Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 525.1 |
$q$-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 | \(0.604766\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −4.65685 | −0.582107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.48528 | −0.373226 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 23.1421 | 1.02275 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −64.5685 | −1.76983 | −0.884916 | − | 0.465751i | \(-0.845784\pi\) | ||||
−0.884916 | + | 0.465751i | \(0.845784\pi\) | |||||||
\(12\) | −13.9706 | −0.336080 | ||||||||
\(13\) | 32.3431 | 0.690029 | 0.345014 | − | 0.938597i | \(-0.387874\pi\) | ||||
0.345014 | + | 0.938597i | \(0.387874\pi\) | |||||||
\(14\) | −12.7990 | −0.244334 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.05887 | −0.0790449 | ||||||||
\(17\) | 56.3431 | 0.803836 | 0.401918 | − | 0.915676i | \(-0.368344\pi\) | ||||
0.401918 | + | 0.915676i | \(0.368344\pi\) | |||||||
\(18\) | −16.4558 | −0.215482 | ||||||||
\(19\) | −2.74517 | −0.0331465 | −0.0165733 | − | 0.999863i | \(-0.505276\pi\) | ||||
−0.0165733 | + | 0.999863i | \(0.505276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 118.059 | 1.14410 | ||||||||
\(23\) | −88.1665 | −0.799304 | −0.399652 | − | 0.916667i | \(-0.630869\pi\) | ||||
−0.399652 | + | 0.916667i | \(0.630869\pi\) | |||||||
\(24\) | 69.4264 | 0.590484 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −59.1371 | −0.446067 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −32.5980 | −0.220016 | ||||||||
\(29\) | 246.735 | 1.57992 | 0.789958 | − | 0.613161i | \(-0.210102\pi\) | ||||
0.789958 | + | 0.613161i | \(0.210102\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −110.912 | −0.642591 | −0.321296 | − | 0.946979i | \(-0.604118\pi\) | ||||
−0.321296 | + | 0.946979i | \(0.604118\pi\) | |||||||
\(32\) | −175.887 | −0.971649 | ||||||||
\(33\) | −193.706 | −1.02181 | ||||||||
\(34\) | −103.019 | −0.519637 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −41.9117 | −0.194036 | ||||||||
\(37\) | −120.676 | −0.536190 | −0.268095 | − | 0.963392i | \(-0.586394\pi\) | ||||
−0.268095 | + | 0.963392i | \(0.586394\pi\) | |||||||
\(38\) | 5.01934 | 0.0214275 | ||||||||
\(39\) | 97.0294 | 0.398388 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −176.274 | −0.671449 | −0.335724 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335724 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(42\) | −38.3970 | −0.141066 | ||||||||
\(43\) | 443.362 | 1.57238 | 0.786188 | − | 0.617988i | \(-0.212052\pi\) | ||||
0.786188 | + | 0.617988i | \(0.212052\pi\) | |||||||
\(44\) | 300.686 | 1.03023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 161.206 | 0.516707 | ||||||||
\(47\) | 345.206 | 1.07135 | 0.535675 | − | 0.844424i | \(-0.320057\pi\) | ||||
0.535675 | + | 0.844424i | \(0.320057\pi\) | |||||||
\(48\) | −15.1766 | −0.0456366 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 169.029 | 0.464095 | ||||||||
\(52\) | −150.617 | −0.401670 | ||||||||
\(53\) | −260.981 | −0.676386 | −0.338193 | − | 0.941077i | \(-0.609816\pi\) | ||||
−0.338193 | + | 0.941077i | \(0.609816\pi\) | |||||||
\(54\) | −49.3675 | −0.124409 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 161.995 | 0.386562 | ||||||||
\(57\) | −8.23550 | −0.0191372 | ||||||||
\(58\) | −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 | \(-0.538580\pi\) | ||||
−0.120907 | + | 0.992664i | \(0.538580\pi\) | |||||||
\(62\) | 202.794 | 0.415401 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 362.068 | 0.707164 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 354.177 | 0.660547 | ||||||||
\(67\) | 951.480 | 1.73495 | 0.867476 | − | 0.497479i | \(-0.165741\pi\) | ||||
0.867476 | + | 0.497479i | \(0.165741\pi\) | |||||||
\(68\) | −262.382 | −0.467919 | ||||||||
\(69\) | −264.500 | −0.461478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 356.264 | 0.595504 | 0.297752 | − | 0.954643i | \(-0.403763\pi\) | ||||
0.297752 | + | 0.954643i | \(0.403763\pi\) | |||||||
\(72\) | 208.279 | 0.340916 | ||||||||
\(73\) | 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 | ||||||||
\(77\) | −451.980 | −0.668933 | ||||||||
\(78\) | −177.411 | −0.257537 | ||||||||
\(79\) | 440.195 | 0.626909 | 0.313455 | − | 0.949603i | \(-0.398514\pi\) | ||||
0.313455 | + | 0.949603i | \(0.398514\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 322.304 | 0.434056 | ||||||||
\(83\) | 54.4121 | 0.0719579 | 0.0359790 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359790 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(84\) | −97.7939 | −0.127026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −810.656 | −1.01646 | ||||||||
\(87\) | 740.205 | 0.912165 | ||||||||
\(88\) | −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 | ||||||||
\(91\) | 226.402 | 0.260806 | ||||||||
\(92\) | 410.579 | 0.465280 | ||||||||
\(93\) | −332.735 | −0.371000 | ||||||||
\(94\) | −631.184 | −0.692571 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −527.662 | −0.560982 | ||||||||
\(97\) | 724.108 | 0.757959 | 0.378979 | − | 0.925405i | \(-0.376275\pi\) | ||||
0.378979 | + | 0.925405i | \(0.376275\pi\) | |||||||
\(98\) | −89.5929 | −0.0923495 | ||||||||
\(99\) | −581.117 | −0.589944 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 268.725 | 0.264744 | 0.132372 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132372 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(102\) | −309.058 | −0.300013 | ||||||||
\(103\) | 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 | \(0.464975\pi\) | |||||||
\(108\) | −125.735 | −0.112027 | ||||||||
\(109\) | −405.176 | −0.356044 | −0.178022 | − | 0.984027i | \(-0.556970\pi\) | ||||
−0.178022 | + | 0.984027i | \(0.556970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −362.029 | −0.309570 | ||||||||
\(112\) | −35.4121 | −0.0298762 | ||||||||
\(113\) | 28.1766 | 0.0234569 | 0.0117285 | − | 0.999931i | \(-0.496267\pi\) | ||||
0.0117285 | + | 0.999931i | \(0.496267\pi\) | |||||||
\(114\) | 15.0580 | 0.0123712 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1149.01 | −0.919680 | ||||||||
\(117\) | 291.088 | 0.230010 | ||||||||
\(118\) | −1150.08 | −0.897232 | ||||||||
\(119\) | 394.402 | 0.303822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2838.10 | 2.13230 | ||||||||
\(122\) | 210.646 | 0.156320 | ||||||||
\(123\) | −528.823 | −0.387661 | ||||||||
\(124\) | 516.500 | 0.374057 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −115.191 | −0.0814446 | ||||||||
\(127\) | 2740.90 | 1.91508 | 0.957541 | − | 0.288298i | \(-0.0930892\pi\) | ||||
0.957541 | + | 0.288298i | \(0.0930892\pi\) | |||||||
\(128\) | 745.083 | 0.514505 | ||||||||
\(129\) | 1330.09 | 0.907811 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1832.04 | −1.22188 | −0.610938 | − | 0.791678i | \(-0.709208\pi\) | ||||
−0.610938 | + | 0.791678i | \(0.709208\pi\) | |||||||
\(132\) | 902.059 | 0.594804 | ||||||||
\(133\) | −19.2162 | −0.0125282 | ||||||||
\(134\) | −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 | \(0.538079\pi\) | |||||||
\(138\) | 483.618 | 0.298321 | ||||||||
\(139\) | 3053.60 | 1.86333 | 0.931667 | − | 0.363314i | \(-0.118355\pi\) | ||||
0.931667 | + | 0.363314i | \(0.118355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1035.62 | 0.618545 | ||||||||
\(142\) | −651.403 | −0.384961 | ||||||||
\(143\) | −2088.35 | −1.22123 | ||||||||
\(144\) | −45.5299 | −0.0263483 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1200.83 | −0.680692 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 561.971 | 0.312120 | ||||||||
\(149\) | 3560.60 | 1.95769 | 0.978843 | − | 0.204611i | \(-0.0655929\pi\) | ||||
0.978843 | + | 0.204611i | \(0.0655929\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 507.088 | 0.267945 | ||||||||
\(154\) | 826.412 | 0.432430 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −451.852 | −0.231905 | ||||||||
\(157\) | −2878.46 | −1.46322 | −0.731611 | − | 0.681723i | \(-0.761231\pi\) | ||||
−0.731611 | + | 0.681723i | \(0.761231\pi\) | |||||||
\(158\) | −804.865 | −0.405263 | ||||||||
\(159\) | −782.942 | −0.390512 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −617.166 | −0.302108 | ||||||||
\(162\) | −148.103 | −0.0718274 | ||||||||
\(163\) | 927.537 | 0.445708 | 0.222854 | − | 0.974852i | \(-0.428463\pi\) | ||||
0.222854 | + | 0.974852i | \(0.428463\pi\) | |||||||
\(164\) | 820.883 | 0.390855 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −99.4886 | −0.0465169 | ||||||||
\(167\) | −1094.52 | −0.507164 | −0.253582 | − | 0.967314i | \(-0.581609\pi\) | ||||
−0.253582 | + | 0.967314i | \(0.581609\pi\) | |||||||
\(168\) | 485.985 | 0.223182 | ||||||||
\(169\) | −1150.92 | −0.523860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.7065 | −0.0110488 | ||||||||
\(172\) | −2064.67 | −0.915290 | ||||||||
\(173\) | 1713.25 | 0.752926 | 0.376463 | − | 0.926432i | \(-0.377140\pi\) | ||||
0.376463 | + | 0.926432i | \(0.377140\pi\) | |||||||
\(174\) | −1353.41 | −0.589666 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 326.644 | 0.139896 | ||||||||
\(177\) | 1887.00 | 0.801330 | ||||||||
\(178\) | 1862.77 | 0.784386 | ||||||||
\(179\) | −4065.58 | −1.69763 | −0.848816 | − | 0.528689i | \(-0.822684\pi\) | ||||
−0.848816 | + | 0.528689i | \(0.822684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2791.40 | −1.14631 | −0.573157 | − | 0.819445i | \(-0.694282\pi\) | ||||
−0.573157 | + | 0.819445i | \(0.694282\pi\) | |||||||
\(182\) | −413.960 | −0.168597 | ||||||||
\(183\) | −345.618 | −0.139611 | ||||||||
\(184\) | −2040.36 | −0.817486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 608.382 | 0.239832 | ||||||||
\(187\) | −3637.99 | −1.42266 | ||||||||
\(188\) | −1607.57 | −0.623640 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −634.185 | −0.240251 | −0.120126 | − | 0.992759i | \(-0.538330\pi\) | ||||
−0.120126 | + | 0.992759i | \(0.538330\pi\) | |||||||
\(192\) | 1086.20 | 0.408281 | ||||||||
\(193\) | 254.999 | 0.0951049 | 0.0475524 | − | 0.998869i | \(-0.484858\pi\) | ||||
0.0475524 | + | 0.998869i | \(0.484858\pi\) | |||||||
\(194\) | −1323.98 | −0.489980 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −228.186 | −0.0831581 | ||||||||
\(197\) | −4172.37 | −1.50898 | −0.754490 | − | 0.656311i | \(-0.772116\pi\) | ||||
−0.754490 | + | 0.656311i | \(0.772116\pi\) | |||||||
\(198\) | 1062.53 | 0.381367 | ||||||||
\(199\) | −4626.48 | −1.64805 | −0.824026 | − | 0.566552i | \(-0.808277\pi\) | ||||
−0.824026 | + | 0.566552i | \(0.808277\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2854.44 | 1.00168 | ||||||||
\(202\) | −491.344 | −0.171143 | ||||||||
\(203\) | 1727.15 | 0.597152 | ||||||||
\(204\) | −787.145 | −0.270153 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3365.45 | −1.13826 | ||||||||
\(207\) | −793.499 | −0.266435 | ||||||||
\(208\) | −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 | ||||||||
\(213\) | 1068.79 | 0.343814 | ||||||||
\(214\) | −444.466 | −0.141977 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 624.838 | 0.196828 | ||||||||
\(217\) | −776.382 | −0.242877 | ||||||||
\(218\) | 740.834 | 0.230163 | ||||||||
\(219\) | 1970.26 | 0.607935 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1822.31 | 0.554670 | ||||||||
\(222\) | 661.943 | 0.200120 | ||||||||
\(223\) | 1236.39 | 0.371278 | 0.185639 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185639 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(224\) | −1231.21 | −0.367249 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.5189 | −0.0151637 | ||||||||
\(227\) | −4181.82 | −1.22272 | −0.611359 | − | 0.791353i | \(-0.709377\pi\) | ||||
−0.611359 | + | 0.791353i | \(0.709377\pi\) | |||||||
\(228\) | 38.3515 | 0.0111399 | ||||||||
\(229\) | −484.774 | −0.139890 | −0.0699449 | − | 0.997551i | \(-0.522282\pi\) | ||||
−0.0699449 | + | 0.997551i | \(0.522282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1355.94 | −0.386209 | ||||||||
\(232\) | 5709.98 | 1.61585 | ||||||||
\(233\) | −2080.54 | −0.584982 | −0.292491 | − | 0.956268i | \(-0.594484\pi\) | ||||
−0.292491 | + | 0.956268i | \(0.594484\pi\) | |||||||
\(234\) | −532.234 | −0.148689 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2929.16 | −0.807932 | ||||||||
\(237\) | 1320.59 | 0.361946 | ||||||||
\(238\) | −721.135 | −0.196404 | ||||||||
\(239\) | 6814.10 | 1.84422 | 0.922108 | − | 0.386933i | \(-0.126466\pi\) | ||||
0.922108 | + | 0.386933i | \(0.126466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3921.84 | −1.04825 | −0.524125 | − | 0.851642i | \(-0.675607\pi\) | ||||
−0.524125 | + | 0.851642i | \(0.675607\pi\) | |||||||
\(242\) | −5189.25 | −1.37842 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 536.498 | 0.140761 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 966.913 | 0.250602 | ||||||||
\(247\) | −88.7873 | −0.0228721 | ||||||||
\(248\) | −2566.73 | −0.657209 | ||||||||
\(249\) | 163.236 | 0.0415449 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5219.10 | −1.31246 | −0.656228 | − | 0.754562i | \(-0.727849\pi\) | ||||
−0.656228 | + | 0.754562i | \(0.727849\pi\) | |||||||
\(252\) | −293.382 | −0.0733386 | ||||||||
\(253\) | 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 | \(-0.821332\pi\) | ||||
−0.846562 | + | 0.532289i | \(0.821332\pi\) | |||||||
\(258\) | −2431.97 | −0.586852 | ||||||||
\(259\) | −844.733 | −0.202661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2220.62 | 0.526639 | ||||||||
\(262\) | 3349.75 | 0.789878 | ||||||||
\(263\) | 3607.36 | 0.845776 | 0.422888 | − | 0.906182i | \(-0.361016\pi\) | ||||
0.422888 | + | 0.906182i | \(0.361016\pi\) | |||||||
\(264\) | −4482.76 | −1.04506 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 35.1354 | 0.00809882 | ||||||||
\(267\) | −3056.35 | −0.700546 | ||||||||
\(268\) | −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 | \(-0.217669\pi\) | ||||
0.775160 | + | 0.631765i | \(0.217669\pi\) | |||||||
\(272\) | −285.033 | −0.0635392 | ||||||||
\(273\) | 679.206 | 0.150577 | ||||||||
\(274\) | 699.825 | 0.154299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1231.74 | 0.268630 | ||||||||
\(277\) | 2119.46 | 0.459733 | 0.229867 | − | 0.973222i | \(-0.426171\pi\) | ||||
0.229867 | + | 0.973222i | \(0.426171\pi\) | |||||||
\(278\) | −5583.29 | −1.20455 | ||||||||
\(279\) | −998.205 | −0.214197 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −239.917 | −0.0509334 | −0.0254667 | − | 0.999676i | \(-0.508107\pi\) | ||||
−0.0254667 | + | 0.999676i | \(0.508107\pi\) | |||||||
\(282\) | −1893.55 | −0.399856 | ||||||||
\(283\) | 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 | ||||||||
\(287\) | −1233.92 | −0.253784 | ||||||||
\(288\) | −1582.99 | −0.323883 | ||||||||
\(289\) | −1738.45 | −0.353847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2172.32 | 0.437608 | ||||||||
\(292\) | −3058.41 | −0.612944 | ||||||||
\(293\) | 2171.70 | 0.433010 | 0.216505 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216505 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(294\) | −268.779 | −0.0533180 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2792.70 | −0.548387 | ||||||||
\(297\) | −1743.35 | −0.340604 | ||||||||
\(298\) | −6510.29 | −1.26554 | ||||||||
\(299\) | −2851.58 | −0.551543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3103.54 | 0.594302 | ||||||||
\(302\) | −5963.96 | −1.13638 | ||||||||
\(303\) | 806.175 | 0.152850 | ||||||||
\(304\) | 13.8875 | 0.00262007 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −927.174 | −0.173212 | ||||||||
\(307\) | 3508.64 | 0.652276 | 0.326138 | − | 0.945322i | \(-0.394253\pi\) | ||||
0.326138 | + | 0.945322i | \(0.394253\pi\) | |||||||
\(308\) | 2104.80 | 0.389391 | ||||||||
\(309\) | 5521.88 | 1.01660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3133.25 | −0.571287 | −0.285643 | − | 0.958336i | \(-0.592207\pi\) | ||||
−0.285643 | + | 0.958336i | \(0.592207\pi\) | |||||||
\(312\) | 2245.47 | 0.407451 | ||||||||
\(313\) | −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 | \(0.546252\pi\) | |||||||
\(318\) | 1431.55 | 0.252445 | ||||||||
\(319\) | −15931.3 | −2.79618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 729.260 | 0.126802 | ||||||||
\(322\) | 1128.44 | 0.195297 | ||||||||
\(323\) | −154.671 | −0.0266444 | ||||||||
\(324\) | −377.205 | −0.0646785 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1695.93 | −0.288126 | ||||||||
\(327\) | −1215.53 | −0.205562 | ||||||||
\(328\) | −4079.36 | −0.686723 | ||||||||
\(329\) | 2416.44 | 0.404932 | ||||||||
\(330\) | 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 | ||||||||
\(333\) | −1086.09 | −0.178730 | ||||||||
\(334\) | 2001.25 | 0.327854 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −106.236 | −0.0172490 | ||||||||
\(337\) | −1713.98 | −0.277051 | −0.138526 | − | 0.990359i | \(-0.544236\pi\) | ||||
−0.138526 | + | 0.990359i | \(0.544236\pi\) | |||||||
\(338\) | 2104.38 | 0.338648 | ||||||||
\(339\) | 84.5299 | 0.0135429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7161.41 | 1.13728 | ||||||||
\(342\) | 45.1740 | 0.00714249 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 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 | \(0.456907\pi\) | |||||||
\(348\) | −3447.03 | −0.530977 | ||||||||
\(349\) | 7046.78 | 1.08082 | 0.540409 | − | 0.841403i | \(-0.318270\pi\) | ||||
0.540409 | + | 0.841403i | \(0.318270\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 873.265 | 0.132796 | ||||||||
\(352\) | 11356.8 | 1.71966 | ||||||||
\(353\) | 12668.5 | 1.91013 | 0.955064 | − | 0.296400i | \(-0.0957863\pi\) | ||||
0.955064 | + | 0.296400i | \(0.0957863\pi\) | |||||||
\(354\) | −3450.24 | −0.518017 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4744.33 | 0.706317 | ||||||||
\(357\) | 1183.21 | 0.175411 | ||||||||
\(358\) | 7433.62 | 1.09743 | ||||||||
\(359\) | 37.7844 | 0.00555483 | 0.00277742 | − | 0.999996i | \(-0.499116\pi\) | ||||
0.00277742 | + | 0.999996i | \(0.499116\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6851.46 | −0.998901 | ||||||||
\(362\) | 5103.87 | 0.741031 | ||||||||
\(363\) | 8514.29 | 1.23109 | ||||||||
\(364\) | −1054.32 | −0.151817 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 631.938 | 0.0902511 | ||||||||
\(367\) | 759.829 | 0.108073 | 0.0540364 | − | 0.998539i | \(-0.482791\pi\) | ||||
0.0540364 | + | 0.998539i | \(0.482791\pi\) | |||||||
\(368\) | 446.023 | 0.0631809 | ||||||||
\(369\) | −1586.47 | −0.223816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1826.86 | −0.255650 | ||||||||
\(372\) | 1549.50 | 0.215962 | ||||||||
\(373\) | −719.320 | −0.0998525 | −0.0499263 | − | 0.998753i | \(-0.515899\pi\) | ||||
−0.0499263 | + | 0.998753i | \(0.515899\pi\) | |||||||
\(374\) | 6651.81 | 0.919671 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7988.81 | 1.09572 | ||||||||
\(377\) | 7980.19 | 1.09019 | ||||||||
\(378\) | −345.573 | −0.0470221 | ||||||||
\(379\) | 572.559 | 0.0775999 | 0.0388000 | − | 0.999247i | \(-0.487646\pi\) | ||||
0.0388000 | + | 0.999247i | \(0.487646\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8222.69 | 1.10567 | ||||||||
\(382\) | 1159.56 | 0.155310 | ||||||||
\(383\) | −4513.18 | −0.602122 | −0.301061 | − | 0.953605i | \(-0.597341\pi\) | ||||
−0.301061 | + | 0.953605i | \(0.597341\pi\) | |||||||
\(384\) | 2235.25 | 0.297050 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −466.247 | −0.0614802 | ||||||||
\(387\) | 3990.26 | 0.524125 | ||||||||
\(388\) | −3372.06 | −0.441213 | ||||||||
\(389\) | −6902.13 | −0.899619 | −0.449810 | − | 0.893124i | \(-0.648508\pi\) | ||||
−0.449810 | + | 0.893124i | \(0.648508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4967.58 | −0.642510 | ||||||||
\(392\) | 1133.96 | 0.146107 | ||||||||
\(393\) | −5496.11 | −0.705451 | ||||||||
\(394\) | 7628.88 | 0.975475 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2706.18 | 0.343410 | ||||||||
\(397\) | −4124.58 | −0.521427 | −0.260714 | − | 0.965416i | \(-0.583958\pi\) | ||||
−0.260714 | + | 0.965416i | \(0.583958\pi\) | |||||||
\(398\) | 8459.18 | 1.06538 | ||||||||
\(399\) | −57.6485 | −0.00723317 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1002.50 | −0.124844 | −0.0624219 | − | 0.998050i | \(-0.519882\pi\) | ||||
−0.0624219 | + | 0.998050i | \(0.519882\pi\) | |||||||
\(402\) | −5219.14 | −0.647530 | ||||||||
\(403\) | −3587.23 | −0.443406 | ||||||||
\(404\) | −1251.41 | −0.154109 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3157.96 | −0.386027 | ||||||||
\(407\) | 7791.89 | 0.948967 | ||||||||
\(408\) | 3911.70 | 0.474652 | ||||||||
\(409\) | 10335.0 | 1.24947 | 0.624736 | − | 0.780836i | \(-0.285206\pi\) | ||||
0.624736 | + | 0.780836i | \(0.285206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1148.24 | −0.137807 | ||||||||
\(412\) | −8571.53 | −1.02497 | ||||||||
\(413\) | 4402.99 | 0.524594 | ||||||||
\(414\) | 1450.85 | 0.172236 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5688.75 | −0.670466 | ||||||||
\(417\) | 9160.81 | 1.07580 | ||||||||
\(418\) | −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 | ||||||||
\(423\) | 3106.85 | 0.357117 | ||||||||
\(424\) | −6039.65 | −0.691772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1954.21 | −0.222258 | ||||||||
\(427\) | −806.442 | −0.0913969 | ||||||||
\(428\) | −1132.02 | −0.127846 | ||||||||
\(429\) | −6265.05 | −0.705080 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3868.41 | 0.432331 | 0.216166 | − | 0.976357i | \(-0.430645\pi\) | ||||
0.216166 | + | 0.976357i | \(0.430645\pi\) | |||||||
\(432\) | −136.590 | −0.0152122 | ||||||||
\(433\) | 6132.96 | 0.680673 | 0.340336 | − | 0.940304i | \(-0.389459\pi\) | ||||
0.340336 | + | 0.940304i | \(0.389459\pi\) | |||||||
\(434\) | 1419.56 | 0.157007 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1886.84 | 0.207256 | ||||||||
\(437\) | 242.032 | 0.0264942 | ||||||||
\(438\) | −3602.48 | −0.392998 | ||||||||
\(439\) | −4090.14 | −0.444673 | −0.222337 | − | 0.974970i | \(-0.571368\pi\) | ||||
−0.222337 | + | 0.974970i | \(0.571368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −3331.97 | −0.358565 | ||||||||
\(443\) | −12434.5 | −1.33359 | −0.666795 | − | 0.745241i | \(-0.732334\pi\) | ||||
−0.666795 | + | 0.745241i | \(0.732334\pi\) | |||||||
\(444\) | 1685.91 | 0.180203 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2260.66 | −0.240012 | ||||||||
\(447\) | 10681.8 | 1.13027 | ||||||||
\(448\) | 2534.48 | 0.267283 | ||||||||
\(449\) | 883.046 | 0.0928141 | 0.0464071 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464071 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11381.8 | 1.18835 | ||||||||
\(452\) | −131.214 | −0.0136544 | ||||||||
\(453\) | 9785.40 | 1.01492 | ||||||||
\(454\) | 7646.15 | 0.790422 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −190.587 | −0.0195725 | ||||||||
\(457\) | 9068.44 | 0.928235 | 0.464118 | − | 0.885774i | \(-0.346371\pi\) | ||||
0.464118 | + | 0.885774i | \(0.346371\pi\) | |||||||
\(458\) | 886.373 | 0.0904312 | ||||||||
\(459\) | 1521.26 | 0.154698 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12508.9 | 1.26377 | 0.631885 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631885 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(462\) | 2479.24 | 0.249663 | ||||||||
\(463\) | −12688.7 | −1.27363 | −0.636817 | − | 0.771015i | \(-0.719749\pi\) | ||||
−0.636817 | + | 0.771015i | \(0.719749\pi\) | |||||||
\(464\) | −1248.20 | −0.124884 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3804.12 | 0.378160 | ||||||||
\(467\) | 10136.5 | 1.00442 | 0.502208 | − | 0.864747i | \(-0.332521\pi\) | ||||
0.502208 | + | 0.864747i | \(0.332521\pi\) | |||||||
\(468\) | −1355.56 | −0.133890 | ||||||||
\(469\) | 6660.36 | 0.655750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8635.37 | −0.844791 | ||||||||
\(472\) | 14556.4 | 1.41952 | ||||||||
\(473\) | −28627.3 | −2.78284 | ||||||||
\(474\) | −2414.59 | −0.233979 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1836.67 | −0.176857 | ||||||||
\(477\) | −2348.83 | −0.225462 | ||||||||
\(478\) | −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 | ||||||||
\(483\) | −1851.50 | −0.174422 | ||||||||
\(484\) | −13216.6 | −1.24123 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −444.308 | −0.0414696 | ||||||||
\(487\) | −7929.53 | −0.737826 | −0.368913 | − | 0.929464i | \(-0.620270\pi\) | ||||
−0.368913 | + | 0.929464i | \(0.620270\pi\) | |||||||
\(488\) | −2666.11 | −0.247314 | ||||||||
\(489\) | 2782.61 | 0.257329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8111.51 | 0.745555 | 0.372777 | − | 0.927921i | \(-0.378405\pi\) | ||||
0.372777 | + | 0.927921i | \(0.378405\pi\) | |||||||
\(492\) | 2462.65 | 0.225660 | ||||||||
\(493\) | 13901.8 | 1.26999 | ||||||||
\(494\) | 162.341 | 0.0147856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 561.088 | 0.0507936 | ||||||||
\(497\) | 2493.85 | 0.225079 | ||||||||
\(498\) | −298.466 | −0.0268566 | ||||||||
\(499\) | 16816.6 | 1.50865 | 0.754324 | − | 0.656502i | \(-0.227965\pi\) | ||||
0.754324 | + | 0.656502i | \(0.227965\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3283.55 | −0.292811 | ||||||||
\(502\) | 9542.74 | 0.848433 | ||||||||
\(503\) | 17764.6 | 1.57472 | 0.787362 | − | 0.616491i | \(-0.211446\pi\) | ||||
0.787362 | + | 0.616491i | \(0.211446\pi\) | |||||||
\(504\) | 1457.95 | 0.128854 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10408.8 | −0.914485 | ||||||||
\(507\) | −3452.76 | −0.302451 | ||||||||
\(508\) | −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 | ||||||||
\(511\) | 4597.27 | 0.397987 | ||||||||
\(512\) | 1826.38 | 0.157647 | ||||||||
\(513\) | −74.1195 | −0.00637905 | ||||||||
\(514\) | 12754.6 | 1.09451 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6194.02 | −0.528443 | ||||||||
\(517\) | −22289.5 | −1.89611 | ||||||||
\(518\) | 1544.53 | 0.131009 | ||||||||
\(519\) | 5139.76 | 0.434702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8639.68 | −0.726510 | −0.363255 | − | 0.931690i | \(-0.618335\pi\) | ||||
−0.363255 | + | 0.931690i | \(0.618335\pi\) | |||||||
\(522\) | −4060.23 | −0.340444 | ||||||||
\(523\) | −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 | ||||||||
\(528\) | 979.932 | 0.0807691 | ||||||||
\(529\) | −4393.66 | −0.361113 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5660.99 | 0.462648 | ||||||||
\(532\) | 89.4869 | 0.00729276 | ||||||||
\(533\) | −5701.26 | −0.463319 | ||||||||
\(534\) | 5588.32 | 0.452865 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22019.3 | 1.77442 | ||||||||
\(537\) | −12196.8 | −0.980128 | ||||||||
\(538\) | −10.7616 | −0.000862390 0 | ||||||||
\(539\) | −3163.86 | −0.252833 | ||||||||
\(540\) | 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 | ||||||||
\(543\) | −8374.19 | −0.661825 | ||||||||
\(544\) | −9910.04 | −0.781047 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1241.88 | −0.0973398 | ||||||||
\(547\) | 7870.21 | 0.615184 | 0.307592 | − | 0.951518i | \(-0.400477\pi\) | ||||
0.307592 | + | 0.951518i | \(0.400477\pi\) | |||||||
\(548\) | 1782.40 | 0.138942 | ||||||||
\(549\) | −1036.85 | −0.0806045 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −677.329 | −0.0523687 | ||||||||
\(552\) | −6121.08 | −0.471976 | ||||||||
\(553\) | 3081.37 | 0.236949 | ||||||||
\(554\) | −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 | \(0.736236\pi\) | |||||||
\(558\) | 1825.15 | 0.138467 | ||||||||
\(559\) | 14339.7 | 1.08498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10914.0 | −0.821370 | ||||||||
\(562\) | 438.672 | 0.0329257 | ||||||||
\(563\) | −15192.8 | −1.13730 | −0.568651 | − | 0.822579i | \(-0.692534\pi\) | ||||
−0.568651 | + | 0.822579i | \(0.692534\pi\) | |||||||
\(564\) | −4822.72 | −0.360059 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8304.93 | −0.616753 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 8244.71 | 0.609050 | ||||||||
\(569\) | −23300.0 | −1.71667 | −0.858335 | − | 0.513090i | \(-0.828501\pi\) | ||||
−0.858335 | + | 0.513090i | \(0.828501\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −1902.55 | −0.138709 | ||||||||
\(574\) | 2256.13 | 0.164058 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3258.61 | 0.235721 | ||||||||
\(577\) | 897.258 | 0.0647372 | 0.0323686 | − | 0.999476i | \(-0.489695\pi\) | ||||
0.0323686 | + | 0.999476i | \(0.489695\pi\) | |||||||
\(578\) | 3178.63 | 0.228743 | ||||||||
\(579\) | 764.997 | 0.0549088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 380.885 | 0.0271975 | ||||||||
\(582\) | −3971.93 | −0.282890 | ||||||||
\(583\) | 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 | \(-0.326952\pi\) | ||||
0.517261 | + | 0.855828i | \(0.326952\pi\) | |||||||
\(588\) | −684.558 | −0.0480114 | ||||||||
\(589\) | 304.471 | 0.0212997 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12517.1 | −0.871210 | ||||||||
\(592\) | 610.486 | 0.0423831 | ||||||||
\(593\) | 7216.29 | 0.499726 | 0.249863 | − | 0.968281i | \(-0.419614\pi\) | ||||
0.249863 | + | 0.968281i | \(0.419614\pi\) | |||||||
\(594\) | 3187.59 | 0.220182 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16581.2 | −1.13958 | ||||||||
\(597\) | −13879.4 | −0.951503 | ||||||||
\(598\) | 5213.91 | 0.356543 | ||||||||
\(599\) | −20885.5 | −1.42464 | −0.712320 | − | 0.701855i | \(-0.752355\pi\) | ||||
−0.712320 | + | 0.701855i | \(0.752355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11047.7 | −0.749823 | −0.374911 | − | 0.927061i | \(-0.622327\pi\) | ||||
−0.374911 | + | 0.927061i | \(0.622327\pi\) | |||||||
\(602\) | −5674.59 | −0.384185 | ||||||||
\(603\) | 8563.32 | 0.578317 | ||||||||
\(604\) | −15189.7 | −1.02328 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1474.03 | −0.0988093 | ||||||||
\(607\) | 9434.94 | 0.630894 | 0.315447 | − | 0.948943i | \(-0.397846\pi\) | ||||
0.315447 | + | 0.948943i | \(0.397846\pi\) | |||||||
\(608\) | 482.840 | 0.0322068 | ||||||||
\(609\) | 5181.44 | 0.344766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11165.0 | 0.739263 | ||||||||
\(612\) | −2361.44 | −0.155973 | ||||||||
\(613\) | 17662.6 | 1.16376 | 0.581881 | − | 0.813274i | \(-0.302317\pi\) | ||||
0.581881 | + | 0.813274i | \(0.302317\pi\) | |||||||
\(614\) | −6415.30 | −0.421662 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10459.8 | −0.684150 | ||||||||
\(617\) | 10817.4 | 0.705820 | 0.352910 | − | 0.935657i | \(-0.385192\pi\) | ||||
0.352910 | + | 0.935657i | \(0.385192\pi\) | |||||||
\(618\) | −10096.3 | −0.657176 | ||||||||
\(619\) | 29073.9 | 1.88785 | 0.943926 | − | 0.330158i | \(-0.107102\pi\) | ||||
0.943926 | + | 0.330158i | \(0.107102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2380.50 | −0.153826 | ||||||||
\(622\) | 5728.92 | 0.369306 | ||||||||
\(623\) | −7131.49 | −0.458615 | ||||||||
\(624\) | −490.860 | −0.0314906 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11682.9 | 0.745915 | ||||||||
\(627\) | 531.754 | 0.0338696 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | −4687.93 | −0.294358 | ||||||||
\(634\) | 2988.45 | 0.187203 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3646.05 | 0.227319 | ||||||||
\(637\) | 1584.81 | 0.0985755 | ||||||||
\(638\) | 29129.3 | 1.80758 | ||||||||
\(639\) | 3206.38 | 0.198501 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22466.5 | 1.38436 | 0.692180 | − | 0.721725i | \(-0.256651\pi\) | ||||
0.692180 | + | 0.721725i | \(0.256651\pi\) | |||||||
\(642\) | −1333.40 | −0.0819705 | ||||||||
\(643\) | 12347.0 | 0.757257 | 0.378629 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378629 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(644\) | 2874.05 | 0.175859 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 282.805 | 0.0172242 | ||||||||
\(647\) | 24114.0 | 1.46525 | 0.732626 | − | 0.680631i | \(-0.238294\pi\) | ||||
0.732626 | + | 0.680631i | \(0.238294\pi\) | |||||||
\(648\) | 1874.51 | 0.113639 | ||||||||
\(649\) | −40613.6 | −2.45643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2329.15 | −0.140225 | ||||||||
\(652\) | −4319.41 | −0.259449 | ||||||||
\(653\) | −7843.33 | −0.470035 | −0.235018 | − | 0.971991i | \(-0.575515\pi\) | ||||
−0.235018 | + | 0.971991i | \(0.575515\pi\) | |||||||
\(654\) | 2222.50 | 0.132885 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 891.749 | 0.0530746 | ||||||||
\(657\) | 5910.78 | 0.350992 | ||||||||
\(658\) | −4418.29 | −0.261767 | ||||||||
\(659\) | 21242.8 | 1.25569 | 0.627846 | − | 0.778338i | \(-0.283937\pi\) | ||||
0.627846 | + | 0.778338i | \(0.283937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22221.7 | −1.30760 | −0.653801 | − | 0.756667i | \(-0.726827\pi\) | ||||
−0.653801 | + | 0.756667i | \(0.726827\pi\) | |||||||
\(662\) | −8019.79 | −0.470843 | ||||||||
\(663\) | 5466.94 | 0.320239 | ||||||||
\(664\) | 1259.21 | 0.0735948 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1985.83 | 0.115539 | ||||||||
\(667\) | −21753.8 | −1.26283 | ||||||||
\(668\) | 5097.01 | 0.295223 | ||||||||
\(669\) | 3709.18 | 0.214358 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7438.69 | 0.427969 | ||||||||
\(672\) | −3693.63 | −0.212031 | ||||||||
\(673\) | 3787.85 | 0.216955 | 0.108478 | − | 0.994099i | \(-0.465402\pi\) | ||||
0.108478 | + | 0.994099i | \(0.465402\pi\) | |||||||
\(674\) | 3133.88 | 0.179099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5359.67 | 0.304943 | ||||||||
\(677\) | 11296.8 | 0.641314 | 0.320657 | − | 0.947195i | \(-0.396096\pi\) | ||||
0.320657 | + | 0.947195i | \(0.396096\pi\) | |||||||
\(678\) | −154.557 | −0.00875474 | ||||||||
\(679\) | 5068.75 | 0.286481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12545.5 | −0.705937 | ||||||||
\(682\) | −13094.1 | −0.735190 | ||||||||
\(683\) | −4807.14 | −0.269312 | −0.134656 | − | 0.990892i | \(-0.542993\pi\) | ||||
−0.134656 | + | 0.990892i | \(0.542993\pi\) | |||||||
\(684\) | 115.055 | 0.00643161 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −627.151 | −0.0349048 | ||||||||
\(687\) | −1454.32 | −0.0807654 | ||||||||
\(688\) | −2242.92 | −0.124288 | ||||||||
\(689\) | −8440.94 | −0.466726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5393.47 | 0.296928 | 0.148464 | − | 0.988918i | \(-0.452567\pi\) | ||||
0.148464 | + | 0.988918i | \(0.452567\pi\) | |||||||
\(692\) | −7978.37 | −0.438283 | ||||||||
\(693\) | −4067.82 | −0.222978 | ||||||||
\(694\) | −3190.29 | −0.174498 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17129.9 | 0.932914 | ||||||||
\(697\) | −9931.84 | −0.539735 | ||||||||
\(698\) | −12884.5 | −0.698691 | ||||||||
\(699\) | −6241.63 | −0.337740 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2404.77 | 0.129568 | 0.0647838 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647838 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(702\) | −1596.70 | −0.0858456 | ||||||||
\(703\) | 331.276 | 0.0177729 | ||||||||
\(704\) | −23378.2 | −1.25156 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23163.4 | −1.23480 | ||||||||
\(707\) | 1881.07 | 0.100064 | ||||||||
\(708\) | −8787.47 | −0.466460 | ||||||||
\(709\) | −21617.3 | −1.14507 | −0.572535 | − | 0.819881i | \(-0.694040\pi\) | ||||
−0.572535 | + | 0.819881i | \(0.694040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3961.76 | 0.208970 | ||||||||
\(712\) | −23576.8 | −1.24098 | ||||||||
\(713\) | 9778.70 | 0.513626 | ||||||||
\(714\) | −2163.41 | −0.113394 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18932.8 | 0.988203 | ||||||||
\(717\) | 20442.3 | 1.06476 | ||||||||
\(718\) | −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 | ||||||||
\(721\) | 12884.4 | 0.665519 | ||||||||
\(722\) | 12527.4 | 0.645736 | ||||||||
\(723\) | −11765.5 | −0.605207 | ||||||||
\(724\) | 12999.1 | 0.667278 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15567.8 | −0.795832 | ||||||||
\(727\) | −20196.5 | −1.03033 | −0.515164 | − | 0.857092i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857092i | \(0.672269\pi\) | |||||||
\(728\) | 5239.43 | 0.266739 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24980.4 | 1.26393 | ||||||||
\(732\) | 1609.49 | 0.0812686 | ||||||||
\(733\) | 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 | ||||||||
\(738\) | 2900.74 | 0.144685 | ||||||||
\(739\) | 13906.0 | 0.692207 | 0.346103 | − | 0.938196i | \(-0.387505\pi\) | ||||
0.346103 | + | 0.938196i | \(0.387505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −266.362 | −0.0132052 | ||||||||
\(742\) | 3340.29 | 0.165264 | ||||||||
\(743\) | −4592.87 | −0.226778 | −0.113389 | − | 0.993551i | \(-0.536171\pi\) | ||||
−0.113389 | + | 0.993551i | \(0.536171\pi\) | |||||||
\(744\) | −7700.20 | −0.379440 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1315.22 | 0.0645493 | ||||||||
\(747\) | 489.709 | 0.0239860 | ||||||||
\(748\) | 16941.6 | 0.828137 | ||||||||
\(749\) | 1701.61 | 0.0830111 | ||||||||
\(750\) | 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 | ||||||||
\(753\) | −15657.3 | −0.757747 | ||||||||
\(754\) | −14591.2 | −0.704748 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −880.145 | −0.0423420 | ||||||||
\(757\) | 1368.89 | 0.0657240 | 0.0328620 | − | 0.999460i | \(-0.489538\pi\) | ||||
0.0328620 | + | 0.999460i | \(0.489538\pi\) | |||||||
\(758\) | −1046.88 | −0.0501642 | ||||||||
\(759\) | 17078.4 | 0.816739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1623.77 | −0.0773478 | −0.0386739 | − | 0.999252i | \(-0.512313\pi\) | ||||
−0.0386739 | + | 0.999252i | \(0.512313\pi\) | |||||||
\(762\) | −15034.6 | −0.714759 | ||||||||
\(763\) | −2836.23 | −0.134572 | ||||||||
\(764\) | 2953.31 | 0.139852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8252.03 | 0.389240 | ||||||||
\(767\) | 20343.8 | 0.957722 | ||||||||
\(768\) | −12776.6 | −0.600308 | ||||||||
\(769\) | −26842.5 | −1.25873 | −0.629366 | − | 0.777109i | \(-0.716685\pi\) | ||||
−0.629366 | + | 0.777109i | \(0.716685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20927.1 | −0.977526 | ||||||||
\(772\) | −1187.49 | −0.0553612 | ||||||||
\(773\) | 20961.4 | 0.975330 | 0.487665 | − | 0.873031i | \(-0.337849\pi\) | ||||
0.487665 | + | 0.873031i | \(0.337849\pi\) | |||||||
\(774\) | −7295.90 | −0.338819 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16757.4 | 0.775200 | ||||||||
\(777\) | −2534.20 | −0.117006 | ||||||||
\(778\) | 12620.0 | 0.581556 | ||||||||
\(779\) | 483.902 | 0.0222562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23003.5 | −1.05394 | ||||||||
\(782\) | 9082.86 | 0.415348 | ||||||||
\(783\) | 6661.85 | 0.304055 | ||||||||
\(784\) | −247.885 | −0.0112921 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10049.2 | 0.456036 | ||||||||
\(787\) | −35333.2 | −1.60037 | −0.800187 | − | 0.599751i | \(-0.795266\pi\) | ||||
−0.800187 | + | 0.599751i | \(0.795266\pi\) | |||||||
\(788\) | 19430.1 | 0.878388 | ||||||||
\(789\) | 10822.1 | 0.488309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 197.236 | 0.00886589 | ||||||||
\(792\) | −13448.3 | −0.603364 | ||||||||
\(793\) | −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 | \(-0.442125\pi\) | ||||
0.180821 | + | 0.983516i | \(0.442125\pi\) | |||||||
\(798\) | 105.406 | 0.00467586 | ||||||||
\(799\) | 19450.0 | 0.861191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9169.05 | −0.404460 | ||||||||
\(802\) | 1832.99 | 0.0807049 | ||||||||
\(803\) | −42405.6 | −1.86359 | ||||||||
\(804\) | −13292.7 | −0.583082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6558.99 | 0.286639 | ||||||||
\(807\) | 17.6572 | 0.000770212 0 | ||||||||
\(808\) | 6218.87 | 0.270766 | ||||||||
\(809\) | −36281.0 | −1.57673 | −0.788364 | − | 0.615209i | \(-0.789072\pi\) | ||||
−0.788364 | + | 0.615209i | \(0.789072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34237.2 | −1.48240 | −0.741202 | − | 0.671282i | \(-0.765744\pi\) | ||||
−0.741202 | + | 0.671282i | \(0.765744\pi\) | |||||||
\(812\) | −8043.06 | −0.347606 | ||||||||
\(813\) | 20749.0 | 0.895077 | ||||||||
\(814\) | −14246.9 | −0.613456 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −855.099 | −0.0366844 | ||||||||
\(817\) | −1217.10 | −0.0521188 | ||||||||
\(818\) | −18896.8 | −0.807717 | ||||||||
\(819\) | 2037.62 | 0.0869355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23247.8 | −0.988250 | −0.494125 | − | 0.869391i | \(-0.664511\pi\) | ||||
−0.494125 | + | 0.869391i | \(0.664511\pi\) | |||||||
\(822\) | 2099.47 | 0.0890846 | ||||||||
\(823\) | −42934.0 | −1.81845 | −0.909225 | − | 0.416306i | \(-0.863325\pi\) | ||||
−0.909225 | + | 0.416306i | \(0.863325\pi\) | |||||||
\(824\) | 42596.0 | 1.80085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8050.55 | −0.339122 | ||||||||
\(827\) | 781.391 | 0.0328557 | 0.0164278 | − | 0.999865i | \(-0.494771\pi\) | ||||
0.0164278 | + | 0.999865i | \(0.494771\pi\) | |||||||
\(828\) | 3695.21 | 0.155093 | ||||||||
\(829\) | −33493.3 | −1.40322 | −0.701611 | − | 0.712561i | \(-0.747535\pi\) | ||||
−0.701611 | + | 0.712561i | \(0.747535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6358.39 | 0.265427 | ||||||||
\(832\) | 11710.4 | 0.487964 | ||||||||
\(833\) | 2760.81 | 0.114834 | ||||||||
\(834\) | −16749.9 | −0.695445 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −825.434 | −0.0341486 | ||||||||
\(837\) | −2994.62 | −0.123667 | ||||||||
\(838\) | −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 | ||||||||
\(843\) | −719.752 | −0.0294064 | ||||||||
\(844\) | 7277.01 | 0.296783 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5680.66 | −0.230857 | ||||||||
\(847\) | 19866.7 | 0.805935 | ||||||||
\(848\) | 1320.27 | 0.0534649 | ||||||||
\(849\) | 13626.4 | 0.550831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10639.6 | 0.428579 | ||||||||
\(852\) | −4977.21 | −0.200137 | ||||||||
\(853\) | 2917.48 | 0.117107 | 0.0585537 | − | 0.998284i | \(-0.481351\pi\) | ||||
0.0585537 | + | 0.998284i | \(0.481351\pi\) | |||||||
\(854\) | 1474.52 | 0.0590832 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5625.54 | 0.224623 | ||||||||
\(857\) | 31560.7 | 1.25799 | 0.628993 | − | 0.777411i | \(-0.283468\pi\) | ||||
0.628993 | + | 0.777411i | \(0.283468\pi\) | |||||||
\(858\) | 11455.2 | 0.455797 | ||||||||
\(859\) | −1404.81 | −0.0557991 | −0.0278995 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0278995 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3701.76 | −0.146522 | ||||||||
\(862\) | −7073.11 | −0.279479 | ||||||||
\(863\) | 9808.24 | 0.386879 | 0.193439 | − | 0.981112i | \(-0.438036\pi\) | ||||
0.193439 | + | 0.981112i | \(0.438036\pi\) | |||||||
\(864\) | −4748.96 | −0.186994 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11213.7 | −0.440018 | ||||||||
\(867\) | −5215.35 | −0.204294 | ||||||||
\(868\) | 3615.50 | 0.141380 | ||||||||
\(869\) | −28422.8 | −1.10952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30773.9 | 1.19717 | ||||||||
\(872\) | −9376.63 | −0.364143 | ||||||||
\(873\) | 6516.97 | 0.252653 | ||||||||
\(874\) | −442.537 | −0.0171271 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9175.22 | −0.353883 | ||||||||
\(877\) | 7196.05 | 0.277073 | 0.138537 | − | 0.990357i | \(-0.455760\pi\) | ||||
0.138537 | + | 0.990357i | \(0.455760\pi\) | |||||||
\(878\) | 7478.52 | 0.287458 | ||||||||
\(879\) | 6515.10 | 0.249999 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3183.27 | −0.121733 | −0.0608667 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608667 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(882\) | −806.336 | −0.0307832 | ||||||||
\(883\) | −25392.5 | −0.967751 | −0.483876 | − | 0.875137i | \(-0.660771\pi\) | ||||
−0.483876 | + | 0.875137i | \(0.660771\pi\) | |||||||
\(884\) | −8486.25 | −0.322877 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22735.6 | 0.862095 | ||||||||
\(887\) | 30634.2 | 1.15964 | 0.579818 | − | 0.814746i | \(-0.303124\pi\) | ||||
0.579818 | + | 0.814746i | \(0.303124\pi\) | |||||||
\(888\) | −8378.11 | −0.316612 | ||||||||
\(889\) | 19186.3 | 0.723833 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5230.05 | −0.196648 | ||||||||
\(892\) | −5757.71 | −0.216124 | ||||||||
\(893\) | −947.648 | −0.0355116 | ||||||||
\(894\) | −19530.9 | −0.730660 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5215.58 | 0.194465 | ||||||||
\(897\) | −8554.75 | −0.318433 | ||||||||
\(898\) | −1614.59 | −0.0599994 | ||||||||
\(899\) | −27365.8 | −1.01524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14704.5 | −0.543704 | ||||||||
\(902\) | −20810.7 | −0.768206 | ||||||||
\(903\) | 9310.61 | 0.343120 | ||||||||
\(904\) | 652.067 | 0.0239905 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17891.9 | −0.656091 | ||||||||
\(907\) | 28089.9 | 1.02834 | 0.514172 | − | 0.857687i | \(-0.328099\pi\) | ||||
0.514172 | + | 0.857687i | \(0.328099\pi\) | |||||||
\(908\) | 19474.1 | 0.711753 | ||||||||
\(909\) | 2418.52 | 0.0882480 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36102.7 | −1.31299 | −0.656495 | − | 0.754330i | \(-0.727962\pi\) | ||||
−0.656495 | + | 0.754330i | \(0.727962\pi\) | |||||||
\(912\) | 41.6624 | 0.00151270 | ||||||||
\(913\) | −3513.31 | −0.127353 | ||||||||
\(914\) | −16581.0 | −0.600055 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2257.52 | 0.0814308 | ||||||||
\(917\) | −12824.3 | −0.461826 | ||||||||
\(918\) | −2781.52 | −0.100004 | ||||||||
\(919\) | −14533.8 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10525.9 | 0.376592 | ||||||||
\(922\) | −22871.6 | −0.816959 | ||||||||
\(923\) | 11522.7 | 0.410915 | ||||||||
\(924\) | 6314.41 | 0.224815 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23200.3 | 0.823336 | ||||||||
\(927\) | 16565.6 | 0.586933 | ||||||||
\(928\) | −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 | ||||||||
\(931\) | −134.513 | −0.00473522 | ||||||||
\(932\) | 9688.79 | 0.340522 | ||||||||
\(933\) | −9399.74 | −0.329833 | ||||||||
\(934\) | −18533.9 | −0.649301 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6736.41 | 0.235242 | ||||||||
\(937\) | −30212.3 | −1.05335 | −0.526677 | − | 0.850065i | \(-0.676562\pi\) | ||||
−0.526677 | + | 0.850065i | \(0.676562\pi\) | |||||||
\(938\) | −12178.0 | −0.423908 | ||||||||
\(939\) | −19168.8 | −0.666187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26414.4 | −0.915074 | −0.457537 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457537 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(942\) | 15789.1 | 0.546112 | ||||||||
\(943\) | 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 | \(0.555923\pi\) | |||||||
\(948\) | −6149.77 | −0.210691 | ||||||||
\(949\) | 21241.5 | 0.726583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4903.31 | −0.167193 | ||||||||
\(952\) | 9127.31 | 0.310733 | ||||||||
\(953\) | −2211.39 | −0.0751669 | −0.0375834 | − | 0.999293i | \(-0.511966\pi\) | ||||
−0.0375834 | + | 0.999293i | \(0.511966\pi\) | |||||||
\(954\) | 4294.66 | 0.145749 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31732.3 | −1.07353 | ||||||||
\(957\) | −47794.0 | −1.61438 | ||||||||
\(958\) | 20773.0 | 0.700569 | ||||||||
\(959\) | −2679.23 | −0.0902156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17489.6 | −0.587077 | ||||||||
\(962\) | 7136.44 | 0.239177 | ||||||||
\(963\) | 2187.78 | 0.0732089 | ||||||||
\(964\) | 18263.4 | 0.610193 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3385.33 | 0.112755 | ||||||||
\(967\) | −7955.89 | −0.264575 | −0.132287 | − | 0.991211i | \(-0.542232\pi\) | ||||
−0.132287 | + | 0.991211i | \(0.542232\pi\) | |||||||
\(968\) | 65679.6 | 2.18081 | ||||||||
\(969\) | −464.014 | −0.0153832 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53071.2 | 1.75400 | 0.877001 | − | 0.480488i | \(-0.159541\pi\) | ||||
0.877001 | + | 0.480488i | \(0.159541\pi\) | |||||||
\(972\) | −1131.62 | −0.0373422 | ||||||||
\(973\) | 21375.2 | 0.704274 | ||||||||
\(974\) | 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 | \(0.380199\pi\) | |||||||
\(978\) | −5087.80 | −0.166350 | ||||||||
\(979\) | 65781.4 | 2.14748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3646.58 | −0.118681 | ||||||||
\(982\) | −14831.3 | −0.481961 | ||||||||
\(983\) | −21712.8 | −0.704509 | −0.352254 | − | 0.935904i | \(-0.614585\pi\) | ||||
−0.352254 | + | 0.935904i | \(0.614585\pi\) | |||||||
\(984\) | −12238.1 | −0.396479 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25418.5 | −0.820983 | ||||||||
\(987\) | 7249.33 | 0.233788 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 13158.5 | 0.420516 | ||||||||
\(994\) | −4559.82 | −0.145502 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −760.168 | −0.0241836 | ||||||||
\(997\) | 39573.1 | 1.25707 | 0.628533 | − | 0.777783i | \(-0.283656\pi\) | ||||
0.628533 | + | 0.777783i | \(0.283656\pi\) | |||||||
\(998\) | −30748.0 | −0.975261 | ||||||||
\(999\) | −3258.26 | −0.103190 |
(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 | 525.4.a.l.1.1 | 2 | ||
3.2 | odd | 2 | 1575.4.a.q.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.l.274.2 | 4 | |||
5.3 | odd | 4 | 525.4.d.l.274.3 | 4 | |||
5.4 | even | 2 | 105.4.a.e.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 315.4.a.k.1.1 | 2 | |||
20.19 | odd | 2 | 1680.4.a.bo.1.2 | 2 | |||
35.34 | odd | 2 | 735.4.a.o.1.2 | 2 | |||
105.104 | even | 2 | 2205.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
315.4.a.k.1.1 | 2 | 15.14 | odd | 2 | |||
525.4.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
525.4.d.l.274.2 | 4 | 5.2 | odd | 4 | |||
525.4.d.l.274.3 | 4 | 5.3 | odd | 4 | |||
735.4.a.o.1.2 | 2 | 35.34 | odd | 2 | |||
1575.4.a.q.1.2 | 2 | 3.2 | odd | 2 | |||
1680.4.a.bo.1.2 | 2 | 20.19 | odd | 2 | |||
2205.4.a.bb.1.1 | 2 | 105.104 | even | 2 |