Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, 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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 151x^{4} - 212x^{3} + 4412x^{2} + 8656x - 19148 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.01416\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.4813 | −0.565937 | −0.282968 | − | 0.959129i | \(-0.591319\pi\) | ||||
−0.282968 | + | 0.959129i | \(0.591319\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.3429 | −0.913932 | −0.456966 | − | 0.889484i | \(-0.651064\pi\) | ||||
−0.456966 | + | 0.889484i | \(0.651064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.9383 | −0.510714 | −0.255357 | − | 0.966847i | \(-0.582193\pi\) | ||||
−0.255357 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 72.5536 | 1.03511 | 0.517554 | − | 0.855651i | \(-0.326843\pi\) | ||||
0.517554 | + | 0.855651i | \(0.326843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45.9922 | −0.555333 | −0.277667 | − | 0.960678i | \(-0.589561\pi\) | ||||
−0.277667 | + | 0.960678i | \(0.589561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 163.189 | 1.47944 | 0.739721 | − | 0.672914i | \(-0.234957\pi\) | ||||
0.739721 | + | 0.672914i | \(0.234957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.9773 | 0.198357 | 0.0991783 | − | 0.995070i | \(-0.468379\pi\) | ||||
0.0991783 | + | 0.995070i | \(0.468379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 304.799 | 1.76592 | 0.882960 | − | 0.469448i | \(-0.155547\pi\) | ||||
0.882960 | + | 0.469448i | \(0.155547\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −52.4065 | −0.253095 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 150.155 | 0.667171 | 0.333586 | − | 0.942720i | \(-0.391741\pi\) | ||||
0.333586 | + | 0.942720i | \(0.391741\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −409.065 | −1.55818 | −0.779088 | − | 0.626915i | \(-0.784317\pi\) | ||||
−0.779088 | + | 0.626915i | \(0.784317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −249.174 | −0.883689 | −0.441845 | − | 0.897092i | \(-0.645676\pi\) | ||||
−0.441845 | + | 0.897092i | \(0.645676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −155.899 | −0.483835 | −0.241917 | − | 0.970297i | \(-0.577776\pi\) | ||||
−0.241917 | + | 0.970297i | \(0.577776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −233.142 | −0.679716 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 263.062 | 0.681780 | 0.340890 | − | 0.940103i | \(-0.389272\pi\) | ||||
0.340890 | + | 0.940103i | \(0.389272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −166.714 | −0.408723 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −245.829 | −0.542445 | −0.271223 | − | 0.962517i | \(-0.587428\pi\) | ||||
−0.271223 | + | 0.962517i | \(0.587428\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −466.473 | −0.979110 | −0.489555 | − | 0.871972i | \(-0.662841\pi\) | ||||
−0.489555 | + | 0.871972i | \(0.662841\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −119.691 | −0.228398 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −177.016 | −0.322775 | −0.161387 | − | 0.986891i | \(-0.551597\pi\) | ||||
−0.161387 | + | 0.986891i | \(0.551597\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.2138 | 0.0755759 | 0.0377879 | − | 0.999286i | \(-0.487969\pi\) | ||||
0.0377879 | + | 0.999286i | \(0.487969\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −949.331 | −1.52207 | −0.761033 | − | 0.648713i | \(-0.775307\pi\) | ||||
−0.761033 | + | 0.648713i | \(0.775307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 349.476 | 0.517228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 496.917 | 0.707690 | 0.353845 | − | 0.935304i | \(-0.384874\pi\) | ||||
0.353845 | + | 0.935304i | \(0.384874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 354.636 | 0.468992 | 0.234496 | − | 0.972117i | \(-0.424656\pi\) | ||||
0.234496 | + | 0.972117i | \(0.424656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 362.768 | 0.462914 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1193.20 | −1.42111 | −0.710554 | − | 0.703643i | \(-0.751556\pi\) | ||||
−0.710554 | + | 0.703643i | \(0.751556\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 250.904 | 0.289032 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −229.961 | −0.248353 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −408.798 | −0.427908 | −0.213954 | − | 0.976844i | \(-0.568634\pi\) | ||||
−0.213954 | + | 0.976844i | \(0.568634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −890.427 | −0.877235 | −0.438618 | − | 0.898674i | \(-0.644532\pi\) | ||||
−0.438618 | + | 0.898674i | \(0.644532\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1531.17 | 1.46476 | 0.732381 | − | 0.680895i | \(-0.238409\pi\) | ||||
0.732381 | + | 0.680895i | \(0.238409\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −989.489 | −0.893996 | −0.446998 | − | 0.894535i | \(-0.647507\pi\) | ||||
−0.446998 | + | 0.894535i | \(0.647507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −296.637 | −0.260667 | −0.130334 | − | 0.991470i | \(-0.541605\pi\) | ||||
−0.130334 | + | 0.991470i | \(0.541605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1036.15 | −0.862588 | −0.431294 | − | 0.902211i | \(-0.641943\pi\) | ||||
−0.431294 | + | 0.902211i | \(0.641943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 815.943 | 0.661627 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −760.456 | −0.585806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −219.254 | −0.164729 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1040.10 | −0.726726 | −0.363363 | − | 0.931648i | \(-0.618372\pi\) | ||||
−0.363363 | + | 0.931648i | \(0.618372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −316.994 | −0.211419 | −0.105709 | − | 0.994397i | \(-0.533711\pi\) | ||||
−0.105709 | + | 0.994397i | \(0.533711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 482.058 | 0.314283 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1701.23 | −1.06092 | −0.530459 | − | 0.847711i | \(-0.677980\pi\) | ||||
−0.530459 | + | 0.847711i | \(0.677980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2756.36 | 1.68196 | 0.840978 | − | 0.541070i | \(-0.181981\pi\) | ||||
0.840978 | + | 0.541070i | \(0.181981\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 798.170 | 0.466757 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 154.887 | 0.0887078 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 328.707 | 0.180730 | 0.0903648 | − | 0.995909i | \(-0.471197\pi\) | ||||
0.0903648 | + | 0.995909i | \(0.471197\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −316.280 | −0.170454 | −0.0852269 | − | 0.996362i | \(-0.527162\pi\) | ||||
−0.0852269 | + | 0.996362i | \(0.527162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1524.00 | 0.789744 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3521.19 | 1.78995 | 0.894973 | − | 0.446120i | \(-0.147194\pi\) | ||||
0.894973 | + | 0.446120i | \(0.147194\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1710.43 | −0.837271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1988.65 | −0.955602 | −0.477801 | − | 0.878468i | \(-0.658566\pi\) | ||||
−0.477801 | + | 0.878468i | \(0.658566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2632.95 | −1.22002 | −0.610011 | − | 0.792393i | \(-0.708835\pi\) | ||||
−0.610011 | + | 0.792393i | \(0.708835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1623.96 | −0.739172 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1683.23 | −0.739732 | −0.369866 | − | 0.929085i | \(-0.620596\pi\) | ||||
−0.369866 | + | 0.929085i | \(0.620596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −262.032 | −0.113187 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2341.61 | −0.977767 | −0.488884 | − | 0.872349i | \(-0.662596\pi\) | ||||
−0.488884 | + | 0.872349i | \(0.662596\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 469.689 | 0.192882 | 0.0964412 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964412 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 750.775 | 0.298368 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2419.14 | −0.946018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1276.72 | −0.483666 | −0.241833 | − | 0.970318i | \(-0.577749\pi\) | ||||
−0.241833 | + | 0.970318i | \(0.577749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1106.88 | −0.412822 | −0.206411 | − | 0.978465i | \(-0.566178\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566178\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1945.23 | −0.703513 | −0.351757 | − | 0.936092i | \(-0.614416\pi\) | ||||
−0.351757 | + | 0.936092i | \(0.614416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −426.899 | −0.152071 | −0.0760353 | − | 0.997105i | \(-0.524226\pi\) | ||||
−0.0760353 | + | 0.997105i | \(0.524226\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −324.682 | −0.112257 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2045.32 | −0.696837 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1533.51 | 0.507537 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4343.21 | 1.41706 | 0.708529 | − | 0.705682i | \(-0.249359\pi\) | ||||
0.708529 | + | 0.705682i | \(0.249359\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1245.87 | −0.395198 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3194.69 | −0.999399 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1736.81 | −0.528644 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2854.90 | −0.857302 | −0.428651 | − | 0.903470i | \(-0.641011\pi\) | ||||
−0.428651 | + | 0.903470i | \(0.641011\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 377.834 | 0.110475 | 0.0552373 | − | 0.998473i | \(-0.482408\pi\) | ||||
0.0552373 | + | 0.998473i | \(0.482408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6143.68 | 1.77286 | 0.886432 | − | 0.462858i | \(-0.153176\pi\) | ||||
0.886432 | + | 0.462858i | \(0.153176\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4323.86 | −1.21573 | −0.607866 | − | 0.794040i | \(-0.707974\pi\) | ||||
−0.607866 | + | 0.794040i | \(0.707974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −779.496 | −0.216378 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1827.21 | −0.494528 | −0.247264 | − | 0.968948i | \(-0.579531\pi\) | ||||
−0.247264 | + | 0.968948i | \(0.579531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 447.748 | 0.119676 | 0.0598381 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598381 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1165.71 | −0.303978 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1100.97 | 0.283616 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4046.98 | 1.01770 | 0.508851 | − | 0.860855i | \(-0.330071\pi\) | ||||
0.508851 | + | 0.860855i | \(0.330071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5441.17 | −1.35211 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2283.13 | −0.554155 | −0.277077 | − | 0.960848i | \(-0.589366\pi\) | ||||
−0.277077 | + | 0.960848i | \(0.589366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1573.82 | −0.377577 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3423.31 | −0.802625 | −0.401312 | − | 0.915941i | \(-0.631446\pi\) | ||||
−0.401312 | + | 0.915941i | \(0.631446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1315.31 | 0.304901 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2257.48 | 0.511676 | 0.255838 | − | 0.966720i | \(-0.417649\pi\) | ||||
0.255838 | + | 0.966720i | \(0.417649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8085.45 | −1.81239 | −0.906193 | − | 0.422865i | \(-0.861024\pi\) | ||||
−0.906193 | + | 0.422865i | \(0.861024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −833.571 | −0.182786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4840.74 | 1.05001 | 0.525004 | − | 0.851100i | \(-0.324064\pi\) | ||||
0.525004 | + | 0.851100i | \(0.324064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6555.12 | −1.39162 | −0.695811 | − | 0.718225i | \(-0.744955\pi\) | ||||
−0.695811 | + | 0.718225i | \(0.744955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4103.01 | 0.861832 | 0.430916 | − | 0.902392i | \(-0.358191\pi\) | ||||
0.430916 | + | 0.902392i | \(0.358191\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4287.53 | 0.881829 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 351.026 | 0.0714485 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8500.10 | −1.69482 | −0.847408 | − | 0.530942i | \(-0.821838\pi\) | ||||
−0.847408 | + | 0.530942i | \(0.821838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1229.15 | −0.242589 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3906.45 | −0.755571 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2611.66 | 0.500112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2332.36 | −0.437871 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5386.01 | 1.00129 | 0.500645 | − | 0.865653i | \(-0.333096\pi\) | ||||
0.500645 | + | 0.865653i | \(0.333096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1489.18 | 0.271522 | 0.135761 | − | 0.990742i | \(-0.456652\pi\) | ||||
0.135761 | + | 0.990742i | \(0.456652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4425.29 | −0.799144 | −0.399572 | − | 0.916702i | \(-0.630841\pi\) | ||||
−0.399572 | + | 0.916702i | \(0.630841\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3235.94 | −0.573340 | −0.286670 | − | 0.958029i | \(-0.592548\pi\) | ||||
−0.286670 | + | 0.958029i | \(0.592548\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1032.87 | −0.181284 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3336.90 | −0.574830 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −598.456 | −0.102143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1634.03 | 0.273820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −871.620 | −0.144739 | −0.0723694 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723694 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −885.079 | −0.144349 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3114.15 | 0.503378 | 0.251689 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251689 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10162.9 | −1.61393 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6038.72 | 0.950613 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7418.63 | 1.14770 | 0.573851 | − | 0.818960i | \(-0.305449\pi\) | ||||
0.573851 | + | 0.818960i | \(0.305449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6016.68 | 0.922824 | 0.461412 | − | 0.887186i | \(-0.347343\pi\) | ||||
0.461412 | + | 0.887186i | \(0.347343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5745.76 | 0.866334 | 0.433167 | − | 0.901314i | \(-0.357396\pi\) | ||||
0.433167 | + | 0.901314i | \(0.357396\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 226.069 | 0.0337986 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5133.25 | −0.754659 | −0.377329 | − | 0.926079i | \(-0.623158\pi\) | ||||
−0.377329 | + | 0.926079i | \(0.623158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4743.72 | −0.691605 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4746.66 | −0.680689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1679.48 | −0.238878 | −0.119439 | − | 0.992842i | \(-0.538110\pi\) | ||||
−0.119439 | + | 0.992842i | \(0.538110\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2757.23 | −0.385844 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4910.54 | −0.681658 | −0.340829 | − | 0.940125i | \(-0.610708\pi\) | ||||
−0.340829 | + | 0.940125i | \(0.610708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −741.543 | −0.101303 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9065.83 | −1.22871 | −0.614354 | − | 0.789030i | \(-0.710583\pi\) | ||||
−0.614354 | + | 0.789030i | \(0.710583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8273.28 | −1.10377 | −0.551886 | − | 0.833919i | \(-0.686092\pi\) | ||||
−0.551886 | + | 0.833919i | \(0.686092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1747.38 | 0.231311 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3008.56 | −0.392134 | −0.196067 | − | 0.980591i | \(-0.562817\pi\) | ||||
−0.196067 | + | 0.980591i | \(0.562817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11839.9 | 1.53138 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2484.59 | 0.316489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11495.3 | −1.45324 | −0.726618 | − | 0.687042i | \(-0.758909\pi\) | ||||
−0.726618 | + | 0.687042i | \(0.758909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10883.5 | 1.35535 | 0.677674 | − | 0.735362i | \(-0.262988\pi\) | ||||
0.677674 | + | 0.735362i | \(0.262988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7296.36 | −0.901880 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5006.60 | −0.609749 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6255.00 | −0.756210 | −0.378105 | − | 0.925763i | \(-0.623424\pi\) | ||||
−0.378105 | + | 0.925763i | \(0.623424\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2576.61 | 0.306990 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1773.18 | 0.209740 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10131.2 | −1.18125 | −0.590623 | − | 0.806947i | \(-0.701118\pi\) | ||||
−0.590623 | + | 0.806947i | \(0.701118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2585.12 | 0.299266 | 0.149633 | − | 0.988742i | \(-0.452191\pi\) | ||||
0.149633 | + | 0.988742i | \(0.452191\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1813.84 | 0.207022 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4889.24 | 0.554114 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5184.08 | 0.579370 | 0.289685 | − | 0.957122i | \(-0.406449\pi\) | ||||
0.289685 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4384.88 | 0.486660 | 0.243330 | − | 0.969944i | \(-0.421760\pi\) | ||||
0.243330 | + | 0.969944i | \(0.421760\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7505.40 | −0.821583 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8649.17 | −0.940324 | −0.470162 | − | 0.882580i | \(-0.655805\pi\) | ||||
−0.470162 | + | 0.882580i | \(0.655805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17120.9 | 1.83620 | 0.918100 | − | 0.396349i | \(-0.129723\pi\) | ||||
0.918100 | + | 0.396349i | \(0.129723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5965.98 | −0.635539 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2688.80 | 0.282611 | 0.141306 | − | 0.989966i | \(-0.454870\pi\) | ||||
0.141306 | + | 0.989966i | \(0.454870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13639.4 | 1.42407 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1254.52 | 0.129259 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1679.09 | 0.171870 | 0.0859350 | − | 0.996301i | \(-0.472612\pi\) | ||||
0.0859350 | + | 0.996301i | \(0.472612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2403.50 | 0.242825 | 0.121412 | − | 0.992602i | \(-0.461258\pi\) | ||||
0.121412 | + | 0.992602i | \(0.461258\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3048.56 | 0.306002 | 0.153001 | − | 0.988226i | \(-0.451106\pi\) | ||||
0.153001 | + | 0.988226i | \(0.451106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6256.23 | −0.619923 | −0.309961 | − | 0.950749i | \(-0.600316\pi\) | ||||
−0.309961 | + | 0.950749i | \(0.600316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1855.35 | 0.182670 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8308.16 | 0.807632 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1149.80 | −0.111067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4633.25 | 0.441960 | 0.220980 | − | 0.975278i | \(-0.429075\pi\) | ||||
0.220980 | + | 0.975278i | \(0.429075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3594.45 | −0.340733 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2043.99 | −0.191366 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9823.94 | 0.914097 | 0.457049 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457049 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2269.91 | 0.208634 | 0.104317 | − | 0.994544i | \(-0.466734\pi\) | ||||
0.104317 | + | 0.994544i | \(0.466734\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2247.52 | 0.205321 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −473.899 | −0.0427712 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4652.31 | 0.417367 | 0.208684 | − | 0.977983i | \(-0.433082\pi\) | ||||
0.208684 | + | 0.977983i | \(0.433082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13783.4 | −1.22181 | −0.610906 | − | 0.791703i | \(-0.709195\pi\) | ||||
−0.610906 | + | 0.791703i | \(0.709195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4452.13 | −0.392312 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 649.278 | 0.0565397 | 0.0282699 | − | 0.999600i | \(-0.491000\pi\) | ||||
0.0282699 | + | 0.999600i | \(0.491000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9950.22 | 0.861393 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7655.84 | 0.655062 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5198.13 | 0.442192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21010.9 | 1.76680 | 0.883402 | − | 0.468616i | \(-0.155247\pi\) | ||||
0.883402 | + | 0.468616i | \(0.155247\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16162.4 | −1.35130 | −0.675652 | − | 0.737221i | \(-0.736138\pi\) | ||||
−0.675652 | + | 0.737221i | \(0.736138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22114.3 | 1.82792 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14463.5 | 1.18875 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9792.30 | 0.795781 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4947.45 | −0.399807 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7773.64 | 0.621214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20812.9 | 1.65400 | 0.827002 | − | 0.562199i | \(-0.190044\pi\) | ||||
0.827002 | + | 0.562199i | \(0.190044\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1483.19 | −0.116574 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1000.02 | −0.0781675 | −0.0390838 | − | 0.999236i | \(-0.512444\pi\) | ||||
−0.0390838 | + | 0.999236i | \(0.512444\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1424.71 | −0.110154 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5208.33 | −0.400508 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4720.42 | 0.359085 | 0.179543 | − | 0.983750i | \(-0.442538\pi\) | ||||
0.179543 | + | 0.983750i | \(0.442538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5964.78 | 0.451312 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7863.47 | 0.588643 | 0.294321 | − | 0.955707i | \(-0.404906\pi\) | ||||
0.294321 | + | 0.955707i | \(0.404906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5180.73 | −0.385761 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22555.2 | −1.66180 | −0.830900 | − | 0.556422i | \(-0.812174\pi\) | ||||
−0.830900 | + | 0.556422i | \(0.812174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12656.8 | −0.927619 | −0.463810 | − | 0.885935i | \(-0.653518\pi\) | ||||
−0.463810 | + | 0.885935i | \(0.653518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4079.71 | 0.295888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11720.0 | 0.845601 | 0.422801 | − | 0.906223i | \(-0.361047\pi\) | ||||
0.422801 | + | 0.906223i | \(0.361047\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3717.05 | −0.265420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8771.24 | −0.623100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −949.761 | −0.0667817 | −0.0333908 | − | 0.999442i | \(-0.510631\pi\) | ||||
−0.0333908 | + | 0.999442i | \(0.510631\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14018.4 | −0.980674 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11575.2 | −0.801580 | −0.400790 | − | 0.916170i | \(-0.631264\pi\) | ||||
−0.400790 | + | 0.916170i | \(0.631264\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3802.28 | −0.261980 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27076.3 | 1.84692 | 0.923461 | − | 0.383693i | \(-0.125348\pi\) | ||||
0.923461 | + | 0.383693i | \(0.125348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19863.3 | 1.34815 | 0.674077 | − | 0.738661i | \(-0.264542\pi\) | ||||
0.674077 | + | 0.738661i | \(0.264542\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1096.27 | −0.0736689 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15270.4 | −1.02110 | −0.510550 | − | 0.859848i | \(-0.670558\pi\) | ||||
−0.510550 | + | 0.859848i | \(0.670558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3731.95 | 0.247101 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13256.0 | −0.873418 | −0.436709 | − | 0.899603i | \(-0.643856\pi\) | ||||
−0.436709 | + | 0.899603i | \(0.643856\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14348.4 | −0.936214 | −0.468107 | − | 0.883672i | \(-0.655064\pi\) | ||||
−0.468107 | + | 0.883672i | \(0.655064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24004.8 | −1.55870 | −0.779348 | − | 0.626591i | \(-0.784450\pi\) | ||||
−0.779348 | + | 0.626591i | \(0.784450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12506.2 | 0.804257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10894.3 | 0.690594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28832.3 | 1.81901 | 0.909505 | − | 0.415693i | \(-0.136461\pi\) | ||||
0.909505 | + | 0.415693i | \(0.136461\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5200.52 | −0.325002 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5581.02 | 0.347140 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25123.6 | −1.54808 | −0.774042 | − | 0.633134i | \(-0.781768\pi\) | ||||
−0.774042 | + | 0.633134i | \(0.781768\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31360.0 | −1.92335 | −0.961676 | − | 0.274187i | \(-0.911591\pi\) | ||||
−0.961676 | + | 0.274187i | \(0.911591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7235.97 | 0.439684 | 0.219842 | − | 0.975536i | \(-0.429446\pi\) | ||||
0.219842 | + | 0.975536i | \(0.429446\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8196.66 | 0.495758 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21525.6 | −1.28999 | −0.644995 | − | 0.764187i | \(-0.723141\pi\) | ||||
−0.644995 | + | 0.764187i | \(0.723141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1584.97 | −0.0945494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19452.1 | 1.14984 | 0.574920 | − | 0.818209i | \(-0.305033\pi\) | ||||
0.574920 | + | 0.818209i | \(0.305033\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −716.749 | −0.0421760 | −0.0210880 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210880 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2410.29 | 0.140552 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5055.14 | 0.293457 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15553.5 | 0.894840 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22459.7 | 1.28641 | 0.643207 | − | 0.765692i | \(-0.277603\pi\) | ||||
0.643207 | + | 0.765692i | \(0.277603\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1671.06 | −0.0948654 | −0.0474327 | − | 0.998874i | \(-0.515104\pi\) | ||||
−0.0474327 | + | 0.998874i | \(0.515104\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4284.73 | 0.242169 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22202.2 | 1.24384 | 0.621921 | − | 0.783080i | \(-0.286353\pi\) | ||||
0.621921 | + | 0.783080i | \(0.286353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8506.14 | −0.474457 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6297.24 | −0.348194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3871.94 | −0.213163 | −0.106582 | − | 0.994304i | \(-0.533991\pi\) | ||||
−0.106582 | + | 0.994304i | \(0.533991\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13781.8 | 0.752193 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29679.1 | −1.61288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21918.3 | −1.18095 | −0.590474 | − | 0.807057i | \(-0.701059\pi\) | ||||
−0.590474 | + | 0.807057i | \(0.701059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6905.96 | −0.370502 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9332.83 | 0.496460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22333.8 | 1.18302 | 0.591512 | − | 0.806296i | \(-0.298531\pi\) | ||||
0.591512 | + | 0.806296i | \(0.298531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 49739.7 | 2.61258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3990.85 | 0.208740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33133.5 | 1.71859 | 0.859297 | − | 0.511477i | \(-0.170901\pi\) | ||||
0.859297 | + | 0.511477i | \(0.170901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16048.6 | −0.828963 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 774.433 | 0.0396713 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11182.1 | 0.570457 | 0.285228 | − | 0.958460i | \(-0.407931\pi\) | ||||
0.285228 | + | 0.958460i | \(0.407931\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18078.5 | −0.914714 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32311.7 | −1.62819 | −0.814093 | − | 0.580735i | \(-0.802765\pi\) | ||||
−0.814093 | + | 0.580735i | \(0.802765\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5902.21 | 0.294994 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16348.4 | 0.813784 | 0.406892 | − | 0.913476i | \(-0.366613\pi\) | ||||
0.406892 | + | 0.913476i | \(0.366613\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13984.2 | −0.690486 | −0.345243 | − | 0.938513i | \(-0.612204\pi\) | ||||
−0.345243 | + | 0.938513i | \(0.612204\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1643.53 | 0.0808248 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10371.1 | 0.505945 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24688.8 | 1.19961 | 0.599805 | − | 0.800146i | \(-0.295245\pi\) | ||||
0.599805 | + | 0.800146i | \(0.295245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1581.40 | −0.0762293 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21515.4 | 1.03301 | 0.516507 | − | 0.856283i | \(-0.327232\pi\) | ||||
0.516507 | + | 0.856283i | \(0.327232\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19156.0 | 0.912487 | 0.456244 | − | 0.889855i | \(-0.349195\pi\) | ||||
0.456244 | + | 0.889855i | \(0.349195\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3109.14 | 0.147521 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5884.73 | 0.277034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39460.0 | −1.85041 | −0.925203 | − | 0.379473i | \(-0.876105\pi\) | ||||
−0.925203 | + | 0.379473i | \(0.876105\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2246.03 | 0.104507 | 0.0522537 | − | 0.998634i | \(-0.483360\pi\) | ||||
0.0522537 | + | 0.998634i | \(0.483360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7619.98 | 0.353184 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18813.8 | 0.865307 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1507.56 | −0.0690712 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17606.0 | 0.800488 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5801.11 | −0.262754 | −0.131377 | − | 0.991332i | \(-0.541940\pi\) | ||||
−0.131377 | + | 0.991332i | \(0.541940\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10860.2 | 0.488170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11166.5 | 0.500045 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40399.1 | 1.79549 | 0.897747 | − | 0.440512i | \(-0.145203\pi\) | ||||
0.897747 | + | 0.440512i | \(0.145203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11311.1 | −0.500821 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31653.4 | 1.39106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8552.14 | −0.374439 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30986.8 | −1.34665 | −0.673324 | − | 0.739348i | \(-0.735134\pi\) | ||||
−0.673324 | + | 0.739348i | \(0.735134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8658.08 | 0.374878 | 0.187439 | − | 0.982276i | \(-0.439981\pi\) | ||||
0.187439 | + | 0.982276i | \(0.439981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9943.25 | −0.427358 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11460.0 | 0.490742 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30463.1 | −1.29497 | −0.647484 | − | 0.762079i | \(-0.724179\pi\) | ||||
−0.647484 | + | 0.762079i | \(0.724179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10357.9 | −0.438704 | −0.219352 | − | 0.975646i | \(-0.570394\pi\) | ||||
−0.219352 | + | 0.975646i | \(0.570394\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30108.4 | 1.26599 | 0.632993 | − | 0.774157i | \(-0.281826\pi\) | ||||
0.632993 | + | 0.774157i | \(0.281826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6248.62 | 0.261789 | 0.130895 | − | 0.991396i | \(-0.458215\pi\) | ||||
0.130895 | + | 0.991396i | \(0.458215\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16915.3 | −0.703579 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13164.7 | −0.545610 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10579.6 | −0.435339 | −0.217669 | − | 0.976023i | \(-0.569845\pi\) | ||||
−0.217669 | + | 0.976023i | \(0.569845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23429.4 | −0.960655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8119.80 | −0.330568 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2298.07 | 0.0932260 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24503.6 | 0.987041 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20228.7 | −0.811980 | −0.405990 | − | 0.913878i | \(-0.633073\pi\) | ||||
−0.405990 | + | 0.913878i | \(0.633073\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43333.4 | −1.72724 | −0.863618 | − | 0.504146i | \(-0.831807\pi\) | ||||
−0.863618 | + | 0.504146i | \(0.831807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16584.0 | 0.658718 | 0.329359 | − | 0.944205i | \(-0.393167\pi\) | ||||
0.329359 | + | 0.944205i | \(0.393167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3281.90 | 0.129452 | 0.0647261 | − | 0.997903i | \(-0.479383\pi\) | ||||
0.0647261 | + | 0.997903i | \(0.479383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8416.15 | −0.330818 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16568.6 | −0.646781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4237.45 | 0.164846 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1310.16 | −0.0506189 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18214.8 | 0.701333 | 0.350666 | − | 0.936500i | \(-0.385955\pi\) | ||||
0.350666 | + | 0.936500i | \(0.385955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29408.8 | 1.12464 | 0.562320 | − | 0.826920i | \(-0.309909\pi\) | ||||
0.562320 | + | 0.826920i | \(0.309909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7442.63 | −0.283652 | −0.141826 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141826 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20306.7 | 0.768696 | 0.384348 | − | 0.923188i | \(-0.374426\pi\) | ||||
0.384348 | + | 0.923188i | \(0.374426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10901.6 | 0.411281 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7170.14 | 0.268690 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11708.1 | −0.437271 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9441.86 | 0.350282 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19086.1 | 0.705716 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2348.45 | 0.0862597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6400.36 | 0.234311 | 0.117156 | − | 0.993114i | \(-0.462622\pi\) | ||||
0.117156 | + | 0.993114i | \(0.462622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9303.31 | −0.338345 | −0.169173 | − | 0.985586i | \(-0.554110\pi\) | ||||
−0.169173 | + | 0.985586i | \(0.554110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11824.6 | −0.428627 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3322.51 | 0.119650 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15110.9 | 0.542397 | 0.271198 | − | 0.962523i | \(-0.412580\pi\) | ||||
0.271198 | + | 0.962523i | \(0.412580\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1082.34 | −0.0385976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3753.87 | 0.133434 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48972.2 | 1.72952 | 0.864761 | − | 0.502184i | \(-0.167470\pi\) | ||||
0.864761 | + | 0.502184i | \(0.167470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10722.7 | 0.377469 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12095.7 | −0.423072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41808.1 | 1.45764 | 0.728821 | − | 0.684705i | \(-0.240069\pi\) | ||||
0.728821 | + | 0.684705i | \(0.240069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54568.7 | 1.89042 | 0.945212 | − | 0.326456i | \(-0.105855\pi\) | ||||
0.945212 | + | 0.326456i | \(0.105855\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −66754.7 | −2.30523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38799.9 | 1.33139 | 0.665695 | − | 0.746224i | \(-0.268135\pi\) | ||||
0.665695 | + | 0.746224i | \(0.268135\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22725.3 | 0.777340 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38007.3 | −1.29190 | −0.645948 | − | 0.763382i | \(-0.723538\pi\) | ||||
−0.645948 | + | 0.763382i | \(0.723538\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6383.59 | −0.216302 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17831.1 | 0.600412 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63111.5 | 2.11848 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5534.38 | −0.184620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42906.7 | 1.42687 | 0.713437 | − | 0.700719i | \(-0.247137\pi\) | ||||
0.713437 | + | 0.700719i | \(0.247137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38855.2 | 1.28416 | 0.642082 | − | 0.766636i | \(-0.278071\pi\) | ||||
0.642082 | + | 0.766636i | \(0.278071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28890.3 | −0.951880 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48239.0 | −1.57963 | −0.789817 | − | 0.613342i | \(-0.789825\pi\) | ||||
−0.789817 | + | 0.613342i | \(0.789825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39784.6 | 1.29880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43167.5 | 1.40064 | 0.700320 | − | 0.713829i | \(-0.253041\pi\) | ||||
0.700320 | + | 0.713829i | \(0.253041\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9726.16 | −0.314621 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40662.3 | −1.30737 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57081.7 | 1.82973 | 0.914863 | − | 0.403764i | \(-0.132298\pi\) | ||||
0.914863 | + | 0.403764i | \(0.132298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2134.49 | −0.0680080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47673.1 | 1.51436 | 0.757182 | − | 0.653203i | \(-0.226575\pi\) | ||||
0.757182 | + | 0.653203i | \(0.226575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1620.4.a.j.1.2 | yes | 6 | |
3.2 | odd | 2 | 1620.4.a.i.1.2 | ✓ | 6 | ||
9.2 | odd | 6 | 1620.4.i.x.1081.5 | 12 | |||
9.4 | even | 3 | 1620.4.i.w.541.5 | 12 | |||
9.5 | odd | 6 | 1620.4.i.x.541.5 | 12 | |||
9.7 | even | 3 | 1620.4.i.w.1081.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.i.1.2 | ✓ | 6 | 3.2 | odd | 2 | ||
1620.4.a.j.1.2 | yes | 6 | 1.1 | even | 1 | trivial | |
1620.4.i.w.541.5 | 12 | 9.4 | even | 3 | |||
1620.4.i.w.1081.5 | 12 | 9.7 | even | 3 | |||
1620.4.i.x.541.5 | 12 | 9.5 | odd | 6 | |||
1620.4.i.x.1081.5 | 12 | 9.2 | odd | 6 |