Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,2,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(16.0738859269\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2x^{10} - 14x^{9} + 27x^{8} + 66x^{7} - 125x^{6} - 115x^{5} + 227x^{4} + 40x^{3} - 129x^{2} + 26x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.70023\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70023 | −1.90935 | −0.954674 | − | 0.297654i | \(-0.903796\pi\) | ||||
−0.954674 | + | 0.297654i | \(0.903796\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.29122 | 2.64561 | ||||||||
\(5\) | 2.21957 | 0.992620 | 0.496310 | − | 0.868145i | \(-0.334688\pi\) | ||||
0.496310 | + | 0.868145i | \(0.334688\pi\) | |||||||
\(6\) | 2.70023 | 1.10236 | ||||||||
\(7\) | −2.11895 | −0.800889 | −0.400444 | − | 0.916321i | \(-0.631144\pi\) | ||||
−0.400444 | + | 0.916321i | \(0.631144\pi\) | |||||||
\(8\) | −8.88702 | −3.14204 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.99333 | −1.89526 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −5.29122 | −1.52744 | ||||||||
\(13\) | −2.52367 | −0.699941 | −0.349971 | − | 0.936761i | \(-0.613808\pi\) | ||||
−0.349971 | + | 0.936761i | \(0.613808\pi\) | |||||||
\(14\) | 5.72165 | 1.52918 | ||||||||
\(15\) | −2.21957 | −0.573089 | ||||||||
\(16\) | 13.4145 | 3.35363 | ||||||||
\(17\) | 1.86251 | 0.451726 | 0.225863 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225863 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(18\) | −2.70023 | −0.636449 | ||||||||
\(19\) | −1.62262 | −0.372255 | −0.186127 | − | 0.982526i | \(-0.559594\pi\) | ||||
−0.186127 | + | 0.982526i | \(0.559594\pi\) | |||||||
\(20\) | 11.7442 | 2.62608 | ||||||||
\(21\) | 2.11895 | 0.462393 | ||||||||
\(22\) | −2.70023 | −0.575690 | ||||||||
\(23\) | 0.232397 | 0.0484581 | 0.0242291 | − | 0.999706i | \(-0.492287\pi\) | ||||
0.0242291 | + | 0.999706i | \(0.492287\pi\) | |||||||
\(24\) | 8.88702 | 1.81406 | ||||||||
\(25\) | −0.0735266 | −0.0147053 | ||||||||
\(26\) | 6.81449 | 1.33643 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −11.2118 | −2.11884 | ||||||||
\(29\) | 8.99969 | 1.67120 | 0.835601 | − | 0.549337i | \(-0.185120\pi\) | ||||
0.835601 | + | 0.549337i | \(0.185120\pi\) | |||||||
\(30\) | 5.99333 | 1.09423 | ||||||||
\(31\) | −0.0529540 | −0.00951081 | −0.00475541 | − | 0.999989i | \(-0.501514\pi\) | ||||
−0.00475541 | + | 0.999989i | \(0.501514\pi\) | |||||||
\(32\) | −18.4482 | −3.26121 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | −5.02921 | −0.862502 | ||||||||
\(35\) | −4.70316 | −0.794978 | ||||||||
\(36\) | 5.29122 | 0.881869 | ||||||||
\(37\) | −1.12092 | −0.184278 | −0.0921389 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921389 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(38\) | 4.38144 | 0.710764 | ||||||||
\(39\) | 2.52367 | 0.404111 | ||||||||
\(40\) | −19.7253 | −3.11885 | ||||||||
\(41\) | −8.95321 | −1.39826 | −0.699128 | − | 0.714996i | \(-0.746428\pi\) | ||||
−0.699128 | + | 0.714996i | \(0.746428\pi\) | |||||||
\(42\) | −5.72165 | −0.882870 | ||||||||
\(43\) | −8.83041 | −1.34662 | −0.673312 | − | 0.739358i | \(-0.735129\pi\) | ||||
−0.673312 | + | 0.739358i | \(0.735129\pi\) | |||||||
\(44\) | 5.29122 | 0.797681 | ||||||||
\(45\) | 2.21957 | 0.330873 | ||||||||
\(46\) | −0.627524 | −0.0925234 | ||||||||
\(47\) | −8.15644 | −1.18974 | −0.594869 | − | 0.803822i | \(-0.702796\pi\) | ||||
−0.594869 | + | 0.803822i | \(0.702796\pi\) | |||||||
\(48\) | −13.4145 | −1.93622 | ||||||||
\(49\) | −2.51004 | −0.358577 | ||||||||
\(50\) | 0.198539 | 0.0280776 | ||||||||
\(51\) | −1.86251 | −0.260804 | ||||||||
\(52\) | −13.3533 | −1.85177 | ||||||||
\(53\) | 11.4915 | 1.57847 | 0.789237 | − | 0.614089i | \(-0.210476\pi\) | ||||
0.789237 | + | 0.614089i | \(0.210476\pi\) | |||||||
\(54\) | 2.70023 | 0.367454 | ||||||||
\(55\) | 2.21957 | 0.299286 | ||||||||
\(56\) | 18.8312 | 2.51642 | ||||||||
\(57\) | 1.62262 | 0.214921 | ||||||||
\(58\) | −24.3012 | −3.19090 | ||||||||
\(59\) | −1.89372 | −0.246542 | −0.123271 | − | 0.992373i | \(-0.539338\pi\) | ||||
−0.123271 | + | 0.992373i | \(0.539338\pi\) | |||||||
\(60\) | −11.7442 | −1.51617 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 0.142988 | 0.0181594 | ||||||||
\(63\) | −2.11895 | −0.266963 | ||||||||
\(64\) | 22.9853 | 2.87316 | ||||||||
\(65\) | −5.60146 | −0.694776 | ||||||||
\(66\) | 2.70023 | 0.332375 | ||||||||
\(67\) | −1.07486 | −0.131315 | −0.0656577 | − | 0.997842i | \(-0.520915\pi\) | ||||
−0.0656577 | + | 0.997842i | \(0.520915\pi\) | |||||||
\(68\) | 9.85497 | 1.19509 | ||||||||
\(69\) | −0.232397 | −0.0279773 | ||||||||
\(70\) | 12.6996 | 1.51789 | ||||||||
\(71\) | 5.42037 | 0.643279 | 0.321640 | − | 0.946862i | \(-0.395766\pi\) | ||||
0.321640 | + | 0.946862i | \(0.395766\pi\) | |||||||
\(72\) | −8.88702 | −1.04735 | ||||||||
\(73\) | −8.03508 | −0.940435 | −0.470217 | − | 0.882551i | \(-0.655824\pi\) | ||||
−0.470217 | + | 0.882551i | \(0.655824\pi\) | |||||||
\(74\) | 3.02673 | 0.351850 | ||||||||
\(75\) | 0.0735266 | 0.00849013 | ||||||||
\(76\) | −8.58564 | −0.984840 | ||||||||
\(77\) | −2.11895 | −0.241477 | ||||||||
\(78\) | −6.81449 | −0.771589 | ||||||||
\(79\) | −6.67275 | −0.750743 | −0.375371 | − | 0.926875i | \(-0.622485\pi\) | ||||
−0.375371 | + | 0.926875i | \(0.622485\pi\) | |||||||
\(80\) | 29.7744 | 3.32888 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 24.1757 | 2.66976 | ||||||||
\(83\) | 3.06257 | 0.336161 | 0.168081 | − | 0.985773i | \(-0.446243\pi\) | ||||
0.168081 | + | 0.985773i | \(0.446243\pi\) | |||||||
\(84\) | 11.2118 | 1.22331 | ||||||||
\(85\) | 4.13397 | 0.448392 | ||||||||
\(86\) | 23.8441 | 2.57117 | ||||||||
\(87\) | −8.99969 | −0.964869 | ||||||||
\(88\) | −8.88702 | −0.947360 | ||||||||
\(89\) | 5.40932 | 0.573387 | 0.286693 | − | 0.958022i | \(-0.407444\pi\) | ||||
0.286693 | + | 0.958022i | \(0.407444\pi\) | |||||||
\(90\) | −5.99333 | −0.631752 | ||||||||
\(91\) | 5.34755 | 0.560575 | ||||||||
\(92\) | 1.22966 | 0.128201 | ||||||||
\(93\) | 0.0529540 | 0.00549107 | ||||||||
\(94\) | 22.0242 | 2.27162 | ||||||||
\(95\) | −3.60151 | −0.369508 | ||||||||
\(96\) | 18.4482 | 1.88286 | ||||||||
\(97\) | 12.0599 | 1.22450 | 0.612251 | − | 0.790664i | \(-0.290264\pi\) | ||||
0.612251 | + | 0.790664i | \(0.290264\pi\) | |||||||
\(98\) | 6.77767 | 0.684648 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −0.389045 | −0.0389045 | ||||||||
\(101\) | −10.2401 | −1.01893 | −0.509464 | − | 0.860492i | \(-0.670156\pi\) | ||||
−0.509464 | + | 0.860492i | \(0.670156\pi\) | |||||||
\(102\) | 5.02921 | 0.497966 | ||||||||
\(103\) | −10.9576 | −1.07968 | −0.539842 | − | 0.841766i | \(-0.681516\pi\) | ||||
−0.539842 | + | 0.841766i | \(0.681516\pi\) | |||||||
\(104\) | 22.4280 | 2.19924 | ||||||||
\(105\) | 4.70316 | 0.458981 | ||||||||
\(106\) | −31.0295 | −3.01386 | ||||||||
\(107\) | 0.334129 | 0.0323015 | 0.0161507 | − | 0.999870i | \(-0.494859\pi\) | ||||
0.0161507 | + | 0.999870i | \(0.494859\pi\) | |||||||
\(108\) | −5.29122 | −0.509147 | ||||||||
\(109\) | 8.41756 | 0.806256 | 0.403128 | − | 0.915144i | \(-0.367923\pi\) | ||||
0.403128 | + | 0.915144i | \(0.367923\pi\) | |||||||
\(110\) | −5.99333 | −0.571441 | ||||||||
\(111\) | 1.12092 | 0.106393 | ||||||||
\(112\) | −28.4248 | −2.68589 | ||||||||
\(113\) | 13.6712 | 1.28608 | 0.643038 | − | 0.765834i | \(-0.277674\pi\) | ||||
0.643038 | + | 0.765834i | \(0.277674\pi\) | |||||||
\(114\) | −4.38144 | −0.410360 | ||||||||
\(115\) | 0.515820 | 0.0481005 | ||||||||
\(116\) | 47.6193 | 4.42134 | ||||||||
\(117\) | −2.52367 | −0.233314 | ||||||||
\(118\) | 5.11348 | 0.470734 | ||||||||
\(119\) | −3.94658 | −0.361782 | ||||||||
\(120\) | 19.7253 | 1.80067 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.70023 | −0.244467 | ||||||||
\(123\) | 8.95321 | 0.807284 | ||||||||
\(124\) | −0.280191 | −0.0251619 | ||||||||
\(125\) | −11.2610 | −1.00722 | ||||||||
\(126\) | 5.72165 | 0.509725 | ||||||||
\(127\) | −3.78595 | −0.335949 | −0.167974 | − | 0.985791i | \(-0.553723\pi\) | ||||
−0.167974 | + | 0.985791i | \(0.553723\pi\) | |||||||
\(128\) | −25.1690 | −2.22464 | ||||||||
\(129\) | 8.83041 | 0.777474 | ||||||||
\(130\) | 15.1252 | 1.32657 | ||||||||
\(131\) | 10.5360 | 0.920533 | 0.460267 | − | 0.887781i | \(-0.347754\pi\) | ||||
0.460267 | + | 0.887781i | \(0.347754\pi\) | |||||||
\(132\) | −5.29122 | −0.460541 | ||||||||
\(133\) | 3.43826 | 0.298135 | ||||||||
\(134\) | 2.90237 | 0.250727 | ||||||||
\(135\) | −2.21957 | −0.191030 | ||||||||
\(136\) | −16.5522 | −1.41934 | ||||||||
\(137\) | −17.4642 | −1.49207 | −0.746033 | − | 0.665909i | \(-0.768044\pi\) | ||||
−0.746033 | + | 0.665909i | \(0.768044\pi\) | |||||||
\(138\) | 0.627524 | 0.0534184 | ||||||||
\(139\) | −0.0929980 | −0.00788799 | −0.00394399 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394399 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(140\) | −24.8854 | −2.10320 | ||||||||
\(141\) | 8.15644 | 0.686896 | ||||||||
\(142\) | −14.6362 | −1.22824 | ||||||||
\(143\) | −2.52367 | −0.211040 | ||||||||
\(144\) | 13.4145 | 1.11788 | ||||||||
\(145\) | 19.9754 | 1.65887 | ||||||||
\(146\) | 21.6965 | 1.79562 | ||||||||
\(147\) | 2.51004 | 0.207025 | ||||||||
\(148\) | −5.93102 | −0.487527 | ||||||||
\(149\) | −9.89650 | −0.810753 | −0.405376 | − | 0.914150i | \(-0.632860\pi\) | ||||
−0.405376 | + | 0.914150i | \(0.632860\pi\) | |||||||
\(150\) | −0.198539 | −0.0162106 | ||||||||
\(151\) | −7.47873 | −0.608611 | −0.304305 | − | 0.952575i | \(-0.598424\pi\) | ||||
−0.304305 | + | 0.952575i | \(0.598424\pi\) | |||||||
\(152\) | 14.4203 | 1.16964 | ||||||||
\(153\) | 1.86251 | 0.150575 | ||||||||
\(154\) | 5.72165 | 0.461064 | ||||||||
\(155\) | −0.117535 | −0.00944062 | ||||||||
\(156\) | 13.3533 | 1.06912 | ||||||||
\(157\) | −15.5758 | −1.24309 | −0.621543 | − | 0.783380i | \(-0.713494\pi\) | ||||
−0.621543 | + | 0.783380i | \(0.713494\pi\) | |||||||
\(158\) | 18.0179 | 1.43343 | ||||||||
\(159\) | −11.4915 | −0.911332 | ||||||||
\(160\) | −40.9470 | −3.23715 | ||||||||
\(161\) | −0.492438 | −0.0388096 | ||||||||
\(162\) | −2.70023 | −0.212150 | ||||||||
\(163\) | 7.47058 | 0.585141 | 0.292571 | − | 0.956244i | \(-0.405489\pi\) | ||||
0.292571 | + | 0.956244i | \(0.405489\pi\) | |||||||
\(164\) | −47.3734 | −3.69924 | ||||||||
\(165\) | −2.21957 | −0.172793 | ||||||||
\(166\) | −8.26964 | −0.641848 | ||||||||
\(167\) | −17.0129 | −1.31650 | −0.658248 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658248 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(168\) | −18.8312 | −1.45286 | ||||||||
\(169\) | −6.63107 | −0.510082 | ||||||||
\(170\) | −11.1627 | −0.856137 | ||||||||
\(171\) | −1.62262 | −0.124085 | ||||||||
\(172\) | −46.7236 | −3.56264 | ||||||||
\(173\) | −7.59030 | −0.577079 | −0.288540 | − | 0.957468i | \(-0.593170\pi\) | ||||
−0.288540 | + | 0.957468i | \(0.593170\pi\) | |||||||
\(174\) | 24.3012 | 1.84227 | ||||||||
\(175\) | 0.155799 | 0.0117773 | ||||||||
\(176\) | 13.4145 | 1.01116 | ||||||||
\(177\) | 1.89372 | 0.142341 | ||||||||
\(178\) | −14.6064 | −1.09479 | ||||||||
\(179\) | 5.63139 | 0.420910 | 0.210455 | − | 0.977604i | \(-0.432505\pi\) | ||||
0.210455 | + | 0.977604i | \(0.432505\pi\) | |||||||
\(180\) | 11.7442 | 0.875361 | ||||||||
\(181\) | 23.6253 | 1.75605 | 0.878027 | − | 0.478610i | \(-0.158859\pi\) | ||||
0.878027 | + | 0.478610i | \(0.158859\pi\) | |||||||
\(182\) | −14.4396 | −1.07033 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −2.06532 | −0.152257 | ||||||||
\(185\) | −2.48795 | −0.182918 | ||||||||
\(186\) | −0.142988 | −0.0104844 | ||||||||
\(187\) | 1.86251 | 0.136201 | ||||||||
\(188\) | −43.1575 | −3.14758 | ||||||||
\(189\) | 2.11895 | 0.154131 | ||||||||
\(190\) | 9.72490 | 0.705518 | ||||||||
\(191\) | −12.1022 | −0.875681 | −0.437841 | − | 0.899053i | \(-0.644257\pi\) | ||||
−0.437841 | + | 0.899053i | \(0.644257\pi\) | |||||||
\(192\) | −22.9853 | −1.65882 | ||||||||
\(193\) | 0.690719 | 0.0497190 | 0.0248595 | − | 0.999691i | \(-0.492086\pi\) | ||||
0.0248595 | + | 0.999691i | \(0.492086\pi\) | |||||||
\(194\) | −32.5646 | −2.33800 | ||||||||
\(195\) | 5.60146 | 0.401129 | ||||||||
\(196\) | −13.2812 | −0.948654 | ||||||||
\(197\) | −12.5268 | −0.892500 | −0.446250 | − | 0.894908i | \(-0.647241\pi\) | ||||
−0.446250 | + | 0.894908i | \(0.647241\pi\) | |||||||
\(198\) | −2.70023 | −0.191897 | ||||||||
\(199\) | −10.6668 | −0.756146 | −0.378073 | − | 0.925776i | \(-0.623413\pi\) | ||||
−0.378073 | + | 0.925776i | \(0.623413\pi\) | |||||||
\(200\) | 0.653433 | 0.0462047 | ||||||||
\(201\) | 1.07486 | 0.0758149 | ||||||||
\(202\) | 27.6506 | 1.94549 | ||||||||
\(203\) | −19.0699 | −1.33845 | ||||||||
\(204\) | −9.85497 | −0.689986 | ||||||||
\(205\) | −19.8722 | −1.38794 | ||||||||
\(206\) | 29.5880 | 2.06149 | ||||||||
\(207\) | 0.232397 | 0.0161527 | ||||||||
\(208\) | −33.8539 | −2.34735 | ||||||||
\(209\) | −1.62262 | −0.112239 | ||||||||
\(210\) | −12.6996 | −0.876354 | ||||||||
\(211\) | −11.3412 | −0.780764 | −0.390382 | − | 0.920653i | \(-0.627657\pi\) | ||||
−0.390382 | + | 0.920653i | \(0.627657\pi\) | |||||||
\(212\) | 60.8038 | 4.17602 | ||||||||
\(213\) | −5.42037 | −0.371398 | ||||||||
\(214\) | −0.902224 | −0.0616748 | ||||||||
\(215\) | −19.5997 | −1.33669 | ||||||||
\(216\) | 8.88702 | 0.604685 | ||||||||
\(217\) | 0.112207 | 0.00761710 | ||||||||
\(218\) | −22.7293 | −1.53942 | ||||||||
\(219\) | 8.03508 | 0.542960 | ||||||||
\(220\) | 11.7442 | 0.791794 | ||||||||
\(221\) | −4.70038 | −0.316182 | ||||||||
\(222\) | −3.02673 | −0.203141 | ||||||||
\(223\) | −10.0996 | −0.676318 | −0.338159 | − | 0.941089i | \(-0.609804\pi\) | ||||
−0.338159 | + | 0.941089i | \(0.609804\pi\) | |||||||
\(224\) | 39.0909 | 2.61187 | ||||||||
\(225\) | −0.0735266 | −0.00490178 | ||||||||
\(226\) | −36.9153 | −2.45557 | ||||||||
\(227\) | −24.4371 | −1.62195 | −0.810973 | − | 0.585084i | \(-0.801061\pi\) | ||||
−0.810973 | + | 0.585084i | \(0.801061\pi\) | |||||||
\(228\) | 8.58564 | 0.568598 | ||||||||
\(229\) | −13.2077 | −0.872787 | −0.436393 | − | 0.899756i | \(-0.643744\pi\) | ||||
−0.436393 | + | 0.899756i | \(0.643744\pi\) | |||||||
\(230\) | −1.39283 | −0.0918406 | ||||||||
\(231\) | 2.11895 | 0.139417 | ||||||||
\(232\) | −79.9805 | −5.25098 | ||||||||
\(233\) | −0.140516 | −0.00920550 | −0.00460275 | − | 0.999989i | \(-0.501465\pi\) | ||||
−0.00460275 | + | 0.999989i | \(0.501465\pi\) | |||||||
\(234\) | 6.81449 | 0.445477 | ||||||||
\(235\) | −18.1037 | −1.18096 | ||||||||
\(236\) | −10.0201 | −0.652253 | ||||||||
\(237\) | 6.67275 | 0.433442 | ||||||||
\(238\) | 10.6567 | 0.690768 | ||||||||
\(239\) | 4.97217 | 0.321623 | 0.160812 | − | 0.986985i | \(-0.448589\pi\) | ||||
0.160812 | + | 0.986985i | \(0.448589\pi\) | |||||||
\(240\) | −29.7744 | −1.92193 | ||||||||
\(241\) | −12.4794 | −0.803871 | −0.401936 | − | 0.915668i | \(-0.631662\pi\) | ||||
−0.401936 | + | 0.915668i | \(0.631662\pi\) | |||||||
\(242\) | −2.70023 | −0.173577 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.29122 | 0.338735 | ||||||||
\(245\) | −5.57120 | −0.355931 | ||||||||
\(246\) | −24.1757 | −1.54139 | ||||||||
\(247\) | 4.09497 | 0.260556 | ||||||||
\(248\) | 0.470603 | 0.0298833 | ||||||||
\(249\) | −3.06257 | −0.194083 | ||||||||
\(250\) | 30.4073 | 1.92313 | ||||||||
\(251\) | 5.84977 | 0.369234 | 0.184617 | − | 0.982811i | \(-0.440896\pi\) | ||||
0.184617 | + | 0.982811i | \(0.440896\pi\) | |||||||
\(252\) | −11.2118 | −0.706279 | ||||||||
\(253\) | 0.232397 | 0.0146107 | ||||||||
\(254\) | 10.2229 | 0.641443 | ||||||||
\(255\) | −4.13397 | −0.258880 | ||||||||
\(256\) | 21.9913 | 1.37446 | ||||||||
\(257\) | 13.3927 | 0.835414 | 0.417707 | − | 0.908582i | \(-0.362834\pi\) | ||||
0.417707 | + | 0.908582i | \(0.362834\pi\) | |||||||
\(258\) | −23.8441 | −1.48447 | ||||||||
\(259\) | 2.37517 | 0.147586 | ||||||||
\(260\) | −29.6385 | −1.83810 | ||||||||
\(261\) | 8.99969 | 0.557067 | ||||||||
\(262\) | −28.4495 | −1.75762 | ||||||||
\(263\) | 21.6822 | 1.33698 | 0.668490 | − | 0.743721i | \(-0.266941\pi\) | ||||
0.668490 | + | 0.743721i | \(0.266941\pi\) | |||||||
\(264\) | 8.88702 | 0.546959 | ||||||||
\(265\) | 25.5061 | 1.56682 | ||||||||
\(266\) | −9.28407 | −0.569243 | ||||||||
\(267\) | −5.40932 | −0.331045 | ||||||||
\(268\) | −5.68733 | −0.347409 | ||||||||
\(269\) | −27.6844 | −1.68795 | −0.843974 | − | 0.536383i | \(-0.819790\pi\) | ||||
−0.843974 | + | 0.536383i | \(0.819790\pi\) | |||||||
\(270\) | 5.99333 | 0.364742 | ||||||||
\(271\) | −17.6848 | −1.07428 | −0.537138 | − | 0.843494i | \(-0.680495\pi\) | ||||
−0.537138 | + | 0.843494i | \(0.680495\pi\) | |||||||
\(272\) | 24.9848 | 1.51492 | ||||||||
\(273\) | −5.34755 | −0.323648 | ||||||||
\(274\) | 47.1572 | 2.84887 | ||||||||
\(275\) | −0.0735266 | −0.00443382 | ||||||||
\(276\) | −1.22966 | −0.0740170 | ||||||||
\(277\) | 28.1120 | 1.68908 | 0.844542 | − | 0.535489i | \(-0.179873\pi\) | ||||
0.844542 | + | 0.535489i | \(0.179873\pi\) | |||||||
\(278\) | 0.251116 | 0.0150609 | ||||||||
\(279\) | −0.0529540 | −0.00317027 | ||||||||
\(280\) | 41.7971 | 2.49785 | ||||||||
\(281\) | 28.9616 | 1.72770 | 0.863851 | − | 0.503748i | \(-0.168046\pi\) | ||||
0.863851 | + | 0.503748i | \(0.168046\pi\) | |||||||
\(282\) | −22.0242 | −1.31152 | ||||||||
\(283\) | 16.5238 | 0.982236 | 0.491118 | − | 0.871093i | \(-0.336588\pi\) | ||||
0.491118 | + | 0.871093i | \(0.336588\pi\) | |||||||
\(284\) | 28.6803 | 1.70187 | ||||||||
\(285\) | 3.60151 | 0.213335 | ||||||||
\(286\) | 6.81449 | 0.402949 | ||||||||
\(287\) | 18.9714 | 1.11985 | ||||||||
\(288\) | −18.4482 | −1.08707 | ||||||||
\(289\) | −13.5310 | −0.795943 | ||||||||
\(290\) | −53.9381 | −3.16736 | ||||||||
\(291\) | −12.0599 | −0.706966 | ||||||||
\(292\) | −42.5153 | −2.48802 | ||||||||
\(293\) | −25.5646 | −1.49350 | −0.746750 | − | 0.665105i | \(-0.768387\pi\) | ||||
−0.746750 | + | 0.665105i | \(0.768387\pi\) | |||||||
\(294\) | −6.77767 | −0.395282 | ||||||||
\(295\) | −4.20324 | −0.244722 | ||||||||
\(296\) | 9.96163 | 0.579008 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 26.7228 | 1.54801 | ||||||||
\(299\) | −0.586494 | −0.0339178 | ||||||||
\(300\) | 0.389045 | 0.0224615 | ||||||||
\(301\) | 18.7112 | 1.07850 | ||||||||
\(302\) | 20.1943 | 1.16205 | ||||||||
\(303\) | 10.2401 | 0.588279 | ||||||||
\(304\) | −21.7667 | −1.24841 | ||||||||
\(305\) | 2.21957 | 0.127092 | ||||||||
\(306\) | −5.02921 | −0.287501 | ||||||||
\(307\) | 14.8707 | 0.848717 | 0.424358 | − | 0.905494i | \(-0.360500\pi\) | ||||
0.424358 | + | 0.905494i | \(0.360500\pi\) | |||||||
\(308\) | −11.2118 | −0.638854 | ||||||||
\(309\) | 10.9576 | 0.623356 | ||||||||
\(310\) | 0.317371 | 0.0180254 | ||||||||
\(311\) | −26.8797 | −1.52421 | −0.762104 | − | 0.647454i | \(-0.775834\pi\) | ||||
−0.762104 | + | 0.647454i | \(0.775834\pi\) | |||||||
\(312\) | −22.4280 | −1.26973 | ||||||||
\(313\) | −32.7560 | −1.85148 | −0.925738 | − | 0.378166i | \(-0.876555\pi\) | ||||
−0.925738 | + | 0.378166i | \(0.876555\pi\) | |||||||
\(314\) | 42.0582 | 2.37348 | ||||||||
\(315\) | −4.70316 | −0.264993 | ||||||||
\(316\) | −35.3069 | −1.98617 | ||||||||
\(317\) | −8.10496 | −0.455220 | −0.227610 | − | 0.973752i | \(-0.573091\pi\) | ||||
−0.227610 | + | 0.973752i | \(0.573091\pi\) | |||||||
\(318\) | 31.0295 | 1.74005 | ||||||||
\(319\) | 8.99969 | 0.503886 | ||||||||
\(320\) | 51.0173 | 2.85195 | ||||||||
\(321\) | −0.334129 | −0.0186493 | ||||||||
\(322\) | 1.32969 | 0.0741010 | ||||||||
\(323\) | −3.02216 | −0.168157 | ||||||||
\(324\) | 5.29122 | 0.293956 | ||||||||
\(325\) | 0.185557 | 0.0102929 | ||||||||
\(326\) | −20.1723 | −1.11724 | ||||||||
\(327\) | −8.41756 | −0.465492 | ||||||||
\(328\) | 79.5674 | 4.39337 | ||||||||
\(329\) | 17.2831 | 0.952848 | ||||||||
\(330\) | 5.99333 | 0.329922 | ||||||||
\(331\) | −13.6297 | −0.749158 | −0.374579 | − | 0.927195i | \(-0.622213\pi\) | ||||
−0.374579 | + | 0.927195i | \(0.622213\pi\) | |||||||
\(332\) | 16.2047 | 0.889351 | ||||||||
\(333\) | −1.12092 | −0.0614259 | ||||||||
\(334\) | 45.9386 | 2.51365 | ||||||||
\(335\) | −2.38573 | −0.130346 | ||||||||
\(336\) | 28.4248 | 1.55070 | ||||||||
\(337\) | 8.22312 | 0.447942 | 0.223971 | − | 0.974596i | \(-0.428098\pi\) | ||||
0.223971 | + | 0.974596i | \(0.428098\pi\) | |||||||
\(338\) | 17.9054 | 0.973924 | ||||||||
\(339\) | −13.6712 | −0.742516 | ||||||||
\(340\) | 21.8738 | 1.18627 | ||||||||
\(341\) | −0.0529540 | −0.00286762 | ||||||||
\(342\) | 4.38144 | 0.236921 | ||||||||
\(343\) | 20.1513 | 1.08807 | ||||||||
\(344\) | 78.4760 | 4.23114 | ||||||||
\(345\) | −0.515820 | −0.0277708 | ||||||||
\(346\) | 20.4955 | 1.10185 | ||||||||
\(347\) | 6.21388 | 0.333579 | 0.166789 | − | 0.985993i | \(-0.446660\pi\) | ||||
0.166789 | + | 0.985993i | \(0.446660\pi\) | |||||||
\(348\) | −47.6193 | −2.55266 | ||||||||
\(349\) | −9.65556 | −0.516850 | −0.258425 | − | 0.966031i | \(-0.583204\pi\) | ||||
−0.258425 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(350\) | −0.420694 | −0.0224870 | ||||||||
\(351\) | 2.52367 | 0.134704 | ||||||||
\(352\) | −18.4482 | −0.983293 | ||||||||
\(353\) | 9.59868 | 0.510886 | 0.255443 | − | 0.966824i | \(-0.417779\pi\) | ||||
0.255443 | + | 0.966824i | \(0.417779\pi\) | |||||||
\(354\) | −5.11348 | −0.271778 | ||||||||
\(355\) | 12.0309 | 0.638532 | ||||||||
\(356\) | 28.6219 | 1.51696 | ||||||||
\(357\) | 3.94658 | 0.208875 | ||||||||
\(358\) | −15.2060 | −0.803663 | ||||||||
\(359\) | −8.24709 | −0.435265 | −0.217632 | − | 0.976031i | \(-0.569833\pi\) | ||||
−0.217632 | + | 0.976031i | \(0.569833\pi\) | |||||||
\(360\) | −19.7253 | −1.03962 | ||||||||
\(361\) | −16.3671 | −0.861426 | ||||||||
\(362\) | −63.7936 | −3.35292 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 28.2950 | 1.48306 | ||||||||
\(365\) | −17.8344 | −0.933494 | ||||||||
\(366\) | 2.70023 | 0.141143 | ||||||||
\(367\) | −14.0837 | −0.735164 | −0.367582 | − | 0.929991i | \(-0.619814\pi\) | ||||
−0.367582 | + | 0.929991i | \(0.619814\pi\) | |||||||
\(368\) | 3.11750 | 0.162511 | ||||||||
\(369\) | −8.95321 | −0.466086 | ||||||||
\(370\) | 6.71803 | 0.349254 | ||||||||
\(371\) | −24.3499 | −1.26418 | ||||||||
\(372\) | 0.280191 | 0.0145272 | ||||||||
\(373\) | 27.9601 | 1.44772 | 0.723859 | − | 0.689948i | \(-0.242367\pi\) | ||||
0.723859 | + | 0.689948i | \(0.242367\pi\) | |||||||
\(374\) | −5.02921 | −0.260054 | ||||||||
\(375\) | 11.2610 | 0.581517 | ||||||||
\(376\) | 72.4864 | 3.73820 | ||||||||
\(377\) | −22.7123 | −1.16974 | ||||||||
\(378\) | −5.72165 | −0.294290 | ||||||||
\(379\) | −14.9564 | −0.768258 | −0.384129 | − | 0.923279i | \(-0.625498\pi\) | ||||
−0.384129 | + | 0.923279i | \(0.625498\pi\) | |||||||
\(380\) | −19.0564 | −0.977572 | ||||||||
\(381\) | 3.78595 | 0.193960 | ||||||||
\(382\) | 32.6785 | 1.67198 | ||||||||
\(383\) | −35.7729 | −1.82791 | −0.913954 | − | 0.405818i | \(-0.866987\pi\) | ||||
−0.913954 | + | 0.405818i | \(0.866987\pi\) | |||||||
\(384\) | 25.1690 | 1.28440 | ||||||||
\(385\) | −4.70316 | −0.239695 | ||||||||
\(386\) | −1.86510 | −0.0949309 | ||||||||
\(387\) | −8.83041 | −0.448875 | ||||||||
\(388\) | 63.8118 | 3.23955 | ||||||||
\(389\) | 15.8009 | 0.801136 | 0.400568 | − | 0.916267i | \(-0.368813\pi\) | ||||
0.400568 | + | 0.916267i | \(0.368813\pi\) | |||||||
\(390\) | −15.1252 | −0.765895 | ||||||||
\(391\) | 0.432843 | 0.0218898 | ||||||||
\(392\) | 22.3068 | 1.12666 | ||||||||
\(393\) | −10.5360 | −0.531470 | ||||||||
\(394\) | 33.8253 | 1.70409 | ||||||||
\(395\) | −14.8106 | −0.745202 | ||||||||
\(396\) | 5.29122 | 0.265894 | ||||||||
\(397\) | 13.4452 | 0.674794 | 0.337397 | − | 0.941362i | \(-0.390454\pi\) | ||||
0.337397 | + | 0.941362i | \(0.390454\pi\) | |||||||
\(398\) | 28.8026 | 1.44375 | ||||||||
\(399\) | −3.43826 | −0.172128 | ||||||||
\(400\) | −0.986326 | −0.0493163 | ||||||||
\(401\) | 11.2339 | 0.560995 | 0.280498 | − | 0.959855i | \(-0.409501\pi\) | ||||
0.280498 | + | 0.959855i | \(0.409501\pi\) | |||||||
\(402\) | −2.90237 | −0.144757 | ||||||||
\(403\) | 0.133639 | 0.00665701 | ||||||||
\(404\) | −54.1826 | −2.69569 | ||||||||
\(405\) | 2.21957 | 0.110291 | ||||||||
\(406\) | 51.4931 | 2.55556 | ||||||||
\(407\) | −1.12092 | −0.0555619 | ||||||||
\(408\) | 16.5522 | 0.819457 | ||||||||
\(409\) | 22.0149 | 1.08857 | 0.544284 | − | 0.838901i | \(-0.316802\pi\) | ||||
0.544284 | + | 0.838901i | \(0.316802\pi\) | |||||||
\(410\) | 53.6595 | 2.65006 | ||||||||
\(411\) | 17.4642 | 0.861444 | ||||||||
\(412\) | −57.9790 | −2.85642 | ||||||||
\(413\) | 4.01271 | 0.197452 | ||||||||
\(414\) | −0.627524 | −0.0308411 | ||||||||
\(415\) | 6.79758 | 0.333680 | ||||||||
\(416\) | 46.5573 | 2.28266 | ||||||||
\(417\) | 0.0929980 | 0.00455413 | ||||||||
\(418\) | 4.38144 | 0.214303 | ||||||||
\(419\) | −10.0502 | −0.490982 | −0.245491 | − | 0.969399i | \(-0.578949\pi\) | ||||
−0.245491 | + | 0.969399i | \(0.578949\pi\) | |||||||
\(420\) | 24.8854 | 1.21428 | ||||||||
\(421\) | −32.7041 | −1.59390 | −0.796950 | − | 0.604046i | \(-0.793555\pi\) | ||||
−0.796950 | + | 0.604046i | \(0.793555\pi\) | |||||||
\(422\) | 30.6239 | 1.49075 | ||||||||
\(423\) | −8.15644 | −0.396580 | ||||||||
\(424\) | −102.125 | −4.95962 | ||||||||
\(425\) | −0.136944 | −0.00664278 | ||||||||
\(426\) | 14.6362 | 0.709127 | ||||||||
\(427\) | −2.11895 | −0.102543 | ||||||||
\(428\) | 1.76795 | 0.0854571 | ||||||||
\(429\) | 2.52367 | 0.121844 | ||||||||
\(430\) | 52.9235 | 2.55220 | ||||||||
\(431\) | −27.2073 | −1.31053 | −0.655264 | − | 0.755400i | \(-0.727443\pi\) | ||||
−0.655264 | + | 0.755400i | \(0.727443\pi\) | |||||||
\(432\) | −13.4145 | −0.645407 | ||||||||
\(433\) | 6.25089 | 0.300399 | 0.150199 | − | 0.988656i | \(-0.452008\pi\) | ||||
0.150199 | + | 0.988656i | \(0.452008\pi\) | |||||||
\(434\) | −0.302984 | −0.0145437 | ||||||||
\(435\) | −19.9754 | −0.957748 | ||||||||
\(436\) | 44.5391 | 2.13304 | ||||||||
\(437\) | −0.377092 | −0.0180388 | ||||||||
\(438\) | −21.6965 | −1.03670 | ||||||||
\(439\) | −6.23945 | −0.297793 | −0.148896 | − | 0.988853i | \(-0.547572\pi\) | ||||
−0.148896 | + | 0.988853i | \(0.547572\pi\) | |||||||
\(440\) | −19.7253 | −0.940369 | ||||||||
\(441\) | −2.51004 | −0.119526 | ||||||||
\(442\) | 12.6921 | 0.603701 | ||||||||
\(443\) | −27.2602 | −1.29517 | −0.647586 | − | 0.761993i | \(-0.724221\pi\) | ||||
−0.647586 | + | 0.761993i | \(0.724221\pi\) | |||||||
\(444\) | 5.93102 | 0.281474 | ||||||||
\(445\) | 12.0063 | 0.569155 | ||||||||
\(446\) | 27.2711 | 1.29133 | ||||||||
\(447\) | 9.89650 | 0.468088 | ||||||||
\(448\) | −48.7047 | −2.30108 | ||||||||
\(449\) | −3.39049 | −0.160007 | −0.0800036 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800036 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(450\) | 0.198539 | 0.00935919 | ||||||||
\(451\) | −8.95321 | −0.421590 | ||||||||
\(452\) | 72.3371 | 3.40245 | ||||||||
\(453\) | 7.47873 | 0.351381 | ||||||||
\(454\) | 65.9856 | 3.09686 | ||||||||
\(455\) | 11.8692 | 0.556438 | ||||||||
\(456\) | −14.4203 | −0.675291 | ||||||||
\(457\) | −6.49576 | −0.303859 | −0.151929 | − | 0.988391i | \(-0.548549\pi\) | ||||
−0.151929 | + | 0.988391i | \(0.548549\pi\) | |||||||
\(458\) | 35.6637 | 1.66645 | ||||||||
\(459\) | −1.86251 | −0.0869347 | ||||||||
\(460\) | 2.72932 | 0.127255 | ||||||||
\(461\) | 6.12439 | 0.285241 | 0.142621 | − | 0.989777i | \(-0.454447\pi\) | ||||
0.142621 | + | 0.989777i | \(0.454447\pi\) | |||||||
\(462\) | −5.72165 | −0.266195 | ||||||||
\(463\) | −38.3973 | −1.78447 | −0.892237 | − | 0.451567i | \(-0.850865\pi\) | ||||
−0.892237 | + | 0.451567i | \(0.850865\pi\) | |||||||
\(464\) | 120.727 | 5.60460 | ||||||||
\(465\) | 0.117535 | 0.00545055 | ||||||||
\(466\) | 0.379424 | 0.0175765 | ||||||||
\(467\) | 12.3597 | 0.571941 | 0.285970 | − | 0.958238i | \(-0.407684\pi\) | ||||
0.285970 | + | 0.958238i | \(0.407684\pi\) | |||||||
\(468\) | −13.3533 | −0.617257 | ||||||||
\(469\) | 2.27758 | 0.105169 | ||||||||
\(470\) | 48.8842 | 2.25486 | ||||||||
\(471\) | 15.5758 | 0.717696 | ||||||||
\(472\) | 16.8296 | 0.774643 | ||||||||
\(473\) | −8.83041 | −0.406022 | ||||||||
\(474\) | −18.0179 | −0.827590 | ||||||||
\(475\) | 0.119306 | 0.00547413 | ||||||||
\(476\) | −20.8822 | −0.957135 | ||||||||
\(477\) | 11.4915 | 0.526158 | ||||||||
\(478\) | −13.4260 | −0.614090 | ||||||||
\(479\) | 19.7415 | 0.902012 | 0.451006 | − | 0.892521i | \(-0.351065\pi\) | ||||
0.451006 | + | 0.892521i | \(0.351065\pi\) | |||||||
\(480\) | 40.9470 | 1.86897 | ||||||||
\(481\) | 2.82883 | 0.128984 | ||||||||
\(482\) | 33.6973 | 1.53487 | ||||||||
\(483\) | 0.492438 | 0.0224067 | ||||||||
\(484\) | 5.29122 | 0.240510 | ||||||||
\(485\) | 26.7678 | 1.21546 | ||||||||
\(486\) | 2.70023 | 0.122485 | ||||||||
\(487\) | 31.5416 | 1.42929 | 0.714644 | − | 0.699488i | \(-0.246589\pi\) | ||||
0.714644 | + | 0.699488i | \(0.246589\pi\) | |||||||
\(488\) | −8.88702 | −0.402297 | ||||||||
\(489\) | −7.47058 | −0.337831 | ||||||||
\(490\) | 15.0435 | 0.679595 | ||||||||
\(491\) | −40.3483 | −1.82089 | −0.910446 | − | 0.413628i | \(-0.864261\pi\) | ||||
−0.910446 | + | 0.413628i | \(0.864261\pi\) | |||||||
\(492\) | 47.3734 | 2.13576 | ||||||||
\(493\) | 16.7621 | 0.754925 | ||||||||
\(494\) | −11.0573 | −0.497493 | ||||||||
\(495\) | 2.21957 | 0.0997621 | ||||||||
\(496\) | −0.710353 | −0.0318958 | ||||||||
\(497\) | −11.4855 | −0.515195 | ||||||||
\(498\) | 8.26964 | 0.370571 | ||||||||
\(499\) | 25.0651 | 1.12207 | 0.561034 | − | 0.827793i | \(-0.310404\pi\) | ||||
0.561034 | + | 0.827793i | \(0.310404\pi\) | |||||||
\(500\) | −59.5845 | −2.66470 | ||||||||
\(501\) | 17.0129 | 0.760080 | ||||||||
\(502\) | −15.7957 | −0.704996 | ||||||||
\(503\) | 12.7643 | 0.569131 | 0.284565 | − | 0.958657i | \(-0.408151\pi\) | ||||
0.284565 | + | 0.958657i | \(0.408151\pi\) | |||||||
\(504\) | 18.8312 | 0.838808 | ||||||||
\(505\) | −22.7286 | −1.01141 | ||||||||
\(506\) | −0.627524 | −0.0278969 | ||||||||
\(507\) | 6.63107 | 0.294496 | ||||||||
\(508\) | −20.0323 | −0.888788 | ||||||||
\(509\) | 5.82491 | 0.258184 | 0.129092 | − | 0.991633i | \(-0.458794\pi\) | ||||
0.129092 | + | 0.991633i | \(0.458794\pi\) | |||||||
\(510\) | 11.1627 | 0.494291 | ||||||||
\(511\) | 17.0260 | 0.753184 | ||||||||
\(512\) | −9.04363 | −0.399676 | ||||||||
\(513\) | 1.62262 | 0.0716405 | ||||||||
\(514\) | −36.1633 | −1.59509 | ||||||||
\(515\) | −24.3211 | −1.07172 | ||||||||
\(516\) | 46.7236 | 2.05689 | ||||||||
\(517\) | −8.15644 | −0.358720 | ||||||||
\(518\) | −6.41350 | −0.281793 | ||||||||
\(519\) | 7.59030 | 0.333177 | ||||||||
\(520\) | 49.7803 | 2.18301 | ||||||||
\(521\) | 24.0360 | 1.05304 | 0.526518 | − | 0.850164i | \(-0.323497\pi\) | ||||
0.526518 | + | 0.850164i | \(0.323497\pi\) | |||||||
\(522\) | −24.3012 | −1.06363 | ||||||||
\(523\) | −36.6082 | −1.60076 | −0.800382 | − | 0.599491i | \(-0.795370\pi\) | ||||
−0.800382 | + | 0.599491i | \(0.795370\pi\) | |||||||
\(524\) | 55.7482 | 2.43537 | ||||||||
\(525\) | −0.155799 | −0.00679965 | ||||||||
\(526\) | −58.5467 | −2.55276 | ||||||||
\(527\) | −0.0986275 | −0.00429628 | ||||||||
\(528\) | −13.4145 | −0.583793 | ||||||||
\(529\) | −22.9460 | −0.997652 | ||||||||
\(530\) | −68.8721 | −2.99161 | ||||||||
\(531\) | −1.89372 | −0.0821805 | ||||||||
\(532\) | 18.1926 | 0.788748 | ||||||||
\(533\) | 22.5950 | 0.978697 | ||||||||
\(534\) | 14.6064 | 0.632080 | ||||||||
\(535\) | 0.741622 | 0.0320631 | ||||||||
\(536\) | 9.55233 | 0.412598 | ||||||||
\(537\) | −5.63139 | −0.243012 | ||||||||
\(538\) | 74.7542 | 3.22288 | ||||||||
\(539\) | −2.51004 | −0.108115 | ||||||||
\(540\) | −11.7442 | −0.505390 | ||||||||
\(541\) | 27.1649 | 1.16791 | 0.583956 | − | 0.811786i | \(-0.301504\pi\) | ||||
0.583956 | + | 0.811786i | \(0.301504\pi\) | |||||||
\(542\) | 47.7530 | 2.05117 | ||||||||
\(543\) | −23.6253 | −1.01386 | ||||||||
\(544\) | −34.3601 | −1.47318 | ||||||||
\(545\) | 18.6833 | 0.800306 | ||||||||
\(546\) | 14.4396 | 0.617957 | ||||||||
\(547\) | −13.8935 | −0.594043 | −0.297022 | − | 0.954871i | \(-0.595993\pi\) | ||||
−0.297022 | + | 0.954871i | \(0.595993\pi\) | |||||||
\(548\) | −92.4067 | −3.94742 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | 0.198539 | 0.00846571 | ||||||||
\(551\) | −14.6031 | −0.622113 | ||||||||
\(552\) | 2.06532 | 0.0879058 | ||||||||
\(553\) | 14.1392 | 0.601261 | ||||||||
\(554\) | −75.9086 | −3.22505 | ||||||||
\(555\) | 2.48795 | 0.105608 | ||||||||
\(556\) | −0.492073 | −0.0208685 | ||||||||
\(557\) | −4.83132 | −0.204710 | −0.102355 | − | 0.994748i | \(-0.532638\pi\) | ||||
−0.102355 | + | 0.994748i | \(0.532638\pi\) | |||||||
\(558\) | 0.142988 | 0.00605315 | ||||||||
\(559\) | 22.2851 | 0.942558 | ||||||||
\(560\) | −63.0906 | −2.66607 | ||||||||
\(561\) | −1.86251 | −0.0786354 | ||||||||
\(562\) | −78.2027 | −3.29878 | ||||||||
\(563\) | 15.6746 | 0.660606 | 0.330303 | − | 0.943875i | \(-0.392849\pi\) | ||||
0.330303 | + | 0.943875i | \(0.392849\pi\) | |||||||
\(564\) | 43.1575 | 1.81726 | ||||||||
\(565\) | 30.3441 | 1.27658 | ||||||||
\(566\) | −44.6179 | −1.87543 | ||||||||
\(567\) | −2.11895 | −0.0889877 | ||||||||
\(568\) | −48.1709 | −2.02121 | ||||||||
\(569\) | −16.9647 | −0.711199 | −0.355600 | − | 0.934638i | \(-0.615723\pi\) | ||||
−0.355600 | + | 0.934638i | \(0.615723\pi\) | |||||||
\(570\) | −9.72490 | −0.407331 | ||||||||
\(571\) | −0.161872 | −0.00677414 | −0.00338707 | − | 0.999994i | \(-0.501078\pi\) | ||||
−0.00338707 | + | 0.999994i | \(0.501078\pi\) | |||||||
\(572\) | −13.3533 | −0.558330 | ||||||||
\(573\) | 12.1022 | 0.505575 | ||||||||
\(574\) | −51.2271 | −2.13818 | ||||||||
\(575\) | −0.0170874 | −0.000712593 0 | ||||||||
\(576\) | 22.9853 | 0.957719 | ||||||||
\(577\) | −23.1526 | −0.963854 | −0.481927 | − | 0.876211i | \(-0.660063\pi\) | ||||
−0.481927 | + | 0.876211i | \(0.660063\pi\) | |||||||
\(578\) | 36.5369 | 1.51973 | ||||||||
\(579\) | −0.690719 | −0.0287053 | ||||||||
\(580\) | 105.694 | 4.38871 | ||||||||
\(581\) | −6.48945 | −0.269228 | ||||||||
\(582\) | 32.5646 | 1.34984 | ||||||||
\(583\) | 11.4915 | 0.475928 | ||||||||
\(584\) | 71.4079 | 2.95488 | ||||||||
\(585\) | −5.60146 | −0.231592 | ||||||||
\(586\) | 69.0302 | 2.85161 | ||||||||
\(587\) | −29.9787 | −1.23735 | −0.618677 | − | 0.785645i | \(-0.712331\pi\) | ||||
−0.618677 | + | 0.785645i | \(0.712331\pi\) | |||||||
\(588\) | 13.2812 | 0.547706 | ||||||||
\(589\) | 0.0859242 | 0.00354045 | ||||||||
\(590\) | 11.3497 | 0.467260 | ||||||||
\(591\) | 12.5268 | 0.515285 | ||||||||
\(592\) | −15.0366 | −0.618000 | ||||||||
\(593\) | −23.2983 | −0.956747 | −0.478374 | − | 0.878156i | \(-0.658774\pi\) | ||||
−0.478374 | + | 0.878156i | \(0.658774\pi\) | |||||||
\(594\) | 2.70023 | 0.110792 | ||||||||
\(595\) | −8.75970 | −0.359113 | ||||||||
\(596\) | −52.3645 | −2.14493 | ||||||||
\(597\) | 10.6668 | 0.436561 | ||||||||
\(598\) | 1.58367 | 0.0647609 | ||||||||
\(599\) | 8.01939 | 0.327664 | 0.163832 | − | 0.986488i | \(-0.447615\pi\) | ||||
0.163832 | + | 0.986488i | \(0.447615\pi\) | |||||||
\(600\) | −0.653433 | −0.0266763 | ||||||||
\(601\) | −16.6438 | −0.678914 | −0.339457 | − | 0.940622i | \(-0.610243\pi\) | ||||
−0.339457 | + | 0.940622i | \(0.610243\pi\) | |||||||
\(602\) | −50.5245 | −2.05922 | ||||||||
\(603\) | −1.07486 | −0.0437718 | ||||||||
\(604\) | −39.5716 | −1.61015 | ||||||||
\(605\) | 2.21957 | 0.0902382 | ||||||||
\(606\) | −27.6506 | −1.12323 | ||||||||
\(607\) | −0.200635 | −0.00814351 | −0.00407175 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407175 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(608\) | 29.9345 | 1.21400 | ||||||||
\(609\) | 19.0699 | 0.772752 | ||||||||
\(610\) | −5.99333 | −0.242663 | ||||||||
\(611\) | 20.5842 | 0.832747 | ||||||||
\(612\) | 9.85497 | 0.398363 | ||||||||
\(613\) | −23.3942 | −0.944884 | −0.472442 | − | 0.881362i | \(-0.656627\pi\) | ||||
−0.472442 | + | 0.881362i | \(0.656627\pi\) | |||||||
\(614\) | −40.1543 | −1.62050 | ||||||||
\(615\) | 19.8722 | 0.801326 | ||||||||
\(616\) | 18.8312 | 0.758730 | ||||||||
\(617\) | 20.5613 | 0.827765 | 0.413882 | − | 0.910330i | \(-0.364172\pi\) | ||||
0.413882 | + | 0.910330i | \(0.364172\pi\) | |||||||
\(618\) | −29.5880 | −1.19020 | ||||||||
\(619\) | −31.0796 | −1.24920 | −0.624598 | − | 0.780947i | \(-0.714737\pi\) | ||||
−0.624598 | + | 0.780947i | \(0.714737\pi\) | |||||||
\(620\) | −0.621902 | −0.0249762 | ||||||||
\(621\) | −0.232397 | −0.00932577 | ||||||||
\(622\) | 72.5813 | 2.91024 | ||||||||
\(623\) | −11.4621 | −0.459219 | ||||||||
\(624\) | 33.8539 | 1.35524 | ||||||||
\(625\) | −24.6270 | −0.985078 | ||||||||
\(626\) | 88.4485 | 3.53511 | ||||||||
\(627\) | 1.62262 | 0.0648012 | ||||||||
\(628\) | −82.4150 | −3.28872 | ||||||||
\(629\) | −2.08773 | −0.0832431 | ||||||||
\(630\) | 12.6996 | 0.505963 | ||||||||
\(631\) | −8.46876 | −0.337136 | −0.168568 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168568 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(632\) | 59.3009 | 2.35886 | ||||||||
\(633\) | 11.3412 | 0.450774 | ||||||||
\(634\) | 21.8852 | 0.869173 | ||||||||
\(635\) | −8.40316 | −0.333469 | ||||||||
\(636\) | −60.8038 | −2.41103 | ||||||||
\(637\) | 6.33452 | 0.250983 | ||||||||
\(638\) | −24.3012 | −0.962094 | ||||||||
\(639\) | 5.42037 | 0.214426 | ||||||||
\(640\) | −55.8642 | −2.20823 | ||||||||
\(641\) | 30.1870 | 1.19231 | 0.596157 | − | 0.802868i | \(-0.296693\pi\) | ||||
0.596157 | + | 0.802868i | \(0.296693\pi\) | |||||||
\(642\) | 0.902224 | 0.0356080 | ||||||||
\(643\) | −18.9252 | −0.746337 | −0.373168 | − | 0.927764i | \(-0.621729\pi\) | ||||
−0.373168 | + | 0.927764i | \(0.621729\pi\) | |||||||
\(644\) | −2.60560 | −0.102675 | ||||||||
\(645\) | 19.5997 | 0.771736 | ||||||||
\(646\) | 8.16050 | 0.321071 | ||||||||
\(647\) | 19.0510 | 0.748973 | 0.374486 | − | 0.927232i | \(-0.377819\pi\) | ||||
0.374486 | + | 0.927232i | \(0.377819\pi\) | |||||||
\(648\) | −8.88702 | −0.349115 | ||||||||
\(649\) | −1.89372 | −0.0743351 | ||||||||
\(650\) | −0.501046 | −0.0196527 | ||||||||
\(651\) | −0.112207 | −0.00439774 | ||||||||
\(652\) | 39.5285 | 1.54805 | ||||||||
\(653\) | −34.8338 | −1.36315 | −0.681576 | − | 0.731748i | \(-0.738705\pi\) | ||||
−0.681576 | + | 0.731748i | \(0.738705\pi\) | |||||||
\(654\) | 22.7293 | 0.888786 | ||||||||
\(655\) | 23.3853 | 0.913740 | ||||||||
\(656\) | −120.103 | −4.68924 | ||||||||
\(657\) | −8.03508 | −0.313478 | ||||||||
\(658\) | −46.6683 | −1.81932 | ||||||||
\(659\) | −18.0958 | −0.704912 | −0.352456 | − | 0.935828i | \(-0.614653\pi\) | ||||
−0.352456 | + | 0.935828i | \(0.614653\pi\) | |||||||
\(660\) | −11.7442 | −0.457142 | ||||||||
\(661\) | −5.52684 | −0.214969 | −0.107485 | − | 0.994207i | \(-0.534280\pi\) | ||||
−0.107485 | + | 0.994207i | \(0.534280\pi\) | |||||||
\(662\) | 36.8033 | 1.43040 | ||||||||
\(663\) | 4.70038 | 0.182548 | ||||||||
\(664\) | −27.2172 | −1.05623 | ||||||||
\(665\) | 7.63144 | 0.295935 | ||||||||
\(666\) | 3.02673 | 0.117283 | ||||||||
\(667\) | 2.09150 | 0.0809833 | ||||||||
\(668\) | −90.0188 | −3.48293 | ||||||||
\(669\) | 10.0996 | 0.390472 | ||||||||
\(670\) | 6.44200 | 0.248876 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | −39.0909 | −1.50796 | ||||||||
\(673\) | 31.0228 | 1.19584 | 0.597921 | − | 0.801555i | \(-0.295994\pi\) | ||||
0.597921 | + | 0.801555i | \(0.295994\pi\) | |||||||
\(674\) | −22.2043 | −0.855277 | ||||||||
\(675\) | 0.0735266 | 0.00283004 | ||||||||
\(676\) | −35.0864 | −1.34948 | ||||||||
\(677\) | −7.79875 | −0.299730 | −0.149865 | − | 0.988706i | \(-0.547884\pi\) | ||||
−0.149865 | + | 0.988706i | \(0.547884\pi\) | |||||||
\(678\) | 36.9153 | 1.41772 | ||||||||
\(679\) | −25.5544 | −0.980690 | ||||||||
\(680\) | −36.7387 | −1.40887 | ||||||||
\(681\) | 24.4371 | 0.936430 | ||||||||
\(682\) | 0.142988 | 0.00547528 | ||||||||
\(683\) | 4.80839 | 0.183988 | 0.0919940 | − | 0.995760i | \(-0.470676\pi\) | ||||
0.0919940 | + | 0.995760i | \(0.470676\pi\) | |||||||
\(684\) | −8.58564 | −0.328280 | ||||||||
\(685\) | −38.7629 | −1.48105 | ||||||||
\(686\) | −54.4131 | −2.07750 | ||||||||
\(687\) | 13.2077 | 0.503904 | ||||||||
\(688\) | −118.456 | −4.51608 | ||||||||
\(689\) | −29.0007 | −1.10484 | ||||||||
\(690\) | 1.39283 | 0.0530242 | ||||||||
\(691\) | 38.0308 | 1.44676 | 0.723381 | − | 0.690449i | \(-0.242587\pi\) | ||||
0.723381 | + | 0.690449i | \(0.242587\pi\) | |||||||
\(692\) | −40.1619 | −1.52673 | ||||||||
\(693\) | −2.11895 | −0.0804924 | ||||||||
\(694\) | −16.7789 | −0.636918 | ||||||||
\(695\) | −0.206415 | −0.00782977 | ||||||||
\(696\) | 79.9805 | 3.03165 | ||||||||
\(697\) | −16.6755 | −0.631629 | ||||||||
\(698\) | 26.0722 | 0.986847 | ||||||||
\(699\) | 0.140516 | 0.00531480 | ||||||||
\(700\) | 0.824369 | 0.0311582 | ||||||||
\(701\) | 31.4813 | 1.18903 | 0.594517 | − | 0.804083i | \(-0.297343\pi\) | ||||
0.594517 | + | 0.804083i | \(0.297343\pi\) | |||||||
\(702\) | −6.81449 | −0.257196 | ||||||||
\(703\) | 1.81883 | 0.0685983 | ||||||||
\(704\) | 22.9853 | 0.866290 | ||||||||
\(705\) | 18.1037 | 0.681827 | ||||||||
\(706\) | −25.9186 | −0.975459 | ||||||||
\(707\) | 21.6983 | 0.816049 | ||||||||
\(708\) | 10.0201 | 0.376578 | ||||||||
\(709\) | 35.2230 | 1.32283 | 0.661414 | − | 0.750021i | \(-0.269957\pi\) | ||||
0.661414 | + | 0.750021i | \(0.269957\pi\) | |||||||
\(710\) | −32.4860 | −1.21918 | ||||||||
\(711\) | −6.67275 | −0.250248 | ||||||||
\(712\) | −48.0727 | −1.80160 | ||||||||
\(713\) | −0.0123063 | −0.000460876 0 | ||||||||
\(714\) | −10.6567 | −0.398815 | ||||||||
\(715\) | −5.60146 | −0.209483 | ||||||||
\(716\) | 29.7969 | 1.11356 | ||||||||
\(717\) | −4.97217 | −0.185689 | ||||||||
\(718\) | 22.2690 | 0.831072 | ||||||||
\(719\) | 44.5756 | 1.66239 | 0.831195 | − | 0.555982i | \(-0.187658\pi\) | ||||
0.831195 | + | 0.555982i | \(0.187658\pi\) | |||||||
\(720\) | 29.7744 | 1.10963 | ||||||||
\(721\) | 23.2186 | 0.864707 | ||||||||
\(722\) | 44.1949 | 1.64476 | ||||||||
\(723\) | 12.4794 | 0.464115 | ||||||||
\(724\) | 125.007 | 4.64583 | ||||||||
\(725\) | −0.661717 | −0.0245756 | ||||||||
\(726\) | 2.70023 | 0.100215 | ||||||||
\(727\) | 30.1879 | 1.11961 | 0.559804 | − | 0.828625i | \(-0.310876\pi\) | ||||
0.559804 | + | 0.828625i | \(0.310876\pi\) | |||||||
\(728\) | −47.5238 | −1.76135 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 48.1569 | 1.78237 | ||||||||
\(731\) | −16.4468 | −0.608305 | ||||||||
\(732\) | −5.29122 | −0.195569 | ||||||||
\(733\) | 37.2407 | 1.37552 | 0.687758 | − | 0.725940i | \(-0.258595\pi\) | ||||
0.687758 | + | 0.725940i | \(0.258595\pi\) | |||||||
\(734\) | 38.0292 | 1.40368 | ||||||||
\(735\) | 5.57120 | 0.205497 | ||||||||
\(736\) | −4.28731 | −0.158032 | ||||||||
\(737\) | −1.07486 | −0.0395931 | ||||||||
\(738\) | 24.1757 | 0.889919 | ||||||||
\(739\) | −12.8770 | −0.473687 | −0.236844 | − | 0.971548i | \(-0.576113\pi\) | ||||
−0.236844 | + | 0.971548i | \(0.576113\pi\) | |||||||
\(740\) | −13.1643 | −0.483929 | ||||||||
\(741\) | −4.09497 | −0.150432 | ||||||||
\(742\) | 65.7501 | 2.41376 | ||||||||
\(743\) | 4.28620 | 0.157245 | 0.0786227 | − | 0.996904i | \(-0.474948\pi\) | ||||
0.0786227 | + | 0.996904i | \(0.474948\pi\) | |||||||
\(744\) | −0.470603 | −0.0172532 | ||||||||
\(745\) | −21.9659 | −0.804770 | ||||||||
\(746\) | −75.4985 | −2.76420 | ||||||||
\(747\) | 3.06257 | 0.112054 | ||||||||
\(748\) | 9.85497 | 0.360333 | ||||||||
\(749\) | −0.708004 | −0.0258699 | ||||||||
\(750\) | −30.4073 | −1.11032 | ||||||||
\(751\) | −27.8015 | −1.01449 | −0.507246 | − | 0.861801i | \(-0.669336\pi\) | ||||
−0.507246 | + | 0.861801i | \(0.669336\pi\) | |||||||
\(752\) | −109.415 | −3.98995 | ||||||||
\(753\) | −5.84977 | −0.213177 | ||||||||
\(754\) | 61.3283 | 2.23345 | ||||||||
\(755\) | −16.5995 | −0.604119 | ||||||||
\(756\) | 11.2118 | 0.407771 | ||||||||
\(757\) | −34.7648 | −1.26355 | −0.631775 | − | 0.775152i | \(-0.717673\pi\) | ||||
−0.631775 | + | 0.775152i | \(0.717673\pi\) | |||||||
\(758\) | 40.3856 | 1.46687 | ||||||||
\(759\) | −0.232397 | −0.00843548 | ||||||||
\(760\) | 32.0067 | 1.16101 | ||||||||
\(761\) | −33.2917 | −1.20682 | −0.603412 | − | 0.797430i | \(-0.706192\pi\) | ||||
−0.603412 | + | 0.797430i | \(0.706192\pi\) | |||||||
\(762\) | −10.2229 | −0.370337 | ||||||||
\(763\) | −17.8364 | −0.645721 | ||||||||
\(764\) | −64.0351 | −2.31671 | ||||||||
\(765\) | 4.13397 | 0.149464 | ||||||||
\(766\) | 96.5948 | 3.49011 | ||||||||
\(767\) | 4.77914 | 0.172565 | ||||||||
\(768\) | −21.9913 | −0.793544 | ||||||||
\(769\) | 24.8893 | 0.897530 | 0.448765 | − | 0.893650i | \(-0.351864\pi\) | ||||
0.448765 | + | 0.893650i | \(0.351864\pi\) | |||||||
\(770\) | 12.6996 | 0.457661 | ||||||||
\(771\) | −13.3927 | −0.482326 | ||||||||
\(772\) | 3.65474 | 0.131537 | ||||||||
\(773\) | 0.379382 | 0.0136454 | 0.00682270 | − | 0.999977i | \(-0.497828\pi\) | ||||
0.00682270 | + | 0.999977i | \(0.497828\pi\) | |||||||
\(774\) | 23.8441 | 0.857058 | ||||||||
\(775\) | 0.00389353 | 0.000139860 0 | ||||||||
\(776\) | −107.177 | −3.84743 | ||||||||
\(777\) | −2.37517 | −0.0852089 | ||||||||
\(778\) | −42.6659 | −1.52965 | ||||||||
\(779\) | 14.5277 | 0.520508 | ||||||||
\(780\) | 29.6385 | 1.06123 | ||||||||
\(781\) | 5.42037 | 0.193956 | ||||||||
\(782\) | −1.16877 | −0.0417952 | ||||||||
\(783\) | −8.99969 | −0.321623 | ||||||||
\(784\) | −33.6710 | −1.20254 | ||||||||
\(785\) | −34.5716 | −1.23391 | ||||||||
\(786\) | 28.4495 | 1.01476 | ||||||||
\(787\) | 51.6649 | 1.84165 | 0.920827 | − | 0.389971i | \(-0.127515\pi\) | ||||
0.920827 | + | 0.389971i | \(0.127515\pi\) | |||||||
\(788\) | −66.2822 | −2.36120 | ||||||||
\(789\) | −21.6822 | −0.771906 | ||||||||
\(790\) | 39.9920 | 1.42285 | ||||||||
\(791\) | −28.9686 | −1.03000 | ||||||||
\(792\) | −8.88702 | −0.315787 | ||||||||
\(793\) | −2.52367 | −0.0896183 | ||||||||
\(794\) | −36.3050 | −1.28842 | ||||||||
\(795\) | −25.5061 | −0.904607 | ||||||||
\(796\) | −56.4401 | −2.00047 | ||||||||
\(797\) | 45.8832 | 1.62527 | 0.812634 | − | 0.582775i | \(-0.198033\pi\) | ||||
0.812634 | + | 0.582775i | \(0.198033\pi\) | |||||||
\(798\) | 9.28407 | 0.328652 | ||||||||
\(799\) | −15.1915 | −0.537436 | ||||||||
\(800\) | 1.35644 | 0.0479572 | ||||||||
\(801\) | 5.40932 | 0.191129 | ||||||||
\(802\) | −30.3341 | −1.07113 | ||||||||
\(803\) | −8.03508 | −0.283552 | ||||||||
\(804\) | 5.68733 | 0.200577 | ||||||||
\(805\) | −1.09300 | −0.0385232 | ||||||||
\(806\) | −0.360854 | −0.0127105 | ||||||||
\(807\) | 27.6844 | 0.974538 | ||||||||
\(808\) | 91.0041 | 3.20151 | ||||||||
\(809\) | 38.7974 | 1.36405 | 0.682023 | − | 0.731331i | \(-0.261101\pi\) | ||||
0.682023 | + | 0.731331i | \(0.261101\pi\) | |||||||
\(810\) | −5.99333 | −0.210584 | ||||||||
\(811\) | 8.13554 | 0.285678 | 0.142839 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142839 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(812\) | −100.903 | −3.54100 | ||||||||
\(813\) | 17.6848 | 0.620233 | ||||||||
\(814\) | 3.02673 | 0.106087 | ||||||||
\(815\) | 16.5814 | 0.580823 | ||||||||
\(816\) | −24.9848 | −0.874642 | ||||||||
\(817\) | 14.3284 | 0.501287 | ||||||||
\(818\) | −59.4452 | −2.07845 | ||||||||
\(819\) | 5.34755 | 0.186858 | ||||||||
\(820\) | −105.148 | −3.67194 | ||||||||
\(821\) | 10.5549 | 0.368370 | 0.184185 | − | 0.982892i | \(-0.441035\pi\) | ||||
0.184185 | + | 0.982892i | \(0.441035\pi\) | |||||||
\(822\) | −47.1572 | −1.64480 | ||||||||
\(823\) | 26.5350 | 0.924953 | 0.462477 | − | 0.886632i | \(-0.346961\pi\) | ||||
0.462477 | + | 0.886632i | \(0.346961\pi\) | |||||||
\(824\) | 97.3804 | 3.39241 | ||||||||
\(825\) | 0.0735266 | 0.00255987 | ||||||||
\(826\) | −10.8352 | −0.377005 | ||||||||
\(827\) | 42.2012 | 1.46748 | 0.733739 | − | 0.679431i | \(-0.237773\pi\) | ||||
0.733739 | + | 0.679431i | \(0.237773\pi\) | |||||||
\(828\) | 1.22966 | 0.0427337 | ||||||||
\(829\) | 32.9471 | 1.14430 | 0.572150 | − | 0.820149i | \(-0.306109\pi\) | ||||
0.572150 | + | 0.820149i | \(0.306109\pi\) | |||||||
\(830\) | −18.3550 | −0.637112 | ||||||||
\(831\) | −28.1120 | −0.975193 | ||||||||
\(832\) | −58.0073 | −2.01104 | ||||||||
\(833\) | −4.67498 | −0.161979 | ||||||||
\(834\) | −0.251116 | −0.00869542 | ||||||||
\(835\) | −37.7612 | −1.30678 | ||||||||
\(836\) | −8.58564 | −0.296941 | ||||||||
\(837\) | 0.0529540 | 0.00183036 | ||||||||
\(838\) | 27.1377 | 0.937455 | ||||||||
\(839\) | −27.8310 | −0.960831 | −0.480416 | − | 0.877041i | \(-0.659514\pi\) | ||||
−0.480416 | + | 0.877041i | \(0.659514\pi\) | |||||||
\(840\) | −41.7971 | −1.44214 | ||||||||
\(841\) | 51.9945 | 1.79291 | ||||||||
\(842\) | 88.3084 | 3.04331 | ||||||||
\(843\) | −28.9616 | −0.997489 | ||||||||
\(844\) | −60.0090 | −2.06559 | ||||||||
\(845\) | −14.7181 | −0.506318 | ||||||||
\(846\) | 22.0242 | 0.757208 | ||||||||
\(847\) | −2.11895 | −0.0728081 | ||||||||
\(848\) | 154.153 | 5.29362 | ||||||||
\(849\) | −16.5238 | −0.567094 | ||||||||
\(850\) | 0.369781 | 0.0126834 | ||||||||
\(851\) | −0.260498 | −0.00892976 | ||||||||
\(852\) | −28.6803 | −0.982572 | ||||||||
\(853\) | −16.5400 | −0.566319 | −0.283159 | − | 0.959073i | \(-0.591383\pi\) | ||||
−0.283159 | + | 0.959073i | \(0.591383\pi\) | |||||||
\(854\) | 5.72165 | 0.195791 | ||||||||
\(855\) | −3.60151 | −0.123169 | ||||||||
\(856\) | −2.96942 | −0.101493 | ||||||||
\(857\) | 34.2189 | 1.16890 | 0.584448 | − | 0.811431i | \(-0.301311\pi\) | ||||
0.584448 | + | 0.811431i | \(0.301311\pi\) | |||||||
\(858\) | −6.81449 | −0.232643 | ||||||||
\(859\) | −41.1854 | −1.40523 | −0.702615 | − | 0.711571i | \(-0.747984\pi\) | ||||
−0.702615 | + | 0.711571i | \(0.747984\pi\) | |||||||
\(860\) | −103.706 | −3.53635 | ||||||||
\(861\) | −18.9714 | −0.646545 | ||||||||
\(862\) | 73.4657 | 2.50225 | ||||||||
\(863\) | 45.1683 | 1.53755 | 0.768774 | − | 0.639520i | \(-0.220867\pi\) | ||||
0.768774 | + | 0.639520i | \(0.220867\pi\) | |||||||
\(864\) | 18.4482 | 0.627621 | ||||||||
\(865\) | −16.8472 | −0.572821 | ||||||||
\(866\) | −16.8788 | −0.573566 | ||||||||
\(867\) | 13.5310 | 0.459538 | ||||||||
\(868\) | 0.593711 | 0.0201519 | ||||||||
\(869\) | −6.67275 | −0.226357 | ||||||||
\(870\) | 53.9381 | 1.82867 | ||||||||
\(871\) | 2.71260 | 0.0919130 | ||||||||
\(872\) | −74.8070 | −2.53329 | ||||||||
\(873\) | 12.0599 | 0.408167 | ||||||||
\(874\) | 1.01823 | 0.0344423 | ||||||||
\(875\) | 23.8616 | 0.806669 | ||||||||
\(876\) | 42.5153 | 1.43646 | ||||||||
\(877\) | 56.3413 | 1.90251 | 0.951256 | − | 0.308404i | \(-0.0997948\pi\) | ||||
0.951256 | + | 0.308404i | \(0.0997948\pi\) | |||||||
\(878\) | 16.8479 | 0.568590 | ||||||||
\(879\) | 25.5646 | 0.862272 | ||||||||
\(880\) | 29.7744 | 1.00370 | ||||||||
\(881\) | 48.9192 | 1.64813 | 0.824065 | − | 0.566495i | \(-0.191701\pi\) | ||||
0.824065 | + | 0.566495i | \(0.191701\pi\) | |||||||
\(882\) | 6.77767 | 0.228216 | ||||||||
\(883\) | 3.36882 | 0.113370 | 0.0566849 | − | 0.998392i | \(-0.481947\pi\) | ||||
0.0566849 | + | 0.998392i | \(0.481947\pi\) | |||||||
\(884\) | −24.8707 | −0.836493 | ||||||||
\(885\) | 4.20324 | 0.141290 | ||||||||
\(886\) | 73.6087 | 2.47293 | ||||||||
\(887\) | 16.3667 | 0.549539 | 0.274770 | − | 0.961510i | \(-0.411398\pi\) | ||||
0.274770 | + | 0.961510i | \(0.411398\pi\) | |||||||
\(888\) | −9.96163 | −0.334290 | ||||||||
\(889\) | 8.02225 | 0.269058 | ||||||||
\(890\) | −32.4198 | −1.08671 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −53.4390 | −1.78927 | ||||||||
\(893\) | 13.2348 | 0.442886 | ||||||||
\(894\) | −26.7228 | −0.893743 | ||||||||
\(895\) | 12.4992 | 0.417804 | ||||||||
\(896\) | 53.3318 | 1.78169 | ||||||||
\(897\) | 0.586494 | 0.0195825 | ||||||||
\(898\) | 9.15510 | 0.305509 | ||||||||
\(899\) | −0.476570 | −0.0158945 | ||||||||
\(900\) | −0.389045 | −0.0129682 | ||||||||
\(901\) | 21.4030 | 0.713038 | ||||||||
\(902\) | 24.1757 | 0.804962 | ||||||||
\(903\) | −18.7112 | −0.622670 | ||||||||
\(904\) | −121.496 | −4.04090 | ||||||||
\(905\) | 52.4379 | 1.74310 | ||||||||
\(906\) | −20.1943 | −0.670909 | ||||||||
\(907\) | 44.5370 | 1.47883 | 0.739413 | − | 0.673252i | \(-0.235103\pi\) | ||||
0.739413 | + | 0.673252i | \(0.235103\pi\) | |||||||
\(908\) | −129.302 | −4.29103 | ||||||||
\(909\) | −10.2401 | −0.339643 | ||||||||
\(910\) | −32.0496 | −1.06243 | ||||||||
\(911\) | −32.4292 | −1.07443 | −0.537214 | − | 0.843446i | \(-0.680523\pi\) | ||||
−0.537214 | + | 0.843446i | \(0.680523\pi\) | |||||||
\(912\) | 21.7667 | 0.720768 | ||||||||
\(913\) | 3.06257 | 0.101356 | ||||||||
\(914\) | 17.5400 | 0.580172 | ||||||||
\(915\) | −2.21957 | −0.0733766 | ||||||||
\(916\) | −69.8846 | −2.30905 | ||||||||
\(917\) | −22.3253 | −0.737245 | ||||||||
\(918\) | 5.02921 | 0.165989 | ||||||||
\(919\) | 43.4762 | 1.43415 | 0.717074 | − | 0.696997i | \(-0.245481\pi\) | ||||
0.717074 | + | 0.696997i | \(0.245481\pi\) | |||||||
\(920\) | −4.58411 | −0.151134 | ||||||||
\(921\) | −14.8707 | −0.490007 | ||||||||
\(922\) | −16.5372 | −0.544624 | ||||||||
\(923\) | −13.6792 | −0.450258 | ||||||||
\(924\) | 11.2118 | 0.368842 | ||||||||
\(925\) | 0.0824174 | 0.00270987 | ||||||||
\(926\) | 103.681 | 3.40718 | ||||||||
\(927\) | −10.9576 | −0.359895 | ||||||||
\(928\) | −166.028 | −5.45015 | ||||||||
\(929\) | −2.48926 | −0.0816699 | −0.0408349 | − | 0.999166i | \(-0.513002\pi\) | ||||
−0.0408349 | + | 0.999166i | \(0.513002\pi\) | |||||||
\(930\) | −0.317371 | −0.0104070 | ||||||||
\(931\) | 4.07284 | 0.133482 | ||||||||
\(932\) | −0.743500 | −0.0243541 | ||||||||
\(933\) | 26.8797 | 0.880002 | ||||||||
\(934\) | −33.3741 | −1.09203 | ||||||||
\(935\) | 4.13397 | 0.135195 | ||||||||
\(936\) | 22.4280 | 0.733081 | ||||||||
\(937\) | −37.0461 | −1.21024 | −0.605122 | − | 0.796133i | \(-0.706876\pi\) | ||||
−0.605122 | + | 0.796133i | \(0.706876\pi\) | |||||||
\(938\) | −6.14998 | −0.200804 | ||||||||
\(939\) | 32.7560 | 1.06895 | ||||||||
\(940\) | −95.7908 | −3.12435 | ||||||||
\(941\) | 20.6828 | 0.674239 | 0.337119 | − | 0.941462i | \(-0.390547\pi\) | ||||
0.337119 | + | 0.941462i | \(0.390547\pi\) | |||||||
\(942\) | −42.0582 | −1.37033 | ||||||||
\(943\) | −2.08070 | −0.0677569 | ||||||||
\(944\) | −25.4034 | −0.826810 | ||||||||
\(945\) | 4.70316 | 0.152994 | ||||||||
\(946\) | 23.8441 | 0.775238 | ||||||||
\(947\) | 5.40266 | 0.175563 | 0.0877814 | − | 0.996140i | \(-0.472022\pi\) | ||||
0.0877814 | + | 0.996140i | \(0.472022\pi\) | |||||||
\(948\) | 35.3069 | 1.14672 | ||||||||
\(949\) | 20.2779 | 0.658249 | ||||||||
\(950\) | −0.322153 | −0.0104520 | ||||||||
\(951\) | 8.10496 | 0.262821 | ||||||||
\(952\) | 35.0734 | 1.13673 | ||||||||
\(953\) | −38.9975 | −1.26325 | −0.631627 | − | 0.775272i | \(-0.717613\pi\) | ||||
−0.631627 | + | 0.775272i | \(0.717613\pi\) | |||||||
\(954\) | −31.0295 | −1.00462 | ||||||||
\(955\) | −26.8615 | −0.869219 | ||||||||
\(956\) | 26.3088 | 0.850888 | ||||||||
\(957\) | −8.99969 | −0.290919 | ||||||||
\(958\) | −53.3065 | −1.72225 | ||||||||
\(959\) | 37.0058 | 1.19498 | ||||||||
\(960\) | −51.0173 | −1.64658 | ||||||||
\(961\) | −30.9972 | −0.999910 | ||||||||
\(962\) | −7.63848 | −0.246275 | ||||||||
\(963\) | 0.334129 | 0.0107672 | ||||||||
\(964\) | −66.0314 | −2.12673 | ||||||||
\(965\) | 1.53310 | 0.0493521 | ||||||||
\(966\) | −1.32969 | −0.0427822 | ||||||||
\(967\) | −41.4580 | −1.33320 | −0.666600 | − | 0.745416i | \(-0.732251\pi\) | ||||
−0.666600 | + | 0.745416i | \(0.732251\pi\) | |||||||
\(968\) | −8.88702 | −0.285640 | ||||||||
\(969\) | 3.02216 | 0.0970856 | ||||||||
\(970\) | −72.2792 | −2.32075 | ||||||||
\(971\) | −26.4228 | −0.847946 | −0.423973 | − | 0.905675i | \(-0.639365\pi\) | ||||
−0.423973 | + | 0.905675i | \(0.639365\pi\) | |||||||
\(972\) | −5.29122 | −0.169716 | ||||||||
\(973\) | 0.197058 | 0.00631740 | ||||||||
\(974\) | −85.1696 | −2.72901 | ||||||||
\(975\) | −0.185557 | −0.00594259 | ||||||||
\(976\) | 13.4145 | 0.429389 | ||||||||
\(977\) | 32.0940 | 1.02678 | 0.513388 | − | 0.858156i | \(-0.328390\pi\) | ||||
0.513388 | + | 0.858156i | \(0.328390\pi\) | |||||||
\(978\) | 20.1723 | 0.645038 | ||||||||
\(979\) | 5.40932 | 0.172883 | ||||||||
\(980\) | −29.4784 | −0.941653 | ||||||||
\(981\) | 8.41756 | 0.268752 | ||||||||
\(982\) | 108.949 | 3.47672 | ||||||||
\(983\) | −52.2389 | −1.66616 | −0.833082 | − | 0.553150i | \(-0.813426\pi\) | ||||
−0.833082 | + | 0.553150i | \(0.813426\pi\) | |||||||
\(984\) | −79.5674 | −2.53652 | ||||||||
\(985\) | −27.8041 | −0.885913 | ||||||||
\(986\) | −45.2613 | −1.44141 | ||||||||
\(987\) | −17.2831 | −0.550127 | ||||||||
\(988\) | 21.6674 | 0.689330 | ||||||||
\(989\) | −2.05216 | −0.0652549 | ||||||||
\(990\) | −5.99333 | −0.190480 | ||||||||
\(991\) | −9.78273 | −0.310759 | −0.155379 | − | 0.987855i | \(-0.549660\pi\) | ||||
−0.155379 | + | 0.987855i | \(0.549660\pi\) | |||||||
\(992\) | 0.976906 | 0.0310168 | ||||||||
\(993\) | 13.6297 | 0.432526 | ||||||||
\(994\) | 31.0134 | 0.983687 | ||||||||
\(995\) | −23.6756 | −0.750566 | ||||||||
\(996\) | −16.2047 | −0.513467 | ||||||||
\(997\) | 13.5943 | 0.430537 | 0.215268 | − | 0.976555i | \(-0.430937\pi\) | ||||
0.215268 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(998\) | −67.6814 | −2.14242 | ||||||||
\(999\) | 1.12092 | 0.0354643 |
(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 | 2013.2.a.b.1.1 | ✓ | 11 | |
3.2 | odd | 2 | 6039.2.a.c.1.11 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.b.1.1 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6039.2.a.c.1.11 | 11 | 3.2 | odd | 2 |