Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [840,2,Mod(209,840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("840.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 840.k (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: | \(6.70743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.22 | ||
Character | \(\chi\) | \(=\) | 840.209 |
Dual form | 840.2.k.b.209.21 |
$q$-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 \(\left(\mathbb{Z}/840\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(281\) | \(337\) | \(421\) | \(631\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.64602 | + | 0.539084i | 0.950331 | + | 0.311240i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30213 | − | 1.81782i | −0.582329 | − | 0.812954i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.19974 | − | 1.47008i | 0.831424 | − | 0.555638i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.41878 | + | 1.77469i | 0.806259 | + | 0.591562i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.958461i | − | 0.288987i | −0.989506 | − | 0.144493i | \(-0.953845\pi\) | ||
0.989506 | − | 0.144493i | \(-0.0461553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.157315 | −0.0436315 | −0.0218157 | − | 0.999762i | \(-0.506945\pi\) | ||||
−0.0218157 | + | 0.999762i | \(0.506945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.16337 | − | 3.69413i | −0.300381 | − | 0.953819i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.51337i | − | 0.609581i | −0.952419 | − | 0.304791i | \(-0.901414\pi\) | ||
0.952419 | − | 0.304791i | \(-0.0985865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.98260i | − | 0.454840i | −0.973797 | − | 0.227420i | \(-0.926971\pi\) | ||
0.973797 | − | 0.227420i | \(-0.0730290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.41332 | − | 1.23394i | 0.963065 | − | 0.269268i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67280 | 0.557317 | 0.278658 | − | 0.960390i | \(-0.410110\pi\) | ||||
0.278658 | + | 0.960390i | \(0.410110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.60893 | + | 4.73406i | −0.321787 | + | 0.946812i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.02466 | + | 4.22510i | 0.582095 | + | 0.813121i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.25028i | − | 0.232171i | −0.993239 | − | 0.116086i | \(-0.962965\pi\) | ||
0.993239 | − | 0.116086i | \(-0.0370347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.66804i | − | 1.55683i | −0.627753 | − | 0.778413i | \(-0.716025\pi\) | ||
0.627753 | − | 0.778413i | \(-0.283975\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.516691 | − | 1.57765i | 0.0899443 | − | 0.274633i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.53668 | − | 2.08450i | −0.935870 | − | 0.352345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.29909i | 0.377969i | 0.981980 | + | 0.188984i | \(0.0605195\pi\) | ||||
−0.981980 | + | 0.188984i | \(0.939480\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.258945 | − | 0.0848062i | −0.0414643 | − | 0.0135799i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.74507 | 0.741056 | 0.370528 | − | 0.928821i | \(-0.379177\pi\) | ||||
0.370528 | + | 0.928821i | \(0.379177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.58424i | 1.00409i | 0.864842 | + | 0.502043i | \(0.167418\pi\) | ||||
−0.864842 | + | 0.502043i | \(0.832582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0765078 | − | 6.70777i | 0.0114051 | − | 0.999935i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 5.60727i | − | 0.817904i | −0.912556 | − | 0.408952i | \(-0.865894\pi\) | ||
0.912556 | − | 0.408952i | \(-0.134106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.67772 | − | 6.46760i | 0.382532 | − | 0.923942i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.35492 | − | 4.13706i | 0.189726 | − | 0.579304i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.59262 | 1.18029 | 0.590144 | − | 0.807298i | \(-0.299071\pi\) | ||||
0.590144 | + | 0.807298i | \(0.299071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.74231 | + | 1.24804i | −0.234933 | + | 0.168285i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.06879 | − | 3.26340i | 0.141564 | − | 0.432248i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4488 | −1.36032 | −0.680159 | − | 0.733065i | \(-0.738089\pi\) | ||||
−0.680159 | + | 0.733065i | \(0.738089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.27757i | − | 0.547686i | −0.961774 | − | 0.273843i | \(-0.911705\pi\) | ||
0.961774 | − | 0.273843i | \(-0.0882949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.92962 | + | 0.348054i | 0.999038 | + | 0.0438506i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.204845 | + | 0.285971i | 0.0254078 | + | 0.0354704i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.8282i | 1.68938i | 0.535255 | + | 0.844690i | \(0.320215\pi\) | ||||
−0.535255 | + | 0.844690i | \(0.679785\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.39948 | + | 1.44086i | 0.529635 | + | 0.173459i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.75994i | 1.15829i | 0.815224 | + | 0.579146i | \(0.196614\pi\) | ||||
−0.815224 | + | 0.579146i | \(0.803386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43474 | 0.519047 | 0.259524 | − | 0.965737i | \(-0.416434\pi\) | ||||
0.259524 | + | 0.965737i | \(0.416434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.20040 | + | 6.92502i | −0.600490 | + | 0.799632i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.40902 | − | 2.10837i | −0.160572 | − | 0.240271i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.517890 | 0.0582671 | 0.0291336 | − | 0.999576i | \(-0.490725\pi\) | ||||
0.0291336 | + | 0.999576i | \(0.490725\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70097 | + | 8.58515i | 0.300108 | + | 0.953905i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18.1293i | 1.98995i | 0.100105 | + | 0.994977i | \(0.468082\pi\) | ||||
−0.100105 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.56885 | + | 3.27272i | −0.495561 | + | 0.354977i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.674006 | − | 2.05799i | 0.0722611 | − | 0.220640i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.954423 | −0.101169 | −0.0505843 | − | 0.998720i | \(-0.516108\pi\) | ||||
−0.0505843 | + | 0.998720i | \(0.516108\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.346053 | + | 0.231267i | −0.0362762 | + | 0.0242433i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.67280 | − | 14.2678i | 0.484546 | − | 1.47950i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.60401 | + | 2.58160i | −0.369764 | + | 0.264866i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0907 | −1.43070 | −0.715348 | − | 0.698768i | \(-0.753732\pi\) | ||||
−0.715348 | + | 0.698768i | \(0.753732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.70097 | − | 2.31830i | 0.170954 | − | 0.232998i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.87371 | 0.882967 | 0.441484 | − | 0.897269i | \(-0.354452\pi\) | ||||
0.441484 | + | 0.897269i | \(0.354452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.26288 | −0.222968 | −0.111484 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111484 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.98978 | − | 6.41587i | −0.779723 | − | 0.626125i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.2677 | −1.57266 | −0.786331 | − | 0.617806i | \(-0.788022\pi\) | ||||
−0.786331 | + | 0.617806i | \(0.788022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4109 | −1.28453 | −0.642264 | − | 0.766483i | \(-0.722005\pi\) | ||||
−0.642264 | + | 0.766483i | \(0.722005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.23940 | + | 3.78436i | −0.117639 | + | 0.359195i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.0284 | 1.41375 | 0.706875 | − | 0.707339i | \(-0.250104\pi\) | ||||
0.706875 | + | 0.707339i | \(0.250104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.48032 | − | 4.85866i | −0.324541 | − | 0.453073i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.380511 | − | 0.279186i | −0.0351783 | − | 0.0258107i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.69485 | − | 5.52876i | −0.338707 | − | 0.506820i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0814 | 0.916487 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.81049 | + | 2.55799i | 0.704248 | + | 0.230646i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.7007 | − | 3.23959i | 0.957100 | − | 0.289758i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.39261i | 0.301046i | 0.988607 | + | 0.150523i | \(0.0480957\pi\) | ||||
−0.988607 | + | 0.150523i | \(0.951904\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.54945 | + | 10.8378i | −0.312512 | + | 0.954215i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.388687 | 0.0339598 | 0.0169799 | − | 0.999856i | \(-0.494595\pi\) | ||||
0.0169799 | + | 0.999856i | \(0.494595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91458 | − | 4.36121i | −0.252726 | − | 0.378165i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.74198 | − | 10.9999i | 0.322059 | − | 0.946720i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.32628 | −0.796798 | −0.398399 | − | 0.917212i | \(-0.630434\pi\) | ||||
−0.398399 | + | 0.917212i | \(0.630434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5321i | 1.23260i | 0.787511 | + | 0.616300i | \(0.211369\pi\) | ||||
−0.787511 | + | 0.616300i | \(0.788631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.02279 | − | 9.22969i | 0.254565 | − | 0.777280i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.150781i | 0.0126089i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.27279 | + | 1.62802i | −0.188745 | + | 0.135200i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.89417 | − | 9.20229i | 0.651100 | − | 0.758992i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.9872i | − | 0.900110i | −0.893001 | − | 0.450055i | \(-0.851404\pi\) | ||
0.893001 | − | 0.450055i | \(-0.148596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5486 | −1.67222 | −0.836109 | − | 0.548563i | \(-0.815175\pi\) | ||||
−0.836109 | + | 0.548563i | \(0.815175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.46044 | − | 6.07928i | 0.360605 | − | 0.491480i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.7569 | + | 11.2869i | −1.26563 | + | 0.906584i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.876066 | −0.0699177 | −0.0349588 | − | 0.999389i | \(-0.511130\pi\) | ||||
−0.0349588 | + | 0.999389i | \(0.511130\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.1436 | + | 4.63214i | 1.12166 | + | 0.367353i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.87946 | − | 3.92923i | 0.463366 | − | 0.309667i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.9513i | − | 1.71936i | −0.510833 | − | 0.859680i | \(-0.670663\pi\) | ||
0.510833 | − | 0.859680i | \(-0.329337\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.54068 | + | 1.11505i | −0.275641 | + | 0.0868063i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.7288i | − | 0.907602i | −0.891103 | − | 0.453801i | \(-0.850068\pi\) | ||
0.891103 | − | 0.453801i | \(-0.149932\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9753 | −0.998096 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.51850 | − | 4.79547i | 0.269066 | − | 0.366719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.8779i | 1.43526i | 0.696423 | + | 0.717632i | \(0.254774\pi\) | ||||
−0.696423 | + | 0.717632i | \(0.745226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.42021 | + | 12.7790i | 0.258544 | + | 0.966000i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.1989 | − | 5.63278i | −1.29275 | − | 0.423385i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.3237i | − | 0.921118i | −0.887629 | − | 0.460559i | \(-0.847649\pi\) | ||
0.887629 | − | 0.460559i | \(-0.152351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2694i | 1.35795i | 0.734160 | + | 0.678976i | \(0.237576\pi\) | ||||
−0.734160 | + | 0.678976i | \(0.762424\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.30597 | − | 7.04097i | 0.170462 | − | 0.520484i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.17934 | − | 2.99371i | 0.307271 | − | 0.220102i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.40897 | −0.176161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.8647 | + | 4.84763i | 0.935769 | + | 0.352613i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4184i | 0.898565i | 0.893390 | + | 0.449283i | \(0.148320\pi\) | ||||
−0.893390 | + | 0.449283i | \(0.851680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0849i | 1.44574i | 0.690983 | + | 0.722871i | \(0.257178\pi\) | ||||
−0.690983 | + | 0.722871i | \(0.742822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.183016 | + | 0.581143i | 0.0131061 | + | 0.0416165i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5756 | 0.967223 | 0.483612 | − | 0.875283i | \(-0.339325\pi\) | ||||
0.483612 | + | 0.875283i | \(0.339325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.36196i | 0.380099i | 0.981774 | + | 0.190050i | \(0.0608649\pi\) | ||||
−0.981774 | + | 0.190050i | \(0.939135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.45455 | + | 22.7615i | −0.525803 | + | 1.60547i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.83802 | − | 2.75030i | −0.129003 | − | 0.193033i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.17868 | − | 8.62568i | −0.431538 | − | 0.602444i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.46490 | + | 4.74338i | 0.449342 | + | 0.329688i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.90025 | −0.131443 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4010 | −1.19794 | −0.598968 | − | 0.800773i | \(-0.704422\pi\) | ||||
−0.598968 | + | 0.800773i | \(0.704422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.26143 | + | 16.0651i | −0.360507 | + | 1.10076i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.9690 | − | 8.57351i | 0.816276 | − | 0.584708i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.7427 | − | 19.0674i | −0.865032 | − | 1.29438i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.29968 | + | 2.39070i | 0.493267 | + | 0.161548i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.395392i | 0.0265969i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.7794 | −1.05666 | −0.528332 | − | 0.849038i | \(-0.677182\pi\) | ||||
−0.528332 | + | 0.849038i | \(0.677182\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.2931 | + | 8.59528i | −0.819542 | + | 0.573019i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.69704i | 0.245381i | 0.992445 | + | 0.122690i | \(0.0391522\pi\) | ||||
−0.992445 | + | 0.122690i | \(0.960848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.9567i | − | 0.922286i | −0.887326 | − | 0.461143i | \(-0.847440\pi\) | ||
0.887326 | − | 0.461143i | \(-0.152560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.18269 | − | 4.23000i | −0.0778150 | − | 0.278313i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.7836 | 1.09953 | 0.549767 | − | 0.835318i | \(-0.314717\pi\) | ||||
0.549767 | + | 0.835318i | \(0.314717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1930 | + | 7.30137i | −0.664918 | + | 0.476289i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.852458 | + | 0.279186i | 0.0553731 | + | 0.0181351i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.2421i | 1.17998i | 0.807410 | + | 0.589991i | \(0.200869\pi\) | ||||
−0.807410 | + | 0.589991i | \(0.799131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.36648i | 0.345685i | 0.984949 | + | 0.172843i | \(0.0552952\pi\) | ||||
−0.984949 | + | 0.172843i | \(0.944705\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.182259 | + | 15.5874i | −0.0116919 | + | 0.999932i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.2437 | + | 3.55401i | −0.973881 | + | 0.227057i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.311894i | 0.0198453i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.77323 | + | 29.8413i | −0.619353 | + | 1.89112i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.5862 | −1.93058 | −0.965292 | − | 0.261172i | \(-0.915891\pi\) | ||||
−0.965292 | + | 0.261172i | \(0.915891\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.56177i | − | 0.161057i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.28470 | + | 2.92398i | −0.581430 | + | 0.183107i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6305i | 1.09976i | 0.835243 | + | 0.549881i | \(0.185327\pi\) | ||||
−0.835243 | + | 0.549881i | \(0.814673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.37985 | + | 5.05741i | 0.210014 | + | 0.314252i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.21886 | − | 3.02415i | 0.137344 | − | 0.187190i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.0858 | 1.67018 | 0.835090 | − | 0.550113i | \(-0.185416\pi\) | ||||
0.835090 | + | 0.550113i | \(0.185416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.1887 | − | 15.6198i | −0.687315 | − | 0.959519i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.57100 | − | 0.514514i | −0.0961437 | − | 0.0314877i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.4642 | −0.759954 | −0.379977 | − | 0.924996i | \(-0.624068\pi\) | ||||
−0.379977 | + | 0.924996i | \(0.624068\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.1528i | − | 0.677484i | −0.940879 | − | 0.338742i | \(-0.889999\pi\) | ||
0.940879 | − | 0.338742i | \(-0.110001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.694283 | + | 0.194118i | −0.0420199 | + | 0.0117486i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.53741 | + | 1.54210i | 0.273616 | + | 0.0929922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.2365i | 1.57640i | 0.615422 | + | 0.788198i | \(0.288986\pi\) | ||||
−0.615422 | + | 0.788198i | \(0.711014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.3831 | − | 20.9660i | 0.920959 | − | 1.25520i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.9648i | − | 0.892722i | −0.894853 | − | 0.446361i | \(-0.852720\pi\) | ||
0.894853 | − | 0.446361i | \(-0.147280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.613047 | −0.0364418 | −0.0182209 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182209 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.32397 | + | 2.30650i | −0.433835 | + | 0.136625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4379 | − | 6.97564i | 0.616132 | − | 0.411759i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.6830 | 0.628411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.1937 | − | 7.59608i | −1.35964 | − | 0.445290i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.76313i | − | 0.511947i | −0.966684 | − | 0.255974i | \(-0.917604\pi\) | ||
0.966684 | − | 0.255974i | \(-0.0823960\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6056 | + | 18.9940i | 0.792152 | + | 1.10587i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.04959 | − | 2.89902i | 0.234981 | − | 0.168218i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.420472 | −0.0243165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.67936 | + | 14.4836i | 0.557909 | + | 0.834822i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.6063 | + | 4.78367i | 0.839111 | + | 0.274815i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.77585 | + | 5.56993i | −0.445244 | + | 0.318933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8865 | 1.02084 | 0.510418 | − | 0.859926i | \(-0.329491\pi\) | ||||
0.510418 | + | 0.859926i | \(0.329491\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.72474 | − | 1.21988i | −0.211893 | − | 0.0693965i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9594 | 0.734859 | 0.367430 | − | 0.930051i | \(-0.380238\pi\) | ||||
0.367430 | + | 0.930051i | \(0.380238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4080 | 1.49267 | 0.746334 | − | 0.665572i | \(-0.231812\pi\) | ||||
0.746334 | + | 0.665572i | \(0.231812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.69267 | − | 14.8678i | −0.546120 | − | 0.837707i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.5973 | −1.04453 | −0.522263 | − | 0.852785i | \(-0.674912\pi\) | ||||
−0.522263 | + | 0.852785i | \(0.674912\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.19835 | −0.0670945 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −26.7770 | − | 8.76967i | −1.49455 | − | 0.489475i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.98300 | −0.277262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.253110 | − | 0.744741i | 0.0140400 | − | 0.0413108i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.0746 | − | 7.22958i | −1.22073 | − | 0.399797i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.24314 | − | 12.3345i | −0.454459 | − | 0.680025i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.45274 | −0.0798496 | −0.0399248 | − | 0.999203i | \(-0.512712\pi\) | ||||
−0.0399248 | + | 0.999203i | \(0.512712\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.08017 | + | 5.56100i | −0.223592 | + | 0.304741i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 25.1371 | − | 18.0060i | 1.37339 | − | 0.983775i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.2863i | − | 0.723753i | −0.932226 | − | 0.361876i | \(-0.882136\pi\) | ||
0.932226 | − | 0.361876i | \(-0.117864\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 24.7370 | + | 8.10155i | 1.34353 | + | 0.440016i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.30797 | −0.449902 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.61760 | − | 18.1635i | −0.195332 | − | 0.980737i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.10946 | − | 9.87365i | −0.167407 | − | 0.531579i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.62840 | 0.194783 | 0.0973914 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973914 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.91682i | − | 0.156134i | −0.996948 | − | 0.0780670i | \(-0.975125\pi\) | ||
0.996948 | − | 0.0780670i | \(-0.0248748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.475825 | − | 0.664673i | −0.0253977 | − | 0.0354776i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2988i | 0.761049i | 0.924771 | + | 0.380525i | \(0.124257\pi\) | ||||
−0.924771 | + | 0.380525i | \(0.875743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7418 | − | 12.7087i | 0.941638 | − | 0.674506i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.10135 | − | 11.0923i | −0.164141 | − | 0.587066i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.66998i | 0.299250i | 0.988743 | + | 0.149625i | \(0.0478067\pi\) | ||||
−0.988743 | + | 0.149625i | \(0.952193\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0693 | 0.793121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.5941 | + | 5.43469i | 0.870966 | + | 0.285247i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.77459 | − | 8.06156i | −0.302256 | − | 0.421961i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.46586 | −0.0765170 | −0.0382585 | − | 0.999268i | \(-0.512181\pi\) | ||||
−0.0382585 | + | 0.999268i | \(0.512181\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4773 | + | 8.42102i | 0.597483 | + | 0.438381i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9015 | − | 12.6319i | 0.981320 | − | 0.655813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.24635i | − | 0.219868i | −0.993939 | − | 0.109934i | \(-0.964936\pi\) | ||
0.993939 | − | 0.109934i | \(-0.0350639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.3600 | + | 0.436136i | 0.999746 | + | 0.0225220i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.196689i | 0.0101300i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6426 | 1.47127 | 0.735636 | − | 0.677377i | \(-0.236883\pi\) | ||||
0.735636 | + | 0.677377i | \(0.236883\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.82890 | + | 5.58431i | −0.0936975 | + | 0.286093i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 19.9108i | − | 1.01740i | −0.860945 | − | 0.508698i | \(-0.830127\pi\) | ||
0.860945 | − | 0.508698i | \(-0.169873\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.99791 | + | 5.30670i | −0.101823 | + | 0.270454i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.6850 | + | 15.9258i | −0.593980 | + | 0.809554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0461i | 0.712168i | 0.934454 | + | 0.356084i | \(0.115888\pi\) | ||||
−0.934454 | + | 0.356084i | \(0.884112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.71772i | − | 0.339730i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.639788 | + | 0.209535i | 0.0322730 | + | 0.0105696i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.674358 | − | 0.941430i | −0.0339306 | − | 0.0473685i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.1172 | 1.71230 | 0.856148 | − | 0.516731i | \(-0.172851\pi\) | ||||
0.856148 | + | 0.516731i | \(0.172851\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.44641 | − | 8.74985i | −0.122474 | − | 0.438040i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 29.9190i | − | 1.49408i | −0.664778 | − | 0.747041i | \(-0.731474\pi\) | ||
0.664778 | − | 0.747041i | \(-0.268526\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36362i | 0.0679266i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.0892 | − | 16.0888i | 0.600719 | − | 0.799460i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.20359 | 0.109228 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 14.1069i | − | 0.697540i | −0.937208 | − | 0.348770i | \(-0.886599\pi\) | ||
0.937208 | − | 0.348770i | \(-0.113401\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3513 | − | 5.02765i | −0.757222 | − | 0.247996i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.9846 | + | 15.3606i | −1.13100 | + | 0.755845i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.9559 | − | 23.6067i | 1.61774 | − | 1.15881i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.83404 | + | 23.9202i | −0.383635 | + | 1.17138i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.5078 | −0.757606 | −0.378803 | − | 0.925477i | \(-0.623664\pi\) | ||||
−0.378803 | + | 0.925477i | \(0.623664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.90788 | 0.336669 | 0.168335 | − | 0.985730i | \(-0.446161\pi\) | ||||
0.168335 | + | 0.985730i | \(0.446161\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.95115 | − | 13.5627i | 0.483841 | − | 0.659443i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.8984 | + | 4.04384i | 0.577159 | + | 0.196155i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.28837 | − | 9.40954i | −0.304316 | − | 0.455360i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0812835 | + | 0.248188i | −0.00392440 | + | 0.0119827i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6636i | 0.513646i | 0.966458 | + | 0.256823i | \(0.0826757\pi\) | ||||
−0.966458 | + | 0.256823i | \(0.917324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7128 | 1.37985 | 0.689924 | − | 0.723882i | \(-0.257644\pi\) | ||||
0.689924 | + | 0.723882i | \(0.257644\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.61870 | + | 1.45454i | −0.221450 | + | 0.0697399i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5.29909i | − | 0.253490i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.4819i | − | 1.45482i | −0.686203 | − | 0.727410i | \(-0.740724\pi\) | ||
0.686203 | − | 0.727410i | \(-0.259276\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.9548 | − | 10.8916i | 0.854989 | − | 0.518646i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.91751 | −0.233638 | −0.116819 | − | 0.993153i | \(-0.537270\pi\) | ||||
−0.116819 | + | 0.993153i | \(0.537270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.24278 | + | 1.73497i | 0.0589134 | + | 0.0822454i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.92304 | − | 18.0852i | 0.280150 | − | 0.855402i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 37.5082i | − | 1.77012i | −0.465477 | − | 0.885060i | \(-0.654117\pi\) | ||
0.465477 | − | 0.885060i | \(-0.345883\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.54797i | − | 0.214155i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.8234 | − | 11.0774i | −1.58916 | − | 0.520462i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.871006 | + | 0.327924i | 0.0408334 | + | 0.0153733i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.50935i | 0.257717i | 0.991663 | + | 0.128858i | \(0.0411313\pi\) | ||||
−0.991663 | + | 0.128858i | \(0.958869\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.6192 | − | 7.60207i | 0.495663 | − | 0.354834i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2515 | −1.45553 | −0.727763 | − | 0.685828i | \(-0.759440\pi\) | ||||
−0.727763 | + | 0.685828i | \(0.759440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.75214i | 0.406746i | 0.979101 | + | 0.203373i | \(0.0651905\pi\) | ||||
−0.979101 | + | 0.203373i | \(0.934810\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −32.0208 | + | 10.0841i | −1.48493 | + | 0.467641i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.527427i | 0.0244064i | 0.999926 | + | 0.0122032i | \(0.00388450\pi\) | ||||
−0.999926 | + | 0.0122032i | \(0.996116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.3285 | + | 30.4184i | 0.938685 | + | 1.40459i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.44202 | − | 0.472273i | −0.0664450 | − | 0.0217612i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.31073 | 0.290168 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.38575 | + | 3.18987i | 0.430648 | + | 0.146361i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.7836 | + | 15.2492i | 0.951618 | + | 0.698214i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.2855 | −0.926869 | −0.463435 | − | 0.886131i | \(-0.653383\pi\) | ||||
−0.463435 | + | 0.886131i | \(0.653383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.361683i | − | 0.0164913i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.7959 | − | 3.29807i | 0.536732 | − | 0.150068i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.3479 | + | 25.6144i | 0.833136 | + | 1.16309i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 10.5659i | − | 0.478787i | −0.970923 | − | 0.239393i | \(-0.923051\pi\) | ||
0.970923 | − | 0.239393i | \(-0.0769485\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.8336 | − | 36.1324i | 0.535134 | − | 1.63396i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.7844i | 1.75032i | 0.483836 | + | 0.875159i | \(0.339243\pi\) | ||||
−0.483836 | + | 0.875159i | \(0.660757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.14242 | −0.141527 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.42913 | − | 0.0733297i | −0.288968 | − | 0.00329593i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.3479 | + | 21.4693i | 0.643592 | + | 0.963032i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.89045 | 0.263693 | 0.131846 | − | 0.991270i | \(-0.457909\pi\) | ||||
0.131846 | + | 0.991270i | \(0.457909\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.32281 | − | 19.3059i | 0.282482 | − | 0.862523i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 14.4764i | − | 0.645471i | −0.946489 | − | 0.322736i | \(-0.895398\pi\) | ||
0.946489 | − | 0.322736i | \(-0.104602\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.5547 | − | 16.1308i | −0.514177 | − | 0.717811i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.3576 | − | 6.99475i | −0.948522 | − | 0.310648i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.2013 | −1.29433 | −0.647163 | − | 0.762351i | \(-0.724045\pi\) | ||||
−0.647163 | + | 0.762351i | \(0.724045\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.75528 | − | 6.51943i | 0.431548 | − | 0.288403i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.37668 | − | 5.99668i | 0.369839 | − | 0.264760i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.94655 | + | 4.11350i | 0.129841 | + | 0.181262i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.37435 | −0.236364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.1768 | + | 31.0735i | −0.446712 | + | 1.36398i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.4599 | 1.72877 | 0.864385 | − | 0.502830i | \(-0.167708\pi\) | ||||
0.864385 | + | 0.502830i | \(0.167708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9475 | 0.741061 | 0.370531 | − | 0.928820i | \(-0.379176\pi\) | ||||
0.370531 | + | 0.928820i | \(0.379176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.25919 | + | 22.8783i | −0.0549555 | + | 0.998489i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.7860 | −0.949011 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8562 | −0.689398 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.2733 | − | 18.5433i | −1.09677 | − | 0.804713i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.746473 | −0.0323333 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.1826 | + | 29.5718i | 0.915805 | + | 1.27850i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.64352 | − | 20.2851i | 0.286689 | − | 0.875367i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.19894 | − | 2.56649i | −0.267007 | − | 0.110547i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.9754 | 0.901802 | 0.450901 | − | 0.892574i | \(-0.351103\pi\) | ||||
0.450901 | + | 0.892574i | \(0.351103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.84873 | + | 30.0718i | −0.422649 | + | 1.29050i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.4626 | + | 24.3785i | 0.748017 | + | 1.04426i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.09174i | − | 0.388735i | −0.980929 | − | 0.194367i | \(-0.937735\pi\) | ||
0.980929 | − | 0.194367i | \(-0.0622654\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.59135 | − | 10.3465i | 0.323991 | − | 0.441577i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.47881 | −0.105601 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.13922 | − | 0.761340i | 0.0484447 | − | 0.0323755i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.49314 | − | 2.67470i | 0.360514 | − | 0.113535i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.77459 | −0.244677 | −0.122339 | − | 0.992488i | \(-0.539039\pi\) | ||||
−0.122339 | + | 0.992488i | \(0.539039\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.03580i | − | 0.0438098i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.96521 | − | 1.29863i | −0.167411 | − | 0.0548284i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.378414i | 0.0159483i | 0.999968 | + | 0.00797413i | \(0.00253827\pi\) | ||||
−0.999968 | + | 0.00797413i | \(0.997462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.5688 | − | 27.3188i | −0.823267 | − | 1.14931i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.5623 | + | 14.9145i | 0.779543 | + | 0.626348i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 25.5314i | − | 1.07033i | −0.844747 | − | 0.535166i | \(-0.820249\pi\) | ||
0.844747 | − | 0.535166i | \(-0.179751\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5308 | −0.608097 | −0.304048 | − | 0.952657i | \(-0.598338\pi\) | ||||
−0.304048 | + | 0.952657i | \(0.598338\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.69457 | + | 20.4410i | −0.279670 | + | 0.853935i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.30036 | + | 12.6532i | −0.179337 | + | 0.527674i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.4901 | 0.644863 | 0.322432 | − | 0.946593i | \(-0.395500\pi\) | ||||
0.322432 | + | 0.946593i | \(0.395500\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8274 | + | 33.0602i | −0.449973 | + | 1.37393i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.6516 | + | 39.8799i | 1.10569 | + | 1.65450i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8.23570i | − | 0.341088i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0120359 | + | 1.05524i | −0.000497621 | + | 0.0436286i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.9975i | 0.907933i | 0.891019 | + | 0.453967i | \(0.149991\pi\) | ||||
−0.891019 | + | 0.453967i | \(0.850009\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.1852 | −0.708106 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.3458 | + | 7.31840i | 0.919183 | + | 0.301039i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.3606i | − | 0.466523i | −0.972414 | − | 0.233261i | \(-0.925060\pi\) | ||
0.972414 | − | 0.233261i | \(-0.0749397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.23912 | + | 13.9157i | −0.214783 | + | 0.570489i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.89054 | + | 8.82590i | −0.118302 | + | 0.361220i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 35.8691i | − | 1.46557i | −0.680460 | − | 0.732785i | \(-0.738220\pi\) | ||
0.680460 | − | 0.732785i | \(-0.261780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.9788i | 0.937326i | 0.883377 | + | 0.468663i | \(0.155264\pi\) | ||||
−0.883377 | + | 0.468663i | \(0.844736\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24.5407 | + | 33.4473i | −0.999374 | + | 1.36208i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.1272 | − | 18.3261i | −0.533696 | − | 0.745061i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.58776 | −0.145623 | −0.0728114 | − | 0.997346i | \(-0.523197\pi\) | ||||
−0.0728114 | + | 0.997346i | \(0.523197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.54277 | − | 5.51789i | −0.0625164 | − | 0.223596i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.882110i | 0.0356864i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.9840i | − | 0.847535i | −0.905771 | − | 0.423768i | \(-0.860707\pi\) | ||
0.905771 | − | 0.423768i | \(-0.139293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.52028 | − | 17.5289i | −0.222599 | − | 0.706833i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3786 | 1.38403 | 0.692015 | − | 0.721883i | \(-0.256723\pi\) | ||||
0.692015 | + | 0.721883i | \(0.256723\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.34530i | 0.255039i | 0.991836 | + | 0.127520i | \(0.0407016\pi\) | ||||
−0.991836 | + | 0.127520i | \(0.959298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.08429 | + | 11.2928i | 0.324411 | + | 0.453166i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.09948 | + | 1.40308i | −0.0841140 | + | 0.0562132i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.8227 | − | 15.2336i | −0.792906 | − | 0.609344i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.12785 | − | 1.02439i | −0.124914 | − | 0.0409102i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.77847 | 0.230403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4326 | 0.614363 | 0.307181 | − | 0.951651i | \(-0.400614\pi\) | ||||
0.307181 | + | 0.951651i | \(0.400614\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28.6425 | − | 9.38061i | −1.13844 | − | 0.372846i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.16715 | − | 4.41761i | 0.244736 | − | 0.175307i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.421247 | + | 1.01745i | −0.0166904 | + | 0.0403130i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.3208 | + | 23.6071i | −0.685202 | + | 0.933883i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5106i | 0.928614i | 0.885674 | + | 0.464307i | \(0.153696\pi\) | ||||
−0.885674 | + | 0.464307i | \(0.846304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9541 | −0.944658 | −0.472329 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472329 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.3230 | − | 7.65991i | 0.957717 | − | 0.301609i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3039i | 1.15205i | 0.817431 | + | 0.576027i | \(0.195398\pi\) | ||||
−0.817431 | + | 0.576027i | \(0.804602\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0148i | 0.393114i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6958 | − | 38.2548i | −0.419203 | − | 1.49932i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.8097 | −1.51874 | −0.759370 | − | 0.650659i | \(-0.774493\pi\) | ||||
−0.759370 | + | 0.650659i | \(0.774493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.506120 | − | 0.706564i | −0.0197758 | − | 0.0276077i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.7267 | + | 7.87028i | 0.418487 | + | 0.307049i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 30.2584i | − | 1.17870i | −0.807878 | − | 0.589349i | \(-0.799384\pi\) | ||
0.807878 | − | 0.589349i | \(-0.200616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18.7051i | − | 0.727542i | −0.931488 | − | 0.363771i | \(-0.881489\pi\) | ||
0.931488 | − | 0.363771i | \(-0.118511\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.213149 | + | 0.650823i | −0.00827803 | + | 0.0252759i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.13273 | + | 10.9770i | −0.160260 | + | 0.425671i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.34175i | − | 0.129393i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.9732 | − | 8.50639i | −1.00418 | − | 0.328876i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.09988 | −0.158274 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.1399i | 0.853432i | 0.904386 | + | 0.426716i | \(0.140330\pi\) | ||||
−0.904386 | + | 0.426716i | \(0.859670\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.8683 | + | 7.52100i | −0.957183 | + | 0.289483i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 45.2632i | − | 1.73961i | −0.493400 | − | 0.869803i | \(-0.664246\pi\) | ||
0.493400 | − | 0.869803i | \(-0.335754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.9960 | + | 20.7145i | −1.18952 | + | 0.794950i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.99301 | + | 6.08540i | −0.0763724 | + | 0.233193i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.71527 | 0.180425 | 0.0902124 | − | 0.995923i | \(-0.471245\pi\) | ||||
0.0902124 | + | 0.995923i | \(0.471245\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.1440 | + | 16.9535i | 0.463998 | + | 0.647760i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.52384 | − | 22.9731i | 0.287052 | − | 0.876477i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.35175 | −0.0514977 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 19.5451i | − | 0.743531i | −0.928327 | − | 0.371766i | \(-0.878753\pi\) | ||
0.928327 | − | 0.371766i | \(-0.121247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.333596 | − | 7.60023i | 0.0126723 | − | 0.288709i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.4168 | − | 18.9227i | 1.00205 | − | 0.717778i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11.9261i | − | 0.451734i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.6263 | + | 9.04779i | 1.04492 | + | 0.342219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.0912i | − | 1.02322i | −0.859217 | − | 0.511611i | \(-0.829049\pi\) | ||
0.859217 | − | 0.511611i | \(-0.170951\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.55818 | 0.171915 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20.7140 | + | 6.52334i | −0.780133 | + | 0.245683i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.5199 | − | 13.0451i | 0.734120 | − | 0.490611i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.3683 | 0.614723 | 0.307362 | − | 0.951593i | \(-0.400554\pi\) | ||||
0.307362 | + | 0.951593i | \(0.400554\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.25266 | + | 0.919092i | 0.0469784 | + | 0.0344686i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 23.1679i | − | 0.867644i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.274092 | − | 0.196336i | 0.0102505 | − | 0.00734254i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.83401 | + | 30.0269i | −0.367258 | + | 1.12137i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4591 | −0.800289 | −0.400145 | − | 0.916452i | \(-0.631040\pi\) | ||||
−0.400145 | + | 0.916452i | \(0.631040\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.97774 | + | 3.32661i | −0.185381 | + | 0.123890i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.89298 | + | 8.83334i | −0.107591 | + | 0.328515i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.91891 | + | 2.01162i | 0.219823 | + | 0.0747097i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.9291 | −0.553690 | −0.276845 | − | 0.960915i | \(-0.589289\pi\) | ||||
−0.276845 | + | 0.960915i | \(0.589289\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.70291 | + | 25.5589i | −0.322330 | + | 0.946627i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5486 | 0.612072 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7630 | −0.545284 | −0.272642 | − | 0.962116i | \(-0.587897\pi\) | ||||
−0.272642 | + | 0.962116i | \(0.587897\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −27.0073 | − | 2.36762i | −0.996179 | − | 0.0873312i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.2538 | 0.488209 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.3148 | 1.55658 | 0.778288 | − | 0.627908i | \(-0.216088\pi\) | ||||
0.778288 | + | 0.627908i | \(0.216088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.168137 | + | 0.513384i | −0.00617666 | + | 0.0188596i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.3503 | −1.40693 | −0.703467 | − | 0.710728i | \(-0.748366\pi\) | ||||
−0.703467 | + | 0.710728i | \(0.748366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.9728 | + | 14.3068i | −0.731747 | + | 0.524160i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.1739 | + | 43.8508i | −1.17718 | + | 1.60442i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.7848 | + | 23.9149i | −1.30755 | + | 0.873831i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9483 | −0.581961 | −0.290981 | − | 0.956729i | \(-0.593981\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593981\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.3456 | − | 16.4885i | −1.83469 | − | 0.600875i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.7568 | + | 37.3536i | 0.973781 | + | 1.35944i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.3428i | − | 1.35725i | −0.734486 | − | 0.678624i | \(-0.762577\pi\) | ||
0.734486 | − | 0.678624i | \(-0.237423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.38101 | − | 4.21673i | 0.0501275 | − | 0.153058i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.9251 | 0.758536 | 0.379268 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379268 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.5004 | + | 19.7151i | −1.06799 | + | 0.713733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.8591 | − | 0.192292i | −0.609542 | − | 0.00695234i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.64376 | 0.0593526 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.7908i | 0.821856i | 0.911668 | + | 0.410928i | \(0.134795\pi\) | ||||
−0.911668 | + | 0.410928i | \(0.865205\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.50433 | + | 29.0202i | −0.342290 | + | 1.04514i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 35.5488i | − | 1.27860i | −0.768958 | − | 0.639300i | \(-0.779224\pi\) | ||
0.768958 | − | 0.639300i | \(-0.220776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.0350 | + | 13.9463i | 1.47402 | + | 0.500966i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.83695 | + | 10.1466i | 0.101775 | + | 0.364008i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 9.40758i | − | 0.337062i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.35452 | 0.334731 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28256 | − | 3.78167i | 0.188783 | − | 0.135146i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.14075 | + | 1.59253i | 0.0407151 | + | 0.0568398i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.01968 | 0.107640 | 0.0538201 | − | 0.998551i | \(-0.482860\pi\) | ||||
0.0538201 | + | 0.998551i | \(0.482860\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 44.5838 | + | 14.6015i | 1.58722 | + | 0.519827i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.0585 | − | 22.0929i | 1.17543 | − | 0.785534i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.672928i | 0.0238964i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.99642 | − | 31.7422i | −0.354536 | − | 1.12578i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.0365i | 0.497198i | 0.968607 | + | 0.248599i | \(0.0799701\pi\) | ||||
−0.968607 | + | 0.248599i | \(0.920030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0931 | −0.498579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.30854 | − | 1.69380i | −0.0815681 | − | 0.0598475i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 4.25053i | − | 0.149998i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.7984 | − | 5.57145i | −0.521576 | − | 0.196368i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.5163 | − | 6.71923i | −0.722208 | − | 0.236528i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.9966i | 1.65231i | 0.563442 | + | 0.826156i | \(0.309477\pi\) | ||||
−0.563442 | + | 0.826156i | \(0.690523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 52.8375i | 1.85537i | 0.373358 | + | 0.927687i | \(0.378206\pi\) | ||||
−0.373358 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.01229 | − | 18.3577i | 0.210860 | − | 0.643834i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −39.9035 | + | 28.5834i | −1.39776 | + | 1.00123i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.0539 | 0.456698 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.24745 | − | 0.0547542i | −0.0435895 | − | 0.00191327i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.1985i | 1.85664i | 0.371783 | + | 0.928320i | \(0.378747\pi\) | ||||
−0.371783 | + | 0.928320i | \(0.621253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3931i | − | 0.920006i | −0.887917 | − | 0.460003i | \(-0.847848\pi\) | ||
0.887917 | − | 0.460003i | \(-0.152152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.63736 | + | 4.98438i | 0.231083 | + | 0.173534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.3363 | −0.707161 | −0.353580 | − | 0.935404i | \(-0.615036\pi\) | ||||
−0.353580 | + | 0.935404i | \(0.615036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.14232i | − | 0.178600i | −0.996005 | − | 0.0893000i | \(-0.971537\pi\) | ||
0.996005 | − | 0.0893000i | \(-0.0284630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.1436 | + | 43.1858i | −0.490638 | + | 1.49810i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.2554 | − | 6.73010i | −0.563218 | − | 0.233184i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.3208 | + | 15.2724i | −0.737838 | + | 0.528523i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.6233 | − | 26.2178i | 1.26589 | − | 0.906221i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.1161 | 0.867103 | 0.433552 | − | 0.901129i | \(-0.357260\pi\) | ||||
0.433552 | + | 0.901129i | \(0.357260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4368 | 0.946096 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.06725 | − | 24.6323i | 0.277851 | − | 0.848382i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.8954 | + | 23.5867i | 0.581220 | + | 0.811406i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.1764 | − | 14.8204i | 0.761989 | − | 0.509235i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.00909 | − | 0.330483i | −0.0346318 | − | 0.0113422i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.14501i | 0.210648i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.0408 | −0.823141 | −0.411570 | − | 0.911378i | \(-0.635020\pi\) | ||||
−0.411570 | + | 0.911378i | \(0.635020\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.2988 | − | 0.151684i | −0.454810 | − | 0.00518749i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 52.0141i | − | 1.77677i | −0.459102 | − | 0.888384i | \(-0.651829\pi\) | ||
0.459102 | − | 0.888384i | \(-0.348171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8217i | 0.676309i | 0.941091 | + | 0.338154i | \(0.109803\pi\) | ||||
−0.941091 | + | 0.338154i | \(0.890197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.9415 | − | 5.85514i | 0.713685 | − | 0.199543i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.2461 | −0.927468 | −0.463734 | − | 0.885974i | \(-0.653491\pi\) | ||||
−0.463734 | + | 0.885974i | \(0.653491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.3167 | − | 24.5815i | 1.16680 | − | 0.835795i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.5844 | + | 5.75902i | 0.597198 | + | 0.195587i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 0.496377i | − | 0.0168384i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.17539i | − | 0.0737102i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.0823 | − | 25.0066i | −1.15351 | − | 0.846346i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.7763 | − | 22.8572i | 0.634755 | − | 0.772713i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6226i | 0.730145i | 0.930979 | + | 0.365072i | \(0.118956\pi\) | ||||
−0.930979 | + | 0.365072i | \(0.881044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.72406 | − | 14.4243i | 0.159339 | − | 0.486520i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.4204 | −1.29442 | −0.647209 | − | 0.762313i | \(-0.724064\pi\) | ||||
−0.647209 | + | 0.762313i | \(0.724064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.7562i | − | 1.13599i | −0.823033 | − | 0.567993i | \(-0.807720\pi\) | ||
0.823033 | − | 0.567993i | \(-0.192280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.1558 | + | 38.5992i | 0.408614 | + | 1.29750i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.9418i | 1.27396i | 0.770879 | + | 0.636981i | \(0.219817\pi\) | ||||
−0.770879 | + | 0.636981i | \(0.780183\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.98741 | + | 7.46287i | 0.167273 | + | 0.250297i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.22853 | − | 2.58877i | 0.275666 | − | 0.0867272i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.1170 | −0.372015 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.4023 | + | 16.0470i | −0.748826 | + | 0.536393i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.692107 | − | 0.226670i | −0.0231088 | − | 0.00756828i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8375 | −0.361450 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 21.5964i | − | 0.719481i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.12456 | + | 29.0583i | 0.270369 | + | 0.967001i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.2104 | − | 23.7890i | 1.10395 | − | 0.790774i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 5.51100i | − | 0.182990i | −0.995806 | − | 0.0914949i | \(-0.970835\pi\) | ||
0.995806 | − | 0.0914949i | \(-0.0291645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.4635 | + | 15.7481i | 0.711900 | + | 0.522330i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.8419i | − | 1.08810i | −0.839052 | − | 0.544051i | \(-0.816890\pi\) | ||
0.839052 | − | 0.544051i | \(-0.183110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.3763 | 0.575071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −15.8019 | + | 4.97640i | −0.522394 | + | 0.164515i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.855012 | − | 0.571402i | 0.0282350 | − | 0.0188694i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.1954 | −1.45787 | −0.728935 | − | 0.684583i | \(-0.759984\pi\) | ||||
−0.728935 | + | 0.684583i | \(0.759984\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.4416 | + | 9.64232i | 0.970133 | + | 0.317725i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.53539i | − | 0.0505380i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8840 | − | 3.69909i | −0.357865 | − | 0.121625i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.47339 | − | 4.01590i | −0.179770 | − | 0.131899i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.66334 | −0.185808 | −0.0929040 | − | 0.995675i | \(-0.529615\pi\) | ||||
−0.0929040 | + | 0.995675i | \(0.529615\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.8227 | − | 5.30885i | −0.420246 | − | 0.173991i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.3314 | + | 6.98619i | 0.698360 | + | 0.228718i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.13678 | + | 4.37906i | 0.102584 | + | 0.143211i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.8981 | −1.49943 | −0.749713 | − | 0.661763i | \(-0.769809\pi\) | ||||
−0.749713 | + | 0.661763i | \(0.769809\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.4681 | + | 14.2361i | 1.41853 | + | 0.464578i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.0654 | 1.63209 | 0.816043 | − | 0.577991i | \(-0.196163\pi\) | ||||
0.816043 | + | 0.577991i | \(0.196163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6826 | 0.413003 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.93934 | − | 29.6979i | −0.258267 | − | 0.966074i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.8322 | 0.904426 | 0.452213 | − | 0.891910i | \(-0.350635\pi\) | ||||
0.452213 | + | 0.891910i | \(0.350635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.697653 | −0.0226468 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.6115 | − | 10.0255i | −0.992645 | − | 0.325098i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.3099 | −0.560721 | −0.280361 | − | 0.959895i | \(-0.590454\pi\) | ||||
−0.280361 | + | 0.959895i | \(0.590454\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.5744 | − | 16.1703i | 0.730492 | − | 0.523260i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.97250 | − | 0.646009i | −0.0637620 | − | 0.0208825i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.5154 | + | 13.7104i | −0.662477 | + | 0.442732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.1348 | −1.42370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.3480 | − | 28.8701i | −1.26797 | − | 0.930327i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.5107 | − | 26.1531i | 1.17532 | − | 0.841897i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.0313i | 0.612006i | 0.952031 | + | 0.306003i | \(0.0989917\pi\) | ||||
−0.952031 | + | 0.306003i | \(0.901008\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.20213 | − | 2.68626i | −0.263490 | − | 0.0862950i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.307918 | 0.00988156 | 0.00494078 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494078 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3634 | + | 31.9670i | 0.684880 | + | 1.02481i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.818103 | − | 1.08941i | 0.0262003 | − | 0.0348891i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.3493 | −1.06694 | −0.533469 | − | 0.845820i | \(-0.679112\pi\) | ||||
−0.533469 | + | 0.845820i | \(0.679112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.914777i | 0.0292364i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32.4379 | − | 23.8001i | −1.03566 | − | 0.759879i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.9932i | 1.24369i | 0.783140 | + | 0.621845i | \(0.213617\pi\) | ||||
−0.783140 | + | 0.621845i | \(0.786383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6772 | − | 24.6780i | −0.563242 | − | 0.786308i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.91904 | − | 24.7467i | −0.220235 | − | 0.787695i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.5983i | 0.559594i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.8271 | 0.820424 | 0.410212 | − | 0.911990i | \(-0.365455\pi\) | ||||
0.410212 | + | 0.911990i | \(0.365455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.39124 | − | 0.783146i | −0.0758836 | − | 0.0248524i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.74707 | − | 6.98195i | 0.309003 | − | 0.221343i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.68987 | −0.148530 | −0.0742649 | − | 0.997239i | \(-0.523661\pi\) | ||||
−0.0742649 | + | 0.997239i | \(0.523661\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.71390 | + | 6.95397i | −0.307334 | + | 0.220014i |
(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 | 840.2.k.b.209.22 | yes | 24 | |
3.2 | odd | 2 | 840.2.k.a.209.21 | yes | 24 | ||
4.3 | odd | 2 | 1680.2.k.h.209.3 | 24 | |||
5.4 | even | 2 | 840.2.k.a.209.3 | ✓ | 24 | ||
7.6 | odd | 2 | inner | 840.2.k.b.209.3 | yes | 24 | |
12.11 | even | 2 | 1680.2.k.i.209.4 | 24 | |||
15.14 | odd | 2 | inner | 840.2.k.b.209.4 | yes | 24 | |
20.19 | odd | 2 | 1680.2.k.i.209.22 | 24 | |||
21.20 | even | 2 | 840.2.k.a.209.4 | yes | 24 | ||
28.27 | even | 2 | 1680.2.k.h.209.22 | 24 | |||
35.34 | odd | 2 | 840.2.k.a.209.22 | yes | 24 | ||
60.59 | even | 2 | 1680.2.k.h.209.21 | 24 | |||
84.83 | odd | 2 | 1680.2.k.i.209.21 | 24 | |||
105.104 | even | 2 | inner | 840.2.k.b.209.21 | yes | 24 | |
140.139 | even | 2 | 1680.2.k.i.209.3 | 24 | |||
420.419 | odd | 2 | 1680.2.k.h.209.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.3 | ✓ | 24 | 5.4 | even | 2 | ||
840.2.k.a.209.4 | yes | 24 | 21.20 | even | 2 | ||
840.2.k.a.209.21 | yes | 24 | 3.2 | odd | 2 | ||
840.2.k.a.209.22 | yes | 24 | 35.34 | odd | 2 | ||
840.2.k.b.209.3 | yes | 24 | 7.6 | odd | 2 | inner | |
840.2.k.b.209.4 | yes | 24 | 15.14 | odd | 2 | inner | |
840.2.k.b.209.21 | yes | 24 | 105.104 | even | 2 | inner | |
840.2.k.b.209.22 | yes | 24 | 1.1 | even | 1 | trivial | |
1680.2.k.h.209.3 | 24 | 4.3 | odd | 2 | |||
1680.2.k.h.209.4 | 24 | 420.419 | odd | 2 | |||
1680.2.k.h.209.21 | 24 | 60.59 | even | 2 | |||
1680.2.k.h.209.22 | 24 | 28.27 | even | 2 | |||
1680.2.k.i.209.3 | 24 | 140.139 | even | 2 | |||
1680.2.k.i.209.4 | 24 | 12.11 | even | 2 | |||
1680.2.k.i.209.21 | 24 | 84.83 | odd | 2 | |||
1680.2.k.i.209.22 | 24 | 20.19 | odd | 2 |