Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 18x^{8} + 32x^{7} + 110x^{6} - 154x^{5} - 282x^{4} + 256x^{3} + 253x^{2} - 126x - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.729469\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 | ||||||||
\(3\) | −0.729469 | −0.421159 | −0.210580 | − | 0.977577i | \(-0.567535\pi\) | ||||
−0.210580 | + | 0.977577i | \(0.567535\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.02160 | 1.35130 | 0.675651 | − | 0.737222i | \(-0.263863\pi\) | ||||
0.675651 | + | 0.737222i | \(0.263863\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46788 | −0.822625 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63548 | −0.794627 | −0.397314 | − | 0.917683i | \(-0.630057\pi\) | ||||
−0.397314 | + | 0.917683i | \(0.630057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.419531 | −0.116357 | −0.0581785 | − | 0.998306i | \(-0.518529\pi\) | ||||
−0.0581785 | + | 0.998306i | \(0.518529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.20416 | −0.569113 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.48814 | 1.08853 | 0.544267 | − | 0.838912i | \(-0.316808\pi\) | ||||
0.544267 | + | 0.838912i | \(0.316808\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.82614 | −1.10719 | −0.553596 | − | 0.832785i | \(-0.686745\pi\) | ||||
−0.553596 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.672994 | 0.140329 | 0.0701644 | − | 0.997535i | \(-0.477648\pi\) | ||||
0.0701644 | + | 0.997535i | \(0.477648\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.13008 | 0.826016 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.98864 | 0.767615 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.40739 | −1.37552 | −0.687759 | − | 0.725939i | \(-0.741405\pi\) | ||||
−0.687759 | + | 0.725939i | \(0.741405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.91525 | 0.703200 | 0.351600 | − | 0.936150i | \(-0.385638\pi\) | ||||
0.351600 | + | 0.936150i | \(0.385638\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.92250 | 0.334664 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.78938 | −0.458572 | −0.229286 | − | 0.973359i | \(-0.573639\pi\) | ||||
−0.229286 | + | 0.973359i | \(0.573639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.306035 | 0.0490048 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.85531 | 1.50292 | 0.751460 | − | 0.659779i | \(-0.229350\pi\) | ||||
0.751460 | + | 0.659779i | \(0.229350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.45694 | −1.11161 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2186 | 1.78227 | 0.891134 | − | 0.453741i | \(-0.149911\pi\) | ||||
0.891134 | + | 0.453741i | \(0.149911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.27396 | −0.458446 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.6009 | −1.73087 | −0.865434 | − | 0.501023i | \(-0.832957\pi\) | ||||
−0.865434 | + | 0.501023i | \(0.832957\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.96337 | −1.07378 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.52052 | 0.466304 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.17437 | −1.06421 | −0.532106 | − | 0.846678i | \(-0.678599\pi\) | ||||
−0.532106 | + | 0.846678i | \(0.678599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.69538 | 0.729218 | 0.364609 | − | 0.931161i | \(-0.381203\pi\) | ||||
0.364609 | + | 0.931161i | \(0.381203\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.26766 | −0.157233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.13105 | −0.504688 | −0.252344 | − | 0.967638i | \(-0.581201\pi\) | ||||
−0.252344 | + | 0.967638i | \(0.581201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.490928 | −0.0591008 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.7449 | 1.98726 | 0.993629 | − | 0.112696i | \(-0.0359487\pi\) | ||||
0.993629 | + | 0.112696i | \(0.0359487\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9924 | −1.40360 | −0.701800 | − | 0.712374i | \(-0.747620\pi\) | ||||
−0.701800 | + | 0.712374i | \(0.747620\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.01276 | −0.347884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.02996 | −0.565915 | −0.282957 | − | 0.959132i | \(-0.591316\pi\) | ||||
−0.282957 | + | 0.959132i | \(0.591316\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.49403 | 0.499337 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.57801 | −0.502502 | −0.251251 | − | 0.967922i | \(-0.580842\pi\) | ||||
−0.251251 | + | 0.967922i | \(0.580842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.5614 | 1.47094 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.40346 | 0.579312 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.8020 | 1.35701 | 0.678504 | − | 0.734596i | \(-0.262628\pi\) | ||||
0.678504 | + | 0.734596i | \(0.262628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.85605 | −0.296159 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.5827 | −1.49615 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.57826 | −0.464852 | −0.232426 | − | 0.972614i | \(-0.574666\pi\) | ||||
−0.232426 | + | 0.972614i | \(0.574666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.50404 | 0.653680 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.02429 | −0.698943 | −0.349472 | − | 0.936947i | \(-0.613639\pi\) | ||||
−0.349472 | + | 0.936947i | \(0.613639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.94473 | −0.585752 | −0.292876 | − | 0.956150i | \(-0.594612\pi\) | ||||
−0.292876 | + | 0.956150i | \(0.594612\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.94944 | −0.671828 | −0.335914 | − | 0.941893i | \(-0.609045\pi\) | ||||
−0.335914 | + | 0.941893i | \(0.609045\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.6652 | −1.78780 | −0.893900 | − | 0.448267i | \(-0.852042\pi\) | ||||
−0.893900 | + | 0.448267i | \(0.852042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.03477 | 0.193132 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0598 | −1.41671 | −0.708355 | − | 0.705857i | \(-0.750562\pi\) | ||||
−0.708355 | + | 0.705857i | \(0.750562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.03352 | 0.189627 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.03535 | 0.0957181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.05424 | −0.368568 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.729469 | 0.0657740 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.62855 | −0.235105 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.79505 | 0.336756 | 0.168378 | − | 0.985722i | \(-0.446147\pi\) | ||||
0.168378 | + | 0.985722i | \(0.446147\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.18914 | −0.632968 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.172315 | 0.0150552 | 0.00752761 | − | 0.999972i | \(-0.497604\pi\) | ||||
0.00752761 | + | 0.999972i | \(0.497604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.0521 | 1.03728 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.94598 | 0.166256 | 0.0831282 | − | 0.996539i | \(-0.473509\pi\) | ||||
0.0831282 | + | 0.996539i | \(0.473509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5097 | −1.40033 | −0.700166 | − | 0.713980i | \(-0.746891\pi\) | ||||
−0.700166 | + | 0.713980i | \(0.746891\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.91310 | −0.750618 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.10567 | 0.0924604 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.3822 | −1.85874 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.14372 | −0.175620 | −0.0878101 | − | 0.996137i | \(-0.527987\pi\) | ||||
−0.0878101 | + | 0.996137i | \(0.527987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6070 | 1.10732 | 0.553659 | − | 0.832743i | \(-0.313231\pi\) | ||||
0.553659 | + | 0.832743i | \(0.313231\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.0762 | −0.895455 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.8303 | 0.950235 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.6320 | −1.32738 | −0.663690 | − | 0.748008i | \(-0.731010\pi\) | ||||
−0.663690 | + | 0.748008i | \(0.731010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.19197 | 0.728971 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.94527 | 0.230691 | 0.115346 | − | 0.993325i | \(-0.463202\pi\) | ||||
0.115346 | + | 0.993325i | \(0.463202\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.80903 | 0.452233 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6880 | −1.29136 | −0.645678 | − | 0.763610i | \(-0.723425\pi\) | ||||
−0.645678 | + | 0.763610i | \(0.723425\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8240 | −0.986461 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9103 | 0.910804 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1557 | −1.53241 | −0.766203 | − | 0.642598i | \(-0.777856\pi\) | ||||
−0.766203 | + | 0.642598i | \(0.777856\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.96295 | 0.448203 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.3960 | −1.44972 | −0.724861 | − | 0.688895i | \(-0.758096\pi\) | ||||
−0.724861 | + | 0.688895i | \(0.758096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.65214 | −0.122802 | −0.0614012 | − | 0.998113i | \(-0.519557\pi\) | ||||
−0.0614012 | + | 0.998113i | \(0.519557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.15460 | −0.307117 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.42841 | −0.619669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8284 | −0.864979 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.4468 | 1.69655 | 0.848274 | − | 0.529557i | \(-0.177642\pi\) | ||||
0.848274 | + | 0.529557i | \(0.177642\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2357 | 1.16867 | 0.584334 | − | 0.811513i | \(-0.301356\pi\) | ||||
0.584334 | + | 0.811513i | \(0.301356\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.924715 | 0.0662202 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.0901 | −1.07512 | −0.537561 | − | 0.843225i | \(-0.680654\pi\) | ||||
−0.537561 | + | 0.843225i | \(0.680654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9859 | −0.778772 | −0.389386 | − | 0.921075i | \(-0.627313\pi\) | ||||
−0.389386 | + | 0.921075i | \(0.627313\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.01347 | 0.212554 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.02160 | −0.211038 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.66086 | −0.115438 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.7192 | 0.879805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.7238 | 1.63321 | 0.816606 | − | 0.577196i | \(-0.195853\pi\) | ||||
0.816606 | + | 0.577196i | \(0.195853\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.2149 | −0.836952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 29.7788 | 2.03090 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.74805 | 0.591139 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.88291 | −0.126658 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.5235 | 1.44132 | 0.720659 | − | 0.693290i | \(-0.243839\pi\) | ||||
0.720659 | + | 0.693290i | \(0.243839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.1925 | −0.679501 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.57776 | −0.303837 | −0.151918 | − | 0.988393i | \(-0.548545\pi\) | ||||
−0.151918 | + | 0.988393i | \(0.548545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.92402 | 0.325389 | 0.162694 | − | 0.986677i | \(-0.447982\pi\) | ||||
0.162694 | + | 0.986677i | \(0.447982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.6354 | −1.15534 | −0.577668 | − | 0.816272i | \(-0.696037\pi\) | ||||
−0.577668 | + | 0.816272i | \(0.696037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.9198 | 2.40838 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.66920 | 0.238340 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.532642 | 0.0344538 | 0.0172269 | − | 0.999852i | \(-0.494516\pi\) | ||||
0.0172269 | + | 0.999852i | \(0.494516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4604 | −0.673814 | −0.336907 | − | 0.941538i | \(-0.609381\pi\) | ||||
−0.336907 | + | 0.941538i | \(0.609381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2442 | −0.977915 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.02471 | 0.128830 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.33952 | 0.211633 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.4434 | −1.54286 | −0.771428 | − | 0.636317i | \(-0.780457\pi\) | ||||
−0.771428 | + | 0.636317i | \(0.780457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.77366 | −0.111509 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.89260 | −0.619499 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.1025 | 0.817309 | 0.408655 | − | 0.912689i | \(-0.365998\pi\) | ||||
0.408655 | + | 0.912689i | \(0.365998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.2805 | 1.13153 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.37037 | 0.269489 | 0.134744 | − | 0.990880i | \(-0.456979\pi\) | ||||
0.134744 | + | 0.990880i | \(0.456979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.0749 | −2.33892 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.33866 | −0.571517 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.3721 | −1.30308 | −0.651540 | − | 0.758615i | \(-0.725877\pi\) | ||||
−0.651540 | + | 0.758615i | \(0.725877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.3061 | 0.990526 | 0.495263 | − | 0.868743i | \(-0.335072\pi\) | ||||
0.495263 | + | 0.868743i | \(0.335072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8847 | −0.656375 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.3362 | −1.16180 | −0.580901 | − | 0.813974i | \(-0.697300\pi\) | ||||
−0.580901 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.66235 | −0.578470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.9338 | 1.48743 | 0.743714 | − | 0.668498i | \(-0.233062\pi\) | ||||
0.743714 | + | 0.668498i | \(0.233062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.46955 | −0.206243 | −0.103122 | − | 0.994669i | \(-0.532883\pi\) | ||||
−0.103122 | + | 0.994669i | \(0.532883\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.6376 | 0.630117 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.14340 | 0.184906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.33970 | 0.195777 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.5746 | 1.02672 | 0.513359 | − | 0.858174i | \(-0.328401\pi\) | ||||
0.513359 | + | 0.858174i | \(0.328401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.6997 | −1.43807 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5120 | −0.609968 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.282342 | −0.0163282 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.12400 | 0.294366 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.2092 | 0.985393 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.7869 | −1.07222 | −0.536112 | − | 0.844147i | \(-0.680108\pi\) | ||||
−0.536112 | + | 0.844147i | \(0.680108\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.33650 | 0.246695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.4618 | −1.38710 | −0.693550 | − | 0.720408i | \(-0.743954\pi\) | ||||
−0.693550 | + | 0.720408i | \(0.743954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.0320 | −1.01923 | −0.509613 | − | 0.860404i | \(-0.670211\pi\) | ||||
−0.509613 | + | 0.860404i | \(0.670211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.26355 | 0.183299 | 0.0916496 | − | 0.995791i | \(-0.470786\pi\) | ||||
0.0916496 | + | 0.995791i | \(0.470786\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.5220 | 1.09302 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.06940 | 0.282946 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6604 | −1.20522 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.73270 | −0.0961127 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6157 | 0.752948 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1594 | 0.558411 | 0.279206 | − | 0.960231i | \(-0.409929\pi\) | ||||
0.279206 | + | 0.960231i | \(0.409929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.88385 | 0.377233 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4824 | −0.681985 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.3482 | 0.727124 | 0.363562 | − | 0.931570i | \(-0.381561\pi\) | ||||
0.363562 | + | 0.931570i | \(0.381561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9857 | 0.596660 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3186 | −0.558782 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.48339 | −0.0798630 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.32015 | −0.339283 | −0.169642 | − | 0.985506i | \(-0.554261\pi\) | ||||
−0.169642 | + | 0.985506i | \(0.554261\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.29144 | 0.443831 | 0.221915 | − | 0.975066i | \(-0.428769\pi\) | ||||
0.221915 | + | 0.975066i | \(0.428769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.67336 | −0.0893173 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.3657 | 1.61620 | 0.808102 | − | 0.589043i | \(-0.200495\pi\) | ||||
0.808102 | + | 0.589043i | \(0.200495\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.5966 | 2.68539 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.3876 | 1.70935 | 0.854675 | − | 0.519163i | \(-0.173756\pi\) | ||||
0.854675 | + | 0.519163i | \(0.173756\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.29162 | 0.225875 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.95744 | 0.155226 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.2361 | −1.89669 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0161 | −0.836031 | −0.418016 | − | 0.908440i | \(-0.637274\pi\) | ||||
−0.418016 | + | 0.908440i | \(0.637274\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.46788 | 0.128472 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.50112 | 0.491949 | 0.245975 | − | 0.969276i | \(-0.420892\pi\) | ||||
0.245975 | + | 0.969276i | \(0.420892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.91745 | 0.0990166 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.10763 | 0.160051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.18315 | 0.420340 | 0.210170 | − | 0.977665i | \(-0.432598\pi\) | ||||
0.210170 | + | 0.977665i | \(0.432598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.76837 | −0.141828 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.5295 | −0.895713 | −0.447857 | − | 0.894105i | \(-0.647812\pi\) | ||||
−0.447857 | + | 0.894105i | \(0.647812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.3217 | −1.23634 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.9349 | −0.909336 | −0.454668 | − | 0.890661i | \(-0.650242\pi\) | ||||
−0.454668 | + | 0.890661i | \(0.650242\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.02049 | 0.152753 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.125698 | −0.00634064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1985 | −0.764722 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.4109 | 1.27534 | 0.637668 | − | 0.770311i | \(-0.279899\pi\) | ||||
0.637668 | + | 0.770311i | \(0.279899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.64011 | 0.131841 | 0.0659204 | − | 0.997825i | \(-0.479002\pi\) | ||||
0.0659204 | + | 0.997825i | \(0.479002\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.64257 | −0.0818222 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.5792 | 0.674755 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.35137 | 0.364394 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.1419 | 1.29263 | 0.646317 | − | 0.763069i | \(-0.276308\pi\) | ||||
0.646317 | + | 0.763069i | \(0.276308\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.41953 | −0.0700204 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.8329 | −0.679032 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0433 | 0.589763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.11337 | −0.103245 | −0.0516224 | − | 0.998667i | \(-0.516439\pi\) | ||||
−0.0516224 | + | 0.998667i | \(0.516439\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5523 | 0.660500 | 0.330250 | − | 0.943894i | \(-0.392867\pi\) | ||||
0.330250 | + | 0.943894i | \(0.392867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.1540 | −1.46614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 18.5364 | 0.899146 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.806549 | −0.0389405 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.8099 | −0.665200 | −0.332600 | − | 0.943068i | \(-0.607926\pi\) | ||||
−0.332600 | + | 0.943068i | \(0.607926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.72356 | −0.130886 | −0.0654429 | − | 0.997856i | \(-0.520846\pi\) | ||||
−0.0654429 | + | 0.997856i | \(0.520846\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.3271 | 0.782825 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.24796 | −0.155371 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3395 | −0.588931 | −0.294465 | − | 0.955662i | \(-0.595142\pi\) | ||||
−0.294465 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.66457 | −0.269132 | −0.134566 | − | 0.990905i | \(-0.542964\pi\) | ||||
−0.134566 | + | 0.990905i | \(0.542964\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.6825 | 1.83373 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.56378 | 0.0739640 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.6028 | −1.11388 | −0.556942 | − | 0.830552i | \(-0.688025\pi\) | ||||
−0.556942 | + | 0.830552i | \(0.688025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.63548 | 0.124100 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.92585 | −0.466357 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8068 | 0.645854 | 0.322927 | − | 0.946424i | \(-0.395333\pi\) | ||||
0.322927 | + | 0.946424i | \(0.395333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.9016 | 0.835575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.33393 | −0.341575 | −0.170788 | − | 0.985308i | \(-0.554631\pi\) | ||||
−0.170788 | + | 0.985308i | \(0.554631\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3928 | −1.50542 | −0.752710 | − | 0.658352i | \(-0.771254\pi\) | ||||
−0.752710 | + | 0.658352i | \(0.771254\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.62986 | −0.400200 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.471234 | 0.0218061 | 0.0109030 | − | 0.999941i | \(-0.496529\pi\) | ||||
0.0109030 | + | 0.999941i | \(0.496529\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.1325 | 0.559038 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.9735 | −1.19426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.9323 | −0.914558 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.0975 | 1.42386 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.2215 | 1.70069 | 0.850346 | − | 0.526224i | \(-0.176393\pi\) | ||||
0.850346 | + | 0.526224i | \(0.176393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.17023 | 0.0533580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.8337 | −0.628155 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.3423 | −1.73745 | −0.868727 | − | 0.495292i | \(-0.835061\pi\) | ||||
−0.868727 | + | 0.495292i | \(0.835061\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.14848 | −0.0971578 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.220444 | 0.00994850 | 0.00497425 | − | 0.999988i | \(-0.498417\pi\) | ||||
0.00497425 | + | 0.999988i | \(0.498417\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.2454 | −1.49730 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.6526 | 0.883319 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.31343 | −0.0587971 | −0.0293985 | − | 0.999568i | \(-0.509359\pi\) | ||||
−0.0293985 | + | 0.999568i | \(0.509359\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.1734 | 0.543866 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.5426 | −1.09430 | −0.547151 | − | 0.837034i | \(-0.684288\pi\) | ||||
−0.547151 | + | 0.837034i | \(0.684288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.2246 | −0.944483 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.35470 | 0.415457 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.1233 | 0.581679 | 0.290839 | − | 0.956772i | \(-0.406066\pi\) | ||||
0.290839 | + | 0.956772i | \(0.406066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.2498 | −0.849897 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.9626 | −0.791528 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.2019 | −1.41624 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7029 | 0.645387 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6139 | −1.38503 | −0.692515 | − | 0.721403i | \(-0.743497\pi\) | ||||
−0.692515 | + | 0.721403i | \(0.743497\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.75542 | 0.120486 | 0.0602431 | − | 0.998184i | \(-0.480812\pi\) | ||||
0.0602431 | + | 0.998184i | \(0.480812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.5722 | 0.765457 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5471 | −0.980308 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.1733 | 0.875448 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.419531 | 0.0181719 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.9984 | −0.907842 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.1487 | 0.610564 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.02547 | −0.302049 | −0.151024 | − | 0.988530i | \(-0.548257\pi\) | ||||
−0.151024 | + | 0.988530i | \(0.548257\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.20518 | 0.0517193 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −56.3987 | −2.41586 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.3015 | 0.568732 | 0.284366 | − | 0.958716i | \(-0.408217\pi\) | ||||
0.284366 | + | 0.958716i | \(0.408217\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.0555 | −0.599873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.7491 | 1.52296 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.14826 | 0.260979 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9873 | 1.65194 | 0.825972 | − | 0.563711i | \(-0.190627\pi\) | ||||
0.825972 | + | 0.563711i | \(0.190627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.13461 | −0.174875 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.62845 | 0.364294 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.28994 | 0.222945 | 0.111472 | − | 0.993768i | \(-0.464443\pi\) | ||||
0.111472 | + | 0.993768i | \(0.464443\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −45.5048 | −1.91440 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.3456 | 1.64945 | 0.824726 | − | 0.565533i | \(-0.191329\pi\) | ||||
0.824726 | + | 0.565533i | \(0.191329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8773 | 0.664446 | 0.332223 | − | 0.943201i | \(-0.392201\pi\) | ||||
0.332223 | + | 0.943201i | \(0.392201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1037 | −0.714517 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.77952 | 0.115914 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.01458 | −0.333651 | −0.166826 | − | 0.985986i | \(-0.553352\pi\) | ||||
−0.166826 | + | 0.985986i | \(0.553352\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.8434 | −0.492195 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.2094 | 1.37539 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.12842 | 0.129344 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.48213 | −0.267546 | −0.133773 | − | 0.991012i | \(-0.542709\pi\) | ||||
−0.133773 | + | 0.991012i | \(0.542709\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.8955 | −0.778577 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0077 | 0.452798 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.02097 | −0.288317 | −0.144158 | − | 0.989555i | \(-0.546047\pi\) | ||||
−0.144158 | + | 0.989555i | \(0.546047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.01390 | 0.327987 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5721 | −0.595399 | −0.297699 | − | 0.954660i | \(-0.596219\pi\) | ||||
−0.297699 | + | 0.954660i | \(0.596219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.94938 | 0.324262 | 0.162131 | − | 0.986769i | \(-0.448163\pi\) | ||||
0.162131 | + | 0.986769i | \(0.448163\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1949 | 0.415169 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.2503 | −0.498046 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.44728 | 0.221098 | 0.110549 | − | 0.993871i | \(-0.464739\pi\) | ||||
0.110549 | + | 0.993871i | \(0.464739\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.12609 | −0.207379 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.9589 | 1.25042 | 0.625209 | − | 0.780458i | \(-0.285014\pi\) | ||||
0.625209 | + | 0.780458i | \(0.285014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.20416 | 0.0888805 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.7514 | −1.11723 | −0.558615 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558615 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.2653 | −0.533176 | −0.266588 | − | 0.963811i | \(-0.585896\pi\) | ||||
−0.266588 | + | 0.963811i | \(0.585896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.68433 | 0.107719 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5928 | −1.14371 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.27826 | −0.370538 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.5191 | −0.499171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6466 | −1.02097 | −0.510487 | − | 0.859885i | \(-0.670535\pi\) | ||||
−0.510487 | + | 0.859885i | \(0.670535\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.3057 | −0.687842 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.4671 | 0.455059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.3244 | −1.63477 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.47574 | −0.0582884 | −0.0291442 | − | 0.999575i | \(-0.509278\pi\) | ||||
−0.0291442 | + | 0.999575i | \(0.509278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4628 | −0.530922 | −0.265461 | − | 0.964122i | \(-0.585524\pi\) | ||||
−0.265461 | + | 0.964122i | \(0.585524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.7227 | −0.855331 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.7466 | −1.71986 | −0.859929 | − | 0.510414i | \(-0.829492\pi\) | ||||
−0.859929 | + | 0.510414i | \(0.829492\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.5434 | 0.845652 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.6172 | −1.66774 | −0.833869 | − | 0.551962i | \(-0.813879\pi\) | ||||
−0.833869 | + | 0.551962i | \(0.813879\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.520667 | 0.0203441 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 29.5956 | 1.15464 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4790 | 0.525068 | 0.262534 | − | 0.964923i | \(-0.415442\pi\) | ||||
0.262534 | + | 0.964923i | \(0.415442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6145 | 1.03518 | 0.517592 | − | 0.855628i | \(-0.326829\pi\) | ||||
0.517592 | + | 0.855628i | \(0.326829\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.37353 | 0.0533434 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.98512 | −0.193025 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.7007 | −0.607024 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0100 | −0.579456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.8109 | 1.34186 | 0.670930 | − | 0.741521i | \(-0.265895\pi\) | ||||
0.670930 | + | 0.741521i | \(0.265895\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.4734 | 0.634062 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.2444 | −0.547455 | −0.273728 | − | 0.961807i | \(-0.588257\pi\) | ||||
−0.273728 | + | 0.961807i | \(0.588257\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.33933 | 0.127964 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.2620 | 1.11968 | 0.559839 | − | 0.828601i | \(-0.310863\pi\) | ||||
0.559839 | + | 0.828601i | \(0.310863\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.87998 | 0.224663 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.59192 | −0.137040 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.28647 | 0.201398 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.59879 | 0.327113 | 0.163557 | − | 0.986534i | \(-0.447703\pi\) | ||||
0.163557 | + | 0.986534i | \(0.447703\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.8857 | −1.89227 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.48814 | −0.170000 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.8645 | 0.486580 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.1495 | −0.572188 | −0.286094 | − | 0.958201i | \(-0.592357\pi\) | ||||
−0.286094 | + | 0.958201i | \(0.592357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.4620 | 0.507727 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.9318 | −1.01431 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.4893 | −0.581713 | −0.290857 | − | 0.956767i | \(-0.593940\pi\) | ||||
−0.290857 | + | 0.956767i | \(0.593940\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.4133 | 0.465536 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.63494 | 0.0986792 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.34088 | 0.124942 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.388546 | −0.0145105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.8745 | −1.67353 | −0.836767 | − | 0.547559i | \(-0.815557\pi\) | ||||
−0.836767 | + | 0.547559i | \(0.815557\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.63054 | 0.283783 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.5931 | −1.13620 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9602 | −0.740284 | −0.370142 | − | 0.928975i | \(-0.620691\pi\) | ||||
−0.370142 | + | 0.928975i | \(0.620691\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.36194 | −0.0874791 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.2320 | 1.63598 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0255 | 0.370299 | 0.185150 | − | 0.982710i | \(-0.440723\pi\) | ||||
0.185150 | + | 0.982710i | \(0.440723\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.8873 | 0.401039 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.4879 | 0.532947 | 0.266474 | − | 0.963842i | \(-0.414141\pi\) | ||||
0.266474 | + | 0.963842i | \(0.414141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.47697 | −0.0542577 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.2464 | −0.706081 | −0.353041 | − | 0.935608i | \(-0.614852\pi\) | ||||
−0.353041 | + | 0.935608i | \(0.614852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.47746 | −0.237316 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2980 | 0.413371 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.3680 | −0.633766 | −0.316883 | − | 0.948465i | \(-0.602636\pi\) | ||||
−0.316883 | + | 0.948465i | \(0.602636\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.8307 | 0.649787 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 41.1148 | 1.49632 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.55997 | −0.311117 | −0.155559 | − | 0.987827i | \(-0.549718\pi\) | ||||
−0.155559 | + | 0.987827i | \(0.549718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.29383 | 0.0469631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.8820 | −0.829474 | −0.414737 | − | 0.909941i | \(-0.636126\pi\) | ||||
−0.414737 | + | 0.909941i | \(0.636126\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −33.4678 | −1.21003 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.42940 | 0.123829 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.5966 | 1.53607 | 0.768036 | − | 0.640407i | \(-0.221234\pi\) | ||||
0.768036 | + | 0.640407i | \(0.221234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.55784 | −0.344217 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.0856 | 1.40581 | 0.702906 | − | 0.711282i | \(-0.251885\pi\) | ||||
0.702906 | + | 0.711282i | \(0.251885\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.1703 | 0.580854 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.82614 | 0.172914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.1310 | −1.57913 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.5454 | −1.05587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −50.2553 | −1.79369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.56896 | −0.198512 | −0.0992561 | − | 0.995062i | \(-0.531646\pi\) | ||||
−0.0992561 | + | 0.995062i | \(0.531646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.18805 | −0.113498 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.38939 | −0.0848496 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.7745 | 0.985059 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0942 | 0.782616 | 0.391308 | − | 0.920260i | \(-0.372023\pi\) | ||||
0.391308 | + | 0.920260i | \(0.372023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.8388 | 1.94006 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.5937 | −1.11631 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.6056 | 1.11534 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.5903 | 0.548804 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.2610 | −0.536548 | −0.268274 | − | 0.963343i | \(-0.586453\pi\) | ||||
−0.268274 | + | 0.963343i | \(0.586453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.3582 | 0.890446 | 0.445223 | − | 0.895420i | \(-0.353124\pi\) | ||||
0.445223 | + | 0.895420i | \(0.353124\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.8948 | −0.417169 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.89944 | 0.311734 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.5631 | −1.66402 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2829 | 0.603178 | 0.301589 | − | 0.953438i | \(-0.402483\pi\) | ||||
0.301589 | + | 0.953438i | \(0.402483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.8641 | −1.42443 | −0.712216 | − | 0.701960i | \(-0.752308\pi\) | ||||
−0.712216 | + | 0.701960i | \(0.752308\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.94008 | 0.276438 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5665 | 0.471755 | 0.235877 | − | 0.971783i | \(-0.424204\pi\) | ||||
0.235877 | + | 0.971783i | \(0.424204\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0661 | 0.349609 | 0.174805 | − | 0.984603i | \(-0.444071\pi\) | ||||
0.174805 | + | 0.984603i | \(0.444071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1052 | 0.489303 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −50.4245 | −1.74501 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.6165 | 0.539787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.4731 | 1.53538 | 0.767691 | − | 0.640820i | \(-0.221405\pi\) | ||||
0.767691 | + | 0.640820i | \(0.221405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.8694 | 0.892048 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.1885 | −0.626444 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −38.7490 | −1.33301 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.53093 | 0.0868612 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.87724 | −0.0643509 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.7118 | −1.42818 | −0.714092 | − | 0.700051i | \(-0.753160\pi\) | ||||
−0.714092 | + | 0.700051i | \(0.753160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35.9882 | 1.23077 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.3777 | −1.10600 | −0.553000 | − | 0.833181i | \(-0.686517\pi\) | ||||
−0.553000 | + | 0.833181i | \(0.686517\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.3027 | −0.351525 | −0.175762 | − | 0.984433i | \(-0.556239\pi\) | ||||
−0.175762 | + | 0.984433i | \(0.556239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.4435 | −0.389543 | −0.194771 | − | 0.980849i | \(-0.562396\pi\) | ||||
−0.194771 | + | 0.980849i | \(0.562396\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.9024 | −2.07074 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.29301 | −0.0778748 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.2564 | 0.449691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.73310 | 0.0587239 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.2986 | 0.382399 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.8720 | −1.41392 | −0.706959 | − | 0.707255i | \(-0.749933\pi\) | ||||
−0.706959 | + | 0.707255i | \(0.749933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.8201 | −0.432411 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.7494 | 0.362158 | 0.181079 | − | 0.983469i | \(-0.442041\pi\) | ||||
0.181079 | + | 0.983469i | \(0.442041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8468 | 0.566940 | 0.283470 | − | 0.958981i | \(-0.408514\pi\) | ||||
0.283470 | + | 0.958981i | \(0.408514\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0177 | 0.605657 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.6898 | 0.996887 | 0.498444 | − | 0.866922i | \(-0.333905\pi\) | ||||
0.498444 | + | 0.866922i | \(0.333905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.8439 | −0.396787 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −58.9687 | −1.97331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −58.6069 | −1.95901 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.205959 | 0.00687679 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.0018 | −0.967263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −56.5546 | −1.88411 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.99210 | −0.165943 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.9752 | −0.630060 | −0.315030 | − | 0.949082i | \(-0.602015\pi\) | ||||
−0.315030 | + | 0.949082i | \(0.602015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.3351 | 0.574968 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1631 | −0.966216 | −0.483108 | − | 0.875561i | \(-0.660492\pi\) | ||||
−0.483108 | + | 0.875561i | \(0.660492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0653 | 0.399302 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.5535 | −0.415007 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2264 | −0.469286 | −0.234643 | − | 0.972082i | \(-0.575392\pi\) | ||||
−0.234643 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.7045 | 0.451577 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.02502 | −0.231231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.5204 | −0.378788 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6709 | 0.481854 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.29313 | −0.304898 | −0.152449 | − | 0.988311i | \(-0.548716\pi\) | ||||
−0.152449 | + | 0.988311i | \(0.548716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.8441 | 0.584190 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.7407 | −1.16885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.4919 | −1.32281 | −0.661406 | − | 0.750028i | \(-0.730040\pi\) | ||||
−0.661406 | + | 0.750028i | \(0.730040\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.1537 | 0.429256 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.7076 | −1.32703 | −0.663515 | − | 0.748163i | \(-0.730936\pi\) | ||||
−0.663515 | + | 0.748163i | \(0.730936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.672994 | −0.0219157 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0839 | 0.880107 | 0.440054 | − | 0.897972i | \(-0.354959\pi\) | ||||
0.440054 | + | 0.897972i | \(0.354959\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.03117 | 0.163319 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.38066 | −0.0771981 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.2939 | 1.75875 | 0.879376 | − | 0.476128i | \(-0.157960\pi\) | ||||
0.879376 | + | 0.476128i | \(0.157960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 70.8468 | 2.29255 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.2407 | −0.460337 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.6708 | −0.505510 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.1503 | 0.552662 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.0577 | 1.57922 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.2843 | −0.362878 | −0.181439 | − | 0.983402i | \(-0.558075\pi\) | ||||
−0.181439 | + | 0.983402i | \(0.558075\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.8006 | 0.507588 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.7201 | 1.75605 | 0.878025 | − | 0.478614i | \(-0.158861\pi\) | ||||
0.878025 | + | 0.478614i | \(0.158861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.26395 | 0.0404787 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.2859 | −1.44882 | −0.724412 | − | 0.689368i | \(-0.757889\pi\) | ||||
−0.724412 | + | 0.689368i | \(0.757889\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.7394 | −1.07832 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.0633 | 1.47069 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.0163 | −0.766000 | −0.383000 | − | 0.923748i | \(-0.625109\pi\) | ||||
−0.383000 | + | 0.923748i | \(0.625109\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −45.5962 | −1.45282 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.63256 | 0.210903 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.1437 | 0.608119 | 0.304060 | − | 0.952653i | \(-0.401658\pi\) | ||||
0.304060 | + | 0.952653i | \(0.401658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.41097 | −0.235180 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.1951 | −1.05236 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.60423 | −0.0508066 | −0.0254033 | − | 0.999677i | \(-0.508087\pi\) | ||||
−0.0254033 | + | 0.999677i | \(0.508087\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.1259 | −0.352007 |
(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 | 8036.2.a.o.1.5 | ✓ | 10 | |
7.6 | odd | 2 | 8036.2.a.p.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.o.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8036.2.a.p.1.6 | yes | 10 | 7.6 | odd | 2 |