729323\pi\) | |||||||
\(878\) | −16.6853 | −0.563101 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −43.3151 | −1.46015 | ||||||||
\(881\) | −44.2340 | −1.49028 | −0.745141 | − | 0.666907i | \(-0.767618\pi\) | ||||
−0.745141 | + | 0.666907i | \(0.767618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8625 | −0.735733 | −0.367866 | − | 0.929879i | \(-0.619912\pi\) | ||||
−0.367866 | + | 0.929879i | \(0.619912\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.4182 | −0.853943 | ||||||||
\(887\) | 0.437004 | 0.0146731 | 0.00733657 | − | 0.999973i | \(-0.497665\pi\) | ||||
0.00733657 | + | 0.999973i | \(0.497665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.9551 | 0.501578 | ||||||||
\(890\) | 5.12940 | 0.171938 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.381143 | 0.0127616 | ||||||||
\(893\) | −29.2896 | −0.980139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −43.9961 | −1.47063 | ||||||||
\(896\) | 52.7664 | 1.76280 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 50.5739 | 1.68767 | ||||||||
\(899\) | 13.1940 | 0.440046 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 3.02762 | 0.100809 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.21727 | 0.0737453 | ||||||||
\(905\) | −27.8127 | −0.924524 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.0070 | −0.564710 | −0.282355 | − | 0.959310i | \(-0.591116\pi\) | ||||
−0.282355 | + | 0.959310i | \(0.591116\pi\) | |||||||
\(908\) | 0.121888 | 0.00404499 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.3750 | −0.575975 | ||||||||
\(911\) | 19.1396 | 0.634122 | 0.317061 | − | 0.948405i | \(-0.397304\pi\) | ||||
0.317061 | + | 0.948405i | \(0.397304\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.1549 | −0.667030 | ||||||||
\(914\) | 35.4472 | 1.17249 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0270869 | −0.000894975 0 | ||||||||
\(917\) | −6.39456 | −0.211167 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.0934 | −1.58645 | −0.793227 | − | 0.608926i | \(-0.791601\pi\) | ||||
−0.793227 | + | 0.608926i | \(0.791601\pi\) | |||||||
\(920\) | −4.01709 | −0.132439 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.44509 | 0.0475916 | ||||||||
\(923\) | −17.9052 | −0.589358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.11552 | −0.102438 | ||||||||
\(926\) | −29.4451 | −0.967625 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.607727 | 0.0199496 | ||||||||
\(929\) | 5.22230 | 0.171338 | 0.0856691 | − | 0.996324i | \(-0.472697\pi\) | ||||
0.0856691 | + | 0.996324i | \(0.472697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 61.9410 | 2.03003 | ||||||||
\(932\) | −0.637841 | −0.0208932 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −50.6092 | −1.65598 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.53593 | −0.213520 | −0.106760 | − | 0.994285i | \(-0.534048\pi\) | ||||
−0.106760 | + | 0.994285i | \(0.534048\pi\) | |||||||
\(938\) | −23.7668 | −0.776012 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.991172 | 0.0323285 | ||||||||
\(941\) | −8.45197 | −0.275526 | −0.137763 | − | 0.990465i | \(-0.543991\pi\) | ||||
−0.137763 | + | 0.990465i | \(0.543991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.290788 | 0.00946935 | ||||||||
\(944\) | −43.0378 | −1.40076 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.85362 | 0.320369 | ||||||||
\(947\) | −46.3276 | −1.50544 | −0.752722 | − | 0.658338i | \(-0.771260\pi\) | ||||
−0.752722 | + | 0.658338i | \(0.771260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.17377 | −0.103025 | ||||||||
\(950\) | 2.48147 | 0.0805097 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.8809 | −1.12990 | −0.564951 | − | 0.825124i | \(-0.691105\pi\) | ||||
−0.564951 | + | 0.825124i | \(0.691105\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.6245 | 1.67053 | ||||||||
\(956\) | 0.477468 | 0.0154424 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.55111 | −0.179348 | ||||||||
\(959\) | −34.9530 | −1.12869 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.3164 | 1.46182 | ||||||||
\(962\) | −14.8639 | −0.479233 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.629095 | 0.0202618 | ||||||||
\(965\) | −8.08934 | −0.260405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.1412 | 1.45164 | 0.725821 | − | 0.687884i | \(-0.241460\pi\) | ||||
0.725821 | + | 0.687884i | \(0.241460\pi\) | |||||||
\(968\) | −26.2915 | −0.845039 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.7839 | −0.410466 | ||||||||
\(971\) | −42.2005 | −1.35428 | −0.677139 | − | 0.735855i | \(-0.736780\pi\) | ||||
−0.677139 | + | 0.735855i | \(0.736780\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −43.6526 | −1.39944 | ||||||||
\(974\) | −29.3140 | −0.939281 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.5865 | 0.338867 | ||||||||
\(977\) | 38.0075 | 1.21597 | 0.607983 | − | 0.793950i | \(-0.291979\pi\) | ||||
0.607983 | + | 0.793950i | \(0.291979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.96915 | 0.222735 | ||||||||
\(980\) | −2.09611 | −0.0669577 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.19154 | 0.293314 | ||||||||
\(983\) | −43.3779 | −1.38354 | −0.691770 | − | 0.722118i | \(-0.743169\pi\) | ||||
−0.691770 | + | 0.722118i | \(0.743169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.7610 | 0.884539 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.406786 | 0.0129416 | ||||||||
\(989\) | 0.946392 | 0.0300935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.2588 | −1.27886 | −0.639431 | − | 0.768848i | \(-0.720830\pi\) | ||||
−0.639431 | + | 0.768848i | \(0.720830\pi\) | |||||||
\(992\) | 3.51519 | 0.111607 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −97.4377 | −3.09054 | ||||||||
\(995\) | 9.30787 | 0.295079 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.8282 | 1.00801 | 0.504005 | − | 0.863701i | \(-0.331859\pi\) | ||||
0.504005 | + | 0.863701i | \(0.331859\pi\) | |||||||
\(998\) | −2.36575 | −0.0748865 | ||||||||
\(999\) | 0 | 0 |
(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 | 2601.2.a.bh.1.5 | 6 | ||
3.2 | odd | 2 | 867.2.a.o.1.2 | ✓ | 6 | ||
17.16 | even | 2 | 2601.2.a.bi.1.5 | 6 | |||
51.2 | odd | 8 | 867.2.e.k.616.3 | 24 | |||
51.5 | even | 16 | 867.2.h.m.688.10 | 48 | |||
51.8 | odd | 8 | 867.2.e.k.829.10 | 24 | |||
51.11 | even | 16 | 867.2.h.m.733.4 | 48 | |||
51.14 | even | 16 | 867.2.h.m.757.4 | 48 | |||
51.20 | even | 16 | 867.2.h.m.757.3 | 48 | |||
51.23 | even | 16 | 867.2.h.m.733.3 | 48 | |||
51.26 | odd | 8 | 867.2.e.k.829.9 | 24 | |||
51.29 | even | 16 | 867.2.h.m.688.9 | 48 | |||
51.32 | odd | 8 | 867.2.e.k.616.4 | 24 | |||
51.38 | odd | 4 | 867.2.d.g.577.10 | 12 | |||
51.41 | even | 16 | 867.2.h.m.712.10 | 48 | |||
51.44 | even | 16 | 867.2.h.m.712.9 | 48 | |||
51.47 | odd | 4 | 867.2.d.g.577.9 | 12 | |||
51.50 | odd | 2 | 867.2.a.p.1.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
867.2.a.o.1.2 | ✓ | 6 | 3.2 | odd | 2 | ||
867.2.a.p.1.2 | yes | 6 | 51.50 | odd | 2 | ||
867.2.d.g.577.9 | 12 | 51.47 | odd | 4 | |||
867.2.d.g.577.10 | 12 | 51.38 | odd | 4 | |||
867.2.e.k.616.3 | 24 | 51.2 | odd | 8 | |||
867.2.e.k.616.4 | 24 | 51.32 | odd | 8 | |||
867.2.e.k.829.9 | 24 | 51.26 | odd | 8 | |||
867.2.e.k.829.10 | 24 | 51.8 | odd | 8 | |||
867.2.h.m.688.9 | 48 | 51.29 | even | 16 | |||
867.2.h.m.688.10 | 48 | 51.5 | even | 16 | |||
867.2.h.m.712.9 | 48 | 51.44 | even | 16 | |||
867.2.h.m.712.10 | 48 | 51.41 | even | 16 | |||
867.2.h.m.733.3 | 48 | 51.23 | even | 16 | |||
867.2.h.m.733.4 | 48 | 51.11 | even | 16 | |||
867.2.h.m.757.3 | 48 | 51.20 | even | 16 | |||
867.2.h.m.757.4 | 48 | 51.14 | even | 16 | |||
2601.2.a.bh.1.5 | 6 | 1.1 | even | 1 | trivial | ||
2601.2.a.bi.1.5 | 6 | 17.16 | even | 2 |