Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.20087896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 21x^{3} + 5x^{2} + 84x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.27399\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.55148 | 1.34233 | 0.671167 | − | 0.741306i | \(-0.265793\pi\) | ||||
0.671167 | + | 0.741306i | \(0.265793\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.79304 | 0.842134 | 0.421067 | − | 0.907030i | \(-0.361656\pi\) | ||||
0.421067 | + | 0.907030i | \(0.361656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73151 | 1.03493 | 0.517467 | − | 0.855703i | \(-0.326875\pi\) | ||||
0.517467 | + | 0.855703i | \(0.326875\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.83097 | −1.89929 | −0.949644 | − | 0.313330i | \(-0.898555\pi\) | ||||
−0.949644 | + | 0.313330i | \(0.898555\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.27949 | −1.44061 | −0.720307 | − | 0.693656i | \(-0.755999\pi\) | ||||
−0.720307 | + | 0.693656i | \(0.755999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.55148 | 0.774997 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.75844 | 0.512229 | 0.256115 | − | 0.966646i | \(-0.417558\pi\) | ||||
0.256115 | + | 0.966646i | \(0.417558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.48995 | 0.447208 | 0.223604 | − | 0.974680i | \(-0.428218\pi\) | ||||
0.223604 | + | 0.974680i | \(0.428218\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.79304 | 0.486206 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.55148 | 0.600310 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.55148 | −0.255062 | −0.127531 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127531 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.73151 | 0.597519 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.78954 | 0.904174 | 0.452087 | − | 0.891974i | \(-0.350680\pi\) | ||||
0.452087 | + | 0.891974i | \(0.350680\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.54798 | 0.693560 | 0.346780 | − | 0.937946i | \(-0.387275\pi\) | ||||
0.346780 | + | 0.937946i | \(0.387275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.27949 | 0.915957 | 0.457979 | − | 0.888963i | \(-0.348574\pi\) | ||||
0.457979 | + | 0.888963i | \(0.348574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.61301 | 0.801859 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.83097 | −1.09655 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.89250 | 1.22148 | 0.610739 | − | 0.791832i | \(-0.290872\pi\) | ||||
0.610739 | + | 0.791832i | \(0.290872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.79304 | 0.376614 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.27949 | −0.831738 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.31342 | −0.431371 | −0.215685 | − | 0.976463i | \(-0.569199\pi\) | ||||
−0.215685 | + | 0.976463i | \(0.569199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2180 | 1.43631 | 0.718156 | − | 0.695882i | \(-0.244986\pi\) | ||||
0.718156 | + | 0.695882i | \(0.244986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.55148 | 0.447444 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.73151 | 0.462837 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.52105 | −0.674503 | −0.337252 | − | 0.941415i | \(-0.609497\pi\) | ||||
−0.337252 | + | 0.941415i | \(0.609497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.34452 | −0.752956 | −0.376478 | − | 0.926426i | \(-0.622865\pi\) | ||||
−0.376478 | + | 0.926426i | \(0.622865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3824 | 1.80038 | 0.900190 | − | 0.435498i | \(-0.143428\pi\) | ||||
0.900190 | + | 0.435498i | \(0.143428\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.91943 | 1.13042 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.62051 | 1.08239 | 0.541196 | − | 0.840897i | \(-0.317972\pi\) | ||||
0.541196 | + | 0.840897i | \(0.317972\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.83097 | −0.640032 | −0.320016 | − | 0.947412i | \(-0.603688\pi\) | ||||
−0.320016 | + | 0.947412i | \(0.603688\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.83097 | −0.849388 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.75844 | 0.295736 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.390487 | 0.0413915 | 0.0206958 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206958 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.2524 | 1.38923 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.48995 | 0.258195 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.27949 | −0.644262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.961896 | 0.0976657 | 0.0488329 | − | 0.998807i | \(-0.484450\pi\) | ||||
0.0488329 | + | 0.998807i | \(0.484450\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.79304 | 0.280711 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9035 | −1.68196 | −0.840980 | − | 0.541066i | \(-0.818021\pi\) | ||||
−0.840980 | + | 0.541066i | \(0.818021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.04143 | 0.595280 | 0.297640 | − | 0.954678i | \(-0.403801\pi\) | ||||
0.297640 | + | 0.954678i | \(0.403801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.55148 | 0.346589 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.3141 | −1.19045 | −0.595224 | − | 0.803560i | \(-0.702937\pi\) | ||||
−0.595224 | + | 0.803560i | \(0.702937\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8579 | 1.42313 | 0.711564 | − | 0.702621i | \(-0.247987\pi\) | ||||
0.711564 | + | 0.702621i | \(0.247987\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.55148 | −0.147260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.21113 | 0.302077 | 0.151039 | − | 0.988528i | \(-0.451738\pi\) | ||||
0.151039 | + | 0.988528i | \(0.451738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.73151 | 0.344978 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.8115 | −2.54948 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.19892 | −0.290811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.78954 | 0.522025 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.145425 | −0.0129043 | −0.00645217 | − | 0.999979i | \(-0.502054\pi\) | ||||
−0.00645217 | + | 0.999979i | \(0.502054\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.54798 | 0.400427 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.3015 | −1.93378 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.16450 | −0.526668 | −0.263334 | − | 0.964705i | \(-0.584822\pi\) | ||||
−0.263334 | + | 0.964705i | \(0.584822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.0690 | −1.19332 | −0.596660 | − | 0.802494i | \(-0.703506\pi\) | ||||
−0.596660 | + | 0.802494i | \(0.703506\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.27949 | 0.528828 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.4223 | 0.871553 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.75844 | 0.229076 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.61301 | 0.462954 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7964 | 1.13024 | 0.565121 | − | 0.825008i | \(-0.308829\pi\) | ||||
0.565121 | + | 0.825008i | \(0.308829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.1989 | −1.31825 | −0.659125 | − | 0.752034i | \(-0.729073\pi\) | ||||
−0.659125 | + | 0.752034i | \(0.729073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.83097 | −0.633096 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.48995 | 0.199997 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1105 | −1.12614 | −0.563068 | − | 0.826410i | \(-0.690379\pi\) | ||||
−0.563068 | + | 0.826410i | \(0.690379\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.89250 | 0.705221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.55148 | 0.279896 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2480 | −1.66427 | −0.832137 | − | 0.554571i | \(-0.812882\pi\) | ||||
−0.832137 | + | 0.554571i | \(0.812882\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.79304 | 0.217438 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.3895 | −1.50040 | −0.750200 | − | 0.661211i | \(-0.770043\pi\) | ||||
−0.750200 | + | 0.661211i | \(0.770043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.924149 | 0.0710884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.27949 | −0.480204 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.1030 | −0.996200 | −0.498100 | − | 0.867120i | \(-0.665969\pi\) | ||||
−0.498100 | + | 0.867120i | \(0.665969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.55148 | 0.268467 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.31342 | −0.249052 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.0759 | 1.05208 | 0.526039 | − | 0.850460i | \(-0.323676\pi\) | ||||
0.526039 | + | 0.850460i | \(0.323676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1374 | 1.57113 | 0.785565 | − | 0.618779i | \(-0.212373\pi\) | ||||
0.785565 | + | 0.618779i | \(0.212373\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2180 | 0.829255 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.55148 | −0.114067 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.8722 | −1.59945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.55148 | 0.258332 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.81647 | −0.203793 | −0.101896 | − | 0.994795i | \(-0.532491\pi\) | ||||
−0.101896 | + | 0.994795i | \(0.532491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4560 | 1.11255 | 0.556274 | − | 0.830999i | \(-0.312230\pi\) | ||||
0.556274 | + | 0.830999i | \(0.312230\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.73151 | 0.267219 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.7311 | 1.83327 | 0.916634 | − | 0.399728i | \(-0.130895\pi\) | ||||
0.916634 | + | 0.399728i | \(0.130895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.95857 | −0.422392 | −0.211196 | − | 0.977444i | \(-0.567736\pi\) | ||||
−0.211196 | + | 0.977444i | \(0.567736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.52105 | −0.389425 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.79654 | 0.687583 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.78954 | 0.404359 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.5389 | −1.21319 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.06903 | 0.417809 | 0.208905 | − | 0.977936i | \(-0.433010\pi\) | ||||
0.208905 | + | 0.977936i | \(0.433010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.34452 | −0.434719 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.54798 | 0.310170 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.84300 | 0.600302 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.3824 | 1.03945 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.2213 | −1.96564 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.57509 | 0.105476 | 0.0527379 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527379 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.7034 | 1.44050 | 0.720251 | − | 0.693713i | \(-0.244026\pi\) | ||||
0.720251 | + | 0.693713i | \(0.244026\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2136 | 1.53400 | 0.766999 | − | 0.641649i | \(-0.221749\pi\) | ||||
0.766999 | + | 0.641649i | \(0.221749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.91943 | 0.652651 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.1989 | −1.19225 | −0.596125 | − | 0.802891i | \(-0.703294\pi\) | ||||
−0.596125 | + | 0.802891i | \(0.703294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.27949 | 0.409629 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.62051 | 0.624919 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9236 | −1.41812 | −0.709060 | − | 0.705148i | \(-0.750880\pi\) | ||||
−0.709060 | + | 0.705148i | \(0.750880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7964 | 1.14636 | 0.573182 | − | 0.819428i | \(-0.305709\pi\) | ||||
0.573182 | + | 0.819428i | \(0.305709\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.61301 | 0.358602 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.4320 | −1.49094 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.83097 | −0.369523 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.2785 | 1.46932 | 0.734661 | − | 0.678434i | \(-0.237341\pi\) | ||||
0.734661 | + | 0.678434i | \(0.237341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.79304 | 0.175597 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.83097 | −0.490394 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5884 | 1.59616 | 0.798079 | − | 0.602552i | \(-0.205850\pi\) | ||||
0.798079 | + | 0.602552i | \(0.205850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.51005 | −0.342378 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.75844 | 0.170743 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.57051 | 0.528481 | 0.264240 | − | 0.964457i | \(-0.414879\pi\) | ||||
0.264240 | + | 0.964457i | \(0.414879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.89250 | 0.546262 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.390487 | 0.0238974 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.4405 | −0.819481 | −0.409740 | − | 0.912202i | \(-0.634381\pi\) | ||||
−0.409740 | + | 0.912202i | \(0.634381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.38699 | −0.205745 | −0.102872 | − | 0.994695i | \(-0.532803\pi\) | ||||
−0.102872 | + | 0.994695i | \(0.532803\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.2524 | 0.802070 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.79304 | 0.168427 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7469 | −1.12639 | −0.563196 | − | 0.826323i | \(-0.690428\pi\) | ||||
−0.563196 | + | 0.826323i | \(0.690428\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.48995 | 0.149069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.21396 | −0.311039 | −0.155519 | − | 0.987833i | \(-0.549705\pi\) | ||||
−0.155519 | + | 0.987833i | \(0.549705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9771 | 1.12807 | 0.564035 | − | 0.825751i | \(-0.309248\pi\) | ||||
0.564035 | + | 0.825751i | \(0.309248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.27949 | −0.371965 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.5614 | 1.21370 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.3240 | 2.60730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.961896 | 0.0563873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.3976 | −1.60059 | −0.800293 | − | 0.599609i | \(-0.795323\pi\) | ||||
−0.800293 | + | 0.599609i | \(0.795323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.31342 | −0.192915 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.79304 | 0.162069 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.73151 | 0.215799 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.1521 | 0.930989 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.9035 | −0.971080 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.2180 | 0.642338 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.18353 | −0.0675475 | −0.0337738 | − | 0.999430i | \(-0.510753\pi\) | ||||
−0.0337738 | + | 0.999430i | \(0.510753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.04143 | 0.343685 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5770 | −1.05340 | −0.526702 | − | 0.850050i | \(-0.676572\pi\) | ||||
−0.526702 | + | 0.850050i | \(0.676572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.50094 | −0.480502 | −0.240251 | − | 0.970711i | \(-0.577230\pi\) | ||||
−0.240251 | + | 0.970711i | \(0.577230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.55148 | 0.200103 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5884 | 1.21252 | 0.606262 | − | 0.795265i | \(-0.292668\pi\) | ||||
0.606262 | + | 0.795265i | \(0.292668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.70443 | 0.431366 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3141 | −0.687305 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.1745 | 2.73614 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.73151 | 0.206987 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.8579 | 0.821644 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.3015 | 1.22952 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0288 | −1.32074 | −0.660372 | − | 0.750939i | \(-0.729601\pi\) | ||||
−0.660372 | + | 0.750939i | \(0.729601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.55148 | −0.0850206 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.52105 | −0.301647 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.7960 | −1.07836 | −0.539178 | − | 0.842192i | \(-0.681265\pi\) | ||||
−0.539178 | + | 0.842192i | \(0.681265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.21113 | 0.174405 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.95452 | 0.376609 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.92585 | −0.265971 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.52388 | −0.189172 | −0.0945859 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945859 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.10979 | 0.487636 | 0.243818 | − | 0.969821i | \(-0.421600\pi\) | ||||
0.243818 | + | 0.969821i | \(0.421600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.73151 | 0.199173 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.7224 | −1.31584 | −0.657920 | − | 0.753088i | \(-0.728564\pi\) | ||||
−0.657920 | + | 0.753088i | \(0.728564\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.34452 | −0.336732 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.8115 | −1.47194 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.3895 | −0.601112 | −0.300556 | − | 0.953764i | \(-0.597172\pi\) | ||||
−0.300556 | + | 0.953764i | \(0.597172\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.4320 | 1.07537 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.19892 | −0.167900 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3824 | 0.805154 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1306 | −0.581011 | −0.290505 | − | 0.956873i | \(-0.593823\pi\) | ||||
−0.290505 | + | 0.956873i | \(0.593823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.78954 | 0.301391 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.5815 | 1.63963 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.51755 | 0.441022 | 0.220511 | − | 0.975385i | \(-0.429228\pi\) | ||||
0.220511 | + | 0.975385i | \(0.429228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2931 | 0.530123 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.1320 | 1.08548 | 0.542738 | − | 0.839902i | \(-0.317388\pi\) | ||||
0.542738 | + | 0.839902i | \(0.317388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.145425 | −0.00745033 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.37562 | −0.479072 | −0.239536 | − | 0.970887i | \(-0.576995\pi\) | ||||
−0.239536 | + | 0.970887i | \(0.576995\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.91943 | 0.505541 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.54798 | 0.231187 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6352 | −0.843437 | −0.421719 | − | 0.906727i | \(-0.638573\pi\) | ||||
−0.421719 | + | 0.906727i | \(0.638573\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.83097 | −0.396029 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.62051 | 0.484060 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9261 | 1.20081 | 0.600407 | − | 0.799694i | \(-0.295005\pi\) | ||||
0.600407 | + | 0.799694i | \(0.295005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.3015 | −1.11647 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.4457 | −0.621508 | −0.310754 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310754 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.29125 | 0.462830 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.33335 | −0.214796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0419 | 1.33714 | 0.668568 | − | 0.743651i | \(-0.266907\pi\) | ||||
0.668568 | + | 0.743651i | \(0.266907\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.16450 | −0.304072 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.7676 | −0.579043 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.83097 | −0.286231 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.0690 | −0.688963 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.0949 | −0.493169 | −0.246585 | − | 0.969121i | \(-0.579308\pi\) | ||||
−0.246585 | + | 0.969121i | \(0.579308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.5268 | −1.39031 | −0.695156 | − | 0.718858i | \(-0.744665\pi\) | ||||
−0.695156 | + | 0.718858i | \(0.744665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.27949 | 0.305319 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.83097 | −0.379858 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.8403 | 1.92801 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4223 | 0.503191 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.6081 | −1.04082 | −0.520412 | − | 0.853915i | \(-0.674222\pi\) | ||||
−0.520412 | + | 0.853915i | \(0.674222\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.21009 | −0.394552 | −0.197276 | − | 0.980348i | \(-0.563209\pi\) | ||||
−0.197276 | + | 0.980348i | \(0.563209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.75844 | 0.132257 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.27949 | −0.300389 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.4429 | −1.16660 | −0.583298 | − | 0.812258i | \(-0.698238\pi\) | ||||
−0.583298 | + | 0.812258i | \(0.698238\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.61301 | 0.267286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.5074 | −1.54447 | −0.772237 | − | 0.635335i | \(-0.780862\pi\) | ||||
−0.772237 | + | 0.635335i | \(0.780862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.390487 | 0.0185109 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.7964 | 0.652546 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.5635 | −1.15922 | −0.579612 | − | 0.814893i | \(-0.696796\pi\) | ||||
−0.579612 | + | 0.814893i | \(0.696796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.1704 | 0.761436 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.1989 | −0.761092 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.2524 | 0.621281 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.6798 | −1.38836 | −0.694180 | − | 0.719801i | \(-0.744233\pi\) | ||||
−0.694180 | + | 0.719801i | \(0.744233\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.83097 | −0.365518 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.2239 | −1.59397 | −0.796983 | − | 0.604001i | \(-0.793572\pi\) | ||||
−0.796983 | + | 0.604001i | \(0.793572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8074 | 1.29232 | 0.646159 | − | 0.763203i | \(-0.276374\pi\) | ||||
0.646159 | + | 0.763203i | \(0.276374\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.48995 | 0.115469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.3207 | −1.03288 | −0.516440 | − | 0.856323i | \(-0.672743\pi\) | ||||
−0.516440 | + | 0.856323i | \(0.672743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6079 | −0.905408 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1105 | −0.650175 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.7027 | 0.584070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.27949 | −0.288123 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.89250 | 0.407160 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 32.7535 | 1.49655 | 0.748274 | − | 0.663390i | \(-0.230883\pi\) | ||||
0.748274 | + | 0.663390i | \(0.230883\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.78936 | −0.263972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.55148 | 0.161598 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.961896 | 0.0436774 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9996 | 1.17816 | 0.589078 | − | 0.808076i | \(-0.299491\pi\) | ||||
0.589078 | + | 0.808076i | \(0.299491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.2480 | −0.960869 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.67348 | 0.346299 | 0.173150 | − | 0.984896i | \(-0.444606\pi\) | ||||
0.173150 | + | 0.984896i | \(0.444606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.6012 | −0.972871 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.79304 | 0.125538 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5324 | −1.01072 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.2951 | −0.684701 | −0.342350 | − | 0.939572i | \(-0.611223\pi\) | ||||
−0.342350 | + | 0.939572i | \(0.611223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.3895 | −0.866257 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.79654 | 0.436806 | 0.218403 | − | 0.975859i | \(-0.429915\pi\) | ||||
0.218403 | + | 0.975859i | \(0.429915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9035 | −0.752196 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.924149 | 0.0410429 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.25713 | 0.277342 | 0.138671 | − | 0.990338i | \(-0.455717\pi\) | ||||
0.138671 | + | 0.990338i | \(0.455717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.6305 | 2.41671 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.27949 | −0.277246 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.04143 | 0.266217 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.5389 | 0.771358 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.1030 | −0.575156 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.72384 | −0.382198 | −0.191099 | − | 0.981571i | \(-0.561205\pi\) | ||||
−0.191099 | + | 0.981571i | \(0.561205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.66404 | 0.378852 | 0.189426 | − | 0.981895i | \(-0.439337\pi\) | ||||
0.189426 | + | 0.981895i | \(0.439337\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.55148 | 0.154999 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4987 | −0.849376 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.31342 | −0.143790 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.6037 | 0.935761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3141 | −0.532384 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.0759 | 0.607418 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.6774 | 0.675273 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.5660 | −1.57209 | −0.786047 | − | 0.618167i | \(-0.787876\pi\) | ||||
−0.786047 | + | 0.618167i | \(0.787876\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1374 | 0.907092 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.8579 | 0.636442 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.827834 | 0.0353956 | 0.0176978 | − | 0.999843i | \(-0.494366\pi\) | ||||
0.0176978 | + | 0.999843i | \(0.494366\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.2180 | 0.478771 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.3216 | −0.737924 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.1670 | 1.45293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.55148 | −0.0658567 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.125533 | 0.00531902 | 0.00265951 | − | 0.999996i | \(-0.499153\pi\) | ||||
0.00265951 | + | 0.999996i | \(0.499153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.9708 | 0.717789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.8722 | −0.923446 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.3207 | 1.61503 | 0.807513 | − | 0.589849i | \(-0.200813\pi\) | ||||
0.807513 | + | 0.589849i | \(0.200813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.21113 | 0.135093 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.55148 | 0.149148 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.8715 | −1.21036 | −0.605179 | − | 0.796090i | \(-0.706898\pi\) | ||||
−0.605179 | + | 0.796090i | \(0.706898\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.0514 | −0.629881 | −0.314940 | − | 0.949111i | \(-0.601985\pi\) | ||||
−0.314940 | + | 0.949111i | \(0.601985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.81647 | −0.117660 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.0561 | −0.876577 | −0.438288 | − | 0.898834i | \(-0.644415\pi\) | ||||
−0.438288 | + | 0.898834i | \(0.644415\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.4560 | 0.642330 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.7086 | −0.859136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.8371 | 1.02865 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.73151 | 0.154279 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −22.2751 | −0.919393 | −0.459696 | − | 0.888076i | \(-0.652042\pi\) | ||||
−0.459696 | + | 0.888076i | \(0.652042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6356 | −0.644253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.7311 | 1.05844 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.45642 | −0.347263 | −0.173632 | − | 0.984811i | \(-0.555550\pi\) | ||||
−0.173632 | + | 0.984811i | \(0.555550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.8115 | −1.14016 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.95857 | −0.243868 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.0040 | 0.408752 | 0.204376 | − | 0.978892i | \(-0.434483\pi\) | ||||
0.204376 | + | 0.978892i | \(0.434483\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8119 | 0.604191 | 0.302096 | − | 0.953278i | \(-0.402314\pi\) | ||||
0.302096 | + | 0.953278i | \(0.402314\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.52105 | −0.224834 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.19892 | −0.130055 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.8883 | −0.441944 | −0.220972 | − | 0.975280i | \(-0.570923\pi\) | ||||
−0.220972 | + | 0.975280i | \(0.570923\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.79654 | 0.396976 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.4320 | 0.947955 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.35238 | 0.135401 | 0.0677007 | − | 0.997706i | \(-0.478434\pi\) | ||||
0.0677007 | + | 0.997706i | \(0.478434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.78954 | 0.233457 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8848 | −0.881050 | −0.440525 | − | 0.897740i | \(-0.645208\pi\) | ||||
−0.440525 | + | 0.897740i | \(0.645208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0762 | 0.404997 | 0.202498 | − | 0.979283i | \(-0.435094\pi\) | ||||
0.202498 | + | 0.979283i | \(0.435094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.38681 | 0.0555613 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.5389 | −0.700435 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.1496 | 0.484436 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.50485 | −0.258954 | −0.129477 | − | 0.991582i | \(-0.541330\pi\) | ||||
−0.129477 | + | 0.991582i | \(0.541330\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.06903 | 0.241222 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.145425 | −0.00577100 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.9450 | 0.829871 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.34452 | −0.250985 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.60723 | −0.0634816 | −0.0317408 | − | 0.999496i | \(-0.510105\pi\) | ||||
−0.0317408 | + | 0.999496i | \(0.510105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.73605 | 0.305080 | 0.152540 | − | 0.988297i | \(-0.451255\pi\) | ||||
0.152540 | + | 0.988297i | \(0.451255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.54798 | 0.179076 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.89232 | 0.349593 | 0.174797 | − | 0.984605i | \(-0.444073\pi\) | ||||
0.174797 | + | 0.984605i | \(0.444073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.25452 | −0.363272 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.84300 | 0.346584 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.2055 | 1.22117 | 0.610583 | − | 0.791952i | \(-0.290935\pi\) | ||||
0.610583 | + | 0.791952i | \(0.290935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.3824 | 0.600126 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.7051 | 0.845509 | 0.422755 | − | 0.906244i | \(-0.361063\pi\) | ||||
0.422755 | + | 0.906244i | \(0.361063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0564 | 1.16906 | 0.584529 | − | 0.811372i | \(-0.301279\pi\) | ||||
0.584529 | + | 0.811372i | \(0.301279\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.2213 | −1.13486 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.3015 | −0.864814 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.75844 | 0.106807 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.57509 | 0.0608965 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.3322 | 1.20957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.2795 | 0.627528 | 0.313764 | − | 0.949501i | \(-0.398410\pi\) | ||||
0.313764 | + | 0.949501i | \(0.398410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.70723 | −0.180914 | −0.0904568 | − | 0.995900i | \(-0.528833\pi\) | ||||
−0.0904568 | + | 0.995900i | \(0.528833\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.41616 | 0.131100 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.7034 | 0.831675 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.82536 | −0.375957 | −0.187978 | − | 0.982173i | \(-0.560193\pi\) | ||||
−0.187978 | + | 0.982173i | \(0.560193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.16450 | −0.235533 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.2136 | 0.885654 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.1824 | 1.26415 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.1718 | 1.64233 | 0.821167 | − | 0.570689i | \(-0.193324\pi\) | ||||
0.821167 | + | 0.570689i | \(0.193324\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.91943 | 0.376808 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0690 | −0.533669 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.3377 | −1.71729 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.1989 | −0.688346 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.44539 | −0.0545915 | −0.0272957 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272957 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.74250 | 0.367445 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.27949 | 0.236499 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60.0324 | −2.25775 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.9697 | −1.08798 | −0.543991 | − | 0.839091i | \(-0.683087\pi\) | ||||
−0.543991 | + | 0.839091i | \(0.683087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.62051 | 0.360797 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.48995 | 0.0932492 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4223 | 0.389770 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.9236 | −0.818752 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.4742 | −1.58402 | −0.792011 | − | 0.610507i | \(-0.790966\pi\) | ||||
−0.792011 | + | 0.610507i | \(0.790966\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.4560 | 0.799064 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.7964 | 0.661854 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.75844 | 0.102446 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.10857 | 0.115291 | 0.0576453 | − | 0.998337i | \(-0.481641\pi\) | ||||
0.0576453 | + | 0.998337i | \(0.481641\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.6151 | −1.31727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.20453 | 0.229170 | 0.114585 | − | 0.993413i | \(-0.463446\pi\) | ||||
0.114585 | + | 0.993413i | \(0.463446\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.61301 | 0.207039 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.4205 | −0.568022 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5010 | 0.790926 | 0.395463 | − | 0.918482i | \(-0.370584\pi\) | ||||
0.395463 | + | 0.918482i | \(0.370584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.4320 | −0.860794 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4469 | 0.933558 | 0.466779 | − | 0.884374i | \(-0.345414\pi\) | ||||
0.466779 | + | 0.884374i | \(0.345414\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.7964 | 0.505460 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.83097 | −0.213344 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −43.7332 | −1.59798 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.9066 | −1.82112 | −0.910560 | − | 0.413378i | \(-0.864349\pi\) | ||||
−0.910560 | + | 0.413378i | \(0.864349\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.2785 | 0.848314 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.1989 | −0.589539 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.8486 | 1.15756 | 0.578778 | − | 0.815485i | \(-0.303530\pi\) | ||||
0.578778 | + | 0.815485i | \(0.303530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.79304 | 0.101381 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.63541 | 0.276783 | 0.138392 | − | 0.990378i | \(-0.455807\pi\) | ||||
0.138392 | + | 0.990378i | \(0.455807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 52.7675 | 1.91031 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.83097 | −0.283129 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.3641 | −0.446440 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.36880 | −0.121482 | −0.0607410 | − | 0.998154i | \(-0.519346\pi\) | ||||
−0.0607410 | + | 0.998154i | \(0.519346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.5884 | 0.921543 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.77800 | 0.207820 | 0.103910 | − | 0.994587i | \(-0.466865\pi\) | ||||
0.103910 | + | 0.994587i | \(0.466865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.48995 | 0.0894415 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.51005 | −0.197672 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.3553 | −1.30257 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7205 | −0.634090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.75844 | 0.0985786 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.1105 | −0.503624 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.46988 | −0.230626 | −0.115313 | − | 0.993329i | \(-0.536787\pi\) | ||||
−0.115313 | + | 0.993329i | \(0.536787\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.57051 | 0.305118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4043 | 0.405489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 41.8599 | 1.48649 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.89250 | 0.315385 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9636 | −0.777990 | −0.388995 | − | 0.921240i | \(-0.627178\pi\) | ||||
−0.388995 | + | 0.921240i | \(0.627178\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.1745 | −1.73967 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.390487 | 0.0137972 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.9638 | 1.51616 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.55148 | 0.125173 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.4405 | −0.473127 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.7222 | −1.50203 | −0.751017 | − | 0.660283i | \(-0.770436\pi\) | ||||
−0.751017 | + | 0.660283i | \(0.770436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2347 | 1.06169 | 0.530843 | − | 0.847470i | \(-0.321876\pi\) | ||||
0.530843 | + | 0.847470i | \(0.321876\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.38699 | −0.118787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.2480 | −0.744286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.5590 | −0.999152 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.2524 | 0.463076 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.3260 | −0.639581 | −0.319791 | − | 0.947488i | \(-0.603613\pi\) | ||||
−0.319791 | + | 0.947488i | \(0.603613\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5081 | 0.505721 | 0.252861 | − | 0.967503i | \(-0.418629\pi\) | ||||
0.252861 | + | 0.967503i | \(0.418629\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.79304 | 0.0972412 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0452 | 0.975228 | 0.487614 | − | 0.873059i | \(-0.337867\pi\) | ||||
0.487614 | + | 0.873059i | \(0.337867\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2281 | −0.910939 | −0.455470 | − | 0.890251i | \(-0.650529\pi\) | ||||
−0.455470 | + | 0.890251i | \(0.650529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.7469 | −0.650323 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.9553 | −1.52296 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.3895 | −0.671000 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.48995 | 0.0860651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2129 | −0.421637 | −0.210819 | − | 0.977525i | \(-0.567613\pi\) | ||||
−0.210819 | + | 0.977525i | \(0.567613\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.3910 | −0.737621 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.21396 | −0.179578 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.924149 | 0.0317917 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.3609 | −0.390365 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.9771 | 0.651291 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55148 | −0.0531841 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 54.2928 | 1.85895 | 0.929474 | − | 0.368886i | \(-0.120261\pi\) | ||||
0.929474 | + | 0.368886i | \(0.120261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.27949 | −0.214754 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.0491 | 0.514067 | 0.257034 | − | 0.966402i | \(-0.417255\pi\) | ||||
0.257034 | + | 0.966402i | \(0.417255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.2351 | −1.16809 | −0.584043 | − | 0.811723i | \(-0.698530\pi\) | ||||
−0.584043 | + | 0.811723i | \(0.698530\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.5614 | 0.700732 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.6488 | −0.498652 | −0.249326 | − | 0.968420i | \(-0.580209\pi\) | ||||
−0.249326 | + | 0.968420i | \(0.580209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1030 | −0.445514 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.3240 | 1.50532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.8705 | 0.911518 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6018 | −0.698066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.961896 | 0.0325552 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.55148 | 0.120062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.2319 | −1.83128 | −0.915641 | − | 0.401998i | \(-0.868316\pi\) | ||||
−0.915641 | + | 0.401998i | \(0.868316\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.3976 | −0.924098 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.3162 | 1.49305 | 0.746525 | − | 0.665357i | \(-0.231721\pi\) | ||||
0.746525 | + | 0.665357i | \(0.231721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2704 | −1.28790 | −0.643951 | − | 0.765067i | \(-0.722706\pi\) | ||||
−0.643951 | + | 0.765067i | \(0.722706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.31342 | −0.111379 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.80699 | 0.194980 | 0.0974898 | − | 0.995237i | \(-0.468919\pi\) | ||||
0.0974898 | + | 0.995237i | \(0.468919\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.516473 | −0.0173219 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.79304 | 0.0935704 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −39.4320 | −1.31954 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.0759 | 0.470504 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.73151 | 0.124591 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.86837 | 0.229073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.6369 | −2.31994 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.1521 | 0.537507 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.1374 | 0.702630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3419 | 0.409805 | 0.204903 | − | 0.978782i | \(-0.434312\pi\) | ||||
0.204903 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.9035 | −0.560654 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.2190 | −0.901807 | −0.450903 | − | 0.892573i | \(-0.648898\pi\) | ||||
−0.450903 | + | 0.892573i | \(0.648898\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.2861 | −0.538992 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.2180 | 0.370854 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.6836 | −1.27605 | −0.638027 | − | 0.770014i | \(-0.720249\pi\) | ||||
−0.638027 | + | 0.770014i | \(0.720249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.18353 | −0.0389986 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.6746 | −0.779260 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.55148 | −0.0510124 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.04143 | 0.198427 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.1365 | −0.562230 | −0.281115 | − | 0.959674i | \(-0.590704\pi\) | ||||
−0.281115 | + | 0.959674i | \(0.590704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.2468 | −1.15517 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.5770 | −0.608183 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.8722 | −0.715298 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4382 | 1.45173 | 0.725866 | − | 0.687836i | \(-0.241439\pi\) | ||||
0.725866 | + | 0.687836i | \(0.241439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.50094 | −0.277418 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1745 | −0.625069 | −0.312535 | − | 0.949906i | \(-0.601178\pi\) | ||||
−0.312535 | + | 0.949906i | \(0.601178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.78954 | 0.188533 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.55148 | 0.115530 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −56.7662 | −1.84465 | −0.922327 | − | 0.386410i | \(-0.873715\pi\) | ||||
−0.922327 | + | 0.386410i | \(0.873715\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.3997 | 1.86327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.5884 | 0.700051 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.8953 | 1.22755 | 0.613774 | − | 0.789482i | \(-0.289651\pi\) | ||||
0.613774 | + | 0.789482i | \(0.289651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.81647 | −0.0911389 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.70443 | 0.249049 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.8931 | −0.706965 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.8002 | −0.800005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.3141 | −0.396816 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4560 | 0.497547 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −58.9924 | −1.89707 | −0.948534 | − | 0.316674i | \(-0.897434\pi\) | ||||
−0.948534 | + | 0.316674i | \(0.897434\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.1745 | 1.57971 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.9675 | −0.640787 | −0.320394 | − | 0.947284i | \(-0.603815\pi\) | ||||
−0.320394 | + | 0.947284i | \(0.603815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.9659 | −1.60183 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.73151 | 0.119504 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.54712 | −0.177468 | −0.0887341 | − | 0.996055i | \(-0.528282\pi\) | ||||
−0.0887341 | + | 0.996055i | \(0.528282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.09065 | 0.0348572 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.8579 | 0.474376 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.1636 | −0.387959 | −0.193979 | − | 0.981006i | \(-0.562139\pi\) | ||||
−0.193979 | + | 0.981006i | \(0.562139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.7311 | 0.819862 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.3015 | 0.709864 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.54798 | 0.144617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.1991 | −0.578113 | −0.289057 | − | 0.957312i | \(-0.593342\pi\) | ||||
−0.289057 | + | 0.957312i | \(0.593342\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.0288 | −0.762531 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.95857 | −0.188899 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.4097 | 1.56482 | 0.782411 | − | 0.622762i | \(-0.213990\pi\) | ||||
0.782411 | + | 0.622762i | \(0.213990\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.55148 | −0.0490867 |
(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 | 5520.2.a.cc.1.4 | 5 | ||
4.3 | odd | 2 | 2760.2.a.w.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 8280.2.a.br.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.w.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
5520.2.a.cc.1.4 | 5 | 1.1 | even | 1 | trivial | ||
8280.2.a.br.1.2 | 5 | 12.11 | even | 2 |