Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(0.536547i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.151 |
Dual form | 375.2.g.d.226.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.165802 | − | 0.510286i | −0.117240 | − | 0.360827i | 0.875168 | − | 0.483820i | \(-0.160751\pi\) |
−0.992408 | + | 0.122993i | \(0.960751\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | ||||
\(4\) | 1.38513 | − | 1.00636i | 0.692566 | − | 0.503179i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.434076 | − | 0.315374i | −0.177211 | − | 0.128751i | ||||
\(7\) | −2.57318 | −0.972570 | −0.486285 | − | 0.873800i | \(-0.661648\pi\) | ||||
−0.486285 | + | 0.873800i | \(0.661648\pi\) | |||||||
\(8\) | −1.61134 | − | 1.17071i | −0.569695 | − | 0.413907i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.58949 | − | 4.89194i | −0.479248 | − | 1.47497i | −0.840141 | − | 0.542368i | \(-0.817528\pi\) |
0.360893 | − | 0.932607i | \(-0.382472\pi\) | |||||||
\(12\) | 0.529073 | − | 1.62832i | 0.152730 | − | 0.470056i | ||||
\(13\) | 0.455776 | − | 1.40274i | 0.126410 | − | 0.389049i | −0.867746 | − | 0.497009i | \(-0.834432\pi\) |
0.994155 | + | 0.107960i | \(0.0344318\pi\) | |||||||
\(14\) | 0.426639 | + | 1.31306i | 0.114024 | + | 0.350930i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.727915 | − | 2.24029i | 0.181979 | − | 0.560073i | ||||
\(17\) | 0.556490 | + | 0.404314i | 0.134969 | + | 0.0980605i | 0.653221 | − | 0.757167i | \(-0.273417\pi\) |
−0.518252 | + | 0.855228i | \(0.673417\pi\) | |||||||
\(18\) | −0.536547 | −0.126465 | ||||||||
\(19\) | 6.54709 | + | 4.75674i | 1.50201 | + | 1.09127i | 0.969574 | + | 0.244799i | \(0.0787219\pi\) |
0.532432 | + | 0.846473i | \(0.321278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.08175 | + | 1.51248i | −0.454274 | + | 0.330050i | ||||
\(22\) | −2.23275 | + | 1.62219i | −0.476024 | + | 0.345852i | ||||
\(23\) | −0.115186 | − | 0.354506i | −0.0240180 | − | 0.0739197i | 0.938329 | − | 0.345743i | \(-0.112373\pi\) |
−0.962347 | + | 0.271824i | \(0.912373\pi\) | |||||||
\(24\) | −1.99173 | −0.406559 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.791365 | −0.155200 | ||||||||
\(27\) | −0.309017 | − | 0.951057i | −0.0594703 | − | 0.183031i | ||||
\(28\) | −3.56419 | + | 2.58954i | −0.673569 | + | 0.489377i | ||||
\(29\) | −0.0288595 | + | 0.0209676i | −0.00535907 | + | 0.00389359i | −0.590462 | − | 0.807066i | \(-0.701054\pi\) |
0.585102 | + | 0.810959i | \(0.301054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.63169 | + | 2.63858i | 0.652272 | + | 0.473903i | 0.864044 | − | 0.503416i | \(-0.167924\pi\) |
−0.211773 | + | 0.977319i | \(0.567924\pi\) | |||||||
\(32\) | −5.24733 | −0.927606 | ||||||||
\(33\) | −4.16133 | − | 3.02338i | −0.724395 | − | 0.526304i | ||||
\(34\) | 0.114049 | − | 0.351005i | 0.0195592 | − | 0.0601969i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.529073 | − | 1.62832i | −0.0881789 | − | 0.271387i | ||||
\(37\) | −0.590022 | + | 1.81590i | −0.0969991 | + | 0.298532i | −0.987770 | − | 0.155921i | \(-0.950165\pi\) |
0.890770 | + | 0.454454i | \(0.150165\pi\) | |||||||
\(38\) | 1.34178 | − | 4.12957i | 0.217665 | − | 0.669905i | ||||
\(39\) | −0.455776 | − | 1.40274i | −0.0729826 | − | 0.224617i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.59739 | + | 4.91625i | −0.249470 | + | 0.767789i | 0.745399 | + | 0.666618i | \(0.232259\pi\) |
−0.994869 | + | 0.101171i | \(0.967741\pi\) | |||||||
\(42\) | 1.11695 | + | 0.811515i | 0.172350 | + | 0.125219i | ||||
\(43\) | 11.4506 | 1.74620 | 0.873099 | − | 0.487543i | \(-0.162107\pi\) | ||||
0.873099 | + | 0.487543i | \(0.162107\pi\) | |||||||
\(44\) | −7.12469 | − | 5.17639i | −1.07409 | − | 0.780370i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.161802 | + | 0.117556i | −0.0238564 | + | 0.0173327i | ||||
\(47\) | 6.89374 | − | 5.00860i | 1.00556 | − | 0.730579i | 0.0422836 | − | 0.999106i | \(-0.486537\pi\) |
0.963272 | + | 0.268527i | \(0.0865367\pi\) | |||||||
\(48\) | −0.727915 | − | 2.24029i | −0.105065 | − | 0.323358i | ||||
\(49\) | −0.378747 | −0.0541067 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.687859 | 0.0963196 | ||||||||
\(52\) | −0.780343 | − | 2.40165i | −0.108214 | − | 0.333049i | ||||
\(53\) | −7.38080 | + | 5.36247i | −1.01383 | + | 0.736592i | −0.965009 | − | 0.262216i | \(-0.915547\pi\) |
−0.0488220 | + | 0.998807i | \(0.515547\pi\) | |||||||
\(54\) | −0.434076 | + | 0.315374i | −0.0590702 | + | 0.0429170i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.14627 | + | 3.01244i | 0.554068 | + | 0.402554i | ||||
\(57\) | 8.09265 | 1.07190 | ||||||||
\(58\) | 0.0154845 | + | 0.0112501i | 0.00203321 | + | 0.00147721i | ||||
\(59\) | −0.0544457 | + | 0.167567i | −0.00708822 | + | 0.0218153i | −0.954538 | − | 0.298089i | \(-0.903651\pi\) |
0.947450 | + | 0.319904i | \(0.103651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.98127 | − | 6.09772i | −0.253676 | − | 0.780733i | −0.994088 | − | 0.108580i | \(-0.965370\pi\) |
0.740412 | − | 0.672153i | \(-0.234630\pi\) | |||||||
\(62\) | 0.744289 | − | 2.29069i | 0.0945248 | − | 0.290918i | ||||
\(63\) | −0.795156 | + | 2.44724i | −0.100180 | + | 0.308323i | ||||
\(64\) | −0.585811 | − | 1.80294i | −0.0732263 | − | 0.225367i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.852834 | + | 2.62475i | −0.104977 | + | 0.323085i | ||||
\(67\) | 0.0675025 | + | 0.0490435i | 0.00824675 | + | 0.00599161i | 0.591901 | − | 0.806011i | \(-0.298378\pi\) |
−0.583654 | + | 0.812002i | \(0.698378\pi\) | |||||||
\(68\) | 1.17770 | 0.142817 | ||||||||
\(69\) | −0.301561 | − | 0.219097i | −0.0363037 | − | 0.0263762i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.83589 | + | 7.14619i | −1.16731 | + | 0.848097i | −0.990684 | − | 0.136182i | \(-0.956517\pi\) |
−0.176622 | + | 0.984279i | \(0.556517\pi\) | |||||||
\(72\) | −1.61134 | + | 1.17071i | −0.189898 | + | 0.137969i | ||||
\(73\) | 3.72421 | + | 11.4619i | 0.435886 | + | 1.34152i | 0.892176 | + | 0.451688i | \(0.149178\pi\) |
−0.456290 | + | 0.889831i | \(0.650822\pi\) | |||||||
\(74\) | 1.02446 | 0.119091 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.8556 | 1.58934 | ||||||||
\(77\) | 4.09004 | + | 12.5878i | 0.466103 | + | 1.43452i | ||||
\(78\) | −0.640228 | + | 0.465153i | −0.0724916 | + | 0.0526682i | ||||
\(79\) | −4.01019 | + | 2.91357i | −0.451182 | + | 0.327803i | −0.790062 | − | 0.613027i | \(-0.789952\pi\) |
0.338881 | + | 0.940829i | \(0.389952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 2.77354 | 0.306287 | ||||||||
\(83\) | 7.57501 | + | 5.50356i | 0.831465 | + | 0.604095i | 0.919973 | − | 0.391981i | \(-0.128210\pi\) |
−0.0885084 | + | 0.996075i | \(0.528210\pi\) | |||||||
\(84\) | −1.36140 | + | 4.18996i | −0.148541 | + | 0.457162i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.89853 | − | 5.84308i | −0.204724 | − | 0.630075i | ||||
\(87\) | −0.0110233 | + | 0.0339264i | −0.00118183 | + | 0.00363729i | ||||
\(88\) | −3.16582 | + | 9.74340i | −0.337478 | + | 1.03865i | ||||
\(89\) | −0.00380677 | − | 0.0117160i | −0.000403517 | − | 0.00124190i | 0.950855 | − | 0.309638i | \(-0.100208\pi\) |
−0.951258 | + | 0.308396i | \(0.900208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.17279 | + | 3.60949i | −0.122942 | + | 0.378377i | ||||
\(92\) | −0.516308 | − | 0.375120i | −0.0538288 | − | 0.0391089i | ||||
\(93\) | 4.48902 | 0.465490 | ||||||||
\(94\) | −3.69882 | − | 2.68735i | −0.381504 | − | 0.277179i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.24518 | + | 3.08430i | −0.433272 | + | 0.314790i | ||||
\(97\) | −6.16504 | + | 4.47917i | −0.625965 | + | 0.454790i | −0.855000 | − | 0.518628i | \(-0.826443\pi\) |
0.229035 | + | 0.973418i | \(0.426443\pi\) | |||||||
\(98\) | 0.0627970 | + | 0.193269i | 0.00634345 | + | 0.0195231i | ||||
\(99\) | −5.14369 | −0.516960 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.27518 | 0.823411 | 0.411706 | − | 0.911317i | \(-0.364933\pi\) | ||||
0.411706 | + | 0.911317i | \(0.364933\pi\) | |||||||
\(102\) | −0.114049 | − | 0.351005i | −0.0112925 | − | 0.0347547i | ||||
\(103\) | 8.40247 | − | 6.10475i | 0.827920 | − | 0.601519i | −0.0910504 | − | 0.995846i | \(-0.529022\pi\) |
0.918970 | + | 0.394328i | \(0.129022\pi\) | |||||||
\(104\) | −2.37660 | + | 1.72670i | −0.233045 | + | 0.169317i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.96015 | + | 2.87722i | 0.384643 | + | 0.279460i | ||||
\(107\) | 12.2737 | 1.18655 | 0.593274 | − | 0.805001i | \(-0.297835\pi\) | ||||
0.593274 | + | 0.805001i | \(0.297835\pi\) | |||||||
\(108\) | −1.38513 | − | 1.00636i | −0.133284 | − | 0.0968368i | ||||
\(109\) | −1.30684 | + | 4.02203i | −0.125172 | + | 0.385241i | −0.993932 | − | 0.109992i | \(-0.964917\pi\) |
0.868760 | + | 0.495233i | \(0.164917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.590022 | + | 1.81590i | 0.0560024 | + | 0.172358i | ||||
\(112\) | −1.87305 | + | 5.76467i | −0.176987 | + | 0.544710i | ||||
\(113\) | 5.67623 | − | 17.4696i | 0.533974 | − | 1.64340i | −0.211880 | − | 0.977296i | \(-0.567959\pi\) |
0.745855 | − | 0.666109i | \(-0.232041\pi\) | |||||||
\(114\) | −1.34178 | − | 4.12957i | −0.125669 | − | 0.386770i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0188733 | + | 0.0580859i | −0.00175234 | + | 0.00539314i | ||||
\(117\) | −1.19324 | − | 0.866938i | −0.110315 | − | 0.0801485i | ||||
\(118\) | 0.0945341 | 0.00870257 | ||||||||
\(119\) | −1.43195 | − | 1.04037i | −0.131267 | − | 0.0953707i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5054 | + | 9.08571i | −1.13685 | + | 0.825974i | ||||
\(122\) | −2.78309 | + | 2.02203i | −0.251969 | + | 0.183066i | ||||
\(123\) | 1.59739 | + | 4.91625i | 0.144031 | + | 0.443283i | ||||
\(124\) | 7.68573 | 0.690199 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.38063 | 0.122996 | ||||||||
\(127\) | −0.106766 | − | 0.328591i | −0.00947391 | − | 0.0291577i | 0.946208 | − | 0.323560i | \(-0.104880\pi\) |
−0.955682 | + | 0.294402i | \(0.904880\pi\) | |||||||
\(128\) | −9.31325 | + | 6.76647i | −0.823182 | + | 0.598077i | ||||
\(129\) | 9.26372 | − | 6.73048i | 0.815625 | − | 0.592586i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.69438 | + | 2.68413i | 0.322780 | + | 0.234513i | 0.737361 | − | 0.675499i | \(-0.236072\pi\) |
−0.414581 | + | 0.910012i | \(0.636072\pi\) | |||||||
\(132\) | −8.80660 | −0.766516 | ||||||||
\(133\) | −16.8468 | − | 12.2400i | −1.46081 | − | 1.06134i | ||||
\(134\) | 0.0138342 | − | 0.0425771i | 0.00119509 | − | 0.00367810i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.423362 | − | 1.30297i | −0.0363030 | − | 0.111729i | ||||
\(137\) | 1.48870 | − | 4.58174i | 0.127188 | − | 0.391445i | −0.867105 | − | 0.498125i | \(-0.834022\pi\) |
0.994293 | + | 0.106680i | \(0.0340221\pi\) | |||||||
\(138\) | −0.0618027 | + | 0.190209i | −0.00526100 | + | 0.0161917i | ||||
\(139\) | −1.15595 | − | 3.55766i | −0.0980468 | − | 0.301757i | 0.889989 | − | 0.455982i | \(-0.150712\pi\) |
−0.988036 | + | 0.154225i | \(0.950712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.63318 | − | 8.10408i | 0.221753 | − | 0.682487i | ||||
\(142\) | 5.27742 | + | 3.83427i | 0.442871 | + | 0.321765i | ||||
\(143\) | −7.58655 | −0.634419 | ||||||||
\(144\) | −1.90570 | − | 1.38458i | −0.158809 | − | 0.115381i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.23139 | − | 3.80083i | 0.432953 | − | 0.314559i | ||||
\(147\) | −0.306412 | + | 0.222622i | −0.0252725 | + | 0.0183615i | ||||
\(148\) | 1.01019 | + | 3.10904i | 0.0830369 | + | 0.255561i | ||||
\(149\) | 8.64621 | 0.708325 | 0.354163 | − | 0.935184i | \(-0.384766\pi\) | ||||
0.354163 | + | 0.935184i | \(0.384766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24898 | −0.101641 | −0.0508205 | − | 0.998708i | \(-0.516184\pi\) | ||||
−0.0508205 | + | 0.998708i | \(0.516184\pi\) | |||||||
\(152\) | −4.98084 | − | 15.3295i | −0.404000 | − | 1.24338i | ||||
\(153\) | 0.556490 | − | 0.404314i | 0.0449895 | − | 0.0326868i | ||||
\(154\) | 5.74527 | − | 4.17418i | 0.462967 | − | 0.336365i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.04296 | − | 1.48430i | −0.163568 | − | 0.118839i | ||||
\(157\) | −3.86574 | −0.308520 | −0.154260 | − | 0.988030i | \(-0.549299\pi\) | ||||
−0.154260 | + | 0.988030i | \(0.549299\pi\) | |||||||
\(158\) | 2.15166 | + | 1.56327i | 0.171176 | + | 0.124367i | ||||
\(159\) | −2.81922 | + | 8.67665i | −0.223578 | + | 0.688103i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.296394 | + | 0.912208i | 0.0233592 | + | 0.0718921i | ||||
\(162\) | −0.165802 | + | 0.510286i | −0.0130266 | + | 0.0400919i | ||||
\(163\) | 2.15512 | − | 6.63277i | 0.168802 | − | 0.519519i | −0.830494 | − | 0.557027i | \(-0.811942\pi\) |
0.999296 | + | 0.0375081i | \(0.0119420\pi\) | |||||||
\(164\) | 2.73491 | + | 8.41719i | 0.213561 | + | 0.657272i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.55244 | − | 4.77793i | 0.120493 | − | 0.370839i | ||||
\(167\) | −12.9114 | − | 9.38069i | −0.999115 | − | 0.725900i | −0.0372169 | − | 0.999307i | \(-0.511849\pi\) |
−0.961898 | + | 0.273408i | \(0.911849\pi\) | |||||||
\(168\) | 5.12507 | 0.395407 | ||||||||
\(169\) | 8.75729 | + | 6.36254i | 0.673637 | + | 0.489426i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.54709 | − | 4.75674i | 0.500669 | − | 0.363757i | ||||
\(172\) | 15.8606 | − | 11.5234i | 1.20936 | − | 0.878649i | ||||
\(173\) | 2.37118 | + | 7.29774i | 0.180277 | + | 0.554837i | 0.999835 | − | 0.0181597i | \(-0.00578074\pi\) |
−0.819558 | + | 0.572997i | \(0.805781\pi\) | |||||||
\(174\) | 0.0191399 | 0.00145099 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.1164 | −0.913306 | ||||||||
\(177\) | 0.0544457 | + | 0.167567i | 0.00409239 | + | 0.0125951i | ||||
\(178\) | −0.00534737 | + | 0.00388509i | −0.000400802 | + | 0.000291200i | ||||
\(179\) | −8.58312 | + | 6.23600i | −0.641532 | + | 0.466100i | −0.860376 | − | 0.509659i | \(-0.829771\pi\) |
0.218844 | + | 0.975760i | \(0.429771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2223 | − | 8.88005i | −0.908480 | − | 0.660049i | 0.0321503 | − | 0.999483i | \(-0.489764\pi\) |
−0.940630 | + | 0.339434i | \(0.889764\pi\) | |||||||
\(182\) | 2.03633 | 0.150942 | ||||||||
\(183\) | −5.18703 | − | 3.76860i | −0.383436 | − | 0.278583i | ||||
\(184\) | −0.229419 | + | 0.706079i | −0.0169130 | + | 0.0520528i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.744289 | − | 2.29069i | −0.0545739 | − | 0.167961i | ||||
\(187\) | 1.09334 | − | 3.36497i | 0.0799532 | − | 0.246071i | ||||
\(188\) | 4.50831 | − | 13.8751i | 0.328802 | − | 1.01195i | ||||
\(189\) | 0.795156 | + | 2.44724i | 0.0578391 | + | 0.178010i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.78359 | − | 11.6447i | 0.273771 | − | 0.842580i | −0.715771 | − | 0.698335i | \(-0.753925\pi\) |
0.989542 | − | 0.144245i | \(-0.0460754\pi\) | |||||||
\(192\) | −1.53367 | − | 1.11428i | −0.110683 | − | 0.0804161i | ||||
\(193\) | −14.2421 | −1.02517 | −0.512585 | − | 0.858637i | \(-0.671312\pi\) | ||||
−0.512585 | + | 0.858637i | \(0.671312\pi\) | |||||||
\(194\) | 3.30783 | + | 2.40328i | 0.237489 | + | 0.172546i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.524614 | + | 0.381154i | −0.0374724 | + | 0.0272253i | ||||
\(197\) | −14.3591 | + | 10.4325i | −1.02304 | + | 0.743286i | −0.966905 | − | 0.255137i | \(-0.917879\pi\) |
−0.0561399 | + | 0.998423i | \(0.517879\pi\) | |||||||
\(198\) | 0.852834 | + | 2.62475i | 0.0606083 | + | 0.186533i | ||||
\(199\) | −18.9550 | −1.34369 | −0.671843 | − | 0.740693i | \(-0.734497\pi\) | ||||
−0.671843 | + | 0.740693i | \(0.734497\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0834377 | 0.00588524 | ||||||||
\(202\) | −1.37204 | − | 4.22271i | −0.0965366 | − | 0.297109i | ||||
\(203\) | 0.0742606 | − | 0.0539535i | 0.00521207 | − | 0.00378679i | ||||
\(204\) | 0.952776 | − | 0.692232i | 0.0667077 | − | 0.0484660i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.50832 | − | 3.27548i | −0.314109 | − | 0.228214i | ||||
\(207\) | −0.372750 | −0.0259079 | ||||||||
\(208\) | −2.81077 | − | 2.04214i | −0.194892 | − | 0.141597i | ||||
\(209\) | 12.8632 | − | 39.5888i | 0.889764 | − | 2.73841i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.33022 | − | 10.2494i | −0.229262 | − | 0.705596i | −0.997831 | − | 0.0658288i | \(-0.979031\pi\) |
0.768569 | − | 0.639767i | \(-0.220969\pi\) | |||||||
\(212\) | −4.82683 | + | 14.8555i | −0.331508 | + | 1.02028i | ||||
\(213\) | −3.75698 | + | 11.5628i | −0.257424 | + | 0.792269i | ||||
\(214\) | −2.03501 | − | 6.26312i | −0.139111 | − | 0.428138i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.615477 | + | 1.89424i | −0.0418779 | + | 0.128887i | ||||
\(217\) | −9.34500 | − | 6.78954i | −0.634380 | − | 0.460904i | ||||
\(218\) | 2.26907 | 0.153681 | ||||||||
\(219\) | 9.75012 | + | 7.08387i | 0.658852 | + | 0.478684i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.820780 | − | 0.596332i | 0.0552116 | − | 0.0401136i | ||||
\(222\) | 0.828803 | − | 0.602161i | 0.0556256 | − | 0.0404144i | ||||
\(223\) | −8.51983 | − | 26.2213i | −0.570530 | − | 1.75591i | −0.650920 | − | 0.759147i | \(-0.725617\pi\) |
0.0803900 | − | 0.996763i | \(-0.474383\pi\) | |||||||
\(224\) | 13.5023 | 0.902162 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.85565 | −0.655588 | ||||||||
\(227\) | 1.23057 | + | 3.78731i | 0.0816758 | + | 0.251372i | 0.983553 | − | 0.180620i | \(-0.0578106\pi\) |
−0.901877 | + | 0.431993i | \(0.857811\pi\) | |||||||
\(228\) | 11.2094 | − | 8.14410i | 0.742360 | − | 0.539356i | ||||
\(229\) | −9.68373 | + | 7.03564i | −0.639919 | + | 0.464928i | −0.859822 | − | 0.510593i | \(-0.829426\pi\) |
0.219903 | + | 0.975522i | \(0.429426\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7079 | + | 7.77971i | 0.704525 | + | 0.511867i | ||||
\(232\) | 0.0710494 | 0.00466462 | ||||||||
\(233\) | 17.0849 | + | 12.4129i | 1.11927 | + | 0.813197i | 0.984098 | − | 0.177625i | \(-0.0568413\pi\) |
0.135172 | + | 0.990822i | \(0.456841\pi\) | |||||||
\(234\) | −0.244545 | + | 0.752633i | −0.0159864 | + | 0.0492012i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.0932174 | + | 0.286894i | 0.00606793 | + | 0.0186752i | ||||
\(237\) | −1.53176 | + | 4.71426i | −0.0994983 | + | 0.306224i | ||||
\(238\) | −0.293467 | + | 0.903200i | −0.0190227 | + | 0.0585457i | ||||
\(239\) | 8.09778 | + | 24.9224i | 0.523802 | + | 1.61210i | 0.766673 | + | 0.642038i | \(0.221911\pi\) |
−0.242871 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.52607 | + | 7.77443i | −0.162718 | + | 0.500795i | −0.998861 | − | 0.0477169i | \(-0.984805\pi\) |
0.836143 | + | 0.548512i | \(0.184805\pi\) | |||||||
\(242\) | 6.70974 | + | 4.87491i | 0.431318 | + | 0.313371i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −8.88081 | − | 6.45228i | −0.568535 | − | 0.413065i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.24384 | − | 1.63025i | 0.143062 | − | 0.103941i | ||||
\(247\) | 9.65646 | − | 7.01583i | 0.614426 | − | 0.446406i | ||||
\(248\) | −2.76289 | − | 8.50330i | −0.175444 | − | 0.539960i | ||||
\(249\) | 9.36322 | 0.593370 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.8145 | 1.56628 | 0.783139 | − | 0.621847i | \(-0.213618\pi\) | ||||
0.783139 | + | 0.621847i | \(0.213618\pi\) | |||||||
\(252\) | 1.36140 | + | 4.18996i | 0.0857602 | + | 0.263943i | ||||
\(253\) | −1.55114 | + | 1.12697i | −0.0975191 | + | 0.0708518i | ||||
\(254\) | −0.149973 | + | 0.108962i | −0.00941017 | + | 0.00683689i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.92965 | + | 1.40197i | 0.120603 | + | 0.0876232i | ||||
\(257\) | −24.2995 | −1.51576 | −0.757882 | − | 0.652392i | \(-0.773766\pi\) | ||||
−0.757882 | + | 0.652392i | \(0.773766\pi\) | |||||||
\(258\) | −4.97042 | − | 3.61122i | −0.309445 | − | 0.224825i | ||||
\(259\) | 1.51823 | − | 4.67264i | 0.0943384 | − | 0.290344i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0110233 | + | 0.0339264i | 0.000682328 | + | 0.00209999i | ||||
\(262\) | 0.757137 | − | 2.33023i | 0.0467761 | − | 0.143962i | ||||
\(263\) | −2.63366 | + | 8.10556i | −0.162398 | + | 0.499810i | −0.998835 | − | 0.0482528i | \(-0.984635\pi\) |
0.836437 | + | 0.548063i | \(0.184635\pi\) | |||||||
\(264\) | 3.16582 | + | 9.74340i | 0.194843 | + | 0.599665i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.45264 | + | 10.6261i | −0.211695 | + | 0.651530i | ||||
\(267\) | −0.00996627 | − | 0.00724092i | −0.000609926 | − | 0.000443137i | ||||
\(268\) | 0.142855 | 0.00872627 | ||||||||
\(269\) | −2.08979 | − | 1.51832i | −0.127417 | − | 0.0925737i | 0.522252 | − | 0.852791i | \(-0.325092\pi\) |
−0.649668 | + | 0.760218i | \(0.725092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9940 | − | 7.98759i | 0.667837 | − | 0.485212i | −0.201464 | − | 0.979496i | \(-0.564570\pi\) |
0.869300 | + | 0.494284i | \(0.164570\pi\) | |||||||
\(272\) | 1.31086 | − | 0.952393i | 0.0794824 | − | 0.0577473i | ||||
\(273\) | 1.17279 | + | 3.60949i | 0.0709807 | + | 0.218456i | ||||
\(274\) | −2.58483 | −0.156155 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.638192 | −0.0384146 | ||||||||
\(277\) | −2.82434 | − | 8.69242i | −0.169698 | − | 0.522277i | 0.829654 | − | 0.558278i | \(-0.188538\pi\) |
−0.999352 | + | 0.0360015i | \(0.988538\pi\) | |||||||
\(278\) | −1.62377 | + | 1.17974i | −0.0973870 | + | 0.0707558i | ||||
\(279\) | 3.63169 | − | 2.63858i | 0.217424 | − | 0.157968i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.42195 | − | 6.11890i | −0.502411 | − | 0.365023i | 0.307526 | − | 0.951540i | \(-0.400499\pi\) |
−0.809937 | + | 0.586517i | \(0.800499\pi\) | |||||||
\(282\) | −4.57199 | −0.272258 | ||||||||
\(283\) | 3.89611 | + | 2.83069i | 0.231600 | + | 0.168267i | 0.697533 | − | 0.716553i | \(-0.254281\pi\) |
−0.465933 | + | 0.884820i | \(0.654281\pi\) | |||||||
\(284\) | −6.43238 | + | 19.7968i | −0.381692 | + | 1.17473i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.25787 | + | 3.87131i | 0.0743791 | + | 0.228915i | ||||
\(287\) | 4.11036 | − | 12.6504i | 0.242627 | − | 0.746729i | ||||
\(288\) | −1.62151 | + | 4.99051i | −0.0955486 | + | 0.294068i | ||||
\(289\) | −5.10708 | − | 15.7180i | −0.300416 | − | 0.924586i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.35484 | + | 7.24744i | −0.138043 | + | 0.424853i | ||||
\(292\) | 16.6933 | + | 12.1284i | 0.976904 | + | 0.709762i | ||||
\(293\) | −24.4506 | −1.42842 | −0.714210 | − | 0.699932i | \(-0.753214\pi\) | ||||
−0.714210 | + | 0.699932i | \(0.753214\pi\) | |||||||
\(294\) | 0.164405 | + | 0.119447i | 0.00958827 | + | 0.00696629i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.07661 | − | 2.23529i | 0.178825 | − | 0.129924i | ||||
\(297\) | −4.16133 | + | 3.02338i | −0.241465 | + | 0.175435i | ||||
\(298\) | −1.43356 | − | 4.41205i | −0.0830439 | − | 0.255583i | ||||
\(299\) | −0.549778 | −0.0317945 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.4644 | −1.69830 | ||||||||
\(302\) | 0.207084 | + | 0.637340i | 0.0119164 | + | 0.0366748i | ||||
\(303\) | 6.69476 | − | 4.86403i | 0.384604 | − | 0.279431i | ||||
\(304\) | 15.4222 | − | 11.2049i | 0.884524 | − | 0.642645i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.298583 | − | 0.216933i | −0.0170689 | − | 0.0124012i | ||||
\(307\) | 9.51655 | 0.543138 | 0.271569 | − | 0.962419i | \(-0.412457\pi\) | ||||
0.271569 | + | 0.962419i | \(0.412457\pi\) | |||||||
\(308\) | 18.3331 | + | 13.3198i | 1.04463 | + | 0.758965i | ||||
\(309\) | 3.20946 | − | 9.87769i | 0.182580 | − | 0.561922i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.71967 | + | 23.7587i | 0.437742 | + | 1.34723i | 0.890250 | + | 0.455471i | \(0.150529\pi\) |
−0.452508 | + | 0.891760i | \(0.649471\pi\) | |||||||
\(312\) | −0.907781 | + | 2.79386i | −0.0513930 | + | 0.158171i | ||||
\(313\) | −3.05359 | + | 9.39797i | −0.172599 | + | 0.531205i | −0.999516 | − | 0.0311197i | \(-0.990093\pi\) |
0.826917 | + | 0.562324i | \(0.190093\pi\) | |||||||
\(314\) | 0.640948 | + | 1.97264i | 0.0361708 | + | 0.111322i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.62255 | + | 8.07137i | −0.147530 | + | 0.454050i | ||||
\(317\) | 20.0078 | + | 14.5365i | 1.12375 | + | 0.816453i | 0.984773 | − | 0.173842i | \(-0.0556184\pi\) |
0.138978 | + | 0.990296i | \(0.455618\pi\) | |||||||
\(318\) | 4.89501 | 0.274499 | ||||||||
\(319\) | 0.148444 | + | 0.107851i | 0.00831128 | + | 0.00603850i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.92967 | − | 7.21433i | 0.554220 | − | 0.402664i | ||||
\(322\) | 0.416345 | − | 0.302492i | 0.0232020 | − | 0.0168572i | ||||
\(323\) | 1.72018 | + | 5.29416i | 0.0957132 | + | 0.294575i | ||||
\(324\) | −1.71212 | −0.0951176 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.74194 | −0.207247 | ||||||||
\(327\) | 1.30684 | + | 4.02203i | 0.0722683 | + | 0.222419i | ||||
\(328\) | 8.32941 | − | 6.05167i | 0.459915 | − | 0.334148i | ||||
\(329\) | −17.7388 | + | 12.8880i | −0.977974 | + | 0.710540i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.872336 | − | 0.633789i | −0.0479479 | − | 0.0348362i | 0.563553 | − | 0.826080i | \(-0.309434\pi\) |
−0.611501 | + | 0.791244i | \(0.709434\pi\) | |||||||
\(332\) | 16.0309 | 0.879812 | ||||||||
\(333\) | 1.54470 | + | 1.12229i | 0.0846490 | + | 0.0615011i | ||||
\(334\) | −2.64610 | + | 8.14386i | −0.144788 | + | 0.445612i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.87305 | + | 5.76467i | 0.102184 | + | 0.314489i | ||||
\(337\) | 4.34507 | − | 13.3727i | 0.236691 | − | 0.728460i | −0.760202 | − | 0.649687i | \(-0.774900\pi\) |
0.996893 | − | 0.0787727i | \(-0.0251001\pi\) | |||||||
\(338\) | 1.79474 | − | 5.52365i | 0.0976211 | − | 0.300447i | ||||
\(339\) | −5.67623 | − | 17.4696i | −0.308290 | − | 0.948820i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.13524 | − | 21.9600i | 0.386395 | − | 1.18920i | ||||
\(342\) | −3.51282 | − | 2.55222i | −0.189952 | − | 0.138008i | ||||
\(343\) | 18.9868 | 1.02519 | ||||||||
\(344\) | −18.4508 | − | 13.4053i | −0.994799 | − | 0.722764i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.33079 | − | 2.41996i | 0.179064 | − | 0.130098i | ||||
\(347\) | −4.60804 | + | 3.34793i | −0.247372 | + | 0.179726i | −0.704561 | − | 0.709643i | \(-0.748856\pi\) |
0.457189 | + | 0.889369i | \(0.348856\pi\) | |||||||
\(348\) | 0.0188733 | + | 0.0580859i | 0.00101171 | + | 0.00311373i | ||||
\(349\) | −28.4950 | −1.52530 | −0.762651 | − | 0.646810i | \(-0.776103\pi\) | ||||
−0.762651 | + | 0.646810i | \(0.776103\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.47492 | −0.0787256 | ||||||||
\(352\) | 8.34056 | + | 25.6696i | 0.444554 | + | 1.36820i | ||||
\(353\) | −10.3276 | + | 7.50341i | −0.549681 | + | 0.399366i | −0.827668 | − | 0.561218i | \(-0.810333\pi\) |
0.277987 | + | 0.960585i | \(0.410333\pi\) | |||||||
\(354\) | 0.0764797 | − | 0.0555658i | 0.00406485 | − | 0.00295329i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.0170634 | − | 0.0123973i | −0.000904359 | − | 0.000657056i | ||||
\(357\) | −1.76999 | −0.0936776 | ||||||||
\(358\) | 4.60524 | + | 3.34591i | 0.243395 | + | 0.176837i | ||||
\(359\) | −1.39620 | + | 4.29707i | −0.0736888 | + | 0.226791i | −0.981117 | − | 0.193417i | \(-0.938043\pi\) |
0.907428 | + | 0.420208i | \(0.138043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3665 | + | 44.2156i | 0.756132 | + | 2.32714i | ||||
\(362\) | −2.50488 | + | 7.70923i | −0.131654 | + | 0.405188i | ||||
\(363\) | −4.77664 | + | 14.7010i | −0.250709 | + | 0.771602i | ||||
\(364\) | 2.00796 | + | 6.17987i | 0.105246 | + | 0.323913i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.06304 | + | 3.27171i | −0.0555662 | + | 0.171015i | ||||
\(367\) | −2.45493 | − | 1.78361i | −0.128146 | − | 0.0931039i | 0.521866 | − | 0.853028i | \(-0.325236\pi\) |
−0.650012 | + | 0.759924i | \(0.725236\pi\) | |||||||
\(368\) | −0.878043 | −0.0457711 | ||||||||
\(369\) | 4.18201 | + | 3.03841i | 0.217707 | + | 0.158173i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.9921 | − | 13.7986i | 0.986022 | − | 0.716387i | ||||
\(372\) | 6.21789 | − | 4.51756i | 0.322382 | − | 0.234225i | ||||
\(373\) | 4.74831 | + | 14.6138i | 0.245858 | + | 0.756674i | 0.995494 | + | 0.0948232i | \(0.0302286\pi\) |
−0.749636 | + | 0.661850i | \(0.769771\pi\) | |||||||
\(374\) | −1.89838 | −0.0981626 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −16.9718 | −0.875252 | ||||||||
\(377\) | 0.0162586 | + | 0.0500388i | 0.000837359 | + | 0.00257713i | ||||
\(378\) | 1.11695 | − | 0.811515i | 0.0574499 | − | 0.0417398i | ||||
\(379\) | −8.38117 | + | 6.08927i | −0.430512 | + | 0.312785i | −0.781853 | − | 0.623462i | \(-0.785725\pi\) |
0.351342 | + | 0.936247i | \(0.385725\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.279516 | − | 0.203080i | −0.0143200 | − | 0.0104041i | ||||
\(382\) | −6.56946 | −0.336123 | ||||||||
\(383\) | 12.5289 | + | 9.10278i | 0.640197 | + | 0.465130i | 0.859918 | − | 0.510432i | \(-0.170515\pi\) |
−0.219721 | + | 0.975563i | \(0.570515\pi\) | |||||||
\(384\) | −3.55734 | + | 10.9484i | −0.181535 | + | 0.558707i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.36137 | + | 7.26756i | 0.120191 | + | 0.369909i | ||||
\(387\) | 3.53843 | − | 10.8902i | 0.179868 | − | 0.553578i | ||||
\(388\) | −4.03176 | + | 12.4085i | −0.204681 | + | 0.629945i | ||||
\(389\) | −6.61139 | − | 20.3478i | −0.335211 | − | 1.03167i | −0.966618 | − | 0.256221i | \(-0.917522\pi\) |
0.631407 | − | 0.775451i | \(-0.282478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0792318 | − | 0.243850i | 0.00400693 | − | 0.0123320i | ||||
\(392\) | 0.610289 | + | 0.443401i | 0.0308243 | + | 0.0223951i | ||||
\(393\) | 4.56651 | 0.230350 | ||||||||
\(394\) | 7.70434 | + | 5.59753i | 0.388139 | + | 0.282000i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.12469 | + | 5.17639i | −0.358029 | + | 0.260123i | ||||
\(397\) | −10.1140 | + | 7.34827i | −0.507608 | + | 0.368799i | −0.811916 | − | 0.583775i | \(-0.801575\pi\) |
0.304307 | + | 0.952574i | \(0.401575\pi\) | |||||||
\(398\) | 3.14278 | + | 9.67249i | 0.157534 | + | 0.484838i | ||||
\(399\) | −20.8238 | −1.04250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.0478 | −1.65033 | −0.825164 | − | 0.564893i | \(-0.808917\pi\) | ||||
−0.825164 | + | 0.564893i | \(0.808917\pi\) | |||||||
\(402\) | −0.0138342 | − | 0.0425771i | −0.000689985 | − | 0.00212355i | ||||
\(403\) | 5.35647 | − | 3.89170i | 0.266825 | − | 0.193860i | ||||
\(404\) | 11.4622 | − | 8.32779i | 0.570267 | − | 0.414323i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0398443 | − | 0.0289486i | −0.00197744 | − | 0.00143669i | ||||
\(407\) | 9.82111 | 0.486815 | ||||||||
\(408\) | −1.10837 | − | 0.805282i | −0.0548727 | − | 0.0398674i | ||||
\(409\) | 0.932426 | − | 2.86971i | 0.0461055 | − | 0.141898i | −0.925354 | − | 0.379105i | \(-0.876232\pi\) |
0.971459 | + | 0.237207i | \(0.0762319\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.48870 | − | 4.58174i | −0.0734321 | − | 0.226001i | ||||
\(412\) | 5.49497 | − | 16.9118i | 0.270718 | − | 0.833183i | ||||
\(413\) | 0.140098 | − | 0.431179i | 0.00689379 | − | 0.0212169i | ||||
\(414\) | 0.0618027 | + | 0.190209i | 0.00303744 | + | 0.00934827i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.39161 | + | 7.36062i | −0.117258 | + | 0.360884i | ||||
\(417\) | −3.02633 | − | 2.19876i | −0.148200 | − | 0.107674i | ||||
\(418\) | −22.3343 | −1.09241 | ||||||||
\(419\) | −5.75511 | − | 4.18133i | −0.281156 | − | 0.204272i | 0.438266 | − | 0.898845i | \(-0.355593\pi\) |
−0.719421 | + | 0.694574i | \(0.755593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6826 | − | 12.8472i | 0.861798 | − | 0.626133i | −0.0665758 | − | 0.997781i | \(-0.521207\pi\) |
0.928373 | + | 0.371649i | \(0.121207\pi\) | |||||||
\(422\) | −4.67796 | + | 3.39873i | −0.227719 | + | 0.165448i | ||||
\(423\) | −2.63318 | − | 8.10408i | −0.128029 | − | 0.394034i | ||||
\(424\) | 18.1709 | 0.882455 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.52325 | 0.316052 | ||||||||
\(427\) | 5.09816 | + | 15.6905i | 0.246717 | + | 0.759318i | ||||
\(428\) | 17.0008 | − | 12.3518i | 0.821763 | − | 0.597045i | ||||
\(429\) | −6.13764 | + | 4.45926i | −0.296328 | + | 0.215295i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.23115 | − | 2.34757i | −0.155639 | − | 0.113078i | 0.507240 | − | 0.861805i | \(-0.330666\pi\) |
−0.662879 | + | 0.748726i | \(0.730666\pi\) | |||||||
\(432\) | −2.35558 | −0.113333 | ||||||||
\(433\) | −20.3802 | − | 14.8071i | −0.979410 | − | 0.711583i | −0.0218335 | − | 0.999762i | \(-0.506950\pi\) |
−0.957577 | + | 0.288178i | \(0.906950\pi\) | |||||||
\(434\) | −1.91519 | + | 5.89435i | −0.0919321 | + | 0.282938i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.23746 | + | 6.88620i | 0.107155 | + | 0.329789i | ||||
\(437\) | 0.932161 | − | 2.86890i | 0.0445913 | − | 0.137238i | ||||
\(438\) | 1.99822 | − | 6.14987i | 0.0954784 | − | 0.293852i | ||||
\(439\) | −0.529997 | − | 1.63116i | −0.0252954 | − | 0.0778511i | 0.937612 | − | 0.347684i | \(-0.113032\pi\) |
−0.962907 | + | 0.269833i | \(0.913032\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.117039 | + | 0.360209i | −0.00557329 | + | 0.0171528i | ||||
\(442\) | −0.440387 | − | 0.319960i | −0.0209471 | − | 0.0152189i | ||||
\(443\) | −11.7475 | −0.558140 | −0.279070 | − | 0.960271i | \(-0.590026\pi\) | ||||
−0.279070 | + | 0.960271i | \(0.590026\pi\) | |||||||
\(444\) | 2.64471 | + | 1.92149i | 0.125512 | + | 0.0911899i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.9678 | + | 8.69510i | −0.566691 | + | 0.411725i | ||||
\(447\) | 6.99493 | − | 5.08212i | 0.330849 | − | 0.240376i | ||||
\(448\) | 1.50740 | + | 4.63929i | 0.0712178 | + | 0.219186i | ||||
\(449\) | 12.8415 | 0.606030 | 0.303015 | − | 0.952986i | \(-0.402007\pi\) | ||||
0.303015 | + | 0.952986i | \(0.402007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.5890 | 1.25203 | ||||||||
\(452\) | −9.71837 | − | 29.9101i | −0.457114 | − | 1.40685i | ||||
\(453\) | −1.01045 | + | 0.734135i | −0.0474751 | + | 0.0344927i | ||||
\(454\) | 1.72858 | − | 1.25589i | 0.0811263 | − | 0.0589417i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.0400 | − | 9.47412i | −0.610654 | − | 0.443666i | ||||
\(457\) | 13.6882 | 0.640309 | 0.320155 | − | 0.947365i | \(-0.396265\pi\) | ||||
0.320155 | + | 0.947365i | \(0.396265\pi\) | |||||||
\(458\) | 5.19577 | + | 3.77495i | 0.242783 | + | 0.176392i | ||||
\(459\) | 0.212560 | − | 0.654193i | 0.00992146 | − | 0.0305351i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00160 | + | 9.23799i | 0.139799 | + | 0.430256i | 0.996306 | − | 0.0858796i | \(-0.0273700\pi\) |
−0.856507 | + | 0.516136i | \(0.827370\pi\) | |||||||
\(462\) | 2.19450 | − | 6.75396i | 0.102097 | − | 0.314223i | ||||
\(463\) | −6.57403 | + | 20.2328i | −0.305521 | + | 0.940297i | 0.673961 | + | 0.738767i | \(0.264592\pi\) |
−0.979482 | + | 0.201531i | \(0.935408\pi\) | |||||||
\(464\) | 0.0259664 | + | 0.0799163i | 0.00120546 | + | 0.00371002i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.50143 | − | 10.7763i | 0.162201 | − | 0.499202i | ||||
\(467\) | −11.2465 | − | 8.17106i | −0.520426 | − | 0.378112i | 0.296338 | − | 0.955083i | \(-0.404234\pi\) |
−0.816764 | + | 0.576971i | \(0.804234\pi\) | |||||||
\(468\) | −2.52524 | −0.116729 | ||||||||
\(469\) | −0.173696 | − | 0.126198i | −0.00802054 | − | 0.00582727i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.12745 | + | 2.27223i | −0.144105 | + | 0.104699i | ||||
\(472\) | 0.283902 | − | 0.206267i | 0.0130676 | − | 0.00949419i | ||||
\(473\) | −18.2006 | − | 56.0156i | −0.836862 | − | 2.57560i | ||||
\(474\) | 2.65959 | 0.122159 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.03042 | −0.138899 | ||||||||
\(477\) | 2.81922 | + | 8.67665i | 0.129083 | + | 0.397277i | ||||
\(478\) | 11.3749 | − | 8.26438i | 0.520278 | − | 0.378004i | ||||
\(479\) | 10.0057 | − | 7.26958i | 0.457173 | − | 0.332155i | −0.335249 | − | 0.942130i | \(-0.608820\pi\) |
0.792421 | + | 0.609974i | \(0.208820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.27831 | + | 1.65529i | 0.103882 | + | 0.0754747i | ||||
\(482\) | 4.38601 | 0.199777 | ||||||||
\(483\) | 0.775971 | + | 0.563776i | 0.0353079 | + | 0.0256527i | ||||
\(484\) | −8.17817 | + | 25.1698i | −0.371735 | + | 1.14408i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.165802 | + | 0.510286i | 0.00752094 | + | 0.0231471i | ||||
\(487\) | −10.9170 | + | 33.5990i | −0.494695 | + | 1.52251i | 0.322737 | + | 0.946489i | \(0.395397\pi\) |
−0.817432 | + | 0.576026i | \(0.804603\pi\) | |||||||
\(488\) | −3.94614 | + | 12.1450i | −0.178634 | + | 0.549778i | ||||
\(489\) | −2.15512 | − | 6.63277i | −0.0974578 | − | 0.299944i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.70374 | + | 20.6320i | −0.302536 | + | 0.931109i | 0.678050 | + | 0.735016i | \(0.262825\pi\) |
−0.980585 | + | 0.196093i | \(0.937175\pi\) | |||||||
\(492\) | 7.16009 | + | 5.20211i | 0.322802 | + | 0.234529i | ||||
\(493\) | −0.0245375 | −0.00110511 | ||||||||
\(494\) | −5.18114 | − | 3.76432i | −0.233111 | − | 0.169365i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.55475 | − | 6.21539i | 0.384120 | − | 0.279079i | ||||
\(497\) | 25.3095 | − | 18.3884i | 1.13529 | − | 0.824834i | ||||
\(498\) | −1.55244 | − | 4.77793i | −0.0695666 | − | 0.214104i | ||||
\(499\) | 38.7869 | 1.73634 | 0.868171 | − | 0.496265i | \(-0.165296\pi\) | ||||
0.868171 | + | 0.496265i | \(0.165296\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.9594 | −0.713013 | ||||||||
\(502\) | −4.11430 | − | 12.6625i | −0.183630 | − | 0.565155i | ||||
\(503\) | −5.19360 | + | 3.77337i | −0.231571 | + | 0.168246i | −0.697520 | − | 0.716565i | \(-0.745713\pi\) |
0.465949 | + | 0.884812i | \(0.345713\pi\) | |||||||
\(504\) | 4.14627 | − | 3.01244i | 0.184689 | − | 0.134185i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.832257 | + | 0.604670i | 0.0369983 | + | 0.0268809i | ||||
\(507\) | 10.8246 | 0.480737 | ||||||||
\(508\) | −0.478564 | − | 0.347697i | −0.0212328 | − | 0.0154266i | ||||
\(509\) | −2.22343 | + | 6.84300i | −0.0985516 | + | 0.303311i | −0.988163 | − | 0.153408i | \(-0.950975\pi\) |
0.889611 | + | 0.456718i | \(0.150975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.58307 | − | 29.4937i | −0.423930 | − | 1.30472i | ||||
\(512\) | −6.71922 | + | 20.6796i | −0.296950 | + | 0.913919i | ||||
\(513\) | 2.50077 | − | 7.69657i | 0.110412 | − | 0.339812i | ||||
\(514\) | 4.02891 | + | 12.3997i | 0.177708 | + | 0.546928i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.05820 | − | 18.6452i | 0.266697 | − | 0.820810i | ||||
\(517\) | −35.4593 | − | 25.7627i | −1.55950 | − | 1.13304i | ||||
\(518\) | −2.63611 | −0.115824 | ||||||||
\(519\) | 6.20783 | + | 4.51025i | 0.272493 | + | 0.197978i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.51120 | − | 6.18375i | 0.372882 | − | 0.270915i | −0.385523 | − | 0.922698i | \(-0.625979\pi\) |
0.758405 | + | 0.651783i | \(0.225979\pi\) | |||||||
\(522\) | 0.0154845 | − | 0.0112501i | 0.000677737 | − | 0.000492404i | ||||
\(523\) | −3.49938 | − | 10.7700i | −0.153017 | − | 0.470938i | 0.844938 | − | 0.534865i | \(-0.179638\pi\) |
−0.997955 | + | 0.0639269i | \(0.979638\pi\) | |||||||
\(524\) | 7.81840 | 0.341548 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.57282 | 0.199385 | ||||||||
\(527\) | 0.954188 | + | 2.93669i | 0.0415651 | + | 0.127924i | ||||
\(528\) | −9.80235 | + | 7.12183i | −0.426593 | + | 0.309938i | ||||
\(529\) | 18.4950 | − | 13.4374i | 0.804130 | − | 0.584234i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.142541 | + | 0.103562i | 0.00618573 | + | 0.00449420i | ||||
\(532\) | −35.6529 | −1.54575 | ||||||||
\(533\) | 6.16814 | + | 4.48142i | 0.267172 | + | 0.194112i | ||||
\(534\) | −0.00204251 | + | 0.00628621i | −8.83882e−5 | + | 0.000272031i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.0513540 | − | 0.158051i | −0.00221815 | − | 0.00682678i | ||||
\(537\) | −3.27846 | + | 10.0901i | −0.141476 | + | 0.435418i | ||||
\(538\) | −0.428287 | + | 1.31813i | −0.0184648 | + | 0.0568287i | ||||
\(539\) | 0.602013 | + | 1.85281i | 0.0259305 | + | 0.0798060i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.22898 | − | 16.0931i | 0.224811 | − | 0.691898i | −0.773499 | − | 0.633797i | \(-0.781495\pi\) |
0.998311 | − | 0.0581012i | \(-0.0185046\pi\) | |||||||
\(542\) | −5.89879 | − | 4.28572i | −0.253375 | − | 0.184087i | ||||
\(543\) | −15.1076 | −0.648331 | ||||||||
\(544\) | −2.92009 | − | 2.12157i | −0.125198 | − | 0.0909614i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.64742 | − | 1.19692i | 0.0705032 | − | 0.0512235i | ||||
\(547\) | −35.7073 | + | 25.9429i | −1.52674 | + | 1.10924i | −0.568717 | + | 0.822533i | \(0.692560\pi\) |
−0.958019 | + | 0.286705i | \(0.907440\pi\) | |||||||
\(548\) | −2.54883 | − | 7.84448i | −0.108881 | − | 0.335100i | ||||
\(549\) | −6.41152 | −0.273637 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.288683 | −0.0122983 | ||||||||
\(552\) | 0.229419 | + | 0.706079i | 0.00976472 | + | 0.0300527i | ||||
\(553\) | 10.3189 | − | 7.49715i | 0.438806 | − | 0.318811i | ||||
\(554\) | −3.96734 | + | 2.88244i | −0.168556 | + | 0.122463i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.18143 | − | 3.76453i | −0.219741 | − | 0.159652i | ||||
\(557\) | −17.8472 | −0.756210 | −0.378105 | − | 0.925763i | \(-0.623424\pi\) | ||||
−0.378105 | + | 0.925763i | \(0.623424\pi\) | |||||||
\(558\) | −1.94857 | − | 1.41572i | −0.0824897 | − | 0.0599323i | ||||
\(559\) | 5.21891 | − | 16.0621i | 0.220736 | − | 0.679356i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.09334 | − | 3.36497i | −0.0461610 | − | 0.142069i | ||||
\(562\) | −1.72602 | + | 5.31213i | −0.0728076 | + | 0.224079i | ||||
\(563\) | 6.61490 | − | 20.3586i | 0.278785 | − | 0.858012i | −0.709408 | − | 0.704798i | \(-0.751038\pi\) |
0.988193 | − | 0.153214i | \(-0.0489623\pi\) | |||||||
\(564\) | −4.50831 | − | 13.8751i | −0.189834 | − | 0.584249i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.798480 | − | 2.45747i | 0.0335626 | − | 0.103295i | ||||
\(567\) | 2.08175 | + | 1.51248i | 0.0874251 | + | 0.0635181i | ||||
\(568\) | 24.2151 | 1.01604 | ||||||||
\(569\) | 21.0929 | + | 15.3249i | 0.884262 | + | 0.642454i | 0.934376 | − | 0.356289i | \(-0.115958\pi\) |
−0.0501135 | + | 0.998744i | \(0.515958\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.71705 | − | 5.60676i | 0.322948 | − | 0.234636i | −0.414484 | − | 0.910057i | \(-0.636038\pi\) |
0.737433 | + | 0.675421i | \(0.236038\pi\) | |||||||
\(572\) | −10.5084 | + | 7.63478i | −0.439377 | + | 0.319226i | ||||
\(573\) | −3.78359 | − | 11.6447i | −0.158062 | − | 0.486464i | ||||
\(574\) | −7.13683 | −0.297885 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.89572 | −0.0789885 | ||||||||
\(577\) | −2.81361 | − | 8.65941i | −0.117132 | − | 0.360496i | 0.875254 | − | 0.483664i | \(-0.160694\pi\) |
−0.992386 | + | 0.123169i | \(0.960694\pi\) | |||||||
\(578\) | −7.17390 | + | 5.21214i | −0.298395 | + | 0.216797i | ||||
\(579\) | −11.5221 | + | 8.37130i | −0.478843 | + | 0.347900i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.4919 | − | 14.1617i | −0.808658 | − | 0.587525i | ||||
\(582\) | 4.08871 | 0.169482 | ||||||||
\(583\) | 37.9646 | + | 27.5829i | 1.57233 | + | 1.14237i | ||||
\(584\) | 7.41761 | − | 22.8291i | 0.306943 | − | 0.944673i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.05396 | + | 12.4768i | 0.167468 | + | 0.515412i | ||||
\(587\) | 9.10008 | − | 28.0072i | 0.375600 | − | 1.15598i | −0.567472 | − | 0.823393i | \(-0.692079\pi\) |
0.943073 | − | 0.332587i | \(-0.107921\pi\) | |||||||
\(588\) | −0.200385 | + | 0.616721i | −0.00826373 | + | 0.0254331i | ||||
\(589\) | 11.2260 | + | 34.5501i | 0.462559 | + | 1.42361i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.48469 | + | 16.8802i | −0.225610 | + | 0.694357i | ||||
\(592\) | 3.63866 | + | 2.64364i | 0.149548 | + | 0.108653i | ||||
\(593\) | 33.7757 | 1.38700 | 0.693501 | − | 0.720456i | \(-0.256067\pi\) | ||||
0.693501 | + | 0.720456i | \(0.256067\pi\) | |||||||
\(594\) | 2.23275 | + | 1.62219i | 0.0916108 | + | 0.0665592i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.9761 | − | 8.70118i | 0.490562 | − | 0.356414i | ||||
\(597\) | −15.3349 | + | 11.1415i | −0.627617 | + | 0.455991i | ||||
\(598\) | 0.0911543 | + | 0.280544i | 0.00372758 | + | 0.0114723i | ||||
\(599\) | −12.0575 | −0.492656 | −0.246328 | − | 0.969187i | \(-0.579224\pi\) | ||||
−0.246328 | + | 0.969187i | \(0.579224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0653240 | 0.00266462 | 0.00133231 | − | 0.999999i | \(-0.499576\pi\) | ||||
0.00133231 | + | 0.999999i | \(0.499576\pi\) | |||||||
\(602\) | 4.88526 | + | 15.0353i | 0.199108 | + | 0.612793i | ||||
\(603\) | 0.0675025 | − | 0.0490435i | 0.00274892 | − | 0.00199720i | ||||
\(604\) | −1.73001 | + | 1.25692i | −0.0703930 | + | 0.0511435i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.59205 | − | 2.60978i | −0.145917 | − | 0.106015i | ||||
\(607\) | 25.9556 | 1.05350 | 0.526752 | − | 0.850019i | \(-0.323410\pi\) | ||||
0.526752 | + | 0.850019i | \(0.323410\pi\) | |||||||
\(608\) | −34.3548 | − | 24.9602i | −1.39327 | − | 1.01227i | ||||
\(609\) | 0.0283650 | − | 0.0872986i | 0.00114941 | − | 0.00353752i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.88373 | − | 11.9529i | −0.157119 | − | 0.483563i | ||||
\(612\) | 0.363928 | − | 1.12006i | 0.0147109 | − | 0.0452756i | ||||
\(613\) | −3.88472 | + | 11.9559i | −0.156902 | + | 0.482896i | −0.998349 | − | 0.0574448i | \(-0.981705\pi\) |
0.841446 | + | 0.540341i | \(0.181705\pi\) | |||||||
\(614\) | −1.57786 | − | 4.85617i | −0.0636774 | − | 0.195979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.14623 | − | 25.0715i | 0.328221 | − | 1.01016i | ||||
\(617\) | −1.50253 | − | 1.09165i | −0.0604896 | − | 0.0439483i | 0.557130 | − | 0.830426i | \(-0.311903\pi\) |
−0.617619 | + | 0.786477i | \(0.711903\pi\) | |||||||
\(618\) | −5.57259 | −0.224162 | ||||||||
\(619\) | 14.5814 | + | 10.5940i | 0.586077 | + | 0.425810i | 0.840910 | − | 0.541175i | \(-0.182020\pi\) |
−0.254833 | + | 0.966985i | \(0.582020\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.301561 | + | 0.219097i | −0.0121012 | + | 0.00879206i | ||||
\(622\) | 10.8438 | − | 7.87848i | 0.434797 | − | 0.315898i | ||||
\(623\) | 0.00979552 | + | 0.0301475i | 0.000392449 | + | 0.00120783i | ||||
\(624\) | −3.47430 | −0.139083 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5.30195 | 0.211908 | ||||||||
\(627\) | −12.8632 | − | 39.5888i | −0.513705 | − | 1.58102i | ||||
\(628\) | −5.35456 | + | 3.89032i | −0.213670 | + | 0.155241i | ||||
\(629\) | −1.06254 | + | 0.771977i | −0.0423661 | + | 0.0307807i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3636 | − | 12.6154i | −0.691233 | − | 0.502210i | 0.185832 | − | 0.982582i | \(-0.440502\pi\) |
−0.877065 | + | 0.480371i | \(0.840502\pi\) | |||||||
\(632\) | 9.87272 | 0.392716 | ||||||||
\(633\) | −8.71864 | − | 6.33446i | −0.346535 | − | 0.251772i | ||||
\(634\) | 4.10046 | − | 12.6199i | 0.162850 | − | 0.501201i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.82683 | + | 14.8555i | 0.191396 | + | 0.589057i | ||||
\(637\) | −0.172624 | + | 0.531281i | −0.00683960 | + | 0.0210501i | ||||
\(638\) | 0.0304225 | − | 0.0936310i | 0.00120444 | − | 0.00370689i | ||||
\(639\) | 3.75698 | + | 11.5628i | 0.148624 | + | 0.457417i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.2648 | − | 37.7471i | 0.484430 | − | 1.49092i | −0.348374 | − | 0.937355i | \(-0.613266\pi\) |
0.832805 | − | 0.553567i | \(-0.186734\pi\) | |||||||
\(642\) | −5.32773 | − | 3.87082i | −0.210269 | − | 0.152769i | ||||
\(643\) | 1.26211 | 0.0497729 | 0.0248864 | − | 0.999690i | \(-0.492078\pi\) | ||||
0.0248864 | + | 0.999690i | \(0.492078\pi\) | |||||||
\(644\) | 1.32855 | + | 0.965250i | 0.0523523 | + | 0.0380362i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.41633 | − | 1.75557i | 0.0950692 | − | 0.0690718i | ||||
\(647\) | 23.4029 | − | 17.0032i | 0.920064 | − | 0.668466i | −0.0234758 | − | 0.999724i | \(-0.507473\pi\) |
0.943540 | + | 0.331259i | \(0.107473\pi\) | |||||||
\(648\) | 0.615477 | + | 1.89424i | 0.0241782 | + | 0.0744129i | ||||
\(649\) | 0.906266 | 0.0355740 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.5511 | −0.452722 | ||||||||
\(652\) | −3.68982 | − | 11.3561i | −0.144504 | − | 0.444739i | ||||
\(653\) | −14.1413 | + | 10.2743i | −0.553393 | + | 0.402063i | −0.829035 | − | 0.559197i | \(-0.811110\pi\) |
0.275642 | + | 0.961260i | \(0.411110\pi\) | |||||||
\(654\) | 1.83571 | − | 1.33372i | 0.0717821 | − | 0.0521527i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.85106 | + | 7.15721i | 0.384619 | + | 0.279442i | ||||
\(657\) | 12.0518 | 0.470186 | ||||||||
\(658\) | 9.51772 | + | 6.91503i | 0.371039 | + | 0.269576i | ||||
\(659\) | 3.50406 | − | 10.7844i | 0.136499 | − | 0.420100i | −0.859321 | − | 0.511436i | \(-0.829114\pi\) |
0.995820 | + | 0.0913359i | \(0.0291137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.43350 | + | 4.41185i | 0.0557565 | + | 0.171601i | 0.975057 | − | 0.221956i | \(-0.0712443\pi\) |
−0.919300 | + | 0.393557i | \(0.871244\pi\) | |||||||
\(662\) | −0.178779 | + | 0.550225i | −0.00694844 | + | 0.0213851i | ||||
\(663\) | 0.313510 | − | 0.964885i | 0.0121757 | − | 0.0374730i | ||||
\(664\) | −5.76285 | − | 17.7362i | −0.223642 | − | 0.688299i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.316575 | − | 0.974317i | 0.0122670 | − | 0.0377540i | ||||
\(667\) | 0.0107574 | + | 0.00781569i | 0.000416527 | + | 0.000302625i | ||||
\(668\) | −27.3243 | −1.05721 | ||||||||
\(669\) | −22.3052 | − | 16.2057i | −0.862369 | − | 0.626547i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.6805 | + | 19.3845i | −1.02999 | + | 0.748330i | ||||
\(672\) | 10.9236 | − | 7.93647i | 0.421387 | − | 0.306156i | ||||
\(673\) | 2.32741 | + | 7.16302i | 0.0897149 | + | 0.276114i | 0.985840 | − | 0.167687i | \(-0.0536298\pi\) |
−0.896125 | + | 0.443801i | \(0.853630\pi\) | |||||||
\(674\) | −7.54435 | −0.290598 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5330 | 0.712807 | ||||||||
\(677\) | 9.77055 | + | 30.0707i | 0.375513 | + | 1.15571i | 0.943132 | + | 0.332418i | \(0.107864\pi\) |
−0.567619 | + | 0.823291i | \(0.692136\pi\) | |||||||
\(678\) | −7.97338 | + | 5.79300i | −0.306216 | + | 0.222479i | ||||
\(679\) | 15.8638 | − | 11.5257i | 0.608795 | − | 0.442316i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.22167 | + | 2.34068i | 0.123455 | + | 0.0896952i | ||||
\(682\) | −12.3889 | −0.474397 | ||||||||
\(683\) | −24.8045 | − | 18.0215i | −0.949118 | − | 0.689575i | 0.00148011 | − | 0.999999i | \(-0.499529\pi\) |
−0.950598 | + | 0.310424i | \(0.899529\pi\) | |||||||
\(684\) | 4.28161 | − | 13.1774i | 0.163711 | − | 0.503852i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.14806 | − | 9.68873i | −0.120193 | − | 0.369917i | ||||
\(687\) | −3.69886 | + | 11.3839i | −0.141120 | + | 0.434323i | ||||
\(688\) | 8.33505 | − | 25.6526i | 0.317771 | − | 0.977998i | ||||
\(689\) | 4.15813 | + | 12.7974i | 0.158412 | + | 0.487542i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.7334 | + | 33.0341i | −0.408318 | + | 1.25667i | 0.509774 | + | 0.860308i | \(0.329729\pi\) |
−0.918092 | + | 0.396366i | \(0.870271\pi\) | |||||||
\(692\) | 10.6285 | + | 7.72208i | 0.404036 | + | 0.293550i | ||||
\(693\) | 13.2356 | 0.502780 | ||||||||
\(694\) | 2.47243 | + | 1.79632i | 0.0938520 | + | 0.0681875i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.0574802 | − | 0.0417618i | 0.00217878 | − | 0.00158298i | ||||
\(697\) | −2.87663 | + | 2.09000i | −0.108960 | + | 0.0791643i | ||||
\(698\) | 4.72453 | + | 14.5406i | 0.178826 | + | 0.550370i | ||||
\(699\) | 21.1181 | 0.798761 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5437 | −0.738154 | −0.369077 | − | 0.929399i | \(-0.620326\pi\) | ||||
−0.369077 | + | 0.929399i | \(0.620326\pi\) | |||||||
\(702\) | 0.244545 | + | 0.752633i | 0.00922977 | + | 0.0284063i | ||||
\(703\) | −12.5007 | + | 9.08230i | −0.471473 | + | 0.342545i | ||||
\(704\) | −7.88873 | + | 5.73150i | −0.297318 | + | 0.216014i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.54122 | + | 4.02593i | 0.208547 | + | 0.151518i | ||||
\(707\) | −21.2935 | −0.800825 | ||||||||
\(708\) | 0.244046 | + | 0.177310i | 0.00917182 | + | 0.00666372i | ||||
\(709\) | −7.82140 | + | 24.0718i | −0.293739 | + | 0.904035i | 0.689904 | + | 0.723901i | \(0.257653\pi\) |
−0.983642 | + | 0.180133i | \(0.942347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.53176 | + | 4.71426i | 0.0574453 | + | 0.176799i | ||||
\(712\) | −0.00758205 | + | 0.0233351i | −0.000284149 | + | 0.000874522i | ||||
\(713\) | 0.517073 | − | 1.59139i | 0.0193645 | − | 0.0595979i | ||||
\(714\) | 0.293467 | + | 0.903200i | 0.0109827 | + | 0.0338014i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.61311 | + | 17.2754i | −0.209772 | + | 0.645611i | ||||
\(717\) | 21.2003 | + | 15.4029i | 0.791738 | + | 0.575232i | ||||
\(718\) | 2.42423 | 0.0904715 | ||||||||
\(719\) | 7.43539 | + | 5.40213i | 0.277293 | + | 0.201465i | 0.717736 | − | 0.696315i | \(-0.245178\pi\) |
−0.440443 | + | 0.897781i | \(0.645178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.6211 | + | 15.7086i | −0.805210 | + | 0.585019i | ||||
\(722\) | 20.1806 | − | 14.6621i | 0.751045 | − | 0.545666i | ||||
\(723\) | 2.52607 | + | 7.77443i | 0.0939454 | + | 0.289134i | ||||
\(724\) | −25.8661 | −0.961305 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.29369 | 0.307808 | ||||||||
\(727\) | −4.03726 | − | 12.4254i | −0.149734 | − | 0.460833i | 0.847856 | − | 0.530227i | \(-0.177893\pi\) |
−0.997589 | + | 0.0693942i | \(0.977893\pi\) | |||||||
\(728\) | 6.11542 | − | 4.44312i | 0.226653 | − | 0.164673i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.37213 | + | 4.62963i | 0.235682 | + | 0.171233i | ||||
\(732\) | −10.9773 | −0.405732 | ||||||||
\(733\) | 7.83202 | + | 5.69030i | 0.289282 | + | 0.210176i | 0.722956 | − | 0.690894i | \(-0.242783\pi\) |
−0.433674 | + | 0.901070i | \(0.642783\pi\) | |||||||
\(734\) | −0.503121 | + | 1.54845i | −0.0185705 | + | 0.0571542i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.604419 | + | 1.86021i | 0.0222792 | + | 0.0685683i | ||||
\(737\) | 0.132623 | − | 0.408172i | 0.00488524 | − | 0.0150352i | ||||
\(738\) | 0.857072 | − | 2.63780i | 0.0315493 | − | 0.0970986i | ||||
\(739\) | 2.82260 | + | 8.68707i | 0.103831 | + | 0.319559i | 0.989454 | − | 0.144845i | \(-0.0462684\pi\) |
−0.885623 | + | 0.464404i | \(0.846268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.68844 | − | 11.3518i | 0.135498 | − | 0.417021i | ||||
\(742\) | −10.1902 | − | 7.40359i | −0.374093 | − | 0.271794i | ||||
\(743\) | −6.35760 | −0.233238 | −0.116619 | − | 0.993177i | \(-0.537206\pi\) | ||||
−0.116619 | + | 0.993177i | \(0.537206\pi\) | |||||||
\(744\) | −7.23334 | − | 5.25533i | −0.265187 | − | 0.192670i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.66994 | − | 4.84600i | 0.244204 | − | 0.177425i | ||||
\(747\) | 7.57501 | − | 5.50356i | 0.277155 | − | 0.201365i | ||||
\(748\) | −1.87193 | − | 5.76122i | −0.0684446 | − | 0.210651i | ||||
\(749\) | −31.5825 | −1.15400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0142 | 1.27768 | 0.638842 | − | 0.769338i | \(-0.279414\pi\) | ||||
0.638842 | + | 0.769338i | \(0.279414\pi\) | |||||||
\(752\) | −6.20266 | − | 19.0898i | −0.226188 | − | 0.696134i | ||||
\(753\) | 20.0754 | − | 14.5856i | 0.731586 | − | 0.531529i | ||||
\(754\) | 0.0228384 | − | 0.0165931i | 0.000831725 | − | 0.000604284i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.56419 | + | 2.58954i | 0.129628 | + | 0.0941806i | ||||
\(757\) | 11.5175 | 0.418609 | 0.209305 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209305 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(758\) | 4.49689 | + | 3.26718i | 0.163334 | + | 0.118669i | ||||
\(759\) | −0.592481 | + | 1.82347i | −0.0215057 | + | 0.0661878i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.6925 | + | 39.0635i | 0.460102 | + | 1.41605i | 0.865039 | + | 0.501705i | \(0.167294\pi\) |
−0.404936 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(762\) | −0.0572847 | + | 0.176304i | −0.00207521 | + | 0.00638683i | ||||
\(763\) | 3.36273 | − | 10.3494i | 0.121739 | − | 0.374674i | ||||
\(764\) | −6.47795 | − | 19.9371i | −0.234364 | − | 0.721298i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.56771 | − | 7.90259i | 0.0927750 | − | 0.285532i | ||||
\(767\) | 0.210236 | + | 0.152746i | 0.00759120 | + | 0.00551533i | ||||
\(768\) | 2.38518 | 0.0860677 | ||||||||
\(769\) | −14.5193 | − | 10.5489i | −0.523578 | − | 0.380402i | 0.294372 | − | 0.955691i | \(-0.404889\pi\) |
−0.817950 | + | 0.575289i | \(0.804889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.6587 | + | 14.2829i | −0.707992 | + | 0.514386i | ||||
\(772\) | −19.7272 | + | 14.3327i | −0.709998 | + | 0.515844i | ||||
\(773\) | 16.0762 | + | 49.4776i | 0.578222 | + | 1.77958i | 0.624935 | + | 0.780676i | \(0.285125\pi\) |
−0.0467133 | + | 0.998908i | \(0.514875\pi\) | |||||||
\(774\) | −6.14378 | −0.220833 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.1778 | 0.544850 | ||||||||
\(777\) | −1.51823 | − | 4.67264i | −0.0544663 | − | 0.167630i | ||||
\(778\) | −9.28701 | + | 6.74741i | −0.332955 | + | 0.241906i | ||||
\(779\) | −33.8435 | + | 24.5888i | −1.21257 | + | 0.880984i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.5928 | + | 36.7578i | 1.81035 | + | 1.31530i | ||||
\(782\) | −0.137570 | −0.00491951 | ||||||||
\(783\) | 0.0288595 | + | 0.0209676i | 0.00103135 | + | 0.000749322i | ||||
\(784\) | −0.275695 | + | 0.848502i | −0.00984626 | + | 0.0303037i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.757137 | − | 2.33023i | −0.0270062 | − | 0.0831165i | ||||
\(787\) | −3.87021 | + | 11.9113i | −0.137958 | + | 0.424592i | −0.996038 | − | 0.0889240i | \(-0.971657\pi\) |
0.858080 | + | 0.513516i | \(0.171657\pi\) | |||||||
\(788\) | −9.39044 | + | 28.9008i | −0.334521 | + | 1.02955i | ||||
\(789\) | 2.63366 | + | 8.10556i | 0.0937607 | + | 0.288566i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.6060 | + | 44.9525i | −0.519328 | + | 1.59833i | ||||
\(792\) | 8.28823 | + | 6.02175i | 0.294509 | + | 0.213974i | ||||
\(793\) | −9.45650 | −0.335810 | ||||||||
\(794\) | 5.42665 | + | 3.94269i | 0.192585 | + | 0.139921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.2552 | + | 19.0755i | −0.930591 | + | 0.676114i | ||||
\(797\) | −20.3400 | + | 14.7779i | −0.720481 | + | 0.523460i | −0.886538 | − | 0.462656i | \(-0.846896\pi\) |
0.166057 | + | 0.986116i | \(0.446896\pi\) | |||||||
\(798\) | 3.45264 | + | 10.6261i | 0.122222 | + | 0.376161i | ||||
\(799\) | 5.86134 | 0.207359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0123190 | −0.000435270 | ||||||||
\(802\) | 5.47939 | + | 16.8638i | 0.193484 | + | 0.595483i | ||||
\(803\) | 50.1516 | − | 36.4372i | 1.76981 | − | 1.28584i | ||||
\(804\) | 0.115572 | − | 0.0839682i | 0.00407592 | − | 0.00296133i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.87400 | − | 2.08808i | −0.101232 | − | 0.0735495i | ||||
\(807\) | −2.58312 | −0.0909302 | ||||||||
\(808\) | −13.3341 | − | 9.68781i | −0.469093 | − | 0.340816i | ||||
\(809\) | −1.49157 | + | 4.59059i | −0.0524409 | + | 0.161396i | −0.973847 | − | 0.227204i | \(-0.927041\pi\) |
0.921406 | + | 0.388601i | \(0.127041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.3898 | − | 35.0543i | −0.399952 | − | 1.23092i | −0.925038 | − | 0.379875i | \(-0.875967\pi\) |
0.525086 | − | 0.851049i | \(-0.324033\pi\) | |||||||
\(812\) | 0.0485643 | − | 0.149465i | 0.00170427 | − | 0.00524521i | ||||
\(813\) | 4.19933 | − | 12.9242i | 0.147277 | − | 0.453271i | ||||
\(814\) | −1.62836 | − | 5.01158i | −0.0570740 | − | 0.175656i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.500703 | − | 1.54100i | 0.0175281 | − | 0.0539460i | ||||
\(817\) | 74.9680 | + | 54.4675i | 2.62280 | + | 1.90558i | ||||
\(818\) | −1.61897 | −0.0566061 | ||||||||
\(819\) | 3.07042 | + | 2.23079i | 0.107289 | + | 0.0779500i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.4772 | + | 8.33868i | −0.400557 | + | 0.291022i | −0.769768 | − | 0.638324i | \(-0.779628\pi\) |
0.369211 | + | 0.929346i | \(0.379628\pi\) | |||||||
\(822\) | −2.09117 | + | 1.51933i | −0.0729380 | + | 0.0529926i | ||||
\(823\) | 8.03241 | + | 24.7212i | 0.279992 | + | 0.861728i | 0.987855 | + | 0.155378i | \(0.0496595\pi\) |
−0.707863 | + | 0.706350i | \(0.750340\pi\) | |||||||
\(824\) | −20.6861 | −0.720634 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.243253 | −0.00846386 | ||||||||
\(827\) | 13.2673 | + | 40.8326i | 0.461350 | + | 1.41989i | 0.863516 | + | 0.504322i | \(0.168257\pi\) |
−0.402166 | + | 0.915567i | \(0.631743\pi\) | |||||||
\(828\) | −0.516308 | + | 0.375120i | −0.0179429 | + | 0.0130363i | ||||
\(829\) | 4.56100 | − | 3.31376i | 0.158410 | − | 0.115092i | −0.505756 | − | 0.862676i | \(-0.668787\pi\) |
0.664167 | + | 0.747585i | \(0.268787\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.39421 | − | 5.37221i | −0.256502 | − | 0.186360i | ||||
\(832\) | −2.79605 | −0.0969355 | ||||||||
\(833\) | −0.210769 | − | 0.153132i | −0.00730270 | − | 0.00530572i | ||||
\(834\) | −0.620224 | + | 1.90885i | −0.0214766 | + | 0.0660981i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −22.0233 | − | 67.7806i | −0.761690 | − | 2.34424i | ||||
\(837\) | 1.38718 | − | 4.26931i | 0.0479481 | − | 0.147569i | ||||
\(838\) | −1.17947 | + | 3.63003i | −0.0407441 | + | 0.125397i | ||||
\(839\) | −7.12687 | − | 21.9343i | −0.246047 | − | 0.757255i | −0.995463 | − | 0.0951546i | \(-0.969665\pi\) |
0.749416 | − | 0.662100i | \(-0.230335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96110 | + | 27.5794i | −0.309003 | + | 0.951015i | ||||
\(842\) | −9.48755 | − | 6.89311i | −0.326963 | − | 0.237552i | ||||
\(843\) | −10.4101 | −0.358543 | ||||||||
\(844\) | −14.9273 | − | 10.8453i | −0.513820 | − | 0.373312i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.69882 | + | 2.68735i | −0.127168 | + | 0.0923929i | ||||
\(847\) | 32.1787 | − | 23.3792i | 1.10567 | − | 0.803317i | ||||
\(848\) | 6.64089 | + | 20.4386i | 0.228049 | + | 0.701863i | ||||
\(849\) | 4.81586 | 0.165280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.711711 | 0.0243971 | ||||||||
\(852\) | 6.43238 | + | 19.7968i | 0.220370 | + | 0.678229i | ||||
\(853\) | −31.5886 | + | 22.9504i | −1.08157 | + | 0.785808i | −0.977956 | − | 0.208809i | \(-0.933041\pi\) |
−0.103616 | + | 0.994617i | \(0.533041\pi\) | |||||||
\(854\) | 7.16138 | − | 5.20305i | 0.245057 | − | 0.178045i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.7772 | − | 14.3690i | −0.675970 | − | 0.491121i | ||||
\(857\) | 12.7315 | 0.434899 | 0.217450 | − | 0.976072i | \(-0.430226\pi\) | ||||
0.217450 | + | 0.976072i | \(0.430226\pi\) | |||||||
\(858\) | 3.29313 | + | 2.39260i | 0.112426 | + | 0.0816821i | ||||
\(859\) | 4.50752 | − | 13.8727i | 0.153795 | − | 0.473331i | −0.844242 | − | 0.535962i | \(-0.819949\pi\) |
0.998037 | + | 0.0626308i | \(0.0199491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.11036 | − | 12.6504i | −0.140081 | − | 0.431124i | ||||
\(862\) | −0.662201 | + | 2.03805i | −0.0225547 | + | 0.0694161i | ||||
\(863\) | −5.41229 | + | 16.6573i | −0.184236 | + | 0.567021i | −0.999934 | − | 0.0114567i | \(-0.996353\pi\) |
0.815698 | + | 0.578478i | \(0.196353\pi\) | |||||||
\(864\) | 1.62151 | + | 4.99051i | 0.0551650 | + | 0.169781i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.17677 | + | 12.8548i | −0.141933 | + | 0.436824i | ||||
\(867\) | −13.3705 | − | 9.71424i | −0.454086 | − | 0.329913i | ||||
\(868\) | −19.7768 | −0.671267 | ||||||||
\(869\) | 20.6272 | + | 14.9865i | 0.699729 | + | 0.508383i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0995611 | − | 0.0723353i | 0.00337350 | − | 0.00245099i | ||||
\(872\) | 6.81438 | − | 4.95094i | 0.230764 | − | 0.167660i | ||||
\(873\) | 2.35484 | + | 7.24744i | 0.0796992 | + | 0.245289i | ||||
\(874\) | −1.61851 | −0.0547470 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.6341 | 0.697162 | ||||||||
\(877\) | 2.81435 | + | 8.66169i | 0.0950340 | + | 0.292485i | 0.987263 | − | 0.159100i | \(-0.0508591\pi\) |
−0.892229 | + | 0.451584i | \(0.850859\pi\) | |||||||
\(878\) | −0.744485 | + | 0.540900i | −0.0251252 | + | 0.0182545i | ||||
\(879\) | −19.7809 | + | 14.3717i | −0.667195 | + | 0.484745i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.5744 | + | 26.5728i | 1.23222 | + | 0.895261i | 0.997055 | − | 0.0766939i | \(-0.0244364\pi\) |
0.235167 | + | 0.971955i | \(0.424436\pi\) | |||||||
\(882\) | 0.203215 | 0.00684262 | ||||||||
\(883\) | 3.43206 | + | 2.49354i | 0.115498 | + | 0.0839142i | 0.644035 | − | 0.764996i | \(-0.277259\pi\) |
−0.528537 | + | 0.848910i | \(0.677259\pi\) | |||||||
\(884\) | 0.536766 | − | 1.65200i | 0.0180534 | − | 0.0555626i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.94776 | + | 5.99458i | 0.0654362 | + | 0.201392i | ||||
\(887\) | −3.95124 | + | 12.1607i | −0.132670 | + | 0.408316i | −0.995220 | − | 0.0976554i | \(-0.968866\pi\) |
0.862551 | + | 0.505971i | \(0.168866\pi\) | |||||||
\(888\) | 1.17516 | − | 3.61678i | 0.0394359 | − | 0.121371i | ||||
\(889\) | 0.274727 | + | 0.845523i | 0.00921405 | + | 0.0283579i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.58949 | + | 4.89194i | −0.0532498 | + | 0.163886i | ||||
\(892\) | −38.1891 | − | 27.7460i | −1.27867 | − | 0.929005i | ||||
\(893\) | 68.9586 | 2.30761 | ||||||||
\(894\) | −3.75311 | − | 2.72679i | −0.125523 | − | 0.0911976i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23.9647 | − | 17.4113i | 0.800603 | − | 0.581672i | ||||
\(897\) | −0.444779 | + | 0.323151i | −0.0148508 | + | 0.0107897i | ||||
\(898\) | −2.12916 | − | 6.55287i | −0.0710508 | − | 0.218672i | ||||
\(899\) | −0.160134 | −0.00534076 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.27546 | −0.209066 | ||||||||
\(902\) | −4.40851 | − | 13.5680i | −0.146787 | − | 0.451765i | ||||
\(903\) | −23.8372 | + | 17.3187i | −0.793253 | + | 0.576332i | ||||
\(904\) | −29.5981 | + | 21.5043i | −0.984419 | + | 0.715223i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.542154 | + | 0.393898i | 0.0180118 | + | 0.0130864i | ||||
\(907\) | 9.51928 | 0.316082 | 0.158041 | − | 0.987433i | \(-0.449482\pi\) | ||||
0.158041 | + | 0.987433i | \(0.449482\pi\) | |||||||
\(908\) | 5.51589 | + | 4.00753i | 0.183051 | + | 0.132994i | ||||
\(909\) | 2.55717 | − | 7.87016i | 0.0848160 | − | 0.261037i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.8107 | − | 39.4274i | −0.424438 | − | 1.30629i | −0.903531 | − | 0.428522i | \(-0.859034\pi\) |
0.479093 | − | 0.877764i | \(-0.340966\pi\) | |||||||
\(912\) | 5.89076 | − | 18.1299i | 0.195063 | − | 0.600341i | ||||
\(913\) | 14.8827 | − | 45.8043i | 0.492546 | − | 1.51590i | ||||
\(914\) | −2.26954 | − | 6.98492i | −0.0750697 | − | 0.231041i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.33287 | + | 19.4906i | −0.209244 | + | 0.643987i | ||||
\(917\) | −9.50631 | − | 6.90674i | −0.313926 | − | 0.228081i | ||||
\(918\) | −0.369069 | −0.0121811 | ||||||||
\(919\) | −12.8372 | − | 9.32675i | −0.423459 | − | 0.307661i | 0.355569 | − | 0.934650i | \(-0.384287\pi\) |
−0.779028 | + | 0.626989i | \(0.784287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.69905 | − | 5.59369i | 0.253692 | − | 0.184318i | ||||
\(922\) | 4.21635 | − | 3.06336i | 0.138858 | − | 0.100886i | ||||
\(923\) | 5.54125 | + | 17.0542i | 0.182393 | + | 0.561346i | ||||
\(924\) | 22.6610 | 0.745491 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.4145 | 0.375104 | ||||||||
\(927\) | −3.20946 | − | 9.87769i | −0.105412 | − | 0.324426i | ||||
\(928\) | 0.151435 | − | 0.110024i | 0.00497110 | − | 0.00361172i | ||||
\(929\) | 23.7938 | − | 17.2872i | 0.780650 | − | 0.567175i | −0.124524 | − | 0.992217i | \(-0.539740\pi\) |
0.905174 | + | 0.425041i | \(0.139740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.47969 | − | 1.80160i | −0.0812685 | − | 0.0590451i | ||||
\(932\) | 36.1567 | 1.18435 | ||||||||
\(933\) | 20.2103 | + | 14.6837i | 0.661657 | + | 0.480722i | ||||
\(934\) | −2.30489 | + | 7.09372i | −0.0754182 | + | 0.232114i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.907781 | + | 2.79386i | 0.0296718 | + | 0.0913203i | ||||
\(937\) | 17.9579 | − | 55.2688i | 0.586660 | − | 1.80555i | −0.00583887 | − | 0.999983i | \(-0.501859\pi\) |
0.592499 | − | 0.805571i | \(-0.298141\pi\) | |||||||
\(938\) | −0.0355978 | + | 0.109559i | −0.00116231 | + | 0.00357722i | ||||
\(939\) | 3.05359 | + | 9.39797i | 0.0996500 | + | 0.306691i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5779 | − | 32.5553i | 0.344828 | − | 1.06127i | −0.616848 | − | 0.787083i | \(-0.711591\pi\) |
0.961676 | − | 0.274189i | \(-0.0884095\pi\) | |||||||
\(942\) | 1.67802 | + | 1.21916i | 0.0546730 | + | 0.0397222i | ||||
\(943\) | 1.92684 | 0.0627464 | ||||||||
\(944\) | 0.335766 | + | 0.243948i | 0.0109282 | + | 0.00793984i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.5663 | + | 18.5750i | −0.831232 | + | 0.603925i | ||||
\(947\) | −30.7511 | + | 22.3420i | −0.999275 | + | 0.726016i | −0.961933 | − | 0.273286i | \(-0.911889\pi\) |
−0.0373427 | + | 0.999303i | \(0.511889\pi\) | |||||||
\(948\) | 2.62255 | + | 8.07137i | 0.0851764 | + | 0.262146i | ||||
\(949\) | 17.7755 | 0.577017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.7310 | 0.801958 | ||||||||
\(952\) | 1.08939 | + | 3.35278i | 0.0353072 | + | 0.108664i | ||||
\(953\) | −13.6845 | + | 9.94235i | −0.443284 | + | 0.322064i | −0.786938 | − | 0.617032i | \(-0.788335\pi\) |
0.343655 | + | 0.939096i | \(0.388335\pi\) | |||||||
\(954\) | 3.96015 | − | 2.87722i | 0.128214 | − | 0.0931533i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.2973 | + | 26.3716i | 1.17394 | + | 0.852917i | ||||
\(957\) | 0.183487 | 0.00593130 | ||||||||
\(958\) | −5.36853 | − | 3.90047i | −0.173449 | − | 0.126018i | ||||
\(959\) | −3.83069 | + | 11.7897i | −0.123699 | + | 0.380708i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.35243 | − | 10.3177i | −0.108143 | − | 0.332829i | ||||
\(962\) | 0.466923 | − | 1.43704i | 0.0150542 | − | 0.0463321i | ||||
\(963\) | 3.79280 | − | 11.6730i | 0.122221 | − | 0.376158i | ||||
\(964\) | 4.32492 | + | 13.3107i | 0.139296 | + | 0.428710i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.159030 | − | 0.489443i | 0.00511669 | − | 0.0157476i | ||||
\(967\) | 18.4330 | + | 13.3924i | 0.592767 | + | 0.430670i | 0.843304 | − | 0.537437i | \(-0.180607\pi\) |
−0.250537 | + | 0.968107i | \(0.580607\pi\) | |||||||
\(968\) | 30.7872 | 0.989537 | ||||||||
\(969\) | 4.50348 | + | 3.27197i | 0.144673 | + | 0.105111i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.5849 | + | 25.8539i | −1.14197 | + | 0.829692i | −0.987393 | − | 0.158288i | \(-0.949402\pi\) |
−0.154580 | + | 0.987980i | \(0.549402\pi\) | |||||||
\(972\) | −1.38513 | + | 1.00636i | −0.0444281 | + | 0.0322789i | ||||
\(973\) | 2.97448 | + | 9.15450i | 0.0953574 | + | 0.293480i | ||||
\(974\) | 18.9552 | 0.607362 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.1029 | −0.483431 | ||||||||
\(977\) | −5.75794 | − | 17.7211i | −0.184213 | − | 0.566948i | 0.815721 | − | 0.578445i | \(-0.196340\pi\) |
−0.999934 | + | 0.0114968i | \(0.996340\pi\) | |||||||
\(978\) | −3.02729 | + | 2.19946i | −0.0968021 | + | 0.0703308i | ||||
\(979\) | −0.0512634 | + | 0.0372450i | −0.00163838 | + | 0.00119036i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.42135 | + | 2.48575i | 0.109235 | + | 0.0793640i | ||||
\(982\) | 11.6397 | 0.371438 | ||||||||
\(983\) | −44.0975 | − | 32.0387i | −1.40649 | − | 1.02188i | −0.993821 | − | 0.110998i | \(-0.964595\pi\) |
−0.412672 | − | 0.910880i | \(-0.635405\pi\) | |||||||
\(984\) | 3.18155 | − | 9.79181i | 0.101424 | − | 0.312152i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.00406837 | + | 0.0125212i | 0.000129563 | + | 0.000398755i | ||||
\(987\) | −6.77563 | + | 20.8533i | −0.215671 | + | 0.663767i | ||||
\(988\) | 6.31504 | − | 19.4357i | 0.200908 | − | 0.618332i | ||||
\(989\) | −1.31895 | − | 4.05930i | −0.0419401 | − | 0.129078i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.1881 | − | 34.4335i | 0.355403 | − | 1.09382i | −0.600373 | − | 0.799720i | \(-0.704981\pi\) |
0.955776 | − | 0.294097i | \(-0.0950188\pi\) | |||||||
\(992\) | −19.0567 | − | 13.8455i | −0.605051 | − | 0.439595i | ||||
\(993\) | −1.07827 | −0.0342178 | ||||||||
\(994\) | −13.5797 | − | 9.86626i | −0.430723 | − | 0.312939i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12.9693 | − | 9.42275i | 0.410948 | − | 0.298571i | ||||
\(997\) | 5.81865 | − | 4.22750i | 0.184279 | − | 0.133886i | −0.491821 | − | 0.870696i | \(-0.663669\pi\) |
0.676100 | + | 0.736810i | \(0.263669\pi\) | |||||||
\(998\) | −6.43096 | − | 19.7924i | −0.203568 | − | 0.626519i | ||||
\(999\) | 1.90935 | 0.0604092 |
(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 | 375.2.g.d.151.2 | 16 | ||
5.2 | odd | 4 | 375.2.i.c.349.3 | 16 | |||
5.3 | odd | 4 | 75.2.i.a.19.2 | yes | 16 | ||
5.4 | even | 2 | 375.2.g.e.151.3 | 16 | |||
15.8 | even | 4 | 225.2.m.b.19.3 | 16 | |||
25.2 | odd | 20 | 1875.2.b.h.1249.7 | 16 | |||
25.3 | odd | 20 | 375.2.i.c.274.3 | 16 | |||
25.4 | even | 10 | 375.2.g.e.226.3 | 16 | |||
25.11 | even | 5 | 1875.2.a.p.1.3 | 8 | |||
25.14 | even | 10 | 1875.2.a.m.1.6 | 8 | |||
25.21 | even | 5 | inner | 375.2.g.d.226.2 | 16 | ||
25.22 | odd | 20 | 75.2.i.a.4.2 | ✓ | 16 | ||
25.23 | odd | 20 | 1875.2.b.h.1249.10 | 16 | |||
75.11 | odd | 10 | 5625.2.a.t.1.6 | 8 | |||
75.14 | odd | 10 | 5625.2.a.bd.1.3 | 8 | |||
75.47 | even | 20 | 225.2.m.b.154.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.2 | ✓ | 16 | 25.22 | odd | 20 | ||
75.2.i.a.19.2 | yes | 16 | 5.3 | odd | 4 | ||
225.2.m.b.19.3 | 16 | 15.8 | even | 4 | |||
225.2.m.b.154.3 | 16 | 75.47 | even | 20 | |||
375.2.g.d.151.2 | 16 | 1.1 | even | 1 | trivial | ||
375.2.g.d.226.2 | 16 | 25.21 | even | 5 | inner | ||
375.2.g.e.151.3 | 16 | 5.4 | even | 2 | |||
375.2.g.e.226.3 | 16 | 25.4 | even | 10 | |||
375.2.i.c.274.3 | 16 | 25.3 | odd | 20 | |||
375.2.i.c.349.3 | 16 | 5.2 | odd | 4 | |||
1875.2.a.m.1.6 | 8 | 25.14 | even | 10 | |||
1875.2.a.p.1.3 | 8 | 25.11 | even | 5 | |||
1875.2.b.h.1249.7 | 16 | 25.2 | odd | 20 | |||
1875.2.b.h.1249.10 | 16 | 25.23 | odd | 20 | |||
5625.2.a.t.1.6 | 8 | 75.11 | odd | 10 | |||
5625.2.a.bd.1.3 | 8 | 75.14 | odd | 10 |