Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(391,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.391");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.2 | ||
Root | \(1.40376 - 0.171630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.391 |
Dual form | 588.2.b.a.391.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40376 | + | 0.171630i | −0.992608 | + | 0.121361i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.94109 | − | 0.481855i | 0.970543 | − | 0.240928i | ||||
\(5\) | − | 0.963711i | − | 0.430985i | −0.976506 | − | 0.215492i | \(-0.930864\pi\) | ||
0.976506 | − | 0.215492i | \(-0.0691356\pi\) | |||||||
\(6\) | 1.40376 | − | 0.171630i | 0.573083 | − | 0.0700677i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.64212 | + | 1.00956i | −0.934130 | + | 0.356933i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.165402 | + | 1.35282i | 0.0523047 | + | 0.427799i | ||||
\(11\) | − | 5.48322i | − | 1.65325i | −0.562751 | − | 0.826626i | \(-0.690257\pi\) | ||
0.562751 | − | 0.826626i | \(-0.309743\pi\) | |||||||
\(12\) | −1.94109 | + | 0.481855i | −0.560343 | + | 0.139100i | ||||
\(13\) | 3.75117i | 1.04039i | 0.854048 | + | 0.520193i | \(0.174140\pi\) | ||||
−0.854048 | + | 0.520193i | \(0.825860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.963711i | 0.248829i | ||||||||
\(16\) | 3.53563 | − | 1.87065i | 0.883908 | − | 0.467661i | ||||
\(17\) | − | 0.686521i | − | 0.166506i | −0.996528 | − | 0.0832529i | \(-0.973469\pi\) | ||
0.996528 | − | 0.0832529i | \(-0.0265309\pi\) | |||||||
\(18\) | −1.40376 | + | 0.171630i | −0.330869 | + | 0.0404536i | ||||
\(19\) | −4.88217 | −1.12005 | −0.560024 | − | 0.828477i | \(-0.689208\pi\) | ||||
−0.560024 | + | 0.828477i | \(0.689208\pi\) | |||||||
\(20\) | −0.464369 | − | 1.87065i | −0.103836 | − | 0.418289i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.941086 | + | 7.69713i | 0.200640 | + | 1.64103i | ||||
\(23\) | − | 1.24090i | − | 0.258746i | −0.991596 | − | 0.129373i | \(-0.958704\pi\) | ||
0.991596 | − | 0.129373i | \(-0.0412964\pi\) | |||||||
\(24\) | 2.64212 | − | 1.00956i | 0.539320 | − | 0.206075i | ||||
\(25\) | 4.07126 | 0.814252 | ||||||||
\(26\) | −0.643814 | − | 5.26574i | −0.126262 | − | 1.03270i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.48011 | −0.460544 | −0.230272 | − | 0.973126i | \(-0.573962\pi\) | ||||
−0.230272 | + | 0.973126i | \(0.573962\pi\) | |||||||
\(30\) | −0.165402 | − | 1.35282i | −0.0301981 | − | 0.246990i | ||||
\(31\) | −4.82802 | −0.867138 | −0.433569 | − | 0.901120i | \(-0.642746\pi\) | ||||
−0.433569 | + | 0.901120i | \(0.642746\pi\) | |||||||
\(32\) | −4.64212 | + | 3.23276i | −0.820618 | + | 0.571477i | ||||
\(33\) | 5.48322i | 0.954506i | ||||||||
\(34\) | 0.117828 | + | 0.963711i | 0.0202073 | + | 0.165275i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94109 | − | 0.481855i | 0.323514 | − | 0.0803092i | ||||
\(37\) | −2.73287 | −0.449281 | −0.224640 | − | 0.974442i | \(-0.572121\pi\) | ||||
−0.224640 | + | 0.974442i | \(0.572121\pi\) | |||||||
\(38\) | 6.85340 | − | 0.837928i | 1.11177 | − | 0.135930i | ||||
\(39\) | − | 3.75117i | − | 0.600668i | ||||||
\(40\) | 0.972923 | + | 2.54624i | 0.153833 | + | 0.402596i | ||||
\(41\) | − | 9.42976i | − | 1.47268i | −0.676611 | − | 0.736340i | \(-0.736552\pi\) | ||
0.676611 | − | 0.736340i | \(-0.263448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.97437i | − | 0.911083i | −0.890215 | − | 0.455541i | \(-0.849446\pi\) | ||
0.890215 | − | 0.455541i | \(-0.150554\pi\) | |||||||
\(44\) | −2.64212 | − | 10.6434i | −0.398314 | − | 1.60455i | ||||
\(45\) | − | 0.963711i | − | 0.143662i | ||||||
\(46\) | 0.212976 | + | 1.74193i | 0.0314016 | + | 0.256833i | ||||
\(47\) | −3.61504 | −0.527308 | −0.263654 | − | 0.964617i | \(-0.584928\pi\) | ||||
−0.263654 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(48\) | −3.53563 | + | 1.87065i | −0.510324 | + | 0.270004i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.71508 | + | 0.698752i | −0.808234 | + | 0.0988184i | ||||
\(51\) | 0.686521i | 0.0961322i | ||||||||
\(52\) | 1.80752 | + | 7.28134i | 0.250658 | + | 1.00974i | ||||
\(53\) | −4.09515 | −0.562512 | −0.281256 | − | 0.959633i | \(-0.590751\pi\) | ||||
−0.281256 | + | 0.959633i | \(0.590751\pi\) | |||||||
\(54\) | 1.40376 | − | 0.171630i | 0.191028 | − | 0.0233559i | ||||
\(55\) | −5.28424 | −0.712526 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.88217 | 0.646660 | ||||||||
\(58\) | 3.48148 | − | 0.425661i | 0.457140 | − | 0.0558921i | ||||
\(59\) | −12.6863 | −1.65162 | −0.825808 | − | 0.563951i | \(-0.809281\pi\) | ||||
−0.825808 | + | 0.563951i | \(0.809281\pi\) | |||||||
\(60\) | 0.464369 | + | 1.87065i | 0.0599498 | + | 0.241499i | ||||
\(61\) | − | 10.4121i | − | 1.33313i | −0.745448 | − | 0.666564i | \(-0.767764\pi\) | ||
0.745448 | − | 0.666564i | \(-0.232236\pi\) | |||||||
\(62\) | 6.77738 | − | 0.828634i | 0.860728 | − | 0.105237i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.96158 | − | 5.33475i | 0.745198 | − | 0.666843i | ||||
\(65\) | 3.61504 | 0.448391 | ||||||||
\(66\) | −0.941086 | − | 7.69713i | −0.115840 | − | 0.947451i | ||||
\(67\) | − | 9.43847i | − | 1.15309i | −0.817064 | − | 0.576546i | \(-0.804400\pi\) | ||
0.817064 | − | 0.576546i | \(-0.195600\pi\) | |||||||
\(68\) | −0.330804 | − | 1.33260i | −0.0401159 | − | 0.161601i | ||||
\(69\) | 1.24090i | 0.149387i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1163i | − | 1.20058i | −0.799782 | − | 0.600291i | \(-0.795052\pi\) | ||
0.799782 | − | 0.600291i | \(-0.204948\pi\) | |||||||
\(72\) | −2.64212 | + | 1.00956i | −0.311377 | + | 0.118978i | ||||
\(73\) | − | 6.66089i | − | 0.779598i | −0.920900 | − | 0.389799i | \(-0.872544\pi\) | ||
0.920900 | − | 0.389799i | \(-0.127456\pi\) | |||||||
\(74\) | 3.83629 | − | 0.469043i | 0.445960 | − | 0.0545251i | ||||
\(75\) | −4.07126 | −0.470109 | ||||||||
\(76\) | −9.47672 | + | 2.35250i | −1.08705 | + | 0.269850i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.643814 | + | 5.26574i | 0.0728976 | + | 0.596228i | ||||
\(79\) | 1.41442i | 0.159134i | 0.996830 | + | 0.0795671i | \(0.0253538\pi\) | ||||
−0.996830 | + | 0.0795671i | \(0.974646\pi\) | |||||||
\(80\) | −1.80276 | − | 3.40733i | −0.201555 | − | 0.380951i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.61843 | + | 13.2371i | 0.178726 | + | 1.46180i | ||||
\(83\) | −0.543780 | −0.0596876 | −0.0298438 | − | 0.999555i | \(-0.509501\pi\) | ||||
−0.0298438 | + | 0.999555i | \(0.509501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.661608 | −0.0717614 | ||||||||
\(86\) | 1.02538 | + | 8.38658i | 0.110570 | + | 0.904348i | ||||
\(87\) | 2.48011 | 0.265895 | ||||||||
\(88\) | 5.53563 | + | 14.4873i | 0.590100 | + | 1.54435i | ||||
\(89\) | − | 0.554380i | − | 0.0587641i | −0.999568 | − | 0.0293821i | \(-0.990646\pi\) | ||
0.999568 | − | 0.0293821i | \(-0.00935395\pi\) | |||||||
\(90\) | 0.165402 | + | 1.35282i | 0.0174349 | + | 0.142600i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.597935 | − | 2.40870i | −0.0623390 | − | 0.251124i | ||||
\(93\) | 4.82802 | 0.500642 | ||||||||
\(94\) | 5.07465 | − | 0.620450i | 0.523410 | − | 0.0639946i | ||||
\(95\) | 4.70500i | 0.482723i | ||||||||
\(96\) | 4.64212 | − | 3.23276i | 0.473784 | − | 0.329942i | ||||
\(97\) | 10.8747i | 1.10416i | 0.833790 | + | 0.552081i | \(0.186166\pi\) | ||||
−0.833790 | + | 0.552081i | \(0.813834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.48322i | − | 0.551084i | ||||||
\(100\) | 7.90267 | − | 1.96176i | 0.790267 | − | 0.196176i | ||||
\(101\) | 14.4305i | 1.43589i | 0.696099 | + | 0.717946i | \(0.254918\pi\) | ||||
−0.696099 | + | 0.717946i | \(0.745082\pi\) | |||||||
\(102\) | −0.117828 | − | 0.963711i | −0.0116667 | − | 0.0954216i | ||||
\(103\) | 15.0247 | 1.48043 | 0.740214 | − | 0.672372i | \(-0.234724\pi\) | ||||
0.740214 | + | 0.672372i | \(0.234724\pi\) | |||||||
\(104\) | −3.78702 | − | 9.91103i | −0.371348 | − | 0.971857i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.74861 | − | 0.702851i | 0.558354 | − | 0.0682669i | ||||
\(107\) | 12.1156i | 1.17126i | 0.810577 | + | 0.585632i | \(0.199153\pi\) | ||||
−0.810577 | + | 0.585632i | \(0.800847\pi\) | |||||||
\(108\) | −1.94109 | + | 0.481855i | −0.186781 | + | 0.0463666i | ||||
\(109\) | −6.07126 | −0.581521 | −0.290761 | − | 0.956796i | \(-0.593908\pi\) | ||||
−0.290761 | + | 0.956796i | \(0.593908\pi\) | |||||||
\(110\) | 7.41780 | − | 0.906935i | 0.707260 | − | 0.0864729i | ||||
\(111\) | 2.73287 | 0.259392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.37939 | −0.694194 | −0.347097 | − | 0.937829i | \(-0.612833\pi\) | ||||
−0.347097 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(114\) | −6.85340 | + | 0.837928i | −0.641880 | + | 0.0784792i | ||||
\(115\) | −1.19587 | −0.111515 | ||||||||
\(116\) | −4.81410 | + | 1.19505i | −0.446978 | + | 0.110958i | ||||
\(117\) | 3.75117i | 0.346796i | ||||||||
\(118\) | 17.8085 | − | 2.17735i | 1.63941 | − | 0.200442i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.972923 | − | 2.54624i | −0.0888153 | − | 0.232439i | ||||
\(121\) | −19.0657 | −1.73324 | ||||||||
\(122\) | 1.78702 | + | 14.6160i | 0.161790 | + | 1.32327i | ||||
\(123\) | 9.42976i | 0.850253i | ||||||||
\(124\) | −9.37160 | + | 2.32641i | −0.841594 | + | 0.208917i | ||||
\(125\) | − | 8.74207i | − | 0.781915i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6431i | 1.03316i | 0.856240 | + | 0.516578i | \(0.172794\pi\) | ||||
−0.856240 | + | 0.516578i | \(0.827206\pi\) | |||||||
\(128\) | −7.45303 | + | 8.51189i | −0.658761 | + | 0.752352i | ||||
\(129\) | 5.97437i | 0.526014i | ||||||||
\(130\) | −5.07465 | + | 0.620450i | −0.445076 | + | 0.0544171i | ||||
\(131\) | 9.26156 | 0.809186 | 0.404593 | − | 0.914497i | \(-0.367413\pi\) | ||||
0.404593 | + | 0.914497i | \(0.367413\pi\) | |||||||
\(132\) | 2.64212 | + | 10.6434i | 0.229967 | + | 0.926389i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.61993 | + | 13.2494i | 0.139940 | + | 1.14457i | ||||
\(135\) | 0.963711i | 0.0829430i | ||||||||
\(136\) | 0.693083 | + | 1.81387i | 0.0594314 | + | 0.155538i | ||||
\(137\) | 7.23008 | 0.617708 | 0.308854 | − | 0.951110i | \(-0.400055\pi\) | ||||
0.308854 | + | 0.951110i | \(0.400055\pi\) | |||||||
\(138\) | −0.212976 | − | 1.74193i | −0.0181297 | − | 0.148283i | ||||
\(139\) | 5.30812 | 0.450229 | 0.225115 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225115 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.61504 | 0.304441 | ||||||||
\(142\) | 1.73626 | + | 14.2008i | 0.145704 | + | 1.19171i | ||||
\(143\) | 20.5685 | 1.72002 | ||||||||
\(144\) | 3.53563 | − | 1.87065i | 0.294636 | − | 0.155887i | ||||
\(145\) | 2.39011i | 0.198488i | ||||||||
\(146\) | 1.14321 | + | 9.35029i | 0.0946127 | + | 0.773836i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.30473 | + | 1.31685i | −0.436046 | + | 0.108244i | ||||
\(149\) | 4.66161 | 0.381894 | 0.190947 | − | 0.981600i | \(-0.438844\pi\) | ||||
0.190947 | + | 0.981600i | \(0.438844\pi\) | |||||||
\(150\) | 5.71508 | − | 0.698752i | 0.466634 | − | 0.0570528i | ||||
\(151\) | 12.2062i | 0.993324i | 0.867944 | + | 0.496662i | \(0.165441\pi\) | ||||
−0.867944 | + | 0.496662i | \(0.834559\pi\) | |||||||
\(152\) | 12.8993 | − | 4.92884i | 1.04627 | − | 0.399782i | ||||
\(153\) | − | 0.686521i | − | 0.0555019i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.65281i | 0.373723i | ||||||||
\(156\) | −1.80752 | − | 7.28134i | −0.144717 | − | 0.582974i | ||||
\(157\) | − | 21.9329i | − | 1.75043i | −0.483731 | − | 0.875217i | \(-0.660719\pi\) | ||
0.483731 | − | 0.875217i | \(-0.339281\pi\) | |||||||
\(158\) | −0.242756 | − | 1.98550i | −0.0193127 | − | 0.157958i | ||||
\(159\) | 4.09515 | 0.324766 | ||||||||
\(160\) | 3.11545 | + | 4.47366i | 0.246298 | + | 0.353674i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.40376 | + | 0.171630i | −0.110290 | + | 0.0134845i | ||||
\(163\) | 4.01848i | 0.314752i | 0.987539 | + | 0.157376i | \(0.0503034\pi\) | ||||
−0.987539 | + | 0.157376i | \(0.949697\pi\) | |||||||
\(164\) | −4.54378 | − | 18.3040i | −0.354810 | − | 1.42930i | ||||
\(165\) | 5.28424 | 0.411377 | ||||||||
\(166\) | 0.763337 | − | 0.0933291i | 0.0592464 | − | 0.00724374i | ||||
\(167\) | 14.7178 | 1.13890 | 0.569448 | − | 0.822027i | \(-0.307157\pi\) | ||||
0.569448 | + | 0.822027i | \(0.307157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07126 | −0.0824047 | ||||||||
\(170\) | 0.928739 | − | 0.113552i | 0.0712310 | − | 0.00870903i | ||||
\(171\) | −4.88217 | −0.373349 | ||||||||
\(172\) | −2.87878 | − | 11.5968i | −0.219505 | − | 0.884245i | ||||
\(173\) | 11.6530i | 0.885958i | 0.896532 | + | 0.442979i | \(0.146078\pi\) | ||||
−0.896532 | + | 0.442979i | \(0.853922\pi\) | |||||||
\(174\) | −3.48148 | + | 0.425661i | −0.263930 | + | 0.0322693i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2572 | − | 19.3866i | −0.773163 | − | 1.46132i | ||||
\(177\) | 12.6863 | 0.953561 | ||||||||
\(178\) | 0.0951483 | + | 0.778216i | 0.00713167 | + | 0.0583298i | ||||
\(179\) | − | 2.59419i | − | 0.193899i | −0.995289 | − | 0.0969494i | \(-0.969091\pi\) | ||
0.995289 | − | 0.0969494i | \(-0.0309085\pi\) | |||||||
\(180\) | −0.464369 | − | 1.87065i | −0.0346120 | − | 0.139430i | ||||
\(181\) | − | 9.53343i | − | 0.708615i | −0.935129 | − | 0.354307i | \(-0.884717\pi\) | ||
0.935129 | − | 0.354307i | \(-0.115283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4121i | 0.769681i | ||||||||
\(184\) | 1.25276 | + | 3.27861i | 0.0923548 | + | 0.241702i | ||||
\(185\) | 2.63370i | 0.193633i | ||||||||
\(186\) | −6.77738 | + | 0.828634i | −0.496942 | + | 0.0607584i | ||||
\(187\) | −3.76434 | −0.275276 | ||||||||
\(188\) | −7.01711 | + | 1.74193i | −0.511775 | + | 0.127043i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.807521 | − | 6.60470i | −0.0585837 | − | 0.479155i | ||||
\(191\) | − | 8.33274i | − | 0.602936i | −0.953476 | − | 0.301468i | \(-0.902523\pi\) | ||
0.953476 | − | 0.301468i | \(-0.0974767\pi\) | |||||||
\(192\) | −5.96158 | + | 5.33475i | −0.430240 | + | 0.385002i | ||||
\(193\) | −12.3726 | −0.890600 | −0.445300 | − | 0.895382i | \(-0.646903\pi\) | ||||
−0.445300 | + | 0.895382i | \(0.646903\pi\) | |||||||
\(194\) | −1.86643 | − | 15.2655i | −0.134002 | − | 1.09600i | ||||
\(195\) | −3.61504 | −0.258878 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.23686 | 0.230617 | 0.115308 | − | 0.993330i | \(-0.463214\pi\) | ||||
0.115308 | + | 0.993330i | \(0.463214\pi\) | |||||||
\(198\) | 0.941086 | + | 7.69713i | 0.0668801 | + | 0.547011i | ||||
\(199\) | 19.2301 | 1.36318 | 0.681592 | − | 0.731732i | \(-0.261288\pi\) | ||||
0.681592 | + | 0.731732i | \(0.261288\pi\) | |||||||
\(200\) | −10.7568 | + | 4.11018i | −0.760618 | + | 0.290633i | ||||
\(201\) | 9.43847i | 0.665738i | ||||||||
\(202\) | −2.47672 | − | 20.2570i | −0.174261 | − | 1.42528i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.330804 | + | 1.33260i | 0.0231609 | + | 0.0933004i | ||||
\(205\) | −9.08756 | −0.634703 | ||||||||
\(206\) | −21.0911 | + | 2.57869i | −1.46948 | + | 0.179666i | ||||
\(207\) | − | 1.24090i | − | 0.0862486i | ||||||
\(208\) | 7.01711 | + | 13.2627i | 0.486549 | + | 0.919606i | ||||
\(209\) | 26.7700i | 1.85172i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.24637i | − | 0.636546i | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||
0.947999 | − | 0.318273i | \(-0.103103\pi\) | |||||||
\(212\) | −7.94904 | + | 1.97327i | −0.545942 | + | 0.135525i | ||||
\(213\) | 10.1163i | 0.693156i | ||||||||
\(214\) | −2.07941 | − | 17.0075i | −0.142146 | − | 1.16261i | ||||
\(215\) | −5.75756 | −0.392663 | ||||||||
\(216\) | 2.64212 | − | 1.00956i | 0.179773 | − | 0.0686918i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.52260 | − | 1.04201i | 0.577223 | − | 0.0705740i | ||||
\(219\) | 6.66089i | 0.450101i | ||||||||
\(220\) | −10.2572 | + | 2.54624i | −0.691538 | + | 0.171667i | ||||
\(221\) | 2.57526 | 0.173230 | ||||||||
\(222\) | −3.83629 | + | 0.469043i | −0.257475 | + | 0.0314801i | ||||
\(223\) | 1.94585 | 0.130303 | 0.0651517 | − | 0.997875i | \(-0.479247\pi\) | ||||
0.0651517 | + | 0.997875i | \(0.479247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.07126 | 0.271417 | ||||||||
\(226\) | 10.3589 | − | 1.26653i | 0.689063 | − | 0.0842480i | ||||
\(227\) | −8.64531 | −0.573809 | −0.286905 | − | 0.957959i | \(-0.592626\pi\) | ||||
−0.286905 | + | 0.957959i | \(0.592626\pi\) | |||||||
\(228\) | 9.47672 | − | 2.35250i | 0.627611 | − | 0.155798i | ||||
\(229\) | − | 16.7889i | − | 1.10944i | −0.832036 | − | 0.554721i | \(-0.812825\pi\) | ||
0.832036 | − | 0.554721i | \(-0.187175\pi\) | |||||||
\(230\) | 1.67871 | − | 0.205247i | 0.110691 | − | 0.0135336i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.55274 | − | 2.50381i | 0.430208 | − | 0.164383i | ||||
\(233\) | −1.04657 | −0.0685628 | −0.0342814 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342814 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(234\) | −0.643814 | − | 5.26574i | −0.0420874 | − | 0.344232i | ||||
\(235\) | 3.48385i | 0.227262i | ||||||||
\(236\) | −24.6252 | + | 6.11296i | −1.60296 | + | 0.397920i | ||||
\(237\) | − | 1.41442i | − | 0.0918761i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2479i | 1.24505i | 0.782602 | + | 0.622523i | \(0.213892\pi\) | ||||
−0.782602 | + | 0.622523i | \(0.786108\pi\) | |||||||
\(240\) | 1.80276 | + | 3.40733i | 0.116368 | + | 0.219942i | ||||
\(241\) | − | 2.75689i | − | 0.177587i | −0.996050 | − | 0.0887934i | \(-0.971699\pi\) | ||
0.996050 | − | 0.0887934i | \(-0.0283011\pi\) | |||||||
\(242\) | 26.7637 | − | 3.27225i | 1.72043 | − | 0.210348i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −5.01711 | − | 20.2107i | −0.321187 | − | 1.29386i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.61843 | − | 13.2371i | −0.103187 | − | 0.843968i | ||||
\(247\) | − | 18.3138i | − | 1.16528i | ||||||
\(248\) | 12.7562 | − | 4.87417i | 0.810019 | − | 0.309510i | ||||
\(249\) | 0.543780 | 0.0344607 | ||||||||
\(250\) | 1.50040 | + | 12.2718i | 0.0948939 | + | 0.776135i | ||||
\(251\) | −20.7493 | −1.30968 | −0.654841 | − | 0.755767i | \(-0.727264\pi\) | ||||
−0.654841 | + | 0.755767i | \(0.727264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80413 | −0.427772 | ||||||||
\(254\) | −1.99830 | − | 16.3441i | −0.125385 | − | 1.02552i | ||||
\(255\) | 0.661608 | 0.0414315 | ||||||||
\(256\) | 9.00137 | − | 13.2278i | 0.562586 | − | 0.826739i | ||||
\(257\) | − | 7.45109i | − | 0.464786i | −0.972622 | − | 0.232393i | \(-0.925344\pi\) | ||
0.972622 | − | 0.232393i | \(-0.0746555\pi\) | |||||||
\(258\) | −1.02538 | − | 8.38658i | −0.0638375 | − | 0.522126i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.01711 | − | 1.74193i | 0.435182 | − | 0.108030i | ||||
\(261\) | −2.48011 | −0.153515 | ||||||||
\(262\) | −13.0010 | + | 1.58956i | −0.803205 | + | 0.0982036i | ||||
\(263\) | 29.6797i | 1.83013i | 0.403305 | + | 0.915066i | \(0.367861\pi\) | ||||
−0.403305 | + | 0.915066i | \(0.632139\pi\) | |||||||
\(264\) | −5.53563 | − | 14.4873i | −0.340695 | − | 0.891633i | ||||
\(265\) | 3.94654i | 0.242434i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.554380i | 0.0339275i | ||||||||
\(268\) | −4.54798 | − | 18.3209i | −0.277812 | − | 1.11913i | ||||
\(269\) | − | 4.31542i | − | 0.263116i | −0.991308 | − | 0.131558i | \(-0.958002\pi\) | ||
0.991308 | − | 0.131558i | \(-0.0419980\pi\) | |||||||
\(270\) | −0.165402 | − | 1.35282i | −0.0100660 | − | 0.0823299i | ||||
\(271\) | −13.5828 | −0.825099 | −0.412550 | − | 0.910935i | \(-0.635362\pi\) | ||||
−0.412550 | + | 0.910935i | \(0.635362\pi\) | |||||||
\(272\) | −1.28424 | − | 2.42728i | −0.0778683 | − | 0.147176i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1493 | + | 1.24090i | −0.613142 | + | 0.0749656i | ||||
\(275\) | − | 22.3236i | − | 1.34616i | ||||||
\(276\) | 0.597935 | + | 2.40870i | 0.0359914 | + | 0.144986i | ||||
\(277\) | 2.07126 | 0.124450 | 0.0622250 | − | 0.998062i | \(-0.480180\pi\) | ||||
0.0622250 | + | 0.998062i | \(0.480180\pi\) | |||||||
\(278\) | −7.45133 | + | 0.911035i | −0.446901 | + | 0.0546402i | ||||
\(279\) | −4.82802 | −0.289046 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7122 | 1.41455 | 0.707276 | − | 0.706938i | \(-0.249924\pi\) | ||||
0.707276 | + | 0.706938i | \(0.249924\pi\) | |||||||
\(282\) | −5.07465 | + | 0.620450i | −0.302191 | + | 0.0369473i | ||||
\(283\) | 12.2548 | 0.728471 | 0.364235 | − | 0.931307i | \(-0.381330\pi\) | ||||
0.364235 | + | 0.931307i | \(0.381330\pi\) | |||||||
\(284\) | −4.87458 | − | 19.6366i | −0.289253 | − | 1.16522i | ||||
\(285\) | − | 4.70500i | − | 0.278700i | ||||||
\(286\) | −28.8732 | + | 3.53017i | −1.70731 | + | 0.208743i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.64212 | + | 3.23276i | −0.273539 | + | 0.190492i | ||||
\(289\) | 16.5287 | 0.972276 | ||||||||
\(290\) | −0.410214 | − | 3.35514i | −0.0240886 | − | 0.197020i | ||||
\(291\) | − | 10.8747i | − | 0.637489i | ||||||
\(292\) | −3.20959 | − | 12.9294i | −0.187827 | − | 0.756634i | ||||
\(293\) | − | 10.7090i | − | 0.625626i | −0.949815 | − | 0.312813i | \(-0.898729\pi\) | ||
0.949815 | − | 0.312813i | \(-0.101271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2259i | 0.711821i | ||||||||
\(296\) | 7.22056 | − | 2.75899i | 0.419687 | − | 0.160363i | ||||
\(297\) | 5.48322i | 0.318169i | ||||||||
\(298\) | −6.54378 | + | 0.800073i | −0.379071 | + | 0.0463470i | ||||
\(299\) | 4.65483 | 0.269196 | ||||||||
\(300\) | −7.90267 | + | 1.96176i | −0.456261 | + | 0.113262i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.09495 | − | 17.1345i | −0.120551 | − | 0.985982i | ||||
\(303\) | − | 14.4305i | − | 0.829013i | ||||||
\(304\) | −17.2616 | + | 9.13281i | −0.990018 | + | 0.523803i | ||||
\(305\) | −10.0342 | −0.574557 | ||||||||
\(306\) | 0.117828 | + | 0.963711i | 0.00673576 | + | 0.0550917i | ||||
\(307\) | 4.22056 | 0.240880 | 0.120440 | − | 0.992721i | \(-0.461569\pi\) | ||||
0.120440 | + | 0.992721i | \(0.461569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0247 | −0.854725 | ||||||||
\(310\) | −0.798563 | − | 6.53143i | −0.0453554 | − | 0.370961i | ||||
\(311\) | 9.70139 | 0.550116 | 0.275058 | − | 0.961428i | \(-0.411303\pi\) | ||||
0.275058 | + | 0.961428i | \(0.411303\pi\) | |||||||
\(312\) | 3.78702 | + | 9.91103i | 0.214398 | + | 0.561102i | ||||
\(313\) | − | 13.6634i | − | 0.772299i | −0.922436 | − | 0.386149i | \(-0.873805\pi\) | ||
0.922436 | − | 0.386149i | \(-0.126195\pi\) | |||||||
\(314\) | 3.76434 | + | 30.7885i | 0.212434 | + | 1.73750i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.681544 | + | 2.74550i | 0.0383398 | + | 0.154447i | ||||
\(317\) | 20.0884 | 1.12828 | 0.564138 | − | 0.825681i | \(-0.309209\pi\) | ||||
0.564138 | + | 0.825681i | \(0.309209\pi\) | |||||||
\(318\) | −5.74861 | + | 0.702851i | −0.322366 | + | 0.0394139i | ||||
\(319\) | 13.5990i | 0.761396i | ||||||||
\(320\) | −5.14115 | − | 5.74524i | −0.287399 | − | 0.321169i | ||||
\(321\) | − | 12.1156i | − | 0.676229i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.35171i | 0.186494i | ||||||||
\(324\) | 1.94109 | − | 0.481855i | 0.107838 | − | 0.0267697i | ||||
\(325\) | 15.2720i | 0.847137i | ||||||||
\(326\) | −0.689693 | − | 5.64098i | −0.0381986 | − | 0.312425i | ||||
\(327\) | 6.07126 | 0.335742 | ||||||||
\(328\) | 9.51989 | + | 24.9145i | 0.525648 | + | 1.37568i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.41780 | + | 0.906935i | −0.408337 | + | 0.0499251i | ||||
\(331\) | − | 9.42104i | − | 0.517827i | −0.965900 | − | 0.258914i | \(-0.916635\pi\) | ||
0.965900 | − | 0.258914i | \(-0.0833645\pi\) | |||||||
\(332\) | −1.05552 | + | 0.262023i | −0.0579294 | + | 0.0143804i | ||||
\(333\) | −2.73287 | −0.149760 | ||||||||
\(334\) | −20.6602 | + | 2.52602i | −1.13048 | + | 0.138217i | ||||
\(335\) | −9.09596 | −0.496965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4411 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(338\) | 1.50379 | − | 0.183861i | 0.0817956 | − | 0.0100007i | ||||
\(339\) | 7.37939 | 0.400793 | ||||||||
\(340\) | −1.28424 | + | 0.318799i | −0.0696476 | + | 0.0172893i | ||||
\(341\) | 26.4731i | 1.43360i | ||||||||
\(342\) | 6.85340 | − | 0.837928i | 0.370589 | − | 0.0453100i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.03148 | + | 15.7850i | 0.325195 | + | 0.851070i | ||||
\(345\) | 1.19587 | 0.0643835 | ||||||||
\(346\) | −2.00000 | − | 16.3580i | −0.107521 | − | 0.879409i | ||||
\(347\) | − | 22.6194i | − | 1.21427i | −0.794598 | − | 0.607136i | \(-0.792318\pi\) | ||
0.794598 | − | 0.607136i | \(-0.207682\pi\) | |||||||
\(348\) | 4.81410 | − | 1.19505i | 0.258063 | − | 0.0640616i | ||||
\(349\) | − | 2.48180i | − | 0.132848i | −0.997791 | − | 0.0664239i | \(-0.978841\pi\) | ||
0.997791 | − | 0.0664239i | \(-0.0211590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.75117i | − | 0.200223i | ||||||
\(352\) | 17.7259 | + | 25.4538i | 0.944795 | + | 1.35669i | ||||
\(353\) | − | 9.11423i | − | 0.485101i | −0.970139 | − | 0.242551i | \(-0.922016\pi\) | ||
0.970139 | − | 0.242551i | \(-0.0779841\pi\) | |||||||
\(354\) | −17.8085 | + | 2.17735i | −0.946513 | + | 0.115725i | ||||
\(355\) | −9.74917 | −0.517432 | ||||||||
\(356\) | −0.267131 | − | 1.07610i | −0.0141579 | − | 0.0570331i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.445241 | + | 3.64162i | 0.0235317 | + | 0.192466i | ||||
\(359\) | 6.92820i | 0.365657i | 0.983145 | + | 0.182828i | \(0.0585252\pi\) | ||||
−0.983145 | + | 0.182828i | \(0.941475\pi\) | |||||||
\(360\) | 0.972923 | + | 2.54624i | 0.0512775 | + | 0.134199i | ||||
\(361\) | 4.83561 | 0.254506 | ||||||||
\(362\) | 1.63623 | + | 13.3827i | 0.0859981 | + | 0.703377i | ||||
\(363\) | 19.0657 | 1.00069 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.41917 | −0.335995 | ||||||||
\(366\) | −1.78702 | − | 14.6160i | −0.0934092 | − | 0.763992i | ||||
\(367\) | 3.83359 | 0.200112 | 0.100056 | − | 0.994982i | \(-0.468098\pi\) | ||||
0.100056 | + | 0.994982i | \(0.468098\pi\) | |||||||
\(368\) | −2.32129 | − | 4.38737i | −0.121005 | − | 0.228707i | ||||
\(369\) | − | 9.42976i | − | 0.490894i | ||||||
\(370\) | −0.452022 | − | 3.69708i | −0.0234995 | − | 0.192202i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.37160 | − | 2.32641i | 0.485895 | − | 0.120619i | ||||
\(373\) | −26.8300 | −1.38921 | −0.694603 | − | 0.719393i | \(-0.744420\pi\) | ||||
−0.694603 | + | 0.719393i | \(0.744420\pi\) | |||||||
\(374\) | 5.28424 | − | 0.646075i | 0.273241 | − | 0.0334078i | ||||
\(375\) | 8.74207i | 0.451439i | ||||||||
\(376\) | 9.55137 | − | 3.64960i | 0.492574 | − | 0.188214i | ||||
\(377\) | − | 9.30330i | − | 0.479144i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.93692i | − | 0.356325i | −0.984001 | − | 0.178163i | \(-0.942985\pi\) | ||
0.984001 | − | 0.178163i | \(-0.0570153\pi\) | |||||||
\(380\) | 2.26713 | + | 9.13281i | 0.116301 | + | 0.468504i | ||||
\(381\) | − | 11.6431i | − | 0.596493i | ||||||
\(382\) | 1.43015 | + | 11.6972i | 0.0731729 | + | 0.598479i | ||||
\(383\) | −2.25761 | −0.115359 | −0.0576793 | − | 0.998335i | \(-0.518370\pi\) | ||||
−0.0576793 | + | 0.998335i | \(0.518370\pi\) | |||||||
\(384\) | 7.45303 | − | 8.51189i | 0.380336 | − | 0.434371i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3682 | − | 2.12351i | 0.884017 | − | 0.108084i | ||||
\(387\) | − | 5.97437i | − | 0.303694i | ||||||
\(388\) | 5.24005 | + | 21.1088i | 0.266023 | + | 1.07164i | ||||
\(389\) | 30.6095 | 1.55196 | 0.775981 | − | 0.630756i | \(-0.217255\pi\) | ||||
0.775981 | + | 0.630756i | \(0.217255\pi\) | |||||||
\(390\) | 5.07465 | − | 0.620450i | 0.256965 | − | 0.0314177i | ||||
\(391\) | −0.851904 | −0.0430827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.26156 | −0.467184 | ||||||||
\(394\) | −4.54378 | + | 0.555544i | −0.228912 | + | 0.0279879i | ||||
\(395\) | 1.36309 | 0.0685844 | ||||||||
\(396\) | −2.64212 | − | 10.6434i | −0.132771 | − | 0.534851i | ||||
\(397\) | 13.8989i | 0.697568i | 0.937203 | + | 0.348784i | \(0.113405\pi\) | ||||
−0.937203 | + | 0.348784i | \(0.886595\pi\) | |||||||
\(398\) | −26.9944 | + | 3.30046i | −1.35311 | + | 0.165437i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.3945 | − | 7.61589i | 0.719724 | − | 0.380794i | ||||
\(401\) | −10.2766 | −0.513191 | −0.256596 | − | 0.966519i | \(-0.582601\pi\) | ||||
−0.256596 | + | 0.966519i | \(0.582601\pi\) | |||||||
\(402\) | −1.61993 | − | 13.2494i | −0.0807946 | − | 0.660818i | ||||
\(403\) | − | 18.1107i | − | 0.902158i | ||||||
\(404\) | 6.95343 | + | 28.0109i | 0.345946 | + | 1.39360i | ||||
\(405\) | − | 0.963711i | − | 0.0478872i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9849i | 0.742775i | ||||||||
\(408\) | −0.693083 | − | 1.81387i | −0.0343127 | − | 0.0897999i | ||||
\(409\) | 12.1639i | 0.601464i | 0.953709 | + | 0.300732i | \(0.0972310\pi\) | ||||
−0.953709 | + | 0.300732i | \(0.902769\pi\) | |||||||
\(410\) | 12.7568 | − | 1.55970i | 0.630011 | − | 0.0770281i | ||||
\(411\) | −7.23008 | −0.356634 | ||||||||
\(412\) | 29.1642 | − | 7.23973i | 1.43682 | − | 0.356676i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.212976 | + | 1.74193i | 0.0104672 | + | 0.0856111i | ||||
\(415\) | 0.524047i | 0.0257244i | ||||||||
\(416\) | −12.1266 | − | 17.4134i | −0.594557 | − | 0.853761i | ||||
\(417\) | −5.30812 | −0.259940 | ||||||||
\(418\) | −4.59454 | − | 37.5787i | −0.224727 | − | 1.83803i | ||||
\(419\) | 16.2245 | 0.792619 | 0.396310 | − | 0.918117i | \(-0.370291\pi\) | ||||
0.396310 | + | 0.918117i | \(0.370291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.58477 | −0.467133 | −0.233567 | − | 0.972341i | \(-0.575040\pi\) | ||||
−0.233567 | + | 0.972341i | \(0.575040\pi\) | |||||||
\(422\) | 1.58696 | + | 12.9797i | 0.0772518 | + | 0.631841i | ||||
\(423\) | −3.61504 | −0.175769 | ||||||||
\(424\) | 10.8199 | − | 4.13429i | 0.525459 | − | 0.200779i | ||||
\(425\) | − | 2.79501i | − | 0.135578i | ||||||
\(426\) | −1.73626 | − | 14.2008i | −0.0841220 | − | 0.688032i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.83799 | + | 23.5175i | 0.282190 | + | 1.13676i | ||||
\(429\) | −20.5685 | −0.993055 | ||||||||
\(430\) | 8.08224 | − | 0.988172i | 0.389760 | − | 0.0476539i | ||||
\(431\) | − | 0.151894i | − | 0.00731648i | −0.999993 | − | 0.00365824i | \(-0.998836\pi\) | ||
0.999993 | − | 0.00365824i | \(-0.00116446\pi\) | |||||||
\(432\) | −3.53563 | + | 1.87065i | −0.170108 | + | 0.0900015i | ||||
\(433\) | − | 9.46997i | − | 0.455098i | −0.973767 | − | 0.227549i | \(-0.926929\pi\) | ||
0.973767 | − | 0.227549i | \(-0.0730711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.39011i | − | 0.114597i | ||||||
\(436\) | −11.7848 | + | 2.92547i | −0.564392 | + | 0.140105i | ||||
\(437\) | 6.05829i | 0.289807i | ||||||||
\(438\) | −1.14321 | − | 9.35029i | −0.0546247 | − | 0.446774i | ||||
\(439\) | 33.4745 | 1.59765 | 0.798826 | − | 0.601562i | \(-0.205455\pi\) | ||||
0.798826 | + | 0.601562i | \(0.205455\pi\) | |||||||
\(440\) | 13.9616 | − | 5.33475i | 0.665592 | − | 0.254324i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.61504 | + | 0.441992i | −0.171950 | + | 0.0210234i | ||||
\(443\) | 26.1554i | 1.24268i | 0.783540 | + | 0.621341i | \(0.213412\pi\) | ||||
−0.783540 | + | 0.621341i | \(0.786588\pi\) | |||||||
\(444\) | 5.30473 | − | 1.31685i | 0.251752 | − | 0.0624948i | ||||
\(445\) | −0.534262 | −0.0253264 | ||||||||
\(446\) | −2.73150 | + | 0.333966i | −0.129340 | + | 0.0158137i | ||||
\(447\) | −4.66161 | −0.220486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2918 | 0.485701 | 0.242851 | − | 0.970064i | \(-0.421918\pi\) | ||||
0.242851 | + | 0.970064i | \(0.421918\pi\) | |||||||
\(450\) | −5.71508 | + | 0.698752i | −0.269411 | + | 0.0329395i | ||||
\(451\) | −51.7054 | −2.43471 | ||||||||
\(452\) | −14.3240 | + | 3.55580i | −0.673745 | + | 0.167251i | ||||
\(453\) | − | 12.2062i | − | 0.573496i | ||||||
\(454\) | 12.1359 | − | 1.48380i | 0.569568 | − | 0.0696380i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.8993 | + | 4.92884i | −0.604064 | + | 0.230814i | ||||
\(457\) | 11.9315 | 0.558131 | 0.279065 | − | 0.960272i | \(-0.409975\pi\) | ||||
0.279065 | + | 0.960272i | \(0.409975\pi\) | |||||||
\(458\) | 2.88148 | + | 23.5676i | 0.134643 | + | 1.10124i | ||||
\(459\) | 0.686521i | 0.0320441i | ||||||||
\(460\) | −2.32129 | + | 0.576236i | −0.108231 | + | 0.0268672i | ||||
\(461\) | 30.0093i | 1.39767i | 0.715281 | + | 0.698837i | \(0.246299\pi\) | ||||
−0.715281 | + | 0.698837i | \(0.753701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2736i | 0.616875i | 0.951245 | + | 0.308437i | \(0.0998060\pi\) | ||||
−0.951245 | + | 0.308437i | \(0.900194\pi\) | |||||||
\(464\) | −8.76874 | + | 4.63940i | −0.407079 | + | 0.215379i | ||||
\(465\) | − | 4.65281i | − | 0.215769i | ||||||
\(466\) | 1.46913 | − | 0.179622i | 0.0680561 | − | 0.00832085i | ||||
\(467\) | −29.6493 | −1.37200 | −0.686002 | − | 0.727600i | \(-0.740636\pi\) | ||||
−0.686002 | + | 0.727600i | \(0.740636\pi\) | |||||||
\(468\) | 1.80752 | + | 7.28134i | 0.0835527 | + | 0.336580i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.597935 | − | 4.89050i | −0.0275807 | − | 0.225582i | ||||
\(471\) | 21.9329i | 1.01061i | ||||||||
\(472\) | 33.5187 | − | 12.8076i | 1.54282 | − | 0.589516i | ||||
\(473\) | −32.7588 | −1.50625 | ||||||||
\(474\) | 0.242756 | + | 1.98550i | 0.0111502 | + | 0.0911970i | ||||
\(475\) | −19.8766 | −0.912001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.09515 | −0.187504 | ||||||||
\(478\) | −3.30353 | − | 27.0195i | −0.151100 | − | 1.23584i | ||||
\(479\) | 11.5355 | 0.527069 | 0.263535 | − | 0.964650i | \(-0.415112\pi\) | ||||
0.263535 | + | 0.964650i | \(0.415112\pi\) | |||||||
\(480\) | −3.11545 | − | 4.47366i | −0.142200 | − | 0.204194i | ||||
\(481\) | − | 10.2515i | − | 0.467426i | ||||||
\(482\) | 0.473165 | + | 3.87001i | 0.0215521 | + | 0.176274i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.0081 | + | 9.18691i | −1.68219 | + | 0.417587i | ||||
\(485\) | 10.4801 | 0.475877 | ||||||||
\(486\) | 1.40376 | − | 0.171630i | 0.0636759 | − | 0.00778531i | ||||
\(487\) | − | 9.75517i | − | 0.442049i | −0.975268 | − | 0.221024i | \(-0.929060\pi\) | ||
0.975268 | − | 0.221024i | \(-0.0709400\pi\) | |||||||
\(488\) | 10.5116 | + | 27.5099i | 0.475837 | + | 1.24531i | ||||
\(489\) | − | 4.01848i | − | 0.181722i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.4736i | − | 1.82655i | −0.407346 | − | 0.913274i | \(-0.633546\pi\) | ||
0.407346 | − | 0.913274i | \(-0.366454\pi\) | |||||||
\(492\) | 4.54378 | + | 18.3040i | 0.204849 | + | 0.825207i | ||||
\(493\) | 1.70265i | 0.0766833i | ||||||||
\(494\) | 3.14321 | + | 25.7083i | 0.141420 | + | 1.15667i | ||||
\(495\) | −5.28424 | −0.237509 | ||||||||
\(496\) | −17.0701 | + | 9.03151i | −0.766470 | + | 0.405527i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.763337 | + | 0.0933291i | −0.0342059 | + | 0.00418218i | ||||
\(499\) | 31.9652i | 1.43096i | 0.698633 | + | 0.715480i | \(0.253792\pi\) | ||||
−0.698633 | + | 0.715480i | \(0.746208\pi\) | |||||||
\(500\) | −4.21242 | − | 16.9691i | −0.188385 | − | 0.758882i | ||||
\(501\) | −14.7178 | −0.657542 | ||||||||
\(502\) | 29.1270 | − | 3.56120i | 1.30000 | − | 0.158944i | ||||
\(503\) | 22.7110 | 1.01263 | 0.506317 | − | 0.862348i | \(-0.331007\pi\) | ||||
0.506317 | + | 0.862348i | \(0.331007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9069 | 0.618847 | ||||||||
\(506\) | 9.55137 | − | 1.16779i | 0.424610 | − | 0.0519148i | ||||
\(507\) | 1.07126 | 0.0475764 | ||||||||
\(508\) | 5.61028 | + | 22.6002i | 0.248916 | + | 1.00272i | ||||
\(509\) | 2.29725i | 0.101824i | 0.998703 | + | 0.0509118i | \(0.0162128\pi\) | ||||
−0.998703 | + | 0.0509118i | \(0.983787\pi\) | |||||||
\(510\) | −0.928739 | + | 0.113552i | −0.0411252 | + | 0.00502816i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.3655 | + | 20.1136i | −0.458093 | + | 0.888904i | ||||
\(513\) | 4.88217 | 0.215553 | ||||||||
\(514\) | 1.27883 | + | 10.4595i | 0.0564068 | + | 0.461350i | ||||
\(515\) | − | 14.4795i | − | 0.638041i | ||||||
\(516\) | 2.87878 | + | 11.5968i | 0.126731 | + | 0.510519i | ||||
\(517\) | 19.8221i | 0.871773i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 11.6530i | − | 0.511508i | ||||||
\(520\) | −9.55137 | + | 3.64960i | −0.418855 | + | 0.160045i | ||||
\(521\) | − | 37.6100i | − | 1.64772i | −0.566791 | − | 0.823862i | \(-0.691815\pi\) | ||
0.566791 | − | 0.823862i | \(-0.308185\pi\) | |||||||
\(522\) | 3.48148 | − | 0.425661i | 0.152380 | − | 0.0186307i | ||||
\(523\) | 35.6887 | 1.56056 | 0.780279 | − | 0.625431i | \(-0.215077\pi\) | ||||
0.780279 | + | 0.625431i | \(0.215077\pi\) | |||||||
\(524\) | 17.9775 | − | 4.46273i | 0.785350 | − | 0.194955i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.09394 | − | 41.6632i | −0.222106 | − | 1.81660i | ||||
\(527\) | 3.31454i | 0.144383i | ||||||||
\(528\) | 10.2572 | + | 19.3866i | 0.446386 | + | 0.843695i | ||||
\(529\) | 21.4602 | 0.933051 | ||||||||
\(530\) | −0.677345 | − | 5.53999i | −0.0294220 | − | 0.240642i | ||||
\(531\) | −12.6863 | −0.550539 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.3726 | 1.53216 | ||||||||
\(534\) | −0.0951483 | − | 0.778216i | −0.00411747 | − | 0.0336767i | ||||
\(535\) | 11.6760 | 0.504796 | ||||||||
\(536\) | 9.52869 | + | 24.9376i | 0.411577 | + | 1.07714i | ||||
\(537\) | 2.59419i | 0.111948i | ||||||||
\(538\) | 0.740657 | + | 6.05782i | 0.0319320 | + | 0.261171i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.464369 | + | 1.87065i | 0.0199833 | + | 0.0804998i | ||||
\(541\) | 37.0203 | 1.59163 | 0.795814 | − | 0.605541i | \(-0.207043\pi\) | ||||
0.795814 | + | 0.605541i | \(0.207043\pi\) | |||||||
\(542\) | 19.0671 | − | 2.33123i | 0.819000 | − | 0.100135i | ||||
\(543\) | 9.53343i | 0.409119i | ||||||||
\(544\) | 2.21936 | + | 3.18691i | 0.0951541 | + | 0.136638i | ||||
\(545\) | 5.85094i | 0.250627i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.09106i | − | 0.0894073i | −0.999000 | − | 0.0447036i | \(-0.985766\pi\) | ||
0.999000 | − | 0.0447036i | \(-0.0142344\pi\) | |||||||
\(548\) | 14.0342 | − | 3.48385i | 0.599512 | − | 0.148823i | ||||
\(549\) | − | 10.4121i | − | 0.444376i | ||||||
\(550\) | 3.83141 | + | 31.3370i | 0.163372 | + | 1.33621i | ||||
\(551\) | 12.1083 | 0.515831 | ||||||||
\(552\) | −1.25276 | − | 3.27861i | −0.0533211 | − | 0.139547i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.90755 | + | 0.355491i | −0.123530 | + | 0.0151034i | ||||
\(555\) | − | 2.63370i | − | 0.111794i | ||||||
\(556\) | 10.3035 | − | 2.55775i | 0.436967 | − | 0.108473i | ||||
\(557\) | −16.7977 | −0.711743 | −0.355872 | − | 0.934535i | \(-0.615816\pi\) | ||||
−0.355872 | + | 0.934535i | \(0.615816\pi\) | |||||||
\(558\) | 6.77738 | − | 0.828634i | 0.286909 | − | 0.0350789i | ||||
\(559\) | 22.4109 | 0.947878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.76434 | 0.158931 | ||||||||
\(562\) | −33.2863 | + | 4.06973i | −1.40410 | + | 0.171671i | ||||
\(563\) | −17.3957 | −0.733141 | −0.366570 | − | 0.930390i | \(-0.619468\pi\) | ||||
−0.366570 | + | 0.930390i | \(0.619468\pi\) | |||||||
\(564\) | 7.01711 | − | 1.74193i | 0.295473 | − | 0.0733484i | ||||
\(565\) | 7.11159i | 0.299187i | ||||||||
\(566\) | −17.2028 | + | 2.10329i | −0.723086 | + | 0.0884079i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2130 | + | 26.7284i | 0.428527 | + | 1.12150i | ||||
\(569\) | −34.2850 | −1.43730 | −0.718652 | − | 0.695370i | \(-0.755241\pi\) | ||||
−0.718652 | + | 0.695370i | \(0.755241\pi\) | |||||||
\(570\) | 0.807521 | + | 6.60470i | 0.0338233 | + | 0.276640i | ||||
\(571\) | 5.93719i | 0.248464i | 0.992253 | + | 0.124232i | \(0.0396467\pi\) | ||||
−0.992253 | + | 0.124232i | \(0.960353\pi\) | |||||||
\(572\) | 39.9252 | − | 9.91103i | 1.66936 | − | 0.414401i | ||||
\(573\) | 8.33274i | 0.348105i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.05203i | − | 0.210684i | ||||||
\(576\) | 5.96158 | − | 5.33475i | 0.248399 | − | 0.222281i | ||||
\(577\) | 39.0208i | 1.62446i | 0.583338 | + | 0.812229i | \(0.301746\pi\) | ||||
−0.583338 | + | 0.812229i | \(0.698254\pi\) | |||||||
\(578\) | −23.2023 | + | 2.83682i | −0.965089 | + | 0.117996i | ||||
\(579\) | 12.3726 | 0.514188 | ||||||||
\(580\) | 1.15169 | + | 4.63940i | 0.0478211 | + | 0.192641i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.86643 | + | 15.2655i | 0.0773662 | + | 0.632777i | ||||
\(583\) | 22.4546i | 0.929974i | ||||||||
\(584\) | 6.72456 | + | 17.5989i | 0.278264 | + | 0.728246i | ||||
\(585\) | 3.61504 | 0.149464 | ||||||||
\(586\) | 1.83799 | + | 15.0329i | 0.0759266 | + | 0.621002i | ||||
\(587\) | −7.71931 | −0.318610 | −0.159305 | − | 0.987229i | \(-0.550925\pi\) | ||||
−0.159305 | + | 0.987229i | \(0.550925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5712 | 0.971235 | ||||||||
\(590\) | −2.09834 | − | 17.1623i | −0.0863872 | − | 0.706560i | ||||
\(591\) | −3.23686 | −0.133147 | ||||||||
\(592\) | −9.66242 | + | 5.11223i | −0.397123 | + | 0.210111i | ||||
\(593\) | − | 0.388414i | − | 0.0159503i | −0.999968 | − | 0.00797513i | \(-0.997461\pi\) | ||
0.999968 | − | 0.00797513i | \(-0.00253859\pi\) | |||||||
\(594\) | −0.941086 | − | 7.69713i | −0.0386132 | − | 0.315817i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.04858 | − | 2.24622i | 0.370644 | − | 0.0920088i | ||||
\(597\) | −19.2301 | −0.787035 | ||||||||
\(598\) | −6.53426 | + | 0.798909i | −0.267206 | + | 0.0326698i | ||||
\(599\) | 20.7846i | 0.849236i | 0.905373 | + | 0.424618i | \(0.139592\pi\) | ||||
−0.905373 | + | 0.424618i | \(0.860408\pi\) | |||||||
\(600\) | 10.7568 | − | 4.11018i | 0.439143 | − | 0.167797i | ||||
\(601\) | − | 26.4110i | − | 1.07733i | −0.842521 | − | 0.538664i | \(-0.818929\pi\) | ||
0.842521 | − | 0.538664i | \(-0.181071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.43847i | − | 0.384364i | ||||||
\(604\) | 5.88161 | + | 23.6932i | 0.239319 | + | 0.964064i | ||||
\(605\) | 18.3738i | 0.747002i | ||||||||
\(606\) | 2.47672 | + | 20.2570i | 0.100610 | + | 0.822885i | ||||
\(607\) | −40.7061 | −1.65221 | −0.826106 | − | 0.563515i | \(-0.809449\pi\) | ||||
−0.826106 | + | 0.563515i | \(0.809449\pi\) | |||||||
\(608\) | 22.6636 | − | 15.7829i | 0.919131 | − | 0.640081i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0856 | − | 1.72217i | 0.570310 | − | 0.0697288i | ||||
\(611\) | − | 13.5606i | − | 0.548604i | ||||||
\(612\) | −0.330804 | − | 1.33260i | −0.0133720 | − | 0.0538670i | ||||
\(613\) | 17.3384 | 0.700291 | 0.350146 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350146 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(614\) | −5.92466 | + | 0.724376i | −0.239100 | + | 0.0292335i | ||||
\(615\) | 9.08756 | 0.366446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.4753 | −1.87103 | −0.935513 | − | 0.353291i | \(-0.885062\pi\) | ||||
−0.935513 | + | 0.353291i | \(0.885062\pi\) | |||||||
\(618\) | 21.0911 | − | 2.57869i | 0.848407 | − | 0.103730i | ||||
\(619\) | −26.3821 | −1.06039 | −0.530194 | − | 0.847877i | \(-0.677881\pi\) | ||||
−0.530194 | + | 0.847877i | \(0.677881\pi\) | |||||||
\(620\) | 2.24198 | + | 9.03151i | 0.0900402 | + | 0.362714i | ||||
\(621\) | 1.24090i | 0.0497956i | ||||||||
\(622\) | −13.6184 | + | 1.66505i | −0.546049 | + | 0.0667625i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.01711 | − | 13.2627i | −0.280909 | − | 0.530935i | ||||
\(625\) | 11.9315 | 0.477259 | ||||||||
\(626\) | 2.34505 | + | 19.1801i | 0.0937269 | + | 0.766590i | ||||
\(627\) | − | 26.7700i | − | 1.06909i | ||||||
\(628\) | −10.5685 | − | 42.5736i | −0.421728 | − | 1.69887i | ||||
\(629\) | 1.87617i | 0.0748079i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 41.0696i | − | 1.63495i | −0.575961 | − | 0.817477i | \(-0.695372\pi\) | ||
0.575961 | − | 0.817477i | \(-0.304628\pi\) | |||||||
\(632\) | −1.42794 | − | 3.73705i | −0.0568002 | − | 0.148652i | ||||
\(633\) | 9.24637i | 0.367510i | ||||||||
\(634\) | −28.1993 | + | 3.44777i | −1.11994 | + | 0.136928i | ||||
\(635\) | 11.2206 | 0.445275 | ||||||||
\(636\) | 7.94904 | − | 1.97327i | 0.315200 | − | 0.0782452i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.33399 | − | 19.0897i | −0.0924037 | − | 0.755768i | ||||
\(639\) | − | 10.1163i | − | 0.400194i | ||||||
\(640\) | 8.20301 | + | 7.18257i | 0.324252 | + | 0.283916i | ||||
\(641\) | 45.4478 | 1.79508 | 0.897540 | − | 0.440932i | \(-0.145352\pi\) | ||||
0.897540 | + | 0.440932i | \(0.145352\pi\) | |||||||
\(642\) | 2.07941 | + | 17.0075i | 0.0820678 | + | 0.671231i | ||||
\(643\) | −30.5534 | −1.20491 | −0.602454 | − | 0.798154i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.75756 | 0.226704 | ||||||||
\(646\) | −0.575255 | − | 4.70500i | −0.0226331 | − | 0.185116i | ||||
\(647\) | −36.1792 | −1.42235 | −0.711175 | − | 0.703015i | \(-0.751836\pi\) | ||||
−0.711175 | + | 0.703015i | \(0.751836\pi\) | |||||||
\(648\) | −2.64212 | + | 1.00956i | −0.103792 | + | 0.0396592i | ||||
\(649\) | 69.5618i | 2.73054i | ||||||||
\(650\) | −2.62113 | − | 21.4382i | −0.102809 | − | 0.840876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93633 | + | 7.80022i | 0.0758324 | + | 0.305480i | ||||
\(653\) | −8.23089 | −0.322100 | −0.161050 | − | 0.986946i | \(-0.551488\pi\) | ||||
−0.161050 | + | 0.986946i | \(0.551488\pi\) | |||||||
\(654\) | −8.52260 | + | 1.04201i | −0.333260 | + | 0.0407459i | ||||
\(655\) | − | 8.92546i | − | 0.348747i | ||||||
\(656\) | −17.6397 | − | 33.3401i | −0.688716 | − | 1.30171i | ||||
\(657\) | − | 6.66089i | − | 0.259866i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.8837i | − | 0.891422i | −0.895177 | − | 0.445711i | \(-0.852951\pi\) | ||
0.895177 | − | 0.445711i | \(-0.147049\pi\) | |||||||
\(660\) | 10.2572 | − | 2.54624i | 0.399259 | − | 0.0991122i | ||||
\(661\) | − | 20.4627i | − | 0.795906i | −0.917406 | − | 0.397953i | \(-0.869721\pi\) | ||
0.917406 | − | 0.397953i | \(-0.130279\pi\) | |||||||
\(662\) | 1.61694 | + | 13.2249i | 0.0628440 | + | 0.514000i | ||||
\(663\) | −2.57526 | −0.100015 | ||||||||
\(664\) | 1.43673 | − | 0.548978i | 0.0557560 | − | 0.0213045i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.83629 | − | 0.469043i | 0.148653 | − | 0.0181750i | ||||
\(667\) | 3.07757i | 0.119164i | ||||||||
\(668\) | 28.5685 | − | 7.09184i | 1.10535 | − | 0.274392i | ||||
\(669\) | −1.94585 | −0.0752307 | ||||||||
\(670\) | 12.7685 | − | 1.56114i | 0.493292 | − | 0.0603121i | ||||
\(671\) | −57.0916 | −2.20400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23008 | 0.163058 | 0.0815289 | − | 0.996671i | \(-0.474020\pi\) | ||||
0.0815289 | + | 0.996671i | \(0.474020\pi\) | |||||||
\(674\) | 18.8681 | − | 2.30690i | 0.726773 | − | 0.0888586i | ||||
\(675\) | −4.07126 | −0.156703 | ||||||||
\(676\) | −2.07941 | + | 0.516193i | −0.0799773 | + | 0.0198536i | ||||
\(677\) | − | 24.0134i | − | 0.922908i | −0.887164 | − | 0.461454i | \(-0.847328\pi\) | ||
0.887164 | − | 0.461454i | \(-0.152672\pi\) | |||||||
\(678\) | −10.3589 | + | 1.26653i | −0.397831 | + | 0.0486406i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.74805 | − | 0.667932i | 0.0670345 | − | 0.0256140i | ||||
\(681\) | 8.64531 | 0.331289 | ||||||||
\(682\) | −4.54358 | − | 37.1619i | −0.173983 | − | 1.42300i | ||||
\(683\) | − | 8.19781i | − | 0.313680i | −0.987624 | − | 0.156840i | \(-0.949869\pi\) | ||
0.987624 | − | 0.156840i | \(-0.0501307\pi\) | |||||||
\(684\) | −9.47672 | + | 2.35250i | −0.362351 | + | 0.0899501i | ||||
\(685\) | − | 6.96771i | − | 0.266222i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.7889i | 0.640537i | ||||||||
\(688\) | −11.1759 | − | 21.1232i | −0.426078 | − | 0.805313i | ||||
\(689\) | − | 15.3616i | − | 0.585230i | ||||||
\(690\) | −1.67871 | + | 0.205247i | −0.0639076 | + | 0.00781363i | ||||
\(691\) | −35.9849 | −1.36893 | −0.684465 | − | 0.729046i | \(-0.739964\pi\) | ||||
−0.684465 | + | 0.729046i | \(0.739964\pi\) | |||||||
\(692\) | 5.61504 | + | 22.6194i | 0.213452 | + | 0.859860i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.88217 | + | 31.7522i | 0.147365 | + | 1.20530i | ||||
\(695\) | − | 5.11550i | − | 0.194042i | ||||||
\(696\) | −6.55274 | + | 2.50381i | −0.248381 | + | 0.0949068i | ||||
\(697\) | −6.47373 | −0.245210 | ||||||||
\(698\) | 0.425952 | + | 3.48385i | 0.0161225 | + | 0.131866i | ||||
\(699\) | 1.04657 | 0.0395848 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9471 | −0.489003 | −0.244502 | − | 0.969649i | \(-0.578624\pi\) | ||||
−0.244502 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(702\) | 0.643814 | + | 5.26574i | 0.0242992 | + | 0.198743i | ||||
\(703\) | 13.3423 | 0.503216 | ||||||||
\(704\) | −29.2516 | − | 32.6887i | −1.10246 | − | 1.23200i | ||||
\(705\) | − | 3.48385i | − | 0.131210i | ||||||
\(706\) | 1.56428 | + | 12.7942i | 0.0588723 | + | 0.481516i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 24.6252 | − | 6.11296i | 0.925472 | − | 0.229739i | ||||
\(709\) | 13.3121 | 0.499945 | 0.249973 | − | 0.968253i | \(-0.419578\pi\) | ||||
0.249973 | + | 0.968253i | \(0.419578\pi\) | |||||||
\(710\) | 13.6855 | − | 1.67325i | 0.513607 | − | 0.0627960i | ||||
\(711\) | 1.41442i | 0.0530447i | ||||||||
\(712\) | 0.559679 | + | 1.46474i | 0.0209749 | + | 0.0548934i | ||||
\(713\) | 5.99109i | 0.224368i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.8221i | − | 0.741303i | ||||||
\(716\) | −1.25002 | − | 5.03555i | −0.0467156 | − | 0.188187i | ||||
\(717\) | − | 19.2479i | − | 0.718827i | ||||||
\(718\) | −1.18909 | − | 9.72554i | −0.0443764 | − | 0.362954i | ||||
\(719\) | 47.5040 | 1.77160 | 0.885800 | − | 0.464068i | \(-0.153611\pi\) | ||||
0.885800 | + | 0.464068i | \(0.153611\pi\) | |||||||
\(720\) | −1.80276 | − | 3.40733i | −0.0671850 | − | 0.126984i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.78803 | + | 0.829936i | −0.252624 | + | 0.0308870i | ||||
\(723\) | 2.75689i | 0.102530i | ||||||||
\(724\) | −4.59374 | − | 18.5052i | −0.170725 | − | 0.687741i | ||||
\(725\) | −10.0972 | −0.374999 | ||||||||
\(726\) | −26.7637 | + | 3.27225i | −0.993292 | + | 0.121445i | ||||
\(727\) | 24.3567 | 0.903340 | 0.451670 | − | 0.892185i | \(-0.350828\pi\) | ||||
0.451670 | + | 0.892185i | \(0.350828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.01098 | − | 1.10172i | 0.333511 | − | 0.0407766i | ||||
\(731\) | −4.10153 | −0.151701 | ||||||||
\(732\) | 5.01711 | + | 20.2107i | 0.185438 | + | 0.747009i | ||||
\(733\) | − | 3.87763i | − | 0.143223i | −0.997433 | − | 0.0716117i | \(-0.977186\pi\) | ||
0.997433 | − | 0.0716117i | \(-0.0228142\pi\) | |||||||
\(734\) | −5.38144 | + | 0.657960i | −0.198633 | + | 0.0242857i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.01153 | + | 5.76041i | 0.147867 | + | 0.212331i | ||||
\(737\) | −51.7532 | −1.90635 | ||||||||
\(738\) | 1.61843 | + | 13.2371i | 0.0595753 | + | 0.487265i | ||||
\(739\) | − | 8.61981i | − | 0.317085i | −0.987352 | − | 0.158542i | \(-0.949321\pi\) | ||
0.987352 | − | 0.158542i | \(-0.0506795\pi\) | |||||||
\(740\) | 1.26906 | + | 5.11223i | 0.0466516 | + | 0.187929i | ||||
\(741\) | 18.3138i | 0.672776i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.12929i | 0.224862i | 0.993660 | + | 0.112431i | \(0.0358637\pi\) | ||||
−0.993660 | + | 0.112431i | \(0.964136\pi\) | |||||||
\(744\) | −12.7562 | + | 4.87417i | −0.467665 | + | 0.178696i | ||||
\(745\) | − | 4.49244i | − | 0.164590i | ||||||
\(746\) | 37.6629 | − | 4.60484i | 1.37894 | − | 0.168595i | ||||
\(747\) | −0.543780 | −0.0198959 | ||||||||
\(748\) | −7.30692 | + | 1.81387i | −0.267167 | + | 0.0663216i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50040 | − | 12.2718i | −0.0547870 | − | 0.448102i | ||||
\(751\) | − | 35.4662i | − | 1.29418i | −0.762414 | − | 0.647090i | \(-0.775986\pi\) | ||
0.762414 | − | 0.647090i | \(-0.224014\pi\) | |||||||
\(752\) | −12.7815 | + | 6.76246i | −0.466092 | + | 0.246602i | ||||
\(753\) | 20.7493 | 0.756145 | ||||||||
\(754\) | 1.59673 | + | 13.0596i | 0.0581494 | + | 0.475603i | ||||
\(755\) | 11.7632 | 0.428108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4204 | 1.06930 | 0.534651 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(758\) | 1.19058 | + | 9.73777i | 0.0432440 | + | 0.353692i | ||||
\(759\) | 6.80413 | 0.246974 | ||||||||
\(760\) | −4.74998 | − | 12.4312i | −0.172300 | − | 0.450926i | ||||
\(761\) | − | 50.2950i | − | 1.82319i | −0.411086 | − | 0.911597i | \(-0.634850\pi\) | ||
0.411086 | − | 0.911597i | \(-0.365150\pi\) | |||||||
\(762\) | 1.99830 | + | 16.3441i | 0.0723909 | + | 0.592084i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.01518 | − | 16.1746i | −0.145264 | − | 0.585175i | ||||
\(765\) | −0.661608 | −0.0239205 | ||||||||
\(766\) | 3.16915 | − | 0.387475i | 0.114506 | − | 0.0140000i | ||||
\(767\) | − | 47.5885i | − | 1.71832i | ||||||
\(768\) | −9.00137 | + | 13.2278i | −0.324809 | + | 0.477318i | ||||
\(769\) | − | 20.2817i | − | 0.731377i | −0.930737 | − | 0.365689i | \(-0.880833\pi\) | ||
0.930737 | − | 0.365689i | \(-0.119167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.45109i | 0.268344i | ||||||||
\(772\) | −24.0163 | + | 5.96181i | −0.864365 | + | 0.214570i | ||||
\(773\) | − | 21.7255i | − | 0.781413i | −0.920515 | − | 0.390706i | \(-0.872231\pi\) | ||
0.920515 | − | 0.390706i | \(-0.127769\pi\) | |||||||
\(774\) | 1.02538 | + | 8.38658i | 0.0368566 | + | 0.301449i | ||||
\(775\) | −19.6561 | −0.706069 | ||||||||
\(776\) | −10.9787 | − | 28.7324i | −0.394112 | − | 1.03143i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.9684 | + | 5.25351i | −1.54049 | + | 0.188347i | ||||
\(779\) | 46.0377i | 1.64947i | ||||||||
\(780\) | −7.01711 | + | 1.74193i | −0.251253 | + | 0.0623710i | ||||
\(781\) | −55.4698 | −1.98486 | ||||||||
\(782\) | 1.19587 | − | 0.146213i | 0.0427642 | − | 0.00522855i | ||||
\(783\) | 2.48011 | 0.0886318 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.1369 | −0.754410 | ||||||||
\(786\) | 13.0010 | − | 1.58956i | 0.463731 | − | 0.0566978i | ||||
\(787\) | −0.598657 | −0.0213398 | −0.0106699 | − | 0.999943i | \(-0.503396\pi\) | ||||
−0.0106699 | + | 0.999943i | \(0.503396\pi\) | |||||||
\(788\) | 6.28303 | − | 1.55970i | 0.223824 | − | 0.0555620i | ||||
\(789\) | − | 29.6797i | − | 1.05663i | ||||||
\(790\) | −1.91345 | + | 0.233947i | −0.0680774 | + | 0.00832346i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.53563 | + | 14.4873i | 0.196700 | + | 0.514784i | ||||
\(793\) | 39.0574 | 1.38697 | ||||||||
\(794\) | −2.38548 | − | 19.5108i | −0.0846575 | − | 0.692412i | ||||
\(795\) | − | 3.94654i | − | 0.139969i | ||||||
\(796\) | 37.3272 | − | 9.26612i | 1.32303 | − | 0.328429i | ||||
\(797\) | − | 36.1789i | − | 1.28152i | −0.767741 | − | 0.640760i | \(-0.778619\pi\) | ||
0.767741 | − | 0.640760i | \(-0.221381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.48180i | 0.0877998i | ||||||||
\(800\) | −18.8993 | + | 13.1614i | −0.668190 | + | 0.465326i | ||||
\(801\) | − | 0.554380i | − | 0.0195880i | ||||||
\(802\) | 14.4260 | − | 1.76378i | 0.509398 | − | 0.0622814i | ||||
\(803\) | −36.5231 | −1.28887 | ||||||||
\(804\) | 4.54798 | + | 18.3209i | 0.160395 | + | 0.646128i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.10834 | + | 25.4231i | 0.109487 | + | 0.895490i | ||||
\(807\) | 4.31542i | 0.151910i | ||||||||
\(808\) | −14.5685 | − | 38.1272i | −0.512517 | − | 1.34131i | ||||
\(809\) | −30.1206 | −1.05898 | −0.529491 | − | 0.848315i | \(-0.677617\pi\) | ||||
−0.529491 | + | 0.848315i | \(0.677617\pi\) | |||||||
\(810\) | 0.165402 | + | 1.35282i | 0.00581163 | + | 0.0475332i | ||||
\(811\) | 21.5947 | 0.758292 | 0.379146 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379146 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5828 | 0.476371 | ||||||||
\(814\) | −2.57187 | − | 21.0352i | −0.0901438 | − | 0.737285i | ||||
\(815\) | 3.87265 | 0.135653 | ||||||||
\(816\) | 1.28424 | + | 2.42728i | 0.0449573 | + | 0.0849720i | ||||
\(817\) | 29.1679i | 1.02046i | ||||||||
\(818\) | −2.08769 | − | 17.0751i | −0.0729942 | − | 0.597018i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.6397 | + | 4.37889i | −0.616006 | + | 0.152917i | ||||
\(821\) | 50.2528 | 1.75384 | 0.876918 | − | 0.480640i | \(-0.159595\pi\) | ||||
0.876918 | + | 0.480640i | \(0.159595\pi\) | |||||||
\(822\) | 10.1493 | − | 1.24090i | 0.353998 | − | 0.0432814i | ||||
\(823\) | 3.31789i | 0.115654i | 0.998327 | + | 0.0578272i | \(0.0184172\pi\) | ||||
−0.998327 | + | 0.0578272i | \(0.981583\pi\) | |||||||
\(824\) | −39.6970 | + | 15.1683i | −1.38291 | + | 0.528413i | ||||
\(825\) | 22.3236i | 0.777209i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3948i | 1.02216i | 0.859534 | + | 0.511078i | \(0.170754\pi\) | ||||
−0.859534 | + | 0.511078i | \(0.829246\pi\) | |||||||
\(828\) | −0.597935 | − | 2.40870i | −0.0207797 | − | 0.0837079i | ||||
\(829\) | 32.6757i | 1.13487i | 0.823417 | + | 0.567437i | \(0.192065\pi\) | ||||
−0.823417 | + | 0.567437i | \(0.807935\pi\) | |||||||
\(830\) | −0.0899422 | − | 0.735636i | −0.00312194 | − | 0.0255343i | ||||
\(831\) | −2.07126 | −0.0718513 | ||||||||
\(832\) | 20.0115 | + | 22.3629i | 0.693775 | + | 0.775294i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.45133 | − | 0.911035i | 0.258019 | − | 0.0315465i | ||||
\(835\) | − | 14.1837i | − | 0.490847i | ||||||
\(836\) | 12.8993 | + | 51.9629i | 0.446131 | + | 1.79717i | ||||
\(837\) | 4.82802 | 0.166881 | ||||||||
\(838\) | −22.7753 | + | 2.78462i | −0.786760 | + | 0.0961930i | ||||
\(839\) | 8.66161 | 0.299032 | 0.149516 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149516 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8491 | −0.787899 | ||||||||
\(842\) | 13.4547 | − | 1.64504i | 0.463680 | − | 0.0566917i | ||||
\(843\) | −23.7122 | −0.816692 | ||||||||
\(844\) | −4.45541 | − | 17.9480i | −0.153362 | − | 0.617795i | ||||
\(845\) | 1.03239i | 0.0355152i | ||||||||
\(846\) | 5.07465 | − | 0.620450i | 0.174470 | − | 0.0213315i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.4789 | + | 7.66057i | −0.497209 | + | 0.263065i | ||||
\(849\) | −12.2548 | −0.420583 | ||||||||
\(850\) | 0.479708 | + | 3.92352i | 0.0164538 | + | 0.134576i | ||||
\(851\) | 3.39122i | 0.116250i | ||||||||
\(852\) | 4.87458 | + | 19.6366i | 0.167000 | + | 0.672738i | ||||
\(853\) | 7.17809i | 0.245773i | 0.992421 | + | 0.122887i | \(0.0392151\pi\) | ||||
−0.992421 | + | 0.122887i | \(0.960785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.70500i | 0.160908i | ||||||||
\(856\) | −12.2315 | − | 32.0110i | −0.418062 | − | 1.09411i | ||||
\(857\) | 45.6493i | 1.55935i | 0.626184 | + | 0.779675i | \(0.284616\pi\) | ||||
−0.626184 | + | 0.779675i | \(0.715384\pi\) | |||||||
\(858\) | 28.8732 | − | 3.53017i | 0.985715 | − | 0.120518i | ||||
\(859\) | 13.5589 | 0.462623 | 0.231311 | − | 0.972880i | \(-0.425698\pi\) | ||||
0.231311 | + | 0.972880i | \(0.425698\pi\) | |||||||
\(860\) | −11.1759 | + | 2.77431i | −0.381096 | + | 0.0946033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0260696 | + | 0.213223i | 0.000887934 | + | 0.00726240i | ||||
\(863\) | − | 41.6327i | − | 1.41719i | −0.705614 | − | 0.708597i | \(-0.749329\pi\) | ||
0.705614 | − | 0.708597i | \(-0.250671\pi\) | |||||||
\(864\) | 4.64212 | − | 3.23276i | 0.157928 | − | 0.109981i | ||||
\(865\) | 11.2301 | 0.381834 | ||||||||
\(866\) | 1.62533 | + | 13.2936i | 0.0552311 | + | 0.451734i | ||||
\(867\) | −16.5287 | −0.561344 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.75555 | 0.263089 | ||||||||
\(870\) | 0.410214 | + | 3.35514i | 0.0139076 | + | 0.113750i | ||||
\(871\) | 35.4053 | 1.19966 | ||||||||
\(872\) | 16.0410 | − | 6.12929i | 0.543217 | − | 0.207564i | ||||
\(873\) | 10.8747i | 0.368054i | ||||||||
\(874\) | −1.03979 | − | 8.50439i | −0.0351713 | − | 0.287665i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.20959 | + | 12.9294i | 0.108442 | + | 0.436843i | ||||
\(877\) | −19.6848 | −0.664708 | −0.332354 | − | 0.943155i | \(-0.607843\pi\) | ||||
−0.332354 | + | 0.943155i | \(0.607843\pi\) | |||||||
\(878\) | −46.9902 | + | 5.74524i | −1.58584 | + | 0.193893i | ||||
\(879\) | 10.7090i | 0.361206i | ||||||||
\(880\) | −18.6831 | + | 9.88494i | −0.629808 | + | 0.333221i | ||||
\(881\) | − | 7.24606i | − | 0.244126i | −0.992522 | − | 0.122063i | \(-0.961049\pi\) | ||
0.992522 | − | 0.122063i | \(-0.0389510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4533i | 1.19310i | 0.802577 | + | 0.596549i | \(0.203462\pi\) | ||||
−0.802577 | + | 0.596549i | \(0.796538\pi\) | |||||||
\(884\) | 4.99879 | − | 1.24090i | 0.168128 | − | 0.0417360i | ||||
\(885\) | − | 12.2259i | − | 0.410970i | ||||||
\(886\) | −4.48906 | − | 36.7160i | −0.150813 | − | 1.23350i | ||||
\(887\) | −17.9737 | −0.603497 | −0.301749 | − | 0.953388i | \(-0.597570\pi\) | ||||
−0.301749 | + | 0.953388i | \(0.597570\pi\) | |||||||
\(888\) | −7.22056 | + | 2.75899i | −0.242306 | + | 0.0925857i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.749976 | − | 0.0916955i | 0.0251392 | − | 0.00307364i | ||||
\(891\) | − | 5.48322i | − | 0.183695i | ||||||
\(892\) | 3.77705 | − | 0.937616i | 0.126465 | − | 0.0313937i | ||||
\(893\) | 17.6493 | 0.590610 | ||||||||
\(894\) | 6.54378 | − | 0.800073i | 0.218857 | − | 0.0267584i | ||||
\(895\) | −2.50005 | −0.0835674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.65483 | −0.155420 | ||||||||
\(898\) | −14.4473 | + | 1.76639i | −0.482111 | + | 0.0589451i | ||||
\(899\) | 11.9740 | 0.399355 | ||||||||
\(900\) | 7.90267 | − | 1.96176i | 0.263422 | − | 0.0653920i | ||||
\(901\) | 2.81141i | 0.0936615i | ||||||||
\(902\) | 72.5820 | − | 8.87421i | 2.41672 | − | 0.295479i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4972 | − | 7.44992i | 0.648468 | − | 0.247781i | ||||
\(905\) | −9.18747 | −0.305402 | ||||||||
\(906\) | 2.09495 | + | 17.1345i | 0.0696000 | + | 0.569257i | ||||
\(907\) | − | 8.78577i | − | 0.291727i | −0.989305 | − | 0.145863i | \(-0.953404\pi\) | ||
0.989305 | − | 0.145863i | \(-0.0465960\pi\) | |||||||
\(908\) | −16.7813 | + | 4.16579i | −0.556907 | + | 0.138247i | ||||
\(909\) | 14.4305i | 0.478631i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5478i | 0.713911i | 0.934121 | + | 0.356955i | \(0.116185\pi\) | ||||
−0.934121 | + | 0.356955i | \(0.883815\pi\) | |||||||
\(912\) | 17.2616 | − | 9.13281i | 0.571587 | − | 0.302418i | ||||
\(913\) | 2.98166i | 0.0986787i | ||||||||
\(914\) | −16.7489 | + | 2.04780i | −0.554005 | + | 0.0677353i | ||||
\(915\) | 10.0342 | 0.331721 | ||||||||
\(916\) | −8.08983 | − | 32.5887i | −0.267295 | − | 1.07676i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.117828 | − | 0.963711i | −0.00388890 | − | 0.0318072i | ||||
\(919\) | 31.8627i | 1.05105i | 0.850777 | + | 0.525527i | \(0.176132\pi\) | ||||
−0.850777 | + | 0.525527i | \(0.823868\pi\) | |||||||
\(920\) | 3.15963 | − | 1.20730i | 0.104170 | − | 0.0398035i | ||||
\(921\) | −4.22056 | −0.139072 | ||||||||
\(922\) | −5.15051 | − | 42.1259i | −0.169623 | − | 1.38734i | ||||
\(923\) | 37.9479 | 1.24907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1262 | −0.365828 | ||||||||
\(926\) | −2.27814 | − | 18.6329i | −0.0748645 | − | 0.612315i | ||||
\(927\) | 15.0247 | 0.493476 | ||||||||
\(928\) | 11.5130 | − | 8.01759i | 0.377931 | − | 0.263190i | ||||
\(929\) | − | 51.0088i | − | 1.67355i | −0.547550 | − | 0.836773i | \(-0.684439\pi\) | ||
0.547550 | − | 0.836773i | \(-0.315561\pi\) | |||||||
\(930\) | 0.798563 | + | 6.53143i | 0.0261859 | + | 0.214174i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.03148 | + | 0.504294i | −0.0665432 | + | 0.0165187i | ||||
\(933\) | −9.70139 | −0.317609 | ||||||||
\(934\) | 41.6204 | − | 5.08871i | 1.36186 | − | 0.166508i | ||||
\(935\) | 3.62774i | 0.118640i | ||||||||
\(936\) | −3.78702 | − | 9.91103i | −0.123783 | − | 0.323952i | ||||
\(937\) | − | 2.65742i | − | 0.0868141i | −0.999057 | − | 0.0434071i | \(-0.986179\pi\) | ||
0.999057 | − | 0.0434071i | \(-0.0138212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6634i | 0.445887i | ||||||||
\(940\) | 1.67871 | + | 6.76246i | 0.0547536 | + | 0.220567i | ||||
\(941\) | 30.3594i | 0.989689i | 0.868982 | + | 0.494844i | \(0.164775\pi\) | ||||
−0.868982 | + | 0.494844i | \(0.835225\pi\) | |||||||
\(942\) | −3.76434 | − | 30.7885i | −0.122649 | − | 1.00314i | ||||
\(943\) | −11.7014 | −0.381050 | ||||||||
\(944\) | −44.8541 | + | 23.7316i | −1.45988 | + | 0.772397i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.9855 | − | 5.62240i | 1.49512 | − | 0.182800i | ||||
\(947\) | − | 43.4750i | − | 1.41275i | −0.707839 | − | 0.706374i | \(-0.750330\pi\) | ||
0.707839 | − | 0.706374i | \(-0.249670\pi\) | |||||||
\(948\) | −0.681544 | − | 2.74550i | −0.0221355 | − | 0.0891698i | ||||
\(949\) | 24.9861 | 0.811084 | ||||||||
\(950\) | 27.9020 | − | 3.41143i | 0.905260 | − | 0.110681i | ||||
\(951\) | −20.0884 | −0.651410 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.8683 | −1.74497 | −0.872483 | − | 0.488645i | \(-0.837491\pi\) | ||||
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(954\) | 5.74861 | − | 0.702851i | 0.186118 | − | 0.0227556i | ||||
\(955\) | −8.03035 | −0.259856 | ||||||||
\(956\) | 9.27472 | + | 37.3619i | 0.299966 | + | 1.20837i | ||||
\(957\) | − | 13.5990i | − | 0.439592i | ||||||
\(958\) | −16.1930 | + | 1.97984i | −0.523173 | + | 0.0639656i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.14115 | + | 5.74524i | 0.165930 | + | 0.185427i | ||||
\(961\) | −7.69025 | −0.248073 | ||||||||
\(962\) | 1.75946 | + | 14.3906i | 0.0567272 | + | 0.463971i | ||||
\(963\) | 12.1156i | 0.390421i | ||||||||
\(964\) | −1.32842 | − | 5.35136i | −0.0427856 | − | 0.172356i | ||||
\(965\) | 11.9236i | 0.383835i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.9529i | 1.44559i | 0.691064 | + | 0.722794i | \(0.257142\pi\) | ||||
−0.691064 | + | 0.722794i | \(0.742858\pi\) | |||||||
\(968\) | 50.3738 | − | 19.2479i | 1.61908 | − | 0.618652i | ||||
\(969\) | − | 3.35171i | − | 0.107673i | ||||||
\(970\) | −14.7116 | + | 1.79870i | −0.472360 | + | 0.0577529i | ||||
\(971\) | −1.28352 | −0.0411900 | −0.0205950 | − | 0.999788i | \(-0.506556\pi\) | ||||
−0.0205950 | + | 0.999788i | \(0.506556\pi\) | |||||||
\(972\) | −1.94109 | + | 0.481855i | −0.0622604 | + | 0.0154555i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.67428 | + | 13.6939i | 0.0536474 | + | 0.438781i | ||||
\(975\) | − | 15.2720i | − | 0.489095i | ||||||
\(976\) | −19.4773 | − | 36.8132i | −0.623452 | − | 1.17836i | ||||
\(977\) | 19.3536 | 0.619176 | 0.309588 | − | 0.950871i | \(-0.399809\pi\) | ||||
0.309588 | + | 0.950871i | \(0.399809\pi\) | |||||||
\(978\) | 0.689693 | + | 5.64098i | 0.0220539 | + | 0.180379i | ||||
\(979\) | −3.03979 | −0.0971520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.07126 | −0.193840 | ||||||||
\(982\) | 6.94649 | + | 56.8152i | 0.221671 | + | 1.81305i | ||||
\(983\) | 8.43273 | 0.268962 | 0.134481 | − | 0.990916i | \(-0.457063\pi\) | ||||
0.134481 | + | 0.990916i | \(0.457063\pi\) | |||||||
\(984\) | −9.51989 | − | 24.9145i | −0.303483 | − | 0.794247i | ||||
\(985\) | − | 3.11940i | − | 0.0993923i | ||||||
\(986\) | −0.292225 | − | 2.39011i | −0.00930635 | − | 0.0761165i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.82463 | − | 35.5488i | −0.280749 | − | 1.13096i | ||||
\(989\) | −7.41360 | −0.235739 | ||||||||
\(990\) | 7.41780 | − | 0.906935i | 0.235753 | − | 0.0288243i | ||||
\(991\) | 24.4758i | 0.777500i | 0.921343 | + | 0.388750i | \(0.127093\pi\) | ||||
−0.921343 | + | 0.388750i | \(0.872907\pi\) | |||||||
\(992\) | 22.4122 | − | 15.6078i | 0.711589 | − | 0.495549i | ||||
\(993\) | 9.42104i | 0.298968i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.5322i | − | 0.587511i | ||||||
\(996\) | 1.05552 | − | 0.262023i | 0.0334455 | − | 0.00830253i | ||||
\(997\) | − | 33.5179i | − | 1.06152i | −0.847522 | − | 0.530761i | \(-0.821906\pi\) | ||
0.847522 | − | 0.530761i | \(-0.178094\pi\) | |||||||
\(998\) | −5.48620 | − | 44.8715i | −0.173663 | − | 1.42038i | ||||
\(999\) | 2.73287 | 0.0864642 |
(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 | 588.2.b.a.391.2 | 8 | ||
3.2 | odd | 2 | 1764.2.b.j.1567.7 | 8 | |||
4.3 | odd | 2 | 588.2.b.b.391.1 | 8 | |||
7.2 | even | 3 | 588.2.o.d.31.3 | 8 | |||
7.3 | odd | 6 | 588.2.o.b.19.3 | 8 | |||
7.4 | even | 3 | 84.2.o.b.19.3 | yes | 8 | ||
7.5 | odd | 6 | 84.2.o.a.31.3 | yes | 8 | ||
7.6 | odd | 2 | 588.2.b.b.391.2 | 8 | |||
12.11 | even | 2 | 1764.2.b.i.1567.8 | 8 | |||
21.5 | even | 6 | 252.2.bf.g.199.2 | 8 | |||
21.11 | odd | 6 | 252.2.bf.f.19.2 | 8 | |||
21.20 | even | 2 | 1764.2.b.i.1567.7 | 8 | |||
28.3 | even | 6 | 588.2.o.d.19.3 | 8 | |||
28.11 | odd | 6 | 84.2.o.a.19.3 | ✓ | 8 | ||
28.19 | even | 6 | 84.2.o.b.31.3 | yes | 8 | ||
28.23 | odd | 6 | 588.2.o.b.31.3 | 8 | |||
28.27 | even | 2 | inner | 588.2.b.a.391.1 | 8 | ||
56.5 | odd | 6 | 1344.2.bl.j.703.2 | 8 | |||
56.11 | odd | 6 | 1344.2.bl.j.1279.2 | 8 | |||
56.19 | even | 6 | 1344.2.bl.i.703.2 | 8 | |||
56.53 | even | 6 | 1344.2.bl.i.1279.2 | 8 | |||
84.11 | even | 6 | 252.2.bf.g.19.2 | 8 | |||
84.47 | odd | 6 | 252.2.bf.f.199.2 | 8 | |||
84.83 | odd | 2 | 1764.2.b.j.1567.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.3 | ✓ | 8 | 28.11 | odd | 6 | ||
84.2.o.a.31.3 | yes | 8 | 7.5 | odd | 6 | ||
84.2.o.b.19.3 | yes | 8 | 7.4 | even | 3 | ||
84.2.o.b.31.3 | yes | 8 | 28.19 | even | 6 | ||
252.2.bf.f.19.2 | 8 | 21.11 | odd | 6 | |||
252.2.bf.f.199.2 | 8 | 84.47 | odd | 6 | |||
252.2.bf.g.19.2 | 8 | 84.11 | even | 6 | |||
252.2.bf.g.199.2 | 8 | 21.5 | even | 6 | |||
588.2.b.a.391.1 | 8 | 28.27 | even | 2 | inner | ||
588.2.b.a.391.2 | 8 | 1.1 | even | 1 | trivial | ||
588.2.b.b.391.1 | 8 | 4.3 | odd | 2 | |||
588.2.b.b.391.2 | 8 | 7.6 | odd | 2 | |||
588.2.o.b.19.3 | 8 | 7.3 | odd | 6 | |||
588.2.o.b.31.3 | 8 | 28.23 | odd | 6 | |||
588.2.o.d.19.3 | 8 | 28.3 | even | 6 | |||
588.2.o.d.31.3 | 8 | 7.2 | even | 3 | |||
1344.2.bl.i.703.2 | 8 | 56.19 | even | 6 | |||
1344.2.bl.i.1279.2 | 8 | 56.53 | even | 6 | |||
1344.2.bl.j.703.2 | 8 | 56.5 | odd | 6 | |||
1344.2.bl.j.1279.2 | 8 | 56.11 | odd | 6 | |||
1764.2.b.i.1567.7 | 8 | 21.20 | even | 2 | |||
1764.2.b.i.1567.8 | 8 | 12.11 | even | 2 | |||
1764.2.b.j.1567.7 | 8 | 3.2 | odd | 2 | |||
1764.2.b.j.1567.8 | 8 | 84.83 | odd | 2 |