Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82843 | −0.646447 | −0.323223 | − | 0.946323i | \(-0.604766\pi\) | ||||
−0.323223 | + | 0.946323i | \(0.604766\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.65685 | −0.582107 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 23.1421 | 1.02275 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.14214 | −0.289100 | ||||||||
\(11\) | 64.5685 | 1.76983 | 0.884916 | − | 0.465751i | \(-0.154216\pi\) | ||||
0.884916 | + | 0.465751i | \(0.154216\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.3431 | 0.690029 | 0.345014 | − | 0.938597i | \(-0.387874\pi\) | ||||
0.345014 | + | 0.938597i | \(0.387874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.05887 | −0.0790449 | ||||||||
\(17\) | −56.3431 | −0.803836 | −0.401918 | − | 0.915676i | \(-0.631656\pi\) | ||||
−0.401918 | + | 0.915676i | \(0.631656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.74517 | 0.0331465 | 0.0165733 | − | 0.999863i | \(-0.494724\pi\) | ||||
0.0165733 | + | 0.999863i | \(0.494724\pi\) | |||||||
\(20\) | −23.2843 | −0.260326 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −118.059 | −1.14410 | ||||||||
\(23\) | −88.1665 | −0.799304 | −0.399652 | − | 0.916667i | \(-0.630869\pi\) | ||||
−0.399652 | + | 0.916667i | \(0.630869\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −59.1371 | −0.446067 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −246.735 | −1.57992 | −0.789958 | − | 0.613161i | \(-0.789898\pi\) | ||||
−0.789958 | + | 0.613161i | \(0.789898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 110.912 | 0.642591 | 0.321296 | − | 0.946979i | \(-0.395882\pi\) | ||||
0.321296 | + | 0.946979i | \(0.395882\pi\) | |||||||
\(32\) | −175.887 | −0.971649 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 103.019 | 0.519637 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 120.676 | 0.536190 | 0.268095 | − | 0.963392i | \(-0.413606\pi\) | ||||
0.268095 | + | 0.963392i | \(0.413606\pi\) | |||||||
\(38\) | −5.01934 | −0.0214275 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 115.711 | 0.457387 | ||||||||
\(41\) | −176.274 | −0.671449 | −0.335724 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335724 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −443.362 | −1.57238 | −0.786188 | − | 0.617988i | \(-0.787948\pi\) | ||||
−0.786188 | + | 0.617988i | \(0.787948\pi\) | |||||||
\(44\) | −300.686 | −1.03023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 161.206 | 0.516707 | ||||||||
\(47\) | −345.206 | −1.07135 | −0.535675 | − | 0.844424i | \(-0.679943\pi\) | ||||
−0.535675 | + | 0.844424i | \(0.679943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −45.7107 | −0.129289 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −150.617 | −0.401670 | ||||||||
\(53\) | −260.981 | −0.676386 | −0.338193 | − | 0.941077i | \(-0.609816\pi\) | ||||
−0.338193 | + | 0.941077i | \(0.609816\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 322.843 | 0.791493 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 451.137 | 1.02133 | ||||||||
\(59\) | 628.999 | 1.38794 | 0.693972 | − | 0.720002i | \(-0.255859\pi\) | ||||
0.693972 | + | 0.720002i | \(0.255859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 115.206 | 0.241814 | 0.120907 | − | 0.992664i | \(-0.461420\pi\) | ||||
0.120907 | + | 0.992664i | \(0.461420\pi\) | |||||||
\(62\) | −202.794 | −0.415401 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 362.068 | 0.707164 | ||||||||
\(65\) | 161.716 | 0.308590 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −951.480 | −1.73495 | −0.867476 | − | 0.497479i | \(-0.834259\pi\) | ||||
−0.867476 | + | 0.497479i | \(0.834259\pi\) | |||||||
\(68\) | 262.382 | 0.467919 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −356.264 | −0.595504 | −0.297752 | − | 0.954643i | \(-0.596237\pi\) | ||||
−0.297752 | + | 0.954643i | \(0.596237\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 656.754 | 1.05298 | 0.526488 | − | 0.850183i | \(-0.323509\pi\) | ||||
0.526488 | + | 0.850183i | \(0.323509\pi\) | |||||||
\(74\) | −220.648 | −0.346618 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.7838 | −0.0192948 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 440.195 | 0.626909 | 0.313455 | − | 0.949603i | \(-0.398514\pi\) | ||||
0.313455 | + | 0.949603i | \(0.398514\pi\) | |||||||
\(80\) | −25.2944 | −0.0353500 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 322.304 | 0.434056 | ||||||||
\(83\) | −54.4121 | −0.0719579 | −0.0359790 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359790 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −281.716 | −0.359487 | ||||||||
\(86\) | 810.656 | 1.01646 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1494.25 | 1.81009 | ||||||||
\(89\) | −1018.78 | −1.21338 | −0.606690 | − | 0.794938i | \(-0.707503\pi\) | ||||
−0.606690 | + | 0.794938i | \(0.707503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 410.579 | 0.465280 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 631.184 | 0.692571 | ||||||||
\(95\) | 13.7258 | 0.0148236 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 724.108 | 0.757959 | 0.378979 | − | 0.925405i | \(-0.376275\pi\) | ||||
0.378979 | + | 0.925405i | \(0.376275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −116.421 | −0.116421 | ||||||||
\(101\) | 268.725 | 0.264744 | 0.132372 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132372 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1840.63 | 1.76080 | 0.880399 | − | 0.474233i | \(-0.157275\pi\) | ||||
0.880399 | + | 0.474233i | \(0.157275\pi\) | |||||||
\(104\) | 748.489 | 0.705725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 477.184 | 0.437247 | ||||||||
\(107\) | 243.087 | 0.219627 | 0.109813 | − | 0.993952i | \(-0.464975\pi\) | ||||
0.109813 | + | 0.993952i | \(0.464975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −405.176 | −0.356044 | −0.178022 | − | 0.984027i | \(-0.556970\pi\) | ||||
−0.178022 | + | 0.984027i | \(0.556970\pi\) | |||||||
\(110\) | −590.294 | −0.511658 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28.1766 | 0.0234569 | 0.0117285 | − | 0.999931i | \(-0.496267\pi\) | ||||
0.0117285 | + | 0.999931i | \(0.496267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −440.833 | −0.357460 | ||||||||
\(116\) | 1149.01 | 0.919680 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1150.08 | −0.897232 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2838.10 | 2.13230 | ||||||||
\(122\) | −210.646 | −0.156320 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −516.500 | −0.374057 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2740.90 | −1.91508 | −0.957541 | − | 0.288298i | \(-0.906911\pi\) | ||||
−0.957541 | + | 0.288298i | \(0.906911\pi\) | |||||||
\(128\) | 745.083 | 0.514505 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −295.685 | −0.199487 | ||||||||
\(131\) | −1832.04 | −1.22188 | −0.610938 | − | 0.791678i | \(-0.709208\pi\) | ||||
−0.610938 | + | 0.791678i | \(0.709208\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1739.71 | 1.12155 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1303.90 | −0.822122 | ||||||||
\(137\) | −382.747 | −0.238688 | −0.119344 | − | 0.992853i | \(-0.538079\pi\) | ||||
−0.119344 | + | 0.992853i | \(0.538079\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3053.60 | −1.86333 | −0.931667 | − | 0.363314i | \(-0.881645\pi\) | ||||
−0.931667 | + | 0.363314i | \(0.881645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 651.403 | 0.384961 | ||||||||
\(143\) | 2088.35 | 1.22123 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1233.68 | −0.706560 | ||||||||
\(146\) | −1200.83 | −0.680692 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −561.971 | −0.312120 | ||||||||
\(149\) | −3560.60 | −1.95769 | −0.978843 | − | 0.204611i | \(-0.934407\pi\) | ||||
−0.978843 | + | 0.204611i | \(0.934407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3261.80 | 1.75789 | 0.878945 | − | 0.476923i | \(-0.158248\pi\) | ||||
0.878945 | + | 0.476923i | \(0.158248\pi\) | |||||||
\(152\) | 63.5290 | 0.0339005 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 554.558 | 0.287376 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2878.46 | −1.46322 | −0.731611 | − | 0.681723i | \(-0.761231\pi\) | ||||
−0.731611 | + | 0.681723i | \(0.761231\pi\) | |||||||
\(158\) | −804.865 | −0.405263 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −879.437 | −0.434535 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −927.537 | −0.445708 | −0.222854 | − | 0.974852i | \(-0.571537\pi\) | ||||
−0.222854 | + | 0.974852i | \(0.571537\pi\) | |||||||
\(164\) | 820.883 | 0.390855 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 99.4886 | 0.0465169 | ||||||||
\(167\) | 1094.52 | 0.507164 | 0.253582 | − | 0.967314i | \(-0.418391\pi\) | ||||
0.253582 | + | 0.967314i | \(0.418391\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1150.92 | −0.523860 | ||||||||
\(170\) | 515.097 | 0.232389 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2064.67 | 0.915290 | ||||||||
\(173\) | −1713.25 | −0.752926 | −0.376463 | − | 0.926432i | \(-0.622860\pi\) | ||||
−0.376463 | + | 0.926432i | \(0.622860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −326.644 | −0.139896 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1862.77 | 0.784386 | ||||||||
\(179\) | 4065.58 | 1.69763 | 0.848816 | − | 0.528689i | \(-0.177316\pi\) | ||||
0.848816 | + | 0.528689i | \(0.177316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2791.40 | 1.14631 | 0.573157 | − | 0.819445i | \(-0.305718\pi\) | ||||
0.573157 | + | 0.819445i | \(0.305718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2040.36 | −0.817486 | ||||||||
\(185\) | 603.381 | 0.239792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3637.99 | −1.42266 | ||||||||
\(188\) | 1607.57 | 0.623640 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −25.0967 | −0.00958266 | ||||||||
\(191\) | 634.185 | 0.240251 | 0.120126 | − | 0.992759i | \(-0.461670\pi\) | ||||
0.120126 | + | 0.992759i | \(0.461670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −254.999 | −0.0951049 | −0.0475524 | − | 0.998869i | \(-0.515142\pi\) | ||||
−0.0475524 | + | 0.998869i | \(0.515142\pi\) | |||||||
\(194\) | −1323.98 | −0.489980 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4172.37 | −1.50898 | −0.754490 | − | 0.656311i | \(-0.772116\pi\) | ||||
−0.754490 | + | 0.656311i | \(0.772116\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4626.48 | 1.64805 | 0.824026 | − | 0.566552i | \(-0.191723\pi\) | ||||
0.824026 | + | 0.566552i | \(0.191723\pi\) | |||||||
\(200\) | 578.553 | 0.204550 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −491.344 | −0.171143 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −881.371 | −0.300281 | ||||||||
\(206\) | −3365.45 | −1.13826 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −163.620 | −0.0545433 | ||||||||
\(209\) | 177.251 | 0.0586638 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1562.64 | −0.509843 | −0.254921 | − | 0.966962i | \(-0.582050\pi\) | ||||
−0.254921 | + | 0.966962i | \(0.582050\pi\) | |||||||
\(212\) | 1215.35 | 0.393729 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −444.466 | −0.141977 | ||||||||
\(215\) | −2216.81 | −0.703188 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 740.834 | 0.230163 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1503.43 | −0.460733 | ||||||||
\(221\) | −1822.31 | −0.554670 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1236.39 | 0.371278 | 0.185639 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185639 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.5189 | −0.0151637 | ||||||||
\(227\) | 4181.82 | 1.22272 | 0.611359 | − | 0.791353i | \(-0.290623\pi\) | ||||
0.611359 | + | 0.791353i | \(0.290623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 484.774 | 0.139890 | 0.0699449 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699449 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(230\) | 806.030 | 0.231079 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5709.98 | −1.61585 | ||||||||
\(233\) | −2080.54 | −0.584982 | −0.292491 | − | 0.956268i | \(-0.594484\pi\) | ||||
−0.292491 | + | 0.956268i | \(0.594484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1726.03 | −0.479123 | ||||||||
\(236\) | −2929.16 | −0.807932 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6814.10 | −1.84422 | −0.922108 | − | 0.386933i | \(-0.873534\pi\) | ||||
−0.922108 | + | 0.386933i | \(0.873534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3921.84 | 1.04825 | 0.524125 | − | 0.851642i | \(-0.324393\pi\) | ||||
0.524125 | + | 0.851642i | \(0.324393\pi\) | |||||||
\(242\) | −5189.25 | −1.37842 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −536.498 | −0.140761 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88.7873 | 0.0228721 | ||||||||
\(248\) | 2566.73 | 0.657209 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −228.553 | −0.0578199 | ||||||||
\(251\) | −5219.10 | −1.31246 | −0.656228 | − | 0.754562i | \(-0.727849\pi\) | ||||
−0.656228 | + | 0.754562i | \(0.727849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5692.78 | −1.41463 | ||||||||
\(254\) | 5011.53 | 1.23800 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4258.88 | −1.03976 | ||||||||
\(257\) | 6975.71 | 1.69312 | 0.846562 | − | 0.532289i | \(-0.178668\pi\) | ||||
0.846562 | + | 0.532289i | \(0.178668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −753.087 | −0.179632 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3349.75 | 0.789878 | ||||||||
\(263\) | 3607.36 | 0.845776 | 0.422888 | − | 0.906182i | \(-0.361016\pi\) | ||||
0.422888 | + | 0.906182i | \(0.361016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1304.90 | −0.302489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4430.90 | 1.00993 | ||||||||
\(269\) | 5.88572 | 0.00133405 | 0.000667023 | − | 1.00000i | \(-0.499788\pi\) | ||||
0.000667023 | 1.00000i | \(0.499788\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6916.32 | −1.55032 | −0.775160 | − | 0.631765i | \(-0.782331\pi\) | ||||
−0.775160 | + | 0.631765i | \(0.782331\pi\) | |||||||
\(272\) | 285.033 | 0.0635392 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 699.825 | 0.154299 | ||||||||
\(275\) | 1614.21 | 0.353966 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2119.46 | −0.459733 | −0.229867 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229867 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(278\) | 5583.29 | 1.20455 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 239.917 | 0.0509334 | 0.0254667 | − | 0.999676i | \(-0.491893\pi\) | ||||
0.0254667 | + | 0.999676i | \(0.491893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4542.12 | 0.954067 | 0.477034 | − | 0.878885i | \(-0.341712\pi\) | ||||
0.477034 | + | 0.878885i | \(0.341712\pi\) | |||||||
\(284\) | 1659.07 | 0.346647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3818.40 | −0.789463 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1738.45 | −0.353847 | ||||||||
\(290\) | 2255.69 | 0.456753 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3058.41 | −0.612944 | ||||||||
\(293\) | −2171.70 | −0.433010 | −0.216505 | − | 0.976281i | \(-0.569466\pi\) | ||||
−0.216505 | + | 0.976281i | \(0.569466\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3145.00 | 0.620708 | ||||||||
\(296\) | 2792.70 | 0.548387 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6510.29 | 1.26554 | ||||||||
\(299\) | −2851.58 | −0.551543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5963.96 | −1.13638 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.8875 | −0.00262007 | ||||||||
\(305\) | 576.030 | 0.108142 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3508.64 | 0.652276 | 0.326138 | − | 0.945322i | \(-0.394253\pi\) | ||||
0.326138 | + | 0.945322i | \(0.394253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1013.97 | −0.185773 | ||||||||
\(311\) | −3133.25 | −0.571287 | −0.285643 | − | 0.958336i | \(-0.592207\pi\) | ||||
−0.285643 | + | 0.958336i | \(0.592207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6389.59 | −1.15387 | −0.576935 | − | 0.816790i | \(-0.695751\pi\) | ||||
−0.576935 | + | 0.816790i | \(0.695751\pi\) | |||||||
\(314\) | 5263.05 | 0.945895 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2049.92 | −0.364928 | ||||||||
\(317\) | −1634.44 | −0.289587 | −0.144794 | − | 0.989462i | \(-0.546252\pi\) | ||||
−0.144794 | + | 0.989462i | \(0.546252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15931.3 | −2.79618 | ||||||||
\(320\) | 1810.34 | 0.316253 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −154.671 | −0.0266444 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 808.579 | 0.138006 | ||||||||
\(326\) | 1695.93 | 0.288126 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4079.36 | −0.686723 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4386.17 | 0.728355 | 0.364177 | − | 0.931330i | \(-0.381350\pi\) | ||||
0.364177 | + | 0.931330i | \(0.381350\pi\) | |||||||
\(332\) | 253.389 | 0.0418872 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2001.25 | −0.327854 | ||||||||
\(335\) | −4757.40 | −0.775894 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1713.98 | 0.277051 | 0.138526 | − | 0.990359i | \(-0.455764\pi\) | ||||
0.138526 | + | 0.990359i | \(0.455764\pi\) | |||||||
\(338\) | 2104.38 | 0.338648 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1311.91 | 0.209260 | ||||||||
\(341\) | 7161.41 | 1.13728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10260.4 | −1.60814 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3132.56 | 0.486727 | ||||||||
\(347\) | 1744.83 | 0.269935 | 0.134967 | − | 0.990850i | \(-0.456907\pi\) | ||||
0.134967 | + | 0.990850i | \(0.456907\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7046.78 | −1.08082 | −0.540409 | − | 0.841403i | \(-0.681730\pi\) | ||||
−0.540409 | + | 0.841403i | \(0.681730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11356.8 | −1.71966 | ||||||||
\(353\) | −12668.5 | −1.91013 | −0.955064 | − | 0.296400i | \(-0.904214\pi\) | ||||
−0.955064 | + | 0.296400i | \(0.904214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1781.32 | −0.266317 | ||||||||
\(356\) | 4744.33 | 0.706317 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7433.62 | −1.09743 | ||||||||
\(359\) | −37.7844 | −0.00555483 | −0.00277742 | − | 0.999996i | \(-0.500884\pi\) | ||||
−0.00277742 | + | 0.999996i | \(0.500884\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6851.46 | −0.998901 | ||||||||
\(362\) | −5103.87 | −0.741031 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3283.77 | 0.470905 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 759.829 | 0.108073 | 0.0540364 | − | 0.998539i | \(-0.482791\pi\) | ||||
0.0540364 | + | 0.998539i | \(0.482791\pi\) | |||||||
\(368\) | 446.023 | 0.0631809 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1103.24 | −0.155012 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 719.320 | 0.0998525 | 0.0499263 | − | 0.998753i | \(-0.484101\pi\) | ||||
0.0499263 | + | 0.998753i | \(0.484101\pi\) | |||||||
\(374\) | 6651.81 | 0.919671 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7988.81 | −1.09572 | ||||||||
\(377\) | −7980.19 | −1.09019 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 572.559 | 0.0775999 | 0.0388000 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388000 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(380\) | −63.9192 | −0.00862891 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1159.56 | −0.155310 | ||||||||
\(383\) | 4513.18 | 0.602122 | 0.301061 | − | 0.953605i | \(-0.402659\pi\) | ||||
0.301061 | + | 0.953605i | \(0.402659\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 466.247 | 0.0614802 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3372.06 | −0.441213 | ||||||||
\(389\) | 6902.13 | 0.899619 | 0.449810 | − | 0.893124i | \(-0.351492\pi\) | ||||
0.449810 | + | 0.893124i | \(0.351492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4967.58 | 0.642510 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7628.88 | 0.975475 | ||||||||
\(395\) | 2200.98 | 0.280362 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4124.58 | −0.521427 | −0.260714 | − | 0.965416i | \(-0.583958\pi\) | ||||
−0.260714 | + | 0.965416i | \(0.583958\pi\) | |||||||
\(398\) | −8459.18 | −1.06538 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −126.472 | −0.0158090 | ||||||||
\(401\) | 1002.50 | 0.124844 | 0.0624219 | − | 0.998050i | \(-0.480118\pi\) | ||||
0.0624219 | + | 0.998050i | \(0.480118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3587.23 | 0.443406 | ||||||||
\(404\) | −1251.41 | −0.154109 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7791.89 | 0.948967 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10335.0 | −1.24947 | −0.624736 | − | 0.780836i | \(-0.714794\pi\) | ||||
−0.624736 | + | 0.780836i | \(0.714794\pi\) | |||||||
\(410\) | 1611.52 | 0.194116 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8571.53 | −1.02497 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −272.061 | −0.0321806 | ||||||||
\(416\) | −5688.75 | −0.670466 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −324.091 | −0.0379230 | ||||||||
\(419\) | 3183.21 | 0.371145 | 0.185573 | − | 0.982631i | \(-0.440586\pi\) | ||||
0.185573 | + | 0.982631i | \(0.440586\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6944.34 | −0.803911 | −0.401956 | − | 0.915659i | \(-0.631669\pi\) | ||||
−0.401956 | + | 0.915659i | \(0.631669\pi\) | |||||||
\(422\) | 2857.18 | 0.329586 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6039.65 | −0.691772 | ||||||||
\(425\) | −1408.58 | −0.160767 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1132.02 | −0.127846 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4053.28 | 0.454573 | ||||||||
\(431\) | −3868.41 | −0.432331 | −0.216166 | − | 0.976357i | \(-0.569355\pi\) | ||||
−0.216166 | + | 0.976357i | \(0.569355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6132.96 | 0.680673 | 0.340336 | − | 0.940304i | \(-0.389459\pi\) | ||||
0.340336 | + | 0.940304i | \(0.389459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1886.84 | 0.207256 | ||||||||
\(437\) | −242.032 | −0.0264942 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4090.14 | 0.444673 | 0.222337 | − | 0.974970i | \(-0.428632\pi\) | ||||
0.222337 | + | 0.974970i | \(0.428632\pi\) | |||||||
\(440\) | 7471.27 | 0.809497 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3331.97 | 0.358565 | ||||||||
\(443\) | −12434.5 | −1.33359 | −0.666795 | − | 0.745241i | \(-0.732334\pi\) | ||||
−0.666795 | + | 0.745241i | \(0.732334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5093.92 | −0.542640 | ||||||||
\(446\) | −2260.66 | −0.240012 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −883.046 | −0.0928141 | −0.0464071 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464071 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11381.8 | −1.18835 | ||||||||
\(452\) | −131.214 | −0.0136544 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7646.15 | −0.790422 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9068.44 | −0.928235 | −0.464118 | − | 0.885774i | \(-0.653629\pi\) | ||||
−0.464118 | + | 0.885774i | \(0.653629\pi\) | |||||||
\(458\) | −886.373 | −0.0904312 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2052.89 | 0.208080 | ||||||||
\(461\) | 12508.9 | 1.26377 | 0.631885 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631885 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12688.7 | 1.27363 | 0.636817 | − | 0.771015i | \(-0.280251\pi\) | ||||
0.636817 | + | 0.771015i | \(0.280251\pi\) | |||||||
\(464\) | 1248.20 | 0.124884 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3804.12 | 0.378160 | ||||||||
\(467\) | −10136.5 | −1.00442 | −0.502208 | − | 0.864747i | \(-0.667479\pi\) | ||||
−0.502208 | + | 0.864747i | \(0.667479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3155.92 | 0.309727 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14556.4 | 1.41952 | ||||||||
\(473\) | −28627.3 | −2.78284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 68.6292 | 0.00662931 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12459.1 | 1.19219 | ||||||||
\(479\) | −11361.1 | −1.08372 | −0.541861 | − | 0.840468i | \(-0.682280\pi\) | ||||
−0.541861 | + | 0.840468i | \(0.682280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3903.05 | 0.369987 | ||||||||
\(482\) | −7170.80 | −0.677637 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13216.6 | −1.24123 | ||||||||
\(485\) | 3620.54 | 0.338969 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7929.53 | 0.737826 | 0.368913 | − | 0.929464i | \(-0.379730\pi\) | ||||
0.368913 | + | 0.929464i | \(0.379730\pi\) | |||||||
\(488\) | 2666.11 | 0.247314 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8111.51 | −0.745555 | −0.372777 | − | 0.927921i | \(-0.621595\pi\) | ||||
−0.372777 | + | 0.927921i | \(0.621595\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13901.8 | 1.26999 | ||||||||
\(494\) | −162.341 | −0.0147856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −561.088 | −0.0507936 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16816.6 | 1.50865 | 0.754324 | − | 0.656502i | \(-0.227965\pi\) | ||||
0.754324 | + | 0.656502i | \(0.227965\pi\) | |||||||
\(500\) | −582.107 | −0.0520652 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9542.74 | 0.848433 | ||||||||
\(503\) | −17764.6 | −1.57472 | −0.787362 | − | 0.616491i | \(-0.788554\pi\) | ||||
−0.787362 | + | 0.616491i | \(0.788554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1343.62 | 0.118397 | ||||||||
\(506\) | 10408.8 | 0.914485 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12764.0 | 1.11478 | ||||||||
\(509\) | 13908.8 | 1.21120 | 0.605598 | − | 0.795771i | \(-0.292934\pi\) | ||||
0.605598 | + | 0.795771i | \(0.292934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1826.38 | 0.157647 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12754.6 | −1.09451 | ||||||||
\(515\) | 9203.13 | 0.787453 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22289.5 | −1.89611 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3742.45 | 0.315610 | ||||||||
\(521\) | −8639.68 | −0.726510 | −0.363255 | − | 0.931690i | \(-0.618335\pi\) | ||||
−0.363255 | + | 0.931690i | \(0.618335\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23242.2 | −1.94323 | −0.971617 | − | 0.236561i | \(-0.923980\pi\) | ||||
−0.971617 | + | 0.236561i | \(0.923980\pi\) | |||||||
\(524\) | 8531.53 | 0.711263 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6595.79 | −0.546749 | ||||||||
\(527\) | −6249.11 | −0.516538 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4393.66 | −0.361113 | ||||||||
\(530\) | 2385.92 | 0.195543 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5701.26 | −0.463319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1215.43 | 0.0982201 | ||||||||
\(536\) | −22019.3 | −1.77442 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.7616 | −0.000862390 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11395.2 | 0.905577 | 0.452789 | − | 0.891618i | \(-0.350429\pi\) | ||||
0.452789 | + | 0.891618i | \(0.350429\pi\) | |||||||
\(542\) | 12646.0 | 1.00220 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9910.04 | 0.781047 | ||||||||
\(545\) | −2025.88 | −0.159228 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7870.21 | −0.615184 | −0.307592 | − | 0.951518i | \(-0.599523\pi\) | ||||
−0.307592 | + | 0.951518i | \(0.599523\pi\) | |||||||
\(548\) | 1782.40 | 0.138942 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2951.47 | −0.228820 | ||||||||
\(551\) | −677.329 | −0.0523687 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3875.28 | 0.297193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14220.2 | 1.08466 | ||||||||
\(557\) | −17769.8 | −1.35176 | −0.675880 | − | 0.737012i | \(-0.736236\pi\) | ||||
−0.675880 | + | 0.737012i | \(0.736236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14339.7 | −1.08498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −438.672 | −0.0329257 | ||||||||
\(563\) | 15192.8 | 1.13730 | 0.568651 | − | 0.822579i | \(-0.307466\pi\) | ||||
0.568651 | + | 0.822579i | \(0.307466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 140.883 | 0.0104903 | ||||||||
\(566\) | −8304.93 | −0.616753 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8244.71 | −0.609050 | ||||||||
\(569\) | 23300.0 | 1.71667 | 0.858335 | − | 0.513090i | \(-0.171499\pi\) | ||||
0.858335 | + | 0.513090i | \(0.171499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10638.2 | 0.779673 | 0.389837 | − | 0.920884i | \(-0.372531\pi\) | ||||
0.389837 | + | 0.920884i | \(0.372531\pi\) | |||||||
\(572\) | −9725.14 | −0.710889 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2204.16 | −0.159861 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 897.258 | 0.0647372 | 0.0323686 | − | 0.999476i | \(-0.489695\pi\) | ||||
0.0323686 | + | 0.999476i | \(0.489695\pi\) | |||||||
\(578\) | 3178.63 | 0.228743 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5745.05 | 0.411293 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16851.1 | −1.19709 | ||||||||
\(584\) | 15198.7 | 1.07693 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3970.79 | 0.279918 | ||||||||
\(587\) | −14712.9 | −1.03452 | −0.517261 | − | 0.855828i | \(-0.673048\pi\) | ||||
−0.517261 | + | 0.855828i | \(0.673048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 304.471 | 0.0212997 | ||||||||
\(590\) | −5750.40 | −0.401254 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −610.486 | −0.0423831 | ||||||||
\(593\) | −7216.29 | −0.499726 | −0.249863 | − | 0.968281i | \(-0.580386\pi\) | ||||
−0.249863 | + | 0.968281i | \(0.580386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16581.2 | 1.13958 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5213.91 | 0.356543 | ||||||||
\(599\) | 20885.5 | 1.42464 | 0.712320 | − | 0.701855i | \(-0.247645\pi\) | ||||
0.712320 | + | 0.701855i | \(0.247645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11047.7 | 0.749823 | 0.374911 | − | 0.927061i | \(-0.377673\pi\) | ||||
0.374911 | + | 0.927061i | \(0.377673\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15189.7 | −1.02328 | ||||||||
\(605\) | 14190.5 | 0.953595 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9434.94 | 0.630894 | 0.315447 | − | 0.948943i | \(-0.397846\pi\) | ||||
0.315447 | + | 0.948943i | \(0.397846\pi\) | |||||||
\(608\) | −482.840 | −0.0322068 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1053.23 | −0.0699082 | ||||||||
\(611\) | −11165.0 | −0.739263 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17662.6 | −1.16376 | −0.581881 | − | 0.813274i | \(-0.697683\pi\) | ||||
−0.581881 | + | 0.813274i | \(0.697683\pi\) | |||||||
\(614\) | −6415.30 | −0.421662 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10817.4 | 0.705820 | 0.352910 | − | 0.935657i | \(-0.385192\pi\) | ||||
0.352910 | + | 0.935657i | \(0.385192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29073.9 | −1.88785 | −0.943926 | − | 0.330158i | \(-0.892898\pi\) | ||||
−0.943926 | + | 0.330158i | \(0.892898\pi\) | |||||||
\(620\) | −2582.50 | −0.167283 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5728.92 | 0.369306 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 11682.9 | 0.745915 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13404.5 | 0.851751 | ||||||||
\(629\) | −6799.28 | −0.431009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2203.17 | −0.138996 | −0.0694981 | − | 0.997582i | \(-0.522140\pi\) | ||||
−0.0694981 | + | 0.997582i | \(0.522140\pi\) | |||||||
\(632\) | 10187.1 | 0.641170 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2988.45 | 0.187203 | ||||||||
\(635\) | −13704.5 | −0.856451 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29129.3 | 1.80758 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3725.42 | 0.230094 | ||||||||
\(641\) | −22466.5 | −1.38436 | −0.692180 | − | 0.721725i | \(-0.743349\pi\) | ||||
−0.692180 | + | 0.721725i | \(0.743349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12347.0 | 0.757257 | 0.378629 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378629 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 282.805 | 0.0172242 | ||||||||
\(647\) | −24114.0 | −1.46525 | −0.732626 | − | 0.680631i | \(-0.761706\pi\) | ||||
−0.732626 | + | 0.680631i | \(0.761706\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40613.6 | 2.45643 | ||||||||
\(650\) | −1478.43 | −0.0892134 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4319.41 | 0.259449 | ||||||||
\(653\) | −7843.33 | −0.470035 | −0.235018 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235018 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9160.18 | −0.546440 | ||||||||
\(656\) | 891.749 | 0.0530746 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21242.8 | −1.25569 | −0.627846 | − | 0.778338i | \(-0.716063\pi\) | ||||
−0.627846 | + | 0.778338i | \(0.716063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22221.7 | 1.30760 | 0.653801 | − | 0.756667i | \(-0.273173\pi\) | ||||
0.653801 | + | 0.756667i | \(0.273173\pi\) | |||||||
\(662\) | −8019.79 | −0.470843 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1259.21 | −0.0735948 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21753.8 | 1.26283 | ||||||||
\(668\) | −5097.01 | −0.295223 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8698.56 | 0.501574 | ||||||||
\(671\) | 7438.69 | 0.427969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3787.85 | −0.216955 | −0.108478 | − | 0.994099i | \(-0.534598\pi\) | ||||
−0.108478 | + | 0.994099i | \(0.534598\pi\) | |||||||
\(674\) | −3133.88 | −0.179099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5359.67 | 0.304943 | ||||||||
\(677\) | −11296.8 | −0.641314 | −0.320657 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320657 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6519.50 | −0.367664 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13094.1 | −0.735190 | ||||||||
\(683\) | −4807.14 | −0.269312 | −0.134656 | − | 0.990892i | \(-0.542993\pi\) | ||||
−0.134656 | + | 0.990892i | \(0.542993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1913.73 | −0.106745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2242.92 | 0.124288 | ||||||||
\(689\) | −8440.94 | −0.466726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5393.47 | −0.296928 | −0.148464 | − | 0.988918i | \(-0.547433\pi\) | ||||
−0.148464 | + | 0.988918i | \(0.547433\pi\) | |||||||
\(692\) | 7978.37 | 0.438283 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3190.29 | −0.174498 | ||||||||
\(695\) | −15268.0 | −0.833308 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9931.84 | 0.539735 | ||||||||
\(698\) | 12884.5 | 0.698691 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2404.77 | −0.129568 | −0.0647838 | − | 0.997899i | \(-0.520636\pi\) | ||||
−0.0647838 | + | 0.997899i | \(0.520636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 331.276 | 0.0177729 | ||||||||
\(704\) | 23378.2 | 1.25156 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23163.4 | 1.23480 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21617.3 | −1.14507 | −0.572535 | − | 0.819881i | \(-0.694040\pi\) | ||||
−0.572535 | + | 0.819881i | \(0.694040\pi\) | |||||||
\(710\) | 3257.01 | 0.172160 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23576.8 | −1.24098 | ||||||||
\(713\) | −9778.70 | −0.513626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10441.7 | 0.546153 | ||||||||
\(716\) | −18932.8 | −0.988203 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 69.0860 | 0.00359090 | ||||||||
\(719\) | −18228.6 | −0.945498 | −0.472749 | − | 0.881197i | \(-0.656738\pi\) | ||||
−0.472749 | + | 0.881197i | \(0.656738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12527.4 | 0.645736 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12999.1 | −0.667278 | ||||||||
\(725\) | −6168.38 | −0.315983 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20196.5 | −1.03033 | −0.515164 | − | 0.857092i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857092i | \(0.672269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6004.13 | −0.304415 | ||||||||
\(731\) | 24980.4 | 1.26393 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15264.9 | 0.769196 | 0.384598 | − | 0.923084i | \(-0.374340\pi\) | ||||
0.384598 | + | 0.923084i | \(0.374340\pi\) | |||||||
\(734\) | −1389.29 | −0.0698633 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15507.4 | 0.776643 | ||||||||
\(737\) | −61435.7 | −3.07057 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13906.0 | 0.692207 | 0.346103 | − | 0.938196i | \(-0.387505\pi\) | ||||
0.346103 | + | 0.938196i | \(0.387505\pi\) | |||||||
\(740\) | −2809.86 | −0.139584 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4592.87 | −0.226778 | −0.113389 | − | 0.993551i | \(-0.536171\pi\) | ||||
−0.113389 | + | 0.993551i | \(0.536171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17803.0 | −0.875504 | ||||||||
\(746\) | −1315.22 | −0.0645493 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16941.6 | 0.828137 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8390.80 | −0.407702 | −0.203851 | − | 0.979002i | \(-0.565346\pi\) | ||||
−0.203851 | + | 0.979002i | \(0.565346\pi\) | |||||||
\(752\) | 1746.35 | 0.0846848 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14591.2 | 0.704748 | ||||||||
\(755\) | 16309.0 | 0.786153 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1368.89 | −0.0657240 | −0.0328620 | − | 0.999460i | \(-0.510462\pi\) | ||||
−0.0328620 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(758\) | −1046.88 | −0.0501642 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 317.645 | 0.0151608 | ||||||||
\(761\) | −1623.77 | −0.0773478 | −0.0386739 | − | 0.999252i | \(-0.512313\pi\) | ||||
−0.0386739 | + | 0.999252i | \(0.512313\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2953.31 | −0.139852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8252.03 | −0.389240 | ||||||||
\(767\) | 20343.8 | 0.957722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26842.5 | 1.25873 | 0.629366 | − | 0.777109i | \(-0.283315\pi\) | ||||
0.629366 | + | 0.777109i | \(0.283315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1187.49 | 0.0553612 | ||||||||
\(773\) | −20961.4 | −0.975330 | −0.487665 | − | 0.873031i | \(-0.662151\pi\) | ||||
−0.487665 | + | 0.873031i | \(0.662151\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2772.79 | 0.128518 | ||||||||
\(776\) | 16757.4 | 0.775200 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12620.0 | −0.581556 | ||||||||
\(779\) | −483.902 | −0.0222562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23003.5 | −1.05394 | ||||||||
\(782\) | −9082.86 | −0.415348 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14392.3 | −0.654373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35333.2 | −1.60037 | −0.800187 | − | 0.599751i | \(-0.795266\pi\) | ||||
−0.800187 | + | 0.599751i | \(0.795266\pi\) | |||||||
\(788\) | 19430.1 | 0.878388 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4024.32 | −0.181239 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3726.13 | 0.166858 | ||||||||
\(794\) | 7541.49 | 0.337075 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21544.8 | −0.959342 | ||||||||
\(797\) | −8137.04 | −0.361642 | −0.180821 | − | 0.983516i | \(-0.557875\pi\) | ||||
−0.180821 | + | 0.983516i | \(0.557875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19450.0 | 0.861191 | ||||||||
\(800\) | −4397.18 | −0.194330 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1832.99 | −0.0807049 | ||||||||
\(803\) | 42405.6 | 1.86359 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6558.99 | −0.286639 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6218.87 | 0.270766 | ||||||||
\(809\) | 36281.0 | 1.57673 | 0.788364 | − | 0.615209i | \(-0.210928\pi\) | ||||
0.788364 | + | 0.615209i | \(0.210928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34237.2 | 1.48240 | 0.741202 | − | 0.671282i | \(-0.234256\pi\) | ||||
0.741202 | + | 0.671282i | \(0.234256\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14246.9 | −0.613456 | ||||||||
\(815\) | −4637.69 | −0.199326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1217.10 | −0.0521188 | ||||||||
\(818\) | 18896.8 | 0.807717 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4104.42 | 0.174796 | ||||||||
\(821\) | 23247.8 | 0.988250 | 0.494125 | − | 0.869391i | \(-0.335489\pi\) | ||||
0.494125 | + | 0.869391i | \(0.335489\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42934.0 | 1.81845 | 0.909225 | − | 0.416306i | \(-0.136675\pi\) | ||||
0.909225 | + | 0.416306i | \(0.136675\pi\) | |||||||
\(824\) | 42596.0 | 1.80085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 781.391 | 0.0328557 | 0.0164278 | − | 0.999865i | \(-0.494771\pi\) | ||||
0.0164278 | + | 0.999865i | \(0.494771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33493.3 | 1.40322 | 0.701611 | − | 0.712561i | \(-0.252465\pi\) | ||||
0.701611 | + | 0.712561i | \(0.252465\pi\) | |||||||
\(830\) | 497.443 | 0.0208030 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11710.4 | 0.487964 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5472.59 | 0.226811 | ||||||||
\(836\) | −825.434 | −0.0341486 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5820.27 | −0.239926 | ||||||||
\(839\) | 15155.7 | 0.623639 | 0.311819 | − | 0.950141i | \(-0.399062\pi\) | ||||
0.311819 | + | 0.950141i | \(0.399062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36489.2 | 1.49613 | ||||||||
\(842\) | 12697.2 | 0.519686 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7277.01 | 0.296783 | ||||||||
\(845\) | −5754.60 | −0.234277 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1320.27 | 0.0534649 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2575.48 | 0.103927 | ||||||||
\(851\) | −10639.6 | −0.428579 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2917.48 | 0.117107 | 0.0585537 | − | 0.998284i | \(-0.481351\pi\) | ||||
0.0585537 | + | 0.998284i | \(0.481351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5625.54 | 0.224623 | ||||||||
\(857\) | −31560.7 | −1.25799 | −0.628993 | − | 0.777411i | \(-0.716532\pi\) | ||||
−0.628993 | + | 0.777411i | \(0.716532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1404.81 | 0.0557991 | 0.0278995 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0278995 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(860\) | 10323.4 | 0.409330 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7073.11 | 0.279479 | ||||||||
\(863\) | 9808.24 | 0.386879 | 0.193439 | − | 0.981112i | \(-0.438036\pi\) | ||||
0.193439 | + | 0.981112i | \(0.438036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8566.27 | −0.336719 | ||||||||
\(866\) | −11213.7 | −0.440018 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28422.8 | 1.10952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30773.9 | −1.19717 | ||||||||
\(872\) | −9376.63 | −0.364143 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 442.537 | 0.0171271 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7196.05 | −0.277073 | −0.138537 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138537 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(878\) | −7478.52 | −0.287458 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1633.22 | −0.0625635 | ||||||||
\(881\) | −3183.27 | −0.121733 | −0.0608667 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608667 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25392.5 | 0.967751 | 0.483876 | − | 0.875137i | \(-0.339229\pi\) | ||||
0.483876 | + | 0.875137i | \(0.339229\pi\) | |||||||
\(884\) | 8486.25 | 0.322877 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22735.6 | 0.862095 | ||||||||
\(887\) | −30634.2 | −1.15964 | −0.579818 | − | 0.814746i | \(-0.696876\pi\) | ||||
−0.579818 | + | 0.814746i | \(0.696876\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9313.86 | 0.350788 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5757.71 | −0.216124 | ||||||||
\(893\) | −947.648 | −0.0355116 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20327.9 | 0.759204 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1614.59 | 0.0599994 | ||||||||
\(899\) | −27365.8 | −1.01524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14704.5 | 0.543704 | ||||||||
\(902\) | 20810.7 | 0.768206 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 652.067 | 0.0239905 | ||||||||
\(905\) | 13957.0 | 0.512648 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28089.9 | −1.02834 | −0.514172 | − | 0.857687i | \(-0.671901\pi\) | ||||
−0.514172 | + | 0.857687i | \(0.671901\pi\) | |||||||
\(908\) | −19474.1 | −0.711753 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36102.7 | 1.31299 | 0.656495 | − | 0.754330i | \(-0.272038\pi\) | ||||
0.656495 | + | 0.754330i | \(0.272038\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3513.31 | −0.127353 | ||||||||
\(914\) | 16581.0 | 0.600055 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2257.52 | −0.0814308 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14533.8 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(920\) | −10201.8 | −0.365591 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22871.6 | −0.816959 | ||||||||
\(923\) | −11522.7 | −0.410915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3016.90 | 0.107238 | ||||||||
\(926\) | −23200.3 | −0.823336 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 43397.6 | 1.53512 | ||||||||
\(929\) | 16539.6 | 0.584118 | 0.292059 | − | 0.956400i | \(-0.405660\pi\) | ||||
0.292059 | + | 0.956400i | \(0.405660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9688.79 | 0.340522 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18533.9 | 0.649301 | ||||||||
\(935\) | −18190.0 | −0.636231 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30212.3 | −1.05335 | −0.526677 | − | 0.850065i | \(-0.676562\pi\) | ||||
−0.526677 | + | 0.850065i | \(0.676562\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8037.87 | 0.278900 | ||||||||
\(941\) | −26414.4 | −0.915074 | −0.457537 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457537 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15541.5 | 0.536692 | ||||||||
\(944\) | −3182.03 | −0.109710 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52342.9 | 1.79896 | ||||||||
\(947\) | −10187.3 | −0.349570 | −0.174785 | − | 0.984607i | \(-0.555923\pi\) | ||||
−0.174785 | + | 0.984607i | \(0.555923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21241.5 | 0.726583 | ||||||||
\(950\) | −125.483 | −0.00428549 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2211.39 | −0.0751669 | −0.0375834 | − | 0.999293i | \(-0.511966\pi\) | ||||
−0.0375834 | + | 0.999293i | \(0.511966\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3170.92 | 0.107444 | ||||||||
\(956\) | 31732.3 | 1.07353 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20773.0 | 0.700569 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17489.6 | −0.587077 | ||||||||
\(962\) | −7136.44 | −0.239177 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18263.4 | −0.610193 | ||||||||
\(965\) | −1275.00 | −0.0425322 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7955.89 | 0.264575 | 0.132287 | − | 0.991211i | \(-0.457768\pi\) | ||||
0.132287 | + | 0.991211i | \(0.457768\pi\) | |||||||
\(968\) | 65679.6 | 2.18081 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6619.89 | −0.219126 | ||||||||
\(971\) | 53071.2 | 1.75400 | 0.877001 | − | 0.480488i | \(-0.159541\pi\) | ||||
0.877001 | + | 0.480488i | \(0.159541\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14498.6 | −0.476965 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −582.813 | −0.0191141 | ||||||||
\(977\) | 22448.2 | 0.735089 | 0.367545 | − | 0.930006i | \(-0.380199\pi\) | ||||
0.367545 | + | 0.930006i | \(0.380199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −65781.4 | −2.14748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14831.3 | 0.481961 | ||||||||
\(983\) | 21712.8 | 0.704509 | 0.352254 | − | 0.935904i | \(-0.385415\pi\) | ||||
0.352254 | + | 0.935904i | \(0.385415\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20861.9 | −0.674837 | ||||||||
\(986\) | −25418.5 | −0.820983 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −413.470 | −0.0133140 | ||||||||
\(989\) | 39089.7 | 1.25681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37849.2 | −1.21324 | −0.606620 | − | 0.794992i | \(-0.707475\pi\) | ||||
−0.606620 | + | 0.794992i | \(0.707475\pi\) | |||||||
\(992\) | −19508.0 | −0.624373 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23132.4 | 0.737031 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39573.1 | 1.25707 | 0.628533 | − | 0.777783i | \(-0.283656\pi\) | ||||
0.628533 | + | 0.777783i | \(0.283656\pi\) | |||||||
\(998\) | −30748.0 | −0.975261 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2205.4.a.bb.1.1 | 2 | ||
3.2 | odd | 2 | 735.4.a.o.1.2 | 2 | |||
7.6 | odd | 2 | 315.4.a.k.1.1 | 2 | |||
21.20 | even | 2 | 105.4.a.e.1.2 | ✓ | 2 | ||
35.34 | odd | 2 | 1575.4.a.q.1.2 | 2 | |||
84.83 | odd | 2 | 1680.4.a.bo.1.2 | 2 | |||
105.62 | odd | 4 | 525.4.d.l.274.3 | 4 | |||
105.83 | odd | 4 | 525.4.d.l.274.2 | 4 | |||
105.104 | even | 2 | 525.4.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.2 | ✓ | 2 | 21.20 | even | 2 | ||
315.4.a.k.1.1 | 2 | 7.6 | odd | 2 | |||
525.4.a.l.1.1 | 2 | 105.104 | even | 2 | |||
525.4.d.l.274.2 | 4 | 105.83 | odd | 4 | |||
525.4.d.l.274.3 | 4 | 105.62 | odd | 4 | |||
735.4.a.o.1.2 | 2 | 3.2 | odd | 2 | |||
1575.4.a.q.1.2 | 2 | 35.34 | odd | 2 | |||
1680.4.a.bo.1.2 | 2 | 84.83 | odd | 2 | |||
2205.4.a.bb.1.1 | 2 | 1.1 | even | 1 | trivial |