Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + 14484 x^{12} - 24566 x^{11} - 36791 x^{10} + 59410 x^{9} + 52109 x^{8} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(0.762638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.762638 | 0.539266 | 0.269633 | − | 0.962963i | \(-0.413098\pi\) | ||||
0.269633 | + | 0.962963i | \(0.413098\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.41838 | −0.709192 | ||||||||
\(5\) | −4.10409 | −1.83540 | −0.917702 | − | 0.397270i | \(-0.869958\pi\) | ||||
−0.917702 | + | 0.397270i | \(0.869958\pi\) | |||||||
\(6\) | 0.762638 | 0.311346 | ||||||||
\(7\) | −2.37592 | −0.898013 | −0.449007 | − | 0.893528i | \(-0.648222\pi\) | ||||
−0.449007 | + | 0.893528i | \(0.648222\pi\) | |||||||
\(8\) | −2.60699 | −0.921710 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.12993 | −0.989771 | ||||||||
\(11\) | −4.76863 | −1.43780 | −0.718898 | − | 0.695116i | \(-0.755353\pi\) | ||||
−0.718898 | + | 0.695116i | \(0.755353\pi\) | |||||||
\(12\) | −1.41838 | −0.409452 | ||||||||
\(13\) | 5.19051 | 1.43959 | 0.719794 | − | 0.694188i | \(-0.244236\pi\) | ||||
0.719794 | + | 0.694188i | \(0.244236\pi\) | |||||||
\(14\) | −1.81197 | −0.484268 | ||||||||
\(15\) | −4.10409 | −1.05967 | ||||||||
\(16\) | 0.848580 | 0.212145 | ||||||||
\(17\) | −2.80912 | −0.681312 | −0.340656 | − | 0.940188i | \(-0.610649\pi\) | ||||
−0.340656 | + | 0.940188i | \(0.610649\pi\) | |||||||
\(18\) | 0.762638 | 0.179755 | ||||||||
\(19\) | −0.644865 | −0.147942 | −0.0739710 | − | 0.997260i | \(-0.523567\pi\) | ||||
−0.0739710 | + | 0.997260i | \(0.523567\pi\) | |||||||
\(20\) | 5.82117 | 1.30165 | ||||||||
\(21\) | −2.37592 | −0.518468 | ||||||||
\(22\) | −3.63674 | −0.775355 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.60699 | −0.532149 | ||||||||
\(25\) | 11.8435 | 2.36871 | ||||||||
\(26\) | 3.95848 | 0.776321 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.36997 | 0.636864 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −3.12993 | −0.571445 | ||||||||
\(31\) | 0.195443 | 0.0351026 | 0.0175513 | − | 0.999846i | \(-0.494413\pi\) | ||||
0.0175513 | + | 0.999846i | \(0.494413\pi\) | |||||||
\(32\) | 5.86114 | 1.03611 | ||||||||
\(33\) | −4.76863 | −0.830111 | ||||||||
\(34\) | −2.14234 | −0.367409 | ||||||||
\(35\) | 9.75098 | 1.64822 | ||||||||
\(36\) | −1.41838 | −0.236397 | ||||||||
\(37\) | 4.46849 | 0.734616 | 0.367308 | − | 0.930099i | \(-0.380280\pi\) | ||||
0.367308 | + | 0.930099i | \(0.380280\pi\) | |||||||
\(38\) | −0.491798 | −0.0797802 | ||||||||
\(39\) | 5.19051 | 0.831146 | ||||||||
\(40\) | 10.6993 | 1.69171 | ||||||||
\(41\) | 2.20248 | 0.343969 | 0.171985 | − | 0.985100i | \(-0.444982\pi\) | ||||
0.171985 | + | 0.985100i | \(0.444982\pi\) | |||||||
\(42\) | −1.81197 | −0.279592 | ||||||||
\(43\) | 10.7899 | 1.64545 | 0.822725 | − | 0.568440i | \(-0.192453\pi\) | ||||
0.822725 | + | 0.568440i | \(0.192453\pi\) | |||||||
\(44\) | 6.76374 | 1.01967 | ||||||||
\(45\) | −4.10409 | −0.611801 | ||||||||
\(46\) | 0.762638 | 0.112445 | ||||||||
\(47\) | −10.3878 | −1.51522 | −0.757610 | − | 0.652708i | \(-0.773633\pi\) | ||||
−0.757610 | + | 0.652708i | \(0.773633\pi\) | |||||||
\(48\) | 0.848580 | 0.122482 | ||||||||
\(49\) | −1.35501 | −0.193572 | ||||||||
\(50\) | 9.03232 | 1.27736 | ||||||||
\(51\) | −2.80912 | −0.393356 | ||||||||
\(52\) | −7.36213 | −1.02094 | ||||||||
\(53\) | −3.71349 | −0.510088 | −0.255044 | − | 0.966930i | \(-0.582090\pi\) | ||||
−0.255044 | + | 0.966930i | \(0.582090\pi\) | |||||||
\(54\) | 0.762638 | 0.103782 | ||||||||
\(55\) | 19.5709 | 2.63893 | ||||||||
\(56\) | 6.19400 | 0.827707 | ||||||||
\(57\) | −0.644865 | −0.0854144 | ||||||||
\(58\) | 0.762638 | 0.100139 | ||||||||
\(59\) | −6.79452 | −0.884572 | −0.442286 | − | 0.896874i | \(-0.645832\pi\) | ||||
−0.442286 | + | 0.896874i | \(0.645832\pi\) | |||||||
\(60\) | 5.82117 | 0.751510 | ||||||||
\(61\) | 12.5542 | 1.60740 | 0.803698 | − | 0.595037i | \(-0.202863\pi\) | ||||
0.803698 | + | 0.595037i | \(0.202863\pi\) | |||||||
\(62\) | 0.149052 | 0.0189296 | ||||||||
\(63\) | −2.37592 | −0.299338 | ||||||||
\(64\) | 2.77276 | 0.346596 | ||||||||
\(65\) | −21.3023 | −2.64222 | ||||||||
\(66\) | −3.63674 | −0.447651 | ||||||||
\(67\) | −2.80619 | −0.342831 | −0.171415 | − | 0.985199i | \(-0.554834\pi\) | ||||
−0.171415 | + | 0.985199i | \(0.554834\pi\) | |||||||
\(68\) | 3.98441 | 0.483181 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 7.43647 | 0.888828 | ||||||||
\(71\) | 14.2651 | 1.69295 | 0.846476 | − | 0.532428i | \(-0.178720\pi\) | ||||
0.846476 | + | 0.532428i | \(0.178720\pi\) | |||||||
\(72\) | −2.60699 | −0.307237 | ||||||||
\(73\) | −7.86909 | −0.921007 | −0.460504 | − | 0.887658i | \(-0.652331\pi\) | ||||
−0.460504 | + | 0.887658i | \(0.652331\pi\) | |||||||
\(74\) | 3.40784 | 0.396153 | ||||||||
\(75\) | 11.8435 | 1.36757 | ||||||||
\(76\) | 0.914665 | 0.104919 | ||||||||
\(77\) | 11.3299 | 1.29116 | ||||||||
\(78\) | 3.95848 | 0.448209 | ||||||||
\(79\) | −9.62495 | −1.08289 | −0.541446 | − | 0.840736i | \(-0.682123\pi\) | ||||
−0.541446 | + | 0.840736i | \(0.682123\pi\) | |||||||
\(80\) | −3.48264 | −0.389371 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.67969 | 0.185491 | ||||||||
\(83\) | 14.6215 | 1.60492 | 0.802458 | − | 0.596708i | \(-0.203525\pi\) | ||||
0.802458 | + | 0.596708i | \(0.203525\pi\) | |||||||
\(84\) | 3.36997 | 0.367693 | ||||||||
\(85\) | 11.5289 | 1.25048 | ||||||||
\(86\) | 8.22881 | 0.887336 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 12.4318 | 1.32523 | ||||||||
\(89\) | −8.72169 | −0.924497 | −0.462249 | − | 0.886750i | \(-0.652957\pi\) | ||||
−0.462249 | + | 0.886750i | \(0.652957\pi\) | |||||||
\(90\) | −3.12993 | −0.329924 | ||||||||
\(91\) | −12.3322 | −1.29277 | ||||||||
\(92\) | −1.41838 | −0.147877 | ||||||||
\(93\) | 0.195443 | 0.0202665 | ||||||||
\(94\) | −7.92214 | −0.817107 | ||||||||
\(95\) | 2.64658 | 0.271533 | ||||||||
\(96\) | 5.86114 | 0.598200 | ||||||||
\(97\) | −13.7648 | −1.39761 | −0.698804 | − | 0.715314i | \(-0.746284\pi\) | ||||
−0.698804 | + | 0.715314i | \(0.746284\pi\) | |||||||
\(98\) | −1.03338 | −0.104387 | ||||||||
\(99\) | −4.76863 | −0.479265 | ||||||||
\(100\) | −16.7987 | −1.67987 | ||||||||
\(101\) | −0.857700 | −0.0853444 | −0.0426722 | − | 0.999089i | \(-0.513587\pi\) | ||||
−0.0426722 | + | 0.999089i | \(0.513587\pi\) | |||||||
\(102\) | −2.14234 | −0.212124 | ||||||||
\(103\) | 3.84676 | 0.379033 | 0.189516 | − | 0.981878i | \(-0.439308\pi\) | ||||
0.189516 | + | 0.981878i | \(0.439308\pi\) | |||||||
\(104\) | −13.5316 | −1.32688 | ||||||||
\(105\) | 9.75098 | 0.951598 | ||||||||
\(106\) | −2.83205 | −0.275073 | ||||||||
\(107\) | 18.4797 | 1.78650 | 0.893248 | − | 0.449565i | \(-0.148421\pi\) | ||||
0.893248 | + | 0.449565i | \(0.148421\pi\) | |||||||
\(108\) | −1.41838 | −0.136484 | ||||||||
\(109\) | −3.88301 | −0.371925 | −0.185963 | − | 0.982557i | \(-0.559540\pi\) | ||||
−0.185963 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(110\) | 14.9255 | 1.42309 | ||||||||
\(111\) | 4.46849 | 0.424131 | ||||||||
\(112\) | −2.01616 | −0.190509 | ||||||||
\(113\) | 0.238682 | 0.0224533 | 0.0112267 | − | 0.999937i | \(-0.496426\pi\) | ||||
0.0112267 | + | 0.999937i | \(0.496426\pi\) | |||||||
\(114\) | −0.491798 | −0.0460611 | ||||||||
\(115\) | −4.10409 | −0.382708 | ||||||||
\(116\) | −1.41838 | −0.131694 | ||||||||
\(117\) | 5.19051 | 0.479862 | ||||||||
\(118\) | −5.18176 | −0.477020 | ||||||||
\(119\) | 6.67425 | 0.611827 | ||||||||
\(120\) | 10.6993 | 0.976709 | ||||||||
\(121\) | 11.7398 | 1.06726 | ||||||||
\(122\) | 9.57428 | 0.866815 | ||||||||
\(123\) | 2.20248 | 0.198591 | ||||||||
\(124\) | −0.277213 | −0.0248944 | ||||||||
\(125\) | −28.0864 | −2.51213 | ||||||||
\(126\) | −1.81197 | −0.161423 | ||||||||
\(127\) | 6.03868 | 0.535846 | 0.267923 | − | 0.963440i | \(-0.413663\pi\) | ||||
0.267923 | + | 0.963440i | \(0.413663\pi\) | |||||||
\(128\) | −9.60766 | −0.849205 | ||||||||
\(129\) | 10.7899 | 0.950001 | ||||||||
\(130\) | −16.2459 | −1.42486 | ||||||||
\(131\) | 16.4899 | 1.44073 | 0.720364 | − | 0.693596i | \(-0.243975\pi\) | ||||
0.720364 | + | 0.693596i | \(0.243975\pi\) | |||||||
\(132\) | 6.76374 | 0.588708 | ||||||||
\(133\) | 1.53215 | 0.132854 | ||||||||
\(134\) | −2.14011 | −0.184877 | ||||||||
\(135\) | −4.10409 | −0.353224 | ||||||||
\(136\) | 7.32335 | 0.627972 | ||||||||
\(137\) | 4.51947 | 0.386124 | 0.193062 | − | 0.981187i | \(-0.438158\pi\) | ||||
0.193062 | + | 0.981187i | \(0.438158\pi\) | |||||||
\(138\) | 0.762638 | 0.0649200 | ||||||||
\(139\) | 23.3271 | 1.97858 | 0.989288 | − | 0.145976i | \(-0.0466323\pi\) | ||||
0.989288 | + | 0.145976i | \(0.0466323\pi\) | |||||||
\(140\) | −13.8306 | −1.16890 | ||||||||
\(141\) | −10.3878 | −0.874812 | ||||||||
\(142\) | 10.8791 | 0.912952 | ||||||||
\(143\) | −24.7516 | −2.06983 | ||||||||
\(144\) | 0.848580 | 0.0707150 | ||||||||
\(145\) | −4.10409 | −0.340826 | ||||||||
\(146\) | −6.00127 | −0.496668 | ||||||||
\(147\) | −1.35501 | −0.111759 | ||||||||
\(148\) | −6.33804 | −0.520983 | ||||||||
\(149\) | −12.3873 | −1.01481 | −0.507403 | − | 0.861709i | \(-0.669395\pi\) | ||||
−0.507403 | + | 0.861709i | \(0.669395\pi\) | |||||||
\(150\) | 9.03232 | 0.737486 | ||||||||
\(151\) | −8.79395 | −0.715642 | −0.357821 | − | 0.933790i | \(-0.616480\pi\) | ||||
−0.357821 | + | 0.933790i | \(0.616480\pi\) | |||||||
\(152\) | 1.68115 | 0.136360 | ||||||||
\(153\) | −2.80912 | −0.227104 | ||||||||
\(154\) | 8.64059 | 0.696279 | ||||||||
\(155\) | −0.802114 | −0.0644274 | ||||||||
\(156\) | −7.36213 | −0.589442 | ||||||||
\(157\) | −12.9451 | −1.03313 | −0.516564 | − | 0.856249i | \(-0.672789\pi\) | ||||
−0.516564 | + | 0.856249i | \(0.672789\pi\) | |||||||
\(158\) | −7.34035 | −0.583967 | ||||||||
\(159\) | −3.71349 | −0.294499 | ||||||||
\(160\) | −24.0546 | −1.90168 | ||||||||
\(161\) | −2.37592 | −0.187249 | ||||||||
\(162\) | 0.762638 | 0.0599185 | ||||||||
\(163\) | 8.06894 | 0.632008 | 0.316004 | − | 0.948758i | \(-0.397659\pi\) | ||||
0.316004 | + | 0.948758i | \(0.397659\pi\) | |||||||
\(164\) | −3.12396 | −0.243940 | ||||||||
\(165\) | 19.5709 | 1.52359 | ||||||||
\(166\) | 11.1509 | 0.865477 | ||||||||
\(167\) | 17.7452 | 1.37317 | 0.686584 | − | 0.727051i | \(-0.259109\pi\) | ||||
0.686584 | + | 0.727051i | \(0.259109\pi\) | |||||||
\(168\) | 6.19400 | 0.477877 | ||||||||
\(169\) | 13.9413 | 1.07241 | ||||||||
\(170\) | 8.79236 | 0.674343 | ||||||||
\(171\) | −0.644865 | −0.0493140 | ||||||||
\(172\) | −15.3043 | −1.16694 | ||||||||
\(173\) | 23.9022 | 1.81725 | 0.908624 | − | 0.417615i | \(-0.137134\pi\) | ||||
0.908624 | + | 0.417615i | \(0.137134\pi\) | |||||||
\(174\) | 0.762638 | 0.0578154 | ||||||||
\(175\) | −28.1393 | −2.12713 | ||||||||
\(176\) | −4.04656 | −0.305021 | ||||||||
\(177\) | −6.79452 | −0.510708 | ||||||||
\(178\) | −6.65149 | −0.498550 | ||||||||
\(179\) | −17.4110 | −1.30136 | −0.650678 | − | 0.759353i | \(-0.725515\pi\) | ||||
−0.650678 | + | 0.759353i | \(0.725515\pi\) | |||||||
\(180\) | 5.82117 | 0.433884 | ||||||||
\(181\) | −8.86252 | −0.658746 | −0.329373 | − | 0.944200i | \(-0.606837\pi\) | ||||
−0.329373 | + | 0.944200i | \(0.606837\pi\) | |||||||
\(182\) | −9.40502 | −0.697146 | ||||||||
\(183\) | 12.5542 | 0.928031 | ||||||||
\(184\) | −2.60699 | −0.192190 | ||||||||
\(185\) | −18.3391 | −1.34832 | ||||||||
\(186\) | 0.149052 | 0.0109290 | ||||||||
\(187\) | 13.3957 | 0.979587 | ||||||||
\(188\) | 14.7339 | 1.07458 | ||||||||
\(189\) | −2.37592 | −0.172823 | ||||||||
\(190\) | 2.01838 | 0.146429 | ||||||||
\(191\) | 12.9011 | 0.933493 | 0.466746 | − | 0.884391i | \(-0.345426\pi\) | ||||
0.466746 | + | 0.884391i | \(0.345426\pi\) | |||||||
\(192\) | 2.77276 | 0.200107 | ||||||||
\(193\) | 3.46564 | 0.249463 | 0.124731 | − | 0.992191i | \(-0.460193\pi\) | ||||
0.124731 | + | 0.992191i | \(0.460193\pi\) | |||||||
\(194\) | −10.4976 | −0.753683 | ||||||||
\(195\) | −21.3023 | −1.52549 | ||||||||
\(196\) | 1.92192 | 0.137280 | ||||||||
\(197\) | −10.0118 | −0.713310 | −0.356655 | − | 0.934236i | \(-0.616083\pi\) | ||||
−0.356655 | + | 0.934236i | \(0.616083\pi\) | |||||||
\(198\) | −3.63674 | −0.258452 | ||||||||
\(199\) | 9.14492 | 0.648266 | 0.324133 | − | 0.946012i | \(-0.394927\pi\) | ||||
0.324133 | + | 0.946012i | \(0.394927\pi\) | |||||||
\(200\) | −30.8759 | −2.18326 | ||||||||
\(201\) | −2.80619 | −0.197933 | ||||||||
\(202\) | −0.654115 | −0.0460234 | ||||||||
\(203\) | −2.37592 | −0.166757 | ||||||||
\(204\) | 3.98441 | 0.278965 | ||||||||
\(205\) | −9.03916 | −0.631322 | ||||||||
\(206\) | 2.93369 | 0.204400 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 4.40456 | 0.305401 | ||||||||
\(209\) | 3.07512 | 0.212710 | ||||||||
\(210\) | 7.43647 | 0.513165 | ||||||||
\(211\) | 3.26744 | 0.224940 | 0.112470 | − | 0.993655i | \(-0.464124\pi\) | ||||
0.112470 | + | 0.993655i | \(0.464124\pi\) | |||||||
\(212\) | 5.26716 | 0.361750 | ||||||||
\(213\) | 14.2651 | 0.977426 | ||||||||
\(214\) | 14.0933 | 0.963397 | ||||||||
\(215\) | −44.2828 | −3.02006 | ||||||||
\(216\) | −2.60699 | −0.177383 | ||||||||
\(217\) | −0.464356 | −0.0315226 | ||||||||
\(218\) | −2.96133 | −0.200567 | ||||||||
\(219\) | −7.86909 | −0.531744 | ||||||||
\(220\) | −27.7590 | −1.87151 | ||||||||
\(221\) | −14.5808 | −0.980808 | ||||||||
\(222\) | 3.40784 | 0.228719 | ||||||||
\(223\) | −16.3511 | −1.09495 | −0.547477 | − | 0.836821i | \(-0.684412\pi\) | ||||
−0.547477 | + | 0.836821i | \(0.684412\pi\) | |||||||
\(224\) | −13.9256 | −0.930442 | ||||||||
\(225\) | 11.8435 | 0.789569 | ||||||||
\(226\) | 0.182028 | 0.0121083 | ||||||||
\(227\) | 6.26229 | 0.415643 | 0.207822 | − | 0.978167i | \(-0.433363\pi\) | ||||
0.207822 | + | 0.978167i | \(0.433363\pi\) | |||||||
\(228\) | 0.914665 | 0.0605752 | ||||||||
\(229\) | −2.82769 | −0.186859 | −0.0934293 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934293 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(230\) | −3.12993 | −0.206382 | ||||||||
\(231\) | 11.3299 | 0.745451 | ||||||||
\(232\) | −2.60699 | −0.171157 | ||||||||
\(233\) | −6.61733 | −0.433515 | −0.216758 | − | 0.976225i | \(-0.569548\pi\) | ||||
−0.216758 | + | 0.976225i | \(0.569548\pi\) | |||||||
\(234\) | 3.95848 | 0.258774 | ||||||||
\(235\) | 42.6325 | 2.78104 | ||||||||
\(236\) | 9.63724 | 0.627331 | ||||||||
\(237\) | −9.62495 | −0.625207 | ||||||||
\(238\) | 5.09003 | 0.329938 | ||||||||
\(239\) | 17.3956 | 1.12523 | 0.562615 | − | 0.826719i | \(-0.309796\pi\) | ||||
0.562615 | + | 0.826719i | \(0.309796\pi\) | |||||||
\(240\) | −3.48264 | −0.224804 | ||||||||
\(241\) | 3.26312 | 0.210196 | 0.105098 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105098 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(242\) | 8.95322 | 0.575535 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −17.8066 | −1.13995 | ||||||||
\(245\) | 5.56106 | 0.355283 | ||||||||
\(246\) | 1.67969 | 0.107093 | ||||||||
\(247\) | −3.34717 | −0.212976 | ||||||||
\(248\) | −0.509517 | −0.0323544 | ||||||||
\(249\) | 14.6215 | 0.926599 | ||||||||
\(250\) | −21.4198 | −1.35471 | ||||||||
\(251\) | −23.6292 | −1.49146 | −0.745731 | − | 0.666247i | \(-0.767900\pi\) | ||||
−0.745731 | + | 0.666247i | \(0.767900\pi\) | |||||||
\(252\) | 3.36997 | 0.212288 | ||||||||
\(253\) | −4.76863 | −0.299801 | ||||||||
\(254\) | 4.60533 | 0.288964 | ||||||||
\(255\) | 11.5289 | 0.721966 | ||||||||
\(256\) | −12.8727 | −0.804543 | ||||||||
\(257\) | 4.73508 | 0.295366 | 0.147683 | − | 0.989035i | \(-0.452818\pi\) | ||||
0.147683 | + | 0.989035i | \(0.452818\pi\) | |||||||
\(258\) | 8.22881 | 0.512304 | ||||||||
\(259\) | −10.6168 | −0.659695 | ||||||||
\(260\) | 30.2148 | 1.87384 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 12.5758 | 0.776937 | ||||||||
\(263\) | 31.4462 | 1.93906 | 0.969529 | − | 0.244978i | \(-0.0787807\pi\) | ||||
0.969529 | + | 0.244978i | \(0.0787807\pi\) | |||||||
\(264\) | 12.4318 | 0.765122 | ||||||||
\(265\) | 15.2405 | 0.936216 | ||||||||
\(266\) | 1.16847 | 0.0716437 | ||||||||
\(267\) | −8.72169 | −0.533759 | ||||||||
\(268\) | 3.98025 | 0.243133 | ||||||||
\(269\) | −13.8706 | −0.845704 | −0.422852 | − | 0.906199i | \(-0.638971\pi\) | ||||
−0.422852 | + | 0.906199i | \(0.638971\pi\) | |||||||
\(270\) | −3.12993 | −0.190482 | ||||||||
\(271\) | 14.7222 | 0.894311 | 0.447156 | − | 0.894456i | \(-0.352437\pi\) | ||||
0.447156 | + | 0.894456i | \(0.352437\pi\) | |||||||
\(272\) | −2.38376 | −0.144537 | ||||||||
\(273\) | −12.3322 | −0.746380 | ||||||||
\(274\) | 3.44672 | 0.208224 | ||||||||
\(275\) | −56.4774 | −3.40571 | ||||||||
\(276\) | −1.41838 | −0.0853767 | ||||||||
\(277\) | 28.6108 | 1.71906 | 0.859528 | − | 0.511088i | \(-0.170757\pi\) | ||||
0.859528 | + | 0.511088i | \(0.170757\pi\) | |||||||
\(278\) | 17.7901 | 1.06698 | ||||||||
\(279\) | 0.195443 | 0.0117009 | ||||||||
\(280\) | −25.4207 | −1.51918 | ||||||||
\(281\) | −1.91196 | −0.114058 | −0.0570289 | − | 0.998373i | \(-0.518163\pi\) | ||||
−0.0570289 | + | 0.998373i | \(0.518163\pi\) | |||||||
\(282\) | −7.92214 | −0.471757 | ||||||||
\(283\) | −13.5965 | −0.808230 | −0.404115 | − | 0.914708i | \(-0.632420\pi\) | ||||
−0.404115 | + | 0.914708i | \(0.632420\pi\) | |||||||
\(284\) | −20.2333 | −1.20063 | ||||||||
\(285\) | 2.64658 | 0.156770 | ||||||||
\(286\) | −18.8765 | −1.11619 | ||||||||
\(287\) | −5.23291 | −0.308889 | ||||||||
\(288\) | 5.86114 | 0.345371 | ||||||||
\(289\) | −9.10883 | −0.535814 | ||||||||
\(290\) | −3.12993 | −0.183796 | ||||||||
\(291\) | −13.7648 | −0.806909 | ||||||||
\(292\) | 11.1614 | 0.653171 | ||||||||
\(293\) | −2.08364 | −0.121727 | −0.0608637 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608637 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(294\) | −1.03338 | −0.0602678 | ||||||||
\(295\) | 27.8853 | 1.62355 | ||||||||
\(296\) | −11.6493 | −0.677102 | ||||||||
\(297\) | −4.76863 | −0.276704 | ||||||||
\(298\) | −9.44702 | −0.547251 | ||||||||
\(299\) | 5.19051 | 0.300175 | ||||||||
\(300\) | −16.7987 | −0.969871 | ||||||||
\(301\) | −25.6360 | −1.47764 | ||||||||
\(302\) | −6.70660 | −0.385921 | ||||||||
\(303\) | −0.857700 | −0.0492736 | ||||||||
\(304\) | −0.547219 | −0.0313852 | ||||||||
\(305\) | −51.5234 | −2.95022 | ||||||||
\(306\) | −2.14234 | −0.122470 | ||||||||
\(307\) | −30.9157 | −1.76445 | −0.882227 | − | 0.470824i | \(-0.843957\pi\) | ||||
−0.882227 | + | 0.470824i | \(0.843957\pi\) | |||||||
\(308\) | −16.0701 | −0.915680 | ||||||||
\(309\) | 3.84676 | 0.218835 | ||||||||
\(310\) | −0.611722 | −0.0347435 | ||||||||
\(311\) | 12.6680 | 0.718334 | 0.359167 | − | 0.933273i | \(-0.383061\pi\) | ||||
0.359167 | + | 0.933273i | \(0.383061\pi\) | |||||||
\(312\) | −13.5316 | −0.766075 | ||||||||
\(313\) | 23.5046 | 1.32856 | 0.664280 | − | 0.747484i | \(-0.268738\pi\) | ||||
0.664280 | + | 0.747484i | \(0.268738\pi\) | |||||||
\(314\) | −9.87239 | −0.557131 | ||||||||
\(315\) | 9.75098 | 0.549406 | ||||||||
\(316\) | 13.6519 | 0.767977 | ||||||||
\(317\) | −9.06839 | −0.509332 | −0.254666 | − | 0.967029i | \(-0.581965\pi\) | ||||
−0.254666 | + | 0.967029i | \(0.581965\pi\) | |||||||
\(318\) | −2.83205 | −0.158814 | ||||||||
\(319\) | −4.76863 | −0.266992 | ||||||||
\(320\) | −11.3797 | −0.636143 | ||||||||
\(321\) | 18.4797 | 1.03143 | ||||||||
\(322\) | −1.81197 | −0.100977 | ||||||||
\(323\) | 1.81150 | 0.100795 | ||||||||
\(324\) | −1.41838 | −0.0787991 | ||||||||
\(325\) | 61.4739 | 3.40996 | ||||||||
\(326\) | 6.15368 | 0.340821 | ||||||||
\(327\) | −3.88301 | −0.214731 | ||||||||
\(328\) | −5.74183 | −0.317040 | ||||||||
\(329\) | 24.6806 | 1.36069 | ||||||||
\(330\) | 14.9255 | 0.821620 | ||||||||
\(331\) | −17.1154 | −0.940748 | −0.470374 | − | 0.882467i | \(-0.655881\pi\) | ||||
−0.470374 | + | 0.882467i | \(0.655881\pi\) | |||||||
\(332\) | −20.7389 | −1.13819 | ||||||||
\(333\) | 4.46849 | 0.244872 | ||||||||
\(334\) | 13.5332 | 0.740503 | ||||||||
\(335\) | 11.5168 | 0.629232 | ||||||||
\(336\) | −2.01616 | −0.109990 | ||||||||
\(337\) | 9.73964 | 0.530552 | 0.265276 | − | 0.964172i | \(-0.414537\pi\) | ||||
0.265276 | + | 0.964172i | \(0.414537\pi\) | |||||||
\(338\) | 10.6322 | 0.578315 | ||||||||
\(339\) | 0.238682 | 0.0129634 | ||||||||
\(340\) | −16.3524 | −0.886832 | ||||||||
\(341\) | −0.931994 | −0.0504703 | ||||||||
\(342\) | −0.491798 | −0.0265934 | ||||||||
\(343\) | 19.8508 | 1.07184 | ||||||||
\(344\) | −28.1292 | −1.51663 | ||||||||
\(345\) | −4.10409 | −0.220957 | ||||||||
\(346\) | 18.2287 | 0.979981 | ||||||||
\(347\) | −0.652189 | −0.0350113 | −0.0175057 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175057 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(348\) | −1.41838 | −0.0760333 | ||||||||
\(349\) | 0.388734 | 0.0208085 | 0.0104042 | − | 0.999946i | \(-0.496688\pi\) | ||||
0.0104042 | + | 0.999946i | \(0.496688\pi\) | |||||||
\(350\) | −21.4601 | −1.14709 | ||||||||
\(351\) | 5.19051 | 0.277049 | ||||||||
\(352\) | −27.9496 | −1.48972 | ||||||||
\(353\) | 33.9129 | 1.80500 | 0.902501 | − | 0.430688i | \(-0.141729\pi\) | ||||
0.902501 | + | 0.430688i | \(0.141729\pi\) | |||||||
\(354\) | −5.18176 | −0.275407 | ||||||||
\(355\) | −58.5450 | −3.10725 | ||||||||
\(356\) | 12.3707 | 0.655646 | ||||||||
\(357\) | 6.67425 | 0.353239 | ||||||||
\(358\) | −13.2783 | −0.701778 | ||||||||
\(359\) | 19.5828 | 1.03354 | 0.516770 | − | 0.856124i | \(-0.327134\pi\) | ||||
0.516770 | + | 0.856124i | \(0.327134\pi\) | |||||||
\(360\) | 10.6993 | 0.563903 | ||||||||
\(361\) | −18.5841 | −0.978113 | ||||||||
\(362\) | −6.75890 | −0.355240 | ||||||||
\(363\) | 11.7398 | 0.616180 | ||||||||
\(364\) | 17.4918 | 0.916821 | ||||||||
\(365\) | 32.2954 | 1.69042 | ||||||||
\(366\) | 9.57428 | 0.500456 | ||||||||
\(367\) | 11.8792 | 0.620091 | 0.310045 | − | 0.950722i | \(-0.399656\pi\) | ||||
0.310045 | + | 0.950722i | \(0.399656\pi\) | |||||||
\(368\) | 0.848580 | 0.0442353 | ||||||||
\(369\) | 2.20248 | 0.114656 | ||||||||
\(370\) | −13.9861 | −0.727101 | ||||||||
\(371\) | 8.82296 | 0.458065 | ||||||||
\(372\) | −0.277213 | −0.0143728 | ||||||||
\(373\) | 35.5289 | 1.83962 | 0.919808 | − | 0.392370i | \(-0.128345\pi\) | ||||
0.919808 | + | 0.392370i | \(0.128345\pi\) | |||||||
\(374\) | 10.2160 | 0.528258 | ||||||||
\(375\) | −28.0864 | −1.45038 | ||||||||
\(376\) | 27.0809 | 1.39659 | ||||||||
\(377\) | 5.19051 | 0.267325 | ||||||||
\(378\) | −1.81197 | −0.0931975 | ||||||||
\(379\) | 20.2070 | 1.03796 | 0.518982 | − | 0.854785i | \(-0.326311\pi\) | ||||
0.518982 | + | 0.854785i | \(0.326311\pi\) | |||||||
\(380\) | −3.75387 | −0.192569 | ||||||||
\(381\) | 6.03868 | 0.309371 | ||||||||
\(382\) | 9.83889 | 0.503401 | ||||||||
\(383\) | −5.97382 | −0.305248 | −0.152624 | − | 0.988284i | \(-0.548772\pi\) | ||||
−0.152624 | + | 0.988284i | \(0.548772\pi\) | |||||||
\(384\) | −9.60766 | −0.490289 | ||||||||
\(385\) | −46.4988 | −2.36980 | ||||||||
\(386\) | 2.64303 | 0.134527 | ||||||||
\(387\) | 10.7899 | 0.548483 | ||||||||
\(388\) | 19.5238 | 0.991172 | ||||||||
\(389\) | −10.8957 | −0.552436 | −0.276218 | − | 0.961095i | \(-0.589081\pi\) | ||||
−0.276218 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(390\) | −16.2459 | −0.822644 | ||||||||
\(391\) | −2.80912 | −0.142063 | ||||||||
\(392\) | 3.53248 | 0.178417 | ||||||||
\(393\) | 16.4899 | 0.831805 | ||||||||
\(394\) | −7.63537 | −0.384664 | ||||||||
\(395\) | 39.5016 | 1.98754 | ||||||||
\(396\) | 6.76374 | 0.339891 | ||||||||
\(397\) | 24.4605 | 1.22764 | 0.613819 | − | 0.789447i | \(-0.289632\pi\) | ||||
0.613819 | + | 0.789447i | \(0.289632\pi\) | |||||||
\(398\) | 6.97426 | 0.349588 | ||||||||
\(399\) | 1.53215 | 0.0767033 | ||||||||
\(400\) | 10.0502 | 0.502509 | ||||||||
\(401\) | 18.6658 | 0.932126 | 0.466063 | − | 0.884751i | \(-0.345672\pi\) | ||||
0.466063 | + | 0.884751i | \(0.345672\pi\) | |||||||
\(402\) | −2.14011 | −0.106739 | ||||||||
\(403\) | 1.01445 | 0.0505332 | ||||||||
\(404\) | 1.21655 | 0.0605255 | ||||||||
\(405\) | −4.10409 | −0.203934 | ||||||||
\(406\) | −1.81197 | −0.0899264 | ||||||||
\(407\) | −21.3086 | −1.05623 | ||||||||
\(408\) | 7.32335 | 0.362560 | ||||||||
\(409\) | 23.3006 | 1.15214 | 0.576071 | − | 0.817400i | \(-0.304585\pi\) | ||||
0.576071 | + | 0.817400i | \(0.304585\pi\) | |||||||
\(410\) | −6.89360 | −0.340451 | ||||||||
\(411\) | 4.51947 | 0.222929 | ||||||||
\(412\) | −5.45619 | −0.268807 | ||||||||
\(413\) | 16.1432 | 0.794357 | ||||||||
\(414\) | 0.762638 | 0.0374816 | ||||||||
\(415\) | −60.0078 | −2.94567 | ||||||||
\(416\) | 30.4223 | 1.49157 | ||||||||
\(417\) | 23.3271 | 1.14233 | ||||||||
\(418\) | 2.34520 | 0.114708 | ||||||||
\(419\) | −11.7063 | −0.571890 | −0.285945 | − | 0.958246i | \(-0.592307\pi\) | ||||
−0.285945 | + | 0.958246i | \(0.592307\pi\) | |||||||
\(420\) | −13.8306 | −0.674866 | ||||||||
\(421\) | −8.76302 | −0.427083 | −0.213542 | − | 0.976934i | \(-0.568500\pi\) | ||||
−0.213542 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(422\) | 2.49187 | 0.121302 | ||||||||
\(423\) | −10.3878 | −0.505073 | ||||||||
\(424\) | 9.68104 | 0.470153 | ||||||||
\(425\) | −33.2699 | −1.61383 | ||||||||
\(426\) | 10.8791 | 0.527093 | ||||||||
\(427\) | −29.8277 | −1.44346 | ||||||||
\(428\) | −26.2112 | −1.26697 | ||||||||
\(429\) | −24.7516 | −1.19502 | ||||||||
\(430\) | −33.7718 | −1.62862 | ||||||||
\(431\) | 25.2322 | 1.21539 | 0.607697 | − | 0.794169i | \(-0.292094\pi\) | ||||
0.607697 | + | 0.794169i | \(0.292094\pi\) | |||||||
\(432\) | 0.848580 | 0.0408273 | ||||||||
\(433\) | 24.3713 | 1.17121 | 0.585606 | − | 0.810596i | \(-0.300857\pi\) | ||||
0.585606 | + | 0.810596i | \(0.300857\pi\) | |||||||
\(434\) | −0.354136 | −0.0169991 | ||||||||
\(435\) | −4.10409 | −0.196776 | ||||||||
\(436\) | 5.50760 | 0.263766 | ||||||||
\(437\) | −0.644865 | −0.0308481 | ||||||||
\(438\) | −6.00127 | −0.286752 | ||||||||
\(439\) | 40.8264 | 1.94854 | 0.974270 | − | 0.225386i | \(-0.0723643\pi\) | ||||
0.974270 | + | 0.225386i | \(0.0723643\pi\) | |||||||
\(440\) | −51.0210 | −2.43233 | ||||||||
\(441\) | −1.35501 | −0.0645241 | ||||||||
\(442\) | −11.1198 | −0.528917 | ||||||||
\(443\) | −27.5392 | −1.30842 | −0.654212 | − | 0.756311i | \(-0.727000\pi\) | ||||
−0.654212 | + | 0.756311i | \(0.727000\pi\) | |||||||
\(444\) | −6.33804 | −0.300790 | ||||||||
\(445\) | 35.7946 | 1.69683 | ||||||||
\(446\) | −12.4700 | −0.590472 | ||||||||
\(447\) | −12.3873 | −0.585899 | ||||||||
\(448\) | −6.58786 | −0.311247 | ||||||||
\(449\) | −27.1392 | −1.28078 | −0.640389 | − | 0.768051i | \(-0.721227\pi\) | ||||
−0.640389 | + | 0.768051i | \(0.721227\pi\) | |||||||
\(450\) | 9.03232 | 0.425788 | ||||||||
\(451\) | −10.5028 | −0.494557 | ||||||||
\(452\) | −0.338543 | −0.0159237 | ||||||||
\(453\) | −8.79395 | −0.413176 | ||||||||
\(454\) | 4.77586 | 0.224142 | ||||||||
\(455\) | 50.6125 | 2.37275 | ||||||||
\(456\) | 1.68115 | 0.0787273 | ||||||||
\(457\) | −11.4419 | −0.535230 | −0.267615 | − | 0.963526i | \(-0.586236\pi\) | ||||
−0.267615 | + | 0.963526i | \(0.586236\pi\) | |||||||
\(458\) | −2.15650 | −0.100767 | ||||||||
\(459\) | −2.80912 | −0.131119 | ||||||||
\(460\) | 5.82117 | 0.271413 | ||||||||
\(461\) | 18.6583 | 0.869004 | 0.434502 | − | 0.900671i | \(-0.356924\pi\) | ||||
0.434502 | + | 0.900671i | \(0.356924\pi\) | |||||||
\(462\) | 8.64059 | 0.401997 | ||||||||
\(463\) | 14.6373 | 0.680254 | 0.340127 | − | 0.940380i | \(-0.389530\pi\) | ||||
0.340127 | + | 0.940380i | \(0.389530\pi\) | |||||||
\(464\) | 0.848580 | 0.0393943 | ||||||||
\(465\) | −0.802114 | −0.0371971 | ||||||||
\(466\) | −5.04662 | −0.233780 | ||||||||
\(467\) | 10.6700 | 0.493749 | 0.246874 | − | 0.969047i | \(-0.420596\pi\) | ||||
0.246874 | + | 0.969047i | \(0.420596\pi\) | |||||||
\(468\) | −7.36213 | −0.340314 | ||||||||
\(469\) | 6.66728 | 0.307866 | ||||||||
\(470\) | 32.5132 | 1.49972 | ||||||||
\(471\) | −12.9451 | −0.596477 | ||||||||
\(472\) | 17.7132 | 0.815318 | ||||||||
\(473\) | −51.4532 | −2.36582 | ||||||||
\(474\) | −7.34035 | −0.337153 | ||||||||
\(475\) | −7.63747 | −0.350431 | ||||||||
\(476\) | −9.46664 | −0.433903 | ||||||||
\(477\) | −3.71349 | −0.170029 | ||||||||
\(478\) | 13.2666 | 0.606798 | ||||||||
\(479\) | 32.0589 | 1.46481 | 0.732405 | − | 0.680870i | \(-0.238398\pi\) | ||||
0.732405 | + | 0.680870i | \(0.238398\pi\) | |||||||
\(480\) | −24.0546 | −1.09794 | ||||||||
\(481\) | 23.1937 | 1.05754 | ||||||||
\(482\) | 2.48857 | 0.113351 | ||||||||
\(483\) | −2.37592 | −0.108108 | ||||||||
\(484\) | −16.6515 | −0.756889 | ||||||||
\(485\) | 56.4921 | 2.56517 | ||||||||
\(486\) | 0.762638 | 0.0345940 | ||||||||
\(487\) | −23.8137 | −1.07910 | −0.539551 | − | 0.841953i | \(-0.681406\pi\) | ||||
−0.539551 | + | 0.841953i | \(0.681406\pi\) | |||||||
\(488\) | −32.7286 | −1.48155 | ||||||||
\(489\) | 8.06894 | 0.364890 | ||||||||
\(490\) | 4.24107 | 0.191592 | ||||||||
\(491\) | −18.2787 | −0.824905 | −0.412453 | − | 0.910979i | \(-0.635328\pi\) | ||||
−0.412453 | + | 0.910979i | \(0.635328\pi\) | |||||||
\(492\) | −3.12396 | −0.140839 | ||||||||
\(493\) | −2.80912 | −0.126516 | ||||||||
\(494\) | −2.55268 | −0.114851 | ||||||||
\(495\) | 19.5709 | 0.879645 | ||||||||
\(496\) | 0.165849 | 0.00744683 | ||||||||
\(497\) | −33.8926 | −1.52029 | ||||||||
\(498\) | 11.1509 | 0.499684 | ||||||||
\(499\) | 4.85298 | 0.217249 | 0.108625 | − | 0.994083i | \(-0.465355\pi\) | ||||
0.108625 | + | 0.994083i | \(0.465355\pi\) | |||||||
\(500\) | 39.8373 | 1.78158 | ||||||||
\(501\) | 17.7452 | 0.792799 | ||||||||
\(502\) | −18.0205 | −0.804295 | ||||||||
\(503\) | −12.1670 | −0.542499 | −0.271249 | − | 0.962509i | \(-0.587437\pi\) | ||||
−0.271249 | + | 0.962509i | \(0.587437\pi\) | |||||||
\(504\) | 6.19400 | 0.275902 | ||||||||
\(505\) | 3.52008 | 0.156641 | ||||||||
\(506\) | −3.63674 | −0.161673 | ||||||||
\(507\) | 13.9413 | 0.619157 | ||||||||
\(508\) | −8.56517 | −0.380018 | ||||||||
\(509\) | 13.0048 | 0.576429 | 0.288214 | − | 0.957566i | \(-0.406938\pi\) | ||||
0.288214 | + | 0.957566i | \(0.406938\pi\) | |||||||
\(510\) | 8.79236 | 0.389332 | ||||||||
\(511\) | 18.6963 | 0.827077 | ||||||||
\(512\) | 9.39811 | 0.415342 | ||||||||
\(513\) | −0.644865 | −0.0284715 | ||||||||
\(514\) | 3.61115 | 0.159281 | ||||||||
\(515\) | −15.7874 | −0.695678 | ||||||||
\(516\) | −15.3043 | −0.673733 | ||||||||
\(517\) | 49.5356 | 2.17857 | ||||||||
\(518\) | −8.09676 | −0.355751 | ||||||||
\(519\) | 23.9022 | 1.04919 | ||||||||
\(520\) | 55.5348 | 2.43536 | ||||||||
\(521\) | −24.7847 | −1.08584 | −0.542919 | − | 0.839785i | \(-0.682681\pi\) | ||||
−0.542919 | + | 0.839785i | \(0.682681\pi\) | |||||||
\(522\) | 0.762638 | 0.0333797 | ||||||||
\(523\) | 1.69891 | 0.0742879 | 0.0371440 | − | 0.999310i | \(-0.488174\pi\) | ||||
0.0371440 | + | 0.999310i | \(0.488174\pi\) | |||||||
\(524\) | −23.3890 | −1.02175 | ||||||||
\(525\) | −28.1393 | −1.22810 | ||||||||
\(526\) | 23.9821 | 1.04567 | ||||||||
\(527\) | −0.549023 | −0.0239158 | ||||||||
\(528\) | −4.04656 | −0.176104 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 11.6230 | 0.504870 | ||||||||
\(531\) | −6.79452 | −0.294857 | ||||||||
\(532\) | −2.17317 | −0.0942189 | ||||||||
\(533\) | 11.4320 | 0.495174 | ||||||||
\(534\) | −6.65149 | −0.287838 | ||||||||
\(535\) | −75.8421 | −3.27894 | ||||||||
\(536\) | 7.31570 | 0.315990 | ||||||||
\(537\) | −17.4110 | −0.751339 | ||||||||
\(538\) | −10.5782 | −0.456060 | ||||||||
\(539\) | 6.46152 | 0.278317 | ||||||||
\(540\) | 5.82117 | 0.250503 | ||||||||
\(541\) | −24.7795 | −1.06535 | −0.532677 | − | 0.846319i | \(-0.678814\pi\) | ||||
−0.532677 | + | 0.846319i | \(0.678814\pi\) | |||||||
\(542\) | 11.2277 | 0.482272 | ||||||||
\(543\) | −8.86252 | −0.380327 | ||||||||
\(544\) | −16.4646 | −0.705916 | ||||||||
\(545\) | 15.9362 | 0.682633 | ||||||||
\(546\) | −9.40502 | −0.402498 | ||||||||
\(547\) | −24.2508 | −1.03689 | −0.518444 | − | 0.855112i | \(-0.673489\pi\) | ||||
−0.518444 | + | 0.855112i | \(0.673489\pi\) | |||||||
\(548\) | −6.41034 | −0.273836 | ||||||||
\(549\) | 12.5542 | 0.535799 | ||||||||
\(550\) | −43.0718 | −1.83659 | ||||||||
\(551\) | −0.644865 | −0.0274722 | ||||||||
\(552\) | −2.60699 | −0.110961 | ||||||||
\(553\) | 22.8681 | 0.972451 | ||||||||
\(554\) | 21.8197 | 0.927029 | ||||||||
\(555\) | −18.3391 | −0.778451 | ||||||||
\(556\) | −33.0867 | −1.40319 | ||||||||
\(557\) | −21.1596 | −0.896559 | −0.448280 | − | 0.893893i | \(-0.647963\pi\) | ||||
−0.448280 | + | 0.893893i | \(0.647963\pi\) | |||||||
\(558\) | 0.149052 | 0.00630988 | ||||||||
\(559\) | 56.0052 | 2.36877 | ||||||||
\(560\) | 8.27448 | 0.349661 | ||||||||
\(561\) | 13.3957 | 0.565565 | ||||||||
\(562\) | −1.45813 | −0.0615075 | ||||||||
\(563\) | −47.1640 | −1.98773 | −0.993864 | − | 0.110613i | \(-0.964719\pi\) | ||||
−0.993864 | + | 0.110613i | \(0.964719\pi\) | |||||||
\(564\) | 14.7339 | 0.620410 | ||||||||
\(565\) | −0.979572 | −0.0412109 | ||||||||
\(566\) | −10.3692 | −0.435851 | ||||||||
\(567\) | −2.37592 | −0.0997793 | ||||||||
\(568\) | −37.1888 | −1.56041 | ||||||||
\(569\) | −11.1557 | −0.467673 | −0.233836 | − | 0.972276i | \(-0.575128\pi\) | ||||
−0.233836 | + | 0.972276i | \(0.575128\pi\) | |||||||
\(570\) | 2.01838 | 0.0845407 | ||||||||
\(571\) | 16.5122 | 0.691013 | 0.345506 | − | 0.938416i | \(-0.387707\pi\) | ||||
0.345506 | + | 0.938416i | \(0.387707\pi\) | |||||||
\(572\) | 35.1072 | 1.46791 | ||||||||
\(573\) | 12.9011 | 0.538952 | ||||||||
\(574\) | −3.99082 | −0.166573 | ||||||||
\(575\) | 11.8435 | 0.493909 | ||||||||
\(576\) | 2.77276 | 0.115532 | ||||||||
\(577\) | −6.85661 | −0.285444 | −0.142722 | − | 0.989763i | \(-0.545586\pi\) | ||||
−0.142722 | + | 0.989763i | \(0.545586\pi\) | |||||||
\(578\) | −6.94674 | −0.288946 | ||||||||
\(579\) | 3.46564 | 0.144027 | ||||||||
\(580\) | 5.82117 | 0.241711 | ||||||||
\(581\) | −34.7395 | −1.44124 | ||||||||
\(582\) | −10.4976 | −0.435139 | ||||||||
\(583\) | 17.7083 | 0.733402 | ||||||||
\(584\) | 20.5146 | 0.848901 | ||||||||
\(585\) | −21.3023 | −0.880741 | ||||||||
\(586\) | −1.58906 | −0.0656435 | ||||||||
\(587\) | −16.3914 | −0.676545 | −0.338273 | − | 0.941048i | \(-0.609843\pi\) | ||||
−0.338273 | + | 0.941048i | \(0.609843\pi\) | |||||||
\(588\) | 1.92192 | 0.0792585 | ||||||||
\(589\) | −0.126034 | −0.00519315 | ||||||||
\(590\) | 21.2664 | 0.875524 | ||||||||
\(591\) | −10.0118 | −0.411830 | ||||||||
\(592\) | 3.79187 | 0.155845 | ||||||||
\(593\) | −40.1902 | −1.65041 | −0.825207 | − | 0.564830i | \(-0.808942\pi\) | ||||
−0.825207 | + | 0.564830i | \(0.808942\pi\) | |||||||
\(594\) | −3.63674 | −0.149217 | ||||||||
\(595\) | −27.3917 | −1.12295 | ||||||||
\(596\) | 17.5699 | 0.719693 | ||||||||
\(597\) | 9.14492 | 0.374277 | ||||||||
\(598\) | 3.95848 | 0.161874 | ||||||||
\(599\) | 28.8613 | 1.17924 | 0.589621 | − | 0.807680i | \(-0.299277\pi\) | ||||
0.589621 | + | 0.807680i | \(0.299277\pi\) | |||||||
\(600\) | −30.8759 | −1.26050 | ||||||||
\(601\) | −24.5658 | −1.00206 | −0.501031 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501031 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(602\) | −19.5510 | −0.796839 | ||||||||
\(603\) | −2.80619 | −0.114277 | ||||||||
\(604\) | 12.4732 | 0.507527 | ||||||||
\(605\) | −48.1812 | −1.95884 | ||||||||
\(606\) | −0.654115 | −0.0265716 | ||||||||
\(607\) | 29.3832 | 1.19263 | 0.596314 | − | 0.802751i | \(-0.296631\pi\) | ||||
0.596314 | + | 0.802751i | \(0.296631\pi\) | |||||||
\(608\) | −3.77964 | −0.153285 | ||||||||
\(609\) | −2.37592 | −0.0962771 | ||||||||
\(610\) | −39.2937 | −1.59095 | ||||||||
\(611\) | −53.9180 | −2.18129 | ||||||||
\(612\) | 3.98441 | 0.161060 | ||||||||
\(613\) | 22.8059 | 0.921122 | 0.460561 | − | 0.887628i | \(-0.347648\pi\) | ||||
0.460561 | + | 0.887628i | \(0.347648\pi\) | |||||||
\(614\) | −23.5775 | −0.951511 | ||||||||
\(615\) | −9.03916 | −0.364494 | ||||||||
\(616\) | −29.5369 | −1.19007 | ||||||||
\(617\) | 20.2767 | 0.816309 | 0.408154 | − | 0.912913i | \(-0.366172\pi\) | ||||
0.408154 | + | 0.912913i | \(0.366172\pi\) | |||||||
\(618\) | 2.93369 | 0.118010 | ||||||||
\(619\) | −20.2300 | −0.813113 | −0.406556 | − | 0.913626i | \(-0.633271\pi\) | ||||
−0.406556 | + | 0.913626i | \(0.633271\pi\) | |||||||
\(620\) | 1.13771 | 0.0456914 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 9.66107 | 0.387374 | ||||||||
\(623\) | 20.7220 | 0.830211 | ||||||||
\(624\) | 4.40456 | 0.176323 | ||||||||
\(625\) | 56.0515 | 2.24206 | ||||||||
\(626\) | 17.9255 | 0.716448 | ||||||||
\(627\) | 3.07512 | 0.122808 | ||||||||
\(628\) | 18.3611 | 0.732686 | ||||||||
\(629\) | −12.5525 | −0.500503 | ||||||||
\(630\) | 7.43647 | 0.296276 | ||||||||
\(631\) | 22.9942 | 0.915385 | 0.457693 | − | 0.889110i | \(-0.348676\pi\) | ||||
0.457693 | + | 0.889110i | \(0.348676\pi\) | |||||||
\(632\) | 25.0921 | 0.998111 | ||||||||
\(633\) | 3.26744 | 0.129869 | ||||||||
\(634\) | −6.91590 | −0.274665 | ||||||||
\(635\) | −24.7833 | −0.983494 | ||||||||
\(636\) | 5.26716 | 0.208856 | ||||||||
\(637\) | −7.03316 | −0.278664 | ||||||||
\(638\) | −3.63674 | −0.143980 | ||||||||
\(639\) | 14.2651 | 0.564317 | ||||||||
\(640\) | 39.4307 | 1.55863 | ||||||||
\(641\) | 30.1570 | 1.19113 | 0.595565 | − | 0.803307i | \(-0.296928\pi\) | ||||
0.595565 | + | 0.803307i | \(0.296928\pi\) | |||||||
\(642\) | 14.0933 | 0.556217 | ||||||||
\(643\) | −0.607328 | −0.0239507 | −0.0119753 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119753 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(644\) | 3.36997 | 0.132795 | ||||||||
\(645\) | −44.2828 | −1.74364 | ||||||||
\(646\) | 1.38152 | 0.0543552 | ||||||||
\(647\) | 11.4460 | 0.449989 | 0.224994 | − | 0.974360i | \(-0.427764\pi\) | ||||
0.224994 | + | 0.974360i | \(0.427764\pi\) | |||||||
\(648\) | −2.60699 | −0.102412 | ||||||||
\(649\) | 32.4006 | 1.27183 | ||||||||
\(650\) | 46.8823 | 1.83888 | ||||||||
\(651\) | −0.464356 | −0.0181996 | ||||||||
\(652\) | −11.4449 | −0.448215 | ||||||||
\(653\) | −24.7401 | −0.968153 | −0.484077 | − | 0.875026i | \(-0.660844\pi\) | ||||
−0.484077 | + | 0.875026i | \(0.660844\pi\) | |||||||
\(654\) | −2.96133 | −0.115797 | ||||||||
\(655\) | −67.6760 | −2.64432 | ||||||||
\(656\) | 1.86898 | 0.0729713 | ||||||||
\(657\) | −7.86909 | −0.307002 | ||||||||
\(658\) | 18.8224 | 0.733773 | ||||||||
\(659\) | 18.8865 | 0.735715 | 0.367858 | − | 0.929882i | \(-0.380091\pi\) | ||||
0.367858 | + | 0.929882i | \(0.380091\pi\) | |||||||
\(660\) | −27.7590 | −1.08052 | ||||||||
\(661\) | −0.433103 | −0.0168457 | −0.00842287 | − | 0.999965i | \(-0.502681\pi\) | ||||
−0.00842287 | + | 0.999965i | \(0.502681\pi\) | |||||||
\(662\) | −13.0529 | −0.507314 | ||||||||
\(663\) | −14.5808 | −0.566270 | ||||||||
\(664\) | −38.1180 | −1.47927 | ||||||||
\(665\) | −6.28806 | −0.243841 | ||||||||
\(666\) | 3.40784 | 0.132051 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −25.1696 | −0.973839 | ||||||||
\(669\) | −16.3511 | −0.632172 | ||||||||
\(670\) | 8.78318 | 0.339324 | ||||||||
\(671\) | −59.8661 | −2.31111 | ||||||||
\(672\) | −13.9256 | −0.537191 | ||||||||
\(673\) | 7.37791 | 0.284398 | 0.142199 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142199 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(674\) | 7.42782 | 0.286109 | ||||||||
\(675\) | 11.8435 | 0.455858 | ||||||||
\(676\) | −19.7742 | −0.760545 | ||||||||
\(677\) | −38.0288 | −1.46156 | −0.730782 | − | 0.682611i | \(-0.760844\pi\) | ||||
−0.730782 | + | 0.682611i | \(0.760844\pi\) | |||||||
\(678\) | 0.182028 | 0.00699075 | ||||||||
\(679\) | 32.7041 | 1.25507 | ||||||||
\(680\) | −30.0557 | −1.15258 | ||||||||
\(681\) | 6.26229 | 0.239972 | ||||||||
\(682\) | −0.710774 | −0.0272169 | ||||||||
\(683\) | 2.89906 | 0.110929 | 0.0554647 | − | 0.998461i | \(-0.482336\pi\) | ||||
0.0554647 | + | 0.998461i | \(0.482336\pi\) | |||||||
\(684\) | 0.914665 | 0.0349731 | ||||||||
\(685\) | −18.5483 | −0.708694 | ||||||||
\(686\) | 15.1390 | 0.578009 | ||||||||
\(687\) | −2.82769 | −0.107883 | ||||||||
\(688\) | 9.15612 | 0.349074 | ||||||||
\(689\) | −19.2749 | −0.734316 | ||||||||
\(690\) | −3.12993 | −0.119154 | ||||||||
\(691\) | 2.97532 | 0.113186 | 0.0565932 | − | 0.998397i | \(-0.481976\pi\) | ||||
0.0565932 | + | 0.998397i | \(0.481976\pi\) | |||||||
\(692\) | −33.9024 | −1.28878 | ||||||||
\(693\) | 11.3299 | 0.430386 | ||||||||
\(694\) | −0.497384 | −0.0188804 | ||||||||
\(695\) | −95.7363 | −3.63149 | ||||||||
\(696\) | −2.60699 | −0.0988176 | ||||||||
\(697\) | −6.18703 | −0.234350 | ||||||||
\(698\) | 0.296463 | 0.0112213 | ||||||||
\(699\) | −6.61733 | −0.250290 | ||||||||
\(700\) | 39.9123 | 1.50854 | ||||||||
\(701\) | −39.2450 | −1.48226 | −0.741132 | − | 0.671359i | \(-0.765711\pi\) | ||||
−0.741132 | + | 0.671359i | \(0.765711\pi\) | |||||||
\(702\) | 3.95848 | 0.149403 | ||||||||
\(703\) | −2.88157 | −0.108681 | ||||||||
\(704\) | −13.2223 | −0.498333 | ||||||||
\(705\) | 42.6325 | 1.60563 | ||||||||
\(706\) | 25.8633 | 0.973377 | ||||||||
\(707\) | 2.03783 | 0.0766404 | ||||||||
\(708\) | 9.63724 | 0.362190 | ||||||||
\(709\) | 21.1537 | 0.794445 | 0.397223 | − | 0.917722i | \(-0.369974\pi\) | ||||
0.397223 | + | 0.917722i | \(0.369974\pi\) | |||||||
\(710\) | −44.6487 | −1.67563 | ||||||||
\(711\) | −9.62495 | −0.360964 | ||||||||
\(712\) | 22.7373 | 0.852118 | ||||||||
\(713\) | 0.195443 | 0.00731939 | ||||||||
\(714\) | 5.09003 | 0.190490 | ||||||||
\(715\) | 101.583 | 3.79898 | ||||||||
\(716\) | 24.6954 | 0.922912 | ||||||||
\(717\) | 17.3956 | 0.649651 | ||||||||
\(718\) | 14.9346 | 0.557353 | ||||||||
\(719\) | −28.2170 | −1.05232 | −0.526159 | − | 0.850386i | \(-0.676368\pi\) | ||||
−0.526159 | + | 0.850386i | \(0.676368\pi\) | |||||||
\(720\) | −3.48264 | −0.129790 | ||||||||
\(721\) | −9.13960 | −0.340377 | ||||||||
\(722\) | −14.1730 | −0.527463 | ||||||||
\(723\) | 3.26312 | 0.121357 | ||||||||
\(724\) | 12.5705 | 0.467177 | ||||||||
\(725\) | 11.8435 | 0.439858 | ||||||||
\(726\) | 8.95322 | 0.332285 | ||||||||
\(727\) | −1.17513 | −0.0435833 | −0.0217917 | − | 0.999763i | \(-0.506937\pi\) | ||||
−0.0217917 | + | 0.999763i | \(0.506937\pi\) | |||||||
\(728\) | 32.1500 | 1.19156 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 24.6297 | 0.911587 | ||||||||
\(731\) | −30.3103 | −1.12107 | ||||||||
\(732\) | −17.8066 | −0.658152 | ||||||||
\(733\) | −30.9783 | −1.14421 | −0.572105 | − | 0.820181i | \(-0.693873\pi\) | ||||
−0.572105 | + | 0.820181i | \(0.693873\pi\) | |||||||
\(734\) | 9.05955 | 0.334394 | ||||||||
\(735\) | 5.56106 | 0.205123 | ||||||||
\(736\) | 5.86114 | 0.216044 | ||||||||
\(737\) | 13.3817 | 0.492920 | ||||||||
\(738\) | 1.67969 | 0.0618303 | ||||||||
\(739\) | 4.13263 | 0.152021 | 0.0760106 | − | 0.997107i | \(-0.475782\pi\) | ||||
0.0760106 | + | 0.997107i | \(0.475782\pi\) | |||||||
\(740\) | 26.0119 | 0.956215 | ||||||||
\(741\) | −3.34717 | −0.122961 | ||||||||
\(742\) | 6.72872 | 0.247019 | ||||||||
\(743\) | 29.3385 | 1.07633 | 0.538163 | − | 0.842841i | \(-0.319119\pi\) | ||||
0.538163 | + | 0.842841i | \(0.319119\pi\) | |||||||
\(744\) | −0.509517 | −0.0186798 | ||||||||
\(745\) | 50.8385 | 1.86258 | ||||||||
\(746\) | 27.0957 | 0.992043 | ||||||||
\(747\) | 14.6215 | 0.534972 | ||||||||
\(748\) | −19.0002 | −0.694715 | ||||||||
\(749\) | −43.9062 | −1.60430 | ||||||||
\(750\) | −21.4198 | −0.782140 | ||||||||
\(751\) | −31.0677 | −1.13368 | −0.566838 | − | 0.823830i | \(-0.691833\pi\) | ||||
−0.566838 | + | 0.823830i | \(0.691833\pi\) | |||||||
\(752\) | −8.81489 | −0.321446 | ||||||||
\(753\) | −23.6292 | −0.861096 | ||||||||
\(754\) | 3.95848 | 0.144159 | ||||||||
\(755\) | 36.0911 | 1.31349 | ||||||||
\(756\) | 3.36997 | 0.122564 | ||||||||
\(757\) | −34.1761 | −1.24215 | −0.621076 | − | 0.783750i | \(-0.713304\pi\) | ||||
−0.621076 | + | 0.783750i | \(0.713304\pi\) | |||||||
\(758\) | 15.4106 | 0.559739 | ||||||||
\(759\) | −4.76863 | −0.173090 | ||||||||
\(760\) | −6.89960 | −0.250275 | ||||||||
\(761\) | 22.4770 | 0.814791 | 0.407395 | − | 0.913252i | \(-0.366437\pi\) | ||||
0.407395 | + | 0.913252i | \(0.366437\pi\) | |||||||
\(762\) | 4.60533 | 0.166833 | ||||||||
\(763\) | 9.22573 | 0.333994 | ||||||||
\(764\) | −18.2987 | −0.662025 | ||||||||
\(765\) | 11.5289 | 0.416828 | ||||||||
\(766\) | −4.55586 | −0.164610 | ||||||||
\(767\) | −35.2670 | −1.27342 | ||||||||
\(768\) | −12.8727 | −0.464503 | ||||||||
\(769\) | 18.3350 | 0.661175 | 0.330588 | − | 0.943775i | \(-0.392753\pi\) | ||||
0.330588 | + | 0.943775i | \(0.392753\pi\) | |||||||
\(770\) | −35.4617 | −1.27795 | ||||||||
\(771\) | 4.73508 | 0.170530 | ||||||||
\(772\) | −4.91561 | −0.176917 | ||||||||
\(773\) | 20.4086 | 0.734046 | 0.367023 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367023 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(774\) | 8.22881 | 0.295779 | ||||||||
\(775\) | 2.31473 | 0.0831476 | ||||||||
\(776\) | 35.8848 | 1.28819 | ||||||||
\(777\) | −10.6168 | −0.380875 | ||||||||
\(778\) | −8.30950 | −0.297910 | ||||||||
\(779\) | −1.42030 | −0.0508875 | ||||||||
\(780\) | 30.2148 | 1.08186 | ||||||||
\(781\) | −68.0248 | −2.43412 | ||||||||
\(782\) | −2.14234 | −0.0766100 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −1.14983 | −0.0410654 | ||||||||
\(785\) | 53.1276 | 1.89621 | ||||||||
\(786\) | 12.5758 | 0.448565 | ||||||||
\(787\) | −2.03075 | −0.0723884 | −0.0361942 | − | 0.999345i | \(-0.511523\pi\) | ||||
−0.0361942 | + | 0.999345i | \(0.511523\pi\) | |||||||
\(788\) | 14.2006 | 0.505874 | ||||||||
\(789\) | 31.4462 | 1.11952 | ||||||||
\(790\) | 30.1254 | 1.07181 | ||||||||
\(791\) | −0.567090 | −0.0201634 | ||||||||
\(792\) | 12.4318 | 0.441743 | ||||||||
\(793\) | 65.1625 | 2.31399 | ||||||||
\(794\) | 18.6545 | 0.662024 | ||||||||
\(795\) | 15.2405 | 0.540525 | ||||||||
\(796\) | −12.9710 | −0.459745 | ||||||||
\(797\) | 41.4799 | 1.46929 | 0.734647 | − | 0.678450i | \(-0.237348\pi\) | ||||
0.734647 | + | 0.678450i | \(0.237348\pi\) | |||||||
\(798\) | 1.16847 | 0.0413635 | ||||||||
\(799\) | 29.1806 | 1.03234 | ||||||||
\(800\) | 69.4165 | 2.45424 | ||||||||
\(801\) | −8.72169 | −0.308166 | ||||||||
\(802\) | 14.2353 | 0.502664 | ||||||||
\(803\) | 37.5248 | 1.32422 | ||||||||
\(804\) | 3.98025 | 0.140373 | ||||||||
\(805\) | 9.75098 | 0.343677 | ||||||||
\(806\) | 0.773655 | 0.0272508 | ||||||||
\(807\) | −13.8706 | −0.488267 | ||||||||
\(808\) | 2.23602 | 0.0786627 | ||||||||
\(809\) | −53.1717 | −1.86942 | −0.934710 | − | 0.355412i | \(-0.884340\pi\) | ||||
−0.934710 | + | 0.355412i | \(0.884340\pi\) | |||||||
\(810\) | −3.12993 | −0.109975 | ||||||||
\(811\) | −52.5852 | −1.84652 | −0.923258 | − | 0.384181i | \(-0.874484\pi\) | ||||
−0.923258 | + | 0.384181i | \(0.874484\pi\) | |||||||
\(812\) | 3.36997 | 0.118263 | ||||||||
\(813\) | 14.7222 | 0.516331 | ||||||||
\(814\) | −16.2507 | −0.569588 | ||||||||
\(815\) | −33.1156 | −1.15999 | ||||||||
\(816\) | −2.38376 | −0.0834484 | ||||||||
\(817\) | −6.95805 | −0.243431 | ||||||||
\(818\) | 17.7699 | 0.621311 | ||||||||
\(819\) | −12.3322 | −0.430923 | ||||||||
\(820\) | 12.8210 | 0.447729 | ||||||||
\(821\) | 47.8814 | 1.67107 | 0.835536 | − | 0.549436i | \(-0.185157\pi\) | ||||
0.835536 | + | 0.549436i | \(0.185157\pi\) | |||||||
\(822\) | 3.44672 | 0.120218 | ||||||||
\(823\) | 38.1344 | 1.32928 | 0.664641 | − | 0.747162i | \(-0.268584\pi\) | ||||
0.664641 | + | 0.747162i | \(0.268584\pi\) | |||||||
\(824\) | −10.0285 | −0.349358 | ||||||||
\(825\) | −56.4774 | −1.96629 | ||||||||
\(826\) | 12.3114 | 0.428370 | ||||||||
\(827\) | 43.3718 | 1.50818 | 0.754092 | − | 0.656769i | \(-0.228077\pi\) | ||||
0.754092 | + | 0.656769i | \(0.228077\pi\) | |||||||
\(828\) | −1.41838 | −0.0492922 | ||||||||
\(829\) | −17.1770 | −0.596581 | −0.298290 | − | 0.954475i | \(-0.596416\pi\) | ||||
−0.298290 | + | 0.954475i | \(0.596416\pi\) | |||||||
\(830\) | −45.7642 | −1.58850 | ||||||||
\(831\) | 28.6108 | 0.992498 | ||||||||
\(832\) | 14.3920 | 0.498954 | ||||||||
\(833\) | 3.80638 | 0.131883 | ||||||||
\(834\) | 17.7901 | 0.616021 | ||||||||
\(835\) | −72.8280 | −2.52032 | ||||||||
\(836\) | −4.36170 | −0.150853 | ||||||||
\(837\) | 0.195443 | 0.00675549 | ||||||||
\(838\) | −8.92766 | −0.308401 | ||||||||
\(839\) | 50.2700 | 1.73551 | 0.867756 | − | 0.496991i | \(-0.165562\pi\) | ||||
0.867756 | + | 0.496991i | \(0.165562\pi\) | |||||||
\(840\) | −25.4207 | −0.877097 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −6.68301 | −0.230312 | ||||||||
\(843\) | −1.91196 | −0.0658513 | ||||||||
\(844\) | −4.63448 | −0.159525 | ||||||||
\(845\) | −57.2165 | −1.96831 | ||||||||
\(846\) | −7.92214 | −0.272369 | ||||||||
\(847\) | −27.8928 | −0.958409 | ||||||||
\(848\) | −3.15120 | −0.108212 | ||||||||
\(849\) | −13.5965 | −0.466632 | ||||||||
\(850\) | −25.3729 | −0.870283 | ||||||||
\(851\) | 4.46849 | 0.153178 | ||||||||
\(852\) | −20.2333 | −0.693182 | ||||||||
\(853\) | 18.6995 | 0.640258 | 0.320129 | − | 0.947374i | \(-0.396274\pi\) | ||||
0.320129 | + | 0.947374i | \(0.396274\pi\) | |||||||
\(854\) | −22.7477 | −0.778411 | ||||||||
\(855\) | 2.64658 | 0.0905111 | ||||||||
\(856\) | −48.1762 | −1.64663 | ||||||||
\(857\) | 6.86614 | 0.234543 | 0.117271 | − | 0.993100i | \(-0.462585\pi\) | ||||
0.117271 | + | 0.993100i | \(0.462585\pi\) | |||||||
\(858\) | −18.8765 | −0.644433 | ||||||||
\(859\) | −30.9629 | −1.05644 | −0.528220 | − | 0.849108i | \(-0.677140\pi\) | ||||
−0.528220 | + | 0.849108i | \(0.677140\pi\) | |||||||
\(860\) | 62.8101 | 2.14181 | ||||||||
\(861\) | −5.23291 | −0.178337 | ||||||||
\(862\) | 19.2430 | 0.655421 | ||||||||
\(863\) | 34.0856 | 1.16029 | 0.580143 | − | 0.814515i | \(-0.302997\pi\) | ||||
0.580143 | + | 0.814515i | \(0.302997\pi\) | |||||||
\(864\) | 5.86114 | 0.199400 | ||||||||
\(865\) | −98.0966 | −3.33538 | ||||||||
\(866\) | 18.5865 | 0.631595 | ||||||||
\(867\) | −9.10883 | −0.309352 | ||||||||
\(868\) | 0.658635 | 0.0223555 | ||||||||
\(869\) | 45.8978 | 1.55698 | ||||||||
\(870\) | −3.12993 | −0.106115 | ||||||||
\(871\) | −14.5655 | −0.493535 | ||||||||
\(872\) | 10.1230 | 0.342807 | ||||||||
\(873\) | −13.7648 | −0.465869 | ||||||||
\(874\) | −0.491798 | −0.0166353 | ||||||||
\(875\) | 66.7311 | 2.25592 | ||||||||
\(876\) | 11.1614 | 0.377108 | ||||||||
\(877\) | 14.0788 | 0.475406 | 0.237703 | − | 0.971338i | \(-0.423605\pi\) | ||||
0.237703 | + | 0.971338i | \(0.423605\pi\) | |||||||
\(878\) | 31.1358 | 1.05078 | ||||||||
\(879\) | −2.08364 | −0.0702794 | ||||||||
\(880\) | 16.6074 | 0.559836 | ||||||||
\(881\) | −24.2508 | −0.817030 | −0.408515 | − | 0.912751i | \(-0.633953\pi\) | ||||
−0.408515 | + | 0.912751i | \(0.633953\pi\) | |||||||
\(882\) | −1.03338 | −0.0347957 | ||||||||
\(883\) | 52.0180 | 1.75054 | 0.875272 | − | 0.483631i | \(-0.160682\pi\) | ||||
0.875272 | + | 0.483631i | \(0.160682\pi\) | |||||||
\(884\) | 20.6811 | 0.695581 | ||||||||
\(885\) | 27.8853 | 0.937355 | ||||||||
\(886\) | −21.0024 | −0.705589 | ||||||||
\(887\) | 10.3246 | 0.346665 | 0.173333 | − | 0.984863i | \(-0.444546\pi\) | ||||
0.173333 | + | 0.984863i | \(0.444546\pi\) | |||||||
\(888\) | −11.6493 | −0.390925 | ||||||||
\(889\) | −14.3474 | −0.481197 | ||||||||
\(890\) | 27.2983 | 0.915041 | ||||||||
\(891\) | −4.76863 | −0.159755 | ||||||||
\(892\) | 23.1922 | 0.776532 | ||||||||
\(893\) | 6.69874 | 0.224165 | ||||||||
\(894\) | −9.44702 | −0.315956 | ||||||||
\(895\) | 71.4561 | 2.38851 | ||||||||
\(896\) | 22.8270 | 0.762597 | ||||||||
\(897\) | 5.19051 | 0.173306 | ||||||||
\(898\) | −20.6974 | −0.690680 | ||||||||
\(899\) | 0.195443 | 0.00651838 | ||||||||
\(900\) | −16.7987 | −0.559956 | ||||||||
\(901\) | 10.4317 | 0.347529 | ||||||||
\(902\) | −8.00983 | −0.266698 | ||||||||
\(903\) | −25.6360 | −0.853114 | ||||||||
\(904\) | −0.622242 | −0.0206955 | ||||||||
\(905\) | 36.3726 | 1.20907 | ||||||||
\(906\) | −6.70660 | −0.222812 | ||||||||
\(907\) | −36.6028 | −1.21538 | −0.607689 | − | 0.794175i | \(-0.707903\pi\) | ||||
−0.607689 | + | 0.794175i | \(0.707903\pi\) | |||||||
\(908\) | −8.88234 | −0.294771 | ||||||||
\(909\) | −0.857700 | −0.0284481 | ||||||||
\(910\) | 38.5990 | 1.27954 | ||||||||
\(911\) | −25.3597 | −0.840205 | −0.420102 | − | 0.907477i | \(-0.638006\pi\) | ||||
−0.420102 | + | 0.907477i | \(0.638006\pi\) | |||||||
\(912\) | −0.547219 | −0.0181202 | ||||||||
\(913\) | −69.7244 | −2.30754 | ||||||||
\(914\) | −8.72604 | −0.288632 | ||||||||
\(915\) | −51.5234 | −1.70331 | ||||||||
\(916\) | 4.01074 | 0.132519 | ||||||||
\(917\) | −39.1787 | −1.29379 | ||||||||
\(918\) | −2.14234 | −0.0707078 | ||||||||
\(919\) | −9.02212 | −0.297612 | −0.148806 | − | 0.988866i | \(-0.547543\pi\) | ||||
−0.148806 | + | 0.988866i | \(0.547543\pi\) | |||||||
\(920\) | 10.6993 | 0.352746 | ||||||||
\(921\) | −30.9157 | −1.01871 | ||||||||
\(922\) | 14.2295 | 0.468624 | ||||||||
\(923\) | 74.0429 | 2.43715 | ||||||||
\(924\) | −16.0701 | −0.528668 | ||||||||
\(925\) | 52.9227 | 1.74009 | ||||||||
\(926\) | 11.1630 | 0.366838 | ||||||||
\(927\) | 3.84676 | 0.126344 | ||||||||
\(928\) | 5.86114 | 0.192401 | ||||||||
\(929\) | 34.1265 | 1.11965 | 0.559827 | − | 0.828610i | \(-0.310868\pi\) | ||||
0.559827 | + | 0.828610i | \(0.310868\pi\) | |||||||
\(930\) | −0.611722 | −0.0200592 | ||||||||
\(931\) | 0.873795 | 0.0286375 | ||||||||
\(932\) | 9.38591 | 0.307446 | ||||||||
\(933\) | 12.6680 | 0.414731 | ||||||||
\(934\) | 8.13735 | 0.266262 | ||||||||
\(935\) | −54.9769 | −1.79794 | ||||||||
\(936\) | −13.5316 | −0.442294 | ||||||||
\(937\) | −34.4584 | −1.12571 | −0.562854 | − | 0.826557i | \(-0.690297\pi\) | ||||
−0.562854 | + | 0.826557i | \(0.690297\pi\) | |||||||
\(938\) | 5.08472 | 0.166022 | ||||||||
\(939\) | 23.5046 | 0.767045 | ||||||||
\(940\) | −60.4693 | −1.97229 | ||||||||
\(941\) | 9.00188 | 0.293453 | 0.146727 | − | 0.989177i | \(-0.453126\pi\) | ||||
0.146727 | + | 0.989177i | \(0.453126\pi\) | |||||||
\(942\) | −9.87239 | −0.321660 | ||||||||
\(943\) | 2.20248 | 0.0717225 | ||||||||
\(944\) | −5.76570 | −0.187657 | ||||||||
\(945\) | 9.75098 | 0.317199 | ||||||||
\(946\) | −39.2401 | −1.27581 | ||||||||
\(947\) | 51.1277 | 1.66143 | 0.830713 | − | 0.556701i | \(-0.187933\pi\) | ||||
0.830713 | + | 0.556701i | \(0.187933\pi\) | |||||||
\(948\) | 13.6519 | 0.443392 | ||||||||
\(949\) | −40.8446 | −1.32587 | ||||||||
\(950\) | −5.82462 | −0.188976 | ||||||||
\(951\) | −9.06839 | −0.294063 | ||||||||
\(952\) | −17.3997 | −0.563927 | ||||||||
\(953\) | 7.73247 | 0.250479 | 0.125240 | − | 0.992127i | \(-0.460030\pi\) | ||||
0.125240 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(954\) | −2.83205 | −0.0916910 | ||||||||
\(955\) | −52.9473 | −1.71334 | ||||||||
\(956\) | −24.6737 | −0.798003 | ||||||||
\(957\) | −4.76863 | −0.154148 | ||||||||
\(958\) | 24.4493 | 0.789922 | ||||||||
\(959\) | −10.7379 | −0.346745 | ||||||||
\(960\) | −11.3797 | −0.367277 | ||||||||
\(961\) | −30.9618 | −0.998768 | ||||||||
\(962\) | 17.6884 | 0.570297 | ||||||||
\(963\) | 18.4797 | 0.595499 | ||||||||
\(964\) | −4.62835 | −0.149069 | ||||||||
\(965\) | −14.2233 | −0.457864 | ||||||||
\(966\) | −1.81197 | −0.0582991 | ||||||||
\(967\) | 15.6598 | 0.503586 | 0.251793 | − | 0.967781i | \(-0.418980\pi\) | ||||
0.251793 | + | 0.967781i | \(0.418980\pi\) | |||||||
\(968\) | −30.6055 | −0.983699 | ||||||||
\(969\) | 1.81150 | 0.0581939 | ||||||||
\(970\) | 43.0830 | 1.38331 | ||||||||
\(971\) | −21.6197 | −0.693810 | −0.346905 | − | 0.937900i | \(-0.612767\pi\) | ||||
−0.346905 | + | 0.937900i | \(0.612767\pi\) | |||||||
\(972\) | −1.41838 | −0.0454947 | ||||||||
\(973\) | −55.4232 | −1.77679 | ||||||||
\(974\) | −18.1612 | −0.581924 | ||||||||
\(975\) | 61.4739 | 1.96874 | ||||||||
\(976\) | 10.6532 | 0.341001 | ||||||||
\(977\) | 5.57404 | 0.178329 | 0.0891647 | − | 0.996017i | \(-0.471580\pi\) | ||||
0.0891647 | + | 0.996017i | \(0.471580\pi\) | |||||||
\(978\) | 6.15368 | 0.196773 | ||||||||
\(979\) | 41.5905 | 1.32924 | ||||||||
\(980\) | −7.88772 | −0.251964 | ||||||||
\(981\) | −3.88301 | −0.123975 | ||||||||
\(982\) | −13.9400 | −0.444843 | ||||||||
\(983\) | −43.2735 | −1.38021 | −0.690105 | − | 0.723710i | \(-0.742435\pi\) | ||||
−0.690105 | + | 0.723710i | \(0.742435\pi\) | |||||||
\(984\) | −5.74183 | −0.183043 | ||||||||
\(985\) | 41.0892 | 1.30921 | ||||||||
\(986\) | −2.14234 | −0.0682261 | ||||||||
\(987\) | 24.6806 | 0.785593 | ||||||||
\(988\) | 4.74758 | 0.151041 | ||||||||
\(989\) | 10.7899 | 0.343100 | ||||||||
\(990\) | 14.9255 | 0.474363 | ||||||||
\(991\) | 9.95405 | 0.316201 | 0.158100 | − | 0.987423i | \(-0.449463\pi\) | ||||
0.158100 | + | 0.987423i | \(0.449463\pi\) | |||||||
\(992\) | 1.14552 | 0.0363702 | ||||||||
\(993\) | −17.1154 | −0.543141 | ||||||||
\(994\) | −25.8478 | −0.819843 | ||||||||
\(995\) | −37.5315 | −1.18983 | ||||||||
\(996\) | −20.7389 | −0.657136 | ||||||||
\(997\) | 9.24724 | 0.292863 | 0.146431 | − | 0.989221i | \(-0.453221\pi\) | ||||
0.146431 | + | 0.989221i | \(0.453221\pi\) | |||||||
\(998\) | 3.70106 | 0.117155 | ||||||||
\(999\) | 4.46849 | 0.141377 |
(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 | 2001.2.a.o.1.13 | ✓ | 20 | |
3.2 | odd | 2 | 6003.2.a.s.1.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.13 | ✓ | 20 | 1.1 | even | 1 | trivial | |
6003.2.a.s.1.8 | 20 | 3.2 | odd | 2 |