Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Character | \(\chi\) | \(=\) | 108.65 |
Dual form | 108.3.k.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.95183 | − | 2.27824i | −0.650610 | − | 0.759412i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.25030 | + | 8.93012i | −0.650060 | + | 1.78602i | −0.0325374 | + | 0.999471i | \(0.510359\pi\) |
−0.617522 | + | 0.786553i | \(0.711863\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.410040 | − | 2.32545i | 0.0585771 | − | 0.332207i | −0.941410 | − | 0.337264i | \(-0.890499\pi\) |
0.999987 | + | 0.00505674i | \(0.00160962\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.38071 | + | 8.89346i | −0.153413 | + | 0.988162i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.40911 | + | 12.1139i | 0.400828 | + | 1.10127i | 0.961877 | + | 0.273483i | \(0.0881757\pi\) |
−0.561049 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.2099 | + | 10.2453i | −0.939224 | + | 0.788103i | −0.977450 | − | 0.211166i | \(-0.932274\pi\) |
0.0382260 | + | 0.999269i | \(0.487829\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 26.6889 | − | 10.0251i | 1.77926 | − | 0.668343i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 12.2018 | − | 7.04474i | 0.717755 | − | 0.414396i | −0.0961707 | − | 0.995365i | \(-0.530659\pi\) |
0.813926 | + | 0.580969i | \(0.197326\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.29274 | + | 5.70319i | −0.173302 | + | 0.300168i | −0.939572 | − | 0.342350i | \(-0.888777\pi\) |
0.766270 | + | 0.642518i | \(0.222110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.09825 | + | 3.60472i | −0.290393 | + | 0.171653i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −25.9779 | + | 4.58061i | −1.12947 | + | 0.199157i | −0.706997 | − | 0.707217i | \(-0.749950\pi\) |
−0.422477 | + | 0.906374i | \(0.638839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −50.0315 | − | 41.9814i | −2.00126 | − | 1.67926i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 22.9563 | − | 14.2129i | 0.850234 | − | 0.526405i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.977913 | − | 1.16543i | 0.0337211 | − | 0.0401873i | −0.748920 | − | 0.662660i | \(-0.769427\pi\) |
0.782641 | + | 0.622473i | \(0.213872\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.620995 | − | 3.52184i | −0.0200321 | − | 0.113608i | 0.973152 | − | 0.230163i | \(-0.0739259\pi\) |
−0.993184 | + | 0.116555i | \(0.962815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18.9925 | − | 33.6893i | 0.575531 | − | 1.02089i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.4338 | + | 11.2201i | 0.555252 | + | 0.320575i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0926 | − | 19.2129i | −0.299800 | − | 0.519269i | 0.676290 | − | 0.736635i | \(-0.263587\pi\) |
−0.976090 | + | 0.217367i | \(0.930253\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 47.1730 | + | 7.81990i | 1.20956 | + | 0.200510i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 31.4714 | + | 37.5062i | 0.767595 | + | 0.914784i | 0.998303 | − | 0.0582388i | \(-0.0185485\pi\) |
−0.230707 | + | 0.973023i | \(0.574104\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 78.8159 | − | 28.6866i | 1.83293 | − | 0.667131i | 0.840888 | − | 0.541210i | \(-0.182033\pi\) |
0.992040 | − | 0.125921i | \(-0.0401887\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −74.9319 | − | 41.2363i | −1.66515 | − | 0.916363i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −34.9622 | − | 6.16478i | −0.743877 | − | 0.131166i | −0.211151 | − | 0.977453i | \(-0.567721\pi\) |
−0.532726 | + | 0.846288i | \(0.678832\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 40.8053 | + | 14.8519i | 0.832762 | + | 0.303101i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −39.8655 | − | 14.0485i | −0.781676 | − | 0.275461i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 65.8880i | 1.24317i | 0.783347 | + | 0.621585i | \(0.213511\pi\) | ||||
−0.783347 | + | 0.621585i | \(0.786489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −122.510 | −2.22745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19.4201 | − | 3.63003i | 0.340703 | − | 0.0636847i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −17.2513 | + | 47.3976i | −0.292395 | + | 0.803349i | 0.703320 | + | 0.710874i | \(0.251700\pi\) |
−0.995715 | + | 0.0924754i | \(0.970522\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5793 | + | 65.6697i | −0.189825 | + | 1.07655i | 0.729772 | + | 0.683690i | \(0.239626\pi\) |
−0.919597 | + | 0.392862i | \(0.871485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.1152 | + | 6.85745i | 0.319288 | + | 0.108848i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −51.8062 | − | 142.336i | −0.797019 | − | 2.18979i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 72.5027 | − | 60.8370i | 1.08213 | − | 0.908015i | 0.0860340 | − | 0.996292i | \(-0.472581\pi\) |
0.996096 | + | 0.0882774i | \(0.0281362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 61.1402 | + | 50.2432i | 0.886089 | + | 0.728163i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 71.8787 | − | 41.4992i | 1.01238 | − | 0.584496i | 0.100490 | − | 0.994938i | \(-0.467959\pi\) |
0.911887 | + | 0.410442i | \(0.134626\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −47.8713 | + | 82.9155i | −0.655771 | + | 1.13583i | 0.325929 | + | 0.945394i | \(0.394323\pi\) |
−0.981700 | + | 0.190434i | \(0.939010\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00947 | + | 195.924i | 0.0267929 | + | 2.61232i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.9782 | − | 5.28597i | 0.389328 | − | 0.0686490i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −25.9904 | − | 21.8086i | −0.328993 | − | 0.276058i | 0.463296 | − | 0.886203i | \(-0.346667\pi\) |
−0.792289 | + | 0.610146i | \(0.791111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −77.1873 | − | 24.5587i | −0.952929 | − | 0.303193i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.14066 | − | 8.50991i | 0.0860321 | − | 0.102529i | −0.721311 | − | 0.692611i | \(-0.756460\pi\) |
0.807343 | + | 0.590082i | \(0.200905\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.2507 | + | 131.861i | 0.273538 | + | 1.55131i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.56385 | + | 0.0468084i | −0.0524580 | + | 0.000538028i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.83930 | − | 5.10337i | −0.0993180 | − | 0.0573412i | 0.449518 | − | 0.893271i | \(-0.351596\pi\) |
−0.548836 | + | 0.835930i | \(0.684929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.8185 | + | 32.5945i | 0.206796 | + | 0.358182i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.81149 | + | 8.28880i | −0.0732419 | + | 0.0891269i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −40.2278 | − | 47.9416i | −0.423450 | − | 0.504648i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.7584 | − | 24.2981i | 0.688231 | − | 0.250496i | 0.0258533 | − | 0.999666i | \(-0.491770\pi\) |
0.662378 | + | 0.749170i | \(0.269547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −113.822 | + | 22.4863i | −1.14972 | + | 0.227135i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −60.9870 | − | 10.7536i | −0.603831 | − | 0.106472i | −0.136629 | − | 0.990622i | \(-0.543627\pi\) |
−0.467202 | + | 0.884151i | \(0.654738\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98.6549 | + | 35.9074i | 0.957814 | + | 0.348616i | 0.773177 | − | 0.634191i | \(-0.218667\pi\) |
0.184638 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.3694 | − | 66.1745i | −0.117804 | − | 0.630234i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 20.2740i | − | 0.189477i | −0.995502 | − | 0.0947385i | \(-0.969799\pi\) | ||
0.995502 | − | 0.0947385i | \(-0.0302015\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 145.914 | 1.33866 | 0.669328 | − | 0.742967i | \(-0.266582\pi\) | ||||
0.669328 | + | 0.742967i | \(0.266582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.1207 | + | 62.7719i | −0.199286 | + | 0.565513i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −22.6555 | + | 62.2454i | −0.200491 | + | 0.550844i | −0.998669 | − | 0.0515773i | \(-0.983575\pi\) |
0.798178 | + | 0.602422i | \(0.205797\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 43.5306 | − | 246.874i | 0.378527 | − | 2.14673i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −74.2581 | − | 122.734i | −0.634684 | − | 1.04901i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3789 | − | 31.2634i | −0.0956214 | − | 0.262718i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −34.6155 | + | 29.0458i | −0.286078 | + | 0.240048i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 24.0210 | − | 144.905i | 0.195293 | − | 1.17809i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 331.765 | − | 191.545i | 2.65412 | − | 1.53236i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.5642 | − | 33.8862i | 0.154049 | − | 0.266820i | −0.778663 | − | 0.627442i | \(-0.784102\pi\) |
0.932712 | + | 0.360621i | \(0.117435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −219.190 | − | 123.570i | −1.69915 | − | 0.957905i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −225.050 | + | 39.6824i | −1.71794 | + | 0.302919i | −0.943903 | − | 0.330223i | \(-0.892876\pi\) |
−0.774036 | + | 0.633142i | \(0.781765\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.9123 | + | 9.99563i | 0.0895664 | + | 0.0751551i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 52.3083 | + | 251.199i | 0.387469 | + | 1.86073i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 90.7406 | − | 108.140i | 0.662340 | − | 0.789346i | −0.325379 | − | 0.945584i | \(-0.605492\pi\) |
0.987720 | + | 0.156237i | \(0.0499364\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8432 | + | 89.8510i | 0.113980 | + | 0.646410i | 0.987250 | + | 0.159175i | \(0.0508835\pi\) |
−0.873271 | + | 0.487235i | \(0.838005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 54.1955 | + | 91.6847i | 0.384365 | + | 0.650246i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −177.946 | − | 102.737i | −1.24438 | − | 0.718442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.22893 | + | 12.5209i | 0.0498547 | + | 0.0863509i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −45.8089 | − | 121.953i | −0.311625 | − | 0.829610i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1684 | + | 24.0358i | 0.135358 | + | 0.161314i | 0.829466 | − | 0.558558i | \(-0.188645\pi\) |
−0.694107 | + | 0.719872i | \(0.744201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −91.3198 | + | 33.2377i | −0.604767 | + | 0.220117i | −0.626212 | − | 0.779653i | \(-0.715396\pi\) |
0.0214449 | + | 0.999770i | \(0.493173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 45.8048 | + | 118.243i | 0.299378 | + | 0.772832i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.4688 | + | 5.90146i | 0.215928 | + | 0.0380739i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.8874 | + | 4.32668i | 0.0757162 | + | 0.0275584i | 0.379601 | − | 0.925150i | \(-0.376061\pi\) |
−0.303884 | + | 0.952709i | \(0.598284\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 150.108 | − | 128.602i | 0.944078 | − | 0.808819i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 62.2886i | 0.386885i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −167.367 | −1.02679 | −0.513397 | − | 0.858151i | \(-0.671613\pi\) | ||||
−0.513397 | + | 0.858151i | \(0.671613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 239.118 | + | 279.106i | 1.44920 | + | 1.69155i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.44485 | − | 17.7071i | 0.0385919 | − | 0.106030i | −0.918900 | − | 0.394491i | \(-0.870921\pi\) |
0.957492 | + | 0.288460i | \(0.0931433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.7686 | − | 83.7568i | 0.0873881 | − | 0.495602i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −46.1748 | − | 37.1583i | −0.270028 | − | 0.217300i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 70.3332 | + | 193.239i | 0.406550 | + | 1.11699i | 0.958991 | + | 0.283436i | \(0.0914743\pi\) |
−0.552441 | + | 0.833552i | \(0.686303\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −118.141 | + | 99.1317i | −0.675089 | + | 0.566467i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 141.655 | − | 53.2095i | 0.800308 | − | 0.300619i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −125.847 | + | 72.6580i | −0.703058 | + | 0.405911i | −0.808485 | − | 0.588516i | \(-0.799712\pi\) |
0.105427 | + | 0.994427i | \(0.466379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −60.7901 | + | 105.292i | −0.335857 | + | 0.581721i | −0.983649 | − | 0.180096i | \(-0.942359\pi\) |
0.647792 | + | 0.761817i | \(0.275693\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 172.212 | − | 101.796i | 0.941049 | − | 0.556260i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 207.628 | − | 36.6104i | 1.12231 | − | 0.197894i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 139.139 | + | 116.751i | 0.744057 | + | 0.624338i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.6385 | − | 59.2117i | −0.125071 | − | 0.313289i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −58.7864 | + | 70.0589i | −0.307782 | + | 0.366801i | −0.897658 | − | 0.440694i | \(-0.854732\pi\) |
0.589875 | + | 0.807494i | \(0.299177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −56.8849 | − | 322.610i | −0.294740 | − | 1.67156i | −0.668256 | − | 0.743932i | \(-0.732959\pi\) |
0.373515 | − | 0.927624i | \(-0.378152\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −223.159 | + | 395.843i | −1.14440 | + | 2.02997i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −43.6830 | − | 25.2204i | −0.221741 | − | 0.128022i | 0.385015 | − | 0.922910i | \(-0.374196\pi\) |
−0.606756 | + | 0.794888i | \(0.707530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.02449 | − | 5.23856i | −0.0151984 | − | 0.0263244i | 0.858326 | − | 0.513104i | \(-0.171505\pi\) |
−0.873525 | + | 0.486780i | \(0.838171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −280.114 | − | 46.4347i | −1.39360 | − | 0.231019i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.30917 | − | 2.75196i | −0.0113752 | − | 0.0135565i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −437.226 | + | 159.137i | −2.13281 | + | 0.776279i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.86937 | − | 237.358i | −0.0235235 | − | 1.14666i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −83.6060 | − | 14.7420i | −0.400029 | − | 0.0705359i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4132 | + | 6.70185i | 0.0872663 | + | 0.0317623i | 0.385284 | − | 0.922798i | \(-0.374103\pi\) |
−0.298018 | + | 0.954560i | \(0.596326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −234.840 | − | 82.7573i | −1.10254 | − | 0.388532i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 797.076i | 3.70733i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.44449 | −0.0389147 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 282.338 | − | 52.7749i | 1.28921 | − | 0.240981i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −76.8077 | + | 211.028i | −0.347546 | + | 0.954876i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4949 | − | 99.2183i | 0.0784523 | − | 0.444925i | −0.920126 | − | 0.391622i | \(-0.871914\pi\) |
0.998578 | − | 0.0533028i | \(-0.0169748\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 442.439 | − | 386.989i | 1.96640 | − | 1.71995i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2532 | − | 33.6653i | −0.0539787 | − | 0.148305i | 0.909773 | − | 0.415106i | \(-0.136256\pi\) |
−0.963752 | + | 0.266801i | \(0.914033\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 131.729 | − | 110.534i | 0.575235 | − | 0.482679i | −0.308144 | − | 0.951340i | \(-0.599708\pi\) |
0.883378 | + | 0.468661i | \(0.155263\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −70.5551 | − | 57.9802i | −0.305433 | − | 0.250996i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 110.221 | − | 63.6363i | 0.473053 | − | 0.273117i | −0.244464 | − | 0.969658i | \(-0.578612\pi\) |
0.717517 | + | 0.696541i | \(0.245279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 168.690 | − | 292.179i | 0.717829 | − | 1.24332i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04388 | + | 101.779i | 0.00440456 | + | 0.429447i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 343.656 | − | 60.5957i | 1.43789 | − | 0.253539i | 0.600272 | − | 0.799796i | \(-0.295059\pi\) |
0.837617 | + | 0.546257i | \(0.183948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 361.538 | + | 303.367i | 1.50016 | + | 1.25878i | 0.880626 | + | 0.473811i | \(0.157122\pi\) |
0.619532 | + | 0.784971i | \(0.287322\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 94.7061 | + | 223.785i | 0.389737 | + | 0.920926i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −265.259 | + | 316.123i | −1.08269 | + | 1.29030i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.2270 | − | 103.371i | −0.0737937 | − | 0.418505i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33.3249 | + | 0.341792i | −0.133835 | + | 0.00137266i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −321.947 | − | 185.876i | −1.28266 | − | 0.740542i | −0.305323 | − | 0.952249i | \(-0.598764\pi\) |
−0.977333 | + | 0.211707i | \(0.932098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −170.028 | − | 294.498i | −0.672049 | − | 1.16402i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 255.030 | − | 310.342i | 1.00012 | − | 1.21703i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 65.9115 | + | 78.5502i | 0.256465 | + | 0.305643i | 0.878879 | − | 0.477045i | \(-0.158292\pi\) |
−0.622414 | + | 0.782688i | \(0.713848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −49.2271 | + | 17.9172i | −0.190066 | + | 0.0691784i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.01450 | + | 10.3062i | 0.0345383 | + | 0.0394872i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 225.681 | + | 39.7937i | 0.858103 | + | 0.151307i | 0.585353 | − | 0.810778i | \(-0.300956\pi\) |
0.272750 | + | 0.962085i | \(0.412067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −588.388 | − | 214.156i | −2.22033 | − | 0.808134i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.62613 | + | 30.0989i | 0.0210717 | + | 0.112730i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 111.782i | − | 0.415546i | −0.978177 | − | 0.207773i | \(-0.933378\pi\) | ||
0.978177 | − | 0.207773i | \(-0.0666215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −107.229 | −0.395680 | −0.197840 | − | 0.980234i | \(-0.563393\pi\) | ||||
−0.197840 | + | 0.980234i | \(0.563393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 37.5276 | − | 106.492i | 0.137464 | − | 0.390080i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 287.965 | − | 791.178i | 1.04715 | − | 2.87701i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −74.3484 | + | 421.651i | −0.268406 | + | 1.52221i | 0.490752 | + | 0.871299i | \(0.336722\pi\) |
−0.759158 | + | 0.650906i | \(0.774389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 32.1787 | − | 0.660142i | 0.115336 | − | 0.00236610i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −46.0248 | − | 126.452i | −0.163789 | − | 0.450007i | 0.830463 | − | 0.557074i | \(-0.188076\pi\) |
−0.994252 | + | 0.107067i | \(0.965854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.267348 | + | 0.224332i | −0.000944693 | + | 0.000792692i | −0.643260 | − | 0.765648i | \(-0.722418\pi\) |
0.642315 | + | 0.766441i | \(0.277974\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −30.7045 | + | 185.222i | −0.107735 | + | 0.649903i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 100.123 | − | 57.8062i | 0.348862 | − | 0.201415i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.2434 | + | 78.3639i | −0.156552 | + | 0.271155i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −185.658 | − | 104.666i | −0.637999 | − | 0.359676i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −454.925 | + | 80.2156i | −1.55265 | + | 0.273773i | −0.883167 | − | 0.469059i | \(-0.844593\pi\) |
−0.669478 | + | 0.742832i | \(0.733482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −367.194 | − | 308.113i | −1.24473 | − | 1.04445i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 273.391 | + | 215.425i | 0.920509 | + | 0.725336i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 270.258 | − | 322.081i | 0.903873 | − | 1.07719i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.3917 | − | 195.045i | −0.114258 | − | 0.647991i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 94.5369 | + | 159.932i | 0.312003 | + | 0.527828i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −548.802 | − | 316.851i | −1.79935 | − | 1.03886i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 164.184 | + | 284.376i | 0.534803 | + | 0.926305i | 0.999173 | + | 0.0406640i | \(0.0129473\pi\) |
−0.464370 | + | 0.885641i | \(0.653719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −110.752 | − | 294.844i | −0.358421 | − | 0.954188i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 104.035 | + | 123.985i | 0.334519 | + | 0.398664i | 0.906915 | − | 0.421313i | \(-0.138431\pi\) |
−0.572396 | + | 0.819977i | \(0.693986\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 219.058 | − | 79.7305i | 0.699865 | − | 0.254730i | 0.0325118 | − | 0.999471i | \(-0.489649\pi\) |
0.667353 | + | 0.744741i | \(0.267427\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −126.618 | + | 157.342i | −0.401962 | + | 0.499498i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 391.166 | + | 68.9732i | 1.23396 | + | 0.217581i | 0.752327 | − | 0.658790i | \(-0.228932\pi\) |
0.481636 | + | 0.876371i | \(0.340043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.4297 | + | 6.70785i | 0.0577732 | + | 0.0210277i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −46.1890 | + | 39.5715i | −0.143891 | + | 0.123276i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 92.7859i | 0.287263i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1040.99 | 3.20306 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −284.799 | − | 332.425i | −0.870944 | − | 1.01659i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.6718 | + | 78.7751i | −0.0871483 | + | 0.239438i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −60.1296 | + | 341.012i | −0.181660 | + | 1.03025i | 0.748511 | + | 0.663122i | \(0.230769\pi\) |
−0.930172 | + | 0.367125i | \(0.880342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 186.185 | − | 72.1240i | 0.559115 | − | 0.216588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 307.626 | + | 845.196i | 0.918287 | + | 2.52297i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.9604 | + | 23.4615i | −0.0829685 | + | 0.0696188i | −0.683329 | − | 0.730111i | \(-0.739468\pi\) |
0.600360 | + | 0.799730i | \(0.295024\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 186.029 | − | 69.8780i | 0.548759 | − | 0.206130i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.9252 | − | 23.0508i | 0.117083 | − | 0.0675977i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 109.122 | − | 189.004i | 0.318139 | − | 0.551033i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −647.402 | + | 382.684i | −1.87653 | + | 1.10923i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.2515 | − | 5.86314i | 0.0958257 | − | 0.0168967i | −0.125530 | − | 0.992090i | \(-0.540063\pi\) |
0.221355 | + | 0.975193i | \(0.428952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −128.274 | − | 107.635i | −0.367548 | − | 0.308410i | 0.440242 | − | 0.897879i | \(-0.354893\pi\) |
−0.807791 | + | 0.589469i | \(0.799337\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −134.678 | + | 408.734i | −0.383699 | + | 1.16448i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −249.417 | + | 297.244i | −0.706564 | + | 0.842050i | −0.993252 | − | 0.115974i | \(-0.963001\pi\) |
0.286689 | + | 0.958024i | \(0.407445\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 136.966 | + | 776.771i | 0.385819 | + | 2.18809i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −49.0156 | + | 86.9448i | −0.137299 | + | 0.243543i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −309.401 | − | 178.633i | −0.861841 | − | 0.497584i | 0.00278752 | − | 0.999996i | \(-0.499113\pi\) |
−0.864628 | + | 0.502412i | \(0.832446\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 158.816 | + | 275.077i | 0.439933 | + | 0.761986i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 133.737 | + | 22.1697i | 0.368421 | + | 0.0610735i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −584.849 | − | 696.996i | −1.60233 | − | 1.90958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 530.990 | − | 193.265i | 1.44684 | − | 0.526606i | 0.505133 | − | 0.863042i | \(-0.331444\pi\) |
0.941707 | + | 0.336435i | \(0.109221\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −377.013 | + | 228.104i | −1.02171 | + | 0.618169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 153.219 | + | 27.0167i | 0.412990 | + | 0.0728213i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −68.7050 | − | 25.0066i | −0.184196 | − | 0.0670417i | 0.248276 | − | 0.968689i | \(-0.420136\pi\) |
−0.432471 | + | 0.901648i | \(0.642358\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1083.93 | − | 381.976i | −2.89049 | − | 1.01860i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.2489i | 0.0643206i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 63.3568 | 0.167168 | 0.0835841 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835841 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −115.387 | + | 21.5682i | −0.302852 | + | 0.0566095i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.5538 | + | 59.2185i | −0.0562762 | + | 0.154618i | −0.964645 | − | 0.263552i | \(-0.915106\pi\) |
0.908369 | + | 0.418169i | \(0.137328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −50.2338 | + | 284.890i | −0.130477 | + | 0.739975i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 146.301 | + | 740.554i | 0.378039 | + | 1.91358i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.7172 | + | 29.4454i | 0.0275508 | + | 0.0756951i | 0.952706 | − | 0.303895i | \(-0.0982872\pi\) |
−0.925155 | + | 0.379590i | \(0.876065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −284.709 | + | 238.899i | −0.728156 | + | 0.610996i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 529.665 | + | 435.264i | 1.34775 | + | 1.10754i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 279.230 | − | 161.213i | 0.706911 | − | 0.408135i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 247.263 | − | 428.273i | 0.622830 | − | 1.07877i | −0.366126 | − | 0.930565i | \(-0.619316\pi\) |
0.988956 | − | 0.148208i | \(-0.0473505\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.478447 | − | 46.6489i | −0.00119912 | − | 0.116914i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 671.249 | − | 118.359i | 1.67394 | − | 0.295160i | 0.745460 | − | 0.666550i | \(-0.232230\pi\) |
0.928477 | + | 0.371390i | \(0.121119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.6647 | + | 36.6390i | 0.108349 | + | 0.0909157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 470.193 | − | 609.469i | 1.16097 | − | 1.50486i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 183.836 | − | 219.087i | 0.451684 | − | 0.538297i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −82.5079 | − | 467.926i | −0.201731 | − | 1.14407i | −0.902502 | − | 0.430686i | \(-0.858272\pi\) |
0.700771 | − | 0.713386i | \(-0.252840\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −423.480 | + | 4.34336i | −1.03036 | + | 0.0105678i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 103.147 | + | 59.5520i | 0.249751 | + | 0.144194i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 52.7852 | + | 91.4267i | 0.127193 | + | 0.220305i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 173.779 | − | 211.468i | 0.416735 | − | 0.507119i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −150.860 | − | 179.788i | −0.360048 | − | 0.429088i | 0.555364 | − | 0.831608i | \(-0.312579\pi\) |
−0.915411 | + | 0.402519i | \(0.868135\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −121.158 | + | 44.0979i | −0.287786 | + | 0.104746i | −0.481879 | − | 0.876238i | \(-0.660046\pi\) |
0.194094 | + | 0.980983i | \(0.437823\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 103.099 | − | 302.423i | 0.243733 | − | 0.714948i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −906.224 | − | 159.792i | −2.13229 | − | 0.375981i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 147.964 | + | 53.8544i | 0.346519 | + | 0.126123i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 113.261 | + | 605.928i | 0.264012 | + | 1.41242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 270.719i | − | 0.628119i | −0.949403 | − | 0.314059i | \(-0.898311\pi\) | ||
0.949403 | − | 0.314059i | \(-0.101689\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −89.2999 | −0.206235 | −0.103118 | − | 0.994669i | \(-0.532882\pi\) | ||||
−0.103118 | + | 0.994669i | \(0.532882\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.4159 | − | 40.9078i | 0.0331399 | − | 0.0940410i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 59.4144 | − | 163.240i | 0.135960 | − | 0.373546i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −108.018 | + | 612.599i | −0.246054 | + | 1.39544i | 0.571978 | + | 0.820269i | \(0.306176\pi\) |
−0.818032 | + | 0.575172i | \(0.804935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −188.426 | + | 342.394i | −0.427269 | + | 0.776405i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −213.946 | − | 587.813i | −0.482949 | − | 1.32689i | −0.906953 | − | 0.421231i | \(-0.861598\pi\) |
0.424005 | − | 0.905660i | \(-0.360624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 74.3041 | − | 62.3485i | 0.166975 | − | 0.140109i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.3938 | − | 92.8621i | 0.0344381 | − | 0.207745i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 86.6015 | − | 49.9994i | 0.192876 | − | 0.111357i | −0.400452 | − | 0.916318i | \(-0.631147\pi\) |
0.593328 | + | 0.804960i | \(0.297814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −315.586 | + | 546.611i | −0.699747 | + | 1.21200i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 253.964 | + | 143.174i | 0.560627 | + | 0.316057i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −352.239 | + | 62.1092i | −0.774151 | + | 0.136504i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −134.065 | − | 112.494i | −0.293359 | − | 0.246158i | 0.484214 | − | 0.874949i | \(-0.339105\pi\) |
−0.777574 | + | 0.628792i | \(0.783550\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 179.983 | − | 335.145i | 0.392120 | − | 0.730164i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 494.766 | − | 589.639i | 1.07325 | − | 1.27904i | 0.114917 | − | 0.993375i | \(-0.463340\pi\) |
0.958328 | − | 0.285669i | \(-0.0922159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −86.2655 | − | 489.236i | −0.186319 | − | 1.05667i | −0.924249 | − | 0.381789i | \(-0.875308\pi\) |
0.737931 | − | 0.674876i | \(-0.235803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.8806 | − | 87.7685i | −0.111571 | − | 0.188750i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −368.842 | − | 212.951i | −0.789811 | − | 0.455997i | 0.0500853 | − | 0.998745i | \(-0.484051\pi\) |
−0.839896 | + | 0.542748i | \(0.817384\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −111.744 | − | 193.547i | −0.238261 | − | 0.412680i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.3451 | − | 35.5273i | −0.0283335 | − | 0.0754296i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 695.015 | + | 828.287i | 1.46938 | + | 1.75114i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 404.169 | − | 147.105i | 0.850881 | − | 0.309695i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −585.972 | − | 90.9725i | −1.22845 | − | 0.190718i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 696.066 | + | 122.735i | 1.45316 | + | 0.256232i | 0.843800 | − | 0.536658i | \(-0.180313\pi\) |
0.609365 | + | 0.792890i | \(0.291424\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 332.283 | + | 120.941i | 0.690816 | + | 0.251437i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 141.908 | − | 121.577i | 0.293805 | − | 0.251712i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 675.136i | 1.39203i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −835.437 | −1.71548 | −0.857738 | − | 0.514087i | \(-0.828131\pi\) | ||||
−0.857738 | + | 0.514087i | \(0.828131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 326.673 | + | 381.302i | 0.668042 | + | 0.779759i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 218.847 | − | 601.277i | 0.445717 | − | 1.22460i | −0.489961 | − | 0.871744i | \(-0.662989\pi\) |
0.935679 | − | 0.352854i | \(-0.114789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.72218 | − | 21.1095i | 0.00755007 | − | 0.0428185i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 169.151 | − | 1089.53i | 0.341719 | − | 2.20108i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −67.0312 | − | 184.167i | −0.134872 | − | 0.370557i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 517.161 | − | 433.949i | 1.03639 | − | 0.869638i | 0.0447962 | − | 0.998996i | \(-0.485736\pi\) |
0.991598 | + | 0.129358i | \(0.0412917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −52.9201 | + | 19.8783i | −0.105629 | + | 0.0396773i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −530.717 | + | 306.409i | −1.05510 | + | 0.609164i | −0.924074 | − | 0.382215i | \(-0.875162\pi\) |
−0.131029 | + | 0.991378i | \(0.541828\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 294.257 | − | 509.668i | 0.582687 | − | 1.00924i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −219.643 | + | 129.833i | −0.433222 | + | 0.256080i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 473.492 | − | 83.4894i | 0.930239 | − | 0.164026i | 0.312059 | − | 0.950063i | \(-0.398981\pi\) |
0.618180 | + | 0.786036i | \(0.287870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 173.187 | + | 145.321i | 0.338917 | + | 0.284385i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.46993 | + | 177.724i | 0.0106626 | + | 0.346440i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −641.315 | + | 764.290i | −1.24527 | + | 1.48406i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −79.4724 | − | 450.711i | −0.153718 | − | 0.871781i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 302.965 | − | 537.405i | 0.583748 | − | 1.03546i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 194.362 | + | 112.215i | 0.373055 | + | 0.215383i | 0.674792 | − | 0.738008i | \(-0.264233\pi\) |
−0.301737 | + | 0.953391i | \(0.597567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −317.364 | − | 549.691i | −0.606815 | − | 1.05104i | −0.991762 | − | 0.128096i | \(-0.959113\pi\) |
0.384946 | − | 0.922939i | \(-0.374220\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 456.436 | + | 75.6638i | 0.869402 | + | 0.144121i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.3877 | − | 38.5981i | −0.0614567 | − | 0.0732412i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 156.772 | − | 57.0604i | 0.296355 | − | 0.107865i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −397.709 | − | 218.866i | −0.748982 | − | 0.412178i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −768.526 | − | 135.512i | −1.44189 | − | 0.254244i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 181.050 | + | 65.8967i | 0.338410 | + | 0.123171i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 411.165 | + | 144.894i | 0.765670 | + | 0.269821i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 559.797i | 1.03858i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −322.531 | −0.596176 | −0.298088 | − | 0.954538i | \(-0.596349\pi\) | ||||
−0.298088 | + | 0.954538i | \(0.596349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 358.531 | − | 67.0171i | 0.660278 | − | 0.123420i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −474.263 | + | 1303.03i | −0.870207 | + | 2.39087i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 63.9102 | − | 362.453i | 0.116838 | − | 0.662619i | −0.868986 | − | 0.494836i | \(-0.835228\pi\) |
0.985824 | − | 0.167783i | \(-0.0536608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −568.043 | − | 193.651i | −1.03469 | − | 0.352735i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.42666 | + | 9.41468i | 0.00621899 | + | 0.0170865i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −61.3719 | + | 51.4971i | −0.110980 | + | 0.0931232i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −488.662 | − | 401.568i | −0.880472 | − | 0.723546i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 218.606 | − | 126.212i | 0.392470 | − | 0.226593i | −0.290760 | − | 0.956796i | \(-0.593908\pi\) |
0.683230 | + | 0.730203i | \(0.260575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −668.431 | + | 1157.76i | −1.19576 | + | 2.07112i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.58837 | − | 544.869i | −0.00996144 | − | 0.971246i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −654.162 | + | 115.346i | −1.16192 | + | 0.204878i | −0.721175 | − | 0.692753i | \(-0.756398\pi\) |
−0.440747 | + | 0.897631i | \(0.645287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −482.222 | − | 404.632i | −0.853490 | − | 0.716163i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −88.7598 | + | 169.425i | −0.156543 | + | 0.298810i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −173.933 | + | 207.286i | −0.305682 | + | 0.364298i | −0.896915 | − | 0.442203i | \(-0.854197\pi\) |
0.591233 | + | 0.806501i | \(0.298641\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 64.4159 | + | 365.321i | 0.112812 | + | 0.639791i | 0.987810 | + | 0.155664i | \(0.0497517\pi\) |
−0.874998 | + | 0.484127i | \(0.839137\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 274.352 | − | 2.81385i | 0.478799 | − | 0.00491073i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1492.01 | + | 861.414i | 2.59481 | + | 1.49811i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 172.890 | + | 299.454i | 0.299636 | + | 0.518985i | 0.976053 | − | 0.217535i | \(-0.0698015\pi\) |
−0.676417 | + | 0.736519i | \(0.736468\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −623.953 | + | 759.278i | −1.07764 | + | 1.31136i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.8614 | − | 20.0947i | −0.0290214 | − | 0.0345863i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −798.162 | + | 290.507i | −1.36906 | + | 0.498297i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1337.39 | − | 264.211i | 2.28614 | − | 0.451642i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 390.919 | + | 68.9295i | 0.665960 | + | 0.117427i | 0.496401 | − | 0.868093i | \(-0.334655\pi\) |
0.169559 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.1305 | + | 8.05483i | 0.0375730 | + | 0.0136754i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.8038 | + | 148.746i | 0.0470454 | + | 0.251685i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 453.585i | − | 0.764899i | −0.923976 | − | 0.382449i | \(-0.875081\pi\) | ||
0.923976 | − | 0.382449i | \(-0.124919\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 316.171 | 0.531380 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.03140 | + | 17.1153i | −0.0101028 | + | 0.0286688i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −127.690 | + | 350.827i | −0.213173 | + | 0.585687i | −0.999483 | − | 0.0321442i | \(-0.989766\pi\) |
0.786310 | + | 0.617832i | \(0.211989\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 162.521 | − | 921.701i | 0.270417 | − | 1.53361i | −0.482736 | − | 0.875766i | \(-0.660357\pi\) |
0.753153 | − | 0.657846i | \(-0.228532\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 440.946 | + | 728.798i | 0.731253 | + | 1.20862i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −146.872 | − | 403.528i | −0.242764 | − | 0.666989i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −825.430 | + | 692.618i | −1.35985 | + | 1.14105i | −0.383824 | + | 0.923406i | \(0.625393\pi\) |
−0.976028 | + | 0.217645i | \(0.930163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.76251 | + | 10.6322i | −0.00289410 | + | 0.0174585i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 490.046 | − | 282.928i | 0.802039 | − | 0.463057i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 51.2650 | − | 88.7935i | 0.0836296 | − | 0.144851i | −0.821177 | − | 0.570674i | \(-0.806682\pi\) |
0.904806 | + | 0.425823i | \(0.140015\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1215.94 | + | 685.495i | 1.97714 | + | 1.11463i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −104.533 | + | 18.4319i | −0.169421 | + | 0.0298735i | −0.257715 | − | 0.966221i | \(-0.582970\pi\) |
0.0882941 | + | 0.996094i | \(0.471858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 59.1978 | + | 49.6728i | 0.0956345 | + | 0.0802469i | 0.689351 | − | 0.724427i | \(-0.257896\pi\) |
−0.593717 | + | 0.804674i | \(0.702340\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −531.253 | + | 474.376i | −0.855480 | + | 0.763891i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.4921 | + | 18.4628i | −0.0248669 | + | 0.0296353i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 348.651 | + | 1977.30i | 0.557842 | + | 3.16368i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 129.599 | + | 219.248i | 0.206697 | + | 0.349678i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −270.700 | − | 156.289i | −0.430366 | − | 0.248472i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −489.646 | − | 848.091i | −0.775983 | − | 1.34404i | −0.934240 | − | 0.356645i | \(-0.883921\pi\) |
0.158257 | − | 0.987398i | \(-0.449413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.6710 | − | 55.0304i | −0.0326556 | − | 0.0869359i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 239.018 | + | 284.851i | 0.376407 | + | 0.448584i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −650.393 | + | 236.724i | −1.02102 | + | 0.371623i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 269.828 | + | 696.549i | 0.422265 | + | 1.09006i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 489.106 | + | 86.2426i | 0.763036 | + | 0.134544i | 0.541606 | − | 0.840633i | \(-0.317817\pi\) |
0.221430 | + | 0.975176i | \(0.428928\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −789.739 | − | 287.442i | −1.22821 | − | 0.447032i | −0.355226 | − | 0.934780i | \(-0.615596\pi\) |
−0.872984 | + | 0.487748i | \(0.837818\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1815.93 | − | 1555.76i | 2.81539 | − | 2.41203i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1032.02i | − | 1.59508i | −0.603263 | − | 0.797542i | \(-0.706133\pi\) | ||
0.603263 | − | 0.797542i | \(-0.293867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −650.234 | −1.00190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.4822 | + | 19.2385i | 0.0253183 | + | 0.0295523i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −318.739 | + | 875.728i | −0.488115 | + | 1.34108i | 0.414270 | + | 0.910154i | \(0.364037\pi\) |
−0.902385 | + | 0.430930i | \(0.858185\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 377.111 | − | 2138.70i | 0.575742 | − | 3.26519i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −671.309 | − | 540.224i | −1.02178 | − | 0.822258i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 137.332 | + | 377.318i | 0.208395 | + | 0.572561i | 0.999220 | − | 0.0394813i | \(-0.0125705\pi\) |
−0.790825 | + | 0.612042i | \(0.790348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −51.6587 | + | 43.3468i | −0.0781523 | + | 0.0655776i | −0.681027 | − | 0.732258i | \(-0.738466\pi\) |
0.602875 | + | 0.797836i | \(0.294022\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 630.686 | − | 236.904i | 0.951261 | − | 0.357321i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −127.981 | + | 73.8898i | −0.192452 | + | 0.111112i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0657 | + | 34.7549i | −0.0300836 | + | 0.0521063i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −260.190 | + | 153.800i | −0.388923 | + | 0.229895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −846.572 | + | 149.273i | −1.26166 | + | 0.222464i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.3494 | + | 12.0405i | 0.0213215 | + | 0.0178909i | 0.653386 | − | 0.757025i | \(-0.273348\pi\) |
−0.632065 | + | 0.774916i | \(0.717792\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1745.22 | − | 252.644i | −2.58551 | − | 0.374288i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 165.239 | − | 196.924i | 0.244075 | − | 0.290877i | −0.630074 | − | 0.776535i | \(-0.716975\pi\) |
0.874149 | + | 0.485658i | \(0.161420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1304 | − | 165.207i | −0.0429019 | − | 0.243309i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −52.7813 | + | 93.6245i | −0.0775056 | + | 0.137481i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 266.287 | + | 153.741i | 0.389879 | + | 0.225097i | 0.682108 | − | 0.731252i | \(-0.261064\pi\) |
−0.292229 | + | 0.956348i | \(0.594397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 670.773 | + | 1161.81i | 0.979231 | + | 1.69608i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −508.934 | − | 84.3664i | −0.740806 | − | 0.122804i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −675.044 | − | 804.487i | −0.979745 | − | 1.16761i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 280.337 | − | 102.034i | 0.405697 | − | 0.147662i | −0.131108 | − | 0.991368i | \(-0.541853\pi\) |
0.536805 | + | 0.843707i | \(0.319631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.61920 | + | 273.909i | 0.00810851 | + | 0.395251i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −853.876 | − | 150.561i | −1.22860 | − | 0.216635i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 648.230 | + | 235.936i | 0.930029 | + | 0.338503i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −360.112 | − | 126.903i | −0.515181 | − | 0.181549i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 274.104i | − | 0.391019i | −0.980702 | − | 0.195510i | \(-0.937364\pi\) | ||
0.980702 | − | 0.195510i | \(-0.0626361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 146.100 | 0.207824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −994.907 | + | 185.969i | −1.41122 | + | 0.263786i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.0142 | + | 137.413i | −0.0707414 | + | 0.194360i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 68.7370 | − | 389.827i | 0.0969492 | − | 0.549826i | −0.897183 | − | 0.441658i | \(-0.854390\pi\) |
0.994133 | − | 0.108168i | \(-0.0344985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 229.839 | − | 201.034i | 0.323262 | − | 0.282748i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.2643 | + | 88.6454i | 0.0452514 | + | 0.124327i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1495.83 | − | 1255.15i | 2.09207 | − | 1.75546i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −808.809 | − | 664.656i | −1.12805 | − | 0.926995i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 80.2851 | − | 46.3526i | 0.111662 | − | 0.0644682i | −0.443129 | − | 0.896458i | \(-0.646132\pi\) |
0.554791 | + | 0.831990i | \(0.312798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 123.953 | − | 214.694i | 0.171919 | − | 0.297772i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.5208 | − | 1415.79i | −0.0200841 | − | 1.95821i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −97.8529 | + | 17.2541i | −0.134970 | + | 0.0237988i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 458.479 | + | 384.709i | 0.630645 | + | 0.529174i | 0.901129 | − | 0.433550i | \(-0.142739\pi\) |
−0.270484 | + | 0.962724i | \(0.587184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 324.985 | − | 652.553i | 0.445796 | − | 0.895135i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 759.609 | − | 905.267i | 1.03914 | − | 1.23840i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −127.319 | − | 722.063i | −0.173696 | − | 0.985079i | −0.939638 | − | 0.342170i | \(-0.888838\pi\) |
0.765942 | − | 0.642910i | \(-0.222273\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1237.94 | − | 12.6968i | 1.68428 | − | 0.0172746i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1056.65 | + | 610.055i | 1.43371 | + | 0.827755i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 208.119 | + | 360.472i | 0.281622 | + | 0.487784i | 0.971784 | − | 0.235871i | \(-0.0757942\pi\) |
−0.690162 | + | 0.723655i | \(0.742461\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −199.927 | + | 243.287i | −0.269806 | + | 0.328323i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 852.915 | + | 1016.46i | 1.14793 | + | 1.36805i | 0.918830 | + | 0.394653i | \(0.129135\pi\) |
0.229104 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −280.196 | + | 101.983i | −0.376101 | + | 0.136890i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 65.8233 | + | 75.2550i | 0.0881169 | + | 0.100743i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −47.1463 | − | 8.31316i | −0.0629456 | − | 0.0110990i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1209.13 | + | 440.087i | 1.61002 | + | 0.586001i | 0.981445 | − | 0.191744i | \(-0.0614145\pi\) |
0.628579 | + | 0.777745i | \(0.283637\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 204.916 | + | 1096.27i | 0.272133 | + | 1.45587i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 923.530i | − | 1.22322i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −519.945 | −0.686849 | −0.343425 | − | 0.939180i | \(-0.611587\pi\) | ||||
−0.343425 | + | 0.939180i | \(0.611587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −339.069 | + | 962.175i | −0.446731 | + | 1.26769i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 129.215 | − | 355.015i | 0.169796 | − | 0.466511i | −0.825384 | − | 0.564571i | \(-0.809042\pi\) |
0.995180 | + | 0.0980603i | \(0.0312638\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 59.8304 | − | 339.315i | 0.0784146 | − | 0.444711i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1204.81 | + | 24.7164i | −1.57491 | + | 0.0323091i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −274.967 | − | 755.466i | −0.358497 | − | 0.984962i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −176.852 | + | 148.396i | −0.229976 | + | 0.192973i | −0.750493 | − | 0.660879i | \(-0.770184\pi\) |
0.520517 | + | 0.853851i | \(0.325739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.3079 | − | 303.479i | 0.0652502 | − | 0.393617i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −184.241 | + | 106.372i | −0.238346 | + | 0.137609i | −0.614416 | − | 0.788982i | \(-0.710608\pi\) |
0.376070 | + | 0.926591i | \(0.377275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −116.782 | + | 202.273i | −0.150687 | + | 0.260997i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 136.903 | + | 77.1797i | 0.176194 | + | 0.0993303i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −317.532 | + | 55.9894i | −0.407615 | + | 0.0718735i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 819.639 | + | 687.759i | 1.04947 | + | 0.880613i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.88508 | − | 40.6530i | 0.00751607 | − | 0.0519196i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −77.2755 | + | 92.0933i | −0.0984401 | + | 0.117316i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 106.636 | + | 604.766i | 0.135497 | + | 0.768444i | 0.974512 | + | 0.224335i | \(0.0720211\pi\) |
−0.839015 | + | 0.544109i | \(0.816868\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −349.832 | − | 591.825i | −0.443387 | − | 0.750095i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 135.459 | + | 78.2073i | 0.171250 | + | 0.0988714i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −531.425 | − | 920.455i | −0.670145 | − | 1.16073i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 660.536 | + | 1758.48i | 0.830863 | + | 2.21193i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −71.3427 | − | 85.0229i | −0.0895141 | − | 0.106679i | 0.719428 | − | 0.694567i | \(-0.244404\pi\) |
−0.808942 | + | 0.587888i | \(0.799960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −470.032 | + | 171.078i | −0.588276 | + | 0.214115i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 57.5912 | − | 71.5656i | 0.0718991 | − | 0.0893454i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1215.50 | − | 214.326i | −1.51370 | − | 0.266906i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −556.244 | − | 202.456i | −0.690987 | − | 0.251499i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −254.665 | + | 218.179i | −0.315570 | + | 0.270358i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1040.29i | − | 1.28589i | −0.765910 | − | 0.642947i | \(-0.777711\pi\) | ||
0.765910 | − | 0.642947i | \(-0.222289\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 869.156 | 1.07171 | 0.535855 | − | 0.844310i | \(-0.319989\pi\) | ||||
0.535855 | + | 0.844310i | \(0.319989\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 209.293 | + | 244.293i | 0.257433 | + | 0.300484i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 543.994 | − | 1494.61i | 0.667477 | − | 1.83388i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −95.9147 | + | 543.960i | −0.117399 | + | 0.665801i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −315.861 | + | 122.358i | −0.385667 | + | 0.149399i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −344.284 | − | 945.912i | −0.419347 | − | 1.15215i | −0.952076 | − | 0.305861i | \(-0.901056\pi\) |
0.532729 | − | 0.846286i | \(-0.321166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −681.106 | + | 571.516i | −0.827589 | + | 0.694430i | −0.954736 | − | 0.297454i | \(-0.903863\pi\) |
0.127147 | + | 0.991884i | \(0.459418\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2364.55 | + | 888.193i | −2.86612 | + | 1.07660i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1179.72 | + | 681.112i | −1.42651 | + | 0.823594i | −0.996843 | − | 0.0793955i | \(-0.974701\pi\) |
−0.429663 | + | 0.902989i | \(0.641368\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −392.123 | + | 679.177i | −0.473007 | + | 0.819273i | −0.999523 | − | 0.0308929i | \(-0.990165\pi\) |
0.526515 | + | 0.850166i | \(0.323498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1105.74 | − | 653.608i | 1.33061 | − | 0.786532i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 602.528 | − | 106.242i | 0.723323 | − | 0.127541i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 137.179 | + | 115.107i | 0.164286 | + | 0.137852i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −64.3114 | − | 72.0222i | −0.0768356 | − | 0.0860481i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 170.797 | − | 203.547i | 0.203572 | − | 0.242607i | −0.654593 | − | 0.755981i | \(-0.727160\pi\) |
0.858165 | + | 0.513374i | \(0.171605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 145.636 | + | 825.944i | 0.173170 | + | 0.982097i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −198.255 | + | 351.668i | −0.235178 | + | 0.417163i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 699.956 | + | 404.120i | 0.828350 | + | 0.478248i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.3510 | + | 92.4066i | 0.0629881 | + | 0.109099i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.03290 | + | 0.171225i | 0.00121661 | + | 0.000201678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 376.169 | + | 448.301i | 0.442032 | + | 0.526793i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1525.03 | − | 555.065i | 1.78784 | − | 0.650721i | 0.788478 | − | 0.615063i | \(-0.210870\pi\) |
0.999364 | − | 0.0356577i | \(-0.0113526\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 481.910 | − | 291.571i | 0.563637 | − | 0.341018i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −153.201 | − | 27.0135i | −0.178764 | − | 0.0315210i | 0.0835493 | − | 0.996504i | \(-0.473374\pi\) |
−0.262314 | + | 0.964983i | \(0.584485\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1005.06 | + | 365.813i | 1.17004 | + | 0.425860i | 0.852674 | − | 0.522443i | \(-0.174979\pi\) |
0.317366 | + | 0.948303i | \(0.397202\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −327.120 | − | 115.276i | −0.379930 | − | 0.133887i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 634.524i | 0.735254i | 0.929973 | + | 0.367627i | \(0.119830\pi\) | ||||
−0.929973 | + | 0.367627i | \(0.880170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1954.25 | −2.25925 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 266.839 | − | 49.8779i | 0.307773 | − | 0.0575293i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 149.593 | − | 411.002i | 0.172143 | − | 0.472960i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −261.956 | + | 1485.63i | −0.300754 | + | 1.70566i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 123.920 | + | 627.262i | 0.141947 | + | 0.718513i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −309.391 | − | 850.045i | −0.353590 | − | 0.971480i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 373.651 | − | 313.530i | 0.426055 | − | 0.357503i | −0.404406 | − | 0.914580i | \(-0.632522\pi\) |
0.830461 | + | 0.557077i | \(0.188077\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1070.69 | + | 879.859i | 1.21807 | + | 1.00098i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 481.009 | − | 277.711i | 0.545981 | − | 0.315222i | −0.201518 | − | 0.979485i | \(-0.564588\pi\) |
0.747499 | + | 0.664262i | \(0.231254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 348.544 | − | 603.697i | 0.394728 | − | 0.683688i | −0.598339 | − | 0.801243i | \(-0.704172\pi\) |
0.993066 | + | 0.117555i | \(0.0375056\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.7480 | + | 1437.94i | 0.0166644 | + | 1.62479i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 210.497 | − | 37.1164i | 0.237314 | − | 0.0418448i | −0.0537262 | − | 0.998556i | \(-0.517110\pi\) |
0.291040 | + | 0.956711i | \(0.405999\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −70.7785 | − | 59.3902i | −0.0796159 | − | 0.0668057i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.8252 | − | 1043.32i | −0.0480642 | − | 1.17096i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 150.280 | − | 179.097i | 0.168287 | − | 0.200557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −239.803 | − | 1359.99i | −0.267937 | − | 1.51954i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1261.27 | + | 12.9361i | −1.40610 | + | 0.0144215i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.71174 | − | 2.72032i | −0.00524109 | − | 0.00302594i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 464.163 | + | 803.955i | 0.515165 | + | 0.892291i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −377.232 | + | 459.048i | −0.417754 | + | 0.508358i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −742.680 | − | 885.092i | −0.820641 | − | 0.978002i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −105.132 | + | 38.2650i | −0.115912 | + | 0.0421886i | −0.399325 | − | 0.916809i | \(-0.630756\pi\) |
0.283413 | + | 0.958998i | \(0.408533\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 179.843 | − | 527.537i | 0.197847 | − | 0.580349i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −782.305 | − | 137.941i | −0.858732 | − | 0.151418i | −0.273091 | − | 0.961988i | \(-0.588046\pi\) |
−0.585641 | + | 0.810571i | \(0.699157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 134.572 | + | 48.9803i | 0.147396 | + | 0.0536477i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 349.307 | + | 1868.74i | 0.381757 | + | 2.04234i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 539.614i | 0.588456i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1706.42 | 1.85682 | 0.928412 | − | 0.371553i | \(-0.121175\pi\) | ||||
0.928412 | + | 0.371553i | \(0.121175\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 327.415 | − | 929.104i | 0.355499 | − | 1.00880i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −452.460 | + | 1243.12i | −0.490206 | + | 1.34683i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −251.607 | + | 1426.93i | −0.272008 | + | 1.54263i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −455.555 | + | 827.805i | −0.491430 | + | 0.892994i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 538.296 | + | 1478.96i | 0.579436 | + | 1.59199i | 0.789135 | + | 0.614220i | \(0.210529\pi\) |
−0.209699 | + | 0.977766i | \(0.567248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −219.065 | + | 183.817i | −0.235300 | + | 0.197441i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 79.4066 | − | 479.014i | 0.0851089 | − | 0.513413i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1494.84 | + | 863.048i | −1.59876 | + | 0.923046i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −570.487 | + | 988.113i | −0.608844 | + | 1.05455i | 0.382587 | + | 0.923920i | \(0.375033\pi\) |
−0.991431 | + | 0.130630i | \(0.958300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −609.209 | − | 343.445i | −0.648784 | − | 0.365756i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1330.02 | − | 234.519i | 1.41341 | − | 0.249223i | 0.585769 | − | 0.810478i | \(-0.300793\pi\) |
0.827643 | + | 0.561255i | \(0.189681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −989.362 | − | 830.173i | −1.04916 | − | 0.880353i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 605.599 | − | 18.6389i | 0.640846 | − | 0.0197238i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −842.221 | + | 1003.72i | −0.889357 | + | 1.05989i | 0.108476 | + | 0.994099i | \(0.465403\pi\) |
−0.997833 | + | 0.0657950i | \(0.979042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −264.993 | − | 1502.85i | −0.279234 | − | 1.58361i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −606.353 | − | 1025.79i | −0.637595 | − | 1.07865i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 638.686 | + | 368.745i | 0.670184 | + | 0.386931i | 0.796146 | − | 0.605104i | \(-0.206868\pi\) |
−0.125962 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −434.561 | − | 752.682i | −0.455038 | − | 0.788149i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.6895 | − | 55.0797i | −0.0216191 | − | 0.0575546i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −214.268 | − | 255.355i | −0.223429 | − | 0.266272i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 891.027 | − | 324.307i | 0.927187 | − | 0.337469i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 180.306 | + | 27.9927i | 0.187234 | + | 0.0290682i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3065.84 | + | 540.591i | 3.17704 | + | 0.560197i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 468.930 | + | 170.677i | 0.484933 | + | 0.176501i | 0.572905 | − | 0.819622i | \(-0.305816\pi\) |
−0.0879722 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 211.388 | − | 181.102i | 0.218151 | − | 0.186896i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 981.048i | − | 1.01035i | −0.863018 | − | 0.505174i | \(-0.831428\pi\) | ||
0.863018 | − | 0.505174i | \(-0.168572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 215.441 | 0.221419 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2031.84 | − | 2371.63i | −2.08394 | − | 2.43244i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −118.283 | + | 324.980i | −0.121068 | + | 0.332630i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) |
0.864324 | + | 0.502936i | \(0.167747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.8484 | − | 129.580i | 0.0233385 | − | 0.132359i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −201.465 | + | 1297.68i | −0.205367 | + | 1.32281i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 67.6176 | + | 185.778i | 0.0687870 | + | 0.188991i | 0.969323 | − | 0.245791i | \(-0.0790477\pi\) |
−0.900536 | + | 0.434782i | \(0.856826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 367.204 | − | 308.120i | 0.372796 | − | 0.312813i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 235.431 | − | 88.4345i | 0.238532 | − | 0.0895993i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1916.07 | + | 1106.24i | −1.93738 | + | 1.11855i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 734.120 | − | 1271.53i | 0.740787 | − | 1.28308i | −0.211351 | − | 0.977410i | \(-0.567786\pi\) |
0.952138 | − | 0.305670i | \(-0.0988804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 894.268 | − | 528.608i | 0.900572 | − | 0.532334i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 56.6115 | − | 9.98213i | 0.0568960 | − | 0.0100323i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.1521 | + | 11.0359i | 0.0131917 | + | 0.0110691i | 0.649360 | − | 0.760481i | \(-0.275037\pi\) |
−0.636168 | + | 0.771551i | \(0.719481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −527.717 | − | 283.400i | −0.528246 | − | 0.283684i |
(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 | 108.3.k.a.65.2 | yes | 36 | |
3.2 | odd | 2 | 324.3.k.a.197.6 | 36 | |||
4.3 | odd | 2 | 432.3.bc.b.65.5 | 36 | |||
27.5 | odd | 18 | inner | 108.3.k.a.5.2 | ✓ | 36 | |
27.7 | even | 9 | 2916.3.c.b.1457.1 | 36 | |||
27.20 | odd | 18 | 2916.3.c.b.1457.36 | 36 | |||
27.22 | even | 9 | 324.3.k.a.125.6 | 36 | |||
108.59 | even | 18 | 432.3.bc.b.113.5 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.5.2 | ✓ | 36 | 27.5 | odd | 18 | inner | |
108.3.k.a.65.2 | yes | 36 | 1.1 | even | 1 | trivial | |
324.3.k.a.125.6 | 36 | 27.22 | even | 9 | |||
324.3.k.a.197.6 | 36 | 3.2 | odd | 2 | |||
432.3.bc.b.65.5 | 36 | 4.3 | odd | 2 | |||
432.3.bc.b.113.5 | 36 | 108.59 | even | 18 | |||
2916.3.c.b.1457.1 | 36 | 27.7 | even | 9 | |||
2916.3.c.b.1457.36 | 36 | 27.20 | odd | 18 |