Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9280,2,Mod(1,9280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9280, 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("9280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9280 = 2^{6} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9280.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: | \(74.1011730757\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 3x + 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 580) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9280.1 |
$q$-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 | ||||||||
\(3\) | 2.90321 | 1.67617 | 0.838085 | − | 0.545540i | \(-0.183675\pi\) | ||||
0.838085 | + | 0.545540i | \(0.183675\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.52543 | 0.576557 | 0.288279 | − | 0.957547i | \(-0.406917\pi\) | ||||
0.288279 | + | 0.957547i | \(0.406917\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.42864 | 1.80955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.52543 | −0.459934 | −0.229967 | − | 0.973198i | \(-0.573862\pi\) | ||||
−0.229967 | + | 0.973198i | \(0.573862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.622216 | −0.172572 | −0.0862858 | − | 0.996270i | \(-0.527500\pi\) | ||||
−0.0862858 | + | 0.996270i | \(0.527500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.90321 | −0.749606 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.52543 | 1.34011 | 0.670057 | − | 0.742310i | \(-0.266270\pi\) | ||||
0.670057 | + | 0.742310i | \(0.266270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.90321 | 0.666042 | 0.333021 | − | 0.942919i | \(-0.391932\pi\) | ||||
0.333021 | + | 0.942919i | \(0.391932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.42864 | 0.966408 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.90321 | 0.605362 | 0.302681 | − | 0.953092i | \(-0.402118\pi\) | ||||
0.302681 | + | 0.953092i | \(0.402118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.05086 | 1.35694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.90321 | 0.521432 | 0.260716 | − | 0.965416i | \(-0.416041\pi\) | ||||
0.260716 | + | 0.965416i | \(0.416041\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.42864 | −0.770927 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52543 | −0.257844 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.47457 | −0.406817 | −0.203409 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203409 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.80642 | −0.289259 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.23506 | −1.28610 | −0.643050 | − | 0.765824i | \(-0.722331\pi\) | ||||
−0.643050 | + | 0.765824i | \(0.722331\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65878 | −0.862956 | −0.431478 | − | 0.902123i | \(-0.642008\pi\) | ||||
−0.431478 | + | 0.902123i | \(0.642008\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.42864 | −0.809254 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.70964 | 0.686971 | 0.343485 | − | 0.939158i | \(-0.388392\pi\) | ||||
0.343485 | + | 0.939158i | \(0.388392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.67307 | −0.667582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.0415 | 2.24626 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2859 | 1.55024 | 0.775120 | − | 0.631814i | \(-0.217689\pi\) | ||||
0.775120 | + | 0.631814i | \(0.217689\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.52543 | 0.205689 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.42864 | 1.11640 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2351 | 1.33249 | 0.666246 | − | 0.745732i | \(-0.267900\pi\) | ||||
0.666246 | + | 0.745732i | \(0.267900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.93978 | 1.01658 | 0.508292 | − | 0.861185i | \(-0.330277\pi\) | ||||
0.508292 | + | 0.861185i | \(0.330277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.28100 | 1.04331 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.622216 | 0.0771764 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.90321 | −0.354684 | −0.177342 | − | 0.984149i | \(-0.556750\pi\) | ||||
−0.177342 | + | 0.984149i | \(0.556750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.42864 | 1.01469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.47949 | −0.887653 | −0.443826 | − | 0.896113i | \(-0.646379\pi\) | ||||
−0.443826 | + | 0.896113i | \(0.646379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.90321 | 0.339795 | 0.169898 | − | 0.985462i | \(-0.445656\pi\) | ||||
0.169898 | + | 0.985462i | \(0.445656\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.90321 | 0.335234 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.32693 | −0.265178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.5763 | 1.86498 | 0.932489 | − | 0.361199i | \(-0.117632\pi\) | ||||
0.932489 | + | 0.361199i | \(0.117632\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18421 | 0.464912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.76986 | −0.743089 | −0.371544 | − | 0.928415i | \(-0.621172\pi\) | ||||
−0.371544 | + | 0.928415i | \(0.621172\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.52543 | −0.599317 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.90321 | −0.311257 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.9081 | 1.47426 | 0.737130 | − | 0.675751i | \(-0.236181\pi\) | ||||
0.737130 | + | 0.675751i | \(0.236181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.949145 | −0.0994974 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.42864 | 0.874009 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.90321 | −0.297863 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.5669 | 1.78365 | 0.891825 | − | 0.452381i | \(-0.149425\pi\) | ||||
0.891825 | + | 0.452381i | \(0.149425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.28100 | −0.832271 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.05086 | −0.502579 | −0.251289 | − | 0.967912i | \(-0.580855\pi\) | ||||
−0.251289 | + | 0.967912i | \(0.580855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.56691 | −0.942656 | −0.471328 | − | 0.881958i | \(-0.656225\pi\) | ||||
−0.471328 | + | 0.881958i | \(0.656225\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.42864 | −0.432191 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.576283 | −0.0557113 | −0.0278557 | − | 0.999612i | \(-0.508868\pi\) | ||||
−0.0278557 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.28592 | −0.697864 | −0.348932 | − | 0.937148i | \(-0.613456\pi\) | ||||
−0.348932 | + | 0.937148i | \(0.613456\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.18421 | −0.681895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7605 | 1.10633 | 0.553167 | − | 0.833070i | \(-0.313419\pi\) | ||||
0.553167 | + | 0.833070i | \(0.313419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.90321 | −0.270726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.37778 | −0.312276 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.42864 | 0.772652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.67307 | −0.788461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.9081 | −2.15572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5161 | 1.28809 | 0.644046 | − | 0.764987i | \(-0.277255\pi\) | ||||
0.644046 | + | 0.764987i | \(0.277255\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.4286 | −1.44646 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.7605 | −1.37700 | −0.688500 | − | 0.725236i | \(-0.741731\pi\) | ||||
−0.688500 | + | 0.725236i | \(0.741731\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.42864 | 0.384012 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.05086 | −0.606841 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.52543 | 0.472069 | 0.236035 | − | 0.971745i | \(-0.424152\pi\) | ||||
0.236035 | + | 0.971745i | \(0.424152\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4193 | −1.47748 | −0.738742 | − | 0.673989i | \(-0.764580\pi\) | ||||
−0.738742 | + | 0.673989i | \(0.764580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.6731 | 1.15148 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.949145 | 0.0793715 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.5669 | −1.11898 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.00000 | −0.163846 | −0.0819232 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819232 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.37778 | 0.437638 | 0.218819 | − | 0.975765i | \(-0.429780\pi\) | ||||
0.218819 | + | 0.975765i | \(0.429780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.9956 | 2.42500 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.90321 | −0.233192 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.39207 | 0.111100 | 0.0555498 | − | 0.998456i | \(-0.482309\pi\) | ||||
0.0555498 | + | 0.998456i | \(0.482309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 32.7654 | 2.59847 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.42864 | 0.349026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.19850 | 0.563830 | 0.281915 | − | 0.959439i | \(-0.409030\pi\) | ||||
0.281915 | + | 0.959439i | \(0.409030\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.42864 | 0.344769 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.7605 | −1.21958 | −0.609792 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609792 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6128 | −0.970219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.7605 | 1.20523 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.4795 | −1.02483 | −0.512413 | − | 0.858739i | \(-0.671248\pi\) | ||||
−0.512413 | + | 0.858739i | \(0.671248\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.52543 | 0.115311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.7146 | 2.23348 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.266706 | −0.0199346 | −0.00996728 | − | 0.999950i | \(-0.503173\pi\) | ||||
−0.00996728 | + | 0.999950i | \(0.503173\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7971 | 1.54583 | 0.772916 | − | 0.634508i | \(-0.218797\pi\) | ||||
0.772916 | + | 0.634508i | \(0.218797\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.0509 | 1.70397 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.47457 | 0.181934 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.42864 | −0.616363 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.7556 | 0.782353 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.43356 | 0.682589 | 0.341294 | − | 0.939956i | \(-0.389135\pi\) | ||||
0.341294 | + | 0.939956i | \(0.389135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.23014 | 0.376474 | 0.188237 | − | 0.982124i | \(-0.439723\pi\) | ||||
0.188237 | + | 0.982124i | \(0.439723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.80642 | 0.129361 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.5397 | −0.822171 | −0.411085 | − | 0.911597i | \(-0.634850\pi\) | ||||
−0.411085 | + | 0.911597i | \(0.634850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.33677 | −0.590978 | −0.295489 | − | 0.955346i | \(-0.595483\pi\) | ||||
−0.295489 | + | 0.955346i | \(0.595483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.42864 | −0.594510 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52543 | −0.107064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.23506 | 0.575162 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.7605 | 1.09543 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.42864 | −0.306335 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.79213 | 0.674118 | 0.337059 | − | 0.941483i | \(-0.390568\pi\) | ||||
0.337059 | + | 0.941483i | \(0.390568\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.7146 | −1.48786 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65878 | 0.385926 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.42864 | 0.300636 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.42864 | 0.569555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.43801 | −0.231265 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0558 | −1.07517 | −0.537587 | − | 0.843208i | \(-0.680664\pi\) | ||||
−0.537587 | + | 0.843208i | \(0.680664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.42864 | 0.361909 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.1985 | 1.27425 | 0.637125 | − | 0.770761i | \(-0.280124\pi\) | ||||
0.637125 | + | 0.770761i | \(0.280124\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5906 | 0.699845 | 0.349922 | − | 0.936779i | \(-0.386208\pi\) | ||||
0.349922 | + | 0.936779i | \(0.386208\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.75557 | −0.444484 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1240 | 1.51490 | 0.757451 | − | 0.652892i | \(-0.226444\pi\) | ||||
0.757451 | + | 0.652892i | \(0.226444\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.70964 | −0.307223 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 48.1245 | 3.12602 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9906 | 1.09903 | 0.549516 | − | 0.835483i | \(-0.314812\pi\) | ||||
0.549516 | + | 0.835483i | \(0.314812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.368416 | 0.0237318 | 0.0118659 | − | 0.999930i | \(-0.496223\pi\) | ||||
0.0118659 | + | 0.999930i | \(0.496223\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.00492 | −0.577666 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.67307 | 0.298552 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.80642 | −0.114940 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.6543 | −1.24554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7190 | 0.992175 | 0.496087 | − | 0.868273i | \(-0.334770\pi\) | ||||
0.496087 | + | 0.868273i | \(0.334770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.42864 | −0.278426 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.0415 | −1.00456 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.6035 | 1.16045 | 0.580227 | − | 0.814455i | \(-0.302964\pi\) | ||||
0.580227 | + | 0.814455i | \(0.302964\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.77478 | −0.234553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.42864 | −0.336024 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.7096 | 0.783710 | 0.391855 | − | 0.920027i | \(-0.371834\pi\) | ||||
0.391855 | + | 0.920027i | \(0.371834\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.2859 | −0.693288 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.3783 | 2.47111 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.7462 | −1.32589 | −0.662945 | − | 0.748668i | \(-0.730694\pi\) | ||||
−0.662945 | + | 0.748668i | \(0.730694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3827 | 1.11667 | 0.558335 | − | 0.829616i | \(-0.311440\pi\) | ||||
0.558335 | + | 0.829616i | \(0.311440\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.75557 | −0.166775 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.52543 | −0.0919867 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7971 | −0.768901 | −0.384450 | − | 0.923146i | \(-0.625609\pi\) | ||||
−0.384450 | + | 0.923146i | \(0.625609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.7605 | 0.943556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.1842 | 1.26374 | 0.631872 | − | 0.775073i | \(-0.282287\pi\) | ||||
0.631872 | + | 0.775073i | \(0.282287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.68736 | −0.338079 | −0.169039 | − | 0.985609i | \(-0.554066\pi\) | ||||
−0.169039 | + | 0.985609i | \(0.554066\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.42864 | −0.499270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5620 | −0.741511 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5303 | 0.795903 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 51.0005 | 2.98970 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.0879 | 1.46565 | 0.732825 | − | 0.680417i | \(-0.238201\pi\) | ||||
0.732825 | + | 0.680417i | \(0.238201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2351 | −0.595908 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.7556 | −0.624101 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.80642 | −0.104468 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.63206 | −0.497544 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.6637 | −0.842408 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.93978 | −0.454630 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.8113 | 1.75850 | 0.879248 | − | 0.476364i | \(-0.158046\pi\) | ||||
0.879248 | + | 0.476364i | \(0.158046\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −27.7748 | −1.58005 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.0370 | −1.70324 | −0.851622 | − | 0.524156i | \(-0.824381\pi\) | ||||
−0.851622 | + | 0.524156i | \(0.824381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3368 | −1.03646 | −0.518228 | − | 0.855243i | \(-0.673408\pi\) | ||||
−0.518228 | + | 0.855243i | \(0.673408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.28100 | −0.466581 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.4558 | −1.14891 | −0.574457 | − | 0.818535i | \(-0.694787\pi\) | ||||
−0.574457 | + | 0.818535i | \(0.694787\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.52543 | 0.0854075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.67307 | −0.0933817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0415 | 0.892572 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.622216 | −0.0345143 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.1526 | −1.16974 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.18421 | 0.396078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0272 | −0.661075 | −0.330537 | − | 0.943793i | \(-0.607230\pi\) | ||||
−0.330537 | + | 0.943793i | \(0.607230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.4336 | −0.736155 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.90321 | 0.158619 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.2306 | −1.75571 | −0.877857 | − | 0.478923i | \(-0.841027\pi\) | ||||
−0.877857 | + | 0.478923i | \(0.841027\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.1432 | 1.85440 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.42864 | −0.239824 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8064 | −0.961457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.42864 | −0.453783 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.9037 | −1.60531 | −0.802657 | − | 0.596441i | \(-0.796581\pi\) | ||||
−0.802657 | + | 0.596441i | \(0.796581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.8163 | −1.59603 | −0.798014 | − | 0.602639i | \(-0.794116\pi\) | ||||
−0.798014 | + | 0.602639i | \(0.794116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.38715 | −0.234169 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1842 | 1.12752 | 0.563761 | − | 0.825938i | \(-0.309354\pi\) | ||||
0.563761 | + | 0.825938i | \(0.309354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.47949 | 0.396970 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.4701 | 1.29510 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1985 | −0.591034 | −0.295517 | − | 0.955337i | \(-0.595492\pi\) | ||||
−0.295517 | + | 0.955337i | \(0.595492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5714 | −0.556387 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.1798 | −1.32159 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.90321 | −0.151961 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.95407 | 0.519598 | 0.259799 | − | 0.965663i | \(-0.416344\pi\) | ||||
0.259799 | + | 0.965663i | \(0.416344\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −44.7052 | −2.32726 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.2159 | 0.893802 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.29529 | −0.118845 | −0.0594227 | − | 0.998233i | \(-0.518926\pi\) | ||||
−0.0594227 | + | 0.998233i | \(0.518926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.90321 | −0.149921 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.622216 | 0.0320457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.61729 | 0.494007 | 0.247004 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247004 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.1432 | 2.15906 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.86172 | 0.350618 | 0.175309 | − | 0.984513i | \(-0.443908\pi\) | ||||
0.175309 | + | 0.984513i | \(0.443908\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.32693 | 0.118591 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.7195 | −1.56156 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.3590 | −1.28575 | −0.642877 | − | 0.765969i | \(-0.722260\pi\) | ||||
−0.642877 | + | 0.765969i | \(0.722260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0415 | 0.811253 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −45.7560 | −2.30809 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.5763 | −0.834043 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.2766 | −1.21841 | −0.609203 | − | 0.793015i | \(-0.708510\pi\) | ||||
−0.609203 | + | 0.793015i | \(0.708510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.8573 | 0.643669 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.30465 | 0.264902 | 0.132451 | − | 0.991190i | \(-0.457715\pi\) | ||||
0.132451 | + | 0.991190i | \(0.457715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.80642 | −0.0899844 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.18421 | −0.207915 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.77478 | 0.187109 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.714082 | 0.0353091 | 0.0176545 | − | 0.999844i | \(-0.494380\pi\) | ||||
0.0176545 | + | 0.999844i | \(0.494380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.0415 | 0.791268 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.6128 | 0.768258 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.76986 | 0.332319 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.5718 | −2.47651 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.6321 | −0.812529 | −0.406265 | − | 0.913755i | \(-0.633169\pi\) | ||||
−0.406265 | + | 0.913755i | \(0.633169\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.4286 | 1.48300 | 0.741501 | − | 0.670952i | \(-0.234114\pi\) | ||||
0.741501 | + | 0.670952i | \(0.234114\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.5669 | 1.24311 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.52543 | 0.268023 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1116 | 0.586119 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.75557 | 0.133040 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.2257 | 1.50409 | 0.752044 | − | 0.659112i | \(-0.229068\pi\) | ||||
0.752044 | + | 0.659112i | \(0.229068\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.2400 | 1.69353 | 0.846763 | − | 0.531971i | \(-0.178548\pi\) | ||||
0.846763 | + | 0.531971i | \(0.178548\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.90321 | 0.139198 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.42864 | 0.403197 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.6133 | −1.46109 | −0.730547 | − | 0.682862i | \(-0.760735\pi\) | ||||
−0.730547 | + | 0.682862i | \(0.760735\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.3684 | −1.20802 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.4938 | 1.49631 | 0.748157 | − | 0.663521i | \(-0.230939\pi\) | ||||
0.748157 | + | 0.663521i | \(0.230939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.9081 | −0.659309 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.80642 | −0.274634 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.6321 | −0.879301 | −0.439651 | − | 0.898169i | \(-0.644898\pi\) | ||||
−0.439651 | + | 0.898169i | \(0.644898\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.5620 | 0.591521 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.6128 | 0.733556 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.949145 | 0.0444966 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.2859 | −1.46349 | −0.731747 | − | 0.681577i | \(-0.761295\pi\) | ||||
−0.731747 | + | 0.681577i | \(0.761295\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 38.9590 | 1.81845 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.9304 | 1.34742 | 0.673712 | − | 0.738994i | \(-0.264699\pi\) | ||||
0.673712 | + | 0.738994i | \(0.264699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.1289 | 0.656626 | 0.328313 | − | 0.944569i | \(-0.393520\pi\) | ||||
0.328313 | + | 0.944569i | \(0.393520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.42864 | −0.390869 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6909 | 1.42021 | 0.710103 | − | 0.704098i | \(-0.248648\pi\) | ||||
0.710103 | + | 0.704098i | \(0.248648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.42864 | −0.204496 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.04149 | 0.186222 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.63206 | 0.396903 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.90321 | 0.133208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 61.2672 | 2.80523 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.04641 | −0.413341 | −0.206670 | − | 0.978411i | \(-0.566263\pi\) | ||||
−0.206670 | + | 0.978411i | \(0.566263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.53972 | 0.0702051 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.8573 | 0.585026 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.5669 | −0.797673 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6494 | 0.663828 | 0.331914 | − | 0.943310i | \(-0.392306\pi\) | ||||
0.331914 | + | 0.943310i | \(0.392306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.8988 | 0.945075 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.1289 | −0.998664 | −0.499332 | − | 0.866411i | \(-0.666421\pi\) | ||||
−0.499332 | + | 0.866411i | \(0.666421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.52543 | −0.248853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.28100 | 0.372203 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4094 | −0.511783 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.9813 | 1.34215 | 0.671073 | − | 0.741391i | \(-0.265834\pi\) | ||||
0.671073 | + | 0.741391i | \(0.265834\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −45.7560 | −2.04423 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6874 | 0.788640 | 0.394320 | − | 0.918973i | \(-0.370980\pi\) | ||||
0.394320 | + | 0.918973i | \(0.370980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.05086 | 0.224760 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.6178 | −1.62625 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.45091 | −0.0643107 | −0.0321553 | − | 0.999483i | \(-0.510237\pi\) | ||||
−0.0321553 | + | 0.999483i | \(0.510237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.42864 | 0.195911 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.4701 | 0.903778 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.56691 | 0.421569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.18421 | −0.315961 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −39.1338 | −1.71778 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.8765 | −1.39653 | −0.698267 | − | 0.715837i | \(-0.746045\pi\) | ||||
−0.698267 | + | 0.715837i | \(0.746045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9032 | 0.651672 | 0.325836 | − | 0.945426i | \(-0.394354\pi\) | ||||
0.325836 | + | 0.945426i | \(0.394354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.42864 | 0.193282 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.0415 | 0.698778 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5714 | −0.633537 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 55.5625 | 2.41121 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.12399 | 0.221944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.576283 | 0.0249149 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.774305 | −0.0334137 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.12843 | 0.307043 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7841 | 0.549633 | 0.274817 | − | 0.961497i | \(-0.411383\pi\) | ||||
0.274817 | + | 0.961497i | \(0.411383\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.3783 | 2.59108 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.28592 | 0.312094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.8617 | −0.806469 | −0.403235 | − | 0.915097i | \(-0.632114\pi\) | ||||
−0.403235 | + | 0.915097i | \(0.632114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 43.1022 | 1.83956 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.90321 | −0.123681 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.2859 | 1.07527 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.18421 | 0.304953 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.6316 | 0.662331 | 0.331166 | − | 0.943573i | \(-0.392558\pi\) | ||||
0.331166 | + | 0.943573i | \(0.392558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.52098 | 0.148922 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.4701 | −1.03313 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.18865 | −0.0500958 | −0.0250479 | − | 0.999686i | \(-0.507974\pi\) | ||||
−0.0250479 | + | 0.999686i | \(0.507974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.7605 | −0.494768 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.38271 | 0.268048 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.5303 | 1.19605 | 0.598027 | − | 0.801476i | \(-0.295951\pi\) | ||||
0.598027 | + | 0.801476i | \(0.295951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.8385 | −0.955763 | −0.477882 | − | 0.878424i | \(-0.658595\pi\) | ||||
−0.477882 | + | 0.878424i | \(0.658595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.3876 | 1.14413 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.90321 | 0.121072 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.18913 | 0.174396 | 0.0871979 | − | 0.996191i | \(-0.472209\pi\) | ||||
0.0871979 | + | 0.996191i | \(0.472209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.1842 | 0.631034 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3269 | −0.428433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2159 | −0.713008 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.37778 | 0.139654 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.2815 | 1.62132 | 0.810660 | − | 0.585517i | \(-0.199109\pi\) | ||||
0.810660 | + | 0.585517i | \(0.199109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.42864 | 0.347296 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −33.5022 | −1.37810 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.4509 | −0.880883 | −0.440442 | − | 0.897781i | \(-0.645178\pi\) | ||||
−0.440442 | + | 0.897781i | \(0.645178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.42864 | −0.345541 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.2034 | −0.990580 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.3827 | −0.751097 | −0.375549 | − | 0.926803i | \(-0.622546\pi\) | ||||
−0.375549 | + | 0.926803i | \(0.622546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.3555 | −0.503992 | −0.251996 | − | 0.967728i | \(-0.581087\pi\) | ||||
−0.251996 | + | 0.967728i | \(0.581087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.7605 | −0.641817 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.67307 | 0.352610 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −48.4340 | −1.96588 | −0.982938 | − | 0.183935i | \(-0.941117\pi\) | ||||
−0.982938 | + | 0.183935i | \(0.941117\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.42864 | −0.179458 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.93041 | −0.118552 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.958989 | 0.0387332 | 0.0193666 | − | 0.999812i | \(-0.493835\pi\) | ||||
0.0193666 | + | 0.999812i | \(0.493835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23.9081 | 0.964069 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.09679 | 0.205189 | 0.102594 | − | 0.994723i | \(-0.467286\pi\) | ||||
0.102594 | + | 0.994723i | \(0.467286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0142901 | 0.000574368 0 | 0.000287184 | − | 1.00000i | \(-0.499909\pi\) | ||||
0.000287184 | 1.00000i | \(0.499909\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.4701 | 0.821438 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.2159 | 0.849995 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.8573 | −0.513470 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.6731 | −0.545181 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8859 | 0.512978 | 0.256489 | − | 0.966547i | \(-0.417434\pi\) | ||||
0.256489 | + | 0.966547i | \(0.417434\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.4286 | 1.12994 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.5161 | −0.576052 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.90766 | 0.115206 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.6035 | −1.60625 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.6865 | −1.84400 | −0.922002 | − | 0.387185i | \(-0.873447\pi\) | ||||
−0.922002 | + | 0.387185i | \(0.873447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.1388 | −1.10968 | −0.554842 | − | 0.831956i | \(-0.687221\pi\) | ||||
−0.554842 | + | 0.831956i | \(0.687221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.4286 | 0.646877 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 47.5067 | 1.86768 | 0.933840 | − | 0.357690i | \(-0.116436\pi\) | ||||
0.933840 | + | 0.357690i | \(0.116436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.6128 | −0.612858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8573 | 0.503916 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.5383 | −0.999392 | −0.499696 | − | 0.866201i | \(-0.666555\pi\) | ||||
−0.499696 | + | 0.866201i | \(0.666555\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.7605 | 0.615813 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.7605 | 0.614875 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4938 | 0.447734 | 0.223867 | − | 0.974620i | \(-0.428132\pi\) | ||||
0.223867 | + | 0.974620i | \(0.428132\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.4929 | −1.88615 | −0.943077 | − | 0.332574i | \(-0.892083\pi\) | ||||
−0.943077 | + | 0.332574i | \(0.892083\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.98126 | −0.387640 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.42864 | −0.171735 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.90321 | −0.112413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −46.6133 | −1.80218 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.1116 | −0.467561 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1526 | −0.584088 | −0.292044 | − | 0.956405i | \(-0.594335\pi\) | ||||
−0.292044 | + | 0.956405i | \(0.594335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.05086 | 0.271388 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.8943 | −1.49483 | −0.747415 | − | 0.664357i | \(-0.768705\pi\) | ||||
−0.747415 | + | 0.664357i | \(0.768705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.7971 | 1.02838 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 55.7373 | 2.13586 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.3733 | 0.435189 | 0.217594 | − | 0.976039i | \(-0.430179\pi\) | ||||
0.217594 | + | 0.976039i | \(0.430179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.52543 | −0.211116 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.7467 | 1.17306 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.02227 | −0.267527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.4893 | −1.12183 | −0.560914 | − | 0.827874i | \(-0.689550\pi\) | ||||
−0.560914 | + | 0.827874i | \(0.689550\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.6321 | −0.479852 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.4193 | 0.660751 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.5022 | −1.72352 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 67.1338 | 2.53923 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.2895 | −1.97495 | −0.987473 | − | 0.157789i | \(-0.949563\pi\) | ||||
−0.987473 | + | 0.157789i | \(0.949563\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.18421 | −0.270958 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6731 | −0.514958 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.70471 | −0.289766 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.18421 | −0.344920 | −0.172460 | − | 0.985017i | \(-0.555172\pi\) | ||||
−0.172460 | + | 0.985017i | \(0.555172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 89.9867 | 3.37476 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.42864 | 0.315655 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.949145 | −0.0354960 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 49.3274 | 1.84217 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.74620 | 0.288885 | 0.144442 | − | 0.989513i | \(-0.453861\pi\) | ||||
0.144442 | + | 0.989513i | \(0.453861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5936 | −0.543495 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.06959 | 0.0397785 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.06821 | −0.187969 | −0.0939847 | − | 0.995574i | \(-0.529960\pi\) | ||||
−0.0939847 | + | 0.995574i | \(0.529960\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6958 | −1.43318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.2672 | −1.15646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.659257 | 0.0243502 | 0.0121751 | − | 0.999926i | \(-0.496124\pi\) | ||||
0.0121751 | + | 0.999926i | \(0.496124\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.5669 | 0.500423 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.42864 | 0.163131 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.07805 | −0.260370 | −0.130185 | − | 0.991490i | \(-0.541557\pi\) | ||||
−0.130185 | + | 0.991490i | \(0.541557\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.24443 | −0.192659 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3412 | 0.966366 | 0.483183 | − | 0.875519i | \(-0.339481\pi\) | ||||
0.483183 | + | 0.875519i | \(0.339481\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | 0.0732743 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.7511 | −1.34465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.879077 | −0.0321208 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.92195 | −0.179604 | −0.0898022 | − | 0.995960i | \(-0.528623\pi\) | ||||
−0.0898022 | + | 0.995960i | \(0.528623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.6356 | 1.66305 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.37778 | −0.195718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9032 | −1.12320 | −0.561598 | − | 0.827410i | \(-0.689813\pi\) | ||||
−0.561598 | + | 0.827410i | \(0.689813\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.8573 | −0.466690 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3274 | 1.13562 | 0.567809 | − | 0.823160i | \(-0.307791\pi\) | ||||
0.567809 | + | 0.823160i | \(0.307791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.1141 | −0.402359 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −29.9956 | −1.08449 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.36842 | −0.229950 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.5620 | −0.957850 | −0.478925 | − | 0.877856i | \(-0.658973\pi\) | ||||
−0.478925 | + | 0.877856i | \(0.658973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.0098 | 1.94512 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.8528 | 0.534219 | 0.267110 | − | 0.963666i | \(-0.413931\pi\) | ||||
0.267110 | + | 0.963666i | \(0.413931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.90321 | 0.104286 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.9590 | −0.393152 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.9081 | −0.856598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4094 | 0.408261 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.05086 | −0.251977 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.39207 | −0.0496853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5540 | −0.910902 | −0.455451 | − | 0.890261i | \(-0.650522\pi\) | ||||
−0.455451 | + | 0.890261i | \(0.650522\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.8988 | 1.31363 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.9398 | 0.637865 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.94025 | −0.175434 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.7654 | −1.16207 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.2208 | 0.362038 | 0.181019 | − | 0.983480i | \(-0.442060\pi\) | ||||
0.181019 | + | 0.983480i | \(0.442060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.0228 | 0.920619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 75.5022 | 2.66774 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.42864 | −0.156283 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.42864 | −0.156089 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −63.1338 | −2.22242 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.44155 | −0.0858402 | −0.0429201 | − | 0.999079i | \(-0.513666\pi\) | ||||
−0.0429201 | + | 0.999079i | \(0.513666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.33984 | −0.0821628 | −0.0410814 | − | 0.999156i | \(-0.513080\pi\) | ||||
−0.0410814 | + | 0.999156i | \(0.513080\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 53.3689 | 1.87173 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.19850 | −0.252152 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.4286 | −0.574765 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.15257 | −0.180045 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6539 | −0.511423 | −0.255712 | − | 0.966753i | \(-0.582310\pi\) | ||||
−0.255712 | + | 0.966753i | \(0.582310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.3733 | −1.65133 | −0.825665 | − | 0.564160i | \(-0.809200\pi\) | ||||
−0.825665 | + | 0.564160i | \(0.809200\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.42864 | −0.154185 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.3412 | −0.637787 | −0.318893 | − | 0.947791i | \(-0.603311\pi\) | ||||
−0.318893 | + | 0.947791i | \(0.603311\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.5625 | −1.58245 | −0.791225 | − | 0.611525i | \(-0.790556\pi\) | ||||
−0.791225 | + | 0.611525i | \(0.790556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −37.1526 | −1.28881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.8207 | −0.894635 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.7605 | 0.545414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.4701 | 0.707551 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.9733 | 1.06932 | 0.534658 | − | 0.845068i | \(-0.320440\pi\) | ||||
0.534658 | + | 0.845068i | \(0.320440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 61.5022 | 2.11825 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6128 | 0.433895 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.2301 | −0.454593 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.5116 | −0.566677 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.18421 | −0.246271 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.4050 | −0.869850 | −0.434925 | − | 0.900467i | \(-0.643225\pi\) | ||||
−0.434925 | + | 0.900467i | \(0.643225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.7605 | −0.538997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.2573 | −0.657818 | −0.328909 | − | 0.944362i | \(-0.606681\pi\) | ||||
−0.328909 | + | 0.944362i | \(0.606681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.2623 | 1.44197 | 0.720985 | − | 0.692951i | \(-0.243690\pi\) | ||||
0.720985 | + | 0.692951i | \(0.243690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −36.4701 | −1.24290 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.88400 | 0.336455 | 0.168228 | − | 0.985748i | \(-0.446196\pi\) | ||||
0.168228 | + | 0.985748i | \(0.446196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.4795 | 0.458317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.2815 | 1.33407 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.2859 | −0.857766 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.80642 | 0.0612083 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 95.3644 | 3.22760 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.52543 | −0.0515689 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6508 | 0.427187 | 0.213594 | − | 0.976923i | \(-0.431483\pi\) | ||||
0.213594 | + | 0.976923i | \(0.431483\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 72.8355 | 2.45668 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.0888033 | −0.00299186 | −0.00149593 | − | 0.999999i | \(-0.500476\pi\) | ||||
−0.00149593 | + | 0.999999i | \(0.500476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 57.3131 | 1.92874 | 0.964370 | − | 0.264557i | \(-0.0852258\pi\) | ||||
0.964370 | + | 0.264557i | \(0.0852258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29.7146 | −0.998844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.0781 | −0.909192 | −0.454596 | − | 0.890698i | \(-0.650216\pi\) | ||||
−0.454596 | + | 0.890698i | \(0.650216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.1432 | 0.742659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.38271 | −0.213829 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.6731 | 0.457552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.266706 | 0.00891500 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.24443 | −0.175106 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.90321 | −0.0968275 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.3595 | 2.07750 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.0607 | −0.833968 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.7971 | −0.691318 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.6276 | −1.28261 | −0.641304 | − | 0.767287i | \(-0.721606\pi\) | ||||
−0.641304 | + | 0.767287i | \(0.721606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.4193 | −0.909440 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.27163 | −0.174657 | −0.0873284 | − | 0.996180i | \(-0.527833\pi\) | ||||
−0.0873284 | + | 0.996180i | \(0.527833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.3269 | 0.341771 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.0509 | −0.762038 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.0415 | −0.793920 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6632 | −0.384734 | −0.192367 | − | 0.981323i | \(-0.561616\pi\) | ||||
−0.192367 | + | 0.981323i | \(0.561616\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 89.4519 | 2.94754 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.65386 | 0.153184 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.47457 | −0.0813634 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.9353 | −1.70578 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.8198 | −1.53611 | −0.768054 | − | 0.640385i | \(-0.778775\pi\) | ||||
−0.768054 | + | 0.640385i | \(0.778775\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.5669 | −0.444638 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −87.2039 | −2.85493 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.42864 | 0.275646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.44738 | 0.145289 | 0.0726447 | − | 0.997358i | \(-0.476856\pi\) | ||||
0.0726447 | + | 0.997358i | \(0.476856\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −53.2355 | −1.73728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.6726 | 0.413115 | 0.206557 | − | 0.978434i | \(-0.433774\pi\) | ||||
0.206557 | + | 0.978434i | \(0.433774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.9081 | −0.778556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.7556 | −0.349879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.2306 | −0.657407 | −0.328703 | − | 0.944433i | \(-0.606612\pi\) | ||||
−0.328703 | + | 0.944433i | \(0.606612\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.80642 | −0.0586390 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.3876 | −1.92578 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.5718 | −0.795960 | −0.397980 | − | 0.917394i | \(-0.630289\pi\) | ||||
−0.397980 | + | 0.917394i | \(0.630289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.43356 | −0.305263 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.42864 | 0.143158 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.42864 | 0.272175 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5714 | −0.728108 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.12843 | −0.100812 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.23014 | −0.168364 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.9960 | −1.70424 | −0.852119 | − | 0.523349i | \(-0.824683\pi\) | ||||
−0.852119 | + | 0.523349i | \(0.824683\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46.5718 | 1.49610 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.02720 | 0.129239 | 0.0646195 | − | 0.997910i | \(-0.479417\pi\) | ||||
0.0646195 | + | 0.997910i | \(0.479417\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.5718 | −0.851854 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.80642 | −0.0578519 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2761 | 0.424739 | 0.212370 | − | 0.977189i | \(-0.431882\pi\) | ||||
0.212370 | + | 0.977189i | \(0.431882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.2159 | −0.678062 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.5526 | −1.26282 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.5857 | 0.752265 | 0.376133 | − | 0.926566i | \(-0.377254\pi\) | ||||
0.376133 | + | 0.926566i | \(0.377254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5397 | 0.367686 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.8573 | 0.663895 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.4286 | −0.522400 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.7882 | −1.61334 | −0.806670 | − | 0.591003i | \(-0.798732\pi\) | ||||
−0.806670 | + | 0.591003i | \(0.798732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.9175 | −1.10807 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.33677 | 0.264293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.5705 | 1.72826 | 0.864132 | − | 0.503266i | \(-0.167868\pi\) | ||||
0.864132 | + | 0.503266i | \(0.167868\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −17.4479 | −0.552026 |
(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 | 9280.2.a.bt.1.3 | 3 | ||
4.3 | odd | 2 | 9280.2.a.bh.1.1 | 3 | |||
8.3 | odd | 2 | 580.2.a.d.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 2320.2.a.o.1.1 | 3 | |||
24.11 | even | 2 | 5220.2.a.w.1.1 | 3 | |||
40.3 | even | 4 | 2900.2.c.g.349.6 | 6 | |||
40.19 | odd | 2 | 2900.2.a.f.1.1 | 3 | |||
40.27 | even | 4 | 2900.2.c.g.349.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
580.2.a.d.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
2320.2.a.o.1.1 | 3 | 8.5 | even | 2 | |||
2900.2.a.f.1.1 | 3 | 40.19 | odd | 2 | |||
2900.2.c.g.349.1 | 6 | 40.27 | even | 4 | |||
2900.2.c.g.349.6 | 6 | 40.3 | even | 4 | |||
5220.2.a.w.1.1 | 3 | 24.11 | even | 2 | |||
9280.2.a.bh.1.1 | 3 | 4.3 | odd | 2 | |||
9280.2.a.bt.1.3 | 3 | 1.1 | even | 1 | trivial |