Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.241849\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.65606 | 0.585506 | 0.292753 | − | 0.956188i | \(-0.405429\pi\) | ||||
0.292753 | + | 0.956188i | \(0.405429\pi\) | |||||||
\(3\) | 0.332888 | 0.0640643 | 0.0320321 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320321 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(4\) | −5.25746 | −0.657182 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0.551283 | 0.0375100 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.9552 | −0.970291 | ||||||||
\(9\) | −26.8892 | −0.995896 | ||||||||
\(10\) | 8.28031 | 0.261846 | ||||||||
\(11\) | 69.5726 | 1.90699 | 0.953497 | − | 0.301402i | \(-0.0974546\pi\) | ||||
0.953497 | + | 0.301402i | \(0.0974546\pi\) | |||||||
\(12\) | −1.75014 | −0.0421019 | ||||||||
\(13\) | −68.4326 | −1.45998 | −0.729991 | − | 0.683456i | \(-0.760476\pi\) | ||||
−0.729991 | + | 0.683456i | \(0.760476\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.66444 | 0.0286504 | ||||||||
\(16\) | 5.70053 | 0.0890707 | ||||||||
\(17\) | −104.332 | −1.48848 | −0.744240 | − | 0.667912i | \(-0.767188\pi\) | ||||
−0.744240 | + | 0.667912i | \(0.767188\pi\) | |||||||
\(18\) | −44.5302 | −0.583103 | ||||||||
\(19\) | −71.8929 | −0.868072 | −0.434036 | − | 0.900896i | \(-0.642911\pi\) | ||||
−0.434036 | + | 0.900896i | \(0.642911\pi\) | |||||||
\(20\) | −26.2873 | −0.293901 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 115.217 | 1.11656 | ||||||||
\(23\) | −101.031 | −0.915929 | −0.457964 | − | 0.888970i | \(-0.651421\pi\) | ||||
−0.457964 | + | 0.888970i | \(0.651421\pi\) | |||||||
\(24\) | −7.30861 | −0.0621610 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −113.329 | −0.854829 | ||||||||
\(27\) | −17.9390 | −0.127866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −114.661 | −0.734205 | −0.367102 | − | 0.930181i | \(-0.619650\pi\) | ||||
−0.367102 | + | 0.930181i | \(0.619650\pi\) | |||||||
\(30\) | 2.75641 | 0.0167750 | ||||||||
\(31\) | 73.6505 | 0.426710 | 0.213355 | − | 0.976975i | \(-0.431561\pi\) | ||||
0.213355 | + | 0.976975i | \(0.431561\pi\) | |||||||
\(32\) | 185.082 | 1.02244 | ||||||||
\(33\) | 23.1599 | 0.122170 | ||||||||
\(34\) | −172.780 | −0.871514 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 141.369 | 0.654485 | ||||||||
\(37\) | −200.933 | −0.892790 | −0.446395 | − | 0.894836i | \(-0.647292\pi\) | ||||
−0.446395 | + | 0.894836i | \(0.647292\pi\) | |||||||
\(38\) | −119.059 | −0.508262 | ||||||||
\(39\) | −22.7803 | −0.0935327 | ||||||||
\(40\) | −109.776 | −0.433927 | ||||||||
\(41\) | −417.308 | −1.58957 | −0.794786 | − | 0.606889i | \(-0.792417\pi\) | ||||
−0.794786 | + | 0.606889i | \(0.792417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 311.175 | 1.10357 | 0.551787 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551787 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(44\) | −365.775 | −1.25324 | ||||||||
\(45\) | −134.446 | −0.445378 | ||||||||
\(46\) | −167.313 | −0.536282 | ||||||||
\(47\) | −149.697 | −0.464586 | −0.232293 | − | 0.972646i | \(-0.574623\pi\) | ||||
−0.232293 | + | 0.972646i | \(0.574623\pi\) | |||||||
\(48\) | 1.89763 | 0.00570625 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 41.4016 | 0.117101 | ||||||||
\(51\) | −34.7307 | −0.0953583 | ||||||||
\(52\) | 359.781 | 0.959475 | ||||||||
\(53\) | 271.474 | 0.703582 | 0.351791 | − | 0.936078i | \(-0.385573\pi\) | ||||
0.351791 | + | 0.936078i | \(0.385573\pi\) | |||||||
\(54\) | −29.7082 | −0.0748661 | ||||||||
\(55\) | 347.863 | 0.852834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23.9323 | −0.0556124 | ||||||||
\(58\) | −189.885 | −0.429882 | ||||||||
\(59\) | 518.028 | 1.14308 | 0.571538 | − | 0.820575i | \(-0.306347\pi\) | ||||
0.571538 | + | 0.820575i | \(0.306347\pi\) | |||||||
\(60\) | −8.75071 | −0.0188285 | ||||||||
\(61\) | 219.926 | 0.461616 | 0.230808 | − | 0.972999i | \(-0.425863\pi\) | ||||
0.230808 | + | 0.972999i | \(0.425863\pi\) | |||||||
\(62\) | 121.970 | 0.249842 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 260.903 | 0.509576 | ||||||||
\(65\) | −342.163 | −0.652924 | ||||||||
\(66\) | 38.3542 | 0.0715314 | ||||||||
\(67\) | 80.6950 | 0.147141 | 0.0735706 | − | 0.997290i | \(-0.476561\pi\) | ||||
0.0735706 | + | 0.997290i | \(0.476561\pi\) | |||||||
\(68\) | 548.520 | 0.978202 | ||||||||
\(69\) | −33.6319 | −0.0586783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −91.0463 | −0.152186 | −0.0760930 | − | 0.997101i | \(-0.524245\pi\) | ||||
−0.0760930 | + | 0.997101i | \(0.524245\pi\) | |||||||
\(72\) | 590.357 | 0.966309 | ||||||||
\(73\) | −882.282 | −1.41457 | −0.707283 | − | 0.706931i | \(-0.750079\pi\) | ||||
−0.707283 | + | 0.706931i | \(0.750079\pi\) | |||||||
\(74\) | −332.758 | −0.522734 | ||||||||
\(75\) | 8.32219 | 0.0128129 | ||||||||
\(76\) | 377.974 | 0.570481 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −37.7257 | −0.0547640 | ||||||||
\(79\) | 599.877 | 0.854322 | 0.427161 | − | 0.904175i | \(-0.359514\pi\) | ||||
0.427161 | + | 0.904175i | \(0.359514\pi\) | |||||||
\(80\) | 28.5026 | 0.0398336 | ||||||||
\(81\) | 720.036 | 0.987704 | ||||||||
\(82\) | −691.087 | −0.930705 | ||||||||
\(83\) | −70.8820 | −0.0937387 | −0.0468694 | − | 0.998901i | \(-0.514924\pi\) | ||||
−0.0468694 | + | 0.998901i | \(0.514924\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −521.659 | −0.665668 | ||||||||
\(86\) | 515.325 | 0.646150 | ||||||||
\(87\) | −38.1691 | −0.0470363 | ||||||||
\(88\) | −1527.48 | −1.85034 | ||||||||
\(89\) | −802.592 | −0.955894 | −0.477947 | − | 0.878389i | \(-0.658619\pi\) | ||||
−0.477947 | + | 0.878389i | \(0.658619\pi\) | |||||||
\(90\) | −222.651 | −0.260772 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 531.165 | 0.601932 | ||||||||
\(93\) | 24.5173 | 0.0273369 | ||||||||
\(94\) | −247.908 | −0.272018 | ||||||||
\(95\) | −359.465 | −0.388214 | ||||||||
\(96\) | 61.6114 | 0.0655020 | ||||||||
\(97\) | −145.648 | −0.152457 | −0.0762283 | − | 0.997090i | \(-0.524288\pi\) | ||||
−0.0762283 | + | 0.997090i | \(0.524288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1870.75 | −1.89917 | ||||||||
\(100\) | −131.436 | −0.131436 | ||||||||
\(101\) | 619.435 | 0.610259 | 0.305129 | − | 0.952311i | \(-0.401300\pi\) | ||||
0.305129 | + | 0.952311i | \(0.401300\pi\) | |||||||
\(102\) | −57.5163 | −0.0558329 | ||||||||
\(103\) | 1822.08 | 1.74306 | 0.871528 | − | 0.490345i | \(-0.163129\pi\) | ||||
0.871528 | + | 0.490345i | \(0.163129\pi\) | |||||||
\(104\) | 1502.45 | 1.41661 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 449.578 | 0.411952 | ||||||||
\(107\) | 1089.70 | 0.984536 | 0.492268 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492268 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(108\) | 94.3138 | 0.0840310 | ||||||||
\(109\) | 589.667 | 0.518164 | 0.259082 | − | 0.965855i | \(-0.416580\pi\) | ||||
0.259082 | + | 0.965855i | \(0.416580\pi\) | |||||||
\(110\) | 576.083 | 0.499340 | ||||||||
\(111\) | −66.8882 | −0.0571959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −900.358 | −0.749544 | −0.374772 | − | 0.927117i | \(-0.622279\pi\) | ||||
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(114\) | −39.6333 | −0.0325614 | ||||||||
\(115\) | −505.154 | −0.409616 | ||||||||
\(116\) | 602.823 | 0.482506 | ||||||||
\(117\) | 1840.10 | 1.45399 | ||||||||
\(118\) | 857.887 | 0.669279 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −36.5430 | −0.0277992 | ||||||||
\(121\) | 3509.35 | 2.63663 | ||||||||
\(122\) | 364.210 | 0.270279 | ||||||||
\(123\) | −138.917 | −0.101835 | ||||||||
\(124\) | −387.214 | −0.280426 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1755.75 | −1.22676 | −0.613378 | − | 0.789790i | \(-0.710190\pi\) | ||||
−0.613378 | + | 0.789790i | \(0.710190\pi\) | |||||||
\(128\) | −1048.58 | −0.724082 | ||||||||
\(129\) | 103.586 | 0.0706996 | ||||||||
\(130\) | −566.643 | −0.382291 | ||||||||
\(131\) | −1809.10 | −1.20658 | −0.603289 | − | 0.797523i | \(-0.706143\pi\) | ||||
−0.603289 | + | 0.797523i | \(0.706143\pi\) | |||||||
\(132\) | −121.762 | −0.0802881 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 133.636 | 0.0861521 | ||||||||
\(135\) | −89.6952 | −0.0571832 | ||||||||
\(136\) | 2290.62 | 1.44426 | ||||||||
\(137\) | −18.5134 | −0.0115453 | −0.00577265 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577265 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(138\) | −55.6965 | −0.0343565 | ||||||||
\(139\) | 625.608 | 0.381751 | 0.190875 | − | 0.981614i | \(-0.438867\pi\) | ||||
0.190875 | + | 0.981614i | \(0.438867\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −49.8323 | −0.0297634 | ||||||||
\(142\) | −150.778 | −0.0891059 | ||||||||
\(143\) | −4761.03 | −2.78418 | ||||||||
\(144\) | −153.283 | −0.0887052 | ||||||||
\(145\) | −573.303 | −0.328346 | ||||||||
\(146\) | −1461.11 | −0.828237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1056.40 | 0.586725 | ||||||||
\(149\) | −1028.63 | −0.565563 | −0.282782 | − | 0.959184i | \(-0.591257\pi\) | ||||
−0.282782 | + | 0.959184i | \(0.591257\pi\) | |||||||
\(150\) | 13.7821 | 0.00750201 | ||||||||
\(151\) | 71.0073 | 0.0382682 | 0.0191341 | − | 0.999817i | \(-0.493909\pi\) | ||||
0.0191341 | + | 0.999817i | \(0.493909\pi\) | |||||||
\(152\) | 1578.42 | 0.842282 | ||||||||
\(153\) | 2805.39 | 1.48237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 368.252 | 0.190831 | ||||||||
\(156\) | 119.767 | 0.0614680 | ||||||||
\(157\) | 2061.32 | 1.04784 | 0.523922 | − | 0.851767i | \(-0.324468\pi\) | ||||
0.523922 | + | 0.851767i | \(0.324468\pi\) | |||||||
\(158\) | 993.434 | 0.500211 | ||||||||
\(159\) | 90.3704 | 0.0450745 | ||||||||
\(160\) | 925.409 | 0.457250 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1192.42 | 0.578307 | ||||||||
\(163\) | −1963.80 | −0.943660 | −0.471830 | − | 0.881690i | \(-0.656406\pi\) | ||||
−0.471830 | + | 0.881690i | \(0.656406\pi\) | |||||||
\(164\) | 2193.98 | 1.04464 | ||||||||
\(165\) | 115.799 | 0.0546362 | ||||||||
\(166\) | −117.385 | −0.0548846 | ||||||||
\(167\) | −2855.04 | −1.32293 | −0.661467 | − | 0.749974i | \(-0.730066\pi\) | ||||
−0.661467 | + | 0.749974i | \(0.730066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2486.01 | 1.13155 | ||||||||
\(170\) | −863.899 | −0.389753 | ||||||||
\(171\) | 1933.14 | 0.864509 | ||||||||
\(172\) | −1635.99 | −0.725249 | ||||||||
\(173\) | 1553.21 | 0.682590 | 0.341295 | − | 0.939956i | \(-0.389134\pi\) | ||||
0.341295 | + | 0.939956i | \(0.389134\pi\) | |||||||
\(174\) | −63.2104 | −0.0275400 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 396.601 | 0.169857 | ||||||||
\(177\) | 172.445 | 0.0732303 | ||||||||
\(178\) | −1329.14 | −0.559682 | ||||||||
\(179\) | 269.841 | 0.112675 | 0.0563376 | − | 0.998412i | \(-0.482058\pi\) | ||||
0.0563376 | + | 0.998412i | \(0.482058\pi\) | |||||||
\(180\) | 706.844 | 0.292695 | ||||||||
\(181\) | −2229.61 | −0.915613 | −0.457806 | − | 0.889052i | \(-0.651365\pi\) | ||||
−0.457806 | + | 0.889052i | \(0.651365\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73.2105 | 0.0295731 | ||||||||
\(184\) | 2218.15 | 0.888717 | ||||||||
\(185\) | −1004.67 | −0.399268 | ||||||||
\(186\) | 40.6022 | 0.0160059 | ||||||||
\(187\) | −7258.63 | −2.83852 | ||||||||
\(188\) | 787.026 | 0.305318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −595.296 | −0.227302 | ||||||||
\(191\) | −465.920 | −0.176507 | −0.0882533 | − | 0.996098i | \(-0.528129\pi\) | ||||
−0.0882533 | + | 0.996098i | \(0.528129\pi\) | |||||||
\(192\) | 86.8513 | 0.0326456 | ||||||||
\(193\) | −4414.46 | −1.64642 | −0.823212 | − | 0.567734i | \(-0.807820\pi\) | ||||
−0.823212 | + | 0.567734i | \(0.807820\pi\) | |||||||
\(194\) | −241.202 | −0.0892643 | ||||||||
\(195\) | −113.902 | −0.0418291 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −289.812 | −0.104814 | −0.0524068 | − | 0.998626i | \(-0.516689\pi\) | ||||
−0.0524068 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(198\) | −3098.08 | −1.11197 | ||||||||
\(199\) | −4817.73 | −1.71618 | −0.858091 | − | 0.513498i | \(-0.828349\pi\) | ||||
−0.858091 | + | 0.513498i | \(0.828349\pi\) | |||||||
\(200\) | −548.879 | −0.194058 | ||||||||
\(201\) | 26.8624 | 0.00942649 | ||||||||
\(202\) | 1025.82 | 0.357310 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 182.595 | 0.0626678 | ||||||||
\(205\) | −2086.54 | −0.710879 | ||||||||
\(206\) | 3017.48 | 1.02057 | ||||||||
\(207\) | 2716.63 | 0.912170 | ||||||||
\(208\) | −390.102 | −0.130042 | ||||||||
\(209\) | −5001.78 | −1.65541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2022.01 | 0.659719 | 0.329859 | − | 0.944030i | \(-0.392999\pi\) | ||||
0.329859 | + | 0.944030i | \(0.392999\pi\) | |||||||
\(212\) | −1427.26 | −0.462382 | ||||||||
\(213\) | −30.3082 | −0.00974968 | ||||||||
\(214\) | 1804.61 | 0.576452 | ||||||||
\(215\) | 1555.87 | 0.493533 | ||||||||
\(216\) | 393.855 | 0.124067 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 976.525 | 0.303388 | ||||||||
\(219\) | −293.701 | −0.0906231 | ||||||||
\(220\) | −1828.88 | −0.560467 | ||||||||
\(221\) | 7139.69 | 2.17315 | ||||||||
\(222\) | −110.771 | −0.0334886 | ||||||||
\(223\) | −4343.86 | −1.30442 | −0.652211 | − | 0.758037i | \(-0.726158\pi\) | ||||
−0.652211 | + | 0.758037i | \(0.726158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −672.230 | −0.199179 | ||||||||
\(226\) | −1491.05 | −0.438863 | ||||||||
\(227\) | 2647.59 | 0.774127 | 0.387064 | − | 0.922053i | \(-0.373489\pi\) | ||||
0.387064 | + | 0.922053i | \(0.373489\pi\) | |||||||
\(228\) | 125.823 | 0.0365475 | ||||||||
\(229\) | 1445.09 | 0.417006 | 0.208503 | − | 0.978022i | \(-0.433141\pi\) | ||||
0.208503 | + | 0.978022i | \(0.433141\pi\) | |||||||
\(230\) | −836.566 | −0.239833 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2517.39 | 0.712392 | ||||||||
\(233\) | −6245.91 | −1.75615 | −0.878076 | − | 0.478522i | \(-0.841173\pi\) | ||||
−0.878076 | + | 0.478522i | \(0.841173\pi\) | |||||||
\(234\) | 3047.31 | 0.851321 | ||||||||
\(235\) | −748.485 | −0.207769 | ||||||||
\(236\) | −2723.51 | −0.751209 | ||||||||
\(237\) | 199.692 | 0.0547315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1340.24 | 0.362731 | 0.181366 | − | 0.983416i | \(-0.441948\pi\) | ||||
0.181366 | + | 0.983416i | \(0.441948\pi\) | |||||||
\(240\) | 9.48817 | 0.00255191 | ||||||||
\(241\) | −3369.92 | −0.900729 | −0.450364 | − | 0.892845i | \(-0.648706\pi\) | ||||
−0.450364 | + | 0.892845i | \(0.648706\pi\) | |||||||
\(242\) | 5811.70 | 1.54376 | ||||||||
\(243\) | 724.045 | 0.191142 | ||||||||
\(244\) | −1156.25 | −0.303366 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −230.054 | −0.0596249 | ||||||||
\(247\) | 4919.82 | 1.26737 | ||||||||
\(248\) | −1617.01 | −0.414033 | ||||||||
\(249\) | −23.5958 | −0.00600530 | ||||||||
\(250\) | 207.008 | 0.0523693 | ||||||||
\(251\) | 3592.64 | 0.903449 | 0.451724 | − | 0.892158i | \(-0.350809\pi\) | ||||
0.451724 | + | 0.892158i | \(0.350809\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7028.97 | −1.74667 | ||||||||
\(254\) | −2907.64 | −0.718273 | ||||||||
\(255\) | −173.654 | −0.0426455 | ||||||||
\(256\) | −3823.74 | −0.933531 | ||||||||
\(257\) | 2.84763 | 0.000691167 0 | 0.000345584 | − | 1.00000i | \(-0.499890\pi\) | ||||
0.000345584 | 1.00000i | \(0.499890\pi\) | ||||||||
\(258\) | 171.545 | 0.0413951 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1798.91 | 0.429090 | ||||||||
\(261\) | 3083.13 | 0.731191 | ||||||||
\(262\) | −2995.98 | −0.706459 | ||||||||
\(263\) | −2817.07 | −0.660488 | −0.330244 | − | 0.943896i | \(-0.607131\pi\) | ||||
−0.330244 | + | 0.943896i | \(0.607131\pi\) | |||||||
\(264\) | −508.479 | −0.118541 | ||||||||
\(265\) | 1357.37 | 0.314652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −267.173 | −0.0612386 | ||||||||
\(268\) | −424.250 | −0.0966986 | ||||||||
\(269\) | 1447.43 | 0.328072 | 0.164036 | − | 0.986454i | \(-0.447549\pi\) | ||||
0.164036 | + | 0.986454i | \(0.447549\pi\) | |||||||
\(270\) | −148.541 | −0.0334811 | ||||||||
\(271\) | −8054.50 | −1.80545 | −0.902724 | − | 0.430221i | \(-0.858436\pi\) | ||||
−0.902724 | + | 0.430221i | \(0.858436\pi\) | |||||||
\(272\) | −594.746 | −0.132580 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.6593 | −0.00675985 | ||||||||
\(275\) | 1739.32 | 0.381399 | ||||||||
\(276\) | 176.818 | 0.0385623 | ||||||||
\(277\) | −571.300 | −0.123921 | −0.0619604 | − | 0.998079i | \(-0.519735\pi\) | ||||
−0.0619604 | + | 0.998079i | \(0.519735\pi\) | |||||||
\(278\) | 1036.05 | 0.223518 | ||||||||
\(279\) | −1980.40 | −0.424959 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1784.48 | −0.378837 | −0.189418 | − | 0.981896i | \(-0.560660\pi\) | ||||
−0.189418 | + | 0.981896i | \(0.560660\pi\) | |||||||
\(282\) | −82.5254 | −0.0174267 | ||||||||
\(283\) | −3321.05 | −0.697582 | −0.348791 | − | 0.937201i | \(-0.613408\pi\) | ||||
−0.348791 | + | 0.937201i | \(0.613408\pi\) | |||||||
\(284\) | 478.672 | 0.100014 | ||||||||
\(285\) | −119.661 | −0.0248706 | ||||||||
\(286\) | −7884.57 | −1.63015 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4976.70 | −1.01825 | ||||||||
\(289\) | 5972.11 | 1.21557 | ||||||||
\(290\) | −949.425 | −0.192249 | ||||||||
\(291\) | −48.4843 | −0.00976701 | ||||||||
\(292\) | 4638.56 | 0.929627 | ||||||||
\(293\) | 5049.54 | 1.00682 | 0.503408 | − | 0.864049i | \(-0.332079\pi\) | ||||
0.503408 | + | 0.864049i | \(0.332079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2590.14 | 0.511199 | ||||||||
\(296\) | 4411.52 | 0.866266 | ||||||||
\(297\) | −1248.07 | −0.243839 | ||||||||
\(298\) | −1703.48 | −0.331141 | ||||||||
\(299\) | 6913.79 | 1.33724 | ||||||||
\(300\) | −43.7536 | −0.00842038 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 117.593 | 0.0224063 | ||||||||
\(303\) | 206.202 | 0.0390958 | ||||||||
\(304\) | −409.828 | −0.0773198 | ||||||||
\(305\) | 1099.63 | 0.206441 | ||||||||
\(306\) | 4645.91 | 0.867938 | ||||||||
\(307\) | 1535.73 | 0.285500 | 0.142750 | − | 0.989759i | \(-0.454405\pi\) | ||||
0.142750 | + | 0.989759i | \(0.454405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 606.548 | 0.111668 | ||||||||
\(310\) | 609.849 | 0.111733 | ||||||||
\(311\) | 9283.05 | 1.69258 | 0.846291 | − | 0.532720i | \(-0.178830\pi\) | ||||
0.846291 | + | 0.532720i | \(0.178830\pi\) | |||||||
\(312\) | 500.147 | 0.0907539 | ||||||||
\(313\) | −6025.43 | −1.08811 | −0.544054 | − | 0.839050i | \(-0.683111\pi\) | ||||
−0.544054 | + | 0.839050i | \(0.683111\pi\) | |||||||
\(314\) | 3413.68 | 0.613519 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3153.83 | −0.561445 | ||||||||
\(317\) | −6977.58 | −1.23628 | −0.618139 | − | 0.786069i | \(-0.712113\pi\) | ||||
−0.618139 | + | 0.786069i | \(0.712113\pi\) | |||||||
\(318\) | 149.659 | 0.0263914 | ||||||||
\(319\) | −7977.24 | −1.40012 | ||||||||
\(320\) | 1304.51 | 0.227889 | ||||||||
\(321\) | 362.748 | 0.0630736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7500.71 | 1.29211 | ||||||||
\(324\) | −3785.56 | −0.649102 | ||||||||
\(325\) | −1710.81 | −0.291997 | ||||||||
\(326\) | −3252.17 | −0.552519 | ||||||||
\(327\) | 196.293 | 0.0331958 | ||||||||
\(328\) | 9162.06 | 1.54235 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 191.771 | 0.0319898 | ||||||||
\(331\) | 984.878 | 0.163546 | 0.0817731 | − | 0.996651i | \(-0.473942\pi\) | ||||
0.0817731 | + | 0.996651i | \(0.473942\pi\) | |||||||
\(332\) | 372.659 | 0.0616034 | ||||||||
\(333\) | 5402.93 | 0.889125 | ||||||||
\(334\) | −4728.13 | −0.774586 | ||||||||
\(335\) | 403.475 | 0.0658035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 51.9653 | 0.00839979 | 0.00419990 | − | 0.999991i | \(-0.498663\pi\) | ||||
0.00419990 | + | 0.999991i | \(0.498663\pi\) | |||||||
\(338\) | 4116.99 | 0.662529 | ||||||||
\(339\) | −299.718 | −0.0480190 | ||||||||
\(340\) | 2742.60 | 0.437465 | ||||||||
\(341\) | 5124.06 | 0.813734 | ||||||||
\(342\) | 3201.40 | 0.506176 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6831.89 | −1.07079 | ||||||||
\(345\) | −168.159 | −0.0262417 | ||||||||
\(346\) | 2572.21 | 0.399661 | ||||||||
\(347\) | −11300.5 | −1.74825 | −0.874123 | − | 0.485704i | \(-0.838563\pi\) | ||||
−0.874123 | + | 0.485704i | \(0.838563\pi\) | |||||||
\(348\) | 200.672 | 0.0309114 | ||||||||
\(349\) | 2016.91 | 0.309349 | 0.154674 | − | 0.987966i | \(-0.450567\pi\) | ||||
0.154674 | + | 0.987966i | \(0.450567\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1227.61 | 0.186682 | ||||||||
\(352\) | 12876.6 | 1.94979 | ||||||||
\(353\) | 7589.41 | 1.14432 | 0.572158 | − | 0.820143i | \(-0.306106\pi\) | ||||
0.572158 | + | 0.820143i | \(0.306106\pi\) | |||||||
\(354\) | 285.580 | 0.0428768 | ||||||||
\(355\) | −455.232 | −0.0680597 | ||||||||
\(356\) | 4219.59 | 0.628196 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 446.873 | 0.0659720 | ||||||||
\(359\) | 8734.24 | 1.28405 | 0.642027 | − | 0.766682i | \(-0.278094\pi\) | ||||
0.642027 | + | 0.766682i | \(0.278094\pi\) | |||||||
\(360\) | 2951.78 | 0.432146 | ||||||||
\(361\) | −1690.41 | −0.246451 | ||||||||
\(362\) | −3692.38 | −0.536097 | ||||||||
\(363\) | 1168.22 | 0.168914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4411.41 | −0.632613 | ||||||||
\(366\) | 121.241 | 0.0173152 | ||||||||
\(367\) | 1890.54 | 0.268898 | 0.134449 | − | 0.990921i | \(-0.457074\pi\) | ||||
0.134449 | + | 0.990921i | \(0.457074\pi\) | |||||||
\(368\) | −575.928 | −0.0815825 | ||||||||
\(369\) | 11221.1 | 1.58305 | ||||||||
\(370\) | −1663.79 | −0.233774 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −128.899 | −0.0179653 | ||||||||
\(373\) | 2713.88 | 0.376728 | 0.188364 | − | 0.982099i | \(-0.439682\pi\) | ||||
0.188364 | + | 0.982099i | \(0.439682\pi\) | |||||||
\(374\) | −12020.7 | −1.66197 | ||||||||
\(375\) | 41.6110 | 0.00573008 | ||||||||
\(376\) | 3286.63 | 0.450784 | ||||||||
\(377\) | 7846.52 | 1.07193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8941.19 | 1.21182 | 0.605908 | − | 0.795535i | \(-0.292810\pi\) | ||||
0.605908 | + | 0.795535i | \(0.292810\pi\) | |||||||
\(380\) | 1889.87 | 0.255127 | ||||||||
\(381\) | −584.469 | −0.0785912 | ||||||||
\(382\) | −771.592 | −0.103346 | ||||||||
\(383\) | 9293.88 | 1.23994 | 0.619968 | − | 0.784627i | \(-0.287146\pi\) | ||||
0.619968 | + | 0.784627i | \(0.287146\pi\) | |||||||
\(384\) | −349.060 | −0.0463878 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7310.62 | −0.963992 | ||||||||
\(387\) | −8367.23 | −1.09904 | ||||||||
\(388\) | 765.737 | 0.100192 | ||||||||
\(389\) | 10454.8 | 1.36267 | 0.681333 | − | 0.731974i | \(-0.261401\pi\) | ||||
0.681333 | + | 0.731974i | \(0.261401\pi\) | |||||||
\(390\) | −188.628 | −0.0244912 | ||||||||
\(391\) | 10540.7 | 1.36334 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −602.226 | −0.0772985 | ||||||||
\(394\) | −479.947 | −0.0613690 | ||||||||
\(395\) | 2999.39 | 0.382065 | ||||||||
\(396\) | 9835.40 | 1.24810 | ||||||||
\(397\) | 3626.03 | 0.458401 | 0.229200 | − | 0.973379i | \(-0.426389\pi\) | ||||
0.229200 | + | 0.973379i | \(0.426389\pi\) | |||||||
\(398\) | −7978.47 | −1.00484 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 142.513 | 0.0178141 | ||||||||
\(401\) | −8422.52 | −1.04888 | −0.524440 | − | 0.851448i | \(-0.675725\pi\) | ||||
−0.524440 | + | 0.851448i | \(0.675725\pi\) | |||||||
\(402\) | 44.4857 | 0.00551927 | ||||||||
\(403\) | −5040.09 | −0.622989 | ||||||||
\(404\) | −3256.65 | −0.401051 | ||||||||
\(405\) | 3600.18 | 0.441715 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13979.5 | −1.70254 | ||||||||
\(408\) | 762.519 | 0.0925253 | ||||||||
\(409\) | 14580.7 | 1.76276 | 0.881379 | − | 0.472409i | \(-0.156616\pi\) | ||||
0.881379 | + | 0.472409i | \(0.156616\pi\) | |||||||
\(410\) | −3455.44 | −0.416224 | ||||||||
\(411\) | −6.16288 | −0.000739641 0 | ||||||||
\(412\) | −9579.51 | −1.14551 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4498.92 | 0.534081 | ||||||||
\(415\) | −354.410 | −0.0419212 | ||||||||
\(416\) | −12665.6 | −1.49275 | ||||||||
\(417\) | 208.257 | 0.0244566 | ||||||||
\(418\) | −8283.26 | −0.969252 | ||||||||
\(419\) | 2537.53 | 0.295863 | 0.147931 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147931 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9649.52 | 1.11708 | 0.558538 | − | 0.829479i | \(-0.311363\pi\) | ||||
0.558538 | + | 0.829479i | \(0.311363\pi\) | |||||||
\(422\) | 3348.57 | 0.386269 | ||||||||
\(423\) | 4025.23 | 0.462680 | ||||||||
\(424\) | −5960.27 | −0.682680 | ||||||||
\(425\) | −2608.29 | −0.297696 | ||||||||
\(426\) | −50.1922 | −0.00570850 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5729.06 | −0.647020 | ||||||||
\(429\) | −1584.89 | −0.178366 | ||||||||
\(430\) | 2576.62 | 0.288967 | ||||||||
\(431\) | −7262.56 | −0.811660 | −0.405830 | − | 0.913949i | \(-0.633017\pi\) | ||||
−0.405830 | + | 0.913949i | \(0.633017\pi\) | |||||||
\(432\) | −102.262 | −0.0113891 | ||||||||
\(433\) | −11345.0 | −1.25914 | −0.629570 | − | 0.776944i | \(-0.716769\pi\) | ||||
−0.629570 | + | 0.776944i | \(0.716769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −190.845 | −0.0210353 | ||||||||
\(436\) | −3100.15 | −0.340528 | ||||||||
\(437\) | 7263.40 | 0.795092 | ||||||||
\(438\) | −486.387 | −0.0530604 | ||||||||
\(439\) | −11705.9 | −1.27265 | −0.636323 | − | 0.771423i | \(-0.719545\pi\) | ||||
−0.636323 | + | 0.771423i | \(0.719545\pi\) | |||||||
\(440\) | −7637.40 | −0.827497 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11823.8 | 1.27240 | ||||||||
\(443\) | 15078.0 | 1.61710 | 0.808551 | − | 0.588426i | \(-0.200252\pi\) | ||||
0.808551 | + | 0.588426i | \(0.200252\pi\) | |||||||
\(444\) | 351.662 | 0.0375881 | ||||||||
\(445\) | −4012.96 | −0.427489 | ||||||||
\(446\) | −7193.70 | −0.763747 | ||||||||
\(447\) | −342.419 | −0.0362324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1075.45 | 0.113037 | 0.0565185 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565185 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(450\) | −1113.25 | −0.116621 | ||||||||
\(451\) | −29033.2 | −3.03131 | ||||||||
\(452\) | 4733.59 | 0.492587 | ||||||||
\(453\) | 23.6375 | 0.00245162 | ||||||||
\(454\) | 4384.58 | 0.453257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 525.437 | 0.0539602 | ||||||||
\(457\) | −10736.9 | −1.09902 | −0.549511 | − | 0.835487i | \(-0.685186\pi\) | ||||
−0.549511 | + | 0.835487i | \(0.685186\pi\) | |||||||
\(458\) | 2393.16 | 0.244159 | ||||||||
\(459\) | 1871.61 | 0.190325 | ||||||||
\(460\) | 2655.82 | 0.269192 | ||||||||
\(461\) | −452.568 | −0.0457228 | −0.0228614 | − | 0.999739i | \(-0.507278\pi\) | ||||
−0.0228614 | + | 0.999739i | \(0.507278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7118.15 | 0.714489 | 0.357244 | − | 0.934011i | \(-0.383716\pi\) | ||||
0.357244 | + | 0.934011i | \(0.383716\pi\) | |||||||
\(464\) | −653.626 | −0.0653962 | ||||||||
\(465\) | 122.587 | 0.0122254 | ||||||||
\(466\) | −10343.6 | −1.02824 | ||||||||
\(467\) | −973.800 | −0.0964927 | −0.0482463 | − | 0.998835i | \(-0.515363\pi\) | ||||
−0.0482463 | + | 0.998835i | \(0.515363\pi\) | |||||||
\(468\) | −9674.23 | −0.955537 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1239.54 | −0.121650 | ||||||||
\(471\) | 686.188 | 0.0671293 | ||||||||
\(472\) | −11373.4 | −1.10912 | ||||||||
\(473\) | 21649.2 | 2.10451 | ||||||||
\(474\) | 330.702 | 0.0320457 | ||||||||
\(475\) | −1797.32 | −0.173614 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7299.72 | −0.700695 | ||||||||
\(478\) | 2219.52 | 0.212381 | ||||||||
\(479\) | −9714.00 | −0.926606 | −0.463303 | − | 0.886200i | \(-0.653336\pi\) | ||||
−0.463303 | + | 0.886200i | \(0.653336\pi\) | |||||||
\(480\) | 308.057 | 0.0292934 | ||||||||
\(481\) | 13750.4 | 1.30346 | ||||||||
\(482\) | −5580.80 | −0.527383 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18450.3 | −1.73274 | ||||||||
\(485\) | −728.239 | −0.0681806 | ||||||||
\(486\) | 1199.06 | 0.111915 | ||||||||
\(487\) | 923.389 | 0.0859194 | 0.0429597 | − | 0.999077i | \(-0.486321\pi\) | ||||
0.0429597 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(488\) | −4828.50 | −0.447902 | ||||||||
\(489\) | −653.724 | −0.0604549 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1289.11 | 0.118486 | 0.0592430 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592430 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(492\) | 730.348 | 0.0669240 | ||||||||
\(493\) | 11962.7 | 1.09285 | ||||||||
\(494\) | 8147.52 | 0.742053 | ||||||||
\(495\) | −9353.76 | −0.849334 | ||||||||
\(496\) | 419.846 | 0.0380074 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −39.0760 | −0.00351614 | ||||||||
\(499\) | −19338.3 | −1.73487 | −0.867436 | − | 0.497549i | \(-0.834234\pi\) | ||||
−0.867436 | + | 0.497549i | \(0.834234\pi\) | |||||||
\(500\) | −657.182 | −0.0587802 | ||||||||
\(501\) | −950.409 | −0.0847528 | ||||||||
\(502\) | 5949.64 | 0.528975 | ||||||||
\(503\) | 1772.84 | 0.157151 | 0.0785757 | − | 0.996908i | \(-0.474963\pi\) | ||||
0.0785757 | + | 0.996908i | \(0.474963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3097.18 | 0.272916 | ||||||||
\(506\) | −11640.4 | −1.02269 | ||||||||
\(507\) | 827.563 | 0.0724919 | ||||||||
\(508\) | 9230.80 | 0.806202 | ||||||||
\(509\) | −3151.75 | −0.274458 | −0.137229 | − | 0.990539i | \(-0.543820\pi\) | ||||
−0.137229 | + | 0.990539i | \(0.543820\pi\) | |||||||
\(510\) | −287.581 | −0.0249692 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2056.31 | 0.177494 | ||||||||
\(513\) | 1289.69 | 0.110997 | ||||||||
\(514\) | 4.71585 | 0.000404683 0 | ||||||||
\(515\) | 9110.40 | 0.779519 | ||||||||
\(516\) | −544.600 | −0.0464626 | ||||||||
\(517\) | −10414.8 | −0.885964 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 517.043 | 0.0437296 | ||||||||
\(520\) | 7512.24 | 0.633526 | ||||||||
\(521\) | 11029.4 | 0.927458 | 0.463729 | − | 0.885977i | \(-0.346511\pi\) | ||||
0.463729 | + | 0.885977i | \(0.346511\pi\) | |||||||
\(522\) | 5105.85 | 0.428117 | ||||||||
\(523\) | −14448.4 | −1.20800 | −0.604002 | − | 0.796983i | \(-0.706428\pi\) | ||||
−0.604002 | + | 0.796983i | \(0.706428\pi\) | |||||||
\(524\) | 9511.26 | 0.792941 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4665.25 | −0.386720 | ||||||||
\(527\) | −7684.08 | −0.635149 | ||||||||
\(528\) | 132.023 | 0.0108818 | ||||||||
\(529\) | −1959.79 | −0.161074 | ||||||||
\(530\) | 2247.89 | 0.184231 | ||||||||
\(531\) | −13929.4 | −1.13838 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28557.4 | 2.32075 | ||||||||
\(534\) | −442.455 | −0.0358556 | ||||||||
\(535\) | 5448.51 | 0.440298 | ||||||||
\(536\) | −1771.67 | −0.142770 | ||||||||
\(537\) | 89.8266 | 0.00721845 | ||||||||
\(538\) | 2397.04 | 0.192089 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 471.569 | 0.0375798 | ||||||||
\(541\) | −22274.8 | −1.77018 | −0.885091 | − | 0.465418i | \(-0.845904\pi\) | ||||
−0.885091 | + | 0.465418i | \(0.845904\pi\) | |||||||
\(542\) | −13338.8 | −1.05710 | ||||||||
\(543\) | −742.211 | −0.0586580 | ||||||||
\(544\) | −19309.9 | −1.52188 | ||||||||
\(545\) | 2948.33 | 0.231730 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18642.6 | 1.45722 | 0.728609 | − | 0.684930i | \(-0.240167\pi\) | ||||
0.728609 | + | 0.684930i | \(0.240167\pi\) | |||||||
\(548\) | 97.3334 | 0.00758737 | ||||||||
\(549\) | −5913.62 | −0.459721 | ||||||||
\(550\) | 2880.42 | 0.223311 | ||||||||
\(551\) | 8243.28 | 0.637343 | ||||||||
\(552\) | 738.394 | 0.0569350 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −946.108 | −0.0725565 | ||||||||
\(555\) | −334.441 | −0.0255788 | ||||||||
\(556\) | −3289.11 | −0.250880 | ||||||||
\(557\) | −21431.8 | −1.63033 | −0.815165 | − | 0.579229i | \(-0.803354\pi\) | ||||
−0.815165 | + | 0.579229i | \(0.803354\pi\) | |||||||
\(558\) | −3279.67 | −0.248816 | ||||||||
\(559\) | −21294.5 | −1.61120 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2416.31 | −0.181848 | ||||||||
\(562\) | −2955.21 | −0.221811 | ||||||||
\(563\) | 6154.85 | 0.460739 | 0.230370 | − | 0.973103i | \(-0.426007\pi\) | ||||
0.230370 | + | 0.973103i | \(0.426007\pi\) | |||||||
\(564\) | 261.991 | 0.0195600 | ||||||||
\(565\) | −4501.79 | −0.335206 | ||||||||
\(566\) | −5499.86 | −0.408439 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1998.94 | 0.147665 | ||||||||
\(569\) | −8389.99 | −0.618149 | −0.309074 | − | 0.951038i | \(-0.600019\pi\) | ||||
−0.309074 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(570\) | −198.167 | −0.0145619 | ||||||||
\(571\) | −600.502 | −0.0440109 | −0.0220055 | − | 0.999758i | \(-0.507005\pi\) | ||||
−0.0220055 | + | 0.999758i | \(0.507005\pi\) | |||||||
\(572\) | 25030.9 | 1.82971 | ||||||||
\(573\) | −155.099 | −0.0113078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2525.77 | −0.183186 | ||||||||
\(576\) | −7015.46 | −0.507484 | ||||||||
\(577\) | −4062.35 | −0.293098 | −0.146549 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146549 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(578\) | 9890.18 | 0.711725 | ||||||||
\(579\) | −1469.52 | −0.105477 | ||||||||
\(580\) | 3014.12 | 0.215783 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −80.2931 | −0.00571865 | ||||||||
\(583\) | 18887.2 | 1.34173 | ||||||||
\(584\) | 19370.6 | 1.37254 | ||||||||
\(585\) | 9200.48 | 0.650244 | ||||||||
\(586\) | 8362.35 | 0.589498 | ||||||||
\(587\) | 8387.50 | 0.589760 | 0.294880 | − | 0.955534i | \(-0.404720\pi\) | ||||
0.294880 | + | 0.955534i | \(0.404720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5294.95 | −0.370415 | ||||||||
\(590\) | 4289.43 | 0.299310 | ||||||||
\(591\) | −96.4749 | −0.00671480 | ||||||||
\(592\) | −1145.43 | −0.0795214 | ||||||||
\(593\) | 15342.6 | 1.06247 | 0.531236 | − | 0.847224i | \(-0.321728\pi\) | ||||
0.531236 | + | 0.847224i | \(0.321728\pi\) | |||||||
\(594\) | −2066.88 | −0.142769 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5408.00 | 0.371678 | ||||||||
\(597\) | −1603.76 | −0.109946 | ||||||||
\(598\) | 11449.7 | 0.782963 | ||||||||
\(599\) | −19708.5 | −1.34435 | −0.672175 | − | 0.740392i | \(-0.734640\pi\) | ||||
−0.672175 | + | 0.740392i | \(0.734640\pi\) | |||||||
\(600\) | −182.715 | −0.0124322 | ||||||||
\(601\) | 19002.5 | 1.28973 | 0.644866 | − | 0.764295i | \(-0.276913\pi\) | ||||
0.644866 | + | 0.764295i | \(0.276913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2169.82 | −0.146537 | ||||||||
\(604\) | −373.318 | −0.0251492 | ||||||||
\(605\) | 17546.8 | 1.17914 | ||||||||
\(606\) | 341.484 | 0.0228908 | ||||||||
\(607\) | −29453.1 | −1.96946 | −0.984732 | − | 0.174076i | \(-0.944306\pi\) | ||||
−0.984732 | + | 0.174076i | \(0.944306\pi\) | |||||||
\(608\) | −13306.1 | −0.887553 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1821.05 | 0.120873 | ||||||||
\(611\) | 10244.2 | 0.678288 | ||||||||
\(612\) | −14749.2 | −0.974188 | ||||||||
\(613\) | 9987.27 | 0.658045 | 0.329023 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329023 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(614\) | 2543.26 | 0.167162 | ||||||||
\(615\) | −694.583 | −0.0455419 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21076.1 | −1.37519 | −0.687593 | − | 0.726096i | \(-0.741333\pi\) | ||||
−0.687593 | + | 0.726096i | \(0.741333\pi\) | |||||||
\(618\) | 1004.48 | 0.0653821 | ||||||||
\(619\) | 314.668 | 0.0204323 | 0.0102161 | − | 0.999948i | \(-0.496748\pi\) | ||||
0.0102161 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(620\) | −1936.07 | −0.125410 | ||||||||
\(621\) | 1812.39 | 0.117116 | ||||||||
\(622\) | 15373.3 | 0.991018 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −129.860 | −0.00833103 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −9978.49 | −0.637094 | ||||||||
\(627\) | −1665.03 | −0.106052 | ||||||||
\(628\) | −10837.3 | −0.688624 | ||||||||
\(629\) | 20963.7 | 1.32890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3314.96 | 0.209138 | 0.104569 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104569 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(632\) | −13170.4 | −0.828941 | ||||||||
\(633\) | 673.101 | 0.0422644 | ||||||||
\(634\) | −11555.3 | −0.723849 | ||||||||
\(635\) | −8778.77 | −0.548622 | ||||||||
\(636\) | −475.119 | −0.0296221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13210.8 | −0.819782 | ||||||||
\(639\) | 2448.16 | 0.151561 | ||||||||
\(640\) | −5242.92 | −0.323820 | ||||||||
\(641\) | 3005.12 | 0.185172 | 0.0925858 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925858 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(642\) | 600.733 | 0.0369300 | ||||||||
\(643\) | −21225.7 | −1.30180 | −0.650902 | − | 0.759162i | \(-0.725609\pi\) | ||||
−0.650902 | + | 0.759162i | \(0.725609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 517.931 | 0.0316178 | ||||||||
\(646\) | 12421.6 | 0.756537 | ||||||||
\(647\) | 2740.35 | 0.166514 | 0.0832568 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832568 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(648\) | −15808.5 | −0.958360 | ||||||||
\(649\) | 36040.6 | 2.17984 | ||||||||
\(650\) | −2833.21 | −0.170966 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10324.6 | 0.620157 | ||||||||
\(653\) | 22790.7 | 1.36580 | 0.682900 | − | 0.730511i | \(-0.260718\pi\) | ||||
0.682900 | + | 0.730511i | \(0.260718\pi\) | |||||||
\(654\) | 325.073 | 0.0194363 | ||||||||
\(655\) | −9045.49 | −0.539598 | ||||||||
\(656\) | −2378.87 | −0.141584 | ||||||||
\(657\) | 23723.8 | 1.40876 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19405.1 | 1.14706 | 0.573532 | − | 0.819183i | \(-0.305573\pi\) | ||||
0.573532 | + | 0.819183i | \(0.305573\pi\) | |||||||
\(660\) | −608.810 | −0.0359059 | ||||||||
\(661\) | −15637.3 | −0.920150 | −0.460075 | − | 0.887880i | \(-0.652177\pi\) | ||||
−0.460075 | + | 0.887880i | \(0.652177\pi\) | |||||||
\(662\) | 1631.02 | 0.0957574 | ||||||||
\(663\) | 2376.71 | 0.139222 | ||||||||
\(664\) | 1556.23 | 0.0909538 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8947.59 | 0.520589 | ||||||||
\(667\) | 11584.2 | 0.672479 | ||||||||
\(668\) | 15010.3 | 0.869409 | ||||||||
\(669\) | −1446.02 | −0.0835668 | ||||||||
\(670\) | 668.179 | 0.0385284 | ||||||||
\(671\) | 15300.8 | 0.880299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2579.54 | −0.147747 | −0.0738735 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738735 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(674\) | 86.0578 | 0.00491813 | ||||||||
\(675\) | −448.476 | −0.0255731 | ||||||||
\(676\) | −13070.1 | −0.743634 | ||||||||
\(677\) | −8159.56 | −0.463216 | −0.231608 | − | 0.972809i | \(-0.574399\pi\) | ||||
−0.231608 | + | 0.972809i | \(0.574399\pi\) | |||||||
\(678\) | −496.351 | −0.0281154 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11453.1 | 0.645892 | ||||||||
\(681\) | 881.351 | 0.0495939 | ||||||||
\(682\) | 8485.76 | 0.476446 | ||||||||
\(683\) | −20529.3 | −1.15012 | −0.575059 | − | 0.818112i | \(-0.695021\pi\) | ||||
−0.575059 | + | 0.818112i | \(0.695021\pi\) | |||||||
\(684\) | −10163.4 | −0.568140 | ||||||||
\(685\) | −92.5670 | −0.00516321 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 481.053 | 0.0267151 | ||||||||
\(688\) | 1773.86 | 0.0982961 | ||||||||
\(689\) | −18577.7 | −1.02722 | ||||||||
\(690\) | −278.482 | −0.0153647 | ||||||||
\(691\) | 917.295 | 0.0505001 | 0.0252500 | − | 0.999681i | \(-0.491962\pi\) | ||||
0.0252500 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(692\) | −8165.92 | −0.448586 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18714.3 | −1.02361 | ||||||||
\(695\) | 3128.04 | 0.170724 | ||||||||
\(696\) | 838.009 | 0.0456389 | ||||||||
\(697\) | 43538.4 | 2.36605 | ||||||||
\(698\) | 3340.13 | 0.181126 | ||||||||
\(699\) | −2079.19 | −0.112507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10491.3 | −0.565266 | −0.282633 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282633 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(702\) | 2033.01 | 0.109303 | ||||||||
\(703\) | 14445.7 | 0.775006 | ||||||||
\(704\) | 18151.7 | 0.971758 | ||||||||
\(705\) | −249.162 | −0.0133106 | ||||||||
\(706\) | 12568.5 | 0.670005 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −906.623 | −0.0481257 | ||||||||
\(709\) | 23837.6 | 1.26268 | 0.631339 | − | 0.775507i | \(-0.282506\pi\) | ||||
0.631339 | + | 0.775507i | \(0.282506\pi\) | |||||||
\(710\) | −753.892 | −0.0398494 | ||||||||
\(711\) | −16130.2 | −0.850816 | ||||||||
\(712\) | 17621.0 | 0.927495 | ||||||||
\(713\) | −7440.96 | −0.390836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23805.2 | −1.24512 | ||||||||
\(716\) | −1418.68 | −0.0740481 | ||||||||
\(717\) | 446.148 | 0.0232381 | ||||||||
\(718\) | 14464.4 | 0.751822 | ||||||||
\(719\) | 3926.19 | 0.203647 | 0.101824 | − | 0.994802i | \(-0.467532\pi\) | ||||
0.101824 | + | 0.994802i | \(0.467532\pi\) | |||||||
\(720\) | −766.413 | −0.0396702 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2799.42 | −0.144299 | ||||||||
\(723\) | −1121.80 | −0.0577045 | ||||||||
\(724\) | 11722.1 | 0.601724 | ||||||||
\(725\) | −2866.51 | −0.146841 | ||||||||
\(726\) | 1934.64 | 0.0989000 | ||||||||
\(727\) | 21071.2 | 1.07495 | 0.537474 | − | 0.843281i | \(-0.319379\pi\) | ||||
0.537474 | + | 0.843281i | \(0.319379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19200.0 | −0.975459 | ||||||||
\(730\) | −7305.57 | −0.370399 | ||||||||
\(731\) | −32465.4 | −1.64265 | ||||||||
\(732\) | −384.901 | −0.0194349 | ||||||||
\(733\) | 22840.7 | 1.15094 | 0.575470 | − | 0.817823i | \(-0.304819\pi\) | ||||
0.575470 | + | 0.817823i | \(0.304819\pi\) | |||||||
\(734\) | 3130.86 | 0.157441 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18699.0 | −0.936485 | ||||||||
\(737\) | 5614.16 | 0.280597 | ||||||||
\(738\) | 18582.8 | 0.926885 | ||||||||
\(739\) | 10837.3 | 0.539456 | 0.269728 | − | 0.962937i | \(-0.413066\pi\) | ||||
0.269728 | + | 0.962937i | \(0.413066\pi\) | |||||||
\(740\) | 5281.99 | 0.262392 | ||||||||
\(741\) | 1637.75 | 0.0811931 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21631.9 | −1.06810 | −0.534050 | − | 0.845453i | \(-0.679331\pi\) | ||||
−0.534050 | + | 0.845453i | \(0.679331\pi\) | |||||||
\(744\) | −538.282 | −0.0265247 | ||||||||
\(745\) | −5143.17 | −0.252928 | ||||||||
\(746\) | 4494.36 | 0.220577 | ||||||||
\(747\) | 1905.96 | 0.0933540 | ||||||||
\(748\) | 38161.9 | 1.86543 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 68.9103 | 0.00335500 | ||||||||
\(751\) | −16179.2 | −0.786133 | −0.393067 | − | 0.919510i | \(-0.628586\pi\) | ||||
−0.393067 | + | 0.919510i | \(0.628586\pi\) | |||||||
\(752\) | −853.352 | −0.0413811 | ||||||||
\(753\) | 1195.95 | 0.0578788 | ||||||||
\(754\) | 12994.3 | 0.627620 | ||||||||
\(755\) | 355.037 | 0.0171140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40930.9 | −1.96520 | −0.982601 | − | 0.185727i | \(-0.940536\pi\) | ||||
−0.982601 | + | 0.185727i | \(0.940536\pi\) | |||||||
\(758\) | 14807.2 | 0.709526 | ||||||||
\(759\) | −2339.86 | −0.111899 | ||||||||
\(760\) | 7892.11 | 0.376680 | ||||||||
\(761\) | −3183.97 | −0.151667 | −0.0758337 | − | 0.997120i | \(-0.524162\pi\) | ||||
−0.0758337 | + | 0.997120i | \(0.524162\pi\) | |||||||
\(762\) | −967.917 | −0.0460157 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2449.55 | 0.115997 | ||||||||
\(765\) | 14027.0 | 0.662936 | ||||||||
\(766\) | 15391.2 | 0.725990 | ||||||||
\(767\) | −35450.0 | −1.66887 | ||||||||
\(768\) | −1272.88 | −0.0598059 | ||||||||
\(769\) | −33595.8 | −1.57542 | −0.787708 | − | 0.616048i | \(-0.788733\pi\) | ||||
−0.787708 | + | 0.616048i | \(0.788733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.947940 | 4.42791e−5 0 | ||||||||
\(772\) | 23208.8 | 1.08200 | ||||||||
\(773\) | −34386.0 | −1.59997 | −0.799986 | − | 0.600019i | \(-0.795160\pi\) | ||||
−0.799986 | + | 0.600019i | \(0.795160\pi\) | |||||||
\(774\) | −13856.7 | −0.643498 | ||||||||
\(775\) | 1841.26 | 0.0853420 | ||||||||
\(776\) | 3197.72 | 0.147927 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17313.7 | 0.797849 | ||||||||
\(779\) | 30001.5 | 1.37986 | ||||||||
\(780\) | 598.834 | 0.0274893 | ||||||||
\(781\) | −6334.33 | −0.290218 | ||||||||
\(782\) | 17456.1 | 0.798245 | ||||||||
\(783\) | 2056.90 | 0.0938795 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10306.6 | 0.468610 | ||||||||
\(786\) | −997.324 | −0.0452588 | ||||||||
\(787\) | 8212.43 | 0.371972 | 0.185986 | − | 0.982552i | \(-0.440452\pi\) | ||||
0.185986 | + | 0.982552i | \(0.440452\pi\) | |||||||
\(788\) | 1523.68 | 0.0688816 | ||||||||
\(789\) | −937.769 | −0.0423136 | ||||||||
\(790\) | 4967.17 | 0.223701 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 41072.7 | 1.84274 | ||||||||
\(793\) | −15050.1 | −0.673951 | ||||||||
\(794\) | 6004.92 | 0.268396 | ||||||||
\(795\) | 451.852 | 0.0201579 | ||||||||
\(796\) | 25329.0 | 1.12784 | ||||||||
\(797\) | −36798.3 | −1.63546 | −0.817732 | − | 0.575600i | \(-0.804769\pi\) | ||||
−0.817732 | + | 0.575600i | \(0.804769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15618.2 | 0.691528 | ||||||||
\(800\) | 4627.05 | 0.204488 | ||||||||
\(801\) | 21581.0 | 0.951971 | ||||||||
\(802\) | −13948.2 | −0.614125 | ||||||||
\(803\) | −61382.7 | −2.69757 | ||||||||
\(804\) | −141.228 | −0.00619492 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8346.70 | −0.364764 | ||||||||
\(807\) | 481.832 | 0.0210177 | ||||||||
\(808\) | −13599.8 | −0.592128 | ||||||||
\(809\) | 10186.2 | 0.442678 | 0.221339 | − | 0.975197i | \(-0.428957\pi\) | ||||
0.221339 | + | 0.975197i | \(0.428957\pi\) | |||||||
\(810\) | 5962.12 | 0.258627 | ||||||||
\(811\) | −21196.9 | −0.917786 | −0.458893 | − | 0.888492i | \(-0.651754\pi\) | ||||
−0.458893 | + | 0.888492i | \(0.651754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2681.24 | −0.115665 | ||||||||
\(814\) | −23150.8 | −0.996851 | ||||||||
\(815\) | −9818.99 | −0.422018 | ||||||||
\(816\) | −197.983 | −0.00849364 | ||||||||
\(817\) | −22371.3 | −0.957982 | ||||||||
\(818\) | 24146.5 | 1.03211 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10969.9 | 0.467177 | ||||||||
\(821\) | 7563.94 | 0.321539 | 0.160769 | − | 0.986992i | \(-0.448602\pi\) | ||||
0.160769 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(822\) | −10.2061 | −0.000433065 0 | ||||||||
\(823\) | 8399.80 | 0.355770 | 0.177885 | − | 0.984051i | \(-0.443075\pi\) | ||||
0.177885 | + | 0.984051i | \(0.443075\pi\) | |||||||
\(824\) | −40004.1 | −1.69127 | ||||||||
\(825\) | 578.997 | 0.0244340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5479.54 | 0.230402 | 0.115201 | − | 0.993342i | \(-0.463249\pi\) | ||||
0.115201 | + | 0.993342i | \(0.463249\pi\) | |||||||
\(828\) | −14282.6 | −0.599462 | ||||||||
\(829\) | −9252.56 | −0.387641 | −0.193821 | − | 0.981037i | \(-0.562088\pi\) | ||||
−0.193821 | + | 0.981037i | \(0.562088\pi\) | |||||||
\(830\) | −586.925 | −0.0245452 | ||||||||
\(831\) | −190.179 | −0.00793890 | ||||||||
\(832\) | −17854.2 | −0.743972 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 344.887 | 0.0143195 | ||||||||
\(835\) | −14275.2 | −0.591634 | ||||||||
\(836\) | 26296.6 | 1.08790 | ||||||||
\(837\) | −1321.22 | −0.0545615 | ||||||||
\(838\) | 4202.31 | 0.173230 | ||||||||
\(839\) | 34517.6 | 1.42036 | 0.710178 | − | 0.704022i | \(-0.248614\pi\) | ||||
0.710178 | + | 0.704022i | \(0.248614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11241.9 | −0.460943 | ||||||||
\(842\) | 15980.2 | 0.654055 | ||||||||
\(843\) | −594.031 | −0.0242699 | ||||||||
\(844\) | −10630.6 | −0.433555 | ||||||||
\(845\) | 12430.1 | 0.506044 | ||||||||
\(846\) | 6666.04 | 0.270902 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1547.55 | 0.0626686 | ||||||||
\(849\) | −1105.54 | −0.0446901 | ||||||||
\(850\) | −4319.50 | −0.174303 | ||||||||
\(851\) | 20300.4 | 0.817732 | ||||||||
\(852\) | 159.344 | 0.00640732 | ||||||||
\(853\) | 1498.57 | 0.0601525 | 0.0300763 | − | 0.999548i | \(-0.490425\pi\) | ||||
0.0300763 | + | 0.999548i | \(0.490425\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9665.71 | 0.386620 | ||||||||
\(856\) | −23924.6 | −0.955287 | ||||||||
\(857\) | 9357.02 | 0.372963 | 0.186482 | − | 0.982458i | \(-0.440291\pi\) | ||||
0.186482 | + | 0.982458i | \(0.440291\pi\) | |||||||
\(858\) | −2624.67 | −0.104435 | ||||||||
\(859\) | 29960.9 | 1.19005 | 0.595025 | − | 0.803707i | \(-0.297142\pi\) | ||||
0.595025 | + | 0.803707i | \(0.297142\pi\) | |||||||
\(860\) | −8179.94 | −0.324341 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12027.3 | −0.475232 | ||||||||
\(863\) | −33941.0 | −1.33878 | −0.669389 | − | 0.742912i | \(-0.733444\pi\) | ||||
−0.669389 | + | 0.742912i | \(0.733444\pi\) | |||||||
\(864\) | −3320.19 | −0.130735 | ||||||||
\(865\) | 7766.03 | 0.305264 | ||||||||
\(866\) | −18788.1 | −0.737235 | ||||||||
\(867\) | 1988.04 | 0.0778747 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41735.0 | 1.62919 | ||||||||
\(870\) | −316.052 | −0.0123163 | ||||||||
\(871\) | −5522.16 | −0.214824 | ||||||||
\(872\) | −12946.2 | −0.502769 | ||||||||
\(873\) | 3916.35 | 0.151831 | ||||||||
\(874\) | 12028.6 | 0.465532 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1544.12 | 0.0595559 | ||||||||
\(877\) | −39436.6 | −1.51845 | −0.759224 | − | 0.650830i | \(-0.774421\pi\) | ||||
−0.759224 | + | 0.650830i | \(0.774421\pi\) | |||||||
\(878\) | −19385.7 | −0.745142 | ||||||||
\(879\) | 1680.93 | 0.0645010 | ||||||||
\(880\) | 1983.00 | 0.0759625 | ||||||||
\(881\) | −32411.4 | −1.23946 | −0.619732 | − | 0.784813i | \(-0.712759\pi\) | ||||
−0.619732 | + | 0.784813i | \(0.712759\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17121.4 | −0.652526 | −0.326263 | − | 0.945279i | \(-0.605790\pi\) | ||||
−0.326263 | + | 0.945279i | \(0.605790\pi\) | |||||||
\(884\) | −37536.6 | −1.42816 | ||||||||
\(885\) | 862.226 | 0.0327496 | ||||||||
\(886\) | 24970.1 | 0.946824 | ||||||||
\(887\) | 687.797 | 0.0260360 | 0.0130180 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130180 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(888\) | 1468.54 | 0.0554967 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6645.71 | −0.250297 | ||||||||
\(891\) | 50094.8 | 1.88355 | ||||||||
\(892\) | 22837.6 | 0.857243 | ||||||||
\(893\) | 10762.2 | 0.403294 | ||||||||
\(894\) | −567.068 | −0.0212143 | ||||||||
\(895\) | 1349.20 | 0.0503898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2301.52 | 0.0856693 | ||||||||
\(898\) | 1781.01 | 0.0661839 | ||||||||
\(899\) | −8444.81 | −0.313293 | ||||||||
\(900\) | 3534.22 | 0.130897 | ||||||||
\(901\) | −28323.4 | −1.04727 | ||||||||
\(902\) | −48080.8 | −1.77485 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19767.5 | 0.727276 | ||||||||
\(905\) | −11148.1 | −0.409474 | ||||||||
\(906\) | 39.1451 | 0.00143544 | ||||||||
\(907\) | 19104.2 | 0.699388 | 0.349694 | − | 0.936864i | \(-0.386286\pi\) | ||||
0.349694 | + | 0.936864i | \(0.386286\pi\) | |||||||
\(908\) | −13919.6 | −0.508743 | ||||||||
\(909\) | −16656.1 | −0.607754 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23135.3 | 0.841390 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(912\) | −136.427 | −0.00495344 | ||||||||
\(913\) | −4931.45 | −0.178759 | ||||||||
\(914\) | −17781.0 | −0.643484 | ||||||||
\(915\) | 366.052 | 0.0132255 | ||||||||
\(916\) | −7597.50 | −0.274049 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3099.50 | 0.111437 | ||||||||
\(919\) | 47373.9 | 1.70046 | 0.850230 | − | 0.526412i | \(-0.176463\pi\) | ||||
0.850230 | + | 0.526412i | \(0.176463\pi\) | |||||||
\(920\) | 11090.7 | 0.397447 | ||||||||
\(921\) | 511.224 | 0.0182903 | ||||||||
\(922\) | −749.481 | −0.0267710 | ||||||||
\(923\) | 6230.53 | 0.222189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5023.33 | −0.178558 | ||||||||
\(926\) | 11788.1 | 0.418338 | ||||||||
\(927\) | −48994.2 | −1.73590 | ||||||||
\(928\) | −21221.6 | −0.750682 | ||||||||
\(929\) | 7617.72 | 0.269031 | 0.134515 | − | 0.990912i | \(-0.457052\pi\) | ||||
0.134515 | + | 0.990912i | \(0.457052\pi\) | |||||||
\(930\) | 203.011 | 0.00715806 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32837.6 | 1.15411 | ||||||||
\(933\) | 3090.21 | 0.108434 | ||||||||
\(934\) | −1612.67 | −0.0564971 | ||||||||
\(935\) | −36293.2 | −1.26943 | ||||||||
\(936\) | −40399.6 | −1.41079 | ||||||||
\(937\) | 52091.2 | 1.81616 | 0.908082 | − | 0.418792i | \(-0.137546\pi\) | ||||
0.908082 | + | 0.418792i | \(0.137546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2005.79 | −0.0697088 | ||||||||
\(940\) | 3935.13 | 0.136542 | ||||||||
\(941\) | 56765.1 | 1.96651 | 0.983257 | − | 0.182225i | \(-0.0583299\pi\) | ||||
0.983257 | + | 0.182225i | \(0.0583299\pi\) | |||||||
\(942\) | 1136.37 | 0.0393046 | ||||||||
\(943\) | 42160.9 | 1.45594 | ||||||||
\(944\) | 2953.03 | 0.101815 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35852.5 | 1.23220 | ||||||||
\(947\) | −47629.2 | −1.63436 | −0.817181 | − | 0.576381i | \(-0.804465\pi\) | ||||
−0.817181 | + | 0.576381i | \(0.804465\pi\) | |||||||
\(948\) | −1049.87 | −0.0359686 | ||||||||
\(949\) | 60376.8 | 2.06524 | ||||||||
\(950\) | −2976.48 | −0.101652 | ||||||||
\(951\) | −2322.75 | −0.0792012 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12893.5 | 0.438259 | 0.219129 | − | 0.975696i | \(-0.429678\pi\) | ||||
0.219129 | + | 0.975696i | \(0.429678\pi\) | |||||||
\(954\) | −12088.8 | −0.410261 | ||||||||
\(955\) | −2329.60 | −0.0789362 | ||||||||
\(956\) | −7046.24 | −0.238380 | ||||||||
\(957\) | −2655.52 | −0.0896979 | ||||||||
\(958\) | −16087.0 | −0.542534 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 434.257 | 0.0145996 | ||||||||
\(961\) | −24366.6 | −0.817918 | ||||||||
\(962\) | 22771.5 | 0.763183 | ||||||||
\(963\) | −29301.2 | −0.980496 | ||||||||
\(964\) | 17717.2 | 0.591943 | ||||||||
\(965\) | −22072.3 | −0.736303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28420.0 | −0.945114 | −0.472557 | − | 0.881300i | \(-0.656669\pi\) | ||||
−0.472557 | + | 0.881300i | \(0.656669\pi\) | |||||||
\(968\) | −77048.4 | −2.55830 | ||||||||
\(969\) | 2496.89 | 0.0827779 | ||||||||
\(970\) | −1206.01 | −0.0399202 | ||||||||
\(971\) | −29273.8 | −0.967497 | −0.483749 | − | 0.875207i | \(-0.660725\pi\) | ||||
−0.483749 | + | 0.875207i | \(0.660725\pi\) | |||||||
\(972\) | −3806.64 | −0.125615 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1529.19 | 0.0503063 | ||||||||
\(975\) | −569.509 | −0.0187065 | ||||||||
\(976\) | 1253.69 | 0.0411165 | ||||||||
\(977\) | 12055.0 | 0.394753 | 0.197377 | − | 0.980328i | \(-0.436758\pi\) | ||||
0.197377 | + | 0.980328i | \(0.436758\pi\) | |||||||
\(978\) | −1082.61 | −0.0353967 | ||||||||
\(979\) | −55838.4 | −1.82288 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15855.7 | −0.516037 | ||||||||
\(982\) | 2134.84 | 0.0693743 | ||||||||
\(983\) | −10605.1 | −0.344099 | −0.172049 | − | 0.985088i | \(-0.555039\pi\) | ||||
−0.172049 | + | 0.985088i | \(0.555039\pi\) | |||||||
\(984\) | 3049.94 | 0.0988094 | ||||||||
\(985\) | −1449.06 | −0.0468740 | ||||||||
\(986\) | 19811.0 | 0.639870 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25865.7 | −0.832893 | ||||||||
\(989\) | −31438.2 | −1.01080 | ||||||||
\(990\) | −15490.4 | −0.497290 | ||||||||
\(991\) | 45229.1 | 1.44980 | 0.724898 | − | 0.688856i | \(-0.241887\pi\) | ||||
0.724898 | + | 0.688856i | \(0.241887\pi\) | |||||||
\(992\) | 13631.4 | 0.436287 | ||||||||
\(993\) | 327.854 | 0.0104775 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24088.7 | −0.767500 | ||||||||
\(996\) | 124.054 | 0.00394658 | ||||||||
\(997\) | 49676.8 | 1.57802 | 0.789008 | − | 0.614383i | \(-0.210595\pi\) | ||||
0.789008 | + | 0.614383i | \(0.210595\pi\) | |||||||
\(998\) | −32025.4 | −1.01578 | ||||||||
\(999\) | 3604.55 | 0.114157 |
(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 | 245.4.a.o.1.5 | ✓ | 6 | |
3.2 | odd | 2 | 2205.4.a.bz.1.2 | 6 | |||
5.4 | even | 2 | 1225.4.a.bj.1.2 | 6 | |||
7.2 | even | 3 | 245.4.e.q.116.2 | 12 | |||
7.3 | odd | 6 | 245.4.e.p.226.2 | 12 | |||
7.4 | even | 3 | 245.4.e.q.226.2 | 12 | |||
7.5 | odd | 6 | 245.4.e.p.116.2 | 12 | |||
7.6 | odd | 2 | 245.4.a.p.1.5 | yes | 6 | ||
21.20 | even | 2 | 2205.4.a.ca.1.2 | 6 | |||
35.34 | odd | 2 | 1225.4.a.bi.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
245.4.a.p.1.5 | yes | 6 | 7.6 | odd | 2 | ||
245.4.e.p.116.2 | 12 | 7.5 | odd | 6 | |||
245.4.e.p.226.2 | 12 | 7.3 | odd | 6 | |||
245.4.e.q.116.2 | 12 | 7.2 | even | 3 | |||
245.4.e.q.226.2 | 12 | 7.4 | even | 3 | |||
1225.4.a.bi.1.2 | 6 | 35.34 | odd | 2 | |||
1225.4.a.bj.1.2 | 6 | 5.4 | even | 2 | |||
2205.4.a.bz.1.2 | 6 | 3.2 | odd | 2 | |||
2205.4.a.ca.1.2 | 6 | 21.20 | even | 2 |