Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(251,1050)]
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, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.251");
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.b (of order \(2\), degree \(1\), 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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.12 | ||
Root | \(1.68439 - 0.403509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.251 |
Dual form | 1050.2.b.e.251.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.68439 | + | 0.403509i | 0.972485 | + | 0.232966i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.403509 | + | 1.68439i | −0.164732 | + | 0.687651i | ||||
\(7\) | 2.31502 | + | 1.28088i | 0.874997 | + | 0.484129i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.67436 | + | 1.35934i | 0.891454 | + | 0.453112i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.34872i | − | 1.61270i | −0.591439 | − | 0.806350i | \(-0.701440\pi\) | ||
0.591439 | − | 0.806350i | \(-0.298560\pi\) | |||||||
\(12\) | −1.68439 | − | 0.403509i | −0.486242 | − | 0.116483i | ||||
\(13\) | − | 3.95617i | − | 1.09724i | −0.836070 | − | 0.548622i | \(-0.815153\pi\) | ||
0.836070 | − | 0.548622i | \(-0.184847\pi\) | |||||||
\(14\) | −1.28088 | + | 2.31502i | −0.342331 | + | 0.618716i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.32496 | 1.77656 | 0.888281 | − | 0.459300i | \(-0.151900\pi\) | ||||
0.888281 | + | 0.459300i | \(0.151900\pi\) | |||||||
\(18\) | −1.35934 | + | 2.67436i | −0.320399 | + | 0.630353i | ||||
\(19\) | − | 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 | ||||
\(22\) | 5.34872 | 1.14035 | ||||||||
\(23\) | − | 0.281327i | − | 0.0586607i | −0.999570 | − | 0.0293304i | \(-0.990663\pi\) | ||
0.999570 | − | 0.0293304i | \(-0.00933749\pi\) | |||||||
\(24\) | 0.403509 | − | 1.68439i | 0.0823660 | − | 0.343825i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.95617 | 0.775869 | ||||||||
\(27\) | 3.95617 | + | 3.36879i | 0.761365 | + | 0.648323i | ||||
\(28\) | −2.31502 | − | 1.28088i | −0.437498 | − | 0.242064i | ||||
\(29\) | 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 | \(0.303473\pi\) | ||||
−0.578924 | + | 0.815382i | \(0.696527\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.15826 | − | 9.00935i | 0.375705 | − | 1.56833i | ||||
\(34\) | 7.32496i | 1.25622i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.67436 | − | 1.35934i | −0.445727 | − | 0.226556i | ||||
\(37\) | −6.06739 | −0.997473 | −0.498737 | − | 0.866754i | \(-0.666203\pi\) | ||||
−0.498737 | + | 0.866754i | \(0.666203\pi\) | |||||||
\(38\) | 0.807019 | 0.130916 | ||||||||
\(39\) | 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 | \(0.659454\pi\) | |||||||
\(42\) | −3.09165 | + | 3.38256i | −0.477051 | + | 0.521941i | ||||
\(43\) | −6.34872 | −0.968171 | −0.484085 | − | 0.875021i | \(-0.660848\pi\) | ||||
−0.484085 | + | 0.875021i | \(0.660848\pi\) | |||||||
\(44\) | 5.34872i | 0.806350i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.281327 | 0.0414794 | ||||||||
\(47\) | −5.78984 | −0.844535 | −0.422268 | − | 0.906471i | \(-0.638766\pi\) | ||||
−0.422268 | + | 0.906471i | \(0.638766\pi\) | |||||||
\(48\) | 1.68439 | + | 0.403509i | 0.243121 | + | 0.0582415i | ||||
\(49\) | 3.71867 | + | 5.93055i | 0.531239 | + | 0.847222i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.3381 | + | 2.95569i | 1.72768 | + | 0.413879i | ||||
\(52\) | 3.95617i | 0.548622i | ||||||||
\(53\) | − | 10.9788i | − | 1.50805i | −0.656846 | − | 0.754025i | \(-0.728110\pi\) | ||
0.656846 | − | 0.754025i | \(-0.271890\pi\) | |||||||
\(54\) | −3.36879 | + | 3.95617i | −0.458434 | + | 0.538367i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.28088 | − | 2.31502i | 0.171165 | − | 0.309358i | ||||
\(57\) | 0.325639 | − | 1.35934i | 0.0431320 | − | 0.180049i | ||||
\(58\) | −0.281327 | −0.0369401 | ||||||||
\(59\) | 4.90390 | 0.638433 | 0.319217 | − | 0.947682i | \(-0.396580\pi\) | ||||
0.319217 | + | 0.947682i | \(0.396580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.2555i | 1.69719i | 0.529040 | + | 0.848597i | \(0.322552\pi\) | ||||
−0.529040 | + | 0.848597i | \(0.677448\pi\) | |||||||
\(62\) | −9.07971 | −1.15312 | ||||||||
\(63\) | 4.45006 | + | 6.57244i | 0.560654 | + | 0.828050i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.00935 | + | 2.15826i | 1.10897 | + | 0.265663i | ||||
\(67\) | 6.71867 | 0.820817 | 0.410408 | − | 0.911902i | \(-0.365386\pi\) | ||||
0.410408 | + | 0.911902i | \(0.365386\pi\) | |||||||
\(68\) | −7.32496 | −0.888281 | ||||||||
\(69\) | 0.113518 | − | 0.473865i | 0.0136660 | − | 0.0570467i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.36995i | 0.399940i | 0.979802 | + | 0.199970i | \(0.0640844\pi\) | ||||
−0.979802 | + | 0.199970i | \(0.935916\pi\) | |||||||
\(72\) | 1.35934 | − | 2.67436i | 0.160199 | − | 0.315176i | ||||
\(73\) | 4.98282i | 0.583195i | 0.956541 | + | 0.291598i | \(0.0941868\pi\) | ||||
−0.956541 | + | 0.291598i | \(0.905813\pi\) | |||||||
\(74\) | − | 6.06739i | − | 0.705320i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.807019i | 0.0925714i | ||||||||
\(77\) | 6.85109 | − | 12.3824i | 0.780754 | − | 1.41111i | ||||
\(78\) | 6.66375 | + | 1.59635i | 0.754521 | + | 0.180751i | ||||
\(79\) | −3.26010 | −0.366789 | −0.183395 | − | 0.983039i | \(-0.558709\pi\) | ||||
−0.183395 | + | 0.983039i | \(0.558709\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.30441 | + | 7.27071i | 0.589379 | + | 0.807857i | ||||
\(82\) | − | 6.15019i | − | 0.679175i | ||||||
\(83\) | −1.53511 | −0.168501 | −0.0842503 | − | 0.996445i | \(-0.526850\pi\) | ||||
−0.0842503 | + | 0.996445i | \(0.526850\pi\) | |||||||
\(84\) | −3.38256 | − | 3.09165i | −0.369068 | − | 0.337326i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.34872i | − | 0.684600i | ||||||
\(87\) | −0.113518 | + | 0.473865i | −0.0121704 | + | 0.0508037i | ||||
\(88\) | −5.34872 | −0.570176 | ||||||||
\(89\) | 4.31652 | 0.457550 | 0.228775 | − | 0.973479i | \(-0.426528\pi\) | ||||
0.228775 | + | 0.973479i | \(0.426528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.06739 | − | 9.15863i | 0.531207 | − | 0.960085i | ||||
\(92\) | 0.281327i | 0.0293304i | ||||||||
\(93\) | −3.66375 | + | 15.2938i | −0.379913 | + | 1.58589i | ||||
\(94\) | − | 5.78984i | − | 0.597177i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.403509 | + | 1.68439i | −0.0411830 | + | 0.171913i | ||||
\(97\) | 15.0892i | 1.53207i | 0.642796 | + | 0.766037i | \(0.277774\pi\) | ||||
−0.642796 | + | 0.766037i | \(0.722226\pi\) | |||||||
\(98\) | −5.93055 | + | 3.71867i | −0.599076 | + | 0.375643i | ||||
\(99\) | 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 | \(0.406991\pi\) | |||||||
\(102\) | −2.95569 | + | 12.3381i | −0.292657 | + | 1.22165i | ||||
\(103\) | − | 6.95721i | − | 0.685514i | −0.939424 | − | 0.342757i | \(-0.888639\pi\) | ||
0.939424 | − | 0.342757i | \(-0.111361\pi\) | |||||||
\(104\) | −3.95617 | −0.387934 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.9788 | 1.06635 | ||||||||
\(107\) | − | 10.6088i | − | 1.02559i | −0.858510 | − | 0.512797i | \(-0.828610\pi\) | ||
0.858510 | − | 0.512797i | \(-0.171390\pi\) | |||||||
\(108\) | −3.95617 | − | 3.36879i | −0.380683 | − | 0.324162i | ||||
\(109\) | −18.1348 | −1.73700 | −0.868499 | − | 0.495691i | \(-0.834915\pi\) | ||||
−0.868499 | + | 0.495691i | \(0.834915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.2199 | − | 2.44825i | −0.970028 | − | 0.232378i | ||||
\(112\) | 2.31502 | + | 1.28088i | 0.218749 | + | 0.121032i | ||||
\(113\) | − | 8.54142i | − | 0.803510i | −0.915747 | − | 0.401755i | \(-0.868400\pi\) | ||
0.915747 | − | 0.401755i | \(-0.131600\pi\) | |||||||
\(114\) | 1.35934 | + | 0.325639i | 0.127314 | + | 0.0304989i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 0.281327i | − | 0.0261206i | ||||||
\(117\) | 5.37777 | − | 10.5802i | 0.497175 | − | 0.978142i | ||||
\(118\) | 4.90390i | 0.451441i | ||||||||
\(119\) | 16.9574 | + | 9.38242i | 1.55449 | + | 0.860085i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.6088 | −1.60080 | ||||||||
\(122\) | −13.2555 | −1.20010 | ||||||||
\(123\) | −10.3593 | − | 2.48166i | −0.934070 | − | 0.223764i | ||||
\(124\) | − | 9.07971i | − | 0.815382i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −6.57244 | + | 4.45006i | −0.585520 | + | 0.396443i | ||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −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 | \(0.757140\pi\) | |||||||
\(132\) | −2.15826 | + | 9.00935i | −0.187852 | + | 0.784163i | ||||
\(133\) | 1.03370 | − | 1.86827i | 0.0896329 | − | 0.161999i | ||||
\(134\) | 6.71867i | 0.580405i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 7.32496i | − | 0.628110i | ||||||
\(137\) | 7.41612i | 0.633601i | 0.948492 | + | 0.316801i | \(0.102609\pi\) | ||||
−0.948492 | + | 0.316801i | \(0.897391\pi\) | |||||||
\(138\) | 0.473865 | + | 0.113518i | 0.0403381 | + | 0.00966330i | ||||
\(139\) | 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 | ||||
\(142\) | −3.36995 | −0.282800 | ||||||||
\(143\) | −21.1604 | −1.76953 | ||||||||
\(144\) | 2.67436 | + | 1.35934i | 0.222863 | + | 0.113278i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.98282 | −0.412381 | ||||||||
\(147\) | 3.87067 | + | 11.4899i | 0.319248 | + | 0.947671i | ||||
\(148\) | 6.06739 | 0.498737 | ||||||||
\(149\) | 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 | \(0.560328\pi\) | |||||||
\(152\) | −0.807019 | −0.0654578 | ||||||||
\(153\) | 19.5896 | + | 9.95708i | 1.58372 | + | 0.804982i | ||||
\(154\) | 12.3824 | + | 6.85109i | 0.997804 | + | 0.552077i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.59635 | + | 6.66375i | −0.127810 | + | 0.533527i | ||||
\(157\) | − | 15.3162i | − | 1.22237i | −0.791489 | − | 0.611184i | \(-0.790694\pi\) | ||
0.791489 | − | 0.611184i | \(-0.209306\pi\) | |||||||
\(158\) | − | 3.26010i | − | 0.259359i | ||||||
\(159\) | 4.43004 | − | 18.4926i | 0.351325 | − | 1.46656i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.360347 | − | 0.651279i | 0.0283993 | − | 0.0513280i | ||||
\(162\) | −7.27071 | + | 5.30441i | −0.571241 | + | 0.416754i | ||||
\(163\) | 3.06739 | 0.240257 | 0.120128 | − | 0.992758i | \(-0.461669\pi\) | ||||
0.120128 | + | 0.992758i | \(0.461669\pi\) | |||||||
\(164\) | 6.15019 | 0.480249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 1.53511i | − | 0.119148i | ||||||
\(167\) | −1.89546 | −0.146675 | −0.0733376 | − | 0.997307i | \(-0.523365\pi\) | ||||
−0.0733376 | + | 0.997307i | \(0.523365\pi\) | |||||||
\(168\) | 3.09165 | − | 3.38256i | 0.238526 | − | 0.260970i | ||||
\(169\) | −2.65128 | −0.203945 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.09701 | − | 2.15826i | 0.0838904 | − | 0.165046i | ||||
\(172\) | 6.34872 | 0.484085 | ||||||||
\(173\) | 8.86007 | 0.673619 | 0.336809 | − | 0.941573i | \(-0.390652\pi\) | ||||
0.336809 | + | 0.941573i | \(0.390652\pi\) | |||||||
\(174\) | −0.473865 | − | 0.113518i | −0.0359236 | − | 0.00860578i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.34872i | − | 0.403175i | ||||||
\(177\) | 8.26010 | + | 1.97877i | 0.620867 | + | 0.148733i | ||||
\(178\) | 4.31652i | 0.323537i | ||||||||
\(179\) | − | 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 | \(-0.896033\pi\) | ||
0.947132 | − | 0.320844i | \(-0.103967\pi\) | |||||||
\(182\) | 9.15863 | + | 5.06739i | 0.678883 | + | 0.375620i | ||||
\(183\) | −5.34872 | + | 22.3275i | −0.395389 | + | 1.65050i | ||||
\(184\) | −0.281327 | −0.0207397 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.2938 | − | 3.66375i | −1.12140 | − | 0.268639i | ||||
\(187\) | − | 39.1791i | − | 2.86506i | ||||||
\(188\) | 5.78984 | 0.422268 | ||||||||
\(189\) | 4.84360 | + | 12.8662i | 0.352320 | + | 0.935879i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.78607i | 0.563380i | 0.959505 | + | 0.281690i | \(0.0908950\pi\) | ||||
−0.959505 | + | 0.281690i | \(0.909105\pi\) | |||||||
\(192\) | −1.68439 | − | 0.403509i | −0.121561 | − | 0.0291208i | ||||
\(193\) | 25.1715 | 1.81188 | 0.905941 | − | 0.423404i | \(-0.139165\pi\) | ||||
0.905941 | + | 0.423404i | \(0.139165\pi\) | |||||||
\(194\) | −15.0892 | −1.08334 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.71867 | − | 5.93055i | −0.265619 | − | 0.423611i | ||||
\(197\) | 2.52597i | 0.179968i | 0.995943 | + | 0.0899840i | \(0.0286816\pi\) | ||||
−0.995943 | + | 0.0899840i | \(0.971318\pi\) | |||||||
\(198\) | 14.3044 | + | 7.27071i | 1.01657 | + | 0.516707i | ||||
\(199\) | − | 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 | ||||
\(202\) | 5.78984i | 0.407372i | ||||||||
\(203\) | −0.360347 | + | 0.651279i | −0.0252914 | + | 0.0457108i | ||||
\(204\) | −12.3381 | − | 2.95569i | −0.863840 | − | 0.206940i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.95721 | 0.484732 | ||||||||
\(207\) | 0.382418 | − | 0.752370i | 0.0265799 | − | 0.0522933i | ||||
\(208\) | − | 3.95617i | − | 0.274311i | ||||||
\(209\) | −4.31652 | −0.298580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.8901 | −0.887394 | −0.443697 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443697 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(212\) | 10.9788i | 0.754025i | ||||||||
\(213\) | −1.35981 | + | 5.67632i | −0.0931724 | + | 0.388935i | ||||
\(214\) | 10.6088 | 0.725204 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.36879 | − | 3.95617i | 0.229217 | − | 0.269183i | ||||
\(217\) | −11.6300 | + | 21.0197i | −0.789499 | + | 1.42691i | ||||
\(218\) | − | 18.1348i | − | 1.22824i | ||||||
\(219\) | −2.01062 | + | 8.39303i | −0.135865 | + | 0.567149i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.9788i | − | 1.94932i | ||||||
\(222\) | 2.44825 | − | 10.2199i | 0.164316 | − | 0.685913i | ||||
\(223\) | 23.7296i | 1.58905i | 0.607230 | + | 0.794526i | \(0.292281\pi\) | ||||
−0.607230 | + | 0.794526i | \(0.707719\pi\) | |||||||
\(224\) | −1.28088 | + | 2.31502i | −0.0855827 | + | 0.154679i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.54142 | 0.568167 | ||||||||
\(227\) | 10.4667 | 0.694700 | 0.347350 | − | 0.937736i | \(-0.387082\pi\) | ||||
0.347350 | + | 0.937736i | \(0.387082\pi\) | |||||||
\(228\) | −0.325639 | + | 1.35934i | −0.0215660 | + | 0.0900243i | ||||
\(229\) | − | 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 | ||||
\(232\) | 0.281327 | 0.0184700 | ||||||||
\(233\) | − | 27.9575i | − | 1.83156i | −0.401681 | − | 0.915780i | \(-0.631574\pi\) | ||
0.401681 | − | 0.915780i | \(-0.368426\pi\) | |||||||
\(234\) | 10.5802 | + | 5.37777i | 0.691651 | + | 0.351556i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.90390 | −0.319217 | ||||||||
\(237\) | −5.49128 | − | 1.31548i | −0.356697 | − | 0.0854495i | ||||
\(238\) | −9.38242 | + | 16.9574i | −0.608172 | + | 1.09919i | ||||
\(239\) | 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 | \(-0.787870\pi\) | ||
0.786037 | − | 0.618180i | \(-0.212130\pi\) | |||||||
\(242\) | − | 17.6088i | − | 1.13194i | ||||||
\(243\) | 6.00091 | + | 14.3871i | 0.384959 | + | 0.922934i | ||||
\(244\) | − | 13.2555i | − | 0.848597i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.48166 | − | 10.3593i | 0.158225 | − | 0.660487i | ||||
\(247\) | −3.19270 | −0.203147 | ||||||||
\(248\) | 9.07971 | 0.576562 | ||||||||
\(249\) | −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 | \(0.730977\pi\) | |||||||
\(252\) | −4.45006 | − | 6.57244i | −0.280327 | − | 0.414025i | ||||
\(253\) | −1.50474 | −0.0946022 | ||||||||
\(254\) | − | 2.00000i | − | 0.125491i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.5881 | −0.909982 | −0.454991 | − | 0.890496i | \(-0.650358\pi\) | ||||
−0.454991 | + | 0.890496i | \(0.650358\pi\) | |||||||
\(258\) | 2.56177 | − | 10.6937i | 0.159489 | − | 0.665763i | ||||
\(259\) | −14.0462 | − | 7.77163i | −0.872786 | − | 0.482905i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.382418 | + | 0.752370i | −0.0236711 | + | 0.0465705i | ||||
\(262\) | − | 16.5454i | − | 1.02218i | ||||||
\(263\) | 8.91138i | 0.549499i | 0.961516 | + | 0.274749i | \(0.0885949\pi\) | ||||
−0.961516 | + | 0.274749i | \(0.911405\pi\) | |||||||
\(264\) | −9.00935 | − | 2.15826i | −0.554487 | − | 0.132832i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.86827 | + | 1.03370i | 0.114551 | + | 0.0633800i | ||||
\(267\) | 7.27071 | + | 1.74175i | 0.444960 | + | 0.106594i | ||||
\(268\) | −6.71867 | −0.410408 | ||||||||
\(269\) | −22.3352 | −1.36180 | −0.680901 | − | 0.732375i | \(-0.738412\pi\) | ||||
−0.680901 | + | 0.732375i | \(0.738412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.17684i | 0.435962i | 0.975953 | + | 0.217981i | \(0.0699471\pi\) | ||||
−0.975953 | + | 0.217981i | \(0.930053\pi\) | |||||||
\(272\) | 7.32496 | 0.444141 | ||||||||
\(273\) | 12.2311 | − | 13.3820i | 0.740258 | − | 0.809915i | ||||
\(274\) | −7.41612 | −0.448024 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.113518 | + | 0.473865i | −0.00683298 | + | 0.0285233i | ||||
\(277\) | −9.32749 | −0.560435 | −0.280217 | − | 0.959937i | \(-0.590407\pi\) | ||||
−0.280217 | + | 0.959937i | \(0.590407\pi\) | |||||||
\(278\) | −6.36982 | −0.382037 | ||||||||
\(279\) | −12.3424 | + | 24.2824i | −0.738919 | + | 1.45375i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4373i | 1.04022i | 0.854098 | + | 0.520112i | \(0.174110\pi\) | ||||
−0.854098 | + | 0.520112i | \(0.825890\pi\) | |||||||
\(282\) | 2.33625 | − | 9.75237i | 0.139122 | − | 0.580745i | ||||
\(283\) | − | 16.1776i | − | 0.961660i | −0.876814 | − | 0.480830i | \(-0.840335\pi\) | ||
0.876814 | − | 0.480830i | \(-0.159665\pi\) | |||||||
\(284\) | − | 3.36995i | − | 0.199970i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 21.1604i | − | 1.25124i | ||||||
\(287\) | −14.2378 | − | 7.87768i | −0.840433 | − | 0.465005i | ||||
\(288\) | −1.35934 | + | 2.67436i | −0.0800997 | + | 0.157588i | ||||
\(289\) | 36.6550 | 2.15618 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.08862 | + | 25.4161i | −0.356922 | + | 1.48992i | ||||
\(292\) | − | 4.98282i | − | 0.291598i | ||||||
\(293\) | 22.5623 | 1.31810 | 0.659050 | − | 0.752099i | \(-0.270958\pi\) | ||||
0.659050 | + | 0.752099i | \(0.270958\pi\) | |||||||
\(294\) | −11.4899 | + | 3.87067i | −0.670105 | + | 0.225742i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.06739i | 0.352660i | ||||||||
\(297\) | 18.0187 | − | 21.1604i | 1.04555 | − | 1.22785i | ||||
\(298\) | −7.60882 | −0.440767 | ||||||||
\(299\) | −1.11298 | −0.0643652 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.6974 | − | 8.13197i | −0.847146 | − | 0.468719i | ||||
\(302\) | − | 4.63005i | − | 0.266429i | ||||||
\(303\) | 9.75237 | + | 2.33625i | 0.560259 | + | 0.134214i | ||||
\(304\) | − | 0.807019i | − | 0.0462857i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.95708 | + | 19.5896i | −0.569208 | + | 1.11986i | ||||
\(307\) | 19.4057i | 1.10754i | 0.832669 | + | 0.553771i | \(0.186812\pi\) | ||||
−0.832669 | + | 0.553771i | \(0.813188\pi\) | |||||||
\(308\) | −6.85109 | + | 12.3824i | −0.390377 | + | 0.705554i | ||||
\(309\) | 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 | \(0.561182\pi\) | |||||||
\(312\) | −6.66375 | − | 1.59635i | −0.377260 | − | 0.0903756i | ||||
\(313\) | − | 21.3875i | − | 1.20889i | −0.796646 | − | 0.604446i | \(-0.793394\pi\) | ||
0.796646 | − | 0.604446i | \(-0.206606\pi\) | |||||||
\(314\) | 15.3162 | 0.864344 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.26010 | 0.183395 | ||||||||
\(317\) | 3.47403i | 0.195121i | 0.995230 | + | 0.0975605i | \(0.0311039\pi\) | ||||
−0.995230 | + | 0.0975605i | \(0.968896\pi\) | |||||||
\(318\) | 18.4926 | + | 4.43004i | 1.03701 | + | 0.248424i | ||||
\(319\) | 1.50474 | 0.0842493 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.28076 | − | 17.8694i | 0.238929 | − | 0.997374i | ||||
\(322\) | 0.651279 | + | 0.360347i | 0.0362944 | + | 0.0200814i | ||||
\(323\) | − | 5.91138i | − | 0.328918i | ||||||
\(324\) | −5.30441 | − | 7.27071i | −0.294689 | − | 0.403928i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.06739i | 0.169887i | ||||||||
\(327\) | −30.5461 | − | 7.31755i | −1.68920 | − | 0.404662i | ||||
\(328\) | 6.15019i | 0.339587i | ||||||||
\(329\) | −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 | \(0.578949\pi\) | |||||||
\(332\) | 1.53511 | 0.0842503 | ||||||||
\(333\) | −16.2264 | − | 8.24763i | −0.889201 | − | 0.451967i | ||||
\(334\) | − | 1.89546i | − | 0.103715i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.38256 | + | 3.09165i | 0.184534 | + | 0.168663i | ||||
\(337\) | −34.2176 | −1.86395 | −0.931977 | − | 0.362518i | \(-0.881917\pi\) | ||||
−0.931977 | + | 0.362518i | \(0.881917\pi\) | |||||||
\(338\) | − | 2.65128i | − | 0.144211i | ||||||
\(339\) | 3.44654 | − | 14.3871i | 0.187191 | − | 0.781401i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 48.5648 | 2.62993 | ||||||||
\(342\) | 2.15826 | + | 1.09701i | 0.116705 | + | 0.0593195i | ||||
\(343\) | 1.01247 | + | 18.4926i | 0.0546680 | + | 0.998505i | ||||
\(344\) | 6.34872i | 0.342300i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.86007i | 0.476320i | ||||||||
\(347\) | − | 11.5260i | − | 0.618747i | −0.950941 | − | 0.309373i | \(-0.899881\pi\) | ||
0.950941 | − | 0.309373i | \(-0.100119\pi\) | |||||||
\(348\) | 0.113518 | − | 0.473865i | 0.00608521 | − | 0.0254018i | ||||
\(349\) | 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 | ||||
\(352\) | 5.34872 | 0.285088 | ||||||||
\(353\) | −4.84211 | −0.257720 | −0.128860 | − | 0.991663i | \(-0.541132\pi\) | ||||
−0.128860 | + | 0.991663i | \(0.541132\pi\) | |||||||
\(354\) | −1.97877 | + | 8.26010i | −0.105170 | + | 0.439019i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.31652 | −0.228775 | ||||||||
\(357\) | 24.7771 | + | 22.6462i | 1.31134 | + | 1.19856i | ||||
\(358\) | 11.3487 | 0.599799 | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | 8.63303 | 0.453742 | ||||||||
\(363\) | −29.6602 | − | 7.10532i | −1.55676 | − | 0.372933i | ||||
\(364\) | −5.06739 | + | 9.15863i | −0.265604 | + | 0.480043i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −22.3275 | − | 5.34872i | −1.16708 | − | 0.279582i | ||||
\(367\) | 13.9910i | 0.730325i | 0.930944 | + | 0.365162i | \(0.118987\pi\) | ||||
−0.930944 | + | 0.365162i | \(0.881013\pi\) | |||||||
\(368\) | − | 0.281327i | − | 0.0146652i | ||||||
\(369\) | −16.4478 | − | 8.36018i | −0.856239 | − | 0.435213i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.0625 | − | 25.4161i | 0.730090 | − | 1.31954i | ||||
\(372\) | 3.66375 | − | 15.2938i | 0.189956 | − | 0.792946i | ||||
\(373\) | −4.24464 | −0.219779 | −0.109890 | − | 0.993944i | \(-0.535050\pi\) | ||||
−0.109890 | + | 0.993944i | \(0.535050\pi\) | |||||||
\(374\) | 39.1791 | 2.02591 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.78984i | 0.298588i | ||||||||
\(377\) | 1.11298 | 0.0573213 | ||||||||
\(378\) | −12.8662 | + | 4.84360i | −0.661767 | + | 0.249128i | ||||
\(379\) | −1.63005 | −0.0837299 | −0.0418650 | − | 0.999123i | \(-0.513330\pi\) | ||||
−0.0418650 | + | 0.999123i | \(0.513330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.36879 | − | 0.807019i | −0.172588 | − | 0.0413448i | ||||
\(382\) | −7.78607 | −0.398370 | ||||||||
\(383\) | −16.9994 | −0.868631 | −0.434316 | − | 0.900761i | \(-0.643010\pi\) | ||||
−0.434316 | + | 0.900761i | \(0.643010\pi\) | |||||||
\(384\) | 0.403509 | − | 1.68439i | 0.0205915 | − | 0.0859563i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1715i | 1.28119i | ||||||||
\(387\) | −16.9788 | − | 8.63005i | −0.863079 | − | 0.438690i | ||||
\(388\) | − | 15.0892i | − | 0.766037i | ||||||
\(389\) | 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 | ||||||
\(392\) | 5.93055 | − | 3.71867i | 0.299538 | − | 0.187821i | ||||
\(393\) | −27.8689 | − | 6.67621i | −1.40580 | − | 0.336770i | ||||
\(394\) | −2.52597 | −0.127257 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.27071 | + | 14.3044i | −0.365367 | + | 0.718824i | ||||
\(397\) | − | 17.8706i | − | 0.896899i | −0.893808 | − | 0.448449i | \(-0.851976\pi\) | ||
0.893808 | − | 0.448449i | \(-0.148024\pi\) | |||||||
\(398\) | 0.947731 | 0.0475054 | ||||||||
\(399\) | 2.49502 | − | 2.72979i | 0.124907 | − | 0.136660i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.6762i | − | 0.633020i | −0.948589 | − | 0.316510i | \(-0.897489\pi\) | ||
0.948589 | − | 0.316510i | \(-0.102511\pi\) | |||||||
\(402\) | −2.71105 | + | 11.3169i | −0.135215 | + | 0.564435i | ||||
\(403\) | 35.9209 | 1.78935 | ||||||||
\(404\) | −5.78984 | −0.288055 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.651279 | − | 0.360347i | −0.0323224 | − | 0.0178837i | ||||
\(407\) | 32.4528i | 1.60863i | ||||||||
\(408\) | 2.95569 | − | 12.3381i | 0.146328 | − | 0.610827i | ||||
\(409\) | − | 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 | ||||
\(412\) | 6.95721i | 0.342757i | ||||||||
\(413\) | 11.3526 | + | 6.28133i | 0.558627 | + | 0.309084i | ||||
\(414\) | 0.752370 | + | 0.382418i | 0.0369770 | + | 0.0187948i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.95617 | 0.193967 | ||||||||
\(417\) | −2.57028 | + | 10.7293i | −0.125867 | + | 0.525416i | ||||
\(418\) | − | 4.31652i | − | 0.211128i | ||||||
\(419\) | 13.1148 | 0.640700 | 0.320350 | − | 0.947299i | \(-0.396200\pi\) | ||||
0.320350 | + | 0.947299i | \(0.396200\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.86521 | 0.188379 | 0.0941895 | − | 0.995554i | \(-0.469974\pi\) | ||||
0.0941895 | + | 0.995554i | \(0.469974\pi\) | |||||||
\(422\) | − | 12.8901i | − | 0.627482i | ||||||
\(423\) | −15.4841 | − | 7.87034i | −0.752864 | − | 0.382669i | ||||
\(424\) | −10.9788 | −0.533176 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.67632 | − | 1.35981i | −0.275019 | − | 0.0658829i | ||||
\(427\) | −16.9788 | + | 30.6868i | −0.821660 | + | 1.48504i | ||||
\(428\) | 10.6088i | 0.512797i | ||||||||
\(429\) | −35.6425 | − | 8.53844i | −1.72084 | − | 0.412240i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2389i | 0.493189i | 0.969119 | + | 0.246594i | \(0.0793115\pi\) | ||||
−0.969119 | + | 0.246594i | \(0.920688\pi\) | |||||||
\(432\) | 3.95617 | + | 3.36879i | 0.190341 | + | 0.162081i | ||||
\(433\) | − | 22.7030i | − | 1.09103i | −0.838099 | − | 0.545517i | \(-0.816333\pi\) | ||
0.838099 | − | 0.545517i | \(-0.183667\pi\) | |||||||
\(434\) | −21.0197 | − | 11.6300i | −1.00898 | − | 0.558260i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.1348 | 0.868499 | ||||||||
\(437\) | −0.227036 | −0.0108606 | ||||||||
\(438\) | −8.39303 | − | 2.01062i | −0.401035 | − | 0.0960709i | ||||
\(439\) | − | 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 | ||||
\(442\) | 28.9788 | 1.37838 | ||||||||
\(443\) | 27.8689i | 1.32409i | 0.749463 | + | 0.662046i | \(0.230312\pi\) | ||||
−0.749463 | + | 0.662046i | \(0.769688\pi\) | |||||||
\(444\) | 10.2199 | + | 2.44825i | 0.485014 | + | 0.116189i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −23.7296 | −1.12363 | ||||||||
\(447\) | −3.07023 | + | 12.8162i | −0.145217 | + | 0.606187i | ||||
\(448\) | −2.31502 | − | 1.28088i | −0.109375 | − | 0.0605161i | ||||
\(449\) | 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 | ||||||||
\(452\) | 8.54142i | 0.401755i | ||||||||
\(453\) | −7.79882 | − | 1.86827i | −0.366421 | − | 0.0877789i | ||||
\(454\) | 10.4667i | 0.491227i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.35934 | − | 0.325639i | −0.0636568 | − | 0.0152495i | ||||
\(457\) | 31.8322 | 1.48905 | 0.744524 | − | 0.667595i | \(-0.232676\pi\) | ||||
0.744524 | + | 0.667595i | \(0.232676\pi\) | |||||||
\(458\) | 16.4762 | 0.769881 | ||||||||
\(459\) | 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 | \(0.579638\pi\) | |||||||
\(462\) | 18.0924 | + | 16.5364i | 0.841734 | + | 0.769341i | ||||
\(463\) | 12.8322 | 0.596364 | 0.298182 | − | 0.954509i | \(-0.403620\pi\) | ||||
0.298182 | + | 0.954509i | \(0.403620\pi\) | |||||||
\(464\) | 0.281327i | 0.0130603i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.9575 | 1.29511 | ||||||||
\(467\) | −20.8716 | −0.965824 | −0.482912 | − | 0.875669i | \(-0.660421\pi\) | ||||
−0.482912 | + | 0.875669i | \(0.660421\pi\) | |||||||
\(468\) | −5.37777 | + | 10.5802i | −0.248587 | + | 0.489071i | ||||
\(469\) | 15.5539 | + | 8.60584i | 0.718212 | + | 0.397381i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18024 | − | 25.7985i | 0.284770 | − | 1.18873i | ||||
\(472\) | − | 4.90390i | − | 0.225720i | ||||||
\(473\) | 33.9575i | 1.56137i | ||||||||
\(474\) | 1.31548 | − | 5.49128i | 0.0604220 | − | 0.252223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −16.9574 | − | 9.38242i | −0.777243 | − | 0.430042i | ||||
\(477\) | 14.9238 | − | 29.3612i | 0.683316 | − | 1.34436i | ||||
\(478\) | −17.2601 | −0.789458 | ||||||||
\(479\) | −33.6879 | −1.53924 | −0.769619 | − | 0.638504i | \(-0.779554\pi\) | ||||
−0.769619 | + | 0.638504i | \(0.779554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.0036i | 1.09447i | ||||||||
\(482\) | 19.1935 | 0.874238 | ||||||||
\(483\) | 0.869764 | − | 0.951606i | 0.0395756 | − | 0.0432996i | ||||
\(484\) | 17.6088 | 0.800401 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −14.3871 | + | 6.00091i | −0.652613 | + | 0.272207i | ||||
\(487\) | 33.3524 | 1.51134 | 0.755671 | − | 0.654951i | \(-0.227311\pi\) | ||||
0.755671 | + | 0.654951i | \(0.227311\pi\) | |||||||
\(488\) | 13.2555 | 0.600049 | ||||||||
\(489\) | 5.16670 | + | 1.23772i | 0.233646 | + | 0.0559717i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000i | 1.35388i | 0.736038 | + | 0.676941i | \(0.236695\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(492\) | 10.3593 | + | 2.48166i | 0.467035 | + | 0.111882i | ||||
\(493\) | 2.06071i | 0.0928096i | ||||||||
\(494\) | − | 3.19270i | − | 0.143646i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.07971i | 0.407691i | ||||||||
\(497\) | −4.31652 | + | 7.80152i | −0.193622 | + | 0.349946i | ||||
\(498\) | 0.619433 | − | 2.58574i | 0.0277574 | − | 0.115870i | ||||
\(499\) | −19.1810 | −0.858657 | −0.429329 | − | 0.903148i | \(-0.641250\pi\) | ||||
−0.429329 | + | 0.903148i | \(0.641250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.19270 | − | 0.764836i | −0.142639 | − | 0.0341704i | ||||
\(502\) | − | 21.0271i | − | 0.938487i | ||||||
\(503\) | −36.9851 | −1.64909 | −0.824543 | − | 0.565800i | \(-0.808568\pi\) | ||||
−0.824543 | + | 0.565800i | \(0.808568\pi\) | |||||||
\(504\) | 6.57244 | − | 4.45006i | 0.292760 | − | 0.198221i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.50474i | − | 0.0668938i | ||||||
\(507\) | −4.46580 | − | 1.06982i | −0.198333 | − | 0.0475122i | ||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | 36.0374 | 1.59733 | 0.798665 | − | 0.601776i | \(-0.205540\pi\) | ||||
0.798665 | + | 0.601776i | \(0.205540\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.38242 | + | 11.5354i | −0.282342 | + | 0.510294i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.71867 | − | 3.19270i | 0.120032 | − | 0.140961i | ||||
\(514\) | − | 14.5881i | − | 0.643455i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.6937 | + | 2.56177i | 0.470766 | + | 0.112776i | ||||
\(517\) | 30.9682i | 1.36198i | ||||||||
\(518\) | 7.77163 | − | 14.0462i | 0.341466 | − | 0.617153i | ||||
\(519\) | 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 | \(0.474469\pi\) | |||||||
\(522\) | −0.752370 | − | 0.382418i | −0.0329303 | − | 0.0167380i | ||||
\(523\) | 2.26321i | 0.0989633i | 0.998775 | + | 0.0494816i | \(0.0157569\pi\) | ||||
−0.998775 | + | 0.0494816i | \(0.984243\pi\) | |||||||
\(524\) | 16.5454 | 0.722788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.91138 | −0.388554 | ||||||||
\(527\) | 66.5084i | 2.89715i | ||||||||
\(528\) | 2.15826 | − | 9.00935i | 0.0939261 | − | 0.392082i | ||||
\(529\) | 22.9209 | 0.996559 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.1148 | + | 6.66605i | 0.569134 | + | 0.289282i | ||||
\(532\) | −1.03370 | + | 1.86827i | −0.0448164 | + | 0.0809997i | ||||
\(533\) | 24.3312i | 1.05390i | ||||||||
\(534\) | −1.74175 | + | 7.27071i | −0.0753731 | + | 0.314634i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 6.71867i | − | 0.290202i | ||||||
\(537\) | 4.57931 | − | 19.1157i | 0.197612 | − | 0.824904i | ||||
\(538\) | − | 22.3352i | − | 0.962940i | ||||||
\(539\) | 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 | \(0.394407\pi\) | |||||||
\(542\) | −7.17684 | −0.308272 | ||||||||
\(543\) | 3.48351 | − | 14.5414i | 0.149492 | − | 0.624032i | ||||
\(544\) | 7.32496i | 0.314055i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.3820 | + | 12.2311i | 0.572696 | + | 0.523442i | ||||
\(547\) | 2.89014 | 0.123574 | 0.0617868 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617868 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(548\) | − | 7.41612i | − | 0.316801i | ||||||
\(549\) | −18.0187 | + | 35.4500i | −0.769019 | + | 1.51297i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.227036 | 0.00967206 | ||||||||
\(552\) | −0.473865 | − | 0.113518i | −0.0201690 | − | 0.00483165i | ||||
\(553\) | −7.54720 | − | 4.17580i | −0.320940 | − | 0.177573i | ||||
\(554\) | − | 9.32749i | − | 0.396287i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 6.36982i | − | 0.270141i | ||||||
\(557\) | − | 32.4777i | − | 1.37613i | −0.725651 | − | 0.688063i | \(-0.758461\pi\) | ||
0.725651 | − | 0.688063i | \(-0.241539\pi\) | |||||||
\(558\) | −24.2824 | − | 12.3424i | −1.02796 | − | 0.522494i | ||||
\(559\) | 25.1166i | 1.06232i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8091 | − | 65.9931i | 0.667463 | − | 2.78623i | ||||
\(562\) | −17.4373 | −0.735550 | ||||||||
\(563\) | −10.9208 | −0.460256 | −0.230128 | − | 0.973160i | \(-0.573914\pi\) | ||||
−0.230128 | + | 0.973160i | \(0.573914\pi\) | |||||||
\(564\) | 9.75237 | + | 2.33625i | 0.410649 | + | 0.0983741i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.1776 | 0.679996 | ||||||||
\(567\) | 2.96690 | + | 23.6262i | 0.124598 | + | 0.992207i | ||||
\(568\) | 3.36995 | 0.141400 | ||||||||
\(569\) | 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 | \(0.461083\pi\) | |||||||
\(572\) | 21.1604 | 0.884763 | ||||||||
\(573\) | −3.14175 | + | 13.1148i | −0.131248 | + | 0.547879i | ||||
\(574\) | 7.87768 | − | 14.2378i | 0.328808 | − | 0.594276i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.67436 | − | 1.35934i | −0.111432 | − | 0.0566390i | ||||
\(577\) | − | 9.82493i | − | 0.409017i | −0.978865 | − | 0.204509i | \(-0.934440\pi\) | ||
0.978865 | − | 0.204509i | \(-0.0655597\pi\) | |||||||
\(578\) | 36.6550i | 1.52465i | ||||||||
\(579\) | 42.3987 | + | 10.1569i | 1.76203 | + | 0.422107i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.55383 | − | 1.96630i | −0.147438 | − | 0.0815760i | ||||
\(582\) | −25.4161 | − | 6.08862i | −1.05353 | − | 0.252382i | ||||
\(583\) | −58.7224 | −2.43203 | ||||||||
\(584\) | 4.98282 | 0.206191 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.5623i | 0.932038i | ||||||||
\(587\) | 27.3106 | 1.12723 | 0.563615 | − | 0.826037i | \(-0.309410\pi\) | ||||
0.563615 | + | 0.826037i | \(0.309410\pi\) | |||||||
\(588\) | −3.87067 | − | 11.4899i | −0.159624 | − | 0.473836i | ||||
\(589\) | 7.32749 | 0.301924 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.01925 | + | 4.25473i | −0.0419264 | + | 0.175016i | ||||
\(592\) | −6.06739 | −0.249368 | ||||||||
\(593\) | 26.8788 | 1.10378 | 0.551889 | − | 0.833917i | \(-0.313907\pi\) | ||||
0.551889 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(594\) | 21.1604 | + | 18.0187i | 0.868224 | + | 0.739316i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.60882i | − | 0.311669i | ||||||
\(597\) | 0.382418 | − | 1.59635i | 0.0156513 | − | 0.0653343i | ||||
\(598\) | − | 1.11298i | − | 0.0455130i | ||||||
\(599\) | − | 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 | \(0.00854120\pi\) | ||||
−0.999640 | + | 0.0268298i | \(0.991459\pi\) | |||||||
\(602\) | 8.13197 | − | 14.6974i | 0.331435 | − | 0.599023i | ||||
\(603\) | 17.9682 | + | 9.13294i | 0.731720 | + | 0.371922i | ||||
\(604\) | 4.63005 | 0.188394 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.33625 | + | 9.75237i | −0.0949039 | + | 0.396163i | ||||
\(607\) | 26.9651i | 1.09448i | 0.836976 | + | 0.547240i | \(0.184321\pi\) | ||||
−0.836976 | + | 0.547240i | \(0.815679\pi\) | |||||||
\(608\) | 0.807019 | 0.0327289 | ||||||||
\(609\) | −0.869764 | + | 0.951606i | −0.0352446 | + | 0.0385610i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.9056i | 0.926661i | ||||||||
\(612\) | −19.5896 | − | 9.95708i | −0.791862 | − | 0.402491i | ||||
\(613\) | −33.9151 | −1.36982 | −0.684909 | − | 0.728629i | \(-0.740158\pi\) | ||||
−0.684909 | + | 0.728629i | \(0.740158\pi\) | |||||||
\(614\) | −19.4057 | −0.783150 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3824 | − | 6.85109i | −0.498902 | − | 0.276038i | ||||
\(617\) | 13.1253i | 0.528405i | 0.964467 | + | 0.264203i | \(0.0851087\pi\) | ||||
−0.964467 | + | 0.264203i | \(0.914891\pi\) | |||||||
\(618\) | 11.7187 | + | 2.80730i | 0.471394 | + | 0.112926i | ||||
\(619\) | 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 | ||||
\(622\) | − | 6.73757i | − | 0.270152i | ||||||
\(623\) | 9.99284 | + | 5.52896i | 0.400355 | + | 0.221513i | ||||
\(624\) | 1.59635 | − | 6.66375i | 0.0639052 | − | 0.266763i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.3875 | 0.854816 | ||||||||
\(627\) | −7.27071 | − | 1.74175i | −0.290364 | − | 0.0695590i | ||||
\(628\) | 15.3162i | 0.611184i | ||||||||
\(629\) | −44.4434 | −1.77207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.0674 | −0.480395 | −0.240198 | − | 0.970724i | \(-0.577212\pi\) | ||||
−0.240198 | + | 0.970724i | \(0.577212\pi\) | |||||||
\(632\) | 3.26010i | 0.129680i | ||||||||
\(633\) | −21.7121 | − | 5.20129i | −0.862977 | − | 0.206733i | ||||
\(634\) | −3.47403 | −0.137971 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.43004 | + | 18.4926i | −0.175662 | + | 0.733278i | ||||
\(637\) | 23.4623 | − | 14.7117i | 0.929609 | − | 0.582899i | ||||
\(638\) | 1.50474i | 0.0595732i | ||||||||
\(639\) | −4.58090 | + | 9.01247i | −0.181218 | + | 0.356528i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 17.4373i | − | 0.688734i | −0.938835 | − | 0.344367i | \(-0.888094\pi\) | ||
0.938835 | − | 0.344367i | \(-0.111906\pi\) | |||||||
\(642\) | 17.8694 | + | 4.28076i | 0.705250 | + | 0.168948i | ||||
\(643\) | 6.01688i | 0.237283i | 0.992937 | + | 0.118641i | \(0.0378538\pi\) | ||||
−0.992937 | + | 0.118641i | \(0.962146\pi\) | |||||||
\(644\) | −0.360347 | + | 0.651279i | −0.0141997 | + | 0.0256640i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.91138 | 0.232580 | ||||||||
\(647\) | −36.7581 | −1.44511 | −0.722555 | − | 0.691314i | \(-0.757032\pi\) | ||||
−0.722555 | + | 0.691314i | \(0.757032\pi\) | |||||||
\(648\) | 7.27071 | − | 5.30441i | 0.285621 | − | 0.208377i | ||||
\(649\) | − | 26.2296i | − | 1.02960i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.0712 | + | 30.7127i | −1.10020 | + | 1.20372i | ||||
\(652\) | −3.06739 | −0.120128 | ||||||||
\(653\) | − | 14.8073i | − | 0.579454i | −0.957109 | − | 0.289727i | \(-0.906435\pi\) | ||
0.957109 | − | 0.289727i | \(-0.0935646\pi\) | |||||||
\(654\) | 7.31755 | − | 30.5461i | 0.286139 | − | 1.19445i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.15019 | −0.240125 | ||||||||
\(657\) | −6.77333 | + | 13.3259i | −0.264253 | + | 0.519892i | ||||
\(658\) | 7.41612 | − | 13.4036i | 0.289110 | − | 0.522528i | ||||
\(659\) | − | 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 | \(0.125179\pi\) | ||||
−0.923664 | + | 0.383203i | \(0.874821\pi\) | |||||||
\(662\) | − | 8.93261i | − | 0.347176i | ||||||
\(663\) | 11.6932 | − | 48.8116i | 0.454126 | − | 1.89569i | ||||
\(664\) | 1.53511i | 0.0595740i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.24763 | − | 16.2264i | 0.319589 | − | 0.628760i | ||||
\(667\) | 0.0791449 | 0.00306450 | ||||||||
\(668\) | 1.89546 | 0.0733376 | ||||||||
\(669\) | −9.57512 | + | 39.9700i | −0.370196 | + | 1.54533i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 70.9000 | 2.73707 | ||||||||
\(672\) | −3.09165 | + | 3.38256i | −0.119263 | + | 0.130485i | ||||
\(673\) | 21.7861 | 0.839791 | 0.419896 | − | 0.907572i | \(-0.362067\pi\) | ||||
0.419896 | + | 0.907572i | \(0.362067\pi\) | |||||||
\(674\) | − | 34.2176i | − | 1.31801i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.65128 | 0.101972 | ||||||||
\(677\) | 15.3706 | 0.590740 | 0.295370 | − | 0.955383i | \(-0.404557\pi\) | ||||
0.295370 | + | 0.955383i | \(0.404557\pi\) | |||||||
\(678\) | 14.3871 | + | 3.44654i | 0.552534 | + | 0.132364i | ||||
\(679\) | −19.3275 | + | 34.9318i | −0.741721 | + | 1.34056i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6300 | + | 4.22341i | 0.675585 | + | 0.161842i | ||||
\(682\) | 48.5648i | 1.85964i | ||||||||
\(683\) | 22.0462i | 0.843573i | 0.906695 | + | 0.421786i | \(0.138597\pi\) | ||||
−0.906695 | + | 0.421786i | \(0.861403\pi\) | |||||||
\(684\) | −1.09701 | + | 2.15826i | −0.0419452 | + | 0.0825231i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.4926 | + | 1.01247i | −0.706049 | + | 0.0386561i | ||||
\(687\) | 6.64829 | − | 27.7524i | 0.253648 | − | 1.05882i | ||||
\(688\) | −6.34872 | −0.242043 | ||||||||
\(689\) | −43.4339 | −1.65470 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.7209i | 1.20672i | 0.797469 | + | 0.603360i | \(0.206172\pi\) | ||||
−0.797469 | + | 0.603360i | \(0.793828\pi\) | |||||||
\(692\) | −8.86007 | −0.336809 | ||||||||
\(693\) | 35.1542 | − | 23.8021i | 1.33540 | − | 0.904168i | ||||
\(694\) | 11.5260 | 0.437520 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.473865 | + | 0.113518i | 0.0179618 | + | 0.00430289i | ||||
\(697\) | −45.0499 | −1.70639 | ||||||||
\(698\) | −21.8342 | −0.826435 | ||||||||
\(699\) | 11.2811 | − | 47.0915i | 0.426691 | − | 1.78116i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.4316i | 1.86700i | 0.358571 | + | 0.933502i | \(0.383264\pi\) | ||||
−0.358571 | + | 0.933502i | \(0.616736\pi\) | |||||||
\(702\) | 15.6513 | + | 13.3275i | 0.590719 | + | 0.503014i | ||||
\(703\) | 4.89650i | 0.184675i | ||||||||
\(704\) | 5.34872i | 0.201588i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 4.84211i | − | 0.182235i | ||||||
\(707\) | 13.4036 | + | 7.41612i | 0.504095 | + | 0.278912i | ||||
\(708\) | −8.26010 | − | 1.97877i | −0.310433 | − | 0.0743667i | ||||
\(709\) | −0.697442 | −0.0261930 | −0.0130965 | − | 0.999914i | \(-0.504169\pi\) | ||||
−0.0130965 | + | 0.999914i | \(0.504169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.71867 | − | 4.43157i | −0.326976 | − | 0.166197i | ||||
\(712\) | − | 4.31652i | − | 0.161768i | ||||||
\(713\) | 2.55437 | 0.0956618 | ||||||||
\(714\) | −22.6462 | + | 24.7771i | −0.847512 | + | 0.927260i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3487i | 0.424122i | ||||||||
\(717\) | −6.96461 | + | 29.0728i | −0.260098 | + | 1.08574i | ||||
\(718\) | 30.3063 | 1.13102 | ||||||||
\(719\) | −32.1430 | −1.19873 | −0.599366 | − | 0.800475i | \(-0.704581\pi\) | ||||
−0.599366 | + | 0.800475i | \(0.704581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.91138 | − | 16.1061i | 0.331877 | − | 0.599823i | ||||
\(722\) | 18.3487i | 0.682869i | ||||||||
\(723\) | 7.74474 | − | 32.3293i | 0.288030 | − | 1.20234i | ||||
\(724\) | 8.63303i | 0.320844i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.10532 | − | 29.6602i | 0.263703 | − | 1.10079i | ||||
\(727\) | − | 27.3970i | − | 1.01610i | −0.861328 | − | 0.508049i | \(-0.830367\pi\) | ||
0.861328 | − | 0.508049i | \(-0.169633\pi\) | |||||||
\(728\) | −9.15863 | − | 5.06739i | −0.339441 | − | 0.187810i | ||||
\(729\) | 4.30256 | + | 26.6550i | 0.159354 | + | 0.987222i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −46.5041 | −1.72002 | ||||||||
\(732\) | 5.34872 | − | 22.3275i | 0.197694 | − | 0.825248i | ||||
\(733\) | − | 0.0617893i | − | 0.00228224i | −0.999999 | − | 0.00114112i | \(-0.999637\pi\) | ||
0.999999 | − | 0.00114112i | \(-0.000363230\pi\) | |||||||
\(734\) | −13.9910 | −0.516417 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.281327 | 0.0103699 | ||||||||
\(737\) | − | 35.9363i | − | 1.32373i | ||||||
\(738\) | 8.36018 | − | 16.4478i | 0.307742 | − | 0.605453i | ||||
\(739\) | −45.0037 | −1.65549 | −0.827744 | − | 0.561106i | \(-0.810376\pi\) | ||||
−0.827744 | + | 0.561106i | \(0.810376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.37777 | − | 1.28828i | −0.197557 | − | 0.0473263i | ||||
\(742\) | 25.4161 | + | 14.0625i | 0.933055 | + | 0.516252i | ||||
\(743\) | − | 38.1655i | − | 1.40016i | −0.714066 | − | 0.700078i | \(-0.753148\pi\) | ||
0.714066 | − | 0.700078i | \(-0.246852\pi\) | |||||||
\(744\) | 15.2938 | + | 3.66375i | 0.560698 | + | 0.134319i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.24464i | − | 0.155407i | ||||||
\(747\) | −4.10545 | − | 2.08674i | −0.150211 | − | 0.0763497i | ||||
\(748\) | 39.1791i | 1.43253i | ||||||||
\(749\) | 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 | \(0.669934\pi\) | |||||||
\(752\) | −5.78984 | −0.211134 | ||||||||
\(753\) | −35.4180 | − | 8.48464i | −1.29070 | − | 0.309198i | ||||
\(754\) | 1.11298i | 0.0405323i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.84360 | − | 12.8662i | −0.176160 | − | 0.467940i | ||||
\(757\) | 38.5876 | 1.40249 | 0.701245 | − | 0.712921i | \(-0.252628\pi\) | ||||
0.701245 | + | 0.712921i | \(0.252628\pi\) | |||||||
\(758\) | − | 1.63005i | − | 0.0592060i | ||||||
\(759\) | −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 | \(0.324392\pi\) | |||||||
\(762\) | 0.807019 | − | 3.36879i | 0.0292352 | − | 0.122038i | ||||
\(763\) | −41.9825 | − | 23.2286i | −1.51987 | − | 0.840930i | ||||
\(764\) | − | 7.78607i | − | 0.281690i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 16.9994i | − | 0.614215i | ||||||
\(767\) | − | 19.4007i | − | 0.700517i | ||||||
\(768\) | 1.68439 | + | 0.403509i | 0.0607803 | + | 0.0145604i | ||||
\(769\) | − | 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 | ||||
\(772\) | −25.1715 | −0.905941 | ||||||||
\(773\) | 23.7370 | 0.853761 | 0.426881 | − | 0.904308i | \(-0.359612\pi\) | ||||
0.426881 | + | 0.904308i | \(0.359612\pi\) | |||||||
\(774\) | 8.63005 | − | 16.9788i | 0.310201 | − | 0.610289i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.0892 | 0.541670 | ||||||||
\(777\) | −20.5233 | − | 18.7582i | −0.736271 | − | 0.672948i | ||||
\(778\) | −29.4623 | −1.05627 | ||||||||
\(779\) | 4.96332i | 0.177829i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0249 | 0.644983 | ||||||||
\(782\) | 2.06071 | 0.0736908 | ||||||||
\(783\) | −0.947731 | + | 1.11298i | −0.0338691 | + | 0.0397746i | ||||
\(784\) | 3.71867 | + | 5.93055i | 0.132810 | + | 0.211806i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.67621 | − | 27.8689i | 0.238133 | − | 0.994051i | ||||
\(787\) | − | 30.7560i | − | 1.09633i | −0.836369 | − | 0.548167i | \(-0.815326\pi\) | ||
0.836369 | − | 0.548167i | \(-0.184674\pi\) | |||||||
\(788\) | − | 2.52597i | − | 0.0899840i | ||||||
\(789\) | −3.59582 | + | 15.0103i | −0.128015 | + | 0.534379i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.9406 | − | 19.7736i | 0.389002 | − | 0.703068i | ||||
\(792\) | −14.3044 | − | 7.27071i | −0.508285 | − | 0.258353i | ||||
\(793\) | 52.4410 | 1.86224 | ||||||||
\(794\) | 17.8706 | 0.634203 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.947731i | 0.0335914i | ||||||||
\(797\) | 14.1958 | 0.502842 | 0.251421 | − | 0.967878i | \(-0.419102\pi\) | ||||
0.251421 | + | 0.967878i | \(0.419102\pi\) | |||||||
\(798\) | 2.72979 | + | 2.49502i | 0.0966335 | + | 0.0883226i | ||||
\(799\) | −42.4103 | −1.50037 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.5439 | + | 5.86760i | 0.407884 | + | 0.207321i | ||||
\(802\) | 12.6762 | 0.447613 | ||||||||
\(803\) | 26.6517 | 0.940519 | ||||||||
\(804\) | −11.3169 | − | 2.71105i | −0.399116 | − | 0.0956112i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.9209i | 1.26526i | ||||||||
\(807\) | −37.6213 | − | 9.01247i | −1.32433 | − | 0.317254i | ||||
\(808\) | − | 5.78984i | − | 0.203686i | ||||||
\(809\) | − | 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 | \(-0.728225\pi\) | ||
0.657118 | − | 0.753788i | \(-0.271775\pi\) | |||||||
\(812\) | 0.360347 | − | 0.651279i | 0.0126457 | − | 0.0228554i | ||||
\(813\) | −2.89592 | + | 12.0886i | −0.101564 | + | 0.423967i | ||||
\(814\) | −32.4528 | −1.13747 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.3381 | + | 2.95569i | 0.431920 | + | 0.103470i | ||||
\(817\) | 5.12354i | 0.179250i | ||||||||
\(818\) | 5.26425 | 0.184060 | ||||||||
\(819\) | 26.0017 | − | 17.6052i | 0.908573 | − | 0.615175i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.45280i | − | 0.0856033i | −0.999084 | − | 0.0428016i | \(-0.986372\pi\) | ||
0.999084 | − | 0.0428016i | \(-0.0136283\pi\) | |||||||
\(822\) | −12.4917 | − | 2.99247i | −0.435696 | − | 0.104374i | ||||
\(823\) | 30.6300 | 1.06770 | 0.533848 | − | 0.845580i | \(-0.320745\pi\) | ||||
0.533848 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(824\) | −6.95721 | −0.242366 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.28133 | + | 11.3526i | −0.218555 | + | 0.395009i | ||||
\(827\) | − | 37.8265i | − | 1.31535i | −0.753300 | − | 0.657677i | \(-0.771539\pi\) | ||
0.753300 | − | 0.657677i | \(-0.228461\pi\) | |||||||
\(828\) | −0.382418 | + | 0.752370i | −0.0132899 | + | 0.0261467i | ||||
\(829\) | − | 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 | ||||
\(832\) | 3.95617i | 0.137156i | ||||||||
\(833\) | 27.2391 | + | 43.4410i | 0.943779 | + | 1.50514i | ||||
\(834\) | −10.7293 | − | 2.57028i | −0.371525 | − | 0.0890016i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.31652 | 0.149290 | ||||||||
\(837\) | −30.5876 | + | 35.9209i | −1.05726 | + | 1.24161i | ||||
\(838\) | 13.1148i | 0.453043i | ||||||||
\(839\) | 21.1604 | 0.730540 | 0.365270 | − | 0.930902i | \(-0.380977\pi\) | ||||
0.365270 | + | 0.930902i | \(0.380977\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9209 | 0.997271 | ||||||||
\(842\) | 3.86521i | 0.133204i | ||||||||
\(843\) | −7.03613 | + | 29.3713i | −0.242337 | + | 1.01160i | ||||
\(844\) | 12.8901 | 0.443697 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.87034 | − | 15.4841i | 0.270588 | − | 0.532355i | ||||
\(847\) | −40.7648 | − | 22.5549i | −1.40070 | − | 0.774994i | ||||
\(848\) | − | 10.9788i | − | 0.377012i | ||||||
\(849\) | 6.52782 | − | 27.2495i | 0.224034 | − | 0.935200i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.70692i | 0.0585125i | ||||||||
\(852\) | 1.35981 | − | 5.67632i | 0.0465862 | − | 0.194468i | ||||
\(853\) | 18.3790i | 0.629287i | 0.949210 | + | 0.314643i | \(0.101885\pi\) | ||||
−0.949210 | + | 0.314643i | \(0.898115\pi\) | |||||||
\(854\) | −30.6868 | − | 16.9788i | −1.05008 | − | 0.581002i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6088 | −0.362602 | ||||||||
\(857\) | 47.0915 | 1.60861 | 0.804307 | − | 0.594214i | \(-0.202537\pi\) | ||||
0.804307 | + | 0.594214i | \(0.202537\pi\) | |||||||
\(858\) | 8.53844 | − | 35.6425i | 0.291497 | − | 1.21682i | ||||
\(859\) | 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 | ||||
\(862\) | −10.2389 | −0.348737 | ||||||||
\(863\) | 32.2696i | 1.09847i | 0.835668 | + | 0.549235i | \(0.185081\pi\) | ||||
−0.835668 | + | 0.549235i | \(0.814919\pi\) | |||||||
\(864\) | −3.36879 | + | 3.95617i | −0.114608 | + | 0.134592i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 22.7030 | 0.771478 | ||||||||
\(867\) | 61.7414 | + | 14.7906i | 2.09685 | + | 0.502316i | ||||
\(868\) | 11.6300 | − | 21.0197i | 0.394750 | − | 0.713456i | ||||
\(869\) | 17.4373i | 0.591521i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 26.5802i | − | 0.900636i | ||||||
\(872\) | 18.1348i | 0.614121i | ||||||||
\(873\) | −20.5113 | + | 40.3539i | −0.694202 | + | 1.36577i | ||||
\(874\) | − | 0.227036i | − | 0.00767961i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.01062 | − | 8.39303i | 0.0679324 | − | 0.283574i | ||||
\(877\) | 9.61460 | 0.324662 | 0.162331 | − | 0.986736i | \(-0.448099\pi\) | ||||
0.162331 | + | 0.986736i | \(0.448099\pi\) | |||||||
\(878\) | 26.4492 | 0.892618 | ||||||||
\(879\) | 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 | \(0.378884\pi\) | |||||||
\(882\) | −20.9154 | + | 1.88345i | −0.704257 | + | 0.0634192i | ||||
\(883\) | −31.5876 | −1.06301 | −0.531503 | − | 0.847056i | \(-0.678373\pi\) | ||||
−0.531503 | + | 0.847056i | \(0.678373\pi\) | |||||||
\(884\) | 28.9788i | 0.974661i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.8689 | −0.936274 | ||||||||
\(887\) | −17.9472 | −0.602607 | −0.301304 | − | 0.953528i | \(-0.597422\pi\) | ||||
−0.301304 | + | 0.953528i | \(0.597422\pi\) | |||||||
\(888\) | −2.44825 | + | 10.2199i | −0.0821579 | + | 0.342957i | ||||
\(889\) | −4.63005 | − | 2.56177i | −0.155287 | − | 0.0859189i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38.8890 | − | 28.3718i | 1.30283 | − | 0.950491i | ||||
\(892\) | − | 23.7296i | − | 0.794526i | ||||||
\(893\) | 4.67251i | 0.156360i | ||||||||
\(894\) | −12.8162 | − | 3.07023i | −0.428639 | − | 0.102684i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.28088 | − | 2.31502i | 0.0427913 | − | 0.0773395i | ||||
\(897\) | −1.87469 | − | 0.449097i | −0.0625941 | − | 0.0149949i | ||||
\(898\) | −9.45858 | −0.315637 | ||||||||
\(899\) | −2.55437 | −0.0851929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 80.4190i | − | 2.67915i | ||||||
\(902\) | −32.8956 | −1.09531 | ||||||||
\(903\) | −21.4749 | − | 19.6280i | −0.714641 | − | 0.653179i | ||||
\(904\) | −8.54142 | −0.284084 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.86827 | − | 7.79882i | 0.0620690 | − | 0.259098i | ||||
\(907\) | 39.9942 | 1.32799 | 0.663993 | − | 0.747739i | \(-0.268860\pi\) | ||||
0.663993 | + | 0.747739i | \(0.268860\pi\) | |||||||
\(908\) | −10.4667 | −0.347350 | ||||||||
\(909\) | 15.4841 | + | 7.87034i | 0.513576 | + | 0.261043i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.4740i | 0.512677i | 0.966587 | + | 0.256339i | \(0.0825163\pi\) | ||||
−0.966587 | + | 0.256339i | \(0.917484\pi\) | |||||||
\(912\) | 0.325639 | − | 1.35934i | 0.0107830 | − | 0.0450121i | ||||
\(913\) | 8.21090i | 0.271741i | ||||||||
\(914\) | 31.8322i | 1.05292i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.4762i | 0.544388i | ||||||||
\(917\) | −38.3029 | − | 21.1927i | −1.26487 | − | 0.699845i | ||||
\(918\) | −24.6762 | + | 28.9788i | −0.814436 | + | 0.956442i | ||||
\(919\) | 25.5721 | 0.843547 | 0.421773 | − | 0.906701i | \(-0.361408\pi\) | ||||
0.421773 | + | 0.906701i | \(0.361408\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.83038 | + | 32.6868i | −0.258020 | + | 1.07707i | ||||
\(922\) | − | 10.6320i | − | 0.350145i | ||||||
\(923\) | 13.3321 | 0.438831 | ||||||||
\(924\) | −16.5364 | + | 18.0924i | −0.544006 | + | 0.595196i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.8322i | 0.421693i | ||||||||
\(927\) | 9.45719 | − | 18.6061i | 0.310615 | − | 0.611104i | ||||
\(928\) | −0.281327 | −0.00923501 | ||||||||
\(929\) | 27.6092 | 0.905828 | 0.452914 | − | 0.891554i | \(-0.350384\pi\) | ||||
0.452914 | + | 0.891554i | \(0.350384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.78607 | − | 3.00104i | 0.156857 | − | 0.0983550i | ||||
\(932\) | 27.9575i | 0.915780i | ||||||||
\(933\) | −11.3487 | − | 2.71867i | −0.371540 | − | 0.0890054i | ||||
\(934\) | − | 20.8716i | − | 0.682940i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.5802 | − | 5.37777i | −0.345825 | − | 0.175778i | ||||
\(937\) | − | 36.8988i | − | 1.20543i | −0.797956 | − | 0.602716i | \(-0.794085\pi\) | ||
0.797956 | − | 0.602716i | \(-0.205915\pi\) | |||||||
\(938\) | −8.60584 | + | 15.5539i | −0.280991 | + | 0.507852i | ||||
\(939\) | 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 | \(0.763057\pi\) | |||||||
\(942\) | 25.7985 | + | 6.18024i | 0.840562 | + | 0.201363i | ||||
\(943\) | 1.73021i | 0.0563435i | ||||||||
\(944\) | 4.90390 | 0.159608 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.9575 | −1.10405 | ||||||||
\(947\) | 13.3524i | 0.433895i | 0.976183 | + | 0.216948i | \(0.0696101\pi\) | ||||
−0.976183 | + | 0.216948i | \(0.930390\pi\) | |||||||
\(948\) | 5.49128 | + | 1.31548i | 0.178349 | + | 0.0427248i | ||||
\(949\) | 19.7129 | 0.639908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.40180 | + | 5.85163i | −0.0454566 | + | 0.189752i | ||||
\(952\) | 9.38242 | − | 16.9574i | 0.304086 | − | 0.549594i | ||||
\(953\) | − | 52.2483i | − | 1.69249i | −0.532794 | − | 0.846245i | \(-0.678858\pi\) | ||
0.532794 | − | 0.846245i | \(-0.321142\pi\) | |||||||
\(954\) | 29.3612 | + | 14.9238i | 0.950604 | + | 0.483177i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 17.2601i | − | 0.558231i | ||||||
\(957\) | 2.53457 | + | 0.607177i | 0.0819311 | + | 0.0196272i | ||||
\(958\) | − | 33.6879i | − | 1.08841i | ||||||
\(959\) | −9.49918 | + | 17.1685i | −0.306745 | + | 0.554399i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −51.4410 | −1.65939 | ||||||||
\(962\) | −24.0036 | −0.773908 | ||||||||
\(963\) | 14.4210 | − | 28.3718i | 0.464709 | − | 0.914269i | ||||
\(964\) | 19.1935i | 0.618180i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.951606 | + | 0.869764i | 0.0306174 | + | 0.0279842i | ||||
\(967\) | 3.46228 | 0.111339 | 0.0556697 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556697 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(968\) | 17.6088i | 0.565969i | ||||||||
\(969\) | 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 | \(0.737839\pi\) | |||||||
\(972\) | −6.00091 | − | 14.3871i | −0.192479 | − | 0.461467i | ||||
\(973\) | −8.15901 | + | 14.7463i | −0.261566 | + | 0.472745i | ||||
\(974\) | 33.3524i | 1.06868i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2555i | 0.424299i | ||||||||
\(977\) | 16.2483i | 0.519831i | 0.965631 | + | 0.259915i | \(0.0836947\pi\) | ||||
−0.965631 | + | 0.259915i | \(0.916305\pi\) | |||||||
\(978\) | −1.23772 | + | 5.16670i | −0.0395780 | + | 0.165213i | ||||
\(979\) | − | 23.0878i | − | 0.737891i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −48.4990 | − | 24.6513i | −1.54845 | − | 0.787055i | ||||
\(982\) | −30.0000 | −0.957338 | ||||||||
\(983\) | 33.9149 | 1.08172 | 0.540859 | − | 0.841114i | \(-0.318099\pi\) | ||||
0.540859 | + | 0.841114i | \(0.318099\pi\) | |||||||
\(984\) | −2.48166 | + | 10.3593i | −0.0791124 | + | 0.330244i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.06071 | −0.0656263 | ||||||||
\(987\) | −19.5845 | − | 17.9001i | −0.623382 | − | 0.569768i | ||||
\(988\) | 3.19270 | 0.101573 | ||||||||
\(989\) | 1.78607i | 0.0567936i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.5971 | −1.32137 | −0.660687 | − | 0.750661i | \(-0.729735\pi\) | ||||
−0.660687 | + | 0.750661i | \(0.729735\pi\) | |||||||
\(992\) | −9.07971 | −0.288281 | ||||||||
\(993\) | −15.0460 | − | 3.60439i | −0.477471 | − | 0.114382i | ||||
\(994\) | −7.80152 | − | 4.31652i | −0.247449 | − | 0.136912i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.58574 | + | 0.619433i | 0.0819322 | + | 0.0196275i | ||||
\(997\) | 9.45719i | 0.299512i | 0.988723 | + | 0.149756i | \(0.0478488\pi\) | ||||
−0.988723 | + | 0.149756i | \(0.952151\pi\) | |||||||
\(998\) | − | 19.1810i | − | 0.607162i | ||||||
\(999\) | −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.b.e.251.12 | yes | 12 | |
3.2 | odd | 2 | inner | 1050.2.b.e.251.1 | yes | 12 | |
5.2 | odd | 4 | 1050.2.d.g.1049.7 | 12 | |||
5.3 | odd | 4 | 1050.2.d.h.1049.6 | 12 | |||
5.4 | even | 2 | 1050.2.b.d.251.1 | ✓ | 12 | ||
7.6 | odd | 2 | inner | 1050.2.b.e.251.7 | yes | 12 | |
15.2 | even | 4 | 1050.2.d.h.1049.8 | 12 | |||
15.8 | even | 4 | 1050.2.d.g.1049.5 | 12 | |||
15.14 | odd | 2 | 1050.2.b.d.251.12 | yes | 12 | ||
21.20 | even | 2 | inner | 1050.2.b.e.251.6 | yes | 12 | |
35.13 | even | 4 | 1050.2.d.h.1049.7 | 12 | |||
35.27 | even | 4 | 1050.2.d.g.1049.6 | 12 | |||
35.34 | odd | 2 | 1050.2.b.d.251.6 | yes | 12 | ||
105.62 | odd | 4 | 1050.2.d.h.1049.5 | 12 | |||
105.83 | odd | 4 | 1050.2.d.g.1049.8 | 12 | |||
105.104 | even | 2 | 1050.2.b.d.251.7 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.2.b.d.251.1 | ✓ | 12 | 5.4 | even | 2 | ||
1050.2.b.d.251.6 | yes | 12 | 35.34 | odd | 2 | ||
1050.2.b.d.251.7 | yes | 12 | 105.104 | even | 2 | ||
1050.2.b.d.251.12 | yes | 12 | 15.14 | odd | 2 | ||
1050.2.b.e.251.1 | yes | 12 | 3.2 | odd | 2 | inner | |
1050.2.b.e.251.6 | yes | 12 | 21.20 | even | 2 | inner | |
1050.2.b.e.251.7 | yes | 12 | 7.6 | odd | 2 | inner | |
1050.2.b.e.251.12 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.2.d.g.1049.5 | 12 | 15.8 | even | 4 | |||
1050.2.d.g.1049.6 | 12 | 35.27 | even | 4 | |||
1050.2.d.g.1049.7 | 12 | 5.2 | odd | 4 | |||
1050.2.d.g.1049.8 | 12 | 105.83 | odd | 4 | |||
1050.2.d.h.1049.5 | 12 | 105.62 | odd | 4 | |||
1050.2.d.h.1049.6 | 12 | 5.3 | odd | 4 | |||
1050.2.d.h.1049.7 | 12 | 35.13 | even | 4 | |||
1050.2.d.h.1049.8 | 12 | 15.2 | even | 4 |