Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.273891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | 1.27389 | 0.735481 | 0.367741 | − | 0.929928i | \(-0.380131\pi\) | ||||
0.367741 | + | 0.929928i | \(0.380131\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.726109 | 0.274444 | 0.137222 | − | 0.990540i | \(-0.456183\pi\) | ||||
0.137222 | + | 0.990540i | \(0.456183\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.37720 | −0.459068 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.273891 | 0.0825811 | 0.0412906 | − | 0.999147i | \(-0.486853\pi\) | ||||
0.0412906 | + | 0.999147i | \(0.486853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.95328 | 1.65114 | 0.825571 | − | 0.564298i | \(-0.190853\pi\) | ||||
0.825571 | + | 0.564298i | \(0.190853\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.27389 | −1.27911 | −0.639553 | − | 0.768747i | \(-0.720881\pi\) | ||||
−0.639553 | + | 0.768747i | \(0.720881\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.924984 | 0.201848 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.67939 | −0.767206 | −0.383603 | − | 0.923498i | \(-0.625317\pi\) | ||||
−0.383603 | + | 0.923498i | \(0.625317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.57608 | −1.07312 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27389 | −0.422251 | −0.211125 | − | 0.977459i | \(-0.567713\pi\) | ||||
−0.211125 | + | 0.977459i | \(0.567713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.19887 | −0.574535 | −0.287267 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287267 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.348907 | 0.0607368 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.12386 | −1.33555 | −0.667777 | − | 0.744361i | \(-0.732754\pi\) | ||||
−0.667777 | + | 0.744361i | \(0.732754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.58383 | 1.21438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.43380 | −1.47331 | −0.736656 | − | 0.676268i | \(-0.763596\pi\) | ||||
−0.736656 | + | 0.676268i | \(0.763596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.81100 | 1.49616 | 0.748082 | − | 0.663607i | \(-0.230975\pi\) | ||||
0.748082 | + | 0.663607i | \(0.230975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1599 | 1.77370 | 0.886852 | − | 0.462053i | \(-0.152887\pi\) | ||||
0.886852 | + | 0.462053i | \(0.152887\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47277 | −0.924681 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.71836 | −0.940758 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.69781 | −0.782655 | −0.391327 | − | 0.920252i | \(-0.627984\pi\) | ||||
−0.391327 | + | 0.920252i | \(0.627984\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.27389 | −0.168731 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.20662 | 0.547656 | 0.273828 | − | 0.961779i | \(-0.411710\pi\) | ||||
0.273828 | + | 0.961779i | \(0.411710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.103312 | −0.0132278 | −0.00661389 | − | 0.999978i | \(-0.502105\pi\) | ||||
−0.00661389 | + | 0.999978i | \(0.502105\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.7827 | −1.43949 | −0.719743 | − | 0.694241i | \(-0.755740\pi\) | ||||
−0.719743 | + | 0.694241i | \(0.755740\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.68714 | −0.564265 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.75441 | −0.682922 | −0.341461 | − | 0.939896i | \(-0.610922\pi\) | ||||
−0.341461 | + | 0.939896i | \(0.610922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.67939 | −0.781763 | −0.390882 | − | 0.920441i | \(-0.627830\pi\) | ||||
−0.390882 | + | 0.920441i | \(0.627830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.198875 | 0.0226639 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.87826 | −0.436339 | −0.218169 | − | 0.975911i | \(-0.570009\pi\) | ||||
−0.218169 | + | 0.975911i | \(0.570009\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.97170 | −0.330189 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.488265 | −0.0535941 | −0.0267970 | − | 0.999641i | \(-0.508531\pi\) | ||||
−0.0267970 | + | 0.999641i | \(0.508531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.89669 | −0.310558 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.4338 | −1.74198 | −0.870989 | − | 0.491302i | \(-0.836521\pi\) | ||||
−0.870989 | + | 0.491302i | \(0.836521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.32273 | 0.453146 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.07502 | −0.422559 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.44447 | 0.451267 | 0.225634 | − | 0.974212i | \(-0.427555\pi\) | ||||
0.225634 | + | 0.974212i | \(0.427555\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.377203 | −0.0379103 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38495 | 0.436319 | 0.218160 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218160 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33048 | 0.328162 | 0.164081 | − | 0.986447i | \(-0.447534\pi\) | ||||
0.164081 | + | 0.986447i | \(0.447534\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4904 | 1.59419 | 0.797093 | − | 0.603857i | \(-0.206370\pi\) | ||||
0.797093 | + | 0.603857i | \(0.206370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.79045 | 0.746190 | 0.373095 | − | 0.927793i | \(-0.378297\pi\) | ||||
0.373095 | + | 0.927793i | \(0.378297\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3489 | −0.982275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.142282 | 0.0133848 | 0.00669238 | − | 0.999978i | \(-0.497870\pi\) | ||||
0.00669238 | + | 0.999978i | \(0.497870\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.19887 | −0.757986 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.82942 | −0.351043 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9250 | −0.993180 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.0176 | −1.08359 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1316 | −1.34271 | −0.671357 | − | 0.741135i | \(-0.734288\pi\) | ||||
−0.671357 | + | 0.741135i | \(0.734288\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4981 | 1.10040 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.58383 | −0.487861 | −0.243931 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243931 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.726109 | −0.0629617 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8294 | −1.09609 | −0.548046 | − | 0.836448i | \(-0.684628\pi\) | ||||
−0.548046 | + | 0.836448i | \(0.684628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2477 | 1.29329 | 0.646647 | − | 0.762789i | \(-0.276171\pi\) | ||||
0.646647 | + | 0.762789i | \(0.276171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4904 | 1.30453 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.63055 | 0.136353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.24559 | −0.680085 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.8315 | 1.13312 | 0.566562 | − | 0.824019i | \(-0.308273\pi\) | ||||
0.566562 | + | 0.824019i | \(0.308273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7077 | 0.952758 | 0.476379 | − | 0.879240i | \(-0.341949\pi\) | ||||
0.476379 | + | 0.879240i | \(0.341949\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.26322 | 0.587196 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.79045 | 0.382320 | 0.191160 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191160 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.25839 | −0.575628 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.67164 | −0.210555 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.8011 | 1.00266 | 0.501331 | − | 0.865256i | \(-0.332844\pi\) | ||||
0.501331 | + | 0.865256i | \(0.332844\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.9426 | −1.62059 | −0.810294 | − | 0.586024i | \(-0.800692\pi\) | ||||
−0.810294 | + | 0.586024i | \(0.800692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4415 | 1.72627 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.37720 | 0.105317 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.7282 | −1.19580 | −0.597898 | − | 0.801572i | \(-0.703997\pi\) | ||||
−0.597898 | + | 0.801572i | \(0.703997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.35878 | 0.402791 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.41325 | −0.255118 | −0.127559 | − | 0.991831i | \(-0.540714\pi\) | ||||
−0.127559 | + | 0.991831i | \(0.540714\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.5109 | 1.74755 | 0.873777 | − | 0.486327i | \(-0.161664\pi\) | ||||
0.873777 | + | 0.486327i | \(0.161664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.131609 | −0.00972878 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.44447 | −0.105630 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.04884 | −0.294510 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4650 | −0.901937 | −0.450968 | − | 0.892540i | \(-0.648921\pi\) | ||||
−0.450968 | + | 0.892540i | \(0.648921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.2993 | −1.38919 | −0.694596 | − | 0.719400i | \(-0.744417\pi\) | ||||
−0.694596 | + | 0.719400i | \(0.744417\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.63055 | −0.472407 | −0.236203 | − | 0.971704i | \(-0.575903\pi\) | ||||
−0.236203 | + | 0.971704i | \(0.575903\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.0849 | 1.63644 | 0.818222 | − | 0.574902i | \(-0.194960\pi\) | ||||
0.818222 | + | 0.574902i | \(0.194960\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0099 | −1.05871 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.65109 | −0.115884 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.06727 | 0.352199 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.273891 | −0.0189454 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54778 | 0.519611 | 0.259805 | − | 0.965661i | \(-0.416342\pi\) | ||||
0.259805 | + | 0.965661i | \(0.416342\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.33048 | −0.502276 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.32273 | −0.157677 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.50881 | −0.574972 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.3969 | −2.11199 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.09344 | −0.0732221 | −0.0366111 | − | 0.999330i | \(-0.511656\pi\) | ||||
−0.0366111 | + | 0.999330i | \(0.511656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.1316 | −1.33618 | −0.668091 | − | 0.744080i | \(-0.732888\pi\) | ||||
−0.668091 | + | 0.744080i | \(0.732888\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.51656 | −0.364545 | −0.182272 | − | 0.983248i | \(-0.558345\pi\) | ||||
−0.182272 | + | 0.983248i | \(0.558345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.253344 | 0.0166688 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.1805 | 1.19104 | 0.595520 | − | 0.803340i | \(-0.296946\pi\) | ||||
0.595520 | + | 0.803340i | \(0.296946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.94048 | −0.320919 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.9164 | −1.41766 | −0.708828 | − | 0.705381i | \(-0.750776\pi\) | ||||
−0.708828 | + | 0.705381i | \(0.750776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.1882 | −1.81576 | −0.907881 | − | 0.419228i | \(-0.862301\pi\) | ||||
−0.907881 | + | 0.419228i | \(0.862301\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.9426 | 0.830269 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.95328 | −0.378798 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.621996 | −0.0394174 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.00987 | −0.568698 | −0.284349 | − | 0.958721i | \(-0.591777\pi\) | ||||
−0.284349 | + | 0.958721i | \(0.591777\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00775 | −0.0633567 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.86064 | −0.427955 | −0.213978 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213978 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.89881 | −0.366534 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.13161 | 0.193842 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.25547 | −0.570717 | −0.285358 | − | 0.958421i | \(-0.592113\pi\) | ||||
−0.285358 | + | 0.958421i | \(0.592113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.9349 | −1.28119 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.498939 | 0.0304208 | 0.0152104 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152104 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.71061 | −0.225403 | −0.112702 | − | 0.993629i | \(-0.535950\pi\) | ||||
−0.112702 | + | 0.993629i | \(0.535950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.50669 | 0.333280 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.58675 | −0.275591 | −0.137796 | − | 0.990461i | \(-0.544002\pi\) | ||||
−0.137796 | + | 0.990461i | \(0.544002\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.40550 | 0.263750 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2653 | 1.62651 | 0.813257 | − | 0.581905i | \(-0.197692\pi\) | ||||
0.813257 | + | 0.581905i | \(0.197692\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2661 | −0.610259 | −0.305129 | − | 0.952311i | \(-0.598700\pi\) | ||||
−0.305129 | + | 0.952311i | \(0.598700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.84997 | −0.404341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8139 | 0.636113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.66177 | 0.331899 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.87051 | 0.109277 | 0.0546383 | − | 0.998506i | \(-0.482599\pi\) | ||||
0.0546383 | + | 0.998506i | \(0.482599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.52723 | −0.0886192 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.9044 | −1.26677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.12386 | 0.410612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.58595 | 0.320904 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.227171 | 0.0129653 | 0.00648266 | − | 0.999979i | \(-0.497936\pi\) | ||||
0.00648266 | + | 0.999979i | \(0.497936\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.24267 | 0.241357 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9554 | −1.18827 | −0.594136 | − | 0.804365i | \(-0.702506\pi\) | ||||
−0.594136 | + | 0.804365i | \(0.702506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2349 | 0.635035 | 0.317518 | − | 0.948252i | \(-0.397151\pi\) | ||||
0.317518 | + | 0.948252i | \(0.397151\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.6228 | −1.04596 | −0.522980 | − | 0.852345i | \(-0.675180\pi\) | ||||
−0.522980 | + | 0.852345i | \(0.675180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.622797 | −0.0348699 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.0069 | 1.17249 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.27389 | 0.293447 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.92418 | 0.548809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.82942 | 0.486782 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1054 | 0.775305 | 0.387652 | − | 0.921806i | \(-0.373286\pi\) | ||||
0.387652 | + | 0.921806i | \(0.373286\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.1882 | 0.613110 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.9709 | −1.25130 | −0.625652 | − | 0.780102i | \(-0.715167\pi\) | ||||
−0.625652 | + | 0.780102i | \(0.715167\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.181252 | 0.00984424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.876142 | −0.0474457 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.78270 | −0.528216 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.93273 | −0.211120 | −0.105560 | − | 0.994413i | \(-0.533664\pi\) | ||||
−0.105560 | + | 0.994413i | \(0.533664\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.4252 | −1.84274 | −0.921371 | − | 0.388685i | \(-0.872929\pi\) | ||||
−0.921371 | + | 0.388685i | \(0.872929\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.1960 | −1.77187 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.25547 | 0.226496 | 0.113248 | − | 0.993567i | \(-0.463875\pi\) | ||||
0.113248 | + | 0.993567i | \(0.463875\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.87826 | −0.258185 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.2944 | 1.07110 | 0.535550 | − | 0.844504i | \(-0.320104\pi\) | ||||
0.535550 | + | 0.844504i | \(0.320104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13.9172 | −0.730465 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.85289 | 0.201119 | 0.100560 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100560 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.9922 | 0.676350 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.13724 | −0.214795 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6356 | −0.757802 | −0.378901 | − | 0.925437i | \(-0.623698\pi\) | ||||
−0.378901 | + | 0.925437i | \(0.623698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.5371 | −0.697197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.0099 | 1.13057 | 0.565286 | − | 0.824895i | \(-0.308766\pi\) | ||||
0.565286 | + | 0.824895i | \(0.308766\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.2760 | −0.987540 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.08569 | −0.157671 | −0.0788357 | − | 0.996888i | \(-0.525120\pi\) | ||||
−0.0788357 | + | 0.996888i | \(0.525120\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.5117 | −0.686840 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.77203 | 0.444760 | 0.222380 | − | 0.974960i | \(-0.428618\pi\) | ||||
0.222380 | + | 0.974960i | \(0.428618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4047 | 0.981338 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.11319 | −0.358813 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.59450 | 0.0800257 | 0.0400129 | − | 0.999199i | \(-0.487260\pi\) | ||||
0.0400129 | + | 0.999199i | \(0.487260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.924984 | −0.0463071 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.5526 | −0.876535 | −0.438268 | − | 0.898844i | \(-0.644408\pi\) | ||||
−0.438268 | + | 0.898844i | \(0.644408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0438 | −0.948639 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.22505 | −0.110292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.6815 | 1.81378 | 0.906892 | − | 0.421363i | \(-0.138448\pi\) | ||||
0.906892 | + | 0.421363i | \(0.138448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.3433 | −0.806155 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.05447 | 0.150301 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.4239 | 0.951194 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.8187 | 0.919356 | 0.459678 | − | 0.888086i | \(-0.347965\pi\) | ||||
0.459678 | + | 0.888086i | \(0.347965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.7819 | −1.64643 | −0.823215 | − | 0.567730i | \(-0.807822\pi\) | ||||
−0.823215 | + | 0.567730i | \(0.807822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.7467 | −0.814250 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0750160 | −0.00363028 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.07714 | 0.100285 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7651 | 0.614872 | 0.307436 | − | 0.951569i | \(-0.400529\pi\) | ||||
0.307436 | + | 0.951569i | \(0.400529\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0771 | 0.772618 | 0.386309 | − | 0.922369i | \(-0.373750\pi\) | ||||
0.386309 | + | 0.922369i | \(0.373750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.67939 | 0.176009 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.36945 | −0.0653604 | −0.0326802 | − | 0.999466i | \(-0.510404\pi\) | ||||
−0.0326802 | + | 0.999466i | \(0.510404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.91431 | 0.424491 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.62280 | 0.219636 | 0.109818 | − | 0.993952i | \(-0.464973\pi\) | ||||
0.109818 | + | 0.993952i | \(0.464973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.6199 | 0.833391 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2555 | 1.09749 | 0.548747 | − | 0.835989i | \(-0.315105\pi\) | ||||
0.548747 | + | 0.835989i | \(0.315105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.58383 | −0.121668 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.9143 | 0.700735 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.8443 | 1.67673 | 0.838364 | − | 0.545111i | \(-0.183513\pi\) | ||||
0.838364 | + | 0.545111i | \(0.183513\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.4076 | 1.37263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.8812 | −0.693086 | −0.346543 | − | 0.938034i | \(-0.612645\pi\) | ||||
−0.346543 | + | 0.938034i | \(0.612645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9554 | −1.39215 | −0.696073 | − | 0.717971i | \(-0.745071\pi\) | ||||
−0.696073 | + | 0.717971i | \(0.745071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.73598 | −0.311704 | −0.155852 | − | 0.987780i | \(-0.549812\pi\) | ||||
−0.155852 | + | 0.987780i | \(0.549812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.55553 | −0.395058 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.10251 | 0.281189 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.68714 | 0.123555 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.84704 | 0.359291 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.6978 | −0.762943 | −0.381471 | − | 0.924381i | \(-0.624582\pi\) | ||||
−0.381471 | + | 0.924381i | \(0.624582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.3636 | −2.20519 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.40338 | −0.154859 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.64042 | 0.164963 | 0.0824816 | − | 0.996593i | \(-0.473715\pi\) | ||||
0.0824816 | + | 0.996593i | \(0.473715\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.3072 | 0.737439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.3249 | 1.50393 | 0.751965 | − | 0.659203i | \(-0.229106\pi\) | ||||
0.751965 | + | 0.659203i | \(0.229106\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.9922 | 0.540104 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.17833 | −0.187424 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.9914 | 1.70073 | 0.850365 | − | 0.526193i | \(-0.176381\pi\) | ||||
0.850365 | + | 0.526193i | \(0.176381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.6786 | −1.19191 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.1826 | −1.88083 | −0.940414 | − | 0.340032i | \(-0.889562\pi\) | ||||
−0.940414 | + | 0.340032i | \(0.889562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 28.5881 | 1.26964 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.9971 | −0.975003 | −0.487502 | − | 0.873122i | \(-0.662092\pi\) | ||||
−0.487502 | + | 0.873122i | \(0.662092\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.84997 | −0.214550 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.57608 | 0.246190 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.33048 | 0.146474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.0360 | −0.879485 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0977 | 0.880496 | 0.440248 | − | 0.897876i | \(-0.354891\pi\) | ||||
0.440248 | + | 0.897876i | \(0.354891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.64817 | −0.203250 | −0.101625 | − | 0.994823i | \(-0.532404\pi\) | ||||
−0.101625 | + | 0.994823i | \(0.532404\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.8705 | 0.734891 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.46209 | −0.411395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.79338 | −0.251411 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −56.1620 | −2.43265 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.34811 | −0.187635 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.77283 | −0.0763612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0673 | 0.862759 | 0.431380 | − | 0.902171i | \(-0.358027\pi\) | ||||
0.431380 | + | 0.902171i | \(0.358027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.9504 | 1.28529 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2010 | −1.59060 | −0.795300 | − | 0.606216i | \(-0.792687\pi\) | ||||
−0.795300 | + | 0.606216i | \(0.792687\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.142282 | 0.00607245 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.27389 | 0.0968710 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.81604 | −0.119750 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.8393 | −1.89990 | −0.949951 | − | 0.312399i | \(-0.898867\pi\) | ||||
−0.949951 | + | 0.312399i | \(0.898867\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 58.4076 | 2.47038 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.84010 | −0.0776889 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.9172 | −0.923701 | −0.461851 | − | 0.886958i | \(-0.652814\pi\) | ||||
−0.461851 | + | 0.886958i | \(0.652814\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.15778 | −0.0906183 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.90656 | 0.415305 | 0.207652 | − | 0.978203i | \(-0.433418\pi\) | ||||
0.207652 | + | 0.978203i | \(0.433418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.6404 | −0.738229 | −0.369114 | − | 0.929384i | \(-0.620339\pi\) | ||||
−0.369114 | + | 0.929384i | \(0.620339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.8791 | −0.663357 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.7048 | 0.528906 | 0.264453 | − | 0.964399i | \(-0.414809\pi\) | ||||
0.264453 | + | 0.964399i | \(0.414809\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.5851 | −1.02172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.354534 | −0.0147085 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.56058 | −0.0646325 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.0438 | 0.620924 | 0.310462 | − | 0.950586i | \(-0.399516\pi\) | ||||
0.310462 | + | 0.950586i | \(0.399516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.19887 | 0.131807 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.44659 | −0.347446 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4231 | 0.674417 | 0.337208 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337208 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 29.4076 | 1.20357 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.1260 | 0.781466 | 0.390733 | − | 0.920504i | \(-0.372222\pi\) | ||||
0.390733 | + | 0.920504i | \(0.372222\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.4124 | 1.28134 | 0.640670 | − | 0.767816i | \(-0.278657\pi\) | ||||
0.640670 | + | 0.767816i | \(0.278657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.2272 | 0.660821 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.5315 | −1.68571 | −0.842855 | − | 0.538140i | \(-0.819127\pi\) | ||||
−0.842855 | + | 0.538140i | \(0.819127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.10331 | −0.0852305 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 72.3913 | 2.92864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7274 | −0.877563 | −0.438781 | − | 0.898594i | \(-0.644590\pi\) | ||||
−0.438781 | + | 0.898594i | \(0.644590\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6065 | −1.35295 | −0.676473 | − | 0.736467i | \(-0.736493\pi\) | ||||
−0.676473 | + | 0.736467i | \(0.736493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.6036 | 1.10948 | 0.554741 | − | 0.832023i | \(-0.312817\pi\) | ||||
0.554741 | + | 0.832023i | \(0.312817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.5166 | 0.823301 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.9327 | −0.478075 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.348907 | −0.0139340 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 42.8443 | 1.70832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.94048 | −0.0772495 | −0.0386247 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386247 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.61505 | 0.382164 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.5342 | −1.52678 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.92498 | 0.313508 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.01975 | 0.0402775 | 0.0201388 | − | 0.999797i | \(-0.493589\pi\) | ||||
0.0201388 | + | 0.999797i | \(0.493589\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9866 | 1.45861 | 0.729305 | − | 0.684189i | \(-0.239844\pi\) | ||||
0.729305 | + | 0.684189i | \(0.239844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.1182 | 0.948186 | 0.474093 | − | 0.880475i | \(-0.342776\pi\) | ||||
0.474093 | + | 0.880475i | \(0.342776\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.15215 | 0.0452260 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.95891 | −0.115969 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.2603 | −1.45811 | −0.729054 | − | 0.684456i | \(-0.760040\pi\) | ||||
−0.729054 | + | 0.684456i | \(0.760040\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.19887 | 0.358882 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4386 | −0.835130 | −0.417565 | − | 0.908647i | \(-0.637116\pi\) | ||||
−0.417565 | + | 0.908647i | \(0.637116\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.783503 | 0.0304747 | 0.0152374 | − | 0.999884i | \(-0.495150\pi\) | ||||
0.0152374 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39.9963 | −1.55333 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.36653 | 0.323953 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.39292 | −0.0538535 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0282963 | −0.00109237 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.1903 | 1.93469 | 0.967347 | − | 0.253454i | \(-0.0815667\pi\) | ||||
0.967347 | + | 0.253454i | \(0.0815667\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.8804 | 1.14840 | 0.574198 | − | 0.818716i | \(-0.305314\pi\) | ||||
0.574198 | + | 0.818716i | \(0.305314\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.22717 | 0.123847 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.6455 | −0.982736 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.3326 | 0.471894 | 0.235947 | − | 0.971766i | \(-0.424181\pi\) | ||||
0.235947 | + | 0.971766i | \(0.424181\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.02750 | −0.268116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.9207 | −1.29227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.62200 | −0.137787 | −0.0688936 | − | 0.997624i | \(-0.521947\pi\) | ||||
−0.0688936 | + | 0.997624i | \(0.521947\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.273891 | −0.0104042 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 49.7528 | 1.88452 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.1599 | 0.875988 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.1209 | 1.28873 | 0.644365 | − | 0.764718i | \(-0.277122\pi\) | ||||
0.644365 | + | 0.764718i | \(0.277122\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.12386 | 0.306397 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.18396 | 0.119745 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1209 | −0.642990 | −0.321495 | − | 0.946911i | \(-0.604185\pi\) | ||||
−0.321495 | + | 0.946911i | \(0.604185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.34116 | 0.200309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.7699 | 0.440786 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.9191 | −1.04266 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.02750 | 0.262081 | 0.131041 | − | 0.991377i | \(-0.458168\pi\) | ||||
0.131041 | + | 0.991377i | \(0.458168\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.41830 | 0.0900620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −35.9087 | −1.33546 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8938 | −0.441115 | −0.220558 | − | 0.975374i | \(-0.570788\pi\) | ||||
−0.220558 | + | 0.975374i | \(0.570788\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4026 | 0.940836 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.7421 | −1.91375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7154 | −0.765142 | −0.382571 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382571 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.22717 | −0.118874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.8620 | −1.24563 | −0.622816 | − | 0.782368i | \(-0.714012\pi\) | ||||
−0.622816 | + | 0.782368i | \(0.714012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.58383 | −0.278599 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.7381 | 1.56791 | 0.783955 | − | 0.620818i | \(-0.213200\pi\) | ||||
0.783955 | + | 0.620818i | \(0.213200\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.672440 | 0.0246033 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.9738 | 0.437514 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.9581 | −0.436358 | −0.218179 | − | 0.975909i | \(-0.570012\pi\) | ||||
−0.218179 | + | 0.975909i | \(0.570012\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4776 | −0.418267 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1103 | −1.05803 | −0.529015 | − | 0.848612i | \(-0.677439\pi\) | ||||
−0.529015 | + | 0.848612i | \(0.677439\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.28376 | −0.0465977 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.3014 | −0.808425 | −0.404212 | − | 0.914665i | \(-0.632454\pi\) | ||||
−0.404212 | + | 0.914665i | \(0.632454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.65672 | 0.204787 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0432 | 0.904258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.95891 | 0.142762 | 0.0713809 | − | 0.997449i | \(-0.477259\pi\) | ||||
0.0713809 | + | 0.997449i | \(0.477259\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.73971 | −0.314753 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.8139 | −1.00040 | −0.500199 | − | 0.865911i | \(-0.666740\pi\) | ||||
−0.500199 | + | 0.865911i | \(0.666740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.51444 | −0.269579 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.43380 | 0.338001 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.57608 | −0.0563965 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.6794 | 0.453124 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.82460 | −0.0650398 | −0.0325199 | − | 0.999471i | \(-0.510353\pi\) | ||||
−0.0325199 | + | 0.999471i | \(0.510353\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.7905 | −0.419751 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.103312 | 0.00367336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.615047 | −0.0218410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.0360 | 0.745135 | 0.372567 | − | 0.928005i | \(-0.378478\pi\) | ||||
0.372567 | + | 0.928005i | \(0.378478\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −64.1300 | −2.26876 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.6327 | 0.799686 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.82942 | −0.0645589 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.635593 | 0.0223739 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.0819654 | −0.00288175 | −0.00144088 | − | 0.999999i | \(-0.500459\pi\) | ||||
−0.00144088 | + | 0.999999i | \(0.500459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.72531 | 0.236158 | 0.118079 | − | 0.993004i | \(-0.462326\pi\) | ||||
0.118079 | + | 0.993004i | \(0.462326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.72691 | −0.165780 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.81100 | −0.343243 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.95328 | −0.208024 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9426 | 1.07990 | 0.539952 | − | 0.841696i | \(-0.318442\pi\) | ||||
0.539952 | + | 0.841696i | \(0.318442\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5908 | 0.926896 | 0.463448 | − | 0.886124i | \(-0.346612\pi\) | ||||
0.463448 | + | 0.886124i | \(0.346612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.57900 | −0.194001 | −0.0970004 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0970004 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9765 | 0.659082 | 0.329541 | − | 0.944141i | \(-0.393106\pi\) | ||||
0.329541 | + | 0.944141i | \(0.393106\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.84302 | −0.202692 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.1367 | 1.18276 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.8372 | 0.616543 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9143 | −0.445852 | −0.222926 | − | 0.974835i | \(-0.571561\pi\) | ||||
−0.222926 | + | 0.974835i | \(0.571561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8294 | −0.821704 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.7331 | 1.19627 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.93273 | −0.272572 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0779 | −0.448834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.8908 | 1.02464 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.46077 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4055 | 0.423764 | 0.211882 | − | 0.977295i | \(-0.432041\pi\) | ||||
0.211882 | + | 0.977295i | \(0.432041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.3425 | −1.37647 | −0.688234 | − | 0.725489i | \(-0.741614\pi\) | ||||
−0.688234 | + | 0.725489i | \(0.741614\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.72611 | −0.297385 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.83235 | 0.0623738 | 0.0311869 | − | 0.999514i | \(-0.490071\pi\) | ||||
0.0311869 | + | 0.999514i | \(0.490071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.7758 | 0.467849 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.06222 | −0.0360333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −70.1457 | −2.37680 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.12094 | −0.207162 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.14419 | 0.275010 | 0.137505 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137505 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.38283 | 0.0803709 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1706 | 0.410037 | 0.205019 | − | 0.978758i | \(-0.434275\pi\) | ||||
0.205019 | + | 0.978758i | \(0.434275\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7614 | 1.57364 | 0.786822 | − | 0.617179i | \(-0.211725\pi\) | ||||
0.786822 | + | 0.617179i | \(0.211725\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.8804 | −1.17117 | −0.585584 | − | 0.810611i | \(-0.699135\pi\) | ||||
−0.585584 | + | 0.810611i | \(0.699135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9872 | −0.368499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.813922 | −0.0272674 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.1599 | −0.406916 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.9039 | −0.931683 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.27389 | 0.242598 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0496 | 1.00110 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.07502 | 0.301998 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5080 | −0.846980 | −0.423490 | − | 0.905901i | \(-0.639195\pi\) | ||||
−0.423490 | + | 0.905901i | \(0.639195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.03897 | −0.200300 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5032 | 0.712432 | 0.356216 | − | 0.934404i | \(-0.384067\pi\) | ||||
0.356216 | + | 0.934404i | \(0.384067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.133731 | −0.00442586 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.05447 | −0.133890 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.1386 | −1.22509 | −0.612544 | − | 0.790436i | \(-0.709854\pi\) | ||||
−0.612544 | + | 0.790436i | \(0.709854\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.289391 | 0.00953575 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −34.2576 | −1.12760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.58675 | −0.150649 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.36170 | −0.110294 | −0.0551469 | − | 0.998478i | \(-0.517563\pi\) | ||||
−0.0551469 | + | 0.998478i | \(0.517563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.47277 | 0.212136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.6949 | −0.873951 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.0694 | −0.328953 | −0.164476 | − | 0.986381i | \(-0.552593\pi\) | ||||
−0.164476 | + | 0.986381i | \(0.552593\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.3121 | 0.467056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.8139 | 0.678514 | 0.339257 | − | 0.940694i | \(-0.389824\pi\) | ||||
0.339257 | + | 0.940694i | \(0.389824\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.7106 | 1.13033 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.4904 | −0.990804 | −0.495402 | − | 0.868664i | \(-0.664979\pi\) | ||||
−0.495402 | + | 0.868664i | \(0.664979\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.7643 | −1.29080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.7234 | −0.769284 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.58383 | −0.245664 | −0.122832 | − | 0.992427i | \(-0.539198\pi\) | ||||
−0.122832 | + | 0.992427i | \(0.539198\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.793375 | −0.0256462 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.31556 | −0.300815 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7672 | −0.669910 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.7106 | −0.731839 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.6687 | 1.75803 | 0.879014 | − | 0.476797i | \(-0.158202\pi\) | ||||
0.879014 | + | 0.476797i | \(0.158202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.71836 | 0.215825 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9632 | 1.28248 | 0.641239 | − | 0.767341i | \(-0.278421\pi\) | ||||
0.641239 | + | 0.767341i | \(0.278421\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0715 | 0.354936 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.2400 | −0.487570 | −0.243785 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243785 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.50106 | −0.143855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.7290 | −0.342552 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.3609 | −1.44679 | −0.723394 | − | 0.690435i | \(-0.757419\pi\) | ||||
−0.723394 | + | 0.690435i | \(0.757419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.2477 | 0.358019 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0985 | −1.14787 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3537 | 0.519493 | 0.259747 | − | 0.965677i | \(-0.416361\pi\) | ||||
0.259747 | + | 0.965677i | \(0.416361\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.9688 | 0.570222 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.2037 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.2993 | 1.43321 |
(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 | 7600.2.a.cc.1.2 | 3 | ||
4.3 | odd | 2 | 475.2.a.e.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bh.1.2 | 3 | |||
12.11 | even | 2 | 4275.2.a.bm.1.3 | 3 | |||
20.3 | even | 4 | 475.2.b.b.324.6 | 6 | |||
20.7 | even | 4 | 475.2.b.b.324.1 | 6 | |||
20.19 | odd | 2 | 475.2.a.g.1.3 | yes | 3 | ||
60.59 | even | 2 | 4275.2.a.ba.1.1 | 3 | |||
76.75 | even | 2 | 9025.2.a.bc.1.3 | 3 | |||
380.379 | even | 2 | 9025.2.a.y.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.e.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
475.2.a.g.1.3 | yes | 3 | 20.19 | odd | 2 | ||
475.2.b.b.324.1 | 6 | 20.7 | even | 4 | |||
475.2.b.b.324.6 | 6 | 20.3 | even | 4 | |||
4275.2.a.ba.1.1 | 3 | 60.59 | even | 2 | |||
4275.2.a.bm.1.3 | 3 | 12.11 | even | 2 | |||
7600.2.a.bh.1.2 | 3 | 5.4 | even | 2 | |||
7600.2.a.cc.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.y.1.1 | 3 | 380.379 | even | 2 | |||
9025.2.a.bc.1.3 | 3 | 76.75 | even | 2 |