Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
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: | \( x^{12} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.07880\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.07880 | −1.46993 | −0.734966 | − | 0.678104i | \(-0.762802\pi\) | ||||
−0.734966 | + | 0.678104i | \(0.762802\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.32140 | 1.16070 | ||||||||
\(5\) | 2.51557 | 1.12500 | 0.562498 | − | 0.826799i | \(-0.309841\pi\) | ||||
0.562498 | + | 0.826799i | \(0.309841\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.31485 | 1.25289 | 0.626447 | − | 0.779464i | \(-0.284509\pi\) | ||||
0.626447 | + | 0.779464i | \(0.284509\pi\) | |||||||
\(8\) | −0.668123 | −0.236217 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.22935 | −1.65367 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.69636 | −1.30254 | −0.651268 | − | 0.758848i | \(-0.725762\pi\) | ||||
−0.651268 | + | 0.758848i | \(0.725762\pi\) | |||||||
\(14\) | −6.89089 | −1.84167 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.25391 | −0.813476 | ||||||||
\(17\) | −2.84744 | −0.690606 | −0.345303 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345303 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.33856 | −1.68358 | −0.841790 | − | 0.539805i | \(-0.818498\pi\) | ||||
−0.841790 | + | 0.539805i | \(0.818498\pi\) | |||||||
\(20\) | 5.83963 | 1.30578 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.07880 | −0.443201 | ||||||||
\(23\) | 2.08156 | 0.434036 | 0.217018 | − | 0.976168i | \(-0.430367\pi\) | ||||
0.217018 | + | 0.976168i | \(0.430367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.32807 | 0.265614 | ||||||||
\(26\) | 9.76278 | 1.91464 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.69508 | 1.45423 | ||||||||
\(29\) | −0.764221 | −0.141912 | −0.0709561 | − | 0.997479i | \(-0.522605\pi\) | ||||
−0.0709561 | + | 0.997479i | \(0.522605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.67183 | 0.479875 | 0.239938 | − | 0.970788i | \(-0.422873\pi\) | ||||
0.239938 | + | 0.970788i | \(0.422873\pi\) | |||||||
\(32\) | 8.10046 | 1.43197 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.91926 | 1.01514 | ||||||||
\(35\) | 8.33871 | 1.40950 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.93137 | 0.481914 | 0.240957 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240957 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(38\) | 15.2554 | 2.47475 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.68071 | −0.265743 | ||||||||
\(41\) | −3.67795 | −0.574399 | −0.287199 | − | 0.957871i | \(-0.592724\pi\) | ||||
−0.287199 | + | 0.957871i | \(0.592724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.30987 | −1.41974 | −0.709871 | − | 0.704332i | \(-0.751247\pi\) | ||||
−0.709871 | + | 0.704332i | \(0.751247\pi\) | |||||||
\(44\) | 2.32140 | 0.349964 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.32715 | −0.638003 | ||||||||
\(47\) | 0.466652 | 0.0680682 | 0.0340341 | − | 0.999421i | \(-0.489165\pi\) | ||||
0.0340341 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.98820 | 0.569743 | ||||||||
\(50\) | −2.76079 | −0.390435 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.9021 | −1.51185 | ||||||||
\(53\) | 7.82503 | 1.07485 | 0.537425 | − | 0.843311i | \(-0.319397\pi\) | ||||
0.537425 | + | 0.843311i | \(0.319397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.51557 | 0.339199 | ||||||||
\(56\) | −2.21472 | −0.295955 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.58866 | 0.208601 | ||||||||
\(59\) | 7.75368 | 1.00944 | 0.504722 | − | 0.863282i | \(-0.331595\pi\) | ||||
0.504722 | + | 0.863282i | \(0.331595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −5.55420 | −0.705384 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.3314 | −1.29142 | ||||||||
\(65\) | −11.8140 | −1.46535 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.65473 | −0.568666 | −0.284333 | − | 0.958726i | \(-0.591772\pi\) | ||||
−0.284333 | + | 0.958726i | \(0.591772\pi\) | |||||||
\(68\) | −6.61005 | −0.801586 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −17.3345 | −2.07187 | ||||||||
\(71\) | −7.30894 | −0.867412 | −0.433706 | − | 0.901054i | \(-0.642794\pi\) | ||||
−0.433706 | + | 0.901054i | \(0.642794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.71256 | −0.785645 | −0.392823 | − | 0.919614i | \(-0.628501\pi\) | ||||
−0.392823 | + | 0.919614i | \(0.628501\pi\) | |||||||
\(74\) | −6.09372 | −0.708381 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.0357 | −1.95413 | ||||||||
\(77\) | 3.31485 | 0.377762 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.44921 | −0.725593 | −0.362797 | − | 0.931868i | \(-0.618178\pi\) | ||||
−0.362797 | + | 0.931868i | \(0.618178\pi\) | |||||||
\(80\) | −8.18541 | −0.915157 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.64571 | 0.844327 | ||||||||
\(83\) | −2.42650 | −0.266343 | −0.133172 | − | 0.991093i | \(-0.542516\pi\) | ||||
−0.133172 | + | 0.991093i | \(0.542516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.16293 | −0.776929 | ||||||||
\(86\) | 19.3533 | 2.08692 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.668123 | −0.0712222 | ||||||||
\(89\) | 2.54789 | 0.270076 | 0.135038 | − | 0.990840i | \(-0.456884\pi\) | ||||
0.135038 | + | 0.990840i | \(0.456884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.5677 | −1.63194 | ||||||||
\(92\) | 4.83214 | 0.503785 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.970075 | −0.100056 | ||||||||
\(95\) | −18.4606 | −1.89402 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8241 | −1.20055 | −0.600277 | − | 0.799793i | \(-0.704943\pi\) | ||||
−0.600277 | + | 0.799793i | \(0.704943\pi\) | |||||||
\(98\) | −8.29066 | −0.837483 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.08298 | 0.308298 | ||||||||
\(101\) | 12.8545 | 1.27907 | 0.639537 | − | 0.768760i | \(-0.279126\pi\) | ||||
0.639537 | + | 0.768760i | \(0.279126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.74643 | −0.763279 | −0.381639 | − | 0.924311i | \(-0.624640\pi\) | ||||
−0.381639 | + | 0.924311i | \(0.624640\pi\) | |||||||
\(104\) | 3.13774 | 0.307681 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.2667 | −1.57996 | ||||||||
\(107\) | −15.8933 | −1.53646 | −0.768230 | − | 0.640174i | \(-0.778862\pi\) | ||||
−0.768230 | + | 0.640174i | \(0.778862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.51888 | −0.337048 | −0.168524 | − | 0.985698i | \(-0.553900\pi\) | ||||
−0.168524 | + | 0.985698i | \(0.553900\pi\) | |||||||
\(110\) | −5.22935 | −0.498599 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.7862 | −1.01920 | ||||||||
\(113\) | −8.00502 | −0.753049 | −0.376524 | − | 0.926407i | \(-0.622881\pi\) | ||||
−0.376524 | + | 0.926407i | \(0.622881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.23631 | 0.488288 | ||||||||
\(116\) | −1.77406 | −0.164717 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.1183 | −1.48381 | ||||||||
\(119\) | −9.43883 | −0.865256 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.07880 | 0.188205 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.20239 | 0.556991 | ||||||||
\(125\) | −9.23698 | −0.826180 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.63027 | 0.499605 | 0.249803 | − | 0.968297i | \(-0.419634\pi\) | ||||
0.249803 | + | 0.968297i | \(0.419634\pi\) | |||||||
\(128\) | 5.27597 | 0.466334 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.5589 | 2.15396 | ||||||||
\(131\) | −4.25978 | −0.372179 | −0.186089 | − | 0.982533i | \(-0.559581\pi\) | ||||
−0.186089 | + | 0.982533i | \(0.559581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.3262 | −2.10935 | ||||||||
\(134\) | 9.67624 | 0.835900 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.90244 | 0.163133 | ||||||||
\(137\) | −0.938042 | −0.0801423 | −0.0400712 | − | 0.999197i | \(-0.512758\pi\) | ||||
−0.0400712 | + | 0.999197i | \(0.512758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0152 | 1.69767 | 0.848834 | − | 0.528660i | \(-0.177305\pi\) | ||||
0.848834 | + | 0.528660i | \(0.177305\pi\) | |||||||
\(140\) | 19.3575 | 1.63601 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.1938 | 1.27504 | ||||||||
\(143\) | −4.69636 | −0.392729 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.92245 | −0.159651 | ||||||||
\(146\) | 13.9540 | 1.15484 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.80487 | 0.559357 | ||||||||
\(149\) | −13.2774 | −1.08773 | −0.543864 | − | 0.839173i | \(-0.683039\pi\) | ||||
−0.543864 | + | 0.839173i | \(0.683039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8307 | 0.962771 | 0.481385 | − | 0.876509i | \(-0.340134\pi\) | ||||
0.481385 | + | 0.876509i | \(0.340134\pi\) | |||||||
\(152\) | 4.90306 | 0.397691 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.89089 | −0.555284 | ||||||||
\(155\) | 6.72117 | 0.539858 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.3071 | −0.982216 | −0.491108 | − | 0.871099i | \(-0.663408\pi\) | ||||
−0.491108 | + | 0.871099i | \(0.663408\pi\) | |||||||
\(158\) | 13.4066 | 1.06657 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 20.3772 | 1.61096 | ||||||||
\(161\) | 6.90006 | 0.543801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.8550 | 1.63349 | 0.816744 | − | 0.577001i | \(-0.195777\pi\) | ||||
0.816744 | + | 0.577001i | \(0.195777\pi\) | |||||||
\(164\) | −8.53798 | −0.666704 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.04421 | 0.391506 | ||||||||
\(167\) | 3.99278 | 0.308970 | 0.154485 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154485 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.05577 | 0.696598 | ||||||||
\(170\) | 14.8903 | 1.14203 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −21.6119 | −1.64789 | ||||||||
\(173\) | 25.5150 | 1.93987 | 0.969937 | − | 0.243358i | \(-0.0782490\pi\) | ||||
0.969937 | + | 0.243358i | \(0.0782490\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.40235 | 0.332787 | ||||||||
\(176\) | −3.25391 | −0.245272 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.29655 | −0.396993 | ||||||||
\(179\) | −20.3940 | −1.52432 | −0.762158 | − | 0.647391i | \(-0.775860\pi\) | ||||
−0.762158 | + | 0.647391i | \(0.775860\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3544 | −0.769633 | −0.384816 | − | 0.922993i | \(-0.625735\pi\) | ||||
−0.384816 | + | 0.922993i | \(0.625735\pi\) | |||||||
\(182\) | 32.3621 | 2.39884 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.39074 | −0.102527 | ||||||||
\(185\) | 7.37405 | 0.542151 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.84744 | −0.208226 | ||||||||
\(188\) | 1.08329 | 0.0790067 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 38.3759 | 2.78408 | ||||||||
\(191\) | −2.57556 | −0.186361 | −0.0931805 | − | 0.995649i | \(-0.529703\pi\) | ||||
−0.0931805 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0757 | 1.51706 | 0.758530 | − | 0.651638i | \(-0.225918\pi\) | ||||
0.758530 | + | 0.651638i | \(0.225918\pi\) | |||||||
\(194\) | 24.5799 | 1.76473 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.25820 | 0.661300 | ||||||||
\(197\) | −21.1509 | −1.50694 | −0.753469 | − | 0.657484i | \(-0.771621\pi\) | ||||
−0.753469 | + | 0.657484i | \(0.771621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.63056 | −0.540916 | −0.270458 | − | 0.962732i | \(-0.587175\pi\) | ||||
−0.270458 | + | 0.962732i | \(0.587175\pi\) | |||||||
\(200\) | −0.887315 | −0.0627427 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −26.7220 | −1.88015 | ||||||||
\(203\) | −2.53327 | −0.177801 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.25212 | −0.646196 | ||||||||
\(206\) | 16.1033 | 1.12197 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.2815 | 1.05958 | ||||||||
\(209\) | −7.33856 | −0.507619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.6471 | −1.76562 | −0.882811 | − | 0.469728i | \(-0.844352\pi\) | ||||
−0.882811 | + | 0.469728i | \(0.844352\pi\) | |||||||
\(212\) | 18.1650 | 1.24758 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 33.0389 | 2.25849 | ||||||||
\(215\) | −23.4196 | −1.59720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.85671 | 0.601233 | ||||||||
\(218\) | 7.31505 | 0.495437 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.83963 | 0.393708 | ||||||||
\(221\) | 13.3726 | 0.899539 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6223 | −1.44794 | −0.723968 | − | 0.689834i | \(-0.757684\pi\) | ||||
−0.723968 | + | 0.689834i | \(0.757684\pi\) | |||||||
\(224\) | 26.8518 | 1.79411 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.6408 | 1.10693 | ||||||||
\(227\) | −7.41119 | −0.491898 | −0.245949 | − | 0.969283i | \(-0.579100\pi\) | ||||
−0.245949 | + | 0.969283i | \(0.579100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2381 | 0.808718 | 0.404359 | − | 0.914600i | \(-0.367495\pi\) | ||||
0.404359 | + | 0.914600i | \(0.367495\pi\) | |||||||
\(230\) | −10.8852 | −0.717750 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.510594 | 0.0335221 | ||||||||
\(233\) | −9.92929 | −0.650489 | −0.325245 | − | 0.945630i | \(-0.605447\pi\) | ||||
−0.325245 | + | 0.945630i | \(0.605447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.17389 | 0.0765764 | ||||||||
\(236\) | 17.9994 | 1.17166 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 19.6214 | 1.27187 | ||||||||
\(239\) | −11.4528 | −0.740823 | −0.370412 | − | 0.928868i | \(-0.620783\pi\) | ||||
−0.370412 | + | 0.928868i | \(0.620783\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.38803 | 0.0894111 | 0.0447055 | − | 0.999000i | \(-0.485765\pi\) | ||||
0.0447055 | + | 0.999000i | \(0.485765\pi\) | |||||||
\(242\) | −2.07880 | −0.133630 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.32140 | −0.148612 | ||||||||
\(245\) | 10.0326 | 0.640958 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.4645 | 2.19292 | ||||||||
\(248\) | −1.78511 | −0.113355 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.2018 | 1.21443 | ||||||||
\(251\) | 10.9919 | 0.693801 | 0.346900 | − | 0.937902i | \(-0.387234\pi\) | ||||
0.346900 | + | 0.937902i | \(0.387234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.08156 | 0.130867 | ||||||||
\(254\) | −11.7042 | −0.734386 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.69512 | 0.605945 | ||||||||
\(257\) | −24.1795 | −1.50827 | −0.754137 | − | 0.656718i | \(-0.771944\pi\) | ||||
−0.754137 | + | 0.656718i | \(0.771944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.71703 | 0.603787 | ||||||||
\(260\) | −27.4250 | −1.70083 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.85522 | 0.547077 | ||||||||
\(263\) | −0.0653591 | −0.00403021 | −0.00201511 | − | 0.999998i | \(-0.500641\pi\) | ||||
−0.00201511 | + | 0.999998i | \(0.500641\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.6844 | 1.20920 | ||||||||
\(266\) | 50.5692 | 3.10060 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.8055 | −0.660050 | ||||||||
\(269\) | −5.24648 | −0.319884 | −0.159942 | − | 0.987126i | \(-0.551131\pi\) | ||||
−0.159942 | + | 0.987126i | \(0.551131\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.61564 | −0.462617 | −0.231308 | − | 0.972880i | \(-0.574301\pi\) | ||||
−0.231308 | + | 0.972880i | \(0.574301\pi\) | |||||||
\(272\) | 9.26531 | 0.561792 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.95000 | 0.117804 | ||||||||
\(275\) | 1.32807 | 0.0800857 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.4198 | 0.986570 | 0.493285 | − | 0.869868i | \(-0.335796\pi\) | ||||
0.493285 | + | 0.869868i | \(0.335796\pi\) | |||||||
\(278\) | −41.6075 | −2.49545 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.57129 | −0.332948 | ||||||||
\(281\) | 6.84038 | 0.408063 | 0.204032 | − | 0.978964i | \(-0.434595\pi\) | ||||
0.204032 | + | 0.978964i | \(0.434595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.59236 | −0.391875 | −0.195937 | − | 0.980616i | \(-0.562775\pi\) | ||||
−0.195937 | + | 0.980616i | \(0.562775\pi\) | |||||||
\(284\) | −16.9670 | −1.00680 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.76278 | 0.577285 | ||||||||
\(287\) | −12.1918 | −0.719661 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.89207 | −0.523063 | ||||||||
\(290\) | 3.99638 | 0.234676 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.5825 | −0.911898 | ||||||||
\(293\) | 0.825657 | 0.0482354 | 0.0241177 | − | 0.999709i | \(-0.492322\pi\) | ||||
0.0241177 | + | 0.999709i | \(0.492322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.5049 | 1.13562 | ||||||||
\(296\) | −1.95851 | −0.113836 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.6010 | 1.59889 | ||||||||
\(299\) | −9.77576 | −0.565347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.8608 | −1.77879 | ||||||||
\(302\) | −24.5937 | −1.41521 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.8790 | 1.36955 | ||||||||
\(305\) | −2.51557 | −0.144041 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.6787 | −0.609463 | −0.304732 | − | 0.952438i | \(-0.598567\pi\) | ||||
−0.304732 | + | 0.952438i | \(0.598567\pi\) | |||||||
\(308\) | 7.69508 | 0.438468 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −13.9720 | −0.793554 | ||||||||
\(311\) | 3.76872 | 0.213704 | 0.106852 | − | 0.994275i | \(-0.465923\pi\) | ||||
0.106852 | + | 0.994275i | \(0.465923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.2136 | 1.02950 | 0.514748 | − | 0.857342i | \(-0.327886\pi\) | ||||
0.514748 | + | 0.857342i | \(0.327886\pi\) | |||||||
\(314\) | 25.5840 | 1.44379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.9712 | −0.842196 | ||||||||
\(317\) | −18.1257 | −1.01804 | −0.509019 | − | 0.860755i | \(-0.669992\pi\) | ||||
−0.509019 | + | 0.860755i | \(0.669992\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.764221 | −0.0427882 | ||||||||
\(320\) | −25.9893 | −1.45285 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.3438 | −0.799350 | ||||||||
\(323\) | 20.8961 | 1.16269 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23710 | −0.345972 | ||||||||
\(326\) | −43.3533 | −2.40111 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.45732 | 0.135683 | ||||||||
\(329\) | 1.54688 | 0.0852822 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.3048 | −1.28095 | −0.640475 | − | 0.767979i | \(-0.721262\pi\) | ||||
−0.640475 | + | 0.767979i | \(0.721262\pi\) | |||||||
\(332\) | −5.63288 | −0.309144 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.30017 | −0.454165 | ||||||||
\(335\) | −11.7093 | −0.639746 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0798 | −0.875924 | −0.437962 | − | 0.898993i | \(-0.644300\pi\) | ||||
−0.437962 | + | 0.898993i | \(0.644300\pi\) | |||||||
\(338\) | −18.8251 | −1.02395 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.6280 | −0.901781 | ||||||||
\(341\) | 2.67183 | 0.144688 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.98366 | −0.539067 | ||||||||
\(344\) | 6.22014 | 0.335368 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −53.0406 | −2.85148 | ||||||||
\(347\) | −2.04396 | −0.109725 | −0.0548627 | − | 0.998494i | \(-0.517472\pi\) | ||||
−0.0548627 | + | 0.998494i | \(0.517472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4212 | −1.46782 | −0.733912 | − | 0.679244i | \(-0.762308\pi\) | ||||
−0.733912 | + | 0.679244i | \(0.762308\pi\) | |||||||
\(350\) | −9.15160 | −0.489173 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.10046 | 0.431756 | ||||||||
\(353\) | 26.7877 | 1.42576 | 0.712882 | − | 0.701284i | \(-0.247390\pi\) | ||||
0.712882 | + | 0.701284i | \(0.247390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.3861 | −0.975835 | ||||||||
\(356\) | 5.91467 | 0.313477 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 42.3949 | 2.24064 | ||||||||
\(359\) | 20.1894 | 1.06556 | 0.532778 | − | 0.846255i | \(-0.321148\pi\) | ||||
0.532778 | + | 0.846255i | \(0.321148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 34.8544 | 1.83444 | ||||||||
\(362\) | 21.5246 | 1.13131 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −36.1388 | −1.89419 | ||||||||
\(365\) | −16.8859 | −0.883847 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.71927 | −0.455142 | −0.227571 | − | 0.973761i | \(-0.573078\pi\) | ||||
−0.227571 | + | 0.973761i | \(0.573078\pi\) | |||||||
\(368\) | −6.77321 | −0.353078 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.3292 | −0.796925 | ||||||||
\(371\) | 25.9388 | 1.34667 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.10112 | 0.419460 | 0.209730 | − | 0.977759i | \(-0.432742\pi\) | ||||
0.209730 | + | 0.977759i | \(0.432742\pi\) | |||||||
\(374\) | 5.91926 | 0.306077 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.311781 | −0.0160789 | ||||||||
\(377\) | 3.58905 | 0.184846 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1829 | 0.831259 | 0.415629 | − | 0.909534i | \(-0.363561\pi\) | ||||
0.415629 | + | 0.909534i | \(0.363561\pi\) | |||||||
\(380\) | −42.8545 | −2.19839 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.35407 | 0.273938 | ||||||||
\(383\) | 11.5062 | 0.587940 | 0.293970 | − | 0.955815i | \(-0.405023\pi\) | ||||
0.293970 | + | 0.955815i | \(0.405023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.33871 | 0.424980 | ||||||||
\(386\) | −43.8120 | −2.22997 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.4484 | −1.39348 | ||||||||
\(389\) | 17.6156 | 0.893147 | 0.446573 | − | 0.894747i | \(-0.352644\pi\) | ||||
0.446573 | + | 0.894747i | \(0.352644\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.92713 | −0.299748 | ||||||||
\(392\) | −2.66461 | −0.134583 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 43.9684 | 2.21509 | ||||||||
\(395\) | −16.2234 | −0.816289 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6556 | 0.936298 | 0.468149 | − | 0.883649i | \(-0.344921\pi\) | ||||
0.468149 | + | 0.883649i | \(0.344921\pi\) | |||||||
\(398\) | 15.8624 | 0.795110 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.32142 | −0.216071 | ||||||||
\(401\) | 26.6759 | 1.33213 | 0.666066 | − | 0.745893i | \(-0.267977\pi\) | ||||
0.666066 | + | 0.745893i | \(0.267977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5479 | −0.625055 | ||||||||
\(404\) | 29.8405 | 1.48462 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.26616 | 0.261355 | ||||||||
\(407\) | 2.93137 | 0.145303 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.2979 | −1.89371 | −0.946856 | − | 0.321658i | \(-0.895760\pi\) | ||||
−0.946856 | + | 0.321658i | \(0.895760\pi\) | |||||||
\(410\) | 19.2333 | 0.949864 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.9826 | −0.885937 | ||||||||
\(413\) | 25.7023 | 1.26473 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.10402 | −0.299635 | ||||||||
\(416\) | −38.0426 | −1.86519 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.2554 | 0.746165 | ||||||||
\(419\) | 4.67442 | 0.228360 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7448 | 1.44967 | 0.724836 | − | 0.688922i | \(-0.241916\pi\) | ||||
0.724836 | + | 0.688922i | \(0.241916\pi\) | |||||||
\(422\) | 53.3152 | 2.59534 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.22808 | −0.253898 | ||||||||
\(425\) | −3.78161 | −0.183435 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.31485 | −0.160417 | ||||||||
\(428\) | −36.8946 | −1.78337 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.6846 | 2.34778 | ||||||||
\(431\) | −14.2615 | −0.686950 | −0.343475 | − | 0.939162i | \(-0.611604\pi\) | ||||
−0.343475 | + | 0.939162i | \(0.611604\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.0835 | 1.92629 | 0.963145 | − | 0.268983i | \(-0.0866875\pi\) | ||||
0.963145 | + | 0.268983i | \(0.0866875\pi\) | |||||||
\(434\) | −18.4113 | −0.883771 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.16873 | −0.391211 | ||||||||
\(437\) | −15.2757 | −0.730734 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.7801 | −1.99405 | −0.997027 | − | 0.0770534i | \(-0.975449\pi\) | ||||
−0.997027 | + | 0.0770534i | \(0.975449\pi\) | |||||||
\(440\) | −1.68071 | −0.0801246 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −27.7989 | −1.32226 | ||||||||
\(443\) | 22.6161 | 1.07452 | 0.537262 | − | 0.843415i | \(-0.319459\pi\) | ||||
0.537262 | + | 0.843415i | \(0.319459\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.40939 | 0.303834 | ||||||||
\(446\) | 44.9484 | 2.12837 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −34.2470 | −1.61802 | ||||||||
\(449\) | −0.296481 | −0.0139918 | −0.00699590 | − | 0.999976i | \(-0.502227\pi\) | ||||
−0.00699590 | + | 0.999976i | \(0.502227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.67795 | −0.173188 | ||||||||
\(452\) | −18.5828 | −0.874063 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.4064 | 0.723056 | ||||||||
\(455\) | −39.1616 | −1.83592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.4014 | −1.65601 | −0.828004 | − | 0.560722i | \(-0.810524\pi\) | ||||
−0.828004 | + | 0.560722i | \(0.810524\pi\) | |||||||
\(458\) | −25.4406 | −1.18876 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.1556 | 0.566756 | ||||||||
\(461\) | −24.8643 | −1.15804 | −0.579022 | − | 0.815312i | \(-0.696566\pi\) | ||||
−0.579022 | + | 0.815312i | \(0.696566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.6296 | −1.09816 | −0.549080 | − | 0.835770i | \(-0.685022\pi\) | ||||
−0.549080 | + | 0.835770i | \(0.685022\pi\) | |||||||
\(464\) | 2.48670 | 0.115442 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.6410 | 0.956175 | ||||||||
\(467\) | 24.7168 | 1.14376 | 0.571879 | − | 0.820338i | \(-0.306215\pi\) | ||||
0.571879 | + | 0.820338i | \(0.306215\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4297 | −0.712478 | ||||||||
\(470\) | −2.44029 | −0.112562 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.18042 | −0.238448 | ||||||||
\(473\) | −9.30987 | −0.428068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.74613 | −0.447183 | ||||||||
\(476\) | −21.9113 | −1.00430 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.8081 | 1.08896 | ||||||||
\(479\) | 3.86168 | 0.176445 | 0.0882223 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882223 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7668 | −0.627710 | ||||||||
\(482\) | −2.88544 | −0.131428 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.32140 | 0.105518 | ||||||||
\(485\) | −29.7442 | −1.35062 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.58072 | 0.207572 | 0.103786 | − | 0.994600i | \(-0.466904\pi\) | ||||
0.103786 | + | 0.994600i | \(0.466904\pi\) | |||||||
\(488\) | 0.668123 | 0.0302445 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.8557 | −0.942164 | ||||||||
\(491\) | 33.5912 | 1.51595 | 0.757974 | − | 0.652284i | \(-0.226189\pi\) | ||||
0.757974 | + | 0.652284i | \(0.226189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.17608 | 0.0980055 | ||||||||
\(494\) | −71.6447 | −3.22345 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.69389 | −0.390367 | ||||||||
\(497\) | −24.2280 | −1.08678 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.2036 | 1.44163 | 0.720816 | − | 0.693127i | \(-0.243767\pi\) | ||||
0.720816 | + | 0.693127i | \(0.243767\pi\) | |||||||
\(500\) | −21.4427 | −0.958947 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.8499 | −1.01984 | ||||||||
\(503\) | 39.4574 | 1.75932 | 0.879660 | − | 0.475603i | \(-0.157770\pi\) | ||||
0.879660 | + | 0.475603i | \(0.157770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.3364 | 1.43895 | ||||||||
\(506\) | −4.32715 | −0.192365 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.0701 | 0.579892 | ||||||||
\(509\) | −21.0465 | −0.932871 | −0.466436 | − | 0.884555i | \(-0.654462\pi\) | ||||
−0.466436 | + | 0.884555i | \(0.654462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.2511 | −0.984330 | ||||||||
\(512\) | −30.7061 | −1.35703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 50.2642 | 2.21706 | ||||||||
\(515\) | −19.4867 | −0.858685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.466652 | 0.0205233 | ||||||||
\(518\) | −20.1997 | −0.887526 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.89320 | 0.346140 | ||||||||
\(521\) | −25.8419 | −1.13216 | −0.566078 | − | 0.824352i | \(-0.691540\pi\) | ||||
−0.566078 | + | 0.824352i | \(0.691540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0550 | 0.483400 | 0.241700 | − | 0.970351i | \(-0.422295\pi\) | ||||
0.241700 | + | 0.970351i | \(0.422295\pi\) | |||||||
\(524\) | −9.88865 | −0.431988 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.135868 | 0.00592414 | ||||||||
\(527\) | −7.60789 | −0.331405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6671 | −0.811613 | ||||||||
\(530\) | −40.9198 | −1.77744 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −56.4708 | −2.44832 | ||||||||
\(533\) | 17.2730 | 0.748175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.9805 | −1.72851 | ||||||||
\(536\) | 3.10993 | 0.134329 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.9064 | 0.470207 | ||||||||
\(539\) | 3.98820 | 0.171784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.1200 | −1.38095 | −0.690473 | − | 0.723358i | \(-0.742598\pi\) | ||||
−0.690473 | + | 0.723358i | \(0.742598\pi\) | |||||||
\(542\) | 15.8314 | 0.680015 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.0656 | −0.988929 | ||||||||
\(545\) | −8.85198 | −0.379177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4050 | −0.915211 | −0.457605 | − | 0.889155i | \(-0.651293\pi\) | ||||
−0.457605 | + | 0.889155i | \(0.651293\pi\) | |||||||
\(548\) | −2.17757 | −0.0930211 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.76079 | −0.117721 | ||||||||
\(551\) | 5.60828 | 0.238921 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.3781 | −0.909091 | ||||||||
\(554\) | −34.1334 | −1.45019 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 46.4633 | 1.97048 | ||||||||
\(557\) | 14.8084 | 0.627453 | 0.313726 | − | 0.949513i | \(-0.398423\pi\) | ||||
0.313726 | + | 0.949513i | \(0.398423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.7225 | 1.84926 | ||||||||
\(560\) | −27.1334 | −1.14659 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.2198 | −0.599825 | ||||||||
\(563\) | −41.4376 | −1.74639 | −0.873193 | − | 0.487374i | \(-0.837955\pi\) | ||||
−0.873193 | + | 0.487374i | \(0.837955\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1371 | −0.847176 | ||||||||
\(566\) | 13.7042 | 0.576029 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.88327 | 0.204898 | ||||||||
\(569\) | 24.3931 | 1.02261 | 0.511306 | − | 0.859399i | \(-0.329162\pi\) | ||||
0.511306 | + | 0.859399i | \(0.329162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.7749 | −1.20419 | −0.602097 | − | 0.798423i | \(-0.705668\pi\) | ||||
−0.602097 | + | 0.798423i | \(0.705668\pi\) | |||||||
\(572\) | −10.9021 | −0.455840 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 25.3443 | 1.05785 | ||||||||
\(575\) | 2.76446 | 0.115286 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.15803 | 0.214732 | 0.107366 | − | 0.994220i | \(-0.465758\pi\) | ||||
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(578\) | 18.4848 | 0.768867 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.46277 | −0.185306 | ||||||||
\(581\) | −8.04348 | −0.333700 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.82503 | 0.324080 | ||||||||
\(584\) | 4.48481 | 0.185583 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.71637 | −0.0709028 | ||||||||
\(587\) | 36.0284 | 1.48705 | 0.743525 | − | 0.668708i | \(-0.233152\pi\) | ||||
0.743525 | + | 0.668708i | \(0.233152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.6074 | −0.807909 | ||||||||
\(590\) | −40.5467 | −1.66928 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.53839 | −0.392026 | ||||||||
\(593\) | 18.1163 | 0.743946 | 0.371973 | − | 0.928243i | \(-0.378681\pi\) | ||||
0.371973 | + | 0.928243i | \(0.378681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.7440 | −0.973409 | ||||||||
\(596\) | −30.8222 | −1.26252 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.3218 | 0.831021 | ||||||||
\(599\) | 8.70761 | 0.355783 | 0.177892 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177892 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7422 | 0.968464 | 0.484232 | − | 0.874940i | \(-0.339099\pi\) | ||||
0.484232 | + | 0.874940i | \(0.339099\pi\) | |||||||
\(602\) | 64.1533 | 2.61469 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.4638 | 1.11749 | ||||||||
\(605\) | 2.51557 | 0.102272 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.604695 | 0.0245438 | 0.0122719 | − | 0.999925i | \(-0.496094\pi\) | ||||
0.0122719 | + | 0.999925i | \(0.496094\pi\) | |||||||
\(608\) | −59.4457 | −2.41084 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.22935 | 0.211730 | ||||||||
\(611\) | −2.19156 | −0.0886612 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6301 | 0.792853 | 0.396426 | − | 0.918067i | \(-0.370250\pi\) | ||||
0.396426 | + | 0.918067i | \(0.370250\pi\) | |||||||
\(614\) | 22.1988 | 0.895870 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.21472 | −0.0892338 | ||||||||
\(617\) | 10.4332 | 0.420025 | 0.210012 | − | 0.977699i | \(-0.432650\pi\) | ||||
0.210012 | + | 0.977699i | \(0.432650\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.6981 | 0.872121 | 0.436060 | − | 0.899917i | \(-0.356373\pi\) | ||||
0.436060 | + | 0.899917i | \(0.356373\pi\) | |||||||
\(620\) | 15.6025 | 0.626612 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.83440 | −0.314131 | ||||||||
\(623\) | 8.44586 | 0.338376 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.8766 | −1.19506 | ||||||||
\(626\) | −37.8625 | −1.51329 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.5697 | −1.14006 | ||||||||
\(629\) | −8.34690 | −0.332813 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.07442 | 0.0825814 | 0.0412907 | − | 0.999147i | \(-0.486853\pi\) | ||||
0.0412907 | + | 0.999147i | \(0.486853\pi\) | |||||||
\(632\) | 4.30887 | 0.171398 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 37.6796 | 1.49645 | ||||||||
\(635\) | 14.1633 | 0.562054 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.7300 | −0.742110 | ||||||||
\(638\) | 1.58866 | 0.0628957 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13.2720 | 0.524624 | ||||||||
\(641\) | 13.9661 | 0.551628 | 0.275814 | − | 0.961211i | \(-0.411053\pi\) | ||||
0.275814 | + | 0.961211i | \(0.411053\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.4874 | −0.807943 | −0.403971 | − | 0.914772i | \(-0.632370\pi\) | ||||
−0.403971 | + | 0.914772i | \(0.632370\pi\) | |||||||
\(644\) | 16.0178 | 0.631189 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −43.4388 | −1.70908 | ||||||||
\(647\) | −11.4213 | −0.449018 | −0.224509 | − | 0.974472i | \(-0.572078\pi\) | ||||
−0.224509 | + | 0.974472i | \(0.572078\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.75368 | 0.304359 | ||||||||
\(650\) | 12.9657 | 0.508555 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 48.4127 | 1.89599 | ||||||||
\(653\) | −17.7057 | −0.692876 | −0.346438 | − | 0.938073i | \(-0.612609\pi\) | ||||
−0.346438 | + | 0.938073i | \(0.612609\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7158 | −0.418699 | ||||||||
\(656\) | 11.9677 | 0.467260 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.21565 | −0.125359 | ||||||||
\(659\) | −17.5526 | −0.683753 | −0.341877 | − | 0.939745i | \(-0.611063\pi\) | ||||
−0.341877 | + | 0.939745i | \(0.611063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.1442 | −1.44474 | −0.722370 | − | 0.691506i | \(-0.756947\pi\) | ||||
−0.722370 | + | 0.691506i | \(0.756947\pi\) | |||||||
\(662\) | 48.4460 | 1.88291 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.62120 | 0.0629148 | ||||||||
\(665\) | −61.1941 | −2.37301 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.59077 | −0.0615950 | ||||||||
\(668\) | 9.26883 | 0.358622 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.3412 | 0.940384 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.8198 | −0.956733 | −0.478366 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478366 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(674\) | 33.4267 | 1.28755 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.0221 | 0.808541 | ||||||||
\(677\) | −20.8171 | −0.800064 | −0.400032 | − | 0.916501i | \(-0.631001\pi\) | ||||
−0.400032 | + | 0.916501i | \(0.631001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.1950 | −1.50417 | ||||||||
\(680\) | 4.78572 | 0.183524 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.55420 | −0.212681 | ||||||||
\(683\) | 21.9543 | 0.840058 | 0.420029 | − | 0.907511i | \(-0.362020\pi\) | ||||
0.420029 | + | 0.907511i | \(0.362020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.35971 | −0.0901597 | ||||||||
\(686\) | 20.7540 | 0.792391 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.2934 | 1.15493 | ||||||||
\(689\) | −36.7491 | −1.40003 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.279975 | −0.0106508 | −0.00532538 | − | 0.999986i | \(-0.501695\pi\) | ||||
−0.00532538 | + | 0.999986i | \(0.501695\pi\) | |||||||
\(692\) | 59.2306 | 2.25161 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.24897 | 0.161289 | ||||||||
\(695\) | 50.3496 | 1.90987 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4727 | 0.396683 | ||||||||
\(698\) | 57.0032 | 2.15760 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.2196 | 0.386265 | ||||||||
\(701\) | −26.9968 | −1.01965 | −0.509827 | − | 0.860277i | \(-0.670290\pi\) | ||||
−0.509827 | + | 0.860277i | \(0.670290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.5120 | −0.811341 | ||||||||
\(704\) | −10.3314 | −0.389379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −55.6861 | −2.09578 | ||||||||
\(707\) | 42.6108 | 1.60254 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4492 | 0.655319 | 0.327659 | − | 0.944796i | \(-0.393740\pi\) | ||||
0.327659 | + | 0.944796i | \(0.393740\pi\) | |||||||
\(710\) | 38.2210 | 1.43441 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.70230 | −0.0637966 | ||||||||
\(713\) | 5.56159 | 0.208283 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.8140 | −0.441818 | ||||||||
\(716\) | −47.3425 | −1.76927 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −41.9697 | −1.56629 | ||||||||
\(719\) | −24.9061 | −0.928839 | −0.464420 | − | 0.885615i | \(-0.653737\pi\) | ||||
−0.464420 | + | 0.885615i | \(0.653737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.6782 | −0.956307 | ||||||||
\(722\) | −72.4553 | −2.69651 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −24.0366 | −0.893312 | ||||||||
\(725\) | −1.01494 | −0.0376939 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.4670 | −0.796166 | −0.398083 | − | 0.917349i | \(-0.630324\pi\) | ||||
−0.398083 | + | 0.917349i | \(0.630324\pi\) | |||||||
\(728\) | 10.4011 | 0.385492 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 35.1023 | 1.29919 | ||||||||
\(731\) | 26.5093 | 0.980483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.10577 | −0.0777784 | −0.0388892 | − | 0.999244i | \(-0.512382\pi\) | ||||
−0.0388892 | + | 0.999244i | \(0.512382\pi\) | |||||||
\(734\) | 18.1256 | 0.669028 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.8616 | 0.621527 | ||||||||
\(737\) | −4.65473 | −0.171459 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0592 | 0.443604 | 0.221802 | − | 0.975092i | \(-0.428806\pi\) | ||||
0.221802 | + | 0.975092i | \(0.428806\pi\) | |||||||
\(740\) | 17.1181 | 0.629274 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −53.9214 | −1.97952 | ||||||||
\(743\) | −5.58320 | −0.204828 | −0.102414 | − | 0.994742i | \(-0.532657\pi\) | ||||
−0.102414 | + | 0.994742i | \(0.532657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.4002 | −1.22369 | ||||||||
\(746\) | −16.8406 | −0.616577 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.61005 | −0.241687 | ||||||||
\(749\) | −52.6837 | −1.92502 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.1470 | 1.46499 | 0.732493 | − | 0.680775i | \(-0.238357\pi\) | ||||
0.732493 | + | 0.680775i | \(0.238357\pi\) | |||||||
\(752\) | −1.51844 | −0.0553719 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.46092 | −0.271711 | ||||||||
\(755\) | 29.7610 | 1.08311 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.2101 | 0.371091 | 0.185546 | − | 0.982636i | \(-0.440595\pi\) | ||||
0.185546 | + | 0.982636i | \(0.440595\pi\) | |||||||
\(758\) | −33.6409 | −1.22189 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.3340 | 0.447400 | ||||||||
\(761\) | −41.3818 | −1.50009 | −0.750045 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750045 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.6646 | −0.422285 | ||||||||
\(764\) | −5.97890 | −0.216309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.9191 | −0.864232 | ||||||||
\(767\) | −36.4141 | −1.31484 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.86294 | −0.0671793 | −0.0335896 | − | 0.999436i | \(-0.510694\pi\) | ||||
−0.0335896 | + | 0.999436i | \(0.510694\pi\) | |||||||
\(770\) | −17.3345 | −0.624692 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 48.9250 | 1.76085 | ||||||||
\(773\) | 8.28658 | 0.298048 | 0.149024 | − | 0.988834i | \(-0.452387\pi\) | ||||
0.149024 | + | 0.988834i | \(0.452387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.54839 | 0.127462 | ||||||||
\(776\) | 7.89994 | 0.283591 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36.6193 | −1.31286 | ||||||||
\(779\) | 26.9908 | 0.967046 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.30894 | −0.261535 | ||||||||
\(782\) | 12.3213 | 0.440609 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.9772 | −0.463472 | ||||||||
\(785\) | −30.9594 | −1.10499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03420 | 0.0368654 | 0.0184327 | − | 0.999830i | \(-0.494132\pi\) | ||||
0.0184327 | + | 0.999830i | \(0.494132\pi\) | |||||||
\(788\) | −49.0996 | −1.74910 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 33.7252 | 1.19989 | ||||||||
\(791\) | −26.5354 | −0.943490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.69636 | 0.166773 | ||||||||
\(794\) | −38.7812 | −1.37629 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.7136 | −0.627841 | ||||||||
\(797\) | 22.6893 | 0.803696 | 0.401848 | − | 0.915706i | \(-0.368368\pi\) | ||||
0.401848 | + | 0.915706i | \(0.368368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.32877 | −0.0470083 | ||||||||
\(800\) | 10.7580 | 0.380352 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −55.4538 | −1.95814 | ||||||||
\(803\) | −6.71256 | −0.236881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.3575 | 0.611773 | ||||||||
\(806\) | 26.0845 | 0.918788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.58841 | −0.302139 | ||||||||
\(809\) | 19.9728 | 0.702206 | 0.351103 | − | 0.936337i | \(-0.385807\pi\) | ||||
0.351103 | + | 0.936337i | \(0.385807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.5452 | 1.81000 | 0.904999 | − | 0.425414i | \(-0.139871\pi\) | ||||
0.904999 | + | 0.425414i | \(0.139871\pi\) | |||||||
\(812\) | −5.88074 | −0.206374 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.09372 | −0.213585 | ||||||||
\(815\) | 52.4621 | 1.83767 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68.3210 | 2.39025 | ||||||||
\(818\) | 79.6137 | 2.78363 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.4779 | −0.750039 | ||||||||
\(821\) | −14.9141 | −0.520506 | −0.260253 | − | 0.965541i | \(-0.583806\pi\) | ||||
−0.260253 | + | 0.965541i | \(0.583806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.5932 | −1.93786 | −0.968929 | − | 0.247340i | \(-0.920444\pi\) | ||||
−0.968929 | + | 0.247340i | \(0.920444\pi\) | |||||||
\(824\) | 5.17557 | 0.180300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −53.4298 | −1.85906 | ||||||||
\(827\) | 9.76170 | 0.339448 | 0.169724 | − | 0.985492i | \(-0.445712\pi\) | ||||
0.169724 | + | 0.985492i | \(0.445712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8861 | −0.378090 | −0.189045 | − | 0.981968i | \(-0.560539\pi\) | ||||
−0.189045 | + | 0.981968i | \(0.560539\pi\) | |||||||
\(830\) | 12.6890 | 0.440443 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 48.5199 | 1.68213 | ||||||||
\(833\) | −11.3562 | −0.393468 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0441 | 0.347590 | ||||||||
\(836\) | −17.0357 | −0.589193 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.71717 | −0.335674 | ||||||||
\(839\) | −30.5135 | −1.05344 | −0.526722 | − | 0.850038i | \(-0.676579\pi\) | ||||
−0.526722 | + | 0.850038i | \(0.676579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4160 | −0.979861 | ||||||||
\(842\) | −61.8334 | −2.13092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −59.5373 | −2.04936 | ||||||||
\(845\) | 22.7804 | 0.783669 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.31485 | 0.113899 | ||||||||
\(848\) | −25.4619 | −0.874365 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.86120 | 0.269637 | ||||||||
\(851\) | 6.10183 | 0.209168 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.5861 | 1.59508 | 0.797539 | − | 0.603267i | \(-0.206135\pi\) | ||||
0.797539 | + | 0.603267i | \(0.206135\pi\) | |||||||
\(854\) | 6.89089 | 0.235801 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.6187 | 0.362938 | ||||||||
\(857\) | 23.3679 | 0.798233 | 0.399116 | − | 0.916900i | \(-0.369317\pi\) | ||||
0.399116 | + | 0.916900i | \(0.369317\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.1184 | −0.993506 | −0.496753 | − | 0.867892i | \(-0.665475\pi\) | ||||
−0.496753 | + | 0.867892i | \(0.665475\pi\) | |||||||
\(860\) | −54.3662 | −1.85387 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.6467 | 1.00977 | ||||||||
\(863\) | −20.8386 | −0.709353 | −0.354676 | − | 0.934989i | \(-0.615409\pi\) | ||||
−0.354676 | + | 0.934989i | \(0.615409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 64.1848 | 2.18235 | ||||||||
\(866\) | −83.3255 | −2.83151 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.5600 | 0.697851 | ||||||||
\(869\) | −6.44921 | −0.218775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8603 | 0.740707 | ||||||||
\(872\) | 2.35105 | 0.0796165 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31.7550 | 1.07413 | ||||||||
\(875\) | −30.6192 | −1.03512 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.3955 | 1.36406 | 0.682030 | − | 0.731324i | \(-0.261097\pi\) | ||||
0.682030 | + | 0.731324i | \(0.261097\pi\) | |||||||
\(878\) | 86.8523 | 2.93112 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.18541 | −0.275930 | ||||||||
\(881\) | −28.4606 | −0.958863 | −0.479432 | − | 0.877579i | \(-0.659157\pi\) | ||||
−0.479432 | + | 0.877579i | \(0.659157\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.3212 | 1.25596 | 0.627980 | − | 0.778230i | \(-0.283882\pi\) | ||||
0.627980 | + | 0.778230i | \(0.283882\pi\) | |||||||
\(884\) | 31.0432 | 1.04409 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.0143 | −1.57948 | ||||||||
\(887\) | 5.69722 | 0.191294 | 0.0956470 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956470 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6635 | 0.625953 | ||||||||
\(890\) | −13.3238 | −0.446615 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −50.1940 | −1.68062 | ||||||||
\(893\) | −3.42455 | −0.114598 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.3024 | −1.71485 | ||||||||
\(896\) | 17.4890 | 0.584267 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.616324 | 0.0205670 | ||||||||
\(899\) | −2.04187 | −0.0681002 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.2813 | −0.742299 | ||||||||
\(902\) | 7.64571 | 0.254574 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.34834 | 0.177883 | ||||||||
\(905\) | −26.0470 | −0.865833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0847 | −0.932536 | −0.466268 | − | 0.884644i | \(-0.654402\pi\) | ||||
−0.466268 | + | 0.884644i | \(0.654402\pi\) | |||||||
\(908\) | −17.2043 | −0.570946 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 81.4090 | 2.69868 | ||||||||
\(911\) | −5.56419 | −0.184350 | −0.0921749 | − | 0.995743i | \(-0.529382\pi\) | ||||
−0.0921749 | + | 0.995743i | \(0.529382\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.42650 | −0.0803055 | ||||||||
\(914\) | 73.5924 | 2.43422 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.4096 | 0.938679 | ||||||||
\(917\) | −14.1205 | −0.466301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.22080 | 0.304166 | 0.152083 | − | 0.988368i | \(-0.451402\pi\) | ||||
0.152083 | + | 0.988368i | \(0.451402\pi\) | |||||||
\(920\) | −3.49850 | −0.115342 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51.6878 | 1.70225 | ||||||||
\(923\) | 34.3254 | 1.12983 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.89307 | 0.128003 | ||||||||
\(926\) | 49.1211 | 1.61422 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.19054 | −0.203214 | ||||||||
\(929\) | 18.9686 | 0.622339 | 0.311170 | − | 0.950354i | \(-0.399279\pi\) | ||||
0.311170 | + | 0.950354i | \(0.399279\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.2676 | −0.959208 | ||||||||
\(932\) | −23.0498 | −0.755022 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −51.3812 | −1.68124 | ||||||||
\(935\) | −7.16293 | −0.234253 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0732 | 0.982449 | 0.491224 | − | 0.871033i | \(-0.336550\pi\) | ||||
0.491224 | + | 0.871033i | \(0.336550\pi\) | |||||||
\(938\) | 32.0752 | 1.04729 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.72508 | 0.0888822 | ||||||||
\(941\) | 23.3429 | 0.760956 | 0.380478 | − | 0.924790i | \(-0.375760\pi\) | ||||
0.380478 | + | 0.924790i | \(0.375760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.65588 | −0.249310 | ||||||||
\(944\) | −25.2298 | −0.821159 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.3533 | 0.629231 | ||||||||
\(947\) | 16.1738 | 0.525579 | 0.262790 | − | 0.964853i | \(-0.415358\pi\) | ||||
0.262790 | + | 0.964853i | \(0.415358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.5246 | 1.02333 | ||||||||
\(950\) | 20.2602 | 0.657329 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.30630 | 0.204388 | ||||||||
\(953\) | 53.5723 | 1.73538 | 0.867689 | − | 0.497107i | \(-0.165604\pi\) | ||||
0.867689 | + | 0.497107i | \(0.165604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.47899 | −0.209655 | ||||||||
\(956\) | −26.5866 | −0.859873 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.02765 | −0.259361 | ||||||||
\(959\) | −3.10946 | −0.100410 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.8613 | −0.769720 | ||||||||
\(962\) | 28.6183 | 0.922691 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.22218 | 0.103779 | ||||||||
\(965\) | 53.0172 | 1.70668 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8918 | −0.864781 | −0.432390 | − | 0.901686i | \(-0.642330\pi\) | ||||
−0.432390 | + | 0.901686i | \(0.642330\pi\) | |||||||
\(968\) | −0.668123 | −0.0214743 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 61.8323 | 1.98531 | ||||||||
\(971\) | −4.19888 | −0.134749 | −0.0673743 | − | 0.997728i | \(-0.521462\pi\) | ||||
−0.0673743 | + | 0.997728i | \(0.521462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66.3473 | 2.12700 | ||||||||
\(974\) | −9.52238 | −0.305117 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.25391 | 0.104155 | ||||||||
\(977\) | −4.88596 | −0.156316 | −0.0781578 | − | 0.996941i | \(-0.524904\pi\) | ||||
−0.0781578 | + | 0.996941i | \(0.524904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.54789 | 0.0814309 | ||||||||
\(980\) | 23.2896 | 0.743959 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −69.8293 | −2.22834 | ||||||||
\(983\) | 41.8812 | 1.33580 | 0.667902 | − | 0.744250i | \(-0.267193\pi\) | ||||
0.667902 | + | 0.744250i | \(0.267193\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53.2064 | −1.69530 | ||||||||
\(986\) | −4.52362 | −0.144061 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 80.0058 | 2.54532 | ||||||||
\(989\) | −19.3791 | −0.616219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.1386 | 0.639724 | 0.319862 | − | 0.947464i | \(-0.396363\pi\) | ||||
0.319862 | + | 0.947464i | \(0.396363\pi\) | |||||||
\(992\) | 21.6431 | 0.687168 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 50.3651 | 1.59749 | ||||||||
\(995\) | −19.1952 | −0.608528 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.25885 | −0.0715385 | −0.0357692 | − | 0.999360i | \(-0.511388\pi\) | ||||
−0.0357692 | + | 0.999360i | \(0.511388\pi\) | |||||||
\(998\) | −66.9448 | −2.11910 | ||||||||
\(999\) | 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 | 6039.2.a.e.1.2 | 12 | ||
3.2 | odd | 2 | 2013.2.a.d.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.d.1.11 | ✓ | 12 | 3.2 | odd | 2 | ||
6039.2.a.e.1.2 | 12 | 1.1 | even | 1 | trivial |