Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2401,4,Mod(1,2401)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2401, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2401.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2401 = 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2401.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: | \(141.663585924\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | no (minimal twist has level 49) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 2401.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08878 | −0.738494 | −0.369247 | − | 0.929331i | \(-0.620384\pi\) | ||||
−0.369247 | + | 0.929331i | \(0.620384\pi\) | |||||||
\(3\) | 2.27918 | 0.438628 | 0.219314 | − | 0.975654i | \(-0.429618\pi\) | ||||
0.219314 | + | 0.975654i | \(0.429618\pi\) | |||||||
\(4\) | −3.63702 | −0.454627 | ||||||||
\(5\) | 20.5308 | 1.83633 | 0.918165 | − | 0.396199i | \(-0.129671\pi\) | ||||
0.918165 | + | 0.396199i | \(0.129671\pi\) | |||||||
\(6\) | −4.76069 | −0.323924 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.3071 | 1.07423 | ||||||||
\(9\) | −21.8054 | −0.807606 | ||||||||
\(10\) | −42.8842 | −1.35612 | ||||||||
\(11\) | 24.3738 | 0.668088 | 0.334044 | − | 0.942557i | \(-0.391587\pi\) | ||||
0.334044 | + | 0.942557i | \(0.391587\pi\) | |||||||
\(12\) | −8.28940 | −0.199412 | ||||||||
\(13\) | −49.9160 | −1.06494 | −0.532470 | − | 0.846449i | \(-0.678736\pi\) | ||||
−0.532470 | + | 0.846449i | \(0.678736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 46.7933 | 0.805465 | ||||||||
\(16\) | −21.6760 | −0.338687 | ||||||||
\(17\) | −91.1860 | −1.30093 | −0.650466 | − | 0.759535i | \(-0.725426\pi\) | ||||
−0.650466 | + | 0.759535i | \(0.725426\pi\) | |||||||
\(18\) | 45.5465 | 0.596412 | ||||||||
\(19\) | 0.874881 | 0.0105638 | 0.00528188 | − | 0.999986i | \(-0.498319\pi\) | ||||
0.00528188 | + | 0.999986i | \(0.498319\pi\) | |||||||
\(20\) | −74.6708 | −0.834845 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −50.9113 | −0.493379 | ||||||||
\(23\) | −20.0588 | −0.181850 | −0.0909250 | − | 0.995858i | \(-0.528982\pi\) | ||||
−0.0909250 | + | 0.995858i | \(0.528982\pi\) | |||||||
\(24\) | 55.4002 | 0.471188 | ||||||||
\(25\) | 296.513 | 2.37211 | ||||||||
\(26\) | 104.263 | 0.786451 | ||||||||
\(27\) | −111.236 | −0.792866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 264.040 | 1.69072 | 0.845361 | − | 0.534195i | \(-0.179385\pi\) | ||||
0.845361 | + | 0.534195i | \(0.179385\pi\) | |||||||
\(30\) | −97.7407 | −0.594831 | ||||||||
\(31\) | −62.5307 | −0.362286 | −0.181143 | − | 0.983457i | \(-0.557980\pi\) | ||||
−0.181143 | + | 0.983457i | \(0.557980\pi\) | |||||||
\(32\) | −149.181 | −0.824115 | ||||||||
\(33\) | 55.5521 | 0.293042 | ||||||||
\(34\) | 190.467 | 0.960730 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 79.3064 | 0.367159 | ||||||||
\(37\) | 24.1476 | 0.107293 | 0.0536465 | − | 0.998560i | \(-0.482916\pi\) | ||||
0.0536465 | + | 0.998560i | \(0.482916\pi\) | |||||||
\(38\) | −1.82743 | −0.00780127 | ||||||||
\(39\) | −113.767 | −0.467112 | ||||||||
\(40\) | 499.044 | 1.97265 | ||||||||
\(41\) | 173.543 | 0.661045 | 0.330522 | − | 0.943798i | \(-0.392775\pi\) | ||||
0.330522 | + | 0.943798i | \(0.392775\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 268.798 | 0.953286 | 0.476643 | − | 0.879097i | \(-0.341853\pi\) | ||||
0.476643 | + | 0.879097i | \(0.341853\pi\) | |||||||
\(44\) | −88.6478 | −0.303731 | ||||||||
\(45\) | −447.681 | −1.48303 | ||||||||
\(46\) | 41.8983 | 0.134295 | ||||||||
\(47\) | −595.968 | −1.84959 | −0.924796 | − | 0.380464i | \(-0.875764\pi\) | ||||
−0.924796 | + | 0.380464i | \(0.875764\pi\) | |||||||
\(48\) | −49.4034 | −0.148558 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −619.349 | −1.75178 | ||||||||
\(51\) | −207.829 | −0.570625 | ||||||||
\(52\) | 181.545 | 0.484150 | ||||||||
\(53\) | 99.8604 | 0.258809 | 0.129405 | − | 0.991592i | \(-0.458693\pi\) | ||||
0.129405 | + | 0.991592i | \(0.458693\pi\) | |||||||
\(54\) | 232.347 | 0.585526 | ||||||||
\(55\) | 500.413 | 1.22683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.99401 | 0.00463356 | ||||||||
\(58\) | −551.520 | −1.24859 | ||||||||
\(59\) | −228.887 | −0.505061 | −0.252531 | − | 0.967589i | \(-0.581263\pi\) | ||||
−0.252531 | + | 0.967589i | \(0.581263\pi\) | |||||||
\(60\) | −170.188 | −0.366186 | ||||||||
\(61\) | −78.5131 | −0.164796 | −0.0823981 | − | 0.996599i | \(-0.526258\pi\) | ||||
−0.0823981 | + | 0.996599i | \(0.526258\pi\) | |||||||
\(62\) | 130.613 | 0.267546 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 485.013 | 0.947290 | ||||||||
\(65\) | −1024.82 | −1.95558 | ||||||||
\(66\) | −116.036 | −0.216410 | ||||||||
\(67\) | −500.417 | −0.912472 | −0.456236 | − | 0.889859i | \(-0.650803\pi\) | ||||
−0.456236 | + | 0.889859i | \(0.650803\pi\) | |||||||
\(68\) | 331.645 | 0.591439 | ||||||||
\(69\) | −45.7176 | −0.0797645 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −915.119 | −1.52964 | −0.764822 | − | 0.644242i | \(-0.777173\pi\) | ||||
−0.764822 | + | 0.644242i | \(0.777173\pi\) | |||||||
\(72\) | −530.025 | −0.867557 | ||||||||
\(73\) | −773.956 | −1.24089 | −0.620443 | − | 0.784251i | \(-0.713047\pi\) | ||||
−0.620443 | + | 0.784251i | \(0.713047\pi\) | |||||||
\(74\) | −50.4389 | −0.0792352 | ||||||||
\(75\) | 675.806 | 1.04047 | ||||||||
\(76\) | −3.18196 | −0.00480257 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 237.635 | 0.344959 | ||||||||
\(79\) | 268.708 | 0.382683 | 0.191342 | − | 0.981523i | \(-0.438716\pi\) | ||||
0.191342 | + | 0.981523i | \(0.438716\pi\) | |||||||
\(80\) | −445.025 | −0.621941 | ||||||||
\(81\) | 335.218 | 0.459833 | ||||||||
\(82\) | −362.492 | −0.488178 | ||||||||
\(83\) | −23.3499 | −0.0308793 | −0.0154397 | − | 0.999881i | \(-0.504915\pi\) | ||||
−0.0154397 | + | 0.999881i | \(0.504915\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1872.12 | −2.38894 | ||||||||
\(86\) | −561.459 | −0.703996 | ||||||||
\(87\) | 601.793 | 0.741598 | ||||||||
\(88\) | 592.456 | 0.717682 | ||||||||
\(89\) | 583.579 | 0.695048 | 0.347524 | − | 0.937671i | \(-0.387023\pi\) | ||||
0.347524 | + | 0.937671i | \(0.387023\pi\) | |||||||
\(90\) | 935.105 | 1.09521 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 72.9542 | 0.0826740 | ||||||||
\(93\) | −142.519 | −0.158908 | ||||||||
\(94\) | 1244.84 | 1.36591 | ||||||||
\(95\) | 17.9620 | 0.0193985 | ||||||||
\(96\) | −340.009 | −0.361480 | ||||||||
\(97\) | −1244.88 | −1.30308 | −0.651538 | − | 0.758616i | \(-0.725876\pi\) | ||||
−0.651538 | + | 0.758616i | \(0.725876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −531.479 | −0.539552 | ||||||||
\(100\) | −1078.42 | −1.07842 | ||||||||
\(101\) | 213.825 | 0.210657 | 0.105328 | − | 0.994437i | \(-0.466411\pi\) | ||||
0.105328 | + | 0.994437i | \(0.466411\pi\) | |||||||
\(102\) | 434.108 | 0.421403 | ||||||||
\(103\) | 511.261 | 0.489088 | 0.244544 | − | 0.969638i | \(-0.421362\pi\) | ||||
0.244544 | + | 0.969638i | \(0.421362\pi\) | |||||||
\(104\) | −1213.31 | −1.14399 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −208.586 | −0.191129 | ||||||||
\(107\) | 1458.89 | 1.31809 | 0.659046 | − | 0.752103i | \(-0.270960\pi\) | ||||
0.659046 | + | 0.752103i | \(0.270960\pi\) | |||||||
\(108\) | 404.567 | 0.360458 | ||||||||
\(109\) | −909.184 | −0.798936 | −0.399468 | − | 0.916747i | \(-0.630805\pi\) | ||||
−0.399468 | + | 0.916747i | \(0.630805\pi\) | |||||||
\(110\) | −1045.25 | −0.906006 | ||||||||
\(111\) | 55.0367 | 0.0470617 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −603.064 | −0.502049 | −0.251024 | − | 0.967981i | \(-0.580767\pi\) | ||||
−0.251024 | + | 0.967981i | \(0.580767\pi\) | |||||||
\(114\) | −4.16504 | −0.00342185 | ||||||||
\(115\) | −411.823 | −0.333937 | ||||||||
\(116\) | −960.317 | −0.768649 | ||||||||
\(117\) | 1088.44 | 0.860051 | ||||||||
\(118\) | 478.094 | 0.372984 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1137.41 | 0.865257 | ||||||||
\(121\) | −736.919 | −0.553658 | ||||||||
\(122\) | 163.996 | 0.121701 | ||||||||
\(123\) | 395.535 | 0.289953 | ||||||||
\(124\) | 227.425 | 0.164705 | ||||||||
\(125\) | 3521.30 | 2.51964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 374.982 | 0.262002 | 0.131001 | − | 0.991382i | \(-0.458181\pi\) | ||||
0.131001 | + | 0.991382i | \(0.458181\pi\) | |||||||
\(128\) | 180.363 | 0.124547 | ||||||||
\(129\) | 612.638 | 0.418138 | ||||||||
\(130\) | 2140.61 | 1.44418 | ||||||||
\(131\) | −2712.98 | −1.80942 | −0.904710 | − | 0.426027i | \(-0.859913\pi\) | ||||
−0.904710 | + | 0.426027i | \(0.859913\pi\) | |||||||
\(132\) | −202.044 | −0.133225 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1045.26 | 0.673855 | ||||||||
\(135\) | −2283.76 | −1.45596 | ||||||||
\(136\) | −2216.47 | −1.39750 | ||||||||
\(137\) | −1102.74 | −0.687688 | −0.343844 | − | 0.939027i | \(-0.611729\pi\) | ||||
−0.343844 | + | 0.939027i | \(0.611729\pi\) | |||||||
\(138\) | 95.4937 | 0.0589055 | ||||||||
\(139\) | 382.063 | 0.233138 | 0.116569 | − | 0.993183i | \(-0.462810\pi\) | ||||
0.116569 | + | 0.993183i | \(0.462810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1358.32 | −0.811282 | ||||||||
\(142\) | 1911.48 | 1.12963 | ||||||||
\(143\) | −1216.64 | −0.711473 | ||||||||
\(144\) | 472.652 | 0.273526 | ||||||||
\(145\) | 5420.95 | 3.10472 | ||||||||
\(146\) | 1616.62 | 0.916387 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −87.8252 | −0.0487783 | ||||||||
\(149\) | −1050.96 | −0.577840 | −0.288920 | − | 0.957353i | \(-0.593296\pi\) | ||||
−0.288920 | + | 0.957353i | \(0.593296\pi\) | |||||||
\(150\) | −1411.61 | −0.768381 | ||||||||
\(151\) | −1815.20 | −0.978271 | −0.489135 | − | 0.872208i | \(-0.662688\pi\) | ||||
−0.489135 | + | 0.872208i | \(0.662688\pi\) | |||||||
\(152\) | 21.2658 | 0.0113479 | ||||||||
\(153\) | 1988.34 | 1.05064 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1283.81 | −0.665276 | ||||||||
\(156\) | 413.774 | 0.212362 | ||||||||
\(157\) | −549.193 | −0.279174 | −0.139587 | − | 0.990210i | \(-0.544578\pi\) | ||||
−0.139587 | + | 0.990210i | \(0.544578\pi\) | |||||||
\(158\) | −561.270 | −0.282609 | ||||||||
\(159\) | 227.599 | 0.113521 | ||||||||
\(160\) | −3062.80 | −1.51335 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −700.195 | −0.339584 | ||||||||
\(163\) | 3283.18 | 1.57766 | 0.788830 | − | 0.614612i | \(-0.210687\pi\) | ||||
0.788830 | + | 0.614612i | \(0.210687\pi\) | |||||||
\(164\) | −631.178 | −0.300529 | ||||||||
\(165\) | 1140.53 | 0.538122 | ||||||||
\(166\) | 48.7727 | 0.0228042 | ||||||||
\(167\) | −211.964 | −0.0982172 | −0.0491086 | − | 0.998793i | \(-0.515638\pi\) | ||||
−0.0491086 | + | 0.998793i | \(0.515638\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 294.610 | 0.134096 | ||||||||
\(170\) | 3910.44 | 1.76422 | ||||||||
\(171\) | −19.0771 | −0.00853135 | ||||||||
\(172\) | −977.623 | −0.433390 | ||||||||
\(173\) | 259.070 | 0.113854 | 0.0569270 | − | 0.998378i | \(-0.481870\pi\) | ||||
0.0569270 | + | 0.998378i | \(0.481870\pi\) | |||||||
\(174\) | −1257.01 | −0.547665 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −528.325 | −0.226273 | ||||||||
\(177\) | −521.675 | −0.221534 | ||||||||
\(178\) | −1218.97 | −0.513289 | ||||||||
\(179\) | −6.04772 | −0.00252530 | −0.00126265 | − | 0.999999i | \(-0.500402\pi\) | ||||
−0.00126265 | + | 0.999999i | \(0.500402\pi\) | |||||||
\(180\) | 1628.22 | 0.674226 | ||||||||
\(181\) | −3792.72 | −1.55752 | −0.778759 | − | 0.627324i | \(-0.784150\pi\) | ||||
−0.778759 | + | 0.627324i | \(0.784150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −178.945 | −0.0722842 | ||||||||
\(184\) | −487.572 | −0.195349 | ||||||||
\(185\) | 495.769 | 0.197025 | ||||||||
\(186\) | 297.689 | 0.117353 | ||||||||
\(187\) | −2222.55 | −0.869137 | ||||||||
\(188\) | 2167.54 | 0.840875 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −37.5186 | −0.0143257 | ||||||||
\(191\) | 2705.30 | 1.02486 | 0.512430 | − | 0.858729i | \(-0.328745\pi\) | ||||
0.512430 | + | 0.858729i | \(0.328745\pi\) | |||||||
\(192\) | 1105.43 | 0.415508 | ||||||||
\(193\) | −1540.63 | −0.574596 | −0.287298 | − | 0.957841i | \(-0.592757\pi\) | ||||
−0.287298 | + | 0.957841i | \(0.592757\pi\) | |||||||
\(194\) | 2600.27 | 0.962313 | ||||||||
\(195\) | −2335.73 | −0.857771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5226.84 | 1.89034 | 0.945170 | − | 0.326578i | \(-0.105896\pi\) | ||||
0.945170 | + | 0.326578i | \(0.105896\pi\) | |||||||
\(198\) | 1110.14 | 0.398456 | ||||||||
\(199\) | −2040.75 | −0.726960 | −0.363480 | − | 0.931602i | \(-0.618411\pi\) | ||||
−0.363480 | + | 0.931602i | \(0.618411\pi\) | |||||||
\(200\) | 7207.38 | 2.54819 | ||||||||
\(201\) | −1140.54 | −0.400236 | ||||||||
\(202\) | −446.632 | −0.155569 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 755.877 | 0.259422 | ||||||||
\(205\) | 3562.97 | 1.21390 | ||||||||
\(206\) | −1067.91 | −0.361188 | ||||||||
\(207\) | 437.389 | 0.146863 | ||||||||
\(208\) | 1081.98 | 0.360681 | ||||||||
\(209\) | 21.3242 | 0.00705752 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2812.63 | −0.917675 | −0.458837 | − | 0.888520i | \(-0.651734\pi\) | ||||
−0.458837 | + | 0.888520i | \(0.651734\pi\) | |||||||
\(212\) | −363.194 | −0.117662 | ||||||||
\(213\) | −2085.72 | −0.670944 | ||||||||
\(214\) | −3047.28 | −0.973402 | ||||||||
\(215\) | 5518.64 | 1.75055 | ||||||||
\(216\) | −2703.83 | −0.851723 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1899.08 | 0.590009 | ||||||||
\(219\) | −1763.98 | −0.544287 | ||||||||
\(220\) | −1820.01 | −0.557750 | ||||||||
\(221\) | 4551.64 | 1.38541 | ||||||||
\(222\) | −114.959 | −0.0347548 | ||||||||
\(223\) | −4569.13 | −1.37207 | −0.686035 | − | 0.727568i | \(-0.740650\pi\) | ||||
−0.686035 | + | 0.727568i | \(0.740650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6465.57 | −1.91573 | ||||||||
\(226\) | 1259.67 | 0.370760 | ||||||||
\(227\) | −946.517 | −0.276751 | −0.138376 | − | 0.990380i | \(-0.544188\pi\) | ||||
−0.138376 | + | 0.990380i | \(0.544188\pi\) | |||||||
\(228\) | −7.25224 | −0.00210654 | ||||||||
\(229\) | 1781.16 | 0.513984 | 0.256992 | − | 0.966414i | \(-0.417269\pi\) | ||||
0.256992 | + | 0.966414i | \(0.417269\pi\) | |||||||
\(230\) | 860.206 | 0.246610 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6418.05 | 1.81623 | ||||||||
\(233\) | 5121.25 | 1.43993 | 0.719966 | − | 0.694009i | \(-0.244157\pi\) | ||||
0.719966 | + | 0.694009i | \(0.244157\pi\) | |||||||
\(234\) | −2273.50 | −0.635142 | ||||||||
\(235\) | −12235.7 | −3.39646 | ||||||||
\(236\) | 832.467 | 0.229614 | ||||||||
\(237\) | 612.433 | 0.167856 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2203.02 | −0.596240 | −0.298120 | − | 0.954528i | \(-0.596360\pi\) | ||||
−0.298120 | + | 0.954528i | \(0.596360\pi\) | |||||||
\(240\) | −1014.29 | −0.272801 | ||||||||
\(241\) | −2441.83 | −0.652665 | −0.326333 | − | 0.945255i | \(-0.605813\pi\) | ||||
−0.326333 | + | 0.945255i | \(0.605813\pi\) | |||||||
\(242\) | 1539.26 | 0.408873 | ||||||||
\(243\) | 3767.39 | 0.994561 | ||||||||
\(244\) | 285.553 | 0.0749208 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −826.183 | −0.214128 | ||||||||
\(247\) | −43.6706 | −0.0112498 | ||||||||
\(248\) | −1519.94 | −0.389179 | ||||||||
\(249\) | −53.2185 | −0.0135445 | ||||||||
\(250\) | −7355.21 | −1.86074 | ||||||||
\(251\) | 4069.78 | 1.02344 | 0.511718 | − | 0.859154i | \(-0.329009\pi\) | ||||
0.511718 | + | 0.859154i | \(0.329009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −488.909 | −0.121492 | ||||||||
\(254\) | −783.254 | −0.193487 | ||||||||
\(255\) | −4266.89 | −1.04786 | ||||||||
\(256\) | −4256.84 | −1.03927 | ||||||||
\(257\) | 2994.94 | 0.726924 | 0.363462 | − | 0.931609i | \(-0.381595\pi\) | ||||
0.363462 | + | 0.931609i | \(0.381595\pi\) | |||||||
\(258\) | −1279.66 | −0.308792 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3727.27 | 0.889060 | ||||||||
\(261\) | −5757.48 | −1.36544 | ||||||||
\(262\) | 5666.80 | 1.33625 | ||||||||
\(263\) | −2821.40 | −0.661501 | −0.330750 | − | 0.943718i | \(-0.607302\pi\) | ||||
−0.330750 | + | 0.943718i | \(0.607302\pi\) | |||||||
\(264\) | 1350.31 | 0.314795 | ||||||||
\(265\) | 2050.21 | 0.475259 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1330.08 | 0.304867 | ||||||||
\(268\) | 1820.02 | 0.414835 | ||||||||
\(269\) | −1882.02 | −0.426575 | −0.213288 | − | 0.976989i | \(-0.568417\pi\) | ||||
−0.213288 | + | 0.976989i | \(0.568417\pi\) | |||||||
\(270\) | 4770.27 | 1.07522 | ||||||||
\(271\) | 288.668 | 0.0647061 | 0.0323530 | − | 0.999477i | \(-0.489700\pi\) | ||||
0.0323530 | + | 0.999477i | \(0.489700\pi\) | |||||||
\(272\) | 1976.54 | 0.440609 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2303.37 | 0.507853 | ||||||||
\(275\) | 7227.14 | 1.58478 | ||||||||
\(276\) | 166.276 | 0.0362631 | ||||||||
\(277\) | 1269.10 | 0.275281 | 0.137641 | − | 0.990482i | \(-0.456048\pi\) | ||||
0.137641 | + | 0.990482i | \(0.456048\pi\) | |||||||
\(278\) | −798.044 | −0.172171 | ||||||||
\(279\) | 1363.50 | 0.292584 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1506.72 | 0.319869 | 0.159934 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159934 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(282\) | 2837.22 | 0.599127 | ||||||||
\(283\) | −2530.42 | −0.531513 | −0.265756 | − | 0.964040i | \(-0.585622\pi\) | ||||
−0.265756 | + | 0.964040i | \(0.585622\pi\) | |||||||
\(284\) | 3328.30 | 0.695417 | ||||||||
\(285\) | 40.9386 | 0.00850874 | ||||||||
\(286\) | 2541.29 | 0.525419 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3252.94 | 0.665560 | ||||||||
\(289\) | 3401.88 | 0.692424 | ||||||||
\(290\) | −11323.1 | −2.29282 | ||||||||
\(291\) | −2837.30 | −0.571565 | ||||||||
\(292\) | 2814.89 | 0.564141 | ||||||||
\(293\) | −7190.40 | −1.43368 | −0.716839 | − | 0.697239i | \(-0.754412\pi\) | ||||
−0.716839 | + | 0.697239i | \(0.754412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4699.24 | −0.927458 | ||||||||
\(296\) | 586.959 | 0.115258 | ||||||||
\(297\) | −2711.24 | −0.529704 | ||||||||
\(298\) | 2195.22 | 0.426731 | ||||||||
\(299\) | 1001.26 | 0.193659 | ||||||||
\(300\) | −2457.92 | −0.473026 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3791.55 | 0.722447 | ||||||||
\(303\) | 487.344 | 0.0924000 | ||||||||
\(304\) | −18.9639 | −0.00357781 | ||||||||
\(305\) | −1611.94 | −0.302620 | ||||||||
\(306\) | −4153.20 | −0.775891 | ||||||||
\(307\) | 7446.38 | 1.38432 | 0.692162 | − | 0.721743i | \(-0.256659\pi\) | ||||
0.692162 | + | 0.721743i | \(0.256659\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1165.25 | 0.214528 | ||||||||
\(310\) | 2681.58 | 0.491302 | ||||||||
\(311\) | −7695.36 | −1.40310 | −0.701550 | − | 0.712620i | \(-0.747508\pi\) | ||||
−0.701550 | + | 0.712620i | \(0.747508\pi\) | |||||||
\(312\) | −2765.36 | −0.501787 | ||||||||
\(313\) | 2167.97 | 0.391504 | 0.195752 | − | 0.980653i | \(-0.437285\pi\) | ||||
0.195752 | + | 0.980653i | \(0.437285\pi\) | |||||||
\(314\) | 1147.14 | 0.206169 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −977.295 | −0.173978 | ||||||||
\(317\) | −4138.08 | −0.733179 | −0.366590 | − | 0.930383i | \(-0.619475\pi\) | ||||
−0.366590 | + | 0.930383i | \(0.619475\pi\) | |||||||
\(318\) | −475.404 | −0.0838344 | ||||||||
\(319\) | 6435.65 | 1.12955 | ||||||||
\(320\) | 9957.69 | 1.73954 | ||||||||
\(321\) | 3325.06 | 0.578151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −79.7769 | −0.0137427 | ||||||||
\(324\) | −1219.19 | −0.209052 | ||||||||
\(325\) | −14800.8 | −2.52615 | ||||||||
\(326\) | −6857.82 | −1.16509 | ||||||||
\(327\) | −2072.19 | −0.350435 | ||||||||
\(328\) | 4218.33 | 0.710116 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2382.31 | −0.397399 | ||||||||
\(331\) | −9319.56 | −1.54758 | −0.773791 | − | 0.633441i | \(-0.781642\pi\) | ||||
−0.773791 | + | 0.633441i | \(0.781642\pi\) | |||||||
\(332\) | 84.9239 | 0.0140386 | ||||||||
\(333\) | −526.547 | −0.0866505 | ||||||||
\(334\) | 442.745 | 0.0725328 | ||||||||
\(335\) | −10274.0 | −1.67560 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2030.58 | −0.328228 | −0.164114 | − | 0.986441i | \(-0.552477\pi\) | ||||
−0.164114 | + | 0.986441i | \(0.552477\pi\) | |||||||
\(338\) | −615.373 | −0.0990293 | ||||||||
\(339\) | −1374.49 | −0.220212 | ||||||||
\(340\) | 6808.93 | 1.08608 | ||||||||
\(341\) | −1524.11 | −0.242039 | ||||||||
\(342\) | 39.8478 | 0.00630035 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6533.71 | 1.02405 | ||||||||
\(345\) | −938.617 | −0.146474 | ||||||||
\(346\) | −541.139 | −0.0840804 | ||||||||
\(347\) | 10513.8 | 1.62655 | 0.813274 | − | 0.581881i | \(-0.197683\pi\) | ||||
0.813274 | + | 0.581881i | \(0.197683\pi\) | |||||||
\(348\) | −2188.73 | −0.337151 | ||||||||
\(349\) | −2497.11 | −0.383001 | −0.191500 | − | 0.981493i | \(-0.561335\pi\) | ||||
−0.191500 | + | 0.981493i | \(0.561335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5552.46 | 0.844354 | ||||||||
\(352\) | −3636.10 | −0.550581 | ||||||||
\(353\) | −5138.62 | −0.774791 | −0.387396 | − | 0.921914i | \(-0.626625\pi\) | ||||
−0.387396 | + | 0.921914i | \(0.626625\pi\) | |||||||
\(354\) | 1089.66 | 0.163601 | ||||||||
\(355\) | −18788.1 | −2.80893 | ||||||||
\(356\) | −2122.49 | −0.315988 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6323 | 0.00186492 | ||||||||
\(359\) | −1201.94 | −0.176702 | −0.0883511 | − | 0.996089i | \(-0.528160\pi\) | ||||
−0.0883511 | + | 0.996089i | \(0.528160\pi\) | |||||||
\(360\) | −10881.8 | −1.59312 | ||||||||
\(361\) | −6858.23 | −0.999888 | ||||||||
\(362\) | 7922.14 | 1.15022 | ||||||||
\(363\) | −1679.57 | −0.242850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15889.9 | −2.27868 | ||||||||
\(366\) | 373.776 | 0.0533814 | ||||||||
\(367\) | −6075.31 | −0.864111 | −0.432055 | − | 0.901847i | \(-0.642212\pi\) | ||||
−0.432055 | + | 0.901847i | \(0.642212\pi\) | |||||||
\(368\) | 434.794 | 0.0615902 | ||||||||
\(369\) | −3784.16 | −0.533864 | ||||||||
\(370\) | −1035.55 | −0.145502 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 518.343 | 0.0722441 | ||||||||
\(373\) | −12687.3 | −1.76120 | −0.880598 | − | 0.473864i | \(-0.842859\pi\) | ||||
−0.880598 | + | 0.473864i | \(0.842859\pi\) | |||||||
\(374\) | 4642.40 | 0.641852 | ||||||||
\(375\) | 8025.66 | 1.10518 | ||||||||
\(376\) | −14486.3 | −1.98689 | ||||||||
\(377\) | −13179.8 | −1.80052 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8715.12 | −1.18118 | −0.590588 | − | 0.806973i | \(-0.701104\pi\) | ||||
−0.590588 | + | 0.806973i | \(0.701104\pi\) | |||||||
\(380\) | −65.3281 | −0.00881911 | ||||||||
\(381\) | 854.651 | 0.114922 | ||||||||
\(382\) | −5650.75 | −0.756853 | ||||||||
\(383\) | 7951.29 | 1.06081 | 0.530407 | − | 0.847743i | \(-0.322039\pi\) | ||||
0.530407 | + | 0.847743i | \(0.322039\pi\) | |||||||
\(384\) | 411.079 | 0.0546296 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3218.03 | 0.424336 | ||||||||
\(387\) | −5861.24 | −0.769880 | ||||||||
\(388\) | 4527.65 | 0.592414 | ||||||||
\(389\) | −498.244 | −0.0649408 | −0.0324704 | − | 0.999473i | \(-0.510337\pi\) | ||||
−0.0324704 | + | 0.999473i | \(0.510337\pi\) | |||||||
\(390\) | 4878.83 | 0.633459 | ||||||||
\(391\) | 1829.08 | 0.236574 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6183.36 | −0.793662 | ||||||||
\(394\) | −10917.7 | −1.39600 | ||||||||
\(395\) | 5516.78 | 0.702733 | ||||||||
\(396\) | 1933.00 | 0.245295 | ||||||||
\(397\) | −1099.37 | −0.138982 | −0.0694908 | − | 0.997583i | \(-0.522137\pi\) | ||||
−0.0694908 | + | 0.997583i | \(0.522137\pi\) | |||||||
\(398\) | 4262.67 | 0.536855 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6427.21 | −0.803401 | ||||||||
\(401\) | −10258.2 | −1.27748 | −0.638740 | − | 0.769423i | \(-0.720544\pi\) | ||||
−0.638740 | + | 0.769423i | \(0.720544\pi\) | |||||||
\(402\) | 2382.33 | 0.295572 | ||||||||
\(403\) | 3121.29 | 0.385812 | ||||||||
\(404\) | −777.684 | −0.0957703 | ||||||||
\(405\) | 6882.29 | 0.844404 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 588.568 | 0.0716812 | ||||||||
\(408\) | −5051.72 | −0.612984 | ||||||||
\(409\) | 8368.94 | 1.01178 | 0.505889 | − | 0.862598i | \(-0.331164\pi\) | ||||
0.505889 | + | 0.862598i | \(0.331164\pi\) | |||||||
\(410\) | −7442.25 | −0.896455 | ||||||||
\(411\) | −2513.33 | −0.301639 | ||||||||
\(412\) | −1859.47 | −0.222353 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −913.608 | −0.108457 | ||||||||
\(415\) | −479.391 | −0.0567046 | ||||||||
\(416\) | 7446.51 | 0.877632 | ||||||||
\(417\) | 870.789 | 0.102261 | ||||||||
\(418\) | −44.5414 | −0.00521194 | ||||||||
\(419\) | 1051.17 | 0.122561 | 0.0612806 | − | 0.998121i | \(-0.480482\pi\) | ||||
0.0612806 | + | 0.998121i | \(0.480482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6470.30 | 0.749034 | 0.374517 | − | 0.927220i | \(-0.377809\pi\) | ||||
0.374517 | + | 0.927220i | \(0.377809\pi\) | |||||||
\(422\) | 5874.95 | 0.677697 | ||||||||
\(423\) | 12995.3 | 1.49374 | ||||||||
\(424\) | 2427.32 | 0.278021 | ||||||||
\(425\) | −27037.8 | −3.08595 | ||||||||
\(426\) | 4356.60 | 0.495488 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5305.99 | −0.599240 | ||||||||
\(429\) | −2772.94 | −0.312072 | ||||||||
\(430\) | −11527.2 | −1.29277 | ||||||||
\(431\) | −6691.40 | −0.747827 | −0.373913 | − | 0.927464i | \(-0.621984\pi\) | ||||
−0.373913 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(432\) | 2411.15 | 0.268533 | ||||||||
\(433\) | −5239.21 | −0.581478 | −0.290739 | − | 0.956802i | \(-0.593901\pi\) | ||||
−0.290739 | + | 0.956802i | \(0.593901\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12355.3 | 1.36182 | ||||||||
\(436\) | 3306.72 | 0.363218 | ||||||||
\(437\) | −17.5491 | −0.00192102 | ||||||||
\(438\) | 3684.56 | 0.401953 | ||||||||
\(439\) | −1750.33 | −0.190293 | −0.0951467 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951467 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(440\) | 12163.6 | 1.31790 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9507.36 | −1.02312 | ||||||||
\(443\) | 14582.9 | 1.56401 | 0.782005 | − | 0.623272i | \(-0.214197\pi\) | ||||
0.782005 | + | 0.623272i | \(0.214197\pi\) | |||||||
\(444\) | −200.169 | −0.0213955 | ||||||||
\(445\) | 11981.3 | 1.27634 | ||||||||
\(446\) | 9543.89 | 1.01327 | ||||||||
\(447\) | −2395.33 | −0.253457 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4892.76 | −0.514262 | −0.257131 | − | 0.966377i | \(-0.582777\pi\) | ||||
−0.257131 | + | 0.966377i | \(0.582777\pi\) | |||||||
\(450\) | 13505.1 | 1.41475 | ||||||||
\(451\) | 4229.89 | 0.441636 | ||||||||
\(452\) | 2193.35 | 0.228245 | ||||||||
\(453\) | −4137.16 | −0.429097 | ||||||||
\(454\) | 1977.06 | 0.204379 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 48.4686 | 0.00497752 | ||||||||
\(457\) | 6729.37 | 0.688811 | 0.344406 | − | 0.938821i | \(-0.388080\pi\) | ||||
0.344406 | + | 0.938821i | \(0.388080\pi\) | |||||||
\(458\) | −3720.44 | −0.379574 | ||||||||
\(459\) | 10143.2 | 1.03146 | ||||||||
\(460\) | 1497.81 | 0.151817 | ||||||||
\(461\) | 5647.28 | 0.570542 | 0.285271 | − | 0.958447i | \(-0.407916\pi\) | ||||
0.285271 | + | 0.958447i | \(0.407916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18097.8 | 1.81658 | 0.908289 | − | 0.418343i | \(-0.137389\pi\) | ||||
0.908289 | + | 0.418343i | \(0.137389\pi\) | |||||||
\(464\) | −5723.32 | −0.572626 | ||||||||
\(465\) | −2926.02 | −0.291808 | ||||||||
\(466\) | −10697.1 | −1.06338 | ||||||||
\(467\) | 8762.53 | 0.868269 | 0.434134 | − | 0.900848i | \(-0.357054\pi\) | ||||
0.434134 | + | 0.900848i | \(0.357054\pi\) | |||||||
\(468\) | −3958.66 | −0.391003 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 25557.6 | 2.50826 | ||||||||
\(471\) | −1251.71 | −0.122454 | ||||||||
\(472\) | −5563.59 | −0.542553 | ||||||||
\(473\) | 6551.62 | 0.636879 | ||||||||
\(474\) | −1279.23 | −0.123960 | ||||||||
\(475\) | 259.414 | 0.0250584 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2177.49 | −0.209016 | ||||||||
\(478\) | 4601.61 | 0.440319 | ||||||||
\(479\) | −1606.66 | −0.153258 | −0.0766288 | − | 0.997060i | \(-0.524416\pi\) | ||||
−0.0766288 | + | 0.997060i | \(0.524416\pi\) | |||||||
\(480\) | −6980.65 | −0.663795 | ||||||||
\(481\) | −1205.35 | −0.114261 | ||||||||
\(482\) | 5100.44 | 0.481989 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2680.19 | 0.251708 | ||||||||
\(485\) | −25558.4 | −2.39288 | ||||||||
\(486\) | −7869.24 | −0.734477 | ||||||||
\(487\) | −17179.8 | −1.59854 | −0.799270 | − | 0.600971i | \(-0.794781\pi\) | ||||
−0.799270 | + | 0.600971i | \(0.794781\pi\) | |||||||
\(488\) | −1908.43 | −0.177030 | ||||||||
\(489\) | 7482.94 | 0.692005 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8314.93 | 0.764251 | 0.382126 | − | 0.924110i | \(-0.375192\pi\) | ||||
0.382126 | + | 0.924110i | \(0.375192\pi\) | |||||||
\(492\) | −1438.57 | −0.131820 | ||||||||
\(493\) | −24076.7 | −2.19952 | ||||||||
\(494\) | 91.2180 | 0.00830788 | ||||||||
\(495\) | −10911.7 | −0.990795 | ||||||||
\(496\) | 1355.41 | 0.122701 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 111.162 | 0.0100025 | ||||||||
\(499\) | −16410.9 | −1.47225 | −0.736126 | − | 0.676845i | \(-0.763347\pi\) | ||||
−0.736126 | + | 0.676845i | \(0.763347\pi\) | |||||||
\(500\) | −12807.0 | −1.14550 | ||||||||
\(501\) | −483.104 | −0.0430808 | ||||||||
\(502\) | −8500.86 | −0.755801 | ||||||||
\(503\) | −10041.7 | −0.890137 | −0.445069 | − | 0.895497i | \(-0.646821\pi\) | ||||
−0.445069 | + | 0.895497i | \(0.646821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4389.99 | 0.386835 | ||||||||
\(506\) | 1021.22 | 0.0897209 | ||||||||
\(507\) | 671.467 | 0.0588184 | ||||||||
\(508\) | −1363.82 | −0.119113 | ||||||||
\(509\) | 9837.36 | 0.856647 | 0.428323 | − | 0.903625i | \(-0.359104\pi\) | ||||
0.428323 | + | 0.903625i | \(0.359104\pi\) | |||||||
\(510\) | 8912.58 | 0.773834 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7448.68 | 0.642946 | ||||||||
\(513\) | −97.3183 | −0.00837565 | ||||||||
\(514\) | −6255.76 | −0.536828 | ||||||||
\(515\) | 10496.6 | 0.898127 | ||||||||
\(516\) | −2228.18 | −0.190097 | ||||||||
\(517\) | −14526.0 | −1.23569 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 590.467 | 0.0499395 | ||||||||
\(520\) | −24910.3 | −2.10075 | ||||||||
\(521\) | −8901.28 | −0.748507 | −0.374253 | − | 0.927326i | \(-0.622101\pi\) | ||||
−0.374253 | + | 0.927326i | \(0.622101\pi\) | |||||||
\(522\) | 12026.1 | 1.00837 | ||||||||
\(523\) | −2325.18 | −0.194403 | −0.0972017 | − | 0.995265i | \(-0.530989\pi\) | ||||
−0.0972017 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(524\) | 9867.15 | 0.822612 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5893.26 | 0.488514 | ||||||||
\(527\) | 5701.93 | 0.471309 | ||||||||
\(528\) | −1204.15 | −0.0992495 | ||||||||
\(529\) | −11764.6 | −0.966931 | ||||||||
\(530\) | −4282.43 | −0.350976 | ||||||||
\(531\) | 4990.97 | 0.407890 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8662.57 | −0.703973 | ||||||||
\(534\) | −2778.24 | −0.225143 | ||||||||
\(535\) | 29952.1 | 2.42045 | ||||||||
\(536\) | −12163.7 | −0.980208 | ||||||||
\(537\) | −13.7838 | −0.00110767 | ||||||||
\(538\) | 3931.12 | 0.315023 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8306.08 | 0.661920 | ||||||||
\(541\) | 2563.04 | 0.203685 | 0.101843 | − | 0.994801i | \(-0.467526\pi\) | ||||
0.101843 | + | 0.994801i | \(0.467526\pi\) | |||||||
\(542\) | −602.963 | −0.0477850 | ||||||||
\(543\) | −8644.28 | −0.683170 | ||||||||
\(544\) | 13603.2 | 1.07212 | ||||||||
\(545\) | −18666.3 | −1.46711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −116.302 | −0.00909090 | −0.00454545 | − | 0.999990i | \(-0.501447\pi\) | ||||
−0.00454545 | + | 0.999990i | \(0.501447\pi\) | |||||||
\(548\) | 4010.68 | 0.312642 | ||||||||
\(549\) | 1712.01 | 0.133090 | ||||||||
\(550\) | −15095.9 | −1.17035 | ||||||||
\(551\) | 231.003 | 0.0178604 | ||||||||
\(552\) | −1111.26 | −0.0856856 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2650.87 | −0.203293 | ||||||||
\(555\) | 1129.95 | 0.0864208 | ||||||||
\(556\) | −1389.57 | −0.105991 | ||||||||
\(557\) | 12812.1 | 0.974623 | 0.487311 | − | 0.873228i | \(-0.337978\pi\) | ||||
0.487311 | + | 0.873228i | \(0.337978\pi\) | |||||||
\(558\) | −2848.06 | −0.216071 | ||||||||
\(559\) | −13417.3 | −1.01519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5065.57 | −0.381228 | ||||||||
\(562\) | −3147.19 | −0.236221 | ||||||||
\(563\) | −20955.4 | −1.56868 | −0.784338 | − | 0.620333i | \(-0.786997\pi\) | ||||
−0.784338 | + | 0.620333i | \(0.786997\pi\) | |||||||
\(564\) | 4940.22 | 0.368831 | ||||||||
\(565\) | −12381.4 | −0.921926 | ||||||||
\(566\) | 5285.49 | 0.392519 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22243.9 | −1.64319 | ||||||||
\(569\) | 19329.9 | 1.42417 | 0.712086 | − | 0.702093i | \(-0.247751\pi\) | ||||
0.712086 | + | 0.702093i | \(0.247751\pi\) | |||||||
\(570\) | −85.5115 | −0.00628365 | ||||||||
\(571\) | −19167.8 | −1.40481 | −0.702406 | − | 0.711776i | \(-0.747891\pi\) | ||||
−0.702406 | + | 0.711776i | \(0.747891\pi\) | |||||||
\(572\) | 4424.95 | 0.323455 | ||||||||
\(573\) | 6165.84 | 0.449532 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5947.70 | −0.431367 | ||||||||
\(576\) | −10575.9 | −0.765037 | ||||||||
\(577\) | 18882.2 | 1.36235 | 0.681177 | − | 0.732119i | \(-0.261469\pi\) | ||||
0.681177 | + | 0.732119i | \(0.261469\pi\) | |||||||
\(578\) | −7105.76 | −0.511351 | ||||||||
\(579\) | −3511.37 | −0.252034 | ||||||||
\(580\) | −19716.1 | −1.41149 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5926.48 | 0.422097 | ||||||||
\(583\) | 2433.97 | 0.172907 | ||||||||
\(584\) | −18812.6 | −1.33300 | ||||||||
\(585\) | 22346.5 | 1.57934 | ||||||||
\(586\) | 15019.1 | 1.05876 | ||||||||
\(587\) | 13230.8 | 0.930314 | 0.465157 | − | 0.885228i | \(-0.345998\pi\) | ||||
0.465157 | + | 0.885228i | \(0.345998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −54.7070 | −0.00382710 | ||||||||
\(590\) | 9815.65 | 0.684922 | ||||||||
\(591\) | 11912.9 | 0.829156 | ||||||||
\(592\) | −523.423 | −0.0363388 | ||||||||
\(593\) | −22547.2 | −1.56139 | −0.780695 | − | 0.624912i | \(-0.785135\pi\) | ||||
−0.780695 | + | 0.624912i | \(0.785135\pi\) | |||||||
\(594\) | 5663.17 | 0.391183 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3822.36 | 0.262702 | ||||||||
\(597\) | −4651.23 | −0.318865 | ||||||||
\(598\) | −2091.40 | −0.143016 | ||||||||
\(599\) | −14486.6 | −0.988157 | −0.494078 | − | 0.869417i | \(-0.664494\pi\) | ||||
−0.494078 | + | 0.869417i | \(0.664494\pi\) | |||||||
\(600\) | 16426.9 | 1.11771 | ||||||||
\(601\) | −19651.1 | −1.33375 | −0.666875 | − | 0.745170i | \(-0.732368\pi\) | ||||
−0.666875 | + | 0.745170i | \(0.732368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10911.8 | 0.736918 | ||||||||
\(604\) | 6601.91 | 0.444748 | ||||||||
\(605\) | −15129.5 | −1.01670 | ||||||||
\(606\) | −1017.95 | −0.0682368 | ||||||||
\(607\) | −4346.08 | −0.290613 | −0.145306 | − | 0.989387i | \(-0.546417\pi\) | ||||
−0.145306 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(608\) | −130.515 | −0.00870575 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3366.97 | 0.223483 | ||||||||
\(611\) | 29748.3 | 1.96970 | ||||||||
\(612\) | −7231.63 | −0.477650 | ||||||||
\(613\) | 516.796 | 0.0340509 | 0.0170254 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170254 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(614\) | −15553.8 | −1.02231 | ||||||||
\(615\) | 8120.64 | 0.532449 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14901.6 | −0.972313 | −0.486157 | − | 0.873872i | \(-0.661602\pi\) | ||||
−0.486157 | + | 0.873872i | \(0.661602\pi\) | |||||||
\(618\) | −2433.95 | −0.158427 | ||||||||
\(619\) | −13377.5 | −0.868642 | −0.434321 | − | 0.900758i | \(-0.643012\pi\) | ||||
−0.434321 | + | 0.900758i | \(0.643012\pi\) | |||||||
\(620\) | 4669.22 | 0.302452 | ||||||||
\(621\) | 2231.26 | 0.144183 | ||||||||
\(622\) | 16073.9 | 1.03618 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2466.02 | 0.158205 | ||||||||
\(625\) | 35230.9 | 2.25478 | ||||||||
\(626\) | −4528.40 | −0.289124 | ||||||||
\(627\) | 48.6015 | 0.00309563 | ||||||||
\(628\) | 1997.42 | 0.126920 | ||||||||
\(629\) | −2201.92 | −0.139581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13482.3 | −0.850588 | −0.425294 | − | 0.905055i | \(-0.639829\pi\) | ||||
−0.425294 | + | 0.905055i | \(0.639829\pi\) | |||||||
\(632\) | 6531.51 | 0.411091 | ||||||||
\(633\) | −6410.48 | −0.402518 | ||||||||
\(634\) | 8643.53 | 0.541448 | ||||||||
\(635\) | 7698.68 | 0.481123 | ||||||||
\(636\) | −827.783 | −0.0516096 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13442.6 | −0.834167 | ||||||||
\(639\) | 19954.5 | 1.23535 | ||||||||
\(640\) | 3702.99 | 0.228709 | ||||||||
\(641\) | 7659.21 | 0.471951 | 0.235975 | − | 0.971759i | \(-0.424172\pi\) | ||||
0.235975 | + | 0.971759i | \(0.424172\pi\) | |||||||
\(642\) | −6945.30 | −0.426961 | ||||||||
\(643\) | 4148.58 | 0.254439 | 0.127219 | − | 0.991875i | \(-0.459395\pi\) | ||||
0.127219 | + | 0.991875i | \(0.459395\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12577.9 | 0.767839 | ||||||||
\(646\) | 166.636 | 0.0101489 | ||||||||
\(647\) | −462.800 | −0.0281214 | −0.0140607 | − | 0.999901i | \(-0.504476\pi\) | ||||
−0.0140607 | + | 0.999901i | \(0.504476\pi\) | |||||||
\(648\) | 8148.18 | 0.493967 | ||||||||
\(649\) | −5578.85 | −0.337425 | ||||||||
\(650\) | 30915.5 | 1.86554 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11941.0 | −0.717247 | ||||||||
\(653\) | 17137.3 | 1.02700 | 0.513502 | − | 0.858088i | \(-0.328348\pi\) | ||||
0.513502 | + | 0.858088i | \(0.328348\pi\) | |||||||
\(654\) | 4328.34 | 0.258794 | ||||||||
\(655\) | −55699.6 | −3.32269 | ||||||||
\(656\) | −3761.71 | −0.223887 | ||||||||
\(657\) | 16876.4 | 1.00215 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4894.60 | −0.289327 | −0.144664 | − | 0.989481i | \(-0.546210\pi\) | ||||
−0.144664 | + | 0.989481i | \(0.546210\pi\) | |||||||
\(660\) | −4148.12 | −0.244645 | ||||||||
\(661\) | 8147.59 | 0.479432 | 0.239716 | − | 0.970843i | \(-0.422946\pi\) | ||||
0.239716 | + | 0.970843i | \(0.422946\pi\) | |||||||
\(662\) | 19466.5 | 1.14288 | ||||||||
\(663\) | 10374.0 | 0.607681 | ||||||||
\(664\) | −567.568 | −0.0331716 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1099.84 | 0.0639908 | ||||||||
\(667\) | −5296.32 | −0.307458 | ||||||||
\(668\) | 770.917 | 0.0446522 | ||||||||
\(669\) | −10413.9 | −0.601828 | ||||||||
\(670\) | 21460.0 | 1.23742 | ||||||||
\(671\) | −1913.66 | −0.110098 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22544.1 | 1.29125 | 0.645626 | − | 0.763654i | \(-0.276597\pi\) | ||||
0.645626 | + | 0.763654i | \(0.276597\pi\) | |||||||
\(674\) | 4241.43 | 0.242394 | ||||||||
\(675\) | −32982.9 | −1.88076 | ||||||||
\(676\) | −1071.50 | −0.0609638 | ||||||||
\(677\) | −32030.8 | −1.81838 | −0.909191 | − | 0.416379i | \(-0.863299\pi\) | ||||
−0.909191 | + | 0.416379i | \(0.863299\pi\) | |||||||
\(678\) | 2871.00 | 0.162625 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −45505.8 | −2.56628 | ||||||||
\(681\) | −2157.28 | −0.121391 | ||||||||
\(682\) | 3183.52 | 0.178744 | ||||||||
\(683\) | 13530.4 | 0.758018 | 0.379009 | − | 0.925393i | \(-0.376265\pi\) | ||||
0.379009 | + | 0.925393i | \(0.376265\pi\) | |||||||
\(684\) | 69.3837 | 0.00387859 | ||||||||
\(685\) | −22640.1 | −1.26282 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4059.58 | 0.225448 | ||||||||
\(688\) | −5826.46 | −0.322866 | ||||||||
\(689\) | −4984.63 | −0.275616 | ||||||||
\(690\) | 1960.56 | 0.108170 | ||||||||
\(691\) | −15794.5 | −0.869537 | −0.434768 | − | 0.900542i | \(-0.643170\pi\) | ||||
−0.434768 | + | 0.900542i | \(0.643170\pi\) | |||||||
\(692\) | −942.242 | −0.0517611 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21961.0 | −1.20119 | ||||||||
\(695\) | 7844.06 | 0.428118 | ||||||||
\(696\) | 14627.9 | 0.796649 | ||||||||
\(697\) | −15824.7 | −0.859975 | ||||||||
\(698\) | 5215.91 | 0.282844 | ||||||||
\(699\) | 11672.2 | 0.631594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28545.2 | −1.53800 | −0.769000 | − | 0.639249i | \(-0.779245\pi\) | ||||
−0.769000 | + | 0.639249i | \(0.779245\pi\) | |||||||
\(702\) | −11597.8 | −0.623550 | ||||||||
\(703\) | 21.1263 | 0.00113342 | ||||||||
\(704\) | 11821.6 | 0.632874 | ||||||||
\(705\) | −27887.3 | −1.48978 | ||||||||
\(706\) | 10733.4 | 0.572178 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1897.34 | 0.100715 | ||||||||
\(709\) | −21174.1 | −1.12160 | −0.560798 | − | 0.827953i | \(-0.689506\pi\) | ||||
−0.560798 | + | 0.827953i | \(0.689506\pi\) | |||||||
\(710\) | 39244.2 | 2.07438 | ||||||||
\(711\) | −5859.27 | −0.309057 | ||||||||
\(712\) | 14185.1 | 0.746643 | ||||||||
\(713\) | 1254.29 | 0.0658816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24978.6 | −1.30650 | ||||||||
\(716\) | 21.9957 | 0.00114807 | ||||||||
\(717\) | −5021.06 | −0.261527 | ||||||||
\(718\) | 2510.59 | 0.130493 | ||||||||
\(719\) | 30681.3 | 1.59140 | 0.795702 | − | 0.605688i | \(-0.207102\pi\) | ||||
0.795702 | + | 0.605688i | \(0.207102\pi\) | |||||||
\(720\) | 9703.92 | 0.502283 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 14325.3 | 0.738411 | ||||||||
\(723\) | −5565.37 | −0.286277 | ||||||||
\(724\) | 13794.2 | 0.708090 | ||||||||
\(725\) | 78291.3 | 4.01057 | ||||||||
\(726\) | 3508.24 | 0.179343 | ||||||||
\(727\) | 20800.5 | 1.06114 | 0.530570 | − | 0.847641i | \(-0.321978\pi\) | ||||
0.530570 | + | 0.847641i | \(0.321978\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −464.333 | −0.0235906 | ||||||||
\(730\) | 33190.5 | 1.68279 | ||||||||
\(731\) | −24510.6 | −1.24016 | ||||||||
\(732\) | 650.827 | 0.0328624 | ||||||||
\(733\) | −22114.2 | −1.11434 | −0.557168 | − | 0.830400i | \(-0.688112\pi\) | ||||
−0.557168 | + | 0.830400i | \(0.688112\pi\) | |||||||
\(734\) | 12690.0 | 0.638140 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2992.39 | 0.149865 | ||||||||
\(737\) | −12197.0 | −0.609612 | ||||||||
\(738\) | 7904.27 | 0.394255 | ||||||||
\(739\) | −10808.8 | −0.538033 | −0.269017 | − | 0.963136i | \(-0.586699\pi\) | ||||
−0.269017 | + | 0.963136i | \(0.586699\pi\) | |||||||
\(740\) | −1803.12 | −0.0895731 | ||||||||
\(741\) | −99.5330 | −0.00493446 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4092.59 | −0.202076 | −0.101038 | − | 0.994883i | \(-0.532216\pi\) | ||||
−0.101038 | + | 0.994883i | \(0.532216\pi\) | |||||||
\(744\) | −3464.22 | −0.170705 | ||||||||
\(745\) | −21577.1 | −1.06110 | ||||||||
\(746\) | 26501.0 | 1.30063 | ||||||||
\(747\) | 509.152 | 0.0249383 | ||||||||
\(748\) | 8083.44 | 0.395133 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16763.8 | −0.816170 | ||||||||
\(751\) | 23601.3 | 1.14677 | 0.573384 | − | 0.819287i | \(-0.305630\pi\) | ||||
0.573384 | + | 0.819287i | \(0.305630\pi\) | |||||||
\(752\) | 12918.2 | 0.626433 | ||||||||
\(753\) | 9275.75 | 0.448907 | ||||||||
\(754\) | 27529.7 | 1.32967 | ||||||||
\(755\) | −37267.5 | −1.79643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6445.81 | −0.309481 | −0.154740 | − | 0.987955i | \(-0.549454\pi\) | ||||
−0.154740 | + | 0.987955i | \(0.549454\pi\) | |||||||
\(758\) | 18203.9 | 0.872291 | ||||||||
\(759\) | −1114.31 | −0.0532897 | ||||||||
\(760\) | 436.604 | 0.0208386 | ||||||||
\(761\) | −29152.5 | −1.38867 | −0.694334 | − | 0.719653i | \(-0.744301\pi\) | ||||
−0.694334 | + | 0.719653i | \(0.744301\pi\) | |||||||
\(762\) | −1785.17 | −0.0848688 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9839.20 | −0.465929 | ||||||||
\(765\) | 40822.2 | 1.92932 | ||||||||
\(766\) | −16608.4 | −0.783404 | ||||||||
\(767\) | 11425.2 | 0.537860 | ||||||||
\(768\) | −9702.09 | −0.455851 | ||||||||
\(769\) | −4567.02 | −0.214162 | −0.107081 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107081 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6826.00 | 0.318849 | ||||||||
\(772\) | 5603.30 | 0.261227 | ||||||||
\(773\) | 26020.5 | 1.21073 | 0.605363 | − | 0.795950i | \(-0.293028\pi\) | ||||
0.605363 | + | 0.795950i | \(0.293028\pi\) | |||||||
\(774\) | 12242.8 | 0.568551 | ||||||||
\(775\) | −18541.2 | −0.859379 | ||||||||
\(776\) | −30259.4 | −1.39981 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1040.72 | 0.0479584 | ||||||||
\(779\) | 151.829 | 0.00698312 | ||||||||
\(780\) | 8495.11 | 0.389966 | ||||||||
\(781\) | −22304.9 | −1.02194 | ||||||||
\(782\) | −3820.54 | −0.174709 | ||||||||
\(783\) | −29370.7 | −1.34052 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11275.4 | −0.512656 | ||||||||
\(786\) | 12915.6 | 0.586114 | ||||||||
\(787\) | 26814.9 | 1.21455 | 0.607274 | − | 0.794493i | \(-0.292263\pi\) | ||||
0.607274 | + | 0.794493i | \(0.292263\pi\) | |||||||
\(788\) | −19010.1 | −0.859400 | ||||||||
\(789\) | −6430.46 | −0.290153 | ||||||||
\(790\) | −11523.3 | −0.518964 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −12918.7 | −0.579604 | ||||||||
\(793\) | 3919.06 | 0.175498 | ||||||||
\(794\) | 2296.33 | 0.102637 | ||||||||
\(795\) | 4672.80 | 0.208462 | ||||||||
\(796\) | 7422.25 | 0.330496 | ||||||||
\(797\) | −21488.7 | −0.955044 | −0.477522 | − | 0.878620i | \(-0.658465\pi\) | ||||
−0.477522 | + | 0.878620i | \(0.658465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54343.9 | 2.40619 | ||||||||
\(800\) | −44234.0 | −1.95489 | ||||||||
\(801\) | −12725.2 | −0.561325 | ||||||||
\(802\) | 21427.1 | 0.943411 | ||||||||
\(803\) | −18864.2 | −0.829021 | ||||||||
\(804\) | 4148.16 | 0.181958 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6519.67 | −0.284920 | ||||||||
\(807\) | −4289.46 | −0.187108 | ||||||||
\(808\) | 5197.46 | 0.226295 | ||||||||
\(809\) | −26285.8 | −1.14235 | −0.571174 | − | 0.820829i | \(-0.693512\pi\) | ||||
−0.571174 | + | 0.820829i | \(0.693512\pi\) | |||||||
\(810\) | −14375.6 | −0.623587 | ||||||||
\(811\) | 14137.3 | 0.612119 | 0.306060 | − | 0.952012i | \(-0.400989\pi\) | ||||
0.306060 | + | 0.952012i | \(0.400989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 657.926 | 0.0283819 | ||||||||
\(814\) | −1229.39 | −0.0529361 | ||||||||
\(815\) | 67406.2 | 2.89710 | ||||||||
\(816\) | 4504.89 | 0.193263 | ||||||||
\(817\) | 235.166 | 0.0100703 | ||||||||
\(818\) | −17480.8 | −0.747192 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12958.6 | −0.551870 | ||||||||
\(821\) | 14694.2 | 0.624641 | 0.312320 | − | 0.949977i | \(-0.398894\pi\) | ||||
0.312320 | + | 0.949977i | \(0.398894\pi\) | |||||||
\(822\) | 5249.79 | 0.222759 | ||||||||
\(823\) | −33610.9 | −1.42358 | −0.711788 | − | 0.702394i | \(-0.752114\pi\) | ||||
−0.711788 | + | 0.702394i | \(0.752114\pi\) | |||||||
\(824\) | 12427.3 | 0.525394 | ||||||||
\(825\) | 16471.9 | 0.695126 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41704.4 | 1.75357 | 0.876786 | − | 0.480881i | \(-0.159683\pi\) | ||||
0.876786 | + | 0.480881i | \(0.159683\pi\) | |||||||
\(828\) | −1590.79 | −0.0667680 | ||||||||
\(829\) | 23189.8 | 0.971550 | 0.485775 | − | 0.874084i | \(-0.338537\pi\) | ||||
0.485775 | + | 0.874084i | \(0.338537\pi\) | |||||||
\(830\) | 1001.34 | 0.0418760 | ||||||||
\(831\) | 2892.50 | 0.120746 | ||||||||
\(832\) | −24209.9 | −1.00881 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1818.88 | −0.0755189 | ||||||||
\(835\) | −4351.79 | −0.180359 | ||||||||
\(836\) | −77.5563 | −0.00320854 | ||||||||
\(837\) | 6955.67 | 0.287244 | ||||||||
\(838\) | −2195.66 | −0.0905107 | ||||||||
\(839\) | −28313.4 | −1.16506 | −0.582531 | − | 0.812808i | \(-0.697938\pi\) | ||||
−0.582531 | + | 0.812808i | \(0.697938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45328.0 | 1.85854 | ||||||||
\(842\) | −13515.0 | −0.553157 | ||||||||
\(843\) | 3434.07 | 0.140303 | ||||||||
\(844\) | 10229.6 | 0.417200 | ||||||||
\(845\) | 6048.57 | 0.246245 | ||||||||
\(846\) | −27144.2 | −1.10312 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2164.57 | −0.0876553 | ||||||||
\(849\) | −5767.28 | −0.233136 | ||||||||
\(850\) | 56476.0 | 2.27895 | ||||||||
\(851\) | −484.372 | −0.0195112 | ||||||||
\(852\) | 7585.79 | 0.305029 | ||||||||
\(853\) | −27586.3 | −1.10731 | −0.553656 | − | 0.832746i | \(-0.686768\pi\) | ||||
−0.553656 | + | 0.832746i | \(0.686768\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −391.668 | −0.0156664 | ||||||||
\(856\) | 35461.3 | 1.41594 | ||||||||
\(857\) | −19048.4 | −0.759253 | −0.379627 | − | 0.925140i | \(-0.623948\pi\) | ||||
−0.379627 | + | 0.925140i | \(0.623948\pi\) | |||||||
\(858\) | 5792.05 | 0.230463 | ||||||||
\(859\) | 35648.5 | 1.41596 | 0.707981 | − | 0.706232i | \(-0.249606\pi\) | ||||
0.707981 | + | 0.706232i | \(0.249606\pi\) | |||||||
\(860\) | −20071.4 | −0.795847 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13976.8 | 0.552265 | ||||||||
\(863\) | −1685.56 | −0.0664856 | −0.0332428 | − | 0.999447i | \(-0.510583\pi\) | ||||
−0.0332428 | + | 0.999447i | \(0.510583\pi\) | |||||||
\(864\) | 16594.3 | 0.653412 | ||||||||
\(865\) | 5318.91 | 0.209073 | ||||||||
\(866\) | 10943.5 | 0.429418 | ||||||||
\(867\) | 7753.48 | 0.303716 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6549.42 | 0.255666 | ||||||||
\(870\) | −25807.4 | −1.00569 | ||||||||
\(871\) | 24978.8 | 0.971728 | ||||||||
\(872\) | −22099.6 | −0.858243 | ||||||||
\(873\) | 27145.0 | 1.05237 | ||||||||
\(874\) | 36.6561 | 0.00141866 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6415.63 | 0.247448 | ||||||||
\(877\) | 15774.7 | 0.607382 | 0.303691 | − | 0.952771i | \(-0.401781\pi\) | ||||
0.303691 | + | 0.952771i | \(0.401781\pi\) | |||||||
\(878\) | 3656.05 | 0.140530 | ||||||||
\(879\) | −16388.2 | −0.628851 | ||||||||
\(880\) | −10846.9 | −0.415511 | ||||||||
\(881\) | 31146.1 | 1.19108 | 0.595539 | − | 0.803327i | \(-0.296939\pi\) | ||||
0.595539 | + | 0.803327i | \(0.296939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39795.7 | 1.51668 | 0.758341 | − | 0.651857i | \(-0.226010\pi\) | ||||
0.758341 | + | 0.651857i | \(0.226010\pi\) | |||||||
\(884\) | −16554.4 | −0.629847 | ||||||||
\(885\) | −10710.4 | −0.406809 | ||||||||
\(886\) | −30460.5 | −1.15501 | ||||||||
\(887\) | 22050.6 | 0.834710 | 0.417355 | − | 0.908743i | \(-0.362957\pi\) | ||||
0.417355 | + | 0.908743i | \(0.362957\pi\) | |||||||
\(888\) | 1337.78 | 0.0505552 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25026.3 | −0.942567 | ||||||||
\(891\) | 8170.53 | 0.307209 | ||||||||
\(892\) | 16618.0 | 0.623781 | ||||||||
\(893\) | −521.401 | −0.0195386 | ||||||||
\(894\) | 5003.30 | 0.187176 | ||||||||
\(895\) | −124.165 | −0.00463728 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2282.04 | 0.0849443 | ||||||||
\(898\) | 10219.9 | 0.379779 | ||||||||
\(899\) | −16510.6 | −0.612524 | ||||||||
\(900\) | 23515.4 | 0.870941 | ||||||||
\(901\) | −9105.87 | −0.336693 | ||||||||
\(902\) | −8835.30 | −0.326146 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14658.7 | −0.539317 | ||||||||
\(905\) | −77867.5 | −2.86011 | ||||||||
\(906\) | 8641.60 | 0.316885 | ||||||||
\(907\) | −50823.3 | −1.86060 | −0.930298 | − | 0.366804i | \(-0.880452\pi\) | ||||
−0.930298 | + | 0.366804i | \(0.880452\pi\) | |||||||
\(908\) | 3442.50 | 0.125819 | ||||||||
\(909\) | −4662.52 | −0.170128 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7063.91 | 0.256902 | 0.128451 | − | 0.991716i | \(-0.458999\pi\) | ||||
0.128451 | + | 0.991716i | \(0.458999\pi\) | |||||||
\(912\) | −43.2221 | −0.00156933 | ||||||||
\(913\) | −569.125 | −0.0206301 | ||||||||
\(914\) | −14056.1 | −0.508683 | ||||||||
\(915\) | −3673.88 | −0.132738 | ||||||||
\(916\) | −6478.11 | −0.233671 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −21186.8 | −0.761730 | ||||||||
\(919\) | −48153.9 | −1.72846 | −0.864228 | − | 0.503101i | \(-0.832192\pi\) | ||||
−0.864228 | + | 0.503101i | \(0.832192\pi\) | |||||||
\(920\) | −10010.2 | −0.358726 | ||||||||
\(921\) | 16971.6 | 0.607203 | ||||||||
\(922\) | −11795.9 | −0.421342 | ||||||||
\(923\) | 45679.1 | 1.62898 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7160.08 | 0.254510 | ||||||||
\(926\) | −37802.2 | −1.34153 | ||||||||
\(927\) | −11148.2 | −0.394990 | ||||||||
\(928\) | −39389.6 | −1.39335 | ||||||||
\(929\) | −13847.3 | −0.489038 | −0.244519 | − | 0.969644i | \(-0.578630\pi\) | ||||
−0.244519 | + | 0.969644i | \(0.578630\pi\) | |||||||
\(930\) | 6111.80 | 0.215499 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18626.1 | −0.654632 | ||||||||
\(933\) | −17539.1 | −0.615438 | ||||||||
\(934\) | −18303.0 | −0.641211 | ||||||||
\(935\) | −45630.6 | −1.59602 | ||||||||
\(936\) | 26456.8 | 0.923895 | ||||||||
\(937\) | 28414.4 | 0.990670 | 0.495335 | − | 0.868702i | \(-0.335045\pi\) | ||||
0.495335 | + | 0.868702i | \(0.335045\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4941.18 | 0.171725 | ||||||||
\(940\) | 44501.4 | 1.54412 | ||||||||
\(941\) | 43222.9 | 1.49737 | 0.748685 | − | 0.662926i | \(-0.230685\pi\) | ||||
0.748685 | + | 0.662926i | \(0.230685\pi\) | |||||||
\(942\) | 2614.54 | 0.0904312 | ||||||||
\(943\) | −3481.06 | −0.120211 | ||||||||
\(944\) | 4961.36 | 0.171058 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13684.9 | −0.470331 | ||||||||
\(947\) | −12157.9 | −0.417189 | −0.208594 | − | 0.978002i | \(-0.566889\pi\) | ||||
−0.208594 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(948\) | −2227.43 | −0.0763117 | ||||||||
\(949\) | 38632.8 | 1.32147 | ||||||||
\(950\) | −541.857 | −0.0185054 | ||||||||
\(951\) | −9431.42 | −0.321593 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39467.4 | 1.34153 | 0.670763 | − | 0.741671i | \(-0.265967\pi\) | ||||
0.670763 | + | 0.741671i | \(0.265967\pi\) | |||||||
\(954\) | 4548.29 | 0.154357 | ||||||||
\(955\) | 55541.8 | 1.88198 | ||||||||
\(956\) | 8012.41 | 0.271067 | ||||||||
\(957\) | 14668.0 | 0.495453 | ||||||||
\(958\) | 3355.96 | 0.113180 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 22695.3 | 0.763009 | ||||||||
\(961\) | −25880.9 | −0.868749 | ||||||||
\(962\) | 2517.71 | 0.0843807 | ||||||||
\(963\) | −31811.5 | −1.06450 | ||||||||
\(964\) | 8880.99 | 0.296719 | ||||||||
\(965\) | −31630.4 | −1.05515 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34059.6 | −1.13266 | −0.566330 | − | 0.824178i | \(-0.691637\pi\) | ||||
−0.566330 | + | 0.824178i | \(0.691637\pi\) | |||||||
\(968\) | −17912.4 | −0.594758 | ||||||||
\(969\) | −181.826 | −0.00602794 | ||||||||
\(970\) | 53385.7 | 1.76712 | ||||||||
\(971\) | 24314.8 | 0.803604 | 0.401802 | − | 0.915726i | \(-0.368384\pi\) | ||||
0.401802 | + | 0.915726i | \(0.368384\pi\) | |||||||
\(972\) | −13702.1 | −0.452155 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 35884.7 | 1.18051 | ||||||||
\(975\) | −33733.5 | −1.10804 | ||||||||
\(976\) | 1701.85 | 0.0558143 | ||||||||
\(977\) | 25995.9 | 0.851261 | 0.425631 | − | 0.904897i | \(-0.360052\pi\) | ||||
0.425631 | + | 0.904897i | \(0.360052\pi\) | |||||||
\(978\) | −15630.2 | −0.511041 | ||||||||
\(979\) | 14224.0 | 0.464353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19825.1 | 0.645225 | ||||||||
\(982\) | −17368.0 | −0.564395 | ||||||||
\(983\) | −1311.35 | −0.0425490 | −0.0212745 | − | 0.999774i | \(-0.506772\pi\) | ||||
−0.0212745 | + | 0.999774i | \(0.506772\pi\) | |||||||
\(984\) | 9614.31 | 0.311477 | ||||||||
\(985\) | 107311. | 3.47129 | ||||||||
\(986\) | 50290.9 | 1.62433 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 158.831 | 0.00511445 | ||||||||
\(989\) | −5391.77 | −0.173355 | ||||||||
\(990\) | 22792.0 | 0.731696 | ||||||||
\(991\) | 25733.0 | 0.824859 | 0.412429 | − | 0.910990i | \(-0.364680\pi\) | ||||
0.412429 | + | 0.910990i | \(0.364680\pi\) | |||||||
\(992\) | 9328.38 | 0.298565 | ||||||||
\(993\) | −21240.9 | −0.678812 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41898.2 | −1.33494 | ||||||||
\(996\) | 193.557 | 0.00615771 | ||||||||
\(997\) | 42804.5 | 1.35971 | 0.679855 | − | 0.733347i | \(-0.262043\pi\) | ||||
0.679855 | + | 0.733347i | \(0.262043\pi\) | |||||||
\(998\) | 34278.7 | 1.08725 | ||||||||
\(999\) | −2686.08 | −0.0850690 |
(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 | 2401.4.a.c.1.14 | 39 | ||
7.6 | odd | 2 | 2401.4.a.d.1.14 | 39 | |||
49.13 | odd | 14 | 49.4.e.a.22.10 | ✓ | 78 | ||
49.34 | odd | 14 | 49.4.e.a.29.10 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.e.a.22.10 | ✓ | 78 | 49.13 | odd | 14 | ||
49.4.e.a.29.10 | yes | 78 | 49.34 | odd | 14 | ||
2401.4.a.c.1.14 | 39 | 1.1 | even | 1 | trivial | ||
2401.4.a.d.1.14 | 39 | 7.6 | odd | 2 |