Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(34,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.34");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.p (of order \(4\), degree \(2\), 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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 265.3 | ||
Root | \(1.85068 + 1.85068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.265 |
Dual form | 273.2.p.f.34.3 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.786556 | + | 0.786556i | −0.556179 | + | 0.556179i | −0.928217 | − | 0.372038i | \(-0.878659\pi\) |
0.372038 | + | 0.928217i | \(0.378659\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0.762660i | 0.381330i | ||||||||
\(5\) | 2.85068 | + | 2.85068i | 1.27486 | + | 1.27486i | 0.943506 | + | 0.331356i | \(0.107506\pi\) |
0.331356 | + | 0.943506i | \(0.392494\pi\) | |||||||
\(6\) | 0.786556 | + | 0.786556i | 0.321110 | + | 0.321110i | ||||
\(7\) | −1.83993 | + | 1.90123i | −0.695427 | + | 0.718597i | ||||
\(8\) | −2.17299 | − | 2.17299i | −0.768267 | − | 0.768267i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −4.48443 | −1.41810 | ||||||||
\(11\) | −1.37164 | − | 1.37164i | −0.413565 | − | 0.413565i | 0.469414 | − | 0.882978i | \(-0.344465\pi\) |
−0.882978 | + | 0.469414i | \(0.844465\pi\) | |||||||
\(12\) | 0.762660 | 0.220161 | ||||||||
\(13\) | 2.79665 | + | 2.27569i | 0.775651 | + | 0.631162i | ||||
\(14\) | −0.0482190 | − | 2.94263i | −0.0128871 | − | 0.786450i | ||||
\(15\) | 2.85068 | − | 2.85068i | 0.736042 | − | 0.736042i | ||||
\(16\) | 1.89303 | 0.473257 | ||||||||
\(17\) | −3.67985 | −0.892495 | −0.446248 | − | 0.894910i | \(-0.647240\pi\) | ||||
−0.446248 | + | 0.894910i | \(0.647240\pi\) | |||||||
\(18\) | 0.786556 | − | 0.786556i | 0.185393 | − | 0.185393i | ||||
\(19\) | 1.10886 | + | 1.10886i | 0.254391 | + | 0.254391i | 0.822768 | − | 0.568377i | \(-0.192429\pi\) |
−0.568377 | + | 0.822768i | \(0.692429\pi\) | |||||||
\(20\) | −2.17410 | + | 2.17410i | −0.486143 | + | 0.486143i | ||||
\(21\) | 1.90123 | + | 1.83993i | 0.414882 | + | 0.401505i | ||||
\(22\) | 2.15774 | 0.460032 | ||||||||
\(23\) | − | 0.653796i | − | 0.136326i | −0.997674 | − | 0.0681630i | \(-0.978286\pi\) | ||
0.997674 | − | 0.0681630i | \(-0.0217138\pi\) | |||||||
\(24\) | −2.17299 | + | 2.17299i | −0.443559 | + | 0.443559i | ||||
\(25\) | 11.2527i | 2.25055i | ||||||||
\(26\) | −3.98968 | + | 0.409765i | −0.782440 | + | 0.0803616i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.44999 | − | 1.40324i | −0.274023 | − | 0.265187i | ||||
\(29\) | −1.78095 | −0.330715 | −0.165357 | − | 0.986234i | \(-0.552878\pi\) | ||||
−0.165357 | + | 0.986234i | \(0.552878\pi\) | |||||||
\(30\) | 4.48443i | 0.818742i | ||||||||
\(31\) | 5.70136 | + | 5.70136i | 1.02399 | + | 1.02399i | 0.999705 | + | 0.0242888i | \(0.00773213\pi\) |
0.0242888 | + | 0.999705i | \(0.492268\pi\) | |||||||
\(32\) | 2.85700 | − | 2.85700i | 0.505051 | − | 0.505051i | ||||
\(33\) | −1.37164 | + | 1.37164i | −0.238772 | + | 0.238772i | ||||
\(34\) | 2.89441 | − | 2.89441i | 0.496387 | − | 0.496387i | ||||
\(35\) | −10.6648 | + | 0.174758i | −1.80269 | + | 0.0295395i | ||||
\(36\) | − | 0.762660i | − | 0.127110i | ||||||
\(37\) | 3.46293 | + | 3.46293i | 0.569302 | + | 0.569302i | 0.931933 | − | 0.362631i | \(-0.118121\pi\) |
−0.362631 | + | 0.931933i | \(0.618121\pi\) | |||||||
\(38\) | −1.74437 | −0.282974 | ||||||||
\(39\) | 2.27569 | − | 2.79665i | 0.364402 | − | 0.447822i | ||||
\(40\) | − | 12.3890i | − | 1.95887i | ||||||
\(41\) | 2.67464 | + | 2.67464i | 0.417709 | + | 0.417709i | 0.884413 | − | 0.466704i | \(-0.154559\pi\) |
−0.466704 | + | 0.884413i | \(0.654559\pi\) | |||||||
\(42\) | −2.94263 | + | 0.0482190i | −0.454057 | + | 0.00744035i | ||||
\(43\) | − | 11.0076i | − | 1.67865i | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||
0.543632 | − | 0.839324i | \(-0.317049\pi\) | |||||||
\(44\) | 1.04609 | − | 1.04609i | 0.157705 | − | 0.157705i | ||||
\(45\) | −2.85068 | − | 2.85068i | −0.424954 | − | 0.424954i | ||||
\(46\) | 0.514247 | + | 0.514247i | 0.0758216 | + | 0.0758216i | ||||
\(47\) | 3.84609 | − | 3.84609i | 0.561010 | − | 0.561010i | −0.368585 | − | 0.929594i | \(-0.620158\pi\) |
0.929594 | + | 0.368585i | \(0.120158\pi\) | |||||||
\(48\) | − | 1.89303i | − | 0.273235i | ||||||
\(49\) | −0.229348 | − | 6.99624i | −0.0327640 | − | 0.999463i | ||||
\(50\) | −8.85090 | − | 8.85090i | −1.25171 | − | 1.25171i | ||||
\(51\) | 3.67985i | 0.515282i | ||||||||
\(52\) | −1.73558 | + | 2.13289i | −0.240681 | + | 0.295779i | ||||
\(53\) | −0.919315 | −0.126278 | −0.0631388 | − | 0.998005i | \(-0.520111\pi\) | ||||
−0.0631388 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(54\) | −0.786556 | − | 0.786556i | −0.107037 | − | 0.107037i | ||||
\(55\) | − | 7.82021i | − | 1.05448i | ||||||
\(56\) | 8.12948 | − | 0.133213i | 1.08635 | − | 0.0178013i | ||||
\(57\) | 1.10886 | − | 1.10886i | 0.146873 | − | 0.146873i | ||||
\(58\) | 1.40082 | − | 1.40082i | 0.183937 | − | 0.183937i | ||||
\(59\) | 8.69367 | − | 8.69367i | 1.13182 | − | 1.13182i | 0.141944 | − | 0.989875i | \(-0.454665\pi\) |
0.989875 | − | 0.141944i | \(-0.0453354\pi\) | |||||||
\(60\) | 2.17410 | + | 2.17410i | 0.280675 | + | 0.280675i | ||||
\(61\) | 5.92939i | 0.759180i | 0.925155 | + | 0.379590i | \(0.123935\pi\) | ||||
−0.925155 | + | 0.379590i | \(0.876065\pi\) | |||||||
\(62\) | −8.96887 | −1.13905 | ||||||||
\(63\) | 1.83993 | − | 1.90123i | 0.231809 | − | 0.239532i | ||||
\(64\) | 8.28044i | 1.03505i | ||||||||
\(65\) | 1.48509 | + | 14.4596i | 0.184203 | + | 1.79349i | ||||
\(66\) | − | 2.15774i | − | 0.265600i | ||||||
\(67\) | −8.44464 | + | 8.44464i | −1.03168 | + | 1.03168i | −0.0321948 | + | 0.999482i | \(0.510250\pi\) |
−0.999482 | + | 0.0321948i | \(0.989750\pi\) | |||||||
\(68\) | − | 2.80648i | − | 0.340335i | ||||||
\(69\) | −0.653796 | −0.0787078 | ||||||||
\(70\) | 8.25103 | − | 8.52594i | 0.986186 | − | 1.01904i | ||||
\(71\) | 8.55531 | − | 8.55531i | 1.01533 | − | 1.01533i | 0.0154474 | − | 0.999881i | \(-0.495083\pi\) |
0.999881 | − | 0.0154474i | \(-0.00491724\pi\) | |||||||
\(72\) | 2.17299 | + | 2.17299i | 0.256089 | + | 0.256089i | ||||
\(73\) | 6.74551 | − | 6.74551i | 0.789503 | − | 0.789503i | −0.191910 | − | 0.981413i | \(-0.561468\pi\) |
0.981413 | + | 0.191910i | \(0.0614681\pi\) | |||||||
\(74\) | −5.44757 | −0.633268 | ||||||||
\(75\) | 11.2527 | 1.29935 | ||||||||
\(76\) | −0.845686 | + | 0.845686i | −0.0970069 | + | 0.0970069i | ||||
\(77\) | 5.13152 | − | 0.0840870i | 0.584791 | − | 0.00958260i | ||||
\(78\) | 0.409765 | + | 3.98968i | 0.0463968 | + | 0.451742i | ||||
\(79\) | 9.87363 | 1.11087 | 0.555435 | − | 0.831560i | \(-0.312552\pi\) | ||||
0.555435 | + | 0.831560i | \(0.312552\pi\) | |||||||
\(80\) | 5.39642 | + | 5.39642i | 0.603338 | + | 0.603338i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.20751 | −0.464642 | ||||||||
\(83\) | −8.71517 | − | 8.71517i | −0.956614 | − | 0.956614i | 0.0424828 | − | 0.999097i | \(-0.486473\pi\) |
−0.999097 | + | 0.0424828i | \(0.986473\pi\) | |||||||
\(84\) | −1.40324 | + | 1.44999i | −0.153106 | + | 0.158207i | ||||
\(85\) | −10.4901 | − | 10.4901i | −1.13781 | − | 1.13781i | ||||
\(86\) | 8.65811 | + | 8.65811i | 0.933629 | + | 0.933629i | ||||
\(87\) | 1.78095i | 0.190938i | ||||||||
\(88\) | 5.96111i | 0.635456i | ||||||||
\(89\) | −4.94580 | + | 4.94580i | −0.524254 | + | 0.524254i | −0.918853 | − | 0.394600i | \(-0.870883\pi\) |
0.394600 | + | 0.918853i | \(0.370883\pi\) | |||||||
\(90\) | 4.48443 | 0.472701 | ||||||||
\(91\) | −9.47223 | + | 1.12998i | −0.992960 | + | 0.118454i | ||||
\(92\) | 0.498624 | 0.0519852 | ||||||||
\(93\) | 5.70136 | − | 5.70136i | 0.591203 | − | 0.591203i | ||||
\(94\) | 6.05033i | 0.624043i | ||||||||
\(95\) | 6.32203i | 0.648626i | ||||||||
\(96\) | −2.85700 | − | 2.85700i | −0.291591 | − | 0.291591i | ||||
\(97\) | −0.857049 | − | 0.857049i | −0.0870201 | − | 0.0870201i | 0.662257 | − | 0.749277i | \(-0.269599\pi\) |
−0.749277 | + | 0.662257i | \(0.769599\pi\) | |||||||
\(98\) | 5.68333 | + | 5.32254i | 0.574103 | + | 0.537658i | ||||
\(99\) | 1.37164 | + | 1.37164i | 0.137855 | + | 0.137855i | ||||
\(100\) | −8.58201 | −0.858201 | ||||||||
\(101\) | 7.21984 | 0.718401 | 0.359200 | − | 0.933260i | \(-0.383049\pi\) | ||||
0.359200 | + | 0.933260i | \(0.383049\pi\) | |||||||
\(102\) | −2.89441 | − | 2.89441i | −0.286589 | − | 0.286589i | ||||
\(103\) | −12.1497 | −1.19715 | −0.598575 | − | 0.801067i | \(-0.704266\pi\) | ||||
−0.598575 | + | 0.801067i | \(0.704266\pi\) | |||||||
\(104\) | −1.13204 | − | 11.0221i | −0.111006 | − | 1.08081i | ||||
\(105\) | 0.174758 | + | 10.6648i | 0.0170546 | + | 1.04078i | ||||
\(106\) | 0.723093 | − | 0.723093i | 0.0702330 | − | 0.0702330i | ||||
\(107\) | −14.3968 | −1.39180 | −0.695898 | − | 0.718141i | \(-0.744993\pi\) | ||||
−0.695898 | + | 0.718141i | \(0.744993\pi\) | |||||||
\(108\) | −0.762660 | −0.0733870 | ||||||||
\(109\) | 11.6047 | − | 11.6047i | 1.11153 | − | 1.11153i | 0.118583 | − | 0.992944i | \(-0.462165\pi\) |
0.992944 | − | 0.118583i | \(-0.0378353\pi\) | |||||||
\(110\) | 6.15103 | + | 6.15103i | 0.586477 | + | 0.586477i | ||||
\(111\) | 3.46293 | − | 3.46293i | 0.328687 | − | 0.328687i | ||||
\(112\) | −3.48303 | + | 3.59908i | −0.329116 | + | 0.340081i | ||||
\(113\) | 8.39121 | 0.789378 | 0.394689 | − | 0.918815i | \(-0.370852\pi\) | ||||
0.394689 | + | 0.918815i | \(0.370852\pi\) | |||||||
\(114\) | 1.74437i | 0.163375i | ||||||||
\(115\) | 1.86376 | − | 1.86376i | 0.173797 | − | 0.173797i | ||||
\(116\) | − | 1.35826i | − | 0.126112i | ||||||
\(117\) | −2.79665 | − | 2.27569i | −0.258550 | − | 0.210387i | ||||
\(118\) | 13.6761i | 1.25899i | ||||||||
\(119\) | 6.77065 | − | 6.99624i | 0.620665 | − | 0.641344i | ||||
\(120\) | −12.3890 | −1.13095 | ||||||||
\(121\) | − | 7.23721i | − | 0.657928i | ||||||
\(122\) | −4.66379 | − | 4.66379i | −0.422240 | − | 0.422240i | ||||
\(123\) | 2.67464 | − | 2.67464i | 0.241164 | − | 0.241164i | ||||
\(124\) | −4.34820 | + | 4.34820i | −0.390480 | + | 0.390480i | ||||
\(125\) | −17.8245 | + | 17.8245i | −1.59427 | + | 1.59427i | ||||
\(126\) | 0.0482190 | + | 2.94263i | 0.00429569 | + | 0.262150i | ||||
\(127\) | − | 1.87363i | − | 0.166258i | −0.996539 | − | 0.0831291i | \(-0.973509\pi\) | ||
0.996539 | − | 0.0831291i | \(-0.0264914\pi\) | |||||||
\(128\) | −0.799026 | − | 0.799026i | −0.0706246 | − | 0.0706246i | ||||
\(129\) | −11.0076 | −0.969168 | ||||||||
\(130\) | −12.5414 | − | 10.2052i | −1.09995 | − | 0.895053i | ||||
\(131\) | 15.5987i | 1.36287i | 0.731880 | + | 0.681433i | \(0.238643\pi\) | ||||
−0.731880 | + | 0.681433i | \(0.761357\pi\) | |||||||
\(132\) | −1.04609 | − | 1.04609i | −0.0910509 | − | 0.0910509i | ||||
\(133\) | −4.14843 | + | 0.0679778i | −0.359715 | + | 0.00589442i | ||||
\(134\) | − | 13.2844i | − | 1.14759i | ||||||
\(135\) | −2.85068 | + | 2.85068i | −0.245347 | + | 0.245347i | ||||
\(136\) | 7.99627 | + | 7.99627i | 0.685674 | + | 0.685674i | ||||
\(137\) | 11.6472 | + | 11.6472i | 0.995087 | + | 0.995087i | 0.999988 | − | 0.00490102i | \(-0.00156005\pi\) |
−0.00490102 | + | 0.999988i | \(0.501560\pi\) | |||||||
\(138\) | 0.514247 | − | 0.514247i | 0.0437756 | − | 0.0437756i | ||||
\(139\) | − | 2.12226i | − | 0.180008i | −0.995941 | − | 0.0900039i | \(-0.971312\pi\) | ||
0.995941 | − | 0.0900039i | \(-0.0286880\pi\) | |||||||
\(140\) | −0.133281 | − | 8.13364i | −0.0112643 | − | 0.687418i | ||||
\(141\) | −3.84609 | − | 3.84609i | −0.323899 | − | 0.323899i | ||||
\(142\) | 13.4584i | 1.12941i | ||||||||
\(143\) | −0.714571 | − | 6.95742i | −0.0597555 | − | 0.581809i | ||||
\(144\) | −1.89303 | −0.157752 | ||||||||
\(145\) | −5.07693 | − | 5.07693i | −0.421616 | − | 0.421616i | ||||
\(146\) | 10.6114i | 0.878209i | ||||||||
\(147\) | −6.99624 | + | 0.229348i | −0.577040 | + | 0.0189163i | ||||
\(148\) | −2.64104 | + | 2.64104i | −0.217092 | + | 0.217092i | ||||
\(149\) | −0.409314 | + | 0.409314i | −0.0335323 | + | 0.0335323i | −0.723674 | − | 0.690142i | \(-0.757548\pi\) |
0.690142 | + | 0.723674i | \(0.257548\pi\) | |||||||
\(150\) | −8.85090 | + | 8.85090i | −0.722673 | + | 0.722673i | ||||
\(151\) | 1.06906 | + | 1.06906i | 0.0869993 | + | 0.0869993i | 0.749267 | − | 0.662268i | \(-0.230406\pi\) |
−0.662268 | + | 0.749267i | \(0.730406\pi\) | |||||||
\(152\) | − | 4.81909i | − | 0.390880i | ||||||
\(153\) | 3.67985 | 0.297498 | ||||||||
\(154\) | −3.97008 | + | 4.10236i | −0.319919 | + | 0.330578i | ||||
\(155\) | 32.5055i | 2.61090i | ||||||||
\(156\) | 2.13289 | + | 1.73558i | 0.170768 | + | 0.138957i | ||||
\(157\) | 0.372554i | 0.0297330i | 0.999889 | + | 0.0148665i | \(0.00473233\pi\) | ||||
−0.999889 | + | 0.0148665i | \(0.995268\pi\) | |||||||
\(158\) | −7.76616 | + | 7.76616i | −0.617843 | + | 0.617843i | ||||
\(159\) | 0.919315i | 0.0729064i | ||||||||
\(160\) | 16.2888 | 1.28774 | ||||||||
\(161\) | 1.24302 | + | 1.20294i | 0.0979635 | + | 0.0948047i | ||||
\(162\) | −0.786556 | + | 0.786556i | −0.0617977 | + | 0.0617977i | ||||
\(163\) | 4.28689 | + | 4.28689i | 0.335775 | + | 0.335775i | 0.854775 | − | 0.518999i | \(-0.173695\pi\) |
−0.518999 | + | 0.854775i | \(0.673695\pi\) | |||||||
\(164\) | −2.03984 | + | 2.03984i | −0.159285 | + | 0.159285i | ||||
\(165\) | −7.82021 | −0.608802 | ||||||||
\(166\) | 13.7099 | 1.06410 | ||||||||
\(167\) | 0.407205 | − | 0.407205i | 0.0315104 | − | 0.0315104i | −0.691176 | − | 0.722686i | \(-0.742907\pi\) |
0.722686 | + | 0.691176i | \(0.242907\pi\) | |||||||
\(168\) | −0.133213 | − | 8.12948i | −0.0102776 | − | 0.627203i | ||||
\(169\) | 2.64249 | + | 12.7286i | 0.203269 | + | 0.979123i | ||||
\(170\) | 16.5021 | 1.26565 | ||||||||
\(171\) | −1.10886 | − | 1.10886i | −0.0847969 | − | 0.0847969i | ||||
\(172\) | 8.39508 | 0.640119 | ||||||||
\(173\) | −23.8232 | −1.81124 | −0.905622 | − | 0.424085i | \(-0.860596\pi\) | ||||
−0.905622 | + | 0.424085i | \(0.860596\pi\) | |||||||
\(174\) | −1.40082 | − | 1.40082i | −0.106196 | − | 0.106196i | ||||
\(175\) | −21.3940 | − | 20.7042i | −1.61724 | − | 1.56509i | ||||
\(176\) | −2.59655 | − | 2.59655i | −0.195723 | − | 0.195723i | ||||
\(177\) | −8.69367 | − | 8.69367i | −0.653456 | − | 0.653456i | ||||
\(178\) | − | 7.78029i | − | 0.583157i | ||||||
\(179\) | 0.227613i | 0.0170126i | 0.999964 | + | 0.00850628i | \(0.00270767\pi\) | ||||
−0.999964 | + | 0.00850628i | \(0.997292\pi\) | |||||||
\(180\) | 2.17410 | − | 2.17410i | 0.162048 | − | 0.162048i | ||||
\(181\) | 20.5214 | 1.52535 | 0.762674 | − | 0.646784i | \(-0.223886\pi\) | ||||
0.762674 | + | 0.646784i | \(0.223886\pi\) | |||||||
\(182\) | 6.56165 | − | 8.33923i | 0.486382 | − | 0.618145i | ||||
\(183\) | 5.92939 | 0.438313 | ||||||||
\(184\) | −1.42069 | + | 1.42069i | −0.104735 | + | 0.104735i | ||||
\(185\) | 19.7434i | 1.45156i | ||||||||
\(186\) | 8.96887i | 0.657629i | ||||||||
\(187\) | 5.04743 | + | 5.04743i | 0.369105 | + | 0.369105i | ||||
\(188\) | 2.93326 | + | 2.93326i | 0.213930 | + | 0.213930i | ||||
\(189\) | −1.90123 | − | 1.83993i | −0.138294 | − | 0.133835i | ||||
\(190\) | −4.97263 | − | 4.97263i | −0.360752 | − | 0.360752i | ||||
\(191\) | 0.119527 | 0.00864867 | 0.00432433 | − | 0.999991i | \(-0.498624\pi\) | ||||
0.00432433 | + | 0.999991i | \(0.498624\pi\) | |||||||
\(192\) | 8.28044 | 0.597589 | ||||||||
\(193\) | −8.53068 | − | 8.53068i | −0.614051 | − | 0.614051i | 0.329948 | − | 0.943999i | \(-0.392969\pi\) |
−0.943999 | + | 0.329948i | \(0.892969\pi\) | |||||||
\(194\) | 1.34823 | 0.0967975 | ||||||||
\(195\) | 14.4596 | − | 1.48509i | 1.03547 | − | 0.106350i | ||||
\(196\) | 5.33576 | − | 0.174914i | 0.381125 | − | 0.0124939i | ||||
\(197\) | 14.3031 | − | 14.3031i | 1.01906 | − | 1.01906i | 0.0192413 | − | 0.999815i | \(-0.493875\pi\) |
0.999815 | − | 0.0192413i | \(-0.00612508\pi\) | |||||||
\(198\) | −2.15774 | −0.153344 | ||||||||
\(199\) | −2.32628 | −0.164905 | −0.0824527 | − | 0.996595i | \(-0.526275\pi\) | ||||
−0.0824527 | + | 0.996595i | \(0.526275\pi\) | |||||||
\(200\) | 24.4520 | − | 24.4520i | 1.72902 | − | 1.72902i | ||||
\(201\) | 8.44464 | + | 8.44464i | 0.595639 | + | 0.595639i | ||||
\(202\) | −5.67880 | + | 5.67880i | −0.399559 | + | 0.399559i | ||||
\(203\) | 3.27682 | − | 3.38600i | 0.229988 | − | 0.237651i | ||||
\(204\) | −2.80648 | −0.196493 | ||||||||
\(205\) | 15.2491i | 1.06504i | ||||||||
\(206\) | 9.55646 | − | 9.55646i | 0.665830 | − | 0.665830i | ||||
\(207\) | 0.653796i | 0.0454420i | ||||||||
\(208\) | 5.29414 | + | 4.30794i | 0.367082 | + | 0.298702i | ||||
\(209\) | − | 3.04192i | − | 0.210414i | ||||||
\(210\) | −8.52594 | − | 8.25103i | −0.588346 | − | 0.569375i | ||||
\(211\) | −9.48119 | −0.652712 | −0.326356 | − | 0.945247i | \(-0.605821\pi\) | ||||
−0.326356 | + | 0.945247i | \(0.605821\pi\) | |||||||
\(212\) | − | 0.701125i | − | 0.0481535i | ||||||
\(213\) | −8.55531 | − | 8.55531i | −0.586200 | − | 0.586200i | ||||
\(214\) | 11.3239 | − | 11.3239i | 0.774087 | − | 0.774087i | ||||
\(215\) | 31.3792 | − | 31.3792i | 2.14004 | − | 2.14004i | ||||
\(216\) | 2.17299 | − | 2.17299i | 0.147853 | − | 0.147853i | ||||
\(217\) | −21.3297 | + | 0.349516i | −1.44795 | + | 0.0237267i | ||||
\(218\) | 18.2555i | 1.23642i | ||||||||
\(219\) | −6.74551 | − | 6.74551i | −0.455820 | − | 0.455820i | ||||
\(220\) | 5.96416 | 0.402104 | ||||||||
\(221\) | −10.2913 | − | 8.37419i | −0.692265 | − | 0.563309i | ||||
\(222\) | 5.44757i | 0.365617i | ||||||||
\(223\) | −3.56512 | − | 3.56512i | −0.238738 | − | 0.238738i | 0.577589 | − | 0.816327i | \(-0.303993\pi\) |
−0.816327 | + | 0.577589i | \(0.803993\pi\) | |||||||
\(224\) | 0.175145 | + | 10.6885i | 0.0117024 | + | 0.714154i | ||||
\(225\) | − | 11.2527i | − | 0.750182i | ||||||
\(226\) | −6.60015 | + | 6.60015i | −0.439036 | + | 0.439036i | ||||
\(227\) | −1.89144 | − | 1.89144i | −0.125539 | − | 0.125539i | 0.641546 | − | 0.767085i | \(-0.278293\pi\) |
−0.767085 | + | 0.641546i | \(0.778293\pi\) | |||||||
\(228\) | 0.845686 | + | 0.845686i | 0.0560069 | + | 0.0560069i | ||||
\(229\) | −8.57080 | + | 8.57080i | −0.566374 | + | 0.566374i | −0.931111 | − | 0.364737i | \(-0.881159\pi\) |
0.364737 | + | 0.931111i | \(0.381159\pi\) | |||||||
\(230\) | 2.93191i | 0.193324i | ||||||||
\(231\) | −0.0840870 | − | 5.13152i | −0.00553252 | − | 0.337629i | ||||
\(232\) | 3.86999 | + | 3.86999i | 0.254077 | + | 0.254077i | ||||
\(233\) | 3.54231i | 0.232064i | 0.993245 | + | 0.116032i | \(0.0370176\pi\) | ||||
−0.993245 | + | 0.116032i | \(0.962982\pi\) | |||||||
\(234\) | 3.98968 | − | 0.409765i | 0.260813 | − | 0.0267872i | ||||
\(235\) | 21.9279 | 1.43042 | ||||||||
\(236\) | 6.63031 | + | 6.63031i | 0.431597 | + | 0.431597i | ||||
\(237\) | − | 9.87363i | − | 0.641361i | ||||||
\(238\) | 0.177439 | + | 10.8284i | 0.0115016 | + | 0.701903i | ||||
\(239\) | −17.2035 | + | 17.2035i | −1.11280 | + | 1.11280i | −0.120029 | + | 0.992770i | \(0.538299\pi\) |
−0.992770 | + | 0.120029i | \(0.961701\pi\) | |||||||
\(240\) | 5.39642 | − | 5.39642i | 0.348337 | − | 0.348337i | ||||
\(241\) | −6.62291 | + | 6.62291i | −0.426619 | + | 0.426619i | −0.887475 | − | 0.460856i | \(-0.847542\pi\) |
0.460856 | + | 0.887475i | \(0.347542\pi\) | |||||||
\(242\) | 5.69247 | + | 5.69247i | 0.365926 | + | 0.365926i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −4.52211 | −0.289498 | ||||||||
\(245\) | 19.2902 | − | 20.5978i | 1.23241 | − | 1.31595i | ||||
\(246\) | 4.20751i | 0.268261i | ||||||||
\(247\) | 0.577675 | + | 5.62453i | 0.0367566 | + | 0.357880i | ||||
\(248\) | − | 24.7779i | − | 1.57340i | ||||||
\(249\) | −8.71517 | + | 8.71517i | −0.552302 | + | 0.552302i | ||||
\(250\) | − | 28.0400i | − | 1.77340i | ||||||
\(251\) | 7.62601 | 0.481349 | 0.240675 | − | 0.970606i | \(-0.422631\pi\) | ||||
0.240675 | + | 0.970606i | \(0.422631\pi\) | |||||||
\(252\) | 1.44999 | + | 1.40324i | 0.0913409 | + | 0.0883957i | ||||
\(253\) | −0.896773 | + | 0.896773i | −0.0563796 | + | 0.0563796i | ||||
\(254\) | 1.47372 | + | 1.47372i | 0.0924693 | + | 0.0924693i | ||||
\(255\) | −10.4901 | + | 10.4901i | −0.656914 | + | 0.656914i | ||||
\(256\) | −15.3039 | −0.956495 | ||||||||
\(257\) | −19.9162 | −1.24234 | −0.621170 | − | 0.783676i | \(-0.713342\pi\) | ||||
−0.621170 | + | 0.783676i | \(0.713342\pi\) | |||||||
\(258\) | 8.65811 | − | 8.65811i | 0.539031 | − | 0.539031i | ||||
\(259\) | −12.9554 | + | 0.212291i | −0.805007 | + | 0.0131911i | ||||
\(260\) | −11.0278 | + | 1.13262i | −0.683913 | + | 0.0702422i | ||||
\(261\) | 1.78095 | 0.110238 | ||||||||
\(262\) | −12.2693 | − | 12.2693i | −0.757998 | − | 0.757998i | ||||
\(263\) | 0.224683 | 0.0138545 | 0.00692727 | − | 0.999976i | \(-0.497795\pi\) | ||||
0.00692727 | + | 0.999976i | \(0.497795\pi\) | |||||||
\(264\) | 5.96111 | 0.366881 | ||||||||
\(265\) | −2.62067 | − | 2.62067i | −0.160987 | − | 0.160987i | ||||
\(266\) | 3.20950 | − | 3.31644i | 0.196787 | − | 0.203344i | ||||
\(267\) | 4.94580 | + | 4.94580i | 0.302678 | + | 0.302678i | ||||
\(268\) | −6.44039 | − | 6.44039i | −0.393409 | − | 0.393409i | ||||
\(269\) | − | 11.2518i | − | 0.686034i | −0.939329 | − | 0.343017i | \(-0.888551\pi\) | ||
0.939329 | − | 0.343017i | \(-0.111449\pi\) | |||||||
\(270\) | − | 4.48443i | − | 0.272914i | ||||||
\(271\) | −9.55246 | + | 9.55246i | −0.580271 | + | 0.580271i | −0.934978 | − | 0.354707i | \(-0.884581\pi\) |
0.354707 | + | 0.934978i | \(0.384581\pi\) | |||||||
\(272\) | −6.96607 | −0.422380 | ||||||||
\(273\) | 1.12998 | + | 9.47223i | 0.0683893 | + | 0.573285i | ||||
\(274\) | −18.3223 | −1.10689 | ||||||||
\(275\) | 15.4347 | − | 15.4347i | 0.930747 | − | 0.930747i | ||||
\(276\) | − | 0.498624i | − | 0.0300137i | ||||||
\(277\) | − | 23.8151i | − | 1.43091i | −0.698658 | − | 0.715456i | \(-0.746219\pi\) | ||
0.698658 | − | 0.715456i | \(-0.253781\pi\) | |||||||
\(278\) | 1.66928 | + | 1.66928i | 0.100117 | + | 0.100117i | ||||
\(279\) | −5.70136 | − | 5.70136i | −0.341331 | − | 0.341331i | ||||
\(280\) | 23.5543 | + | 22.7948i | 1.40764 | + | 1.36225i | ||||
\(281\) | 0.540489 | + | 0.540489i | 0.0322429 | + | 0.0322429i | 0.723044 | − | 0.690802i | \(-0.242742\pi\) |
−0.690802 | + | 0.723044i | \(0.742742\pi\) | |||||||
\(282\) | 6.05033 | 0.360292 | ||||||||
\(283\) | −6.04531 | −0.359356 | −0.179678 | − | 0.983725i | \(-0.557506\pi\) | ||||
−0.179678 | + | 0.983725i | \(0.557506\pi\) | |||||||
\(284\) | 6.52479 | + | 6.52479i | 0.387175 | + | 0.387175i | ||||
\(285\) | 6.32203 | 0.374485 | ||||||||
\(286\) | 6.03445 | + | 4.91035i | 0.356824 | + | 0.290355i | ||||
\(287\) | −10.0063 | + | 0.163966i | −0.590650 | + | 0.00967862i | ||||
\(288\) | −2.85700 | + | 2.85700i | −0.168350 | + | 0.168350i | ||||
\(289\) | −3.45870 | −0.203453 | ||||||||
\(290\) | 7.98657 | 0.468988 | ||||||||
\(291\) | −0.857049 | + | 0.857049i | −0.0502411 | + | 0.0502411i | ||||
\(292\) | 5.14454 | + | 5.14454i | 0.301061 | + | 0.301061i | ||||
\(293\) | −15.4775 | + | 15.4775i | −0.904204 | + | 0.904204i | −0.995797 | − | 0.0915927i | \(-0.970804\pi\) |
0.0915927 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(294\) | 5.32254 | − | 5.68333i | 0.310417 | − | 0.331458i | ||||
\(295\) | 49.5657 | 2.88583 | ||||||||
\(296\) | − | 15.0498i | − | 0.874752i | ||||||
\(297\) | 1.37164 | − | 1.37164i | 0.0795906 | − | 0.0795906i | ||||
\(298\) | − | 0.643897i | − | 0.0373000i | ||||||
\(299\) | 1.48784 | − | 1.82844i | 0.0860438 | − | 0.105741i | ||||
\(300\) | 8.58201i | 0.495483i | ||||||||
\(301\) | 20.9280 | + | 20.2532i | 1.20627 | + | 1.16738i | ||||
\(302\) | −1.68176 | −0.0967743 | ||||||||
\(303\) | − | 7.21984i | − | 0.414769i | ||||||
\(304\) | 2.09911 | + | 2.09911i | 0.120392 | + | 0.120392i | ||||
\(305\) | −16.9028 | + | 16.9028i | −0.967850 | + | 0.967850i | ||||
\(306\) | −2.89441 | + | 2.89441i | −0.165462 | + | 0.165462i | ||||
\(307\) | 23.2206 | − | 23.2206i | 1.32527 | − | 1.32527i | 0.415821 | − | 0.909446i | \(-0.363494\pi\) |
0.909446 | − | 0.415821i | \(-0.136506\pi\) | |||||||
\(308\) | 0.0641298 | + | 3.91360i | 0.00365413 | + | 0.222998i | ||||
\(309\) | 12.1497i | 0.691175i | ||||||||
\(310\) | −25.5674 | − | 25.5674i | −1.45213 | − | 1.45213i | ||||
\(311\) | −6.55258 | −0.371563 | −0.185781 | − | 0.982591i | \(-0.559482\pi\) | ||||
−0.185781 | + | 0.982591i | \(0.559482\pi\) | |||||||
\(312\) | −11.0221 | + | 1.13204i | −0.624005 | + | 0.0640893i | ||||
\(313\) | − | 27.9268i | − | 1.57852i | −0.614062 | − | 0.789258i | \(-0.710465\pi\) | ||
0.614062 | − | 0.789258i | \(-0.289535\pi\) | |||||||
\(314\) | −0.293034 | − | 0.293034i | −0.0165369 | − | 0.0165369i | ||||
\(315\) | 10.6648 | − | 0.174758i | 0.600895 | − | 0.00984649i | ||||
\(316\) | 7.53023i | 0.423608i | ||||||||
\(317\) | 5.67885 | − | 5.67885i | 0.318956 | − | 0.318956i | −0.529410 | − | 0.848366i | \(-0.677587\pi\) |
0.848366 | + | 0.529410i | \(0.177587\pi\) | |||||||
\(318\) | −0.723093 | − | 0.723093i | −0.0405490 | − | 0.0405490i | ||||
\(319\) | 2.44283 | + | 2.44283i | 0.136772 | + | 0.136772i | ||||
\(320\) | −23.6049 | + | 23.6049i | −1.31955 | + | 1.31955i | ||||
\(321\) | 14.3968i | 0.803553i | ||||||||
\(322\) | −1.92388 | + | 0.0315254i | −0.107214 | + | 0.00175684i | ||||
\(323\) | −4.08045 | − | 4.08045i | −0.227043 | − | 0.227043i | ||||
\(324\) | 0.762660i | 0.0423700i | ||||||||
\(325\) | −25.6077 | + | 31.4699i | −1.42046 | + | 1.74564i | ||||
\(326\) | −6.74376 | −0.373502 | ||||||||
\(327\) | −11.6047 | − | 11.6047i | −0.641741 | − | 0.641741i | ||||
\(328\) | − | 11.6239i | − | 0.641824i | ||||||
\(329\) | 0.235780 | + | 14.3888i | 0.0129990 | + | 0.793281i | ||||
\(330\) | 6.15103 | − | 6.15103i | 0.338603 | − | 0.338603i | ||||
\(331\) | −4.44838 | + | 4.44838i | −0.244505 | + | 0.244505i | −0.818711 | − | 0.574206i | \(-0.805311\pi\) |
0.574206 | + | 0.818711i | \(0.305311\pi\) | |||||||
\(332\) | 6.64671 | − | 6.64671i | 0.364786 | − | 0.364786i | ||||
\(333\) | −3.46293 | − | 3.46293i | −0.189767 | − | 0.189767i | ||||
\(334\) | 0.640578i | 0.0350509i | ||||||||
\(335\) | −48.1459 | −2.63049 | ||||||||
\(336\) | 3.59908 | + | 3.48303i | 0.196346 | + | 0.190015i | ||||
\(337\) | − | 9.53772i | − | 0.519552i | −0.965669 | − | 0.259776i | \(-0.916351\pi\) | ||
0.965669 | − | 0.259776i | \(-0.0836488\pi\) | |||||||
\(338\) | −12.0902 | − | 7.93329i | −0.657621 | − | 0.431514i | ||||
\(339\) | − | 8.39121i | − | 0.455748i | ||||||
\(340\) | 8.00036 | − | 8.00036i | 0.433880 | − | 0.433880i | ||||
\(341\) | − | 15.6404i | − | 0.846976i | ||||||
\(342\) | 1.74437 | 0.0943245 | ||||||||
\(343\) | 13.7234 | + | 12.4365i | 0.740996 | + | 0.671509i | ||||
\(344\) | −23.9194 | + | 23.9194i | −1.28965 | + | 1.28965i | ||||
\(345\) | −1.86376 | − | 1.86376i | −0.100342 | − | 0.100342i | ||||
\(346\) | 18.7383 | − | 18.7383i | 1.00738 | − | 1.00738i | ||||
\(347\) | −2.22056 | −0.119206 | −0.0596029 | − | 0.998222i | \(-0.518983\pi\) | ||||
−0.0596029 | + | 0.998222i | \(0.518983\pi\) | |||||||
\(348\) | −1.35826 | −0.0728105 | ||||||||
\(349\) | −7.80156 | + | 7.80156i | −0.417608 | + | 0.417608i | −0.884378 | − | 0.466771i | \(-0.845417\pi\) |
0.466771 | + | 0.884378i | \(0.345417\pi\) | |||||||
\(350\) | 33.1126 | − | 0.542595i | 1.76994 | − | 0.0290029i | ||||
\(351\) | −2.27569 | + | 2.79665i | −0.121467 | + | 0.149274i | ||||
\(352\) | −7.83755 | −0.417743 | ||||||||
\(353\) | 20.7785 | + | 20.7785i | 1.10593 | + | 1.10593i | 0.993680 | + | 0.112246i | \(0.0358046\pi\) |
0.112246 | + | 0.993680i | \(0.464195\pi\) | |||||||
\(354\) | 13.6761 | 0.726877 | ||||||||
\(355\) | 48.7768 | 2.58881 | ||||||||
\(356\) | −3.77196 | − | 3.77196i | −0.199914 | − | 0.199914i | ||||
\(357\) | −6.99624 | − | 6.77065i | −0.370280 | − | 0.358341i | ||||
\(358\) | −0.179030 | − | 0.179030i | −0.00946203 | − | 0.00946203i | ||||
\(359\) | −20.4570 | − | 20.4570i | −1.07968 | − | 1.07968i | −0.996538 | − | 0.0831407i | \(-0.973505\pi\) |
−0.0831407 | − | 0.996538i | \(-0.526495\pi\) | |||||||
\(360\) | 12.3890i | 0.652956i | ||||||||
\(361\) | − | 16.5408i | − | 0.870571i | ||||||
\(362\) | −16.1413 | + | 16.1413i | −0.848366 | + | 0.848366i | ||||
\(363\) | −7.23721 | −0.379855 | ||||||||
\(364\) | −0.861788 | − | 7.22409i | −0.0451700 | − | 0.378645i | ||||
\(365\) | 38.4586 | 2.01301 | ||||||||
\(366\) | −4.66379 | + | 4.66379i | −0.243780 | + | 0.243780i | ||||
\(367\) | 8.38088i | 0.437478i | 0.975783 | + | 0.218739i | \(0.0701944\pi\) | ||||
−0.975783 | + | 0.218739i | \(0.929806\pi\) | |||||||
\(368\) | − | 1.23766i | − | 0.0645173i | ||||||
\(369\) | −2.67464 | − | 2.67464i | −0.139236 | − | 0.139236i | ||||
\(370\) | −15.5293 | − | 15.5293i | −0.807329 | − | 0.807329i | ||||
\(371\) | 1.69147 | − | 1.74783i | 0.0878168 | − | 0.0907428i | ||||
\(372\) | 4.34820 | + | 4.34820i | 0.225444 | + | 0.225444i | ||||
\(373\) | −0.652524 | −0.0337864 | −0.0168932 | − | 0.999857i | \(-0.505378\pi\) | ||||
−0.0168932 | + | 0.999857i | \(0.505378\pi\) | |||||||
\(374\) | −7.94017 | −0.410576 | ||||||||
\(375\) | 17.8245 | + | 17.8245i | 0.920454 | + | 0.920454i | ||||
\(376\) | −16.7150 | −0.862010 | ||||||||
\(377\) | −4.98070 | − | 4.05290i | −0.256519 | − | 0.208735i | ||||
\(378\) | 2.94263 | − | 0.0482190i | 0.151352 | − | 0.00248012i | ||||
\(379\) | 16.5305 | − | 16.5305i | 0.849115 | − | 0.849115i | −0.140907 | − | 0.990023i | \(-0.545002\pi\) |
0.990023 | + | 0.140907i | \(0.0450020\pi\) | |||||||
\(380\) | −4.82156 | −0.247341 | ||||||||
\(381\) | −1.87363 | −0.0959892 | ||||||||
\(382\) | −0.0940146 | + | 0.0940146i | −0.00481021 | + | 0.00481021i | ||||
\(383\) | 13.9994 | + | 13.9994i | 0.715335 | + | 0.715335i | 0.967646 | − | 0.252311i | \(-0.0811907\pi\) |
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(384\) | −0.799026 | + | 0.799026i | −0.0407751 | + | 0.0407751i | ||||
\(385\) | 14.8680 | + | 14.3886i | 0.757744 | + | 0.733311i | ||||
\(386\) | 13.4197 | 0.683045 | ||||||||
\(387\) | 11.0076i | 0.559549i | ||||||||
\(388\) | 0.653637 | − | 0.653637i | 0.0331834 | − | 0.0331834i | ||||
\(389\) | − | 17.3926i | − | 0.881838i | −0.897547 | − | 0.440919i | \(-0.854653\pi\) | ||
0.897547 | − | 0.440919i | \(-0.145347\pi\) | |||||||
\(390\) | −10.2052 | + | 12.5414i | −0.516759 | + | 0.635058i | ||||
\(391\) | 2.40587i | 0.121670i | ||||||||
\(392\) | −14.7044 | + | 15.7011i | −0.742683 | + | 0.793026i | ||||
\(393\) | 15.5987 | 0.786851 | ||||||||
\(394\) | 22.5004i | 1.13356i | ||||||||
\(395\) | 28.1466 | + | 28.1466i | 1.41621 | + | 1.41621i | ||||
\(396\) | −1.04609 | + | 1.04609i | −0.0525682 | + | 0.0525682i | ||||
\(397\) | −16.2242 | + | 16.2242i | −0.814268 | + | 0.814268i | −0.985271 | − | 0.171002i | \(-0.945299\pi\) |
0.171002 | + | 0.985271i | \(0.445299\pi\) | |||||||
\(398\) | 1.82975 | − | 1.82975i | 0.0917168 | − | 0.0917168i | ||||
\(399\) | 0.0679778 | + | 4.14843i | 0.00340314 | + | 0.207681i | ||||
\(400\) | 21.3017i | 1.06509i | ||||||||
\(401\) | −7.53850 | − | 7.53850i | −0.376454 | − | 0.376454i | 0.493367 | − | 0.869821i | \(-0.335766\pi\) |
−0.869821 | + | 0.493367i | \(0.835766\pi\) | |||||||
\(402\) | −13.2844 | −0.662563 | ||||||||
\(403\) | 2.97019 | + | 28.9192i | 0.147956 | + | 1.44057i | ||||
\(404\) | 5.50628i | 0.273948i | ||||||||
\(405\) | 2.85068 | + | 2.85068i | 0.141651 | + | 0.141651i | ||||
\(406\) | 0.0858758 | + | 5.24068i | 0.00426194 | + | 0.260091i | ||||
\(407\) | − | 9.49978i | − | 0.470887i | ||||||
\(408\) | 7.99627 | − | 7.99627i | 0.395874 | − | 0.395874i | ||||
\(409\) | −2.07779 | − | 2.07779i | −0.102740 | − | 0.102740i | 0.653868 | − | 0.756608i | \(-0.273145\pi\) |
−0.756608 | + | 0.653868i | \(0.773145\pi\) | |||||||
\(410\) | −11.9943 | − | 11.9943i | −0.592354 | − | 0.592354i | ||||
\(411\) | 11.6472 | − | 11.6472i | 0.574514 | − | 0.574514i | ||||
\(412\) | − | 9.26613i | − | 0.456509i | ||||||
\(413\) | 0.532956 | + | 32.5244i | 0.0262251 | + | 1.60042i | ||||
\(414\) | −0.514247 | − | 0.514247i | −0.0252739 | − | 0.0252739i | ||||
\(415\) | − | 49.6883i | − | 2.43910i | ||||||
\(416\) | 14.4917 | − | 1.48839i | 0.710512 | − | 0.0729742i | ||||
\(417\) | −2.12226 | −0.103928 | ||||||||
\(418\) | 2.39264 | + | 2.39264i | 0.117028 | + | 0.117028i | ||||
\(419\) | 17.6403i | 0.861784i | 0.902403 | + | 0.430892i | \(0.141801\pi\) | ||||
−0.902403 | + | 0.430892i | \(0.858199\pi\) | |||||||
\(420\) | −8.13364 | + | 0.133281i | −0.396881 | + | 0.00650344i | ||||
\(421\) | −22.6337 | + | 22.6337i | −1.10310 | + | 1.10310i | −0.109062 | + | 0.994035i | \(0.534785\pi\) |
−0.994035 | + | 0.109062i | \(0.965215\pi\) | |||||||
\(422\) | 7.45748 | − | 7.45748i | 0.363025 | − | 0.363025i | ||||
\(423\) | −3.84609 | + | 3.84609i | −0.187003 | + | 0.187003i | ||||
\(424\) | 1.99766 | + | 1.99766i | 0.0970149 | + | 0.0970149i | ||||
\(425\) | − | 41.4084i | − | 2.00860i | ||||||
\(426\) | 13.4584 | 0.652064 | ||||||||
\(427\) | −11.2731 | − | 10.9096i | −0.545545 | − | 0.527954i | ||||
\(428\) | − | 10.9799i | − | 0.530734i | ||||||
\(429\) | −6.95742 | + | 0.714571i | −0.335907 | + | 0.0344998i | ||||
\(430\) | 49.3630i | 2.38050i | ||||||||
\(431\) | −13.0173 | + | 13.0173i | −0.627023 | + | 0.627023i | −0.947318 | − | 0.320295i | \(-0.896218\pi\) |
0.320295 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(432\) | 1.89303i | 0.0910784i | ||||||||
\(433\) | −0.894979 | −0.0430099 | −0.0215050 | − | 0.999769i | \(-0.506846\pi\) | ||||
−0.0215050 | + | 0.999769i | \(0.506846\pi\) | |||||||
\(434\) | 16.5021 | − | 17.0519i | 0.792124 | − | 0.818516i | ||||
\(435\) | −5.07693 | + | 5.07693i | −0.243420 | + | 0.243420i | ||||
\(436\) | 8.85043 | + | 8.85043i | 0.423859 | + | 0.423859i | ||||
\(437\) | 0.724971 | − | 0.724971i | 0.0346801 | − | 0.0346801i | ||||
\(438\) | 10.6114 | 0.507034 | ||||||||
\(439\) | 12.4360 | 0.593539 | 0.296770 | − | 0.954949i | \(-0.404091\pi\) | ||||
0.296770 | + | 0.954949i | \(0.404091\pi\) | |||||||
\(440\) | −16.9932 | + | 16.9932i | −0.810119 | + | 0.810119i | ||||
\(441\) | 0.229348 | + | 6.99624i | 0.0109213 | + | 0.333154i | ||||
\(442\) | 14.6814 | − | 1.50788i | 0.698324 | − | 0.0717223i | ||||
\(443\) | −13.4521 | −0.639129 | −0.319565 | − | 0.947564i | \(-0.603537\pi\) | ||||
−0.319565 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(444\) | 2.64104 | + | 2.64104i | 0.125338 | + | 0.125338i | ||||
\(445\) | −28.1978 | −1.33670 | ||||||||
\(446\) | 5.60833 | 0.265562 | ||||||||
\(447\) | 0.409314 | + | 0.409314i | 0.0193599 | + | 0.0193599i | ||||
\(448\) | −15.7430 | − | 15.2354i | −0.743787 | − | 0.719804i | ||||
\(449\) | −13.7721 | − | 13.7721i | −0.649945 | − | 0.649945i | 0.303034 | − | 0.952980i | \(-0.402000\pi\) |
−0.952980 | + | 0.303034i | \(0.902000\pi\) | |||||||
\(450\) | 8.85090 | + | 8.85090i | 0.417235 | + | 0.417235i | ||||
\(451\) | − | 7.33729i | − | 0.345500i | ||||||
\(452\) | 6.39964i | 0.301014i | ||||||||
\(453\) | 1.06906 | − | 1.06906i | 0.0502290 | − | 0.0502290i | ||||
\(454\) | 2.97544 | 0.139645 | ||||||||
\(455\) | −30.2235 | − | 23.7811i | −1.41690 | − | 1.11487i | ||||
\(456\) | −4.81909 | −0.225675 | ||||||||
\(457\) | 15.6164 | − | 15.6164i | 0.730505 | − | 0.730505i | −0.240214 | − | 0.970720i | \(-0.577218\pi\) |
0.970720 | + | 0.240214i | \(0.0772177\pi\) | |||||||
\(458\) | − | 13.4828i | − | 0.630011i | ||||||
\(459\) | − | 3.67985i | − | 0.171761i | ||||||
\(460\) | 1.42142 | + | 1.42142i | 0.0662740 | + | 0.0662740i | ||||
\(461\) | 9.65686 | + | 9.65686i | 0.449765 | + | 0.449765i | 0.895276 | − | 0.445511i | \(-0.146978\pi\) |
−0.445511 | + | 0.895276i | \(0.646978\pi\) | |||||||
\(462\) | 4.10236 | + | 3.97008i | 0.190859 | + | 0.184705i | ||||
\(463\) | −9.70922 | − | 9.70922i | −0.451226 | − | 0.451226i | 0.444536 | − | 0.895761i | \(-0.353369\pi\) |
−0.895761 | + | 0.444536i | \(0.853369\pi\) | |||||||
\(464\) | −3.37140 | −0.156513 | ||||||||
\(465\) | 32.5055 | 1.50740 | ||||||||
\(466\) | −2.78622 | − | 2.78622i | −0.129069 | − | 0.129069i | ||||
\(467\) | −15.6220 | −0.722898 | −0.361449 | − | 0.932392i | \(-0.617718\pi\) | ||||
−0.361449 | + | 0.932392i | \(0.617718\pi\) | |||||||
\(468\) | 1.73558 | − | 2.13289i | 0.0802270 | − | 0.0985930i | ||||
\(469\) | −0.517690 | − | 31.5927i | −0.0239047 | − | 1.45881i | ||||
\(470\) | −17.2475 | + | 17.2475i | −0.795569 | + | 0.795569i | ||||
\(471\) | 0.372554 | 0.0171664 | ||||||||
\(472\) | −37.7824 | −1.73908 | ||||||||
\(473\) | −15.0985 | + | 15.0985i | −0.694230 | + | 0.694230i | ||||
\(474\) | 7.76616 | + | 7.76616i | 0.356712 | + | 0.356712i | ||||
\(475\) | −12.4777 | + | 12.4777i | −0.572518 | + | 0.572518i | ||||
\(476\) | 5.33576 | + | 5.16371i | 0.244564 | + | 0.236678i | ||||
\(477\) | 0.919315 | 0.0420925 | ||||||||
\(478\) | − | 27.0630i | − | 1.23783i | ||||||
\(479\) | −7.85952 | + | 7.85952i | −0.359110 | + | 0.359110i | −0.863485 | − | 0.504375i | \(-0.831723\pi\) |
0.504375 | + | 0.863485i | \(0.331723\pi\) | |||||||
\(480\) | − | 16.2888i | − | 0.743477i | ||||||
\(481\) | 1.80405 | + | 17.5651i | 0.0822577 | + | 0.800902i | ||||
\(482\) | − | 10.4186i | − | 0.474553i | ||||||
\(483\) | 1.20294 | − | 1.24302i | 0.0547355 | − | 0.0565592i | ||||
\(484\) | 5.51953 | 0.250888 | ||||||||
\(485\) | − | 4.88634i | − | 0.221877i | ||||||
\(486\) | 0.786556 | + | 0.786556i | 0.0356789 | + | 0.0356789i | ||||
\(487\) | −26.4643 | + | 26.4643i | −1.19921 | + | 1.19921i | −0.224807 | + | 0.974403i | \(0.572175\pi\) |
−0.974403 | + | 0.224807i | \(0.927825\pi\) | |||||||
\(488\) | 12.8845 | − | 12.8845i | 0.583253 | − | 0.583253i | ||||
\(489\) | 4.28689 | − | 4.28689i | 0.193860 | − | 0.193860i | ||||
\(490\) | 1.02849 | + | 31.3742i | 0.0464627 | + | 1.41734i | ||||
\(491\) | − | 41.4045i | − | 1.86856i | −0.356543 | − | 0.934279i | \(-0.616045\pi\) | ||
0.356543 | − | 0.934279i | \(-0.383955\pi\) | |||||||
\(492\) | 2.03984 | + | 2.03984i | 0.0919632 | + | 0.0919632i | ||||
\(493\) | 6.55365 | 0.295161 | ||||||||
\(494\) | −4.87838 | − | 3.96963i | −0.219489 | − | 0.178602i | ||||
\(495\) | 7.82021i | 0.351492i | ||||||||
\(496\) | 10.7928 | + | 10.7928i | 0.484613 | + | 0.484613i | ||||
\(497\) | 0.524474 | + | 32.0067i | 0.0235259 | + | 1.43570i | ||||
\(498\) | − | 13.7099i | − | 0.614357i | ||||||
\(499\) | 17.1634 | − | 17.1634i | 0.768340 | − | 0.768340i | −0.209474 | − | 0.977814i | \(-0.567175\pi\) |
0.977814 | + | 0.209474i | \(0.0671751\pi\) | |||||||
\(500\) | −13.5941 | − | 13.5941i | −0.607945 | − | 0.607945i | ||||
\(501\) | −0.407205 | − | 0.407205i | −0.0181926 | − | 0.0181926i | ||||
\(502\) | −5.99828 | + | 5.99828i | −0.267716 | + | 0.267716i | ||||
\(503\) | 9.14068i | 0.407563i | 0.979016 | + | 0.203781i | \(0.0653232\pi\) | ||||
−0.979016 | + | 0.203781i | \(0.934677\pi\) | |||||||
\(504\) | −8.12948 | + | 0.133213i | −0.362116 | + | 0.00593376i | ||||
\(505\) | 20.5814 | + | 20.5814i | 0.915862 | + | 0.915862i | ||||
\(506\) | − | 1.41072i | − | 0.0627143i | ||||||
\(507\) | 12.7286 | − | 2.64249i | 0.565297 | − | 0.117357i | ||||
\(508\) | 1.42895 | 0.0633992 | ||||||||
\(509\) | −5.44750 | − | 5.44750i | −0.241456 | − | 0.241456i | 0.575996 | − | 0.817452i | \(-0.304614\pi\) |
−0.817452 | + | 0.575996i | \(0.804614\pi\) | |||||||
\(510\) | − | 16.5021i | − | 0.730723i | ||||||
\(511\) | 0.413527 | + | 25.2360i | 0.0182933 | + | 1.11638i | ||||
\(512\) | 13.6354 | − | 13.6354i | 0.602607 | − | 0.602607i | ||||
\(513\) | −1.10886 | + | 1.10886i | −0.0489575 | + | 0.0489575i | ||||
\(514\) | 15.6652 | − | 15.6652i | 0.690964 | − | 0.690964i | ||||
\(515\) | −34.6350 | − | 34.6350i | −1.52620 | − | 1.52620i | ||||
\(516\) | − | 8.39508i | − | 0.369573i | ||||||
\(517\) | −10.5509 | −0.464028 | ||||||||
\(518\) | 10.0231 | − | 10.3571i | 0.440391 | − | 0.455064i | ||||
\(519\) | 23.8232i | 1.04572i | ||||||||
\(520\) | 28.1934 | − | 34.6476i | 1.23636 | − | 1.51940i | ||||
\(521\) | − | 11.4764i | − | 0.502791i | −0.967885 | − | 0.251395i | \(-0.919111\pi\) | ||
0.967885 | − | 0.251395i | \(-0.0808894\pi\) | |||||||
\(522\) | −1.40082 | + | 1.40082i | −0.0613122 | + | 0.0613122i | ||||
\(523\) | 10.4153i | 0.455431i | 0.973728 | + | 0.227715i | \(0.0731256\pi\) | ||||
−0.973728 | + | 0.227715i | \(0.926874\pi\) | |||||||
\(524\) | −11.8965 | −0.519702 | ||||||||
\(525\) | −20.7042 | + | 21.3940i | −0.903605 | + | 0.933712i | ||||
\(526\) | −0.176726 | + | 0.176726i | −0.00770560 | + | 0.00770560i | ||||
\(527\) | −20.9801 | − | 20.9801i | −0.913909 | − | 0.913909i | ||||
\(528\) | −2.59655 | + | 2.59655i | −0.113000 | + | 0.113000i | ||||
\(529\) | 22.5726 | 0.981415 | ||||||||
\(530\) | 4.12261 | 0.179075 | ||||||||
\(531\) | −8.69367 | + | 8.69367i | −0.377273 | + | 0.377273i | ||||
\(532\) | −0.0518439 | − | 3.16384i | −0.00224772 | − | 0.137170i | ||||
\(533\) | 1.39339 | + | 13.5667i | 0.0603542 | + | 0.587638i | ||||
\(534\) | −7.78029 | −0.336686 | ||||||||
\(535\) | −41.0408 | − | 41.0408i | −1.77435 | − | 1.77435i | ||||
\(536\) | 36.7002 | 1.58521 | ||||||||
\(537\) | 0.227613 | 0.00982221 | ||||||||
\(538\) | 8.85016 | + | 8.85016i | 0.381558 | + | 0.381558i | ||||
\(539\) | −9.28174 | + | 9.91090i | −0.399793 | + | 0.426893i | ||||
\(540\) | −2.17410 | − | 2.17410i | −0.0935583 | − | 0.0935583i | ||||
\(541\) | 30.0820 | + | 30.0820i | 1.29333 | + | 1.29333i | 0.932717 | + | 0.360610i | \(0.117432\pi\) |
0.360610 | + | 0.932717i | \(0.382568\pi\) | |||||||
\(542\) | − | 15.0271i | − | 0.645469i | ||||||
\(543\) | − | 20.5214i | − | 0.880660i | ||||||
\(544\) | −10.5133 | + | 10.5133i | −0.450755 | + | 0.450755i | ||||
\(545\) | 66.1625 | 2.83409 | ||||||||
\(546\) | −8.33923 | − | 6.56165i | −0.356886 | − | 0.280813i | ||||
\(547\) | −4.22100 | −0.180477 | −0.0902384 | − | 0.995920i | \(-0.528763\pi\) | ||||
−0.0902384 | + | 0.995920i | \(0.528763\pi\) | |||||||
\(548\) | −8.88285 | + | 8.88285i | −0.379457 | + | 0.379457i | ||||
\(549\) | − | 5.92939i | − | 0.253060i | ||||||
\(550\) | 24.2805i | 1.03532i | ||||||||
\(551\) | −1.97484 | − | 1.97484i | −0.0841308 | − | 0.0841308i | ||||
\(552\) | 1.42069 | + | 1.42069i | 0.0604686 | + | 0.0604686i | ||||
\(553\) | −18.1668 | + | 18.7720i | −0.772529 | + | 0.798269i | ||||
\(554\) | 18.7319 | + | 18.7319i | 0.795843 | + | 0.795843i | ||||
\(555\) | 19.7434 | 0.838060 | ||||||||
\(556\) | 1.61856 | 0.0686424 | ||||||||
\(557\) | 24.4288 | + | 24.4288i | 1.03508 | + | 1.03508i | 0.999362 | + | 0.0357207i | \(0.0113727\pi\) |
0.0357207 | + | 0.999362i | \(0.488627\pi\) | |||||||
\(558\) | 8.96887 | 0.379682 | ||||||||
\(559\) | 25.0499 | − | 30.7845i | 1.05950 | − | 1.30204i | ||||
\(560\) | −20.1888 | + | 0.330822i | −0.853134 | + | 0.0139798i | ||||
\(561\) | 5.04743 | − | 5.04743i | 0.213103 | − | 0.213103i | ||||
\(562\) | −0.850249 | −0.0358656 | ||||||||
\(563\) | −7.55703 | −0.318491 | −0.159245 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159245 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(564\) | 2.93326 | − | 2.93326i | 0.123512 | − | 0.123512i | ||||
\(565\) | 23.9206 | + | 23.9206i | 1.00635 | + | 1.00635i | ||||
\(566\) | 4.75497 | − | 4.75497i | 0.199866 | − | 0.199866i | ||||
\(567\) | −1.83993 | + | 1.90123i | −0.0772696 | + | 0.0798441i | ||||
\(568\) | −37.1811 | −1.56009 | ||||||||
\(569\) | 30.8175i | 1.29193i | 0.763365 | + | 0.645967i | \(0.223546\pi\) | ||||
−0.763365 | + | 0.645967i | \(0.776454\pi\) | |||||||
\(570\) | −4.97263 | + | 4.97263i | −0.208280 | + | 0.208280i | ||||
\(571\) | 21.7092i | 0.908500i | 0.890874 | + | 0.454250i | \(0.150093\pi\) | ||||
−0.890874 | + | 0.454250i | \(0.849907\pi\) | |||||||
\(572\) | 5.30615 | − | 0.544975i | 0.221861 | − | 0.0227866i | ||||
\(573\) | − | 0.119527i | − | 0.00499331i | ||||||
\(574\) | 7.74151 | − | 7.99944i | 0.323124 | − | 0.333890i | ||||
\(575\) | 7.35700 | 0.306808 | ||||||||
\(576\) | − | 8.28044i | − | 0.345018i | ||||||
\(577\) | −25.9426 | − | 25.9426i | −1.08000 | − | 1.08000i | −0.996508 | − | 0.0834969i | \(-0.973391\pi\) |
−0.0834969 | − | 0.996508i | \(-0.526609\pi\) | |||||||
\(578\) | 2.72046 | − | 2.72046i | 0.113156 | − | 0.113156i | ||||
\(579\) | −8.53068 | + | 8.53068i | −0.354523 | + | 0.354523i | ||||
\(580\) | 3.87197 | − | 3.87197i | 0.160775 | − | 0.160775i | ||||
\(581\) | 32.6048 | − | 0.534275i | 1.35268 | − | 0.0221654i | ||||
\(582\) | − | 1.34823i | − | 0.0558861i | ||||||
\(583\) | 1.26097 | + | 1.26097i | 0.0522240 | + | 0.0522240i | ||||
\(584\) | −29.3158 | −1.21310 | ||||||||
\(585\) | −1.48509 | − | 14.4596i | −0.0614011 | − | 0.597831i | ||||
\(586\) | − | 24.3478i | − | 1.00580i | ||||||
\(587\) | 9.91583 | + | 9.91583i | 0.409270 | + | 0.409270i | 0.881484 | − | 0.472214i | \(-0.156545\pi\) |
−0.472214 | + | 0.881484i | \(0.656545\pi\) | |||||||
\(588\) | −0.174914 | − | 5.33576i | −0.00721335 | − | 0.220043i | ||||
\(589\) | 12.6441i | 0.520989i | ||||||||
\(590\) | −38.9862 | + | 38.9862i | −1.60504 | + | 1.60504i | ||||
\(591\) | −14.3031 | − | 14.3031i | −0.588352 | − | 0.588352i | ||||
\(592\) | 6.55543 | + | 6.55543i | 0.269426 | + | 0.269426i | ||||
\(593\) | −14.3032 | + | 14.3032i | −0.587360 | + | 0.587360i | −0.936916 | − | 0.349555i | \(-0.886333\pi\) |
0.349555 | + | 0.936916i | \(0.386333\pi\) | |||||||
\(594\) | 2.15774i | 0.0885332i | ||||||||
\(595\) | 39.2450 | − | 0.643083i | 1.60889 | − | 0.0263638i | ||||
\(596\) | −0.312168 | − | 0.312168i | −0.0127869 | − | 0.0127869i | ||||
\(597\) | 2.32628i | 0.0952081i | ||||||||
\(598\) | 0.267903 | + | 2.60844i | 0.0109554 | + | 0.106667i | ||||
\(599\) | 12.3813 | 0.505886 | 0.252943 | − | 0.967481i | \(-0.418601\pi\) | ||||
0.252943 | + | 0.967481i | \(0.418601\pi\) | |||||||
\(600\) | −24.4520 | − | 24.4520i | −0.998250 | − | 0.998250i | ||||
\(601\) | − | 32.7835i | − | 1.33727i | −0.743592 | − | 0.668634i | \(-0.766879\pi\) | ||
0.743592 | − | 0.668634i | \(-0.233121\pi\) | |||||||
\(602\) | −32.3914 | + | 0.530777i | −1.32017 | + | 0.0216328i | ||||
\(603\) | 8.44464 | − | 8.44464i | 0.343892 | − | 0.343892i | ||||
\(604\) | −0.815333 | + | 0.815333i | −0.0331754 | + | 0.0331754i | ||||
\(605\) | 20.6310 | − | 20.6310i | 0.838768 | − | 0.838768i | ||||
\(606\) | 5.67880 | + | 5.67880i | 0.230686 | + | 0.230686i | ||||
\(607\) | − | 26.5960i | − | 1.07950i | −0.841826 | − | 0.539749i | \(-0.818519\pi\) | ||
0.841826 | − | 0.539749i | \(-0.181481\pi\) | |||||||
\(608\) | 6.33605 | 0.256961 | ||||||||
\(609\) | −3.38600 | − | 3.27682i | −0.137208 | − | 0.132784i | ||||
\(610\) | − | 26.5899i | − | 1.07660i | ||||||
\(611\) | 19.5087 | − | 2.00366i | 0.789236 | − | 0.0810596i | ||||
\(612\) | 2.80648i | 0.113445i | ||||||||
\(613\) | 10.6735 | − | 10.6735i | 0.431099 | − | 0.431099i | −0.457903 | − | 0.889002i | \(-0.651399\pi\) |
0.889002 | + | 0.457903i | \(0.151399\pi\) | |||||||
\(614\) | 36.5285i | 1.47417i | ||||||||
\(615\) | 15.2491 | 0.614903 | ||||||||
\(616\) | −11.3334 | − | 10.9680i | −0.456637 | − | 0.441913i | ||||
\(617\) | 25.3375 | − | 25.3375i | 1.02005 | − | 1.02005i | 0.0202541 | − | 0.999795i | \(-0.493552\pi\) |
0.999795 | − | 0.0202541i | \(-0.00644752\pi\) | |||||||
\(618\) | −9.55646 | − | 9.55646i | −0.384417 | − | 0.384417i | ||||
\(619\) | 20.2261 | − | 20.2261i | 0.812955 | − | 0.812955i | −0.172121 | − | 0.985076i | \(-0.555062\pi\) |
0.985076 | + | 0.172121i | \(0.0550620\pi\) | |||||||
\(620\) | −24.7906 | −0.995615 | ||||||||
\(621\) | 0.653796 | 0.0262359 | ||||||||
\(622\) | 5.15397 | − | 5.15397i | 0.206655 | − | 0.206655i | ||||
\(623\) | −0.303197 | − | 18.5030i | −0.0121473 | − | 0.741307i | ||||
\(624\) | 4.30794 | − | 5.29414i | 0.172456 | − | 0.211935i | ||||
\(625\) | −45.3603 | −1.81441 | ||||||||
\(626\) | 21.9660 | + | 21.9660i | 0.877937 | + | 0.877937i | ||||
\(627\) | −3.04192 | −0.121483 | ||||||||
\(628\) | −0.284132 | −0.0113381 | ||||||||
\(629\) | −12.7431 | − | 12.7431i | −0.508099 | − | 0.508099i | ||||
\(630\) | −8.25103 | + | 8.52594i | −0.328729 | + | 0.339682i | ||||
\(631\) | 6.74447 | + | 6.74447i | 0.268493 | + | 0.268493i | 0.828493 | − | 0.560000i | \(-0.189199\pi\) |
−0.560000 | + | 0.828493i | \(0.689199\pi\) | |||||||
\(632\) | −21.4553 | − | 21.4553i | −0.853445 | − | 0.853445i | ||||
\(633\) | 9.48119i | 0.376843i | ||||||||
\(634\) | 8.93346i | 0.354793i | ||||||||
\(635\) | 5.34113 | − | 5.34113i | 0.211956 | − | 0.211956i | ||||
\(636\) | −0.701125 | −0.0278014 | ||||||||
\(637\) | 15.2799 | − | 20.0880i | 0.605410 | − | 0.795914i | ||||
\(638\) | −3.84284 | −0.152139 | ||||||||
\(639\) | −8.55531 | + | 8.55531i | −0.338443 | + | 0.338443i | ||||
\(640\) | − | 4.55553i | − | 0.180073i | ||||||
\(641\) | − | 42.7458i | − | 1.68836i | −0.536062 | − | 0.844179i | \(-0.680089\pi\) | ||
0.536062 | − | 0.844179i | \(-0.319911\pi\) | |||||||
\(642\) | −11.3239 | − | 11.3239i | −0.446919 | − | 0.446919i | ||||
\(643\) | 24.5416 | + | 24.5416i | 0.967827 | + | 0.967827i | 0.999498 | − | 0.0316713i | \(-0.0100830\pi\) |
−0.0316713 | + | 0.999498i | \(0.510083\pi\) | |||||||
\(644\) | −0.917432 | + | 0.948000i | −0.0361519 | + | 0.0373564i | ||||
\(645\) | −31.3792 | − | 31.3792i | −1.23556 | − | 1.23556i | ||||
\(646\) | 6.41901 | 0.252553 | ||||||||
\(647\) | 32.2371 | 1.26737 | 0.633685 | − | 0.773591i | \(-0.281541\pi\) | ||||
0.633685 | + | 0.773591i | \(0.281541\pi\) | |||||||
\(648\) | −2.17299 | − | 2.17299i | −0.0853630 | − | 0.0853630i | ||||
\(649\) | −23.8492 | −0.936161 | ||||||||
\(650\) | −4.61098 | − | 44.8947i | −0.180857 | − | 1.76092i | ||||
\(651\) | 0.349516 | + | 21.3297i | 0.0136986 | + | 0.835975i | ||||
\(652\) | −3.26944 | + | 3.26944i | −0.128041 | + | 0.128041i | ||||
\(653\) | 33.3640 | 1.30563 | 0.652817 | − | 0.757516i | \(-0.273587\pi\) | ||||
0.652817 | + | 0.757516i | \(0.273587\pi\) | |||||||
\(654\) | 18.2555 | 0.713845 | ||||||||
\(655\) | −44.4669 | + | 44.4669i | −1.73747 | + | 1.73747i | ||||
\(656\) | 5.06318 | + | 5.06318i | 0.197684 | + | 0.197684i | ||||
\(657\) | −6.74551 | + | 6.74551i | −0.263168 | + | 0.263168i | ||||
\(658\) | −11.5031 | − | 11.1321i | −0.448436 | − | 0.433976i | ||||
\(659\) | −6.27743 | −0.244534 | −0.122267 | − | 0.992497i | \(-0.539016\pi\) | ||||
−0.122267 | + | 0.992497i | \(0.539016\pi\) | |||||||
\(660\) | − | 5.96416i | − | 0.232155i | ||||||
\(661\) | 27.2446 | − | 27.2446i | 1.05969 | − | 1.05969i | 0.0615924 | − | 0.998101i | \(-0.480382\pi\) |
0.998101 | − | 0.0615924i | \(-0.0196179\pi\) | |||||||
\(662\) | − | 6.99780i | − | 0.271977i | ||||||
\(663\) | −8.37419 | + | 10.2913i | −0.325227 | + | 0.399679i | ||||
\(664\) | 37.8759i | 1.46987i | ||||||||
\(665\) | −12.0196 | − | 11.6321i | −0.466101 | − | 0.451072i | ||||
\(666\) | 5.44757 | 0.211089 | ||||||||
\(667\) | 1.16438i | 0.0450850i | ||||||||
\(668\) | 0.310559 | + | 0.310559i | 0.0120159 | + | 0.0120159i | ||||
\(669\) | −3.56512 | + | 3.56512i | −0.137835 | + | 0.137835i | ||||
\(670\) | 37.8694 | − | 37.8694i | 1.46302 | − | 1.46302i | ||||
\(671\) | 8.13298 | − | 8.13298i | 0.313970 | − | 0.313970i | ||||
\(672\) | 10.6885 | − | 0.175145i | 0.412317 | − | 0.00675638i | ||||
\(673\) | 0.229492i | 0.00884627i | 0.999990 | + | 0.00442313i | \(0.00140793\pi\) | ||||
−0.999990 | + | 0.00442313i | \(0.998592\pi\) | |||||||
\(674\) | 7.50194 | + | 7.50194i | 0.288964 | + | 0.288964i | ||||
\(675\) | −11.2527 | −0.433118 | ||||||||
\(676\) | −9.70760 | + | 2.01532i | −0.373369 | + | 0.0775124i | ||||
\(677\) | − | 4.51279i | − | 0.173441i | −0.996233 | − | 0.0867204i | \(-0.972361\pi\) | ||
0.996233 | − | 0.0867204i | \(-0.0276387\pi\) | |||||||
\(678\) | 6.60015 | + | 6.60015i | 0.253477 | + | 0.253477i | ||||
\(679\) | 3.20635 | − | 0.0525405i | 0.123049 | − | 0.00201632i | ||||
\(680\) | 45.5896i | 1.74828i | ||||||||
\(681\) | −1.89144 | + | 1.89144i | −0.0724801 | + | 0.0724801i | ||||
\(682\) | 12.3021 | + | 12.3021i | 0.471070 | + | 0.471070i | ||||
\(683\) | 15.0159 | + | 15.0159i | 0.574568 | + | 0.574568i | 0.933402 | − | 0.358833i | \(-0.116825\pi\) |
−0.358833 | + | 0.933402i | \(0.616825\pi\) | |||||||
\(684\) | 0.845686 | − | 0.845686i | 0.0323356 | − | 0.0323356i | ||||
\(685\) | 66.4048i | 2.53720i | ||||||||
\(686\) | −20.5763 | + | 1.01224i | −0.785606 | + | 0.0386474i | ||||
\(687\) | 8.57080 | + | 8.57080i | 0.326996 | + | 0.326996i | ||||
\(688\) | − | 20.8378i | − | 0.794432i | ||||||
\(689\) | −2.57100 | − | 2.09207i | −0.0979474 | − | 0.0797017i | ||||
\(690\) | 2.93191 | 0.111616 | ||||||||
\(691\) | 13.7088 | + | 13.7088i | 0.521506 | + | 0.521506i | 0.918026 | − | 0.396520i | \(-0.129782\pi\) |
−0.396520 | + | 0.918026i | \(0.629782\pi\) | |||||||
\(692\) | − | 18.1690i | − | 0.690682i | ||||||
\(693\) | −5.13152 | + | 0.0840870i | −0.194930 | + | 0.00319420i | ||||
\(694\) | 1.74659 | − | 1.74659i | 0.0662998 | − | 0.0662998i | ||||
\(695\) | 6.04988 | − | 6.04988i | 0.229485 | − | 0.229485i | ||||
\(696\) | 3.86999 | − | 3.86999i | 0.146692 | − | 0.146692i | ||||
\(697\) | −9.84229 | − | 9.84229i | −0.372803 | − | 0.372803i | ||||
\(698\) | − | 12.2727i | − | 0.464529i | ||||||
\(699\) | 3.54231 | 0.133982 | ||||||||
\(700\) | 15.7903 | − | 16.3164i | 0.596816 | − | 0.616701i | ||||
\(701\) | − | 24.9025i | − | 0.940553i | −0.882519 | − | 0.470277i | \(-0.844154\pi\) | ||
0.882519 | − | 0.470277i | \(-0.155846\pi\) | |||||||
\(702\) | −0.409765 | − | 3.98968i | −0.0154656 | − | 0.150581i | ||||
\(703\) | 7.67983i | 0.289650i | ||||||||
\(704\) | 11.3578 | − | 11.3578i | 0.428062 | − | 0.428062i | ||||
\(705\) | − | 21.9279i | − | 0.825853i | ||||||
\(706\) | −32.6869 | −1.23019 | ||||||||
\(707\) | −13.2840 | + | 13.7266i | −0.499595 | + | 0.516241i | ||||
\(708\) | 6.63031 | − | 6.63031i | 0.249182 | − | 0.249182i | ||||
\(709\) | −26.6069 | − | 26.6069i | −0.999245 | − | 0.999245i | 0.000754806 | − | 1.00000i | \(-0.499760\pi\) |
−1.00000 | 0.000754806i | \(0.999760\pi\) | ||||||||
\(710\) | −38.3657 | + | 38.3657i | −1.43984 | + | 1.43984i | ||||
\(711\) | −9.87363 | −0.370290 | ||||||||
\(712\) | 21.4943 | 0.805533 | ||||||||
\(713\) | 3.72753 | − | 3.72753i | 0.139597 | − | 0.139597i | ||||
\(714\) | 10.8284 | − | 0.177439i | 0.405244 | − | 0.00664048i | ||||
\(715\) | 17.7963 | − | 21.8704i | 0.665546 | − | 0.817906i | ||||
\(716\) | −0.173591 | −0.00648740 | ||||||||
\(717\) | 17.2035 | + | 17.2035i | 0.642475 | + | 0.642475i | ||||
\(718\) | 32.1811 | 1.20099 | ||||||||
\(719\) | −11.7193 | −0.437054 | −0.218527 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218527 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(720\) | −5.39642 | − | 5.39642i | −0.201113 | − | 0.201113i | ||||
\(721\) | 22.3546 | − | 23.0995i | 0.832530 | − | 0.860269i | ||||
\(722\) | 13.0103 | + | 13.0103i | 0.484193 | + | 0.484193i | ||||
\(723\) | 6.62291 | + | 6.62291i | 0.246309 | + | 0.246309i | ||||
\(724\) | 15.6509i | 0.581661i | ||||||||
\(725\) | − | 20.0406i | − | 0.744289i | ||||||
\(726\) | 5.69247 | − | 5.69247i | 0.211267 | − | 0.211267i | ||||
\(727\) | −1.29408 | −0.0479949 | −0.0239975 | − | 0.999712i | \(-0.507639\pi\) | ||||
−0.0239975 | + | 0.999712i | \(0.507639\pi\) | |||||||
\(728\) | 23.0384 | + | 18.1276i | 0.853862 | + | 0.671854i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −30.2498 | + | 30.2498i | −1.11960 | + | 1.11960i | ||||
\(731\) | 40.5064i | 1.49818i | ||||||||
\(732\) | 4.52211i | 0.167142i | ||||||||
\(733\) | −9.51083 | − | 9.51083i | −0.351291 | − | 0.351291i | 0.509299 | − | 0.860590i | \(-0.329905\pi\) |
−0.860590 | + | 0.509299i | \(0.829905\pi\) | |||||||
\(734\) | −6.59203 | − | 6.59203i | −0.243316 | − | 0.243316i | ||||
\(735\) | −20.5978 | − | 19.2902i | −0.759762 | − | 0.711531i | ||||
\(736\) | −1.86790 | − | 1.86790i | −0.0688516 | − | 0.0688516i | ||||
\(737\) | 23.1660 | 0.853330 | ||||||||
\(738\) | 4.20751 | 0.154881 | ||||||||
\(739\) | 13.5044 | + | 13.5044i | 0.496766 | + | 0.496766i | 0.910430 | − | 0.413663i | \(-0.135751\pi\) |
−0.413663 | + | 0.910430i | \(0.635751\pi\) | |||||||
\(740\) | −15.0575 | −0.553525 | ||||||||
\(741\) | 5.62453 | − | 0.577675i | 0.206622 | − | 0.0212214i | ||||
\(742\) | 0.0443284 | + | 2.70520i | 0.00162735 | + | 0.0993111i | ||||
\(743\) | −27.2778 | + | 27.2778i | −1.00073 | + | 1.00073i | −0.000725386 | 1.00000i | \(0.500231\pi\) | |
−1.00000 | 0.000725386i | \(0.999769\pi\) | ||||||||
\(744\) | −24.7779 | −0.908403 | ||||||||
\(745\) | −2.33365 | −0.0854982 | ||||||||
\(746\) | 0.513246 | − | 0.513246i | 0.0187913 | − | 0.0187913i | ||||
\(747\) | 8.71517 | + | 8.71517i | 0.318871 | + | 0.318871i | ||||
\(748\) | −3.84947 | + | 3.84947i | −0.140751 | + | 0.140751i | ||||
\(749\) | 26.4891 | − | 27.3717i | 0.967891 | − | 1.00014i | ||||
\(750\) | −28.0400 | −1.02387 | ||||||||
\(751\) | 17.3413i | 0.632792i | 0.948627 | + | 0.316396i | \(0.102473\pi\) | ||||
−0.948627 | + | 0.316396i | \(0.897527\pi\) | |||||||
\(752\) | 7.28076 | − | 7.28076i | 0.265502 | − | 0.265502i | ||||
\(753\) | − | 7.62601i | − | 0.277907i | ||||||
\(754\) | 7.10543 | − | 0.729773i | 0.258764 | − | 0.0265768i | ||||
\(755\) | 6.09512i | 0.221824i | ||||||||
\(756\) | 1.40324 | − | 1.44999i | 0.0510353 | − | 0.0527357i | ||||
\(757\) | 14.0722 | 0.511464 | 0.255732 | − | 0.966748i | \(-0.417684\pi\) | ||||
0.255732 | + | 0.966748i | \(0.417684\pi\) | |||||||
\(758\) | 26.0043i | 0.944520i | ||||||||
\(759\) | 0.896773 | + | 0.896773i | 0.0325508 | + | 0.0325508i | ||||
\(760\) | 13.7377 | − | 13.7377i | 0.498318 | − | 0.498318i | ||||
\(761\) | 17.8688 | − | 17.8688i | 0.647742 | − | 0.647742i | −0.304705 | − | 0.952447i | \(-0.598558\pi\) |
0.952447 | + | 0.304705i | \(0.0985579\pi\) | |||||||
\(762\) | 1.47372 | − | 1.47372i | 0.0533872 | − | 0.0533872i | ||||
\(763\) | 0.711413 | + | 43.4149i | 0.0257549 | + | 1.57173i | ||||
\(764\) | 0.0911585i | 0.00329800i | ||||||||
\(765\) | 10.4901 | + | 10.4901i | 0.379269 | + | 0.379269i | ||||
\(766\) | −22.0226 | −0.795708 | ||||||||
\(767\) | 44.0972 | − | 4.52907i | 1.59226 | − | 0.163535i | ||||
\(768\) | 15.3039i | 0.552233i | ||||||||
\(769\) | −24.0788 | − | 24.0788i | −0.868302 | − | 0.868302i | 0.123982 | − | 0.992284i | \(-0.460433\pi\) |
−0.992284 | + | 0.123982i | \(0.960433\pi\) | |||||||
\(770\) | −23.0119 | + | 0.377082i | −0.829293 | + | 0.0135891i | ||||
\(771\) | 19.9162i | 0.717266i | ||||||||
\(772\) | 6.50601 | − | 6.50601i | 0.234156 | − | 0.234156i | ||||
\(773\) | 16.3658 | + | 16.3658i | 0.588636 | + | 0.588636i | 0.937262 | − | 0.348626i | \(-0.113352\pi\) |
−0.348626 | + | 0.937262i | \(0.613352\pi\) | |||||||
\(774\) | −8.65811 | − | 8.65811i | −0.311210 | − | 0.311210i | ||||
\(775\) | −64.1558 | + | 64.1558i | −2.30455 | + | 2.30455i | ||||
\(776\) | 3.72471i | 0.133709i | ||||||||
\(777\) | 0.212291 | + | 12.9554i | 0.00761591 | + | 0.464771i | ||||
\(778\) | 13.6802 | + | 13.6802i | 0.490460 | + | 0.490460i | ||||
\(779\) | 5.93163i | 0.212523i | ||||||||
\(780\) | 1.13262 | + | 11.0278i | 0.0405544 | + | 0.394857i | ||||
\(781\) | −23.4696 | −0.839808 | ||||||||
\(782\) | −1.89235 | − | 1.89235i | −0.0676704 | − | 0.0676704i | ||||
\(783\) | − | 1.78095i | − | 0.0636461i | ||||||
\(784\) | −0.434162 | − | 13.2441i | −0.0155058 | − | 0.473003i | ||||
\(785\) | −1.06203 | + | 1.06203i | −0.0379055 | + | 0.0379055i | ||||
\(786\) | −12.2693 | + | 12.2693i | −0.437630 | + | 0.437630i | ||||
\(787\) | −9.35789 | + | 9.35789i | −0.333573 | + | 0.333573i | −0.853942 | − | 0.520369i | \(-0.825794\pi\) |
0.520369 | + | 0.853942i | \(0.325794\pi\) | |||||||
\(788\) | 10.9084 | + | 10.9084i | 0.388597 | + | 0.388597i | ||||
\(789\) | − | 0.224683i | − | 0.00799892i | ||||||
\(790\) | −44.2777 | −1.57533 | ||||||||
\(791\) | −15.4392 | + | 15.9536i | −0.548955 | + | 0.567245i | ||||
\(792\) | − | 5.96111i | − | 0.211819i | ||||||
\(793\) | −13.4934 | + | 16.5824i | −0.479166 | + | 0.588859i | ||||
\(794\) | − | 25.5224i | − | 0.905758i | ||||||
\(795\) | −2.62067 | + | 2.62067i | −0.0929456 | + | 0.0929456i | ||||
\(796\) | − | 1.77416i | − | 0.0628834i | ||||||
\(797\) | 8.50189 | 0.301152 | 0.150576 | − | 0.988598i | \(-0.451887\pi\) | ||||
0.150576 | + | 0.988598i | \(0.451887\pi\) | |||||||
\(798\) | −3.31644 | − | 3.20950i | −0.117401 | − | 0.113615i | ||||
\(799\) | −14.1530 | + | 14.1530i | −0.500698 | + | 0.500698i | ||||
\(800\) | 32.1490 | + | 32.1490i | 1.13664 | + | 1.13664i | ||||
\(801\) | 4.94580 | − | 4.94580i | 0.174751 | − | 0.174751i | ||||
\(802\) | 11.8589 | 0.418752 | ||||||||
\(803\) | −18.5048 | −0.653021 | ||||||||
\(804\) | −6.44039 | + | 6.44039i | −0.227135 | + | 0.227135i | ||||
\(805\) | 0.114256 | + | 6.97263i | 0.00402700 | + | 0.245753i | ||||
\(806\) | −25.0828 | − | 20.4103i | −0.883503 | − | 0.718924i | ||||
\(807\) | −11.2518 | −0.396082 | ||||||||
\(808\) | −15.6886 | − | 15.6886i | −0.551923 | − | 0.551923i | ||||
\(809\) | 4.57041 | 0.160687 | 0.0803434 | − | 0.996767i | \(-0.474398\pi\) | ||||
0.0803434 | + | 0.996767i | \(0.474398\pi\) | |||||||
\(810\) | −4.48443 | −0.157567 | ||||||||
\(811\) | −29.0467 | − | 29.0467i | −1.01997 | − | 1.01997i | −0.999797 | − | 0.0201724i | \(-0.993578\pi\) |
−0.0201724 | − | 0.999797i | \(-0.506422\pi\) | |||||||
\(812\) | 2.58237 | + | 2.49910i | 0.0906234 | + | 0.0877013i | ||||
\(813\) | 9.55246 | + | 9.55246i | 0.335019 | + | 0.335019i | ||||
\(814\) | 7.47211 | + | 7.47211i | 0.261897 | + | 0.261897i | ||||
\(815\) | 24.4411i | 0.856135i | ||||||||
\(816\) | 6.96607i | 0.243861i | ||||||||
\(817\) | 12.2060 | − | 12.2060i | 0.427033 | − | 0.427033i | ||||
\(818\) | 3.26859 | 0.114284 | ||||||||
\(819\) | 9.47223 | − | 1.12998i | 0.330987 | − | 0.0394846i | ||||
\(820\) | −11.6299 | −0.406133 | ||||||||
\(821\) | 24.7896 | − | 24.7896i | 0.865163 | − | 0.865163i | −0.126769 | − | 0.991932i | \(-0.540461\pi\) |
0.991932 | + | 0.126769i | \(0.0404606\pi\) | |||||||
\(822\) | 18.3223i | 0.639065i | ||||||||
\(823\) | − | 29.6585i | − | 1.03383i | −0.856036 | − | 0.516916i | \(-0.827080\pi\) | ||
0.856036 | − | 0.516916i | \(-0.172920\pi\) | |||||||
\(824\) | 26.4012 | + | 26.4012i | 0.919731 | + | 0.919731i | ||||
\(825\) | −15.4347 | − | 15.4347i | −0.537367 | − | 0.537367i | ||||
\(826\) | −26.0014 | − | 25.1630i | −0.904705 | − | 0.875533i | ||||
\(827\) | 28.6388 | + | 28.6388i | 0.995870 | + | 0.995870i | 0.999992 | − | 0.00412144i | \(-0.00131190\pi\) |
−0.00412144 | + | 0.999992i | \(0.501312\pi\) | |||||||
\(828\) | −0.498624 | −0.0173284 | ||||||||
\(829\) | 11.4568 | 0.397912 | 0.198956 | − | 0.980008i | \(-0.436245\pi\) | ||||
0.198956 | + | 0.980008i | \(0.436245\pi\) | |||||||
\(830\) | 39.0826 | + | 39.0826i | 1.35658 | + | 1.35658i | ||||
\(831\) | −23.8151 | −0.826138 | ||||||||
\(832\) | −18.8437 | + | 23.1575i | −0.653287 | + | 0.802841i | ||||
\(833\) | 0.843965 | + | 25.7451i | 0.0292417 | + | 0.892016i | ||||
\(834\) | 1.66928 | − | 1.66928i | 0.0578023 | − | 0.0578023i | ||||
\(835\) | 2.32162 | 0.0803429 | ||||||||
\(836\) | 2.31995 | 0.0802373 | ||||||||
\(837\) | −5.70136 | + | 5.70136i | −0.197068 | + | 0.197068i | ||||
\(838\) | −13.8751 | − | 13.8751i | −0.479306 | − | 0.479306i | ||||
\(839\) | −22.2494 | + | 22.2494i | −0.768133 | + | 0.768133i | −0.977778 | − | 0.209644i | \(-0.932769\pi\) |
0.209644 | + | 0.977778i | \(0.432769\pi\) | |||||||
\(840\) | 22.7948 | − | 23.5543i | 0.786495 | − | 0.812700i | ||||
\(841\) | −25.8282 | −0.890628 | ||||||||
\(842\) | − | 35.6053i | − | 1.22704i | ||||||
\(843\) | 0.540489 | − | 0.540489i | 0.0186154 | − | 0.0186154i | ||||
\(844\) | − | 7.23093i | − | 0.248899i | ||||||
\(845\) | −28.7522 | + | 43.8180i | −0.989107 | + | 1.50739i | ||||
\(846\) | − | 6.05033i | − | 0.208014i | ||||||
\(847\) | 13.7596 | + | 13.3159i | 0.472785 | + | 0.457541i | ||||
\(848\) | −1.74029 | −0.0597618 | ||||||||
\(849\) | 6.04531i | 0.207474i | ||||||||
\(850\) | 32.5700 | + | 32.5700i | 1.11714 | + | 1.11714i | ||||
\(851\) | 2.26405 | − | 2.26405i | 0.0776107 | − | 0.0776107i | ||||
\(852\) | 6.52479 | − | 6.52479i | 0.223536 | − | 0.223536i | ||||
\(853\) | −7.32728 | + | 7.32728i | −0.250881 | + | 0.250881i | −0.821332 | − | 0.570451i | \(-0.806769\pi\) |
0.570451 | + | 0.821332i | \(0.306769\pi\) | |||||||
\(854\) | 17.4480 | − | 0.285909i | 0.597057 | − | 0.00978360i | ||||
\(855\) | − | 6.32203i | − | 0.216209i | ||||||
\(856\) | 31.2841 | + | 31.2841i | 1.06927 | + | 1.06927i | ||||
\(857\) | 17.5648 | 0.600004 | 0.300002 | − | 0.953939i | \(-0.403013\pi\) | ||||
0.300002 | + | 0.953939i | \(0.403013\pi\) | |||||||
\(858\) | 4.91035 | − | 6.03445i | 0.167636 | − | 0.206013i | ||||
\(859\) | 17.1020i | 0.583514i | 0.956492 | + | 0.291757i | \(0.0942399\pi\) | ||||
−0.956492 | + | 0.291757i | \(0.905760\pi\) | |||||||
\(860\) | 23.9317 | + | 23.9317i | 0.816063 | + | 0.816063i | ||||
\(861\) | 0.163966 | + | 10.0063i | 0.00558795 | + | 0.341012i | ||||
\(862\) | − | 20.4777i | − | 0.697474i | ||||||
\(863\) | −16.9381 | + | 16.9381i | −0.576579 | + | 0.576579i | −0.933959 | − | 0.357380i | \(-0.883670\pi\) |
0.357380 | + | 0.933959i | \(0.383670\pi\) | |||||||
\(864\) | 2.85700 | + | 2.85700i | 0.0971971 | + | 0.0971971i | ||||
\(865\) | −67.9123 | − | 67.9123i | −2.30909 | − | 2.30909i | ||||
\(866\) | 0.703951 | − | 0.703951i | 0.0239212 | − | 0.0239212i | ||||
\(867\) | 3.45870i | 0.117463i | ||||||||
\(868\) | −0.266562 | − | 16.2673i | −0.00904770 | − | 0.552148i | ||||
\(869\) | −13.5431 | − | 13.5431i | −0.459417 | − | 0.459417i | ||||
\(870\) | − | 7.98657i | − | 0.270770i | ||||||
\(871\) | −42.8340 | + | 4.39933i | −1.45138 | + | 0.149066i | ||||
\(872\) | −50.4336 | −1.70790 | ||||||||
\(873\) | 0.857049 | + | 0.857049i | 0.0290067 | + | 0.0290067i | ||||
\(874\) | 1.14046i | 0.0385766i | ||||||||
\(875\) | −1.09271 | − | 66.6843i | −0.0369405 | − | 2.25434i | ||||
\(876\) | 5.14454 | − | 5.14454i | 0.173818 | − | 0.173818i | ||||
\(877\) | −7.32085 | + | 7.32085i | −0.247208 | + | 0.247208i | −0.819824 | − | 0.572616i | \(-0.805929\pi\) |
0.572616 | + | 0.819824i | \(0.305929\pi\) | |||||||
\(878\) | −9.78163 | + | 9.78163i | −0.330114 | + | 0.330114i | ||||
\(879\) | 15.4775 | + | 15.4775i | 0.522042 | + | 0.522042i | ||||
\(880\) | − | 14.8039i | − | 0.499039i | ||||||
\(881\) | −40.4345 | −1.36227 | −0.681136 | − | 0.732157i | \(-0.738514\pi\) | ||||
−0.681136 | + | 0.732157i | \(0.738514\pi\) | |||||||
\(882\) | −5.68333 | − | 5.32254i | −0.191368 | − | 0.179219i | ||||
\(883\) | − | 19.4706i | − | 0.655238i | −0.944810 | − | 0.327619i | \(-0.893754\pi\) | ||
0.944810 | − | 0.327619i | \(-0.106246\pi\) | |||||||
\(884\) | 6.38666 | − | 7.84873i | 0.214807 | − | 0.263981i | ||||
\(885\) | − | 49.5657i | − | 1.66613i | ||||||
\(886\) | 10.5808 | − | 10.5808i | 0.355470 | − | 0.355470i | ||||
\(887\) | − | 31.1044i | − | 1.04438i | −0.852828 | − | 0.522192i | \(-0.825114\pi\) | ||
0.852828 | − | 0.522192i | \(-0.174886\pi\) | |||||||
\(888\) | −15.0498 | −0.505038 | ||||||||
\(889\) | 3.56221 | + | 3.44735i | 0.119473 | + | 0.115620i | ||||
\(890\) | 22.1791 | − | 22.1791i | 0.743445 | − | 0.743445i | ||||
\(891\) | −1.37164 | − | 1.37164i | −0.0459517 | − | 0.0459517i | ||||
\(892\) | 2.71897 | − | 2.71897i | 0.0910380 | − | 0.0910380i | ||||
\(893\) | 8.52958 | 0.285431 | ||||||||
\(894\) | −0.643897 | −0.0215351 | ||||||||
\(895\) | −0.648850 | + | 0.648850i | −0.0216887 | + | 0.0216887i | ||||
\(896\) | 2.98928 | − | 0.0489835i | 0.0998648 | − | 0.00163642i | ||||
\(897\) | −1.82844 | − | 1.48784i | −0.0610498 | − | 0.0496774i | ||||
\(898\) | 21.6650 | 0.722972 | ||||||||
\(899\) | −10.1539 | − | 10.1539i | −0.338650 | − | 0.338650i | ||||
\(900\) | 8.58201 | 0.286067 | ||||||||
\(901\) | 3.38294 | 0.112702 | ||||||||
\(902\) | 5.77119 | + | 5.77119i | 0.192160 | + | 0.192160i | ||||
\(903\) | 20.2532 | − | 20.9280i | 0.673985 | − | 0.696441i | ||||
\(904\) | −18.2340 | − | 18.2340i | −0.606453 | − | 0.606453i | ||||
\(905\) | 58.5000 | + | 58.5000i | 1.94461 | + | 1.94461i | ||||
\(906\) | 1.68176i | 0.0558727i | ||||||||
\(907\) | 1.02572i | 0.0340584i | 0.999855 | + | 0.0170292i | \(0.00542082\pi\) | ||||
−0.999855 | + | 0.0170292i | \(0.994579\pi\) | |||||||
\(908\) | 1.44253 | − | 1.44253i | 0.0478719 | − | 0.0478719i | ||||
\(909\) | −7.21984 | −0.239467 | ||||||||
\(910\) | 42.4776 | − | 5.06730i | 1.40812 | − | 0.167979i | ||||
\(911\) | −41.0344 | −1.35953 | −0.679766 | − | 0.733429i | \(-0.737919\pi\) | ||||
−0.679766 | + | 0.733429i | \(0.737919\pi\) | |||||||
\(912\) | 2.09911 | − | 2.09911i | 0.0695085 | − | 0.0695085i | ||||
\(913\) | 23.9082i | 0.791244i | ||||||||
\(914\) | 24.5664i | 0.812583i | ||||||||
\(915\) | 16.9028 | + | 16.9028i | 0.558788 | + | 0.558788i | ||||
\(916\) | −6.53661 | − | 6.53661i | −0.215976 | − | 0.215976i | ||||
\(917\) | −29.6567 | − | 28.7005i | −0.979352 | − | 0.947773i | ||||
\(918\) | 2.89441 | + | 2.89441i | 0.0955297 | + | 0.0955297i | ||||
\(919\) | −15.4977 | −0.511222 | −0.255611 | − | 0.966780i | \(-0.582277\pi\) | ||||
−0.255611 | + | 0.966780i | \(0.582277\pi\) | |||||||
\(920\) | −8.09986 | −0.267045 | ||||||||
\(921\) | −23.2206 | − | 23.2206i | −0.765144 | − | 0.765144i | ||||
\(922\) | −15.1913 | −0.500299 | ||||||||
\(923\) | 43.3954 | − | 4.45699i | 1.42838 | − | 0.146703i | ||||
\(924\) | 3.91360 | − | 0.0641298i | 0.128748 | − | 0.00210971i | ||||
\(925\) | −38.9674 | + | 38.9674i | −1.28124 | + | 1.28124i | ||||
\(926\) | 15.2737 | 0.501924 | ||||||||
\(927\) | 12.1497 | 0.399050 | ||||||||
\(928\) | −5.08818 | + | 5.08818i | −0.167028 | + | 0.167028i | ||||
\(929\) | 23.0704 | + | 23.0704i | 0.756914 | + | 0.756914i | 0.975760 | − | 0.218845i | \(-0.0702290\pi\) |
−0.218845 | + | 0.975760i | \(0.570229\pi\) | |||||||
\(930\) | −25.5674 | + | 25.5674i | −0.838387 | + | 0.838387i | ||||
\(931\) | 7.50356 | − | 8.01219i | 0.245919 | − | 0.262589i | ||||
\(932\) | −2.70158 | −0.0884932 | ||||||||
\(933\) | 6.55258i | 0.214522i | ||||||||
\(934\) | 12.2875 | − | 12.2875i | 0.402061 | − | 0.402061i | ||||
\(935\) | 28.7772i | 0.941115i | ||||||||
\(936\) | 1.13204 | + | 11.0221i | 0.0370020 | + | 0.360269i | ||||
\(937\) | − | 23.9494i | − | 0.782391i | −0.920308 | − | 0.391196i | \(-0.872062\pi\) | ||
0.920308 | − | 0.391196i | \(-0.127938\pi\) | |||||||
\(938\) | 25.2566 | + | 24.4422i | 0.824657 | + | 0.798067i | ||||
\(939\) | −27.9268 | −0.911357 | ||||||||
\(940\) | 16.7235i | 0.545462i | ||||||||
\(941\) | −35.7947 | − | 35.7947i | −1.16687 | − | 1.16687i | −0.982938 | − | 0.183935i | \(-0.941116\pi\) |
−0.183935 | − | 0.982938i | \(-0.558884\pi\) | |||||||
\(942\) | −0.293034 | + | 0.293034i | −0.00954758 | + | 0.00954758i | ||||
\(943\) | 1.74867 | − | 1.74867i | 0.0569446 | − | 0.0569446i | ||||
\(944\) | 16.4574 | − | 16.4574i | 0.535642 | − | 0.535642i | ||||
\(945\) | −0.174758 | − | 10.6648i | −0.00568487 | − | 0.346927i | ||||
\(946\) | − | 23.7516i | − | 0.772232i | ||||||
\(947\) | 24.7804 | + | 24.7804i | 0.805256 | + | 0.805256i | 0.983912 | − | 0.178656i | \(-0.0571748\pi\) |
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(948\) | 7.53023 | 0.244570 | ||||||||
\(949\) | 34.2155 | − | 3.51415i | 1.11068 | − | 0.114074i | ||||
\(950\) | − | 19.6289i | − | 0.636845i | ||||||
\(951\) | −5.67885 | − | 5.67885i | −0.184149 | − | 0.184149i | ||||
\(952\) | −29.9153 | + | 0.490203i | −0.969559 | + | 0.0158876i | ||||
\(953\) | 45.1262i | 1.46178i | 0.682494 | + | 0.730891i | \(0.260895\pi\) | ||||
−0.682494 | + | 0.730891i | \(0.739105\pi\) | |||||||
\(954\) | −0.723093 | + | 0.723093i | −0.0234110 | + | 0.0234110i | ||||
\(955\) | 0.340733 | + | 0.340733i | 0.0110259 | + | 0.0110259i | ||||
\(956\) | −13.1204 | − | 13.1204i | −0.424344 | − | 0.424344i | ||||
\(957\) | 2.44283 | − | 2.44283i | 0.0789654 | − | 0.0789654i | ||||
\(958\) | − | 12.3639i | − | 0.399459i | ||||||
\(959\) | −43.5740 | + | 0.714019i | −1.40708 | + | 0.0230569i | ||||
\(960\) | 23.6049 | + | 23.6049i | 0.761844 | + | 0.761844i | ||||
\(961\) | 34.0109i | 1.09713i | ||||||||
\(962\) | −15.2350 | − | 12.3970i | −0.491195 | − | 0.399695i | ||||
\(963\) | 14.3968 | 0.463932 | ||||||||
\(964\) | −5.05103 | − | 5.05103i | −0.162683 | − | 0.162683i | ||||
\(965\) | − | 48.6364i | − | 1.56566i | ||||||
\(966\) | 0.0315254 | + | 1.92388i | 0.00101431 | + | 0.0618998i | ||||
\(967\) | 14.6545 | − | 14.6545i | 0.471257 | − | 0.471257i | −0.431065 | − | 0.902321i | \(-0.641862\pi\) |
0.902321 | + | 0.431065i | \(0.141862\pi\) | |||||||
\(968\) | −15.7264 | + | 15.7264i | −0.505464 | + | 0.505464i | ||||
\(969\) | −4.08045 | + | 4.08045i | −0.131083 | + | 0.131083i | ||||
\(970\) | 3.84338 | + | 3.84338i | 0.123403 | + | 0.123403i | ||||
\(971\) | − | 44.5224i | − | 1.42879i | −0.699742 | − | 0.714396i | \(-0.746702\pi\) | ||
0.699742 | − | 0.714396i | \(-0.253298\pi\) | |||||||
\(972\) | 0.762660 | 0.0244623 | ||||||||
\(973\) | 4.03491 | + | 3.90480i | 0.129353 | + | 0.125182i | ||||
\(974\) | − | 41.6312i | − | 1.33395i | ||||||
\(975\) | 31.4699 | + | 25.6077i | 1.00784 | + | 0.820103i | ||||
\(976\) | 11.2245i | 0.359287i | ||||||||
\(977\) | −0.515539 | + | 0.515539i | −0.0164935 | + | 0.0164935i | −0.715305 | − | 0.698812i | \(-0.753712\pi\) |
0.698812 | + | 0.715305i | \(0.253712\pi\) | |||||||
\(978\) | 6.74376i | 0.215642i | ||||||||
\(979\) | 13.5677 | 0.433626 | ||||||||
\(980\) | 15.7091 | + | 14.7119i | 0.501810 | + | 0.469954i | ||||
\(981\) | −11.6047 | + | 11.6047i | −0.370509 | + | 0.370509i | ||||
\(982\) | 32.5669 | + | 32.5669i | 1.03925 | + | 1.03925i | ||||
\(983\) | −16.5350 | + | 16.5350i | −0.527386 | + | 0.527386i | −0.919792 | − | 0.392406i | \(-0.871643\pi\) |
0.392406 | + | 0.919792i | \(0.371643\pi\) | |||||||
\(984\) | −11.6239 | −0.370557 | ||||||||
\(985\) | 81.5473 | 2.59831 | ||||||||
\(986\) | −5.15481 | + | 5.15481i | −0.164163 | + | 0.164163i | ||||
\(987\) | 14.3888 | − | 0.235780i | 0.458001 | − | 0.00750498i | ||||
\(988\) | −4.28961 | + | 0.440570i | −0.136471 | + | 0.0140164i | ||||
\(989\) | −7.19675 | −0.228843 | ||||||||
\(990\) | −6.15103 | − | 6.15103i | −0.195492 | − | 0.195492i | ||||
\(991\) | −35.2705 | −1.12040 | −0.560202 | − | 0.828356i | \(-0.689277\pi\) | ||||
−0.560202 | + | 0.828356i | \(0.689277\pi\) | |||||||
\(992\) | 32.5775 | 1.03434 | ||||||||
\(993\) | 4.44838 | + | 4.44838i | 0.141165 | + | 0.141165i | ||||
\(994\) | −25.5876 | − | 24.7625i | −0.811589 | − | 0.785420i | ||||
\(995\) | −6.63146 | − | 6.63146i | −0.210232 | − | 0.210232i | ||||
\(996\) | −6.64671 | − | 6.64671i | −0.210609 | − | 0.210609i | ||||
\(997\) | − | 60.2109i | − | 1.90690i | −0.301554 | − | 0.953449i | \(-0.597505\pi\) | ||
0.301554 | − | 0.953449i | \(-0.402495\pi\) | |||||||
\(998\) | 27.0000i | 0.854669i | ||||||||
\(999\) | −3.46293 | + | 3.46293i | −0.109562 | + | 0.109562i |
(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 | 273.2.p.f.265.3 | yes | 12 | |
3.2 | odd | 2 | 819.2.y.f.811.4 | 12 | |||
7.6 | odd | 2 | 273.2.p.e.265.3 | yes | 12 | ||
13.8 | odd | 4 | 273.2.p.e.34.3 | ✓ | 12 | ||
21.20 | even | 2 | 819.2.y.g.811.4 | 12 | |||
39.8 | even | 4 | 819.2.y.g.307.4 | 12 | |||
91.34 | even | 4 | inner | 273.2.p.f.34.3 | yes | 12 | |
273.125 | odd | 4 | 819.2.y.f.307.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.p.e.34.3 | ✓ | 12 | 13.8 | odd | 4 | ||
273.2.p.e.265.3 | yes | 12 | 7.6 | odd | 2 | ||
273.2.p.f.34.3 | yes | 12 | 91.34 | even | 4 | inner | |
273.2.p.f.265.3 | yes | 12 | 1.1 | even | 1 | trivial | |
819.2.y.f.307.4 | 12 | 273.125 | odd | 4 | |||
819.2.y.f.811.4 | 12 | 3.2 | odd | 2 | |||
819.2.y.g.307.4 | 12 | 39.8 | even | 4 | |||
819.2.y.g.811.4 | 12 | 21.20 | even | 2 |