Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(11,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.l (of order \(6\), degree \(2\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.116304318664704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + x^{10} + 6x^{9} - 9x^{8} - 2x^{7} + 18x^{6} - 4x^{5} - 36x^{4} + 48x^{3} + 16x^{2} - 64x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(0.578188 - 1.29062i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.101 |
Dual form | 370.2.l.c.11.3 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.40680 | + | 2.43665i | 0.812218 | + | 1.40680i | 0.911308 | + | 0.411725i | \(0.135073\pi\) |
−0.0990900 | + | 0.995078i | \(0.531593\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | − | 2.81361i | − | 1.14865i | ||||||
\(7\) | 1.97465 | + | 3.42019i | 0.746348 | + | 1.29271i | 0.949562 | + | 0.313578i | \(0.101528\pi\) |
−0.203215 | + | 0.979134i | \(0.565139\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.45819 | + | 4.25771i | −0.819397 | + | 1.41924i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.23847 | −1.57946 | −0.789729 | − | 0.613456i | \(-0.789779\pi\) | ||||
−0.789729 | + | 0.613456i | \(0.789779\pi\) | |||||||
\(12\) | −1.40680 | + | 2.43665i | −0.406109 | + | 0.703402i | ||||
\(13\) | 2.55417 | − | 1.47465i | 0.708399 | − | 0.408994i | −0.102069 | − | 0.994777i | \(-0.532546\pi\) |
0.810468 | + | 0.585783i | \(0.199213\pi\) | |||||||
\(14\) | − | 3.94930i | − | 1.05550i | ||||||
\(15\) | −2.43665 | − | 1.40680i | −0.629142 | − | 0.363235i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.18900 | − | 1.26382i | −0.530910 | − | 0.306521i | 0.210477 | − | 0.977599i | \(-0.432498\pi\) |
−0.741387 | + | 0.671078i | \(0.765832\pi\) | |||||||
\(18\) | 4.25771 | − | 2.45819i | 1.00355 | − | 0.579401i | ||||
\(19\) | 4.20751 | − | 2.42920i | 0.965268 | − | 0.557298i | 0.0674777 | − | 0.997721i | \(-0.478505\pi\) |
0.897790 | + | 0.440423i | \(0.145172\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | −5.55589 | + | 9.62308i | −1.21239 | + | 2.09993i | ||||
\(22\) | 4.53665 | + | 2.61923i | 0.967217 | + | 0.558423i | ||||
\(23\) | − | 2.92572i | − | 0.610054i | −0.952344 | − | 0.305027i | \(-0.901334\pi\) | ||
0.952344 | − | 0.305027i | \(-0.0986655\pi\) | |||||||
\(24\) | 2.43665 | − | 1.40680i | 0.497380 | − | 0.287163i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −2.94930 | −0.578406 | ||||||||
\(27\) | −5.39194 | −1.03768 | ||||||||
\(28\) | −1.97465 | + | 3.42019i | −0.373174 | + | 0.646356i | ||||
\(29\) | 9.66965i | 1.79561i | 0.440394 | + | 0.897805i | \(0.354839\pi\) | ||||
−0.440394 | + | 0.897805i | \(0.645161\pi\) | |||||||
\(30\) | 1.40680 | + | 2.43665i | 0.256846 | + | 0.444870i | ||||
\(31\) | − | 3.14682i | − | 0.565186i | −0.959240 | − | 0.282593i | \(-0.908805\pi\) | ||
0.959240 | − | 0.282593i | \(-0.0911946\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −7.36950 | − | 12.7643i | −1.28286 | − | 2.22199i | ||||
\(34\) | 1.26382 | + | 2.18900i | 0.216743 | + | 0.375410i | ||||
\(35\) | −3.42019 | − | 1.97465i | −0.578118 | − | 0.333777i | ||||
\(36\) | −4.91638 | −0.819397 | ||||||||
\(37\) | −6.01944 | + | 0.875392i | −0.989590 | + | 0.143914i | ||||
\(38\) | −4.85841 | −0.788138 | ||||||||
\(39\) | 7.18643 | + | 4.14909i | 1.15075 | + | 0.664386i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.88220 | + | 6.72417i | 0.606298 | + | 1.05014i | 0.991845 | + | 0.127450i | \(0.0406793\pi\) |
−0.385547 | + | 0.922688i | \(0.625987\pi\) | |||||||
\(42\) | 9.62308 | − | 5.55589i | 1.48487 | − | 0.857292i | ||||
\(43\) | 1.68060i | 0.256289i | 0.991756 | + | 0.128144i | \(0.0409021\pi\) | ||||
−0.991756 | + | 0.128144i | \(0.959098\pi\) | |||||||
\(44\) | −2.61923 | − | 4.53665i | −0.394864 | − | 0.683925i | ||||
\(45\) | − | 4.91638i | − | 0.732891i | ||||||
\(46\) | −1.46286 | + | 2.53375i | −0.215687 | + | 0.373580i | ||||
\(47\) | 11.8205 | 1.72420 | 0.862102 | − | 0.506735i | \(-0.169148\pi\) | ||||
0.862102 | + | 0.506735i | \(0.169148\pi\) | |||||||
\(48\) | −2.81361 | −0.406109 | ||||||||
\(49\) | −4.29849 | + | 7.44520i | −0.614070 | + | 1.06360i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | − | 7.11178i | − | 0.995848i | ||||||
\(52\) | 2.55417 | + | 1.47465i | 0.354200 | + | 0.204497i | ||||
\(53\) | −1.72422 | + | 2.98644i | −0.236840 | + | 0.410219i | −0.959806 | − | 0.280665i | \(-0.909445\pi\) |
0.722966 | + | 0.690884i | \(0.242778\pi\) | |||||||
\(54\) | 4.66956 | + | 2.69597i | 0.635447 | + | 0.366875i | ||||
\(55\) | 4.53665 | − | 2.61923i | 0.611721 | − | 0.353178i | ||||
\(56\) | 3.42019 | − | 1.97465i | 0.457043 | − | 0.263874i | ||||
\(57\) | 11.8383 | + | 6.83483i | 1.56802 | + | 0.905295i | ||||
\(58\) | 4.83483 | − | 8.37416i | 0.634844 | − | 1.09958i | ||||
\(59\) | 6.01430 | + | 3.47236i | 0.782995 | + | 0.452062i | 0.837491 | − | 0.546452i | \(-0.184022\pi\) |
−0.0544958 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(60\) | − | 2.81361i | − | 0.363235i | ||||||
\(61\) | 8.76366 | − | 5.05970i | 1.12207 | − | 0.647829i | 0.180143 | − | 0.983640i | \(-0.442344\pi\) |
0.941929 | + | 0.335812i | \(0.109011\pi\) | |||||||
\(62\) | −1.57341 | + | 2.72523i | −0.199823 | + | 0.346104i | ||||
\(63\) | −19.4163 | −2.44622 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.47465 | + | 2.55417i | −0.182908 | + | 0.316806i | ||||
\(66\) | 14.7390i | 1.81424i | ||||||||
\(67\) | 3.44554 | + | 5.96786i | 0.420940 | + | 0.729090i | 0.996032 | − | 0.0889992i | \(-0.0283669\pi\) |
−0.575091 | + | 0.818089i | \(0.695034\pi\) | |||||||
\(68\) | − | 2.52764i | − | 0.306521i | ||||||
\(69\) | 7.12896 | − | 4.11591i | 0.858226 | − | 0.495497i | ||||
\(70\) | 1.97465 | + | 3.42019i | 0.236016 | + | 0.408791i | ||||
\(71\) | −5.54009 | − | 9.59572i | −0.657488 | − | 1.13880i | −0.981264 | − | 0.192669i | \(-0.938286\pi\) |
0.323776 | − | 0.946134i | \(-0.395048\pi\) | |||||||
\(72\) | 4.25771 | + | 2.45819i | 0.501776 | + | 0.289701i | ||||
\(73\) | 1.02217 | 0.119636 | 0.0598182 | − | 0.998209i | \(-0.480948\pi\) | ||||
0.0598182 | + | 0.998209i | \(0.480948\pi\) | |||||||
\(74\) | 5.65069 | + | 2.25161i | 0.656879 | + | 0.261744i | ||||
\(75\) | 2.81361 | 0.324887 | ||||||||
\(76\) | 4.20751 | + | 2.42920i | 0.482634 | + | 0.278649i | ||||
\(77\) | −10.3441 | − | 17.9166i | −1.17882 | − | 2.04178i | ||||
\(78\) | −4.14909 | − | 7.18643i | −0.469792 | − | 0.813703i | ||||
\(79\) | −7.07449 | + | 4.08446i | −0.795942 | + | 0.459537i | −0.842050 | − | 0.539399i | \(-0.818651\pi\) |
0.0461082 | + | 0.998936i | \(0.485318\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | −0.210831 | − | 0.365171i | −0.0234257 | − | 0.0405745i | ||||
\(82\) | − | 7.76440i | − | 0.857434i | ||||||
\(83\) | 8.20899 | − | 14.2184i | 0.901054 | − | 1.56067i | 0.0749251 | − | 0.997189i | \(-0.476128\pi\) |
0.826129 | − | 0.563482i | \(-0.190538\pi\) | |||||||
\(84\) | −11.1118 | −1.21239 | ||||||||
\(85\) | 2.52764 | 0.274161 | ||||||||
\(86\) | 0.840298 | − | 1.45544i | 0.0906117 | − | 0.156944i | ||||
\(87\) | −23.5616 | + | 13.6033i | −2.52607 | + | 1.45843i | ||||
\(88\) | 5.23847i | 0.558423i | ||||||||
\(89\) | 2.14759 | + | 1.23991i | 0.227644 | + | 0.131430i | 0.609485 | − | 0.792798i | \(-0.291376\pi\) |
−0.381841 | + | 0.924228i | \(0.624710\pi\) | |||||||
\(90\) | −2.45819 | + | 4.25771i | −0.259116 | + | 0.448802i | ||||
\(91\) | 10.0872 | + | 5.82384i | 1.05742 | + | 0.610504i | ||||
\(92\) | 2.53375 | − | 1.46286i | 0.264161 | − | 0.152514i | ||||
\(93\) | 7.66772 | − | 4.42696i | 0.795106 | − | 0.459054i | ||||
\(94\) | −10.2369 | − | 5.91027i | −1.05586 | − | 0.609598i | ||||
\(95\) | −2.42920 | + | 4.20751i | −0.249231 | + | 0.431681i | ||||
\(96\) | 2.43665 | + | 1.40680i | 0.248690 | + | 0.143581i | ||||
\(97\) | − | 4.96273i | − | 0.503889i | −0.967742 | − | 0.251945i | \(-0.918930\pi\) | ||
0.967742 | − | 0.251945i | \(-0.0810701\pi\) | |||||||
\(98\) | 7.44520 | − | 4.29849i | 0.752079 | − | 0.434213i | ||||
\(99\) | 12.8772 | − | 22.3039i | 1.29420 | − | 2.24163i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.755513 | −0.0751763 | −0.0375882 | − | 0.999293i | \(-0.511968\pi\) | ||||
−0.0375882 | + | 0.999293i | \(0.511968\pi\) | |||||||
\(102\) | −3.55589 | + | 6.15898i | −0.352086 | + | 0.609830i | ||||
\(103\) | − | 16.5377i | − | 1.62951i | −0.579808 | − | 0.814753i | \(-0.696873\pi\) | ||
0.579808 | − | 0.814753i | \(-0.303127\pi\) | |||||||
\(104\) | −1.47465 | − | 2.55417i | −0.144601 | − | 0.250457i | ||||
\(105\) | − | 11.1118i | − | 1.08440i | ||||||
\(106\) | 2.98644 | − | 1.72422i | 0.290069 | − | 0.167471i | ||||
\(107\) | −6.32318 | − | 10.9521i | −0.611285 | − | 1.05878i | −0.991024 | − | 0.133684i | \(-0.957319\pi\) |
0.379739 | − | 0.925094i | \(-0.376014\pi\) | |||||||
\(108\) | −2.69597 | − | 4.66956i | −0.259420 | − | 0.449329i | ||||
\(109\) | −4.60707 | − | 2.65989i | −0.441277 | − | 0.254772i | 0.262862 | − | 0.964833i | \(-0.415334\pi\) |
−0.704139 | + | 0.710062i | \(0.748667\pi\) | |||||||
\(110\) | −5.23847 | −0.499468 | ||||||||
\(111\) | −10.6012 | − | 13.4358i | −1.00622 | − | 1.27527i | ||||
\(112\) | −3.94930 | −0.373174 | ||||||||
\(113\) | 7.48250 | + | 4.32003i | 0.703895 | + | 0.406394i | 0.808796 | − | 0.588089i | \(-0.200119\pi\) |
−0.104902 | + | 0.994483i | \(0.533453\pi\) | |||||||
\(114\) | −6.83483 | − | 11.8383i | −0.640140 | − | 1.10876i | ||||
\(115\) | 1.46286 | + | 2.53375i | 0.136412 | + | 0.236273i | ||||
\(116\) | −8.37416 | + | 4.83483i | −0.777522 | + | 0.448902i | ||||
\(117\) | 14.4999i | 1.34052i | ||||||||
\(118\) | −3.47236 | − | 6.01430i | −0.319656 | − | 0.553661i | ||||
\(119\) | − | 9.98240i | − | 0.915085i | ||||||
\(120\) | −1.40680 | + | 2.43665i | −0.128423 | + | 0.222435i | ||||
\(121\) | 16.4416 | 1.49469 | ||||||||
\(122\) | −10.1194 | −0.916168 | ||||||||
\(123\) | −10.9230 | + | 18.9192i | −0.984892 | + | 1.70588i | ||||
\(124\) | 2.72523 | − | 1.57341i | 0.244733 | − | 0.141297i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 16.8150 | + | 9.70814i | 1.49800 | + | 0.864869i | ||||
\(127\) | 4.04603 | − | 7.00792i | 0.359027 | − | 0.621852i | −0.628772 | − | 0.777590i | \(-0.716442\pi\) |
0.987798 | + | 0.155737i | \(0.0497754\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.09503 | + | 2.36427i | −0.360548 | + | 0.208162i | ||||
\(130\) | 2.55417 | − | 1.47465i | 0.224015 | − | 0.129335i | ||||
\(131\) | 3.43829 | + | 1.98510i | 0.300405 | + | 0.173439i | 0.642625 | − | 0.766181i | \(-0.277845\pi\) |
−0.342220 | + | 0.939620i | \(0.611179\pi\) | |||||||
\(132\) | 7.36950 | − | 12.7643i | 0.641432 | − | 1.11099i | ||||
\(133\) | 16.6167 | + | 9.59366i | 1.44085 | + | 0.831876i | ||||
\(134\) | − | 6.89109i | − | 0.595299i | ||||||
\(135\) | 4.66956 | − | 2.69597i | 0.401892 | − | 0.232032i | ||||
\(136\) | −1.26382 | + | 2.18900i | −0.108372 | + | 0.187705i | ||||
\(137\) | 20.7501 | 1.77280 | 0.886401 | − | 0.462918i | \(-0.153197\pi\) | ||||
0.886401 | + | 0.462918i | \(0.153197\pi\) | |||||||
\(138\) | −8.23182 | −0.700739 | ||||||||
\(139\) | −9.05622 | + | 15.6858i | −0.768139 | + | 1.33046i | 0.170433 | + | 0.985369i | \(0.445484\pi\) |
−0.938571 | + | 0.345086i | \(0.887850\pi\) | |||||||
\(140\) | − | 3.94930i | − | 0.333777i | ||||||
\(141\) | 16.6292 | + | 28.8026i | 1.40043 | + | 2.42562i | ||||
\(142\) | 11.0802i | 0.929829i | ||||||||
\(143\) | −13.3799 | + | 7.72491i | −1.11889 | + | 0.645990i | ||||
\(144\) | −2.45819 | − | 4.25771i | −0.204849 | − | 0.354809i | ||||
\(145\) | −4.83483 | − | 8.37416i | −0.401510 | − | 0.695436i | ||||
\(146\) | −0.885228 | − | 0.511087i | −0.0732620 | − | 0.0422978i | ||||
\(147\) | −24.1885 | −1.99504 | ||||||||
\(148\) | −3.76783 | − | 4.77529i | −0.309714 | − | 0.392527i | ||||
\(149\) | −16.1234 | −1.32088 | −0.660441 | − | 0.750878i | \(-0.729631\pi\) | ||||
−0.660441 | + | 0.750878i | \(0.729631\pi\) | |||||||
\(150\) | −2.43665 | − | 1.40680i | −0.198952 | − | 0.114865i | ||||
\(151\) | 2.67163 | + | 4.62739i | 0.217414 | + | 0.376572i | 0.954017 | − | 0.299754i | \(-0.0969045\pi\) |
−0.736603 | + | 0.676326i | \(0.763571\pi\) | |||||||
\(152\) | −2.42920 | − | 4.20751i | −0.197035 | − | 0.341274i | ||||
\(153\) | 10.7620 | − | 6.21342i | 0.870052 | − | 0.502325i | ||||
\(154\) | 20.6883i | 1.66711i | ||||||||
\(155\) | 1.57341 | + | 2.72523i | 0.126379 | + | 0.218896i | ||||
\(156\) | 8.29817i | 0.664386i | ||||||||
\(157\) | −7.08298 | + | 12.2681i | −0.565283 | + | 0.979099i | 0.431740 | + | 0.901998i | \(0.357900\pi\) |
−0.997023 | + | 0.0771012i | \(0.975434\pi\) | |||||||
\(158\) | 8.16892 | 0.649884 | ||||||||
\(159\) | −9.70257 | −0.769464 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 10.0065 | − | 5.77727i | 0.788625 | − | 0.455313i | ||||
\(162\) | 0.421663i | 0.0331290i | ||||||||
\(163\) | −0.975743 | − | 0.563345i | −0.0764261 | − | 0.0441246i | 0.461300 | − | 0.887244i | \(-0.347383\pi\) |
−0.537726 | + | 0.843120i | \(0.680717\pi\) | |||||||
\(164\) | −3.88220 | + | 6.72417i | −0.303149 | + | 0.525069i | ||||
\(165\) | 12.7643 | + | 7.36950i | 0.993703 | + | 0.573714i | ||||
\(166\) | −14.2184 | + | 8.20899i | −1.10356 | + | 0.637141i | ||||
\(167\) | −9.17780 | + | 5.29881i | −0.710200 | + | 0.410034i | −0.811135 | − | 0.584859i | \(-0.801150\pi\) |
0.100935 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(168\) | 9.62308 | + | 5.55589i | 0.742437 | + | 0.428646i | ||||
\(169\) | −2.15081 | + | 3.72532i | −0.165447 | + | 0.286563i | ||||
\(170\) | −2.18900 | − | 1.26382i | −0.167889 | − | 0.0969305i | ||||
\(171\) | 23.8858i | 1.82659i | ||||||||
\(172\) | −1.45544 | + | 0.840298i | −0.110976 | + | 0.0640722i | ||||
\(173\) | 7.75419 | − | 13.4307i | 0.589540 | − | 1.02111i | −0.404752 | − | 0.914426i | \(-0.632642\pi\) |
0.994293 | − | 0.106688i | \(-0.0340245\pi\) | |||||||
\(174\) | 27.2066 | 2.06253 | ||||||||
\(175\) | 3.94930 | 0.298539 | ||||||||
\(176\) | 2.61923 | − | 4.53665i | 0.197432 | − | 0.341963i | ||||
\(177\) | 19.5397i | 1.46869i | ||||||||
\(178\) | −1.23991 | − | 2.14759i | −0.0929351 | − | 0.160968i | ||||
\(179\) | 8.16858i | 0.610548i | 0.952265 | + | 0.305274i | \(0.0987481\pi\) | ||||
−0.952265 | + | 0.305274i | \(0.901252\pi\) | |||||||
\(180\) | 4.25771 | − | 2.45819i | 0.317351 | − | 0.183223i | ||||
\(181\) | −2.99877 | − | 5.19403i | −0.222897 | − | 0.386069i | 0.732789 | − | 0.680455i | \(-0.238218\pi\) |
−0.955686 | + | 0.294387i | \(0.904885\pi\) | |||||||
\(182\) | −5.82384 | − | 10.0872i | −0.431692 | − | 0.747712i | ||||
\(183\) | 24.6575 | + | 14.2360i | 1.82273 | + | 1.05236i | ||||
\(184\) | −2.92572 | −0.215687 | ||||||||
\(185\) | 4.77529 | − | 3.76783i | 0.351087 | − | 0.277017i | ||||
\(186\) | −8.85392 | −0.649201 | ||||||||
\(187\) | 11.4670 | + | 6.62048i | 0.838550 | + | 0.484137i | ||||
\(188\) | 5.91027 | + | 10.2369i | 0.431051 | + | 0.746602i | ||||
\(189\) | −10.6472 | − | 18.4415i | −0.774470 | − | 1.34142i | ||||
\(190\) | 4.20751 | − | 2.42920i | 0.305245 | − | 0.176233i | ||||
\(191\) | − | 12.8486i | − | 0.929693i | −0.885391 | − | 0.464847i | \(-0.846109\pi\) | ||
0.885391 | − | 0.464847i | \(-0.153891\pi\) | |||||||
\(192\) | −1.40680 | − | 2.43665i | −0.101527 | − | 0.175850i | ||||
\(193\) | − | 12.8968i | − | 0.928330i | −0.885749 | − | 0.464165i | \(-0.846354\pi\) | ||
0.885749 | − | 0.464165i | \(-0.153646\pi\) | |||||||
\(194\) | −2.48137 | + | 4.29785i | −0.178152 | + | 0.308568i | ||||
\(195\) | −8.29817 | −0.594244 | ||||||||
\(196\) | −8.59698 | −0.614070 | ||||||||
\(197\) | 5.03868 | − | 8.72726i | 0.358991 | − | 0.621791i | −0.628801 | − | 0.777566i | \(-0.716454\pi\) |
0.987793 | + | 0.155775i | \(0.0497874\pi\) | |||||||
\(198\) | −22.3039 | + | 12.8772i | −1.58507 | + | 0.915140i | ||||
\(199\) | − | 0.913815i | − | 0.0647786i | −0.999475 | − | 0.0323893i | \(-0.989688\pi\) | ||
0.999475 | − | 0.0323893i | \(-0.0103116\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | −9.69441 | + | 16.7912i | −0.683791 | + | 1.18436i | ||||
\(202\) | 0.654293 | + | 0.377756i | 0.0460359 | + | 0.0265788i | ||||
\(203\) | −33.0721 | + | 19.0942i | −2.32121 | + | 1.34015i | ||||
\(204\) | 6.15898 | − | 3.55589i | 0.431215 | − | 0.248962i | ||||
\(205\) | −6.72417 | − | 3.88220i | −0.469636 | − | 0.271145i | ||||
\(206\) | −8.26884 | + | 14.3220i | −0.576117 | + | 0.997864i | ||||
\(207\) | 12.4569 | + | 7.19197i | 0.865812 | + | 0.499877i | ||||
\(208\) | 2.94930i | 0.204497i | ||||||||
\(209\) | −22.0409 | + | 12.7253i | −1.52460 | + | 0.880228i | ||||
\(210\) | −5.55589 | + | 9.62308i | −0.383393 | + | 0.664056i | ||||
\(211\) | −5.47592 | −0.376978 | −0.188489 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188489 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(212\) | −3.44845 | −0.236840 | ||||||||
\(213\) | 15.5876 | − | 26.9986i | 1.06805 | − | 1.84991i | ||||
\(214\) | 12.6464i | 0.864488i | ||||||||
\(215\) | −0.840298 | − | 1.45544i | −0.0573079 | − | 0.0992602i | ||||
\(216\) | 5.39194i | 0.366875i | ||||||||
\(217\) | 10.7627 | − | 6.21388i | 0.730623 | − | 0.421825i | ||||
\(218\) | 2.65989 | + | 4.60707i | 0.180151 | + | 0.312030i | ||||
\(219\) | 1.43800 | + | 2.49068i | 0.0971708 | + | 0.168305i | ||||
\(220\) | 4.53665 | + | 2.61923i | 0.305861 | + | 0.176589i | ||||
\(221\) | −7.45477 | −0.501462 | ||||||||
\(222\) | 2.46301 | + | 16.9363i | 0.165306 | + | 1.13669i | ||||
\(223\) | 12.6320 | 0.845899 | 0.422949 | − | 0.906153i | \(-0.360995\pi\) | ||||
0.422949 | + | 0.906153i | \(0.360995\pi\) | |||||||
\(224\) | 3.42019 | + | 1.97465i | 0.228521 | + | 0.131937i | ||||
\(225\) | 2.45819 | + | 4.25771i | 0.163879 | + | 0.283847i | ||||
\(226\) | −4.32003 | − | 7.48250i | −0.287364 | − | 0.497729i | ||||
\(227\) | 20.6340 | − | 11.9131i | 1.36953 | − | 0.790697i | 0.378660 | − | 0.925536i | \(-0.376385\pi\) |
0.990868 | + | 0.134838i | \(0.0430515\pi\) | |||||||
\(228\) | 13.6697i | 0.905295i | ||||||||
\(229\) | −4.62224 | − | 8.00596i | −0.305446 | − | 0.529049i | 0.671914 | − | 0.740629i | \(-0.265472\pi\) |
−0.977361 | + | 0.211580i | \(0.932139\pi\) | |||||||
\(230\) | − | 2.92572i | − | 0.192916i | ||||||
\(231\) | 29.1044 | − | 50.4102i | 1.91493 | − | 3.31675i | ||||
\(232\) | 9.66965 | 0.634844 | ||||||||
\(233\) | −1.79691 | −0.117719 | −0.0588596 | − | 0.998266i | \(-0.518746\pi\) | ||||
−0.0588596 | + | 0.998266i | \(0.518746\pi\) | |||||||
\(234\) | 7.24994 | − | 12.5573i | 0.473944 | − | 0.820895i | ||||
\(235\) | −10.2369 | + | 5.91027i | −0.667781 | + | 0.385544i | ||||
\(236\) | 6.94471i | 0.452062i | ||||||||
\(237\) | −19.9048 | − | 11.4921i | −1.29296 | − | 0.746489i | ||||
\(238\) | −4.99120 | + | 8.64502i | −0.323532 | + | 0.560373i | ||||
\(239\) | 0.845001 | + | 0.487862i | 0.0546586 | + | 0.0315571i | 0.527080 | − | 0.849816i | \(-0.323287\pi\) |
−0.472422 | + | 0.881373i | \(0.656620\pi\) | |||||||
\(240\) | 2.43665 | − | 1.40680i | 0.157285 | − | 0.0908088i | ||||
\(241\) | 5.29039 | − | 3.05441i | 0.340784 | − | 0.196752i | −0.319835 | − | 0.947473i | \(-0.603627\pi\) |
0.660619 | + | 0.750722i | \(0.270294\pi\) | |||||||
\(242\) | −14.2388 | − | 8.22078i | −0.915305 | − | 0.528452i | ||||
\(243\) | −7.49472 | + | 12.9812i | −0.480786 | + | 0.832747i | ||||
\(244\) | 8.76366 | + | 5.05970i | 0.561036 | + | 0.323914i | ||||
\(245\) | − | 8.59698i | − | 0.549241i | ||||||
\(246\) | 18.9192 | − | 10.9230i | 1.20624 | − | 0.696424i | ||||
\(247\) | 7.16446 | − | 12.4092i | 0.455863 | − | 0.789579i | ||||
\(248\) | −3.14682 | −0.199823 | ||||||||
\(249\) | 46.1937 | 2.92741 | ||||||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 11.8413i | 0.747418i | 0.927546 | + | 0.373709i | \(0.121914\pi\) | ||||
−0.927546 | + | 0.373709i | \(0.878086\pi\) | |||||||
\(252\) | −9.70814 | − | 16.8150i | −0.611555 | − | 1.05924i | ||||
\(253\) | 15.3263i | 0.963555i | ||||||||
\(254\) | −7.00792 | + | 4.04603i | −0.439716 | + | 0.253870i | ||||
\(255\) | 3.55589 | + | 6.15898i | 0.222678 | + | 0.385690i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 12.3403 | + | 7.12467i | 0.769767 | + | 0.444425i | 0.832791 | − | 0.553587i | \(-0.186741\pi\) |
−0.0630248 | + | 0.998012i | \(0.520075\pi\) | |||||||
\(258\) | 4.72854 | 0.294386 | ||||||||
\(259\) | −14.8803 | − | 18.8591i | −0.924617 | − | 1.17185i | ||||
\(260\) | −2.94930 | −0.182908 | ||||||||
\(261\) | −41.1706 | − | 23.7698i | −2.54840 | − | 1.47132i | ||||
\(262\) | −1.98510 | − | 3.43829i | −0.122640 | − | 0.212418i | ||||
\(263\) | −9.83222 | − | 17.0299i | −0.606281 | − | 1.05011i | −0.991848 | − | 0.127429i | \(-0.959327\pi\) |
0.385567 | − | 0.922680i | \(-0.374006\pi\) | |||||||
\(264\) | −12.7643 | + | 7.36950i | −0.785591 | + | 0.453561i | ||||
\(265\) | − | 3.44845i | − | 0.211836i | ||||||
\(266\) | −9.59366 | − | 16.6167i | −0.588225 | − | 1.01884i | ||||
\(267\) | 6.97723i | 0.427000i | ||||||||
\(268\) | −3.44554 | + | 5.96786i | −0.210470 | + | 0.364545i | ||||
\(269\) | 0.526562 | 0.0321051 | 0.0160525 | − | 0.999871i | \(-0.494890\pi\) | ||||
0.0160525 | + | 0.999871i | \(0.494890\pi\) | |||||||
\(270\) | −5.39194 | −0.328143 | ||||||||
\(271\) | 4.54386 | − | 7.87019i | 0.276020 | − | 0.478080i | −0.694372 | − | 0.719616i | \(-0.744318\pi\) |
0.970392 | + | 0.241536i | \(0.0776512\pi\) | |||||||
\(272\) | 2.18900 | − | 1.26382i | 0.132728 | − | 0.0766303i | ||||
\(273\) | 32.7720i | 1.98345i | ||||||||
\(274\) | −17.9701 | − | 10.3751i | −1.08562 | − | 0.626780i | ||||
\(275\) | −2.61923 | + | 4.53665i | −0.157946 | + | 0.273570i | ||||
\(276\) | 7.12896 | + | 4.11591i | 0.429113 | + | 0.247749i | ||||
\(277\) | −26.5155 | + | 15.3087i | −1.59316 | + | 0.919813i | −0.600402 | + | 0.799698i | \(0.704993\pi\) |
−0.992760 | + | 0.120115i | \(0.961674\pi\) | |||||||
\(278\) | 15.6858 | − | 9.05622i | 0.940774 | − | 0.543156i | ||||
\(279\) | 13.3983 | + | 7.73549i | 0.802133 | + | 0.463112i | ||||
\(280\) | −1.97465 | + | 3.42019i | −0.118008 | + | 0.204396i | ||||
\(281\) | −14.2745 | − | 8.24138i | −0.851545 | − | 0.491640i | 0.00962696 | − | 0.999954i | \(-0.496936\pi\) |
−0.861172 | + | 0.508314i | \(0.830269\pi\) | |||||||
\(282\) | − | 33.2584i | − | 1.98051i | ||||||
\(283\) | −24.8151 | + | 14.3270i | −1.47510 | + | 0.851652i | −0.999606 | − | 0.0280655i | \(-0.991065\pi\) |
−0.475498 | + | 0.879717i | \(0.657732\pi\) | |||||||
\(284\) | 5.54009 | − | 9.59572i | 0.328744 | − | 0.569401i | ||||
\(285\) | −13.6697 | −0.809720 | ||||||||
\(286\) | 15.4498 | 0.913567 | ||||||||
\(287\) | −15.3320 | + | 26.5558i | −0.905018 | + | 1.56754i | ||||
\(288\) | 4.91638i | 0.289701i | ||||||||
\(289\) | −5.30552 | − | 9.18944i | −0.312090 | − | 0.540555i | ||||
\(290\) | 9.66965i | 0.567822i | ||||||||
\(291\) | 12.0925 | − | 6.98159i | 0.708873 | − | 0.409268i | ||||
\(292\) | 0.511087 | + | 0.885228i | 0.0299091 | + | 0.0518041i | ||||
\(293\) | −10.5371 | − | 18.2509i | −0.615587 | − | 1.06623i | −0.990281 | − | 0.139079i | \(-0.955586\pi\) |
0.374695 | − | 0.927148i | \(-0.377748\pi\) | |||||||
\(294\) | 20.9479 | + | 12.0943i | 1.22170 | + | 0.705351i | ||||
\(295\) | −6.94471 | −0.404337 | ||||||||
\(296\) | 0.875392 | + | 6.01944i | 0.0508811 | + | 0.349873i | ||||
\(297\) | 28.2455 | 1.63897 | ||||||||
\(298\) | 13.9633 | + | 8.06171i | 0.808872 | + | 0.467003i | ||||
\(299\) | −4.31441 | − | 7.47278i | −0.249509 | − | 0.432162i | ||||
\(300\) | 1.40680 | + | 2.43665i | 0.0812218 | + | 0.140680i | ||||
\(301\) | −5.74797 | + | 3.31859i | −0.331307 | + | 0.191280i | ||||
\(302\) | − | 5.34326i | − | 0.307470i | ||||||
\(303\) | −1.06286 | − | 1.84092i | −0.0610596 | − | 0.105758i | ||||
\(304\) | 4.85841i | 0.278649i | ||||||||
\(305\) | −5.05970 | + | 8.76366i | −0.289718 | + | 0.501806i | ||||
\(306\) | −12.4268 | −0.710395 | ||||||||
\(307\) | 4.76704 | 0.272069 | 0.136035 | − | 0.990704i | \(-0.456564\pi\) | ||||
0.136035 | + | 0.990704i | \(0.456564\pi\) | |||||||
\(308\) | 10.3441 | − | 17.9166i | 0.589412 | − | 1.02089i | ||||
\(309\) | 40.2966 | − | 23.2653i | 2.29239 | − | 1.32351i | ||||
\(310\) | − | 3.14682i | − | 0.178728i | ||||||
\(311\) | −15.9677 | − | 9.21894i | −0.905444 | − | 0.522758i | −0.0264814 | − | 0.999649i | \(-0.508430\pi\) |
−0.878962 | + | 0.476891i | \(0.841764\pi\) | |||||||
\(312\) | 4.14909 | − | 7.18643i | 0.234896 | − | 0.406851i | ||||
\(313\) | −14.9405 | − | 8.62591i | −0.844487 | − | 0.487565i | 0.0142997 | − | 0.999898i | \(-0.495448\pi\) |
−0.858787 | + | 0.512333i | \(0.828781\pi\) | |||||||
\(314\) | 12.2681 | − | 7.08298i | 0.692328 | − | 0.399716i | ||||
\(315\) | 16.8150 | − | 9.70814i | 0.947417 | − | 0.546991i | ||||
\(316\) | −7.07449 | − | 4.08446i | −0.397971 | − | 0.229769i | ||||
\(317\) | −16.3282 | + | 28.2813i | −0.917085 | + | 1.58844i | −0.113264 | + | 0.993565i | \(0.536131\pi\) |
−0.803820 | + | 0.594872i | \(0.797203\pi\) | |||||||
\(318\) | 8.40267 | + | 4.85129i | 0.471199 | + | 0.272047i | ||||
\(319\) | − | 50.6542i | − | 2.83609i | ||||||
\(320\) | 0.866025 | − | 0.500000i | 0.0484123 | − | 0.0279508i | ||||
\(321\) | 17.7910 | − | 30.8148i | 0.992994 | − | 1.71992i | ||||
\(322\) | −11.5545 | −0.643909 | ||||||||
\(323\) | −12.2803 | −0.683294 | ||||||||
\(324\) | 0.210831 | − | 0.365171i | 0.0117129 | − | 0.0202873i | ||||
\(325\) | − | 2.94930i | − | 0.163598i | ||||||
\(326\) | 0.563345 | + | 0.975743i | 0.0312008 | + | 0.0540414i | ||||
\(327\) | − | 14.9678i | − | 0.827720i | ||||||
\(328\) | 6.72417 | − | 3.88220i | 0.371280 | − | 0.214359i | ||||
\(329\) | 23.3415 | + | 40.4286i | 1.28686 | + | 2.22890i | ||||
\(330\) | −7.36950 | − | 12.7643i | −0.405677 | − | 0.702654i | ||||
\(331\) | −12.2922 | − | 7.09688i | −0.675638 | − | 0.390080i | 0.122571 | − | 0.992460i | \(-0.460886\pi\) |
−0.798210 | + | 0.602380i | \(0.794219\pi\) | |||||||
\(332\) | 16.4180 | 0.901054 | ||||||||
\(333\) | 11.0698 | − | 27.7809i | 0.606620 | − | 1.52239i | ||||
\(334\) | 10.5976 | 0.579876 | ||||||||
\(335\) | −5.96786 | − | 3.44554i | −0.326059 | − | 0.188250i | ||||
\(336\) | −5.55589 | − | 9.62308i | −0.303099 | − | 0.524982i | ||||
\(337\) | 12.3658 | + | 21.4182i | 0.673608 | + | 1.16672i | 0.976874 | + | 0.213818i | \(0.0685898\pi\) |
−0.303265 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(338\) | 3.72532 | − | 2.15081i | 0.202630 | − | 0.116989i | ||||
\(339\) | 24.3097i | 1.32032i | ||||||||
\(340\) | 1.26382 | + | 2.18900i | 0.0685402 | + | 0.118715i | ||||
\(341\) | 16.4845i | 0.892688i | ||||||||
\(342\) | 11.9429 | − | 20.6857i | 0.645798 | − | 1.11855i | ||||
\(343\) | −6.30695 | −0.340543 | ||||||||
\(344\) | 1.68060 | 0.0906117 | ||||||||
\(345\) | −4.11591 | + | 7.12896i | −0.221593 | + | 0.383811i | ||||
\(346\) | −13.4307 | + | 7.75419i | −0.722037 | + | 0.416868i | ||||
\(347\) | − | 8.11360i | − | 0.435561i | −0.975998 | − | 0.217780i | \(-0.930118\pi\) | ||
0.975998 | − | 0.217780i | \(-0.0698817\pi\) | |||||||
\(348\) | −23.5616 | − | 13.6033i | −1.26303 | − | 0.729213i | ||||
\(349\) | −12.0052 | + | 20.7936i | −0.642622 | + | 1.11305i | 0.342223 | + | 0.939619i | \(0.388820\pi\) |
−0.984845 | + | 0.173435i | \(0.944513\pi\) | |||||||
\(350\) | −3.42019 | − | 1.97465i | −0.182817 | − | 0.105550i | ||||
\(351\) | −13.7719 | + | 7.95123i | −0.735092 | + | 0.424405i | ||||
\(352\) | −4.53665 | + | 2.61923i | −0.241804 | + | 0.139606i | ||||
\(353\) | 18.8909 | + | 10.9067i | 1.00546 | + | 0.580504i | 0.909860 | − | 0.414915i | \(-0.136189\pi\) |
0.0956030 | + | 0.995420i | \(0.469522\pi\) | |||||||
\(354\) | 9.76984 | − | 16.9219i | 0.519261 | − | 0.899387i | ||||
\(355\) | 9.59572 | + | 5.54009i | 0.509288 | + | 0.294038i | ||||
\(356\) | 2.47982i | 0.131430i | ||||||||
\(357\) | 24.3237 | − | 14.0433i | 1.28735 | − | 0.743249i | ||||
\(358\) | 4.08429 | − | 7.07419i | 0.215861 | − | 0.373883i | ||||
\(359\) | −14.6216 | −0.771696 | −0.385848 | − | 0.922562i | \(-0.626091\pi\) | ||||
−0.385848 | + | 0.922562i | \(0.626091\pi\) | |||||||
\(360\) | −4.91638 | −0.259116 | ||||||||
\(361\) | 2.30207 | − | 3.98730i | 0.121162 | − | 0.209858i | ||||
\(362\) | 5.99754i | 0.315224i | ||||||||
\(363\) | 23.1300 | + | 40.0624i | 1.21401 | + | 2.10273i | ||||
\(364\) | 11.6477i | 0.610504i | ||||||||
\(365\) | −0.885228 | + | 0.511087i | −0.0463350 | + | 0.0267515i | ||||
\(366\) | −14.2360 | − | 24.6575i | −0.744128 | − | 1.28887i | ||||
\(367\) | −4.67210 | − | 8.09232i | −0.243882 | − | 0.422415i | 0.717935 | − | 0.696110i | \(-0.245088\pi\) |
−0.961817 | + | 0.273695i | \(0.911754\pi\) | |||||||
\(368\) | 2.53375 | + | 1.46286i | 0.132081 | + | 0.0762568i | ||||
\(369\) | −38.1727 | −1.98719 | ||||||||
\(370\) | −6.01944 | + | 0.875392i | −0.312936 | + | 0.0455095i | ||||
\(371\) | −13.6190 | −0.707061 | ||||||||
\(372\) | 7.66772 | + | 4.42696i | 0.397553 | + | 0.229527i | ||||
\(373\) | 1.13370 | + | 1.96362i | 0.0587007 | + | 0.101673i | 0.893882 | − | 0.448301i | \(-0.147971\pi\) |
−0.835182 | + | 0.549974i | \(0.814638\pi\) | |||||||
\(374\) | −6.62048 | − | 11.4670i | −0.342337 | − | 0.592945i | ||||
\(375\) | −2.43665 | + | 1.40680i | −0.125828 | + | 0.0726470i | ||||
\(376\) | − | 11.8205i | − | 0.609598i | ||||||
\(377\) | 14.2594 | + | 24.6979i | 0.734394 | + | 1.27201i | ||||
\(378\) | 21.2944i | 1.09527i | ||||||||
\(379\) | 1.23608 | − | 2.14096i | 0.0634932 | − | 0.109974i | −0.832531 | − | 0.553978i | \(-0.813109\pi\) |
0.896025 | + | 0.444004i | \(0.146443\pi\) | |||||||
\(380\) | −4.85841 | −0.249231 | ||||||||
\(381\) | 22.7678 | 1.16643 | ||||||||
\(382\) | −6.42431 | + | 11.1272i | −0.328696 | + | 0.569319i | ||||
\(383\) | 30.3399 | − | 17.5167i | 1.55029 | − | 0.895063i | 0.552177 | − | 0.833727i | \(-0.313797\pi\) |
0.998117 | − | 0.0613362i | \(-0.0195362\pi\) | |||||||
\(384\) | 2.81361i | 0.143581i | ||||||||
\(385\) | 17.9166 | + | 10.3441i | 0.913114 | + | 0.527187i | ||||
\(386\) | −6.44839 | + | 11.1689i | −0.328214 | + | 0.568484i | ||||
\(387\) | −7.15550 | − | 4.13123i | −0.363734 | − | 0.210002i | ||||
\(388\) | 4.29785 | − | 2.48137i | 0.218190 | − | 0.125972i | ||||
\(389\) | 23.5689 | − | 13.6075i | 1.19499 | − | 0.689927i | 0.235555 | − | 0.971861i | \(-0.424309\pi\) |
0.959434 | + | 0.281934i | \(0.0909758\pi\) | |||||||
\(390\) | 7.18643 | + | 4.14909i | 0.363899 | + | 0.210097i | ||||
\(391\) | −3.69758 | + | 6.40439i | −0.186995 | + | 0.323884i | ||||
\(392\) | 7.44520 | + | 4.29849i | 0.376039 | + | 0.217106i | ||||
\(393\) | 11.1706i | 0.563481i | ||||||||
\(394\) | −8.72726 | + | 5.03868i | −0.439673 | + | 0.253845i | ||||
\(395\) | 4.08446 | − | 7.07449i | 0.205511 | − | 0.355956i | ||||
\(396\) | 25.7543 | 1.29420 | ||||||||
\(397\) | 2.34614 | 0.117750 | 0.0588748 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588748 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(398\) | −0.456907 | + | 0.791387i | −0.0229027 | + | 0.0396686i | ||||
\(399\) | 53.9856i | 2.70266i | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | − | 20.5055i | − | 1.02400i | −0.858987 | − | 0.511998i | \(-0.828906\pi\) | ||
0.858987 | − | 0.511998i | \(-0.171094\pi\) | |||||||
\(402\) | 16.7912 | − | 9.69441i | 0.837469 | − | 0.483513i | ||||
\(403\) | −4.64046 | − | 8.03752i | −0.231158 | − | 0.400377i | ||||
\(404\) | −0.377756 | − | 0.654293i | −0.0187941 | − | 0.0325523i | ||||
\(405\) | 0.365171 | + | 0.210831i | 0.0181455 | + | 0.0104763i | ||||
\(406\) | 38.1884 | 1.89526 | ||||||||
\(407\) | 31.5327 | − | 4.58572i | 1.56302 | − | 0.227305i | ||||
\(408\) | −7.11178 | −0.352086 | ||||||||
\(409\) | −31.9761 | − | 18.4614i | −1.58112 | − | 0.912859i | −0.994697 | − | 0.102853i | \(-0.967203\pi\) |
−0.586421 | − | 0.810006i | \(-0.699464\pi\) | |||||||
\(410\) | 3.88220 | + | 6.72417i | 0.191728 | + | 0.332083i | ||||
\(411\) | 29.1913 | + | 50.5609i | 1.43990 | + | 2.49398i | ||||
\(412\) | 14.3220 | − | 8.26884i | 0.705597 | − | 0.407376i | ||||
\(413\) | 27.4268i | 1.34958i | ||||||||
\(414\) | −7.19197 | − | 12.4569i | −0.353466 | − | 0.612221i | ||||
\(415\) | 16.4180i | 0.805927i | ||||||||
\(416\) | 1.47465 | − | 2.55417i | 0.0723007 | − | 0.125228i | ||||
\(417\) | −50.9613 | −2.49558 | ||||||||
\(418\) | 25.4506 | 1.24483 | ||||||||
\(419\) | 4.73126 | − | 8.19479i | 0.231137 | − | 0.400342i | −0.727006 | − | 0.686631i | \(-0.759089\pi\) |
0.958143 | + | 0.286290i | \(0.0924220\pi\) | |||||||
\(420\) | 9.62308 | − | 5.55589i | 0.469558 | − | 0.271100i | ||||
\(421\) | 12.5632i | 0.612293i | 0.951984 | + | 0.306146i | \(0.0990397\pi\) | ||||
−0.951984 | + | 0.306146i | \(0.900960\pi\) | |||||||
\(422\) | 4.74229 | + | 2.73796i | 0.230851 | + | 0.133282i | ||||
\(423\) | −29.0572 | + | 50.3285i | −1.41281 | + | 2.44705i | ||||
\(424\) | 2.98644 | + | 1.72422i | 0.145034 | + | 0.0837357i | ||||
\(425\) | −2.18900 | + | 1.26382i | −0.106182 | + | 0.0613042i | ||||
\(426\) | −26.9986 | + | 15.5876i | −1.30809 | + | 0.755224i | ||||
\(427\) | 34.6103 | + | 19.9823i | 1.67491 | + | 0.967011i | ||||
\(428\) | 6.32318 | − | 10.9521i | 0.305643 | − | 0.529389i | ||||
\(429\) | −37.6459 | − | 21.7349i | −1.81756 | − | 1.04937i | ||||
\(430\) | 1.68060i | 0.0810456i | ||||||||
\(431\) | 24.7659 | − | 14.2986i | 1.19293 | − | 0.688740i | 0.233962 | − | 0.972246i | \(-0.424831\pi\) |
0.958971 | + | 0.283506i | \(0.0914975\pi\) | |||||||
\(432\) | 2.69597 | − | 4.66956i | 0.129710 | − | 0.224664i | ||||
\(433\) | −10.2506 | −0.492613 | −0.246306 | − | 0.969192i | \(-0.579217\pi\) | ||||
−0.246306 | + | 0.969192i | \(0.579217\pi\) | |||||||
\(434\) | −12.4278 | −0.596551 | ||||||||
\(435\) | 13.6033 | − | 23.5616i | 0.652228 | − | 1.12969i | ||||
\(436\) | − | 5.31979i | − | 0.254772i | ||||||
\(437\) | −7.10717 | − | 12.3100i | −0.339982 | − | 0.588866i | ||||
\(438\) | − | 2.87599i | − | 0.137420i | ||||||
\(439\) | −9.52996 | + | 5.50213i | −0.454840 | + | 0.262602i | −0.709872 | − | 0.704330i | \(-0.751247\pi\) |
0.255032 | + | 0.966933i | \(0.417914\pi\) | |||||||
\(440\) | −2.61923 | − | 4.53665i | −0.124867 | − | 0.216276i | ||||
\(441\) | −21.1330 | − | 36.6035i | −1.00633 | − | 1.74302i | ||||
\(442\) | 6.45602 | + | 3.72738i | 0.307081 | + | 0.177294i | ||||
\(443\) | 3.49848 | 0.166218 | 0.0831089 | − | 0.996540i | \(-0.473515\pi\) | ||||
0.0831089 | + | 0.996540i | \(0.473515\pi\) | |||||||
\(444\) | 6.33514 | − | 15.8988i | 0.300653 | − | 0.754524i | ||||
\(445\) | −2.47982 | −0.117555 | ||||||||
\(446\) | −10.9396 | − | 6.31598i | −0.518005 | − | 0.299070i | ||||
\(447\) | −22.6825 | − | 39.2872i | −1.07284 | − | 1.85822i | ||||
\(448\) | −1.97465 | − | 3.42019i | −0.0932935 | − | 0.161589i | ||||
\(449\) | 13.6898 | − | 7.90382i | 0.646063 | − | 0.373005i | −0.140883 | − | 0.990026i | \(-0.544994\pi\) |
0.786946 | + | 0.617022i | \(0.211661\pi\) | |||||||
\(450\) | − | 4.91638i | − | 0.231760i | ||||||
\(451\) | −20.3368 | − | 35.2243i | −0.957622 | − | 1.65865i | ||||
\(452\) | 8.64005i | 0.406394i | ||||||||
\(453\) | −7.51691 | + | 13.0197i | −0.353175 | + | 0.611717i | ||||
\(454\) | −23.8261 | −1.11821 | ||||||||
\(455\) | −11.6477 | −0.546052 | ||||||||
\(456\) | 6.83483 | − | 11.8383i | 0.320070 | − | 0.554378i | ||||
\(457\) | 23.8050 | − | 13.7438i | 1.11355 | − | 0.642908i | 0.173803 | − | 0.984780i | \(-0.444394\pi\) |
0.939746 | + | 0.341873i | \(0.111061\pi\) | |||||||
\(458\) | 9.24449i | 0.431967i | ||||||||
\(459\) | 11.8030 | + | 6.81444i | 0.550915 | + | 0.318071i | ||||
\(460\) | −1.46286 | + | 2.53375i | −0.0682061 | + | 0.118137i | ||||
\(461\) | −17.9712 | − | 10.3757i | −0.837002 | − | 0.483243i | 0.0192421 | − | 0.999815i | \(-0.493875\pi\) |
−0.856244 | + | 0.516572i | \(0.827208\pi\) | |||||||
\(462\) | −50.4102 | + | 29.1044i | −2.34530 | + | 1.35406i | ||||
\(463\) | 12.5685 | − | 7.25643i | 0.584108 | − | 0.337235i | −0.178656 | − | 0.983912i | \(-0.557175\pi\) |
0.762764 | + | 0.646677i | \(0.223842\pi\) | |||||||
\(464\) | −8.37416 | − | 4.83483i | −0.388761 | − | 0.224451i | ||||
\(465\) | −4.42696 | + | 7.66772i | −0.205295 | + | 0.355582i | ||||
\(466\) | 1.55617 | + | 0.898453i | 0.0720880 | + | 0.0416200i | ||||
\(467\) | 1.19790i | 0.0554322i | 0.999616 | + | 0.0277161i | \(0.00882343\pi\) | ||||
−0.999616 | + | 0.0277161i | \(0.991177\pi\) | |||||||
\(468\) | −12.5573 | + | 7.24994i | −0.580460 | + | 0.335129i | ||||
\(469\) | −13.6075 | + | 23.5689i | −0.628336 | + | 1.08831i | ||||
\(470\) | 11.8205 | 0.545241 | ||||||||
\(471\) | −39.8574 | −1.83653 | ||||||||
\(472\) | 3.47236 | − | 6.01430i | 0.159828 | − | 0.276830i | ||||
\(473\) | − | 8.80376i | − | 0.404797i | ||||||
\(474\) | 11.4921 | + | 19.9048i | 0.527848 | + | 0.914259i | ||||
\(475\) | − | 4.85841i | − | 0.222919i | ||||||
\(476\) | 8.64502 | − | 4.99120i | 0.396244 | − | 0.228771i | ||||
\(477\) | −8.47694 | − | 14.6825i | −0.388132 | − | 0.672265i | ||||
\(478\) | −0.487862 | − | 0.845001i | −0.0223143 | − | 0.0386495i | ||||
\(479\) | 12.0118 | + | 6.93504i | 0.548835 | + | 0.316870i | 0.748652 | − | 0.662963i | \(-0.230701\pi\) |
−0.199817 | + | 0.979833i | \(0.564035\pi\) | |||||||
\(480\) | −2.81361 | −0.128423 | ||||||||
\(481\) | −14.0838 | + | 11.1125i | −0.642165 | + | 0.506685i | ||||
\(482\) | −6.10881 | −0.278249 | ||||||||
\(483\) | 28.1544 | + | 16.2550i | 1.28107 | + | 0.739626i | ||||
\(484\) | 8.22078 | + | 14.2388i | 0.373672 | + | 0.647219i | ||||
\(485\) | 2.48137 | + | 4.29785i | 0.112673 | + | 0.195155i | ||||
\(486\) | 12.9812 | − | 7.49472i | 0.588841 | − | 0.339967i | ||||
\(487\) | − | 35.3465i | − | 1.60170i | −0.598862 | − | 0.800852i | \(-0.704380\pi\) | ||
0.598862 | − | 0.800852i | \(-0.295620\pi\) | |||||||
\(488\) | −5.05970 | − | 8.76366i | −0.229042 | − | 0.396712i | ||||
\(489\) | − | 3.17006i | − | 0.143355i | ||||||
\(490\) | −4.29849 | + | 7.44520i | −0.194186 | + | 0.336340i | ||||
\(491\) | −2.11115 | −0.0952751 | −0.0476375 | − | 0.998865i | \(-0.515169\pi\) | ||||
−0.0476375 | + | 0.998865i | \(0.515169\pi\) | |||||||
\(492\) | −21.8460 | −0.984892 | ||||||||
\(493\) | 12.2207 | − | 21.1669i | 0.550392 | − | 0.953307i | ||||
\(494\) | −12.4092 | + | 7.16446i | −0.558316 | + | 0.322344i | ||||
\(495\) | 25.7543i | 1.15757i | ||||||||
\(496\) | 2.72523 | + | 1.57341i | 0.122366 | + | 0.0706483i | ||||
\(497\) | 21.8795 | − | 37.8964i | 0.981430 | − | 1.69989i | ||||
\(498\) | −40.0049 | − | 23.0969i | −1.79266 | − | 1.03500i | ||||
\(499\) | 5.62547 | − | 3.24787i | 0.251831 | − | 0.145395i | −0.368772 | − | 0.929520i | \(-0.620222\pi\) |
0.620602 | + | 0.784126i | \(0.286888\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | −25.8227 | − | 14.9088i | −1.15367 | − | 0.666074i | ||||
\(502\) | 5.92066 | − | 10.2549i | 0.264252 | − | 0.457698i | ||||
\(503\) | −27.3930 | − | 15.8153i | −1.22139 | − | 0.705171i | −0.256177 | − | 0.966630i | \(-0.582463\pi\) |
−0.965215 | + | 0.261459i | \(0.915796\pi\) | |||||||
\(504\) | 19.4163i | 0.864869i | ||||||||
\(505\) | 0.654293 | − | 0.377756i | 0.0291157 | − | 0.0168099i | ||||
\(506\) | 7.66314 | − | 13.2730i | 0.340668 | − | 0.590055i | ||||
\(507\) | −12.1031 | −0.537516 | ||||||||
\(508\) | 8.09205 | 0.359027 | ||||||||
\(509\) | −19.7306 | + | 34.1744i | −0.874543 | + | 1.51475i | −0.0172943 | + | 0.999850i | \(0.505505\pi\) |
−0.857249 | + | 0.514903i | \(0.827828\pi\) | |||||||
\(510\) | − | 7.11178i | − | 0.314915i | ||||||
\(511\) | 2.01844 | + | 3.49603i | 0.0892903 | + | 0.154655i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −22.6866 | + | 13.0981i | −1.00164 | + | 0.578297i | ||||
\(514\) | −7.12467 | − | 12.3403i | −0.314256 | − | 0.544307i | ||||
\(515\) | 8.26884 | + | 14.3220i | 0.364369 | + | 0.631105i | ||||
\(516\) | −4.09503 | − | 2.36427i | −0.180274 | − | 0.104081i | ||||
\(517\) | −61.9216 | −2.72331 | ||||||||
\(518\) | 3.45719 | + | 23.7726i | 0.151900 | + | 1.04451i | ||||
\(519\) | 43.6345 | 1.91534 | ||||||||
\(520\) | 2.55417 | + | 1.47465i | 0.112008 | + | 0.0646677i | ||||
\(521\) | −3.16429 | − | 5.48070i | −0.138630 | − | 0.240114i | 0.788348 | − | 0.615229i | \(-0.210937\pi\) |
−0.926978 | + | 0.375115i | \(0.877603\pi\) | |||||||
\(522\) | 23.7698 | + | 41.1706i | 1.04038 | + | 1.80199i | ||||
\(523\) | 2.77181 | − | 1.60030i | 0.121203 | − | 0.0699764i | −0.438173 | − | 0.898891i | \(-0.644374\pi\) |
0.559376 | + | 0.828914i | \(0.311041\pi\) | |||||||
\(524\) | 3.97020i | 0.173439i | ||||||||
\(525\) | 5.55589 | + | 9.62308i | 0.242479 | + | 0.419986i | ||||
\(526\) | 19.6644i | 0.857410i | ||||||||
\(527\) | −3.97701 | + | 6.88839i | −0.173241 | + | 0.300063i | ||||
\(528\) | 14.7390 | 0.641432 | ||||||||
\(529\) | 14.4402 | 0.627834 | ||||||||
\(530\) | −1.72422 | + | 2.98644i | −0.0748955 | + | 0.129723i | ||||
\(531\) | −29.5686 | + | 17.0714i | −1.28317 | + | 0.740837i | ||||
\(532\) | 19.1873i | 0.831876i | ||||||||
\(533\) | 19.8316 | + | 11.4498i | 0.859002 | + | 0.495945i | ||||
\(534\) | 3.48862 | − | 6.04246i | 0.150967 | − | 0.261483i | ||||
\(535\) | 10.9521 | + | 6.32318i | 0.473500 | + | 0.273375i | ||||
\(536\) | 5.96786 | − | 3.44554i | 0.257772 | − | 0.148825i | ||||
\(537\) | −19.9040 | + | 11.4916i | −0.858921 | + | 0.495898i | ||||
\(538\) | −0.456016 | − | 0.263281i | −0.0196603 | − | 0.0113509i | ||||
\(539\) | 22.5175 | − | 39.0015i | 0.969898 | − | 1.67991i | ||||
\(540\) | 4.66956 | + | 2.69597i | 0.200946 | + | 0.116016i | ||||
\(541\) | − | 6.72644i | − | 0.289192i | −0.989491 | − | 0.144596i | \(-0.953812\pi\) | ||
0.989491 | − | 0.144596i | \(-0.0461883\pi\) | |||||||
\(542\) | −7.87019 | + | 4.54386i | −0.338054 | + | 0.195175i | ||||
\(543\) | 8.43736 | − | 14.6139i | 0.362082 | − | 0.627144i | ||||
\(544\) | −2.52764 | −0.108372 | ||||||||
\(545\) | 5.31979 | 0.227875 | ||||||||
\(546\) | 16.3860 | − | 28.3814i | 0.701256 | − | 1.21461i | ||||
\(547\) | − | 34.7721i | − | 1.48675i | −0.668877 | − | 0.743373i | \(-0.733225\pi\) | ||
0.668877 | − | 0.743373i | \(-0.266775\pi\) | |||||||
\(548\) | 10.3751 | + | 17.9701i | 0.443201 | + | 0.767646i | ||||
\(549\) | 49.7509i | 2.12331i | ||||||||
\(550\) | 4.53665 | − | 2.61923i | 0.193443 | − | 0.111685i | ||||
\(551\) | 23.4896 | + | 40.6851i | 1.00069 | + | 1.73324i | ||||
\(552\) | −4.11591 | − | 7.12896i | −0.175185 | − | 0.303429i | ||||
\(553\) | −27.9393 | − | 16.1308i | −1.18810 | − | 0.685949i | ||||
\(554\) | 30.6175 | 1.30081 | ||||||||
\(555\) | 15.8988 | + | 6.33514i | 0.674867 | + | 0.268912i | ||||
\(556\) | −18.1124 | −0.768139 | ||||||||
\(557\) | −5.21849 | − | 3.01290i | −0.221115 | − | 0.127661i | 0.385352 | − | 0.922770i | \(-0.374080\pi\) |
−0.606466 | + | 0.795109i | \(0.707413\pi\) | |||||||
\(558\) | −7.73549 | − | 13.3983i | −0.327469 | − | 0.567194i | ||||
\(559\) | 2.47829 | + | 4.29253i | 0.104821 | + | 0.181555i | ||||
\(560\) | 3.42019 | − | 1.97465i | 0.144530 | − | 0.0834442i | ||||
\(561\) | 37.2548i | 1.57290i | ||||||||
\(562\) | 8.24138 | + | 14.2745i | 0.347642 | + | 0.602133i | ||||
\(563\) | 30.3059i | 1.27724i | 0.769522 | + | 0.638620i | \(0.220495\pi\) | ||||
−0.769522 | + | 0.638620i | \(0.779505\pi\) | |||||||
\(564\) | −16.6292 | + | 28.8026i | −0.700215 | + | 1.21281i | ||||
\(565\) | −8.64005 | −0.363490 | ||||||||
\(566\) | 28.6540 | 1.20442 | ||||||||
\(567\) | 0.832637 | − | 1.44217i | 0.0349675 | − | 0.0605654i | ||||
\(568\) | −9.59572 | + | 5.54009i | −0.402628 | + | 0.232457i | ||||
\(569\) | − | 9.64599i | − | 0.404381i | −0.979346 | − | 0.202190i | \(-0.935194\pi\) | ||
0.979346 | − | 0.202190i | \(-0.0648060\pi\) | |||||||
\(570\) | 11.8383 | + | 6.83483i | 0.495850 | + | 0.286279i | ||||
\(571\) | 11.5120 | − | 19.9394i | 0.481762 | − | 0.834436i | −0.518019 | − | 0.855369i | \(-0.673330\pi\) |
0.999781 | + | 0.0209328i | \(0.00666361\pi\) | |||||||
\(572\) | −13.3799 | − | 7.72491i | −0.559443 | − | 0.322995i | ||||
\(573\) | 31.3076 | − | 18.0755i | 1.30790 | − | 0.755114i | ||||
\(574\) | 26.5558 | − | 15.3320i | 1.10842 | − | 0.639944i | ||||
\(575\) | −2.53375 | − | 1.46286i | −0.105665 | − | 0.0610054i | ||||
\(576\) | 2.45819 | − | 4.25771i | 0.102425 | − | 0.177405i | ||||
\(577\) | 28.1896 | + | 16.2753i | 1.17355 | + | 0.677548i | 0.954513 | − | 0.298169i | \(-0.0963760\pi\) |
0.219034 | + | 0.975717i | \(0.429709\pi\) | |||||||
\(578\) | 10.6110i | 0.441361i | ||||||||
\(579\) | 31.4250 | − | 18.1432i | 1.30598 | − | 0.754007i | ||||
\(580\) | 4.83483 | − | 8.37416i | 0.200755 | − | 0.347718i | ||||
\(581\) | 64.8395 | 2.69000 | ||||||||
\(582\) | −13.9632 | −0.578792 | ||||||||
\(583\) | 9.03229 | − | 15.6444i | 0.374079 | − | 0.647924i | ||||
\(584\) | − | 1.02217i | − | 0.0422978i | ||||||
\(585\) | −7.24994 | − | 12.5573i | −0.299748 | − | 0.519179i | ||||
\(586\) | 21.0743i | 0.870571i | ||||||||
\(587\) | −28.9200 | + | 16.6969i | −1.19365 | + | 0.689157i | −0.959133 | − | 0.282954i | \(-0.908685\pi\) |
−0.234521 | + | 0.972111i | \(0.575352\pi\) | |||||||
\(588\) | −12.0943 | − | 20.9479i | −0.498759 | − | 0.863876i | ||||
\(589\) | −7.64428 | − | 13.2403i | −0.314977 | − | 0.545556i | ||||
\(590\) | 6.01430 | + | 3.47236i | 0.247605 | + | 0.142955i | ||||
\(591\) | 28.3537 | 1.16632 | ||||||||
\(592\) | 2.25161 | − | 5.65069i | 0.0925406 | − | 0.232242i | ||||
\(593\) | 19.1069 | 0.784626 | 0.392313 | − | 0.919832i | \(-0.371675\pi\) | ||||
0.392313 | + | 0.919832i | \(0.371675\pi\) | |||||||
\(594\) | −24.4613 | − | 14.1228i | −1.00366 | − | 0.579464i | ||||
\(595\) | 4.99120 | + | 8.64502i | 0.204619 | + | 0.354411i | ||||
\(596\) | −8.06171 | − | 13.9633i | −0.330221 | − | 0.571959i | ||||
\(597\) | 2.22665 | − | 1.28556i | 0.0911308 | − | 0.0526144i | ||||
\(598\) | 8.62882i | 0.352859i | ||||||||
\(599\) | 0.677086 | + | 1.17275i | 0.0276650 | + | 0.0479172i | 0.879526 | − | 0.475850i | \(-0.157860\pi\) |
−0.851861 | + | 0.523767i | \(0.824526\pi\) | |||||||
\(600\) | − | 2.81361i | − | 0.114865i | ||||||
\(601\) | −14.4676 | + | 25.0586i | −0.590145 | + | 1.02216i | 0.404067 | + | 0.914729i | \(0.367596\pi\) |
−0.994212 | + | 0.107432i | \(0.965737\pi\) | |||||||
\(602\) | 6.63718 | 0.270511 | ||||||||
\(603\) | −33.8792 | −1.37967 | ||||||||
\(604\) | −2.67163 | + | 4.62739i | −0.108707 | + | 0.188286i | ||||
\(605\) | −14.2388 | + | 8.22078i | −0.578890 | + | 0.334222i | ||||
\(606\) | 2.12572i | 0.0863513i | ||||||||
\(607\) | −7.40617 | − | 4.27596i | −0.300607 | − | 0.173556i | 0.342108 | − | 0.939661i | \(-0.388859\pi\) |
−0.642716 | + | 0.766105i | \(0.722192\pi\) | |||||||
\(608\) | 2.42920 | − | 4.20751i | 0.0985173 | − | 0.170637i | ||||
\(609\) | −93.0519 | − | 53.7235i | −3.77065 | − | 2.17699i | ||||
\(610\) | 8.76366 | − | 5.05970i | 0.354830 | − | 0.204861i | ||||
\(611\) | 30.1917 | − | 17.4312i | 1.22142 | − | 0.705190i | ||||
\(612\) | 10.7620 | + | 6.21342i | 0.435026 | + | 0.251162i | ||||
\(613\) | −20.0120 | + | 34.6618i | −0.808278 | + | 1.39998i | 0.105777 | + | 0.994390i | \(0.466267\pi\) |
−0.914056 | + | 0.405589i | \(0.867066\pi\) | |||||||
\(614\) | −4.12838 | − | 2.38352i | −0.166608 | − | 0.0961911i | ||||
\(615\) | − | 21.8460i | − | 0.880914i | ||||||
\(616\) | −17.9166 | + | 10.3441i | −0.721880 | + | 0.416778i | ||||
\(617\) | 0.0533952 | − | 0.0924832i | 0.00214961 | − | 0.00372323i | −0.864949 | − | 0.501860i | \(-0.832649\pi\) |
0.867098 | + | 0.498137i | \(0.165982\pi\) | |||||||
\(618\) | −46.5305 | −1.87173 | ||||||||
\(619\) | 34.5582 | 1.38901 | 0.694505 | − | 0.719488i | \(-0.255623\pi\) | ||||
0.694505 | + | 0.719488i | \(0.255623\pi\) | |||||||
\(620\) | −1.57341 | + | 2.72523i | −0.0631897 | + | 0.109448i | ||||
\(621\) | 15.7753i | 0.633041i | ||||||||
\(622\) | 9.21894 | + | 15.9677i | 0.369646 | + | 0.640245i | ||||
\(623\) | 9.79355i | 0.392370i | ||||||||
\(624\) | −7.18643 | + | 4.14909i | −0.287687 | + | 0.166096i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 8.62591 | + | 14.9405i | 0.344761 | + | 0.597143i | ||||
\(627\) | −62.0144 | − | 35.8040i | −2.47662 | − | 1.42988i | ||||
\(628\) | −14.1660 | −0.565283 | ||||||||
\(629\) | 14.2829 | + | 5.69125i | 0.569496 | + | 0.226925i | ||||
\(630\) | −19.4163 | −0.773563 | ||||||||
\(631\) | 5.54791 | + | 3.20309i | 0.220859 | + | 0.127513i | 0.606348 | − | 0.795199i | \(-0.292634\pi\) |
−0.385489 | + | 0.922712i | \(0.625967\pi\) | |||||||
\(632\) | 4.08446 | + | 7.07449i | 0.162471 | + | 0.281408i | ||||
\(633\) | −7.70355 | − | 13.3429i | −0.306188 | − | 0.530334i | ||||
\(634\) | 28.2813 | − | 16.3282i | 1.12319 | − | 0.648477i | ||||
\(635\) | 8.09205i | 0.321123i | ||||||||
\(636\) | −4.85129 | − | 8.40267i | −0.192366 | − | 0.333188i | ||||
\(637\) | 25.3551i | 1.00460i | ||||||||
\(638\) | −25.3271 | + | 43.8678i | −1.00271 | + | 1.73674i | ||||
\(639\) | 54.4744 | 2.15497 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −14.9665 | + | 25.9228i | −0.591142 | + | 1.02389i | 0.402936 | + | 0.915228i | \(0.367990\pi\) |
−0.994079 | + | 0.108661i | \(0.965344\pi\) | |||||||
\(642\) | −30.8148 | + | 17.7910i | −1.21616 | + | 0.702153i | ||||
\(643\) | − | 15.8086i | − | 0.623431i | −0.950175 | − | 0.311716i | \(-0.899096\pi\) | ||
0.950175 | − | 0.311716i | \(-0.100904\pi\) | |||||||
\(644\) | 10.0065 | + | 5.77727i | 0.394312 | + | 0.227656i | ||||
\(645\) | 2.36427 | − | 4.09503i | 0.0930930 | − | 0.161242i | ||||
\(646\) | 10.6351 | + | 6.14015i | 0.418431 | + | 0.241581i | ||||
\(647\) | −9.27416 | + | 5.35444i | −0.364605 | + | 0.210505i | −0.671099 | − | 0.741368i | \(-0.734177\pi\) |
0.306494 | + | 0.951873i | \(0.400844\pi\) | |||||||
\(648\) | −0.365171 | + | 0.210831i | −0.0143453 | + | 0.00828224i | ||||
\(649\) | −31.5057 | − | 18.1898i | −1.23671 | − | 0.714013i | ||||
\(650\) | −1.47465 | + | 2.55417i | −0.0578406 | + | 0.100183i | ||||
\(651\) | 30.2821 | + | 17.4834i | 1.18685 | + | 0.685228i | ||||
\(652\) | − | 1.12669i | − | 0.0441246i | ||||||
\(653\) | −19.5406 | + | 11.2818i | −0.764682 | + | 0.441489i | −0.830974 | − | 0.556311i | \(-0.812216\pi\) |
0.0662922 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(654\) | −7.48389 | + | 12.9625i | −0.292643 | + | 0.506873i | ||||
\(655\) | −3.97020 | −0.155129 | ||||||||
\(656\) | −7.76440 | −0.303149 | ||||||||
\(657\) | −2.51270 | + | 4.35212i | −0.0980297 | + | 0.169792i | ||||
\(658\) | − | 46.6829i | − | 1.81989i | ||||||
\(659\) | 24.5615 | + | 42.5417i | 0.956779 | + | 1.65719i | 0.730243 | + | 0.683187i | \(0.239407\pi\) |
0.226536 | + | 0.974003i | \(0.427260\pi\) | |||||||
\(660\) | 14.7390i | 0.573714i | ||||||||
\(661\) | 10.6409 | − | 6.14350i | 0.413882 | − | 0.238955i | −0.278575 | − | 0.960415i | \(-0.589862\pi\) |
0.692456 | + | 0.721460i | \(0.256529\pi\) | |||||||
\(662\) | 7.09688 | + | 12.2922i | 0.275828 | + | 0.477749i | ||||
\(663\) | −10.4874 | − | 18.1647i | −0.407296 | − | 0.705458i | ||||
\(664\) | −14.2184 | − | 8.20899i | −0.551780 | − | 0.318571i | ||||
\(665\) | −19.1873 | −0.744052 | ||||||||
\(666\) | −23.4772 | + | 18.5241i | −0.909722 | + | 0.717795i | ||||
\(667\) | 28.2907 | 1.09542 | ||||||||
\(668\) | −9.17780 | − | 5.29881i | −0.355100 | − | 0.205017i | ||||
\(669\) | 17.7707 | + | 30.7797i | 0.687054 | + | 1.19001i | ||||
\(670\) | 3.44554 | + | 5.96786i | 0.133113 | + | 0.230558i | ||||
\(671\) | −45.9082 | + | 26.5051i | −1.77227 | + | 1.02322i | ||||
\(672\) | 11.1118i | 0.428646i | ||||||||
\(673\) | −8.94312 | − | 15.4899i | −0.344732 | − | 0.597093i | 0.640573 | − | 0.767897i | \(-0.278697\pi\) |
−0.985305 | + | 0.170804i | \(0.945364\pi\) | |||||||
\(674\) | − | 24.7316i | − | 0.952626i | ||||||
\(675\) | −2.69597 | + | 4.66956i | −0.103768 | + | 0.179731i | ||||
\(676\) | −4.30162 | −0.165447 | ||||||||
\(677\) | −39.4953 | −1.51793 | −0.758964 | − | 0.651133i | \(-0.774294\pi\) | ||||
−0.758964 | + | 0.651133i | \(0.774294\pi\) | |||||||
\(678\) | 12.1549 | − | 21.0528i | 0.466804 | − | 0.808529i | ||||
\(679\) | 16.9735 | − | 9.79966i | 0.651384 | − | 0.376076i | ||||
\(680\) | − | 2.52764i | − | 0.0969305i | ||||||
\(681\) | 58.0560 | + | 33.5187i | 2.22471 | + | 1.28444i | ||||
\(682\) | 8.24227 | − | 14.2760i | 0.315613 | − | 0.546657i | ||||
\(683\) | 16.2450 | + | 9.37906i | 0.621598 | + | 0.358880i | 0.777491 | − | 0.628894i | \(-0.216492\pi\) |
−0.155893 | + | 0.987774i | \(0.549825\pi\) | |||||||
\(684\) | −20.6857 | + | 11.9429i | −0.790938 | + | 0.456648i | ||||
\(685\) | −17.9701 | + | 10.3751i | −0.686603 | + | 0.396411i | ||||
\(686\) | 5.46198 | + | 3.15347i | 0.208539 | + | 0.120400i | ||||
\(687\) | 13.0052 | − | 22.5256i | 0.496178 | − | 0.859406i | ||||
\(688\) | −1.45544 | − | 0.840298i | −0.0554881 | − | 0.0320361i | ||||
\(689\) | 10.1705i | 0.387465i | ||||||||
\(690\) | 7.12896 | − | 4.11591i | 0.271395 | − | 0.156690i | ||||
\(691\) | 18.8718 | − | 32.6869i | 0.717916 | − | 1.24347i | −0.243907 | − | 0.969799i | \(-0.578429\pi\) |
0.961824 | − | 0.273669i | \(-0.0882374\pi\) | |||||||
\(692\) | 15.5084 | 0.589540 | ||||||||
\(693\) | 101.712 | 3.86370 | ||||||||
\(694\) | −4.05680 | + | 7.02659i | −0.153994 | + | 0.266726i | ||||
\(695\) | − | 18.1124i | − | 0.687044i | ||||||
\(696\) | 13.6033 | + | 23.5616i | 0.515632 | + | 0.893100i | ||||
\(697\) | − | 19.6256i | − | 0.743372i | ||||||
\(698\) | 20.7936 | − | 12.0052i | 0.787048 | − | 0.454402i | ||||
\(699\) | −2.52789 | − | 4.37844i | −0.0956137 | − | 0.165608i | ||||
\(700\) | 1.97465 | + | 3.42019i | 0.0746348 | + | 0.129271i | ||||
\(701\) | −8.56876 | − | 4.94718i | −0.323638 | − | 0.186852i | 0.329375 | − | 0.944199i | \(-0.393162\pi\) |
−0.653013 | + | 0.757347i | \(0.726495\pi\) | |||||||
\(702\) | 15.9025 | 0.600200 | ||||||||
\(703\) | −23.2003 | + | 18.3057i | −0.875017 | + | 0.690412i | ||||
\(704\) | 5.23847 | 0.197432 | ||||||||
\(705\) | −28.8026 | − | 16.6292i | −1.08477 | − | 0.626291i | ||||
\(706\) | −10.9067 | − | 18.8909i | −0.410479 | − | 0.710970i | ||||
\(707\) | −1.49187 | − | 2.58400i | −0.0561077 | − | 0.0971813i | ||||
\(708\) | −16.9219 | + | 9.76984i | −0.635963 | + | 0.367173i | ||||
\(709\) | 8.15882i | 0.306411i | 0.988194 | + | 0.153206i | \(0.0489597\pi\) | ||||
−0.988194 | + | 0.153206i | \(0.951040\pi\) | |||||||
\(710\) | −5.54009 | − | 9.59572i | −0.207916 | − | 0.360121i | ||||
\(711\) | − | 40.1615i | − | 1.50617i | ||||||
\(712\) | 1.23991 | − | 2.14759i | 0.0464676 | − | 0.0804842i | ||||
\(713\) | −9.20671 | −0.344794 | ||||||||
\(714\) | −28.0866 | −1.05111 | ||||||||
\(715\) | 7.72491 | − | 13.3799i | 0.288895 | − | 0.500381i | ||||
\(716\) | −7.07419 | + | 4.08429i | −0.264375 | + | 0.152637i | ||||
\(717\) | 2.74530i | 0.102525i | ||||||||
\(718\) | 12.6626 | + | 7.31078i | 0.472565 | + | 0.272836i | ||||
\(719\) | −21.5544 | + | 37.3334i | −0.803845 | + | 1.39230i | 0.113223 | + | 0.993570i | \(0.463883\pi\) |
−0.917068 | + | 0.398731i | \(0.869451\pi\) | |||||||
\(720\) | 4.25771 | + | 2.45819i | 0.158676 | + | 0.0916114i | ||||
\(721\) | 56.5621 | − | 32.6561i | 2.10648 | − | 1.21618i | ||||
\(722\) | −3.98730 | + | 2.30207i | −0.148392 | + | 0.0856742i | ||||
\(723\) | 14.8851 | + | 8.59390i | 0.553582 | + | 0.319611i | ||||
\(724\) | 2.99877 | − | 5.19403i | 0.111448 | − | 0.193034i | ||||
\(725\) | 8.37416 | + | 4.83483i | 0.311009 | + | 0.179561i | ||||
\(726\) | − | 46.2601i | − | 1.71687i | ||||||
\(727\) | 40.4823 | − | 23.3724i | 1.50140 | − | 0.866836i | 0.501406 | − | 0.865212i | \(-0.332816\pi\) |
0.999999 | − | 0.00162370i | \(-0.000516841\pi\) | |||||||
\(728\) | 5.82384 | − | 10.0872i | 0.215846 | − | 0.373856i | ||||
\(729\) | −43.4394 | −1.60887 | ||||||||
\(730\) | 1.02217 | 0.0378323 | ||||||||
\(731\) | 2.12397 | − | 3.67882i | 0.0785579 | − | 0.136066i | ||||
\(732\) | 28.4720i | 1.05236i | ||||||||
\(733\) | −4.55451 | − | 7.88864i | −0.168225 | − | 0.291373i | 0.769571 | − | 0.638561i | \(-0.220470\pi\) |
−0.937796 | + | 0.347188i | \(0.887137\pi\) | |||||||
\(734\) | 9.34420i | 0.344901i | ||||||||
\(735\) | 20.9479 | − | 12.0943i | 0.772674 | − | 0.446103i | ||||
\(736\) | −1.46286 | − | 2.53375i | −0.0539217 | − | 0.0933951i | ||||
\(737\) | −18.0494 | − | 31.2624i | −0.664857 | − | 1.15157i | ||||
\(738\) | 33.0586 | + | 19.0864i | 1.21690 | + | 0.702579i | ||||
\(739\) | −22.5334 | −0.828905 | −0.414453 | − | 0.910071i | \(-0.636027\pi\) | ||||
−0.414453 | + | 0.910071i | \(0.636027\pi\) | |||||||
\(740\) | 5.65069 | + | 2.25161i | 0.207723 | + | 0.0827708i | ||||
\(741\) | 40.3159 | 1.48104 | ||||||||
\(742\) | 11.7944 | + | 6.80948i | 0.432985 | + | 0.249984i | ||||
\(743\) | −4.07129 | − | 7.05169i | −0.149361 | − | 0.258701i | 0.781630 | − | 0.623742i | \(-0.214388\pi\) |
−0.930992 | + | 0.365041i | \(0.881055\pi\) | |||||||
\(744\) | −4.42696 | − | 7.66772i | −0.162300 | − | 0.281112i | ||||
\(745\) | 13.9633 | − | 8.06171i | 0.511576 | − | 0.295358i | ||||
\(746\) | − | 2.26740i | − | 0.0830154i | ||||||
\(747\) | 40.3585 | + | 69.9030i | 1.47664 | + | 2.55762i | ||||
\(748\) | 13.2410i | 0.484137i | ||||||||
\(749\) | 24.9722 | − | 43.2530i | 0.912463 | − | 1.58043i | ||||
\(750\) | 2.81361 | 0.102738 | ||||||||
\(751\) | −49.7026 | −1.81367 | −0.906837 | − | 0.421481i | \(-0.861511\pi\) | ||||
−0.906837 | + | 0.421481i | \(0.861511\pi\) | |||||||
\(752\) | −5.91027 | + | 10.2369i | −0.215526 | + | 0.373301i | ||||
\(753\) | −28.8532 | + | 16.6584i | −1.05147 | + | 0.607066i | ||||
\(754\) | − | 28.5187i | − | 1.03859i | ||||||
\(755\) | −4.62739 | − | 2.67163i | −0.168408 | − | 0.0972305i | ||||
\(756\) | 10.6472 | − | 18.4415i | 0.387235 | − | 0.670711i | ||||
\(757\) | 9.10485 | + | 5.25669i | 0.330921 | + | 0.191057i | 0.656250 | − | 0.754543i | \(-0.272142\pi\) |
−0.325329 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(758\) | −2.14096 | + | 1.23608i | −0.0777630 | + | 0.0448965i | ||||
\(759\) | −37.3449 | + | 21.5611i | −1.35553 | + | 0.782617i | ||||
\(760\) | 4.20751 | + | 2.42920i | 0.152622 | + | 0.0881165i | ||||
\(761\) | 1.43338 | − | 2.48268i | 0.0519598 | − | 0.0899971i | −0.838876 | − | 0.544323i | \(-0.816787\pi\) |
0.890835 | + | 0.454326i | \(0.150120\pi\) | |||||||
\(762\) | −19.7175 | − | 11.3839i | −0.714291 | − | 0.412396i | ||||
\(763\) | − | 21.0094i | − | 0.760593i | ||||||
\(764\) | 11.1272 | − | 6.42431i | 0.402569 | − | 0.232423i | ||||
\(765\) | −6.21342 | + | 10.7620i | −0.224647 | + | 0.389099i | ||||
\(766\) | −35.0335 | −1.26581 | ||||||||
\(767\) | 20.4820 | 0.739564 | ||||||||
\(768\) | 1.40680 | − | 2.43665i | 0.0507636 | − | 0.0879252i | ||||
\(769\) | 18.9984i | 0.685099i | 0.939500 | + | 0.342549i | \(0.111290\pi\) | ||||
−0.939500 | + | 0.342549i | \(0.888710\pi\) | |||||||
\(770\) | −10.3441 | − | 17.9166i | −0.372777 | − | 0.645669i | ||||
\(771\) | 40.0921i | 1.44388i | ||||||||
\(772\) | 11.1689 | − | 6.44839i | 0.401979 | − | 0.232083i | ||||
\(773\) | −1.36501 | − | 2.36427i | −0.0490960 | − | 0.0850368i | 0.840433 | − | 0.541915i | \(-0.182301\pi\) |
−0.889529 | + | 0.456879i | \(0.848967\pi\) | |||||||
\(774\) | 4.13123 | + | 7.15550i | 0.148494 | + | 0.257199i | ||||
\(775\) | −2.72523 | − | 1.57341i | −0.0978931 | − | 0.0565186i | ||||
\(776\) | −4.96273 | −0.178152 | ||||||||
\(777\) | 25.0194 | − | 62.7892i | 0.897565 | − | 2.25255i | ||||
\(778\) | −27.2150 | −0.975704 | ||||||||
\(779\) | 32.6688 | + | 18.8613i | 1.17048 | + | 0.675777i | ||||
\(780\) | −4.14909 | − | 7.18643i | −0.148561 | − | 0.257315i | ||||
\(781\) | 29.0216 | + | 50.2669i | 1.03847 | + | 1.79869i | ||||
\(782\) | 6.40439 | − | 3.69758i | 0.229021 | − | 0.132225i | ||||
\(783\) | − | 52.1382i | − | 1.86327i | ||||||
\(784\) | −4.29849 | − | 7.44520i | −0.153517 | − | 0.265900i | ||||
\(785\) | − | 14.1660i | − | 0.505605i | ||||||
\(786\) | 5.58529 | − | 9.67401i | 0.199221 | − | 0.345060i | ||||
\(787\) | 1.07558 | 0.0383404 | 0.0191702 | − | 0.999816i | \(-0.493898\pi\) | ||||
0.0191702 | + | 0.999816i | \(0.493898\pi\) | |||||||
\(788\) | 10.0774 | 0.358991 | ||||||||
\(789\) | 27.6640 | − | 47.9154i | 0.984864 | − | 1.70584i | ||||
\(790\) | −7.07449 | + | 4.08446i | −0.251699 | + | 0.145318i | ||||
\(791\) | 34.1222i | 1.21324i | ||||||||
\(792\) | −22.3039 | − | 12.8772i | −0.792534 | − | 0.457570i | ||||
\(793\) | 14.9226 | − | 25.8467i | 0.529917 | − | 0.917842i | ||||
\(794\) | −2.03182 | − | 1.17307i | −0.0721066 | − | 0.0416308i | ||||
\(795\) | 8.40267 | − | 4.85129i | 0.298012 | − | 0.172057i | ||||
\(796\) | 0.791387 | − | 0.456907i | 0.0280500 | − | 0.0161947i | ||||
\(797\) | −10.9159 | − | 6.30233i | −0.386663 | − | 0.223240i | 0.294050 | − | 0.955790i | \(-0.404997\pi\) |
−0.680713 | + | 0.732550i | \(0.738330\pi\) | |||||||
\(798\) | 26.9928 | − | 46.7529i | 0.955534 | − | 1.65503i | ||||
\(799\) | −25.8752 | − | 14.9390i | −0.915398 | − | 0.528505i | ||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −10.5584 | + | 6.09587i | −0.373061 | + | 0.215387i | ||||
\(802\) | −10.2527 | + | 17.7583i | −0.362037 | + | 0.627067i | ||||
\(803\) | −5.35463 | −0.188961 | ||||||||
\(804\) | −19.3888 | −0.683791 | ||||||||
\(805\) | −5.77727 | + | 10.0065i | −0.203622 | + | 0.352684i | ||||
\(806\) | 9.28093i | 0.326907i | ||||||||
\(807\) | 0.740770 | + | 1.28305i | 0.0260763 | + | 0.0451655i | ||||
\(808\) | 0.755513i | 0.0265788i | ||||||||
\(809\) | −7.43655 | + | 4.29349i | −0.261455 | + | 0.150951i | −0.624998 | − | 0.780626i | \(-0.714900\pi\) |
0.363543 | + | 0.931577i | \(0.381567\pi\) | |||||||
\(810\) | −0.210831 | − | 0.365171i | −0.00740786 | − | 0.0128308i | ||||
\(811\) | 8.94230 | + | 15.4885i | 0.314007 | + | 0.543876i | 0.979226 | − | 0.202773i | \(-0.0649952\pi\) |
−0.665219 | + | 0.746648i | \(0.731662\pi\) | |||||||
\(812\) | −33.0721 | − | 19.0942i | −1.16060 | − | 0.670074i | ||||
\(813\) | 25.5693 | 0.896753 | ||||||||
\(814\) | −29.6009 | − | 11.7950i | −1.03751 | − | 0.413414i | ||||
\(815\) | 1.12669 | 0.0394662 | ||||||||
\(816\) | 6.15898 | + | 3.55589i | 0.215607 | + | 0.124481i | ||||
\(817\) | 4.08251 | + | 7.07112i | 0.142829 | + | 0.247387i | ||||
\(818\) | 18.4614 | + | 31.9761i | 0.645489 | + | 1.11802i | ||||
\(819\) | −49.5924 | + | 28.6322i | −1.73290 | + | 1.00049i | ||||
\(820\) | − | 7.76440i | − | 0.271145i | ||||||
\(821\) | −12.4019 | − | 21.4808i | −0.432831 | − | 0.749685i | 0.564285 | − | 0.825580i | \(-0.309152\pi\) |
−0.997116 | + | 0.0758952i | \(0.975819\pi\) | |||||||
\(822\) | − | 58.3827i | − | 2.03633i | ||||||
\(823\) | −7.01240 | + | 12.1458i | −0.244437 | + | 0.423377i | −0.961973 | − | 0.273144i | \(-0.911936\pi\) |
0.717536 | + | 0.696521i | \(0.245270\pi\) | |||||||
\(824\) | −16.5377 | −0.576117 | ||||||||
\(825\) | −14.7390 | −0.513146 | ||||||||
\(826\) | 13.7134 | − | 23.7523i | 0.477150 | − | 0.826447i | ||||
\(827\) | −39.5761 | + | 22.8493i | −1.37620 | + | 0.794548i | −0.991699 | − | 0.128578i | \(-0.958959\pi\) |
−0.384498 | + | 0.923126i | \(0.625625\pi\) | |||||||
\(828\) | 14.3839i | 0.499877i | ||||||||
\(829\) | 15.8025 | + | 9.12361i | 0.548845 | + | 0.316876i | 0.748656 | − | 0.662959i | \(-0.230699\pi\) |
−0.199811 | + | 0.979834i | \(0.564033\pi\) | |||||||
\(830\) | 8.20899 | − | 14.2184i | 0.284938 | − | 0.493527i | ||||
\(831\) | −74.6042 | − | 43.0728i | −2.58799 | − | 1.49418i | ||||
\(832\) | −2.55417 | + | 1.47465i | −0.0885499 | + | 0.0511243i | ||||
\(833\) | 18.8188 | − | 10.8650i | 0.652032 | − | 0.376451i | ||||
\(834\) | 44.1338 | + | 25.4806i | 1.52823 | + | 0.882322i | ||||
\(835\) | 5.29881 | − | 9.17780i | 0.183373 | − | 0.317611i | ||||
\(836\) | −22.0409 | − | 12.7253i | −0.762300 | − | 0.440114i | ||||
\(837\) | 16.9675i | 0.586482i | ||||||||
\(838\) | −8.19479 | + | 4.73126i | −0.283084 | + | 0.163439i | ||||
\(839\) | 21.0651 | − | 36.4858i | 0.727247 | − | 1.25963i | −0.230795 | − | 0.973002i | \(-0.574133\pi\) |
0.958042 | − | 0.286627i | \(-0.0925341\pi\) | |||||||
\(840\) | −11.1118 | −0.383393 | ||||||||
\(841\) | −64.5022 | −2.22421 | ||||||||
\(842\) | 6.28160 | − | 10.8800i | 0.216478 | − | 0.374951i | ||||
\(843\) | − | 46.3760i | − | 1.59727i | ||||||
\(844\) | −2.73796 | − | 4.74229i | −0.0942445 | − | 0.163236i | ||||
\(845\) | − | 4.30162i | − | 0.147980i | ||||||
\(846\) | 50.3285 | − | 29.0572i | 1.73033 | − | 0.999006i | ||||
\(847\) | 32.4663 | + | 56.2334i | 1.11556 | + | 1.93220i | ||||
\(848\) | −1.72422 | − | 2.98644i | −0.0592101 | − | 0.102555i | ||||
\(849\) | −69.8199 | − | 40.3105i | −2.39621 | − | 1.38345i | ||||
\(850\) | 2.52764 | 0.0866973 | ||||||||
\(851\) | 2.56115 | + | 17.6112i | 0.0877951 | + | 0.603704i | ||||
\(852\) | 31.1753 | 1.06805 | ||||||||
\(853\) | 14.9470 | + | 8.62964i | 0.511775 | + | 0.295473i | 0.733563 | − | 0.679622i | \(-0.237856\pi\) |
−0.221788 | + | 0.975095i | \(0.571189\pi\) | |||||||
\(854\) | −19.9823 | − | 34.6103i | −0.683780 | − | 1.18434i | ||||
\(855\) | −11.9429 | − | 20.6857i | −0.408438 | − | 0.707436i | ||||
\(856\) | −10.9521 | + | 6.32318i | −0.374334 | + | 0.216122i | ||||
\(857\) | − | 35.1582i | − | 1.20098i | −0.799631 | − | 0.600491i | \(-0.794972\pi\) | ||
0.799631 | − | 0.600491i | \(-0.205028\pi\) | |||||||
\(858\) | 21.7349 | + | 37.6459i | 0.742016 | + | 1.28521i | ||||
\(859\) | 12.8084i | 0.437018i | 0.975835 | + | 0.218509i | \(0.0701193\pi\) | ||||
−0.975835 | + | 0.218509i | \(0.929881\pi\) | |||||||
\(860\) | 0.840298 | − | 1.45544i | 0.0286539 | − | 0.0496301i | ||||
\(861\) | −86.2763 | −2.94029 | ||||||||
\(862\) | −28.5972 | −0.974025 | ||||||||
\(863\) | 7.35393 | − | 12.7374i | 0.250331 | − | 0.433585i | −0.713286 | − | 0.700873i | \(-0.752794\pi\) |
0.963617 | + | 0.267288i | \(0.0861274\pi\) | |||||||
\(864\) | −4.66956 | + | 2.69597i | −0.158862 | + | 0.0917188i | ||||
\(865\) | 15.5084i | 0.527301i | ||||||||
\(866\) | 8.87728 | + | 5.12530i | 0.301662 | + | 0.174165i | ||||
\(867\) | 14.9277 | − | 25.8555i | 0.506970 | − | 0.878097i | ||||
\(868\) | 10.7627 | + | 6.21388i | 0.365311 | + | 0.210913i | ||||
\(869\) | 37.0595 | − | 21.3963i | 1.25716 | − | 0.725820i | ||||
\(870\) | −23.5616 | + | 13.6033i | −0.798813 | + | 0.461195i | ||||
\(871\) | 17.6010 | + | 10.1619i | 0.596387 | + | 0.344324i | ||||
\(872\) | −2.65989 | + | 4.60707i | −0.0900753 | + | 0.156015i | ||||
\(873\) | 21.1299 | + | 12.1993i | 0.715138 | + | 0.412885i | ||||
\(874\) | 14.2143i | 0.480807i | ||||||||
\(875\) | −3.42019 | + | 1.97465i | −0.115624 | + | 0.0667554i | ||||
\(876\) | −1.43800 | + | 2.49068i | −0.0485854 | + | 0.0841524i | ||||
\(877\) | 32.7004 | 1.10422 | 0.552108 | − | 0.833773i | \(-0.313824\pi\) | ||||
0.552108 | + | 0.833773i | \(0.313824\pi\) | |||||||
\(878\) | 11.0043 | 0.371376 | ||||||||
\(879\) | 29.6474 | − | 51.3508i | 0.999981 | − | 1.73202i | ||||
\(880\) | 5.23847i | 0.176589i | ||||||||
\(881\) | 14.8534 | + | 25.7268i | 0.500423 | + | 0.866759i | 1.00000 | 0.000488989i | \(0.000155650\pi\) | |
−0.499576 | + | 0.866270i | \(0.666511\pi\) | |||||||
\(882\) | 42.2660i | 1.42317i | ||||||||
\(883\) | −26.6656 | + | 15.3954i | −0.897368 | + | 0.518096i | −0.876345 | − | 0.481683i | \(-0.840026\pi\) |
−0.0210227 | + | 0.999779i | \(0.506692\pi\) | |||||||
\(884\) | −3.72738 | − | 6.45602i | −0.125365 | − | 0.217139i | ||||
\(885\) | −9.76984 | − | 16.9219i | −0.328410 | − | 0.568822i | ||||
\(886\) | −3.02977 | − | 1.74924i | −0.101787 | − | 0.0587669i | ||||
\(887\) | 1.18778 | 0.0398817 | 0.0199409 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199409 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(888\) | −13.4358 | + | 10.6012i | −0.450876 | + | 0.355753i | ||||
\(889\) | 31.9579 | 1.07184 | ||||||||
\(890\) | 2.14759 | + | 1.23991i | 0.0719872 | + | 0.0415619i | ||||
\(891\) | 1.10443 | + | 1.91294i | 0.0369999 | + | 0.0640858i | ||||
\(892\) | 6.31598 | + | 10.9396i | 0.211475 | + | 0.366285i | ||||
\(893\) | 49.7350 | − | 28.7145i | 1.66432 | − | 0.960895i | ||||
\(894\) | 45.3650i | 1.51723i | ||||||||
\(895\) | −4.08429 | − | 7.07419i | −0.136523 | − | 0.236464i | ||||
\(896\) | 3.94930i | 0.131937i | ||||||||
\(897\) | 12.1391 | − | 21.0255i | 0.405311 | − | 0.702020i | ||||
\(898\) | −15.8076 | −0.527508 | ||||||||
\(899\) | 30.4287 | 1.01485 | ||||||||
\(900\) | −2.45819 | + | 4.25771i | −0.0819397 | + | 0.141924i | ||||
\(901\) | 7.54864 | − | 4.35821i | 0.251482 | − | 0.145193i | ||||
\(902\) | 40.6736i | 1.35428i | ||||||||
\(903\) | −16.1725 | − | 9.33721i | −0.538188 | − | 0.310723i | ||||
\(904\) | 4.32003 | − | 7.48250i | 0.143682 | − | 0.248864i | ||||
\(905\) | 5.19403 | + | 2.99877i | 0.172655 | + | 0.0996825i | ||||
\(906\) | 13.0197 | − | 7.51691i | 0.432549 | − | 0.249733i | ||||
\(907\) | 23.3777 | − | 13.4971i | 0.776244 | − | 0.448165i | −0.0588537 | − | 0.998267i | \(-0.518745\pi\) |
0.835097 | + | 0.550102i | \(0.185411\pi\) | |||||||
\(908\) | 20.6340 | + | 11.9131i | 0.684764 | + | 0.395349i | ||||
\(909\) | 1.85719 | − | 3.21675i | 0.0615992 | − | 0.106693i | ||||
\(910\) | 10.0872 | + | 5.82384i | 0.334387 | + | 0.193058i | ||||
\(911\) | 28.3992i | 0.940908i | 0.882425 | + | 0.470454i | \(0.155910\pi\) | ||||
−0.882425 | + | 0.470454i | \(0.844090\pi\) | |||||||
\(912\) | −11.8383 | + | 6.83483i | −0.392004 | + | 0.226324i | ||||
\(913\) | −43.0025 | + | 74.4826i | −1.42318 | + | 2.46501i | ||||
\(914\) | −27.4876 | −0.909209 | ||||||||
\(915\) | −28.4720 | −0.941256 | ||||||||
\(916\) | 4.62224 | − | 8.00596i | 0.152723 | − | 0.264524i | ||||
\(917\) | 15.6795i | 0.517783i | ||||||||
\(918\) | −6.81444 | − | 11.8030i | −0.224910 | − | 0.389556i | ||||
\(919\) | − | 33.2492i | − | 1.09679i | −0.836219 | − | 0.548395i | \(-0.815239\pi\) | ||
0.836219 | − | 0.548395i | \(-0.184761\pi\) | |||||||
\(920\) | 2.53375 | − | 1.46286i | 0.0835351 | − | 0.0482290i | ||||
\(921\) | 6.70629 | + | 11.6156i | 0.220980 | + | 0.382748i | ||||
\(922\) | 10.3757 | + | 17.9712i | 0.341705 | + | 0.591850i | ||||
\(923\) | −28.3007 | − | 16.3394i | −0.931528 | − | 0.537818i | ||||
\(924\) | 58.2087 | 1.91493 | ||||||||
\(925\) | −2.25161 | + | 5.65069i | −0.0740325 | + | 0.185793i | ||||
\(926\) | −14.5129 | −0.476922 | ||||||||
\(927\) | 70.4127 | + | 40.6528i | 2.31265 | + | 1.33521i | ||||
\(928\) | 4.83483 | + | 8.37416i | 0.158711 | + | 0.274895i | ||||
\(929\) | 20.2744 | + | 35.1164i | 0.665183 | + | 1.15213i | 0.979236 | + | 0.202725i | \(0.0649797\pi\) |
−0.314053 | + | 0.949405i | \(0.601687\pi\) | |||||||
\(930\) | 7.66772 | − | 4.42696i | 0.251434 | − | 0.145166i | ||||
\(931\) | 41.7676i | 1.36888i | ||||||||
\(932\) | −0.898453 | − | 1.55617i | −0.0294298 | − | 0.0509739i | ||||
\(933\) | − | 51.8769i | − | 1.69838i | ||||||
\(934\) | 0.598950 | − | 1.03741i | 0.0195982 | − | 0.0339451i | ||||
\(935\) | −13.2410 | −0.433026 | ||||||||
\(936\) | 14.4999 | 0.473944 | ||||||||
\(937\) | 21.3445 | − | 36.9697i | 0.697294 | − | 1.20775i | −0.272107 | − | 0.962267i | \(-0.587721\pi\) |
0.969401 | − | 0.245482i | \(-0.0789461\pi\) | |||||||
\(938\) | 23.5689 | − | 13.6075i | 0.769551 | − | 0.444300i | ||||
\(939\) | − | 48.5398i | − | 1.58404i | ||||||
\(940\) | −10.2369 | − | 5.91027i | −0.333891 | − | 0.192772i | ||||
\(941\) | 13.5253 | − | 23.4265i | 0.440912 | − | 0.763682i | −0.556845 | − | 0.830616i | \(-0.687988\pi\) |
0.997757 | + | 0.0669343i | \(0.0213218\pi\) | |||||||
\(942\) | 34.5175 | + | 19.9287i | 1.12464 | + | 0.649313i | ||||
\(943\) | 19.6730 | − | 11.3582i | 0.640641 | − | 0.369874i | ||||
\(944\) | −6.01430 | + | 3.47236i | −0.195749 | + | 0.113016i | ||||
\(945\) | 18.4415 | + | 10.6472i | 0.599902 | + | 0.346354i | ||||
\(946\) | −4.40188 | + | 7.62428i | −0.143117 | + | 0.247887i | ||||
\(947\) | −7.62016 | − | 4.39950i | −0.247622 | − | 0.142965i | 0.371053 | − | 0.928612i | \(-0.378997\pi\) |
−0.618675 | + | 0.785647i | \(0.712330\pi\) | |||||||
\(948\) | − | 22.9841i | − | 0.746489i | ||||||
\(949\) | 2.61080 | − | 1.50735i | 0.0847503 | − | 0.0489306i | ||||
\(950\) | −2.42920 | + | 4.20751i | −0.0788138 | + | 0.136510i | ||||
\(951\) | −91.8824 | −2.97949 | ||||||||
\(952\) | −9.98240 | −0.323532 | ||||||||
\(953\) | −13.9400 | + | 24.1447i | −0.451559 | + | 0.782124i | −0.998483 | − | 0.0550587i | \(-0.982465\pi\) |
0.546924 | + | 0.837182i | \(0.315799\pi\) | |||||||
\(954\) | 16.9539i | 0.548902i | ||||||||
\(955\) | 6.42431 | + | 11.1272i | 0.207886 | + | 0.360069i | ||||
\(956\) | 0.975723i | 0.0315571i | ||||||||
\(957\) | 123.427 | − | 71.2605i | 3.98982 | − | 2.30352i | ||||
\(958\) | −6.93504 | − | 12.0118i | −0.224061 | − | 0.388085i | ||||
\(959\) | 40.9742 | + | 70.9695i | 1.32313 | + | 2.29172i | ||||
\(960\) | 2.43665 | + | 1.40680i | 0.0786427 | + | 0.0454044i | ||||
\(961\) | 21.0975 | 0.680565 | ||||||||
\(962\) | 17.7531 | − | 2.58180i | 0.572384 | − | 0.0832404i | ||||
\(963\) | 62.1744 | 2.00354 | ||||||||
\(964\) | 5.29039 | + | 3.05441i | 0.170392 | + | 0.0983758i | ||||
\(965\) | 6.44839 | + | 11.1689i | 0.207581 | + | 0.359541i | ||||
\(966\) | −16.2550 | − | 28.1544i | −0.522995 | − | 0.905854i | ||||
\(967\) | −23.6814 | + | 13.6724i | −0.761541 | + | 0.439676i | −0.829849 | − | 0.557988i | \(-0.811573\pi\) |
0.0683075 | + | 0.997664i | \(0.478240\pi\) | |||||||
\(968\) | − | 16.4416i | − | 0.528452i | ||||||
\(969\) | −17.2760 | − | 29.9229i | −0.554984 | − | 0.961260i | ||||
\(970\) | − | 4.96273i | − | 0.159344i | ||||||
\(971\) | −13.2341 | + | 22.9221i | −0.424702 | + | 0.735606i | −0.996393 | − | 0.0848636i | \(-0.972955\pi\) |
0.571690 | + | 0.820469i | \(0.306288\pi\) | |||||||
\(972\) | −14.9894 | −0.480786 | ||||||||
\(973\) | −71.5315 | −2.29319 | ||||||||
\(974\) | −17.6733 | + | 30.6110i | −0.566288 | + | 0.980840i | ||||
\(975\) | 7.18643 | − | 4.14909i | 0.230150 | − | 0.132877i | ||||
\(976\) | 10.1194i | 0.323914i | ||||||||
\(977\) | −22.2269 | − | 12.8327i | −0.711101 | − | 0.410554i | 0.100367 | − | 0.994950i | \(-0.467998\pi\) |
−0.811469 | + | 0.584396i | \(0.801332\pi\) | |||||||
\(978\) | −1.58503 | + | 2.74536i | −0.0506837 | + | 0.0877868i | ||||
\(979\) | −11.2501 | − | 6.49523i | −0.359554 | − | 0.207588i | ||||
\(980\) | 7.44520 | − | 4.29849i | 0.237828 | − | 0.137310i | ||||
\(981\) | 22.6501 | − | 13.0770i | 0.723162 | − | 0.417518i | ||||
\(982\) | 1.82831 | + | 1.05558i | 0.0583438 | + | 0.0336848i | ||||
\(983\) | −7.32713 | + | 12.6910i | −0.233699 | + | 0.404779i | −0.958894 | − | 0.283765i | \(-0.908416\pi\) |
0.725195 | + | 0.688544i | \(0.241750\pi\) | |||||||
\(984\) | 18.9192 | + | 10.9230i | 0.603121 | + | 0.348212i | ||||
\(985\) | 10.0774i | 0.321092i | ||||||||
\(986\) | −21.1669 | + | 12.2207i | −0.674090 | + | 0.389186i | ||||
\(987\) | −65.6737 | + | 113.750i | −2.09042 | + | 3.62071i | ||||
\(988\) | 14.3289 | 0.455863 | ||||||||
\(989\) | 4.91695 | 0.156350 | ||||||||
\(990\) | 12.8772 | − | 22.3039i | 0.409263 | − | 0.708864i | ||||
\(991\) | 53.0936i | 1.68657i | 0.537463 | + | 0.843287i | \(0.319383\pi\) | ||||
−0.537463 | + | 0.843287i | \(0.680617\pi\) | |||||||
\(992\) | −1.57341 | − | 2.72523i | −0.0499559 | − | 0.0865261i | ||||
\(993\) | − | 39.9357i | − | 1.26732i | ||||||
\(994\) | −37.8964 | + | 21.8795i | −1.20200 | + | 0.693975i | ||||
\(995\) | 0.456907 | + | 0.791387i | 0.0144849 | + | 0.0250887i | ||||
\(996\) | 23.0969 | + | 40.0049i | 0.731852 | + | 1.26761i | ||||
\(997\) | 10.2660 | + | 5.92705i | 0.325126 | + | 0.187712i | 0.653675 | − | 0.756775i | \(-0.273226\pi\) |
−0.328549 | + | 0.944487i | \(0.606560\pi\) | |||||||
\(998\) | −6.49573 | −0.205619 | ||||||||
\(999\) | 32.4565 | − | 4.72007i | 1.02688 | − | 0.149336i |
(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 | 370.2.l.c.101.3 | yes | 12 | |
37.11 | even | 6 | inner | 370.2.l.c.11.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.l.c.11.3 | ✓ | 12 | 37.11 | even | 6 | inner | |
370.2.l.c.101.3 | yes | 12 | 1.1 | even | 1 | trivial |