Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 386x^{10} + 54793x^{8} + 3447408x^{6} + 90154296x^{4} + 707138208x^{2} + 525876624 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.11 | ||
Root | \(0.910182i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.e.673.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.8002i | 1.23433i | 0.786833 | + | 0.617166i | \(0.211719\pi\) | ||||
−0.786833 | + | 0.617166i | \(0.788281\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 9.03959i | − 0.247776i | −0.992296 | − | 0.123888i | \(-0.960464\pi\) | ||||
0.992296 | − | 0.123888i | \(-0.0395364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 50.6976i | − 1.08161i | −0.841146 | − | 0.540807i | \(-0.818119\pi\) | ||||
0.841146 | − | 0.540807i | \(-0.181881\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −41.4007 | −0.712642 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.30157 | 0.0185692 | 0.00928460 | − | 0.999957i | \(-0.497045\pi\) | ||||
0.00928460 | + | 0.999957i | \(0.497045\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.9067i | 0.179991i | 0.995942 | + | 0.0899953i | \(0.0286852\pi\) | ||||
−0.995942 | + | 0.0899953i | \(0.971315\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 21.0000i | − 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 62.4329 | 0.566007 | 0.283003 | − | 0.959119i | \(-0.408669\pi\) | ||||
0.283003 | + | 0.959119i | \(0.408669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −65.4469 | −0.523575 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 37.3470i | − 0.239143i | −0.992826 | − | 0.119572i | \(-0.961848\pi\) | ||||
0.992826 | − | 0.119572i | \(-0.0381521\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32.6466 | 0.189145 | 0.0945727 | − | 0.995518i | \(-0.469852\pi\) | ||||
0.0945727 | + | 0.995518i | \(0.469852\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 27.1188 | 0.143054 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 96.6017i | − 0.466534i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 307.226i | − 1.36507i | −0.730852 | − | 0.682536i | \(-0.760877\pi\) | ||||
0.730852 | − | 0.682536i | \(-0.239123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 152.093 | 0.624471 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19.4537 | 0.0741014 | 0.0370507 | − | 0.999313i | \(-0.488204\pi\) | ||||
0.0370507 | + | 0.999313i | \(0.488204\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 201.834i | − 0.715799i | −0.933760 | − | 0.357899i | \(-0.883493\pi\) | ||||
0.933760 | − | 0.357899i | \(-0.116507\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 124.202i | − 0.411444i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 273.997 | 0.850351 | 0.425176 | − | 0.905111i | \(-0.360212\pi\) | ||||
0.425176 | + | 0.905111i | \(0.360212\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.90470i | 0.0107209i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 29.5266i | − 0.0765245i | −0.999268 | − | 0.0382622i | \(-0.987818\pi\) | ||||
0.999268 | − | 0.0382622i | \(-0.0121822\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 124.749 | 0.305838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −44.7200 | −0.103918 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 625.595i | − 1.38043i | −0.723603 | − | 0.690216i | \(-0.757515\pi\) | ||||
0.723603 | − | 0.690216i | \(-0.242485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 758.719i | − 1.59253i | −0.604951 | − | 0.796263i | \(-0.706807\pi\) | ||||
0.604951 | − | 0.796263i | \(-0.293193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 699.640 | 1.33507 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 733.451i | 1.33739i | 0.743536 | + | 0.668696i | \(0.233147\pi\) | ||||
−0.743536 | + | 0.668696i | \(0.766853\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 187.299i | 0.326784i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 107.407 | 0.179533 | 0.0897665 | − | 0.995963i | \(-0.471388\pi\) | ||||
0.0897665 | + | 0.995963i | \(0.471388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 342.209 | 0.548665 | 0.274333 | − | 0.961635i | \(-0.411543\pi\) | ||||
0.274333 | + | 0.961635i | \(0.411543\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 196.341i | − 0.302286i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 63.2771i | 0.0936506i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −800.686 | −1.14031 | −0.570153 | − | 0.821538i | \(-0.693116\pi\) | ||||
−0.570153 | + | 0.821538i | \(0.693116\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1097.68i | 1.45164i | 0.687884 | + | 0.725821i | \(0.258540\pi\) | ||||
−0.687884 | + | 0.725821i | \(0.741460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.9620i | 0.0229206i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 112.041 | 0.138069 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1295.70 | 1.54319 | 0.771594 | − | 0.636115i | \(-0.219460\pi\) | ||||
0.771594 | + | 0.636115i | \(0.219460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 354.883i | 0.408812i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 97.9399i | 0.109203i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −205.716 | −0.222168 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −301.872 | −0.315984 | −0.157992 | − | 0.987440i | \(-0.550502\pi\) | ||||
−0.157992 | + | 0.987440i | \(0.550502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 81.3563i | 0.0825921i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 404.892i | 0.398893i | 0.979909 | + | 0.199447i | \(0.0639145\pi\) | ||||
−0.979909 | + | 0.199447i | \(0.936086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −444.944 | −0.425647 | −0.212823 | − | 0.977091i | \(-0.568266\pi\) | ||||
−0.212823 | + | 0.977091i | \(0.568266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 289.805 | 0.269353 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 264.030i | − 0.238549i | −0.992861 | − | 0.119275i | \(-0.961943\pi\) | ||||
0.992861 | − | 0.119275i | \(-0.0380569\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 93.4086i | − 0.0820818i | −0.999157 | − | 0.0410409i | \(-0.986933\pi\) | ||||
0.999157 | − | 0.0410409i | \(-0.0130674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 921.679 | 0.788125 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 536.170 | 0.446359 | 0.223180 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223180 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 861.589i | 0.698640i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 456.279i | 0.360538i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.11097 | −0.00701850 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1249.29 | 0.938607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 58.3611i | 0.0427824i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 821.848i | 0.588067i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −63.7997 | −0.0445772 | −0.0222886 | − | 0.999752i | \(-0.507095\pi\) | ||||
−0.0222886 | + | 0.999752i | \(0.507095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 605.501 | 0.413267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 878.089i | 0.585641i | 0.956167 | + | 0.292821i | \(0.0945939\pi\) | ||||
−0.956167 | + | 0.292821i | \(0.905406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 104.347i | − 0.0680301i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 372.607 | 0.237547 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 582.172 | 0.363054 | 0.181527 | − | 0.983386i | \(-0.441896\pi\) | ||||
0.181527 | + | 0.983386i | \(0.441896\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1968.29i | 1.20106i | 0.799601 | + | 0.600532i | \(0.205044\pi\) | ||||
−0.799601 | + | 0.600532i | \(0.794956\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 821.990i | 0.490950i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −458.286 | −0.267998 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 515.397 | 0.295182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1085.29i | − 0.596712i | −0.954455 | − | 0.298356i | \(-0.903562\pi\) | ||||
0.954455 | − | 0.298356i | \(-0.0964383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 784.336 | 0.422705 | 0.211352 | − | 0.977410i | \(-0.432213\pi\) | ||||
0.211352 | + | 0.977410i | \(0.432213\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.7141 | −0.00618974 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 450.532i | 0.233468i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 2495.67i | − 1.26864i | −0.773071 | − | 0.634320i | \(-0.781280\pi\) | ||||
0.773071 | − | 0.634320i | \(-0.218720\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 88.5799 | 0.0441814 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −437.030 | −0.213930 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 896.461i | 0.430774i | 0.976529 | + | 0.215387i | \(0.0691014\pi\) | ||||
−0.976529 | + | 0.215387i | \(0.930899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 374.246i | 0.176576i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1159.58 | 0.537312 | 0.268656 | − | 0.963236i | \(-0.413420\pi\) | ||||
0.268656 | + | 0.963236i | \(0.413420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −373.249 | −0.169890 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 134.160i | − 0.0599969i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 3822.75i | − 1.67999i | −0.542595 | − | 0.839995i | \(-0.682558\pi\) | ||||
0.542595 | − | 0.839995i | \(-0.317442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 458.128 | 0.197893 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1876.78 | 0.796993 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3849.44i | 1.60738i | 0.595050 | + | 0.803689i | \(0.297132\pi\) | ||||
−0.595050 | + | 0.803689i | \(0.702868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 334.288i | − 0.137278i | −0.997642 | − | 0.0686392i | \(-0.978134\pi\) | ||||
0.997642 | − | 0.0686392i | \(-0.0218657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2276.16 | 0.919445 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4239.80 | 1.68495 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 11.7656i | − 0.00460101i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1230.68 | −0.466223 | −0.233112 | − | 0.972450i | \(-0.574891\pi\) | ||||
−0.233112 | + | 0.972450i | \(0.574891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3026.92 | −1.12893 | −0.564463 | − | 0.825459i | \(-0.690917\pi\) | ||||
−0.564463 | + | 0.825459i | \(0.690917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2098.92i | 0.770804i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 202.135i | − 0.0731041i | −0.999332 | − | 0.0365520i | \(-0.988363\pi\) | ||||
0.999332 | − | 0.0365520i | \(-0.0116375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 138.229 | 0.0492402 | 0.0246201 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246201 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2200.35 | −0.772144 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 261.429i | 0.0903877i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 268.466i | 0.0914657i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −561.896 | −0.188669 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 134.750 | 0.0445974 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4519.96i | 1.47472i | 0.675498 | + | 0.737362i | \(0.263929\pi\) | ||||
−0.675498 | + | 0.737362i | \(0.736071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 322.220i | 0.103653i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2785.35 | 0.883533 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −228.526 | −0.0714903 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1026.63i | 0.316772i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 65.9864i | − 0.0200847i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3151.11 | 0.946252 | 0.473126 | − | 0.880995i | \(-0.343126\pi\) | ||||
0.473126 | + | 0.880995i | \(0.343126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 589.022 | 0.174525 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4211.08i | − 1.23127i | −0.788030 | − | 0.615637i | \(-0.788899\pi\) | ||||
0.788030 | − | 0.615637i | \(-0.211101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 1822.48i | − 0.525909i | −0.964808 | − | 0.262954i | \(-0.915303\pi\) | ||||
0.964808 | − | 0.262954i | \(-0.0846969\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −189.831 | −0.0540692 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3714.19 | 1.04431 | 0.522156 | − | 0.852850i | \(-0.325128\pi\) | ||||
0.522156 | + | 0.852850i | \(0.325128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3781.22i | 1.04962i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2402.06i | − 0.658356i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5149.09 | 1.39359 | 0.696793 | − | 0.717272i | \(-0.254610\pi\) | ||||
0.696793 | + | 0.717272i | \(0.254610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7286.99 | 1.94770 | 0.973851 | − | 0.227188i | \(-0.0729533\pi\) | ||||
0.973851 | + | 0.227188i | \(0.0729533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 676.212i | 0.176333i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 755.732 | 0.194680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3293.04 | −0.838105 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2202.95i | − 0.553981i | −0.960873 | − | 0.276991i | \(-0.910663\pi\) | ||||
0.960873 | − | 0.276991i | \(-0.0893371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 564.368i | − 0.140243i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −53.8859 | −0.0132332 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −382.218 | −0.0927708 | −0.0463854 | − | 0.998924i | \(-0.514770\pi\) | ||||
−0.0463854 | + | 0.998924i | \(0.514770\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2150.58i | 0.515949i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 336.123i | 0.0797145i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4374.34 | 1.02560 | 0.512801 | − | 0.858508i | \(-0.328608\pi\) | ||||
0.512801 | + | 0.858508i | \(0.328608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 407.475 | 0.0944566 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3887.09i | 0.890960i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 4182.99i | − 0.948110i | −0.880495 | − | 0.474055i | \(-0.842790\pi\) | ||||
0.880495 | − | 0.474055i | \(-0.157210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1227.13 | 0.275065 | 0.137533 | − | 0.990497i | \(-0.456083\pi\) | ||||
0.137533 | + | 0.990497i | \(0.456083\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1064.65 | −0.236028 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 591.613i | 0.129729i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2468.15i | 0.535368i | 0.963507 | + | 0.267684i | \(0.0862584\pi\) | ||||
−0.963507 | + | 0.267684i | \(0.913742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −293.820 | −0.0630485 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1588.55 | −0.337241 | −0.168621 | − | 0.985681i | \(-0.553931\pi\) | ||||
−0.168621 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1186.01i | − 0.249121i | −0.992212 | − | 0.124560i | \(-0.960248\pi\) | ||||
0.992212 | − | 0.124560i | \(-0.0397520\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 617.147i | − 0.128269i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −136.176 | −0.0280077 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4911.31 | −0.999655 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 905.616i | − 0.182433i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 3491.33i | − 0.696128i | −0.937471 | − | 0.348064i | \(-0.886839\pi\) | ||||
0.937471 | − | 0.348064i | \(-0.113161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8633.36 | 1.70391 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −244.069 | −0.0476846 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3165.20i | − 0.612201i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1412.84i | 0.270547i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1214.68 | −0.230301 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10470.5 | 1.96570 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1230.87i | − 0.228826i | −0.993433 | − | 0.114413i | \(-0.963501\pi\) | ||||
0.993433 | − | 0.114413i | \(-0.0364987\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1334.83i | − 0.245747i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5625.29 | −1.02566 | −0.512831 | − | 0.858490i | \(-0.671403\pi\) | ||||
−0.512831 | + | 0.858490i | \(0.671403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3114.06 | 0.562355 | 0.281178 | − | 0.959656i | \(-0.409275\pi\) | ||||
0.281178 | + | 0.959656i | \(0.409275\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 869.416i | 0.155511i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 6729.84i | − 1.19238i | −0.802842 | − | 0.596192i | \(-0.796680\pi\) | ||||
0.802842 | − | 0.596192i | \(-0.203320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −337.601 | −0.0592541 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 792.091 | 0.137727 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.4020i | 0.00334228i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3318.00i | 0.566306i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 280.226 | 0.0473900 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1917.98 | −0.321402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 2942.02i | − 0.488543i | −0.969707 | − | 0.244272i | \(-0.921451\pi\) | ||||
0.969707 | − | 0.244272i | \(-0.0785488\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2765.04i | 0.455024i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10121.8 | −1.65079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2629.36 | −0.425016 | −0.212508 | − | 0.977159i | \(-0.568163\pi\) | ||||
−0.212508 | + | 0.977159i | \(0.568163\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1608.51i | 0.257706i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 295.112i | − 0.0468658i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2584.77 | −0.403360 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2984.39i | 0.461701i | 0.972989 | + | 0.230851i | \(0.0741509\pi\) | ||||
−0.972989 | + | 0.230851i | \(0.925849\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2450.58i | 0.375864i | 0.982182 | + | 0.187932i | \(0.0601784\pi\) | ||||
−0.982182 | + | 0.187932i | \(0.939822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1368.84 | −0.208157 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3980.70 | 0.600202 | 0.300101 | − | 0.953907i | \(-0.402980\pi\) | ||||
0.300101 | + | 0.953907i | \(0.402980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1482.24i | 0.221603i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 27.3329i | − 0.00405213i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1807.77 | −0.265767 | −0.132883 | − | 0.991132i | \(-0.542424\pi\) | ||||
−0.132883 | + | 0.991132i | \(0.542424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6636.79 | 0.967603 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3747.86i | 0.541905i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4722.57i | 0.677235i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1718.88 | 0.244481 | 0.122241 | − | 0.992500i | \(-0.460992\pi\) | ||||
0.122241 | + | 0.992500i | \(0.460992\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −175.083 | −0.0247005 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 206.687i | 0.0289235i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8236.73i | 1.14338i | 0.820469 | + | 0.571691i | \(0.193712\pi\) | ||||
−0.820469 | + | 0.571691i | \(0.806288\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2465.54 | −0.339520 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1893.40 | −0.258661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 702.905i | 0.0952659i | 0.998865 | + | 0.0476330i | \(0.0151678\pi\) | ||||
−0.998865 | + | 0.0476330i | \(0.984832\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 191.399i | − 0.0257367i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8552.42 | −1.14101 | −0.570507 | − | 0.821293i | \(-0.693253\pi\) | ||||
−0.570507 | + | 0.821293i | \(0.693253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −873.240 | −0.115596 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1816.50i | 0.238600i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5627.96i | − 0.733545i | −0.930311 | − | 0.366773i | \(-0.880463\pi\) | ||||
0.930311 | − | 0.366773i | \(-0.119537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 81.2606 | 0.0105103 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2634.27 | −0.338120 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 11049.7i | − 1.40752i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 9872.80i | − 1.24811i | −0.781379 | − | 0.624057i | \(-0.785483\pi\) | ||||
0.781379 | − | 0.624057i | \(-0.214517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 313.040 | 0.0392772 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15672.1 | 1.95168 | 0.975842 | − | 0.218479i | \(-0.0701095\pi\) | ||||
0.975842 | + | 0.218479i | \(0.0701095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1655.11i | − 0.204582i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1117.82i | 0.137148i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2777.20 | −0.338233 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12951.5 | 1.56580 | 0.782898 | − | 0.622150i | \(-0.213740\pi\) | ||||
0.782898 | + | 0.622150i | \(0.213740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1746.52i | 0.209609i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4379.16i | 0.521754i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15148.3 | −1.79181 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5904.86 | −0.693434 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 4474.53i | − 0.521707i | −0.965378 | − | 0.260853i | \(-0.915996\pi\) | ||||
0.965378 | − | 0.260853i | \(-0.0840039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11461.4i | 1.32683i | 0.748250 | + | 0.663416i | \(0.230894\pi\) | ||||
−0.748250 | + | 0.663416i | \(0.769106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2465.97 | −0.283450 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −85.1835 | −0.00972237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5311.04i | 0.601918i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1374.86i | − 0.154729i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11478.6 | −1.28284 | −0.641418 | − | 0.767191i | \(-0.721654\pi\) | ||||
−0.641418 | + | 0.767191i | \(0.721654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6977.91 | −0.774450 | −0.387225 | − | 0.921985i | \(-0.626566\pi\) | ||||
−0.387225 | + | 0.921985i | \(0.626566\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1546.19i | 0.170424i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 930.666i | 0.101876i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12332.6 | 1.34078 | 0.670391 | − | 0.742008i | \(-0.266126\pi\) | ||||
0.670391 | + | 0.742008i | \(0.266126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6404.12i | 0.686838i | 0.939182 | + | 0.343419i | \(0.111585\pi\) | ||||
−0.939182 | + | 0.343419i | \(0.888415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17881.0i | 1.90481i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3255.86 | 0.344512 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1011.06 | 0.106269 | 0.0531346 | − | 0.998587i | \(-0.483079\pi\) | ||||
0.0531346 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 175.853i | − 0.0183606i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2353.01i | 0.244049i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4897.48 | −0.504610 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8076.06 | −0.826657 | −0.413328 | − | 0.910582i | \(-0.635634\pi\) | ||||
−0.413328 | + | 0.910582i | \(0.635634\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 35.1423i | − 0.00357365i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 10882.8i | − 1.09948i | −0.835335 | − | 0.549742i | \(-0.814726\pi\) | ||||
0.835335 | − | 0.549742i | \(-0.185274\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7423.39 | 0.745128 | 0.372564 | − | 0.928007i | \(-0.378479\pi\) | ||||
0.372564 | + | 0.928007i | \(0.378479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1351.60 | −0.134793 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 15704.8i | − 1.55617i | −0.628160 | − | 0.778084i | \(-0.716192\pi\) | ||||
0.628160 | − | 0.778084i | \(-0.283808\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 5134.16i | − 0.505487i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7487.02 | 0.732450 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1824.49 | −0.177358 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 975.594i | − 0.0942386i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 265.740i | 0.0255082i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12984.5 | −1.23857 | −0.619286 | − | 0.785166i | \(-0.712578\pi\) | ||||
−0.619286 | + | 0.785166i | \(0.712578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15575.6 | −1.47648 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 1311.09i | − 0.123513i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4165.91i | − 0.390029i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10080.4 | 0.937960 | 0.468980 | − | 0.883209i | \(-0.344622\pi\) | ||||
0.468980 | + | 0.883209i | \(0.344622\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2689.38 | −0.248708 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 15508.0i | − 1.42539i | −0.701474 | − | 0.712695i | \(-0.747474\pi\) | ||||
0.701474 | − | 0.712695i | \(-0.252526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 48.6096i | − 0.00444070i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1122.74 | −0.101946 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −751.848 | −0.0678571 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 15965.8i | − 1.43232i | −0.697936 | − | 0.716161i | \(-0.745898\pi\) | ||||
0.697936 | − | 0.716161i | \(-0.254102\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3478.75i | 0.310217i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4854.84 | 0.430351 | 0.215175 | − | 0.976575i | \(-0.430968\pi\) | ||||
0.215175 | + | 0.976575i | \(0.430968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5587.61 | −0.492367 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 1119.75i | − 0.0980862i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 17962.8i | − 1.56422i | −0.623142 | − | 0.782108i | \(-0.714144\pi\) | ||||
0.623142 | − | 0.782108i | \(-0.285856\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2395.46 | −0.207376 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 402.480 | 0.0346392 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 6140.34i | − 0.525390i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 2476.82i | − 0.210697i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11468.2 | 0.969942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6089.86 | −0.512095 | −0.256048 | − | 0.966664i | \(-0.582420\pi\) | ||||
−0.256048 | + | 0.966664i | \(0.582420\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10064.6i | 0.841481i | 0.907181 | + | 0.420740i | \(0.138230\pi\) | ||||
−0.907181 | + | 0.420740i | \(0.861770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1374.38i | 0.114253i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.4918 | 0.00351228 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8269.14 | −0.679636 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5630.35i | 0.460144i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 986.256i | − 0.0801491i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3643.68 | 0.294449 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11548.3 | −0.928020 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 442.940i | − 0.0353966i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1714.23i | 0.136230i | 0.997677 | + | 0.0681149i | \(0.0216984\pi\) | ||||
−0.997677 | + | 0.0681149i | \(0.978302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1002.86 | 0.0792578 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1289.06 | 0.101316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 21550.4i | − 1.68451i | −0.539079 | − | 0.842255i | \(-0.681227\pi\) | ||||
0.539079 | − | 0.842255i | \(-0.318773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6828.47i | 0.530842i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 556.718 | 0.0430436 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5604.80 | 0.430995 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12719.4i | 0.972808i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19313.9i | 1.46922i | 0.678489 | + | 0.734610i | \(0.262635\pi\) | ||||
−0.678489 | + | 0.734610i | \(0.737365\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10232.5 | −0.774218 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.2969 | 0.00265639 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 16117.4i | − 1.20651i | −0.797547 | − | 0.603257i | \(-0.793869\pi\) | ||||
0.797547 | − | 0.603257i | \(-0.206131\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7399.28i | 0.550956i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6162.20 | −0.454012 | −0.227006 | − | 0.973893i | \(-0.572894\pi\) | ||||
−0.227006 | + | 0.973893i | \(0.572894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 305.052i | 0.0223573i | 0.999938 | + | 0.0111787i | \(0.00355835\pi\) | ||||
−0.999938 | + | 0.0111787i | \(0.996442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3692.03i | − 0.269174i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4086.04 | −0.296347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23824.2 | −1.71892 | −0.859458 | − | 0.511206i | \(-0.829199\pi\) | ||||
−0.859458 | + | 0.511206i | \(0.829199\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9080.77i | − 0.651785i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7683.77i | − 0.548669i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −266.909 | −0.0189610 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6296.76 | −0.445024 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4028.40i | − 0.283254i | −0.989920 | − | 0.141627i | \(-0.954767\pi\) | ||||
0.989920 | − | 0.141627i | \(-0.0452333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 486.652i | 0.0340444i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 606.404 | 0.0422067 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5755.42 | 0.398562 | 0.199281 | − | 0.979942i | \(-0.436139\pi\) | ||||
0.199281 | + | 0.979942i | \(0.436139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 125.734i | − 0.00866316i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 414.687i | 0.0284288i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4561.05 | 0.311117 | 0.155559 | − | 0.987827i | \(-0.450282\pi\) | ||||
0.155559 | + | 0.987827i | \(0.450282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20192.3 | −1.37049 | −0.685243 | − | 0.728314i | \(-0.740304\pi\) | ||||
−0.685243 | + | 0.728314i | \(0.740304\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 6601.06i | − 0.445797i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17240.5i | 1.15855i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11163.2 | −0.746462 | −0.373231 | − | 0.927738i | \(-0.621750\pi\) | ||||
−0.373231 | + | 0.927738i | \(0.621750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −784.286 | −0.0521854 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 13891.0i | − 0.919752i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 15405.0i | − 1.01501i | −0.861648 | − | 0.507506i | \(-0.830568\pi\) | ||||
0.861648 | − | 0.507506i | \(-0.169432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −805.397 | −0.0528077 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20356.8 | 1.32825 | 0.664127 | − | 0.747620i | \(-0.268803\pi\) | ||||
0.664127 | + | 0.747620i | \(0.268803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19443.1i | 1.26250i | 0.775581 | + | 0.631249i | \(0.217457\pi\) | ||||
−0.775581 | + | 0.631249i | \(0.782543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1685.69i | − 0.108928i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9069.89 | −0.583270 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19522.6 | −1.24944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 404.250i | 0.0257483i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 399.876i | − 0.0253483i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1972.21 | −0.124425 | −0.0622126 | − | 0.998063i | \(-0.519816\pi\) | ||||
−0.0622126 | + | 0.998063i | \(0.519816\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13559.9 | −0.851432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 880.452i | − 0.0550231i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2484.18i | − 0.154516i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −966.661 | −0.0598443 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2538.56 | −0.156423 | −0.0782115 | − | 0.996937i | \(-0.524921\pi\) | ||||
−0.0782115 | + | 0.996937i | \(0.524921\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8973.74i | 0.550373i | 0.961391 | + | 0.275186i | \(0.0887396\pi\) | ||||
−0.961391 | + | 0.275186i | \(0.911260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8356.06i | 0.510108i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 31664.1 | 1.92403 | 0.962013 | − | 0.273003i | \(-0.0880170\pi\) | ||||
0.962013 | + | 0.273003i | \(0.0880170\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5655.12 | −0.342038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 685.579i | − 0.0412749i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19639.4i | 1.17695i | 0.808514 | + | 0.588477i | \(0.200272\pi\) | ||||
−0.808514 | + | 0.588477i | \(0.799728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12117.9 | −0.722876 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3079.88 | −0.182888 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 20127.3i | − 1.18975i | −0.803817 | − | 0.594876i | \(-0.797201\pi\) | ||||
0.803817 | − | 0.594876i | \(-0.202799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10898.2i | 0.641290i | 0.947199 | + | 0.320645i | \(0.103900\pi\) | ||||
−0.947199 | + | 0.320645i | \(0.896100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 197.959 | 0.0115959 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1440.01 | 0.0839717 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2331.68i | − 0.135357i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9453.34i | 0.546319i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6858.51 | −0.394590 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14208.3 | −0.813802 | −0.406901 | − | 0.913472i | \(-0.633391\pi\) | ||||
−0.406901 | + | 0.913472i | \(0.633391\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1767.07i | 0.100762i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8372.78i | − 0.475321i | −0.971348 | − | 0.237660i | \(-0.923619\pi\) | ||||
0.971348 | − | 0.237660i | \(-0.0763805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2113.10 | 0.119431 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12633.2 | 0.710876 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 34724.7i | − 1.94539i | −0.232081 | − | 0.972696i | \(-0.574554\pi\) | ||||
0.232081 | − | 0.972696i | \(-0.425446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8034.12i | 0.448129i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5467.45 | 0.303634 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1496.93 | −0.0827700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10289.8i | 0.566489i | 0.959048 | + | 0.283245i | \(0.0914108\pi\) | ||||
−0.959048 | + | 0.283245i | \(0.908589\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 569.494i | − 0.0312169i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27162.8 | −1.48251 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.3203 | 0.00137600 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11142.6i | 0.602933i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14676.9i | 0.790782i | 0.918513 | + | 0.395391i | \(0.129391\pi\) | ||||
−0.918513 | + | 0.395391i | \(0.870609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4579.72 | 0.245700 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11343.7 | −0.605996 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 2834.24i | − 0.150768i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 896.286i | − 0.0474764i | −0.999718 | − | 0.0237382i | \(-0.992443\pi\) | ||||
0.999718 | − | 0.0237382i | \(-0.00755681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7206.18 | 0.380102 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2038.22 | 0.107058 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6324.46i | − 0.330799i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15447.3i | 0.804587i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8717.37 | −0.452160 | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226080 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3114.61 | 0.160879 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21861.0i | 1.12451i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2444.24i | 0.125209i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2221.29 | −0.113319 | −0.0566595 | − | 0.998394i | \(-0.518045\pi\) | ||||
−0.0566595 | + | 0.998394i | \(0.518045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 262.700i | − 0.0132918i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32736.2i | − 1.64958i | −0.565442 | − | 0.824788i | \(-0.691295\pi\) | ||||
0.565442 | − | 0.824788i | \(-0.308705\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2028.64 | −0.101806 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6630.09 | 0.331374 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17029.1i | 0.847667i | 0.905740 | + | 0.423834i | \(0.139316\pi\) | ||||
−0.905740 | + | 0.423834i | \(0.860684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2267.20i | 0.112399i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30283.4 | 1.49528 | 0.747639 | − | 0.664105i | \(-0.231187\pi\) | ||||
0.747639 | + | 0.664105i | \(0.231187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14977.2 | 0.736541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 9879.13i | − 0.483880i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1848.21i | 0.0901632i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39087.9 | −1.89925 | −0.949625 | − | 0.313387i | \(-0.898536\pi\) | ||||
−0.949625 | + | 0.313387i | \(0.898536\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6608.86 | 0.319841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10824.0i | 0.521758i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16887.7i | 0.810824i | 0.914134 | + | 0.405412i | \(0.132872\pi\) | ||||
−0.914134 | + | 0.405412i | \(0.867128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1693.10 | 0.0809694 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20357.1 | −0.969705 | −0.484852 | − | 0.874596i | \(-0.661127\pi\) | ||||
−0.484852 | + | 0.874596i | \(0.661127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 653.860i | 0.0310240i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 161.658i | − 0.00764019i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31716.2 | −1.49310 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31570.3 | −1.48044 | −0.740218 | − | 0.672367i | \(-0.765278\pi\) | ||||
−0.740218 | + | 0.672367i | \(0.765278\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 1146.65i | − 0.0535613i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3695.86i | 0.171968i | 0.996297 | + | 0.0859838i | \(0.0274033\pi\) | ||||
−0.996297 | + | 0.0859838i | \(0.972597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2136.62 | −0.0990318 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6451.75 | −0.297883 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 289.989i | 0.0133376i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 970.914i | − 0.0444840i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1008.37 | −0.0460232 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34440.9 | 1.56592 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36218.2i | 1.64046i | 0.572036 | + | 0.820229i | \(0.306154\pi\) | ||||
−0.572036 | + | 0.820229i | \(0.693846\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13123.0i | 0.592131i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3753.19 | −0.168708 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38465.3 | −1.72250 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1222.43i | 0.0545345i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 12815.9i | − 0.569587i | −0.958589 | − | 0.284794i | \(-0.908075\pi\) | ||||
0.958589 | − | 0.284794i | \(-0.0919251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 356.625 | 0.0157903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11661.3 | −0.514396 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3093.43i | − 0.135946i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6031.12i | − 0.264061i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12549.0 | 0.547392 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16477.2 | 0.716080 | 0.358040 | − | 0.933706i | \(-0.383445\pi\) | ||||
0.358040 | + | 0.933706i | \(0.383445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 28389.1i | − 1.22919i | −0.788842 | − | 0.614596i | \(-0.789319\pi\) | ||||
0.788842 | − | 0.614596i | \(-0.210681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3681.38i | 0.158809i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12371.4 | −0.531718 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3008.67 | 0.128837 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 3193.95i | − 0.136271i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 45205.5i | − 1.92166i | −0.277138 | − | 0.960830i | \(-0.589386\pi\) | ||||
0.277138 | − | 0.960830i | \(-0.410614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4872.70 | 0.206381 | 0.103191 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103191 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1774.84 | −0.0748993 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 20947.1i | − 0.880778i | −0.897807 | − | 0.440389i | \(-0.854840\pi\) | ||||
0.897807 | − | 0.440389i | \(-0.145160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25995.0i | 1.08907i | 0.838737 | + | 0.544537i | \(0.183295\pi\) | ||||
−0.838737 | + | 0.544537i | \(0.816705\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7404.46 | −0.309095 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 63.7768 | 0.00265274 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16002.5i | 0.663222i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 881.459i | − 0.0364011i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31337.3 | −1.28949 | −0.644746 | − | 0.764397i | \(-0.723037\pi\) | ||||
−0.644746 | + | 0.764397i | \(0.723037\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22994.2 | 0.942810 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 4765.64i | − 0.194706i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 5150.93i | − 0.209701i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8745.00 | −0.354760 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3558.04 | 0.143830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 19181.0i | − 0.772640i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7641.96i | − 0.306748i | −0.988168 | − | 0.153374i | \(-0.950986\pi\) | ||||
0.988168 | − | 0.153374i | \(-0.0490138\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1851.44 | 0.0740560 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18271.5 | −0.728290 | −0.364145 | − | 0.931342i | \(-0.618639\pi\) | ||||
−0.364145 | + | 0.931342i | \(0.618639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18836.6i | 0.748190i | 0.927390 | + | 0.374095i | \(0.122047\pi\) | ||||
−0.927390 | + | 0.374095i | \(0.877953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 408.528i | − 0.0161702i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26302.5 | 1.03748 | 0.518742 | − | 0.854931i | \(-0.326401\pi\) | ||||
0.518742 | + | 0.854931i | \(0.326401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52754.9 | 2.07366 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 14733.9i | − 0.577151i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7237.88i | 0.282541i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37184.2 | 1.44654 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2716.85 | 0.105328 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5752.94i | − 0.222268i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39775.9i | 1.53151i | 0.643130 | + | 0.765757i | \(0.277635\pi\) | ||||
−0.643130 | + | 0.765757i | \(0.722365\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10474.0 | 0.401910 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35303.3 | 1.35005 | 0.675027 | − | 0.737793i | \(-0.264132\pi\) | ||||
0.675027 | + | 0.737793i | \(0.264132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 21710.3i | − 0.827416i | −0.910410 | − | 0.413708i | \(-0.864233\pi\) | ||||
0.910410 | − | 0.413708i | \(-0.135767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25900.1i | 0.983754i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15410.7 | −0.583359 | −0.291680 | − | 0.956516i | \(-0.594214\pi\) | ||||
−0.291680 | + | 0.956516i | \(0.594214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 446.598 | 0.0168486 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 732.207i | − 0.0275307i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4084.37i | 0.153055i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −53123.2 | −1.98404 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9495.60 | 0.353455 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1219.25i | − 0.0452329i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 38.4309i | − 0.00142100i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4238.51 | −0.156200 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4613.25 | 0.169447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7462.18i | − 0.273184i | −0.990627 | − | 0.136592i | \(-0.956385\pi\) | ||||
0.990627 | − | 0.136592i | \(-0.0436149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3644.03i | − 0.132964i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4681.98 | −0.170276 | −0.0851378 | − | 0.996369i | \(-0.527133\pi\) | ||||
−0.0851378 | + | 0.996369i | \(0.527133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9922.59 | 0.359682 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31411.5i | 1.13490i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6146.63i | − 0.221352i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2846.62 | 0.102178 | 0.0510888 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510888 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3692.62 | 0.132113 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5445.27i | − 0.194186i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20107.0i | 0.714718i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4004.50 | 0.141882 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35272.0 | −1.24568 | −0.622839 | − | 0.782350i | \(-0.714021\pi\) | ||||
−0.622839 | + | 0.782350i | \(0.714021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 730.426i | 0.0257129i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 16875.9i | − 0.592166i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 162.369 | 0.00567917 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6983.20 | 0.243470 | 0.121735 | − | 0.992563i | \(-0.461154\pi\) | ||||
0.121735 | + | 0.992563i | \(0.461154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9342.19i | 0.324676i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4614.35i | 0.159855i | 0.996801 | + | 0.0799274i | \(0.0254688\pi\) | ||||
−0.996801 | + | 0.0799274i | \(0.974531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1214.55 | 0.0419419 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2608.25 | −0.0897844 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36604.3i | 1.25605i | 0.778194 | + | 0.628025i | \(0.216136\pi\) | ||||
−0.778194 | + | 0.628025i | \(0.783864\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 17349.2i | − 0.593444i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20189.5 | 0.688423 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52783.0 | 1.79413 | 0.897067 | − | 0.441895i | \(-0.145694\pi\) | ||||
0.897067 | + | 0.441895i | \(0.145694\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 16983.6i | − 0.575474i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 1012.80i | − 0.0342104i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4075.21 | −0.137221 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28725.2 | −0.964224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2376.27i | 0.0795165i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 41772.3i | − 1.39347i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49366.0 | 1.64168 | 0.820840 | − | 0.571158i | \(-0.193506\pi\) | ||||
0.820840 | + | 0.571158i | \(0.193506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −58.2061 | −0.00192967 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 12250.5i | − 0.404878i | −0.979295 | − | 0.202439i | \(-0.935113\pi\) | ||||
0.979295 | − | 0.202439i | \(-0.0648868\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 13778.0i | − 0.453959i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9954.00 | −0.326957 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9536.66 | −0.312287 | −0.156144 | − | 0.987734i | \(-0.549906\pi\) | ||||
−0.156144 | + | 0.987734i | \(0.549906\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 11712.6i | − 0.382365i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 840.677i | 0.0273606i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47967.2 | 1.55638 | 0.778188 | − | 0.628032i | \(-0.216139\pi\) | ||||
0.778188 | + | 0.628032i | \(0.216139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2789.51 | 0.0902347 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5753.93i | − 0.185562i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 12601.1i | − 0.405147i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43201.5 | 1.38480 | 0.692401 | − | 0.721513i | \(-0.256553\pi\) | ||||
0.692401 | + | 0.721513i | \(0.256553\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8826.05 | 0.282061 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1907.59i | 0.0607787i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 13736.8i | − 0.436359i | −0.975909 | − | 0.218180i | \(-0.929988\pi\) | ||||
0.975909 | − | 0.218180i | \(-0.0700119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8295.11 | −0.262708 |
(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 | 1344.4.c.e.673.11 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.h.673.5 | yes | 12 | ||
8.3 | odd | 2 | 1344.4.c.h.673.8 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.e.673.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.e.673.2 | ✓ | 12 | 8.5 | even | 2 | inner | |
1344.4.c.e.673.11 | yes | 12 | 1.1 | even | 1 | trivial | |
1344.4.c.h.673.5 | yes | 12 | 4.3 | odd | 2 | ||
1344.4.c.h.673.8 | yes | 12 | 8.3 | odd | 2 |