Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-2.27289\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.27289 | 1.60718 | 0.803589 | − | 0.595185i | \(-0.202921\pi\) | ||||
0.803589 | + | 0.595185i | \(0.202921\pi\) | |||||||
\(3\) | −1.88926 | −1.09076 | −0.545382 | − | 0.838187i | \(-0.683616\pi\) | ||||
−0.545382 | + | 0.838187i | \(0.683616\pi\) | |||||||
\(4\) | 3.16604 | 1.58302 | ||||||||
\(5\) | −1.72209 | −0.770143 | −0.385071 | − | 0.922887i | \(-0.625823\pi\) | ||||
−0.385071 | + | 0.922887i | \(0.625823\pi\) | |||||||
\(6\) | −4.29408 | −1.75305 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.65028 | 0.937015 | ||||||||
\(9\) | 0.569302 | 0.189767 | ||||||||
\(10\) | −3.91413 | −1.23776 | ||||||||
\(11\) | −2.87184 | −0.865892 | −0.432946 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432946 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(12\) | −5.98147 | −1.72670 | ||||||||
\(13\) | 1.56496 | 0.434043 | 0.217021 | − | 0.976167i | \(-0.430366\pi\) | ||||
0.217021 | + | 0.976167i | \(0.430366\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.25348 | 0.840044 | ||||||||
\(16\) | −0.308281 | −0.0770702 | ||||||||
\(17\) | −5.43502 | −1.31819 | −0.659094 | − | 0.752061i | \(-0.729060\pi\) | ||||
−0.659094 | + | 0.752061i | \(0.729060\pi\) | |||||||
\(18\) | 1.29396 | 0.304990 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −5.45221 | −1.21915 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.52738 | −1.39164 | ||||||||
\(23\) | −6.09715 | −1.27134 | −0.635672 | − | 0.771959i | \(-0.719277\pi\) | ||||
−0.635672 | + | 0.771959i | \(0.719277\pi\) | |||||||
\(24\) | −5.00706 | −1.02206 | ||||||||
\(25\) | −2.03440 | −0.406880 | ||||||||
\(26\) | 3.55699 | 0.697583 | ||||||||
\(27\) | 4.59222 | 0.883773 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17391 | 0.589380 | 0.294690 | − | 0.955593i | \(-0.404784\pi\) | ||||
0.294690 | + | 0.955593i | \(0.404784\pi\) | |||||||
\(30\) | 7.39480 | 1.35010 | ||||||||
\(31\) | 1.03449 | 0.185800 | 0.0929000 | − | 0.995675i | \(-0.470386\pi\) | ||||
0.0929000 | + | 0.995675i | \(0.470386\pi\) | |||||||
\(32\) | −6.00124 | −1.06088 | ||||||||
\(33\) | 5.42565 | 0.944484 | ||||||||
\(34\) | −12.3532 | −2.11856 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.80243 | 0.300405 | ||||||||
\(37\) | 8.44727 | 1.38872 | 0.694361 | − | 0.719626i | \(-0.255687\pi\) | ||||
0.694361 | + | 0.719626i | \(0.255687\pi\) | |||||||
\(38\) | −2.27289 | −0.368712 | ||||||||
\(39\) | −2.95662 | −0.473438 | ||||||||
\(40\) | −4.56402 | −0.721635 | ||||||||
\(41\) | −10.4075 | −1.62538 | −0.812691 | − | 0.582694i | \(-0.801999\pi\) | ||||
−0.812691 | + | 0.582694i | \(0.801999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.21975 | −0.491008 | −0.245504 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245504 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(44\) | −9.09235 | −1.37072 | ||||||||
\(45\) | −0.980390 | −0.146148 | ||||||||
\(46\) | −13.8582 | −2.04327 | ||||||||
\(47\) | 5.50514 | 0.803008 | 0.401504 | − | 0.915857i | \(-0.368488\pi\) | ||||
0.401504 | + | 0.915857i | \(0.368488\pi\) | |||||||
\(48\) | 0.582422 | 0.0840654 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.62398 | −0.653929 | ||||||||
\(51\) | 10.2682 | 1.43783 | ||||||||
\(52\) | 4.95473 | 0.687097 | ||||||||
\(53\) | −12.9804 | −1.78299 | −0.891495 | − | 0.453030i | \(-0.850343\pi\) | ||||
−0.891495 | + | 0.453030i | \(0.850343\pi\) | |||||||
\(54\) | 10.4376 | 1.42038 | ||||||||
\(55\) | 4.94557 | 0.666860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.88926 | 0.250239 | ||||||||
\(58\) | 7.21396 | 0.947239 | ||||||||
\(59\) | 6.21573 | 0.809219 | 0.404609 | − | 0.914490i | \(-0.367407\pi\) | ||||
0.404609 | + | 0.914490i | \(0.367407\pi\) | |||||||
\(60\) | 10.3006 | 1.32981 | ||||||||
\(61\) | −9.76784 | −1.25064 | −0.625322 | − | 0.780367i | \(-0.715032\pi\) | ||||
−0.625322 | + | 0.780367i | \(0.715032\pi\) | |||||||
\(62\) | 2.35128 | 0.298613 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −13.0236 | −1.62795 | ||||||||
\(65\) | −2.69501 | −0.334275 | ||||||||
\(66\) | 12.3319 | 1.51795 | ||||||||
\(67\) | −2.55851 | −0.312572 | −0.156286 | − | 0.987712i | \(-0.549952\pi\) | ||||
−0.156286 | + | 0.987712i | \(0.549952\pi\) | |||||||
\(68\) | −17.2075 | −2.08672 | ||||||||
\(69\) | 11.5191 | 1.38674 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3595 | 1.46681 | 0.733404 | − | 0.679793i | \(-0.237930\pi\) | ||||
0.733404 | + | 0.679793i | \(0.237930\pi\) | |||||||
\(72\) | 1.50881 | 0.177815 | ||||||||
\(73\) | 10.5517 | 1.23498 | 0.617491 | − | 0.786578i | \(-0.288149\pi\) | ||||
0.617491 | + | 0.786578i | \(0.288149\pi\) | |||||||
\(74\) | 19.1997 | 2.23192 | ||||||||
\(75\) | 3.84351 | 0.443811 | ||||||||
\(76\) | −3.16604 | −0.363169 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.72008 | −0.760899 | ||||||||
\(79\) | 12.9952 | 1.46208 | 0.731040 | − | 0.682335i | \(-0.239035\pi\) | ||||
0.731040 | + | 0.682335i | \(0.239035\pi\) | |||||||
\(80\) | 0.530887 | 0.0593550 | ||||||||
\(81\) | −10.3838 | −1.15376 | ||||||||
\(82\) | −23.6552 | −2.61228 | ||||||||
\(83\) | −5.38474 | −0.591052 | −0.295526 | − | 0.955335i | \(-0.595495\pi\) | ||||
−0.295526 | + | 0.955335i | \(0.595495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.35961 | 1.01519 | ||||||||
\(86\) | −7.31815 | −0.789136 | ||||||||
\(87\) | −5.99634 | −0.642875 | ||||||||
\(88\) | −7.61117 | −0.811354 | ||||||||
\(89\) | −7.45375 | −0.790096 | −0.395048 | − | 0.918661i | \(-0.629272\pi\) | ||||
−0.395048 | + | 0.918661i | \(0.629272\pi\) | |||||||
\(90\) | −2.22832 | −0.234886 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −19.3038 | −2.01256 | ||||||||
\(93\) | −1.95442 | −0.202664 | ||||||||
\(94\) | 12.5126 | 1.29058 | ||||||||
\(95\) | 1.72209 | 0.176683 | ||||||||
\(96\) | 11.3379 | 1.15717 | ||||||||
\(97\) | 2.45162 | 0.248925 | 0.124462 | − | 0.992224i | \(-0.460279\pi\) | ||||
0.124462 | + | 0.992224i | \(0.460279\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63494 | −0.164318 | ||||||||
\(100\) | −6.44099 | −0.644099 | ||||||||
\(101\) | 1.46770 | 0.146041 | 0.0730207 | − | 0.997330i | \(-0.476736\pi\) | ||||
0.0730207 | + | 0.997330i | \(0.476736\pi\) | |||||||
\(102\) | 23.3384 | 2.31085 | ||||||||
\(103\) | 11.2451 | 1.10802 | 0.554008 | − | 0.832511i | \(-0.313098\pi\) | ||||
0.554008 | + | 0.832511i | \(0.313098\pi\) | |||||||
\(104\) | 4.14759 | 0.406704 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.5030 | −2.86558 | ||||||||
\(107\) | −0.243353 | −0.0235258 | −0.0117629 | − | 0.999931i | \(-0.503744\pi\) | ||||
−0.0117629 | + | 0.999931i | \(0.503744\pi\) | |||||||
\(108\) | 14.5391 | 1.39903 | ||||||||
\(109\) | 16.1331 | 1.54527 | 0.772636 | − | 0.634849i | \(-0.218938\pi\) | ||||
0.772636 | + | 0.634849i | \(0.218938\pi\) | |||||||
\(110\) | 11.2407 | 1.07176 | ||||||||
\(111\) | −15.9591 | −1.51477 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0613 | 1.60499 | 0.802495 | − | 0.596659i | \(-0.203505\pi\) | ||||
0.802495 | + | 0.596659i | \(0.203505\pi\) | |||||||
\(114\) | 4.29408 | 0.402178 | ||||||||
\(115\) | 10.4998 | 0.979116 | ||||||||
\(116\) | 10.0487 | 0.933000 | ||||||||
\(117\) | 0.890937 | 0.0823671 | ||||||||
\(118\) | 14.1277 | 1.30056 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 8.62262 | 0.787134 | ||||||||
\(121\) | −2.75254 | −0.250231 | ||||||||
\(122\) | −22.2013 | −2.01001 | ||||||||
\(123\) | 19.6625 | 1.77291 | ||||||||
\(124\) | 3.27524 | 0.294125 | ||||||||
\(125\) | 12.1139 | 1.08350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.51261 | −0.311693 | −0.155847 | − | 0.987781i | \(-0.549811\pi\) | ||||
−0.155847 | + | 0.987781i | \(0.549811\pi\) | |||||||
\(128\) | −17.5988 | −1.55553 | ||||||||
\(129\) | 6.08295 | 0.535574 | ||||||||
\(130\) | −6.12546 | −0.537239 | ||||||||
\(131\) | −9.87558 | −0.862834 | −0.431417 | − | 0.902153i | \(-0.641986\pi\) | ||||
−0.431417 | + | 0.902153i | \(0.641986\pi\) | |||||||
\(132\) | 17.1778 | 1.49514 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.81521 | −0.502358 | ||||||||
\(135\) | −7.90822 | −0.680631 | ||||||||
\(136\) | −14.4043 | −1.23516 | ||||||||
\(137\) | 0.428635 | 0.0366207 | 0.0183104 | − | 0.999832i | \(-0.494171\pi\) | ||||
0.0183104 | + | 0.999832i | \(0.494171\pi\) | |||||||
\(138\) | 26.1817 | 2.22873 | ||||||||
\(139\) | −20.1401 | −1.70826 | −0.854130 | − | 0.520059i | \(-0.825910\pi\) | ||||
−0.854130 | + | 0.520059i | \(0.825910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4006 | −0.875892 | ||||||||
\(142\) | 28.0919 | 2.35742 | ||||||||
\(143\) | −4.49432 | −0.375834 | ||||||||
\(144\) | −0.175505 | −0.0146254 | ||||||||
\(145\) | −5.46576 | −0.453907 | ||||||||
\(146\) | 23.9829 | 1.98484 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 26.7444 | 2.19837 | ||||||||
\(149\) | −9.30332 | −0.762158 | −0.381079 | − | 0.924543i | \(-0.624447\pi\) | ||||
−0.381079 | + | 0.924543i | \(0.624447\pi\) | |||||||
\(150\) | 8.73589 | 0.713282 | ||||||||
\(151\) | −13.1140 | −1.06720 | −0.533602 | − | 0.845735i | \(-0.679162\pi\) | ||||
−0.533602 | + | 0.845735i | \(0.679162\pi\) | |||||||
\(152\) | −2.65028 | −0.214966 | ||||||||
\(153\) | −3.09417 | −0.250149 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.78149 | −0.143092 | ||||||||
\(156\) | −9.36077 | −0.749462 | ||||||||
\(157\) | −16.6033 | −1.32509 | −0.662543 | − | 0.749024i | \(-0.730523\pi\) | ||||
−0.662543 | + | 0.749024i | \(0.730523\pi\) | |||||||
\(158\) | 29.5368 | 2.34982 | ||||||||
\(159\) | 24.5233 | 1.94482 | ||||||||
\(160\) | 10.3347 | 0.817029 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −23.6013 | −1.85429 | ||||||||
\(163\) | −4.67202 | −0.365941 | −0.182970 | − | 0.983118i | \(-0.558571\pi\) | ||||
−0.182970 | + | 0.983118i | \(0.558571\pi\) | |||||||
\(164\) | −32.9506 | −2.57301 | ||||||||
\(165\) | −9.34346 | −0.727388 | ||||||||
\(166\) | −12.2389 | −0.949926 | ||||||||
\(167\) | −3.21131 | −0.248499 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5509 | −0.811607 | ||||||||
\(170\) | 21.2734 | 1.63159 | ||||||||
\(171\) | −0.569302 | −0.0435356 | ||||||||
\(172\) | −10.1939 | −0.777274 | ||||||||
\(173\) | −7.38250 | −0.561281 | −0.280641 | − | 0.959813i | \(-0.590547\pi\) | ||||
−0.280641 | + | 0.959813i | \(0.590547\pi\) | |||||||
\(174\) | −13.6290 | −1.03321 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.885332 | 0.0667344 | ||||||||
\(177\) | −11.7431 | −0.882667 | ||||||||
\(178\) | −16.9416 | −1.26982 | ||||||||
\(179\) | −26.1139 | −1.95185 | −0.975924 | − | 0.218111i | \(-0.930010\pi\) | ||||
−0.975924 | + | 0.218111i | \(0.930010\pi\) | |||||||
\(180\) | −3.10395 | −0.231355 | ||||||||
\(181\) | 3.30215 | 0.245447 | 0.122723 | − | 0.992441i | \(-0.460837\pi\) | ||||
0.122723 | + | 0.992441i | \(0.460837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.4540 | 1.36416 | ||||||||
\(184\) | −16.1591 | −1.19127 | ||||||||
\(185\) | −14.5470 | −1.06951 | ||||||||
\(186\) | −4.44219 | −0.325717 | ||||||||
\(187\) | 15.6085 | 1.14141 | ||||||||
\(188\) | 17.4295 | 1.27118 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.91413 | 0.283961 | ||||||||
\(191\) | 7.00807 | 0.507086 | 0.253543 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253543 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(192\) | 24.6050 | 1.77571 | ||||||||
\(193\) | 6.61313 | 0.476024 | 0.238012 | − | 0.971262i | \(-0.423504\pi\) | ||||
0.238012 | + | 0.971262i | \(0.423504\pi\) | |||||||
\(194\) | 5.57227 | 0.400066 | ||||||||
\(195\) | 5.09157 | 0.364615 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.23496 | −0.372976 | −0.186488 | − | 0.982457i | \(-0.559710\pi\) | ||||
−0.186488 | + | 0.982457i | \(0.559710\pi\) | |||||||
\(198\) | −3.71605 | −0.264088 | ||||||||
\(199\) | 13.3552 | 0.946724 | 0.473362 | − | 0.880868i | \(-0.343040\pi\) | ||||
0.473362 | + | 0.880868i | \(0.343040\pi\) | |||||||
\(200\) | −5.39173 | −0.381253 | ||||||||
\(201\) | 4.83369 | 0.340942 | ||||||||
\(202\) | 3.33592 | 0.234714 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 32.5094 | 2.27611 | ||||||||
\(205\) | 17.9227 | 1.25178 | ||||||||
\(206\) | 25.5590 | 1.78078 | ||||||||
\(207\) | −3.47112 | −0.241260 | ||||||||
\(208\) | −0.482448 | −0.0334517 | ||||||||
\(209\) | 2.87184 | 0.198649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1468 | 0.905061 | 0.452531 | − | 0.891749i | \(-0.350521\pi\) | ||||
0.452531 | + | 0.891749i | \(0.350521\pi\) | |||||||
\(212\) | −41.0963 | −2.82251 | ||||||||
\(213\) | −23.3504 | −1.59994 | ||||||||
\(214\) | −0.553114 | −0.0378101 | ||||||||
\(215\) | 5.54471 | 0.378146 | ||||||||
\(216\) | 12.1707 | 0.828108 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 36.6688 | 2.48353 | ||||||||
\(219\) | −19.9349 | −1.34707 | ||||||||
\(220\) | 15.6579 | 1.05565 | ||||||||
\(221\) | −8.50561 | −0.572149 | ||||||||
\(222\) | −36.2733 | −2.43450 | ||||||||
\(223\) | −11.1267 | −0.745099 | −0.372549 | − | 0.928012i | \(-0.621516\pi\) | ||||
−0.372549 | + | 0.928012i | \(0.621516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.15819 | −0.0772126 | ||||||||
\(226\) | 38.7784 | 2.57950 | ||||||||
\(227\) | 25.2738 | 1.67748 | 0.838740 | − | 0.544532i | \(-0.183293\pi\) | ||||
0.838740 | + | 0.544532i | \(0.183293\pi\) | |||||||
\(228\) | 5.98147 | 0.396132 | ||||||||
\(229\) | 4.09982 | 0.270923 | 0.135462 | − | 0.990783i | \(-0.456748\pi\) | ||||
0.135462 | + | 0.990783i | \(0.456748\pi\) | |||||||
\(230\) | 23.8650 | 1.57361 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.41175 | 0.552258 | ||||||||
\(233\) | −28.7409 | −1.88288 | −0.941439 | − | 0.337183i | \(-0.890526\pi\) | ||||
−0.941439 | + | 0.337183i | \(0.890526\pi\) | |||||||
\(234\) | 2.02500 | 0.132379 | ||||||||
\(235\) | −9.48036 | −0.618430 | ||||||||
\(236\) | 19.6792 | 1.28101 | ||||||||
\(237\) | −24.5514 | −1.59478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1082 | 0.847900 | 0.423950 | − | 0.905686i | \(-0.360643\pi\) | ||||
0.423950 | + | 0.905686i | \(0.360643\pi\) | |||||||
\(240\) | −1.00298 | −0.0647423 | ||||||||
\(241\) | 0.00249380 | 0.000160640 0 | 8.03200e−5 | − | 1.00000i | \(-0.499974\pi\) | ||||
8.03200e−5 | 1.00000i | \(0.499974\pi\) | ||||||||
\(242\) | −6.25623 | −0.402165 | ||||||||
\(243\) | 5.84104 | 0.374703 | ||||||||
\(244\) | −30.9254 | −1.97979 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 44.6908 | 2.84938 | ||||||||
\(247\) | −1.56496 | −0.0995762 | ||||||||
\(248\) | 2.74169 | 0.174097 | ||||||||
\(249\) | 10.1732 | 0.644699 | ||||||||
\(250\) | 27.5335 | 1.74137 | ||||||||
\(251\) | −13.5644 | −0.856175 | −0.428087 | − | 0.903737i | \(-0.640812\pi\) | ||||
−0.428087 | + | 0.903737i | \(0.640812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.5100 | 1.10085 | ||||||||
\(254\) | −7.98377 | −0.500947 | ||||||||
\(255\) | −17.6827 | −1.10734 | ||||||||
\(256\) | −13.9529 | −0.872057 | ||||||||
\(257\) | −25.9001 | −1.61560 | −0.807801 | − | 0.589456i | \(-0.799342\pi\) | ||||
−0.807801 | + | 0.589456i | \(0.799342\pi\) | |||||||
\(258\) | 13.8259 | 0.860762 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.53250 | −0.529163 | ||||||||
\(261\) | 1.80691 | 0.111845 | ||||||||
\(262\) | −22.4461 | −1.38673 | ||||||||
\(263\) | 19.2508 | 1.18705 | 0.593526 | − | 0.804814i | \(-0.297735\pi\) | ||||
0.593526 | + | 0.804814i | \(0.297735\pi\) | |||||||
\(264\) | 14.3795 | 0.884996 | ||||||||
\(265\) | 22.3534 | 1.37316 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.0821 | 0.861809 | ||||||||
\(268\) | −8.10033 | −0.494807 | ||||||||
\(269\) | −19.2999 | −1.17673 | −0.588367 | − | 0.808594i | \(-0.700229\pi\) | ||||
−0.588367 | + | 0.808594i | \(0.700229\pi\) | |||||||
\(270\) | −17.9745 | −1.09390 | ||||||||
\(271\) | 18.4313 | 1.11962 | 0.559812 | − | 0.828620i | \(-0.310874\pi\) | ||||
0.559812 | + | 0.828620i | \(0.310874\pi\) | |||||||
\(272\) | 1.67551 | 0.101593 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.974241 | 0.0588560 | ||||||||
\(275\) | 5.84247 | 0.352314 | ||||||||
\(276\) | 36.4699 | 2.19523 | ||||||||
\(277\) | −15.7856 | −0.948463 | −0.474231 | − | 0.880400i | \(-0.657274\pi\) | ||||
−0.474231 | + | 0.880400i | \(0.657274\pi\) | |||||||
\(278\) | −45.7763 | −2.74548 | ||||||||
\(279\) | 0.588938 | 0.0352588 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.2255 | −1.44517 | −0.722587 | − | 0.691280i | \(-0.757047\pi\) | ||||
−0.722587 | + | 0.691280i | \(0.757047\pi\) | |||||||
\(282\) | −23.6395 | −1.40771 | ||||||||
\(283\) | −7.99693 | −0.475368 | −0.237684 | − | 0.971343i | \(-0.576388\pi\) | ||||
−0.237684 | + | 0.971343i | \(0.576388\pi\) | |||||||
\(284\) | 39.1308 | 2.32198 | ||||||||
\(285\) | −3.25348 | −0.192719 | ||||||||
\(286\) | −10.2151 | −0.604032 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.41652 | −0.201320 | ||||||||
\(289\) | 12.5395 | 0.737617 | ||||||||
\(290\) | −12.4231 | −0.729509 | ||||||||
\(291\) | −4.63175 | −0.271518 | ||||||||
\(292\) | 33.4071 | 1.95500 | ||||||||
\(293\) | 17.3236 | 1.01206 | 0.506028 | − | 0.862517i | \(-0.331113\pi\) | ||||
0.506028 | + | 0.862517i | \(0.331113\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7040 | −0.623214 | ||||||||
\(296\) | 22.3876 | 1.30125 | ||||||||
\(297\) | −13.1881 | −0.765252 | ||||||||
\(298\) | −21.1454 | −1.22492 | ||||||||
\(299\) | −9.54181 | −0.551817 | ||||||||
\(300\) | 12.1687 | 0.702561 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −29.8068 | −1.71519 | ||||||||
\(303\) | −2.77286 | −0.159297 | ||||||||
\(304\) | 0.308281 | 0.0176811 | ||||||||
\(305\) | 16.8211 | 0.963174 | ||||||||
\(306\) | −7.03272 | −0.402034 | ||||||||
\(307\) | −5.30000 | −0.302487 | −0.151244 | − | 0.988497i | \(-0.548328\pi\) | ||||
−0.151244 | + | 0.988497i | \(0.548328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.2450 | −1.20859 | ||||||||
\(310\) | −4.04913 | −0.229975 | ||||||||
\(311\) | −6.02144 | −0.341444 | −0.170722 | − | 0.985319i | \(-0.554610\pi\) | ||||
−0.170722 | + | 0.985319i | \(0.554610\pi\) | |||||||
\(312\) | −7.83587 | −0.443619 | ||||||||
\(313\) | −17.5310 | −0.990908 | −0.495454 | − | 0.868634i | \(-0.664998\pi\) | ||||
−0.495454 | + | 0.868634i | \(0.664998\pi\) | |||||||
\(314\) | −37.7374 | −2.12965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 41.1434 | 2.31450 | ||||||||
\(317\) | −20.3083 | −1.14063 | −0.570313 | − | 0.821427i | \(-0.693178\pi\) | ||||
−0.570313 | + | 0.821427i | \(0.693178\pi\) | |||||||
\(318\) | 55.7388 | 3.12568 | ||||||||
\(319\) | −9.11496 | −0.510340 | ||||||||
\(320\) | 22.4279 | 1.25376 | ||||||||
\(321\) | 0.459756 | 0.0256611 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.43502 | 0.302413 | ||||||||
\(324\) | −32.8755 | −1.82642 | ||||||||
\(325\) | −3.18376 | −0.176603 | ||||||||
\(326\) | −10.6190 | −0.588132 | ||||||||
\(327\) | −30.4796 | −1.68553 | ||||||||
\(328\) | −27.5828 | −1.52301 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −21.2367 | −1.16904 | ||||||||
\(331\) | −13.9894 | −0.768929 | −0.384464 | − | 0.923140i | \(-0.625614\pi\) | ||||
−0.384464 | + | 0.923140i | \(0.625614\pi\) | |||||||
\(332\) | −17.0483 | −0.935647 | ||||||||
\(333\) | 4.80905 | 0.263534 | ||||||||
\(334\) | −7.29897 | −0.399382 | ||||||||
\(335\) | 4.40598 | 0.240725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.6696 | −1.39831 | −0.699157 | − | 0.714969i | \(-0.746441\pi\) | ||||
−0.699157 | + | 0.714969i | \(0.746441\pi\) | |||||||
\(338\) | −23.9810 | −1.30440 | ||||||||
\(339\) | −32.2332 | −1.75067 | ||||||||
\(340\) | 29.6329 | 1.60707 | ||||||||
\(341\) | −2.97089 | −0.160883 | ||||||||
\(342\) | −1.29396 | −0.0699695 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.53324 | −0.460081 | ||||||||
\(345\) | −19.8369 | −1.06798 | ||||||||
\(346\) | −16.7796 | −0.902078 | ||||||||
\(347\) | 26.5340 | 1.42442 | 0.712210 | − | 0.701966i | \(-0.247694\pi\) | ||||
0.712210 | + | 0.701966i | \(0.247694\pi\) | |||||||
\(348\) | −18.9846 | −1.01768 | ||||||||
\(349\) | −32.7352 | −1.75228 | −0.876139 | − | 0.482059i | \(-0.839889\pi\) | ||||
−0.876139 | + | 0.482059i | \(0.839889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.18665 | 0.383595 | ||||||||
\(352\) | 17.2346 | 0.918608 | ||||||||
\(353\) | 6.36333 | 0.338686 | 0.169343 | − | 0.985557i | \(-0.445835\pi\) | ||||
0.169343 | + | 0.985557i | \(0.445835\pi\) | |||||||
\(354\) | −26.6909 | −1.41860 | ||||||||
\(355\) | −21.2843 | −1.12965 | ||||||||
\(356\) | −23.5989 | −1.25074 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −59.3542 | −3.13697 | ||||||||
\(359\) | 17.9081 | 0.945152 | 0.472576 | − | 0.881290i | \(-0.343324\pi\) | ||||
0.472576 | + | 0.881290i | \(0.343324\pi\) | |||||||
\(360\) | −2.59831 | −0.136943 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 7.50543 | 0.394477 | ||||||||
\(363\) | 5.20026 | 0.272943 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.1710 | −0.951113 | ||||||||
\(366\) | 41.9439 | 2.19244 | ||||||||
\(367\) | 18.9798 | 0.990736 | 0.495368 | − | 0.868683i | \(-0.335033\pi\) | ||||
0.495368 | + | 0.868683i | \(0.335033\pi\) | |||||||
\(368\) | 1.87963 | 0.0979826 | ||||||||
\(369\) | −5.92503 | −0.308445 | ||||||||
\(370\) | −33.0637 | −1.71890 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.18777 | −0.320821 | ||||||||
\(373\) | 1.89525 | 0.0981321 | 0.0490660 | − | 0.998796i | \(-0.484376\pi\) | ||||
0.0490660 | + | 0.998796i | \(0.484376\pi\) | |||||||
\(374\) | 35.4765 | 1.83444 | ||||||||
\(375\) | −22.8863 | −1.18184 | ||||||||
\(376\) | 14.5902 | 0.752430 | ||||||||
\(377\) | 4.96705 | 0.255816 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8480 | −0.916790 | −0.458395 | − | 0.888748i | \(-0.651576\pi\) | ||||
−0.458395 | + | 0.888748i | \(0.651576\pi\) | |||||||
\(380\) | 5.45221 | 0.279692 | ||||||||
\(381\) | 6.63623 | 0.339984 | ||||||||
\(382\) | 15.9286 | 0.814977 | ||||||||
\(383\) | 24.9132 | 1.27301 | 0.636503 | − | 0.771274i | \(-0.280380\pi\) | ||||
0.636503 | + | 0.771274i | \(0.280380\pi\) | |||||||
\(384\) | 33.2487 | 1.69671 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.0309 | 0.765054 | ||||||||
\(387\) | −1.83301 | −0.0931773 | ||||||||
\(388\) | 7.76193 | 0.394052 | ||||||||
\(389\) | 20.4631 | 1.03752 | 0.518760 | − | 0.854920i | \(-0.326394\pi\) | ||||
0.518760 | + | 0.854920i | \(0.326394\pi\) | |||||||
\(390\) | 11.5726 | 0.586001 | ||||||||
\(391\) | 33.1382 | 1.67587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.6575 | 0.941149 | ||||||||
\(394\) | −11.8985 | −0.599438 | ||||||||
\(395\) | −22.3790 | −1.12601 | ||||||||
\(396\) | −5.17630 | −0.260119 | ||||||||
\(397\) | −34.7628 | −1.74469 | −0.872347 | − | 0.488888i | \(-0.837403\pi\) | ||||
−0.872347 | + | 0.488888i | \(0.837403\pi\) | |||||||
\(398\) | 30.3549 | 1.52155 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.627167 | 0.0313583 | ||||||||
\(401\) | 21.9956 | 1.09841 | 0.549205 | − | 0.835688i | \(-0.314931\pi\) | ||||
0.549205 | + | 0.835688i | \(0.314931\pi\) | |||||||
\(402\) | 10.9864 | 0.547954 | ||||||||
\(403\) | 1.61894 | 0.0806451 | ||||||||
\(404\) | 4.64679 | 0.231186 | ||||||||
\(405\) | 17.8819 | 0.888556 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.2592 | −1.20248 | ||||||||
\(408\) | 27.2135 | 1.34727 | ||||||||
\(409\) | −3.51585 | −0.173847 | −0.0869237 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869237 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(410\) | 40.7364 | 2.01183 | ||||||||
\(411\) | −0.809802 | −0.0399446 | ||||||||
\(412\) | 35.6025 | 1.75401 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.88948 | −0.387747 | ||||||||
\(415\) | 9.27302 | 0.455194 | ||||||||
\(416\) | −9.39172 | −0.460467 | ||||||||
\(417\) | 38.0499 | 1.86331 | ||||||||
\(418\) | 6.52738 | 0.319265 | ||||||||
\(419\) | −38.5514 | −1.88336 | −0.941679 | − | 0.336514i | \(-0.890752\pi\) | ||||
−0.941679 | + | 0.336514i | \(0.890752\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.44685 | −0.411674 | −0.205837 | − | 0.978586i | \(-0.565992\pi\) | ||||
−0.205837 | + | 0.978586i | \(0.565992\pi\) | |||||||
\(422\) | 29.8812 | 1.45459 | ||||||||
\(423\) | 3.13409 | 0.152385 | ||||||||
\(424\) | −34.4016 | −1.67069 | ||||||||
\(425\) | 11.0570 | 0.536344 | ||||||||
\(426\) | −53.0729 | −2.57139 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.770463 | −0.0372418 | ||||||||
\(429\) | 8.49094 | 0.409946 | ||||||||
\(430\) | 12.6025 | 0.607748 | ||||||||
\(431\) | −3.55584 | −0.171279 | −0.0856394 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856394 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(432\) | −1.41569 | −0.0681125 | ||||||||
\(433\) | −1.09300 | −0.0525264 | −0.0262632 | − | 0.999655i | \(-0.508361\pi\) | ||||
−0.0262632 | + | 0.999655i | \(0.508361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3262 | 0.495106 | ||||||||
\(436\) | 51.0781 | 2.44620 | ||||||||
\(437\) | 6.09715 | 0.291666 | ||||||||
\(438\) | −45.3098 | −2.16499 | ||||||||
\(439\) | 8.19098 | 0.390934 | 0.195467 | − | 0.980710i | \(-0.437378\pi\) | ||||
0.195467 | + | 0.980710i | \(0.437378\pi\) | |||||||
\(440\) | 13.1071 | 0.624858 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.3323 | −0.919545 | ||||||||
\(443\) | 10.2973 | 0.489239 | 0.244620 | − | 0.969619i | \(-0.421337\pi\) | ||||
0.244620 | + | 0.969619i | \(0.421337\pi\) | |||||||
\(444\) | −50.5271 | −2.39791 | ||||||||
\(445\) | 12.8360 | 0.608486 | ||||||||
\(446\) | −25.2898 | −1.19751 | ||||||||
\(447\) | 17.5764 | 0.831335 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0244 | 1.03940 | 0.519699 | − | 0.854350i | \(-0.326044\pi\) | ||||
0.519699 | + | 0.854350i | \(0.326044\pi\) | |||||||
\(450\) | −2.63244 | −0.124094 | ||||||||
\(451\) | 29.8887 | 1.40741 | ||||||||
\(452\) | 54.0166 | 2.54073 | ||||||||
\(453\) | 24.7758 | 1.16407 | ||||||||
\(454\) | 57.4446 | 2.69601 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.00706 | 0.234477 | ||||||||
\(457\) | −11.7275 | −0.548591 | −0.274296 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274296 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(458\) | 9.31844 | 0.435422 | ||||||||
\(459\) | −24.9588 | −1.16498 | ||||||||
\(460\) | 33.2429 | 1.54996 | ||||||||
\(461\) | 19.1133 | 0.890194 | 0.445097 | − | 0.895482i | \(-0.353169\pi\) | ||||
0.445097 | + | 0.895482i | \(0.353169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.75469 | 0.174495 | 0.0872475 | − | 0.996187i | \(-0.472193\pi\) | ||||
0.0872475 | + | 0.996187i | \(0.472193\pi\) | |||||||
\(464\) | −0.978455 | −0.0454236 | ||||||||
\(465\) | 3.36569 | 0.156080 | ||||||||
\(466\) | −65.3249 | −3.02612 | ||||||||
\(467\) | −3.15207 | −0.145860 | −0.0729302 | − | 0.997337i | \(-0.523235\pi\) | ||||
−0.0729302 | + | 0.997337i | \(0.523235\pi\) | |||||||
\(468\) | 2.82074 | 0.130389 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −21.5478 | −0.993927 | ||||||||
\(471\) | 31.3679 | 1.44536 | ||||||||
\(472\) | 16.4734 | 0.758250 | ||||||||
\(473\) | 9.24661 | 0.425160 | ||||||||
\(474\) | −55.8027 | −2.56310 | ||||||||
\(475\) | 2.03440 | 0.0933448 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.38975 | −0.338354 | ||||||||
\(478\) | 29.7936 | 1.36273 | ||||||||
\(479\) | −6.14080 | −0.280580 | −0.140290 | − | 0.990110i | \(-0.544804\pi\) | ||||
−0.140290 | + | 0.990110i | \(0.544804\pi\) | |||||||
\(480\) | −19.5249 | −0.891186 | ||||||||
\(481\) | 13.2197 | 0.602765 | ||||||||
\(482\) | 0.00566815 | 0.000258177 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.71465 | −0.396120 | ||||||||
\(485\) | −4.22192 | −0.191707 | ||||||||
\(486\) | 13.2761 | 0.602214 | ||||||||
\(487\) | 40.4699 | 1.83387 | 0.916934 | − | 0.399038i | \(-0.130656\pi\) | ||||
0.916934 | + | 0.399038i | \(0.130656\pi\) | |||||||
\(488\) | −25.8875 | −1.17187 | ||||||||
\(489\) | 8.82666 | 0.399155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0490 | −0.814538 | −0.407269 | − | 0.913308i | \(-0.633519\pi\) | ||||
−0.407269 | + | 0.913308i | \(0.633519\pi\) | |||||||
\(492\) | 62.2523 | 2.80655 | ||||||||
\(493\) | −17.2503 | −0.776914 | ||||||||
\(494\) | −3.55699 | −0.160037 | ||||||||
\(495\) | 2.81552 | 0.126548 | ||||||||
\(496\) | −0.318913 | −0.0143196 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 23.1225 | 1.03615 | ||||||||
\(499\) | −35.5880 | −1.59314 | −0.796569 | − | 0.604548i | \(-0.793354\pi\) | ||||
−0.796569 | + | 0.604548i | \(0.793354\pi\) | |||||||
\(500\) | 38.3530 | 1.71520 | ||||||||
\(501\) | 6.06700 | 0.271054 | ||||||||
\(502\) | −30.8303 | −1.37602 | ||||||||
\(503\) | 27.3502 | 1.21949 | 0.609744 | − | 0.792599i | \(-0.291272\pi\) | ||||
0.609744 | + | 0.792599i | \(0.291272\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.52751 | −0.112473 | ||||||||
\(506\) | 39.7984 | 1.76926 | ||||||||
\(507\) | 19.9334 | 0.885272 | ||||||||
\(508\) | −11.1210 | −0.493417 | ||||||||
\(509\) | −41.1163 | −1.82245 | −0.911225 | − | 0.411909i | \(-0.864862\pi\) | ||||
−0.911225 | + | 0.411909i | \(0.864862\pi\) | |||||||
\(510\) | −40.1909 | −1.77968 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.48413 | 0.153978 | ||||||||
\(513\) | −4.59222 | −0.202751 | ||||||||
\(514\) | −58.8680 | −2.59656 | ||||||||
\(515\) | −19.3652 | −0.853331 | ||||||||
\(516\) | 19.2588 | 0.847823 | ||||||||
\(517\) | −15.8099 | −0.695318 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9475 | 0.612226 | ||||||||
\(520\) | −7.14252 | −0.313220 | ||||||||
\(521\) | 12.8696 | 0.563828 | 0.281914 | − | 0.959440i | \(-0.409031\pi\) | ||||
0.281914 | + | 0.959440i | \(0.409031\pi\) | |||||||
\(522\) | 4.10692 | 0.179755 | ||||||||
\(523\) | 14.5744 | 0.637294 | 0.318647 | − | 0.947873i | \(-0.396772\pi\) | ||||
0.318647 | + | 0.947873i | \(0.396772\pi\) | |||||||
\(524\) | −31.2665 | −1.36588 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.7549 | 1.90780 | ||||||||
\(527\) | −5.62248 | −0.244919 | ||||||||
\(528\) | −1.67262 | −0.0727916 | ||||||||
\(529\) | 14.1752 | 0.616315 | ||||||||
\(530\) | 50.8068 | 2.20691 | ||||||||
\(531\) | 3.53863 | 0.153563 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.2874 | −0.705485 | ||||||||
\(534\) | 32.0070 | 1.38508 | ||||||||
\(535\) | 0.419075 | 0.0181182 | ||||||||
\(536\) | −6.78076 | −0.292884 | ||||||||
\(537\) | 49.3360 | 2.12901 | ||||||||
\(538\) | −43.8665 | −1.89122 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −25.0377 | −1.07745 | ||||||||
\(541\) | −17.5194 | −0.753219 | −0.376609 | − | 0.926372i | \(-0.622910\pi\) | ||||
−0.376609 | + | 0.926372i | \(0.622910\pi\) | |||||||
\(542\) | 41.8924 | 1.79943 | ||||||||
\(543\) | −6.23862 | −0.267725 | ||||||||
\(544\) | 32.6169 | 1.39844 | ||||||||
\(545\) | −27.7827 | −1.19008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.50159 | −0.0642032 | −0.0321016 | − | 0.999485i | \(-0.510220\pi\) | ||||
−0.0321016 | + | 0.999485i | \(0.510220\pi\) | |||||||
\(548\) | 1.35707 | 0.0579713 | ||||||||
\(549\) | −5.56086 | −0.237332 | ||||||||
\(550\) | 13.2793 | 0.566232 | ||||||||
\(551\) | −3.17391 | −0.135213 | ||||||||
\(552\) | 30.5288 | 1.29939 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35.8789 | −1.52435 | ||||||||
\(555\) | 27.4830 | 1.16659 | ||||||||
\(556\) | −63.7643 | −2.70421 | ||||||||
\(557\) | −29.5856 | −1.25358 | −0.626790 | − | 0.779188i | \(-0.715632\pi\) | ||||
−0.626790 | + | 0.779188i | \(0.715632\pi\) | |||||||
\(558\) | 1.33859 | 0.0566671 | ||||||||
\(559\) | −5.03879 | −0.213118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.4885 | −1.24501 | ||||||||
\(562\) | −55.0620 | −2.32265 | ||||||||
\(563\) | 5.40462 | 0.227778 | 0.113889 | − | 0.993493i | \(-0.463669\pi\) | ||||
0.113889 | + | 0.993493i | \(0.463669\pi\) | |||||||
\(564\) | −32.9288 | −1.38655 | ||||||||
\(565\) | −29.3811 | −1.23607 | ||||||||
\(566\) | −18.1762 | −0.764001 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 32.7562 | 1.37442 | ||||||||
\(569\) | 14.9850 | 0.628205 | 0.314102 | − | 0.949389i | \(-0.398296\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398296\pi\) | |||||||
\(570\) | −7.39480 | −0.309734 | ||||||||
\(571\) | 30.1295 | 1.26088 | 0.630441 | − | 0.776237i | \(-0.282874\pi\) | ||||
0.630441 | + | 0.776237i | \(0.282874\pi\) | |||||||
\(572\) | −14.2292 | −0.594952 | ||||||||
\(573\) | −13.2401 | −0.553111 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.4041 | 0.517285 | ||||||||
\(576\) | −7.41438 | −0.308932 | ||||||||
\(577\) | 22.0535 | 0.918101 | 0.459050 | − | 0.888410i | \(-0.348190\pi\) | ||||
0.459050 | + | 0.888410i | \(0.348190\pi\) | |||||||
\(578\) | 28.5009 | 1.18548 | ||||||||
\(579\) | −12.4939 | −0.519230 | ||||||||
\(580\) | −17.3048 | −0.718543 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −10.5275 | −0.436378 | ||||||||
\(583\) | 37.2775 | 1.54388 | ||||||||
\(584\) | 27.9649 | 1.15720 | ||||||||
\(585\) | −1.53427 | −0.0634344 | ||||||||
\(586\) | 39.3747 | 1.62655 | ||||||||
\(587\) | −23.6848 | −0.977575 | −0.488788 | − | 0.872403i | \(-0.662561\pi\) | ||||
−0.488788 | + | 0.872403i | \(0.662561\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03449 | −0.0426254 | ||||||||
\(590\) | −24.3291 | −1.00162 | ||||||||
\(591\) | 9.89020 | 0.406829 | ||||||||
\(592\) | −2.60413 | −0.107029 | ||||||||
\(593\) | 28.5028 | 1.17047 | 0.585235 | − | 0.810864i | \(-0.301002\pi\) | ||||
0.585235 | + | 0.810864i | \(0.301002\pi\) | |||||||
\(594\) | −29.9752 | −1.22990 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.4547 | −1.20651 | ||||||||
\(597\) | −25.2314 | −1.03265 | ||||||||
\(598\) | −21.6875 | −0.886868 | ||||||||
\(599\) | 4.10267 | 0.167630 | 0.0838152 | − | 0.996481i | \(-0.473289\pi\) | ||||
0.0838152 | + | 0.996481i | \(0.473289\pi\) | |||||||
\(600\) | 10.1864 | 0.415857 | ||||||||
\(601\) | −10.6311 | −0.433651 | −0.216825 | − | 0.976210i | \(-0.569570\pi\) | ||||
−0.216825 | + | 0.976210i | \(0.569570\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.45656 | −0.0593159 | ||||||||
\(604\) | −41.5195 | −1.68941 | ||||||||
\(605\) | 4.74012 | 0.192713 | ||||||||
\(606\) | −6.30242 | −0.256018 | ||||||||
\(607\) | −28.7604 | −1.16735 | −0.583674 | − | 0.811988i | \(-0.698385\pi\) | ||||
−0.583674 | + | 0.811988i | \(0.698385\pi\) | |||||||
\(608\) | 6.00124 | 0.243383 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 38.2326 | 1.54799 | ||||||||
\(611\) | 8.61534 | 0.348539 | ||||||||
\(612\) | −9.79627 | −0.395991 | ||||||||
\(613\) | 19.8663 | 0.802390 | 0.401195 | − | 0.915993i | \(-0.368595\pi\) | ||||
0.401195 | + | 0.915993i | \(0.368595\pi\) | |||||||
\(614\) | −12.0463 | −0.486150 | ||||||||
\(615\) | −33.8607 | −1.36539 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.6057 | 1.47369 | 0.736846 | − | 0.676061i | \(-0.236314\pi\) | ||||
0.736846 | + | 0.676061i | \(0.236314\pi\) | |||||||
\(618\) | −48.2876 | −1.94241 | ||||||||
\(619\) | 40.2839 | 1.61915 | 0.809574 | − | 0.587018i | \(-0.199698\pi\) | ||||
0.809574 | + | 0.587018i | \(0.199698\pi\) | |||||||
\(620\) | −5.64025 | −0.226518 | ||||||||
\(621\) | −27.9994 | −1.12358 | ||||||||
\(622\) | −13.6861 | −0.548761 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.911469 | 0.0364880 | ||||||||
\(625\) | −10.6892 | −0.427568 | ||||||||
\(626\) | −39.8460 | −1.59257 | ||||||||
\(627\) | −5.42565 | −0.216680 | ||||||||
\(628\) | −52.5666 | −2.09763 | ||||||||
\(629\) | −45.9111 | −1.83060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7789 | 0.667956 | 0.333978 | − | 0.942581i | \(-0.391609\pi\) | ||||
0.333978 | + | 0.942581i | \(0.391609\pi\) | |||||||
\(632\) | 34.4410 | 1.36999 | ||||||||
\(633\) | −24.8377 | −0.987209 | ||||||||
\(634\) | −46.1585 | −1.83319 | ||||||||
\(635\) | 6.04903 | 0.240048 | ||||||||
\(636\) | 77.6416 | 3.07869 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −20.7173 | −0.820207 | ||||||||
\(639\) | 7.03631 | 0.278352 | ||||||||
\(640\) | 30.3067 | 1.19798 | ||||||||
\(641\) | −33.0517 | −1.30546 | −0.652732 | − | 0.757589i | \(-0.726377\pi\) | ||||
−0.652732 | + | 0.757589i | \(0.726377\pi\) | |||||||
\(642\) | 1.04498 | 0.0412419 | ||||||||
\(643\) | 45.2538 | 1.78463 | 0.892317 | − | 0.451409i | \(-0.149078\pi\) | ||||
0.892317 | + | 0.451409i | \(0.149078\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4754 | −0.412468 | ||||||||
\(646\) | 12.3532 | 0.486031 | ||||||||
\(647\) | 16.0011 | 0.629068 | 0.314534 | − | 0.949246i | \(-0.398152\pi\) | ||||
0.314534 | + | 0.949246i | \(0.398152\pi\) | |||||||
\(648\) | −27.5200 | −1.08109 | ||||||||
\(649\) | −17.8506 | −0.700696 | ||||||||
\(650\) | −7.23635 | −0.283833 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.7918 | −0.579291 | ||||||||
\(653\) | 13.3269 | 0.521520 | 0.260760 | − | 0.965404i | \(-0.416027\pi\) | ||||
0.260760 | + | 0.965404i | \(0.416027\pi\) | |||||||
\(654\) | −69.2769 | −2.70894 | ||||||||
\(655\) | 17.0067 | 0.664505 | ||||||||
\(656\) | 3.20844 | 0.125269 | ||||||||
\(657\) | 6.00710 | 0.234359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.7239 | −1.07997 | −0.539985 | − | 0.841675i | \(-0.681570\pi\) | ||||
−0.539985 | + | 0.841675i | \(0.681570\pi\) | |||||||
\(660\) | −29.5818 | −1.15147 | ||||||||
\(661\) | 11.1407 | 0.433325 | 0.216662 | − | 0.976247i | \(-0.430483\pi\) | ||||
0.216662 | + | 0.976247i | \(0.430483\pi\) | |||||||
\(662\) | −31.7965 | −1.23580 | ||||||||
\(663\) | 16.0693 | 0.624080 | ||||||||
\(664\) | −14.2711 | −0.553824 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9305 | 0.423546 | ||||||||
\(667\) | −19.3518 | −0.749305 | ||||||||
\(668\) | −10.1671 | −0.393378 | ||||||||
\(669\) | 21.0212 | 0.812727 | ||||||||
\(670\) | 10.0143 | 0.386887 | ||||||||
\(671\) | 28.0517 | 1.08292 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.3885 | 0.516087 | 0.258043 | − | 0.966133i | \(-0.416922\pi\) | ||||
0.258043 | + | 0.966133i | \(0.416922\pi\) | |||||||
\(674\) | −58.3443 | −2.24734 | ||||||||
\(675\) | −9.34242 | −0.359590 | ||||||||
\(676\) | −33.4045 | −1.28479 | ||||||||
\(677\) | −16.3781 | −0.629462 | −0.314731 | − | 0.949181i | \(-0.601914\pi\) | ||||
−0.314731 | + | 0.949181i | \(0.601914\pi\) | |||||||
\(678\) | −73.2625 | −2.81363 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 24.8056 | 0.951250 | ||||||||
\(681\) | −47.7488 | −1.82974 | ||||||||
\(682\) | −6.75251 | −0.258567 | ||||||||
\(683\) | −3.38340 | −0.129462 | −0.0647311 | − | 0.997903i | \(-0.520619\pi\) | ||||
−0.0647311 | + | 0.997903i | \(0.520619\pi\) | |||||||
\(684\) | −1.80243 | −0.0689177 | ||||||||
\(685\) | −0.738148 | −0.0282032 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.74562 | −0.295514 | ||||||||
\(688\) | 0.992587 | 0.0378420 | ||||||||
\(689\) | −20.3138 | −0.773894 | ||||||||
\(690\) | −45.0872 | −1.71644 | ||||||||
\(691\) | 34.1321 | 1.29845 | 0.649223 | − | 0.760598i | \(-0.275094\pi\) | ||||
0.649223 | + | 0.760598i | \(0.275094\pi\) | |||||||
\(692\) | −23.3733 | −0.888519 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 60.3089 | 2.28930 | ||||||||
\(695\) | 34.6831 | 1.31560 | ||||||||
\(696\) | −15.8920 | −0.602384 | ||||||||
\(697\) | 56.5652 | 2.14256 | ||||||||
\(698\) | −74.4037 | −2.81622 | ||||||||
\(699\) | 54.2990 | 2.05378 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5338 | 0.473395 | 0.236697 | − | 0.971583i | \(-0.423935\pi\) | ||||
0.236697 | + | 0.971583i | \(0.423935\pi\) | |||||||
\(702\) | 16.3345 | 0.616505 | ||||||||
\(703\) | −8.44727 | −0.318595 | ||||||||
\(704\) | 37.4017 | 1.40963 | ||||||||
\(705\) | 17.9109 | 0.674562 | ||||||||
\(706\) | 14.4632 | 0.544328 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −37.1792 | −1.39728 | ||||||||
\(709\) | 16.7799 | 0.630184 | 0.315092 | − | 0.949061i | \(-0.397965\pi\) | ||||
0.315092 | + | 0.949061i | \(0.397965\pi\) | |||||||
\(710\) | −48.3768 | −1.81555 | ||||||||
\(711\) | 7.39822 | 0.277455 | ||||||||
\(712\) | −19.7545 | −0.740331 | ||||||||
\(713\) | −6.30744 | −0.236216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.73963 | 0.289446 | ||||||||
\(716\) | −82.6777 | −3.08981 | ||||||||
\(717\) | −24.7648 | −0.924860 | ||||||||
\(718\) | 40.7031 | 1.51903 | ||||||||
\(719\) | −40.0031 | −1.49186 | −0.745932 | − | 0.666022i | \(-0.767996\pi\) | ||||
−0.745932 | + | 0.666022i | \(0.767996\pi\) | |||||||
\(720\) | 0.302235 | 0.0112636 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.27289 | 0.0845883 | ||||||||
\(723\) | −0.00471144 | −0.000175221 0 | ||||||||
\(724\) | 10.4547 | 0.388547 | ||||||||
\(725\) | −6.45701 | −0.239807 | ||||||||
\(726\) | 11.8196 | 0.438668 | ||||||||
\(727\) | −17.6291 | −0.653828 | −0.326914 | − | 0.945054i | \(-0.606009\pi\) | ||||
−0.326914 | + | 0.945054i | \(0.606009\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.1162 | 0.745043 | ||||||||
\(730\) | −41.3007 | −1.52861 | ||||||||
\(731\) | 17.4994 | 0.647240 | ||||||||
\(732\) | 58.4260 | 2.15949 | ||||||||
\(733\) | −2.33685 | −0.0863136 | −0.0431568 | − | 0.999068i | \(-0.513742\pi\) | ||||
−0.0431568 | + | 0.999068i | \(0.513742\pi\) | |||||||
\(734\) | 43.1390 | 1.59229 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36.5905 | 1.34874 | ||||||||
\(737\) | 7.34762 | 0.270653 | ||||||||
\(738\) | −13.4670 | −0.495725 | ||||||||
\(739\) | −31.7072 | −1.16637 | −0.583184 | − | 0.812340i | \(-0.698193\pi\) | ||||
−0.583184 | + | 0.812340i | \(0.698193\pi\) | |||||||
\(740\) | −46.0563 | −1.69306 | ||||||||
\(741\) | 2.95662 | 0.108614 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.1449 | 0.812418 | 0.406209 | − | 0.913780i | \(-0.366851\pi\) | ||||
0.406209 | + | 0.913780i | \(0.366851\pi\) | |||||||
\(744\) | −5.17976 | −0.189899 | ||||||||
\(745\) | 16.0212 | 0.586970 | ||||||||
\(746\) | 4.30769 | 0.157716 | ||||||||
\(747\) | −3.06555 | −0.112162 | ||||||||
\(748\) | 49.4172 | 1.80687 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −52.0180 | −1.89943 | ||||||||
\(751\) | −49.6623 | −1.81220 | −0.906102 | − | 0.423059i | \(-0.860956\pi\) | ||||
−0.906102 | + | 0.423059i | \(0.860956\pi\) | |||||||
\(752\) | −1.69713 | −0.0618879 | ||||||||
\(753\) | 25.6266 | 0.933885 | ||||||||
\(754\) | 11.2896 | 0.411142 | ||||||||
\(755\) | 22.5836 | 0.821900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.1148 | −0.949158 | −0.474579 | − | 0.880213i | \(-0.657400\pi\) | ||||
−0.474579 | + | 0.880213i | \(0.657400\pi\) | |||||||
\(758\) | −40.5666 | −1.47344 | ||||||||
\(759\) | −33.0810 | −1.20076 | ||||||||
\(760\) | 4.56402 | 0.165554 | ||||||||
\(761\) | −31.4608 | −1.14045 | −0.570226 | − | 0.821488i | \(-0.693144\pi\) | ||||
−0.570226 | + | 0.821488i | \(0.693144\pi\) | |||||||
\(762\) | 15.0834 | 0.546415 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.1878 | 0.802726 | ||||||||
\(765\) | 5.32845 | 0.192650 | ||||||||
\(766\) | 56.6250 | 2.04595 | ||||||||
\(767\) | 9.72738 | 0.351235 | ||||||||
\(768\) | 26.3607 | 0.951209 | ||||||||
\(769\) | 31.4360 | 1.13361 | 0.566806 | − | 0.823851i | \(-0.308179\pi\) | ||||
0.566806 | + | 0.823851i | \(0.308179\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.9319 | 1.76224 | ||||||||
\(772\) | 20.9374 | 0.753554 | ||||||||
\(773\) | 10.7968 | 0.388334 | 0.194167 | − | 0.980969i | \(-0.437800\pi\) | ||||
0.194167 | + | 0.980969i | \(0.437800\pi\) | |||||||
\(774\) | −4.16624 | −0.149752 | ||||||||
\(775\) | −2.10457 | −0.0755983 | ||||||||
\(776\) | 6.49748 | 0.233246 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 46.5104 | 1.66748 | ||||||||
\(779\) | 10.4075 | 0.372888 | ||||||||
\(780\) | 16.1201 | 0.577192 | ||||||||
\(781\) | −35.4946 | −1.27010 | ||||||||
\(782\) | 75.3195 | 2.69342 | ||||||||
\(783\) | 14.5753 | 0.520879 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.5923 | 1.02050 | ||||||||
\(786\) | 42.4066 | 1.51259 | ||||||||
\(787\) | 46.7996 | 1.66823 | 0.834113 | − | 0.551594i | \(-0.185980\pi\) | ||||
0.834113 | + | 0.551594i | \(0.185980\pi\) | |||||||
\(788\) | −16.5741 | −0.590427 | ||||||||
\(789\) | −36.3697 | −1.29480 | ||||||||
\(790\) | −50.8651 | −1.80970 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.33306 | −0.153968 | ||||||||
\(793\) | −15.2863 | −0.542833 | ||||||||
\(794\) | −79.0120 | −2.80403 | ||||||||
\(795\) | −42.2313 | −1.49779 | ||||||||
\(796\) | 42.2830 | 1.49868 | ||||||||
\(797\) | −16.9067 | −0.598864 | −0.299432 | − | 0.954118i | \(-0.596797\pi\) | ||||
−0.299432 | + | 0.954118i | \(0.596797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.9206 | −1.05851 | ||||||||
\(800\) | 12.2089 | 0.431651 | ||||||||
\(801\) | −4.24344 | −0.149934 | ||||||||
\(802\) | 49.9937 | 1.76534 | ||||||||
\(803\) | −30.3028 | −1.06936 | ||||||||
\(804\) | 15.3036 | 0.539718 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.67967 | 0.129611 | ||||||||
\(807\) | 36.4625 | 1.28354 | ||||||||
\(808\) | 3.88981 | 0.136843 | ||||||||
\(809\) | −13.3420 | −0.469081 | −0.234540 | − | 0.972106i | \(-0.575358\pi\) | ||||
−0.234540 | + | 0.972106i | \(0.575358\pi\) | |||||||
\(810\) | 40.6435 | 1.42807 | ||||||||
\(811\) | −20.7826 | −0.729777 | −0.364888 | − | 0.931051i | \(-0.618893\pi\) | ||||
−0.364888 | + | 0.931051i | \(0.618893\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.8216 | −1.22125 | ||||||||
\(814\) | −55.1386 | −1.93261 | ||||||||
\(815\) | 8.04564 | 0.281827 | ||||||||
\(816\) | −3.16548 | −0.110814 | ||||||||
\(817\) | 3.21975 | 0.112645 | ||||||||
\(818\) | −7.99114 | −0.279404 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 56.7440 | 1.98159 | ||||||||
\(821\) | −10.2489 | −0.357690 | −0.178845 | − | 0.983877i | \(-0.557236\pi\) | ||||
−0.178845 | + | 0.983877i | \(0.557236\pi\) | |||||||
\(822\) | −1.84059 | −0.0641981 | ||||||||
\(823\) | −42.0328 | −1.46517 | −0.732585 | − | 0.680675i | \(-0.761687\pi\) | ||||
−0.732585 | + | 0.680675i | \(0.761687\pi\) | |||||||
\(824\) | 29.8027 | 1.03823 | ||||||||
\(825\) | −11.0380 | −0.384292 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.3468 | 0.464112 | 0.232056 | − | 0.972702i | \(-0.425455\pi\) | ||||
0.232056 | + | 0.972702i | \(0.425455\pi\) | |||||||
\(828\) | −10.9897 | −0.381919 | ||||||||
\(829\) | 33.9734 | 1.17994 | 0.589972 | − | 0.807424i | \(-0.299139\pi\) | ||||
0.589972 | + | 0.807424i | \(0.299139\pi\) | |||||||
\(830\) | 21.0766 | 0.731578 | ||||||||
\(831\) | 29.8230 | 1.03455 | ||||||||
\(832\) | −20.3815 | −0.706600 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 86.4832 | 2.99467 | ||||||||
\(835\) | 5.53017 | 0.191380 | ||||||||
\(836\) | 9.09235 | 0.314466 | ||||||||
\(837\) | 4.75061 | 0.164205 | ||||||||
\(838\) | −87.6231 | −3.02689 | ||||||||
\(839\) | −38.4347 | −1.32691 | −0.663457 | − | 0.748215i | \(-0.730911\pi\) | ||||
−0.663457 | + | 0.748215i | \(0.730911\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9263 | −0.652631 | ||||||||
\(842\) | −19.1988 | −0.661633 | ||||||||
\(843\) | 45.7683 | 1.57634 | ||||||||
\(844\) | 41.6232 | 1.43273 | ||||||||
\(845\) | 18.1696 | 0.625053 | ||||||||
\(846\) | 7.12345 | 0.244909 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.00160 | 0.137415 | ||||||||
\(849\) | 15.1083 | 0.518515 | ||||||||
\(850\) | 25.1314 | 0.862001 | ||||||||
\(851\) | −51.5043 | −1.76554 | ||||||||
\(852\) | −73.9282 | −2.53274 | ||||||||
\(853\) | 55.0017 | 1.88322 | 0.941611 | − | 0.336701i | \(-0.109311\pi\) | ||||
0.941611 | + | 0.336701i | \(0.109311\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.980390 | 0.0335286 | ||||||||
\(856\) | −0.644952 | −0.0220440 | ||||||||
\(857\) | −15.7299 | −0.537325 | −0.268662 | − | 0.963234i | \(-0.586582\pi\) | ||||
−0.268662 | + | 0.963234i | \(0.586582\pi\) | |||||||
\(858\) | 19.2990 | 0.658857 | ||||||||
\(859\) | 38.6992 | 1.32040 | 0.660200 | − | 0.751090i | \(-0.270471\pi\) | ||||
0.660200 | + | 0.751090i | \(0.270471\pi\) | |||||||
\(860\) | 17.5548 | 0.598612 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.08204 | −0.275275 | ||||||||
\(863\) | 49.0091 | 1.66829 | 0.834145 | − | 0.551545i | \(-0.185961\pi\) | ||||
0.834145 | + | 0.551545i | \(0.185961\pi\) | |||||||
\(864\) | −27.5590 | −0.937577 | ||||||||
\(865\) | 12.7133 | 0.432267 | ||||||||
\(866\) | −2.48428 | −0.0844192 | ||||||||
\(867\) | −23.6904 | −0.804567 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.3203 | −1.26600 | ||||||||
\(870\) | 23.4704 | 0.795723 | ||||||||
\(871\) | −4.00397 | −0.135669 | ||||||||
\(872\) | 42.7572 | 1.44794 | ||||||||
\(873\) | 1.39571 | 0.0472378 | ||||||||
\(874\) | 13.8582 | 0.468759 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −63.1146 | −2.13245 | ||||||||
\(877\) | 45.1810 | 1.52565 | 0.762827 | − | 0.646602i | \(-0.223811\pi\) | ||||
0.762827 | + | 0.646602i | \(0.223811\pi\) | |||||||
\(878\) | 18.6172 | 0.628300 | ||||||||
\(879\) | −32.7288 | −1.10392 | ||||||||
\(880\) | −1.52462 | −0.0513950 | ||||||||
\(881\) | −3.43242 | −0.115641 | −0.0578206 | − | 0.998327i | \(-0.518415\pi\) | ||||
−0.0578206 | + | 0.998327i | \(0.518415\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.3441 | 0.650980 | 0.325490 | − | 0.945545i | \(-0.394471\pi\) | ||||
0.325490 | + | 0.945545i | \(0.394471\pi\) | |||||||
\(884\) | −26.9291 | −0.905723 | ||||||||
\(885\) | 20.2227 | 0.679780 | ||||||||
\(886\) | 23.4046 | 0.786294 | ||||||||
\(887\) | 35.3049 | 1.18542 | 0.592712 | − | 0.805415i | \(-0.298057\pi\) | ||||
0.592712 | + | 0.805415i | \(0.298057\pi\) | |||||||
\(888\) | −42.2960 | −1.41936 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 29.1749 | 0.977946 | ||||||||
\(891\) | 29.8206 | 0.999028 | ||||||||
\(892\) | −35.2275 | −1.17951 | ||||||||
\(893\) | −5.50514 | −0.184223 | ||||||||
\(894\) | 39.9492 | 1.33610 | ||||||||
\(895\) | 44.9706 | 1.50320 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.0270 | 0.601903 | ||||||||
\(898\) | 50.0591 | 1.67050 | ||||||||
\(899\) | 3.28338 | 0.109507 | ||||||||
\(900\) | −3.66687 | −0.122229 | ||||||||
\(901\) | 70.5486 | 2.35032 | ||||||||
\(902\) | 67.9339 | 2.26195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 45.2171 | 1.50390 | ||||||||
\(905\) | −5.68660 | −0.189029 | ||||||||
\(906\) | 56.3127 | 1.87087 | ||||||||
\(907\) | −24.5319 | −0.814569 | −0.407284 | − | 0.913301i | \(-0.633524\pi\) | ||||
−0.407284 | + | 0.913301i | \(0.633524\pi\) | |||||||
\(908\) | 80.0178 | 2.65548 | ||||||||
\(909\) | 0.835564 | 0.0277139 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.4707 | −1.73843 | −0.869216 | − | 0.494433i | \(-0.835376\pi\) | ||||
−0.869216 | + | 0.494433i | \(0.835376\pi\) | |||||||
\(912\) | −0.582422 | −0.0192859 | ||||||||
\(913\) | 15.4641 | 0.511787 | ||||||||
\(914\) | −26.6554 | −0.881683 | ||||||||
\(915\) | −31.7795 | −1.05060 | ||||||||
\(916\) | 12.9802 | 0.428877 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −56.7287 | −1.87233 | ||||||||
\(919\) | −5.27938 | −0.174151 | −0.0870753 | − | 0.996202i | \(-0.527752\pi\) | ||||
−0.0870753 | + | 0.996202i | \(0.527752\pi\) | |||||||
\(920\) | 27.8275 | 0.917446 | ||||||||
\(921\) | 10.0131 | 0.329942 | ||||||||
\(922\) | 43.4424 | 1.43070 | ||||||||
\(923\) | 19.3422 | 0.636657 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1851 | −0.565044 | ||||||||
\(926\) | 8.53399 | 0.280444 | ||||||||
\(927\) | 6.40188 | 0.210265 | ||||||||
\(928\) | −19.0474 | −0.625262 | ||||||||
\(929\) | 17.7720 | 0.583080 | 0.291540 | − | 0.956559i | \(-0.405832\pi\) | ||||
0.291540 | + | 0.956559i | \(0.405832\pi\) | |||||||
\(930\) | 7.64985 | 0.250849 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −90.9947 | −2.98063 | ||||||||
\(933\) | 11.3761 | 0.372435 | ||||||||
\(934\) | −7.16431 | −0.234423 | ||||||||
\(935\) | −26.8793 | −0.879047 | ||||||||
\(936\) | 2.36123 | 0.0771792 | ||||||||
\(937\) | 37.1004 | 1.21202 | 0.606008 | − | 0.795458i | \(-0.292770\pi\) | ||||
0.606008 | + | 0.795458i | \(0.292770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.1205 | 1.08085 | ||||||||
\(940\) | −30.0152 | −0.978987 | ||||||||
\(941\) | −8.01455 | −0.261267 | −0.130633 | − | 0.991431i | \(-0.541701\pi\) | ||||
−0.130633 | + | 0.991431i | \(0.541701\pi\) | |||||||
\(942\) | 71.2958 | 2.32294 | ||||||||
\(943\) | 63.4563 | 2.06642 | ||||||||
\(944\) | −1.91619 | −0.0623666 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.0165 | 0.683307 | ||||||||
\(947\) | −36.1009 | −1.17312 | −0.586560 | − | 0.809905i | \(-0.699518\pi\) | ||||
−0.586560 | + | 0.809905i | \(0.699518\pi\) | |||||||
\(948\) | −77.7307 | −2.52457 | ||||||||
\(949\) | 16.5130 | 0.536035 | ||||||||
\(950\) | 4.62398 | 0.150022 | ||||||||
\(951\) | 38.3676 | 1.24416 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.8308 | −1.48461 | −0.742303 | − | 0.670065i | \(-0.766266\pi\) | ||||
−0.742303 | + | 0.670065i | \(0.766266\pi\) | |||||||
\(954\) | −16.7961 | −0.543794 | ||||||||
\(955\) | −12.0685 | −0.390528 | ||||||||
\(956\) | 41.5011 | 1.34224 | ||||||||
\(957\) | 17.2205 | 0.556661 | ||||||||
\(958\) | −13.9574 | −0.450942 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −42.3720 | −1.36755 | ||||||||
\(961\) | −29.9298 | −0.965478 | ||||||||
\(962\) | 30.0469 | 0.968750 | ||||||||
\(963\) | −0.138541 | −0.00446443 | ||||||||
\(964\) | 0.00789548 | 0.000254296 0 | ||||||||
\(965\) | −11.3884 | −0.366606 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.3040 | −0.459985 | −0.229993 | − | 0.973192i | \(-0.573870\pi\) | ||||
−0.229993 | + | 0.973192i | \(0.573870\pi\) | |||||||
\(968\) | −7.29500 | −0.234470 | ||||||||
\(969\) | −10.2682 | −0.329861 | ||||||||
\(970\) | −9.59596 | −0.308108 | ||||||||
\(971\) | 27.0679 | 0.868651 | 0.434325 | − | 0.900756i | \(-0.356987\pi\) | ||||
0.434325 | + | 0.900756i | \(0.356987\pi\) | |||||||
\(972\) | 18.4930 | 0.593162 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 91.9838 | 2.94735 | ||||||||
\(975\) | 6.01495 | 0.192633 | ||||||||
\(976\) | 3.01124 | 0.0963873 | ||||||||
\(977\) | 28.6282 | 0.915898 | 0.457949 | − | 0.888978i | \(-0.348584\pi\) | ||||
0.457949 | + | 0.888978i | \(0.348584\pi\) | |||||||
\(978\) | 20.0620 | 0.641513 | ||||||||
\(979\) | 21.4060 | 0.684138 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.18462 | 0.293242 | ||||||||
\(982\) | −41.0233 | −1.30911 | ||||||||
\(983\) | −39.6198 | −1.26368 | −0.631838 | − | 0.775100i | \(-0.717699\pi\) | ||||
−0.631838 | + | 0.775100i | \(0.717699\pi\) | |||||||
\(984\) | 52.1112 | 1.66124 | ||||||||
\(985\) | 9.01508 | 0.287244 | ||||||||
\(986\) | −39.2080 | −1.24864 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.95473 | −0.157631 | ||||||||
\(989\) | 19.6313 | 0.624239 | ||||||||
\(990\) | 6.39938 | 0.203386 | ||||||||
\(991\) | −4.20741 | −0.133653 | −0.0668264 | − | 0.997765i | \(-0.521287\pi\) | ||||
−0.0668264 | + | 0.997765i | \(0.521287\pi\) | |||||||
\(992\) | −6.20823 | −0.197111 | ||||||||
\(993\) | 26.4297 | 0.838720 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9989 | −0.729113 | ||||||||
\(996\) | 32.2087 | 1.02057 | ||||||||
\(997\) | 21.5597 | 0.682803 | 0.341401 | − | 0.939918i | \(-0.389098\pi\) | ||||
0.341401 | + | 0.939918i | \(0.389098\pi\) | |||||||
\(998\) | −80.8877 | −2.56045 | ||||||||
\(999\) | 38.7917 | 1.22732 |
(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 | 931.2.a.p.1.10 | ✓ | 10 | |
3.2 | odd | 2 | 8379.2.a.ct.1.1 | 10 | |||
7.2 | even | 3 | 931.2.f.r.704.1 | 20 | |||
7.3 | odd | 6 | 931.2.f.q.324.1 | 20 | |||
7.4 | even | 3 | 931.2.f.r.324.1 | 20 | |||
7.5 | odd | 6 | 931.2.f.q.704.1 | 20 | |||
7.6 | odd | 2 | 931.2.a.q.1.10 | yes | 10 | ||
21.20 | even | 2 | 8379.2.a.cs.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.p.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial | |
931.2.a.q.1.10 | yes | 10 | 7.6 | odd | 2 | ||
931.2.f.q.324.1 | 20 | 7.3 | odd | 6 | |||
931.2.f.q.704.1 | 20 | 7.5 | odd | 6 | |||
931.2.f.r.324.1 | 20 | 7.4 | even | 3 | |||
931.2.f.r.704.1 | 20 | 7.2 | even | 3 | |||
8379.2.a.cs.1.1 | 10 | 21.20 | even | 2 | |||
8379.2.a.ct.1.1 | 10 | 3.2 | odd | 2 |