Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.414214 | −0.185242 | −0.0926210 | − | 0.995701i | \(-0.529524\pi\) | ||||
−0.0926210 | + | 0.995701i | \(0.529524\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.414214 | −0.124890 | −0.0624450 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624450 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.82843 | −0.685994 | −0.342997 | − | 0.939336i | \(-0.611442\pi\) | ||||
−0.342997 | + | 0.939336i | \(0.611442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.82843 | −0.419470 | −0.209735 | − | 0.977758i | \(-0.567260\pi\) | ||||
−0.209735 | + | 0.977758i | \(0.567260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.24264 | −0.676137 | −0.338069 | − | 0.941121i | \(-0.609774\pi\) | ||||
−0.338069 | + | 0.941121i | \(0.609774\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.82843 | −0.965685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.65685 | −1.19561 | −0.597803 | − | 0.801643i | \(-0.703960\pi\) | ||||
−0.597803 | + | 0.801643i | \(0.703960\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.414214 | −0.0700149 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.82843 | 0.958188 | 0.479094 | − | 0.877764i | \(-0.340965\pi\) | ||||
0.479094 | + | 0.877764i | \(0.340965\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.0711 | 1.88518 | 0.942592 | − | 0.333946i | \(-0.108380\pi\) | ||||
0.942592 | + | 0.333946i | \(0.108380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.828427 | −0.126334 | −0.0631670 | − | 0.998003i | \(-0.520120\pi\) | ||||
−0.0631670 | + | 0.998003i | \(0.520120\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6569 | 1.70033 | 0.850163 | − | 0.526519i | \(-0.176503\pi\) | ||||
0.850163 | + | 0.526519i | \(0.176503\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00000 | −0.549442 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.171573 | 0.0231349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.65685 | 0.996838 | 0.498419 | − | 0.866936i | \(-0.333914\pi\) | ||||
0.498419 | + | 0.866936i | \(0.333914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3137 | 1.44857 | 0.724286 | − | 0.689500i | \(-0.242170\pi\) | ||||
0.724286 | + | 0.689500i | \(0.242170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.17157 | 0.145316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853 | 1.52532 | 0.762660 | − | 0.646800i | \(-0.223893\pi\) | ||||
0.762660 | + | 0.646800i | \(0.223893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.41421 | 0.998583 | 0.499292 | − | 0.866434i | \(-0.333594\pi\) | ||||
0.499292 | + | 0.866434i | \(0.333594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.82843 | −1.03329 | −0.516645 | − | 0.856200i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856200i | \(0.672819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.414214 | −0.0472040 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.828427 | 0.0932053 | 0.0466027 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466027 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.17157 | 0.567654 | 0.283827 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283827 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.17157 | 0.127075 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.24264 | −0.767718 | −0.383859 | − | 0.923392i | \(-0.625405\pi\) | ||||
−0.383859 | + | 0.923392i | \(0.625405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | −0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.757359 | 0.0777034 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.65685 | 0.168228 | 0.0841140 | − | 0.996456i | \(-0.473194\pi\) | ||||
0.0841140 | + | 0.996456i | \(0.473194\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.48528 | 0.446302 | 0.223151 | − | 0.974784i | \(-0.428366\pi\) | ||||
0.223151 | + | 0.974784i | \(0.428366\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.65685 | 0.458853 | 0.229427 | − | 0.973326i | \(-0.426315\pi\) | ||||
0.229427 | + | 0.973326i | \(0.426315\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.3137 | 1.67378 | 0.836890 | − | 0.547372i | \(-0.184372\pi\) | ||||
0.836890 | + | 0.547372i | \(0.184372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.31371 | −0.413178 | −0.206589 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206589 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.1421 | −1.51852 | −0.759262 | − | 0.650785i | \(-0.774440\pi\) | ||||
−0.759262 | + | 0.650785i | \(0.774440\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.34315 | 0.125249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82843 | −0.259281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.07107 | 0.364127 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.82843 | 0.250982 | 0.125491 | − | 0.992095i | \(-0.459949\pi\) | ||||
0.125491 | + | 0.992095i | \(0.459949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | 0.174741 | 0.0873704 | − | 0.996176i | \(-0.472154\pi\) | ||||
0.0873704 | + | 0.996176i | \(0.472154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.82843 | −0.158545 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843 | 0.241649 | 0.120824 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120824 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.65685 | −0.819084 | −0.409542 | − | 0.912291i | \(-0.634311\pi\) | ||||
−0.409542 | + | 0.912291i | \(0.634311\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.17157 | 0.0979718 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.17157 | −0.0972938 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.82843 | 0.723253 | 0.361626 | − | 0.932323i | \(-0.382222\pi\) | ||||
0.361626 | + | 0.932323i | \(0.382222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.3137 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.75736 | 0.221476 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1421 | 1.12867 | 0.564333 | − | 0.825547i | \(-0.309134\pi\) | ||||
0.564333 | + | 0.825547i | \(0.309134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.24264 | −0.255556 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.485281 | 0.0380102 | 0.0190051 | − | 0.999819i | \(-0.493950\pi\) | ||||
0.0190051 | + | 0.999819i | \(0.493950\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.4853 | 1.43043 | 0.715217 | − | 0.698902i | \(-0.246328\pi\) | ||||
0.715217 | + | 0.698902i | \(0.246328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.757359 | 0.0575810 | 0.0287905 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287905 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.82843 | −0.364995 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.34315 | 0.623596 | 0.311798 | − | 0.950148i | \(-0.399069\pi\) | ||||
0.311798 | + | 0.950148i | \(0.399069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.34315 | 0.620141 | 0.310071 | − | 0.950714i | \(-0.399647\pi\) | ||||
0.310071 | + | 0.950714i | \(0.399647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.41421 | −0.177497 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17157 | 0.0856739 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.58579 | 0.693603 | 0.346802 | − | 0.937939i | \(-0.387268\pi\) | ||||
0.346802 | + | 0.937939i | \(0.387268\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.65685 | 0.551152 | 0.275576 | − | 0.961279i | \(-0.411131\pi\) | ||||
0.275576 | + | 0.961279i | \(0.411131\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1716 | −1.36592 | −0.682959 | − | 0.730457i | \(-0.739307\pi\) | ||||
−0.682959 | + | 0.730457i | \(0.739307\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.4853 | 0.955946 | 0.477973 | − | 0.878374i | \(-0.341372\pi\) | ||||
0.477973 | + | 0.878374i | \(0.341372\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | 0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.00000 | −0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.757359 | 0.0523876 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | −0.413057 | −0.206529 | − | 0.978441i | \(-0.566217\pi\) | ||||
−0.206529 | + | 0.978441i | \(0.566217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.343146 | 0.0234023 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.65685 | −0.451897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.00000 | 0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7990 | 0.991014 | 0.495507 | − | 0.868604i | \(-0.334982\pi\) | ||||
0.495507 | + | 0.868604i | \(0.334982\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.1716 | 1.00697 | 0.503486 | − | 0.864003i | \(-0.332050\pi\) | ||||
0.503486 | + | 0.864003i | \(0.332050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.31371 | −0.218976 | −0.109488 | − | 0.993988i | \(-0.534921\pi\) | ||||
−0.109488 | + | 0.993988i | \(0.534921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.17157 | −0.469825 | −0.234913 | − | 0.972016i | \(-0.575480\pi\) | ||||
−0.234913 | + | 0.972016i | \(0.575480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.82843 | −0.314972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.34315 | 0.280935 | 0.140467 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140467 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.14214 | 0.266818 | 0.133409 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133409 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.414214 | −0.0264631 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.17157 | 0.329059 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.97056 | −0.566217 | −0.283108 | − | 0.959088i | \(-0.591366\pi\) | ||||
−0.283108 | + | 0.959088i | \(0.591366\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34315 | 0.0844428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.7279 | 1.97913 | 0.989567 | − | 0.144075i | \(-0.0460208\pi\) | ||||
0.989567 | + | 0.144075i | \(0.0460208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.82843 | 0.362161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3848 | 1.44197 | 0.720984 | − | 0.692952i | \(-0.243690\pi\) | ||||
0.720984 | + | 0.692952i | \(0.243690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.65685 | 0.101780 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4142 | −1.12273 | −0.561367 | − | 0.827567i | \(-0.689724\pi\) | ||||
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.17157 | 0.490982 | 0.245491 | − | 0.969399i | \(-0.421051\pi\) | ||||
0.245491 | + | 0.969399i | \(0.421051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.31371 | 0.434755 | 0.217377 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217377 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0711 | 0.712533 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.8284 | 0.866286 | 0.433143 | − | 0.901325i | \(-0.357405\pi\) | ||||
0.433143 | + | 0.901325i | \(0.357405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.17157 | −0.184656 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.17157 | 0.530406 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.828427 | −0.0477497 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.68629 | −0.268336 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.17157 | −0.466376 | −0.233188 | − | 0.972432i | \(-0.574916\pi\) | ||||
−0.233188 | + | 0.972432i | \(0.574916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.4853 | 0.934795 | 0.467397 | − | 0.884047i | \(-0.345192\pi\) | ||||
0.467397 | + | 0.884047i | \(0.345192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1716 | −0.744501 | −0.372251 | − | 0.928132i | \(-0.621414\pi\) | ||||
−0.372251 | + | 0.928132i | \(0.621414\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.2843 | −1.25161 | −0.625805 | − | 0.779980i | \(-0.715229\pi\) | ||||
−0.625805 | + | 0.779980i | \(0.715229\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.17157 | −0.0655955 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.17157 | 0.287754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.6569 | 0.757546 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.6569 | 0.642663 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6274 | 0.584136 | 0.292068 | − | 0.956398i | \(-0.405657\pi\) | ||||
0.292068 | + | 0.956398i | \(0.405657\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.17157 | −0.282553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.6274 | −1.06917 | −0.534587 | − | 0.845114i | \(-0.679533\pi\) | ||||
−0.534587 | + | 0.845114i | \(0.679533\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.75736 | 0.149319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.92893 | 0.210916 | 0.105458 | − | 0.994424i | \(-0.466369\pi\) | ||||
0.105458 | + | 0.994424i | \(0.466369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.34315 | 0.446598 | 0.223299 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223299 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.41421 | −0.128496 | −0.0642478 | − | 0.997934i | \(-0.520465\pi\) | ||||
−0.0642478 | + | 0.997934i | \(0.520465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.48528 | −0.184980 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.31371 | −0.0693349 | −0.0346674 | − | 0.999399i | \(-0.511037\pi\) | ||||
−0.0346674 | + | 0.999399i | \(0.511037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6569 | −0.824045 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.65685 | 0.191408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4853 | −1.01712 | −0.508562 | − | 0.861026i | \(-0.669823\pi\) | ||||
−0.508562 | + | 0.861026i | \(0.669823\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.3137 | 1.36247 | 0.681236 | − | 0.732064i | \(-0.261443\pi\) | ||||
0.681236 | + | 0.732064i | \(0.261443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48528 | 0.127660 | 0.0638302 | − | 0.997961i | \(-0.479668\pi\) | ||||
0.0638302 | + | 0.997961i | \(0.479668\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.4558 | −0.789757 | −0.394878 | − | 0.918733i | \(-0.629213\pi\) | ||||
−0.394878 | + | 0.918733i | \(0.629213\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.171573 | 0.00874416 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.3137 | 0.573628 | 0.286814 | − | 0.957986i | \(-0.407404\pi\) | ||||
0.286814 | + | 0.957986i | \(0.407404\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.17157 | 0.463826 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.343146 | −0.0172655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.65685 | 0.384286 | 0.192143 | − | 0.981367i | \(-0.438456\pi\) | ||||
0.192143 | + | 0.981367i | \(0.438456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1716 | 0.857507 | 0.428754 | − | 0.903421i | \(-0.358953\pi\) | ||||
0.428754 | + | 0.903421i | \(0.358953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.8284 | 0.937911 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.41421 | −0.119668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.5147 | −0.866047 | −0.433024 | − | 0.901383i | \(-0.642553\pi\) | ||||
−0.433024 | + | 0.901383i | \(0.642553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.65685 | 0.376769 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.14214 | −0.105153 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.1421 | 1.37483 | 0.687417 | − | 0.726263i | \(-0.258745\pi\) | ||||
0.687417 | + | 0.726263i | \(0.258745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4853 | 1.33955 | 0.669775 | − | 0.742564i | \(-0.266390\pi\) | ||||
0.669775 | + | 0.742564i | \(0.266390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.6569 | 0.662455 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.3137 | 0.547509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2132 | 0.973636 | 0.486818 | − | 0.873503i | \(-0.338158\pi\) | ||||
0.486818 | + | 0.873503i | \(0.338158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.4558 | −1.41556 | −0.707779 | − | 0.706434i | \(-0.750303\pi\) | ||||
−0.707779 | + | 0.706434i | \(0.750303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.92893 | 0.283619 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00000 | −0.381819 | −0.190910 | − | 0.981608i | \(-0.561144\pi\) | ||||
−0.190910 | + | 0.981608i | \(0.561144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0711 | 0.668537 | 0.334268 | − | 0.942478i | \(-0.391511\pi\) | ||||
0.334268 | + | 0.942478i | \(0.391511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | 0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −23.1716 | −1.09353 | −0.546767 | − | 0.837285i | \(-0.684142\pi\) | ||||
−0.546767 | + | 0.837285i | \(0.684142\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | −0.235441 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.17157 | 0.0549242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.65685 | 0.124282 | 0.0621412 | − | 0.998067i | \(-0.480207\pi\) | ||||
0.0621412 | + | 0.998067i | \(0.480207\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.7574 | 0.780468 | 0.390234 | − | 0.920716i | \(-0.372394\pi\) | ||||
0.390234 | + | 0.920716i | \(0.372394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6569 | 1.09943 | 0.549714 | − | 0.835353i | \(-0.314737\pi\) | ||||
0.549714 | + | 0.835353i | \(0.314737\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.6274 | 1.32472 | 0.662359 | − | 0.749186i | \(-0.269555\pi\) | ||||
0.662359 | + | 0.749186i | \(0.269555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.4853 | 0.576517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.343146 | 0.0157779 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.82843 | 0.405076 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.02944 | 0.138419 | 0.0692093 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692093 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.4853 | −0.751664 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.686292 | −0.0311629 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.51472 | 0.249896 | 0.124948 | − | 0.992163i | \(-0.460124\pi\) | ||||
0.124948 | + | 0.992163i | \(0.460124\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8701 | 1.16750 | 0.583750 | − | 0.811934i | \(-0.301585\pi\) | ||||
0.583750 | + | 0.811934i | \(0.301585\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.00000 | −0.360302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.41421 | 0.377429 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.7696 | −1.73556 | −0.867782 | − | 0.496945i | \(-0.834455\pi\) | ||||
−0.867782 | + | 0.496945i | \(0.834455\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1421 | 0.808918 | 0.404459 | − | 0.914556i | \(-0.367460\pi\) | ||||
0.404459 | + | 0.914556i | \(0.367460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.85786 | −0.0826739 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.5147 | 0.687678 | 0.343839 | − | 0.939029i | \(-0.388273\pi\) | ||||
0.343839 | + | 0.939029i | \(0.388273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.82843 | −0.390547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.92893 | −0.0849989 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.82843 | −0.212354 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7574 | −0.821775 | −0.410887 | − | 0.911686i | \(-0.634781\pi\) | ||||
−0.410887 | + | 0.911686i | \(0.634781\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.9706 | −0.960706 | −0.480353 | − | 0.877075i | \(-0.659491\pi\) | ||||
−0.480353 | + | 0.877075i | \(0.659491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.8284 | 0.820179 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4853 | −0.542838 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.1421 | −1.47886 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.17157 | −0.310054 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.414214 | −0.0178414 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7990 | 0.636258 | 0.318129 | − | 0.948047i | \(-0.396945\pi\) | ||||
0.318129 | + | 0.948047i | \(0.396945\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.78680 | 0.0765380 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.9706 | −0.725609 | −0.362804 | − | 0.931865i | \(-0.618181\pi\) | ||||
−0.362804 | + | 0.931865i | \(0.618181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.17157 | −0.220316 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.828427 | 0.0352283 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.7696 | −1.81220 | −0.906102 | − | 0.423059i | \(-0.860956\pi\) | ||||
−0.906102 | + | 0.423059i | \(0.860956\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.34315 | 0.0991045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.7990 | −0.665848 | −0.332924 | − | 0.942954i | \(-0.608035\pi\) | ||||
−0.332924 | + | 0.942954i | \(0.608035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.68629 | 0.281294 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.7990 | 1.24924 | 0.624619 | − | 0.780929i | \(-0.285254\pi\) | ||||
0.624619 | + | 0.780929i | \(0.285254\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.6274 | −1.36541 | −0.682707 | − | 0.730692i | \(-0.739198\pi\) | ||||
−0.682707 | + | 0.730692i | \(0.739198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.6569 | 0.652936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.9411 | 1.16320 | 0.581602 | − | 0.813473i | \(-0.302426\pi\) | ||||
0.581602 | + | 0.813473i | \(0.302426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.17157 | 0.214553 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.65685 | 0.0686199 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.4558 | −0.803029 | −0.401514 | − | 0.915853i | \(-0.631516\pi\) | ||||
−0.401514 | + | 0.915853i | \(0.631516\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.1716 | 0.501521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.7574 | −0.441752 | −0.220876 | − | 0.975302i | \(-0.570892\pi\) | ||||
−0.220876 | + | 0.975302i | \(0.570892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.17157 | 0.0480298 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0416 | −0.859738 | −0.429869 | − | 0.902891i | \(-0.641440\pi\) | ||||
−0.429869 | + | 0.902891i | \(0.641440\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.1421 | −1.55585 | −0.777925 | − | 0.628357i | \(-0.783728\pi\) | ||||
−0.777925 | + | 0.628357i | \(0.783728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.48528 | 0.182353 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3431 | −0.582170 | −0.291085 | − | 0.956697i | \(-0.594016\pi\) | ||||
−0.291085 | + | 0.956697i | \(0.594016\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −32.9706 | −1.33385 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.9706 | 1.69518 | 0.847588 | − | 0.530656i | \(-0.178054\pi\) | ||||
0.847588 | + | 0.530656i | \(0.178054\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2843 | 0.414029 | 0.207015 | − | 0.978338i | \(-0.433625\pi\) | ||||
0.207015 | + | 0.978338i | \(0.433625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.6863 | 0.710872 | 0.355436 | − | 0.934701i | \(-0.384332\pi\) | ||||
0.355436 | + | 0.934701i | \(0.384332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.24264 | −0.290170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4558 | 0.898234 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.4853 | −0.657311 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.1421 | 1.27956 | 0.639779 | − | 0.768559i | \(-0.279026\pi\) | ||||
0.639779 | + | 0.768559i | \(0.279026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.17157 | −0.0464925 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.82843 | −0.112066 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4853 | −0.888115 | −0.444058 | − | 0.895998i | \(-0.646461\pi\) | ||||
−0.444058 | + | 0.895998i | \(0.646461\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.4853 | 0.531808 | 0.265904 | − | 0.964000i | \(-0.414330\pi\) | ||||
0.265904 | + | 0.964000i | \(0.414330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.3137 | −1.30970 | −0.654849 | − | 0.755760i | \(-0.727268\pi\) | ||||
−0.654849 | + | 0.755760i | \(0.727268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.17157 | −0.124495 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.9706 | 1.52504 | 0.762518 | − | 0.646967i | \(-0.223963\pi\) | ||||
0.762518 | + | 0.646967i | \(0.223963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.828427 | −0.0323693 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.1005 | −0.666141 | −0.333071 | − | 0.942902i | \(-0.608085\pi\) | ||||
−0.333071 | + | 0.942902i | \(0.608085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.17157 | 0.201151 | 0.100575 | − | 0.994929i | \(-0.467932\pi\) | ||||
0.100575 | + | 0.994929i | \(0.467932\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.757359 | 0.0293691 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.17157 | −0.355125 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.68629 | −0.180912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.2843 | −0.858996 | −0.429498 | − | 0.903068i | \(-0.641309\pi\) | ||||
−0.429498 | + | 0.903068i | \(0.641309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.0416 | 1.65422 | 0.827112 | − | 0.562037i | \(-0.189982\pi\) | ||||
0.827112 | + | 0.562037i | \(0.189982\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.65685 | 0.0635842 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.89949 | −0.264002 | −0.132001 | − | 0.991250i | \(-0.542140\pi\) | ||||
−0.132001 | + | 0.991250i | \(0.542140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.17157 | −0.0447635 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.3137 | 0.431018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.3137 | 1.79990 | 0.899949 | − | 0.435995i | \(-0.143603\pi\) | ||||
0.899949 | + | 0.435995i | \(0.143603\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.1421 | −1.29323 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.4853 | −1.83126 | −0.915632 | − | 0.402018i | \(-0.868309\pi\) | ||||
−0.915632 | + | 0.402018i | \(0.868309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6569 | −0.401931 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.48528 | 0.168686 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.68629 | 0.138442 | 0.0692208 | − | 0.997601i | \(-0.477949\pi\) | ||||
0.0692208 | + | 0.997601i | \(0.477949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.5858 | 0.808394 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.485281 | −0.0181485 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.65685 | −0.136378 | −0.0681888 | − | 0.997672i | \(-0.521722\pi\) | ||||
−0.0681888 | + | 0.997672i | \(0.521722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.65685 | 0.173430 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6569 | −0.507203 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.6274 | −1.43261 | −0.716306 | − | 0.697787i | \(-0.754168\pi\) | ||||
−0.716306 | + | 0.697787i | \(0.754168\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.34315 | 0.0866644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.82843 | 0.178342 | 0.0891710 | − | 0.996016i | \(-0.471578\pi\) | ||||
0.0891710 | + | 0.996016i | \(0.471578\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.17157 | −0.190497 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.97056 | 0.109274 | 0.0546370 | − | 0.998506i | \(-0.482600\pi\) | ||||
0.0546370 | + | 0.998506i | \(0.482600\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.89949 | −0.106372 | −0.0531861 | − | 0.998585i | \(-0.516938\pi\) | ||||
−0.0531861 | + | 0.998585i | \(0.516938\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.65685 | −0.133977 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3137 | 0.632629 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5147 | 1.22297 | 0.611485 | − | 0.791256i | \(-0.290573\pi\) | ||||
0.611485 | + | 0.791256i | \(0.290573\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.17157 | 0.261000 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.2843 | −0.955318 | −0.477659 | − | 0.878545i | \(-0.658515\pi\) | ||||
−0.477659 | + | 0.878545i | \(0.658515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.20101 | 0.297286 | 0.148643 | − | 0.988891i | \(-0.452509\pi\) | ||||
0.148643 | + | 0.988891i | \(0.452509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.31371 | −0.156167 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.6569 | −0.781984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.1421 | 1.08695 | 0.543477 | − | 0.839424i | \(-0.317108\pi\) | ||||
0.543477 | + | 0.839424i | \(0.317108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.5858 | −1.27993 | −0.639966 | − | 0.768403i | \(-0.721052\pi\) | ||||
−0.639966 | + | 0.768403i | \(0.721052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.1421 | 1.15458 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.0711 | −0.790778 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.48528 | −0.124713 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.85786 | −0.209076 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.9411 | 1.49504 | 0.747520 | − | 0.664239i | \(-0.231244\pi\) | ||||
0.747520 | + | 0.664239i | \(0.231244\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.1421 | −0.573948 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.1005 | 0.747418 | 0.373709 | − | 0.927546i | \(-0.378086\pi\) | ||||
0.373709 | + | 0.927546i | \(0.378086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9706 | −1.16641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.65685 | 0.129048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.34315 | 0.0473397 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.5147 | −1.10800 | −0.553999 | − | 0.832517i | \(-0.686899\pi\) | ||||
−0.553999 | + | 0.832517i | \(0.686899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.6569 | −0.725360 | −0.362680 | − | 0.931914i | \(-0.618138\pi\) | ||||
−0.362680 | + | 0.931914i | \(0.618138\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.201010 | −0.00704108 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.51472 | 0.0529933 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.2843 | 1.75493 | 0.877467 | − | 0.479638i | \(-0.159232\pi\) | ||||
0.877467 | + | 0.479638i | \(0.159232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.37258 | −0.117561 | −0.0587804 | − | 0.998271i | \(-0.518721\pi\) | ||||
−0.0587804 | + | 0.998271i | \(0.518721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.4142 | 0.362138 | 0.181069 | − | 0.983470i | \(-0.442044\pi\) | ||||
0.181069 | + | 0.983470i | \(0.442044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.1421 | −0.699565 | −0.349783 | − | 0.936831i | \(-0.613745\pi\) | ||||
−0.349783 | + | 0.936831i | \(0.613745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.82843 | −0.0979992 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.65685 | −0.264976 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.85786 | −0.202236 | −0.101118 | − | 0.994874i | \(-0.532242\pi\) | ||||
−0.101118 | + | 0.994874i | \(0.532242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.07107 | 0.0712469 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.8284 | −0.372069 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8995 | −0.647866 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.9706 | 1.53976 | 0.769881 | − | 0.638187i | \(-0.220315\pi\) | ||||
0.769881 | + | 0.638187i | \(0.220315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.5563 | −1.31706 | −0.658530 | − | 0.752555i | \(-0.728821\pi\) | ||||
−0.658530 | + | 0.752555i | \(0.728821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1127 | 0.549758 | 0.274879 | − | 0.961479i | \(-0.411362\pi\) | ||||
0.274879 | + | 0.961479i | \(0.411362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.3431 | −0.828650 | −0.414325 | − | 0.910129i | \(-0.635982\pi\) | ||||
−0.414325 | + | 0.910129i | \(0.635982\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.313708 | −0.0106664 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.343146 | −0.0116404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.3137 | −1.19656 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.07107 | 0.137627 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.9411 | −0.943505 | −0.471752 | − | 0.881731i | \(-0.656378\pi\) | ||||
−0.471752 | + | 0.881731i | \(0.656378\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.27208 | 0.211312 | 0.105656 | − | 0.994403i | \(-0.466306\pi\) | ||||
0.105656 | + | 0.994403i | \(0.466306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.3137 | −1.32301 | −0.661506 | − | 0.749940i | \(-0.730082\pi\) | ||||
−0.661506 | + | 0.749940i | \(0.730082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.7696 | 1.36891 | 0.684454 | − | 0.729056i | \(-0.260041\pi\) | ||||
0.684454 | + | 0.729056i | \(0.260041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.82843 | 0.0948624 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.3137 | −0.713236 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.45584 | −0.115516 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.8284 | −0.627963 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3137 | 0.376914 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.45584 | −0.114876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3137 | 1.10616 | 0.553082 | − | 0.833127i | \(-0.313452\pi\) | ||||
0.553082 | + | 0.833127i | \(0.313452\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.9706 | −1.42368 | −0.711839 | − | 0.702343i | \(-0.752137\pi\) | ||||
−0.711839 | + | 0.702343i | \(0.752137\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.14214 | −0.0708943 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.00000 | 0.0660458 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.6569 | 1.37413 | 0.687066 | − | 0.726595i | \(-0.258898\pi\) | ||||
0.687066 | + | 0.726595i | \(0.258898\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.7990 | −0.783353 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.1421 | −0.925308 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.8579 | 0.585898 | 0.292949 | − | 0.956128i | \(-0.405363\pi\) | ||||
0.292949 | + | 0.956128i | \(0.405363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82843 | −0.0599243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.485281 | −0.0158704 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.3137 | 0.369603 | 0.184801 | − | 0.982776i | \(-0.440836\pi\) | ||||
0.184801 | + | 0.982776i | \(0.440836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3848 | −0.957916 | −0.478958 | − | 0.877838i | \(-0.658985\pi\) | ||||
−0.478958 | + | 0.877838i | \(0.658985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −39.1421 | −1.27464 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.7279 | 0.706063 | 0.353031 | − | 0.935612i | \(-0.385151\pi\) | ||||
0.353031 | + | 0.935612i | \(0.385151\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9706 | 0.810579 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.8284 | −1.90564 | −0.952820 | − | 0.303536i | \(-0.901833\pi\) | ||||
−0.952820 | + | 0.303536i | \(0.901833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.97056 | −0.128484 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.82843 | 0.0913347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.3137 | 0.429474 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.17157 | −0.102097 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.2843 | −1.48840 | −0.744201 | − | 0.667956i | \(-0.767169\pi\) | ||||
−0.744201 | + | 0.667956i | \(0.767169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.8284 | −1.50280 | −0.751398 | − | 0.659849i | \(-0.770620\pi\) | ||||
−0.751398 | + | 0.659849i | \(0.770620\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.65685 | −0.309585 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.9706 | 1.56671 | 0.783354 | − | 0.621576i | \(-0.213507\pi\) | ||||
0.783354 | + | 0.621576i | \(0.213507\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00000 | 0.0958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.5980 | 1.70951 | 0.854755 | − | 0.519032i | \(-0.173707\pi\) | ||||
0.854755 | + | 0.519032i | \(0.173707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.94113 | 0.253025 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.68629 | 0.0854191 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4558 | 0.427439 | 0.213719 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213719 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.58579 | −0.177081 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.3137 | 1.43510 | 0.717550 | − | 0.696507i | \(-0.245264\pi\) | ||||
0.717550 | + | 0.696507i | \(0.245264\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.a.bj.1.1 | yes | 2 | |
3.2 | odd | 2 | 6048.2.a.ba.1.2 | yes | 2 | ||
4.3 | odd | 2 | 6048.2.a.bg.1.1 | yes | 2 | ||
12.11 | even | 2 | 6048.2.a.z.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.z.1.2 | ✓ | 2 | 12.11 | even | 2 | ||
6048.2.a.ba.1.2 | yes | 2 | 3.2 | odd | 2 | ||
6048.2.a.bg.1.1 | yes | 2 | 4.3 | odd | 2 | ||
6048.2.a.bj.1.1 | yes | 2 | 1.1 | even | 1 | trivial |