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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.4 | ||
Root | \(1.72689 + 0.133595i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.k.1601.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.747749 | − | 1.56233i | 0.431713 | − | 0.902011i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.456468 | + | 2.60608i | 0.172529 | + | 0.985004i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.88174 | − | 2.33646i | −0.627248 | − | 0.778820i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.698384 | − | 0.403212i | −0.210571 | − | 0.121573i | 0.391006 | − | 0.920388i | \(-0.372127\pi\) |
−0.601577 | + | 0.798815i | \(0.705461\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.86649i | 1.07237i | 0.844100 | + | 0.536186i | \(0.180136\pi\) | ||||
−0.844100 | + | 0.536186i | \(0.819864\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.05989 | + | 1.83578i | −0.257061 | + | 0.445242i | −0.965453 | − | 0.260577i | \(-0.916087\pi\) |
0.708393 | + | 0.705819i | \(0.249421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70603 | − | 1.56233i | 0.620807 | − | 0.358423i | −0.156376 | − | 0.987698i | \(-0.549981\pi\) |
0.777183 | + | 0.629275i | \(0.216648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41287 | + | 1.23554i | 0.962968 | + | 0.269617i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.21989 | − | 2.43635i | 0.879908 | − | 0.508015i | 0.00927994 | − | 0.999957i | \(-0.497046\pi\) |
0.870628 | + | 0.491942i | \(0.163713\pi\) | |||||||
\(24\) | 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 | 0.912590 | − | 0.408876i | \(-0.134079\pi\) |
0.102198 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.15217 | + | 0.789604i | −0.200566 | + | 0.137452i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.89991 | + | 6.75485i | 0.641142 | + | 1.11049i | 0.985178 | + | 0.171534i | \(0.0548724\pi\) |
−0.344036 | + | 0.938956i | \(0.611794\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.04074 | + | 2.89117i | 0.967292 | + | 0.462957i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.44841 | 1.31942 | 0.659710 | − | 0.751520i | \(-0.270679\pi\) | ||||
0.659710 | + | 0.751520i | \(0.270679\pi\) | |||||||
\(42\) | 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 | \(-0.101784\pi\) |
−0.746883 | + | 0.664955i | \(0.768451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58327 | + | 2.37918i | −0.940468 | + | 0.339883i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.07556 | + | 3.02860i | 0.290637 | + | 0.424088i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5565 | + | 6.67216i | 1.58741 | + | 0.916492i | 0.993732 | + | 0.111789i | \(0.0356581\pi\) |
0.593678 | + | 0.804703i | \(0.297675\pi\) | |||||||
\(54\) | 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 | \(-0.954935\pi\) |
0.617198 | + | 0.786808i | \(0.288268\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.79397 | − | 1.03575i | 0.229694 | − | 0.132614i | −0.380737 | − | 0.924683i | \(-0.624330\pi\) |
0.610431 | + | 0.792070i | \(0.290996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.23004 | − | 5.97049i | 0.658923 | − | 0.752211i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.45110 | − | 9.44157i | 0.665957 | − | 1.15347i | −0.313067 | − | 0.949731i | \(-0.601357\pi\) |
0.979025 | − | 0.203741i | \(-0.0653101\pi\) | |||||||
\(68\) | 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 | 0.335413 | − | 0.942071i | \(-0.391124\pi\) |
−0.648151 | + | 0.761512i | \(0.724457\pi\) | |||||||
\(74\) | 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 | 0.942364 | + | 0.334589i | \(0.108597\pi\) |
−0.181420 | + | 0.983406i | \(0.558069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.91809 | + | 8.79323i | −0.213121 | + | 0.977026i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.8948 | 1.41539 | 0.707694 | − | 0.706519i | \(-0.249735\pi\) | ||||
0.707694 | + | 0.706519i | \(0.249735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4317 | − | 4.99273i | −1.11839 | − | 0.535277i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60530 | + | 2.78046i | 0.170161 | + | 0.294728i | 0.938476 | − | 0.345344i | \(-0.112238\pi\) |
−0.768315 | + | 0.640072i | \(0.778904\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0764 | + | 1.76493i | −1.05629 | + | 0.185015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.32131 | − | 6.38809i | 0.966574 | − | 0.662414i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.01388i | − | 0.102944i | −0.998674 | − | 0.0514721i | \(-0.983609\pi\) | ||
0.998674 | − | 0.0514721i | \(-0.0163913\pi\) | |||||||
\(98\) | 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 | \(-0.693371\pi\) |
0.996483 | + | 0.0837947i | \(0.0267040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.46835 | + | 4.88921i | −0.834411 | + | 0.481748i | −0.855361 | − | 0.518033i | \(-0.826664\pi\) |
0.0209492 | + | 0.999781i | \(0.493331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8336 | + | 9.14150i | −1.53069 | + | 0.883743i | −0.531357 | + | 0.847148i | \(0.678318\pi\) |
−0.999330 | + | 0.0365946i | \(0.988349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.74840 | + | 15.1527i | −0.837945 | + | 1.45136i | 0.0536658 | + | 0.998559i | \(0.482909\pi\) |
−0.891610 | + | 0.452804i | \(0.850424\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | 9.03391 | − | 7.27575i | 0.835185 | − | 0.672643i | ||||
\(118\) | 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 | ||||||||
\(123\) | 6.31729 | − | 13.1992i | 0.569611 | − | 1.19013i | ||||
\(124\) | 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 | ||||||||
\(129\) | 0.612463 | − | 1.27967i | 0.0539244 | − | 0.112668i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.93761 | + | 10.2842i | 0.518772 | + | 0.898539i | 0.999762 | + | 0.0218131i | \(0.00694387\pi\) |
−0.480990 | + | 0.876726i | \(0.659723\pi\) | |||||||
\(132\) | 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 | \(-0.366822\pi\) |
−0.588179 | + | 0.808730i | \(0.700155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.81335i | − | 0.238625i | −0.992857 | − | 0.119313i | \(-0.961931\pi\) | ||
0.992857 | − | 0.119313i | \(-0.0380691\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −1.20557 | + | 12.0643i | −0.0994339 | + | 0.995044i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8234 | − | 7.40357i | 1.05053 | − | 0.606524i | 0.127733 | − | 0.991809i | \(-0.459230\pi\) |
0.922798 | + | 0.385285i | \(0.125897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.427898 | − | 0.741141i | 0.0348218 | − | 0.0603132i | −0.848089 | − | 0.529853i | \(-0.822247\pi\) |
0.882911 | + | 0.469540i | \(0.155580\pi\) | |||||||
\(152\) | 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 | −0.958748 | − | 0.284256i | \(-0.908254\pi\) |
−0.725547 | − | 0.688173i | \(-0.758413\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.0655 | − | 13.0660i | 1.51199 | − | 1.03620i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.27557 | + | 9.88524i | 0.652207 | + | 0.779066i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.789402 | + | 1.36728i | 0.0618307 | + | 0.107094i | 0.895284 | − | 0.445496i | \(-0.146973\pi\) |
−0.833453 | + | 0.552590i | \(0.813639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9264 | 1.30980 | 0.654902 | − | 0.755714i | \(-0.272710\pi\) | ||||
0.654902 | + | 0.755714i | \(0.272710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.94978 | −0.149983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.74238 | − | 3.38264i | −0.668546 | − | 0.258677i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.33037 | − | 4.03633i | −0.177175 | − | 0.306876i | 0.763737 | − | 0.645528i | \(-0.223363\pi\) |
−0.940912 | + | 0.338652i | \(0.890029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.60756 | + | 8.18238i | 0.421490 | + | 0.615025i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.11674 | − | 1.79945i | −0.232956 | − | 0.134497i | 0.378979 | − | 0.925405i | \(-0.376275\pi\) |
−0.611935 | + | 0.790908i | \(0.709609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.5821i | − | 1.67851i | −0.543737 | − | 0.839256i | \(-0.682991\pi\) | ||
0.543737 | − | 0.839256i | \(-0.317009\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | −5.41711 | − | 12.6355i | −0.394037 | − | 0.919095i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.92355 | − | 1.68791i | 0.211541 | − | 0.122133i | −0.390486 | − | 0.920609i | \(-0.627693\pi\) |
0.602027 | + | 0.798475i | \(0.294360\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.54524 | + | 9.60463i | −0.399155 | + | 0.691357i | −0.993622 | − | 0.112763i | \(-0.964030\pi\) |
0.594467 | + | 0.804120i | \(0.297363\pi\) | |||||||
\(194\) | 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 | 0.461245 | − | 0.887273i | \(-0.347403\pi\) |
−0.537779 | + | 0.843086i | \(0.680736\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6748 | − | 15.5763i | −0.752942 | − | 1.09867i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.4008 | − | 3.04784i | 1.22130 | − | 0.213917i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −13.6332 | − | 5.27501i | −0.947573 | − | 0.366639i | ||||
\(208\) | 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 | ||||||||
\(213\) | −16.2249 | − | 7.76541i | −1.11171 | − | 0.532077i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.92216 | + | 16.2136i | −0.402022 | + | 1.10065i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.40821 | + | 3.02104i | −0.297879 | + | 0.204143i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.09803 | − | 4.09805i | −0.477465 | − | 0.275665i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9369i | 1.40204i | 0.713143 | + | 0.701019i | \(0.247271\pi\) | ||||
−0.713143 | + | 0.701019i | \(0.752729\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.29103 | + | 3.96818i | −0.152061 | + | 0.263377i | −0.931985 | − | 0.362497i | \(-0.881924\pi\) |
0.779924 | + | 0.625874i | \(0.215258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.845272 | − | 0.488018i | 0.0558572 | − | 0.0322492i | −0.471811 | − | 0.881700i | \(-0.656400\pi\) |
0.527669 | + | 0.849450i | \(0.323066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.58370 | − | 2.64220i | −0.169995 | − | 0.173844i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.2382 | + | 9.95247i | −1.12931 | + | 0.652008i | −0.943762 | − | 0.330627i | \(-0.892740\pi\) |
−0.185550 | + | 0.982635i | \(0.559407\pi\) | |||||||
\(234\) | 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 | 0.812794 | − | 0.582551i | \(-0.197945\pi\) |
−0.0981065 | + | 0.995176i | \(0.531279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.3037 | + | 9.57181i | 0.789281 | + | 0.614032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.04074 | + | 10.4629i | 0.384363 | + | 0.665736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.64207 | − | 20.1459i | 0.611042 | − | 1.27670i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.3349 | 0.652335 | 0.326167 | − | 0.945312i | \(-0.394243\pi\) | ||||
0.326167 | + | 0.945312i | \(0.394243\pi\) | |||||||
\(252\) | 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 | −0.742315 | − | 0.670052i | \(-0.766272\pi\) |
−0.209124 | − | 0.977889i | \(-0.567061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.8235 | + | 13.2469i | −0.983223 | + | 0.823119i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.6006 | + | 12.5644i | −0.965651 | + | 0.777718i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.9054 | − | 10.3377i | −1.10409 | − | 0.637447i | −0.166799 | − | 0.985991i | \(-0.553343\pi\) |
−0.937293 | + | 0.348543i | \(0.886676\pi\) | |||||||
\(264\) | 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 | −0.187948 | − | 0.982179i | \(-0.560184\pi\) |
0.944566 | − | 0.328322i | \(-0.106483\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8571 | − | 10.8871i | 1.14548 | − | 0.661346i | 0.197702 | − | 0.980262i | \(-0.436652\pi\) |
0.947783 | + | 0.318916i | \(0.103319\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.77720 | + | 17.0623i | −0.289129 | + | 1.03266i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.61126 | − | 13.1831i | 0.457316 | − | 0.792095i | −0.541502 | − | 0.840699i | \(-0.682144\pi\) |
0.998818 | + | 0.0486048i | \(0.0154775\pi\) | |||||||
\(278\) | 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 | 0.993245 | − | 0.116033i | \(-0.0370178\pi\) |
0.396135 | + | 0.918192i | \(0.370351\pi\) | |||||||
\(284\) | 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 | ||||||||
\(291\) | −1.58402 | − | 0.758129i | −0.0928567 | − | 0.0444423i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.4450 | −0.843887 | −0.421944 | − | 0.906622i | \(-0.638652\pi\) | ||||
−0.421944 | + | 0.906622i | \(0.638652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.01296 | + | 1.20616i | 0.232855 | + | 0.0699884i | ||||
\(298\) | 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 | ||||||||
\(303\) | −8.37747 | − | 12.2241i | −0.481273 | − | 0.702259i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.34543i | 0.533372i | 0.963783 | + | 0.266686i | \(0.0859287\pi\) | ||||
−0.963783 | + | 0.266686i | \(0.914071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.30635 | + | 16.8862i | 0.0743154 | + | 0.960625i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.6664 | + | 25.4029i | −0.831654 | + | 1.44047i | 0.0650722 | + | 0.997881i | \(0.479272\pi\) |
−0.896726 | + | 0.442586i | \(0.854061\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.55728 | + | 5.51790i | −0.540209 | + | 0.311890i | −0.745164 | − | 0.666881i | \(-0.767629\pi\) |
0.204954 | + | 0.978772i | \(0.434295\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6987 | + | 8.48631i | −0.825563 | + | 0.476639i | −0.852331 | − | 0.523003i | \(-0.824812\pi\) |
0.0267682 | + | 0.999642i | \(0.491478\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | 17.1318 | + | 24.9983i | 0.947393 | + | 1.38241i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.63070 | + | 4.71382i | −0.310430 | + | 0.259881i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.82739 | + | 10.0933i | 0.320302 | + | 0.554780i | 0.980550 | − | 0.196268i | \(-0.0628822\pi\) |
−0.660248 | + | 0.751048i | \(0.729549\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.44380 | − | 21.8229i | 0.462717 | − | 1.19589i | ||||
\(334\) | 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 | ||||||||
\(339\) | −10.8741 | − | 5.20449i | −0.590602 | − | 0.282669i | ||||
\(340\) | 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 | \(-0.319712\pi\) |
−0.462494 | + | 0.886622i | \(0.653045\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.4812i | 0.828690i | 0.910120 | + | 0.414345i | \(0.135989\pi\) | ||||
−0.910120 | + | 0.414345i | \(0.864011\pi\) | |||||||
\(350\) | 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 | \(-0.943986\pi\) |
0.643889 | + | 0.765119i | \(0.277320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.94533 | + | 6.79153i | −0.367586 | + | 0.359446i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.66697 | + | 3.27183i | −0.299091 | + | 0.172680i | −0.642035 | − | 0.766676i | \(-0.721909\pi\) |
0.342943 | + | 0.939356i | \(0.388576\pi\) | |||||||
\(360\) | 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 | 0.837497 | − | 0.546442i | \(-0.184018\pi\) |
−0.0544847 | + | 0.998515i | \(0.517352\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.8977 | − | 19.7394i | −0.827603 | − | 1.02759i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.1130 | + | 33.1628i | −0.628875 | + | 1.72173i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.497933 | − | 0.862445i | −0.0257820 | − | 0.0446557i | 0.852847 | − | 0.522162i | \(-0.174874\pi\) |
−0.878629 | + | 0.477506i | \(0.841541\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | −5.81105 | + | 12.1415i | −0.297709 | + | 0.622026i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.93736 | − | 17.2120i | −0.507776 | − | 0.879493i | −0.999959 | − | 0.00900178i | \(-0.997135\pi\) |
0.492184 | − | 0.870491i | \(-0.336199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.54129 | − | 1.91374i | −0.0783482 | − | 0.0972808i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.56923 | + | 0.905994i | 0.0795630 | + | 0.0459357i | 0.539254 | − | 0.842143i | \(-0.318706\pi\) |
−0.459691 | + | 0.888079i | \(0.652040\pi\) | |||||||
\(390\) | 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 | 0.512384 | − | 0.858757i | \(-0.328763\pi\) |
0.999897 | − | 0.0143590i | \(-0.00457078\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.8717 | − | 3.55095i | 0.694453 | − | 0.177770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.5121 | + | 18.7709i | −1.62358 | + | 0.937374i | −0.637627 | + | 0.770345i | \(0.720084\pi\) |
−0.985952 | + | 0.167029i | \(0.946583\pi\) | |||||||
\(402\) | 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 | 0.578140 | − | 0.815937i | \(-0.303779\pi\) |
−0.417552 | + | 0.908653i | \(0.637112\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.51225 | + | 2.40702i | −0.173246 | + | 0.118729i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.2326 | − | 5.19856i | −0.700339 | − | 0.255804i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.39538 | − | 2.10368i | −0.215242 | − | 0.103018i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0547 | −1.46827 | −0.734134 | − | 0.679005i | \(-0.762411\pi\) | ||||
−0.734134 | + | 0.679005i | \(0.762411\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5447 | 1.00129 | 0.500643 | − | 0.865654i | \(-0.333097\pi\) | ||||
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00468 | − | 7.76556i | 0.146093 | − | 0.377574i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.51813 | + | 4.20243i | 0.170254 | + | 0.203370i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.05300 | − | 4.45484i | −0.147400 | − | 0.215082i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.7400 | − | 18.3251i | −1.52886 | − | 0.882688i | −0.999410 | − | 0.0343478i | \(-0.989065\pi\) |
−0.529451 | − | 0.848340i | \(-0.677602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.4397i | − | 1.75118i | −0.483057 | − | 0.875589i | \(-0.660474\pi\) | ||
0.483057 | − | 0.875589i | \(-0.339526\pi\) | |||||||
\(434\) | 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 | −0.677807 | − | 0.735240i | \(-0.737070\pi\) |
0.297833 | + | 0.954618i | \(0.403736\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.9469 | + | 10.9045i | 0.854614 | + | 0.519264i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7332 | + | 11.9703i | −0.985063 | + | 0.568727i | −0.903795 | − | 0.427966i | \(-0.859230\pi\) |
−0.0812683 | + | 0.996692i | \(0.525897\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | −0.837945 | − | 1.22270i | −0.0393701 | − | 0.0574476i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.33585 | + | 5.77786i | 0.156044 | + | 0.270277i | 0.933439 | − | 0.358737i | \(-0.116792\pi\) |
−0.777394 | + | 0.629013i | \(0.783459\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.17052 | − | 10.5485i | 0.147987 | − | 0.492362i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.6895 | 1.24305 | 0.621527 | − | 0.783393i | \(-0.286513\pi\) | ||||
0.621527 | + | 0.783393i | \(0.286513\pi\) | |||||||
\(462\) | 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 | \(-0.174765\pi\) |
−0.878464 | + | 0.477808i | \(0.841431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.0937 | + | 9.89620i | 1.25107 | + | 0.456964i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −34.8168 | + | 23.8607i | −1.60427 | + | 1.09944i | ||||
\(472\) | 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 | \(-0.730985\pi\) |
0.979655 | + | 0.200689i | \(0.0643180\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.1176 | + | 15.0790i | −1.19086 | + | 0.687543i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.6320 | − | 5.53749i | 0.984292 | − | 0.251964i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.8416 | + | 27.4385i | −0.717854 | + | 1.24336i | 0.243995 | + | 0.969776i | \(0.421542\pi\) |
−0.961849 | + | 0.273582i | \(0.911791\pi\) | |||||||
\(488\) | 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 | 0.962480 | − | 0.271352i | \(-0.0874706\pi\) |
−0.716237 | + | 0.697857i | \(0.754137\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.6567 | − | 26.4446i | 0.565460 | − | 1.18146i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.2246 | −0.901772 | −0.450886 | − | 0.892582i | \(-0.648892\pi\) | ||||
−0.450886 | + | 0.892582i | \(0.648892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.45795 | + | 3.04620i | −0.0647497 | + | 0.135287i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24557 | + | 9.08560i | 0.232506 | + | 0.402712i | 0.958545 | − | 0.284941i | \(-0.0919742\pi\) |
−0.726039 | + | 0.687654i | \(0.758641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.80069 | − | 7.66771i | 0.123895 | − | 0.339199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11.8219 | + | 11.1291i | −0.521949 | + | 0.491362i | ||||
\(514\) | 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 | \(-0.918019\pi\) |
0.704095 | + | 0.710105i | \(0.251353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.74038 | − | 4.46891i | 0.338463 | − | 0.195412i | −0.321129 | − | 0.947035i | \(-0.604062\pi\) |
0.659592 | + | 0.751624i | \(0.270729\pi\) | |||||||
\(524\) | 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 | ||||||||
\(537\) | −5.14187 | + | 3.52383i | −0.221888 | + | 0.152065i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.55697 | + | 0.992874i | 0.239356 | + | 0.0427661i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.9695 | − | 27.6599i | −0.686581 | − | 1.18919i | −0.972937 | − | 0.231069i | \(-0.925778\pi\) |
0.286357 | − | 0.958123i | \(-0.407556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.2806 | − | 16.8857i | −1.51404 | − | 0.724635i | ||||
\(544\) | 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 | ||||||||
\(549\) | −5.79577 | − | 2.24252i | −0.247357 | − | 0.0957085i | ||||
\(550\) | 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 | \(-0.261236\pi\) |
−0.292747 | + | 0.956190i | \(0.594569\pi\) | |||||||
\(558\) | 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 | \(-0.848739\pi\) |
0.840821 | + | 0.541313i | \(0.182073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.7914 | − | 0.984852i | −0.999144 | − | 0.0413599i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1648 | − | 13.9515i | 1.01304 | − | 0.584878i | 0.100959 | − | 0.994891i | \(-0.467809\pi\) |
0.912080 | + | 0.410012i | \(0.134476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.11649 | − | 5.39791i | 0.130421 | − | 0.225896i | −0.793418 | − | 0.608677i | \(-0.791700\pi\) |
0.923839 | + | 0.382782i | \(0.125034\pi\) | |||||||
\(572\) | 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 | 0.241687 | − | 0.970354i | \(-0.422299\pi\) |
−0.719508 | + | 0.694484i | \(0.755632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8592 | + | 15.8453i | 0.451291 | + | 0.658510i | ||||
\(580\) | 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 | \(-0.374448\pi\) | ||||
0.384284 | + | 0.923215i | \(0.374448\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.3858 | 0.839982 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.4011 | − | 12.1572i | −1.04486 | − | 0.500082i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.37822 | − | 2.38715i | −0.0565967 | − | 0.0980284i | 0.836339 | − | 0.548213i | \(-0.184692\pi\) |
−0.892936 | + | 0.450184i | \(0.851358\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.78115 | + | 1.22066i | −0.0728976 | + | 0.0499583i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.2530 | − | 9.38368i | −0.664080 | − | 0.383407i | 0.129750 | − | 0.991547i | \(-0.458583\pi\) |
−0.793830 | + | 0.608140i | \(0.791916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.5669i | − | 0.675779i | −0.941186 | − | 0.337890i | \(-0.890287\pi\) | ||
0.941186 | − | 0.337890i | \(-0.109713\pi\) | |||||||
\(602\) | 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 | −0.955122 | − | 0.296213i | \(-0.904276\pi\) |
−0.221032 | + | 0.975266i | \(0.570943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.24971 | − | 29.4648i | 0.334295 | − | 1.19397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.29381 | + | 5.36578i | −0.375987 | + | 0.217076i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7772 | + | 32.5231i | −0.758404 | + | 1.31359i | 0.185260 | + | 0.982690i | \(0.440687\pi\) |
−0.943664 | + | 0.330905i | \(0.892646\pi\) | |||||||
\(614\) | 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 | −0.0498816 | − | 0.998755i | \(-0.515884\pi\) |
−0.889888 | + | 0.456179i | \(0.849218\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4355 | + | 17.3551i | −0.739791 | + | 0.696438i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.51332 | + | 5.45272i | −0.260951 | + | 0.218459i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.88418 | + | 3.93676i | −0.0752468 | + | 0.157219i | ||||
\(628\) | 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 | ||||||||
\(633\) | −5.72376 | + | 11.9591i | −0.227499 | + | 0.475331i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.19909 | − | 25.4542i | −0.364481 | − | 1.00853i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.2642 | + | 19.5420i | −0.959878 | + | 0.773069i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.6664 | − | 15.3959i | −1.05326 | − | 0.608100i | −0.129700 | − | 0.991553i | \(-0.541401\pi\) |
−0.923560 | + | 0.383453i | \(0.874735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.42929i | − | 0.135238i | −0.997711 | − | 0.0676189i | \(-0.978460\pi\) | ||
0.997711 | − | 0.0676189i | \(-0.0215402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.2967 | + | 43.8152i | −0.994516 | + | 1.72255i | −0.406689 | + | 0.913567i | \(0.633317\pi\) |
−0.587828 | + | 0.808986i | \(0.700017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.99966 | − | 2.30920i | 0.157000 | − | 0.0906441i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9027 | + | 21.3761i | 0.819243 | + | 0.837795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.57643 | − | 2.64220i | 0.179090 | − | 0.103397i | −0.407775 | − | 0.913082i | \(-0.633695\pi\) |
0.586865 | + | 0.809685i | \(0.300362\pi\) | |||||||
\(654\) | 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 | −0.166481 | − | 0.986045i | \(-0.553241\pi\) |
−0.937180 | + | 0.348845i | \(0.886574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.7101 | + | 8.02515i | −0.454781 | + | 0.311671i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.2676 | − | 28.1763i | −0.629883 | − | 1.09099i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 32.7103 | + | 15.6555i | 1.26465 | + | 0.605278i | ||||
\(670\) | 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 | \(-0.0466387\pi\) |
−0.621079 | + | 0.783748i | \(0.713305\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.64225 | − | 0.462805i | 0.101400 | − | 0.0177608i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.48649 | + | 6.54654i | 0.171923 | + | 0.250864i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.0821 | + | 14.4812i | 0.959741 | + | 0.554107i | 0.896093 | − | 0.443866i | \(-0.146393\pi\) |
0.0636479 | + | 0.997972i | \(0.479727\pi\) | |||||||
\(684\) | 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 | 0.501024 | − | 0.865433i | \(-0.332957\pi\) |
0.999999 | − | 0.00118303i | \(-0.000376571\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.05995 | + | 2.06088i | −0.230198 | + | 0.0782862i | ||||
\(694\) | 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 | 0.618506 | − | 0.785780i | \(-0.287738\pi\) |
−0.989759 | + | 0.142752i | \(0.954405\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6436 | − | 37.8463i | 0.549180 | − | 1.41935i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.7904 | 1.19056 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.1675 | + | 21.1391i | 1.64947 | + | 0.789454i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.740641 | + | 1.28283i | 0.0276212 | + | 0.0478414i | 0.879506 | − | 0.475889i | \(-0.157873\pi\) |
−0.851884 | + | 0.523730i | \(0.824540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6072 | − | 19.8374i | −0.618484 | − | 0.738784i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.3040 | − | 12.5441i | 0.680733 | − | 0.466521i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.35193i | − | 0.235580i | −0.993039 | − | 0.117790i | \(-0.962419\pi\) | ||
0.993039 | − | 0.117790i | \(-0.0375810\pi\) | |||||||
\(728\) | 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 | 0.283857 | − | 0.958866i | \(-0.408386\pi\) |
0.972331 | + | 0.233605i | \(0.0750524\pi\) | |||||||
\(734\) | 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 | −0.580139 | − | 0.814518i | \(-0.697002\pi\) |
0.995462 | + | 0.0951558i | \(0.0303349\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | −24.2647 | − | 30.1282i | −0.887799 | − | 1.10233i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.0510 | − | 37.0906i | −1.13458 | − | 1.35526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.62709 | + | 14.9426i | 0.314807 | + | 0.545262i | 0.979396 | − | 0.201947i | \(-0.0647268\pi\) |
−0.664589 | + | 0.747209i | \(0.731393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.72793 | − | 16.1466i | 0.281621 | − | 0.588413i | ||||
\(754\) | 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 | ||||||||
\(759\) | −2.93826 | + | 6.13913i | −0.106652 | + | 0.222836i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.00796126 | + | 0.0137893i | 0.000288596 | + | 0.000499862i | 0.866170 | − | 0.499750i | \(-0.166575\pi\) |
−0.865881 | + | 0.500250i | \(0.833241\pi\) | |||||||
\(762\) | 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 | \(0.0755213\pi\) | ||||
−0.971986 | + | 0.235037i | \(0.924479\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52.6796 | + | 4.07537i | −1.89721 | + | 0.146771i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.7085 | + | 25.4758i | −0.529027 | + | 0.916301i | 0.470400 | + | 0.882453i | \(0.344110\pi\) |
−0.999427 | + | 0.0338481i | \(0.989224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.86395 | + | 34.6268i | 0.317993 | + | 1.24223i | ||||
\(778\) | 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 | 0.464664 | − | 0.885487i | \(-0.346175\pi\) |
−0.534522 | + | 0.845154i | \(0.679508\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.5395 | + | 20.2441i | −1.05164 | + | 0.720708i | ||||
\(790\) | 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 | \(-0.386988\pi\) | ||||
0.347625 | + | 0.937634i | \(0.386988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.88350 | −0.208143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.47567 | − | 8.98283i | 0.122807 | − | 0.317393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.24407 | + | 2.15479i | 0.0439022 | + | 0.0760409i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.3012 | − | 35.4596i | −0.855444 | − | 1.24824i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.2506 | + | 12.2690i | 0.747130 | + | 0.431356i | 0.824656 | − | 0.565635i | \(-0.191369\pi\) |
−0.0775260 | + | 0.996990i | \(0.524702\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.7927i | 1.36220i | 0.732192 | + | 0.681098i | \(0.238497\pi\) | ||||
−0.732192 | + | 0.681098i | \(0.761503\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 23.0849 | + | 20.2219i | 0.806650 | + | 0.706611i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.8734 | + | 6.85513i | −0.414386 | + | 0.239246i | −0.692672 | − | 0.721252i | \(-0.743567\pi\) |
0.278287 | + | 0.960498i | \(0.410233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04168 | − | 7.00040i | 0.140884 | − | 0.244019i | −0.786946 | − | 0.617022i | \(-0.788339\pi\) |
0.927830 | + | 0.373004i | \(0.121672\pi\) | |||||||
\(824\) | 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 | 0.743665 | − | 0.668552i | \(-0.233086\pi\) |
−0.207150 | + | 0.978309i | \(0.566419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.9050 | − | 21.7489i | −0.517049 | − | 0.754462i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.60988 | − | 14.6071i | 0.0904269 | − | 0.506106i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.4658 | − | 9.75811i | −1.12218 | − | 0.337290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.49497 | −0.155183 | −0.0775917 | − | 0.996985i | \(-0.524723\pi\) | ||||
−0.0775917 | + | 0.996985i | \(0.524723\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5825 | −0.537329 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.0419 | − | 13.4212i | −0.965814 | − | 0.462250i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.9963 | − | 17.5774i | 0.721443 | − | 0.603966i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 38.5598 | − | 26.4259i | 1.32337 | − | 0.906934i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.9144 | + | 19.0032i | 1.12829 | + | 0.651420i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.0503i | − | 1.13162i | −0.824535 | − | 0.565811i | \(-0.808563\pi\) | ||
0.824535 | − | 0.565811i | \(-0.191437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.210762 | + | 0.365051i | −0.00719949 | + | 0.0124699i | −0.869603 | − | 0.493752i | \(-0.835625\pi\) |
0.862403 | + | 0.506222i | \(0.168958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0294 | + | 9.83192i | −0.581035 | + | 0.335461i | −0.761545 | − | 0.648112i | \(-0.775559\pi\) |
0.180509 | + | 0.983573i | \(0.442225\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.2818 | + | 10.4383i | 1.27056 | + | 0.355737i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.782575 | + | 0.451820i | −0.0266392 | + | 0.0153801i | −0.513260 | − | 0.858233i | \(-0.671563\pi\) |
0.486621 | + | 0.873613i | \(0.338229\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | −2.36889 | + | 1.90787i | −0.0801749 | + | 0.0645715i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.65916 | − | 13.2661i | −0.258632 | − | 0.447963i | 0.707244 | − | 0.706970i | \(-0.249938\pi\) |
−0.965876 | + | 0.259006i | \(0.916605\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8013 | + | 22.5679i | −0.364317 | + | 0.761196i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.8614 | 1.47773 | 0.738863 | − | 0.673855i | \(-0.235363\pi\) | ||||
0.738863 | + | 0.673855i | \(0.235363\pi\) | |||||||
\(882\) | 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 | \(-0.247122\pi\) |
−0.963547 | + | 0.267541i | \(0.913789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.54739 | − | 20.2528i | −0.118976 | − | 0.679259i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.88510 | − | 5.36766i | 0.163657 | − | 0.179823i | ||||
\(892\) | 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 | ||||||||
\(903\) | 3.61448 | + | 1.01200i | 0.120282 | + | 0.0336772i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.54899 | − | 16.5393i | 0.317069 | − | 0.549180i | −0.662806 | − | 0.748791i | \(-0.730635\pi\) |
0.979875 | + | 0.199611i | \(0.0639679\pi\) | |||||||
\(908\) | 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 | 0.510668 | − | 0.859778i | \(-0.329398\pi\) |
−0.999924 | + | 0.0123630i | \(0.996065\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.6006 | + | 6.98804i | 0.481107 | + | 0.230264i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.1537 | 1.32168 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 27.3587 | + | 10.5857i | 0.898577 | + | 0.347681i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.8256 | − | 29.1428i | −0.552030 | − | 0.956144i | −0.998128 | − | 0.0611601i | \(-0.980520\pi\) |
0.446098 | − | 0.894984i | \(-0.352813\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.0975 | + | 16.7234i | −0.462027 | + | 0.548087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.7209 | + | 41.9087i | 0.940281 | + | 1.37203i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.99276i | 0.261112i | 0.991441 | + | 0.130556i | \(0.0416762\pi\) | ||||
−0.991441 | + | 0.130556i | \(0.958324\pi\) | |||||||
\(938\) | 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 | \(-0.741862\pi\) |
0.972226 | + | 0.234043i | \(0.0751955\pi\) | |||||||
\(942\) | 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 | \(-0.907842\pi\) |
−0.231943 | + | 0.972729i | \(0.574508\pi\) | |||||||
\(948\) | 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 | ||||||||
\(957\) | 5.27220 | + | 7.69303i | 0.170426 | + | 0.248680i | ||||
\(958\) | 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 | ||||||||
\(963\) | 51.1534 | + | 19.7925i | 1.64840 | + | 0.637804i | ||||
\(964\) | 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 | ||||||||
\(969\) | 10.3482 | + | 4.95277i | 0.332432 | + | 0.159106i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.5452 | + | 37.3173i | 0.691418 | + | 1.19757i | 0.971373 | + | 0.237558i | \(0.0763469\pi\) |
−0.279956 | + | 0.960013i | \(0.590320\pi\) | |||||||
\(972\) | 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 | \(-0.452135\pi\) |
−0.781350 | + | 0.624093i | \(0.785469\pi\) | |||||||
\(978\) | 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 | −0.240157 | − | 0.970734i | \(-0.577199\pi\) |
0.960759 | − | 0.277385i | \(-0.0894677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.15419 | + | 12.3218i | 0.100399 | + | 0.392206i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.45641 | − | 1.99556i | 0.109907 | − | 0.0634551i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2760 | + | 43.7793i | −0.802919 | + | 1.39070i | 0.114768 | + | 0.993392i | \(0.463388\pi\) |
−0.917687 | + | 0.397304i | \(0.869946\pi\) | |||||||
\(992\) | 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 | 0.812760 | − | 0.582599i | \(-0.197964\pi\) |
−0.0981654 | + | 0.995170i | \(0.531297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.7807 | − | 29.5100i | −0.878942 | − | 0.933656i |
(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.k.101.4 | 10 | ||
3.2 | odd | 2 | 2100.2.bi.j.101.2 | 10 | |||
5.2 | odd | 4 | 2100.2.bo.h.1949.3 | 20 | |||
5.3 | odd | 4 | 2100.2.bo.h.1949.8 | 20 | |||
5.4 | even | 2 | 420.2.bh.a.101.2 | ✓ | 10 | ||
7.5 | odd | 6 | 2100.2.bi.j.1601.2 | 10 | |||
15.2 | even | 4 | 2100.2.bo.g.1949.9 | 20 | |||
15.8 | even | 4 | 2100.2.bo.g.1949.2 | 20 | |||
15.14 | odd | 2 | 420.2.bh.b.101.4 | yes | 10 | ||
21.5 | even | 6 | inner | 2100.2.bi.k.1601.4 | 10 | ||
35.4 | even | 6 | 2940.2.d.b.881.9 | 10 | |||
35.12 | even | 12 | 2100.2.bo.g.1349.2 | 20 | |||
35.19 | odd | 6 | 420.2.bh.b.341.4 | yes | 10 | ||
35.24 | odd | 6 | 2940.2.d.a.881.2 | 10 | |||
35.33 | even | 12 | 2100.2.bo.g.1349.9 | 20 | |||
105.47 | odd | 12 | 2100.2.bo.h.1349.8 | 20 | |||
105.59 | even | 6 | 2940.2.d.b.881.10 | 10 | |||
105.68 | odd | 12 | 2100.2.bo.h.1349.3 | 20 | |||
105.74 | odd | 6 | 2940.2.d.a.881.1 | 10 | |||
105.89 | even | 6 | 420.2.bh.a.341.2 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bh.a.101.2 | ✓ | 10 | 5.4 | even | 2 | ||
420.2.bh.a.341.2 | yes | 10 | 105.89 | even | 6 | ||
420.2.bh.b.101.4 | yes | 10 | 15.14 | odd | 2 | ||
420.2.bh.b.341.4 | yes | 10 | 35.19 | odd | 6 | ||
2100.2.bi.j.101.2 | 10 | 3.2 | odd | 2 | |||
2100.2.bi.j.1601.2 | 10 | 7.5 | odd | 6 | |||
2100.2.bi.k.101.4 | 10 | 1.1 | even | 1 | trivial | ||
2100.2.bi.k.1601.4 | 10 | 21.5 | even | 6 | inner | ||
2100.2.bo.g.1349.2 | 20 | 35.12 | even | 12 | |||
2100.2.bo.g.1349.9 | 20 | 35.33 | even | 12 | |||
2100.2.bo.g.1949.2 | 20 | 15.8 | even | 4 | |||
2100.2.bo.g.1949.9 | 20 | 15.2 | even | 4 | |||
2100.2.bo.h.1349.3 | 20 | 105.68 | odd | 12 | |||
2100.2.bo.h.1349.8 | 20 | 105.47 | odd | 12 | |||
2100.2.bo.h.1949.3 | 20 | 5.2 | odd | 4 | |||
2100.2.bo.h.1949.8 | 20 | 5.3 | odd | 4 | |||
2940.2.d.a.881.1 | 10 | 105.74 | odd | 6 | |||
2940.2.d.a.881.2 | 10 | 35.24 | odd | 6 | |||
2940.2.d.b.881.9 | 10 | 35.4 | even | 6 | |||
2940.2.d.b.881.10 | 10 | 105.59 | even | 6 |