Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(143,1600)]
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([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.j (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: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 400) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.12 | ||
Character | \(\chi\) | \(=\) | 1600.143 |
Dual form | 1600.2.j.e.1007.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 3.25766i | 1.88081i | 0.340052 | + | 0.940407i | \(0.389555\pi\) | ||||
−0.340052 | + | 0.940407i | \(0.610445\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54012 | + | 2.54012i | −0.960075 | + | 0.960075i | −0.999233 | − | 0.0391576i | \(-0.987533\pi\) |
0.0391576 | + | 0.999233i | \(0.487533\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.61238 | −2.53746 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.462406 | − | 0.462406i | 0.139421 | − | 0.139421i | −0.633952 | − | 0.773372i | \(-0.718568\pi\) |
0.773372 | + | 0.633952i | \(0.218568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.33473 | 0.370188 | 0.185094 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185094 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.37342 | + | 2.37342i | −0.575640 | + | 0.575640i | −0.933699 | − | 0.358059i | \(-0.883439\pi\) |
0.358059 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.69776 | + | 2.69776i | −0.618909 | + | 0.618909i | −0.945251 | − | 0.326343i | \(-0.894184\pi\) |
0.326343 | + | 0.945251i | \(0.394184\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.27486 | − | 8.27486i | −1.80572 | − | 1.80572i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.10420 | + | 2.10420i | 0.438755 | + | 0.438755i | 0.891593 | − | 0.452838i | \(-0.149588\pi\) |
−0.452838 | + | 0.891593i | \(0.649588\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 15.0256i | − | 2.89168i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.97767 | − | 1.97767i | −0.367245 | − | 0.367245i | 0.499227 | − | 0.866471i | \(-0.333618\pi\) |
−0.866471 | + | 0.499227i | \(0.833618\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.03054i | − | 1.26272i | −0.775489 | − | 0.631361i | \(-0.782497\pi\) | ||
0.775489 | − | 0.631361i | \(-0.217503\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50636 | + | 1.50636i | 0.262224 | + | 0.262224i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.81135 | 1.28418 | 0.642089 | − | 0.766630i | \(-0.278068\pi\) | ||||
0.642089 | + | 0.766630i | \(0.278068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.34811i | 0.696255i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.17459i | 0.339614i | 0.985477 | + | 0.169807i | \(0.0543144\pi\) | ||||
−0.985477 | + | 0.169807i | \(0.945686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.10070 | −0.472852 | −0.236426 | − | 0.971650i | \(-0.575976\pi\) | ||||
−0.236426 | + | 0.971650i | \(0.575976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0727309 | + | 0.0727309i | 0.0106089 | + | 0.0106089i | 0.712391 | − | 0.701782i | \(-0.247612\pi\) |
−0.701782 | + | 0.712391i | \(0.747612\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.90443i | − | 0.843490i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.73182 | − | 7.73182i | −1.08267 | − | 1.08267i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 0.719718i | − | 0.0988609i | −0.998778 | − | 0.0494304i | \(-0.984259\pi\) | ||
0.998778 | − | 0.0494304i | \(-0.0157406\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.78840 | − | 8.78840i | −1.16405 | − | 1.16405i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.67421 | − | 8.67421i | −1.12929 | − | 1.12929i | −0.990293 | − | 0.138993i | \(-0.955613\pi\) |
−0.138993 | − | 0.990293i | \(-0.544387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.10027 | + | 7.10027i | −0.909097 | + | 0.909097i | −0.996199 | − | 0.0871025i | \(-0.972239\pi\) |
0.0871025 | + | 0.996199i | \(0.472239\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.3364 | − | 19.3364i | 2.43615 | − | 2.43615i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.8172 | −1.32153 | −0.660765 | − | 0.750593i | \(-0.729768\pi\) | ||||
−0.660765 | + | 0.750593i | \(0.729768\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.85476 | + | 6.85476i | −0.825217 | + | 0.825217i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.3474 | 1.82140 | 0.910698 | − | 0.413072i | \(-0.135544\pi\) | ||||
0.910698 | + | 0.413072i | \(0.135544\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.905052 | + | 0.905052i | −0.105928 | + | 0.105928i | −0.758085 | − | 0.652156i | \(-0.773865\pi\) |
0.652156 | + | 0.758085i | \(0.273865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34913i | 0.267709i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.90167 | 0.438972 | 0.219486 | − | 0.975616i | \(-0.429562\pi\) | ||||
0.219486 | + | 0.975616i | \(0.429562\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 26.1112 | 2.90124 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.02206i | − | 0.661007i | −0.943805 | − | 0.330503i | \(-0.892782\pi\) | ||
0.943805 | − | 0.330503i | \(-0.107218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.44260 | − | 6.44260i | 0.690719 | − | 0.690719i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.46664 | 0.791462 | 0.395731 | − | 0.918366i | \(-0.370491\pi\) | ||||
0.395731 | + | 0.918366i | \(0.370491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.39038 | + | 3.39038i | −0.355408 | + | 0.355408i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.9031 | 2.37494 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.74551 | + | 3.74551i | −0.380299 | + | 0.380299i | −0.871210 | − | 0.490911i | \(-0.836664\pi\) |
0.490911 | + | 0.871210i | \(0.336664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.52001 | + | 3.52001i | −0.353774 | + | 0.353774i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.39232 | + | 4.39232i | 0.437052 | + | 0.437052i | 0.891019 | − | 0.453966i | \(-0.149991\pi\) |
−0.453966 | + | 0.891019i | \(0.649991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.36518 | + | 6.36518i | 0.627179 | + | 0.627179i | 0.947357 | − | 0.320178i | \(-0.103743\pi\) |
−0.320178 | + | 0.947357i | \(0.603743\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.8172i | 1.04574i | 0.852413 | + | 0.522869i | \(0.175138\pi\) | ||||
−0.852413 | + | 0.522869i | \(0.824862\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.56691 | − | 7.56691i | −0.724779 | − | 0.724779i | 0.244796 | − | 0.969575i | \(-0.421279\pi\) |
−0.969575 | + | 0.244796i | \(0.921279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.4468i | 2.41530i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.2142 | − | 12.2142i | −1.14902 | − | 1.14902i | −0.986746 | − | 0.162270i | \(-0.948118\pi\) |
−0.162270 | − | 0.986746i | \(-0.551882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1605 | −0.939337 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 12.0576i | − | 1.10532i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.5724i | 0.961124i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.08408 | −0.638750 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.98272 | + | 8.98272i | 0.797087 | + | 0.797087i | 0.982635 | − | 0.185548i | \(-0.0594059\pi\) |
−0.185548 | + | 0.982635i | \(0.559406\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 10.1010i | − | 0.889346i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.01718 | + | 5.01718i | 0.438353 | + | 0.438353i | 0.891458 | − | 0.453104i | \(-0.149683\pi\) |
−0.453104 | + | 0.891458i | \(0.649683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 13.7053i | − | 1.18840i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.21068 | + | 3.21068i | 0.274307 | + | 0.274307i | 0.830831 | − | 0.556524i | \(-0.187865\pi\) |
−0.556524 | + | 0.830831i | \(0.687865\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.102562 | − | 0.102562i | −0.00869923 | − | 0.00869923i | 0.702744 | − | 0.711443i | \(-0.251958\pi\) |
−0.711443 | + | 0.702744i | \(0.751958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.236933 | + | 0.236933i | −0.0199533 | + | 0.0199533i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.617188 | − | 0.617188i | 0.0516118 | − | 0.0516118i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.2346 | 1.58645 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.12805 | + | 2.12805i | −0.174337 | + | 0.174337i | −0.788882 | − | 0.614545i | \(-0.789340\pi\) |
0.614545 | + | 0.788882i | \(0.289340\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.6723 | −1.76366 | −0.881832 | − | 0.471564i | \(-0.843690\pi\) | ||||
−0.881832 | + | 0.471564i | \(0.843690\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.0674 | − | 18.0674i | 1.46066 | − | 1.46066i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.3539i | − | 1.38499i | −0.721421 | − | 0.692496i | \(-0.756511\pi\) | ||
0.721421 | − | 0.692496i | \(-0.243489\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.34460 | 0.185939 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.6898 | −0.842476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.29032i | 0.492696i | 0.969181 | + | 0.246348i | \(0.0792306\pi\) | ||||
−0.969181 | + | 0.246348i | \(0.920769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.61495 | + | 6.61495i | −0.511880 | + | 0.511880i | −0.915102 | − | 0.403222i | \(-0.867890\pi\) |
0.403222 | + | 0.915102i | \(0.367890\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2185 | −0.862961 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.5364 | − | 20.5364i | 1.57046 | − | 1.57046i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.857921 | −0.0652265 | −0.0326133 | − | 0.999468i | \(-0.510383\pi\) | ||||
−0.0326133 | + | 0.999468i | \(0.510383\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 28.2577 | − | 28.2577i | 2.12398 | − | 2.12398i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.571652 | + | 0.571652i | −0.0427273 | + | 0.0427273i | −0.728148 | − | 0.685420i | \(-0.759618\pi\) |
0.685420 | + | 0.728148i | \(0.259618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3879 | − | 10.3879i | −0.772130 | − | 0.772130i | 0.206349 | − | 0.978478i | \(-0.433842\pi\) |
−0.978478 | + | 0.206349i | \(0.933842\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.1303 | − | 23.1303i | −1.70984 | − | 1.70984i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.19497i | 0.160512i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 38.1668 | + | 38.1668i | 2.77623 | + | 2.77623i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.5293i | 1.63017i | 0.579344 | + | 0.815083i | \(0.303309\pi\) | ||||
−0.579344 | + | 0.815083i | \(0.696691\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.95941 | − | 7.95941i | −0.572931 | − | 0.572931i | 0.360015 | − | 0.932946i | \(-0.382771\pi\) |
−0.932946 | + | 0.360015i | \(0.882771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5546 | −1.25071 | −0.625357 | − | 0.780338i | \(-0.715047\pi\) | ||||
−0.625357 | + | 0.780338i | \(0.715047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 18.7910i | − | 1.33206i | −0.745924 | − | 0.666031i | \(-0.767992\pi\) | ||
0.745924 | − | 0.666031i | \(-0.232008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 35.2388i | − | 2.48555i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.0471 | 0.705165 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.0179 | − | 16.0179i | −1.11332 | − | 1.11332i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.49492i | 0.172577i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00592 | − | 9.00592i | −0.619993 | − | 0.619993i | 0.325536 | − | 0.945530i | \(-0.394455\pi\) |
−0.945530 | + | 0.325536i | \(0.894455\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 49.9965i | 3.42571i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.8584 | + | 17.8584i | 1.21231 | + | 1.21231i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.94836 | − | 2.94836i | −0.199232 | − | 0.199232i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.16788 | + | 3.16788i | −0.213095 | + | 0.213095i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.16630 | + | 9.16630i | −0.613821 | + | 0.613821i | −0.943939 | − | 0.330119i | \(-0.892911\pi\) |
0.330119 | + | 0.943939i | \(0.392911\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.2474 | −1.41024 | −0.705120 | − | 0.709088i | \(-0.749107\pi\) | ||||
−0.705120 | + | 0.709088i | \(0.749107\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0502 | − | 14.0502i | 0.928461 | − | 0.928461i | −0.0691452 | − | 0.997607i | \(-0.522027\pi\) |
0.997607 | + | 0.0691452i | \(0.0220272\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.65269 | −0.503510 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.7571 | + | 19.7571i | −1.29433 | + | 1.29433i | −0.362244 | + | 0.932083i | \(0.617989\pi\) |
−0.932083 | + | 0.362244i | \(0.882011\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.7103i | 0.825625i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.51630 | −0.0980814 | −0.0490407 | − | 0.998797i | \(-0.515616\pi\) | ||||
−0.0490407 | + | 0.998797i | \(0.515616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.91616 | 0.381094 | 0.190547 | − | 0.981678i | \(-0.438974\pi\) | ||||
0.190547 | + | 0.981678i | \(0.438974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 39.9847i | 2.56502i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.60079 | + | 3.60079i | −0.229112 | + | 0.229112i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.6178 | 1.24323 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8723 | − | 11.8723i | 0.749376 | − | 0.749376i | −0.224986 | − | 0.974362i | \(-0.572234\pi\) |
0.974362 | + | 0.224986i | \(0.0722336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.94598 | 0.122343 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.39452 | + | 8.39452i | −0.523636 | + | 0.523636i | −0.918667 | − | 0.395032i | \(-0.870734\pi\) |
0.395032 | + | 0.918667i | \(0.370734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.8418 | + | 19.8418i | −1.23291 | + | 1.23291i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0548 | + | 15.0548i | 0.931869 | + | 0.931869i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.8623 | + | 10.8623i | 0.669798 | + | 0.669798i | 0.957669 | − | 0.287871i | \(-0.0929474\pi\) |
−0.287871 | + | 0.957669i | \(0.592947\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.3238i | 1.48859i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9373 | − | 12.9373i | −0.788804 | − | 0.788804i | 0.192494 | − | 0.981298i | \(-0.438342\pi\) |
−0.981298 | + | 0.192494i | \(0.938342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.44017i | 0.0874842i | 0.999043 | + | 0.0437421i | \(0.0139280\pi\) | ||||
−0.999043 | + | 0.0437421i | \(0.986072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.0447 | − | 11.0447i | −0.668457 | − | 0.668457i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0758 | −0.785647 | −0.392823 | − | 0.919614i | \(-0.628502\pi\) | ||||
−0.392823 | + | 0.919614i | \(0.628502\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 53.5191i | 3.20411i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.00639i | − | 0.358311i | −0.983821 | − | 0.179156i | \(-0.942663\pi\) | ||
0.983821 | − | 0.179156i | \(-0.0573366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.542533 | 0.0322502 | 0.0161251 | − | 0.999870i | \(-0.494867\pi\) | ||||
0.0161251 | + | 0.999870i | \(0.494867\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.52372 | − | 5.52372i | −0.326055 | − | 0.326055i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.73372i | 0.337278i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2016 | − | 12.2016i | −0.715271 | − | 0.715271i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.6018i | 1.55409i | 0.629443 | + | 0.777046i | \(0.283283\pi\) | ||||
−0.629443 | + | 0.777046i | \(0.716717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.94792 | − | 6.94792i | −0.403159 | − | 0.403159i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80854 | + | 2.80854i | 0.162422 | + | 0.162422i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.87615 | − | 7.87615i | 0.453973 | − | 0.453973i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3087 | + | 14.3087i | −0.822014 | + | 0.822014i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.72156 | 0.383619 | 0.191810 | − | 0.981432i | \(-0.438564\pi\) | ||||
0.191810 | + | 0.981432i | \(0.438564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.7356 | + | 20.7356i | −1.17961 | + | 1.17961i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.636143 | −0.0360723 | −0.0180362 | − | 0.999837i | \(-0.505741\pi\) | ||||
−0.0180362 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.109268 | − | 0.109268i | 0.00617619 | − | 0.00617619i | −0.704012 | − | 0.710188i | \(-0.748610\pi\) |
0.710188 | + | 0.704012i | \(0.248610\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.6913i | 1.94846i | 0.225566 | + | 0.974228i | \(0.427577\pi\) | ||||
−0.225566 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.82898 | −0.102403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −35.2388 | −1.96684 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.8059i | − | 0.712537i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.6505 | − | 24.6505i | 1.36317 | − | 1.36317i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.369490 | −0.0203707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.51089 | + | 7.51089i | −0.412836 | + | 0.412836i | −0.882725 | − | 0.469890i | \(-0.844294\pi\) |
0.469890 | + | 0.882725i | \(0.344294\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −59.4630 | −3.25855 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00053 | + | 6.00053i | −0.326870 | + | 0.326870i | −0.851395 | − | 0.524525i | \(-0.824243\pi\) |
0.524525 | + | 0.851395i | \(0.324243\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 39.7898 | − | 39.7898i | 2.16109 | − | 2.16109i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.25096 | − | 3.25096i | −0.176049 | − | 0.176049i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.78289 | − | 2.78289i | −0.150262 | − | 0.150262i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.5337i | 1.26336i | 0.775231 | + | 0.631678i | \(0.217634\pi\) | ||||
−0.775231 | + | 0.631678i | \(0.782366\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.4715 | − | 14.4715i | −0.774643 | − | 0.774643i | 0.204271 | − | 0.978914i | \(-0.434518\pi\) |
−0.978914 | + | 0.204271i | \(0.934518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 20.0551i | − | 1.07046i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.4898 | + | 20.4898i | 1.09056 | + | 1.09056i | 0.995468 | + | 0.0950957i | \(0.0303157\pi\) |
0.0950957 | + | 0.995468i | \(0.469684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 39.2795 | 2.07889 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.83355i | − | 0.518995i | −0.965744 | − | 0.259498i | \(-0.916443\pi\) | ||
0.965744 | − | 0.259498i | \(-0.0835570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.44419i | 0.233905i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −34.4412 | −1.80769 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.2123 | + | 25.2123i | 1.31607 | + | 1.31607i | 0.916858 | + | 0.399214i | \(0.130717\pi\) |
0.399214 | + | 0.916858i | \(0.369283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 16.5538i | − | 0.861756i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.82817 | + | 1.82817i | 0.0949139 | + | 0.0949139i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.6020i | − | 0.807839i | −0.914794 | − | 0.403920i | \(-0.867648\pi\) | ||
0.914794 | − | 0.403920i | \(-0.132352\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.63966 | − | 2.63966i | −0.135950 | − | 0.135950i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.1868 | + | 11.1868i | 0.574627 | + | 0.574627i | 0.933418 | − | 0.358791i | \(-0.116811\pi\) |
−0.358791 | + | 0.933418i | \(0.616811\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.2627 | + | 29.2627i | −1.49917 | + | 1.49917i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.3975 | + | 11.3975i | −0.582386 | + | 0.582386i | −0.935558 | − | 0.353172i | \(-0.885103\pi\) |
0.353172 | + | 0.935558i | \(0.385103\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.6037 | 1.19984 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.8767 | + | 11.8767i | −0.602170 | + | 0.602170i | −0.940888 | − | 0.338718i | \(-0.890007\pi\) |
0.338718 | + | 0.940888i | \(0.390007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.98829 | −0.505130 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.3443 | + | 16.3443i | −0.824461 | + | 0.824461i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.0768i | − | 0.806870i | −0.915008 | − | 0.403435i | \(-0.867816\pi\) | ||
0.915008 | − | 0.403435i | \(-0.132184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 44.6472 | 2.23515 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.8966 | 1.09346 | 0.546731 | − | 0.837308i | \(-0.315872\pi\) | ||||
0.546731 | + | 0.837308i | \(0.315872\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9.38388i | − | 0.467444i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.61201 | − | 3.61201i | 0.179041 | − | 0.179041i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.1426 | 0.995987 | 0.497993 | − | 0.867181i | \(-0.334070\pi\) | ||||
0.497993 | + | 0.867181i | \(0.334070\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4593 | + | 10.4593i | −0.515921 | + | 0.515921i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 44.0671 | 2.16840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.334114 | − | 0.334114i | 0.0163616 | − | 0.0163616i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.87077 | + | 2.87077i | −0.140246 | + | 0.140246i | −0.773744 | − | 0.633498i | \(-0.781619\pi\) |
0.633498 | + | 0.773744i | \(0.281619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9834 | + | 12.9834i | 0.632774 | + | 0.632774i | 0.948763 | − | 0.315989i | \(-0.102336\pi\) |
−0.315989 | + | 0.948763i | \(0.602336\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.553655 | − | 0.553655i | −0.0269196 | − | 0.0269196i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 36.0711i | − | 1.74560i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.01059 | + | 2.01059i | 0.0970722 | + | 0.0970722i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 11.2042i | − | 0.539686i | −0.962904 | − | 0.269843i | \(-0.913028\pi\) | ||
0.962904 | − | 0.269843i | \(-0.0869719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.8634 | − | 20.8634i | −1.00263 | − | 1.00263i | −0.999997 | − | 0.00263391i | \(-0.999162\pi\) |
−0.00263391 | − | 0.999997i | \(-0.500838\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.3532 | −0.543099 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.6495i | − | 1.27191i | −0.771726 | − | 0.635956i | \(-0.780606\pi\) | ||
0.771726 | − | 0.635956i | \(-0.219394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44.9467i | 2.14032i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.97706 | 0.283979 | 0.141989 | − | 0.989868i | \(-0.454650\pi\) | ||||
0.141989 | + | 0.989868i | \(0.454650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.93247 | − | 6.93247i | −0.327895 | − | 0.327895i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.5495i | 1.39453i | 0.716814 | + | 0.697264i | \(0.245600\pi\) | ||||
−0.716814 | + | 0.697264i | \(0.754400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00554 | + | 1.00554i | 0.0473492 | + | 0.0473492i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 70.6010i | − | 3.31712i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.1813 | + | 19.1813i | 0.897262 | + | 0.897262i | 0.995193 | − | 0.0979311i | \(-0.0312225\pi\) |
−0.0979311 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.6621 | + | 35.6621i | 1.66456 | + | 1.66456i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.3016 | − | 18.3016i | 0.852390 | − | 0.852390i | −0.138037 | − | 0.990427i | \(-0.544079\pi\) |
0.990427 | + | 0.138037i | \(0.0440794\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.71513 | − | 2.71513i | 0.126183 | − | 0.126183i | −0.641195 | − | 0.767378i | \(-0.721561\pi\) |
0.767378 | + | 0.641195i | \(0.221561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.1096 | −1.25448 | −0.627241 | − | 0.778826i | \(-0.715816\pi\) | ||||
−0.627241 | + | 0.778826i | \(0.715816\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.4770 | − | 27.4770i | 1.26877 | − | 1.26877i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 56.5332 | 2.60491 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.43378 | + | 1.43378i | −0.0659253 | + | 0.0659253i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.47877i | 0.250855i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.86610 | 0.405102 | 0.202551 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202551 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.4261 | 0.475387 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 34.8239i | − | 1.58454i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.24646 | + | 8.24646i | −0.373683 | + | 0.373683i | −0.868817 | − | 0.495134i | \(-0.835119\pi\) |
0.495134 | + | 0.868817i | \(0.335119\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.4918 | −0.926670 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.4901 | + | 23.4901i | −1.06010 | + | 1.06010i | −0.0620205 | + | 0.998075i | \(0.519754\pi\) |
−0.998075 | + | 0.0620205i | \(0.980246\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.38771 | 0.422801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −38.9841 | + | 38.9841i | −1.74868 | + | 1.74868i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8371 | + | 15.8371i | −0.708965 | + | 0.708965i | −0.966317 | − | 0.257353i | \(-0.917150\pi\) |
0.257353 | + | 0.966317i | \(0.417150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.5493 | − | 21.5493i | −0.962751 | − | 0.962751i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.4080 | + | 16.4080i | 0.731597 | + | 0.731597i | 0.970936 | − | 0.239339i | \(-0.0769307\pi\) |
−0.239339 | + | 0.970936i | \(0.576931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 36.5461i | − | 1.62307i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.698178 | + | 0.698178i | 0.0309462 | + | 0.0309462i | 0.722411 | − | 0.691464i | \(-0.243034\pi\) |
−0.691464 | + | 0.722411i | \(0.743034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.59789i | − | 0.203398i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.5354 | + | 40.5354i | 1.78968 | + | 1.78968i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0672624 | 0.00295819 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.79482i | − | 0.122679i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0336i | 1.05293i | 0.850196 | + | 0.526466i | \(0.176483\pi\) | ||||
−0.850196 | + | 0.526466i | \(0.823517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.7876 | −0.952705 | −0.476353 | − | 0.879254i | \(-0.658041\pi\) | ||||
−0.476353 | + | 0.879254i | \(0.658041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.6864 | + | 16.6864i | 0.726873 | + | 0.726873i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 14.1447i | − | 0.614988i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 66.0314 | + | 66.0314i | 2.86552 | + | 2.86552i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.90249i | 0.125721i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.86225 | − | 1.86225i | −0.0803620 | − | 0.0803620i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.73024 | − | 2.73024i | −0.117600 | − | 0.117600i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1010 | − | 12.1010i | 0.520264 | − | 0.520264i | −0.397387 | − | 0.917651i | \(-0.630083\pi\) |
0.917651 | + | 0.397387i | \(0.130083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.8404 | − | 33.8404i | 1.45223 | − | 1.45223i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.3827 | 1.17080 | 0.585399 | − | 0.810745i | \(-0.300938\pi\) | ||||
0.585399 | + | 0.810745i | \(0.300938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 54.0500 | − | 54.0500i | 2.30680 | − | 2.30680i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6706 | 0.454582 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.91071 | + | 9.91071i | −0.421446 | + | 0.421446i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.8103i | − | 0.797018i | −0.917164 | − | 0.398509i | \(-0.869528\pi\) | ||
0.917164 | − | 0.398509i | \(-0.130472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.13860 | −0.175044 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.15048 | −0.301893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.43590i | 0.186951i | 0.995622 | + | 0.0934755i | \(0.0297977\pi\) | ||||
−0.995622 | + | 0.0934755i | \(0.970202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −66.3256 | + | 66.3256i | −2.78541 | + | 2.78541i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.76043 | 0.367256 | 0.183628 | − | 0.982996i | \(-0.441216\pi\) | ||||
0.183628 | + | 0.982996i | \(0.441216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.44131 | − | 4.44131i | 0.185863 | − | 0.185863i | −0.608042 | − | 0.793905i | \(-0.708045\pi\) |
0.793905 | + | 0.608042i | \(0.208045\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −73.3930 | −3.06604 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.25383 | − | 9.25383i | 0.385242 | − | 0.385242i | −0.487745 | − | 0.872986i | \(-0.662180\pi\) |
0.872986 | + | 0.487745i | \(0.162180\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.9291 | − | 25.9291i | 1.07758 | − | 1.07758i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.2968 | + | 15.2968i | 0.634616 | + | 0.634616i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.332802 | − | 0.332802i | −0.0137832 | − | 0.0137832i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.9676i | − | 0.906700i | −0.891333 | − | 0.453350i | \(-0.850229\pi\) | ||
0.891333 | − | 0.453350i | \(-0.149771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9667 | + | 18.9667i | 0.781509 | + | 0.781509i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 57.1871i | − | 2.35236i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.10461 | + | 9.10461i | 0.373881 | + | 0.373881i | 0.868889 | − | 0.495007i | \(-0.164835\pi\) |
−0.495007 | + | 0.868889i | \(0.664835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.2149 | 2.50536 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.3551i | 1.15856i | 0.815130 | + | 0.579279i | \(0.196666\pi\) | ||||
−0.815130 | + | 0.579279i | \(0.803334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.3072i | 1.64417i | 0.569368 | + | 0.822083i | \(0.307188\pi\) | ||||
−0.569368 | + | 0.822083i | \(0.692812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 82.3446 | 3.35333 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.3427 | − | 33.3427i | −1.35334 | − | 1.35334i | −0.881897 | − | 0.471442i | \(-0.843734\pi\) |
−0.471442 | − | 0.881897i | \(-0.656266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 32.7300i | 1.32628i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.0970762 | + | 0.0970762i | 0.00392728 | + | 0.00392728i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.1895i | − | 0.896227i | −0.893977 | − | 0.448113i | \(-0.852096\pi\) | ||
0.893977 | − | 0.448113i | \(-0.147904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7719 | − | 15.7719i | −0.634954 | − | 0.634954i | 0.314353 | − | 0.949306i | \(-0.398213\pi\) |
−0.949306 | + | 0.314353i | \(0.898213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.07600 | − | 5.07600i | −0.204022 | − | 0.204022i | 0.597699 | − | 0.801721i | \(-0.296082\pi\) |
−0.801721 | + | 0.597699i | \(0.796082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.6168 | − | 31.6168i | 1.26874 | − | 1.26874i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9662 | + | 18.9662i | −0.759863 | + | 0.759863i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.12761 | −0.324586 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.5396 | + | 18.5396i | −0.739224 | + | 0.739224i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2617 | −1.24451 | −0.622254 | − | 0.782816i | \(-0.713783\pi\) | ||||
−0.622254 | + | 0.782816i | \(0.713783\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.3383 | − | 29.3383i | 1.16609 | − | 1.16609i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.88083i | − | 0.312250i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −116.830 | −4.62172 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.38681 | −0.173269 | −0.0866343 | − | 0.996240i | \(-0.527611\pi\) | ||||
−0.0866343 | + | 0.996240i | \(0.527611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28.1726i | − | 1.11102i | −0.831511 | − | 0.555509i | \(-0.812524\pi\) | ||
0.831511 | − | 0.555509i | \(-0.187476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.3260 | − | 13.3260i | 0.523900 | − | 0.523900i | −0.394847 | − | 0.918747i | \(-0.629202\pi\) |
0.918747 | + | 0.394847i | \(0.129202\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.02201 | −0.314892 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −58.1767 | + | 58.1767i | −2.28013 | + | 2.28013i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.61001 | 0.141271 | 0.0706354 | − | 0.997502i | \(-0.477497\pi\) | ||||
0.0706354 | + | 0.997502i | \(0.477497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.88960 | − | 6.88960i | 0.268789 | − | 0.268789i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.6066 | + | 10.6066i | −0.413173 | + | 0.413173i | −0.882842 | − | 0.469669i | \(-0.844373\pi\) |
0.469669 | + | 0.882842i | \(0.344373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.7397 | − | 14.7397i | −0.573307 | − | 0.573307i | 0.359744 | − | 0.933051i | \(-0.382864\pi\) |
−0.933051 | + | 0.359744i | \(0.882864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.3199 | − | 10.3199i | −0.400792 | − | 0.400792i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.32282i | − | 0.322261i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.8607 | − | 29.8607i | −1.15448 | − | 1.15448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.56642i | 0.253494i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.21655 | − | 1.21655i | −0.0468946 | − | 0.0468946i | 0.683271 | − | 0.730165i | \(-0.260557\pi\) |
−0.730165 | + | 0.683271i | \(0.760557\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.4713 | 1.13267 | 0.566337 | − | 0.824174i | \(-0.308360\pi\) | ||||
0.566337 | + | 0.824174i | \(0.308360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 19.0281i | − | 0.730231i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 69.2169i | − | 2.65240i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.5003 | −1.74102 | −0.870510 | − | 0.492151i | \(-0.836211\pi\) | ||||
−0.870510 | + | 0.492151i | \(0.836211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 45.7707 | + | 45.7707i | 1.74626 | + | 1.74626i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.960630i | − | 0.0365971i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4526 | − | 21.4526i | −0.816096 | − | 0.816096i | 0.169444 | − | 0.985540i | \(-0.445803\pi\) |
−0.985540 | + | 0.169444i | \(0.945803\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 17.8825i | − | 0.679300i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.16122 | − | 5.16122i | −0.195495 | − | 0.195495i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −64.3618 | − | 64.3618i | −2.43439 | − | 2.43439i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.4263 | + | 17.4263i | −0.658183 | + | 0.658183i | −0.954950 | − | 0.296767i | \(-0.904091\pi\) |
0.296767 | + | 0.954950i | \(0.404091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.0731 | + | 21.0731i | −0.794789 | + | 0.794789i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.3141 | −0.839207 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.0431 | + | 14.0431i | −0.527401 | + | 0.527401i | −0.919796 | − | 0.392396i | \(-0.871646\pi\) |
0.392396 | + | 0.919796i | \(0.371646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.7010 | −1.11387 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.7936 | − | 14.7936i | 0.554025 | − | 0.554025i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 4.93960i | − | 0.184473i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.8139 | 1.37293 | 0.686463 | − | 0.727165i | \(-0.259162\pi\) | ||||
0.686463 | + | 0.727165i | \(0.259162\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.3366 | −1.20428 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.2729i | 0.716766i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9475 | − | 21.9475i | 0.813989 | − | 0.813989i | −0.171240 | − | 0.985229i | \(-0.554778\pi\) |
0.985229 | + | 0.171240i | \(0.0547775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −51.9233 | −1.92308 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.35927 | − | 7.35927i | 0.272192 | − | 0.272192i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.2145 | 1.26374 | 0.631870 | − | 0.775074i | \(-0.282288\pi\) | ||||
0.631870 | + | 0.775074i | \(0.282288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00193 | + | 5.00193i | −0.184249 | + | 0.184249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.64086 | + | 5.64086i | −0.207502 | + | 0.207502i | −0.803205 | − | 0.595703i | \(-0.796874\pi\) |
0.595703 | + | 0.803205i | \(0.296874\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.7302 | − | 11.7302i | −0.430918 | − | 0.430918i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.765980 | + | 0.765980i | 0.0281011 | + | 0.0281011i | 0.721018 | − | 0.692917i | \(-0.243675\pi\) |
−0.692917 | + | 0.721018i | \(0.743675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 45.8422i | 1.67728i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.4770 | − | 27.4770i | −1.00399 | − | 1.00399i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 9.66983i | − | 0.352857i | −0.984313 | − | 0.176429i | \(-0.943546\pi\) | ||
0.984313 | − | 0.176429i | \(-0.0564544\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.6761 | + | 38.6761i | 1.40944 | + | 1.40944i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.33702 | −0.157632 | −0.0788158 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788158 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.33937i | 0.230104i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 49.2936i | − | 1.78689i | −0.449170 | − | 0.893446i | \(-0.648280\pi\) | ||
0.449170 | − | 0.893446i | \(-0.351720\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.4417 | 1.39168 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.5777 | − | 11.5777i | −0.418048 | − | 0.418048i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.9736i | 1.11694i | 0.829526 | + | 0.558468i | \(0.188611\pi\) | ||||
−0.829526 | + | 0.558468i | \(0.811389\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.3465 | − | 27.3465i | −0.984861 | − | 0.984861i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.1058i | 0.543319i | 0.962393 | + | 0.271660i | \(0.0875725\pi\) | ||||
−0.962393 | + | 0.271660i | \(0.912427\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −64.6378 | − | 64.6378i | −2.31887 | − | 2.31887i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.86652 | − | 5.86652i | −0.210190 | − | 0.210190i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.09671 | − | 7.09671i | 0.253940 | − | 0.253940i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.7157 | + | 29.7157i | −1.06195 | + | 1.06195i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.2095 | 1.07685 | 0.538426 | − | 0.842673i | \(-0.319019\pi\) | ||||
0.538426 | + | 0.842673i | \(0.319019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.3857 | + | 35.3857i | −1.25977 | + | 1.25977i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.0512 | 2.20629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.47696 | + | 9.47696i | −0.336537 | + | 0.336537i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 9.39226i | − | 0.332691i | −0.986068 | − | 0.166346i | \(-0.946803\pi\) | ||
0.986068 | − | 0.166346i | \(-0.0531967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.345242 | −0.0122138 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −56.8389 | −2.00830 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.837003i | 0.0295372i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.1455 | − | 42.1455i | 1.48359 | − | 1.48359i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.0307 | 1.72383 | 0.861914 | − | 0.507054i | \(-0.169266\pi\) | ||||
0.861914 | + | 0.507054i | \(0.169266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4561 | − | 20.4561i | 0.718311 | − | 0.718311i | −0.249948 | − | 0.968259i | \(-0.580414\pi\) |
0.968259 | + | 0.249948i | \(0.0804137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.69160 | −0.164541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.36494 | − | 8.36494i | 0.292652 | − | 0.292652i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.8089 | − | 25.8089i | 0.901834 | − | 0.901834i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.8437 | + | 34.8437i | 1.21605 | + | 1.21605i | 0.969003 | + | 0.247050i | \(0.0794610\pi\) |
0.247050 | + | 0.969003i | \(0.420539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.05406 | + | 8.05406i | 0.280747 | + | 0.280747i | 0.833407 | − | 0.552660i | \(-0.186387\pi\) |
−0.552660 | + | 0.833407i | \(0.686387\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.7148i | 1.38102i | 0.723323 | + | 0.690510i | \(0.242614\pi\) | ||||
−0.723323 | + | 0.690510i | \(0.757386\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7529 | + | 20.7529i | 0.720778 | + | 0.720778i | 0.968764 | − | 0.247985i | \(-0.0797685\pi\) |
−0.247985 | + | 0.968764i | \(0.579769\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 42.5965i | − | 1.47765i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.0137 | + | 14.0137i | 0.485546 | + | 0.485546i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −105.638 | −3.65138 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.3056i | 1.52960i | 0.644267 | + | 0.764800i | \(0.277162\pi\) | ||||
−0.644267 | + | 0.764800i | \(0.722838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 21.1776i | − | 0.730262i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5668 | 0.673917 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8551 | − | 26.8551i | −0.922751 | − | 0.922751i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.76739i | 0.0606567i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.4366 | + | 16.4366i | 0.563440 | + | 0.563440i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5903i | 1.01315i | 0.862195 | + | 0.506577i | \(0.169089\pi\) | ||||
−0.862195 | + | 0.506577i | \(0.830911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.9315 | − | 22.9315i | −0.783326 | − | 0.783326i | 0.197064 | − | 0.980391i | \(-0.436859\pi\) |
−0.980391 | + | 0.197064i | \(0.936859\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.1388 | + | 23.1388i | 0.789486 | + | 0.789486i | 0.981410 | − | 0.191924i | \(-0.0614727\pi\) |
−0.191924 | + | 0.981410i | \(0.561473\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.9944 | − | 17.9944i | 0.613248 | − | 0.613248i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.8789 | − | 10.8789i | 0.370322 | − | 0.370322i | −0.497273 | − | 0.867594i | \(-0.665665\pi\) |
0.867594 | + | 0.497273i | \(0.165665\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6786 | −0.634357 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.80415 | − | 1.80415i | 0.0612018 | − | 0.0612018i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4381 | −0.489215 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.5122 | − | 28.5122i | 0.964993 | − | 0.964993i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.3146i | − | 0.719742i | −0.933002 | − | 0.359871i | \(-0.882821\pi\) | ||
0.933002 | − | 0.359871i | \(-0.117179\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −86.6597 | −2.92296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.6540 | 1.47074 | 0.735370 | − | 0.677666i | \(-0.237009\pi\) | ||||
0.735370 | + | 0.677666i | \(0.237009\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.9408i | 0.435492i | 0.976006 | + | 0.217746i | \(0.0698704\pi\) | ||||
−0.976006 | + | 0.217746i | \(0.930130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.9454 | + | 28.9454i | −0.971892 | + | 0.971892i | −0.999616 | − | 0.0277234i | \(-0.991174\pi\) |
0.0277234 | + | 0.999616i | \(0.491174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.6344 | −1.53053 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.0740 | − | 12.0740i | 0.404493 | − | 0.404493i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.392421 | −0.0131319 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.14927 | + | 9.14927i | −0.305485 | + | 0.305485i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.9041 | + | 13.9041i | −0.463728 | + | 0.463728i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.70820 | + | 1.70820i | 0.0569082 | + | 0.0569082i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.6578 | + | 25.6578i | 0.853840 | + | 0.853840i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.83334i | 0.226897i | 0.993544 | + | 0.113449i | \(0.0361898\pi\) | ||||
−0.993544 | + | 0.113449i | \(0.963810\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.4360 | − | 33.4360i | −1.10900 | − | 1.10900i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 25.5381i | − | 0.846114i | −0.906103 | − | 0.423057i | \(-0.860957\pi\) | ||
0.906103 | − | 0.423057i | \(-0.139043\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.78463 | − | 2.78463i | −0.0921579 | − | 0.0921579i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.4885 | −0.841704 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.49036i | − | 0.0821493i | −0.999156 | − | 0.0410746i | \(-0.986922\pi\) | ||
0.999156 | − | 0.0410746i | \(-0.0130781\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.8966i | 0.721517i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.4846 | 0.674259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −48.4541 | − | 48.4541i | −1.59144 | − | 1.59144i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.45665i | − | 0.277454i | −0.990331 | − | 0.138727i | \(-0.955699\pi\) | ||
0.990331 | − | 0.138727i | \(-0.0443010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.9287 | + | 15.9287i | 0.522043 | + | 0.522043i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 2.07234i | − | 0.0678453i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.1339 | + | 40.1339i | 1.31112 | + | 1.31112i | 0.920593 | + | 0.390523i | \(0.127706\pi\) |
0.390523 | + | 0.920593i | \(0.372294\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.355959 | + | 0.355959i | 0.0116163 | + | 0.0116163i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3857 | − | 35.3857i | 1.15354 | − | 1.15354i | 0.167704 | − | 0.985837i | \(-0.446365\pi\) |
0.985837 | − | 0.167704i | \(-0.0536354\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.57576 | + | 4.57576i | −0.149007 | + | 0.149007i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.4999 | −0.341200 | −0.170600 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170600 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.20800 | + | 1.20800i | −0.0392134 | + | 0.0392134i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −113.013 | −3.66468 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.72367 | + | 4.72367i | −0.153015 | + | 0.153015i | −0.779463 | − | 0.626448i | \(-0.784508\pi\) |
0.626448 | + | 0.779463i | \(0.284508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 5.95819i | − | 0.192601i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.3111 | −0.526711 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4284 | −0.594466 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 82.3446i | − | 2.65352i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.08577 | + | 4.08577i | −0.131390 | + | 0.131390i | −0.769743 | − | 0.638354i | \(-0.779616\pi\) |
0.638354 | + | 0.769743i | \(0.279616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.7172 | 1.34015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5569 | − | 13.5569i | 0.435062 | − | 0.435062i | −0.455284 | − | 0.890346i | \(-0.650462\pi\) |
0.890346 | + | 0.455284i | \(0.150462\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.521042 | 0.0167038 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7102 | − | 24.7102i | 0.790550 | − | 0.790550i | −0.191034 | − | 0.981584i | \(-0.561184\pi\) |
0.981584 | + | 0.191034i | \(0.0611839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.45262 | − | 3.45262i | 0.110346 | − | 0.110346i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.6022 | + | 57.6022i | 1.83910 | + | 1.83910i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.4292 | − | 15.4292i | −0.492115 | − | 0.492115i | 0.416857 | − | 0.908972i | \(-0.363132\pi\) |
−0.908972 | + | 0.416857i | \(0.863132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.20368i | − | 0.0383134i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.52447 | − | 6.52447i | −0.207466 | − | 0.207466i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6537i | 0.941981i | 0.882138 | + | 0.470990i | \(0.156103\pi\) | ||||
−0.882138 | + | 0.470990i | \(0.843897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.4680 | − | 24.4680i | −0.776467 | − | 0.776467i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.4336 | −1.15386 | −0.576932 | − | 0.816792i | \(-0.695750\pi\) | ||||
−0.576932 | + | 0.816792i | \(0.695750\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 117.370i | − | 3.71343i |
(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.j.e.143.12 | 24 | ||
4.3 | odd | 2 | 400.2.j.e.43.11 | yes | 24 | ||
5.2 | odd | 4 | 1600.2.s.e.207.12 | 24 | |||
5.3 | odd | 4 | 1600.2.s.e.207.1 | 24 | |||
5.4 | even | 2 | inner | 1600.2.j.e.143.1 | 24 | ||
16.3 | odd | 4 | 1600.2.s.e.943.12 | 24 | |||
16.13 | even | 4 | 400.2.s.e.243.5 | yes | 24 | ||
20.3 | even | 4 | 400.2.s.e.107.8 | yes | 24 | ||
20.7 | even | 4 | 400.2.s.e.107.5 | yes | 24 | ||
20.19 | odd | 2 | 400.2.j.e.43.2 | ✓ | 24 | ||
80.3 | even | 4 | inner | 1600.2.j.e.1007.12 | 24 | ||
80.13 | odd | 4 | 400.2.j.e.307.2 | yes | 24 | ||
80.19 | odd | 4 | 1600.2.s.e.943.1 | 24 | |||
80.29 | even | 4 | 400.2.s.e.243.8 | yes | 24 | ||
80.67 | even | 4 | inner | 1600.2.j.e.1007.1 | 24 | ||
80.77 | odd | 4 | 400.2.j.e.307.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.j.e.43.2 | ✓ | 24 | 20.19 | odd | 2 | ||
400.2.j.e.43.11 | yes | 24 | 4.3 | odd | 2 | ||
400.2.j.e.307.2 | yes | 24 | 80.13 | odd | 4 | ||
400.2.j.e.307.11 | yes | 24 | 80.77 | odd | 4 | ||
400.2.s.e.107.5 | yes | 24 | 20.7 | even | 4 | ||
400.2.s.e.107.8 | yes | 24 | 20.3 | even | 4 | ||
400.2.s.e.243.5 | yes | 24 | 16.13 | even | 4 | ||
400.2.s.e.243.8 | yes | 24 | 80.29 | even | 4 | ||
1600.2.j.e.143.1 | 24 | 5.4 | even | 2 | inner | ||
1600.2.j.e.143.12 | 24 | 1.1 | even | 1 | trivial | ||
1600.2.j.e.1007.1 | 24 | 80.67 | even | 4 | inner | ||
1600.2.j.e.1007.12 | 24 | 80.3 | even | 4 | inner | ||
1600.2.s.e.207.1 | 24 | 5.3 | odd | 4 | |||
1600.2.s.e.207.12 | 24 | 5.2 | odd | 4 | |||
1600.2.s.e.943.1 | 24 | 80.19 | odd | 4 | |||
1600.2.s.e.943.12 | 24 | 16.3 | odd | 4 |