Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1890,2,Mod(1889,1890)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1890, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1890.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1890.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(15.0917259820\) |
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: | \( x^{16} - 3 x^{15} + 3 x^{14} + 5 x^{12} + 15 x^{11} - 12 x^{10} + 381 x^{9} - 1356 x^{8} + 1905 x^{7} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.15 | ||
Root | \(0.599527 - 2.15420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1890.1889 |
Dual form | 1890.2.d.e.1889.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(1081\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.16535 | − | 0.557894i | 0.968375 | − | 0.249498i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39492 | − | 2.24815i | −0.527230 | − | 0.849722i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.16535 | + | 0.557894i | −0.684745 | + | 0.176421i | ||||
\(11\) | − | 3.69641i | − | 1.11451i | −0.830341 | − | 0.557256i | \(-0.811854\pi\) | ||
0.830341 | − | 0.557256i | \(-0.188146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.958131 | 0.265738 | 0.132869 | − | 0.991134i | \(-0.457581\pi\) | ||||
0.132869 | + | 0.991134i | \(0.457581\pi\) | |||||||
\(14\) | 1.39492 | + | 2.24815i | 0.372808 | + | 0.600844i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.53776i | − | 0.372962i | −0.982459 | − | 0.186481i | \(-0.940292\pi\) | ||
0.982459 | − | 0.186481i | \(-0.0597083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.31008i | − | 0.300552i | −0.988644 | − | 0.150276i | \(-0.951984\pi\) | ||
0.988644 | − | 0.150276i | \(-0.0480162\pi\) | |||||||
\(20\) | 2.16535 | − | 0.557894i | 0.484188 | − | 0.124749i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.69641i | 0.788078i | ||||||||
\(23\) | −7.48590 | −1.56092 | −0.780459 | − | 0.625207i | \(-0.785015\pi\) | ||||
−0.780459 | + | 0.625207i | \(0.785015\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.37751 | − | 2.41607i | 0.875502 | − | 0.483215i | ||||
\(26\) | −0.958131 | −0.187905 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.39492 | − | 2.24815i | −0.263615 | − | 0.424861i | ||||
\(29\) | − | 3.86433i | − | 0.717589i | −0.933417 | − | 0.358794i | \(-0.883188\pi\) | ||
0.933417 | − | 0.358794i | \(-0.116812\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.04213i | 0.546382i | 0.961960 | + | 0.273191i | \(0.0880791\pi\) | ||||
−0.961960 | + | 0.273191i | \(0.911921\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.53776i | 0.263724i | ||||||||
\(35\) | −4.27473 | − | 4.08983i | −0.722561 | − | 0.691307i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00470i | 0.493969i | 0.969019 | + | 0.246984i | \(0.0794397\pi\) | ||||
−0.969019 | + | 0.246984i | \(0.920560\pi\) | |||||||
\(38\) | 1.31008i | 0.212522i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.16535 | + | 0.557894i | −0.342372 | + | 0.0882107i | ||||
\(41\) | −2.07167 | −0.323541 | −0.161770 | − | 0.986828i | \(-0.551720\pi\) | ||||
−0.161770 | + | 0.986828i | \(0.551720\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.66423i | 0.711288i | 0.934621 | + | 0.355644i | \(0.115738\pi\) | ||||
−0.934621 | + | 0.355644i | \(0.884262\pi\) | |||||||
\(44\) | − | 3.69641i | − | 0.557256i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.48590 | 1.10374 | ||||||||
\(47\) | − | 12.3497i | − | 1.80139i | −0.434453 | − | 0.900694i | \(-0.643058\pi\) | ||
0.434453 | − | 0.900694i | \(-0.356942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.10839 | + | 6.27199i | −0.444056 | + | 0.895999i | ||||
\(50\) | −4.37751 | + | 2.41607i | −0.619073 | + | 0.341684i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.958131 | 0.132869 | ||||||||
\(53\) | −7.82242 | −1.07449 | −0.537246 | − | 0.843426i | \(-0.680535\pi\) | ||||
−0.537246 | + | 0.843426i | \(0.680535\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.06221 | − | 8.00404i | −0.278068 | − | 1.07927i | ||||
\(56\) | 1.39492 | + | 2.24815i | 0.186404 | + | 0.300422i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.86433i | 0.507412i | ||||||||
\(59\) | −10.1504 | −1.32146 | −0.660732 | − | 0.750622i | \(-0.729754\pi\) | ||||
−0.660732 | + | 0.750622i | \(0.729754\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | − | 3.04213i | − | 0.386350i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.07469 | − | 0.534535i | 0.257334 | − | 0.0663009i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.34516i | − | 0.164338i | −0.996618 | − | 0.0821690i | \(-0.973815\pi\) | ||
0.996618 | − | 0.0821690i | \(-0.0261847\pi\) | |||||||
\(68\) | − | 1.53776i | − | 0.186481i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.27473 | + | 4.08983i | 0.510928 | + | 0.488828i | ||||
\(71\) | 5.46412i | 0.648472i | 0.945976 | + | 0.324236i | \(0.105107\pi\) | ||||
−0.945976 | + | 0.324236i | \(0.894893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.94324 | 0.929686 | 0.464843 | − | 0.885393i | \(-0.346111\pi\) | ||||
0.464843 | + | 0.885393i | \(0.346111\pi\) | |||||||
\(74\) | − | 3.00470i | − | 0.349289i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.31008i | − | 0.150276i | ||||||
\(77\) | −8.31011 | + | 5.15621i | −0.947025 | + | 0.587604i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6876 | −1.42747 | −0.713734 | − | 0.700417i | \(-0.752998\pi\) | ||||
−0.713734 | + | 0.700417i | \(0.752998\pi\) | |||||||
\(80\) | 2.16535 | − | 0.557894i | 0.242094 | − | 0.0623744i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.07167 | 0.228778 | ||||||||
\(83\) | 0.194288i | 0.0213259i | 0.999943 | + | 0.0106629i | \(0.00339419\pi\) | ||||
−0.999943 | + | 0.0106629i | \(0.996606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.857908 | − | 3.32980i | −0.0930532 | − | 0.361167i | ||||
\(86\) | − | 4.66423i | − | 0.502957i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.69641i | 0.394039i | ||||||||
\(89\) | 1.16442 | 0.123429 | 0.0617144 | − | 0.998094i | \(-0.480343\pi\) | ||||
0.0617144 | + | 0.998094i | \(0.480343\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.33652 | − | 2.15403i | −0.140105 | − | 0.225803i | ||||
\(92\) | −7.48590 | −0.780459 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.3497i | 1.27377i | ||||||||
\(95\) | −0.730883 | − | 2.83678i | −0.0749870 | − | 0.291047i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.91039 | 1.00625 | 0.503124 | − | 0.864214i | \(-0.332184\pi\) | ||||
0.503124 | + | 0.864214i | \(0.332184\pi\) | |||||||
\(98\) | 3.10839 | − | 6.27199i | 0.313995 | − | 0.633567i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.37751 | − | 2.41607i | 0.437751 | − | 0.241607i | ||||
\(101\) | 15.0638 | 1.49890 | 0.749452 | − | 0.662059i | \(-0.230317\pi\) | ||||
0.749452 | + | 0.662059i | \(0.230317\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.54787 | 0.743714 | 0.371857 | − | 0.928290i | \(-0.378721\pi\) | ||||
0.371857 | + | 0.928290i | \(0.378721\pi\) | |||||||
\(104\) | −0.958131 | −0.0939525 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.82242 | 0.759780 | ||||||||
\(107\) | 1.93260 | 0.186832 | 0.0934158 | − | 0.995627i | \(-0.470221\pi\) | ||||
0.0934158 | + | 0.995627i | \(0.470221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.59608 | 0.344442 | 0.172221 | − | 0.985058i | \(-0.444906\pi\) | ||||
0.172221 | + | 0.985058i | \(0.444906\pi\) | |||||||
\(110\) | 2.06221 | + | 8.00404i | 0.196624 | + | 0.763156i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.39492 | − | 2.24815i | −0.131808 | − | 0.212431i | ||||
\(113\) | −7.59608 | −0.714579 | −0.357290 | − | 0.933994i | \(-0.616299\pi\) | ||||
−0.357290 | + | 0.933994i | \(0.616299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.2096 | + | 4.17634i | −1.51155 | + | 0.389445i | ||||
\(116\) | − | 3.86433i | − | 0.358794i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1504 | 0.934416 | ||||||||
\(119\) | −3.45713 | + | 2.14506i | −0.316914 | + | 0.196637i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.66348 | −0.242135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.04213i | 0.273191i | ||||||||
\(125\) | 8.13094 | − | 7.67384i | 0.727254 | − | 0.686369i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.908067i | 0.0805779i | 0.999188 | + | 0.0402890i | \(0.0128278\pi\) | ||||
−0.999188 | + | 0.0402890i | \(0.987172\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.07469 | + | 0.534535i | −0.181963 | + | 0.0468818i | ||||
\(131\) | 5.13343 | 0.448510 | 0.224255 | − | 0.974531i | \(-0.428005\pi\) | ||||
0.224255 | + | 0.974531i | \(0.428005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.94525 | + | 1.82745i | −0.255386 | + | 0.158460i | ||||
\(134\) | 1.34516i | 0.116204i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.53776i | 0.131862i | ||||||||
\(137\) | −8.55330 | −0.730758 | −0.365379 | − | 0.930859i | \(-0.619061\pi\) | ||||
−0.365379 | + | 0.930859i | \(0.619061\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 12.4272i | − | 1.05407i | −0.849845 | − | 0.527033i | \(-0.823305\pi\) | ||
0.849845 | − | 0.527033i | \(-0.176695\pi\) | |||||||
\(140\) | −4.27473 | − | 4.08983i | −0.361280 | − | 0.345654i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 5.46412i | − | 0.458539i | ||||||
\(143\) | − | 3.54165i | − | 0.296168i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.15589 | − | 8.36765i | −0.179037 | − | 0.694895i | ||||
\(146\) | −7.94324 | −0.657387 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00470i | 0.246984i | ||||||||
\(149\) | − | 14.7059i | − | 1.20475i | −0.798212 | − | 0.602376i | \(-0.794221\pi\) | ||
0.798212 | − | 0.602376i | \(-0.205779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0392 | −1.38663 | −0.693315 | − | 0.720634i | \(-0.743851\pi\) | ||||
−0.693315 | + | 0.720634i | \(0.743851\pi\) | |||||||
\(152\) | 1.31008i | 0.106261i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.31011 | − | 5.15621i | 0.669648 | − | 0.415499i | ||||
\(155\) | 1.69718 | + | 6.58728i | 0.136321 | + | 0.529103i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.60949 | −0.687112 | −0.343556 | − | 0.939132i | \(-0.611631\pi\) | ||||
−0.343556 | + | 0.939132i | \(0.611631\pi\) | |||||||
\(158\) | 12.6876 | 1.00937 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.16535 | + | 0.557894i | −0.171186 | + | 0.0441054i | ||||
\(161\) | 10.4422 | + | 16.8295i | 0.822964 | + | 1.32635i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4044i | 0.814939i | 0.913219 | + | 0.407469i | \(0.133589\pi\) | ||||
−0.913219 | + | 0.407469i | \(0.866411\pi\) | |||||||
\(164\) | −2.07167 | −0.161770 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 0.194288i | − | 0.0150797i | ||||||
\(167\) | 14.0483i | 1.08709i | 0.839379 | + | 0.543547i | \(0.182919\pi\) | ||||
−0.839379 | + | 0.543547i | \(0.817081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0820 | −0.929383 | ||||||||
\(170\) | 0.857908 | + | 3.32980i | 0.0657985 | + | 0.255384i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.66423i | 0.355644i | ||||||||
\(173\) | − | 14.1282i | − | 1.07415i | −0.843534 | − | 0.537075i | \(-0.819529\pi\) | ||
0.843534 | − | 0.537075i | \(-0.180471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.5380 | − | 6.47108i | −0.872190 | − | 0.489168i | ||||
\(176\) | − | 3.69641i | − | 0.278628i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.16442 | −0.0872773 | ||||||||
\(179\) | − | 25.3580i | − | 1.89535i | −0.319240 | − | 0.947674i | \(-0.603428\pi\) | ||
0.319240 | − | 0.947674i | \(-0.396572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 19.0502i | − | 1.41599i | −0.706217 | − | 0.707996i | \(-0.749600\pi\) | ||
0.706217 | − | 0.707996i | \(-0.250400\pi\) | |||||||
\(182\) | 1.33652 | + | 2.15403i | 0.0990692 | + | 0.159667i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.48590 | 0.551868 | ||||||||
\(185\) | 1.67630 | + | 6.50623i | 0.123244 | + | 0.478347i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.68421 | −0.415671 | ||||||||
\(188\) | − | 12.3497i | − | 0.900694i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.730883 | + | 2.83678i | 0.0530238 | + | 0.205801i | ||||
\(191\) | − | 10.8616i | − | 0.785916i | −0.919556 | − | 0.392958i | \(-0.871452\pi\) | ||
0.919556 | − | 0.392958i | \(-0.128548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 18.0865i | − | 1.30189i | −0.759123 | − | 0.650947i | \(-0.774372\pi\) | ||
0.759123 | − | 0.650947i | \(-0.225628\pi\) | |||||||
\(194\) | −9.91039 | −0.711525 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.10839 | + | 6.27199i | −0.222028 | + | 0.448000i | ||||
\(197\) | −4.20172 | −0.299360 | −0.149680 | − | 0.988734i | \(-0.547824\pi\) | ||||
−0.149680 | + | 0.988734i | \(0.547824\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 26.2395i | − | 1.86007i | −0.367472 | − | 0.930035i | \(-0.619777\pi\) | ||
0.367472 | − | 0.930035i | \(-0.380223\pi\) | |||||||
\(200\) | −4.37751 | + | 2.41607i | −0.309537 | + | 0.170842i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.0638 | −1.05988 | ||||||||
\(203\) | −8.68762 | + | 5.39044i | −0.609751 | + | 0.378335i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.48590 | + | 1.15577i | −0.313309 | + | 0.0807227i | ||||
\(206\) | −7.54787 | −0.525885 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.958131 | 0.0664344 | ||||||||
\(209\) | −4.84258 | −0.334968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1735 | −1.38880 | −0.694401 | − | 0.719588i | \(-0.744331\pi\) | ||||
−0.694401 | + | 0.719588i | \(0.744331\pi\) | |||||||
\(212\) | −7.82242 | −0.537246 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.93260 | −0.132110 | ||||||||
\(215\) | 2.60214 | + | 10.0997i | 0.177465 | + | 0.688794i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.83917 | − | 4.24353i | 0.464273 | − | 0.288069i | ||||
\(218\) | −3.59608 | −0.243557 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.06221 | − | 8.00404i | −0.139034 | − | 0.539633i | ||||
\(221\) | − | 1.47338i | − | 0.0991101i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.1775 | 1.21725 | 0.608627 | − | 0.793457i | \(-0.291721\pi\) | ||||
0.608627 | + | 0.793457i | \(0.291721\pi\) | |||||||
\(224\) | 1.39492 | + | 2.24815i | 0.0932021 | + | 0.150211i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.59608 | 0.505284 | ||||||||
\(227\) | − | 21.5928i | − | 1.43317i | −0.697502 | − | 0.716583i | \(-0.745705\pi\) | ||
0.697502 | − | 0.716583i | \(-0.254295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.08425i | 0.402059i | 0.979585 | + | 0.201029i | \(0.0644287\pi\) | ||||
−0.979585 | + | 0.201029i | \(0.935571\pi\) | |||||||
\(230\) | 16.2096 | − | 4.17634i | 1.06883 | − | 0.275379i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.86433i | 0.253706i | ||||||||
\(233\) | 15.1061 | 0.989635 | 0.494817 | − | 0.868997i | \(-0.335235\pi\) | ||||
0.494817 | + | 0.868997i | \(0.335235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88982 | − | 26.7415i | −0.449442 | − | 1.74442i | ||||
\(236\) | −10.1504 | −0.660732 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.45713 | − | 2.14506i | 0.224092 | − | 0.139043i | ||||
\(239\) | 25.3781i | 1.64157i | 0.571237 | + | 0.820785i | \(0.306464\pi\) | ||||
−0.571237 | + | 0.820785i | \(0.693536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0530i | 1.48498i | 0.669859 | + | 0.742488i | \(0.266354\pi\) | ||||
−0.669859 | + | 0.742488i | \(0.733646\pi\) | |||||||
\(242\) | 2.66348 | 0.171215 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.23166 | + | 15.3152i | −0.206463 | + | 0.978454i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.25522i | − | 0.0798680i | ||||||
\(248\) | − | 3.04213i | − | 0.193175i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.13094 | + | 7.67384i | −0.514246 | + | 0.485336i | ||||
\(251\) | −13.3864 | −0.844945 | −0.422473 | − | 0.906376i | \(-0.638838\pi\) | ||||
−0.422473 | + | 0.906376i | \(0.638838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.6710i | 1.73966i | ||||||||
\(254\) | − | 0.908067i | − | 0.0569772i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0037i | 0.624015i | 0.950080 | + | 0.312008i | \(0.101001\pi\) | ||||
−0.950080 | + | 0.312008i | \(0.898999\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.75502 | − | 4.19131i | 0.419736 | − | 0.260435i | ||||
\(260\) | 2.07469 | − | 0.534535i | 0.128667 | − | 0.0331505i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.13343 | −0.317144 | ||||||||
\(263\) | 12.8129 | 0.790075 | 0.395038 | − | 0.918665i | \(-0.370732\pi\) | ||||
0.395038 | + | 0.918665i | \(0.370732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9383 | + | 4.36408i | −1.04051 | + | 0.268083i | ||||
\(266\) | 2.94525 | − | 1.82745i | 0.180585 | − | 0.112048i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 1.34516i | − | 0.0821690i | ||||||
\(269\) | −16.7411 | −1.02073 | −0.510363 | − | 0.859959i | \(-0.670489\pi\) | ||||
−0.510363 | + | 0.859959i | \(0.670489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.3956i | − | 1.54267i | −0.636429 | − | 0.771335i | \(-0.719589\pi\) | ||
0.636429 | − | 0.771335i | \(-0.280411\pi\) | |||||||
\(272\) | − | 1.53776i | − | 0.0932406i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.55330 | 0.516724 | ||||||||
\(275\) | −8.93081 | − | 16.1811i | −0.538548 | − | 0.975756i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 30.0040i | − | 1.80277i | −0.433022 | − | 0.901383i | \(-0.642553\pi\) | ||
0.433022 | − | 0.901383i | \(-0.357447\pi\) | |||||||
\(278\) | 12.4272i | 0.745337i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.27473 | + | 4.08983i | 0.255464 | + | 0.244414i | ||||
\(281\) | 25.7354i | 1.53524i | 0.640903 | + | 0.767622i | \(0.278560\pi\) | ||||
−0.640903 | + | 0.767622i | \(0.721440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 33.2739 | 1.97793 | 0.988964 | − | 0.148158i | \(-0.0473343\pi\) | ||||
0.988964 | + | 0.148158i | \(0.0473343\pi\) | |||||||
\(284\) | 5.46412i | 0.324236i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.54165i | 0.209422i | ||||||||
\(287\) | 2.88982 | + | 4.65744i | 0.170581 | + | 0.274920i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.6353 | 0.860899 | ||||||||
\(290\) | 2.15589 | + | 8.36765i | 0.126598 | + | 0.491365i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.94324 | 0.464843 | ||||||||
\(293\) | 10.0037i | 0.584424i | 0.956354 | + | 0.292212i | \(0.0943913\pi\) | ||||
−0.956354 | + | 0.292212i | \(0.905609\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.9791 | + | 5.66282i | −1.27967 | + | 0.329702i | ||||
\(296\) | − | 3.00470i | − | 0.174644i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.7059i | 0.851888i | ||||||||
\(299\) | −7.17247 | −0.414795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4859 | − | 6.50623i | 0.604397 | − | 0.375013i | ||||
\(302\) | 17.0392 | 0.980496 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1.31008i | − | 0.0751380i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.23005 | −0.0702024 | −0.0351012 | − | 0.999384i | \(-0.511175\pi\) | ||||
−0.0351012 | + | 0.999384i | \(0.511175\pi\) | |||||||
\(308\) | −8.31011 | + | 5.15621i | −0.473512 | + | 0.293802i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.69718 | − | 6.58728i | −0.0963935 | − | 0.374132i | ||||
\(311\) | 32.4192 | 1.83833 | 0.919163 | − | 0.393877i | \(-0.128866\pi\) | ||||
0.919163 | + | 0.393877i | \(0.128866\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.3146 | 1.03520 | 0.517602 | − | 0.855622i | \(-0.326825\pi\) | ||||
0.517602 | + | 0.855622i | \(0.326825\pi\) | |||||||
\(314\) | 8.60949 | 0.485861 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.6876 | −0.713734 | ||||||||
\(317\) | 14.0669 | 0.790077 | 0.395038 | − | 0.918665i | \(-0.370731\pi\) | ||||
0.395038 | + | 0.918665i | \(0.370731\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.2842 | −0.799761 | ||||||||
\(320\) | 2.16535 | − | 0.557894i | 0.121047 | − | 0.0311872i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.4422 | − | 16.8295i | −0.581923 | − | 0.937869i | ||||
\(323\) | −2.01459 | −0.112095 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.19423 | − | 2.31492i | 0.232654 | − | 0.128408i | ||||
\(326\) | − | 10.4044i | − | 0.576249i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.07167 | 0.114389 | ||||||||
\(329\) | −27.7640 | + | 17.2269i | −1.53068 | + | 0.949747i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5287 | −0.578709 | −0.289354 | − | 0.957222i | \(-0.593441\pi\) | ||||
−0.289354 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(332\) | 0.194288i | 0.0106629i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 14.0483i | − | 0.768692i | ||||||
\(335\) | −0.750459 | − | 2.91276i | −0.0410019 | − | 0.159141i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.9186i | 1.24846i | 0.781242 | + | 0.624229i | \(0.214587\pi\) | ||||
−0.781242 | + | 0.624229i | \(0.785413\pi\) | |||||||
\(338\) | 12.0820 | 0.657173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.857908 | − | 3.32980i | −0.0465266 | − | 0.180584i | ||||
\(341\) | 11.2450 | 0.608949 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4364 | − | 1.76079i | 0.995470 | − | 0.0950737i | ||||
\(344\) | − | 4.66423i | − | 0.251478i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.1282i | 0.759539i | ||||||||
\(347\) | 32.2651 | 1.73208 | 0.866039 | − | 0.499976i | \(-0.166658\pi\) | ||||
0.866039 | + | 0.499976i | \(0.166658\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.6731i | 1.74895i | 0.485068 | + | 0.874477i | \(0.338795\pi\) | ||||
−0.485068 | + | 0.874477i | \(0.661205\pi\) | |||||||
\(350\) | 11.5380 | + | 6.47108i | 0.616731 | + | 0.345894i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.69641i | 0.197020i | ||||||||
\(353\) | 12.0852i | 0.643228i | 0.946871 | + | 0.321614i | \(0.104225\pi\) | ||||
−0.946871 | + | 0.321614i | \(0.895775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.04840 | + | 11.8318i | 0.161792 | + | 0.627964i | ||||
\(356\) | 1.16442 | 0.0617144 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 25.3580i | 1.34021i | ||||||||
\(359\) | − | 32.9275i | − | 1.73785i | −0.494947 | − | 0.868923i | \(-0.664812\pi\) | ||
0.494947 | − | 0.868923i | \(-0.335188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.2837 | 0.909669 | ||||||||
\(362\) | 19.0502i | 1.00126i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.33652 | − | 2.15403i | −0.0700525 | − | 0.112902i | ||||
\(365\) | 17.1999 | − | 4.43149i | 0.900285 | − | 0.231955i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9811 | −0.886406 | −0.443203 | − | 0.896421i | \(-0.646158\pi\) | ||||
−0.443203 | + | 0.896421i | \(0.646158\pi\) | |||||||
\(368\) | −7.48590 | −0.390230 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.67630 | − | 6.50623i | −0.0871467 | − | 0.338243i | ||||
\(371\) | 10.9117 | + | 17.5860i | 0.566505 | + | 0.913020i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.1739i | 1.51057i | 0.655397 | + | 0.755284i | \(0.272501\pi\) | ||||
−0.655397 | + | 0.755284i | \(0.727499\pi\) | |||||||
\(374\) | 5.68421 | 0.293923 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.3497i | 0.636887i | ||||||||
\(377\) | − | 3.70254i | − | 0.190690i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.9718 | 0.563584 | 0.281792 | − | 0.959476i | \(-0.409071\pi\) | ||||
0.281792 | + | 0.959476i | \(0.409071\pi\) | |||||||
\(380\) | −0.730883 | − | 2.83678i | −0.0374935 | − | 0.145524i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.8616i | 0.555727i | ||||||||
\(383\) | − | 8.16073i | − | 0.416994i | −0.978023 | − | 0.208497i | \(-0.933143\pi\) | ||
0.978023 | − | 0.208497i | \(-0.0668571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.1177 | + | 15.8012i | −0.770470 | + | 0.805302i | ||||
\(386\) | 18.0865i | 0.920578i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.91039 | 0.503124 | ||||||||
\(389\) | − | 9.75100i | − | 0.494395i | −0.968965 | − | 0.247198i | \(-0.920490\pi\) | ||
0.968965 | − | 0.247198i | \(-0.0795097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5115i | 0.582164i | ||||||||
\(392\) | 3.10839 | − | 6.27199i | 0.156998 | − | 0.316783i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.20172 | 0.211679 | ||||||||
\(395\) | −27.4732 | + | 7.07834i | −1.38233 | + | 0.356150i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.1533 | −1.31260 | −0.656299 | − | 0.754501i | \(-0.727879\pi\) | ||||
−0.656299 | + | 0.754501i | \(0.727879\pi\) | |||||||
\(398\) | 26.2395i | 1.31527i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.37751 | − | 2.41607i | 0.218875 | − | 0.120804i | ||||
\(401\) | − | 22.2753i | − | 1.11238i | −0.831056 | − | 0.556189i | \(-0.812263\pi\) | ||
0.831056 | − | 0.556189i | \(-0.187737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.91476i | 0.145194i | ||||||||
\(404\) | 15.0638 | 0.749452 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.68762 | − | 5.39044i | 0.431159 | − | 0.267523i | ||||
\(407\) | 11.1066 | 0.550534 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.8617i | − | 0.932652i | −0.884613 | − | 0.466326i | \(-0.845577\pi\) | ||
0.884613 | − | 0.466326i | \(-0.154423\pi\) | |||||||
\(410\) | 4.48590 | − | 1.15577i | 0.221543 | − | 0.0570795i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.54787 | 0.371857 | ||||||||
\(413\) | 14.1589 | + | 22.8196i | 0.696716 | + | 1.12288i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.108392 | + | 0.420702i | 0.00532076 | + | 0.0206515i | ||||
\(416\) | −0.958131 | −0.0469762 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.84258 | 0.236858 | ||||||||
\(419\) | −15.2501 | −0.745017 | −0.372508 | − | 0.928029i | \(-0.621502\pi\) | ||||
−0.372508 | + | 0.928029i | \(0.621502\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.9869 | 1.02284 | 0.511419 | − | 0.859332i | \(-0.329120\pi\) | ||||
0.511419 | + | 0.859332i | \(0.329120\pi\) | |||||||
\(422\) | 20.1735 | 0.982032 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.82242 | 0.379890 | ||||||||
\(425\) | −3.71535 | − | 6.73157i | −0.180221 | − | 0.326529i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.93260 | 0.0934158 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.60214 | − | 10.0997i | −0.125486 | − | 0.487051i | ||||
\(431\) | 19.9737i | 0.962099i | 0.876694 | + | 0.481049i | \(0.159744\pi\) | ||||
−0.876694 | + | 0.481049i | \(0.840256\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1103 | 0.630043 | 0.315021 | − | 0.949085i | \(-0.397988\pi\) | ||||
0.315021 | + | 0.949085i | \(0.397988\pi\) | |||||||
\(434\) | −6.83917 | + | 4.24353i | −0.328291 | + | 0.203696i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.59608 | 0.172221 | ||||||||
\(437\) | 9.80710i | 0.469137i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3928i | 0.686930i | 0.939166 | + | 0.343465i | \(0.111601\pi\) | ||||
−0.939166 | + | 0.343465i | \(0.888399\pi\) | |||||||
\(440\) | 2.06221 | + | 8.00404i | 0.0983118 | + | 0.381578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.47338i | 0.0700815i | ||||||||
\(443\) | 28.4180 | 1.35018 | 0.675090 | − | 0.737735i | \(-0.264105\pi\) | ||||
0.675090 | + | 0.737735i | \(0.264105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.52139 | − | 0.649625i | 0.119525 | − | 0.0307952i | ||||
\(446\) | −18.1775 | −0.860728 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.39492 | − | 2.24815i | −0.0659038 | − | 0.106215i | ||||
\(449\) | 4.07377i | 0.192253i | 0.995369 | + | 0.0961265i | \(0.0306453\pi\) | ||||
−0.995369 | + | 0.0961265i | \(0.969355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.65776i | 0.360590i | ||||||||
\(452\) | −7.59608 | −0.357290 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.5928i | 1.01340i | ||||||||
\(455\) | −4.09575 | − | 3.91859i | −0.192012 | − | 0.183706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.89136i | − | 0.415920i | −0.978137 | − | 0.207960i | \(-0.933318\pi\) | ||
0.978137 | − | 0.207960i | \(-0.0666824\pi\) | |||||||
\(458\) | − | 6.08425i | − | 0.284298i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.2096 | + | 4.17634i | −0.755777 | + | 0.194723i | ||||
\(461\) | 11.4649 | 0.533976 | 0.266988 | − | 0.963700i | \(-0.413972\pi\) | ||||
0.266988 | + | 0.963700i | \(0.413972\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.42495i | − | 0.0662230i | −0.999452 | − | 0.0331115i | \(-0.989458\pi\) | ||
0.999452 | − | 0.0331115i | \(-0.0105417\pi\) | |||||||
\(464\) | − | 3.86433i | − | 0.179397i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.1061 | −0.699778 | ||||||||
\(467\) | 26.0118i | 1.20368i | 0.798615 | + | 0.601842i | \(0.205566\pi\) | ||||
−0.798615 | + | 0.601842i | \(0.794434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.02414 | + | 1.87640i | −0.139642 | + | 0.0866440i | ||||
\(470\) | 6.88982 | + | 26.7415i | 0.317804 | + | 1.23349i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1504 | 0.467208 | ||||||||
\(473\) | 17.2409 | 0.792738 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.16524 | − | 5.73487i | −0.145231 | − | 0.263134i | ||||
\(476\) | −3.45713 | + | 2.14506i | −0.158457 | + | 0.0983185i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 25.3781i | − | 1.16077i | ||||||
\(479\) | 22.0479 | 1.00739 | 0.503696 | − | 0.863881i | \(-0.331973\pi\) | ||||
0.503696 | + | 0.863881i | \(0.331973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.87889i | 0.131266i | ||||||||
\(482\) | − | 23.0530i | − | 1.05004i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.66348 | −0.121067 | ||||||||
\(485\) | 21.4595 | − | 5.52894i | 0.974425 | − | 0.251056i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.9355i | − | 1.12993i | −0.825113 | − | 0.564967i | \(-0.808889\pi\) | ||
0.825113 | − | 0.564967i | \(-0.191111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.23166 | − | 15.3152i | 0.145992 | − | 0.691872i | ||||
\(491\) | 15.2511i | 0.688275i | 0.938919 | + | 0.344137i | \(0.111829\pi\) | ||||
−0.938919 | + | 0.344137i | \(0.888171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.94243 | −0.267634 | ||||||||
\(494\) | 1.25522i | 0.0564752i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.04213i | 0.136596i | ||||||||
\(497\) | 12.2842 | − | 7.62202i | 0.551021 | − | 0.341894i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.8370 | −0.485131 | −0.242565 | − | 0.970135i | \(-0.577989\pi\) | ||||
−0.242565 | + | 0.970135i | \(0.577989\pi\) | |||||||
\(500\) | 8.13094 | − | 7.67384i | 0.363627 | − | 0.343184i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.3864 | 0.597466 | ||||||||
\(503\) | 42.4860i | 1.89436i | 0.320705 | + | 0.947179i | \(0.396080\pi\) | ||||
−0.320705 | + | 0.947179i | \(0.603920\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.6184 | − | 8.40399i | 1.45150 | − | 0.373973i | ||||
\(506\) | − | 27.6710i | − | 1.23013i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.908067i | 0.0402890i | ||||||||
\(509\) | −19.3226 | −0.856459 | −0.428230 | − | 0.903670i | \(-0.640863\pi\) | ||||
−0.428230 | + | 0.903670i | \(0.640863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0802 | − | 17.8576i | −0.490159 | − | 0.789975i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10.0037i | − | 0.441246i | ||||||
\(515\) | 16.3438 | − | 4.21091i | 0.720194 | − | 0.185555i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −45.6496 | −2.00767 | ||||||||
\(518\) | −6.75502 | + | 4.19131i | −0.296798 | + | 0.184156i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.07469 | + | 0.534535i | −0.0909813 | + | 0.0234409i | ||||
\(521\) | −19.0689 | −0.835426 | −0.417713 | − | 0.908579i | \(-0.637168\pi\) | ||||
−0.417713 | + | 0.908579i | \(0.637168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0556 | 0.702062 | 0.351031 | − | 0.936364i | \(-0.385831\pi\) | ||||
0.351031 | + | 0.936364i | \(0.385831\pi\) | |||||||
\(524\) | 5.13343 | 0.224255 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.8129 | −0.558668 | ||||||||
\(527\) | 4.67807 | 0.203780 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.0387 | 1.43647 | ||||||||
\(530\) | 16.9383 | − | 4.36408i | 0.735753 | − | 0.189563i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.94525 | + | 1.82745i | −0.127693 | + | 0.0792301i | ||||
\(533\) | −1.98493 | −0.0859770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.18476 | − | 1.07819i | 0.180923 | − | 0.0466140i | ||||
\(536\) | 1.34516i | 0.0581022i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.7411 | 0.721762 | ||||||||
\(539\) | 23.1839 | + | 11.4899i | 0.998601 | + | 0.494905i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.40392 | 0.275326 | 0.137663 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137663 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(542\) | 25.3956i | 1.09083i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.53776i | 0.0659310i | ||||||||
\(545\) | 7.78679 | − | 2.00623i | 0.333549 | − | 0.0859375i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 27.9854i | − | 1.19657i | −0.801284 | − | 0.598284i | \(-0.795849\pi\) | ||
0.801284 | − | 0.598284i | \(-0.204151\pi\) | |||||||
\(548\) | −8.55330 | −0.365379 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.93081 | + | 16.1811i | 0.380811 | + | 0.689964i | ||||
\(551\) | −5.06257 | −0.215673 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.6982 | + | 28.5237i | 0.752605 | + | 1.21295i | ||||
\(554\) | 30.0040i | 1.27475i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 12.4272i | − | 0.527033i | ||||||
\(557\) | −8.24092 | −0.349179 | −0.174589 | − | 0.984641i | \(-0.555860\pi\) | ||||
−0.174589 | + | 0.984641i | \(0.555860\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.46894i | 0.189016i | ||||||||
\(560\) | −4.27473 | − | 4.08983i | −0.180640 | − | 0.172827i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 25.7354i | − | 1.08558i | ||||||
\(563\) | − | 2.96458i | − | 0.124942i | −0.998047 | − | 0.0624710i | \(-0.980102\pi\) | ||
0.998047 | − | 0.0624710i | \(-0.0198981\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.4482 | + | 4.23781i | −0.691981 | + | 0.178286i | ||||
\(566\) | −33.2739 | −1.39861 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 5.46412i | − | 0.229269i | ||||||
\(569\) | − | 34.9443i | − | 1.46494i | −0.680798 | − | 0.732471i | \(-0.738367\pi\) | ||
0.680798 | − | 0.732471i | \(-0.261633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.0105 | 1.79993 | 0.899967 | − | 0.435958i | \(-0.143590\pi\) | ||||
0.899967 | + | 0.435958i | \(0.143590\pi\) | |||||||
\(572\) | − | 3.54165i | − | 0.148084i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.88982 | − | 4.65744i | −0.120619 | − | 0.194398i | ||||
\(575\) | −32.7696 | + | 18.0865i | −1.36659 | + | 0.754259i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.44707 | 0.101873 | 0.0509364 | − | 0.998702i | \(-0.483779\pi\) | ||||
0.0509364 | + | 0.998702i | \(0.483779\pi\) | |||||||
\(578\) | −14.6353 | −0.608748 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.15589 | − | 8.36765i | −0.0895184 | − | 0.347448i | ||||
\(581\) | 0.436790 | − | 0.271017i | 0.0181211 | − | 0.0112437i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.9149i | 1.19753i | ||||||||
\(584\) | −7.94324 | −0.328694 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 10.0037i | − | 0.413250i | ||||||
\(587\) | − | 4.76687i | − | 0.196750i | −0.995149 | − | 0.0983750i | \(-0.968636\pi\) | ||
0.995149 | − | 0.0983750i | \(-0.0313645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.98541 | 0.164216 | ||||||||
\(590\) | 21.9791 | − | 5.66282i | 0.904865 | − | 0.233134i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00470i | 0.123492i | ||||||||
\(593\) | − | 44.4850i | − | 1.82678i | −0.407088 | − | 0.913389i | \(-0.633456\pi\) | ||
0.407088 | − | 0.913389i | \(-0.366544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.28919 | + | 6.57352i | −0.257832 | + | 0.269488i | ||||
\(596\) | − | 14.7059i | − | 0.602376i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.17247 | 0.293304 | ||||||||
\(599\) | 45.6945i | 1.86703i | 0.358543 | + | 0.933513i | \(0.383274\pi\) | ||||
−0.358543 | + | 0.933513i | \(0.616726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.7774i | 1.09227i | 0.837696 | + | 0.546136i | \(0.183902\pi\) | ||||
−0.837696 | + | 0.546136i | \(0.816098\pi\) | |||||||
\(602\) | −10.4859 | + | 6.50623i | −0.427373 | + | 0.265174i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.0392 | −0.693315 | ||||||||
\(605\) | −5.76738 | + | 1.48594i | −0.234477 | + | 0.0604121i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.0757 | −1.22073 | −0.610367 | − | 0.792119i | \(-0.708978\pi\) | ||||
−0.610367 | + | 0.792119i | \(0.708978\pi\) | |||||||
\(608\) | 1.31008i | 0.0531306i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.8326i | − | 0.478697i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5002i | 0.545270i | 0.962118 | + | 0.272635i | \(0.0878951\pi\) | ||||
−0.962118 | + | 0.272635i | \(0.912105\pi\) | |||||||
\(614\) | 1.23005 | 0.0496406 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.31011 | − | 5.15621i | 0.334824 | − | 0.207749i | ||||
\(617\) | −31.6740 | −1.27515 | −0.637574 | − | 0.770389i | \(-0.720062\pi\) | ||||
−0.637574 | + | 0.770389i | \(0.720062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.3662i | − | 0.416653i | −0.978059 | − | 0.208327i | \(-0.933198\pi\) | ||
0.978059 | − | 0.208327i | \(-0.0668017\pi\) | |||||||
\(620\) | 1.69718 | + | 6.58728i | 0.0681605 | + | 0.264551i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.4192 | −1.29989 | ||||||||
\(623\) | −1.62428 | − | 2.61781i | −0.0650754 | − | 0.104880i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3252 | − | 21.1528i | 0.533007 | − | 0.846111i | ||||
\(626\) | −18.3146 | −0.732000 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.60949 | −0.343556 | ||||||||
\(629\) | 4.62051 | 0.184232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.62022 | 0.263547 | 0.131773 | − | 0.991280i | \(-0.457933\pi\) | ||||
0.131773 | + | 0.991280i | \(0.457933\pi\) | |||||||
\(632\) | 12.6876 | 0.504686 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0669 | −0.558669 | ||||||||
\(635\) | 0.506605 | + | 1.96629i | 0.0201040 | + | 0.0780297i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.97825 | + | 6.00939i | −0.118002 | + | 0.238101i | ||||
\(638\) | 14.2842 | 0.565516 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.16535 | + | 0.557894i | −0.0855931 | + | 0.0220527i | ||||
\(641\) | 0.866555i | 0.0342269i | 0.999854 | + | 0.0171134i | \(0.00544764\pi\) | ||||
−0.999854 | + | 0.0171134i | \(0.994552\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.3339 | −1.19625 | −0.598126 | − | 0.801402i | \(-0.704088\pi\) | ||||
−0.598126 | + | 0.801402i | \(0.704088\pi\) | |||||||
\(644\) | 10.4422 | + | 16.8295i | 0.411482 | + | 0.663174i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.01459 | 0.0792628 | ||||||||
\(647\) | 5.19960i | 0.204417i | 0.994763 | + | 0.102209i | \(0.0325909\pi\) | ||||
−0.994763 | + | 0.102209i | \(0.967409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.5199i | 1.47279i | ||||||||
\(650\) | −4.19423 | + | 2.31492i | −0.164511 | + | 0.0907984i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.4044i | 0.407469i | ||||||||
\(653\) | −0.510519 | −0.0199782 | −0.00998908 | − | 0.999950i | \(-0.503180\pi\) | ||||
−0.00998908 | + | 0.999950i | \(0.503180\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.1157 | − | 2.86391i | 0.434326 | − | 0.111902i | ||||
\(656\) | −2.07167 | −0.0808852 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.7640 | − | 17.2269i | 1.08235 | − | 0.671573i | ||||
\(659\) | 8.38903i | 0.326790i | 0.986561 | + | 0.163395i | \(0.0522445\pi\) | ||||
−0.986561 | + | 0.163395i | \(0.947755\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.1672i | 1.13447i | 0.823555 | + | 0.567237i | \(0.191988\pi\) | ||||
−0.823555 | + | 0.567237i | \(0.808012\pi\) | |||||||
\(662\) | 10.5287 | 0.409209 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 0.194288i | − | 0.00753984i | ||||||
\(665\) | −5.35799 | + | 5.60021i | −0.207774 | + | 0.217167i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.9280i | 1.12010i | ||||||||
\(668\) | 14.0483i | 0.543547i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.750459 | + | 2.91276i | 0.0289927 | + | 0.112530i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.75616i | 0.144789i | 0.997376 | + | 0.0723947i | \(0.0230641\pi\) | ||||
−0.997376 | + | 0.0723947i | \(0.976936\pi\) | |||||||
\(674\) | − | 22.9186i | − | 0.882793i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.0820 | −0.464692 | ||||||||
\(677\) | 35.3252i | 1.35766i | 0.734297 | + | 0.678828i | \(0.237512\pi\) | ||||
−0.734297 | + | 0.678828i | \(0.762488\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8242 | − | 22.2801i | −0.530524 | − | 0.855031i | ||||
\(680\) | 0.857908 | + | 3.32980i | 0.0328993 | + | 0.127692i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −11.2450 | −0.430592 | ||||||||
\(683\) | −11.0428 | −0.422540 | −0.211270 | − | 0.977428i | \(-0.567760\pi\) | ||||
−0.211270 | + | 0.977428i | \(0.567760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.5209 | + | 4.77183i | −0.707648 | + | 0.182322i | ||||
\(686\) | −18.4364 | + | 1.76079i | −0.703904 | + | 0.0672273i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.66423i | 0.177822i | ||||||||
\(689\) | −7.49490 | −0.285533 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.1353i | − | 1.22248i | −0.791444 | − | 0.611241i | \(-0.790670\pi\) | ||
0.791444 | − | 0.611241i | \(-0.209330\pi\) | |||||||
\(692\) | − | 14.1282i | − | 0.537075i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.2651 | −1.22476 | ||||||||
\(695\) | −6.93308 | − | 26.9094i | −0.262987 | − | 1.02073i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.18574i | 0.120668i | ||||||||
\(698\) | − | 32.6731i | − | 1.23670i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.5380 | − | 6.47108i | −0.436095 | − | 0.244584i | ||||
\(701\) | 20.0505i | 0.757297i | 0.925541 | + | 0.378649i | \(0.123611\pi\) | ||||
−0.925541 | + | 0.378649i | \(0.876389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.93638 | 0.148463 | ||||||||
\(704\) | − | 3.69641i | − | 0.139314i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 12.0852i | − | 0.454831i | ||||||
\(707\) | −21.0128 | − | 33.8657i | −0.790268 | − | 1.27365i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.7792 | 0.893045 | 0.446522 | − | 0.894772i | \(-0.352662\pi\) | ||||
0.446522 | + | 0.894772i | \(0.352662\pi\) | |||||||
\(710\) | −3.04840 | − | 11.8318i | −0.114404 | − | 0.444038i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.16442 | −0.0436387 | ||||||||
\(713\) | − | 22.7731i | − | 0.852858i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.97586 | − | 7.66892i | −0.0738931 | − | 0.286801i | ||||
\(716\) | − | 25.3580i | − | 0.947674i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.9275i | 1.22884i | ||||||||
\(719\) | 22.3854 | 0.834834 | 0.417417 | − | 0.908715i | \(-0.362935\pi\) | ||||
0.417417 | + | 0.908715i | \(0.362935\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.5287 | − | 16.9688i | −0.392109 | − | 0.631950i | ||||
\(722\) | −17.2837 | −0.643233 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 19.0502i | − | 0.707996i | ||||||
\(725\) | −9.33652 | − | 16.9162i | −0.346750 | − | 0.628250i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.2104 | 1.75094 | 0.875469 | − | 0.483274i | \(-0.160552\pi\) | ||||
0.875469 | + | 0.483274i | \(0.160552\pi\) | |||||||
\(728\) | 1.33652 | + | 2.15403i | 0.0495346 | + | 0.0798335i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.1999 | + | 4.43149i | −0.636598 | + | 0.164017i | ||||
\(731\) | 7.17247 | 0.265284 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.2291 | 1.30121 | 0.650607 | − | 0.759414i | \(-0.274514\pi\) | ||||
0.650607 | + | 0.759414i | \(0.274514\pi\) | |||||||
\(734\) | 16.9811 | 0.626784 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.48590 | 0.275934 | ||||||||
\(737\) | −4.97228 | −0.183156 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.97180 | −0.256462 | −0.128231 | − | 0.991744i | \(-0.540930\pi\) | ||||
−0.128231 | + | 0.991744i | \(0.540930\pi\) | |||||||
\(740\) | 1.67630 | + | 6.50623i | 0.0616220 | + | 0.239174i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.9117 | − | 17.5860i | −0.400579 | − | 0.645602i | ||||
\(743\) | 11.9195 | 0.437283 | 0.218641 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218641 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.20431 | − | 31.8434i | −0.300583 | − | 1.16665i | ||||
\(746\) | − | 29.1739i | − | 1.06813i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.68421 | −0.207835 | ||||||||
\(749\) | −2.69582 | − | 4.34478i | −0.0985033 | − | 0.158755i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3078 | −1.28840 | −0.644201 | − | 0.764857i | \(-0.722810\pi\) | ||||
−0.644201 | + | 0.764857i | \(0.722810\pi\) | |||||||
\(752\) | − | 12.3497i | − | 0.450347i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.70254i | 0.134839i | ||||||||
\(755\) | −36.8959 | + | 9.50606i | −1.34278 | + | 0.345961i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.51232i | 0.273040i | 0.990637 | + | 0.136520i | \(0.0435918\pi\) | ||||
−0.990637 | + | 0.136520i | \(0.956408\pi\) | |||||||
\(758\) | −10.9718 | −0.398514 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.730883 | + | 2.83678i | 0.0265119 | + | 0.102901i | ||||
\(761\) | 45.2360 | 1.63980 | 0.819901 | − | 0.572505i | \(-0.194028\pi\) | ||||
0.819901 | + | 0.572505i | \(0.194028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.01625 | − | 8.08455i | −0.181600 | − | 0.292680i | ||||
\(764\) | − | 10.8616i | − | 0.392958i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.16073i | 0.294859i | ||||||||
\(767\) | −9.72537 | −0.351163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.2725i | 0.875287i | 0.899148 | + | 0.437644i | \(0.144187\pi\) | ||||
−0.899148 | + | 0.437644i | \(0.855813\pi\) | |||||||
\(770\) | 15.1177 | − | 15.8012i | 0.544804 | − | 0.569434i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 18.0865i | − | 0.650947i | ||||||
\(773\) | − | 12.0018i | − | 0.431676i | −0.976429 | − | 0.215838i | \(-0.930752\pi\) | ||
0.976429 | − | 0.215838i | \(-0.0692482\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.35000 | + | 13.3169i | 0.264020 | + | 0.478358i | ||||
\(776\) | −9.91039 | −0.355762 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.75100i | 0.349590i | ||||||||
\(779\) | 2.71405i | 0.0972408i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1977 | 0.722729 | ||||||||
\(782\) | − | 11.5115i | − | 0.411652i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.10839 | + | 6.27199i | −0.111014 | + | 0.224000i | ||||
\(785\) | −18.6426 | + | 4.80318i | −0.665382 | + | 0.171433i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.9585 | 1.06790 | 0.533952 | − | 0.845515i | \(-0.320706\pi\) | ||||
0.533952 | + | 0.845515i | \(0.320706\pi\) | |||||||
\(788\) | −4.20172 | −0.149680 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.4732 | − | 7.07834i | 0.977452 | − | 0.251836i | ||||
\(791\) | 10.5959 | + | 17.0772i | 0.376748 | + | 0.607194i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 26.1533 | 0.928147 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 26.2395i | − | 0.930035i | ||||||
\(797\) | − | 36.0109i | − | 1.27557i | −0.770214 | − | 0.637785i | \(-0.779851\pi\) | ||
0.770214 | − | 0.637785i | \(-0.220149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.9909 | −0.671850 | ||||||||
\(800\) | −4.37751 | + | 2.41607i | −0.154768 | + | 0.0854211i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.2753i | 0.786570i | ||||||||
\(803\) | − | 29.3615i | − | 1.03615i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.0002 | + | 30.6161i | 1.12786 | + | 1.07907i | ||||
\(806\) | − | 2.91476i | − | 0.102668i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0638 | −0.529942 | ||||||||
\(809\) | − | 36.4258i | − | 1.28066i | −0.768099 | − | 0.640331i | \(-0.778797\pi\) | ||
0.768099 | − | 0.640331i | \(-0.221203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.9870i | 1.61482i | 0.589990 | + | 0.807411i | \(0.299132\pi\) | ||||
−0.589990 | + | 0.807411i | \(0.700868\pi\) | |||||||
\(812\) | −8.68762 | + | 5.39044i | −0.304876 | + | 0.189167i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.1066 | −0.389286 | ||||||||
\(815\) | 5.80457 | + | 22.5293i | 0.203325 | + | 0.789167i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.11049 | 0.213779 | ||||||||
\(818\) | 18.8617i | 0.659485i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.48590 | + | 1.15577i | −0.156654 | + | 0.0403613i | ||||
\(821\) | − | 9.20205i | − | 0.321154i | −0.987023 | − | 0.160577i | \(-0.948665\pi\) | ||
0.987023 | − | 0.160577i | \(-0.0513354\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 47.9339i | − | 1.67087i | −0.549589 | − | 0.835435i | \(-0.685216\pi\) | ||
0.549589 | − | 0.835435i | \(-0.314784\pi\) | |||||||
\(824\) | −7.54787 | −0.262943 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.1589 | − | 22.8196i | −0.492652 | − | 0.793994i | ||||
\(827\) | −10.6539 | −0.370474 | −0.185237 | − | 0.982694i | \(-0.559305\pi\) | ||||
−0.185237 | + | 0.982694i | \(0.559305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.30336i | 0.149462i | 0.997204 | + | 0.0747310i | \(0.0238098\pi\) | ||||
−0.997204 | + | 0.0747310i | \(0.976190\pi\) | |||||||
\(830\) | −0.108392 | − | 0.420702i | −0.00376235 | − | 0.0146028i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.958131 | 0.0332172 | ||||||||
\(833\) | 9.64484 | + | 4.77997i | 0.334174 | + | 0.165616i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.83749 | + | 30.4196i | 0.271227 | + | 1.05272i | ||||
\(836\) | −4.84258 | −0.167484 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.2501 | 0.526806 | ||||||||
\(839\) | 38.1028 | 1.31545 | 0.657727 | − | 0.753256i | \(-0.271518\pi\) | ||||
0.657727 | + | 0.753256i | \(0.271518\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0669 | 0.485066 | ||||||||
\(842\) | −20.9869 | −0.723255 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.1735 | −0.694401 | ||||||||
\(845\) | −26.1618 | + | 6.74046i | −0.899992 | + | 0.231879i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.71535 | + | 5.98792i | 0.127661 | + | 0.205747i | ||||
\(848\) | −7.82242 | −0.268623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.71535 | + | 6.73157i | 0.127435 | + | 0.230891i | ||||
\(851\) | − | 22.4929i | − | 0.771045i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.3707 | 1.93010 | 0.965048 | − | 0.262072i | \(-0.0844059\pi\) | ||||
0.965048 | + | 0.262072i | \(0.0844059\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.93260 | −0.0660549 | ||||||||
\(857\) | 15.7781i | 0.538968i | 0.963005 | + | 0.269484i | \(0.0868532\pi\) | ||||
−0.963005 | + | 0.269484i | \(0.913147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.7024i | 0.399280i | 0.979869 | + | 0.199640i | \(0.0639773\pi\) | ||||
−0.979869 | + | 0.199640i | \(0.936023\pi\) | |||||||
\(860\) | 2.60214 | + | 10.0997i | 0.0887323 | + | 0.344397i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 19.9737i | − | 0.680306i | ||||||
\(863\) | −42.5925 | −1.44987 | −0.724933 | − | 0.688820i | \(-0.758129\pi\) | ||||
−0.724933 | + | 0.688820i | \(0.758129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.88206 | − | 30.5926i | −0.267998 | − | 1.04018i | ||||
\(866\) | −13.1103 | −0.445507 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.83917 | − | 4.24353i | 0.232136 | − | 0.144035i | ||||
\(869\) | 46.8987i | 1.59093i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.28884i | − | 0.0436708i | ||||||
\(872\) | −3.59608 | −0.121779 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 9.80710i | − | 0.331730i | ||||||
\(875\) | −28.5940 | − | 7.57521i | −0.966653 | − | 0.256089i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6401i | 0.730735i | 0.930863 | + | 0.365368i | \(0.119057\pi\) | ||||
−0.930863 | + | 0.365368i | \(0.880943\pi\) | |||||||
\(878\) | − | 14.3928i | − | 0.485733i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.06221 | − | 8.00404i | −0.0695170 | − | 0.269816i | ||||
\(881\) | 42.0251 | 1.41586 | 0.707931 | − | 0.706282i | \(-0.249629\pi\) | ||||
0.707931 | + | 0.706282i | \(0.249629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.89798i | 0.198483i | 0.995063 | + | 0.0992414i | \(0.0316416\pi\) | ||||
−0.995063 | + | 0.0992414i | \(0.968358\pi\) | |||||||
\(884\) | − | 1.47338i | − | 0.0495551i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.4180 | −0.954722 | ||||||||
\(887\) | 24.9068i | 0.836288i | 0.908381 | + | 0.418144i | \(0.137319\pi\) | ||||
−0.908381 | + | 0.418144i | \(0.862681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.04147 | − | 1.26668i | 0.0684688 | − | 0.0424831i | ||||
\(890\) | −2.52139 | + | 0.649625i | −0.0845172 | + | 0.0217755i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.1775 | 0.608627 | ||||||||
\(893\) | −16.1790 | −0.541411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.1471 | − | 54.9091i | −0.472885 | − | 1.83541i | ||||
\(896\) | 1.39492 | + | 2.24815i | 0.0466010 | + | 0.0751056i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 4.07377i | − | 0.135943i | ||||||
\(899\) | 11.7558 | 0.392078 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0290i | 0.400745i | ||||||||
\(902\) | − | 7.65776i | − | 0.254975i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.59608 | 0.252642 | ||||||||
\(905\) | −10.6280 | − | 41.2504i | −0.353286 | − | 1.37121i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.8831i | − | 0.627005i | −0.949587 | − | 0.313502i | \(-0.898498\pi\) | ||
0.949587 | − | 0.313502i | \(-0.101502\pi\) | |||||||
\(908\) | − | 21.5928i | − | 0.716583i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.09575 | + | 3.91859i | 0.135773 | + | 0.129900i | ||||
\(911\) | 27.4634i | 0.909902i | 0.890516 | + | 0.454951i | \(0.150343\pi\) | ||||
−0.890516 | + | 0.454951i | \(0.849657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.718170 | 0.0237679 | ||||||||
\(914\) | 8.89136i | 0.294100i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.08425i | 0.201029i | ||||||||
\(917\) | −7.16073 | − | 11.5407i | −0.236468 | − | 0.381109i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.2460 | −1.32759 | −0.663796 | − | 0.747914i | \(-0.731056\pi\) | ||||
−0.663796 | + | 0.747914i | \(0.731056\pi\) | |||||||
\(920\) | 16.2096 | − | 4.17634i | 0.534415 | − | 0.137690i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.4649 | −0.377578 | ||||||||
\(923\) | 5.23534i | 0.172323i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.25957 | + | 13.1531i | 0.238693 | + | 0.432471i | ||||
\(926\) | 1.42495i | 0.0468268i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.86433i | 0.126853i | ||||||||
\(929\) | −9.56970 | −0.313972 | −0.156986 | − | 0.987601i | \(-0.550178\pi\) | ||||
−0.156986 | + | 0.987601i | \(0.550178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.21678 | + | 4.07223i | 0.269294 | + | 0.133462i | ||||
\(932\) | 15.1061 | 0.494817 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 26.0118i | − | 0.851133i | ||||||
\(935\) | −12.3083 | + | 3.17118i | −0.402525 | + | 0.103709i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.31701 | −0.141031 | −0.0705153 | − | 0.997511i | \(-0.522464\pi\) | ||||
−0.0705153 | + | 0.997511i | \(0.522464\pi\) | |||||||
\(938\) | 3.02414 | − | 1.87640i | 0.0987415 | − | 0.0612665i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.88982 | − | 26.7415i | −0.224721 | − | 0.872210i | ||||
\(941\) | 1.57282 | 0.0512724 | 0.0256362 | − | 0.999671i | \(-0.491839\pi\) | ||||
0.0256362 | + | 0.999671i | \(0.491839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.5083 | 0.505021 | ||||||||
\(944\) | −10.1504 | −0.330366 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.2409 | −0.560551 | ||||||||
\(947\) | −3.27867 | −0.106542 | −0.0532712 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532712 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.61067 | 0.247053 | ||||||||
\(950\) | 3.16524 | + | 5.73487i | 0.102694 | + | 0.186064i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.45713 | − | 2.14506i | 0.112046 | − | 0.0695217i | ||||
\(953\) | 12.7887 | 0.414268 | 0.207134 | − | 0.978313i | \(-0.433586\pi\) | ||||
0.207134 | + | 0.978313i | \(0.433586\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.05961 | − | 23.5192i | −0.196084 | − | 0.761062i | ||||
\(956\) | 25.3781i | 0.820785i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.0479 | −0.712334 | ||||||||
\(959\) | 11.9312 | + | 19.2291i | 0.385278 | + | 0.620941i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.7455 | 0.701467 | ||||||||
\(962\) | − | 2.87889i | − | 0.0928192i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.0530i | 0.742488i | ||||||||
\(965\) | −10.0903 | − | 39.1636i | −0.324819 | − | 1.26072i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 35.1053i | − | 1.12891i | −0.825463 | − | 0.564456i | \(-0.809086\pi\) | ||
0.825463 | − | 0.564456i | \(-0.190914\pi\) | |||||||
\(968\) | 2.66348 | 0.0856076 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.4595 | + | 5.52894i | −0.689023 | + | 0.177524i | ||||
\(971\) | 3.97005 | 0.127405 | 0.0637024 | − | 0.997969i | \(-0.479709\pi\) | ||||
0.0637024 | + | 0.997969i | \(0.479709\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.9384 | + | 17.3350i | −0.895663 | + | 0.555735i | ||||
\(974\) | 24.9355i | 0.798984i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25.9285 | −0.829527 | −0.414764 | − | 0.909929i | \(-0.636136\pi\) | ||||
−0.414764 | + | 0.909929i | \(0.636136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.30420i | − | 0.137563i | ||||||
\(980\) | −3.23166 | + | 15.3152i | −0.103232 | + | 0.489227i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 15.2511i | − | 0.486684i | ||||||
\(983\) | − | 45.4172i | − | 1.44858i | −0.689493 | − | 0.724292i | \(-0.742167\pi\) | ||
0.689493 | − | 0.724292i | \(-0.257833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.09820 | + | 2.34411i | −0.289893 | + | 0.0746896i | ||||
\(986\) | 5.94243 | 0.189246 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.25522i | − | 0.0399340i | ||||||
\(989\) | − | 34.9159i | − | 1.11026i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.7751 | −1.58116 | −0.790579 | − | 0.612360i | \(-0.790220\pi\) | ||||
−0.790579 | + | 0.612360i | \(0.790220\pi\) | |||||||
\(992\) | − | 3.04213i | − | 0.0965876i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.2842 | + | 7.62202i | −0.389631 | + | 0.241756i | ||||
\(995\) | −14.6389 | − | 56.8178i | −0.464083 | − | 1.80125i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.3630 | −1.05662 | −0.528309 | − | 0.849052i | \(-0.677174\pi\) | ||||
−0.528309 | + | 0.849052i | \(0.677174\pi\) | |||||||
\(998\) | 10.8370 | 0.343039 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1890.2.d.e.1889.15 | yes | 16 | |
3.2 | odd | 2 | 1890.2.d.f.1889.2 | yes | 16 | ||
5.4 | even | 2 | 1890.2.d.f.1889.16 | yes | 16 | ||
7.6 | odd | 2 | inner | 1890.2.d.e.1889.2 | yes | 16 | |
15.14 | odd | 2 | inner | 1890.2.d.e.1889.1 | ✓ | 16 | |
21.20 | even | 2 | 1890.2.d.f.1889.15 | yes | 16 | ||
35.34 | odd | 2 | 1890.2.d.f.1889.1 | yes | 16 | ||
105.104 | even | 2 | inner | 1890.2.d.e.1889.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.d.e.1889.1 | ✓ | 16 | 15.14 | odd | 2 | inner | |
1890.2.d.e.1889.2 | yes | 16 | 7.6 | odd | 2 | inner | |
1890.2.d.e.1889.15 | yes | 16 | 1.1 | even | 1 | trivial | |
1890.2.d.e.1889.16 | yes | 16 | 105.104 | even | 2 | inner | |
1890.2.d.f.1889.1 | yes | 16 | 35.34 | odd | 2 | ||
1890.2.d.f.1889.2 | yes | 16 | 3.2 | odd | 2 | ||
1890.2.d.f.1889.15 | yes | 16 | 21.20 | even | 2 | ||
1890.2.d.f.1889.16 | yes | 16 | 5.4 | even | 2 |