Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(440,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.440");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 48 x^{14} + 1647 x^{12} - 27620 x^{10} + 336765 x^{8} - 1200006 x^{6} + 3242464 x^{4} + \cdots + 810000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 440.10 | ||
Root | \(-0.648633 - 0.374489i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.440 |
Dual form | 441.4.c.a.440.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.748977i | 0.264803i | 0.991196 | + | 0.132402i | \(0.0422689\pi\) | ||||
−0.991196 | + | 0.132402i | \(0.957731\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.43903 | 0.929879 | ||||||||
\(5\) | 10.8554 | 0.970933 | 0.485466 | − | 0.874255i | \(-0.338650\pi\) | ||||
0.485466 | + | 0.874255i | \(0.338650\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 11.5635i | 0.511039i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.13042i | 0.257106i | ||||||||
\(11\) | − 51.8611i | − 1.42152i | −0.703435 | − | 0.710760i | \(-0.748351\pi\) | ||||
0.703435 | − | 0.710760i | \(-0.251649\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 32.1880i | − 0.686719i | −0.939204 | − | 0.343360i | \(-0.888435\pi\) | ||||
0.939204 | − | 0.343360i | \(-0.111565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 50.8515 | 0.794554 | ||||||||
\(17\) | 81.4649 | 1.16224 | 0.581121 | − | 0.813817i | \(-0.302614\pi\) | ||||
0.581121 | + | 0.813817i | \(0.302614\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0485737i | 0 0.000586504i | 1.00000 | 0.000293252i | \(9.33450e-5\pi\) | |||||
−1.00000 | 0.000293252i | \(0.999907\pi\) | ||||||||
\(20\) | 80.7534 | 0.902850 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 38.8428 | 0.376423 | ||||||||
\(23\) | − 89.2956i | − 0.809540i | −0.914419 | − | 0.404770i | \(-0.867352\pi\) | ||||
0.914419 | − | 0.404770i | \(-0.132648\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.16119 | −0.0572896 | ||||||||
\(26\) | 24.1081 | 0.181846 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 175.246i | − 1.12215i | −0.827766 | − | 0.561074i | \(-0.810388\pi\) | ||||
0.827766 | − | 0.561074i | \(-0.189612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 215.049i | 1.24593i | 0.782249 | + | 0.622966i | \(0.214073\pi\) | ||||
−0.782249 | + | 0.622966i | \(0.785927\pi\) | |||||||
\(32\) | 130.594i | 0.721439i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 61.0153i | 0.307766i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 64.5458 | 0.286791 | 0.143395 | − | 0.989665i | \(-0.454198\pi\) | ||||
0.143395 | + | 0.989665i | \(0.454198\pi\) | |||||||
\(38\) | −0.0363806 | −0.000155308 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 125.526i | 0.496184i | ||||||||
\(41\) | −411.485 | −1.56740 | −0.783698 | − | 0.621142i | \(-0.786669\pi\) | ||||
−0.783698 | + | 0.621142i | \(0.786669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −234.771 | −0.832611 | −0.416305 | − | 0.909225i | \(-0.636675\pi\) | ||||
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(44\) | − 385.797i | − 1.32184i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 66.8803 | 0.214369 | ||||||||
\(47\) | 632.152 | 1.96189 | 0.980946 | − | 0.194283i | \(-0.0622379\pi\) | ||||
0.980946 | + | 0.194283i | \(0.0622379\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 5.36357i | − 0.0151705i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 239.448i | − 0.638566i | ||||||||
\(53\) | − 265.638i | − 0.688456i | −0.938886 | − | 0.344228i | \(-0.888141\pi\) | ||||
0.938886 | − | 0.344228i | \(-0.111859\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 562.971i | − 1.38020i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 131.255 | 0.297149 | ||||||||
\(59\) | 351.059 | 0.774645 | 0.387322 | − | 0.921944i | \(-0.373400\pi\) | ||||
0.387322 | + | 0.921944i | \(0.373400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 778.069i | 1.63314i | 0.577247 | + | 0.816569i | \(0.304127\pi\) | ||||
−0.577247 | + | 0.816569i | \(0.695873\pi\) | |||||||
\(62\) | −161.067 | −0.329927 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 309.000 | 0.603515 | ||||||||
\(65\) | − 349.412i | − 0.666758i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −196.009 | −0.357407 | −0.178703 | − | 0.983903i | \(-0.557190\pi\) | ||||
−0.178703 | + | 0.983903i | \(0.557190\pi\) | |||||||
\(68\) | 606.020 | 1.08075 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 142.632i | 0.238412i | 0.992870 | + | 0.119206i | \(0.0380349\pi\) | ||||
−0.992870 | + | 0.119206i | \(0.961965\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 780.879i | 1.25199i | 0.779829 | + | 0.625993i | \(0.215306\pi\) | ||||
−0.779829 | + | 0.625993i | \(0.784694\pi\) | |||||||
\(74\) | 48.3433i | 0.0759432i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.361341i | 0 0.000545378i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1289.05 | 1.83582 | 0.917908 | − | 0.396794i | \(-0.129877\pi\) | ||||
0.917908 | + | 0.396794i | \(0.129877\pi\) | |||||||
\(80\) | 552.011 | 0.771459 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 308.193i | − 0.415052i | ||||||||
\(83\) | 235.123 | 0.310940 | 0.155470 | − | 0.987841i | \(-0.450311\pi\) | ||||
0.155470 | + | 0.987841i | \(0.450311\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 884.330 | 1.12846 | ||||||||
\(86\) | − 175.838i | − 0.220478i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 599.695 | 0.726452 | ||||||||
\(89\) | −670.780 | −0.798905 | −0.399453 | − | 0.916754i | \(-0.630800\pi\) | ||||
−0.399453 | + | 0.916754i | \(0.630800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 664.273i | − 0.752774i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 473.468i | 0.519515i | ||||||||
\(95\) | 0.527285i | 0 0.000569456i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 655.891i | 0.686553i | 0.939234 | + | 0.343276i | \(0.111537\pi\) | ||||
−0.939234 | + | 0.343276i | \(0.888463\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −53.2724 | −0.0532724 | ||||||||
\(101\) | 1163.24 | 1.14600 | 0.573002 | − | 0.819554i | \(-0.305779\pi\) | ||||
0.573002 | + | 0.819554i | \(0.305779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 26.4198i | − 0.0252740i | −0.999920 | − | 0.0126370i | \(-0.995977\pi\) | ||||
0.999920 | − | 0.0126370i | \(-0.00402258\pi\) | |||||||
\(104\) | 372.206 | 0.350940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 198.957 | 0.182305 | ||||||||
\(107\) | − 1467.08i | − 1.32549i | −0.748844 | − | 0.662746i | \(-0.769391\pi\) | ||||
0.748844 | − | 0.662746i | \(-0.230609\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −135.069 | −0.118690 | −0.0593450 | − | 0.998238i | \(-0.518901\pi\) | ||||
−0.0593450 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(110\) | 421.653 | 0.365482 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 288.471i | 0.240151i | 0.992765 | + | 0.120076i | \(0.0383137\pi\) | ||||
−0.992765 | + | 0.120076i | \(0.961686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 969.335i | − 0.786009i | ||||||||
\(116\) | − 1303.66i | − 1.04346i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 262.935i | 0.205129i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1358.58 | −1.02072 | ||||||||
\(122\) | −582.756 | −0.432461 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1599.75i | 1.15857i | ||||||||
\(125\) | −1434.66 | −1.02656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2269.80 | −1.58592 | −0.792961 | − | 0.609273i | \(-0.791461\pi\) | ||||
−0.792961 | + | 0.609273i | \(0.791461\pi\) | |||||||
\(128\) | 1276.19i | 0.881252i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 261.702 | 0.176560 | ||||||||
\(131\) | 389.692 | 0.259905 | 0.129952 | − | 0.991520i | \(-0.458518\pi\) | ||||
0.129952 | + | 0.991520i | \(0.458518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 146.806i | − 0.0946425i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 942.017i | 0.593951i | ||||||||
\(137\) | 1468.69i | 0.915905i | 0.888977 | + | 0.457953i | \(0.151417\pi\) | ||||
−0.888977 | + | 0.457953i | \(0.848583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 624.712i | − 0.381204i | −0.981667 | − | 0.190602i | \(-0.938956\pi\) | ||||
0.981667 | − | 0.190602i | \(-0.0610440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −106.828 | −0.0631323 | ||||||||
\(143\) | −1669.31 | −0.976185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 1902.35i | − 1.08953i | ||||||||
\(146\) | −584.860 | −0.331530 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 480.158 | 0.266681 | ||||||||
\(149\) | 1601.86i | 0.880735i | 0.897818 | + | 0.440367i | \(0.145152\pi\) | ||||
−0.897818 | + | 0.440367i | \(0.854848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 404.376 | 0.217931 | 0.108966 | − | 0.994046i | \(-0.465246\pi\) | ||||
0.108966 | + | 0.994046i | \(0.465246\pi\) | |||||||
\(152\) | −0.561681 | −0.000299726 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2334.43i | 1.20972i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2412.07i | − 1.22614i | −0.790028 | − | 0.613071i | \(-0.789934\pi\) | ||||
0.790028 | − | 0.613071i | \(-0.210066\pi\) | |||||||
\(158\) | 965.469i | 0.486130i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1417.65i | 0.700469i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −945.367 | −0.454275 | −0.227138 | − | 0.973863i | \(-0.572937\pi\) | ||||
−0.227138 | + | 0.973863i | \(0.572937\pi\) | |||||||
\(164\) | −3061.05 | −1.45749 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 176.101i | 0.0823381i | ||||||||
\(167\) | 1271.18 | 0.589022 | 0.294511 | − | 0.955648i | \(-0.404843\pi\) | ||||
0.294511 | + | 0.955648i | \(0.404843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1160.93 | 0.528417 | ||||||||
\(170\) | 662.343i | 0.298820i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1746.47 | −0.774228 | ||||||||
\(173\) | −4434.99 | −1.94905 | −0.974525 | − | 0.224278i | \(-0.927998\pi\) | ||||
−0.974525 | + | 0.224278i | \(0.927998\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 2637.22i | − 1.12947i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 502.399i | − 0.211553i | ||||||||
\(179\) | 1087.54i | 0.454114i | 0.973881 | + | 0.227057i | \(0.0729103\pi\) | ||||
−0.973881 | + | 0.227057i | \(0.927090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2916.08i | − 1.19752i | −0.800930 | − | 0.598758i | \(-0.795661\pi\) | ||||
0.800930 | − | 0.598758i | \(-0.204339\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1032.57 | 0.413706 | ||||||||
\(185\) | 700.667 | 0.278455 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4224.86i | − 1.65215i | ||||||||
\(188\) | 4702.60 | 1.82432 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.394924 | −0.000150794 0 | ||||||||
\(191\) | 4559.87i | 1.72744i | 0.503973 | + | 0.863719i | \(0.331871\pi\) | ||||
−0.503973 | + | 0.863719i | \(0.668129\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3757.20 | −1.40129 | −0.700645 | − | 0.713510i | \(-0.747104\pi\) | ||||
−0.700645 | + | 0.713510i | \(0.747104\pi\) | |||||||
\(194\) | −491.247 | −0.181802 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2014.34i | 0.728507i | 0.931300 | + | 0.364253i | \(0.118676\pi\) | ||||
−0.931300 | + | 0.364253i | \(0.881324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5118i | 0.00445698i | 0.999998 | + | 0.00222849i | \(0.000709351\pi\) | ||||
−0.999998 | + | 0.00222849i | \(0.999291\pi\) | |||||||
\(200\) | − 82.8083i | − 0.0292772i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 871.238i | 0.303466i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4466.82 | −1.52184 | ||||||||
\(206\) | 19.7878 | 0.00669263 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1636.81i | − 0.545636i | ||||||||
\(209\) | 2.51909 | 0.000833727 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2915.84 | −0.951349 | −0.475675 | − | 0.879621i | \(-0.657796\pi\) | ||||
−0.475675 | + | 0.879621i | \(0.657796\pi\) | |||||||
\(212\) | − 1976.09i | − 0.640181i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1098.81 | 0.350995 | ||||||||
\(215\) | −2548.53 | −0.808409 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 101.163i | − 0.0314295i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 4187.96i | − 1.28342i | ||||||||
\(221\) | − 2622.19i | − 0.798135i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1097.87i | 0.329681i | 0.986320 | + | 0.164841i | \(0.0527110\pi\) | ||||
−0.986320 | + | 0.164841i | \(0.947289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −216.058 | −0.0635929 | ||||||||
\(227\) | −500.594 | −0.146368 | −0.0731841 | − | 0.997318i | \(-0.523316\pi\) | ||||
−0.0731841 | + | 0.997318i | \(0.523316\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1133.53i | 0.327099i | 0.986535 | + | 0.163549i | \(0.0522943\pi\) | ||||
−0.986535 | + | 0.163549i | \(0.947706\pi\) | |||||||
\(230\) | 726.010 | 0.208138 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2026.45 | 0.573461 | ||||||||
\(233\) | 3435.37i | 0.965916i | 0.875643 | + | 0.482958i | \(0.160438\pi\) | ||||
−0.875643 | + | 0.482958i | \(0.839562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6862.24 | 1.90486 | ||||||||
\(236\) | 2611.54 | 0.720326 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2213.97i | 0.599203i | 0.954064 | + | 0.299602i | \(0.0968537\pi\) | ||||
−0.954064 | + | 0.299602i | \(0.903146\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5951.96i | 1.59087i | 0.606040 | + | 0.795435i | \(0.292757\pi\) | ||||
−0.606040 | + | 0.795435i | \(0.707243\pi\) | |||||||
\(242\) | − 1017.54i | − 0.270290i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5788.08i | 1.51862i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.56349 | 0.000402763 0 | ||||||||
\(248\) | −2486.71 | −0.636719 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1074.53i | − 0.271836i | ||||||||
\(251\) | −4889.86 | −1.22966 | −0.614831 | − | 0.788659i | \(-0.710776\pi\) | ||||
−0.614831 | + | 0.788659i | \(0.710776\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4630.97 | −1.15078 | ||||||||
\(254\) | − 1700.03i | − 0.419957i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1516.16 | 0.370156 | ||||||||
\(257\) | −3196.42 | −0.775825 | −0.387913 | − | 0.921696i | \(-0.626804\pi\) | ||||
−0.387913 | + | 0.921696i | \(0.626804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 2599.29i | − 0.620005i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 291.870i | 0.0688237i | ||||||||
\(263\) | − 748.464i | − 0.175484i | −0.996143 | − | 0.0877419i | \(-0.972035\pi\) | ||||
0.996143 | − | 0.0877419i | \(-0.0279651\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 2883.59i | − 0.668444i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1458.11 | −0.332345 | ||||||||
\(269\) | −1299.26 | −0.294487 | −0.147244 | − | 0.989100i | \(-0.547040\pi\) | ||||
−0.147244 | + | 0.989100i | \(0.547040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 83.5611i | − 0.0187305i | −0.999956 | − | 0.00936527i | \(-0.997019\pi\) | ||||
0.999956 | − | 0.00936527i | \(-0.00298110\pi\) | |||||||
\(272\) | 4142.61 | 0.923465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1100.02 | −0.242535 | ||||||||
\(275\) | 371.388i | 0.0814382i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4641.86 | −1.00687 | −0.503434 | − | 0.864034i | \(-0.667930\pi\) | ||||
−0.503434 | + | 0.864034i | \(0.667930\pi\) | |||||||
\(278\) | 467.895 | 0.100944 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 179.289i | − 0.0380622i | −0.999819 | − | 0.0190311i | \(-0.993942\pi\) | ||||
0.999819 | − | 0.0190311i | \(-0.00605816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 4048.54i | − 0.850391i | −0.905101 | − | 0.425196i | \(-0.860205\pi\) | ||||
0.905101 | − | 0.425196i | \(-0.139795\pi\) | |||||||
\(284\) | 1061.04i | 0.221694i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 1250.27i | − 0.258497i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1723.52 | 0.350808 | ||||||||
\(290\) | 1424.82 | 0.288511 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5808.98i | 1.16420i | ||||||||
\(293\) | −3389.52 | −0.675828 | −0.337914 | − | 0.941177i | \(-0.609721\pi\) | ||||
−0.337914 | + | 0.941177i | \(0.609721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3810.88 | 0.752128 | ||||||||
\(296\) | 746.374i | 0.146561i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1199.76 | −0.233222 | ||||||||
\(299\) | −2874.25 | −0.555927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 302.868i | 0.0577089i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.47004i | 0 0.000466009i | ||||||||
\(305\) | 8446.21i | 1.58567i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2014.64i | 0.374534i | 0.982309 | + | 0.187267i | \(0.0599629\pi\) | ||||
−0.982309 | + | 0.187267i | \(0.940037\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1748.44 | −0.320337 | ||||||||
\(311\) | 5844.02 | 1.06554 | 0.532772 | − | 0.846259i | \(-0.321150\pi\) | ||||
0.532772 | + | 0.846259i | \(0.321150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2449.45i | − 0.442336i | −0.975236 | − | 0.221168i | \(-0.929013\pi\) | ||||
0.975236 | − | 0.221168i | \(-0.0709870\pi\) | |||||||
\(314\) | 1806.59 | 0.324686 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9589.28 | 1.70709 | ||||||||
\(317\) | − 6123.66i | − 1.08498i | −0.840062 | − | 0.542490i | \(-0.817481\pi\) | ||||
0.840062 | − | 0.542490i | \(-0.182519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9088.44 | −1.59516 | ||||||||
\(320\) | 3354.30 | 0.585972 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.95705i | 0 0.000681660i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 230.505i | 0.0393418i | ||||||||
\(326\) | − 708.059i | − 0.120294i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 4758.20i | − 0.801000i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7597.04 | 1.26154 | 0.630772 | − | 0.775968i | \(-0.282738\pi\) | ||||
0.630772 | + | 0.775968i | \(0.282738\pi\) | |||||||
\(332\) | 1749.08 | 0.289137 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 952.083i | 0.155975i | ||||||||
\(335\) | −2127.74 | −0.347018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3863.22 | −0.624460 | −0.312230 | − | 0.950007i | \(-0.601076\pi\) | ||||
−0.312230 | + | 0.950007i | \(0.601076\pi\) | |||||||
\(338\) | 869.511i | 0.139927i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6578.56 | 1.04933 | ||||||||
\(341\) | 11152.7 | 1.77112 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 2714.77i | − 0.425496i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 3321.70i | − 0.516115i | ||||||||
\(347\) | − 1824.41i | − 0.282246i | −0.989992 | − | 0.141123i | \(-0.954929\pi\) | ||||
0.989992 | − | 0.141123i | \(-0.0450713\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 1537.52i | − 0.235822i | −0.993024 | − | 0.117911i | \(-0.962380\pi\) | ||||
0.993024 | − | 0.117911i | \(-0.0376197\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6772.78 | 1.02554 | ||||||||
\(353\) | −5927.33 | −0.893711 | −0.446855 | − | 0.894606i | \(-0.647456\pi\) | ||||
−0.446855 | + | 0.894606i | \(0.647456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1548.32i | 0.231482i | ||||||||
\(356\) | −4989.96 | −0.742885 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −814.541 | −0.120251 | ||||||||
\(359\) | − 4839.49i | − 0.711472i | −0.934587 | − | 0.355736i | \(-0.884230\pi\) | ||||
0.934587 | − | 0.355736i | \(-0.115770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6859.00 | 1.00000 | ||||||||
\(362\) | 2184.08 | 0.317106 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8476.72i | 1.21559i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11509.1i | 1.63698i | 0.574519 | + | 0.818491i | \(0.305189\pi\) | ||||
−0.574519 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(368\) | − 4540.81i | − 0.643223i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 524.784i | 0.0737357i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 187.497 | 0.0260275 | 0.0130137 | − | 0.999915i | \(-0.495857\pi\) | ||||
0.0130137 | + | 0.999915i | \(0.495857\pi\) | |||||||
\(374\) | 3164.32 | 0.437495 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7309.88i | 1.00260i | ||||||||
\(377\) | −5640.81 | −0.770601 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3515.82 | 0.476506 | 0.238253 | − | 0.971203i | \(-0.423425\pi\) | ||||
0.238253 | + | 0.971203i | \(0.423425\pi\) | |||||||
\(380\) | 3.92249i | 0 0.000529525i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3415.24 | −0.457432 | ||||||||
\(383\) | 2029.38 | 0.270748 | 0.135374 | − | 0.990795i | \(-0.456776\pi\) | ||||
0.135374 | + | 0.990795i | \(0.456776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 2814.06i | − 0.371067i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4879.19i | 0.638411i | ||||||||
\(389\) | − 6439.94i | − 0.839378i | −0.907668 | − | 0.419689i | \(-0.862139\pi\) | ||||
0.907668 | − | 0.419689i | \(-0.137861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 7274.45i | − 0.940882i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1508.70 | −0.192911 | ||||||||
\(395\) | 13993.1 | 1.78245 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9664.61i | 1.22180i | 0.791709 | + | 0.610898i | \(0.209191\pi\) | ||||
−0.791709 | + | 0.610898i | \(0.790809\pi\) | |||||||
\(398\) | −9.37106 | −0.00118022 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −364.157 | −0.0455197 | ||||||||
\(401\) | − 11762.8i | − 1.46485i | −0.680846 | − | 0.732426i | \(-0.738388\pi\) | ||||
0.680846 | − | 0.732426i | \(-0.261612\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6921.99 | 0.855606 | ||||||||
\(404\) | 8653.36 | 1.06565 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 3347.42i | − 0.407679i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 5272.03i | − 0.637371i | −0.947860 | − | 0.318686i | \(-0.896759\pi\) | ||||
0.947860 | − | 0.318686i | \(-0.103241\pi\) | |||||||
\(410\) | − 3345.55i | − 0.402987i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 196.538i | − 0.0235017i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2552.34 | 0.301902 | ||||||||
\(416\) | 4203.58 | 0.495426 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.88674i | 0 0.000220774i | ||||||||
\(419\) | 5103.18 | 0.595003 | 0.297502 | − | 0.954721i | \(-0.403847\pi\) | ||||
0.297502 | + | 0.954721i | \(0.403847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8395.31 | −0.971882 | −0.485941 | − | 0.873992i | \(-0.661523\pi\) | ||||
−0.485941 | + | 0.873992i | \(0.661523\pi\) | |||||||
\(422\) | − 2183.90i | − 0.251921i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3071.70 | 0.351827 | ||||||||
\(425\) | −583.386 | −0.0665844 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 10913.6i | − 1.23255i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 1908.79i | − 0.214070i | ||||||||
\(431\) | − 2088.48i | − 0.233408i | −0.993167 | − | 0.116704i | \(-0.962767\pi\) | ||||
0.993167 | − | 0.116704i | \(-0.0372329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11495.3i | 1.27582i | 0.770111 | + | 0.637910i | \(0.220201\pi\) | ||||
−0.770111 | + | 0.637910i | \(0.779799\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1004.78 | −0.110367 | ||||||||
\(437\) | 4.33742 | 0.000474798 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 4252.70i | − 0.462347i | −0.972913 | − | 0.231173i | \(-0.925744\pi\) | ||||
0.972913 | − | 0.231173i | \(-0.0742565\pi\) | |||||||
\(440\) | 6509.91 | 0.705336 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1963.96 | 0.211349 | ||||||||
\(443\) | − 3304.79i | − 0.354437i | −0.984172 | − | 0.177218i | \(-0.943290\pi\) | ||||
0.984172 | − | 0.177218i | \(-0.0567098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7281.56 | −0.775683 | ||||||||
\(446\) | −822.280 | −0.0873007 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 6952.63i | − 0.730768i | −0.930857 | − | 0.365384i | \(-0.880938\pi\) | ||||
0.930857 | − | 0.365384i | \(-0.119062\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21340.1i | 2.22808i | ||||||||
\(452\) | 2145.95i | 0.223312i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 374.933i | − 0.0387588i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9741.14 | 0.997093 | 0.498546 | − | 0.866863i | \(-0.333867\pi\) | ||||
0.498546 | + | 0.866863i | \(0.333867\pi\) | |||||||
\(458\) | −848.987 | −0.0866169 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 7210.92i | − 0.730893i | ||||||||
\(461\) | −5563.15 | −0.562043 | −0.281021 | − | 0.959702i | \(-0.590673\pi\) | ||||
−0.281021 | + | 0.959702i | \(0.590673\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4114.02 | 0.412948 | 0.206474 | − | 0.978452i | \(-0.433801\pi\) | ||||
0.206474 | + | 0.978452i | \(0.433801\pi\) | |||||||
\(464\) | − 8911.50i | − 0.891608i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2573.01 | −0.255778 | ||||||||
\(467\) | −6061.59 | −0.600636 | −0.300318 | − | 0.953839i | \(-0.597093\pi\) | ||||
−0.300318 | + | 0.953839i | \(0.597093\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5139.66i | 0.504415i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4059.47i | 0.395873i | ||||||||
\(473\) | 12175.5i | 1.18357i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.347846i | 0 3.36005e-5i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1658.21 | −0.158671 | ||||||||
\(479\) | 8246.66 | 0.786638 | 0.393319 | − | 0.919402i | \(-0.371327\pi\) | ||||
0.393319 | + | 0.919402i | \(0.371327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 2077.60i | − 0.196945i | ||||||||
\(482\) | −4457.88 | −0.421268 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10106.5 | −0.949145 | ||||||||
\(485\) | 7119.93i | 0.666597i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11744.2 | 1.09277 | 0.546385 | − | 0.837534i | \(-0.316004\pi\) | ||||
0.546385 | + | 0.837534i | \(0.316004\pi\) | |||||||
\(488\) | −8997.18 | −0.834597 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 6008.34i | − 0.552246i | −0.961122 | − | 0.276123i | \(-0.910950\pi\) | ||||
0.961122 | − | 0.276123i | \(-0.0890497\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 14276.4i | − 1.30421i | ||||||||
\(494\) | 1.17102i | 0 0.000106653i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10935.5i | 0.989961i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13649.9 | −1.22455 | −0.612276 | − | 0.790644i | \(-0.709746\pi\) | ||||
−0.612276 | + | 0.790644i | \(0.709746\pi\) | |||||||
\(500\) | −10672.5 | −0.954574 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 3662.39i | − 0.325619i | ||||||||
\(503\) | 4862.69 | 0.431047 | 0.215524 | − | 0.976499i | \(-0.430854\pi\) | ||||
0.215524 | + | 0.976499i | \(0.430854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12627.4 | 1.11269 | ||||||||
\(506\) | − 3468.49i | − 0.304730i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −16885.1 | −1.47472 | ||||||||
\(509\) | 17722.7 | 1.54331 | 0.771653 | − | 0.636043i | \(-0.219430\pi\) | ||||
0.771653 | + | 0.636043i | \(0.219430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11345.1i | 0.979271i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 2394.04i | − 0.205441i | ||||||||
\(515\) | − 286.796i | − 0.0245393i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 32784.1i | − 2.78887i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4040.43 | 0.340739 | ||||||||
\(521\) | −13755.9 | −1.15673 | −0.578366 | − | 0.815777i | \(-0.696309\pi\) | ||||
−0.578366 | + | 0.815777i | \(0.696309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1311.94i | − 0.109689i | −0.998495 | − | 0.0548443i | \(-0.982534\pi\) | ||||
0.998495 | − | 0.0548443i | \(-0.0174663\pi\) | |||||||
\(524\) | 2898.93 | 0.241680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 560.582 | 0.0464687 | ||||||||
\(527\) | 17518.9i | 1.44808i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4193.30 | 0.344645 | ||||||||
\(530\) | 2159.75 | 0.177006 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13244.9i | 1.07636i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 15925.6i | − 1.28696i | ||||||||
\(536\) | − 2266.54i | − 0.182649i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 973.114i | − 0.0779812i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1195.91 | 0.0950389 | 0.0475195 | − | 0.998870i | \(-0.484868\pi\) | ||||
0.0475195 | + | 0.998870i | \(0.484868\pi\) | |||||||
\(542\) | 62.5854 | 0.00495991 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10638.9i | 0.838488i | ||||||||
\(545\) | −1466.22 | −0.115240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6178.59 | −0.482957 | −0.241478 | − | 0.970406i | \(-0.577632\pi\) | ||||
−0.241478 | + | 0.970406i | \(0.577632\pi\) | |||||||
\(548\) | 10925.7i | 0.851681i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −278.161 | −0.0215651 | ||||||||
\(551\) | 8.51233 | 0.000658144 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 3476.65i | − 0.266622i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 4647.26i | − 0.354474i | ||||||||
\(557\) | − 3356.20i | − 0.255309i | −0.991819 | − | 0.127654i | \(-0.959255\pi\) | ||||
0.991819 | − | 0.127654i | \(-0.0407448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7556.82i | 0.571770i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 134.283 | 0.0100790 | ||||||||
\(563\) | −3585.28 | −0.268386 | −0.134193 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134193 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3131.46i | 0.233171i | ||||||||
\(566\) | 3032.26 | 0.225187 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1649.32 | −0.121838 | ||||||||
\(569\) | 18285.7i | 1.34723i | 0.739081 | + | 0.673617i | \(0.235260\pi\) | ||||
−0.739081 | + | 0.673617i | \(0.764740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16363.0 | −1.19925 | −0.599624 | − | 0.800282i | \(-0.704683\pi\) | ||||
−0.599624 | + | 0.800282i | \(0.704683\pi\) | |||||||
\(572\) | −12418.0 | −0.907734 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 639.463i | 0.0463782i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 7711.39i | − 0.556376i | −0.960527 | − | 0.278188i | \(-0.910266\pi\) | ||||
0.960527 | − | 0.278188i | \(-0.0897339\pi\) | |||||||
\(578\) | 1290.88i | 0.0928953i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 14151.7i | − 1.01313i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13776.3 | −0.978653 | ||||||||
\(584\) | −9029.68 | −0.639813 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 2538.67i | − 0.178962i | ||||||||
\(587\) | −4182.21 | −0.294069 | −0.147034 | − | 0.989131i | \(-0.546973\pi\) | ||||
−0.147034 | + | 0.989131i | \(0.546973\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4457 | −0.000730744 0 | ||||||||
\(590\) | 2854.26i | 0.199166i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3282.25 | 0.227871 | ||||||||
\(593\) | −16189.3 | −1.12110 | −0.560552 | − | 0.828119i | \(-0.689411\pi\) | ||||
−0.560552 | + | 0.828119i | \(0.689411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11916.3i | 0.818977i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 2152.75i | − 0.147211i | ||||||||
\(599\) | − 12777.3i | − 0.871566i | −0.900052 | − | 0.435783i | \(-0.856471\pi\) | ||||
0.900052 | − | 0.435783i | \(-0.143529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24022.7i | 1.63046i | 0.579137 | + | 0.815231i | \(0.303390\pi\) | ||||
−0.579137 | + | 0.815231i | \(0.696610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3008.16 | 0.202650 | ||||||||
\(605\) | −14747.8 | −0.991050 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 9666.83i | − 0.646400i | −0.946331 | − | 0.323200i | \(-0.895241\pi\) | ||||
0.946331 | − | 0.323200i | \(-0.104759\pi\) | |||||||
\(608\) | −6.34346 | −0.000423127 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6326.02 | −0.419890 | ||||||||
\(611\) | − 20347.7i | − 1.34727i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14385.5 | 0.947836 | 0.473918 | − | 0.880569i | \(-0.342839\pi\) | ||||
0.473918 | + | 0.880569i | \(0.342839\pi\) | |||||||
\(614\) | −1508.92 | −0.0991778 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7712.69i | 0.503244i | 0.967826 | + | 0.251622i | \(0.0809639\pi\) | ||||
−0.967826 | + | 0.251622i | \(0.919036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14317.0i | 0.929645i | 0.885404 | + | 0.464822i | \(0.153882\pi\) | ||||
−0.885404 | + | 0.464822i | \(0.846118\pi\) | |||||||
\(620\) | 17365.9i | 1.12489i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4377.04i | 0.282160i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14678.6 | −0.939428 | ||||||||
\(626\) | 1834.58 | 0.117132 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 17943.5i | − 1.14016i | ||||||||
\(629\) | 5258.21 | 0.333320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4971.96 | 0.313678 | 0.156839 | − | 0.987624i | \(-0.449870\pi\) | ||||
0.156839 | + | 0.987624i | \(0.449870\pi\) | |||||||
\(632\) | 14905.9i | 0.938172i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4586.48 | 0.287307 | ||||||||
\(635\) | −24639.5 | −1.53982 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 6807.03i | − 0.422403i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13853.5i | 0.855637i | ||||||||
\(641\) | 29423.8i | 1.81306i | 0.422145 | + | 0.906529i | \(0.361277\pi\) | ||||
−0.422145 | + | 0.906529i | \(0.638723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31273.9i | 1.91807i | 0.283283 | + | 0.959036i | \(0.408576\pi\) | ||||
−0.283283 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.96374 | −0.000180506 0 | ||||||||
\(647\) | 8011.64 | 0.486816 | 0.243408 | − | 0.969924i | \(-0.421735\pi\) | ||||
0.243408 | + | 0.969924i | \(0.421735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 18206.3i | − 1.10117i | ||||||||
\(650\) | −172.643 | −0.0104179 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7032.62 | −0.422421 | ||||||||
\(653\) | 15440.6i | 0.925327i | 0.886534 | + | 0.462664i | \(0.153106\pi\) | ||||
−0.886534 | + | 0.462664i | \(0.846894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4230.24 | 0.252350 | ||||||||
\(656\) | −20924.6 | −1.24538 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 31288.9i | − 1.84953i | −0.380537 | − | 0.924766i | \(-0.624261\pi\) | ||||
0.380537 | − | 0.924766i | \(-0.375739\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 30326.1i | − 1.78449i | −0.451550 | − | 0.892246i | \(-0.649129\pi\) | ||||
0.451550 | − | 0.892246i | \(-0.350871\pi\) | |||||||
\(662\) | 5690.01i | 0.334061i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2718.84i | 0.158903i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15648.7 | −0.908424 | ||||||||
\(668\) | 9456.33 | 0.547719 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1593.63i | − 0.0918915i | ||||||||
\(671\) | 40351.5 | 2.32154 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12067.9 | 0.691207 | 0.345604 | − | 0.938381i | \(-0.387674\pi\) | ||||
0.345604 | + | 0.938381i | \(0.387674\pi\) | |||||||
\(674\) | − 2893.46i | − 0.165359i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8636.21 | 0.491364 | ||||||||
\(677\) | 6544.82 | 0.371548 | 0.185774 | − | 0.982593i | \(-0.440521\pi\) | ||||
0.185774 | + | 0.982593i | \(0.440521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10225.9i | 0.576686i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8353.10i | 0.468998i | ||||||||
\(683\) | − 31485.3i | − 1.76391i | −0.471332 | − | 0.881956i | \(-0.656227\pi\) | ||||
0.471332 | − | 0.881956i | \(-0.343773\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15943.2i | 0.889282i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11938.5 | −0.661555 | ||||||||
\(689\) | −8550.35 | −0.472776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10035.3i | 0.552476i | 0.961089 | + | 0.276238i | \(0.0890879\pi\) | ||||
−0.961089 | + | 0.276238i | \(0.910912\pi\) | |||||||
\(692\) | −32992.0 | −1.81238 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1366.44 | 0.0747397 | ||||||||
\(695\) | − 6781.48i | − 0.370124i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33521.6 | −1.82169 | ||||||||
\(698\) | 1151.57 | 0.0624464 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 768.196i | − 0.0413900i | −0.999786 | − | 0.0206950i | \(-0.993412\pi\) | ||||
0.999786 | − | 0.0206950i | \(-0.00658789\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.13523i | 0 0.000168204i | ||||||||
\(704\) | − 16025.1i | − 0.857908i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 4439.43i | − 0.236658i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13968.6 | 0.739918 | 0.369959 | − | 0.929048i | \(-0.379372\pi\) | ||||
0.369959 | + | 0.929048i | \(0.379372\pi\) | |||||||
\(710\) | −1159.65 | −0.0612973 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 7756.56i | − 0.408271i | ||||||||
\(713\) | 19202.9 | 1.00863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18120.9 | −0.947810 | ||||||||
\(716\) | 8090.23i | 0.422271i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3624.67 | 0.188400 | ||||||||
\(719\) | −11969.6 | −0.620847 | −0.310424 | − | 0.950598i | \(-0.600471\pi\) | ||||
−0.310424 | + | 0.950598i | \(0.600471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5137.23i | 0.264803i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 21692.8i | − 1.11354i | ||||||||
\(725\) | 1254.97i | 0.0642874i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 12223.3i | − 0.623575i | −0.950152 | − | 0.311787i | \(-0.899072\pi\) | ||||
0.950152 | − | 0.311787i | \(-0.100928\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6348.87 | −0.321893 | ||||||||
\(731\) | −19125.6 | −0.967696 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23785.0i | 1.19853i | 0.800552 | + | 0.599264i | \(0.204540\pi\) | ||||
−0.800552 | + | 0.599264i | \(0.795460\pi\) | |||||||
\(734\) | −8620.09 | −0.433478 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11661.5 | 0.584034 | ||||||||
\(737\) | 10165.2i | 0.508061i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11478.1 | 0.571351 | 0.285675 | − | 0.958326i | \(-0.407782\pi\) | ||||
0.285675 | + | 0.958326i | \(0.407782\pi\) | |||||||
\(740\) | 5212.29 | 0.258929 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18604.0i | 0.918593i | 0.888283 | + | 0.459297i | \(0.151899\pi\) | ||||
−0.888283 | + | 0.459297i | \(0.848101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17388.8i | 0.855134i | ||||||||
\(746\) | 140.431i | 0.00689217i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 31428.9i | − 1.53630i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31012.5 | 1.50687 | 0.753436 | − | 0.657522i | \(-0.228395\pi\) | ||||
0.753436 | + | 0.657522i | \(0.228395\pi\) | |||||||
\(752\) | 32145.9 | 1.55883 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 4224.84i | − 0.204058i | ||||||||
\(755\) | 4389.64 | 0.211597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19065.9 | −0.915407 | −0.457703 | − | 0.889105i | \(-0.651328\pi\) | ||||
−0.457703 | + | 0.889105i | \(0.651328\pi\) | |||||||
\(758\) | 2633.27i | 0.126180i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.09725 | −0.000291014 0 | ||||||||
\(761\) | 14679.2 | 0.699236 | 0.349618 | − | 0.936892i | \(-0.386311\pi\) | ||||
0.349618 | + | 0.936892i | \(0.386311\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 33921.0i | 1.60631i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1519.96i | 0.0716949i | ||||||||
\(767\) | − 11299.9i | − 0.531963i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 29972.5i | − 1.40551i | −0.711434 | − | 0.702753i | \(-0.751954\pi\) | ||||
0.711434 | − | 0.702753i | \(-0.248046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −27949.9 | −1.30303 | ||||||||
\(773\) | −22687.8 | −1.05566 | −0.527828 | − | 0.849351i | \(-0.676993\pi\) | ||||
−0.527828 | + | 0.849351i | \(0.676993\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1540.01i | − 0.0713789i | ||||||||
\(776\) | −7584.38 | −0.350855 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4823.37 | 0.222270 | ||||||||
\(779\) | − 19.9874i | 0 0.000919284i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7397.04 | 0.338908 | ||||||||
\(782\) | 5448.40 | 0.249149 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 26183.9i | − 1.19050i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 20937.9i | − 0.948357i | −0.880429 | − | 0.474178i | \(-0.842745\pi\) | ||||
0.880429 | − | 0.474178i | \(-0.157255\pi\) | |||||||
\(788\) | 14984.7i | 0.677423i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10480.5i | 0.472000i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25044.5 | 1.12151 | ||||||||
\(794\) | −7238.57 | −0.323536 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 93.0758i | 0.00414445i | ||||||||
\(797\) | −27393.4 | −1.21747 | −0.608735 | − | 0.793373i | \(-0.708323\pi\) | ||||
−0.608735 | + | 0.793373i | \(0.708323\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51498.2 | 2.28019 | ||||||||
\(800\) | − 935.212i | − 0.0413309i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8810.06 | 0.387898 | ||||||||
\(803\) | 40497.3 | 1.77972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5184.41i | 0.226567i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13451.1i | 0.585652i | ||||||||
\(809\) | 26805.4i | 1.16493i | 0.812856 | + | 0.582465i | \(0.197912\pi\) | ||||
−0.812856 | + | 0.582465i | \(0.802088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17139.6i | 0.742113i | 0.928610 | + | 0.371056i | \(0.121004\pi\) | ||||
−0.928610 | + | 0.371056i | \(0.878996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2507.14 | 0.107955 | ||||||||
\(815\) | −10262.3 | −0.441071 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 11.4037i | 0 0.000488329i | ||||||||
\(818\) | 3948.63 | 0.168778 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33228.8 | −1.41512 | ||||||||
\(821\) | − 8629.28i | − 0.366826i | −0.983036 | − | 0.183413i | \(-0.941285\pi\) | ||||
0.983036 | − | 0.183413i | \(-0.0587145\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5284.96 | −0.223842 | −0.111921 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111921 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(824\) | 305.505 | 0.0129160 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1845.35i | 0.0775926i | 0.999247 | + | 0.0387963i | \(0.0123523\pi\) | ||||
−0.999247 | + | 0.0387963i | \(0.987648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19493.2i | 0.816677i | 0.912831 | + | 0.408339i | \(0.133892\pi\) | ||||
−0.912831 | + | 0.408339i | \(0.866108\pi\) | |||||||
\(830\) | 1911.64i | 0.0799447i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 9946.08i | − 0.414445i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13799.1 | 0.571901 | ||||||||
\(836\) | 18.7396 | 0.000775265 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3822.16i | 0.157559i | ||||||||
\(839\) | 27816.7 | 1.14462 | 0.572312 | − | 0.820036i | \(-0.306047\pi\) | ||||
0.572312 | + | 0.820036i | \(0.306047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6322.03 | −0.259217 | ||||||||
\(842\) | − 6287.90i | − 0.257358i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21691.0 | −0.884640 | ||||||||
\(845\) | 12602.3 | 0.513057 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 13508.1i | − 0.547015i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 436.942i | − 0.0176318i | ||||||||
\(851\) | − 5763.65i | − 0.232168i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 9210.41i | − 0.369705i | −0.982766 | − | 0.184852i | \(-0.940819\pi\) | ||||
0.982766 | − | 0.184852i | \(-0.0591807\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16964.5 | 0.677377 | ||||||||
\(857\) | 34500.9 | 1.37518 | 0.687589 | − | 0.726100i | \(-0.258669\pi\) | ||||
0.687589 | + | 0.726100i | \(0.258669\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43698.0i | 1.73569i | 0.496836 | + | 0.867845i | \(0.334495\pi\) | ||||
−0.496836 | + | 0.867845i | \(0.665505\pi\) | |||||||
\(860\) | −18958.6 | −0.751723 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1564.23 | 0.0618072 | ||||||||
\(863\) | − 28333.6i | − 1.11760i | −0.829303 | − | 0.558800i | \(-0.811262\pi\) | ||||
0.829303 | − | 0.558800i | \(-0.188738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48143.4 | −1.89240 | ||||||||
\(866\) | −8609.73 | −0.337841 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 66851.6i | − 2.60965i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6309.13i | 0.245438i | ||||||||
\(872\) | − 1561.86i | − 0.0606552i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.24863i | 0 0.000125728i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45125.8 | −1.73750 | −0.868751 | − | 0.495249i | \(-0.835077\pi\) | ||||
−0.868751 | + | 0.495249i | \(0.835077\pi\) | |||||||
\(878\) | 3185.17 | 0.122431 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 28627.9i | − 1.09664i | ||||||||
\(881\) | −4244.09 | −0.162301 | −0.0811504 | − | 0.996702i | \(-0.525859\pi\) | ||||
−0.0811504 | + | 0.996702i | \(0.525859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.9077 | −0.000834939 0 | −0.000417470 | − | 1.00000i | \(-0.500133\pi\) | ||||
−0.000417470 | 1.00000i | \(0.500133\pi\) | ||||||||
\(884\) | − 19506.6i | − 0.742169i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2475.21 | 0.0938560 | ||||||||
\(887\) | −7501.63 | −0.283969 | −0.141984 | − | 0.989869i | \(-0.545348\pi\) | ||||
−0.141984 | + | 0.989869i | \(0.545348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 5453.72i | − 0.205404i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8167.10i | 0.306564i | ||||||||
\(893\) | 30.7060i | 0.00115066i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11805.6i | 0.440914i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5207.36 | 0.193510 | ||||||||
\(899\) | 37686.4 | 1.39812 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 21640.1i | − 0.800153i | ||||||||
\(902\) | −15983.2 | −0.590004 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3335.73 | −0.122727 | ||||||||
\(905\) | − 31655.1i | − 1.16271i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41137.3 | 1.50600 | 0.753001 | − | 0.658020i | \(-0.228606\pi\) | ||||
0.753001 | + | 0.658020i | \(0.228606\pi\) | |||||||
\(908\) | −3723.94 | −0.136105 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14080.6i | 0.512086i | 0.966665 | + | 0.256043i | \(0.0824189\pi\) | ||||
−0.966665 | + | 0.256043i | \(0.917581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 12193.7i | − 0.442008i | ||||||||
\(914\) | 7295.89i | 0.264034i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8432.35i | 0.304162i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12623.2 | 0.453101 | 0.226550 | − | 0.973999i | \(-0.427255\pi\) | ||||
0.226550 | + | 0.973999i | \(0.427255\pi\) | |||||||
\(920\) | 11208.9 | 0.401681 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 4166.67i | − 0.148831i | ||||||||
\(923\) | 4591.03 | 0.163722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −462.225 | −0.0164301 | ||||||||
\(926\) | 3081.31i | 0.109350i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22886.1 | 0.809562 | ||||||||
\(929\) | 33473.7 | 1.18217 | 0.591085 | − | 0.806609i | \(-0.298700\pi\) | ||||
0.591085 | + | 0.806609i | \(0.298700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25555.8i | 0.898186i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 4539.99i | − 0.159050i | ||||||||
\(935\) | − 45862.4i | − 1.60413i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 25652.3i | − 0.894371i | −0.894441 | − | 0.447185i | \(-0.852426\pi\) | ||||
0.894441 | − | 0.447185i | \(-0.147574\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 51048.4 | 1.77129 | ||||||||
\(941\) | −2602.96 | −0.0901744 | −0.0450872 | − | 0.998983i | \(-0.514357\pi\) | ||||
−0.0450872 | + | 0.998983i | \(0.514357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36743.8i | 1.26887i | ||||||||
\(944\) | 17851.9 | 0.615497 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9119.17 | −0.313414 | ||||||||
\(947\) | − 37616.8i | − 1.29079i | −0.763847 | − | 0.645397i | \(-0.776692\pi\) | ||||
0.763847 | − | 0.645397i | \(-0.223308\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25134.9 | 0.859763 | ||||||||
\(950\) | 0.260528 | 8.89754e−6 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 23444.5i | − 0.796896i | −0.917191 | − | 0.398448i | \(-0.869549\pi\) | ||||
0.917191 | − | 0.398448i | \(-0.130451\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49499.1i | 1.67723i | ||||||||
\(956\) | 16469.8i | 0.557187i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6176.56i | 0.208304i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16455.0 | −0.552347 | ||||||||
\(962\) | 1556.07 | 0.0521516 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 44276.8i | 1.47932i | ||||||||
\(965\) | −40785.7 | −1.36056 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4312.24 | 0.143405 | 0.0717023 | − | 0.997426i | \(-0.477157\pi\) | ||||
0.0717023 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(968\) | − 15709.9i | − 0.521627i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5332.66 | −0.176517 | ||||||||
\(971\) | 47052.7 | 1.55509 | 0.777545 | − | 0.628827i | \(-0.216465\pi\) | ||||
0.777545 | + | 0.628827i | \(0.216465\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8796.11i | 0.289369i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39565.9i | 1.29762i | ||||||||
\(977\) | − 20463.0i | − 0.670082i | −0.942204 | − | 0.335041i | \(-0.891250\pi\) | ||||
0.942204 | − | 0.335041i | \(-0.108750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34787.4i | 1.13566i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4500.11 | 0.146237 | ||||||||
\(983\) | 44629.0 | 1.44806 | 0.724031 | − | 0.689767i | \(-0.242287\pi\) | ||||
0.724031 | + | 0.689767i | \(0.242287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21866.4i | 0.707331i | ||||||||
\(986\) | 10692.7 | 0.345359 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.6309 | 0.000374521 0 | ||||||||
\(989\) | 20964.0i | 0.674032i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43131.0 | 1.38254 | 0.691272 | − | 0.722594i | \(-0.257051\pi\) | ||||
0.691272 | + | 0.722594i | \(0.257051\pi\) | |||||||
\(992\) | −28084.2 | −0.898864 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 135.820i | 0.00432743i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3622.25i | 0.115063i | 0.998344 | + | 0.0575315i | \(0.0183230\pi\) | ||||
−0.998344 | + | 0.0575315i | \(0.981677\pi\) | |||||||
\(998\) | − 10223.4i | − 0.324266i | ||||||||
\(999\) | 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 | 441.4.c.a.440.10 | 16 | ||
3.2 | odd | 2 | inner | 441.4.c.a.440.7 | 16 | ||
7.2 | even | 3 | 441.4.p.c.80.5 | 16 | |||
7.3 | odd | 6 | 441.4.p.c.215.4 | 16 | |||
7.4 | even | 3 | 63.4.p.a.26.4 | yes | 16 | ||
7.5 | odd | 6 | 63.4.p.a.17.5 | yes | 16 | ||
7.6 | odd | 2 | inner | 441.4.c.a.440.9 | 16 | ||
21.2 | odd | 6 | 441.4.p.c.80.4 | 16 | |||
21.5 | even | 6 | 63.4.p.a.17.4 | ✓ | 16 | ||
21.11 | odd | 6 | 63.4.p.a.26.5 | yes | 16 | ||
21.17 | even | 6 | 441.4.p.c.215.5 | 16 | |||
21.20 | even | 2 | inner | 441.4.c.a.440.8 | 16 | ||
28.11 | odd | 6 | 1008.4.bt.a.593.3 | 16 | |||
28.19 | even | 6 | 1008.4.bt.a.17.6 | 16 | |||
84.11 | even | 6 | 1008.4.bt.a.593.6 | 16 | |||
84.47 | odd | 6 | 1008.4.bt.a.17.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.p.a.17.4 | ✓ | 16 | 21.5 | even | 6 | ||
63.4.p.a.17.5 | yes | 16 | 7.5 | odd | 6 | ||
63.4.p.a.26.4 | yes | 16 | 7.4 | even | 3 | ||
63.4.p.a.26.5 | yes | 16 | 21.11 | odd | 6 | ||
441.4.c.a.440.7 | 16 | 3.2 | odd | 2 | inner | ||
441.4.c.a.440.8 | 16 | 21.20 | even | 2 | inner | ||
441.4.c.a.440.9 | 16 | 7.6 | odd | 2 | inner | ||
441.4.c.a.440.10 | 16 | 1.1 | even | 1 | trivial | ||
441.4.p.c.80.4 | 16 | 21.2 | odd | 6 | |||
441.4.p.c.80.5 | 16 | 7.2 | even | 3 | |||
441.4.p.c.215.4 | 16 | 7.3 | odd | 6 | |||
441.4.p.c.215.5 | 16 | 21.17 | even | 6 | |||
1008.4.bt.a.17.3 | 16 | 84.47 | odd | 6 | |||
1008.4.bt.a.17.6 | 16 | 28.19 | even | 6 | |||
1008.4.bt.a.593.3 | 16 | 28.11 | odd | 6 | |||
1008.4.bt.a.593.6 | 16 | 84.11 | even | 6 |