Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 8x + 10 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.59774\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59774 | −0.981852 | −0.490926 | − | 0.871201i | \(-0.663341\pi\) | ||||
−0.490926 | + | 0.871201i | \(0.663341\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −4.74823 | −1.43164 | −0.715822 | − | 0.698282i | \(-0.753948\pi\) | ||||
−0.715822 | + | 0.698282i | \(0.753948\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.69193 | 1.85601 | 0.928003 | − | 0.372572i | \(-0.121524\pi\) | ||||
0.928003 | + | 0.372572i | \(0.121524\pi\) | |||||||
\(14\) | 2.59774 | 0.694274 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.748228 | 0.181472 | 0.0907360 | − | 0.995875i | \(-0.471078\pi\) | ||||
0.0907360 | + | 0.995875i | \(0.471078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.34596 | −0.767617 | −0.383808 | − | 0.923413i | \(-0.625388\pi\) | ||||
−0.383808 | + | 0.923413i | \(0.625388\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.74823 | 1.01233 | ||||||||
\(23\) | −1.49646 | −0.312033 | −0.156016 | − | 0.987754i | \(-0.549865\pi\) | ||||
−0.156016 | + | 0.987754i | \(0.549865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.69193 | −1.31239 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.59774 | −0.490926 | ||||||||
\(29\) | −3.94370 | −0.732326 | −0.366163 | − | 0.930551i | \(-0.619329\pi\) | ||||
−0.366163 | + | 0.930551i | \(0.619329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.79321 | 1.39970 | 0.699851 | − | 0.714289i | \(-0.253250\pi\) | ||||
0.699851 | + | 0.714289i | \(0.253250\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.748228 | −0.128320 | ||||||||
\(35\) | −2.59774 | −0.439097 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 3.34596 | 0.542787 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 6.44724 | 1.00689 | 0.503445 | − | 0.864027i | \(-0.332066\pi\) | ||||
0.503445 | + | 0.864027i | \(0.332066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.94370 | 0.296411 | 0.148206 | − | 0.988957i | \(-0.452650\pi\) | ||||
0.148206 | + | 0.988957i | \(0.452650\pi\) | |||||||
\(44\) | −4.74823 | −0.715822 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.49646 | 0.220640 | ||||||||
\(47\) | −1.84951 | −0.269778 | −0.134889 | − | 0.990861i | \(-0.543068\pi\) | ||||
−0.134889 | + | 0.990861i | \(0.543068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.251772 | −0.0359674 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.69193 | 0.928003 | ||||||||
\(53\) | −10.4472 | −1.43504 | −0.717520 | − | 0.696538i | \(-0.754723\pi\) | ||||
−0.717520 | + | 0.696538i | \(0.754723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.74823 | −0.640251 | ||||||||
\(56\) | 2.59774 | 0.347137 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.94370 | 0.517833 | ||||||||
\(59\) | −5.84951 | −0.761541 | −0.380770 | − | 0.924670i | \(-0.624341\pi\) | ||||
−0.380770 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.94370 | 1.01709 | 0.508543 | − | 0.861036i | \(-0.330184\pi\) | ||||
0.508543 | + | 0.861036i | \(0.330184\pi\) | |||||||
\(62\) | −7.79321 | −0.989738 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.69193 | 0.830031 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.84951 | 0.225953 | 0.112977 | − | 0.993598i | \(-0.463961\pi\) | ||||
0.112977 | + | 0.993598i | \(0.463961\pi\) | |||||||
\(68\) | 0.748228 | 0.0907360 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.59774 | 0.310489 | ||||||||
\(71\) | 3.88740 | 0.461349 | 0.230675 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230675 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.49646 | −0.877394 | −0.438697 | − | 0.898635i | \(-0.644560\pi\) | ||||
−0.438697 | + | 0.898635i | \(0.644560\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.34596 | −0.383808 | ||||||||
\(77\) | 12.3346 | 1.40566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.5414 | −1.86106 | −0.930528 | − | 0.366220i | \(-0.880652\pi\) | ||||
−0.930528 | + | 0.366220i | \(0.880652\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.44724 | −0.711979 | ||||||||
\(83\) | −15.2334 | −1.67208 | −0.836039 | − | 0.548670i | \(-0.815134\pi\) | ||||
−0.836039 | + | 0.548670i | \(0.815134\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.748228 | 0.0811567 | ||||||||
\(86\) | −1.94370 | −0.209594 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.74823 | 0.506163 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3839 | −1.82232 | ||||||||
\(92\) | −1.49646 | −0.156016 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.84951 | 0.190762 | ||||||||
\(95\) | −3.34596 | −0.343289 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4472 | −1.06076 | −0.530378 | − | 0.847761i | \(-0.677950\pi\) | ||||
−0.530378 | + | 0.847761i | \(0.677950\pi\) | |||||||
\(98\) | 0.251772 | 0.0254328 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.1884 | 1.21279 | 0.606395 | − | 0.795164i | \(-0.292615\pi\) | ||||
0.606395 | + | 0.795164i | \(0.292615\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.30807 | −0.128888 | −0.0644442 | − | 0.997921i | \(-0.520527\pi\) | ||||
−0.0644442 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(104\) | −6.69193 | −0.656197 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.4472 | 1.01473 | ||||||||
\(107\) | 3.04498 | 0.294369 | 0.147185 | − | 0.989109i | \(-0.452979\pi\) | ||||
0.147185 | + | 0.989109i | \(0.452979\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.44015 | −0.137942 | −0.0689709 | − | 0.997619i | \(-0.521972\pi\) | ||||
−0.0689709 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(110\) | 4.74823 | 0.452726 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.59774 | −0.245463 | ||||||||
\(113\) | −11.1392 | −1.04788 | −0.523942 | − | 0.851754i | \(-0.675539\pi\) | ||||
−0.523942 | + | 0.851754i | \(0.675539\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.49646 | −0.139545 | ||||||||
\(116\) | −3.94370 | −0.366163 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.84951 | 0.538491 | ||||||||
\(119\) | −1.94370 | −0.178179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.5457 | 1.04961 | ||||||||
\(122\) | −7.94370 | −0.719189 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.79321 | 0.699851 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.84242 | −0.784638 | −0.392319 | − | 0.919829i | \(-0.628327\pi\) | ||||
−0.392319 | + | 0.919829i | \(0.628327\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.69193 | −0.586921 | ||||||||
\(131\) | −6.15049 | −0.537371 | −0.268686 | − | 0.963228i | \(-0.586589\pi\) | ||||
−0.268686 | + | 0.963228i | \(0.586589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.69193 | 0.753686 | ||||||||
\(134\) | −1.84951 | −0.159773 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.748228 | −0.0641600 | ||||||||
\(137\) | −10.8945 | −0.930779 | −0.465389 | − | 0.885106i | \(-0.654086\pi\) | ||||
−0.465389 | + | 0.885106i | \(0.654086\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.04921 | 0.0889932 | 0.0444966 | − | 0.999010i | \(-0.485832\pi\) | ||||
0.0444966 | + | 0.999010i | \(0.485832\pi\) | |||||||
\(140\) | −2.59774 | −0.219549 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.88740 | −0.326223 | ||||||||
\(143\) | −31.7748 | −2.65714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.94370 | −0.327506 | ||||||||
\(146\) | 7.49646 | 0.620411 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | 4.18838 | 0.343126 | 0.171563 | − | 0.985173i | \(-0.445118\pi\) | ||||
0.171563 | + | 0.985173i | \(0.445118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.69193 | −0.544581 | −0.272291 | − | 0.962215i | \(-0.587781\pi\) | ||||
−0.272291 | + | 0.962215i | \(0.587781\pi\) | |||||||
\(152\) | 3.34596 | 0.271393 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.3346 | −0.993954 | ||||||||
\(155\) | 7.79321 | 0.625965 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.94370 | −0.314741 | −0.157371 | − | 0.987540i | \(-0.550302\pi\) | ||||
−0.157371 | + | 0.987540i | \(0.550302\pi\) | |||||||
\(158\) | 16.5414 | 1.31597 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 3.88740 | 0.306370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1463 | −0.951368 | −0.475684 | − | 0.879616i | \(-0.657799\pi\) | ||||
−0.475684 | + | 0.879616i | \(0.657799\pi\) | |||||||
\(164\) | 6.44724 | 0.503445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.2334 | 1.18234 | ||||||||
\(167\) | −17.0829 | −1.32191 | −0.660956 | − | 0.750425i | \(-0.729849\pi\) | ||||
−0.660956 | + | 0.750425i | \(0.729849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.7819 | 2.44476 | ||||||||
\(170\) | −0.748228 | −0.0573865 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.94370 | 0.148206 | ||||||||
\(173\) | 15.3417 | 1.16641 | 0.583205 | − | 0.812325i | \(-0.301798\pi\) | ||||
0.583205 | + | 0.812325i | \(0.301798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.59774 | −0.196370 | ||||||||
\(176\) | −4.74823 | −0.357911 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −2.45148 | −0.183232 | −0.0916161 | − | 0.995794i | \(-0.529203\pi\) | ||||
−0.0916161 | + | 0.995794i | \(0.529203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1955 | 0.980812 | 0.490406 | − | 0.871494i | \(-0.336849\pi\) | ||||
0.490406 | + | 0.871494i | \(0.336849\pi\) | |||||||
\(182\) | 17.3839 | 1.28858 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.49646 | 0.110320 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.55276 | −0.259803 | ||||||||
\(188\) | −1.84951 | −0.134889 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.34596 | 0.242742 | ||||||||
\(191\) | 21.7790 | 1.57588 | 0.787938 | − | 0.615755i | \(-0.211149\pi\) | ||||
0.787938 | + | 0.615755i | \(0.211149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9929 | −0.935250 | −0.467625 | − | 0.883927i | \(-0.654890\pi\) | ||||
−0.467625 | + | 0.883927i | \(0.654890\pi\) | |||||||
\(194\) | 10.4472 | 0.750068 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.251772 | −0.0179837 | ||||||||
\(197\) | −0.616147 | −0.0438986 | −0.0219493 | − | 0.999759i | \(-0.506987\pi\) | ||||
−0.0219493 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.54852 | −0.109772 | −0.0548859 | − | 0.998493i | \(-0.517480\pi\) | ||||
−0.0548859 | + | 0.998493i | \(0.517480\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.1884 | −0.857572 | ||||||||
\(203\) | 10.2447 | 0.719036 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.44724 | 0.450295 | ||||||||
\(206\) | 1.30807 | 0.0911378 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.69193 | 0.464002 | ||||||||
\(209\) | 15.8874 | 1.09895 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9366 | 1.44134 | 0.720668 | − | 0.693280i | \(-0.243835\pi\) | ||||
0.720668 | + | 0.693280i | \(0.243835\pi\) | |||||||
\(212\) | −10.4472 | −0.717520 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.04498 | −0.208150 | ||||||||
\(215\) | 1.94370 | 0.132559 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.2447 | −1.37430 | ||||||||
\(218\) | 1.44015 | 0.0975396 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.74823 | −0.320125 | ||||||||
\(221\) | 5.00709 | 0.336813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.71034 | −0.181498 | −0.0907488 | − | 0.995874i | \(-0.528926\pi\) | ||||
−0.0907488 | + | 0.995874i | \(0.528926\pi\) | |||||||
\(224\) | 2.59774 | 0.173568 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.1392 | 0.740966 | ||||||||
\(227\) | −26.1321 | −1.73445 | −0.867224 | − | 0.497919i | \(-0.834098\pi\) | ||||
−0.867224 | + | 0.497919i | \(0.834098\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.7677 | −1.63670 | −0.818348 | − | 0.574723i | \(-0.805110\pi\) | ||||
−0.818348 | + | 0.574723i | \(0.805110\pi\) | |||||||
\(230\) | 1.49646 | 0.0986734 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.94370 | 0.258916 | ||||||||
\(233\) | 12.2783 | 0.804381 | 0.402190 | − | 0.915556i | \(-0.368249\pi\) | ||||
0.402190 | + | 0.915556i | \(0.368249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.84951 | −0.120649 | ||||||||
\(236\) | −5.84951 | −0.380770 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.94370 | 0.125991 | ||||||||
\(239\) | 17.1771 | 1.11109 | 0.555546 | − | 0.831486i | \(-0.312509\pi\) | ||||
0.555546 | + | 0.831486i | \(0.312509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2713 | −0.983708 | −0.491854 | − | 0.870678i | \(-0.663681\pi\) | ||||
−0.491854 | + | 0.870678i | \(0.663681\pi\) | |||||||
\(242\) | −11.5457 | −0.742184 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.94370 | 0.508543 | ||||||||
\(245\) | −0.251772 | −0.0160851 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.3909 | −1.42470 | ||||||||
\(248\) | −7.79321 | −0.494869 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −10.0379 | −0.633586 | −0.316793 | − | 0.948495i | \(-0.602606\pi\) | ||||
−0.316793 | + | 0.948495i | \(0.602606\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.10552 | 0.446720 | ||||||||
\(254\) | 8.84242 | 0.554823 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.9703 | 1.30809 | 0.654045 | − | 0.756456i | \(-0.273071\pi\) | ||||
0.654045 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.59774 | 0.161415 | ||||||||
\(260\) | 6.69193 | 0.415016 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.15049 | 0.379979 | ||||||||
\(263\) | −22.3725 | −1.37955 | −0.689775 | − | 0.724024i | \(-0.742290\pi\) | ||||
−0.689775 | + | 0.724024i | \(0.742290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4472 | −0.641769 | ||||||||
\(266\) | −8.69193 | −0.532936 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.84951 | 0.112977 | ||||||||
\(269\) | 4.18838 | 0.255370 | 0.127685 | − | 0.991815i | \(-0.459245\pi\) | ||||
0.127685 | + | 0.991815i | \(0.459245\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1126 | −0.735788 | −0.367894 | − | 0.929868i | \(-0.619921\pi\) | ||||
−0.367894 | + | 0.929868i | \(0.619921\pi\) | |||||||
\(272\) | 0.748228 | 0.0453680 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.8945 | 0.658160 | ||||||||
\(275\) | −4.74823 | −0.286329 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.30807 | −0.559268 | −0.279634 | − | 0.960107i | \(-0.590213\pi\) | ||||
−0.279634 | + | 0.960107i | \(0.590213\pi\) | |||||||
\(278\) | −1.04921 | −0.0629277 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.59774 | 0.155244 | ||||||||
\(281\) | −19.2713 | −1.14963 | −0.574813 | − | 0.818285i | \(-0.694925\pi\) | ||||
−0.574813 | + | 0.818285i | \(0.694925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6848 | −0.813479 | −0.406740 | − | 0.913544i | \(-0.633334\pi\) | ||||
−0.406740 | + | 0.913544i | \(0.633334\pi\) | |||||||
\(284\) | 3.88740 | 0.230675 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31.7748 | 1.87888 | ||||||||
\(287\) | −16.7482 | −0.988617 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4402 | −0.967068 | ||||||||
\(290\) | 3.94370 | 0.231582 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.49646 | −0.438697 | ||||||||
\(293\) | 10.4472 | 0.610334 | 0.305167 | − | 0.952299i | \(-0.401288\pi\) | ||||
0.305167 | + | 0.952299i | \(0.401288\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.84951 | −0.340571 | ||||||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.18838 | −0.242627 | ||||||||
\(299\) | −10.0142 | −0.579135 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.04921 | −0.291032 | ||||||||
\(302\) | 6.69193 | 0.385077 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.34596 | −0.191904 | ||||||||
\(305\) | 7.94370 | 0.454855 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.95502 | −0.282798 | −0.141399 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141399 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(308\) | 12.3346 | 0.702831 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.79321 | −0.442624 | ||||||||
\(311\) | −3.68060 | −0.208708 | −0.104354 | − | 0.994540i | \(-0.533277\pi\) | ||||
−0.104354 | + | 0.994540i | \(0.533277\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.992912 | −0.0561227 | −0.0280614 | − | 0.999606i | \(-0.508933\pi\) | ||||
−0.0280614 | + | 0.999606i | \(0.508933\pi\) | |||||||
\(314\) | 3.94370 | 0.222556 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5414 | −0.930528 | ||||||||
\(317\) | 6.55985 | 0.368438 | 0.184219 | − | 0.982885i | \(-0.441024\pi\) | ||||
0.184219 | + | 0.982885i | \(0.441024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.7256 | 1.04843 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.88740 | −0.216636 | ||||||||
\(323\) | −2.50354 | −0.139301 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.69193 | 0.371201 | ||||||||
\(326\) | 12.1463 | 0.672719 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.44724 | −0.355989 | ||||||||
\(329\) | 4.80453 | 0.264882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.0379 | −0.991452 | −0.495726 | − | 0.868479i | \(-0.665098\pi\) | ||||
−0.495726 | + | 0.868479i | \(0.665098\pi\) | |||||||
\(332\) | −15.2334 | −0.836039 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.0829 | 0.934733 | ||||||||
\(335\) | 1.84951 | 0.101049 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8945 | −0.811354 | −0.405677 | − | 0.914016i | \(-0.632964\pi\) | ||||
−0.405677 | + | 0.914016i | \(0.632964\pi\) | |||||||
\(338\) | −31.7819 | −1.72871 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.748228 | 0.0405784 | ||||||||
\(341\) | −37.0039 | −2.00387 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.8382 | 1.01717 | ||||||||
\(344\) | −1.94370 | −0.104797 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.3417 | −0.824776 | ||||||||
\(347\) | 9.38385 | 0.503752 | 0.251876 | − | 0.967760i | \(-0.418953\pi\) | ||||
0.251876 | + | 0.967760i | \(0.418953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.9703 | −1.76486 | −0.882429 | − | 0.470446i | \(-0.844093\pi\) | ||||
−0.882429 | + | 0.470446i | \(0.844093\pi\) | |||||||
\(350\) | 2.59774 | 0.138855 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.74823 | 0.253081 | ||||||||
\(353\) | −27.4260 | −1.45974 | −0.729869 | − | 0.683587i | \(-0.760419\pi\) | ||||
−0.729869 | + | 0.683587i | \(0.760419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.88740 | 0.206322 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.45148 | 0.129565 | ||||||||
\(359\) | 25.0829 | 1.32382 | 0.661912 | − | 0.749582i | \(-0.269745\pi\) | ||||
0.661912 | + | 0.749582i | \(0.269745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.80453 | −0.410765 | ||||||||
\(362\) | −13.1955 | −0.693539 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.3839 | −0.911161 | ||||||||
\(365\) | −7.49646 | −0.392382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.48513 | 0.129723 | 0.0648614 | − | 0.997894i | \(-0.479339\pi\) | ||||
0.0648614 | + | 0.997894i | \(0.479339\pi\) | |||||||
\(368\) | −1.49646 | −0.0780082 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | 27.1392 | 1.40900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.1586 | −1.82045 | −0.910223 | − | 0.414119i | \(-0.864090\pi\) | ||||
−0.910223 | + | 0.414119i | \(0.864090\pi\) | |||||||
\(374\) | 3.55276 | 0.183709 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.84951 | 0.0953810 | ||||||||
\(377\) | −26.3909 | −1.35920 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.6778 | 1.26761 | 0.633805 | − | 0.773492i | \(-0.281492\pi\) | ||||
0.633805 | + | 0.773492i | \(0.281492\pi\) | |||||||
\(380\) | −3.34596 | −0.171644 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.7790 | −1.11431 | ||||||||
\(383\) | 13.3839 | 0.683883 | 0.341941 | − | 0.939721i | \(-0.388916\pi\) | ||||
0.341941 | + | 0.939721i | \(0.388916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.3346 | 0.628631 | ||||||||
\(386\) | 12.9929 | 0.661322 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.4472 | −0.530378 | ||||||||
\(389\) | −18.2220 | −0.923894 | −0.461947 | − | 0.886908i | \(-0.652849\pi\) | ||||
−0.461947 | + | 0.886908i | \(0.652849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11969 | −0.0566252 | ||||||||
\(392\) | 0.251772 | 0.0127164 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.616147 | 0.0310410 | ||||||||
\(395\) | −16.5414 | −0.832290 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.22521 | −0.111680 | −0.0558399 | − | 0.998440i | \(-0.517784\pi\) | ||||
−0.0558399 | + | 0.998440i | \(0.517784\pi\) | |||||||
\(398\) | 1.54852 | 0.0776204 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −12.3909 | −0.618774 | −0.309387 | − | 0.950936i | \(-0.600124\pi\) | ||||
−0.309387 | + | 0.950936i | \(0.600124\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 52.1516 | 2.59785 | ||||||||
\(404\) | 12.1884 | 0.606395 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.2447 | −0.508435 | ||||||||
\(407\) | 4.74823 | 0.235361 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.27125 | 0.359540 | 0.179770 | − | 0.983709i | \(-0.442465\pi\) | ||||
0.179770 | + | 0.983709i | \(0.442465\pi\) | |||||||
\(410\) | −6.44724 | −0.318407 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.30807 | −0.0644442 | ||||||||
\(413\) | 15.1955 | 0.747720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.2334 | −0.747776 | ||||||||
\(416\) | −6.69193 | −0.328099 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.8874 | −0.777078 | ||||||||
\(419\) | −28.4809 | −1.39138 | −0.695691 | − | 0.718341i | \(-0.744902\pi\) | ||||
−0.695691 | + | 0.718341i | \(0.744902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | −20.9366 | −1.01918 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4472 | 0.507363 | ||||||||
\(425\) | 0.748228 | 0.0362944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.6356 | −0.998628 | ||||||||
\(428\) | 3.04498 | 0.147185 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.94370 | −0.0937335 | ||||||||
\(431\) | −1.51487 | −0.0729686 | −0.0364843 | − | 0.999334i | \(-0.511616\pi\) | ||||
−0.0364843 | + | 0.999334i | \(0.511616\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.9929 | 1.20108 | 0.600541 | − | 0.799594i | \(-0.294952\pi\) | ||||
0.600541 | + | 0.799594i | \(0.294952\pi\) | |||||||
\(434\) | 20.2447 | 0.971776 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.44015 | −0.0689709 | ||||||||
\(437\) | 5.00709 | 0.239521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.10128 | −0.243471 | −0.121735 | − | 0.992563i | \(-0.538846\pi\) | ||||
−0.121735 | + | 0.992563i | \(0.538846\pi\) | |||||||
\(440\) | 4.74823 | 0.226363 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.00709 | −0.238163 | ||||||||
\(443\) | −25.7369 | −1.22280 | −0.611399 | − | 0.791323i | \(-0.709393\pi\) | ||||
−0.611399 | + | 0.791323i | \(0.709393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | 2.71034 | 0.128338 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.59774 | −0.122731 | ||||||||
\(449\) | 17.7748 | 0.838844 | 0.419422 | − | 0.907791i | \(-0.362233\pi\) | ||||
0.419422 | + | 0.907791i | \(0.362233\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −30.6130 | −1.44151 | ||||||||
\(452\) | −11.1392 | −0.523942 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.1321 | 1.22644 | ||||||||
\(455\) | −17.3839 | −0.814968 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.3346 | 1.60611 | 0.803053 | − | 0.595907i | \(-0.203207\pi\) | ||||
0.803053 | + | 0.595907i | \(0.203207\pi\) | |||||||
\(458\) | 24.7677 | 1.15732 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.49646 | −0.0697726 | ||||||||
\(461\) | 16.9508 | 0.789477 | 0.394738 | − | 0.918794i | \(-0.370835\pi\) | ||||
0.394738 | + | 0.918794i | \(0.370835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9929 | 0.510884 | 0.255442 | − | 0.966824i | \(-0.417779\pi\) | ||||
0.255442 | + | 0.966824i | \(0.417779\pi\) | |||||||
\(464\) | −3.94370 | −0.183082 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.2783 | −0.568783 | ||||||||
\(467\) | −37.4175 | −1.73148 | −0.865738 | − | 0.500498i | \(-0.833150\pi\) | ||||
−0.865738 | + | 0.500498i | \(0.833150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.80453 | −0.221853 | ||||||||
\(470\) | 1.84951 | 0.0853114 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.84951 | 0.269245 | ||||||||
\(473\) | −9.22912 | −0.424356 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.34596 | −0.153523 | ||||||||
\(476\) | −1.94370 | −0.0890893 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.1771 | −0.785660 | ||||||||
\(479\) | 0.465654 | 0.0212763 | 0.0106381 | − | 0.999943i | \(-0.496614\pi\) | ||||
0.0106381 | + | 0.999943i | \(0.496614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.69193 | −0.305126 | ||||||||
\(482\) | 15.2713 | 0.695586 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.5457 | 0.524803 | ||||||||
\(485\) | −10.4472 | −0.474385 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.9561 | 1.58401 | 0.792006 | − | 0.610514i | \(-0.209037\pi\) | ||||
0.792006 | + | 0.610514i | \(0.209037\pi\) | |||||||
\(488\) | −7.94370 | −0.359594 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.251772 | 0.0113739 | ||||||||
\(491\) | 24.7819 | 1.11839 | 0.559195 | − | 0.829036i | \(-0.311110\pi\) | ||||
0.559195 | + | 0.829036i | \(0.311110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.95079 | −0.132897 | ||||||||
\(494\) | 22.3909 | 1.00742 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.79321 | 0.349925 | ||||||||
\(497\) | −10.0984 | −0.452976 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.33888 | −0.104702 | −0.0523512 | − | 0.998629i | \(-0.516672\pi\) | ||||
−0.0523512 | + | 0.998629i | \(0.516672\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0379 | 0.448013 | ||||||||
\(503\) | 18.6161 | 0.830053 | 0.415026 | − | 0.909809i | \(-0.363772\pi\) | ||||
0.415026 | + | 0.909809i | \(0.363772\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.1884 | 0.542376 | ||||||||
\(506\) | −7.10552 | −0.315879 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.84242 | −0.392319 | ||||||||
\(509\) | −6.89448 | −0.305593 | −0.152796 | − | 0.988258i | \(-0.548828\pi\) | ||||
−0.152796 | + | 0.988258i | \(0.548828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.4738 | 0.861471 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.9703 | −0.924959 | ||||||||
\(515\) | −1.30807 | −0.0576406 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.78188 | 0.386227 | ||||||||
\(518\) | −2.59774 | −0.114138 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.69193 | −0.293460 | ||||||||
\(521\) | −4.86083 | −0.212957 | −0.106478 | − | 0.994315i | \(-0.533958\pi\) | ||||
−0.106478 | + | 0.994315i | \(0.533958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.7677 | 0.995562 | 0.497781 | − | 0.867303i | \(-0.334148\pi\) | ||||
0.497781 | + | 0.867303i | \(0.334148\pi\) | |||||||
\(524\) | −6.15049 | −0.268686 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.3725 | 0.975489 | ||||||||
\(527\) | 5.83110 | 0.254007 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7606 | −0.902636 | ||||||||
\(530\) | 10.4472 | 0.453799 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.69193 | 0.376843 | ||||||||
\(533\) | 43.1445 | 1.86879 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.04498 | 0.131646 | ||||||||
\(536\) | −1.84951 | −0.0798865 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.18838 | −0.180574 | ||||||||
\(539\) | 1.19547 | 0.0514926 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.99291 | 0.386636 | 0.193318 | − | 0.981136i | \(-0.438075\pi\) | ||||
0.193318 | + | 0.981136i | \(0.438075\pi\) | |||||||
\(542\) | 12.1126 | 0.520281 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.748228 | −0.0320800 | ||||||||
\(545\) | −1.44015 | −0.0616894 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8382 | −0.805463 | −0.402731 | − | 0.915318i | \(-0.631939\pi\) | ||||
−0.402731 | + | 0.915318i | \(0.631939\pi\) | |||||||
\(548\) | −10.8945 | −0.465389 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.74823 | 0.202465 | ||||||||
\(551\) | 13.1955 | 0.562146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.9703 | 1.82728 | ||||||||
\(554\) | 9.30807 | 0.395462 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.04921 | 0.0444966 | ||||||||
\(557\) | −3.69901 | −0.156732 | −0.0783661 | − | 0.996925i | \(-0.524970\pi\) | ||||
−0.0783661 | + | 0.996925i | \(0.524970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.0071 | 0.550141 | ||||||||
\(560\) | −2.59774 | −0.109774 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.2713 | 0.812909 | ||||||||
\(563\) | 14.3488 | 0.604730 | 0.302365 | − | 0.953192i | \(-0.402224\pi\) | ||||
0.302365 | + | 0.953192i | \(0.402224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1392 | −0.468628 | ||||||||
\(566\) | 13.6848 | 0.575217 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.88740 | −0.163112 | ||||||||
\(569\) | −15.9858 | −0.670161 | −0.335080 | − | 0.942190i | \(-0.608763\pi\) | ||||
−0.335080 | + | 0.942190i | \(0.608763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.2079 | −1.26416 | −0.632080 | − | 0.774903i | \(-0.717799\pi\) | ||||
−0.632080 | + | 0.774903i | \(0.717799\pi\) | |||||||
\(572\) | −31.7748 | −1.32857 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 16.7482 | 0.699058 | ||||||||
\(575\) | −1.49646 | −0.0624065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1813 | −0.798528 | −0.399264 | − | 0.916836i | \(-0.630734\pi\) | ||||
−0.399264 | + | 0.916836i | \(0.630734\pi\) | |||||||
\(578\) | 16.4402 | 0.683820 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.94370 | −0.163753 | ||||||||
\(581\) | 39.5722 | 1.64173 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.6059 | 2.05447 | ||||||||
\(584\) | 7.49646 | 0.310206 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.4472 | −0.431572 | ||||||||
\(587\) | 26.6130 | 1.09844 | 0.549218 | − | 0.835679i | \(-0.314926\pi\) | ||||
0.549218 | + | 0.835679i | \(0.314926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.0758 | −1.07443 | ||||||||
\(590\) | 5.84951 | 0.240820 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | −26.2642 | −1.07854 | −0.539270 | − | 0.842133i | \(-0.681300\pi\) | ||||
−0.539270 | + | 0.842133i | \(0.681300\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.94370 | −0.0796839 | ||||||||
\(596\) | 4.18838 | 0.171563 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.0142 | 0.409510 | ||||||||
\(599\) | 38.2415 | 1.56251 | 0.781253 | − | 0.624215i | \(-0.214581\pi\) | ||||
0.781253 | + | 0.624215i | \(0.214581\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2447 | 1.23371 | 0.616853 | − | 0.787078i | \(-0.288407\pi\) | ||||
0.616853 | + | 0.787078i | \(0.288407\pi\) | |||||||
\(602\) | 5.04921 | 0.205791 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.69193 | −0.272291 | ||||||||
\(605\) | 11.5457 | 0.469398 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.90157 | −0.239537 | −0.119769 | − | 0.992802i | \(-0.538215\pi\) | ||||
−0.119769 | + | 0.992802i | \(0.538215\pi\) | |||||||
\(608\) | 3.34596 | 0.135697 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.94370 | −0.321631 | ||||||||
\(611\) | −12.3768 | −0.500710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.15473 | 0.248587 | 0.124294 | − | 0.992245i | \(-0.460334\pi\) | ||||
0.124294 | + | 0.992245i | \(0.460334\pi\) | |||||||
\(614\) | 4.95502 | 0.199968 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3346 | −0.496977 | ||||||||
\(617\) | −16.5035 | −0.664408 | −0.332204 | − | 0.943208i | \(-0.607792\pi\) | ||||
−0.332204 | + | 0.943208i | \(0.607792\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.04921 | 0.363719 | 0.181859 | − | 0.983325i | \(-0.441788\pi\) | ||||
0.181859 | + | 0.983325i | \(0.441788\pi\) | |||||||
\(620\) | 7.79321 | 0.312983 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.68060 | 0.147579 | ||||||||
\(623\) | 15.5864 | 0.624456 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.992912 | 0.0396848 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.94370 | −0.157371 | ||||||||
\(629\) | −0.748228 | −0.0298338 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.507780 | −0.0202144 | −0.0101072 | − | 0.999949i | \(-0.503217\pi\) | ||||
−0.0101072 | + | 0.999949i | \(0.503217\pi\) | |||||||
\(632\) | 16.5414 | 0.657983 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.55985 | −0.260525 | ||||||||
\(635\) | −8.84242 | −0.350901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.68484 | −0.0667558 | ||||||||
\(638\) | −18.7256 | −0.741353 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 40.6356 | 1.60501 | 0.802505 | − | 0.596645i | \(-0.203500\pi\) | ||||
0.802505 | + | 0.596645i | \(0.203500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.53011 | −0.375831 | −0.187915 | − | 0.982185i | \(-0.560173\pi\) | ||||
−0.187915 | + | 0.982185i | \(0.560173\pi\) | |||||||
\(644\) | 3.88740 | 0.153185 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.50354 | 0.0985006 | ||||||||
\(647\) | 21.0071 | 0.825874 | 0.412937 | − | 0.910760i | \(-0.364503\pi\) | ||||
0.412937 | + | 0.910760i | \(0.364503\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.7748 | 1.09026 | ||||||||
\(650\) | −6.69193 | −0.262479 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.1463 | −0.475684 | ||||||||
\(653\) | 45.5496 | 1.78249 | 0.891247 | − | 0.453519i | \(-0.149832\pi\) | ||||
0.891247 | + | 0.453519i | \(0.149832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.15049 | −0.240320 | ||||||||
\(656\) | 6.44724 | 0.251723 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.80453 | −0.187300 | ||||||||
\(659\) | −9.38385 | −0.365543 | −0.182772 | − | 0.983155i | \(-0.558507\pi\) | ||||
−0.182772 | + | 0.983155i | \(0.558507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.05630 | 0.157772 | 0.0788859 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788859 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(662\) | 18.0379 | 0.701062 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.2334 | 0.591169 | ||||||||
\(665\) | 8.69193 | 0.337058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.90157 | 0.228510 | ||||||||
\(668\) | −17.0829 | −0.660956 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.84951 | −0.0714527 | ||||||||
\(671\) | −37.7185 | −1.45611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.60906 | 0.293308 | 0.146654 | − | 0.989188i | \(-0.453150\pi\) | ||||
0.146654 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(674\) | 14.8945 | 0.573714 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.7819 | 1.22238 | ||||||||
\(677\) | −28.7677 | −1.10563 | −0.552816 | − | 0.833303i | \(-0.686447\pi\) | ||||
−0.552816 | + | 0.833303i | \(0.686447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.1392 | 1.04151 | ||||||||
\(680\) | −0.748228 | −0.0286932 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 37.0039 | 1.41695 | ||||||||
\(683\) | −0.0704767 | −0.00269671 | −0.00134836 | − | 0.999999i | \(-0.500429\pi\) | ||||
−0.00134836 | + | 0.999999i | \(0.500429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.8945 | −0.416257 | ||||||||
\(686\) | −18.8382 | −0.719245 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.94370 | 0.0741028 | ||||||||
\(689\) | −69.9122 | −2.66344 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.6498 | 0.405137 | 0.202569 | − | 0.979268i | \(-0.435071\pi\) | ||||
0.202569 | + | 0.979268i | \(0.435071\pi\) | |||||||
\(692\) | 15.3417 | 0.583205 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.38385 | −0.356206 | ||||||||
\(695\) | 1.04921 | 0.0397990 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.82401 | 0.182722 | ||||||||
\(698\) | 32.9703 | 1.24794 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.59774 | −0.0981852 | ||||||||
\(701\) | 7.98582 | 0.301620 | 0.150810 | − | 0.988563i | \(-0.451812\pi\) | ||||
0.150810 | + | 0.988563i | \(0.451812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.34596 | 0.126195 | ||||||||
\(704\) | −4.74823 | −0.178956 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.4260 | 1.03219 | ||||||||
\(707\) | −31.6622 | −1.19078 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.2149 | −1.39764 | −0.698818 | − | 0.715299i | \(-0.746290\pi\) | ||||
−0.698818 | + | 0.715299i | \(0.746290\pi\) | |||||||
\(710\) | −3.88740 | −0.145891 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | −11.6622 | −0.436752 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31.7748 | −1.18831 | ||||||||
\(716\) | −2.45148 | −0.0916161 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.0829 | −0.936084 | ||||||||
\(719\) | −30.1742 | −1.12531 | −0.562654 | − | 0.826692i | \(-0.690220\pi\) | ||||
−0.562654 | + | 0.826692i | \(0.690220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.39803 | 0.126549 | ||||||||
\(722\) | 7.80453 | 0.290455 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.1955 | 0.490406 | ||||||||
\(725\) | −3.94370 | −0.146465 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.7677 | −0.696056 | −0.348028 | − | 0.937484i | \(-0.613149\pi\) | ||||
−0.348028 | + | 0.937484i | \(0.613149\pi\) | |||||||
\(728\) | 17.3839 | 0.644288 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.49646 | 0.277456 | ||||||||
\(731\) | 1.45433 | 0.0537903 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.1094 | 0.964374 | 0.482187 | − | 0.876068i | \(-0.339843\pi\) | ||||
0.482187 | + | 0.876068i | \(0.339843\pi\) | |||||||
\(734\) | −2.48513 | −0.0917279 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.49646 | 0.0551601 | ||||||||
\(737\) | −8.78188 | −0.323485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.6130 | 1.56754 | 0.783772 | − | 0.621049i | \(-0.213293\pi\) | ||||
0.783772 | + | 0.621049i | \(0.213293\pi\) | |||||||
\(740\) | −1.00000 | −0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27.1392 | −0.996310 | ||||||||
\(743\) | 35.4922 | 1.30208 | 0.651042 | − | 0.759042i | \(-0.274332\pi\) | ||||
0.651042 | + | 0.759042i | \(0.274332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.18838 | 0.153450 | ||||||||
\(746\) | 35.1586 | 1.28725 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.55276 | −0.129902 | ||||||||
\(749\) | −7.91005 | −0.289027 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.5722 | 0.787182 | 0.393591 | − | 0.919286i | \(-0.371233\pi\) | ||||
0.393591 | + | 0.919286i | \(0.371233\pi\) | |||||||
\(752\) | −1.84951 | −0.0674446 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.3909 | 0.961101 | ||||||||
\(755\) | −6.69193 | −0.243544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.7890 | −0.864625 | −0.432312 | − | 0.901724i | \(-0.642302\pi\) | ||||
−0.432312 | + | 0.901724i | \(0.642302\pi\) | |||||||
\(758\) | −24.6778 | −0.896336 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.34596 | 0.121371 | ||||||||
\(761\) | 18.6724 | 0.676876 | 0.338438 | − | 0.940989i | \(-0.390102\pi\) | ||||
0.338438 | + | 0.940989i | \(0.390102\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.74114 | 0.135438 | ||||||||
\(764\) | 21.7790 | 0.787938 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.3839 | −0.483578 | ||||||||
\(767\) | −39.1445 | −1.41342 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.48937 | −0.0897689 | −0.0448845 | − | 0.998992i | \(-0.514292\pi\) | ||||
−0.0448845 | + | 0.998992i | \(0.514292\pi\) | |||||||
\(770\) | −12.3346 | −0.444510 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.9929 | −0.467625 | ||||||||
\(773\) | −0.950786 | −0.0341974 | −0.0170987 | − | 0.999854i | \(-0.505443\pi\) | ||||
−0.0170987 | + | 0.999854i | \(0.505443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.79321 | 0.279940 | ||||||||
\(776\) | 10.4472 | 0.375034 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.2220 | 0.653292 | ||||||||
\(779\) | −21.5722 | −0.772906 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4582 | −0.660488 | ||||||||
\(782\) | 1.11969 | 0.0400401 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.251772 | −0.00899185 | ||||||||
\(785\) | −3.94370 | −0.140757 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.4359 | −1.04928 | −0.524639 | − | 0.851325i | \(-0.675800\pi\) | ||||
−0.524639 | + | 0.851325i | \(0.675800\pi\) | |||||||
\(788\) | −0.616147 | −0.0219493 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.5414 | 0.588518 | ||||||||
\(791\) | 28.9366 | 1.02887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.1586 | 1.88772 | ||||||||
\(794\) | 2.22521 | 0.0789696 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.54852 | −0.0548859 | ||||||||
\(797\) | 14.1742 | 0.502076 | 0.251038 | − | 0.967977i | \(-0.419228\pi\) | ||||
0.251038 | + | 0.967977i | \(0.419228\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.38385 | −0.0489572 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.3909 | 0.437539 | ||||||||
\(803\) | 35.5949 | 1.25612 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.88740 | 0.137013 | ||||||||
\(806\) | −52.1516 | −1.83696 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.1884 | −0.428786 | ||||||||
\(809\) | 32.9929 | 1.15997 | 0.579985 | − | 0.814627i | \(-0.303059\pi\) | ||||
0.579985 | + | 0.814627i | \(0.303059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.5567 | 1.42414 | 0.712069 | − | 0.702110i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702110i | \(0.247758\pi\) | |||||||
\(812\) | 10.2447 | 0.359518 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.74823 | −0.166425 | ||||||||
\(815\) | −12.1463 | −0.425465 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.50354 | −0.227530 | ||||||||
\(818\) | −7.27125 | −0.254233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.44724 | 0.225147 | ||||||||
\(821\) | 38.8661 | 1.35644 | 0.678219 | − | 0.734860i | \(-0.262752\pi\) | ||||
0.678219 | + | 0.734860i | \(0.262752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.6243 | −1.72979 | −0.864897 | − | 0.501949i | \(-0.832616\pi\) | ||||
−0.864897 | + | 0.501949i | \(0.832616\pi\) | |||||||
\(824\) | 1.30807 | 0.0455689 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.1955 | −0.528718 | ||||||||
\(827\) | 30.0195 | 1.04388 | 0.521940 | − | 0.852982i | \(-0.325209\pi\) | ||||
0.521940 | + | 0.852982i | \(0.325209\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5598 | 0.366759 | 0.183379 | − | 0.983042i | \(-0.441296\pi\) | ||||
0.183379 | + | 0.983042i | \(0.441296\pi\) | |||||||
\(830\) | 15.2334 | 0.528758 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.69193 | 0.232001 | ||||||||
\(833\) | −0.188383 | −0.00652708 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.0829 | −0.591177 | ||||||||
\(836\) | 15.8874 | 0.549477 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.4809 | 0.983856 | ||||||||
\(839\) | −29.3839 | −1.01444 | −0.507222 | − | 0.861816i | \(-0.669327\pi\) | ||||
−0.507222 | + | 0.861816i | \(0.669327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.4472 | −0.463698 | ||||||||
\(842\) | −22.0000 | −0.758170 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.9366 | 0.720668 | ||||||||
\(845\) | 31.7819 | 1.09333 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.9926 | −1.03056 | ||||||||
\(848\) | −10.4472 | −0.358760 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.748228 | −0.0256640 | ||||||||
\(851\) | 1.49646 | 0.0512979 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.22521 | 0.213147 | 0.106573 | − | 0.994305i | \(-0.466012\pi\) | ||||
0.106573 | + | 0.994305i | \(0.466012\pi\) | |||||||
\(854\) | 20.6356 | 0.706137 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.04498 | −0.104075 | ||||||||
\(857\) | 3.65119 | 0.124722 | 0.0623611 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623611 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.3162 | −1.23909 | −0.619547 | − | 0.784960i | \(-0.712684\pi\) | ||||
−0.619547 | + | 0.784960i | \(0.712684\pi\) | |||||||
\(860\) | 1.94370 | 0.0662796 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.51487 | 0.0515966 | ||||||||
\(863\) | −24.5751 | −0.836546 | −0.418273 | − | 0.908321i | \(-0.637364\pi\) | ||||
−0.418273 | + | 0.908321i | \(0.637364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.3417 | 0.521634 | ||||||||
\(866\) | −24.9929 | −0.849294 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −20.2447 | −0.687149 | ||||||||
\(869\) | 78.5425 | 2.66437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.3768 | 0.419371 | ||||||||
\(872\) | 1.44015 | 0.0487698 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.00709 | −0.169367 | ||||||||
\(875\) | −2.59774 | −0.0878195 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0563 | 0.677253 | 0.338627 | − | 0.940921i | \(-0.390038\pi\) | ||||
0.338627 | + | 0.940921i | \(0.390038\pi\) | |||||||
\(878\) | 5.10128 | 0.172160 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.74823 | −0.160063 | ||||||||
\(881\) | 15.0266 | 0.506258 | 0.253129 | − | 0.967433i | \(-0.418540\pi\) | ||||
0.253129 | + | 0.967433i | \(0.418540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.62145 | −0.222830 | −0.111415 | − | 0.993774i | \(-0.535538\pi\) | ||||
−0.111415 | + | 0.993774i | \(0.535538\pi\) | |||||||
\(884\) | 5.00709 | 0.168407 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.7369 | 0.864648 | ||||||||
\(887\) | 37.5538 | 1.26093 | 0.630467 | − | 0.776216i | \(-0.282863\pi\) | ||||
0.630467 | + | 0.776216i | \(0.282863\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.9703 | 0.770398 | ||||||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.71034 | −0.0907488 | ||||||||
\(893\) | 6.18838 | 0.207086 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.45148 | −0.0819439 | ||||||||
\(896\) | 2.59774 | 0.0867842 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.7748 | −0.593153 | ||||||||
\(899\) | −30.7341 | −1.02504 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.81692 | −0.260419 | ||||||||
\(902\) | 30.6130 | 1.01930 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.1392 | 0.370483 | ||||||||
\(905\) | 13.1955 | 0.438632 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.4667 | 1.67572 | 0.837860 | − | 0.545885i | \(-0.183807\pi\) | ||||
0.837860 | + | 0.545885i | \(0.183807\pi\) | |||||||
\(908\) | −26.1321 | −0.867224 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.3839 | 0.576269 | ||||||||
\(911\) | −15.9395 | −0.528098 | −0.264049 | − | 0.964509i | \(-0.585058\pi\) | ||||
−0.264049 | + | 0.964509i | \(0.585058\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72.3315 | 2.39382 | ||||||||
\(914\) | −34.3346 | −1.13569 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.7677 | −0.818348 | ||||||||
\(917\) | 15.9774 | 0.527619 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.5414 | 1.07344 | 0.536721 | − | 0.843760i | \(-0.319663\pi\) | ||||
0.536721 | + | 0.843760i | \(0.319663\pi\) | |||||||
\(920\) | 1.49646 | 0.0493367 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.9508 | −0.558244 | ||||||||
\(923\) | 26.0142 | 0.856267 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | −10.9929 | −0.361250 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.94370 | 0.129458 | ||||||||
\(929\) | 34.1094 | 1.11909 | 0.559547 | − | 0.828799i | \(-0.310975\pi\) | ||||
0.559547 | + | 0.828799i | \(0.310975\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.842420 | 0.0276092 | ||||||||
\(932\) | 12.2783 | 0.402190 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.4175 | 1.22434 | ||||||||
\(935\) | −3.55276 | −0.116188 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.0141751 | 0.000463082 0 | 0.000231541 | − | 1.00000i | \(-0.499926\pi\) | ||||
0.000231541 | 1.00000i | \(0.499926\pi\) | ||||||||
\(938\) | 4.80453 | 0.156873 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.84951 | −0.0603243 | ||||||||
\(941\) | −11.1813 | −0.364500 | −0.182250 | − | 0.983252i | \(-0.558338\pi\) | ||||
−0.182250 | + | 0.983252i | \(0.558338\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.64802 | −0.314183 | ||||||||
\(944\) | −5.84951 | −0.190385 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.22912 | 0.300065 | ||||||||
\(947\) | 53.6427 | 1.74315 | 0.871577 | − | 0.490259i | \(-0.163098\pi\) | ||||
0.871577 | + | 0.490259i | \(0.163098\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −50.1657 | −1.62845 | ||||||||
\(950\) | 3.34596 | 0.108557 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.94370 | 0.0629956 | ||||||||
\(953\) | 9.88740 | 0.320284 | 0.160142 | − | 0.987094i | \(-0.448805\pi\) | ||||
0.160142 | + | 0.987094i | \(0.448805\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.7790 | 0.704753 | ||||||||
\(956\) | 17.1771 | 0.555546 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.465654 | −0.0150446 | ||||||||
\(959\) | 28.3010 | 0.913886 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.7341 | 0.959163 | ||||||||
\(962\) | 6.69193 | 0.215756 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.2713 | −0.491854 | ||||||||
\(965\) | −12.9929 | −0.418257 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51.6254 | 1.66016 | 0.830080 | − | 0.557644i | \(-0.188295\pi\) | ||||
0.830080 | + | 0.557644i | \(0.188295\pi\) | |||||||
\(968\) | −11.5457 | −0.371092 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.4472 | 0.335441 | ||||||||
\(971\) | −20.5598 | −0.659797 | −0.329898 | − | 0.944016i | \(-0.607014\pi\) | ||||
−0.329898 | + | 0.944016i | \(0.607014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.72558 | −0.0873781 | ||||||||
\(974\) | −34.9561 | −1.12007 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.94370 | 0.254272 | ||||||||
\(977\) | −38.4472 | −1.23004 | −0.615018 | − | 0.788513i | \(-0.710851\pi\) | ||||
−0.615018 | + | 0.788513i | \(0.710851\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.4894 | 0.910524 | ||||||||
\(980\) | −0.251772 | −0.00804256 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −24.7819 | −0.790822 | ||||||||
\(983\) | −11.8973 | −0.379466 | −0.189733 | − | 0.981836i | \(-0.560762\pi\) | ||||
−0.189733 | + | 0.981836i | \(0.560762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.616147 | −0.0196321 | ||||||||
\(986\) | 2.95079 | 0.0939722 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.3909 | −0.712351 | ||||||||
\(989\) | −2.90866 | −0.0924900 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.7932 | −0.628752 | −0.314376 | − | 0.949299i | \(-0.601795\pi\) | ||||
−0.314376 | + | 0.949299i | \(0.601795\pi\) | |||||||
\(992\) | −7.79321 | −0.247435 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.0984 | 0.320303 | ||||||||
\(995\) | −1.54852 | −0.0490914 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.88740 | 0.186456 | 0.0932279 | − | 0.995645i | \(-0.470281\pi\) | ||||
0.0932279 | + | 0.995645i | \(0.470281\pi\) | |||||||
\(998\) | 2.33888 | 0.0740358 | ||||||||
\(999\) | 0 | 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 | 3330.2.a.bg.1.1 | 3 | ||
3.2 | odd | 2 | 370.2.a.g.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 2960.2.a.u.1.3 | 3 | |||
15.2 | even | 4 | 1850.2.b.o.149.6 | 6 | |||
15.8 | even | 4 | 1850.2.b.o.149.1 | 6 | |||
15.14 | odd | 2 | 1850.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.g.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1850.2.a.z.1.3 | 3 | 15.14 | odd | 2 | |||
1850.2.b.o.149.1 | 6 | 15.8 | even | 4 | |||
1850.2.b.o.149.6 | 6 | 15.2 | even | 4 | |||
2960.2.a.u.1.3 | 3 | 12.11 | even | 2 | |||
3330.2.a.bg.1.1 | 3 | 1.1 | even | 1 | trivial |