Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(401,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.l (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1201.1 | ||
Root | \(0.719139 - 1.21772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1201 |
Dual form | 1600.2.l.g.401.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.66783 | + | 1.66783i | −0.962922 | + | 0.962922i | −0.999337 | − | 0.0364144i | \(-0.988406\pi\) |
0.0364144 | + | 0.999337i | \(0.488406\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87372i | 0.708198i | 0.935208 | + | 0.354099i | \(0.115212\pi\) | ||||
−0.935208 | + | 0.354099i | \(0.884788\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.56332i | − | 0.854439i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.29695 | + | 3.29695i | 0.994068 | + | 0.994068i | 0.999983 | − | 0.00591443i | \(-0.00188263\pi\) |
−0.00591443 | + | 0.999983i | \(0.501883\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.90022 | − | 1.90022i | 0.527027 | − | 0.527027i | −0.392658 | − | 0.919685i | \(-0.628444\pi\) |
0.919685 | + | 0.392658i | \(0.128444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.57148 | 0.623675 | 0.311838 | − | 0.950135i | \(-0.399056\pi\) | ||||
0.311838 | + | 0.950135i | \(0.399056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.76636 | − | 5.76636i | 1.32289 | − | 1.32289i | 0.411472 | − | 0.911422i | \(-0.365015\pi\) |
0.911422 | − | 0.411472i | \(-0.134985\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12504 | − | 3.12504i | −0.681940 | − | 0.681940i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.58574i | 1.58174i | 0.611987 | + | 0.790868i | \(0.290371\pi\) | ||||
−0.611987 | + | 0.790868i | \(0.709629\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.728312 | − | 0.728312i | −0.140164 | − | 0.140164i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.45786 | − | 6.45786i | 1.19919 | − | 1.19919i | 0.224787 | − | 0.974408i | \(-0.427831\pi\) |
0.974408 | − | 0.224787i | \(-0.0721685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.799135 | 0.143529 | 0.0717644 | − | 0.997422i | \(-0.477137\pi\) | ||||
0.0717644 | + | 0.997422i | \(0.477137\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.9975 | −1.91442 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.69652 | + | 2.69652i | 0.443305 | + | 0.443305i | 0.893121 | − | 0.449816i | \(-0.148511\pi\) |
−0.449816 | + | 0.893121i | \(0.648511\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.33850i | 1.01497i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.946984i | 0.147894i | 0.997262 | + | 0.0739471i | \(0.0235596\pi\) | ||||
−0.997262 | + | 0.0739471i | \(0.976440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.829986 | − | 0.829986i | −0.126572 | − | 0.126572i | 0.640983 | − | 0.767555i | \(-0.278527\pi\) |
−0.767555 | + | 0.640983i | \(0.778527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.52421 | −0.222329 | −0.111165 | − | 0.993802i | \(-0.535458\pi\) | ||||
−0.111165 | + | 0.993802i | \(0.535458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.48919 | 0.498456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.28879 | + | 4.28879i | −0.600551 | + | 0.600551i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.97225 | + | 6.97225i | 0.957712 | + | 0.957712i | 0.999141 | − | 0.0414296i | \(-0.0131912\pi\) |
−0.0414296 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.2346i | 2.54769i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.84418 | − | 6.84418i | −0.891036 | − | 0.891036i | 0.103585 | − | 0.994621i | \(-0.466969\pi\) |
−0.994621 | + | 0.103585i | \(0.966969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87247 | + | 6.87247i | −0.879930 | + | 0.879930i | −0.993527 | − | 0.113597i | \(-0.963763\pi\) |
0.113597 | + | 0.993527i | \(0.463763\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.80293 | 0.605112 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.73647 | − | 3.73647i | 0.456483 | − | 0.456483i | −0.441016 | − | 0.897499i | \(-0.645382\pi\) |
0.897499 | + | 0.441016i | \(0.145382\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.6517 | − | 12.6517i | −1.52309 | − | 1.52309i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.34417i | 1.10895i | 0.832201 | + | 0.554475i | \(0.187081\pi\) | ||||
−0.832201 | + | 0.554475i | \(0.812919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.886316i | − | 0.103735i | −0.998654 | − | 0.0518677i | \(-0.983483\pi\) | ||
0.998654 | − | 0.0518677i | \(-0.0165174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.17755 | + | 6.17755i | −0.703997 | + | 0.703997i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.07575 | −0.346049 | −0.173024 | − | 0.984918i | \(-0.555354\pi\) | ||||
−0.173024 | + | 0.984918i | \(0.555354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1194 | 1.12437 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.989393 | − | 0.989393i | 0.108600 | − | 0.108600i | −0.650719 | − | 0.759319i | \(-0.725532\pi\) |
0.759319 | + | 0.650719i | \(0.225532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.5412i | 2.30946i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0942i | 1.06998i | 0.844859 | + | 0.534990i | \(0.179684\pi\) | ||||
−0.844859 | + | 0.534990i | \(0.820316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.56048 | + | 3.56048i | 0.373239 | + | 0.373239i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.33282 | + | 1.33282i | −0.138207 | + | 0.138207i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.16829 | −0.727830 | −0.363915 | − | 0.931432i | \(-0.618560\pi\) | ||||
−0.363915 | + | 0.931432i | \(0.618560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.45113 | − | 8.45113i | 0.849371 | − | 0.849371i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05091 | − | 1.05091i | −0.104570 | − | 0.104570i | 0.652886 | − | 0.757456i | \(-0.273558\pi\) |
−0.757456 | + | 0.652886i | \(0.773558\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.20690i | − | 0.808649i | −0.914616 | − | 0.404325i | \(-0.867507\pi\) | ||
0.914616 | − | 0.404325i | \(-0.132493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.85743 | + | 2.85743i | 0.276238 | + | 0.276238i | 0.831605 | − | 0.555367i | \(-0.187422\pi\) |
−0.555367 | + | 0.831605i | \(0.687422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3735 | + | 11.3735i | −1.08939 | + | 1.08939i | −0.0937940 | + | 0.995592i | \(0.529900\pi\) |
−0.995592 | + | 0.0937940i | \(0.970100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.99467 | −0.853736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.54221 | −0.333223 | −0.166611 | − | 0.986023i | \(-0.553283\pi\) | ||||
−0.166611 | + | 0.986023i | \(0.553283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.87088 | − | 4.87088i | −0.450313 | − | 0.450313i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.81822i | 0.441685i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7398i | 0.976343i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.57941 | − | 1.57941i | −0.142411 | − | 0.142411i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0693 | −1.60339 | −0.801693 | − | 0.597735i | \(-0.796067\pi\) | ||||
−0.801693 | + | 0.597735i | \(0.796067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.76855 | 0.243757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.39614 | − | 6.39614i | 0.558834 | − | 0.558834i | −0.370142 | − | 0.928975i | \(-0.620691\pi\) |
0.928975 | + | 0.370142i | \(0.120691\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8045 | + | 10.8045i | 0.936871 | + | 0.936871i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.7357i | − | 0.917212i | −0.888640 | − | 0.458606i | \(-0.848349\pi\) | ||
0.888640 | − | 0.458606i | \(-0.151651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.31086 | + | 2.31086i | 0.196005 | + | 0.196005i | 0.798285 | − | 0.602280i | \(-0.205741\pi\) |
−0.602280 | + | 0.798285i | \(0.705741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54213 | − | 2.54213i | 0.214086 | − | 0.214086i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.5299 | 1.04780 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.81938 | + | 5.81938i | −0.479974 | + | 0.479974i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.38743 | + | 1.38743i | 0.113663 | + | 0.113663i | 0.761651 | − | 0.647988i | \(-0.224389\pi\) |
−0.647988 | + | 0.761651i | \(0.724389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.68590i | 0.462712i | 0.972869 | + | 0.231356i | \(0.0743163\pi\) | ||||
−0.972869 | + | 0.231356i | \(0.925684\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.59152i | − | 0.532892i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.48874 | + | 2.48874i | −0.198623 | + | 0.198623i | −0.799409 | − | 0.600787i | \(-0.794854\pi\) |
0.600787 | + | 0.799409i | \(0.294854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.2571 | −1.84440 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2135 | −1.12018 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7091 | + | 12.7091i | −0.995451 | + | 0.995451i | −0.999990 | − | 0.00453842i | \(-0.998555\pi\) |
0.00453842 | + | 0.999990i | \(0.498555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.00982i | 0.387672i | 0.981034 | + | 0.193836i | \(0.0620929\pi\) | ||||
−0.981034 | + | 0.193836i | \(0.937907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.77830i | 0.444485i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.7810 | − | 14.7810i | −1.13033 | − | 1.13033i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.19546 | − | 6.19546i | 0.471032 | − | 0.471032i | −0.431216 | − | 0.902249i | \(-0.641915\pi\) |
0.902249 | + | 0.431216i | \(0.141915\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.8299 | 1.71600 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.51628 | − | 5.51628i | 0.412306 | − | 0.412306i | −0.470235 | − | 0.882541i | \(-0.655831\pi\) |
0.882541 | + | 0.470235i | \(0.155831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8993 | + | 11.8993i | 0.884470 | + | 0.884470i | 0.993985 | − | 0.109515i | \(-0.0349298\pi\) |
−0.109515 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 22.9242i | − | 1.69461i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.47804 | + | 8.47804i | 0.619976 | + | 0.619976i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.36465 | − | 1.36465i | 0.0992637 | − | 0.0992637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1278 | −0.805180 | −0.402590 | − | 0.915380i | \(-0.631890\pi\) | ||||
−0.402590 | + | 0.915380i | \(0.631890\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7821 | 1.49593 | 0.747965 | − | 0.663738i | \(-0.231031\pi\) | ||||
0.747965 | + | 0.663738i | \(0.231031\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0309 | − | 14.0309i | −0.999663 | − | 0.999663i | 0.000337236 | − | 1.00000i | \(-0.499893\pi\) |
−1.00000 | 0.000337236i | \(0.999893\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.24727i | 0.230193i | 0.993354 | + | 0.115096i | \(0.0367177\pi\) | ||||
−0.993354 | + | 0.115096i | \(0.963282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4636i | 0.879115i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1002 | + | 12.1002i | 0.849267 | + | 0.849267i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.4447 | 1.35150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.0228 | 2.63009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1821 | − | 10.1821i | 0.700964 | − | 0.700964i | −0.263654 | − | 0.964617i | \(-0.584928\pi\) |
0.964617 | + | 0.263654i | \(0.0849276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.5845 | − | 15.5845i | −1.06783 | − | 1.06783i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.49735i | 0.101647i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.47822 | + | 1.47822i | 0.0998892 | + | 0.0998892i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88638 | − | 4.88638i | 0.328694 | − | 0.328694i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0469 | −1.61030 | −0.805151 | − | 0.593070i | \(-0.797916\pi\) | ||||
−0.805151 | + | 0.593070i | \(0.797916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9863 | − | 11.9863i | 0.795562 | − | 0.795562i | −0.186830 | − | 0.982392i | \(-0.559821\pi\) |
0.982392 | + | 0.186830i | \(0.0598215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.1972 | − | 20.1972i | −1.33467 | − | 1.33467i | −0.901140 | − | 0.433529i | \(-0.857268\pi\) |
−0.433529 | − | 0.901140i | \(-0.642732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 20.6062i | − | 1.35579i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0655i | 0.659410i | 0.944084 | + | 0.329705i | \(0.106949\pi\) | ||||
−0.944084 | + | 0.329705i | \(0.893051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.12983 | − | 5.12983i | 0.333218 | − | 0.333218i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.992801 | −0.0642189 | −0.0321095 | − | 0.999484i | \(-0.510223\pi\) | ||||
−0.0321095 | + | 0.999484i | \(0.510223\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1229 | 0.909738 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6924 | + | 14.6924i | −0.942520 | + | 0.942520i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.9148i | − | 1.39440i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.30028i | 0.209147i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.56681 | − | 1.56681i | −0.0988961 | − | 0.0988961i | 0.655928 | − | 0.754824i | \(-0.272278\pi\) |
−0.754824 | + | 0.655928i | \(0.772278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.0098 | + | 25.0098i | −1.57235 | + | 1.57235i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2593 | 0.639960 | 0.319980 | − | 0.947424i | \(-0.396324\pi\) | ||||
0.319980 | + | 0.947424i | \(0.396324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.05251 | + | 5.05251i | −0.313948 | + | 0.313948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.5535 | − | 16.5535i | −1.02464 | − | 1.02464i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 19.0630i | − | 1.17548i | −0.809051 | − | 0.587739i | \(-0.800018\pi\) | ||
0.809051 | − | 0.587739i | \(-0.199982\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.8354 | − | 16.8354i | −1.03031 | − | 1.03031i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.48459 | − | 3.48459i | 0.212459 | − | 0.212459i | −0.592852 | − | 0.805311i | \(-0.701998\pi\) |
0.805311 | + | 0.592852i | \(0.201998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.0045 | 1.82264 | 0.911322 | − | 0.411695i | \(-0.135063\pi\) | ||||
0.911322 | + | 0.411695i | \(0.135063\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.8765 | −0.718801 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.43732 | − | 8.43732i | −0.506949 | − | 0.506949i | 0.406639 | − | 0.913589i | \(-0.366701\pi\) |
−0.913589 | + | 0.406639i | \(0.866701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.04844i | − | 0.122637i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.44714i | − | 0.384604i | −0.981336 | − | 0.192302i | \(-0.938405\pi\) | ||
0.981336 | − | 0.192302i | \(-0.0615954\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.61000 | + | 2.61000i | 0.155148 | + | 0.155148i | 0.780413 | − | 0.625264i | \(-0.215009\pi\) |
−0.625264 | + | 0.780413i | \(0.715009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.77438 | −0.104738 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3875 | −0.611029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9555 | − | 11.9555i | 0.700844 | − | 0.700844i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.52428 | + | 7.52428i | 0.439573 | + | 0.439573i | 0.891868 | − | 0.452295i | \(-0.149395\pi\) |
−0.452295 | + | 0.891868i | \(0.649395\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.80242i | − | 0.278665i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.4146 | + | 14.4146i | 0.833618 | + | 0.833618i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55516 | − | 1.55516i | 0.0896377 | − | 0.0896377i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.50549 | 0.201385 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7130 | − | 12.7130i | 0.725571 | − | 0.725571i | −0.244163 | − | 0.969734i | \(-0.578513\pi\) |
0.969734 | + | 0.244163i | \(0.0785133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6877 | + | 13.6877i | 0.778667 | + | 0.778667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9313i | 0.676563i | 0.941045 | + | 0.338281i | \(0.109846\pi\) | ||||
−0.941045 | + | 0.338281i | \(0.890154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 34.3458i | − | 1.94134i | −0.240414 | − | 0.970670i | \(-0.577283\pi\) | ||
0.240414 | − | 0.970670i | \(-0.422717\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.1112 | − | 17.1112i | 0.961060 | − | 0.961060i | −0.0382097 | − | 0.999270i | \(-0.512165\pi\) |
0.999270 | + | 0.0382097i | \(0.0121655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.5825 | 2.38416 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.53141 | −0.531992 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.8281 | − | 14.8281i | 0.825056 | − | 0.825056i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 37.9382i | − | 2.09799i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.85594i | − | 0.157453i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.80246 | − | 9.80246i | −0.538792 | − | 0.538792i | 0.384382 | − | 0.923174i | \(-0.374415\pi\) |
−0.923174 | + | 0.384382i | \(0.874415\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.91203 | − | 6.91203i | 0.378777 | − | 0.378777i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.07501 | −0.330927 | −0.165463 | − | 0.986216i | \(-0.552912\pi\) | ||||
−0.165463 | + | 0.986216i | \(0.552912\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.90780 | − | 5.90780i | 0.320868 | − | 0.320868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63471 | + | 2.63471i | 0.142677 | + | 0.142677i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6538i | 1.06120i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.77231 | + | 5.77231i | 0.309874 | + | 0.309874i | 0.844860 | − | 0.534987i | \(-0.179683\pi\) |
−0.534987 | + | 0.844860i | \(0.679683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.58851 | + | 7.58851i | −0.406203 | + | 0.406203i | −0.880412 | − | 0.474209i | \(-0.842734\pi\) |
0.474209 | + | 0.880412i | \(0.342734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.76791 | −0.147740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.2285 | 0.863753 | 0.431877 | − | 0.901933i | \(-0.357852\pi\) | ||||
0.431877 | + | 0.901933i | \(0.357852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.03597 | − | 8.03597i | −0.425309 | − | 0.425309i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.77298i | 0.357464i | 0.983898 | + | 0.178732i | \(0.0571996\pi\) | ||||
−0.983898 | + | 0.178732i | \(0.942800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 47.5019i | − | 2.50010i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.9121 | − | 17.9121i | −0.940142 | − | 0.940142i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.35705 | −0.331835 | −0.165918 | − | 0.986140i | \(-0.553059\pi\) | ||||
−0.165918 | + | 0.986140i | \(0.553059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.42742 | 0.126367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.0640 | + | 13.0640i | −0.678250 | + | 0.678250i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.20937 | − | 9.20937i | −0.476843 | − | 0.476843i | 0.427278 | − | 0.904121i | \(-0.359473\pi\) |
−0.904121 | + | 0.427278i | \(0.859473\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 24.5428i | − | 1.26402i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.41600 | − | 5.41600i | −0.278201 | − | 0.278201i | 0.554189 | − | 0.832391i | \(-0.313028\pi\) |
−0.832391 | + | 0.554189i | \(0.813028\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.1365 | − | 30.1365i | 1.54394 | − | 1.54394i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.1626 | 1.43904 | 0.719520 | − | 0.694472i | \(-0.244362\pi\) | ||||
0.719520 | + | 0.694472i | \(0.244362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.12752 | + | 2.12752i | −0.108148 | + | 0.108148i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.59783 | + | 9.59783i | 0.486629 | + | 0.486629i | 0.907241 | − | 0.420611i | \(-0.138184\pi\) |
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.5066i | 0.986490i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.3354i | 1.07623i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.4884 | + | 10.4884i | −0.526399 | + | 0.526399i | −0.919497 | − | 0.393098i | \(-0.871403\pi\) |
0.393098 | + | 0.919497i | \(0.371403\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −36.0402 | −1.80427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.44221 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.51853 | − | 1.51853i | 0.0756436 | − | 0.0756436i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.7806i | 0.881350i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6628i | 1.21950i | 0.792596 | + | 0.609748i | \(0.208729\pi\) | ||||
−0.792596 | + | 0.609748i | \(0.791271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.9053 | + | 17.9053i | 0.883204 | + | 0.883204i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.8240 | − | 12.8240i | 0.631030 | − | 0.631030i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.70826 | −0.377475 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.1661 | + | 19.1661i | −0.936326 | + | 0.936326i | −0.998091 | − | 0.0617649i | \(-0.980327\pi\) |
0.0617649 | + | 0.998091i | \(0.480327\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.43469 | − | 7.43469i | −0.362345 | − | 0.362345i | 0.502331 | − | 0.864676i | \(-0.332476\pi\) |
−0.864676 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.90704i | 0.189967i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.8771 | − | 12.8771i | −0.623164 | − | 0.623164i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.8977 | + | 20.8977i | −1.00895 | + | 1.00895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5647 | −1.08690 | −0.543451 | − | 0.839441i | \(-0.682883\pi\) | ||||
−0.543451 | + | 0.839441i | \(0.682883\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4811 | −1.27260 | −0.636301 | − | 0.771441i | \(-0.719536\pi\) | ||||
−0.636301 | + | 0.771441i | \(0.719536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43.7421 | + | 43.7421i | 2.09247 | + | 2.09247i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.765288i | − | 0.0365252i | −0.999833 | − | 0.0182626i | \(-0.994187\pi\) | ||
0.999833 | − | 0.0182626i | \(-0.00581349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8.94390i | − | 0.425900i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.2685 | + | 20.2685i | 0.962985 | + | 0.962985i | 0.999339 | − | 0.0363537i | \(-0.0115743\pi\) |
−0.0363537 | + | 0.999339i | \(0.511574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.62800 | −0.218897 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.2717 | −1.66457 | −0.832287 | − | 0.554345i | \(-0.812969\pi\) | ||||
−0.832287 | + | 0.554345i | \(0.812969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.12216 | + | 3.12216i | −0.147017 | + | 0.147017i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.48312 | − | 9.48312i | −0.445556 | − | 0.445556i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.01188i | − | 0.421558i | −0.977534 | − | 0.210779i | \(-0.932400\pi\) | ||
0.977534 | − | 0.210779i | \(-0.0676000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.87284 | − | 1.87284i | −0.0874167 | − | 0.0874167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8247 | + | 22.8247i | −1.06305 | + | 1.06305i | −0.0651807 | + | 0.997873i | \(0.520762\pi\) |
−0.997873 | + | 0.0651807i | \(0.979238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.72721 | 0.173218 | 0.0866090 | − | 0.996242i | \(-0.472397\pi\) | ||||
0.0866090 | + | 0.996242i | \(0.472397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.23477 | + | 3.23477i | −0.149687 | + | 0.149687i | −0.777978 | − | 0.628291i | \(-0.783755\pi\) |
0.628291 | + | 0.777978i | \(0.283755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.00109 | + | 7.00109i | 0.323280 | + | 0.323280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.30158i | − | 0.382517i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.47284i | − | 0.251642i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.8721 | − | 17.8721i | 0.818307 | − | 0.818307i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0636 | 0.505508 | 0.252754 | − | 0.967531i | \(-0.418664\pi\) | ||||
0.252754 | + | 0.967531i | \(0.418664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2480 | 0.467267 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.7057 | − | 23.7057i | 1.07865 | − | 1.07865i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.68176i | − | 0.302779i | −0.988474 | − | 0.151390i | \(-0.951625\pi\) | ||
0.988474 | − | 0.151390i | \(-0.0483748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 42.3932i | − | 1.91708i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.4274 | + | 18.4274i | 0.831618 | + | 0.831618i | 0.987738 | − | 0.156120i | \(-0.0498986\pi\) |
−0.156120 | + | 0.987738i | \(0.549899\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.6063 | − | 16.6063i | 0.747908 | − | 0.747908i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.5083 | −0.785356 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.84615 | + | 8.84615i | −0.396008 | + | 0.396008i | −0.876822 | − | 0.480814i | \(-0.840341\pi\) |
0.480814 | + | 0.876822i | \(0.340341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.35554 | − | 8.35554i | −0.373298 | − | 0.373298i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.8746i | 0.752401i | 0.926538 | + | 0.376201i | \(0.122770\pi\) | ||||
−0.926538 | + | 0.376201i | \(0.877230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.63723 | − | 9.63723i | −0.428004 | − | 0.428004i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.5691 | − | 20.5691i | 0.911707 | − | 0.911707i | −0.0846994 | − | 0.996407i | \(-0.526993\pi\) |
0.996407 | + | 0.0846994i | \(0.0269930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.66070 | 0.0734652 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.39943 | −0.370844 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.02526 | − | 5.02526i | −0.221011 | − | 0.221011i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.6660i | 0.907135i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6708i | 0.555118i | 0.960709 | + | 0.277559i | \(0.0895253\pi\) | ||||
−0.960709 | + | 0.277559i | \(0.910475\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8509 | − | 27.8509i | −1.21784 | − | 1.21784i | −0.968388 | − | 0.249448i | \(-0.919751\pi\) |
−0.249448 | − | 0.968388i | \(-0.580249\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.05496 | 0.0895154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −34.5435 | −1.50189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −17.5438 | + | 17.5438i | −0.761336 | + | 0.761336i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.79948 | + | 1.79948i | 0.0779442 | + | 0.0779442i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.4005i | 0.794038i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.5037 | + | 11.5037i | 0.495499 | + | 0.495499i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4122 | + | 23.4122i | −1.00657 | + | 1.00657i | −0.00659048 | + | 0.999978i | \(0.502098\pi\) |
−0.999978 | + | 0.00659048i | \(0.997902\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.6921 | −1.70335 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.3745 | − | 17.3745i | 0.742878 | − | 0.742878i | −0.230253 | − | 0.973131i | \(-0.573955\pi\) |
0.973131 | + | 0.230253i | \(0.0739552\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.6163 | + | 17.6163i | 0.751846 | + | 0.751846i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 74.4767i | − | 3.17282i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 5.76308i | − | 0.245071i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8889 | + | 22.8889i | −0.969832 | + | 0.969832i | −0.999558 | − | 0.0297261i | \(-0.990536\pi\) |
0.0297261 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.15432 | −0.133413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.2799 | −1.19398 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.2489 | − | 19.2489i | 0.811246 | − | 0.811246i | −0.173574 | − | 0.984821i | \(-0.555532\pi\) |
0.984821 | + | 0.173574i | \(0.0555317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.9608i | 0.796278i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.4274i | 1.44327i | 0.692273 | + | 0.721635i | \(0.256609\pi\) | ||||
−0.692273 | + | 0.721635i | \(0.743391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.85059 | − | 5.85059i | −0.244840 | − | 0.244840i | 0.574009 | − | 0.818849i | \(-0.305387\pi\) |
−0.818849 | + | 0.574009i | \(0.805387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5593 | − | 18.5593i | 0.775326 | − | 0.775326i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.5042 | −1.35317 | −0.676585 | − | 0.736365i | \(-0.736541\pi\) | ||||
−0.676585 | + | 0.736365i | \(0.736541\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34.6611 | + | 34.6611i | −1.44047 | + | 1.44047i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85384 | + | 1.85384i | 0.0769103 | + | 0.0769103i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.9743i | 1.90406i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.7519 | − | 14.7519i | −0.608875 | − | 0.608875i | 0.333777 | − | 0.942652i | \(-0.391677\pi\) |
−0.942652 | + | 0.333777i | \(0.891677\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.60810 | − | 4.60810i | 0.189873 | − | 0.189873i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.8024 | 1.92520 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5310 | 0.843108 | 0.421554 | − | 0.906803i | \(-0.361485\pi\) | ||||
0.421554 | + | 0.906803i | \(0.361485\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.41590 | − | 5.41590i | −0.221658 | − | 0.221658i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 12.3998i | − | 0.506644i | −0.967382 | − | 0.253322i | \(-0.918477\pi\) | ||
0.967382 | − | 0.253322i | \(-0.0815232\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3980i | 0.505723i | 0.967502 | + | 0.252862i | \(0.0813718\pi\) | ||||
−0.967502 | + | 0.252862i | \(0.918628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.57777 | − | 9.57777i | −0.390037 | − | 0.390037i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.90398 | 0.199046 | 0.0995232 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995232 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.3621 | −1.63556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.89635 | + | 2.89635i | −0.117174 | + | 0.117174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.408547 | + | 0.408547i | 0.0165011 | + | 0.0165011i | 0.715309 | − | 0.698808i | \(-0.246286\pi\) |
−0.698808 | + | 0.715309i | \(0.746286\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.17186i | 0.248470i | 0.992253 | + | 0.124235i | \(0.0396476\pi\) | ||||
−0.992253 | + | 0.124235i | \(0.960352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.5138 | − | 18.5138i | −0.744132 | − | 0.744132i | 0.229238 | − | 0.973370i | \(-0.426377\pi\) |
−0.973370 | + | 0.229238i | \(0.926377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.52479 | − | 5.52479i | 0.221702 | − | 0.221702i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9136 | −0.757757 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −63.4156 | + | 63.4156i | −2.53258 | + | 2.53258i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.93404 | + | 6.93404i | 0.276478 | + | 0.276478i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.7940i | 0.827795i | 0.910323 | + | 0.413897i | \(0.135833\pi\) | ||||
−0.910323 | + | 0.413897i | \(0.864167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.9640i | 1.34995i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.63024 | − | 6.63024i | 0.262700 | − | 0.262700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.9521 | 0.947530 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1179 | 0.636620 | 0.318310 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.3733 | − | 10.3733i | 0.409082 | − | 0.409082i | −0.472336 | − | 0.881419i | \(-0.656589\pi\) |
0.881419 | + | 0.472336i | \(0.156589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 32.5724i | − | 1.28055i | −0.768145 | − | 0.640276i | \(-0.778820\pi\) | ||
0.768145 | − | 0.640276i | \(-0.221180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 45.1298i | − | 1.77150i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.49733 | − | 2.49733i | −0.0978780 | − | 0.0978780i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31962 | + | 4.31962i | −0.169040 | + | 0.169040i | −0.786557 | − | 0.617517i | \(-0.788139\pi\) |
0.617517 | + | 0.786557i | \(0.288139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.27191 | −0.0886356 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.19711 | − | 4.19711i | 0.163496 | − | 0.163496i | −0.620617 | − | 0.784114i | \(-0.713118\pi\) |
0.784114 | + | 0.620617i | \(0.213118\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2310 | + | 21.2310i | 0.825790 | + | 0.825790i | 0.986931 | − | 0.161141i | \(-0.0515175\pi\) |
−0.161141 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.2993i | 0.633013i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.9877 | + | 48.9877i | 1.89681 | + | 1.89681i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.1062 | − | 40.1062i | 1.55060 | − | 1.55060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −45.3164 | −1.74942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.08317 | 0.234489 | 0.117244 | − | 0.993103i | \(-0.462594\pi\) | ||||
0.117244 | + | 0.993103i | \(0.462594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.42443 | + | 8.42443i | 0.323777 | + | 0.323777i | 0.850214 | − | 0.526437i | \(-0.176472\pi\) |
−0.526437 | + | 0.850214i | \(0.676472\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.4313i | − | 0.515447i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.9824i | 1.53213i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.7609 | + | 14.7609i | 0.564812 | + | 0.564812i | 0.930670 | − | 0.365859i | \(-0.119225\pi\) |
−0.365859 | + | 0.930670i | \(0.619225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.3710 | 2.57036 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.4977 | 1.00948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.06268 | − | 4.06268i | 0.154552 | − | 0.154552i | −0.625596 | − | 0.780147i | \(-0.715144\pi\) |
0.780147 | + | 0.625596i | \(0.215144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.8350 | + | 15.8350i | 0.601523 | + | 0.601523i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43515i | 0.0922379i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.7875 | − | 16.7875i | −0.634961 | − | 0.634961i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1049 | − | 11.1049i | 0.419428 | − | 0.419428i | −0.465578 | − | 0.885007i | \(-0.654154\pi\) |
0.885007 | + | 0.465578i | \(0.154154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.0982 | 1.17289 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.96911 | − | 1.96911i | 0.0740561 | − | 0.0740561i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.0114 | + | 13.0114i | 0.488652 | + | 0.488652i | 0.907881 | − | 0.419229i | \(-0.137700\pi\) |
−0.419229 | + | 0.907881i | \(0.637700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.88412i | 0.295678i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.06203i | 0.227025i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.65582 | − | 1.65582i | 0.0618378 | − | 0.0618378i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.0570 | 1.86681 | 0.933406 | − | 0.358821i | \(-0.116821\pi\) | ||||
0.933406 | + | 0.358821i | \(0.116821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3774 | 0.572684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.5547 | + | 23.5547i | −0.876007 | + | 0.876007i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.7141i | 1.02786i | 0.857832 | + | 0.513930i | \(0.171811\pi\) | ||||
−0.857832 | + | 0.513930i | \(0.828189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 18.6509i | − | 0.690775i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.13429 | − | 2.13429i | −0.0789396 | − | 0.0789396i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.8860 | + | 16.8860i | −0.623698 | + | 0.623698i | −0.946475 | − | 0.322777i | \(-0.895384\pi\) |
0.322777 | + | 0.946475i | \(0.395384\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.6379 | 0.907550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.6286 | − | 23.6286i | 0.869193 | − | 0.869193i | −0.123190 | − | 0.992383i | \(-0.539312\pi\) |
0.992383 | + | 0.123190i | \(0.0393124\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.5501 | + | 36.5501i | 1.34270 | + | 1.34270i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.53356i | − | 0.239693i | −0.992792 | − | 0.119846i | \(-0.961760\pi\) | ||
0.992792 | − | 0.119846i | \(-0.0382402\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53613 | − | 2.53613i | −0.0927921 | − | 0.0927921i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.35401 | + | 5.35401i | −0.195631 | + | 0.195631i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.8483 | 0.833746 | 0.416873 | − | 0.908965i | \(-0.363126\pi\) | ||||
0.416873 | + | 0.908965i | \(0.363126\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.22634 | 0.190459 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.0190 | + | 24.0190i | 0.872985 | + | 0.872985i | 0.992797 | − | 0.119811i | \(-0.0382290\pi\) |
−0.119811 | + | 0.992797i | \(0.538229\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 83.4243i | − | 3.02811i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.51772i | − | 0.200017i | −0.994987 | − | 0.100009i | \(-0.968113\pi\) | ||
0.994987 | − | 0.100009i | \(-0.0318871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.3107 | − | 21.3107i | −0.771501 | − | 0.771501i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0109 | −0.939200 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0124 | 0.505299 | 0.252649 | − | 0.967558i | \(-0.418698\pi\) | ||||
0.252649 | + | 0.967558i | \(0.418698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.1108 | + | 17.1108i | −0.616231 | + | 0.616231i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.753043 | − | 0.753043i | −0.0270851 | − | 0.0270851i | 0.693435 | − | 0.720520i | \(-0.256097\pi\) |
−0.720520 | + | 0.693435i | \(0.756097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 16.8535i | − | 0.604614i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.46066 | + | 5.46066i | 0.195648 | + | 0.195648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.8073 | + | 30.8073i | −1.10237 | + | 1.10237i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.40668 | −0.336167 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.2752 | + | 29.2752i | −1.04355 | + | 1.04355i | −0.0445395 | + | 0.999008i | \(0.514182\pi\) |
−0.999008 | + | 0.0445395i | \(0.985818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.7939 | + | 31.7939i | 1.13189 | + | 1.13189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.63709i | − | 0.235988i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.1185i | 0.927494i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.09658 | − | 6.09658i | 0.215952 | − | 0.215952i | −0.590838 | − | 0.806790i | \(-0.701203\pi\) |
0.806790 | + | 0.590838i | \(0.201203\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.91948 | −0.138661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.8745 | 0.914232 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.92214 | − | 2.92214i | 0.103120 | − | 0.103120i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6234i | 0.409163i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 31.5083i | − | 1.10777i | −0.832592 | − | 0.553886i | \(-0.813144\pi\) | ||
0.832592 | − | 0.553886i | \(-0.186856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.2317 | − | 20.2317i | −0.710431 | − | 0.710431i | 0.256194 | − | 0.966625i | \(-0.417531\pi\) |
−0.966625 | + | 0.256194i | \(0.917531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.0424 | + | 50.0424i | −1.75506 | + | 1.75506i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.57200 | −0.334882 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.12664 | − | 9.12664i | 0.318910 | − | 0.318910i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1821 | − | 19.1821i | −0.669459 | − | 0.669459i | 0.288132 | − | 0.957591i | \(-0.406966\pi\) |
−0.957591 | + | 0.288132i | \(0.906966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 11.4746i | − | 0.399979i | −0.979798 | − | 0.199989i | \(-0.935909\pi\) | ||
0.979798 | − | 0.199989i | \(-0.0640907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.7573 | + | 17.7573i | 0.617482 | + | 0.617482i | 0.944885 | − | 0.327403i | \(-0.106173\pi\) |
−0.327403 | + | 0.944885i | \(0.606173\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0071 | + | 20.0071i | −0.694876 | + | 0.694876i | −0.963301 | − | 0.268424i | \(-0.913497\pi\) |
0.268424 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.1440 | 0.976306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.97238 | 0.310874 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.582020 | − | 0.582020i | −0.0201175 | − | 0.0201175i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 20.3936i | − | 0.704065i | −0.935988 | − | 0.352033i | \(-0.885491\pi\) | ||
0.935988 | − | 0.352033i | \(-0.114509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 54.4079i | − | 1.87614i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.7527 | + | 10.7527i | 0.370344 | + | 0.370344i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.1233 | −0.691444 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.70608 | −0.298792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4551 | + | 20.4551i | −0.701191 | + | 0.701191i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.4481 | − | 37.4481i | −1.28220 | − | 1.28220i | −0.939414 | − | 0.342784i | \(-0.888630\pi\) |
−0.342784 | − | 0.939414i | \(-0.611370\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 12.7258i | − | 0.434706i | −0.976093 | − | 0.217353i | \(-0.930258\pi\) | ||
0.976093 | − | 0.217353i | \(-0.0697422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.4318 | − | 17.4318i | −0.594766 | − | 0.594766i | 0.344149 | − | 0.938915i | \(-0.388167\pi\) |
−0.938915 | + | 0.344149i | \(0.888167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95936 | − | 2.95936i | 0.100855 | − | 0.100855i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.6976 | −1.14708 | −0.573540 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573540 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3246 | − | 17.3246i | 0.588374 | − | 0.588374i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1406 | − | 10.1406i | −0.343996 | − | 0.343996i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.2003i | − | 0.481158i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.3746i | 0.621886i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.8386 | − | 21.8386i | 0.737436 | − | 0.737436i | −0.234645 | − | 0.972081i | \(-0.575393\pi\) |
0.972081 | + | 0.234645i | \(0.0753927\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −25.0985 | −0.846550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3274 | −1.32497 | −0.662487 | − | 0.749073i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.80206 | + | 6.80206i | −0.228907 | + | 0.228907i | −0.812236 | − | 0.583329i | \(-0.801750\pi\) |
0.583329 | + | 0.812236i | \(0.301750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.4190i | 0.987793i | 0.869521 | + | 0.493897i | \(0.164428\pi\) | ||||
−0.869521 | + | 0.493897i | \(0.835572\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 33.8566i | − | 1.13552i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.3630 | + | 33.3630i | 1.11770 | + | 1.11770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.78917 | + | 8.78917i | −0.294118 | + | 0.294118i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −48.0822 | −1.60542 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.16070 | − | 5.16070i | 0.172119 | − | 0.172119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9290 | + | 17.9290i | 0.597301 | + | 0.597301i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.18748i | 0.172628i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6137 | + | 16.6137i | 0.551649 | + | 0.551649i | 0.926917 | − | 0.375267i | \(-0.122449\pi\) |
−0.375267 | + | 0.926917i | \(0.622449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.69382 | + | 2.69382i | −0.0893485 | + | 0.0893485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.7299 | −1.34944 | −0.674721 | − | 0.738073i | \(-0.735736\pi\) | ||||
−0.674721 | + | 0.738073i | \(0.735736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.52396 | 0.215912 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.9846 | + | 11.9846i | 0.395765 | + | 0.395765i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.6125i | − | 1.17475i | −0.809316 | − | 0.587373i | \(-0.800162\pi\) | ||
0.809316 | − | 0.587373i | \(-0.199838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.4064i | 1.39734i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.7560 | + | 17.7560i | 0.584446 | + | 0.584446i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.0369 | −0.690942 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.570971 | −0.0187329 | −0.00936647 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936647 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.1199 | − | 20.1199i | 0.659404 | − | 0.659404i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.8994 | − | 19.8994i | −0.651477 | − | 0.651477i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3585i | 0.697750i | 0.937169 | + | 0.348875i | \(0.113436\pi\) | ||||
−0.937169 | + | 0.348875i | \(0.886564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 57.2830 | + | 57.2830i | 1.86936 | + | 1.86936i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.6914 | − | 33.6914i | 1.09831 | − | 1.09831i | 0.103700 | − | 0.994609i | \(-0.466932\pi\) |
0.994609 | − | 0.103700i | \(-0.0330681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.18358 | −0.233929 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.421834 | − | 0.421834i | 0.0137078 | − | 0.0137078i | −0.700220 | − | 0.713927i | \(-0.746915\pi\) |
0.713927 | + | 0.700220i | \(0.246915\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.68420 | − | 1.68420i | −0.0546714 | − | 0.0546714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.0771i | 1.85085i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7261i | 0.898137i | 0.893497 | + | 0.449069i | \(0.148244\pi\) | ||||
−0.893497 | + | 0.449069i | \(0.851756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −71.0204 | + | 71.0204i | −2.29576 | + | 2.29576i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.1156 | 0.649567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3614 | −0.979399 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.32450 | − | 7.32450i | 0.236029 | − | 0.236029i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 41.9640i | − | 1.34947i | −0.738060 | − | 0.674735i | \(-0.764258\pi\) | ||
0.738060 | − | 0.674735i | \(-0.235742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 49.4614i | 1.58893i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0549 | − | 30.0549i | −0.964508 | − | 0.964508i | 0.0348833 | − | 0.999391i | \(-0.488894\pi\) |
−0.999391 | + | 0.0348833i | \(0.988894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.32990 | + | 4.32990i | −0.138810 | + | 0.138810i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.3389 | 1.41853 | 0.709263 | − | 0.704944i | \(-0.249028\pi\) | ||||
0.709263 | + | 0.704944i | \(0.249028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.2800 | + | 33.2800i | −1.06363 | + | 1.06363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.1539 | + | 29.1539i | 0.930814 | + | 0.930814i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 27.0764i | − | 0.863604i | −0.901968 | − | 0.431802i | \(-0.857878\pi\) | ||
0.901968 | − | 0.431802i | \(-0.142122\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.76323 | + | 4.76323i | 0.151615 | + | 0.151615i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.29606 | − | 6.29606i | 0.200203 | − | 0.200203i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3780 | −0.615564 | −0.307782 | − | 0.951457i | \(-0.599587\pi\) | ||||
−0.307782 | + | 0.951457i | \(0.599587\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.6977 | 1.03763 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.69453 | + | 8.69453i | 0.275359 | + | 0.275359i | 0.831253 | − | 0.555894i | \(-0.187624\pi\) |
−0.555894 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 3.92782i | − | 0.124271i |
(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 | 1600.2.l.g.1201.1 | 12 | ||
4.3 | odd | 2 | 400.2.l.f.101.3 | ✓ | 12 | ||
5.2 | odd | 4 | 1600.2.q.e.49.6 | 12 | |||
5.3 | odd | 4 | 1600.2.q.f.49.1 | 12 | |||
5.4 | even | 2 | 1600.2.l.f.1201.6 | 12 | |||
16.3 | odd | 4 | 400.2.l.f.301.3 | yes | 12 | ||
16.13 | even | 4 | inner | 1600.2.l.g.401.1 | 12 | ||
20.3 | even | 4 | 400.2.q.f.149.5 | 12 | |||
20.7 | even | 4 | 400.2.q.e.149.2 | 12 | |||
20.19 | odd | 2 | 400.2.l.g.101.4 | yes | 12 | ||
80.3 | even | 4 | 400.2.q.e.349.2 | 12 | |||
80.13 | odd | 4 | 1600.2.q.e.849.6 | 12 | |||
80.19 | odd | 4 | 400.2.l.g.301.4 | yes | 12 | ||
80.29 | even | 4 | 1600.2.l.f.401.6 | 12 | |||
80.67 | even | 4 | 400.2.q.f.349.5 | 12 | |||
80.77 | odd | 4 | 1600.2.q.f.849.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.3 | ✓ | 12 | 4.3 | odd | 2 | ||
400.2.l.f.301.3 | yes | 12 | 16.3 | odd | 4 | ||
400.2.l.g.101.4 | yes | 12 | 20.19 | odd | 2 | ||
400.2.l.g.301.4 | yes | 12 | 80.19 | odd | 4 | ||
400.2.q.e.149.2 | 12 | 20.7 | even | 4 | |||
400.2.q.e.349.2 | 12 | 80.3 | even | 4 | |||
400.2.q.f.149.5 | 12 | 20.3 | even | 4 | |||
400.2.q.f.349.5 | 12 | 80.67 | even | 4 | |||
1600.2.l.f.401.6 | 12 | 80.29 | even | 4 | |||
1600.2.l.f.1201.6 | 12 | 5.4 | even | 2 | |||
1600.2.l.g.401.1 | 12 | 16.13 | even | 4 | inner | ||
1600.2.l.g.1201.1 | 12 | 1.1 | even | 1 | trivial | ||
1600.2.q.e.49.6 | 12 | 5.2 | odd | 4 | |||
1600.2.q.e.849.6 | 12 | 80.13 | odd | 4 | |||
1600.2.q.f.49.1 | 12 | 5.3 | odd | 4 | |||
1600.2.q.f.849.1 | 12 | 80.77 | odd | 4 |