Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.57047\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.57047 | 1.11049 | 0.555246 | − | 0.831686i | \(-0.312624\pi\) | ||||
0.555246 | + | 0.831686i | \(0.312624\pi\) | |||||||
\(3\) | −2.28502 | −1.31926 | −0.659628 | − | 0.751592i | \(-0.729286\pi\) | ||||
−0.659628 | + | 0.751592i | \(0.729286\pi\) | |||||||
\(4\) | 0.466387 | 0.233193 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.58856 | −1.46502 | ||||||||
\(7\) | −4.01337 | −1.51691 | −0.758455 | − | 0.651725i | \(-0.774045\pi\) | ||||
−0.758455 | + | 0.651725i | \(0.774045\pi\) | |||||||
\(8\) | −2.40850 | −0.851533 | ||||||||
\(9\) | 2.22131 | 0.740437 | ||||||||
\(10\) | −1.57047 | −0.496627 | ||||||||
\(11\) | 2.76620 | 0.834041 | 0.417021 | − | 0.908897i | \(-0.363074\pi\) | ||||
0.417021 | + | 0.908897i | \(0.363074\pi\) | |||||||
\(12\) | −1.06570 | −0.307642 | ||||||||
\(13\) | −2.78732 | −0.773065 | −0.386532 | − | 0.922276i | \(-0.626327\pi\) | ||||
−0.386532 | + | 0.922276i | \(0.626327\pi\) | |||||||
\(14\) | −6.30289 | −1.68452 | ||||||||
\(15\) | 2.28502 | 0.589989 | ||||||||
\(16\) | −4.71526 | −1.17881 | ||||||||
\(17\) | −3.60673 | −0.874761 | −0.437381 | − | 0.899277i | \(-0.644094\pi\) | ||||
−0.437381 | + | 0.899277i | \(0.644094\pi\) | |||||||
\(18\) | 3.48851 | 0.822250 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.466387 | −0.104287 | ||||||||
\(21\) | 9.17062 | 2.00119 | ||||||||
\(22\) | 4.34425 | 0.926197 | ||||||||
\(23\) | 1.36746 | 0.285136 | 0.142568 | − | 0.989785i | \(-0.454464\pi\) | ||||
0.142568 | + | 0.989785i | \(0.454464\pi\) | |||||||
\(24\) | 5.50347 | 1.12339 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.37742 | −0.858482 | ||||||||
\(27\) | 1.77932 | 0.342430 | ||||||||
\(28\) | −1.87178 | −0.353733 | ||||||||
\(29\) | 9.50940 | 1.76585 | 0.882926 | − | 0.469512i | \(-0.155570\pi\) | ||||
0.882926 | + | 0.469512i | \(0.155570\pi\) | |||||||
\(30\) | 3.58856 | 0.655179 | ||||||||
\(31\) | −1.55371 | −0.279054 | −0.139527 | − | 0.990218i | \(-0.544558\pi\) | ||||
−0.139527 | + | 0.990218i | \(0.544558\pi\) | |||||||
\(32\) | −2.58819 | −0.457531 | ||||||||
\(33\) | −6.32083 | −1.10031 | ||||||||
\(34\) | −5.66428 | −0.971415 | ||||||||
\(35\) | 4.01337 | 0.678383 | ||||||||
\(36\) | 1.03599 | 0.172665 | ||||||||
\(37\) | −8.51183 | −1.39934 | −0.699668 | − | 0.714468i | \(-0.746669\pi\) | ||||
−0.699668 | + | 0.714468i | \(0.746669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.36909 | 1.01987 | ||||||||
\(40\) | 2.40850 | 0.380817 | ||||||||
\(41\) | 6.60899 | 1.03215 | 0.516075 | − | 0.856543i | \(-0.327393\pi\) | ||||
0.516075 | + | 0.856543i | \(0.327393\pi\) | |||||||
\(42\) | 14.4022 | 2.22231 | ||||||||
\(43\) | −6.25476 | −0.953842 | −0.476921 | − | 0.878946i | \(-0.658247\pi\) | ||||
−0.476921 | + | 0.878946i | \(0.658247\pi\) | |||||||
\(44\) | 1.29012 | 0.194493 | ||||||||
\(45\) | −2.22131 | −0.331134 | ||||||||
\(46\) | 2.14756 | 0.316641 | ||||||||
\(47\) | 9.10988 | 1.32881 | 0.664406 | − | 0.747371i | \(-0.268684\pi\) | ||||
0.664406 | + | 0.747371i | \(0.268684\pi\) | |||||||
\(48\) | 10.7745 | 1.55516 | ||||||||
\(49\) | 9.10711 | 1.30102 | ||||||||
\(50\) | 1.57047 | 0.222098 | ||||||||
\(51\) | 8.24145 | 1.15403 | ||||||||
\(52\) | −1.29997 | −0.180274 | ||||||||
\(53\) | 3.94456 | 0.541827 | 0.270913 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270913 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(54\) | 2.79437 | 0.380265 | ||||||||
\(55\) | −2.76620 | −0.372995 | ||||||||
\(56\) | 9.66619 | 1.29170 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.9343 | 1.96096 | ||||||||
\(59\) | −3.61183 | −0.470220 | −0.235110 | − | 0.971969i | \(-0.575545\pi\) | ||||
−0.235110 | + | 0.971969i | \(0.575545\pi\) | |||||||
\(60\) | 1.06570 | 0.137582 | ||||||||
\(61\) | −7.48908 | −0.958879 | −0.479439 | − | 0.877575i | \(-0.659160\pi\) | ||||
−0.479439 | + | 0.877575i | \(0.659160\pi\) | |||||||
\(62\) | −2.44005 | −0.309887 | ||||||||
\(63\) | −8.91494 | −1.12318 | ||||||||
\(64\) | 5.36583 | 0.670729 | ||||||||
\(65\) | 2.78732 | 0.345725 | ||||||||
\(66\) | −9.92669 | −1.22189 | ||||||||
\(67\) | 14.5720 | 1.78025 | 0.890125 | − | 0.455717i | \(-0.150617\pi\) | ||||
0.890125 | + | 0.455717i | \(0.150617\pi\) | |||||||
\(68\) | −1.68213 | −0.203988 | ||||||||
\(69\) | −3.12468 | −0.376167 | ||||||||
\(70\) | 6.30289 | 0.753339 | ||||||||
\(71\) | 3.31888 | 0.393879 | 0.196940 | − | 0.980416i | \(-0.436900\pi\) | ||||
0.196940 | + | 0.980416i | \(0.436900\pi\) | |||||||
\(72\) | −5.35003 | −0.630507 | ||||||||
\(73\) | −10.0077 | −1.17132 | −0.585659 | − | 0.810558i | \(-0.699164\pi\) | ||||
−0.585659 | + | 0.810558i | \(0.699164\pi\) | |||||||
\(74\) | −13.3676 | −1.55395 | ||||||||
\(75\) | −2.28502 | −0.263851 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.1018 | −1.26517 | ||||||||
\(78\) | 10.0025 | 1.13256 | ||||||||
\(79\) | 1.94735 | 0.219094 | 0.109547 | − | 0.993982i | \(-0.465060\pi\) | ||||
0.109547 | + | 0.993982i | \(0.465060\pi\) | |||||||
\(80\) | 4.71526 | 0.527182 | ||||||||
\(81\) | −10.7297 | −1.19219 | ||||||||
\(82\) | 10.3792 | 1.14619 | ||||||||
\(83\) | 1.61868 | 0.177673 | 0.0888365 | − | 0.996046i | \(-0.471685\pi\) | ||||
0.0888365 | + | 0.996046i | \(0.471685\pi\) | |||||||
\(84\) | 4.27705 | 0.466665 | ||||||||
\(85\) | 3.60673 | 0.391205 | ||||||||
\(86\) | −9.82294 | −1.05923 | ||||||||
\(87\) | −21.7292 | −2.32961 | ||||||||
\(88\) | −6.66240 | −0.710214 | ||||||||
\(89\) | 12.2510 | 1.29860 | 0.649300 | − | 0.760532i | \(-0.275062\pi\) | ||||
0.649300 | + | 0.760532i | \(0.275062\pi\) | |||||||
\(90\) | −3.48851 | −0.367721 | ||||||||
\(91\) | 11.1866 | 1.17267 | ||||||||
\(92\) | 0.637766 | 0.0664917 | ||||||||
\(93\) | 3.55025 | 0.368143 | ||||||||
\(94\) | 14.3068 | 1.47564 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.91406 | 0.603601 | ||||||||
\(97\) | 11.5912 | 1.17690 | 0.588452 | − | 0.808532i | \(-0.299738\pi\) | ||||
0.588452 | + | 0.808532i | \(0.299738\pi\) | |||||||
\(98\) | 14.3025 | 1.44477 | ||||||||
\(99\) | 6.14460 | 0.617555 | ||||||||
\(100\) | 0.466387 | 0.0466387 | ||||||||
\(101\) | −6.98240 | −0.694774 | −0.347387 | − | 0.937722i | \(-0.612931\pi\) | ||||
−0.347387 | + | 0.937722i | \(0.612931\pi\) | |||||||
\(102\) | 12.9430 | 1.28155 | ||||||||
\(103\) | −10.1338 | −0.998510 | −0.499255 | − | 0.866455i | \(-0.666393\pi\) | ||||
−0.499255 | + | 0.866455i | \(0.666393\pi\) | |||||||
\(104\) | 6.71327 | 0.658290 | ||||||||
\(105\) | −9.17062 | −0.894961 | ||||||||
\(106\) | 6.19482 | 0.601694 | ||||||||
\(107\) | 11.7835 | 1.13916 | 0.569578 | − | 0.821937i | \(-0.307107\pi\) | ||||
0.569578 | + | 0.821937i | \(0.307107\pi\) | |||||||
\(108\) | 0.829849 | 0.0798523 | ||||||||
\(109\) | 1.60407 | 0.153642 | 0.0768212 | − | 0.997045i | \(-0.475523\pi\) | ||||
0.0768212 | + | 0.997045i | \(0.475523\pi\) | |||||||
\(110\) | −4.34425 | −0.414208 | ||||||||
\(111\) | 19.4497 | 1.84608 | ||||||||
\(112\) | 18.9241 | 1.78815 | ||||||||
\(113\) | −12.9449 | −1.21775 | −0.608876 | − | 0.793266i | \(-0.708379\pi\) | ||||
−0.608876 | + | 0.793266i | \(0.708379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36746 | −0.127517 | ||||||||
\(116\) | 4.43506 | 0.411785 | ||||||||
\(117\) | −6.19152 | −0.572406 | ||||||||
\(118\) | −5.67228 | −0.522175 | ||||||||
\(119\) | 14.4751 | 1.32693 | ||||||||
\(120\) | −5.50347 | −0.502395 | ||||||||
\(121\) | −3.34812 | −0.304375 | ||||||||
\(122\) | −11.7614 | −1.06483 | ||||||||
\(123\) | −15.1017 | −1.36167 | ||||||||
\(124\) | −0.724627 | −0.0650735 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −14.0007 | −1.24728 | ||||||||
\(127\) | 8.29802 | 0.736331 | 0.368165 | − | 0.929760i | \(-0.379986\pi\) | ||||
0.368165 | + | 0.929760i | \(0.379986\pi\) | |||||||
\(128\) | 13.6033 | 1.20237 | ||||||||
\(129\) | 14.2923 | 1.25836 | ||||||||
\(130\) | 4.37742 | 0.383925 | ||||||||
\(131\) | −6.51185 | −0.568943 | −0.284471 | − | 0.958685i | \(-0.591818\pi\) | ||||
−0.284471 | + | 0.958685i | \(0.591818\pi\) | |||||||
\(132\) | −2.94795 | −0.256586 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 22.8849 | 1.97695 | ||||||||
\(135\) | −1.77932 | −0.153139 | ||||||||
\(136\) | 8.68681 | 0.744888 | ||||||||
\(137\) | 14.8686 | 1.27031 | 0.635156 | − | 0.772384i | \(-0.280936\pi\) | ||||
0.635156 | + | 0.772384i | \(0.280936\pi\) | |||||||
\(138\) | −4.90722 | −0.417731 | ||||||||
\(139\) | 9.95823 | 0.844646 | 0.422323 | − | 0.906445i | \(-0.361215\pi\) | ||||
0.422323 | + | 0.906445i | \(0.361215\pi\) | |||||||
\(140\) | 1.87178 | 0.158194 | ||||||||
\(141\) | −20.8163 | −1.75304 | ||||||||
\(142\) | 5.21222 | 0.437400 | ||||||||
\(143\) | −7.71030 | −0.644768 | ||||||||
\(144\) | −10.4741 | −0.872838 | ||||||||
\(145\) | −9.50940 | −0.789713 | ||||||||
\(146\) | −15.7169 | −1.30074 | ||||||||
\(147\) | −20.8099 | −1.71637 | ||||||||
\(148\) | −3.96980 | −0.326316 | ||||||||
\(149\) | −1.43162 | −0.117283 | −0.0586416 | − | 0.998279i | \(-0.518677\pi\) | ||||
−0.0586416 | + | 0.998279i | \(0.518677\pi\) | |||||||
\(150\) | −3.58856 | −0.293005 | ||||||||
\(151\) | 8.18383 | 0.665990 | 0.332995 | − | 0.942929i | \(-0.391941\pi\) | ||||
0.332995 | + | 0.942929i | \(0.391941\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.01168 | −0.647706 | ||||||||
\(154\) | −17.4351 | −1.40496 | ||||||||
\(155\) | 1.55371 | 0.124797 | ||||||||
\(156\) | 2.97046 | 0.237827 | ||||||||
\(157\) | −7.83512 | −0.625311 | −0.312655 | − | 0.949867i | \(-0.601218\pi\) | ||||
−0.312655 | + | 0.949867i | \(0.601218\pi\) | |||||||
\(158\) | 3.05827 | 0.243303 | ||||||||
\(159\) | −9.01339 | −0.714808 | ||||||||
\(160\) | 2.58819 | 0.204614 | ||||||||
\(161\) | −5.48813 | −0.432525 | ||||||||
\(162\) | −16.8507 | −1.32392 | ||||||||
\(163\) | −19.2994 | −1.51164 | −0.755821 | − | 0.654778i | \(-0.772762\pi\) | ||||
−0.755821 | + | 0.654778i | \(0.772762\pi\) | |||||||
\(164\) | 3.08234 | 0.240690 | ||||||||
\(165\) | 6.32083 | 0.492076 | ||||||||
\(166\) | 2.54209 | 0.197304 | ||||||||
\(167\) | −9.38968 | −0.726595 | −0.363297 | − | 0.931673i | \(-0.618349\pi\) | ||||
−0.363297 | + | 0.931673i | \(0.618349\pi\) | |||||||
\(168\) | −22.0874 | −1.70408 | ||||||||
\(169\) | −5.23082 | −0.402371 | ||||||||
\(170\) | 5.66428 | 0.434430 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.91714 | −0.222430 | ||||||||
\(173\) | −8.31084 | −0.631861 | −0.315931 | − | 0.948782i | \(-0.602317\pi\) | ||||
−0.315931 | + | 0.948782i | \(0.602317\pi\) | |||||||
\(174\) | −34.1251 | −2.58702 | ||||||||
\(175\) | −4.01337 | −0.303382 | ||||||||
\(176\) | −13.0434 | −0.983180 | ||||||||
\(177\) | 8.25309 | 0.620340 | ||||||||
\(178\) | 19.2398 | 1.44209 | ||||||||
\(179\) | 18.5319 | 1.38514 | 0.692568 | − | 0.721352i | \(-0.256479\pi\) | ||||
0.692568 | + | 0.721352i | \(0.256479\pi\) | |||||||
\(180\) | −1.03599 | −0.0772182 | ||||||||
\(181\) | −11.3292 | −0.842094 | −0.421047 | − | 0.907039i | \(-0.638337\pi\) | ||||
−0.421047 | + | 0.907039i | \(0.638337\pi\) | |||||||
\(182\) | 17.5682 | 1.30224 | ||||||||
\(183\) | 17.1127 | 1.26501 | ||||||||
\(184\) | −3.29353 | −0.242802 | ||||||||
\(185\) | 8.51183 | 0.625802 | ||||||||
\(186\) | 5.57557 | 0.408820 | ||||||||
\(187\) | −9.97695 | −0.729587 | ||||||||
\(188\) | 4.24873 | 0.309870 | ||||||||
\(189\) | −7.14105 | −0.519435 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8879 | 0.860175 | 0.430088 | − | 0.902787i | \(-0.358483\pi\) | ||||
0.430088 | + | 0.902787i | \(0.358483\pi\) | |||||||
\(192\) | −12.2610 | −0.884864 | ||||||||
\(193\) | 0.957834 | 0.0689464 | 0.0344732 | − | 0.999406i | \(-0.489025\pi\) | ||||
0.0344732 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(194\) | 18.2036 | 1.30694 | ||||||||
\(195\) | −6.36909 | −0.456100 | ||||||||
\(196\) | 4.24743 | 0.303388 | ||||||||
\(197\) | 14.2776 | 1.01724 | 0.508619 | − | 0.860991i | \(-0.330156\pi\) | ||||
0.508619 | + | 0.860991i | \(0.330156\pi\) | |||||||
\(198\) | 9.64993 | 0.685791 | ||||||||
\(199\) | −7.76571 | −0.550497 | −0.275248 | − | 0.961373i | \(-0.588760\pi\) | ||||
−0.275248 | + | 0.961373i | \(0.588760\pi\) | |||||||
\(200\) | −2.40850 | −0.170307 | ||||||||
\(201\) | −33.2972 | −2.34861 | ||||||||
\(202\) | −10.9657 | −0.771542 | ||||||||
\(203\) | −38.1647 | −2.67864 | ||||||||
\(204\) | 3.84370 | 0.269113 | ||||||||
\(205\) | −6.60899 | −0.461592 | ||||||||
\(206\) | −15.9148 | −1.10884 | ||||||||
\(207\) | 3.03756 | 0.211125 | ||||||||
\(208\) | 13.1430 | 0.911300 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −14.4022 | −0.993847 | ||||||||
\(211\) | −7.62274 | −0.524771 | −0.262386 | − | 0.964963i | \(-0.584509\pi\) | ||||
−0.262386 | + | 0.964963i | \(0.584509\pi\) | |||||||
\(212\) | 1.83969 | 0.126350 | ||||||||
\(213\) | −7.58371 | −0.519627 | ||||||||
\(214\) | 18.5057 | 1.26502 | ||||||||
\(215\) | 6.25476 | 0.426571 | ||||||||
\(216\) | −4.28548 | −0.291590 | ||||||||
\(217\) | 6.23559 | 0.423299 | ||||||||
\(218\) | 2.51916 | 0.170619 | ||||||||
\(219\) | 22.8679 | 1.54527 | ||||||||
\(220\) | −1.29012 | −0.0869799 | ||||||||
\(221\) | 10.0531 | 0.676247 | ||||||||
\(222\) | 30.5452 | 2.05006 | ||||||||
\(223\) | 8.00331 | 0.535942 | 0.267971 | − | 0.963427i | \(-0.413647\pi\) | ||||
0.267971 | + | 0.963427i | \(0.413647\pi\) | |||||||
\(224\) | 10.3873 | 0.694034 | ||||||||
\(225\) | 2.22131 | 0.148087 | ||||||||
\(226\) | −20.3296 | −1.35230 | ||||||||
\(227\) | 17.7409 | 1.17750 | 0.588752 | − | 0.808314i | \(-0.299619\pi\) | ||||
0.588752 | + | 0.808314i | \(0.299619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.2231 | −1.60071 | −0.800354 | − | 0.599528i | \(-0.795355\pi\) | ||||
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(230\) | −2.14756 | −0.141606 | ||||||||
\(231\) | 25.3678 | 1.66908 | ||||||||
\(232\) | −22.9034 | −1.50368 | ||||||||
\(233\) | 13.6491 | 0.894183 | 0.447092 | − | 0.894488i | \(-0.352460\pi\) | ||||
0.447092 | + | 0.894488i | \(0.352460\pi\) | |||||||
\(234\) | −9.72361 | −0.635653 | ||||||||
\(235\) | −9.10988 | −0.594263 | ||||||||
\(236\) | −1.68451 | −0.109652 | ||||||||
\(237\) | −4.44974 | −0.289042 | ||||||||
\(238\) | 22.7328 | 1.47355 | ||||||||
\(239\) | 3.73764 | 0.241768 | 0.120884 | − | 0.992667i | \(-0.461427\pi\) | ||||
0.120884 | + | 0.992667i | \(0.461427\pi\) | |||||||
\(240\) | −10.7745 | −0.695488 | ||||||||
\(241\) | 5.28146 | 0.340209 | 0.170104 | − | 0.985426i | \(-0.445590\pi\) | ||||
0.170104 | + | 0.985426i | \(0.445590\pi\) | |||||||
\(242\) | −5.25814 | −0.338006 | ||||||||
\(243\) | 19.1796 | 1.23037 | ||||||||
\(244\) | −3.49281 | −0.223604 | ||||||||
\(245\) | −9.10711 | −0.581832 | ||||||||
\(246\) | −23.7168 | −1.51212 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.74210 | 0.237623 | ||||||||
\(249\) | −3.69871 | −0.234396 | ||||||||
\(250\) | −1.57047 | −0.0993255 | ||||||||
\(251\) | −12.5445 | −0.791801 | −0.395900 | − | 0.918293i | \(-0.629567\pi\) | ||||
−0.395900 | + | 0.918293i | \(0.629567\pi\) | |||||||
\(252\) | −4.15781 | −0.261917 | ||||||||
\(253\) | 3.78268 | 0.237815 | ||||||||
\(254\) | 13.0318 | 0.817689 | ||||||||
\(255\) | −8.24145 | −0.516100 | ||||||||
\(256\) | 10.6319 | 0.664494 | ||||||||
\(257\) | −8.59982 | −0.536442 | −0.268221 | − | 0.963357i | \(-0.586436\pi\) | ||||
−0.268221 | + | 0.963357i | \(0.586436\pi\) | |||||||
\(258\) | 22.4456 | 1.39740 | ||||||||
\(259\) | 34.1611 | 2.12267 | ||||||||
\(260\) | 1.29997 | 0.0806208 | ||||||||
\(261\) | 21.1234 | 1.30750 | ||||||||
\(262\) | −10.2267 | −0.631806 | ||||||||
\(263\) | 26.6903 | 1.64580 | 0.822898 | − | 0.568189i | \(-0.192356\pi\) | ||||
0.822898 | + | 0.568189i | \(0.192356\pi\) | |||||||
\(264\) | 15.2237 | 0.936954 | ||||||||
\(265\) | −3.94456 | −0.242312 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −27.9937 | −1.71319 | ||||||||
\(268\) | 6.79617 | 0.415142 | ||||||||
\(269\) | 3.30320 | 0.201400 | 0.100700 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100700 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(270\) | −2.79437 | −0.170060 | ||||||||
\(271\) | −18.3875 | −1.11696 | −0.558482 | − | 0.829517i | \(-0.688616\pi\) | ||||
−0.558482 | + | 0.829517i | \(0.688616\pi\) | |||||||
\(272\) | 17.0067 | 1.03118 | ||||||||
\(273\) | −25.5615 | −1.54705 | ||||||||
\(274\) | 23.3508 | 1.41067 | ||||||||
\(275\) | 2.76620 | 0.166808 | ||||||||
\(276\) | −1.45731 | −0.0877196 | ||||||||
\(277\) | 26.7787 | 1.60898 | 0.804488 | − | 0.593969i | \(-0.202440\pi\) | ||||
0.804488 | + | 0.593969i | \(0.202440\pi\) | |||||||
\(278\) | 15.6391 | 0.937973 | ||||||||
\(279\) | −3.45126 | −0.206622 | ||||||||
\(280\) | −9.66619 | −0.577665 | ||||||||
\(281\) | −21.5462 | −1.28534 | −0.642669 | − | 0.766144i | \(-0.722173\pi\) | ||||
−0.642669 | + | 0.766144i | \(0.722173\pi\) | |||||||
\(282\) | −32.6914 | −1.94674 | ||||||||
\(283\) | 18.3471 | 1.09062 | 0.545311 | − | 0.838234i | \(-0.316412\pi\) | ||||
0.545311 | + | 0.838234i | \(0.316412\pi\) | |||||||
\(284\) | 1.54788 | 0.0918499 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.1088 | −0.716010 | ||||||||
\(287\) | −26.5243 | −1.56568 | ||||||||
\(288\) | −5.74917 | −0.338773 | ||||||||
\(289\) | −3.99148 | −0.234793 | ||||||||
\(290\) | −14.9343 | −0.876970 | ||||||||
\(291\) | −26.4860 | −1.55264 | ||||||||
\(292\) | −4.66748 | −0.273143 | ||||||||
\(293\) | 9.28872 | 0.542653 | 0.271326 | − | 0.962487i | \(-0.412538\pi\) | ||||
0.271326 | + | 0.962487i | \(0.412538\pi\) | |||||||
\(294\) | −32.6814 | −1.90602 | ||||||||
\(295\) | 3.61183 | 0.210289 | ||||||||
\(296\) | 20.5007 | 1.19158 | ||||||||
\(297\) | 4.92195 | 0.285600 | ||||||||
\(298\) | −2.24833 | −0.130242 | ||||||||
\(299\) | −3.81156 | −0.220428 | ||||||||
\(300\) | −1.06570 | −0.0615284 | ||||||||
\(301\) | 25.1027 | 1.44689 | ||||||||
\(302\) | 12.8525 | 0.739577 | ||||||||
\(303\) | 15.9549 | 0.916585 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.48908 | 0.428824 | ||||||||
\(306\) | −12.5821 | −0.719272 | ||||||||
\(307\) | 11.0151 | 0.628666 | 0.314333 | − | 0.949313i | \(-0.398219\pi\) | ||||
0.314333 | + | 0.949313i | \(0.398219\pi\) | |||||||
\(308\) | −5.17772 | −0.295028 | ||||||||
\(309\) | 23.1559 | 1.31729 | ||||||||
\(310\) | 2.44005 | 0.138586 | ||||||||
\(311\) | 25.3821 | 1.43929 | 0.719644 | − | 0.694343i | \(-0.244305\pi\) | ||||
0.719644 | + | 0.694343i | \(0.244305\pi\) | |||||||
\(312\) | −15.3399 | −0.868453 | ||||||||
\(313\) | 21.0559 | 1.19015 | 0.595074 | − | 0.803671i | \(-0.297123\pi\) | ||||
0.595074 | + | 0.803671i | \(0.297123\pi\) | |||||||
\(314\) | −12.3048 | −0.694403 | ||||||||
\(315\) | 8.91494 | 0.502300 | ||||||||
\(316\) | 0.908220 | 0.0510914 | ||||||||
\(317\) | −4.00986 | −0.225216 | −0.112608 | − | 0.993639i | \(-0.535920\pi\) | ||||
−0.112608 | + | 0.993639i | \(0.535920\pi\) | |||||||
\(318\) | −14.1553 | −0.793789 | ||||||||
\(319\) | 26.3049 | 1.47279 | ||||||||
\(320\) | −5.36583 | −0.299959 | ||||||||
\(321\) | −26.9256 | −1.50284 | ||||||||
\(322\) | −8.61896 | −0.480316 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.00419 | −0.278011 | ||||||||
\(325\) | −2.78732 | −0.154613 | ||||||||
\(326\) | −30.3091 | −1.67867 | ||||||||
\(327\) | −3.66534 | −0.202694 | ||||||||
\(328\) | −15.9177 | −0.878910 | ||||||||
\(329\) | −36.5613 | −2.01569 | ||||||||
\(330\) | 9.92669 | 0.546446 | ||||||||
\(331\) | 32.1360 | 1.76635 | 0.883176 | − | 0.469042i | \(-0.155401\pi\) | ||||
0.883176 | + | 0.469042i | \(0.155401\pi\) | |||||||
\(332\) | 0.754929 | 0.0414321 | ||||||||
\(333\) | −18.9074 | −1.03612 | ||||||||
\(334\) | −14.7462 | −0.806878 | ||||||||
\(335\) | −14.5720 | −0.796152 | ||||||||
\(336\) | −43.2418 | −2.35903 | ||||||||
\(337\) | −23.4476 | −1.27727 | −0.638636 | − | 0.769509i | \(-0.720501\pi\) | ||||
−0.638636 | + | 0.769509i | \(0.720501\pi\) | |||||||
\(338\) | −8.21487 | −0.446830 | ||||||||
\(339\) | 29.5793 | 1.60653 | ||||||||
\(340\) | 1.68213 | 0.0912264 | ||||||||
\(341\) | −4.29786 | −0.232742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.45661 | −0.456614 | ||||||||
\(344\) | 15.0646 | 0.812228 | ||||||||
\(345\) | 3.12468 | 0.168227 | ||||||||
\(346\) | −13.0519 | −0.701677 | ||||||||
\(347\) | 6.49353 | 0.348591 | 0.174295 | − | 0.984693i | \(-0.444235\pi\) | ||||
0.174295 | + | 0.984693i | \(0.444235\pi\) | |||||||
\(348\) | −10.1342 | −0.543250 | ||||||||
\(349\) | −27.2008 | −1.45603 | −0.728013 | − | 0.685563i | \(-0.759556\pi\) | ||||
−0.728013 | + | 0.685563i | \(0.759556\pi\) | |||||||
\(350\) | −6.30289 | −0.336903 | ||||||||
\(351\) | −4.95953 | −0.264720 | ||||||||
\(352\) | −7.15945 | −0.381600 | ||||||||
\(353\) | −6.56125 | −0.349220 | −0.174610 | − | 0.984638i | \(-0.555866\pi\) | ||||
−0.174610 | + | 0.984638i | \(0.555866\pi\) | |||||||
\(354\) | 12.9613 | 0.688883 | ||||||||
\(355\) | −3.31888 | −0.176148 | ||||||||
\(356\) | 5.71369 | 0.302825 | ||||||||
\(357\) | −33.0760 | −1.75057 | ||||||||
\(358\) | 29.1038 | 1.53818 | ||||||||
\(359\) | −2.73194 | −0.144186 | −0.0720932 | − | 0.997398i | \(-0.522968\pi\) | ||||
−0.0720932 | + | 0.997398i | \(0.522968\pi\) | |||||||
\(360\) | 5.35003 | 0.281971 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −17.7922 | −0.935139 | ||||||||
\(363\) | 7.65053 | 0.401549 | ||||||||
\(364\) | 5.21726 | 0.273459 | ||||||||
\(365\) | 10.0077 | 0.523829 | ||||||||
\(366\) | 26.8750 | 1.40478 | ||||||||
\(367\) | 6.57903 | 0.343423 | 0.171711 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171711 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(368\) | −6.44794 | −0.336122 | ||||||||
\(369\) | 14.6806 | 0.764243 | ||||||||
\(370\) | 13.3676 | 0.694949 | ||||||||
\(371\) | −15.8310 | −0.821902 | ||||||||
\(372\) | 1.65579 | 0.0858486 | ||||||||
\(373\) | 8.55993 | 0.443216 | 0.221608 | − | 0.975136i | \(-0.428869\pi\) | ||||
0.221608 | + | 0.975136i | \(0.428869\pi\) | |||||||
\(374\) | −15.6685 | −0.810201 | ||||||||
\(375\) | 2.28502 | 0.117998 | ||||||||
\(376\) | −21.9411 | −1.13153 | ||||||||
\(377\) | −26.5058 | −1.36512 | ||||||||
\(378\) | −11.2148 | −0.576828 | ||||||||
\(379\) | −14.2477 | −0.731856 | −0.365928 | − | 0.930643i | \(-0.619248\pi\) | ||||
−0.365928 | + | 0.930643i | \(0.619248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.9611 | −0.971409 | ||||||||
\(382\) | 18.6696 | 0.955218 | ||||||||
\(383\) | −21.3664 | −1.09177 | −0.545885 | − | 0.837860i | \(-0.683807\pi\) | ||||
−0.545885 | + | 0.837860i | \(0.683807\pi\) | |||||||
\(384\) | −31.0837 | −1.58624 | ||||||||
\(385\) | 11.1018 | 0.565799 | ||||||||
\(386\) | 1.50425 | 0.0765644 | ||||||||
\(387\) | −13.8938 | −0.706261 | ||||||||
\(388\) | 5.40596 | 0.274446 | ||||||||
\(389\) | 15.2926 | 0.775367 | 0.387683 | − | 0.921793i | \(-0.373275\pi\) | ||||
0.387683 | + | 0.921793i | \(0.373275\pi\) | |||||||
\(390\) | −10.0025 | −0.506496 | ||||||||
\(391\) | −4.93207 | −0.249426 | ||||||||
\(392\) | −21.9345 | −1.10786 | ||||||||
\(393\) | 14.8797 | 0.750581 | ||||||||
\(394\) | 22.4226 | 1.12964 | ||||||||
\(395\) | −1.94735 | −0.0979820 | ||||||||
\(396\) | 2.86576 | 0.144010 | ||||||||
\(397\) | 32.6020 | 1.63625 | 0.818124 | − | 0.575042i | \(-0.195014\pi\) | ||||
0.818124 | + | 0.575042i | \(0.195014\pi\) | |||||||
\(398\) | −12.1958 | −0.611322 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.71526 | −0.235763 | ||||||||
\(401\) | 17.3119 | 0.864517 | 0.432258 | − | 0.901750i | \(-0.357717\pi\) | ||||
0.432258 | + | 0.901750i | \(0.357717\pi\) | |||||||
\(402\) | −52.2924 | −2.60811 | ||||||||
\(403\) | 4.33068 | 0.215727 | ||||||||
\(404\) | −3.25650 | −0.162017 | ||||||||
\(405\) | 10.7297 | 0.533164 | ||||||||
\(406\) | −59.9367 | −2.97461 | ||||||||
\(407\) | −23.5455 | −1.16710 | ||||||||
\(408\) | −19.8495 | −0.982698 | ||||||||
\(409\) | 10.8272 | 0.535370 | 0.267685 | − | 0.963506i | \(-0.413741\pi\) | ||||
0.267685 | + | 0.963506i | \(0.413741\pi\) | |||||||
\(410\) | −10.3792 | −0.512594 | ||||||||
\(411\) | −33.9751 | −1.67587 | ||||||||
\(412\) | −4.72625 | −0.232846 | ||||||||
\(413\) | 14.4956 | 0.713281 | ||||||||
\(414\) | 4.77041 | 0.234453 | ||||||||
\(415\) | −1.61868 | −0.0794577 | ||||||||
\(416\) | 7.21412 | 0.353701 | ||||||||
\(417\) | −22.7547 | −1.11430 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.9763 | 1.65985 | 0.829925 | − | 0.557876i | \(-0.188383\pi\) | ||||
0.829925 | + | 0.557876i | \(0.188383\pi\) | |||||||
\(420\) | −4.27705 | −0.208699 | ||||||||
\(421\) | −8.30825 | −0.404919 | −0.202460 | − | 0.979291i | \(-0.564894\pi\) | ||||
−0.202460 | + | 0.979291i | \(0.564894\pi\) | |||||||
\(422\) | −11.9713 | −0.582754 | ||||||||
\(423\) | 20.2359 | 0.983903 | ||||||||
\(424\) | −9.50046 | −0.461383 | ||||||||
\(425\) | −3.60673 | −0.174952 | ||||||||
\(426\) | −11.9100 | −0.577042 | ||||||||
\(427\) | 30.0564 | 1.45453 | ||||||||
\(428\) | 5.49568 | 0.265644 | ||||||||
\(429\) | 17.6182 | 0.850614 | ||||||||
\(430\) | 9.82294 | 0.473704 | ||||||||
\(431\) | 12.1298 | 0.584271 | 0.292135 | − | 0.956377i | \(-0.405634\pi\) | ||||
0.292135 | + | 0.956377i | \(0.405634\pi\) | |||||||
\(432\) | −8.38993 | −0.403661 | ||||||||
\(433\) | 5.43541 | 0.261209 | 0.130605 | − | 0.991435i | \(-0.458308\pi\) | ||||
0.130605 | + | 0.991435i | \(0.458308\pi\) | |||||||
\(434\) | 9.79283 | 0.470071 | ||||||||
\(435\) | 21.7292 | 1.04183 | ||||||||
\(436\) | 0.748119 | 0.0358284 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 35.9134 | 1.71601 | ||||||||
\(439\) | 25.3807 | 1.21136 | 0.605678 | − | 0.795710i | \(-0.292902\pi\) | ||||
0.605678 | + | 0.795710i | \(0.292902\pi\) | |||||||
\(440\) | 6.66240 | 0.317617 | ||||||||
\(441\) | 20.2297 | 0.963321 | ||||||||
\(442\) | 15.7882 | 0.750967 | ||||||||
\(443\) | −4.92125 | −0.233816 | −0.116908 | − | 0.993143i | \(-0.537298\pi\) | ||||
−0.116908 | + | 0.993143i | \(0.537298\pi\) | |||||||
\(444\) | 9.07108 | 0.430494 | ||||||||
\(445\) | −12.2510 | −0.580752 | ||||||||
\(446\) | 12.5690 | 0.595159 | ||||||||
\(447\) | 3.27129 | 0.154727 | ||||||||
\(448\) | −21.5351 | −1.01744 | ||||||||
\(449\) | −4.06649 | −0.191910 | −0.0959548 | − | 0.995386i | \(-0.530590\pi\) | ||||
−0.0959548 | + | 0.995386i | \(0.530590\pi\) | |||||||
\(450\) | 3.48851 | 0.164450 | ||||||||
\(451\) | 18.2818 | 0.860856 | ||||||||
\(452\) | −6.03732 | −0.283971 | ||||||||
\(453\) | −18.7002 | −0.878612 | ||||||||
\(454\) | 27.8616 | 1.30761 | ||||||||
\(455\) | −11.1866 | −0.524434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5517 | −0.633922 | −0.316961 | − | 0.948439i | \(-0.602662\pi\) | ||||
−0.316961 | + | 0.948439i | \(0.602662\pi\) | |||||||
\(458\) | −38.0418 | −1.77757 | ||||||||
\(459\) | −6.41752 | −0.299544 | ||||||||
\(460\) | −0.637766 | −0.0297360 | ||||||||
\(461\) | 17.8812 | 0.832812 | 0.416406 | − | 0.909179i | \(-0.363290\pi\) | ||||
0.416406 | + | 0.909179i | \(0.363290\pi\) | |||||||
\(462\) | 39.8394 | 1.85350 | ||||||||
\(463\) | 1.30695 | 0.0607393 | 0.0303696 | − | 0.999539i | \(-0.490332\pi\) | ||||
0.0303696 | + | 0.999539i | \(0.490332\pi\) | |||||||
\(464\) | −44.8393 | −2.08161 | ||||||||
\(465\) | −3.55025 | −0.164639 | ||||||||
\(466\) | 21.4356 | 0.992983 | ||||||||
\(467\) | 27.0266 | 1.25064 | 0.625321 | − | 0.780368i | \(-0.284968\pi\) | ||||
0.625321 | + | 0.780368i | \(0.284968\pi\) | |||||||
\(468\) | −2.88764 | −0.133481 | ||||||||
\(469\) | −58.4826 | −2.70048 | ||||||||
\(470\) | −14.3068 | −0.659925 | ||||||||
\(471\) | 17.9034 | 0.824945 | ||||||||
\(472\) | 8.69908 | 0.400408 | ||||||||
\(473\) | −17.3019 | −0.795544 | ||||||||
\(474\) | −6.98820 | −0.320979 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.75101 | 0.309432 | ||||||||
\(477\) | 8.76210 | 0.401189 | ||||||||
\(478\) | 5.86987 | 0.268481 | ||||||||
\(479\) | 0.289474 | 0.0132264 | 0.00661321 | − | 0.999978i | \(-0.497895\pi\) | ||||
0.00661321 | + | 0.999978i | \(0.497895\pi\) | |||||||
\(480\) | −5.91406 | −0.269939 | ||||||||
\(481\) | 23.7252 | 1.08178 | ||||||||
\(482\) | 8.29439 | 0.377799 | ||||||||
\(483\) | 12.5405 | 0.570611 | ||||||||
\(484\) | −1.56152 | −0.0709782 | ||||||||
\(485\) | −11.5912 | −0.526327 | ||||||||
\(486\) | 30.1211 | 1.36632 | ||||||||
\(487\) | −15.3711 | −0.696530 | −0.348265 | − | 0.937396i | \(-0.613229\pi\) | ||||
−0.348265 | + | 0.937396i | \(0.613229\pi\) | |||||||
\(488\) | 18.0374 | 0.816517 | ||||||||
\(489\) | 44.0994 | 1.99424 | ||||||||
\(490\) | −14.3025 | −0.646120 | ||||||||
\(491\) | 14.5101 | 0.654834 | 0.327417 | − | 0.944880i | \(-0.393822\pi\) | ||||
0.327417 | + | 0.944880i | \(0.393822\pi\) | |||||||
\(492\) | −7.04321 | −0.317532 | ||||||||
\(493\) | −34.2979 | −1.54470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.14460 | −0.276179 | ||||||||
\(496\) | 7.32612 | 0.328952 | ||||||||
\(497\) | −13.3199 | −0.597479 | ||||||||
\(498\) | −5.80872 | −0.260295 | ||||||||
\(499\) | −14.7379 | −0.659761 | −0.329880 | − | 0.944023i | \(-0.607008\pi\) | ||||
−0.329880 | + | 0.944023i | \(0.607008\pi\) | |||||||
\(500\) | −0.466387 | −0.0208574 | ||||||||
\(501\) | 21.4556 | 0.958565 | ||||||||
\(502\) | −19.7008 | −0.879289 | ||||||||
\(503\) | 4.35253 | 0.194070 | 0.0970348 | − | 0.995281i | \(-0.469064\pi\) | ||||
0.0970348 | + | 0.995281i | \(0.469064\pi\) | |||||||
\(504\) | 21.4716 | 0.956422 | ||||||||
\(505\) | 6.98240 | 0.310713 | ||||||||
\(506\) | 5.94060 | 0.264092 | ||||||||
\(507\) | 11.9525 | 0.530830 | ||||||||
\(508\) | 3.87009 | 0.171707 | ||||||||
\(509\) | −8.59364 | −0.380906 | −0.190453 | − | 0.981696i | \(-0.560996\pi\) | ||||
−0.190453 | + | 0.981696i | \(0.560996\pi\) | |||||||
\(510\) | −12.9430 | −0.573125 | ||||||||
\(511\) | 40.1647 | 1.77678 | ||||||||
\(512\) | −10.5094 | −0.464455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5058 | −0.595715 | ||||||||
\(515\) | 10.1338 | 0.446547 | ||||||||
\(516\) | 6.66571 | 0.293442 | ||||||||
\(517\) | 25.1998 | 1.10828 | ||||||||
\(518\) | 53.6491 | 2.35721 | ||||||||
\(519\) | 18.9904 | 0.833587 | ||||||||
\(520\) | −6.71327 | −0.294396 | ||||||||
\(521\) | −2.06951 | −0.0906668 | −0.0453334 | − | 0.998972i | \(-0.514435\pi\) | ||||
−0.0453334 | + | 0.998972i | \(0.514435\pi\) | |||||||
\(522\) | 33.1737 | 1.45197 | ||||||||
\(523\) | −14.0120 | −0.612702 | −0.306351 | − | 0.951919i | \(-0.599108\pi\) | ||||
−0.306351 | + | 0.951919i | \(0.599108\pi\) | |||||||
\(524\) | −3.03704 | −0.132674 | ||||||||
\(525\) | 9.17062 | 0.400239 | ||||||||
\(526\) | 41.9164 | 1.82764 | ||||||||
\(527\) | 5.60380 | 0.244105 | ||||||||
\(528\) | 29.8043 | 1.29707 | ||||||||
\(529\) | −21.1300 | −0.918698 | ||||||||
\(530\) | −6.19482 | −0.269086 | ||||||||
\(531\) | −8.02299 | −0.348168 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.4214 | −0.797919 | ||||||||
\(534\) | −43.9634 | −1.90248 | ||||||||
\(535\) | −11.7835 | −0.509446 | ||||||||
\(536\) | −35.0966 | −1.51594 | ||||||||
\(537\) | −42.3457 | −1.82735 | ||||||||
\(538\) | 5.18759 | 0.223653 | ||||||||
\(539\) | 25.1921 | 1.08510 | ||||||||
\(540\) | −0.829849 | −0.0357110 | ||||||||
\(541\) | −16.6193 | −0.714520 | −0.357260 | − | 0.934005i | \(-0.616289\pi\) | ||||
−0.357260 | + | 0.934005i | \(0.616289\pi\) | |||||||
\(542\) | −28.8771 | −1.24038 | ||||||||
\(543\) | 25.8875 | 1.11094 | ||||||||
\(544\) | 9.33490 | 0.400230 | ||||||||
\(545\) | −1.60407 | −0.0687110 | ||||||||
\(546\) | −40.1436 | −1.71799 | ||||||||
\(547\) | 6.03456 | 0.258019 | 0.129010 | − | 0.991643i | \(-0.458820\pi\) | ||||
0.129010 | + | 0.991643i | \(0.458820\pi\) | |||||||
\(548\) | 6.93453 | 0.296228 | ||||||||
\(549\) | −16.6356 | −0.709990 | ||||||||
\(550\) | 4.34425 | 0.185239 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 7.52578 | 0.320319 | ||||||||
\(553\) | −7.81545 | −0.332347 | ||||||||
\(554\) | 42.0552 | 1.78676 | ||||||||
\(555\) | −19.4497 | −0.825594 | ||||||||
\(556\) | 4.64439 | 0.196966 | ||||||||
\(557\) | −28.1274 | −1.19180 | −0.595898 | − | 0.803060i | \(-0.703204\pi\) | ||||
−0.595898 | + | 0.803060i | \(0.703204\pi\) | |||||||
\(558\) | −5.42012 | −0.229452 | ||||||||
\(559\) | 17.4341 | 0.737382 | ||||||||
\(560\) | −18.9241 | −0.799687 | ||||||||
\(561\) | 22.7975 | 0.962512 | ||||||||
\(562\) | −33.8377 | −1.42736 | ||||||||
\(563\) | 1.21155 | 0.0510609 | 0.0255305 | − | 0.999674i | \(-0.491873\pi\) | ||||
0.0255305 | + | 0.999674i | \(0.491873\pi\) | |||||||
\(564\) | −9.70842 | −0.408798 | ||||||||
\(565\) | 12.9449 | 0.544595 | ||||||||
\(566\) | 28.8136 | 1.21113 | ||||||||
\(567\) | 43.0623 | 1.80844 | ||||||||
\(568\) | −7.99353 | −0.335401 | ||||||||
\(569\) | 17.5814 | 0.737049 | 0.368524 | − | 0.929618i | \(-0.379863\pi\) | ||||
0.368524 | + | 0.929618i | \(0.379863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.6982 | 1.78686 | 0.893432 | − | 0.449198i | \(-0.148290\pi\) | ||||
0.893432 | + | 0.449198i | \(0.148290\pi\) | |||||||
\(572\) | −3.59598 | −0.150356 | ||||||||
\(573\) | −27.1640 | −1.13479 | ||||||||
\(574\) | −41.6557 | −1.73867 | ||||||||
\(575\) | 1.36746 | 0.0570271 | ||||||||
\(576\) | 11.9192 | 0.496633 | ||||||||
\(577\) | 5.49356 | 0.228700 | 0.114350 | − | 0.993441i | \(-0.463521\pi\) | ||||
0.114350 | + | 0.993441i | \(0.463521\pi\) | |||||||
\(578\) | −6.26852 | −0.260736 | ||||||||
\(579\) | −2.18867 | −0.0909579 | ||||||||
\(580\) | −4.43506 | −0.184156 | ||||||||
\(581\) | −6.49635 | −0.269514 | ||||||||
\(582\) | −41.5956 | −1.72419 | ||||||||
\(583\) | 10.9114 | 0.451906 | ||||||||
\(584\) | 24.1036 | 0.997415 | ||||||||
\(585\) | 6.19152 | 0.255988 | ||||||||
\(586\) | 14.5877 | 0.602611 | ||||||||
\(587\) | −12.4236 | −0.512778 | −0.256389 | − | 0.966574i | \(-0.582533\pi\) | ||||
−0.256389 | + | 0.966574i | \(0.582533\pi\) | |||||||
\(588\) | −9.70547 | −0.400247 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.67228 | 0.233524 | ||||||||
\(591\) | −32.6247 | −1.34200 | ||||||||
\(592\) | 40.1355 | 1.64956 | ||||||||
\(593\) | −1.11776 | −0.0459009 | −0.0229505 | − | 0.999737i | \(-0.507306\pi\) | ||||
−0.0229505 | + | 0.999737i | \(0.507306\pi\) | |||||||
\(594\) | 7.72979 | 0.317157 | ||||||||
\(595\) | −14.4751 | −0.593423 | ||||||||
\(596\) | −0.667690 | −0.0273497 | ||||||||
\(597\) | 17.7448 | 0.726246 | ||||||||
\(598\) | −5.98596 | −0.244784 | ||||||||
\(599\) | 27.5096 | 1.12401 | 0.562007 | − | 0.827133i | \(-0.310030\pi\) | ||||
0.562007 | + | 0.827133i | \(0.310030\pi\) | |||||||
\(600\) | 5.50347 | 0.224678 | ||||||||
\(601\) | −14.0537 | −0.573263 | −0.286631 | − | 0.958041i | \(-0.592536\pi\) | ||||
−0.286631 | + | 0.958041i | \(0.592536\pi\) | |||||||
\(602\) | 39.4230 | 1.60676 | ||||||||
\(603\) | 32.3689 | 1.31816 | ||||||||
\(604\) | 3.81683 | 0.155305 | ||||||||
\(605\) | 3.34812 | 0.136121 | ||||||||
\(606\) | 25.0568 | 1.01786 | ||||||||
\(607\) | 16.1942 | 0.657304 | 0.328652 | − | 0.944451i | \(-0.393406\pi\) | ||||
0.328652 | + | 0.944451i | \(0.393406\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 87.2071 | 3.53381 | ||||||||
\(610\) | 11.7614 | 0.476205 | ||||||||
\(611\) | −25.3922 | −1.02726 | ||||||||
\(612\) | −3.73654 | −0.151041 | ||||||||
\(613\) | 27.6779 | 1.11790 | 0.558949 | − | 0.829202i | \(-0.311205\pi\) | ||||
0.558949 | + | 0.829202i | \(0.311205\pi\) | |||||||
\(614\) | 17.2990 | 0.698129 | ||||||||
\(615\) | 15.1017 | 0.608958 | ||||||||
\(616\) | 26.7386 | 1.07733 | ||||||||
\(617\) | 6.09559 | 0.245399 | 0.122700 | − | 0.992444i | \(-0.460845\pi\) | ||||
0.122700 | + | 0.992444i | \(0.460845\pi\) | |||||||
\(618\) | 36.3656 | 1.46284 | ||||||||
\(619\) | −11.7187 | −0.471014 | −0.235507 | − | 0.971873i | \(-0.575675\pi\) | ||||
−0.235507 | + | 0.971873i | \(0.575675\pi\) | |||||||
\(620\) | 0.724627 | 0.0291017 | ||||||||
\(621\) | 2.43315 | 0.0976389 | ||||||||
\(622\) | 39.8619 | 1.59832 | ||||||||
\(623\) | −49.1677 | −1.96986 | ||||||||
\(624\) | −30.0319 | −1.20224 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 33.0677 | 1.32165 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.65419 | −0.145818 | ||||||||
\(629\) | 30.6999 | 1.22409 | ||||||||
\(630\) | 14.0007 | 0.557800 | ||||||||
\(631\) | 20.9211 | 0.832856 | 0.416428 | − | 0.909169i | \(-0.363282\pi\) | ||||
0.416428 | + | 0.909169i | \(0.363282\pi\) | |||||||
\(632\) | −4.69020 | −0.186566 | ||||||||
\(633\) | 17.4181 | 0.692308 | ||||||||
\(634\) | −6.29738 | −0.250101 | ||||||||
\(635\) | −8.29802 | −0.329297 | ||||||||
\(636\) | −4.20372 | −0.166689 | ||||||||
\(637\) | −25.3845 | −1.00577 | ||||||||
\(638\) | 41.3112 | 1.63553 | ||||||||
\(639\) | 7.37228 | 0.291643 | ||||||||
\(640\) | −13.6033 | −0.537717 | ||||||||
\(641\) | 9.48683 | 0.374707 | 0.187354 | − | 0.982293i | \(-0.440009\pi\) | ||||
0.187354 | + | 0.982293i | \(0.440009\pi\) | |||||||
\(642\) | −42.2859 | −1.66889 | ||||||||
\(643\) | 12.5393 | 0.494500 | 0.247250 | − | 0.968952i | \(-0.420473\pi\) | ||||
0.247250 | + | 0.968952i | \(0.420473\pi\) | |||||||
\(644\) | −2.55959 | −0.100862 | ||||||||
\(645\) | −14.2923 | −0.562757 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.6504 | −0.615281 | −0.307640 | − | 0.951503i | \(-0.599539\pi\) | ||||
−0.307640 | + | 0.951503i | \(0.599539\pi\) | |||||||
\(648\) | 25.8425 | 1.01519 | ||||||||
\(649\) | −9.99104 | −0.392183 | ||||||||
\(650\) | −4.37742 | −0.171696 | ||||||||
\(651\) | −14.2484 | −0.558440 | ||||||||
\(652\) | −9.00096 | −0.352505 | ||||||||
\(653\) | 19.0906 | 0.747071 | 0.373536 | − | 0.927616i | \(-0.378145\pi\) | ||||
0.373536 | + | 0.927616i | \(0.378145\pi\) | |||||||
\(654\) | −5.75632 | −0.225090 | ||||||||
\(655\) | 6.51185 | 0.254439 | ||||||||
\(656\) | −31.1631 | −1.21671 | ||||||||
\(657\) | −22.2303 | −0.867287 | ||||||||
\(658\) | −57.4185 | −2.23841 | ||||||||
\(659\) | 10.4682 | 0.407783 | 0.203891 | − | 0.978994i | \(-0.434641\pi\) | ||||
0.203891 | + | 0.978994i | \(0.434641\pi\) | |||||||
\(660\) | 2.94795 | 0.114749 | ||||||||
\(661\) | 29.1420 | 1.13349 | 0.566745 | − | 0.823893i | \(-0.308202\pi\) | ||||
0.566745 | + | 0.823893i | \(0.308202\pi\) | |||||||
\(662\) | 50.4687 | 1.96152 | ||||||||
\(663\) | −22.9716 | −0.892143 | ||||||||
\(664\) | −3.89858 | −0.151294 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −29.6936 | −1.15060 | ||||||||
\(667\) | 13.0038 | 0.503507 | ||||||||
\(668\) | −4.37922 | −0.169437 | ||||||||
\(669\) | −18.2877 | −0.707044 | ||||||||
\(670\) | −22.8849 | −0.884120 | ||||||||
\(671\) | −20.7163 | −0.799745 | ||||||||
\(672\) | −23.7353 | −0.915608 | ||||||||
\(673\) | 14.5550 | 0.561052 | 0.280526 | − | 0.959846i | \(-0.409491\pi\) | ||||
0.280526 | + | 0.959846i | \(0.409491\pi\) | |||||||
\(674\) | −36.8239 | −1.41840 | ||||||||
\(675\) | 1.77932 | 0.0684859 | ||||||||
\(676\) | −2.43959 | −0.0938302 | ||||||||
\(677\) | 10.9800 | 0.421995 | 0.210998 | − | 0.977487i | \(-0.432329\pi\) | ||||
0.210998 | + | 0.977487i | \(0.432329\pi\) | |||||||
\(678\) | 46.4535 | 1.78404 | ||||||||
\(679\) | −46.5196 | −1.78526 | ||||||||
\(680\) | −8.68681 | −0.333124 | ||||||||
\(681\) | −40.5383 | −1.55343 | ||||||||
\(682\) | −6.74968 | −0.258459 | ||||||||
\(683\) | 43.3449 | 1.65854 | 0.829272 | − | 0.558844i | \(-0.188755\pi\) | ||||
0.829272 | + | 0.558844i | \(0.188755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8686 | −0.568101 | ||||||||
\(686\) | −13.2809 | −0.507066 | ||||||||
\(687\) | 55.3503 | 2.11174 | ||||||||
\(688\) | 29.4928 | 1.12440 | ||||||||
\(689\) | −10.9948 | −0.418867 | ||||||||
\(690\) | 4.90722 | 0.186815 | ||||||||
\(691\) | 30.4057 | 1.15669 | 0.578344 | − | 0.815793i | \(-0.303699\pi\) | ||||
0.578344 | + | 0.815793i | \(0.303699\pi\) | |||||||
\(692\) | −3.87606 | −0.147346 | ||||||||
\(693\) | −24.6605 | −0.936776 | ||||||||
\(694\) | 10.1979 | 0.387107 | ||||||||
\(695\) | −9.95823 | −0.377737 | ||||||||
\(696\) | 52.3347 | 1.98374 | ||||||||
\(697\) | −23.8368 | −0.902885 | ||||||||
\(698\) | −42.7181 | −1.61691 | ||||||||
\(699\) | −31.1885 | −1.17966 | ||||||||
\(700\) | −1.87178 | −0.0707466 | ||||||||
\(701\) | 21.3688 | 0.807088 | 0.403544 | − | 0.914960i | \(-0.367778\pi\) | ||||
0.403544 | + | 0.914960i | \(0.367778\pi\) | |||||||
\(702\) | −7.78881 | −0.293970 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 14.8430 | 0.559416 | ||||||||
\(705\) | 20.8163 | 0.783985 | ||||||||
\(706\) | −10.3043 | −0.387806 | ||||||||
\(707\) | 28.0229 | 1.05391 | ||||||||
\(708\) | 3.84913 | 0.144659 | ||||||||
\(709\) | −20.0113 | −0.751541 | −0.375770 | − | 0.926713i | \(-0.622622\pi\) | ||||
−0.375770 | + | 0.926713i | \(0.622622\pi\) | |||||||
\(710\) | −5.21222 | −0.195611 | ||||||||
\(711\) | 4.32568 | 0.162226 | ||||||||
\(712\) | −29.5065 | −1.10580 | ||||||||
\(713\) | −2.12463 | −0.0795682 | ||||||||
\(714\) | −51.9449 | −1.94399 | ||||||||
\(715\) | 7.71030 | 0.288349 | ||||||||
\(716\) | 8.64301 | 0.323005 | ||||||||
\(717\) | −8.54058 | −0.318954 | ||||||||
\(718\) | −4.29045 | −0.160118 | ||||||||
\(719\) | −4.10144 | −0.152958 | −0.0764790 | − | 0.997071i | \(-0.524368\pi\) | ||||
−0.0764790 | + | 0.997071i | \(0.524368\pi\) | |||||||
\(720\) | 10.4741 | 0.390345 | ||||||||
\(721\) | 40.6705 | 1.51465 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.0682 | −0.448822 | ||||||||
\(724\) | −5.28379 | −0.196371 | ||||||||
\(725\) | 9.50940 | 0.353170 | ||||||||
\(726\) | 12.0149 | 0.445917 | ||||||||
\(727\) | −35.7495 | −1.32588 | −0.662938 | − | 0.748674i | \(-0.730691\pi\) | ||||
−0.662938 | + | 0.748674i | \(0.730691\pi\) | |||||||
\(728\) | −26.9428 | −0.998567 | ||||||||
\(729\) | −11.6367 | −0.430990 | ||||||||
\(730\) | 15.7169 | 0.581708 | ||||||||
\(731\) | 22.5593 | 0.834384 | ||||||||
\(732\) | 7.98113 | 0.294991 | ||||||||
\(733\) | −31.2944 | −1.15589 | −0.577943 | − | 0.816077i | \(-0.696145\pi\) | ||||
−0.577943 | + | 0.816077i | \(0.696145\pi\) | |||||||
\(734\) | 10.3322 | 0.381368 | ||||||||
\(735\) | 20.8099 | 0.767586 | ||||||||
\(736\) | −3.53925 | −0.130458 | ||||||||
\(737\) | 40.3090 | 1.48480 | ||||||||
\(738\) | 23.0555 | 0.848686 | ||||||||
\(739\) | 32.5127 | 1.19600 | 0.597999 | − | 0.801497i | \(-0.295963\pi\) | ||||
0.597999 | + | 0.801497i | \(0.295963\pi\) | |||||||
\(740\) | 3.96980 | 0.145933 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.8621 | −0.912716 | ||||||||
\(743\) | −38.8471 | −1.42516 | −0.712580 | − | 0.701590i | \(-0.752474\pi\) | ||||
−0.712580 | + | 0.701590i | \(0.752474\pi\) | |||||||
\(744\) | −8.55076 | −0.313486 | ||||||||
\(745\) | 1.43162 | 0.0524506 | ||||||||
\(746\) | 13.4431 | 0.492188 | ||||||||
\(747\) | 3.59559 | 0.131556 | ||||||||
\(748\) | −4.65312 | −0.170135 | ||||||||
\(749\) | −47.2916 | −1.72800 | ||||||||
\(750\) | 3.58856 | 0.131036 | ||||||||
\(751\) | 1.80781 | 0.0659681 | 0.0329840 | − | 0.999456i | \(-0.489499\pi\) | ||||
0.0329840 | + | 0.999456i | \(0.489499\pi\) | |||||||
\(752\) | −42.9554 | −1.56642 | ||||||||
\(753\) | 28.6644 | 1.04459 | ||||||||
\(754\) | −41.6266 | −1.51595 | ||||||||
\(755\) | −8.18383 | −0.297840 | ||||||||
\(756\) | −3.33049 | −0.121129 | ||||||||
\(757\) | 22.5632 | 0.820074 | 0.410037 | − | 0.912069i | \(-0.365516\pi\) | ||||
0.410037 | + | 0.912069i | \(0.365516\pi\) | |||||||
\(758\) | −22.3757 | −0.812721 | ||||||||
\(759\) | −8.64349 | −0.313739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.85080 | 0.103341 | 0.0516707 | − | 0.998664i | \(-0.483545\pi\) | ||||
0.0516707 | + | 0.998664i | \(0.483545\pi\) | |||||||
\(762\) | −29.7780 | −1.07874 | ||||||||
\(763\) | −6.43774 | −0.233062 | ||||||||
\(764\) | 5.54434 | 0.200587 | ||||||||
\(765\) | 8.01168 | 0.289663 | ||||||||
\(766\) | −33.5553 | −1.21240 | ||||||||
\(767\) | 10.0673 | 0.363510 | ||||||||
\(768\) | −24.2941 | −0.876639 | ||||||||
\(769\) | 6.11973 | 0.220683 | 0.110342 | − | 0.993894i | \(-0.464806\pi\) | ||||
0.110342 | + | 0.993894i | \(0.464806\pi\) | |||||||
\(770\) | 17.4351 | 0.628316 | ||||||||
\(771\) | 19.6508 | 0.707705 | ||||||||
\(772\) | 0.446721 | 0.0160778 | ||||||||
\(773\) | −50.1577 | −1.80405 | −0.902023 | − | 0.431688i | \(-0.857918\pi\) | ||||
−0.902023 | + | 0.431688i | \(0.857918\pi\) | |||||||
\(774\) | −21.8198 | −0.784297 | ||||||||
\(775\) | −1.55371 | −0.0558107 | ||||||||
\(776\) | −27.9173 | −1.00217 | ||||||||
\(777\) | −78.0588 | −2.80034 | ||||||||
\(778\) | 24.0167 | 0.861039 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.97046 | −0.106359 | ||||||||
\(781\) | 9.18070 | 0.328511 | ||||||||
\(782\) | −7.74569 | −0.276985 | ||||||||
\(783\) | 16.9202 | 0.604680 | ||||||||
\(784\) | −42.9424 | −1.53366 | ||||||||
\(785\) | 7.83512 | 0.279647 | ||||||||
\(786\) | 23.3682 | 0.833515 | ||||||||
\(787\) | 33.0203 | 1.17705 | 0.588524 | − | 0.808480i | \(-0.299709\pi\) | ||||
0.588524 | + | 0.808480i | \(0.299709\pi\) | |||||||
\(788\) | 6.65889 | 0.237213 | ||||||||
\(789\) | −60.9879 | −2.17123 | ||||||||
\(790\) | −3.05827 | −0.108808 | ||||||||
\(791\) | 51.9525 | 1.84722 | ||||||||
\(792\) | −14.7993 | −0.525869 | ||||||||
\(793\) | 20.8745 | 0.741275 | ||||||||
\(794\) | 51.2006 | 1.81704 | ||||||||
\(795\) | 9.01339 | 0.319672 | ||||||||
\(796\) | −3.62182 | −0.128372 | ||||||||
\(797\) | −47.2358 | −1.67318 | −0.836590 | − | 0.547830i | \(-0.815454\pi\) | ||||
−0.836590 | + | 0.547830i | \(0.815454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.8569 | −1.16239 | ||||||||
\(800\) | −2.58819 | −0.0915062 | ||||||||
\(801\) | 27.2132 | 0.961533 | ||||||||
\(802\) | 27.1879 | 0.960039 | ||||||||
\(803\) | −27.6834 | −0.976927 | ||||||||
\(804\) | −15.5294 | −0.547679 | ||||||||
\(805\) | 5.48813 | 0.193431 | ||||||||
\(806\) | 6.80122 | 0.239563 | ||||||||
\(807\) | −7.54788 | −0.265698 | ||||||||
\(808\) | 16.8171 | 0.591623 | ||||||||
\(809\) | 4.38236 | 0.154076 | 0.0770378 | − | 0.997028i | \(-0.475454\pi\) | ||||
0.0770378 | + | 0.997028i | \(0.475454\pi\) | |||||||
\(810\) | 16.8507 | 0.592074 | ||||||||
\(811\) | 33.9613 | 1.19254 | 0.596271 | − | 0.802783i | \(-0.296649\pi\) | ||||
0.596271 | + | 0.802783i | \(0.296649\pi\) | |||||||
\(812\) | −17.7995 | −0.624640 | ||||||||
\(813\) | 42.0159 | 1.47356 | ||||||||
\(814\) | −36.9775 | −1.29606 | ||||||||
\(815\) | 19.2994 | 0.676027 | ||||||||
\(816\) | −38.8606 | −1.36039 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.0038 | 0.594525 | ||||||||
\(819\) | 24.8488 | 0.868288 | ||||||||
\(820\) | −3.08234 | −0.107640 | ||||||||
\(821\) | 40.1364 | 1.40077 | 0.700385 | − | 0.713766i | \(-0.253012\pi\) | ||||
0.700385 | + | 0.713766i | \(0.253012\pi\) | |||||||
\(822\) | −53.3570 | −1.86104 | ||||||||
\(823\) | 6.31582 | 0.220156 | 0.110078 | − | 0.993923i | \(-0.464890\pi\) | ||||
0.110078 | + | 0.993923i | \(0.464890\pi\) | |||||||
\(824\) | 24.4072 | 0.850264 | ||||||||
\(825\) | −6.32083 | −0.220063 | ||||||||
\(826\) | 22.7649 | 0.792093 | ||||||||
\(827\) | −21.3614 | −0.742808 | −0.371404 | − | 0.928471i | \(-0.621123\pi\) | ||||
−0.371404 | + | 0.928471i | \(0.621123\pi\) | |||||||
\(828\) | 1.41668 | 0.0492330 | ||||||||
\(829\) | −49.0602 | −1.70393 | −0.851966 | − | 0.523597i | \(-0.824590\pi\) | ||||
−0.851966 | + | 0.523597i | \(0.824590\pi\) | |||||||
\(830\) | −2.54209 | −0.0882372 | ||||||||
\(831\) | −61.1898 | −2.12265 | ||||||||
\(832\) | −14.9563 | −0.518517 | ||||||||
\(833\) | −32.8469 | −1.13808 | ||||||||
\(834\) | −35.7357 | −1.23743 | ||||||||
\(835\) | 9.38968 | 0.324943 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.76453 | −0.0955562 | ||||||||
\(838\) | 53.3588 | 1.84325 | ||||||||
\(839\) | 7.38997 | 0.255130 | 0.127565 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127565 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(840\) | 22.0874 | 0.762089 | ||||||||
\(841\) | 61.4287 | 2.11823 | ||||||||
\(842\) | −13.0479 | −0.449660 | ||||||||
\(843\) | 49.2334 | 1.69569 | ||||||||
\(844\) | −3.55514 | −0.122373 | ||||||||
\(845\) | 5.23082 | 0.179946 | ||||||||
\(846\) | 31.7799 | 1.09262 | ||||||||
\(847\) | 13.4372 | 0.461709 | ||||||||
\(848\) | −18.5996 | −0.638713 | ||||||||
\(849\) | −41.9235 | −1.43881 | ||||||||
\(850\) | −5.66428 | −0.194283 | ||||||||
\(851\) | −11.6396 | −0.399001 | ||||||||
\(852\) | −3.53694 | −0.121174 | ||||||||
\(853\) | 2.75310 | 0.0942642 | 0.0471321 | − | 0.998889i | \(-0.484992\pi\) | ||||
0.0471321 | + | 0.998889i | \(0.484992\pi\) | |||||||
\(854\) | 47.2028 | 1.61525 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.3806 | −0.970029 | ||||||||
\(857\) | 44.1261 | 1.50732 | 0.753659 | − | 0.657266i | \(-0.228287\pi\) | ||||
0.753659 | + | 0.657266i | \(0.228287\pi\) | |||||||
\(858\) | 27.6689 | 0.944601 | ||||||||
\(859\) | −11.7531 | −0.401010 | −0.200505 | − | 0.979693i | \(-0.564258\pi\) | ||||
−0.200505 | + | 0.979693i | \(0.564258\pi\) | |||||||
\(860\) | 2.91714 | 0.0994736 | ||||||||
\(861\) | 60.6085 | 2.06553 | ||||||||
\(862\) | 19.0495 | 0.648828 | ||||||||
\(863\) | 34.2831 | 1.16701 | 0.583504 | − | 0.812110i | \(-0.301681\pi\) | ||||
0.583504 | + | 0.812110i | \(0.301681\pi\) | |||||||
\(864\) | −4.60520 | −0.156672 | ||||||||
\(865\) | 8.31084 | 0.282577 | ||||||||
\(866\) | 8.53617 | 0.290071 | ||||||||
\(867\) | 9.12061 | 0.309752 | ||||||||
\(868\) | 2.90820 | 0.0987106 | ||||||||
\(869\) | 5.38678 | 0.182734 | ||||||||
\(870\) | 34.1251 | 1.15695 | ||||||||
\(871\) | −40.6168 | −1.37625 | ||||||||
\(872\) | −3.86341 | −0.130832 | ||||||||
\(873\) | 25.7476 | 0.871423 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.01337 | 0.135677 | ||||||||
\(876\) | 10.6653 | 0.360346 | ||||||||
\(877\) | 24.2041 | 0.817313 | 0.408656 | − | 0.912688i | \(-0.365997\pi\) | ||||
0.408656 | + | 0.912688i | \(0.365997\pi\) | |||||||
\(878\) | 39.8597 | 1.34520 | ||||||||
\(879\) | −21.2249 | −0.715898 | ||||||||
\(880\) | 13.0434 | 0.439691 | ||||||||
\(881\) | −39.1733 | −1.31978 | −0.659892 | − | 0.751361i | \(-0.729398\pi\) | ||||
−0.659892 | + | 0.751361i | \(0.729398\pi\) | |||||||
\(882\) | 31.7703 | 1.06976 | ||||||||
\(883\) | 32.3695 | 1.08932 | 0.544660 | − | 0.838657i | \(-0.316659\pi\) | ||||
0.544660 | + | 0.838657i | \(0.316659\pi\) | |||||||
\(884\) | 4.68865 | 0.157696 | ||||||||
\(885\) | −8.25309 | −0.277425 | ||||||||
\(886\) | −7.72870 | −0.259651 | ||||||||
\(887\) | −0.380819 | −0.0127866 | −0.00639332 | − | 0.999980i | \(-0.502035\pi\) | ||||
−0.00639332 | + | 0.999980i | \(0.502035\pi\) | |||||||
\(888\) | −46.8446 | −1.57200 | ||||||||
\(889\) | −33.3030 | −1.11695 | ||||||||
\(890\) | −19.2398 | −0.644921 | ||||||||
\(891\) | −29.6805 | −0.994336 | ||||||||
\(892\) | 3.73264 | 0.124978 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 5.13747 | 0.171823 | ||||||||
\(895\) | −18.5319 | −0.619452 | ||||||||
\(896\) | −54.5949 | −1.82389 | ||||||||
\(897\) | 8.70949 | 0.290801 | ||||||||
\(898\) | −6.38632 | −0.213114 | ||||||||
\(899\) | −14.7748 | −0.492767 | ||||||||
\(900\) | 1.03599 | 0.0345330 | ||||||||
\(901\) | −14.2270 | −0.473969 | ||||||||
\(902\) | 28.7111 | 0.955974 | ||||||||
\(903\) | −57.3600 | −1.90882 | ||||||||
\(904\) | 31.1777 | 1.03696 | ||||||||
\(905\) | 11.3292 | 0.376596 | ||||||||
\(906\) | −29.3682 | −0.975692 | ||||||||
\(907\) | 4.92616 | 0.163571 | 0.0817853 | − | 0.996650i | \(-0.473938\pi\) | ||||
0.0817853 | + | 0.996650i | \(0.473938\pi\) | |||||||
\(908\) | 8.27411 | 0.274586 | ||||||||
\(909\) | −15.5101 | −0.514437 | ||||||||
\(910\) | −17.5682 | −0.582380 | ||||||||
\(911\) | −20.6775 | −0.685075 | −0.342537 | − | 0.939504i | \(-0.611286\pi\) | ||||
−0.342537 | + | 0.939504i | \(0.611286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.47759 | 0.148187 | ||||||||
\(914\) | −21.2826 | −0.703965 | ||||||||
\(915\) | −17.1127 | −0.565728 | ||||||||
\(916\) | −11.2973 | −0.373274 | ||||||||
\(917\) | 26.1344 | 0.863035 | ||||||||
\(918\) | −10.0785 | −0.332641 | ||||||||
\(919\) | −60.5868 | −1.99857 | −0.999287 | − | 0.0377591i | \(-0.987978\pi\) | ||||
−0.999287 | + | 0.0377591i | \(0.987978\pi\) | |||||||
\(920\) | 3.29353 | 0.108585 | ||||||||
\(921\) | −25.1698 | −0.829372 | ||||||||
\(922\) | 28.0820 | 0.924831 | ||||||||
\(923\) | −9.25080 | −0.304494 | ||||||||
\(924\) | 11.8312 | 0.389218 | ||||||||
\(925\) | −8.51183 | −0.279867 | ||||||||
\(926\) | 2.05254 | 0.0674505 | ||||||||
\(927\) | −22.5103 | −0.739334 | ||||||||
\(928\) | −24.6121 | −0.807932 | ||||||||
\(929\) | −0.290620 | −0.00953494 | −0.00476747 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476747 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(930\) | −5.57557 | −0.182830 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.36576 | 0.208517 | ||||||||
\(933\) | −57.9986 | −1.89879 | ||||||||
\(934\) | 42.4446 | 1.38883 | ||||||||
\(935\) | 9.97695 | 0.326281 | ||||||||
\(936\) | 14.9123 | 0.487423 | ||||||||
\(937\) | 5.30585 | 0.173335 | 0.0866673 | − | 0.996237i | \(-0.472378\pi\) | ||||
0.0866673 | + | 0.996237i | \(0.472378\pi\) | |||||||
\(938\) | −91.8454 | −2.99886 | ||||||||
\(939\) | −48.1131 | −1.57011 | ||||||||
\(940\) | −4.24873 | −0.138578 | ||||||||
\(941\) | 28.4255 | 0.926646 | 0.463323 | − | 0.886189i | \(-0.346657\pi\) | ||||
0.463323 | + | 0.886189i | \(0.346657\pi\) | |||||||
\(942\) | 28.1168 | 0.916095 | ||||||||
\(943\) | 9.03754 | 0.294303 | ||||||||
\(944\) | 17.0307 | 0.554302 | ||||||||
\(945\) | 7.14105 | 0.232298 | ||||||||
\(946\) | −27.1722 | −0.883446 | ||||||||
\(947\) | −49.9790 | −1.62410 | −0.812049 | − | 0.583589i | \(-0.801648\pi\) | ||||
−0.812049 | + | 0.583589i | \(0.801648\pi\) | |||||||
\(948\) | −2.07530 | −0.0674026 | ||||||||
\(949\) | 27.8948 | 0.905504 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.16261 | 0.297118 | ||||||||
\(952\) | −34.8634 | −1.12993 | ||||||||
\(953\) | 12.1003 | 0.391966 | 0.195983 | − | 0.980607i | \(-0.437210\pi\) | ||||
0.195983 | + | 0.980607i | \(0.437210\pi\) | |||||||
\(954\) | 13.7606 | 0.445517 | ||||||||
\(955\) | −11.8879 | −0.384682 | ||||||||
\(956\) | 1.74319 | 0.0563787 | ||||||||
\(957\) | −60.1073 | −1.94299 | ||||||||
\(958\) | 0.454611 | 0.0146878 | ||||||||
\(959\) | −59.6732 | −1.92695 | ||||||||
\(960\) | 12.2610 | 0.395723 | ||||||||
\(961\) | −28.5860 | −0.922129 | ||||||||
\(962\) | 37.2599 | 1.20131 | ||||||||
\(963\) | 26.1749 | 0.843474 | ||||||||
\(964\) | 2.46320 | 0.0793344 | ||||||||
\(965\) | −0.957834 | −0.0308338 | ||||||||
\(966\) | 19.6945 | 0.633660 | ||||||||
\(967\) | 13.1688 | 0.423480 | 0.211740 | − | 0.977326i | \(-0.432087\pi\) | ||||
0.211740 | + | 0.977326i | \(0.432087\pi\) | |||||||
\(968\) | 8.06395 | 0.259185 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.2036 | −0.584482 | ||||||||
\(971\) | 17.5135 | 0.562035 | 0.281018 | − | 0.959703i | \(-0.409328\pi\) | ||||
0.281018 | + | 0.959703i | \(0.409328\pi\) | |||||||
\(972\) | 8.94513 | 0.286915 | ||||||||
\(973\) | −39.9660 | −1.28125 | ||||||||
\(974\) | −24.1399 | −0.773491 | ||||||||
\(975\) | 6.36909 | 0.203974 | ||||||||
\(976\) | 35.3129 | 1.13034 | ||||||||
\(977\) | 10.5361 | 0.337081 | 0.168541 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168541 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(978\) | 69.2569 | 2.21459 | ||||||||
\(979\) | 33.8887 | 1.08309 | ||||||||
\(980\) | −4.24743 | −0.135679 | ||||||||
\(981\) | 3.56315 | 0.113763 | ||||||||
\(982\) | 22.7878 | 0.727188 | ||||||||
\(983\) | −51.9781 | −1.65784 | −0.828922 | − | 0.559364i | \(-0.811046\pi\) | ||||
−0.828922 | + | 0.559364i | \(0.811046\pi\) | |||||||
\(984\) | 36.3723 | 1.15951 | ||||||||
\(985\) | −14.2776 | −0.454923 | ||||||||
\(986\) | −53.8639 | −1.71538 | ||||||||
\(987\) | 83.5433 | 2.65921 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.55315 | −0.271974 | ||||||||
\(990\) | −9.64993 | −0.306695 | ||||||||
\(991\) | −6.77628 | −0.215256 | −0.107628 | − | 0.994191i | \(-0.534326\pi\) | ||||
−0.107628 | + | 0.994191i | \(0.534326\pi\) | |||||||
\(992\) | 4.02128 | 0.127676 | ||||||||
\(993\) | −73.4313 | −2.33027 | ||||||||
\(994\) | −20.9185 | −0.663496 | ||||||||
\(995\) | 7.76571 | 0.246190 | ||||||||
\(996\) | −1.72503 | −0.0546596 | ||||||||
\(997\) | −40.2693 | −1.27534 | −0.637671 | − | 0.770309i | \(-0.720102\pi\) | ||||
−0.637671 | + | 0.770309i | \(0.720102\pi\) | |||||||
\(998\) | −23.1455 | −0.732659 | ||||||||
\(999\) | −15.1452 | −0.479174 |
(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 | 1805.2.a.u.1.8 | 9 | ||
5.4 | even | 2 | 9025.2.a.cd.1.2 | 9 | |||
19.14 | odd | 18 | 95.2.k.b.6.1 | ✓ | 18 | ||
19.15 | odd | 18 | 95.2.k.b.16.1 | yes | 18 | ||
19.18 | odd | 2 | 1805.2.a.t.1.2 | 9 | |||
57.14 | even | 18 | 855.2.bs.b.766.3 | 18 | |||
57.53 | even | 18 | 855.2.bs.b.586.3 | 18 | |||
95.14 | odd | 18 | 475.2.l.b.101.3 | 18 | |||
95.33 | even | 36 | 475.2.u.c.424.5 | 36 | |||
95.34 | odd | 18 | 475.2.l.b.301.3 | 18 | |||
95.52 | even | 36 | 475.2.u.c.424.2 | 36 | |||
95.53 | even | 36 | 475.2.u.c.149.2 | 36 | |||
95.72 | even | 36 | 475.2.u.c.149.5 | 36 | |||
95.94 | odd | 2 | 9025.2.a.ce.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.6.1 | ✓ | 18 | 19.14 | odd | 18 | ||
95.2.k.b.16.1 | yes | 18 | 19.15 | odd | 18 | ||
475.2.l.b.101.3 | 18 | 95.14 | odd | 18 | |||
475.2.l.b.301.3 | 18 | 95.34 | odd | 18 | |||
475.2.u.c.149.2 | 36 | 95.53 | even | 36 | |||
475.2.u.c.149.5 | 36 | 95.72 | even | 36 | |||
475.2.u.c.424.2 | 36 | 95.52 | even | 36 | |||
475.2.u.c.424.5 | 36 | 95.33 | even | 36 | |||
855.2.bs.b.586.3 | 18 | 57.53 | even | 18 | |||
855.2.bs.b.766.3 | 18 | 57.14 | even | 18 | |||
1805.2.a.t.1.2 | 9 | 19.18 | odd | 2 | |||
1805.2.a.u.1.8 | 9 | 1.1 | even | 1 | trivial | ||
9025.2.a.cd.1.2 | 9 | 5.4 | even | 2 | |||
9025.2.a.ce.1.8 | 9 | 95.94 | odd | 2 |