Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3744,2,Mod(1,3744)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3744, 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("3744.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.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: | \(29.8959905168\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3744.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35114 | −0.888648 | −0.444324 | − | 0.895866i | \(-0.646556\pi\) | ||||
−0.444324 | + | 0.895866i | \(0.646556\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.15537 | 1.85591 | 0.927957 | − | 0.372689i | \(-0.121564\pi\) | ||||
0.927957 | + | 0.372689i | \(0.121564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.47214 | −1.56972 | −0.784862 | − | 0.619671i | \(-0.787266\pi\) | ||||
−0.784862 | + | 0.619671i | \(0.787266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.25731 | −1.20611 | −0.603055 | − | 0.797700i | \(-0.706050\pi\) | ||||
−0.603055 | + | 0.797700i | \(0.706050\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.35114 | −0.422277 | −0.211139 | − | 0.977456i | \(-0.567717\pi\) | ||||
−0.211139 | + | 0.977456i | \(0.567717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.90617 | −0.491232 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9443 | −1.79923 | −0.899614 | − | 0.436687i | \(-0.856152\pi\) | ||||
−0.899614 | + | 0.436687i | \(0.856152\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.23607 | −0.817736 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.60845 | 1.16028 | 0.580139 | − | 0.814517i | \(-0.302998\pi\) | ||||
0.580139 | + | 0.814517i | \(0.302998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.06154 | −1.32176 | −0.660881 | − | 0.750491i | \(-0.729817\pi\) | ||||
−0.660881 | + | 0.750491i | \(0.729817\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.47214 | −0.210305 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.94427 | 0.679148 | 0.339574 | − | 0.940579i | \(-0.389717\pi\) | ||||
0.339574 | + | 0.940579i | \(0.389717\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.60845 | 1.02592 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.06154 | 1.17971 | 0.589856 | − | 0.807509i | \(-0.299185\pi\) | ||||
0.589856 | + | 0.807509i | \(0.299185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.47214 | 0.572598 | 0.286299 | − | 0.958140i | \(-0.407575\pi\) | ||||
0.286299 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.23607 | 0.153315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.6619 | 1.79123 | 0.895617 | − | 0.444827i | \(-0.146735\pi\) | ||||
0.895617 | + | 0.444827i | \(0.146735\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.15537 | 0.730508 | 0.365254 | − | 0.930908i | \(-0.380982\pi\) | ||||
0.365254 | + | 0.930908i | \(0.380982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.4721 | −1.64925 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.2169 | −1.71204 | −0.856018 | − | 0.516946i | \(-0.827069\pi\) | ||||
−0.856018 | + | 0.516946i | \(0.827069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.24920 | −0.356646 | −0.178323 | − | 0.983972i | \(-0.557067\pi\) | ||||
−0.178323 | + | 0.983972i | \(0.557067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.7082 | −1.66507 | −0.832533 | − | 0.553975i | \(-0.813110\pi\) | ||||
−0.832533 | + | 0.553975i | \(0.813110\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.35114 | −0.246467 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.49839 | −0.666721 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9443 | 1.11122 | 0.555611 | − | 0.831442i | \(-0.312484\pi\) | ||||
0.555611 | + | 0.831442i | \(0.312484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.52786 | −0.550043 | −0.275022 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275022 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0130 | 1.67634 | 0.838171 | − | 0.545407i | \(-0.183625\pi\) | ||||
0.838171 | + | 0.545407i | \(0.183625\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.2169 | −1.47107 | −0.735537 | − | 0.677485i | \(-0.763070\pi\) | ||||
−0.735537 | + | 0.677485i | \(0.763070\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9443 | −1.43140 | −0.715701 | − | 0.698407i | \(-0.753893\pi\) | ||||
−0.715701 | + | 0.698407i | \(0.753893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.00000 | −0.376288 | −0.188144 | − | 0.982141i | \(-0.560247\pi\) | ||||
−0.188144 | + | 0.982141i | \(0.560247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.2169 | 1.39493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.8885 | 2.44441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.70228 | −0.417260 | −0.208630 | − | 0.977995i | \(-0.566900\pi\) | ||||
−0.208630 | + | 0.977995i | \(0.566900\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.40456 | −0.821681 | −0.410840 | − | 0.911707i | \(-0.634765\pi\) | ||||
−0.410840 | + | 0.911707i | \(0.634765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.3607 | 1.07181 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.291796 | −0.0249298 | −0.0124649 | − | 0.999922i | \(-0.503968\pi\) | ||||
−0.0124649 | + | 0.999922i | \(0.503968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.90617 | 0.246498 | 0.123249 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123249 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.15537 | 0.514738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.94427 | −0.410599 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2361 | −1.41203 | −0.706017 | − | 0.708195i | \(-0.749510\pi\) | ||||
−0.706017 | + | 0.708195i | \(0.749510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.2703 | −1.81233 | −0.906167 | − | 0.422921i | \(-0.861005\pi\) | ||||
−0.906167 | + | 0.422921i | \(0.861005\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.90617 | −0.233429 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.41641 | 0.432276 | 0.216138 | − | 0.976363i | \(-0.430654\pi\) | ||||
0.216138 | + | 0.976363i | \(0.430654\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.95959 | −0.780096 | −0.390048 | − | 0.920795i | \(-0.627542\pi\) | ||||
−0.390048 | + | 0.920795i | \(0.627542\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.06154 | −0.701203 | −0.350601 | − | 0.936525i | \(-0.614023\pi\) | ||||
−0.350601 | + | 0.936525i | \(0.614023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.4721 | −0.796182 | −0.398091 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398091 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.16348 | 0.617101 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7153 | −1.62308 | −0.811539 | − | 0.584299i | \(-0.801370\pi\) | ||||
−0.811539 | + | 0.584299i | \(0.801370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.4721 | −1.22436 | −0.612182 | − | 0.790717i | \(-0.709708\pi\) | ||||
−0.612182 | + | 0.790717i | \(0.709708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.5279 | −0.994588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.8384 | −2.91327 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.49839 | 0.470207 | 0.235104 | − | 0.971970i | \(-0.424457\pi\) | ||||
0.235104 | + | 0.971970i | \(0.424457\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.94427 | −0.211933 | −0.105967 | − | 0.994370i | \(-0.533794\pi\) | ||||
−0.105967 | + | 0.994370i | \(0.533794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1803 | 1.01031 | 0.505154 | − | 0.863029i | \(-0.331436\pi\) | ||||
0.505154 | + | 0.863029i | \(0.331436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.1068 | 1.00001 | 0.500004 | − | 0.866023i | \(-0.333332\pi\) | ||||
0.500004 | + | 0.866023i | \(0.333332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.40456 | 0.660071 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.47214 | −0.452034 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.3607 | −2.23844 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.81234 | −0.400138 | −0.200069 | − | 0.979782i | \(-0.564117\pi\) | ||||
−0.200069 | + | 0.979782i | \(0.564117\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.40456 | 0.641386 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.52786 | 0.375256 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.47214 | −0.435363 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2703 | 1.49133 | 0.745666 | − | 0.666320i | \(-0.232132\pi\) | ||||
0.745666 | + | 0.666320i | \(0.232132\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.8707 | 1.84984 | 0.924921 | − | 0.380161i | \(-0.124131\pi\) | ||||
0.924921 | + | 0.380161i | \(0.124131\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41641 | 0.485865 | 0.242933 | − | 0.970043i | \(-0.421891\pi\) | ||||
0.242933 | + | 0.970043i | \(0.421891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2007 | −0.730652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8707 | −1.80280 | −0.901402 | − | 0.432984i | \(-0.857461\pi\) | ||||
−0.901402 | + | 0.432984i | \(0.857461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.88854 | 0.508146 | 0.254073 | − | 0.967185i | \(-0.418230\pi\) | ||||
0.254073 | + | 0.967185i | \(0.418230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.81966 | −0.116254 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.25731 | −0.334515 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.1231 | 1.14392 | 0.571959 | − | 0.820282i | \(-0.306184\pi\) | ||||
0.571959 | + | 0.820282i | \(0.306184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5279 | −0.843845 | −0.421922 | − | 0.906632i | \(-0.638645\pi\) | ||||
−0.421922 | + | 0.906632i | \(0.638645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.7315 | 1.59888 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3107 | 0.759112 | 0.379556 | − | 0.925169i | \(-0.376077\pi\) | ||||
0.379556 | + | 0.925169i | \(0.376077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.11146 | 0.375424 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0000 | 1.21942 | 0.609711 | − | 0.792624i | \(-0.291286\pi\) | ||||
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.35114 | −0.142822 | −0.0714108 | − | 0.997447i | \(-0.522750\pi\) | ||||
−0.0714108 | + | 0.997447i | \(0.522750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −21.3723 | −1.28880 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.291796 | −0.0174071 | −0.00870355 | − | 0.999962i | \(-0.502770\pi\) | ||||
−0.00870355 | + | 0.999962i | \(0.502770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1068 | 0.838565 | 0.419282 | − | 0.907856i | \(-0.362282\pi\) | ||||
0.419282 | + | 0.907856i | \(0.362282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.3107 | 0.726680 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.8885 | 1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1246 | −1.11727 | −0.558636 | − | 0.829413i | \(-0.688675\pi\) | ||||
−0.558636 | + | 0.829413i | \(0.688675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2007 | 0.652129 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.8885 | −1.03108 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.52786 | 0.316525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.95959 | 0.568424 | 0.284212 | − | 0.958761i | \(-0.408268\pi\) | ||||
0.284212 | + | 0.958761i | \(0.408268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8885 | 1.35026 | 0.675130 | − | 0.737699i | \(-0.264087\pi\) | ||||
0.675130 | + | 0.737699i | \(0.264087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.5967 | −1.21299 | −0.606497 | − | 0.795086i | \(-0.707426\pi\) | ||||
−0.606497 | + | 0.795086i | \(0.707426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.6215 | −1.37854 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.0260 | 1.89326 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.47214 | −0.192599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 21.3050 | 1.17458 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.25731 | 0.288968 | 0.144484 | − | 0.989507i | \(-0.453848\pi\) | ||||
0.144484 | + | 0.989507i | \(0.453848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.1231 | 0.990169 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.4721 | −0.783710 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9192 | 1.07553 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.6215 | 1.32175 | 0.660875 | − | 0.750496i | \(-0.270185\pi\) | ||||
0.660875 | + | 0.750496i | \(0.270185\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.88854 | −0.422264 | −0.211132 | − | 0.977458i | \(-0.567715\pi\) | ||||
−0.211132 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.7639 | 0.998703 | 0.499352 | − | 0.866399i | \(-0.333572\pi\) | ||||
0.499352 | + | 0.866399i | \(0.333572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.60845 | 0.403815 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6538 | −0.667840 | −0.333920 | − | 0.942601i | \(-0.608372\pi\) | ||||
−0.333920 | + | 0.942601i | \(0.608372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.63932 | 0.454701 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.41641 | 0.388193 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1231 | 0.946017 | 0.473008 | − | 0.881058i | \(-0.343168\pi\) | ||||
0.473008 | + | 0.881058i | \(0.343168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6247 | −0.603523 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.95959 | 0.511590 | 0.255795 | − | 0.966731i | \(-0.417663\pi\) | ||||
0.255795 | + | 0.966731i | \(0.417663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9677 | −0.611521 | −0.305761 | − | 0.952108i | \(-0.598911\pi\) | ||||
−0.305761 | + | 0.952108i | \(0.598911\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.8885 | −0.911685 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4721 | −0.733766 | −0.366883 | − | 0.930267i | \(-0.619575\pi\) | ||||
−0.366883 | + | 0.930267i | \(0.619575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.8091 | −0.946390 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.8328 | 1.24632 | 0.623162 | − | 0.782093i | \(-0.285848\pi\) | ||||
0.623162 | + | 0.782093i | \(0.285848\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.7082 | −1.58343 | −0.791716 | − | 0.610889i | \(-0.790812\pi\) | ||||
−0.791716 | + | 0.610889i | \(0.790812\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.35114 | −0.117119 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −67.3660 | −3.33921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.8885 | −0.587851 | −0.293925 | − | 0.955828i | \(-0.594962\pi\) | ||||
−0.293925 | + | 0.955828i | \(0.594962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.3050 | −1.04835 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.01623 | −0.197149 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.0292 | 1.02735 | 0.513673 | − | 0.857986i | \(-0.328284\pi\) | ||||
0.513673 | + | 0.857986i | \(0.328284\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.4721 | 1.09006 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.5146 | −0.508838 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.6538 | 0.609510 | 0.304755 | − | 0.952431i | \(-0.401425\pi\) | ||||
0.304755 | + | 0.952431i | \(0.401425\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.41641 | −0.452524 | −0.226262 | − | 0.974067i | \(-0.572651\pi\) | ||||
−0.226262 | + | 0.974067i | \(0.572651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.4176 | −1.26084 | −0.630421 | − | 0.776253i | \(-0.717118\pi\) | ||||
−0.630421 | + | 0.776253i | \(0.717118\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.2169 | −0.722977 | −0.361488 | − | 0.932377i | \(-0.617731\pi\) | ||||
−0.361488 | + | 0.932377i | \(0.617731\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.4164 | −0.920426 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.1803 | 1.23553 | 0.617763 | − | 0.786364i | \(-0.288039\pi\) | ||||
0.617763 | + | 0.786364i | \(0.288039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.2299 | −1.51765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.90617 | −0.136243 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9443 | 1.26040 | 0.630200 | − | 0.776433i | \(-0.282973\pi\) | ||||
0.630200 | + | 0.776433i | \(0.282973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0689 | 1.12100 | 0.560500 | − | 0.828155i | \(-0.310609\pi\) | ||||
0.560500 | + | 0.828155i | \(0.310609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.7557 | −0.546334 | −0.273167 | − | 0.961967i | \(-0.588071\pi\) | ||||
−0.273167 | + | 0.961967i | \(0.588071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.49839 | −0.300710 | −0.150355 | − | 0.988632i | \(-0.548042\pi\) | ||||
−0.150355 | + | 0.988632i | \(0.548042\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.4721 | −1.59178 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.8328 | 2.15338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.2541 | 0.837556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.5599 | −0.710951 | −0.355476 | − | 0.934686i | \(-0.615681\pi\) | ||||
−0.355476 | + | 0.934686i | \(0.615681\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.9443 | −0.499016 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.5279 | 0.614269 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7849 | −1.48563 | −0.742814 | − | 0.669498i | \(-0.766509\pi\) | ||||
−0.742814 | + | 0.669498i | \(0.766509\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.9322 | −1.66673 | −0.833363 | − | 0.552725i | \(-0.813588\pi\) | ||||
−0.833363 | + | 0.552725i | \(0.813588\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8885 | 1.16596 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.4721 | −0.649164 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.0697 | 0.495546 | 0.247773 | − | 0.968818i | \(-0.420301\pi\) | ||||
0.247773 | + | 0.968818i | \(0.420301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1231 | 0.808068 | 0.404034 | − | 0.914744i | \(-0.367608\pi\) | ||||
0.404034 | + | 0.914744i | \(0.367608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.83282 | −0.304056 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2918 | 0.544824 | 0.272412 | − | 0.962181i | \(-0.412179\pi\) | ||||
0.272412 | + | 0.962181i | \(0.412179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.1068 | −0.624050 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.0292 | 0.926659 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −55.7771 | −2.45307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.11146 | 0.0925046 | 0.0462523 | − | 0.998930i | \(-0.485272\pi\) | ||||
0.0462523 | + | 0.998930i | \(0.485272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.90617 | 0.127078 | 0.0635390 | − | 0.997979i | \(-0.479761\pi\) | ||||
0.0635390 | + | 0.997979i | \(0.479761\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.2169 | 0.662859 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.23607 | −0.226799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.8091 | −0.813190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.06154 | −0.390308 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.9443 | 0.470531 | 0.235266 | − | 0.971931i | \(-0.424404\pi\) | ||||
0.235266 | + | 0.971931i | \(0.424404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4721 | −0.791259 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.90617 | −0.124259 | −0.0621294 | − | 0.998068i | \(-0.519789\pi\) | ||||
−0.0621294 | + | 0.998068i | \(0.519789\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0292 | 0.895876 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.7771 | 1.52140 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.5967 | 0.915084 | 0.457542 | − | 0.889188i | \(-0.348730\pi\) | ||||
0.457542 | + | 0.889188i | \(0.348730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.60845 | 0.321803 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.90617 | −0.122480 | −0.0612402 | − | 0.998123i | \(-0.519506\pi\) | ||||
−0.0612402 | + | 0.998123i | \(0.519506\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.94427 | −0.208007 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.52786 | −0.231740 | −0.115870 | − | 0.993264i | \(-0.536966\pi\) | ||||
−0.115870 | + | 0.993264i | \(0.536966\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.5407 | −1.86397 | −0.931984 | − | 0.362499i | \(-0.881924\pi\) | ||||
−0.931984 | + | 0.362499i | \(0.881924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.9443 | 1.28823 | 0.644113 | − | 0.764930i | \(-0.277226\pi\) | ||||
0.644113 | + | 0.764930i | \(0.277226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.63932 | 0.316932 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.4338 | 1.26044 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6538 | −0.522277 | −0.261138 | − | 0.965301i | \(-0.584098\pi\) | ||||
−0.261138 | + | 0.965301i | \(0.584098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3607 | 0.509313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.2918 | 1.32607 | 0.663033 | − | 0.748591i | \(-0.269269\pi\) | ||||
0.663033 | + | 0.748591i | \(0.269269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.8091 | 0.771099 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.49839 | −0.265517 | −0.132759 | − | 0.991148i | \(-0.542383\pi\) | ||||
−0.132759 | + | 0.991148i | \(0.542383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.88854 | 0.321780 | 0.160890 | − | 0.986972i | \(-0.448563\pi\) | ||||
0.160890 | + | 0.986972i | \(0.448563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.2361 | 1.35124 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.71851 | 0.353873 | 0.176937 | − | 0.984222i | \(-0.443381\pi\) | ||||
0.176937 | + | 0.984222i | \(0.443381\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.06154 | −0.366591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0689 | −1.45208 | −0.726039 | − | 0.687653i | \(-0.758641\pi\) | ||||
−0.726039 | + | 0.687653i | \(0.758641\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.7687 | 1.15631 | 0.578156 | − | 0.815926i | \(-0.303772\pi\) | ||||
0.578156 | + | 0.815926i | \(0.303772\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.9322 | 1.47966 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.8328 | 2.82429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.9758 | 0.556369 | 0.278184 | − | 0.960528i | \(-0.410267\pi\) | ||||
0.278184 | + | 0.960528i | \(0.410267\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.81234 | −0.230656 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.47214 | −0.0583282 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.3607 | −0.962189 | −0.481095 | − | 0.876669i | \(-0.659761\pi\) | ||||
−0.481095 | + | 0.876669i | \(0.659761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.36737 | −0.251105 | −0.125552 | − | 0.992087i | \(-0.540070\pi\) | ||||
−0.125552 | + | 0.992087i | \(0.540070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 55.7771 | 2.18944 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.9443 | −1.28921 | −0.644604 | − | 0.764516i | \(-0.722978\pi\) | ||||
−0.644604 | + | 0.764516i | \(0.722978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.6247 | −0.454214 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.81234 | 0.226417 | 0.113208 | − | 0.993571i | \(-0.463887\pi\) | ||||
0.113208 | + | 0.993571i | \(0.463887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7771 | 1.78052 | 0.890261 | − | 0.455450i | \(-0.150522\pi\) | ||||
0.890261 | + | 0.455450i | \(0.150522\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.2786 | 0.592480 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.5276 | 1.06269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4164 | 0.671353 | 0.335677 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335677 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.7771 | 1.06756 | 0.533780 | − | 0.845623i | \(-0.320771\pi\) | ||||
0.533780 | + | 0.845623i | \(0.320771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.7315 | −0.987485 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.06154 | −0.346730 | −0.173365 | − | 0.984858i | \(-0.555464\pi\) | ||||
−0.173365 | + | 0.984858i | \(0.555464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.360680 | −0.0137809 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.94427 | 0.188362 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.7719 | −0.599993 | −0.299996 | − | 0.953940i | \(-0.596985\pi\) | ||||
−0.299996 | + | 0.953940i | \(0.596985\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.59222 | 0.136261 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.8885 | 1.28362 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.47214 | −0.244449 | −0.122225 | − | 0.992502i | \(-0.539003\pi\) | ||||
−0.122225 | + | 0.992502i | \(0.539003\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.5374 | 2.17007 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.9968 | 0.488795 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.7771 | 0.968079 | 0.484039 | − | 0.875046i | \(-0.339169\pi\) | ||||
0.484039 | + | 0.875046i | \(0.339169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.60845 | 0.284540 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.81234 | −0.216764 | −0.108382 | − | 0.994109i | \(-0.534567\pi\) | ||||
−0.108382 | + | 0.994109i | \(0.534567\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0000 | −1.48968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8885 | 0.515808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.11006 | 0.0411698 | 0.0205849 | − | 0.999788i | \(-0.493447\pi\) | ||||
0.0205849 | + | 0.999788i | \(0.493447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −49.2429 | −1.82132 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9443 | −0.847466 | −0.423733 | − | 0.905787i | \(-0.639281\pi\) | ||||
−0.423733 | + | 0.905787i | \(0.639281\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 90.2492 | 3.32437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.84953 | −0.325535 | −0.162768 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162768 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.46931 | −0.200650 | −0.100325 | − | 0.994955i | \(-0.531988\pi\) | ||||
−0.100325 | + | 0.994955i | \(0.531988\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3050 | −0.780553 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.7771 | 1.30727 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2007 | −0.408718 | −0.204359 | − | 0.978896i | \(-0.565511\pi\) | ||||
−0.204359 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.5276 | −1.00183 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.5836 | −0.675432 | −0.337716 | − | 0.941248i | \(-0.609654\pi\) | ||||
−0.337716 | + | 0.941248i | \(0.609654\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6525 | 0.748652 | 0.374326 | − | 0.927297i | \(-0.377874\pi\) | ||||
0.374326 | + | 0.927297i | \(0.377874\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 35.1361 | 1.27201 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.06154 | 0.327193 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.8328 | −1.32823 | −0.664113 | − | 0.747633i | \(-0.731190\pi\) | ||||
−0.664113 | + | 0.747633i | \(0.731190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.7082 | 1.28433 | 0.642167 | − | 0.766564i | \(-0.278035\pi\) | ||||
0.642167 | + | 0.766564i | \(0.278035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.16348 | 0.293241 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.5276 | 0.986280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37.8885 | 1.35576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.69505 | 0.238957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.2057 | 1.64706 | 0.823528 | − | 0.567275i | \(-0.192002\pi\) | ||||
0.823528 | + | 0.567275i | \(0.192002\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.40456 | 0.334388 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.47214 | 0.158810 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.4164 | −0.404390 | −0.202195 | − | 0.979345i | \(-0.564807\pi\) | ||||
−0.202195 | + | 0.979345i | \(0.564807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.6475 | 2.07480 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.9322 | 1.30331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.00000 | 0.140633 | 0.0703163 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703163 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.7980 | 1.74864 | 0.874322 | − | 0.485347i | \(-0.161307\pi\) | ||||
0.874322 | + | 0.485347i | \(0.161307\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.3107 | −0.431226 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −40.0000 | −1.39942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.5967 | 1.31214 | 0.656068 | − | 0.754702i | \(-0.272219\pi\) | ||||
0.656068 | + | 0.754702i | \(0.272219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8254 | −0.795642 | −0.397821 | − | 0.917463i | \(-0.630233\pi\) | ||||
−0.397821 | + | 0.917463i | \(0.630233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.1814 | 1.39724 | 0.698622 | − | 0.715491i | \(-0.253797\pi\) | ||||
0.698622 | + | 0.715491i | \(0.253797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.472136 | 0.0163980 | 0.00819898 | − | 0.999966i | \(-0.497390\pi\) | ||||
0.00819898 | + | 0.999966i | \(0.497390\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.52786 | 0.330121 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.2007 | −0.387615 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.5892 | −1.26320 | −0.631599 | − | 0.775295i | \(-0.717601\pi\) | ||||
−0.631599 | + | 0.775295i | \(0.717601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.23607 | 0.0425220 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −63.2188 | −2.17222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.8328 | −0.713302 | −0.356651 | − | 0.934238i | \(-0.616081\pi\) | ||||
−0.356651 | + | 0.934238i | \(0.616081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.3050 | −1.68423 | −0.842113 | − | 0.539302i | \(-0.818688\pi\) | ||||
−0.842113 | + | 0.539302i | \(0.818688\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2169 | −0.519194 | −0.259597 | − | 0.965717i | \(-0.583590\pi\) | ||||
−0.259597 | + | 0.965717i | \(0.583590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.9677 | −0.407385 | −0.203693 | − | 0.979035i | \(-0.565294\pi\) | ||||
−0.203693 | + | 0.979035i | \(0.565294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.9443 | −0.440118 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −93.6656 | −3.17739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6619 | 0.496799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.6215 | 0.832358 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.9443 | 1.04491 | 0.522457 | − | 0.852666i | \(-0.325016\pi\) | ||||
0.522457 | + | 0.852666i | \(0.325016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.36068 | 0.146915 | 0.0734575 | − | 0.997298i | \(-0.476597\pi\) | ||||
0.0734575 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.1329 | −1.61980 | −0.809900 | − | 0.586568i | \(-0.800479\pi\) | ||||
−0.809900 | + | 0.586568i | \(0.800479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.7445 | 1.43522 | 0.717611 | − | 0.696445i | \(-0.245236\pi\) | ||||
0.717611 | + | 0.696445i | \(0.245236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.0557 | 0.370797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.6393 | 1.59419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8416 | −0.897215 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.40456 | 0.313660 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.0000 | −1.06607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.3607 | −0.676812 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.70228 | 0.156137 | 0.0780684 | − | 0.996948i | \(-0.475125\pi\) | ||||
0.0780684 | + | 0.996948i | \(0.475125\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.9322 | 1.22362 | 0.611809 | − | 0.791005i | \(-0.290442\pi\) | ||||
0.611809 | + | 0.791005i | \(0.290442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.0000 | −0.661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.1115 | 0.730185 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2169 | −0.501959 | −0.250980 | − | 0.967992i | \(-0.580753\pi\) | ||||
−0.250980 | + | 0.967992i | \(0.580753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.15537 | 0.202606 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.0000 | 1.24943 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8197 | 0.453408 | 0.226704 | − | 0.973964i | \(-0.427205\pi\) | ||||
0.226704 | + | 0.973964i | \(0.427205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.73948 | 0.253651 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49.2429 | −1.61042 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.5279 | 0.899296 | 0.449648 | − | 0.893206i | \(-0.351549\pi\) | ||||
0.449648 | + | 0.893206i | \(0.351549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7082 | 0.381677 | 0.190838 | − | 0.981621i | \(-0.438879\pi\) | ||||
0.190838 | + | 0.981621i | \(0.438879\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.46931 | 0.177729 | 0.0888644 | − | 0.996044i | \(-0.471676\pi\) | ||||
0.0888644 | + | 0.996044i | \(0.471676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.4164 | 1.27682 | 0.638411 | − | 0.769695i | \(-0.279592\pi\) | ||||
0.638411 | + | 0.769695i | \(0.279592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.03246 | 0.259924 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.686054 | 0.0221538 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.4721 | −0.821682 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.63932 | −0.117154 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0795 | 1.32103 | 0.660513 | − | 0.750815i | \(-0.270339\pi\) | ||||
0.660513 | + | 0.750815i | \(0.270339\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.4338 | −0.976667 | −0.488334 | − | 0.872657i | \(-0.662395\pi\) | ||||
−0.488334 | + | 0.872657i | \(0.662395\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.83282 | −0.219050 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.1246 | 1.50765 | 0.753825 | − | 0.657075i | \(-0.228207\pi\) | ||||
0.753825 | + | 0.657075i | \(0.228207\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −96.6898 | −3.09022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −55.3983 | −1.76693 | −0.883466 | − | 0.468496i | \(-0.844796\pi\) | ||||
−0.883466 | + | 0.468496i | \(0.844796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5279 | 0.558484 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.3400 | −1.05908 | −0.529540 | − | 0.848285i | \(-0.677635\pi\) | ||||
−0.529540 | + | 0.848285i | \(0.677635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.4370 | 0.552791 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.11146 | 0.130211 | 0.0651056 | − | 0.997878i | \(-0.479262\pi\) | ||||
0.0651056 | + | 0.997878i | \(0.479262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3744.2.a.bb.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 3744.2.a.bf.1.1 | yes | 4 | ||
4.3 | odd | 2 | inner | 3744.2.a.bb.1.4 | yes | 4 | |
8.3 | odd | 2 | 7488.2.a.dd.1.2 | 4 | |||
8.5 | even | 2 | 7488.2.a.dd.1.1 | 4 | |||
12.11 | even | 2 | 3744.2.a.bf.1.2 | yes | 4 | ||
24.5 | odd | 2 | 7488.2.a.cz.1.3 | 4 | |||
24.11 | even | 2 | 7488.2.a.cz.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3744.2.a.bb.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
3744.2.a.bb.1.4 | yes | 4 | 4.3 | odd | 2 | inner | |
3744.2.a.bf.1.1 | yes | 4 | 3.2 | odd | 2 | ||
3744.2.a.bf.1.2 | yes | 4 | 12.11 | even | 2 | ||
7488.2.a.cz.1.3 | 4 | 24.5 | odd | 2 | |||
7488.2.a.cz.1.4 | 4 | 24.11 | even | 2 | |||
7488.2.a.dd.1.1 | 4 | 8.5 | even | 2 | |||
7488.2.a.dd.1.2 | 4 | 8.3 | odd | 2 |