Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2523,2,Mod(1,2523)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2523, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2523.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2523 = 3 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2523.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: | \(20.1462564300\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 87) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2523.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | −4.23607 | −1.60108 | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.23607 | −1.65579 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | −0.618034 | −0.178411 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −6.85410 | −1.83184 | ||||||||
\(15\) | 3.23607 | 0.835549 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 1.61803 | 0.381374 | ||||||||
\(19\) | −7.70820 | −1.76838 | −0.884192 | − | 0.467124i | \(-0.845290\pi\) | ||||
−0.884192 | + | 0.467124i | \(0.845290\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 4.23607 | 0.924386 | ||||||||
\(22\) | −3.61803 | −0.771367 | ||||||||
\(23\) | 1.23607 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 1.61803 | 0.317323 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.61803 | −0.494762 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 5.23607 | 0.955971 | ||||||||
\(31\) | 7.23607 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 4.85410 | 0.832472 | ||||||||
\(35\) | 13.7082 | 2.31711 | ||||||||
\(36\) | 0.618034 | 0.103006 | ||||||||
\(37\) | 4.76393 | 0.783186 | 0.391593 | − | 0.920139i | \(-0.371924\pi\) | ||||
0.391593 | + | 0.920139i | \(0.371924\pi\) | |||||||
\(38\) | −12.4721 | −2.02325 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 7.23607 | 1.14412 | ||||||||
\(41\) | −4.47214 | −0.698430 | −0.349215 | − | 0.937043i | \(-0.613552\pi\) | ||||
−0.349215 | + | 0.937043i | \(0.613552\pi\) | |||||||
\(42\) | 6.85410 | 1.05761 | ||||||||
\(43\) | 0.472136 | 0.0720001 | 0.0360000 | − | 0.999352i | \(-0.488538\pi\) | ||||
0.0360000 | + | 0.999352i | \(0.488538\pi\) | |||||||
\(44\) | −1.38197 | −0.208339 | ||||||||
\(45\) | −3.23607 | −0.482405 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | −10.2361 | −1.49308 | −0.746542 | − | 0.665338i | \(-0.768287\pi\) | ||||
−0.746542 | + | 0.665338i | \(0.768287\pi\) | |||||||
\(48\) | 4.85410 | 0.700629 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 8.85410 | 1.25216 | ||||||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0.618034 | 0.0857059 | ||||||||
\(53\) | 6.76393 | 0.929098 | 0.464549 | − | 0.885548i | \(-0.346217\pi\) | ||||
0.464549 | + | 0.885548i | \(0.346217\pi\) | |||||||
\(54\) | −1.61803 | −0.220187 | ||||||||
\(55\) | 7.23607 | 0.975711 | ||||||||
\(56\) | 9.47214 | 1.26577 | ||||||||
\(57\) | 7.70820 | 1.02098 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | −2.76393 | −0.353885 | −0.176943 | − | 0.984221i | \(-0.556621\pi\) | ||||
−0.176943 | + | 0.984221i | \(0.556621\pi\) | |||||||
\(62\) | 11.7082 | 1.48694 | ||||||||
\(63\) | −4.23607 | −0.533694 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | −3.23607 | −0.401385 | ||||||||
\(66\) | 3.61803 | 0.445349 | ||||||||
\(67\) | −4.70820 | −0.575199 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287599 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(68\) | 1.85410 | 0.224843 | ||||||||
\(69\) | −1.23607 | −0.148805 | ||||||||
\(70\) | 22.1803 | 2.65106 | ||||||||
\(71\) | −4.76393 | −0.565375 | −0.282687 | − | 0.959212i | \(-0.591226\pi\) | ||||
−0.282687 | + | 0.959212i | \(0.591226\pi\) | |||||||
\(72\) | −2.23607 | −0.263523 | ||||||||
\(73\) | −7.70820 | −0.902177 | −0.451089 | − | 0.892479i | \(-0.648964\pi\) | ||||
−0.451089 | + | 0.892479i | \(0.648964\pi\) | |||||||
\(74\) | 7.70820 | 0.896061 | ||||||||
\(75\) | −5.47214 | −0.631868 | ||||||||
\(76\) | −4.76393 | −0.546460 | ||||||||
\(77\) | 9.47214 | 1.07945 | ||||||||
\(78\) | −1.61803 | −0.183206 | ||||||||
\(79\) | 2.29180 | 0.257847 | 0.128924 | − | 0.991655i | \(-0.458848\pi\) | ||||
0.128924 | + | 0.991655i | \(0.458848\pi\) | |||||||
\(80\) | 15.7082 | 1.75623 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.23607 | −0.799090 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 2.61803 | 0.285651 | ||||||||
\(85\) | −9.70820 | −1.05300 | ||||||||
\(86\) | 0.763932 | 0.0823769 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 0.0557281 | 0.00590717 | 0.00295358 | − | 0.999996i | \(-0.499060\pi\) | ||||
0.00295358 | + | 0.999996i | \(0.499060\pi\) | |||||||
\(90\) | −5.23607 | −0.551930 | ||||||||
\(91\) | −4.23607 | −0.444061 | ||||||||
\(92\) | 0.763932 | 0.0796454 | ||||||||
\(93\) | −7.23607 | −0.750345 | ||||||||
\(94\) | −16.5623 | −1.70827 | ||||||||
\(95\) | 24.9443 | 2.55923 | ||||||||
\(96\) | 3.38197 | 0.345170 | ||||||||
\(97\) | 18.1803 | 1.84593 | 0.922967 | − | 0.384879i | \(-0.125757\pi\) | ||||
0.922967 | + | 0.384879i | \(0.125757\pi\) | |||||||
\(98\) | 17.7082 | 1.78880 | ||||||||
\(99\) | −2.23607 | −0.224733 | ||||||||
\(100\) | 3.38197 | 0.338197 | ||||||||
\(101\) | 3.94427 | 0.392470 | 0.196235 | − | 0.980557i | \(-0.437129\pi\) | ||||
0.196235 | + | 0.980557i | \(0.437129\pi\) | |||||||
\(102\) | −4.85410 | −0.480628 | ||||||||
\(103\) | −19.4164 | −1.91316 | −0.956578 | − | 0.291477i | \(-0.905853\pi\) | ||||
−0.956578 | + | 0.291477i | \(0.905853\pi\) | |||||||
\(104\) | −2.23607 | −0.219265 | ||||||||
\(105\) | −13.7082 | −1.33778 | ||||||||
\(106\) | 10.9443 | 1.06300 | ||||||||
\(107\) | 0.763932 | 0.0738521 | 0.0369260 | − | 0.999318i | \(-0.488243\pi\) | ||||
0.0369260 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(108\) | −0.618034 | −0.0594703 | ||||||||
\(109\) | −5.00000 | −0.478913 | −0.239457 | − | 0.970907i | \(-0.576969\pi\) | ||||
−0.239457 | + | 0.970907i | \(0.576969\pi\) | |||||||
\(110\) | 11.7082 | 1.11633 | ||||||||
\(111\) | −4.76393 | −0.452172 | ||||||||
\(112\) | 20.5623 | 1.94296 | ||||||||
\(113\) | 4.52786 | 0.425946 | 0.212973 | − | 0.977058i | \(-0.431685\pi\) | ||||
0.212973 | + | 0.977058i | \(0.431685\pi\) | |||||||
\(114\) | 12.4721 | 1.16812 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 14.4721 | 1.33227 | ||||||||
\(119\) | −12.7082 | −1.16496 | ||||||||
\(120\) | −7.23607 | −0.660560 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | −4.47214 | −0.404888 | ||||||||
\(123\) | 4.47214 | 0.403239 | ||||||||
\(124\) | 4.47214 | 0.401610 | ||||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | −6.85410 | −0.610612 | ||||||||
\(127\) | 12.4721 | 1.10672 | 0.553362 | − | 0.832941i | \(-0.313345\pi\) | ||||
0.553362 | + | 0.832941i | \(0.313345\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | −0.472136 | −0.0415693 | ||||||||
\(130\) | −5.23607 | −0.459234 | ||||||||
\(131\) | 12.2361 | 1.06907 | 0.534535 | − | 0.845146i | \(-0.320487\pi\) | ||||
0.534535 | + | 0.845146i | \(0.320487\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | 32.6525 | 2.83133 | ||||||||
\(134\) | −7.61803 | −0.658098 | ||||||||
\(135\) | 3.23607 | 0.278516 | ||||||||
\(136\) | −6.70820 | −0.575224 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | −2.00000 | −0.170251 | ||||||||
\(139\) | −6.70820 | −0.568982 | −0.284491 | − | 0.958679i | \(-0.591825\pi\) | ||||
−0.284491 | + | 0.958679i | \(0.591825\pi\) | |||||||
\(140\) | 8.47214 | 0.716026 | ||||||||
\(141\) | 10.2361 | 0.862032 | ||||||||
\(142\) | −7.70820 | −0.646858 | ||||||||
\(143\) | −2.23607 | −0.186989 | ||||||||
\(144\) | −4.85410 | −0.404508 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.4721 | −1.03220 | ||||||||
\(147\) | −10.9443 | −0.902668 | ||||||||
\(148\) | 2.94427 | 0.242018 | ||||||||
\(149\) | 5.52786 | 0.452860 | 0.226430 | − | 0.974027i | \(-0.427295\pi\) | ||||
0.226430 | + | 0.974027i | \(0.427295\pi\) | |||||||
\(150\) | −8.85410 | −0.722934 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 17.2361 | 1.39803 | ||||||||
\(153\) | 3.00000 | 0.242536 | ||||||||
\(154\) | 15.3262 | 1.23502 | ||||||||
\(155\) | −23.4164 | −1.88085 | ||||||||
\(156\) | −0.618034 | −0.0494823 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 3.70820 | 0.295009 | ||||||||
\(159\) | −6.76393 | −0.536415 | ||||||||
\(160\) | 10.9443 | 0.865221 | ||||||||
\(161\) | −5.23607 | −0.412660 | ||||||||
\(162\) | 1.61803 | 0.127125 | ||||||||
\(163\) | 7.41641 | 0.580898 | 0.290449 | − | 0.956890i | \(-0.406195\pi\) | ||||
0.290449 | + | 0.956890i | \(0.406195\pi\) | |||||||
\(164\) | −2.76393 | −0.215827 | ||||||||
\(165\) | −7.23607 | −0.563327 | ||||||||
\(166\) | −9.70820 | −0.753503 | ||||||||
\(167\) | −15.8885 | −1.22949 | −0.614746 | − | 0.788725i | \(-0.710742\pi\) | ||||
−0.614746 | + | 0.788725i | \(0.710742\pi\) | |||||||
\(168\) | −9.47214 | −0.730791 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −15.7082 | −1.20476 | ||||||||
\(171\) | −7.70820 | −0.589461 | ||||||||
\(172\) | 0.291796 | 0.0222492 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.1803 | −1.75227 | ||||||||
\(176\) | 10.8541 | 0.818159 | ||||||||
\(177\) | −8.94427 | −0.672293 | ||||||||
\(178\) | 0.0901699 | 0.00675852 | ||||||||
\(179\) | 17.2361 | 1.28828 | 0.644142 | − | 0.764906i | \(-0.277215\pi\) | ||||
0.644142 | + | 0.764906i | \(0.277215\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 20.4164 | 1.51754 | 0.758770 | − | 0.651359i | \(-0.225801\pi\) | ||||
0.758770 | + | 0.651359i | \(0.225801\pi\) | |||||||
\(182\) | −6.85410 | −0.508060 | ||||||||
\(183\) | 2.76393 | 0.204316 | ||||||||
\(184\) | −2.76393 | −0.203760 | ||||||||
\(185\) | −15.4164 | −1.13344 | ||||||||
\(186\) | −11.7082 | −0.858487 | ||||||||
\(187\) | −6.70820 | −0.490552 | ||||||||
\(188\) | −6.32624 | −0.461388 | ||||||||
\(189\) | 4.23607 | 0.308129 | ||||||||
\(190\) | 40.3607 | 2.92807 | ||||||||
\(191\) | −8.94427 | −0.647185 | −0.323592 | − | 0.946197i | \(-0.604891\pi\) | ||||
−0.323592 | + | 0.946197i | \(0.604891\pi\) | |||||||
\(192\) | −4.23607 | −0.305712 | ||||||||
\(193\) | −17.4164 | −1.25366 | −0.626830 | − | 0.779156i | \(-0.715648\pi\) | ||||
−0.626830 | + | 0.779156i | \(0.715648\pi\) | |||||||
\(194\) | 29.4164 | 2.11198 | ||||||||
\(195\) | 3.23607 | 0.231740 | ||||||||
\(196\) | 6.76393 | 0.483138 | ||||||||
\(197\) | −3.70820 | −0.264199 | −0.132099 | − | 0.991236i | \(-0.542172\pi\) | ||||
−0.132099 | + | 0.991236i | \(0.542172\pi\) | |||||||
\(198\) | −3.61803 | −0.257122 | ||||||||
\(199\) | −20.1246 | −1.42660 | −0.713298 | − | 0.700861i | \(-0.752799\pi\) | ||||
−0.713298 | + | 0.700861i | \(0.752799\pi\) | |||||||
\(200\) | −12.2361 | −0.865221 | ||||||||
\(201\) | 4.70820 | 0.332091 | ||||||||
\(202\) | 6.38197 | 0.449034 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.85410 | −0.129813 | ||||||||
\(205\) | 14.4721 | 1.01078 | ||||||||
\(206\) | −31.4164 | −2.18888 | ||||||||
\(207\) | 1.23607 | 0.0859127 | ||||||||
\(208\) | −4.85410 | −0.336571 | ||||||||
\(209\) | 17.2361 | 1.19224 | ||||||||
\(210\) | −22.1803 | −1.53059 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | 4.18034 | 0.287107 | ||||||||
\(213\) | 4.76393 | 0.326419 | ||||||||
\(214\) | 1.23607 | 0.0844959 | ||||||||
\(215\) | −1.52786 | −0.104199 | ||||||||
\(216\) | 2.23607 | 0.152145 | ||||||||
\(217\) | −30.6525 | −2.08083 | ||||||||
\(218\) | −8.09017 | −0.547935 | ||||||||
\(219\) | 7.70820 | 0.520872 | ||||||||
\(220\) | 4.47214 | 0.301511 | ||||||||
\(221\) | 3.00000 | 0.201802 | ||||||||
\(222\) | −7.70820 | −0.517341 | ||||||||
\(223\) | −12.7082 | −0.851004 | −0.425502 | − | 0.904957i | \(-0.639903\pi\) | ||||
−0.425502 | + | 0.904957i | \(0.639903\pi\) | |||||||
\(224\) | 14.3262 | 0.957212 | ||||||||
\(225\) | 5.47214 | 0.364809 | ||||||||
\(226\) | 7.32624 | 0.487334 | ||||||||
\(227\) | 9.05573 | 0.601050 | 0.300525 | − | 0.953774i | \(-0.402838\pi\) | ||||
0.300525 | + | 0.953774i | \(0.402838\pi\) | |||||||
\(228\) | 4.76393 | 0.315499 | ||||||||
\(229\) | 22.1803 | 1.46572 | 0.732859 | − | 0.680380i | \(-0.238185\pi\) | ||||
0.732859 | + | 0.680380i | \(0.238185\pi\) | |||||||
\(230\) | −6.47214 | −0.426760 | ||||||||
\(231\) | −9.47214 | −0.623221 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4721 | −0.686052 | −0.343026 | − | 0.939326i | \(-0.611452\pi\) | ||||
−0.343026 | + | 0.939326i | \(0.611452\pi\) | |||||||
\(234\) | 1.61803 | 0.105774 | ||||||||
\(235\) | 33.1246 | 2.16081 | ||||||||
\(236\) | 5.52786 | 0.359833 | ||||||||
\(237\) | −2.29180 | −0.148868 | ||||||||
\(238\) | −20.5623 | −1.33286 | ||||||||
\(239\) | 26.1803 | 1.69347 | 0.846733 | − | 0.532019i | \(-0.178566\pi\) | ||||
0.846733 | + | 0.532019i | \(0.178566\pi\) | |||||||
\(240\) | −15.7082 | −1.01396 | ||||||||
\(241\) | 3.00000 | 0.193247 | 0.0966235 | − | 0.995321i | \(-0.469196\pi\) | ||||
0.0966235 | + | 0.995321i | \(0.469196\pi\) | |||||||
\(242\) | −9.70820 | −0.624067 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.70820 | −0.109357 | ||||||||
\(245\) | −35.4164 | −2.26267 | ||||||||
\(246\) | 7.23607 | 0.461355 | ||||||||
\(247\) | −7.70820 | −0.490461 | ||||||||
\(248\) | −16.1803 | −1.02745 | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | −2.47214 | −0.156352 | ||||||||
\(251\) | 12.2361 | 0.772334 | 0.386167 | − | 0.922429i | \(-0.373799\pi\) | ||||
0.386167 | + | 0.922429i | \(0.373799\pi\) | |||||||
\(252\) | −2.61803 | −0.164921 | ||||||||
\(253\) | −2.76393 | −0.173767 | ||||||||
\(254\) | 20.1803 | 1.26623 | ||||||||
\(255\) | 9.70820 | 0.607951 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −26.4721 | −1.65129 | −0.825643 | − | 0.564193i | \(-0.809188\pi\) | ||||
−0.825643 | + | 0.564193i | \(0.809188\pi\) | |||||||
\(258\) | −0.763932 | −0.0475603 | ||||||||
\(259\) | −20.1803 | −1.25395 | ||||||||
\(260\) | −2.00000 | −0.124035 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.7984 | 1.22315 | ||||||||
\(263\) | 4.94427 | 0.304877 | 0.152438 | − | 0.988313i | \(-0.451287\pi\) | ||||
0.152438 | + | 0.988313i | \(0.451287\pi\) | |||||||
\(264\) | −5.00000 | −0.307729 | ||||||||
\(265\) | −21.8885 | −1.34460 | ||||||||
\(266\) | 52.8328 | 3.23939 | ||||||||
\(267\) | −0.0557281 | −0.00341050 | ||||||||
\(268\) | −2.90983 | −0.177746 | ||||||||
\(269\) | −21.3607 | −1.30238 | −0.651192 | − | 0.758913i | \(-0.725731\pi\) | ||||
−0.651192 | + | 0.758913i | \(0.725731\pi\) | |||||||
\(270\) | 5.23607 | 0.318657 | ||||||||
\(271\) | −23.4164 | −1.42245 | −0.711223 | − | 0.702967i | \(-0.751858\pi\) | ||||
−0.711223 | + | 0.702967i | \(0.751858\pi\) | |||||||
\(272\) | −14.5623 | −0.882969 | ||||||||
\(273\) | 4.23607 | 0.256378 | ||||||||
\(274\) | 5.70820 | 0.344845 | ||||||||
\(275\) | −12.2361 | −0.737863 | ||||||||
\(276\) | −0.763932 | −0.0459833 | ||||||||
\(277\) | 6.41641 | 0.385525 | 0.192762 | − | 0.981245i | \(-0.438255\pi\) | ||||
0.192762 | + | 0.981245i | \(0.438255\pi\) | |||||||
\(278\) | −10.8541 | −0.650986 | ||||||||
\(279\) | 7.23607 | 0.433212 | ||||||||
\(280\) | −30.6525 | −1.83184 | ||||||||
\(281\) | −1.41641 | −0.0844958 | −0.0422479 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422479 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(282\) | 16.5623 | 0.986271 | ||||||||
\(283\) | 13.8885 | 0.825588 | 0.412794 | − | 0.910824i | \(-0.364553\pi\) | ||||
0.412794 | + | 0.910824i | \(0.364553\pi\) | |||||||
\(284\) | −2.94427 | −0.174710 | ||||||||
\(285\) | −24.9443 | −1.47757 | ||||||||
\(286\) | −3.61803 | −0.213939 | ||||||||
\(287\) | 18.9443 | 1.11825 | ||||||||
\(288\) | −3.38197 | −0.199284 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1803 | −1.06575 | ||||||||
\(292\) | −4.76393 | −0.278788 | ||||||||
\(293\) | 29.9443 | 1.74936 | 0.874682 | − | 0.484698i | \(-0.161071\pi\) | ||||
0.874682 | + | 0.484698i | \(0.161071\pi\) | |||||||
\(294\) | −17.7082 | −1.03276 | ||||||||
\(295\) | −28.9443 | −1.68520 | ||||||||
\(296\) | −10.6525 | −0.619163 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | 8.94427 | 0.518128 | ||||||||
\(299\) | 1.23607 | 0.0714837 | ||||||||
\(300\) | −3.38197 | −0.195258 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | −19.4164 | −1.11729 | ||||||||
\(303\) | −3.94427 | −0.226593 | ||||||||
\(304\) | 37.4164 | 2.14598 | ||||||||
\(305\) | 8.94427 | 0.512148 | ||||||||
\(306\) | 4.85410 | 0.277491 | ||||||||
\(307\) | −28.1803 | −1.60834 | −0.804168 | − | 0.594401i | \(-0.797389\pi\) | ||||
−0.804168 | + | 0.594401i | \(0.797389\pi\) | |||||||
\(308\) | 5.85410 | 0.333568 | ||||||||
\(309\) | 19.4164 | 1.10456 | ||||||||
\(310\) | −37.8885 | −2.15192 | ||||||||
\(311\) | 15.6525 | 0.887570 | 0.443785 | − | 0.896133i | \(-0.353635\pi\) | ||||
0.443785 | + | 0.896133i | \(0.353635\pi\) | |||||||
\(312\) | 2.23607 | 0.126592 | ||||||||
\(313\) | −5.47214 | −0.309303 | −0.154652 | − | 0.987969i | \(-0.549426\pi\) | ||||
−0.154652 | + | 0.987969i | \(0.549426\pi\) | |||||||
\(314\) | 3.23607 | 0.182622 | ||||||||
\(315\) | 13.7082 | 0.772370 | ||||||||
\(316\) | 1.41641 | 0.0796792 | ||||||||
\(317\) | 23.8328 | 1.33858 | 0.669292 | − | 0.742999i | \(-0.266597\pi\) | ||||
0.669292 | + | 0.742999i | \(0.266597\pi\) | |||||||
\(318\) | −10.9443 | −0.613724 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −13.7082 | −0.766312 | ||||||||
\(321\) | −0.763932 | −0.0426385 | ||||||||
\(322\) | −8.47214 | −0.472134 | ||||||||
\(323\) | −23.1246 | −1.28669 | ||||||||
\(324\) | 0.618034 | 0.0343352 | ||||||||
\(325\) | 5.47214 | 0.303539 | ||||||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 5.00000 | 0.276501 | ||||||||
\(328\) | 10.0000 | 0.552158 | ||||||||
\(329\) | 43.3607 | 2.39055 | ||||||||
\(330\) | −11.7082 | −0.644515 | ||||||||
\(331\) | −8.29180 | −0.455758 | −0.227879 | − | 0.973689i | \(-0.573179\pi\) | ||||
−0.227879 | + | 0.973689i | \(0.573179\pi\) | |||||||
\(332\) | −3.70820 | −0.203514 | ||||||||
\(333\) | 4.76393 | 0.261062 | ||||||||
\(334\) | −25.7082 | −1.40669 | ||||||||
\(335\) | 15.2361 | 0.832435 | ||||||||
\(336\) | −20.5623 | −1.12177 | ||||||||
\(337\) | 19.2361 | 1.04786 | 0.523928 | − | 0.851763i | \(-0.324466\pi\) | ||||
0.523928 | + | 0.851763i | \(0.324466\pi\) | |||||||
\(338\) | −19.4164 | −1.05611 | ||||||||
\(339\) | −4.52786 | −0.245920 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | −16.1803 | −0.876215 | ||||||||
\(342\) | −12.4721 | −0.674416 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | −1.05573 | −0.0569210 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 9.70820 | 0.521916 | ||||||||
\(347\) | 22.6525 | 1.21605 | 0.608024 | − | 0.793918i | \(-0.291962\pi\) | ||||
0.608024 | + | 0.793918i | \(0.291962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | −37.5066 | −2.00481 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 7.56231 | 0.403072 | ||||||||
\(353\) | −4.65248 | −0.247626 | −0.123813 | − | 0.992306i | \(-0.539512\pi\) | ||||
−0.123813 | + | 0.992306i | \(0.539512\pi\) | |||||||
\(354\) | −14.4721 | −0.769185 | ||||||||
\(355\) | 15.4164 | 0.818218 | ||||||||
\(356\) | 0.0344419 | 0.00182541 | ||||||||
\(357\) | 12.7082 | 0.672589 | ||||||||
\(358\) | 27.8885 | 1.47396 | ||||||||
\(359\) | 25.3050 | 1.33554 | 0.667772 | − | 0.744366i | \(-0.267248\pi\) | ||||
0.667772 | + | 0.744366i | \(0.267248\pi\) | |||||||
\(360\) | 7.23607 | 0.381374 | ||||||||
\(361\) | 40.4164 | 2.12718 | ||||||||
\(362\) | 33.0344 | 1.73625 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | −2.61803 | −0.137222 | ||||||||
\(365\) | 24.9443 | 1.30564 | ||||||||
\(366\) | 4.47214 | 0.233762 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | −4.47214 | −0.232810 | ||||||||
\(370\) | −24.9443 | −1.29679 | ||||||||
\(371\) | −28.6525 | −1.48756 | ||||||||
\(372\) | −4.47214 | −0.231869 | ||||||||
\(373\) | −3.88854 | −0.201341 | −0.100671 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100671 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(374\) | −10.8541 | −0.561252 | ||||||||
\(375\) | 1.52786 | 0.0788986 | ||||||||
\(376\) | 22.8885 | 1.18039 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 6.85410 | 0.352537 | ||||||||
\(379\) | −14.2918 | −0.734120 | −0.367060 | − | 0.930197i | \(-0.619636\pi\) | ||||
−0.367060 | + | 0.930197i | \(0.619636\pi\) | |||||||
\(380\) | 15.4164 | 0.790845 | ||||||||
\(381\) | −12.4721 | −0.638967 | ||||||||
\(382\) | −14.4721 | −0.740459 | ||||||||
\(383\) | 5.34752 | 0.273246 | 0.136623 | − | 0.990623i | \(-0.456375\pi\) | ||||
0.136623 | + | 0.990623i | \(0.456375\pi\) | |||||||
\(384\) | −13.6180 | −0.694942 | ||||||||
\(385\) | −30.6525 | −1.56219 | ||||||||
\(386\) | −28.1803 | −1.43434 | ||||||||
\(387\) | 0.472136 | 0.0240000 | ||||||||
\(388\) | 11.2361 | 0.570425 | ||||||||
\(389\) | −13.4721 | −0.683064 | −0.341532 | − | 0.939870i | \(-0.610946\pi\) | ||||
−0.341532 | + | 0.939870i | \(0.610946\pi\) | |||||||
\(390\) | 5.23607 | 0.265139 | ||||||||
\(391\) | 3.70820 | 0.187532 | ||||||||
\(392\) | −24.4721 | −1.23603 | ||||||||
\(393\) | −12.2361 | −0.617228 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −7.41641 | −0.373160 | ||||||||
\(396\) | −1.38197 | −0.0694464 | ||||||||
\(397\) | 6.94427 | 0.348523 | 0.174262 | − | 0.984699i | \(-0.444246\pi\) | ||||
0.174262 | + | 0.984699i | \(0.444246\pi\) | |||||||
\(398\) | −32.5623 | −1.63220 | ||||||||
\(399\) | −32.6525 | −1.63467 | ||||||||
\(400\) | −26.5623 | −1.32812 | ||||||||
\(401\) | 33.7082 | 1.68331 | 0.841654 | − | 0.540018i | \(-0.181582\pi\) | ||||
0.841654 | + | 0.540018i | \(0.181582\pi\) | |||||||
\(402\) | 7.61803 | 0.379953 | ||||||||
\(403\) | 7.23607 | 0.360454 | ||||||||
\(404\) | 2.43769 | 0.121280 | ||||||||
\(405\) | −3.23607 | −0.160802 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6525 | −0.528024 | ||||||||
\(408\) | 6.70820 | 0.332106 | ||||||||
\(409\) | 10.5836 | 0.523325 | 0.261662 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261662 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(410\) | 23.4164 | 1.15645 | ||||||||
\(411\) | −3.52786 | −0.174017 | ||||||||
\(412\) | −12.0000 | −0.591198 | ||||||||
\(413\) | −37.8885 | −1.86437 | ||||||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | 19.4164 | 0.953114 | ||||||||
\(416\) | −3.38197 | −0.165815 | ||||||||
\(417\) | 6.70820 | 0.328502 | ||||||||
\(418\) | 27.8885 | 1.36407 | ||||||||
\(419\) | −3.81966 | −0.186603 | −0.0933013 | − | 0.995638i | \(-0.529742\pi\) | ||||
−0.0933013 | + | 0.995638i | \(0.529742\pi\) | |||||||
\(420\) | −8.47214 | −0.413398 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 16.1803 | 0.787647 | ||||||||
\(423\) | −10.2361 | −0.497695 | ||||||||
\(424\) | −15.1246 | −0.734516 | ||||||||
\(425\) | 16.4164 | 0.796313 | ||||||||
\(426\) | 7.70820 | 0.373464 | ||||||||
\(427\) | 11.7082 | 0.566600 | ||||||||
\(428\) | 0.472136 | 0.0228216 | ||||||||
\(429\) | 2.23607 | 0.107958 | ||||||||
\(430\) | −2.47214 | −0.119217 | ||||||||
\(431\) | 14.3607 | 0.691730 | 0.345865 | − | 0.938284i | \(-0.387586\pi\) | ||||
0.345865 | + | 0.938284i | \(0.387586\pi\) | |||||||
\(432\) | 4.85410 | 0.233543 | ||||||||
\(433\) | −14.2918 | −0.686820 | −0.343410 | − | 0.939186i | \(-0.611582\pi\) | ||||
−0.343410 | + | 0.939186i | \(0.611582\pi\) | |||||||
\(434\) | −49.5967 | −2.38072 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.09017 | −0.147992 | ||||||||
\(437\) | −9.52786 | −0.455780 | ||||||||
\(438\) | 12.4721 | 0.595942 | ||||||||
\(439\) | −13.2918 | −0.634383 | −0.317191 | − | 0.948362i | \(-0.602740\pi\) | ||||
−0.317191 | + | 0.948362i | \(0.602740\pi\) | |||||||
\(440\) | −16.1803 | −0.771367 | ||||||||
\(441\) | 10.9443 | 0.521156 | ||||||||
\(442\) | 4.85410 | 0.230886 | ||||||||
\(443\) | 9.65248 | 0.458603 | 0.229301 | − | 0.973355i | \(-0.426356\pi\) | ||||
0.229301 | + | 0.973355i | \(0.426356\pi\) | |||||||
\(444\) | −2.94427 | −0.139729 | ||||||||
\(445\) | −0.180340 | −0.00854893 | ||||||||
\(446\) | −20.5623 | −0.973653 | ||||||||
\(447\) | −5.52786 | −0.261459 | ||||||||
\(448\) | −17.9443 | −0.847787 | ||||||||
\(449\) | −18.8885 | −0.891405 | −0.445703 | − | 0.895181i | \(-0.647046\pi\) | ||||
−0.445703 | + | 0.895181i | \(0.647046\pi\) | |||||||
\(450\) | 8.85410 | 0.417386 | ||||||||
\(451\) | 10.0000 | 0.470882 | ||||||||
\(452\) | 2.79837 | 0.131624 | ||||||||
\(453\) | 12.0000 | 0.563809 | ||||||||
\(454\) | 14.6525 | 0.687675 | ||||||||
\(455\) | 13.7082 | 0.642651 | ||||||||
\(456\) | −17.2361 | −0.807153 | ||||||||
\(457\) | −6.41641 | −0.300147 | −0.150073 | − | 0.988675i | \(-0.547951\pi\) | ||||
−0.150073 | + | 0.988675i | \(0.547951\pi\) | |||||||
\(458\) | 35.8885 | 1.67696 | ||||||||
\(459\) | −3.00000 | −0.140028 | ||||||||
\(460\) | −2.47214 | −0.115264 | ||||||||
\(461\) | −18.9443 | −0.882323 | −0.441161 | − | 0.897428i | \(-0.645433\pi\) | ||||
−0.441161 | + | 0.897428i | \(0.645433\pi\) | |||||||
\(462\) | −15.3262 | −0.713041 | ||||||||
\(463\) | −0.708204 | −0.0329130 | −0.0164565 | − | 0.999865i | \(-0.505239\pi\) | ||||
−0.0164565 | + | 0.999865i | \(0.505239\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23.4164 | 1.08591 | ||||||||
\(466\) | −16.9443 | −0.784928 | ||||||||
\(467\) | 13.5279 | 0.625995 | 0.312997 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312997 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(468\) | 0.618034 | 0.0285686 | ||||||||
\(469\) | 19.9443 | 0.920941 | ||||||||
\(470\) | 53.5967 | 2.47223 | ||||||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | −20.0000 | −0.920575 | ||||||||
\(473\) | −1.05573 | −0.0485424 | ||||||||
\(474\) | −3.70820 | −0.170323 | ||||||||
\(475\) | −42.1803 | −1.93537 | ||||||||
\(476\) | −7.85410 | −0.359992 | ||||||||
\(477\) | 6.76393 | 0.309699 | ||||||||
\(478\) | 42.3607 | 1.93753 | ||||||||
\(479\) | 10.4721 | 0.478484 | 0.239242 | − | 0.970960i | \(-0.423101\pi\) | ||||
0.239242 | + | 0.970960i | \(0.423101\pi\) | |||||||
\(480\) | −10.9443 | −0.499535 | ||||||||
\(481\) | 4.76393 | 0.217217 | ||||||||
\(482\) | 4.85410 | 0.221098 | ||||||||
\(483\) | 5.23607 | 0.238249 | ||||||||
\(484\) | −3.70820 | −0.168555 | ||||||||
\(485\) | −58.8328 | −2.67146 | ||||||||
\(486\) | −1.61803 | −0.0733955 | ||||||||
\(487\) | 20.3607 | 0.922630 | 0.461315 | − | 0.887236i | \(-0.347378\pi\) | ||||
0.461315 | + | 0.887236i | \(0.347378\pi\) | |||||||
\(488\) | 6.18034 | 0.279771 | ||||||||
\(489\) | −7.41641 | −0.335382 | ||||||||
\(490\) | −57.3050 | −2.58877 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 2.76393 | 0.124608 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −12.4721 | −0.561148 | ||||||||
\(495\) | 7.23607 | 0.325237 | ||||||||
\(496\) | −35.1246 | −1.57714 | ||||||||
\(497\) | 20.1803 | 0.905212 | ||||||||
\(498\) | 9.70820 | 0.435035 | ||||||||
\(499\) | −21.1803 | −0.948162 | −0.474081 | − | 0.880481i | \(-0.657220\pi\) | ||||
−0.474081 | + | 0.880481i | \(0.657220\pi\) | |||||||
\(500\) | −0.944272 | −0.0422291 | ||||||||
\(501\) | 15.8885 | 0.709848 | ||||||||
\(502\) | 19.7984 | 0.883645 | ||||||||
\(503\) | 25.1803 | 1.12274 | 0.561368 | − | 0.827566i | \(-0.310275\pi\) | ||||
0.561368 | + | 0.827566i | \(0.310275\pi\) | |||||||
\(504\) | 9.47214 | 0.421922 | ||||||||
\(505\) | −12.7639 | −0.567988 | ||||||||
\(506\) | −4.47214 | −0.198811 | ||||||||
\(507\) | 12.0000 | 0.532939 | ||||||||
\(508\) | 7.70820 | 0.341996 | ||||||||
\(509\) | −26.8328 | −1.18934 | −0.594672 | − | 0.803969i | \(-0.702718\pi\) | ||||
−0.594672 | + | 0.803969i | \(0.702718\pi\) | |||||||
\(510\) | 15.7082 | 0.695571 | ||||||||
\(511\) | 32.6525 | 1.44446 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 7.70820 | 0.340326 | ||||||||
\(514\) | −42.8328 | −1.88927 | ||||||||
\(515\) | 62.8328 | 2.76874 | ||||||||
\(516\) | −0.291796 | −0.0128456 | ||||||||
\(517\) | 22.8885 | 1.00664 | ||||||||
\(518\) | −32.6525 | −1.43467 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 7.23607 | 0.317323 | ||||||||
\(521\) | 3.52786 | 0.154559 | 0.0772793 | − | 0.997009i | \(-0.475377\pi\) | ||||
0.0772793 | + | 0.997009i | \(0.475377\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.0689 | 1.44600 | 0.723001 | − | 0.690847i | \(-0.242762\pi\) | ||||
0.723001 | + | 0.690847i | \(0.242762\pi\) | |||||||
\(524\) | 7.56231 | 0.330361 | ||||||||
\(525\) | 23.1803 | 1.01167 | ||||||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | 21.7082 | 0.945624 | ||||||||
\(528\) | −10.8541 | −0.472364 | ||||||||
\(529\) | −21.4721 | −0.933571 | ||||||||
\(530\) | −35.4164 | −1.53839 | ||||||||
\(531\) | 8.94427 | 0.388148 | ||||||||
\(532\) | 20.1803 | 0.874929 | ||||||||
\(533\) | −4.47214 | −0.193710 | ||||||||
\(534\) | −0.0901699 | −0.00390204 | ||||||||
\(535\) | −2.47214 | −0.106880 | ||||||||
\(536\) | 10.5279 | 0.454734 | ||||||||
\(537\) | −17.2361 | −0.743791 | ||||||||
\(538\) | −34.5623 | −1.49009 | ||||||||
\(539\) | −24.4721 | −1.05409 | ||||||||
\(540\) | 2.00000 | 0.0860663 | ||||||||
\(541\) | 10.6525 | 0.457986 | 0.228993 | − | 0.973428i | \(-0.426457\pi\) | ||||
0.228993 | + | 0.973428i | \(0.426457\pi\) | |||||||
\(542\) | −37.8885 | −1.62745 | ||||||||
\(543\) | −20.4164 | −0.876152 | ||||||||
\(544\) | −10.1459 | −0.435002 | ||||||||
\(545\) | 16.1803 | 0.693090 | ||||||||
\(546\) | 6.85410 | 0.293328 | ||||||||
\(547\) | −6.34752 | −0.271401 | −0.135700 | − | 0.990750i | \(-0.543328\pi\) | ||||
−0.135700 | + | 0.990750i | \(0.543328\pi\) | |||||||
\(548\) | 2.18034 | 0.0931395 | ||||||||
\(549\) | −2.76393 | −0.117962 | ||||||||
\(550\) | −19.7984 | −0.844205 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 2.76393 | 0.117641 | ||||||||
\(553\) | −9.70820 | −0.412835 | ||||||||
\(554\) | 10.3820 | 0.441087 | ||||||||
\(555\) | 15.4164 | 0.654390 | ||||||||
\(556\) | −4.14590 | −0.175825 | ||||||||
\(557\) | 16.4721 | 0.697947 | 0.348973 | − | 0.937133i | \(-0.386530\pi\) | ||||
0.348973 | + | 0.937133i | \(0.386530\pi\) | |||||||
\(558\) | 11.7082 | 0.495648 | ||||||||
\(559\) | 0.472136 | 0.0199692 | ||||||||
\(560\) | −66.5410 | −2.81187 | ||||||||
\(561\) | 6.70820 | 0.283221 | ||||||||
\(562\) | −2.29180 | −0.0966736 | ||||||||
\(563\) | 13.0689 | 0.550788 | 0.275394 | − | 0.961331i | \(-0.411192\pi\) | ||||
0.275394 | + | 0.961331i | \(0.411192\pi\) | |||||||
\(564\) | 6.32624 | 0.266383 | ||||||||
\(565\) | −14.6525 | −0.616434 | ||||||||
\(566\) | 22.4721 | 0.944574 | ||||||||
\(567\) | −4.23607 | −0.177898 | ||||||||
\(568\) | 10.6525 | 0.446968 | ||||||||
\(569\) | 21.0000 | 0.880366 | 0.440183 | − | 0.897908i | \(-0.354914\pi\) | ||||
0.440183 | + | 0.897908i | \(0.354914\pi\) | |||||||
\(570\) | −40.3607 | −1.69052 | ||||||||
\(571\) | 18.8328 | 0.788129 | 0.394064 | − | 0.919083i | \(-0.371069\pi\) | ||||
0.394064 | + | 0.919083i | \(0.371069\pi\) | |||||||
\(572\) | −1.38197 | −0.0577829 | ||||||||
\(573\) | 8.94427 | 0.373652 | ||||||||
\(574\) | 30.6525 | 1.27941 | ||||||||
\(575\) | 6.76393 | 0.282075 | ||||||||
\(576\) | 4.23607 | 0.176503 | ||||||||
\(577\) | −24.8328 | −1.03380 | −0.516902 | − | 0.856045i | \(-0.672915\pi\) | ||||
−0.516902 | + | 0.856045i | \(0.672915\pi\) | |||||||
\(578\) | −12.9443 | −0.538411 | ||||||||
\(579\) | 17.4164 | 0.723801 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.4164 | 1.05445 | ||||||||
\(582\) | −29.4164 | −1.21935 | ||||||||
\(583\) | −15.1246 | −0.626397 | ||||||||
\(584\) | 17.2361 | 0.713234 | ||||||||
\(585\) | −3.23607 | −0.133795 | ||||||||
\(586\) | 48.4508 | 2.00149 | ||||||||
\(587\) | −0.944272 | −0.0389743 | −0.0194871 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194871 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(588\) | −6.76393 | −0.278940 | ||||||||
\(589\) | −55.7771 | −2.29825 | ||||||||
\(590\) | −46.8328 | −1.92808 | ||||||||
\(591\) | 3.70820 | 0.152535 | ||||||||
\(592\) | −23.1246 | −0.950416 | ||||||||
\(593\) | −40.1803 | −1.65001 | −0.825004 | − | 0.565126i | \(-0.808827\pi\) | ||||
−0.825004 | + | 0.565126i | \(0.808827\pi\) | |||||||
\(594\) | 3.61803 | 0.148450 | ||||||||
\(595\) | 41.1246 | 1.68594 | ||||||||
\(596\) | 3.41641 | 0.139942 | ||||||||
\(597\) | 20.1246 | 0.823646 | ||||||||
\(598\) | 2.00000 | 0.0817861 | ||||||||
\(599\) | 1.76393 | 0.0720723 | 0.0360362 | − | 0.999350i | \(-0.488527\pi\) | ||||
0.0360362 | + | 0.999350i | \(0.488527\pi\) | |||||||
\(600\) | 12.2361 | 0.499535 | ||||||||
\(601\) | 18.5410 | 0.756304 | 0.378152 | − | 0.925744i | \(-0.376560\pi\) | ||||
0.378152 | + | 0.925744i | \(0.376560\pi\) | |||||||
\(602\) | −3.23607 | −0.131892 | ||||||||
\(603\) | −4.70820 | −0.191733 | ||||||||
\(604\) | −7.41641 | −0.301769 | ||||||||
\(605\) | 19.4164 | 0.789389 | ||||||||
\(606\) | −6.38197 | −0.259250 | ||||||||
\(607\) | 25.4164 | 1.03162 | 0.515810 | − | 0.856703i | \(-0.327491\pi\) | ||||
0.515810 | + | 0.856703i | \(0.327491\pi\) | |||||||
\(608\) | 26.0689 | 1.05723 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.4721 | 0.585960 | ||||||||
\(611\) | −10.2361 | −0.414107 | ||||||||
\(612\) | 1.85410 | 0.0749476 | ||||||||
\(613\) | 24.4164 | 0.986169 | 0.493085 | − | 0.869981i | \(-0.335869\pi\) | ||||
0.493085 | + | 0.869981i | \(0.335869\pi\) | |||||||
\(614\) | −45.5967 | −1.84013 | ||||||||
\(615\) | −14.4721 | −0.583573 | ||||||||
\(616\) | −21.1803 | −0.853380 | ||||||||
\(617\) | 19.8885 | 0.800683 | 0.400341 | − | 0.916366i | \(-0.368892\pi\) | ||||
0.400341 | + | 0.916366i | \(0.368892\pi\) | |||||||
\(618\) | 31.4164 | 1.26375 | ||||||||
\(619\) | −32.5410 | −1.30793 | −0.653967 | − | 0.756523i | \(-0.726896\pi\) | ||||
−0.653967 | + | 0.756523i | \(0.726896\pi\) | |||||||
\(620\) | −14.4721 | −0.581215 | ||||||||
\(621\) | −1.23607 | −0.0496017 | ||||||||
\(622\) | 25.3262 | 1.01549 | ||||||||
\(623\) | −0.236068 | −0.00945786 | ||||||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −8.85410 | −0.353881 | ||||||||
\(627\) | −17.2361 | −0.688342 | ||||||||
\(628\) | 1.23607 | 0.0493245 | ||||||||
\(629\) | 14.2918 | 0.569851 | ||||||||
\(630\) | 22.1803 | 0.883686 | ||||||||
\(631\) | −28.7082 | −1.14286 | −0.571428 | − | 0.820652i | \(-0.693610\pi\) | ||||
−0.571428 | + | 0.820652i | \(0.693610\pi\) | |||||||
\(632\) | −5.12461 | −0.203846 | ||||||||
\(633\) | −10.0000 | −0.397464 | ||||||||
\(634\) | 38.5623 | 1.53150 | ||||||||
\(635\) | −40.3607 | −1.60166 | ||||||||
\(636\) | −4.18034 | −0.165761 | ||||||||
\(637\) | 10.9443 | 0.433628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.76393 | −0.188458 | ||||||||
\(640\) | −44.0689 | −1.74198 | ||||||||
\(641\) | 19.4721 | 0.769103 | 0.384552 | − | 0.923104i | \(-0.374356\pi\) | ||||
0.384552 | + | 0.923104i | \(0.374356\pi\) | |||||||
\(642\) | −1.23607 | −0.0487837 | ||||||||
\(643\) | −0.708204 | −0.0279288 | −0.0139644 | − | 0.999902i | \(-0.504445\pi\) | ||||
−0.0139644 | + | 0.999902i | \(0.504445\pi\) | |||||||
\(644\) | −3.23607 | −0.127519 | ||||||||
\(645\) | 1.52786 | 0.0601596 | ||||||||
\(646\) | −37.4164 | −1.47213 | ||||||||
\(647\) | −17.5967 | −0.691800 | −0.345900 | − | 0.938271i | \(-0.612426\pi\) | ||||
−0.345900 | + | 0.938271i | \(0.612426\pi\) | |||||||
\(648\) | −2.23607 | −0.0878410 | ||||||||
\(649\) | −20.0000 | −0.785069 | ||||||||
\(650\) | 8.85410 | 0.347286 | ||||||||
\(651\) | 30.6525 | 1.20137 | ||||||||
\(652\) | 4.58359 | 0.179507 | ||||||||
\(653\) | −32.3050 | −1.26419 | −0.632095 | − | 0.774891i | \(-0.717805\pi\) | ||||
−0.632095 | + | 0.774891i | \(0.717805\pi\) | |||||||
\(654\) | 8.09017 | 0.316351 | ||||||||
\(655\) | −39.5967 | −1.54717 | ||||||||
\(656\) | 21.7082 | 0.847563 | ||||||||
\(657\) | −7.70820 | −0.300726 | ||||||||
\(658\) | 70.1591 | 2.73508 | ||||||||
\(659\) | 26.2361 | 1.02201 | 0.511006 | − | 0.859577i | \(-0.329273\pi\) | ||||
0.511006 | + | 0.859577i | \(0.329273\pi\) | |||||||
\(660\) | −4.47214 | −0.174078 | ||||||||
\(661\) | −29.8328 | −1.16036 | −0.580181 | − | 0.814488i | \(-0.697018\pi\) | ||||
−0.580181 | + | 0.814488i | \(0.697018\pi\) | |||||||
\(662\) | −13.4164 | −0.521443 | ||||||||
\(663\) | −3.00000 | −0.116510 | ||||||||
\(664\) | 13.4164 | 0.520658 | ||||||||
\(665\) | −105.666 | −4.09754 | ||||||||
\(666\) | 7.70820 | 0.298687 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.81966 | −0.379934 | ||||||||
\(669\) | 12.7082 | 0.491328 | ||||||||
\(670\) | 24.6525 | 0.952408 | ||||||||
\(671\) | 6.18034 | 0.238589 | ||||||||
\(672\) | −14.3262 | −0.552647 | ||||||||
\(673\) | 4.41641 | 0.170240 | 0.0851200 | − | 0.996371i | \(-0.472873\pi\) | ||||
0.0851200 | + | 0.996371i | \(0.472873\pi\) | |||||||
\(674\) | 31.1246 | 1.19888 | ||||||||
\(675\) | −5.47214 | −0.210623 | ||||||||
\(676\) | −7.41641 | −0.285246 | ||||||||
\(677\) | 18.0557 | 0.693938 | 0.346969 | − | 0.937877i | \(-0.387211\pi\) | ||||
0.346969 | + | 0.937877i | \(0.387211\pi\) | |||||||
\(678\) | −7.32624 | −0.281362 | ||||||||
\(679\) | −77.0132 | −2.95549 | ||||||||
\(680\) | 21.7082 | 0.832472 | ||||||||
\(681\) | −9.05573 | −0.347016 | ||||||||
\(682\) | −26.1803 | −1.00250 | ||||||||
\(683\) | 32.9443 | 1.26058 | 0.630289 | − | 0.776361i | \(-0.282936\pi\) | ||||
0.630289 | + | 0.776361i | \(0.282936\pi\) | |||||||
\(684\) | −4.76393 | −0.182153 | ||||||||
\(685\) | −11.4164 | −0.436199 | ||||||||
\(686\) | −27.0344 | −1.03218 | ||||||||
\(687\) | −22.1803 | −0.846233 | ||||||||
\(688\) | −2.29180 | −0.0873739 | ||||||||
\(689\) | 6.76393 | 0.257685 | ||||||||
\(690\) | 6.47214 | 0.246390 | ||||||||
\(691\) | −30.2361 | −1.15023 | −0.575117 | − | 0.818071i | \(-0.695044\pi\) | ||||
−0.575117 | + | 0.818071i | \(0.695044\pi\) | |||||||
\(692\) | 3.70820 | 0.140965 | ||||||||
\(693\) | 9.47214 | 0.359817 | ||||||||
\(694\) | 36.6525 | 1.39131 | ||||||||
\(695\) | 21.7082 | 0.823439 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.4164 | −0.508183 | ||||||||
\(698\) | 16.1803 | 0.612435 | ||||||||
\(699\) | 10.4721 | 0.396093 | ||||||||
\(700\) | −14.3262 | −0.541481 | ||||||||
\(701\) | −8.18034 | −0.308967 | −0.154484 | − | 0.987995i | \(-0.549371\pi\) | ||||
−0.154484 | + | 0.987995i | \(0.549371\pi\) | |||||||
\(702\) | −1.61803 | −0.0610688 | ||||||||
\(703\) | −36.7214 | −1.38497 | ||||||||
\(704\) | −9.47214 | −0.356995 | ||||||||
\(705\) | −33.1246 | −1.24755 | ||||||||
\(706\) | −7.52786 | −0.283315 | ||||||||
\(707\) | −16.7082 | −0.628377 | ||||||||
\(708\) | −5.52786 | −0.207750 | ||||||||
\(709\) | 13.4164 | 0.503864 | 0.251932 | − | 0.967745i | \(-0.418934\pi\) | ||||
0.251932 | + | 0.967745i | \(0.418934\pi\) | |||||||
\(710\) | 24.9443 | 0.936142 | ||||||||
\(711\) | 2.29180 | 0.0859491 | ||||||||
\(712\) | −0.124612 | −0.00467002 | ||||||||
\(713\) | 8.94427 | 0.334966 | ||||||||
\(714\) | 20.5623 | 0.769525 | ||||||||
\(715\) | 7.23607 | 0.270614 | ||||||||
\(716\) | 10.6525 | 0.398102 | ||||||||
\(717\) | −26.1803 | −0.977723 | ||||||||
\(718\) | 40.9443 | 1.52803 | ||||||||
\(719\) | −30.0000 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(720\) | 15.7082 | 0.585410 | ||||||||
\(721\) | 82.2492 | 3.06312 | ||||||||
\(722\) | 65.3951 | 2.43375 | ||||||||
\(723\) | −3.00000 | −0.111571 | ||||||||
\(724\) | 12.6180 | 0.468946 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.70820 | 0.360305 | ||||||||
\(727\) | −5.81966 | −0.215839 | −0.107920 | − | 0.994160i | \(-0.534419\pi\) | ||||
−0.107920 | + | 0.994160i | \(0.534419\pi\) | |||||||
\(728\) | 9.47214 | 0.351061 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 40.3607 | 1.49382 | ||||||||
\(731\) | 1.41641 | 0.0523877 | ||||||||
\(732\) | 1.70820 | 0.0631370 | ||||||||
\(733\) | 8.47214 | 0.312925 | 0.156463 | − | 0.987684i | \(-0.449991\pi\) | ||||
0.156463 | + | 0.987684i | \(0.449991\pi\) | |||||||
\(734\) | 29.1246 | 1.07501 | ||||||||
\(735\) | 35.4164 | 1.30635 | ||||||||
\(736\) | −4.18034 | −0.154089 | ||||||||
\(737\) | 10.5279 | 0.387799 | ||||||||
\(738\) | −7.23607 | −0.266363 | ||||||||
\(739\) | −12.1803 | −0.448061 | −0.224031 | − | 0.974582i | \(-0.571922\pi\) | ||||
−0.224031 | + | 0.974582i | \(0.571922\pi\) | |||||||
\(740\) | −9.52786 | −0.350251 | ||||||||
\(741\) | 7.70820 | 0.283168 | ||||||||
\(742\) | −46.3607 | −1.70195 | ||||||||
\(743\) | 43.0689 | 1.58004 | 0.790022 | − | 0.613078i | \(-0.210069\pi\) | ||||
0.790022 | + | 0.613078i | \(0.210069\pi\) | |||||||
\(744\) | 16.1803 | 0.593200 | ||||||||
\(745\) | −17.8885 | −0.655386 | ||||||||
\(746\) | −6.29180 | −0.230359 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | −4.14590 | −0.151589 | ||||||||
\(749\) | −3.23607 | −0.118243 | ||||||||
\(750\) | 2.47214 | 0.0902696 | ||||||||
\(751\) | 26.8328 | 0.979143 | 0.489572 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489572 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(752\) | 49.6869 | 1.81190 | ||||||||
\(753\) | −12.2361 | −0.445907 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.8328 | 1.41327 | ||||||||
\(756\) | 2.61803 | 0.0952170 | ||||||||
\(757\) | 38.0000 | 1.38113 | 0.690567 | − | 0.723269i | \(-0.257361\pi\) | ||||
0.690567 | + | 0.723269i | \(0.257361\pi\) | |||||||
\(758\) | −23.1246 | −0.839924 | ||||||||
\(759\) | 2.76393 | 0.100324 | ||||||||
\(760\) | −55.7771 | −2.02325 | ||||||||
\(761\) | 2.65248 | 0.0961522 | 0.0480761 | − | 0.998844i | \(-0.484691\pi\) | ||||
0.0480761 | + | 0.998844i | \(0.484691\pi\) | |||||||
\(762\) | −20.1803 | −0.731057 | ||||||||
\(763\) | 21.1803 | 0.766780 | ||||||||
\(764\) | −5.52786 | −0.199991 | ||||||||
\(765\) | −9.70820 | −0.351001 | ||||||||
\(766\) | 8.65248 | 0.312627 | ||||||||
\(767\) | 8.94427 | 0.322959 | ||||||||
\(768\) | −13.5623 | −0.489388 | ||||||||
\(769\) | −40.1803 | −1.44894 | −0.724470 | − | 0.689306i | \(-0.757915\pi\) | ||||
−0.724470 | + | 0.689306i | \(0.757915\pi\) | |||||||
\(770\) | −49.5967 | −1.78734 | ||||||||
\(771\) | 26.4721 | 0.953371 | ||||||||
\(772\) | −10.7639 | −0.387402 | ||||||||
\(773\) | −31.8885 | −1.14695 | −0.573476 | − | 0.819223i | \(-0.694405\pi\) | ||||
−0.573476 | + | 0.819223i | \(0.694405\pi\) | |||||||
\(774\) | 0.763932 | 0.0274590 | ||||||||
\(775\) | 39.5967 | 1.42236 | ||||||||
\(776\) | −40.6525 | −1.45934 | ||||||||
\(777\) | 20.1803 | 0.723966 | ||||||||
\(778\) | −21.7984 | −0.781510 | ||||||||
\(779\) | 34.4721 | 1.23509 | ||||||||
\(780\) | 2.00000 | 0.0716115 | ||||||||
\(781\) | 10.6525 | 0.381176 | ||||||||
\(782\) | 6.00000 | 0.214560 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −53.1246 | −1.89731 | ||||||||
\(785\) | −6.47214 | −0.231000 | ||||||||
\(786\) | −19.7984 | −0.706185 | ||||||||
\(787\) | 12.0000 | 0.427754 | 0.213877 | − | 0.976861i | \(-0.431391\pi\) | ||||
0.213877 | + | 0.976861i | \(0.431391\pi\) | |||||||
\(788\) | −2.29180 | −0.0816419 | ||||||||
\(789\) | −4.94427 | −0.176021 | ||||||||
\(790\) | −12.0000 | −0.426941 | ||||||||
\(791\) | −19.1803 | −0.681974 | ||||||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | −2.76393 | −0.0981501 | ||||||||
\(794\) | 11.2361 | 0.398753 | ||||||||
\(795\) | 21.8885 | 0.776307 | ||||||||
\(796\) | −12.4377 | −0.440842 | ||||||||
\(797\) | 44.8328 | 1.58806 | 0.794030 | − | 0.607879i | \(-0.207979\pi\) | ||||
0.794030 | + | 0.607879i | \(0.207979\pi\) | |||||||
\(798\) | −52.8328 | −1.87026 | ||||||||
\(799\) | −30.7082 | −1.08638 | ||||||||
\(800\) | −18.5066 | −0.654306 | ||||||||
\(801\) | 0.0557281 | 0.00196906 | ||||||||
\(802\) | 54.5410 | 1.92591 | ||||||||
\(803\) | 17.2361 | 0.608248 | ||||||||
\(804\) | 2.90983 | 0.102622 | ||||||||
\(805\) | 16.9443 | 0.597207 | ||||||||
\(806\) | 11.7082 | 0.412404 | ||||||||
\(807\) | 21.3607 | 0.751932 | ||||||||
\(808\) | −8.81966 | −0.310275 | ||||||||
\(809\) | 43.3607 | 1.52448 | 0.762240 | − | 0.647294i | \(-0.224100\pi\) | ||||
0.762240 | + | 0.647294i | \(0.224100\pi\) | |||||||
\(810\) | −5.23607 | −0.183977 | ||||||||
\(811\) | −46.5967 | −1.63623 | −0.818117 | − | 0.575052i | \(-0.804982\pi\) | ||||
−0.818117 | + | 0.575052i | \(0.804982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.4164 | 0.821249 | ||||||||
\(814\) | −17.2361 | −0.604124 | ||||||||
\(815\) | −24.0000 | −0.840683 | ||||||||
\(816\) | 14.5623 | 0.509783 | ||||||||
\(817\) | −3.63932 | −0.127324 | ||||||||
\(818\) | 17.1246 | 0.598748 | ||||||||
\(819\) | −4.23607 | −0.148020 | ||||||||
\(820\) | 8.94427 | 0.312348 | ||||||||
\(821\) | 12.4721 | 0.435281 | 0.217640 | − | 0.976029i | \(-0.430164\pi\) | ||||
0.217640 | + | 0.976029i | \(0.430164\pi\) | |||||||
\(822\) | −5.70820 | −0.199096 | ||||||||
\(823\) | −26.3607 | −0.918876 | −0.459438 | − | 0.888210i | \(-0.651949\pi\) | ||||
−0.459438 | + | 0.888210i | \(0.651949\pi\) | |||||||
\(824\) | 43.4164 | 1.51248 | ||||||||
\(825\) | 12.2361 | 0.426005 | ||||||||
\(826\) | −61.3050 | −2.13307 | ||||||||
\(827\) | 29.8885 | 1.03933 | 0.519663 | − | 0.854371i | \(-0.326057\pi\) | ||||
0.519663 | + | 0.854371i | \(0.326057\pi\) | |||||||
\(828\) | 0.763932 | 0.0265485 | ||||||||
\(829\) | −27.3050 | −0.948340 | −0.474170 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474170 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(830\) | 31.4164 | 1.09048 | ||||||||
\(831\) | −6.41641 | −0.222583 | ||||||||
\(832\) | 4.23607 | 0.146859 | ||||||||
\(833\) | 32.8328 | 1.13759 | ||||||||
\(834\) | 10.8541 | 0.375847 | ||||||||
\(835\) | 51.4164 | 1.77934 | ||||||||
\(836\) | 10.6525 | 0.368424 | ||||||||
\(837\) | −7.23607 | −0.250115 | ||||||||
\(838\) | −6.18034 | −0.213496 | ||||||||
\(839\) | −0.708204 | −0.0244499 | −0.0122250 | − | 0.999925i | \(-0.503891\pi\) | ||||
−0.0122250 | + | 0.999925i | \(0.503891\pi\) | |||||||
\(840\) | 30.6525 | 1.05761 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 32.3607 | 1.11522 | ||||||||
\(843\) | 1.41641 | 0.0487837 | ||||||||
\(844\) | 6.18034 | 0.212736 | ||||||||
\(845\) | 38.8328 | 1.33589 | ||||||||
\(846\) | −16.5623 | −0.569424 | ||||||||
\(847\) | 25.4164 | 0.873318 | ||||||||
\(848\) | −32.8328 | −1.12748 | ||||||||
\(849\) | −13.8885 | −0.476654 | ||||||||
\(850\) | 26.5623 | 0.911080 | ||||||||
\(851\) | 5.88854 | 0.201857 | ||||||||
\(852\) | 2.94427 | 0.100869 | ||||||||
\(853\) | −45.1935 | −1.54740 | −0.773698 | − | 0.633555i | \(-0.781595\pi\) | ||||
−0.773698 | + | 0.633555i | \(0.781595\pi\) | |||||||
\(854\) | 18.9443 | 0.648260 | ||||||||
\(855\) | 24.9443 | 0.853076 | ||||||||
\(856\) | −1.70820 | −0.0583852 | ||||||||
\(857\) | 37.5967 | 1.28428 | 0.642140 | − | 0.766587i | \(-0.278047\pi\) | ||||
0.642140 | + | 0.766587i | \(0.278047\pi\) | |||||||
\(858\) | 3.61803 | 0.123518 | ||||||||
\(859\) | −36.3607 | −1.24061 | −0.620305 | − | 0.784361i | \(-0.712991\pi\) | ||||
−0.620305 | + | 0.784361i | \(0.712991\pi\) | |||||||
\(860\) | −0.944272 | −0.0321994 | ||||||||
\(861\) | −18.9443 | −0.645619 | ||||||||
\(862\) | 23.2361 | 0.791424 | ||||||||
\(863\) | 46.6525 | 1.58807 | 0.794034 | − | 0.607873i | \(-0.207977\pi\) | ||||
0.794034 | + | 0.607873i | \(0.207977\pi\) | |||||||
\(864\) | 3.38197 | 0.115057 | ||||||||
\(865\) | −19.4164 | −0.660178 | ||||||||
\(866\) | −23.1246 | −0.785806 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | −18.9443 | −0.643010 | ||||||||
\(869\) | −5.12461 | −0.173841 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.70820 | −0.159531 | ||||||||
\(872\) | 11.1803 | 0.378614 | ||||||||
\(873\) | 18.1803 | 0.615311 | ||||||||
\(874\) | −15.4164 | −0.521468 | ||||||||
\(875\) | 6.47214 | 0.218798 | ||||||||
\(876\) | 4.76393 | 0.160958 | ||||||||
\(877\) | 32.4721 | 1.09651 | 0.548253 | − | 0.836312i | \(-0.315293\pi\) | ||||
0.548253 | + | 0.836312i | \(0.315293\pi\) | |||||||
\(878\) | −21.5066 | −0.725812 | ||||||||
\(879\) | −29.9443 | −1.01000 | ||||||||
\(880\) | −35.1246 | −1.18405 | ||||||||
\(881\) | 55.2492 | 1.86139 | 0.930697 | − | 0.365792i | \(-0.119202\pi\) | ||||
0.930697 | + | 0.365792i | \(0.119202\pi\) | |||||||
\(882\) | 17.7082 | 0.596266 | ||||||||
\(883\) | −34.2492 | −1.15258 | −0.576289 | − | 0.817246i | \(-0.695500\pi\) | ||||
−0.576289 | + | 0.817246i | \(0.695500\pi\) | |||||||
\(884\) | 1.85410 | 0.0623602 | ||||||||
\(885\) | 28.9443 | 0.972951 | ||||||||
\(886\) | 15.6180 | 0.524698 | ||||||||
\(887\) | 17.0689 | 0.573117 | 0.286559 | − | 0.958063i | \(-0.407489\pi\) | ||||
0.286559 | + | 0.958063i | \(0.407489\pi\) | |||||||
\(888\) | 10.6525 | 0.357474 | ||||||||
\(889\) | −52.8328 | −1.77196 | ||||||||
\(890\) | −0.291796 | −0.00978103 | ||||||||
\(891\) | −2.23607 | −0.0749111 | ||||||||
\(892\) | −7.85410 | −0.262975 | ||||||||
\(893\) | 78.9017 | 2.64034 | ||||||||
\(894\) | −8.94427 | −0.299141 | ||||||||
\(895\) | −55.7771 | −1.86442 | ||||||||
\(896\) | −57.6869 | −1.92718 | ||||||||
\(897\) | −1.23607 | −0.0412711 | ||||||||
\(898\) | −30.5623 | −1.01988 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 3.38197 | 0.112732 | ||||||||
\(901\) | 20.2918 | 0.676018 | ||||||||
\(902\) | 16.1803 | 0.538746 | ||||||||
\(903\) | 2.00000 | 0.0665558 | ||||||||
\(904\) | −10.1246 | −0.336740 | ||||||||
\(905\) | −66.0689 | −2.19620 | ||||||||
\(906\) | 19.4164 | 0.645067 | ||||||||
\(907\) | 26.4721 | 0.878993 | 0.439496 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439496 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(908\) | 5.59675 | 0.185735 | ||||||||
\(909\) | 3.94427 | 0.130823 | ||||||||
\(910\) | 22.1803 | 0.735271 | ||||||||
\(911\) | −51.1803 | −1.69568 | −0.847840 | − | 0.530252i | \(-0.822097\pi\) | ||||
−0.847840 | + | 0.530252i | \(0.822097\pi\) | |||||||
\(912\) | −37.4164 | −1.23898 | ||||||||
\(913\) | 13.4164 | 0.444018 | ||||||||
\(914\) | −10.3820 | −0.343405 | ||||||||
\(915\) | −8.94427 | −0.295689 | ||||||||
\(916\) | 13.7082 | 0.452932 | ||||||||
\(917\) | −51.8328 | −1.71167 | ||||||||
\(918\) | −4.85410 | −0.160209 | ||||||||
\(919\) | −25.6525 | −0.846197 | −0.423099 | − | 0.906084i | \(-0.639058\pi\) | ||||
−0.423099 | + | 0.906084i | \(0.639058\pi\) | |||||||
\(920\) | 8.94427 | 0.294884 | ||||||||
\(921\) | 28.1803 | 0.928574 | ||||||||
\(922\) | −30.6525 | −1.00949 | ||||||||
\(923\) | −4.76393 | −0.156807 | ||||||||
\(924\) | −5.85410 | −0.192586 | ||||||||
\(925\) | 26.0689 | 0.857140 | ||||||||
\(926\) | −1.14590 | −0.0376565 | ||||||||
\(927\) | −19.4164 | −0.637719 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.3607 | −1.06172 | −0.530860 | − | 0.847460i | \(-0.678131\pi\) | ||||
−0.530860 | + | 0.847460i | \(0.678131\pi\) | |||||||
\(930\) | 37.8885 | 1.24241 | ||||||||
\(931\) | −84.3607 | −2.76481 | ||||||||
\(932\) | −6.47214 | −0.212002 | ||||||||
\(933\) | −15.6525 | −0.512439 | ||||||||
\(934\) | 21.8885 | 0.716215 | ||||||||
\(935\) | 21.7082 | 0.709934 | ||||||||
\(936\) | −2.23607 | −0.0730882 | ||||||||
\(937\) | −33.0000 | −1.07806 | −0.539032 | − | 0.842286i | \(-0.681210\pi\) | ||||
−0.539032 | + | 0.842286i | \(0.681210\pi\) | |||||||
\(938\) | 32.2705 | 1.05367 | ||||||||
\(939\) | 5.47214 | 0.178576 | ||||||||
\(940\) | 20.4721 | 0.667727 | ||||||||
\(941\) | 44.8328 | 1.46151 | 0.730754 | − | 0.682641i | \(-0.239169\pi\) | ||||
0.730754 | + | 0.682641i | \(0.239169\pi\) | |||||||
\(942\) | −3.23607 | −0.105437 | ||||||||
\(943\) | −5.52786 | −0.180012 | ||||||||
\(944\) | −43.4164 | −1.41308 | ||||||||
\(945\) | −13.7082 | −0.445928 | ||||||||
\(946\) | −1.70820 | −0.0555385 | ||||||||
\(947\) | 16.8197 | 0.546566 | 0.273283 | − | 0.961934i | \(-0.411891\pi\) | ||||
0.273283 | + | 0.961934i | \(0.411891\pi\) | |||||||
\(948\) | −1.41641 | −0.0460028 | ||||||||
\(949\) | −7.70820 | −0.250219 | ||||||||
\(950\) | −68.2492 | −2.21430 | ||||||||
\(951\) | −23.8328 | −0.772832 | ||||||||
\(952\) | 28.4164 | 0.920981 | ||||||||
\(953\) | −59.6656 | −1.93276 | −0.966380 | − | 0.257119i | \(-0.917227\pi\) | ||||
−0.966380 | + | 0.257119i | \(0.917227\pi\) | |||||||
\(954\) | 10.9443 | 0.354334 | ||||||||
\(955\) | 28.9443 | 0.936615 | ||||||||
\(956\) | 16.1803 | 0.523310 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.9443 | 0.547445 | ||||||||
\(959\) | −14.9443 | −0.482576 | ||||||||
\(960\) | 13.7082 | 0.442430 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | 7.70820 | 0.248522 | ||||||||
\(963\) | 0.763932 | 0.0246174 | ||||||||
\(964\) | 1.85410 | 0.0597166 | ||||||||
\(965\) | 56.3607 | 1.81431 | ||||||||
\(966\) | 8.47214 | 0.272587 | ||||||||
\(967\) | 27.1246 | 0.872269 | 0.436134 | − | 0.899882i | \(-0.356347\pi\) | ||||
0.436134 | + | 0.899882i | \(0.356347\pi\) | |||||||
\(968\) | 13.4164 | 0.431220 | ||||||||
\(969\) | 23.1246 | 0.742870 | ||||||||
\(970\) | −95.1935 | −3.05648 | ||||||||
\(971\) | −16.5836 | −0.532193 | −0.266096 | − | 0.963946i | \(-0.585734\pi\) | ||||
−0.266096 | + | 0.963946i | \(0.585734\pi\) | |||||||
\(972\) | −0.618034 | −0.0198234 | ||||||||
\(973\) | 28.4164 | 0.910988 | ||||||||
\(974\) | 32.9443 | 1.05560 | ||||||||
\(975\) | −5.47214 | −0.175249 | ||||||||
\(976\) | 13.4164 | 0.429449 | ||||||||
\(977\) | 51.0132 | 1.63206 | 0.816028 | − | 0.578013i | \(-0.196172\pi\) | ||||
0.816028 | + | 0.578013i | \(0.196172\pi\) | |||||||
\(978\) | −12.0000 | −0.383718 | ||||||||
\(979\) | −0.124612 | −0.00398261 | ||||||||
\(980\) | −21.8885 | −0.699204 | ||||||||
\(981\) | −5.00000 | −0.159638 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8885 | −0.442976 | −0.221488 | − | 0.975163i | \(-0.571091\pi\) | ||||
−0.221488 | + | 0.975163i | \(0.571091\pi\) | |||||||
\(984\) | −10.0000 | −0.318788 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.3607 | −1.38019 | ||||||||
\(988\) | −4.76393 | −0.151561 | ||||||||
\(989\) | 0.583592 | 0.0185572 | ||||||||
\(990\) | 11.7082 | 0.372111 | ||||||||
\(991\) | 21.2918 | 0.676356 | 0.338178 | − | 0.941082i | \(-0.390189\pi\) | ||||
0.338178 | + | 0.941082i | \(0.390189\pi\) | |||||||
\(992\) | −24.4721 | −0.776991 | ||||||||
\(993\) | 8.29180 | 0.263132 | ||||||||
\(994\) | 32.6525 | 1.03567 | ||||||||
\(995\) | 65.1246 | 2.06459 | ||||||||
\(996\) | 3.70820 | 0.117499 | ||||||||
\(997\) | 24.5836 | 0.778570 | 0.389285 | − | 0.921117i | \(-0.372722\pi\) | ||||
0.389285 | + | 0.921117i | \(0.372722\pi\) | |||||||
\(998\) | −34.2705 | −1.08481 | ||||||||
\(999\) | −4.76393 | −0.150724 |
(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 | 2523.2.a.e.1.2 | 2 | ||
3.2 | odd | 2 | 7569.2.a.f.1.1 | 2 | |||
29.12 | odd | 4 | 87.2.c.a.28.4 | yes | 4 | ||
29.17 | odd | 4 | 87.2.c.a.28.1 | ✓ | 4 | ||
29.28 | even | 2 | 2523.2.a.d.1.1 | 2 | |||
87.17 | even | 4 | 261.2.c.b.28.4 | 4 | |||
87.41 | even | 4 | 261.2.c.b.28.1 | 4 | |||
87.86 | odd | 2 | 7569.2.a.n.1.2 | 2 | |||
116.75 | even | 4 | 1392.2.o.i.289.2 | 4 | |||
116.99 | even | 4 | 1392.2.o.i.289.4 | 4 | |||
145.12 | even | 4 | 2175.2.f.a.724.1 | 4 | |||
145.17 | even | 4 | 2175.2.f.b.724.3 | 4 | |||
145.99 | odd | 4 | 2175.2.d.e.376.1 | 4 | |||
145.104 | odd | 4 | 2175.2.d.e.376.4 | 4 | |||
145.128 | even | 4 | 2175.2.f.b.724.4 | 4 | |||
145.133 | even | 4 | 2175.2.f.a.724.2 | 4 | |||
348.191 | odd | 4 | 4176.2.o.l.289.2 | 4 | |||
348.215 | odd | 4 | 4176.2.o.l.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
87.2.c.a.28.1 | ✓ | 4 | 29.17 | odd | 4 | ||
87.2.c.a.28.4 | yes | 4 | 29.12 | odd | 4 | ||
261.2.c.b.28.1 | 4 | 87.41 | even | 4 | |||
261.2.c.b.28.4 | 4 | 87.17 | even | 4 | |||
1392.2.o.i.289.2 | 4 | 116.75 | even | 4 | |||
1392.2.o.i.289.4 | 4 | 116.99 | even | 4 | |||
2175.2.d.e.376.1 | 4 | 145.99 | odd | 4 | |||
2175.2.d.e.376.4 | 4 | 145.104 | odd | 4 | |||
2175.2.f.a.724.1 | 4 | 145.12 | even | 4 | |||
2175.2.f.a.724.2 | 4 | 145.133 | even | 4 | |||
2175.2.f.b.724.3 | 4 | 145.17 | even | 4 | |||
2175.2.f.b.724.4 | 4 | 145.128 | even | 4 | |||
2523.2.a.d.1.1 | 2 | 29.28 | even | 2 | |||
2523.2.a.e.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4176.2.o.l.289.1 | 4 | 348.215 | odd | 4 | |||
4176.2.o.l.289.2 | 4 | 348.191 | odd | 4 | |||
7569.2.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
7569.2.a.n.1.2 | 2 | 87.86 | odd | 2 |