Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(1049,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.1049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{8} - 30x^{6} + 36x^{4} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1049.5 | ||
Root | \(1.68439 - 0.403509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.1049 |
Dual form | 1050.2.d.h.1049.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.403509 | − | 1.68439i | −0.232966 | − | 0.972485i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.403509 | − | 1.68439i | −0.164732 | − | 0.687651i | ||||
\(7\) | 1.28088 | + | 2.31502i | 0.484129 | + | 0.874997i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.67436 | + | 1.35934i | −0.891454 | + | 0.453112i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.34872i | 1.61270i | 0.591439 | + | 0.806350i | \(0.298560\pi\) | ||||
−0.591439 | + | 0.806350i | \(0.701440\pi\) | |||||||
\(12\) | −0.403509 | − | 1.68439i | −0.116483 | − | 0.486242i | ||||
\(13\) | 3.95617 | 1.09724 | 0.548622 | − | 0.836070i | \(-0.315153\pi\) | ||||
0.548622 | + | 0.836070i | \(0.315153\pi\) | |||||||
\(14\) | 1.28088 | + | 2.31502i | 0.342331 | + | 0.618716i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.32496i | 1.77656i | 0.459300 | + | 0.888281i | \(0.348100\pi\) | ||||
−0.459300 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(18\) | −2.67436 | + | 1.35934i | −0.630353 | + | 0.320399i | ||||
\(19\) | − | 0.807019i | − | 0.185143i | −0.995706 | − | 0.0925714i | \(-0.970491\pi\) | ||
0.995706 | − | 0.0925714i | \(-0.0295086\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.38256 | − | 3.09165i | 0.738136 | − | 0.674652i | ||||
\(22\) | 5.34872i | 1.14035i | ||||||||
\(23\) | 0.281327 | 0.0586607 | 0.0293304 | − | 0.999570i | \(-0.490663\pi\) | ||||
0.0293304 | + | 0.999570i | \(0.490663\pi\) | |||||||
\(24\) | −0.403509 | − | 1.68439i | −0.0823660 | − | 0.343825i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.95617 | 0.775869 | ||||||||
\(27\) | 3.36879 | + | 3.95617i | 0.648323 | + | 0.761365i | ||||
\(28\) | 1.28088 | + | 2.31502i | 0.242064 | + | 0.437498i | ||||
\(29\) | 0.281327i | 0.0522411i | 0.999659 | + | 0.0261206i | \(0.00831538\pi\) | ||||
−0.999659 | + | 0.0261206i | \(0.991685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.07971i | − | 1.63076i | −0.578924 | − | 0.815382i | \(-0.696527\pi\) | ||
0.578924 | − | 0.815382i | \(-0.303473\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 9.00935 | − | 2.15826i | 1.56833 | − | 0.375705i | ||||
\(34\) | 7.32496i | 1.25622i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.67436 | + | 1.35934i | −0.445727 | + | 0.226556i | ||||
\(37\) | − | 6.06739i | − | 0.997473i | −0.866754 | − | 0.498737i | \(-0.833797\pi\) | ||
0.866754 | − | 0.498737i | \(-0.166203\pi\) | |||||||
\(38\) | − | 0.807019i | − | 0.130916i | ||||||
\(39\) | −1.59635 | − | 6.66375i | −0.255621 | − | 1.06705i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.15019 | −0.960498 | −0.480249 | − | 0.877132i | \(-0.659454\pi\) | ||||
−0.480249 | + | 0.877132i | \(0.659454\pi\) | |||||||
\(42\) | 3.38256 | − | 3.09165i | 0.521941 | − | 0.477051i | ||||
\(43\) | 6.34872i | 0.968171i | 0.875021 | + | 0.484085i | \(0.160848\pi\) | ||||
−0.875021 | + | 0.484085i | \(0.839152\pi\) | |||||||
\(44\) | 5.34872i | 0.806350i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.281327 | 0.0414794 | ||||||||
\(47\) | − | 5.78984i | − | 0.844535i | −0.906471 | − | 0.422268i | \(-0.861234\pi\) | ||
0.906471 | − | 0.422268i | \(-0.138766\pi\) | |||||||
\(48\) | −0.403509 | − | 1.68439i | −0.0582415 | − | 0.243121i | ||||
\(49\) | −3.71867 | + | 5.93055i | −0.531239 | + | 0.847222i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.3381 | − | 2.95569i | 1.72768 | − | 0.413879i | ||||
\(52\) | 3.95617 | 0.548622 | ||||||||
\(53\) | 10.9788 | 1.50805 | 0.754025 | − | 0.656846i | \(-0.228110\pi\) | ||||
0.754025 | + | 0.656846i | \(0.228110\pi\) | |||||||
\(54\) | 3.36879 | + | 3.95617i | 0.458434 | + | 0.538367i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.28088 | + | 2.31502i | 0.171165 | + | 0.309358i | ||||
\(57\) | −1.35934 | + | 0.325639i | −0.180049 | + | 0.0431320i | ||||
\(58\) | 0.281327i | 0.0369401i | ||||||||
\(59\) | −4.90390 | −0.638433 | −0.319217 | − | 0.947682i | \(-0.603420\pi\) | ||||
−0.319217 | + | 0.947682i | \(0.603420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.2555i | − | 1.69719i | −0.529040 | − | 0.848597i | \(-0.677448\pi\) | ||
0.529040 | − | 0.848597i | \(-0.322552\pi\) | |||||||
\(62\) | − | 9.07971i | − | 1.15312i | ||||||
\(63\) | −6.57244 | − | 4.45006i | −0.828050 | − | 0.560654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.00935 | − | 2.15826i | 1.10897 | − | 0.265663i | ||||
\(67\) | 6.71867i | 0.820817i | 0.911902 | + | 0.410408i | \(0.134614\pi\) | ||||
−0.911902 | + | 0.410408i | \(0.865386\pi\) | |||||||
\(68\) | 7.32496i | 0.888281i | ||||||||
\(69\) | −0.113518 | − | 0.473865i | −0.0136660 | − | 0.0570467i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.36995i | − | 0.399940i | −0.979802 | − | 0.199970i | \(-0.935916\pi\) | ||
0.979802 | − | 0.199970i | \(-0.0640844\pi\) | |||||||
\(72\) | −2.67436 | + | 1.35934i | −0.315176 | + | 0.160199i | ||||
\(73\) | −4.98282 | −0.583195 | −0.291598 | − | 0.956541i | \(-0.594187\pi\) | ||||
−0.291598 | + | 0.956541i | \(0.594187\pi\) | |||||||
\(74\) | − | 6.06739i | − | 0.705320i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.807019i | − | 0.0925714i | ||||||
\(77\) | −12.3824 | + | 6.85109i | −1.41111 | + | 0.780754i | ||||
\(78\) | −1.59635 | − | 6.66375i | −0.180751 | − | 0.754521i | ||||
\(79\) | 3.26010 | 0.366789 | 0.183395 | − | 0.983039i | \(-0.441291\pi\) | ||||
0.183395 | + | 0.983039i | \(0.441291\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.30441 | − | 7.27071i | 0.589379 | − | 0.807857i | ||||
\(82\) | −6.15019 | −0.679175 | ||||||||
\(83\) | 1.53511i | 0.168501i | 0.996445 | + | 0.0842503i | \(0.0268495\pi\) | ||||
−0.996445 | + | 0.0842503i | \(0.973150\pi\) | |||||||
\(84\) | 3.38256 | − | 3.09165i | 0.369068 | − | 0.337326i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.34872i | 0.684600i | ||||||||
\(87\) | 0.473865 | − | 0.113518i | 0.0508037 | − | 0.0121704i | ||||
\(88\) | 5.34872i | 0.570176i | ||||||||
\(89\) | −4.31652 | −0.457550 | −0.228775 | − | 0.973479i | \(-0.573472\pi\) | ||||
−0.228775 | + | 0.973479i | \(0.573472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.06739 | + | 9.15863i | 0.531207 | + | 0.960085i | ||||
\(92\) | 0.281327 | 0.0293304 | ||||||||
\(93\) | −15.2938 | + | 3.66375i | −1.58589 | + | 0.379913i | ||||
\(94\) | − | 5.78984i | − | 0.597177i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.403509 | − | 1.68439i | −0.0411830 | − | 0.171913i | ||||
\(97\) | 15.0892 | 1.53207 | 0.766037 | − | 0.642796i | \(-0.222226\pi\) | ||||
0.766037 | + | 0.642796i | \(0.222226\pi\) | |||||||
\(98\) | −3.71867 | + | 5.93055i | −0.375643 | + | 0.599076i | ||||
\(99\) | −7.27071 | − | 14.3044i | −0.730734 | − | 1.43765i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.78984 | 0.576111 | 0.288055 | − | 0.957614i | \(-0.406991\pi\) | ||||
0.288055 | + | 0.957614i | \(0.406991\pi\) | |||||||
\(102\) | 12.3381 | − | 2.95569i | 1.22165 | − | 0.292657i | ||||
\(103\) | 6.95721 | 0.685514 | 0.342757 | − | 0.939424i | \(-0.388639\pi\) | ||||
0.342757 | + | 0.939424i | \(0.388639\pi\) | |||||||
\(104\) | 3.95617 | 0.387934 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9788 | 1.06635 | ||||||||
\(107\) | −10.6088 | −1.02559 | −0.512797 | − | 0.858510i | \(-0.671390\pi\) | ||||
−0.512797 | + | 0.858510i | \(0.671390\pi\) | |||||||
\(108\) | 3.36879 | + | 3.95617i | 0.324162 | + | 0.380683i | ||||
\(109\) | 18.1348 | 1.73700 | 0.868499 | − | 0.495691i | \(-0.165085\pi\) | ||||
0.868499 | + | 0.495691i | \(0.165085\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2199 | + | 2.44825i | −0.970028 | + | 0.232378i | ||||
\(112\) | 1.28088 | + | 2.31502i | 0.121032 | + | 0.218749i | ||||
\(113\) | 8.54142 | 0.803510 | 0.401755 | − | 0.915747i | \(-0.368400\pi\) | ||||
0.401755 | + | 0.915747i | \(0.368400\pi\) | |||||||
\(114\) | −1.35934 | + | 0.325639i | −0.127314 | + | 0.0304989i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.281327i | 0.0261206i | ||||||||
\(117\) | −10.5802 | + | 5.37777i | −0.978142 | + | 0.497175i | ||||
\(118\) | −4.90390 | −0.451441 | ||||||||
\(119\) | −16.9574 | + | 9.38242i | −1.55449 | + | 0.860085i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.6088 | −1.60080 | ||||||||
\(122\) | − | 13.2555i | − | 1.20010i | ||||||
\(123\) | 2.48166 | + | 10.3593i | 0.223764 | + | 0.934070i | ||||
\(124\) | − | 9.07971i | − | 0.815382i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.57244 | − | 4.45006i | −0.585520 | − | 0.396443i | ||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.6937 | − | 2.56177i | 0.941532 | − | 0.225551i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5454 | −1.44558 | −0.722788 | − | 0.691070i | \(-0.757140\pi\) | ||||
−0.722788 | + | 0.691070i | \(0.757140\pi\) | |||||||
\(132\) | 9.00935 | − | 2.15826i | 0.784163 | − | 0.187852i | ||||
\(133\) | 1.86827 | − | 1.03370i | 0.161999 | − | 0.0896329i | ||||
\(134\) | 6.71867i | 0.580405i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.32496i | 0.628110i | ||||||||
\(137\) | 7.41612 | 0.633601 | 0.316801 | − | 0.948492i | \(-0.397391\pi\) | ||||
0.316801 | + | 0.948492i | \(0.397391\pi\) | |||||||
\(138\) | −0.113518 | − | 0.473865i | −0.00966330 | − | 0.0403381i | ||||
\(139\) | 6.36982i | 0.540281i | 0.962821 | + | 0.270141i | \(0.0870702\pi\) | ||||
−0.962821 | + | 0.270141i | \(0.912930\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.75237 | + | 2.33625i | −0.821298 | + | 0.196748i | ||||
\(142\) | − | 3.36995i | − | 0.282800i | ||||||
\(143\) | 21.1604i | 1.76953i | ||||||||
\(144\) | −2.67436 | + | 1.35934i | −0.222863 | + | 0.113278i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.98282 | −0.412381 | ||||||||
\(147\) | 11.4899 | + | 3.87067i | 0.947671 | + | 0.319248i | ||||
\(148\) | − | 6.06739i | − | 0.498737i | ||||||
\(149\) | 7.60882i | 0.623339i | 0.950191 | + | 0.311669i | \(0.100888\pi\) | ||||
−0.950191 | + | 0.311669i | \(0.899112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.63005 | −0.376788 | −0.188394 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188394 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(152\) | − | 0.807019i | − | 0.0654578i | ||||||
\(153\) | −9.95708 | − | 19.5896i | −0.804982 | − | 1.58372i | ||||
\(154\) | −12.3824 | + | 6.85109i | −0.997804 | + | 0.552077i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.59635 | − | 6.66375i | −0.127810 | − | 0.533527i | ||||
\(157\) | −15.3162 | −1.22237 | −0.611184 | − | 0.791489i | \(-0.709306\pi\) | ||||
−0.611184 | + | 0.791489i | \(0.709306\pi\) | |||||||
\(158\) | 3.26010 | 0.259359 | ||||||||
\(159\) | −4.43004 | − | 18.4926i | −0.351325 | − | 1.46656i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.360347 | + | 0.651279i | 0.0283993 | + | 0.0513280i | ||||
\(162\) | 5.30441 | − | 7.27071i | 0.416754 | − | 0.571241i | ||||
\(163\) | − | 3.06739i | − | 0.240257i | −0.992758 | − | 0.120128i | \(-0.961669\pi\) | ||
0.992758 | − | 0.120128i | \(-0.0383306\pi\) | |||||||
\(164\) | −6.15019 | −0.480249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.53511i | 0.119148i | ||||||||
\(167\) | − | 1.89546i | − | 0.146675i | −0.997307 | − | 0.0733376i | \(-0.976635\pi\) | ||
0.997307 | − | 0.0733376i | \(-0.0233651\pi\) | |||||||
\(168\) | 3.38256 | − | 3.09165i | 0.260970 | − | 0.238526i | ||||
\(169\) | 2.65128 | 0.203945 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.09701 | + | 2.15826i | 0.0838904 | + | 0.165046i | ||||
\(172\) | 6.34872i | 0.484085i | ||||||||
\(173\) | − | 8.86007i | − | 0.673619i | −0.941573 | − | 0.336809i | \(-0.890652\pi\) | ||
0.941573 | − | 0.336809i | \(-0.109348\pi\) | |||||||
\(174\) | 0.473865 | − | 0.113518i | 0.0359236 | − | 0.00860578i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.34872i | 0.403175i | ||||||||
\(177\) | 1.97877 | + | 8.26010i | 0.148733 | + | 0.620867i | ||||
\(178\) | −4.31652 | −0.323537 | ||||||||
\(179\) | − | 11.3487i | − | 0.848243i | −0.905605 | − | 0.424122i | \(-0.860583\pi\) | ||
0.905605 | − | 0.424122i | \(-0.139417\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.63303i | 0.641688i | 0.947132 | + | 0.320844i | \(0.103967\pi\) | ||||
−0.947132 | + | 0.320844i | \(0.896033\pi\) | |||||||
\(182\) | 5.06739 | + | 9.15863i | 0.375620 | + | 0.678883i | ||||
\(183\) | −22.3275 | + | 5.34872i | −1.65050 | + | 0.395389i | ||||
\(184\) | 0.281327 | 0.0207397 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.2938 | + | 3.66375i | −1.12140 | + | 0.268639i | ||||
\(187\) | −39.1791 | −2.86506 | ||||||||
\(188\) | − | 5.78984i | − | 0.422268i | ||||||
\(189\) | −4.84360 | + | 12.8662i | −0.352320 | + | 0.935879i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.78607i | − | 0.563380i | −0.959505 | − | 0.281690i | \(-0.909105\pi\) | ||
0.959505 | − | 0.281690i | \(-0.0908950\pi\) | |||||||
\(192\) | −0.403509 | − | 1.68439i | −0.0291208 | − | 0.121561i | ||||
\(193\) | − | 25.1715i | − | 1.81188i | −0.423404 | − | 0.905941i | \(-0.639165\pi\) | ||
0.423404 | − | 0.905941i | \(-0.360835\pi\) | |||||||
\(194\) | 15.0892 | 1.08334 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.71867 | + | 5.93055i | −0.265619 | + | 0.423611i | ||||
\(197\) | 2.52597 | 0.179968 | 0.0899840 | − | 0.995943i | \(-0.471318\pi\) | ||||
0.0899840 | + | 0.995943i | \(0.471318\pi\) | |||||||
\(198\) | −7.27071 | − | 14.3044i | −0.516707 | − | 1.01657i | ||||
\(199\) | − | 0.947731i | − | 0.0671828i | −0.999436 | − | 0.0335914i | \(-0.989306\pi\) | ||
0.999436 | − | 0.0335914i | \(-0.0106945\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3169 | − | 2.71105i | 0.798232 | − | 0.191222i | ||||
\(202\) | 5.78984 | 0.407372 | ||||||||
\(203\) | −0.651279 | + | 0.360347i | −0.0457108 | + | 0.0252914i | ||||
\(204\) | 12.3381 | − | 2.95569i | 0.863840 | − | 0.206940i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.95721 | 0.484732 | ||||||||
\(207\) | −0.752370 | + | 0.382418i | −0.0522933 | + | 0.0265799i | ||||
\(208\) | 3.95617 | 0.274311 | ||||||||
\(209\) | 4.31652 | 0.298580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8901 | −0.887394 | −0.443697 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443697 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(212\) | 10.9788 | 0.754025 | ||||||||
\(213\) | −5.67632 | + | 1.35981i | −0.388935 | + | 0.0931724i | ||||
\(214\) | −10.6088 | −0.725204 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.36879 | + | 3.95617i | 0.229217 | + | 0.269183i | ||||
\(217\) | 21.0197 | − | 11.6300i | 1.42691 | − | 0.789499i | ||||
\(218\) | 18.1348 | 1.22824 | ||||||||
\(219\) | 2.01062 | + | 8.39303i | 0.135865 | + | 0.567149i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.9788i | 1.94932i | ||||||||
\(222\) | −10.2199 | + | 2.44825i | −0.685913 | + | 0.164316i | ||||
\(223\) | −23.7296 | −1.58905 | −0.794526 | − | 0.607230i | \(-0.792281\pi\) | ||||
−0.794526 | + | 0.607230i | \(0.792281\pi\) | |||||||
\(224\) | 1.28088 | + | 2.31502i | 0.0855827 | + | 0.154679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.54142 | 0.568167 | ||||||||
\(227\) | 10.4667i | 0.694700i | 0.937736 | + | 0.347350i | \(0.112918\pi\) | ||||
−0.937736 | + | 0.347350i | \(0.887082\pi\) | |||||||
\(228\) | −1.35934 | + | 0.325639i | −0.0900243 | + | 0.0215660i | ||||
\(229\) | − | 16.4762i | − | 1.08878i | −0.838833 | − | 0.544388i | \(-0.816762\pi\) | ||
0.838833 | − | 0.544388i | \(-0.183238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.5364 | + | 18.0924i | 1.08801 | + | 1.19039i | ||||
\(232\) | 0.281327i | 0.0184700i | ||||||||
\(233\) | 27.9575 | 1.83156 | 0.915780 | − | 0.401681i | \(-0.131574\pi\) | ||||
0.915780 | + | 0.401681i | \(0.131574\pi\) | |||||||
\(234\) | −10.5802 | + | 5.37777i | −0.691651 | + | 0.351556i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.90390 | −0.319217 | ||||||||
\(237\) | −1.31548 | − | 5.49128i | −0.0854495 | − | 0.356697i | ||||
\(238\) | −16.9574 | + | 9.38242i | −1.09919 | + | 0.608172i | ||||
\(239\) | 17.2601i | 1.11646i | 0.829685 | + | 0.558231i | \(0.188520\pi\) | ||||
−0.829685 | + | 0.558231i | \(0.811480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1935i | 1.23636i | 0.786037 | + | 0.618180i | \(0.212130\pi\) | ||||
−0.786037 | + | 0.618180i | \(0.787870\pi\) | |||||||
\(242\) | −17.6088 | −1.13194 | ||||||||
\(243\) | −14.3871 | − | 6.00091i | −0.922934 | − | 0.384959i | ||||
\(244\) | − | 13.2555i | − | 0.848597i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.48166 | + | 10.3593i | 0.158225 | + | 0.660487i | ||||
\(247\) | − | 3.19270i | − | 0.203147i | ||||||
\(248\) | − | 9.07971i | − | 0.576562i | ||||||
\(249\) | 2.58574 | − | 0.619433i | 0.163864 | − | 0.0392550i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0271 | −1.32722 | −0.663611 | − | 0.748078i | \(-0.730977\pi\) | ||||
−0.663611 | + | 0.748078i | \(0.730977\pi\) | |||||||
\(252\) | −6.57244 | − | 4.45006i | −0.414025 | − | 0.280327i | ||||
\(253\) | 1.50474i | 0.0946022i | ||||||||
\(254\) | − | 2.00000i | − | 0.125491i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.5881i | − | 0.909982i | −0.890496 | − | 0.454991i | \(-0.849642\pi\) | ||
0.890496 | − | 0.454991i | \(-0.150358\pi\) | |||||||
\(258\) | 10.6937 | − | 2.56177i | 0.665763 | − | 0.159489i | ||||
\(259\) | 14.0462 | − | 7.77163i | 0.872786 | − | 0.482905i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.382418 | − | 0.752370i | −0.0236711 | − | 0.0465705i | ||||
\(262\) | −16.5454 | −1.02218 | ||||||||
\(263\) | −8.91138 | −0.549499 | −0.274749 | − | 0.961516i | \(-0.588595\pi\) | ||||
−0.274749 | + | 0.961516i | \(0.588595\pi\) | |||||||
\(264\) | 9.00935 | − | 2.15826i | 0.554487 | − | 0.132832i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.86827 | − | 1.03370i | 0.114551 | − | 0.0633800i | ||||
\(267\) | 1.74175 | + | 7.27071i | 0.106594 | + | 0.444960i | ||||
\(268\) | 6.71867i | 0.410408i | ||||||||
\(269\) | 22.3352 | 1.36180 | 0.680901 | − | 0.732375i | \(-0.261588\pi\) | ||||
0.680901 | + | 0.732375i | \(0.261588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.17684i | − | 0.435962i | −0.975953 | − | 0.217981i | \(-0.930053\pi\) | ||
0.975953 | − | 0.217981i | \(-0.0699471\pi\) | |||||||
\(272\) | 7.32496i | 0.444141i | ||||||||
\(273\) | 13.3820 | − | 12.2311i | 0.809915 | − | 0.740258i | ||||
\(274\) | 7.41612 | 0.448024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.113518 | − | 0.473865i | −0.00683298 | − | 0.0285233i | ||||
\(277\) | − | 9.32749i | − | 0.560435i | −0.959937 | − | 0.280217i | \(-0.909593\pi\) | ||
0.959937 | − | 0.280217i | \(-0.0904065\pi\) | |||||||
\(278\) | 6.36982i | 0.382037i | ||||||||
\(279\) | 12.3424 | + | 24.2824i | 0.738919 | + | 1.45375i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.4373i | − | 1.04022i | −0.854098 | − | 0.520112i | \(-0.825890\pi\) | ||
0.854098 | − | 0.520112i | \(-0.174110\pi\) | |||||||
\(282\) | −9.75237 | + | 2.33625i | −0.580745 | + | 0.139122i | ||||
\(283\) | 16.1776 | 0.961660 | 0.480830 | − | 0.876814i | \(-0.340335\pi\) | ||||
0.480830 | + | 0.876814i | \(0.340335\pi\) | |||||||
\(284\) | − | 3.36995i | − | 0.199970i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.1604i | 1.25124i | ||||||||
\(287\) | −7.87768 | − | 14.2378i | −0.465005 | − | 0.840433i | ||||
\(288\) | −2.67436 | + | 1.35934i | −0.157588 | + | 0.0800997i | ||||
\(289\) | −36.6550 | −2.15618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.08862 | − | 25.4161i | −0.356922 | − | 1.48992i | ||||
\(292\) | −4.98282 | −0.291598 | ||||||||
\(293\) | − | 22.5623i | − | 1.31810i | −0.752099 | − | 0.659050i | \(-0.770958\pi\) | ||
0.752099 | − | 0.659050i | \(-0.229042\pi\) | |||||||
\(294\) | 11.4899 | + | 3.87067i | 0.670105 | + | 0.225742i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 6.06739i | − | 0.352660i | ||||||
\(297\) | −21.1604 | + | 18.0187i | −1.22785 | + | 1.04555i | ||||
\(298\) | 7.60882i | 0.440767i | ||||||||
\(299\) | 1.11298 | 0.0643652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.6974 | + | 8.13197i | −0.847146 | + | 0.468719i | ||||
\(302\) | −4.63005 | −0.266429 | ||||||||
\(303\) | −2.33625 | − | 9.75237i | −0.134214 | − | 0.560259i | ||||
\(304\) | − | 0.807019i | − | 0.0462857i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.95708 | − | 19.5896i | −0.569208 | − | 1.11986i | ||||
\(307\) | 19.4057 | 1.10754 | 0.553771 | − | 0.832669i | \(-0.313188\pi\) | ||||
0.553771 | + | 0.832669i | \(0.313188\pi\) | |||||||
\(308\) | −12.3824 | + | 6.85109i | −0.705554 | + | 0.390377i | ||||
\(309\) | −2.80730 | − | 11.7187i | −0.159702 | − | 0.666652i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.73757 | −0.382053 | −0.191026 | − | 0.981585i | \(-0.561182\pi\) | ||||
−0.191026 | + | 0.981585i | \(0.561182\pi\) | |||||||
\(312\) | −1.59635 | − | 6.66375i | −0.0903756 | − | 0.377260i | ||||
\(313\) | 21.3875 | 1.20889 | 0.604446 | − | 0.796646i | \(-0.293394\pi\) | ||||
0.604446 | + | 0.796646i | \(0.293394\pi\) | |||||||
\(314\) | −15.3162 | −0.864344 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.26010 | 0.183395 | ||||||||
\(317\) | 3.47403 | 0.195121 | 0.0975605 | − | 0.995230i | \(-0.468896\pi\) | ||||
0.0975605 | + | 0.995230i | \(0.468896\pi\) | |||||||
\(318\) | −4.43004 | − | 18.4926i | −0.248424 | − | 1.03701i | ||||
\(319\) | −1.50474 | −0.0842493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.28076 | + | 17.8694i | 0.238929 | + | 0.997374i | ||||
\(322\) | 0.360347 | + | 0.651279i | 0.0200814 | + | 0.0362944i | ||||
\(323\) | 5.91138 | 0.328918 | ||||||||
\(324\) | 5.30441 | − | 7.27071i | 0.294689 | − | 0.403928i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 3.06739i | − | 0.169887i | ||||||
\(327\) | −7.31755 | − | 30.5461i | −0.404662 | − | 1.68920i | ||||
\(328\) | −6.15019 | −0.339587 | ||||||||
\(329\) | 13.4036 | − | 7.41612i | 0.738966 | − | 0.408864i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.93261 | −0.490980 | −0.245490 | − | 0.969399i | \(-0.578949\pi\) | ||||
−0.245490 | + | 0.969399i | \(0.578949\pi\) | |||||||
\(332\) | 1.53511i | 0.0842503i | ||||||||
\(333\) | 8.24763 | + | 16.2264i | 0.451967 | + | 0.889201i | ||||
\(334\) | − | 1.89546i | − | 0.103715i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.38256 | − | 3.09165i | 0.184534 | − | 0.168663i | ||||
\(337\) | − | 34.2176i | − | 1.86395i | −0.362518 | − | 0.931977i | \(-0.618083\pi\) | ||
0.362518 | − | 0.931977i | \(-0.381917\pi\) | |||||||
\(338\) | 2.65128 | 0.144211 | ||||||||
\(339\) | −3.44654 | − | 14.3871i | −0.187191 | − | 0.781401i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.5648 | 2.62993 | ||||||||
\(342\) | 1.09701 | + | 2.15826i | 0.0593195 | + | 0.116705i | ||||
\(343\) | −18.4926 | − | 1.01247i | −0.998505 | − | 0.0546680i | ||||
\(344\) | 6.34872i | 0.342300i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.86007i | − | 0.476320i | ||||||
\(347\) | −11.5260 | −0.618747 | −0.309373 | − | 0.950941i | \(-0.600119\pi\) | ||||
−0.309373 | + | 0.950941i | \(0.600119\pi\) | |||||||
\(348\) | 0.473865 | − | 0.113518i | 0.0254018 | − | 0.00608521i | ||||
\(349\) | 21.8342i | 1.16876i | 0.811482 | + | 0.584378i | \(0.198661\pi\) | ||||
−0.811482 | + | 0.584378i | \(0.801339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.3275 | + | 15.6513i | 0.711369 | + | 0.835403i | ||||
\(352\) | 5.34872i | 0.285088i | ||||||||
\(353\) | 4.84211i | 0.257720i | 0.991663 | + | 0.128860i | \(0.0411317\pi\) | ||||
−0.991663 | + | 0.128860i | \(0.958868\pi\) | |||||||
\(354\) | 1.97877 | + | 8.26010i | 0.105170 | + | 0.439019i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.31652 | −0.228775 | ||||||||
\(357\) | 22.6462 | + | 24.7771i | 1.19856 | + | 1.31134i | ||||
\(358\) | − | 11.3487i | − | 0.599799i | ||||||
\(359\) | − | 30.3063i | − | 1.59950i | −0.600331 | − | 0.799752i | \(-0.704965\pi\) | ||
0.600331 | − | 0.799752i | \(-0.295035\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3487 | 0.965722 | ||||||||
\(362\) | 8.63303i | 0.453742i | ||||||||
\(363\) | 7.10532 | + | 29.6602i | 0.372933 | + | 1.55676i | ||||
\(364\) | 5.06739 | + | 9.15863i | 0.265604 | + | 0.480043i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.3275 | + | 5.34872i | −1.16708 | + | 0.279582i | ||||
\(367\) | 13.9910 | 0.730325 | 0.365162 | − | 0.930944i | \(-0.381013\pi\) | ||||
0.365162 | + | 0.930944i | \(0.381013\pi\) | |||||||
\(368\) | 0.281327 | 0.0146652 | ||||||||
\(369\) | 16.4478 | − | 8.36018i | 0.856239 | − | 0.435213i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0625 | + | 25.4161i | 0.730090 | + | 1.31954i | ||||
\(372\) | −15.2938 | + | 3.66375i | −0.792946 | + | 0.189956i | ||||
\(373\) | 4.24464i | 0.219779i | 0.993944 | + | 0.109890i | \(0.0350497\pi\) | ||||
−0.993944 | + | 0.109890i | \(0.964950\pi\) | |||||||
\(374\) | −39.1791 | −2.02591 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 5.78984i | − | 0.298588i | ||||||
\(377\) | 1.11298i | 0.0573213i | ||||||||
\(378\) | −4.84360 | + | 12.8662i | −0.249128 | + | 0.661767i | ||||
\(379\) | 1.63005 | 0.0837299 | 0.0418650 | − | 0.999123i | \(-0.486670\pi\) | ||||
0.0418650 | + | 0.999123i | \(0.486670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.36879 | + | 0.807019i | −0.172588 | + | 0.0413448i | ||||
\(382\) | − | 7.78607i | − | 0.398370i | ||||||
\(383\) | 16.9994i | 0.868631i | 0.900761 | + | 0.434316i | \(0.143010\pi\) | ||||
−0.900761 | + | 0.434316i | \(0.856990\pi\) | |||||||
\(384\) | −0.403509 | − | 1.68439i | −0.0205915 | − | 0.0859563i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 25.1715i | − | 1.28119i | ||||||
\(387\) | −8.63005 | − | 16.9788i | −0.438690 | − | 0.863079i | ||||
\(388\) | 15.0892 | 0.766037 | ||||||||
\(389\) | 29.4623i | 1.49380i | 0.664938 | + | 0.746898i | \(0.268458\pi\) | ||||
−0.664938 | + | 0.746898i | \(0.731542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.06071i | 0.104214i | ||||||||
\(392\) | −3.71867 | + | 5.93055i | −0.187821 | + | 0.299538i | ||||
\(393\) | 6.67621 | + | 27.8689i | 0.336770 | + | 1.40580i | ||||
\(394\) | 2.52597 | 0.127257 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.27071 | − | 14.3044i | −0.365367 | − | 0.718824i | ||||
\(397\) | −17.8706 | −0.896899 | −0.448449 | − | 0.893808i | \(-0.648024\pi\) | ||||
−0.448449 | + | 0.893808i | \(0.648024\pi\) | |||||||
\(398\) | − | 0.947731i | − | 0.0475054i | ||||||
\(399\) | −2.49502 | − | 2.72979i | −0.124907 | − | 0.136660i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.6762i | 0.633020i | 0.948589 | + | 0.316510i | \(0.102511\pi\) | ||||
−0.948589 | + | 0.316510i | \(0.897489\pi\) | |||||||
\(402\) | 11.3169 | − | 2.71105i | 0.564435 | − | 0.135215i | ||||
\(403\) | − | 35.9209i | − | 1.78935i | ||||||
\(404\) | 5.78984 | 0.288055 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.651279 | + | 0.360347i | −0.0323224 | + | 0.0178837i | ||||
\(407\) | 32.4528 | 1.60863 | ||||||||
\(408\) | 12.3381 | − | 2.95569i | 0.610827 | − | 0.146328i | ||||
\(409\) | − | 5.26425i | − | 0.260300i | −0.991494 | − | 0.130150i | \(-0.958454\pi\) | ||
0.991494 | − | 0.130150i | \(-0.0415459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.99247 | − | 12.4917i | −0.147608 | − | 0.616168i | ||||
\(412\) | 6.95721 | 0.342757 | ||||||||
\(413\) | −6.28133 | − | 11.3526i | −0.309084 | − | 0.558627i | ||||
\(414\) | −0.752370 | + | 0.382418i | −0.0369770 | + | 0.0187948i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.95617 | 0.193967 | ||||||||
\(417\) | 10.7293 | − | 2.57028i | 0.525416 | − | 0.125867i | ||||
\(418\) | 4.31652 | 0.211128 | ||||||||
\(419\) | −13.1148 | −0.640700 | −0.320350 | − | 0.947299i | \(-0.603800\pi\) | ||||
−0.320350 | + | 0.947299i | \(0.603800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.86521 | 0.188379 | 0.0941895 | − | 0.995554i | \(-0.469974\pi\) | ||||
0.0941895 | + | 0.995554i | \(0.469974\pi\) | |||||||
\(422\) | −12.8901 | −0.627482 | ||||||||
\(423\) | 7.87034 | + | 15.4841i | 0.382669 | + | 0.752864i | ||||
\(424\) | 10.9788 | 0.533176 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.67632 | + | 1.35981i | −0.275019 | + | 0.0658829i | ||||
\(427\) | 30.6868 | − | 16.9788i | 1.48504 | − | 0.821660i | ||||
\(428\) | −10.6088 | −0.512797 | ||||||||
\(429\) | 35.6425 | − | 8.53844i | 1.72084 | − | 0.412240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.2389i | − | 0.493189i | −0.969119 | − | 0.246594i | \(-0.920688\pi\) | ||
0.969119 | − | 0.246594i | \(-0.0793115\pi\) | |||||||
\(432\) | 3.36879 | + | 3.95617i | 0.162081 | + | 0.190341i | ||||
\(433\) | 22.7030 | 1.09103 | 0.545517 | − | 0.838099i | \(-0.316333\pi\) | ||||
0.545517 | + | 0.838099i | \(0.316333\pi\) | |||||||
\(434\) | 21.0197 | − | 11.6300i | 1.00898 | − | 0.558260i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.1348 | 0.868499 | ||||||||
\(437\) | − | 0.227036i | − | 0.0108606i | ||||||
\(438\) | 2.01062 | + | 8.39303i | 0.0960709 | + | 0.401035i | ||||
\(439\) | − | 26.4492i | − | 1.26235i | −0.775639 | − | 0.631176i | \(-0.782572\pi\) | ||
0.775639 | − | 0.631176i | \(-0.217428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.88345 | − | 20.9154i | 0.0896883 | − | 0.995970i | ||||
\(442\) | 28.9788i | 1.37838i | ||||||||
\(443\) | −27.8689 | −1.32409 | −0.662046 | − | 0.749463i | \(-0.730312\pi\) | ||||
−0.662046 | + | 0.749463i | \(0.730312\pi\) | |||||||
\(444\) | −10.2199 | + | 2.44825i | −0.485014 | + | 0.116189i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.7296 | −1.12363 | ||||||||
\(447\) | 12.8162 | − | 3.07023i | 0.606187 | − | 0.145217i | ||||
\(448\) | 1.28088 | + | 2.31502i | 0.0605161 | + | 0.109375i | ||||
\(449\) | 9.45858i | 0.446378i | 0.974775 | + | 0.223189i | \(0.0716467\pi\) | ||||
−0.974775 | + | 0.223189i | \(0.928353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 32.8956i | − | 1.54900i | ||||||
\(452\) | 8.54142 | 0.401755 | ||||||||
\(453\) | 1.86827 | + | 7.79882i | 0.0877789 | + | 0.366421i | ||||
\(454\) | 10.4667i | 0.491227i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35934 | + | 0.325639i | −0.0636568 | + | 0.0152495i | ||||
\(457\) | 31.8322i | 1.48905i | 0.667595 | + | 0.744524i | \(0.267324\pi\) | ||||
−0.667595 | + | 0.744524i | \(0.732676\pi\) | |||||||
\(458\) | − | 16.4762i | − | 0.769881i | ||||||
\(459\) | −28.9788 | + | 24.6762i | −1.35261 | + | 1.15179i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.6320 | −0.495179 | −0.247590 | − | 0.968865i | \(-0.579638\pi\) | ||||
−0.247590 | + | 0.968865i | \(0.579638\pi\) | |||||||
\(462\) | 16.5364 | + | 18.0924i | 0.769341 | + | 0.841734i | ||||
\(463\) | − | 12.8322i | − | 0.596364i | −0.954509 | − | 0.298182i | \(-0.903620\pi\) | ||
0.954509 | − | 0.298182i | \(-0.0963803\pi\) | |||||||
\(464\) | 0.281327i | 0.0130603i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.9575 | 1.29511 | ||||||||
\(467\) | − | 20.8716i | − | 0.965824i | −0.875669 | − | 0.482912i | \(-0.839579\pi\) | ||
0.875669 | − | 0.482912i | \(-0.160421\pi\) | |||||||
\(468\) | −10.5802 | + | 5.37777i | −0.489071 | + | 0.248587i | ||||
\(469\) | −15.5539 | + | 8.60584i | −0.718212 | + | 0.397381i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18024 | + | 25.7985i | 0.284770 | + | 1.18873i | ||||
\(472\) | −4.90390 | −0.225720 | ||||||||
\(473\) | −33.9575 | −1.56137 | ||||||||
\(474\) | −1.31548 | − | 5.49128i | −0.0604220 | − | 0.252223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.9574 | + | 9.38242i | −0.777243 | + | 0.430042i | ||||
\(477\) | −29.3612 | + | 14.9238i | −1.34436 | + | 0.683316i | ||||
\(478\) | 17.2601i | 0.789458i | ||||||||
\(479\) | 33.6879 | 1.53924 | 0.769619 | − | 0.638504i | \(-0.220446\pi\) | ||||
0.769619 | + | 0.638504i | \(0.220446\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 24.0036i | − | 1.09447i | ||||||
\(482\) | 19.1935i | 0.874238i | ||||||||
\(483\) | 0.951606 | − | 0.869764i | 0.0432996 | − | 0.0395756i | ||||
\(484\) | −17.6088 | −0.800401 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.3871 | − | 6.00091i | −0.652613 | − | 0.272207i | ||||
\(487\) | 33.3524i | 1.51134i | 0.654951 | + | 0.755671i | \(0.272689\pi\) | ||||
−0.654951 | + | 0.755671i | \(0.727311\pi\) | |||||||
\(488\) | − | 13.2555i | − | 0.600049i | ||||||
\(489\) | −5.16670 | + | 1.23772i | −0.233646 | + | 0.0559717i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.0000i | − | 1.35388i | −0.736038 | − | 0.676941i | \(-0.763305\pi\) | ||
0.736038 | − | 0.676941i | \(-0.236695\pi\) | |||||||
\(492\) | 2.48166 | + | 10.3593i | 0.111882 | + | 0.467035i | ||||
\(493\) | −2.06071 | −0.0928096 | ||||||||
\(494\) | − | 3.19270i | − | 0.143646i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 9.07971i | − | 0.407691i | ||||||
\(497\) | 7.80152 | − | 4.31652i | 0.349946 | − | 0.193622i | ||||
\(498\) | 2.58574 | − | 0.619433i | 0.115870 | − | 0.0277574i | ||||
\(499\) | 19.1810 | 0.858657 | 0.429329 | − | 0.903148i | \(-0.358750\pi\) | ||||
0.429329 | + | 0.903148i | \(0.358750\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.19270 | + | 0.764836i | −0.142639 | + | 0.0341704i | ||||
\(502\) | −21.0271 | −0.938487 | ||||||||
\(503\) | 36.9851i | 1.64909i | 0.565800 | + | 0.824543i | \(0.308568\pi\) | ||||
−0.565800 | + | 0.824543i | \(0.691432\pi\) | |||||||
\(504\) | −6.57244 | − | 4.45006i | −0.292760 | − | 0.198221i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.50474i | 0.0668938i | ||||||||
\(507\) | −1.06982 | − | 4.46580i | −0.0475122 | − | 0.198333i | ||||
\(508\) | − | 2.00000i | − | 0.0887357i | ||||||
\(509\) | −36.0374 | −1.59733 | −0.798665 | − | 0.601776i | \(-0.794460\pi\) | ||||
−0.798665 | + | 0.601776i | \(0.794460\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.38242 | − | 11.5354i | −0.282342 | − | 0.510294i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.19270 | − | 2.71867i | 0.140961 | − | 0.120032i | ||||
\(514\) | − | 14.5881i | − | 0.643455i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.6937 | − | 2.56177i | 0.470766 | − | 0.112776i | ||||
\(517\) | 30.9682 | 1.36198 | ||||||||
\(518\) | 14.0462 | − | 7.77163i | 0.617153 | − | 0.341466i | ||||
\(519\) | −14.9238 | + | 3.57512i | −0.655084 | + | 0.156930i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.65761 | 0.160243 | 0.0801214 | − | 0.996785i | \(-0.474469\pi\) | ||||
0.0801214 | + | 0.996785i | \(0.474469\pi\) | |||||||
\(522\) | −0.382418 | − | 0.752370i | −0.0167380 | − | 0.0329303i | ||||
\(523\) | −2.26321 | −0.0989633 | −0.0494816 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494816 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(524\) | −16.5454 | −0.722788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.91138 | −0.388554 | ||||||||
\(527\) | 66.5084 | 2.89715 | ||||||||
\(528\) | 9.00935 | − | 2.15826i | 0.392082 | − | 0.0939261i | ||||
\(529\) | −22.9209 | −0.996559 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.1148 | − | 6.66605i | 0.569134 | − | 0.289282i | ||||
\(532\) | 1.86827 | − | 1.03370i | 0.0809997 | − | 0.0448164i | ||||
\(533\) | −24.3312 | −1.05390 | ||||||||
\(534\) | 1.74175 | + | 7.27071i | 0.0753731 | + | 0.314634i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.71867i | 0.290202i | ||||||||
\(537\) | −19.1157 | + | 4.57931i | −0.824904 | + | 0.197612i | ||||
\(538\) | 22.3352 | 0.962940 | ||||||||
\(539\) | −31.7209 | − | 19.8901i | −1.36632 | − | 0.856729i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.1502 | 0.651360 | 0.325680 | − | 0.945480i | \(-0.394407\pi\) | ||||
0.325680 | + | 0.945480i | \(0.394407\pi\) | |||||||
\(542\) | − | 7.17684i | − | 0.308272i | ||||||
\(543\) | 14.5414 | − | 3.48351i | 0.624032 | − | 0.149492i | ||||
\(544\) | 7.32496i | 0.314055i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.3820 | − | 12.2311i | 0.572696 | − | 0.523442i | ||||
\(547\) | 2.89014i | 0.123574i | 0.998089 | + | 0.0617868i | \(0.0196799\pi\) | ||||
−0.998089 | + | 0.0617868i | \(0.980320\pi\) | |||||||
\(548\) | 7.41612 | 0.316801 | ||||||||
\(549\) | 18.0187 | + | 35.4500i | 0.769019 | + | 1.51297i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.227036 | 0.00967206 | ||||||||
\(552\) | −0.113518 | − | 0.473865i | −0.00483165 | − | 0.0201690i | ||||
\(553\) | 4.17580 | + | 7.54720i | 0.177573 | + | 0.320940i | ||||
\(554\) | − | 9.32749i | − | 0.396287i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.36982i | 0.270141i | ||||||||
\(557\) | −32.4777 | −1.37613 | −0.688063 | − | 0.725651i | \(-0.741539\pi\) | ||||
−0.688063 | + | 0.725651i | \(0.741539\pi\) | |||||||
\(558\) | 12.3424 | + | 24.2824i | 0.522494 | + | 1.02796i | ||||
\(559\) | 25.1166i | 1.06232i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8091 | + | 65.9931i | 0.667463 | + | 2.78623i | ||||
\(562\) | − | 17.4373i | − | 0.735550i | ||||||
\(563\) | 10.9208i | 0.460256i | 0.973160 | + | 0.230128i | \(0.0739145\pi\) | ||||
−0.973160 | + | 0.230128i | \(0.926086\pi\) | |||||||
\(564\) | −9.75237 | + | 2.33625i | −0.410649 | + | 0.0983741i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.1776 | 0.679996 | ||||||||
\(567\) | 23.6262 | + | 2.96690i | 0.992207 | + | 0.124598i | ||||
\(568\) | − | 3.36995i | − | 0.141400i | ||||||
\(569\) | 4.58388i | 0.192166i | 0.995373 | + | 0.0960832i | \(0.0306315\pi\) | ||||
−0.995373 | + | 0.0960832i | \(0.969369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.82853 | 0.243916 | 0.121958 | − | 0.992535i | \(-0.461083\pi\) | ||||
0.121958 | + | 0.992535i | \(0.461083\pi\) | |||||||
\(572\) | 21.1604i | 0.884763i | ||||||||
\(573\) | −13.1148 | + | 3.14175i | −0.547879 | + | 0.131248i | ||||
\(574\) | −7.87768 | − | 14.2378i | −0.328808 | − | 0.594276i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.67436 | + | 1.35934i | −0.111432 | + | 0.0566390i | ||||
\(577\) | −9.82493 | −0.409017 | −0.204509 | − | 0.978865i | \(-0.565560\pi\) | ||||
−0.204509 | + | 0.978865i | \(0.565560\pi\) | |||||||
\(578\) | −36.6550 | −1.52465 | ||||||||
\(579\) | −42.3987 | + | 10.1569i | −1.76203 | + | 0.422107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.55383 | + | 1.96630i | −0.147438 | + | 0.0815760i | ||||
\(582\) | −6.08862 | − | 25.4161i | −0.252382 | − | 1.05353i | ||||
\(583\) | 58.7224i | 2.43203i | ||||||||
\(584\) | −4.98282 | −0.206191 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 22.5623i | − | 0.932038i | ||||||
\(587\) | 27.3106i | 1.12723i | 0.826037 | + | 0.563615i | \(0.190590\pi\) | ||||
−0.826037 | + | 0.563615i | \(0.809410\pi\) | |||||||
\(588\) | 11.4899 | + | 3.87067i | 0.473836 | + | 0.159624i | ||||
\(589\) | −7.32749 | −0.301924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.01925 | − | 4.25473i | −0.0419264 | − | 0.175016i | ||||
\(592\) | − | 6.06739i | − | 0.249368i | ||||||
\(593\) | − | 26.8788i | − | 1.10378i | −0.833917 | − | 0.551889i | \(-0.813907\pi\) | ||
0.833917 | − | 0.551889i | \(-0.186093\pi\) | |||||||
\(594\) | −21.1604 | + | 18.0187i | −0.868224 | + | 0.739316i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.60882i | 0.311669i | ||||||||
\(597\) | −1.59635 | + | 0.382418i | −0.0653343 | + | 0.0156513i | ||||
\(598\) | 1.11298 | 0.0455130 | ||||||||
\(599\) | − | 6.45858i | − | 0.263890i | −0.991257 | − | 0.131945i | \(-0.957878\pi\) | ||
0.991257 | − | 0.131945i | \(-0.0421223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.31548i | − | 0.0536595i | −0.999640 | − | 0.0268298i | \(-0.991459\pi\) | ||
0.999640 | − | 0.0268298i | \(-0.00854120\pi\) | |||||||
\(602\) | −14.6974 | + | 8.13197i | −0.599023 | + | 0.331435i | ||||
\(603\) | −9.13294 | − | 17.9682i | −0.371922 | − | 0.731720i | ||||
\(604\) | −4.63005 | −0.188394 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.33625 | − | 9.75237i | −0.0949039 | − | 0.396163i | ||||
\(607\) | 26.9651 | 1.09448 | 0.547240 | − | 0.836976i | \(-0.315679\pi\) | ||||
0.547240 | + | 0.836976i | \(0.315679\pi\) | |||||||
\(608\) | − | 0.807019i | − | 0.0327289i | ||||||
\(609\) | 0.869764 | + | 0.951606i | 0.0352446 | + | 0.0385610i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 22.9056i | − | 0.926661i | ||||||
\(612\) | −9.95708 | − | 19.5896i | −0.402491 | − | 0.791862i | ||||
\(613\) | 33.9151i | 1.36982i | 0.728629 | + | 0.684909i | \(0.240158\pi\) | ||||
−0.728629 | + | 0.684909i | \(0.759842\pi\) | |||||||
\(614\) | 19.4057 | 0.783150 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3824 | + | 6.85109i | −0.498902 | + | 0.276038i | ||||
\(617\) | 13.1253 | 0.528405 | 0.264203 | − | 0.964467i | \(-0.414891\pi\) | ||||
0.264203 | + | 0.964467i | \(0.414891\pi\) | |||||||
\(618\) | −2.80730 | − | 11.7187i | −0.112926 | − | 0.471394i | ||||
\(619\) | 38.0907i | 1.53099i | 0.643439 | + | 0.765497i | \(0.277507\pi\) | ||||
−0.643439 | + | 0.765497i | \(0.722493\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.947731 | + | 1.11298i | 0.0380311 | + | 0.0446623i | ||||
\(622\) | −6.73757 | −0.270152 | ||||||||
\(623\) | −5.52896 | − | 9.99284i | −0.221513 | − | 0.400355i | ||||
\(624\) | −1.59635 | − | 6.66375i | −0.0639052 | − | 0.266763i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.3875 | 0.854816 | ||||||||
\(627\) | −1.74175 | − | 7.27071i | −0.0695590 | − | 0.290364i | ||||
\(628\) | −15.3162 | −0.611184 | ||||||||
\(629\) | 44.4434 | 1.77207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0674 | −0.480395 | −0.240198 | − | 0.970724i | \(-0.577212\pi\) | ||||
−0.240198 | + | 0.970724i | \(0.577212\pi\) | |||||||
\(632\) | 3.26010 | 0.129680 | ||||||||
\(633\) | 5.20129 | + | 21.7121i | 0.206733 | + | 0.862977i | ||||
\(634\) | 3.47403 | 0.137971 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.43004 | − | 18.4926i | −0.175662 | − | 0.733278i | ||||
\(637\) | −14.7117 | + | 23.4623i | −0.582899 | + | 0.929609i | ||||
\(638\) | −1.50474 | −0.0595732 | ||||||||
\(639\) | 4.58090 | + | 9.01247i | 0.181218 | + | 0.356528i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4373i | 0.688734i | 0.938835 | + | 0.344367i | \(0.111906\pi\) | ||||
−0.938835 | + | 0.344367i | \(0.888094\pi\) | |||||||
\(642\) | 4.28076 | + | 17.8694i | 0.168948 | + | 0.705250i | ||||
\(643\) | −6.01688 | −0.237283 | −0.118641 | − | 0.992937i | \(-0.537854\pi\) | ||||
−0.118641 | + | 0.992937i | \(0.537854\pi\) | |||||||
\(644\) | 0.360347 | + | 0.651279i | 0.0141997 | + | 0.0256640i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.91138 | 0.232580 | ||||||||
\(647\) | − | 36.7581i | − | 1.44511i | −0.691314 | − | 0.722555i | \(-0.742968\pi\) | ||
0.691314 | − | 0.722555i | \(-0.257032\pi\) | |||||||
\(648\) | 5.30441 | − | 7.27071i | 0.208377 | − | 0.285621i | ||||
\(649\) | − | 26.2296i | − | 1.02960i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.0712 | − | 30.7127i | −1.10020 | − | 1.20372i | ||||
\(652\) | − | 3.06739i | − | 0.120128i | ||||||
\(653\) | 14.8073 | 0.579454 | 0.289727 | − | 0.957109i | \(-0.406435\pi\) | ||||
0.289727 | + | 0.957109i | \(0.406435\pi\) | |||||||
\(654\) | −7.31755 | − | 30.5461i | −0.286139 | − | 1.19445i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.15019 | −0.240125 | ||||||||
\(657\) | 13.3259 | − | 6.77333i | 0.519892 | − | 0.264253i | ||||
\(658\) | 13.4036 | − | 7.41612i | 0.522528 | − | 0.289110i | ||||
\(659\) | − | 11.3487i | − | 0.442083i | −0.975264 | − | 0.221042i | \(-0.929054\pi\) | ||
0.975264 | − | 0.221042i | \(-0.0709457\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 19.7043i | − | 0.766407i | −0.923664 | − | 0.383203i | \(-0.874821\pi\) | ||
0.923664 | − | 0.383203i | \(-0.125179\pi\) | |||||||
\(662\) | −8.93261 | −0.347176 | ||||||||
\(663\) | 48.8116 | − | 11.6932i | 1.89569 | − | 0.454126i | ||||
\(664\) | 1.53511i | 0.0595740i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.24763 | + | 16.2264i | 0.319589 | + | 0.628760i | ||||
\(667\) | 0.0791449i | 0.00306450i | ||||||||
\(668\) | − | 1.89546i | − | 0.0733376i | ||||||
\(669\) | 9.57512 | + | 39.9700i | 0.370196 | + | 1.54533i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.9000 | 2.73707 | ||||||||
\(672\) | 3.38256 | − | 3.09165i | 0.130485 | − | 0.119263i | ||||
\(673\) | − | 21.7861i | − | 0.839791i | −0.907572 | − | 0.419896i | \(-0.862067\pi\) | ||
0.907572 | − | 0.419896i | \(-0.137933\pi\) | |||||||
\(674\) | − | 34.2176i | − | 1.31801i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.65128 | 0.101972 | ||||||||
\(677\) | 15.3706i | 0.590740i | 0.955383 | + | 0.295370i | \(0.0954430\pi\) | ||||
−0.955383 | + | 0.295370i | \(0.904557\pi\) | |||||||
\(678\) | −3.44654 | − | 14.3871i | −0.132364 | − | 0.552534i | ||||
\(679\) | 19.3275 | + | 34.9318i | 0.741721 | + | 1.34056i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6300 | − | 4.22341i | 0.675585 | − | 0.161842i | ||||
\(682\) | 48.5648 | 1.85964 | ||||||||
\(683\) | −22.0462 | −0.843573 | −0.421786 | − | 0.906695i | \(-0.638597\pi\) | ||||
−0.421786 | + | 0.906695i | \(0.638597\pi\) | |||||||
\(684\) | 1.09701 | + | 2.15826i | 0.0419452 | + | 0.0825231i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.4926 | − | 1.01247i | −0.706049 | − | 0.0386561i | ||||
\(687\) | −27.7524 | + | 6.64829i | −1.05882 | + | 0.253648i | ||||
\(688\) | 6.34872i | 0.242043i | ||||||||
\(689\) | 43.4339 | 1.65470 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 31.7209i | − | 1.20672i | −0.797469 | − | 0.603360i | \(-0.793828\pi\) | ||
0.797469 | − | 0.603360i | \(-0.206172\pi\) | |||||||
\(692\) | − | 8.86007i | − | 0.336809i | ||||||
\(693\) | 23.8021 | − | 35.1542i | 0.904168 | − | 1.33540i | ||||
\(694\) | −11.5260 | −0.437520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.473865 | − | 0.113518i | 0.0179618 | − | 0.00430289i | ||||
\(697\) | − | 45.0499i | − | 1.70639i | ||||||
\(698\) | 21.8342i | 0.826435i | ||||||||
\(699\) | −11.2811 | − | 47.0915i | −0.426691 | − | 1.78116i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 49.4316i | − | 1.86700i | −0.358571 | − | 0.933502i | \(-0.616736\pi\) | ||
0.358571 | − | 0.933502i | \(-0.383264\pi\) | |||||||
\(702\) | 13.3275 | + | 15.6513i | 0.503014 | + | 0.590719i | ||||
\(703\) | −4.89650 | −0.184675 | ||||||||
\(704\) | 5.34872i | 0.201588i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.84211i | 0.182235i | ||||||||
\(707\) | 7.41612 | + | 13.4036i | 0.278912 | + | 0.504095i | ||||
\(708\) | 1.97877 | + | 8.26010i | 0.0743667 | + | 0.310433i | ||||
\(709\) | 0.697442 | 0.0261930 | 0.0130965 | − | 0.999914i | \(-0.495831\pi\) | ||||
0.0130965 | + | 0.999914i | \(0.495831\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.71867 | + | 4.43157i | −0.326976 | + | 0.166197i | ||||
\(712\) | −4.31652 | −0.161768 | ||||||||
\(713\) | − | 2.55437i | − | 0.0956618i | ||||||
\(714\) | 22.6462 | + | 24.7771i | 0.847512 | + | 0.927260i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.3487i | − | 0.424122i | ||||||
\(717\) | 29.0728 | − | 6.96461i | 1.08574 | − | 0.260098i | ||||
\(718\) | − | 30.3063i | − | 1.13102i | ||||||
\(719\) | 32.1430 | 1.19873 | 0.599366 | − | 0.800475i | \(-0.295419\pi\) | ||||
0.599366 | + | 0.800475i | \(0.295419\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.91138 | + | 16.1061i | 0.331877 | + | 0.599823i | ||||
\(722\) | 18.3487 | 0.682869 | ||||||||
\(723\) | 32.3293 | − | 7.74474i | 1.20234 | − | 0.288030i | ||||
\(724\) | 8.63303i | 0.320844i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.10532 | + | 29.6602i | 0.263703 | + | 1.10079i | ||||
\(727\) | −27.3970 | −1.01610 | −0.508049 | − | 0.861328i | \(-0.669633\pi\) | ||||
−0.508049 | + | 0.861328i | \(0.669633\pi\) | |||||||
\(728\) | 5.06739 | + | 9.15863i | 0.187810 | + | 0.339441i | ||||
\(729\) | −4.30256 | + | 26.6550i | −0.159354 | + | 0.987222i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.5041 | −1.72002 | ||||||||
\(732\) | −22.3275 | + | 5.34872i | −0.825248 | + | 0.197694i | ||||
\(733\) | 0.0617893 | 0.00228224 | 0.00114112 | − | 0.999999i | \(-0.499637\pi\) | ||||
0.00114112 | + | 0.999999i | \(0.499637\pi\) | |||||||
\(734\) | 13.9910 | 0.516417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.281327 | 0.0103699 | ||||||||
\(737\) | −35.9363 | −1.32373 | ||||||||
\(738\) | 16.4478 | − | 8.36018i | 0.605453 | − | 0.307742i | ||||
\(739\) | 45.0037 | 1.65549 | 0.827744 | − | 0.561106i | \(-0.189624\pi\) | ||||
0.827744 | + | 0.561106i | \(0.189624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.37777 | + | 1.28828i | −0.197557 | + | 0.0473263i | ||||
\(742\) | 14.0625 | + | 25.4161i | 0.516252 | + | 0.933055i | ||||
\(743\) | 38.1655 | 1.40016 | 0.700078 | − | 0.714066i | \(-0.253148\pi\) | ||||
0.700078 | + | 0.714066i | \(0.253148\pi\) | |||||||
\(744\) | −15.2938 | + | 3.66375i | −0.560698 | + | 0.134319i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.24464i | 0.155407i | ||||||||
\(747\) | −2.08674 | − | 4.10545i | −0.0763497 | − | 0.150211i | ||||
\(748\) | −39.1791 | −1.43253 | ||||||||
\(749\) | −13.5887 | − | 24.5597i | −0.496519 | − | 0.897391i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8901 | −1.01773 | −0.508863 | − | 0.860848i | \(-0.669934\pi\) | ||||
−0.508863 | + | 0.860848i | \(0.669934\pi\) | |||||||
\(752\) | − | 5.78984i | − | 0.211134i | ||||||
\(753\) | 8.48464 | + | 35.4180i | 0.309198 | + | 1.29070i | ||||
\(754\) | 1.11298i | 0.0405323i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.84360 | + | 12.8662i | −0.176160 | + | 0.467940i | ||||
\(757\) | 38.5876i | 1.40249i | 0.712921 | + | 0.701245i | \(0.247372\pi\) | ||||
−0.712921 | + | 0.701245i | \(0.752628\pi\) | |||||||
\(758\) | 1.63005 | 0.0592060 | ||||||||
\(759\) | 2.53457 | − | 0.607177i | 0.0919992 | − | 0.0220391i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.9173 | 1.04825 | 0.524125 | − | 0.851641i | \(-0.324392\pi\) | ||||
0.524125 | + | 0.851641i | \(0.324392\pi\) | |||||||
\(762\) | −3.36879 | + | 0.807019i | −0.122038 | + | 0.0292352i | ||||
\(763\) | 23.2286 | + | 41.9825i | 0.840930 | + | 1.51987i | ||||
\(764\) | − | 7.78607i | − | 0.281690i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.9994i | 0.614215i | ||||||||
\(767\) | −19.4007 | −0.700517 | ||||||||
\(768\) | −0.403509 | − | 1.68439i | −0.0145604 | − | 0.0607803i | ||||
\(769\) | − | 30.3191i | − | 1.09333i | −0.837350 | − | 0.546667i | \(-0.815896\pi\) | ||
0.837350 | − | 0.546667i | \(-0.184104\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.5721 | + | 5.88644i | −0.884944 | + | 0.211995i | ||||
\(772\) | − | 25.1715i | − | 0.905941i | ||||||
\(773\) | − | 23.7370i | − | 0.853761i | −0.904308 | − | 0.426881i | \(-0.859612\pi\) | ||
0.904308 | − | 0.426881i | \(-0.140388\pi\) | |||||||
\(774\) | −8.63005 | − | 16.9788i | −0.310201 | − | 0.610289i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.0892 | 0.541670 | ||||||||
\(777\) | −18.7582 | − | 20.5233i | −0.672948 | − | 0.736271i | ||||
\(778\) | 29.4623i | 1.05627i | ||||||||
\(779\) | 4.96332i | 0.177829i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0249 | 0.644983 | ||||||||
\(782\) | 2.06071i | 0.0736908i | ||||||||
\(783\) | −1.11298 | + | 0.947731i | −0.0397746 | + | 0.0338691i | ||||
\(784\) | −3.71867 | + | 5.93055i | −0.132810 | + | 0.211806i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.67621 | + | 27.8689i | 0.238133 | + | 0.994051i | ||||
\(787\) | −30.7560 | −1.09633 | −0.548167 | − | 0.836369i | \(-0.684674\pi\) | ||||
−0.548167 | + | 0.836369i | \(0.684674\pi\) | |||||||
\(788\) | 2.52597 | 0.0899840 | ||||||||
\(789\) | 3.59582 | + | 15.0103i | 0.128015 | + | 0.534379i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9406 | + | 19.7736i | 0.389002 | + | 0.703068i | ||||
\(792\) | −7.27071 | − | 14.3044i | −0.258353 | − | 0.508285i | ||||
\(793\) | − | 52.4410i | − | 1.86224i | ||||||
\(794\) | −17.8706 | −0.634203 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 0.947731i | − | 0.0335914i | ||||||
\(797\) | 14.1958i | 0.502842i | 0.967878 | + | 0.251421i | \(0.0808979\pi\) | ||||
−0.967878 | + | 0.251421i | \(0.919102\pi\) | |||||||
\(798\) | −2.49502 | − | 2.72979i | −0.0883226 | − | 0.0966335i | ||||
\(799\) | 42.4103 | 1.50037 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.5439 | − | 5.86760i | 0.407884 | − | 0.207321i | ||||
\(802\) | 12.6762i | 0.447613i | ||||||||
\(803\) | − | 26.6517i | − | 0.940519i | ||||||
\(804\) | 11.3169 | − | 2.71105i | 0.399116 | − | 0.0956112i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 35.9209i | − | 1.26526i | ||||||
\(807\) | −9.01247 | − | 37.6213i | −0.317254 | − | 1.32433i | ||||
\(808\) | 5.78984 | 0.203686 | ||||||||
\(809\) | − | 39.0404i | − | 1.37259i | −0.727325 | − | 0.686293i | \(-0.759237\pi\) | ||
0.727325 | − | 0.686293i | \(-0.240763\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.9328i | 1.50758i | 0.657118 | + | 0.753788i | \(0.271775\pi\) | ||||
−0.657118 | + | 0.753788i | \(0.728225\pi\) | |||||||
\(812\) | −0.651279 | + | 0.360347i | −0.0228554 | + | 0.0126457i | ||||
\(813\) | −12.0886 | + | 2.89592i | −0.423967 | + | 0.101564i | ||||
\(814\) | 32.4528 | 1.13747 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.3381 | − | 2.95569i | 0.431920 | − | 0.103470i | ||||
\(817\) | 5.12354 | 0.179250 | ||||||||
\(818\) | − | 5.26425i | − | 0.184060i | ||||||
\(819\) | −26.0017 | − | 17.6052i | −0.908573 | − | 0.615175i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.45280i | 0.0856033i | 0.999084 | + | 0.0428016i | \(0.0136283\pi\) | ||||
−0.999084 | + | 0.0428016i | \(0.986372\pi\) | |||||||
\(822\) | −2.99247 | − | 12.4917i | −0.104374 | − | 0.435696i | ||||
\(823\) | − | 30.6300i | − | 1.06770i | −0.845580 | − | 0.533848i | \(-0.820745\pi\) | ||
0.845580 | − | 0.533848i | \(-0.179255\pi\) | |||||||
\(824\) | 6.95721 | 0.242366 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.28133 | − | 11.3526i | −0.218555 | − | 0.395009i | ||||
\(827\) | −37.8265 | −1.31535 | −0.657677 | − | 0.753300i | \(-0.728461\pi\) | ||||
−0.657677 | + | 0.753300i | \(0.728461\pi\) | |||||||
\(828\) | −0.752370 | + | 0.382418i | −0.0261467 | + | 0.0132899i | ||||
\(829\) | − | 18.6605i | − | 0.648105i | −0.946039 | − | 0.324052i | \(-0.894955\pi\) | ||
0.946039 | − | 0.324052i | \(-0.105045\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.7112 | + | 3.76373i | −0.545014 | + | 0.130562i | ||||
\(832\) | 3.95617 | 0.137156 | ||||||||
\(833\) | −43.4410 | − | 27.2391i | −1.50514 | − | 0.943779i | ||||
\(834\) | 10.7293 | − | 2.57028i | 0.371525 | − | 0.0890016i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.31652 | 0.149290 | ||||||||
\(837\) | 35.9209 | − | 30.5876i | 1.24161 | − | 1.05726i | ||||
\(838\) | −13.1148 | −0.453043 | ||||||||
\(839\) | −21.1604 | −0.730540 | −0.365270 | − | 0.930902i | \(-0.619023\pi\) | ||||
−0.365270 | + | 0.930902i | \(0.619023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9209 | 0.997271 | ||||||||
\(842\) | 3.86521 | 0.133204 | ||||||||
\(843\) | −29.3713 | + | 7.03613i | −1.01160 | + | 0.242337i | ||||
\(844\) | −12.8901 | −0.443697 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.87034 | + | 15.4841i | 0.270588 | + | 0.532355i | ||||
\(847\) | −22.5549 | − | 40.7648i | −0.774994 | − | 1.40070i | ||||
\(848\) | 10.9788 | 0.377012 | ||||||||
\(849\) | −6.52782 | − | 27.2495i | −0.224034 | − | 0.935200i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.70692i | − | 0.0585125i | ||||||
\(852\) | −5.67632 | + | 1.35981i | −0.194468 | + | 0.0465862i | ||||
\(853\) | −18.3790 | −0.629287 | −0.314643 | − | 0.949210i | \(-0.601885\pi\) | ||||
−0.314643 | + | 0.949210i | \(0.601885\pi\) | |||||||
\(854\) | 30.6868 | − | 16.9788i | 1.05008 | − | 0.581002i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6088 | −0.362602 | ||||||||
\(857\) | 47.0915i | 1.60861i | 0.594214 | + | 0.804307i | \(0.297463\pi\) | ||||
−0.594214 | + | 0.804307i | \(0.702537\pi\) | |||||||
\(858\) | 35.6425 | − | 8.53844i | 1.21682 | − | 0.291497i | ||||
\(859\) | 30.5313i | 1.04171i | 0.853644 | + | 0.520857i | \(0.174388\pi\) | ||||
−0.853644 | + | 0.520857i | \(0.825612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.8034 | + | 19.0142i | −0.708978 | + | 0.648002i | ||||
\(862\) | − | 10.2389i | − | 0.348737i | ||||||
\(863\) | −32.2696 | −1.09847 | −0.549235 | − | 0.835668i | \(-0.685081\pi\) | ||||
−0.549235 | + | 0.835668i | \(0.685081\pi\) | |||||||
\(864\) | 3.36879 | + | 3.95617i | 0.114608 | + | 0.134592i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.7030 | 0.771478 | ||||||||
\(867\) | 14.7906 | + | 61.7414i | 0.502316 | + | 2.09685i | ||||
\(868\) | 21.0197 | − | 11.6300i | 0.713456 | − | 0.394750i | ||||
\(869\) | 17.4373i | 0.591521i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.5802i | 0.900636i | ||||||||
\(872\) | 18.1348 | 0.614121 | ||||||||
\(873\) | −40.3539 | + | 20.5113i | −1.36577 | + | 0.694202i | ||||
\(874\) | − | 0.227036i | − | 0.00767961i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.01062 | + | 8.39303i | 0.0679324 | + | 0.283574i | ||||
\(877\) | 9.61460i | 0.324662i | 0.986736 | + | 0.162331i | \(0.0519012\pi\) | ||||
−0.986736 | + | 0.162331i | \(0.948099\pi\) | |||||||
\(878\) | − | 26.4492i | − | 0.892618i | ||||||
\(879\) | −38.0037 | + | 9.10408i | −1.28183 | + | 0.307073i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0464 | 0.742762 | 0.371381 | − | 0.928481i | \(-0.378884\pi\) | ||||
0.371381 | + | 0.928481i | \(0.378884\pi\) | |||||||
\(882\) | 1.88345 | − | 20.9154i | 0.0634192 | − | 0.704257i | ||||
\(883\) | 31.5876i | 1.06301i | 0.847056 | + | 0.531503i | \(0.178373\pi\) | ||||
−0.847056 | + | 0.531503i | \(0.821627\pi\) | |||||||
\(884\) | 28.9788i | 0.974661i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.8689 | −0.936274 | ||||||||
\(887\) | − | 17.9472i | − | 0.602607i | −0.953528 | − | 0.301304i | \(-0.902578\pi\) | ||
0.953528 | − | 0.301304i | \(-0.0974218\pi\) | |||||||
\(888\) | −10.2199 | + | 2.44825i | −0.342957 | + | 0.0821579i | ||||
\(889\) | 4.63005 | − | 2.56177i | 0.155287 | − | 0.0859189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.8890 | + | 28.3718i | 1.30283 | + | 0.950491i | ||||
\(892\) | −23.7296 | −0.794526 | ||||||||
\(893\) | −4.67251 | −0.156360 | ||||||||
\(894\) | 12.8162 | − | 3.07023i | 0.428639 | − | 0.102684i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.28088 | + | 2.31502i | 0.0427913 | + | 0.0773395i | ||||
\(897\) | −0.449097 | − | 1.87469i | −0.0149949 | − | 0.0625941i | ||||
\(898\) | 9.45858i | 0.315637i | ||||||||
\(899\) | 2.55437 | 0.0851929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80.4190i | 2.67915i | ||||||||
\(902\) | − | 32.8956i | − | 1.09531i | ||||||
\(903\) | 19.6280 | + | 21.4749i | 0.653179 | + | 0.714641i | ||||
\(904\) | 8.54142 | 0.284084 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.86827 | + | 7.79882i | 0.0620690 | + | 0.259098i | ||||
\(907\) | 39.9942i | 1.32799i | 0.747739 | + | 0.663993i | \(0.231140\pi\) | ||||
−0.747739 | + | 0.663993i | \(0.768860\pi\) | |||||||
\(908\) | 10.4667i | 0.347350i | ||||||||
\(909\) | −15.4841 | + | 7.87034i | −0.513576 | + | 0.261043i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.4740i | − | 0.512677i | −0.966587 | − | 0.256339i | \(-0.917484\pi\) | ||
0.966587 | − | 0.256339i | \(-0.0825163\pi\) | |||||||
\(912\) | −1.35934 | + | 0.325639i | −0.0450121 | + | 0.0107830i | ||||
\(913\) | −8.21090 | −0.271741 | ||||||||
\(914\) | 31.8322i | 1.05292i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 16.4762i | − | 0.544388i | ||||||
\(917\) | −21.1927 | − | 38.3029i | −0.699845 | − | 1.26487i | ||||
\(918\) | −28.9788 | + | 24.6762i | −0.956442 | + | 0.814436i | ||||
\(919\) | −25.5721 | −0.843547 | −0.421773 | − | 0.906701i | \(-0.638592\pi\) | ||||
−0.421773 | + | 0.906701i | \(0.638592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.83038 | − | 32.6868i | −0.258020 | − | 1.07707i | ||||
\(922\) | −10.6320 | −0.350145 | ||||||||
\(923\) | − | 13.3321i | − | 0.438831i | ||||||
\(924\) | 16.5364 | + | 18.0924i | 0.544006 | + | 0.595196i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 12.8322i | − | 0.421693i | ||||||
\(927\) | −18.6061 | + | 9.45719i | −0.611104 | + | 0.310615i | ||||
\(928\) | 0.281327i | 0.00923501i | ||||||||
\(929\) | −27.6092 | −0.905828 | −0.452914 | − | 0.891554i | \(-0.649616\pi\) | ||||
−0.452914 | + | 0.891554i | \(0.649616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.78607 | + | 3.00104i | 0.156857 | + | 0.0983550i | ||||
\(932\) | 27.9575 | 0.915780 | ||||||||
\(933\) | 2.71867 | + | 11.3487i | 0.0890054 | + | 0.371540i | ||||
\(934\) | − | 20.8716i | − | 0.682940i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.5802 | + | 5.37777i | −0.345825 | + | 0.175778i | ||||
\(937\) | −36.8988 | −1.20543 | −0.602716 | − | 0.797956i | \(-0.705915\pi\) | ||||
−0.602716 | + | 0.797956i | \(0.705915\pi\) | |||||||
\(938\) | −15.5539 | + | 8.60584i | −0.507852 | + | 0.280991i | ||||
\(939\) | −8.63005 | − | 36.0249i | −0.281631 | − | 1.17563i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.1245 | −1.47102 | −0.735508 | − | 0.677516i | \(-0.763057\pi\) | ||||
−0.735508 | + | 0.677516i | \(0.763057\pi\) | |||||||
\(942\) | 6.18024 | + | 25.7985i | 0.201363 | + | 0.840562i | ||||
\(943\) | −1.73021 | −0.0563435 | ||||||||
\(944\) | −4.90390 | −0.159608 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.9575 | −1.10405 | ||||||||
\(947\) | 13.3524 | 0.433895 | 0.216948 | − | 0.976183i | \(-0.430390\pi\) | ||||
0.216948 | + | 0.976183i | \(0.430390\pi\) | |||||||
\(948\) | −1.31548 | − | 5.49128i | −0.0427248 | − | 0.178349i | ||||
\(949\) | −19.7129 | −0.639908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.40180 | − | 5.85163i | −0.0454566 | − | 0.189752i | ||||
\(952\) | −16.9574 | + | 9.38242i | −0.549594 | + | 0.304086i | ||||
\(953\) | 52.2483 | 1.69249 | 0.846245 | − | 0.532794i | \(-0.178858\pi\) | ||||
0.846245 | + | 0.532794i | \(0.178858\pi\) | |||||||
\(954\) | −29.3612 | + | 14.9238i | −0.950604 | + | 0.483177i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 17.2601i | 0.558231i | ||||||||
\(957\) | 0.607177 | + | 2.53457i | 0.0196272 | + | 0.0819311i | ||||
\(958\) | 33.6879 | 1.08841 | ||||||||
\(959\) | 9.49918 | + | 17.1685i | 0.306745 | + | 0.554399i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.4410 | −1.65939 | ||||||||
\(962\) | − | 24.0036i | − | 0.773908i | ||||||
\(963\) | 28.3718 | − | 14.4210i | 0.914269 | − | 0.464709i | ||||
\(964\) | 19.1935i | 0.618180i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.951606 | − | 0.869764i | 0.0306174 | − | 0.0279842i | ||||
\(967\) | 3.46228i | 0.111339i | 0.998449 | + | 0.0556697i | \(0.0177294\pi\) | ||||
−0.998449 | + | 0.0556697i | \(0.982271\pi\) | |||||||
\(968\) | −17.6088 | −0.565969 | ||||||||
\(969\) | −2.38529 | − | 9.95708i | −0.0766267 | − | 0.319867i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.3528 | −1.35917 | −0.679584 | − | 0.733598i | \(-0.737839\pi\) | ||||
−0.679584 | + | 0.733598i | \(0.737839\pi\) | |||||||
\(972\) | −14.3871 | − | 6.00091i | −0.461467 | − | 0.192479i | ||||
\(973\) | −14.7463 | + | 8.15901i | −0.472745 | + | 0.261566i | ||||
\(974\) | 33.3524i | 1.06868i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 13.2555i | − | 0.424299i | ||||||
\(977\) | 16.2483 | 0.519831 | 0.259915 | − | 0.965631i | \(-0.416305\pi\) | ||||
0.259915 | + | 0.965631i | \(0.416305\pi\) | |||||||
\(978\) | −5.16670 | + | 1.23772i | −0.165213 | + | 0.0395780i | ||||
\(979\) | − | 23.0878i | − | 0.737891i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.4990 | + | 24.6513i | −1.54845 | + | 0.787055i | ||||
\(982\) | − | 30.0000i | − | 0.957338i | ||||||
\(983\) | − | 33.9149i | − | 1.08172i | −0.841114 | − | 0.540859i | \(-0.818099\pi\) | ||
0.841114 | − | 0.540859i | \(-0.181901\pi\) | |||||||
\(984\) | 2.48166 | + | 10.3593i | 0.0791124 | + | 0.330244i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.06071 | −0.0656263 | ||||||||
\(987\) | −17.9001 | − | 19.5845i | −0.569768 | − | 0.623382i | ||||
\(988\) | − | 3.19270i | − | 0.101573i | ||||||
\(989\) | 1.78607i | 0.0567936i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5971 | −1.32137 | −0.660687 | − | 0.750661i | \(-0.729735\pi\) | ||||
−0.660687 | + | 0.750661i | \(0.729735\pi\) | |||||||
\(992\) | − | 9.07971i | − | 0.288281i | ||||||
\(993\) | 3.60439 | + | 15.0460i | 0.114382 | + | 0.477471i | ||||
\(994\) | 7.80152 | − | 4.31652i | 0.247449 | − | 0.136912i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.58574 | − | 0.619433i | 0.0819322 | − | 0.0196275i | ||||
\(997\) | 9.45719 | 0.299512 | 0.149756 | − | 0.988723i | \(-0.452151\pi\) | ||||
0.149756 | + | 0.988723i | \(0.452151\pi\) | |||||||
\(998\) | 19.1810 | 0.607162 | ||||||||
\(999\) | 24.0036 | − | 20.4398i | 0.759442 | − | 0.646685i |
(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 | 1050.2.d.h.1049.5 | 12 | ||
3.2 | odd | 2 | 1050.2.d.g.1049.6 | 12 | |||
5.2 | odd | 4 | 1050.2.b.d.251.7 | yes | 12 | ||
5.3 | odd | 4 | 1050.2.b.e.251.6 | yes | 12 | ||
5.4 | even | 2 | 1050.2.d.g.1049.8 | 12 | |||
7.6 | odd | 2 | inner | 1050.2.d.h.1049.8 | 12 | ||
15.2 | even | 4 | 1050.2.b.d.251.6 | yes | 12 | ||
15.8 | even | 4 | 1050.2.b.e.251.7 | yes | 12 | ||
15.14 | odd | 2 | inner | 1050.2.d.h.1049.7 | 12 | ||
21.20 | even | 2 | 1050.2.d.g.1049.7 | 12 | |||
35.13 | even | 4 | 1050.2.b.e.251.1 | yes | 12 | ||
35.27 | even | 4 | 1050.2.b.d.251.12 | yes | 12 | ||
35.34 | odd | 2 | 1050.2.d.g.1049.5 | 12 | |||
105.62 | odd | 4 | 1050.2.b.d.251.1 | ✓ | 12 | ||
105.83 | odd | 4 | 1050.2.b.e.251.12 | yes | 12 | ||
105.104 | even | 2 | inner | 1050.2.d.h.1049.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.1 | ✓ | 12 | 105.62 | odd | 4 | ||
1050.2.b.d.251.6 | yes | 12 | 15.2 | even | 4 | ||
1050.2.b.d.251.7 | yes | 12 | 5.2 | odd | 4 | ||
1050.2.b.d.251.12 | yes | 12 | 35.27 | even | 4 | ||
1050.2.b.e.251.1 | yes | 12 | 35.13 | even | 4 | ||
1050.2.b.e.251.6 | yes | 12 | 5.3 | odd | 4 | ||
1050.2.b.e.251.7 | yes | 12 | 15.8 | even | 4 | ||
1050.2.b.e.251.12 | yes | 12 | 105.83 | odd | 4 | ||
1050.2.d.g.1049.5 | 12 | 35.34 | odd | 2 | |||
1050.2.d.g.1049.6 | 12 | 3.2 | odd | 2 | |||
1050.2.d.g.1049.7 | 12 | 21.20 | even | 2 | |||
1050.2.d.g.1049.8 | 12 | 5.4 | even | 2 | |||
1050.2.d.h.1049.5 | 12 | 1.1 | even | 1 | trivial | ||
1050.2.d.h.1049.6 | 12 | 105.104 | even | 2 | inner | ||
1050.2.d.h.1049.7 | 12 | 15.14 | odd | 2 | inner | ||
1050.2.d.h.1049.8 | 12 | 7.6 | odd | 2 | inner |