Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.588238\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.213700 | −0.0755543 | −0.0377772 | − | 0.999286i | \(-0.512028\pi\) | ||||
−0.0377772 | + | 0.999286i | \(0.512028\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.95433 | −0.994292 | ||||||||
\(5\) | −15.3391 | −1.37197 | −0.685987 | − | 0.727614i | \(-0.740629\pi\) | ||||
−0.685987 | + | 0.727614i | \(0.740629\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −32.3928 | −1.74905 | −0.874523 | − | 0.484984i | \(-0.838825\pi\) | ||||
−0.874523 | + | 0.484984i | \(0.838825\pi\) | |||||||
\(8\) | 3.40944 | 0.150677 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.27797 | 0.103659 | ||||||||
\(11\) | −29.5925 | −0.811135 | −0.405567 | − | 0.914065i | \(-0.632926\pi\) | ||||
−0.405567 | + | 0.914065i | \(0.632926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.92233 | 0.132148 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 62.9061 | 0.982907 | ||||||||
\(17\) | 78.1958 | 1.11560 | 0.557802 | − | 0.829974i | \(-0.311645\pi\) | ||||
0.557802 | + | 0.829974i | \(0.311645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.6600 | 0.128715 | 0.0643574 | − | 0.997927i | \(-0.479500\pi\) | ||||
0.0643574 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(20\) | 122.013 | 1.36414 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.32392 | 0.0612847 | ||||||||
\(23\) | 26.8789 | 0.243680 | 0.121840 | − | 0.992550i | \(-0.461121\pi\) | ||||
0.121840 | + | 0.992550i | \(0.461121\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 110.289 | 0.882314 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 257.663 | 1.73906 | ||||||||
\(29\) | 190.785 | 1.22165 | 0.610824 | − | 0.791766i | \(-0.290838\pi\) | ||||
0.610824 | + | 0.791766i | \(0.290838\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.108 | −0.742222 | −0.371111 | − | 0.928589i | \(-0.621023\pi\) | ||||
−0.371111 | + | 0.928589i | \(0.621023\pi\) | |||||||
\(32\) | −40.7185 | −0.224940 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −16.7104 | −0.0842887 | ||||||||
\(35\) | 496.877 | 2.39965 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −379.934 | −1.68813 | −0.844065 | − | 0.536241i | \(-0.819844\pi\) | ||||
−0.844065 | + | 0.536241i | \(0.819844\pi\) | |||||||
\(38\) | −2.27805 | −0.00972496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −52.2979 | −0.206725 | ||||||||
\(41\) | 464.631 | 1.76983 | 0.884917 | − | 0.465749i | \(-0.154215\pi\) | ||||
0.884917 | + | 0.465749i | \(0.154215\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 322.758 | 1.14466 | 0.572328 | − | 0.820025i | \(-0.306041\pi\) | ||||
0.572328 | + | 0.820025i | \(0.306041\pi\) | |||||||
\(44\) | 235.389 | 0.806504 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.74401 | −0.0184110 | ||||||||
\(47\) | 248.529 | 0.771314 | 0.385657 | − | 0.922642i | \(-0.373975\pi\) | ||||
0.385657 | + | 0.922642i | \(0.373975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 706.292 | 2.05916 | ||||||||
\(50\) | −23.5688 | −0.0666626 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −740.167 | −1.91830 | −0.959148 | − | 0.282904i | \(-0.908702\pi\) | ||||
−0.959148 | + | 0.282904i | \(0.908702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 453.924 | 1.11286 | ||||||||
\(56\) | −110.441 | −0.263542 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −40.7706 | −0.0923008 | ||||||||
\(59\) | 340.673 | 0.751727 | 0.375864 | − | 0.926675i | \(-0.377346\pi\) | ||||
0.375864 | + | 0.926675i | \(0.377346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −590.834 | −1.24014 | −0.620070 | − | 0.784547i | \(-0.712896\pi\) | ||||
−0.620070 | + | 0.784547i | \(0.712896\pi\) | |||||||
\(62\) | 27.3767 | 0.0560781 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −494.547 | −0.965912 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −340.777 | −0.621382 | −0.310691 | − | 0.950511i | \(-0.600560\pi\) | ||||
−0.310691 | + | 0.950511i | \(0.600560\pi\) | |||||||
\(68\) | −621.995 | −1.10924 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −106.183 | −0.181304 | ||||||||
\(71\) | 36.2243 | 0.0605498 | 0.0302749 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302749 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −164.572 | −0.263859 | −0.131929 | − | 0.991259i | \(-0.542117\pi\) | ||||
−0.131929 | + | 0.991259i | \(0.542117\pi\) | |||||||
\(74\) | 81.1919 | 0.127546 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −84.7935 | −0.127980 | ||||||||
\(77\) | 958.584 | 1.41871 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −327.242 | −0.466046 | −0.233023 | − | 0.972471i | \(-0.574862\pi\) | ||||
−0.233023 | + | 0.972471i | \(0.574862\pi\) | |||||||
\(80\) | −964.925 | −1.34852 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −99.2916 | −0.133719 | ||||||||
\(83\) | 1404.48 | 1.85737 | 0.928684 | − | 0.370871i | \(-0.120941\pi\) | ||||
0.928684 | + | 0.370871i | \(0.120941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1199.46 | −1.53058 | ||||||||
\(86\) | −68.9734 | −0.0864837 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −100.894 | −0.122220 | ||||||||
\(89\) | −736.986 | −0.877756 | −0.438878 | − | 0.898547i | \(-0.644624\pi\) | ||||
−0.438878 | + | 0.898547i | \(0.644624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −213.803 | −0.242289 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −53.1107 | −0.0582761 | ||||||||
\(95\) | −163.516 | −0.176593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1494.87 | 1.56476 | 0.782378 | − | 0.622804i | \(-0.214007\pi\) | ||||
0.782378 | + | 0.622804i | \(0.214007\pi\) | |||||||
\(98\) | −150.935 | −0.155578 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −877.277 | −0.877277 | ||||||||
\(101\) | 484.010 | 0.476839 | 0.238420 | − | 0.971162i | \(-0.423371\pi\) | ||||
0.238420 | + | 0.971162i | \(0.423371\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 214.049 | 0.204766 | 0.102383 | − | 0.994745i | \(-0.467353\pi\) | ||||
0.102383 | + | 0.994745i | \(0.467353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 158.174 | 0.144936 | ||||||||
\(107\) | −148.288 | −0.133977 | −0.0669884 | − | 0.997754i | \(-0.521339\pi\) | ||||
−0.0669884 | + | 0.997754i | \(0.521339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −504.881 | −0.443659 | −0.221829 | − | 0.975086i | \(-0.571203\pi\) | ||||
−0.221829 | + | 0.975086i | \(0.571203\pi\) | |||||||
\(110\) | −97.0035 | −0.0840811 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2037.70 | −1.71915 | ||||||||
\(113\) | 1136.49 | 0.946120 | 0.473060 | − | 0.881030i | \(-0.343149\pi\) | ||||
0.473060 | + | 0.881030i | \(0.343149\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −412.299 | −0.334322 | ||||||||
\(116\) | −1517.56 | −1.21467 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −72.8019 | −0.0567962 | ||||||||
\(119\) | −2532.98 | −1.95124 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −455.282 | −0.342060 | ||||||||
\(122\) | 126.261 | 0.0936979 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1019.01 | 0.737985 | ||||||||
\(125\) | 225.651 | 0.161463 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1286.84 | −0.899122 | −0.449561 | − | 0.893250i | \(-0.648420\pi\) | ||||
−0.449561 | + | 0.893250i | \(0.648420\pi\) | |||||||
\(128\) | 431.433 | 0.297919 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2229.88 | −1.48722 | −0.743610 | − | 0.668614i | \(-0.766888\pi\) | ||||
−0.743610 | + | 0.668614i | \(0.766888\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −345.308 | −0.225128 | ||||||||
\(134\) | 72.8241 | 0.0469481 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 266.604 | 0.168096 | ||||||||
\(137\) | −474.745 | −0.296060 | −0.148030 | − | 0.988983i | \(-0.547293\pi\) | ||||
−0.148030 | + | 0.988983i | \(0.547293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1927.02 | 1.17588 | 0.587941 | − | 0.808904i | \(-0.299939\pi\) | ||||
0.587941 | + | 0.808904i | \(0.299939\pi\) | |||||||
\(140\) | −3952.33 | −2.38595 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.74113 | −0.00457480 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2926.47 | −1.67607 | ||||||||
\(146\) | 35.1690 | 0.0199357 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3022.12 | 1.67849 | ||||||||
\(149\) | 1065.73 | 0.585959 | 0.292979 | − | 0.956119i | \(-0.405353\pi\) | ||||
0.292979 | + | 0.956119i | \(0.405353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −877.888 | −0.473123 | −0.236561 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236561 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(152\) | 36.3448 | 0.0193944 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −204.849 | −0.107190 | ||||||||
\(155\) | 1965.07 | 1.01831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2314.94 | 1.17676 | 0.588382 | − | 0.808583i | \(-0.299765\pi\) | ||||
0.588382 | + | 0.808583i | \(0.299765\pi\) | |||||||
\(158\) | 69.9317 | 0.0352118 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 624.587 | 0.308612 | ||||||||
\(161\) | −870.681 | −0.426207 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −331.399 | −0.159246 | −0.0796232 | − | 0.996825i | \(-0.525372\pi\) | ||||
−0.0796232 | + | 0.996825i | \(0.525372\pi\) | |||||||
\(164\) | −3695.83 | −1.75973 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −300.137 | −0.140332 | ||||||||
\(167\) | −2171.62 | −1.00626 | −0.503129 | − | 0.864212i | \(-0.667818\pi\) | ||||
−0.503129 | + | 0.864212i | \(0.667818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 256.324 | 0.115642 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2567.33 | −1.13812 | ||||||||
\(173\) | 2936.69 | 1.29059 | 0.645295 | − | 0.763933i | \(-0.276734\pi\) | ||||
0.645295 | + | 0.763933i | \(0.276734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3572.57 | −1.54321 | ||||||||
\(176\) | −1861.55 | −0.797270 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 157.494 | 0.0663183 | ||||||||
\(179\) | −1615.57 | −0.674599 | −0.337300 | − | 0.941397i | \(-0.609514\pi\) | ||||
−0.337300 | + | 0.941397i | \(0.609514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 725.019 | 0.297736 | 0.148868 | − | 0.988857i | \(-0.452437\pi\) | ||||
0.148868 | + | 0.988857i | \(0.452437\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 91.6419 | 0.0367170 | ||||||||
\(185\) | 5827.87 | 2.31607 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2314.01 | −0.904905 | ||||||||
\(188\) | −1976.89 | −0.766911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 34.9433 | 0.0133424 | ||||||||
\(191\) | −1717.08 | −0.650490 | −0.325245 | − | 0.945630i | \(-0.605447\pi\) | ||||
−0.325245 | + | 0.945630i | \(0.605447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −435.830 | −0.162548 | −0.0812740 | − | 0.996692i | \(-0.525899\pi\) | ||||
−0.0812740 | + | 0.996692i | \(0.525899\pi\) | |||||||
\(194\) | −319.454 | −0.118224 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5618.08 | −2.04741 | ||||||||
\(197\) | 694.556 | 0.251193 | 0.125597 | − | 0.992081i | \(-0.459915\pi\) | ||||
0.125597 | + | 0.992081i | \(0.459915\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2899.24 | 1.03277 | 0.516386 | − | 0.856356i | \(-0.327277\pi\) | ||||
0.516386 | + | 0.856356i | \(0.327277\pi\) | |||||||
\(200\) | 376.024 | 0.132945 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −103.433 | −0.0360273 | ||||||||
\(203\) | −6180.04 | −2.13672 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7127.04 | −2.42817 | ||||||||
\(206\) | −45.7423 | −0.0154709 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −315.457 | −0.104405 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5250.30 | 1.71301 | 0.856507 | − | 0.516136i | \(-0.172630\pi\) | ||||
0.856507 | + | 0.516136i | \(0.172630\pi\) | |||||||
\(212\) | 5887.53 | 1.90735 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 31.6891 | 0.0101225 | ||||||||
\(215\) | −4950.84 | −1.57044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4149.77 | 1.29818 | ||||||||
\(218\) | 107.893 | 0.0335203 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3610.66 | −1.10650 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1382.46 | 0.415141 | 0.207570 | − | 0.978220i | \(-0.433444\pi\) | ||||
0.207570 | + | 0.978220i | \(0.433444\pi\) | |||||||
\(224\) | 1318.99 | 0.393431 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −242.867 | −0.0714835 | ||||||||
\(227\) | 1223.57 | 0.357760 | 0.178880 | − | 0.983871i | \(-0.442753\pi\) | ||||
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4019.61 | 1.15993 | 0.579964 | − | 0.814642i | \(-0.303067\pi\) | ||||
0.579964 | + | 0.814642i | \(0.303067\pi\) | |||||||
\(230\) | 88.1082 | 0.0252595 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 650.468 | 0.184075 | ||||||||
\(233\) | −1658.40 | −0.466290 | −0.233145 | − | 0.972442i | \(-0.574902\pi\) | ||||
−0.233145 | + | 0.972442i | \(0.574902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3812.23 | −1.05822 | ||||||||
\(236\) | −2709.83 | −0.747436 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 541.297 | 0.147425 | ||||||||
\(239\) | −618.554 | −0.167410 | −0.0837049 | − | 0.996491i | \(-0.526675\pi\) | ||||
−0.0837049 | + | 0.996491i | \(0.526675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1135.25 | 0.303434 | 0.151717 | − | 0.988424i | \(-0.451520\pi\) | ||||
0.151717 | + | 0.988424i | \(0.451520\pi\) | |||||||
\(242\) | 97.2938 | 0.0258441 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4699.69 | 1.23306 | ||||||||
\(245\) | −10833.9 | −2.82512 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −436.777 | −0.111836 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −48.2215 | −0.0121992 | ||||||||
\(251\) | −2287.83 | −0.575326 | −0.287663 | − | 0.957732i | \(-0.592878\pi\) | ||||
−0.287663 | + | 0.957732i | \(0.592878\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −795.414 | −0.197657 | ||||||||
\(254\) | 274.997 | 0.0679326 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3864.18 | 0.943403 | ||||||||
\(257\) | 5113.49 | 1.24113 | 0.620566 | − | 0.784154i | \(-0.286903\pi\) | ||||
0.620566 | + | 0.784154i | \(0.286903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12307.1 | 2.95262 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 476.526 | 0.112366 | ||||||||
\(263\) | −2760.17 | −0.647145 | −0.323573 | − | 0.946203i | \(-0.604884\pi\) | ||||
−0.323573 | + | 0.946203i | \(0.604884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11353.5 | 2.63185 | ||||||||
\(266\) | 73.7923 | 0.0170094 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2710.66 | 0.617834 | ||||||||
\(269\) | 3310.32 | 0.750312 | 0.375156 | − | 0.926962i | \(-0.377589\pi\) | ||||
0.375156 | + | 0.926962i | \(0.377589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2522.26 | −0.565374 | −0.282687 | − | 0.959212i | \(-0.591226\pi\) | ||||
−0.282687 | + | 0.959212i | \(0.591226\pi\) | |||||||
\(272\) | 4918.99 | 1.09654 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 101.453 | 0.0223686 | ||||||||
\(275\) | −3263.74 | −0.715675 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3455.48 | −0.749530 | −0.374765 | − | 0.927120i | \(-0.622277\pi\) | ||||
−0.374765 | + | 0.927120i | \(0.622277\pi\) | |||||||
\(278\) | −411.804 | −0.0888430 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1694.07 | 0.361572 | ||||||||
\(281\) | −981.649 | −0.208400 | −0.104200 | − | 0.994556i | \(-0.533228\pi\) | ||||
−0.104200 | + | 0.994556i | \(0.533228\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5331.10 | 1.11979 | 0.559896 | − | 0.828563i | \(-0.310841\pi\) | ||||
0.559896 | + | 0.828563i | \(0.310841\pi\) | |||||||
\(284\) | −288.140 | −0.0602041 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15050.7 | −3.09552 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1201.58 | 0.244572 | ||||||||
\(290\) | 625.387 | 0.126634 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1309.06 | 0.262353 | ||||||||
\(293\) | −2420.39 | −0.482597 | −0.241299 | − | 0.970451i | \(-0.577573\pi\) | ||||
−0.241299 | + | 0.970451i | \(0.577573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5225.64 | −1.03135 | ||||||||
\(296\) | −1295.36 | −0.254363 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −227.746 | −0.0442717 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10455.0 | −2.00205 | ||||||||
\(302\) | 187.605 | 0.0357465 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 670.581 | 0.126515 | ||||||||
\(305\) | 9062.88 | 1.70144 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 875.509 | 0.162762 | 0.0813810 | − | 0.996683i | \(-0.474067\pi\) | ||||
0.0813810 | + | 0.996683i | \(0.474067\pi\) | |||||||
\(308\) | −7624.90 | −1.41061 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −419.935 | −0.0769377 | ||||||||
\(311\) | −6419.10 | −1.17040 | −0.585199 | − | 0.810890i | \(-0.698984\pi\) | ||||
−0.585199 | + | 0.810890i | \(0.698984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5015.58 | −0.905742 | −0.452871 | − | 0.891576i | \(-0.649600\pi\) | ||||
−0.452871 | + | 0.891576i | \(0.649600\pi\) | |||||||
\(314\) | −494.701 | −0.0889096 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2602.99 | 0.463386 | ||||||||
\(317\) | 5228.81 | 0.926433 | 0.463217 | − | 0.886245i | \(-0.346695\pi\) | ||||
0.463217 | + | 0.886245i | \(0.346695\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5645.80 | −0.990922 | ||||||||
\(320\) | 7585.92 | 1.32521 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 186.064 | 0.0322018 | ||||||||
\(323\) | 833.570 | 0.143595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 70.8199 | 0.0120318 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1584.13 | 0.266674 | ||||||||
\(329\) | −8050.56 | −1.34906 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3186.81 | 0.529193 | 0.264596 | − | 0.964359i | \(-0.414761\pi\) | ||||
0.264596 | + | 0.964359i | \(0.414761\pi\) | |||||||
\(332\) | −11171.7 | −1.84677 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 464.075 | 0.0760271 | ||||||||
\(335\) | 5227.23 | 0.852520 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5600.69 | −0.905309 | −0.452655 | − | 0.891686i | \(-0.649523\pi\) | ||||
−0.452655 | + | 0.891686i | \(0.649523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9540.87 | 1.52184 | ||||||||
\(341\) | 3791.04 | 0.602042 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11768.0 | −1.85252 | ||||||||
\(344\) | 1100.42 | 0.172474 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −627.570 | −0.0975097 | ||||||||
\(347\) | 6982.33 | 1.08020 | 0.540102 | − | 0.841599i | \(-0.318386\pi\) | ||||
0.540102 | + | 0.841599i | \(0.318386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2872.20 | −0.440531 | −0.220265 | − | 0.975440i | \(-0.570692\pi\) | ||||
−0.220265 | + | 0.975440i | \(0.570692\pi\) | |||||||
\(350\) | 763.459 | 0.116596 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1204.96 | 0.182457 | ||||||||
\(353\) | −5104.55 | −0.769655 | −0.384827 | − | 0.922989i | \(-0.625739\pi\) | ||||
−0.384827 | + | 0.922989i | \(0.625739\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −555.650 | −0.0830728 | ||||||||
\(356\) | 5862.23 | 0.872746 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 345.247 | 0.0509689 | ||||||||
\(359\) | −10771.0 | −1.58348 | −0.791741 | − | 0.610857i | \(-0.790825\pi\) | ||||
−0.791741 | + | 0.610857i | \(0.790825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6745.36 | −0.983433 | ||||||||
\(362\) | −154.936 | −0.0224952 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2524.39 | 0.362008 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11380.5 | −1.61868 | −0.809340 | − | 0.587340i | \(-0.800175\pi\) | ||||
−0.809340 | + | 0.587340i | \(0.800175\pi\) | |||||||
\(368\) | 1690.84 | 0.239514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1245.41 | −0.174989 | ||||||||
\(371\) | 23976.1 | 3.35519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3196.75 | 0.443758 | 0.221879 | − | 0.975074i | \(-0.428781\pi\) | ||||
0.221879 | + | 0.975074i | \(0.428781\pi\) | |||||||
\(374\) | 494.504 | 0.0683695 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 847.346 | 0.116220 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2050.75 | −0.277942 | −0.138971 | − | 0.990296i | \(-0.544379\pi\) | ||||
−0.138971 | + | 0.990296i | \(0.544379\pi\) | |||||||
\(380\) | 1300.66 | 0.175585 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 366.940 | 0.0491473 | ||||||||
\(383\) | −3507.54 | −0.467955 | −0.233978 | − | 0.972242i | \(-0.575174\pi\) | ||||
−0.233978 | + | 0.972242i | \(0.575174\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14703.9 | −1.94644 | ||||||||
\(386\) | 93.1369 | 0.0122812 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11890.7 | −1.55582 | ||||||||
\(389\) | 6572.66 | 0.856676 | 0.428338 | − | 0.903618i | \(-0.359099\pi\) | ||||
0.428338 | + | 0.903618i | \(0.359099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2101.81 | 0.271850 | ||||||||
\(392\) | 2408.06 | 0.310269 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −148.427 | −0.0189787 | ||||||||
\(395\) | 5019.62 | 0.639403 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5285.98 | −0.668251 | −0.334126 | − | 0.942529i | \(-0.608441\pi\) | ||||
−0.334126 | + | 0.942529i | \(0.608441\pi\) | |||||||
\(398\) | −619.567 | −0.0780304 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6937.86 | 0.867233 | ||||||||
\(401\) | 919.541 | 0.114513 | 0.0572565 | − | 0.998360i | \(-0.481765\pi\) | ||||
0.0572565 | + | 0.998360i | \(0.481765\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3849.97 | −0.474117 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1320.67 | 0.161438 | ||||||||
\(407\) | 11243.2 | 1.36930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1539.17 | −0.186081 | −0.0930403 | − | 0.995662i | \(-0.529659\pi\) | ||||
−0.0930403 | + | 0.995662i | \(0.529659\pi\) | |||||||
\(410\) | 1523.05 | 0.183458 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1702.62 | −0.203597 | ||||||||
\(413\) | −11035.4 | −1.31481 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21543.5 | −2.54826 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 67.4132 | 0.00788825 | ||||||||
\(419\) | −10579.9 | −1.23357 | −0.616783 | − | 0.787133i | \(-0.711564\pi\) | ||||
−0.616783 | + | 0.787133i | \(0.711564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 74.9351 | 0.00867485 | 0.00433743 | − | 0.999991i | \(-0.498619\pi\) | ||||
0.00433743 | + | 0.999991i | \(0.498619\pi\) | |||||||
\(422\) | −1121.99 | −0.129426 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2523.55 | −0.289044 | ||||||||
\(425\) | 8624.15 | 0.984313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19138.8 | 2.16906 | ||||||||
\(428\) | 1179.53 | 0.133212 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1057.99 | 0.118653 | ||||||||
\(431\) | 12165.6 | 1.35962 | 0.679810 | − | 0.733388i | \(-0.262062\pi\) | ||||
0.679810 | + | 0.733388i | \(0.262062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2869.23 | −0.318445 | −0.159222 | − | 0.987243i | \(-0.550899\pi\) | ||||
−0.159222 | + | 0.987243i | \(0.550899\pi\) | |||||||
\(434\) | −886.806 | −0.0980831 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4015.99 | 0.441126 | ||||||||
\(437\) | 286.530 | 0.0313652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3845.12 | −0.418035 | −0.209018 | − | 0.977912i | \(-0.567027\pi\) | ||||
−0.209018 | + | 0.977912i | \(0.567027\pi\) | |||||||
\(440\) | 1547.63 | 0.167682 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3858.30 | 0.413799 | 0.206900 | − | 0.978362i | \(-0.433663\pi\) | ||||
0.206900 | + | 0.978362i | \(0.433663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11304.7 | 1.20426 | ||||||||
\(446\) | −295.432 | −0.0313657 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16019.7 | 1.68942 | ||||||||
\(449\) | 5550.51 | 0.583395 | 0.291698 | − | 0.956511i | \(-0.405780\pi\) | ||||
0.291698 | + | 0.956511i | \(0.405780\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13749.6 | −1.43557 | ||||||||
\(452\) | −9039.99 | −0.940719 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −261.478 | −0.0270303 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8102.42 | 0.829355 | 0.414677 | − | 0.909968i | \(-0.363894\pi\) | ||||
0.414677 | + | 0.909968i | \(0.363894\pi\) | |||||||
\(458\) | −858.991 | −0.0876376 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3279.56 | 0.332414 | ||||||||
\(461\) | −9230.86 | −0.932590 | −0.466295 | − | 0.884629i | \(-0.654412\pi\) | ||||
−0.466295 | + | 0.884629i | \(0.654412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13934.7 | −1.39870 | −0.699352 | − | 0.714777i | \(-0.746528\pi\) | ||||
−0.699352 | + | 0.714777i | \(0.746528\pi\) | |||||||
\(464\) | 12001.5 | 1.20077 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 354.400 | 0.0352302 | ||||||||
\(467\) | −10918.0 | −1.08185 | −0.540926 | − | 0.841070i | \(-0.681926\pi\) | ||||
−0.540926 | + | 0.841070i | \(0.681926\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11038.7 | 1.08682 | ||||||||
\(470\) | 814.673 | 0.0799533 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1161.51 | 0.113268 | ||||||||
\(473\) | −9551.23 | −0.928470 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1175.69 | 0.113567 | ||||||||
\(476\) | 20148.2 | 1.94010 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 132.185 | 0.0126485 | ||||||||
\(479\) | 11028.4 | 1.05198 | 0.525992 | − | 0.850490i | \(-0.323694\pi\) | ||||
0.525992 | + | 0.850490i | \(0.323694\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −242.602 | −0.0229258 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3621.47 | 0.340108 | ||||||||
\(485\) | −22930.0 | −2.14680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1078.10 | −0.100315 | −0.0501576 | − | 0.998741i | \(-0.515972\pi\) | ||||
−0.0501576 | + | 0.998741i | \(0.515972\pi\) | |||||||
\(488\) | −2014.41 | −0.186861 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2315.21 | 0.213450 | ||||||||
\(491\) | −6572.88 | −0.604134 | −0.302067 | − | 0.953287i | \(-0.597677\pi\) | ||||
−0.302067 | + | 0.953287i | \(0.597677\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14918.6 | 1.36288 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8058.77 | −0.729535 | ||||||||
\(497\) | −1173.41 | −0.105904 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9956.79 | −0.893241 | −0.446620 | − | 0.894724i | \(-0.647373\pi\) | ||||
−0.446620 | + | 0.894724i | \(0.647373\pi\) | |||||||
\(500\) | −1794.90 | −0.160541 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 488.910 | 0.0434683 | ||||||||
\(503\) | 11965.0 | 1.06062 | 0.530310 | − | 0.847804i | \(-0.322076\pi\) | ||||
0.530310 | + | 0.847804i | \(0.322076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7424.29 | −0.654211 | ||||||||
\(506\) | 169.980 | 0.0149338 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10235.9 | 0.893990 | ||||||||
\(509\) | −7160.44 | −0.623538 | −0.311769 | − | 0.950158i | \(-0.600922\pi\) | ||||
−0.311769 | + | 0.950158i | \(0.600922\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5330.94 | 0.461501 | ||||||||
\(512\) | −4277.24 | −0.369197 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1092.75 | −0.0937729 | ||||||||
\(515\) | −3283.33 | −0.280933 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7354.61 | −0.625639 | ||||||||
\(518\) | −2630.03 | −0.223083 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17213.1 | 1.44745 | 0.723725 | − | 0.690089i | \(-0.242428\pi\) | ||||
0.723725 | + | 0.690089i | \(0.242428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10110.1 | −0.845281 | −0.422640 | − | 0.906297i | \(-0.638897\pi\) | ||||
−0.422640 | + | 0.906297i | \(0.638897\pi\) | |||||||
\(524\) | 17737.2 | 1.47873 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 589.847 | 0.0488946 | ||||||||
\(527\) | −10017.5 | −0.828026 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11444.5 | −0.940620 | ||||||||
\(530\) | −2426.25 | −0.198848 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2746.70 | 0.223843 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2274.61 | 0.183813 | ||||||||
\(536\) | −1161.86 | −0.0936281 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −707.416 | −0.0566893 | ||||||||
\(539\) | −20901.0 | −1.67026 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5951.54 | 0.472970 | 0.236485 | − | 0.971635i | \(-0.424005\pi\) | ||||
0.236485 | + | 0.971635i | \(0.424005\pi\) | |||||||
\(542\) | 539.007 | 0.0427165 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3184.02 | −0.250944 | ||||||||
\(545\) | 7744.43 | 0.608688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5157.62 | 0.403152 | 0.201576 | − | 0.979473i | \(-0.435394\pi\) | ||||
0.201576 | + | 0.979473i | \(0.435394\pi\) | |||||||
\(548\) | 3776.28 | 0.294370 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 697.460 | 0.0540724 | ||||||||
\(551\) | 2033.77 | 0.157244 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10600.3 | 0.815136 | ||||||||
\(554\) | 738.436 | 0.0566302 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15328.2 | −1.16917 | ||||||||
\(557\) | 23314.4 | 1.77354 | 0.886772 | − | 0.462206i | \(-0.152942\pi\) | ||||
0.886772 | + | 0.462206i | \(0.152942\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 31256.6 | 2.35863 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 209.778 | 0.0157455 | ||||||||
\(563\) | −2329.12 | −0.174353 | −0.0871764 | − | 0.996193i | \(-0.527784\pi\) | ||||
−0.0871764 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17432.7 | −1.29805 | ||||||||
\(566\) | −1139.26 | −0.0846051 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 123.505 | 0.00912348 | ||||||||
\(569\) | 17446.6 | 1.28541 | 0.642706 | − | 0.766113i | \(-0.277812\pi\) | ||||
0.642706 | + | 0.766113i | \(0.277812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −413.526 | −0.0303074 | −0.0151537 | − | 0.999885i | \(-0.504824\pi\) | ||||
−0.0151537 | + | 0.999885i | \(0.504824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3216.33 | 0.233880 | ||||||||
\(575\) | 2964.45 | 0.215002 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21258.8 | −1.53382 | −0.766911 | − | 0.641754i | \(-0.778207\pi\) | ||||
−0.766911 | + | 0.641754i | \(0.778207\pi\) | |||||||
\(578\) | −256.778 | −0.0184785 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23278.1 | 1.66650 | ||||||||
\(581\) | −45495.0 | −3.24862 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21903.4 | 1.55600 | ||||||||
\(584\) | −561.098 | −0.0397575 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 517.238 | 0.0364623 | ||||||||
\(587\) | −2965.69 | −0.208530 | −0.104265 | − | 0.994550i | \(-0.533249\pi\) | ||||
−0.104265 | + | 0.994550i | \(0.533249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1365.64 | −0.0955349 | ||||||||
\(590\) | 1116.72 | 0.0779230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23900.2 | −1.65928 | ||||||||
\(593\) | 17786.8 | 1.23173 | 0.615865 | − | 0.787852i | \(-0.288807\pi\) | ||||
0.615865 | + | 0.787852i | \(0.288807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38853.7 | 2.67705 | ||||||||
\(596\) | −8477.16 | −0.582614 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21796.4 | −1.48677 | −0.743387 | − | 0.668861i | \(-0.766782\pi\) | ||||
−0.743387 | + | 0.668861i | \(0.766782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20468.7 | 1.38924 | 0.694622 | − | 0.719375i | \(-0.255572\pi\) | ||||
0.694622 | + | 0.719375i | \(0.255572\pi\) | |||||||
\(602\) | 2234.24 | 0.151264 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6983.01 | 0.470422 | ||||||||
\(605\) | 6983.64 | 0.469298 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7852.53 | 0.525081 | 0.262541 | − | 0.964921i | \(-0.415440\pi\) | ||||
0.262541 | + | 0.964921i | \(0.415440\pi\) | |||||||
\(608\) | −434.061 | −0.0289531 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1936.74 | −0.128551 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2460.21 | −0.162099 | −0.0810497 | − | 0.996710i | \(-0.525827\pi\) | ||||
−0.0810497 | + | 0.996710i | \(0.525827\pi\) | |||||||
\(614\) | −187.096 | −0.0122974 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3268.23 | 0.213768 | ||||||||
\(617\) | 17829.3 | 1.16334 | 0.581670 | − | 0.813425i | \(-0.302400\pi\) | ||||
0.581670 | + | 0.813425i | \(0.302400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16901.7 | 1.09748 | 0.548739 | − | 0.835994i | \(-0.315108\pi\) | ||||
0.548739 | + | 0.835994i | \(0.315108\pi\) | |||||||
\(620\) | −15630.8 | −1.01250 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1371.76 | 0.0884286 | ||||||||
\(623\) | 23873.0 | 1.53524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17247.4 | −1.10384 | ||||||||
\(626\) | 1071.83 | 0.0684327 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18413.8 | −1.17005 | ||||||||
\(629\) | −29709.3 | −1.88328 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1833.82 | −0.115695 | −0.0578473 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578473 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(632\) | −1115.71 | −0.0702226 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1117.40 | −0.0699960 | ||||||||
\(635\) | 19739.0 | 1.23357 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1206.51 | 0.0748684 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6617.81 | −0.408737 | ||||||||
\(641\) | −29172.1 | −1.79755 | −0.898773 | − | 0.438414i | \(-0.855540\pi\) | ||||
−0.898773 | + | 0.438414i | \(0.855540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25103.8 | −1.53965 | −0.769826 | − | 0.638254i | \(-0.779657\pi\) | ||||
−0.769826 | + | 0.638254i | \(0.779657\pi\) | |||||||
\(644\) | 6925.69 | 0.423774 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −178.134 | −0.0108492 | ||||||||
\(647\) | 24471.6 | 1.48698 | 0.743492 | − | 0.668745i | \(-0.233168\pi\) | ||||
0.743492 | + | 0.668745i | \(0.233168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10081.4 | −0.609752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2636.06 | 0.158337 | ||||||||
\(653\) | −6632.68 | −0.397484 | −0.198742 | − | 0.980052i | \(-0.563686\pi\) | ||||
−0.198742 | + | 0.980052i | \(0.563686\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34204.5 | 2.04043 | ||||||||
\(656\) | 29228.1 | 1.73958 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1720.40 | 0.101928 | ||||||||
\(659\) | −26436.9 | −1.56272 | −0.781361 | − | 0.624080i | \(-0.785474\pi\) | ||||
−0.781361 | + | 0.624080i | \(0.785474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27596.7 | −1.62389 | −0.811943 | − | 0.583737i | \(-0.801590\pi\) | ||||
−0.811943 | + | 0.583737i | \(0.801590\pi\) | |||||||
\(662\) | −681.020 | −0.0399828 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4788.49 | 0.279863 | ||||||||
\(665\) | 5296.73 | 0.308870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5128.07 | 0.297691 | ||||||||
\(668\) | 17273.8 | 1.00051 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1117.06 | −0.0644115 | ||||||||
\(671\) | 17484.3 | 1.00592 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18860.1 | 1.08024 | 0.540122 | − | 0.841587i | \(-0.318378\pi\) | ||||
0.540122 | + | 0.841587i | \(0.318378\pi\) | |||||||
\(674\) | 1196.87 | 0.0684000 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14705.5 | 0.834825 | 0.417412 | − | 0.908717i | \(-0.362937\pi\) | ||||
0.417412 | + | 0.908717i | \(0.362937\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48423.1 | −2.73683 | ||||||||
\(680\) | −4089.47 | −0.230624 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −810.145 | −0.0454869 | ||||||||
\(683\) | −17950.2 | −1.00563 | −0.502814 | − | 0.864395i | \(-0.667702\pi\) | ||||
−0.502814 | + | 0.864395i | \(0.667702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7282.18 | 0.406186 | ||||||||
\(686\) | 2514.83 | 0.139966 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20303.5 | 1.12509 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8692.38 | 0.478544 | 0.239272 | − | 0.970953i | \(-0.423091\pi\) | ||||
0.239272 | + | 0.970953i | \(0.423091\pi\) | |||||||
\(692\) | −23359.4 | −1.28322 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1492.12 | −0.0816141 | ||||||||
\(695\) | −29558.8 | −1.61328 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36332.2 | 1.97443 | ||||||||
\(698\) | 613.789 | 0.0332840 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28417.4 | 1.53440 | ||||||||
\(701\) | −23275.9 | −1.25409 | −0.627047 | − | 0.778982i | \(-0.715736\pi\) | ||||
−0.627047 | + | 0.778982i | \(0.715736\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4050.11 | −0.217287 | ||||||||
\(704\) | 14634.9 | 0.783485 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1090.84 | 0.0581507 | ||||||||
\(707\) | −15678.4 | −0.834014 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34164.7 | 1.80971 | 0.904854 | − | 0.425722i | \(-0.139980\pi\) | ||||
0.904854 | + | 0.425722i | \(0.139980\pi\) | |||||||
\(710\) | 118.742 | 0.00627651 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2512.71 | −0.132258 | ||||||||
\(713\) | −3443.40 | −0.180864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12850.8 | 0.670748 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2301.75 | 0.119639 | ||||||||
\(719\) | 8391.74 | 0.435270 | 0.217635 | − | 0.976030i | \(-0.430166\pi\) | ||||
0.217635 | + | 0.976030i | \(0.430166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6933.64 | −0.358145 | ||||||||
\(722\) | 1441.48 | 0.0743026 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5767.04 | −0.296036 | ||||||||
\(725\) | 21041.5 | 1.07788 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23500.4 | 1.19887 | 0.599436 | − | 0.800423i | \(-0.295392\pi\) | ||||
0.599436 | + | 0.800423i | \(0.295392\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −539.462 | −0.0273512 | ||||||||
\(731\) | 25238.3 | 1.27698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1289.07 | −0.0649563 | −0.0324781 | − | 0.999472i | \(-0.510340\pi\) | ||||
−0.0324781 | + | 0.999472i | \(0.510340\pi\) | |||||||
\(734\) | 2432.01 | 0.122298 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1094.47 | −0.0548133 | ||||||||
\(737\) | 10084.5 | 0.504024 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18197.8 | 0.905844 | 0.452922 | − | 0.891550i | \(-0.350382\pi\) | ||||
0.452922 | + | 0.891550i | \(0.350382\pi\) | |||||||
\(740\) | −46356.8 | −2.30285 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5123.68 | −0.253499 | ||||||||
\(743\) | 21277.2 | 1.05059 | 0.525294 | − | 0.850921i | \(-0.323956\pi\) | ||||
0.525294 | + | 0.850921i | \(0.323956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16347.4 | −0.803920 | ||||||||
\(746\) | −683.146 | −0.0335278 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18406.4 | 0.899739 | ||||||||
\(749\) | 4803.45 | 0.234331 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25653.4 | −1.24648 | −0.623240 | − | 0.782030i | \(-0.714184\pi\) | ||||
−0.623240 | + | 0.782030i | \(0.714184\pi\) | |||||||
\(752\) | 15634.0 | 0.758130 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13466.0 | 0.649112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26521.2 | 1.27336 | 0.636678 | − | 0.771130i | \(-0.280308\pi\) | ||||
0.636678 | + | 0.771130i | \(0.280308\pi\) | |||||||
\(758\) | 438.245 | 0.0209997 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −557.497 | −0.0266086 | ||||||||
\(761\) | 21607.2 | 1.02925 | 0.514625 | − | 0.857415i | \(-0.327931\pi\) | ||||
0.514625 | + | 0.857415i | \(0.327931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16354.5 | 0.775979 | ||||||||
\(764\) | 13658.2 | 0.646776 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 749.560 | 0.0353560 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17179.2 | 0.805591 | 0.402795 | − | 0.915290i | \(-0.368039\pi\) | ||||
0.402795 | + | 0.915290i | \(0.368039\pi\) | |||||||
\(770\) | 3142.21 | 0.147062 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3466.74 | 0.161620 | ||||||||
\(773\) | −12822.1 | −0.596609 | −0.298304 | − | 0.954471i | \(-0.596421\pi\) | ||||
−0.298304 | + | 0.954471i | \(0.596421\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14128.9 | −0.654873 | ||||||||
\(776\) | 5096.67 | 0.235773 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1404.58 | −0.0647256 | ||||||||
\(779\) | 4952.98 | 0.227804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1071.97 | −0.0491140 | ||||||||
\(782\) | −449.157 | −0.0205394 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 44430.0 | 2.02396 | ||||||||
\(785\) | −35509.1 | −1.61449 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35213.4 | 1.59495 | 0.797474 | − | 0.603354i | \(-0.206169\pi\) | ||||
0.797474 | + | 0.603354i | \(0.206169\pi\) | |||||||
\(788\) | −5524.73 | −0.249759 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1072.69 | −0.0483097 | ||||||||
\(791\) | −36813.9 | −1.65481 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 1129.61 | 0.0504893 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23061.5 | −1.02688 | ||||||||
\(797\) | −7500.15 | −0.333336 | −0.166668 | − | 0.986013i | \(-0.553301\pi\) | ||||
−0.166668 | + | 0.986013i | \(0.553301\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19434.0 | 0.860481 | ||||||||
\(800\) | −4490.82 | −0.198468 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −196.506 | −0.00865195 | ||||||||
\(803\) | 4870.10 | 0.214025 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13355.5 | 0.584745 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1650.20 | 0.0718489 | ||||||||
\(809\) | 22020.5 | 0.956982 | 0.478491 | − | 0.878092i | \(-0.341184\pi\) | ||||
0.478491 | + | 0.878092i | \(0.341184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20444.6 | −0.885210 | −0.442605 | − | 0.896717i | \(-0.645946\pi\) | ||||
−0.442605 | + | 0.896717i | \(0.645946\pi\) | |||||||
\(812\) | 49158.1 | 2.12452 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2402.67 | −0.103457 | ||||||||
\(815\) | 5083.37 | 0.218482 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3440.62 | 0.147334 | ||||||||
\(818\) | 328.920 | 0.0140592 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56690.8 | 2.41431 | ||||||||
\(821\) | 40353.0 | 1.71538 | 0.857692 | − | 0.514164i | \(-0.171898\pi\) | ||||
0.857692 | + | 0.514164i | \(0.171898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33110.7 | −1.40239 | −0.701194 | − | 0.712971i | \(-0.747349\pi\) | ||||
−0.701194 | + | 0.712971i | \(0.747349\pi\) | |||||||
\(824\) | 729.787 | 0.0308536 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2358.26 | 0.0993392 | ||||||||
\(827\) | −43410.4 | −1.82531 | −0.912653 | − | 0.408735i | \(-0.865970\pi\) | ||||
−0.912653 | + | 0.408735i | \(0.865970\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5502.87 | −0.230546 | −0.115273 | − | 0.993334i | \(-0.536774\pi\) | ||||
−0.115273 | + | 0.993334i | \(0.536774\pi\) | |||||||
\(830\) | 4603.84 | 0.192532 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 55229.1 | 2.29721 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33310.8 | 1.38056 | ||||||||
\(836\) | 2509.25 | 0.103809 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2260.93 | 0.0932013 | ||||||||
\(839\) | −1698.27 | −0.0698819 | −0.0349409 | − | 0.999389i | \(-0.511124\pi\) | ||||
−0.0349409 | + | 0.999389i | \(0.511124\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12009.8 | 0.492425 | ||||||||
\(842\) | −16.0136 | −0.000655423 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −41762.7 | −1.70323 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14747.9 | 0.598279 | ||||||||
\(848\) | −46561.0 | −1.88551 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1842.98 | −0.0743691 | ||||||||
\(851\) | −10212.2 | −0.411363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18686.8 | −0.750087 | −0.375044 | − | 0.927007i | \(-0.622372\pi\) | ||||
−0.375044 | + | 0.927007i | \(0.622372\pi\) | |||||||
\(854\) | −4089.95 | −0.163882 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −505.578 | −0.0201873 | ||||||||
\(857\) | 9659.16 | 0.385007 | 0.192503 | − | 0.981296i | \(-0.438339\pi\) | ||||
0.192503 | + | 0.981296i | \(0.438339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1559.90 | −0.0619595 | −0.0309798 | − | 0.999520i | \(-0.509863\pi\) | ||||
−0.0309798 | + | 0.999520i | \(0.509863\pi\) | |||||||
\(860\) | 39380.6 | 1.56147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2599.79 | −0.102725 | ||||||||
\(863\) | −11358.7 | −0.448034 | −0.224017 | − | 0.974585i | \(-0.571917\pi\) | ||||
−0.224017 | + | 0.974585i | \(0.571917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45046.3 | −1.77066 | ||||||||
\(866\) | 613.155 | 0.0240599 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33008.7 | −1.29077 | ||||||||
\(869\) | 9683.93 | 0.378026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1721.36 | −0.0668493 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −61.2314 | −0.00236977 | ||||||||
\(875\) | −7309.45 | −0.282405 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33301.6 | 1.28223 | 0.641115 | − | 0.767444i | \(-0.278472\pi\) | ||||
0.641115 | + | 0.767444i | \(0.278472\pi\) | |||||||
\(878\) | 821.701 | 0.0315844 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28554.6 | 1.09383 | ||||||||
\(881\) | −28912.3 | −1.10565 | −0.552826 | − | 0.833296i | \(-0.686451\pi\) | ||||
−0.552826 | + | 0.833296i | \(0.686451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49100.9 | −1.87132 | −0.935661 | − | 0.352901i | \(-0.885195\pi\) | ||||
−0.935661 | + | 0.352901i | \(0.885195\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −824.517 | −0.0312643 | ||||||||
\(887\) | −4566.49 | −0.172861 | −0.0864304 | − | 0.996258i | \(-0.527546\pi\) | ||||
−0.0864304 | + | 0.996258i | \(0.527546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41684.3 | 1.57261 | ||||||||
\(890\) | −2415.82 | −0.0909870 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10996.5 | −0.412771 | ||||||||
\(893\) | 2649.33 | 0.0992795 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24781.4 | 0.925533 | ||||||||
\(896\) | −13975.3 | −0.521074 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1186.14 | −0.0440780 | ||||||||
\(899\) | −24441.0 | −0.906734 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −57877.9 | −2.14006 | ||||||||
\(902\) | 2938.29 | 0.108464 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3874.78 | 0.142559 | ||||||||
\(905\) | −11121.2 | −0.408486 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48873.3 | 1.78921 | 0.894604 | − | 0.446860i | \(-0.147458\pi\) | ||||
0.894604 | + | 0.446860i | \(0.147458\pi\) | |||||||
\(908\) | −9732.72 | −0.355718 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31550.1 | −1.14742 | −0.573710 | − | 0.819058i | \(-0.694497\pi\) | ||||
−0.573710 | + | 0.819058i | \(0.694497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −41562.1 | −1.50658 | ||||||||
\(914\) | −1731.49 | −0.0626613 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31973.3 | −1.15331 | ||||||||
\(917\) | 72232.1 | 2.60121 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11720.3 | −0.420694 | −0.210347 | − | 0.977627i | \(-0.567459\pi\) | ||||
−0.210347 | + | 0.977627i | \(0.567459\pi\) | |||||||
\(920\) | −1405.71 | −0.0503748 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1972.63 | 0.0704612 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41902.7 | −1.48946 | ||||||||
\(926\) | 2977.84 | 0.105678 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7768.47 | −0.274798 | ||||||||
\(929\) | −6911.23 | −0.244080 | −0.122040 | − | 0.992525i | \(-0.538944\pi\) | ||||
−0.122040 | + | 0.992525i | \(0.538944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7529.10 | 0.265044 | ||||||||
\(932\) | 13191.5 | 0.463628 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2333.18 | 0.0817386 | ||||||||
\(935\) | 35494.9 | 1.24151 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28673.9 | −0.999717 | −0.499858 | − | 0.866107i | \(-0.666615\pi\) | ||||
−0.499858 | + | 0.866107i | \(0.666615\pi\) | |||||||
\(938\) | −2358.97 | −0.0821143 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30323.7 | 1.05218 | ||||||||
\(941\) | 22463.6 | 0.778207 | 0.389103 | − | 0.921194i | \(-0.372785\pi\) | ||||
0.389103 | + | 0.921194i | \(0.372785\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12488.8 | 0.431272 | ||||||||
\(944\) | 21430.4 | 0.738878 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2041.10 | 0.0701499 | ||||||||
\(947\) | 36806.6 | 1.26299 | 0.631497 | − | 0.775379i | \(-0.282441\pi\) | ||||
0.631497 | + | 0.775379i | \(0.282441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −251.244 | −0.00858046 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8636.04 | −0.294008 | ||||||||
\(953\) | 1781.07 | 0.0605400 | 0.0302700 | − | 0.999542i | \(-0.490363\pi\) | ||||
0.0302700 | + | 0.999542i | \(0.490363\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26338.5 | 0.892455 | ||||||||
\(956\) | 4920.19 | 0.166454 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2356.77 | −0.0794819 | ||||||||
\(959\) | 15378.3 | 0.517822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13379.3 | −0.449107 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9030.12 | −0.301702 | ||||||||
\(965\) | 6685.26 | 0.223012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54777.2 | −1.82163 | −0.910815 | − | 0.412815i | \(-0.864545\pi\) | ||||
−0.910815 | + | 0.412815i | \(0.864545\pi\) | |||||||
\(968\) | −1552.26 | −0.0515408 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4900.15 | 0.162200 | ||||||||
\(971\) | 2391.54 | 0.0790403 | 0.0395201 | − | 0.999219i | \(-0.487417\pi\) | ||||
0.0395201 | + | 0.999219i | \(0.487417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62421.5 | −2.05667 | ||||||||
\(974\) | 230.391 | 0.00757925 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37167.0 | −1.21894 | ||||||||
\(977\) | −43738.5 | −1.43226 | −0.716130 | − | 0.697967i | \(-0.754088\pi\) | ||||
−0.716130 | + | 0.697967i | \(0.754088\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21809.3 | 0.711979 | ||||||||
\(980\) | 86176.5 | 2.80899 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1404.62 | 0.0456449 | ||||||||
\(983\) | 27712.4 | 0.899174 | 0.449587 | − | 0.893236i | \(-0.351571\pi\) | ||||
0.449587 | + | 0.893236i | \(0.351571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10653.9 | −0.344631 | ||||||||
\(986\) | −3188.09 | −0.102971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8675.38 | 0.278929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3550.23 | 0.113801 | 0.0569005 | − | 0.998380i | \(-0.481878\pi\) | ||||
0.0569005 | + | 0.998380i | \(0.481878\pi\) | |||||||
\(992\) | 5216.37 | 0.166956 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 250.757 | 0.00800153 | ||||||||
\(995\) | −44471.8 | −1.41694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28338.4 | −0.900188 | −0.450094 | − | 0.892981i | \(-0.648610\pi\) | ||||
−0.450094 | + | 0.892981i | \(0.648610\pi\) | |||||||
\(998\) | 2127.76 | 0.0674882 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.bi.1.4 | 9 | ||
3.2 | odd | 2 | 507.4.a.o.1.6 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.bf.1.6 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.9 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.10 | 18 | |||
39.38 | odd | 2 | 507.4.a.p.1.4 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.6 | ✓ | 9 | 3.2 | odd | 2 | ||
507.4.a.p.1.4 | yes | 9 | 39.38 | odd | 2 | ||
507.4.b.k.337.9 | 18 | 39.5 | even | 4 | |||
507.4.b.k.337.10 | 18 | 39.8 | even | 4 | |||
1521.4.a.bf.1.6 | 9 | 13.12 | even | 2 | |||
1521.4.a.bi.1.4 | 9 | 1.1 | even | 1 | trivial |