Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0631532 | 0.0446561 | 0.0223280 | − | 0.999751i | \(-0.492892\pi\) | ||||
0.0223280 | + | 0.999751i | \(0.492892\pi\) | |||||||
\(3\) | 0.00106429 | 0.000614468 0 | 0.000307234 | − | 1.00000i | \(-0.499902\pi\) | ||||
0.000307234 | 1.00000i | \(0.499902\pi\) | ||||||||
\(4\) | −1.99601 | −0.998006 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 6.72133e−5 0 | 2.74397e−5 0 | ||||||||
\(7\) | 3.26238 | 1.23306 | 0.616531 | − | 0.787330i | \(-0.288537\pi\) | ||||
0.616531 | + | 0.787330i | \(0.288537\pi\) | |||||||
\(8\) | −0.252361 | −0.0892231 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0.0631532 | 0.0199708 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.00212434 | −0.000613243 0 | ||||||||
\(13\) | 0.254914 | 0.0707004 | 0.0353502 | − | 0.999375i | \(-0.488745\pi\) | ||||
0.0353502 | + | 0.999375i | \(0.488745\pi\) | |||||||
\(14\) | 0.206030 | 0.0550637 | ||||||||
\(15\) | 0.00106429 | 0.000274798 0 | ||||||||
\(16\) | 3.97609 | 0.994021 | ||||||||
\(17\) | −5.08854 | −1.23415 | −0.617077 | − | 0.786903i | \(-0.711683\pi\) | ||||
−0.617077 | + | 0.786903i | \(0.711683\pi\) | |||||||
\(18\) | −0.189460 | −0.0446560 | ||||||||
\(19\) | −0.0662831 | −0.0152064 | −0.00760319 | − | 0.999971i | \(-0.502420\pi\) | ||||
−0.00760319 | + | 0.999971i | \(0.502420\pi\) | |||||||
\(20\) | −1.99601 | −0.446322 | ||||||||
\(21\) | 0.00347211 | 0.000757678 0 | ||||||||
\(22\) | −0.0631532 | −0.0134643 | ||||||||
\(23\) | 3.74775 | 0.781460 | 0.390730 | − | 0.920505i | \(-0.372223\pi\) | ||||
0.390730 | + | 0.920505i | \(0.372223\pi\) | |||||||
\(24\) | −0.000268585 0 | −5.48247e−5 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.0160986 | 0.00315720 | ||||||||
\(27\) | −0.00638574 | −0.00122894 | ||||||||
\(28\) | −6.51174 | −1.23060 | ||||||||
\(29\) | 3.06459 | 0.569081 | 0.284540 | − | 0.958664i | \(-0.408159\pi\) | ||||
0.284540 | + | 0.958664i | \(0.408159\pi\) | |||||||
\(30\) | 6.72133e−5 0 | 1.22714e−5 0 | ||||||||
\(31\) | 0.0370196 | 0.00664892 | 0.00332446 | − | 0.999994i | \(-0.498942\pi\) | ||||
0.00332446 | + | 0.999994i | \(0.498942\pi\) | |||||||
\(32\) | 0.755825 | 0.133612 | ||||||||
\(33\) | −0.00106429 | −0.000185269 0 | ||||||||
\(34\) | −0.321358 | −0.0551124 | ||||||||
\(35\) | 3.26238 | 0.551442 | ||||||||
\(36\) | 5.98803 | 0.998005 | ||||||||
\(37\) | 1.75949 | 0.289259 | 0.144629 | − | 0.989486i | \(-0.453801\pi\) | ||||
0.144629 | + | 0.989486i | \(0.453801\pi\) | |||||||
\(38\) | −0.00418599 | −0.000679057 0 | ||||||||
\(39\) | 0.000271302 0 | 4.34431e−5 0 | ||||||||
\(40\) | −0.252361 | −0.0399018 | ||||||||
\(41\) | −4.05583 | −0.633414 | −0.316707 | − | 0.948523i | \(-0.602577\pi\) | ||||
−0.316707 | + | 0.948523i | \(0.602577\pi\) | |||||||
\(42\) | 0.000219275 0 | 3.38349e−5 0 | ||||||||
\(43\) | 5.35006 | 0.815877 | 0.407938 | − | 0.913010i | \(-0.366248\pi\) | ||||
0.407938 | + | 0.913010i | \(0.366248\pi\) | |||||||
\(44\) | 1.99601 | 0.300910 | ||||||||
\(45\) | −3.00000 | −0.447213 | ||||||||
\(46\) | 0.236682 | 0.0348969 | ||||||||
\(47\) | −6.11964 | −0.892641 | −0.446321 | − | 0.894873i | \(-0.647266\pi\) | ||||
−0.446321 | + | 0.894873i | \(0.647266\pi\) | |||||||
\(48\) | 0.00423171 | 0.000610795 0 | ||||||||
\(49\) | 3.64310 | 0.520443 | ||||||||
\(50\) | 0.0631532 | 0.00893121 | ||||||||
\(51\) | −0.00541569 | −0.000758348 0 | ||||||||
\(52\) | −0.508811 | −0.0705594 | ||||||||
\(53\) | 7.61455 | 1.04594 | 0.522970 | − | 0.852351i | \(-0.324824\pi\) | ||||
0.522970 | + | 0.852351i | \(0.324824\pi\) | |||||||
\(54\) | −0.000403280 0 | −5.48794e−5 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −0.823297 | −0.110018 | ||||||||
\(57\) | −7.05444e−5 0 | −9.34384e−6 0 | ||||||||
\(58\) | 0.193539 | 0.0254129 | ||||||||
\(59\) | 7.27764 | 0.947468 | 0.473734 | − | 0.880668i | \(-0.342906\pi\) | ||||
0.473734 | + | 0.880668i | \(0.342906\pi\) | |||||||
\(60\) | −0.00212434 | −0.000274250 0 | ||||||||
\(61\) | −4.70371 | −0.602249 | −0.301124 | − | 0.953585i | \(-0.597362\pi\) | ||||
−0.301124 | + | 0.953585i | \(0.597362\pi\) | |||||||
\(62\) | 0.00233791 | 0.000296915 0 | ||||||||
\(63\) | −9.78713 | −1.23306 | ||||||||
\(64\) | −7.90444 | −0.988055 | ||||||||
\(65\) | 0.254914 | 0.0316182 | ||||||||
\(66\) | −6.72133e−5 0 | −8.27339e−6 0 | ||||||||
\(67\) | 9.97468 | 1.21860 | 0.609301 | − | 0.792939i | \(-0.291450\pi\) | ||||
0.609301 | + | 0.792939i | \(0.291450\pi\) | |||||||
\(68\) | 10.1568 | 1.23169 | ||||||||
\(69\) | 0.00398869 | 0.000480182 0 | ||||||||
\(70\) | 0.206030 | 0.0246252 | ||||||||
\(71\) | 10.3177 | 1.22449 | 0.612243 | − | 0.790669i | \(-0.290267\pi\) | ||||
0.612243 | + | 0.790669i | \(0.290267\pi\) | |||||||
\(72\) | 0.757083 | 0.0892230 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | 0.111118 | 0.0129172 | ||||||||
\(75\) | 0.00106429 | 0.000122894 0 | ||||||||
\(76\) | 0.132302 | 0.0151761 | ||||||||
\(77\) | −3.26238 | −0.371782 | ||||||||
\(78\) | 1.71336e−5 0 | 1.94000e−6 0 | ||||||||
\(79\) | −4.96069 | −0.558122 | −0.279061 | − | 0.960273i | \(-0.590023\pi\) | ||||
−0.279061 | + | 0.960273i | \(0.590023\pi\) | |||||||
\(80\) | 3.97609 | 0.444540 | ||||||||
\(81\) | 8.99999 | 0.999999 | ||||||||
\(82\) | −0.256139 | −0.0282858 | ||||||||
\(83\) | 17.7671 | 1.95020 | 0.975098 | − | 0.221776i | \(-0.0711855\pi\) | ||||
0.975098 | + | 0.221776i | \(0.0711855\pi\) | |||||||
\(84\) | −0.00693038 | −0.000756167 0 | ||||||||
\(85\) | −5.08854 | −0.551930 | ||||||||
\(86\) | 0.337873 | 0.0364338 | ||||||||
\(87\) | 0.00326162 | 0.000349682 0 | ||||||||
\(88\) | 0.252361 | 0.0269018 | ||||||||
\(89\) | −17.6804 | −1.87412 | −0.937059 | − | 0.349171i | \(-0.886463\pi\) | ||||
−0.937059 | + | 0.349171i | \(0.886463\pi\) | |||||||
\(90\) | −0.189460 | −0.0199708 | ||||||||
\(91\) | 0.831625 | 0.0871780 | ||||||||
\(92\) | −7.48055 | −0.779901 | ||||||||
\(93\) | 3.93996e−5 0 | 4.08555e−6 0 | ||||||||
\(94\) | −0.386475 | −0.0398619 | ||||||||
\(95\) | −0.0662831 | −0.00680050 | ||||||||
\(96\) | 0.000804417 0 | 8.21004e−5 0 | ||||||||
\(97\) | −9.81498 | −0.996560 | −0.498280 | − | 0.867016i | \(-0.666035\pi\) | ||||
−0.498280 | + | 0.867016i | \(0.666035\pi\) | |||||||
\(98\) | 0.230073 | 0.0232409 | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | −1.99601 | −0.199601 | ||||||||
\(101\) | 10.2545 | 1.02036 | 0.510181 | − | 0.860067i | \(-0.329579\pi\) | ||||
0.510181 | + | 0.860067i | \(0.329579\pi\) | |||||||
\(102\) | −0.000342018 0 | −3.38648e−5 0 | ||||||||
\(103\) | 17.1779 | 1.69259 | 0.846294 | − | 0.532717i | \(-0.178829\pi\) | ||||
0.846294 | + | 0.532717i | \(0.178829\pi\) | |||||||
\(104\) | −0.0643303 | −0.00630811 | ||||||||
\(105\) | 0.00347211 | 0.000338844 0 | ||||||||
\(106\) | 0.480884 | 0.0467075 | ||||||||
\(107\) | −0.870329 | −0.0841379 | −0.0420689 | − | 0.999115i | \(-0.513395\pi\) | ||||
−0.0420689 | + | 0.999115i | \(0.513395\pi\) | |||||||
\(108\) | 0.0127460 | 0.00122649 | ||||||||
\(109\) | −12.3116 | −1.17924 | −0.589618 | − | 0.807682i | \(-0.700722\pi\) | ||||
−0.589618 | + | 0.807682i | \(0.700722\pi\) | |||||||
\(110\) | −0.0631532 | −0.00602142 | ||||||||
\(111\) | 0.00187261 | 0.000177740 0 | ||||||||
\(112\) | 12.9715 | 1.22569 | ||||||||
\(113\) | 5.72645 | 0.538700 | 0.269350 | − | 0.963042i | \(-0.413191\pi\) | ||||
0.269350 | + | 0.963042i | \(0.413191\pi\) | |||||||
\(114\) | −4.45511e−6 0 | −4.17259e−7 0 | ||||||||
\(115\) | 3.74775 | 0.349479 | ||||||||
\(116\) | −6.11696 | −0.567946 | ||||||||
\(117\) | −0.764741 | −0.0707004 | ||||||||
\(118\) | 0.459606 | 0.0423102 | ||||||||
\(119\) | −16.6007 | −1.52179 | ||||||||
\(120\) | −0.000268585 0 | −2.45184e−5 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.297055 | −0.0268941 | ||||||||
\(123\) | −0.00431658 | −0.000389213 0 | ||||||||
\(124\) | −0.0738916 | −0.00663566 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.618088 | −0.0550637 | ||||||||
\(127\) | −2.22009 | −0.197001 | −0.0985006 | − | 0.995137i | \(-0.531405\pi\) | ||||
−0.0985006 | + | 0.995137i | \(0.531405\pi\) | |||||||
\(128\) | −2.01084 | −0.177735 | ||||||||
\(129\) | 0.00569402 | 0.000501330 0 | ||||||||
\(130\) | 0.0160986 | 0.00141194 | ||||||||
\(131\) | 8.77822 | 0.766956 | 0.383478 | − | 0.923550i | \(-0.374726\pi\) | ||||
0.383478 | + | 0.923550i | \(0.374726\pi\) | |||||||
\(132\) | 0.00212434 | 0.000184900 0 | ||||||||
\(133\) | −0.216240 | −0.0187504 | ||||||||
\(134\) | 0.629933 | 0.0544180 | ||||||||
\(135\) | −0.00638574 | −0.000549597 0 | ||||||||
\(136\) | 1.28415 | 0.110115 | ||||||||
\(137\) | 12.3371 | 1.05403 | 0.527016 | − | 0.849856i | \(-0.323311\pi\) | ||||
0.527016 | + | 0.849856i | \(0.323311\pi\) | |||||||
\(138\) | 0.000251899 0 | 2.14430e−5 0 | ||||||||
\(139\) | 4.62376 | 0.392182 | 0.196091 | − | 0.980586i | \(-0.437175\pi\) | ||||
0.196091 | + | 0.980586i | \(0.437175\pi\) | |||||||
\(140\) | −6.51174 | −0.550343 | ||||||||
\(141\) | −0.00651307 | −0.000548500 0 | ||||||||
\(142\) | 0.651596 | 0.0546808 | ||||||||
\(143\) | −0.254914 | −0.0213170 | ||||||||
\(144\) | −11.9283 | −0.994021 | ||||||||
\(145\) | 3.06459 | 0.254501 | ||||||||
\(146\) | −0.0631532 | −0.00522660 | ||||||||
\(147\) | 0.00387731 | 0.000319796 0 | ||||||||
\(148\) | −3.51197 | −0.288682 | ||||||||
\(149\) | 11.1476 | 0.913251 | 0.456625 | − | 0.889659i | \(-0.349058\pi\) | ||||
0.456625 | + | 0.889659i | \(0.349058\pi\) | |||||||
\(150\) | 6.72133e−5 0 | 5.48795e−6 0 | ||||||||
\(151\) | −16.4135 | −1.33571 | −0.667856 | − | 0.744291i | \(-0.732788\pi\) | ||||
−0.667856 | + | 0.744291i | \(0.732788\pi\) | |||||||
\(152\) | 0.0167273 | 0.00135676 | ||||||||
\(153\) | 15.2656 | 1.23415 | ||||||||
\(154\) | −0.206030 | −0.0166023 | ||||||||
\(155\) | 0.0370196 | 0.00297349 | ||||||||
\(156\) | −0.000541523 0 | −4.33565e−5 0 | ||||||||
\(157\) | 9.34001 | 0.745414 | 0.372707 | − | 0.927949i | \(-0.378430\pi\) | ||||
0.372707 | + | 0.927949i | \(0.378430\pi\) | |||||||
\(158\) | −0.313284 | −0.0249235 | ||||||||
\(159\) | 0.00810409 | 0.000642696 0 | ||||||||
\(160\) | 0.755825 | 0.0597532 | ||||||||
\(161\) | 12.2266 | 0.963588 | ||||||||
\(162\) | 0.568378 | 0.0446560 | ||||||||
\(163\) | −4.17767 | −0.327220 | −0.163610 | − | 0.986525i | \(-0.552314\pi\) | ||||
−0.163610 | + | 0.986525i | \(0.552314\pi\) | |||||||
\(164\) | 8.09548 | 0.632151 | ||||||||
\(165\) | −0.00106429 | −8.28549e−5 0 | ||||||||
\(166\) | 1.12205 | 0.0870880 | ||||||||
\(167\) | 2.04778 | 0.158462 | 0.0792308 | − | 0.996856i | \(-0.474754\pi\) | ||||
0.0792308 | + | 0.996856i | \(0.474754\pi\) | |||||||
\(168\) | −0.000876226 0 | −6.76023e−5 0 | ||||||||
\(169\) | −12.9350 | −0.995001 | ||||||||
\(170\) | −0.321358 | −0.0246470 | ||||||||
\(171\) | 0.198849 | 0.0152064 | ||||||||
\(172\) | −10.6788 | −0.814250 | ||||||||
\(173\) | 15.0891 | 1.14721 | 0.573603 | − | 0.819133i | \(-0.305545\pi\) | ||||
0.573603 | + | 0.819133i | \(0.305545\pi\) | |||||||
\(174\) | 0.000205981 0 | 1.56154e−5 0 | ||||||||
\(175\) | 3.26238 | 0.246612 | ||||||||
\(176\) | −3.97609 | −0.299709 | ||||||||
\(177\) | 0.00774552 | 0.000582189 0 | ||||||||
\(178\) | −1.11657 | −0.0836907 | ||||||||
\(179\) | 14.9557 | 1.11784 | 0.558919 | − | 0.829222i | \(-0.311216\pi\) | ||||
0.558919 | + | 0.829222i | \(0.311216\pi\) | |||||||
\(180\) | 5.98803 | 0.446322 | ||||||||
\(181\) | 16.8041 | 1.24904 | 0.624519 | − | 0.781009i | \(-0.285295\pi\) | ||||
0.624519 | + | 0.781009i | \(0.285295\pi\) | |||||||
\(182\) | 0.0525198 | 0.00389303 | ||||||||
\(183\) | −0.00500611 | −0.000370063 0 | ||||||||
\(184\) | −0.945786 | −0.0697242 | ||||||||
\(185\) | 1.75949 | 0.129361 | ||||||||
\(186\) | 2.48821e−6 0 | 1.82444e−7 0 | ||||||||
\(187\) | 5.08854 | 0.372111 | ||||||||
\(188\) | 12.2149 | 0.890861 | ||||||||
\(189\) | −0.0208327 | −0.00151535 | ||||||||
\(190\) | −0.00418599 | −0.000303684 0 | ||||||||
\(191\) | 3.11170 | 0.225154 | 0.112577 | − | 0.993643i | \(-0.464089\pi\) | ||||
0.112577 | + | 0.993643i | \(0.464089\pi\) | |||||||
\(192\) | −0.00841262 | −0.000607128 0 | ||||||||
\(193\) | 2.24990 | 0.161952 | 0.0809758 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809758 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(194\) | −0.619848 | −0.0445025 | ||||||||
\(195\) | 0.000271302 0 | 1.94284e−5 0 | ||||||||
\(196\) | −7.27167 | −0.519405 | ||||||||
\(197\) | −13.2229 | −0.942091 | −0.471046 | − | 0.882109i | \(-0.656123\pi\) | ||||
−0.471046 | + | 0.882109i | \(0.656123\pi\) | |||||||
\(198\) | 0.189460 | 0.0134643 | ||||||||
\(199\) | −12.1146 | −0.858782 | −0.429391 | − | 0.903119i | \(-0.641272\pi\) | ||||
−0.429391 | + | 0.903119i | \(0.641272\pi\) | |||||||
\(200\) | −0.252361 | −0.0178446 | ||||||||
\(201\) | 0.0106160 | 0.000748792 0 | ||||||||
\(202\) | 0.647605 | 0.0455653 | ||||||||
\(203\) | 9.99786 | 0.701712 | ||||||||
\(204\) | 0.0108098 | 0.000756835 0 | ||||||||
\(205\) | −4.05583 | −0.283271 | ||||||||
\(206\) | 1.08484 | 0.0755843 | ||||||||
\(207\) | −11.2432 | −0.781459 | ||||||||
\(208\) | 1.01356 | 0.0702777 | ||||||||
\(209\) | 0.0662831 | 0.00458490 | ||||||||
\(210\) | 0.000219275 0 | 1.51314e−5 0 | ||||||||
\(211\) | −15.9343 | −1.09696 | −0.548482 | − | 0.836163i | \(-0.684794\pi\) | ||||
−0.548482 | + | 0.836163i | \(0.684794\pi\) | |||||||
\(212\) | −15.1987 | −1.04385 | ||||||||
\(213\) | 0.0109810 | 0.000752408 0 | ||||||||
\(214\) | −0.0549641 | −0.00375727 | ||||||||
\(215\) | 5.35006 | 0.364871 | ||||||||
\(216\) | 0.00161151 | 0.000109649 0 | ||||||||
\(217\) | 0.120772 | 0.00819853 | ||||||||
\(218\) | −0.777517 | −0.0526601 | ||||||||
\(219\) | −0.00106429 | −7.19181e−5 0 | ||||||||
\(220\) | 1.99601 | 0.134571 | ||||||||
\(221\) | −1.29714 | −0.0872551 | ||||||||
\(222\) | 0.000118261 0 | 7.93719e−6 0 | ||||||||
\(223\) | 16.0190 | 1.07271 | 0.536356 | − | 0.843992i | \(-0.319800\pi\) | ||||
0.536356 | + | 0.843992i | \(0.319800\pi\) | |||||||
\(224\) | 2.46578 | 0.164752 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0.361644 | 0.0240562 | ||||||||
\(227\) | 23.6668 | 1.57082 | 0.785412 | − | 0.618974i | \(-0.212451\pi\) | ||||
0.785412 | + | 0.618974i | \(0.212451\pi\) | |||||||
\(228\) | 0.000140808 0 | 9.32521e−6 0 | ||||||||
\(229\) | 9.85560 | 0.651276 | 0.325638 | − | 0.945494i | \(-0.394421\pi\) | ||||
0.325638 | + | 0.945494i | \(0.394421\pi\) | |||||||
\(230\) | 0.236682 | 0.0156064 | ||||||||
\(231\) | −0.00347211 | −0.000228448 0 | ||||||||
\(232\) | −0.773384 | −0.0507751 | ||||||||
\(233\) | 5.82922 | 0.381885 | 0.190942 | − | 0.981601i | \(-0.438846\pi\) | ||||
0.190942 | + | 0.981601i | \(0.438846\pi\) | |||||||
\(234\) | −0.0482959 | −0.00315720 | ||||||||
\(235\) | −6.11964 | −0.399201 | ||||||||
\(236\) | −14.5263 | −0.945579 | ||||||||
\(237\) | −0.00527962 | −0.000342948 0 | ||||||||
\(238\) | −1.04839 | −0.0679571 | ||||||||
\(239\) | 10.4625 | 0.676762 | 0.338381 | − | 0.941009i | \(-0.390121\pi\) | ||||
0.338381 | + | 0.941009i | \(0.390121\pi\) | |||||||
\(240\) | 0.00423171 | 0.000273156 0 | ||||||||
\(241\) | 2.23340 | 0.143866 | 0.0719330 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719330 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(242\) | 0.0631532 | 0.00405964 | ||||||||
\(243\) | 0.0287358 | 0.00184340 | ||||||||
\(244\) | 9.38866 | 0.601048 | ||||||||
\(245\) | 3.64310 | 0.232749 | ||||||||
\(246\) | −0.000272606 0 | −1.73807e−5 0 | ||||||||
\(247\) | −0.0168965 | −0.00107510 | ||||||||
\(248\) | −0.00934230 | −0.000593237 0 | ||||||||
\(249\) | 0.0189094 | 0.00119833 | ||||||||
\(250\) | 0.0631532 | 0.00399416 | ||||||||
\(251\) | −17.8490 | −1.12662 | −0.563309 | − | 0.826246i | \(-0.690472\pi\) | ||||
−0.563309 | + | 0.826246i | \(0.690472\pi\) | |||||||
\(252\) | 19.5352 | 1.23060 | ||||||||
\(253\) | −3.74775 | −0.235619 | ||||||||
\(254\) | −0.140206 | −0.00879730 | ||||||||
\(255\) | −0.00541569 | −0.000339143 0 | ||||||||
\(256\) | 15.6819 | 0.980118 | ||||||||
\(257\) | −2.98972 | −0.186494 | −0.0932469 | − | 0.995643i | \(-0.529725\pi\) | ||||
−0.0932469 | + | 0.995643i | \(0.529725\pi\) | |||||||
\(258\) | 0.000359595 0 | 2.23874e−5 0 | ||||||||
\(259\) | 5.74013 | 0.356674 | ||||||||
\(260\) | −0.508811 | −0.0315551 | ||||||||
\(261\) | −9.19378 | −0.569080 | ||||||||
\(262\) | 0.554373 | 0.0342493 | ||||||||
\(263\) | 16.6314 | 1.02554 | 0.512768 | − | 0.858527i | \(-0.328620\pi\) | ||||
0.512768 | + | 0.858527i | \(0.328620\pi\) | |||||||
\(264\) | 0.000268585 0 | 1.65303e−5 0 | ||||||||
\(265\) | 7.61455 | 0.467758 | ||||||||
\(266\) | −0.0136563 | −0.000837320 0 | ||||||||
\(267\) | −0.0188171 | −0.00115159 | ||||||||
\(268\) | −19.9096 | −1.21617 | ||||||||
\(269\) | −7.90925 | −0.482235 | −0.241118 | − | 0.970496i | \(-0.577514\pi\) | ||||
−0.241118 | + | 0.970496i | \(0.577514\pi\) | |||||||
\(270\) | −0.000403280 0 | −2.45428e−5 0 | ||||||||
\(271\) | 20.0247 | 1.21642 | 0.608208 | − | 0.793778i | \(-0.291889\pi\) | ||||
0.608208 | + | 0.793778i | \(0.291889\pi\) | |||||||
\(272\) | −20.2325 | −1.22677 | ||||||||
\(273\) | 0.000885090 0 | 5.35681e−5 0 | ||||||||
\(274\) | 0.779129 | 0.0470689 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −0.00796147 | −0.000479224 0 | ||||||||
\(277\) | 22.3812 | 1.34476 | 0.672379 | − | 0.740207i | \(-0.265273\pi\) | ||||
0.672379 | + | 0.740207i | \(0.265273\pi\) | |||||||
\(278\) | 0.292005 | 0.0175133 | ||||||||
\(279\) | −0.111059 | −0.00664892 | ||||||||
\(280\) | −0.823297 | −0.0492014 | ||||||||
\(281\) | 10.9747 | 0.654699 | 0.327349 | − | 0.944903i | \(-0.393845\pi\) | ||||
0.327349 | + | 0.944903i | \(0.393845\pi\) | |||||||
\(282\) | −0.000411321 0 | −2.44938e−5 0 | ||||||||
\(283\) | 14.2906 | 0.849487 | 0.424743 | − | 0.905314i | \(-0.360364\pi\) | ||||
0.424743 | + | 0.905314i | \(0.360364\pi\) | |||||||
\(284\) | −20.5943 | −1.22204 | ||||||||
\(285\) | −7.05444e−5 0 | −4.17869e−6 0 | ||||||||
\(286\) | −0.0160986 | −0.000951932 0 | ||||||||
\(287\) | −13.2316 | −0.781039 | ||||||||
\(288\) | −2.26747 | −0.133612 | ||||||||
\(289\) | 8.89327 | 0.523134 | ||||||||
\(290\) | 0.193539 | 0.0113650 | ||||||||
\(291\) | −0.0104460 | −0.000612355 0 | ||||||||
\(292\) | 1.99601 | 0.116808 | ||||||||
\(293\) | 16.8457 | 0.984136 | 0.492068 | − | 0.870557i | \(-0.336241\pi\) | ||||
0.492068 | + | 0.870557i | \(0.336241\pi\) | |||||||
\(294\) | 0.000244865 0 | 1.42808e−5 0 | ||||||||
\(295\) | 7.27764 | 0.423721 | ||||||||
\(296\) | −0.444028 | −0.0258086 | ||||||||
\(297\) | 0.00638574 | 0.000370538 0 | ||||||||
\(298\) | 0.704010 | 0.0407822 | ||||||||
\(299\) | 0.955353 | 0.0552495 | ||||||||
\(300\) | −0.00212434 | −0.000122649 0 | ||||||||
\(301\) | 17.4539 | 1.00603 | ||||||||
\(302\) | −1.03657 | −0.0596476 | ||||||||
\(303\) | 0.0109138 | 0.000626980 0 | ||||||||
\(304\) | −0.263547 | −0.0151155 | ||||||||
\(305\) | −4.70371 | −0.269334 | ||||||||
\(306\) | 0.964073 | 0.0551124 | ||||||||
\(307\) | 19.4949 | 1.11263 | 0.556317 | − | 0.830970i | \(-0.312214\pi\) | ||||
0.556317 | + | 0.830970i | \(0.312214\pi\) | |||||||
\(308\) | 6.51174 | 0.371041 | ||||||||
\(309\) | 0.0182823 | 0.00104004 | ||||||||
\(310\) | 0.00233791 | 0.000132784 0 | ||||||||
\(311\) | 33.0423 | 1.87366 | 0.936829 | − | 0.349787i | \(-0.113746\pi\) | ||||
0.936829 | + | 0.349787i | \(0.113746\pi\) | |||||||
\(312\) | −6.84661e−5 0 | −3.87613e−6 0 | ||||||||
\(313\) | −8.88168 | −0.502022 | −0.251011 | − | 0.967984i | \(-0.580763\pi\) | ||||
−0.251011 | + | 0.967984i | \(0.580763\pi\) | |||||||
\(314\) | 0.589852 | 0.0332873 | ||||||||
\(315\) | −9.78713 | −0.551442 | ||||||||
\(316\) | 9.90160 | 0.557009 | ||||||||
\(317\) | 10.8131 | 0.607324 | 0.303662 | − | 0.952780i | \(-0.401791\pi\) | ||||
0.303662 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(318\) | 0.000511800 0 | 2.87003e−5 0 | ||||||||
\(319\) | −3.06459 | −0.171584 | ||||||||
\(320\) | −7.90444 | −0.441872 | ||||||||
\(321\) | −0.000926283 0 | −5.17001e−5 0 | ||||||||
\(322\) | 0.772147 | 0.0430301 | ||||||||
\(323\) | 0.337284 | 0.0187670 | ||||||||
\(324\) | −17.9641 | −0.998005 | ||||||||
\(325\) | 0.254914 | 0.0141401 | ||||||||
\(326\) | −0.263833 | −0.0146124 | ||||||||
\(327\) | −0.0131031 | −0.000724603 0 | ||||||||
\(328\) | 1.02353 | 0.0565152 | ||||||||
\(329\) | −19.9646 | −1.10068 | ||||||||
\(330\) | −6.72133e−5 0 | −3.69997e−6 0 | ||||||||
\(331\) | 10.7780 | 0.592414 | 0.296207 | − | 0.955124i | \(-0.404278\pi\) | ||||
0.296207 | + | 0.955124i | \(0.404278\pi\) | |||||||
\(332\) | −35.4634 | −1.94631 | ||||||||
\(333\) | −5.27848 | −0.289259 | ||||||||
\(334\) | 0.129324 | 0.00707627 | ||||||||
\(335\) | 9.97468 | 0.544975 | ||||||||
\(336\) | 0.0138054 | 0.000753148 0 | ||||||||
\(337\) | −20.7896 | −1.13248 | −0.566241 | − | 0.824239i | \(-0.691603\pi\) | ||||
−0.566241 | + | 0.824239i | \(0.691603\pi\) | |||||||
\(338\) | −0.816888 | −0.0444329 | ||||||||
\(339\) | 0.00609461 | 0.000331014 0 | ||||||||
\(340\) | 10.1568 | 0.550829 | ||||||||
\(341\) | −0.0370196 | −0.00200472 | ||||||||
\(342\) | 0.0125580 | 0.000679057 0 | ||||||||
\(343\) | −10.9515 | −0.591324 | ||||||||
\(344\) | −1.35015 | −0.0727950 | ||||||||
\(345\) | 0.00398869 | 0.000214744 0 | ||||||||
\(346\) | 0.952927 | 0.0512297 | ||||||||
\(347\) | −1.42004 | −0.0762317 | −0.0381158 | − | 0.999273i | \(-0.512136\pi\) | ||||
−0.0381158 | + | 0.999273i | \(0.512136\pi\) | |||||||
\(348\) | −0.00651022 | −0.000348985 0 | ||||||||
\(349\) | 9.51158 | 0.509143 | 0.254572 | − | 0.967054i | \(-0.418066\pi\) | ||||
0.254572 | + | 0.967054i | \(0.418066\pi\) | |||||||
\(350\) | 0.206030 | 0.0110127 | ||||||||
\(351\) | −0.00162781 | −8.68863e−5 0 | ||||||||
\(352\) | −0.755825 | −0.0402856 | ||||||||
\(353\) | −14.7799 | −0.786656 | −0.393328 | − | 0.919398i | \(-0.628676\pi\) | ||||
−0.393328 | + | 0.919398i | \(0.628676\pi\) | |||||||
\(354\) | 0.000489154 0 | 2.59983e−5 0 | ||||||||
\(355\) | 10.3177 | 0.547607 | ||||||||
\(356\) | 35.2903 | 1.87038 | ||||||||
\(357\) | −0.0176680 | −0.000935090 0 | ||||||||
\(358\) | 0.944498 | 0.0499183 | ||||||||
\(359\) | 5.67824 | 0.299686 | 0.149843 | − | 0.988710i | \(-0.452123\pi\) | ||||
0.149843 | + | 0.988710i | \(0.452123\pi\) | |||||||
\(360\) | 0.757083 | 0.0399018 | ||||||||
\(361\) | −18.9956 | −0.999769 | ||||||||
\(362\) | 1.06123 | 0.0557771 | ||||||||
\(363\) | 0.00106429 | 5.58607e−5 0 | ||||||||
\(364\) | −1.65993 | −0.0870042 | ||||||||
\(365\) | −1.00000 | −0.0523424 | ||||||||
\(366\) | −0.000316152 0 | −1.65255e−5 0 | ||||||||
\(367\) | 16.9362 | 0.884065 | 0.442032 | − | 0.896999i | \(-0.354258\pi\) | ||||
0.442032 | + | 0.896999i | \(0.354258\pi\) | |||||||
\(368\) | 14.9014 | 0.776788 | ||||||||
\(369\) | 12.1675 | 0.633414 | ||||||||
\(370\) | 0.111118 | 0.00577673 | ||||||||
\(371\) | 24.8415 | 1.28971 | ||||||||
\(372\) | −7.86421e−5 0 | −4.07740e−6 0 | ||||||||
\(373\) | −19.5040 | −1.00988 | −0.504940 | − | 0.863155i | \(-0.668485\pi\) | ||||
−0.504940 | + | 0.863155i | \(0.668485\pi\) | |||||||
\(374\) | 0.321358 | 0.0166170 | ||||||||
\(375\) | 0.00106429 | 5.49597e−5 0 | ||||||||
\(376\) | 1.54436 | 0.0796442 | ||||||||
\(377\) | 0.781207 | 0.0402342 | ||||||||
\(378\) | −0.00131565 | −6.76698e−5 0 | ||||||||
\(379\) | 1.31499 | 0.0675464 | 0.0337732 | − | 0.999430i | \(-0.489248\pi\) | ||||
0.0337732 | + | 0.999430i | \(0.489248\pi\) | |||||||
\(380\) | 0.132302 | 0.00678694 | ||||||||
\(381\) | −0.00236282 | −0.000121051 0 | ||||||||
\(382\) | 0.196514 | 0.0100545 | ||||||||
\(383\) | 18.3648 | 0.938395 | 0.469198 | − | 0.883093i | \(-0.344543\pi\) | ||||
0.469198 | + | 0.883093i | \(0.344543\pi\) | |||||||
\(384\) | −0.00214012 | −0.000109212 0 | ||||||||
\(385\) | −3.26238 | −0.166266 | ||||||||
\(386\) | 0.142089 | 0.00723212 | ||||||||
\(387\) | −16.0502 | −0.815876 | ||||||||
\(388\) | 19.5908 | 0.994573 | ||||||||
\(389\) | 26.7354 | 1.35554 | 0.677770 | − | 0.735274i | \(-0.262946\pi\) | ||||
0.677770 | + | 0.735274i | \(0.262946\pi\) | |||||||
\(390\) | 1.71336e−5 0 | 8.67594e−7 0 | ||||||||
\(391\) | −19.0706 | −0.964441 | ||||||||
\(392\) | −0.919376 | −0.0464355 | ||||||||
\(393\) | 0.00934257 | 0.000471270 0 | ||||||||
\(394\) | −0.835067 | −0.0420701 | ||||||||
\(395\) | −4.96069 | −0.249600 | ||||||||
\(396\) | −5.98803 | −0.300910 | ||||||||
\(397\) | 21.3300 | 1.07052 | 0.535261 | − | 0.844687i | \(-0.320213\pi\) | ||||
0.535261 | + | 0.844687i | \(0.320213\pi\) | |||||||
\(398\) | −0.765077 | −0.0383498 | ||||||||
\(399\) | −0.000230142 0 | −1.15215e−5 0 | ||||||||
\(400\) | 3.97609 | 0.198804 | ||||||||
\(401\) | −15.6774 | −0.782890 | −0.391445 | − | 0.920201i | \(-0.628025\pi\) | ||||
−0.391445 | + | 0.920201i | \(0.628025\pi\) | |||||||
\(402\) | 0.000670432 0 | 3.34381e−5 0 | ||||||||
\(403\) | 0.00943681 | 0.000470081 0 | ||||||||
\(404\) | −20.4681 | −1.01833 | ||||||||
\(405\) | 8.99999 | 0.447213 | ||||||||
\(406\) | 0.631397 | 0.0313357 | ||||||||
\(407\) | −1.75949 | −0.0872149 | ||||||||
\(408\) | 0.00136671 | 6.76621e−5 0 | ||||||||
\(409\) | 17.4130 | 0.861019 | 0.430510 | − | 0.902586i | \(-0.358334\pi\) | ||||
0.430510 | + | 0.902586i | \(0.358334\pi\) | |||||||
\(410\) | −0.256139 | −0.0126498 | ||||||||
\(411\) | 0.0131303 | 0.000647669 0 | ||||||||
\(412\) | −34.2873 | −1.68921 | ||||||||
\(413\) | 23.7424 | 1.16829 | ||||||||
\(414\) | −0.710047 | −0.0348969 | ||||||||
\(415\) | 17.7671 | 0.872154 | ||||||||
\(416\) | 0.192670 | 0.00944643 | ||||||||
\(417\) | 0.00492102 | 0.000240984 0 | ||||||||
\(418\) | 0.00418599 | 0.000204743 0 | ||||||||
\(419\) | 11.9497 | 0.583780 | 0.291890 | − | 0.956452i | \(-0.405716\pi\) | ||||
0.291890 | + | 0.956452i | \(0.405716\pi\) | |||||||
\(420\) | −0.00693038 | −0.000338168 0 | ||||||||
\(421\) | −22.2895 | −1.08632 | −0.543161 | − | 0.839629i | \(-0.682773\pi\) | ||||
−0.543161 | + | 0.839629i | \(0.682773\pi\) | |||||||
\(422\) | −1.00630 | −0.0489861 | ||||||||
\(423\) | 18.3589 | 0.892641 | ||||||||
\(424\) | −1.92162 | −0.0933219 | ||||||||
\(425\) | −5.08854 | −0.246831 | ||||||||
\(426\) | 0.000693488 0 | 3.35996e−5 0 | ||||||||
\(427\) | −15.3453 | −0.742610 | ||||||||
\(428\) | 1.73719 | 0.0839701 | ||||||||
\(429\) | −0.000271302 0 | −1.30986e−5 0 | ||||||||
\(430\) | 0.337873 | 0.0162937 | ||||||||
\(431\) | 35.6192 | 1.71572 | 0.857858 | − | 0.513887i | \(-0.171795\pi\) | ||||
0.857858 | + | 0.513887i | \(0.171795\pi\) | |||||||
\(432\) | −0.0253902 | −0.00122159 | ||||||||
\(433\) | −22.6944 | −1.09062 | −0.545312 | − | 0.838233i | \(-0.683589\pi\) | ||||
−0.545312 | + | 0.838233i | \(0.683589\pi\) | |||||||
\(434\) | 0.00762713 | 0.000366114 0 | ||||||||
\(435\) | 0.00326162 | 0.000156382 0 | ||||||||
\(436\) | 24.5741 | 1.17689 | ||||||||
\(437\) | −0.248412 | −0.0118832 | ||||||||
\(438\) | −6.72133e−5 0 | −3.21158e−6 0 | ||||||||
\(439\) | −8.14202 | −0.388597 | −0.194299 | − | 0.980942i | \(-0.562243\pi\) | ||||
−0.194299 | + | 0.980942i | \(0.562243\pi\) | |||||||
\(440\) | 0.252361 | 0.0120308 | ||||||||
\(441\) | −10.9293 | −0.520443 | ||||||||
\(442\) | −0.0819186 | −0.00389647 | ||||||||
\(443\) | −20.2241 | −0.960878 | −0.480439 | − | 0.877028i | \(-0.659523\pi\) | ||||
−0.480439 | + | 0.877028i | \(0.659523\pi\) | |||||||
\(444\) | −0.00373775 | −0.000177386 0 | ||||||||
\(445\) | −17.6804 | −0.838131 | ||||||||
\(446\) | 1.01165 | 0.0479031 | ||||||||
\(447\) | 0.0118643 | 0.000561164 0 | ||||||||
\(448\) | −25.7873 | −1.21833 | ||||||||
\(449\) | −23.8717 | −1.12658 | −0.563288 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563288 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(450\) | −0.189460 | −0.00893121 | ||||||||
\(451\) | 4.05583 | 0.190982 | ||||||||
\(452\) | −11.4301 | −0.537625 | ||||||||
\(453\) | −0.0174687 | −0.000820752 0 | ||||||||
\(454\) | 1.49464 | 0.0701468 | ||||||||
\(455\) | 0.831625 | 0.0389872 | ||||||||
\(456\) | 1.78027e−5 0 | 8.33686e−7 0 | ||||||||
\(457\) | −18.1558 | −0.849295 | −0.424647 | − | 0.905359i | \(-0.639602\pi\) | ||||
−0.424647 | + | 0.905359i | \(0.639602\pi\) | |||||||
\(458\) | 0.622413 | 0.0290834 | ||||||||
\(459\) | 0.0324941 | 0.00151670 | ||||||||
\(460\) | −7.48055 | −0.348782 | ||||||||
\(461\) | −35.5196 | −1.65431 | −0.827155 | − | 0.561973i | \(-0.810042\pi\) | ||||
−0.827155 | + | 0.561973i | \(0.810042\pi\) | |||||||
\(462\) | −0.000219275 0 | −1.02016e−5 0 | ||||||||
\(463\) | −17.0672 | −0.793181 | −0.396590 | − | 0.917996i | \(-0.629807\pi\) | ||||
−0.396590 | + | 0.917996i | \(0.629807\pi\) | |||||||
\(464\) | 12.1851 | 0.565678 | ||||||||
\(465\) | 3.93996e−5 0 | 1.82711e−6 0 | ||||||||
\(466\) | 0.368134 | 0.0170535 | ||||||||
\(467\) | −40.0403 | −1.85285 | −0.926423 | − | 0.376485i | \(-0.877133\pi\) | ||||
−0.926423 | + | 0.376485i | \(0.877133\pi\) | |||||||
\(468\) | 1.52643 | 0.0705594 | ||||||||
\(469\) | 32.5412 | 1.50261 | ||||||||
\(470\) | −0.386475 | −0.0178268 | ||||||||
\(471\) | 0.00994048 | 0.000458033 0 | ||||||||
\(472\) | −1.83659 | −0.0845360 | ||||||||
\(473\) | −5.35006 | −0.245996 | ||||||||
\(474\) | −0.000333425 0 | −1.53147e−5 0 | ||||||||
\(475\) | −0.0662831 | −0.00304128 | ||||||||
\(476\) | 33.1353 | 1.51875 | ||||||||
\(477\) | −22.8437 | −1.04594 | ||||||||
\(478\) | 0.660739 | 0.0302215 | ||||||||
\(479\) | −9.06436 | −0.414161 | −0.207081 | − | 0.978324i | \(-0.566396\pi\) | ||||
−0.207081 | + | 0.978324i | \(0.566396\pi\) | |||||||
\(480\) | 0.000804417 0 | 3.67164e−5 0 | ||||||||
\(481\) | 0.448519 | 0.0204507 | ||||||||
\(482\) | 0.141047 | 0.00642449 | ||||||||
\(483\) | 0.0130126 | 0.000592094 0 | ||||||||
\(484\) | −1.99601 | −0.0907278 | ||||||||
\(485\) | −9.81498 | −0.445675 | ||||||||
\(486\) | 0.00181476 | 8.23191e−5 0 | ||||||||
\(487\) | 30.5982 | 1.38654 | 0.693269 | − | 0.720679i | \(-0.256170\pi\) | ||||
0.693269 | + | 0.720679i | \(0.256170\pi\) | |||||||
\(488\) | 1.18703 | 0.0537345 | ||||||||
\(489\) | −0.00444625 | −0.000201066 0 | ||||||||
\(490\) | 0.230073 | 0.0103937 | ||||||||
\(491\) | 9.61409 | 0.433878 | 0.216939 | − | 0.976185i | \(-0.430393\pi\) | ||||
0.216939 | + | 0.976185i | \(0.430393\pi\) | |||||||
\(492\) | 0.00861594 | 0.000388437 0 | ||||||||
\(493\) | −15.5943 | −0.702333 | ||||||||
\(494\) | −0.00106707 | −4.80096e−5 0 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 0.147193 | 0.00660917 | ||||||||
\(497\) | 33.6602 | 1.50987 | ||||||||
\(498\) | 0.00119419 | 5.35128e−5 0 | ||||||||
\(499\) | −15.3505 | −0.687181 | −0.343591 | − | 0.939120i | \(-0.611643\pi\) | ||||
−0.343591 | + | 0.939120i | \(0.611643\pi\) | |||||||
\(500\) | −1.99601 | −0.0892644 | ||||||||
\(501\) | 0.00217943 | 9.73696e−5 0 | ||||||||
\(502\) | −1.12722 | −0.0503104 | ||||||||
\(503\) | −26.7037 | −1.19066 | −0.595330 | − | 0.803482i | \(-0.702978\pi\) | ||||
−0.595330 | + | 0.803482i | \(0.702978\pi\) | |||||||
\(504\) | 2.46989 | 0.110018 | ||||||||
\(505\) | 10.2545 | 0.456320 | ||||||||
\(506\) | −0.236682 | −0.0105218 | ||||||||
\(507\) | −0.0137666 | −0.000611397 0 | ||||||||
\(508\) | 4.43133 | 0.196608 | ||||||||
\(509\) | −32.2882 | −1.43115 | −0.715575 | − | 0.698536i | \(-0.753835\pi\) | ||||
−0.715575 | + | 0.698536i | \(0.753835\pi\) | |||||||
\(510\) | −0.000342018 0 | −1.51448e−5 0 | ||||||||
\(511\) | −3.26238 | −0.144319 | ||||||||
\(512\) | 5.01204 | 0.221503 | ||||||||
\(513\) | 0.000423267 0 | 1.86877e−5 0 | ||||||||
\(514\) | −0.188811 | −0.00832808 | ||||||||
\(515\) | 17.1779 | 0.756948 | ||||||||
\(516\) | −0.0113653 | −0.000500330 0 | ||||||||
\(517\) | 6.11964 | 0.269142 | ||||||||
\(518\) | 0.362508 | 0.0159277 | ||||||||
\(519\) | 0.0160592 | 0.000704921 0 | ||||||||
\(520\) | −0.0643303 | −0.00282107 | ||||||||
\(521\) | 27.7374 | 1.21520 | 0.607598 | − | 0.794245i | \(-0.292133\pi\) | ||||
0.607598 | + | 0.794245i | \(0.292133\pi\) | |||||||
\(522\) | −0.580616 | −0.0254129 | ||||||||
\(523\) | 10.6335 | 0.464972 | 0.232486 | − | 0.972600i | \(-0.425314\pi\) | ||||
0.232486 | + | 0.972600i | \(0.425314\pi\) | |||||||
\(524\) | −17.5214 | −0.765427 | ||||||||
\(525\) | 0.00347211 | 0.000151536 0 | ||||||||
\(526\) | 1.05033 | 0.0457964 | ||||||||
\(527\) | −0.188376 | −0.00820578 | ||||||||
\(528\) | −0.00423171 | −0.000184161 0 | ||||||||
\(529\) | −8.95438 | −0.389321 | ||||||||
\(530\) | 0.480884 | 0.0208882 | ||||||||
\(531\) | −21.8329 | −0.947468 | ||||||||
\(532\) | 0.431618 | 0.0187130 | ||||||||
\(533\) | −1.03389 | −0.0447826 | ||||||||
\(534\) | −0.00118836 | −5.14253e−5 0 | ||||||||
\(535\) | −0.870329 | −0.0376276 | ||||||||
\(536\) | −2.51722 | −0.108727 | ||||||||
\(537\) | 0.0159172 | 0.000686876 0 | ||||||||
\(538\) | −0.499494 | −0.0215347 | ||||||||
\(539\) | −3.64310 | −0.156919 | ||||||||
\(540\) | 0.0127460 | 0.000548501 0 | ||||||||
\(541\) | 18.7924 | 0.807950 | 0.403975 | − | 0.914770i | \(-0.367628\pi\) | ||||
0.403975 | + | 0.914770i | \(0.367628\pi\) | |||||||
\(542\) | 1.26463 | 0.0543204 | ||||||||
\(543\) | 0.0178844 | 0.000767494 0 | ||||||||
\(544\) | −3.84605 | −0.164898 | ||||||||
\(545\) | −12.3116 | −0.527371 | ||||||||
\(546\) | 5.58963e−5 0 | 2.39214e−6 0 | ||||||||
\(547\) | −17.9650 | −0.768128 | −0.384064 | − | 0.923307i | \(-0.625476\pi\) | ||||
−0.384064 | + | 0.923307i | \(0.625476\pi\) | |||||||
\(548\) | −24.6250 | −1.05193 | ||||||||
\(549\) | 14.1111 | 0.602248 | ||||||||
\(550\) | −0.0631532 | −0.00269286 | ||||||||
\(551\) | −0.203131 | −0.00865366 | ||||||||
\(552\) | −0.00100659 | −4.28433e−5 0 | ||||||||
\(553\) | −16.1837 | −0.688199 | ||||||||
\(554\) | 1.41345 | 0.0600516 | ||||||||
\(555\) | 0.00187261 | 7.94879e−5 0 | ||||||||
\(556\) | −9.22908 | −0.391400 | ||||||||
\(557\) | 4.21692 | 0.178677 | 0.0893384 | − | 0.996001i | \(-0.471525\pi\) | ||||
0.0893384 | + | 0.996001i | \(0.471525\pi\) | |||||||
\(558\) | −0.00701372 | −0.000296914 0 | ||||||||
\(559\) | 1.36380 | 0.0576828 | ||||||||
\(560\) | 12.9715 | 0.548145 | ||||||||
\(561\) | 0.00541569 | 0.000228650 0 | ||||||||
\(562\) | 0.693091 | 0.0292363 | ||||||||
\(563\) | −31.6279 | −1.33296 | −0.666478 | − | 0.745525i | \(-0.732199\pi\) | ||||
−0.666478 | + | 0.745525i | \(0.732199\pi\) | |||||||
\(564\) | 0.0130002 | 0.000547406 0 | ||||||||
\(565\) | 5.72645 | 0.240914 | ||||||||
\(566\) | 0.902496 | 0.0379347 | ||||||||
\(567\) | 29.3614 | 1.23306 | ||||||||
\(568\) | −2.60379 | −0.109252 | ||||||||
\(569\) | 17.5387 | 0.735259 | 0.367629 | − | 0.929972i | \(-0.380170\pi\) | ||||
0.367629 | + | 0.929972i | \(0.380170\pi\) | |||||||
\(570\) | −4.45511e−6 0 | −1.86604e−7 0 | ||||||||
\(571\) | −21.1700 | −0.885938 | −0.442969 | − | 0.896537i | \(-0.646075\pi\) | ||||
−0.442969 | + | 0.896537i | \(0.646075\pi\) | |||||||
\(572\) | 0.508811 | 0.0212745 | ||||||||
\(573\) | 0.00331175 | 0.000138350 0 | ||||||||
\(574\) | −0.835621 | −0.0348781 | ||||||||
\(575\) | 3.74775 | 0.156292 | ||||||||
\(576\) | 23.7133 | 0.988055 | ||||||||
\(577\) | −11.8444 | −0.493090 | −0.246545 | − | 0.969131i | \(-0.579295\pi\) | ||||
−0.246545 | + | 0.969131i | \(0.579295\pi\) | |||||||
\(578\) | 0.561639 | 0.0233611 | ||||||||
\(579\) | 0.00239455 | 9.95141e−5 0 | ||||||||
\(580\) | −6.11696 | −0.253993 | ||||||||
\(581\) | 57.9630 | 2.40471 | ||||||||
\(582\) | −0.000659698 0 | −2.73453e−5 0 | ||||||||
\(583\) | −7.61455 | −0.315363 | ||||||||
\(584\) | 0.252361 | 0.0104428 | ||||||||
\(585\) | −0.764741 | −0.0316182 | ||||||||
\(586\) | 1.06386 | 0.0439477 | ||||||||
\(587\) | −34.1740 | −1.41051 | −0.705255 | − | 0.708953i | \(-0.749168\pi\) | ||||
−0.705255 | + | 0.708953i | \(0.749168\pi\) | |||||||
\(588\) | −0.00773917 | −0.000319158 0 | ||||||||
\(589\) | −0.00245377 | −0.000101106 0 | ||||||||
\(590\) | 0.459606 | 0.0189217 | ||||||||
\(591\) | −0.0140730 | −0.000578885 0 | ||||||||
\(592\) | 6.99590 | 0.287530 | ||||||||
\(593\) | −32.5358 | −1.33609 | −0.668043 | − | 0.744123i | \(-0.732868\pi\) | ||||
−0.668043 | + | 0.744123i | \(0.732868\pi\) | |||||||
\(594\) | 0.000403280 0 | 1.65468e−5 0 | ||||||||
\(595\) | −16.6007 | −0.680564 | ||||||||
\(596\) | −22.2508 | −0.911430 | ||||||||
\(597\) | −0.0128935 | −0.000527694 0 | ||||||||
\(598\) | 0.0603336 | 0.00246723 | ||||||||
\(599\) | −21.5192 | −0.879251 | −0.439626 | − | 0.898181i | \(-0.644889\pi\) | ||||
−0.439626 | + | 0.898181i | \(0.644889\pi\) | |||||||
\(600\) | −0.000268585 0 | −1.09649e−5 0 | ||||||||
\(601\) | 7.47402 | 0.304872 | 0.152436 | − | 0.988313i | \(-0.451288\pi\) | ||||
0.152436 | + | 0.988313i | \(0.451288\pi\) | |||||||
\(602\) | 1.10227 | 0.0449252 | ||||||||
\(603\) | −29.9240 | −1.21860 | ||||||||
\(604\) | 32.7615 | 1.33305 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0.000689239 0 | 2.79984e−5 0 | ||||||||
\(607\) | −11.7249 | −0.475897 | −0.237949 | − | 0.971278i | \(-0.576475\pi\) | ||||
−0.237949 | + | 0.971278i | \(0.576475\pi\) | |||||||
\(608\) | −0.0500984 | −0.00203176 | ||||||||
\(609\) | 0.0106406 | 0.000431180 0 | ||||||||
\(610\) | −0.297055 | −0.0120274 | ||||||||
\(611\) | −1.55998 | −0.0631101 | ||||||||
\(612\) | −30.4704 | −1.23169 | ||||||||
\(613\) | −13.5687 | −0.548034 | −0.274017 | − | 0.961725i | \(-0.588353\pi\) | ||||
−0.274017 | + | 0.961725i | \(0.588353\pi\) | |||||||
\(614\) | 1.23117 | 0.0496859 | ||||||||
\(615\) | −0.00431658 | −0.000174061 0 | ||||||||
\(616\) | 0.823297 | 0.0331716 | ||||||||
\(617\) | −2.26287 | −0.0910996 | −0.0455498 | − | 0.998962i | \(-0.514504\pi\) | ||||
−0.0455498 | + | 0.998962i | \(0.514504\pi\) | |||||||
\(618\) | 0.00115458 | 4.64441e−5 0 | ||||||||
\(619\) | −6.84013 | −0.274928 | −0.137464 | − | 0.990507i | \(-0.543895\pi\) | ||||
−0.137464 | + | 0.990507i | \(0.543895\pi\) | |||||||
\(620\) | −0.0738916 | −0.00296756 | ||||||||
\(621\) | −0.0239321 | −0.000960364 0 | ||||||||
\(622\) | 2.08673 | 0.0836702 | ||||||||
\(623\) | −57.6801 | −2.31090 | ||||||||
\(624\) | 0.00107872 | 4.31834e−5 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −0.560907 | −0.0224183 | ||||||||
\(627\) | 7.05444e−5 0 | 2.81727e−6 0 | ||||||||
\(628\) | −18.6428 | −0.743928 | ||||||||
\(629\) | −8.95326 | −0.356990 | ||||||||
\(630\) | −0.618088 | −0.0246252 | ||||||||
\(631\) | −28.0119 | −1.11514 | −0.557569 | − | 0.830131i | \(-0.688266\pi\) | ||||
−0.557569 | + | 0.830131i | \(0.688266\pi\) | |||||||
\(632\) | 1.25189 | 0.0497973 | ||||||||
\(633\) | −0.0169587 | −0.000674049 0 | ||||||||
\(634\) | 0.682882 | 0.0271207 | ||||||||
\(635\) | −2.22009 | −0.0881016 | ||||||||
\(636\) | −0.0161759 | −0.000641415 0 | ||||||||
\(637\) | 0.928677 | 0.0367955 | ||||||||
\(638\) | −0.193539 | −0.00766228 | ||||||||
\(639\) | −30.9531 | −1.22449 | ||||||||
\(640\) | −2.01084 | −0.0794854 | ||||||||
\(641\) | −7.37703 | −0.291375 | −0.145688 | − | 0.989331i | \(-0.546539\pi\) | ||||
−0.145688 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(642\) | −5.84977e−5 0 | −2.30872e−6 0 | ||||||||
\(643\) | 2.79668 | 0.110290 | 0.0551452 | − | 0.998478i | \(-0.482438\pi\) | ||||
0.0551452 | + | 0.998478i | \(0.482438\pi\) | |||||||
\(644\) | −24.4044 | −0.961667 | ||||||||
\(645\) | 0.00569402 | 0.000224202 0 | ||||||||
\(646\) | 0.0213006 | 0.000838061 0 | ||||||||
\(647\) | −0.576232 | −0.0226540 | −0.0113270 | − | 0.999936i | \(-0.503606\pi\) | ||||
−0.0113270 | + | 0.999936i | \(0.503606\pi\) | |||||||
\(648\) | −2.27125 | −0.0892230 | ||||||||
\(649\) | −7.27764 | −0.285672 | ||||||||
\(650\) | 0.0160986 | 0.000631440 0 | ||||||||
\(651\) | 0.000128536 0 | 5.03774e−6 0 | ||||||||
\(652\) | 8.33868 | 0.326568 | ||||||||
\(653\) | −38.1607 | −1.49334 | −0.746672 | − | 0.665192i | \(-0.768350\pi\) | ||||
−0.746672 | + | 0.665192i | \(0.768350\pi\) | |||||||
\(654\) | −0.000827503 0 | −3.23579e−5 0 | ||||||||
\(655\) | 8.77822 | 0.342993 | ||||||||
\(656\) | −16.1263 | −0.629627 | ||||||||
\(657\) | 3.00000 | 0.117041 | ||||||||
\(658\) | −1.26083 | −0.0491522 | ||||||||
\(659\) | −7.41673 | −0.288915 | −0.144457 | − | 0.989511i | \(-0.546144\pi\) | ||||
−0.144457 | + | 0.989511i | \(0.546144\pi\) | |||||||
\(660\) | 0.00212434 | 8.26896e−5 0 | ||||||||
\(661\) | 44.1623 | 1.71771 | 0.858857 | − | 0.512216i | \(-0.171175\pi\) | ||||
0.858857 | + | 0.512216i | \(0.171175\pi\) | |||||||
\(662\) | 0.680667 | 0.0264549 | ||||||||
\(663\) | −0.00138053 | −5.36155e−5 0 | ||||||||
\(664\) | −4.48373 | −0.174002 | ||||||||
\(665\) | −0.216240 | −0.00838544 | ||||||||
\(666\) | −0.333353 | −0.0129172 | ||||||||
\(667\) | 11.4853 | 0.444714 | ||||||||
\(668\) | −4.08738 | −0.158146 | ||||||||
\(669\) | 0.0170489 | 0.000659147 0 | ||||||||
\(670\) | 0.629933 | 0.0243364 | ||||||||
\(671\) | 4.70371 | 0.181585 | ||||||||
\(672\) | 0.00262431 | 0.000101235 0 | ||||||||
\(673\) | −38.1718 | −1.47141 | −0.735707 | − | 0.677299i | \(-0.763150\pi\) | ||||
−0.735707 | + | 0.677299i | \(0.763150\pi\) | |||||||
\(674\) | −1.31293 | −0.0505722 | ||||||||
\(675\) | −0.00638574 | −0.000245787 0 | ||||||||
\(676\) | 25.8184 | 0.993017 | ||||||||
\(677\) | −23.8700 | −0.917399 | −0.458700 | − | 0.888591i | \(-0.651685\pi\) | ||||
−0.458700 | + | 0.888591i | \(0.651685\pi\) | |||||||
\(678\) | 0.000384894 0 | 1.47818e−5 0 | ||||||||
\(679\) | −32.0202 | −1.22882 | ||||||||
\(680\) | 1.28415 | 0.0492449 | ||||||||
\(681\) | 0.0251884 | 0.000965221 0 | ||||||||
\(682\) | −0.00233791 | −8.95231e−5 0 | ||||||||
\(683\) | −19.7030 | −0.753914 | −0.376957 | − | 0.926231i | \(-0.623030\pi\) | ||||
−0.376957 | + | 0.926231i | \(0.623030\pi\) | |||||||
\(684\) | −0.396905 | −0.0151761 | ||||||||
\(685\) | 12.3371 | 0.471377 | ||||||||
\(686\) | −0.691621 | −0.0264062 | ||||||||
\(687\) | 0.0104892 | 0.000400189 0 | ||||||||
\(688\) | 21.2723 | 0.810999 | ||||||||
\(689\) | 1.94106 | 0.0739483 | ||||||||
\(690\) | 0.000251899 0 | 9.58962e−6 0 | ||||||||
\(691\) | −5.47088 | −0.208122 | −0.104061 | − | 0.994571i | \(-0.533184\pi\) | ||||
−0.104061 | + | 0.994571i | \(0.533184\pi\) | |||||||
\(692\) | −30.1181 | −1.14492 | ||||||||
\(693\) | 9.78713 | 0.371782 | ||||||||
\(694\) | −0.0896800 | −0.00340421 | ||||||||
\(695\) | 4.62376 | 0.175389 | ||||||||
\(696\) | −0.000823104 0 | −3.11997e−5 0 | ||||||||
\(697\) | 20.6383 | 0.781730 | ||||||||
\(698\) | 0.600687 | 0.0227363 | ||||||||
\(699\) | 0.00620398 | 0.000234656 0 | ||||||||
\(700\) | −6.51174 | −0.246121 | ||||||||
\(701\) | −15.2038 | −0.574241 | −0.287121 | − | 0.957894i | \(-0.592698\pi\) | ||||
−0.287121 | + | 0.957894i | \(0.592698\pi\) | |||||||
\(702\) | −0.000102802 0 | −3.88000e−6 0 | ||||||||
\(703\) | −0.116625 | −0.00439858 | ||||||||
\(704\) | 7.90444 | 0.297910 | ||||||||
\(705\) | −0.00651307 | −0.000245297 0 | ||||||||
\(706\) | −0.933400 | −0.0351290 | ||||||||
\(707\) | 33.4541 | 1.25817 | ||||||||
\(708\) | −0.0154601 | −0.000581028 0 | ||||||||
\(709\) | −4.44185 | −0.166817 | −0.0834086 | − | 0.996515i | \(-0.526581\pi\) | ||||
−0.0834086 | + | 0.996515i | \(0.526581\pi\) | |||||||
\(710\) | 0.651596 | 0.0244540 | ||||||||
\(711\) | 14.8821 | 0.558121 | ||||||||
\(712\) | 4.46184 | 0.167215 | ||||||||
\(713\) | 0.138740 | 0.00519586 | ||||||||
\(714\) | −0.00111579 | −4.17574e−5 0 | ||||||||
\(715\) | −0.254914 | −0.00953324 | ||||||||
\(716\) | −29.8517 | −1.11561 | ||||||||
\(717\) | 0.0111351 | 0.000415848 0 | ||||||||
\(718\) | 0.358599 | 0.0133828 | ||||||||
\(719\) | 16.6451 | 0.620757 | 0.310379 | − | 0.950613i | \(-0.399544\pi\) | ||||
0.310379 | + | 0.950613i | \(0.399544\pi\) | |||||||
\(720\) | −11.9283 | −0.444540 | ||||||||
\(721\) | 56.0407 | 2.08707 | ||||||||
\(722\) | −1.19963 | −0.0446457 | ||||||||
\(723\) | 0.00237699 | 8.84011e−5 0 | ||||||||
\(724\) | −33.5412 | −1.24655 | ||||||||
\(725\) | 3.06459 | 0.113816 | ||||||||
\(726\) | 6.72133e−5 0 | 2.49452e−6 0 | ||||||||
\(727\) | −7.07068 | −0.262237 | −0.131118 | − | 0.991367i | \(-0.541857\pi\) | ||||
−0.131118 | + | 0.991367i | \(0.541857\pi\) | |||||||
\(728\) | −0.209870 | −0.00777829 | ||||||||
\(729\) | −26.9999 | −0.999998 | ||||||||
\(730\) | −0.0631532 | −0.00233741 | ||||||||
\(731\) | −27.2240 | −1.00692 | ||||||||
\(732\) | 0.00999226 | 0.000369325 0 | ||||||||
\(733\) | −15.6106 | −0.576590 | −0.288295 | − | 0.957542i | \(-0.593088\pi\) | ||||
−0.288295 | + | 0.957542i | \(0.593088\pi\) | |||||||
\(734\) | 1.06958 | 0.0394789 | ||||||||
\(735\) | 0.00387731 | 0.000143017 0 | ||||||||
\(736\) | 2.83264 | 0.104413 | ||||||||
\(737\) | −9.97468 | −0.367422 | ||||||||
\(738\) | 0.768416 | 0.0282858 | ||||||||
\(739\) | 22.1076 | 0.813241 | 0.406620 | − | 0.913597i | \(-0.366707\pi\) | ||||
0.406620 | + | 0.913597i | \(0.366707\pi\) | |||||||
\(740\) | −3.51197 | −0.129103 | ||||||||
\(741\) | −1.79828e−5 0 | −6.60613e−7 0 | ||||||||
\(742\) | 1.56882 | 0.0575933 | ||||||||
\(743\) | −7.11975 | −0.261198 | −0.130599 | − | 0.991435i | \(-0.541690\pi\) | ||||
−0.130599 | + | 0.991435i | \(0.541690\pi\) | |||||||
\(744\) | −9.94292e−6 0 | −3.64525e−7 0 | ||||||||
\(745\) | 11.1476 | 0.408418 | ||||||||
\(746\) | −1.23174 | −0.0450972 | ||||||||
\(747\) | −53.3014 | −1.95019 | ||||||||
\(748\) | −10.1568 | −0.371369 | ||||||||
\(749\) | −2.83934 | −0.103747 | ||||||||
\(750\) | 6.72133e−5 0 | 2.45428e−6 0 | ||||||||
\(751\) | 4.91245 | 0.179258 | 0.0896288 | − | 0.995975i | \(-0.471432\pi\) | ||||
0.0896288 | + | 0.995975i | \(0.471432\pi\) | |||||||
\(752\) | −24.3322 | −0.887305 | ||||||||
\(753\) | −0.0189965 | −0.000692271 0 | ||||||||
\(754\) | 0.0493358 | 0.00179670 | ||||||||
\(755\) | −16.4135 | −0.597348 | ||||||||
\(756\) | 0.0415823 | 0.00151233 | ||||||||
\(757\) | 19.1094 | 0.694542 | 0.347271 | − | 0.937765i | \(-0.387108\pi\) | ||||
0.347271 | + | 0.937765i | \(0.387108\pi\) | |||||||
\(758\) | 0.0830457 | 0.00301636 | ||||||||
\(759\) | −0.00398869 | −0.000144780 0 | ||||||||
\(760\) | 0.0167273 | 0.000606762 0 | ||||||||
\(761\) | 46.0902 | 1.67077 | 0.835385 | − | 0.549666i | \(-0.185245\pi\) | ||||
0.835385 | + | 0.549666i | \(0.185245\pi\) | |||||||
\(762\) | −0.000149220 0 | −5.40566e−6 0 | ||||||||
\(763\) | −40.1651 | −1.45407 | ||||||||
\(764\) | −6.21098 | −0.224705 | ||||||||
\(765\) | 15.2656 | 0.551930 | ||||||||
\(766\) | 1.15979 | 0.0419050 | ||||||||
\(767\) | 1.85517 | 0.0669864 | ||||||||
\(768\) | 0.0166901 | 0.000602251 0 | ||||||||
\(769\) | −18.5542 | −0.669082 | −0.334541 | − | 0.942381i | \(-0.608581\pi\) | ||||
−0.334541 | + | 0.942381i | \(0.608581\pi\) | |||||||
\(770\) | −0.206030 | −0.00742479 | ||||||||
\(771\) | −0.00318193 | −0.000114594 0 | ||||||||
\(772\) | −4.49083 | −0.161629 | ||||||||
\(773\) | 14.4351 | 0.519193 | 0.259597 | − | 0.965717i | \(-0.416410\pi\) | ||||
0.259597 | + | 0.965717i | \(0.416410\pi\) | |||||||
\(774\) | −1.01362 | −0.0364338 | ||||||||
\(775\) | 0.0370196 | 0.00132978 | ||||||||
\(776\) | 2.47692 | 0.0889162 | ||||||||
\(777\) | 0.00610916 | 0.000219165 0 | ||||||||
\(778\) | 1.68843 | 0.0605331 | ||||||||
\(779\) | 0.268833 | 0.00963194 | ||||||||
\(780\) | −0.000541523 0 | −1.93896e−5 0 | ||||||||
\(781\) | −10.3177 | −0.369197 | ||||||||
\(782\) | −1.20437 | −0.0430681 | ||||||||
\(783\) | −0.0195697 | −0.000699364 0 | ||||||||
\(784\) | 14.4853 | 0.517331 | ||||||||
\(785\) | 9.34001 | 0.333359 | ||||||||
\(786\) | 0.000590013 0 | 2.10451e−5 0 | ||||||||
\(787\) | −3.77220 | −0.134464 | −0.0672322 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672322 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(788\) | 26.3930 | 0.940212 | ||||||||
\(789\) | 0.0177006 | 0.000630159 0 | ||||||||
\(790\) | −0.313284 | −0.0111461 | ||||||||
\(791\) | 18.6819 | 0.664250 | ||||||||
\(792\) | −0.757083 | −0.0269018 | ||||||||
\(793\) | −1.19904 | −0.0425792 | ||||||||
\(794\) | 1.34706 | 0.0478053 | ||||||||
\(795\) | 0.00810409 | 0.000287423 0 | ||||||||
\(796\) | 24.1809 | 0.857070 | ||||||||
\(797\) | −15.8205 | −0.560390 | −0.280195 | − | 0.959943i | \(-0.590399\pi\) | ||||
−0.280195 | + | 0.959943i | \(0.590399\pi\) | |||||||
\(798\) | −1.45342e−5 0 | −5.14506e−7 0 | ||||||||
\(799\) | 31.1401 | 1.10166 | ||||||||
\(800\) | 0.755825 | 0.0267224 | ||||||||
\(801\) | 53.0412 | 1.87412 | ||||||||
\(802\) | −0.990076 | −0.0349608 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | −0.0211896 | −0.000747299 0 | ||||||||
\(805\) | 12.2266 | 0.430930 | ||||||||
\(806\) | 0.000595965 0 | 2.09920e−5 0 | ||||||||
\(807\) | −0.00841773 | −0.000296318 0 | ||||||||
\(808\) | −2.58784 | −0.0910398 | ||||||||
\(809\) | 0.567396 | 0.0199486 | 0.00997428 | − | 0.999950i | \(-0.496825\pi\) | ||||
0.00997428 | + | 0.999950i | \(0.496825\pi\) | |||||||
\(810\) | 0.568378 | 0.0199708 | ||||||||
\(811\) | −22.0944 | −0.775841 | −0.387921 | − | 0.921693i | \(-0.626806\pi\) | ||||
−0.387921 | + | 0.921693i | \(0.626806\pi\) | |||||||
\(812\) | −19.9558 | −0.700313 | ||||||||
\(813\) | 0.0213121 | 0.000747449 0 | ||||||||
\(814\) | −0.111118 | −0.00389467 | ||||||||
\(815\) | −4.17767 | −0.146337 | ||||||||
\(816\) | −0.0215332 | −0.000753814 0 | ||||||||
\(817\) | −0.354619 | −0.0124065 | ||||||||
\(818\) | 1.09969 | 0.0384497 | ||||||||
\(819\) | −2.49487 | −0.0871780 | ||||||||
\(820\) | 8.09548 | 0.282707 | ||||||||
\(821\) | 48.6514 | 1.69795 | 0.848973 | − | 0.528437i | \(-0.177222\pi\) | ||||
0.848973 | + | 0.528437i | \(0.177222\pi\) | |||||||
\(822\) | 0.000829219 0 | 2.89223e−5 0 | ||||||||
\(823\) | 43.8945 | 1.53007 | 0.765033 | − | 0.643992i | \(-0.222723\pi\) | ||||
0.765033 | + | 0.643992i | \(0.222723\pi\) | |||||||
\(824\) | −4.33503 | −0.151018 | ||||||||
\(825\) | −0.00106429 | −3.70538e−5 0 | ||||||||
\(826\) | 1.49941 | 0.0521711 | ||||||||
\(827\) | −4.78980 | −0.166558 | −0.0832788 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832788 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(828\) | 22.4416 | 0.779901 | ||||||||
\(829\) | 47.3407 | 1.64421 | 0.822106 | − | 0.569335i | \(-0.192799\pi\) | ||||
0.822106 | + | 0.569335i | \(0.192799\pi\) | |||||||
\(830\) | 1.12205 | 0.0389470 | ||||||||
\(831\) | 0.0238201 | 0.000826311 0 | ||||||||
\(832\) | −2.01495 | −0.0698559 | ||||||||
\(833\) | −18.5381 | −0.642306 | ||||||||
\(834\) | 0.000310778 0 | 1.07614e−5 0 | ||||||||
\(835\) | 2.04778 | 0.0708662 | ||||||||
\(836\) | −0.132302 | −0.00457575 | ||||||||
\(837\) | −0.000236398 0 | −8.17109e−6 0 | ||||||||
\(838\) | 0.754661 | 0.0260693 | ||||||||
\(839\) | 6.70780 | 0.231579 | 0.115789 | − | 0.993274i | \(-0.463060\pi\) | ||||
0.115789 | + | 0.993274i | \(0.463060\pi\) | |||||||
\(840\) | −0.000876226 0 | −3.02327e−5 0 | ||||||||
\(841\) | −19.6083 | −0.676147 | ||||||||
\(842\) | −1.40765 | −0.0485108 | ||||||||
\(843\) | 0.0116803 | 0.000402291 0 | ||||||||
\(844\) | 31.8051 | 1.09478 | ||||||||
\(845\) | −12.9350 | −0.444978 | ||||||||
\(846\) | 1.15942 | 0.0398618 | ||||||||
\(847\) | 3.26238 | 0.112097 | ||||||||
\(848\) | 30.2761 | 1.03969 | ||||||||
\(849\) | 0.0152093 | 0.000521983 0 | ||||||||
\(850\) | −0.321358 | −0.0110225 | ||||||||
\(851\) | 6.59414 | 0.226044 | ||||||||
\(852\) | −0.0219183 | −0.000750908 0 | ||||||||
\(853\) | 22.1954 | 0.759955 | 0.379977 | − | 0.924996i | \(-0.375932\pi\) | ||||
0.379977 | + | 0.924996i | \(0.375932\pi\) | |||||||
\(854\) | −0.969104 | −0.0331620 | ||||||||
\(855\) | 0.198849 | 0.00680050 | ||||||||
\(856\) | 0.219637 | 0.00750704 | ||||||||
\(857\) | 3.79894 | 0.129769 | 0.0648846 | − | 0.997893i | \(-0.479332\pi\) | ||||
0.0648846 | + | 0.997893i | \(0.479332\pi\) | |||||||
\(858\) | −1.71336e−5 0 | −5.84932e−7 0 | ||||||||
\(859\) | −42.6990 | −1.45687 | −0.728436 | − | 0.685114i | \(-0.759752\pi\) | ||||
−0.728436 | + | 0.685114i | \(0.759752\pi\) | |||||||
\(860\) | −10.6788 | −0.364143 | ||||||||
\(861\) | −0.0140823 | −0.000479924 0 | ||||||||
\(862\) | 2.24947 | 0.0766171 | ||||||||
\(863\) | 31.7569 | 1.08102 | 0.540509 | − | 0.841338i | \(-0.318232\pi\) | ||||
0.540509 | + | 0.841338i | \(0.318232\pi\) | |||||||
\(864\) | −0.00482650 | −0.000164201 0 | ||||||||
\(865\) | 15.0891 | 0.513046 | ||||||||
\(866\) | −1.43323 | −0.0487030 | ||||||||
\(867\) | 0.00946502 | 0.000321449 0 | ||||||||
\(868\) | −0.241062 | −0.00818218 | ||||||||
\(869\) | 4.96069 | 0.168280 | ||||||||
\(870\) | 0.000205981 0 | 6.98343e−6 0 | ||||||||
\(871\) | 2.54269 | 0.0861556 | ||||||||
\(872\) | 3.10697 | 0.105215 | ||||||||
\(873\) | 29.4449 | 0.996560 | ||||||||
\(874\) | −0.0156880 | −0.000530656 0 | ||||||||
\(875\) | 3.26238 | 0.110288 | ||||||||
\(876\) | 0.00212434 | 7.17746e−5 0 | ||||||||
\(877\) | −22.2820 | −0.752410 | −0.376205 | − | 0.926537i | \(-0.622771\pi\) | ||||
−0.376205 | + | 0.926537i | \(0.622771\pi\) | |||||||
\(878\) | −0.514195 | −0.0173532 | ||||||||
\(879\) | 0.0179287 | 0.000604720 0 | ||||||||
\(880\) | −3.97609 | −0.134034 | ||||||||
\(881\) | 20.9055 | 0.704325 | 0.352163 | − | 0.935939i | \(-0.385446\pi\) | ||||
0.352163 | + | 0.935939i | \(0.385446\pi\) | |||||||
\(882\) | −0.690220 | −0.0232409 | ||||||||
\(883\) | 41.0009 | 1.37979 | 0.689894 | − | 0.723910i | \(-0.257657\pi\) | ||||
0.689894 | + | 0.723910i | \(0.257657\pi\) | |||||||
\(884\) | 2.58911 | 0.0870811 | ||||||||
\(885\) | 0.00774552 | 0.000260363 0 | ||||||||
\(886\) | −1.27722 | −0.0429090 | ||||||||
\(887\) | 20.7799 | 0.697721 | 0.348861 | − | 0.937175i | \(-0.386569\pi\) | ||||
0.348861 | + | 0.937175i | \(0.386569\pi\) | |||||||
\(888\) | −0.000472574 0 | −1.58585e−5 0 | ||||||||
\(889\) | −7.24277 | −0.242915 | ||||||||
\(890\) | −1.11657 | −0.0374276 | ||||||||
\(891\) | −8.99999 | −0.301511 | ||||||||
\(892\) | −31.9741 | −1.07057 | ||||||||
\(893\) | 0.405629 | 0.0135738 | ||||||||
\(894\) | 0.000749271 0 | 2.50594e−5 0 | ||||||||
\(895\) | 14.9557 | 0.499913 | ||||||||
\(896\) | −6.56012 | −0.219158 | ||||||||
\(897\) | 0.00101677 | 3.39491e−5 0 | ||||||||
\(898\) | −1.50757 | −0.0503084 | ||||||||
\(899\) | 0.113450 | 0.00378377 | ||||||||
\(900\) | 5.98803 | 0.199601 | ||||||||
\(901\) | −38.7470 | −1.29085 | ||||||||
\(902\) | 0.256139 | 0.00852848 | ||||||||
\(903\) | 0.0185760 | 0.000618171 0 | ||||||||
\(904\) | −1.44513 | −0.0480644 | ||||||||
\(905\) | 16.8041 | 0.558587 | ||||||||
\(906\) | −0.00110321 | −3.66516e−5 0 | ||||||||
\(907\) | 32.2773 | 1.07175 | 0.535875 | − | 0.844297i | \(-0.319982\pi\) | ||||
0.535875 | + | 0.844297i | \(0.319982\pi\) | |||||||
\(908\) | −47.2393 | −1.56769 | ||||||||
\(909\) | −30.7635 | −1.02036 | ||||||||
\(910\) | 0.0525198 | 0.00174101 | ||||||||
\(911\) | −17.2673 | −0.572091 | −0.286046 | − | 0.958216i | \(-0.592341\pi\) | ||||
−0.286046 | + | 0.958216i | \(0.592341\pi\) | |||||||
\(912\) | −0.000280491 0 | −9.28798e−6 0 | ||||||||
\(913\) | −17.7671 | −0.588006 | ||||||||
\(914\) | −1.14660 | −0.0379262 | ||||||||
\(915\) | −0.00500611 | −0.000165497 0 | ||||||||
\(916\) | −19.6719 | −0.649978 | ||||||||
\(917\) | 28.6379 | 0.945705 | ||||||||
\(918\) | 0.00205211 | 6.77296e−5 0 | ||||||||
\(919\) | 27.4609 | 0.905851 | 0.452926 | − | 0.891548i | \(-0.350380\pi\) | ||||
0.452926 | + | 0.891548i | \(0.350380\pi\) | |||||||
\(920\) | −0.945786 | −0.0311816 | ||||||||
\(921\) | 0.0207483 | 0.000683678 0 | ||||||||
\(922\) | −2.24317 | −0.0738750 | ||||||||
\(923\) | 2.63013 | 0.0865717 | ||||||||
\(924\) | 0.00693038 | 0.000227993 0 | ||||||||
\(925\) | 1.75949 | 0.0578518 | ||||||||
\(926\) | −1.07785 | −0.0354203 | ||||||||
\(927\) | −51.5336 | −1.69259 | ||||||||
\(928\) | 2.31629 | 0.0760361 | ||||||||
\(929\) | 0.370745 | 0.0121637 | 0.00608187 | − | 0.999982i | \(-0.498064\pi\) | ||||
0.00608187 | + | 0.999982i | \(0.498064\pi\) | |||||||
\(930\) | 2.48821e−6 0 | 8.15917e−8 0 | ||||||||
\(931\) | −0.241476 | −0.00791405 | ||||||||
\(932\) | −11.6352 | −0.381123 | ||||||||
\(933\) | 0.0351666 | 0.00115130 | ||||||||
\(934\) | −2.52868 | −0.0827408 | ||||||||
\(935\) | 5.08854 | 0.166413 | ||||||||
\(936\) | 0.192991 | 0.00630811 | ||||||||
\(937\) | −46.6770 | −1.52487 | −0.762435 | − | 0.647064i | \(-0.775997\pi\) | ||||
−0.762435 | + | 0.647064i | \(0.775997\pi\) | |||||||
\(938\) | 2.05508 | 0.0671007 | ||||||||
\(939\) | −0.00945269 | −0.000308477 0 | ||||||||
\(940\) | 12.2149 | 0.398405 | ||||||||
\(941\) | −11.2596 | −0.367053 | −0.183527 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183527 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(942\) | 0.000627774 0 | 2.04540e−5 0 | ||||||||
\(943\) | −15.2002 | −0.494988 | ||||||||
\(944\) | 28.9365 | 0.941804 | ||||||||
\(945\) | −0.0208327 | −0.000677687 0 | ||||||||
\(946\) | −0.337873 | −0.0109852 | ||||||||
\(947\) | 13.7970 | 0.448343 | 0.224171 | − | 0.974550i | \(-0.428032\pi\) | ||||
0.224171 | + | 0.974550i | \(0.428032\pi\) | |||||||
\(948\) | 0.0105382 | 0.000342264 0 | ||||||||
\(949\) | −0.254914 | −0.00827486 | ||||||||
\(950\) | −0.00418599 | −0.000135811 0 | ||||||||
\(951\) | 0.0115083 | 0.000373181 0 | ||||||||
\(952\) | 4.18938 | 0.135779 | ||||||||
\(953\) | 4.98932 | 0.161620 | 0.0808100 | − | 0.996730i | \(-0.474249\pi\) | ||||
0.0808100 | + | 0.996730i | \(0.474249\pi\) | |||||||
\(954\) | −1.44265 | −0.0467075 | ||||||||
\(955\) | 3.11170 | 0.100692 | ||||||||
\(956\) | −20.8832 | −0.675412 | ||||||||
\(957\) | −0.00326162 | −0.000105433 0 | ||||||||
\(958\) | −0.572443 | −0.0184948 | ||||||||
\(959\) | 40.2483 | 1.29969 | ||||||||
\(960\) | −0.00841262 | −0.000271516 0 | ||||||||
\(961\) | −30.9986 | −0.999956 | ||||||||
\(962\) | 0.0283254 | 0.000913249 0 | ||||||||
\(963\) | 2.61099 | 0.0841379 | ||||||||
\(964\) | −4.45790 | −0.143579 | ||||||||
\(965\) | 2.24990 | 0.0724269 | ||||||||
\(966\) | 0.000821788 0 | 2.64406e−5 0 | ||||||||
\(967\) | −33.9405 | −1.09145 | −0.545726 | − | 0.837964i | \(-0.683746\pi\) | ||||
−0.545726 | + | 0.837964i | \(0.683746\pi\) | |||||||
\(968\) | −0.252361 | −0.00811119 | ||||||||
\(969\) | 0.000358968 0 | 1.15317e−5 0 | ||||||||
\(970\) | −0.619848 | −0.0199021 | ||||||||
\(971\) | 23.4339 | 0.752028 | 0.376014 | − | 0.926614i | \(-0.377294\pi\) | ||||
0.376014 | + | 0.926614i | \(0.377294\pi\) | |||||||
\(972\) | −0.0573570 | −0.00183973 | ||||||||
\(973\) | 15.0845 | 0.483585 | ||||||||
\(974\) | 1.93238 | 0.0619174 | ||||||||
\(975\) | 0.000271302 0 | 8.68863e−6 0 | ||||||||
\(976\) | −18.7024 | −0.598648 | ||||||||
\(977\) | −5.23561 | −0.167502 | −0.0837511 | − | 0.996487i | \(-0.526690\pi\) | ||||
−0.0837511 | + | 0.996487i | \(0.526690\pi\) | |||||||
\(978\) | −0.000280795 0 | −8.97884e−6 0 | ||||||||
\(979\) | 17.6804 | 0.565068 | ||||||||
\(980\) | −7.27167 | −0.232285 | ||||||||
\(981\) | 36.9348 | 1.17924 | ||||||||
\(982\) | 0.607161 | 0.0193753 | ||||||||
\(983\) | 60.4833 | 1.92912 | 0.964559 | − | 0.263866i | \(-0.0849975\pi\) | ||||
0.964559 | + | 0.263866i | \(0.0849975\pi\) | |||||||
\(984\) | 0.00108934 | 3.47268e−5 0 | ||||||||
\(985\) | −13.2229 | −0.421316 | ||||||||
\(986\) | −0.984831 | −0.0313634 | ||||||||
\(987\) | −0.0212481 | −0.000676334 0 | ||||||||
\(988\) | 0.0337256 | 0.00107295 | ||||||||
\(989\) | 20.0507 | 0.637575 | ||||||||
\(990\) | 0.189460 | 0.00602142 | ||||||||
\(991\) | 9.86087 | 0.313241 | 0.156620 | − | 0.987659i | \(-0.449940\pi\) | ||||
0.156620 | + | 0.987659i | \(0.449940\pi\) | |||||||
\(992\) | 0.0279803 | 0.000888376 0 | ||||||||
\(993\) | 0.0114709 | 0.000364019 0 | ||||||||
\(994\) | 2.12575 | 0.0674248 | ||||||||
\(995\) | −12.1146 | −0.384059 | ||||||||
\(996\) | −0.0377433 | −0.00119594 | ||||||||
\(997\) | 14.8379 | 0.469921 | 0.234961 | − | 0.972005i | \(-0.424504\pi\) | ||||
0.234961 | + | 0.972005i | \(0.424504\pi\) | |||||||
\(998\) | −0.969431 | −0.0306868 | ||||||||
\(999\) | −0.0112357 | −0.000355481 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4015.2.a.i.1.20 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.i.1.20 | ✓ | 38 | 1.1 | even | 1 | trivial |