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 | 209.21 | ||
Character | \(\chi\) | \(=\) | 840.209 |
Dual form | 840.2.k.a.209.22 |
$q$-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 | \(0.0461553\pi\) | ||||
−0.989506 | + | 0.144493i | \(0.953845\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.157315 | −0.0436315 | −0.0218157 | − | 0.999762i | \(-0.506945\pi\) | ||||
−0.0218157 | + | 0.999762i | \(0.506945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.12329 | + | 2.29022i | 0.806429 | + | 0.591331i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.51337i | 0.609581i | 0.952419 | + | 0.304791i | \(0.0985865\pi\) | ||||
−0.952419 | + | 0.304791i | \(0.901414\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.98260i | − | 0.454840i | −0.973797 | − | 0.227420i | \(-0.926971\pi\) | ||
0.973797 | − | 0.227420i | \(-0.0730290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82833 | − | 3.60563i | 0.617191 | − | 0.786813i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.67280 | −0.557317 | −0.278658 | − | 0.960390i | \(-0.589890\pi\) | ||||
−0.278658 | + | 0.960390i | \(0.589890\pi\) | |||||||
\(24\) | 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 | \(0.0370347\pi\) | ||||
−0.993239 | + | 0.116086i | \(0.962965\pi\) | |||||||
\(30\) | 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 | \(-0.620823\pi\) | ||||
−0.370528 | + | 0.928821i | \(0.620823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.58424i | 1.00409i | 0.864842 | + | 0.502043i | \(0.167418\pi\) | ||||
−0.864842 | + | 0.502043i | \(0.832582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.37561 | + | 2.08603i | 0.950421 | + | 0.310968i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.60727i | 0.817904i | 0.912556 | + | 0.408952i | \(0.134106\pi\) | ||||
−0.912556 | + | 0.408952i | \(0.865894\pi\) | |||||||
\(48\) | 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 | \(-0.700929\pi\) | ||||
−0.590144 | + | 0.807298i | \(0.700929\pi\) | |||||||
\(54\) | 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 | \(-0.261911\pi\) | ||||
0.680159 | + | 0.733065i | \(0.261911\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.27757i | − | 0.547686i | −0.961774 | − | 0.273843i | \(-0.911705\pi\) | ||
0.961774 | − | 0.273843i | \(-0.0882949\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.71175 | − | 7.45965i | 0.341648 | − | 0.939828i | ||||
\(64\) | 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 | \(-0.803386\pi\) | ||
0.815224 | − | 0.579146i | \(-0.196614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.43474 | 0.519047 | 0.259524 | − | 0.965737i | \(-0.416434\pi\) | ||||
0.259524 | + | 0.965737i | \(0.416434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0962871 | + | 8.65972i | −0.0111183 | + | 0.999938i | ||||
\(76\) | 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 | \(-0.531918\pi\) | ||
0.100105 | − | 0.994977i | \(-0.468082\pi\) | |||||||
\(84\) | 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 | \(-0.483892\pi\) | ||||
0.0505843 | + | 0.998720i | \(0.483892\pi\) | |||||||
\(90\) | 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 | \(-0.645548\pi\) | ||||
−0.441484 | + | 0.897269i | \(0.645548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.26288 | −0.222968 | −0.111484 | − | 0.993766i | \(-0.535560\pi\) | ||||
−0.111484 | + | 0.993766i | \(0.535560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.2372 | + | 0.446399i | 0.999051 | + | 0.0435641i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.2677 | 1.57266 | 0.786331 | − | 0.617806i | \(-0.211978\pi\) | ||||
0.786331 | + | 0.617806i | \(0.211978\pi\) | |||||||
\(108\) | 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 | \(-0.749896\pi\) | ||||
−0.706875 | + | 0.707339i | \(0.749896\pi\) | |||||||
\(114\) | 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 | \(-0.505405\pi\) | ||||
−0.0169799 | + | 0.999856i | \(0.505405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91458 | − | 4.36121i | −0.252726 | − | 0.378165i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.6189 | − | 0.00333277i | 1.00000 | − | 0.000286839i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.32628 | 0.796798 | 0.398399 | − | 0.917212i | \(-0.369566\pi\) | ||||
0.398399 | + | 0.917212i | \(0.369566\pi\) | |||||||
\(138\) | 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 | ||||||||
\(147\) | 0.921014 | − | 12.0893i | 0.0759640 | − | 0.997111i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9872i | 0.900110i | 0.893001 | + | 0.450055i | \(0.148596\pi\) | ||||
−0.893001 | + | 0.450055i | \(0.851404\pi\) | |||||||
\(150\) | 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 | ||||||||
\(165\) | −2.19508 | + | 2.99355i | −0.170887 | + | 0.233047i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.7288i | 0.907602i | 0.891103 | + | 0.453801i | \(0.149932\pi\) | ||||
−0.891103 | + | 0.453801i | \(0.850068\pi\) | |||||||
\(168\) | 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 | \(-0.745226\pi\) | ||
0.696423 | − | 0.717632i | \(-0.254774\pi\) | |||||||
\(174\) | 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 | \(0.152351\pi\) | ||||
−0.887629 | + | 0.460559i | \(0.847649\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | 0.442223 | − | 13.7406i | 0.0321670 | − | 0.999483i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.4184i | − | 0.898565i | −0.893390 | − | 0.449283i | \(-0.851680\pi\) | ||
0.893390 | − | 0.449283i | \(-0.148320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0849i | 1.44574i | 0.690983 | + | 0.722871i | \(0.257178\pi\) | ||||
−0.690983 | + | 0.722871i | \(0.742822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.491341 | − | 0.360286i | −0.0351857 | − | 0.0258006i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.5756 | −0.967223 | −0.483612 | − | 0.875283i | \(-0.660675\pi\) | ||||
−0.483612 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(198\) | 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 | ||||||||
\(225\) | 4.50982 | + | 14.3060i | 0.300655 | + | 0.953733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.69704i | − | 0.245381i | −0.992445 | − | 0.122690i | \(-0.960848\pi\) | ||
0.992445 | − | 0.122690i | \(-0.0391522\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 13.9567i | − | 0.922286i | −0.887326 | − | 0.461143i | \(-0.847440\pi\) | ||
0.887326 | − | 0.461143i | \(-0.152560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.45586 | + | 2.71084i | 0.227379 | + | 0.178360i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.7836 | −1.09953 | −0.549767 | − | 0.835318i | \(-0.685283\pi\) | ||||
−0.549767 | + | 0.835318i | \(0.685283\pi\) | |||||||
\(234\) | 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 | \(-0.799131\pi\) | ||
0.807410 | − | 0.589991i | \(-0.200869\pi\) | |||||||
\(240\) | 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 | \(-0.0841091\pi\) | ||||
0.965292 | + | 0.261172i | \(0.0841091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.56177i | − | 0.161057i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.75615 | + | 7.84996i | −0.360464 | + | 0.491584i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 17.6305i | − | 1.09976i | −0.835243 | − | 0.549881i | \(-0.814673\pi\) | ||
0.835243 | − | 0.549881i | \(-0.185327\pi\) | |||||||
\(258\) | 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 | \(-0.814584\pi\) | ||||
−0.835090 | + | 0.550113i | \(0.814584\pi\) | |||||||
\(264\) | 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 | \(-0.375932\pi\) | ||||
0.379977 | + | 0.924996i | \(0.375932\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 11.1528i | − | 0.677484i | −0.940879 | − | 0.338742i | \(-0.889999\pi\) | ||
0.940879 | − | 0.338742i | \(-0.110001\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.444939 | + | 0.567222i | −0.0269290 | + | 0.0343298i | ||||
\(274\) | 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 | \(0.147280\pi\) | ||||
−0.894853 | + | 0.446361i | \(0.852720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.613047 | −0.0364418 | −0.0182209 | − | 0.999834i | \(-0.505800\pi\) | ||||
−0.0182209 | + | 0.999834i | \(0.505800\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.54058 | − | 6.19223i | 0.268961 | − | 0.366796i | ||||
\(286\) | 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 | \(0.0823960\pi\) | ||||
−0.966684 | + | 0.255974i | \(0.917604\pi\) | |||||||
\(294\) | 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 | \(-0.619762\pi\) | ||||
−0.367430 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.4080 | 1.49267 | 0.746334 | − | 0.665572i | \(-0.231812\pi\) | ||||
0.746334 | + | 0.665572i | \(0.231812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 17.0913 | − | 4.78394i | 0.962988 | − | 0.269544i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.5973 | 1.04453 | 0.522263 | − | 0.852785i | \(-0.325088\pi\) | ||||
0.522263 | + | 0.852785i | \(0.325088\pi\) | |||||||
\(318\) | 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 | ||||||||
\(345\) | −8.34791 | − | 6.12128i | −0.449436 | − | 0.329559i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.62840 | −0.194783 | −0.0973914 | − | 0.995246i | \(-0.531050\pi\) | ||||
−0.0973914 | + | 0.995246i | \(0.531050\pi\) | |||||||
\(348\) | 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 | \(-0.875743\pi\) | ||
0.924771 | − | 0.380525i | \(-0.124257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7418 | − | 12.7087i | 0.941638 | − | 0.674506i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.06228 | + | 7.10862i | 0.479627 | + | 0.376228i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5.66998i | − | 0.299250i | −0.988743 | − | 0.149625i | \(-0.952193\pi\) | ||
0.988743 | − | 0.149625i | \(-0.0478067\pi\) | |||||||
\(360\) | 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 | ||||||||
\(375\) | −15.8672 | + | 11.1010i | −0.819378 | + | 0.573254i | ||||
\(376\) | 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 | \(0.169873\pi\) | ||||
−0.860945 | + | 0.508698i | \(0.830127\pi\) | |||||||
\(384\) | 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 | \(-0.884112\pi\) | ||
0.934454 | − | 0.356084i | \(-0.115888\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −7.14852 | − | 5.60744i | −0.357874 | − | 0.280723i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.9190i | 1.49408i | 0.664778 | + | 0.747041i | \(0.268526\pi\) | ||||
−0.664778 | + | 0.747041i | \(0.731474\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.36362i | 0.0679266i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.1233 | − | 6.26907i | 0.950242 | − | 0.311513i | ||||
\(406\) | 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 | \(-0.376336\pi\) | ||||
0.378803 | + | 0.925477i | \(0.376336\pi\) | |||||||
\(420\) | 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 | \(-0.917324\pi\) | ||
0.966458 | − | 0.256823i | \(-0.0826757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.7128 | 1.37985 | 0.689924 | − | 0.723882i | \(-0.257644\pi\) | ||||
0.689924 | + | 0.723882i | \(0.257644\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.86341 | + | 3.90499i | −0.137290 | + | 0.187230i | ||||
\(436\) | 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 | ||||||||
\(441\) | −5.00115 | − | 20.3958i | −0.238150 | − | 0.971228i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.91751 | 0.233638 | 0.116819 | − | 0.993153i | \(-0.462730\pi\) | ||||
0.116819 | + | 0.993153i | \(0.462730\pi\) | |||||||
\(444\) | 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 | \(0.345883\pi\) | ||||
−0.465477 | + | 0.885060i | \(0.654117\pi\) | |||||||
\(450\) | 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 | \(-0.240560\pi\) | ||||
0.727763 | + | 0.685828i | \(0.240560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.75214i | 0.406746i | 0.979101 | + | 0.203373i | \(0.0651905\pi\) | ||||
−0.979101 | + | 0.203373i | \(0.934810\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.8517 | − | 27.0727i | 0.920599 | − | 1.25547i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 0.527427i | − | 0.0244064i | −0.999926 | − | 0.0122032i | \(-0.996116\pi\) | ||
0.999926 | − | 0.0122032i | \(-0.00388450\pi\) | |||||||
\(468\) | 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 | \(-0.346617\pi\) | ||||
0.463435 | + | 0.886131i | \(0.346617\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.361683i | − | 0.0164913i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.55954 | + | 9.63712i | −0.343971 | + | 0.438504i | ||||
\(484\) | 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 | \(-0.660757\pi\) | ||
0.483836 | − | 0.875159i | \(-0.339243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.14242 | −0.141527 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.99938 | + | 6.11078i | −0.0898655 | + | 0.274659i | ||||
\(496\) | 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 | \(0.104602\pi\) | ||||
−0.946489 | + | 0.322736i | \(0.895398\pi\) | |||||||
\(504\) | 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 | \(-0.275955\pi\) | ||||
0.647163 | + | 0.762351i | \(0.275955\pi\) | |||||||
\(510\) | 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 | \(-0.832292\pi\) | ||||
−0.864385 | + | 0.502830i | \(0.832292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9475 | 0.741061 | 0.370531 | − | 0.928820i | \(-0.379176\pi\) | ||||
0.370531 | + | 0.928820i | \(0.379176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5187 | + | 19.1907i | 0.546360 | + | 0.837550i | ||||
\(526\) | 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 | ||||||||
\(555\) | −5.26542 | + | 7.18073i | −0.223505 | + | 0.304805i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.77459 | 0.244677 | 0.122339 | − | 0.992488i | \(-0.460961\pi\) | ||||
0.122339 | + | 0.992488i | \(0.460961\pi\) | |||||||
\(558\) | 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 | \(-0.997462\pi\) | ||
0.999968 | − | 0.00797413i | \(-0.00253827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.5688 | − | 27.3188i | −0.823267 | − | 1.14931i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.67943 | − | 22.8557i | −0.280510 | − | 0.959851i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.5314i | 1.07033i | 0.844747 | + | 0.535166i | \(0.179751\pi\) | ||||
−0.844747 | + | 0.535166i | \(0.820249\pi\) | |||||||
\(570\) | 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 | ||||||||
\(585\) | −1.00298 | − | 0.328165i | −0.0414682 | − | 0.0135680i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 21.9975i | − | 0.907933i | −0.891019 | − | 0.453967i | \(-0.850009\pi\) | ||
0.891019 | − | 0.453967i | \(-0.149991\pi\) | |||||||
\(588\) | 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 | \(0.0749397\pi\) | ||||
−0.972414 | + | 0.233261i | \(0.925060\pi\) | |||||||
\(594\) | 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 | \(0.261780\pi\) | ||||
−0.680460 | + | 0.732785i | \(0.738220\pi\) | |||||||
\(600\) | 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 | ||||||||
\(609\) | 4.50805 | + | 3.53620i | 0.182676 | + | 0.143294i | ||||
\(610\) | 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 | ||||||||
\(615\) | −14.8202 | − | 10.8672i | −0.597609 | − | 0.438209i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.3786 | −1.38403 | −0.692015 | − | 0.721883i | \(-0.743277\pi\) | ||||
−0.692015 | + | 0.721883i | \(0.743277\pi\) | |||||||
\(618\) | 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 | \(-0.846304\pi\) | ||
0.885674 | − | 0.464307i | \(-0.153696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9541 | −0.944658 | −0.472329 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472329 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.0793 | + | 20.5644i | −0.593748 | + | 0.809724i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 29.3039i | − | 1.15205i | −0.817431 | − | 0.576027i | \(-0.804602\pi\) | ||
0.817431 | − | 0.576027i | \(-0.195398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0148i | 0.393114i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.2537 | − | 24.5160i | −1.22493 | − | 0.960859i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.8097 | 1.51874 | 0.759370 | − | 0.650659i | \(-0.225507\pi\) | ||||
0.759370 | + | 0.650659i | \(0.225507\pi\) | |||||||
\(654\) | 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 | \(0.200616\pi\) | ||||
−0.807878 | + | 0.589349i | \(0.799384\pi\) | |||||||
\(660\) | 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 | ||||||||
\(675\) | 15.1354 | + | 21.1168i | 0.582562 | + | 0.812786i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.2632i | 1.73961i | 0.493400 | + | 0.869803i | \(0.335754\pi\) | ||||
−0.493400 | + | 0.869803i | \(0.664246\pi\) | |||||||
\(678\) | 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 | \(-0.528755\pi\) | ||||
−0.0902124 | + | 0.995923i | \(0.528755\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 7.14979 | + | 2.59911i | 0.271598 | + | 0.0987319i | ||||
\(694\) | 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 | \(0.170951\pi\) | ||||
−0.859217 | + | 0.511611i | \(0.829049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.55818 | 0.171915 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.8419 | + | 17.5131i | −0.483652 | + | 0.659581i | ||||
\(706\) | 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 | \(-0.368960\pi\) | ||||
0.400145 | + | 0.916452i | \(0.368960\pi\) | |||||||
\(720\) | 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 | ||||||||
\(735\) | 23.1755 | − | 14.0676i | 0.854841 | − | 0.518891i | ||||
\(736\) | 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 | \(-0.251634\pi\) | ||||
0.703467 | + | 0.710728i | \(0.251634\pi\) | |||||||
\(744\) | 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 | \(-0.623824\pi\) | ||||
−0.379268 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.5004 | + | 19.7151i | −1.06799 | + | 0.713733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.24297 | + | 16.0243i | −0.189560 | + | 0.579358i | ||||
\(766\) | 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 | \(0.220776\pi\) | ||||
−0.768958 | + | 0.639300i | \(0.779224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 41.0350 | + | 13.9463i | 1.47402 | + | 0.500966i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.28968 | + | 6.50259i | 0.297391 | + | 0.233279i | ||||
\(778\) | 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 | ||||||||
\(795\) | −26.8372 | − | 19.6790i | −0.951818 | − | 0.697941i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 14.0365i | − | 0.497198i | −0.968607 | − | 0.248599i | \(-0.920030\pi\) | ||
0.968607 | − | 0.248599i | \(-0.0799701\pi\) | |||||||
\(798\) | 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 | \(-0.690523\pi\) | ||
0.563442 | − | 0.826156i | \(-0.309477\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | −0.426600 | + | 1.17352i | −0.0149066 | + | 0.0410061i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 53.1985i | − | 1.85664i | −0.371783 | − | 0.928320i | \(-0.621253\pi\) | ||
0.371783 | − | 0.928320i | \(-0.378747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 26.3931i | − | 0.920006i | −0.887917 | − | 0.460003i | \(-0.847848\pi\) | ||
0.887917 | − | 0.460003i | \(-0.152152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.30000 | − | 0.0922875i | −0.288969 | − | 0.00321304i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.3363 | 0.707161 | 0.353580 | − | 0.935404i | \(-0.384964\pi\) | ||||
0.353580 | + | 0.935404i | \(0.384964\pi\) | |||||||
\(828\) | 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 | \(-0.642740\pi\) | ||||
−0.433552 | + | 0.901129i | \(0.642740\pi\) | |||||||
\(840\) | 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 | ||||||||
\(855\) | 4.13577 | − | 12.6403i | 0.141440 | − | 0.432289i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.0141i | 1.77677i | 0.459102 | + | 0.888384i | \(0.348171\pi\) | ||||
−0.459102 | + | 0.888384i | \(0.651829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8217i | 0.676309i | 0.941091 | + | 0.338154i | \(0.109803\pi\) | ||||
−0.941091 | + | 0.338154i | \(0.890197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.4206 | + | 17.1090i | −0.457373 | + | 0.583072i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.2461 | 0.927468 | 0.463734 | − | 0.885974i | \(-0.346509\pi\) | ||||
0.463734 | + | 0.885974i | \(0.346509\pi\) | |||||||
\(864\) | 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 | \(-0.275936\pi\) | ||||
0.647209 | + | 0.762313i | \(0.275936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 33.7562i | − | 1.13599i | −0.823033 | − | 0.567993i | \(-0.807720\pi\) | ||
0.823033 | − | 0.567993i | \(-0.192280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.6346 | + | 23.9300i | 1.09700 | + | 0.804398i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 37.9418i | − | 1.27396i | −0.770879 | − | 0.636981i | \(-0.780183\pi\) | ||
0.770879 | − | 0.636981i | \(-0.219817\pi\) | |||||||
\(888\) | 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 | ||||||||
\(903\) | 23.7403 | + | 18.6224i | 0.790029 | + | 0.619713i | ||||
\(904\) | 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 | \(0.183110\pi\) | ||||
−0.839052 | + | 0.544051i | \(0.816890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.3763 | 0.575071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.79655 | − | 13.3601i | 0.323864 | − | 0.441670i | ||||
\(916\) | 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 | \(-0.470385\pi\) | ||||
0.0929040 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(930\) | 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 | \(-0.803837\pi\) | ||||
−0.816043 | + | 0.577991i | \(0.803837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6826 | 0.413003 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 25.5538 | − | 17.0881i | 0.831265 | − | 0.555877i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.8322 | −0.904426 | −0.452213 | − | 0.891910i | \(-0.649365\pi\) | ||||
−0.452213 | + | 0.891910i | \(0.649365\pi\) | |||||||
\(948\) | 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 | \(-0.409546\pi\) | ||||
0.280361 | + | 0.959895i | \(0.409546\pi\) | |||||||
\(954\) | 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 | \(-0.501573\pi\) | ||||
−0.00494078 | + | 0.999988i | \(0.501573\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3634 | + | 31.9670i | 0.684880 | + | 1.02481i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0151475 | − | 1.36231i | 0.000485107 | − | 0.0436288i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.3493 | 1.06694 | 0.533469 | − | 0.845820i | \(-0.320888\pi\) | ||||
0.533469 | + | 0.845820i | \(0.320888\pi\) | |||||||
\(978\) | 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 | \(-0.786383\pi\) | ||
0.783140 | − | 0.621845i | \(-0.213617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6772 | − | 24.6780i | −0.563242 | − | 0.786308i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.2177 | + | 15.8592i | 0.643538 | + | 0.504803i | ||||
\(988\) | 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.a.209.21 | yes | 24 | |
3.2 | odd | 2 | 840.2.k.b.209.22 | yes | 24 | ||
4.3 | odd | 2 | 1680.2.k.i.209.4 | 24 | |||
5.4 | even | 2 | 840.2.k.b.209.4 | yes | 24 | ||
7.6 | odd | 2 | inner | 840.2.k.a.209.4 | yes | 24 | |
12.11 | even | 2 | 1680.2.k.h.209.3 | 24 | |||
15.14 | odd | 2 | inner | 840.2.k.a.209.3 | ✓ | 24 | |
20.19 | odd | 2 | 1680.2.k.h.209.21 | 24 | |||
21.20 | even | 2 | 840.2.k.b.209.3 | yes | 24 | ||
28.27 | even | 2 | 1680.2.k.i.209.21 | 24 | |||
35.34 | odd | 2 | 840.2.k.b.209.21 | yes | 24 | ||
60.59 | even | 2 | 1680.2.k.i.209.22 | 24 | |||
84.83 | odd | 2 | 1680.2.k.h.209.22 | 24 | |||
105.104 | even | 2 | inner | 840.2.k.a.209.22 | yes | 24 | |
140.139 | even | 2 | 1680.2.k.h.209.4 | 24 | |||
420.419 | odd | 2 | 1680.2.k.i.209.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.k.a.209.3 | ✓ | 24 | 15.14 | odd | 2 | inner | |
840.2.k.a.209.4 | yes | 24 | 7.6 | odd | 2 | inner | |
840.2.k.a.209.21 | yes | 24 | 1.1 | even | 1 | trivial | |
840.2.k.a.209.22 | yes | 24 | 105.104 | even | 2 | inner | |
840.2.k.b.209.3 | yes | 24 | 21.20 | even | 2 | ||
840.2.k.b.209.4 | yes | 24 | 5.4 | even | 2 | ||
840.2.k.b.209.21 | yes | 24 | 35.34 | odd | 2 | ||
840.2.k.b.209.22 | yes | 24 | 3.2 | odd | 2 | ||
1680.2.k.h.209.3 | 24 | 12.11 | even | 2 | |||
1680.2.k.h.209.4 | 24 | 140.139 | even | 2 | |||
1680.2.k.h.209.21 | 24 | 20.19 | odd | 2 | |||
1680.2.k.h.209.22 | 24 | 84.83 | odd | 2 | |||
1680.2.k.i.209.3 | 24 | 420.419 | odd | 2 | |||
1680.2.k.i.209.4 | 24 | 4.3 | odd | 2 | |||
1680.2.k.i.209.21 | 24 | 28.27 | even | 2 | |||
1680.2.k.i.209.22 | 24 | 60.59 | even | 2 |