Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 52x^{6} + 805x^{4} - 4210x^{2} + 4992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 117) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.39589\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.39589 | −1.90774 | −0.953868 | − | 0.300228i | \(-0.902937\pi\) | ||||
−0.953868 | + | 0.300228i | \(0.902937\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 21.1156 | 2.63945 | ||||||||
\(5\) | −13.0421 | −1.16653 | −0.583263 | − | 0.812284i | \(-0.698224\pi\) | ||||
−0.583263 | + | 0.812284i | \(0.698224\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.42494 | 0.346914 | 0.173457 | − | 0.984841i | \(-0.444506\pi\) | ||||
0.173457 | + | 0.984841i | \(0.444506\pi\) | |||||||
\(8\) | −70.7705 | −3.12764 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 70.3740 | 2.22542 | ||||||||
\(11\) | −26.2056 | −0.718298 | −0.359149 | − | 0.933280i | \(-0.616933\pi\) | ||||
−0.359149 | + | 0.933280i | \(0.616933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −34.6683 | −0.661820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 212.945 | 3.32726 | ||||||||
\(17\) | −123.877 | −1.76733 | −0.883663 | − | 0.468124i | \(-0.844930\pi\) | ||||
−0.883663 | + | 0.468124i | \(0.844930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −109.667 | −1.32417 | −0.662086 | − | 0.749428i | \(-0.730329\pi\) | ||||
−0.662086 | + | 0.749428i | \(0.730329\pi\) | |||||||
\(20\) | −275.393 | −3.07899 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 141.402 | 1.37032 | ||||||||
\(23\) | −63.4094 | −0.574860 | −0.287430 | − | 0.957802i | \(-0.592801\pi\) | ||||
−0.287430 | + | 0.957802i | \(0.592801\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 45.0976 | 0.360781 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 135.667 | 0.915664 | ||||||||
\(29\) | 225.410 | 1.44337 | 0.721683 | − | 0.692224i | \(-0.243369\pi\) | ||||
0.721683 | + | 0.692224i | \(0.243369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −200.732 | −1.16298 | −0.581491 | − | 0.813553i | \(-0.697530\pi\) | ||||
−0.581491 | + | 0.813553i | \(0.697530\pi\) | |||||||
\(32\) | −582.863 | −3.21989 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 668.426 | 3.37159 | ||||||||
\(35\) | −83.7950 | −0.404684 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −252.509 | −1.12195 | −0.560976 | − | 0.827832i | \(-0.689574\pi\) | ||||
−0.560976 | + | 0.827832i | \(0.689574\pi\) | |||||||
\(38\) | 591.749 | 2.52617 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 922.999 | 3.64847 | ||||||||
\(41\) | −227.423 | −0.866282 | −0.433141 | − | 0.901326i | \(-0.642595\pi\) | ||||
−0.433141 | + | 0.901326i | \(0.642595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −384.032 | −1.36196 | −0.680980 | − | 0.732302i | \(-0.738446\pi\) | ||||
−0.680980 | + | 0.732302i | \(0.738446\pi\) | |||||||
\(44\) | −553.348 | −1.89592 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 342.150 | 1.09668 | ||||||||
\(47\) | −34.6646 | −0.107582 | −0.0537910 | − | 0.998552i | \(-0.517130\pi\) | ||||
−0.0537910 | + | 0.998552i | \(0.517130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −301.720 | −0.879651 | ||||||||
\(50\) | −243.342 | −0.688274 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −61.0601 | −0.158250 | −0.0791251 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791251 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 341.777 | 0.837913 | ||||||||
\(56\) | −454.696 | −1.08502 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1216.29 | −2.75356 | ||||||||
\(59\) | 80.5562 | 0.177755 | 0.0888774 | − | 0.996043i | \(-0.471672\pi\) | ||||
0.0888774 | + | 0.996043i | \(0.471672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.1383 | −0.0548634 | −0.0274317 | − | 0.999624i | \(-0.508733\pi\) | ||||
−0.0274317 | + | 0.999624i | \(0.508733\pi\) | |||||||
\(62\) | 1083.13 | 2.21866 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1441.50 | 2.81544 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 931.510 | 1.69854 | 0.849269 | − | 0.527960i | \(-0.177043\pi\) | ||||
0.849269 | + | 0.527960i | \(0.177043\pi\) | |||||||
\(68\) | −2615.74 | −4.66477 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 452.149 | 0.772030 | ||||||||
\(71\) | −427.608 | −0.714757 | −0.357379 | − | 0.933960i | \(-0.616329\pi\) | ||||
−0.357379 | + | 0.933960i | \(0.616329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −108.518 | −0.173987 | −0.0869935 | − | 0.996209i | \(-0.527726\pi\) | ||||
−0.0869935 | + | 0.996209i | \(0.527726\pi\) | |||||||
\(74\) | 1362.51 | 2.14039 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2315.68 | −3.49509 | ||||||||
\(77\) | −168.369 | −0.249188 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 384.590 | 0.547718 | 0.273859 | − | 0.961770i | \(-0.411700\pi\) | ||||
0.273859 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(80\) | −2777.26 | −3.88133 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1227.15 | 1.65264 | ||||||||
\(83\) | 85.9758 | 0.113700 | 0.0568498 | − | 0.998383i | \(-0.481894\pi\) | ||||
0.0568498 | + | 0.998383i | \(0.481894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1615.62 | 2.06163 | ||||||||
\(86\) | 2072.19 | 2.59826 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1854.58 | 2.24658 | ||||||||
\(89\) | 495.903 | 0.590625 | 0.295313 | − | 0.955401i | \(-0.404576\pi\) | ||||
0.295313 | + | 0.955401i | \(0.404576\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1338.93 | −1.51732 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 187.046 | 0.205238 | ||||||||
\(95\) | 1430.29 | 1.54468 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −190.857 | −0.199780 | −0.0998898 | − | 0.994999i | \(-0.531849\pi\) | ||||
−0.0998898 | + | 0.994999i | \(0.531849\pi\) | |||||||
\(98\) | 1628.05 | 1.67814 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 952.264 | 0.952264 | ||||||||
\(101\) | −850.980 | −0.838373 | −0.419186 | − | 0.907900i | \(-0.637685\pi\) | ||||
−0.419186 | + | 0.907900i | \(0.637685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1309.50 | −1.25270 | −0.626352 | − | 0.779540i | \(-0.715453\pi\) | ||||
−0.626352 | + | 0.779540i | \(0.715453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 329.474 | 0.301899 | ||||||||
\(107\) | −962.302 | −0.869432 | −0.434716 | − | 0.900567i | \(-0.643151\pi\) | ||||
−0.434716 | + | 0.900567i | \(0.643151\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −891.973 | −0.783812 | −0.391906 | − | 0.920005i | \(-0.628184\pi\) | ||||
−0.391906 | + | 0.920005i | \(0.628184\pi\) | |||||||
\(110\) | −1844.19 | −1.59852 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1368.16 | 1.15427 | ||||||||
\(113\) | −263.839 | −0.219645 | −0.109823 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109823 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 826.995 | 0.670588 | ||||||||
\(116\) | 4759.68 | 3.80970 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −434.673 | −0.339109 | ||||||||
\(119\) | −795.901 | −0.613110 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −644.267 | −0.484047 | ||||||||
\(122\) | 141.039 | 0.104665 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4238.57 | −3.06964 | ||||||||
\(125\) | 1042.10 | 0.745665 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1543.97 | −1.07878 | −0.539391 | − | 0.842056i | \(-0.681345\pi\) | ||||
−0.539391 | + | 0.842056i | \(0.681345\pi\) | |||||||
\(128\) | −3115.30 | −2.15122 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 776.790 | 0.518080 | 0.259040 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259040 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −704.602 | −0.459374 | ||||||||
\(134\) | −5026.33 | −3.24036 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8766.82 | 5.52756 | ||||||||
\(137\) | −2434.71 | −1.51833 | −0.759166 | − | 0.650897i | \(-0.774393\pi\) | ||||
−0.759166 | + | 0.650897i | \(0.774393\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1251.40 | 0.763615 | 0.381807 | − | 0.924242i | \(-0.375302\pi\) | ||||
0.381807 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(140\) | −1769.38 | −1.06814 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2307.33 | 1.36357 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2939.83 | −1.68372 | ||||||||
\(146\) | 585.550 | 0.331921 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5331.88 | −2.96134 | ||||||||
\(149\) | −783.619 | −0.430850 | −0.215425 | − | 0.976520i | \(-0.569114\pi\) | ||||
−0.215425 | + | 0.976520i | \(0.569114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −162.220 | −0.0874255 | −0.0437128 | − | 0.999044i | \(-0.513919\pi\) | ||||
−0.0437128 | + | 0.999044i | \(0.513919\pi\) | |||||||
\(152\) | 7761.16 | 4.14154 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 908.503 | 0.475385 | ||||||||
\(155\) | 2617.97 | 1.35665 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2355.76 | −1.19752 | −0.598758 | − | 0.800930i | \(-0.704339\pi\) | ||||
−0.598758 | + | 0.800930i | \(0.704339\pi\) | |||||||
\(158\) | −2075.20 | −1.04490 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7601.78 | 3.75608 | ||||||||
\(161\) | −407.402 | −0.199427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1574.29 | −0.756488 | −0.378244 | − | 0.925706i | \(-0.623472\pi\) | ||||
−0.378244 | + | 0.925706i | \(0.623472\pi\) | |||||||
\(164\) | −4802.19 | −2.28651 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −463.916 | −0.216909 | ||||||||
\(167\) | −3574.56 | −1.65633 | −0.828166 | − | 0.560483i | \(-0.810616\pi\) | ||||
−0.828166 | + | 0.560483i | \(0.810616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −8717.70 | −3.93304 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8109.07 | −3.59483 | ||||||||
\(173\) | 1.44108 | 0.000633314 0 | 0.000316657 | − | 1.00000i | \(-0.499899\pi\) | ||||
0.000316657 | 1.00000i | \(0.499899\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 289.749 | 0.125160 | ||||||||
\(176\) | −5580.34 | −2.38997 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2675.84 | −1.12676 | ||||||||
\(179\) | −2082.28 | −0.869478 | −0.434739 | − | 0.900556i | \(-0.643159\pi\) | ||||
−0.434739 | + | 0.900556i | \(0.643159\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −464.500 | −0.190751 | −0.0953756 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953756 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4487.51 | 1.79796 | ||||||||
\(185\) | 3293.26 | 1.30878 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3246.26 | 1.26947 | ||||||||
\(188\) | −731.965 | −0.283957 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7717.68 | −2.94684 | ||||||||
\(191\) | −4866.28 | −1.84352 | −0.921758 | − | 0.387765i | \(-0.873247\pi\) | ||||
−0.921758 | + | 0.387765i | \(0.873247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 856.339 | 0.319381 | 0.159691 | − | 0.987167i | \(-0.448950\pi\) | ||||
0.159691 | + | 0.987167i | \(0.448950\pi\) | |||||||
\(194\) | 1029.84 | 0.381127 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6371.01 | −2.32180 | ||||||||
\(197\) | 1571.93 | 0.568504 | 0.284252 | − | 0.958750i | \(-0.408255\pi\) | ||||
0.284252 | + | 0.958750i | \(0.408255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3126.61 | 1.11377 | 0.556883 | − | 0.830591i | \(-0.311997\pi\) | ||||
0.556883 | + | 0.830591i | \(0.311997\pi\) | |||||||
\(200\) | −3191.58 | −1.12839 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4591.79 | 1.59939 | ||||||||
\(203\) | 1448.25 | 0.500724 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2966.09 | 1.01054 | ||||||||
\(206\) | 7065.90 | 2.38983 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2873.88 | 0.951150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 123.392 | 0.0402590 | 0.0201295 | − | 0.999797i | \(-0.493592\pi\) | ||||
0.0201295 | + | 0.999797i | \(0.493592\pi\) | |||||||
\(212\) | −1289.32 | −0.417694 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5192.48 | 1.65865 | ||||||||
\(215\) | 5008.60 | 1.58876 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1289.69 | −0.403455 | ||||||||
\(218\) | 4812.99 | 1.49531 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7216.84 | 2.21163 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2503.69 | 0.751836 | 0.375918 | − | 0.926653i | \(-0.377327\pi\) | ||||
0.375918 | + | 0.926653i | \(0.377327\pi\) | |||||||
\(224\) | −3744.86 | −1.11703 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1423.65 | 0.419025 | ||||||||
\(227\) | −579.270 | −0.169372 | −0.0846861 | − | 0.996408i | \(-0.526989\pi\) | ||||
−0.0846861 | + | 0.996408i | \(0.526989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 768.922 | 0.221886 | 0.110943 | − | 0.993827i | \(-0.464613\pi\) | ||||
0.110943 | + | 0.993827i | \(0.464613\pi\) | |||||||
\(230\) | −4462.37 | −1.27930 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15952.4 | −4.51433 | ||||||||
\(233\) | 845.695 | 0.237783 | 0.118891 | − | 0.992907i | \(-0.462066\pi\) | ||||
0.118891 | + | 0.992907i | \(0.462066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 452.101 | 0.125497 | ||||||||
\(236\) | 1701.00 | 0.469175 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4294.59 | 1.16965 | ||||||||
\(239\) | 6552.78 | 1.77349 | 0.886744 | − | 0.462260i | \(-0.152961\pi\) | ||||
0.886744 | + | 0.462260i | \(0.152961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5176.75 | −1.38367 | −0.691834 | − | 0.722056i | \(-0.743197\pi\) | ||||
−0.691834 | + | 0.722056i | \(0.743197\pi\) | |||||||
\(242\) | 3476.39 | 0.923434 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −551.927 | −0.144809 | ||||||||
\(245\) | 3935.08 | 1.02613 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14205.9 | 3.63739 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5623.05 | −1.42253 | ||||||||
\(251\) | 4296.82 | 1.08053 | 0.540264 | − | 0.841495i | \(-0.318324\pi\) | ||||
0.540264 | + | 0.841495i | \(0.318324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1661.68 | 0.412921 | ||||||||
\(254\) | 8331.10 | 2.05803 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5277.77 | 1.28852 | ||||||||
\(257\) | −1383.94 | −0.335906 | −0.167953 | − | 0.985795i | \(-0.553716\pi\) | ||||
−0.167953 | + | 0.985795i | \(0.553716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1622.35 | −0.389221 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4191.47 | −0.988359 | ||||||||
\(263\) | −2478.68 | −0.581147 | −0.290574 | − | 0.956853i | \(-0.593846\pi\) | ||||
−0.290574 | + | 0.956853i | \(0.593846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 796.355 | 0.184603 | ||||||||
\(266\) | 3801.95 | 0.876364 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19669.4 | 4.48321 | ||||||||
\(269\) | −2452.64 | −0.555911 | −0.277956 | − | 0.960594i | \(-0.589657\pi\) | ||||
−0.277956 | + | 0.960594i | \(0.589657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5980.74 | 1.34060 | 0.670302 | − | 0.742088i | \(-0.266164\pi\) | ||||
0.670302 | + | 0.742088i | \(0.266164\pi\) | |||||||
\(272\) | −26378.9 | −5.88036 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13137.4 | 2.89658 | ||||||||
\(275\) | −1181.81 | −0.259148 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7377.99 | −1.60036 | −0.800182 | − | 0.599758i | \(-0.795264\pi\) | ||||
−0.800182 | + | 0.599758i | \(0.795264\pi\) | |||||||
\(278\) | −6752.42 | −1.45677 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5930.22 | 1.26571 | ||||||||
\(281\) | 5937.17 | 1.26043 | 0.630217 | − | 0.776419i | \(-0.282966\pi\) | ||||
0.630217 | + | 0.776419i | \(0.282966\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1486.52 | 0.312241 | 0.156121 | − | 0.987738i | \(-0.450101\pi\) | ||||
0.156121 | + | 0.987738i | \(0.450101\pi\) | |||||||
\(284\) | −9029.22 | −1.88657 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1461.18 | −0.300526 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10432.5 | 2.12344 | ||||||||
\(290\) | 15863.0 | 3.21210 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2291.42 | −0.459231 | ||||||||
\(293\) | −3580.05 | −0.713818 | −0.356909 | − | 0.934139i | \(-0.616169\pi\) | ||||
−0.356909 | + | 0.934139i | \(0.616169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1050.63 | −0.207355 | ||||||||
\(296\) | 17870.2 | 3.50906 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4228.32 | 0.821947 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2467.38 | −0.472483 | ||||||||
\(302\) | 875.320 | 0.166785 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23352.9 | −4.40587 | ||||||||
\(305\) | 340.900 | 0.0639995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 415.013 | 0.0771533 | 0.0385767 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385767 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(308\) | −3555.23 | −0.657720 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14126.3 | −2.58812 | ||||||||
\(311\) | −3009.05 | −0.548642 | −0.274321 | − | 0.961638i | \(-0.588453\pi\) | ||||
−0.274321 | + | 0.961638i | \(0.588453\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3760.84 | 0.679154 | 0.339577 | − | 0.940578i | \(-0.389716\pi\) | ||||
0.339577 | + | 0.940578i | \(0.389716\pi\) | |||||||
\(314\) | 12711.4 | 2.28454 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8120.86 | 1.44568 | ||||||||
\(317\) | 2772.04 | 0.491146 | 0.245573 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245573 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5907.01 | −1.03677 | ||||||||
\(320\) | −18800.3 | −3.28428 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2198.29 | 0.380454 | ||||||||
\(323\) | 13585.2 | 2.34024 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8494.67 | 1.44318 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16094.9 | 2.70942 | ||||||||
\(329\) | −222.718 | −0.0373217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6558.16 | −1.08903 | −0.544515 | − | 0.838751i | \(-0.683286\pi\) | ||||
−0.544515 | + | 0.838751i | \(0.683286\pi\) | |||||||
\(332\) | 1815.43 | 0.300105 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19287.9 | 3.15984 | ||||||||
\(335\) | −12148.9 | −1.98139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9509.17 | 1.53708 | 0.768542 | − | 0.639799i | \(-0.220983\pi\) | ||||
0.768542 | + | 0.639799i | \(0.220983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 34114.8 | 5.44158 | ||||||||
\(341\) | 5260.29 | 0.835368 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4142.29 | −0.652077 | ||||||||
\(344\) | 27178.1 | 4.25973 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.77591 | −0.00120820 | ||||||||
\(347\) | −9808.78 | −1.51747 | −0.758736 | − | 0.651398i | \(-0.774183\pi\) | ||||
−0.758736 | + | 0.651398i | \(0.774183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −794.952 | −0.121928 | −0.0609639 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609639 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(350\) | −1563.46 | −0.238772 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15274.3 | 2.31284 | ||||||||
\(353\) | 7115.60 | 1.07288 | 0.536438 | − | 0.843940i | \(-0.319770\pi\) | ||||
0.536438 | + | 0.843940i | \(0.319770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5576.93 | 0.833782 | ||||||||
\(356\) | 10471.3 | 1.55893 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11235.7 | 1.65873 | ||||||||
\(359\) | 6907.19 | 1.01545 | 0.507726 | − | 0.861518i | \(-0.330486\pi\) | ||||
0.507726 | + | 0.861518i | \(0.330486\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5167.78 | 0.753430 | ||||||||
\(362\) | 2506.39 | 0.363903 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1415.31 | 0.202960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −459.533 | −0.0653609 | −0.0326804 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326804 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(368\) | −13502.7 | −1.91271 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −17770.1 | −2.49681 | ||||||||
\(371\) | −392.308 | −0.0548992 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5359.92 | 0.744038 | 0.372019 | − | 0.928225i | \(-0.378666\pi\) | ||||
0.372019 | + | 0.928225i | \(0.378666\pi\) | |||||||
\(374\) | −17516.5 | −2.42181 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2453.23 | 0.336478 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8594.06 | −1.16477 | −0.582384 | − | 0.812914i | \(-0.697880\pi\) | ||||
−0.582384 | + | 0.812914i | \(0.697880\pi\) | |||||||
\(380\) | 30201.4 | 4.07711 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26257.9 | 3.51694 | ||||||||
\(383\) | −9336.49 | −1.24562 | −0.622810 | − | 0.782373i | \(-0.714009\pi\) | ||||
−0.622810 | + | 0.782373i | \(0.714009\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2195.90 | 0.290684 | ||||||||
\(386\) | −4620.71 | −0.609295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4030.07 | −0.527309 | ||||||||
\(389\) | 12792.1 | 1.66732 | 0.833659 | − | 0.552279i | \(-0.186242\pi\) | ||||
0.833659 | + | 0.552279i | \(0.186242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7854.95 | 1.01596 | ||||||||
\(392\) | 21352.9 | 2.75123 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8481.96 | −1.08456 | ||||||||
\(395\) | −5015.88 | −0.638927 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13384.5 | 1.69206 | 0.846030 | − | 0.533135i | \(-0.178986\pi\) | ||||
0.846030 | + | 0.533135i | \(0.178986\pi\) | |||||||
\(398\) | −16870.8 | −2.12477 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9603.30 | 1.20041 | ||||||||
\(401\) | 6357.41 | 0.791706 | 0.395853 | − | 0.918314i | \(-0.370449\pi\) | ||||
0.395853 | + | 0.918314i | \(0.370449\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −17969.0 | −2.21285 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7814.58 | −0.955249 | ||||||||
\(407\) | 6617.14 | 0.805896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5301.63 | 0.640950 | 0.320475 | − | 0.947257i | \(-0.396157\pi\) | ||||
0.320475 | + | 0.947257i | \(0.396157\pi\) | |||||||
\(410\) | −16004.7 | −1.92784 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27650.8 | −3.30645 | ||||||||
\(413\) | 517.569 | 0.0616656 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1121.31 | −0.132633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15507.1 | −1.81454 | ||||||||
\(419\) | 16395.8 | 1.91167 | 0.955835 | − | 0.293905i | \(-0.0949551\pi\) | ||||
0.955835 | + | 0.293905i | \(0.0949551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8484.68 | −0.982227 | −0.491114 | − | 0.871095i | \(-0.663410\pi\) | ||||
−0.491114 | + | 0.871095i | \(0.663410\pi\) | |||||||
\(422\) | −665.808 | −0.0768034 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4321.26 | 0.494950 | ||||||||
\(425\) | −5586.55 | −0.637617 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −167.937 | −0.0190329 | ||||||||
\(428\) | −20319.6 | −2.29483 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −27025.8 | −3.03094 | ||||||||
\(431\) | −1594.74 | −0.178227 | −0.0891136 | − | 0.996021i | \(-0.528403\pi\) | ||||
−0.0891136 | + | 0.996021i | \(0.528403\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3387.57 | −0.375973 | −0.187987 | − | 0.982172i | \(-0.560196\pi\) | ||||
−0.187987 | + | 0.982172i | \(0.560196\pi\) | |||||||
\(434\) | 6959.02 | 0.769685 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18834.6 | −2.06884 | ||||||||
\(437\) | 6953.90 | 0.761213 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7211.54 | −0.784027 | −0.392014 | − | 0.919959i | \(-0.628221\pi\) | ||||
−0.392014 | + | 0.919959i | \(0.628221\pi\) | |||||||
\(440\) | −24187.7 | −2.62069 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7500.66 | −0.804441 | −0.402220 | − | 0.915543i | \(-0.631761\pi\) | ||||
−0.402220 | + | 0.915543i | \(0.631761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6467.65 | −0.688979 | ||||||||
\(446\) | −13509.6 | −1.43430 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9261.58 | 0.976715 | ||||||||
\(449\) | 7649.53 | 0.804017 | 0.402009 | − | 0.915636i | \(-0.368312\pi\) | ||||
0.402009 | + | 0.915636i | \(0.368312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5959.77 | 0.622249 | ||||||||
\(452\) | −5571.13 | −0.579743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3125.67 | 0.323117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9001.79 | 0.921414 | 0.460707 | − | 0.887552i | \(-0.347596\pi\) | ||||
0.460707 | + | 0.887552i | \(0.347596\pi\) | |||||||
\(458\) | −4149.02 | −0.423299 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17462.5 | 1.76999 | ||||||||
\(461\) | 1347.83 | 0.136171 | 0.0680854 | − | 0.997679i | \(-0.478311\pi\) | ||||
0.0680854 | + | 0.997679i | \(0.478311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 94.9035 | 0.00952600 | 0.00476300 | − | 0.999989i | \(-0.498484\pi\) | ||||
0.00476300 | + | 0.999989i | \(0.498484\pi\) | |||||||
\(464\) | 47999.9 | 4.80246 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4563.28 | −0.453626 | ||||||||
\(467\) | 13290.9 | 1.31698 | 0.658489 | − | 0.752591i | \(-0.271196\pi\) | ||||
0.658489 | + | 0.752591i | \(0.271196\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5984.90 | 0.589247 | ||||||||
\(470\) | −2439.49 | −0.239415 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5701.00 | −0.555953 | ||||||||
\(473\) | 10063.8 | 0.978294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4945.70 | −0.477736 | ||||||||
\(476\) | −16806.0 | −1.61828 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −35358.1 | −3.38335 | ||||||||
\(479\) | 3801.59 | 0.362628 | 0.181314 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181314 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 27933.2 | 2.63967 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13604.1 | −1.27762 | ||||||||
\(485\) | 2489.19 | 0.233048 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8747.34 | 0.813922 | 0.406961 | − | 0.913446i | \(-0.366588\pi\) | ||||
0.406961 | + | 0.913446i | \(0.366588\pi\) | |||||||
\(488\) | 1849.82 | 0.171593 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21233.2 | −1.95759 | ||||||||
\(491\) | 15085.4 | 1.38655 | 0.693273 | − | 0.720675i | \(-0.256168\pi\) | ||||
0.693273 | + | 0.720675i | \(0.256168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27923.1 | −2.55090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42744.7 | −3.86955 | ||||||||
\(497\) | −2747.36 | −0.247959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14593.9 | −1.30925 | −0.654623 | − | 0.755955i | \(-0.727173\pi\) | ||||
−0.654623 | + | 0.755955i | \(0.727173\pi\) | |||||||
\(500\) | 22004.6 | 1.96815 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −23185.2 | −2.06136 | ||||||||
\(503\) | −18204.9 | −1.61375 | −0.806876 | − | 0.590721i | \(-0.798843\pi\) | ||||
−0.806876 | + | 0.590721i | \(0.798843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11098.6 | 0.977983 | ||||||||
\(506\) | −8966.25 | −0.787744 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32601.9 | −2.84739 | ||||||||
\(509\) | 7891.92 | 0.687236 | 0.343618 | − | 0.939109i | \(-0.388347\pi\) | ||||
0.343618 | + | 0.939109i | \(0.388347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −697.221 | −0.0603586 | ||||||||
\(512\) | −3555.88 | −0.306932 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7467.59 | 0.640819 | ||||||||
\(515\) | 17078.6 | 1.46131 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 908.406 | 0.0772759 | ||||||||
\(518\) | 8754.05 | 0.742530 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 647.902 | 0.0544820 | 0.0272410 | − | 0.999629i | \(-0.491328\pi\) | ||||
0.0272410 | + | 0.999629i | \(0.491328\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9269.99 | 0.775044 | 0.387522 | − | 0.921860i | \(-0.373331\pi\) | ||||
0.387522 | + | 0.921860i | \(0.373331\pi\) | |||||||
\(524\) | 16402.4 | 1.36745 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13374.7 | 1.10867 | ||||||||
\(527\) | 24866.0 | 2.05537 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8146.25 | −0.669536 | ||||||||
\(530\) | −4297.05 | −0.352173 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14878.1 | −1.21250 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12550.5 | 1.01421 | ||||||||
\(536\) | −65923.4 | −5.31242 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13234.2 | 1.06053 | ||||||||
\(539\) | 7906.75 | 0.631852 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3844.83 | −0.305549 | −0.152775 | − | 0.988261i | \(-0.548821\pi\) | ||||
−0.152775 | + | 0.988261i | \(0.548821\pi\) | |||||||
\(542\) | −32271.4 | −2.55752 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 72203.1 | 5.69060 | ||||||||
\(545\) | 11633.2 | 0.914337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20245.4 | −1.58251 | −0.791253 | − | 0.611489i | \(-0.790571\pi\) | ||||
−0.791253 | + | 0.611489i | \(0.790571\pi\) | |||||||
\(548\) | −51410.5 | −4.00757 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6376.91 | 0.494386 | ||||||||
\(551\) | −24720.0 | −1.91126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2470.97 | 0.190011 | ||||||||
\(554\) | 39810.8 | 3.05307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26424.1 | 2.01553 | ||||||||
\(557\) | 7223.34 | 0.549485 | 0.274742 | − | 0.961518i | \(-0.411407\pi\) | ||||
0.274742 | + | 0.961518i | \(0.411407\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −17843.7 | −1.34649 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32036.3 | −2.40458 | ||||||||
\(563\) | 17290.3 | 1.29431 | 0.647156 | − | 0.762358i | \(-0.275958\pi\) | ||||
0.647156 | + | 0.762358i | \(0.275958\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3441.03 | 0.256221 | ||||||||
\(566\) | −8021.09 | −0.595674 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30262.0 | 2.23551 | ||||||||
\(569\) | −17364.0 | −1.27933 | −0.639663 | − | 0.768655i | \(-0.720926\pi\) | ||||
−0.639663 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 158.149 | 0.0115908 | 0.00579540 | − | 0.999983i | \(-0.498155\pi\) | ||||
0.00579540 | + | 0.999983i | \(0.498155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7884.38 | 0.573323 | ||||||||
\(575\) | −2859.61 | −0.207398 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9627.04 | −0.694591 | −0.347295 | − | 0.937756i | \(-0.612900\pi\) | ||||
−0.347295 | + | 0.937756i | \(0.612900\pi\) | |||||||
\(578\) | −56292.4 | −4.05096 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −62076.4 | −4.44411 | ||||||||
\(581\) | 552.389 | 0.0394440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1600.12 | 0.113671 | ||||||||
\(584\) | 7679.86 | 0.544169 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19317.6 | 1.36178 | ||||||||
\(587\) | −13321.2 | −0.936668 | −0.468334 | − | 0.883551i | \(-0.655146\pi\) | ||||
−0.468334 | + | 0.883551i | \(0.655146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22013.6 | 1.53999 | ||||||||
\(590\) | 5669.06 | 0.395579 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −53770.4 | −3.73303 | ||||||||
\(593\) | 16723.4 | 1.15809 | 0.579044 | − | 0.815296i | \(-0.303426\pi\) | ||||
0.579044 | + | 0.815296i | \(0.303426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10380.3 | 0.715209 | ||||||||
\(596\) | −16546.6 | −1.13721 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17160.0 | −1.17051 | −0.585256 | − | 0.810849i | \(-0.699006\pi\) | ||||
−0.585256 | + | 0.810849i | \(0.699006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11048.6 | 0.749885 | 0.374942 | − | 0.927048i | \(-0.377663\pi\) | ||||
0.374942 | + | 0.927048i | \(0.377663\pi\) | |||||||
\(602\) | 13313.7 | 0.901373 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3425.37 | −0.230756 | ||||||||
\(605\) | 8402.62 | 0.564653 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21119.6 | 1.41222 | 0.706110 | − | 0.708102i | \(-0.250448\pi\) | ||||
0.706110 | + | 0.708102i | \(0.250448\pi\) | |||||||
\(608\) | 63920.6 | 4.26369 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1839.46 | −0.122094 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6233.83 | 0.410737 | 0.205369 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205369 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(614\) | −2239.37 | −0.147188 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11915.6 | 0.779371 | ||||||||
\(617\) | −5598.36 | −0.365286 | −0.182643 | − | 0.983179i | \(-0.558465\pi\) | ||||
−0.182643 | + | 0.983179i | \(0.558465\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15874.3 | 1.03076 | 0.515382 | − | 0.856961i | \(-0.327650\pi\) | ||||
0.515382 | + | 0.856961i | \(0.327650\pi\) | |||||||
\(620\) | 55280.1 | 3.58081 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16236.5 | 1.04666 | ||||||||
\(623\) | 3186.15 | 0.204896 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19228.4 | −1.23062 | ||||||||
\(626\) | −20293.1 | −1.29565 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −49743.3 | −3.16079 | ||||||||
\(629\) | 31280.0 | 1.98285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11249.0 | −0.709693 | −0.354846 | − | 0.934925i | \(-0.615467\pi\) | ||||
−0.354846 | + | 0.934925i | \(0.615467\pi\) | |||||||
\(632\) | −27217.6 | −1.71307 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14957.6 | −0.936976 | ||||||||
\(635\) | 20136.7 | 1.25843 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 31873.6 | 1.97788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40630.2 | 2.50945 | ||||||||
\(641\) | −23768.3 | −1.46457 | −0.732287 | − | 0.680996i | \(-0.761547\pi\) | ||||
−0.732287 | + | 0.680996i | \(0.761547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4368.95 | 0.267954 | 0.133977 | − | 0.990984i | \(-0.457225\pi\) | ||||
0.133977 | + | 0.990984i | \(0.457225\pi\) | |||||||
\(644\) | −8602.54 | −0.526378 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −73304.0 | −4.46456 | ||||||||
\(647\) | −21305.2 | −1.29458 | −0.647290 | − | 0.762244i | \(-0.724098\pi\) | ||||
−0.647290 | + | 0.762244i | \(0.724098\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2111.02 | −0.127681 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33242.0 | −1.99672 | ||||||||
\(653\) | −27958.3 | −1.67549 | −0.837744 | − | 0.546064i | \(-0.816126\pi\) | ||||
−0.837744 | + | 0.546064i | \(0.816126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10131.0 | −0.604353 | ||||||||
\(656\) | −48428.6 | −2.88235 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1201.76 | 0.0711999 | ||||||||
\(659\) | 9619.46 | 0.568621 | 0.284310 | − | 0.958732i | \(-0.408235\pi\) | ||||
0.284310 | + | 0.958732i | \(0.408235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4414.40 | −0.259759 | −0.129879 | − | 0.991530i | \(-0.541459\pi\) | ||||
−0.129879 | + | 0.991530i | \(0.541459\pi\) | |||||||
\(662\) | 35387.1 | 2.07758 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6084.55 | −0.355612 | ||||||||
\(665\) | 9189.52 | 0.535871 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14293.1 | −0.829733 | ||||||||
\(668\) | −75479.0 | −4.37181 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 65554.1 | 3.77996 | ||||||||
\(671\) | 684.970 | 0.0394083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18001.8 | −1.03108 | −0.515540 | − | 0.856865i | \(-0.672409\pi\) | ||||
−0.515540 | + | 0.856865i | \(0.672409\pi\) | |||||||
\(674\) | −51310.4 | −2.93235 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11192.0 | −0.635369 | −0.317684 | − | 0.948197i | \(-0.602905\pi\) | ||||
−0.317684 | + | 0.948197i | \(0.602905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1226.25 | −0.0693064 | ||||||||
\(680\) | −114338. | −6.44804 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28383.9 | −1.59366 | ||||||||
\(683\) | −35122.3 | −1.96767 | −0.983835 | − | 0.179076i | \(-0.942689\pi\) | ||||
−0.983835 | + | 0.179076i | \(0.942689\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31753.9 | 1.77117 | ||||||||
\(686\) | 22351.3 | 1.24399 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −81777.5 | −4.53160 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29534.6 | −1.62597 | −0.812987 | − | 0.582282i | \(-0.802160\pi\) | ||||
−0.812987 | + | 0.582282i | \(0.802160\pi\) | |||||||
\(692\) | 30.4293 | 0.00167160 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 52927.1 | 2.89494 | ||||||||
\(695\) | −16321.0 | −0.890776 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28172.5 | 1.53100 | ||||||||
\(698\) | 4289.47 | 0.232606 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6118.24 | 0.330354 | ||||||||
\(701\) | 8804.19 | 0.474365 | 0.237182 | − | 0.971465i | \(-0.423776\pi\) | ||||
0.237182 | + | 0.971465i | \(0.423776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27691.8 | 1.48566 | ||||||||
\(704\) | −37775.5 | −2.02232 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38395.0 | −2.04676 | ||||||||
\(707\) | −5467.49 | −0.290843 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27138.2 | −1.43752 | −0.718758 | − | 0.695261i | \(-0.755289\pi\) | ||||
−0.718758 | + | 0.695261i | \(0.755289\pi\) | |||||||
\(710\) | −30092.5 | −1.59064 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −35095.3 | −1.84727 | ||||||||
\(713\) | 12728.3 | 0.668552 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43968.6 | −2.29495 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −37270.4 | −1.93721 | ||||||||
\(719\) | 17337.4 | 0.899274 | 0.449637 | − | 0.893211i | \(-0.351553\pi\) | ||||
0.449637 | + | 0.893211i | \(0.351553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8413.44 | −0.434581 | ||||||||
\(722\) | −27884.8 | −1.43735 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9808.20 | −0.503479 | ||||||||
\(725\) | 10165.5 | 0.520739 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25771.3 | 1.31473 | 0.657363 | − | 0.753574i | \(-0.271672\pi\) | ||||
0.657363 | + | 0.753574i | \(0.271672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7636.83 | −0.387194 | ||||||||
\(731\) | 47572.6 | 2.40703 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21784.2 | −1.09771 | −0.548853 | − | 0.835919i | \(-0.684935\pi\) | ||||
−0.548853 | + | 0.835919i | \(0.684935\pi\) | |||||||
\(734\) | 2479.59 | 0.124691 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36959.0 | 1.85099 | ||||||||
\(737\) | −24410.8 | −1.22006 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22353.8 | −1.11272 | −0.556360 | − | 0.830942i | \(-0.687802\pi\) | ||||
−0.556360 | + | 0.830942i | \(0.687802\pi\) | |||||||
\(740\) | 69539.2 | 3.45448 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2116.85 | 0.104733 | ||||||||
\(743\) | 18382.6 | 0.907662 | 0.453831 | − | 0.891088i | \(-0.350057\pi\) | ||||
0.453831 | + | 0.891088i | \(0.350057\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10220.1 | 0.502597 | ||||||||
\(746\) | −28921.5 | −1.41943 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 68546.9 | 3.35070 | ||||||||
\(749\) | −6182.74 | −0.301618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13782.8 | 0.669694 | 0.334847 | − | 0.942272i | \(-0.391315\pi\) | ||||
0.334847 | + | 0.942272i | \(0.391315\pi\) | |||||||
\(752\) | −7381.64 | −0.357953 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2115.69 | 0.101984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25639.5 | 1.23102 | 0.615510 | − | 0.788129i | \(-0.288950\pi\) | ||||
0.615510 | + | 0.788129i | \(0.288950\pi\) | |||||||
\(758\) | 46372.6 | 2.22207 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −101222. | −4.83121 | ||||||||
\(761\) | −43.4757 | −0.00207095 | −0.00103548 | − | 0.999999i | \(-0.500330\pi\) | ||||
−0.00103548 | + | 0.999999i | \(0.500330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5730.88 | −0.271916 | ||||||||
\(764\) | −102755. | −4.86588 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50378.7 | 2.37631 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20485.7 | 0.960641 | 0.480321 | − | 0.877093i | \(-0.340520\pi\) | ||||
0.480321 | + | 0.877093i | \(0.340520\pi\) | |||||||
\(770\) | −11848.8 | −0.554548 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18082.1 | 0.842992 | ||||||||
\(773\) | −29450.3 | −1.37031 | −0.685157 | − | 0.728395i | \(-0.740266\pi\) | ||||
−0.685157 | + | 0.728395i | \(0.740266\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9052.51 | −0.419582 | ||||||||
\(776\) | 13507.1 | 0.624839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −69025.0 | −3.18080 | ||||||||
\(779\) | 24940.8 | 1.14711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11205.7 | 0.513409 | ||||||||
\(782\) | −42384.5 | −1.93819 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −64249.7 | −2.92683 | ||||||||
\(785\) | 30724.1 | 1.39693 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9751.10 | −0.441664 | −0.220832 | − | 0.975312i | \(-0.570877\pi\) | ||||
−0.220832 | + | 0.975312i | \(0.570877\pi\) | |||||||
\(788\) | 33192.3 | 1.50054 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27065.1 | 1.21890 | ||||||||
\(791\) | −1695.15 | −0.0761980 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −72221.2 | −3.22800 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 66020.3 | 2.93973 | ||||||||
\(797\) | −37750.8 | −1.67779 | −0.838896 | − | 0.544291i | \(-0.816799\pi\) | ||||
−0.838896 | + | 0.544291i | \(0.816799\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4294.14 | 0.190132 | ||||||||
\(800\) | −26285.7 | −1.16167 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −34303.9 | −1.51037 | ||||||||
\(803\) | 2843.77 | 0.124975 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5313.39 | 0.232637 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 60224.2 | 2.62213 | ||||||||
\(809\) | −6999.45 | −0.304187 | −0.152094 | − | 0.988366i | \(-0.548602\pi\) | ||||
−0.152094 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35792.1 | 1.54973 | 0.774864 | − | 0.632128i | \(-0.217818\pi\) | ||||
0.774864 | + | 0.632128i | \(0.217818\pi\) | |||||||
\(812\) | 30580.6 | 1.32164 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −35705.4 | −1.53744 | ||||||||
\(815\) | 20532.1 | 0.882463 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42115.5 | 1.80347 | ||||||||
\(818\) | −28607.0 | −1.22276 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 62630.9 | 2.66727 | ||||||||
\(821\) | −9776.62 | −0.415599 | −0.207799 | − | 0.978171i | \(-0.566630\pi\) | ||||
−0.207799 | + | 0.978171i | \(0.566630\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19662.0 | 0.832777 | 0.416389 | − | 0.909187i | \(-0.363296\pi\) | ||||
0.416389 | + | 0.909187i | \(0.363296\pi\) | |||||||
\(824\) | 92673.7 | 3.91801 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2792.75 | −0.117642 | ||||||||
\(827\) | −5281.22 | −0.222063 | −0.111032 | − | 0.993817i | \(-0.535415\pi\) | ||||
−0.111032 | + | 0.993817i | \(0.535415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21735.5 | 0.910621 | 0.455310 | − | 0.890333i | \(-0.349528\pi\) | ||||
0.455310 | + | 0.890333i | \(0.349528\pi\) | |||||||
\(830\) | 6050.46 | 0.253030 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37376.1 | 1.55463 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46619.9 | 1.93215 | ||||||||
\(836\) | 60683.8 | 2.51052 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −88470.2 | −3.64696 | ||||||||
\(839\) | 28574.7 | 1.17582 | 0.587908 | − | 0.808928i | \(-0.299952\pi\) | ||||
0.587908 | + | 0.808928i | \(0.299952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26420.7 | 1.08330 | ||||||||
\(842\) | 45782.4 | 1.87383 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2605.49 | 0.106262 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4139.38 | −0.167923 | ||||||||
\(848\) | −13002.4 | −0.526540 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30144.4 | 1.21640 | ||||||||
\(851\) | 16011.4 | 0.644965 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5251.39 | −0.210791 | −0.105395 | − | 0.994430i | \(-0.533611\pi\) | ||||
−0.105395 | + | 0.994430i | \(0.533611\pi\) | |||||||
\(854\) | 906.170 | 0.0363097 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 68102.6 | 2.71927 | ||||||||
\(857\) | −34851.0 | −1.38913 | −0.694566 | − | 0.719429i | \(-0.744404\pi\) | ||||
−0.694566 | + | 0.719429i | \(0.744404\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41697.5 | 1.65623 | 0.828114 | − | 0.560559i | \(-0.189414\pi\) | ||||
0.828114 | + | 0.560559i | \(0.189414\pi\) | |||||||
\(860\) | 105760. | 4.19346 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8605.05 | 0.340010 | ||||||||
\(863\) | −28648.9 | −1.13004 | −0.565018 | − | 0.825079i | \(-0.691131\pi\) | ||||
−0.565018 | + | 0.825079i | \(0.691131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.7948 | −0.000738777 0 | ||||||||
\(866\) | 18279.0 | 0.717257 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −27232.6 | −1.06490 | ||||||||
\(869\) | −10078.4 | −0.393425 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 63125.4 | 2.45149 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37522.5 | −1.45219 | ||||||||
\(875\) | 6695.42 | 0.258682 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31516.8 | 1.21351 | 0.606754 | − | 0.794890i | \(-0.292471\pi\) | ||||
0.606754 | + | 0.794890i | \(0.292471\pi\) | |||||||
\(878\) | 38912.7 | 1.49572 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 72779.7 | 2.78796 | ||||||||
\(881\) | 31246.1 | 1.19490 | 0.597451 | − | 0.801905i | \(-0.296180\pi\) | ||||
0.597451 | + | 0.801905i | \(0.296180\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16181.8 | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 40472.8 | 1.53466 | ||||||||
\(887\) | −13289.0 | −0.503046 | −0.251523 | − | 0.967851i | \(-0.580931\pi\) | ||||
−0.251523 | + | 0.967851i | \(0.580931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9919.92 | −0.374245 | ||||||||
\(890\) | 34898.7 | 1.31439 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 52867.0 | 1.98444 | ||||||||
\(893\) | 3801.55 | 0.142457 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27157.4 | 1.01427 | ||||||||
\(896\) | −20015.6 | −0.746288 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41276.0 | −1.53385 | ||||||||
\(899\) | −45246.9 | −1.67861 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7563.94 | 0.279679 | ||||||||
\(902\) | −32158.2 | −1.18709 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18672.0 | 0.686971 | ||||||||
\(905\) | 6058.07 | 0.222516 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47128.4 | 1.72533 | 0.862664 | − | 0.505778i | \(-0.168795\pi\) | ||||
0.862664 | + | 0.505778i | \(0.168795\pi\) | |||||||
\(908\) | −12231.6 | −0.447050 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2884.69 | −0.104911 | −0.0524556 | − | 0.998623i | \(-0.516705\pi\) | ||||
−0.0524556 | + | 0.998623i | \(0.516705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2253.05 | −0.0816703 | ||||||||
\(914\) | −48572.7 | −1.75781 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16236.3 | 0.585657 | ||||||||
\(917\) | 4990.83 | 0.179729 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25752.2 | −0.924359 | −0.462179 | − | 0.886787i | \(-0.652932\pi\) | ||||
−0.462179 | + | 0.886787i | \(0.652932\pi\) | |||||||
\(920\) | −58526.8 | −2.09736 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7272.75 | −0.259778 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11387.5 | −0.404779 | ||||||||
\(926\) | −512.089 | −0.0181731 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −131383. | −4.64748 | ||||||||
\(929\) | 51394.7 | 1.81508 | 0.907539 | − | 0.419969i | \(-0.137959\pi\) | ||||
0.907539 | + | 0.419969i | \(0.137959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33088.6 | 1.16481 | ||||||||
\(932\) | 17857.4 | 0.627616 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −71716.1 | −2.51244 | ||||||||
\(935\) | −42338.3 | −1.48087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6781.86 | 0.236450 | 0.118225 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118225 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(938\) | −32293.9 | −1.12413 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9546.39 | 0.331244 | ||||||||
\(941\) | −22038.2 | −0.763470 | −0.381735 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381735 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14420.8 | 0.497991 | ||||||||
\(944\) | 17154.0 | 0.591436 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −54303.0 | −1.86633 | ||||||||
\(947\) | −45531.0 | −1.56236 | −0.781182 | − | 0.624304i | \(-0.785383\pi\) | ||||
−0.781182 | + | 0.624304i | \(0.785383\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 26686.5 | 0.911393 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 56326.3 | 1.91759 | ||||||||
\(953\) | 26541.2 | 0.902154 | 0.451077 | − | 0.892485i | \(-0.351040\pi\) | ||||
0.451077 | + | 0.892485i | \(0.351040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63466.7 | 2.15051 | ||||||||
\(956\) | 138366. | 4.68104 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20513.0 | −0.691799 | ||||||||
\(959\) | −15642.9 | −0.526731 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10502.1 | 0.352527 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −109310. | −3.65213 | ||||||||
\(965\) | −11168.5 | −0.372566 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48269.6 | −1.60522 | −0.802609 | − | 0.596506i | \(-0.796555\pi\) | ||||
−0.802609 | + | 0.596506i | \(0.796555\pi\) | |||||||
\(968\) | 45595.1 | 1.51393 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13431.4 | −0.444594 | ||||||||
\(971\) | −34161.3 | −1.12903 | −0.564515 | − | 0.825423i | \(-0.690937\pi\) | ||||
−0.564515 | + | 0.825423i | \(0.690937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8040.18 | 0.264909 | ||||||||
\(974\) | −47199.7 | −1.55275 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5566.02 | −0.182545 | ||||||||
\(977\) | 24124.2 | 0.789971 | 0.394985 | − | 0.918687i | \(-0.370750\pi\) | ||||
0.394985 | + | 0.918687i | \(0.370750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12995.4 | −0.424245 | ||||||||
\(980\) | 83091.7 | 2.70843 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −81399.1 | −2.64516 | ||||||||
\(983\) | −19023.4 | −0.617246 | −0.308623 | − | 0.951185i | \(-0.599868\pi\) | ||||
−0.308623 | + | 0.951185i | \(0.599868\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20501.3 | −0.663175 | ||||||||
\(986\) | 150670. | 4.86644 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24351.2 | 0.782936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −229.962 | −0.00737131 | −0.00368566 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368566 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(992\) | 116999. | 3.74468 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14824.4 | 0.473041 | ||||||||
\(995\) | −40777.7 | −1.29924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26991.1 | 0.857389 | 0.428694 | − | 0.903450i | \(-0.358974\pi\) | ||||
0.428694 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(998\) | 78747.2 | 2.49769 | ||||||||
\(999\) | 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 | 1521.4.a.bd.1.1 | 8 | ||
3.2 | odd | 2 | inner | 1521.4.a.bd.1.8 | 8 | ||
13.4 | even | 6 | 117.4.g.f.55.1 | ✓ | 16 | ||
13.10 | even | 6 | 117.4.g.f.100.1 | yes | 16 | ||
13.12 | even | 2 | 1521.4.a.bc.1.8 | 8 | |||
39.17 | odd | 6 | 117.4.g.f.55.8 | yes | 16 | ||
39.23 | odd | 6 | 117.4.g.f.100.8 | yes | 16 | ||
39.38 | odd | 2 | 1521.4.a.bc.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.4.g.f.55.1 | ✓ | 16 | 13.4 | even | 6 | ||
117.4.g.f.55.8 | yes | 16 | 39.17 | odd | 6 | ||
117.4.g.f.100.1 | yes | 16 | 13.10 | even | 6 | ||
117.4.g.f.100.8 | yes | 16 | 39.23 | odd | 6 | ||
1521.4.a.bc.1.1 | 8 | 39.38 | odd | 2 | |||
1521.4.a.bc.1.8 | 8 | 13.12 | even | 2 | |||
1521.4.a.bd.1.1 | 8 | 1.1 | even | 1 | trivial | ||
1521.4.a.bd.1.8 | 8 | 3.2 | odd | 2 | inner |