Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6900,2,Mod(6349,6900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6900, 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("6900.6349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6900.f (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: | \(55.0967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.158155776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 24x^{3} + 81x^{2} + 54x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6349.1 | ||
Root | \(-1.42234 + 1.42234i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6900.6349 |
Dual form | 6900.2.f.r.6349.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6900\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(1201\) | \(3451\) | \(4601\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 3.73549i | − 1.41188i | −0.708270 | − | 0.705941i | \(-0.750524\pi\) | ||||
0.708270 | − | 0.705941i | \(-0.249476\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.84469 | 1.46073 | 0.730364 | − | 0.683058i | \(-0.239351\pi\) | ||||
0.730364 | + | 0.683058i | \(0.239351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.84469i | 0.788974i | 0.918902 | + | 0.394487i | \(0.129078\pi\) | ||||
−0.918902 | + | 0.394487i | \(0.870922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.890804i | 0.216052i | 0.994148 | + | 0.108026i | \(0.0344529\pi\) | ||||
−0.994148 | + | 0.108026i | \(0.965547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.84469 | −1.57028 | −0.785139 | − | 0.619319i | \(-0.787409\pi\) | ||||
−0.785139 | + | 0.619319i | \(0.787409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.73549 | −0.815151 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.890804 | 0.165418 | 0.0827091 | − | 0.996574i | \(-0.473643\pi\) | ||||
0.0827091 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.73549 | 1.38933 | 0.694667 | − | 0.719331i | \(-0.255552\pi\) | ||||
0.694667 | + | 0.719331i | \(0.255552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 4.84469i | − 0.843352i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.95388i | − 0.321216i | −0.987018 | − | 0.160608i | \(-0.948654\pi\) | ||||
0.987018 | − | 0.160608i | \(-0.0513455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.84469 | 0.455514 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.3618 | 1.93059 | 0.965293 | − | 0.261169i | \(-0.0841080\pi\) | ||||
0.965293 | + | 0.261169i | \(0.0841080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.47098i | 0.529319i | 0.964342 | + | 0.264660i | \(0.0852596\pi\) | ||||
−0.964342 | + | 0.264660i | \(0.914740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.62629i | − 0.966544i | −0.875470 | − | 0.483272i | \(-0.839448\pi\) | ||||
0.875470 | − | 0.483272i | \(-0.160552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95388 | −0.993412 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.890804 | 0.124737 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 12.3618i | − 1.69802i | −0.528376 | − | 0.849011i | \(-0.677199\pi\) | ||||
0.528376 | − | 0.849011i | \(-0.322801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.84469i | 0.906601i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.890804 | −0.115973 | −0.0579864 | − | 0.998317i | \(-0.518468\pi\) | ||||
−0.0579864 | + | 0.998317i | \(0.518468\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.62629 | 1.10448 | 0.552242 | − | 0.833684i | \(-0.313773\pi\) | ||||
0.552242 | + | 0.833684i | \(0.313773\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.73549i | 0.470627i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.73549i | 0.945040i | 0.881320 | + | 0.472520i | \(0.156656\pi\) | ||||
−0.881320 | + | 0.472520i | \(0.843344\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.3618 | −1.46707 | −0.733537 | − | 0.679650i | \(-0.762132\pi\) | ||||
−0.733537 | + | 0.679650i | \(0.762132\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 16.5341i | − 1.93516i | −0.252555 | − | 0.967582i | \(-0.581271\pi\) | ||||
0.252555 | − | 0.967582i | \(-0.418729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 18.0973i | − 2.06238i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4710 | −1.51560 | −0.757802 | − | 0.652485i | \(-0.773727\pi\) | ||||
−0.757802 | + | 0.652485i | \(0.773727\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.58018i | 0.502740i | 0.967891 | + | 0.251370i | \(0.0808810\pi\) | ||||
−0.967891 | + | 0.251370i | \(0.919119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 0.890804i | − 0.0955042i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.1604 | 1.60699 | 0.803497 | − | 0.595309i | \(-0.202970\pi\) | ||||
0.803497 | + | 0.595309i | \(0.202970\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6263 | 1.11394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.73549i | − 0.802133i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 17.2526i | − 1.75173i | −0.482552 | − | 0.875867i | \(-0.660290\pi\) | ||||
0.482552 | − | 0.875867i | \(-0.339710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.84469 | −0.486909 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.67241 | −0.265915 | −0.132957 | − | 0.991122i | \(-0.542447\pi\) | ||||
−0.132957 | + | 0.991122i | \(0.542447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.21839i | − 0.612716i | −0.951916 | − | 0.306358i | \(-0.900889\pi\) | ||||
0.951916 | − | 0.306358i | \(-0.0991105\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14.7986i | − 1.43063i | −0.698801 | − | 0.715316i | \(-0.746283\pi\) | ||||
0.698801 | − | 0.715316i | \(-0.253717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5341 | 1.20054 | 0.600272 | − | 0.799796i | \(-0.295059\pi\) | ||||
0.600272 | + | 0.799796i | \(0.295059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.95388 | −0.185454 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 12.3618i | − 1.16290i | −0.813583 | − | 0.581449i | \(-0.802486\pi\) | ||||
0.813583 | − | 0.581449i | \(-0.197514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.84469i | − 0.262991i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.32759 | 0.305040 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4710 | 1.13373 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 12.3618i | − 1.11462i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.7866i | 1.04590i | 0.852365 | + | 0.522948i | \(0.175168\pi\) | ||||
−0.852365 | + | 0.522948i | \(0.824832\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.47098 | 0.305603 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4710 | −1.52645 | −0.763223 | − | 0.646135i | \(-0.776384\pi\) | ||||
−0.763223 | + | 0.646135i | \(0.776384\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.5683i | 2.21705i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1604i | 1.29524i | 0.761965 | + | 0.647618i | \(0.224235\pi\) | ||||
−0.761965 | + | 0.647618i | \(0.775765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.51710 | 0.467954 | 0.233977 | − | 0.972242i | \(-0.424826\pi\) | ||||
0.233977 | + | 0.972242i | \(0.424826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.62629 | −0.558035 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.7816i | 1.15248i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.95388i | 0.573547i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.15531 | −0.0946470 | −0.0473235 | − | 0.998880i | \(-0.515069\pi\) | ||||
−0.0473235 | + | 0.998880i | \(0.515069\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4710 | −1.25901 | −0.629505 | − | 0.776996i | \(-0.716742\pi\) | ||||
−0.629505 | + | 0.776996i | \(0.716742\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 0.890804i | − 0.0720172i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6774i | 1.49062i | 0.666717 | + | 0.745311i | \(0.267699\pi\) | ||||
−0.666717 | + | 0.745311i | \(0.732301\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.3618 | −0.980353 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.73549 | −0.294398 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.0922364i | − 0.00722451i | −0.999993 | − | 0.00361226i | \(-0.998850\pi\) | ||||
0.999993 | − | 0.00361226i | \(-0.00114982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 5.37371i | − 0.415830i | −0.978147 | − | 0.207915i | \(-0.933332\pi\) | ||||
0.978147 | − | 0.207915i | \(-0.0666677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.90776 | 0.377520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.84469 | 0.523426 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.890804i | 0.0669569i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.56322 | 0.714788 | 0.357394 | − | 0.933954i | \(-0.383665\pi\) | ||||
0.357394 | + | 0.933954i | \(0.383665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.16035 | −0.532225 | −0.266112 | − | 0.963942i | \(-0.585739\pi\) | ||||
−0.266112 | + | 0.963942i | \(0.585739\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 8.62629i | − 0.637674i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.31566i | 0.315593i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.73549 | 0.271717 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0050 | 1.01337 | 0.506684 | − | 0.862132i | \(-0.330871\pi\) | ||||
0.506684 | + | 0.862132i | \(0.330871\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 26.7236i | − 1.92360i | −0.273745 | − | 0.961802i | \(-0.588263\pi\) | ||||
0.273745 | − | 0.961802i | \(-0.411737\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.16035i | 0.652648i | 0.945258 | + | 0.326324i | \(0.105810\pi\) | ||||
−0.945258 | + | 0.326324i | \(0.894190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.310629 | 0.0220199 | 0.0110099 | − | 0.999939i | \(-0.496495\pi\) | ||||
0.0110099 | + | 0.999939i | \(0.496495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.73549 | 0.545619 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.32759i | − 0.233551i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.1604 | −2.29375 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.95388 | 0.409882 | 0.204941 | − | 0.978774i | \(-0.434300\pi\) | ||||
0.204941 | + | 0.978774i | \(0.434300\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.3618i | 0.847015i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 28.8958i | − 1.96158i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.5341 | −1.11727 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.53406 | −0.170459 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.9078i | 0.797403i | 0.917081 | + | 0.398701i | \(0.130539\pi\) | ||||
−0.917081 | + | 0.398701i | \(0.869461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.37874i | 0.489744i | 0.969555 | + | 0.244872i | \(0.0787460\pi\) | ||||
−0.969555 | + | 0.244872i | \(0.921254\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.1604 | −1.53048 | −0.765240 | − | 0.643746i | \(-0.777379\pi\) | ||||
−0.765240 | + | 0.643746i | \(0.777379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.0973 | −1.19071 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9420i | 1.50298i | 0.659746 | + | 0.751489i | \(0.270664\pi\) | ||||
−0.659746 | + | 0.751489i | \(0.729336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.4710i | 0.875034i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.361783 | −0.0234018 | −0.0117009 | − | 0.999932i | \(-0.503725\pi\) | ||||
−0.0117009 | + | 0.999932i | \(0.503725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5341 | 1.83804 | 0.919020 | − | 0.394211i | \(-0.128982\pi\) | ||||
0.919020 | + | 0.394211i | \(0.128982\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 19.4710i | − 1.23891i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.58018 | 0.290257 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.8497 | −1.94722 | −0.973609 | − | 0.228224i | \(-0.926708\pi\) | ||||
−0.973609 | + | 0.228224i | \(0.926708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.84469i | − 0.304583i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 12.7524i | − 0.795476i | −0.917499 | − | 0.397738i | \(-0.869795\pi\) | ||||
0.917499 | − | 0.397738i | \(-0.130205\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.29870 | −0.453519 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.890804 | −0.0551394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 6.36178i | − 0.392284i | −0.980575 | − | 0.196142i | \(-0.937159\pi\) | ||||
0.980575 | − | 0.196142i | \(-0.0628414\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 15.1604i | − 0.927798i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5802 | −0.645085 | −0.322542 | − | 0.946555i | \(-0.604537\pi\) | ||||
−0.322542 | + | 0.946555i | \(0.604537\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.26451 | −0.259051 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 10.6263i | − 0.643133i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 29.3787i | − 1.76520i | −0.470127 | − | 0.882599i | \(-0.655792\pi\) | ||||
0.470127 | − | 0.882599i | \(-0.344208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.73549 | −0.463112 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7524 | −1.11868 | −0.559339 | − | 0.828939i | \(-0.688945\pi\) | ||||
−0.559339 | + | 0.828939i | \(0.688945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.8958i | 0.766578i | 0.923628 | + | 0.383289i | \(0.125209\pi\) | ||||
−0.923628 | + | 0.383289i | \(0.874791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 46.1773i | − 2.72576i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.2065 | 0.953322 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.2526 | −1.01136 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 8.79857i | − 0.514018i | −0.966409 | − | 0.257009i | \(-0.917263\pi\) | ||||
0.966409 | − | 0.257009i | \(-0.0827370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.84469i | 0.281117i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.84469 | 0.164512 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.9658 | 0.747337 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.67241i | 0.153526i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0050i | 0.571018i | 0.958376 | + | 0.285509i | \(0.0921626\pi\) | ||||
−0.958376 | + | 0.285509i | \(0.907837\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.21839 | −0.353752 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5290 | −1.05068 | −0.525342 | − | 0.850891i | \(-0.676063\pi\) | ||||
−0.525342 | + | 0.850891i | \(0.676063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 2.39067i | − 0.135128i | −0.997715 | − | 0.0675642i | \(-0.978477\pi\) | ||||
0.997715 | − | 0.0675642i | \(-0.0215228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 16.3157i | − 0.916379i | −0.888855 | − | 0.458190i | \(-0.848498\pi\) | ||||
0.888855 | − | 0.458190i | \(-0.151502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.31566 | 0.241631 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.7986 | −0.825975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.09727i | − 0.339261i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 12.5341i | − 0.693135i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.7524 | −1.36465 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.8958 | −1.36840 | −0.684200 | − | 0.729295i | \(-0.739848\pi\) | ||||
−0.684200 | + | 0.729295i | \(0.739848\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.95388i | 0.107072i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 27.4710i | − 1.49644i | −0.663451 | − | 0.748220i | \(-0.730909\pi\) | ||||
0.663451 | − | 0.748220i | \(-0.269091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3618 | −0.671400 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.4760 | 2.02944 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 0.172274i | − 0.00930193i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.25259i | − 0.0672424i | −0.999435 | − | 0.0336212i | \(-0.989296\pi\) | ||||
0.999435 | − | 0.0336212i | \(-0.0107040\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.64325 | −0.516192 | −0.258096 | − | 0.966119i | \(-0.583095\pi\) | ||||
−0.258096 | + | 0.966119i | \(0.583095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.84469 | −0.151838 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7524i | 0.678744i | 0.940652 | + | 0.339372i | \(0.110215\pi\) | ||||
−0.940652 | + | 0.339372i | \(0.889785\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.32759i | − 0.176115i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.62629 | 0.349722 | 0.174861 | − | 0.984593i | \(-0.444052\pi\) | ||||
0.174861 | + | 0.984593i | \(0.444052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.8497 | 1.46577 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 12.4710i | − 0.654557i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 9.60933i | − 0.501603i | −0.968039 | − | 0.250802i | \(-0.919306\pi\) | ||||
0.968039 | − | 0.250802i | \(-0.0806942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3618 | −0.643529 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.1773 | −2.39741 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 29.8839i | − 1.54733i | −0.633595 | − | 0.773665i | \(-0.718421\pi\) | ||||
0.633595 | − | 0.773665i | \(-0.281579\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.53406i | 0.130511i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.52902 | −0.129907 | −0.0649535 | − | 0.997888i | \(-0.520690\pi\) | ||||
−0.0649535 | + | 0.997888i | \(0.520690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.7866 | 0.603848 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 25.2115i | − 1.28825i | −0.764921 | − | 0.644124i | \(-0.777222\pi\) | ||||
0.764921 | − | 0.644124i | \(-0.222778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.47098i | − 0.176440i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.0681 | −1.77802 | −0.889012 | − | 0.457884i | \(-0.848608\pi\) | ||||
−0.889012 | + | 0.457884i | \(0.848608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.890804 | 0.0450499 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.4710i | 0.881294i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.84972i | 0.444155i | 0.975029 | + | 0.222077i | \(0.0712838\pi\) | ||||
−0.975029 | + | 0.222077i | \(0.928716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.5683 | 1.28001 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0681 | −1.15197 | −0.575983 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575983 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.0050i | 1.09615i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 9.46594i | − 0.469209i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.29870 | −0.262004 | −0.131002 | − | 0.991382i | \(-0.541819\pi\) | ||||
−0.131002 | + | 0.991382i | \(0.541819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.1604 | 0.747805 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.32759i | 0.163740i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 5.51710i | − 0.270173i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.53406 | −0.123797 | −0.0618984 | − | 0.998082i | \(-0.519715\pi\) | ||||
−0.0618984 | + | 0.998082i | \(0.519715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4079 | 1.09209 | 0.546047 | − | 0.837754i | \(-0.316132\pi\) | ||||
0.546047 | + | 0.837754i | \(0.316132\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.62629i | 0.322181i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 32.2234i | − 1.55940i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.7816 | 0.665382 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.5733 | 1.52083 | 0.760416 | − | 0.649436i | \(-0.224995\pi\) | ||||
0.760416 | + | 0.649436i | \(0.224995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 7.20647i | − 0.346321i | −0.984894 | − | 0.173160i | \(-0.944602\pi\) | ||||
0.984894 | − | 0.173160i | \(-0.0553979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.84469i | 0.327426i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.72357 | 0.225443 | 0.112722 | − | 0.993627i | \(-0.464043\pi\) | ||||
0.112722 | + | 0.993627i | \(0.464043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.95388 | 0.331137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.87888i | 0.374337i | 0.982328 | + | 0.187168i | \(0.0599310\pi\) | ||||
−0.982328 | + | 0.187168i | \(0.940069\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.15531i | 0.0546445i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.70633 | 0.222105 | 0.111053 | − | 0.993815i | \(-0.464578\pi\) | ||||
0.111053 | + | 0.993815i | \(0.464578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 59.8890 | 2.82006 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4710i | 0.726890i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.04612i | − 0.282825i | −0.989951 | − | 0.141413i | \(-0.954836\pi\) | ||||
0.989951 | − | 0.141413i | \(-0.0451645\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.890804 | −0.0415792 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.2526 | −0.896682 | −0.448341 | − | 0.893863i | \(-0.647985\pi\) | ||||
−0.448341 | + | 0.893863i | \(0.647985\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.4418i | 1.22886i | 0.788973 | + | 0.614428i | \(0.210613\pi\) | ||||
−0.788973 | + | 0.614428i | \(0.789387\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.20143i | 0.425792i | 0.977075 | + | 0.212896i | \(0.0682895\pi\) | ||||
−0.977075 | + | 0.212896i | \(0.931711\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.8958 | 1.33429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.6774 | 0.860611 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.8158i | 0.773191i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.3618i | 0.566007i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.7524 | 0.582674 | 0.291337 | − | 0.956620i | \(-0.405900\pi\) | ||||
0.291337 | + | 0.956620i | \(0.405900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.55818 | 0.253431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.73549i | 0.169971i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 30.5341i | − 1.38363i | −0.722075 | − | 0.691815i | \(-0.756811\pi\) | ||||
0.722075 | − | 0.691815i | \(-0.243189\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0922364 | −0.00417107 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.67241 | −0.120604 | −0.0603021 | − | 0.998180i | \(-0.519206\pi\) | ||||
−0.0603021 | + | 0.998180i | \(0.519206\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.793532i | 0.0357389i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.1773i | 2.07134i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8036 | 0.931297 | 0.465649 | − | 0.884970i | \(-0.345821\pi\) | ||||
0.465649 | + | 0.884970i | \(0.345821\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.37371 | −0.240080 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 3.32759i | − 0.148370i | −0.997245 | − | 0.0741849i | \(-0.976364\pi\) | ||||
0.997245 | − | 0.0741849i | \(-0.0236355\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 4.90776i | − 0.217961i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.2184 | −0.718868 | −0.359434 | − | 0.933171i | \(-0.617030\pi\) | ||||
−0.359434 | + | 0.933171i | \(0.617030\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −61.7628 | −2.73223 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 6.84469i | − 0.302200i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 32.1023i | − 1.41186i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.18923 | 0.139723 | 0.0698614 | − | 0.997557i | \(-0.477744\pi\) | ||||
0.0698614 | + | 0.997557i | \(0.477744\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.8155i | − 1.04138i | −0.853746 | − | 0.520690i | \(-0.825675\pi\) | ||||
0.853746 | − | 0.520690i | \(-0.174325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.89080i | 0.300168i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.890804 | 0.0386576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.1654i | 1.52318i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 9.56322i | − 0.412683i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.6894 | −1.45110 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7816 | 0.678504 | 0.339252 | − | 0.940695i | \(-0.389826\pi\) | ||||
0.339252 | + | 0.940695i | \(0.389826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.16035i | 0.307280i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.0000i | − 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.62629 | −0.368161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.09727 | −0.259753 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.3207i | 2.13985i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7405i | 1.34489i | 0.740147 | + | 0.672445i | \(0.234756\pi\) | ||||
−0.740147 | + | 0.672445i | \(0.765244\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.87384 | −0.417619 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31566 | 0.182208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 21.9250i | − 0.924029i | −0.886872 | − | 0.462014i | \(-0.847127\pi\) | ||||
0.886872 | − | 0.462014i | \(-0.152873\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 3.73549i | − 0.156876i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6313 | 0.613377 | 0.306689 | − | 0.951810i | \(-0.400779\pi\) | ||||
0.306689 | + | 0.951810i | \(0.400779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24755 | 0.0522084 | 0.0261042 | − | 0.999659i | \(-0.491690\pi\) | ||||
0.0261042 | + | 0.999659i | \(0.491690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 14.0050i | − 0.585069i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0922i | 0.753190i | 0.926378 | + | 0.376595i | \(0.122905\pi\) | ||||
−0.926378 | + | 0.376595i | \(0.877095\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.7236 | −1.11059 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1092 | 0.709809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 59.8890i | − 2.48035i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.5290i | 0.517128i | 0.965994 | + | 0.258564i | \(0.0832493\pi\) | ||||
−0.965994 | + | 0.258564i | \(0.916751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.9470 | −2.18164 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.16035 | 0.376806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.9470i | 1.02445i | 0.858851 | + | 0.512225i | \(0.171179\pi\) | ||||
−0.858851 | + | 0.512225i | \(0.828821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 0.310629i | − 0.0127132i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.5391 | 1.41123 | 0.705615 | − | 0.708596i | \(-0.250671\pi\) | ||||
0.705615 | + | 0.708596i | \(0.250671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.9300 | 1.54720 | 0.773599 | − | 0.633675i | \(-0.218454\pi\) | ||||
0.773599 | + | 0.633675i | \(0.218454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7.73549i | − 0.315013i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.0973i | 1.05926i | 0.848230 | + | 0.529628i | \(0.177668\pi\) | ||||
−0.848230 | + | 0.529628i | \(0.822332\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.32759 | −0.134841 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.8497 | 0.762578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.84972i | − 0.115099i | −0.998343 | − | 0.0575496i | \(-0.981671\pi\) | ||||
0.998343 | − | 0.0575496i | \(-0.0183287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 9.52213i | − 0.383347i | −0.981459 | − | 0.191673i | \(-0.938609\pi\) | ||||
0.981459 | − | 0.191673i | \(-0.0613914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.9762 | 0.963683 | 0.481841 | − | 0.876258i | \(-0.339968\pi\) | ||||
0.481841 | + | 0.876258i | \(0.339968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 56.6313i | − 2.26889i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.1604i | 1.32430i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.74053 | 0.0693993 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8789 | −0.711747 | −0.355873 | − | 0.934534i | \(-0.615817\pi\) | ||||
−0.355873 | + | 0.934534i | \(0.615817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 5.95388i | − 0.236646i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 19.7816i | − 0.783776i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.3618 | 0.489025 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.93692 | 0.116001 | 0.0580007 | − | 0.998317i | \(-0.481527\pi\) | ||||
0.0580007 | + | 0.998317i | \(0.481527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.895840i | 0.0353285i | 0.999844 | + | 0.0176642i | \(0.00562299\pi\) | ||||
−0.999844 | + | 0.0176642i | \(0.994377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 21.4659i | − 0.843913i | −0.906616 | − | 0.421957i | \(-0.861343\pi\) | ||||
0.906616 | − | 0.421957i | \(-0.138657\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.31566 | −0.169405 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.8958 | −1.13252 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.84469i | 0.189587i | 0.995497 | + | 0.0947936i | \(0.0302191\pi\) | ||||
−0.995497 | + | 0.0947936i | \(0.969781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5341i | 0.645055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0973 | 0.704970 | 0.352485 | − | 0.935818i | \(-0.385337\pi\) | ||||
0.352485 | + | 0.935818i | \(0.385337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.747413 | 0.0290710 | 0.0145355 | − | 0.999894i | \(-0.495373\pi\) | ||||
0.0145355 | + | 0.999894i | \(0.495373\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.53406i | 0.0984146i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.890804i | − 0.0344921i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.9078 | 0.460381 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.7917 | 1.61335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1892i | 0.739691i | 0.929093 | + | 0.369845i | \(0.120589\pi\) | ||||
−0.929093 | + | 0.369845i | \(0.879411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 4.17731i | − 0.160547i | −0.996773 | − | 0.0802735i | \(-0.974421\pi\) | ||||
0.996773 | − | 0.0802735i | \(-0.0255794\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −64.4469 | −2.47324 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.37874 | 0.282754 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0050i | 0.995055i | 0.867448 | + | 0.497528i | \(0.165759\pi\) | ||||
−0.867448 | + | 0.497528i | \(0.834241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.1604i | 0.883622i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.1654 | 1.33969 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8497 | 1.02141 | 0.510706 | − | 0.859756i | \(-0.329384\pi\) | ||||
0.510706 | + | 0.859756i | \(0.329384\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0973i | 0.687459i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0119i | 0.417106i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.9420 | 0.867745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.9027 | 0.449560 | 0.224780 | − | 0.974410i | \(-0.427834\pi\) | ||||
0.224780 | + | 0.974410i | \(0.427834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3737i | 0.504399i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.98277i | 0.375441i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.3737 | 1.47871 | 0.739355 | − | 0.673315i | \(-0.235130\pi\) | ||||
0.739355 | + | 0.673315i | \(0.235130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4710 | 0.505201 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 7.73549i | − 0.289696i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.361783i | 0.0135110i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.6382 | −0.881557 | −0.440778 | − | 0.897616i | \(-0.645298\pi\) | ||||
−0.440778 | + | 0.897616i | \(0.645298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2287 | −0.865083 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 28.5341i | − 1.06119i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.5513i | 0.465502i | 0.972536 | + | 0.232751i | \(0.0747727\pi\) | ||||
−0.972536 | + | 0.232751i | \(0.925227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.09196 | −0.114360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 39.1142i | − 1.44472i | −0.691519 | − | 0.722359i | \(-0.743058\pi\) | ||||
0.691519 | − | 0.722359i | \(-0.256942\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.4760i | 1.38045i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.7456 | −1.31492 | −0.657461 | − | 0.753489i | \(-0.728370\pi\) | ||||
−0.657461 | + | 0.753489i | \(0.728370\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.4710 | −0.715284 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 20.4368i | − 0.749753i | −0.927075 | − | 0.374876i | \(-0.877685\pi\) | ||||
0.927075 | − | 0.374876i | \(-0.122315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.58018i | − 0.167580i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.2799 | −2.01988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.534057 | −0.0194880 | −0.00974401 | − | 0.999953i | \(-0.503102\pi\) | ||||
−0.00974401 | + | 0.999953i | \(0.503102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.8497i | 1.12423i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 29.5171i | − 1.07282i | −0.843958 | − | 0.536409i | \(-0.819781\pi\) | ||||
0.843958 | − | 0.536409i | \(-0.180219\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.84469 | −0.175851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1434 | 1.38270 | 0.691348 | − | 0.722522i | \(-0.257017\pi\) | ||||
0.691348 | + | 0.722522i | \(0.257017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 46.8208i | − 1.69503i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.53406i | − 0.0914995i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.8786 | −0.752902 | −0.376451 | − | 0.926437i | \(-0.622856\pi\) | ||||
−0.376451 | + | 0.926437i | \(0.622856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7524 | −0.459268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 8.31063i | − 0.298913i | −0.988768 | − | 0.149456i | \(-0.952248\pi\) | ||||
0.988768 | − | 0.149456i | \(-0.0477523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.29870i | 0.261840i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −84.6125 | −3.03156 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.8890 | −2.14300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.890804i | 0.0318347i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.95388i | − 0.0696484i | −0.999393 | − | 0.0348242i | \(-0.988913\pi\) | ||||
0.999393 | − | 0.0348242i | \(-0.0110871\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.36178 | −0.226485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.1773 | −1.64188 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5391i | 0.871409i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 16.1773i | − 0.573030i | −0.958076 | − | 0.286515i | \(-0.907503\pi\) | ||||
0.958076 | − | 0.286515i | \(-0.0924968\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.90273 | 0.208823 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1604 | −0.535665 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 80.1023i | − 2.82675i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.5802i | 0.372440i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8670 | 0.944592 | 0.472296 | − | 0.881440i | \(-0.343425\pi\) | ||||
0.472296 | + | 0.881440i | \(0.343425\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.13835 | 0.0750878 | 0.0375439 | − | 0.999295i | \(-0.488047\pi\) | ||||
0.0375439 | + | 0.999295i | \(0.488047\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.26451i | 0.149563i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 23.7578i | − 0.831179i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.6263 | −0.371313 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1604 | 0.529100 | 0.264550 | − | 0.964372i | \(-0.414777\pi\) | ||||
0.264550 | + | 0.964372i | \(0.414777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.1264i | 0.806137i | 0.915170 | + | 0.403068i | \(0.132056\pi\) | ||||
−0.915170 | + | 0.403068i | \(0.867944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.4299i | 1.64930i | 0.565644 | + | 0.824650i | \(0.308628\pi\) | ||||
−0.565644 | + | 0.824650i | \(0.691372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.1723 | 1.04793 | 0.523963 | − | 0.851741i | \(-0.324453\pi\) | ||||
0.523963 | + | 0.851741i | \(0.324453\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3787 | −1.01914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.19454i | − 0.214628i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.73549i | 0.267378i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.8497 | −0.650765 | −0.325382 | − | 0.945583i | \(-0.605493\pi\) | ||||
−0.325382 | + | 0.945583i | \(0.605493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2065 | −0.972637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.7524i | 0.645869i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 46.5852i | − 1.60069i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.8958 | 0.442584 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.95388 | −0.0669782 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 29.7578i | − 1.01889i | −0.860504 | − | 0.509443i | \(-0.829851\pi\) | ||||
0.860504 | − | 0.509443i | \(-0.170149\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 15.2865i | − 0.522177i | −0.965315 | − | 0.261089i | \(-0.915919\pi\) | ||||
0.965315 | − | 0.261089i | \(-0.0840815\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.5171 | −1.14359 | −0.571794 | − | 0.820397i | \(-0.693752\pi\) | ||||
−0.571794 | + | 0.820397i | \(0.693752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −46.1773 | −1.57372 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.0443i | 1.05676i | 0.849008 | + | 0.528380i | \(0.177200\pi\) | ||||
−0.849008 | + | 0.528380i | \(0.822800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 16.2065i | − 0.550401i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.2627 | −2.21388 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0050 | −0.745612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.2526i | 0.583912i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.6313i | 0.358994i | 0.983758 | + | 0.179497i | \(0.0574471\pi\) | ||||
−0.983758 | + | 0.179497i | \(0.942553\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.79857 | −0.296768 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.5341 | 0.691810 | 0.345905 | − | 0.938270i | \(-0.387572\pi\) | ||||
0.345905 | + | 0.938270i | \(0.387572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 36.0390i | − 1.21281i | −0.795157 | − | 0.606404i | \(-0.792612\pi\) | ||||
0.795157 | − | 0.606404i | \(-0.207388\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 24.9759i | − 0.838608i | −0.907846 | − | 0.419304i | \(-0.862274\pi\) | ||||
0.907846 | − | 0.419304i | \(-0.137726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0289 | 1.47668 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.84469 | 0.162303 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.3549i | 1.51774i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.84469i | − 0.0949813i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.89080 | 0.229821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0119 | 0.366860 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 12.9658i | − 0.431475i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.6194i | 1.38195i | 0.722879 | + | 0.690975i | \(0.242818\pi\) | ||||
−0.722879 | + | 0.690975i | \(0.757182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.67241 | 0.0886383 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.81553 | 0.126414 | 0.0632070 | − | 0.998000i | \(-0.479867\pi\) | ||||
0.0632070 | + | 0.998000i | \(0.479867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.1895i | 0.734366i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 65.2627i | 2.15516i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.7917 | 1.31261 | 0.656303 | − | 0.754497i | \(-0.272119\pi\) | ||||
0.656303 | + | 0.754497i | \(0.272119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0050 | 0.329677 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 35.1654i | − 1.15748i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.21839i | 0.204239i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.6141 | −0.413855 | −0.206928 | − | 0.978356i | \(-0.566346\pi\) | ||||
−0.206928 | + | 0.978356i | \(0.566346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.5971 | 1.55993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.5290i | 0.606613i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 22.1262i | − 0.722830i | −0.932405 | − | 0.361415i | \(-0.882294\pi\) | ||||
0.932405 | − | 0.361415i | \(-0.117706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.39067 | −0.0780164 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0392 | −0.359869 | −0.179934 | − | 0.983679i | \(-0.557589\pi\) | ||||
−0.179934 | + | 0.983679i | \(0.557589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 12.3618i | − 0.402555i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.68937i | 0.314862i | 0.987530 | + | 0.157431i | \(0.0503212\pi\) | ||||
−0.987530 | + | 0.157431i | \(0.949679\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.0342 | 1.52679 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3157 | −0.529072 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1845i | 0.459480i | 0.973252 | + | 0.229740i | \(0.0737876\pi\) | ||||
−0.973252 | + | 0.229740i | \(0.926212\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 4.31566i | − 0.139506i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.6313 | 1.82872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8378 | 0.930252 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.7986i | 0.476877i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8447i | 0.413057i | 0.978441 | + | 0.206529i | \(0.0662167\pi\) | ||||
−0.978441 | + | 0.206529i | \(0.933783\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.09727 | −0.195873 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1945 | −0.776440 | −0.388220 | − | 0.921567i | \(-0.626910\pi\) | ||||
−0.388220 | + | 0.921567i | \(0.626910\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 20.6091i | − 0.660696i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.4879i | 0.591482i | 0.955268 | + | 0.295741i | \(0.0955665\pi\) | ||||
−0.955268 | + | 0.295741i | \(0.904434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 73.4471 | 2.34738 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.5341 | −0.400182 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.8325i | 0.919614i | 0.888019 | + | 0.459807i | \(0.152081\pi\) | ||||
−0.888019 | + | 0.459807i | \(0.847919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.7524i | 0.787879i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.47098 | 0.110371 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.8958 | 1.29910 | 0.649550 | − | 0.760319i | \(-0.274957\pi\) | ||||
0.649550 | + | 0.760319i | \(0.274957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.8958i | 0.790046i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 4.65518i | − 0.147431i | −0.997279 | − | 0.0737155i | \(-0.976514\pi\) | ||||
0.997279 | − | 0.0737155i | \(-0.0234857\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.95388 | 0.0618181 |
(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 | 6900.2.f.r.6349.1 | 6 | ||
5.2 | odd | 4 | 6900.2.a.x.1.3 | 3 | |||
5.3 | odd | 4 | 1380.2.a.j.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 6900.2.f.r.6349.6 | 6 | ||
15.8 | even | 4 | 4140.2.a.s.1.1 | 3 | |||
20.3 | even | 4 | 5520.2.a.bv.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.a.j.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
4140.2.a.s.1.1 | 3 | 15.8 | even | 4 | |||
5520.2.a.bv.1.3 | 3 | 20.3 | even | 4 | |||
6900.2.a.x.1.3 | 3 | 5.2 | odd | 4 | |||
6900.2.f.r.6349.1 | 6 | 1.1 | even | 1 | trivial | ||
6900.2.f.r.6349.6 | 6 | 5.4 | even | 2 | inner |