Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(1,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, 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("3332.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.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: | \(26.6061539535\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 4x^{7} - 8x^{6} + 36x^{5} + 17x^{4} - 76x^{3} - 20x^{2} + 44x + 17 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.43314\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.1 |
$q$-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 | ||||||||
\(3\) | 2.43314 | 1.40477 | 0.702387 | − | 0.711795i | \(-0.252118\pi\) | ||||
0.702387 | + | 0.711795i | \(0.252118\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.700514 | 0.313279 | 0.156640 | − | 0.987656i | \(-0.449934\pi\) | ||||
0.156640 | + | 0.987656i | \(0.449934\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.92017 | 0.973391 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.25232 | −1.88514 | −0.942572 | − | 0.334003i | \(-0.891601\pi\) | ||||
−0.942572 | + | 0.334003i | \(0.891601\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.33822 | −0.925855 | −0.462928 | − | 0.886396i | \(-0.653201\pi\) | ||||
−0.462928 | + | 0.886396i | \(0.653201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.70445 | 0.440087 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.78435 | −0.638773 | −0.319387 | − | 0.947625i | \(-0.603477\pi\) | ||||
−0.319387 | + | 0.947625i | \(0.603477\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.97696 | −1.24628 | −0.623141 | − | 0.782110i | \(-0.714144\pi\) | ||||
−0.623141 | + | 0.782110i | \(0.714144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.50928 | −0.901856 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.194229 | −0.0373793 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.96405 | −0.736106 | −0.368053 | − | 0.929805i | \(-0.619976\pi\) | ||||
−0.368053 | + | 0.929805i | \(0.619976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.55695 | −0.279637 | −0.139818 | − | 0.990177i | \(-0.544652\pi\) | ||||
−0.139818 | + | 0.990177i | \(0.544652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −15.2128 | −2.64820 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.53597 | −0.416912 | −0.208456 | − | 0.978032i | \(-0.566844\pi\) | ||||
−0.208456 | + | 0.978032i | \(0.566844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.12236 | −1.30062 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.62122 | −0.877887 | −0.438944 | − | 0.898515i | \(-0.644647\pi\) | ||||
−0.438944 | + | 0.898515i | \(0.644647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.29290 | −0.349664 | −0.174832 | − | 0.984598i | \(-0.555938\pi\) | ||||
−0.174832 | + | 0.984598i | \(0.555938\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.04562 | 0.304943 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.9664 | 1.74548 | 0.872742 | − | 0.488181i | \(-0.162339\pi\) | ||||
0.872742 | + | 0.488181i | \(0.162339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.43314 | 0.340708 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.55500 | 0.900399 | 0.450200 | − | 0.892928i | \(-0.351353\pi\) | ||||
0.450200 | + | 0.892928i | \(0.351353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.37983 | −0.590577 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.77471 | −0.897332 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.78005 | 1.14307 | 0.571533 | − | 0.820579i | \(-0.306349\pi\) | ||||
0.571533 | + | 0.820579i | \(0.306349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.95327 | −0.634201 | −0.317101 | − | 0.948392i | \(-0.602709\pi\) | ||||
−0.317101 | + | 0.948392i | \(0.602709\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.33847 | −0.290051 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1327 | 1.60442 | 0.802210 | − | 0.597042i | \(-0.203657\pi\) | ||||
0.802210 | + | 0.597042i | \(0.203657\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.5428 | −1.75074 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2118 | −1.68663 | −0.843317 | − | 0.537417i | \(-0.819400\pi\) | ||||
−0.843317 | + | 0.537417i | \(0.819400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.40017 | 0.983165 | 0.491583 | − | 0.870831i | \(-0.336419\pi\) | ||||
0.491583 | + | 0.870831i | \(0.336419\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.9717 | −1.26690 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.03170 | 0.341093 | 0.170546 | − | 0.985350i | \(-0.445447\pi\) | ||||
0.170546 | + | 0.985350i | \(0.445447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.23311 | −1.02590 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.93476 | 0.541660 | 0.270830 | − | 0.962627i | \(-0.412702\pi\) | ||||
0.270830 | + | 0.962627i | \(0.412702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.700514 | 0.0759814 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.64510 | −1.03406 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.7216 | −1.56049 | −0.780244 | − | 0.625475i | \(-0.784905\pi\) | ||||
−0.780244 | + | 0.625475i | \(0.784905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.78828 | −0.392826 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.95047 | −0.200114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.898333 | −0.0912119 | −0.0456060 | − | 0.998960i | \(-0.514522\pi\) | ||||
−0.0456060 | + | 0.998960i | \(0.514522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.2578 | −1.83498 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.75291 | 0.671940 | 0.335970 | − | 0.941873i | \(-0.390936\pi\) | ||||
0.335970 | + | 0.941873i | \(0.390936\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.74321 | 0.368830 | 0.184415 | − | 0.982849i | \(-0.440961\pi\) | ||||
0.184415 | + | 0.982849i | \(0.440961\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7611 | 1.23367 | 0.616833 | − | 0.787094i | \(-0.288415\pi\) | ||||
0.616833 | + | 0.787094i | \(0.288415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.26268 | −0.887204 | −0.443602 | − | 0.896224i | \(-0.646300\pi\) | ||||
−0.443602 | + | 0.896224i | \(0.646300\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.17038 | −0.585667 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.64156 | 0.248497 | 0.124248 | − | 0.992251i | \(-0.460348\pi\) | ||||
0.124248 | + | 0.992251i | \(0.460348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.18694 | −0.390434 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.74818 | −0.901220 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.0915 | 2.55377 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.6772 | −1.23323 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.66138 | −0.595812 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.94328 | 0.616117 | 0.308058 | − | 0.951367i | \(-0.400321\pi\) | ||||
0.308058 | + | 0.951367i | \(0.400321\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.57895 | −0.491199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.88103 | 0.775939 | 0.387969 | − | 0.921672i | \(-0.373177\pi\) | ||||
0.387969 | + | 0.921672i | \(0.373177\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.136060 | −0.0117102 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.33823 | 0.370640 | 0.185320 | − | 0.982678i | \(-0.440668\pi\) | ||||
0.185320 | + | 0.982678i | \(0.440668\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.0420 | −1.53030 | −0.765150 | − | 0.643852i | \(-0.777335\pi\) | ||||
−0.765150 | + | 0.643852i | \(0.777335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.1160 | 2.45201 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.8716 | 1.74537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.77687 | −0.230607 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6645 | 1.44713 | 0.723567 | − | 0.690255i | \(-0.242501\pi\) | ||||
0.723567 | + | 0.690255i | \(0.242501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6266 | 0.946159 | 0.473080 | − | 0.881020i | \(-0.343142\pi\) | ||||
0.473080 | + | 0.881020i | \(0.343142\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.92017 | 0.236082 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.09067 | −0.0876043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8397 | −1.50357 | −0.751784 | − | 0.659410i | \(-0.770806\pi\) | ||||
−0.751784 | + | 0.659410i | \(0.770806\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.9492 | 1.26486 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.2038 | −0.799221 | −0.399611 | − | 0.916685i | \(-0.630855\pi\) | ||||
−0.399611 | + | 0.916685i | \(0.630855\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.6568 | −0.829627 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.04752 | −0.158442 | −0.0792210 | − | 0.996857i | \(-0.525243\pi\) | ||||
−0.0792210 | + | 0.996857i | \(0.525243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.85629 | −0.142792 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.13078 | −0.621776 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.51778 | −0.267452 | −0.133726 | − | 0.991018i | \(-0.542694\pi\) | ||||
−0.133726 | + | 0.991018i | \(0.542694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.3631 | 1.60575 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.01805 | 0.300323 | 0.150162 | − | 0.988661i | \(-0.452021\pi\) | ||||
0.150162 | + | 0.988661i | \(0.452021\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00576 | −0.223416 | −0.111708 | − | 0.993741i | \(-0.535632\pi\) | ||||
−0.111708 | + | 0.993741i | \(0.535632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.0520 | −0.890910 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.77648 | −0.130610 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.25232 | −0.457215 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7743 | 0.996670 | 0.498335 | − | 0.866985i | \(-0.333945\pi\) | ||||
0.498335 | + | 0.866985i | \(0.333945\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.29653 | −0.597197 | −0.298599 | − | 0.954379i | \(-0.596519\pi\) | ||||
−0.298599 | + | 0.954379i | \(0.596519\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.68982 | −0.407457 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6075 | 0.755755 | 0.377878 | − | 0.925856i | \(-0.376654\pi\) | ||||
0.377878 | + | 0.925856i | \(0.376654\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.8444 | −1.26495 | −0.632477 | − | 0.774579i | \(-0.717962\pi\) | ||||
−0.632477 | + | 0.774579i | \(0.717962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.9538 | 2.25385 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.93774 | −0.275024 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.4537 | −1.21312 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.4086 | 1.20418 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.90813 | −0.337889 | −0.168945 | − | 0.985626i | \(-0.554036\pi\) | ||||
−0.168945 | + | 0.985626i | \(0.554036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −34.5794 | −2.36934 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.60621 | −0.109542 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 20.4388 | 1.38113 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.33822 | −0.224553 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.7501 | 0.719879 | 0.359940 | − | 0.932976i | \(-0.382797\pi\) | ||||
0.359940 | + | 0.932976i | \(0.382797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.1679 | −0.877859 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.86801 | 0.455846 | 0.227923 | − | 0.973679i | \(-0.426807\pi\) | ||||
0.227923 | + | 0.973679i | \(0.426807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.3348 | −0.947268 | −0.473634 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473634 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.26722 | −0.607116 | −0.303558 | − | 0.952813i | \(-0.598175\pi\) | ||||
−0.303558 | + | 0.952813i | \(0.598175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.38266 | 0.546824 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.37655 | 0.479158 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.9940 | −1.48736 | −0.743680 | − | 0.668536i | \(-0.766921\pi\) | ||||
−0.743680 | + | 0.668536i | \(0.766921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.18312 | 0.333874 | 0.166937 | − | 0.985968i | \(-0.446612\pi\) | ||||
0.166937 | + | 0.985968i | \(0.446612\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.8828 | −1.40378 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.29476 | 0.591412 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.0070 | 0.760910 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.0836 | −1.70950 | −0.854752 | − | 0.519037i | \(-0.826291\pi\) | ||||
−0.854752 | + | 0.519037i | \(0.826291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.3698 | 2.34942 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.70445 | 0.106737 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.655631 | 0.0408972 | 0.0204486 | − | 0.999791i | \(-0.493491\pi\) | ||||
0.0204486 | + | 0.999791i | \(0.493491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.5757 | −0.716520 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.1584 | 1.36635 | 0.683173 | − | 0.730257i | \(-0.260600\pi\) | ||||
0.683173 | + | 0.730257i | \(0.260600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.59187 | 0.282076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.8198 | −2.19213 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.04549 | −0.429571 | −0.214786 | − | 0.976661i | \(-0.568905\pi\) | ||||
−0.214786 | + | 0.976661i | \(0.568905\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4854 | 1.54813 | 0.774064 | − | 0.633107i | \(-0.218221\pi\) | ||||
0.774064 | + | 0.633107i | \(0.218221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 28.1934 | 1.70013 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.4113 | 1.94741 | 0.973704 | − | 0.227815i | \(-0.0731582\pi\) | ||||
0.973704 | + | 0.227815i | \(0.0731582\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.54657 | −0.272196 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.29635 | −0.0773339 | −0.0386669 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386669 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.0050 | −1.48639 | −0.743197 | − | 0.669072i | \(-0.766692\pi\) | ||||
−0.743197 | + | 0.669072i | \(0.766692\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.74578 | −0.281116 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.18577 | −0.128132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.4747 | −1.48825 | −0.744125 | − | 0.668041i | \(-0.767133\pi\) | ||||
−0.744125 | + | 0.668041i | \(0.767133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.15055 | 0.358099 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.21438 | 0.0704654 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.9524 | 1.15388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.4308 | 0.943924 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.46983 | −0.198682 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.5628 | −1.91553 | −0.957764 | − | 0.287555i | \(-0.907158\pi\) | ||||
−0.957764 | + | 0.287555i | \(0.907158\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.10776 | 0.518122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2347 | −1.31752 | −0.658760 | − | 0.752353i | \(-0.728919\pi\) | ||||
−0.658760 | + | 0.752353i | \(0.728919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.2386 | −1.70919 | −0.854593 | − | 0.519299i | \(-0.826193\pi\) | ||||
−0.854593 | + | 0.519299i | \(0.826193\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.4442 | −1.09210 | −0.546049 | − | 0.837753i | \(-0.683869\pi\) | ||||
−0.546049 | + | 0.837753i | \(0.683869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.7845 | 1.38767 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31.0496 | 1.73302 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.78435 | −0.154925 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.0530 | 0.834988 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.5374 | −1.24632 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4473 | −1.50864 | −0.754321 | − | 0.656506i | \(-0.772034\pi\) | ||||
−0.754321 | + | 0.656506i | \(0.772034\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.40549 | −0.405818 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.19967 | 0.502631 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4504 | −0.732688 | −0.366344 | − | 0.930479i | \(-0.619391\pi\) | ||||
−0.366344 | + | 0.930479i | \(0.619391\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.42728 | 0.349082 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.73455 | 0.527155 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.1874 | −0.548472 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.62909 | −0.0874544 | −0.0437272 | − | 0.999044i | \(-0.513923\pi\) | ||||
−0.0437272 | + | 0.999044i | \(0.513923\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.60959 | 0.407332 | 0.203666 | − | 0.979040i | \(-0.434714\pi\) | ||||
0.203666 | + | 0.979040i | \(0.434714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.648378 | 0.0346079 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.3499 | −1.45569 | −0.727843 | − | 0.685744i | \(-0.759477\pi\) | ||||
−0.727843 | + | 0.685744i | \(0.759477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.95558 | −0.528387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.5849 | 1.45588 | 0.727939 | − | 0.685642i | \(-0.240479\pi\) | ||||
0.727939 | + | 0.685642i | \(0.240479\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2474 | −0.591969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 68.3505 | 3.58747 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.88443 | 0.308005 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7116 | 0.767938 | 0.383969 | − | 0.923346i | \(-0.374557\pi\) | ||||
0.383969 | + | 0.923346i | \(0.374557\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4149 | −0.854528 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.0714 | 1.09104 | 0.545518 | − | 0.838099i | \(-0.316333\pi\) | ||||
0.545518 | + | 0.838099i | \(0.316333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −16.2081 | −0.836982 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.2329 | 0.681528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.5227 | −1.56784 | −0.783922 | − | 0.620859i | \(-0.786784\pi\) | ||||
−0.783922 | + | 0.620859i | \(0.786784\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.8940 | 0.865505 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5517 | 0.692458 | 0.346229 | − | 0.938150i | \(-0.387462\pi\) | ||||
0.346229 | + | 0.938150i | \(0.387462\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.69567 | −0.340360 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.02769 | −0.356318 | −0.178159 | − | 0.984002i | \(-0.557014\pi\) | ||||
−0.178159 | + | 0.984002i | \(0.557014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.97696 | −0.302268 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6088 | 1.09002 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.12375 | 0.106857 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2330 | 0.915088 | 0.457544 | − | 0.889187i | \(-0.348729\pi\) | ||||
0.457544 | + | 0.889187i | \(0.348729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.8638 | −0.892077 | −0.446038 | − | 0.895014i | \(-0.647166\pi\) | ||||
−0.446038 | + | 0.895014i | \(0.647166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.19744 | 0.258903 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.46792 | −0.321393 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.8557 | 0.785939 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8428 | 0.536143 | 0.268072 | − | 0.963399i | \(-0.413614\pi\) | ||||
0.268072 | + | 0.963399i | \(0.413614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.5555 | 0.520665 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.45686 | 0.169691 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.8987 | −2.14973 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8813 | −1.16668 | −0.583340 | − | 0.812228i | \(-0.698255\pi\) | ||||
−0.583340 | + | 0.812228i | \(0.698255\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.82824 | −0.332788 | −0.166394 | − | 0.986059i | \(-0.553212\pi\) | ||||
−0.166394 | + | 0.986059i | \(0.553212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.9441 | 1.69904 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.50928 | −0.218732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 50.7835 | 2.45185 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.9429 | −0.527101 | −0.263551 | − | 0.964646i | \(-0.584894\pi\) | ||||
−0.263551 | + | 0.964646i | \(0.584894\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.8182 | 0.904344 | 0.452172 | − | 0.891931i | \(-0.350649\pi\) | ||||
0.452172 | + | 0.891931i | \(0.350649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.75653 | −0.323951 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.6419 | 0.796091 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.35808 | 0.208000 | 0.104000 | − | 0.994577i | \(-0.466836\pi\) | ||||
0.104000 | + | 0.994577i | \(0.466836\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.16946 | −0.388143 | −0.194071 | − | 0.980987i | \(-0.562169\pi\) | ||||
−0.194071 | + | 0.980987i | \(0.562169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.3127 | −0.488869 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 42.9802 | 2.03290 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0508 | 0.710292 | 0.355146 | − | 0.934811i | \(-0.384431\pi\) | ||||
0.355146 | + | 0.934811i | \(0.384431\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 35.1456 | 1.65494 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.2891 | 1.32914 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.2417 | −1.74209 | −0.871047 | − | 0.491199i | \(-0.836559\pi\) | ||||
−0.871047 | + | 0.491199i | \(0.836559\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.194229 | −0.00906582 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6939 | −1.56928 | −0.784642 | − | 0.619949i | \(-0.787153\pi\) | ||||
−0.784642 | + | 0.619949i | \(0.787153\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.90942 | −0.367582 | −0.183791 | − | 0.982965i | \(-0.558837\pi\) | ||||
−0.183791 | + | 0.982965i | \(0.558837\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.65374 | −0.123064 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4018 | 0.573887 | 0.286944 | − | 0.957947i | \(-0.407361\pi\) | ||||
0.286944 | + | 0.957947i | \(0.407361\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −45.8395 | −2.11217 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.3359 | 0.659167 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.5554 | 0.576082 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.1418 | 0.876441 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.175096 | 0.00800033 | 0.00400016 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00400016 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.46564 | 0.386000 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.629295 | −0.0285748 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.8139 | 1.71351 | 0.856755 | − | 0.515724i | \(-0.172477\pi\) | ||||
0.856755 | + | 0.515724i | \(0.172477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.8272 | −1.12273 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.7418 | 1.65814 | 0.829068 | − | 0.559148i | \(-0.188872\pi\) | ||||
0.829068 | + | 0.559148i | \(0.188872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.96405 | −0.178532 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7899 | −0.574862 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.8512 | −1.47062 | −0.735311 | − | 0.677729i | \(-0.762964\pi\) | ||||
−0.735311 | + | 0.677729i | \(0.762964\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.98191 | −0.222575 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.33672 | 0.327128 | 0.163564 | − | 0.986533i | \(-0.447701\pi\) | ||||
0.163564 | + | 0.986533i | \(0.447701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.73051 | 0.210505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.51662 | −0.200590 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.8523 | −0.658318 | −0.329159 | − | 0.944275i | \(-0.606765\pi\) | ||||
−0.329159 | + | 0.944275i | \(0.606765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.540800 | 0.0238769 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.62217 | 0.115547 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −74.8180 | −3.29049 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.55925 | −0.375709 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.695446 | −0.0304680 | −0.0152340 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152340 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.79974 | −0.297332 | −0.148666 | − | 0.988887i | \(-0.547498\pi\) | ||||
−0.148666 | + | 0.988887i | \(0.547498\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.55695 | −0.0678218 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.7240 | 0.553217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.6393 | 1.11265 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.7649 | 0.812797 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.93935 | 0.386482 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.77648 | 0.421886 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.5784 | −1.87358 | −0.936792 | − | 0.349887i | \(-0.886220\pi\) | ||||
−0.936792 | + | 0.349887i | \(0.886220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.31343 | −0.313849 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.48863 | −0.277943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6669 | −1.14019 | −0.570097 | − | 0.821577i | \(-0.693094\pi\) | ||||
−0.570097 | + | 0.821577i | \(0.693094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.4644 | −0.617326 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0373 | 0.470205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.32244 | −0.183477 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.5815 | −0.787322 | −0.393661 | − | 0.919256i | \(-0.628792\pi\) | ||||
−0.393661 | + | 0.919256i | \(0.628792\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.65420 | 0.323738 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2128 | −0.642283 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.61461 | 0.405208 | 0.202604 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202604 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.85045 | 0.0778489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.8304 | −0.915179 | −0.457590 | − | 0.889163i | \(-0.651287\pi\) | ||||
−0.457590 | + | 0.889163i | \(0.651287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.1272 | −0.591207 | −0.295603 | − | 0.955311i | \(-0.595521\pi\) | ||||
−0.295603 | + | 0.955311i | \(0.595521\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.5147 | 1.40010 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.9518 | 1.12397 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.2960 | −1.01146 | −0.505729 | − | 0.862693i | \(-0.668776\pi\) | ||||
−0.505729 | + | 0.862693i | \(0.668776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.1866 | −0.838928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.9840 | −1.69738 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.82873 | −0.282333 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.98164 | −0.164340 | −0.0821700 | − | 0.996618i | \(-0.526185\pi\) | ||||
−0.0821700 | + | 0.996618i | \(0.526185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.33509 | 0.178624 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.8096 | 1.06167 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.4429 | 1.33227 | 0.666135 | − | 0.745831i | \(-0.267947\pi\) | ||||
0.666135 | + | 0.745831i | \(0.267947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −43.4178 | −1.77697 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.4024 | −1.97767 | −0.988835 | − | 0.149016i | \(-0.952389\pi\) | ||||
−0.988835 | + | 0.149016i | \(0.952389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.7447 | −0.601448 | −0.300724 | − | 0.953711i | \(-0.597228\pi\) | ||||
−0.300724 | + | 0.953711i | \(0.597228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.3499 | 1.56173 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.6785 | 0.800043 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.2021 | −0.779390 | −0.389695 | − | 0.920944i | \(-0.627420\pi\) | ||||
−0.389695 | + | 0.920944i | \(0.627420\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.9466 | −1.61607 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.5312 | 1.31392 | 0.656961 | − | 0.753924i | \(-0.271841\pi\) | ||||
0.656961 | + | 0.753924i | \(0.271841\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.58108 | −0.386346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4908 | 1.10674 | 0.553369 | − | 0.832937i | \(-0.313342\pi\) | ||||
0.553369 | + | 0.832937i | \(0.313342\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.33700 | 0.0939321 | 0.0469661 | − | 0.998896i | \(-0.485045\pi\) | ||||
0.0469661 | + | 0.998896i | \(0.485045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.16090 | 0.0465852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8800 | 0.715201 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 42.3576 | 1.69160 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.53597 | −0.101116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.5715 | −1.37627 | −0.688135 | − | 0.725583i | \(-0.741570\pi\) | ||||
−0.688135 | + | 0.725583i | \(0.741570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.9422 | −0.474658 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.86387 | 0.193017 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.5010 | −1.64175 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.9277 | −0.945086 | −0.472543 | − | 0.881308i | \(-0.656664\pi\) | ||||
−0.472543 | + | 0.881308i | \(0.656664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3241 | 0.722632 | 0.361316 | − | 0.932443i | \(-0.382328\pi\) | ||||
0.361316 | + | 0.932443i | \(0.382328\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.90813 | −0.153882 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.3569 | 1.58659 | 0.793297 | − | 0.608834i | \(-0.208363\pi\) | ||||
0.793297 | + | 0.608834i | \(0.208363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.8957 | −2.15484 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.7302 | 0.654705 | 0.327353 | − | 0.944902i | \(-0.393844\pi\) | ||||
0.327353 | + | 0.944902i | \(0.393844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.22128 | 0.243086 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.5299 | 0.957004 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.34497 | −0.208211 | −0.104105 | − | 0.994566i | \(-0.533198\pi\) | ||||
−0.104105 | + | 0.994566i | \(0.533198\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.9109 | 0.696654 | 0.348327 | − | 0.937373i | \(-0.386750\pi\) | ||||
0.348327 | + | 0.937373i | \(0.386750\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.12236 | −0.315446 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6930 | 0.917396 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.1565 | 1.01127 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9694 | 1.19556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.72661 | 0.374933 | 0.187467 | − | 0.982271i | \(-0.439972\pi\) | ||||
0.187467 | + | 0.982271i | \(0.439972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.875832 | 0.0337108 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.35298 | −0.0519993 | −0.0259997 | − | 0.999662i | \(-0.508277\pi\) | ||||
−0.0259997 | + | 0.999662i | \(0.508277\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.7108 | 0.640361 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.2177 | 1.15625 | 0.578125 | − | 0.815948i | \(-0.303785\pi\) | ||||
0.578125 | + | 0.815948i | \(0.303785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.03899 | 0.116114 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.8785 | −1.33070 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.8820 | −0.833639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9535 | −0.568859 | −0.284430 | − | 0.958697i | \(-0.591804\pi\) | ||||
−0.284430 | + | 0.958697i | \(0.591804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.6386 | −0.479411 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.62122 | −0.212919 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.5485 | −0.852861 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.6974 | −1.00835 | −0.504173 | − | 0.863603i | \(-0.668202\pi\) | ||||
−0.504173 | + | 0.863603i | \(0.668202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.06104 | 0.266312 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.3962 | 0.768165 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.43807 | 0.0540077 | 0.0270038 | − | 0.999635i | \(-0.491403\pi\) | ||||
0.0270038 | + | 0.999635i | \(0.491403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.85309 | 0.332017 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.30582 | 0.348506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6208 | 0.546789 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −55.9477 | −2.08940 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.5231 | 1.36208 | 0.681041 | − | 0.732245i | \(-0.261527\pi\) | ||||
0.681041 | + | 0.732245i | \(0.261527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.6113 | 0.469018 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.8750 | 0.663862 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.65584 | 0.135588 | 0.0677938 | − | 0.997699i | \(-0.478404\pi\) | ||||
0.0677938 | + | 0.997699i | \(0.478404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.5445 | −0.946093 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.29290 | −0.0848060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.5214 | −1.01652 | −0.508262 | − | 0.861202i | \(-0.669712\pi\) | ||||
−0.508262 | + | 0.861202i | \(0.669712\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −82.1101 | −3.02456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.0727 | 1.40053 | 0.700264 | − | 0.713884i | \(-0.253066\pi\) | ||||
0.700264 | + | 0.713884i | \(0.253066\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.6155 | 0.830800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.8685 | 1.93956 | 0.969778 | − | 0.243990i | \(-0.0784564\pi\) | ||||
0.969778 | + | 0.243990i | \(0.0784564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3742 | 0.453357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.4103 | 0.527247 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.4052 | 0.379691 | 0.189846 | − | 0.981814i | \(-0.439201\pi\) | ||||
0.189846 | + | 0.981814i | \(0.439201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −65.8983 | −2.40147 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.14459 | 0.296412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.5697 | −0.893000 | −0.446500 | − | 0.894784i | \(-0.647330\pi\) | ||||
−0.446500 | + | 0.894784i | \(0.647330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 90.9260 | 3.30041 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.52282 | −0.127702 | −0.0638511 | − | 0.997959i | \(-0.520338\pi\) | ||||
−0.0638511 | + | 0.997959i | \(0.520338\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.04562 | 0.0739596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.3097 | −1.05831 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0896 | −0.904753 | −0.452377 | − | 0.891827i | \(-0.649424\pi\) | ||||
−0.452377 | + | 0.891827i | \(0.649424\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.59524 | 0.0574513 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.0298 | 1.15203 | 0.576016 | − | 0.817438i | \(-0.304606\pi\) | ||||
0.576016 | + | 0.817438i | \(0.304606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.02073 | 0.252192 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.6514 | 0.560771 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 88.8569 | 3.17955 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.769933 | 0.0275152 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.1974 | −0.471037 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.4077 | 0.442288 | 0.221144 | − | 0.975241i | \(-0.429021\pi\) | ||||
0.221144 | + | 0.975241i | \(0.429021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 53.9145 | 1.91941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.5351 | 0.587179 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.1727 | 0.396254 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.2865 | −1.21449 | −0.607245 | − | 0.794515i | \(-0.707725\pi\) | ||||
−0.607245 | + | 0.794515i | \(0.707725\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.9664 | 0.423342 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.9897 | −1.51897 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.5205 | −1.85341 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17.1427 | −0.603451 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.3540 | 1.77035 | 0.885176 | − | 0.465256i | \(-0.154038\pi\) | ||||
0.885176 | + | 0.465256i | \(0.154038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.5402 | 1.73959 | 0.869796 | − | 0.493412i | \(-0.164250\pi\) | ||||
0.869796 | + | 0.493412i | \(0.164250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 62.0096 | 2.17477 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.14789 | −0.250379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.38423 | 0.223356 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.0853 | 0.421781 | 0.210890 | − | 0.977510i | \(-0.432364\pi\) | ||||
0.210890 | + | 0.977510i | \(0.432364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.2751 | −0.358166 | −0.179083 | − | 0.983834i | \(-0.557313\pi\) | ||||
−0.179083 | + | 0.983834i | \(0.557313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 68.5986 | 2.38830 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 51.7650 | 1.80005 | 0.900023 | − | 0.435843i | \(-0.143550\pi\) | ||||
0.900023 | + | 0.435843i | \(0.143550\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.9968 | 1.66700 | 0.833500 | − | 0.552520i | \(-0.186334\pi\) | ||||
0.833500 | + | 0.552520i | \(0.186334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 78.8614 | 2.73567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.43432 | −0.0496366 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.302405 | 0.0104526 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.5562 | 1.81444 | 0.907220 | − | 0.420656i | \(-0.138200\pi\) | ||||
0.907220 | + | 0.420656i | \(0.138200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2863 | −0.458147 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.15421 | −0.108637 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.30036 | −0.0447337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60.8408 | −2.08805 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.1574 | 0.519589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.65942 | 0.262254 | 0.131127 | − | 0.991366i | \(-0.458141\pi\) | ||||
0.131127 | + | 0.991366i | \(0.458141\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.69572 | −0.194790 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.9114 | −1.67078 | −0.835391 | − | 0.549656i | \(-0.814759\pi\) | ||||
−0.835391 | + | 0.549656i | \(0.814759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7120 | −0.570206 | −0.285103 | − | 0.958497i | \(-0.592028\pi\) | ||||
−0.285103 | + | 0.958497i | \(0.592028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.7856 | 1.55856 | 0.779279 | − | 0.626677i | \(-0.215585\pi\) | ||||
0.779279 | + | 0.626677i | \(0.215585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.46425 | −0.0837871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.43314 | 0.0826338 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9551 | −0.643009 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.8400 | −1.48546 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.62329 | −0.0887849 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.1183 | −0.881952 | −0.440976 | − | 0.897519i | \(-0.645368\pi\) | ||||
−0.440976 | + | 0.897519i | \(0.645368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −61.9836 | −2.09065 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.3437 | −0.786469 | −0.393234 | − | 0.919438i | \(-0.628644\pi\) | ||||
−0.393234 | + | 0.919438i | \(0.628644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.0746 | 1.04574 | 0.522872 | − | 0.852411i | \(-0.324861\pi\) | ||||
0.522872 | + | 0.852411i | \(0.324861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.9651 | 0.503048 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.0640 | 0.841566 | 0.420783 | − | 0.907161i | \(-0.361755\pi\) | ||||
0.420783 | + | 0.907161i | \(0.361755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.7283 | 1.93397 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.3187 | −1.11497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.81470 | 0.0940850 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.5470 | 1.62094 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.17184 | 0.205842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.55500 | 0.218379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.10557 | −0.0699916 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.7568 | 1.88458 | 0.942290 | − | 0.334798i | \(-0.108668\pi\) | ||||
0.942290 | + | 0.334798i | \(0.108668\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.7197 | 0.654060 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.93958 | −0.229919 | −0.114959 | − | 0.993370i | \(-0.536674\pi\) | ||||
−0.114959 | + | 0.993370i | \(0.536674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.8537 | −1.02111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.44259 | −0.279103 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.2004 | 1.39206 | 0.696031 | − | 0.718012i | \(-0.254948\pi\) | ||||
0.696031 | + | 0.718012i | \(0.254948\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −81.6629 | −2.69089 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47.4422 | 1.56158 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.4354 | 0.375994 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.9308 | 0.359015 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.3374 | 1.12657 | 0.563286 | − | 0.826262i | \(-0.309537\pi\) | ||||
0.563286 | + | 0.826262i | \(0.309537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −56.5334 | −1.85082 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.37983 | −0.143236 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.5267 | 0.539903 | 0.269952 | − | 0.962874i | \(-0.412992\pi\) | ||||
0.269952 | + | 0.962874i | \(0.412992\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −73.5747 | −2.40102 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.6133 | −1.22616 | −0.613079 | − | 0.790022i | \(-0.710069\pi\) | ||||
−0.613079 | + | 0.790022i | \(0.710069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.5978 | 1.09409 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.7256 | 0.998448 | 0.499224 | − | 0.866473i | \(-0.333618\pi\) | ||||
0.499224 | + | 0.866473i | \(0.333618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0416 | −0.910269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.3106 | −1.53415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.1120 | 0.327558 | 0.163779 | − | 0.986497i | \(-0.447632\pi\) | ||||
0.163779 | + | 0.986497i | \(0.447632\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.64905 | 0.312236 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 60.3042 | 1.94936 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5759 | −0.921803 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 37.2647 | 1.20084 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.81183 | −0.187090 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.0882 | −0.838940 | −0.419470 | − | 0.907769i | \(-0.637784\pi\) | ||||
−0.419470 | + | 0.907769i | \(0.637784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.77471 | −0.217635 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8527 | 0.380372 | 0.190186 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190186 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 36.6260 | 1.17297 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.1874 | −0.421902 | −0.210951 | − | 0.977497i | \(-0.567656\pi\) | ||||
−0.210951 | + | 0.977497i | \(0.567656\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 92.0442 | 2.94175 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.0486 | −0.863596 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.3555 | 0.617344 | 0.308672 | − | 0.951169i | \(-0.400115\pi\) | ||||
0.308672 | + | 0.951169i | \(0.400115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.43072 | 0.236762 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.7046 | 0.435780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.67221 | −0.180184 | −0.0900918 | − | 0.995933i | \(-0.528716\pi\) | ||||
−0.0900918 | + | 0.995933i | \(0.528716\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −66.7832 | −2.11930 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.5002 | −0.396284 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.7031 | −1.00405 | −0.502023 | − | 0.864854i | \(-0.667411\pi\) | ||||
−0.502023 | + | 0.864854i | \(0.667411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.492559 | 0.0155839 |
(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 | 3332.2.a.t.1.8 | ✓ | 8 | |
7.6 | odd | 2 | 3332.2.a.u.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3332.2.a.t.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
3332.2.a.u.1.1 | yes | 8 | 7.6 | odd | 2 |