Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (of order \(2\), degree \(1\), 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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 3x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.l.4049.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.23607i | − 0.713644i | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
0.934172 | − | 0.356822i | \(-0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.236068i | − 0.0892253i | −0.999004 | − | 0.0446127i | \(-0.985795\pi\) | ||||
0.999004 | − | 0.0446127i | \(-0.0142054\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.47214 | 0.490712 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23607i | 0.620174i | 0.950708 | + | 0.310087i | \(0.100358\pi\) | ||||
−0.950708 | + | 0.310087i | \(0.899642\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47214i | 0.599581i | 0.954005 | + | 0.299791i | \(0.0969168\pi\) | ||||
−0.954005 | + | 0.299791i | \(0.903083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.291796 | −0.0636751 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.52786i | − 1.06384i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.23607 | 1.15801 | 0.579004 | − | 0.815324i | \(-0.303441\pi\) | ||||
0.579004 | + | 0.815324i | \(0.303441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.47214 | −1.52164 | −0.760820 | − | 0.648963i | \(-0.775203\pi\) | ||||
−0.760820 | + | 0.648963i | \(0.775203\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.23607i | − 0.215172i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.76393i | − 1.11198i | −0.831188 | − | 0.555992i | \(-0.812339\pi\) | ||||
0.831188 | − | 0.555992i | \(-0.187661\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.76393 | 0.442583 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.9443 | 1.86538 | 0.932691 | − | 0.360677i | \(-0.117454\pi\) | ||||
0.932691 | + | 0.360677i | \(0.117454\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.4721i | 1.74948i | 0.484589 | + | 0.874742i | \(0.338969\pi\) | ||||
−0.484589 | + | 0.874742i | \(0.661031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.70820i | 0.249167i | 0.992209 | + | 0.124584i | \(0.0397595\pi\) | ||||
−0.992209 | + | 0.124584i | \(0.960241\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.94427 | 0.992039 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.05573 | 0.427888 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 3.23607i | − 0.444508i | −0.974989 | − | 0.222254i | \(-0.928659\pi\) | ||||
0.974989 | − | 0.222254i | \(-0.0713414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.23607i | 0.163721i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.23607 | 0.160922 | 0.0804612 | − | 0.996758i | \(-0.474361\pi\) | ||||
0.0804612 | + | 0.996758i | \(0.474361\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.76393 | −0.353885 | −0.176943 | − | 0.984221i | \(-0.556621\pi\) | ||||
−0.176943 | + | 0.984221i | \(0.556621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 0.347524i | − 0.0437839i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.94427i | 0.604039i | 0.953302 | + | 0.302019i | \(0.0976608\pi\) | ||||
−0.953302 | + | 0.302019i | \(0.902339\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.23607 | −0.148805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.527864i | − 0.0617818i | −0.999523 | − | 0.0308909i | \(-0.990166\pi\) | ||||
0.999523 | − | 0.0308909i | \(-0.00983445\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.236068i | − 0.0269024i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.18034 | 0.807851 | 0.403926 | − | 0.914792i | \(-0.367645\pi\) | ||||
0.403926 | + | 0.914792i | \(0.367645\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.41641 | −0.268490 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.00000i | 0.987878i | 0.869496 | + | 0.493939i | \(0.164443\pi\) | ||||
−0.869496 | + | 0.493939i | \(0.835557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 7.70820i | − 0.826406i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.527864 | 0.0553352 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.4721i | 1.08591i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1803i | 1.64286i | 0.570306 | + | 0.821432i | \(0.306825\pi\) | ||||
−0.570306 | + | 0.821432i | \(0.693175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47214 | 0.147955 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05573 | −0.105049 | −0.0525244 | − | 0.998620i | \(-0.516727\pi\) | ||||
−0.0525244 | + | 0.998620i | \(0.516727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.23607i | 0.220326i | 0.993914 | + | 0.110163i | \(0.0351373\pi\) | ||||
−0.993914 | + | 0.110163i | \(0.964863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.41641i | − 0.716971i | −0.933535 | − | 0.358486i | \(-0.883293\pi\) | ||||
0.933535 | − | 0.358486i | \(-0.116707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2361 | 1.65092 | 0.825458 | − | 0.564464i | \(-0.190917\pi\) | ||||
0.825458 | + | 0.564464i | \(0.190917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.36068 | −0.793561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2361i | 1.05700i | 0.848933 | + | 0.528500i | \(0.177245\pi\) | ||||
−0.848933 | + | 0.528500i | \(0.822755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.29180i | 0.304327i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.583592 | 0.0534978 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 14.7639i | − 1.33122i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 18.1803i | − 1.61324i | −0.591067 | − | 0.806622i | \(-0.701293\pi\) | ||||
0.591067 | − | 0.806622i | \(-0.298707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.1803 | 1.24851 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.94427 | 0.257242 | 0.128621 | − | 0.991694i | \(-0.458945\pi\) | ||||
0.128621 | + | 0.991694i | \(0.458945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.236068i | 0.0204697i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 20.4721i | − 1.74905i | −0.484978 | − | 0.874526i | \(-0.661172\pi\) | ||||
0.484978 | − | 0.874526i | \(-0.338828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.11146 | 0.177817 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.23607i | 0.186989i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 8.58359i | − 0.707963i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.94427 | 0.568897 | 0.284448 | − | 0.958691i | \(-0.408190\pi\) | ||||
0.284448 | + | 0.958691i | \(0.408190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4721 | 1.66600 | 0.832999 | − | 0.553274i | \(-0.186622\pi\) | ||||
0.832999 | + | 0.553274i | \(0.186622\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.63932i | 0.294222i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 13.7082i | − 1.09403i | −0.837122 | − | 0.547017i | \(-0.815763\pi\) | ||||
0.837122 | − | 0.547017i | \(-0.184237\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.236068 | −0.0186048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.70820i | 0.133797i | 0.997760 | + | 0.0668984i | \(0.0213103\pi\) | ||||
−0.997760 | + | 0.0668984i | \(0.978690\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 21.4164i | − 1.65725i | −0.559803 | − | 0.828626i | \(-0.689123\pi\) | ||||
0.559803 | − | 0.828626i | \(-0.310877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.00000 | 0.615385 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.47214 | −0.112577 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.76393i | 0.742338i | 0.928565 | + | 0.371169i | \(0.121043\pi\) | ||||
−0.928565 | + | 0.371169i | \(0.878957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 1.52786i | − 0.114841i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.29180 | 0.171297 | 0.0856484 | − | 0.996325i | \(-0.472704\pi\) | ||||
0.0856484 | + | 0.996325i | \(0.472704\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9443 | 1.25946 | 0.629729 | − | 0.776815i | \(-0.283166\pi\) | ||||
0.629729 | + | 0.776815i | \(0.283166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.41641i | 0.252548i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.47214i | 0.180780i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.30495 | −0.0949213 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.18034 | 0.230121 | 0.115061 | − | 0.993358i | \(-0.463294\pi\) | ||||
0.115061 | + | 0.993358i | \(0.463294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 14.9443i | − 1.07571i | −0.843037 | − | 0.537856i | \(-0.819234\pi\) | ||||
0.843037 | − | 0.537856i | \(-0.180766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.76393i | 0.268169i | 0.990970 | + | 0.134085i | \(0.0428094\pi\) | ||||
−0.990970 | + | 0.134085i | \(0.957191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.708204 | 0.0502032 | 0.0251016 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251016 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.11146 | 0.431069 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1.47214i | − 0.103324i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.47214i | − 0.102321i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.94427 | 0.202692 | 0.101346 | − | 0.994851i | \(-0.467685\pi\) | ||||
0.101346 | + | 0.994851i | \(0.467685\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 12.3607i | − 0.846940i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000i | 0.135769i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.652476 | −0.0440902 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.52786 | −0.371844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.76393i | 0.586876i | 0.955978 | + | 0.293438i | \(0.0947995\pi\) | ||||
−0.955978 | + | 0.293438i | \(0.905201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.94427i | 0.328163i | 0.986447 | + | 0.164081i | \(0.0524660\pi\) | ||||
−0.986447 | + | 0.164081i | \(0.947534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9443 | 0.723218 | 0.361609 | − | 0.932330i | \(-0.382228\pi\) | ||||
0.361609 | + | 0.932330i | \(0.382228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.291796 | −0.0191988 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.4721i | 0.882589i | 0.897362 | + | 0.441294i | \(0.145481\pi\) | ||||
−0.897362 | + | 0.441294i | \(0.854519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.87539i | − 0.576518i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.2361 | −0.726801 | −0.363400 | − | 0.931633i | \(-0.618384\pi\) | ||||
−0.363400 | + | 0.931633i | \(0.618384\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7639 | 1.07986 | 0.539930 | − | 0.841710i | \(-0.318451\pi\) | ||||
0.539930 | + | 0.841710i | \(0.318451\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 13.5967i | − 0.872232i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.23607i | − 0.142278i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1246 | 0.704994 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.4721 | −0.913473 | −0.456737 | − | 0.889602i | \(-0.650982\pi\) | ||||
−0.456737 | + | 0.889602i | \(0.650982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.00000i | − 0.0628695i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000i | 0.873296i | 0.899632 | + | 0.436648i | \(0.143834\pi\) | ||||
−0.899632 | + | 0.436648i | \(0.856166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.59675 | −0.0992171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.18034 | 0.568249 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.00000i | 0.493301i | 0.969104 | + | 0.246651i | \(0.0793300\pi\) | ||||
−0.969104 | + | 0.246651i | \(0.920670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.47214i | 0.151292i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.81966 | 0.171918 | 0.0859589 | − | 0.996299i | \(-0.472605\pi\) | ||||
0.0859589 | + | 0.996299i | \(0.472605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.0689 | 1.58357 | 0.791786 | − | 0.610799i | \(-0.209152\pi\) | ||||
0.791786 | + | 0.610799i | \(0.209152\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 0.652476i | − 0.0394896i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 9.76393i | − 0.586658i | −0.956012 | − | 0.293329i | \(-0.905237\pi\) | ||||
0.956012 | − | 0.293329i | \(-0.0947631\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.4721 | −0.746687 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.180340 | 0.0107582 | 0.00537909 | − | 0.999986i | \(-0.498288\pi\) | ||||
0.00537909 | + | 0.999986i | \(0.498288\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.3607i | − 0.972541i | −0.873808 | − | 0.486271i | \(-0.838357\pi\) | ||||
0.873808 | − | 0.486271i | \(-0.161643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.81966i | − 0.166439i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.0000 | 1.17242 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 5.52786i | − 0.322941i | −0.986878 | − | 0.161471i | \(-0.948376\pi\) | ||||
0.986878 | − | 0.161471i | \(-0.0516237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.52786i | − 0.320759i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.23607 | 0.129315 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.70820 | 0.156098 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30495i | 0.0749675i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 24.0000i | − 1.36975i | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||||
0.728659 | − | 0.684876i | \(-0.240144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.76393 | 0.157235 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.23607 | 0.0700910 | 0.0350455 | − | 0.999386i | \(-0.488842\pi\) | ||||
0.0350455 | + | 0.999386i | \(0.488842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6525i | 1.16735i | 0.811988 | + | 0.583673i | \(0.198385\pi\) | ||||
−0.811988 | + | 0.583673i | \(0.801615\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 18.1246i | − 1.01798i | −0.860773 | − | 0.508990i | \(-0.830019\pi\) | ||||
0.860773 | − | 0.508990i | \(-0.169981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.23607 | 0.349153 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.16718 | −0.511662 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 2.47214i | − 0.137553i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 21.3050i | − 1.17817i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.403252 | 0.0222320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0557 | 0.717608 | 0.358804 | − | 0.933413i | \(-0.383185\pi\) | ||||
0.358804 | + | 0.933413i | \(0.383185\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 9.95743i | − 0.545664i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 6.65248i | − 0.362383i | −0.983448 | − | 0.181192i | \(-0.942005\pi\) | ||||
0.983448 | − | 0.181192i | \(-0.0579955\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.8885 | 0.754322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.47214 | −0.458792 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.29180i | − 0.177740i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 20.9443i | − 1.12435i | −0.827019 | − | 0.562174i | \(-0.809965\pi\) | ||||
0.827019 | − | 0.562174i | \(-0.190035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1803 | −0.919643 | −0.459821 | − | 0.888011i | \(-0.652087\pi\) | ||||
−0.459821 | + | 0.888011i | \(0.652087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.3607 | 0.659764 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.8885i | 1.64403i | 0.569465 | + | 0.822016i | \(0.307150\pi\) | ||||
−0.569465 | + | 0.822016i | \(0.692850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 0.721360i | − 0.0381784i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.2361 | −1.27913 | −0.639565 | − | 0.768737i | \(-0.720886\pi\) | ||||
−0.639565 | + | 0.768737i | \(0.720886\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3607i | 0.648767i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7.65248i | − 0.399456i | −0.979851 | − | 0.199728i | \(-0.935994\pi\) | ||||
0.979851 | − | 0.199728i | \(-0.0640059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.5836 | 0.915365 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.763932 | −0.0396614 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 12.0000i | − 0.621336i | −0.950518 | − | 0.310668i | \(-0.899447\pi\) | ||||
0.950518 | − | 0.310668i | \(-0.100553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.9443i | 0.718167i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.9443 | −1.07583 | −0.537917 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537917 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.4721 | −1.15128 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.23607i | 0.216453i | 0.994126 | + | 0.108226i | \(0.0345172\pi\) | ||||
−0.994126 | + | 0.108226i | \(0.965483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.8885i | 0.858493i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.1803 | 0.820376 | 0.410188 | − | 0.912001i | \(-0.365463\pi\) | ||||
0.410188 | + | 0.912001i | \(0.365463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.47214 | 0.125021 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 3.63932i | − 0.183579i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.3607i | 1.12225i | 0.827731 | + | 0.561125i | \(0.189631\pi\) | ||||
−0.827731 | + | 0.561125i | \(0.810369\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.291796 | 0.0146081 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.1246 | 1.35454 | 0.677269 | − | 0.735735i | \(-0.263163\pi\) | ||||
0.677269 | + | 0.735735i | \(0.263163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 18.9443i | − 0.943681i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.76393i | − 0.335276i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.416408 | −0.0205900 | −0.0102950 | − | 0.999947i | \(-0.503277\pi\) | ||||
−0.0102950 | + | 0.999947i | \(0.503277\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −25.3050 | −1.24820 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 0.291796i | − 0.0143583i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.7214i | 1.21061i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.7771 | −1.69897 | −0.849486 | − | 0.527611i | \(-0.823088\pi\) | ||||
−0.849486 | + | 0.527611i | \(0.823088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8885 | −0.969308 | −0.484654 | − | 0.874706i | \(-0.661055\pi\) | ||||
−0.484654 | + | 0.874706i | \(0.661055\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.51471i | 0.122269i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.652476i | 0.0315755i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.76393 | 0.133444 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.94427 | −0.238157 | −0.119079 | − | 0.992885i | \(-0.537994\pi\) | ||||
−0.119079 | + | 0.992885i | \(0.537994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.1246i | 0.534615i | 0.963611 | + | 0.267307i | \(0.0861339\pi\) | ||||
−0.963611 | + | 0.267307i | \(0.913866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000i | 0.0478365i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3607 | 1.54449 | 0.772245 | − | 0.635324i | \(-0.219134\pi\) | ||||
0.772245 | + | 0.635324i | \(0.219134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.2229 | 0.486805 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10.0000i | − 0.475114i | −0.971374 | − | 0.237557i | \(-0.923653\pi\) | ||||
0.971374 | − | 0.237557i | \(-0.0763467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 8.58359i | − 0.405990i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.8328 | −0.794390 | −0.397195 | − | 0.917734i | \(-0.630016\pi\) | ||||
−0.397195 | + | 0.917734i | \(0.630016\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9443 | 0.562434 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 25.3050i | − 1.18893i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 10.6525i | − 0.498302i | −0.968465 | − | 0.249151i | \(-0.919848\pi\) | ||||
0.968465 | − | 0.249151i | \(-0.0801515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6656 | 0.637857 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.34752 | 0.109335 | 0.0546676 | − | 0.998505i | \(-0.482590\pi\) | ||||
0.0546676 | + | 0.998505i | \(0.482590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17.5279i | − 0.814589i | −0.913297 | − | 0.407294i | \(-0.866472\pi\) | ||||
0.913297 | − | 0.407294i | \(-0.133528\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.0000i | 0.786666i | 0.919396 | + | 0.393333i | \(0.128678\pi\) | ||||
−0.919396 | + | 0.393333i | \(0.871322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.16718 | 0.0538956 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.9443 | −0.780751 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.4721i | 0.527489i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.76393i | − 0.218125i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.1246 | −1.28505 | −0.642523 | − | 0.766266i | \(-0.722112\pi\) | ||||
−0.642523 | + | 0.766266i | \(0.722112\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1246 | 0.689623 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.291796i | 0.0132772i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 1.12461i | − 0.0509610i | −0.999675 | − | 0.0254805i | \(-0.991888\pi\) | ||||
0.999675 | − | 0.0254805i | \(-0.00811158\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.11146 | 0.0954833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.23607 | 0.0557830 | 0.0278915 | − | 0.999611i | \(-0.491121\pi\) | ||||
0.0278915 | + | 0.999611i | \(0.491121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.4164i | 0.694320i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.36068i | − 0.105891i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.5410 | −1.09861 | −0.549303 | − | 0.835623i | \(-0.685107\pi\) | ||||
−0.549303 | + | 0.835623i | \(0.685107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26.4721 | −1.18269 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 32.5967i | − 1.45342i | −0.686946 | − | 0.726709i | \(-0.741049\pi\) | ||||
0.686946 | − | 0.726709i | \(-0.258951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.88854i | − 0.439166i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.3607 | 0.636526 | 0.318263 | − | 0.948002i | \(-0.396901\pi\) | ||||
0.318263 | + | 0.948002i | \(0.396901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.124612 | −0.00551250 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.52786i | 0.244061i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.70820i | 0.0751267i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0689 | 0.529765 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.6525 | 1.78102 | 0.890509 | − | 0.454966i | \(-0.150349\pi\) | ||||
0.890509 | + | 0.454966i | \(0.150349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.8885i | 0.738484i | 0.929333 | + | 0.369242i | \(0.120383\pi\) | ||||
−0.929333 | + | 0.369242i | \(0.879617\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 20.9443i | − 0.912347i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.81966 | 0.0789665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26.7082i | 1.15686i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 2.83282i | − 0.122245i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.94427 | 0.299111 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.70820 | −0.202421 | −0.101211 | − | 0.994865i | \(-0.532272\pi\) | ||||
−0.101211 | + | 0.994865i | \(0.532272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 20.9443i | − 0.898805i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.29180i | 0.0979901i | 0.998799 | + | 0.0489951i | \(0.0156019\pi\) | ||||
−0.998799 | + | 0.0489951i | \(0.984398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.06888 | −0.173656 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.23607 | −0.265665 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 1.69505i | − 0.0720808i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 13.8197i | − 0.585558i | −0.956180 | − | 0.292779i | \(-0.905420\pi\) | ||||
0.956180 | − | 0.292779i | \(-0.0945800\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.6525 | −1.08498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.05573 | 0.129013 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.36068i | 0.225926i | 0.993599 | + | 0.112963i | \(0.0360341\pi\) | ||||
−0.993599 | + | 0.112963i | \(0.963966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.570437i | 0.0239561i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.4164 | −1.65242 | −0.826211 | − | 0.563361i | \(-0.809508\pi\) | ||||
−0.826211 | + | 0.563361i | \(0.809508\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000 | 1.00437 | 0.502184 | − | 0.864761i | \(-0.332530\pi\) | ||||
0.502184 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 3.93112i | − 0.164225i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 9.00000i | − 0.374675i | −0.982296 | − | 0.187337i | \(-0.940014\pi\) | ||||
0.982296 | − | 0.187337i | \(-0.0599858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.4721 | −0.767676 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.12461 | 0.0881437 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 3.23607i | − 0.134024i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.5967i | 0.891393i | 0.895184 | + | 0.445697i | \(0.147044\pi\) | ||||
−0.895184 | + | 0.445697i | \(0.852956\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.47214 | 0.349088 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.65248 | 0.191377 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.11146i | 0.374163i | 0.982344 | + | 0.187081i | \(0.0599028\pi\) | ||||
−0.982344 | + | 0.187081i | \(0.940097\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.875388i | − 0.0358273i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.8328 | 1.50495 | 0.752474 | − | 0.658622i | \(-0.228860\pi\) | ||||
0.752474 | + | 0.658622i | \(0.228860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.94427 | 0.120099 | 0.0600497 | − | 0.998195i | \(-0.480874\pi\) | ||||
0.0600497 | + | 0.998195i | \(0.480874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.27864i | 0.296409i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.1246i | 0.695067i | 0.937668 | + | 0.347533i | \(0.112981\pi\) | ||||
−0.937668 | + | 0.347533i | \(0.887019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.81966 | −0.0737363 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.81966 | −0.154527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.0689i | 1.61837i | 0.587556 | + | 0.809183i | \(0.300090\pi\) | ||||
−0.587556 | + | 0.809183i | \(0.699910\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.3050i | 1.50184i | 0.660393 | + | 0.750920i | \(0.270390\pi\) | ||||
−0.660393 | + | 0.750920i | \(0.729610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.4721 | 0.742458 | 0.371229 | − | 0.928541i | \(-0.378937\pi\) | ||||
0.371229 | + | 0.928541i | \(0.378937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.52786 | −0.221826 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.472136i | 0.0189157i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.23607i | 0.0493638i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.7214 | 0.666724 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1246 | 0.641911 | 0.320955 | − | 0.947094i | \(-0.395996\pi\) | ||||
0.320955 | + | 0.947094i | \(0.395996\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 3.63932i | − 0.144650i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5279i | 0.615236i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.7214 | 0.582368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.7771 | −1.72909 | −0.864546 | − | 0.502555i | \(-0.832394\pi\) | ||||
−0.864546 | + | 0.502555i | \(0.832394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15.9443i | − 0.628781i | −0.949294 | − | 0.314390i | \(-0.898200\pi\) | ||||
0.949294 | − | 0.314390i | \(-0.101800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1803i | 0.478859i | 0.970914 | + | 0.239429i | \(0.0769603\pi\) | ||||
−0.970914 | + | 0.239429i | \(0.923040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23607 | 0.0485199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.47214 | 0.0968906 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.5410i | 1.07776i | 0.842381 | + | 0.538882i | \(0.181153\pi\) | ||||
−0.842381 | + | 0.538882i | \(0.818847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 0.777088i | − 0.0303171i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.52786 | −0.176381 | −0.0881903 | − | 0.996104i | \(-0.528108\pi\) | ||||
−0.0881903 | + | 0.996104i | \(0.528108\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.1803 | −1.71842 | −0.859208 | − | 0.511626i | \(-0.829043\pi\) | ||||
−0.859208 | + | 0.511626i | \(0.829043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.83282i | 0.265365i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.23607i | − 0.241462i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8328 | 0.418821 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.76393 | −0.106700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 14.3050i | − 0.551415i | −0.961242 | − | 0.275708i | \(-0.911088\pi\) | ||||
0.961242 | − | 0.275708i | \(-0.0889122\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.29180i | 0.164947i | 0.996593 | + | 0.0824736i | \(0.0262820\pi\) | ||||
−0.996593 | + | 0.0824736i | \(0.973718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.81966 | 0.146585 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.11146 | 0.234192 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 29.7771i | − 1.13939i | −0.821857 | − | 0.569694i | \(-0.807062\pi\) | ||||
0.821857 | − | 0.569694i | \(-0.192938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 13.5279i | − 0.516120i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.23607 | 0.275672 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.5279 | −1.27546 | −0.637730 | − | 0.770260i | \(-0.720126\pi\) | ||||
−0.637730 | + | 0.770260i | \(0.720126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 0.347524i | − 0.0132014i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.5279i | 1.11845i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.6525 | 0.629854 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.4721 | −1.75523 | −0.877614 | − | 0.479368i | \(-0.840866\pi\) | ||||
−0.877614 | + | 0.479368i | \(0.840866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.76393i | 0.255107i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.249224i | 0.00937302i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4164 | 0.654087 | 0.327043 | − | 0.945009i | \(-0.393948\pi\) | ||||
0.327043 | + | 0.945009i | \(0.393948\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.5704 | 0.396422 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.47214i | 0.317284i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.8885i | 0.518677i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.2918 | −0.905931 | −0.452966 | − | 0.891528i | \(-0.649634\pi\) | ||||
−0.452966 | + | 0.891528i | \(0.649634\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.527864 | 0.0196587 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 20.7214i | − 0.770636i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.7214i | 1.65862i | 0.558786 | + | 0.829312i | \(0.311267\pi\) | ||||
−0.558786 | + | 0.829312i | \(0.688733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.0557 | −0.890953 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.3607 | −1.04896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 48.4721i | − 1.79036i | −0.445706 | − | 0.895180i | \(-0.647047\pi\) | ||||
0.445706 | − | 0.895180i | \(-0.352953\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.94427i | 0.182125i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.9443 | −0.991161 | −0.495581 | − | 0.868562i | \(-0.665045\pi\) | ||||
−0.495581 | + | 0.868562i | \(0.665045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.76393 | −0.101536 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8197i | 0.617053i | 0.951216 | + | 0.308527i | \(0.0998359\pi\) | ||||
−0.951216 | + | 0.308527i | \(0.900164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.2492i | 0.484764i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.75078 | −0.0639720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.5967 | 0.970529 | 0.485265 | − | 0.874367i | \(-0.338723\pi\) | ||||
0.485265 | + | 0.874367i | \(0.338723\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.8885i | 0.651895i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.2361i | 0.771838i | 0.922533 | + | 0.385919i | \(0.126116\pi\) | ||||
−0.922533 | + | 0.385919i | \(0.873884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.23607 | −0.0448664 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.1115 | −0.620290 | −0.310145 | − | 0.950689i | \(-0.600378\pi\) | ||||
−0.310145 | + | 0.950689i | \(0.600378\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 4.06888i | − 0.147303i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.76393i | 0.0997998i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.0689 | −0.435215 | −0.217608 | − | 0.976036i | \(-0.569825\pi\) | ||||
−0.217608 | + | 0.976036i | \(0.569825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.3050 | 0.623223 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 9.23607i | − 0.332198i | −0.986109 | − | 0.166099i | \(-0.946883\pi\) | ||||
0.986109 | − | 0.166099i | \(-0.0531172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.97369i | 0.0708057i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.9443 | −0.427948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 34.4721i | − 1.23193i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.7214i | 1.77238i | 0.463327 | + | 0.886188i | \(0.346656\pi\) | ||||
−0.463327 | + | 0.886188i | \(0.653344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.88854 | 0.352041 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.65248 | 0.0943112 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 6.18034i | − 0.219470i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 10.7639i | − 0.381278i | −0.981660 | − | 0.190639i | \(-0.938944\pi\) | ||||
0.981660 | − | 0.190639i | \(-0.0610560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.22291 | −0.149396 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.94427 | −0.104031 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 0.527864i | − 0.0186279i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 3.48529i | − 0.122688i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.8885 | 1.57820 | 0.789099 | − | 0.614267i | \(-0.210548\pi\) | ||||
0.789099 | + | 0.614267i | \(0.210548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.4164 | −0.400884 | −0.200442 | − | 0.979706i | \(-0.564238\pi\) | ||||
−0.200442 | + | 0.979706i | \(0.564238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 32.2229i | − 1.13011i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 11.4721i | − 0.401359i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.777088 | 0.0271536 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.7639 | −0.619966 | −0.309983 | − | 0.950742i | \(-0.600323\pi\) | ||||
−0.309983 | + | 0.950742i | \(0.600323\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 8.94427i | − 0.311778i | −0.987775 | − | 0.155889i | \(-0.950176\pi\) | ||||
0.987775 | − | 0.155889i | \(-0.0498242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 3.00000i | − 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.236068 | −0.00819898 | −0.00409949 | − | 0.999992i | \(-0.501305\pi\) | ||||
−0.00409949 | + | 0.999992i | \(0.501305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.0689 | −0.418665 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.1672i | 0.594808i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.8328i | 1.61878i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.5967 | 1.40156 | 0.700778 | − | 0.713380i | \(-0.252836\pi\) | ||||
0.700778 | + | 0.713380i | \(0.252836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.88854 | 0.340984 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 0.222912i | − 0.00767751i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.36068i | 0.0811139i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.2229 | −0.694049 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.76393 | −0.231865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7639i | 0.813662i | 0.913504 | + | 0.406831i | \(0.133366\pi\) | ||||
−0.913504 | + | 0.406831i | \(0.866634\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 27.3050i | − 0.932719i | −0.884595 | − | 0.466360i | \(-0.845565\pi\) | ||||
0.884595 | − | 0.466360i | \(-0.154435\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.29180 | 0.282912 | 0.141456 | − | 0.989945i | \(-0.454822\pi\) | ||||
0.141456 | + | 0.989945i | \(0.454822\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.48529 | −0.118778 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 32.5410i | 1.10771i | 0.832613 | + | 0.553855i | \(0.186844\pi\) | ||||
−0.832613 | + | 0.553855i | \(0.813156\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 13.4590i | − 0.457091i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.18034 | 0.243576 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0557 | −0.374609 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.8197i | 0.806173i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.4164i | 0.993322i | 0.867945 | + | 0.496661i | \(0.165441\pi\) | ||||
−0.867945 | + | 0.496661i | \(0.834559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.83282 | −0.230465 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.2918 | 0.818411 | 0.409206 | − | 0.912442i | \(-0.365806\pi\) | ||||
0.409206 | + | 0.912442i | \(0.365806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 20.9443i | − 0.704831i | −0.935844 | − | 0.352415i | \(-0.885360\pi\) | ||||
0.935844 | − | 0.352415i | \(-0.114640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 32.3607i | − 1.08657i | −0.839550 | − | 0.543283i | \(-0.817181\pi\) | ||||
0.839550 | − | 0.543283i | \(-0.182819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.29180 | −0.143942 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.41641 | −0.0809527 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.70820i | − 0.0571629i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.76393i | − 0.0922850i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −52.8328 | −1.76207 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3.34752i | − 0.111399i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.4164i | 1.07637i | 0.842827 | + | 0.538185i | \(0.180890\pi\) | ||||
−0.842827 | + | 0.538185i | \(0.819110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.55418 | −0.0515487 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.0689 | 0.896832 | 0.448416 | − | 0.893825i | \(-0.351988\pi\) | ||||
0.448416 | + | 0.893825i | \(0.351988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00000i | 0.297857i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 0.695048i | − 0.0229525i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7771 | 0.916282 | 0.458141 | − | 0.888880i | \(-0.348516\pi\) | ||||
0.458141 | + | 0.888880i | \(0.348516\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.6656 | −0.977516 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.3607i | 0.736011i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.29180i | 0.108117i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0000 | −1.01708 | −0.508539 | − | 0.861039i | \(-0.669814\pi\) | ||||
−0.508539 | + | 0.861039i | \(0.669814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.94427 | −0.227589 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.52786i | − 0.0500200i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.1246i | 1.08213i | 0.840980 | + | 0.541067i | \(0.181979\pi\) | ||||
−0.840980 | + | 0.541067i | \(0.818021\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.5279 | 0.833070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.76393 | −0.285696 | −0.142848 | − | 0.989745i | \(-0.545626\pi\) | ||||
−0.142848 | + | 0.989745i | \(0.545626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 11.9443i | − 0.388959i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.1935i | 1.72856i | 0.503014 | + | 0.864278i | \(0.332224\pi\) | ||||
−0.503014 | + | 0.864278i | \(0.667776\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.18034 | 0.0383155 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.4033 | −0.726475 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.6525i | 1.18729i | 0.804727 | + | 0.593645i | \(0.202312\pi\) | ||||
−0.804727 | + | 0.593645i | \(0.797688\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.70820i | − 0.249171i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.83282 | −0.156060 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7771 | 1.31539 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10.9180i | − 0.351826i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8885i | 0.961151i | 0.876953 | + | 0.480575i | \(0.159572\pi\) | ||||
−0.876953 | + | 0.480575i | \(0.840428\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.05573 | −0.0981641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.2492 | −1.38793 | −0.693967 | − | 0.720007i | \(-0.744139\pi\) | ||||
−0.693967 | + | 0.720007i | \(0.744139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.72136i | 0.151360i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.5410i | 1.42499i | 0.701675 | + | 0.712497i | \(0.252436\pi\) | ||||
−0.701675 | + | 0.712497i | \(0.747564\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.3738 | 0.810124 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 3.65248i | − 0.116496i | −0.998302 | − | 0.0582479i | \(-0.981449\pi\) | ||||
0.998302 | − | 0.0582479i | \(-0.0185514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 0.498447i | − 0.0158657i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.4721 | 0.364793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.59675 | 0.241319 | 0.120659 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120659 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 16.1378i | − 0.512117i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 38.1246i | − 1.20742i | −0.797205 | − | 0.603709i | \(-0.793689\pi\) | ||||
0.797205 | − | 0.603709i | \(-0.206311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.3901 | −1.18297 |
(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 | 4600.2.e.l.4049.2 | 4 | ||
5.2 | odd | 4 | 4600.2.a.u.1.1 | yes | 2 | ||
5.3 | odd | 4 | 4600.2.a.q.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 4600.2.e.l.4049.3 | 4 | ||
20.3 | even | 4 | 9200.2.a.bz.1.1 | 2 | |||
20.7 | even | 4 | 9200.2.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.q.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
4600.2.a.u.1.1 | yes | 2 | 5.2 | odd | 4 | ||
4600.2.e.l.4049.2 | 4 | 1.1 | even | 1 | trivial | ||
4600.2.e.l.4049.3 | 4 | 5.4 | even | 2 | inner | ||
9200.2.a.bn.1.2 | 2 | 20.7 | even | 4 | |||
9200.2.a.bz.1.1 | 2 | 20.3 | even | 4 |