Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + 21 x^{11} - 17032 x^{10} + 4985 x^{9} + 29792 x^{8} - 13249 x^{7} - 28600 x^{6} + \cdots + 210 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-1.94177\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.94177 | 1.37304 | 0.686520 | − | 0.727111i | \(-0.259137\pi\) | ||||
0.686520 | + | 0.727111i | \(0.259137\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.77048 | 0.885238 | ||||||||
\(5\) | −3.66642 | −1.63967 | −0.819836 | − | 0.572598i | \(-0.805936\pi\) | ||||
−0.819836 | + | 0.572598i | \(0.805936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.445683 | −0.157573 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.11935 | −2.25134 | ||||||||
\(11\) | −2.76439 | −0.833496 | −0.416748 | − | 0.909022i | \(-0.636830\pi\) | ||||
−0.416748 | + | 0.909022i | \(0.636830\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.90363 | −1.08267 | −0.541336 | − | 0.840806i | \(-0.682081\pi\) | ||||
−0.541336 | + | 0.840806i | \(0.682081\pi\) | |||||||
\(14\) | 1.94177 | 0.518960 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.40637 | −1.10159 | ||||||||
\(17\) | −3.65343 | −0.886087 | −0.443043 | − | 0.896500i | \(-0.646101\pi\) | ||||
−0.443043 | + | 0.896500i | \(0.646101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.93631 | −0.673636 | −0.336818 | − | 0.941570i | \(-0.609351\pi\) | ||||
−0.336818 | + | 0.941570i | \(0.609351\pi\) | |||||||
\(20\) | −6.49131 | −1.45150 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.36782 | −1.14442 | ||||||||
\(23\) | 5.90239 | 1.23073 | 0.615367 | − | 0.788241i | \(-0.289008\pi\) | ||||
0.615367 | + | 0.788241i | \(0.289008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.44263 | 1.68853 | ||||||||
\(26\) | −7.57996 | −1.48655 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.77048 | 0.334589 | ||||||||
\(29\) | −1.00996 | −0.187544 | −0.0937720 | − | 0.995594i | \(-0.529892\pi\) | ||||
−0.0937720 | + | 0.995594i | \(0.529892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.885070 | −0.158963 | −0.0794817 | − | 0.996836i | \(-0.525327\pi\) | ||||
−0.0794817 | + | 0.996836i | \(0.525327\pi\) | |||||||
\(32\) | −7.66479 | −1.35496 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.09412 | −1.21663 | ||||||||
\(35\) | −3.66642 | −0.619738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.97192 | 0.981778 | 0.490889 | − | 0.871222i | \(-0.336672\pi\) | ||||
0.490889 | + | 0.871222i | \(0.336672\pi\) | |||||||
\(38\) | −5.70165 | −0.924929 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.63406 | 0.258368 | ||||||||
\(41\) | −7.04246 | −1.09985 | −0.549924 | − | 0.835215i | \(-0.685343\pi\) | ||||
−0.549924 | + | 0.835215i | \(0.685343\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.95501 | 0.908130 | 0.454065 | − | 0.890969i | \(-0.349973\pi\) | ||||
0.454065 | + | 0.890969i | \(0.349973\pi\) | |||||||
\(44\) | −4.89429 | −0.737843 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.4611 | 1.68985 | ||||||||
\(47\) | 5.51094 | 0.803853 | 0.401927 | − | 0.915672i | \(-0.368341\pi\) | ||||
0.401927 | + | 0.915672i | \(0.368341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 16.3937 | 2.31841 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.91129 | −0.958423 | ||||||||
\(53\) | −4.27470 | −0.587176 | −0.293588 | − | 0.955932i | \(-0.594849\pi\) | ||||
−0.293588 | + | 0.955932i | \(0.594849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1354 | 1.36666 | ||||||||
\(56\) | −0.445683 | −0.0595568 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.96110 | −0.257505 | ||||||||
\(59\) | 7.36890 | 0.959349 | 0.479675 | − | 0.877446i | \(-0.340755\pi\) | ||||
0.479675 | + | 0.877446i | \(0.340755\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9371 | 1.52839 | 0.764197 | − | 0.644983i | \(-0.223136\pi\) | ||||
0.764197 | + | 0.644983i | \(0.223136\pi\) | |||||||
\(62\) | −1.71860 | −0.218263 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.07054 | −0.758817 | ||||||||
\(65\) | 14.3124 | 1.77523 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.14451 | 0.995011 | 0.497505 | − | 0.867461i | \(-0.334249\pi\) | ||||
0.497505 | + | 0.867461i | \(0.334249\pi\) | |||||||
\(68\) | −6.46831 | −0.784398 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.11935 | −0.850925 | ||||||||
\(71\) | −4.06599 | −0.482545 | −0.241272 | − | 0.970457i | \(-0.577565\pi\) | ||||
−0.241272 | + | 0.970457i | \(0.577565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.01678 | 0.119005 | 0.0595027 | − | 0.998228i | \(-0.481049\pi\) | ||||
0.0595027 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(74\) | 11.5961 | 1.34802 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.19867 | −0.596329 | ||||||||
\(77\) | −2.76439 | −0.315032 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03997 | 0.117006 | 0.0585029 | − | 0.998287i | \(-0.481367\pi\) | ||||
0.0585029 | + | 0.998287i | \(0.481367\pi\) | |||||||
\(80\) | 16.1556 | 1.80625 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −13.6748 | −1.51013 | ||||||||
\(83\) | −3.97794 | −0.436636 | −0.218318 | − | 0.975878i | \(-0.570057\pi\) | ||||
−0.218318 | + | 0.975878i | \(0.570057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3950 | 1.45289 | ||||||||
\(86\) | 11.5633 | 1.24690 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.23204 | 0.131336 | ||||||||
\(89\) | −10.8011 | −1.14492 | −0.572458 | − | 0.819934i | \(-0.694010\pi\) | ||||
−0.572458 | + | 0.819934i | \(0.694010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.90363 | −0.409212 | ||||||||
\(92\) | 10.4501 | 1.08949 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.7010 | 1.10372 | ||||||||
\(95\) | 10.7658 | 1.10454 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1382 | 1.33398 | 0.666991 | − | 0.745065i | \(-0.267582\pi\) | ||||
0.666991 | + | 0.745065i | \(0.267582\pi\) | |||||||
\(98\) | 1.94177 | 0.196149 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 14.9475 | 1.49475 | ||||||||
\(101\) | 1.59877 | 0.159083 | 0.0795415 | − | 0.996832i | \(-0.474654\pi\) | ||||
0.0795415 | + | 0.996832i | \(0.474654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33183 | 0.131229 | 0.0656144 | − | 0.997845i | \(-0.479099\pi\) | ||||
0.0656144 | + | 0.997845i | \(0.479099\pi\) | |||||||
\(104\) | 1.73978 | 0.170600 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.30050 | −0.806215 | ||||||||
\(107\) | 4.41836 | 0.427139 | 0.213570 | − | 0.976928i | \(-0.431491\pi\) | ||||
0.213570 | + | 0.976928i | \(0.431491\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.80353 | −0.651660 | −0.325830 | − | 0.945428i | \(-0.605644\pi\) | ||||
−0.325830 | + | 0.945428i | \(0.605644\pi\) | |||||||
\(110\) | 19.6807 | 1.87648 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.40637 | −0.416362 | ||||||||
\(113\) | 11.6660 | 1.09744 | 0.548720 | − | 0.836006i | \(-0.315115\pi\) | ||||
0.548720 | + | 0.836006i | \(0.315115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.6407 | −2.01800 | ||||||||
\(116\) | −1.78810 | −0.166021 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.3087 | 1.31722 | ||||||||
\(119\) | −3.65343 | −0.334909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.35813 | −0.305284 | ||||||||
\(122\) | 23.1792 | 2.09855 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.56700 | −0.140720 | ||||||||
\(125\) | −12.6221 | −1.12896 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 3.54198 | 0.313070 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27.7913 | 2.43746 | ||||||||
\(131\) | −5.62011 | −0.491032 | −0.245516 | − | 0.969393i | \(-0.578957\pi\) | ||||
−0.245516 | + | 0.969393i | \(0.578957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.93631 | −0.254611 | ||||||||
\(134\) | 15.8148 | 1.36619 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.62827 | 0.139623 | ||||||||
\(137\) | 7.90120 | 0.675045 | 0.337523 | − | 0.941317i | \(-0.390411\pi\) | ||||
0.337523 | + | 0.941317i | \(0.390411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.4360 | −1.81818 | −0.909089 | − | 0.416601i | \(-0.863221\pi\) | ||||
−0.909089 | + | 0.416601i | \(0.863221\pi\) | |||||||
\(140\) | −6.49131 | −0.548616 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.89523 | −0.662553 | ||||||||
\(143\) | 10.7912 | 0.902404 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.70292 | 0.307511 | ||||||||
\(146\) | 1.97436 | 0.163399 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5731 | 0.869107 | ||||||||
\(149\) | 1.21636 | 0.0996478 | 0.0498239 | − | 0.998758i | \(-0.484134\pi\) | ||||
0.0498239 | + | 0.998758i | \(0.484134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.654350 | 0.0532502 | 0.0266251 | − | 0.999645i | \(-0.491524\pi\) | ||||
0.0266251 | + | 0.999645i | \(0.491524\pi\) | |||||||
\(152\) | 1.30866 | 0.106147 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.36782 | −0.432551 | ||||||||
\(155\) | 3.24504 | 0.260648 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1435 | 0.969158 | 0.484579 | − | 0.874747i | \(-0.338973\pi\) | ||||
0.484579 | + | 0.874747i | \(0.338973\pi\) | |||||||
\(158\) | 2.01938 | 0.160654 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.1023 | 2.22169 | ||||||||
\(161\) | 5.90239 | 0.465174 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1369 | −0.872307 | −0.436154 | − | 0.899872i | \(-0.643660\pi\) | ||||
−0.436154 | + | 0.899872i | \(0.643660\pi\) | |||||||
\(164\) | −12.4685 | −0.973627 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.72426 | −0.599519 | ||||||||
\(167\) | −14.8250 | −1.14719 | −0.573597 | − | 0.819137i | \(-0.694453\pi\) | ||||
−0.573597 | + | 0.819137i | \(0.694453\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.23835 | 0.172181 | ||||||||
\(170\) | 26.0100 | 1.99488 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.5432 | 0.803911 | ||||||||
\(173\) | −10.9026 | −0.828907 | −0.414453 | − | 0.910071i | \(-0.636027\pi\) | ||||
−0.414453 | + | 0.910071i | \(0.636027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.44263 | 0.638203 | ||||||||
\(176\) | 12.1809 | 0.918172 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.9733 | −1.57202 | ||||||||
\(179\) | −1.82536 | −0.136434 | −0.0682168 | − | 0.997671i | \(-0.521731\pi\) | ||||
−0.0682168 | + | 0.997671i | \(0.521731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5199 | −1.59956 | −0.799781 | − | 0.600292i | \(-0.795051\pi\) | ||||
−0.799781 | + | 0.600292i | \(0.795051\pi\) | |||||||
\(182\) | −7.57996 | −0.561864 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.63059 | −0.193930 | ||||||||
\(185\) | −21.8956 | −1.60979 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0995 | 0.738550 | ||||||||
\(188\) | 9.75699 | 0.711602 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.9046 | 1.51658 | ||||||||
\(191\) | 4.98503 | 0.360704 | 0.180352 | − | 0.983602i | \(-0.442276\pi\) | ||||
0.180352 | + | 0.983602i | \(0.442276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.6773 | 1.05649 | 0.528247 | − | 0.849091i | \(-0.322850\pi\) | ||||
0.528247 | + | 0.849091i | \(0.322850\pi\) | |||||||
\(194\) | 25.5114 | 1.83161 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.77048 | 0.126463 | ||||||||
\(197\) | 17.4312 | 1.24192 | 0.620960 | − | 0.783843i | \(-0.286743\pi\) | ||||
0.620960 | + | 0.783843i | \(0.286743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4374 | 1.80321 | 0.901606 | − | 0.432558i | \(-0.142389\pi\) | ||||
0.901606 | + | 0.432558i | \(0.142389\pi\) | |||||||
\(200\) | −3.76274 | −0.266066 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.10444 | 0.218427 | ||||||||
\(203\) | −1.00996 | −0.0708850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.8206 | 1.80339 | ||||||||
\(206\) | 2.58610 | 0.180182 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.2008 | 1.19266 | ||||||||
\(209\) | 8.11713 | 0.561473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.97851 | 0.342735 | 0.171367 | − | 0.985207i | \(-0.445182\pi\) | ||||
0.171367 | + | 0.985207i | \(0.445182\pi\) | |||||||
\(212\) | −7.56826 | −0.519790 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.57945 | 0.586479 | ||||||||
\(215\) | −21.8335 | −1.48904 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.885070 | −0.0600825 | ||||||||
\(218\) | −13.2109 | −0.894755 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.9445 | 1.20982 | ||||||||
\(221\) | 14.2616 | 0.959342 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.48750 | −0.0996106 | −0.0498053 | − | 0.998759i | \(-0.515860\pi\) | ||||
−0.0498053 | + | 0.998759i | \(0.515860\pi\) | |||||||
\(224\) | −7.66479 | −0.512125 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.6526 | 1.50683 | ||||||||
\(227\) | 19.5282 | 1.29613 | 0.648066 | − | 0.761584i | \(-0.275578\pi\) | ||||
0.648066 | + | 0.761584i | \(0.275578\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.26693 | −0.546294 | −0.273147 | − | 0.961972i | \(-0.588065\pi\) | ||||
−0.273147 | + | 0.961972i | \(0.588065\pi\) | |||||||
\(230\) | −42.0212 | −2.77080 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.450119 | 0.0295518 | ||||||||
\(233\) | 23.3515 | 1.52981 | 0.764905 | − | 0.644143i | \(-0.222786\pi\) | ||||
0.764905 | + | 0.644143i | \(0.222786\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.2054 | −1.31806 | ||||||||
\(236\) | 13.0465 | 0.849252 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.09412 | −0.459844 | ||||||||
\(239\) | −14.2016 | −0.918625 | −0.459313 | − | 0.888275i | \(-0.651904\pi\) | ||||
−0.459313 | + | 0.888275i | \(0.651904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.08805 | 0.263335 | 0.131667 | − | 0.991294i | \(-0.457967\pi\) | ||||
0.131667 | + | 0.991294i | \(0.457967\pi\) | |||||||
\(242\) | −6.52071 | −0.419167 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 21.1344 | 1.35299 | ||||||||
\(245\) | −3.66642 | −0.234239 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4623 | 0.729328 | ||||||||
\(248\) | 0.394461 | 0.0250483 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24.5093 | −1.55011 | ||||||||
\(251\) | 24.8954 | 1.57138 | 0.785690 | − | 0.618620i | \(-0.212308\pi\) | ||||
0.785690 | + | 0.618620i | \(0.212308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.3165 | −1.02581 | ||||||||
\(254\) | 1.94177 | 0.121838 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0188 | 1.18867 | ||||||||
\(257\) | 12.2395 | 0.763481 | 0.381740 | − | 0.924270i | \(-0.375325\pi\) | ||||
0.381740 | + | 0.924270i | \(0.375325\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.97192 | 0.371077 | ||||||||
\(260\) | 25.3397 | 1.57150 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9130 | −0.674206 | ||||||||
\(263\) | 1.56340 | 0.0964035 | 0.0482018 | − | 0.998838i | \(-0.484651\pi\) | ||||
0.0482018 | + | 0.998838i | \(0.484651\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.6729 | 0.962776 | ||||||||
\(266\) | −5.70165 | −0.349590 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.4197 | 0.880821 | ||||||||
\(269\) | −21.2587 | −1.29616 | −0.648082 | − | 0.761571i | \(-0.724428\pi\) | ||||
−0.648082 | + | 0.761571i | \(0.724428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.59026 | 0.278838 | 0.139419 | − | 0.990233i | \(-0.455476\pi\) | ||||
0.139419 | + | 0.990233i | \(0.455476\pi\) | |||||||
\(272\) | 16.0983 | 0.976106 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.3423 | 0.926864 | ||||||||
\(275\) | −23.3388 | −1.40738 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.4342 | 0.807183 | 0.403592 | − | 0.914939i | \(-0.367762\pi\) | ||||
0.403592 | + | 0.914939i | \(0.367762\pi\) | |||||||
\(278\) | −41.6238 | −2.49643 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.63406 | 0.0976537 | ||||||||
\(281\) | 20.7151 | 1.23576 | 0.617879 | − | 0.786273i | \(-0.287992\pi\) | ||||
0.617879 | + | 0.786273i | \(0.287992\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.68438 | 0.397345 | 0.198673 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198673 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(284\) | −7.19874 | −0.427167 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.9540 | 1.23904 | ||||||||
\(287\) | −7.04246 | −0.415703 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.65245 | −0.214850 | ||||||||
\(290\) | 7.19022 | 0.422224 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.80019 | 0.105348 | ||||||||
\(293\) | 1.67899 | 0.0980877 | 0.0490438 | − | 0.998797i | \(-0.484383\pi\) | ||||
0.0490438 | + | 0.998797i | \(0.484383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.0175 | −1.57302 | ||||||||
\(296\) | −2.66158 | −0.154701 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.36189 | 0.136820 | ||||||||
\(299\) | −23.0408 | −1.33248 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.95501 | 0.343241 | ||||||||
\(302\) | 1.27060 | 0.0731147 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.9385 | 0.742072 | ||||||||
\(305\) | −43.7666 | −2.50607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.815036 | 0.0465166 | 0.0232583 | − | 0.999729i | \(-0.492596\pi\) | ||||
0.0232583 | + | 0.999729i | \(0.492596\pi\) | |||||||
\(308\) | −4.89429 | −0.278878 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.30113 | 0.357880 | ||||||||
\(311\) | −6.64455 | −0.376778 | −0.188389 | − | 0.982095i | \(-0.560327\pi\) | ||||
−0.188389 | + | 0.982095i | \(0.560327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.290004 | 0.0163920 | 0.00819599 | − | 0.999966i | \(-0.497391\pi\) | ||||
0.00819599 | + | 0.999966i | \(0.497391\pi\) | |||||||
\(314\) | 23.5799 | 1.33069 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.84124 | 0.103578 | ||||||||
\(317\) | −33.6696 | −1.89107 | −0.945536 | − | 0.325518i | \(-0.894461\pi\) | ||||
−0.945536 | + | 0.325518i | \(0.894461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.79191 | 0.156317 | ||||||||
\(320\) | 22.2571 | 1.24421 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.4611 | 0.638702 | ||||||||
\(323\) | 10.7276 | 0.596900 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.9569 | −1.82812 | ||||||||
\(326\) | −21.6253 | −1.19771 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.13870 | 0.173306 | ||||||||
\(329\) | 5.51094 | 0.303828 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.1886 | 0.999734 | 0.499867 | − | 0.866102i | \(-0.333382\pi\) | ||||
0.499867 | + | 0.866102i | \(0.333382\pi\) | |||||||
\(332\) | −7.04285 | −0.386527 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −28.7868 | −1.57514 | ||||||||
\(335\) | −29.8612 | −1.63149 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.22052 | 0.284380 | 0.142190 | − | 0.989839i | \(-0.454586\pi\) | ||||
0.142190 | + | 0.989839i | \(0.454586\pi\) | |||||||
\(338\) | 4.34636 | 0.236411 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 23.7155 | 1.28616 | ||||||||
\(341\) | 2.44668 | 0.132495 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.65404 | −0.143096 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.1703 | −1.13812 | ||||||||
\(347\) | −25.6219 | −1.37546 | −0.687728 | − | 0.725968i | \(-0.741392\pi\) | ||||
−0.687728 | + | 0.725968i | \(0.741392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.47632 | −0.453727 | −0.226863 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226863 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(350\) | 16.3937 | 0.876278 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.1885 | 1.12935 | ||||||||
\(353\) | 29.0703 | 1.54725 | 0.773627 | − | 0.633641i | \(-0.218440\pi\) | ||||
0.773627 | + | 0.633641i | \(0.218440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.9076 | 0.791215 | ||||||||
\(356\) | −19.1231 | −1.01352 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.54443 | −0.187329 | ||||||||
\(359\) | −16.1630 | −0.853049 | −0.426525 | − | 0.904476i | \(-0.640262\pi\) | ||||
−0.426525 | + | 0.904476i | \(0.640262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3781 | −0.546214 | ||||||||
\(362\) | −41.7868 | −2.19626 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.91129 | −0.362250 | ||||||||
\(365\) | −3.72795 | −0.195130 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.02538 | −0.418921 | −0.209461 | − | 0.977817i | \(-0.567171\pi\) | ||||
−0.209461 | + | 0.977817i | \(0.567171\pi\) | |||||||
\(368\) | −26.0081 | −1.35577 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −42.5162 | −2.21031 | ||||||||
\(371\) | −4.27470 | −0.221932 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.5329 | 1.16671 | 0.583355 | − | 0.812217i | \(-0.301740\pi\) | ||||
0.583355 | + | 0.812217i | \(0.301740\pi\) | |||||||
\(374\) | 19.6110 | 1.01406 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.45613 | −0.126665 | ||||||||
\(377\) | 3.94249 | 0.203049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.2331 | −0.782471 | −0.391235 | − | 0.920291i | \(-0.627952\pi\) | ||||
−0.391235 | + | 0.920291i | \(0.627952\pi\) | |||||||
\(380\) | 19.0605 | 0.977784 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.67979 | 0.495261 | ||||||||
\(383\) | 12.0870 | 0.617618 | 0.308809 | − | 0.951124i | \(-0.400070\pi\) | ||||
0.308809 | + | 0.951124i | \(0.400070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.1354 | 0.516549 | ||||||||
\(386\) | 28.4999 | 1.45061 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 23.2609 | 1.18089 | ||||||||
\(389\) | −32.5350 | −1.64959 | −0.824795 | − | 0.565431i | \(-0.808710\pi\) | ||||
−0.824795 | + | 0.565431i | \(0.808710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.5640 | −1.09054 | ||||||||
\(392\) | −0.445683 | −0.0225104 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 33.8473 | 1.70520 | ||||||||
\(395\) | −3.81297 | −0.191851 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.54787 | −0.429005 | −0.214503 | − | 0.976723i | \(-0.568813\pi\) | ||||
−0.214503 | + | 0.976723i | \(0.568813\pi\) | |||||||
\(398\) | 49.3937 | 2.47588 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −37.2013 | −1.86007 | ||||||||
\(401\) | 28.8363 | 1.44002 | 0.720009 | − | 0.693965i | \(-0.244138\pi\) | ||||
0.720009 | + | 0.693965i | \(0.244138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.45499 | 0.172105 | ||||||||
\(404\) | 2.83058 | 0.140826 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.96110 | −0.0973279 | ||||||||
\(407\) | −16.5087 | −0.818308 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.26809 | 0.0627028 | 0.0313514 | − | 0.999508i | \(-0.490019\pi\) | ||||
0.0313514 | + | 0.999508i | \(0.490019\pi\) | |||||||
\(410\) | 50.1377 | 2.47613 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.35797 | 0.116169 | ||||||||
\(413\) | 7.36890 | 0.362600 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.5848 | 0.715940 | ||||||||
\(416\) | 29.9205 | 1.46697 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.7616 | 0.770925 | ||||||||
\(419\) | 31.3924 | 1.53362 | 0.766808 | − | 0.641876i | \(-0.221844\pi\) | ||||
0.766808 | + | 0.641876i | \(0.221844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31725 | −0.112936 | −0.0564679 | − | 0.998404i | \(-0.517984\pi\) | ||||
−0.0564679 | + | 0.998404i | \(0.517984\pi\) | |||||||
\(422\) | 9.66712 | 0.470588 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.90516 | 0.0925228 | ||||||||
\(425\) | −30.8446 | −1.49618 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9371 | 0.577679 | ||||||||
\(428\) | 7.82261 | 0.378120 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −42.3958 | −2.04451 | ||||||||
\(431\) | 17.0872 | 0.823062 | 0.411531 | − | 0.911396i | \(-0.364994\pi\) | ||||
0.411531 | + | 0.911396i | \(0.364994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.3684 | −1.17107 | −0.585534 | − | 0.810648i | \(-0.699115\pi\) | ||||
−0.585534 | + | 0.810648i | \(0.699115\pi\) | |||||||
\(434\) | −1.71860 | −0.0824957 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.0455 | −0.576874 | ||||||||
\(437\) | −17.3313 | −0.829067 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.89424 | 0.376771 | 0.188386 | − | 0.982095i | \(-0.439675\pi\) | ||||
0.188386 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(440\) | −4.51718 | −0.215348 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.6929 | 1.31721 | ||||||||
\(443\) | −20.7191 | −0.984393 | −0.492197 | − | 0.870484i | \(-0.663806\pi\) | ||||
−0.492197 | + | 0.870484i | \(0.663806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.6015 | 1.87729 | ||||||||
\(446\) | −2.88839 | −0.136769 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.07054 | −0.286806 | ||||||||
\(449\) | 30.8777 | 1.45721 | 0.728604 | − | 0.684936i | \(-0.240170\pi\) | ||||
0.728604 | + | 0.684936i | \(0.240170\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4681 | 0.916718 | ||||||||
\(452\) | 20.6543 | 0.971496 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.9193 | 1.77964 | ||||||||
\(455\) | 14.3124 | 0.670974 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3189 | 0.903702 | 0.451851 | − | 0.892094i | \(-0.350764\pi\) | ||||
0.451851 | + | 0.892094i | \(0.350764\pi\) | |||||||
\(458\) | −16.0525 | −0.750083 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −38.3143 | −1.78641 | ||||||||
\(461\) | −4.01040 | −0.186783 | −0.0933915 | − | 0.995629i | \(-0.529771\pi\) | ||||
−0.0933915 | + | 0.995629i | \(0.529771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.67124 | 0.217091 | 0.108546 | − | 0.994091i | \(-0.465381\pi\) | ||||
0.108546 | + | 0.994091i | \(0.465381\pi\) | |||||||
\(464\) | 4.45023 | 0.206597 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.3433 | 2.10049 | ||||||||
\(467\) | −12.3374 | −0.570909 | −0.285454 | − | 0.958392i | \(-0.592144\pi\) | ||||
−0.285454 | + | 0.958392i | \(0.592144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.14451 | 0.376079 | ||||||||
\(470\) | −39.2343 | −1.80974 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.28419 | −0.151167 | ||||||||
\(473\) | −16.4620 | −0.756923 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.7902 | −1.13745 | ||||||||
\(476\) | −6.46831 | −0.296474 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.5763 | −1.26131 | ||||||||
\(479\) | 2.70152 | 0.123436 | 0.0617178 | − | 0.998094i | \(-0.480342\pi\) | ||||
0.0617178 | + | 0.998094i | \(0.480342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.3122 | −1.06294 | ||||||||
\(482\) | 7.93807 | 0.361569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.94548 | −0.270249 | ||||||||
\(485\) | −48.1702 | −2.18730 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.9996 | −1.22347 | −0.611734 | − | 0.791064i | \(-0.709528\pi\) | ||||
−0.611734 | + | 0.791064i | \(0.709528\pi\) | |||||||
\(488\) | −5.32018 | −0.240833 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.11935 | −0.321619 | ||||||||
\(491\) | 25.4643 | 1.14919 | 0.574593 | − | 0.818439i | \(-0.305160\pi\) | ||||
0.574593 | + | 0.818439i | \(0.305160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.68980 | 0.166180 | ||||||||
\(494\) | 22.2571 | 1.00140 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.89994 | 0.175113 | ||||||||
\(497\) | −4.06599 | −0.182385 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.8156 | −1.15566 | −0.577831 | − | 0.816156i | \(-0.696101\pi\) | ||||
−0.577831 | + | 0.816156i | \(0.696101\pi\) | |||||||
\(500\) | −22.3472 | −0.999397 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 48.3411 | 2.15757 | ||||||||
\(503\) | 37.1572 | 1.65676 | 0.828378 | − | 0.560170i | \(-0.189264\pi\) | ||||
0.828378 | + | 0.560170i | \(0.189264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.86174 | −0.260844 | ||||||||
\(506\) | −31.6830 | −1.40848 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.77048 | 0.0785522 | ||||||||
\(509\) | 27.2527 | 1.20796 | 0.603978 | − | 0.797001i | \(-0.293582\pi\) | ||||
0.603978 | + | 0.797001i | \(0.293582\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.01678 | 0.0449798 | ||||||||
\(512\) | 29.8462 | 1.31903 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.7664 | 1.04829 | ||||||||
\(515\) | −4.88304 | −0.215172 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.2344 | −0.670009 | ||||||||
\(518\) | 11.5961 | 0.509504 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.37877 | −0.279727 | ||||||||
\(521\) | 11.6168 | 0.508943 | 0.254471 | − | 0.967080i | \(-0.418099\pi\) | ||||
0.254471 | + | 0.967080i | \(0.418099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.2279 | −1.27805 | −0.639023 | − | 0.769188i | \(-0.720661\pi\) | ||||
−0.639023 | + | 0.769188i | \(0.720661\pi\) | |||||||
\(524\) | −9.95028 | −0.434680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.03577 | 0.132366 | ||||||||
\(527\) | 3.23354 | 0.140855 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8383 | 0.514707 | ||||||||
\(530\) | 30.4331 | 1.32193 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.19867 | −0.225391 | ||||||||
\(533\) | 27.4912 | 1.19077 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.1996 | −0.700369 | ||||||||
\(536\) | −3.62987 | −0.156786 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.2794 | −1.77968 | ||||||||
\(539\) | −2.76439 | −0.119071 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.52150 | 0.409361 | 0.204681 | − | 0.978829i | \(-0.434384\pi\) | ||||
0.204681 | + | 0.978829i | \(0.434384\pi\) | |||||||
\(542\) | 8.91323 | 0.382856 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.0028 | 1.20061 | ||||||||
\(545\) | 24.9446 | 1.06851 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.7437 | 1.69932 | 0.849658 | − | 0.527333i | \(-0.176808\pi\) | ||||
0.849658 | + | 0.527333i | \(0.176808\pi\) | |||||||
\(548\) | 13.9889 | 0.597576 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −45.3186 | −1.93239 | ||||||||
\(551\) | 2.96554 | 0.126336 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03997 | 0.0442240 | ||||||||
\(554\) | 26.0862 | 1.10829 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.9520 | −1.60952 | ||||||||
\(557\) | 11.1132 | 0.470879 | 0.235440 | − | 0.971889i | \(-0.424347\pi\) | ||||
0.235440 | + | 0.971889i | \(0.424347\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.2462 | −0.983207 | ||||||||
\(560\) | 16.1556 | 0.682698 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40.2239 | 1.69674 | ||||||||
\(563\) | −39.4772 | −1.66377 | −0.831883 | − | 0.554950i | \(-0.812737\pi\) | ||||
−0.831883 | + | 0.554950i | \(0.812737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.7723 | −1.79944 | ||||||||
\(566\) | 12.9795 | 0.545571 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.81214 | 0.0760358 | ||||||||
\(569\) | −36.1926 | −1.51727 | −0.758637 | − | 0.651513i | \(-0.774134\pi\) | ||||
−0.758637 | + | 0.651513i | \(0.774134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.8322 | −1.20659 | −0.603295 | − | 0.797518i | \(-0.706146\pi\) | ||||
−0.603295 | + | 0.797518i | \(0.706146\pi\) | |||||||
\(572\) | 19.1055 | 0.798842 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.6748 | −0.570777 | ||||||||
\(575\) | 49.8318 | 2.07813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.6307 | 1.35843 | 0.679217 | − | 0.733937i | \(-0.262319\pi\) | ||||
0.679217 | + | 0.733937i | \(0.262319\pi\) | |||||||
\(578\) | −7.09223 | −0.294998 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.55593 | 0.272220 | ||||||||
\(581\) | −3.97794 | −0.165033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.8170 | 0.489409 | ||||||||
\(584\) | −0.453162 | −0.0187520 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.26022 | 0.134678 | ||||||||
\(587\) | 41.8690 | 1.72812 | 0.864059 | − | 0.503391i | \(-0.167914\pi\) | ||||
0.864059 | + | 0.503391i | \(0.167914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.59884 | 0.107083 | ||||||||
\(590\) | −52.4618 | −2.15982 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −26.3145 | −1.08152 | ||||||||
\(593\) | −17.7488 | −0.728855 | −0.364428 | − | 0.931232i | \(-0.618735\pi\) | ||||
−0.364428 | + | 0.931232i | \(0.618735\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.3950 | 0.549142 | ||||||||
\(596\) | 2.15353 | 0.0882120 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −44.7399 | −1.82955 | ||||||||
\(599\) | 11.2278 | 0.458757 | 0.229379 | − | 0.973337i | \(-0.426331\pi\) | ||||
0.229379 | + | 0.973337i | \(0.426331\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2339 | 0.702987 | 0.351494 | − | 0.936190i | \(-0.385674\pi\) | ||||
0.351494 | + | 0.936190i | \(0.385674\pi\) | |||||||
\(602\) | 11.5633 | 0.471283 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.15851 | 0.0471391 | ||||||||
\(605\) | 12.3123 | 0.500566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.1843 | −1.26573 | −0.632865 | − | 0.774262i | \(-0.718121\pi\) | ||||
−0.632865 | + | 0.774262i | \(0.718121\pi\) | |||||||
\(608\) | 22.5062 | 0.912748 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −84.9847 | −3.44093 | ||||||||
\(611\) | −21.5127 | −0.870310 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.58057 | 0.0638387 | 0.0319193 | − | 0.999490i | \(-0.489838\pi\) | ||||
0.0319193 | + | 0.999490i | \(0.489838\pi\) | |||||||
\(614\) | 1.58261 | 0.0638691 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.23204 | 0.0496404 | ||||||||
\(617\) | 43.3219 | 1.74408 | 0.872038 | − | 0.489439i | \(-0.162798\pi\) | ||||
0.872038 | + | 0.489439i | \(0.162798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0264 | −1.44802 | −0.724011 | − | 0.689789i | \(-0.757703\pi\) | ||||
−0.724011 | + | 0.689789i | \(0.757703\pi\) | |||||||
\(620\) | 5.74527 | 0.230735 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.9022 | −0.517331 | ||||||||
\(623\) | −10.8011 | −0.432738 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.06490 | 0.162596 | ||||||||
\(626\) | 0.563121 | 0.0225069 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.4998 | 0.857936 | ||||||||
\(629\) | −21.8180 | −0.869940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.6150 | −0.780862 | −0.390431 | − | 0.920632i | \(-0.627674\pi\) | ||||
−0.390431 | + | 0.920632i | \(0.627674\pi\) | |||||||
\(632\) | −0.463496 | −0.0184369 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −65.3786 | −2.59652 | ||||||||
\(635\) | −3.66642 | −0.145497 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.90363 | −0.154668 | ||||||||
\(638\) | 5.42126 | 0.214630 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.9864 | −0.513332 | ||||||||
\(641\) | −37.3289 | −1.47440 | −0.737202 | − | 0.675672i | \(-0.763854\pi\) | ||||
−0.737202 | + | 0.675672i | \(0.763854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2063 | 0.599677 | 0.299839 | − | 0.953990i | \(-0.403067\pi\) | ||||
0.299839 | + | 0.953990i | \(0.403067\pi\) | |||||||
\(644\) | 10.4501 | 0.411790 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.8306 | 0.819568 | ||||||||
\(647\) | 33.1334 | 1.30261 | 0.651304 | − | 0.758817i | \(-0.274222\pi\) | ||||
0.651304 | + | 0.758817i | \(0.274222\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.3705 | −0.799614 | ||||||||
\(650\) | −63.9948 | −2.51008 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.7176 | −0.772199 | ||||||||
\(653\) | 2.29910 | 0.0899709 | 0.0449854 | − | 0.998988i | \(-0.485676\pi\) | ||||
0.0449854 | + | 0.998988i | \(0.485676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.6057 | 0.805131 | ||||||||
\(656\) | 31.0316 | 1.21158 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 10.7010 | 0.417168 | ||||||||
\(659\) | 42.2286 | 1.64499 | 0.822496 | − | 0.568771i | \(-0.192581\pi\) | ||||
0.822496 | + | 0.568771i | \(0.192581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4775 | 0.990960 | 0.495480 | − | 0.868619i | \(-0.334992\pi\) | ||||
0.495480 | + | 0.868619i | \(0.334992\pi\) | |||||||
\(662\) | 35.3180 | 1.37267 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.77290 | 0.0688019 | ||||||||
\(665\) | 10.7658 | 0.417478 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.96115 | −0.230817 | ||||||||
\(668\) | −26.2474 | −1.01554 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −57.9836 | −2.24010 | ||||||||
\(671\) | −32.9990 | −1.27391 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.1340 | 0.853204 | 0.426602 | − | 0.904439i | \(-0.359710\pi\) | ||||
0.426602 | + | 0.904439i | \(0.359710\pi\) | |||||||
\(674\) | 10.1371 | 0.390465 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.96294 | 0.152421 | ||||||||
\(677\) | −30.8690 | −1.18639 | −0.593195 | − | 0.805059i | \(-0.702134\pi\) | ||||
−0.593195 | + | 0.805059i | \(0.702134\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1382 | 0.504198 | ||||||||
\(680\) | −5.96992 | −0.228936 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.75090 | 0.181921 | ||||||||
\(683\) | 49.1676 | 1.88135 | 0.940673 | − | 0.339315i | \(-0.110195\pi\) | ||||
0.940673 | + | 0.339315i | \(0.110195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.9691 | −1.10685 | ||||||||
\(686\) | 1.94177 | 0.0741372 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.2399 | −1.00039 | ||||||||
\(689\) | 16.6869 | 0.635719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7873 | −0.638621 | −0.319310 | − | 0.947650i | \(-0.603451\pi\) | ||||
−0.319310 | + | 0.947650i | \(0.603451\pi\) | |||||||
\(692\) | −19.3027 | −0.733780 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −49.7519 | −1.88856 | ||||||||
\(695\) | 78.5934 | 2.98122 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.7291 | 0.974560 | ||||||||
\(698\) | −16.4591 | −0.622985 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 14.9475 | 0.564962 | ||||||||
\(701\) | −3.96675 | −0.149822 | −0.0749110 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749110 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.5354 | −0.661361 | ||||||||
\(704\) | 16.7814 | 0.632471 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 56.4478 | 2.12444 | ||||||||
\(707\) | 1.59877 | 0.0601278 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6827 | −0.476309 | −0.238154 | − | 0.971227i | \(-0.576542\pi\) | ||||
−0.238154 | + | 0.971227i | \(0.576542\pi\) | |||||||
\(710\) | 28.9472 | 1.08637 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.81387 | 0.180408 | ||||||||
\(713\) | −5.22404 | −0.195642 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.5650 | −1.47965 | ||||||||
\(716\) | −3.23175 | −0.120776 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −31.3848 | −1.17127 | ||||||||
\(719\) | −37.0747 | −1.38265 | −0.691327 | − | 0.722542i | \(-0.742973\pi\) | ||||
−0.691327 | + | 0.722542i | \(0.742973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.33183 | 0.0495999 | ||||||||
\(722\) | −20.1518 | −0.749974 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −38.1005 | −1.41599 | ||||||||
\(725\) | −8.52668 | −0.316673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7092 | 1.13894 | 0.569471 | − | 0.822011i | \(-0.307148\pi\) | ||||
0.569471 | + | 0.822011i | \(0.307148\pi\) | |||||||
\(728\) | 1.73978 | 0.0644806 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.23883 | −0.267921 | ||||||||
\(731\) | −21.7562 | −0.804682 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.0346 | 1.58952 | 0.794761 | − | 0.606923i | \(-0.207596\pi\) | ||||
0.794761 | + | 0.606923i | \(0.207596\pi\) | |||||||
\(734\) | −15.5834 | −0.575195 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −45.2406 | −1.66759 | ||||||||
\(737\) | −22.5146 | −0.829338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.5287 | −0.718376 | −0.359188 | − | 0.933265i | \(-0.616946\pi\) | ||||
−0.359188 | + | 0.933265i | \(0.616946\pi\) | |||||||
\(740\) | −38.7656 | −1.42505 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.30050 | −0.304721 | ||||||||
\(743\) | 39.5429 | 1.45069 | 0.725345 | − | 0.688386i | \(-0.241680\pi\) | ||||
0.725345 | + | 0.688386i | \(0.241680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.45967 | −0.163390 | ||||||||
\(746\) | 43.7538 | 1.60194 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.8810 | 0.653793 | ||||||||
\(749\) | 4.41836 | 0.161444 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.05959 | 0.184627 | 0.0923136 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923136 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(752\) | −24.2832 | −0.885518 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.65542 | 0.278794 | ||||||||
\(755\) | −2.39912 | −0.0873129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.35286 | −0.121862 | −0.0609309 | − | 0.998142i | \(-0.519407\pi\) | ||||
−0.0609309 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(758\) | −29.5792 | −1.07436 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.79811 | −0.174046 | ||||||||
\(761\) | −9.15947 | −0.332030 | −0.166015 | − | 0.986123i | \(-0.553090\pi\) | ||||
−0.166015 | + | 0.986123i | \(0.553090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.80353 | −0.246304 | ||||||||
\(764\) | 8.82588 | 0.319309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.4702 | 0.848014 | ||||||||
\(767\) | −28.7655 | −1.03866 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6579 | −0.492517 | −0.246258 | − | 0.969204i | \(-0.579201\pi\) | ||||
−0.246258 | + | 0.969204i | \(0.579201\pi\) | |||||||
\(770\) | 19.6807 | 0.709243 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.9858 | 0.935248 | ||||||||
\(773\) | −2.38910 | −0.0859301 | −0.0429651 | − | 0.999077i | \(-0.513680\pi\) | ||||
−0.0429651 | + | 0.999077i | \(0.513680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.47233 | −0.268414 | ||||||||
\(776\) | −5.85547 | −0.210199 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −63.1756 | −2.26495 | ||||||||
\(779\) | 20.6789 | 0.740897 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2400 | 0.402199 | ||||||||
\(782\) | −41.8723 | −1.49735 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.40637 | −0.157370 | ||||||||
\(785\) | −44.5232 | −1.58910 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.6553 | −0.415465 | −0.207733 | − | 0.978186i | \(-0.566608\pi\) | ||||
−0.207733 | + | 0.978186i | \(0.566608\pi\) | |||||||
\(788\) | 30.8615 | 1.09939 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.40391 | −0.263419 | ||||||||
\(791\) | 11.6660 | 0.414794 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5982 | −1.65475 | ||||||||
\(794\) | −16.5980 | −0.589041 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.0364 | 1.59627 | ||||||||
\(797\) | 52.8237 | 1.87111 | 0.935556 | − | 0.353179i | \(-0.114899\pi\) | ||||
0.935556 | + | 0.353179i | \(0.114899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1338 | −0.712284 | ||||||||
\(800\) | −64.7110 | −2.28788 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 55.9935 | 1.97720 | ||||||||
\(803\) | −2.81079 | −0.0991905 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.6407 | −0.762733 | ||||||||
\(806\) | 6.70880 | 0.236307 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.712542 | −0.0250671 | ||||||||
\(809\) | 14.9711 | 0.526356 | 0.263178 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263178 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8772 | −0.662869 | −0.331434 | − | 0.943478i | \(-0.607533\pi\) | ||||
−0.331434 | + | 0.943478i | \(0.607533\pi\) | |||||||
\(812\) | −1.78810 | −0.0627501 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −32.0562 | −1.12357 | ||||||||
\(815\) | 40.8324 | 1.43030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4858 | −0.611749 | ||||||||
\(818\) | 2.46233 | 0.0860935 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 45.7148 | 1.59643 | ||||||||
\(821\) | 46.1335 | 1.61007 | 0.805035 | − | 0.593227i | \(-0.202146\pi\) | ||||
0.805035 | + | 0.593227i | \(0.202146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.7137 | −1.48891 | −0.744453 | − | 0.667674i | \(-0.767290\pi\) | ||||
−0.744453 | + | 0.667674i | \(0.767290\pi\) | |||||||
\(824\) | −0.593572 | −0.0206781 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.3087 | 0.497864 | ||||||||
\(827\) | −23.2513 | −0.808527 | −0.404263 | − | 0.914643i | \(-0.632472\pi\) | ||||
−0.404263 | + | 0.914643i | \(0.632472\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.6651 | 0.682996 | 0.341498 | − | 0.939883i | \(-0.389066\pi\) | ||||
0.341498 | + | 0.939883i | \(0.389066\pi\) | |||||||
\(830\) | 28.3204 | 0.983014 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23.6972 | 0.821551 | ||||||||
\(833\) | −3.65343 | −0.126584 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.3548 | 1.88102 | ||||||||
\(836\) | 14.3712 | 0.497038 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 60.9568 | 2.10572 | ||||||||
\(839\) | −28.3518 | −0.978812 | −0.489406 | − | 0.872056i | \(-0.662786\pi\) | ||||
−0.489406 | + | 0.872056i | \(0.662786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9800 | −0.964827 | ||||||||
\(842\) | −4.49957 | −0.155065 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.81433 | 0.303402 | ||||||||
\(845\) | −8.20672 | −0.282320 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.35813 | −0.115387 | ||||||||
\(848\) | 18.8359 | 0.646828 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59.8931 | −2.05432 | ||||||||
\(851\) | 35.2486 | 1.20831 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.4795 | 0.461530 | 0.230765 | − | 0.973009i | \(-0.425877\pi\) | ||||
0.230765 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(854\) | 23.1792 | 0.793176 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.96919 | −0.0673055 | ||||||||
\(857\) | −40.5096 | −1.38378 | −0.691891 | − | 0.722002i | \(-0.743222\pi\) | ||||
−0.691891 | + | 0.722002i | \(0.743222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.5206 | −1.82610 | −0.913049 | − | 0.407850i | \(-0.866279\pi\) | ||||
−0.913049 | + | 0.407850i | \(0.866279\pi\) | |||||||
\(860\) | −38.6558 | −1.31815 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.1795 | 1.13010 | ||||||||
\(863\) | 18.8826 | 0.642772 | 0.321386 | − | 0.946948i | \(-0.395851\pi\) | ||||
0.321386 | + | 0.946948i | \(0.395851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.9734 | 1.35914 | ||||||||
\(866\) | −47.3178 | −1.60792 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.56700 | −0.0531873 | ||||||||
\(869\) | −2.87489 | −0.0975238 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.7932 | −1.07727 | ||||||||
\(872\) | 3.03221 | 0.102684 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −33.6534 | −1.13834 | ||||||||
\(875\) | −12.6221 | −0.426706 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.9075 | 0.402089 | 0.201044 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201044 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(878\) | 15.3288 | 0.517322 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −44.6604 | −1.50550 | ||||||||
\(881\) | 21.5448 | 0.725863 | 0.362931 | − | 0.931816i | \(-0.381776\pi\) | ||||
0.362931 | + | 0.931816i | \(0.381776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.8753 | 0.365985 | 0.182992 | − | 0.983114i | \(-0.441422\pi\) | ||||
0.182992 | + | 0.983114i | \(0.441422\pi\) | |||||||
\(884\) | 25.2499 | 0.849246 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −40.2317 | −1.35161 | ||||||||
\(887\) | 4.35531 | 0.146237 | 0.0731186 | − | 0.997323i | \(-0.476705\pi\) | ||||
0.0731186 | + | 0.997323i | \(0.476705\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 76.8970 | 2.57759 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.63359 | −0.0881791 | ||||||||
\(893\) | −16.1818 | −0.541505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.69252 | 0.223706 | ||||||||
\(896\) | 3.54198 | 0.118329 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 59.9574 | 2.00080 | ||||||||
\(899\) | 0.893881 | 0.0298126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.6173 | 0.520288 | ||||||||
\(902\) | 37.8027 | 1.25869 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.19931 | −0.172927 | ||||||||
\(905\) | 78.9010 | 2.62276 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.60721 | 0.285798 | 0.142899 | − | 0.989737i | \(-0.454358\pi\) | ||||
0.142899 | + | 0.989737i | \(0.454358\pi\) | |||||||
\(908\) | 34.5742 | 1.14739 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 27.7913 | 0.921273 | ||||||||
\(911\) | −48.0894 | −1.59327 | −0.796637 | − | 0.604458i | \(-0.793390\pi\) | ||||
−0.796637 | + | 0.604458i | \(0.793390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9966 | 0.363934 | ||||||||
\(914\) | 37.5130 | 1.24082 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.6364 | −0.483600 | ||||||||
\(917\) | −5.62011 | −0.185592 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.97332 | 0.0980807 | 0.0490404 | − | 0.998797i | \(-0.484384\pi\) | ||||
0.0490404 | + | 0.998797i | \(0.484384\pi\) | |||||||
\(920\) | 9.64487 | 0.317982 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.78728 | −0.256460 | ||||||||
\(923\) | 15.8721 | 0.522438 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.4187 | 1.65776 | ||||||||
\(926\) | 9.07049 | 0.298075 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.74110 | 0.254114 | ||||||||
\(929\) | 9.52563 | 0.312526 | 0.156263 | − | 0.987715i | \(-0.450055\pi\) | ||||
0.156263 | + | 0.987715i | \(0.450055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.93631 | −0.0962338 | ||||||||
\(932\) | 41.3433 | 1.35425 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.9565 | −0.783880 | ||||||||
\(935\) | −37.0291 | −1.21098 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.8037 | 1.46367 | 0.731836 | − | 0.681481i | \(-0.238664\pi\) | ||||
0.731836 | + | 0.681481i | \(0.238664\pi\) | |||||||
\(938\) | 15.8148 | 0.516371 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35.7732 | −1.16679 | ||||||||
\(941\) | 24.5478 | 0.800236 | 0.400118 | − | 0.916464i | \(-0.368969\pi\) | ||||
0.400118 | + | 0.916464i | \(0.368969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.5674 | −1.35362 | ||||||||
\(944\) | −32.4701 | −1.05681 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.9654 | −1.03928 | ||||||||
\(947\) | 44.5523 | 1.44775 | 0.723877 | − | 0.689929i | \(-0.242358\pi\) | ||||
0.723877 | + | 0.689929i | \(0.242358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.96914 | −0.128844 | ||||||||
\(950\) | −48.1369 | −1.56177 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.62827 | 0.0527725 | ||||||||
\(953\) | 9.81808 | 0.318039 | 0.159019 | − | 0.987275i | \(-0.449167\pi\) | ||||
0.159019 | + | 0.987275i | \(0.449167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.2772 | −0.591437 | ||||||||
\(956\) | −25.1436 | −0.813202 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.24573 | 0.169482 | ||||||||
\(959\) | 7.90120 | 0.255143 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2167 | −0.974731 | ||||||||
\(962\) | −45.2669 | −1.45946 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.23780 | 0.233114 | ||||||||
\(965\) | −53.8131 | −1.73230 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.7733 | 1.56844 | 0.784222 | − | 0.620480i | \(-0.213062\pi\) | ||||
0.784222 | + | 0.620480i | \(0.213062\pi\) | |||||||
\(968\) | 1.49666 | 0.0481044 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −93.5355 | −3.00324 | ||||||||
\(971\) | −27.9521 | −0.897027 | −0.448514 | − | 0.893776i | \(-0.648046\pi\) | ||||
−0.448514 | + | 0.893776i | \(0.648046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.4360 | −0.687207 | ||||||||
\(974\) | −52.4270 | −1.67987 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −52.5994 | −1.68367 | ||||||||
\(977\) | −9.88220 | −0.316160 | −0.158080 | − | 0.987426i | \(-0.550530\pi\) | ||||
−0.158080 | + | 0.987426i | \(0.550530\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.8586 | 0.954284 | ||||||||
\(980\) | −6.49131 | −0.207357 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 49.4458 | 1.57788 | ||||||||
\(983\) | −35.8839 | −1.14452 | −0.572260 | − | 0.820073i | \(-0.693933\pi\) | ||||
−0.572260 | + | 0.820073i | \(0.693933\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.9100 | −2.03634 | ||||||||
\(986\) | 7.16475 | 0.228172 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.2937 | 0.645629 | ||||||||
\(989\) | 35.1488 | 1.11767 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8528 | 0.630646 | 0.315323 | − | 0.948984i | \(-0.397887\pi\) | ||||
0.315323 | + | 0.948984i | \(0.397887\pi\) | |||||||
\(992\) | 6.78388 | 0.215388 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.89523 | −0.250421 | ||||||||
\(995\) | −93.2643 | −2.95668 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.8307 | 0.786398 | 0.393199 | − | 0.919453i | \(-0.371368\pi\) | ||||
0.393199 | + | 0.919453i | \(0.371368\pi\) | |||||||
\(998\) | −50.1279 | −1.58677 | ||||||||
\(999\) | 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 | 8001.2.a.v.1.17 | 19 | ||
3.2 | odd | 2 | 2667.2.a.q.1.3 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.q.1.3 | ✓ | 19 | 3.2 | odd | 2 | ||
8001.2.a.v.1.17 | 19 | 1.1 | even | 1 | trivial |