Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [140,2,Mod(17,140)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(140, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("140.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.u (of order \(12\), degree \(4\), 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: | \(1.11790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 802 x^{12} - 2264 x^{11} + 5402 x^{10} - 10642 x^{9} + \cdots + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Root | \(0.500000 - 0.617773i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 140.73 |
Dual form | 140.2.u.a.117.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | 0.409133 | + | 1.52691i | 0.236213 | + | 0.881560i | 0.977598 | + | 0.210480i | \(0.0675026\pi\) |
−0.741385 | + | 0.671080i | \(0.765831\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.62046 | − | 1.54081i | 0.724693 | − | 0.689072i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.512081 | + | 2.59572i | −0.193549 | + | 0.981091i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.434025 | − | 0.250584i | 0.144675 | − | 0.0835281i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.342727 | + | 0.593621i | −0.103336 | + | 0.178984i | −0.913057 | − | 0.407831i | \(-0.866285\pi\) |
0.809721 | + | 0.586815i | \(0.199618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.04830 | + | 1.04830i | −0.290747 | + | 0.290747i | −0.837375 | − | 0.546628i | \(-0.815911\pi\) |
0.546628 | + | 0.837375i | \(0.315911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.01566 | + | 1.84390i | 0.778640 | + | 0.476092i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.31940 | + | 0.353532i | −0.320002 | + | 0.0857442i | −0.415244 | − | 0.909710i | \(-0.636304\pi\) |
0.0952428 | + | 0.995454i | \(0.469637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.55949 | − | 2.70111i | −0.357771 | − | 0.619678i | 0.629817 | − | 0.776744i | \(-0.283130\pi\) |
−0.987588 | + | 0.157065i | \(0.949797\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.17293 | + | 0.280096i | −0.910609 | + | 0.0611220i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.18980 | − | 4.44038i | 0.248090 | − | 0.925883i | −0.723716 | − | 0.690098i | \(-0.757567\pi\) |
0.971805 | − | 0.235785i | \(-0.0757661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.251796 | − | 4.99366i | 0.0503591 | − | 0.998731i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.91351 | + | 3.91351i | 0.753155 | + | 0.753155i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.90106i | − | 1.46719i | −0.679587 | − | 0.733595i | \(-0.737841\pi\) | ||
0.679587 | − | 0.733595i | \(-0.262159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.63715 | − | 4.40931i | −1.37167 | − | 0.791936i | −0.380535 | − | 0.924767i | \(-0.624260\pi\) |
−0.991139 | + | 0.132831i | \(0.957593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.04663 | − | 0.280442i | −0.182194 | − | 0.0488187i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.16971 | + | 4.99529i | 0.535779 | + | 0.844358i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.68572 | − | 2.32733i | −1.42792 | − | 0.382611i | −0.539636 | − | 0.841899i | \(-0.681438\pi\) |
−0.888288 | + | 0.459288i | \(0.848105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.02956 | − | 1.17176i | −0.324989 | − | 0.187632i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2469i | 1.60029i | 0.599805 | + | 0.800146i | \(0.295245\pi\) | ||||
−0.599805 | + | 0.800146i | \(0.704755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73689 | + | 3.73689i | 0.569871 | + | 0.569871i | 0.932092 | − | 0.362221i | \(-0.117982\pi\) |
−0.362221 | + | 0.932092i | \(0.617982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.317217 | − | 1.07481i | 0.0472880 | − | 0.160224i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.80577 | + | 6.73924i | −0.263399 | + | 0.983019i | 0.699824 | + | 0.714315i | \(0.253262\pi\) |
−0.963223 | + | 0.268703i | \(0.913405\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.47555 | − | 2.65844i | −0.925078 | − | 0.379777i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.07962 | − | 1.86996i | −0.151177 | − | 0.261847i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.94065 | − | 2.39564i | 1.22809 | − | 0.329066i | 0.414256 | − | 0.910160i | \(-0.364042\pi\) |
0.813837 | + | 0.581094i | \(0.197375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.359282 | + | 1.49002i | 0.0484456 | + | 0.200914i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.48631 | − | 3.48631i | 0.461773 | − | 0.461773i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.10430 | − | 3.64475i | 0.273956 | − | 0.474506i | −0.695915 | − | 0.718124i | \(-0.745001\pi\) |
0.969871 | + | 0.243618i | \(0.0783343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.57882 | − | 2.06623i | 0.458221 | − | 0.264554i | −0.253075 | − | 0.967447i | \(-0.581442\pi\) |
0.711296 | + | 0.702893i | \(0.248109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.428191 | + | 1.25493i | 0.0539470 | + | 0.158106i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0834974 | + | 3.31397i | −0.0103566 | + | 0.411048i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.07466 | − | 4.01070i | −0.131291 | − | 0.489985i | 0.868694 | − | 0.495348i | \(-0.164960\pi\) |
−0.999986 | + | 0.00536291i | \(0.998293\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.26683 | 0.874823 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.5889 | 1.49402 | 0.747011 | − | 0.664812i | \(-0.231488\pi\) | ||||
0.747011 | + | 0.664812i | \(0.231488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.32399 | + | 12.4053i | 0.389044 | + | 1.45193i | 0.831693 | + | 0.555236i | \(0.187372\pi\) |
−0.442649 | + | 0.896695i | \(0.645961\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.72786 | − | 1.65860i | 0.892336 | − | 0.191519i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.36537 | − | 1.19361i | −0.155599 | − | 0.136024i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1515 | + | 7.01566i | −1.36715 | + | 0.789323i | −0.990563 | − | 0.137059i | \(-0.956235\pi\) |
−0.376585 | + | 0.926382i | \(0.622902\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.62266 | + | 6.27464i | −0.402518 | + | 0.697182i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.99595 | + | 3.99595i | −0.438612 | + | 0.438612i | −0.891545 | − | 0.452933i | \(-0.850378\pi\) |
0.452933 | + | 0.891545i | \(0.350378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.59331 | + | 2.60583i | −0.172819 | + | 0.282642i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0642 | − | 3.23259i | 1.29342 | − | 0.346570i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.79949 | + | 10.0450i | 0.614745 | + | 1.06477i | 0.990429 | + | 0.138021i | \(0.0440743\pi\) |
−0.375685 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.18429 | − | 3.25792i | −0.228975 | − | 0.341523i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.60799 | − | 13.4652i | 0.374131 | − | 1.39628i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.68900 | − | 1.97417i | −0.686277 | − | 0.202546i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.60010 | + | 2.60010i | 0.264000 | + | 0.264000i | 0.826677 | − | 0.562677i | \(-0.190228\pi\) |
−0.562677 | + | 0.826677i | \(0.690228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.343528i | 0.0345259i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.65764 | − | 1.53439i | −0.264445 | − | 0.152677i | 0.361915 | − | 0.932211i | \(-0.382123\pi\) |
−0.626361 | + | 0.779533i | \(0.715456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.9958 | − | 4.28607i | −1.57612 | − | 0.422319i | −0.638395 | − | 0.769709i | \(-0.720402\pi\) |
−0.937721 | + | 0.347389i | \(0.887068\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.33050 | + | 6.88359i | −0.617794 | + | 0.671770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.12180 | − | 1.37238i | −0.495143 | − | 0.132673i | 0.00260205 | − | 0.999997i | \(-0.499172\pi\) |
−0.497745 | + | 0.867323i | \(0.665838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.3427 | + | 8.28074i | 1.37378 | + | 0.793151i | 0.991401 | − | 0.130856i | \(-0.0417726\pi\) |
0.382376 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 14.2145i | − | 1.34918i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.21561 | − | 7.21561i | −0.678787 | − | 0.678787i | 0.280939 | − | 0.959726i | \(-0.409354\pi\) |
−0.959726 | + | 0.280939i | \(0.909354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.91377 | − | 9.02872i | −0.458212 | − | 0.841933i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.192301 | + | 0.717677i | −0.0177782 | + | 0.0663493i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.242031 | − | 3.60583i | −0.0221870 | − | 0.330546i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.26508 | + | 9.11938i | 0.478643 | + | 0.829034i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.6460 | + | 4.19233i | −1.41075 | + | 0.378010i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.28626 | − | 8.48000i | −0.651703 | − | 0.758474i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.13026 | + | 2.13026i | −0.189030 | + | 0.189030i | −0.795277 | − | 0.606247i | \(-0.792674\pi\) |
0.606247 | + | 0.795277i | \(0.292674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.17700 | + | 7.23477i | −0.367764 | + | 0.636986i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.47951 | − | 5.47300i | 0.828229 | − | 0.478178i | −0.0250169 | − | 0.999687i | \(-0.507964\pi\) |
0.853246 | + | 0.521509i | \(0.174631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.80993 | − | 2.66481i | 0.677207 | − | 0.231068i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 12.3717 | + | 0.311711i | 1.06478 | + | 0.0268278i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.349978 | + | 1.30614i | 0.0299006 | + | 0.111591i | 0.979263 | − | 0.202592i | \(-0.0649364\pi\) |
−0.949363 | + | 0.314182i | \(0.898270\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.703180 | −0.0596429 | −0.0298215 | − | 0.999555i | \(-0.509494\pi\) | ||||
−0.0298215 | + | 0.999555i | \(0.509494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0290 | −0.928808 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.263013 | − | 0.981577i | −0.0219942 | − | 0.0820836i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.1741 | − | 12.8034i | −1.01100 | − | 1.06326i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.40983 | − | 10.9752i | 0.116281 | − | 0.905220i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.78894 | − | 5.65165i | 0.801941 | − | 0.463001i | −0.0422084 | − | 0.999109i | \(-0.513439\pi\) |
0.844149 | + | 0.536108i | \(0.180106\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.95170 | − | 6.84454i | 0.321585 | − | 0.557001i | −0.659230 | − | 0.751941i | \(-0.729118\pi\) |
0.980815 | + | 0.194940i | \(0.0624512\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.484063 | + | 0.484063i | −0.0391341 | + | 0.0391341i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1696 | + | 4.62229i | −1.53974 | + | 0.371272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.25342 | − | 0.603801i | 0.179842 | − | 0.0481886i | −0.167774 | − | 0.985825i | \(-0.553658\pi\) |
0.347616 | + | 0.937637i | \(0.386991\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.31583 | + | 12.6714i | 0.580183 | + | 1.00491i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9167 | + | 5.36222i | 0.860358 | + | 0.422602i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.292547 | − | 1.09180i | 0.0229140 | − | 0.0855163i | −0.953522 | − | 0.301324i | \(-0.902572\pi\) |
0.976436 | + | 0.215807i | \(0.0692383\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.12813 | + | 1.15821i | −0.165674 | + | 0.0901662i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.76281 | − | 5.76281i | −0.445940 | − | 0.445940i | 0.448062 | − | 0.894002i | \(-0.352114\pi\) |
−0.894002 | + | 0.448062i | \(0.852114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8021i | 0.830933i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.35371 | − | 0.781567i | −0.103521 | − | 0.0597679i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.8911 | − | 4.52596i | −1.28421 | − | 0.344103i | −0.448751 | − | 0.893657i | \(-0.648131\pi\) |
−0.835458 | + | 0.549554i | \(0.814798\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.8332 | + | 3.21075i | 0.970099 | + | 0.242710i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.42613 | + | 1.72188i | 0.483017 | + | 0.129424i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.930020 | − | 0.536947i | −0.0695129 | − | 0.0401333i | 0.464841 | − | 0.885394i | \(-0.346112\pi\) |
−0.534354 | + | 0.845261i | \(0.679445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.93607i | − | 0.664213i | −0.943242 | − | 0.332106i | \(-0.892241\pi\) | ||
0.943242 | − | 0.332106i | \(-0.107759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.61916 | + | 4.61916i | 0.341458 | + | 0.341458i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.6609 | + | 9.61171i | −1.29845 | + | 0.706667i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.242330 | − | 0.904389i | 0.0177210 | − | 0.0661355i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.1624 | + | 8.15435i | −0.884686 | + | 0.593142i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.1898 | + | 21.1133i | 0.882020 | + | 1.52770i | 0.849091 | + | 0.528246i | \(0.177150\pi\) |
0.0329288 | + | 0.999458i | \(0.489517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.72531 | − | 2.33794i | 0.628062 | − | 0.168289i | 0.0692717 | − | 0.997598i | \(-0.477932\pi\) |
0.558790 | + | 0.829309i | \(0.311266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.09429 | + | 1.22836i | −0.364809 | + | 0.0879649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.78673 | − | 1.78673i | 0.127299 | − | 0.127299i | −0.640587 | − | 0.767886i | \(-0.721309\pi\) |
0.767886 | + | 0.640587i | \(0.221309\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.67200 | − | 8.09214i | 0.331189 | − | 0.573637i | −0.651556 | − | 0.758601i | \(-0.725883\pi\) |
0.982745 | + | 0.184964i | \(0.0592168\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.68429 | − | 3.28182i | 0.400939 | − | 0.231482i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5090 | + | 4.04599i | 1.43945 | + | 0.283972i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7885 | + | 16.6047i | 1.10272 | + | 1.15972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.596288 | − | 2.22538i | −0.0414449 | − | 0.154675i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.13792 | 0.147883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.84703 | −0.677898 | −0.338949 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338949 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.15052 | + | 19.2220i | 0.352908 | + | 1.31707i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.8133 | + | 0.297644i | 0.805664 | + | 0.0202991i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.3562 | − | 17.5660i | 1.04245 | − | 1.19246i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.5818 | + | 10.1508i | −1.18807 | + | 0.685931i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.01252 | − | 1.75374i | 0.0681096 | − | 0.117969i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.338625 | + | 0.338625i | −0.0226760 | + | 0.0226760i | −0.718354 | − | 0.695678i | \(-0.755104\pi\) |
0.695678 | + | 0.718354i | \(0.255104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.14205 | − | 2.23047i | −0.0761364 | − | 0.148698i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.3958 | − | 3.58938i | 0.889108 | − | 0.238236i | 0.214775 | − | 0.976664i | \(-0.431098\pi\) |
0.674333 | + | 0.738428i | \(0.264431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.33146 | + | 2.30615i | 0.0879850 | + | 0.152395i | 0.906659 | − | 0.421864i | \(-0.138624\pi\) |
−0.818674 | + | 0.574258i | \(0.805291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.26391 | − | 2.57314i | 0.0831590 | − | 0.169300i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.90012 | − | 18.2875i | 0.321017 | − | 1.19805i | −0.597238 | − | 0.802064i | \(-0.703735\pi\) |
0.918255 | − | 0.395989i | \(-0.129598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.45771 | + | 13.7030i | 0.486487 | + | 0.893888i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.6838 | − | 15.6838i | −1.01877 | − | 1.01877i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.74416i | 0.371559i | 0.982591 | + | 0.185779i | \(0.0594809\pi\) | ||||
−0.982591 | + | 0.185779i | \(0.940519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.82144 | + | 5.09306i | 0.568239 | + | 0.328073i | 0.756446 | − | 0.654057i | \(-0.226934\pi\) |
−0.188207 | + | 0.982129i | \(0.560268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.97494 | + | 1.33303i | 0.319142 | + | 0.0855139i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.5895 | + | 5.66970i | −0.932091 | + | 0.362224i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.46640 | + | 1.19677i | 0.284190 | + | 0.0761486i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.73631 | − | 4.46656i | −0.490268 | − | 0.283057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 7.28871i | − | 0.460059i | −0.973184 | − | 0.230030i | \(-0.926118\pi\) | ||
0.973184 | − | 0.230030i | \(-0.0738823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.22813 | + | 2.22813i | 0.140081 | + | 0.140081i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.63074 | − | 1.36670i | −0.289988 | − | 0.0855863i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.16193 | + | 11.8005i | −0.197236 | + | 0.736095i | 0.794441 | + | 0.607342i | \(0.207764\pi\) |
−0.991677 | + | 0.128753i | \(0.958903\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4889 | − | 21.3539i | 0.651748 | − | 1.32687i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.97988 | − | 3.42926i | −0.122552 | − | 0.212266i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.7745 | + | 5.56652i | −1.28101 | + | 0.343246i | −0.834240 | − | 0.551402i | \(-0.814093\pi\) |
−0.446772 | + | 0.894648i | \(0.647427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7968 | − | 17.6579i | 0.663239 | − | 1.08472i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.9650 | + | 12.9650i | −0.793446 | + | 0.793446i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.2377 | − | 22.9283i | 0.807114 | − | 1.39796i | −0.107741 | − | 0.994179i | \(-0.534362\pi\) |
0.914855 | − | 0.403783i | \(-0.132305\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.4571 | + | 8.92414i | −0.938949 | + | 0.542103i | −0.889631 | − | 0.456680i | \(-0.849038\pi\) |
−0.0493186 | + | 0.998783i | \(0.515705\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.08087 | − | 4.66812i | 0.246986 | − | 0.282528i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.87804 | + | 1.86093i | 0.173553 | + | 0.112219i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.86772 | + | 25.6307i | 0.412641 | + | 1.54000i | 0.789514 | + | 0.613733i | \(0.210333\pi\) |
−0.376873 | + | 0.926265i | \(0.623001\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.41962 | −0.264596 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.7465 | −1.11832 | −0.559161 | − | 0.829059i | \(-0.688877\pi\) | ||||
−0.559161 | + | 0.829059i | \(0.688877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.169240 | + | 0.631614i | 0.0100603 | + | 0.0375456i | 0.970774 | − | 0.239997i | \(-0.0771466\pi\) |
−0.960713 | + | 0.277543i | \(0.910480\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.277685 | − | 11.0212i | 0.0164486 | − | 0.652838i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.5980 | − | 5.24723i | −1.57003 | − | 0.309734i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.1066 | + | 7.56710i | −0.770976 | + | 0.445123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.90632 | + | 5.03390i | −0.170372 | + | 0.295092i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.72555 | − | 1.72555i | 0.100808 | − | 0.100808i | −0.654904 | − | 0.755712i | \(-0.727291\pi\) |
0.755712 | + | 0.654904i | \(0.227291\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.20594 | − | 9.14851i | −0.128435 | − | 0.532647i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.66441 | + | 0.981876i | −0.212631 | + | 0.0569742i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.40760 | + | 5.90213i | 0.197066 | + | 0.341329i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.6135 | + | 7.78634i | −0.669393 | + | 0.448797i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.25554 | − | 4.68574i | 0.0721288 | − | 0.269188i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.61567 | − | 8.86254i | 0.149773 | − | 0.507468i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.5555 | + | 18.5555i | 1.05902 | + | 1.05902i | 0.998145 | + | 0.0608747i | \(0.0193890\pi\) |
0.0608747 | + | 0.998145i | \(0.480611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 26.1777i | − | 1.48920i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.30249 | + | 2.48404i | 0.243972 | + | 0.140857i | 0.617001 | − | 0.786962i | \(-0.288347\pi\) |
−0.373029 | + | 0.927820i | \(0.621681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8215 | − | 3.16757i | −0.668192 | − | 0.179041i | −0.0912515 | − | 0.995828i | \(-0.529087\pi\) |
−0.576940 | + | 0.816787i | \(0.695753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.62747 | + | 1.37380i | 0.148041 | + | 0.0774048i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.0231 | − | 6.70491i | −1.40543 | − | 0.376585i | −0.525142 | − | 0.851015i | \(-0.675988\pi\) |
−0.880293 | + | 0.474430i | \(0.842654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.69024 | + | 2.70791i | 0.262603 | + | 0.151614i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 8.38199i | − | 0.467837i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.01252 | + | 3.01252i | 0.167621 | + | 0.167621i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.97091 | + | 5.49882i | 0.275736 | + | 0.305020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.77585 | + | 25.2878i | −0.374705 | + | 1.39842i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.5685 | − | 8.13832i | −0.913450 | − | 0.448680i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.58313 | − | 13.1344i | −0.416806 | − | 0.721930i | 0.578810 | − | 0.815463i | \(-0.303517\pi\) |
−0.995616 | + | 0.0935328i | \(0.970184\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.35301 | + | 1.16639i | −0.238543 | + | 0.0639175i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.92120 | − | 4.84334i | −0.432781 | − | 0.264620i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.7442 | − | 12.7442i | 0.694218 | − | 0.694218i | −0.268939 | − | 0.963157i | \(-0.586673\pi\) |
0.963157 | + | 0.268939i | \(0.0866729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.06541 | − | 13.9697i | 0.438053 | − | 0.758730i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.23492 | − | 3.02238i | 0.283487 | − | 0.163671i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.2166 | − | 15.4474i | 0.551643 | − | 0.834080i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7756 | − | 11.1968i | 0.633978 | − | 0.602816i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.56558 | + | 5.84281i | 0.0840445 | + | 0.313658i | 0.995132 | − | 0.0985557i | \(-0.0314223\pi\) |
−0.911087 | + | 0.412214i | \(0.864756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.80171 | 0.310558 | 0.155279 | − | 0.987871i | \(-0.450372\pi\) | ||||
0.155279 | + | 0.987871i | \(0.450372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.20509 | −0.437955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.06423 | − | 11.4359i | −0.163093 | − | 0.608670i | −0.998276 | − | 0.0586980i | \(-0.981305\pi\) |
0.835183 | − | 0.549972i | \(-0.185362\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3998 | − | 19.3971i | 1.08271 | − | 1.02949i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.40675 | − | 1.84483i | 0.286155 | − | 0.0976385i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.22275 | − | 2.43801i | 0.222868 | − | 0.128673i | −0.384409 | − | 0.923163i | \(-0.625595\pi\) |
0.607278 | + | 0.794490i | \(0.292262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.63599 | − | 8.02976i | 0.243999 | − | 0.422619i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.7703 | + | 11.7703i | −0.617781 | + | 0.617781i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.5006 | + | 14.9807i | 1.28242 | + | 0.784125i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.97731 | + | 1.60161i | −0.312013 | + | 0.0836036i | −0.411427 | − | 0.911443i | \(-0.634970\pi\) |
0.0994146 | + | 0.995046i | \(0.468303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.56770 | + | 4.44739i | 0.133669 | + | 0.231522i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.64008 | + | 24.4342i | 0.0851485 | + | 1.26856i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.49882 | + | 31.7180i | −0.440052 | + | 1.64230i | 0.288626 | + | 0.957442i | \(0.406801\pi\) |
−0.728679 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.96711 | − | 14.5949i | 0.514699 | − | 0.753677i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.28270 | + | 8.28270i | 0.426581 | + | 0.426581i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.53089i | 0.335469i | 0.985832 | + | 0.167735i | \(0.0536452\pi\) | ||||
−0.985832 | + | 0.167735i | \(0.946355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.12426 | − | 2.38115i | −0.211292 | − | 0.121990i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.830244 | + | 0.222463i | 0.0424235 | + | 0.0113673i | 0.279968 | − | 0.960009i | \(-0.409676\pi\) |
−0.237545 | + | 0.971377i | \(0.576343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.05166 | + | 0.169585i | −0.206492 | + | 0.00864287i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.55831 | + | 0.685497i | 0.130046 | + | 0.0348458i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8241 | − | 13.1775i | −1.15723 | − | 0.668125i | −0.206589 | − | 0.978428i | \(-0.566236\pi\) |
−0.950638 | + | 0.310302i | \(0.899570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.27927i | 0.317556i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.2351 | + | 12.2351i | 0.617181 | + | 0.617181i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.88120 | + | 30.0918i | −0.446862 | + | 1.51408i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.80685 | + | 10.4753i | −0.140872 | + | 0.525741i | 0.859033 | + | 0.511921i | \(0.171066\pi\) |
−0.999905 | + | 0.0138199i | \(0.995601\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.26422 | + | 10.8348i | 0.363666 | + | 0.542417i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.6283 | − | 3.38375i | 0.629063 | − | 0.168557i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.79765 | + | 15.7497i | 0.188707 | + | 0.782606i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.35839 | − | 4.35839i | 0.216037 | − | 0.216037i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.69537 | + | 2.93647i | −0.0838308 | + | 0.145199i | −0.904892 | − | 0.425640i | \(-0.860049\pi\) |
0.821062 | + | 0.570840i | \(0.193382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.85116 | + | 1.06877i | −0.0913109 | + | 0.0527184i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.38319 | + | 7.32858i | 0.412510 | + | 0.360616i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.318277 | + | 12.6323i | −0.0156236 | + | 0.620094i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.287694 | − | 1.07369i | −0.0140884 | − | 0.0525788i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.03776 | 0.0506978 | 0.0253489 | − | 0.999679i | \(-0.491930\pi\) | ||||
0.0253489 | + | 0.999679i | \(0.491930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.683118 | −0.0332931 | −0.0166466 | − | 0.999861i | \(-0.505299\pi\) | ||||
−0.0166466 | + | 0.999861i | \(0.505299\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.904997 | + | 3.37749i | 0.0440024 | + | 0.164219i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.43320 | + | 6.67765i | 0.0695204 | + | 0.323914i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.53072 | + | 10.3477i | 0.170863 | + | 0.500760i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.39117 | − | 0.803191i | 0.0671662 | − | 0.0387784i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.34273 | − | 16.1821i | 0.450023 | − | 0.779463i | −0.548364 | − | 0.836240i | \(-0.684749\pi\) |
0.998387 | + | 0.0567767i | \(0.0180823\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.43170 | + | 7.43170i | −0.357145 | + | 0.357145i | −0.862759 | − | 0.505615i | \(-0.831266\pi\) |
0.505615 | + | 0.862759i | \(0.331266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.5687 | − | 23.8269i | 0.698517 | − | 1.14241i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.8495 | + | 3.71095i | −0.662509 | + | 0.177519i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.5514 | − | 23.4717i | −0.646772 | − | 1.12024i | −0.983889 | − | 0.178779i | \(-0.942785\pi\) |
0.337118 | − | 0.941463i | \(-0.390548\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.47671 | + | 0.468841i | −0.165558 | + | 0.0223258i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.71108 | − | 36.2422i | 0.461387 | − | 1.72192i | −0.207210 | − | 0.978297i | \(-0.566438\pi\) |
0.668597 | − | 0.743625i | \(-0.266895\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.8753 | + | 7.34164i | 1.17920 | + | 0.348027i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6345 | + | 12.6345i | 0.597592 | + | 0.597592i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.36931i | 0.300586i | 0.988641 | + | 0.150293i | \(0.0480217\pi\) | ||||
−0.988641 | + | 0.150293i | \(0.951978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.08276 | − | 3.51188i | −0.286426 | − | 0.165368i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.0677 | + | 3.23354i | 0.566992 | + | 0.151925i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.55939 | − | 1.91376i | −0.401271 | − | 0.0897184i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3652 | − | 3.84913i | −0.671974 | − | 0.180055i | −0.0933301 | − | 0.995635i | \(-0.529751\pi\) |
−0.578644 | + | 0.815580i | \(0.696418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.54704 | − | 3.77993i | −0.305590 | − | 0.176432i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.8860i | 1.95082i | 0.220390 | + | 0.975412i | \(0.429267\pi\) | ||||
−0.220390 | + | 0.975412i | \(0.570733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.8985 | + | 17.8985i | 0.831813 | + | 0.831813i | 0.987765 | − | 0.155952i | \(-0.0498445\pi\) |
−0.155952 | + | 0.987765i | \(0.549845\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.9007 | − | 27.3791i | −0.691006 | − | 1.26968i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.5646 | − | 39.4275i | 0.488870 | − | 1.82449i | −0.0730918 | − | 0.997325i | \(-0.523287\pi\) |
0.561962 | − | 0.827163i | \(-0.310047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9610 | − | 0.735725i | 0.506131 | − | 0.0339726i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.84390 | + | 3.19372i | 0.0849622 | + | 0.147159i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.49904 | + | 0.937564i | −0.160886 | + | 0.0431092i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.8811 | + | 7.10742i | −0.636909 | + | 0.326111i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.28015 | − | 3.28015i | 0.150188 | − | 0.150188i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.44050 | + | 4.22708i | −0.111509 | + | 0.193140i | −0.916379 | − | 0.400312i | \(-0.868902\pi\) |
0.804870 | + | 0.593452i | \(0.202235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5450 | − | 6.66552i | 0.526407 | − | 0.303921i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.72121 | + | 18.8627i | −0.169321 | + | 0.858281i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.21963 | + | 0.207098i | 0.373234 | + | 0.00940384i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.16256 | − | 34.1952i | −0.415195 | − | 1.54953i | −0.784444 | − | 0.620200i | \(-0.787052\pi\) |
0.369249 | − | 0.929331i | \(-0.379615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.78677 | 0.0808003 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.8068 | 1.16464 | 0.582322 | − | 0.812958i | \(-0.302144\pi\) | ||||
0.582322 | + | 0.812958i | \(0.302144\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.79328 | + | 10.4247i | 0.125803 | + | 0.469503i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.529313 | + | 0.556675i | 0.0237908 | + | 0.0250207i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.44652 | + | 32.6772i | −0.289166 | + | 1.46577i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3336 | + | 6.54347i | −0.507363 | + | 0.292926i | −0.731749 | − | 0.681574i | \(-0.761296\pi\) |
0.224386 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.44151 | − | 11.1570i | 0.287786 | − | 0.498459i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.2498 | − | 15.2498i | 0.679955 | − | 0.679955i | −0.280035 | − | 0.959990i | \(-0.590346\pi\) |
0.959990 | + | 0.280035i | \(0.0903460\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.67081 | + | 1.60850i | −0.296847 | + | 0.0715775i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.4938 | + | 4.41951i | −0.732516 | + | 0.196277i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.264712 | + | 0.458495i | 0.0117332 | + | 0.0203224i | 0.871832 | − | 0.489804i | \(-0.162932\pi\) |
−0.860099 | + | 0.510127i | \(0.829598\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.9029 | + | 2.27563i | −1.49978 | + | 0.100668i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.46776 | − | 16.6739i | 0.197257 | − | 0.736172i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.5247 | + | 17.7012i | −1.43321 | + | 0.780006i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.38167 | − | 3.38167i | −0.148726 | − | 0.148726i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 27.6429i | − | 1.21339i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.14066 | + | 1.81326i | 0.137595 | + | 0.0794404i | 0.567217 | − | 0.823568i | \(-0.308020\pi\) |
−0.429622 | + | 0.903009i | \(0.641353\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.9361 | − | 5.34185i | −0.871743 | − | 0.233583i | −0.204902 | − | 0.978783i | \(-0.565687\pi\) |
−0.666841 | + | 0.745200i | \(0.732354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.347978 | + | 20.9087i | 0.0151870 | + | 0.912531i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6353 | + | 3.11767i | 0.506842 | + | 0.135808i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.61722 | + | 0.933702i | 0.0703139 | + | 0.0405957i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 2.10922i | − | 0.0915321i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.7418 | − | 10.7418i | −0.465280 | − | 0.465280i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.4143 | + | 5.66784i | −0.450248 | + | 0.245042i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.439366 | − | 1.63974i | 0.0189600 | − | 0.0707598i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.79745 | − | 2.93290i | 0.163568 | − | 0.126329i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.7743 | − | 23.8578i | −0.592204 | − | 1.02573i | −0.993935 | − | 0.109969i | \(-0.964925\pi\) |
0.401731 | − | 0.915758i | \(-0.368409\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.6445 | − | 3.65604i | 0.585543 | − | 0.156896i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.0008 | − | 8.68072i | 1.54210 | − | 0.371841i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.00886 | − | 5.00886i | 0.214164 | − | 0.214164i | −0.591870 | − | 0.806034i | \(-0.701610\pi\) |
0.806034 | + | 0.591870i | \(0.201610\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.03553 | − | 1.79359i | 0.0441954 | − | 0.0765486i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.3417 | + | 12.3216i | −0.909186 | + | 0.524919i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.9882 | − | 35.1345i | −0.509788 | − | 1.49407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.9018 | − | 23.0340i | −0.929680 | − | 0.977739i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.70252 | + | 10.0860i | 0.114510 | + | 0.427356i | 0.999250 | − | 0.0387290i | \(-0.0123309\pi\) |
−0.884740 | + | 0.466085i | \(0.845664\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.83479 | −0.331376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48006 | 0.0624883 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.15482 | − | 26.7021i | −0.301540 | − | 1.12536i | −0.935883 | − | 0.352310i | \(-0.885396\pi\) |
0.634344 | − | 0.773051i | \(-0.281270\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.8105 | − | 0.574723i | −0.959645 | − | 0.0241788i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.4321 | − | 12.6165i | −0.606092 | − | 0.529845i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.63770 | − | 5.56433i | 0.404033 | − | 0.233269i | −0.284189 | − | 0.958768i | \(-0.591724\pi\) |
0.688223 | + | 0.725499i | \(0.258391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3474 | + | 17.9222i | −0.433025 | + | 0.750022i | −0.997132 | − | 0.0756800i | \(-0.975887\pi\) |
0.564107 | + | 0.825702i | \(0.309221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.2508 | + | 27.2508i | −1.13842 | + | 1.13842i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.8741 | − | 7.05950i | −0.912215 | − | 0.294402i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.00314 | − | 1.87648i | 0.291544 | − | 0.0781191i | −0.110083 | − | 0.993922i | \(-0.535112\pi\) |
0.401627 | + | 0.915803i | \(0.368445\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.13963 | + | 12.3662i | 0.296713 | + | 0.513922i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.32611 | − | 12.4186i | −0.345425 | − | 0.515211i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.64210 | + | 6.12841i | −0.0680090 | + | 0.253813i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.794189 | + | 1.45927i | 0.0328357 | + | 0.0603333i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.87340 | − | 5.87340i | −0.242421 | − | 0.242421i | 0.575430 | − | 0.817851i | \(-0.304835\pi\) |
−0.817851 | + | 0.575430i | \(0.804835\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.5051i | 1.13333i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.45918 | + | 1.99716i | 0.142292 | + | 0.0821521i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.3818 | + | 7.06897i | 1.08337 | + | 0.290288i | 0.755975 | − | 0.654600i | \(-0.227163\pi\) |
0.327394 | + | 0.944888i | \(0.393830\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.94812 | − | 5.47019i | −0.243849 | − | 0.224256i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2674 | + | 3.82294i | 0.583926 | + | 0.156463i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.9641 | + | 12.6810i | 0.897430 | + | 0.518131i | 0.876366 | − | 0.481647i | \(-0.159961\pi\) |
0.0210645 | + | 0.999778i | \(0.493294\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.8045i | − | 0.563099i | −0.959547 | − | 0.281550i | \(-0.909152\pi\) | ||
0.959547 | − | 0.281550i | \(-0.0908484\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.47145 | − | 1.47145i | −0.0599221 | − | 0.0599221i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.5831 | + | 6.66512i | 0.918134 | + | 0.270975i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.79866 | − | 21.6409i | 0.235360 | − | 0.878376i | −0.742626 | − | 0.669707i | \(-0.766420\pi\) |
0.977986 | − | 0.208670i | \(-0.0669134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.21306 | + | 32.9706i | 0.0896776 | + | 1.33604i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.17176 | − | 8.95776i | −0.209227 | − | 0.362392i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.1509 | + | 8.61481i | −1.29856 | + | 0.347949i | −0.840907 | − | 0.541180i | \(-0.817978\pi\) |
−0.457656 | + | 0.889129i | \(0.651311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.8942 | + | 30.9011i | −0.761886 | + | 1.24605i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1167 | − | 21.1167i | 0.850125 | − | 0.850125i | −0.140023 | − | 0.990148i | \(-0.544718\pi\) |
0.990148 | + | 0.140023i | \(0.0447177\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2311 | + | 31.5771i | −0.732768 | + | 1.26919i | 0.222927 | + | 0.974835i | \(0.428439\pi\) |
−0.955696 | + | 0.294357i | \(0.904895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.0338 | − | 12.7212i | 0.884184 | − | 0.510484i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −29.0439 | + | 9.91000i | −1.16362 | + | 0.397036i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8732 | − | 2.51476i | −0.994928 | − | 0.100590i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.874694 | + | 3.26440i | 0.0349319 | + | 0.130368i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12.2827 | 0.489744 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0247 | 1.87203 | 0.936013 | − | 0.351966i | \(-0.114487\pi\) | ||||
0.936013 | + | 0.351966i | \(0.114487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.02875 | − | 15.0355i | −0.160128 | − | 0.597607i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.169675 | + | 6.73433i | −0.00673336 | + | 0.267244i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.57518 | − | 4.00148i | 0.379383 | − | 0.158544i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.46387 | − | 3.15457i | 0.216147 | − | 0.124793i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.05261 | − | 13.9475i | 0.318059 | − | 0.550894i | −0.662024 | − | 0.749483i | \(-0.730302\pi\) |
0.980083 | + | 0.198588i | \(0.0636357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1021 | − | 29.1021i | 1.14768 | − | 1.14768i | 0.160667 | − | 0.987009i | \(-0.448635\pi\) |
0.987009 | − | 0.160667i | \(-0.0513646\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.37876 | + | 18.1596i | 0.172413 | + | 0.715035i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2480 | − | 11.0524i | 1.62163 | − | 0.434513i | 0.670147 | − | 0.742228i | \(-0.266231\pi\) |
0.951479 | + | 0.307715i | \(0.0995642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.44240 | + | 2.49831i | 0.0566192 | + | 0.0980673i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.1044 | + | 16.2606i | 1.29746 | + | 0.637304i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.62895 | + | 32.2037i | −0.337677 | + | 1.26023i | 0.563261 | + | 0.826279i | \(0.309547\pi\) |
−0.900938 | + | 0.433948i | \(0.857120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.92833 | − | 23.4749i | 0.270712 | − | 0.917242i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.55127 | + | 4.55127i | 0.177562 | + | 0.177562i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.01773i | 0.0785996i | 0.999227 | + | 0.0392998i | \(0.0125127\pi\) | ||||
−0.999227 | + | 0.0392998i | \(0.987487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.409726 | + | 0.236556i | 0.0159365 | + | 0.00920095i | 0.507947 | − | 0.861388i | \(-0.330405\pi\) |
−0.492011 | + | 0.870589i | \(0.663738\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.09205 | + | 0.828513i | 0.120085 | + | 0.0321768i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.54972 | − | 16.3519i | 0.331544 | − | 0.634098i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.0837 | − | 9.40065i | −1.35845 | − | 0.363995i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.655592 | − | 0.378506i | −0.0253466 | − | 0.0146339i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.83262i | 0.109352i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.1663 | − | 15.1663i | −0.584616 | − | 0.584616i | 0.351552 | − | 0.936168i | \(-0.385654\pi\) |
−0.936168 | + | 0.351552i | \(0.885654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.5281 | − | 18.5573i | 0.790128 | − | 0.714272i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.67670 | + | 13.7216i | −0.141307 | + | 0.527365i | 0.858585 | + | 0.512671i | \(0.171344\pi\) |
−0.999892 | + | 0.0146937i | \(0.995323\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.08060 | + | 5.41767i | −0.310105 | + | 0.207911i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9613 | + | 18.9855i | 0.420038 | + | 0.727527i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2251 | − | 5.41929i | 0.773891 | − | 0.207363i | 0.149801 | − | 0.988716i | \(-0.452137\pi\) |
0.624090 | + | 0.781353i | \(0.285470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.57964 | + | 1.57729i | 0.0985628 | + | 0.0602653i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.97653 | + | 2.97653i | −0.113562 | + | 0.113562i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.86115 | + | 11.8839i | −0.261389 | + | 0.452739i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.60324 | − | 3.23504i | 0.213157 | − | 0.123067i | −0.389620 | − | 0.920976i | \(-0.627394\pi\) |
0.602778 | + | 0.797909i | \(0.294060\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.891704 | − | 0.175914i | −0.0338730 | − | 0.00668244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.13948 | + | 1.08347i | −0.0432228 | + | 0.0410983i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.62260 | − | 13.5197i | −0.137216 | − | 0.512096i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.9281 | 1.13198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.5423 | 0.587026 | 0.293513 | − | 0.955955i | \(-0.405176\pi\) | ||||
0.293513 | + | 0.955955i | \(0.405176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.25890 | + | 27.0906i | 0.273774 | + | 1.02174i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.8721 | + | 16.9936i | −0.673100 | + | 0.640016i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.34378 | − | 6.11276i | 0.200973 | − | 0.229894i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.77659 | + | 4.48981i | −0.292056 | + | 0.168619i | −0.638869 | − | 0.769316i | \(-0.720597\pi\) |
0.346813 | + | 0.937934i | \(0.387264\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.51603 | + | 6.08994i | −0.131861 | + | 0.228391i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.6657 | + | 28.6657i | −1.07354 | + | 1.07354i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.93863 | − | 1.18536i | −0.0725006 | − | 0.0443298i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.77079 | + | 2.35013i | −0.327551 | + | 0.0877670i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.2758 | + | 35.1187i | 0.756160 | + | 1.30971i | 0.944795 | + | 0.327661i | \(0.106260\pi\) |
−0.188635 | + | 0.982047i | \(0.560406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.3166 | − | 39.3259i | 0.719388 | − | 1.46457i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.16748 | + | 15.5532i | −0.154990 | + | 0.578432i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.4552 | − | 1.98945i | −1.46533 | − | 0.0738864i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9052 | + | 11.9052i | 0.441540 | + | 0.441540i | 0.892529 | − | 0.450990i | \(-0.148929\pi\) |
−0.450990 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8776i | 1.10658i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.25157 | − | 3.60935i | −0.231223 | − | 0.133496i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.98288 | + | 1.60311i | 0.220983 | + | 0.0592121i | 0.367611 | − | 0.929979i | \(-0.380176\pi\) |
−0.146629 | + | 0.989192i | \(0.546842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.6262 | − | 19.9572i | −0.539494 | − | 0.736132i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.74916 | + | 0.736634i | 0.101266 | + | 0.0271343i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.3295 | + | 19.8201i | 1.26283 | + | 0.729095i | 0.973621 | − | 0.228171i | \(-0.0732746\pi\) |
0.289208 | + | 0.957266i | \(0.406608\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.30942i | 0.268518i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7507 | − | 15.7507i | −0.577837 | − | 0.577837i | 0.356470 | − | 0.934307i | \(-0.383980\pi\) |
−0.934307 | + | 0.356470i | \(0.883980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.15448 | − | 24.2412i | 0.262120 | − | 0.888129i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.733018 | + | 2.73566i | −0.0268197 | + | 0.100093i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.18510 | − | 12.5920i | 0.225999 | − | 0.460101i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.16731 | + | 15.8782i | 0.334520 | + | 0.579405i | 0.983392 | − | 0.181492i | \(-0.0580926\pi\) |
−0.648873 | + | 0.760897i | \(0.724759\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.1292 | − | 2.98205i | 0.405570 | − | 0.108672i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.14258 | − | 17.1802i | −0.150764 | − | 0.625250i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.1143 | + | 14.1143i | −0.512994 | + | 0.512994i | −0.915443 | − | 0.402449i | \(-0.868159\pi\) |
0.402449 | + | 0.915443i | \(0.368159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.49054 | + | 4.31374i | −0.0904009 | + | 0.156579i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0843 | − | 5.82217i | 0.365555 | − | 0.211054i | −0.305960 | − | 0.952045i | \(-0.598977\pi\) |
0.671515 | + | 0.740991i | \(0.265644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.8391 | + | 32.9891i | −1.04405 | + | 1.19429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0385556 | + | 1.53025i | −0.00139398 | + | 0.0553265i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.61486 | + | 6.02674i | 0.0583092 | + | 0.217613i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.3371 | −1.63490 | −0.817448 | − | 0.576002i | \(-0.804612\pi\) | ||||
−0.817448 | + | 0.576002i | \(0.804612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.3119 | −0.695501 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.88925 | − | 7.05078i | −0.0679516 | − | 0.253599i | 0.923591 | − | 0.383379i | \(-0.125240\pi\) |
−0.991543 | + | 0.129780i | \(0.958573\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.9416 | + | 37.0271i | −0.860007 | + | 1.33005i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 36.8968 | + | 7.27896i | 1.32367 | + | 0.261131i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.6780 | − | 15.9799i | 0.991666 | − | 0.572539i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.31455 | + | 7.47301i | −0.154387 | + | 0.267405i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9209 | − | 30.9209i | 1.10502 | − | 1.10502i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.72123 | − | 4.45053i | 0.0971250 | − | 0.158846i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.5872 | + | 7.92786i | −1.05467 | + | 0.282598i | −0.744180 | − | 0.667979i | \(-0.767159\pi\) |
−0.310489 | + | 0.950577i | \(0.600493\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.9991 | − | 29.4433i | −0.605184 | − | 1.04821i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.4247 | − | 15.0347i | 0.797330 | − | 0.534574i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.58565 | + | 5.91772i | −0.0563081 | + | 0.210145i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.3793 | + | 9.26119i | 1.11291 | + | 0.328461i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.7751 | − | 30.7751i | −1.09011 | − | 1.09011i | −0.995516 | − | 0.0945938i | \(-0.969845\pi\) |
−0.0945938 | − | 0.995516i | \(-0.530155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.53015i | − | 0.337153i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.03424 | + | 2.90652i | 0.177876 | + | 0.102697i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.50328 | − | 2.27845i | −0.300074 | − | 0.0804046i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.9523 | − | 8.13135i | 0.914698 | − | 0.286592i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 40.4253 | + | 10.8319i | 1.42304 | + | 0.381302i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.6957 | − | 7.32984i | −0.446355 | − | 0.257703i | 0.259934 | − | 0.965626i | \(-0.416299\pi\) |
−0.706290 | + | 0.707923i | \(0.749632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 0.360507i | − | 0.0126591i | −0.999980 | − | 0.00632956i | \(-0.997985\pi\) | ||
0.999980 | − | 0.00632956i | \(-0.00201477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9503 | − | 19.9503i | −0.699688 | − | 0.699688i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.20820 | − | 2.21998i | −0.0423213 | − | 0.0777625i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.26613 | − | 15.9214i | 0.149253 | − | 0.557020i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76442 | − | 0.866669i | −0.0616537 | − | 0.0302839i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.1407 | − | 19.2962i | −0.388812 | − | 0.673442i | 0.603478 | − | 0.797379i | \(-0.293781\pi\) |
−0.992290 | + | 0.123938i | \(0.960448\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.1760 | − | 2.99459i | 0.389569 | − | 0.104385i | −0.0587174 | − | 0.998275i | \(-0.518701\pi\) |
0.448287 | + | 0.893890i | \(0.352034\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.66397 | + | 5.15587i | −0.0579319 | + | 0.179504i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7972 | + | 24.7972i | −0.862283 | + | 0.862283i | −0.991603 | − | 0.129320i | \(-0.958721\pi\) |
0.129320 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.6987 | − | 21.9948i | 0.441044 | − | 0.763911i | −0.556723 | − | 0.830698i | \(-0.687941\pi\) |
0.997767 | + | 0.0667871i | \(0.0212748\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.3258 | + | 20.9727i | −1.26013 | + | 0.727536i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.48368 | + | 1.21823i | 0.328590 | + | 0.0422093i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.2178 | − | 0.459008i | −0.630454 | − | 0.0158846i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.6322 | − | 47.1440i | −0.436632 | − | 1.62953i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.36253 | −0.150611 | −0.0753057 | − | 0.997160i | \(-0.523993\pi\) | ||||
−0.0753057 | + | 0.997160i | \(0.523993\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.4268 | −1.15265 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.66981 | − | 28.6241i | −0.264162 | − | 0.985867i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.6440 | + | 17.5044i | 0.572572 | + | 0.602171i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.3675 | + | 8.99681i | −0.905999 | + | 0.309134i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.895173 | + | 0.516829i | −0.0307223 | + | 0.0177375i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.6685 | + | 35.7988i | −0.708506 | + | 1.22717i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8935 | − | 36.8935i | 1.26321 | − | 1.26321i | 0.313683 | − | 0.949528i | \(-0.398437\pi\) |
0.949528 | − | 0.313683i | \(-0.101563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.39789 | + | 0.819319i | −0.116205 | + | 0.0280201i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.6686 | − | 6.60994i | 0.842665 | − | 0.225791i | 0.188433 | − | 0.982086i | \(-0.439659\pi\) |
0.654231 | + | 0.756295i | \(0.272992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.3819 | − | 28.3743i | −0.558944 | − | 0.968120i | −0.997585 | − | 0.0694571i | \(-0.977873\pi\) |
0.438641 | − | 0.898662i | \(-0.355460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.87011 | − | 42.7595i | −0.0978130 | − | 1.45724i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.22751 | + | 23.2414i | −0.211987 | + | 0.791146i | 0.775219 | + | 0.631693i | \(0.217640\pi\) |
−0.987206 | + | 0.159453i | \(0.949027\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.3451 | + | 18.6919i | −1.16777 | + | 0.635544i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.9166 | − | 16.9166i | −0.574518 | − | 0.574518i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.61784i | − | 0.326263i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.33101 | + | 3.07786i | 0.180634 | + | 0.104289i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.78005 | + | 0.476963i | 0.0602456 | + | 0.0161428i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.7429 | − | 14.5707i | 0.870268 | − | 0.492578i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.7037 | + | 12.5142i | 1.57707 | + | 0.422575i | 0.938018 | − | 0.346586i | \(-0.112659\pi\) |
0.639054 | + | 0.769162i | \(0.279326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.34074 | + | 1.92878i | 0.112680 | + | 0.0650560i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.63541i | − | 0.122480i | −0.998123 | − | 0.0612400i | \(-0.980494\pi\) | ||
0.998123 | − | 0.0612400i | \(-0.0195055\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.50117 | − | 7.50117i | −0.252434 | − | 0.252434i | 0.569534 | − | 0.821968i | \(-0.307124\pi\) |
−0.821968 | + | 0.569534i | \(0.807124\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.0664 | − | 7.11122i | 0.439222 | − | 0.239041i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.92442 | − | 10.9141i | 0.0981924 | − | 0.366459i | −0.899292 | − | 0.437349i | \(-0.855917\pi\) |
0.997484 | + | 0.0708903i | \(0.0225840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.43869 | − | 6.62043i | −0.148869 | − | 0.222042i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.48317 | − | 4.30098i | −0.0831894 | − | 0.144088i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 21.0195 | − | 5.63217i | 0.703392 | − | 0.188473i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.33440 | + | 0.562883i | −0.0780303 | + | 0.0188151i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.61784 | + | 7.61784i | −0.254352 | + | 0.254352i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.8383 | + | 60.3416i | −1.16192 | + | 2.01251i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.9494 | + | 6.32162i | −0.364776 | + | 0.210604i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.6405 | − | 14.5471i | −0.553761 | − | 0.484098i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7688 | − | 14.4806i | −0.457691 | − | 0.481350i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.17302 | + | 15.5739i | 0.138563 | + | 0.517124i | 0.999958 | + | 0.00918798i | \(0.00292467\pi\) |
−0.861395 | + | 0.507936i | \(0.830409\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.53798 | −0.0510114 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.2211 | −1.03440 | −0.517201 | − | 0.855864i | \(-0.673026\pi\) | ||||
−0.517201 | + | 0.855864i | \(0.673026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.00256 | − | 3.74160i | −0.0331798 | − | 0.123829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.6024 | + | 0.367916i | 0.482741 | + | 0.0121629i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.35211 | + | 27.4088i | 0.308834 | + | 0.905118i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.7681 | − | 24.6922i | 1.41079 | − | 0.814520i | 0.415328 | − | 0.909672i | \(-0.363667\pi\) |
0.995463 | + | 0.0951513i | \(0.0303335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.7409 | + | 35.9242i | −0.683435 | + | 1.18374i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.1969 | + | 13.1969i | −0.434382 | + | 0.434382i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8089 | + | 42.7875i | −0.454034 | + | 1.40684i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.01661 | + | 2.14804i | −0.263300 | + | 0.0705510i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.4711 | − | 45.8492i | −0.868487 | − | 1.50426i | −0.863542 | − | 0.504276i | \(-0.831759\pi\) |
−0.00494489 | − | 0.999988i | \(-0.501574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.91779 | + | 21.6370i | 0.0956267 | + | 0.709124i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.03261 | + | 7.58580i | −0.0665447 | + | 0.248348i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.00081 | − | 1.83891i | −0.0327299 | − | 0.0601389i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.9004 | − | 28.9004i | −0.944134 | − | 0.944134i | 0.0543857 | − | 0.998520i | \(-0.482680\pi\) |
−0.998520 | + | 0.0543857i | \(0.982680\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 19.3463i | − | 0.631343i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.1600 | − | 17.9902i | −1.01579 | − | 0.586465i | −0.102906 | − | 0.994691i | \(-0.532814\pi\) |
−0.912881 | + | 0.408226i | \(0.866147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.5000 | + | 12.1917i | 1.48168 | + | 0.397016i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.14442 | + | 31.9538i | −0.232408 | + | 1.03946i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.6929 | + | 5.00874i | 0.607437 | + | 0.162762i | 0.549410 | − | 0.835553i | \(-0.314852\pi\) |
0.0580267 | + | 0.998315i | \(0.481519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.4891 | − | 9.51997i | −0.535258 | − | 0.309031i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 40.9511i | − | 1.32793i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7055 | + | 13.7055i | 0.443965 | + | 0.443965i | 0.893342 | − | 0.449377i | \(-0.148354\pi\) |
−0.449377 | + | 0.893342i | \(0.648354\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.2847 | + | 15.4311i | 1.69189 | + | 0.499340i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.21579 | + | 8.26945i | −0.0716264 | + | 0.267313i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.56958 | + | 0.239598i | −0.115268 | + | 0.00773702i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3841 | + | 40.5024i | 0.754325 | + | 1.30653i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.56688 | + | 0.687794i | −0.0827167 | + | 0.0221639i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.5367 | − | 17.2326i | 0.339189 | − | 0.554737i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.8117 | + | 26.8117i | −0.862207 | + | 0.862207i | −0.991594 | − | 0.129387i | \(-0.958699\pi\) |
0.129387 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.36732 | + | 5.83236i | −0.108174 | + | 0.187362i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.91146 | − | 1.10358i | 0.0613417 | − | 0.0354157i | −0.469015 | − | 0.883190i | \(-0.655391\pi\) |
0.530357 | + | 0.847774i | \(0.322058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.360085 | − | 1.82526i | 0.0115438 | − | 0.0585151i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.36242 | + | 9.83985i | −0.203761 | + | 0.315128i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0366 | + | 52.3853i | 0.449071 | + | 1.67596i | 0.704958 | + | 0.709249i | \(0.250966\pi\) |
−0.255887 | + | 0.966707i | \(0.582368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.95058 | −0.254102 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.30009 | 0.265001 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.12508 | + | 34.0552i | 0.291045 | + | 1.08619i | 0.944308 | + | 0.329063i | \(0.106733\pi\) |
−0.653263 | + | 0.757131i | \(0.726601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.142313 | − | 5.64835i | 0.00453447 | − | 0.179971i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.64774 | − | 28.6282i | 0.179769 | − | 0.911245i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.0394 | − | 12.1471i | 0.669013 | − | 0.386255i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.16103 | + | 7.20712i | −0.132179 | + | 0.228942i | −0.924516 | − | 0.381142i | \(-0.875531\pi\) |
0.792337 | + | 0.610084i | \(0.208864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.9524 | − | 16.9524i | 0.537969 | − | 0.537969i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.89767 | − | 20.3117i | −0.155267 | − | 0.643924i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.5090 | + | 8.17487i | −0.966230 | + | 0.258901i | −0.707235 | − | 0.706978i | \(-0.750058\pi\) |
−0.258995 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.8836 | − | 43.0997i | −0.787283 | − | 1.36361i |
(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 | 140.2.u.a.73.3 | yes | 16 | |
3.2 | odd | 2 | 1260.2.dq.a.73.2 | 16 | |||
4.3 | odd | 2 | 560.2.ci.d.353.2 | 16 | |||
5.2 | odd | 4 | inner | 140.2.u.a.17.3 | ✓ | 16 | |
5.3 | odd | 4 | 700.2.bc.b.157.2 | 16 | |||
5.4 | even | 2 | 700.2.bc.b.493.2 | 16 | |||
7.2 | even | 3 | 980.2.v.a.313.2 | 16 | |||
7.3 | odd | 6 | 980.2.m.a.293.3 | 16 | |||
7.4 | even | 3 | 980.2.m.a.293.6 | 16 | |||
7.5 | odd | 6 | inner | 140.2.u.a.33.3 | yes | 16 | |
7.6 | odd | 2 | 980.2.v.a.913.2 | 16 | |||
15.2 | even | 4 | 1260.2.dq.a.577.1 | 16 | |||
20.7 | even | 4 | 560.2.ci.d.17.2 | 16 | |||
21.5 | even | 6 | 1260.2.dq.a.1153.1 | 16 | |||
28.19 | even | 6 | 560.2.ci.d.33.2 | 16 | |||
35.2 | odd | 12 | 980.2.v.a.117.2 | 16 | |||
35.12 | even | 12 | inner | 140.2.u.a.117.3 | yes | 16 | |
35.17 | even | 12 | 980.2.m.a.97.6 | 16 | |||
35.19 | odd | 6 | 700.2.bc.b.593.2 | 16 | |||
35.27 | even | 4 | 980.2.v.a.717.2 | 16 | |||
35.32 | odd | 12 | 980.2.m.a.97.3 | 16 | |||
35.33 | even | 12 | 700.2.bc.b.257.2 | 16 | |||
105.47 | odd | 12 | 1260.2.dq.a.397.2 | 16 | |||
140.47 | odd | 12 | 560.2.ci.d.257.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.u.a.17.3 | ✓ | 16 | 5.2 | odd | 4 | inner | |
140.2.u.a.33.3 | yes | 16 | 7.5 | odd | 6 | inner | |
140.2.u.a.73.3 | yes | 16 | 1.1 | even | 1 | trivial | |
140.2.u.a.117.3 | yes | 16 | 35.12 | even | 12 | inner | |
560.2.ci.d.17.2 | 16 | 20.7 | even | 4 | |||
560.2.ci.d.33.2 | 16 | 28.19 | even | 6 | |||
560.2.ci.d.257.2 | 16 | 140.47 | odd | 12 | |||
560.2.ci.d.353.2 | 16 | 4.3 | odd | 2 | |||
700.2.bc.b.157.2 | 16 | 5.3 | odd | 4 | |||
700.2.bc.b.257.2 | 16 | 35.33 | even | 12 | |||
700.2.bc.b.493.2 | 16 | 5.4 | even | 2 | |||
700.2.bc.b.593.2 | 16 | 35.19 | odd | 6 | |||
980.2.m.a.97.3 | 16 | 35.32 | odd | 12 | |||
980.2.m.a.97.6 | 16 | 35.17 | even | 12 | |||
980.2.m.a.293.3 | 16 | 7.3 | odd | 6 | |||
980.2.m.a.293.6 | 16 | 7.4 | even | 3 | |||
980.2.v.a.117.2 | 16 | 35.2 | odd | 12 | |||
980.2.v.a.313.2 | 16 | 7.2 | even | 3 | |||
980.2.v.a.717.2 | 16 | 35.27 | even | 4 | |||
980.2.v.a.913.2 | 16 | 7.6 | odd | 2 | |||
1260.2.dq.a.73.2 | 16 | 3.2 | odd | 2 | |||
1260.2.dq.a.397.2 | 16 | 105.47 | odd | 12 | |||
1260.2.dq.a.577.1 | 16 | 15.2 | even | 4 | |||
1260.2.dq.a.1153.1 | 16 | 21.5 | even | 6 |