Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85290 | −1.31020 | −0.655100 | − | 0.755542i | \(-0.727373\pi\) | ||||
−0.655100 | + | 0.755542i | \(0.727373\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.43325 | 0.716623 | ||||||||
\(5\) | −3.21014 | −1.43562 | −0.717809 | − | 0.696240i | \(-0.754855\pi\) | ||||
−0.717809 | + | 0.696240i | \(0.754855\pi\) | |||||||
\(6\) | 1.85290 | 0.756444 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.05014 | 0.371281 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.94808 | 1.88095 | ||||||||
\(11\) | 4.69097 | 1.41438 | 0.707191 | − | 0.707023i | \(-0.249962\pi\) | ||||
0.707191 | + | 0.707023i | \(0.249962\pi\) | |||||||
\(12\) | −1.43325 | −0.413742 | ||||||||
\(13\) | 2.39172 | 0.663345 | 0.331672 | − | 0.943395i | \(-0.392387\pi\) | ||||
0.331672 | + | 0.943395i | \(0.392387\pi\) | |||||||
\(14\) | −1.85290 | −0.495209 | ||||||||
\(15\) | 3.21014 | 0.828855 | ||||||||
\(16\) | −4.81230 | −1.20307 | ||||||||
\(17\) | −5.33525 | −1.29399 | −0.646994 | − | 0.762495i | \(-0.723974\pi\) | ||||
−0.646994 | + | 0.762495i | \(0.723974\pi\) | |||||||
\(18\) | −1.85290 | −0.436733 | ||||||||
\(19\) | −0.312316 | −0.0716503 | −0.0358252 | − | 0.999358i | \(-0.511406\pi\) | ||||
−0.0358252 | + | 0.999358i | \(0.511406\pi\) | |||||||
\(20\) | −4.60092 | −1.02880 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −8.69191 | −1.85312 | ||||||||
\(23\) | −5.88569 | −1.22725 | −0.613625 | − | 0.789597i | \(-0.710289\pi\) | ||||
−0.613625 | + | 0.789597i | \(0.710289\pi\) | |||||||
\(24\) | −1.05014 | −0.214359 | ||||||||
\(25\) | 5.30500 | 1.06100 | ||||||||
\(26\) | −4.43163 | −0.869114 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.43325 | 0.270858 | ||||||||
\(29\) | 7.36152 | 1.36700 | 0.683500 | − | 0.729951i | \(-0.260457\pi\) | ||||
0.683500 | + | 0.729951i | \(0.260457\pi\) | |||||||
\(30\) | −5.94808 | −1.08597 | ||||||||
\(31\) | 0.943195 | 0.169403 | 0.0847014 | − | 0.996406i | \(-0.473006\pi\) | ||||
0.0847014 | + | 0.996406i | \(0.473006\pi\) | |||||||
\(32\) | 6.81644 | 1.20499 | ||||||||
\(33\) | −4.69097 | −0.816594 | ||||||||
\(34\) | 9.88569 | 1.69538 | ||||||||
\(35\) | −3.21014 | −0.542613 | ||||||||
\(36\) | 1.43325 | 0.238874 | ||||||||
\(37\) | 7.38664 | 1.21436 | 0.607178 | − | 0.794566i | \(-0.292301\pi\) | ||||
0.607178 | + | 0.794566i | \(0.292301\pi\) | |||||||
\(38\) | 0.578692 | 0.0938762 | ||||||||
\(39\) | −2.39172 | −0.382982 | ||||||||
\(40\) | −3.37110 | −0.533017 | ||||||||
\(41\) | 2.27743 | 0.355674 | 0.177837 | − | 0.984060i | \(-0.443090\pi\) | ||||
0.177837 | + | 0.984060i | \(0.443090\pi\) | |||||||
\(42\) | 1.85290 | 0.285909 | ||||||||
\(43\) | 5.60881 | 0.855336 | 0.427668 | − | 0.903936i | \(-0.359335\pi\) | ||||
0.427668 | + | 0.903936i | \(0.359335\pi\) | |||||||
\(44\) | 6.72332 | 1.01358 | ||||||||
\(45\) | −3.21014 | −0.478539 | ||||||||
\(46\) | 10.9056 | 1.60794 | ||||||||
\(47\) | 1.72173 | 0.251140 | 0.125570 | − | 0.992085i | \(-0.459924\pi\) | ||||
0.125570 | + | 0.992085i | \(0.459924\pi\) | |||||||
\(48\) | 4.81230 | 0.694595 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.82965 | −1.39012 | ||||||||
\(51\) | 5.33525 | 0.747084 | ||||||||
\(52\) | 3.42793 | 0.475368 | ||||||||
\(53\) | 3.85567 | 0.529617 | 0.264808 | − | 0.964301i | \(-0.414691\pi\) | ||||
0.264808 | + | 0.964301i | \(0.414691\pi\) | |||||||
\(54\) | 1.85290 | 0.252148 | ||||||||
\(55\) | −15.0587 | −2.03051 | ||||||||
\(56\) | 1.05014 | 0.140331 | ||||||||
\(57\) | 0.312316 | 0.0413673 | ||||||||
\(58\) | −13.6402 | −1.79104 | ||||||||
\(59\) | −14.5600 | −1.89556 | −0.947778 | − | 0.318932i | \(-0.896676\pi\) | ||||
−0.947778 | + | 0.318932i | \(0.896676\pi\) | |||||||
\(60\) | 4.60092 | 0.593976 | ||||||||
\(61\) | 10.7348 | 1.37445 | 0.687224 | − | 0.726446i | \(-0.258829\pi\) | ||||
0.687224 | + | 0.726446i | \(0.258829\pi\) | |||||||
\(62\) | −1.74765 | −0.221951 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −3.00559 | −0.375699 | ||||||||
\(65\) | −7.67777 | −0.952310 | ||||||||
\(66\) | 8.69191 | 1.06990 | ||||||||
\(67\) | −7.76670 | −0.948853 | −0.474426 | − | 0.880295i | \(-0.657345\pi\) | ||||
−0.474426 | + | 0.880295i | \(0.657345\pi\) | |||||||
\(68\) | −7.64672 | −0.927301 | ||||||||
\(69\) | 5.88569 | 0.708553 | ||||||||
\(70\) | 5.94808 | 0.710931 | ||||||||
\(71\) | −1.06851 | −0.126809 | −0.0634044 | − | 0.997988i | \(-0.520196\pi\) | ||||
−0.0634044 | + | 0.997988i | \(0.520196\pi\) | |||||||
\(72\) | 1.05014 | 0.123760 | ||||||||
\(73\) | 15.6913 | 1.83653 | 0.918266 | − | 0.395964i | \(-0.129589\pi\) | ||||
0.918266 | + | 0.395964i | \(0.129589\pi\) | |||||||
\(74\) | −13.6867 | −1.59105 | ||||||||
\(75\) | −5.30500 | −0.612569 | ||||||||
\(76\) | −0.447626 | −0.0513463 | ||||||||
\(77\) | 4.69097 | 0.534586 | ||||||||
\(78\) | 4.43163 | 0.501783 | ||||||||
\(79\) | −8.92717 | −1.00438 | −0.502192 | − | 0.864756i | \(-0.667473\pi\) | ||||
−0.502192 | + | 0.864756i | \(0.667473\pi\) | |||||||
\(80\) | 15.4482 | 1.72716 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.21985 | −0.466004 | ||||||||
\(83\) | 12.7810 | 1.40289 | 0.701447 | − | 0.712722i | \(-0.252538\pi\) | ||||
0.701447 | + | 0.712722i | \(0.252538\pi\) | |||||||
\(84\) | −1.43325 | −0.156380 | ||||||||
\(85\) | 17.1269 | 1.85767 | ||||||||
\(86\) | −10.3926 | −1.12066 | ||||||||
\(87\) | −7.36152 | −0.789237 | ||||||||
\(88\) | 4.92618 | 0.525132 | ||||||||
\(89\) | 18.7109 | 1.98335 | 0.991674 | − | 0.128776i | \(-0.0411047\pi\) | ||||
0.991674 | + | 0.128776i | \(0.0411047\pi\) | |||||||
\(90\) | 5.94808 | 0.626982 | ||||||||
\(91\) | 2.39172 | 0.250721 | ||||||||
\(92\) | −8.43564 | −0.879476 | ||||||||
\(93\) | −0.943195 | −0.0978047 | ||||||||
\(94\) | −3.19020 | −0.329044 | ||||||||
\(95\) | 1.00258 | 0.102863 | ||||||||
\(96\) | −6.81644 | −0.695700 | ||||||||
\(97\) | 6.81283 | 0.691738 | 0.345869 | − | 0.938283i | \(-0.387584\pi\) | ||||
0.345869 | + | 0.938283i | \(0.387584\pi\) | |||||||
\(98\) | −1.85290 | −0.187171 | ||||||||
\(99\) | 4.69097 | 0.471461 | ||||||||
\(100\) | 7.60337 | 0.760337 | ||||||||
\(101\) | −13.6015 | −1.35340 | −0.676702 | − | 0.736257i | \(-0.736592\pi\) | ||||
−0.676702 | + | 0.736257i | \(0.736592\pi\) | |||||||
\(102\) | −9.88569 | −0.978830 | ||||||||
\(103\) | −4.83718 | −0.476621 | −0.238311 | − | 0.971189i | \(-0.576594\pi\) | ||||
−0.238311 | + | 0.971189i | \(0.576594\pi\) | |||||||
\(104\) | 2.51165 | 0.246287 | ||||||||
\(105\) | 3.21014 | 0.313278 | ||||||||
\(106\) | −7.14417 | −0.693903 | ||||||||
\(107\) | −12.9339 | −1.25037 | −0.625184 | − | 0.780477i | \(-0.714976\pi\) | ||||
−0.625184 | + | 0.780477i | \(0.714976\pi\) | |||||||
\(108\) | −1.43325 | −0.137914 | ||||||||
\(109\) | 5.11701 | 0.490121 | 0.245061 | − | 0.969508i | \(-0.421192\pi\) | ||||
0.245061 | + | 0.969508i | \(0.421192\pi\) | |||||||
\(110\) | 27.9023 | 2.66038 | ||||||||
\(111\) | −7.38664 | −0.701109 | ||||||||
\(112\) | −4.81230 | −0.454719 | ||||||||
\(113\) | 13.5759 | 1.27711 | 0.638554 | − | 0.769577i | \(-0.279533\pi\) | ||||
0.638554 | + | 0.769577i | \(0.279533\pi\) | |||||||
\(114\) | −0.578692 | −0.0541995 | ||||||||
\(115\) | 18.8939 | 1.76186 | ||||||||
\(116\) | 10.5509 | 0.979623 | ||||||||
\(117\) | 2.39172 | 0.221115 | ||||||||
\(118\) | 26.9783 | 2.48356 | ||||||||
\(119\) | −5.33525 | −0.489081 | ||||||||
\(120\) | 3.37110 | 0.307738 | ||||||||
\(121\) | 11.0052 | 1.00048 | ||||||||
\(122\) | −19.8905 | −1.80080 | ||||||||
\(123\) | −2.27743 | −0.205349 | ||||||||
\(124\) | 1.35183 | 0.121398 | ||||||||
\(125\) | −0.979095 | −0.0875729 | ||||||||
\(126\) | −1.85290 | −0.165070 | ||||||||
\(127\) | 17.8346 | 1.58256 | 0.791282 | − | 0.611451i | \(-0.209414\pi\) | ||||
0.791282 | + | 0.611451i | \(0.209414\pi\) | |||||||
\(128\) | −8.06380 | −0.712746 | ||||||||
\(129\) | −5.60881 | −0.493828 | ||||||||
\(130\) | 14.2262 | 1.24772 | ||||||||
\(131\) | −21.6482 | −1.89142 | −0.945708 | − | 0.325018i | \(-0.894630\pi\) | ||||
−0.945708 | + | 0.325018i | \(0.894630\pi\) | |||||||
\(132\) | −6.72332 | −0.585190 | ||||||||
\(133\) | −0.312316 | −0.0270813 | ||||||||
\(134\) | 14.3909 | 1.24319 | ||||||||
\(135\) | 3.21014 | 0.276285 | ||||||||
\(136\) | −5.60276 | −0.480433 | ||||||||
\(137\) | −2.09823 | −0.179264 | −0.0896320 | − | 0.995975i | \(-0.528569\pi\) | ||||
−0.0896320 | + | 0.995975i | \(0.528569\pi\) | |||||||
\(138\) | −10.9056 | −0.928346 | ||||||||
\(139\) | −18.1952 | −1.54330 | −0.771650 | − | 0.636048i | \(-0.780568\pi\) | ||||
−0.771650 | + | 0.636048i | \(0.780568\pi\) | |||||||
\(140\) | −4.60092 | −0.388849 | ||||||||
\(141\) | −1.72173 | −0.144996 | ||||||||
\(142\) | 1.97985 | 0.166145 | ||||||||
\(143\) | 11.2195 | 0.938223 | ||||||||
\(144\) | −4.81230 | −0.401025 | ||||||||
\(145\) | −23.6315 | −1.96249 | ||||||||
\(146\) | −29.0745 | −2.40622 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 10.5869 | 0.870235 | ||||||||
\(149\) | −17.8336 | −1.46098 | −0.730492 | − | 0.682922i | \(-0.760709\pi\) | ||||
−0.730492 | + | 0.682922i | \(0.760709\pi\) | |||||||
\(150\) | 9.82965 | 0.802587 | ||||||||
\(151\) | 9.35590 | 0.761372 | 0.380686 | − | 0.924704i | \(-0.375688\pi\) | ||||
0.380686 | + | 0.924704i | \(0.375688\pi\) | |||||||
\(152\) | −0.327976 | −0.0266024 | ||||||||
\(153\) | −5.33525 | −0.431329 | ||||||||
\(154\) | −8.69191 | −0.700414 | ||||||||
\(155\) | −3.02779 | −0.243198 | ||||||||
\(156\) | −3.42793 | −0.274454 | ||||||||
\(157\) | −23.3467 | −1.86327 | −0.931635 | − | 0.363396i | \(-0.881617\pi\) | ||||
−0.931635 | + | 0.363396i | \(0.881617\pi\) | |||||||
\(158\) | 16.5412 | 1.31594 | ||||||||
\(159\) | −3.85567 | −0.305774 | ||||||||
\(160\) | −21.8817 | −1.72990 | ||||||||
\(161\) | −5.88569 | −0.463857 | ||||||||
\(162\) | −1.85290 | −0.145578 | ||||||||
\(163\) | 18.9277 | 1.48254 | 0.741268 | − | 0.671210i | \(-0.234225\pi\) | ||||
0.741268 | + | 0.671210i | \(0.234225\pi\) | |||||||
\(164\) | 3.26411 | 0.254884 | ||||||||
\(165\) | 15.0587 | 1.17232 | ||||||||
\(166\) | −23.6819 | −1.83807 | ||||||||
\(167\) | 6.43574 | 0.498012 | 0.249006 | − | 0.968502i | \(-0.419896\pi\) | ||||
0.249006 | + | 0.968502i | \(0.419896\pi\) | |||||||
\(168\) | −1.05014 | −0.0810201 | ||||||||
\(169\) | −7.27966 | −0.559973 | ||||||||
\(170\) | −31.7345 | −2.43392 | ||||||||
\(171\) | −0.312316 | −0.0238834 | ||||||||
\(172\) | 8.03881 | 0.612953 | ||||||||
\(173\) | −15.7641 | −1.19852 | −0.599261 | − | 0.800554i | \(-0.704539\pi\) | ||||
−0.599261 | + | 0.800554i | \(0.704539\pi\) | |||||||
\(174\) | 13.6402 | 1.03406 | ||||||||
\(175\) | 5.30500 | 0.401020 | ||||||||
\(176\) | −22.5744 | −1.70161 | ||||||||
\(177\) | 14.5600 | 1.09440 | ||||||||
\(178\) | −34.6694 | −2.59858 | ||||||||
\(179\) | −7.14886 | −0.534331 | −0.267166 | − | 0.963651i | \(-0.586087\pi\) | ||||
−0.267166 | + | 0.963651i | \(0.586087\pi\) | |||||||
\(180\) | −4.60092 | −0.342932 | ||||||||
\(181\) | −9.10549 | −0.676806 | −0.338403 | − | 0.941001i | \(-0.609887\pi\) | ||||
−0.338403 | + | 0.941001i | \(0.609887\pi\) | |||||||
\(182\) | −4.43163 | −0.328494 | ||||||||
\(183\) | −10.7348 | −0.793538 | ||||||||
\(184\) | −6.18079 | −0.455654 | ||||||||
\(185\) | −23.7122 | −1.74335 | ||||||||
\(186\) | 1.74765 | 0.128144 | ||||||||
\(187\) | −25.0275 | −1.83019 | ||||||||
\(188\) | 2.46766 | 0.179973 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.85768 | −0.134770 | ||||||||
\(191\) | −19.5972 | −1.41800 | −0.709001 | − | 0.705207i | \(-0.750854\pi\) | ||||
−0.709001 | + | 0.705207i | \(0.750854\pi\) | |||||||
\(192\) | 3.00559 | 0.216910 | ||||||||
\(193\) | −5.18417 | −0.373165 | −0.186582 | − | 0.982439i | \(-0.559741\pi\) | ||||
−0.186582 | + | 0.982439i | \(0.559741\pi\) | |||||||
\(194\) | −12.6235 | −0.906314 | ||||||||
\(195\) | 7.67777 | 0.549817 | ||||||||
\(196\) | 1.43325 | 0.102375 | ||||||||
\(197\) | 16.7284 | 1.19185 | 0.595926 | − | 0.803040i | \(-0.296785\pi\) | ||||
0.595926 | + | 0.803040i | \(0.296785\pi\) | |||||||
\(198\) | −8.69191 | −0.617707 | ||||||||
\(199\) | 20.7020 | 1.46752 | 0.733762 | − | 0.679406i | \(-0.237763\pi\) | ||||
0.733762 | + | 0.679406i | \(0.237763\pi\) | |||||||
\(200\) | 5.57099 | 0.393929 | ||||||||
\(201\) | 7.76670 | 0.547820 | ||||||||
\(202\) | 25.2023 | 1.77323 | ||||||||
\(203\) | 7.36152 | 0.516677 | ||||||||
\(204\) | 7.64672 | 0.535378 | ||||||||
\(205\) | −7.31086 | −0.510613 | ||||||||
\(206\) | 8.96281 | 0.624469 | ||||||||
\(207\) | −5.88569 | −0.409083 | ||||||||
\(208\) | −11.5097 | −0.798053 | ||||||||
\(209\) | −1.46507 | −0.101341 | ||||||||
\(210\) | −5.94808 | −0.410456 | ||||||||
\(211\) | 16.8083 | 1.15713 | 0.578567 | − | 0.815635i | \(-0.303612\pi\) | ||||
0.578567 | + | 0.815635i | \(0.303612\pi\) | |||||||
\(212\) | 5.52612 | 0.379535 | ||||||||
\(213\) | 1.06851 | 0.0732131 | ||||||||
\(214\) | 23.9653 | 1.63823 | ||||||||
\(215\) | −18.0051 | −1.22794 | ||||||||
\(216\) | −1.05014 | −0.0714530 | ||||||||
\(217\) | 0.943195 | 0.0640282 | ||||||||
\(218\) | −9.48132 | −0.642156 | ||||||||
\(219\) | −15.6913 | −1.06032 | ||||||||
\(220\) | −21.5828 | −1.45511 | ||||||||
\(221\) | −12.7604 | −0.858360 | ||||||||
\(222\) | 13.6867 | 0.918592 | ||||||||
\(223\) | −21.3467 | −1.42948 | −0.714739 | − | 0.699392i | \(-0.753454\pi\) | ||||
−0.714739 | + | 0.699392i | \(0.753454\pi\) | |||||||
\(224\) | 6.81644 | 0.455442 | ||||||||
\(225\) | 5.30500 | 0.353667 | ||||||||
\(226\) | −25.1547 | −1.67327 | ||||||||
\(227\) | 3.72777 | 0.247421 | 0.123711 | − | 0.992318i | \(-0.460521\pi\) | ||||
0.123711 | + | 0.992318i | \(0.460521\pi\) | |||||||
\(228\) | 0.447626 | 0.0296448 | ||||||||
\(229\) | −14.4009 | −0.951640 | −0.475820 | − | 0.879543i | \(-0.657849\pi\) | ||||
−0.475820 | + | 0.879543i | \(0.657849\pi\) | |||||||
\(230\) | −35.0085 | −2.30839 | ||||||||
\(231\) | −4.69097 | −0.308643 | ||||||||
\(232\) | 7.73062 | 0.507540 | ||||||||
\(233\) | 26.9701 | 1.76687 | 0.883435 | − | 0.468553i | \(-0.155225\pi\) | ||||
0.883435 | + | 0.468553i | \(0.155225\pi\) | |||||||
\(234\) | −4.43163 | −0.289705 | ||||||||
\(235\) | −5.52699 | −0.360541 | ||||||||
\(236\) | −20.8681 | −1.35840 | ||||||||
\(237\) | 8.92717 | 0.579882 | ||||||||
\(238\) | 9.88569 | 0.640794 | ||||||||
\(239\) | −8.73652 | −0.565119 | −0.282559 | − | 0.959250i | \(-0.591183\pi\) | ||||
−0.282559 | + | 0.959250i | \(0.591183\pi\) | |||||||
\(240\) | −15.4482 | −0.997174 | ||||||||
\(241\) | −6.09077 | −0.392341 | −0.196171 | − | 0.980570i | \(-0.562851\pi\) | ||||
−0.196171 | + | 0.980570i | \(0.562851\pi\) | |||||||
\(242\) | −20.3916 | −1.31082 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.3856 | 0.984961 | ||||||||
\(245\) | −3.21014 | −0.205088 | ||||||||
\(246\) | 4.21985 | 0.269048 | ||||||||
\(247\) | −0.746975 | −0.0475289 | ||||||||
\(248\) | 0.990486 | 0.0628959 | ||||||||
\(249\) | −12.7810 | −0.809961 | ||||||||
\(250\) | 1.81417 | 0.114738 | ||||||||
\(251\) | −25.2040 | −1.59086 | −0.795431 | − | 0.606044i | \(-0.792756\pi\) | ||||
−0.795431 | + | 0.606044i | \(0.792756\pi\) | |||||||
\(252\) | 1.43325 | 0.0902860 | ||||||||
\(253\) | −27.6096 | −1.73580 | ||||||||
\(254\) | −33.0458 | −2.07347 | ||||||||
\(255\) | −17.1269 | −1.07253 | ||||||||
\(256\) | 20.9526 | 1.30954 | ||||||||
\(257\) | 7.18529 | 0.448206 | 0.224103 | − | 0.974565i | \(-0.428055\pi\) | ||||
0.224103 | + | 0.974565i | \(0.428055\pi\) | |||||||
\(258\) | 10.3926 | 0.647014 | ||||||||
\(259\) | 7.38664 | 0.458983 | ||||||||
\(260\) | −11.0041 | −0.682447 | ||||||||
\(261\) | 7.36152 | 0.455666 | ||||||||
\(262\) | 40.1121 | 2.47813 | ||||||||
\(263\) | 1.08053 | 0.0666282 | 0.0333141 | − | 0.999445i | \(-0.489394\pi\) | ||||
0.0333141 | + | 0.999445i | \(0.489394\pi\) | |||||||
\(264\) | −4.92618 | −0.303185 | ||||||||
\(265\) | −12.3772 | −0.760327 | ||||||||
\(266\) | 0.578692 | 0.0354819 | ||||||||
\(267\) | −18.7109 | −1.14509 | ||||||||
\(268\) | −11.1316 | −0.679970 | ||||||||
\(269\) | −2.00098 | −0.122002 | −0.0610009 | − | 0.998138i | \(-0.519429\pi\) | ||||
−0.0610009 | + | 0.998138i | \(0.519429\pi\) | |||||||
\(270\) | −5.94808 | −0.361988 | ||||||||
\(271\) | 22.8381 | 1.38732 | 0.693659 | − | 0.720304i | \(-0.255998\pi\) | ||||
0.693659 | + | 0.720304i | \(0.255998\pi\) | |||||||
\(272\) | 25.6748 | 1.55676 | ||||||||
\(273\) | −2.39172 | −0.144754 | ||||||||
\(274\) | 3.88782 | 0.234872 | ||||||||
\(275\) | 24.8856 | 1.50066 | ||||||||
\(276\) | 8.43564 | 0.507766 | ||||||||
\(277\) | 17.6647 | 1.06137 | 0.530686 | − | 0.847569i | \(-0.321934\pi\) | ||||
0.530686 | + | 0.847569i | \(0.321934\pi\) | |||||||
\(278\) | 33.7140 | 2.02203 | ||||||||
\(279\) | 0.943195 | 0.0564676 | ||||||||
\(280\) | −3.37110 | −0.201462 | ||||||||
\(281\) | −8.23815 | −0.491447 | −0.245724 | − | 0.969340i | \(-0.579026\pi\) | ||||
−0.245724 | + | 0.969340i | \(0.579026\pi\) | |||||||
\(282\) | 3.19020 | 0.189973 | ||||||||
\(283\) | 19.0525 | 1.13255 | 0.566277 | − | 0.824215i | \(-0.308383\pi\) | ||||
0.566277 | + | 0.824215i | \(0.308383\pi\) | |||||||
\(284\) | −1.53144 | −0.0908741 | ||||||||
\(285\) | −1.00258 | −0.0593877 | ||||||||
\(286\) | −20.7887 | −1.22926 | ||||||||
\(287\) | 2.27743 | 0.134432 | ||||||||
\(288\) | 6.81644 | 0.401662 | ||||||||
\(289\) | 11.4649 | 0.674405 | ||||||||
\(290\) | 43.7868 | 2.57125 | ||||||||
\(291\) | −6.81283 | −0.399375 | ||||||||
\(292\) | 22.4895 | 1.31610 | ||||||||
\(293\) | 14.1130 | 0.824490 | 0.412245 | − | 0.911073i | \(-0.364745\pi\) | ||||
0.412245 | + | 0.911073i | \(0.364745\pi\) | |||||||
\(294\) | 1.85290 | 0.108063 | ||||||||
\(295\) | 46.7398 | 2.72129 | ||||||||
\(296\) | 7.75701 | 0.450867 | ||||||||
\(297\) | −4.69097 | −0.272198 | ||||||||
\(298\) | 33.0439 | 1.91418 | ||||||||
\(299\) | −14.0769 | −0.814090 | ||||||||
\(300\) | −7.60337 | −0.438981 | ||||||||
\(301\) | 5.60881 | 0.323287 | ||||||||
\(302\) | −17.3356 | −0.997550 | ||||||||
\(303\) | 13.6015 | 0.781389 | ||||||||
\(304\) | 1.50296 | 0.0862007 | ||||||||
\(305\) | −34.4601 | −1.97318 | ||||||||
\(306\) | 9.88569 | 0.565128 | ||||||||
\(307\) | 3.92129 | 0.223800 | 0.111900 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111900 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(308\) | 6.72332 | 0.383097 | ||||||||
\(309\) | 4.83718 | 0.275177 | ||||||||
\(310\) | 5.61019 | 0.318638 | ||||||||
\(311\) | −2.79178 | −0.158307 | −0.0791536 | − | 0.996862i | \(-0.525222\pi\) | ||||
−0.0791536 | + | 0.996862i | \(0.525222\pi\) | |||||||
\(312\) | −2.51165 | −0.142194 | ||||||||
\(313\) | 3.95575 | 0.223592 | 0.111796 | − | 0.993731i | \(-0.464340\pi\) | ||||
0.111796 | + | 0.993731i | \(0.464340\pi\) | |||||||
\(314\) | 43.2591 | 2.44125 | ||||||||
\(315\) | −3.21014 | −0.180871 | ||||||||
\(316\) | −12.7948 | −0.719765 | ||||||||
\(317\) | 5.47919 | 0.307742 | 0.153871 | − | 0.988091i | \(-0.450826\pi\) | ||||
0.153871 | + | 0.988091i | \(0.450826\pi\) | |||||||
\(318\) | 7.14417 | 0.400625 | ||||||||
\(319\) | 34.5327 | 1.93346 | ||||||||
\(320\) | 9.64838 | 0.539361 | ||||||||
\(321\) | 12.9339 | 0.721901 | ||||||||
\(322\) | 10.9056 | 0.607745 | ||||||||
\(323\) | 1.66629 | 0.0927147 | ||||||||
\(324\) | 1.43325 | 0.0796248 | ||||||||
\(325\) | 12.6881 | 0.703809 | ||||||||
\(326\) | −35.0713 | −1.94242 | ||||||||
\(327\) | −5.11701 | −0.282971 | ||||||||
\(328\) | 2.39162 | 0.132055 | ||||||||
\(329\) | 1.72173 | 0.0949220 | ||||||||
\(330\) | −27.9023 | −1.53597 | ||||||||
\(331\) | 2.77529 | 0.152544 | 0.0762719 | − | 0.997087i | \(-0.475698\pi\) | ||||
0.0762719 | + | 0.997087i | \(0.475698\pi\) | |||||||
\(332\) | 18.3183 | 1.00535 | ||||||||
\(333\) | 7.38664 | 0.404785 | ||||||||
\(334\) | −11.9248 | −0.652496 | ||||||||
\(335\) | 24.9322 | 1.36219 | ||||||||
\(336\) | 4.81230 | 0.262532 | ||||||||
\(337\) | −26.2917 | −1.43220 | −0.716101 | − | 0.697997i | \(-0.754075\pi\) | ||||
−0.716101 | + | 0.697997i | \(0.754075\pi\) | |||||||
\(338\) | 13.4885 | 0.733677 | ||||||||
\(339\) | −13.5759 | −0.737339 | ||||||||
\(340\) | 24.5471 | 1.33125 | ||||||||
\(341\) | 4.42450 | 0.239600 | ||||||||
\(342\) | 0.578692 | 0.0312921 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.89004 | 0.317570 | ||||||||
\(345\) | −18.8939 | −1.01721 | ||||||||
\(346\) | 29.2093 | 1.57030 | ||||||||
\(347\) | −30.0569 | −1.61354 | −0.806769 | − | 0.590867i | \(-0.798786\pi\) | ||||
−0.806769 | + | 0.590867i | \(0.798786\pi\) | |||||||
\(348\) | −10.5509 | −0.565586 | ||||||||
\(349\) | −10.6376 | −0.569417 | −0.284708 | − | 0.958614i | \(-0.591897\pi\) | ||||
−0.284708 | + | 0.958614i | \(0.591897\pi\) | |||||||
\(350\) | −9.82965 | −0.525417 | ||||||||
\(351\) | −2.39172 | −0.127661 | ||||||||
\(352\) | 31.9757 | 1.70431 | ||||||||
\(353\) | −22.0385 | −1.17299 | −0.586495 | − | 0.809953i | \(-0.699493\pi\) | ||||
−0.586495 | + | 0.809953i | \(0.699493\pi\) | |||||||
\(354\) | −26.9783 | −1.43388 | ||||||||
\(355\) | 3.43007 | 0.182049 | ||||||||
\(356\) | 26.8173 | 1.42131 | ||||||||
\(357\) | 5.33525 | 0.282371 | ||||||||
\(358\) | 13.2461 | 0.700080 | ||||||||
\(359\) | 2.56691 | 0.135476 | 0.0677382 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677382 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(360\) | −3.37110 | −0.177672 | ||||||||
\(361\) | −18.9025 | −0.994866 | ||||||||
\(362\) | 16.8716 | 0.886750 | ||||||||
\(363\) | −11.0052 | −0.577625 | ||||||||
\(364\) | 3.42793 | 0.179672 | ||||||||
\(365\) | −50.3714 | −2.63656 | ||||||||
\(366\) | 19.8905 | 1.03969 | ||||||||
\(367\) | 5.51924 | 0.288102 | 0.144051 | − | 0.989570i | \(-0.453987\pi\) | ||||
0.144051 | + | 0.989570i | \(0.453987\pi\) | |||||||
\(368\) | 28.3237 | 1.47647 | ||||||||
\(369\) | 2.27743 | 0.118558 | ||||||||
\(370\) | 43.9363 | 2.28414 | ||||||||
\(371\) | 3.85567 | 0.200176 | ||||||||
\(372\) | −1.35183 | −0.0700891 | ||||||||
\(373\) | −4.48940 | −0.232453 | −0.116226 | − | 0.993223i | \(-0.537080\pi\) | ||||
−0.116226 | + | 0.993223i | \(0.537080\pi\) | |||||||
\(374\) | 46.3735 | 2.39792 | ||||||||
\(375\) | 0.979095 | 0.0505602 | ||||||||
\(376\) | 1.80806 | 0.0932434 | ||||||||
\(377\) | 17.6067 | 0.906792 | ||||||||
\(378\) | 1.85290 | 0.0953030 | ||||||||
\(379\) | 31.9282 | 1.64004 | 0.820021 | − | 0.572334i | \(-0.193962\pi\) | ||||
0.820021 | + | 0.572334i | \(0.193962\pi\) | |||||||
\(380\) | 1.43694 | 0.0737136 | ||||||||
\(381\) | −17.8346 | −0.913694 | ||||||||
\(382\) | 36.3117 | 1.85787 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 8.06380 | 0.411504 | ||||||||
\(385\) | −15.0587 | −0.767462 | ||||||||
\(386\) | 9.60576 | 0.488920 | ||||||||
\(387\) | 5.60881 | 0.285112 | ||||||||
\(388\) | 9.76445 | 0.495715 | ||||||||
\(389\) | 25.8081 | 1.30852 | 0.654260 | − | 0.756270i | \(-0.272980\pi\) | ||||
0.654260 | + | 0.756270i | \(0.272980\pi\) | |||||||
\(390\) | −14.2262 | −0.720369 | ||||||||
\(391\) | 31.4016 | 1.58805 | ||||||||
\(392\) | 1.05014 | 0.0530401 | ||||||||
\(393\) | 21.6482 | 1.09201 | ||||||||
\(394\) | −30.9961 | −1.56156 | ||||||||
\(395\) | 28.6575 | 1.44191 | ||||||||
\(396\) | 6.72332 | 0.337859 | ||||||||
\(397\) | −9.61054 | −0.482339 | −0.241170 | − | 0.970483i | \(-0.577531\pi\) | ||||
−0.241170 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(398\) | −38.3587 | −1.92275 | ||||||||
\(399\) | 0.312316 | 0.0156354 | ||||||||
\(400\) | −25.5292 | −1.27646 | ||||||||
\(401\) | −11.7868 | −0.588606 | −0.294303 | − | 0.955712i | \(-0.595087\pi\) | ||||
−0.294303 | + | 0.955712i | \(0.595087\pi\) | |||||||
\(402\) | −14.3909 | −0.717754 | ||||||||
\(403\) | 2.25586 | 0.112372 | ||||||||
\(404\) | −19.4944 | −0.969881 | ||||||||
\(405\) | −3.21014 | −0.159513 | ||||||||
\(406\) | −13.6402 | −0.676950 | ||||||||
\(407\) | 34.6505 | 1.71756 | ||||||||
\(408\) | 5.60276 | 0.277378 | ||||||||
\(409\) | 20.1698 | 0.997333 | 0.498667 | − | 0.866794i | \(-0.333823\pi\) | ||||
0.498667 | + | 0.866794i | \(0.333823\pi\) | |||||||
\(410\) | 13.5463 | 0.669005 | ||||||||
\(411\) | 2.09823 | 0.103498 | ||||||||
\(412\) | −6.93286 | −0.341558 | ||||||||
\(413\) | −14.5600 | −0.716453 | ||||||||
\(414\) | 10.9056 | 0.535981 | ||||||||
\(415\) | −41.0287 | −2.01402 | ||||||||
\(416\) | 16.3030 | 0.799322 | ||||||||
\(417\) | 18.1952 | 0.891024 | ||||||||
\(418\) | 2.71463 | 0.132777 | ||||||||
\(419\) | 10.2205 | 0.499303 | 0.249651 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249651 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(420\) | 4.60092 | 0.224502 | ||||||||
\(421\) | 8.76855 | 0.427353 | 0.213677 | − | 0.976904i | \(-0.431456\pi\) | ||||
0.213677 | + | 0.976904i | \(0.431456\pi\) | |||||||
\(422\) | −31.1442 | −1.51608 | ||||||||
\(423\) | 1.72173 | 0.0837134 | ||||||||
\(424\) | 4.04899 | 0.196636 | ||||||||
\(425\) | −28.3035 | −1.37292 | ||||||||
\(426\) | −1.97985 | −0.0959238 | ||||||||
\(427\) | 10.7348 | 0.519492 | ||||||||
\(428\) | −18.5375 | −0.896043 | ||||||||
\(429\) | −11.2195 | −0.541683 | ||||||||
\(430\) | 33.3616 | 1.60884 | ||||||||
\(431\) | 20.8702 | 1.00528 | 0.502642 | − | 0.864495i | \(-0.332362\pi\) | ||||
0.502642 | + | 0.864495i | \(0.332362\pi\) | |||||||
\(432\) | 4.81230 | 0.231532 | ||||||||
\(433\) | −4.67650 | −0.224738 | −0.112369 | − | 0.993667i | \(-0.535844\pi\) | ||||
−0.112369 | + | 0.993667i | \(0.535844\pi\) | |||||||
\(434\) | −1.74765 | −0.0838897 | ||||||||
\(435\) | 23.6315 | 1.13304 | ||||||||
\(436\) | 7.33394 | 0.351232 | ||||||||
\(437\) | 1.83820 | 0.0879329 | ||||||||
\(438\) | 29.0745 | 1.38923 | ||||||||
\(439\) | −25.5135 | −1.21769 | −0.608847 | − | 0.793288i | \(-0.708368\pi\) | ||||
−0.608847 | + | 0.793288i | \(0.708368\pi\) | |||||||
\(440\) | −15.8137 | −0.753890 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 23.6439 | 1.12462 | ||||||||
\(443\) | −28.1711 | −1.33845 | −0.669224 | − | 0.743060i | \(-0.733373\pi\) | ||||
−0.669224 | + | 0.743060i | \(0.733373\pi\) | |||||||
\(444\) | −10.5869 | −0.502431 | ||||||||
\(445\) | −60.0645 | −2.84733 | ||||||||
\(446\) | 39.5533 | 1.87290 | ||||||||
\(447\) | 17.8336 | 0.843499 | ||||||||
\(448\) | −3.00559 | −0.142001 | ||||||||
\(449\) | −32.6607 | −1.54135 | −0.770677 | − | 0.637226i | \(-0.780082\pi\) | ||||
−0.770677 | + | 0.637226i | \(0.780082\pi\) | |||||||
\(450\) | −9.82965 | −0.463374 | ||||||||
\(451\) | 10.6834 | 0.503059 | ||||||||
\(452\) | 19.4575 | 0.915205 | ||||||||
\(453\) | −9.35590 | −0.439578 | ||||||||
\(454\) | −6.90720 | −0.324171 | ||||||||
\(455\) | −7.67777 | −0.359939 | ||||||||
\(456\) | 0.327976 | 0.0153589 | ||||||||
\(457\) | 24.4618 | 1.14428 | 0.572138 | − | 0.820158i | \(-0.306114\pi\) | ||||
0.572138 | + | 0.820158i | \(0.306114\pi\) | |||||||
\(458\) | 26.6835 | 1.24684 | ||||||||
\(459\) | 5.33525 | 0.249028 | ||||||||
\(460\) | 27.0796 | 1.26259 | ||||||||
\(461\) | 26.0424 | 1.21292 | 0.606459 | − | 0.795115i | \(-0.292590\pi\) | ||||
0.606459 | + | 0.795115i | \(0.292590\pi\) | |||||||
\(462\) | 8.69191 | 0.404384 | ||||||||
\(463\) | 29.2747 | 1.36051 | 0.680256 | − | 0.732975i | \(-0.261869\pi\) | ||||
0.680256 | + | 0.732975i | \(0.261869\pi\) | |||||||
\(464\) | −35.4258 | −1.64460 | ||||||||
\(465\) | 3.02779 | 0.140410 | ||||||||
\(466\) | −49.9730 | −2.31495 | ||||||||
\(467\) | 7.39736 | 0.342309 | 0.171155 | − | 0.985244i | \(-0.445250\pi\) | ||||
0.171155 | + | 0.985244i | \(0.445250\pi\) | |||||||
\(468\) | 3.42793 | 0.158456 | ||||||||
\(469\) | −7.76670 | −0.358633 | ||||||||
\(470\) | 10.2410 | 0.472381 | ||||||||
\(471\) | 23.3467 | 1.07576 | ||||||||
\(472\) | −15.2901 | −0.703783 | ||||||||
\(473\) | 26.3108 | 1.20977 | ||||||||
\(474\) | −16.5412 | −0.759761 | ||||||||
\(475\) | −1.65684 | −0.0760210 | ||||||||
\(476\) | −7.64672 | −0.350487 | ||||||||
\(477\) | 3.85567 | 0.176539 | ||||||||
\(478\) | 16.1879 | 0.740418 | ||||||||
\(479\) | −27.2961 | −1.24719 | −0.623596 | − | 0.781746i | \(-0.714329\pi\) | ||||
−0.623596 | + | 0.781746i | \(0.714329\pi\) | |||||||
\(480\) | 21.8817 | 0.998759 | ||||||||
\(481\) | 17.6668 | 0.805537 | ||||||||
\(482\) | 11.2856 | 0.514045 | ||||||||
\(483\) | 5.88569 | 0.267808 | ||||||||
\(484\) | 15.7732 | 0.716964 | ||||||||
\(485\) | −21.8701 | −0.993071 | ||||||||
\(486\) | 1.85290 | 0.0840493 | ||||||||
\(487\) | −3.17351 | −0.143805 | −0.0719026 | − | 0.997412i | \(-0.522907\pi\) | ||||
−0.0719026 | + | 0.997412i | \(0.522907\pi\) | |||||||
\(488\) | 11.2730 | 0.510306 | ||||||||
\(489\) | −18.9277 | −0.855942 | ||||||||
\(490\) | 5.94808 | 0.268707 | ||||||||
\(491\) | 21.4652 | 0.968711 | 0.484355 | − | 0.874871i | \(-0.339054\pi\) | ||||
0.484355 | + | 0.874871i | \(0.339054\pi\) | |||||||
\(492\) | −3.26411 | −0.147158 | ||||||||
\(493\) | −39.2755 | −1.76888 | ||||||||
\(494\) | 1.38407 | 0.0622723 | ||||||||
\(495\) | −15.0587 | −0.676837 | ||||||||
\(496\) | −4.53893 | −0.203804 | ||||||||
\(497\) | −1.06851 | −0.0479292 | ||||||||
\(498\) | 23.6819 | 1.06121 | ||||||||
\(499\) | 42.1584 | 1.88727 | 0.943634 | − | 0.330990i | \(-0.107383\pi\) | ||||
0.943634 | + | 0.330990i | \(0.107383\pi\) | |||||||
\(500\) | −1.40328 | −0.0627568 | ||||||||
\(501\) | −6.43574 | −0.287528 | ||||||||
\(502\) | 46.7005 | 2.08435 | ||||||||
\(503\) | −24.3838 | −1.08722 | −0.543610 | − | 0.839338i | \(-0.682943\pi\) | ||||
−0.543610 | + | 0.839338i | \(0.682943\pi\) | |||||||
\(504\) | 1.05014 | 0.0467769 | ||||||||
\(505\) | 43.6629 | 1.94297 | ||||||||
\(506\) | 51.1579 | 2.27425 | ||||||||
\(507\) | 7.27966 | 0.323301 | ||||||||
\(508\) | 25.5614 | 1.13410 | ||||||||
\(509\) | −11.0516 | −0.489854 | −0.244927 | − | 0.969541i | \(-0.578764\pi\) | ||||
−0.244927 | + | 0.969541i | \(0.578764\pi\) | |||||||
\(510\) | 31.7345 | 1.40523 | ||||||||
\(511\) | 15.6913 | 0.694144 | ||||||||
\(512\) | −22.6956 | −1.00301 | ||||||||
\(513\) | 0.312316 | 0.0137891 | ||||||||
\(514\) | −13.3136 | −0.587240 | ||||||||
\(515\) | 15.5280 | 0.684246 | ||||||||
\(516\) | −8.03881 | −0.353889 | ||||||||
\(517\) | 8.07659 | 0.355208 | ||||||||
\(518\) | −13.6867 | −0.601360 | ||||||||
\(519\) | 15.7641 | 0.691966 | ||||||||
\(520\) | −8.06273 | −0.353574 | ||||||||
\(521\) | 38.0117 | 1.66532 | 0.832662 | − | 0.553781i | \(-0.186816\pi\) | ||||
0.832662 | + | 0.553781i | \(0.186816\pi\) | |||||||
\(522\) | −13.6402 | −0.597014 | ||||||||
\(523\) | 16.8756 | 0.737917 | 0.368959 | − | 0.929446i | \(-0.379714\pi\) | ||||
0.368959 | + | 0.929446i | \(0.379714\pi\) | |||||||
\(524\) | −31.0272 | −1.35543 | ||||||||
\(525\) | −5.30500 | −0.231529 | ||||||||
\(526\) | −2.00211 | −0.0872962 | ||||||||
\(527\) | −5.03218 | −0.219205 | ||||||||
\(528\) | 22.5744 | 0.982423 | ||||||||
\(529\) | 11.6413 | 0.506144 | ||||||||
\(530\) | 22.9338 | 0.996181 | ||||||||
\(531\) | −14.5600 | −0.631852 | ||||||||
\(532\) | −0.447626 | −0.0194071 | ||||||||
\(533\) | 5.44698 | 0.235935 | ||||||||
\(534\) | 34.6694 | 1.50029 | ||||||||
\(535\) | 41.5197 | 1.79505 | ||||||||
\(536\) | −8.15612 | −0.352291 | ||||||||
\(537\) | 7.14886 | 0.308496 | ||||||||
\(538\) | 3.70762 | 0.159847 | ||||||||
\(539\) | 4.69097 | 0.202055 | ||||||||
\(540\) | 4.60092 | 0.197992 | ||||||||
\(541\) | 31.3415 | 1.34748 | 0.673739 | − | 0.738970i | \(-0.264687\pi\) | ||||
0.673739 | + | 0.738970i | \(0.264687\pi\) | |||||||
\(542\) | −42.3168 | −1.81766 | ||||||||
\(543\) | 9.10549 | 0.390754 | ||||||||
\(544\) | −36.3674 | −1.55924 | ||||||||
\(545\) | −16.4263 | −0.703627 | ||||||||
\(546\) | 4.43163 | 0.189656 | ||||||||
\(547\) | 17.4234 | 0.744970 | 0.372485 | − | 0.928038i | \(-0.378506\pi\) | ||||
0.372485 | + | 0.928038i | \(0.378506\pi\) | |||||||
\(548\) | −3.00728 | −0.128465 | ||||||||
\(549\) | 10.7348 | 0.458149 | ||||||||
\(550\) | −46.1106 | −1.96616 | ||||||||
\(551\) | −2.29912 | −0.0979459 | ||||||||
\(552\) | 6.18079 | 0.263072 | ||||||||
\(553\) | −8.92717 | −0.379622 | ||||||||
\(554\) | −32.7310 | −1.39061 | ||||||||
\(555\) | 23.7122 | 1.00652 | ||||||||
\(556\) | −26.0782 | −1.10596 | ||||||||
\(557\) | −0.331868 | −0.0140617 | −0.00703085 | − | 0.999975i | \(-0.502238\pi\) | ||||
−0.00703085 | + | 0.999975i | \(0.502238\pi\) | |||||||
\(558\) | −1.74765 | −0.0739838 | ||||||||
\(559\) | 13.4147 | 0.567383 | ||||||||
\(560\) | 15.4482 | 0.652804 | ||||||||
\(561\) | 25.0275 | 1.05666 | ||||||||
\(562\) | 15.2645 | 0.643894 | ||||||||
\(563\) | −43.0228 | −1.81319 | −0.906597 | − | 0.421997i | \(-0.861329\pi\) | ||||
−0.906597 | + | 0.421997i | \(0.861329\pi\) | |||||||
\(564\) | −2.46766 | −0.103907 | ||||||||
\(565\) | −43.5804 | −1.83344 | ||||||||
\(566\) | −35.3024 | −1.48387 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −1.12209 | −0.0470817 | ||||||||
\(569\) | 41.3196 | 1.73221 | 0.866104 | − | 0.499864i | \(-0.166617\pi\) | ||||
0.866104 | + | 0.499864i | \(0.166617\pi\) | |||||||
\(570\) | 1.85768 | 0.0778097 | ||||||||
\(571\) | 2.11330 | 0.0884388 | 0.0442194 | − | 0.999022i | \(-0.485920\pi\) | ||||
0.0442194 | + | 0.999022i | \(0.485920\pi\) | |||||||
\(572\) | 16.0803 | 0.672352 | ||||||||
\(573\) | 19.5972 | 0.818684 | ||||||||
\(574\) | −4.21985 | −0.176133 | ||||||||
\(575\) | −31.2236 | −1.30211 | ||||||||
\(576\) | −3.00559 | −0.125233 | ||||||||
\(577\) | −32.0184 | −1.33294 | −0.666472 | − | 0.745530i | \(-0.732196\pi\) | ||||
−0.666472 | + | 0.745530i | \(0.732196\pi\) | |||||||
\(578\) | −21.2433 | −0.883605 | ||||||||
\(579\) | 5.18417 | 0.215447 | ||||||||
\(580\) | −33.8697 | −1.40636 | ||||||||
\(581\) | 12.7810 | 0.530244 | ||||||||
\(582\) | 12.6235 | 0.523261 | ||||||||
\(583\) | 18.0868 | 0.749080 | ||||||||
\(584\) | 16.4781 | 0.681869 | ||||||||
\(585\) | −7.67777 | −0.317437 | ||||||||
\(586\) | −26.1500 | −1.08025 | ||||||||
\(587\) | 43.7137 | 1.80426 | 0.902128 | − | 0.431469i | \(-0.142005\pi\) | ||||
0.902128 | + | 0.431469i | \(0.142005\pi\) | |||||||
\(588\) | −1.43325 | −0.0591061 | ||||||||
\(589\) | −0.294575 | −0.0121378 | ||||||||
\(590\) | −86.6042 | −3.56544 | ||||||||
\(591\) | −16.7284 | −0.688116 | ||||||||
\(592\) | −35.5467 | −1.46096 | ||||||||
\(593\) | 23.8069 | 0.977633 | 0.488816 | − | 0.872387i | \(-0.337429\pi\) | ||||
0.488816 | + | 0.872387i | \(0.337429\pi\) | |||||||
\(594\) | 8.69191 | 0.356634 | ||||||||
\(595\) | 17.1269 | 0.702134 | ||||||||
\(596\) | −25.5599 | −1.04697 | ||||||||
\(597\) | −20.7020 | −0.847276 | ||||||||
\(598\) | 26.0832 | 1.06662 | ||||||||
\(599\) | 26.4572 | 1.08101 | 0.540506 | − | 0.841340i | \(-0.318233\pi\) | ||||
0.540506 | + | 0.841340i | \(0.318233\pi\) | |||||||
\(600\) | −5.57099 | −0.227435 | ||||||||
\(601\) | −42.2007 | −1.72140 | −0.860702 | − | 0.509109i | \(-0.829975\pi\) | ||||
−0.860702 | + | 0.509109i | \(0.829975\pi\) | |||||||
\(602\) | −10.3926 | −0.423570 | ||||||||
\(603\) | −7.76670 | −0.316284 | ||||||||
\(604\) | 13.4093 | 0.545617 | ||||||||
\(605\) | −35.3283 | −1.43630 | ||||||||
\(606\) | −25.2023 | −1.02377 | ||||||||
\(607\) | 24.0184 | 0.974879 | 0.487439 | − | 0.873157i | \(-0.337931\pi\) | ||||
0.487439 | + | 0.873157i | \(0.337931\pi\) | |||||||
\(608\) | −2.12889 | −0.0863377 | ||||||||
\(609\) | −7.36152 | −0.298304 | ||||||||
\(610\) | 63.8513 | 2.58526 | ||||||||
\(611\) | 4.11790 | 0.166593 | ||||||||
\(612\) | −7.64672 | −0.309100 | ||||||||
\(613\) | 43.6832 | 1.76435 | 0.882173 | − | 0.470925i | \(-0.156080\pi\) | ||||
0.882173 | + | 0.470925i | \(0.156080\pi\) | |||||||
\(614\) | −7.26576 | −0.293222 | ||||||||
\(615\) | 7.31086 | 0.294802 | ||||||||
\(616\) | 4.92618 | 0.198481 | ||||||||
\(617\) | −3.55895 | −0.143278 | −0.0716389 | − | 0.997431i | \(-0.522823\pi\) | ||||
−0.0716389 | + | 0.997431i | \(0.522823\pi\) | |||||||
\(618\) | −8.96281 | −0.360537 | ||||||||
\(619\) | −37.1304 | −1.49240 | −0.746199 | − | 0.665723i | \(-0.768123\pi\) | ||||
−0.746199 | + | 0.665723i | \(0.768123\pi\) | |||||||
\(620\) | −4.33956 | −0.174281 | ||||||||
\(621\) | 5.88569 | 0.236184 | ||||||||
\(622\) | 5.17289 | 0.207414 | ||||||||
\(623\) | 18.7109 | 0.749635 | ||||||||
\(624\) | 11.5097 | 0.460756 | ||||||||
\(625\) | −23.3820 | −0.935279 | ||||||||
\(626\) | −7.32961 | −0.292950 | ||||||||
\(627\) | 1.46507 | 0.0585092 | ||||||||
\(628\) | −33.4616 | −1.33526 | ||||||||
\(629\) | −39.4096 | −1.57136 | ||||||||
\(630\) | 5.94808 | 0.236977 | ||||||||
\(631\) | −43.8209 | −1.74448 | −0.872240 | − | 0.489077i | \(-0.837334\pi\) | ||||
−0.872240 | + | 0.489077i | \(0.837334\pi\) | |||||||
\(632\) | −9.37477 | −0.372908 | ||||||||
\(633\) | −16.8083 | −0.668071 | ||||||||
\(634\) | −10.1524 | −0.403204 | ||||||||
\(635\) | −57.2515 | −2.27196 | ||||||||
\(636\) | −5.52612 | −0.219125 | ||||||||
\(637\) | 2.39172 | 0.0947636 | ||||||||
\(638\) | −63.9857 | −2.53322 | ||||||||
\(639\) | −1.06851 | −0.0422696 | ||||||||
\(640\) | 25.8859 | 1.02323 | ||||||||
\(641\) | 27.9201 | 1.10278 | 0.551389 | − | 0.834248i | \(-0.314098\pi\) | ||||
0.551389 | + | 0.834248i | \(0.314098\pi\) | |||||||
\(642\) | −23.9653 | −0.945834 | ||||||||
\(643\) | −4.19824 | −0.165562 | −0.0827812 | − | 0.996568i | \(-0.526380\pi\) | ||||
−0.0827812 | + | 0.996568i | \(0.526380\pi\) | |||||||
\(644\) | −8.43564 | −0.332411 | ||||||||
\(645\) | 18.0051 | 0.708949 | ||||||||
\(646\) | −3.08747 | −0.121475 | ||||||||
\(647\) | −37.2669 | −1.46511 | −0.732557 | − | 0.680706i | \(-0.761673\pi\) | ||||
−0.732557 | + | 0.680706i | \(0.761673\pi\) | |||||||
\(648\) | 1.05014 | 0.0412534 | ||||||||
\(649\) | −68.3008 | −2.68104 | ||||||||
\(650\) | −23.5098 | −0.922130 | ||||||||
\(651\) | −0.943195 | −0.0369667 | ||||||||
\(652\) | 27.1281 | 1.06242 | ||||||||
\(653\) | −21.1806 | −0.828862 | −0.414431 | − | 0.910081i | \(-0.636019\pi\) | ||||
−0.414431 | + | 0.910081i | \(0.636019\pi\) | |||||||
\(654\) | 9.48132 | 0.370749 | ||||||||
\(655\) | 69.4939 | 2.71535 | ||||||||
\(656\) | −10.9597 | −0.427903 | ||||||||
\(657\) | 15.6913 | 0.612177 | ||||||||
\(658\) | −3.19020 | −0.124367 | ||||||||
\(659\) | 2.13751 | 0.0832657 | 0.0416328 | − | 0.999133i | \(-0.486744\pi\) | ||||
0.0416328 | + | 0.999133i | \(0.486744\pi\) | |||||||
\(660\) | 21.5828 | 0.840109 | ||||||||
\(661\) | 18.8595 | 0.733551 | 0.366775 | − | 0.930310i | \(-0.380462\pi\) | ||||
0.366775 | + | 0.930310i | \(0.380462\pi\) | |||||||
\(662\) | −5.14234 | −0.199863 | ||||||||
\(663\) | 12.7604 | 0.495575 | ||||||||
\(664\) | 13.4218 | 0.520867 | ||||||||
\(665\) | 1.00258 | 0.0388784 | ||||||||
\(666\) | −13.6867 | −0.530350 | ||||||||
\(667\) | −43.3276 | −1.67765 | ||||||||
\(668\) | 9.22399 | 0.356887 | ||||||||
\(669\) | 21.3467 | 0.825309 | ||||||||
\(670\) | −46.1969 | −1.78474 | ||||||||
\(671\) | 50.3566 | 1.94399 | ||||||||
\(672\) | −6.81644 | −0.262950 | ||||||||
\(673\) | −14.0290 | −0.540777 | −0.270389 | − | 0.962751i | \(-0.587152\pi\) | ||||
−0.270389 | + | 0.962751i | \(0.587152\pi\) | |||||||
\(674\) | 48.7160 | 1.87647 | ||||||||
\(675\) | −5.30500 | −0.204190 | ||||||||
\(676\) | −10.4335 | −0.401290 | ||||||||
\(677\) | 34.0790 | 1.30976 | 0.654881 | − | 0.755732i | \(-0.272719\pi\) | ||||
0.654881 | + | 0.755732i | \(0.272719\pi\) | |||||||
\(678\) | 25.1547 | 0.966061 | ||||||||
\(679\) | 6.81283 | 0.261452 | ||||||||
\(680\) | 17.9856 | 0.689718 | ||||||||
\(681\) | −3.72777 | −0.142849 | ||||||||
\(682\) | −8.19817 | −0.313924 | ||||||||
\(683\) | 36.4699 | 1.39548 | 0.697740 | − | 0.716351i | \(-0.254189\pi\) | ||||
0.697740 | + | 0.716351i | \(0.254189\pi\) | |||||||
\(684\) | −0.447626 | −0.0171154 | ||||||||
\(685\) | 6.73562 | 0.257355 | ||||||||
\(686\) | −1.85290 | −0.0707441 | ||||||||
\(687\) | 14.4009 | 0.549429 | ||||||||
\(688\) | −26.9913 | −1.02903 | ||||||||
\(689\) | 9.22169 | 0.351318 | ||||||||
\(690\) | 35.0085 | 1.33275 | ||||||||
\(691\) | −7.13401 | −0.271390 | −0.135695 | − | 0.990751i | \(-0.543327\pi\) | ||||
−0.135695 | + | 0.990751i | \(0.543327\pi\) | |||||||
\(692\) | −22.5938 | −0.858888 | ||||||||
\(693\) | 4.69097 | 0.178195 | ||||||||
\(694\) | 55.6924 | 2.11406 | ||||||||
\(695\) | 58.4092 | 2.21559 | ||||||||
\(696\) | −7.73062 | −0.293028 | ||||||||
\(697\) | −12.1506 | −0.460238 | ||||||||
\(698\) | 19.7104 | 0.746050 | ||||||||
\(699\) | −26.9701 | −1.02010 | ||||||||
\(700\) | 7.60337 | 0.287380 | ||||||||
\(701\) | −12.1932 | −0.460533 | −0.230266 | − | 0.973128i | \(-0.573960\pi\) | ||||
−0.230266 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(702\) | 4.43163 | 0.167261 | ||||||||
\(703\) | −2.30697 | −0.0870090 | ||||||||
\(704\) | −14.0992 | −0.531382 | ||||||||
\(705\) | 5.52699 | 0.208159 | ||||||||
\(706\) | 40.8352 | 1.53685 | ||||||||
\(707\) | −13.6015 | −0.511539 | ||||||||
\(708\) | 20.8681 | 0.784272 | ||||||||
\(709\) | 19.9645 | 0.749782 | 0.374891 | − | 0.927069i | \(-0.377680\pi\) | ||||
0.374891 | + | 0.927069i | \(0.377680\pi\) | |||||||
\(710\) | −6.35558 | −0.238521 | ||||||||
\(711\) | −8.92717 | −0.334795 | ||||||||
\(712\) | 19.6490 | 0.736378 | ||||||||
\(713\) | −5.55135 | −0.207900 | ||||||||
\(714\) | −9.88569 | −0.369963 | ||||||||
\(715\) | −36.0162 | −1.34693 | ||||||||
\(716\) | −10.2461 | −0.382914 | ||||||||
\(717\) | 8.73652 | 0.326271 | ||||||||
\(718\) | −4.75624 | −0.177501 | ||||||||
\(719\) | 1.07483 | 0.0400843 | 0.0200422 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200422 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(720\) | 15.4482 | 0.575719 | ||||||||
\(721\) | −4.83718 | −0.180146 | ||||||||
\(722\) | 35.0244 | 1.30347 | ||||||||
\(723\) | 6.09077 | 0.226518 | ||||||||
\(724\) | −13.0504 | −0.485014 | ||||||||
\(725\) | 39.0528 | 1.45039 | ||||||||
\(726\) | 20.3916 | 0.756804 | ||||||||
\(727\) | −21.8309 | −0.809665 | −0.404832 | − | 0.914391i | \(-0.632670\pi\) | ||||
−0.404832 | + | 0.914391i | \(0.632670\pi\) | |||||||
\(728\) | 2.51165 | 0.0930878 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 93.3333 | 3.45442 | ||||||||
\(731\) | −29.9244 | −1.10679 | ||||||||
\(732\) | −15.3856 | −0.568667 | ||||||||
\(733\) | 43.6954 | 1.61393 | 0.806964 | − | 0.590601i | \(-0.201109\pi\) | ||||
0.806964 | + | 0.590601i | \(0.201109\pi\) | |||||||
\(734\) | −10.2266 | −0.377471 | ||||||||
\(735\) | 3.21014 | 0.118408 | ||||||||
\(736\) | −40.1194 | −1.47882 | ||||||||
\(737\) | −36.4334 | −1.34204 | ||||||||
\(738\) | −4.21985 | −0.155335 | ||||||||
\(739\) | −10.7849 | −0.396729 | −0.198364 | − | 0.980128i | \(-0.563563\pi\) | ||||
−0.198364 | + | 0.980128i | \(0.563563\pi\) | |||||||
\(740\) | −33.9853 | −1.24933 | ||||||||
\(741\) | 0.746975 | 0.0274408 | ||||||||
\(742\) | −7.14417 | −0.262271 | ||||||||
\(743\) | 0.991731 | 0.0363831 | 0.0181915 | − | 0.999835i | \(-0.494209\pi\) | ||||
0.0181915 | + | 0.999835i | \(0.494209\pi\) | |||||||
\(744\) | −0.990486 | −0.0363130 | ||||||||
\(745\) | 57.2483 | 2.09741 | ||||||||
\(746\) | 8.31843 | 0.304559 | ||||||||
\(747\) | 12.7810 | 0.467631 | ||||||||
\(748\) | −35.8706 | −1.31156 | ||||||||
\(749\) | −12.9339 | −0.472595 | ||||||||
\(750\) | −1.81417 | −0.0662440 | ||||||||
\(751\) | −31.0574 | −1.13330 | −0.566651 | − | 0.823958i | \(-0.691761\pi\) | ||||
−0.566651 | + | 0.823958i | \(0.691761\pi\) | |||||||
\(752\) | −8.28548 | −0.302140 | ||||||||
\(753\) | 25.2040 | 0.918485 | ||||||||
\(754\) | −32.6235 | −1.18808 | ||||||||
\(755\) | −30.0337 | −1.09304 | ||||||||
\(756\) | −1.43325 | −0.0521266 | ||||||||
\(757\) | −22.7351 | −0.826322 | −0.413161 | − | 0.910658i | \(-0.635575\pi\) | ||||
−0.413161 | + | 0.910658i | \(0.635575\pi\) | |||||||
\(758\) | −59.1598 | −2.14878 | ||||||||
\(759\) | 27.6096 | 1.00216 | ||||||||
\(760\) | 1.05285 | 0.0381908 | ||||||||
\(761\) | 36.9060 | 1.33784 | 0.668920 | − | 0.743334i | \(-0.266757\pi\) | ||||
0.668920 | + | 0.743334i | \(0.266757\pi\) | |||||||
\(762\) | 33.0458 | 1.19712 | ||||||||
\(763\) | 5.11701 | 0.185248 | ||||||||
\(764\) | −28.0876 | −1.01617 | ||||||||
\(765\) | 17.1269 | 0.619224 | ||||||||
\(766\) | 1.85290 | 0.0669481 | ||||||||
\(767\) | −34.8236 | −1.25741 | ||||||||
\(768\) | −20.9526 | −0.756063 | ||||||||
\(769\) | −41.7437 | −1.50532 | −0.752659 | − | 0.658411i | \(-0.771229\pi\) | ||||
−0.752659 | + | 0.658411i | \(0.771229\pi\) | |||||||
\(770\) | 27.9023 | 1.00553 | ||||||||
\(771\) | −7.18529 | −0.258772 | ||||||||
\(772\) | −7.43019 | −0.267418 | ||||||||
\(773\) | 12.5894 | 0.452808 | 0.226404 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226404 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(774\) | −10.3926 | −0.373554 | ||||||||
\(775\) | 5.00365 | 0.179736 | ||||||||
\(776\) | 7.15442 | 0.256829 | ||||||||
\(777\) | −7.38664 | −0.264994 | ||||||||
\(778\) | −47.8198 | −1.71442 | ||||||||
\(779\) | −0.711278 | −0.0254842 | ||||||||
\(780\) | 11.0041 | 0.394011 | ||||||||
\(781\) | −5.01235 | −0.179356 | ||||||||
\(782\) | −58.1841 | −2.08066 | ||||||||
\(783\) | −7.36152 | −0.263079 | ||||||||
\(784\) | −4.81230 | −0.171868 | ||||||||
\(785\) | 74.9462 | 2.67494 | ||||||||
\(786\) | −40.1121 | −1.43075 | ||||||||
\(787\) | −6.94407 | −0.247530 | −0.123765 | − | 0.992312i | \(-0.539497\pi\) | ||||
−0.123765 | + | 0.992312i | \(0.539497\pi\) | |||||||
\(788\) | 23.9760 | 0.854108 | ||||||||
\(789\) | −1.08053 | −0.0384678 | ||||||||
\(790\) | −53.0995 | −1.88919 | ||||||||
\(791\) | 13.5759 | 0.482702 | ||||||||
\(792\) | 4.92618 | 0.175044 | ||||||||
\(793\) | 25.6746 | 0.911733 | ||||||||
\(794\) | 17.8074 | 0.631960 | ||||||||
\(795\) | 12.3772 | 0.438975 | ||||||||
\(796\) | 29.6710 | 1.05166 | ||||||||
\(797\) | −1.86467 | −0.0660499 | −0.0330249 | − | 0.999455i | \(-0.510514\pi\) | ||||
−0.0330249 | + | 0.999455i | \(0.510514\pi\) | |||||||
\(798\) | −0.578692 | −0.0204855 | ||||||||
\(799\) | −9.18586 | −0.324972 | ||||||||
\(800\) | 36.1612 | 1.27849 | ||||||||
\(801\) | 18.7109 | 0.661116 | ||||||||
\(802\) | 21.8398 | 0.771191 | ||||||||
\(803\) | 73.6077 | 2.59756 | ||||||||
\(804\) | 11.1316 | 0.392581 | ||||||||
\(805\) | 18.8939 | 0.665922 | ||||||||
\(806\) | −4.17989 | −0.147230 | ||||||||
\(807\) | 2.00098 | 0.0704377 | ||||||||
\(808\) | −14.2835 | −0.502493 | ||||||||
\(809\) | 8.82350 | 0.310218 | 0.155109 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155109 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(810\) | 5.94808 | 0.208994 | ||||||||
\(811\) | −46.5161 | −1.63340 | −0.816701 | − | 0.577061i | \(-0.804200\pi\) | ||||
−0.816701 | + | 0.577061i | \(0.804200\pi\) | |||||||
\(812\) | 10.5509 | 0.370263 | ||||||||
\(813\) | −22.8381 | −0.800968 | ||||||||
\(814\) | −64.2040 | −2.25035 | ||||||||
\(815\) | −60.7607 | −2.12835 | ||||||||
\(816\) | −25.6748 | −0.898798 | ||||||||
\(817\) | −1.75172 | −0.0612851 | ||||||||
\(818\) | −37.3727 | −1.30671 | ||||||||
\(819\) | 2.39172 | 0.0835736 | ||||||||
\(820\) | −10.4783 | −0.365917 | ||||||||
\(821\) | 35.3062 | 1.23220 | 0.616098 | − | 0.787670i | \(-0.288713\pi\) | ||||
0.616098 | + | 0.787670i | \(0.288713\pi\) | |||||||
\(822\) | −3.88782 | −0.135603 | ||||||||
\(823\) | 31.8375 | 1.10979 | 0.554893 | − | 0.831922i | \(-0.312759\pi\) | ||||
0.554893 | + | 0.831922i | \(0.312759\pi\) | |||||||
\(824\) | −5.07971 | −0.176960 | ||||||||
\(825\) | −24.8856 | −0.866406 | ||||||||
\(826\) | 26.9783 | 0.938696 | ||||||||
\(827\) | 1.29171 | 0.0449172 | 0.0224586 | − | 0.999748i | \(-0.492851\pi\) | ||||
0.0224586 | + | 0.999748i | \(0.492851\pi\) | |||||||
\(828\) | −8.43564 | −0.293159 | ||||||||
\(829\) | 53.0048 | 1.84093 | 0.920467 | − | 0.390821i | \(-0.127809\pi\) | ||||
0.920467 | + | 0.390821i | \(0.127809\pi\) | |||||||
\(830\) | 76.0221 | 2.63877 | ||||||||
\(831\) | −17.6647 | −0.612783 | ||||||||
\(832\) | −7.18855 | −0.249218 | ||||||||
\(833\) | −5.33525 | −0.184855 | ||||||||
\(834\) | −33.7140 | −1.16742 | ||||||||
\(835\) | −20.6596 | −0.714956 | ||||||||
\(836\) | −2.09980 | −0.0726232 | ||||||||
\(837\) | −0.943195 | −0.0326016 | ||||||||
\(838\) | −18.9375 | −0.654186 | ||||||||
\(839\) | 4.78091 | 0.165055 | 0.0825277 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825277 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(840\) | 3.37110 | 0.116314 | ||||||||
\(841\) | 25.1919 | 0.868686 | ||||||||
\(842\) | −16.2473 | −0.559918 | ||||||||
\(843\) | 8.23815 | 0.283737 | ||||||||
\(844\) | 24.0905 | 0.829228 | ||||||||
\(845\) | 23.3687 | 0.803908 | ||||||||
\(846\) | −3.19020 | −0.109681 | ||||||||
\(847\) | 11.0052 | 0.378144 | ||||||||
\(848\) | −18.5546 | −0.637168 | ||||||||
\(849\) | −19.0525 | −0.653880 | ||||||||
\(850\) | 52.4436 | 1.79880 | ||||||||
\(851\) | −43.4754 | −1.49032 | ||||||||
\(852\) | 1.53144 | 0.0524662 | ||||||||
\(853\) | 30.0506 | 1.02891 | 0.514457 | − | 0.857516i | \(-0.327994\pi\) | ||||
0.514457 | + | 0.857516i | \(0.327994\pi\) | |||||||
\(854\) | −19.8905 | −0.680639 | ||||||||
\(855\) | 1.00258 | 0.0342875 | ||||||||
\(856\) | −13.5824 | −0.464238 | ||||||||
\(857\) | 32.6428 | 1.11506 | 0.557529 | − | 0.830157i | \(-0.311749\pi\) | ||||
0.557529 | + | 0.830157i | \(0.311749\pi\) | |||||||
\(858\) | 20.7887 | 0.709713 | ||||||||
\(859\) | 41.5308 | 1.41701 | 0.708506 | − | 0.705705i | \(-0.249370\pi\) | ||||
0.708506 | + | 0.705705i | \(0.249370\pi\) | |||||||
\(860\) | −25.8057 | −0.879967 | ||||||||
\(861\) | −2.27743 | −0.0776145 | ||||||||
\(862\) | −38.6705 | −1.31712 | ||||||||
\(863\) | 25.8555 | 0.880132 | 0.440066 | − | 0.897965i | \(-0.354955\pi\) | ||||
0.440066 | + | 0.897965i | \(0.354955\pi\) | |||||||
\(864\) | −6.81644 | −0.231900 | ||||||||
\(865\) | 50.6049 | 1.72062 | ||||||||
\(866\) | 8.66509 | 0.294452 | ||||||||
\(867\) | −11.4649 | −0.389368 | ||||||||
\(868\) | 1.35183 | 0.0458841 | ||||||||
\(869\) | −41.8771 | −1.42058 | ||||||||
\(870\) | −43.7868 | −1.48451 | ||||||||
\(871\) | −18.5758 | −0.629417 | ||||||||
\(872\) | 5.37358 | 0.181972 | ||||||||
\(873\) | 6.81283 | 0.230579 | ||||||||
\(874\) | −3.40600 | −0.115210 | ||||||||
\(875\) | −0.979095 | −0.0330994 | ||||||||
\(876\) | −22.4895 | −0.759851 | ||||||||
\(877\) | −16.7193 | −0.564569 | −0.282285 | − | 0.959331i | \(-0.591092\pi\) | ||||
−0.282285 | + | 0.959331i | \(0.591092\pi\) | |||||||
\(878\) | 47.2741 | 1.59542 | ||||||||
\(879\) | −14.1130 | −0.476019 | ||||||||
\(880\) | 72.4669 | 2.44286 | ||||||||
\(881\) | −2.58708 | −0.0871611 | −0.0435805 | − | 0.999050i | \(-0.513877\pi\) | ||||
−0.0435805 | + | 0.999050i | \(0.513877\pi\) | |||||||
\(882\) | −1.85290 | −0.0623905 | ||||||||
\(883\) | −13.5192 | −0.454957 | −0.227478 | − | 0.973783i | \(-0.573048\pi\) | ||||
−0.227478 | + | 0.973783i | \(0.573048\pi\) | |||||||
\(884\) | −18.2889 | −0.615121 | ||||||||
\(885\) | −46.7398 | −1.57114 | ||||||||
\(886\) | 52.1983 | 1.75363 | ||||||||
\(887\) | 0.778491 | 0.0261392 | 0.0130696 | − | 0.999915i | \(-0.495840\pi\) | ||||
0.0130696 | + | 0.999915i | \(0.495840\pi\) | |||||||
\(888\) | −7.75701 | −0.260308 | ||||||||
\(889\) | 17.8346 | 0.598153 | ||||||||
\(890\) | 111.294 | 3.73057 | ||||||||
\(891\) | 4.69097 | 0.157154 | ||||||||
\(892\) | −30.5950 | −1.02440 | ||||||||
\(893\) | −0.537725 | −0.0179943 | ||||||||
\(894\) | −33.0439 | −1.10515 | ||||||||
\(895\) | 22.9489 | 0.767096 | ||||||||
\(896\) | −8.06380 | −0.269393 | ||||||||
\(897\) | 14.0769 | 0.470015 | ||||||||
\(898\) | 60.5171 | 2.01948 | ||||||||
\(899\) | 6.94334 | 0.231573 | ||||||||
\(900\) | 7.60337 | 0.253446 | ||||||||
\(901\) | −20.5709 | −0.685318 | ||||||||
\(902\) | −19.7952 | −0.659108 | ||||||||
\(903\) | −5.60881 | −0.186650 | ||||||||
\(904\) | 14.2565 | 0.474166 | ||||||||
\(905\) | 29.2299 | 0.971635 | ||||||||
\(906\) | 17.3356 | 0.575935 | ||||||||
\(907\) | 4.86748 | 0.161622 | 0.0808110 | − | 0.996729i | \(-0.474249\pi\) | ||||
0.0808110 | + | 0.996729i | \(0.474249\pi\) | |||||||
\(908\) | 5.34282 | 0.177308 | ||||||||
\(909\) | −13.6015 | −0.451135 | ||||||||
\(910\) | 14.2262 | 0.471592 | ||||||||
\(911\) | 3.21058 | 0.106371 | 0.0531856 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531856 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(912\) | −1.50296 | −0.0497680 | ||||||||
\(913\) | 59.9552 | 1.98423 | ||||||||
\(914\) | −45.3253 | −1.49923 | ||||||||
\(915\) | 34.4601 | 1.13922 | ||||||||
\(916\) | −20.6401 | −0.681967 | ||||||||
\(917\) | −21.6482 | −0.714888 | ||||||||
\(918\) | −9.88569 | −0.326277 | ||||||||
\(919\) | −5.49041 | −0.181112 | −0.0905559 | − | 0.995891i | \(-0.528864\pi\) | ||||
−0.0905559 | + | 0.995891i | \(0.528864\pi\) | |||||||
\(920\) | 19.8412 | 0.654146 | ||||||||
\(921\) | −3.92129 | −0.129211 | ||||||||
\(922\) | −48.2541 | −1.58916 | ||||||||
\(923\) | −2.55558 | −0.0841180 | ||||||||
\(924\) | −6.72332 | −0.221181 | ||||||||
\(925\) | 39.1861 | 1.28843 | ||||||||
\(926\) | −54.2432 | −1.78254 | ||||||||
\(927\) | −4.83718 | −0.158874 | ||||||||
\(928\) | 50.1793 | 1.64722 | ||||||||
\(929\) | 1.43430 | 0.0470580 | 0.0235290 | − | 0.999723i | \(-0.492510\pi\) | ||||
0.0235290 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(930\) | −5.61019 | −0.183965 | ||||||||
\(931\) | −0.312316 | −0.0102358 | ||||||||
\(932\) | 38.6548 | 1.26618 | ||||||||
\(933\) | 2.79178 | 0.0913987 | ||||||||
\(934\) | −13.7066 | −0.448493 | ||||||||
\(935\) | 80.3418 | 2.62746 | ||||||||
\(936\) | 2.51165 | 0.0820957 | ||||||||
\(937\) | 37.0831 | 1.21145 | 0.605726 | − | 0.795673i | \(-0.292883\pi\) | ||||
0.605726 | + | 0.795673i | \(0.292883\pi\) | |||||||
\(938\) | 14.3909 | 0.469880 | ||||||||
\(939\) | −3.95575 | −0.129091 | ||||||||
\(940\) | −7.92154 | −0.258372 | ||||||||
\(941\) | −19.0673 | −0.621575 | −0.310787 | − | 0.950479i | \(-0.600593\pi\) | ||||
−0.310787 | + | 0.950479i | \(0.600593\pi\) | |||||||
\(942\) | −43.2591 | −1.40946 | ||||||||
\(943\) | −13.4042 | −0.436502 | ||||||||
\(944\) | 70.0672 | 2.28049 | ||||||||
\(945\) | 3.21014 | 0.104426 | ||||||||
\(946\) | −48.7513 | −1.58504 | ||||||||
\(947\) | 29.0946 | 0.945447 | 0.472724 | − | 0.881211i | \(-0.343271\pi\) | ||||
0.472724 | + | 0.881211i | \(0.343271\pi\) | |||||||
\(948\) | 12.7948 | 0.415557 | ||||||||
\(949\) | 37.5294 | 1.21825 | ||||||||
\(950\) | 3.06996 | 0.0996027 | ||||||||
\(951\) | −5.47919 | −0.177675 | ||||||||
\(952\) | −5.60276 | −0.181586 | ||||||||
\(953\) | −13.9007 | −0.450288 | −0.225144 | − | 0.974325i | \(-0.572285\pi\) | ||||
−0.225144 | + | 0.974325i | \(0.572285\pi\) | |||||||
\(954\) | −7.14417 | −0.231301 | ||||||||
\(955\) | 62.9097 | 2.03571 | ||||||||
\(956\) | −12.5216 | −0.404977 | ||||||||
\(957\) | −34.5327 | −1.11628 | ||||||||
\(958\) | 50.5771 | 1.63407 | ||||||||
\(959\) | −2.09823 | −0.0677554 | ||||||||
\(960\) | −9.64838 | −0.311400 | ||||||||
\(961\) | −30.1104 | −0.971303 | ||||||||
\(962\) | −32.7349 | −1.05541 | ||||||||
\(963\) | −12.9339 | −0.416790 | ||||||||
\(964\) | −8.72957 | −0.281161 | ||||||||
\(965\) | 16.6419 | 0.535722 | ||||||||
\(966\) | −10.9056 | −0.350882 | ||||||||
\(967\) | −17.9285 | −0.576542 | −0.288271 | − | 0.957549i | \(-0.593080\pi\) | ||||
−0.288271 | + | 0.957549i | \(0.593080\pi\) | |||||||
\(968\) | 11.5570 | 0.371457 | ||||||||
\(969\) | −1.66629 | −0.0535288 | ||||||||
\(970\) | 40.5232 | 1.30112 | ||||||||
\(971\) | −58.9141 | −1.89064 | −0.945322 | − | 0.326139i | \(-0.894252\pi\) | ||||
−0.945322 | + | 0.326139i | \(0.894252\pi\) | |||||||
\(972\) | −1.43325 | −0.0459714 | ||||||||
\(973\) | −18.1952 | −0.583312 | ||||||||
\(974\) | 5.88019 | 0.188414 | ||||||||
\(975\) | −12.6881 | −0.406344 | ||||||||
\(976\) | −51.6590 | −1.65356 | ||||||||
\(977\) | 0.0288918 | 0.000924330 0 | 0.000462165 | − | 1.00000i | \(-0.499853\pi\) | ||||
0.000462165 | 1.00000i | \(0.499853\pi\) | ||||||||
\(978\) | 35.0713 | 1.12146 | ||||||||
\(979\) | 87.7722 | 2.80521 | ||||||||
\(980\) | −4.60092 | −0.146971 | ||||||||
\(981\) | 5.11701 | 0.163374 | ||||||||
\(982\) | −39.7729 | −1.26920 | ||||||||
\(983\) | 55.3085 | 1.76407 | 0.882034 | − | 0.471185i | \(-0.156174\pi\) | ||||
0.882034 | + | 0.471185i | \(0.156174\pi\) | |||||||
\(984\) | −2.39162 | −0.0762420 | ||||||||
\(985\) | −53.7006 | −1.71104 | ||||||||
\(986\) | 72.7737 | 2.31759 | ||||||||
\(987\) | −1.72173 | −0.0548033 | ||||||||
\(988\) | −1.07060 | −0.0340603 | ||||||||
\(989\) | −33.0117 | −1.04971 | ||||||||
\(990\) | 27.9023 | 0.886792 | ||||||||
\(991\) | −40.3241 | −1.28094 | −0.640468 | − | 0.767985i | \(-0.721260\pi\) | ||||
−0.640468 | + | 0.767985i | \(0.721260\pi\) | |||||||
\(992\) | 6.42923 | 0.204128 | ||||||||
\(993\) | −2.77529 | −0.0880712 | ||||||||
\(994\) | 1.97985 | 0.0627969 | ||||||||
\(995\) | −66.4563 | −2.10681 | ||||||||
\(996\) | −18.3183 | −0.580436 | ||||||||
\(997\) | −31.5092 | −0.997906 | −0.498953 | − | 0.866629i | \(-0.666282\pi\) | ||||
−0.498953 | + | 0.866629i | \(0.666282\pi\) | |||||||
\(998\) | −78.1154 | −2.47270 | ||||||||
\(999\) | −7.38664 | −0.233703 |
(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 | 8043.2.a.t.1.11 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.11 | ✓ | 52 | 1.1 | even | 1 | trivial |