Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1257629.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 9x^{3} + 9x^{2} + 17x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.49431\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.20813 | −0.456630 | −0.228315 | − | 0.973587i | \(-0.573322\pi\) | ||||
−0.228315 | + | 0.973587i | \(0.573322\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.26856 | 1.58853 | 0.794265 | − | 0.607571i | \(-0.207856\pi\) | ||||
0.794265 | + | 0.607571i | \(0.207856\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.221575 | 0.0614538 | 0.0307269 | − | 0.999528i | \(-0.490218\pi\) | ||||
0.0307269 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.28618 | −1.03955 | −0.519776 | − | 0.854303i | \(-0.673984\pi\) | ||||
−0.519776 | + | 0.854303i | \(0.673984\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.28201 | −1.21178 | −0.605888 | − | 0.795550i | \(-0.707182\pi\) | ||||
−0.605888 | + | 0.795550i | \(0.707182\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.20813 | 0.263635 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.67771 | −0.558342 | −0.279171 | − | 0.960241i | \(-0.590060\pi\) | ||||
−0.279171 | + | 0.960241i | \(0.590060\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.52207 | −1.21112 | −0.605559 | − | 0.795800i | \(-0.707050\pi\) | ||||
−0.605559 | + | 0.795800i | \(0.707050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.38432 | 0.428237 | 0.214119 | − | 0.976808i | \(-0.431312\pi\) | ||||
0.214119 | + | 0.976808i | \(0.431312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.26856 | −0.917139 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.20813 | −0.204211 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.84802 | 1.45461 | 0.727303 | − | 0.686316i | \(-0.240773\pi\) | ||||
0.727303 | + | 0.686316i | \(0.240773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.221575 | −0.0354804 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.02055 | −1.09643 | −0.548213 | − | 0.836339i | \(-0.684692\pi\) | ||||
−0.548213 | + | 0.836339i | \(0.684692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.44939 | −1.44102 | −0.720509 | − | 0.693446i | \(-0.756092\pi\) | ||||
−0.720509 | + | 0.693446i | \(0.756092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.74782 | 0.254945 | 0.127473 | − | 0.991842i | \(-0.459313\pi\) | ||||
0.127473 | + | 0.991842i | \(0.459313\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.54042 | −0.791489 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.28618 | 0.600185 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.05419 | −0.694247 | −0.347123 | − | 0.937819i | \(-0.612842\pi\) | ||||
−0.347123 | + | 0.937819i | \(0.612842\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.26856 | 0.710412 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.28201 | 0.699619 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1910 | 1.32675 | 0.663376 | − | 0.748287i | \(-0.269123\pi\) | ||||
0.663376 | + | 0.748287i | \(0.269123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.62352 | −0.335907 | −0.167954 | − | 0.985795i | \(-0.553716\pi\) | ||||
−0.167954 | + | 0.985795i | \(0.553716\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.20813 | −0.152210 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.221575 | 0.0274830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.67771 | 0.322359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.47669 | 0.768642 | 0.384321 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384321 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.83165 | −0.799584 | −0.399792 | − | 0.916606i | \(-0.630918\pi\) | ||||
−0.399792 | + | 0.916606i | \(0.630918\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.36510 | −0.725370 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.6612 | 1.87453 | 0.937265 | − | 0.348618i | \(-0.113349\pi\) | ||||
0.937265 | + | 0.348618i | \(0.113349\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2039 | −1.12002 | −0.560009 | − | 0.828486i | \(-0.689202\pi\) | ||||
−0.560009 | + | 0.828486i | \(0.689202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.28618 | −0.464901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.52207 | 0.699239 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.85648 | −0.514785 | −0.257393 | − | 0.966307i | \(-0.582863\pi\) | ||||
−0.257393 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.267691 | −0.0280617 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.38432 | −0.247243 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.28201 | −0.541922 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8518 | 1.40644 | 0.703218 | − | 0.710974i | \(-0.251746\pi\) | ||||
0.703218 | + | 0.710974i | \(0.251746\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.26856 | 0.529510 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.48797 | −0.347066 | −0.173533 | − | 0.984828i | \(-0.555518\pi\) | ||||
−0.173533 | + | 0.984828i | \(0.555518\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.08149 | −0.205095 | −0.102548 | − | 0.994728i | \(-0.532699\pi\) | ||||
−0.102548 | + | 0.994728i | \(0.532699\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20813 | 0.117901 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.20298 | −0.599665 | −0.299832 | − | 0.953992i | \(-0.596931\pi\) | ||||
−0.299832 | + | 0.953992i | \(0.596931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.50055 | 0.143726 | 0.0718631 | − | 0.997415i | \(-0.477106\pi\) | ||||
0.0718631 | + | 0.997415i | \(0.477106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.84802 | −0.839817 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.71515 | −0.725780 | −0.362890 | − | 0.931832i | \(-0.618210\pi\) | ||||
−0.362890 | + | 0.931832i | \(0.618210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.67771 | −0.249698 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.221575 | 0.0204846 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.17826 | 0.474690 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.7577 | 1.52343 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.02055 | 0.633022 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.2425 | −1.61876 | −0.809380 | − | 0.587286i | \(-0.800196\pi\) | ||||
−0.809380 | + | 0.587286i | \(0.800196\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.44939 | 0.831972 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.94163 | 0.693864 | 0.346932 | − | 0.937890i | \(-0.387224\pi\) | ||||
0.346932 | + | 0.937890i | \(0.387224\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.38134 | 0.553333 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.4964 | −1.23851 | −0.619254 | − | 0.785190i | \(-0.712565\pi\) | ||||
−0.619254 | + | 0.785190i | \(0.712565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8983 | −1.09402 | −0.547010 | − | 0.837126i | \(-0.684234\pi\) | ||||
−0.547010 | + | 0.837126i | \(0.684234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.74782 | −0.147193 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.16738 | 0.0976213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.52207 | −0.541628 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.54042 | 0.456967 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.64431 | 0.216630 | 0.108315 | − | 0.994117i | \(-0.465454\pi\) | ||||
0.108315 | + | 0.994117i | \(0.465454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00344 | 0.0816587 | 0.0408293 | − | 0.999166i | \(-0.487000\pi\) | ||||
0.0408293 | + | 0.999166i | \(0.487000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.28618 | −0.346517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.38432 | 0.191513 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.0151 | −0.799288 | −0.399644 | − | 0.916670i | \(-0.630866\pi\) | ||||
−0.399644 | + | 0.916670i | \(0.630866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.05419 | 0.400824 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.23502 | 0.254955 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5123 | −1.05836 | −0.529182 | − | 0.848508i | \(-0.677501\pi\) | ||||
−0.529182 | + | 0.848508i | \(0.677501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.26856 | −0.410157 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.12997 | 0.242205 | 0.121102 | − | 0.992640i | \(-0.461357\pi\) | ||||
0.121102 | + | 0.992640i | \(0.461357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9509 | −0.996223 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.28201 | −0.403925 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7522 | −1.12159 | −0.560795 | − | 0.827954i | \(-0.689505\pi\) | ||||
−0.560795 | + | 0.827954i | \(0.689505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.20813 | −0.0913260 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1910 | −0.766000 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2500 | 0.915606 | 0.457803 | − | 0.889054i | \(-0.348637\pi\) | ||||
0.457803 | + | 0.889054i | \(0.348637\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.9768 | −0.964556 | −0.482278 | − | 0.876018i | \(-0.660191\pi\) | ||||
−0.482278 | + | 0.876018i | \(0.660191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.62352 | 0.193936 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.84802 | 0.650520 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.5820 | −1.65136 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.20813 | 0.0878784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6718 | 0.916901 | 0.458451 | − | 0.888720i | \(-0.348405\pi\) | ||||
0.458451 | + | 0.888720i | \(0.348405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.9701 | −1.50946 | −0.754731 | − | 0.656034i | \(-0.772233\pi\) | ||||
−0.754731 | + | 0.656034i | \(0.772233\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.221575 | −0.0158673 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.0298715 | −0.00212826 | −0.00106413 | − | 0.999999i | \(-0.500339\pi\) | ||||
−0.00106413 | + | 0.999999i | \(0.500339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.79971 | −0.623795 | −0.311898 | − | 0.950116i | \(-0.600965\pi\) | ||||
−0.311898 | + | 0.950116i | \(0.600965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | 0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.87950 | 0.553033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.02055 | −0.490337 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.67771 | −0.186114 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.8286 | −1.92494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.3630 | −1.05763 | −0.528816 | − | 0.848737i | \(-0.677364\pi\) | ||||
−0.528816 | + | 0.848737i | \(0.677364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.47669 | −0.443775 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.44939 | −0.644443 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.88057 | −0.195546 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.83165 | 0.461640 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.949710 | −0.0638844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.4518 | 1.10169 | 0.550847 | − | 0.834606i | \(-0.314305\pi\) | ||||
0.550847 | + | 0.834606i | \(0.314305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.69592 | −0.311679 | −0.155840 | − | 0.987782i | \(-0.549808\pi\) | ||||
−0.155840 | + | 0.987782i | \(0.549808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.8217 | −1.30985 | −0.654927 | − | 0.755692i | \(-0.727301\pi\) | ||||
−0.654927 | + | 0.755692i | \(0.727301\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.36510 | 0.418793 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.11745 | 0.531792 | 0.265896 | − | 0.964002i | \(-0.414332\pi\) | ||||
0.265896 | + | 0.964002i | \(0.414332\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.74782 | 0.114015 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.6612 | −1.08226 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.19458 | −0.141956 | −0.0709778 | − | 0.997478i | \(-0.522612\pi\) | ||||
−0.0709778 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.89615 | −0.379804 | −0.189902 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189902 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.54042 | −0.353965 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17036 | −0.0744682 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2039 | 0.646643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.5661 | 1.29812 | 0.649060 | − | 0.760738i | \(-0.275163\pi\) | ||||
0.649060 | + | 0.760738i | \(0.275163\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.1077 | −0.886943 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.28618 | 0.268411 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0885 | 1.37784 | 0.688920 | − | 0.724838i | \(-0.258085\pi\) | ||||
0.688920 | + | 0.724838i | \(0.258085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6896 | −0.664217 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.52207 | −0.403706 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.52774 | −0.279193 | −0.139596 | − | 0.990208i | \(-0.544580\pi\) | ||||
−0.139596 | + | 0.990208i | \(0.544580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.05419 | −0.310477 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.85648 | 0.297211 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7766 | −0.900942 | −0.450471 | − | 0.892791i | \(-0.648744\pi\) | ||||
−0.450471 | + | 0.892791i | \(0.648744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.43852 | −0.208875 | −0.104438 | − | 0.994531i | \(-0.533304\pi\) | ||||
−0.104438 | + | 0.994531i | \(0.533304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.267691 | 0.0162014 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.26856 | 0.317706 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.39446 | 0.203954 | 0.101977 | − | 0.994787i | \(-0.467483\pi\) | ||||
0.101977 | + | 0.994787i | \(0.467483\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.38432 | 0.142746 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3562 | 1.51263 | 0.756313 | − | 0.654210i | \(-0.226999\pi\) | ||||
0.756313 | + | 0.654210i | \(0.226999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.2710 | 0.967209 | 0.483605 | − | 0.875287i | \(-0.339327\pi\) | ||||
0.483605 | + | 0.875287i | \(0.339327\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.28201 | 0.312879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.48173 | 0.500661 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37134 | 0.0806668 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.8518 | −0.812007 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.5037 | −0.613634 | −0.306817 | − | 0.951769i | \(-0.599264\pi\) | ||||
−0.306817 | + | 0.951769i | \(0.599264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1910 | 0.593341 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.26856 | −0.305713 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.593314 | −0.0343122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.4161 | 0.658012 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.48797 | 0.200379 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.62352 | −0.150222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.75566 | 0.385566 | 0.192783 | − | 0.981241i | \(-0.438249\pi\) | ||||
0.192783 | + | 0.981241i | \(0.438249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.08149 | 0.118412 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.7675 | −1.57455 | −0.787274 | − | 0.616603i | \(-0.788508\pi\) | ||||
−0.787274 | + | 0.616603i | \(0.788508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.69703 | −0.0959220 | −0.0479610 | − | 0.998849i | \(-0.515272\pi\) | ||||
−0.0479610 | + | 0.998849i | \(0.515272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.20813 | −0.0680703 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6249 | −0.877579 | −0.438790 | − | 0.898590i | \(-0.644593\pi\) | ||||
−0.438790 | + | 0.898590i | \(0.644593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −34.3619 | −1.92390 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.20298 | 0.346217 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.6396 | 1.25970 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.221575 | 0.0122908 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.50055 | −0.0829804 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.11159 | −0.116416 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8890 | 1.20313 | 0.601564 | − | 0.798824i | \(-0.294544\pi\) | ||||
0.601564 | + | 0.798824i | \(0.294544\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.84802 | 0.484869 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.5155 | −1.11755 | −0.558775 | − | 0.829319i | \(-0.688728\pi\) | ||||
−0.558775 | + | 0.829319i | \(0.688728\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.71515 | 0.419029 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5619 | 0.680268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.1504 | 0.818047 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.67771 | 0.144163 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.81881 | 0.312370 | 0.156185 | − | 0.987728i | \(-0.450080\pi\) | ||||
0.156185 | + | 0.987728i | \(0.450080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.1985 | −1.67002 | −0.835010 | − | 0.550235i | \(-0.814538\pi\) | ||||
−0.835010 | + | 0.550235i | \(0.814538\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.221575 | −0.0118268 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0053 | 0.532527 | 0.266263 | − | 0.963900i | \(-0.414211\pi\) | ||||
0.266263 | + | 0.963900i | \(0.414211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.47669 | 0.343747 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.17826 | −0.274062 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.08282 | −0.109927 | −0.0549634 | − | 0.998488i | \(-0.517504\pi\) | ||||
−0.0549634 | + | 0.998488i | \(0.517504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.89959 | 0.468399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.7577 | −0.879552 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.83165 | −0.357585 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.23892 | 0.273469 | 0.136735 | − | 0.990608i | \(-0.456339\pi\) | ||||
0.136735 | + | 0.990608i | \(0.456339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.02055 | −0.365475 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.10612 | 0.317014 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.55057 | 0.0802852 | 0.0401426 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401426 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.44513 | −0.0744278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.2300 | 0.987778 | 0.493889 | − | 0.869525i | \(-0.335575\pi\) | ||||
0.493889 | + | 0.869525i | \(0.335575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.2425 | 0.934591 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.7083 | −1.56912 | −0.784559 | − | 0.620054i | \(-0.787111\pi\) | ||||
−0.784559 | + | 0.620054i | \(0.787111\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.36510 | −0.324395 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.44939 | −0.480339 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.0267 | 1.57312 | 0.786559 | − | 0.617515i | \(-0.211861\pi\) | ||||
0.786559 | + | 0.617515i | \(0.211861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.4772 | 0.580425 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.94163 | −0.400602 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.6612 | 0.838315 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.0597 | −1.10714 | −0.553572 | − | 0.832801i | \(-0.686736\pi\) | ||||
−0.553572 | + | 0.832801i | \(0.686736\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.38134 | −0.319467 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.53299 | 0.326242 | 0.163121 | − | 0.986606i | \(-0.447844\pi\) | ||||
0.163121 | + | 0.986606i | \(0.447844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.528306 | 0.0263168 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.6163 | 2.31069 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9387 | −0.689222 | −0.344611 | − | 0.938746i | \(-0.611989\pi\) | ||||
−0.344611 | + | 0.938746i | \(0.611989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.4964 | 0.715053 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.3120 | −0.605834 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2039 | −0.500887 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.8983 | 0.631633 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0939 | 0.639677 | 0.319839 | − | 0.947472i | \(-0.396371\pi\) | ||||
0.319839 | + | 0.947472i | \(0.396371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.70216 | −0.180432 | −0.0902161 | − | 0.995922i | \(-0.528756\pi\) | ||||
−0.0902161 | + | 0.995922i | \(0.528756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.74782 | 0.0849818 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.28618 | −0.207910 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.16955 | 0.153385 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.16738 | −0.0563617 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.8212 | −0.569407 | −0.284703 | − | 0.958616i | \(-0.591895\pi\) | ||||
−0.284703 | + | 0.958616i | \(0.591895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2560 | −1.45401 | −0.727006 | − | 0.686631i | \(-0.759089\pi\) | ||||
−0.727006 | + | 0.686631i | \(0.759089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.52207 | 0.312709 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.1437 | 0.676584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7871 | 1.27848 | 0.639240 | − | 0.769007i | \(-0.279249\pi\) | ||||
0.639240 | + | 0.769007i | \(0.279249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.54042 | −0.263830 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.3894 | 1.06375 | 0.531876 | − | 0.846822i | \(-0.321487\pi\) | ||||
0.531876 | + | 0.846822i | \(0.321487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.85648 | −0.230219 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.64431 | −0.125071 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7716 | 0.744309 | 0.372155 | − | 0.928171i | \(-0.378619\pi\) | ||||
0.372155 | + | 0.928171i | \(0.378619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.9882 | −1.74171 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.00344 | −0.0471456 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.267691 | −0.0125496 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.3749 | 1.23377 | 0.616883 | − | 0.787055i | \(-0.288395\pi\) | ||||
0.616883 | + | 0.787055i | \(0.288395\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.28618 | 0.200062 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.2864 | −1.73660 | −0.868300 | − | 0.496039i | \(-0.834787\pi\) | ||||
−0.868300 | + | 0.496039i | \(0.834787\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.1519 | −1.40128 | −0.700639 | − | 0.713516i | \(-0.747102\pi\) | ||||
−0.700639 | + | 0.713516i | \(0.747102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.38432 | −0.110570 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.98512 | 0.0918605 | 0.0459303 | − | 0.998945i | \(-0.485375\pi\) | ||||
0.0459303 | + | 0.998945i | \(0.485375\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.20813 | 0.0557862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.0151 | 0.461469 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −49.7847 | −2.28910 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.28201 | −0.242355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.05419 | −0.231416 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.2629 | −1.61120 | −0.805602 | − | 0.592457i | \(-0.798158\pi\) | ||||
−0.805602 | + | 0.592457i | \(0.798158\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.96050 | 0.0893911 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.23502 | −0.147199 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8518 | 0.628978 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.7469 | −0.758875 | −0.379437 | − | 0.925217i | \(-0.623882\pi\) | ||||
−0.379437 | + | 0.925217i | \(0.623882\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.5123 | 0.611047 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.1645 | 1.09053 | 0.545265 | − | 0.838264i | \(-0.316429\pi\) | ||||
0.545265 | + | 0.838264i | \(0.316429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.9548 | 1.25902 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.26856 | 0.236804 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.82467 | −0.350985 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.75145 | 0.436535 | 0.218267 | − | 0.975889i | \(-0.429960\pi\) | ||||
0.218267 | + | 0.975889i | \(0.429960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.12997 | −0.139837 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.65830 | −0.207703 | −0.103852 | − | 0.994593i | \(-0.533117\pi\) | ||||
−0.103852 | + | 0.994593i | \(0.533117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.48797 | −0.155213 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9509 | 0.575170 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.20120 | 0.230539 | 0.115269 | − | 0.993334i | \(-0.463227\pi\) | ||||
0.115269 | + | 0.993334i | \(0.463227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.25351 | 0.365114 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.28201 | 0.233206 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.08149 | −0.0917214 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.20848 | 0.404989 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7522 | 0.647551 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.7719 | −0.690980 | −0.345490 | − | 0.938422i | \(-0.612287\pi\) | ||||
−0.345490 | + | 0.938422i | \(0.612287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.4599 | −1.76919 | −0.884595 | − | 0.466360i | \(-0.845565\pi\) | ||||
−0.884595 | + | 0.466360i | \(0.845565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.20813 | 0.0527271 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.2196 | −0.445174 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8299 | −0.688255 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1910 | 0.442250 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.55558 | −0.0673796 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.20298 | −0.268178 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.2500 | −0.528625 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.1901 | −1.25730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2953 | −0.829571 | −0.414785 | − | 0.909919i | \(-0.636143\pi\) | ||||
−0.414785 | + | 0.909919i | \(0.636143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.9768 | 0.556887 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.50055 | 0.0642763 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.6679 | −1.26851 | −0.634254 | − | 0.773125i | \(-0.718693\pi\) | ||||
−0.634254 | + | 0.773125i | \(0.718693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.62352 | −0.111969 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4496 | 1.46760 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.1289 | −0.855966 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.84802 | −0.375578 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.85195 | 0.120841 | 0.0604204 | − | 0.998173i | \(-0.480756\pi\) | ||||
0.0604204 | + | 0.998173i | \(0.480756\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.09375 | −0.0885561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5820 | 0.953413 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.76040 | 0.284917 | 0.142458 | − | 0.989801i | \(-0.454499\pi\) | ||||
0.142458 | + | 0.989801i | \(0.454499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.71515 | −0.324579 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.20813 | −0.0507366 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.0963 | −0.926326 | −0.463163 | − | 0.886273i | \(-0.653286\pi\) | ||||
−0.463163 | + | 0.886273i | \(0.653286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.2440 | −1.18197 | −0.590987 | − | 0.806681i | \(-0.701262\pi\) | ||||
−0.590987 | + | 0.806681i | \(0.701262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.6718 | −0.529373 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.67771 | −0.111668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.97207 | 0.331882 | 0.165941 | − | 0.986136i | \(-0.446934\pi\) | ||||
0.165941 | + | 0.986136i | \(0.446934\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.9701 | 0.871489 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.3276 | 0.511434 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.6283 | −1.10283 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.221575 | 0.00916100 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.72439 | 0.401369 | 0.200684 | − | 0.979656i | \(-0.435683\pi\) | ||||
0.200684 | + | 0.979656i | \(0.435683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5940 | −0.518927 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0298715 | 0.00122875 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.1802 | 0.992961 | 0.496480 | − | 0.868048i | \(-0.334626\pi\) | ||||
0.496480 | + | 0.868048i | \(0.334626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.17826 | 0.212288 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.79971 | 0.360148 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.26002 | −0.255778 | −0.127889 | − | 0.991789i | \(-0.540820\pi\) | ||||
−0.127889 | + | 0.991789i | \(0.540820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.78039 | −0.113415 | −0.0567073 | − | 0.998391i | \(-0.518060\pi\) | ||||
−0.0567073 | + | 0.998391i | \(0.518060\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.7577 | 0.681298 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3197 | 0.500040 | 0.250020 | − | 0.968241i | \(-0.419563\pi\) | ||||
0.250020 | + | 0.968241i | \(0.419563\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.87950 | −0.319293 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.387273 | 0.0156674 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.3931 | 0.460164 | 0.230082 | − | 0.973171i | \(-0.426101\pi\) | ||||
0.230082 | + | 0.973171i | \(0.426101\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.02055 | 0.283096 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.9748 | −0.482086 | −0.241043 | − | 0.970514i | \(-0.577489\pi\) | ||||
−0.241043 | + | 0.970514i | \(0.577489\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.25911 | 0.331962 | 0.165981 | − | 0.986129i | \(-0.446921\pi\) | ||||
0.165981 | + | 0.986129i | \(0.446921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.67771 | 0.107453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.86725 | 0.235066 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.8286 | 1.11137 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −37.9242 | −1.51214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.5428 | 1.89265 | 0.946325 | − | 0.323218i | \(-0.104765\pi\) | ||||
0.946325 | + | 0.323218i | \(0.104765\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.3630 | 0.610624 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.2425 | −0.723931 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.22762 | −0.0486401 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.47669 | 0.256214 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.4053 | 1.16144 | 0.580720 | − | 0.814103i | \(-0.302771\pi\) | ||||
0.580720 | + | 0.814103i | \(0.302771\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.8999 | 0.705903 | 0.352952 | − | 0.935642i | \(-0.385178\pi\) | ||||
0.352952 | + | 0.935642i | \(0.385178\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.44939 | 0.372069 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.8635 | 1.37063 | 0.685313 | − | 0.728248i | \(-0.259665\pi\) | ||||
0.685313 | + | 0.728248i | \(0.259665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.6917 | 2.10758 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.88057 | 0.112898 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.7869 | 1.40045 | 0.700225 | − | 0.713922i | \(-0.253083\pi\) | ||||
0.700225 | + | 0.713922i | \(0.253083\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.94163 | 0.310305 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.83165 | −0.266528 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7234 | 1.50845 | 0.754225 | − | 0.656616i | \(-0.228013\pi\) | ||||
0.754225 | + | 0.656616i | \(0.228013\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.65942 | 0.142335 | 0.0711675 | − | 0.997464i | \(-0.477328\pi\) | ||||
0.0711675 | + | 0.997464i | \(0.477328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.949710 | 0.0368837 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.38134 | 0.247458 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.4642 | 0.676217 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.4518 | −0.636064 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.8222 | −0.533599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.6162 | 1.48855 | 0.744273 | − | 0.667875i | \(-0.232796\pi\) | ||||
0.744273 | + | 0.667875i | \(0.232796\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.1414 | 1.54276 | 0.771379 | − | 0.636376i | \(-0.219567\pi\) | ||||
0.771379 | + | 0.636376i | \(0.219567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.7348 | −0.642221 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.69592 | 0.179948 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7462 | −0.487720 | −0.243860 | − | 0.969810i | \(-0.578414\pi\) | ||||
−0.243860 | + | 0.969810i | \(0.578414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.4964 | −0.553878 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.8217 | 0.756245 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.11988 | −0.0426641 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8852 | −0.414094 | −0.207047 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207047 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.36510 | −0.241790 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8983 | −0.489261 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30.0913 | 1.13979 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.11745 | −0.307030 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.2030 | 1.02744 | 0.513721 | − | 0.857957i | \(-0.328267\pi\) | ||||
0.513721 | + | 0.857957i | \(0.328267\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −46.7353 | −1.76266 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.74782 | −0.0658266 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.21391 | 0.158481 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.2293 | 1.54840 | 0.774200 | − | 0.632941i | \(-0.218152\pi\) | ||||
0.774200 | + | 0.632941i | \(0.218152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.6612 | 0.624843 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.38453 | −0.239103 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16738 | 0.0436576 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.19458 | 0.0819581 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.7367 | −1.07170 | −0.535848 | − | 0.844314i | \(-0.680008\pi\) | ||||
−0.535848 | + | 0.844314i | \(0.680008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.51471 | 0.0936526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.89615 | 0.219280 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.52207 | −0.242224 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.2623 | −0.603136 | −0.301568 | − | 0.953445i | \(-0.597510\pi\) | ||||
−0.301568 | + | 0.953445i | \(0.597510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.5018 | 1.49801 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.5411 | −1.71904 | −0.859518 | − | 0.511105i | \(-0.829236\pi\) | ||||
−0.859518 | + | 0.511105i | \(0.829236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.54042 | 0.204362 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.26856 | −0.194070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1832 | 1.33102 | 0.665511 | − | 0.746388i | \(-0.268214\pi\) | ||||
0.665511 | + | 0.746388i | \(0.268214\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.17036 | 0.0429943 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3825 | 1.15131 | 0.575657 | − | 0.817691i | \(-0.304746\pi\) | ||||
0.575657 | + | 0.817691i | \(0.304746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.64431 | 0.0968799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.2039 | −0.373339 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.49400 | 0.273825 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0310 | 0.621472 | 0.310736 | − | 0.950496i | \(-0.399425\pi\) | ||||
0.310736 | + | 0.950496i | \(0.399425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −20.5661 | −0.749469 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00344 | 0.0365189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.0230 | −0.727749 | −0.363875 | − | 0.931448i | \(-0.618546\pi\) | ||||
−0.363875 | + | 0.931448i | \(0.618546\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.1077 | 0.512077 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0826 | 0.945493 | 0.472747 | − | 0.881198i | \(-0.343263\pi\) | ||||
0.472747 | + | 0.881198i | \(0.343263\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.81285 | −0.0656297 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.28618 | −0.154967 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.25806 | 0.0815339 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8245 | 0.678829 | 0.339414 | − | 0.940637i | \(-0.389771\pi\) | ||||
0.339414 | + | 0.940637i | \(0.389771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0885 | −0.795496 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.5855 | 0.920248 | 0.460124 | − | 0.887855i | \(-0.347805\pi\) | ||||
0.460124 | + | 0.887855i | \(0.347805\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.38432 | 0.0856474 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.6896 | 0.383486 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.0826 | 1.32862 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.1228 | 1.22101 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.52207 | 0.233080 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0151 | −0.357452 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.06377 | −0.287442 | −0.143721 | − | 0.989618i | \(-0.545907\pi\) | ||||
−0.143721 | + | 0.989618i | \(0.545907\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.52774 | 0.161192 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.32089 | 0.331413 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.581306 | −0.0206428 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.05419 | 0.179254 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.8730 | 0.916468 | 0.458234 | − | 0.888832i | \(-0.348482\pi\) | ||||
0.458234 | + | 0.888832i | \(0.348482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.49146 | −0.265029 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.85648 | −0.171595 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.9929 | −1.27016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.23502 | 0.114020 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.7766 | 0.520159 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.2083 | −0.569854 | −0.284927 | − | 0.958549i | \(-0.591969\pi\) | ||||
−0.284927 | + | 0.958549i | \(0.591969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.9205 | 1.43691 | 0.718457 | − | 0.695571i | \(-0.244849\pi\) | ||||
0.718457 | + | 0.695571i | \(0.244849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.43852 | 0.120594 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.5123 | −0.473315 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 49.9117 | 1.74619 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.267691 | −0.00935388 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.74373 | 0.305158 | 0.152579 | − | 0.988291i | \(-0.451242\pi\) | ||||
0.152579 | + | 0.988291i | \(0.451242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.33914 | 0.151253 | 0.0756265 | − | 0.997136i | \(-0.475904\pi\) | ||||
0.0756265 | + | 0.997136i | \(0.475904\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.26856 | −0.183428 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8600 | −0.481959 | −0.240979 | − | 0.970530i | \(-0.577469\pi\) | ||||
−0.240979 | + | 0.970530i | \(0.577469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5706 | 1.20069 | 0.600343 | − | 0.799742i | \(-0.295031\pi\) | ||||
0.600343 | + | 0.799742i | \(0.295031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.39446 | −0.117753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.7473 | 0.822794 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.12997 | 0.108317 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.38432 | −0.0824143 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.9355 | −1.30968 | −0.654840 | − | 0.755767i | \(-0.727264\pi\) | ||||
−0.654840 | + | 0.755767i | \(0.727264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5374 | 0.466807 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.3562 | −0.873315 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.9509 | −0.445525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2455 | −0.695643 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.2710 | −0.558419 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.6925 | −0.812167 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.2892 | −1.44795 | −0.723977 | − | 0.689824i | \(-0.757688\pi\) | ||||
−0.723977 | + | 0.689824i | \(0.757688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.28201 | −0.180641 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.8774 | −0.474044 | −0.237022 | − | 0.971504i | \(-0.576171\pi\) | ||||
−0.237022 | + | 0.971504i | \(0.576171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.3256 | 1.68297 | 0.841483 | − | 0.540283i | \(-0.181683\pi\) | ||||
0.841483 | + | 0.540283i | \(0.181683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.48173 | −0.289057 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.5871 | 0.768874 | 0.384437 | − | 0.923151i | \(-0.374396\pi\) | ||||
0.384437 | + | 0.923151i | \(0.374396\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.7522 | −0.501591 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.37134 | −0.0465730 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 87.7804 | 2.97775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.221575 | −0.00750778 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.8518 | 0.468812 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.20813 | −0.0408422 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.9314 | −0.808105 | −0.404053 | − | 0.914736i | \(-0.632399\pi\) | ||||
−0.404053 | + | 0.914736i | \(0.632399\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5037 | 0.354281 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.9624 | 0.942079 | 0.471039 | − | 0.882112i | \(-0.343879\pi\) | ||||
0.471039 | + | 0.882112i | \(0.343879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.42710 | −0.148984 | −0.0744920 | − | 0.997222i | \(-0.523734\pi\) | ||||
−0.0744920 | + | 0.997222i | \(0.523734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1910 | −0.342566 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.7480 | 0.998842 | 0.499421 | − | 0.866360i | \(-0.333546\pi\) | ||||
0.499421 | + | 0.866360i | \(0.333546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.0393 | 0.739174 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.26856 | 0.176503 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.23199 | −0.308937 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.2500 | 0.409471 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.593314 | 0.0198102 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.5507 | −0.518646 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.6632 | 0.721705 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.4161 | −0.379903 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.9768 | −0.431363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.3392 | 0.409716 | 0.204858 | − | 0.978792i | \(-0.434327\pi\) | ||||
0.204858 | + | 0.978792i | \(0.434327\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.48797 | −0.115689 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.77581 | −0.0919666 | −0.0459833 | − | 0.998942i | \(-0.514642\pi\) | ||||
−0.0459833 | + | 0.998942i | \(0.514642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −53.7596 | −1.77918 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.62352 | 0.0867308 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.59452 | −0.316839 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2264 | −0.832141 | −0.416070 | − | 0.909332i | \(-0.636593\pi\) | ||||
−0.416070 | + | 0.909332i | \(0.636593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.75566 | −0.222607 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.43507 | 0.0472360 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.84802 | 0.290921 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.08149 | −0.0683651 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.4132 | −1.75243 | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||||
−0.876216 | + | 0.481919i | \(0.839940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.2646 | 0.959107 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.7675 | 0.909066 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.5820 | −0.738510 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.30085 | −0.0424969 | −0.0212485 | − | 0.999774i | \(-0.506764\pi\) | ||||
−0.0212485 | + | 0.999774i | \(0.506764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.69703 | 0.0553806 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.872072 | 0.0284287 | 0.0142144 | − | 0.999899i | \(-0.495475\pi\) | ||||
0.0142144 | + | 0.999899i | \(0.495475\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.7990 | 0.612180 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.20813 | 0.0393004 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.3246 | −1.01791 | −0.508957 | − | 0.860792i | \(-0.669969\pi\) | ||||
−0.508957 | + | 0.860792i | \(0.669969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.51372 | −0.0491375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.6249 | 0.506671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.9757 | 1.29494 | 0.647470 | − | 0.762091i | \(-0.275827\pi\) | ||||
0.647470 | + | 0.762091i | \(0.275827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6718 | 0.410051 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.3619 | 1.11076 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.5135 | 0.565540 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.3150 | −0.816613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.20298 | −0.199888 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20.9701 | −0.675052 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8166 | 0.701576 | 0.350788 | − | 0.936455i | \(-0.385914\pi\) | ||||
0.350788 | + | 0.936455i | \(0.385914\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.6396 | −0.727290 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.1306 | 1.06321 | 0.531606 | − | 0.846992i | \(-0.321589\pi\) | ||||
0.531606 | + | 0.846992i | \(0.321589\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.5828 | 0.499562 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.221575 | −0.00709608 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60.5558 | 1.93735 | 0.968675 | − | 0.248331i | \(-0.0798820\pi\) | ||||
0.968675 | + | 0.248331i | \(0.0798820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.5866 | −0.817752 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.50055 | 0.0479087 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.4291 | 0.811064 | 0.405532 | − | 0.914081i | \(-0.367086\pi\) | ||||
0.405532 | + | 0.914081i | \(0.367086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0298715 | −0.000951786 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.11159 | 0.0672126 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.3027 | 0.804580 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.77341 | 0.119866 | 0.0599332 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599332 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.8890 | −0.694626 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.79971 | −0.278970 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.0286 | −0.792662 | −0.396331 | − | 0.918108i | \(-0.629717\pi\) | ||||
−0.396331 | + | 0.918108i | \(0.629717\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.84802 | −0.279939 |
(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 | 4020.2.a.e.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.e.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial |