Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 10.0.29471584693248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Root | \(1.72689 + 0.133595i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1601 |
Dual form | 2100.2.bi.j.101.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.979142 | − | 1.42873i | −0.565308 | − | 0.824880i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.456468 | − | 2.60608i | 0.172529 | − | 0.985004i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.08256 | + | 2.79787i | −0.360854 | + | 0.932622i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.698384 | − | 0.403212i | 0.210571 | − | 0.121573i | −0.391006 | − | 0.920388i | \(-0.627873\pi\) |
0.601577 | + | 0.798815i | \(0.294539\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.86649i | − | 1.07237i | −0.844100 | − | 0.536186i | \(-0.819864\pi\) | ||
0.844100 | − | 0.536186i | \(-0.180136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.05989 | + | 1.83578i | 0.257061 | + | 0.445242i | 0.965453 | − | 0.260577i | \(-0.0839127\pi\) |
−0.708393 | + | 0.705819i | \(0.750579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70603 | + | 1.56233i | 0.620807 | + | 0.358423i | 0.777183 | − | 0.629275i | \(-0.216648\pi\) |
−0.156376 | + | 0.987698i | \(0.549981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.17034 | + | 1.89955i | −0.910042 | + | 0.414515i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.21989 | − | 2.43635i | −0.879908 | − | 0.508015i | −0.00927994 | − | 0.999957i | \(-0.502954\pi\) |
−0.870628 | + | 0.491942i | \(0.836287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.05739 | − | 1.19282i | 0.973295 | − | 0.229558i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.67701i | − | 1.23989i | −0.784645 | − | 0.619945i | \(-0.787155\pi\) | ||
0.784645 | − | 0.619945i | \(-0.212845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65010 | − | 3.26209i | 1.01479 | − | 0.585888i | 0.102198 | − | 0.994764i | \(-0.467413\pi\) |
0.912590 | + | 0.408876i | \(0.134079\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.25990 | − | 0.603003i | −0.219320 | − | 0.104969i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.89991 | − | 6.75485i | 0.641142 | − | 1.11049i | −0.344036 | − | 0.938956i | \(-0.611794\pi\) |
0.985178 | − | 0.171534i | \(-0.0548724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.52419 | + | 3.78585i | −0.884579 | + | 0.606221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.44841 | −1.31942 | −0.659710 | − | 0.751520i | \(-0.729321\pi\) | ||||
−0.659710 | + | 0.751520i | \(0.729321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.819076 | 0.124908 | 0.0624540 | − | 0.998048i | \(-0.480107\pi\) | ||||
0.0624540 | + | 0.998048i | \(0.480107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.38776 | + | 2.40368i | −0.202426 | + | 0.350612i | −0.949310 | − | 0.314343i | \(-0.898216\pi\) |
0.746883 | + | 0.664955i | \(0.231549\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58327 | − | 2.37918i | −0.940468 | − | 0.339883i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.58506 | − | 3.31179i | 0.221953 | − | 0.463743i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.5565 | + | 6.67216i | −1.58741 | + | 0.916492i | −0.593678 | + | 0.804703i | \(0.702325\pi\) |
−0.993732 | + | 0.111789i | \(0.964342\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.417438 | − | 5.39594i | −0.0552910 | − | 0.714710i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.86351 | + | 4.95974i | 0.372797 | + | 0.645703i | 0.989995 | − | 0.141105i | \(-0.0450655\pi\) |
−0.617198 | + | 0.786808i | \(0.711732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.79397 | + | 1.03575i | 0.229694 | + | 0.132614i | 0.610431 | − | 0.792070i | \(-0.290996\pi\) |
−0.380737 | + | 0.924683i | \(0.624330\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.79730 | + | 4.09838i | 0.856380 | + | 0.516347i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.45110 | + | 9.44157i | 0.665957 | + | 1.15347i | 0.979025 | + | 0.203741i | \(0.0653101\pi\) |
−0.313067 | + | 0.949731i | \(0.601357\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.650969 | + | 8.41464i | 0.0783674 | + | 1.01300i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.3850i | − | 1.23248i | −0.787559 | − | 0.616239i | \(-0.788656\pi\) | ||
0.787559 | − | 0.616239i | \(-0.211344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.67203 | + | 1.54270i | −0.312737 | + | 0.180559i | −0.648151 | − | 0.761512i | \(-0.724457\pi\) |
0.335413 | + | 0.942071i | \(0.391124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.732012 | − | 2.00410i | −0.0834205 | − | 0.228388i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.76342 | − | 11.7146i | 0.760944 | − | 1.31799i | −0.181420 | − | 0.983406i | \(-0.558069\pi\) |
0.942364 | − | 0.334589i | \(-0.108597\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.65612 | − | 6.05773i | −0.739569 | − | 0.673081i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.8948 | −1.41539 | −0.707694 | − | 0.706519i | \(-0.750265\pi\) | ||||
−0.707694 | + | 0.706519i | \(0.750265\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.53968 | + | 6.53775i | −1.02276 | + | 0.700920i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.60530 | + | 2.78046i | −0.170161 | + | 0.294728i | −0.938476 | − | 0.345344i | \(-0.887762\pi\) |
0.768315 | + | 0.640072i | \(0.221096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0764 | − | 1.76493i | −1.05629 | − | 0.185015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.1929 | − | 4.87844i | −1.05695 | − | 0.505871i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01388i | 0.102944i | 0.998674 | + | 0.0514721i | \(0.0163913\pi\) | ||||
−0.998674 | + | 0.0514721i | \(0.983609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.372090 | + | 2.39049i | 0.0373965 | + | 0.240253i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.27796 | − | 7.40965i | −0.425673 | − | 0.737288i | 0.570810 | − | 0.821082i | \(-0.306629\pi\) |
−0.996483 | + | 0.0837947i | \(0.973296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.46835 | − | 4.88921i | −0.834411 | − | 0.481748i | 0.0209492 | − | 0.999781i | \(-0.493331\pi\) |
−0.855361 | + | 0.518033i | \(0.826664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.8336 | + | 9.14150i | 1.53069 | + | 0.883743i | 0.999330 | + | 0.0365946i | \(0.0116510\pi\) |
0.531357 | + | 0.847148i | \(0.321682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.74840 | − | 15.1527i | −0.837945 | − | 1.45136i | −0.891610 | − | 0.452804i | \(-0.850424\pi\) |
0.0536658 | − | 0.998559i | \(-0.482909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.4695 | + | 1.04202i | −1.27846 | + | 0.0989039i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.96021i | − | 0.654761i | −0.944893 | − | 0.327381i | \(-0.893834\pi\) | ||
0.944893 | − | 0.327381i | \(-0.106166\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.8179 | + | 4.18572i | 1.00012 | + | 0.386970i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.26799 | − | 1.92417i | 0.482916 | − | 0.176389i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.17484 | + | 8.96309i | −0.470440 | + | 0.814826i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.27219 | + | 12.0705i | 0.745879 | + | 1.08836i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.77139 | −0.689600 | −0.344800 | − | 0.938676i | \(-0.612053\pi\) | ||||
−0.344800 | + | 0.938676i | \(0.612053\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.801992 | − | 1.17024i | −0.0706114 | − | 0.103034i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.93761 | + | 10.2842i | −0.518772 | + | 0.898539i | 0.480990 | + | 0.876726i | \(0.340277\pi\) |
−0.999762 | + | 0.0218131i | \(0.993056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.30677 | − | 6.33898i | 0.460155 | − | 0.549659i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.12894 | − | 1.22915i | 0.181888 | − | 0.105013i | −0.406291 | − | 0.913744i | \(-0.633178\pi\) |
0.588179 | + | 0.808730i | \(0.299845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.81335i | 0.238625i | 0.992857 | + | 0.119313i | \(0.0380691\pi\) | ||||
−0.992857 | + | 0.119313i | \(0.961931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.79303 | − | 0.370796i | 0.403646 | − | 0.0312267i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.55902 | − | 2.70030i | −0.130372 | − | 0.225810i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.04674 | + | 11.7353i | 0.251291 | + | 0.967912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8234 | − | 7.40357i | −1.05053 | − | 0.606524i | −0.127733 | − | 0.991809i | \(-0.540770\pi\) |
−0.922798 | + | 0.385285i | \(0.874103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.427898 | + | 0.741141i | 0.0348218 | + | 0.0603132i | 0.882911 | − | 0.469540i | \(-0.155580\pi\) |
−0.848089 | + | 0.529853i | \(0.822247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.28366 | + | 0.978080i | −0.508004 | + | 0.0790731i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1042 | + | 12.1845i | −1.68430 | + | 0.972428i | −0.725547 | + | 0.688173i | \(0.758413\pi\) |
−0.958748 | + | 0.284256i | \(0.908254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 20.8482 | + | 9.97820i | 1.65337 | + | 0.791323i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.27557 | + | 9.88524i | −0.652207 | + | 0.779066i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.789402 | − | 1.36728i | 0.0618307 | − | 0.107094i | −0.833453 | − | 0.552590i | \(-0.813639\pi\) |
0.895284 | + | 0.445496i | \(0.146973\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.9264 | −1.30980 | −0.654902 | − | 0.755714i | \(-0.727290\pi\) | ||||
−0.654902 | + | 0.755714i | \(0.727290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.94978 | −0.149983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.30064 | + | 5.87980i | −0.558294 | + | 0.449640i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.33037 | − | 4.03633i | 0.177175 | − | 0.306876i | −0.763737 | − | 0.645528i | \(-0.776637\pi\) |
0.940912 | + | 0.338652i | \(0.109971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.28237 | − | 8.94748i | 0.321883 | − | 0.672534i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.11674 | − | 1.79945i | 0.232956 | − | 0.134497i | −0.378979 | − | 0.925405i | \(-0.623725\pi\) |
0.611935 | + | 0.790908i | \(0.290391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.5821i | 1.67851i | 0.543737 | + | 0.839256i | \(0.317009\pi\) | ||||
−0.543737 | + | 0.839256i | \(0.682991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.276741 | − | 3.57725i | −0.0204573 | − | 0.264438i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.48042 | + | 0.854719i | 0.108259 | + | 0.0625033i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.800034 | − | 13.7244i | −0.0581939 | − | 0.998305i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.92355 | − | 1.68791i | −0.211541 | − | 0.122133i | 0.390486 | − | 0.920609i | \(-0.372307\pi\) |
−0.602027 | + | 0.798475i | \(0.705640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.54524 | − | 9.60463i | −0.399155 | − | 0.691357i | 0.594467 | − | 0.804120i | \(-0.297363\pi\) |
−0.993622 | + | 0.112763i | \(0.964030\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.2585i | − | 1.15837i | −0.815197 | − | 0.579184i | \(-0.803371\pi\) | ||
0.815197 | − | 0.579184i | \(-0.196629\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.07964 | + | 0.623332i | −0.0765338 | + | 0.0441868i | −0.537779 | − | 0.843086i | \(-0.680736\pi\) |
0.461245 | + | 0.887273i | \(0.347403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.15210 | − | 17.0328i | 0.575005 | − | 1.20140i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.4008 | − | 3.04784i | −1.22130 | − | 0.213917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.3849 | − | 9.16919i | 0.791305 | − | 0.637303i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.51980 | 0.174298 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65466 | −0.526968 | −0.263484 | − | 0.964664i | \(-0.584872\pi\) | ||||
−0.263484 | + | 0.964664i | \(0.584872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.8375 | + | 10.1684i | −1.01665 | + | 0.696730i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.92216 | − | 16.2136i | −0.402022 | − | 1.10065i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.82040 | + | 2.30710i | 0.325732 | + | 0.155899i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.09803 | − | 4.09805i | 0.477465 | − | 0.275665i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.9369i | − | 1.40204i | −0.713143 | − | 0.701019i | \(-0.752729\pi\) | ||
0.713143 | − | 0.701019i | \(-0.247271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.29103 | + | 3.96818i | 0.152061 | + | 0.263377i | 0.931985 | − | 0.362497i | \(-0.118076\pi\) |
−0.779924 | + | 0.625874i | \(0.784742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.845272 | + | 0.488018i | 0.0558572 | + | 0.0322492i | 0.527669 | − | 0.849450i | \(-0.323066\pi\) |
−0.471811 | + | 0.881700i | \(0.656400\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.14658 | + | 3.00814i | −0.141234 | + | 0.197921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.2382 | + | 9.95247i | 1.12931 | + | 0.652008i | 0.943762 | − | 0.330627i | \(-0.107260\pi\) |
0.185550 | + | 0.982635i | \(0.440593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.3594 | + | 1.80712i | −1.51736 | + | 0.117385i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.2703i | 1.82865i | 0.404977 | + | 0.914327i | \(0.367279\pi\) | ||||
−0.404977 | + | 0.914327i | \(0.632721\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0949 | − | 6.40567i | 0.714688 | − | 0.412625i | −0.0981065 | − | 0.995176i | \(-0.531279\pi\) |
0.812794 | + | 0.582551i | \(0.197945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.13760 | + | 15.4412i | −0.137127 | + | 0.990553i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.04074 | − | 10.4629i | 0.384363 | − | 0.665736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6258 | + | 18.4232i | 0.800130 | + | 1.16753i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3349 | −0.652335 | −0.326167 | − | 0.945312i | \(-0.605757\pi\) | ||||
−0.326167 | + | 0.945312i | \(0.605757\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.92947 | −0.247044 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2527 | − | 26.4185i | 0.951439 | − | 1.64794i | 0.209124 | − | 0.977889i | \(-0.432939\pi\) |
0.742315 | − | 0.670052i | \(-0.233728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.8235 | − | 13.2469i | −0.983223 | − | 0.823119i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.6814 | + | 7.22828i | 1.15635 | + | 0.447419i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9054 | − | 10.3377i | 1.10409 | − | 0.637447i | 0.166799 | − | 0.985991i | \(-0.446657\pi\) |
0.937293 | + | 0.348543i | \(0.113324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.54435 | − | 0.428919i | 0.339309 | − | 0.0262494i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4095 | − | 21.4938i | −0.756618 | − | 1.31050i | −0.944566 | − | 0.328322i | \(-0.893517\pi\) |
0.187948 | − | 0.982179i | \(-0.439816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8571 | + | 10.8871i | 1.14548 | + | 0.661346i | 0.947783 | − | 0.318916i | \(-0.103319\pi\) |
0.197702 | + | 0.980262i | \(0.436652\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.34459 | + | 16.1246i | 0.444515 | + | 0.975905i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.61126 | + | 13.1831i | 0.457316 | + | 0.792095i | 0.998818 | − | 0.0486048i | \(-0.0154775\pi\) |
−0.541502 | + | 0.840699i | \(0.682144\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.01030 | + | 19.3396i | 0.180222 | + | 1.15783i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.9488i | − | 1.07073i | −0.844619 | − | 0.535367i | \(-0.820173\pi\) | ||
0.844619 | − | 0.535367i | \(-0.179827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.3730 | − | 13.4944i | 1.38938 | − | 0.802159i | 0.396135 | − | 0.918192i | \(-0.370351\pi\) |
0.993245 | + | 0.116033i | \(0.0370178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.85643 | + | 22.0172i | −0.227638 | + | 1.29963i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.25328 | − | 10.8310i | 0.367840 | − | 0.637117i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.44857 | − | 0.992735i | 0.0849166 | − | 0.0581951i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4450 | 0.843887 | 0.421944 | − | 0.906622i | \(-0.361348\pi\) | ||||
0.421944 | + | 0.906622i | \(0.361348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.05104 | − | 2.87224i | 0.177039 | − | 0.166665i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.42015 | + | 16.3162i | −0.544782 | + | 0.943589i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.373882 | − | 2.13457i | 0.0215502 | − | 0.123035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.39768 | + | 13.3672i | −0.367537 | + | 0.767924i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.34543i | − | 0.533372i | −0.963783 | − | 0.266686i | \(-0.914071\pi\) | ||
0.963783 | − | 0.266686i | \(-0.0859287\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.30635 | + | 16.8862i | 0.0743154 | + | 0.960625i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.6664 | + | 25.4029i | 0.831654 | + | 1.44047i | 0.896726 | + | 0.442586i | \(0.145939\pi\) |
−0.0650722 | + | 0.997881i | \(0.520728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.55728 | − | 5.51790i | −0.540209 | − | 0.311890i | 0.204954 | − | 0.978772i | \(-0.434295\pi\) |
−0.745164 | + | 0.666881i | \(0.767629\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.6987 | + | 8.48631i | 0.825563 | + | 0.476639i | 0.852331 | − | 0.523003i | \(-0.175188\pi\) |
−0.0267682 | + | 0.999642i | \(0.508522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.69225 | − | 4.66312i | −0.150737 | − | 0.261085i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.44252 | − | 31.5728i | −0.136328 | − | 1.76222i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.62357i | 0.368546i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.0832 | + | 27.3357i | −0.723503 | + | 1.51167i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.63070 | + | 4.71382i | 0.310430 | + | 0.259881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.82739 | − | 10.0933i | 0.320302 | − | 0.554780i | −0.660248 | − | 0.751048i | \(-0.729549\pi\) |
0.980550 | + | 0.196268i | \(0.0628822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.6773 | + | 18.2240i | 0.804310 | + | 0.998668i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1753 | −0.554286 | −0.277143 | − | 0.960829i | \(-0.589388\pi\) | ||||
−0.277143 | + | 0.960829i | \(0.589388\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.94428 | + | 6.81503i | −0.540099 | + | 0.370142i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63063 | − | 4.55638i | 0.142456 | − | 0.246742i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.20538 | + | 16.0705i | −0.497044 | + | 0.867725i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.38025 | + | 0.796887i | −0.0740956 | + | 0.0427791i | −0.536590 | − | 0.843843i | \(-0.680288\pi\) |
0.462494 | + | 0.886622i | \(0.346955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.4812i | − | 0.828690i | −0.910120 | − | 0.414345i | \(-0.864011\pi\) | ||
0.910120 | − | 0.414345i | \(-0.135989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.61202 | − | 19.5544i | −0.246171 | − | 1.04374i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.40056 | + | 11.0861i | 0.340668 | + | 0.590054i | 0.984557 | − | 0.175065i | \(-0.0560136\pi\) |
−0.643889 | + | 0.765119i | \(0.722680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.90724 | − | 5.64251i | −0.418496 | − | 0.298633i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.66697 | + | 3.27183i | 0.299091 | + | 0.172680i | 0.642035 | − | 0.766676i | \(-0.278091\pi\) |
−0.342943 | + | 0.939356i | \(0.611424\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.61826 | − | 7.99906i | −0.243066 | − | 0.421003i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.8728 | − | 1.38266i | 0.938077 | − | 0.0725710i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0004 | − | 8.66046i | 0.783012 | − | 0.452072i | −0.0544847 | − | 0.998515i | \(-0.517352\pi\) |
0.837497 | + | 0.546442i | \(0.184018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.14593 | − | 23.6375i | 0.476118 | − | 1.23052i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.1130 | + | 33.1628i | 0.628875 | + | 1.72173i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.497933 | + | 0.862445i | −0.0257820 | + | 0.0446557i | −0.878629 | − | 0.477506i | \(-0.841541\pi\) |
0.852847 | + | 0.522162i | \(0.174874\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.8166 | −1.32962 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.2985 | −1.04266 | −0.521331 | − | 0.853355i | \(-0.674564\pi\) | ||||
−0.521331 | + | 0.853355i | \(0.674564\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.60930 | + | 11.1033i | 0.389836 | + | 0.568837i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.93736 | − | 17.2120i | 0.507776 | − | 0.879493i | −0.492184 | − | 0.870491i | \(-0.663801\pi\) |
0.999959 | − | 0.00900178i | \(-0.00286539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.886700 | + | 2.29167i | −0.0450735 | + | 0.116492i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.56923 | + | 0.905994i | −0.0795630 | + | 0.0459357i | −0.539254 | − | 0.842143i | \(-0.681294\pi\) |
0.459691 | + | 0.888079i | \(0.347960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 10.3291i | − | 0.522363i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.5072 | − | 1.58647i | 1.03445 | − | 0.0800268i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.1320 | + | 17.3967i | 1.51228 | + | 0.873116i | 0.999897 | + | 0.0143590i | \(0.00457078\pi\) |
0.512384 | + | 0.858757i | \(0.328763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.2528 | − | 1.37520i | −0.713532 | − | 0.0688461i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.5121 | + | 18.7709i | 1.62358 | + | 0.937374i | 0.985952 | + | 0.167029i | \(0.0534173\pi\) |
0.637627 | + | 0.770345i | \(0.279916\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6128 | − | 21.8461i | −0.628290 | − | 1.08823i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.28997i | − | 0.311782i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.24769 | − | 1.87505i | 0.160588 | − | 0.0927154i | −0.417552 | − | 0.908653i | \(-0.637112\pi\) |
0.578140 | + | 0.815937i | \(0.303779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.84066 | − | 1.83819i | −0.189446 | − | 0.0906710i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.2326 | − | 5.19856i | 0.700339 | − | 0.255804i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.01953 | − | 2.75467i | 0.196837 | − | 0.134897i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0547 | 1.46827 | 0.734134 | − | 0.679005i | \(-0.237589\pi\) | ||||
0.734134 | + | 0.679005i | \(0.237589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5447 | 1.00129 | 0.500643 | − | 0.865654i | \(-0.333097\pi\) | ||||
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.22283 | − | 6.48491i | −0.253943 | − | 0.315307i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.51813 | − | 4.20243i | 0.170254 | − | 0.203370i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.33151 | + | 4.87140i | −0.112566 | + | 0.235193i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.7400 | − | 18.3251i | 1.52886 | − | 0.882688i | 0.529451 | − | 0.848340i | \(-0.322398\pi\) |
0.999410 | − | 0.0343478i | \(-0.0109354\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.4397i | 1.75118i | 0.483057 | + | 0.875589i | \(0.339526\pi\) | ||||
−0.483057 | + | 0.875589i | \(0.660474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.61278 | − | 13.1857i | −0.364168 | − | 0.630758i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.96135 | − | 4.59649i | −0.379975 | − | 0.219378i | 0.297833 | − | 0.954618i | \(-0.403736\pi\) |
−0.677807 | + | 0.735240i | \(0.737070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.7834 | − | 15.8435i | 0.656354 | − | 0.754453i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.7332 | + | 11.9703i | 0.985063 | + | 0.568727i | 0.903795 | − | 0.427966i | \(-0.140770\pi\) |
0.0812683 | + | 0.996692i | \(0.474103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.97816 | + | 25.5703i | 0.0935636 | + | 1.20943i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.0126i | − | 1.13322i | −0.823985 | − | 0.566611i | \(-0.808254\pi\) | ||
0.823985 | − | 0.566611i | \(-0.191746\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.90023 | + | 3.40650i | −0.277831 | + | 0.160406i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.639920 | − | 1.33703i | 0.0300661 | − | 0.0628193i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.33585 | − | 5.77786i | 0.156044 | − | 0.270277i | −0.777394 | − | 0.629013i | \(-0.783459\pi\) |
0.933439 | + | 0.358737i | \(0.116792\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.55001 | + | 8.02000i | 0.352404 | + | 0.374342i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6895 | −1.24305 | −0.621527 | − | 0.783393i | \(-0.713487\pi\) | ||||
−0.621527 | + | 0.783393i | \(0.713487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9550 | −0.509123 | −0.254562 | − | 0.967057i | \(-0.581931\pi\) | ||||
−0.254562 | + | 0.967057i | \(0.581931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.549726 | − | 0.952153i | 0.0254383 | − | 0.0440604i | −0.853026 | − | 0.521868i | \(-0.825235\pi\) |
0.878464 | + | 0.477808i | \(0.158569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.0937 | − | 9.89620i | 1.25107 | − | 0.456964i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.0724 | + | 18.2219i | 1.75428 | + | 0.839620i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.572029 | − | 0.330261i | 0.0263019 | − | 0.0151854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.15717 | − | 39.5566i | −0.281917 | − | 1.81117i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.91657 | − | 11.9798i | −0.316026 | − | 0.547373i | 0.663629 | − | 0.748062i | \(-0.269015\pi\) |
−0.979655 | + | 0.200689i | \(0.935682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1176 | − | 15.0790i | −1.19086 | − | 0.687543i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.2263 | + | 2.14454i | 1.01133 | + | 0.0975799i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8416 | − | 27.4385i | −0.717854 | − | 1.24336i | −0.961849 | − | 0.273582i | \(-0.911791\pi\) |
0.243995 | − | 0.969776i | \(-0.421542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.72642 | + | 0.210920i | −0.123293 | + | 0.00953813i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 37.3388i | − | 1.68508i | −0.538636 | − | 0.842538i | \(-0.681060\pi\) | ||
0.538636 | − | 0.842538i | \(-0.318940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.2575 | − | 7.07689i | 0.552051 | − | 0.318727i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.0642 | − | 4.74044i | −1.21400 | − | 0.212638i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.50065 | − | 9.52740i | 0.246243 | − | 0.426505i | −0.716237 | − | 0.697857i | \(-0.754137\pi\) |
0.962480 | + | 0.271352i | \(0.0874706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.5734 | + | 24.1833i | 0.740443 | + | 1.08043i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2246 | 0.901772 | 0.450886 | − | 0.892582i | \(-0.351108\pi\) | ||||
0.450886 | + | 0.892582i | \(0.351108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.90911 | + | 2.78572i | 0.0847867 | + | 0.123718i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.24557 | + | 9.08560i | −0.232506 | + | 0.402712i | −0.958545 | − | 0.284941i | \(-0.908026\pi\) |
0.726039 | + | 0.687654i | \(0.241359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.80069 | + | 7.66771i | 0.123895 | + | 0.339199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5490 | + | 4.67351i | 0.686507 | + | 0.206340i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.23825i | 0.0984383i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.04860 | + | 0.622652i | −0.353295 | + | 0.0273314i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00130 | + | 10.3946i | 0.262922 | + | 0.455394i | 0.967017 | − | 0.254712i | \(-0.0819806\pi\) |
−0.704095 | + | 0.710105i | \(0.748647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.74038 | + | 4.46891i | 0.338463 | + | 0.195412i | 0.659592 | − | 0.751624i | \(-0.270729\pi\) |
−0.321129 | + | 0.947035i | \(0.604062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.9769 | + | 6.91489i | 0.521724 | + | 0.301217i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.371651 | + | 0.643719i | 0.0161587 | + | 0.0279878i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.9766 | + | 2.64249i | −0.736723 | + | 0.114674i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.6657i | 1.41491i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.62266 | − | 2.69107i | −0.242636 | − | 0.116128i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.55697 | + | 0.992874i | −0.239356 | + | 0.0427661i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9695 | + | 27.6599i | −0.686581 | + | 1.18919i | 0.286357 | + | 0.958123i | \(0.407556\pi\) |
−0.972937 | + | 0.231069i | \(0.925778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.2638 | − | 22.1110i | 1.38457 | − | 0.948876i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.6313 | 1.43797 | 0.718984 | − | 0.695026i | \(-0.244607\pi\) | ||||
0.718984 | + | 0.695026i | \(0.244607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.83996 | + | 3.89802i | −0.206565 | + | 0.166363i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.4317 | − | 18.0682i | 0.444405 | − | 0.769732i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.4418 | − | 22.9733i | −1.16695 | − | 0.976926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.17988 | + | 5.30000i | −0.388964 | + | 0.224568i | −0.681711 | − | 0.731621i | \(-0.738764\pi\) |
0.292747 | + | 0.956190i | \(0.405431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.16695i | − | 0.133948i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.228372 | − | 2.95201i | −0.00964188 | − | 0.124634i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.14796 | + | 1.98833i | 0.0483808 | + | 0.0837980i | 0.889202 | − | 0.457515i | \(-0.151261\pi\) |
−0.840821 | + | 0.541313i | \(0.817927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.8252 | + | 14.5812i | −0.790585 | + | 0.612353i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.1648 | − | 13.9515i | −1.01304 | − | 0.584878i | −0.100959 | − | 0.994891i | \(-0.532191\pi\) |
−0.912080 | + | 0.410012i | \(0.865524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.11649 | + | 5.39791i | 0.130421 | + | 0.225896i | 0.923839 | − | 0.382782i | \(-0.125034\pi\) |
−0.793418 | + | 0.608677i | \(0.791700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.450993 | + | 5.82969i | 0.0188405 | + | 0.243539i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.4776 | + | 6.62662i | −0.477820 | + | 0.275870i | −0.719508 | − | 0.694484i | \(-0.755632\pi\) |
0.241687 | + | 0.970354i | \(0.422299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.29289 | + | 17.3270i | −0.344641 | + | 0.720084i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.88606 | + | 33.6048i | −0.244195 | + | 1.39416i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.38059 | + | 9.31946i | −0.222841 | + | 0.385973i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.6209 | −0.768568 | −0.384284 | − | 0.923215i | \(-0.625552\pi\) | ||||
−0.384284 | + | 0.923215i | \(0.625552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.3858 | 0.839982 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.2290 | + | 15.9193i | −0.955514 | + | 0.654834i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.37822 | − | 2.38715i | 0.0565967 | − | 0.0980284i | −0.836339 | − | 0.548213i | \(-0.815308\pi\) |
0.892936 | + | 0.450184i | \(0.148642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.94770 | + | 0.932191i | 0.0797140 | + | 0.0381520i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.2530 | − | 9.38368i | 0.664080 | − | 0.383407i | −0.129750 | − | 0.991547i | \(-0.541417\pi\) |
0.793830 | + | 0.608140i | \(0.208084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5669i | 0.675779i | 0.941186 | + | 0.337890i | \(0.109713\pi\) | ||||
−0.941186 | + | 0.337890i | \(0.890287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.3174 | + | 5.03035i | −1.31607 | + | 0.204852i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.9773 | − | 16.7301i | −1.17615 | − | 0.679053i | −0.221032 | − | 0.975266i | \(-0.570943\pi\) |
−0.955122 | + | 0.296213i | \(0.904276\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.6833 | + | 27.8454i | 0.513954 | + | 1.12835i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.29381 | + | 5.36578i | 0.375987 | + | 0.217076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7772 | − | 32.5231i | −0.758404 | − | 1.31359i | −0.943664 | − | 0.330905i | \(-0.892646\pi\) |
0.185260 | − | 0.982690i | \(-0.440687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.5088i | − | 0.906172i | −0.891467 | − | 0.453086i | \(-0.850323\pi\) | ||
0.891467 | − | 0.453086i | \(-0.149677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.3812 | + | 13.4991i | −0.939770 | + | 0.542576i | −0.889888 | − | 0.456179i | \(-0.849218\pi\) |
−0.0498816 | + | 0.998755i | \(0.515884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.2478 | − | 7.28804i | −0.973029 | − | 0.292459i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.51332 | + | 5.45272i | 0.260951 | + | 0.218459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.46724 | − | 3.60012i | −0.0985322 | − | 0.143775i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.5339 | 0.659249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.17965 | 0.365436 | 0.182718 | − | 0.983165i | \(-0.441510\pi\) | ||||
0.182718 | + | 0.983165i | \(0.441510\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.49499 | + | 10.9365i | 0.297899 | + | 0.434686i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.19909 | + | 25.4542i | −0.364481 | + | 1.00853i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.0560 | + | 11.2425i | 1.14944 | + | 0.444745i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.6664 | − | 15.3959i | 1.05326 | − | 0.608100i | 0.129700 | − | 0.991553i | \(-0.458599\pi\) |
0.923560 | + | 0.383453i | \(0.125265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.42929i | 0.135238i | 0.997711 | + | 0.0676189i | \(0.0215402\pi\) | ||||
−0.997711 | + | 0.0676189i | \(0.978460\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.2967 | + | 43.8152i | 0.994516 | + | 1.72255i | 0.587828 | + | 0.808986i | \(0.299983\pi\) |
0.406689 | + | 0.913567i | \(0.366683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.99966 | + | 2.30920i | 0.157000 | + | 0.0906441i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3663 | + | 24.3366i | −0.680640 | + | 0.953828i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.57643 | − | 2.64220i | −0.179090 | − | 0.103397i | 0.407775 | − | 0.913082i | \(-0.366305\pi\) |
−0.586865 | + | 0.809685i | \(0.699638\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.42362 | − | 9.14605i | −0.0555408 | − | 0.356821i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.0502i | 1.01477i | 0.861719 | + | 0.507385i | \(0.169388\pi\) | ||||
−0.861719 | + | 0.507385i | \(0.830612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.3751 | + | 16.3823i | −1.10366 | + | 0.637199i | −0.937180 | − | 0.348845i | \(-0.886574\pi\) |
−0.166481 | + | 0.986045i | \(0.553241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.8050 | − | 6.12863i | −0.497305 | − | 0.238016i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.2676 | + | 28.1763i | −0.629883 | + | 1.09099i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.9132 | + | 20.5002i | −1.15651 | + | 0.792583i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67050 | 0.0644891 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.5194 | 1.48481 | 0.742406 | − | 0.669950i | \(-0.233685\pi\) | ||||
0.742406 | + | 0.669950i | \(0.233685\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.58044 | + | 16.5938i | −0.368206 | + | 0.637752i | −0.989285 | − | 0.145996i | \(-0.953361\pi\) |
0.621079 | + | 0.783748i | \(0.286695\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.64225 | + | 0.462805i | 0.101400 | + | 0.0177608i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.42623 | − | 7.15868i | 0.131293 | − | 0.274321i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.0821 | + | 14.4812i | −0.959741 | + | 0.554107i | −0.896093 | − | 0.443866i | \(-0.853607\pi\) |
−0.0636479 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.130393 | − | 1.68551i | −0.00497482 | − | 0.0643062i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.7979 | + | 44.6832i | 0.982821 | + | 1.70230i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.4572 | + | 22.7806i | 1.50102 | + | 0.866616i | 0.999999 | + | 0.00118303i | \(0.000376571\pi\) |
0.501024 | + | 0.865433i | \(0.332957\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.39964 | + | 0.121486i | 0.243102 | + | 0.00461485i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.95437 | − | 15.5094i | −0.339171 | − | 0.587461i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.65920 | − | 34.3737i | −0.100580 | − | 1.30013i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 39.2878i | − | 1.48388i | −0.670466 | − | 0.741940i | \(-0.733906\pi\) | ||
0.670466 | − | 0.741940i | \(-0.266094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.1066 | − | 12.1859i | 0.796050 | − | 0.459600i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.2629 | + | 7.76643i | −0.799672 | + | 0.292087i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.88537 | + | 17.1220i | −0.371253 | + | 0.643029i | −0.989759 | − | 0.142752i | \(-0.954405\pi\) |
0.618506 | + | 0.785780i | \(0.287738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.4540 | + | 31.6049i | 0.954601 | + | 1.18528i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.7904 | −1.19056 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.3907 | − | 27.6806i | 1.50842 | − | 1.03375i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.740641 | + | 1.28283i | −0.0276212 | + | 0.0478414i | −0.879506 | − | 0.475889i | \(-0.842127\pi\) |
0.851884 | + | 0.523730i | \(0.175460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6072 | + | 19.8374i | −0.618484 | + | 0.738784i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.0155 | − | 9.57966i | −0.744385 | − | 0.356271i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.35193i | 0.235580i | 0.993039 | + | 0.117790i | \(0.0375810\pi\) | ||||
−0.993039 | + | 0.117790i | \(0.962419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.1544 | − | 12.0651i | 0.894607 | − | 0.446855i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.868129 | + | 1.50364i | 0.0321089 | + | 0.0556142i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0100 | + | 19.6357i | 1.25619 | + | 0.725261i | 0.972331 | − | 0.233605i | \(-0.0750524\pi\) |
0.283857 | + | 0.958866i | \(0.408386\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.61392 | + | 4.39590i | 0.280462 | + | 0.161925i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2904 | + | 19.5555i | 0.415324 | + | 0.719362i | 0.995462 | − | 0.0951558i | \(-0.0303349\pi\) |
−0.580139 | + | 0.814518i | \(0.697002\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.8634 | + | 1.61402i | −0.766436 | + | 0.0592926i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 26.6330i | − | 0.977070i | −0.872544 | − | 0.488535i | \(-0.837532\pi\) | ||
0.872544 | − | 0.488535i | \(-0.162468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.9594 | − | 36.0779i | 0.510748 | − | 1.32002i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.0510 | − | 37.0906i | 1.13458 | − | 1.35526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.62709 | − | 14.9426i | 0.314807 | − | 0.545262i | −0.664589 | − | 0.747209i | \(-0.731393\pi\) |
0.979396 | + | 0.201947i | \(0.0647268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1194 | + | 14.7659i | 0.368770 | + | 0.538098i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1712 | −0.914863 | −0.457431 | − | 0.889245i | \(-0.651230\pi\) | ||||
−0.457431 | + | 0.889245i | \(0.651230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.84751 | + | 5.61417i | 0.139656 | + | 0.203781i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.00796126 | + | 0.0137893i | −0.000288596 | + | 0.000499862i | −0.866170 | − | 0.499750i | \(-0.833425\pi\) |
0.865881 | + | 0.500250i | \(0.166759\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −43.4824 | + | 15.8823i | −1.57417 | + | 0.574977i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1768 | − | 11.0717i | 0.692435 | − | 0.399777i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.0356i | − | 0.470075i | −0.971986 | − | 0.235037i | \(-0.924479\pi\) | ||
0.971986 | − | 0.235037i | \(-0.0755213\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.6796 | + | 4.07537i | −1.89721 | + | 0.146771i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7085 | + | 25.4758i | 0.529027 | + | 0.916301i | 0.999427 | + | 0.0338481i | \(0.0107762\pi\) |
−0.470400 | + | 0.882453i | \(0.655890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.43280 | + | 35.5781i | −0.123151 | + | 1.27636i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.8617 | − | 13.1992i | −0.819105 | − | 0.472910i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.18738 | − | 7.25275i | −0.149836 | − | 0.259524i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.96445 | − | 33.7683i | −0.284626 | − | 1.20678i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.95977 | + | 1.13148i | −0.0698584 | + | 0.0403327i | −0.534522 | − | 0.845154i | \(-0.679508\pi\) |
0.464664 | + | 0.885487i | \(0.346175\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.3017 | − | 15.4600i | −1.14997 | − | 0.550389i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.1388 | − | 3.17711i | −0.644943 | − | 0.112965i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00471 | − | 6.93636i | 0.142211 | − | 0.246318i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.6277 | −0.695250 | −0.347625 | − | 0.937634i | \(-0.613012\pi\) | ||||
−0.347625 | + | 0.937634i | \(0.613012\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.88350 | −0.208143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.04152 | − | 7.50143i | −0.213467 | − | 0.265050i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.24407 | + | 2.15479i | −0.0439022 | + | 0.0760409i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.5583 | + | 38.7753i | −0.653284 | + | 1.36496i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.2506 | + | 12.2690i | −0.747130 | + | 0.431356i | −0.824656 | − | 0.565635i | \(-0.808631\pi\) |
0.0775260 | + | 0.996990i | \(0.475298\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.7927i | − | 1.36220i | −0.732192 | − | 0.681098i | \(-0.761503\pi\) | ||
0.732192 | − | 0.681098i | \(-0.238497\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.90893 | − | 37.6018i | −0.102021 | − | 1.31875i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.21645 | + | 1.27967i | 0.0775436 | + | 0.0447698i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.8464 | − | 26.2817i | 0.553716 | − | 0.918358i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.8734 | + | 6.85513i | 0.414386 | + | 0.239246i | 0.692672 | − | 0.721252i | \(-0.256433\pi\) |
−0.278287 | + | 0.960498i | \(0.589767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04168 | + | 7.00040i | 0.140884 | + | 0.244019i | 0.927830 | − | 0.373004i | \(-0.121672\pi\) |
−0.786946 | + | 0.617022i | \(0.788339\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37.6581i | − | 1.30950i | −0.755845 | − | 0.654751i | \(-0.772774\pi\) | ||
0.755845 | − | 0.654751i | \(-0.227226\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.4475 | − | 8.91864i | 0.536515 | − | 0.309757i | −0.207150 | − | 0.978309i | \(-0.566419\pi\) |
0.743665 | + | 0.668552i | \(0.233086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3826 | − | 23.7826i | 0.394859 | − | 0.825008i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.60988 | − | 14.6071i | −0.0904269 | − | 0.506106i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.6837 | − | 23.2372i | 0.853193 | − | 0.803194i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.49497 | 0.155183 | 0.0775917 | − | 0.996985i | \(-0.475277\pi\) | ||||
0.0775917 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5825 | −0.537329 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.6440 | + | 17.5744i | −0.883228 | + | 0.605295i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.9963 | + | 17.5774i | 0.721443 | + | 0.603966i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.1654 | − | 20.1809i | −1.44711 | − | 0.692605i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.9144 | + | 19.0032i | −1.12829 | + | 0.651420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0503i | 1.13162i | 0.824535 | + | 0.565811i | \(0.191437\pi\) | ||||
−0.824535 | + | 0.565811i | \(0.808563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.210762 | + | 0.365051i | 0.00719949 | + | 0.0124699i | 0.869603 | − | 0.493752i | \(-0.164375\pi\) |
−0.862403 | + | 0.506222i | \(0.831042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0294 | − | 9.83192i | −0.581035 | − | 0.335461i | 0.180509 | − | 0.983573i | \(-0.442225\pi\) |
−0.761545 | + | 0.648112i | \(0.775559\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.2327 | − | 16.0482i | 1.20073 | − | 0.546920i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.782575 | + | 0.451820i | 0.0266392 | + | 0.0153801i | 0.513260 | − | 0.858233i | \(-0.328437\pi\) |
−0.486621 | + | 0.873613i | \(0.661771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.5974 | + | 1.67081i | −0.733488 | + | 0.0567437i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 10.9084i | − | 0.370041i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.5058 | − | 21.0766i | 1.23695 | − | 0.714154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.83671 | − | 1.09759i | −0.0960080 | − | 0.0371478i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.65916 | + | 13.2661i | −0.258632 | + | 0.447963i | −0.965876 | − | 0.259006i | \(-0.916605\pi\) |
0.707244 | + | 0.706970i | \(0.249938\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.1437 | − | 20.6381i | −0.477056 | − | 0.696106i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.8614 | −1.47773 | −0.738863 | − | 0.673855i | \(-0.764637\pi\) | ||||
−0.738863 | + | 0.673855i | \(0.764637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.91300 | 0.0980304 | 0.0490152 | − | 0.998798i | \(-0.484392\pi\) | ||||
0.0490152 | + | 0.998798i | \(0.484392\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.44790 | − | 12.9001i | 0.250076 | − | 0.433145i | −0.713470 | − | 0.700685i | \(-0.752878\pi\) |
0.963547 | + | 0.267541i | \(0.0862110\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.54739 | + | 20.2528i | −0.118976 | + | 0.679259i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.09108 | − | 1.54679i | −0.237560 | − | 0.0518195i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.51067 | + | 4.33629i | −0.251335 | + | 0.145108i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.5352 | − | 2.51697i | 1.08632 | − | 0.0840391i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.7810 | − | 37.7258i | −0.726437 | − | 1.25823i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4972 | − | 14.1435i | −0.816121 | − | 0.471188i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.41582 | + | 1.55587i | −0.113671 | + | 0.0517762i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.54899 | + | 16.5393i | 0.317069 | + | 0.549180i | 0.979875 | − | 0.199611i | \(-0.0639679\pi\) |
−0.662806 | + | 0.748791i | \(0.730635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 25.3624 | − | 3.94777i | 0.841217 | − | 0.130939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6.16915i | − | 0.204393i | −0.994764 | − | 0.102197i | \(-0.967413\pi\) | ||
0.994764 | − | 0.102197i | \(-0.0325871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00552 | + | 5.19934i | −0.298039 | + | 0.172073i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.0912 | + | 20.1683i | 0.795562 | + | 0.666016i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8318 | + | 25.6894i | −0.489255 | + | 0.847415i | −0.999924 | − | 0.0123630i | \(-0.996065\pi\) |
0.510668 | + | 0.859778i | \(0.329398\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.3521 | + | 9.15051i | −0.439968 | + | 0.301519i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.1537 | −1.32168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.8469 | − | 18.4005i | 0.750389 | − | 0.604350i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.8256 | − | 29.1428i | 0.552030 | − | 0.956144i | −0.446098 | − | 0.894984i | \(-0.647187\pi\) |
0.998128 | − | 0.0611601i | \(-0.0194800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.0975 | − | 16.7234i | −0.462027 | − | 0.548087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.9335 | − | 45.8274i | 0.718072 | − | 1.50032i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.99276i | − | 0.261112i | −0.991441 | − | 0.130556i | \(-0.958324\pi\) | ||
0.991441 | − | 0.130556i | \(-0.0416762\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.47433 | + | 19.0576i | 0.0481128 | + | 0.621922i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.69431 | − | 15.0590i | −0.283426 | − | 0.490909i | 0.688800 | − | 0.724951i | \(-0.258138\pi\) |
−0.972226 | + | 0.234043i | \(0.924804\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.6514 | + | 20.5833i | 1.16097 | + | 0.670285i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.6302 | + | 21.1485i | 1.19032 | + | 0.687233i | 0.958380 | − | 0.285496i | \(-0.0921583\pi\) |
0.231943 | + | 0.972729i | \(0.425492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.96483 | + | 10.3314i | 0.193627 | + | 0.335371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.26746 | − | 29.3099i | −0.0735273 | − | 0.950438i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.5612i | − | 1.31391i | −0.753932 | − | 0.656953i | \(-0.771845\pi\) | ||
0.753932 | − | 0.656953i | \(-0.228155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.02626 | + | 8.41237i | −0.130150 | + | 0.271933i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.23145 | − | 6.10926i | −0.0720574 | − | 0.197278i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.78241 | − | 10.0154i | 0.186529 | − | 0.323078i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.7175 | + | 34.4039i | −1.37655 | + | 1.10865i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.6713 | 1.21143 | 0.605714 | − | 0.795682i | \(-0.292888\pi\) | ||||
0.605714 | + | 0.795682i | \(0.292888\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.46333 | − | 6.48542i | 0.304006 | − | 0.208342i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5452 | + | 37.3173i | −0.691418 | + | 1.19757i | 0.279956 | + | 0.960013i | \(0.409680\pi\) |
−0.971373 | + | 0.237558i | \(0.923653\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.33180 | + | 1.28420i | 0.235047 | + | 0.0411697i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.7402 | − | 11.3970i | 0.631545 | − | 0.364622i | −0.149805 | − | 0.988716i | \(-0.547865\pi\) |
0.781350 | + | 0.624093i | \(0.214531\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.58910i | 0.0827481i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 51.8658 | − | 8.07315i | 1.65595 | − | 0.257756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.5929 | − | 39.1321i | −0.720602 | − | 1.24812i | −0.960759 | − | 0.277385i | \(-0.910532\pi\) |
0.240157 | − | 0.970734i | \(-0.422801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.22154 | − | 12.6603i | 0.0388822 | − | 0.402981i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.45641 | − | 1.99556i | −0.109907 | − | 0.0634551i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2760 | − | 43.7793i | −0.802919 | − | 1.39070i | −0.917687 | − | 0.397304i | \(-0.869946\pi\) |
0.114768 | − | 0.993392i | \(-0.463388\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.1265 | + | 1.55702i | −0.638696 | + | 0.0494105i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.5635 | − | 13.0271i | 0.714595 | − | 0.412571i | −0.0981654 | − | 0.995170i | \(-0.531297\pi\) |
0.812760 | + | 0.582599i | \(0.197964\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.6661 | − | 38.8138i | 0.369099 | − | 1.22801i |
(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 | 2100.2.bi.j.1601.2 | 10 | ||
3.2 | odd | 2 | 2100.2.bi.k.1601.4 | 10 | |||
5.2 | odd | 4 | 2100.2.bo.g.1349.2 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.g.1349.9 | 20 | |||
5.4 | even | 2 | 420.2.bh.b.341.4 | yes | 10 | ||
7.3 | odd | 6 | 2100.2.bi.k.101.4 | 10 | |||
15.2 | even | 4 | 2100.2.bo.h.1349.8 | 20 | |||
15.8 | even | 4 | 2100.2.bo.h.1349.3 | 20 | |||
15.14 | odd | 2 | 420.2.bh.a.341.2 | yes | 10 | ||
21.17 | even | 6 | inner | 2100.2.bi.j.101.2 | 10 | ||
35.3 | even | 12 | 2100.2.bo.h.1949.8 | 20 | |||
35.9 | even | 6 | 2940.2.d.a.881.2 | 10 | |||
35.17 | even | 12 | 2100.2.bo.h.1949.3 | 20 | |||
35.19 | odd | 6 | 2940.2.d.b.881.9 | 10 | |||
35.24 | odd | 6 | 420.2.bh.a.101.2 | ✓ | 10 | ||
105.17 | odd | 12 | 2100.2.bo.g.1949.9 | 20 | |||
105.38 | odd | 12 | 2100.2.bo.g.1949.2 | 20 | |||
105.44 | odd | 6 | 2940.2.d.b.881.10 | 10 | |||
105.59 | even | 6 | 420.2.bh.b.101.4 | yes | 10 | ||
105.89 | even | 6 | 2940.2.d.a.881.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.2 | ✓ | 10 | 35.24 | odd | 6 | ||
420.2.bh.a.341.2 | yes | 10 | 15.14 | odd | 2 | ||
420.2.bh.b.101.4 | yes | 10 | 105.59 | even | 6 | ||
420.2.bh.b.341.4 | yes | 10 | 5.4 | even | 2 | ||
2100.2.bi.j.101.2 | 10 | 21.17 | even | 6 | inner | ||
2100.2.bi.j.1601.2 | 10 | 1.1 | even | 1 | trivial | ||
2100.2.bi.k.101.4 | 10 | 7.3 | odd | 6 | |||
2100.2.bi.k.1601.4 | 10 | 3.2 | odd | 2 | |||
2100.2.bo.g.1349.2 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.g.1349.9 | 20 | 5.3 | odd | 4 | |||
2100.2.bo.g.1949.2 | 20 | 105.38 | odd | 12 | |||
2100.2.bo.g.1949.9 | 20 | 105.17 | odd | 12 | |||
2100.2.bo.h.1349.3 | 20 | 15.8 | even | 4 | |||
2100.2.bo.h.1349.8 | 20 | 15.2 | even | 4 | |||
2100.2.bo.h.1949.3 | 20 | 35.17 | even | 12 | |||
2100.2.bo.h.1949.8 | 20 | 35.3 | even | 12 | |||
2940.2.d.a.881.1 | 10 | 105.89 | even | 6 | |||
2940.2.d.a.881.2 | 10 | 35.9 | even | 6 | |||
2940.2.d.b.881.9 | 10 | 35.19 | odd | 6 | |||
2940.2.d.b.881.10 | 10 | 105.44 | odd | 6 |