Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1920,2,Mod(481,1920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1920, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1920.481");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1920 = 2^{7} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1920.s (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: | \(15.3312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 481.10 | ||
Root | \(1.18701 + 0.768775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1920.481 |
Dual form | 1920.2.s.f.1441.6 |
$q$-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 \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(641\) | \(901\) | \(1537\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.92824i | 1.86270i | 0.364127 | + | 0.931349i | \(0.381368\pi\) | ||||
−0.364127 | + | 0.931349i | \(0.618632\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.45868 | + | 2.45868i | 0.741321 | + | 0.741321i | 0.972832 | − | 0.231511i | \(-0.0743669\pi\) |
−0.231511 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93127 | − | 2.93127i | 0.812987 | − | 0.812987i | −0.172093 | − | 0.985081i | \(-0.555053\pi\) |
0.985081 | + | 0.172093i | \(0.0550531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.77716 | −1.40117 | −0.700584 | − | 0.713570i | \(-0.747077\pi\) | ||||
−0.700584 | + | 0.713570i | \(0.747077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.984104 | + | 0.984104i | −0.225769 | + | 0.225769i | −0.810922 | − | 0.585154i | \(-0.801034\pi\) |
0.585154 | + | 0.810922i | \(0.301034\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.48479 | + | 3.48479i | 0.760444 | + | 0.760444i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.539543i | 0.112502i | 0.998417 | + | 0.0562512i | \(0.0179148\pi\) | ||||
−0.998417 | + | 0.0562512i | \(0.982085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.81092 | + | 6.81092i | −1.26476 | + | 1.26476i | −0.315995 | + | 0.948761i | \(0.602338\pi\) |
−0.948761 | + | 0.315995i | \(0.897662\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.63175 | 0.472677 | 0.236338 | − | 0.971671i | \(-0.424053\pi\) | ||||
0.236338 | + | 0.971671i | \(0.424053\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.47711 | 0.605286 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.48479 | − | 3.48479i | 0.589037 | − | 0.589037i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00637 | + | 6.00637i | 0.987441 | + | 0.987441i | 0.999922 | − | 0.0124815i | \(-0.00397308\pi\) |
−0.0124815 | + | 0.999922i | \(0.503973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 4.14544i | − | 0.663801i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.17728i | 0.808555i | 0.914636 | + | 0.404277i | \(0.132477\pi\) | ||||
−0.914636 | + | 0.404277i | \(0.867523\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.180211 | − | 0.180211i | −0.0274819 | − | 0.0274819i | 0.693232 | − | 0.720714i | \(-0.256186\pi\) |
−0.720714 | + | 0.693232i | \(0.756186\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.707107 | + | 0.707107i | −0.105409 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.57785 | −0.813613 | −0.406806 | − | 0.913514i | \(-0.633358\pi\) | ||||
−0.406806 | + | 0.913514i | \(0.633358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.2875 | −2.46965 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.08507 | + | 4.08507i | −0.572024 | + | 0.572024i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.146862 | + | 0.146862i | 0.0201730 | + | 0.0201730i | 0.717121 | − | 0.696948i | \(-0.245459\pi\) |
−0.696948 | + | 0.717121i | \(0.745459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.47711i | − | 0.468853i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.39173i | 0.184340i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.13789 | + | 3.13789i | 0.408518 | + | 0.408518i | 0.881221 | − | 0.472704i | \(-0.156722\pi\) |
−0.472704 | + | 0.881221i | \(0.656722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.87356 | − | 1.87356i | 0.239884 | − | 0.239884i | −0.576918 | − | 0.816802i | \(-0.695745\pi\) |
0.816802 | + | 0.576918i | \(0.195745\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.92824 | 0.620900 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.14544 | −0.514178 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.02582 | − | 8.02582i | 0.980510 | − | 0.980510i | −0.0193039 | − | 0.999814i | \(-0.506145\pi\) |
0.999814 | + | 0.0193039i | \(0.00614500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.381514 | + | 0.381514i | 0.0459289 | + | 0.0459289i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.40711i | 0.879062i | 0.898227 | + | 0.439531i | \(0.144855\pi\) | ||||
−0.898227 | + | 0.439531i | \(0.855145\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1715i | 1.30753i | 0.756699 | + | 0.653763i | \(0.226811\pi\) | ||||
−0.756699 | + | 0.653763i | \(0.773189\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.707107 | + | 0.707107i | 0.0816497 | + | 0.0816497i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.1170 | + | 12.1170i | −1.38086 | + | 1.38086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.71759 | −0.868297 | −0.434148 | − | 0.900841i | \(-0.642951\pi\) | ||||
−0.434148 | + | 0.900841i | \(0.642951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.62773 | + | 1.62773i | −0.178666 | + | 0.178666i | −0.790774 | − | 0.612108i | \(-0.790322\pi\) |
0.612108 | + | 0.790774i | \(0.290322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.08507 | + | 4.08507i | 0.443088 | + | 0.443088i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.63209i | 1.03267i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.54484i | 1.01175i | 0.862607 | + | 0.505875i | \(0.168830\pi\) | ||||
−0.862607 | + | 0.505875i | \(0.831170\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.4460 | + | 14.4460i | 1.51435 | + | 1.51435i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.86093 | − | 1.86093i | 0.192969 | − | 0.192969i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.39173 | 0.142789 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.39090 | 0.445828 | 0.222914 | − | 0.974838i | \(-0.428443\pi\) | ||||
0.222914 | + | 0.974838i | \(0.428443\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.45868 | − | 2.45868i | 0.247107 | − | 0.247107i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.1289 | − | 10.1289i | −1.00787 | − | 1.00787i | −0.999969 | − | 0.00789816i | \(-0.997486\pi\) |
−0.00789816 | − | 0.999969i | \(-0.502514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.89734i | 0.975214i | 0.873063 | + | 0.487607i | \(0.162130\pi\) | ||||
−0.873063 | + | 0.487607i | \(0.837870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 4.92824i | − | 0.480947i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.45556 | + | 5.45556i | 0.527409 | + | 0.527409i | 0.919799 | − | 0.392390i | \(-0.128352\pi\) |
−0.392390 | + | 0.919799i | \(0.628352\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.08344 | − | 6.08344i | 0.582687 | − | 0.582687i | −0.352953 | − | 0.935641i | \(-0.614823\pi\) |
0.935641 | + | 0.352953i | \(0.114823\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.49429 | 0.806242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.60003 | 0.714951 | 0.357475 | − | 0.933923i | \(-0.383638\pi\) | ||||
0.357475 | + | 0.933923i | \(0.383638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.381514 | − | 0.381514i | 0.0355764 | − | 0.0355764i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.93127 | − | 2.93127i | −0.270996 | − | 0.270996i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 28.4712i | − | 2.60995i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.09026i | 0.0991146i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.66089 | + | 3.66089i | 0.330091 | + | 0.330091i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.0209 | 1.51036 | 0.755179 | − | 0.655519i | \(-0.227550\pi\) | ||||
0.755179 | + | 0.655519i | \(0.227550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.254857 | −0.0224389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.449639 | + | 0.449639i | −0.0392851 | + | 0.0392851i | −0.726476 | − | 0.687191i | \(-0.758843\pi\) |
0.687191 | + | 0.726476i | \(0.258843\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.84990 | − | 4.84990i | −0.420540 | − | 0.420540i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 9.66718i | − | 0.825923i | −0.910749 | − | 0.412961i | \(-0.864494\pi\) | ||
0.910749 | − | 0.412961i | \(-0.135506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.08375 | + | 8.08375i | 0.685655 | + | 0.685655i | 0.961268 | − | 0.275614i | \(-0.0888810\pi\) |
−0.275614 | + | 0.961268i | \(0.588881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.94413 | + | 3.94413i | −0.332156 | + | 0.332156i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4141 | 1.20537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.63209 | 0.799902 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.2241 | + | 12.2241i | −1.00823 | + | 1.00823i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.28504 | + | 5.28504i | 0.432968 | + | 0.432968i | 0.889637 | − | 0.456669i | \(-0.150958\pi\) |
−0.456669 | + | 0.889637i | \(0.650958\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8929i | 0.886451i | 0.896410 | + | 0.443226i | \(0.146166\pi\) | ||||
−0.896410 | + | 0.443226i | \(0.853834\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.77716i | 0.467056i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.86093 | − | 1.86093i | −0.149473 | − | 0.149473i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.56692 | + | 7.56692i | −0.603906 | + | 0.603906i | −0.941347 | − | 0.337441i | \(-0.890439\pi\) |
0.337441 | + | 0.941347i | \(0.390439\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.207694 | 0.0164712 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.65899 | −0.209558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.60466 | − | 8.60466i | 0.673969 | − | 0.673969i | −0.284660 | − | 0.958629i | \(-0.591881\pi\) |
0.958629 | + | 0.284660i | \(0.0918807\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.45868 | − | 2.45868i | −0.191408 | − | 0.191408i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.53289i | − | 0.737677i | −0.929494 | − | 0.368838i | \(-0.879756\pi\) | ||
0.929494 | − | 0.368838i | \(-0.120244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.18465i | − | 0.321896i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.984104 | + | 0.984104i | 0.0752563 | + | 0.0752563i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.20532 | − | 7.20532i | 0.547810 | − | 0.547810i | −0.377997 | − | 0.925807i | \(-0.623387\pi\) |
0.925807 | + | 0.377997i | \(0.123387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.92824 | −0.372540 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.43764 | 0.333553 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.48245 | − | 4.48245i | 0.335034 | − | 0.335034i | −0.519461 | − | 0.854494i | \(-0.673867\pi\) |
0.854494 | + | 0.519461i | \(0.173867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3260 | − | 16.3260i | −1.21350 | − | 1.21350i | −0.969867 | − | 0.243636i | \(-0.921660\pi\) |
−0.243636 | − | 0.969867i | \(-0.578340\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.64961i | − | 0.195865i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 8.49429i | − | 0.624512i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.2042 | − | 14.2042i | −1.03872 | − | 1.03872i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.48479 | − | 3.48479i | 0.253481 | − | 0.253481i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00369 | 0.434412 | 0.217206 | − | 0.976126i | \(-0.430306\pi\) | ||||
0.217206 | + | 0.976126i | \(0.430306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6641 | 1.12753 | 0.563763 | − | 0.825937i | \(-0.309353\pi\) | ||||
0.563763 | + | 0.825937i | \(0.309353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.93127 | + | 2.93127i | −0.209912 | + | 0.209912i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.5309 | − | 10.5309i | −0.750299 | − | 0.750299i | 0.224236 | − | 0.974535i | \(-0.428011\pi\) |
−0.974535 | + | 0.224236i | \(0.928011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4667i | 1.80528i | 0.430393 | + | 0.902642i | \(0.358375\pi\) | ||||
−0.430393 | + | 0.902642i | \(0.641625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 11.3502i | − | 0.800583i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −33.5658 | − | 33.5658i | −2.35586 | − | 2.35586i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.66089 | − | 3.66089i | 0.255687 | − | 0.255687i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.539543 | 0.0375008 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.83920 | −0.334735 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.23633 | + | 1.23633i | −0.0851128 | + | 0.0851128i | −0.748381 | − | 0.663269i | \(-0.769169\pi\) |
0.663269 | + | 0.748381i | \(0.269169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.23762 | + | 5.23762i | 0.358876 | + | 0.358876i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.254857i | 0.0173811i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9699i | 0.880454i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.89945 | + | 7.89945i | 0.533796 | + | 0.533796i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.9344 | + | 16.9344i | −1.13913 | + | 1.13913i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3805 | −0.829061 | −0.414531 | − | 0.910035i | \(-0.636054\pi\) | ||||
−0.414531 | + | 0.910035i | \(0.636054\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.27494 | − | 2.27494i | 0.150993 | − | 0.150993i | −0.627568 | − | 0.778561i | \(-0.715950\pi\) |
0.778561 | + | 0.627568i | \(0.215950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.28770 | + | 9.28770i | 0.613749 | + | 0.613749i | 0.943921 | − | 0.330172i | \(-0.107107\pi\) |
−0.330172 | + | 0.943921i | \(0.607107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.1360i | 1.12747i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00671i | 0.459025i | 0.973306 | + | 0.229512i | \(0.0737131\pi\) | ||||
−0.973306 | + | 0.229512i | \(0.926287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.94413 | + | 3.94413i | 0.257287 | + | 0.257287i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.45716 | + | 5.45716i | −0.354481 | + | 0.354481i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.2607 | 1.31055 | 0.655276 | − | 0.755389i | \(-0.272552\pi\) | ||||
0.655276 | + | 0.755389i | \(0.272552\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.3806 | −1.44166 | −0.720831 | − | 0.693110i | \(-0.756240\pi\) | ||||
−0.720831 | + | 0.693110i | \(0.756240\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2241 | + | 12.2241i | 0.780971 | + | 0.780971i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.76934i | 0.367094i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.30195i | 0.145880i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.8288 | − | 15.8288i | −0.999108 | − | 0.999108i | 0.000891670 | − | 1.00000i | \(-0.499716\pi\) |
−1.00000 | 0.000891670i | \(0.999716\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.32657 | + | 1.32657i | −0.0834004 | + | 0.0834004i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.77716 | 0.361780 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.4018 | −1.33501 | −0.667503 | − | 0.744607i | \(-0.732637\pi\) | ||||
−0.667503 | + | 0.744607i | \(0.732637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.6008 | + | 29.6008i | −1.83930 | + | 1.83930i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.81092 | + | 6.81092i | 0.421585 | + | 0.421585i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 29.4331i | − | 1.81493i | −0.420133 | − | 0.907463i | \(-0.638016\pi\) | ||
0.420133 | − | 0.907463i | \(-0.361984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.207694i | − | 0.0127585i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.74922 | + | 6.74922i | 0.413046 | + | 0.413046i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.28110 | + | 4.28110i | −0.261023 | + | 0.261023i | −0.825470 | − | 0.564446i | \(-0.809090\pi\) |
0.564446 | + | 0.825470i | \(0.309090\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0914 | 0.855989 | 0.427995 | − | 0.903781i | \(-0.359220\pi\) | ||||
0.427995 | + | 0.903781i | \(0.359220\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.4297 | 1.23646 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.45868 | + | 2.45868i | −0.148264 | + | 0.148264i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.97589 | + | 7.97589i | 0.479225 | + | 0.479225i | 0.904884 | − | 0.425659i | \(-0.139958\pi\) |
−0.425659 | + | 0.904884i | \(0.639958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 2.63175i | − | 0.157559i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3.95952i | − | 0.236205i | −0.993001 | − | 0.118103i | \(-0.962319\pi\) | ||
0.993001 | − | 0.118103i | \(-0.0376812\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8192 | − | 14.8192i | −0.880912 | − | 0.880912i | 0.112716 | − | 0.993627i | \(-0.464045\pi\) |
−0.993627 | + | 0.112716i | \(0.964045\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.984104 | − | 0.984104i | 0.0582933 | − | 0.0582933i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.5148 | −1.50609 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3756 | 0.963270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.10483 | − | 3.10483i | 0.182009 | − | 0.182009i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.34880 | − | 3.34880i | −0.195639 | − | 0.195639i | 0.602488 | − | 0.798128i | \(-0.294176\pi\) |
−0.798128 | + | 0.602488i | \(0.794176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.43764i | − | 0.258369i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.47711i | − | 0.201762i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.58154 | + | 1.58154i | 0.0914630 | + | 0.0914630i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.888123 | − | 0.888123i | 0.0511906 | − | 0.0511906i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3245 | −0.822920 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.64961 | −0.151716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.58868 | − | 1.58868i | 0.0906710 | − | 0.0906710i | −0.660316 | − | 0.750987i | \(-0.729578\pi\) |
0.750987 | + | 0.660316i | \(0.229578\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.99848 | + | 6.99848i | 0.398129 | + | 0.398129i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.40357i | 0.533228i | 0.963803 | + | 0.266614i | \(0.0859049\pi\) | ||||
−0.963803 | + | 0.266614i | \(0.914095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.8228i | − | 1.34654i | −0.739396 | − | 0.673271i | \(-0.764889\pi\) | ||
0.739396 | − | 0.673271i | \(-0.235111\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.48479 | − | 3.48479i | −0.196346 | − | 0.196346i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2338 | − | 14.2338i | 0.799450 | − | 0.799450i | −0.183559 | − | 0.983009i | \(-0.558762\pi\) |
0.983009 | + | 0.183559i | \(0.0587618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.4918 | −1.87518 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.71532 | 0.430627 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.68533 | − | 5.68533i | 0.316340 | − | 0.316340i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.93127 | + | 2.93127i | 0.162597 | + | 0.162597i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.60328i | − | 0.475762i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 27.4890i | − | 1.51552i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.54040 | − | 7.54040i | −0.414458 | − | 0.414458i | 0.468831 | − | 0.883288i | \(-0.344676\pi\) |
−0.883288 | + | 0.468831i | \(0.844676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00637 | − | 6.00637i | 0.329147 | − | 0.329147i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.3502 | −0.620129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.57374 | 0.140201 | 0.0701004 | − | 0.997540i | \(-0.477668\pi\) | ||||
0.0701004 | + | 0.997540i | \(0.477668\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.37403 | − | 5.37403i | 0.291877 | − | 0.291877i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.47065 | + | 6.47065i | 0.350405 | + | 0.350405i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 50.6994i | − | 2.73751i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.539543i | − | 0.0290480i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.35992 | − | 1.35992i | −0.0730044 | − | 0.0730044i | 0.669662 | − | 0.742666i | \(-0.266439\pi\) |
−0.742666 | + | 0.669662i | \(0.766439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.76754 | + | 1.76754i | −0.0946143 | + | 0.0946143i | −0.752830 | − | 0.658215i | \(-0.771312\pi\) |
0.658215 | + | 0.752830i | \(0.271312\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.14544 | −0.221267 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.5420 | 0.880442 | 0.440221 | − | 0.897889i | \(-0.354900\pi\) | ||||
0.440221 | + | 0.897889i | \(0.354900\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.23762 | − | 5.23762i | 0.277984 | − | 0.277984i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.1322 | − | 20.1322i | −1.06551 | − | 1.06551i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.25343i | 0.435599i | 0.975993 | + | 0.217800i | \(0.0698880\pi\) | ||||
−0.975993 | + | 0.217800i | \(0.930112\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0631i | 0.898057i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.770930 | + | 0.770930i | 0.0404633 | + | 0.0404633i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.89945 | − | 7.89945i | 0.413476 | − | 0.413476i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.13754 | −0.320377 | −0.160188 | − | 0.987086i | \(-0.551210\pi\) | ||||
−0.160188 | + | 0.987086i | \(0.551210\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.17728 | 0.269518 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.723770 | + | 0.723770i | −0.0375763 | + | 0.0375763i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.29129 | − | 7.29129i | −0.377529 | − | 0.377529i | 0.492681 | − | 0.870210i | \(-0.336017\pi\) |
−0.870210 | + | 0.492681i | \(0.836017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.00000i | − | 0.0516398i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 39.9292i | 2.05646i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.6355 | + | 18.6355i | 0.957239 | + | 0.957239i | 0.999123 | − | 0.0418834i | \(-0.0133358\pi\) |
−0.0418834 | + | 0.999123i | \(0.513336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.0356 | − | 12.0356i | 0.616601 | − | 0.616601i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.03829 | −0.257445 | −0.128722 | − | 0.991681i | \(-0.541088\pi\) | ||||
−0.128722 | + | 0.991681i | \(0.541088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.1360 | 0.873332 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.180211 | + | 0.180211i | −0.00916065 | + | 0.00916065i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.6292 | − | 20.6292i | −1.04594 | − | 1.04594i | −0.998893 | − | 0.0470501i | \(-0.985018\pi\) |
−0.0470501 | − | 0.998893i | \(-0.514982\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.11703i | − | 0.157635i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.635885i | 0.0320762i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.45716 | + | 5.45716i | 0.274580 | + | 0.274580i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.8413 | − | 19.8413i | 0.995804 | − | 0.995804i | −0.00418691 | − | 0.999991i | \(-0.501333\pi\) |
0.999991 | + | 0.00418691i | \(0.00133274\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.85879 | −0.343369 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0994 | −1.15353 | −0.576764 | − | 0.816911i | \(-0.695685\pi\) | ||||
−0.576764 | + | 0.816911i | \(0.695685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.71437 | − | 7.71437i | 0.384280 | − | 0.384280i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.707107 | + | 0.707107i | 0.0351364 | + | 0.0351364i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.5355i | 1.46402i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.1354i | − | 0.896740i | −0.893848 | − | 0.448370i | \(-0.852005\pi\) | ||
0.893848 | − | 0.448370i | \(-0.147995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.83573 | − | 6.83573i | −0.337182 | − | 0.337182i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.4642 | + | 15.4642i | −0.760946 | + | 0.760946i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.30195 | 0.112998 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.4322 | 0.559835 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.63245 | + | 2.63245i | −0.128604 | + | 0.128604i | −0.768479 | − | 0.639875i | \(-0.778986\pi\) |
0.639875 | + | 0.768479i | \(0.278986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.09456 | − | 8.09456i | −0.394505 | − | 0.394505i | 0.481785 | − | 0.876290i | \(-0.339989\pi\) |
−0.876290 | + | 0.481785i | \(0.839989\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.57785i | 0.271204i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.77716i | − | 0.280234i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.23334 | + | 9.23334i | 0.446832 | + | 0.446832i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1923 | − | 10.1923i | 0.492090 | − | 0.492090i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.645299 | 0.0310829 | 0.0155415 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155415 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.0436 | −0.771005 | −0.385503 | − | 0.922707i | \(-0.625972\pi\) | ||||
−0.385503 | + | 0.922707i | \(0.625972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.81092 | − | 6.81092i | 0.326559 | − | 0.326559i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.530966 | − | 0.530966i | −0.0253996 | − | 0.0253996i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.81375i | 0.182020i | 0.995850 | + | 0.0910101i | \(0.0290096\pi\) | ||||
−0.995850 | + | 0.0910101i | \(0.970990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.2875i | 0.823216i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.79697 | − | 2.79697i | −0.132888 | − | 0.132888i | 0.637534 | − | 0.770422i | \(-0.279955\pi\) |
−0.770422 | + | 0.637534i | \(0.779955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.74922 | − | 6.74922i | 0.319944 | − | 0.319944i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.47418 | 0.353517 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.93839 | −0.138671 | −0.0693357 | − | 0.997593i | \(-0.522088\pi\) | ||||
−0.0693357 | + | 0.997593i | \(0.522088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.7293 | + | 12.7293i | −0.599399 | + | 0.599399i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.70244 | + | 7.70244i | 0.361892 | + | 0.361892i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 20.4297i | − | 0.957759i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 29.3145i | − | 1.37127i | −0.727944 | − | 0.685637i | \(-0.759524\pi\) | ||
0.727944 | − | 0.685637i | \(-0.240476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.08507 | + | 4.08507i | 0.190675 | + | 0.190675i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.24108 | + | 2.24108i | −0.104377 | + | 0.104377i | −0.757367 | − | 0.652989i | \(-0.773515\pi\) |
0.652989 | + | 0.757367i | \(0.273515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.7521 | 1.98686 | 0.993429 | − | 0.114452i | \(-0.0365113\pi\) | ||||
0.993429 | + | 0.114452i | \(0.0365113\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.63175 | −0.122045 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.8766 | + | 10.8766i | −0.503309 | + | 0.503309i | −0.912465 | − | 0.409155i | \(-0.865823\pi\) |
0.409155 | + | 0.912465i | \(0.365823\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.5531 | + | 39.5531i | 1.82639 | + | 1.82639i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.7012i | 0.493087i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.886165i | − | 0.0407459i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.984104 | − | 0.984104i | −0.0451538 | − | 0.0451538i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.146862 | − | 0.146862i | 0.00672434 | − | 0.00672434i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.5881 | −0.757932 | −0.378966 | − | 0.925411i | \(-0.623720\pi\) | ||||
−0.378966 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.2125 | 1.60555 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.88019 | + | 1.88019i | −0.0855517 | + | 0.0855517i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.10483 | − | 3.10483i | −0.140983 | − | 0.140983i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.8494i | − | 0.582260i | −0.956683 | − | 0.291130i | \(-0.905969\pi\) | ||
0.956683 | − | 0.291130i | \(-0.0940313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 12.1688i | − | 0.550293i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.2617 | + | 24.2617i | 1.09492 | + | 1.09492i | 0.994995 | + | 0.0999218i | \(0.0318593\pi\) |
0.0999218 | + | 0.994995i | \(0.468141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.3478 | − | 39.3478i | 1.77213 | − | 1.77213i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.47711 | −0.156284 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.5040 | −1.63743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.1785 | − | 27.1785i | 1.21667 | − | 1.21667i | 0.247886 | − | 0.968789i | \(-0.420264\pi\) |
0.968789 | − | 0.247886i | \(-0.0797357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.74077 | − | 6.74077i | −0.301155 | − | 0.301155i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.96618i | 0.132255i | 0.997811 | + | 0.0661276i | \(0.0210644\pi\) | ||||
−0.997811 | + | 0.0661276i | \(0.978936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.3245i | 0.637431i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.95899 | − | 2.95899i | −0.131414 | − | 0.131414i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.38314 | − | 3.38314i | 0.149955 | − | 0.149955i | −0.628143 | − | 0.778098i | \(-0.716185\pi\) |
0.778098 | + | 0.628143i | \(0.216185\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.0559 | −2.43553 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.39173 | 0.0614465 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.99848 | − | 6.99848i | 0.308390 | − | 0.308390i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7142 | − | 13.7142i | −0.603148 | − | 0.603148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.1899i | − | 0.447285i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.6801i | − | 0.862200i | −0.902304 | − | 0.431100i | \(-0.858126\pi\) | ||
0.902304 | − | 0.431100i | \(-0.141874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0799 | − | 20.0799i | −0.878031 | − | 0.878031i | 0.115300 | − | 0.993331i | \(-0.463217\pi\) |
−0.993331 | + | 0.115300i | \(0.963217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.48479 | + | 3.48479i | −0.152089 | + | 0.152089i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.2041 | −0.662299 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7089 | 0.987343 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.13789 | − | 3.13789i | 0.136173 | − | 0.136173i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.1760 | + | 15.1760i | 0.657344 | + | 0.657344i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.71532i | − | 0.333562i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 6.33914i | − | 0.273554i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −42.5046 | − | 42.5046i | −1.83080 | − | 1.83080i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3406 | + | 13.3406i | −0.573555 | + | 0.573555i | −0.933120 | − | 0.359565i | \(-0.882925\pi\) |
0.359565 | + | 0.933120i | \(0.382925\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.0885 | −0.990821 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.60328 | −0.368524 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.1198 | + | 28.1198i | −1.20231 | + | 1.20231i | −0.228854 | + | 0.973461i | \(0.573498\pi\) |
−0.973461 | + | 0.228854i | \(0.926502\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.87356 | − | 1.87356i | −0.0799615 | − | 0.0799615i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.4053i | − | 0.571085i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 38.0341i | − | 1.61738i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.00637 | − | 6.00637i | −0.254956 | − | 0.254956i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.3140 | − | 24.3140i | 1.03022 | − | 1.03022i | 0.0306885 | − | 0.999529i | \(-0.490230\pi\) |
0.999529 | − | 0.0306885i | \(-0.00977000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.05649 | −0.0446849 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.0878 | −0.848108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.7337 | − | 15.7337i | 0.663098 | − | 0.663098i | −0.293011 | − | 0.956109i | \(-0.594657\pi\) |
0.956109 | + | 0.293011i | \(0.0946574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.37403 | − | 5.37403i | −0.226087 | − | 0.226087i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.92824i | − | 0.206967i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.11372i | 0.214378i | 0.994239 | + | 0.107189i | \(0.0341851\pi\) | ||||
−0.994239 | + | 0.107189i | \(0.965815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.8788 | + | 17.8788i | 0.748203 | + | 0.748203i | 0.974142 | − | 0.225938i | \(-0.0725448\pi\) |
−0.225938 | + | 0.974142i | \(0.572545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.24525 | − | 4.24525i | 0.177348 | − | 0.177348i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.539543 | −0.0225005 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.02300 | 0.0425882 | 0.0212941 | − | 0.999773i | \(-0.493221\pi\) | ||||
0.0212941 | + | 0.999773i | \(0.493221\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.0762 | − | 11.0762i | 0.460310 | − | 0.460310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.02183 | − | 8.02183i | −0.332802 | − | 0.332802i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.722174i | 0.0299094i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.14544i | 0.171393i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.3088 | + | 27.3088i | 1.12716 | + | 1.12716i | 0.990637 | + | 0.136519i | \(0.0435915\pi\) |
0.136519 | + | 0.990637i | \(0.456409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.58992 | + | 2.58992i | −0.106716 | + | 0.106716i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.8930 | −0.612616 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.9492 | 0.901346 | 0.450673 | − | 0.892689i | \(-0.351184\pi\) | ||||
0.450673 | + | 0.892689i | \(0.351184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.1322 | + | 20.1322i | −0.825340 | + | 0.825340i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.0076 | + | 18.0076i | 0.737004 | + | 0.737004i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 0.802273i | − | 0.0327800i | −0.999866 | − | 0.0163900i | \(-0.994783\pi\) | ||
0.999866 | − | 0.0163900i | \(-0.00521733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1634i | 0.944853i | 0.881370 | + | 0.472427i | \(0.156622\pi\) | ||||
−0.881370 | + | 0.472427i | \(0.843378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.02582 | − | 8.02582i | −0.326837 | − | 0.326837i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.770930 | − | 0.770930i | 0.0313428 | − | 0.0313428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.0996 | 1.83054 | 0.915268 | − | 0.402846i | \(-0.131979\pi\) | ||||
0.915268 | + | 0.402846i | \(0.131979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −47.4692 | −1.92355 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.3502 | + | 16.3502i | −0.661457 | + | 0.661457i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.01756 | + | 7.01756i | 0.283437 | + | 0.283437i | 0.834478 | − | 0.551041i | \(-0.185769\pi\) |
−0.551041 | + | 0.834478i | \(0.685769\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 5.17728i | − | 0.208768i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.17606i | 0.0473465i | 0.999720 | + | 0.0236733i | \(0.00753614\pi\) | ||||
−0.999720 | + | 0.0236733i | \(0.992464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.8296 | − | 23.8296i | −0.957794 | − | 0.957794i | 0.0413509 | − | 0.999145i | \(-0.486834\pi\) |
−0.999145 | + | 0.0413509i | \(0.986834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.381514 | − | 0.381514i | 0.0153096 | − | 0.0153096i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −47.0392 | −1.88459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.42183 | + | 3.42183i | −0.136655 | + | 0.136655i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.6998 | − | 34.6998i | −1.38357 | − | 1.38357i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.89946i | 0.314473i | 0.987561 | + | 0.157236i | \(0.0502584\pi\) | ||||
−0.987561 | + | 0.157236i | \(0.949742\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.74844i | 0.0694943i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0356 | − | 12.0356i | −0.477617 | − | 0.477617i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −50.6744 | + | 50.6744i | −2.00779 | + | 2.00779i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.40711 | 0.293021 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.2986 | −1.23622 | −0.618111 | − | 0.786091i | \(-0.712102\pi\) | ||||
−0.618111 | + | 0.786091i | \(0.712102\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.7961 | − | 23.7961i | 0.938426 | − | 0.938426i | −0.0597853 | − | 0.998211i | \(-0.519042\pi\) |
0.998211 | + | 0.0597853i | \(0.0190416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.180211 | + | 0.180211i | 0.00709581 | + | 0.00709581i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 36.5905i | − | 1.43852i | −0.694741 | − | 0.719260i | \(-0.744481\pi\) | ||
0.694741 | − | 0.719260i | \(-0.255519\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.4301i | 0.605686i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.17110 | + | 9.17110i | 0.359444 | + | 0.359444i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9694 | − | 26.9694i | 1.05539 | − | 1.05539i | 0.0570212 | − | 0.998373i | \(-0.481840\pi\) |
0.998373 | − | 0.0570212i | \(-0.0181603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.635885 | 0.0248461 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1715 | 0.435842 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.4626 | − | 12.4626i | 0.485476 | − | 0.485476i | −0.421399 | − | 0.906875i | \(-0.638461\pi\) |
0.906875 | + | 0.421399i | \(0.138461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0063 | − | 15.0063i | −0.583676 | − | 0.583676i | 0.352236 | − | 0.935911i | \(-0.385422\pi\) |
−0.935911 | + | 0.352236i | \(0.885422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.9489i | 0.930097i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.85879i | 0.265973i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.67478 | − | 3.67478i | −0.142288 | − | 0.142288i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.75435 | + | 8.75435i | −0.338463 | + | 0.338463i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.21297 | 0.355663 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9004 | 0.458727 | 0.229364 | − | 0.973341i | \(-0.426335\pi\) | ||||
0.229364 | + | 0.973341i | \(0.426335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.707107 | − | 0.707107i | 0.0272166 | − | 0.0272166i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.6457 | + | 33.6457i | 1.29311 | + | 1.29311i | 0.932855 | + | 0.360253i | \(0.117310\pi\) |
0.360253 | + | 0.932855i | \(0.382690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21.6394i | 0.830443i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3.21725i | − | 0.123285i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.3777 | + | 18.3777i | 0.703203 | + | 0.703203i | 0.965097 | − | 0.261894i | \(-0.0843470\pi\) |
−0.261894 | + | 0.965097i | \(0.584347\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.83573 | + | 6.83573i | −0.261180 | + | 0.261180i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.1348 | 0.501124 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.860982 | 0.0328008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.774737 | − | 0.774737i | 0.0294724 | − | 0.0294724i | −0.692217 | − | 0.721689i | \(-0.743366\pi\) |
0.721689 | + | 0.692217i | \(0.243366\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.1170 | + | 12.1170i | 0.460286 | + | 0.460286i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11.4322i | − | 0.433646i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 29.9100i | − | 1.13292i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.95449 | + | 4.95449i | 0.187396 | + | 0.187396i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.34576 | + | 7.34576i | −0.277445 | + | 0.277445i | −0.832088 | − | 0.554643i | \(-0.812855\pi\) |
0.554643 | + | 0.832088i | \(0.312855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.8218 | −0.445867 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.57785 | 0.210074 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 49.9178 | − | 49.9178i | 1.87735 | − | 1.87735i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.80617 | − | 2.80617i | −0.105388 | − | 0.105388i | 0.652447 | − | 0.757835i | \(-0.273743\pi\) |
−0.757835 | + | 0.652447i | \(0.773743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.71759i | 0.289432i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.41994i | 0.0531773i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.1923 | − | 10.1923i | −0.381171 | − | 0.381171i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.3264 | − | 14.3264i | 0.535031 | − | 0.535031i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.1785 | 0.827118 | 0.413559 | − | 0.910477i | \(-0.364286\pi\) | ||||
0.413559 | + | 0.910477i | \(0.364286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.7764 | −1.81653 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.8255 | + | 15.8255i | −0.588556 | + | 0.588556i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.81092 | − | 6.81092i | −0.252951 | − | 0.252951i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0297i | 0.817038i | 0.912750 | + | 0.408519i | \(0.133955\pi\) | ||||
−0.912750 | + | 0.408519i | \(0.866045\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.04111 | + | 1.04111i | 0.0385068 | + | 0.0385068i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.6342 | + | 11.6342i | −0.429720 | + | 0.429720i | −0.888533 | − | 0.458813i | \(-0.848275\pi\) |
0.458813 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.2875 | 0.637660 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.4659 | 1.45375 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.97647 | + | 9.97647i | −0.366990 | + | 0.366990i | −0.866378 | − | 0.499388i | \(-0.833558\pi\) |
0.499388 | + | 0.866378i | \(0.333558\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.07954 | + | 4.07954i | 0.149866 | + | 0.149866i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9003i | 0.730073i | 0.930993 | + | 0.365036i | \(0.118943\pi\) | ||||
−0.930993 | + | 0.365036i | \(0.881057\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.47418i | − | 0.273833i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.62773 | + | 1.62773i | 0.0595554 | + | 0.0595554i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26.8863 | + | 26.8863i | −0.982403 | + | 0.982403i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.5710 | 1.51695 | 0.758473 | − | 0.651704i | \(-0.225946\pi\) | ||||
0.758473 | + | 0.651704i | \(0.225946\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.3854 | −0.815768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.70244 | − | 7.70244i | 0.280320 | − | 0.280320i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.0159 | − | 27.0159i | −0.981909 | − | 0.981909i | 0.0179307 | − | 0.999839i | \(-0.494292\pi\) |
−0.999839 | + | 0.0179307i | \(0.994292\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.87605i | 0.0680962i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.2812i | 0.553944i | 0.960878 | + | 0.276972i | \(0.0893309\pi\) | ||||
−0.960878 | + | 0.276972i | \(0.910669\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.9806 | + | 29.9806i | 1.08537 | + | 1.08537i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.08507 | − | 4.08507i | 0.147696 | − | 0.147696i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.3960 | 0.664240 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.9990 | −0.432694 | −0.216347 | − | 0.976317i | \(-0.569414\pi\) | ||||
−0.216347 | + | 0.976317i | \(0.569414\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.1333 | + | 15.1333i | −0.545014 | + | 0.545014i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.2957 | + | 19.2957i | 0.694020 | + | 0.694020i | 0.963114 | − | 0.269094i | \(-0.0867243\pi\) |
−0.269094 | + | 0.963114i | \(0.586724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.63175i | 0.0945353i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 41.8619i | 1.50179i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.09498 | − | 5.09498i | −0.182546 | − | 0.182546i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.2118 | + | 18.2118i | −0.651668 | + | 0.651668i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.63209 | 0.344223 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7012 | 0.381944 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.5668 | + | 26.5668i | −0.947006 | + | 0.947006i | −0.998665 | − | 0.0516592i | \(-0.983549\pi\) |
0.0516592 | + | 0.998665i | \(0.483549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.8124 | − | 20.8124i | −0.740940 | − | 0.740940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.4548i | 1.33174i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 10.9838i | − | 0.390046i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.146862 | − | 0.146862i | −0.00520865 | − | 0.00520865i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.94914 | − | 4.94914i | 0.175307 | − | 0.175307i | −0.613999 | − | 0.789307i | \(-0.710440\pi\) |
0.789307 | + | 0.613999i | \(0.210440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32.2241 | 1.14001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.54484 | 0.337250 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.4672 | + | 27.4672i | −0.969297 | + | 0.969297i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.88019 | + | 1.88019i | 0.0662681 | + | 0.0662681i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.05439i | 0.213125i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 26.1203i | − | 0.918339i | −0.888349 | − | 0.459170i | \(-0.848147\pi\) | ||
0.888349 | − | 0.459170i | \(-0.151853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.57185 | + | 7.57185i | 0.265884 | + | 0.265884i | 0.827439 | − | 0.561555i | \(-0.189797\pi\) |
−0.561555 | + | 0.827439i | \(0.689797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.96410 | − | 9.96410i | 0.349456 | − | 0.349456i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1688 | −0.426255 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.354693 | 0.0124091 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.4460 | − | 14.4460i | 0.504783 | − | 0.504783i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.4689 | + | 35.4689i | 1.23787 | + | 1.23787i | 0.960869 | + | 0.277004i | \(0.0893416\pi\) |
0.277004 | + | 0.960869i | \(0.410658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 18.2252i | − | 0.635290i | −0.948210 | − | 0.317645i | \(-0.897108\pi\) | ||
0.948210 | − | 0.317645i | \(-0.102892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.47711i | 0.121057i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.88954 | + | 6.88954i | 0.239573 | + | 0.239573i | 0.816673 | − | 0.577100i | \(-0.195816\pi\) |
−0.577100 | + | 0.816673i | \(0.695816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.07707 | − | 7.07707i | 0.245797 | − | 0.245797i | −0.573446 | − | 0.819243i | \(-0.694394\pi\) |
0.819243 | + | 0.573446i | \(0.194394\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2796 | 0.391286 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 99.8729 | 3.46039 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.74077 | + | 6.74077i | −0.233274 | + | 0.233274i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.86093 | − | 1.86093i | −0.0643231 | − | 0.0643231i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.0722i | 0.658445i | 0.944252 | + | 0.329223i | \(0.106787\pi\) | ||||
−0.944252 | + | 0.329223i | \(0.893213\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 63.7772i | − | 2.19921i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.79981 | − | 2.79981i | −0.0964304 | − | 0.0964304i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.95899 | + | 2.95899i | −0.101793 | + | 0.101793i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.37306 | −0.184621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.9576 | −0.719261 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.24069 | + | 3.24069i | −0.111089 | + | 0.111089i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.9330 | + | 19.9330i | 0.682494 | + | 0.682494i | 0.960562 | − | 0.278068i | \(-0.0896939\pi\) |
−0.278068 | + | 0.960562i | \(0.589694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.39173i | − | 0.0475963i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 32.3955i | − | 1.10661i | −0.832979 | − | 0.553304i | \(-0.813367\pi\) | ||
0.832979 | − | 0.553304i | \(-0.186633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5311 | + | 13.5311i | 0.461676 | + | 0.461676i | 0.899205 | − | 0.437529i | \(-0.144146\pi\) |
−0.437529 | + | 0.899205i | \(0.644146\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.0417 | + | 18.0417i | −0.614860 | + | 0.614860i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.8745 | 1.62967 | 0.814833 | − | 0.579695i | \(-0.196828\pi\) | ||||
0.814833 | + | 0.579695i | \(0.196828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.1899 | −0.346466 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.5793 | − | 11.5793i | 0.393254 | − | 0.393254i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9751 | − | 18.9751i | −0.643687 | − | 0.643687i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 47.0516i | − | 1.59428i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 4.39090i | − | 0.148609i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.48479 | + | 3.48479i | 0.117807 | + | 0.117807i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37481 | − | 2.37481i | 0.0801917 | − | 0.0801917i | −0.665873 | − | 0.746065i | \(-0.731941\pi\) |
0.746065 | + | 0.665873i | \(0.231941\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.73592 | −0.159739 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.1626 | 1.92586 | 0.962928 | − | 0.269759i | \(-0.0869442\pi\) | ||||
0.962928 | + | 0.269759i | \(0.0869442\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2888 | − | 12.2888i | 0.413550 | − | 0.413550i | −0.469423 | − | 0.882973i | \(-0.655538\pi\) |
0.882973 | + | 0.469423i | \(0.155538\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.13789 | − | 3.13789i | −0.105479 | − | 0.105479i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.1999i | 0.678248i | 0.940742 | + | 0.339124i | \(0.110131\pi\) | ||||
−0.940742 | + | 0.339124i | \(0.889869\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 83.8829i | 2.81334i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.45868 | − | 2.45868i | −0.0823690 | − | 0.0823690i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.48918 | − | 5.48918i | 0.183688 | − | 0.183688i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.33914 | −0.211894 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.23664 | 0.0746792 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.9246 | + | 17.9246i | −0.597820 | + | 0.597820i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.848444 | − | 0.848444i | −0.0282658 | − | 0.0282658i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.25600i | − | 0.0417969i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.0885i | 0.767486i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.76047 | + | 5.76047i | 0.191273 | + | 0.191273i | 0.796246 | − | 0.604973i | \(-0.206816\pi\) |
−0.604973 | + | 0.796246i | \(0.706816\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.1289 | + | 10.1289i | −0.335956 | + | 0.335956i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.5721 | −0.549057 | −0.274529 | − | 0.961579i | \(-0.588522\pi\) | ||||
−0.274529 | + | 0.961579i | \(0.588522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00414 | −0.264898 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.87356 | + | 1.87356i | −0.0619379 | + | 0.0619379i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.21593 | − | 2.21593i | −0.0731764 | − | 0.0731764i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13.0931i | − | 0.431903i | −0.976404 | − | 0.215952i | \(-0.930715\pi\) | ||
0.976404 | − | 0.215952i | \(-0.0692853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2.24674i | − | 0.0740325i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.7122 | + | 21.7122i | 0.714666 | + | 0.714666i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00637 | + | 6.00637i | −0.197488 | + | 0.197488i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.89734 | 0.325071 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.2834 | 0.567050 | 0.283525 | − | 0.958965i | \(-0.408496\pi\) | ||||
0.283525 | + | 0.958965i | \(0.408496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0127 | − | 17.0127i | 0.557570 | − | 0.557570i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.64933 | + | 6.64933i | 0.217689 | + | 0.217689i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.0878i | 0.656941i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8187i | 1.00680i | 0.864053 | + | 0.503401i | \(0.167918\pi\) | ||||
−0.864053 | + | 0.503401i | \(0.832082\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.8452 | − | 16.8452i | −0.549724 | − | 0.549724i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.2305 | − | 12.2305i | 0.398704 | − | 0.398704i | −0.479072 | − | 0.877776i | \(-0.659027\pi\) |
0.877776 | + | 0.479072i | \(0.159027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.79336 | −0.0909643 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.92824 | −0.160316 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.880251 | + | 0.880251i | −0.0286043 | + | 0.0286043i | −0.721264 | − | 0.692660i | \(-0.756439\pi\) |
0.692660 | + | 0.721264i | \(0.256439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7467 | + | 32.7467i | 1.06300 | + | 1.06300i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 20.1296i | − | 0.652748i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.7271i | 1.74039i | 0.492705 | + | 0.870196i | \(0.336008\pi\) | ||||
−0.492705 | + | 0.870196i | \(0.663992\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.24525 | − | 4.24525i | −0.137373 | − | 0.137373i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.6823 | + | 23.6823i | −0.765539 | + | 0.765539i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.6422 | 1.53845 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0739 | −0.776577 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.45556 | − | 5.45556i | 0.175803 | − | 0.175803i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.0762 | − | 11.0762i | −0.356555 | − | 0.356555i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.3769i | 1.49138i | 0.666294 | + | 0.745690i | \(0.267880\pi\) | ||||
−0.666294 | + | 0.745690i | \(0.732120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.04027i | − | 0.258291i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.7246 | − | 28.7246i | −0.921815 | − | 0.921815i | 0.0753424 | − | 0.997158i | \(-0.475995\pi\) |
−0.997158 | + | 0.0753424i | \(0.975995\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.8387 | + | 39.8387i | −1.27717 | + | 1.27717i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.14544 | 0.132760 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −60.6613 | −1.94073 | −0.970364 | − | 0.241648i | \(-0.922312\pi\) | ||||
−0.970364 | + | 0.241648i | \(0.922312\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4677 | + | 23.4677i | −0.750032 | + | 0.750032i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.08344 | − | 6.08344i | −0.194229 | − | 0.194229i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 9.61371i | − | 0.306630i | −0.988177 | − | 0.153315i | \(-0.951005\pi\) | ||
0.988177 | − | 0.153315i | \(-0.0489949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8930i | 0.474531i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.4376 | − | 19.4376i | −0.618707 | − | 0.618707i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.0972316 | − | 0.0972316i | 0.00309178 | − | 0.00309178i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.3622 | 0.900956 | 0.450478 | − | 0.892788i | \(-0.351254\pi\) | ||||
0.450478 | + | 0.892788i | \(0.351254\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6637 | −0.338403 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.0076 | − | 18.0076i | 0.570881 | − | 0.570881i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9440 | − | 17.9440i | −0.568293 | − | 0.568293i | 0.363357 | − | 0.931650i | \(-0.381630\pi\) |
−0.931650 | + | 0.363357i | \(0.881630\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.49429i | − | 0.268747i |
(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 | 1920.2.s.f.481.10 | 20 | ||
4.3 | odd | 2 | 1920.2.s.e.481.1 | 20 | |||
8.3 | odd | 2 | 240.2.s.c.181.8 | yes | 20 | ||
8.5 | even | 2 | 960.2.s.c.241.5 | 20 | |||
16.3 | odd | 4 | 1920.2.s.e.1441.5 | 20 | |||
16.5 | even | 4 | 960.2.s.c.721.1 | 20 | |||
16.11 | odd | 4 | 240.2.s.c.61.8 | ✓ | 20 | ||
16.13 | even | 4 | inner | 1920.2.s.f.1441.6 | 20 | ||
24.5 | odd | 2 | 2880.2.t.d.2161.5 | 20 | |||
24.11 | even | 2 | 720.2.t.d.181.3 | 20 | |||
48.5 | odd | 4 | 2880.2.t.d.721.1 | 20 | |||
48.11 | even | 4 | 720.2.t.d.541.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.8 | ✓ | 20 | 16.11 | odd | 4 | ||
240.2.s.c.181.8 | yes | 20 | 8.3 | odd | 2 | ||
720.2.t.d.181.3 | 20 | 24.11 | even | 2 | |||
720.2.t.d.541.3 | 20 | 48.11 | even | 4 | |||
960.2.s.c.241.5 | 20 | 8.5 | even | 2 | |||
960.2.s.c.721.1 | 20 | 16.5 | even | 4 | |||
1920.2.s.e.481.1 | 20 | 4.3 | odd | 2 | |||
1920.2.s.e.1441.5 | 20 | 16.3 | odd | 4 | |||
1920.2.s.f.481.10 | 20 | 1.1 | even | 1 | trivial | ||
1920.2.s.f.1441.6 | 20 | 16.13 | even | 4 | inner | ||
2880.2.t.d.721.1 | 20 | 48.5 | odd | 4 | |||
2880.2.t.d.2161.5 | 20 | 24.5 | odd | 2 |