Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.36 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.126650 | −0.0731212 | −0.0365606 | − | 0.999331i | \(-0.511640\pi\) | ||||
−0.0365606 | + | 0.999331i | \(0.511640\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.50247 | 1.11914 | 0.559569 | − | 0.828784i | \(-0.310967\pi\) | ||||
0.559569 | + | 0.828784i | \(0.310967\pi\) | |||||||
\(6\) | −0.126650 | −0.0517045 | ||||||||
\(7\) | −3.12234 | −1.18013 | −0.590067 | − | 0.807354i | \(-0.700899\pi\) | ||||
−0.590067 | + | 0.807354i | \(0.700899\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.98396 | −0.994653 | ||||||||
\(10\) | 2.50247 | 0.791350 | ||||||||
\(11\) | 3.00996 | 0.907538 | 0.453769 | − | 0.891119i | \(-0.350079\pi\) | ||||
0.453769 | + | 0.891119i | \(0.350079\pi\) | |||||||
\(12\) | −0.126650 | −0.0365606 | ||||||||
\(13\) | 0.390555 | 0.108320 | 0.0541602 | − | 0.998532i | \(-0.482752\pi\) | ||||
0.0541602 | + | 0.998532i | \(0.482752\pi\) | |||||||
\(14\) | −3.12234 | −0.834481 | ||||||||
\(15\) | −0.316937 | −0.0818327 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.35775 | −1.05691 | −0.528455 | − | 0.848962i | \(-0.677228\pi\) | ||||
−0.528455 | + | 0.848962i | \(0.677228\pi\) | |||||||
\(18\) | −2.98396 | −0.703326 | ||||||||
\(19\) | −2.72254 | −0.624593 | −0.312297 | − | 0.949985i | \(-0.601098\pi\) | ||||
−0.312297 | + | 0.949985i | \(0.601098\pi\) | |||||||
\(20\) | 2.50247 | 0.559569 | ||||||||
\(21\) | 0.395443 | 0.0862928 | ||||||||
\(22\) | 3.00996 | 0.641726 | ||||||||
\(23\) | 6.27644 | 1.30873 | 0.654364 | − | 0.756179i | \(-0.272936\pi\) | ||||
0.654364 | + | 0.756179i | \(0.272936\pi\) | |||||||
\(24\) | −0.126650 | −0.0258522 | ||||||||
\(25\) | 1.26236 | 0.252471 | ||||||||
\(26\) | 0.390555 | 0.0765941 | ||||||||
\(27\) | 0.757866 | 0.145851 | ||||||||
\(28\) | −3.12234 | −0.590067 | ||||||||
\(29\) | −2.88480 | −0.535695 | −0.267847 | − | 0.963461i | \(-0.586312\pi\) | ||||
−0.267847 | + | 0.963461i | \(0.586312\pi\) | |||||||
\(30\) | −0.316937 | −0.0578645 | ||||||||
\(31\) | −7.34113 | −1.31851 | −0.659253 | − | 0.751921i | \(-0.729127\pi\) | ||||
−0.659253 | + | 0.751921i | \(0.729127\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.381211 | −0.0663603 | ||||||||
\(34\) | −4.35775 | −0.747348 | ||||||||
\(35\) | −7.81357 | −1.32073 | ||||||||
\(36\) | −2.98396 | −0.497327 | ||||||||
\(37\) | 4.63215 | 0.761521 | 0.380761 | − | 0.924674i | \(-0.375662\pi\) | ||||
0.380761 | + | 0.924674i | \(0.375662\pi\) | |||||||
\(38\) | −2.72254 | −0.441654 | ||||||||
\(39\) | −0.0494636 | −0.00792051 | ||||||||
\(40\) | 2.50247 | 0.395675 | ||||||||
\(41\) | −0.369047 | −0.0576354 | −0.0288177 | − | 0.999585i | \(-0.509174\pi\) | ||||
−0.0288177 | + | 0.999585i | \(0.509174\pi\) | |||||||
\(42\) | 0.395443 | 0.0610183 | ||||||||
\(43\) | −7.60429 | −1.15964 | −0.579822 | − | 0.814744i | \(-0.696878\pi\) | ||||
−0.579822 | + | 0.814744i | \(0.696878\pi\) | |||||||
\(44\) | 3.00996 | 0.453769 | ||||||||
\(45\) | −7.46727 | −1.11315 | ||||||||
\(46\) | 6.27644 | 0.925411 | ||||||||
\(47\) | −6.02468 | −0.878789 | −0.439395 | − | 0.898294i | \(-0.644807\pi\) | ||||
−0.439395 | + | 0.898294i | \(0.644807\pi\) | |||||||
\(48\) | −0.126650 | −0.0182803 | ||||||||
\(49\) | 2.74902 | 0.392718 | ||||||||
\(50\) | 1.26236 | 0.178524 | ||||||||
\(51\) | 0.551907 | 0.0772824 | ||||||||
\(52\) | 0.390555 | 0.0541602 | ||||||||
\(53\) | 2.88719 | 0.396587 | 0.198293 | − | 0.980143i | \(-0.436460\pi\) | ||||
0.198293 | + | 0.980143i | \(0.436460\pi\) | |||||||
\(54\) | 0.757866 | 0.103133 | ||||||||
\(55\) | 7.53234 | 1.01566 | ||||||||
\(56\) | −3.12234 | −0.417241 | ||||||||
\(57\) | 0.344809 | 0.0456710 | ||||||||
\(58\) | −2.88480 | −0.378793 | ||||||||
\(59\) | 13.7042 | 1.78413 | 0.892064 | − | 0.451908i | \(-0.149257\pi\) | ||||
0.892064 | + | 0.451908i | \(0.149257\pi\) | |||||||
\(60\) | −0.316937 | −0.0409164 | ||||||||
\(61\) | −12.8491 | −1.64516 | −0.822581 | − | 0.568648i | \(-0.807467\pi\) | ||||
−0.822581 | + | 0.568648i | \(0.807467\pi\) | |||||||
\(62\) | −7.34113 | −0.932325 | ||||||||
\(63\) | 9.31695 | 1.17382 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.977351 | 0.121225 | ||||||||
\(66\) | −0.381211 | −0.0469238 | ||||||||
\(67\) | 1.22549 | 0.149718 | 0.0748590 | − | 0.997194i | \(-0.476149\pi\) | ||||
0.0748590 | + | 0.997194i | \(0.476149\pi\) | |||||||
\(68\) | −4.35775 | −0.528455 | ||||||||
\(69\) | −0.794909 | −0.0956958 | ||||||||
\(70\) | −7.81357 | −0.933900 | ||||||||
\(71\) | −8.76692 | −1.04044 | −0.520221 | − | 0.854032i | \(-0.674150\pi\) | ||||
−0.520221 | + | 0.854032i | \(0.674150\pi\) | |||||||
\(72\) | −2.98396 | −0.351663 | ||||||||
\(73\) | 3.21298 | 0.376051 | 0.188025 | − | 0.982164i | \(-0.439791\pi\) | ||||
0.188025 | + | 0.982164i | \(0.439791\pi\) | |||||||
\(74\) | 4.63215 | 0.538477 | ||||||||
\(75\) | −0.159877 | −0.0184610 | ||||||||
\(76\) | −2.72254 | −0.312297 | ||||||||
\(77\) | −9.39813 | −1.07102 | ||||||||
\(78\) | −0.0494636 | −0.00560065 | ||||||||
\(79\) | −9.72775 | −1.09446 | −0.547229 | − | 0.836983i | \(-0.684317\pi\) | ||||
−0.547229 | + | 0.836983i | \(0.684317\pi\) | |||||||
\(80\) | 2.50247 | 0.279785 | ||||||||
\(81\) | 8.85590 | 0.983988 | ||||||||
\(82\) | −0.369047 | −0.0407544 | ||||||||
\(83\) | −0.802753 | −0.0881136 | −0.0440568 | − | 0.999029i | \(-0.514028\pi\) | ||||
−0.0440568 | + | 0.999029i | \(0.514028\pi\) | |||||||
\(84\) | 0.395443 | 0.0431464 | ||||||||
\(85\) | −10.9051 | −1.18283 | ||||||||
\(86\) | −7.60429 | −0.819991 | ||||||||
\(87\) | 0.365359 | 0.0391706 | ||||||||
\(88\) | 3.00996 | 0.320863 | ||||||||
\(89\) | −8.60368 | −0.911988 | −0.455994 | − | 0.889983i | \(-0.650716\pi\) | ||||
−0.455994 | + | 0.889983i | \(0.650716\pi\) | |||||||
\(90\) | −7.46727 | −0.787119 | ||||||||
\(91\) | −1.21945 | −0.127833 | ||||||||
\(92\) | 6.27644 | 0.654364 | ||||||||
\(93\) | 0.929752 | 0.0964108 | ||||||||
\(94\) | −6.02468 | −0.621398 | ||||||||
\(95\) | −6.81307 | −0.699007 | ||||||||
\(96\) | −0.126650 | −0.0129261 | ||||||||
\(97\) | −0.991788 | −0.100701 | −0.0503504 | − | 0.998732i | \(-0.516034\pi\) | ||||
−0.0503504 | + | 0.998732i | \(0.516034\pi\) | |||||||
\(98\) | 2.74902 | 0.277693 | ||||||||
\(99\) | −8.98161 | −0.902686 | ||||||||
\(100\) | 1.26236 | 0.126236 | ||||||||
\(101\) | −12.0240 | −1.19644 | −0.598218 | − | 0.801334i | \(-0.704124\pi\) | ||||
−0.598218 | + | 0.801334i | \(0.704124\pi\) | |||||||
\(102\) | 0.551907 | 0.0546469 | ||||||||
\(103\) | −12.8902 | −1.27010 | −0.635052 | − | 0.772469i | \(-0.719021\pi\) | ||||
−0.635052 | + | 0.772469i | \(0.719021\pi\) | |||||||
\(104\) | 0.390555 | 0.0382970 | ||||||||
\(105\) | 0.989585 | 0.0965736 | ||||||||
\(106\) | 2.88719 | 0.280429 | ||||||||
\(107\) | −17.0471 | −1.64800 | −0.824002 | − | 0.566587i | \(-0.808263\pi\) | ||||
−0.824002 | + | 0.566587i | \(0.808263\pi\) | |||||||
\(108\) | 0.757866 | 0.0729257 | ||||||||
\(109\) | 14.0833 | 1.34893 | 0.674467 | − | 0.738305i | \(-0.264374\pi\) | ||||
0.674467 | + | 0.738305i | \(0.264374\pi\) | |||||||
\(110\) | 7.53234 | 0.718181 | ||||||||
\(111\) | −0.586661 | −0.0556834 | ||||||||
\(112\) | −3.12234 | −0.295034 | ||||||||
\(113\) | 3.86364 | 0.363461 | 0.181730 | − | 0.983348i | \(-0.441830\pi\) | ||||
0.181730 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(114\) | 0.344809 | 0.0322943 | ||||||||
\(115\) | 15.7066 | 1.46465 | ||||||||
\(116\) | −2.88480 | −0.267847 | ||||||||
\(117\) | −1.16540 | −0.107741 | ||||||||
\(118\) | 13.7042 | 1.26157 | ||||||||
\(119\) | 13.6064 | 1.24729 | ||||||||
\(120\) | −0.316937 | −0.0289322 | ||||||||
\(121\) | −1.94012 | −0.176375 | ||||||||
\(122\) | −12.8491 | −1.16331 | ||||||||
\(123\) | 0.0467396 | 0.00421437 | ||||||||
\(124\) | −7.34113 | −0.659253 | ||||||||
\(125\) | −9.35334 | −0.836588 | ||||||||
\(126\) | 9.31695 | 0.830019 | ||||||||
\(127\) | −0.943810 | −0.0837496 | −0.0418748 | − | 0.999123i | \(-0.513333\pi\) | ||||
−0.0418748 | + | 0.999123i | \(0.513333\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.963080 | 0.0847945 | ||||||||
\(130\) | 0.977351 | 0.0857194 | ||||||||
\(131\) | 11.5999 | 1.01349 | 0.506744 | − | 0.862097i | \(-0.330849\pi\) | ||||
0.506744 | + | 0.862097i | \(0.330849\pi\) | |||||||
\(132\) | −0.381211 | −0.0331801 | ||||||||
\(133\) | 8.50070 | 0.737104 | ||||||||
\(134\) | 1.22549 | 0.105867 | ||||||||
\(135\) | 1.89654 | 0.163228 | ||||||||
\(136\) | −4.35775 | −0.373674 | ||||||||
\(137\) | 8.38292 | 0.716201 | 0.358100 | − | 0.933683i | \(-0.383425\pi\) | ||||
0.358100 | + | 0.933683i | \(0.383425\pi\) | |||||||
\(138\) | −0.794909 | −0.0676672 | ||||||||
\(139\) | 22.5822 | 1.91540 | 0.957699 | − | 0.287773i | \(-0.0929147\pi\) | ||||
0.957699 | + | 0.287773i | \(0.0929147\pi\) | |||||||
\(140\) | −7.81357 | −0.660367 | ||||||||
\(141\) | 0.763023 | 0.0642581 | ||||||||
\(142\) | −8.76692 | −0.735704 | ||||||||
\(143\) | 1.17555 | 0.0983048 | ||||||||
\(144\) | −2.98396 | −0.248663 | ||||||||
\(145\) | −7.21914 | −0.599517 | ||||||||
\(146\) | 3.21298 | 0.265908 | ||||||||
\(147\) | −0.348163 | −0.0287160 | ||||||||
\(148\) | 4.63215 | 0.380761 | ||||||||
\(149\) | −15.9218 | −1.30436 | −0.652181 | − | 0.758063i | \(-0.726146\pi\) | ||||
−0.652181 | + | 0.758063i | \(0.726146\pi\) | |||||||
\(150\) | −0.159877 | −0.0130539 | ||||||||
\(151\) | −10.8518 | −0.883106 | −0.441553 | − | 0.897235i | \(-0.645572\pi\) | ||||
−0.441553 | + | 0.897235i | \(0.645572\pi\) | |||||||
\(152\) | −2.72254 | −0.220827 | ||||||||
\(153\) | 13.0033 | 1.05126 | ||||||||
\(154\) | −9.39813 | −0.757323 | ||||||||
\(155\) | −18.3710 | −1.47559 | ||||||||
\(156\) | −0.0494636 | −0.00396026 | ||||||||
\(157\) | 21.2621 | 1.69690 | 0.848452 | − | 0.529272i | \(-0.177535\pi\) | ||||
0.848452 | + | 0.529272i | \(0.177535\pi\) | |||||||
\(158\) | −9.72775 | −0.773898 | ||||||||
\(159\) | −0.365662 | −0.0289989 | ||||||||
\(160\) | 2.50247 | 0.197838 | ||||||||
\(161\) | −19.5972 | −1.54448 | ||||||||
\(162\) | 8.85590 | 0.695785 | ||||||||
\(163\) | 6.92348 | 0.542289 | 0.271144 | − | 0.962539i | \(-0.412598\pi\) | ||||
0.271144 | + | 0.962539i | \(0.412598\pi\) | |||||||
\(164\) | −0.369047 | −0.0288177 | ||||||||
\(165\) | −0.953968 | −0.0742663 | ||||||||
\(166\) | −0.802753 | −0.0623057 | ||||||||
\(167\) | 10.5567 | 0.816900 | 0.408450 | − | 0.912781i | \(-0.366069\pi\) | ||||
0.408450 | + | 0.912781i | \(0.366069\pi\) | |||||||
\(168\) | 0.395443 | 0.0305091 | ||||||||
\(169\) | −12.8475 | −0.988267 | ||||||||
\(170\) | −10.9051 | −0.836385 | ||||||||
\(171\) | 8.12395 | 0.621254 | ||||||||
\(172\) | −7.60429 | −0.579822 | ||||||||
\(173\) | −23.0655 | −1.75364 | −0.876819 | − | 0.480821i | \(-0.840339\pi\) | ||||
−0.876819 | + | 0.480821i | \(0.840339\pi\) | |||||||
\(174\) | 0.365359 | 0.0276978 | ||||||||
\(175\) | −3.94151 | −0.297950 | ||||||||
\(176\) | 3.00996 | 0.226884 | ||||||||
\(177\) | −1.73563 | −0.130458 | ||||||||
\(178\) | −8.60368 | −0.644873 | ||||||||
\(179\) | 8.05824 | 0.602301 | 0.301150 | − | 0.953577i | \(-0.402629\pi\) | ||||
0.301150 | + | 0.953577i | \(0.402629\pi\) | |||||||
\(180\) | −7.46727 | −0.556577 | ||||||||
\(181\) | 6.14897 | 0.457049 | 0.228525 | − | 0.973538i | \(-0.426610\pi\) | ||||
0.228525 | + | 0.973538i | \(0.426610\pi\) | |||||||
\(182\) | −1.21945 | −0.0903913 | ||||||||
\(183\) | 1.62734 | 0.120296 | ||||||||
\(184\) | 6.27644 | 0.462705 | ||||||||
\(185\) | 11.5918 | 0.852248 | ||||||||
\(186\) | 0.929752 | 0.0681727 | ||||||||
\(187\) | −13.1167 | −0.959185 | ||||||||
\(188\) | −6.02468 | −0.439395 | ||||||||
\(189\) | −2.36632 | −0.172124 | ||||||||
\(190\) | −6.81307 | −0.494272 | ||||||||
\(191\) | −0.0544458 | −0.00393956 | −0.00196978 | − | 0.999998i | \(-0.500627\pi\) | ||||
−0.00196978 | + | 0.999998i | \(0.500627\pi\) | |||||||
\(192\) | −0.126650 | −0.00914015 | ||||||||
\(193\) | −16.1070 | −1.15941 | −0.579705 | − | 0.814826i | \(-0.696832\pi\) | ||||
−0.579705 | + | 0.814826i | \(0.696832\pi\) | |||||||
\(194\) | −0.991788 | −0.0712062 | ||||||||
\(195\) | −0.123781 | −0.00886415 | ||||||||
\(196\) | 2.74902 | 0.196359 | ||||||||
\(197\) | −8.52039 | −0.607053 | −0.303526 | − | 0.952823i | \(-0.598164\pi\) | ||||
−0.303526 | + | 0.952823i | \(0.598164\pi\) | |||||||
\(198\) | −8.98161 | −0.638295 | ||||||||
\(199\) | −21.5290 | −1.52615 | −0.763076 | − | 0.646308i | \(-0.776312\pi\) | ||||
−0.763076 | + | 0.646308i | \(0.776312\pi\) | |||||||
\(200\) | 1.26236 | 0.0892620 | ||||||||
\(201\) | −0.155208 | −0.0109476 | ||||||||
\(202\) | −12.0240 | −0.846007 | ||||||||
\(203\) | 9.00735 | 0.632192 | ||||||||
\(204\) | 0.551907 | 0.0386412 | ||||||||
\(205\) | −0.923529 | −0.0645020 | ||||||||
\(206\) | −12.8902 | −0.898099 | ||||||||
\(207\) | −18.7287 | −1.30173 | ||||||||
\(208\) | 0.390555 | 0.0270801 | ||||||||
\(209\) | −8.19474 | −0.566842 | ||||||||
\(210\) | 0.989585 | 0.0682879 | ||||||||
\(211\) | −1.17635 | −0.0809831 | −0.0404915 | − | 0.999180i | \(-0.512892\pi\) | ||||
−0.0404915 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(212\) | 2.88719 | 0.198293 | ||||||||
\(213\) | 1.11033 | 0.0760783 | ||||||||
\(214\) | −17.0471 | −1.16531 | ||||||||
\(215\) | −19.0295 | −1.29780 | ||||||||
\(216\) | 0.757866 | 0.0515663 | ||||||||
\(217\) | 22.9215 | 1.55602 | ||||||||
\(218\) | 14.0833 | 0.953840 | ||||||||
\(219\) | −0.406922 | −0.0274973 | ||||||||
\(220\) | 7.53234 | 0.507830 | ||||||||
\(221\) | −1.70194 | −0.114485 | ||||||||
\(222\) | −0.586661 | −0.0393741 | ||||||||
\(223\) | 4.45579 | 0.298382 | 0.149191 | − | 0.988808i | \(-0.452333\pi\) | ||||
0.149191 | + | 0.988808i | \(0.452333\pi\) | |||||||
\(224\) | −3.12234 | −0.208620 | ||||||||
\(225\) | −3.76682 | −0.251121 | ||||||||
\(226\) | 3.86364 | 0.257006 | ||||||||
\(227\) | 19.3013 | 1.28107 | 0.640536 | − | 0.767928i | \(-0.278712\pi\) | ||||
0.640536 | + | 0.767928i | \(0.278712\pi\) | |||||||
\(228\) | 0.344809 | 0.0228355 | ||||||||
\(229\) | −26.1577 | −1.72855 | −0.864275 | − | 0.503020i | \(-0.832222\pi\) | ||||
−0.864275 | + | 0.503020i | \(0.832222\pi\) | |||||||
\(230\) | 15.7066 | 1.03566 | ||||||||
\(231\) | 1.19027 | 0.0783140 | ||||||||
\(232\) | −2.88480 | −0.189397 | ||||||||
\(233\) | −20.2416 | −1.32607 | −0.663036 | − | 0.748588i | \(-0.730732\pi\) | ||||
−0.663036 | + | 0.748588i | \(0.730732\pi\) | |||||||
\(234\) | −1.16540 | −0.0761845 | ||||||||
\(235\) | −15.0766 | −0.983487 | ||||||||
\(236\) | 13.7042 | 0.892064 | ||||||||
\(237\) | 1.23202 | 0.0800280 | ||||||||
\(238\) | 13.6064 | 0.881971 | ||||||||
\(239\) | −11.8533 | −0.766728 | −0.383364 | − | 0.923597i | \(-0.625235\pi\) | ||||
−0.383364 | + | 0.923597i | \(0.625235\pi\) | |||||||
\(240\) | −0.316937 | −0.0204582 | ||||||||
\(241\) | 5.11831 | 0.329699 | 0.164850 | − | 0.986319i | \(-0.447286\pi\) | ||||
0.164850 | + | 0.986319i | \(0.447286\pi\) | |||||||
\(242\) | −1.94012 | −0.124716 | ||||||||
\(243\) | −3.39519 | −0.217802 | ||||||||
\(244\) | −12.8491 | −0.822581 | ||||||||
\(245\) | 6.87935 | 0.439505 | ||||||||
\(246\) | 0.0467396 | 0.00298001 | ||||||||
\(247\) | −1.06330 | −0.0676562 | ||||||||
\(248\) | −7.34113 | −0.466162 | ||||||||
\(249\) | 0.101668 | 0.00644297 | ||||||||
\(250\) | −9.35334 | −0.591557 | ||||||||
\(251\) | −19.6617 | −1.24103 | −0.620517 | − | 0.784193i | \(-0.713077\pi\) | ||||
−0.620517 | + | 0.784193i | \(0.713077\pi\) | |||||||
\(252\) | 9.31695 | 0.586912 | ||||||||
\(253\) | 18.8919 | 1.18772 | ||||||||
\(254\) | −0.943810 | −0.0592199 | ||||||||
\(255\) | 1.38113 | 0.0864898 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.77198 | −0.547181 | −0.273590 | − | 0.961846i | \(-0.588211\pi\) | ||||
−0.273590 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(258\) | 0.963080 | 0.0599587 | ||||||||
\(259\) | −14.4632 | −0.898698 | ||||||||
\(260\) | 0.977351 | 0.0606127 | ||||||||
\(261\) | 8.60814 | 0.532831 | ||||||||
\(262\) | 11.5999 | 0.716644 | ||||||||
\(263\) | −12.5090 | −0.771335 | −0.385667 | − | 0.922638i | \(-0.626029\pi\) | ||||
−0.385667 | + | 0.922638i | \(0.626029\pi\) | |||||||
\(264\) | −0.381211 | −0.0234619 | ||||||||
\(265\) | 7.22512 | 0.443835 | ||||||||
\(266\) | 8.50070 | 0.521211 | ||||||||
\(267\) | 1.08965 | 0.0666856 | ||||||||
\(268\) | 1.22549 | 0.0748590 | ||||||||
\(269\) | 27.5019 | 1.67682 | 0.838409 | − | 0.545042i | \(-0.183486\pi\) | ||||
0.838409 | + | 0.545042i | \(0.183486\pi\) | |||||||
\(270\) | 1.89654 | 0.115420 | ||||||||
\(271\) | 10.0589 | 0.611032 | 0.305516 | − | 0.952187i | \(-0.401171\pi\) | ||||
0.305516 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(272\) | −4.35775 | −0.264227 | ||||||||
\(273\) | 0.154442 | 0.00934727 | ||||||||
\(274\) | 8.38292 | 0.506430 | ||||||||
\(275\) | 3.79964 | 0.229127 | ||||||||
\(276\) | −0.794909 | −0.0478479 | ||||||||
\(277\) | −24.5466 | −1.47486 | −0.737430 | − | 0.675424i | \(-0.763961\pi\) | ||||
−0.737430 | + | 0.675424i | \(0.763961\pi\) | |||||||
\(278\) | 22.5822 | 1.35439 | ||||||||
\(279\) | 21.9056 | 1.31146 | ||||||||
\(280\) | −7.81357 | −0.466950 | ||||||||
\(281\) | −4.34867 | −0.259420 | −0.129710 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129710 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(282\) | 0.763023 | 0.0454374 | ||||||||
\(283\) | −7.70675 | −0.458119 | −0.229059 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229059 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(284\) | −8.76692 | −0.520221 | ||||||||
\(285\) | 0.862873 | 0.0511122 | ||||||||
\(286\) | 1.17555 | 0.0695120 | ||||||||
\(287\) | 1.15229 | 0.0680176 | ||||||||
\(288\) | −2.98396 | −0.175832 | ||||||||
\(289\) | 1.98997 | 0.117057 | ||||||||
\(290\) | −7.21914 | −0.423922 | ||||||||
\(291\) | 0.125610 | 0.00736337 | ||||||||
\(292\) | 3.21298 | 0.188025 | ||||||||
\(293\) | −4.11838 | −0.240598 | −0.120299 | − | 0.992738i | \(-0.538385\pi\) | ||||
−0.120299 | + | 0.992738i | \(0.538385\pi\) | |||||||
\(294\) | −0.348163 | −0.0203053 | ||||||||
\(295\) | 34.2942 | 1.99669 | ||||||||
\(296\) | 4.63215 | 0.269238 | ||||||||
\(297\) | 2.28115 | 0.132366 | ||||||||
\(298\) | −15.9218 | −0.922324 | ||||||||
\(299\) | 2.45129 | 0.141762 | ||||||||
\(300\) | −0.159877 | −0.00923049 | ||||||||
\(301\) | 23.7432 | 1.36853 | ||||||||
\(302\) | −10.8518 | −0.624450 | ||||||||
\(303\) | 1.52284 | 0.0874848 | ||||||||
\(304\) | −2.72254 | −0.156148 | ||||||||
\(305\) | −32.1546 | −1.84116 | ||||||||
\(306\) | 13.0033 | 0.743352 | ||||||||
\(307\) | −7.03580 | −0.401554 | −0.200777 | − | 0.979637i | \(-0.564347\pi\) | ||||
−0.200777 | + | 0.979637i | \(0.564347\pi\) | |||||||
\(308\) | −9.39813 | −0.535508 | ||||||||
\(309\) | 1.63253 | 0.0928715 | ||||||||
\(310\) | −18.3710 | −1.04340 | ||||||||
\(311\) | 3.45972 | 0.196183 | 0.0980913 | − | 0.995177i | \(-0.468726\pi\) | ||||
0.0980913 | + | 0.995177i | \(0.468726\pi\) | |||||||
\(312\) | −0.0494636 | −0.00280032 | ||||||||
\(313\) | −20.3659 | −1.15115 | −0.575575 | − | 0.817749i | \(-0.695222\pi\) | ||||
−0.575575 | + | 0.817749i | \(0.695222\pi\) | |||||||
\(314\) | 21.2621 | 1.19989 | ||||||||
\(315\) | 23.3154 | 1.31367 | ||||||||
\(316\) | −9.72775 | −0.547229 | ||||||||
\(317\) | 3.95097 | 0.221908 | 0.110954 | − | 0.993826i | \(-0.464609\pi\) | ||||
0.110954 | + | 0.993826i | \(0.464609\pi\) | |||||||
\(318\) | −0.365662 | −0.0205053 | ||||||||
\(319\) | −8.68316 | −0.486163 | ||||||||
\(320\) | 2.50247 | 0.139892 | ||||||||
\(321\) | 2.15901 | 0.120504 | ||||||||
\(322\) | −19.5972 | −1.09211 | ||||||||
\(323\) | 11.8641 | 0.660139 | ||||||||
\(324\) | 8.85590 | 0.491994 | ||||||||
\(325\) | 0.493019 | 0.0273478 | ||||||||
\(326\) | 6.92348 | 0.383456 | ||||||||
\(327\) | −1.78364 | −0.0986356 | ||||||||
\(328\) | −0.369047 | −0.0203772 | ||||||||
\(329\) | 18.8111 | 1.03709 | ||||||||
\(330\) | −0.953968 | −0.0525142 | ||||||||
\(331\) | 14.1985 | 0.780418 | 0.390209 | − | 0.920726i | \(-0.372403\pi\) | ||||
0.390209 | + | 0.920726i | \(0.372403\pi\) | |||||||
\(332\) | −0.802753 | −0.0440568 | ||||||||
\(333\) | −13.8222 | −0.757450 | ||||||||
\(334\) | 10.5567 | 0.577635 | ||||||||
\(335\) | 3.06676 | 0.167555 | ||||||||
\(336\) | 0.395443 | 0.0215732 | ||||||||
\(337\) | 16.8297 | 0.916772 | 0.458386 | − | 0.888753i | \(-0.348428\pi\) | ||||
0.458386 | + | 0.888753i | \(0.348428\pi\) | |||||||
\(338\) | −12.8475 | −0.698810 | ||||||||
\(339\) | −0.489329 | −0.0265767 | ||||||||
\(340\) | −10.9051 | −0.591414 | ||||||||
\(341\) | −22.0965 | −1.19659 | ||||||||
\(342\) | 8.12395 | 0.439293 | ||||||||
\(343\) | 13.2730 | 0.716675 | ||||||||
\(344\) | −7.60429 | −0.409996 | ||||||||
\(345\) | −1.98924 | −0.107097 | ||||||||
\(346\) | −23.0655 | −1.24001 | ||||||||
\(347\) | −6.72762 | −0.361158 | −0.180579 | − | 0.983561i | \(-0.557797\pi\) | ||||
−0.180579 | + | 0.983561i | \(0.557797\pi\) | |||||||
\(348\) | 0.365359 | 0.0195853 | ||||||||
\(349\) | 21.2764 | 1.13890 | 0.569449 | − | 0.822027i | \(-0.307157\pi\) | ||||
0.569449 | + | 0.822027i | \(0.307157\pi\) | |||||||
\(350\) | −3.94151 | −0.210682 | ||||||||
\(351\) | 0.295988 | 0.0157987 | ||||||||
\(352\) | 3.00996 | 0.160432 | ||||||||
\(353\) | 20.5331 | 1.09286 | 0.546432 | − | 0.837503i | \(-0.315986\pi\) | ||||
0.546432 | + | 0.837503i | \(0.315986\pi\) | |||||||
\(354\) | −1.73563 | −0.0922475 | ||||||||
\(355\) | −21.9390 | −1.16440 | ||||||||
\(356\) | −8.60368 | −0.455994 | ||||||||
\(357\) | −1.72324 | −0.0912037 | ||||||||
\(358\) | 8.05824 | 0.425891 | ||||||||
\(359\) | 27.2939 | 1.44052 | 0.720258 | − | 0.693706i | \(-0.244023\pi\) | ||||
0.720258 | + | 0.693706i | \(0.244023\pi\) | |||||||
\(360\) | −7.46727 | −0.393560 | ||||||||
\(361\) | −11.5878 | −0.609883 | ||||||||
\(362\) | 6.14897 | 0.323182 | ||||||||
\(363\) | 0.245716 | 0.0128967 | ||||||||
\(364\) | −1.21945 | −0.0639163 | ||||||||
\(365\) | 8.04038 | 0.420853 | ||||||||
\(366\) | 1.62734 | 0.0850623 | ||||||||
\(367\) | 10.6571 | 0.556294 | 0.278147 | − | 0.960539i | \(-0.410280\pi\) | ||||
0.278147 | + | 0.960539i | \(0.410280\pi\) | |||||||
\(368\) | 6.27644 | 0.327182 | ||||||||
\(369\) | 1.10122 | 0.0573273 | ||||||||
\(370\) | 11.5918 | 0.602630 | ||||||||
\(371\) | −9.01481 | −0.468026 | ||||||||
\(372\) | 0.929752 | 0.0482054 | ||||||||
\(373\) | 25.7862 | 1.33516 | 0.667579 | − | 0.744539i | \(-0.267330\pi\) | ||||
0.667579 | + | 0.744539i | \(0.267330\pi\) | |||||||
\(374\) | −13.1167 | −0.678246 | ||||||||
\(375\) | 1.18460 | 0.0611723 | ||||||||
\(376\) | −6.02468 | −0.310699 | ||||||||
\(377\) | −1.12667 | −0.0580267 | ||||||||
\(378\) | −2.36632 | −0.121710 | ||||||||
\(379\) | 9.98509 | 0.512900 | 0.256450 | − | 0.966558i | \(-0.417447\pi\) | ||||
0.256450 | + | 0.966558i | \(0.417447\pi\) | |||||||
\(380\) | −6.81307 | −0.349503 | ||||||||
\(381\) | 0.119533 | 0.00612387 | ||||||||
\(382\) | −0.0544458 | −0.00278569 | ||||||||
\(383\) | 29.2565 | 1.49494 | 0.747468 | − | 0.664298i | \(-0.231269\pi\) | ||||
0.747468 | + | 0.664298i | \(0.231269\pi\) | |||||||
\(384\) | −0.126650 | −0.00646306 | ||||||||
\(385\) | −23.5185 | −1.19862 | ||||||||
\(386\) | −16.1070 | −0.819827 | ||||||||
\(387\) | 22.6909 | 1.15344 | ||||||||
\(388\) | −0.991788 | −0.0503504 | ||||||||
\(389\) | 15.2945 | 0.775464 | 0.387732 | − | 0.921772i | \(-0.373259\pi\) | ||||
0.387732 | + | 0.921772i | \(0.373259\pi\) | |||||||
\(390\) | −0.123781 | −0.00626790 | ||||||||
\(391\) | −27.3512 | −1.38321 | ||||||||
\(392\) | 2.74902 | 0.138847 | ||||||||
\(393\) | −1.46912 | −0.0741075 | ||||||||
\(394\) | −8.52039 | −0.429251 | ||||||||
\(395\) | −24.3434 | −1.22485 | ||||||||
\(396\) | −8.98161 | −0.451343 | ||||||||
\(397\) | 6.29432 | 0.315903 | 0.157951 | − | 0.987447i | \(-0.449511\pi\) | ||||
0.157951 | + | 0.987447i | \(0.449511\pi\) | |||||||
\(398\) | −21.5290 | −1.07915 | ||||||||
\(399\) | −1.07661 | −0.0538979 | ||||||||
\(400\) | 1.26236 | 0.0631178 | ||||||||
\(401\) | 10.5056 | 0.524622 | 0.262311 | − | 0.964983i | \(-0.415515\pi\) | ||||
0.262311 | + | 0.964983i | \(0.415515\pi\) | |||||||
\(402\) | −0.155208 | −0.00774109 | ||||||||
\(403\) | −2.86711 | −0.142821 | ||||||||
\(404\) | −12.0240 | −0.598218 | ||||||||
\(405\) | 22.1616 | 1.10122 | ||||||||
\(406\) | 9.00735 | 0.447027 | ||||||||
\(407\) | 13.9426 | 0.691110 | ||||||||
\(408\) | 0.551907 | 0.0273235 | ||||||||
\(409\) | 24.4450 | 1.20873 | 0.604365 | − | 0.796708i | \(-0.293427\pi\) | ||||
0.604365 | + | 0.796708i | \(0.293427\pi\) | |||||||
\(410\) | −0.923529 | −0.0456098 | ||||||||
\(411\) | −1.06169 | −0.0523695 | ||||||||
\(412\) | −12.8902 | −0.635052 | ||||||||
\(413\) | −42.7891 | −2.10551 | ||||||||
\(414\) | −18.7287 | −0.920463 | ||||||||
\(415\) | −2.00887 | −0.0986114 | ||||||||
\(416\) | 0.390555 | 0.0191485 | ||||||||
\(417\) | −2.86003 | −0.140056 | ||||||||
\(418\) | −8.19474 | −0.400818 | ||||||||
\(419\) | 23.6498 | 1.15537 | 0.577684 | − | 0.816260i | \(-0.303957\pi\) | ||||
0.577684 | + | 0.816260i | \(0.303957\pi\) | |||||||
\(420\) | 0.989585 | 0.0482868 | ||||||||
\(421\) | 17.6998 | 0.862638 | 0.431319 | − | 0.902200i | \(-0.358048\pi\) | ||||
0.431319 | + | 0.902200i | \(0.358048\pi\) | |||||||
\(422\) | −1.17635 | −0.0572637 | ||||||||
\(423\) | 17.9774 | 0.874091 | ||||||||
\(424\) | 2.88719 | 0.140215 | ||||||||
\(425\) | −5.50103 | −0.266839 | ||||||||
\(426\) | 1.11033 | 0.0537955 | ||||||||
\(427\) | 40.1194 | 1.94151 | ||||||||
\(428\) | −17.0471 | −0.824002 | ||||||||
\(429\) | −0.148884 | −0.00718817 | ||||||||
\(430\) | −19.0295 | −0.917684 | ||||||||
\(431\) | −35.5338 | −1.71160 | −0.855802 | − | 0.517304i | \(-0.826936\pi\) | ||||
−0.855802 | + | 0.517304i | \(0.826936\pi\) | |||||||
\(432\) | 0.757866 | 0.0364629 | ||||||||
\(433\) | −3.27087 | −0.157188 | −0.0785939 | − | 0.996907i | \(-0.525043\pi\) | ||||
−0.0785939 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(434\) | 22.9215 | 1.10027 | ||||||||
\(435\) | 0.914301 | 0.0438374 | ||||||||
\(436\) | 14.0833 | 0.674467 | ||||||||
\(437\) | −17.0879 | −0.817423 | ||||||||
\(438\) | −0.406922 | −0.0194435 | ||||||||
\(439\) | 22.7977 | 1.08807 | 0.544037 | − | 0.839061i | \(-0.316895\pi\) | ||||
0.544037 | + | 0.839061i | \(0.316895\pi\) | |||||||
\(440\) | 7.53234 | 0.359090 | ||||||||
\(441\) | −8.20298 | −0.390618 | ||||||||
\(442\) | −1.70194 | −0.0809530 | ||||||||
\(443\) | −15.4272 | −0.732967 | −0.366484 | − | 0.930424i | \(-0.619438\pi\) | ||||
−0.366484 | + | 0.930424i | \(0.619438\pi\) | |||||||
\(444\) | −0.586661 | −0.0278417 | ||||||||
\(445\) | −21.5304 | −1.02064 | ||||||||
\(446\) | 4.45579 | 0.210988 | ||||||||
\(447\) | 2.01649 | 0.0953765 | ||||||||
\(448\) | −3.12234 | −0.147517 | ||||||||
\(449\) | −13.6450 | −0.643947 | −0.321973 | − | 0.946749i | \(-0.604346\pi\) | ||||
−0.321973 | + | 0.946749i | \(0.604346\pi\) | |||||||
\(450\) | −3.76682 | −0.177569 | ||||||||
\(451\) | −1.11082 | −0.0523063 | ||||||||
\(452\) | 3.86364 | 0.181730 | ||||||||
\(453\) | 1.37437 | 0.0645737 | ||||||||
\(454\) | 19.3013 | 0.905855 | ||||||||
\(455\) | −3.05163 | −0.143062 | ||||||||
\(456\) | 0.344809 | 0.0161471 | ||||||||
\(457\) | −12.0586 | −0.564080 | −0.282040 | − | 0.959403i | \(-0.591011\pi\) | ||||
−0.282040 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(458\) | −26.1577 | −1.22227 | ||||||||
\(459\) | −3.30259 | −0.154152 | ||||||||
\(460\) | 15.7066 | 0.732324 | ||||||||
\(461\) | −7.53956 | −0.351153 | −0.175576 | − | 0.984466i | \(-0.556179\pi\) | ||||
−0.175576 | + | 0.984466i | \(0.556179\pi\) | |||||||
\(462\) | 1.19027 | 0.0553764 | ||||||||
\(463\) | −11.3090 | −0.525572 | −0.262786 | − | 0.964854i | \(-0.584641\pi\) | ||||
−0.262786 | + | 0.964854i | \(0.584641\pi\) | |||||||
\(464\) | −2.88480 | −0.133924 | ||||||||
\(465\) | 2.32668 | 0.107897 | ||||||||
\(466\) | −20.2416 | −0.937674 | ||||||||
\(467\) | −8.17243 | −0.378175 | −0.189087 | − | 0.981960i | \(-0.560553\pi\) | ||||
−0.189087 | + | 0.981960i | \(0.560553\pi\) | |||||||
\(468\) | −1.16540 | −0.0538706 | ||||||||
\(469\) | −3.82641 | −0.176687 | ||||||||
\(470\) | −15.0766 | −0.695430 | ||||||||
\(471\) | −2.69284 | −0.124080 | ||||||||
\(472\) | 13.7042 | 0.630785 | ||||||||
\(473\) | −22.8886 | −1.05242 | ||||||||
\(474\) | 1.23202 | 0.0565883 | ||||||||
\(475\) | −3.43681 | −0.157692 | ||||||||
\(476\) | 13.6064 | 0.623647 | ||||||||
\(477\) | −8.61527 | −0.394466 | ||||||||
\(478\) | −11.8533 | −0.542159 | ||||||||
\(479\) | 31.2123 | 1.42612 | 0.713062 | − | 0.701101i | \(-0.247308\pi\) | ||||
0.713062 | + | 0.701101i | \(0.247308\pi\) | |||||||
\(480\) | −0.316937 | −0.0144661 | ||||||||
\(481\) | 1.80911 | 0.0824883 | ||||||||
\(482\) | 5.11831 | 0.233133 | ||||||||
\(483\) | 2.48198 | 0.112934 | ||||||||
\(484\) | −1.94012 | −0.0881875 | ||||||||
\(485\) | −2.48192 | −0.112698 | ||||||||
\(486\) | −3.39519 | −0.154009 | ||||||||
\(487\) | 26.7699 | 1.21306 | 0.606529 | − | 0.795061i | \(-0.292561\pi\) | ||||
0.606529 | + | 0.795061i | \(0.292561\pi\) | |||||||
\(488\) | −12.8491 | −0.581653 | ||||||||
\(489\) | −0.876856 | −0.0396528 | ||||||||
\(490\) | 6.87935 | 0.310777 | ||||||||
\(491\) | −40.7714 | −1.83999 | −0.919995 | − | 0.391931i | \(-0.871807\pi\) | ||||
−0.919995 | + | 0.391931i | \(0.871807\pi\) | |||||||
\(492\) | 0.0467396 | 0.00210719 | ||||||||
\(493\) | 12.5713 | 0.566181 | ||||||||
\(494\) | −1.06330 | −0.0478402 | ||||||||
\(495\) | −22.4762 | −1.01023 | ||||||||
\(496\) | −7.34113 | −0.329627 | ||||||||
\(497\) | 27.3733 | 1.22786 | ||||||||
\(498\) | 0.101668 | 0.00455587 | ||||||||
\(499\) | −22.6172 | −1.01249 | −0.506243 | − | 0.862391i | \(-0.668966\pi\) | ||||
−0.506243 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(500\) | −9.35334 | −0.418294 | ||||||||
\(501\) | −1.33700 | −0.0597327 | ||||||||
\(502\) | −19.6617 | −0.877543 | ||||||||
\(503\) | −21.1317 | −0.942216 | −0.471108 | − | 0.882076i | \(-0.656146\pi\) | ||||
−0.471108 | + | 0.882076i | \(0.656146\pi\) | |||||||
\(504\) | 9.31695 | 0.415010 | ||||||||
\(505\) | −30.0898 | −1.33898 | ||||||||
\(506\) | 18.8919 | 0.839846 | ||||||||
\(507\) | 1.62713 | 0.0722632 | ||||||||
\(508\) | −0.943810 | −0.0418748 | ||||||||
\(509\) | −8.33660 | −0.369513 | −0.184757 | − | 0.982784i | \(-0.559150\pi\) | ||||
−0.184757 | + | 0.982784i | \(0.559150\pi\) | |||||||
\(510\) | 1.38113 | 0.0611575 | ||||||||
\(511\) | −10.0320 | −0.443790 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.06332 | −0.0910978 | ||||||||
\(514\) | −8.77198 | −0.386915 | ||||||||
\(515\) | −32.2572 | −1.42142 | ||||||||
\(516\) | 0.963080 | 0.0423972 | ||||||||
\(517\) | −18.1341 | −0.797535 | ||||||||
\(518\) | −14.4632 | −0.635475 | ||||||||
\(519\) | 2.92124 | 0.128228 | ||||||||
\(520\) | 0.977351 | 0.0428597 | ||||||||
\(521\) | 3.41569 | 0.149644 | 0.0748222 | − | 0.997197i | \(-0.476161\pi\) | ||||
0.0748222 | + | 0.997197i | \(0.476161\pi\) | |||||||
\(522\) | 8.60814 | 0.376768 | ||||||||
\(523\) | 25.8922 | 1.13219 | 0.566093 | − | 0.824341i | \(-0.308454\pi\) | ||||
0.566093 | + | 0.824341i | \(0.308454\pi\) | |||||||
\(524\) | 11.5999 | 0.506744 | ||||||||
\(525\) | 0.499190 | 0.0217864 | ||||||||
\(526\) | −12.5090 | −0.545416 | ||||||||
\(527\) | 31.9908 | 1.39354 | ||||||||
\(528\) | −0.381211 | −0.0165901 | ||||||||
\(529\) | 16.3937 | 0.712771 | ||||||||
\(530\) | 7.22512 | 0.313839 | ||||||||
\(531\) | −40.8926 | −1.77459 | ||||||||
\(532\) | 8.50070 | 0.368552 | ||||||||
\(533\) | −0.144133 | −0.00624309 | ||||||||
\(534\) | 1.08965 | 0.0471539 | ||||||||
\(535\) | −42.6598 | −1.84434 | ||||||||
\(536\) | 1.22549 | 0.0529333 | ||||||||
\(537\) | −1.02057 | −0.0440409 | ||||||||
\(538\) | 27.5019 | 1.18569 | ||||||||
\(539\) | 8.27446 | 0.356406 | ||||||||
\(540\) | 1.89654 | 0.0816140 | ||||||||
\(541\) | −34.1036 | −1.46623 | −0.733115 | − | 0.680105i | \(-0.761934\pi\) | ||||
−0.733115 | + | 0.680105i | \(0.761934\pi\) | |||||||
\(542\) | 10.0589 | 0.432065 | ||||||||
\(543\) | −0.778764 | −0.0334200 | ||||||||
\(544\) | −4.35775 | −0.186837 | ||||||||
\(545\) | 35.2430 | 1.50964 | ||||||||
\(546\) | 0.154442 | 0.00660952 | ||||||||
\(547\) | 15.5133 | 0.663300 | 0.331650 | − | 0.943403i | \(-0.392395\pi\) | ||||
0.331650 | + | 0.943403i | \(0.392395\pi\) | |||||||
\(548\) | 8.38292 | 0.358100 | ||||||||
\(549\) | 38.3413 | 1.63637 | ||||||||
\(550\) | 3.79964 | 0.162017 | ||||||||
\(551\) | 7.85400 | 0.334591 | ||||||||
\(552\) | −0.794909 | −0.0338336 | ||||||||
\(553\) | 30.3734 | 1.29161 | ||||||||
\(554\) | −24.5466 | −1.04288 | ||||||||
\(555\) | −1.46810 | −0.0623174 | ||||||||
\(556\) | 22.5822 | 0.957699 | ||||||||
\(557\) | 16.1369 | 0.683744 | 0.341872 | − | 0.939746i | \(-0.388939\pi\) | ||||
0.341872 | + | 0.939746i | \(0.388939\pi\) | |||||||
\(558\) | 21.9056 | 0.927340 | ||||||||
\(559\) | −2.96989 | −0.125613 | ||||||||
\(560\) | −7.81357 | −0.330184 | ||||||||
\(561\) | 1.66122 | 0.0701368 | ||||||||
\(562\) | −4.34867 | −0.183437 | ||||||||
\(563\) | −19.6166 | −0.826742 | −0.413371 | − | 0.910563i | \(-0.635649\pi\) | ||||
−0.413371 | + | 0.910563i | \(0.635649\pi\) | |||||||
\(564\) | 0.763023 | 0.0321291 | ||||||||
\(565\) | 9.66865 | 0.406763 | ||||||||
\(566\) | −7.70675 | −0.323939 | ||||||||
\(567\) | −27.6511 | −1.16124 | ||||||||
\(568\) | −8.76692 | −0.367852 | ||||||||
\(569\) | −29.3645 | −1.23102 | −0.615512 | − | 0.788128i | \(-0.711051\pi\) | ||||
−0.615512 | + | 0.788128i | \(0.711051\pi\) | |||||||
\(570\) | 0.862873 | 0.0361418 | ||||||||
\(571\) | −15.5952 | −0.652639 | −0.326319 | − | 0.945260i | \(-0.605808\pi\) | ||||
−0.326319 | + | 0.945260i | \(0.605808\pi\) | |||||||
\(572\) | 1.17555 | 0.0491524 | ||||||||
\(573\) | 0.00689554 | 0.000288065 0 | ||||||||
\(574\) | 1.15229 | 0.0480957 | ||||||||
\(575\) | 7.92310 | 0.330416 | ||||||||
\(576\) | −2.98396 | −0.124332 | ||||||||
\(577\) | 5.18503 | 0.215856 | 0.107928 | − | 0.994159i | \(-0.465578\pi\) | ||||
0.107928 | + | 0.994159i | \(0.465578\pi\) | |||||||
\(578\) | 1.98997 | 0.0827716 | ||||||||
\(579\) | 2.03995 | 0.0847775 | ||||||||
\(580\) | −7.21914 | −0.299758 | ||||||||
\(581\) | 2.50647 | 0.103986 | ||||||||
\(582\) | 0.125610 | 0.00520669 | ||||||||
\(583\) | 8.69035 | 0.359917 | ||||||||
\(584\) | 3.21298 | 0.132954 | ||||||||
\(585\) | −2.91638 | −0.120577 | ||||||||
\(586\) | −4.11838 | −0.170129 | ||||||||
\(587\) | 13.9974 | 0.577733 | 0.288866 | − | 0.957369i | \(-0.406722\pi\) | ||||
0.288866 | + | 0.957369i | \(0.406722\pi\) | |||||||
\(588\) | −0.348163 | −0.0143580 | ||||||||
\(589\) | 19.9865 | 0.823531 | ||||||||
\(590\) | 34.2942 | 1.41187 | ||||||||
\(591\) | 1.07910 | 0.0443884 | ||||||||
\(592\) | 4.63215 | 0.190380 | ||||||||
\(593\) | −13.0323 | −0.535174 | −0.267587 | − | 0.963534i | \(-0.586226\pi\) | ||||
−0.267587 | + | 0.963534i | \(0.586226\pi\) | |||||||
\(594\) | 2.28115 | 0.0935967 | ||||||||
\(595\) | 34.0496 | 1.39590 | ||||||||
\(596\) | −15.9218 | −0.652181 | ||||||||
\(597\) | 2.72664 | 0.111594 | ||||||||
\(598\) | 2.45129 | 0.100241 | ||||||||
\(599\) | 28.9347 | 1.18224 | 0.591120 | − | 0.806583i | \(-0.298686\pi\) | ||||
0.591120 | + | 0.806583i | \(0.298686\pi\) | |||||||
\(600\) | −0.159877 | −0.00652694 | ||||||||
\(601\) | 12.6610 | 0.516453 | 0.258226 | − | 0.966084i | \(-0.416862\pi\) | ||||
0.258226 | + | 0.966084i | \(0.416862\pi\) | |||||||
\(602\) | 23.7432 | 0.967700 | ||||||||
\(603\) | −3.65683 | −0.148917 | ||||||||
\(604\) | −10.8518 | −0.441553 | ||||||||
\(605\) | −4.85510 | −0.197388 | ||||||||
\(606\) | 1.52284 | 0.0618611 | ||||||||
\(607\) | 43.4709 | 1.76443 | 0.882214 | − | 0.470848i | \(-0.156052\pi\) | ||||
0.882214 | + | 0.470848i | \(0.156052\pi\) | |||||||
\(608\) | −2.72254 | −0.110414 | ||||||||
\(609\) | −1.14078 | −0.0462266 | ||||||||
\(610\) | −32.1546 | −1.30190 | ||||||||
\(611\) | −2.35297 | −0.0951908 | ||||||||
\(612\) | 13.0033 | 0.525629 | ||||||||
\(613\) | −3.49037 | −0.140975 | −0.0704873 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704873 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(614\) | −7.03580 | −0.283942 | ||||||||
\(615\) | 0.116965 | 0.00471647 | ||||||||
\(616\) | −9.39813 | −0.378662 | ||||||||
\(617\) | −4.63108 | −0.186440 | −0.0932201 | − | 0.995646i | \(-0.529716\pi\) | ||||
−0.0932201 | + | 0.995646i | \(0.529716\pi\) | |||||||
\(618\) | 1.63253 | 0.0656701 | ||||||||
\(619\) | −27.4710 | −1.10415 | −0.552076 | − | 0.833794i | \(-0.686164\pi\) | ||||
−0.552076 | + | 0.833794i | \(0.686164\pi\) | |||||||
\(620\) | −18.3710 | −0.737796 | ||||||||
\(621\) | 4.75670 | 0.190880 | ||||||||
\(622\) | 3.45972 | 0.138722 | ||||||||
\(623\) | 26.8636 | 1.07627 | ||||||||
\(624\) | −0.0494636 | −0.00198013 | ||||||||
\(625\) | −29.7182 | −1.18873 | ||||||||
\(626\) | −20.3659 | −0.813986 | ||||||||
\(627\) | 1.03786 | 0.0414482 | ||||||||
\(628\) | 21.2621 | 0.848452 | ||||||||
\(629\) | −20.1858 | −0.804859 | ||||||||
\(630\) | 23.3154 | 0.928907 | ||||||||
\(631\) | 6.00772 | 0.239164 | 0.119582 | − | 0.992824i | \(-0.461845\pi\) | ||||
0.119582 | + | 0.992824i | \(0.461845\pi\) | |||||||
\(632\) | −9.72775 | −0.386949 | ||||||||
\(633\) | 0.148984 | 0.00592158 | ||||||||
\(634\) | 3.95097 | 0.156913 | ||||||||
\(635\) | −2.36186 | −0.0937274 | ||||||||
\(636\) | −0.365662 | −0.0144994 | ||||||||
\(637\) | 1.07364 | 0.0425393 | ||||||||
\(638\) | −8.68316 | −0.343769 | ||||||||
\(639\) | 26.1601 | 1.03488 | ||||||||
\(640\) | 2.50247 | 0.0989188 | ||||||||
\(641\) | −21.1296 | −0.834570 | −0.417285 | − | 0.908776i | \(-0.637018\pi\) | ||||
−0.417285 | + | 0.908776i | \(0.637018\pi\) | |||||||
\(642\) | 2.15901 | 0.0852092 | ||||||||
\(643\) | −3.64782 | −0.143856 | −0.0719279 | − | 0.997410i | \(-0.522915\pi\) | ||||
−0.0719279 | + | 0.997410i | \(0.522915\pi\) | |||||||
\(644\) | −19.5972 | −0.772238 | ||||||||
\(645\) | 2.41008 | 0.0948968 | ||||||||
\(646\) | 11.8641 | 0.466788 | ||||||||
\(647\) | 32.0127 | 1.25855 | 0.629274 | − | 0.777183i | \(-0.283352\pi\) | ||||
0.629274 | + | 0.777183i | \(0.283352\pi\) | |||||||
\(648\) | 8.85590 | 0.347892 | ||||||||
\(649\) | 41.2490 | 1.61916 | ||||||||
\(650\) | 0.493019 | 0.0193378 | ||||||||
\(651\) | −2.90300 | −0.113778 | ||||||||
\(652\) | 6.92348 | 0.271144 | ||||||||
\(653\) | −40.6625 | −1.59125 | −0.795624 | − | 0.605791i | \(-0.792857\pi\) | ||||
−0.795624 | + | 0.605791i | \(0.792857\pi\) | |||||||
\(654\) | −1.78364 | −0.0697459 | ||||||||
\(655\) | 29.0284 | 1.13423 | ||||||||
\(656\) | −0.369047 | −0.0144089 | ||||||||
\(657\) | −9.58739 | −0.374040 | ||||||||
\(658\) | 18.8111 | 0.733333 | ||||||||
\(659\) | −28.9172 | −1.12646 | −0.563228 | − | 0.826302i | \(-0.690441\pi\) | ||||
−0.563228 | + | 0.826302i | \(0.690441\pi\) | |||||||
\(660\) | −0.953968 | −0.0371332 | ||||||||
\(661\) | 19.5479 | 0.760323 | 0.380162 | − | 0.924920i | \(-0.375868\pi\) | ||||
0.380162 | + | 0.924920i | \(0.375868\pi\) | |||||||
\(662\) | 14.1985 | 0.551839 | ||||||||
\(663\) | 0.215550 | 0.00837126 | ||||||||
\(664\) | −0.802753 | −0.0311529 | ||||||||
\(665\) | 21.2728 | 0.824922 | ||||||||
\(666\) | −13.8222 | −0.535598 | ||||||||
\(667\) | −18.1063 | −0.701079 | ||||||||
\(668\) | 10.5567 | 0.408450 | ||||||||
\(669\) | −0.564324 | −0.0218180 | ||||||||
\(670\) | 3.06676 | 0.118479 | ||||||||
\(671\) | −38.6754 | −1.49305 | ||||||||
\(672\) | 0.395443 | 0.0152546 | ||||||||
\(673\) | −4.04802 | −0.156040 | −0.0780198 | − | 0.996952i | \(-0.524860\pi\) | ||||
−0.0780198 | + | 0.996952i | \(0.524860\pi\) | |||||||
\(674\) | 16.8297 | 0.648256 | ||||||||
\(675\) | 0.956696 | 0.0368233 | ||||||||
\(676\) | −12.8475 | −0.494133 | ||||||||
\(677\) | −15.5233 | −0.596609 | −0.298305 | − | 0.954471i | \(-0.596421\pi\) | ||||
−0.298305 | + | 0.954471i | \(0.596421\pi\) | |||||||
\(678\) | −0.489329 | −0.0187926 | ||||||||
\(679\) | 3.09670 | 0.118841 | ||||||||
\(680\) | −10.9051 | −0.418193 | ||||||||
\(681\) | −2.44450 | −0.0936735 | ||||||||
\(682\) | −22.0965 | −0.846120 | ||||||||
\(683\) | −19.5096 | −0.746513 | −0.373257 | − | 0.927728i | \(-0.621759\pi\) | ||||
−0.373257 | + | 0.927728i | \(0.621759\pi\) | |||||||
\(684\) | 8.12395 | 0.310627 | ||||||||
\(685\) | 20.9780 | 0.801528 | ||||||||
\(686\) | 13.2730 | 0.506766 | ||||||||
\(687\) | 3.31286 | 0.126394 | ||||||||
\(688\) | −7.60429 | −0.289911 | ||||||||
\(689\) | 1.12761 | 0.0429584 | ||||||||
\(690\) | −1.98924 | −0.0757289 | ||||||||
\(691\) | 16.2742 | 0.619099 | 0.309550 | − | 0.950883i | \(-0.399822\pi\) | ||||
0.309550 | + | 0.950883i | \(0.399822\pi\) | |||||||
\(692\) | −23.0655 | −0.876819 | ||||||||
\(693\) | 28.0437 | 1.06529 | ||||||||
\(694\) | −6.72762 | −0.255377 | ||||||||
\(695\) | 56.5113 | 2.14360 | ||||||||
\(696\) | 0.365359 | 0.0138489 | ||||||||
\(697\) | 1.60821 | 0.0609154 | ||||||||
\(698\) | 21.2764 | 0.805323 | ||||||||
\(699\) | 2.56359 | 0.0969639 | ||||||||
\(700\) | −3.94151 | −0.148975 | ||||||||
\(701\) | −6.73472 | −0.254367 | −0.127183 | − | 0.991879i | \(-0.540594\pi\) | ||||
−0.127183 | + | 0.991879i | \(0.540594\pi\) | |||||||
\(702\) | 0.295988 | 0.0111714 | ||||||||
\(703\) | −12.6112 | −0.475641 | ||||||||
\(704\) | 3.00996 | 0.113442 | ||||||||
\(705\) | 1.90944 | 0.0719137 | ||||||||
\(706\) | 20.5331 | 0.772772 | ||||||||
\(707\) | 37.5431 | 1.41195 | ||||||||
\(708\) | −1.73563 | −0.0652288 | ||||||||
\(709\) | 4.15033 | 0.155869 | 0.0779344 | − | 0.996958i | \(-0.475168\pi\) | ||||
0.0779344 | + | 0.996958i | \(0.475168\pi\) | |||||||
\(710\) | −21.9390 | −0.823354 | ||||||||
\(711\) | 29.0272 | 1.08861 | ||||||||
\(712\) | −8.60368 | −0.322436 | ||||||||
\(713\) | −46.0762 | −1.72557 | ||||||||
\(714\) | −1.72324 | −0.0644907 | ||||||||
\(715\) | 2.94179 | 0.110017 | ||||||||
\(716\) | 8.05824 | 0.301150 | ||||||||
\(717\) | 1.50122 | 0.0560641 | ||||||||
\(718\) | 27.2939 | 1.01860 | ||||||||
\(719\) | 18.9536 | 0.706848 | 0.353424 | − | 0.935463i | \(-0.385017\pi\) | ||||
0.353424 | + | 0.935463i | \(0.385017\pi\) | |||||||
\(720\) | −7.46727 | −0.278289 | ||||||||
\(721\) | 40.2475 | 1.49889 | ||||||||
\(722\) | −11.5878 | −0.431252 | ||||||||
\(723\) | −0.648232 | −0.0241080 | ||||||||
\(724\) | 6.14897 | 0.228525 | ||||||||
\(725\) | −3.64165 | −0.135247 | ||||||||
\(726\) | 0.245716 | 0.00911938 | ||||||||
\(727\) | −12.3450 | −0.457849 | −0.228925 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228925 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(728\) | −1.21945 | −0.0451957 | ||||||||
\(729\) | −26.1377 | −0.968063 | ||||||||
\(730\) | 8.04038 | 0.297588 | ||||||||
\(731\) | 33.1376 | 1.22564 | ||||||||
\(732\) | 1.62734 | 0.0601481 | ||||||||
\(733\) | 30.6547 | 1.13226 | 0.566128 | − | 0.824317i | \(-0.308441\pi\) | ||||
0.566128 | + | 0.824317i | \(0.308441\pi\) | |||||||
\(734\) | 10.6571 | 0.393359 | ||||||||
\(735\) | −0.871267 | −0.0321372 | ||||||||
\(736\) | 6.27644 | 0.231353 | ||||||||
\(737\) | 3.68869 | 0.135875 | ||||||||
\(738\) | 1.10122 | 0.0405365 | ||||||||
\(739\) | −11.2582 | −0.414140 | −0.207070 | − | 0.978326i | \(-0.566393\pi\) | ||||
−0.207070 | + | 0.978326i | \(0.566393\pi\) | |||||||
\(740\) | 11.5918 | 0.426124 | ||||||||
\(741\) | 0.134667 | 0.00494710 | ||||||||
\(742\) | −9.01481 | −0.330944 | ||||||||
\(743\) | 15.1182 | 0.554634 | 0.277317 | − | 0.960778i | \(-0.410555\pi\) | ||||
0.277317 | + | 0.960778i | \(0.410555\pi\) | |||||||
\(744\) | 0.929752 | 0.0340864 | ||||||||
\(745\) | −39.8438 | −1.45976 | ||||||||
\(746\) | 25.7862 | 0.944100 | ||||||||
\(747\) | 2.39538 | 0.0876425 | ||||||||
\(748\) | −13.1167 | −0.479593 | ||||||||
\(749\) | 53.2268 | 1.94487 | ||||||||
\(750\) | 1.18460 | 0.0432554 | ||||||||
\(751\) | −13.6534 | −0.498219 | −0.249110 | − | 0.968475i | \(-0.580138\pi\) | ||||
−0.249110 | + | 0.968475i | \(0.580138\pi\) | |||||||
\(752\) | −6.02468 | −0.219697 | ||||||||
\(753\) | 2.49014 | 0.0907458 | ||||||||
\(754\) | −1.12667 | −0.0410310 | ||||||||
\(755\) | −27.1563 | −0.988318 | ||||||||
\(756\) | −2.36632 | −0.0860622 | ||||||||
\(757\) | −47.9357 | −1.74225 | −0.871127 | − | 0.491058i | \(-0.836610\pi\) | ||||
−0.871127 | + | 0.491058i | \(0.836610\pi\) | |||||||
\(758\) | 9.98509 | 0.362675 | ||||||||
\(759\) | −2.39265 | −0.0868476 | ||||||||
\(760\) | −6.81307 | −0.247136 | ||||||||
\(761\) | 46.4161 | 1.68258 | 0.841291 | − | 0.540582i | \(-0.181796\pi\) | ||||
0.841291 | + | 0.540582i | \(0.181796\pi\) | |||||||
\(762\) | 0.119533 | 0.00433023 | ||||||||
\(763\) | −43.9728 | −1.59192 | ||||||||
\(764\) | −0.0544458 | −0.00196978 | ||||||||
\(765\) | 32.5405 | 1.17650 | ||||||||
\(766\) | 29.2565 | 1.05708 | ||||||||
\(767\) | 5.35222 | 0.193257 | ||||||||
\(768\) | −0.126650 | −0.00457007 | ||||||||
\(769\) | 18.2813 | 0.659242 | 0.329621 | − | 0.944113i | \(-0.393079\pi\) | ||||
0.329621 | + | 0.944113i | \(0.393079\pi\) | |||||||
\(770\) | −23.5185 | −0.847550 | ||||||||
\(771\) | 1.11097 | 0.0400105 | ||||||||
\(772\) | −16.1070 | −0.579705 | ||||||||
\(773\) | −42.5397 | −1.53005 | −0.765024 | − | 0.644002i | \(-0.777273\pi\) | ||||
−0.765024 | + | 0.644002i | \(0.777273\pi\) | |||||||
\(774\) | 22.6909 | 0.815607 | ||||||||
\(775\) | −9.26712 | −0.332885 | ||||||||
\(776\) | −0.991788 | −0.0356031 | ||||||||
\(777\) | 1.83176 | 0.0657139 | ||||||||
\(778\) | 15.2945 | 0.548336 | ||||||||
\(779\) | 1.00474 | 0.0359987 | ||||||||
\(780\) | −0.123781 | −0.00443208 | ||||||||
\(781\) | −26.3881 | −0.944240 | ||||||||
\(782\) | −27.3512 | −0.978075 | ||||||||
\(783\) | −2.18630 | −0.0781319 | ||||||||
\(784\) | 2.74902 | 0.0981794 | ||||||||
\(785\) | 53.2079 | 1.89907 | ||||||||
\(786\) | −1.46912 | −0.0524019 | ||||||||
\(787\) | 48.7724 | 1.73855 | 0.869274 | − | 0.494330i | \(-0.164587\pi\) | ||||
0.869274 | + | 0.494330i | \(0.164587\pi\) | |||||||
\(788\) | −8.52039 | −0.303526 | ||||||||
\(789\) | 1.58425 | 0.0564009 | ||||||||
\(790\) | −24.3434 | −0.866099 | ||||||||
\(791\) | −12.0636 | −0.428933 | ||||||||
\(792\) | −8.98161 | −0.319148 | ||||||||
\(793\) | −5.01829 | −0.178205 | ||||||||
\(794\) | 6.29432 | 0.223377 | ||||||||
\(795\) | −0.915058 | −0.0324538 | ||||||||
\(796\) | −21.5290 | −0.763076 | ||||||||
\(797\) | 24.1444 | 0.855240 | 0.427620 | − | 0.903959i | \(-0.359352\pi\) | ||||
0.427620 | + | 0.903959i | \(0.359352\pi\) | |||||||
\(798\) | −1.07661 | −0.0381116 | ||||||||
\(799\) | 26.2540 | 0.928800 | ||||||||
\(800\) | 1.26236 | 0.0446310 | ||||||||
\(801\) | 25.6730 | 0.907112 | ||||||||
\(802\) | 10.5056 | 0.370964 | ||||||||
\(803\) | 9.67094 | 0.341280 | ||||||||
\(804\) | −0.155208 | −0.00547378 | ||||||||
\(805\) | −49.0414 | −1.72848 | ||||||||
\(806\) | −2.86711 | −0.100990 | ||||||||
\(807\) | −3.48310 | −0.122611 | ||||||||
\(808\) | −12.0240 | −0.423004 | ||||||||
\(809\) | −20.5369 | −0.722040 | −0.361020 | − | 0.932558i | \(-0.617571\pi\) | ||||
−0.361020 | + | 0.932558i | \(0.617571\pi\) | |||||||
\(810\) | 22.1616 | 0.778680 | ||||||||
\(811\) | −8.92591 | −0.313431 | −0.156716 | − | 0.987644i | \(-0.550091\pi\) | ||||
−0.156716 | + | 0.987644i | \(0.550091\pi\) | |||||||
\(812\) | 9.00735 | 0.316096 | ||||||||
\(813\) | −1.27395 | −0.0446794 | ||||||||
\(814\) | 13.9426 | 0.488688 | ||||||||
\(815\) | 17.3258 | 0.606896 | ||||||||
\(816\) | 0.551907 | 0.0193206 | ||||||||
\(817\) | 20.7030 | 0.724305 | ||||||||
\(818\) | 24.4450 | 0.854701 | ||||||||
\(819\) | 3.63878 | 0.127149 | ||||||||
\(820\) | −0.923529 | −0.0322510 | ||||||||
\(821\) | −28.7099 | −1.00198 | −0.500991 | − | 0.865453i | \(-0.667031\pi\) | ||||
−0.500991 | + | 0.865453i | \(0.667031\pi\) | |||||||
\(822\) | −1.06169 | −0.0370308 | ||||||||
\(823\) | 13.3817 | 0.466457 | 0.233228 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233228 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(824\) | −12.8902 | −0.449050 | ||||||||
\(825\) | −0.481223 | −0.0167540 | ||||||||
\(826\) | −42.7891 | −1.48882 | ||||||||
\(827\) | 8.97382 | 0.312050 | 0.156025 | − | 0.987753i | \(-0.450132\pi\) | ||||
0.156025 | + | 0.987753i | \(0.450132\pi\) | |||||||
\(828\) | −18.7287 | −0.650866 | ||||||||
\(829\) | −43.7005 | −1.51778 | −0.758890 | − | 0.651219i | \(-0.774258\pi\) | ||||
−0.758890 | + | 0.651219i | \(0.774258\pi\) | |||||||
\(830\) | −2.00887 | −0.0697288 | ||||||||
\(831\) | 3.10881 | 0.107844 | ||||||||
\(832\) | 0.390555 | 0.0135400 | ||||||||
\(833\) | −11.9795 | −0.415067 | ||||||||
\(834\) | −2.86003 | −0.0990347 | ||||||||
\(835\) | 26.4177 | 0.914224 | ||||||||
\(836\) | −8.19474 | −0.283421 | ||||||||
\(837\) | −5.56360 | −0.192306 | ||||||||
\(838\) | 23.6498 | 0.816969 | ||||||||
\(839\) | 44.3583 | 1.53142 | 0.765709 | − | 0.643187i | \(-0.222388\pi\) | ||||
0.765709 | + | 0.643187i | \(0.222388\pi\) | |||||||
\(840\) | 0.989585 | 0.0341439 | ||||||||
\(841\) | −20.6779 | −0.713031 | ||||||||
\(842\) | 17.6998 | 0.609977 | ||||||||
\(843\) | 0.550757 | 0.0189691 | ||||||||
\(844\) | −1.17635 | −0.0404915 | ||||||||
\(845\) | −32.1504 | −1.10601 | ||||||||
\(846\) | 17.9774 | 0.618075 | ||||||||
\(847\) | 6.05773 | 0.208146 | ||||||||
\(848\) | 2.88719 | 0.0991467 | ||||||||
\(849\) | 0.976057 | 0.0334982 | ||||||||
\(850\) | −5.50103 | −0.188684 | ||||||||
\(851\) | 29.0735 | 0.996625 | ||||||||
\(852\) | 1.11033 | 0.0380392 | ||||||||
\(853\) | −16.0290 | −0.548824 | −0.274412 | − | 0.961612i | \(-0.588483\pi\) | ||||
−0.274412 | + | 0.961612i | \(0.588483\pi\) | |||||||
\(854\) | 40.1194 | 1.37286 | ||||||||
\(855\) | 20.3299 | 0.695269 | ||||||||
\(856\) | −17.0471 | −0.582657 | ||||||||
\(857\) | −47.0530 | −1.60730 | −0.803649 | − | 0.595103i | \(-0.797111\pi\) | ||||
−0.803649 | + | 0.595103i | \(0.797111\pi\) | |||||||
\(858\) | −0.148884 | −0.00508280 | ||||||||
\(859\) | 57.1503 | 1.94994 | 0.974971 | − | 0.222332i | \(-0.0713668\pi\) | ||||
0.974971 | + | 0.222332i | \(0.0713668\pi\) | |||||||
\(860\) | −19.0295 | −0.648901 | ||||||||
\(861\) | −0.145937 | −0.00497353 | ||||||||
\(862\) | −35.5338 | −1.21029 | ||||||||
\(863\) | 44.6109 | 1.51857 | 0.759286 | − | 0.650757i | \(-0.225548\pi\) | ||||
0.759286 | + | 0.650757i | \(0.225548\pi\) | |||||||
\(864\) | 0.757866 | 0.0257831 | ||||||||
\(865\) | −57.7207 | −1.96256 | ||||||||
\(866\) | −3.27087 | −0.111149 | ||||||||
\(867\) | −0.252028 | −0.00855933 | ||||||||
\(868\) | 22.9215 | 0.778008 | ||||||||
\(869\) | −29.2802 | −0.993261 | ||||||||
\(870\) | 0.914301 | 0.0309977 | ||||||||
\(871\) | 0.478622 | 0.0162175 | ||||||||
\(872\) | 14.0833 | 0.476920 | ||||||||
\(873\) | 2.95946 | 0.100162 | ||||||||
\(874\) | −17.0879 | −0.578006 | ||||||||
\(875\) | 29.2043 | 0.987287 | ||||||||
\(876\) | −0.406922 | −0.0137486 | ||||||||
\(877\) | −28.1902 | −0.951917 | −0.475959 | − | 0.879468i | \(-0.657899\pi\) | ||||
−0.475959 | + | 0.879468i | \(0.657899\pi\) | |||||||
\(878\) | 22.7977 | 0.769385 | ||||||||
\(879\) | 0.521591 | 0.0175928 | ||||||||
\(880\) | 7.53234 | 0.253915 | ||||||||
\(881\) | 20.8092 | 0.701079 | 0.350539 | − | 0.936548i | \(-0.385998\pi\) | ||||
0.350539 | + | 0.936548i | \(0.385998\pi\) | |||||||
\(882\) | −8.20298 | −0.276209 | ||||||||
\(883\) | 46.4087 | 1.56178 | 0.780888 | − | 0.624671i | \(-0.214767\pi\) | ||||
0.780888 | + | 0.624671i | \(0.214767\pi\) | |||||||
\(884\) | −1.70194 | −0.0572424 | ||||||||
\(885\) | −4.34335 | −0.146000 | ||||||||
\(886\) | −15.4272 | −0.518286 | ||||||||
\(887\) | −37.3056 | −1.25260 | −0.626299 | − | 0.779583i | \(-0.715431\pi\) | ||||
−0.626299 | + | 0.779583i | \(0.715431\pi\) | |||||||
\(888\) | −0.586661 | −0.0196870 | ||||||||
\(889\) | 2.94690 | 0.0988358 | ||||||||
\(890\) | −21.5304 | −0.721702 | ||||||||
\(891\) | 26.6559 | 0.893007 | ||||||||
\(892\) | 4.45579 | 0.149191 | ||||||||
\(893\) | 16.4024 | 0.548886 | ||||||||
\(894\) | 2.01649 | 0.0674414 | ||||||||
\(895\) | 20.1655 | 0.674058 | ||||||||
\(896\) | −3.12234 | −0.104310 | ||||||||
\(897\) | −0.310455 | −0.0103658 | ||||||||
\(898\) | −13.6450 | −0.455339 | ||||||||
\(899\) | 21.1777 | 0.706317 | ||||||||
\(900\) | −3.76682 | −0.125561 | ||||||||
\(901\) | −12.5817 | −0.419156 | ||||||||
\(902\) | −1.11082 | −0.0369862 | ||||||||
\(903\) | −3.00707 | −0.100069 | ||||||||
\(904\) | 3.86364 | 0.128503 | ||||||||
\(905\) | 15.3876 | 0.511501 | ||||||||
\(906\) | 1.37437 | 0.0456605 | ||||||||
\(907\) | −10.9397 | −0.363246 | −0.181623 | − | 0.983368i | \(-0.558135\pi\) | ||||
−0.181623 | + | 0.983368i | \(0.558135\pi\) | |||||||
\(908\) | 19.3013 | 0.640536 | ||||||||
\(909\) | 35.8792 | 1.19004 | ||||||||
\(910\) | −3.05163 | −0.101160 | ||||||||
\(911\) | −7.46598 | −0.247359 | −0.123679 | − | 0.992322i | \(-0.539469\pi\) | ||||
−0.123679 | + | 0.992322i | \(0.539469\pi\) | |||||||
\(912\) | 0.344809 | 0.0114178 | ||||||||
\(913\) | −2.41626 | −0.0799665 | ||||||||
\(914\) | −12.0586 | −0.398865 | ||||||||
\(915\) | 4.07236 | 0.134628 | ||||||||
\(916\) | −26.1577 | −0.864275 | ||||||||
\(917\) | −36.2189 | −1.19605 | ||||||||
\(918\) | −3.30259 | −0.109002 | ||||||||
\(919\) | 45.6370 | 1.50543 | 0.752713 | − | 0.658349i | \(-0.228745\pi\) | ||||
0.752713 | + | 0.658349i | \(0.228745\pi\) | |||||||
\(920\) | 15.7066 | 0.517832 | ||||||||
\(921\) | 0.891081 | 0.0293621 | ||||||||
\(922\) | −7.53956 | −0.248302 | ||||||||
\(923\) | −3.42396 | −0.112701 | ||||||||
\(924\) | 1.19027 | 0.0391570 | ||||||||
\(925\) | 5.84742 | 0.192262 | ||||||||
\(926\) | −11.3090 | −0.371635 | ||||||||
\(927\) | 38.4637 | 1.26331 | ||||||||
\(928\) | −2.88480 | −0.0946984 | ||||||||
\(929\) | −7.40149 | −0.242835 | −0.121417 | − | 0.992602i | \(-0.538744\pi\) | ||||
−0.121417 | + | 0.992602i | \(0.538744\pi\) | |||||||
\(930\) | 2.32668 | 0.0762947 | ||||||||
\(931\) | −7.48433 | −0.245289 | ||||||||
\(932\) | −20.2416 | −0.663036 | ||||||||
\(933\) | −0.438172 | −0.0143451 | ||||||||
\(934\) | −8.17243 | −0.267410 | ||||||||
\(935\) | −32.8240 | −1.07346 | ||||||||
\(936\) | −1.16540 | −0.0380923 | ||||||||
\(937\) | −11.2189 | −0.366505 | −0.183253 | − | 0.983066i | \(-0.558663\pi\) | ||||
−0.183253 | + | 0.983066i | \(0.558663\pi\) | |||||||
\(938\) | −3.82641 | −0.124937 | ||||||||
\(939\) | 2.57934 | 0.0841735 | ||||||||
\(940\) | −15.0766 | −0.491744 | ||||||||
\(941\) | −53.1502 | −1.73265 | −0.866323 | − | 0.499484i | \(-0.833523\pi\) | ||||
−0.866323 | + | 0.499484i | \(0.833523\pi\) | |||||||
\(942\) | −2.69284 | −0.0877376 | ||||||||
\(943\) | −2.31630 | −0.0754292 | ||||||||
\(944\) | 13.7042 | 0.446032 | ||||||||
\(945\) | −5.92164 | −0.192631 | ||||||||
\(946\) | −22.8886 | −0.744173 | ||||||||
\(947\) | −9.21451 | −0.299431 | −0.149716 | − | 0.988729i | \(-0.547836\pi\) | ||||
−0.149716 | + | 0.988729i | \(0.547836\pi\) | |||||||
\(948\) | 1.23202 | 0.0400140 | ||||||||
\(949\) | 1.25484 | 0.0407339 | ||||||||
\(950\) | −3.43681 | −0.111505 | ||||||||
\(951\) | −0.500389 | −0.0162262 | ||||||||
\(952\) | 13.6064 | 0.440985 | ||||||||
\(953\) | −7.72435 | −0.250216 | −0.125108 | − | 0.992143i | \(-0.539928\pi\) | ||||
−0.125108 | + | 0.992143i | \(0.539928\pi\) | |||||||
\(954\) | −8.61527 | −0.278930 | ||||||||
\(955\) | −0.136249 | −0.00440891 | ||||||||
\(956\) | −11.8533 | −0.383364 | ||||||||
\(957\) | 1.09972 | 0.0355488 | ||||||||
\(958\) | 31.2123 | 1.00842 | ||||||||
\(959\) | −26.1743 | −0.845213 | ||||||||
\(960\) | −0.316937 | −0.0102291 | ||||||||
\(961\) | 22.8922 | 0.738459 | ||||||||
\(962\) | 1.80911 | 0.0583280 | ||||||||
\(963\) | 50.8678 | 1.63919 | ||||||||
\(964\) | 5.11831 | 0.164850 | ||||||||
\(965\) | −40.3074 | −1.29754 | ||||||||
\(966\) | 2.48198 | 0.0798563 | ||||||||
\(967\) | −1.21696 | −0.0391348 | −0.0195674 | − | 0.999809i | \(-0.506229\pi\) | ||||
−0.0195674 | + | 0.999809i | \(0.506229\pi\) | |||||||
\(968\) | −1.94012 | −0.0623580 | ||||||||
\(969\) | −1.50259 | −0.0482701 | ||||||||
\(970\) | −2.48192 | −0.0796897 | ||||||||
\(971\) | −41.6620 | −1.33700 | −0.668499 | − | 0.743713i | \(-0.733063\pi\) | ||||
−0.668499 | + | 0.743713i | \(0.733063\pi\) | |||||||
\(972\) | −3.39519 | −0.108901 | ||||||||
\(973\) | −70.5094 | −2.26043 | ||||||||
\(974\) | 26.7699 | 0.857762 | ||||||||
\(975\) | −0.0624406 | −0.00199970 | ||||||||
\(976\) | −12.8491 | −0.411291 | ||||||||
\(977\) | −12.3489 | −0.395077 | −0.197539 | − | 0.980295i | \(-0.563295\pi\) | ||||
−0.197539 | + | 0.980295i | \(0.563295\pi\) | |||||||
\(978\) | −0.876856 | −0.0280388 | ||||||||
\(979\) | −25.8967 | −0.827664 | ||||||||
\(980\) | 6.87935 | 0.219753 | ||||||||
\(981\) | −42.0240 | −1.34172 | ||||||||
\(982\) | −40.7714 | −1.30107 | ||||||||
\(983\) | −38.9411 | −1.24203 | −0.621013 | − | 0.783800i | \(-0.713279\pi\) | ||||
−0.621013 | + | 0.783800i | \(0.713279\pi\) | |||||||
\(984\) | 0.0467396 | 0.00149001 | ||||||||
\(985\) | −21.3220 | −0.679376 | ||||||||
\(986\) | 12.5713 | 0.400350 | ||||||||
\(987\) | −2.38242 | −0.0758332 | ||||||||
\(988\) | −1.06330 | −0.0338281 | ||||||||
\(989\) | −47.7279 | −1.51766 | ||||||||
\(990\) | −22.4762 | −0.714341 | ||||||||
\(991\) | 55.8994 | 1.77570 | 0.887852 | − | 0.460130i | \(-0.152197\pi\) | ||||
0.887852 | + | 0.460130i | \(0.152197\pi\) | |||||||
\(992\) | −7.34113 | −0.233081 | ||||||||
\(993\) | −1.79823 | −0.0570651 | ||||||||
\(994\) | 27.3733 | 0.868229 | ||||||||
\(995\) | −53.8758 | −1.70798 | ||||||||
\(996\) | 0.101668 | 0.00322149 | ||||||||
\(997\) | 39.7755 | 1.25970 | 0.629852 | − | 0.776715i | \(-0.283116\pi\) | ||||
0.629852 | + | 0.776715i | \(0.283116\pi\) | |||||||
\(998\) | −22.6172 | −0.715935 | ||||||||
\(999\) | 3.51055 | 0.111069 |
(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 | 8042.2.a.a.1.36 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.36 | ✓ | 67 | 1.1 | even | 1 | trivial |