Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.81361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.81361 | 1.04709 | 0.523543 | − | 0.851999i | \(-0.324610\pi\) | ||||
0.523543 | + | 0.851999i | \(0.324610\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.81361 | −0.685479 | −0.342739 | − | 0.939431i | \(-0.611355\pi\) | ||||
−0.342739 | + | 0.939431i | \(0.611355\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.289169 | 0.0963895 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.28917 | 0.388699 | 0.194349 | − | 0.980932i | \(-0.437740\pi\) | ||||
0.194349 | + | 0.980932i | \(0.437740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.62721 | 1.00601 | 0.503004 | − | 0.864284i | \(-0.332228\pi\) | ||||
0.503004 | + | 0.864284i | \(0.332228\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.81361 | −0.468271 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.20555 | −1.50507 | −0.752533 | − | 0.658554i | \(-0.771168\pi\) | ||||
−0.752533 | + | 0.658554i | \(0.771168\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.10278 | −0.711825 | −0.355913 | − | 0.934519i | \(-0.615830\pi\) | ||||
−0.355913 | + | 0.934519i | \(0.615830\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.28917 | −0.717755 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.42166 | 0.296437 | 0.148219 | − | 0.988955i | \(-0.452646\pi\) | ||||
0.148219 | + | 0.988955i | \(0.452646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.91638 | −0.946158 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.15165 | −0.745659 | −0.372829 | − | 0.927900i | \(-0.621612\pi\) | ||||
−0.372829 | + | 0.927900i | \(0.621612\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.33804 | 0.407001 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.81361 | 0.306555 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.57834 | 1.05338 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.33804 | −1.30218 | −0.651092 | − | 0.758999i | \(-0.725689\pi\) | ||||
−0.651092 | + | 0.758999i | \(0.725689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.57834 | −0.393193 | −0.196596 | − | 0.980485i | \(-0.562989\pi\) | ||||
−0.196596 | + | 0.980485i | \(0.562989\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.289169 | −0.0431067 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.81361 | −0.264542 | −0.132271 | − | 0.991214i | \(-0.542227\pi\) | ||||
−0.132271 | + | 0.991214i | \(0.542227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.71083 | −0.530119 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.2544 | −1.57593 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.49472 | 0.205315 | 0.102658 | − | 0.994717i | \(-0.467265\pi\) | ||||
0.102658 | + | 0.994717i | \(0.467265\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.28917 | −0.173831 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.62721 | −0.745343 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3572 | 1.86915 | 0.934574 | − | 0.355768i | \(-0.115781\pi\) | ||||
0.934574 | + | 0.355768i | \(0.115781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.42166 | −0.438099 | −0.219050 | − | 0.975714i | \(-0.570296\pi\) | ||||
−0.219050 | + | 0.975714i | \(0.570296\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.524438 | −0.0660730 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.62721 | −0.449900 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.897225 | −0.109613 | −0.0548067 | − | 0.998497i | \(-0.517454\pi\) | ||||
−0.0548067 | + | 0.998497i | \(0.517454\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.57834 | 0.310395 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.66196 | 0.197238 | 0.0986189 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986189 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3380 | −1.44406 | −0.722029 | − | 0.691862i | \(-0.756790\pi\) | ||||
−0.722029 | + | 0.691862i | \(0.756790\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.81361 | 0.209417 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.33804 | −0.266445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3572 | 1.16528 | 0.582638 | − | 0.812732i | \(-0.302021\pi\) | ||||
0.582638 | + | 0.812732i | \(0.302021\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.78389 | −1.08710 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1758 | 1.44624 | 0.723118 | − | 0.690725i | \(-0.242708\pi\) | ||||
0.723118 | + | 0.690725i | \(0.242708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.20555 | 0.673086 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.62721 | −0.388878 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8328 | −1.25427 | −0.627135 | − | 0.778910i | \(-0.715773\pi\) | ||||
−0.627135 | + | 0.778910i | \(0.715773\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.57834 | −0.689597 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.52946 | −0.780769 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.10278 | 0.318338 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.67609 | −0.271716 | −0.135858 | − | 0.990728i | \(-0.543379\pi\) | ||||
−0.135858 | + | 0.990728i | \(0.543379\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.372787 | 0.0374665 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.7003 | 1.36323 | 0.681614 | − | 0.731712i | \(-0.261278\pi\) | ||||
0.681614 | + | 0.731712i | \(0.261278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.62721 | −0.751532 | −0.375766 | − | 0.926715i | \(-0.622620\pi\) | ||||
−0.375766 | + | 0.926715i | \(0.622620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.28917 | 0.320990 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.89722 | −0.473433 | −0.236716 | − | 0.971579i | \(-0.576071\pi\) | ||||
−0.236716 | + | 0.971579i | \(0.576071\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9894 | −1.62729 | −0.813646 | − | 0.581360i | \(-0.802521\pi\) | ||||
−0.813646 | + | 0.581360i | \(0.802521\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.81361 | −0.172140 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.37279 | −0.411357 | −0.205679 | − | 0.978620i | \(-0.565940\pi\) | ||||
−0.205679 | + | 0.978620i | \(0.565940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.42166 | −0.132571 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.04888 | 0.0969686 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.2544 | 1.03169 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.33804 | −0.848913 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.1219 | −1.36350 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.34307 | −0.651592 | −0.325796 | − | 0.945440i | \(-0.605632\pi\) | ||||
−0.325796 | + | 0.945440i | \(0.605632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.67609 | −0.411707 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.6705 | −1.80599 | −0.902997 | − | 0.429647i | \(-0.858638\pi\) | ||||
−0.902997 | + | 0.429647i | \(0.858638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.62721 | 0.487941 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.91638 | 0.423135 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.4111 | −0.889480 | −0.444740 | − | 0.895660i | \(-0.646704\pi\) | ||||
−0.444740 | + | 0.895660i | \(0.646704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.09775 | 0.517205 | 0.258602 | − | 0.965984i | \(-0.416738\pi\) | ||||
0.258602 | + | 0.965984i | \(0.416738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.28917 | −0.276998 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.67609 | 0.391034 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.72999 | −0.555080 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.1219 | −1.56653 | −0.783265 | − | 0.621688i | \(-0.786447\pi\) | ||||
−0.783265 | + | 0.621688i | \(0.786447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.6167 | 1.51500 | 0.757501 | − | 0.652834i | \(-0.226420\pi\) | ||||
0.757501 | + | 0.652834i | \(0.226420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.79445 | −0.145073 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.15165 | 0.333469 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.49472 | −0.757761 | −0.378881 | − | 0.925446i | \(-0.623691\pi\) | ||||
−0.378881 | + | 0.925446i | \(0.623691\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.71083 | 0.214983 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.57834 | −0.203201 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.21611 | −0.565210 | −0.282605 | − | 0.959236i | \(-0.591198\pi\) | ||||
−0.282605 | + | 0.959236i | \(0.591198\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.33804 | −0.182017 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.2056 | −0.789729 | −0.394865 | − | 0.918739i | \(-0.629208\pi\) | ||||
−0.394865 | + | 0.918739i | \(0.629208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.156674 | 0.0120519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.897225 | −0.0686125 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5925 | 0.881359 | 0.440680 | − | 0.897664i | \(-0.354737\pi\) | ||||
0.440680 | + | 0.897664i | \(0.354737\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.81361 | −0.137096 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 26.0383 | 1.95716 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.72999 | −0.503023 | −0.251511 | − | 0.967854i | \(-0.580928\pi\) | ||||
−0.251511 | + | 0.967854i | \(0.580928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.96526 | 0.740712 | 0.370356 | − | 0.928890i | \(-0.379236\pi\) | ||||
0.370356 | + | 0.928890i | \(0.379236\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.20555 | −0.458727 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.00000 | −0.585018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.91638 | 0.648571 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1517 | 0.879263 | 0.439631 | − | 0.898178i | \(-0.355109\pi\) | ||||
0.439631 | + | 0.898178i | \(0.355109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.31335 | −0.310482 | −0.155241 | − | 0.987877i | \(-0.549615\pi\) | ||||
−0.155241 | + | 0.987877i | \(0.549615\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.57834 | −0.471085 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8363 | 1.84076 | 0.920381 | − | 0.391022i | \(-0.127878\pi\) | ||||
0.920381 | + | 0.391022i | \(0.127878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.68111 | 0.686276 | 0.343138 | − | 0.939285i | \(-0.388510\pi\) | ||||
0.343138 | + | 0.939285i | \(0.388510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.62721 | −0.114775 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.62721 | 0.254580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.33804 | 0.582354 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.411100 | 0.0285734 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.6030 | −0.729943 | −0.364971 | − | 0.931019i | \(-0.618921\pi\) | ||||
−0.364971 | + | 0.931019i | \(0.618921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.01413 | 0.206525 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.57834 | 0.175841 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.52946 | 0.511133 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −22.3764 | −1.51205 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.5089 | −1.51411 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.5386 | 0.772680 | 0.386340 | − | 0.922356i | \(-0.373739\pi\) | ||||
0.386340 | + | 0.922356i | \(0.373739\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.289169 | 0.0192779 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.79445 | −0.119102 | −0.0595509 | − | 0.998225i | \(-0.518967\pi\) | ||||
−0.0595509 | + | 0.998225i | \(0.518967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1708 | 0.672106 | 0.336053 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336053 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.24029 | −0.278991 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.6655 | 0.895258 | 0.447629 | − | 0.894219i | \(-0.352268\pi\) | ||||
0.447629 | + | 0.894219i | \(0.352268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.81361 | 0.118307 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7839 | 1.22014 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.5733 | 1.39546 | 0.697731 | − | 0.716360i | \(-0.254193\pi\) | ||||
0.697731 | + | 0.716360i | \(0.254193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.843326 | −0.0543234 | −0.0271617 | − | 0.999631i | \(-0.508647\pi\) | ||||
−0.0271617 | + | 0.999631i | \(0.508647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.99498 | −0.192128 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.71083 | 0.237076 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.2544 | −0.716102 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.8958 | 1.51433 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.63224 | 0.292384 | 0.146192 | − | 0.989256i | \(-0.453298\pi\) | ||||
0.146192 | + | 0.989256i | \(0.453298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.83276 | 0.115225 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.2544 | 0.704779 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3033 | 1.01697 | 0.508486 | − | 0.861070i | \(-0.330205\pi\) | ||||
0.508486 | + | 0.861070i | \(0.330205\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.81361 | 0.112692 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.578337 | −0.0357982 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.5280 | −1.63579 | −0.817894 | − | 0.575370i | \(-0.804858\pi\) | ||||
−0.817894 | + | 0.575370i | \(0.804858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.49472 | −0.0918198 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −21.4600 | −1.31333 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.37279 | 0.510498 | 0.255249 | − | 0.966875i | \(-0.417843\pi\) | ||||
0.255249 | + | 0.966875i | \(0.417843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.66196 | 0.100957 | 0.0504783 | − | 0.998725i | \(-0.483925\pi\) | ||||
0.0504783 | + | 0.998725i | \(0.483925\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.9305 | −0.722068 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.28917 | 0.0777398 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.79445 | 0.107818 | 0.0539090 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539090 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.20053 | −0.0718737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.67609 | 0.398262 | 0.199131 | − | 0.979973i | \(-0.436188\pi\) | ||||
0.199131 | + | 0.979973i | \(0.436188\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.61665 | 0.155544 | 0.0777719 | − | 0.996971i | \(-0.475219\pi\) | ||||
0.0777719 | + | 0.996971i | \(0.475219\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.62721 | 0.333327 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.1219 | 0.892619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.5089 | 1.26523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.85337 | −0.284510 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.843326 | −0.0492676 | −0.0246338 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246338 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3572 | −0.835909 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.33804 | −0.367771 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.15667 | 0.298218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.67609 | 0.269525 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.8469 | 1.42742 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.42166 | 0.195924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9008 | 0.850433 | 0.425217 | − | 0.905092i | \(-0.360198\pi\) | ||||
0.425217 | + | 0.905092i | \(0.360198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.8328 | −0.786918 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2005 | 1.20217 | 0.601086 | − | 0.799185i | \(-0.294735\pi\) | ||||
0.601086 | + | 0.799185i | \(0.294735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.15667 | 0.404519 | 0.202260 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202260 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.524438 | 0.0295487 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.25443 | −0.295118 | −0.147559 | − | 0.989053i | \(-0.547142\pi\) | ||||
−0.147559 | + | 0.989053i | \(0.547142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.57834 | −0.144359 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.88164 | −0.495725 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.2544 | 1.07134 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.62721 | 0.201202 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −30.8122 | −1.70392 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.28917 | 0.181338 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3189 | −1.00690 | −0.503449 | − | 0.864025i | \(-0.667936\pi\) | ||||
−0.503449 | + | 0.864025i | \(0.667936\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.289169 | −0.0158463 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.897225 | 0.0490206 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.74914 | −0.476596 | −0.238298 | − | 0.971192i | \(-0.576590\pi\) | ||||
−0.238298 | + | 0.971192i | \(0.576590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.93051 | −0.430726 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.35218 | −0.289837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4252 | 1.04886 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.57834 | −0.138813 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.7350 | −0.844700 | −0.422350 | − | 0.906433i | \(-0.638795\pi\) | ||||
−0.422350 | + | 0.906433i | \(0.638795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.52946 | 0.295985 | 0.147993 | − | 0.988988i | \(-0.452719\pi\) | ||||
0.147993 | + | 0.988988i | \(0.452719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8328 | −0.951842 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.83276 | −0.203997 | −0.101999 | − | 0.994785i | \(-0.532524\pi\) | ||||
−0.101999 | + | 0.994785i | \(0.532524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.66196 | −0.0882074 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 20.4111 | 1.08027 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.95469 | −0.472611 | −0.236305 | − | 0.971679i | \(-0.575937\pi\) | ||||
−0.236305 | + | 0.971679i | \(0.575937\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.37279 | −0.493305 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.9355 | −0.888885 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3380 | 0.645803 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.53500 | −0.497723 | −0.248861 | − | 0.968539i | \(-0.580056\pi\) | ||||
−0.248861 | + | 0.968539i | \(0.580056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.41110 | −0.125517 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.71083 | −0.140739 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.5230 | −1.63220 | −0.816099 | − | 0.577912i | \(-0.803868\pi\) | ||||
−0.816099 | + | 0.577912i | \(0.803868\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.81361 | −0.0936542 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.25443 | −0.373622 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.5436 | 0.849787 | 0.424894 | − | 0.905243i | \(-0.360311\pi\) | ||||
0.424894 | + | 0.905243i | \(0.360311\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.3174 | −0.682273 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.7633 | −0.907661 | −0.453831 | − | 0.891088i | \(-0.649943\pi\) | ||||
−0.453831 | + | 0.891088i | \(0.649943\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.33804 | 0.119158 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.745574 | −0.0378997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.6550 | −1.85848 | −0.929240 | − | 0.369476i | \(-0.879537\pi\) | ||||
−0.929240 | + | 0.369476i | \(0.879537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.82220 | −0.446158 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −37.4882 | −1.89103 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3572 | −0.521127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.7008 | 0.737811 | 0.368906 | − | 0.929467i | \(-0.379733\pi\) | ||||
0.368906 | + | 0.929467i | \(0.379733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.2056 | 0.510917 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.6066 | 1.72817 | 0.864086 | − | 0.503345i | \(-0.167897\pi\) | ||||
0.864086 | + | 0.503345i | \(0.167897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0589 | −0.750138 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.78389 | 0.486165 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.28917 | −0.0639017 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6550 | 1.21911 | 0.609555 | − | 0.792744i | \(-0.291348\pi\) | ||||
0.609555 | + | 0.792744i | \(0.291348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.8816 | −0.931363 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.0383 | −1.28126 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.1758 | −0.646776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.0589 | 0.541558 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0347 | 0.881055 | 0.440527 | − | 0.897739i | \(-0.354791\pi\) | ||||
0.440527 | + | 0.897739i | \(0.354791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.67609 | 0.130425 | 0.0652123 | − | 0.997871i | \(-0.479228\pi\) | ||||
0.0652123 | + | 0.997871i | \(0.479228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.524438 | −0.0254990 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.20555 | −0.301013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20555 | 0.300308 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.48059 | 0.409447 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.88666 | −0.187214 | −0.0936070 | − | 0.995609i | \(-0.529840\pi\) | ||||
−0.0936070 | + | 0.995609i | \(0.529840\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7491 | 1.18937 | 0.594684 | − | 0.803960i | \(-0.297277\pi\) | ||||
0.594684 | + | 0.803960i | \(0.297277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.62721 | 0.173912 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.41110 | −0.211012 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.9950 | −0.524762 | −0.262381 | − | 0.964964i | \(-0.584508\pi\) | ||||
−0.262381 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.07306 | −0.0510979 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.4303 | 1.16072 | 0.580358 | − | 0.814361i | \(-0.302913\pi\) | ||||
0.580358 | + | 0.814361i | \(0.302913\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.8328 | 0.560927 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −34.6797 | −1.64029 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.0872 | 0.712008 | 0.356004 | − | 0.934484i | \(-0.384139\pi\) | ||||
0.356004 | + | 0.934484i | \(0.384139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7491 | −0.506157 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.7633 | 1.58634 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.57834 | 0.308397 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6655 | −0.826358 | −0.413179 | − | 0.910650i | \(-0.635582\pi\) | ||||
−0.413179 | + | 0.910650i | \(0.635582\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 30.5089 | 1.42403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6655 | −0.822766 | −0.411383 | − | 0.911463i | \(-0.634954\pi\) | ||||
−0.411383 | + | 0.911463i | \(0.634954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.51941 | 0.163561 | 0.0817805 | − | 0.996650i | \(-0.473939\pi\) | ||||
0.0817805 | + | 0.996650i | \(0.473939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.52946 | 0.349170 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.6061 | 1.92530 | 0.962650 | − | 0.270749i | \(-0.0872712\pi\) | ||||
0.962650 | + | 0.270749i | \(0.0872712\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.62721 | 0.0751377 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.2197 | −0.793441 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.32391 | −0.152834 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.10278 | −0.142365 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.432226 | 0.0197903 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.67107 | 0.350500 | 0.175250 | − | 0.984524i | \(-0.443927\pi\) | ||||
0.175250 | + | 0.984524i | \(0.443927\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.62721 | −0.165387 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.67609 | −0.212769 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.67609 | 0.121515 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.4600 | 0.791187 | 0.395594 | − | 0.918426i | \(-0.370539\pi\) | ||||
0.395594 | + | 0.918426i | \(0.370539\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.0872 | −0.591823 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.1955 | −0.730893 | −0.365446 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365446 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4111 | 0.558968 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.372787 | −0.0167555 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.01413 | −0.135202 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.41612 | −0.421524 | −0.210762 | − | 0.977537i | \(-0.567594\pi\) | ||||
−0.210762 | + | 0.977537i | \(0.567594\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.5089 | −0.826915 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.2333 | 1.12510 | 0.562549 | − | 0.826764i | \(-0.309821\pi\) | ||||
0.562549 | + | 0.826764i | \(0.309821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7003 | −0.609654 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.284145 | 0.0126193 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.4736 | 1.74964 | 0.874818 | − | 0.484451i | \(-0.160981\pi\) | ||||
0.874818 | + | 0.484451i | \(0.160981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3764 | 0.989872 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.2544 | 0.673499 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.62721 | 0.336095 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.33804 | −0.102827 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0242 | 0.922859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.6413 | 0.991935 | 0.495968 | − | 0.868341i | \(-0.334813\pi\) | ||||
0.495968 | + | 0.868341i | \(0.334813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.8328 | −1.12959 | −0.564794 | − | 0.825232i | \(-0.691044\pi\) | ||||
−0.564794 | + | 0.825232i | \(0.691044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.28917 | −0.143551 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.7633 | 1.12227 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9789 | −0.912125 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.15165 | 0.180166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.2439 | −1.31001 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.89722 | 0.211725 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2056 | −0.526708 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.78389 | −0.206057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.57834 | −0.196838 | −0.0984190 | − | 0.995145i | \(-0.531379\pi\) | ||||
−0.0984190 | + | 0.995145i | \(0.531379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.0731 | 0.775589 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9894 | 0.727748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.7244 | −0.629572 | −0.314786 | − | 0.949163i | \(-0.601933\pi\) | ||||
−0.314786 | + | 0.949163i | \(0.601933\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.989437 | −0.0422282 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.20555 | 0.264365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.7839 | −0.798772 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.81361 | 0.0769833 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.4494 | 0.527499 | 0.263749 | − | 0.964591i | \(-0.415041\pi\) | ||||
0.263749 | + | 0.964591i | \(0.415041\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.35218 | −0.395555 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.5089 | −0.612564 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.83276 | −0.414402 | −0.207201 | − | 0.978298i | \(-0.566435\pi\) | ||||
−0.207201 | + | 0.978298i | \(0.566435\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.37279 | 0.183965 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.7441 | 0.745183 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.2439 | −0.848667 | −0.424333 | − | 0.905506i | \(-0.639492\pi\) | ||||
−0.424333 | + | 0.905506i | \(0.639492\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.6691 | 1.74380 | 0.871899 | − | 0.489686i | \(-0.162889\pi\) | ||||
0.871899 | + | 0.489686i | \(0.162889\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.0383 | 0.920664 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.42166 | 0.0592874 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.04888 | −0.376710 | −0.188355 | − | 0.982101i | \(-0.560315\pi\) | ||||
−0.188355 | + | 0.982101i | \(0.560315\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.82272 | −0.325101 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.8958 | −0.991364 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.92694 | 0.0798059 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.04888 | −0.0433657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.41110 | 0.182066 | 0.0910328 | − | 0.995848i | \(-0.470983\pi\) | ||||
0.0910328 | + | 0.995848i | \(0.470983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8816 | 0.530779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.8569 | 1.92744 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.9269 | −0.489781 | −0.244890 | − | 0.969551i | \(-0.578752\pi\) | ||||
−0.244890 | + | 0.969551i | \(0.578752\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2544 | −0.461386 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.5577 | 0.718590 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.4564 | 1.12184 | 0.560919 | − | 0.827871i | \(-0.310448\pi\) | ||||
0.560919 | + | 0.827871i | \(0.310448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.7038 | 0.640573 | 0.320286 | − | 0.947321i | \(-0.396221\pi\) | ||||
0.320286 | + | 0.947321i | \(0.396221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.259449 | −0.0105656 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.33804 | 0.379645 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1355 | −0.939043 | −0.469521 | − | 0.882921i | \(-0.655574\pi\) | ||||
−0.469521 | + | 0.882921i | \(0.655574\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.57834 | 0.266568 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.57834 | −0.266131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.1013 | −1.70046 | −0.850228 | − | 0.526414i | \(-0.823536\pi\) | ||||
−0.850228 | + | 0.526414i | \(0.823536\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.1219 | 0.609775 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.60303 | −0.185311 | −0.0926556 | − | 0.995698i | \(-0.529536\pi\) | ||||
−0.0926556 | + | 0.995698i | \(0.529536\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.24029 | 0.331205 | 0.165603 | − | 0.986193i | \(-0.447043\pi\) | ||||
0.165603 | + | 0.986193i | \(0.447043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.98944 | −0.280476 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.4600 | 0.859776 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.25443 | −0.289714 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.20555 | 0.247431 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.2772 | −0.687793 | −0.343896 | − | 0.939008i | \(-0.611747\pi\) | ||||
−0.343896 | + | 0.939008i | \(0.611747\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.2297 | −0.764313 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.34307 | 0.291401 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.4600 | −0.533304 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.480585 | 0.0190117 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2091 | 0.482231 | 0.241116 | − | 0.970496i | \(-0.422487\pi\) | ||||
0.241116 | + | 0.970496i | \(0.422487\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.1184 | −0.832827 | −0.416413 | − | 0.909175i | \(-0.636713\pi\) | ||||
−0.416413 | + | 0.909175i | \(0.636713\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.67609 | 0.184121 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.8222 | −1.13312 | −0.566559 | − | 0.824021i | \(-0.691726\pi\) | ||||
−0.566559 | + | 0.824021i | \(0.691726\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.5089 | 0.726536 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.6555 | 0.535200 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.8716 | −1.20810 | −0.604049 | − | 0.796947i | \(-0.706447\pi\) | ||||
−0.604049 | + | 0.796947i | \(0.706447\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.6705 | 0.807665 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.56777 | −0.139192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.5713 | −1.22984 | −0.614922 | − | 0.788588i | \(-0.710813\pi\) | ||||
−0.614922 | + | 0.788588i | \(0.710813\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0872 | −0.586824 | −0.293412 | − | 0.955986i | \(-0.594791\pi\) | ||||
−0.293412 | + | 0.955986i | \(0.594791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.8222 | −1.58540 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.62721 | −0.218214 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.84333 | −0.110094 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.9264 | 0.809062 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.41110 | −0.170289 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.39697 | −0.285132 | −0.142566 | − | 0.989785i | \(-0.545535\pi\) | ||||
−0.142566 | + | 0.989785i | \(0.545535\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.91638 | −0.189232 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.3970 | 0.438021 | 0.219011 | − | 0.975723i | \(-0.429717\pi\) | ||||
0.219011 | + | 0.975723i | \(0.429717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.85337 | 0.186255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.25443 | −0.124710 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.75614 | 0.0671967 | 0.0335984 | − | 0.999435i | \(-0.489303\pi\) | ||||
0.0335984 | + | 0.999435i | \(0.489303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4111 | 0.397788 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.4458 | 0.703753 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.42166 | 0.206549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.2233 | −1.49212 | −0.746061 | − | 0.665877i | \(-0.768058\pi\) | ||||
−0.746061 | + | 0.665877i | \(0.768058\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.676089 | −0.0256825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.09775 | −0.231301 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 51.7422 | 1.95987 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 24.7839 | 0.937413 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.167237 | −0.00631645 | −0.00315823 | − | 0.999995i | \(-0.501005\pi\) | ||||
−0.00315823 | + | 0.999995i | \(0.501005\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.10278 | 0.117023 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.28917 | 0.123877 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.8469 | −0.934464 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.6172 | −0.586515 | −0.293258 | − | 0.956033i | \(-0.594739\pi\) | ||||
−0.293258 | + | 0.956033i | \(0.594739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.99498 | 0.112320 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.90225 | −0.221041 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.67609 | −0.174876 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39.1255 | 1.46117 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.9547 | 1.52735 | 0.763676 | − | 0.645599i | \(-0.223392\pi\) | ||||
0.763676 | + | 0.645599i | \(0.223392\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.8328 | 0.515159 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.52946 | −0.0568813 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | −0.148352 | −0.0741759 | − | 0.997245i | \(-0.523633\pi\) | ||||
−0.0741759 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.9200 | 0.885924 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0000 | 0.591781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.01413 | 0.185201 | 0.0926006 | − | 0.995703i | \(-0.470482\pi\) | ||||
0.0926006 | + | 0.995703i | \(0.470482\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.72999 | 0.248239 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.15667 | −0.0426066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.4358 | 1.34031 | 0.670156 | − | 0.742220i | \(-0.266227\pi\) | ||||
0.670156 | + | 0.742220i | \(0.266227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.4111 | −0.749821 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.66698 | 0.244588 | 0.122294 | − | 0.992494i | \(-0.460975\pi\) | ||||
0.122294 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.1219 | 0.700573 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.81004 | 0.139402 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.88164 | 0.324528 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.1986 | 1.13845 | 0.569226 | − | 0.822181i | \(-0.307243\pi\) | ||||
0.569226 | + | 0.822181i | \(0.307243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.40105 | 0.306151 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.6167 | −0.677529 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −51.9789 | −1.88920 | −0.944602 | − | 0.328218i | \(-0.893552\pi\) | ||||
−0.944602 | + | 0.328218i | \(0.893552\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.32391 | 0.120650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.1320 | −0.548534 | −0.274267 | − | 0.961654i | \(-0.588435\pi\) | ||||
−0.274267 | + | 0.961654i | \(0.588435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.8122 | 1.11547 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.79445 | 0.0648785 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.0766 | 1.88038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.2933 | 1.45301 | 0.726506 | − | 0.687160i | \(-0.241143\pi\) | ||||
0.726506 | + | 0.687160i | \(0.241143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.5678 | 1.06486 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.6691 | −1.13906 | −0.569529 | − | 0.821971i | \(-0.692874\pi\) | ||||
−0.569529 | + | 0.821971i | \(0.692874\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.15165 | −0.149132 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.28917 | 0.117998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.8711 | 0.926928 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.14254 | 0.0766661 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.83276 | 0.351394 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.49472 | 0.338881 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.9880 | −1.42542 | −0.712709 | − | 0.701460i | \(-0.752532\pi\) | ||||
−0.712709 | + | 0.701460i | \(0.752532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −48.1114 | −1.71281 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.93051 | 0.281977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4111 | −0.440731 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.71083 | −0.0961433 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.98995 | 0.212175 | 0.106088 | − | 0.994357i | \(-0.466168\pi\) | ||||
0.106088 | + | 0.994357i | \(0.466168\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2544 | 0.398153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.42166 | −0.120899 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.9058 | −0.561304 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.57834 | 0.0908744 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.1849 | 0.534535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.3522 | 0.961651 | 0.480826 | − | 0.876816i | \(-0.340337\pi\) | ||||
0.480826 | + | 0.876816i | \(0.340337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.9753 | −0.841887 | −0.420943 | − | 0.907087i | \(-0.638301\pi\) | ||||
−0.420943 | + | 0.907087i | \(0.638301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.01413 | 0.105710 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.21611 | 0.252769 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.00000 | 0.279885 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.90225 | −0.0664699 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.1779 | 1.47202 | 0.736010 | − | 0.676970i | \(-0.236707\pi\) | ||||
0.736010 | + | 0.676970i | \(0.236707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.20053 | −0.320710 | −0.160355 | − | 0.987059i | \(-0.551264\pi\) | ||||
−0.160355 | + | 0.987059i | \(0.551264\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.33804 | 0.0814003 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.31386 | 0.323875 | 0.161937 | − | 0.986801i | \(-0.448226\pi\) | ||||
0.161937 | + | 0.986801i | \(0.448226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.167237 | 0.00580838 | 0.00290419 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290419 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.25443 | 0.112895 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.0278 | 0.797864 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.2056 | 0.353178 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.4111 | 0.705511 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.2721 | −1.25225 | −0.626126 | − | 0.779721i | \(-0.715361\pi\) | ||||
−0.626126 | + | 0.779721i | \(0.715361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.1078 | 0.417015 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.156674 | −0.00538976 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.9355 | 0.581912 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.74557 | 0.162868 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.42166 | −0.0487340 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.3133 | −0.421601 | −0.210801 | − | 0.977529i | \(-0.567607\pi\) | ||||
−0.210801 | + | 0.977529i | \(0.567607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.897225 | 0.0306844 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.8716 | −1.05455 | −0.527277 | − | 0.849694i | \(-0.676787\pi\) | ||||
−0.527277 | + | 0.849694i | \(0.676787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5628 | −0.701592 | −0.350796 | − | 0.936452i | \(-0.614089\pi\) | ||||
−0.350796 | + | 0.936452i | \(0.614089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.4252 | 0.934649 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.0816 | 1.39844 | 0.699218 | − | 0.714909i | \(-0.253532\pi\) | ||||
0.699218 | + | 0.714909i | \(0.253532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.5925 | −0.394156 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.0086 | 1.32480 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3522 | 0.452942 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.25443 | −0.110272 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.773841 | −0.0261905 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.81361 | 0.0613111 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.5266 | −1.67239 | −0.836196 | − | 0.548430i | \(-0.815226\pi\) | ||||
−0.836196 | + | 0.548430i | \(0.815226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.52946 | −0.0515874 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.9583 | 1.71683 | 0.858414 | − | 0.512958i | \(-0.171450\pi\) | ||||
0.858414 | + | 0.512958i | \(0.171450\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3421 | −1.32397 | −0.661984 | − | 0.749518i | \(-0.730285\pi\) | ||||
−0.661984 | + | 0.749518i | \(0.730285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.0383 | −0.875268 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.4202 | 1.42433 | 0.712166 | − | 0.702011i | \(-0.247714\pi\) | ||||
0.712166 | + | 0.702011i | \(0.247714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.3174 | 0.446652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6131 | −0.422554 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.62721 | 0.188308 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.72999 | 0.224959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.35218 | 0.312260 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.30330 | 0.276931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.27555 | −0.309013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48059 | 0.282216 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.96526 | −0.331256 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6756 | 0.719726 | 0.359863 | − | 0.933005i | \(-0.382824\pi\) | ||||
0.359863 | + | 0.933005i | \(0.382824\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.96169 | 0.131401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.4444 | −0.644221 | −0.322111 | − | 0.946702i | \(-0.604392\pi\) | ||||
−0.322111 | + | 0.946702i | \(0.604392\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.9859 | 0.562150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.20555 | 0.205149 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.4882 | 1.23797 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.8167 | −1.61031 | −0.805157 | − | 0.593062i | \(-0.797919\pi\) | ||||
−0.805157 | + | 0.593062i | \(0.797919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.0242 | 0.890477 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.02827 | 0.198423 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.20555 | −0.0724398 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.8011 | 1.46988 | 0.734938 | − | 0.678135i | \(-0.237211\pi\) | ||||
0.734938 | + | 0.678135i | \(0.237211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.5139 | 0.377352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.4494 | 1.25878 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.00000 | 0.261628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.2297 | −1.21624 | −0.608121 | − | 0.793844i | \(-0.708077\pi\) | ||||
−0.608121 | + | 0.793844i | \(0.708077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.9794 | 0.423566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.1572 | 0.396313 | 0.198157 | − | 0.980170i | \(-0.436505\pi\) | ||||
0.198157 | + | 0.980170i | \(0.436505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8539 | −0.386016 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.91638 | −0.290050 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.9300 | −0.940099 | −0.470049 | − | 0.882640i | \(-0.655764\pi\) | ||||
−0.470049 | + | 0.882640i | \(0.655764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −44.7527 | −1.45273 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.52946 | −0.309014 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.4842 | −1.57056 | −0.785278 | − | 0.619143i | \(-0.787480\pi\) | ||||
−0.785278 | + | 0.619143i | \(0.787480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.1517 | −0.393218 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.67609 | −0.151156 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.8816 | 0.609720 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7638 | −0.443993 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.41612 | −0.0456339 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.31335 | 0.138852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.6272 | 0.502537 | 0.251269 | − | 0.967917i | \(-0.419152\pi\) | ||||
0.251269 | + | 0.967917i | \(0.419152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.9200 | 1.12179 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.6832 | 1.43395 | 0.716977 | − | 0.697097i | \(-0.245525\pi\) | ||||
0.716977 | + | 0.697097i | \(0.245525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.0589 | −0.354533 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.57834 | 0.210675 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.51941 | 0.304553 | 0.152277 | − | 0.988338i | \(-0.451340\pi\) | ||||
0.152277 | + | 0.988338i | \(0.451340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.2544 | −0.487534 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.91281 | −0.156854 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.77187 | −0.279779 | −0.139890 | − | 0.990167i | \(-0.544675\pi\) | ||||
−0.139890 | + | 0.990167i | \(0.544675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.8363 | −0.823214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.96526 | 0.189876 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.66553 | −0.116557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5033 | −0.587777 | −0.293889 | − | 0.955840i | \(-0.594949\pi\) | ||||
−0.293889 | + | 0.955840i | \(0.594949\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.2233 | −1.05431 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.68111 | −0.306912 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.4877 | 1.21892 | 0.609459 | − | 0.792817i | \(-0.291387\pi\) | ||||
0.609459 | + | 0.792817i | \(0.291387\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.91638 | 0.155547 |
(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 | 2960.2.a.r.1.3 | 3 | ||
4.3 | odd | 2 | 1480.2.a.e.1.1 | ✓ | 3 | ||
20.19 | odd | 2 | 7400.2.a.l.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
2960.2.a.r.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7400.2.a.l.1.3 | 3 | 20.19 | odd | 2 |