Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12654 | −1.50369 | −0.751844 | − | 0.659341i | \(-0.770835\pi\) | ||||
−0.751844 | + | 0.659341i | \(0.770835\pi\) | |||||||
\(3\) | −0.167601 | −0.0967645 | −0.0483822 | − | 0.998829i | \(-0.515407\pi\) | ||||
−0.0483822 | + | 0.998829i | \(0.515407\pi\) | |||||||
\(4\) | 2.52216 | 1.26108 | ||||||||
\(5\) | −1.92531 | −0.861024 | −0.430512 | − | 0.902585i | \(-0.641667\pi\) | ||||
−0.430512 | + | 0.902585i | \(0.641667\pi\) | |||||||
\(6\) | 0.356410 | 0.145504 | ||||||||
\(7\) | 0.0410631 | 0.0155204 | 0.00776020 | − | 0.999970i | \(-0.497530\pi\) | ||||
0.00776020 | + | 0.999970i | \(0.497530\pi\) | |||||||
\(8\) | −1.11038 | −0.392580 | ||||||||
\(9\) | −2.97191 | −0.990637 | ||||||||
\(10\) | 4.09424 | 1.29471 | ||||||||
\(11\) | 3.07732 | 0.927847 | 0.463924 | − | 0.885875i | \(-0.346441\pi\) | ||||
0.463924 | + | 0.885875i | \(0.346441\pi\) | |||||||
\(12\) | −0.422716 | −0.122028 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.0873222 | −0.0233379 | ||||||||
\(15\) | 0.322684 | 0.0833166 | ||||||||
\(16\) | −2.68304 | −0.670760 | ||||||||
\(17\) | −4.74077 | −1.14981 | −0.574903 | − | 0.818222i | \(-0.694960\pi\) | ||||
−0.574903 | + | 0.818222i | \(0.694960\pi\) | |||||||
\(18\) | 6.31987 | 1.48961 | ||||||||
\(19\) | −1.80299 | −0.413634 | −0.206817 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206817 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(20\) | −4.85593 | −1.08582 | ||||||||
\(21\) | −0.00688222 | −0.00150182 | ||||||||
\(22\) | −6.54404 | −1.39519 | ||||||||
\(23\) | −4.58005 | −0.955007 | −0.477503 | − | 0.878630i | \(-0.658458\pi\) | ||||
−0.477503 | + | 0.878630i | \(0.658458\pi\) | |||||||
\(24\) | 0.186102 | 0.0379878 | ||||||||
\(25\) | −1.29318 | −0.258637 | ||||||||
\(26\) | 2.12654 | 0.417048 | ||||||||
\(27\) | 1.00090 | 0.192623 | ||||||||
\(28\) | 0.103568 | 0.0195724 | ||||||||
\(29\) | 2.69979 | 0.501339 | 0.250669 | − | 0.968073i | \(-0.419349\pi\) | ||||
0.250669 | + | 0.968073i | \(0.419349\pi\) | |||||||
\(30\) | −0.686199 | −0.125282 | ||||||||
\(31\) | 8.90052 | 1.59858 | 0.799290 | − | 0.600945i | \(-0.205209\pi\) | ||||
0.799290 | + | 0.600945i | \(0.205209\pi\) | |||||||
\(32\) | 7.92635 | 1.40119 | ||||||||
\(33\) | −0.515762 | −0.0897827 | ||||||||
\(34\) | 10.0814 | 1.72895 | ||||||||
\(35\) | −0.0790592 | −0.0133634 | ||||||||
\(36\) | −7.49562 | −1.24927 | ||||||||
\(37\) | 7.81755 | 1.28520 | 0.642598 | − | 0.766203i | \(-0.277856\pi\) | ||||
0.642598 | + | 0.766203i | \(0.277856\pi\) | |||||||
\(38\) | 3.83412 | 0.621976 | ||||||||
\(39\) | 0.167601 | 0.0268376 | ||||||||
\(40\) | 2.13783 | 0.338021 | ||||||||
\(41\) | 9.02010 | 1.40870 | 0.704351 | − | 0.709852i | \(-0.251238\pi\) | ||||
0.704351 | + | 0.709852i | \(0.251238\pi\) | |||||||
\(42\) | 0.0146353 | 0.00225828 | ||||||||
\(43\) | 5.06430 | 0.772299 | 0.386149 | − | 0.922436i | \(-0.373805\pi\) | ||||
0.386149 | + | 0.922436i | \(0.373805\pi\) | |||||||
\(44\) | 7.76149 | 1.17009 | ||||||||
\(45\) | 5.72185 | 0.852962 | ||||||||
\(46\) | 9.73965 | 1.43603 | ||||||||
\(47\) | 12.4793 | 1.82029 | 0.910145 | − | 0.414290i | \(-0.135970\pi\) | ||||
0.910145 | + | 0.414290i | \(0.135970\pi\) | |||||||
\(48\) | 0.449680 | 0.0649057 | ||||||||
\(49\) | −6.99831 | −0.999759 | ||||||||
\(50\) | 2.75000 | 0.388909 | ||||||||
\(51\) | 0.794558 | 0.111260 | ||||||||
\(52\) | −2.52216 | −0.349760 | ||||||||
\(53\) | −1.95071 | −0.267951 | −0.133976 | − | 0.990985i | \(-0.542774\pi\) | ||||
−0.133976 | + | 0.990985i | \(0.542774\pi\) | |||||||
\(54\) | −2.12845 | −0.289645 | ||||||||
\(55\) | −5.92480 | −0.798899 | ||||||||
\(56\) | −0.0455959 | −0.00609301 | ||||||||
\(57\) | 0.302183 | 0.0400251 | ||||||||
\(58\) | −5.74121 | −0.753857 | ||||||||
\(59\) | −14.0622 | −1.83074 | −0.915370 | − | 0.402613i | \(-0.868102\pi\) | ||||
−0.915370 | + | 0.402613i | \(0.868102\pi\) | |||||||
\(60\) | 0.813859 | 0.105069 | ||||||||
\(61\) | −0.519818 | −0.0665558 | −0.0332779 | − | 0.999446i | \(-0.510595\pi\) | ||||
−0.0332779 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(62\) | −18.9273 | −2.40377 | ||||||||
\(63\) | −0.122036 | −0.0153751 | ||||||||
\(64\) | −11.4896 | −1.43620 | ||||||||
\(65\) | 1.92531 | 0.238805 | ||||||||
\(66\) | 1.09679 | 0.135005 | ||||||||
\(67\) | −14.4946 | −1.77080 | −0.885401 | − | 0.464828i | \(-0.846116\pi\) | ||||
−0.885401 | + | 0.464828i | \(0.846116\pi\) | |||||||
\(68\) | −11.9570 | −1.45000 | ||||||||
\(69\) | 0.767621 | 0.0924107 | ||||||||
\(70\) | 0.168122 | 0.0200945 | ||||||||
\(71\) | −2.74485 | −0.325753 | −0.162877 | − | 0.986646i | \(-0.552077\pi\) | ||||
−0.162877 | + | 0.986646i | \(0.552077\pi\) | |||||||
\(72\) | 3.29996 | 0.388904 | ||||||||
\(73\) | −3.91130 | −0.457783 | −0.228891 | − | 0.973452i | \(-0.573510\pi\) | ||||
−0.228891 | + | 0.973452i | \(0.573510\pi\) | |||||||
\(74\) | −16.6243 | −1.93253 | ||||||||
\(75\) | 0.216739 | 0.0250269 | ||||||||
\(76\) | −4.54742 | −0.521624 | ||||||||
\(77\) | 0.126364 | 0.0144006 | ||||||||
\(78\) | −0.356410 | −0.0403554 | ||||||||
\(79\) | 12.3492 | 1.38939 | 0.694697 | − | 0.719303i | \(-0.255539\pi\) | ||||
0.694697 | + | 0.719303i | \(0.255539\pi\) | |||||||
\(80\) | 5.16568 | 0.577541 | ||||||||
\(81\) | 8.74798 | 0.971998 | ||||||||
\(82\) | −19.1816 | −2.11825 | ||||||||
\(83\) | −2.28778 | −0.251116 | −0.125558 | − | 0.992086i | \(-0.540072\pi\) | ||||
−0.125558 | + | 0.992086i | \(0.540072\pi\) | |||||||
\(84\) | −0.0173580 | −0.00189392 | ||||||||
\(85\) | 9.12745 | 0.990011 | ||||||||
\(86\) | −10.7694 | −1.16130 | ||||||||
\(87\) | −0.452488 | −0.0485118 | ||||||||
\(88\) | −3.41701 | −0.364255 | ||||||||
\(89\) | −6.45962 | −0.684718 | −0.342359 | − | 0.939569i | \(-0.611226\pi\) | ||||
−0.342359 | + | 0.939569i | \(0.611226\pi\) | |||||||
\(90\) | −12.1677 | −1.28259 | ||||||||
\(91\) | −0.0410631 | −0.00430459 | ||||||||
\(92\) | −11.5516 | −1.20434 | ||||||||
\(93\) | −1.49174 | −0.154686 | ||||||||
\(94\) | −26.5376 | −2.73715 | ||||||||
\(95\) | 3.47131 | 0.356149 | ||||||||
\(96\) | −1.32846 | −0.135586 | ||||||||
\(97\) | 5.74742 | 0.583562 | 0.291781 | − | 0.956485i | \(-0.405752\pi\) | ||||
0.291781 | + | 0.956485i | \(0.405752\pi\) | |||||||
\(98\) | 14.8822 | 1.50333 | ||||||||
\(99\) | −9.14552 | −0.919160 | ||||||||
\(100\) | −3.26161 | −0.326161 | ||||||||
\(101\) | −13.4576 | −1.33908 | −0.669539 | − | 0.742777i | \(-0.733508\pi\) | ||||
−0.669539 | + | 0.742777i | \(0.733508\pi\) | |||||||
\(102\) | −1.68966 | −0.167301 | ||||||||
\(103\) | 15.2889 | 1.50646 | 0.753230 | − | 0.657757i | \(-0.228494\pi\) | ||||
0.753230 | + | 0.657757i | \(0.228494\pi\) | |||||||
\(104\) | 1.11038 | 0.108882 | ||||||||
\(105\) | 0.0132504 | 0.00129311 | ||||||||
\(106\) | 4.14826 | 0.402915 | ||||||||
\(107\) | 13.1298 | 1.26931 | 0.634655 | − | 0.772796i | \(-0.281142\pi\) | ||||
0.634655 | + | 0.772796i | \(0.281142\pi\) | |||||||
\(108\) | 2.52442 | 0.242913 | ||||||||
\(109\) | 4.07881 | 0.390679 | 0.195339 | − | 0.980736i | \(-0.437419\pi\) | ||||
0.195339 | + | 0.980736i | \(0.437419\pi\) | |||||||
\(110\) | 12.5993 | 1.20130 | ||||||||
\(111\) | −1.31023 | −0.124361 | ||||||||
\(112\) | −0.110174 | −0.0104105 | ||||||||
\(113\) | 5.48600 | 0.516079 | 0.258040 | − | 0.966134i | \(-0.416923\pi\) | ||||
0.258040 | + | 0.966134i | \(0.416923\pi\) | |||||||
\(114\) | −0.642602 | −0.0601852 | ||||||||
\(115\) | 8.81801 | 0.822284 | ||||||||
\(116\) | 6.80930 | 0.632228 | ||||||||
\(117\) | 2.97191 | 0.274753 | ||||||||
\(118\) | 29.9038 | 2.75286 | ||||||||
\(119\) | −0.194671 | −0.0178455 | ||||||||
\(120\) | −0.358303 | −0.0327085 | ||||||||
\(121\) | −1.53009 | −0.139099 | ||||||||
\(122\) | 1.10541 | 0.100079 | ||||||||
\(123\) | −1.51178 | −0.136312 | ||||||||
\(124\) | 22.4485 | 2.01594 | ||||||||
\(125\) | 12.1163 | 1.08372 | ||||||||
\(126\) | 0.259514 | 0.0231193 | ||||||||
\(127\) | 15.4543 | 1.37135 | 0.685674 | − | 0.727909i | \(-0.259508\pi\) | ||||
0.685674 | + | 0.727909i | \(0.259508\pi\) | |||||||
\(128\) | 8.58034 | 0.758402 | ||||||||
\(129\) | −0.848782 | −0.0747311 | ||||||||
\(130\) | −4.09424 | −0.359089 | ||||||||
\(131\) | −12.8990 | −1.12699 | −0.563495 | − | 0.826119i | \(-0.690544\pi\) | ||||
−0.563495 | + | 0.826119i | \(0.690544\pi\) | |||||||
\(132\) | −1.30083 | −0.113223 | ||||||||
\(133\) | −0.0740363 | −0.00641976 | ||||||||
\(134\) | 30.8234 | 2.66273 | ||||||||
\(135\) | −1.92704 | −0.165853 | ||||||||
\(136\) | 5.26408 | 0.451391 | ||||||||
\(137\) | −17.4507 | −1.49092 | −0.745458 | − | 0.666553i | \(-0.767769\pi\) | ||||
−0.745458 | + | 0.666553i | \(0.767769\pi\) | |||||||
\(138\) | −1.63237 | −0.138957 | ||||||||
\(139\) | −18.0474 | −1.53076 | −0.765378 | − | 0.643580i | \(-0.777448\pi\) | ||||
−0.765378 | + | 0.643580i | \(0.777448\pi\) | |||||||
\(140\) | −0.199400 | −0.0168524 | ||||||||
\(141\) | −2.09154 | −0.176139 | ||||||||
\(142\) | 5.83701 | 0.489831 | ||||||||
\(143\) | −3.07732 | −0.257339 | ||||||||
\(144\) | 7.97375 | 0.664479 | ||||||||
\(145\) | −5.19794 | −0.431665 | ||||||||
\(146\) | 8.31751 | 0.688362 | ||||||||
\(147\) | 1.17292 | 0.0967412 | ||||||||
\(148\) | 19.7171 | 1.62073 | ||||||||
\(149\) | 20.8768 | 1.71030 | 0.855148 | − | 0.518385i | \(-0.173466\pi\) | ||||
0.855148 | + | 0.518385i | \(0.173466\pi\) | |||||||
\(150\) | −0.460904 | −0.0376326 | ||||||||
\(151\) | −4.34170 | −0.353323 | −0.176661 | − | 0.984272i | \(-0.556530\pi\) | ||||
−0.176661 | + | 0.984272i | \(0.556530\pi\) | |||||||
\(152\) | 2.00201 | 0.162384 | ||||||||
\(153\) | 14.0891 | 1.13904 | ||||||||
\(154\) | −0.268719 | −0.0216540 | ||||||||
\(155\) | −17.1363 | −1.37642 | ||||||||
\(156\) | 0.422716 | 0.0338444 | ||||||||
\(157\) | 14.5110 | 1.15810 | 0.579052 | − | 0.815291i | \(-0.303423\pi\) | ||||
0.579052 | + | 0.815291i | \(0.303423\pi\) | |||||||
\(158\) | −26.2610 | −2.08921 | ||||||||
\(159\) | 0.326942 | 0.0259282 | ||||||||
\(160\) | −15.2607 | −1.20646 | ||||||||
\(161\) | −0.188071 | −0.0148221 | ||||||||
\(162\) | −18.6029 | −1.46158 | ||||||||
\(163\) | 23.9646 | 1.87705 | 0.938527 | − | 0.345206i | \(-0.112191\pi\) | ||||
0.938527 | + | 0.345206i | \(0.112191\pi\) | |||||||
\(164\) | 22.7501 | 1.77648 | ||||||||
\(165\) | 0.993002 | 0.0773051 | ||||||||
\(166\) | 4.86504 | 0.377601 | ||||||||
\(167\) | −20.5263 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(168\) | 0.00764192 | 0.000589587 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −19.4099 | −1.48867 | ||||||||
\(171\) | 5.35832 | 0.409761 | ||||||||
\(172\) | 12.7730 | 0.973929 | ||||||||
\(173\) | 1.79921 | 0.136791 | 0.0683956 | − | 0.997658i | \(-0.478212\pi\) | ||||
0.0683956 | + | 0.997658i | \(0.478212\pi\) | |||||||
\(174\) | 0.962232 | 0.0729466 | ||||||||
\(175\) | −0.0531022 | −0.00401415 | ||||||||
\(176\) | −8.25658 | −0.622363 | ||||||||
\(177\) | 2.35684 | 0.177151 | ||||||||
\(178\) | 13.7366 | 1.02960 | ||||||||
\(179\) | −7.36235 | −0.550288 | −0.275144 | − | 0.961403i | \(-0.588725\pi\) | ||||
−0.275144 | + | 0.961403i | \(0.588725\pi\) | |||||||
\(180\) | 14.4314 | 1.07565 | ||||||||
\(181\) | 6.61714 | 0.491848 | 0.245924 | − | 0.969289i | \(-0.420909\pi\) | ||||
0.245924 | + | 0.969289i | \(0.420909\pi\) | |||||||
\(182\) | 0.0873222 | 0.00647276 | ||||||||
\(183\) | 0.0871220 | 0.00644024 | ||||||||
\(184\) | 5.08562 | 0.374917 | ||||||||
\(185\) | −15.0512 | −1.10659 | ||||||||
\(186\) | 3.17223 | 0.232599 | ||||||||
\(187\) | −14.5889 | −1.06684 | ||||||||
\(188\) | 31.4747 | 2.29553 | ||||||||
\(189\) | 0.0411000 | 0.00298959 | ||||||||
\(190\) | −7.38186 | −0.535537 | ||||||||
\(191\) | −13.6371 | −0.986743 | −0.493372 | − | 0.869819i | \(-0.664236\pi\) | ||||
−0.493372 | + | 0.869819i | \(0.664236\pi\) | |||||||
\(192\) | 1.92567 | 0.138973 | ||||||||
\(193\) | 1.01066 | 0.0727488 | 0.0363744 | − | 0.999338i | \(-0.488419\pi\) | ||||
0.0363744 | + | 0.999338i | \(0.488419\pi\) | |||||||
\(194\) | −12.2221 | −0.877496 | ||||||||
\(195\) | −0.322684 | −0.0231079 | ||||||||
\(196\) | −17.6508 | −1.26077 | ||||||||
\(197\) | −0.540203 | −0.0384878 | −0.0192439 | − | 0.999815i | \(-0.506126\pi\) | ||||
−0.0192439 | + | 0.999815i | \(0.506126\pi\) | |||||||
\(198\) | 19.4483 | 1.38213 | ||||||||
\(199\) | 22.3714 | 1.58587 | 0.792933 | − | 0.609309i | \(-0.208553\pi\) | ||||
0.792933 | + | 0.609309i | \(0.208553\pi\) | |||||||
\(200\) | 1.43593 | 0.101536 | ||||||||
\(201\) | 2.42932 | 0.171351 | ||||||||
\(202\) | 28.6180 | 2.01355 | ||||||||
\(203\) | 0.110862 | 0.00778098 | ||||||||
\(204\) | 2.00400 | 0.140308 | ||||||||
\(205\) | −17.3665 | −1.21293 | ||||||||
\(206\) | −32.5124 | −2.26525 | ||||||||
\(207\) | 13.6115 | 0.946065 | ||||||||
\(208\) | 2.68304 | 0.186035 | ||||||||
\(209\) | −5.54837 | −0.383789 | ||||||||
\(210\) | −0.0281775 | −0.00194443 | ||||||||
\(211\) | 2.76956 | 0.190664 | 0.0953321 | − | 0.995446i | \(-0.469609\pi\) | ||||
0.0953321 | + | 0.995446i | \(0.469609\pi\) | |||||||
\(212\) | −4.92001 | −0.337907 | ||||||||
\(213\) | 0.460039 | 0.0315214 | ||||||||
\(214\) | −27.9211 | −1.90865 | ||||||||
\(215\) | −9.75035 | −0.664968 | ||||||||
\(216\) | −1.11138 | −0.0756200 | ||||||||
\(217\) | 0.365483 | 0.0248106 | ||||||||
\(218\) | −8.67373 | −0.587459 | ||||||||
\(219\) | 0.655537 | 0.0442971 | ||||||||
\(220\) | −14.9433 | −1.00747 | ||||||||
\(221\) | 4.74077 | 0.318899 | ||||||||
\(222\) | 2.78625 | 0.187001 | ||||||||
\(223\) | −5.90104 | −0.395163 | −0.197581 | − | 0.980286i | \(-0.563309\pi\) | ||||
−0.197581 | + | 0.980286i | \(0.563309\pi\) | |||||||
\(224\) | 0.325481 | 0.0217471 | ||||||||
\(225\) | 3.84323 | 0.256215 | ||||||||
\(226\) | −11.6662 | −0.776022 | ||||||||
\(227\) | −18.6060 | −1.23492 | −0.617461 | − | 0.786601i | \(-0.711839\pi\) | ||||
−0.617461 | + | 0.786601i | \(0.711839\pi\) | |||||||
\(228\) | 0.762152 | 0.0504747 | ||||||||
\(229\) | 12.8389 | 0.848420 | 0.424210 | − | 0.905564i | \(-0.360552\pi\) | ||||
0.424210 | + | 0.905564i | \(0.360552\pi\) | |||||||
\(230\) | −18.7518 | −1.23646 | ||||||||
\(231\) | −0.0211788 | −0.00139346 | ||||||||
\(232\) | −2.99781 | −0.196816 | ||||||||
\(233\) | −8.40261 | −0.550473 | −0.275237 | − | 0.961377i | \(-0.588756\pi\) | ||||
−0.275237 | + | 0.961377i | \(0.588756\pi\) | |||||||
\(234\) | −6.31987 | −0.413143 | ||||||||
\(235\) | −24.0265 | −1.56731 | ||||||||
\(236\) | −35.4670 | −2.30871 | ||||||||
\(237\) | −2.06974 | −0.134444 | ||||||||
\(238\) | 0.413975 | 0.0268340 | ||||||||
\(239\) | −20.7790 | −1.34408 | −0.672041 | − | 0.740514i | \(-0.734582\pi\) | ||||
−0.672041 | + | 0.740514i | \(0.734582\pi\) | |||||||
\(240\) | −0.865773 | −0.0558854 | ||||||||
\(241\) | −3.84725 | −0.247823 | −0.123912 | − | 0.992293i | \(-0.539544\pi\) | ||||
−0.123912 | + | 0.992293i | \(0.539544\pi\) | |||||||
\(242\) | 3.25379 | 0.209162 | ||||||||
\(243\) | −4.46886 | −0.286678 | ||||||||
\(244\) | −1.31106 | −0.0839321 | ||||||||
\(245\) | 13.4739 | 0.860817 | ||||||||
\(246\) | 3.21485 | 0.204971 | ||||||||
\(247\) | 1.80299 | 0.114721 | ||||||||
\(248\) | −9.88300 | −0.627571 | ||||||||
\(249\) | 0.383434 | 0.0242991 | ||||||||
\(250\) | −25.7658 | −1.62957 | ||||||||
\(251\) | 24.5615 | 1.55031 | 0.775155 | − | 0.631771i | \(-0.217672\pi\) | ||||
0.775155 | + | 0.631771i | \(0.217672\pi\) | |||||||
\(252\) | −0.307794 | −0.0193892 | ||||||||
\(253\) | −14.0943 | −0.886101 | ||||||||
\(254\) | −32.8641 | −2.06208 | ||||||||
\(255\) | −1.52977 | −0.0957979 | ||||||||
\(256\) | 4.73279 | 0.295799 | ||||||||
\(257\) | 2.71235 | 0.169192 | 0.0845959 | − | 0.996415i | \(-0.473040\pi\) | ||||
0.0845959 | + | 0.996415i | \(0.473040\pi\) | |||||||
\(258\) | 1.80497 | 0.112372 | ||||||||
\(259\) | 0.321013 | 0.0199468 | ||||||||
\(260\) | 4.85593 | 0.301152 | ||||||||
\(261\) | −8.02354 | −0.496645 | ||||||||
\(262\) | 27.4302 | 1.69464 | ||||||||
\(263\) | 1.75020 | 0.107922 | 0.0539611 | − | 0.998543i | \(-0.482815\pi\) | ||||
0.0539611 | + | 0.998543i | \(0.482815\pi\) | |||||||
\(264\) | 0.572695 | 0.0352469 | ||||||||
\(265\) | 3.75573 | 0.230712 | ||||||||
\(266\) | 0.157441 | 0.00965332 | ||||||||
\(267\) | 1.08264 | 0.0662564 | ||||||||
\(268\) | −36.5577 | −2.23312 | ||||||||
\(269\) | 4.66312 | 0.284315 | 0.142158 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142158 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(270\) | 4.09792 | 0.249391 | ||||||||
\(271\) | −1.11372 | −0.0676538 | −0.0338269 | − | 0.999428i | \(-0.510769\pi\) | ||||
−0.0338269 | + | 0.999428i | \(0.510769\pi\) | |||||||
\(272\) | 12.7197 | 0.771244 | ||||||||
\(273\) | 0.00688222 | 0.000416531 0 | ||||||||
\(274\) | 37.1096 | 2.24187 | ||||||||
\(275\) | −3.97955 | −0.239976 | ||||||||
\(276\) | 1.93606 | 0.116537 | ||||||||
\(277\) | −3.57329 | −0.214698 | −0.107349 | − | 0.994221i | \(-0.534236\pi\) | ||||
−0.107349 | + | 0.994221i | \(0.534236\pi\) | |||||||
\(278\) | 38.3784 | 2.30178 | ||||||||
\(279\) | −26.4515 | −1.58361 | ||||||||
\(280\) | 0.0877862 | 0.00524623 | ||||||||
\(281\) | −13.2494 | −0.790393 | −0.395196 | − | 0.918597i | \(-0.629323\pi\) | ||||
−0.395196 | + | 0.918597i | \(0.629323\pi\) | |||||||
\(282\) | 4.44774 | 0.264859 | ||||||||
\(283\) | 13.8599 | 0.823884 | 0.411942 | − | 0.911210i | \(-0.364851\pi\) | ||||
0.411942 | + | 0.911210i | \(0.364851\pi\) | |||||||
\(284\) | −6.92293 | −0.410800 | ||||||||
\(285\) | −0.581795 | −0.0344625 | ||||||||
\(286\) | 6.54404 | 0.386957 | ||||||||
\(287\) | 0.370393 | 0.0218636 | ||||||||
\(288\) | −23.5564 | −1.38807 | ||||||||
\(289\) | 5.47491 | 0.322054 | ||||||||
\(290\) | 11.0536 | 0.649090 | ||||||||
\(291\) | −0.963274 | −0.0564681 | ||||||||
\(292\) | −9.86490 | −0.577300 | ||||||||
\(293\) | 31.8458 | 1.86045 | 0.930226 | − | 0.366987i | \(-0.119611\pi\) | ||||
0.930226 | + | 0.366987i | \(0.119611\pi\) | |||||||
\(294\) | −2.49427 | −0.145469 | ||||||||
\(295\) | 27.0741 | 1.57631 | ||||||||
\(296\) | −8.68048 | −0.504543 | ||||||||
\(297\) | 3.08009 | 0.178725 | ||||||||
\(298\) | −44.3953 | −2.57175 | ||||||||
\(299\) | 4.58005 | 0.264871 | ||||||||
\(300\) | 0.546650 | 0.0315608 | ||||||||
\(301\) | 0.207956 | 0.0119864 | ||||||||
\(302\) | 9.23279 | 0.531287 | ||||||||
\(303\) | 2.25550 | 0.129575 | ||||||||
\(304\) | 4.83749 | 0.277449 | ||||||||
\(305\) | 1.00081 | 0.0573062 | ||||||||
\(306\) | −29.9611 | −1.71276 | ||||||||
\(307\) | −0.113410 | −0.00647268 | −0.00323634 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323634 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(308\) | 0.318711 | 0.0181602 | ||||||||
\(309\) | −2.56244 | −0.145772 | ||||||||
\(310\) | 36.4409 | 2.06970 | ||||||||
\(311\) | 18.4376 | 1.04550 | 0.522750 | − | 0.852486i | \(-0.324906\pi\) | ||||
0.522750 | + | 0.852486i | \(0.324906\pi\) | |||||||
\(312\) | −0.186102 | −0.0105359 | ||||||||
\(313\) | −9.47042 | −0.535300 | −0.267650 | − | 0.963516i | \(-0.586247\pi\) | ||||
−0.267650 | + | 0.963516i | \(0.586247\pi\) | |||||||
\(314\) | −30.8581 | −1.74143 | ||||||||
\(315\) | 0.234957 | 0.0132383 | ||||||||
\(316\) | 31.1466 | 1.75213 | ||||||||
\(317\) | −0.327446 | −0.0183912 | −0.00919560 | − | 0.999958i | \(-0.502927\pi\) | ||||
−0.00919560 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(318\) | −0.695253 | −0.0389879 | ||||||||
\(319\) | 8.30813 | 0.465166 | ||||||||
\(320\) | 22.1210 | 1.23660 | ||||||||
\(321\) | −2.20057 | −0.122824 | ||||||||
\(322\) | 0.399940 | 0.0222878 | ||||||||
\(323\) | 8.54755 | 0.475598 | ||||||||
\(324\) | 22.0638 | 1.22577 | ||||||||
\(325\) | 1.29318 | 0.0717330 | ||||||||
\(326\) | −50.9616 | −2.82250 | ||||||||
\(327\) | −0.683612 | −0.0378039 | ||||||||
\(328\) | −10.0158 | −0.553029 | ||||||||
\(329\) | 0.512438 | 0.0282516 | ||||||||
\(330\) | −2.11165 | −0.116243 | ||||||||
\(331\) | −31.2009 | −1.71496 | −0.857479 | − | 0.514519i | \(-0.827971\pi\) | ||||
−0.857479 | + | 0.514519i | \(0.827971\pi\) | |||||||
\(332\) | −5.77014 | −0.316677 | ||||||||
\(333\) | −23.2330 | −1.27316 | ||||||||
\(334\) | 43.6499 | 2.38841 | ||||||||
\(335\) | 27.9067 | 1.52470 | ||||||||
\(336\) | 0.0184653 | 0.00100736 | ||||||||
\(337\) | 2.42583 | 0.132143 | 0.0660717 | − | 0.997815i | \(-0.478953\pi\) | ||||
0.0660717 | + | 0.997815i | \(0.478953\pi\) | |||||||
\(338\) | −2.12654 | −0.115668 | ||||||||
\(339\) | −0.919459 | −0.0499381 | ||||||||
\(340\) | 23.0209 | 1.24848 | ||||||||
\(341\) | 27.3898 | 1.48324 | ||||||||
\(342\) | −11.3947 | −0.616152 | ||||||||
\(343\) | −0.574815 | −0.0310371 | ||||||||
\(344\) | −5.62332 | −0.303189 | ||||||||
\(345\) | −1.47791 | −0.0795679 | ||||||||
\(346\) | −3.82608 | −0.205691 | ||||||||
\(347\) | −26.7225 | −1.43454 | −0.717269 | − | 0.696796i | \(-0.754608\pi\) | ||||
−0.717269 | + | 0.696796i | \(0.754608\pi\) | |||||||
\(348\) | −1.14125 | −0.0611772 | ||||||||
\(349\) | 13.9159 | 0.744903 | 0.372451 | − | 0.928052i | \(-0.378517\pi\) | ||||
0.372451 | + | 0.928052i | \(0.378517\pi\) | |||||||
\(350\) | 0.112924 | 0.00603603 | ||||||||
\(351\) | −1.00090 | −0.0534240 | ||||||||
\(352\) | 24.3919 | 1.30009 | ||||||||
\(353\) | −0.453367 | −0.0241303 | −0.0120651 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120651 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(354\) | −5.01190 | −0.266379 | ||||||||
\(355\) | 5.28468 | 0.280482 | ||||||||
\(356\) | −16.2922 | −0.863484 | ||||||||
\(357\) | 0.0326270 | 0.00172681 | ||||||||
\(358\) | 15.6563 | 0.827461 | ||||||||
\(359\) | −29.9920 | −1.58292 | −0.791460 | − | 0.611221i | \(-0.790678\pi\) | ||||
−0.791460 | + | 0.611221i | \(0.790678\pi\) | |||||||
\(360\) | −6.35345 | −0.334856 | ||||||||
\(361\) | −15.7492 | −0.828907 | ||||||||
\(362\) | −14.0716 | −0.739586 | ||||||||
\(363\) | 0.256445 | 0.0134599 | ||||||||
\(364\) | −0.103568 | −0.00542842 | ||||||||
\(365\) | 7.53045 | 0.394162 | ||||||||
\(366\) | −0.185268 | −0.00968411 | ||||||||
\(367\) | −23.8742 | −1.24622 | −0.623110 | − | 0.782134i | \(-0.714131\pi\) | ||||
−0.623110 | + | 0.782134i | \(0.714131\pi\) | |||||||
\(368\) | 12.2885 | 0.640580 | ||||||||
\(369\) | −26.8069 | −1.39551 | ||||||||
\(370\) | 32.0069 | 1.66396 | ||||||||
\(371\) | −0.0801024 | −0.00415871 | ||||||||
\(372\) | −3.76239 | −0.195071 | ||||||||
\(373\) | −20.1275 | −1.04216 | −0.521081 | − | 0.853507i | \(-0.674471\pi\) | ||||
−0.521081 | + | 0.853507i | \(0.674471\pi\) | |||||||
\(374\) | 31.0238 | 1.60420 | ||||||||
\(375\) | −2.03071 | −0.104865 | ||||||||
\(376\) | −13.8568 | −0.714610 | ||||||||
\(377\) | −2.69979 | −0.139046 | ||||||||
\(378\) | −0.0874007 | −0.00449541 | ||||||||
\(379\) | −30.0630 | −1.54423 | −0.772116 | − | 0.635481i | \(-0.780802\pi\) | ||||
−0.772116 | + | 0.635481i | \(0.780802\pi\) | |||||||
\(380\) | 8.75518 | 0.449131 | ||||||||
\(381\) | −2.59016 | −0.132698 | ||||||||
\(382\) | 28.9997 | 1.48375 | ||||||||
\(383\) | −23.4974 | −1.20066 | −0.600332 | − | 0.799751i | \(-0.704965\pi\) | ||||
−0.600332 | + | 0.799751i | \(0.704965\pi\) | |||||||
\(384\) | −1.43807 | −0.0733863 | ||||||||
\(385\) | −0.243291 | −0.0123992 | ||||||||
\(386\) | −2.14920 | −0.109391 | ||||||||
\(387\) | −15.0506 | −0.765067 | ||||||||
\(388\) | 14.4959 | 0.735918 | ||||||||
\(389\) | −20.9710 | −1.06327 | −0.531637 | − | 0.846973i | \(-0.678423\pi\) | ||||
−0.531637 | + | 0.846973i | \(0.678423\pi\) | |||||||
\(390\) | 0.686199 | 0.0347470 | ||||||||
\(391\) | 21.7130 | 1.09807 | ||||||||
\(392\) | 7.77082 | 0.392486 | ||||||||
\(393\) | 2.16189 | 0.109053 | ||||||||
\(394\) | 1.14876 | 0.0578737 | ||||||||
\(395\) | −23.7760 | −1.19630 | ||||||||
\(396\) | −23.0664 | −1.15913 | ||||||||
\(397\) | −30.4229 | −1.52688 | −0.763442 | − | 0.645876i | \(-0.776492\pi\) | ||||
−0.763442 | + | 0.645876i | \(0.776492\pi\) | |||||||
\(398\) | −47.5736 | −2.38465 | ||||||||
\(399\) | 0.0124086 | 0.000621205 0 | ||||||||
\(400\) | 3.46967 | 0.173483 | ||||||||
\(401\) | 24.0363 | 1.20032 | 0.600159 | − | 0.799881i | \(-0.295104\pi\) | ||||
0.600159 | + | 0.799881i | \(0.295104\pi\) | |||||||
\(402\) | −5.16603 | −0.257658 | ||||||||
\(403\) | −8.90052 | −0.443367 | ||||||||
\(404\) | −33.9421 | −1.68868 | ||||||||
\(405\) | −16.8426 | −0.836914 | ||||||||
\(406\) | −0.235752 | −0.0117002 | ||||||||
\(407\) | 24.0571 | 1.19247 | ||||||||
\(408\) | −0.882265 | −0.0436786 | ||||||||
\(409\) | −14.1843 | −0.701366 | −0.350683 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350683 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(410\) | 36.9304 | 1.82386 | ||||||||
\(411\) | 2.92476 | 0.144268 | ||||||||
\(412\) | 38.5610 | 1.89977 | ||||||||
\(413\) | −0.577437 | −0.0284138 | ||||||||
\(414\) | −28.9453 | −1.42259 | ||||||||
\(415\) | 4.40468 | 0.216217 | ||||||||
\(416\) | −7.92635 | −0.388621 | ||||||||
\(417\) | 3.02476 | 0.148123 | ||||||||
\(418\) | 11.7988 | 0.577099 | ||||||||
\(419\) | −19.3169 | −0.943693 | −0.471846 | − | 0.881681i | \(-0.656412\pi\) | ||||
−0.471846 | + | 0.881681i | \(0.656412\pi\) | |||||||
\(420\) | 0.0334196 | 0.00163071 | ||||||||
\(421\) | 9.36974 | 0.456653 | 0.228327 | − | 0.973585i | \(-0.426675\pi\) | ||||
0.228327 | + | 0.973585i | \(0.426675\pi\) | |||||||
\(422\) | −5.88957 | −0.286700 | ||||||||
\(423\) | −37.0873 | −1.80325 | ||||||||
\(424\) | 2.16604 | 0.105192 | ||||||||
\(425\) | 6.13069 | 0.297382 | ||||||||
\(426\) | −0.978290 | −0.0473983 | ||||||||
\(427\) | −0.0213453 | −0.00103297 | ||||||||
\(428\) | 33.1155 | 1.60070 | ||||||||
\(429\) | 0.515762 | 0.0249012 | ||||||||
\(430\) | 20.7345 | 0.999905 | ||||||||
\(431\) | −11.3595 | −0.547166 | −0.273583 | − | 0.961848i | \(-0.588209\pi\) | ||||
−0.273583 | + | 0.961848i | \(0.588209\pi\) | |||||||
\(432\) | −2.68545 | −0.129204 | ||||||||
\(433\) | 34.1724 | 1.64222 | 0.821110 | − | 0.570769i | \(-0.193355\pi\) | ||||
0.821110 | + | 0.570769i | \(0.193355\pi\) | |||||||
\(434\) | −0.777213 | −0.0373074 | ||||||||
\(435\) | 0.871179 | 0.0417698 | ||||||||
\(436\) | 10.2874 | 0.492677 | ||||||||
\(437\) | 8.25778 | 0.395023 | ||||||||
\(438\) | −1.39402 | −0.0666090 | ||||||||
\(439\) | −22.6638 | −1.08168 | −0.540841 | − | 0.841125i | \(-0.681894\pi\) | ||||
−0.540841 | + | 0.841125i | \(0.681894\pi\) | |||||||
\(440\) | 6.57880 | 0.313632 | ||||||||
\(441\) | 20.7984 | 0.990398 | ||||||||
\(442\) | −10.0814 | −0.479524 | ||||||||
\(443\) | −18.2731 | −0.868179 | −0.434090 | − | 0.900870i | \(-0.642930\pi\) | ||||
−0.434090 | + | 0.900870i | \(0.642930\pi\) | |||||||
\(444\) | −3.30460 | −0.156829 | ||||||||
\(445\) | 12.4368 | 0.589559 | ||||||||
\(446\) | 12.5488 | 0.594202 | ||||||||
\(447\) | −3.49897 | −0.165496 | ||||||||
\(448\) | −0.471799 | −0.0222904 | ||||||||
\(449\) | −5.98117 | −0.282269 | −0.141134 | − | 0.989990i | \(-0.545075\pi\) | ||||
−0.141134 | + | 0.989990i | \(0.545075\pi\) | |||||||
\(450\) | −8.17277 | −0.385268 | ||||||||
\(451\) | 27.7577 | 1.30706 | ||||||||
\(452\) | 13.8365 | 0.650816 | ||||||||
\(453\) | 0.727674 | 0.0341891 | ||||||||
\(454\) | 39.5663 | 1.85694 | ||||||||
\(455\) | 0.0790592 | 0.00370635 | ||||||||
\(456\) | −0.335539 | −0.0157130 | ||||||||
\(457\) | 29.1975 | 1.36580 | 0.682901 | − | 0.730511i | \(-0.260718\pi\) | ||||
0.682901 | + | 0.730511i | \(0.260718\pi\) | |||||||
\(458\) | −27.3024 | −1.27576 | ||||||||
\(459\) | −4.74503 | −0.221479 | ||||||||
\(460\) | 22.2404 | 1.03696 | ||||||||
\(461\) | −18.4840 | −0.860885 | −0.430442 | − | 0.902618i | \(-0.641642\pi\) | ||||
−0.430442 | + | 0.902618i | \(0.641642\pi\) | |||||||
\(462\) | 0.0450375 | 0.00209533 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −7.24365 | −0.336278 | ||||||||
\(465\) | 2.87205 | 0.133188 | ||||||||
\(466\) | 17.8685 | 0.827740 | ||||||||
\(467\) | −24.2985 | −1.12440 | −0.562201 | − | 0.827001i | \(-0.690045\pi\) | ||||
−0.562201 | + | 0.827001i | \(0.690045\pi\) | |||||||
\(468\) | 7.49562 | 0.346485 | ||||||||
\(469\) | −0.595195 | −0.0274836 | ||||||||
\(470\) | 51.0932 | 2.35675 | ||||||||
\(471\) | −2.43206 | −0.112063 | ||||||||
\(472\) | 15.6144 | 0.718713 | ||||||||
\(473\) | 15.5845 | 0.716575 | ||||||||
\(474\) | 4.40137 | 0.202162 | ||||||||
\(475\) | 2.33160 | 0.106981 | ||||||||
\(476\) | −0.490991 | −0.0225045 | ||||||||
\(477\) | 5.79735 | 0.265442 | ||||||||
\(478\) | 44.1873 | 2.02108 | ||||||||
\(479\) | 19.5729 | 0.894309 | 0.447155 | − | 0.894457i | \(-0.352437\pi\) | ||||
0.447155 | + | 0.894457i | \(0.352437\pi\) | |||||||
\(480\) | 2.55770 | 0.116743 | ||||||||
\(481\) | −7.81755 | −0.356449 | ||||||||
\(482\) | 8.18132 | 0.372649 | ||||||||
\(483\) | 0.0315209 | 0.00143425 | ||||||||
\(484\) | −3.85913 | −0.175415 | ||||||||
\(485\) | −11.0656 | −0.502461 | ||||||||
\(486\) | 9.50320 | 0.431074 | ||||||||
\(487\) | −23.1114 | −1.04728 | −0.523639 | − | 0.851941i | \(-0.675426\pi\) | ||||
−0.523639 | + | 0.851941i | \(0.675426\pi\) | |||||||
\(488\) | 0.577198 | 0.0261285 | ||||||||
\(489\) | −4.01649 | −0.181632 | ||||||||
\(490\) | −28.6528 | −1.29440 | ||||||||
\(491\) | 27.6965 | 1.24992 | 0.624962 | − | 0.780655i | \(-0.285114\pi\) | ||||
0.624962 | + | 0.780655i | \(0.285114\pi\) | |||||||
\(492\) | −3.81294 | −0.171901 | ||||||||
\(493\) | −12.7991 | −0.576442 | ||||||||
\(494\) | −3.83412 | −0.172505 | ||||||||
\(495\) | 17.6080 | 0.791419 | ||||||||
\(496\) | −23.8804 | −1.07226 | ||||||||
\(497\) | −0.112712 | −0.00505582 | ||||||||
\(498\) | −0.815386 | −0.0365383 | ||||||||
\(499\) | 0.616476 | 0.0275973 | 0.0137986 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137986 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(500\) | 30.5593 | 1.36665 | ||||||||
\(501\) | 3.44022 | 0.153698 | ||||||||
\(502\) | −52.2310 | −2.33118 | ||||||||
\(503\) | 15.1551 | 0.675731 | 0.337866 | − | 0.941194i | \(-0.390295\pi\) | ||||
0.337866 | + | 0.941194i | \(0.390295\pi\) | |||||||
\(504\) | 0.135507 | 0.00603595 | ||||||||
\(505\) | 25.9100 | 1.15298 | ||||||||
\(506\) | 29.9720 | 1.33242 | ||||||||
\(507\) | −0.167601 | −0.00744342 | ||||||||
\(508\) | 38.9782 | 1.72938 | ||||||||
\(509\) | −36.2041 | −1.60472 | −0.802360 | − | 0.596840i | \(-0.796423\pi\) | ||||
−0.802360 | + | 0.596840i | \(0.796423\pi\) | |||||||
\(510\) | 3.25311 | 0.144050 | ||||||||
\(511\) | −0.160610 | −0.00710497 | ||||||||
\(512\) | −27.2251 | −1.20319 | ||||||||
\(513\) | −1.80461 | −0.0796753 | ||||||||
\(514\) | −5.76791 | −0.254412 | ||||||||
\(515\) | −29.4359 | −1.29710 | ||||||||
\(516\) | −2.14076 | −0.0942418 | ||||||||
\(517\) | 38.4028 | 1.68895 | ||||||||
\(518\) | −0.682646 | −0.0299937 | ||||||||
\(519\) | −0.301549 | −0.0132365 | ||||||||
\(520\) | −2.13783 | −0.0937502 | ||||||||
\(521\) | −7.94924 | −0.348263 | −0.174131 | − | 0.984722i | \(-0.555712\pi\) | ||||
−0.174131 | + | 0.984722i | \(0.555712\pi\) | |||||||
\(522\) | 17.0624 | 0.746799 | ||||||||
\(523\) | 19.5301 | 0.853992 | 0.426996 | − | 0.904254i | \(-0.359572\pi\) | ||||
0.426996 | + | 0.904254i | \(0.359572\pi\) | |||||||
\(524\) | −32.5333 | −1.42122 | ||||||||
\(525\) | 0.00889999 | 0.000388427 0 | ||||||||
\(526\) | −3.72187 | −0.162281 | ||||||||
\(527\) | −42.1953 | −1.83806 | ||||||||
\(528\) | 1.38381 | 0.0602226 | ||||||||
\(529\) | −2.02313 | −0.0879621 | ||||||||
\(530\) | −7.98669 | −0.346920 | ||||||||
\(531\) | 41.7916 | 1.81360 | ||||||||
\(532\) | −0.186731 | −0.00809582 | ||||||||
\(533\) | −9.02010 | −0.390704 | ||||||||
\(534\) | −2.30227 | −0.0996290 | ||||||||
\(535\) | −25.2790 | −1.09291 | ||||||||
\(536\) | 16.0946 | 0.695182 | ||||||||
\(537\) | 1.23394 | 0.0532483 | ||||||||
\(538\) | −9.91629 | −0.427521 | ||||||||
\(539\) | −21.5361 | −0.927624 | ||||||||
\(540\) | −4.86029 | −0.209154 | ||||||||
\(541\) | 32.1231 | 1.38108 | 0.690541 | − | 0.723294i | \(-0.257373\pi\) | ||||
0.690541 | + | 0.723294i | \(0.257373\pi\) | |||||||
\(542\) | 2.36837 | 0.101730 | ||||||||
\(543\) | −1.10904 | −0.0475934 | ||||||||
\(544\) | −37.5770 | −1.61110 | ||||||||
\(545\) | −7.85297 | −0.336384 | ||||||||
\(546\) | −0.0146353 | −0.000626333 0 | ||||||||
\(547\) | −42.0649 | −1.79856 | −0.899282 | − | 0.437370i | \(-0.855910\pi\) | ||||
−0.899282 | + | 0.437370i | \(0.855910\pi\) | |||||||
\(548\) | −44.0134 | −1.88016 | ||||||||
\(549\) | 1.54485 | 0.0659326 | ||||||||
\(550\) | 8.46265 | 0.360849 | ||||||||
\(551\) | −4.86769 | −0.207371 | ||||||||
\(552\) | −0.852355 | −0.0362786 | ||||||||
\(553\) | 0.507097 | 0.0215640 | ||||||||
\(554\) | 7.59874 | 0.322840 | ||||||||
\(555\) | 2.52259 | 0.107078 | ||||||||
\(556\) | −45.5183 | −1.93040 | ||||||||
\(557\) | −19.7273 | −0.835873 | −0.417936 | − | 0.908476i | \(-0.637246\pi\) | ||||
−0.417936 | + | 0.908476i | \(0.637246\pi\) | |||||||
\(558\) | 56.2502 | 2.38126 | ||||||||
\(559\) | −5.06430 | −0.214197 | ||||||||
\(560\) | 0.212119 | 0.00896366 | ||||||||
\(561\) | 2.44511 | 0.103233 | ||||||||
\(562\) | 28.1753 | 1.18850 | ||||||||
\(563\) | −23.6207 | −0.995496 | −0.497748 | − | 0.867322i | \(-0.665839\pi\) | ||||
−0.497748 | + | 0.867322i | \(0.665839\pi\) | |||||||
\(564\) | −5.27519 | −0.222126 | ||||||||
\(565\) | −10.5622 | −0.444357 | ||||||||
\(566\) | −29.4735 | −1.23887 | ||||||||
\(567\) | 0.359219 | 0.0150858 | ||||||||
\(568\) | 3.04784 | 0.127884 | ||||||||
\(569\) | −12.4247 | −0.520871 | −0.260435 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260435 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(570\) | 1.23721 | 0.0518209 | ||||||||
\(571\) | −4.18465 | −0.175122 | −0.0875612 | − | 0.996159i | \(-0.527907\pi\) | ||||
−0.0875612 | + | 0.996159i | \(0.527907\pi\) | |||||||
\(572\) | −7.76149 | −0.324524 | ||||||||
\(573\) | 2.28559 | 0.0954817 | ||||||||
\(574\) | −0.787655 | −0.0328761 | ||||||||
\(575\) | 5.92285 | 0.247000 | ||||||||
\(576\) | 34.1460 | 1.42275 | ||||||||
\(577\) | 13.7380 | 0.571922 | 0.285961 | − | 0.958241i | \(-0.407687\pi\) | ||||
0.285961 | + | 0.958241i | \(0.407687\pi\) | |||||||
\(578\) | −11.6426 | −0.484268 | ||||||||
\(579\) | −0.169387 | −0.00703950 | ||||||||
\(580\) | −13.1100 | −0.544363 | ||||||||
\(581\) | −0.0939434 | −0.00389743 | ||||||||
\(582\) | 2.04844 | 0.0849104 | ||||||||
\(583\) | −6.00297 | −0.248618 | ||||||||
\(584\) | 4.34304 | 0.179716 | ||||||||
\(585\) | −5.72185 | −0.236569 | ||||||||
\(586\) | −67.7213 | −2.79754 | ||||||||
\(587\) | 20.0531 | 0.827678 | 0.413839 | − | 0.910350i | \(-0.364188\pi\) | ||||
0.413839 | + | 0.910350i | \(0.364188\pi\) | |||||||
\(588\) | 2.95830 | 0.121998 | ||||||||
\(589\) | −16.0475 | −0.661227 | ||||||||
\(590\) | −57.5740 | −2.37028 | ||||||||
\(591\) | 0.0905385 | 0.00372426 | ||||||||
\(592\) | −20.9748 | −0.862058 | ||||||||
\(593\) | −19.4705 | −0.799557 | −0.399779 | − | 0.916612i | \(-0.630913\pi\) | ||||
−0.399779 | + | 0.916612i | \(0.630913\pi\) | |||||||
\(594\) | −6.54991 | −0.268746 | ||||||||
\(595\) | 0.374802 | 0.0153654 | ||||||||
\(596\) | 52.6546 | 2.15682 | ||||||||
\(597\) | −3.74947 | −0.153456 | ||||||||
\(598\) | −9.73965 | −0.398284 | ||||||||
\(599\) | −28.6342 | −1.16996 | −0.584980 | − | 0.811048i | \(-0.698898\pi\) | ||||
−0.584980 | + | 0.811048i | \(0.698898\pi\) | |||||||
\(600\) | −0.240664 | −0.00982506 | ||||||||
\(601\) | −13.7836 | −0.562244 | −0.281122 | − | 0.959672i | \(-0.590706\pi\) | ||||
−0.281122 | + | 0.959672i | \(0.590706\pi\) | |||||||
\(602\) | −0.442226 | −0.0180238 | ||||||||
\(603\) | 43.0768 | 1.75422 | ||||||||
\(604\) | −10.9505 | −0.445568 | ||||||||
\(605\) | 2.94590 | 0.119768 | ||||||||
\(606\) | −4.79640 | −0.194841 | ||||||||
\(607\) | −37.5822 | −1.52542 | −0.762708 | − | 0.646743i | \(-0.776130\pi\) | ||||
−0.762708 | + | 0.646743i | \(0.776130\pi\) | |||||||
\(608\) | −14.2911 | −0.579581 | ||||||||
\(609\) | −0.0185806 | −0.000752923 0 | ||||||||
\(610\) | −2.12826 | −0.0861706 | ||||||||
\(611\) | −12.4793 | −0.504858 | ||||||||
\(612\) | 35.5350 | 1.43642 | ||||||||
\(613\) | 0.394258 | 0.0159239 | 0.00796196 | − | 0.999968i | \(-0.497466\pi\) | ||||
0.00796196 | + | 0.999968i | \(0.497466\pi\) | |||||||
\(614\) | 0.241171 | 0.00973289 | ||||||||
\(615\) | 2.91064 | 0.117368 | ||||||||
\(616\) | −0.140313 | −0.00565338 | ||||||||
\(617\) | 48.2584 | 1.94281 | 0.971404 | − | 0.237431i | \(-0.0763055\pi\) | ||||
0.971404 | + | 0.237431i | \(0.0763055\pi\) | |||||||
\(618\) | 5.44911 | 0.219196 | ||||||||
\(619\) | 35.7294 | 1.43608 | 0.718042 | − | 0.696000i | \(-0.245039\pi\) | ||||
0.718042 | + | 0.696000i | \(0.245039\pi\) | |||||||
\(620\) | −43.2203 | −1.73577 | ||||||||
\(621\) | −4.58416 | −0.183956 | ||||||||
\(622\) | −39.2082 | −1.57211 | ||||||||
\(623\) | −0.265252 | −0.0106271 | ||||||||
\(624\) | −0.449680 | −0.0180016 | ||||||||
\(625\) | −16.8617 | −0.674470 | ||||||||
\(626\) | 20.1392 | 0.804924 | ||||||||
\(627\) | 0.929913 | 0.0371371 | ||||||||
\(628\) | 36.5990 | 1.46046 | ||||||||
\(629\) | −37.0612 | −1.47773 | ||||||||
\(630\) | −0.499644 | −0.0199063 | ||||||||
\(631\) | −6.56552 | −0.261369 | −0.130685 | − | 0.991424i | \(-0.541718\pi\) | ||||
−0.130685 | + | 0.991424i | \(0.541718\pi\) | |||||||
\(632\) | −13.7124 | −0.545449 | ||||||||
\(633\) | −0.464181 | −0.0184495 | ||||||||
\(634\) | 0.696326 | 0.0276546 | ||||||||
\(635\) | −29.7543 | −1.18076 | ||||||||
\(636\) | 0.824598 | 0.0326974 | ||||||||
\(637\) | 6.99831 | 0.277283 | ||||||||
\(638\) | −17.6675 | −0.699465 | ||||||||
\(639\) | 8.15744 | 0.322703 | ||||||||
\(640\) | −16.5198 | −0.653002 | ||||||||
\(641\) | 9.86437 | 0.389619 | 0.194810 | − | 0.980841i | \(-0.437591\pi\) | ||||
0.194810 | + | 0.980841i | \(0.437591\pi\) | |||||||
\(642\) | 4.67960 | 0.184689 | ||||||||
\(643\) | −32.7342 | −1.29091 | −0.645455 | − | 0.763798i | \(-0.723332\pi\) | ||||
−0.645455 | + | 0.763798i | \(0.723332\pi\) | |||||||
\(644\) | −0.474345 | −0.0186918 | ||||||||
\(645\) | 1.63417 | 0.0643453 | ||||||||
\(646\) | −18.1767 | −0.715152 | ||||||||
\(647\) | 26.3856 | 1.03732 | 0.518662 | − | 0.854979i | \(-0.326430\pi\) | ||||
0.518662 | + | 0.854979i | \(0.326430\pi\) | |||||||
\(648\) | −9.71362 | −0.381587 | ||||||||
\(649\) | −43.2739 | −1.69865 | ||||||||
\(650\) | −2.75000 | −0.107864 | ||||||||
\(651\) | −0.0612554 | −0.00240079 | ||||||||
\(652\) | 60.4425 | 2.36711 | ||||||||
\(653\) | −47.1434 | −1.84486 | −0.922432 | − | 0.386159i | \(-0.873802\pi\) | ||||
−0.922432 | + | 0.386159i | \(0.873802\pi\) | |||||||
\(654\) | 1.45373 | 0.0568452 | ||||||||
\(655\) | 24.8346 | 0.970366 | ||||||||
\(656\) | −24.2013 | −0.944901 | ||||||||
\(657\) | 11.6240 | 0.453496 | ||||||||
\(658\) | −1.08972 | −0.0424817 | ||||||||
\(659\) | 7.54754 | 0.294010 | 0.147005 | − | 0.989136i | \(-0.453037\pi\) | ||||
0.147005 | + | 0.989136i | \(0.453037\pi\) | |||||||
\(660\) | 2.50451 | 0.0974878 | ||||||||
\(661\) | 39.1731 | 1.52366 | 0.761829 | − | 0.647778i | \(-0.224302\pi\) | ||||
0.761829 | + | 0.647778i | \(0.224302\pi\) | |||||||
\(662\) | 66.3499 | 2.57876 | ||||||||
\(663\) | −0.794558 | −0.0308581 | ||||||||
\(664\) | 2.54031 | 0.0985833 | ||||||||
\(665\) | 0.142543 | 0.00552757 | ||||||||
\(666\) | 49.4059 | 1.91444 | ||||||||
\(667\) | −12.3652 | −0.478782 | ||||||||
\(668\) | −51.7705 | −2.00306 | ||||||||
\(669\) | 0.989020 | 0.0382377 | ||||||||
\(670\) | −59.3445 | −2.29268 | ||||||||
\(671\) | −1.59965 | −0.0617536 | ||||||||
\(672\) | −0.0545509 | −0.00210435 | ||||||||
\(673\) | 23.9209 | 0.922083 | 0.461041 | − | 0.887379i | \(-0.347476\pi\) | ||||
0.461041 | + | 0.887379i | \(0.347476\pi\) | |||||||
\(674\) | −5.15862 | −0.198702 | ||||||||
\(675\) | −1.29435 | −0.0498194 | ||||||||
\(676\) | 2.52216 | 0.0970060 | ||||||||
\(677\) | 29.2001 | 1.12225 | 0.561125 | − | 0.827731i | \(-0.310369\pi\) | ||||
0.561125 | + | 0.827731i | \(0.310369\pi\) | |||||||
\(678\) | 1.95526 | 0.0750914 | ||||||||
\(679\) | 0.236007 | 0.00905712 | ||||||||
\(680\) | −10.1350 | −0.388659 | ||||||||
\(681\) | 3.11838 | 0.119497 | ||||||||
\(682\) | −58.2453 | −2.23033 | ||||||||
\(683\) | −33.8080 | −1.29363 | −0.646813 | − | 0.762649i | \(-0.723898\pi\) | ||||
−0.646813 | + | 0.762649i | \(0.723898\pi\) | |||||||
\(684\) | 13.5145 | 0.516740 | ||||||||
\(685\) | 33.5980 | 1.28371 | ||||||||
\(686\) | 1.22236 | 0.0466701 | ||||||||
\(687\) | −2.15182 | −0.0820969 | ||||||||
\(688\) | −13.5877 | −0.518027 | ||||||||
\(689\) | 1.95071 | 0.0743163 | ||||||||
\(690\) | 3.14283 | 0.119645 | ||||||||
\(691\) | −6.36915 | −0.242294 | −0.121147 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121147 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(692\) | 4.53788 | 0.172504 | ||||||||
\(693\) | −0.375544 | −0.0142657 | ||||||||
\(694\) | 56.8263 | 2.15710 | ||||||||
\(695\) | 34.7467 | 1.31802 | ||||||||
\(696\) | 0.502436 | 0.0190448 | ||||||||
\(697\) | −42.7622 | −1.61973 | ||||||||
\(698\) | −29.5927 | −1.12010 | ||||||||
\(699\) | 1.40829 | 0.0532663 | ||||||||
\(700\) | −0.133932 | −0.00506216 | ||||||||
\(701\) | 9.74768 | 0.368165 | 0.184082 | − | 0.982911i | \(-0.441069\pi\) | ||||
0.184082 | + | 0.982911i | \(0.441069\pi\) | |||||||
\(702\) | 2.12845 | 0.0803330 | ||||||||
\(703\) | −14.0949 | −0.531601 | ||||||||
\(704\) | −35.3572 | −1.33257 | ||||||||
\(705\) | 4.02686 | 0.151660 | ||||||||
\(706\) | 0.964102 | 0.0362844 | ||||||||
\(707\) | −0.552610 | −0.0207830 | ||||||||
\(708\) | 5.94431 | 0.223401 | ||||||||
\(709\) | −12.1235 | −0.455306 | −0.227653 | − | 0.973742i | \(-0.573105\pi\) | ||||
−0.227653 | + | 0.973742i | \(0.573105\pi\) | |||||||
\(710\) | −11.2381 | −0.421757 | ||||||||
\(711\) | −36.7007 | −1.37638 | ||||||||
\(712\) | 7.17267 | 0.268807 | ||||||||
\(713\) | −40.7648 | −1.52666 | ||||||||
\(714\) | −0.0693826 | −0.00259658 | ||||||||
\(715\) | 5.92480 | 0.221575 | ||||||||
\(716\) | −18.5690 | −0.693956 | ||||||||
\(717\) | 3.48258 | 0.130059 | ||||||||
\(718\) | 63.7792 | 2.38022 | ||||||||
\(719\) | 17.1380 | 0.639140 | 0.319570 | − | 0.947563i | \(-0.396461\pi\) | ||||
0.319570 | + | 0.947563i | \(0.396461\pi\) | |||||||
\(720\) | −15.3519 | −0.572133 | ||||||||
\(721\) | 0.627810 | 0.0233809 | ||||||||
\(722\) | 33.4913 | 1.24642 | ||||||||
\(723\) | 0.644804 | 0.0239805 | ||||||||
\(724\) | 16.6895 | 0.620259 | ||||||||
\(725\) | −3.49133 | −0.129665 | ||||||||
\(726\) | −0.545339 | −0.0202394 | ||||||||
\(727\) | 13.1194 | 0.486572 | 0.243286 | − | 0.969955i | \(-0.421775\pi\) | ||||
0.243286 | + | 0.969955i | \(0.421775\pi\) | |||||||
\(728\) | 0.0455959 | 0.00168990 | ||||||||
\(729\) | −25.4949 | −0.944257 | ||||||||
\(730\) | −16.0138 | −0.592697 | ||||||||
\(731\) | −24.0087 | −0.887994 | ||||||||
\(732\) | 0.219735 | 0.00812165 | ||||||||
\(733\) | 45.3647 | 1.67558 | 0.837792 | − | 0.545989i | \(-0.183846\pi\) | ||||
0.837792 | + | 0.545989i | \(0.183846\pi\) | |||||||
\(734\) | 50.7692 | 1.87393 | ||||||||
\(735\) | −2.25824 | −0.0832965 | ||||||||
\(736\) | −36.3031 | −1.33815 | ||||||||
\(737\) | −44.6047 | −1.64303 | ||||||||
\(738\) | 57.0059 | 2.09842 | ||||||||
\(739\) | −10.7344 | −0.394871 | −0.197435 | − | 0.980316i | \(-0.563261\pi\) | ||||
−0.197435 | + | 0.980316i | \(0.563261\pi\) | |||||||
\(740\) | −37.9615 | −1.39549 | ||||||||
\(741\) | −0.302183 | −0.0111010 | ||||||||
\(742\) | 0.170341 | 0.00625340 | ||||||||
\(743\) | −4.77880 | −0.175317 | −0.0876585 | − | 0.996151i | \(-0.527938\pi\) | ||||
−0.0876585 | + | 0.996151i | \(0.527938\pi\) | |||||||
\(744\) | 1.65640 | 0.0607266 | ||||||||
\(745\) | −40.1943 | −1.47261 | ||||||||
\(746\) | 42.8019 | 1.56709 | ||||||||
\(747\) | 6.79907 | 0.248765 | ||||||||
\(748\) | −36.7954 | −1.34537 | ||||||||
\(749\) | 0.539152 | 0.0197002 | ||||||||
\(750\) | 4.31838 | 0.157685 | ||||||||
\(751\) | −9.45753 | −0.345110 | −0.172555 | − | 0.985000i | \(-0.555202\pi\) | ||||
−0.172555 | + | 0.985000i | \(0.555202\pi\) | |||||||
\(752\) | −33.4824 | −1.22098 | ||||||||
\(753\) | −4.11654 | −0.150015 | ||||||||
\(754\) | 5.74121 | 0.209082 | ||||||||
\(755\) | 8.35912 | 0.304219 | ||||||||
\(756\) | 0.103661 | 0.00377010 | ||||||||
\(757\) | 21.9693 | 0.798487 | 0.399243 | − | 0.916845i | \(-0.369273\pi\) | ||||
0.399243 | + | 0.916845i | \(0.369273\pi\) | |||||||
\(758\) | 63.9300 | 2.32204 | ||||||||
\(759\) | 2.36222 | 0.0857431 | ||||||||
\(760\) | −3.85449 | −0.139817 | ||||||||
\(761\) | −53.0060 | −1.92147 | −0.960733 | − | 0.277476i | \(-0.910502\pi\) | ||||
−0.960733 | + | 0.277476i | \(0.910502\pi\) | |||||||
\(762\) | 5.50806 | 0.199536 | ||||||||
\(763\) | 0.167489 | 0.00606350 | ||||||||
\(764\) | −34.3948 | −1.24436 | ||||||||
\(765\) | −27.1260 | −0.980741 | ||||||||
\(766\) | 49.9682 | 1.80542 | ||||||||
\(767\) | 14.0622 | 0.507756 | ||||||||
\(768\) | −0.793221 | −0.0286229 | ||||||||
\(769\) | −29.9712 | −1.08079 | −0.540395 | − | 0.841412i | \(-0.681725\pi\) | ||||
−0.540395 | + | 0.841412i | \(0.681725\pi\) | |||||||
\(770\) | 0.517366 | 0.0186446 | ||||||||
\(771\) | −0.454593 | −0.0163718 | ||||||||
\(772\) | 2.54904 | 0.0917419 | ||||||||
\(773\) | −42.8860 | −1.54250 | −0.771252 | − | 0.636530i | \(-0.780369\pi\) | ||||
−0.771252 | + | 0.636530i | \(0.780369\pi\) | |||||||
\(774\) | 32.0057 | 1.15042 | ||||||||
\(775\) | −11.5100 | −0.413452 | ||||||||
\(776\) | −6.38185 | −0.229095 | ||||||||
\(777\) | −0.0538021 | −0.00193014 | ||||||||
\(778\) | 44.5956 | 1.59883 | ||||||||
\(779\) | −16.2631 | −0.582687 | ||||||||
\(780\) | −0.813859 | −0.0291408 | ||||||||
\(781\) | −8.44677 | −0.302249 | ||||||||
\(782\) | −46.1734 | −1.65116 | ||||||||
\(783\) | 2.70222 | 0.0965694 | ||||||||
\(784\) | 18.7768 | 0.670598 | ||||||||
\(785\) | −27.9381 | −0.997155 | ||||||||
\(786\) | −4.59733 | −0.163981 | ||||||||
\(787\) | 41.1824 | 1.46799 | 0.733996 | − | 0.679153i | \(-0.237653\pi\) | ||||
0.733996 | + | 0.679153i | \(0.237653\pi\) | |||||||
\(788\) | −1.36248 | −0.0485362 | ||||||||
\(789\) | −0.293336 | −0.0104430 | ||||||||
\(790\) | 50.5606 | 1.79886 | ||||||||
\(791\) | 0.225272 | 0.00800976 | ||||||||
\(792\) | 10.1551 | 0.360844 | ||||||||
\(793\) | 0.519818 | 0.0184593 | ||||||||
\(794\) | 64.6955 | 2.29596 | ||||||||
\(795\) | −0.629464 | −0.0223248 | ||||||||
\(796\) | 56.4242 | 1.99990 | ||||||||
\(797\) | 26.5727 | 0.941255 | 0.470627 | − | 0.882332i | \(-0.344028\pi\) | ||||
0.470627 | + | 0.882332i | \(0.344028\pi\) | |||||||
\(798\) | −0.0263873 | −0.000934099 0 | ||||||||
\(799\) | −59.1614 | −2.09298 | ||||||||
\(800\) | −10.2502 | −0.362401 | ||||||||
\(801\) | 19.1974 | 0.678307 | ||||||||
\(802\) | −51.1142 | −1.80490 | ||||||||
\(803\) | −12.0363 | −0.424752 | ||||||||
\(804\) | 6.12711 | 0.216087 | ||||||||
\(805\) | 0.362095 | 0.0127622 | ||||||||
\(806\) | 18.9273 | 0.666685 | ||||||||
\(807\) | −0.781543 | −0.0275116 | ||||||||
\(808\) | 14.9431 | 0.525695 | ||||||||
\(809\) | −23.9655 | −0.842582 | −0.421291 | − | 0.906926i | \(-0.638423\pi\) | ||||
−0.421291 | + | 0.906926i | \(0.638423\pi\) | |||||||
\(810\) | 35.8163 | 1.25846 | ||||||||
\(811\) | 11.3020 | 0.396868 | 0.198434 | − | 0.980114i | \(-0.436414\pi\) | ||||
0.198434 | + | 0.980114i | \(0.436414\pi\) | |||||||
\(812\) | 0.279611 | 0.00981243 | ||||||||
\(813\) | 0.186661 | 0.00654649 | ||||||||
\(814\) | −51.1583 | −1.79310 | ||||||||
\(815\) | −46.1393 | −1.61619 | ||||||||
\(816\) | −2.13183 | −0.0746290 | ||||||||
\(817\) | −9.13087 | −0.319449 | ||||||||
\(818\) | 30.1633 | 1.05464 | ||||||||
\(819\) | 0.122036 | 0.00426428 | ||||||||
\(820\) | −43.8010 | −1.52960 | ||||||||
\(821\) | −22.8285 | −0.796720 | −0.398360 | − | 0.917229i | \(-0.630420\pi\) | ||||
−0.398360 | + | 0.917229i | \(0.630420\pi\) | |||||||
\(822\) | −6.21960 | −0.216934 | ||||||||
\(823\) | −7.37589 | −0.257107 | −0.128554 | − | 0.991703i | \(-0.541033\pi\) | ||||
−0.128554 | + | 0.991703i | \(0.541033\pi\) | |||||||
\(824\) | −16.9766 | −0.591407 | ||||||||
\(825\) | 0.666976 | 0.0232211 | ||||||||
\(826\) | 1.22794 | 0.0427256 | ||||||||
\(827\) | 27.5616 | 0.958412 | 0.479206 | − | 0.877702i | \(-0.340925\pi\) | ||||
0.479206 | + | 0.877702i | \(0.340925\pi\) | |||||||
\(828\) | 34.3303 | 1.19306 | ||||||||
\(829\) | −21.5148 | −0.747240 | −0.373620 | − | 0.927582i | \(-0.621884\pi\) | ||||
−0.373620 | + | 0.927582i | \(0.621884\pi\) | |||||||
\(830\) | −9.36671 | −0.325123 | ||||||||
\(831\) | 0.598888 | 0.0207752 | ||||||||
\(832\) | 11.4896 | 0.398330 | ||||||||
\(833\) | 33.1774 | 1.14953 | ||||||||
\(834\) | −6.43225 | −0.222731 | ||||||||
\(835\) | 39.5194 | 1.36763 | ||||||||
\(836\) | −13.9939 | −0.483988 | ||||||||
\(837\) | 8.90851 | 0.307923 | ||||||||
\(838\) | 41.0781 | 1.41902 | ||||||||
\(839\) | 3.95055 | 0.136388 | 0.0681941 | − | 0.997672i | \(-0.478276\pi\) | ||||
0.0681941 | + | 0.997672i | \(0.478276\pi\) | |||||||
\(840\) | −0.0147130 | −0.000507648 0 | ||||||||
\(841\) | −21.7111 | −0.748659 | ||||||||
\(842\) | −19.9251 | −0.686664 | ||||||||
\(843\) | 2.22061 | 0.0764819 | ||||||||
\(844\) | 6.98526 | 0.240443 | ||||||||
\(845\) | −1.92531 | −0.0662326 | ||||||||
\(846\) | 78.8675 | 2.71152 | ||||||||
\(847\) | −0.0628303 | −0.00215887 | ||||||||
\(848\) | 5.23384 | 0.179731 | ||||||||
\(849\) | −2.32293 | −0.0797227 | ||||||||
\(850\) | −13.0371 | −0.447170 | ||||||||
\(851\) | −35.8048 | −1.22737 | ||||||||
\(852\) | 1.16029 | 0.0397509 | ||||||||
\(853\) | 33.9708 | 1.16314 | 0.581569 | − | 0.813497i | \(-0.302439\pi\) | ||||
0.581569 | + | 0.813497i | \(0.302439\pi\) | |||||||
\(854\) | 0.0453916 | 0.00155327 | ||||||||
\(855\) | −10.3164 | −0.352814 | ||||||||
\(856\) | −14.5792 | −0.498306 | ||||||||
\(857\) | −34.4912 | −1.17820 | −0.589099 | − | 0.808061i | \(-0.700517\pi\) | ||||
−0.589099 | + | 0.808061i | \(0.700517\pi\) | |||||||
\(858\) | −1.09679 | −0.0374437 | ||||||||
\(859\) | −45.2599 | −1.54425 | −0.772124 | − | 0.635471i | \(-0.780806\pi\) | ||||
−0.772124 | + | 0.635471i | \(0.780806\pi\) | |||||||
\(860\) | −24.5919 | −0.838577 | ||||||||
\(861\) | −0.0620783 | −0.00211562 | ||||||||
\(862\) | 24.1563 | 0.822767 | ||||||||
\(863\) | 30.5418 | 1.03966 | 0.519828 | − | 0.854271i | \(-0.325996\pi\) | ||||
0.519828 | + | 0.854271i | \(0.325996\pi\) | |||||||
\(864\) | 7.93347 | 0.269902 | ||||||||
\(865\) | −3.46403 | −0.117780 | ||||||||
\(866\) | −72.6689 | −2.46939 | ||||||||
\(867\) | −0.917601 | −0.0311634 | ||||||||
\(868\) | 0.921806 | 0.0312881 | ||||||||
\(869\) | 38.0025 | 1.28915 | ||||||||
\(870\) | −1.85259 | −0.0628088 | ||||||||
\(871\) | 14.4946 | 0.491132 | ||||||||
\(872\) | −4.52905 | −0.153373 | ||||||||
\(873\) | −17.0808 | −0.578098 | ||||||||
\(874\) | −17.5605 | −0.593991 | ||||||||
\(875\) | 0.497534 | 0.0168197 | ||||||||
\(876\) | 1.65337 | 0.0558621 | ||||||||
\(877\) | −37.6125 | −1.27008 | −0.635042 | − | 0.772477i | \(-0.719017\pi\) | ||||
−0.635042 | + | 0.772477i | \(0.719017\pi\) | |||||||
\(878\) | 48.1953 | 1.62651 | ||||||||
\(879\) | −5.33739 | −0.180026 | ||||||||
\(880\) | 15.8965 | 0.535870 | ||||||||
\(881\) | 14.0753 | 0.474208 | 0.237104 | − | 0.971484i | \(-0.423802\pi\) | ||||
0.237104 | + | 0.971484i | \(0.423802\pi\) | |||||||
\(882\) | −44.2285 | −1.48925 | ||||||||
\(883\) | 37.1421 | 1.24993 | 0.624966 | − | 0.780652i | \(-0.285113\pi\) | ||||
0.624966 | + | 0.780652i | \(0.285113\pi\) | |||||||
\(884\) | 11.9570 | 0.402156 | ||||||||
\(885\) | −4.53764 | −0.152531 | ||||||||
\(886\) | 38.8583 | 1.30547 | ||||||||
\(887\) | −47.6824 | −1.60102 | −0.800510 | − | 0.599320i | \(-0.795438\pi\) | ||||
−0.800510 | + | 0.599320i | \(0.795438\pi\) | |||||||
\(888\) | 1.45486 | 0.0488218 | ||||||||
\(889\) | 0.634602 | 0.0212839 | ||||||||
\(890\) | −26.4472 | −0.886513 | ||||||||
\(891\) | 26.9203 | 0.901865 | ||||||||
\(892\) | −14.8833 | −0.498331 | ||||||||
\(893\) | −22.5000 | −0.752933 | ||||||||
\(894\) | 7.44070 | 0.248854 | ||||||||
\(895\) | 14.1748 | 0.473811 | ||||||||
\(896\) | 0.352335 | 0.0117707 | ||||||||
\(897\) | −0.767621 | −0.0256301 | ||||||||
\(898\) | 12.7192 | 0.424444 | ||||||||
\(899\) | 24.0296 | 0.801431 | ||||||||
\(900\) | 9.69322 | 0.323107 | ||||||||
\(901\) | 9.24789 | 0.308092 | ||||||||
\(902\) | −59.0278 | −1.96541 | ||||||||
\(903\) | −0.0348536 | −0.00115986 | ||||||||
\(904\) | −6.09157 | −0.202603 | ||||||||
\(905\) | −12.7400 | −0.423493 | ||||||||
\(906\) | −1.54742 | −0.0514097 | ||||||||
\(907\) | 21.0593 | 0.699263 | 0.349631 | − | 0.936887i | \(-0.386307\pi\) | ||||
0.349631 | + | 0.936887i | \(0.386307\pi\) | |||||||
\(908\) | −46.9272 | −1.55733 | ||||||||
\(909\) | 39.9947 | 1.32654 | ||||||||
\(910\) | −0.168122 | −0.00557320 | ||||||||
\(911\) | 9.82605 | 0.325552 | 0.162776 | − | 0.986663i | \(-0.447955\pi\) | ||||
0.162776 | + | 0.986663i | \(0.447955\pi\) | |||||||
\(912\) | −0.810768 | −0.0268472 | ||||||||
\(913\) | −7.04023 | −0.232998 | ||||||||
\(914\) | −62.0896 | −2.05374 | ||||||||
\(915\) | −0.167737 | −0.00554520 | ||||||||
\(916\) | 32.3818 | 1.06992 | ||||||||
\(917\) | −0.529673 | −0.0174914 | ||||||||
\(918\) | 10.0905 | 0.333035 | ||||||||
\(919\) | −20.2081 | −0.666603 | −0.333301 | − | 0.942820i | \(-0.608163\pi\) | ||||
−0.333301 | + | 0.942820i | \(0.608163\pi\) | |||||||
\(920\) | −9.79139 | −0.322813 | ||||||||
\(921\) | 0.0190077 | 0.000626325 0 | ||||||||
\(922\) | 39.3069 | 1.29450 | ||||||||
\(923\) | 2.74485 | 0.0903477 | ||||||||
\(924\) | −0.0534163 | −0.00175727 | ||||||||
\(925\) | −10.1095 | −0.332399 | ||||||||
\(926\) | 2.12654 | 0.0698823 | ||||||||
\(927\) | −45.4373 | −1.49236 | ||||||||
\(928\) | 21.3995 | 0.702473 | ||||||||
\(929\) | 33.4399 | 1.09713 | 0.548565 | − | 0.836108i | \(-0.315174\pi\) | ||||
0.548565 | + | 0.836108i | \(0.315174\pi\) | |||||||
\(930\) | −6.10753 | −0.200274 | ||||||||
\(931\) | 12.6179 | 0.413534 | ||||||||
\(932\) | −21.1927 | −0.694190 | ||||||||
\(933\) | −3.09016 | −0.101167 | ||||||||
\(934\) | 51.6717 | 1.69075 | ||||||||
\(935\) | 28.0881 | 0.918579 | ||||||||
\(936\) | −3.29996 | −0.107863 | ||||||||
\(937\) | 11.2836 | 0.368618 | 0.184309 | − | 0.982868i | \(-0.440995\pi\) | ||||
0.184309 | + | 0.982868i | \(0.440995\pi\) | |||||||
\(938\) | 1.26570 | 0.0413267 | ||||||||
\(939\) | 1.58725 | 0.0517980 | ||||||||
\(940\) | −60.5985 | −1.97651 | ||||||||
\(941\) | −20.3569 | −0.663616 | −0.331808 | − | 0.943347i | \(-0.607659\pi\) | ||||
−0.331808 | + | 0.943347i | \(0.607659\pi\) | |||||||
\(942\) | 5.17186 | 0.168508 | ||||||||
\(943\) | −41.3125 | −1.34532 | ||||||||
\(944\) | 37.7294 | 1.22799 | ||||||||
\(945\) | −0.0791302 | −0.00257411 | ||||||||
\(946\) | −33.1410 | −1.07751 | ||||||||
\(947\) | 18.2561 | 0.593243 | 0.296621 | − | 0.954995i | \(-0.404140\pi\) | ||||
0.296621 | + | 0.954995i | \(0.404140\pi\) | |||||||
\(948\) | −5.22020 | −0.169544 | ||||||||
\(949\) | 3.91130 | 0.126966 | ||||||||
\(950\) | −4.95822 | −0.160866 | ||||||||
\(951\) | 0.0548803 | 0.00177961 | ||||||||
\(952\) | 0.216160 | 0.00700577 | ||||||||
\(953\) | 0.106277 | 0.00344265 | 0.00172132 | − | 0.999999i | \(-0.499452\pi\) | ||||
0.00172132 | + | 0.999999i | \(0.499452\pi\) | |||||||
\(954\) | −12.3283 | −0.399142 | ||||||||
\(955\) | 26.2556 | 0.849610 | ||||||||
\(956\) | −52.4079 | −1.69499 | ||||||||
\(957\) | −1.39245 | −0.0450116 | ||||||||
\(958\) | −41.6225 | −1.34476 | ||||||||
\(959\) | −0.716581 | −0.0231396 | ||||||||
\(960\) | −3.70750 | −0.119659 | ||||||||
\(961\) | 48.2193 | 1.55546 | ||||||||
\(962\) | 16.6243 | 0.535989 | ||||||||
\(963\) | −39.0207 | −1.25742 | ||||||||
\(964\) | −9.70338 | −0.312525 | ||||||||
\(965\) | −1.94583 | −0.0626385 | ||||||||
\(966\) | −0.0670304 | −0.00215667 | ||||||||
\(967\) | −37.9888 | −1.22164 | −0.610819 | − | 0.791770i | \(-0.709160\pi\) | ||||
−0.610819 | + | 0.791770i | \(0.709160\pi\) | |||||||
\(968\) | 1.69899 | 0.0546076 | ||||||||
\(969\) | −1.43258 | −0.0460210 | ||||||||
\(970\) | 23.5313 | 0.755545 | ||||||||
\(971\) | −22.5744 | −0.724448 | −0.362224 | − | 0.932091i | \(-0.617983\pi\) | ||||
−0.362224 | + | 0.932091i | \(0.617983\pi\) | |||||||
\(972\) | −11.2712 | −0.361523 | ||||||||
\(973\) | −0.741081 | −0.0237580 | ||||||||
\(974\) | 49.1472 | 1.57478 | ||||||||
\(975\) | −0.216739 | −0.00694121 | ||||||||
\(976\) | 1.39469 | 0.0446430 | ||||||||
\(977\) | 3.94105 | 0.126085 | 0.0630427 | − | 0.998011i | \(-0.479920\pi\) | ||||
0.0630427 | + | 0.998011i | \(0.479920\pi\) | |||||||
\(978\) | 8.54122 | 0.273118 | ||||||||
\(979\) | −19.8783 | −0.635314 | ||||||||
\(980\) | 33.9833 | 1.08556 | ||||||||
\(981\) | −12.1219 | −0.387021 | ||||||||
\(982\) | −58.8975 | −1.87950 | ||||||||
\(983\) | 7.53961 | 0.240476 | 0.120238 | − | 0.992745i | \(-0.461634\pi\) | ||||
0.120238 | + | 0.992745i | \(0.461634\pi\) | |||||||
\(984\) | 1.67865 | 0.0535136 | ||||||||
\(985\) | 1.04006 | 0.0331390 | ||||||||
\(986\) | 27.2178 | 0.866790 | ||||||||
\(987\) | −0.0858852 | −0.00273376 | ||||||||
\(988\) | 4.54742 | 0.144673 | ||||||||
\(989\) | −23.1948 | −0.737550 | ||||||||
\(990\) | −37.4440 | −1.19005 | ||||||||
\(991\) | 22.6447 | 0.719332 | 0.359666 | − | 0.933081i | \(-0.382891\pi\) | ||||
0.359666 | + | 0.933081i | \(0.382891\pi\) | |||||||
\(992\) | 70.5486 | 2.23992 | ||||||||
\(993\) | 5.22931 | 0.165947 | ||||||||
\(994\) | 0.239686 | 0.00760238 | ||||||||
\(995\) | −43.0718 | −1.36547 | ||||||||
\(996\) | 0.967081 | 0.0306431 | ||||||||
\(997\) | 1.86014 | 0.0589113 | 0.0294556 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294556 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(998\) | −1.31096 | −0.0414977 | ||||||||
\(999\) | 7.82457 | 0.247558 |
(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 | 6019.2.a.c.1.20 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.20 | ✓ | 108 | 1.1 | even | 1 | trivial |