Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(25,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 10, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.bq (of order \(9\), degree \(6\), 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(144\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 25.3 | ||
Character | \(\chi\) | \(=\) | 756.25 |
Dual form | 756.2.bq.a.121.3 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.63641 | − | 0.567600i | −0.944781 | − | 0.327704i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.66918 | − | 0.971502i | −1.19369 | − | 0.434469i | −0.332675 | − | 0.943042i | \(-0.607951\pi\) |
−0.861019 | + | 0.508573i | \(0.830173\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.492567 | − | 2.59950i | −0.186173 | − | 0.982517i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.35566 | + | 1.85765i | 0.785220 | + | 0.619216i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.08935 | − | 0.760461i | 0.629962 | − | 0.229288i | −0.00725263 | − | 0.999974i | \(-0.502309\pi\) |
0.637215 | + | 0.770686i | \(0.280086\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.722049 | − | 4.09495i | −0.200260 | − | 1.13573i | −0.904726 | − | 0.425995i | \(-0.859924\pi\) |
0.704465 | − | 0.709739i | \(-0.251187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.81644 | + | 3.10480i | 0.985401 | + | 0.801656i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.23040 | 0.298416 | 0.149208 | − | 0.988806i | \(-0.452328\pi\) | ||||
0.149208 | + | 0.988806i | \(0.452328\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.21574 | −1.65540 | −0.827702 | − | 0.561168i | \(-0.810352\pi\) | ||||
−0.827702 | + | 0.561168i | \(0.810352\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.669432 | + | 4.53342i | −0.146082 | + | 0.989272i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.458850 | + | 2.60226i | 0.0956767 | + | 0.542610i | 0.994538 | + | 0.104376i | \(0.0332846\pi\) |
−0.898861 | + | 0.438234i | \(0.855604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35048 | + | 1.97229i | 0.470096 | + | 0.394458i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.80042 | − | 4.37694i | −0.538942 | − | 0.842343i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.59718 | + | 9.05809i | −0.296590 | + | 1.68204i | 0.364080 | + | 0.931368i | \(0.381383\pi\) |
−0.660670 | + | 0.750677i | \(0.729728\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.68234 | + | 1.41165i | −0.302157 | + | 0.253540i | −0.781242 | − | 0.624229i | \(-0.785413\pi\) |
0.479084 | + | 0.877769i | \(0.340969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.85066 | + | 0.0585105i | −0.670314 | + | 0.0101854i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.21067 | + | 7.41705i | −0.204640 | + | 1.25371i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.96015 | + | 5.12713i | −0.486645 | + | 0.842895i | −0.999882 | − | 0.0153525i | \(-0.995113\pi\) |
0.513237 | + | 0.858247i | \(0.328446\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.14272 | + | 7.11084i | −0.182982 | + | 1.13865i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03634 | + | 5.87737i | 0.161849 | + | 0.917891i | 0.952254 | + | 0.305306i | \(0.0987589\pi\) |
−0.790405 | + | 0.612584i | \(0.790130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.42059 | − | 4.54841i | −0.826632 | − | 0.693626i | 0.127883 | − | 0.991789i | \(-0.459182\pi\) |
−0.954515 | + | 0.298163i | \(0.903626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.48297 | − | 7.24693i | −0.668282 | − | 1.08031i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.60266 | + | 6.37939i | 1.10896 | + | 0.930529i | 0.997995 | − | 0.0632947i | \(-0.0201608\pi\) |
0.110967 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.51476 | + | 2.56085i | −0.930679 | + | 0.365836i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.01343 | − | 0.698374i | −0.281937 | − | 0.0977919i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.892450 | − | 1.54577i | 0.122587 | − | 0.212328i | −0.798200 | − | 0.602393i | \(-0.794214\pi\) |
0.920787 | + | 0.390065i | \(0.127547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.31564 | −0.851600 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.8079 | + | 4.09565i | 1.56399 | + | 0.542482i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.19550 | − | 6.78002i | −0.155641 | − | 0.882683i | −0.958198 | − | 0.286107i | \(-0.907639\pi\) |
0.802557 | − | 0.596576i | \(-0.203472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7272 | + | 9.00123i | 1.37348 | + | 1.15249i | 0.971554 | + | 0.236819i | \(0.0761048\pi\) |
0.401930 | + | 0.915671i | \(0.368340\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.66863 | − | 7.03855i | 0.462204 | − | 0.886774i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.05097 | + | 11.6316i | −0.254391 | + | 1.44272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.04732 | − | 2.20104i | −0.738798 | − | 0.268900i | −0.0549136 | − | 0.998491i | \(-0.517488\pi\) |
−0.683884 | + | 0.729591i | \(0.739711\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.726179 | − | 4.51881i | 0.0874217 | − | 0.544001i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.09591 | − | 12.2905i | −0.842129 | − | 1.45861i | −0.888091 | − | 0.459668i | \(-0.847969\pi\) |
0.0459616 | − | 0.998943i | \(-0.485365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.302622 | + | 0.524156i | 0.0354192 | + | 0.0613479i | 0.883192 | − | 0.469012i | \(-0.155390\pi\) |
−0.847772 | + | 0.530360i | \(0.822057\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.72688 | − | 4.56160i | −0.314873 | − | 0.526728i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.00596 | − | 5.05667i | −0.342561 | − | 0.576261i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.26788 | − | 2.64529i | 0.817700 | − | 0.297619i | 0.100900 | − | 0.994897i | \(-0.467828\pi\) |
0.716801 | + | 0.697278i | \(0.245606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.09828 | + | 8.75198i | 0.233142 | + | 0.972443i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.00883471 | − | 0.0501041i | 0.000969735 | − | 0.00549964i | −0.984319 | − | 0.176397i | \(-0.943556\pi\) |
0.985289 | + | 0.170898i | \(0.0546668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.28416 | − | 1.19534i | −0.356217 | − | 0.129652i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.75501 | − | 13.9162i | 0.831425 | − | 1.49197i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3288 | −1.73085 | −0.865427 | − | 0.501035i | \(-0.832953\pi\) | ||||
−0.865427 | + | 0.501035i | \(0.832953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2891 | + | 3.89400i | −1.07859 | + | 0.408202i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.55425 | − | 1.35514i | 0.368558 | − | 0.140522i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.2601 | + | 7.01010i | 1.97605 | + | 0.719222i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8061 | − | 9.06742i | −1.09720 | − | 0.920657i | −0.0999629 | − | 0.994991i | \(-0.531872\pi\) |
−0.997233 | + | 0.0743341i | \(0.976317\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.33447 | + | 2.08989i | 0.636638 | + | 0.210042i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.55863 | + | 14.5107i | −0.254593 | + | 1.44387i | 0.542521 | + | 0.840042i | \(0.317470\pi\) |
−0.797115 | + | 0.603828i | \(0.793641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8713 | + | 4.68477i | 1.26825 | + | 0.461604i | 0.886528 | − | 0.462675i | \(-0.153110\pi\) |
0.381718 | + | 0.924279i | \(0.375333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.19106 | − | 11.4501i | 0.604185 | − | 1.11742i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.233044 | + | 0.403645i | 0.0225292 | + | 0.0390218i | 0.877070 | − | 0.480362i | \(-0.159495\pi\) |
−0.854541 | + | 0.519384i | \(0.826161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.12987 | − | 7.15314i | 0.395570 | − | 0.685147i | −0.597604 | − | 0.801791i | \(-0.703881\pi\) |
0.993174 | + | 0.116645i | \(0.0372138\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.75417 | − | 6.70989i | 0.735993 | − | 0.636875i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.32727 | + | 1.11371i | −0.124859 | + | 0.104769i | −0.703079 | − | 0.711112i | \(-0.748192\pi\) |
0.578220 | + | 0.815881i | \(0.303747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.30335 | − | 7.39169i | 0.121538 | − | 0.689278i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.90607 | − | 10.9876i | 0.546016 | − | 1.01581i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.606054 | − | 3.19842i | −0.0555569 | − | 0.293198i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.63941 | + | 3.89293i | −0.421765 | + | 0.353903i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.64012 | − | 10.2060i | 0.147885 | − | 0.920244i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.74343 | + | 4.75175i | 0.245380 | + | 0.425010i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.358039 | − | 0.620141i | 0.0317708 | − | 0.0550286i | −0.849703 | − | 0.527262i | \(-0.823219\pi\) |
0.881474 | + | 0.472233i | \(0.156552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.28861 | + | 10.5198i | 0.553682 | + | 0.926215i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.494193 | − | 2.80271i | −0.0431778 | − | 0.244874i | 0.955578 | − | 0.294738i | \(-0.0952323\pi\) |
−0.998756 | + | 0.0498641i | \(0.984121\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.55424 | + | 18.7573i | 0.308191 | + | 1.62646i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.22262 | + | 14.4035i | 0.277359 | + | 1.23965i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.92125 | + | 3.29032i | 0.335015 | + | 0.281111i | 0.794740 | − | 0.606951i | \(-0.207607\pi\) |
−0.459725 | + | 0.888062i | \(0.652052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.0738 | − | 7.67023i | −1.78746 | − | 0.650581i | −0.999388 | − | 0.0349931i | \(-0.988859\pi\) |
−0.788068 | − | 0.615588i | \(-0.788919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.82011 | − | 14.7545i | −0.742787 | − | 1.24256i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.62266 | − | 8.00668i | −0.386566 | − | 0.669552i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.0631 | − | 22.6260i | 1.08483 | − | 1.87899i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1143 | − | 0.492826i | 0.999174 | − | 0.0406476i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4632 | + | 8.77965i | −0.857177 | + | 0.719257i | −0.961358 | − | 0.275301i | \(-0.911222\pi\) |
0.104181 | + | 0.994558i | \(0.466778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.53448 | − | 0.558504i | 0.124874 | − | 0.0454504i | −0.278827 | − | 0.960341i | \(-0.589946\pi\) |
0.403701 | + | 0.914891i | \(0.367724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.89840 | + | 2.28565i | 0.234322 | + | 0.184784i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.86189 | − | 2.13355i | 0.470838 | − | 0.171371i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.48942 | + | 8.44693i | 0.118869 | + | 0.674138i | 0.984762 | + | 0.173909i | \(0.0556399\pi\) |
−0.865893 | + | 0.500229i | \(0.833249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.33779 | + | 2.02295i | −0.185399 | + | 0.160431i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.53856 | − | 2.47457i | 0.515311 | − | 0.195023i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.28752 | − | 5.69416i | −0.257499 | − | 0.446001i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260139i | \(0.916232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.3350 | + | 3.58475i | 0.804575 | + | 0.279073i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.07957 | + | 6.77957i | −0.625216 | + | 0.524619i | −0.899438 | − | 0.437048i | \(-0.856024\pi\) |
0.274222 | + | 0.961666i | \(0.411580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.03122 | + | 1.46725i | −0.310094 | + | 0.112865i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.9978 | − | 13.4043i | −1.29986 | − | 1.02505i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.01856 | − | 17.1191i | 0.229497 | − | 1.30154i | −0.624401 | − | 0.781104i | \(-0.714657\pi\) |
0.853898 | − | 0.520440i | \(-0.174232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.96919 | − | 7.08155i | 0.300042 | − | 0.535315i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.89201 | + | 11.7734i | −0.142212 | + | 0.884946i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.958408 | 0.0716348 | 0.0358174 | − | 0.999358i | \(-0.488597\pi\) | ||||
0.0358174 | + | 0.999358i | \(0.488597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.98698 | − | 17.2980i | 0.742326 | − | 1.28575i | −0.209107 | − | 0.977893i | \(-0.567056\pi\) |
0.951434 | − | 0.307854i | \(-0.0996108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.4451 | − | 20.8185i | −0.919965 | − | 1.53895i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.8822 | − | 10.8094i | 0.947117 | − | 0.794725i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.57073 | − | 0.935670i | 0.187991 | − | 0.0684230i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.99845 | + | 9.43562i | −0.727280 | + | 0.686341i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.682129 | − | 0.248275i | 0.0493571 | − | 0.0179645i | −0.317224 | − | 0.948351i | \(-0.602751\pi\) |
0.366581 | + | 0.930386i | \(0.380528\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.56936 | − | 2.15595i | 0.184947 | − | 0.155189i | −0.545614 | − | 0.838037i | \(-0.683703\pi\) |
0.730560 | + | 0.682848i | \(0.239259\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.95832 | − | 17.8699i | 0.713130 | − | 1.27969i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.27513 | − | 14.3329i | 0.589579 | − | 1.02118i | −0.404709 | − | 0.914446i | \(-0.632627\pi\) |
0.994288 | − | 0.106735i | \(-0.0340395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2879 | −1.22550 | −0.612752 | − | 0.790275i | \(-0.709938\pi\) | ||||
−0.612752 | + | 0.790275i | \(0.709938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.64657 | + | 7.03426i | 0.609882 | + | 0.496159i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.3332 | − | 0.309839i | 1.70785 | − | 0.0217465i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.94370 | − | 16.6946i | 0.205597 | − | 1.16600i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.75320 | + | 6.98244i | −0.260865 | + | 0.485313i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0762 | + | 5.48729i | −1.04284 | + | 0.379563i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.49453 | − | 1.25406i | 0.102887 | − | 0.0863328i | −0.589893 | − | 0.807482i | \(-0.700830\pi\) |
0.692780 | + | 0.721149i | \(0.256386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.63573 | + | 24.1399i | 0.317635 | + | 1.65404i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0497 | + | 17.4066i | 0.685386 | + | 1.18712i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.49825 | + | 3.67790i | 0.305361 | + | 0.249672i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.197702 | − | 1.02950i | −0.0133595 | − | 0.0695673i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.888409 | − | 5.03842i | −0.0597609 | − | 0.338921i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.43245 | − | 0.521370i | 0.0959242 | − | 0.0349135i | −0.293612 | − | 0.955925i | \(-0.594857\pi\) |
0.389536 | + | 0.921011i | \(0.372635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.87312 | + | 9.01242i | 0.124875 | + | 0.600828i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.3767 | + | 5.59667i | −1.02059 | + | 0.371464i | −0.797490 | − | 0.603332i | \(-0.793839\pi\) |
−0.223099 | + | 0.974796i | \(0.571617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.65761 | + | 2.23000i | −0.175620 | + | 0.147362i | −0.726360 | − | 0.687314i | \(-0.758790\pi\) |
0.550741 | + | 0.834676i | \(0.314345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.04881 | + | 9.98096i | 0.134802 | + | 0.656699i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.58173 | + | 13.1319i | −0.496696 | + | 0.860302i | −0.999993 | − | 0.00381143i | \(-0.998787\pi\) |
0.503297 | + | 0.864113i | \(0.332120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.0953 | − | 24.4137i | −0.919474 | − | 1.59258i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3947 | + | 0.203531i | −0.870078 | + | 0.0132208i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.55011 | − | 0.564194i | −0.100268 | − | 0.0364947i | 0.291399 | − | 0.956602i | \(-0.405879\pi\) |
−0.391667 | + | 0.920107i | \(0.628102\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8645 | + | 9.95552i | 0.764262 | + | 0.641292i | 0.939232 | − | 0.343282i | \(-0.111539\pi\) |
−0.174971 | + | 0.984574i | \(0.555983\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.53398 | − | 15.5128i | 0.0984046 | − | 0.995146i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.8769 | − | 0.506276i | 1.26989 | − | 0.0323448i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.21012 | + | 29.5481i | 0.331512 | + | 1.88010i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.0428963 | + | 0.0769762i | −0.00271844 | + | 0.00487817i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.29533 | + | 14.3679i | −0.523597 | + | 0.906896i | 0.476026 | + | 0.879431i | \(0.342077\pi\) |
−0.999623 | + | 0.0274648i | \(0.991257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.93762 | + | 5.08810i | 0.184686 | + | 0.319886i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.69575 | + | 3.82014i | 0.294059 | + | 0.239227i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.6725 | − | 13.1508i | 0.977622 | − | 0.820322i | −0.00610721 | − | 0.999981i | \(-0.501944\pi\) |
0.983729 | + | 0.179659i | \(0.0574996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7860 | + | 5.16944i | 0.918758 | + | 0.321213i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.5892 | + | 18.3708i | −1.27444 | + | 1.13712i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.04301 | + | 11.5865i | −0.125978 | + | 0.714454i | 0.854745 | + | 0.519048i | \(0.173714\pi\) |
−0.980722 | + | 0.195406i | \(0.937398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.88383 | + | 3.25892i | −0.238582 | + | 0.200194i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.7206 | + | 9.26824i | 1.63528 | + | 0.567207i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3873 | + | 17.9913i | −0.633324 | + | 1.09695i | 0.353544 | + | 0.935418i | \(0.384977\pi\) |
−0.986868 | + | 0.161531i | \(0.948357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.22260 | − | 10.7779i | −0.377996 | − | 0.654709i | 0.612774 | − | 0.790258i | \(-0.290053\pi\) |
−0.990771 | + | 0.135549i | \(0.956720\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.0475 | − | 0.532063i | 1.15280 | − | 0.0322019i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.41082 | + | 2.33335i | 0.386587 | + | 0.140706i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.21699 | − | 29.5870i | 0.313458 | − | 1.77771i | −0.267279 | − | 0.963619i | \(-0.586124\pi\) |
0.580737 | − | 0.814091i | \(-0.302765\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.58538 | + | 0.200175i | −0.394256 | + | 0.0119842i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.68561 | − | 3.09260i | −0.219865 | − | 0.184489i | 0.526202 | − | 0.850360i | \(-0.323616\pi\) |
−0.746067 | + | 0.665871i | \(0.768060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.9993 | − | 9.09902i | −1.48606 | − | 0.540880i | −0.533649 | − | 0.845706i | \(-0.679179\pi\) |
−0.952408 | + | 0.304826i | \(0.901402\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.5385 | − | 22.4034i | −1.63124 | − | 1.32706i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7677 | − | 5.58896i | 0.871711 | − | 0.329906i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4861 | −0.910948 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5366 | + | 20.9716i | 0.734907 | + | 1.22937i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.39612 | + | 2.32800i | 0.373665 | + | 0.136003i | 0.522025 | − | 0.852930i | \(-0.325177\pi\) |
−0.148359 | + | 0.988934i | \(0.547399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.39580 | + | 19.2585i | −0.197711 | + | 1.12127i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.17955 | − | 7.01535i | −0.532652 | − | 0.407072i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.3248 | − | 3.75793i | 0.597100 | − | 0.217327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.15358 | + | 16.3312i | −0.527603 | + | 0.941314i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4232 | − | 22.2932i | 0.713696 | − | 1.28071i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.8882 | − | 34.4474i | −1.13880 | − | 1.97245i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.91071 | − | 8.50560i | −0.280269 | − | 0.485440i | 0.691182 | − | 0.722681i | \(-0.257090\pi\) |
−0.971451 | + | 0.237241i | \(0.923757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4036 | − | 14.9719i | −1.04694 | − | 0.851723i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.04368 | − | 2.56369i | −0.399410 | − | 0.145373i | 0.134502 | − | 0.990913i | \(-0.457057\pi\) |
−0.533912 | + | 0.845540i | \(0.679279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.19311 | + | 6.76648i | −0.0674388 | + | 0.382464i | 0.932343 | + | 0.361575i | \(0.117761\pi\) |
−0.999782 | + | 0.0208892i | \(0.993350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.6302 | + | 15.2231i | −0.937005 | + | 0.857723i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.3240 | − | 12.8583i | −0.860680 | − | 0.722196i | 0.101435 | − | 0.994842i | \(-0.467657\pi\) |
−0.962114 | + | 0.272646i | \(0.912101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.55124 | + | 20.1401i | 0.198831 | + | 1.12763i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.152247 | − | 0.792803i | −0.00849760 | − | 0.0442500i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.87824 | −0.493998 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.37925 | − | 11.0492i | 0.353857 | − | 0.612899i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8183 | + | 9.36135i | −0.598252 | + | 0.517684i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.8384 | − | 22.9054i | 0.707802 | − | 1.26281i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.16458 | + | 4.33360i | 0.283871 | + | 0.238196i | 0.773593 | − | 0.633682i | \(-0.218457\pi\) |
−0.489722 | + | 0.871878i | \(0.662902\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.4975 | + | 6.57886i | −0.904058 | + | 0.360519i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0031 | + | 11.7500i | 0.765069 | + | 0.641969i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.41987 | + | 19.3950i | 0.186292 | + | 1.05652i | 0.924284 | + | 0.381706i | \(0.124663\pi\) |
−0.737992 | + | 0.674810i | \(0.764226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.80409 | − | 1.06912i | 0.152297 | − | 0.0580669i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44149 | + | 4.22879i | −0.132214 | + | 0.229002i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.86588 | + | 15.6737i | 0.532707 | + | 0.846300i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.32834 | + | 11.3560i | −0.340706 | + | 0.611388i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.53677 | + | 7.16320i | −0.458278 | + | 0.384541i | −0.842497 | − | 0.538701i | \(-0.818915\pi\) |
0.384219 | + | 0.923242i | \(0.374471\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.18076 | + | 6.69644i | −0.0632048 | + | 0.358452i | 0.936759 | + | 0.349974i | \(0.113810\pi\) |
−0.999964 | + | 0.00847787i | \(0.997301\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.9013 | + | 14.6279i | −0.848749 | + | 0.780782i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.49296 | − | 2.93094i | −0.185911 | − | 0.155998i | 0.545082 | − | 0.838383i | \(-0.316499\pi\) |
−0.730993 | + | 0.682385i | \(0.760943\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.00004 | + | 39.6992i | 0.371523 | + | 2.10701i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.823669 | + | 5.57791i | −0.0435932 | + | 0.295214i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.3481 | −1.86560 | −0.932800 | − | 0.360395i | \(-0.882642\pi\) | ||||
−0.932800 | + | 0.360395i | \(0.882642\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.0669 | 1.74036 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.80160 | − | 3.73709i | 0.514450 | − | 0.196146i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.298533 | − | 1.69307i | −0.0156259 | − | 0.0886191i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.4786 | − | 5.63376i | 0.807978 | − | 0.294080i | 0.0951897 | − | 0.995459i | \(-0.469654\pi\) |
0.712788 | + | 0.701379i | \(0.247432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.47682 | + | 15.7702i | −0.441286 | + | 0.820966i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.45781 | − | 1.55853i | −0.231438 | − | 0.0809146i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.4152 | − | 9.25038i | −1.31595 | − | 0.478966i | −0.413791 | − | 0.910372i | \(-0.635796\pi\) |
−0.902158 | + | 0.431405i | \(0.858018\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.79227 | − | 9.33298i | −0.0925525 | − | 0.481953i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.2456 | 1.96975 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.3318 | 1.19848 | 0.599238 | − | 0.800571i | \(-0.295470\pi\) | ||||
0.599238 | + | 0.800571i | \(0.295470\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.937889 | + | 0.811581i | −0.0480495 | + | 0.0415786i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.8199 | + | 7.57781i | 1.06385 | + | 0.387208i | 0.813872 | − | 0.581045i | \(-0.197356\pi\) |
0.249974 | + | 0.968253i | \(0.419578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.11087 | + | 16.4175i | 0.158545 | + | 0.836712i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.31972 | − | 20.7841i | −0.219583 | − | 1.05651i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.4261 | + | 5.61463i | −0.782133 | + | 0.284673i | −0.702062 | − | 0.712116i | \(-0.747737\pi\) |
−0.0800711 | + | 0.996789i | \(0.525515\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.564568 | + | 3.20182i | 0.0285514 | + | 0.161923i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.782114 | + | 4.86688i | −0.0394524 | + | 0.245501i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.9692 | −1.10539 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.5789 | −1.38415 | −0.692073 | − | 0.721828i | \(-0.743302\pi\) | ||||
−0.692073 | + | 0.721828i | \(0.743302\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.83045 | − | 32.7119i | 0.241825 | − | 1.63765i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.89853 | − | 27.7809i | −0.244621 | − | 1.38731i | −0.821371 | − | 0.570394i | \(-0.806791\pi\) |
0.576750 | − | 0.816920i | \(-0.304321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.99537 | + | 5.86981i | 0.348464 | + | 0.292396i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.90188 | − | 25.3991i | 0.144195 | − | 1.26209i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.28580 | + | 12.9634i | −0.113303 | + | 0.642573i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.978228 | + | 0.820831i | −0.0483703 | + | 0.0405875i | −0.666652 | − | 0.745369i | \(-0.732273\pi\) |
0.618282 | + | 0.785956i | \(0.287829\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.54918 | − | 7.61000i | −0.224394 | − | 0.375374i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0358 | + | 6.44731i | −0.838275 | + | 0.317251i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0722577 | + | 0.125154i | −0.00354699 | + | 0.00614357i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.1317 | + | 24.5131i | 1.47556 | + | 1.20041i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.98110 | − | 16.9067i | −0.145636 | − | 0.825944i | −0.966854 | − | 0.255329i | \(-0.917816\pi\) |
0.821218 | − | 0.570615i | \(-0.193295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.61491 | + | 5.55057i | 0.322391 | + | 0.270518i | 0.789591 | − | 0.613634i | \(-0.210293\pi\) |
−0.467200 | + | 0.884152i | \(0.654737\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.05863 | + | 29.1507i | 0.294581 | + | 1.41736i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.89203 | + | 2.42670i | 0.140284 | + | 0.117712i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1148 | − | 32.3191i | 0.876635 | − | 1.56403i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.01997 | + | 15.7260i | 0.145805 | + | 0.759259i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4964 | − | 19.9124i | 0.553763 | − | 0.959145i | −0.444236 | − | 0.895910i | \(-0.646525\pi\) |
0.997999 | − | 0.0632353i | \(-0.0201419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.47220 | −0.455205 | −0.227603 | − | 0.973754i | \(-0.573089\pi\) | ||||
−0.227603 | + | 0.973754i | \(0.573089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.2191 | + | 29.6107i | −1.64068 | + | 1.41973i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.31094 | − | 18.7773i | −0.158384 | − | 0.898238i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.46610 | − | 5.42570i | −0.308610 | − | 0.258955i | 0.475307 | − | 0.879820i | \(-0.342337\pi\) |
−0.783917 | + | 0.620865i | \(0.786781\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.1037 | − | 6.06963i | −0.957320 | − | 0.289030i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.10216 | + | 34.6071i | −0.289922 | + | 1.64423i | 0.397230 | + | 0.917719i | \(0.369971\pi\) |
−0.687153 | + | 0.726513i | \(0.741140\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.5846 | + | 15.8635i | 2.06611 | + | 0.752002i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.1054 | − | 8.42819i | 1.04555 | − | 0.398640i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.9052 | − | 34.4768i | −0.939383 | − | 1.62706i | −0.766626 | − | 0.642094i | \(-0.778066\pi\) |
−0.172757 | − | 0.984964i | \(-0.555268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.63478 | + | 11.4918i | 0.312420 | + | 0.541126i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.82803 | + | 0.0429718i | −0.132873 | + | 0.00201899i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.2466 | − | 0.397869i | 1.46486 | − | 0.0186524i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.30969 | + | 0.840658i | −0.108043 | + | 0.0393243i | −0.395476 | − | 0.918476i | \(-0.629420\pi\) |
0.287433 | + | 0.957801i | \(0.407198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.44564 | − | 5.38539i | −0.160829 | − | 0.251368i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.11944 | − | 17.6912i | 0.145287 | − | 0.823962i | −0.821850 | − | 0.569704i | \(-0.807058\pi\) |
0.967136 | − | 0.254258i | \(-0.0818312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6713 | − | 6.79580i | −0.867729 | − | 0.315828i | −0.130482 | − | 0.991451i | \(-0.541652\pi\) |
−0.737247 | + | 0.675623i | \(0.763875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.8034 | + | 0.164158i | −0.500998 | + | 0.00761263i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9033 | −0.689644 | −0.344822 | − | 0.938668i | \(-0.612061\pi\) | ||||
−0.344822 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.74289 | + | 16.8041i | −0.126655 | + | 0.775943i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.35717 | − | 14.6680i | 0.108613 | − | 0.675867i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.7844 | − | 5.38108i | −0.679787 | − | 0.247422i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9605 | − | 14.2315i | −0.778200 | − | 0.652987i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.97381 | − | 1.98345i | 0.227735 | − | 0.0908159i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.38451 | + | 30.5371i | −0.246025 | + | 1.39527i | 0.572077 | + | 0.820200i | \(0.306138\pi\) |
−0.818101 | + | 0.575074i | \(0.804973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.1327 | + | 8.41961i | 1.05476 | + | 0.383901i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.1043 | + | 0.338116i | −0.550766 | + | 0.0153848i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.0345 | + | 34.7008i | 0.909719 | + | 1.57568i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.10330 | − | 10.5712i | 0.276567 | − | 0.479028i | −0.693962 | − | 0.720011i | \(-0.744137\pi\) |
0.970529 | + | 0.240984i | \(0.0774700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.14773 | + | 11.1840i | 0.0971236 | + | 0.505756i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.90208 | + | 7.46973i | −0.401745 | + | 0.337104i | −0.821168 | − | 0.570687i | \(-0.806677\pi\) |
0.419423 | + | 0.907791i | \(0.362233\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.96518 | + | 11.1451i | −0.0885070 | + | 0.501948i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.8775 | − | 11.7322i | −0.668694 | − | 0.527325i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.4538 | + | 24.4997i | −1.27633 | + | 1.09896i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.126329 | − | 0.106002i | 0.00565525 | − | 0.00474532i | −0.639956 | − | 0.768412i | \(-0.721047\pi\) |
0.645611 | + | 0.763667i | \(0.276603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0696 | − | 6.50817i | 0.762611 | − | 0.290764i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.1072 | − | 33.0947i | −0.851949 | − | 1.47562i | −0.879447 | − | 0.475998i | \(-0.842087\pi\) |
0.0274972 | − | 0.999622i | \(-0.491246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9266 | − | 36.2460i | 0.931223 | − | 1.61293i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.42953 | − | 0.112891i | 0.329957 | − | 0.00501367i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.133077 | − | 0.754719i | −0.00589855 | − | 0.0334523i | 0.981716 | − | 0.190349i | \(-0.0609621\pi\) |
−0.987615 | + | 0.156897i | \(0.949851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.21348 | − | 1.04485i | 0.0536812 | − | 0.0462213i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.2071 | + | 31.5829i | 0.892166 | + | 1.39442i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.8045 | − | 25.0090i | −1.31334 | − | 1.10203i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.7359 | + | 7.54724i | 0.911963 | + | 0.331927i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.6564 | + | 26.3005i | −0.643345 | + | 1.15447i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.298486 | − | 0.516993i | −0.0130769 | − | 0.0226499i | 0.859413 | − | 0.511282i | \(-0.170829\pi\) |
−0.872490 | + | 0.488632i | \(0.837496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.9406 | + | 36.2703i | −0.915670 | + | 1.58599i | −0.109754 | + | 0.993959i | \(0.535006\pi\) |
−0.805917 | + | 0.592029i | \(0.798327\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.5147 | + | 9.33540i | −0.458899 | + | 0.407430i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.06995 | + | 1.73689i | −0.0901685 | + | 0.0756603i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0517 | − | 5.47837i | 0.654421 | − | 0.238190i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.77870 | − | 18.1922i | 0.424359 | − | 0.789476i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.3192 | − | 8.48750i | 1.01007 | − | 0.367634i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.229896 | − | 1.30380i | −0.00993926 | − | 0.0563683i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.56835 | − | 0.543992i | −0.0676791 | − | 0.0234750i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.6642 | + | 10.3047i | −0.502411 | + | 0.443856i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.10808 | + | 7.11540i | 0.176620 | + | 0.305915i | 0.940721 | − | 0.339182i | \(-0.110150\pi\) |
−0.764101 | + | 0.645097i | \(0.776817\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1611 | + | 22.6379i | −1.12268 | + | 0.971485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.9727 | + | 15.0808i | −0.769864 | + | 0.645993i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.99139 | − | 2.90863i | 0.341687 | − | 0.124364i | −0.165476 | − | 0.986214i | \(-0.552916\pi\) |
0.507164 | + | 0.861850i | \(0.330694\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.54864 | + | 41.1313i | 0.364847 | + | 1.75544i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5249 | − | 65.3608i | 0.490976 | − | 2.78446i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.4563 | − | 17.5898i | −0.444649 | − | 0.747996i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −27.2159 | + | 10.3767i | −1.15525 | + | 0.440467i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.9531 | −0.803067 | −0.401534 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401534 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.7116 | + | 25.4812i | −0.622233 | + | 1.07774i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.73785 | + | 0.0719913i | −0.200032 | + | 0.00303948i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3983 | − | 18.7944i | 0.943976 | − | 0.792090i | −0.0342970 | − | 0.999412i | \(-0.510919\pi\) |
0.978273 | + | 0.207322i | \(0.0664748\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.62468 | − | 1.68325i | 0.194562 | − | 0.0708147i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.7172 | − | 9.76541i | 0.912037 | − | 0.410109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.0155 | − | 4.37329i | 0.503717 | − | 0.183338i | −0.0776483 | − | 0.996981i | \(-0.524741\pi\) |
0.581365 | + | 0.813643i | \(0.302519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9888 | − | 29.3591i | 1.46424 | − | 1.22864i | 0.542946 | − | 0.839767i | \(-0.317309\pi\) |
0.921291 | − | 0.388874i | \(-0.127136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.25716 | + | 0.0191025i | −0.0525187 | + | 0.000798017i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.05390 | + | 7.02156i | −0.169059 | + | 0.292819i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.03738 | 0.251340 | 0.125670 | − | 0.992072i | \(-0.459892\pi\) | ||||
0.125670 | + | 0.992072i | \(0.459892\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.42824 | + | 2.06965i | −0.225590 | + | 0.0860115i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.134597 | + | 0.00171385i | −0.00558403 | + | 7.11026e-5i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.689143 | − | 3.90832i | 0.0285414 | − | 0.161866i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −26.4389 | + | 23.5902i | −1.09311 | + | 0.975334i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.7636 | − | 5.00954i | 0.568084 | − | 0.206766i | −0.0419789 | − | 0.999118i | \(-0.513366\pi\) |
0.610063 | + | 0.792353i | \(0.291144\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.1393 | − | 10.1861i | 0.500192 | − | 0.419711i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.6769 | + | 18.7576i | −0.891667 | + | 0.771584i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.71826 | − | 2.97612i | −0.0705607 | − | 0.122215i | 0.828586 | − | 0.559861i | \(-0.189146\pi\) |
−0.899147 | + | 0.437646i | \(0.855812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.48960 | + | 9.12593i | −0.0610677 | + | 0.374127i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.2900 | + | 9.81259i | 1.15783 | + | 0.401603i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.36954 | + | 19.1096i | 0.137676 | + | 0.780797i | 0.972959 | + | 0.230978i | \(0.0741924\pi\) |
−0.835283 | + | 0.549820i | \(0.814696\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.74705 | + | 3.18367i | −0.356800 | + | 0.129864i | −0.514200 | − | 0.857670i | \(-0.671911\pi\) |
0.157400 | + | 0.987535i | \(0.449689\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.1567 | − | 16.4187i | −0.413612 | − | 0.668622i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.1654 | − | 5.88373i | 0.657218 | − | 0.239208i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.75650 | + | 4.83028i | −0.233649 | + | 0.196055i | −0.752093 | − | 0.659057i | \(-0.770956\pi\) |
0.518444 | + | 0.855111i | \(0.326511\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.9949 | − | 13.3045i | −1.62067 | − | 0.539125i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.6338 | − | 35.7387i | 0.834752 | − | 1.44583i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6494 | + | 20.1773i | 0.470514 | + | 0.814954i | 0.999431 | − | 0.0337194i | \(-0.0107353\pi\) |
−0.528918 | + | 0.848673i | \(0.677402\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.2929 | + | 25.6483i | −0.576346 | + | 1.03424i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.6336 | − | 5.32620i | −0.589128 | − | 0.214425i | 0.0302181 | − | 0.999543i | \(-0.490380\pi\) |
−0.619346 | + | 0.785118i | \(0.712602\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.7896 | + | 15.7663i | 0.755217 | + | 0.633703i | 0.936877 | − | 0.349659i | \(-0.113702\pi\) |
−0.181660 | + | 0.983361i | \(0.558147\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.1050 | − | 9.29580i | 0.405499 | − | 0.373028i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.04305 | + | 42.4467i | 0.322238 | + | 1.70059i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.37042 | − | 30.4571i | −0.214817 | − | 1.21829i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.7854 | − | 0.422197i | 1.10964 | − | 0.0168609i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.64216 | + | 6.30841i | −0.145223 | + | 0.251533i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9402 | + | 25.8773i | 0.594762 | + | 1.03016i | 0.993580 | + | 0.113128i | \(0.0360869\pi\) |
−0.398819 | + | 0.917030i | \(0.630580\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.15745 | + | 1.20385i | −0.125498 | + | 0.0478489i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.55814 | + | 1.30743i | −0.0618328 | + | 0.0518839i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.1905 | + | 24.8285i | 0.601871 | + | 0.983741i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.11583 | − | 42.1339i | 0.241938 | − | 1.66679i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.66603 | − | 9.44853i | 0.0658043 | − | 0.373195i | −0.934066 | − | 0.357100i | \(-0.883766\pi\) |
0.999870 | − | 0.0160947i | \(-0.00512331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.7814 | + | 21.6332i | −1.01672 | + | 0.853129i | −0.989212 | − | 0.146493i | \(-0.953202\pi\) |
−0.0275077 | + | 0.999622i | \(0.508757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.56545 | − | 34.1886i | −0.258515 | − | 1.34617i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00802 | − | 10.4062i | 0.236200 | − | 0.409110i | −0.723421 | − | 0.690407i | \(-0.757431\pi\) |
0.959621 | + | 0.281297i | \(0.0907647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.65375 | − | 13.2567i | −0.300436 | − | 0.520370i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.27339 | − | 8.57175i | −0.206680 | − | 0.335954i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.89469 | − | 3.60137i | −0.387209 | − | 0.140933i | 0.141078 | − | 0.989999i | \(-0.454943\pi\) |
−0.528287 | + | 0.849066i | \(0.677165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.40375 | + | 7.96104i | −0.0548489 | + | 0.311064i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.260824 | + | 1.79690i | −0.0101757 | + | 0.0701037i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.7075 | + | 21.5712i | 1.00142 | + | 0.840294i | 0.987181 | − | 0.159604i | \(-0.0510218\pi\) |
0.0142429 | + | 0.999899i | \(0.495466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.1449 | − | 9.87993i | −1.05581 | − | 0.384285i | −0.244960 | − | 0.969533i | \(-0.578775\pi\) |
−0.810854 | + | 0.585248i | \(0.800997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.40600 | + | 8.74917i | −0.0546047 | + | 0.339790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.73584 | − | 53.5195i | 0.338761 | − | 2.07540i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.3044 | −0.941070 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.64001 | + | 0.0401147i | −0.102069 | + | 0.00155092i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.2580 | + | 10.6491i | 1.12949 | + | 0.411102i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.77748 | − | 38.4370i | 0.261253 | − | 1.48164i | −0.518245 | − | 0.855232i | \(-0.673415\pi\) |
0.779498 | − | 0.626405i | \(-0.215474\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.05025 | − | 15.8112i | 0.0789143 | − | 0.608572i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.9229 | − | 11.2550i | 1.18846 | − | 0.432565i | 0.329279 | − | 0.944233i | \(-0.393194\pi\) |
0.859184 | + | 0.511668i | \(0.170972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.2480 | + | 32.5568i | −0.700293 | + | 1.24942i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.3393 | − | 0.430613i | 1.08596 | − | 0.0165011i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.42785 | + | 2.47311i | 0.0546352 | + | 0.0946309i | 0.892049 | − | 0.451938i | \(-0.149267\pi\) |
−0.837414 | + | 0.546569i | \(0.815934\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.26997 | − | 12.5920i | −0.277771 | − | 0.481114i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.61467 | − | 2.14073i | 0.214213 | − | 0.0816738i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.97424 | − | 2.53841i | −0.265697 | − | 0.0967059i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.65879 | + | 15.0788i | −0.101145 | + | 0.573623i | 0.891545 | + | 0.452932i | \(0.149622\pi\) |
−0.992690 | + | 0.120691i | \(0.961489\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.31250 | − | 17.4958i | 0.0878448 | − | 0.664612i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.7981 | + | 40.9465i | 1.85102 | + | 1.55319i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.27511 | + | 7.23151i | 0.0482982 | + | 0.273913i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8605 | − | 17.1858i | 0.751192 | − | 0.650028i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.7791 | 1.31359 | 0.656795 | − | 0.754070i | \(-0.271912\pi\) | ||||
0.656795 | + | 0.754070i | \(0.271912\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.3597 | − | 36.9960i | 0.805595 | − | 1.39533i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.20839 | + | 47.9513i | 0.346808 | + | 1.80595i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.9808 | − | 0.496351i | 1.46603 | − | 0.0186672i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.34268 | − | 6.16124i | −0.275760 | − | 0.231390i | 0.494410 | − | 0.869229i | \(-0.335384\pi\) |
−0.770170 | + | 0.637839i | \(0.779829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 22.0347 | + | 7.26976i | 0.826365 | + | 0.272637i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.44543 | − | 3.73016i | −0.166483 | − | 0.139696i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.56020 | + | 25.8622i | 0.170542 | + | 0.967191i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.21638 | + | 1.80309i | 0.0827722 | + | 0.0673378i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.2972 | − | 33.4238i | 0.719665 | − | 1.24650i | −0.241468 | − | 0.970409i | \(-0.577629\pi\) |
0.961133 | − | 0.276087i | \(-0.0890378\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.83806 | − | 35.7664i | 0.217421 | − | 1.33201i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.7645 | − | 23.0256i | −0.511906 | − | 0.856331i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.6193 | + | 18.1408i | −0.802921 | + | 0.673731i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.94631 | − | 50.7371i | 0.331800 | − | 1.88173i | −0.124988 | − | 0.992158i | \(-0.539889\pi\) |
0.456789 | − | 0.889575i | \(-0.349000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.3153 | + | 24.5146i | −0.419084 | + | 0.907947i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.66949 | − | 5.59636i | −0.246680 | − | 0.206989i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.01993 | − | 22.7981i | −0.148479 | − | 0.842068i | −0.964507 | − | 0.264056i | \(-0.914940\pi\) |
0.816028 | − | 0.578012i | \(-0.196172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −32.8141 | − | 10.4537i | −1.21037 | − | 0.385589i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.3088 | −0.527070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.9581 | −1.54345 | −0.771727 | − | 0.635954i | \(-0.780607\pi\) | ||||
−0.771727 | + | 0.635954i | \(0.780607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.24558 | − | 51.3099i | 0.302909 | − | 1.88492i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.66867 | − | 49.1625i | −0.318023 | − | 1.80360i | −0.554747 | − | 0.832019i | \(-0.687185\pi\) |
0.236724 | − | 0.971577i | \(-0.423926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.4576 | − | 13.2695i | 1.33570 | − | 0.486156i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.113887 | − | 0.101617i | 0.00416692 | − | 0.00371796i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.934483 | − | 0.804620i | 0.0341453 | − | 0.0294002i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.28250 | + | 0.830761i | 0.0832895 | + | 0.0303149i | 0.383329 | − | 0.923612i | \(-0.374778\pi\) |
−0.300039 | + | 0.953927i | \(0.597000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.7298 | − | 18.8034i | 0.791877 | − | 0.685233i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.63838 | −0.168808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.3823 | 1.46772 | 0.733859 | − | 0.679301i | \(-0.237717\pi\) | ||||
0.733859 | + | 0.679301i | \(0.237717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.91913 | − | 9.99360i | −0.0696602 | − | 0.362745i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.0259 | − | 12.0204i | −1.19719 | − | 0.435741i | −0.334946 | − | 0.942237i | \(-0.608718\pi\) |
−0.862242 | + | 0.506497i | \(0.830940\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.6288 | − | 7.21217i | −0.746813 | − | 0.261098i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.51585 | − | 8.91661i | −0.199426 | − | 0.322381i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.9006 | + | 9.79101i | −0.971324 | + | 0.353533i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.14242 | − | 12.1503i | −0.0772577 | − | 0.438150i | −0.998760 | − | 0.0497781i | \(-0.984149\pi\) |
0.921503 | − | 0.388372i | \(-0.126963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.1109 | + | 12.6243i | −1.19246 | + | 0.454654i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.7847 | 1.50289 | 0.751446 | − | 0.659795i | \(-0.229357\pi\) | ||||
0.751446 | + | 0.659795i | \(0.229357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.73850 | −0.242054 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.2618 | − | 16.8518i | −0.762762 | − | 0.604557i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.47795 | − | 42.4096i | −0.267925 | − | 1.51948i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.1722 | − | 20.2829i | −0.864951 | − | 0.725780i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 44.1195 | − | 18.3757i | 1.57670 | − | 0.656693i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.23068 | − | 23.9934i | 0.150999 | − | 0.856359i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5306 | − | 17.2272i | 0.731838 | − | 0.614085i | −0.198794 | − | 0.980041i | \(-0.563702\pi\) |
0.930632 | + | 0.365956i | \(0.119258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.91970 | − | 17.8006i | 0.353151 | − | 0.633719i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.54885 | + | 2.90164i | 0.126182 | + | 0.103171i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.1139 | − | 50.4268i | 1.03387 | − | 1.79071i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.20529 | − | 3.12846i | 0.291012 | − | 0.110955i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.81502 | + | 44.3212i | 0.276822 | + | 1.56994i | 0.733113 | + | 0.680107i | \(0.238067\pi\) |
−0.456291 | + | 0.889831i | \(0.650822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.35430 | + | 7.84919i | 0.330932 | + | 0.277685i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.4652 | − | 30.3332i | −1.35910 | − | 1.07177i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.03088 | + | 0.865013i | 0.0363791 | + | 0.0305257i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.8566 | + | 0.252839i | −0.699855 | + | 0.00891139i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.2097 | − | 23.5453i | 0.957827 | − | 0.828834i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.7505 | + | 23.8166i | −0.483443 | + | 0.837348i | −0.999819 | − | 0.0190140i | \(-0.993947\pi\) |
0.516376 | + | 0.856362i | \(0.327281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7704 | −1.50187 | −0.750936 | − | 0.660375i | \(-0.770397\pi\) | ||||
−0.750936 | + | 0.660375i | \(0.770397\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.06521 | + | 21.1689i | 0.142573 | + | 0.742427i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.24311 | + | 18.3926i | 0.113601 | + | 0.644264i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.1135 | + | 32.8202i | 1.36841 | + | 1.14823i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.4714 | − | 9.94066i | −1.09970 | − | 0.347355i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.95102 | − | 33.7499i | 0.207692 | − | 1.17788i | −0.685455 | − | 0.728115i | \(-0.740397\pi\) |
0.893147 | − | 0.449765i | \(-0.148492\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.07675 | − | 1.48381i | −0.142106 | − | 0.0517225i | 0.269988 | − | 0.962864i | \(-0.412980\pi\) |
−0.412094 | + | 0.911141i | \(0.635203\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.16632 | − | 7.45709i | −0.319130 | − | 0.259623i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.64312 | + | 8.04211i | 0.161457 | + | 0.279652i | 0.935391 | − | 0.353614i | \(-0.115047\pi\) |
−0.773934 | + | 0.633266i | \(0.781714\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0346 | − | 17.3804i | −0.348515 | − | 0.603646i | 0.637471 | − | 0.770475i | \(-0.279981\pi\) |
−0.985986 | + | 0.166828i | \(0.946647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.3307 | + | 45.4552i | −0.878712 | + | 1.57682i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.01575 | + | 3.15087i | −0.277729 | + | 0.109171i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.1522 | − | 10.2466i | 0.974247 | − | 0.354597i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8900 | + | 3.41029i | 0.376413 | + | 0.117877i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.23820 | + | 52.3924i | −0.318938 | + | 1.80879i | 0.230297 | + | 0.973120i | \(0.426030\pi\) |
−0.549236 | + | 0.835668i | \(0.685081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52.2468 | − | 19.0163i | −1.80161 | − | 0.655734i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.27581 | + | 7.15271i | 0.147267 | + | 0.246352i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1855 | 0.419194 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.4049 | + | 10.1426i | 0.426237 | + | 0.348504i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.7445 | + | 29.0793i | 1.22675 | + | 0.998000i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7004 | − | 5.35051i | −0.503923 | − | 0.183413i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.1219 | + | 23.5971i | 0.962875 | + | 0.807948i | 0.981418 | − | 0.191880i | \(-0.0614584\pi\) |
−0.0185434 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.3480 | + | 52.2919i | 1.10628 | + | 1.78835i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.86132 | − | 44.5838i | 0.268538 | − | 1.52295i | −0.490231 | − | 0.871593i | \(-0.663088\pi\) |
0.758769 | − | 0.651360i | \(-0.225801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7230 | + | 5.35872i | 0.502341 | + | 0.182837i | 0.580746 | − | 0.814084i | \(-0.302761\pi\) |
−0.0784058 | + | 0.996922i | \(0.524983\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3383 | + | 0.763656i | −0.931687 | + | 0.0260253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.2234 | + | 24.6356i | 0.484169 | + | 0.838606i | 0.999835 | − | 0.0181843i | \(-0.00578855\pi\) |
−0.515665 | + | 0.856790i | \(0.672455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24.6884 | + | 42.7615i | −0.839429 | + | 1.45393i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.3416 | + | 8.78991i | 0.860646 | + | 0.298521i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.1735 | − | 11.0539i | 0.446880 | − | 0.374977i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.64669 | + | 26.3527i | −0.157447 | + | 0.892927i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.61150 | − | 41.4338i | −0.291455 | − | 1.40232i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0008 | − | 9.47208i | 0.371896 | − | 0.320215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.7836 | − | 18.2786i | 0.735579 | − | 0.617224i | −0.196067 | − | 0.980590i | \(-0.562817\pi\) |
0.931646 | + | 0.363366i | \(0.118373\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.14529 | − | 7.43999i | −0.308463 | − | 0.250945i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.2485 | + | 40.2676i | 0.783262 | + | 1.35665i | 0.930032 | + | 0.367478i | \(0.119779\pi\) |
−0.146771 | + | 0.989171i | \(0.546888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.72232 | + | 4.71519i | −0.0916132 | + | 0.158679i | −0.908190 | − | 0.418558i | \(-0.862536\pi\) |
0.816577 | + | 0.577237i | \(0.195869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.4880 | − | 29.5873i | 0.554239 | − | 0.994567i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.281794 | + | 1.59813i | 0.00946172 | + | 0.0536601i | 0.989173 | − | 0.146754i | \(-0.0468825\pi\) |
−0.979711 | + | 0.200414i | \(0.935771\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.78841 | − | 0.625259i | −0.0599814 | − | 0.0209705i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.0396 | + | 16.6903i | 0.369840 | + | 0.559145i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54.8588 | − | 46.0320i | −1.83578 | − | 1.54040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.55816 | − | 0.931095i | −0.0855099 | − | 0.0311231i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.0286 | + | 0.289138i | −0.635347 | + | 0.00965405i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.0999 | − | 17.4935i | −0.336849 | − | 0.583439i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09807 | − | 1.90191i | 0.0365820 | − | 0.0633619i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.2486 | − | 21.5289i | 0.806942 | − | 0.716438i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −43.4620 | + | 36.4690i | −1.44473 | + | 1.21227i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6192 | − | 6.04889i | 0.551831 | − | 0.200850i | −0.0510286 | − | 0.998697i | \(-0.516250\pi\) |
0.602860 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.9831 | + | 29.4293i | −1.09398 | + | 0.976108i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8940 | + | 13.7923i | −1.25548 | + | 0.456959i | −0.882251 | − | 0.470779i | \(-0.843973\pi\) |
−0.373233 | + | 0.927738i | \(0.621751\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0196434 | − | 0.111403i | −0.000650102 | − | 0.00368691i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.9929 | + | 67.6586i | 0.429533 | + | 2.23673i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.04220 | + | 2.66517i | −0.232554 | + | 0.0880118i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.08348 | + | 14.0010i | 0.266649 | + | 0.461850i | 0.967994 | − | 0.250972i | \(-0.0807501\pi\) |
−0.701345 | + | 0.712822i | \(0.747417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.20815 | + | 16.7060i | 0.105712 | + | 0.550480i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.2052 | + | 37.9317i | −1.48795 | + | 1.24854i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.0700 | + | 6.21295i | −0.561257 | + | 0.204281i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.6178 | + | 34.9461i | 0.710020 | + | 1.14778i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.31381 | − | 13.1223i | 0.0759136 | − | 0.430528i | −0.923036 | − | 0.384713i | \(-0.874300\pi\) |
0.998950 | − | 0.0458148i | \(-0.0145884\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.0088 | − | 18.4784i | 1.54065 | − | 0.605606i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.0712 | + | 8.19323i | 0.329716 | + | 0.268234i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.77075 | −0.254131 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.2562 | + | 24.6924i | −0.465728 | + | 0.806665i | −0.999234 | − | 0.0391314i | \(-0.987541\pi\) |
0.533506 | + | 0.845796i | \(0.320874\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.79307 | − | 10.3955i | 0.189050 | − | 0.339245i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5773 | + | 13.9100i | −0.540406 | + | 0.453454i | −0.871677 | − | 0.490082i | \(-0.836967\pi\) |
0.331271 | + | 0.943536i | \(0.392523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.8189 | + | 5.39365i | −0.482571 | + | 0.175642i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 35.8544 | − | 15.4719i | 1.16634 | − | 0.503300i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.937338 | + | 0.341163i | −0.0304594 | + | 0.0110863i | −0.357205 | − | 0.934026i | \(-0.616270\pi\) |
0.326746 | + | 0.945112i | \(0.394048\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.92788 | − | 1.61769i | 0.0625818 | − | 0.0525123i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.7779 | + | 29.7394i | 0.576487 | + | 0.964365i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.1992 | + | 45.3784i | −0.848677 | + | 1.46995i | 0.0337131 | + | 0.999432i | \(0.489267\pi\) |
−0.882390 | + | 0.470519i | \(0.844067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.06192 | −0.0667223 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.62023 | − | 34.9731i | 0.181676 | − | 1.13052i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.62169 | − | 11.8140i | 0.213826 | − | 0.381493i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.54558 | + | 25.7793i | −0.146632 | + | 0.831590i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.200856 | + | 1.38376i | −0.00647251 | + | 0.0445912i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.95260 | + | 3.25848i | −0.288194 | + | 0.104894i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.3231 | − | 9.50124i | 0.364128 | − | 0.305539i | −0.442306 | − | 0.896864i | \(-0.645839\pi\) |
0.806433 | + | 0.591325i | \(0.201395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.5284 | + | 5.03928i | 0.466720 | + | 0.161885i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.9123 | + | 43.1494i | 0.799475 | + | 1.38473i | 0.919958 | + | 0.392016i | \(0.128222\pi\) |
−0.120483 | + | 0.992715i | \(0.538444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.55848 | + | 58.5593i | −0.306431 | + | 1.87733i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.7106 | + | 14.4601i | −0.535167 | + | 0.463094i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.65154 | + | 15.0376i | 0.0848301 | + | 0.481096i | 0.997393 | + | 0.0721594i | \(0.0229890\pi\) |
−0.912563 | + | 0.408936i | \(0.865900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.1166 | + | 12.4174i | −1.09037 | + | 0.396863i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.0166 | − | 9.17854i | 0.734863 | − | 0.293048i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.5168 | + | 10.7432i | −0.941439 | + | 0.342656i | −0.766734 | − | 0.641965i | \(-0.778119\pi\) |
−0.174705 | + | 0.984621i | \(0.555897\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0123 | + | 30.2179i | −1.14745 | + | 0.962823i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.0099 | + | 30.1954i | −1.08255 | + | 0.961132i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.34894 | − | 16.1928i | 0.297279 | − | 0.514902i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0599 | + | 41.6729i | 0.764287 | + | 1.32378i | 0.940623 | + | 0.339453i | \(0.110242\pi\) |
−0.176336 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.99161 | − | 10.0229i | −0.190138 | − | 0.318068i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.1444 | + | 16.7952i | 1.46288 | + | 0.532444i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0592 | − | 13.4753i | −0.508601 | − | 0.426767i | 0.352035 | − | 0.935987i | \(-0.385490\pi\) |
−0.860637 | + | 0.509220i | \(0.829934\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.7308 | − | 1.40172i | 0.972280 | − | 0.0443485i |
(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 | 756.2.bq.a.25.3 | yes | 144 | |
7.2 | even | 3 | 756.2.bp.a.457.20 | yes | 144 | ||
27.13 | even | 9 | 756.2.bp.a.445.20 | ✓ | 144 | ||
189.121 | even | 9 | inner | 756.2.bq.a.121.3 | yes | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.bp.a.445.20 | ✓ | 144 | 27.13 | even | 9 | ||
756.2.bp.a.457.20 | yes | 144 | 7.2 | even | 3 | ||
756.2.bq.a.25.3 | yes | 144 | 1.1 | even | 1 | trivial | |
756.2.bq.a.121.3 | yes | 144 | 189.121 | even | 9 | inner |