Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 25 x^{14} + 59 x^{13} + 273 x^{12} - 443 x^{11} - 1620 x^{10} + 1595 x^{9} + 5490 x^{8} - 2787 x^{7} - 10540 x^{6} + 1919 x^{5} + 10822 x^{4} + 132 x^{3} + \cdots + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-2.17558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.17558 | 1.83342 | 0.916710 | − | 0.399552i | \(-0.130834\pi\) | ||||
0.916710 | + | 0.399552i | \(0.130834\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.74937 | 1.22955 | 0.614777 | − | 0.788701i | \(-0.289246\pi\) | ||||
0.614777 | + | 0.788701i | \(0.289246\pi\) | |||||||
\(6\) | 3.17558 | 1.29642 | ||||||||
\(7\) | −3.80515 | −1.43821 | −0.719107 | − | 0.694900i | \(-0.755449\pi\) | ||||
−0.719107 | + | 0.694900i | \(0.755449\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.08430 | 2.36143 | ||||||||
\(10\) | 2.74937 | 0.869426 | ||||||||
\(11\) | −0.994384 | −0.299818 | −0.149909 | − | 0.988700i | \(-0.547898\pi\) | ||||
−0.149909 | + | 0.988700i | \(0.547898\pi\) | |||||||
\(12\) | 3.17558 | 0.916710 | ||||||||
\(13\) | −1.61008 | −0.446555 | −0.223278 | − | 0.974755i | \(-0.571676\pi\) | ||||
−0.223278 | + | 0.974755i | \(0.571676\pi\) | |||||||
\(14\) | −3.80515 | −1.01697 | ||||||||
\(15\) | 8.73083 | 2.25429 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.55443 | −0.862076 | −0.431038 | − | 0.902334i | \(-0.641852\pi\) | ||||
−0.431038 | + | 0.902334i | \(0.641852\pi\) | |||||||
\(18\) | 7.08430 | 1.66978 | ||||||||
\(19\) | 1.37594 | 0.315662 | 0.157831 | − | 0.987466i | \(-0.449550\pi\) | ||||
0.157831 | + | 0.987466i | \(0.449550\pi\) | |||||||
\(20\) | 2.74937 | 0.614777 | ||||||||
\(21\) | −12.0836 | −2.63685 | ||||||||
\(22\) | −0.994384 | −0.212003 | ||||||||
\(23\) | 4.07706 | 0.850126 | 0.425063 | − | 0.905164i | \(-0.360252\pi\) | ||||
0.425063 | + | 0.905164i | \(0.360252\pi\) | |||||||
\(24\) | 3.17558 | 0.648212 | ||||||||
\(25\) | 2.55902 | 0.511805 | ||||||||
\(26\) | −1.61008 | −0.315762 | ||||||||
\(27\) | 12.9700 | 2.49608 | ||||||||
\(28\) | −3.80515 | −0.719107 | ||||||||
\(29\) | 7.53219 | 1.39869 | 0.699346 | − | 0.714783i | \(-0.253475\pi\) | ||||
0.699346 | + | 0.714783i | \(0.253475\pi\) | |||||||
\(30\) | 8.73083 | 1.59402 | ||||||||
\(31\) | −3.04814 | −0.547463 | −0.273731 | − | 0.961806i | \(-0.588258\pi\) | ||||
−0.273731 | + | 0.961806i | \(0.588258\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −3.15774 | −0.549693 | ||||||||
\(34\) | −3.55443 | −0.609580 | ||||||||
\(35\) | −10.4618 | −1.76836 | ||||||||
\(36\) | 7.08430 | 1.18072 | ||||||||
\(37\) | 4.67498 | 0.768562 | 0.384281 | − | 0.923216i | \(-0.374449\pi\) | ||||
0.384281 | + | 0.923216i | \(0.374449\pi\) | |||||||
\(38\) | 1.37594 | 0.223207 | ||||||||
\(39\) | −5.11293 | −0.818723 | ||||||||
\(40\) | 2.74937 | 0.434713 | ||||||||
\(41\) | −7.29785 | −1.13973 | −0.569866 | − | 0.821738i | \(-0.693005\pi\) | ||||
−0.569866 | + | 0.821738i | \(0.693005\pi\) | |||||||
\(42\) | −12.0836 | −1.86453 | ||||||||
\(43\) | −7.79973 | −1.18945 | −0.594724 | − | 0.803930i | \(-0.702739\pi\) | ||||
−0.594724 | + | 0.803930i | \(0.702739\pi\) | |||||||
\(44\) | −0.994384 | −0.149909 | ||||||||
\(45\) | 19.4773 | 2.90351 | ||||||||
\(46\) | 4.07706 | 0.601130 | ||||||||
\(47\) | 5.89187 | 0.859418 | 0.429709 | − | 0.902967i | \(-0.358616\pi\) | ||||
0.429709 | + | 0.902967i | \(0.358616\pi\) | |||||||
\(48\) | 3.17558 | 0.458355 | ||||||||
\(49\) | 7.47920 | 1.06846 | ||||||||
\(50\) | 2.55902 | 0.361900 | ||||||||
\(51\) | −11.2874 | −1.58055 | ||||||||
\(52\) | −1.61008 | −0.223278 | ||||||||
\(53\) | −8.19172 | −1.12522 | −0.562609 | − | 0.826723i | \(-0.690202\pi\) | ||||
−0.562609 | + | 0.826723i | \(0.690202\pi\) | |||||||
\(54\) | 12.9700 | 1.76499 | ||||||||
\(55\) | −2.73393 | −0.368643 | ||||||||
\(56\) | −3.80515 | −0.508485 | ||||||||
\(57\) | 4.36940 | 0.578742 | ||||||||
\(58\) | 7.53219 | 0.989025 | ||||||||
\(59\) | 2.50465 | 0.326078 | 0.163039 | − | 0.986620i | \(-0.447870\pi\) | ||||
0.163039 | + | 0.986620i | \(0.447870\pi\) | |||||||
\(60\) | 8.73083 | 1.12715 | ||||||||
\(61\) | −15.2149 | −1.94807 | −0.974037 | − | 0.226389i | \(-0.927308\pi\) | ||||
−0.974037 | + | 0.226389i | \(0.927308\pi\) | |||||||
\(62\) | −3.04814 | −0.387115 | ||||||||
\(63\) | −26.9568 | −3.39624 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.42669 | −0.549064 | ||||||||
\(66\) | −3.15774 | −0.388691 | ||||||||
\(67\) | 0.0467268 | 0.00570859 | 0.00285430 | − | 0.999996i | \(-0.499091\pi\) | ||||
0.00285430 | + | 0.999996i | \(0.499091\pi\) | |||||||
\(68\) | −3.55443 | −0.431038 | ||||||||
\(69\) | 12.9470 | 1.55864 | ||||||||
\(70\) | −10.4618 | −1.25042 | ||||||||
\(71\) | 10.0920 | 1.19770 | 0.598848 | − | 0.800863i | \(-0.295625\pi\) | ||||
0.598848 | + | 0.800863i | \(0.295625\pi\) | |||||||
\(72\) | 7.08430 | 0.834892 | ||||||||
\(73\) | −6.04356 | −0.707345 | −0.353673 | − | 0.935369i | \(-0.615067\pi\) | ||||
−0.353673 | + | 0.935369i | \(0.615067\pi\) | |||||||
\(74\) | 4.67498 | 0.543456 | ||||||||
\(75\) | 8.12638 | 0.938353 | ||||||||
\(76\) | 1.37594 | 0.157831 | ||||||||
\(77\) | 3.78378 | 0.431202 | ||||||||
\(78\) | −5.11293 | −0.578925 | ||||||||
\(79\) | −5.29564 | −0.595806 | −0.297903 | − | 0.954596i | \(-0.596287\pi\) | ||||
−0.297903 | + | 0.954596i | \(0.596287\pi\) | |||||||
\(80\) | 2.74937 | 0.307389 | ||||||||
\(81\) | 19.9344 | 2.21493 | ||||||||
\(82\) | −7.29785 | −0.805912 | ||||||||
\(83\) | 11.2022 | 1.22960 | 0.614802 | − | 0.788681i | \(-0.289236\pi\) | ||||
0.614802 | + | 0.788681i | \(0.289236\pi\) | |||||||
\(84\) | −12.0836 | −1.31842 | ||||||||
\(85\) | −9.77243 | −1.05997 | ||||||||
\(86\) | −7.79973 | −0.841067 | ||||||||
\(87\) | 23.9191 | 2.56439 | ||||||||
\(88\) | −0.994384 | −0.106002 | ||||||||
\(89\) | −14.6766 | −1.55571 | −0.777857 | − | 0.628442i | \(-0.783693\pi\) | ||||
−0.777857 | + | 0.628442i | \(0.783693\pi\) | |||||||
\(90\) | 19.4773 | 2.05309 | ||||||||
\(91\) | 6.12659 | 0.642241 | ||||||||
\(92\) | 4.07706 | 0.425063 | ||||||||
\(93\) | −9.67962 | −1.00373 | ||||||||
\(94\) | 5.89187 | 0.607700 | ||||||||
\(95\) | 3.78296 | 0.388124 | ||||||||
\(96\) | 3.17558 | 0.324106 | ||||||||
\(97\) | −6.54687 | −0.664734 | −0.332367 | − | 0.943150i | \(-0.607847\pi\) | ||||
−0.332367 | + | 0.943150i | \(0.607847\pi\) | |||||||
\(98\) | 7.47920 | 0.755513 | ||||||||
\(99\) | −7.04451 | −0.708000 | ||||||||
\(100\) | 2.55902 | 0.255902 | ||||||||
\(101\) | −4.04332 | −0.402325 | −0.201163 | − | 0.979558i | \(-0.564472\pi\) | ||||
−0.201163 | + | 0.979558i | \(0.564472\pi\) | |||||||
\(102\) | −11.2874 | −1.11762 | ||||||||
\(103\) | 5.06385 | 0.498956 | 0.249478 | − | 0.968380i | \(-0.419741\pi\) | ||||
0.249478 | + | 0.968380i | \(0.419741\pi\) | |||||||
\(104\) | −1.61008 | −0.157881 | ||||||||
\(105\) | −33.2222 | −3.24215 | ||||||||
\(106\) | −8.19172 | −0.795650 | ||||||||
\(107\) | −9.95084 | −0.961984 | −0.480992 | − | 0.876725i | \(-0.659723\pi\) | ||||
−0.480992 | + | 0.876725i | \(0.659723\pi\) | |||||||
\(108\) | 12.9700 | 1.24804 | ||||||||
\(109\) | −5.88020 | −0.563221 | −0.281610 | − | 0.959529i | \(-0.590869\pi\) | ||||
−0.281610 | + | 0.959529i | \(0.590869\pi\) | |||||||
\(110\) | −2.73393 | −0.260670 | ||||||||
\(111\) | 14.8458 | 1.40910 | ||||||||
\(112\) | −3.80515 | −0.359553 | ||||||||
\(113\) | −16.1497 | −1.51924 | −0.759619 | − | 0.650369i | \(-0.774614\pi\) | ||||
−0.759619 | + | 0.650369i | \(0.774614\pi\) | |||||||
\(114\) | 4.36940 | 0.409232 | ||||||||
\(115\) | 11.2093 | 1.04528 | ||||||||
\(116\) | 7.53219 | 0.699346 | ||||||||
\(117\) | −11.4063 | −1.05451 | ||||||||
\(118\) | 2.50465 | 0.230572 | ||||||||
\(119\) | 13.5252 | 1.23985 | ||||||||
\(120\) | 8.73083 | 0.797012 | ||||||||
\(121\) | −10.0112 | −0.910109 | ||||||||
\(122\) | −15.2149 | −1.37750 | ||||||||
\(123\) | −23.1749 | −2.08961 | ||||||||
\(124\) | −3.04814 | −0.273731 | ||||||||
\(125\) | −6.71114 | −0.600263 | ||||||||
\(126\) | −26.9568 | −2.40151 | ||||||||
\(127\) | −16.6680 | −1.47905 | −0.739524 | − | 0.673130i | \(-0.764949\pi\) | ||||
−0.739524 | + | 0.673130i | \(0.764949\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −24.7687 | −2.18076 | ||||||||
\(130\) | −4.42669 | −0.388247 | ||||||||
\(131\) | 18.6452 | 1.62904 | 0.814520 | − | 0.580136i | \(-0.197001\pi\) | ||||
0.814520 | + | 0.580136i | \(0.197001\pi\) | |||||||
\(132\) | −3.15774 | −0.274846 | ||||||||
\(133\) | −5.23566 | −0.453989 | ||||||||
\(134\) | 0.0467268 | 0.00403658 | ||||||||
\(135\) | 35.6593 | 3.06906 | ||||||||
\(136\) | −3.55443 | −0.304790 | ||||||||
\(137\) | 1.77649 | 0.151776 | 0.0758880 | − | 0.997116i | \(-0.475821\pi\) | ||||
0.0758880 | + | 0.997116i | \(0.475821\pi\) | |||||||
\(138\) | 12.9470 | 1.10212 | ||||||||
\(139\) | 2.27140 | 0.192657 | 0.0963287 | − | 0.995350i | \(-0.469290\pi\) | ||||
0.0963287 | + | 0.995350i | \(0.469290\pi\) | |||||||
\(140\) | −10.4618 | −0.884181 | ||||||||
\(141\) | 18.7101 | 1.57568 | ||||||||
\(142\) | 10.0920 | 0.846899 | ||||||||
\(143\) | 1.60103 | 0.133885 | ||||||||
\(144\) | 7.08430 | 0.590358 | ||||||||
\(145\) | 20.7088 | 1.71977 | ||||||||
\(146\) | −6.04356 | −0.500169 | ||||||||
\(147\) | 23.7508 | 1.95893 | ||||||||
\(148\) | 4.67498 | 0.384281 | ||||||||
\(149\) | 12.1540 | 0.995695 | 0.497848 | − | 0.867264i | \(-0.334124\pi\) | ||||
0.497848 | + | 0.867264i | \(0.334124\pi\) | |||||||
\(150\) | 8.12638 | 0.663516 | ||||||||
\(151\) | −2.34401 | −0.190753 | −0.0953765 | − | 0.995441i | \(-0.530406\pi\) | ||||
−0.0953765 | + | 0.995441i | \(0.530406\pi\) | |||||||
\(152\) | 1.37594 | 0.111603 | ||||||||
\(153\) | −25.1806 | −2.03573 | ||||||||
\(154\) | 3.78378 | 0.304906 | ||||||||
\(155\) | −8.38047 | −0.673135 | ||||||||
\(156\) | −5.11293 | −0.409362 | ||||||||
\(157\) | 17.7604 | 1.41743 | 0.708715 | − | 0.705495i | \(-0.249275\pi\) | ||||
0.708715 | + | 0.705495i | \(0.249275\pi\) | |||||||
\(158\) | −5.29564 | −0.421299 | ||||||||
\(159\) | −26.0134 | −2.06300 | ||||||||
\(160\) | 2.74937 | 0.217357 | ||||||||
\(161\) | −15.5138 | −1.22266 | ||||||||
\(162\) | 19.9344 | 1.56619 | ||||||||
\(163\) | −3.80818 | −0.298280 | −0.149140 | − | 0.988816i | \(-0.547650\pi\) | ||||
−0.149140 | + | 0.988816i | \(0.547650\pi\) | |||||||
\(164\) | −7.29785 | −0.569866 | ||||||||
\(165\) | −8.68180 | −0.675877 | ||||||||
\(166\) | 11.2022 | 0.869461 | ||||||||
\(167\) | 13.7656 | 1.06522 | 0.532608 | − | 0.846362i | \(-0.321212\pi\) | ||||
0.532608 | + | 0.846362i | \(0.321212\pi\) | |||||||
\(168\) | −12.0836 | −0.932267 | ||||||||
\(169\) | −10.4077 | −0.800589 | ||||||||
\(170\) | −9.77243 | −0.749511 | ||||||||
\(171\) | 9.74756 | 0.745415 | ||||||||
\(172\) | −7.79973 | −0.594724 | ||||||||
\(173\) | 19.3413 | 1.47049 | 0.735246 | − | 0.677800i | \(-0.237067\pi\) | ||||
0.735246 | + | 0.677800i | \(0.237067\pi\) | |||||||
\(174\) | 23.9191 | 1.81330 | ||||||||
\(175\) | −9.73748 | −0.736084 | ||||||||
\(176\) | −0.994384 | −0.0749545 | ||||||||
\(177\) | 7.95371 | 0.597837 | ||||||||
\(178\) | −14.6766 | −1.10006 | ||||||||
\(179\) | −0.585208 | −0.0437405 | −0.0218702 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218702 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(180\) | 19.4773 | 1.45175 | ||||||||
\(181\) | −1.34299 | −0.0998240 | −0.0499120 | − | 0.998754i | \(-0.515894\pi\) | ||||
−0.0499120 | + | 0.998754i | \(0.515894\pi\) | |||||||
\(182\) | 6.12659 | 0.454133 | ||||||||
\(183\) | −48.3162 | −3.57164 | ||||||||
\(184\) | 4.07706 | 0.300565 | ||||||||
\(185\) | 12.8532 | 0.944989 | ||||||||
\(186\) | −9.67962 | −0.709744 | ||||||||
\(187\) | 3.53447 | 0.258466 | ||||||||
\(188\) | 5.89187 | 0.429709 | ||||||||
\(189\) | −49.3529 | −3.58989 | ||||||||
\(190\) | 3.78296 | 0.274445 | ||||||||
\(191\) | 24.4599 | 1.76985 | 0.884927 | − | 0.465730i | \(-0.154208\pi\) | ||||
0.884927 | + | 0.465730i | \(0.154208\pi\) | |||||||
\(192\) | 3.17558 | 0.229178 | ||||||||
\(193\) | 20.2681 | 1.45893 | 0.729464 | − | 0.684019i | \(-0.239770\pi\) | ||||
0.729464 | + | 0.684019i | \(0.239770\pi\) | |||||||
\(194\) | −6.54687 | −0.470038 | ||||||||
\(195\) | −14.0573 | −1.00667 | ||||||||
\(196\) | 7.47920 | 0.534228 | ||||||||
\(197\) | 11.6804 | 0.832197 | 0.416098 | − | 0.909320i | \(-0.363397\pi\) | ||||
0.416098 | + | 0.909320i | \(0.363397\pi\) | |||||||
\(198\) | −7.04451 | −0.500632 | ||||||||
\(199\) | 11.4681 | 0.812955 | 0.406477 | − | 0.913661i | \(-0.366757\pi\) | ||||
0.406477 | + | 0.913661i | \(0.366757\pi\) | |||||||
\(200\) | 2.55902 | 0.180950 | ||||||||
\(201\) | 0.148385 | 0.0104662 | ||||||||
\(202\) | −4.04332 | −0.284487 | ||||||||
\(203\) | −28.6611 | −2.01162 | ||||||||
\(204\) | −11.2874 | −0.790274 | ||||||||
\(205\) | −20.0645 | −1.40136 | ||||||||
\(206\) | 5.06385 | 0.352815 | ||||||||
\(207\) | 28.8831 | 2.00751 | ||||||||
\(208\) | −1.61008 | −0.111639 | ||||||||
\(209\) | −1.36821 | −0.0946412 | ||||||||
\(210\) | −33.2222 | −2.29255 | ||||||||
\(211\) | −3.56683 | −0.245551 | −0.122775 | − | 0.992434i | \(-0.539179\pi\) | ||||
−0.122775 | + | 0.992434i | \(0.539179\pi\) | |||||||
\(212\) | −8.19172 | −0.562609 | ||||||||
\(213\) | 32.0478 | 2.19588 | ||||||||
\(214\) | −9.95084 | −0.680226 | ||||||||
\(215\) | −21.4443 | −1.46249 | ||||||||
\(216\) | 12.9700 | 0.882497 | ||||||||
\(217\) | 11.5987 | 0.787368 | ||||||||
\(218\) | −5.88020 | −0.398257 | ||||||||
\(219\) | −19.1918 | −1.29686 | ||||||||
\(220\) | −2.73393 | −0.184321 | ||||||||
\(221\) | 5.72291 | 0.384964 | ||||||||
\(222\) | 14.8458 | 0.996383 | ||||||||
\(223\) | 20.0646 | 1.34362 | 0.671811 | − | 0.740723i | \(-0.265517\pi\) | ||||
0.671811 | + | 0.740723i | \(0.265517\pi\) | |||||||
\(224\) | −3.80515 | −0.254243 | ||||||||
\(225\) | 18.1289 | 1.20859 | ||||||||
\(226\) | −16.1497 | −1.07426 | ||||||||
\(227\) | 16.1415 | 1.07135 | 0.535675 | − | 0.844424i | \(-0.320057\pi\) | ||||
0.535675 | + | 0.844424i | \(0.320057\pi\) | |||||||
\(228\) | 4.36940 | 0.289371 | ||||||||
\(229\) | −21.5723 | −1.42554 | −0.712768 | − | 0.701399i | \(-0.752559\pi\) | ||||
−0.712768 | + | 0.701399i | \(0.752559\pi\) | |||||||
\(230\) | 11.2093 | 0.739122 | ||||||||
\(231\) | 12.0157 | 0.790575 | ||||||||
\(232\) | 7.53219 | 0.494513 | ||||||||
\(233\) | 24.3039 | 1.59220 | 0.796099 | − | 0.605166i | \(-0.206893\pi\) | ||||
0.796099 | + | 0.605166i | \(0.206893\pi\) | |||||||
\(234\) | −11.4063 | −0.745651 | ||||||||
\(235\) | 16.1989 | 1.05670 | ||||||||
\(236\) | 2.50465 | 0.163039 | ||||||||
\(237\) | −16.8167 | −1.09236 | ||||||||
\(238\) | 13.5252 | 0.876705 | ||||||||
\(239\) | 17.5860 | 1.13754 | 0.568771 | − | 0.822496i | \(-0.307419\pi\) | ||||
0.568771 | + | 0.822496i | \(0.307419\pi\) | |||||||
\(240\) | 8.73083 | 0.563573 | ||||||||
\(241\) | 9.83124 | 0.633286 | 0.316643 | − | 0.948545i | \(-0.397444\pi\) | ||||
0.316643 | + | 0.948545i | \(0.397444\pi\) | |||||||
\(242\) | −10.0112 | −0.643544 | ||||||||
\(243\) | 24.3931 | 1.56482 | ||||||||
\(244\) | −15.2149 | −0.974037 | ||||||||
\(245\) | 20.5631 | 1.31373 | ||||||||
\(246\) | −23.1749 | −1.47758 | ||||||||
\(247\) | −2.21537 | −0.140960 | ||||||||
\(248\) | −3.04814 | −0.193557 | ||||||||
\(249\) | 35.5735 | 2.25438 | ||||||||
\(250\) | −6.71114 | −0.424450 | ||||||||
\(251\) | 16.1118 | 1.01697 | 0.508485 | − | 0.861071i | \(-0.330206\pi\) | ||||
0.508485 | + | 0.861071i | \(0.330206\pi\) | |||||||
\(252\) | −26.9568 | −1.69812 | ||||||||
\(253\) | −4.05416 | −0.254883 | ||||||||
\(254\) | −16.6680 | −1.04584 | ||||||||
\(255\) | −31.0331 | −1.94337 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.93245 | 0.245299 | 0.122650 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122650 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(258\) | −24.7687 | −1.54203 | ||||||||
\(259\) | −17.7890 | −1.10536 | ||||||||
\(260\) | −4.42669 | −0.274532 | ||||||||
\(261\) | 53.3603 | 3.30292 | ||||||||
\(262\) | 18.6452 | 1.15190 | ||||||||
\(263\) | −12.7883 | −0.788560 | −0.394280 | − | 0.918990i | \(-0.629006\pi\) | ||||
−0.394280 | + | 0.918990i | \(0.629006\pi\) | |||||||
\(264\) | −3.15774 | −0.194346 | ||||||||
\(265\) | −22.5220 | −1.38352 | ||||||||
\(266\) | −5.23566 | −0.321019 | ||||||||
\(267\) | −46.6066 | −2.85228 | ||||||||
\(268\) | 0.0467268 | 0.00285430 | ||||||||
\(269\) | 27.2182 | 1.65952 | 0.829761 | − | 0.558119i | \(-0.188477\pi\) | ||||
0.829761 | + | 0.558119i | \(0.188477\pi\) | |||||||
\(270\) | 35.6593 | 2.17016 | ||||||||
\(271\) | −15.6191 | −0.948792 | −0.474396 | − | 0.880311i | \(-0.657334\pi\) | ||||
−0.474396 | + | 0.880311i | \(0.657334\pi\) | |||||||
\(272\) | −3.55443 | −0.215519 | ||||||||
\(273\) | 19.4555 | 1.17750 | ||||||||
\(274\) | 1.77649 | 0.107322 | ||||||||
\(275\) | −2.54465 | −0.153448 | ||||||||
\(276\) | 12.9470 | 0.779319 | ||||||||
\(277\) | 15.0948 | 0.906958 | 0.453479 | − | 0.891267i | \(-0.350183\pi\) | ||||
0.453479 | + | 0.891267i | \(0.350183\pi\) | |||||||
\(278\) | 2.27140 | 0.136229 | ||||||||
\(279\) | −21.5940 | −1.29280 | ||||||||
\(280\) | −10.4618 | −0.625210 | ||||||||
\(281\) | −13.1122 | −0.782210 | −0.391105 | − | 0.920346i | \(-0.627907\pi\) | ||||
−0.391105 | + | 0.920346i | \(0.627907\pi\) | |||||||
\(282\) | 18.7101 | 1.11417 | ||||||||
\(283\) | 15.6931 | 0.932859 | 0.466429 | − | 0.884558i | \(-0.345540\pi\) | ||||
0.466429 | + | 0.884558i | \(0.345540\pi\) | |||||||
\(284\) | 10.0920 | 0.598848 | ||||||||
\(285\) | 12.0131 | 0.711594 | ||||||||
\(286\) | 1.60103 | 0.0946712 | ||||||||
\(287\) | 27.7694 | 1.63918 | ||||||||
\(288\) | 7.08430 | 0.417446 | ||||||||
\(289\) | −4.36603 | −0.256825 | ||||||||
\(290\) | 20.7088 | 1.21606 | ||||||||
\(291\) | −20.7901 | −1.21874 | ||||||||
\(292\) | −6.04356 | −0.353673 | ||||||||
\(293\) | 7.06624 | 0.412814 | 0.206407 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206407 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(294\) | 23.7508 | 1.38517 | ||||||||
\(295\) | 6.88620 | 0.400930 | ||||||||
\(296\) | 4.67498 | 0.271728 | ||||||||
\(297\) | −12.8972 | −0.748369 | ||||||||
\(298\) | 12.1540 | 0.704063 | ||||||||
\(299\) | −6.56438 | −0.379628 | ||||||||
\(300\) | 8.12638 | 0.469177 | ||||||||
\(301\) | 29.6792 | 1.71068 | ||||||||
\(302\) | −2.34401 | −0.134883 | ||||||||
\(303\) | −12.8399 | −0.737631 | ||||||||
\(304\) | 1.37594 | 0.0789155 | ||||||||
\(305\) | −41.8315 | −2.39526 | ||||||||
\(306\) | −25.1806 | −1.43948 | ||||||||
\(307\) | −3.77208 | −0.215284 | −0.107642 | − | 0.994190i | \(-0.534330\pi\) | ||||
−0.107642 | + | 0.994190i | \(0.534330\pi\) | |||||||
\(308\) | 3.78378 | 0.215601 | ||||||||
\(309\) | 16.0807 | 0.914796 | ||||||||
\(310\) | −8.38047 | −0.475979 | ||||||||
\(311\) | −19.8737 | −1.12693 | −0.563467 | − | 0.826138i | \(-0.690533\pi\) | ||||
−0.563467 | + | 0.826138i | \(0.690533\pi\) | |||||||
\(312\) | −5.11293 | −0.289462 | ||||||||
\(313\) | −25.6759 | −1.45129 | −0.725644 | − | 0.688070i | \(-0.758458\pi\) | ||||
−0.725644 | + | 0.688070i | \(0.758458\pi\) | |||||||
\(314\) | 17.7604 | 1.00227 | ||||||||
\(315\) | −74.1143 | −4.17587 | ||||||||
\(316\) | −5.29564 | −0.297903 | ||||||||
\(317\) | −13.4370 | −0.754699 | −0.377350 | − | 0.926071i | \(-0.623165\pi\) | ||||
−0.377350 | + | 0.926071i | \(0.623165\pi\) | |||||||
\(318\) | −26.0134 | −1.45876 | ||||||||
\(319\) | −7.48989 | −0.419353 | ||||||||
\(320\) | 2.74937 | 0.153694 | ||||||||
\(321\) | −31.5997 | −1.76372 | ||||||||
\(322\) | −15.5138 | −0.864552 | ||||||||
\(323\) | −4.89068 | −0.272125 | ||||||||
\(324\) | 19.9344 | 1.10747 | ||||||||
\(325\) | −4.12022 | −0.228549 | ||||||||
\(326\) | −3.80818 | −0.210916 | ||||||||
\(327\) | −18.6730 | −1.03262 | ||||||||
\(328\) | −7.29785 | −0.402956 | ||||||||
\(329\) | −22.4195 | −1.23603 | ||||||||
\(330\) | −8.68180 | −0.477917 | ||||||||
\(331\) | 4.05100 | 0.222663 | 0.111332 | − | 0.993783i | \(-0.464488\pi\) | ||||
0.111332 | + | 0.993783i | \(0.464488\pi\) | |||||||
\(332\) | 11.2022 | 0.614802 | ||||||||
\(333\) | 33.1190 | 1.81491 | ||||||||
\(334\) | 13.7656 | 0.753221 | ||||||||
\(335\) | 0.128469 | 0.00701902 | ||||||||
\(336\) | −12.0836 | −0.659212 | ||||||||
\(337\) | −4.81379 | −0.262224 | −0.131112 | − | 0.991368i | \(-0.541855\pi\) | ||||
−0.131112 | + | 0.991368i | \(0.541855\pi\) | |||||||
\(338\) | −10.4077 | −0.566102 | ||||||||
\(339\) | −51.2847 | −2.78540 | ||||||||
\(340\) | −9.77243 | −0.529985 | ||||||||
\(341\) | 3.03103 | 0.164139 | ||||||||
\(342\) | 9.74756 | 0.527088 | ||||||||
\(343\) | −1.82342 | −0.0984555 | ||||||||
\(344\) | −7.79973 | −0.420533 | ||||||||
\(345\) | 35.5961 | 1.91643 | ||||||||
\(346\) | 19.3413 | 1.03979 | ||||||||
\(347\) | −28.0304 | −1.50475 | −0.752377 | − | 0.658733i | \(-0.771093\pi\) | ||||
−0.752377 | + | 0.658733i | \(0.771093\pi\) | |||||||
\(348\) | 23.9191 | 1.28220 | ||||||||
\(349\) | −14.5076 | −0.776573 | −0.388286 | − | 0.921539i | \(-0.626933\pi\) | ||||
−0.388286 | + | 0.921539i | \(0.626933\pi\) | |||||||
\(350\) | −9.73748 | −0.520490 | ||||||||
\(351\) | −20.8827 | −1.11464 | ||||||||
\(352\) | −0.994384 | −0.0530009 | ||||||||
\(353\) | 18.4431 | 0.981626 | 0.490813 | − | 0.871265i | \(-0.336700\pi\) | ||||
0.490813 | + | 0.871265i | \(0.336700\pi\) | |||||||
\(354\) | 7.95371 | 0.422735 | ||||||||
\(355\) | 27.7465 | 1.47263 | ||||||||
\(356\) | −14.6766 | −0.777857 | ||||||||
\(357\) | 42.9502 | 2.27316 | ||||||||
\(358\) | −0.585208 | −0.0309292 | ||||||||
\(359\) | 18.4513 | 0.973821 | 0.486910 | − | 0.873452i | \(-0.338124\pi\) | ||||
0.486910 | + | 0.873452i | \(0.338124\pi\) | |||||||
\(360\) | 19.4773 | 1.02655 | ||||||||
\(361\) | −17.1068 | −0.900357 | ||||||||
\(362\) | −1.34299 | −0.0705862 | ||||||||
\(363\) | −31.7913 | −1.66861 | ||||||||
\(364\) | 6.12659 | 0.321121 | ||||||||
\(365\) | −16.6160 | −0.869719 | ||||||||
\(366\) | −48.3162 | −2.52553 | ||||||||
\(367\) | 29.7137 | 1.55104 | 0.775521 | − | 0.631322i | \(-0.217487\pi\) | ||||
0.775521 | + | 0.631322i | \(0.217487\pi\) | |||||||
\(368\) | 4.07706 | 0.212531 | ||||||||
\(369\) | −51.7001 | −2.69140 | ||||||||
\(370\) | 12.8532 | 0.668208 | ||||||||
\(371\) | 31.1707 | 1.61830 | ||||||||
\(372\) | −9.67962 | −0.501865 | ||||||||
\(373\) | 28.2684 | 1.46368 | 0.731840 | − | 0.681476i | \(-0.238662\pi\) | ||||
0.731840 | + | 0.681476i | \(0.238662\pi\) | |||||||
\(374\) | 3.53447 | 0.182763 | ||||||||
\(375\) | −21.3118 | −1.10053 | ||||||||
\(376\) | 5.89187 | 0.303850 | ||||||||
\(377\) | −12.1274 | −0.624593 | ||||||||
\(378\) | −49.3529 | −2.53844 | ||||||||
\(379\) | −3.52360 | −0.180995 | −0.0904975 | − | 0.995897i | \(-0.528846\pi\) | ||||
−0.0904975 | + | 0.995897i | \(0.528846\pi\) | |||||||
\(380\) | 3.78296 | 0.194062 | ||||||||
\(381\) | −52.9306 | −2.71172 | ||||||||
\(382\) | 24.4599 | 1.25148 | ||||||||
\(383\) | 30.7104 | 1.56923 | 0.784613 | − | 0.619986i | \(-0.212862\pi\) | ||||
0.784613 | + | 0.619986i | \(0.212862\pi\) | |||||||
\(384\) | 3.17558 | 0.162053 | ||||||||
\(385\) | 10.4030 | 0.530187 | ||||||||
\(386\) | 20.2681 | 1.03162 | ||||||||
\(387\) | −55.2556 | −2.80880 | ||||||||
\(388\) | −6.54687 | −0.332367 | ||||||||
\(389\) | −14.8158 | −0.751193 | −0.375597 | − | 0.926783i | \(-0.622562\pi\) | ||||
−0.375597 | + | 0.926783i | \(0.622562\pi\) | |||||||
\(390\) | −14.0573 | −0.711820 | ||||||||
\(391\) | −14.4916 | −0.732873 | ||||||||
\(392\) | 7.47920 | 0.377757 | ||||||||
\(393\) | 59.2093 | 2.98672 | ||||||||
\(394\) | 11.6804 | 0.588452 | ||||||||
\(395\) | −14.5597 | −0.732577 | ||||||||
\(396\) | −7.04451 | −0.354000 | ||||||||
\(397\) | 13.4129 | 0.673174 | 0.336587 | − | 0.941652i | \(-0.390727\pi\) | ||||
0.336587 | + | 0.941652i | \(0.390727\pi\) | |||||||
\(398\) | 11.4681 | 0.574846 | ||||||||
\(399\) | −16.6263 | −0.832354 | ||||||||
\(400\) | 2.55902 | 0.127951 | ||||||||
\(401\) | −37.5566 | −1.87549 | −0.937744 | − | 0.347327i | \(-0.887089\pi\) | ||||
−0.937744 | + | 0.347327i | \(0.887089\pi\) | |||||||
\(402\) | 0.148385 | 0.00740076 | ||||||||
\(403\) | 4.90775 | 0.244472 | ||||||||
\(404\) | −4.04332 | −0.201163 | ||||||||
\(405\) | 54.8069 | 2.72338 | ||||||||
\(406\) | −28.6611 | −1.42243 | ||||||||
\(407\) | −4.64873 | −0.230429 | ||||||||
\(408\) | −11.2874 | −0.558808 | ||||||||
\(409\) | 24.0263 | 1.18802 | 0.594012 | − | 0.804456i | \(-0.297543\pi\) | ||||
0.594012 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(410\) | −20.0645 | −0.990913 | ||||||||
\(411\) | 5.64139 | 0.278269 | ||||||||
\(412\) | 5.06385 | 0.249478 | ||||||||
\(413\) | −9.53058 | −0.468969 | ||||||||
\(414\) | 28.8831 | 1.41953 | ||||||||
\(415\) | 30.7990 | 1.51187 | ||||||||
\(416\) | −1.61008 | −0.0789405 | ||||||||
\(417\) | 7.21300 | 0.353222 | ||||||||
\(418\) | −1.36821 | −0.0669214 | ||||||||
\(419\) | −32.4579 | −1.58567 | −0.792837 | − | 0.609434i | \(-0.791397\pi\) | ||||
−0.792837 | + | 0.609434i | \(0.791397\pi\) | |||||||
\(420\) | −33.2222 | −1.62108 | ||||||||
\(421\) | 14.0767 | 0.686055 | 0.343027 | − | 0.939325i | \(-0.388548\pi\) | ||||
0.343027 | + | 0.939325i | \(0.388548\pi\) | |||||||
\(422\) | −3.56683 | −0.173631 | ||||||||
\(423\) | 41.7398 | 2.02946 | ||||||||
\(424\) | −8.19172 | −0.397825 | ||||||||
\(425\) | −9.09587 | −0.441214 | ||||||||
\(426\) | 32.0478 | 1.55272 | ||||||||
\(427\) | 57.8952 | 2.80175 | ||||||||
\(428\) | −9.95084 | −0.480992 | ||||||||
\(429\) | 5.08421 | 0.245468 | ||||||||
\(430\) | −21.4443 | −1.03414 | ||||||||
\(431\) | −9.86060 | −0.474969 | −0.237484 | − | 0.971391i | \(-0.576323\pi\) | ||||
−0.237484 | + | 0.971391i | \(0.576323\pi\) | |||||||
\(432\) | 12.9700 | 0.624020 | ||||||||
\(433\) | 29.3909 | 1.41244 | 0.706218 | − | 0.707994i | \(-0.250400\pi\) | ||||
0.706218 | + | 0.707994i | \(0.250400\pi\) | |||||||
\(434\) | 11.5987 | 0.556753 | ||||||||
\(435\) | 65.7623 | 3.15306 | ||||||||
\(436\) | −5.88020 | −0.281610 | ||||||||
\(437\) | 5.60979 | 0.268352 | ||||||||
\(438\) | −19.1918 | −0.917019 | ||||||||
\(439\) | −4.57873 | −0.218531 | −0.109266 | − | 0.994013i | \(-0.534850\pi\) | ||||
−0.109266 | + | 0.994013i | \(0.534850\pi\) | |||||||
\(440\) | −2.73393 | −0.130335 | ||||||||
\(441\) | 52.9849 | 2.52309 | ||||||||
\(442\) | 5.72291 | 0.272211 | ||||||||
\(443\) | −36.6705 | −1.74227 | −0.871134 | − | 0.491045i | \(-0.836615\pi\) | ||||
−0.871134 | + | 0.491045i | \(0.836615\pi\) | |||||||
\(444\) | 14.8458 | 0.704549 | ||||||||
\(445\) | −40.3513 | −1.91283 | ||||||||
\(446\) | 20.0646 | 0.950084 | ||||||||
\(447\) | 38.5960 | 1.82553 | ||||||||
\(448\) | −3.80515 | −0.179777 | ||||||||
\(449\) | −10.6630 | −0.503216 | −0.251608 | − | 0.967829i | \(-0.580959\pi\) | ||||
−0.251608 | + | 0.967829i | \(0.580959\pi\) | |||||||
\(450\) | 18.1289 | 0.854603 | ||||||||
\(451\) | 7.25686 | 0.341712 | ||||||||
\(452\) | −16.1497 | −0.759619 | ||||||||
\(453\) | −7.44359 | −0.349731 | ||||||||
\(454\) | 16.1415 | 0.757558 | ||||||||
\(455\) | 16.8443 | 0.789671 | ||||||||
\(456\) | 4.36940 | 0.204616 | ||||||||
\(457\) | 39.1144 | 1.82969 | 0.914847 | − | 0.403801i | \(-0.132311\pi\) | ||||
0.914847 | + | 0.403801i | \(0.132311\pi\) | |||||||
\(458\) | −21.5723 | −1.00801 | ||||||||
\(459\) | −46.1010 | −2.15181 | ||||||||
\(460\) | 11.2093 | 0.522638 | ||||||||
\(461\) | −32.6190 | −1.51922 | −0.759609 | − | 0.650380i | \(-0.774610\pi\) | ||||
−0.759609 | + | 0.650380i | \(0.774610\pi\) | |||||||
\(462\) | 12.0157 | 0.559021 | ||||||||
\(463\) | −7.87682 | −0.366067 | −0.183033 | − | 0.983107i | \(-0.558592\pi\) | ||||
−0.183033 | + | 0.983107i | \(0.558592\pi\) | |||||||
\(464\) | 7.53219 | 0.349673 | ||||||||
\(465\) | −26.6128 | −1.23414 | ||||||||
\(466\) | 24.3039 | 1.12585 | ||||||||
\(467\) | 29.1726 | 1.34995 | 0.674973 | − | 0.737842i | \(-0.264155\pi\) | ||||
0.674973 | + | 0.737842i | \(0.264155\pi\) | |||||||
\(468\) | −11.4063 | −0.527255 | ||||||||
\(469\) | −0.177803 | −0.00821017 | ||||||||
\(470\) | 16.1989 | 0.747201 | ||||||||
\(471\) | 56.3994 | 2.59875 | ||||||||
\(472\) | 2.50465 | 0.115286 | ||||||||
\(473\) | 7.75593 | 0.356618 | ||||||||
\(474\) | −16.8167 | −0.772418 | ||||||||
\(475\) | 3.52106 | 0.161557 | ||||||||
\(476\) | 13.5252 | 0.619924 | ||||||||
\(477\) | −58.0326 | −2.65713 | ||||||||
\(478\) | 17.5860 | 0.804363 | ||||||||
\(479\) | −10.5245 | −0.480877 | −0.240439 | − | 0.970664i | \(-0.577291\pi\) | ||||
−0.240439 | + | 0.970664i | \(0.577291\pi\) | |||||||
\(480\) | 8.73083 | 0.398506 | ||||||||
\(481\) | −7.52708 | −0.343205 | ||||||||
\(482\) | 9.83124 | 0.447801 | ||||||||
\(483\) | −49.2654 | −2.24165 | ||||||||
\(484\) | −10.0112 | −0.455055 | ||||||||
\(485\) | −17.9998 | −0.817327 | ||||||||
\(486\) | 24.3931 | 1.10650 | ||||||||
\(487\) | 40.4170 | 1.83147 | 0.915734 | − | 0.401786i | \(-0.131610\pi\) | ||||
0.915734 | + | 0.401786i | \(0.131610\pi\) | |||||||
\(488\) | −15.2149 | −0.688748 | ||||||||
\(489\) | −12.0932 | −0.546872 | ||||||||
\(490\) | 20.5631 | 0.928945 | ||||||||
\(491\) | 12.7430 | 0.575085 | 0.287543 | − | 0.957768i | \(-0.407162\pi\) | ||||
0.287543 | + | 0.957768i | \(0.407162\pi\) | |||||||
\(492\) | −23.1749 | −1.04480 | ||||||||
\(493\) | −26.7726 | −1.20578 | ||||||||
\(494\) | −2.21537 | −0.0996741 | ||||||||
\(495\) | −19.3680 | −0.870525 | ||||||||
\(496\) | −3.04814 | −0.136866 | ||||||||
\(497\) | −38.4015 | −1.72254 | ||||||||
\(498\) | 35.5735 | 1.59409 | ||||||||
\(499\) | −11.4162 | −0.511061 | −0.255531 | − | 0.966801i | \(-0.582250\pi\) | ||||
−0.255531 | + | 0.966801i | \(0.582250\pi\) | |||||||
\(500\) | −6.71114 | −0.300131 | ||||||||
\(501\) | 43.7138 | 1.95299 | ||||||||
\(502\) | 16.1118 | 0.719106 | ||||||||
\(503\) | −33.8483 | −1.50922 | −0.754610 | − | 0.656174i | \(-0.772174\pi\) | ||||
−0.754610 | + | 0.656174i | \(0.772174\pi\) | |||||||
\(504\) | −26.9568 | −1.20075 | ||||||||
\(505\) | −11.1166 | −0.494681 | ||||||||
\(506\) | −4.05416 | −0.180230 | ||||||||
\(507\) | −33.0503 | −1.46782 | ||||||||
\(508\) | −16.6680 | −0.739524 | ||||||||
\(509\) | −1.42384 | −0.0631106 | −0.0315553 | − | 0.999502i | \(-0.510046\pi\) | ||||
−0.0315553 | + | 0.999502i | \(0.510046\pi\) | |||||||
\(510\) | −31.0331 | −1.37417 | ||||||||
\(511\) | 22.9967 | 1.01731 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.8459 | 0.787917 | ||||||||
\(514\) | 3.93245 | 0.173453 | ||||||||
\(515\) | 13.9224 | 0.613494 | ||||||||
\(516\) | −24.7687 | −1.09038 | ||||||||
\(517\) | −5.85879 | −0.257669 | ||||||||
\(518\) | −17.7890 | −0.781605 | ||||||||
\(519\) | 61.4198 | 2.69603 | ||||||||
\(520\) | −4.42669 | −0.194123 | ||||||||
\(521\) | 14.4693 | 0.633913 | 0.316957 | − | 0.948440i | \(-0.397339\pi\) | ||||
0.316957 | + | 0.948440i | \(0.397339\pi\) | |||||||
\(522\) | 53.3603 | 2.33552 | ||||||||
\(523\) | −41.3027 | −1.80604 | −0.903021 | − | 0.429595i | \(-0.858656\pi\) | ||||
−0.903021 | + | 0.429595i | \(0.858656\pi\) | |||||||
\(524\) | 18.6452 | 0.814520 | ||||||||
\(525\) | −30.9221 | −1.34955 | ||||||||
\(526\) | −12.7883 | −0.557596 | ||||||||
\(527\) | 10.8344 | 0.471954 | ||||||||
\(528\) | −3.15774 | −0.137423 | ||||||||
\(529\) | −6.37759 | −0.277286 | ||||||||
\(530\) | −22.5220 | −0.978295 | ||||||||
\(531\) | 17.7437 | 0.770010 | ||||||||
\(532\) | −5.23566 | −0.226995 | ||||||||
\(533\) | 11.7501 | 0.508953 | ||||||||
\(534\) | −46.6066 | −2.01687 | ||||||||
\(535\) | −27.3585 | −1.18281 | ||||||||
\(536\) | 0.0467268 | 0.00201829 | ||||||||
\(537\) | −1.85837 | −0.0801947 | ||||||||
\(538\) | 27.2182 | 1.17346 | ||||||||
\(539\) | −7.43720 | −0.320343 | ||||||||
\(540\) | 35.6593 | 1.53453 | ||||||||
\(541\) | −31.6641 | −1.36135 | −0.680673 | − | 0.732588i | \(-0.738312\pi\) | ||||
−0.680673 | + | 0.732588i | \(0.738312\pi\) | |||||||
\(542\) | −15.6191 | −0.670897 | ||||||||
\(543\) | −4.26478 | −0.183019 | ||||||||
\(544\) | −3.55443 | −0.152395 | ||||||||
\(545\) | −16.1668 | −0.692511 | ||||||||
\(546\) | 19.4555 | 0.832617 | ||||||||
\(547\) | −11.9782 | −0.512150 | −0.256075 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256075 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(548\) | 1.77649 | 0.0758880 | ||||||||
\(549\) | −107.787 | −4.60024 | ||||||||
\(550\) | −2.54465 | −0.108504 | ||||||||
\(551\) | 10.3638 | 0.441514 | ||||||||
\(552\) | 12.9470 | 0.551062 | ||||||||
\(553\) | 20.1507 | 0.856897 | ||||||||
\(554\) | 15.0948 | 0.641316 | ||||||||
\(555\) | 40.8165 | 1.73256 | ||||||||
\(556\) | 2.27140 | 0.0963287 | ||||||||
\(557\) | −6.47782 | −0.274474 | −0.137237 | − | 0.990538i | \(-0.543822\pi\) | ||||
−0.137237 | + | 0.990538i | \(0.543822\pi\) | |||||||
\(558\) | −21.5940 | −0.914145 | ||||||||
\(559\) | 12.5582 | 0.531154 | ||||||||
\(560\) | −10.4618 | −0.442090 | ||||||||
\(561\) | 11.2240 | 0.473877 | ||||||||
\(562\) | −13.1122 | −0.553106 | ||||||||
\(563\) | 13.1123 | 0.552618 | 0.276309 | − | 0.961069i | \(-0.410889\pi\) | ||||
0.276309 | + | 0.961069i | \(0.410889\pi\) | |||||||
\(564\) | 18.7101 | 0.787838 | ||||||||
\(565\) | −44.4015 | −1.86799 | ||||||||
\(566\) | 15.6931 | 0.659631 | ||||||||
\(567\) | −75.8534 | −3.18554 | ||||||||
\(568\) | 10.0920 | 0.423450 | ||||||||
\(569\) | 40.7627 | 1.70886 | 0.854431 | − | 0.519565i | \(-0.173906\pi\) | ||||
0.854431 | + | 0.519565i | \(0.173906\pi\) | |||||||
\(570\) | 12.0131 | 0.503173 | ||||||||
\(571\) | −2.15286 | −0.0900942 | −0.0450471 | − | 0.998985i | \(-0.514344\pi\) | ||||
−0.0450471 | + | 0.998985i | \(0.514344\pi\) | |||||||
\(572\) | 1.60103 | 0.0669426 | ||||||||
\(573\) | 77.6742 | 3.24489 | ||||||||
\(574\) | 27.7694 | 1.15907 | ||||||||
\(575\) | 10.4333 | 0.435098 | ||||||||
\(576\) | 7.08430 | 0.295179 | ||||||||
\(577\) | 21.6408 | 0.900919 | 0.450459 | − | 0.892797i | \(-0.351260\pi\) | ||||
0.450459 | + | 0.892797i | \(0.351260\pi\) | |||||||
\(578\) | −4.36603 | −0.181603 | ||||||||
\(579\) | 64.3628 | 2.67483 | ||||||||
\(580\) | 20.7088 | 0.859885 | ||||||||
\(581\) | −42.6262 | −1.76843 | ||||||||
\(582\) | −20.7901 | −0.861778 | ||||||||
\(583\) | 8.14571 | 0.337361 | ||||||||
\(584\) | −6.04356 | −0.250084 | ||||||||
\(585\) | −31.3600 | −1.29658 | ||||||||
\(586\) | 7.06624 | 0.291904 | ||||||||
\(587\) | −22.8445 | −0.942894 | −0.471447 | − | 0.881894i | \(-0.656268\pi\) | ||||
−0.471447 | + | 0.881894i | \(0.656268\pi\) | |||||||
\(588\) | 23.7508 | 0.979466 | ||||||||
\(589\) | −4.19406 | −0.172813 | ||||||||
\(590\) | 6.88620 | 0.283500 | ||||||||
\(591\) | 37.0921 | 1.52577 | ||||||||
\(592\) | 4.67498 | 0.192141 | ||||||||
\(593\) | 16.3335 | 0.670735 | 0.335368 | − | 0.942087i | \(-0.391139\pi\) | ||||
0.335368 | + | 0.942087i | \(0.391139\pi\) | |||||||
\(594\) | −12.8972 | −0.529177 | ||||||||
\(595\) | 37.1856 | 1.52446 | ||||||||
\(596\) | 12.1540 | 0.497848 | ||||||||
\(597\) | 36.4180 | 1.49049 | ||||||||
\(598\) | −6.56438 | −0.268437 | ||||||||
\(599\) | −30.5769 | −1.24934 | −0.624668 | − | 0.780890i | \(-0.714766\pi\) | ||||
−0.624668 | + | 0.780890i | \(0.714766\pi\) | |||||||
\(600\) | 8.12638 | 0.331758 | ||||||||
\(601\) | 20.5192 | 0.836997 | 0.418499 | − | 0.908217i | \(-0.362556\pi\) | ||||
0.418499 | + | 0.908217i | \(0.362556\pi\) | |||||||
\(602\) | 29.6792 | 1.20963 | ||||||||
\(603\) | 0.331027 | 0.0134805 | ||||||||
\(604\) | −2.34401 | −0.0953765 | ||||||||
\(605\) | −27.5245 | −1.11903 | ||||||||
\(606\) | −12.8399 | −0.521584 | ||||||||
\(607\) | −18.3804 | −0.746039 | −0.373019 | − | 0.927824i | \(-0.621678\pi\) | ||||
−0.373019 | + | 0.927824i | \(0.621678\pi\) | |||||||
\(608\) | 1.37594 | 0.0558017 | ||||||||
\(609\) | −91.0157 | −3.68814 | ||||||||
\(610\) | −41.8315 | −1.69371 | ||||||||
\(611\) | −9.48637 | −0.383778 | ||||||||
\(612\) | −25.1806 | −1.01787 | ||||||||
\(613\) | −0.655604 | −0.0264796 | −0.0132398 | − | 0.999912i | \(-0.504214\pi\) | ||||
−0.0132398 | + | 0.999912i | \(0.504214\pi\) | |||||||
\(614\) | −3.77208 | −0.152229 | ||||||||
\(615\) | −63.7163 | −2.56929 | ||||||||
\(616\) | 3.78378 | 0.152453 | ||||||||
\(617\) | −23.5073 | −0.946367 | −0.473184 | − | 0.880964i | \(-0.656895\pi\) | ||||
−0.473184 | + | 0.880964i | \(0.656895\pi\) | |||||||
\(618\) | 16.0807 | 0.646859 | ||||||||
\(619\) | 9.69469 | 0.389663 | 0.194831 | − | 0.980837i | \(-0.437584\pi\) | ||||
0.194831 | + | 0.980837i | \(0.437584\pi\) | |||||||
\(620\) | −8.38047 | −0.336568 | ||||||||
\(621\) | 52.8795 | 2.12198 | ||||||||
\(622\) | −19.8737 | −0.796863 | ||||||||
\(623\) | 55.8466 | 2.23745 | ||||||||
\(624\) | −5.11293 | −0.204681 | ||||||||
\(625\) | −31.2465 | −1.24986 | ||||||||
\(626\) | −25.6759 | −1.02622 | ||||||||
\(627\) | −4.34486 | −0.173517 | ||||||||
\(628\) | 17.7604 | 0.708715 | ||||||||
\(629\) | −16.6169 | −0.662559 | ||||||||
\(630\) | −74.1143 | −2.95278 | ||||||||
\(631\) | 31.8474 | 1.26783 | 0.633913 | − | 0.773404i | \(-0.281448\pi\) | ||||
0.633913 | + | 0.773404i | \(0.281448\pi\) | |||||||
\(632\) | −5.29564 | −0.210649 | ||||||||
\(633\) | −11.3268 | −0.450198 | ||||||||
\(634\) | −13.4370 | −0.533653 | ||||||||
\(635\) | −45.8265 | −1.81857 | ||||||||
\(636\) | −26.0134 | −1.03150 | ||||||||
\(637\) | −12.0421 | −0.477125 | ||||||||
\(638\) | −7.48989 | −0.296528 | ||||||||
\(639\) | 71.4945 | 2.82828 | ||||||||
\(640\) | 2.74937 | 0.108678 | ||||||||
\(641\) | 2.87122 | 0.113406 | 0.0567032 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567032 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(642\) | −31.5997 | −1.24714 | ||||||||
\(643\) | −7.13336 | −0.281312 | −0.140656 | − | 0.990058i | \(-0.544921\pi\) | ||||
−0.140656 | + | 0.990058i | \(0.544921\pi\) | |||||||
\(644\) | −15.5138 | −0.611331 | ||||||||
\(645\) | −68.0981 | −2.68136 | ||||||||
\(646\) | −4.89068 | −0.192421 | ||||||||
\(647\) | 7.48721 | 0.294353 | 0.147176 | − | 0.989110i | \(-0.452982\pi\) | ||||
0.147176 | + | 0.989110i | \(0.452982\pi\) | |||||||
\(648\) | 19.9344 | 0.783096 | ||||||||
\(649\) | −2.49058 | −0.0977640 | ||||||||
\(650\) | −4.12022 | −0.161608 | ||||||||
\(651\) | 36.8324 | 1.44358 | ||||||||
\(652\) | −3.80818 | −0.149140 | ||||||||
\(653\) | −43.3869 | −1.69786 | −0.848929 | − | 0.528506i | \(-0.822752\pi\) | ||||
−0.848929 | + | 0.528506i | \(0.822752\pi\) | |||||||
\(654\) | −18.6730 | −0.730173 | ||||||||
\(655\) | 51.2625 | 2.00299 | ||||||||
\(656\) | −7.29785 | −0.284933 | ||||||||
\(657\) | −42.8144 | −1.67035 | ||||||||
\(658\) | −22.4195 | −0.874003 | ||||||||
\(659\) | −44.7861 | −1.74462 | −0.872309 | − | 0.488955i | \(-0.837378\pi\) | ||||
−0.872309 | + | 0.488955i | \(0.837378\pi\) | |||||||
\(660\) | −8.68180 | −0.337939 | ||||||||
\(661\) | −10.0915 | −0.392514 | −0.196257 | − | 0.980552i | \(-0.562879\pi\) | ||||
−0.196257 | + | 0.980552i | \(0.562879\pi\) | |||||||
\(662\) | 4.05100 | 0.157447 | ||||||||
\(663\) | 18.1735 | 0.705802 | ||||||||
\(664\) | 11.2022 | 0.434731 | ||||||||
\(665\) | −14.3948 | −0.558205 | ||||||||
\(666\) | 33.1190 | 1.28333 | ||||||||
\(667\) | 30.7092 | 1.18906 | ||||||||
\(668\) | 13.7656 | 0.532608 | ||||||||
\(669\) | 63.7166 | 2.46342 | ||||||||
\(670\) | 0.128469 | 0.00496320 | ||||||||
\(671\) | 15.1295 | 0.584068 | ||||||||
\(672\) | −12.0836 | −0.466134 | ||||||||
\(673\) | 6.51802 | 0.251251 | 0.125626 | − | 0.992078i | \(-0.459906\pi\) | ||||
0.125626 | + | 0.992078i | \(0.459906\pi\) | |||||||
\(674\) | −4.81379 | −0.185420 | ||||||||
\(675\) | 33.1905 | 1.27750 | ||||||||
\(676\) | −10.4077 | −0.400294 | ||||||||
\(677\) | −0.510876 | −0.0196346 | −0.00981728 | − | 0.999952i | \(-0.503125\pi\) | ||||
−0.00981728 | + | 0.999952i | \(0.503125\pi\) | |||||||
\(678\) | −51.2847 | −1.96958 | ||||||||
\(679\) | 24.9119 | 0.956030 | ||||||||
\(680\) | −9.77243 | −0.374756 | ||||||||
\(681\) | 51.2586 | 1.96423 | ||||||||
\(682\) | 3.03103 | 0.116064 | ||||||||
\(683\) | −11.2651 | −0.431047 | −0.215524 | − | 0.976499i | \(-0.569146\pi\) | ||||
−0.215524 | + | 0.976499i | \(0.569146\pi\) | |||||||
\(684\) | 9.74756 | 0.372707 | ||||||||
\(685\) | 4.88423 | 0.186617 | ||||||||
\(686\) | −1.82342 | −0.0696186 | ||||||||
\(687\) | −68.5045 | −2.61361 | ||||||||
\(688\) | −7.79973 | −0.297362 | ||||||||
\(689\) | 13.1893 | 0.502472 | ||||||||
\(690\) | 35.5961 | 1.35512 | ||||||||
\(691\) | −1.08585 | −0.0413077 | −0.0206539 | − | 0.999787i | \(-0.506575\pi\) | ||||
−0.0206539 | + | 0.999787i | \(0.506575\pi\) | |||||||
\(692\) | 19.3413 | 0.735246 | ||||||||
\(693\) | 26.8055 | 1.01826 | ||||||||
\(694\) | −28.0304 | −1.06402 | ||||||||
\(695\) | 6.24491 | 0.236883 | ||||||||
\(696\) | 23.9191 | 0.906650 | ||||||||
\(697\) | 25.9397 | 0.982536 | ||||||||
\(698\) | −14.5076 | −0.549120 | ||||||||
\(699\) | 77.1788 | 2.91917 | ||||||||
\(700\) | −9.73748 | −0.368042 | ||||||||
\(701\) | −4.11280 | −0.155338 | −0.0776691 | − | 0.996979i | \(-0.524748\pi\) | ||||
−0.0776691 | + | 0.996979i | \(0.524748\pi\) | |||||||
\(702\) | −20.8827 | −0.788167 | ||||||||
\(703\) | 6.43249 | 0.242606 | ||||||||
\(704\) | −0.994384 | −0.0374773 | ||||||||
\(705\) | 51.4410 | 1.93738 | ||||||||
\(706\) | 18.4431 | 0.694114 | ||||||||
\(707\) | 15.3854 | 0.578629 | ||||||||
\(708\) | 7.95371 | 0.298919 | ||||||||
\(709\) | 43.8863 | 1.64819 | 0.824093 | − | 0.566455i | \(-0.191686\pi\) | ||||
0.824093 | + | 0.566455i | \(0.191686\pi\) | |||||||
\(710\) | 27.7465 | 1.04131 | ||||||||
\(711\) | −37.5159 | −1.40696 | ||||||||
\(712\) | −14.6766 | −0.550028 | ||||||||
\(713\) | −12.4275 | −0.465412 | ||||||||
\(714\) | 42.9502 | 1.60737 | ||||||||
\(715\) | 4.40183 | 0.164619 | ||||||||
\(716\) | −0.585208 | −0.0218702 | ||||||||
\(717\) | 55.8456 | 2.08559 | ||||||||
\(718\) | 18.4513 | 0.688595 | ||||||||
\(719\) | −17.6201 | −0.657120 | −0.328560 | − | 0.944483i | \(-0.606563\pi\) | ||||
−0.328560 | + | 0.944483i | \(0.606563\pi\) | |||||||
\(720\) | 19.4773 | 0.725877 | ||||||||
\(721\) | −19.2687 | −0.717605 | ||||||||
\(722\) | −17.1068 | −0.636649 | ||||||||
\(723\) | 31.2199 | 1.16108 | ||||||||
\(724\) | −1.34299 | −0.0499120 | ||||||||
\(725\) | 19.2750 | 0.715857 | ||||||||
\(726\) | −31.7913 | −1.17989 | ||||||||
\(727\) | −3.49375 | −0.129576 | −0.0647881 | − | 0.997899i | \(-0.520637\pi\) | ||||
−0.0647881 | + | 0.997899i | \(0.520637\pi\) | |||||||
\(728\) | 6.12659 | 0.227067 | ||||||||
\(729\) | 17.6592 | 0.654045 | ||||||||
\(730\) | −16.6160 | −0.614984 | ||||||||
\(731\) | 27.7236 | 1.02539 | ||||||||
\(732\) | −48.3162 | −1.78582 | ||||||||
\(733\) | −28.8437 | −1.06537 | −0.532684 | − | 0.846314i | \(-0.678817\pi\) | ||||
−0.532684 | + | 0.846314i | \(0.678817\pi\) | |||||||
\(734\) | 29.7137 | 1.09675 | ||||||||
\(735\) | 65.2996 | 2.40861 | ||||||||
\(736\) | 4.07706 | 0.150282 | ||||||||
\(737\) | −0.0464644 | −0.00171154 | ||||||||
\(738\) | −51.7001 | −1.90311 | ||||||||
\(739\) | 20.2013 | 0.743118 | 0.371559 | − | 0.928409i | \(-0.378823\pi\) | ||||
0.371559 | + | 0.928409i | \(0.378823\pi\) | |||||||
\(740\) | 12.8532 | 0.472495 | ||||||||
\(741\) | −7.03507 | −0.258440 | ||||||||
\(742\) | 31.1707 | 1.14431 | ||||||||
\(743\) | 6.51897 | 0.239158 | 0.119579 | − | 0.992825i | \(-0.461846\pi\) | ||||
0.119579 | + | 0.992825i | \(0.461846\pi\) | |||||||
\(744\) | −9.67962 | −0.354872 | ||||||||
\(745\) | 33.4158 | 1.22426 | ||||||||
\(746\) | 28.2684 | 1.03498 | ||||||||
\(747\) | 79.3599 | 2.90363 | ||||||||
\(748\) | 3.53447 | 0.129233 | ||||||||
\(749\) | 37.8645 | 1.38354 | ||||||||
\(750\) | −21.3118 | −0.778196 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 5.89187 | 0.214855 | ||||||||
\(753\) | 51.1643 | 1.86453 | ||||||||
\(754\) | −12.1274 | −0.441654 | ||||||||
\(755\) | −6.44455 | −0.234541 | ||||||||
\(756\) | −49.3529 | −1.79495 | ||||||||
\(757\) | −46.8268 | −1.70195 | −0.850975 | − | 0.525206i | \(-0.823988\pi\) | ||||
−0.850975 | + | 0.525206i | \(0.823988\pi\) | |||||||
\(758\) | −3.52360 | −0.127983 | ||||||||
\(759\) | −12.8743 | −0.467308 | ||||||||
\(760\) | 3.78296 | 0.137222 | ||||||||
\(761\) | 41.4119 | 1.50118 | 0.750590 | − | 0.660768i | \(-0.229769\pi\) | ||||
0.750590 | + | 0.660768i | \(0.229769\pi\) | |||||||
\(762\) | −52.9306 | −1.91747 | ||||||||
\(763\) | 22.3751 | 0.810032 | ||||||||
\(764\) | 24.4599 | 0.884927 | ||||||||
\(765\) | −69.2308 | −2.50305 | ||||||||
\(766\) | 30.7104 | 1.10961 | ||||||||
\(767\) | −4.03268 | −0.145612 | ||||||||
\(768\) | 3.17558 | 0.114589 | ||||||||
\(769\) | −9.69312 | −0.349543 | −0.174771 | − | 0.984609i | \(-0.555919\pi\) | ||||
−0.174771 | + | 0.984609i | \(0.555919\pi\) | |||||||
\(770\) | 10.4030 | 0.374899 | ||||||||
\(771\) | 12.4878 | 0.449737 | ||||||||
\(772\) | 20.2681 | 0.729464 | ||||||||
\(773\) | −50.4613 | −1.81497 | −0.907484 | − | 0.420087i | \(-0.861999\pi\) | ||||
−0.907484 | + | 0.420087i | \(0.861999\pi\) | |||||||
\(774\) | −55.2556 | −1.98612 | ||||||||
\(775\) | −7.80027 | −0.280194 | ||||||||
\(776\) | −6.54687 | −0.235019 | ||||||||
\(777\) | −56.4904 | −2.02658 | ||||||||
\(778\) | −14.8158 | −0.531174 | ||||||||
\(779\) | −10.0414 | −0.359770 | ||||||||
\(780\) | −14.0573 | −0.503333 | ||||||||
\(781\) | −10.0353 | −0.359091 | ||||||||
\(782\) | −14.4916 | −0.518219 | ||||||||
\(783\) | 97.6925 | 3.49125 | ||||||||
\(784\) | 7.47920 | 0.267114 | ||||||||
\(785\) | 48.8297 | 1.74281 | ||||||||
\(786\) | 59.2093 | 2.11193 | ||||||||
\(787\) | 37.8382 | 1.34878 | 0.674392 | − | 0.738373i | \(-0.264406\pi\) | ||||
0.674392 | + | 0.738373i | \(0.264406\pi\) | |||||||
\(788\) | 11.6804 | 0.416098 | ||||||||
\(789\) | −40.6102 | −1.44576 | ||||||||
\(790\) | −14.5597 | −0.518010 | ||||||||
\(791\) | 61.4522 | 2.18499 | ||||||||
\(792\) | −7.04451 | −0.250316 | ||||||||
\(793\) | 24.4972 | 0.869922 | ||||||||
\(794\) | 13.4129 | 0.476006 | ||||||||
\(795\) | −71.5205 | −2.53657 | ||||||||
\(796\) | 11.4681 | 0.406477 | ||||||||
\(797\) | 30.8500 | 1.09276 | 0.546381 | − | 0.837537i | \(-0.316005\pi\) | ||||
0.546381 | + | 0.837537i | \(0.316005\pi\) | |||||||
\(798\) | −16.6263 | −0.588563 | ||||||||
\(799\) | −20.9423 | −0.740884 | ||||||||
\(800\) | 2.55902 | 0.0904751 | ||||||||
\(801\) | −103.973 | −3.67371 | ||||||||
\(802\) | −37.5566 | −1.32617 | ||||||||
\(803\) | 6.00962 | 0.212075 | ||||||||
\(804\) | 0.148385 | 0.00523312 | ||||||||
\(805\) | −42.6532 | −1.50333 | ||||||||
\(806\) | 4.90775 | 0.172868 | ||||||||
\(807\) | 86.4334 | 3.04260 | ||||||||
\(808\) | −4.04332 | −0.142243 | ||||||||
\(809\) | 23.9700 | 0.842740 | 0.421370 | − | 0.906889i | \(-0.361549\pi\) | ||||
0.421370 | + | 0.906889i | \(0.361549\pi\) | |||||||
\(810\) | 54.8069 | 1.92572 | ||||||||
\(811\) | −49.0754 | −1.72327 | −0.861636 | − | 0.507527i | \(-0.830560\pi\) | ||||
−0.861636 | + | 0.507527i | \(0.830560\pi\) | |||||||
\(812\) | −28.6611 | −1.00581 | ||||||||
\(813\) | −49.5997 | −1.73954 | ||||||||
\(814\) | −4.64873 | −0.162938 | ||||||||
\(815\) | −10.4701 | −0.366751 | ||||||||
\(816\) | −11.2874 | −0.395137 | ||||||||
\(817\) | −10.7320 | −0.375464 | ||||||||
\(818\) | 24.0263 | 0.840060 | ||||||||
\(819\) | 43.4026 | 1.51661 | ||||||||
\(820\) | −20.0645 | −0.700682 | ||||||||
\(821\) | 49.4463 | 1.72569 | 0.862843 | − | 0.505471i | \(-0.168681\pi\) | ||||
0.862843 | + | 0.505471i | \(0.168681\pi\) | |||||||
\(822\) | 5.64139 | 0.196766 | ||||||||
\(823\) | 46.6706 | 1.62683 | 0.813417 | − | 0.581681i | \(-0.197605\pi\) | ||||
0.813417 | + | 0.581681i | \(0.197605\pi\) | |||||||
\(824\) | 5.06385 | 0.176408 | ||||||||
\(825\) | −8.08074 | −0.281335 | ||||||||
\(826\) | −9.53058 | −0.331611 | ||||||||
\(827\) | −2.64911 | −0.0921185 | −0.0460593 | − | 0.998939i | \(-0.514666\pi\) | ||||
−0.0460593 | + | 0.998939i | \(0.514666\pi\) | |||||||
\(828\) | 28.8831 | 1.00376 | ||||||||
\(829\) | −0.533637 | −0.0185340 | −0.00926699 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926699 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(830\) | 30.7990 | 1.06905 | ||||||||
\(831\) | 47.9347 | 1.66284 | ||||||||
\(832\) | −1.61008 | −0.0558194 | ||||||||
\(833\) | −26.5843 | −0.921091 | ||||||||
\(834\) | 7.21300 | 0.249766 | ||||||||
\(835\) | 37.8468 | 1.30974 | ||||||||
\(836\) | −1.36821 | −0.0473206 | ||||||||
\(837\) | −39.5344 | −1.36651 | ||||||||
\(838\) | −32.4579 | −1.12124 | ||||||||
\(839\) | 3.26426 | 0.112695 | 0.0563474 | − | 0.998411i | \(-0.482055\pi\) | ||||
0.0563474 | + | 0.998411i | \(0.482055\pi\) | |||||||
\(840\) | −33.2222 | −1.14627 | ||||||||
\(841\) | 27.7339 | 0.956341 | ||||||||
\(842\) | 14.0767 | 0.485114 | ||||||||
\(843\) | −41.6389 | −1.43412 | ||||||||
\(844\) | −3.56683 | −0.122775 | ||||||||
\(845\) | −28.6145 | −0.984367 | ||||||||
\(846\) | 41.7398 | 1.43504 | ||||||||
\(847\) | 38.0942 | 1.30893 | ||||||||
\(848\) | −8.19172 | −0.281305 | ||||||||
\(849\) | 49.8347 | 1.71032 | ||||||||
\(850\) | −9.09587 | −0.311986 | ||||||||
\(851\) | 19.0602 | 0.653374 | ||||||||
\(852\) | 32.0478 | 1.09794 | ||||||||
\(853\) | 49.6838 | 1.70114 | 0.850571 | − | 0.525860i | \(-0.176256\pi\) | ||||
0.850571 | + | 0.525860i | \(0.176256\pi\) | |||||||
\(854\) | 57.8952 | 1.98113 | ||||||||
\(855\) | 26.7996 | 0.916528 | ||||||||
\(856\) | −9.95084 | −0.340113 | ||||||||
\(857\) | 16.8291 | 0.574870 | 0.287435 | − | 0.957800i | \(-0.407198\pi\) | ||||
0.287435 | + | 0.957800i | \(0.407198\pi\) | |||||||
\(858\) | 5.08421 | 0.173572 | ||||||||
\(859\) | 2.57724 | 0.0879343 | 0.0439671 | − | 0.999033i | \(-0.486000\pi\) | ||||
0.0439671 | + | 0.999033i | \(0.486000\pi\) | |||||||
\(860\) | −21.4443 | −0.731246 | ||||||||
\(861\) | 88.1840 | 3.00530 | ||||||||
\(862\) | −9.86060 | −0.335853 | ||||||||
\(863\) | 24.7556 | 0.842690 | 0.421345 | − | 0.906901i | \(-0.361558\pi\) | ||||
0.421345 | + | 0.906901i | \(0.361558\pi\) | |||||||
\(864\) | 12.9700 | 0.441248 | ||||||||
\(865\) | 53.1764 | 1.80805 | ||||||||
\(866\) | 29.3909 | 0.998743 | ||||||||
\(867\) | −13.8647 | −0.470869 | ||||||||
\(868\) | 11.5987 | 0.393684 | ||||||||
\(869\) | 5.26590 | 0.178634 | ||||||||
\(870\) | 65.7623 | 2.22955 | ||||||||
\(871\) | −0.0752338 | −0.00254920 | ||||||||
\(872\) | −5.88020 | −0.199129 | ||||||||
\(873\) | −46.3800 | −1.56973 | ||||||||
\(874\) | 5.60979 | 0.189754 | ||||||||
\(875\) | 25.5369 | 0.863306 | ||||||||
\(876\) | −19.1918 | −0.648431 | ||||||||
\(877\) | 27.8969 | 0.942012 | 0.471006 | − | 0.882130i | \(-0.343891\pi\) | ||||
0.471006 | + | 0.882130i | \(0.343891\pi\) | |||||||
\(878\) | −4.57873 | −0.154525 | ||||||||
\(879\) | 22.4394 | 0.756863 | ||||||||
\(880\) | −2.73393 | −0.0921607 | ||||||||
\(881\) | −55.8653 | −1.88215 | −0.941074 | − | 0.338200i | \(-0.890182\pi\) | ||||
−0.941074 | + | 0.338200i | \(0.890182\pi\) | |||||||
\(882\) | 52.9849 | 1.78409 | ||||||||
\(883\) | −44.8709 | −1.51003 | −0.755014 | − | 0.655709i | \(-0.772370\pi\) | ||||
−0.755014 | + | 0.655709i | \(0.772370\pi\) | |||||||
\(884\) | 5.72291 | 0.192482 | ||||||||
\(885\) | 21.8677 | 0.735074 | ||||||||
\(886\) | −36.6705 | −1.23197 | ||||||||
\(887\) | −7.01672 | −0.235598 | −0.117799 | − | 0.993037i | \(-0.537584\pi\) | ||||
−0.117799 | + | 0.993037i | \(0.537584\pi\) | |||||||
\(888\) | 14.8458 | 0.498191 | ||||||||
\(889\) | 63.4244 | 2.12719 | ||||||||
\(890\) | −40.3513 | −1.35258 | ||||||||
\(891\) | −19.8224 | −0.664076 | ||||||||
\(892\) | 20.0646 | 0.671811 | ||||||||
\(893\) | 8.10686 | 0.271286 | ||||||||
\(894\) | 38.5960 | 1.29084 | ||||||||
\(895\) | −1.60895 | −0.0537813 | ||||||||
\(896\) | −3.80515 | −0.127121 | ||||||||
\(897\) | −20.8457 | −0.696018 | ||||||||
\(898\) | −10.6630 | −0.355827 | ||||||||
\(899\) | −22.9592 | −0.765732 | ||||||||
\(900\) | 18.1289 | 0.604296 | ||||||||
\(901\) | 29.1169 | 0.970024 | ||||||||
\(902\) | 7.25686 | 0.241627 | ||||||||
\(903\) | 94.2486 | 3.13640 | ||||||||
\(904\) | −16.1497 | −0.537132 | ||||||||
\(905\) | −3.69239 | −0.122739 | ||||||||
\(906\) | −7.44359 | −0.247297 | ||||||||
\(907\) | −4.56437 | −0.151557 | −0.0757787 | − | 0.997125i | \(-0.524144\pi\) | ||||
−0.0757787 | + | 0.997125i | \(0.524144\pi\) | |||||||
\(908\) | 16.1415 | 0.535675 | ||||||||
\(909\) | −28.6441 | −0.950063 | ||||||||
\(910\) | 16.8443 | 0.558382 | ||||||||
\(911\) | 24.8789 | 0.824275 | 0.412138 | − | 0.911122i | \(-0.364782\pi\) | ||||
0.412138 | + | 0.911122i | \(0.364782\pi\) | |||||||
\(912\) | 4.36940 | 0.144685 | ||||||||
\(913\) | −11.1393 | −0.368658 | ||||||||
\(914\) | 39.1144 | 1.29379 | ||||||||
\(915\) | −132.839 | −4.39153 | ||||||||
\(916\) | −21.5723 | −0.712768 | ||||||||
\(917\) | −70.9479 | −2.34291 | ||||||||
\(918\) | −46.1010 | −1.52156 | ||||||||
\(919\) | 21.3410 | 0.703976 | 0.351988 | − | 0.936005i | \(-0.385506\pi\) | ||||
0.351988 | + | 0.936005i | \(0.385506\pi\) | |||||||
\(920\) | 11.2093 | 0.369561 | ||||||||
\(921\) | −11.9785 | −0.394706 | ||||||||
\(922\) | −32.6190 | −1.07425 | ||||||||
\(923\) | −16.2488 | −0.534837 | ||||||||
\(924\) | 12.0157 | 0.395288 | ||||||||
\(925\) | 11.9634 | 0.393354 | ||||||||
\(926\) | −7.87682 | −0.258848 | ||||||||
\(927\) | 35.8738 | 1.17825 | ||||||||
\(928\) | 7.53219 | 0.247256 | ||||||||
\(929\) | −5.14653 | −0.168852 | −0.0844261 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844261 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(930\) | −26.6128 | −0.872669 | ||||||||
\(931\) | 10.2909 | 0.337271 | ||||||||
\(932\) | 24.3039 | 0.796099 | ||||||||
\(933\) | −63.1105 | −2.06614 | ||||||||
\(934\) | 29.1726 | 0.954556 | ||||||||
\(935\) | 9.71755 | 0.317798 | ||||||||
\(936\) | −11.4063 | −0.372825 | ||||||||
\(937\) | 22.1701 | 0.724267 | 0.362134 | − | 0.932126i | \(-0.382048\pi\) | ||||
0.362134 | + | 0.932126i | \(0.382048\pi\) | |||||||
\(938\) | −0.177803 | −0.00580547 | ||||||||
\(939\) | −81.5359 | −2.66082 | ||||||||
\(940\) | 16.1989 | 0.528351 | ||||||||
\(941\) | −13.8102 | −0.450199 | −0.225100 | − | 0.974336i | \(-0.572271\pi\) | ||||
−0.225100 | + | 0.974336i | \(0.572271\pi\) | |||||||
\(942\) | 56.3994 | 1.83759 | ||||||||
\(943\) | −29.7538 | −0.968916 | ||||||||
\(944\) | 2.50465 | 0.0815194 | ||||||||
\(945\) | −135.689 | −4.41397 | ||||||||
\(946\) | 7.75593 | 0.252167 | ||||||||
\(947\) | 2.78480 | 0.0904938 | 0.0452469 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452469 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(948\) | −16.8167 | −0.546182 | ||||||||
\(949\) | 9.73060 | 0.315868 | ||||||||
\(950\) | 3.52106 | 0.114238 | ||||||||
\(951\) | −42.6704 | −1.38368 | ||||||||
\(952\) | 13.5252 | 0.438353 | ||||||||
\(953\) | 10.7432 | 0.348006 | 0.174003 | − | 0.984745i | \(-0.444330\pi\) | ||||
0.174003 | + | 0.984745i | \(0.444330\pi\) | |||||||
\(954\) | −58.0326 | −1.87887 | ||||||||
\(955\) | 67.2492 | 2.17613 | ||||||||
\(956\) | 17.5860 | 0.568771 | ||||||||
\(957\) | −23.7847 | −0.768851 | ||||||||
\(958\) | −10.5245 | −0.340032 | ||||||||
\(959\) | −6.75983 | −0.218286 | ||||||||
\(960\) | 8.73083 | 0.281786 | ||||||||
\(961\) | −21.7088 | −0.700285 | ||||||||
\(962\) | −7.52708 | −0.242683 | ||||||||
\(963\) | −70.4947 | −2.27166 | ||||||||
\(964\) | 9.83124 | 0.316643 | ||||||||
\(965\) | 55.7244 | 1.79383 | ||||||||
\(966\) | −49.2654 | −1.58509 | ||||||||
\(967\) | 28.4197 | 0.913918 | 0.456959 | − | 0.889488i | \(-0.348939\pi\) | ||||
0.456959 | + | 0.889488i | \(0.348939\pi\) | |||||||
\(968\) | −10.0112 | −0.321772 | ||||||||
\(969\) | −15.5307 | −0.498919 | ||||||||
\(970\) | −17.9998 | −0.577938 | ||||||||
\(971\) | −26.3117 | −0.844382 | −0.422191 | − | 0.906507i | \(-0.638739\pi\) | ||||
−0.422191 | + | 0.906507i | \(0.638739\pi\) | |||||||
\(972\) | 24.3931 | 0.782410 | ||||||||
\(973\) | −8.64302 | −0.277083 | ||||||||
\(974\) | 40.4170 | 1.29504 | ||||||||
\(975\) | −13.0841 | −0.419026 | ||||||||
\(976\) | −15.2149 | −0.487019 | ||||||||
\(977\) | 33.3912 | 1.06828 | 0.534139 | − | 0.845396i | \(-0.320636\pi\) | ||||
0.534139 | + | 0.845396i | \(0.320636\pi\) | |||||||
\(978\) | −12.0932 | −0.386697 | ||||||||
\(979\) | 14.5942 | 0.466431 | ||||||||
\(980\) | 20.5631 | 0.656863 | ||||||||
\(981\) | −41.6571 | −1.33001 | ||||||||
\(982\) | 12.7430 | 0.406647 | ||||||||
\(983\) | 14.4612 | 0.461239 | 0.230620 | − | 0.973044i | \(-0.425925\pi\) | ||||
0.230620 | + | 0.973044i | \(0.425925\pi\) | |||||||
\(984\) | −23.1749 | −0.738788 | ||||||||
\(985\) | 32.1138 | 1.02323 | ||||||||
\(986\) | −26.7726 | −0.852615 | ||||||||
\(987\) | −71.1948 | −2.26616 | ||||||||
\(988\) | −2.21537 | −0.0704802 | ||||||||
\(989\) | −31.8000 | −1.01118 | ||||||||
\(990\) | −19.3680 | −0.615554 | ||||||||
\(991\) | −22.3146 | −0.708848 | −0.354424 | − | 0.935085i | \(-0.615323\pi\) | ||||
−0.354424 | + | 0.935085i | \(0.615323\pi\) | |||||||
\(992\) | −3.04814 | −0.0967786 | ||||||||
\(993\) | 12.8643 | 0.408235 | ||||||||
\(994\) | −38.4015 | −1.21802 | ||||||||
\(995\) | 31.5301 | 0.999573 | ||||||||
\(996\) | 35.5735 | 1.12719 | ||||||||
\(997\) | −34.8376 | −1.10332 | −0.551659 | − | 0.834070i | \(-0.686005\pi\) | ||||
−0.551659 | + | 0.834070i | \(0.686005\pi\) | |||||||
\(998\) | −11.4162 | −0.361375 | ||||||||
\(999\) | 60.6345 | 1.91839 |
(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 | 1502.2.a.g.1.16 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.g.1.16 | ✓ | 16 | 1.1 | even | 1 | trivial |