Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.9 | ||
Root | \(0.500000 + 3.43554i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.b.2155.8 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 4.30156i | − | 1.92372i | −0.273546 | − | 0.961859i | \(-0.588197\pi\) | ||
0.273546 | − | 0.961859i | \(-0.411803\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.30156 | 1.36027 | ||||||||
\(11\) | 2.11424 | + | 2.55539i | 0.637466 | + | 0.770478i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −1.00074 | −0.277556 | −0.138778 | − | 0.990324i | \(-0.544317\pi\) | ||||
−0.138778 | + | 0.990324i | \(0.544317\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.30156 | −1.11066 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.33708 | −0.809361 | −0.404681 | − | 0.914458i | \(-0.632617\pi\) | ||||
−0.404681 | + | 0.914458i | \(0.632617\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 3.23111 | 0.741266 | 0.370633 | − | 0.928779i | \(-0.379141\pi\) | ||||
0.370633 | + | 0.928779i | \(0.379141\pi\) | |||||||
\(20\) | 4.30156i | 0.961859i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.55539 | + | 2.11424i | −0.544810 | + | 0.450757i | ||||
\(23\) | −5.72998 | −1.19478 | −0.597392 | − | 0.801950i | \(-0.703796\pi\) | ||||
−0.597392 | + | 0.801950i | \(0.703796\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −13.5035 | −2.70069 | ||||||||
\(26\) | − | 1.00074i | − | 0.196262i | ||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.74872i | − | 1.43890i | −0.694544 | − | 0.719450i | \(-0.744394\pi\) | ||
0.694544 | − | 0.719450i | \(-0.255606\pi\) | |||||||
\(30\) | − | 4.30156i | − | 0.785355i | ||||||
\(31\) | − | 3.20322i | − | 0.575315i | −0.957733 | − | 0.287657i | \(-0.907124\pi\) | ||
0.957733 | − | 0.287657i | \(-0.0928764\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.55539 | − | 2.11424i | 0.444836 | − | 0.368041i | ||||
\(34\) | − | 3.33708i | − | 0.572305i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.52944 | −0.415837 | −0.207918 | − | 0.978146i | \(-0.566669\pi\) | ||||
−0.207918 | + | 0.978146i | \(0.566669\pi\) | |||||||
\(38\) | 3.23111i | 0.524154i | ||||||||
\(39\) | 1.00074i | 0.160247i | ||||||||
\(40\) | −4.30156 | −0.680137 | ||||||||
\(41\) | −1.45111 | −0.226625 | −0.113313 | − | 0.993559i | \(-0.536146\pi\) | ||||
−0.113313 | + | 0.993559i | \(0.536146\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14572i | 0.632216i | 0.948723 | + | 0.316108i | \(0.102376\pi\) | ||||
−0.948723 | + | 0.316108i | \(0.897624\pi\) | |||||||
\(44\) | −2.11424 | − | 2.55539i | −0.318733 | − | 0.385239i | ||||
\(45\) | 4.30156i | 0.641239i | ||||||||
\(46\) | − | 5.72998i | − | 0.844840i | ||||||
\(47\) | − | 3.20101i | − | 0.466915i | −0.972367 | − | 0.233458i | \(-0.924996\pi\) | ||
0.972367 | − | 0.233458i | \(-0.0750040\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 13.5035i | − | 1.90968i | ||||||
\(51\) | 3.33708i | 0.467285i | ||||||||
\(52\) | 1.00074 | 0.138778 | ||||||||
\(53\) | −11.3155 | −1.55430 | −0.777150 | − | 0.629315i | \(-0.783336\pi\) | ||||
−0.777150 | + | 0.629315i | \(0.783336\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 10.9922 | − | 9.09452i | 1.48218 | − | 1.22631i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.23111i | − | 0.427970i | ||||||
\(58\) | 7.74872 | 1.01746 | ||||||||
\(59\) | 3.44231i | 0.448151i | 0.974572 | + | 0.224075i | \(0.0719362\pi\) | ||||
−0.974572 | + | 0.224075i | \(0.928064\pi\) | |||||||
\(60\) | 4.30156 | 0.555330 | ||||||||
\(61\) | 14.8504 | 1.90140 | 0.950702 | − | 0.310106i | \(-0.100365\pi\) | ||||
0.950702 | + | 0.310106i | \(0.100365\pi\) | |||||||
\(62\) | 3.20322 | 0.406809 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.30476i | 0.533940i | ||||||||
\(66\) | 2.11424 | + | 2.55539i | 0.260245 | + | 0.314546i | ||||
\(67\) | −0.330392 | −0.0403638 | −0.0201819 | − | 0.999796i | \(-0.506425\pi\) | ||||
−0.0201819 | + | 0.999796i | \(0.506425\pi\) | |||||||
\(68\) | 3.33708 | 0.404681 | ||||||||
\(69\) | 5.72998i | 0.689809i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.84974 | 0.338201 | 0.169101 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169101 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −14.8958 | −1.74342 | −0.871710 | − | 0.490022i | \(-0.836989\pi\) | ||||
−0.871710 | + | 0.490022i | \(0.836989\pi\) | |||||||
\(74\) | − | 2.52944i | − | 0.294041i | ||||||
\(75\) | 13.5035i | 1.55924i | ||||||||
\(76\) | −3.23111 | −0.370633 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00074 | −0.113312 | ||||||||
\(79\) | 16.0923i | 1.81052i | 0.424855 | + | 0.905261i | \(0.360325\pi\) | ||||
−0.424855 | + | 0.905261i | \(0.639675\pi\) | |||||||
\(80\) | − | 4.30156i | − | 0.480929i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 1.45111i | − | 0.160248i | ||||||
\(83\) | −1.75062 | −0.192155 | −0.0960777 | − | 0.995374i | \(-0.530630\pi\) | ||||
−0.0960777 | + | 0.995374i | \(0.530630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.3547i | 1.55698i | ||||||||
\(86\) | −4.14572 | −0.447044 | ||||||||
\(87\) | −7.74872 | −0.830750 | ||||||||
\(88\) | 2.55539 | − | 2.11424i | 0.272405 | − | 0.225378i | ||||
\(89\) | 2.78460i | 0.295167i | 0.989050 | + | 0.147583i | \(0.0471494\pi\) | ||||
−0.989050 | + | 0.147583i | \(0.952851\pi\) | |||||||
\(90\) | −4.30156 | −0.453425 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.72998 | 0.597392 | ||||||||
\(93\) | −3.20322 | −0.332158 | ||||||||
\(94\) | 3.20101 | 0.330159 | ||||||||
\(95\) | − | 13.8988i | − | 1.42599i | ||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − | 12.3347i | − | 1.25240i | −0.779661 | − | 0.626201i | \(-0.784609\pi\) | ||
0.779661 | − | 0.626201i | \(-0.215391\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.11424 | − | 2.55539i | −0.212489 | − | 0.256826i | ||||
\(100\) | 13.5035 | 1.35035 | ||||||||
\(101\) | 0.0562448 | 0.00559657 | 0.00279828 | − | 0.999996i | \(-0.499109\pi\) | ||||
0.00279828 | + | 0.999996i | \(0.499109\pi\) | |||||||
\(102\) | −3.33708 | −0.330420 | ||||||||
\(103\) | 14.7949i | 1.45779i | 0.684627 | + | 0.728893i | \(0.259965\pi\) | ||||
−0.684627 | + | 0.728893i | \(0.740035\pi\) | |||||||
\(104\) | 1.00074i | 0.0981309i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.3155i | − | 1.09906i | ||||||
\(107\) | − | 10.6139i | − | 1.02608i | −0.858364 | − | 0.513042i | \(-0.828519\pi\) | ||
0.858364 | − | 0.513042i | \(-0.171481\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 0.348204i | − | 0.0333519i | −0.999861 | − | 0.0166759i | \(-0.994692\pi\) | ||
0.999861 | − | 0.0166759i | \(-0.00530836\pi\) | |||||||
\(110\) | 9.09452 | + | 10.9922i | 0.867129 | + | 1.04806i | ||||
\(111\) | 2.52944i | 0.240084i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.9549 | −1.78313 | −0.891564 | − | 0.452895i | \(-0.850391\pi\) | ||||
−0.891564 | + | 0.452895i | \(0.850391\pi\) | |||||||
\(114\) | 3.23111 | 0.302621 | ||||||||
\(115\) | 24.6479i | 2.29843i | ||||||||
\(116\) | 7.74872i | 0.719450i | ||||||||
\(117\) | 1.00074 | 0.0925187 | ||||||||
\(118\) | −3.44231 | −0.316890 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.30156i | 0.392677i | ||||||||
\(121\) | −2.06001 | + | 10.8054i | −0.187273 | + | 0.982308i | ||||
\(122\) | 14.8504i | 1.34450i | ||||||||
\(123\) | 1.45111i | 0.130842i | ||||||||
\(124\) | 3.20322i | 0.287657i | ||||||||
\(125\) | 36.5781i | 3.27165i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 5.90909i | − | 0.524347i | −0.965021 | − | 0.262173i | \(-0.915561\pi\) | ||
0.965021 | − | 0.262173i | \(-0.0844392\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.14572 | 0.365010 | ||||||||
\(130\) | −4.30476 | −0.377552 | ||||||||
\(131\) | −12.1043 | −1.05756 | −0.528778 | − | 0.848760i | \(-0.677349\pi\) | ||||
−0.528778 | + | 0.848760i | \(0.677349\pi\) | |||||||
\(132\) | −2.55539 | + | 2.11424i | −0.222418 | + | 0.184021i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.330392i | − | 0.0285415i | ||||||
\(135\) | 4.30156 | 0.370220 | ||||||||
\(136\) | 3.33708i | 0.286152i | ||||||||
\(137\) | 9.89121 | 0.845063 | 0.422532 | − | 0.906348i | \(-0.361142\pi\) | ||||
0.422532 | + | 0.906348i | \(0.361142\pi\) | |||||||
\(138\) | −5.72998 | −0.487768 | ||||||||
\(139\) | 1.58746 | 0.134647 | 0.0673235 | − | 0.997731i | \(-0.478554\pi\) | ||||
0.0673235 | + | 0.997731i | \(0.478554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.20101 | −0.269574 | ||||||||
\(142\) | 2.84974i | 0.239145i | ||||||||
\(143\) | −2.11581 | − | 2.55729i | −0.176933 | − | 0.213851i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −33.3316 | −2.76804 | ||||||||
\(146\) | − | 14.8958i | − | 1.23278i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.52944 | 0.207918 | ||||||||
\(149\) | 17.0794i | 1.39920i | 0.714535 | + | 0.699599i | \(0.246638\pi\) | ||||
−0.714535 | + | 0.699599i | \(0.753362\pi\) | |||||||
\(150\) | −13.5035 | −1.10255 | ||||||||
\(151\) | − | 8.31552i | − | 0.676707i | −0.941019 | − | 0.338354i | \(-0.890130\pi\) | ||
0.941019 | − | 0.338354i | \(-0.109870\pi\) | |||||||
\(152\) | − | 3.23111i | − | 0.262077i | ||||||
\(153\) | 3.33708 | 0.269787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.7788 | −1.10674 | ||||||||
\(156\) | − | 1.00074i | − | 0.0801236i | ||||||
\(157\) | − | 1.25113i | − | 0.0998510i | −0.998753 | − | 0.0499255i | \(-0.984102\pi\) | ||
0.998753 | − | 0.0499255i | \(-0.0158984\pi\) | |||||||
\(158\) | −16.0923 | −1.28023 | ||||||||
\(159\) | 11.3155i | 0.897376i | ||||||||
\(160\) | 4.30156 | 0.340068 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 7.21571 | 0.565178 | 0.282589 | − | 0.959241i | \(-0.408807\pi\) | ||||
0.282589 | + | 0.959241i | \(0.408807\pi\) | |||||||
\(164\) | 1.45111 | 0.113313 | ||||||||
\(165\) | −9.09452 | − | 10.9922i | −0.708008 | − | 0.855739i | ||||
\(166\) | − | 1.75062i | − | 0.135874i | ||||||
\(167\) | −15.4393 | −1.19473 | −0.597364 | − | 0.801970i | \(-0.703785\pi\) | ||||
−0.597364 | + | 0.801970i | \(0.703785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9985 | −0.922963 | ||||||||
\(170\) | −14.3547 | −1.10095 | ||||||||
\(171\) | −3.23111 | −0.247089 | ||||||||
\(172\) | − | 4.14572i | − | 0.316108i | ||||||
\(173\) | −6.22042 | −0.472930 | −0.236465 | − | 0.971640i | \(-0.575989\pi\) | ||||
−0.236465 | + | 0.971640i | \(0.575989\pi\) | |||||||
\(174\) | − | 7.74872i | − | 0.587429i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.11424 | + | 2.55539i | 0.159367 | + | 0.192620i | ||||
\(177\) | 3.44231 | 0.258740 | ||||||||
\(178\) | −2.78460 | −0.208714 | ||||||||
\(179\) | 3.07893 | 0.230130 | 0.115065 | − | 0.993358i | \(-0.463292\pi\) | ||||
0.115065 | + | 0.993358i | \(0.463292\pi\) | |||||||
\(180\) | − | 4.30156i | − | 0.320620i | ||||||
\(181\) | − | 18.3243i | − | 1.36203i | −0.732268 | − | 0.681016i | \(-0.761538\pi\) | ||
0.732268 | − | 0.681016i | \(-0.238462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.8504i | − | 1.09778i | ||||||
\(184\) | 5.72998i | 0.422420i | ||||||||
\(185\) | 10.8805i | 0.799953i | ||||||||
\(186\) | − | 3.20322i | − | 0.234871i | ||||||
\(187\) | −7.05538 | − | 8.52753i | −0.515940 | − | 0.623595i | ||||
\(188\) | 3.20101i | 0.233458i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.8988 | 1.00833 | ||||||||
\(191\) | 20.8202 | 1.50650 | 0.753248 | − | 0.657736i | \(-0.228486\pi\) | ||||
0.753248 | + | 0.657736i | \(0.228486\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 4.51641i | 0.325099i | 0.986700 | + | 0.162549i | \(0.0519716\pi\) | ||||
−0.986700 | + | 0.162549i | \(0.948028\pi\) | |||||||
\(194\) | 12.3347 | 0.885583 | ||||||||
\(195\) | 4.30476 | 0.308270 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3563i | 1.23659i | 0.785947 | + | 0.618293i | \(0.212176\pi\) | ||||
−0.785947 | + | 0.618293i | \(0.787824\pi\) | |||||||
\(198\) | 2.55539 | − | 2.11424i | 0.181603 | − | 0.150252i | ||||
\(199\) | 7.81660i | 0.554104i | 0.960855 | + | 0.277052i | \(0.0893575\pi\) | ||||
−0.960855 | + | 0.277052i | \(0.910643\pi\) | |||||||
\(200\) | 13.5035i | 0.954838i | ||||||||
\(201\) | 0.330392i | 0.0233040i | ||||||||
\(202\) | 0.0562448i | 0.00395737i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 3.33708i | − | 0.233642i | ||||||
\(205\) | 6.24205i | 0.435963i | ||||||||
\(206\) | −14.7949 | −1.03081 | ||||||||
\(207\) | 5.72998 | 0.398261 | ||||||||
\(208\) | −1.00074 | −0.0693890 | ||||||||
\(209\) | 6.83132 | + | 8.25673i | 0.472532 | + | 0.571130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9923i | 1.51401i | 0.653406 | + | 0.757007i | \(0.273339\pi\) | ||||
−0.653406 | + | 0.757007i | \(0.726661\pi\) | |||||||
\(212\) | 11.3155 | 0.777150 | ||||||||
\(213\) | − | 2.84974i | − | 0.195261i | ||||||
\(214\) | 10.6139 | 0.725550 | ||||||||
\(215\) | 17.8331 | 1.21620 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.348204 | 0.0235833 | ||||||||
\(219\) | 14.8958i | 1.00656i | ||||||||
\(220\) | −10.9922 | + | 9.09452i | −0.741091 | + | 0.613153i | ||||
\(221\) | 3.33956 | 0.224643 | ||||||||
\(222\) | −2.52944 | −0.169765 | ||||||||
\(223\) | 8.30245i | 0.555973i | 0.960585 | + | 0.277987i | \(0.0896671\pi\) | ||||
−0.960585 | + | 0.277987i | \(0.910333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.5035 | 0.900230 | ||||||||
\(226\) | − | 18.9549i | − | 1.26086i | ||||||
\(227\) | 7.91253 | 0.525173 | 0.262587 | − | 0.964908i | \(-0.415424\pi\) | ||||
0.262587 | + | 0.964908i | \(0.415424\pi\) | |||||||
\(228\) | 3.23111i | 0.213985i | ||||||||
\(229\) | 10.7093i | 0.707688i | 0.935304 | + | 0.353844i | \(0.115126\pi\) | ||||
−0.935304 | + | 0.353844i | \(0.884874\pi\) | |||||||
\(230\) | −24.6479 | −1.62523 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.74872 | −0.508728 | ||||||||
\(233\) | − | 17.7106i | − | 1.16026i | −0.814525 | − | 0.580129i | \(-0.803002\pi\) | ||
0.814525 | − | 0.580129i | \(-0.196998\pi\) | |||||||
\(234\) | 1.00074i | 0.0654206i | ||||||||
\(235\) | −13.7693 | −0.898213 | ||||||||
\(236\) | − | 3.44231i | − | 0.224075i | ||||||
\(237\) | 16.0923 | 1.04531 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.6356i | − | 1.72291i | −0.507832 | − | 0.861456i | \(-0.669553\pi\) | ||
0.507832 | − | 0.861456i | \(-0.330447\pi\) | |||||||
\(240\) | −4.30156 | −0.277665 | ||||||||
\(241\) | 3.71041 | 0.239009 | 0.119504 | − | 0.992834i | \(-0.461869\pi\) | ||||
0.119504 | + | 0.992834i | \(0.461869\pi\) | |||||||
\(242\) | −10.8054 | − | 2.06001i | −0.694597 | − | 0.132422i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −14.8504 | −0.950702 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.45111 | −0.0925195 | ||||||||
\(247\) | −3.23351 | −0.205743 | ||||||||
\(248\) | −3.20322 | −0.203404 | ||||||||
\(249\) | 1.75062i | 0.110941i | ||||||||
\(250\) | −36.5781 | −2.31341 | ||||||||
\(251\) | − | 10.6948i | − | 0.675051i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.1145 | − | 14.6423i | −0.761634 | − | 0.920555i | ||||
\(254\) | 5.90909 | 0.370769 | ||||||||
\(255\) | 14.3547 | 0.898924 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 23.8220i | − | 1.48597i | −0.669305 | − | 0.742987i | \(-0.733408\pi\) | ||
0.669305 | − | 0.742987i | \(-0.266592\pi\) | |||||||
\(258\) | 4.14572i | 0.258101i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.30476i | − | 0.266970i | ||||||
\(261\) | 7.74872i | 0.479633i | ||||||||
\(262\) | − | 12.1043i | − | 0.747804i | ||||||
\(263\) | 17.0516i | 1.05145i | 0.850655 | + | 0.525725i | \(0.176206\pi\) | ||||
−0.850655 | + | 0.525725i | \(0.823794\pi\) | |||||||
\(264\) | −2.11424 | − | 2.55539i | −0.130122 | − | 0.157273i | ||||
\(265\) | 48.6743i | 2.99004i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.78460 | 0.170414 | ||||||||
\(268\) | 0.330392 | 0.0201819 | ||||||||
\(269\) | 9.61064i | 0.585971i | 0.956117 | + | 0.292986i | \(0.0946488\pi\) | ||||
−0.956117 | + | 0.292986i | \(0.905351\pi\) | |||||||
\(270\) | 4.30156i | 0.261785i | ||||||||
\(271\) | 5.11228 | 0.310549 | 0.155274 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155274 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(272\) | −3.33708 | −0.202340 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.89121i | 0.597550i | ||||||||
\(275\) | −28.5495 | − | 34.5066i | −1.72160 | − | 2.08082i | ||||
\(276\) | − | 5.72998i | − | 0.344904i | ||||||
\(277\) | 26.3274i | 1.58186i | 0.611906 | + | 0.790931i | \(0.290403\pi\) | ||||
−0.611906 | + | 0.790931i | \(0.709597\pi\) | |||||||
\(278\) | 1.58746i | 0.0952098i | ||||||||
\(279\) | 3.20322i | 0.191772i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.5684i | − | 0.630459i | −0.949015 | − | 0.315230i | \(-0.897918\pi\) | ||
0.949015 | − | 0.315230i | \(-0.102082\pi\) | |||||||
\(282\) | − | 3.20101i | − | 0.190617i | ||||||
\(283\) | −10.4076 | −0.618667 | −0.309333 | − | 0.950954i | \(-0.600106\pi\) | ||||
−0.309333 | + | 0.950954i | \(0.600106\pi\) | |||||||
\(284\) | −2.84974 | −0.169101 | ||||||||
\(285\) | −13.8988 | −0.823294 | ||||||||
\(286\) | 2.55729 | − | 2.11581i | 0.151215 | − | 0.125110i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −5.86389 | −0.344935 | ||||||||
\(290\) | − | 33.3316i | − | 1.95730i | ||||||
\(291\) | −12.3347 | −0.723075 | ||||||||
\(292\) | 14.8958 | 0.871710 | ||||||||
\(293\) | 31.4600 | 1.83792 | 0.918958 | − | 0.394356i | \(-0.129032\pi\) | ||||
0.918958 | + | 0.394356i | \(0.129032\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.8073 | 0.862116 | ||||||||
\(296\) | 2.52944i | 0.147021i | ||||||||
\(297\) | −2.55539 | + | 2.11424i | −0.148279 | + | 0.122680i | ||||
\(298\) | −17.0794 | −0.989383 | ||||||||
\(299\) | 5.73424 | 0.331620 | ||||||||
\(300\) | − | 13.5035i | − | 0.779622i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.31552 | 0.478504 | ||||||||
\(303\) | − | 0.0562448i | − | 0.00323118i | ||||||
\(304\) | 3.23111 | 0.185317 | ||||||||
\(305\) | − | 63.8801i | − | 3.65776i | ||||||
\(306\) | 3.33708i | 0.190768i | ||||||||
\(307\) | −18.4994 | −1.05582 | −0.527910 | − | 0.849301i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849301i | \(0.677024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7949 | 0.841653 | ||||||||
\(310\) | − | 13.7788i | − | 0.782585i | ||||||
\(311\) | − | 30.9979i | − | 1.75773i | −0.477073 | − | 0.878864i | \(-0.658302\pi\) | ||
0.477073 | − | 0.878864i | \(-0.341698\pi\) | |||||||
\(312\) | 1.00074 | 0.0566559 | ||||||||
\(313\) | − | 9.60149i | − | 0.542708i | −0.962480 | − | 0.271354i | \(-0.912529\pi\) | ||
0.962480 | − | 0.271354i | \(-0.0874714\pi\) | |||||||
\(314\) | 1.25113 | 0.0706053 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 16.0923i | − | 0.905261i | ||||||
\(317\) | −11.9425 | −0.670759 | −0.335379 | − | 0.942083i | \(-0.608864\pi\) | ||||
−0.335379 | + | 0.942083i | \(0.608864\pi\) | |||||||
\(318\) | −11.3155 | −0.634541 | ||||||||
\(319\) | 19.8010 | − | 16.3826i | 1.10864 | − | 0.917251i | ||||
\(320\) | 4.30156i | 0.240465i | ||||||||
\(321\) | −10.6139 | −0.592409 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.7825 | −0.599952 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 13.5135 | 0.749593 | ||||||||
\(326\) | 7.21571i | 0.399641i | ||||||||
\(327\) | −0.348204 | −0.0192557 | ||||||||
\(328\) | 1.45111i | 0.0801242i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.9922 | − | 9.09452i | 0.605099 | − | 0.500637i | ||||
\(331\) | 6.49162 | 0.356812 | 0.178406 | − | 0.983957i | \(-0.442906\pi\) | ||||
0.178406 | + | 0.983957i | \(0.442906\pi\) | |||||||
\(332\) | 1.75062 | 0.0960777 | ||||||||
\(333\) | 2.52944 | 0.138612 | ||||||||
\(334\) | − | 15.4393i | − | 0.844800i | ||||||
\(335\) | 1.42120i | 0.0776485i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.74869i | − | 0.313151i | −0.987666 | − | 0.156576i | \(-0.949955\pi\) | ||
0.987666 | − | 0.156576i | \(-0.0500455\pi\) | |||||||
\(338\) | − | 11.9985i | − | 0.652633i | ||||||
\(339\) | 18.9549i | 1.02949i | ||||||||
\(340\) | − | 14.3547i | − | 0.778491i | ||||||
\(341\) | 8.18546 | − | 6.77236i | 0.443267 | − | 0.366744i | ||||
\(342\) | − | 3.23111i | − | 0.174718i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.14572 | 0.223522 | ||||||||
\(345\) | 24.6479 | 1.32700 | ||||||||
\(346\) | − | 6.22042i | − | 0.334412i | ||||||
\(347\) | − | 14.6253i | − | 0.785125i | −0.919725 | − | 0.392563i | \(-0.871589\pi\) | ||
0.919725 | − | 0.392563i | \(-0.128411\pi\) | |||||||
\(348\) | 7.74872 | 0.415375 | ||||||||
\(349\) | −15.2458 | −0.816091 | −0.408046 | − | 0.912962i | \(-0.633790\pi\) | ||||
−0.408046 | + | 0.912962i | \(0.633790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.00074i | − | 0.0534157i | ||||||
\(352\) | −2.55539 | + | 2.11424i | −0.136203 | + | 0.112689i | ||||
\(353\) | − | 27.4483i | − | 1.46093i | −0.682952 | − | 0.730463i | \(-0.739304\pi\) | ||
0.682952 | − | 0.730463i | \(-0.260696\pi\) | |||||||
\(354\) | 3.44231i | 0.182957i | ||||||||
\(355\) | − | 12.2583i | − | 0.650604i | ||||||
\(356\) | − | 2.78460i | − | 0.147583i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.07893i | 0.162726i | ||||||||
\(359\) | − | 16.2962i | − | 0.860078i | −0.902810 | − | 0.430039i | \(-0.858500\pi\) | ||
0.902810 | − | 0.430039i | \(-0.141500\pi\) | |||||||
\(360\) | 4.30156 | 0.226712 | ||||||||
\(361\) | −8.55996 | −0.450524 | ||||||||
\(362\) | 18.3243 | 0.963102 | ||||||||
\(363\) | 10.8054 | + | 2.06001i | 0.567136 | + | 0.108122i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 64.0752i | 3.35385i | ||||||||
\(366\) | 14.8504 | 0.776245 | ||||||||
\(367\) | − | 3.39392i | − | 0.177161i | −0.996069 | − | 0.0885807i | \(-0.971767\pi\) | ||
0.996069 | − | 0.0885807i | \(-0.0282331\pi\) | |||||||
\(368\) | −5.72998 | −0.298696 | ||||||||
\(369\) | 1.45111 | 0.0755418 | ||||||||
\(370\) | −10.8805 | −0.565652 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.20322 | 0.166079 | ||||||||
\(373\) | − | 6.51584i | − | 0.337378i | −0.985669 | − | 0.168689i | \(-0.946047\pi\) | ||
0.985669 | − | 0.168689i | \(-0.0539533\pi\) | |||||||
\(374\) | 8.52753 | − | 7.05538i | 0.440948 | − | 0.364825i | ||||
\(375\) | 36.5781 | 1.88889 | ||||||||
\(376\) | −3.20101 | −0.165079 | ||||||||
\(377\) | 7.75447i | 0.399376i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.4324 | −1.40911 | −0.704555 | − | 0.709650i | \(-0.748853\pi\) | ||||
−0.704555 | + | 0.709650i | \(0.748853\pi\) | |||||||
\(380\) | 13.8988i | 0.712994i | ||||||||
\(381\) | −5.90909 | −0.302732 | ||||||||
\(382\) | 20.8202i | 1.06525i | ||||||||
\(383\) | 8.83690i | 0.451545i | 0.974180 | + | 0.225772i | \(0.0724906\pi\) | ||||
−0.974180 | + | 0.225772i | \(0.927509\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.51641 | −0.229879 | ||||||||
\(387\) | − | 4.14572i | − | 0.210739i | ||||||
\(388\) | 12.3347i | 0.626201i | ||||||||
\(389\) | 8.92306 | 0.452417 | 0.226209 | − | 0.974079i | \(-0.427367\pi\) | ||||
0.226209 | + | 0.974079i | \(0.427367\pi\) | |||||||
\(390\) | 4.30476i | 0.217980i | ||||||||
\(391\) | 19.1214 | 0.967011 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.1043i | 0.610580i | ||||||||
\(394\) | −17.3563 | −0.874399 | ||||||||
\(395\) | 69.2220 | 3.48293 | ||||||||
\(396\) | 2.11424 | + | 2.55539i | 0.106244 | + | 0.128413i | ||||
\(397\) | 4.77555i | 0.239678i | 0.992793 | + | 0.119839i | \(0.0382379\pi\) | ||||
−0.992793 | + | 0.119839i | \(0.961762\pi\) | |||||||
\(398\) | −7.81660 | −0.391811 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.5035 | −0.675173 | ||||||||
\(401\) | 2.53972 | 0.126827 | 0.0634137 | − | 0.997987i | \(-0.479801\pi\) | ||||
0.0634137 | + | 0.997987i | \(0.479801\pi\) | |||||||
\(402\) | −0.330392 | −0.0164784 | ||||||||
\(403\) | 3.20560i | 0.159682i | ||||||||
\(404\) | −0.0562448 | −0.00279828 | ||||||||
\(405\) | − | 4.30156i | − | 0.213746i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.34783 | − | 6.46369i | −0.265082 | − | 0.320393i | ||||
\(408\) | 3.33708 | 0.165210 | ||||||||
\(409\) | −0.0642013 | −0.00317455 | −0.00158728 | − | 0.999999i | \(-0.500505\pi\) | ||||
−0.00158728 | + | 0.999999i | \(0.500505\pi\) | |||||||
\(410\) | −6.24205 | −0.308273 | ||||||||
\(411\) | − | 9.89121i | − | 0.487897i | ||||||
\(412\) | − | 14.7949i | − | 0.728893i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.72998i | 0.281613i | ||||||||
\(415\) | 7.53040i | 0.369653i | ||||||||
\(416\) | − | 1.00074i | − | 0.0490655i | ||||||
\(417\) | − | 1.58746i | − | 0.0777385i | ||||||
\(418\) | −8.25673 | + | 6.83132i | −0.403850 | + | 0.334131i | ||||
\(419\) | − | 23.7720i | − | 1.16134i | −0.814140 | − | 0.580669i | \(-0.802791\pi\) | ||
0.814140 | − | 0.580669i | \(-0.197209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.11501 | −0.0543422 | −0.0271711 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271711 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(422\) | −21.9923 | −1.07057 | ||||||||
\(423\) | 3.20101i | 0.155638i | ||||||||
\(424\) | 11.3155i | 0.549528i | ||||||||
\(425\) | 45.0621 | 2.18583 | ||||||||
\(426\) | 2.84974 | 0.138070 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.6139i | 0.513042i | ||||||||
\(429\) | −2.55729 | + | 2.11581i | −0.123467 | + | 0.102152i | ||||
\(430\) | 17.8331i | 0.859987i | ||||||||
\(431\) | − | 29.3790i | − | 1.41514i | −0.706644 | − | 0.707569i | \(-0.749792\pi\) | ||
0.706644 | − | 0.707569i | \(-0.250208\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 13.1705i | − | 0.632934i | −0.948604 | − | 0.316467i | \(-0.897503\pi\) | ||
0.948604 | − | 0.316467i | \(-0.102497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.3316i | 1.59813i | ||||||||
\(436\) | 0.348204i | 0.0166759i | ||||||||
\(437\) | −18.5142 | −0.885653 | ||||||||
\(438\) | −14.8958 | −0.711748 | ||||||||
\(439\) | −10.2133 | −0.487454 | −0.243727 | − | 0.969844i | \(-0.578370\pi\) | ||||
−0.243727 | + | 0.969844i | \(0.578370\pi\) | |||||||
\(440\) | −9.09452 | − | 10.9922i | −0.433564 | − | 0.524031i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.33956i | 0.158847i | ||||||||
\(443\) | 27.3723 | 1.30050 | 0.650250 | − | 0.759721i | \(-0.274664\pi\) | ||||
0.650250 | + | 0.759721i | \(0.274664\pi\) | |||||||
\(444\) | − | 2.52944i | − | 0.120042i | ||||||
\(445\) | 11.9781 | 0.567817 | ||||||||
\(446\) | −8.30245 | −0.393133 | ||||||||
\(447\) | 17.0794 | 0.807828 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.35953 | 0.0641602 | 0.0320801 | − | 0.999485i | \(-0.489787\pi\) | ||||
0.0320801 | + | 0.999485i | \(0.489787\pi\) | |||||||
\(450\) | 13.5035i | 0.636559i | ||||||||
\(451\) | −3.06799 | − | 3.70815i | −0.144466 | − | 0.174610i | ||||
\(452\) | 18.9549 | 0.891564 | ||||||||
\(453\) | −8.31552 | −0.390697 | ||||||||
\(454\) | 7.91253i | 0.371354i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.23111 | −0.151310 | ||||||||
\(457\) | 21.8981i | 1.02435i | 0.858880 | + | 0.512176i | \(0.171160\pi\) | ||||
−0.858880 | + | 0.512176i | \(0.828840\pi\) | |||||||
\(458\) | −10.7093 | −0.500411 | ||||||||
\(459\) | − | 3.33708i | − | 0.155762i | ||||||
\(460\) | − | 24.6479i | − | 1.14921i | ||||||
\(461\) | 13.4227 | 0.625159 | 0.312579 | − | 0.949892i | \(-0.398807\pi\) | ||||
0.312579 | + | 0.949892i | \(0.398807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1422 | −0.982562 | −0.491281 | − | 0.871001i | \(-0.663471\pi\) | ||||
−0.491281 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(464\) | − | 7.74872i | − | 0.359725i | ||||||
\(465\) | 13.7788i | 0.638978i | ||||||||
\(466\) | 17.7106 | 0.820426 | ||||||||
\(467\) | − | 2.87475i | − | 0.133027i | −0.997786 | − | 0.0665137i | \(-0.978812\pi\) | ||
0.997786 | − | 0.0665137i | \(-0.0211876\pi\) | |||||||
\(468\) | −1.00074 | −0.0462594 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 13.7693i | − | 0.635133i | ||||||
\(471\) | −1.25113 | −0.0576490 | ||||||||
\(472\) | 3.44231 | 0.158445 | ||||||||
\(473\) | −10.5939 | + | 8.76502i | −0.487108 | + | 0.403016i | ||||
\(474\) | 16.0923i | 0.739143i | ||||||||
\(475\) | −43.6311 | −2.00193 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.3155 | 0.518100 | ||||||||
\(478\) | 26.6356 | 1.21828 | ||||||||
\(479\) | −3.83882 | −0.175400 | −0.0877000 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0877000 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(480\) | − | 4.30156i | − | 0.196339i | ||||||
\(481\) | 2.53132 | 0.115418 | ||||||||
\(482\) | 3.71041i | 0.169005i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.06001 | − | 10.8054i | 0.0936367 | − | 0.491154i | ||||
\(485\) | −53.0587 | −2.40927 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −9.68084 | −0.438681 | −0.219340 | − | 0.975648i | \(-0.570391\pi\) | ||||
−0.219340 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(488\) | − | 14.8504i | − | 0.672248i | ||||||
\(489\) | − | 7.21571i | − | 0.326306i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.8886i | − | 0.717041i | −0.933522 | − | 0.358520i | \(-0.883281\pi\) | ||
0.933522 | − | 0.358520i | \(-0.116719\pi\) | |||||||
\(492\) | − | 1.45111i | − | 0.0654211i | ||||||
\(493\) | 25.8581i | 1.16459i | ||||||||
\(494\) | − | 3.23351i | − | 0.145482i | ||||||
\(495\) | −10.9922 | + | 9.09452i | −0.494061 | + | 0.408768i | ||||
\(496\) | − | 3.20322i | − | 0.143829i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.75062 | −0.0784471 | ||||||||
\(499\) | −30.0440 | −1.34495 | −0.672477 | − | 0.740118i | \(-0.734769\pi\) | ||||
−0.672477 | + | 0.740118i | \(0.734769\pi\) | |||||||
\(500\) | − | 36.5781i | − | 1.63582i | ||||||
\(501\) | 15.4393i | 0.689776i | ||||||||
\(502\) | 10.6948 | 0.477333 | ||||||||
\(503\) | −4.66798 | −0.208135 | −0.104067 | − | 0.994570i | \(-0.533186\pi\) | ||||
−0.104067 | + | 0.994570i | \(0.533186\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.241941i | − | 0.0107662i | ||||||
\(506\) | 14.6423 | − | 12.1145i | 0.650931 | − | 0.538557i | ||||
\(507\) | 11.9985i | 0.532873i | ||||||||
\(508\) | 5.90909i | 0.262173i | ||||||||
\(509\) | − | 30.9460i | − | 1.37166i | −0.727763 | − | 0.685829i | \(-0.759440\pi\) | ||
0.727763 | − | 0.685829i | \(-0.240560\pi\) | |||||||
\(510\) | 14.3547i | 0.635635i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.23111i | 0.142657i | ||||||||
\(514\) | 23.8220 | 1.05074 | ||||||||
\(515\) | 63.6413 | 2.80437 | ||||||||
\(516\) | −4.14572 | −0.182505 | ||||||||
\(517\) | 8.17982 | − | 6.76769i | 0.359748 | − | 0.297643i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.22042i | 0.273046i | ||||||||
\(520\) | 4.30476 | 0.188776 | ||||||||
\(521\) | 11.0536i | 0.484267i | 0.970243 | + | 0.242134i | \(0.0778473\pi\) | ||||
−0.970243 | + | 0.242134i | \(0.922153\pi\) | |||||||
\(522\) | −7.74872 | −0.339152 | ||||||||
\(523\) | 4.13481 | 0.180803 | 0.0904013 | − | 0.995905i | \(-0.471185\pi\) | ||||
0.0904013 | + | 0.995905i | \(0.471185\pi\) | |||||||
\(524\) | 12.1043 | 0.528778 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.0516 | −0.743487 | ||||||||
\(527\) | 10.6894i | 0.465637i | ||||||||
\(528\) | 2.55539 | − | 2.11424i | 0.111209 | − | 0.0920103i | ||||
\(529\) | 9.83268 | 0.427508 | ||||||||
\(530\) | −48.6743 | −2.11427 | ||||||||
\(531\) | − | 3.44231i | − | 0.149384i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.45219 | 0.0629013 | ||||||||
\(534\) | 2.78460i | 0.120501i | ||||||||
\(535\) | −45.6563 | −1.97389 | ||||||||
\(536\) | 0.330392i | 0.0142707i | ||||||||
\(537\) | − | 3.07893i | − | 0.132866i | ||||||
\(538\) | −9.61064 | −0.414344 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.30156 | −0.185110 | ||||||||
\(541\) | − | 39.8272i | − | 1.71231i | −0.516723 | − | 0.856153i | \(-0.672848\pi\) | ||
0.516723 | − | 0.856153i | \(-0.327152\pi\) | |||||||
\(542\) | 5.11228i | 0.219591i | ||||||||
\(543\) | −18.3243 | −0.786370 | ||||||||
\(544\) | − | 3.33708i | − | 0.143076i | ||||||
\(545\) | −1.49782 | −0.0641596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7080i | 1.61228i | 0.591728 | + | 0.806138i | \(0.298446\pi\) | ||||
−0.591728 | + | 0.806138i | \(0.701554\pi\) | |||||||
\(548\) | −9.89121 | −0.422532 | ||||||||
\(549\) | −14.8504 | −0.633801 | ||||||||
\(550\) | 34.5066 | − | 28.5495i | 1.47136 | − | 1.21735i | ||||
\(551\) | − | 25.0369i | − | 1.06661i | ||||||
\(552\) | 5.72998 | 0.243884 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −26.3274 | −1.11854 | ||||||||
\(555\) | 10.8805 | 0.461853 | ||||||||
\(556\) | −1.58746 | −0.0673235 | ||||||||
\(557\) | 31.5451i | 1.33661i | 0.743888 | + | 0.668304i | \(0.232979\pi\) | ||||
−0.743888 | + | 0.668304i | \(0.767021\pi\) | |||||||
\(558\) | −3.20322 | −0.135603 | ||||||||
\(559\) | − | 4.14880i | − | 0.175475i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.52753 | + | 7.05538i | −0.360033 | + | 0.297878i | ||||
\(562\) | 10.5684 | 0.445802 | ||||||||
\(563\) | −37.7986 | −1.59302 | −0.796511 | − | 0.604625i | \(-0.793323\pi\) | ||||
−0.796511 | + | 0.604625i | \(0.793323\pi\) | |||||||
\(564\) | 3.20101 | 0.134787 | ||||||||
\(565\) | 81.5357i | 3.43023i | ||||||||
\(566\) | − | 10.4076i | − | 0.437463i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.84974i | − | 0.119572i | ||||||
\(569\) | 18.4881i | 0.775061i | 0.921857 | + | 0.387530i | \(0.126672\pi\) | ||||
−0.921857 | + | 0.387530i | \(0.873328\pi\) | |||||||
\(570\) | − | 13.8988i | − | 0.582157i | ||||||
\(571\) | 15.2403i | 0.637785i | 0.947791 | + | 0.318892i | \(0.103311\pi\) | ||||
−0.947791 | + | 0.318892i | \(0.896689\pi\) | |||||||
\(572\) | 2.11581 | + | 2.55729i | 0.0884664 | + | 0.106926i | ||||
\(573\) | − | 20.8202i | − | 0.869776i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 77.3745 | 3.22674 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 27.3882i | − | 1.14018i | −0.821581 | − | 0.570092i | \(-0.806908\pi\) | ||
0.821581 | − | 0.570092i | \(-0.193092\pi\) | |||||||
\(578\) | − | 5.86389i | − | 0.243906i | ||||||
\(579\) | 4.51641 | 0.187696 | ||||||||
\(580\) | 33.3316 | 1.38402 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 12.3347i | − | 0.511291i | ||||||
\(583\) | −23.9236 | − | 28.9154i | −0.990814 | − | 1.19755i | ||||
\(584\) | 14.8958i | 0.616392i | ||||||||
\(585\) | − | 4.30476i | − | 0.177980i | ||||||
\(586\) | 31.4600i | 1.29960i | ||||||||
\(587\) | − | 17.1517i | − | 0.707927i | −0.935259 | − | 0.353964i | \(-0.884834\pi\) | ||
0.935259 | − | 0.353964i | \(-0.115166\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.3499i | − | 0.426461i | ||||||
\(590\) | 14.8073i | 0.609608i | ||||||||
\(591\) | 17.3563 | 0.713944 | ||||||||
\(592\) | −2.52944 | −0.103959 | ||||||||
\(593\) | −5.26141 | −0.216060 | −0.108030 | − | 0.994148i | \(-0.534454\pi\) | ||||
−0.108030 | + | 0.994148i | \(0.534454\pi\) | |||||||
\(594\) | −2.11424 | − | 2.55539i | −0.0867482 | − | 0.104849i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 17.0794i | − | 0.699599i | ||||||
\(597\) | 7.81660 | 0.319912 | ||||||||
\(598\) | 5.73424i | 0.234490i | ||||||||
\(599\) | −35.6885 | −1.45819 | −0.729096 | − | 0.684411i | \(-0.760059\pi\) | ||||
−0.729096 | + | 0.684411i | \(0.760059\pi\) | |||||||
\(600\) | 13.5035 | 0.551276 | ||||||||
\(601\) | 9.98679 | 0.407370 | 0.203685 | − | 0.979036i | \(-0.434708\pi\) | ||||
0.203685 | + | 0.979036i | \(0.434708\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.330392 | 0.0134546 | ||||||||
\(604\) | 8.31552i | 0.338354i | ||||||||
\(605\) | 46.4801 | + | 8.86125i | 1.88968 | + | 0.360261i | ||||
\(606\) | 0.0562448 | 0.00228479 | ||||||||
\(607\) | 23.6993 | 0.961924 | 0.480962 | − | 0.876742i | \(-0.340288\pi\) | ||||
0.480962 | + | 0.876742i | \(0.340288\pi\) | |||||||
\(608\) | 3.23111i | 0.131039i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 63.8801 | 2.58643 | ||||||||
\(611\) | 3.20339i | 0.129595i | ||||||||
\(612\) | −3.33708 | −0.134894 | ||||||||
\(613\) | 25.8159i | 1.04269i | 0.853345 | + | 0.521347i | \(0.174570\pi\) | ||||
−0.853345 | + | 0.521347i | \(0.825430\pi\) | |||||||
\(614\) | − | 18.4994i | − | 0.746577i | ||||||
\(615\) | 6.24205 | 0.251704 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.44499 | 0.178949 | 0.0894743 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894743 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(618\) | 14.7949i | 0.595139i | ||||||||
\(619\) | − | 34.6603i | − | 1.39311i | −0.717501 | − | 0.696557i | \(-0.754714\pi\) | ||
0.717501 | − | 0.696557i | \(-0.245286\pi\) | |||||||
\(620\) | 13.7788 | 0.553371 | ||||||||
\(621\) | − | 5.72998i | − | 0.229936i | ||||||
\(622\) | 30.9979 | 1.24290 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00074i | 0.0400618i | ||||||||
\(625\) | 89.8260 | 3.59304 | ||||||||
\(626\) | 9.60149 | 0.383753 | ||||||||
\(627\) | 8.25673 | − | 6.83132i | 0.329742 | − | 0.272817i | ||||
\(628\) | 1.25113i | 0.0499255i | ||||||||
\(629\) | 8.44094 | 0.336562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7549 | 1.30395 | 0.651975 | − | 0.758240i | \(-0.273941\pi\) | ||||
0.651975 | + | 0.758240i | \(0.273941\pi\) | |||||||
\(632\) | 16.0923 | 0.640116 | ||||||||
\(633\) | 21.9923 | 0.874117 | ||||||||
\(634\) | − | 11.9425i | − | 0.474298i | ||||||
\(635\) | −25.4183 | −1.00870 | ||||||||
\(636\) | − | 11.3155i | − | 0.448688i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.3826 | + | 19.8010i | 0.648594 | + | 0.783928i | ||||
\(639\) | −2.84974 | −0.112734 | ||||||||
\(640\) | −4.30156 | −0.170034 | ||||||||
\(641\) | −35.0833 | −1.38571 | −0.692854 | − | 0.721078i | \(-0.743647\pi\) | ||||
−0.692854 | + | 0.721078i | \(0.743647\pi\) | |||||||
\(642\) | − | 10.6139i | − | 0.418897i | ||||||
\(643\) | − | 4.02224i | − | 0.158622i | −0.996850 | − | 0.0793109i | \(-0.974728\pi\) | ||
0.996850 | − | 0.0793109i | \(-0.0252720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 17.8331i | − | 0.702176i | ||||||
\(646\) | − | 10.7825i | − | 0.424230i | ||||||
\(647\) | − | 5.70997i | − | 0.224482i | −0.993681 | − | 0.112241i | \(-0.964197\pi\) | ||
0.993681 | − | 0.112241i | \(-0.0358028\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −8.79644 | + | 7.27786i | −0.345290 | + | 0.285681i | ||||
\(650\) | 13.5135i | 0.530043i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.21571 | −0.282589 | ||||||||
\(653\) | −14.3938 | −0.563272 | −0.281636 | − | 0.959521i | \(-0.590877\pi\) | ||||
−0.281636 | + | 0.959521i | \(0.590877\pi\) | |||||||
\(654\) | − | 0.348204i | − | 0.0136158i | ||||||
\(655\) | 52.0673i | 2.03444i | ||||||||
\(656\) | −1.45111 | −0.0566564 | ||||||||
\(657\) | 14.8958 | 0.581140 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.73466i | 0.0675728i | 0.999429 | + | 0.0337864i | \(0.0107566\pi\) | ||||
−0.999429 | + | 0.0337864i | \(0.989243\pi\) | |||||||
\(660\) | 9.09452 | + | 10.9922i | 0.354004 | + | 0.427869i | ||||
\(661\) | − | 28.0265i | − | 1.09010i | −0.838402 | − | 0.545052i | \(-0.816510\pi\) | ||
0.838402 | − | 0.545052i | \(-0.183490\pi\) | |||||||
\(662\) | 6.49162i | 0.252304i | ||||||||
\(663\) | − | 3.33956i | − | 0.129698i | ||||||
\(664\) | 1.75062i | 0.0679372i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.52944i | 0.0980137i | ||||||||
\(667\) | 44.4000i | 1.71917i | ||||||||
\(668\) | 15.4393 | 0.597364 | ||||||||
\(669\) | 8.30245 | 0.320991 | ||||||||
\(670\) | −1.42120 | −0.0549058 | ||||||||
\(671\) | 31.3973 | + | 37.9486i | 1.21208 | + | 1.46499i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 11.9436i | − | 0.460394i | −0.973144 | − | 0.230197i | \(-0.926063\pi\) | ||
0.973144 | − | 0.230197i | \(-0.0739370\pi\) | |||||||
\(674\) | 5.74869 | 0.221431 | ||||||||
\(675\) | − | 13.5035i | − | 0.519748i | ||||||
\(676\) | 11.9985 | 0.461481 | ||||||||
\(677\) | 40.4669 | 1.55527 | 0.777634 | − | 0.628717i | \(-0.216420\pi\) | ||||
0.777634 | + | 0.628717i | \(0.216420\pi\) | |||||||
\(678\) | −18.9549 | −0.727959 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.3547 | 0.550476 | ||||||||
\(681\) | − | 7.91253i | − | 0.303209i | ||||||
\(682\) | 6.77236 | + | 8.18546i | 0.259327 | + | 0.313437i | ||||
\(683\) | −18.3199 | −0.700990 | −0.350495 | − | 0.936565i | \(-0.613987\pi\) | ||||
−0.350495 | + | 0.936565i | \(0.613987\pi\) | |||||||
\(684\) | 3.23111 | 0.123544 | ||||||||
\(685\) | − | 42.5477i | − | 1.62566i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7093 | 0.408584 | ||||||||
\(688\) | 4.14572i | 0.158054i | ||||||||
\(689\) | 11.3239 | 0.431406 | ||||||||
\(690\) | 24.6479i | 0.938329i | ||||||||
\(691\) | − | 44.6823i | − | 1.69980i | −0.526947 | − | 0.849898i | \(-0.676663\pi\) | ||
0.526947 | − | 0.849898i | \(-0.323337\pi\) | |||||||
\(692\) | 6.22042 | 0.236465 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.6253 | 0.555167 | ||||||||
\(695\) | − | 6.82858i | − | 0.259023i | ||||||
\(696\) | 7.74872i | 0.293714i | ||||||||
\(697\) | 4.84248 | 0.183422 | ||||||||
\(698\) | − | 15.2458i | − | 0.577064i | ||||||
\(699\) | −17.7106 | −0.669875 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 18.6437i | − | 0.704161i | −0.935970 | − | 0.352081i | \(-0.885474\pi\) | ||
0.935970 | − | 0.352081i | \(-0.114526\pi\) | |||||||
\(702\) | 1.00074 | 0.0377706 | ||||||||
\(703\) | −8.17288 | −0.308246 | ||||||||
\(704\) | −2.11424 | − | 2.55539i | −0.0796833 | − | 0.0963098i | ||||
\(705\) | 13.7693i | 0.518584i | ||||||||
\(706\) | 27.4483 | 1.03303 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.44231 | −0.129370 | ||||||||
\(709\) | −4.90134 | −0.184074 | −0.0920368 | − | 0.995756i | \(-0.529338\pi\) | ||||
−0.0920368 | + | 0.995756i | \(0.529338\pi\) | |||||||
\(710\) | 12.2583 | 0.460047 | ||||||||
\(711\) | − | 16.0923i | − | 0.603508i | ||||||
\(712\) | 2.78460 | 0.104357 | ||||||||
\(713\) | 18.3544i | 0.687376i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0003 | + | 9.10128i | −0.411389 | + | 0.340369i | ||||
\(716\) | −3.07893 | −0.115065 | ||||||||
\(717\) | −26.6356 | −0.994724 | ||||||||
\(718\) | 16.2962 | 0.608167 | ||||||||
\(719\) | 22.2470i | 0.829674i | 0.909896 | + | 0.414837i | \(0.136161\pi\) | ||||
−0.909896 | + | 0.414837i | \(0.863839\pi\) | |||||||
\(720\) | 4.30156i | 0.160310i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 8.55996i | − | 0.318569i | ||||||
\(723\) | − | 3.71041i | − | 0.137992i | ||||||
\(724\) | 18.3243i | 0.681016i | ||||||||
\(725\) | 104.634i | 3.88603i | ||||||||
\(726\) | −2.06001 | + | 10.8054i | −0.0764541 | + | 0.401025i | ||||
\(727\) | 27.5807i | 1.02291i | 0.859310 | + | 0.511456i | \(0.170894\pi\) | ||||
−0.859310 | + | 0.511456i | \(0.829106\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −64.0752 | −2.37153 | ||||||||
\(731\) | − | 13.8346i | − | 0.511691i | ||||||
\(732\) | 14.8504i | 0.548888i | ||||||||
\(733\) | −17.9014 | −0.661203 | −0.330602 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330602 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(734\) | 3.39392 | 0.125272 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.72998i | − | 0.211210i | ||||||
\(737\) | −0.698526 | − | 0.844279i | −0.0257305 | − | 0.0310994i | ||||
\(738\) | 1.45111i | 0.0534161i | ||||||||
\(739\) | − | 28.8613i | − | 1.06168i | −0.847471 | − | 0.530841i | \(-0.821876\pi\) | ||
0.847471 | − | 0.530841i | \(-0.178124\pi\) | |||||||
\(740\) | − | 10.8805i | − | 0.399976i | ||||||
\(741\) | 3.23351i | 0.118786i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34.0656i | − | 1.24975i | −0.780726 | − | 0.624873i | \(-0.785151\pi\) | ||
0.780726 | − | 0.624873i | \(-0.214849\pi\) | |||||||
\(744\) | 3.20322i | 0.117436i | ||||||||
\(745\) | 73.4681 | 2.69166 | ||||||||
\(746\) | 6.51584 | 0.238562 | ||||||||
\(747\) | 1.75062 | 0.0640518 | ||||||||
\(748\) | 7.05538 | + | 8.52753i | 0.257970 | + | 0.311798i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 36.5781i | 1.33565i | ||||||||
\(751\) | −12.5636 | −0.458452 | −0.229226 | − | 0.973373i | \(-0.573619\pi\) | ||||
−0.229226 | + | 0.973373i | \(0.573619\pi\) | |||||||
\(752\) | − | 3.20101i | − | 0.116729i | ||||||
\(753\) | −10.6948 | −0.389741 | ||||||||
\(754\) | −7.75447 | −0.282401 | ||||||||
\(755\) | −35.7697 | −1.30179 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.03843 | 0.255816 | 0.127908 | − | 0.991786i | \(-0.459174\pi\) | ||||
0.127908 | + | 0.991786i | \(0.459174\pi\) | |||||||
\(758\) | − | 27.4324i | − | 0.996391i | ||||||
\(759\) | −14.6423 | + | 12.1145i | −0.531483 | + | 0.439730i | ||||
\(760\) | −13.8988 | −0.504163 | ||||||||
\(761\) | 1.64145 | 0.0595025 | 0.0297512 | − | 0.999557i | \(-0.490528\pi\) | ||||
0.0297512 | + | 0.999557i | \(0.490528\pi\) | |||||||
\(762\) | − | 5.90909i | − | 0.214064i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20.8202 | −0.753248 | ||||||||
\(765\) | − | 14.3547i | − | 0.518994i | ||||||
\(766\) | −8.83690 | −0.319290 | ||||||||
\(767\) | − | 3.44487i | − | 0.124387i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −5.29585 | −0.190973 | −0.0954867 | − | 0.995431i | \(-0.530441\pi\) | ||||
−0.0954867 | + | 0.995431i | \(0.530441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.8220 | −0.857928 | ||||||||
\(772\) | − | 4.51641i | − | 0.162549i | ||||||
\(773\) | − | 19.7087i | − | 0.708874i | −0.935080 | − | 0.354437i | \(-0.884673\pi\) | ||
0.935080 | − | 0.354437i | \(-0.115327\pi\) | |||||||
\(774\) | 4.14572 | 0.149015 | ||||||||
\(775\) | 43.2545i | 1.55375i | ||||||||
\(776\) | −12.3347 | −0.442791 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.92306i | 0.319907i | ||||||||
\(779\) | −4.68869 | −0.167990 | ||||||||
\(780\) | −4.30476 | −0.154135 | ||||||||
\(781\) | 6.02502 | + | 7.28218i | 0.215592 | + | 0.260577i | ||||
\(782\) | 19.1214i | 0.683780i | ||||||||
\(783\) | 7.74872 | 0.276917 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.38181 | −0.192085 | ||||||||
\(786\) | −12.1043 | −0.431745 | ||||||||
\(787\) | −52.0997 | −1.85715 | −0.928576 | − | 0.371141i | \(-0.878967\pi\) | ||||
−0.928576 | + | 0.371141i | \(0.878967\pi\) | |||||||
\(788\) | − | 17.3563i | − | 0.618293i | ||||||
\(789\) | 17.0516 | 0.607055 | ||||||||
\(790\) | 69.2220i | 2.46281i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.55539 | + | 2.11424i | −0.0908017 | + | 0.0751261i | ||||
\(793\) | −14.8615 | −0.527746 | ||||||||
\(794\) | −4.77555 | −0.169478 | ||||||||
\(795\) | 48.6743 | 1.72630 | ||||||||
\(796\) | − | 7.81660i | − | 0.277052i | ||||||
\(797\) | − | 39.4609i | − | 1.39778i | −0.715230 | − | 0.698889i | \(-0.753678\pi\) | ||
0.715230 | − | 0.698889i | \(-0.246322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.6820i | 0.377903i | ||||||||
\(800\) | − | 13.5035i | − | 0.477419i | ||||||
\(801\) | − | 2.78460i | − | 0.0983888i | ||||||
\(802\) | 2.53972i | 0.0896805i | ||||||||
\(803\) | −31.4932 | − | 38.0645i | −1.11137 | − | 1.34327i | ||||
\(804\) | − | 0.330392i | − | 0.0116520i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.20560 | −0.112912 | ||||||||
\(807\) | 9.61064 | 0.338311 | ||||||||
\(808\) | − | 0.0562448i | − | 0.00197868i | ||||||
\(809\) | 1.64396i | 0.0577984i | 0.999582 | + | 0.0288992i | \(0.00920019\pi\) | ||||
−0.999582 | + | 0.0288992i | \(0.990800\pi\) | |||||||
\(810\) | 4.30156 | 0.151142 | ||||||||
\(811\) | −18.9381 | −0.665006 | −0.332503 | − | 0.943102i | \(-0.607893\pi\) | ||||
−0.332503 | + | 0.943102i | \(0.607893\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.11228i | − | 0.179295i | ||||||
\(814\) | 6.46369 | − | 5.34783i | 0.226552 | − | 0.187441i | ||||
\(815\) | − | 31.0389i | − | 1.08724i | ||||||
\(816\) | 3.33708i | 0.116821i | ||||||||
\(817\) | 13.3952i | 0.468640i | ||||||||
\(818\) | − | 0.0642013i | − | 0.00224475i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 6.24205i | − | 0.217982i | ||||||
\(821\) | − | 16.1682i | − | 0.564274i | −0.959374 | − | 0.282137i | \(-0.908957\pi\) | ||
0.959374 | − | 0.282137i | \(-0.0910433\pi\) | |||||||
\(822\) | 9.89121 | 0.344996 | ||||||||
\(823\) | 3.87280 | 0.134997 | 0.0674986 | − | 0.997719i | \(-0.478498\pi\) | ||||
0.0674986 | + | 0.997719i | \(0.478498\pi\) | |||||||
\(824\) | 14.7949 | 0.515405 | ||||||||
\(825\) | −34.5066 | + | 28.5495i | −1.20136 | + | 0.993966i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.5641i | − | 0.610762i | −0.952230 | − | 0.305381i | \(-0.901216\pi\) | ||
0.952230 | − | 0.305381i | \(-0.0987838\pi\) | |||||||
\(828\) | −5.72998 | −0.199131 | ||||||||
\(829\) | 31.8636i | 1.10667i | 0.832959 | + | 0.553335i | \(0.186645\pi\) | ||||
−0.832959 | + | 0.553335i | \(0.813355\pi\) | |||||||
\(830\) | −7.53040 | −0.261384 | ||||||||
\(831\) | 26.3274 | 0.913288 | ||||||||
\(832\) | 1.00074 | 0.0346945 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.58746 | 0.0549694 | ||||||||
\(835\) | 66.4131i | 2.29832i | ||||||||
\(836\) | −6.83132 | − | 8.25673i | −0.236266 | − | 0.285565i | ||||
\(837\) | 3.20322 | 0.110719 | ||||||||
\(838\) | 23.7720 | 0.821190 | ||||||||
\(839\) | − | 13.8360i | − | 0.477670i | −0.971060 | − | 0.238835i | \(-0.923234\pi\) | ||
0.971060 | − | 0.238835i | \(-0.0767656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.0426 | −1.07043 | ||||||||
\(842\) | − | 1.11501i | − | 0.0384258i | ||||||
\(843\) | −10.5684 | −0.363996 | ||||||||
\(844\) | − | 21.9923i | − | 0.757007i | ||||||
\(845\) | 51.6124i | 1.77552i | ||||||||
\(846\) | −3.20101 | −0.110053 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.3155 | −0.388575 | ||||||||
\(849\) | 10.4076i | 0.357187i | ||||||||
\(850\) | 45.0621i | 1.54562i | ||||||||
\(851\) | 14.4936 | 0.496835 | ||||||||
\(852\) | 2.84974i | 0.0976304i | ||||||||
\(853\) | 9.77894 | 0.334825 | 0.167412 | − | 0.985887i | \(-0.446459\pi\) | ||||
0.167412 | + | 0.985887i | \(0.446459\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.8988i | 0.475329i | ||||||||
\(856\) | −10.6139 | −0.362775 | ||||||||
\(857\) | 43.7118 | 1.49317 | 0.746583 | − | 0.665293i | \(-0.231693\pi\) | ||||
0.746583 | + | 0.665293i | \(0.231693\pi\) | |||||||
\(858\) | −2.11581 | − | 2.55729i | −0.0722325 | − | 0.0873043i | ||||
\(859\) | − | 46.2851i | − | 1.57923i | −0.613604 | − | 0.789614i | \(-0.710281\pi\) | ||
0.613604 | − | 0.789614i | \(-0.289719\pi\) | |||||||
\(860\) | −17.8331 | −0.608102 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.3790 | 1.00065 | ||||||||
\(863\) | −28.6154 | −0.974081 | −0.487041 | − | 0.873379i | \(-0.661924\pi\) | ||||
−0.487041 | + | 0.873379i | \(0.661924\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 26.7576i | 0.909784i | ||||||||
\(866\) | 13.1705 | 0.447552 | ||||||||
\(867\) | 5.86389i | 0.199148i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41.1220 | + | 34.0229i | −1.39497 | + | 1.15415i | ||||
\(870\) | −33.3316 | −1.13005 | ||||||||
\(871\) | 0.330637 | 0.0112032 | ||||||||
\(872\) | −0.348204 | −0.0117917 | ||||||||
\(873\) | 12.3347i | 0.417468i | ||||||||
\(874\) | − | 18.5142i | − | 0.626251i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 14.8958i | − | 0.503282i | ||||||
\(877\) | − | 55.6056i | − | 1.87767i | −0.344370 | − | 0.938834i | \(-0.611907\pi\) | ||
0.344370 | − | 0.938834i | \(-0.388093\pi\) | |||||||
\(878\) | − | 10.2133i | − | 0.344682i | ||||||
\(879\) | − | 31.4600i | − | 1.06112i | ||||||
\(880\) | 10.9922 | − | 9.09452i | 0.370546 | − | 0.306576i | ||||
\(881\) | 31.8585i | 1.07334i | 0.843792 | + | 0.536671i | \(0.180318\pi\) | ||||
−0.843792 | + | 0.536671i | \(0.819682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.9427 | 1.88262 | 0.941311 | − | 0.337539i | \(-0.109595\pi\) | ||||
0.941311 | + | 0.337539i | \(0.109595\pi\) | |||||||
\(884\) | −3.33956 | −0.112322 | ||||||||
\(885\) | − | 14.8073i | − | 0.497743i | ||||||
\(886\) | 27.3723i | 0.919592i | ||||||||
\(887\) | 10.9802 | 0.368678 | 0.184339 | − | 0.982863i | \(-0.440986\pi\) | ||||
0.184339 | + | 0.982863i | \(0.440986\pi\) | |||||||
\(888\) | 2.52944 | 0.0848823 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.9781i | 0.401507i | ||||||||
\(891\) | 2.11424 | + | 2.55539i | 0.0708296 | + | 0.0856087i | ||||
\(892\) | − | 8.30245i | − | 0.277987i | ||||||
\(893\) | − | 10.3428i | − | 0.346109i | ||||||
\(894\) | 17.0794i | 0.571220i | ||||||||
\(895\) | − | 13.2442i | − | 0.442705i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.73424i | − | 0.191461i | ||||||
\(898\) | 1.35953i | 0.0453681i | ||||||||
\(899\) | −24.8208 | −0.827820 | ||||||||
\(900\) | −13.5035 | −0.450115 | ||||||||
\(901\) | 37.7607 | 1.25799 | ||||||||
\(902\) | 3.70815 | − | 3.06799i | 0.123468 | − | 0.102153i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.9549i | 0.630431i | ||||||||
\(905\) | −78.8230 | −2.62017 | ||||||||
\(906\) | − | 8.31552i | − | 0.276265i | ||||||
\(907\) | 2.11933 | 0.0703712 | 0.0351856 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351856 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(908\) | −7.91253 | −0.262587 | ||||||||
\(909\) | −0.0562448 | −0.00186552 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.06472 | 0.0352757 | 0.0176379 | − | 0.999844i | \(-0.494385\pi\) | ||||
0.0176379 | + | 0.999844i | \(0.494385\pi\) | |||||||
\(912\) | − | 3.23111i | − | 0.106993i | ||||||
\(913\) | −3.70122 | − | 4.47351i | −0.122493 | − | 0.148052i | ||||
\(914\) | −21.8981 | −0.724326 | ||||||||
\(915\) | −63.8801 | −2.11181 | ||||||||
\(916\) | − | 10.7093i | − | 0.353844i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.33708 | 0.110140 | ||||||||
\(919\) | 41.2735i | 1.36149i | 0.732522 | + | 0.680744i | \(0.238343\pi\) | ||||
−0.732522 | + | 0.680744i | \(0.761657\pi\) | |||||||
\(920\) | 24.6479 | 0.812617 | ||||||||
\(921\) | 18.4994i | 0.609577i | ||||||||
\(922\) | 13.4227i | 0.442054i | ||||||||
\(923\) | −2.85185 | −0.0938699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.1561 | 1.12305 | ||||||||
\(926\) | − | 21.1422i | − | 0.694776i | ||||||
\(927\) | − | 14.7949i | − | 0.485929i | ||||||
\(928\) | 7.74872 | 0.254364 | ||||||||
\(929\) | − | 20.3459i | − | 0.667528i | −0.942657 | − | 0.333764i | \(-0.891681\pi\) | ||
0.942657 | − | 0.333764i | \(-0.108319\pi\) | |||||||
\(930\) | −13.7788 | −0.451826 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.7106i | 0.580129i | ||||||||
\(933\) | −30.9979 | −1.01482 | ||||||||
\(934\) | 2.87475 | 0.0940646 | ||||||||
\(935\) | −36.6817 | + | 30.3492i | −1.19962 | + | 0.992524i | ||||
\(936\) | − | 1.00074i | − | 0.0327103i | ||||||
\(937\) | 21.9119 | 0.715831 | 0.357916 | − | 0.933754i | \(-0.383488\pi\) | ||||
0.357916 | + | 0.933754i | \(0.383488\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.60149 | −0.313333 | ||||||||
\(940\) | 13.7693 | 0.449107 | ||||||||
\(941\) | 52.6097 | 1.71503 | 0.857514 | − | 0.514460i | \(-0.172008\pi\) | ||||
0.857514 | + | 0.514460i | \(0.172008\pi\) | |||||||
\(942\) | − | 1.25113i | − | 0.0407640i | ||||||
\(943\) | 8.31484 | 0.270768 | ||||||||
\(944\) | 3.44231i | 0.112038i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.76502 | − | 10.5939i | −0.284976 | − | 0.344438i | ||||
\(947\) | −25.0357 | −0.813550 | −0.406775 | − | 0.913528i | \(-0.633347\pi\) | ||||
−0.406775 | + | 0.913528i | \(0.633347\pi\) | |||||||
\(948\) | −16.0923 | −0.522653 | ||||||||
\(949\) | 14.9069 | 0.483897 | ||||||||
\(950\) | − | 43.6311i | − | 1.41558i | ||||||
\(951\) | 11.9425i | 0.387263i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.4386i | 0.888823i | 0.895823 | + | 0.444411i | \(0.146587\pi\) | ||||
−0.895823 | + | 0.444411i | \(0.853413\pi\) | |||||||
\(954\) | 11.3155i | 0.366352i | ||||||||
\(955\) | − | 89.5594i | − | 2.89807i | ||||||
\(956\) | 26.6356i | 0.861456i | ||||||||
\(957\) | −16.3826 | − | 19.8010i | −0.529575 | − | 0.640074i | ||||
\(958\) | − | 3.83882i | − | 0.124027i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.30156 | 0.138832 | ||||||||
\(961\) | 20.7394 | 0.669013 | ||||||||
\(962\) | 2.53132i | 0.0816129i | ||||||||
\(963\) | 10.6139i | 0.342028i | ||||||||
\(964\) | −3.71041 | −0.119504 | ||||||||
\(965\) | 19.4276 | 0.625398 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 44.4870i | − | 1.43061i | −0.698815 | − | 0.715303i | \(-0.746289\pi\) | ||
0.698815 | − | 0.715303i | \(-0.253711\pi\) | |||||||
\(968\) | 10.8054 | + | 2.06001i | 0.347298 | + | 0.0662112i | ||||
\(969\) | 10.7825i | 0.346383i | ||||||||
\(970\) | − | 53.0587i | − | 1.70361i | ||||||
\(971\) | 8.27547i | 0.265573i | 0.991145 | + | 0.132786i | \(0.0423924\pi\) | ||||
−0.991145 | + | 0.132786i | \(0.957608\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 9.68084i | − | 0.310194i | ||||||
\(975\) | − | 13.5135i | − | 0.432778i | ||||||
\(976\) | 14.8504 | 0.475351 | ||||||||
\(977\) | 28.8701 | 0.923637 | 0.461818 | − | 0.886975i | \(-0.347197\pi\) | ||||
0.461818 | + | 0.886975i | \(0.347197\pi\) | |||||||
\(978\) | 7.21571 | 0.230733 | ||||||||
\(979\) | −7.11572 | + | 5.88729i | −0.227419 | + | 0.188159i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.348204i | 0.0111173i | ||||||||
\(982\) | 15.8886 | 0.507025 | ||||||||
\(983\) | 44.6135i | 1.42295i | 0.702711 | + | 0.711476i | \(0.251973\pi\) | ||||
−0.702711 | + | 0.711476i | \(0.748027\pi\) | |||||||
\(984\) | 1.45111 | 0.0462597 | ||||||||
\(985\) | 74.6593 | 2.37884 | ||||||||
\(986\) | −25.8581 | −0.823490 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.23351 | 0.102872 | ||||||||
\(989\) | − | 23.7549i | − | 0.755361i | ||||||
\(990\) | −9.09452 | − | 10.9922i | −0.289043 | − | 0.349354i | ||||
\(991\) | −37.0562 | −1.17713 | −0.588565 | − | 0.808450i | \(-0.700307\pi\) | ||||
−0.588565 | + | 0.808450i | \(0.700307\pi\) | |||||||
\(992\) | 3.20322 | 0.101702 | ||||||||
\(993\) | − | 6.49162i | − | 0.206005i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.6236 | 1.06594 | ||||||||
\(996\) | − | 1.75062i | − | 0.0554705i | ||||||
\(997\) | 34.4937 | 1.09243 | 0.546213 | − | 0.837647i | \(-0.316069\pi\) | ||||
0.546213 | + | 0.837647i | \(0.316069\pi\) | |||||||
\(998\) | − | 30.0440i | − | 0.951025i | ||||||
\(999\) | − | 2.52944i | − | 0.0800278i |
(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 | 3234.2.e.b.2155.9 | 16 | ||
7.4 | even | 3 | 462.2.p.b.439.4 | yes | 16 | ||
7.5 | odd | 6 | 462.2.p.a.241.8 | ✓ | 16 | ||
7.6 | odd | 2 | 3234.2.e.a.2155.16 | 16 | |||
11.10 | odd | 2 | 3234.2.e.a.2155.1 | 16 | |||
21.5 | even | 6 | 1386.2.bk.a.703.1 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.b.901.5 | 16 | |||
77.32 | odd | 6 | 462.2.p.a.439.8 | yes | 16 | ||
77.54 | even | 6 | 462.2.p.b.241.4 | yes | 16 | ||
77.76 | even | 2 | inner | 3234.2.e.b.2155.8 | 16 | ||
231.32 | even | 6 | 1386.2.bk.a.901.1 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.b.703.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.8 | ✓ | 16 | 7.5 | odd | 6 | ||
462.2.p.a.439.8 | yes | 16 | 77.32 | odd | 6 | ||
462.2.p.b.241.4 | yes | 16 | 77.54 | even | 6 | ||
462.2.p.b.439.4 | yes | 16 | 7.4 | even | 3 | ||
1386.2.bk.a.703.1 | 16 | 21.5 | even | 6 | |||
1386.2.bk.a.901.1 | 16 | 231.32 | even | 6 | |||
1386.2.bk.b.703.5 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.b.901.5 | 16 | 21.11 | odd | 6 | |||
3234.2.e.a.2155.1 | 16 | 11.10 | odd | 2 | |||
3234.2.e.a.2155.16 | 16 | 7.6 | odd | 2 | |||
3234.2.e.b.2155.8 | 16 | 77.76 | even | 2 | inner | ||
3234.2.e.b.2155.9 | 16 | 1.1 | even | 1 | trivial |