Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 22x^{10} + 181x^{8} - 692x^{6} + 1240x^{4} - 936x^{2} + 244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.870105\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.870105 | 0.615257 | 0.307628 | − | 0.951507i | \(-0.400465\pi\) | ||||
0.307628 | + | 0.951507i | \(0.400465\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.24292 | −0.621459 | ||||||||
\(5\) | −0.709862 | −0.317460 | −0.158730 | − | 0.987322i | \(-0.550740\pi\) | ||||
−0.158730 | + | 0.987322i | \(0.550740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.82168 | −0.997614 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.617654 | −0.195319 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.47182 | 0.962910 | 0.481455 | − | 0.876471i | \(-0.340109\pi\) | ||||
0.481455 | + | 0.876471i | \(0.340109\pi\) | |||||||
\(14\) | −0.870105 | −0.232545 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0306816 | 0.00767039 | ||||||||
\(17\) | 1.34682 | 0.326652 | 0.163326 | − | 0.986572i | \(-0.447778\pi\) | ||||
0.163326 | + | 0.986572i | \(0.447778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.503149 | −0.115430 | −0.0577151 | − | 0.998333i | \(-0.518382\pi\) | ||||
−0.0577151 | + | 0.998333i | \(0.518382\pi\) | |||||||
\(20\) | 0.882300 | 0.197288 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.69178 | 0.769790 | 0.384895 | − | 0.922960i | \(-0.374238\pi\) | ||||
0.384895 | + | 0.922960i | \(0.374238\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.49610 | −0.899219 | ||||||||
\(26\) | 3.02085 | 0.592437 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.24292 | 0.234889 | ||||||||
\(29\) | −9.21603 | −1.71137 | −0.855687 | − | 0.517494i | \(-0.826865\pi\) | ||||
−0.855687 | + | 0.517494i | \(0.826865\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.39006 | 0.249663 | 0.124832 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124832 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(32\) | 5.67005 | 1.00233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.17188 | 0.200975 | ||||||||
\(35\) | 0.709862 | 0.119989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.24922 | 0.369769 | 0.184884 | − | 0.982760i | \(-0.440809\pi\) | ||||
0.184884 | + | 0.982760i | \(0.440809\pi\) | |||||||
\(38\) | −0.437792 | −0.0710192 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00300 | 0.316702 | ||||||||
\(41\) | 12.4700 | 1.94749 | 0.973745 | − | 0.227641i | \(-0.0731012\pi\) | ||||
0.973745 | + | 0.227641i | \(0.0731012\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.60495 | −0.854747 | −0.427374 | − | 0.904075i | \(-0.640561\pi\) | ||||
−0.427374 | + | 0.904075i | \(0.640561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.21224 | 0.473618 | ||||||||
\(47\) | −5.79140 | −0.844763 | −0.422381 | − | 0.906418i | \(-0.638806\pi\) | ||||
−0.422381 | + | 0.906418i | \(0.638806\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.91207 | −0.553251 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.31519 | −0.598409 | ||||||||
\(53\) | 3.60444 | 0.495108 | 0.247554 | − | 0.968874i | \(-0.420373\pi\) | ||||
0.247554 | + | 0.968874i | \(0.420373\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.82168 | 0.377063 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.01891 | −1.05293 | ||||||||
\(59\) | −7.64892 | −0.995804 | −0.497902 | − | 0.867233i | \(-0.665896\pi\) | ||||
−0.497902 | + | 0.867233i | \(0.665896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.52488 | −0.707389 | −0.353694 | − | 0.935361i | \(-0.615075\pi\) | ||||
−0.353694 | + | 0.935361i | \(0.615075\pi\) | |||||||
\(62\) | 1.20950 | 0.153607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.87217 | 0.609022 | ||||||||
\(65\) | −2.46451 | −0.305685 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.25948 | 0.398208 | 0.199104 | − | 0.979978i | \(-0.436197\pi\) | ||||
0.199104 | + | 0.979978i | \(0.436197\pi\) | |||||||
\(68\) | −1.67399 | −0.203001 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.617654 | 0.0738237 | ||||||||
\(71\) | 8.53290 | 1.01267 | 0.506335 | − | 0.862337i | \(-0.331000\pi\) | ||||
0.506335 | + | 0.862337i | \(0.331000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.35102 | 0.275166 | 0.137583 | − | 0.990490i | \(-0.456067\pi\) | ||||
0.137583 | + | 0.990490i | \(0.456067\pi\) | |||||||
\(74\) | 1.95705 | 0.227503 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.625372 | 0.0717351 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00104 | 0.450152 | 0.225076 | − | 0.974341i | \(-0.427737\pi\) | ||||
0.225076 | + | 0.974341i | \(0.427737\pi\) | |||||||
\(80\) | −0.0217797 | −0.00243504 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.8502 | 1.19821 | ||||||||
\(83\) | 14.6924 | 1.61270 | 0.806352 | − | 0.591436i | \(-0.201439\pi\) | ||||
0.806352 | + | 0.591436i | \(0.201439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.956057 | −0.103699 | ||||||||
\(86\) | −4.87689 | −0.525889 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.42869 | −0.151440 | −0.0757202 | − | 0.997129i | \(-0.524126\pi\) | ||||
−0.0757202 | + | 0.997129i | \(0.524126\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.47182 | −0.363946 | ||||||||
\(92\) | −4.58858 | −0.478393 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.03913 | −0.519746 | ||||||||
\(95\) | 0.357166 | 0.0366444 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.56194 | −0.869333 | −0.434667 | − | 0.900591i | \(-0.643134\pi\) | ||||
−0.434667 | + | 0.900591i | \(0.643134\pi\) | |||||||
\(98\) | 0.870105 | 0.0878938 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.58828 | 0.558828 | ||||||||
\(101\) | 3.97425 | 0.395452 | 0.197726 | − | 0.980257i | \(-0.436644\pi\) | ||||
0.197726 | + | 0.980257i | \(0.436644\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2729 | 1.20929 | 0.604644 | − | 0.796496i | \(-0.293316\pi\) | ||||
0.604644 | + | 0.796496i | \(0.293316\pi\) | |||||||
\(104\) | −9.79636 | −0.960612 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.13624 | 0.304619 | ||||||||
\(107\) | −12.0377 | −1.16373 | −0.581865 | − | 0.813286i | \(-0.697677\pi\) | ||||
−0.581865 | + | 0.813286i | \(0.697677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.18589 | −0.688284 | −0.344142 | − | 0.938918i | \(-0.611830\pi\) | ||||
−0.344142 | + | 0.938918i | \(0.611830\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0306816 | −0.00289914 | ||||||||
\(113\) | −8.67927 | −0.816477 | −0.408238 | − | 0.912875i | \(-0.633857\pi\) | ||||
−0.408238 | + | 0.912875i | \(0.633857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.62065 | −0.244377 | ||||||||
\(116\) | 11.4548 | 1.06355 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.65536 | −0.612675 | ||||||||
\(119\) | −1.34682 | −0.123463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.80723 | −0.435226 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.72774 | −0.155155 | ||||||||
\(125\) | 6.74091 | 0.602926 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.5942 | −1.91618 | −0.958089 | − | 0.286472i | \(-0.907518\pi\) | ||||
−0.958089 | + | 0.286472i | \(0.907518\pi\) | |||||||
\(128\) | −7.10080 | −0.627628 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.14438 | −0.188075 | ||||||||
\(131\) | −8.93177 | −0.780372 | −0.390186 | − | 0.920736i | \(-0.627589\pi\) | ||||
−0.390186 | + | 0.920736i | \(0.627589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.503149 | 0.0436285 | ||||||||
\(134\) | 2.83608 | 0.245000 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.80030 | −0.325873 | ||||||||
\(137\) | −8.70309 | −0.743555 | −0.371778 | − | 0.928322i | \(-0.621252\pi\) | ||||
−0.371778 | + | 0.928322i | \(0.621252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.54256 | 0.724571 | 0.362285 | − | 0.932067i | \(-0.381997\pi\) | ||||
0.362285 | + | 0.932067i | \(0.381997\pi\) | |||||||
\(140\) | −0.882300 | −0.0745679 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.42452 | 0.623052 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.54211 | 0.543292 | ||||||||
\(146\) | 2.04563 | 0.169298 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.79559 | −0.229796 | ||||||||
\(149\) | −2.22541 | −0.182313 | −0.0911563 | − | 0.995837i | \(-0.529056\pi\) | ||||
−0.0911563 | + | 0.995837i | \(0.529056\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0845 | −1.06480 | −0.532400 | − | 0.846493i | \(-0.678710\pi\) | ||||
−0.532400 | + | 0.846493i | \(0.678710\pi\) | |||||||
\(152\) | 1.41972 | 0.115155 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.986754 | −0.0792580 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.7874 | −1.33978 | −0.669889 | − | 0.742461i | \(-0.733658\pi\) | ||||
−0.669889 | + | 0.742461i | \(0.733658\pi\) | |||||||
\(158\) | 3.48132 | 0.276959 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.02495 | −0.318200 | ||||||||
\(161\) | −3.69178 | −0.290953 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.70967 | −0.368890 | −0.184445 | − | 0.982843i | \(-0.559049\pi\) | ||||
−0.184445 | + | 0.982843i | \(0.559049\pi\) | |||||||
\(164\) | −15.4992 | −1.21029 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.7839 | 0.992227 | ||||||||
\(167\) | −3.59383 | −0.278099 | −0.139050 | − | 0.990285i | \(-0.544405\pi\) | ||||
−0.139050 | + | 0.990285i | \(0.544405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.946464 | −0.0728049 | ||||||||
\(170\) | −0.831870 | −0.0638015 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.96650 | 0.531190 | ||||||||
\(173\) | −9.26569 | −0.704457 | −0.352229 | − | 0.935914i | \(-0.614576\pi\) | ||||
−0.352229 | + | 0.935914i | \(0.614576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49610 | 0.339873 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.24311 | −0.0931747 | ||||||||
\(179\) | −6.25994 | −0.467890 | −0.233945 | − | 0.972250i | \(-0.575164\pi\) | ||||
−0.233945 | + | 0.972250i | \(0.575164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1467 | 1.20017 | 0.600087 | − | 0.799935i | \(-0.295133\pi\) | ||||
0.600087 | + | 0.799935i | \(0.295133\pi\) | |||||||
\(182\) | −3.02085 | −0.223920 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.4170 | −0.767953 | ||||||||
\(185\) | −1.59663 | −0.117387 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.19824 | 0.524986 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.310772 | 0.0225457 | ||||||||
\(191\) | −18.5412 | −1.34159 | −0.670797 | − | 0.741641i | \(-0.734048\pi\) | ||||
−0.670797 | + | 0.741641i | \(0.734048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.23992 | −0.593122 | −0.296561 | − | 0.955014i | \(-0.595840\pi\) | ||||
−0.296561 | + | 0.955014i | \(0.595840\pi\) | |||||||
\(194\) | −7.44978 | −0.534863 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.24292 | −0.0887799 | ||||||||
\(197\) | 3.60845 | 0.257092 | 0.128546 | − | 0.991704i | \(-0.458969\pi\) | ||||
0.128546 | + | 0.991704i | \(0.458969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.74954 | 0.549350 | 0.274675 | − | 0.961537i | \(-0.411430\pi\) | ||||
0.274675 | + | 0.961537i | \(0.411430\pi\) | |||||||
\(200\) | 12.6865 | 0.897074 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.45801 | 0.243305 | ||||||||
\(203\) | 9.21603 | 0.646839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.85199 | −0.618250 | ||||||||
\(206\) | 10.6787 | 0.744022 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.106521 | 0.00738590 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.130589 | 0.00899014 | 0.00449507 | − | 0.999990i | \(-0.498569\pi\) | ||||
0.00449507 | + | 0.999990i | \(0.498569\pi\) | |||||||
\(212\) | −4.48002 | −0.307689 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.4741 | −0.715992 | ||||||||
\(215\) | 3.97874 | 0.271348 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.39006 | −0.0943638 | ||||||||
\(218\) | −6.25248 | −0.423471 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.67593 | 0.314537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3141 | −0.824615 | −0.412308 | − | 0.911045i | \(-0.635277\pi\) | ||||
−0.412308 | + | 0.911045i | \(0.635277\pi\) | |||||||
\(224\) | −5.67005 | −0.378846 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.55187 | −0.502343 | ||||||||
\(227\) | 13.9626 | 0.926733 | 0.463367 | − | 0.886167i | \(-0.346641\pi\) | ||||
0.463367 | + | 0.886167i | \(0.346641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9419 | −1.31780 | −0.658898 | − | 0.752233i | \(-0.728977\pi\) | ||||
−0.658898 | + | 0.752233i | \(0.728977\pi\) | |||||||
\(230\) | −2.28024 | −0.150355 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.0047 | 1.70729 | ||||||||
\(233\) | −4.58513 | −0.300382 | −0.150191 | − | 0.988657i | \(-0.547989\pi\) | ||||
−0.150191 | + | 0.988657i | \(0.547989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.11109 | 0.268178 | ||||||||
\(236\) | 9.50698 | 0.618852 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.17188 | −0.0759615 | ||||||||
\(239\) | 2.46796 | 0.159639 | 0.0798195 | − | 0.996809i | \(-0.474566\pi\) | ||||
0.0798195 | + | 0.996809i | \(0.474566\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.1525 | −1.36255 | −0.681276 | − | 0.732027i | \(-0.738575\pi\) | ||||
−0.681276 | + | 0.732027i | \(0.738575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.86698 | 0.439613 | ||||||||
\(245\) | −0.709862 | −0.0453514 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.74684 | −0.111149 | ||||||||
\(248\) | −3.92232 | −0.249067 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.86530 | 0.370954 | ||||||||
\(251\) | −18.8125 | −1.18743 | −0.593717 | − | 0.804674i | \(-0.702340\pi\) | ||||
−0.593717 | + | 0.804674i | \(0.702340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.7892 | −1.17894 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9228 | −0.995174 | ||||||||
\(257\) | −29.1877 | −1.82068 | −0.910339 | − | 0.413862i | \(-0.864179\pi\) | ||||
−0.910339 | + | 0.413862i | \(0.864179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.24922 | −0.139759 | ||||||||
\(260\) | 3.06319 | 0.189971 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.77157 | −0.480129 | ||||||||
\(263\) | −16.5583 | −1.02103 | −0.510516 | − | 0.859868i | \(-0.670545\pi\) | ||||
−0.510516 | + | 0.859868i | \(0.670545\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.55865 | −0.157177 | ||||||||
\(266\) | 0.437792 | 0.0268427 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.05126 | −0.247470 | ||||||||
\(269\) | −22.2756 | −1.35817 | −0.679084 | − | 0.734061i | \(-0.737623\pi\) | ||||
−0.679084 | + | 0.734061i | \(0.737623\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3230 | −1.11304 | −0.556521 | − | 0.830834i | \(-0.687864\pi\) | ||||
−0.556521 | + | 0.830834i | \(0.687864\pi\) | |||||||
\(272\) | 0.0413226 | 0.00250555 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.57260 | −0.457478 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2766 | −1.15822 | −0.579110 | − | 0.815249i | \(-0.696600\pi\) | ||||
−0.579110 | + | 0.815249i | \(0.696600\pi\) | |||||||
\(278\) | 7.43292 | 0.445797 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.00300 | −0.119702 | ||||||||
\(281\) | 16.9012 | 1.00824 | 0.504120 | − | 0.863634i | \(-0.331817\pi\) | ||||
0.504120 | + | 0.863634i | \(0.331817\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0611 | −0.776400 | −0.388200 | − | 0.921575i | \(-0.626903\pi\) | ||||
−0.388200 | + | 0.921575i | \(0.626903\pi\) | |||||||
\(284\) | −10.6057 | −0.629332 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.4700 | −0.736082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1861 | −0.893298 | ||||||||
\(290\) | 5.69232 | 0.334264 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.92212 | −0.171004 | ||||||||
\(293\) | 12.7793 | 0.746577 | 0.373288 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373288 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.42967 | 0.316128 | ||||||||
\(296\) | −6.34656 | −0.368886 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.93634 | −0.112169 | ||||||||
\(299\) | 12.8172 | 0.741238 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.60495 | 0.323064 | ||||||||
\(302\) | −11.3849 | −0.655126 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0154374 | −0.000885395 0 | ||||||||
\(305\) | 3.92190 | 0.224567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9531 | −1.59537 | −0.797685 | − | 0.603074i | \(-0.793942\pi\) | ||||
−0.797685 | + | 0.603074i | \(0.793942\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.858579 | −0.0487640 | ||||||||
\(311\) | −2.60259 | −0.147579 | −0.0737896 | − | 0.997274i | \(-0.523509\pi\) | ||||
−0.0737896 | + | 0.997274i | \(0.523509\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3114 | 0.752405 | 0.376202 | − | 0.926537i | \(-0.377230\pi\) | ||||
0.376202 | + | 0.926537i | \(0.377230\pi\) | |||||||
\(314\) | −14.6068 | −0.824308 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.97297 | −0.279751 | ||||||||
\(317\) | 28.1411 | 1.58056 | 0.790282 | − | 0.612743i | \(-0.209934\pi\) | ||||
0.790282 | + | 0.612743i | \(0.209934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.45857 | −0.193340 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.21224 | −0.179011 | ||||||||
\(323\) | −0.677652 | −0.0377056 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.6096 | −0.865867 | ||||||||
\(326\) | −4.09790 | −0.226962 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −35.1864 | −1.94284 | ||||||||
\(329\) | 5.79140 | 0.319290 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1522 | 1.43746 | 0.718728 | − | 0.695291i | \(-0.244725\pi\) | ||||
0.718728 | + | 0.695291i | \(0.244725\pi\) | |||||||
\(332\) | −18.2615 | −1.00223 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.12701 | −0.171102 | ||||||||
\(335\) | −2.31378 | −0.126415 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8676 | −1.02779 | −0.513893 | − | 0.857854i | \(-0.671797\pi\) | ||||
−0.513893 | + | 0.857854i | \(0.671797\pi\) | |||||||
\(338\) | −0.823522 | −0.0447937 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.18830 | 0.0644447 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 15.8154 | 0.852707 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.06211 | −0.433422 | ||||||||
\(347\) | 11.8666 | 0.637033 | 0.318517 | − | 0.947917i | \(-0.396815\pi\) | ||||
0.318517 | + | 0.947917i | \(0.396815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7072 | −1.37607 | −0.688037 | − | 0.725675i | \(-0.741527\pi\) | ||||
−0.688037 | + | 0.725675i | \(0.741527\pi\) | |||||||
\(350\) | 3.91207 | 0.209109 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4391 | 1.35399 | 0.676993 | − | 0.735990i | \(-0.263283\pi\) | ||||
0.676993 | + | 0.735990i | \(0.263283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.05718 | −0.321482 | ||||||||
\(356\) | 1.77574 | 0.0941140 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.44680 | −0.287872 | ||||||||
\(359\) | −16.9602 | −0.895126 | −0.447563 | − | 0.894252i | \(-0.647708\pi\) | ||||
−0.447563 | + | 0.894252i | \(0.647708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7468 | −0.986676 | ||||||||
\(362\) | 14.0493 | 0.738415 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.31519 | 0.226177 | ||||||||
\(365\) | −1.66890 | −0.0873541 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6589 | 0.608587 | 0.304294 | − | 0.952578i | \(-0.401580\pi\) | ||||
0.304294 | + | 0.952578i | \(0.401580\pi\) | |||||||
\(368\) | 0.113270 | 0.00590459 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.38924 | −0.0722230 | ||||||||
\(371\) | −3.60444 | −0.187133 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1414 | 0.835771 | 0.417886 | − | 0.908500i | \(-0.362771\pi\) | ||||
0.417886 | + | 0.908500i | \(0.362771\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.3415 | 0.842747 | ||||||||
\(377\) | −31.9964 | −1.64790 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.64587 | 0.187276 | 0.0936380 | − | 0.995606i | \(-0.470150\pi\) | ||||
0.0936380 | + | 0.995606i | \(0.470150\pi\) | |||||||
\(380\) | −0.443928 | −0.0227730 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.1328 | −0.825424 | ||||||||
\(383\) | 27.9141 | 1.42634 | 0.713172 | − | 0.700989i | \(-0.247258\pi\) | ||||
0.713172 | + | 0.700989i | \(0.247258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.16959 | −0.364922 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.6418 | 0.540255 | ||||||||
\(389\) | 32.3483 | 1.64013 | 0.820063 | − | 0.572274i | \(-0.193939\pi\) | ||||
0.820063 | + | 0.572274i | \(0.193939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.97217 | 0.251454 | ||||||||
\(392\) | −2.82168 | −0.142516 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.13973 | 0.158177 | ||||||||
\(395\) | −2.84019 | −0.142905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.4932 | 1.12890 | 0.564451 | − | 0.825467i | \(-0.309088\pi\) | ||||
0.564451 | + | 0.825467i | \(0.309088\pi\) | |||||||
\(398\) | 6.74291 | 0.337992 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.137947 | −0.00689737 | ||||||||
\(401\) | 13.2813 | 0.663236 | 0.331618 | − | 0.943414i | \(-0.392406\pi\) | ||||
0.331618 | + | 0.943414i | \(0.392406\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.82606 | 0.240403 | ||||||||
\(404\) | −4.93966 | −0.245757 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.01891 | 0.397972 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.75052 | −0.333792 | −0.166896 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166896 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(410\) | −7.70216 | −0.380382 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.2542 | −0.751522 | ||||||||
\(413\) | 7.64892 | 0.376379 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.4296 | −0.511968 | ||||||||
\(416\) | 19.6854 | 0.965156 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.5259 | 1.24702 | 0.623511 | − | 0.781815i | \(-0.285706\pi\) | ||||
0.623511 | + | 0.781815i | \(0.285706\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.5994 | −0.711529 | −0.355765 | − | 0.934576i | \(-0.615780\pi\) | ||||
−0.355765 | + | 0.934576i | \(0.615780\pi\) | |||||||
\(422\) | 0.113626 | 0.00553124 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.1706 | −0.493926 | ||||||||
\(425\) | −6.05544 | −0.293732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.52488 | 0.267368 | ||||||||
\(428\) | 14.9619 | 0.723210 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46192 | 0.166949 | ||||||||
\(431\) | −3.80384 | −0.183225 | −0.0916123 | − | 0.995795i | \(-0.529202\pi\) | ||||
−0.0916123 | + | 0.995795i | \(0.529202\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.18094 | −0.104809 | −0.0524046 | − | 0.998626i | \(-0.516689\pi\) | ||||
−0.0524046 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(434\) | −1.20950 | −0.0580579 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.93148 | 0.427740 | ||||||||
\(437\) | −1.85752 | −0.0888570 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.6200 | −1.65232 | −0.826162 | − | 0.563433i | \(-0.809480\pi\) | ||||
−0.826162 | + | 0.563433i | \(0.809480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.06854 | 0.193521 | ||||||||
\(443\) | 30.4185 | 1.44523 | 0.722614 | − | 0.691252i | \(-0.242940\pi\) | ||||
0.722614 | + | 0.691252i | \(0.242940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.01417 | 0.0480762 | ||||||||
\(446\) | −10.7146 | −0.507350 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.87217 | −0.230189 | ||||||||
\(449\) | −5.65261 | −0.266763 | −0.133382 | − | 0.991065i | \(-0.542584\pi\) | ||||
−0.133382 | + | 0.991065i | \(0.542584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.7876 | 0.507407 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.1490 | 0.570179 | ||||||||
\(455\) | 2.46451 | 0.115538 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.7755 | −0.925060 | −0.462530 | − | 0.886604i | \(-0.653058\pi\) | ||||
−0.462530 | + | 0.886604i | \(0.653058\pi\) | |||||||
\(458\) | −17.3515 | −0.810782 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.25726 | 0.151870 | ||||||||
\(461\) | −0.336395 | −0.0156675 | −0.00783374 | − | 0.999969i | \(-0.502494\pi\) | ||||
−0.00783374 | + | 0.999969i | \(0.502494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0213 | 0.976941 | 0.488471 | − | 0.872580i | \(-0.337555\pi\) | ||||
0.488471 | + | 0.872580i | \(0.337555\pi\) | |||||||
\(464\) | −0.282762 | −0.0131269 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.98955 | −0.184812 | ||||||||
\(467\) | −11.5498 | −0.534462 | −0.267231 | − | 0.963633i | \(-0.586109\pi\) | ||||
−0.267231 | + | 0.963633i | \(0.586109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25948 | −0.150509 | ||||||||
\(470\) | 3.57708 | 0.164998 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.5828 | 0.993428 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.26220 | 0.103797 | ||||||||
\(476\) | 1.67399 | 0.0767272 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.14738 | 0.0982190 | ||||||||
\(479\) | −33.3819 | −1.52526 | −0.762628 | − | 0.646837i | \(-0.776091\pi\) | ||||
−0.762628 | + | 0.646837i | \(0.776091\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.80887 | 0.356054 | ||||||||
\(482\) | −18.4049 | −0.838319 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.07779 | 0.275978 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.53639 | 0.114935 | 0.0574673 | − | 0.998347i | \(-0.481697\pi\) | ||||
0.0574673 | + | 0.998347i | \(0.481697\pi\) | |||||||
\(488\) | 15.5894 | 0.705701 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.617654 | −0.0279028 | ||||||||
\(491\) | −4.17150 | −0.188257 | −0.0941286 | − | 0.995560i | \(-0.530006\pi\) | ||||
−0.0941286 | + | 0.995560i | \(0.530006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4124 | −0.559024 | ||||||||
\(494\) | −1.51993 | −0.0683851 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0426494 | 0.00191501 | ||||||||
\(497\) | −8.53290 | −0.382753 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.2831 | 1.66902 | 0.834509 | − | 0.550994i | \(-0.185751\pi\) | ||||
0.834509 | + | 0.550994i | \(0.185751\pi\) | |||||||
\(500\) | −8.37840 | −0.374694 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.3688 | −0.730576 | ||||||||
\(503\) | 9.14838 | 0.407906 | 0.203953 | − | 0.978981i | \(-0.434621\pi\) | ||||
0.203953 | + | 0.978981i | \(0.434621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.82117 | −0.125540 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26.8398 | 1.19083 | ||||||||
\(509\) | 21.1205 | 0.936151 | 0.468075 | − | 0.883689i | \(-0.344948\pi\) | ||||
0.468075 | + | 0.883689i | \(0.344948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.35102 | −0.104003 | ||||||||
\(512\) | 0.347113 | 0.0153404 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.3964 | −1.12019 | ||||||||
\(515\) | −8.71208 | −0.383900 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.95705 | −0.0859879 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.95406 | 0.304956 | ||||||||
\(521\) | −20.2060 | −0.885239 | −0.442619 | − | 0.896710i | \(-0.645951\pi\) | ||||
−0.442619 | + | 0.896710i | \(0.645951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.0877 | −0.484830 | −0.242415 | − | 0.970173i | \(-0.577940\pi\) | ||||
−0.242415 | + | 0.970173i | \(0.577940\pi\) | |||||||
\(524\) | 11.1015 | 0.484969 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.4075 | −0.628196 | ||||||||
\(527\) | 1.87217 | 0.0815530 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.37074 | −0.407424 | ||||||||
\(530\) | −2.22630 | −0.0967041 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.625372 | −0.0271133 | ||||||||
\(533\) | 43.2937 | 1.87526 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.54511 | 0.369437 | ||||||||
\(536\) | −9.19719 | −0.397258 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.3821 | −0.835622 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.8592 | −1.11177 | −0.555887 | − | 0.831258i | \(-0.687621\pi\) | ||||
−0.555887 | + | 0.831258i | \(0.687621\pi\) | |||||||
\(542\) | −15.9429 | −0.684806 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.63655 | 0.327414 | ||||||||
\(545\) | 5.10099 | 0.218502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.9691 | 0.469006 | 0.234503 | − | 0.972115i | \(-0.424654\pi\) | ||||
0.234503 | + | 0.972115i | \(0.424654\pi\) | |||||||
\(548\) | 10.8172 | 0.462089 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.63703 | 0.197544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00104 | −0.170142 | ||||||||
\(554\) | −16.7727 | −0.712603 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.6177 | −0.450291 | ||||||||
\(557\) | 18.0302 | 0.763964 | 0.381982 | − | 0.924170i | \(-0.375242\pi\) | ||||
0.381982 | + | 0.924170i | \(0.375242\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.4594 | −0.823044 | ||||||||
\(560\) | 0.0217797 | 0.000920359 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7058 | 0.620326 | ||||||||
\(563\) | −21.5405 | −0.907822 | −0.453911 | − | 0.891047i | \(-0.649972\pi\) | ||||
−0.453911 | + | 0.891047i | \(0.649972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.16108 | 0.259198 | ||||||||
\(566\) | −11.3645 | −0.477685 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −24.0771 | −1.01025 | ||||||||
\(569\) | 21.8568 | 0.916286 | 0.458143 | − | 0.888879i | \(-0.348515\pi\) | ||||
0.458143 | + | 0.888879i | \(0.348515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.01476 | −0.209861 | −0.104930 | − | 0.994480i | \(-0.533462\pi\) | ||||
−0.104930 | + | 0.994480i | \(0.533462\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.8502 | −0.452880 | ||||||||
\(575\) | −16.5986 | −0.692210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.8613 | 0.493793 | 0.246897 | − | 0.969042i | \(-0.420589\pi\) | ||||
0.246897 | + | 0.969042i | \(0.420589\pi\) | |||||||
\(578\) | −13.2135 | −0.549608 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.13130 | −0.337634 | ||||||||
\(581\) | −14.6924 | −0.609545 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.63381 | −0.274509 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.1194 | 0.459336 | ||||||||
\(587\) | 30.1344 | 1.24378 | 0.621890 | − | 0.783104i | \(-0.286365\pi\) | ||||
0.621890 | + | 0.783104i | \(0.286365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.699409 | −0.0288187 | ||||||||
\(590\) | 4.72438 | 0.194500 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0690095 | 0.00283627 | ||||||||
\(593\) | −0.154283 | −0.00633564 | −0.00316782 | − | 0.999995i | \(-0.501008\pi\) | ||||
−0.00316782 | + | 0.999995i | \(0.501008\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.956057 | 0.0391945 | ||||||||
\(596\) | 2.76600 | 0.113300 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.1523 | 0.456052 | ||||||||
\(599\) | 33.8158 | 1.38168 | 0.690838 | − | 0.723010i | \(-0.257242\pi\) | ||||
0.690838 | + | 0.723010i | \(0.257242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.2993 | 1.92938 | 0.964688 | − | 0.263394i | \(-0.0848418\pi\) | ||||
0.964688 | + | 0.263394i | \(0.0848418\pi\) | |||||||
\(602\) | 4.87689 | 0.198767 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.2629 | 0.661730 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.76035 | −0.396160 | −0.198080 | − | 0.980186i | \(-0.563471\pi\) | ||||
−0.198080 | + | 0.980186i | \(0.563471\pi\) | |||||||
\(608\) | −2.85288 | −0.115700 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.41247 | 0.138167 | ||||||||
\(611\) | −20.1067 | −0.813430 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.4957 | −1.67600 | −0.837998 | − | 0.545673i | \(-0.816274\pi\) | ||||
−0.837998 | + | 0.545673i | \(0.816274\pi\) | |||||||
\(614\) | −24.3222 | −0.981562 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2181 | −0.934725 | −0.467362 | − | 0.884066i | \(-0.654796\pi\) | ||||
−0.467362 | + | 0.884066i | \(0.654796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.3371 | −0.817416 | −0.408708 | − | 0.912665i | \(-0.634021\pi\) | ||||
−0.408708 | + | 0.912665i | \(0.634021\pi\) | |||||||
\(620\) | 1.22645 | 0.0492556 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.26452 | −0.0907991 | ||||||||
\(623\) | 1.42869 | 0.0572391 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.6954 | 0.707815 | ||||||||
\(626\) | 11.5823 | 0.462922 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 20.8653 | 0.832617 | ||||||||
\(629\) | 3.02929 | 0.120786 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1617 | 1.32015 | 0.660073 | − | 0.751202i | \(-0.270525\pi\) | ||||
0.660073 | + | 0.751202i | \(0.270525\pi\) | |||||||
\(632\) | −11.2896 | −0.449078 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.4857 | 0.972453 | ||||||||
\(635\) | 15.3289 | 0.608309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.47182 | 0.137559 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.04059 | 0.199247 | ||||||||
\(641\) | 24.7317 | 0.976843 | 0.488422 | − | 0.872608i | \(-0.337573\pi\) | ||||
0.488422 | + | 0.872608i | \(0.337573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.06615 | 0.199789 | 0.0998947 | − | 0.994998i | \(-0.468149\pi\) | ||||
0.0998947 | + | 0.994998i | \(0.468149\pi\) | |||||||
\(644\) | 4.58858 | 0.180816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.589628 | −0.0231986 | ||||||||
\(647\) | 35.4931 | 1.39538 | 0.697690 | − | 0.716400i | \(-0.254211\pi\) | ||||
0.697690 | + | 0.716400i | \(0.254211\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.5820 | −0.532731 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.85373 | 0.229250 | ||||||||
\(653\) | 9.63770 | 0.377152 | 0.188576 | − | 0.982059i | \(-0.439613\pi\) | ||||
0.188576 | + | 0.982059i | \(0.439613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.34032 | 0.247737 | ||||||||
\(656\) | 0.382600 | 0.0149380 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.03913 | 0.196446 | ||||||||
\(659\) | 15.4794 | 0.602992 | 0.301496 | − | 0.953467i | \(-0.402514\pi\) | ||||
0.301496 | + | 0.953467i | \(0.402514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2397 | −0.826128 | −0.413064 | − | 0.910702i | \(-0.635541\pi\) | ||||
−0.413064 | + | 0.910702i | \(0.635541\pi\) | |||||||
\(662\) | 22.7552 | 0.884405 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41.4573 | −1.60886 | ||||||||
\(665\) | −0.357166 | −0.0138503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.0236 | −1.31740 | ||||||||
\(668\) | 4.46684 | 0.172827 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.01323 | −0.0777778 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.16841 | 0.0835861 | 0.0417931 | − | 0.999126i | \(-0.486693\pi\) | ||||
0.0417931 | + | 0.999126i | \(0.486693\pi\) | |||||||
\(674\) | −16.4168 | −0.632352 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.17638 | 0.0452453 | ||||||||
\(677\) | −1.79264 | −0.0688966 | −0.0344483 | − | 0.999406i | \(-0.510967\pi\) | ||||
−0.0344483 | + | 0.999406i | \(0.510967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.56194 | 0.328577 | ||||||||
\(680\) | 2.69769 | 0.103452 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.8000 | −0.681099 | −0.340549 | − | 0.940227i | \(-0.610613\pi\) | ||||
−0.340549 | + | 0.940227i | \(0.610613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.17799 | 0.236049 | ||||||||
\(686\) | −0.870105 | −0.0332207 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.171969 | −0.00655625 | ||||||||
\(689\) | 12.5140 | 0.476744 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8957 | 1.21337 | 0.606686 | − | 0.794942i | \(-0.292499\pi\) | ||||
0.606686 | + | 0.794942i | \(0.292499\pi\) | |||||||
\(692\) | 11.5165 | 0.437791 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.3252 | 0.391939 | ||||||||
\(695\) | −6.06404 | −0.230022 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.7949 | 0.636152 | ||||||||
\(698\) | −22.3679 | −0.846639 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.58828 | −0.211217 | ||||||||
\(701\) | −34.6298 | −1.30795 | −0.653975 | − | 0.756516i | \(-0.726900\pi\) | ||||
−0.653975 | + | 0.756516i | \(0.726900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.13169 | −0.0426825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.1347 | 0.833049 | ||||||||
\(707\) | −3.97425 | −0.149467 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.5584 | −0.922310 | −0.461155 | − | 0.887320i | \(-0.652565\pi\) | ||||
−0.461155 | + | 0.887320i | \(0.652565\pi\) | |||||||
\(710\) | −5.27038 | −0.197794 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.03129 | 0.151079 | ||||||||
\(713\) | 5.13182 | 0.192188 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.78059 | 0.290774 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.7572 | −0.550732 | ||||||||
\(719\) | 30.8151 | 1.14921 | 0.574604 | − | 0.818431i | \(-0.305156\pi\) | ||||
0.574604 | + | 0.818431i | \(0.305156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.2729 | −0.457068 | ||||||||
\(722\) | −16.3117 | −0.607059 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.0690 | −0.745858 | ||||||||
\(725\) | 41.4362 | 1.53890 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.5902 | −0.949090 | −0.474545 | − | 0.880231i | \(-0.657387\pi\) | ||||
−0.474545 | + | 0.880231i | \(0.657387\pi\) | |||||||
\(728\) | 9.79636 | 0.363077 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.45212 | −0.0537452 | ||||||||
\(731\) | −7.54887 | −0.279205 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5577 | −0.943995 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(734\) | 10.1444 | 0.374437 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.9326 | 0.771586 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.5651 | −0.830072 | −0.415036 | − | 0.909805i | \(-0.636231\pi\) | ||||
−0.415036 | + | 0.909805i | \(0.636231\pi\) | |||||||
\(740\) | 1.98448 | 0.0729510 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.13624 | −0.115135 | ||||||||
\(743\) | −5.20368 | −0.190905 | −0.0954523 | − | 0.995434i | \(-0.530430\pi\) | ||||
−0.0954523 | + | 0.995434i | \(0.530430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.57973 | 0.0578769 | ||||||||
\(746\) | 14.0447 | 0.514214 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.0377 | 0.439848 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.3856 | −1.58316 | −0.791581 | − | 0.611065i | \(-0.790742\pi\) | ||||
−0.791581 | + | 0.611065i | \(0.790742\pi\) | |||||||
\(752\) | −0.177689 | −0.00647966 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.8402 | −1.01388 | ||||||||
\(755\) | 9.28818 | 0.338031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.2472 | 0.590513 | 0.295256 | − | 0.955418i | \(-0.404595\pi\) | ||||
0.295256 | + | 0.955418i | \(0.404595\pi\) | |||||||
\(758\) | 3.17229 | 0.115223 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.00781 | −0.0365570 | ||||||||
\(761\) | −27.7710 | −1.00670 | −0.503349 | − | 0.864083i | \(-0.667899\pi\) | ||||
−0.503349 | + | 0.864083i | \(0.667899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.18589 | 0.260147 | ||||||||
\(764\) | 23.0452 | 0.833745 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.2882 | 0.877568 | ||||||||
\(767\) | −26.5557 | −0.958870 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.5109 | −1.71329 | −0.856643 | − | 0.515910i | \(-0.827454\pi\) | ||||
−0.856643 | + | 0.515910i | \(0.827454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.2415 | 0.368601 | ||||||||
\(773\) | 53.7721 | 1.93405 | 0.967023 | − | 0.254689i | \(-0.0819730\pi\) | ||||
0.967023 | + | 0.254689i | \(0.0819730\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.24987 | −0.224502 | ||||||||
\(776\) | 24.1590 | 0.867259 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.1464 | 1.00910 | ||||||||
\(779\) | −6.27427 | −0.224799 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 4.32631 | 0.154709 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0306816 | 0.00109577 | ||||||||
\(785\) | 11.9167 | 0.425326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.9658 | 1.70980 | 0.854898 | − | 0.518796i | \(-0.173619\pi\) | ||||
0.854898 | + | 0.518796i | \(0.173619\pi\) | |||||||
\(788\) | −4.48501 | −0.159772 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.47126 | −0.0879234 | ||||||||
\(791\) | 8.67927 | 0.308599 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.1814 | −0.681152 | ||||||||
\(794\) | 19.5714 | 0.694564 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.63204 | −0.341399 | ||||||||
\(797\) | 21.2494 | 0.752691 | 0.376346 | − | 0.926479i | \(-0.377181\pi\) | ||||
0.376346 | + | 0.926479i | \(0.377181\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.79999 | −0.275944 | ||||||||
\(800\) | −25.4931 | −0.901317 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.5561 | 0.408060 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.62065 | 0.0923659 | ||||||||
\(806\) | 4.19917 | 0.147910 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.2140 | −0.394509 | ||||||||
\(809\) | 35.7295 | 1.25618 | 0.628092 | − | 0.778139i | \(-0.283836\pi\) | ||||
0.628092 | + | 0.778139i | \(0.283836\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0383 | −0.422721 | −0.211360 | − | 0.977408i | \(-0.567789\pi\) | ||||
−0.211360 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(812\) | −11.4548 | −0.401984 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.34321 | 0.117108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.82012 | 0.0986636 | ||||||||
\(818\) | −5.87366 | −0.205368 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.0023 | 0.384217 | ||||||||
\(821\) | 47.0391 | 1.64168 | 0.820838 | − | 0.571162i | \(-0.193507\pi\) | ||||
0.820838 | + | 0.571162i | \(0.193507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.9888 | −1.32421 | −0.662103 | − | 0.749413i | \(-0.730336\pi\) | ||||
−0.662103 | + | 0.749413i | \(0.730336\pi\) | |||||||
\(824\) | −34.6302 | −1.20640 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.65536 | 0.231570 | ||||||||
\(827\) | 1.05716 | 0.0367611 | 0.0183805 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183805 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.4048 | −1.22966 | −0.614831 | − | 0.788659i | \(-0.710776\pi\) | ||||
−0.614831 | + | 0.788659i | \(0.710776\pi\) | |||||||
\(830\) | −9.07483 | −0.314992 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.9153 | 0.586433 | ||||||||
\(833\) | 1.34682 | 0.0466646 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.55112 | 0.0882853 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.2102 | 0.767238 | ||||||||
\(839\) | 41.3140 | 1.42632 | 0.713159 | − | 0.701002i | \(-0.247264\pi\) | ||||
0.713159 | + | 0.701002i | \(0.247264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.9353 | 1.92880 | ||||||||
\(842\) | −12.7030 | −0.437773 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.162312 | −0.00558700 | ||||||||
\(845\) | 0.671858 | 0.0231126 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.110590 | 0.00379767 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.26887 | −0.180721 | ||||||||
\(851\) | 8.30361 | 0.284644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.244685 | 0.00837784 | 0.00418892 | − | 0.999991i | \(-0.498667\pi\) | ||||
0.00418892 | + | 0.999991i | \(0.498667\pi\) | |||||||
\(854\) | 4.80723 | 0.164500 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.9665 | 1.16095 | ||||||||
\(857\) | −50.2741 | −1.71733 | −0.858666 | − | 0.512536i | \(-0.828706\pi\) | ||||
−0.858666 | + | 0.512536i | \(0.828706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3223 | 0.454552 | 0.227276 | − | 0.973830i | \(-0.427018\pi\) | ||||
0.227276 | + | 0.973830i | \(0.427018\pi\) | |||||||
\(860\) | −4.94525 | −0.168632 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.30974 | −0.112730 | ||||||||
\(863\) | −29.5005 | −1.00421 | −0.502105 | − | 0.864807i | \(-0.667441\pi\) | ||||
−0.502105 | + | 0.864807i | \(0.667441\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.57735 | 0.223637 | ||||||||
\(866\) | −1.89764 | −0.0644845 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.72774 | 0.0586432 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3163 | 0.383439 | ||||||||
\(872\) | 20.2763 | 0.686641 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.61623 | −0.0546699 | ||||||||
\(875\) | −6.74091 | −0.227884 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.6648 | 0.765335 | 0.382667 | − | 0.923886i | \(-0.375006\pi\) | ||||
0.382667 | + | 0.923886i | \(0.375006\pi\) | |||||||
\(878\) | −30.1230 | −1.01660 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1422 | −1.52088 | −0.760440 | − | 0.649409i | \(-0.775016\pi\) | ||||
−0.760440 | + | 0.649409i | \(0.775016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7815 | −0.531089 | −0.265545 | − | 0.964099i | \(-0.585552\pi\) | ||||
−0.265545 | + | 0.964099i | \(0.585552\pi\) | |||||||
\(884\) | −5.81179 | −0.195472 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.4673 | 0.889186 | ||||||||
\(887\) | 37.8474 | 1.27079 | 0.635396 | − | 0.772187i | \(-0.280837\pi\) | ||||
0.635396 | + | 0.772187i | \(0.280837\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.5942 | 0.724247 | ||||||||
\(890\) | 0.882433 | 0.0295792 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.3055 | 0.512465 | ||||||||
\(893\) | 2.91394 | 0.0975112 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.44369 | 0.148536 | ||||||||
\(896\) | 7.10080 | 0.237221 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.91836 | −0.164128 | ||||||||
\(899\) | −12.8109 | −0.427267 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.85454 | 0.161728 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.4901 | 0.814528 | ||||||||
\(905\) | −11.4619 | −0.381007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.1259 | −0.502246 | −0.251123 | − | 0.967955i | \(-0.580800\pi\) | ||||
−0.251123 | + | 0.967955i | \(0.580800\pi\) | |||||||
\(908\) | −17.3544 | −0.575927 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.14438 | 0.0710856 | ||||||||
\(911\) | −51.5380 | −1.70753 | −0.853765 | − | 0.520658i | \(-0.825687\pi\) | ||||
−0.853765 | + | 0.520658i | \(0.825687\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −17.2068 | −0.569149 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.7861 | 0.818956 | ||||||||
\(917\) | 8.93177 | 0.294953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1376 | −0.400384 | −0.200192 | − | 0.979757i | \(-0.564157\pi\) | ||||
−0.200192 | + | 0.979757i | \(0.564157\pi\) | |||||||
\(920\) | 7.39464 | 0.243794 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.292699 | −0.00963953 | ||||||||
\(923\) | 29.6247 | 0.975109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1127 | −0.332503 | ||||||||
\(926\) | 18.2907 | 0.601070 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −52.2554 | −1.71537 | ||||||||
\(929\) | 39.7034 | 1.30263 | 0.651314 | − | 0.758808i | \(-0.274218\pi\) | ||||
0.651314 | + | 0.758808i | \(0.274218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.503149 | −0.0164900 | ||||||||
\(932\) | 5.69895 | 0.186675 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.0495 | −0.328831 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5516 | −0.344705 | −0.172353 | − | 0.985035i | \(-0.555137\pi\) | ||||
−0.172353 | + | 0.985035i | \(0.555137\pi\) | |||||||
\(938\) | −2.83608 | −0.0926014 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.10975 | −0.166662 | ||||||||
\(941\) | −27.3882 | −0.892829 | −0.446415 | − | 0.894826i | \(-0.647299\pi\) | ||||
−0.446415 | + | 0.894826i | \(0.647299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.0366 | 1.49916 | ||||||||
\(944\) | −0.234681 | −0.00763821 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.1492 | 0.427292 | 0.213646 | − | 0.976911i | \(-0.431466\pi\) | ||||
0.213646 | + | 0.976911i | \(0.431466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.16231 | 0.264960 | ||||||||
\(950\) | 1.96835 | 0.0638619 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.80030 | 0.123168 | ||||||||
\(953\) | 30.3710 | 0.983815 | 0.491907 | − | 0.870648i | \(-0.336300\pi\) | ||||
0.491907 | + | 0.870648i | \(0.336300\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1617 | 0.425902 | ||||||||
\(956\) | −3.06747 | −0.0992091 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.0457 | −0.938425 | ||||||||
\(959\) | 8.70309 | 0.281038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0677 | −0.937668 | ||||||||
\(962\) | 6.79453 | 0.219065 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.2908 | 0.846770 | ||||||||
\(965\) | 5.84920 | 0.188292 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.6355 | 1.59617 | 0.798085 | − | 0.602545i | \(-0.205847\pi\) | ||||
0.798085 | + | 0.602545i | \(0.205847\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.28832 | 0.169798 | ||||||||
\(971\) | −48.5870 | −1.55923 | −0.779615 | − | 0.626259i | \(-0.784585\pi\) | ||||
−0.779615 | + | 0.626259i | \(0.784585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.54256 | −0.273862 | ||||||||
\(974\) | 2.20692 | 0.0707143 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.169512 | −0.00542595 | ||||||||
\(977\) | −43.9332 | −1.40555 | −0.702773 | − | 0.711414i | \(-0.748055\pi\) | ||||
−0.702773 | + | 0.711414i | \(0.748055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.882300 | 0.0281840 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.62964 | −0.115827 | ||||||||
\(983\) | −33.4481 | −1.06683 | −0.533415 | − | 0.845854i | \(-0.679092\pi\) | ||||
−0.533415 | + | 0.845854i | \(0.679092\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.56150 | −0.0816162 | ||||||||
\(986\) | −10.8000 | −0.343944 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.17118 | 0.0690745 | ||||||||
\(989\) | −20.6923 | −0.657976 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.7034 | −1.35652 | −0.678260 | − | 0.734822i | \(-0.737266\pi\) | ||||
−0.678260 | + | 0.734822i | \(0.737266\pi\) | |||||||
\(992\) | 7.88174 | 0.250245 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.42452 | −0.235491 | ||||||||
\(995\) | −5.50110 | −0.174397 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0468 | −0.539879 | −0.269939 | − | 0.962877i | \(-0.587004\pi\) | ||||
−0.269939 | + | 0.962877i | \(0.587004\pi\) | |||||||
\(998\) | 32.4402 | 1.02688 | ||||||||
\(999\) | 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 | 7623.2.a.cz.1.8 | yes | 12 | |
3.2 | odd | 2 | inner | 7623.2.a.cz.1.5 | ✓ | 12 | |
11.10 | odd | 2 | 7623.2.a.da.1.5 | yes | 12 | ||
33.32 | even | 2 | 7623.2.a.da.1.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cz.1.5 | ✓ | 12 | 3.2 | odd | 2 | inner | |
7623.2.a.cz.1.8 | yes | 12 | 1.1 | even | 1 | trivial | |
7623.2.a.da.1.5 | yes | 12 | 11.10 | odd | 2 | ||
7623.2.a.da.1.8 | yes | 12 | 33.32 | even | 2 |