Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + 6652 x^{11} - 67665 x^{10} - 17345 x^{9} + 174105 x^{8} + 41499 x^{7} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(-0.942024\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.942024 | 0.543878 | 0.271939 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271939 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.85968 | 0.702892 | 0.351446 | − | 0.936208i | \(-0.385690\pi\) | ||||
0.351446 | + | 0.936208i | \(0.385690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.11259 | −0.704197 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46518 | −1.64781 | −0.823907 | − | 0.566725i | \(-0.808210\pi\) | ||||
−0.823907 | + | 0.566725i | \(0.808210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.73017 | −0.479864 | −0.239932 | − | 0.970790i | \(-0.577125\pi\) | ||||
−0.239932 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.942024 | 0.243230 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.05540 | 1.71119 | 0.855593 | − | 0.517650i | \(-0.173193\pi\) | ||||
0.855593 | + | 0.517650i | \(0.173193\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.773935 | −0.177553 | −0.0887765 | − | 0.996052i | \(-0.528296\pi\) | ||||
−0.0887765 | + | 0.996052i | \(0.528296\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.75186 | 0.382288 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81258 | −0.794977 | −0.397489 | − | 0.917607i | \(-0.630118\pi\) | ||||
−0.397489 | + | 0.917607i | \(0.630118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.81618 | −0.926875 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.07852 | −0.943057 | −0.471528 | − | 0.881851i | \(-0.656298\pi\) | ||||
−0.471528 | + | 0.881851i | \(0.656298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.44521 | −0.618778 | −0.309389 | − | 0.950936i | \(-0.600125\pi\) | ||||
−0.309389 | + | 0.950936i | \(0.600125\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.14833 | −0.896210 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85968 | 0.314343 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.1557 | 1.66959 | 0.834793 | − | 0.550563i | \(-0.185587\pi\) | ||||
0.834793 | + | 0.550563i | \(0.185587\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.62987 | −0.260987 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9597 | 1.71162 | 0.855812 | − | 0.517288i | \(-0.173058\pi\) | ||||
0.855812 | + | 0.517288i | \(0.173058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.4006 | −1.73858 | −0.869291 | − | 0.494300i | \(-0.835424\pi\) | ||||
−0.869291 | + | 0.494300i | \(0.835424\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.11259 | −0.314926 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.80816 | 0.701342 | 0.350671 | − | 0.936499i | \(-0.385954\pi\) | ||||
0.350671 | + | 0.936499i | \(0.385954\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.54160 | −0.505942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.64636 | 0.930676 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.9347 | −1.63936 | −0.819678 | − | 0.572825i | \(-0.805848\pi\) | ||||
−0.819678 | + | 0.572825i | \(0.805848\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.46518 | −0.736925 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.729066 | −0.0965671 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.86243 | 1.28398 | 0.641990 | − | 0.766713i | \(-0.278109\pi\) | ||||
0.641990 | + | 0.766713i | \(0.278109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.97110 | −0.380410 | −0.190205 | − | 0.981744i | \(-0.560915\pi\) | ||||
−0.190205 | + | 0.981744i | \(0.560915\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.92874 | −0.494974 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.73017 | −0.214602 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.49773 | 0.182977 | 0.0914886 | − | 0.995806i | \(-0.470838\pi\) | ||||
0.0914886 | + | 0.995806i | \(0.470838\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.59154 | −0.432371 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.03659 | −0.479055 | −0.239527 | − | 0.970890i | \(-0.576992\pi\) | ||||
−0.239527 | + | 0.970890i | \(0.576992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.6541 | −1.24697 | −0.623484 | − | 0.781836i | \(-0.714283\pi\) | ||||
−0.623484 | + | 0.781836i | \(0.714283\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.942024 | 0.108776 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.1635 | −1.15824 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.78333 | −0.763185 | −0.381592 | − | 0.924331i | \(-0.624624\pi\) | ||||
−0.381592 | + | 0.924331i | \(0.624624\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.80081 | 0.200090 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.89233 | −0.976060 | −0.488030 | − | 0.872827i | \(-0.662284\pi\) | ||||
−0.488030 | + | 0.872827i | \(0.662284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.05540 | 0.765265 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.78409 | −0.512908 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.29643 | 0.985420 | 0.492710 | − | 0.870194i | \(-0.336006\pi\) | ||||
0.492710 | + | 0.870194i | \(0.336006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.21756 | −0.337292 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.24547 | −0.336540 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.773935 | −0.0794041 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.2342 | −1.54680 | −0.773398 | − | 0.633920i | \(-0.781445\pi\) | ||||
−0.773398 | + | 0.633920i | \(0.781445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.5457 | 1.16038 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9485 | −1.48743 | −0.743717 | − | 0.668494i | \(-0.766939\pi\) | ||||
−0.743717 | + | 0.668494i | \(0.766939\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6600 | 1.44449 | 0.722244 | − | 0.691638i | \(-0.243111\pi\) | ||||
0.722244 | + | 0.691638i | \(0.243111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.75186 | 0.170964 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.3707 | −1.87264 | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||||
−0.936320 | + | 0.351147i | \(0.885792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.922013 | −0.0883128 | −0.0441564 | − | 0.999025i | \(-0.514060\pi\) | ||||
−0.0441564 | + | 0.999025i | \(0.514060\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.56692 | 0.908052 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.59578 | −0.808623 | −0.404311 | − | 0.914621i | \(-0.632489\pi\) | ||||
−0.404311 | + | 0.914621i | \(0.632489\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.81258 | −0.355525 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.65515 | 0.337918 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.1208 | 1.20278 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8682 | 1.71529 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3243 | 0.930914 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.360098 | −0.0319536 | −0.0159768 | − | 0.999872i | \(-0.505086\pi\) | ||||
−0.0159768 | + | 0.999872i | \(0.505086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7397 | −0.945577 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5951 | −1.27518 | −0.637590 | − | 0.770376i | \(-0.720069\pi\) | ||||
−0.637590 | + | 0.770376i | \(0.720069\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.43927 | −0.124801 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.81618 | −0.414511 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.99895 | −0.170782 | −0.0853909 | − | 0.996348i | \(-0.527214\pi\) | ||||
−0.0853909 | + | 0.996348i | \(0.527214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.25356 | −0.700058 | −0.350029 | − | 0.936739i | \(-0.613828\pi\) | ||||
−0.350029 | + | 0.936739i | \(0.613828\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.52940 | 0.381445 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.45571 | 0.790726 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.07852 | −0.421748 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.33627 | −0.275171 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.09019 | −0.417005 | −0.208502 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208502 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.9052 | −1.20501 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.44521 | −0.276726 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.3985 | −1.78759 | −0.893797 | − | 0.448473i | \(-0.851968\pi\) | ||||
−0.893797 | + | 0.448473i | \(0.851968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2428 | −0.891610 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.09017 | −0.558783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7023 | −0.916599 | −0.458299 | − | 0.888798i | \(-0.651541\pi\) | ||||
−0.458299 | + | 0.888798i | \(0.651541\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.14833 | −0.400797 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.75896 | −0.368260 | −0.184130 | − | 0.982902i | \(-0.558947\pi\) | ||||
−0.184130 | + | 0.982902i | \(0.558947\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0065 | −0.769731 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.63501 | 0.125032 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4915 | 0.949711 | 0.474855 | − | 0.880064i | \(-0.342500\pi\) | ||||
0.474855 | + | 0.880064i | \(0.342500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.85968 | 0.140578 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.29065 | 0.698328 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.79891 | 0.433431 | 0.216715 | − | 0.976235i | \(-0.430466\pi\) | ||||
0.216715 | + | 0.976235i | \(0.430466\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.4230 | 1.51803 | 0.759014 | − | 0.651074i | \(-0.225681\pi\) | ||||
0.759014 | + | 0.651074i | \(0.225681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.79885 | −0.206897 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.1557 | 0.746662 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −38.5590 | −2.81971 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.95655 | −0.651493 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.6833 | −0.917734 | −0.458867 | − | 0.888505i | \(-0.651745\pi\) | ||||
−0.458867 | + | 0.888505i | \(0.651745\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.96373 | 0.213334 | 0.106667 | − | 0.994295i | \(-0.465982\pi\) | ||||
0.106667 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.62987 | −0.116717 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.41769 | 0.528488 | 0.264244 | − | 0.964456i | \(-0.414878\pi\) | ||||
0.264244 | + | 0.964456i | \(0.414878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.5540 | 1.66970 | 0.834851 | − | 0.550476i | \(-0.185554\pi\) | ||||
0.834851 | + | 0.550476i | \(0.185554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.41090 | 0.0995172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.44441 | −0.662867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9597 | 0.765461 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.05441 | 0.559820 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.22970 | 0.292574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.35476 | −0.0932656 | −0.0466328 | − | 0.998912i | \(-0.514849\pi\) | ||||
−0.0466328 | + | 0.998912i | \(0.514849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.80256 | −0.260547 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4006 | −0.777518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.40698 | −0.434934 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.0364 | −0.678199 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.2071 | −0.821136 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.0323 | 0.805743 | 0.402872 | − | 0.915257i | \(-0.368012\pi\) | ||||
0.402872 | + | 0.915257i | \(0.368012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.11259 | −0.140839 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.3601 | −1.21860 | −0.609301 | − | 0.792939i | \(-0.708550\pi\) | ||||
−0.609301 | + | 0.792939i | \(0.708550\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.16790 | −0.143259 | −0.0716294 | − | 0.997431i | \(-0.522820\pi\) | ||||
−0.0716294 | + | 0.997431i | \(0.522820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.57424 | −0.629939 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.07658 | 0.136041 | 0.0680207 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680207 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.80816 | 0.313650 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.39007 | −0.415079 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3456 | −1.05731 | −0.528654 | − | 0.848838i | \(-0.677303\pi\) | ||||
−0.528654 | + | 0.848838i | \(0.677303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.5561 | −0.679981 | −0.339990 | − | 0.940429i | \(-0.610424\pi\) | ||||
−0.339990 | + | 0.940429i | \(0.610424\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1450 | 1.03570 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.54160 | −0.226264 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.33904 | 0.0852012 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.37679 | −0.530857 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.88441 | −0.245182 | −0.122591 | − | 0.992457i | \(-0.539120\pi\) | ||||
−0.122591 | + | 0.992457i | \(0.539120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.8364 | 1.30997 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.64636 | 0.416211 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.6557 | 1.47560 | 0.737802 | − | 0.675017i | \(-0.235864\pi\) | ||||
0.737802 | + | 0.675017i | \(0.235864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.8863 | 1.17354 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.7288 | 0.664098 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.5604 | −1.32947 | −0.664737 | − | 0.747078i | \(-0.731456\pi\) | ||||
−0.664737 | + | 0.747078i | \(0.731456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.9347 | −0.733142 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.75747 | 0.535948 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.1582 | −1.65586 | −0.827932 | − | 0.560829i | \(-0.810483\pi\) | ||||
−0.827932 | + | 0.560829i | \(0.810483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5096 | 1.30661 | 0.653307 | − | 0.757093i | \(-0.273381\pi\) | ||||
0.653307 | + | 0.757093i | \(0.273381\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.03102 | −0.183446 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.46518 | −0.329563 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8380 | 1.13187 | 0.565933 | − | 0.824451i | \(-0.308516\pi\) | ||||
0.565933 | + | 0.824451i | \(0.308516\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.27832 | 0.435742 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.0782 | 1.37673 | 0.688366 | − | 0.725364i | \(-0.258328\pi\) | ||||
0.688366 | + | 0.725364i | \(0.258328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.94744 | −0.591314 | −0.295657 | − | 0.955294i | \(-0.595539\pi\) | ||||
−0.295657 | + | 0.955294i | \(0.595539\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.729066 | −0.0431861 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.3816 | 1.20309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.7787 | 1.92816 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.3510 | −0.841269 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.76914 | 0.161775 | 0.0808875 | − | 0.996723i | \(-0.474225\pi\) | ||||
0.0808875 | + | 0.996723i | \(0.474225\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.86243 | 0.574213 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.3213 | 1.52732 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.59642 | 0.381481 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.2015 | −1.22204 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.0819 | −0.808983 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.97110 | −0.170125 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2009 | 1.49537 | 0.747683 | − | 0.664056i | \(-0.231166\pi\) | ||||
0.747683 | + | 0.664056i | \(0.231166\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8100 | 0.785626 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.6108 | −0.715093 | −0.357546 | − | 0.933895i | \(-0.616387\pi\) | ||||
−0.357546 | + | 0.933895i | \(0.616387\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.59498 | 0.0901534 | 0.0450767 | − | 0.998984i | \(-0.485647\pi\) | ||||
0.0450767 | + | 0.998984i | \(0.485647\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.92874 | −0.221359 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.542764 | −0.0304847 | −0.0152423 | − | 0.999884i | \(-0.504852\pi\) | ||||
−0.0152423 | + | 0.999884i | \(0.504852\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.7550 | 1.55398 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.2477 | −1.01849 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.46042 | −0.303826 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.73017 | −0.0959727 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.868559 | −0.0480314 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.94163 | 0.492968 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.1664 | 1.76802 | 0.884012 | − | 0.467463i | \(-0.154832\pi\) | ||||
0.884012 | + | 0.467463i | \(0.154832\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.4548 | −1.17572 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.49773 | 0.0818299 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6504 | 0.689111 | 0.344555 | − | 0.938766i | \(-0.388030\pi\) | ||||
0.344555 | + | 0.938766i | \(0.388030\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.09743 | −0.439792 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.8287 | 1.01963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6040 | −1.05852 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.59154 | −0.193362 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2603 | −0.658170 | −0.329085 | − | 0.944300i | \(-0.606740\pi\) | ||||
−0.329085 | + | 0.944300i | \(0.606740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.8093 | 1.32801 | 0.664006 | − | 0.747727i | \(-0.268855\pi\) | ||||
0.664006 | + | 0.747727i | \(0.268855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.33283 | 0.444774 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0626 | 1.01460 | 0.507301 | − | 0.861769i | \(-0.330643\pi\) | ||||
0.507301 | + | 0.861769i | \(0.330643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.03659 | −0.214240 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.3601 | 0.654165 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.75013 | −0.356258 | −0.178129 | − | 0.984007i | \(-0.557005\pi\) | ||||
−0.178129 | + | 0.984007i | \(0.557005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.4010 | −0.968475 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.7743 | 0.932908 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6541 | −0.557661 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.6322 | −1.33799 | −0.668995 | − | 0.743267i | \(-0.733275\pi\) | ||||
−0.668995 | + | 0.743267i | \(0.733275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.1534 | −1.20532 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.1947 | −1.15229 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.8673 | 1.49469 | 0.747346 | − | 0.664435i | \(-0.231328\pi\) | ||||
0.747346 | + | 0.664435i | \(0.231328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.942024 | 0.0486459 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.78671 | 0.452539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.1364 | 1.18844 | 0.594218 | − | 0.804304i | \(-0.297462\pi\) | ||||
0.594218 | + | 0.804304i | \(0.297462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.339221 | −0.0173788 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.0043 | 1.58424 | 0.792122 | − | 0.610362i | \(-0.208976\pi\) | ||||
0.792122 | + | 0.610362i | \(0.208976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1635 | −0.517979 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.0849 | 1.22430 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.9191 | 0.908535 | 0.454267 | − | 0.890865i | \(-0.349901\pi\) | ||||
0.454267 | + | 0.890865i | \(0.349901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.8992 | −1.36035 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.7489 | −0.693543 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.78333 | −0.341307 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.93812 | 0.197648 | 0.0988242 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988242 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.35583 | −0.0678763 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.98027 | −0.498391 | −0.249195 | − | 0.968453i | \(-0.580166\pi\) | ||||
−0.249195 | + | 0.968453i | \(0.580166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.96081 | 0.296929 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.80081 | 0.0894828 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −55.5027 | −2.75117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.4497 | 0.615597 | 0.307798 | − | 0.951452i | \(-0.400408\pi\) | ||||
0.307798 | + | 0.951452i | \(0.400408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.88306 | −0.0928844 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.3409 | 0.902499 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.89233 | −0.436507 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.77506 | −0.380746 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.67843 | 0.423969 | 0.211984 | − | 0.977273i | \(-0.432007\pi\) | ||||
0.211984 | + | 0.977273i | \(0.432007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0069 | −1.36497 | −0.682485 | − | 0.730899i | \(-0.739101\pi\) | ||||
−0.682485 | + | 0.730899i | \(0.739101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.1577 | −0.493883 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.05540 | 0.342237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.52529 | −0.267387 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.90751 | 0.430058 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.5263 | 1.75941 | 0.879705 | − | 0.475519i | \(-0.157740\pi\) | ||||
0.879705 | + | 0.475519i | \(0.157740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.40044 | 0.211472 | 0.105736 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105736 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.78409 | −0.229379 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.95069 | 0.141151 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.3479 | −1.78252 | −0.891259 | − | 0.453494i | \(-0.850177\pi\) | ||||
−0.891259 | + | 0.453494i | \(0.850177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.48194 | 0.356283 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.6861 | −1.41043 | −0.705215 | − | 0.708994i | \(-0.749149\pi\) | ||||
−0.705215 | + | 0.708994i | \(0.749149\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.29643 | 0.440693 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.79509 | −0.226800 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.69250 | −0.127067 | −0.0635335 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635335 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −59.8969 | −2.82044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.942024 | 0.0442602 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.21756 | −0.150842 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.46265 | 0.442644 | 0.221322 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221322 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.9801 | −1.58606 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.9597 | −1.06934 | −0.534670 | − | 0.845061i | \(-0.679564\pi\) | ||||
−0.534670 | + | 0.845061i | \(0.679564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.78207 | −0.454611 | −0.227306 | − | 0.973823i | \(-0.572992\pi\) | ||||
−0.227306 | + | 0.973823i | \(0.572992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.24547 | −0.150505 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.4773 | −0.484830 | −0.242415 | − | 0.970173i | \(-0.577940\pi\) | ||||
−0.242415 | + | 0.970173i | \(0.577940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.78530 | 0.128613 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0999 | −0.972233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 62.3066 | 2.86486 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.773935 | −0.0355106 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25.2131 | 1.15443 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9758 | −1.50670 | −0.753352 | − | 0.657617i | \(-0.771565\pi\) | ||||
−0.753352 | + | 0.657617i | \(0.771565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5711 | −0.801174 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.67911 | −0.303910 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2342 | −0.691749 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.119256 | −0.00540400 | −0.00270200 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270200 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.0239 | −0.498518 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.51914 | −0.429593 | −0.214796 | − | 0.976659i | \(-0.568909\pi\) | ||||
−0.214796 | + | 0.976659i | \(0.568909\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.8310 | −1.61375 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.5457 | 0.518940 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.50675 | −0.336724 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.86759 | −0.128371 | −0.0641854 | − | 0.997938i | \(-0.520445\pi\) | ||||
−0.0641854 | + | 0.997938i | \(0.520445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.48306 | −0.200288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.4990 | −1.40447 | −0.702235 | − | 0.711946i | \(-0.747814\pi\) | ||||
−0.702235 | + | 0.711946i | \(0.747814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.9485 | −0.665201 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.42637 | −0.418640 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.2470 | −1.16338 | −0.581690 | − | 0.813411i | \(-0.697608\pi\) | ||||
−0.581690 | + | 0.813411i | \(0.697608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.8132 | −0.876484 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.72741 | 0.164569 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.6600 | 0.645995 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.2775 | −1.15568 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.7673 | 0.516527 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.7628 | 0.778202 | 0.389101 | − | 0.921195i | \(-0.372786\pi\) | ||||
0.389101 | + | 0.921195i | \(0.372786\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.4991 | 1.02754 | 0.513771 | − | 0.857927i | \(-0.328248\pi\) | ||||
0.513771 | + | 0.857927i | \(0.328248\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.75186 | 0.0764575 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.3073 | −1.05884 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.46426 | −0.368011 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.8353 | −0.904174 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9622 | −0.821346 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.3707 | −0.837470 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.46271 | 0.235733 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.3555 | 0.833699 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.8331 | −1.06766 | −0.533830 | − | 0.845592i | \(-0.679248\pi\) | ||||
−0.533830 | + | 0.845592i | \(0.679248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.2389 | 0.825622 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.922013 | −0.0394947 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.12472 | 0.390145 | 0.195073 | − | 0.980789i | \(-0.437506\pi\) | ||||
0.195073 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.27672 | 0.267884 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.93044 | 0.167443 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6148 | −0.536437 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.56692 | 0.406093 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.4976 | 1.75831 | 0.879155 | − | 0.476536i | \(-0.158108\pi\) | ||||
0.879155 | + | 0.476536i | \(0.158108\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.7251 | 0.834283 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.3235 | −1.53358 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.4440 | −0.861611 | −0.430805 | − | 0.902445i | \(-0.641770\pi\) | ||||
−0.430805 | + | 0.902445i | \(0.641770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.59578 | −0.361627 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.34892 | 0.140641 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8637 | 0.790808 | 0.395404 | − | 0.918507i | \(-0.370605\pi\) | ||||
0.395404 | + | 0.918507i | \(0.370605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0690 | 1.38389 | 0.691947 | − | 0.721948i | \(-0.256753\pi\) | ||||
0.691947 | + | 0.721948i | \(0.256753\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.9480 | −0.499135 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.81258 | −0.158995 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4593 | −1.35130 | −0.675648 | − | 0.737224i | \(-0.736136\pi\) | ||||
−0.675648 | + | 0.737224i | \(0.736136\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.79191 | 0.116028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.5369 | −0.686065 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 65.2252 | 2.70135 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.65515 | 0.151122 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.1383 | −1.61541 | −0.807706 | − | 0.589586i | \(-0.799291\pi\) | ||||
−0.807706 | + | 0.589586i | \(0.799291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.66637 | 0.109866 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.98764 | 0.287433 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.16244 | 0.170931 | 0.0854655 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854655 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1208 | 0.537899 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.1885 | 0.908114 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.55066 | −0.104217 | −0.0521086 | − | 0.998641i | \(-0.516594\pi\) | ||||
−0.0521086 | + | 0.998641i | \(0.516594\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.5984 | −1.86000 | −0.929999 | − | 0.367563i | \(-0.880192\pi\) | ||||
−0.929999 | + | 0.367563i | \(0.880192\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.16409 | −0.128852 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.8682 | 0.767101 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.73191 | 0.151473 | 0.0757367 | − | 0.997128i | \(-0.475869\pi\) | ||||
0.0757367 | + | 0.997128i | \(0.475869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.89686 | −0.360519 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.31895 | −0.336549 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.7399 | 0.999235 | 0.499618 | − | 0.866246i | \(-0.333474\pi\) | ||||
0.499618 | + | 0.866246i | \(0.333474\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.3243 | 0.416317 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2583 | 0.412984 | 0.206492 | − | 0.978448i | \(-0.433795\pi\) | ||||
0.206492 | + | 0.978448i | \(0.433795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 40.0207 | 1.60857 | 0.804284 | − | 0.594246i | \(-0.202549\pi\) | ||||
0.804284 | + | 0.594246i | \(0.202549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.3621 | 0.736845 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.2884 | 0.692644 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.98448 | 0.159125 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 71.6525 | 2.85697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8223 | 0.470637 | 0.235318 | − | 0.971918i | \(-0.424387\pi\) | ||||
0.235318 | + | 0.971918i | \(0.424387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.27622 | −0.0507251 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.360098 | −0.0142901 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.12758 | 0.242783 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.52765 | 0.337349 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.3260 | −0.605341 | −0.302670 | − | 0.953095i | \(-0.597878\pi\) | ||||
−0.302670 | + | 0.953095i | \(0.597878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0979 | −0.989765 | −0.494883 | − | 0.868960i | \(-0.664789\pi\) | ||||
−0.494883 | + | 0.868960i | \(0.664789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.7397 | −0.422875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.2560 | −0.639090 | −0.319545 | − | 0.947571i | \(-0.603530\pi\) | ||||
−0.319545 | + | 0.947571i | \(0.603530\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −53.9000 | −2.11576 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.03554 | −0.236551 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.2615 | −1.88862 | −0.944309 | − | 0.329059i | \(-0.893268\pi\) | ||||
−0.944309 | + | 0.329059i | \(0.893268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5951 | −0.570278 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 22.5077 | 0.878111 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.9498 | 1.24459 | 0.622294 | − | 0.782783i | \(-0.286201\pi\) | ||||
0.622294 | + | 0.782783i | \(0.286201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.5313 | 0.876364 | 0.438182 | − | 0.898886i | \(-0.355623\pi\) | ||||
0.438182 | + | 0.898886i | \(0.355623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.4993 | −0.446598 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.43927 | −0.0558125 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.3622 | 0.749709 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.3347 | 0.438226 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.2376 | 0.626845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.7717 | 1.03197 | 0.515987 | − | 0.856597i | \(-0.327425\pi\) | ||||
0.515987 | + | 0.856597i | \(0.327425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.81618 | −0.185375 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −41.9616 | −1.61272 | −0.806358 | − | 0.591427i | \(-0.798565\pi\) | ||||
−0.806358 | + | 0.591427i | \(0.798565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −28.3307 | −1.08723 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.2957 | −0.662771 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.6300 | 1.17202 | 0.586011 | − | 0.810303i | \(-0.300697\pi\) | ||||
0.586011 | + | 0.810303i | \(0.300697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.99895 | −0.0763759 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.04221 | −0.0779153 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.6491 | 0.786667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.191722 | −0.00729344 | −0.00364672 | − | 0.999993i | \(-0.501161\pi\) | ||||
−0.00364672 | + | 0.999993i | \(0.501161\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.4713 | 0.815626 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.25356 | −0.313076 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 77.3253 | 2.92890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.95619 | 0.0739899 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.1570 | −0.496932 | −0.248466 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248466 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.85985 | −0.296440 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.52940 | 0.170587 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.7995 | −1.04551 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.0799 | −0.829226 | −0.414613 | − | 0.909998i | \(-0.636083\pi\) | ||||
−0.414613 | + | 0.909998i | \(0.636083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.3304 | 0.537432 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.1351 | 0.491915 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.45571 | 0.353623 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.3979 | −0.575046 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.30618 | −0.272475 | −0.136237 | − | 0.990676i | \(-0.543501\pi\) | ||||
−0.136237 | + | 0.990676i | \(0.543501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.2628 | 1.01532 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.94414 | −0.369826 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.07852 | −0.188611 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4806 | 1.46425 | 0.732127 | − | 0.681168i | \(-0.238528\pi\) | ||||
0.732127 | + | 0.681168i | \(0.238528\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.80652 | 0.363205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −80.4361 | −2.97504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.7787 | 1.28458 | 0.642290 | − | 0.766462i | \(-0.277985\pi\) | ||||
0.642290 | + | 0.766462i | \(0.277985\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.33627 | −0.123060 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.18538 | −0.301512 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.3828 | −1.15444 | −0.577218 | − | 0.816590i | \(-0.695862\pi\) | ||||
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.26141 | 0.0463391 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.62389 | −0.206320 | −0.103160 | − | 0.994665i | \(-0.532895\pi\) | ||||
−0.103160 | + | 0.994665i | \(0.532895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.09019 | −0.186490 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.7858 | 0.687338 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.0234 | −1.31626 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.71183 | −0.317899 | −0.158950 | − | 0.987287i | \(-0.550811\pi\) | ||||
−0.158950 | + | 0.987287i | \(0.550811\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.65921 | −0.133349 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.94566 | 0.252444 | 0.126222 | − | 0.992002i | \(-0.459715\pi\) | ||||
0.126222 | + | 0.992002i | \(0.459715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.6284 | 0.712466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.9711 | 1.44895 | 0.724476 | − | 0.689300i | \(-0.242082\pi\) | ||||
0.724476 | + | 0.689300i | \(0.242082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.71465 | −0.0620744 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.9052 | −0.538897 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.0637 | −0.616135 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.04056 | 0.217828 | 0.108914 | − | 0.994051i | \(-0.465263\pi\) | ||||
0.108914 | + | 0.994051i | \(0.465263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.2843 | 0.802548 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5620 | 0.487792 | 0.243896 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243896 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.44521 | −0.123756 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.7914 | 0.638262 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.48213 | −0.303904 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0607 | 0.789393 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.4591 | 0.874096 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22.3985 | −0.799436 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7846 | 0.420075 | 0.210038 | − | 0.977693i | \(-0.432641\pi\) | ||||
0.210038 | + | 0.977693i | \(0.432641\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.3105 | −0.723071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.9854 | −0.568375 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.14052 | 0.182545 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.2428 | −0.398740 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8658 | 1.34127 | 0.670637 | − | 0.741786i | \(-0.266021\pi\) | ||||
0.670637 | + | 0.741786i | \(0.266021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.9235 | 1.20013 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.6396 | −0.693930 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.2266 | 2.05477 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.09017 | −0.249895 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.5837 | −0.900588 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.1249 | −0.637238 | −0.318619 | − | 0.947883i | \(-0.603219\pi\) | ||||
−0.318619 | + | 0.947883i | \(0.603219\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.5280 | −0.510145 | −0.255073 | − | 0.966922i | \(-0.582099\pi\) | ||||
−0.255073 | + | 0.966922i | \(0.582099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.2625 | 0.710639 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.7023 | −0.409915 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.82336 | 0.308690 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.79740 | 0.237520 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.80501 | 0.0978956 | 0.0489478 | − | 0.998801i | \(-0.484413\pi\) | ||||
0.0489478 | + | 0.998801i | \(0.484413\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.0462 | −1.29135 | −0.645675 | − | 0.763612i | \(-0.723424\pi\) | ||||
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.14833 | −0.179242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.8953 | 1.59594 | 0.797968 | − | 0.602699i | \(-0.205908\pi\) | ||||
0.797968 | + | 0.602699i | \(0.205908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.1002 | 0.593914 | 0.296957 | − | 0.954891i | \(-0.404028\pi\) | ||||
0.296957 | + | 0.954891i | \(0.404028\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.7459 | 0.615597 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.9874 | −0.865761 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.75896 | −0.164691 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.5928 | 0.573530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.9731 | 1.13836 | 0.569178 | − | 0.822214i | \(-0.307261\pi\) | ||||
0.569178 | + | 0.822214i | \(0.307261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.20866 | −0.110644 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.7402 | 0.748774 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0065 | −0.344234 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.0888 | 1.20566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.37073 | −0.321603 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.7194 | −1.32728 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.0327 | 1.02830 | 0.514150 | − | 0.857701i | \(-0.328108\pi\) | ||||
0.514150 | + | 0.857701i | \(0.328108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.63501 | 0.0559161 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.27381 | 0.316787 | 0.158394 | − | 0.987376i | \(-0.449368\pi\) | ||||
0.158394 | + | 0.987376i | \(0.449368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.7216 | 0.809371 | 0.404686 | − | 0.914456i | \(-0.367381\pi\) | ||||
0.404686 | + | 0.914456i | \(0.367381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.1999 | 0.654332 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.52449 | −0.290177 | −0.145088 | − | 0.989419i | \(-0.546347\pi\) | ||||
−0.145088 | + | 0.989419i | \(0.546347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4915 | 0.424724 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.8783 | 1.04868 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.0721 | 1.25759 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.59134 | −0.0878041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.1836 | 1.08925 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.85968 | 0.0628686 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.9338 | 0.639349 | 0.319675 | − | 0.947527i | \(-0.396426\pi\) | ||||
0.319675 | + | 0.947527i | \(0.396426\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.60860 | 0.0879859 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.7275 | 1.43953 | 0.719763 | − | 0.694220i | \(-0.244250\pi\) | ||||
0.719763 | + | 0.694220i | \(0.244250\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.46336 | 0.318467 | 0.159234 | − | 0.987241i | \(-0.449098\pi\) | ||||
0.159234 | + | 0.987241i | \(0.449098\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.29065 | 0.312302 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.0558 | −1.27779 | −0.638895 | − | 0.769294i | \(-0.720608\pi\) | ||||
−0.638895 | + | 0.769294i | \(0.720608\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.669667 | −0.0224599 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.84173 | −0.329711 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.72120 | −0.124525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.79891 | 0.193836 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.21399 | 0.207479 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.4966 | 0.583543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −84.2040 | −2.80524 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.9724 | −0.664639 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.4230 | 0.678883 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.354493 | −0.0117707 | −0.00588537 | − | 0.999983i | \(-0.501873\pi\) | ||||
−0.00588537 | + | 0.999983i | \(0.501873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.5801 | 1.04745 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1125 | −0.832013 | −0.416007 | − | 0.909362i | \(-0.636571\pi\) | ||||
−0.416007 | + | 0.909362i | \(0.636571\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.5982 | 1.60836 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.79885 | −0.0925271 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.1422 | −0.896314 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.4338 | −1.56470 | −0.782349 | − | 0.622841i | \(-0.785978\pi\) | ||||
−0.782349 | + | 0.622841i | \(0.785978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.6819 | 0.813297 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.98399 | 0.229881 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.1557 | 0.333917 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9705 | −1.01720 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.518160 | −0.0170003 | −0.00850014 | − | 0.999964i | \(-0.502706\pi\) | ||||
−0.00850014 | + | 0.999964i | \(0.502706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.74097 | 0.0898316 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.8797 | −0.388923 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −38.5590 | −1.26101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4387 | −1.12506 | −0.562532 | − | 0.826776i | \(-0.690173\pi\) | ||||
−0.562532 | + | 0.826776i | \(0.690173\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.50251 | 0.0490325 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8006 | −0.482485 | −0.241242 | − | 0.970465i | \(-0.577555\pi\) | ||||
−0.241242 | + | 0.970465i | \(0.577555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.7848 | −1.36070 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.95655 | −0.291357 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.7019 | 0.575234 | 0.287617 | − | 0.957745i | \(-0.407137\pi\) | ||||
0.287617 | + | 0.957745i | \(0.407137\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.4334 | 0.598375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.511297 | −0.0165799 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.6813 | −1.44737 | −0.723685 | − | 0.690130i | \(-0.757553\pi\) | ||||
−0.723685 | + | 0.690130i | \(0.757553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.6833 | −0.410423 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.1459 | 0.845177 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.71740 | −0.120041 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.1305 | −0.617113 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.9224 | 1.31871 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.96373 | 0.0954059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.1012 | 0.582094 | 0.291047 | − | 0.956709i | \(-0.405996\pi\) | ||||
0.291047 | + | 0.956709i | \(0.405996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.14385 | −0.165244 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.1142 | 0.517131 | 0.258565 | − | 0.965994i | \(-0.416750\pi\) | ||||
0.258565 | + | 0.965994i | \(0.416750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.3490 | −0.492065 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.62987 | −0.0521975 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57.1462 | 1.82827 | 0.914135 | − | 0.405411i | \(-0.132871\pi\) | ||||
0.914135 | + | 0.405411i | \(0.132871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.8067 | −1.62379 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.94784 | 0.0621896 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.0265 | −1.40423 | −0.702113 | − | 0.712065i | \(-0.747760\pi\) | ||||
−0.702113 | + | 0.712065i | \(0.747760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.41769 | 0.236347 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.42323 | 0.268114 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.4658 | 1.38213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.7478 | 0.404946 | 0.202473 | − | 0.979288i | \(-0.435102\pi\) | ||||
0.202473 | + | 0.979288i | \(0.435102\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.3015 | 0.961590 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.5540 | 0.746713 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1246 | 0.890715 | 0.445357 | − | 0.895353i | \(-0.353077\pi\) | ||||
0.445357 | + | 0.895353i | \(0.353077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −48.9117 | −1.54750 |
(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 | 6040.2.a.p.1.13 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.13 | ✓ | 19 | 1.1 | even | 1 | trivial |