Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25323 | −1.59327 | −0.796636 | − | 0.604460i | \(-0.793389\pi\) | ||||
−0.796636 | + | 0.604460i | \(0.793389\pi\) | |||||||
\(3\) | −3.09773 | −1.78847 | −0.894237 | − | 0.447595i | \(-0.852281\pi\) | ||||
−0.894237 | + | 0.447595i | \(0.852281\pi\) | |||||||
\(4\) | 3.07703 | 1.53851 | ||||||||
\(5\) | 4.21432 | 1.88470 | 0.942352 | − | 0.334624i | \(-0.108609\pi\) | ||||
0.942352 | + | 0.334624i | \(0.108609\pi\) | |||||||
\(6\) | 6.97988 | 2.84952 | ||||||||
\(7\) | −2.71387 | −1.02575 | −0.512873 | − | 0.858464i | \(-0.671419\pi\) | ||||
−0.512873 | + | 0.858464i | \(0.671419\pi\) | |||||||
\(8\) | −2.42679 | −0.857999 | ||||||||
\(9\) | 6.59591 | 2.19864 | ||||||||
\(10\) | −9.49583 | −3.00284 | ||||||||
\(11\) | −5.27116 | −1.58931 | −0.794657 | − | 0.607059i | \(-0.792349\pi\) | ||||
−0.794657 | + | 0.607059i | \(0.792349\pi\) | |||||||
\(12\) | −9.53179 | −2.75159 | ||||||||
\(13\) | 6.49332 | 1.80092 | 0.900461 | − | 0.434937i | \(-0.143229\pi\) | ||||
0.900461 | + | 0.434937i | \(0.143229\pi\) | |||||||
\(14\) | 6.11496 | 1.63429 | ||||||||
\(15\) | −13.0548 | −3.37074 | ||||||||
\(16\) | −0.685952 | −0.171488 | ||||||||
\(17\) | −6.74728 | −1.63646 | −0.818228 | − | 0.574894i | \(-0.805043\pi\) | ||||
−0.818228 | + | 0.574894i | \(0.805043\pi\) | |||||||
\(18\) | −14.8621 | −3.50302 | ||||||||
\(19\) | 3.73708 | 0.857345 | 0.428673 | − | 0.903460i | \(-0.358981\pi\) | ||||
0.428673 | + | 0.903460i | \(0.358981\pi\) | |||||||
\(20\) | 12.9676 | 2.89964 | ||||||||
\(21\) | 8.40683 | 1.83452 | ||||||||
\(22\) | 11.8771 | 2.53221 | ||||||||
\(23\) | 2.37719 | 0.495679 | 0.247840 | − | 0.968801i | \(-0.420279\pi\) | ||||
0.247840 | + | 0.968801i | \(0.420279\pi\) | |||||||
\(24\) | 7.51753 | 1.53451 | ||||||||
\(25\) | 12.7605 | 2.55211 | ||||||||
\(26\) | −14.6309 | −2.86936 | ||||||||
\(27\) | −11.1391 | −2.14373 | ||||||||
\(28\) | −8.35066 | −1.57813 | ||||||||
\(29\) | −3.48753 | −0.647617 | −0.323809 | − | 0.946123i | \(-0.604963\pi\) | ||||
−0.323809 | + | 0.946123i | \(0.604963\pi\) | |||||||
\(30\) | 29.4155 | 5.37051 | ||||||||
\(31\) | 6.22056 | 1.11725 | 0.558623 | − | 0.829422i | \(-0.311330\pi\) | ||||
0.558623 | + | 0.829422i | \(0.311330\pi\) | |||||||
\(32\) | 6.39918 | 1.13123 | ||||||||
\(33\) | 16.3286 | 2.84244 | ||||||||
\(34\) | 15.2032 | 2.60732 | ||||||||
\(35\) | −11.4371 | −1.93323 | ||||||||
\(36\) | 20.2958 | 3.38263 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | −8.42049 | −1.36598 | ||||||||
\(39\) | −20.1145 | −3.22090 | ||||||||
\(40\) | −10.2273 | −1.61707 | ||||||||
\(41\) | −7.24759 | −1.13188 | −0.565942 | − | 0.824445i | \(-0.691487\pi\) | ||||
−0.565942 | + | 0.824445i | \(0.691487\pi\) | |||||||
\(42\) | −18.9425 | −2.92289 | ||||||||
\(43\) | −2.56694 | −0.391455 | −0.195728 | − | 0.980658i | \(-0.562707\pi\) | ||||
−0.195728 | + | 0.980658i | \(0.562707\pi\) | |||||||
\(44\) | −16.2195 | −2.44518 | ||||||||
\(45\) | 27.7973 | 4.14378 | ||||||||
\(46\) | −5.35635 | −0.789751 | ||||||||
\(47\) | −7.19003 | −1.04877 | −0.524387 | − | 0.851480i | \(-0.675705\pi\) | ||||
−0.524387 | + | 0.851480i | \(0.675705\pi\) | |||||||
\(48\) | 2.12489 | 0.306702 | ||||||||
\(49\) | 0.365094 | 0.0521562 | ||||||||
\(50\) | −28.7524 | −4.06620 | ||||||||
\(51\) | 20.9012 | 2.92676 | ||||||||
\(52\) | 19.9801 | 2.77074 | ||||||||
\(53\) | −2.10804 | −0.289561 | −0.144781 | − | 0.989464i | \(-0.546248\pi\) | ||||
−0.144781 | + | 0.989464i | \(0.546248\pi\) | |||||||
\(54\) | 25.0990 | 3.41554 | ||||||||
\(55\) | −22.2144 | −2.99538 | ||||||||
\(56\) | 6.58599 | 0.880090 | ||||||||
\(57\) | −11.5765 | −1.53334 | ||||||||
\(58\) | 7.85819 | 1.03183 | ||||||||
\(59\) | 11.8319 | 1.54039 | 0.770193 | − | 0.637811i | \(-0.220160\pi\) | ||||
0.770193 | + | 0.637811i | \(0.220160\pi\) | |||||||
\(60\) | −40.1701 | −5.18593 | ||||||||
\(61\) | 3.62469 | 0.464094 | 0.232047 | − | 0.972705i | \(-0.425458\pi\) | ||||
0.232047 | + | 0.972705i | \(0.425458\pi\) | |||||||
\(62\) | −14.0163 | −1.78008 | ||||||||
\(63\) | −17.9004 | −2.25524 | ||||||||
\(64\) | −13.0469 | −1.63086 | ||||||||
\(65\) | 27.3649 | 3.39420 | ||||||||
\(66\) | −36.7920 | −4.52879 | ||||||||
\(67\) | −14.1243 | −1.72556 | −0.862782 | − | 0.505577i | \(-0.831280\pi\) | ||||
−0.862782 | + | 0.505577i | \(0.831280\pi\) | |||||||
\(68\) | −20.7616 | −2.51771 | ||||||||
\(69\) | −7.36389 | −0.886509 | ||||||||
\(70\) | 25.7704 | 3.08016 | ||||||||
\(71\) | −8.75155 | −1.03862 | −0.519309 | − | 0.854586i | \(-0.673811\pi\) | ||||
−0.519309 | + | 0.854586i | \(0.673811\pi\) | |||||||
\(72\) | −16.0069 | −1.88643 | ||||||||
\(73\) | −3.39991 | −0.397930 | −0.198965 | − | 0.980007i | \(-0.563758\pi\) | ||||
−0.198965 | + | 0.980007i | \(0.563758\pi\) | |||||||
\(74\) | −2.25323 | −0.261932 | ||||||||
\(75\) | −39.5286 | −4.56437 | ||||||||
\(76\) | 11.4991 | 1.31904 | ||||||||
\(77\) | 14.3052 | 1.63023 | ||||||||
\(78\) | 45.3226 | 5.13177 | ||||||||
\(79\) | 9.60315 | 1.08044 | 0.540219 | − | 0.841524i | \(-0.318341\pi\) | ||||
0.540219 | + | 0.841524i | \(0.318341\pi\) | |||||||
\(80\) | −2.89083 | −0.323204 | ||||||||
\(81\) | 14.7183 | 1.63536 | ||||||||
\(82\) | 16.3305 | 1.80340 | ||||||||
\(83\) | −8.49065 | −0.931970 | −0.465985 | − | 0.884793i | \(-0.654300\pi\) | ||||
−0.465985 | + | 0.884793i | \(0.654300\pi\) | |||||||
\(84\) | 25.8681 | 2.82244 | ||||||||
\(85\) | −28.4352 | −3.08423 | ||||||||
\(86\) | 5.78391 | 0.623695 | ||||||||
\(87\) | 10.8034 | 1.15825 | ||||||||
\(88\) | 12.7920 | 1.36363 | ||||||||
\(89\) | 7.44998 | 0.789697 | 0.394848 | − | 0.918746i | \(-0.370797\pi\) | ||||
0.394848 | + | 0.918746i | \(0.370797\pi\) | |||||||
\(90\) | −62.6336 | −6.60216 | ||||||||
\(91\) | −17.6220 | −1.84729 | ||||||||
\(92\) | 7.31469 | 0.762609 | ||||||||
\(93\) | −19.2696 | −1.99816 | ||||||||
\(94\) | 16.2008 | 1.67098 | ||||||||
\(95\) | 15.7493 | 1.61584 | ||||||||
\(96\) | −19.8229 | −2.02317 | ||||||||
\(97\) | 0.510399 | 0.0518232 | 0.0259116 | − | 0.999664i | \(-0.491751\pi\) | ||||
0.0259116 | + | 0.999664i | \(0.491751\pi\) | |||||||
\(98\) | −0.822639 | −0.0830991 | ||||||||
\(99\) | −34.7681 | −3.49432 | ||||||||
\(100\) | 39.2645 | 3.92645 | ||||||||
\(101\) | −0.265131 | −0.0263816 | −0.0131908 | − | 0.999913i | \(-0.504199\pi\) | ||||
−0.0131908 | + | 0.999913i | \(0.504199\pi\) | |||||||
\(102\) | −47.0952 | −4.66312 | ||||||||
\(103\) | −19.5995 | −1.93119 | −0.965597 | − | 0.260045i | \(-0.916263\pi\) | ||||
−0.965597 | + | 0.260045i | \(0.916263\pi\) | |||||||
\(104\) | −15.7579 | −1.54519 | ||||||||
\(105\) | 35.4291 | 3.45753 | ||||||||
\(106\) | 4.74988 | 0.461349 | ||||||||
\(107\) | −1.88409 | −0.182142 | −0.0910710 | − | 0.995844i | \(-0.529029\pi\) | ||||
−0.0910710 | + | 0.995844i | \(0.529029\pi\) | |||||||
\(108\) | −34.2754 | −3.29816 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 50.0540 | 4.77246 | ||||||||
\(111\) | −3.09773 | −0.294023 | ||||||||
\(112\) | 1.86159 | 0.175903 | ||||||||
\(113\) | −3.81141 | −0.358547 | −0.179274 | − | 0.983799i | \(-0.557375\pi\) | ||||
−0.179274 | + | 0.983799i | \(0.557375\pi\) | |||||||
\(114\) | 26.0844 | 2.44302 | ||||||||
\(115\) | 10.0183 | 0.934208 | ||||||||
\(116\) | −10.7312 | −0.996369 | ||||||||
\(117\) | 42.8293 | 3.95957 | ||||||||
\(118\) | −26.6600 | −2.45425 | ||||||||
\(119\) | 18.3113 | 1.67859 | ||||||||
\(120\) | 31.6813 | 2.89209 | ||||||||
\(121\) | 16.7851 | 1.52592 | ||||||||
\(122\) | −8.16724 | −0.739427 | ||||||||
\(123\) | 22.4511 | 2.02434 | ||||||||
\(124\) | 19.1408 | 1.71890 | ||||||||
\(125\) | 32.7054 | 2.92526 | ||||||||
\(126\) | 40.3337 | 3.59322 | ||||||||
\(127\) | 10.2357 | 0.908275 | 0.454138 | − | 0.890932i | \(-0.349947\pi\) | ||||
0.454138 | + | 0.890932i | \(0.349947\pi\) | |||||||
\(128\) | 16.5993 | 1.46718 | ||||||||
\(129\) | 7.95169 | 0.700107 | ||||||||
\(130\) | −61.6594 | −5.40789 | ||||||||
\(131\) | 12.1690 | 1.06321 | 0.531604 | − | 0.846993i | \(-0.321590\pi\) | ||||
0.531604 | + | 0.846993i | \(0.321590\pi\) | |||||||
\(132\) | 50.2436 | 4.37314 | ||||||||
\(133\) | −10.1420 | −0.879419 | ||||||||
\(134\) | 31.8253 | 2.74929 | ||||||||
\(135\) | −46.9439 | −4.04029 | ||||||||
\(136\) | 16.3742 | 1.40408 | ||||||||
\(137\) | −8.36979 | −0.715080 | −0.357540 | − | 0.933898i | \(-0.616384\pi\) | ||||
−0.357540 | + | 0.933898i | \(0.616384\pi\) | |||||||
\(138\) | 16.5925 | 1.41245 | ||||||||
\(139\) | 8.79403 | 0.745900 | 0.372950 | − | 0.927851i | \(-0.378346\pi\) | ||||
0.372950 | + | 0.927851i | \(0.378346\pi\) | |||||||
\(140\) | −35.1924 | −2.97430 | ||||||||
\(141\) | 22.2727 | 1.87570 | ||||||||
\(142\) | 19.7192 | 1.65480 | ||||||||
\(143\) | −34.2273 | −2.86223 | ||||||||
\(144\) | −4.52448 | −0.377040 | ||||||||
\(145\) | −14.6976 | −1.22057 | ||||||||
\(146\) | 7.66078 | 0.634010 | ||||||||
\(147\) | −1.13096 | −0.0932800 | ||||||||
\(148\) | 3.07703 | 0.252930 | ||||||||
\(149\) | 0.363686 | 0.0297943 | 0.0148972 | − | 0.999889i | \(-0.495258\pi\) | ||||
0.0148972 | + | 0.999889i | \(0.495258\pi\) | |||||||
\(150\) | 89.0670 | 7.27229 | ||||||||
\(151\) | 19.4246 | 1.58075 | 0.790376 | − | 0.612622i | \(-0.209885\pi\) | ||||
0.790376 | + | 0.612622i | \(0.209885\pi\) | |||||||
\(152\) | −9.06911 | −0.735602 | ||||||||
\(153\) | −44.5045 | −3.59797 | ||||||||
\(154\) | −32.2329 | −2.59740 | ||||||||
\(155\) | 26.2155 | 2.10568 | ||||||||
\(156\) | −61.8929 | −4.95540 | ||||||||
\(157\) | −8.41449 | −0.671550 | −0.335775 | − | 0.941942i | \(-0.608998\pi\) | ||||
−0.335775 | + | 0.941942i | \(0.608998\pi\) | |||||||
\(158\) | −21.6381 | −1.72143 | ||||||||
\(159\) | 6.53012 | 0.517872 | ||||||||
\(160\) | 26.9682 | 2.13203 | ||||||||
\(161\) | −6.45139 | −0.508441 | ||||||||
\(162\) | −33.1636 | −2.60558 | ||||||||
\(163\) | −0.955548 | −0.0748443 | −0.0374222 | − | 0.999300i | \(-0.511915\pi\) | ||||
−0.0374222 | + | 0.999300i | \(0.511915\pi\) | |||||||
\(164\) | −22.3011 | −1.74142 | ||||||||
\(165\) | 68.8140 | 5.35716 | ||||||||
\(166\) | 19.1314 | 1.48488 | ||||||||
\(167\) | 18.8719 | 1.46035 | 0.730175 | − | 0.683260i | \(-0.239438\pi\) | ||||
0.730175 | + | 0.683260i | \(0.239438\pi\) | |||||||
\(168\) | −20.4016 | −1.57402 | ||||||||
\(169\) | 29.1632 | 2.24332 | ||||||||
\(170\) | 64.0710 | 4.91402 | ||||||||
\(171\) | 24.6494 | 1.88499 | ||||||||
\(172\) | −7.89856 | −0.602260 | ||||||||
\(173\) | −1.16604 | −0.0886525 | −0.0443262 | − | 0.999017i | \(-0.514114\pi\) | ||||
−0.0443262 | + | 0.999017i | \(0.514114\pi\) | |||||||
\(174\) | −24.3425 | −1.84540 | ||||||||
\(175\) | −34.6304 | −2.61781 | ||||||||
\(176\) | 3.61576 | 0.272548 | ||||||||
\(177\) | −36.6521 | −2.75494 | ||||||||
\(178\) | −16.7865 | −1.25820 | ||||||||
\(179\) | −11.8652 | −0.886847 | −0.443423 | − | 0.896312i | \(-0.646236\pi\) | ||||
−0.443423 | + | 0.896312i | \(0.646236\pi\) | |||||||
\(180\) | 85.5331 | 6.37526 | ||||||||
\(181\) | −10.0031 | −0.743528 | −0.371764 | − | 0.928327i | \(-0.621247\pi\) | ||||
−0.371764 | + | 0.928327i | \(0.621247\pi\) | |||||||
\(182\) | 39.7064 | 2.94323 | ||||||||
\(183\) | −11.2283 | −0.830019 | ||||||||
\(184\) | −5.76895 | −0.425292 | ||||||||
\(185\) | 4.21432 | 0.309843 | ||||||||
\(186\) | 43.4188 | 3.18362 | ||||||||
\(187\) | 35.5660 | 2.60084 | ||||||||
\(188\) | −22.1239 | −1.61355 | ||||||||
\(189\) | 30.2302 | 2.19892 | ||||||||
\(190\) | −35.4867 | −2.57447 | ||||||||
\(191\) | −14.5262 | −1.05108 | −0.525538 | − | 0.850770i | \(-0.676136\pi\) | ||||
−0.525538 | + | 0.850770i | \(0.676136\pi\) | |||||||
\(192\) | 40.4157 | 2.91675 | ||||||||
\(193\) | 8.88339 | 0.639441 | 0.319720 | − | 0.947512i | \(-0.396411\pi\) | ||||
0.319720 | + | 0.947512i | \(0.396411\pi\) | |||||||
\(194\) | −1.15005 | −0.0825684 | ||||||||
\(195\) | −84.7691 | −6.07044 | ||||||||
\(196\) | 1.12340 | 0.0802431 | ||||||||
\(197\) | −18.4866 | −1.31712 | −0.658559 | − | 0.752529i | \(-0.728834\pi\) | ||||
−0.658559 | + | 0.752529i | \(0.728834\pi\) | |||||||
\(198\) | 78.3403 | 5.56740 | ||||||||
\(199\) | 9.97633 | 0.707203 | 0.353602 | − | 0.935396i | \(-0.384957\pi\) | ||||
0.353602 | + | 0.935396i | \(0.384957\pi\) | |||||||
\(200\) | −30.9671 | −2.18971 | ||||||||
\(201\) | 43.7534 | 3.08612 | ||||||||
\(202\) | 0.597401 | 0.0420330 | ||||||||
\(203\) | 9.46470 | 0.664291 | ||||||||
\(204\) | 64.3137 | 4.50286 | ||||||||
\(205\) | −30.5437 | −2.13327 | ||||||||
\(206\) | 44.1620 | 3.07692 | ||||||||
\(207\) | 15.6797 | 1.08982 | ||||||||
\(208\) | −4.45411 | −0.308837 | ||||||||
\(209\) | −19.6987 | −1.36259 | ||||||||
\(210\) | −79.8298 | −5.50878 | ||||||||
\(211\) | −20.6958 | −1.42476 | −0.712380 | − | 0.701794i | \(-0.752383\pi\) | ||||
−0.712380 | + | 0.701794i | \(0.752383\pi\) | |||||||
\(212\) | −6.48649 | −0.445494 | ||||||||
\(213\) | 27.1099 | 1.85754 | ||||||||
\(214\) | 4.24528 | 0.290202 | ||||||||
\(215\) | −10.8179 | −0.737777 | ||||||||
\(216\) | 27.0323 | 1.83932 | ||||||||
\(217\) | −16.8818 | −1.14601 | ||||||||
\(218\) | −2.25323 | −0.152608 | ||||||||
\(219\) | 10.5320 | 0.711687 | ||||||||
\(220\) | −68.3542 | −4.60844 | ||||||||
\(221\) | −43.8122 | −2.94713 | ||||||||
\(222\) | 6.97988 | 0.468459 | ||||||||
\(223\) | 1.98096 | 0.132655 | 0.0663274 | − | 0.997798i | \(-0.478872\pi\) | ||||
0.0663274 | + | 0.997798i | \(0.478872\pi\) | |||||||
\(224\) | −17.3666 | −1.16035 | ||||||||
\(225\) | 84.1673 | 5.61115 | ||||||||
\(226\) | 8.58797 | 0.571263 | ||||||||
\(227\) | 23.4725 | 1.55792 | 0.778962 | − | 0.627071i | \(-0.215746\pi\) | ||||
0.778962 | + | 0.627071i | \(0.215746\pi\) | |||||||
\(228\) | −35.6211 | −2.35906 | ||||||||
\(229\) | −9.25664 | −0.611696 | −0.305848 | − | 0.952080i | \(-0.598940\pi\) | ||||
−0.305848 | + | 0.952080i | \(0.598940\pi\) | |||||||
\(230\) | −22.5734 | −1.48845 | ||||||||
\(231\) | −44.3137 | −2.91563 | ||||||||
\(232\) | 8.46349 | 0.555655 | ||||||||
\(233\) | 9.61814 | 0.630105 | 0.315053 | − | 0.949074i | \(-0.397978\pi\) | ||||
0.315053 | + | 0.949074i | \(0.397978\pi\) | |||||||
\(234\) | −96.5041 | −6.30867 | ||||||||
\(235\) | −30.3011 | −1.97663 | ||||||||
\(236\) | 36.4072 | 2.36991 | ||||||||
\(237\) | −29.7479 | −1.93234 | ||||||||
\(238\) | −41.2594 | −2.67445 | ||||||||
\(239\) | 11.8012 | 0.763356 | 0.381678 | − | 0.924295i | \(-0.375346\pi\) | ||||
0.381678 | + | 0.924295i | \(0.375346\pi\) | |||||||
\(240\) | 8.95499 | 0.578042 | ||||||||
\(241\) | −9.99901 | −0.644093 | −0.322046 | − | 0.946724i | \(-0.604371\pi\) | ||||
−0.322046 | + | 0.946724i | \(0.604371\pi\) | |||||||
\(242\) | −37.8206 | −2.43120 | ||||||||
\(243\) | −12.1758 | −0.781077 | ||||||||
\(244\) | 11.1533 | 0.714015 | ||||||||
\(245\) | 1.53862 | 0.0982990 | ||||||||
\(246\) | −50.5873 | −3.22533 | ||||||||
\(247\) | 24.2660 | 1.54401 | ||||||||
\(248\) | −15.0960 | −0.958596 | ||||||||
\(249\) | 26.3017 | 1.66680 | ||||||||
\(250\) | −73.6927 | −4.66073 | ||||||||
\(251\) | −4.48969 | −0.283387 | −0.141693 | − | 0.989911i | \(-0.545255\pi\) | ||||
−0.141693 | + | 0.989911i | \(0.545255\pi\) | |||||||
\(252\) | −55.0802 | −3.46972 | ||||||||
\(253\) | −12.5306 | −0.787789 | ||||||||
\(254\) | −23.0634 | −1.44713 | ||||||||
\(255\) | 88.0846 | 5.51607 | ||||||||
\(256\) | −11.3081 | −0.706755 | ||||||||
\(257\) | −1.16187 | −0.0724754 | −0.0362377 | − | 0.999343i | \(-0.511537\pi\) | ||||
−0.0362377 | + | 0.999343i | \(0.511537\pi\) | |||||||
\(258\) | −17.9170 | −1.11546 | ||||||||
\(259\) | −2.71387 | −0.168632 | ||||||||
\(260\) | 84.2027 | 5.22203 | ||||||||
\(261\) | −23.0034 | −1.42388 | ||||||||
\(262\) | −27.4194 | −1.69398 | ||||||||
\(263\) | −17.4847 | −1.07815 | −0.539076 | − | 0.842257i | \(-0.681227\pi\) | ||||
−0.539076 | + | 0.842257i | \(0.681227\pi\) | |||||||
\(264\) | −39.6261 | −2.43882 | ||||||||
\(265\) | −8.88395 | −0.545737 | ||||||||
\(266\) | 22.8521 | 1.40115 | ||||||||
\(267\) | −23.0780 | −1.41235 | ||||||||
\(268\) | −43.4610 | −2.65480 | ||||||||
\(269\) | 10.0133 | 0.610520 | 0.305260 | − | 0.952269i | \(-0.401257\pi\) | ||||
0.305260 | + | 0.952269i | \(0.401257\pi\) | |||||||
\(270\) | 105.775 | 6.43728 | ||||||||
\(271\) | −2.36241 | −0.143506 | −0.0717530 | − | 0.997422i | \(-0.522859\pi\) | ||||
−0.0717530 | + | 0.997422i | \(0.522859\pi\) | |||||||
\(272\) | 4.62831 | 0.280633 | ||||||||
\(273\) | 54.5882 | 3.30383 | ||||||||
\(274\) | 18.8590 | 1.13932 | ||||||||
\(275\) | −67.2627 | −4.05610 | ||||||||
\(276\) | −22.6589 | −1.36391 | ||||||||
\(277\) | −10.9540 | −0.658164 | −0.329082 | − | 0.944301i | \(-0.606739\pi\) | ||||
−0.329082 | + | 0.944301i | \(0.606739\pi\) | |||||||
\(278\) | −19.8149 | −1.18842 | ||||||||
\(279\) | 41.0302 | 2.45642 | ||||||||
\(280\) | 27.7555 | 1.65871 | ||||||||
\(281\) | −3.93808 | −0.234926 | −0.117463 | − | 0.993077i | \(-0.537476\pi\) | ||||
−0.117463 | + | 0.993077i | \(0.537476\pi\) | |||||||
\(282\) | −50.1855 | −2.98850 | ||||||||
\(283\) | 11.2392 | 0.668101 | 0.334050 | − | 0.942555i | \(-0.391584\pi\) | ||||
0.334050 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(284\) | −26.9288 | −1.59793 | ||||||||
\(285\) | −48.7869 | −2.88989 | ||||||||
\(286\) | 77.1218 | 4.56031 | ||||||||
\(287\) | 19.6690 | 1.16103 | ||||||||
\(288\) | 42.2084 | 2.48716 | ||||||||
\(289\) | 28.5258 | 1.67799 | ||||||||
\(290\) | 33.1169 | 1.94469 | ||||||||
\(291\) | −1.58108 | −0.0926844 | ||||||||
\(292\) | −10.4616 | −0.612221 | ||||||||
\(293\) | −17.5614 | −1.02595 | −0.512974 | − | 0.858404i | \(-0.671456\pi\) | ||||
−0.512974 | + | 0.858404i | \(0.671456\pi\) | |||||||
\(294\) | 2.54831 | 0.148620 | ||||||||
\(295\) | 49.8636 | 2.90317 | ||||||||
\(296\) | −2.42679 | −0.141054 | ||||||||
\(297\) | 58.7161 | 3.40706 | ||||||||
\(298\) | −0.819467 | −0.0474705 | ||||||||
\(299\) | 15.4359 | 0.892679 | ||||||||
\(300\) | −121.631 | −7.02235 | ||||||||
\(301\) | 6.96635 | 0.401534 | ||||||||
\(302\) | −43.7680 | −2.51857 | ||||||||
\(303\) | 0.821304 | 0.0471827 | ||||||||
\(304\) | −2.56346 | −0.147024 | ||||||||
\(305\) | 15.2756 | 0.874679 | ||||||||
\(306\) | 100.279 | 5.73255 | ||||||||
\(307\) | −28.0412 | −1.60040 | −0.800199 | − | 0.599735i | \(-0.795273\pi\) | ||||
−0.800199 | + | 0.599735i | \(0.795273\pi\) | |||||||
\(308\) | 44.0176 | 2.50814 | ||||||||
\(309\) | 60.7138 | 3.45389 | ||||||||
\(310\) | −59.0694 | −3.35491 | ||||||||
\(311\) | −16.2213 | −0.919826 | −0.459913 | − | 0.887964i | \(-0.652119\pi\) | ||||
−0.459913 | + | 0.887964i | \(0.652119\pi\) | |||||||
\(312\) | 48.8137 | 2.76353 | ||||||||
\(313\) | 8.63958 | 0.488338 | 0.244169 | − | 0.969733i | \(-0.421485\pi\) | ||||
0.244169 | + | 0.969733i | \(0.421485\pi\) | |||||||
\(314\) | 18.9598 | 1.06996 | ||||||||
\(315\) | −75.4383 | −4.25046 | ||||||||
\(316\) | 29.5492 | 1.66227 | ||||||||
\(317\) | −11.1788 | −0.627862 | −0.313931 | − | 0.949446i | \(-0.601646\pi\) | ||||
−0.313931 | + | 0.949446i | \(0.601646\pi\) | |||||||
\(318\) | −14.7138 | −0.825111 | ||||||||
\(319\) | 18.3833 | 1.02927 | ||||||||
\(320\) | −54.9839 | −3.07369 | ||||||||
\(321\) | 5.83640 | 0.325756 | ||||||||
\(322\) | 14.5365 | 0.810085 | ||||||||
\(323\) | −25.2151 | −1.40301 | ||||||||
\(324\) | 45.2886 | 2.51603 | ||||||||
\(325\) | 82.8582 | 4.59614 | ||||||||
\(326\) | 2.15307 | 0.119247 | ||||||||
\(327\) | −3.09773 | −0.171305 | ||||||||
\(328\) | 17.5884 | 0.971156 | ||||||||
\(329\) | 19.5128 | 1.07578 | ||||||||
\(330\) | −155.054 | −8.53542 | ||||||||
\(331\) | −17.2809 | −0.949841 | −0.474921 | − | 0.880029i | \(-0.657523\pi\) | ||||
−0.474921 | + | 0.880029i | \(0.657523\pi\) | |||||||
\(332\) | −26.1260 | −1.43385 | ||||||||
\(333\) | 6.59591 | 0.361454 | ||||||||
\(334\) | −42.5226 | −2.32673 | ||||||||
\(335\) | −59.5246 | −3.25217 | ||||||||
\(336\) | −5.76668 | −0.314598 | ||||||||
\(337\) | −2.83699 | −0.154541 | −0.0772703 | − | 0.997010i | \(-0.524620\pi\) | ||||
−0.0772703 | + | 0.997010i | \(0.524620\pi\) | |||||||
\(338\) | −65.7112 | −3.57422 | ||||||||
\(339\) | 11.8067 | 0.641252 | ||||||||
\(340\) | −87.4960 | −4.74514 | ||||||||
\(341\) | −32.7895 | −1.77565 | ||||||||
\(342\) | −55.5408 | −3.00330 | ||||||||
\(343\) | 18.0063 | 0.972248 | ||||||||
\(344\) | 6.22943 | 0.335868 | ||||||||
\(345\) | −31.0338 | −1.67081 | ||||||||
\(346\) | 2.62735 | 0.141247 | ||||||||
\(347\) | 20.7927 | 1.11621 | 0.558106 | − | 0.829769i | \(-0.311528\pi\) | ||||
0.558106 | + | 0.829769i | \(0.311528\pi\) | |||||||
\(348\) | 33.2424 | 1.78198 | ||||||||
\(349\) | −26.7752 | −1.43325 | −0.716623 | − | 0.697461i | \(-0.754313\pi\) | ||||
−0.716623 | + | 0.697461i | \(0.754313\pi\) | |||||||
\(350\) | 78.0302 | 4.17089 | ||||||||
\(351\) | −72.3300 | −3.86069 | ||||||||
\(352\) | −33.7311 | −1.79787 | ||||||||
\(353\) | 10.0894 | 0.537007 | 0.268504 | − | 0.963279i | \(-0.413471\pi\) | ||||
0.268504 | + | 0.963279i | \(0.413471\pi\) | |||||||
\(354\) | 82.5854 | 4.38936 | ||||||||
\(355\) | −36.8819 | −1.95749 | ||||||||
\(356\) | 22.9238 | 1.21496 | ||||||||
\(357\) | −56.7232 | −3.00211 | ||||||||
\(358\) | 26.7350 | 1.41299 | ||||||||
\(359\) | 8.14282 | 0.429762 | 0.214881 | − | 0.976640i | \(-0.431064\pi\) | ||||
0.214881 | + | 0.976640i | \(0.431064\pi\) | |||||||
\(360\) | −67.4582 | −3.55536 | ||||||||
\(361\) | −5.03423 | −0.264959 | ||||||||
\(362\) | 22.5393 | 1.18464 | ||||||||
\(363\) | −51.9956 | −2.72906 | ||||||||
\(364\) | −54.2235 | −2.84208 | ||||||||
\(365\) | −14.3283 | −0.749980 | ||||||||
\(366\) | 25.2999 | 1.32245 | ||||||||
\(367\) | −1.58332 | −0.0826489 | −0.0413244 | − | 0.999146i | \(-0.513158\pi\) | ||||
−0.0413244 | + | 0.999146i | \(0.513158\pi\) | |||||||
\(368\) | −1.63064 | −0.0850031 | ||||||||
\(369\) | −47.8045 | −2.48860 | ||||||||
\(370\) | −9.49583 | −0.493665 | ||||||||
\(371\) | 5.72094 | 0.297016 | ||||||||
\(372\) | −59.2931 | −3.07420 | ||||||||
\(373\) | 5.55671 | 0.287715 | 0.143858 | − | 0.989598i | \(-0.454049\pi\) | ||||
0.143858 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(374\) | −80.1382 | −4.14385 | ||||||||
\(375\) | −101.312 | −5.23175 | ||||||||
\(376\) | 17.4487 | 0.899847 | ||||||||
\(377\) | −22.6456 | −1.16631 | ||||||||
\(378\) | −68.1154 | −3.50348 | ||||||||
\(379\) | 20.5129 | 1.05367 | 0.526837 | − | 0.849966i | \(-0.323378\pi\) | ||||
0.526837 | + | 0.849966i | \(0.323378\pi\) | |||||||
\(380\) | 48.4610 | 2.48599 | ||||||||
\(381\) | −31.7075 | −1.62443 | ||||||||
\(382\) | 32.7307 | 1.67465 | ||||||||
\(383\) | −34.9937 | −1.78810 | −0.894048 | − | 0.447971i | \(-0.852147\pi\) | ||||
−0.894048 | + | 0.447971i | \(0.852147\pi\) | |||||||
\(384\) | −51.4200 | −2.62401 | ||||||||
\(385\) | 60.2869 | 3.07250 | ||||||||
\(386\) | −20.0163 | −1.01880 | ||||||||
\(387\) | −16.9313 | −0.860668 | ||||||||
\(388\) | 1.57051 | 0.0797307 | ||||||||
\(389\) | 3.15579 | 0.160005 | 0.0800025 | − | 0.996795i | \(-0.474507\pi\) | ||||
0.0800025 | + | 0.996795i | \(0.474507\pi\) | |||||||
\(390\) | 191.004 | 9.67186 | ||||||||
\(391\) | −16.0396 | −0.811157 | ||||||||
\(392\) | −0.886005 | −0.0447500 | ||||||||
\(393\) | −37.6961 | −1.90152 | ||||||||
\(394\) | 41.6546 | 2.09853 | ||||||||
\(395\) | 40.4708 | 2.03631 | ||||||||
\(396\) | −106.982 | −5.37606 | ||||||||
\(397\) | 17.7287 | 0.889776 | 0.444888 | − | 0.895586i | \(-0.353243\pi\) | ||||
0.444888 | + | 0.895586i | \(0.353243\pi\) | |||||||
\(398\) | −22.4789 | −1.12677 | ||||||||
\(399\) | 31.4170 | 1.57282 | ||||||||
\(400\) | −8.75312 | −0.437656 | ||||||||
\(401\) | −20.8703 | −1.04221 | −0.521106 | − | 0.853492i | \(-0.674481\pi\) | ||||
−0.521106 | + | 0.853492i | \(0.674481\pi\) | |||||||
\(402\) | −98.5862 | −4.91703 | ||||||||
\(403\) | 40.3921 | 2.01207 | ||||||||
\(404\) | −0.815817 | −0.0405884 | ||||||||
\(405\) | 62.0276 | 3.08218 | ||||||||
\(406\) | −21.3261 | −1.05840 | ||||||||
\(407\) | −5.27116 | −0.261281 | ||||||||
\(408\) | −50.7229 | −2.51116 | ||||||||
\(409\) | 15.2990 | 0.756485 | 0.378242 | − | 0.925707i | \(-0.376529\pi\) | ||||
0.378242 | + | 0.925707i | \(0.376529\pi\) | |||||||
\(410\) | 68.8219 | 3.39887 | ||||||||
\(411\) | 25.9273 | 1.27890 | ||||||||
\(412\) | −60.3081 | −2.97117 | ||||||||
\(413\) | −32.1103 | −1.58005 | ||||||||
\(414\) | −35.3300 | −1.73638 | ||||||||
\(415\) | −35.7824 | −1.75649 | ||||||||
\(416\) | 41.5519 | 2.03725 | ||||||||
\(417\) | −27.2415 | −1.33402 | ||||||||
\(418\) | 44.3857 | 2.17098 | ||||||||
\(419\) | 6.42955 | 0.314104 | 0.157052 | − | 0.987590i | \(-0.449801\pi\) | ||||
0.157052 | + | 0.987590i | \(0.449801\pi\) | |||||||
\(420\) | 109.016 | 5.31945 | ||||||||
\(421\) | −24.2121 | −1.18002 | −0.590012 | − | 0.807395i | \(-0.700877\pi\) | ||||
−0.590012 | + | 0.807395i | \(0.700877\pi\) | |||||||
\(422\) | 46.6324 | 2.27003 | ||||||||
\(423\) | −47.4247 | −2.30587 | ||||||||
\(424\) | 5.11576 | 0.248443 | ||||||||
\(425\) | −86.0989 | −4.17641 | ||||||||
\(426\) | −61.0848 | −2.95957 | ||||||||
\(427\) | −9.83693 | −0.476043 | ||||||||
\(428\) | −5.79740 | −0.280228 | ||||||||
\(429\) | 106.027 | 5.11902 | ||||||||
\(430\) | 24.3753 | 1.17548 | ||||||||
\(431\) | 25.1440 | 1.21114 | 0.605572 | − | 0.795790i | \(-0.292944\pi\) | ||||
0.605572 | + | 0.795790i | \(0.292944\pi\) | |||||||
\(432\) | 7.64092 | 0.367624 | ||||||||
\(433\) | 10.3898 | 0.499300 | 0.249650 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249650 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(434\) | 38.0385 | 1.82591 | ||||||||
\(435\) | 45.5290 | 2.18295 | ||||||||
\(436\) | 3.07703 | 0.147363 | ||||||||
\(437\) | 8.88376 | 0.424968 | ||||||||
\(438\) | −23.7310 | −1.13391 | ||||||||
\(439\) | 30.0645 | 1.43490 | 0.717450 | − | 0.696610i | \(-0.245309\pi\) | ||||
0.717450 | + | 0.696610i | \(0.245309\pi\) | |||||||
\(440\) | 53.9096 | 2.57004 | ||||||||
\(441\) | 2.40812 | 0.114673 | ||||||||
\(442\) | 98.7189 | 4.69558 | ||||||||
\(443\) | −7.47006 | −0.354913 | −0.177457 | − | 0.984129i | \(-0.556787\pi\) | ||||
−0.177457 | + | 0.984129i | \(0.556787\pi\) | |||||||
\(444\) | −9.53179 | −0.452359 | ||||||||
\(445\) | 31.3966 | 1.48834 | ||||||||
\(446\) | −4.46355 | −0.211355 | ||||||||
\(447\) | −1.12660 | −0.0532864 | ||||||||
\(448\) | 35.4076 | 1.67285 | ||||||||
\(449\) | −19.4443 | −0.917633 | −0.458817 | − | 0.888531i | \(-0.651726\pi\) | ||||
−0.458817 | + | 0.888531i | \(0.651726\pi\) | |||||||
\(450\) | −189.648 | −8.94009 | ||||||||
\(451\) | 38.2032 | 1.79892 | ||||||||
\(452\) | −11.7278 | −0.551630 | ||||||||
\(453\) | −60.1721 | −2.82713 | ||||||||
\(454\) | −52.8889 | −2.48220 | ||||||||
\(455\) | −74.2649 | −3.48159 | ||||||||
\(456\) | 28.0936 | 1.31560 | ||||||||
\(457\) | −18.4159 | −0.861461 | −0.430731 | − | 0.902481i | \(-0.641744\pi\) | ||||
−0.430731 | + | 0.902481i | \(0.641744\pi\) | |||||||
\(458\) | 20.8573 | 0.974598 | ||||||||
\(459\) | 75.1589 | 3.50812 | ||||||||
\(460\) | 30.8265 | 1.43729 | ||||||||
\(461\) | 33.5363 | 1.56194 | 0.780971 | − | 0.624568i | \(-0.214725\pi\) | ||||
0.780971 | + | 0.624568i | \(0.214725\pi\) | |||||||
\(462\) | 99.8488 | 4.64539 | ||||||||
\(463\) | −22.1475 | −1.02928 | −0.514641 | − | 0.857406i | \(-0.672075\pi\) | ||||
−0.514641 | + | 0.857406i | \(0.672075\pi\) | |||||||
\(464\) | 2.39228 | 0.111059 | ||||||||
\(465\) | −81.2083 | −3.76595 | ||||||||
\(466\) | −21.6718 | −1.00393 | ||||||||
\(467\) | −23.6788 | −1.09572 | −0.547862 | − | 0.836569i | \(-0.684558\pi\) | ||||
−0.547862 | + | 0.836569i | \(0.684558\pi\) | |||||||
\(468\) | 131.787 | 6.09186 | ||||||||
\(469\) | 38.3316 | 1.76999 | ||||||||
\(470\) | 68.2752 | 3.14930 | ||||||||
\(471\) | 26.0658 | 1.20105 | ||||||||
\(472\) | −28.7136 | −1.32165 | ||||||||
\(473\) | 13.5308 | 0.622145 | ||||||||
\(474\) | 67.0288 | 3.07873 | ||||||||
\(475\) | 47.6871 | 2.18804 | ||||||||
\(476\) | 56.3442 | 2.58253 | ||||||||
\(477\) | −13.9044 | −0.636639 | ||||||||
\(478\) | −26.5908 | −1.21623 | ||||||||
\(479\) | −7.06734 | −0.322915 | −0.161457 | − | 0.986880i | \(-0.551619\pi\) | ||||
−0.161457 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(480\) | −83.5402 | −3.81307 | ||||||||
\(481\) | 6.49332 | 0.296070 | ||||||||
\(482\) | 22.5300 | 1.02621 | ||||||||
\(483\) | 19.9847 | 0.909333 | ||||||||
\(484\) | 51.6482 | 2.34764 | ||||||||
\(485\) | 2.15099 | 0.0976713 | ||||||||
\(486\) | 27.4348 | 1.24447 | ||||||||
\(487\) | 0.633314 | 0.0286982 | 0.0143491 | − | 0.999897i | \(-0.495432\pi\) | ||||
0.0143491 | + | 0.999897i | \(0.495432\pi\) | |||||||
\(488\) | −8.79635 | −0.398192 | ||||||||
\(489\) | 2.96003 | 0.133857 | ||||||||
\(490\) | −3.46687 | −0.156617 | ||||||||
\(491\) | 28.2116 | 1.27317 | 0.636586 | − | 0.771206i | \(-0.280346\pi\) | ||||
0.636586 | + | 0.771206i | \(0.280346\pi\) | |||||||
\(492\) | 69.0826 | 3.11448 | ||||||||
\(493\) | 23.5313 | 1.05980 | ||||||||
\(494\) | −54.6769 | −2.46003 | ||||||||
\(495\) | −146.524 | −6.58576 | ||||||||
\(496\) | −4.26701 | −0.191594 | ||||||||
\(497\) | 23.7506 | 1.06536 | ||||||||
\(498\) | −59.2637 | −2.65567 | ||||||||
\(499\) | −40.4238 | −1.80962 | −0.904809 | − | 0.425818i | \(-0.859987\pi\) | ||||
−0.904809 | + | 0.425818i | \(0.859987\pi\) | |||||||
\(500\) | 100.635 | 4.50055 | ||||||||
\(501\) | −58.4599 | −2.61180 | ||||||||
\(502\) | 10.1163 | 0.451512 | ||||||||
\(503\) | −37.3979 | −1.66749 | −0.833746 | − | 0.552149i | \(-0.813808\pi\) | ||||
−0.833746 | + | 0.552149i | \(0.813808\pi\) | |||||||
\(504\) | 43.4406 | 1.93500 | ||||||||
\(505\) | −1.11735 | −0.0497214 | ||||||||
\(506\) | 28.2342 | 1.25516 | ||||||||
\(507\) | −90.3395 | −4.01212 | ||||||||
\(508\) | 31.4957 | 1.39739 | ||||||||
\(509\) | −5.92704 | −0.262711 | −0.131356 | − | 0.991335i | \(-0.541933\pi\) | ||||
−0.131356 | + | 0.991335i | \(0.541933\pi\) | |||||||
\(510\) | −198.474 | −8.78860 | ||||||||
\(511\) | 9.22693 | 0.408175 | ||||||||
\(512\) | −7.71886 | −0.341129 | ||||||||
\(513\) | −41.6279 | −1.83791 | ||||||||
\(514\) | 2.61795 | 0.115473 | ||||||||
\(515\) | −82.5985 | −3.63973 | ||||||||
\(516\) | 24.4676 | 1.07713 | ||||||||
\(517\) | 37.8997 | 1.66683 | ||||||||
\(518\) | 6.11496 | 0.268676 | ||||||||
\(519\) | 3.61208 | 0.158553 | ||||||||
\(520\) | −66.4089 | −2.91222 | ||||||||
\(521\) | 1.99652 | 0.0874692 | 0.0437346 | − | 0.999043i | \(-0.486074\pi\) | ||||
0.0437346 | + | 0.999043i | \(0.486074\pi\) | |||||||
\(522\) | 51.8319 | 2.26862 | ||||||||
\(523\) | −7.00425 | −0.306274 | −0.153137 | − | 0.988205i | \(-0.548938\pi\) | ||||
−0.153137 | + | 0.988205i | \(0.548938\pi\) | |||||||
\(524\) | 37.4443 | 1.63576 | ||||||||
\(525\) | 107.276 | 4.68189 | ||||||||
\(526\) | 39.3970 | 1.71779 | ||||||||
\(527\) | −41.9719 | −1.82832 | ||||||||
\(528\) | −11.2006 | −0.487445 | ||||||||
\(529\) | −17.3490 | −0.754302 | ||||||||
\(530\) | 20.0176 | 0.869507 | ||||||||
\(531\) | 78.0423 | 3.38675 | ||||||||
\(532\) | −31.2071 | −1.35300 | ||||||||
\(533\) | −47.0609 | −2.03843 | ||||||||
\(534\) | 52.0000 | 2.25026 | ||||||||
\(535\) | −7.94017 | −0.343283 | ||||||||
\(536\) | 34.2768 | 1.48053 | ||||||||
\(537\) | 36.7551 | 1.58610 | ||||||||
\(538\) | −22.5622 | −0.972724 | ||||||||
\(539\) | −1.92447 | −0.0828926 | ||||||||
\(540\) | −144.448 | −6.21605 | ||||||||
\(541\) | −25.3987 | −1.09197 | −0.545987 | − | 0.837794i | \(-0.683845\pi\) | ||||
−0.545987 | + | 0.837794i | \(0.683845\pi\) | |||||||
\(542\) | 5.32303 | 0.228644 | ||||||||
\(543\) | 30.9870 | 1.32978 | ||||||||
\(544\) | −43.1771 | −1.85120 | ||||||||
\(545\) | 4.21432 | 0.180522 | ||||||||
\(546\) | −123.000 | −5.26390 | ||||||||
\(547\) | 9.13682 | 0.390662 | 0.195331 | − | 0.980737i | \(-0.437422\pi\) | ||||
0.195331 | + | 0.980737i | \(0.437422\pi\) | |||||||
\(548\) | −25.7541 | −1.10016 | ||||||||
\(549\) | 23.9081 | 1.02037 | ||||||||
\(550\) | 151.558 | 6.46246 | ||||||||
\(551\) | −13.0332 | −0.555232 | ||||||||
\(552\) | 17.8706 | 0.760624 | ||||||||
\(553\) | −26.0617 | −1.10826 | ||||||||
\(554\) | 24.6819 | 1.04863 | ||||||||
\(555\) | −13.0548 | −0.554146 | ||||||||
\(556\) | 27.0595 | 1.14758 | ||||||||
\(557\) | −32.5340 | −1.37851 | −0.689255 | − | 0.724519i | \(-0.742062\pi\) | ||||
−0.689255 | + | 0.724519i | \(0.742062\pi\) | |||||||
\(558\) | −92.4504 | −3.91374 | ||||||||
\(559\) | −16.6680 | −0.704980 | ||||||||
\(560\) | 7.84533 | 0.331526 | ||||||||
\(561\) | −110.174 | −4.65154 | ||||||||
\(562\) | 8.87337 | 0.374301 | ||||||||
\(563\) | −17.3775 | −0.732376 | −0.366188 | − | 0.930541i | \(-0.619337\pi\) | ||||
−0.366188 | + | 0.930541i | \(0.619337\pi\) | |||||||
\(564\) | 68.5338 | 2.88579 | ||||||||
\(565\) | −16.0625 | −0.675755 | ||||||||
\(566\) | −25.3245 | −1.06447 | ||||||||
\(567\) | −39.9435 | −1.67747 | ||||||||
\(568\) | 21.2382 | 0.891134 | ||||||||
\(569\) | −21.3143 | −0.893540 | −0.446770 | − | 0.894649i | \(-0.647426\pi\) | ||||
−0.446770 | + | 0.894649i | \(0.647426\pi\) | |||||||
\(570\) | 109.928 | 4.60438 | ||||||||
\(571\) | −29.8805 | −1.25046 | −0.625230 | − | 0.780440i | \(-0.714995\pi\) | ||||
−0.625230 | + | 0.780440i | \(0.714995\pi\) | |||||||
\(572\) | −105.318 | −4.40358 | ||||||||
\(573\) | 44.9981 | 1.87982 | ||||||||
\(574\) | −44.3188 | −1.84983 | ||||||||
\(575\) | 30.3342 | 1.26503 | ||||||||
\(576\) | −86.0562 | −3.58567 | ||||||||
\(577\) | 5.90022 | 0.245629 | 0.122815 | − | 0.992430i | \(-0.460808\pi\) | ||||
0.122815 | + | 0.992430i | \(0.460808\pi\) | |||||||
\(578\) | −64.2751 | −2.67349 | ||||||||
\(579\) | −27.5183 | −1.14362 | ||||||||
\(580\) | −45.2248 | −1.87786 | ||||||||
\(581\) | 23.0425 | 0.955965 | ||||||||
\(582\) | 3.56252 | 0.147671 | ||||||||
\(583\) | 11.1118 | 0.460203 | ||||||||
\(584\) | 8.25087 | 0.341424 | ||||||||
\(585\) | 180.497 | 7.46262 | ||||||||
\(586\) | 39.5698 | 1.63461 | ||||||||
\(587\) | −34.6413 | −1.42980 | −0.714900 | − | 0.699226i | \(-0.753528\pi\) | ||||
−0.714900 | + | 0.699226i | \(0.753528\pi\) | |||||||
\(588\) | −3.48000 | −0.143513 | ||||||||
\(589\) | 23.2467 | 0.957865 | ||||||||
\(590\) | −112.354 | −4.62554 | ||||||||
\(591\) | 57.2666 | 2.35563 | ||||||||
\(592\) | −0.685952 | −0.0281925 | ||||||||
\(593\) | 4.64599 | 0.190788 | 0.0953940 | − | 0.995440i | \(-0.469589\pi\) | ||||
0.0953940 | + | 0.995440i | \(0.469589\pi\) | |||||||
\(594\) | −132.301 | −5.42837 | ||||||||
\(595\) | 77.1696 | 3.16364 | ||||||||
\(596\) | 1.11907 | 0.0458390 | ||||||||
\(597\) | −30.9039 | −1.26481 | ||||||||
\(598\) | −34.7805 | −1.42228 | ||||||||
\(599\) | −24.8981 | −1.01731 | −0.508654 | − | 0.860971i | \(-0.669857\pi\) | ||||
−0.508654 | + | 0.860971i | \(0.669857\pi\) | |||||||
\(600\) | 95.9276 | 3.91623 | ||||||||
\(601\) | 22.7459 | 0.927823 | 0.463912 | − | 0.885882i | \(-0.346446\pi\) | ||||
0.463912 | + | 0.885882i | \(0.346446\pi\) | |||||||
\(602\) | −15.6968 | −0.639753 | ||||||||
\(603\) | −93.1629 | −3.79389 | ||||||||
\(604\) | 59.7701 | 2.43201 | ||||||||
\(605\) | 70.7378 | 2.87590 | ||||||||
\(606\) | −1.85058 | −0.0751749 | ||||||||
\(607\) | 4.79525 | 0.194633 | 0.0973165 | − | 0.995253i | \(-0.468974\pi\) | ||||
0.0973165 | + | 0.995253i | \(0.468974\pi\) | |||||||
\(608\) | 23.9143 | 0.969851 | ||||||||
\(609\) | −29.3190 | −1.18807 | ||||||||
\(610\) | −34.4194 | −1.39360 | ||||||||
\(611\) | −46.6871 | −1.88876 | ||||||||
\(612\) | −136.941 | −5.53553 | ||||||||
\(613\) | −4.22608 | −0.170690 | −0.0853449 | − | 0.996351i | \(-0.527199\pi\) | ||||
−0.0853449 | + | 0.996351i | \(0.527199\pi\) | |||||||
\(614\) | 63.1832 | 2.54987 | ||||||||
\(615\) | 94.6161 | 3.81529 | ||||||||
\(616\) | −34.7158 | −1.39874 | ||||||||
\(617\) | −0.657747 | −0.0264799 | −0.0132399 | − | 0.999912i | \(-0.504215\pi\) | ||||
−0.0132399 | + | 0.999912i | \(0.504215\pi\) | |||||||
\(618\) | −136.802 | −5.50298 | ||||||||
\(619\) | 47.2382 | 1.89866 | 0.949331 | − | 0.314278i | \(-0.101762\pi\) | ||||
0.949331 | + | 0.314278i | \(0.101762\pi\) | |||||||
\(620\) | 80.6657 | 3.23961 | ||||||||
\(621\) | −26.4799 | −1.06260 | ||||||||
\(622\) | 36.5503 | 1.46553 | ||||||||
\(623\) | −20.2183 | −0.810029 | ||||||||
\(624\) | 13.7976 | 0.552346 | ||||||||
\(625\) | 74.0285 | 2.96114 | ||||||||
\(626\) | −19.4669 | −0.778055 | ||||||||
\(627\) | 61.0213 | 2.43696 | ||||||||
\(628\) | −25.8916 | −1.03319 | ||||||||
\(629\) | −6.74728 | −0.269032 | ||||||||
\(630\) | 169.979 | 6.77214 | ||||||||
\(631\) | −13.7415 | −0.547042 | −0.273521 | − | 0.961866i | \(-0.588188\pi\) | ||||
−0.273521 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(632\) | −23.3048 | −0.927016 | ||||||||
\(633\) | 64.1100 | 2.54814 | ||||||||
\(634\) | 25.1883 | 1.00036 | ||||||||
\(635\) | 43.1367 | 1.71183 | ||||||||
\(636\) | 20.0934 | 0.796754 | ||||||||
\(637\) | 2.37067 | 0.0939293 | ||||||||
\(638\) | −41.4217 | −1.63990 | ||||||||
\(639\) | −57.7244 | −2.28354 | ||||||||
\(640\) | 69.9547 | 2.76520 | ||||||||
\(641\) | −35.4842 | −1.40154 | −0.700771 | − | 0.713387i | \(-0.747160\pi\) | ||||
−0.700771 | + | 0.713387i | \(0.747160\pi\) | |||||||
\(642\) | −13.1507 | −0.519018 | ||||||||
\(643\) | 30.0138 | 1.18363 | 0.591814 | − | 0.806075i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(644\) | −19.8511 | −0.782244 | ||||||||
\(645\) | 33.5110 | 1.31949 | ||||||||
\(646\) | 56.8154 | 2.23537 | ||||||||
\(647\) | −28.1806 | −1.10789 | −0.553947 | − | 0.832552i | \(-0.686879\pi\) | ||||
−0.553947 | + | 0.832552i | \(0.686879\pi\) | |||||||
\(648\) | −35.7182 | −1.40314 | ||||||||
\(649\) | −62.3679 | −2.44816 | ||||||||
\(650\) | −186.698 | −7.32291 | ||||||||
\(651\) | 52.2952 | 2.04961 | ||||||||
\(652\) | −2.94025 | −0.115149 | ||||||||
\(653\) | 40.9791 | 1.60364 | 0.801818 | − | 0.597568i | \(-0.203866\pi\) | ||||
0.801818 | + | 0.597568i | \(0.203866\pi\) | |||||||
\(654\) | 6.97988 | 0.272935 | ||||||||
\(655\) | 51.2840 | 2.00383 | ||||||||
\(656\) | 4.97151 | 0.194105 | ||||||||
\(657\) | −22.4255 | −0.874903 | ||||||||
\(658\) | −43.9668 | −1.71400 | ||||||||
\(659\) | −24.5298 | −0.955547 | −0.477773 | − | 0.878483i | \(-0.658556\pi\) | ||||
−0.477773 | + | 0.878483i | \(0.658556\pi\) | |||||||
\(660\) | 211.743 | 8.24207 | ||||||||
\(661\) | −23.2170 | −0.903038 | −0.451519 | − | 0.892262i | \(-0.649118\pi\) | ||||
−0.451519 | + | 0.892262i | \(0.649118\pi\) | |||||||
\(662\) | 38.9377 | 1.51336 | ||||||||
\(663\) | 135.718 | 5.27086 | ||||||||
\(664\) | 20.6050 | 0.799630 | ||||||||
\(665\) | −42.7415 | −1.65744 | ||||||||
\(666\) | −14.8621 | −0.575894 | ||||||||
\(667\) | −8.29052 | −0.321010 | ||||||||
\(668\) | 58.0693 | 2.24677 | ||||||||
\(669\) | −6.13647 | −0.237250 | ||||||||
\(670\) | 134.122 | 5.18160 | ||||||||
\(671\) | −19.1063 | −0.737590 | ||||||||
\(672\) | 53.7968 | 2.07526 | ||||||||
\(673\) | −37.4165 | −1.44230 | −0.721149 | − | 0.692780i | \(-0.756386\pi\) | ||||
−0.721149 | + | 0.692780i | \(0.756386\pi\) | |||||||
\(674\) | 6.39238 | 0.246225 | ||||||||
\(675\) | −142.141 | −5.47102 | ||||||||
\(676\) | 89.7359 | 3.45138 | ||||||||
\(677\) | 26.6868 | 1.02566 | 0.512828 | − | 0.858491i | \(-0.328598\pi\) | ||||
0.512828 | + | 0.858491i | \(0.328598\pi\) | |||||||
\(678\) | −26.6032 | −1.02169 | ||||||||
\(679\) | −1.38516 | −0.0531575 | ||||||||
\(680\) | 69.0063 | 2.64627 | ||||||||
\(681\) | −72.7114 | −2.78631 | ||||||||
\(682\) | 73.8823 | 2.82910 | ||||||||
\(683\) | −18.4639 | −0.706502 | −0.353251 | − | 0.935529i | \(-0.614924\pi\) | ||||
−0.353251 | + | 0.935529i | \(0.614924\pi\) | |||||||
\(684\) | 75.8470 | 2.90008 | ||||||||
\(685\) | −35.2730 | −1.34771 | ||||||||
\(686\) | −40.5722 | −1.54905 | ||||||||
\(687\) | 28.6745 | 1.09400 | ||||||||
\(688\) | 1.76080 | 0.0671299 | ||||||||
\(689\) | −13.6881 | −0.521477 | ||||||||
\(690\) | 69.9263 | 2.66205 | ||||||||
\(691\) | 3.10743 | 0.118212 | 0.0591061 | − | 0.998252i | \(-0.481175\pi\) | ||||
0.0591061 | + | 0.998252i | \(0.481175\pi\) | |||||||
\(692\) | −3.58794 | −0.136393 | ||||||||
\(693\) | 94.3560 | 3.58429 | ||||||||
\(694\) | −46.8507 | −1.77843 | ||||||||
\(695\) | 37.0609 | 1.40580 | ||||||||
\(696\) | −26.2176 | −0.993775 | ||||||||
\(697\) | 48.9016 | 1.85228 | ||||||||
\(698\) | 60.3307 | 2.28355 | ||||||||
\(699\) | −29.7944 | −1.12693 | ||||||||
\(700\) | −106.559 | −4.02754 | ||||||||
\(701\) | 12.4002 | 0.468350 | 0.234175 | − | 0.972195i | \(-0.424761\pi\) | ||||
0.234175 | + | 0.972195i | \(0.424761\pi\) | |||||||
\(702\) | 162.976 | 6.15112 | ||||||||
\(703\) | 3.73708 | 0.140947 | ||||||||
\(704\) | 68.7723 | 2.59195 | ||||||||
\(705\) | 93.8645 | 3.53514 | ||||||||
\(706\) | −22.7338 | −0.855598 | ||||||||
\(707\) | 0.719532 | 0.0270608 | ||||||||
\(708\) | −112.779 | −4.23851 | ||||||||
\(709\) | −16.3903 | −0.615550 | −0.307775 | − | 0.951459i | \(-0.599584\pi\) | ||||
−0.307775 | + | 0.951459i | \(0.599584\pi\) | |||||||
\(710\) | 83.1032 | 3.11881 | ||||||||
\(711\) | 63.3415 | 2.37549 | ||||||||
\(712\) | −18.0795 | −0.677559 | ||||||||
\(713\) | 14.7875 | 0.553795 | ||||||||
\(714\) | 127.810 | 4.78318 | ||||||||
\(715\) | −144.245 | −5.39445 | ||||||||
\(716\) | −36.5096 | −1.36443 | ||||||||
\(717\) | −36.5569 | −1.36524 | ||||||||
\(718\) | −18.3476 | −0.684727 | ||||||||
\(719\) | −1.85548 | −0.0691978 | −0.0345989 | − | 0.999401i | \(-0.511015\pi\) | ||||
−0.0345989 | + | 0.999401i | \(0.511015\pi\) | |||||||
\(720\) | −19.0676 | −0.710608 | ||||||||
\(721\) | 53.1904 | 1.98091 | ||||||||
\(722\) | 11.3433 | 0.422152 | ||||||||
\(723\) | 30.9742 | 1.15194 | ||||||||
\(724\) | −30.7799 | −1.14393 | ||||||||
\(725\) | −44.5027 | −1.65279 | ||||||||
\(726\) | 117.158 | 4.34813 | ||||||||
\(727\) | 10.0650 | 0.373291 | 0.186646 | − | 0.982427i | \(-0.440238\pi\) | ||||
0.186646 | + | 0.982427i | \(0.440238\pi\) | |||||||
\(728\) | 42.7649 | 1.58497 | ||||||||
\(729\) | −6.43759 | −0.238429 | ||||||||
\(730\) | 32.2850 | 1.19492 | ||||||||
\(731\) | 17.3199 | 0.640599 | ||||||||
\(732\) | −34.5498 | −1.27700 | ||||||||
\(733\) | 34.7477 | 1.28344 | 0.641718 | − | 0.766941i | \(-0.278222\pi\) | ||||
0.641718 | + | 0.766941i | \(0.278222\pi\) | |||||||
\(734\) | 3.56759 | 0.131682 | ||||||||
\(735\) | −4.76623 | −0.175805 | ||||||||
\(736\) | 15.2121 | 0.560725 | ||||||||
\(737\) | 74.4516 | 2.74246 | ||||||||
\(738\) | 107.714 | 3.96502 | ||||||||
\(739\) | 5.89184 | 0.216735 | 0.108367 | − | 0.994111i | \(-0.465438\pi\) | ||||
0.108367 | + | 0.994111i | \(0.465438\pi\) | |||||||
\(740\) | 12.9676 | 0.476698 | ||||||||
\(741\) | −75.1696 | −2.76142 | ||||||||
\(742\) | −12.8906 | −0.473228 | ||||||||
\(743\) | −34.1682 | −1.25351 | −0.626755 | − | 0.779217i | \(-0.715617\pi\) | ||||
−0.626755 | + | 0.779217i | \(0.715617\pi\) | |||||||
\(744\) | 46.7632 | 1.71442 | ||||||||
\(745\) | 1.53269 | 0.0561535 | ||||||||
\(746\) | −12.5205 | −0.458409 | ||||||||
\(747\) | −56.0036 | −2.04906 | ||||||||
\(748\) | 109.438 | 4.00143 | ||||||||
\(749\) | 5.11318 | 0.186831 | ||||||||
\(750\) | 228.280 | 8.33560 | ||||||||
\(751\) | −31.1495 | −1.13666 | −0.568331 | − | 0.822800i | \(-0.692411\pi\) | ||||
−0.568331 | + | 0.822800i | \(0.692411\pi\) | |||||||
\(752\) | 4.93202 | 0.179852 | ||||||||
\(753\) | 13.9078 | 0.506830 | ||||||||
\(754\) | 51.0257 | 1.85825 | ||||||||
\(755\) | 81.8616 | 2.97925 | ||||||||
\(756\) | 93.0191 | 3.38307 | ||||||||
\(757\) | −18.9369 | −0.688275 | −0.344138 | − | 0.938919i | \(-0.611829\pi\) | ||||
−0.344138 | + | 0.938919i | \(0.611829\pi\) | |||||||
\(758\) | −46.2201 | −1.67879 | ||||||||
\(759\) | 38.8162 | 1.40894 | ||||||||
\(760\) | −38.2202 | −1.38639 | ||||||||
\(761\) | 14.4161 | 0.522583 | 0.261292 | − | 0.965260i | \(-0.415852\pi\) | ||||
0.261292 | + | 0.965260i | \(0.415852\pi\) | |||||||
\(762\) | 71.4442 | 2.58815 | ||||||||
\(763\) | −2.71387 | −0.0982487 | ||||||||
\(764\) | −44.6974 | −1.61710 | ||||||||
\(765\) | −187.556 | −6.78111 | ||||||||
\(766\) | 78.8488 | 2.84892 | ||||||||
\(767\) | 76.8284 | 2.77411 | ||||||||
\(768\) | 35.0293 | 1.26401 | ||||||||
\(769\) | −26.4863 | −0.955121 | −0.477561 | − | 0.878599i | \(-0.658479\pi\) | ||||
−0.477561 | + | 0.878599i | \(0.658479\pi\) | |||||||
\(770\) | −135.840 | −4.89533 | ||||||||
\(771\) | 3.59915 | 0.129620 | ||||||||
\(772\) | 27.3345 | 0.983788 | ||||||||
\(773\) | −46.3856 | −1.66838 | −0.834188 | − | 0.551481i | \(-0.814063\pi\) | ||||
−0.834188 | + | 0.551481i | \(0.814063\pi\) | |||||||
\(774\) | 38.1501 | 1.37128 | ||||||||
\(775\) | 79.3777 | 2.85133 | ||||||||
\(776\) | −1.23863 | −0.0444643 | ||||||||
\(777\) | 8.40683 | 0.301593 | ||||||||
\(778\) | −7.11071 | −0.254931 | ||||||||
\(779\) | −27.0848 | −0.970415 | ||||||||
\(780\) | −260.837 | −9.33946 | ||||||||
\(781\) | 46.1308 | 1.65069 | ||||||||
\(782\) | 36.1408 | 1.29239 | ||||||||
\(783\) | 38.8480 | 1.38832 | ||||||||
\(784\) | −0.250437 | −0.00894418 | ||||||||
\(785\) | −35.4614 | −1.26567 | ||||||||
\(786\) | 84.9379 | 3.02964 | ||||||||
\(787\) | 11.2850 | 0.402265 | 0.201133 | − | 0.979564i | \(-0.435538\pi\) | ||||
0.201133 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(788\) | −56.8839 | −2.02641 | ||||||||
\(789\) | 54.1628 | 1.92825 | ||||||||
\(790\) | −91.1898 | −3.24439 | ||||||||
\(791\) | 10.3437 | 0.367779 | ||||||||
\(792\) | 84.3747 | 2.99813 | ||||||||
\(793\) | 23.5362 | 0.835797 | ||||||||
\(794\) | −39.9467 | −1.41765 | ||||||||
\(795\) | 27.5200 | 0.976035 | ||||||||
\(796\) | 30.6975 | 1.08804 | ||||||||
\(797\) | 11.5861 | 0.410399 | 0.205200 | − | 0.978720i | \(-0.434216\pi\) | ||||
0.205200 | + | 0.978720i | \(0.434216\pi\) | |||||||
\(798\) | −70.7896 | −2.50592 | ||||||||
\(799\) | 48.5131 | 1.71627 | ||||||||
\(800\) | 81.6570 | 2.88701 | ||||||||
\(801\) | 49.1394 | 1.73626 | ||||||||
\(802\) | 47.0255 | 1.66053 | ||||||||
\(803\) | 17.9215 | 0.632435 | ||||||||
\(804\) | 134.630 | 4.74805 | ||||||||
\(805\) | −27.1883 | −0.958261 | ||||||||
\(806\) | −91.0125 | −3.20578 | ||||||||
\(807\) | −31.0184 | −1.09190 | ||||||||
\(808\) | 0.643418 | 0.0226354 | ||||||||
\(809\) | 23.5414 | 0.827673 | 0.413837 | − | 0.910351i | \(-0.364189\pi\) | ||||
0.413837 | + | 0.910351i | \(0.364189\pi\) | |||||||
\(810\) | −139.762 | −4.91074 | ||||||||
\(811\) | −23.9526 | −0.841089 | −0.420544 | − | 0.907272i | \(-0.638161\pi\) | ||||
−0.420544 | + | 0.907272i | \(0.638161\pi\) | |||||||
\(812\) | 29.1231 | 1.02202 | ||||||||
\(813\) | 7.31809 | 0.256656 | ||||||||
\(814\) | 11.8771 | 0.416292 | ||||||||
\(815\) | −4.02699 | −0.141059 | ||||||||
\(816\) | −14.3373 | −0.501904 | ||||||||
\(817\) | −9.59288 | −0.335612 | ||||||||
\(818\) | −34.4720 | −1.20529 | ||||||||
\(819\) | −116.233 | −4.06152 | ||||||||
\(820\) | −93.9839 | −3.28206 | ||||||||
\(821\) | 44.1792 | 1.54186 | 0.770932 | − | 0.636918i | \(-0.219791\pi\) | ||||
0.770932 | + | 0.636918i | \(0.219791\pi\) | |||||||
\(822\) | −58.4201 | −2.03764 | ||||||||
\(823\) | −2.86645 | −0.0999183 | −0.0499591 | − | 0.998751i | \(-0.515909\pi\) | ||||
−0.0499591 | + | 0.998751i | \(0.515909\pi\) | |||||||
\(824\) | 47.5638 | 1.65696 | ||||||||
\(825\) | 208.362 | 7.25422 | ||||||||
\(826\) | 72.3518 | 2.51744 | ||||||||
\(827\) | 44.0422 | 1.53150 | 0.765749 | − | 0.643139i | \(-0.222368\pi\) | ||||
0.765749 | + | 0.643139i | \(0.222368\pi\) | |||||||
\(828\) | 48.2470 | 1.67670 | ||||||||
\(829\) | 6.76420 | 0.234930 | 0.117465 | − | 0.993077i | \(-0.462523\pi\) | ||||
0.117465 | + | 0.993077i | \(0.462523\pi\) | |||||||
\(830\) | 80.6258 | 2.79856 | ||||||||
\(831\) | 33.9326 | 1.17711 | ||||||||
\(832\) | −84.7177 | −2.93706 | ||||||||
\(833\) | −2.46339 | −0.0853514 | ||||||||
\(834\) | 61.3813 | 2.12546 | ||||||||
\(835\) | 79.5323 | 2.75233 | ||||||||
\(836\) | −60.6136 | −2.09636 | ||||||||
\(837\) | −69.2917 | −2.39507 | ||||||||
\(838\) | −14.4872 | −0.500453 | ||||||||
\(839\) | −45.9721 | −1.58713 | −0.793566 | − | 0.608484i | \(-0.791778\pi\) | ||||
−0.793566 | + | 0.608484i | \(0.791778\pi\) | |||||||
\(840\) | −85.9790 | −2.96656 | ||||||||
\(841\) | −16.8372 | −0.580592 | ||||||||
\(842\) | 54.5552 | 1.88010 | ||||||||
\(843\) | 12.1991 | 0.420159 | ||||||||
\(844\) | −63.6817 | −2.19201 | ||||||||
\(845\) | 122.903 | 4.22799 | ||||||||
\(846\) | 106.859 | 3.67388 | ||||||||
\(847\) | −45.5525 | −1.56520 | ||||||||
\(848\) | 1.44601 | 0.0496563 | ||||||||
\(849\) | −34.8160 | −1.19488 | ||||||||
\(850\) | 194.000 | 6.65416 | ||||||||
\(851\) | 2.37719 | 0.0814891 | ||||||||
\(852\) | 83.4180 | 2.85785 | ||||||||
\(853\) | −29.1768 | −0.998996 | −0.499498 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499498 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(854\) | 22.1648 | 0.758465 | ||||||||
\(855\) | 103.881 | 3.55265 | ||||||||
\(856\) | 4.57229 | 0.156278 | ||||||||
\(857\) | −3.44148 | −0.117559 | −0.0587793 | − | 0.998271i | \(-0.518721\pi\) | ||||
−0.0587793 | + | 0.998271i | \(0.518721\pi\) | |||||||
\(858\) | −238.902 | −8.15599 | ||||||||
\(859\) | 14.6352 | 0.499346 | 0.249673 | − | 0.968330i | \(-0.419677\pi\) | ||||
0.249673 | + | 0.968330i | \(0.419677\pi\) | |||||||
\(860\) | −33.2871 | −1.13508 | ||||||||
\(861\) | −60.9293 | −2.07646 | ||||||||
\(862\) | −56.6551 | −1.92968 | ||||||||
\(863\) | 10.0899 | 0.343463 | 0.171732 | − | 0.985144i | \(-0.445064\pi\) | ||||
0.171732 | + | 0.985144i | \(0.445064\pi\) | |||||||
\(864\) | −71.2814 | −2.42504 | ||||||||
\(865\) | −4.91407 | −0.167084 | ||||||||
\(866\) | −23.4105 | −0.795521 | ||||||||
\(867\) | −88.3652 | −3.00104 | ||||||||
\(868\) | −51.9458 | −1.76315 | ||||||||
\(869\) | −50.6197 | −1.71716 | ||||||||
\(870\) | −102.587 | −3.47803 | ||||||||
\(871\) | −91.7138 | −3.10760 | ||||||||
\(872\) | −2.42679 | −0.0821814 | ||||||||
\(873\) | 3.36655 | 0.113940 | ||||||||
\(874\) | −20.0171 | −0.677089 | ||||||||
\(875\) | −88.7582 | −3.00058 | ||||||||
\(876\) | 32.4073 | 1.09494 | ||||||||
\(877\) | −15.5836 | −0.526221 | −0.263111 | − | 0.964766i | \(-0.584748\pi\) | ||||
−0.263111 | + | 0.964766i | \(0.584748\pi\) | |||||||
\(878\) | −67.7421 | −2.28618 | ||||||||
\(879\) | 54.4004 | 1.83488 | ||||||||
\(880\) | 15.2380 | 0.513673 | ||||||||
\(881\) | −10.1020 | −0.340345 | −0.170172 | − | 0.985414i | \(-0.554432\pi\) | ||||
−0.170172 | + | 0.985414i | \(0.554432\pi\) | |||||||
\(882\) | −5.42605 | −0.182705 | ||||||||
\(883\) | 33.2059 | 1.11747 | 0.558733 | − | 0.829347i | \(-0.311287\pi\) | ||||
0.558733 | + | 0.829347i | \(0.311287\pi\) | |||||||
\(884\) | −134.812 | −4.53420 | ||||||||
\(885\) | −154.464 | −5.19224 | ||||||||
\(886\) | 16.8317 | 0.565473 | ||||||||
\(887\) | −27.2739 | −0.915767 | −0.457884 | − | 0.889012i | \(-0.651392\pi\) | ||||
−0.457884 | + | 0.889012i | \(0.651392\pi\) | |||||||
\(888\) | 7.51753 | 0.252272 | ||||||||
\(889\) | −27.7785 | −0.931660 | ||||||||
\(890\) | −70.7437 | −2.37134 | ||||||||
\(891\) | −77.5823 | −2.59911 | ||||||||
\(892\) | 6.09547 | 0.204091 | ||||||||
\(893\) | −26.8697 | −0.899160 | ||||||||
\(894\) | 2.53848 | 0.0848996 | ||||||||
\(895\) | −50.0038 | −1.67144 | ||||||||
\(896\) | −45.0482 | −1.50496 | ||||||||
\(897\) | −47.8161 | −1.59653 | ||||||||
\(898\) | 43.8124 | 1.46204 | ||||||||
\(899\) | −21.6944 | −0.723548 | ||||||||
\(900\) | 258.985 | 8.63284 | ||||||||
\(901\) | 14.2235 | 0.473854 | ||||||||
\(902\) | −86.0805 | −2.86617 | ||||||||
\(903\) | −21.5799 | −0.718133 | ||||||||
\(904\) | 9.24949 | 0.307633 | ||||||||
\(905\) | −42.1565 | −1.40133 | ||||||||
\(906\) | 135.581 | 4.50439 | ||||||||
\(907\) | −48.4024 | −1.60717 | −0.803587 | − | 0.595187i | \(-0.797078\pi\) | ||||
−0.803587 | + | 0.595187i | \(0.797078\pi\) | |||||||
\(908\) | 72.2256 | 2.39689 | ||||||||
\(909\) | −1.74878 | −0.0580034 | ||||||||
\(910\) | 167.336 | 5.54712 | ||||||||
\(911\) | −47.0014 | −1.55722 | −0.778612 | − | 0.627505i | \(-0.784076\pi\) | ||||
−0.778612 | + | 0.627505i | \(0.784076\pi\) | |||||||
\(912\) | 7.94089 | 0.262949 | ||||||||
\(913\) | 44.7556 | 1.48119 | ||||||||
\(914\) | 41.4953 | 1.37254 | ||||||||
\(915\) | −47.3197 | −1.56434 | ||||||||
\(916\) | −28.4830 | −0.941103 | ||||||||
\(917\) | −33.0250 | −1.09058 | ||||||||
\(918\) | −169.350 | −5.58938 | ||||||||
\(919\) | −16.8310 | −0.555204 | −0.277602 | − | 0.960696i | \(-0.589540\pi\) | ||||
−0.277602 | + | 0.960696i | \(0.589540\pi\) | |||||||
\(920\) | −24.3122 | −0.801550 | ||||||||
\(921\) | 86.8640 | 2.86227 | ||||||||
\(922\) | −75.5649 | −2.48860 | ||||||||
\(923\) | −56.8266 | −1.87047 | ||||||||
\(924\) | −136.355 | −4.48573 | ||||||||
\(925\) | 12.7605 | 0.419564 | ||||||||
\(926\) | 49.9033 | 1.63992 | ||||||||
\(927\) | −129.276 | −4.24599 | ||||||||
\(928\) | −22.3173 | −0.732602 | ||||||||
\(929\) | 17.0596 | 0.559706 | 0.279853 | − | 0.960043i | \(-0.409714\pi\) | ||||
0.279853 | + | 0.960043i | \(0.409714\pi\) | |||||||
\(930\) | 182.981 | 6.00017 | ||||||||
\(931\) | 1.36438 | 0.0447159 | ||||||||
\(932\) | 29.5953 | 0.969426 | ||||||||
\(933\) | 50.2491 | 1.64508 | ||||||||
\(934\) | 53.3537 | 1.74579 | ||||||||
\(935\) | 149.887 | 4.90181 | ||||||||
\(936\) | −103.938 | −3.39731 | ||||||||
\(937\) | 35.6184 | 1.16360 | 0.581801 | − | 0.813331i | \(-0.302348\pi\) | ||||
0.581801 | + | 0.813331i | \(0.302348\pi\) | |||||||
\(938\) | −86.3699 | −2.82008 | ||||||||
\(939\) | −26.7630 | −0.873379 | ||||||||
\(940\) | −93.2374 | −3.04107 | ||||||||
\(941\) | −26.5251 | −0.864693 | −0.432346 | − | 0.901708i | \(-0.642314\pi\) | ||||
−0.432346 | + | 0.901708i | \(0.642314\pi\) | |||||||
\(942\) | −58.7321 | −1.91360 | ||||||||
\(943\) | −17.2289 | −0.561051 | ||||||||
\(944\) | −8.11614 | −0.264158 | ||||||||
\(945\) | 127.400 | 4.14432 | ||||||||
\(946\) | −30.4879 | −0.991246 | ||||||||
\(947\) | −5.47403 | −0.177882 | −0.0889411 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889411 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(948\) | −91.5352 | −2.97293 | ||||||||
\(949\) | −22.0767 | −0.716641 | ||||||||
\(950\) | −107.450 | −3.48613 | ||||||||
\(951\) | 34.6288 | 1.12291 | ||||||||
\(952\) | −44.4375 | −1.44023 | ||||||||
\(953\) | 12.9858 | 0.420651 | 0.210326 | − | 0.977631i | \(-0.432548\pi\) | ||||
0.210326 | + | 0.977631i | \(0.432548\pi\) | |||||||
\(954\) | 31.3298 | 1.01434 | ||||||||
\(955\) | −61.2180 | −1.98097 | ||||||||
\(956\) | 36.3126 | 1.17443 | ||||||||
\(957\) | −56.9464 | −1.84082 | ||||||||
\(958\) | 15.9243 | 0.514491 | ||||||||
\(959\) | 22.7145 | 0.733491 | ||||||||
\(960\) | 170.325 | 5.49722 | ||||||||
\(961\) | 7.69537 | 0.248238 | ||||||||
\(962\) | −14.6309 | −0.471719 | ||||||||
\(963\) | −12.4273 | −0.400464 | ||||||||
\(964\) | −30.7672 | −0.990946 | ||||||||
\(965\) | 37.4375 | 1.20516 | ||||||||
\(966\) | −45.0300 | −1.44881 | ||||||||
\(967\) | 55.7432 | 1.79258 | 0.896290 | − | 0.443469i | \(-0.146253\pi\) | ||||
0.896290 | + | 0.443469i | \(0.146253\pi\) | |||||||
\(968\) | −40.7339 | −1.30924 | ||||||||
\(969\) | 78.1096 | 2.50924 | ||||||||
\(970\) | −4.84666 | −0.155617 | ||||||||
\(971\) | −47.4591 | −1.52303 | −0.761517 | − | 0.648145i | \(-0.775545\pi\) | ||||
−0.761517 | + | 0.648145i | \(0.775545\pi\) | |||||||
\(972\) | −37.4652 | −1.20170 | ||||||||
\(973\) | −23.8659 | −0.765105 | ||||||||
\(974\) | −1.42700 | −0.0457240 | ||||||||
\(975\) | −256.672 | −8.22008 | ||||||||
\(976\) | −2.48636 | −0.0795866 | ||||||||
\(977\) | 10.3715 | 0.331814 | 0.165907 | − | 0.986141i | \(-0.446945\pi\) | ||||
0.165907 | + | 0.986141i | \(0.446945\pi\) | |||||||
\(978\) | −6.66961 | −0.213271 | ||||||||
\(979\) | −39.2700 | −1.25508 | ||||||||
\(980\) | 4.73439 | 0.151234 | ||||||||
\(981\) | 6.59591 | 0.210591 | ||||||||
\(982\) | −63.5671 | −2.02851 | ||||||||
\(983\) | 17.6788 | 0.563866 | 0.281933 | − | 0.959434i | \(-0.409024\pi\) | ||||
0.281933 | + | 0.959434i | \(0.409024\pi\) | |||||||
\(984\) | −54.4840 | −1.73689 | ||||||||
\(985\) | −77.9087 | −2.48238 | ||||||||
\(986\) | −53.0214 | −1.68855 | ||||||||
\(987\) | −60.4453 | −1.92400 | ||||||||
\(988\) | 74.6673 | 2.37548 | ||||||||
\(989\) | −6.10212 | −0.194036 | ||||||||
\(990\) | 330.151 | 10.4929 | ||||||||
\(991\) | 6.14140 | 0.195088 | 0.0975439 | − | 0.995231i | \(-0.468901\pi\) | ||||
0.0975439 | + | 0.995231i | \(0.468901\pi\) | |||||||
\(992\) | 39.8065 | 1.26386 | ||||||||
\(993\) | 53.5313 | 1.69877 | ||||||||
\(994\) | −53.5154 | −1.69741 | ||||||||
\(995\) | 42.0435 | 1.33287 | ||||||||
\(996\) | 80.9311 | 2.56440 | ||||||||
\(997\) | −26.2703 | −0.831988 | −0.415994 | − | 0.909367i | \(-0.636566\pi\) | ||||
−0.415994 | + | 0.909367i | \(0.636566\pi\) | |||||||
\(998\) | 91.0840 | 2.88321 | ||||||||
\(999\) | −11.1391 | −0.352427 |
(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 | 4033.2.a.c.1.12 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.12 | ✓ | 77 | 1.1 | even | 1 | trivial |