Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(37,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.v (of order \(12\), degree \(4\), 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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 88.5 | ||
Character | \(\chi\) | \(=\) | 105.88 |
Dual form | 105.3.v.a.37.5 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91023 | − | 0.511845i | −0.955116 | − | 0.255922i | −0.252584 | − | 0.967575i | \(-0.581280\pi\) |
−0.702532 | + | 0.711653i | \(0.747947\pi\) | |||||||
\(3\) | −1.67303 | + | 0.448288i | −0.557678 | + | 0.149429i | ||||
\(4\) | −0.0771041 | − | 0.0445161i | −0.0192760 | − | 0.0111290i | ||||
\(5\) | −4.99333 | + | 0.258093i | −0.998667 | + | 0.0516186i | ||||
\(6\) | 3.42533 | 0.570889 | ||||||||
\(7\) | 6.99587 | − | 0.240410i | 0.999410 | − | 0.0343443i | ||||
\(8\) | 5.71805 | + | 5.71805i | 0.714756 | + | 0.714756i | ||||
\(9\) | 2.59808 | − | 1.50000i | 0.288675 | − | 0.166667i | ||||
\(10\) | 9.67053 | + | 2.06280i | 0.967053 | + | 0.206280i | ||||
\(11\) | 1.58449 | − | 2.74441i | 0.144044 | − | 0.249492i | −0.784972 | − | 0.619532i | \(-0.787323\pi\) |
0.929016 | + | 0.370040i | \(0.120656\pi\) | |||||||
\(12\) | 0.148954 | + | 0.0399120i | 0.0124128 | + | 0.00332600i | ||||
\(13\) | 11.0592 | + | 11.0592i | 0.850706 | + | 0.850706i | 0.990220 | − | 0.139514i | \(-0.0445541\pi\) |
−0.139514 | + | 0.990220i | \(0.544554\pi\) | |||||||
\(14\) | −13.4868 | − | 3.12156i | −0.963342 | − | 0.222969i | ||||
\(15\) | 8.23831 | − | 2.67025i | 0.549221 | − | 0.178017i | ||||
\(16\) | −7.81797 | − | 13.5411i | −0.488623 | − | 0.846320i | ||||
\(17\) | 4.27411 | + | 15.9512i | 0.251418 | + | 0.938305i | 0.970048 | + | 0.242912i | \(0.0781027\pi\) |
−0.718630 | + | 0.695392i | \(0.755231\pi\) | |||||||
\(18\) | −5.73069 | + | 1.53553i | −0.318372 | + | 0.0853075i | ||||
\(19\) | 24.9472 | − | 14.4033i | 1.31301 | − | 0.758066i | 0.330416 | − | 0.943836i | \(-0.392811\pi\) |
0.982593 | + | 0.185769i | \(0.0594778\pi\) | |||||||
\(20\) | 0.396496 | + | 0.202384i | 0.0198248 | + | 0.0101192i | ||||
\(21\) | −11.5965 | + | 3.53838i | −0.552216 | + | 0.168494i | ||||
\(22\) | −4.43145 | + | 4.43145i | −0.201429 | + | 0.201429i | ||||
\(23\) | −2.86298 | + | 10.6848i | −0.124477 | + | 0.464556i | −0.999820 | − | 0.0189465i | \(-0.993969\pi\) |
0.875343 | + | 0.483502i | \(0.160635\pi\) | |||||||
\(24\) | −12.1298 | − | 7.00315i | −0.505409 | − | 0.291798i | ||||
\(25\) | 24.8668 | − | 2.57749i | 0.994671 | − | 0.103100i | ||||
\(26\) | −15.4650 | − | 26.7862i | −0.594808 | − | 1.03024i | ||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | −0.550112 | − | 0.292892i | −0.0196469 | − | 0.0104604i | ||||
\(29\) | − | 20.9038i | − | 0.720822i | −0.932794 | − | 0.360411i | \(-0.882636\pi\) | ||
0.932794 | − | 0.360411i | \(-0.117364\pi\) | |||||||
\(30\) | −17.1038 | + | 0.884054i | −0.570128 | + | 0.0294685i | ||||
\(31\) | −30.4426 | + | 52.7281i | −0.982019 | + | 1.70091i | −0.327518 | + | 0.944845i | \(0.606212\pi\) |
−0.654501 | + | 0.756061i | \(0.727121\pi\) | |||||||
\(32\) | −0.368622 | − | 1.37572i | −0.0115194 | − | 0.0429912i | ||||
\(33\) | −1.42061 | + | 5.30179i | −0.0430488 | + | 0.160660i | ||||
\(34\) | − | 32.6581i | − | 0.960533i | ||||||
\(35\) | −34.8707 | + | 3.00603i | −0.996305 | + | 0.0858867i | ||||
\(36\) | −0.267096 | −0.00741934 | ||||||||
\(37\) | −4.96117 | − | 1.32934i | −0.134086 | − | 0.0359281i | 0.191152 | − | 0.981560i | \(-0.438778\pi\) |
−0.325238 | + | 0.945632i | \(0.605444\pi\) | |||||||
\(38\) | −55.0271 | + | 14.7445i | −1.44808 | + | 0.388012i | ||||
\(39\) | −23.4601 | − | 13.5447i | −0.601540 | − | 0.347299i | ||||
\(40\) | −30.0279 | − | 27.0763i | −0.750698 | − | 0.676908i | ||||
\(41\) | 0.605481 | 0.0147678 | 0.00738392 | − | 0.999973i | \(-0.497650\pi\) | ||||
0.00738392 | + | 0.999973i | \(0.497650\pi\) | |||||||
\(42\) | 23.9632 | − | 0.823485i | 0.570552 | − | 0.0196068i | ||||
\(43\) | 16.0752 | + | 16.0752i | 0.373842 | + | 0.373842i | 0.868874 | − | 0.495032i | \(-0.164844\pi\) |
−0.495032 | + | 0.868874i | \(0.664844\pi\) | |||||||
\(44\) | −0.244341 | + | 0.141070i | −0.00555320 | + | 0.00320614i | ||||
\(45\) | −12.5859 | + | 8.16055i | −0.279687 | + | 0.181345i | ||||
\(46\) | 10.9379 | − | 18.9450i | 0.237780 | − | 0.411848i | ||||
\(47\) | 34.1202 | + | 9.14247i | 0.725961 | + | 0.194521i | 0.602830 | − | 0.797870i | \(-0.294040\pi\) |
0.123131 | + | 0.992390i | \(0.460706\pi\) | |||||||
\(48\) | 19.1500 | + | 19.1500i | 0.398959 | + | 0.398959i | ||||
\(49\) | 48.8844 | − | 3.36376i | 0.997641 | − | 0.0686481i | ||||
\(50\) | −48.8206 | − | 7.80433i | −0.976411 | − | 0.156087i | ||||
\(51\) | −14.3014 | − | 24.7708i | −0.280420 | − | 0.485702i | ||||
\(52\) | −0.360397 | − | 1.34502i | −0.00693070 | − | 0.0258657i | ||||
\(53\) | 60.8242 | − | 16.2978i | 1.14763 | − | 0.307506i | 0.365613 | − | 0.930767i | \(-0.380859\pi\) |
0.782014 | + | 0.623261i | \(0.214193\pi\) | |||||||
\(54\) | 8.89928 | − | 5.13800i | 0.164801 | − | 0.0951481i | ||||
\(55\) | −7.20355 | + | 14.1127i | −0.130974 | + | 0.256595i | ||||
\(56\) | 41.3774 | + | 38.6280i | 0.738882 | + | 0.689786i | ||||
\(57\) | −35.2806 | + | 35.2806i | −0.618958 | + | 0.618958i | ||||
\(58\) | −10.6995 | + | 39.9312i | −0.184475 | + | 0.688469i | ||||
\(59\) | 88.6860 | + | 51.2029i | 1.50315 | + | 0.867845i | 0.999993 | + | 0.00365152i | \(0.00116232\pi\) |
0.503159 | + | 0.864194i | \(0.332171\pi\) | |||||||
\(60\) | −0.754076 | − | 0.160850i | −0.0125679 | − | 0.00268084i | ||||
\(61\) | −16.9814 | − | 29.4127i | −0.278384 | − | 0.482175i | 0.692599 | − | 0.721322i | \(-0.256465\pi\) |
−0.970983 | + | 0.239147i | \(0.923132\pi\) | |||||||
\(62\) | 85.1410 | − | 85.1410i | 1.37324 | − | 1.37324i | ||||
\(63\) | 17.8152 | − | 11.1184i | 0.282781 | − | 0.176483i | ||||
\(64\) | 65.3604i | 1.02126i | ||||||||
\(65\) | −58.0765 | − | 52.3679i | −0.893484 | − | 0.805659i | ||||
\(66\) | 5.42739 | − | 9.40052i | 0.0822332 | − | 0.142432i | ||||
\(67\) | −13.4604 | − | 50.2349i | −0.200902 | − | 0.749775i | −0.990660 | − | 0.136357i | \(-0.956461\pi\) |
0.789758 | − | 0.613418i | \(-0.210206\pi\) | |||||||
\(68\) | 0.380533 | − | 1.42017i | 0.00559607 | − | 0.0208848i | ||||
\(69\) | − | 19.1594i | − | 0.277673i | ||||||
\(70\) | 68.1497 | + | 12.1062i | 0.973567 | + | 0.172945i | ||||
\(71\) | 25.3750 | 0.357395 | 0.178697 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178697 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(72\) | 23.4330 | + | 6.27885i | 0.325458 | + | 0.0872063i | ||||
\(73\) | −86.1585 | + | 23.0861i | −1.18025 | + | 0.316248i | −0.795027 | − | 0.606574i | \(-0.792543\pi\) |
−0.385226 | + | 0.922822i | \(0.625877\pi\) | |||||||
\(74\) | 8.79656 | + | 5.07870i | 0.118872 | + | 0.0686310i | ||||
\(75\) | −40.4475 | + | 15.4597i | −0.539300 | + | 0.206129i | ||||
\(76\) | −2.56471 | −0.0337461 | ||||||||
\(77\) | 10.4251 | − | 19.5805i | 0.135391 | − | 0.254292i | ||||
\(78\) | 37.8814 | + | 37.8814i | 0.485658 | + | 0.485658i | ||||
\(79\) | 6.66046 | − | 3.84542i | 0.0843096 | − | 0.0486762i | −0.457253 | − | 0.889337i | \(-0.651166\pi\) |
0.541562 | + | 0.840661i | \(0.317833\pi\) | |||||||
\(80\) | 42.5326 | + | 65.5976i | 0.531658 | + | 0.819970i | ||||
\(81\) | 4.50000 | − | 7.79423i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.15661 | − | 0.309913i | −0.0141050 | − | 0.00377942i | ||||
\(83\) | 81.1873 | + | 81.1873i | 0.978160 | + | 0.978160i | 0.999767 | − | 0.0216065i | \(-0.00687811\pi\) |
−0.0216065 | + | 0.999767i | \(0.506878\pi\) | |||||||
\(84\) | 1.05166 | + | 0.243409i | 0.0125197 | + | 0.00289773i | ||||
\(85\) | −25.4589 | − | 78.5465i | −0.299517 | − | 0.924076i | ||||
\(86\) | −22.4793 | − | 38.9354i | −0.261388 | − | 0.452737i | ||||
\(87\) | 9.37094 | + | 34.9728i | 0.107712 | + | 0.401986i | ||||
\(88\) | 24.7528 | − | 6.63250i | 0.281282 | − | 0.0753693i | ||||
\(89\) | −35.6866 | + | 20.6037i | −0.400973 | + | 0.231502i | −0.686904 | − | 0.726748i | \(-0.741031\pi\) |
0.285931 | + | 0.958250i | \(0.407697\pi\) | |||||||
\(90\) | 28.2190 | − | 9.14649i | 0.313544 | − | 0.101628i | ||||
\(91\) | 80.0273 | + | 74.7098i | 0.879421 | + | 0.820987i | ||||
\(92\) | 0.696392 | − | 0.696392i | 0.00756947 | − | 0.00756947i | ||||
\(93\) | 27.2941 | − | 101.863i | 0.293485 | − | 1.09530i | ||||
\(94\) | −60.4979 | − | 34.9285i | −0.643594 | − | 0.371579i | ||||
\(95\) | −120.852 | + | 78.3590i | −1.27213 | + | 0.824831i | ||||
\(96\) | 1.23343 | + | 2.13637i | 0.0128483 | + | 0.0222539i | ||||
\(97\) | 1.74125 | − | 1.74125i | 0.0179511 | − | 0.0179511i | −0.698074 | − | 0.716025i | \(-0.745959\pi\) |
0.716025 | + | 0.698074i | \(0.245959\pi\) | |||||||
\(98\) | −95.1022 | − | 18.5957i | −0.970431 | − | 0.189752i | ||||
\(99\) | − | 9.50691i | − | 0.0960294i | ||||||
\(100\) | −2.03207 | − | 0.908236i | −0.0203207 | − | 0.00908236i | ||||
\(101\) | 75.1492 | − | 130.162i | 0.744051 | − | 1.28873i | −0.206586 | − | 0.978429i | \(-0.566235\pi\) |
0.950637 | − | 0.310306i | \(-0.100431\pi\) | |||||||
\(102\) | 14.6402 | + | 54.6381i | 0.143532 | + | 0.535668i | ||||
\(103\) | −38.0137 | + | 141.869i | −0.369065 | + | 1.37737i | 0.492760 | + | 0.870165i | \(0.335988\pi\) |
−0.861825 | + | 0.507205i | \(0.830679\pi\) | |||||||
\(104\) | 126.474i | 1.21609i | ||||||||
\(105\) | 56.9922 | − | 20.6613i | 0.542783 | − | 0.196774i | ||||
\(106\) | −124.530 | −1.17481 | ||||||||
\(107\) | −98.2349 | − | 26.3220i | −0.918083 | − | 0.246000i | −0.231317 | − | 0.972878i | \(-0.574304\pi\) |
−0.686766 | + | 0.726879i | \(0.740970\pi\) | |||||||
\(108\) | 0.446861 | − | 0.119736i | 0.00413760 | − | 0.00110867i | ||||
\(109\) | −104.505 | − | 60.3357i | −0.958757 | − | 0.553539i | −0.0629667 | − | 0.998016i | \(-0.520056\pi\) |
−0.895790 | + | 0.444477i | \(0.853390\pi\) | |||||||
\(110\) | 20.9840 | − | 23.2714i | 0.190763 | − | 0.211558i | ||||
\(111\) | 8.89612 | 0.0801452 | ||||||||
\(112\) | −57.9489 | − | 92.8524i | −0.517401 | − | 0.829040i | ||||
\(113\) | −152.659 | − | 152.659i | −1.35097 | − | 1.35097i | −0.884583 | − | 0.466383i | \(-0.845557\pi\) |
−0.466383 | − | 0.884583i | \(-0.654443\pi\) | |||||||
\(114\) | 85.4524 | − | 49.3359i | 0.749582 | − | 0.432771i | ||||
\(115\) | 11.5381 | − | 54.0916i | 0.100332 | − | 0.470362i | ||||
\(116\) | −0.930557 | + | 1.61177i | −0.00802204 | + | 0.0138946i | ||||
\(117\) | 45.3213 | + | 12.1438i | 0.387362 | + | 0.103793i | ||||
\(118\) | −143.203 | − | 143.203i | −1.21358 | − | 1.21358i | ||||
\(119\) | 33.7359 | + | 110.565i | 0.283495 | + | 0.929116i | ||||
\(120\) | 62.3756 | + | 31.8384i | 0.519797 | + | 0.265320i | ||||
\(121\) | 55.4788 | + | 96.0921i | 0.458503 | + | 0.794150i | ||||
\(122\) | 17.3837 | + | 64.8769i | 0.142489 | + | 0.531778i | ||||
\(123\) | −1.01299 | + | 0.271430i | −0.00823569 | + | 0.00220675i | ||||
\(124\) | 4.69449 | − | 2.71037i | 0.0378588 | − | 0.0218578i | ||||
\(125\) | −123.503 | + | 19.2882i | −0.988023 | + | 0.154306i | ||||
\(126\) | −39.7220 | + | 12.1201i | −0.315254 | + | 0.0961914i | ||||
\(127\) | −42.9287 | + | 42.9287i | −0.338021 | + | 0.338021i | −0.855622 | − | 0.517601i | \(-0.826825\pi\) |
0.517601 | + | 0.855622i | \(0.326825\pi\) | |||||||
\(128\) | 31.9799 | − | 119.351i | 0.249843 | − | 0.932426i | ||||
\(129\) | −34.1007 | − | 19.6880i | −0.264346 | − | 0.152620i | ||||
\(130\) | 84.1352 | + | 129.761i | 0.647194 | + | 0.998160i | ||||
\(131\) | −0.332730 | − | 0.576305i | −0.00253992 | − | 0.00439928i | 0.864753 | − | 0.502198i | \(-0.167475\pi\) |
−0.867293 | + | 0.497799i | \(0.834142\pi\) | |||||||
\(132\) | 0.345550 | − | 0.345550i | 0.00261780 | − | 0.00261780i | ||||
\(133\) | 171.064 | − | 106.761i | 1.28620 | − | 0.802713i | ||||
\(134\) | 102.850i | 0.767537i | ||||||||
\(135\) | 17.3984 | − | 19.2950i | 0.128877 | − | 0.142926i | ||||
\(136\) | −66.7700 | + | 115.649i | −0.490956 | + | 0.850361i | ||||
\(137\) | −21.7413 | − | 81.1397i | −0.158696 | − | 0.592261i | −0.998760 | − | 0.0497746i | \(-0.984150\pi\) |
0.840065 | − | 0.542486i | \(-0.182517\pi\) | |||||||
\(138\) | −9.80665 | + | 36.5989i | −0.0710627 | + | 0.265210i | ||||
\(139\) | − | 178.979i | − | 1.28762i | −0.765185 | − | 0.643810i | \(-0.777353\pi\) | ||
0.765185 | − | 0.643810i | \(-0.222647\pi\) | |||||||
\(140\) | 2.82249 | + | 1.32053i | 0.0201606 | + | 0.00943234i | ||||
\(141\) | −61.1826 | −0.433919 | ||||||||
\(142\) | −48.4722 | − | 12.9881i | −0.341353 | − | 0.0914654i | ||||
\(143\) | 47.8740 | − | 12.8278i | 0.334783 | − | 0.0897049i | ||||
\(144\) | −40.6234 | − | 23.4539i | −0.282107 | − | 0.162874i | ||||
\(145\) | 5.39513 | + | 104.380i | 0.0372078 | + | 0.719861i | ||||
\(146\) | 176.399 | 1.20821 | ||||||||
\(147\) | −80.2773 | + | 27.5420i | −0.546104 | + | 0.187360i | ||||
\(148\) | 0.323349 | + | 0.323349i | 0.00218479 | + | 0.00218479i | ||||
\(149\) | −5.12619 | + | 2.95961i | −0.0344039 | + | 0.0198631i | −0.517103 | − | 0.855923i | \(-0.672990\pi\) |
0.482699 | + | 0.875786i | \(0.339656\pi\) | |||||||
\(150\) | 85.1770 | − | 8.82876i | 0.567847 | − | 0.0588584i | ||||
\(151\) | 41.9842 | − | 72.7188i | 0.278041 | − | 0.481581i | −0.692857 | − | 0.721075i | \(-0.743648\pi\) |
0.970898 | + | 0.239494i | \(0.0769815\pi\) | |||||||
\(152\) | 225.008 | + | 60.2906i | 1.48031 | + | 0.396649i | ||||
\(153\) | 35.0312 | + | 35.0312i | 0.228962 | + | 0.228962i | ||||
\(154\) | −29.9365 | + | 32.0672i | −0.194393 | + | 0.208228i | ||||
\(155\) | 138.401 | − | 271.146i | 0.892911 | − | 1.74933i | ||||
\(156\) | 1.20591 | + | 2.08870i | 0.00773020 | + | 0.0133891i | ||||
\(157\) | 22.8585 | + | 85.3089i | 0.145595 | + | 0.543369i | 0.999728 | + | 0.0233142i | \(0.00742182\pi\) |
−0.854133 | + | 0.520055i | \(0.825912\pi\) | |||||||
\(158\) | −14.6913 | + | 3.93651i | −0.0929827 | + | 0.0249146i | ||||
\(159\) | −94.4548 | + | 54.5335i | −0.594055 | + | 0.342978i | ||||
\(160\) | 2.19572 | + | 6.77428i | 0.0137232 | + | 0.0423392i | ||||
\(161\) | −17.4603 | + | 75.4376i | −0.108449 | + | 0.468557i | ||||
\(162\) | −12.5855 | + | 12.5855i | −0.0776881 | + | 0.0776881i | ||||
\(163\) | −43.7619 | + | 163.321i | −0.268478 | + | 1.00197i | 0.691610 | + | 0.722272i | \(0.256902\pi\) |
−0.960087 | + | 0.279701i | \(0.909765\pi\) | |||||||
\(164\) | −0.0466851 | − | 0.0269537i | −0.000284665 | − | 0.000164352i | ||||
\(165\) | 5.72523 | − | 26.8403i | 0.0346984 | − | 0.162668i | ||||
\(166\) | −113.531 | − | 196.642i | −0.683923 | − | 1.18459i | ||||
\(167\) | −152.203 | + | 152.203i | −0.911395 | + | 0.911395i | −0.996382 | − | 0.0849869i | \(-0.972915\pi\) |
0.0849869 | + | 0.996382i | \(0.472915\pi\) | |||||||
\(168\) | −86.5422 | − | 46.0770i | −0.515132 | − | 0.274268i | ||||
\(169\) | 75.6107i | 0.447401i | ||||||||
\(170\) | 8.42883 | + | 163.073i | 0.0495813 | + | 0.959252i | ||||
\(171\) | 43.2098 | − | 74.8415i | 0.252689 | − | 0.437670i | ||||
\(172\) | −0.523859 | − | 1.95507i | −0.00304569 | − | 0.0113667i | ||||
\(173\) | −5.62237 | + | 20.9830i | −0.0324993 | + | 0.121289i | −0.980270 | − | 0.197664i | \(-0.936665\pi\) |
0.947771 | + | 0.318953i | \(0.103331\pi\) | |||||||
\(174\) | − | 71.6026i | − | 0.411509i | ||||||
\(175\) | 173.345 | − | 24.0100i | 0.990543 | − | 0.137200i | ||||
\(176\) | −49.5499 | −0.281533 | ||||||||
\(177\) | −171.328 | − | 45.9072i | −0.967956 | − | 0.259363i | ||||
\(178\) | 78.7155 | − | 21.0918i | 0.442222 | − | 0.118493i | ||||
\(179\) | −106.793 | − | 61.6572i | −0.596612 | − | 0.344454i | 0.171096 | − | 0.985254i | \(-0.445269\pi\) |
−0.767707 | + | 0.640801i | \(0.778603\pi\) | |||||||
\(180\) | 1.33370 | − | 0.0689357i | 0.00740945 | − | 0.000382976i | ||||
\(181\) | −58.5465 | −0.323462 | −0.161731 | − | 0.986835i | \(-0.551708\pi\) | ||||
−0.161731 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(182\) | −114.631 | − | 183.675i | −0.629839 | − | 1.00920i | ||||
\(183\) | 41.5958 | + | 41.5958i | 0.227299 | + | 0.227299i | ||||
\(184\) | −77.4667 | + | 44.7254i | −0.421015 | + | 0.243073i | ||||
\(185\) | 25.1159 | + | 5.35740i | 0.135761 | + | 0.0289589i | ||||
\(186\) | −104.276 | + | 180.611i | −0.560623 | + | 0.971028i | ||||
\(187\) | 50.5488 | + | 13.5445i | 0.270315 | + | 0.0724306i | ||||
\(188\) | −2.22382 | − | 2.22382i | −0.0118288 | − | 0.0118288i | ||||
\(189\) | −24.8211 | + | 26.5878i | −0.131329 | + | 0.140676i | ||||
\(190\) | 270.963 | − | 87.8261i | 1.42612 | − | 0.462243i | ||||
\(191\) | 138.752 | + | 240.325i | 0.726449 | + | 1.25825i | 0.958375 | + | 0.285514i | \(0.0921642\pi\) |
−0.231925 | + | 0.972734i | \(0.574502\pi\) | |||||||
\(192\) | −29.3003 | − | 109.350i | −0.152606 | − | 0.569532i | ||||
\(193\) | 361.420 | − | 96.8423i | 1.87265 | − | 0.501774i | 0.872737 | − | 0.488190i | \(-0.162343\pi\) |
0.999908 | − | 0.0135835i | \(-0.00432391\pi\) | |||||||
\(194\) | −4.21745 | + | 2.43494i | −0.0217394 | + | 0.0125513i | ||||
\(195\) | 120.640 | + | 61.5782i | 0.618665 | + | 0.315786i | ||||
\(196\) | −3.91893 | − | 1.91678i | −0.0199945 | − | 0.00977950i | ||||
\(197\) | 96.9859 | − | 96.9859i | 0.492314 | − | 0.492314i | −0.416720 | − | 0.909035i | \(-0.636821\pi\) |
0.909035 | + | 0.416720i | \(0.136821\pi\) | |||||||
\(198\) | −4.86607 | + | 18.1604i | −0.0245761 | + | 0.0917192i | ||||
\(199\) | −78.0408 | − | 45.0569i | −0.392165 | − | 0.226416i | 0.290933 | − | 0.956743i | \(-0.406034\pi\) |
−0.683098 | + | 0.730327i | \(0.739368\pi\) | |||||||
\(200\) | 156.928 | + | 127.451i | 0.784638 | + | 0.637256i | ||||
\(201\) | 45.0394 | + | 78.0106i | 0.224077 | + | 0.388112i | ||||
\(202\) | −210.175 | + | 210.175i | −1.04047 | + | 1.04047i | ||||
\(203\) | −5.02550 | − | 146.241i | −0.0247562 | − | 0.720397i | ||||
\(204\) | 2.54657i | 0.0124832i | ||||||||
\(205\) | −3.02337 | + | 0.156270i | −0.0147482 | + | 0.000762295i | ||||
\(206\) | 145.230 | − | 251.546i | 0.705000 | − | 1.22110i | ||||
\(207\) | 8.58893 | + | 32.0543i | 0.0414924 | + | 0.154852i | ||||
\(208\) | 63.2934 | − | 236.214i | 0.304295 | − | 1.13564i | ||||
\(209\) | − | 91.2870i | − | 0.436780i | ||||||
\(210\) | −119.444 | + | 10.2967i | −0.568779 | + | 0.0490317i | ||||
\(211\) | −3.83967 | −0.0181975 | −0.00909873 | − | 0.999959i | \(-0.502896\pi\) | ||||
−0.00909873 | + | 0.999959i | \(0.502896\pi\) | |||||||
\(212\) | −5.41531 | − | 1.45103i | −0.0255439 | − | 0.00684447i | ||||
\(213\) | −42.4533 | + | 11.3753i | −0.199311 | + | 0.0534052i | ||||
\(214\) | 174.179 | + | 100.562i | 0.813919 | + | 0.469916i | ||||
\(215\) | −84.4178 | − | 76.1200i | −0.392641 | − | 0.354046i | ||||
\(216\) | −42.0189 | −0.194532 | ||||||||
\(217\) | −200.296 | + | 376.198i | −0.923023 | + | 1.73363i | ||||
\(218\) | 168.745 | + | 168.745i | 0.774061 | + | 0.774061i | ||||
\(219\) | 133.797 | − | 77.2476i | 0.610944 | − | 0.352729i | ||||
\(220\) | 1.18367 | − | 0.767473i | 0.00538030 | − | 0.00348851i | ||||
\(221\) | −129.139 | + | 223.675i | −0.584338 | + | 1.01210i | ||||
\(222\) | −16.9936 | − | 4.55343i | −0.0765480 | − | 0.0205110i | ||||
\(223\) | −68.8218 | − | 68.8218i | −0.308618 | − | 0.308618i | 0.535755 | − | 0.844373i | \(-0.320027\pi\) |
−0.844373 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(224\) | −2.90957 | − | 9.53572i | −0.0129892 | − | 0.0425702i | ||||
\(225\) | 60.7395 | − | 43.9967i | 0.269954 | − | 0.195541i | ||||
\(226\) | 213.476 | + | 369.752i | 0.944586 | + | 1.63607i | ||||
\(227\) | −36.4264 | − | 135.945i | −0.160469 | − | 0.598878i | −0.998575 | − | 0.0533705i | \(-0.983004\pi\) |
0.838106 | − | 0.545508i | \(-0.183663\pi\) | |||||||
\(228\) | 4.29084 | − | 1.14973i | 0.0188195 | − | 0.00504266i | ||||
\(229\) | 143.125 | − | 82.6334i | 0.625001 | − | 0.360844i | −0.153813 | − | 0.988100i | \(-0.549155\pi\) |
0.778813 | + | 0.627256i | \(0.215822\pi\) | |||||||
\(230\) | −49.7270 | + | 97.4217i | −0.216204 | + | 0.423573i | ||||
\(231\) | −8.66381 | + | 37.4322i | −0.0375056 | + | 0.162044i | ||||
\(232\) | 119.529 | − | 119.529i | 0.515212 | − | 0.515212i | ||||
\(233\) | 68.7110 | − | 256.433i | 0.294897 | − | 1.10057i | −0.646402 | − | 0.762997i | \(-0.723727\pi\) |
0.941299 | − | 0.337574i | \(-0.109606\pi\) | |||||||
\(234\) | −80.3585 | − | 46.3950i | −0.343412 | − | 0.198269i | ||||
\(235\) | −172.733 | − | 36.8452i | −0.735034 | − | 0.156788i | ||||
\(236\) | −4.55870 | − | 7.89590i | −0.0193165 | − | 0.0334572i | ||||
\(237\) | −9.41931 | + | 9.41931i | −0.0397439 | + | 0.0397439i | ||||
\(238\) | −7.85135 | − | 228.472i | −0.0329889 | − | 0.959966i | ||||
\(239\) | 373.238i | 1.56167i | 0.624739 | + | 0.780834i | \(0.285205\pi\) | ||||
−0.624739 | + | 0.780834i | \(0.714795\pi\) | |||||||
\(240\) | −100.565 | − | 90.6801i | −0.419021 | − | 0.377834i | ||||
\(241\) | 193.813 | − | 335.694i | 0.804204 | − | 1.39292i | −0.112624 | − | 0.993638i | \(-0.535925\pi\) |
0.916827 | − | 0.399284i | \(-0.130741\pi\) | |||||||
\(242\) | −56.7931 | − | 211.955i | −0.234682 | − | 0.875846i | ||||
\(243\) | −4.03459 | + | 15.0573i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | 3.02378i | 0.0123926i | ||||||||
\(245\) | −243.228 | + | 29.4131i | −0.992767 | + | 0.120053i | ||||
\(246\) | 2.07398 | 0.00843079 | ||||||||
\(247\) | 435.183 | + | 116.607i | 1.76188 | + | 0.472093i | ||||
\(248\) | −475.574 | + | 127.430i | −1.91764 | + | 0.513829i | ||||
\(249\) | −172.224 | − | 99.4337i | −0.691664 | − | 0.399332i | ||||
\(250\) | 245.792 | + | 26.3694i | 0.983167 | + | 0.105478i | ||||
\(251\) | −24.1190 | −0.0960917 | −0.0480458 | − | 0.998845i | \(-0.515299\pi\) | ||||
−0.0480458 | + | 0.998845i | \(0.515299\pi\) | |||||||
\(252\) | −1.86857 | + | 0.0642127i | −0.00741497 | + | 0.000254812i | ||||
\(253\) | 24.7871 | + | 24.7871i | 0.0979726 | + | 0.0979726i | ||||
\(254\) | 103.977 | − | 60.0309i | 0.409357 | − | 0.236342i | ||||
\(255\) | 77.8050 | + | 119.998i | 0.305118 | + | 0.470580i | ||||
\(256\) | 8.54282 | − | 14.7966i | 0.0333704 | − | 0.0577992i | ||||
\(257\) | −194.693 | − | 52.1677i | −0.757558 | − | 0.202987i | −0.140690 | − | 0.990054i | \(-0.544932\pi\) |
−0.616868 | + | 0.787067i | \(0.711599\pi\) | |||||||
\(258\) | 55.0629 | + | 55.0629i | 0.213422 | + | 0.213422i | ||||
\(259\) | −35.0273 | − | 8.10718i | −0.135240 | − | 0.0313019i | ||||
\(260\) | 2.14672 | + | 6.62311i | 0.00825662 | + | 0.0254735i | ||||
\(261\) | −31.3558 | − | 54.3098i | −0.120137 | − | 0.208083i | ||||
\(262\) | 0.340612 | + | 1.27118i | 0.00130005 | + | 0.00485184i | ||||
\(263\) | −156.656 | + | 41.9758i | −0.595649 | + | 0.159604i | −0.544034 | − | 0.839063i | \(-0.683104\pi\) |
−0.0516156 | + | 0.998667i | \(0.516437\pi\) | |||||||
\(264\) | −38.4390 | + | 22.1928i | −0.145602 | + | 0.0840635i | ||||
\(265\) | −299.509 | + | 97.0786i | −1.13022 | + | 0.366334i | ||||
\(266\) | −381.418 | + | 116.379i | −1.43390 | + | 0.437517i | ||||
\(267\) | 50.4685 | − | 50.4685i | 0.189020 | − | 0.189020i | ||||
\(268\) | −1.19841 | + | 4.47252i | −0.00447168 | + | 0.0166885i | ||||
\(269\) | 69.3332 | + | 40.0295i | 0.257744 | + | 0.148809i | 0.623305 | − | 0.781979i | \(-0.285789\pi\) |
−0.365561 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(270\) | −43.1110 | + | 27.9526i | −0.159670 | + | 0.103528i | ||||
\(271\) | −230.600 | − | 399.411i | −0.850923 | − | 1.47384i | −0.880377 | − | 0.474275i | \(-0.842710\pi\) |
0.0294543 | − | 0.999566i | \(-0.490623\pi\) | |||||||
\(272\) | 182.582 | − | 182.582i | 0.671258 | − | 0.671258i | ||||
\(273\) | −167.380 | − | 89.1167i | −0.613113 | − | 0.326435i | ||||
\(274\) | 166.124i | 0.606291i | ||||||||
\(275\) | 32.3274 | − | 72.3286i | 0.117554 | − | 0.263013i | ||||
\(276\) | −0.852902 | + | 1.47727i | −0.00309022 | + | 0.00535243i | ||||
\(277\) | 44.5632 | + | 166.312i | 0.160878 | + | 0.600405i | 0.998530 | + | 0.0542008i | \(0.0172611\pi\) |
−0.837652 | + | 0.546204i | \(0.816072\pi\) | |||||||
\(278\) | −91.6096 | + | 341.892i | −0.329531 | + | 1.22983i | ||||
\(279\) | 182.655i | 0.654679i | ||||||||
\(280\) | −216.581 | − | 182.203i | −0.773503 | − | 0.650727i | ||||
\(281\) | 40.4440 | 0.143929 | 0.0719644 | − | 0.997407i | \(-0.477073\pi\) | ||||
0.0719644 | + | 0.997407i | \(0.477073\pi\) | |||||||
\(282\) | 116.873 | + | 31.3160i | 0.414443 | + | 0.111050i | ||||
\(283\) | −147.124 | + | 39.4218i | −0.519874 | + | 0.139300i | −0.509208 | − | 0.860643i | \(-0.670062\pi\) |
−0.0106656 | + | 0.999943i | \(0.503395\pi\) | |||||||
\(284\) | −1.95652 | − | 1.12960i | −0.00688915 | − | 0.00397745i | ||||
\(285\) | 167.062 | − | 185.274i | 0.586183 | − | 0.650083i | ||||
\(286\) | −98.0163 | −0.342714 | ||||||||
\(287\) | 4.23587 | − | 0.145564i | 0.0147591 | − | 0.000507192i | ||||
\(288\) | −3.02129 | − | 3.02129i | −0.0104906 | − | 0.0104906i | ||||
\(289\) | 14.1092 | − | 8.14597i | 0.0488209 | − | 0.0281867i | ||||
\(290\) | 43.1204 | − | 202.151i | 0.148691 | − | 0.697073i | ||||
\(291\) | −2.13259 | + | 3.69375i | −0.00732849 | + | 0.0126933i | ||||
\(292\) | 7.67087 | + | 2.05540i | 0.0262701 | + | 0.00703906i | ||||
\(293\) | −106.571 | − | 106.571i | −0.363722 | − | 0.363722i | 0.501459 | − | 0.865181i | \(-0.332797\pi\) |
−0.865181 | + | 0.501459i | \(0.832797\pi\) | |||||||
\(294\) | 167.445 | − | 11.5220i | 0.569542 | − | 0.0391904i | ||||
\(295\) | −456.054 | − | 232.784i | −1.54595 | − | 0.789098i | ||||
\(296\) | −20.7670 | − | 35.9694i | −0.0701586 | − | 0.121518i | ||||
\(297\) | 4.26183 | + | 15.9054i | 0.0143496 | + | 0.0535535i | ||||
\(298\) | 11.3071 | − | 3.02972i | 0.0379432 | − | 0.0101668i | ||||
\(299\) | −149.827 | + | 86.5027i | −0.501094 | + | 0.289307i | ||||
\(300\) | 3.80687 | + | 0.608557i | 0.0126896 | + | 0.00202852i | ||||
\(301\) | 116.325 | + | 108.595i | 0.386461 | + | 0.360782i | ||||
\(302\) | −117.420 | + | 117.420i | −0.388809 | + | 0.388809i | ||||
\(303\) | −67.3769 | + | 251.454i | −0.222366 | + | 0.829881i | ||||
\(304\) | −390.073 | − | 225.209i | −1.28313 | − | 0.740817i | ||||
\(305\) | 92.3851 | + | 142.485i | 0.302902 | + | 0.467162i | ||||
\(306\) | −48.9872 | − | 84.8483i | −0.160089 | − | 0.277282i | ||||
\(307\) | 196.397 | − | 196.397i | 0.639729 | − | 0.639729i | −0.310759 | − | 0.950489i | \(-0.600583\pi\) |
0.950489 | + | 0.310759i | \(0.100583\pi\) | |||||||
\(308\) | −1.67546 | + | 1.04565i | −0.00543981 | + | 0.00339497i | ||||
\(309\) | − | 254.393i | − | 0.823277i | ||||||
\(310\) | −403.163 | + | 447.112i | −1.30053 | + | 1.44230i | ||||
\(311\) | 92.9088 | − | 160.923i | 0.298742 | − | 0.517437i | −0.677106 | − | 0.735885i | \(-0.736766\pi\) |
0.975848 | + | 0.218449i | \(0.0700996\pi\) | |||||||
\(312\) | −56.6966 | − | 211.595i | −0.181720 | − | 0.678188i | ||||
\(313\) | −141.985 | + | 529.896i | −0.453627 | + | 1.69296i | 0.238468 | + | 0.971150i | \(0.423355\pi\) |
−0.692094 | + | 0.721807i | \(0.743312\pi\) | |||||||
\(314\) | − | 174.660i | − | 0.556241i | ||||||
\(315\) | −86.0876 | + | 60.1159i | −0.273294 | + | 0.190844i | ||||
\(316\) | −0.684731 | −0.00216687 | ||||||||
\(317\) | −47.1593 | − | 12.6363i | −0.148768 | − | 0.0398622i | 0.183667 | − | 0.982989i | \(-0.441203\pi\) |
−0.332434 | + | 0.943126i | \(0.607870\pi\) | |||||||
\(318\) | 208.343 | − | 55.8254i | 0.655167 | − | 0.175551i | ||||
\(319\) | −57.3687 | − | 33.1218i | −0.179839 | − | 0.103830i | ||||
\(320\) | −16.8691 | − | 326.366i | −0.0527158 | − | 1.01989i | ||||
\(321\) | 176.150 | 0.548754 | ||||||||
\(322\) | 71.9655 | − | 135.166i | 0.223495 | − | 0.419771i | ||||
\(323\) | 336.376 | + | 336.376i | 1.04141 | + | 1.04141i | ||||
\(324\) | −0.693937 | + | 0.400645i | −0.00214178 | + | 0.00123656i | ||||
\(325\) | 303.511 | + | 246.501i | 0.933880 | + | 0.758465i | ||||
\(326\) | 167.191 | − | 289.583i | 0.512854 | − | 0.888290i | ||||
\(327\) | 201.887 | + | 54.0955i | 0.617392 | + | 0.165430i | ||||
\(328\) | 3.46217 | + | 3.46217i | 0.0105554 | + | 0.0105554i | ||||
\(329\) | 240.898 | + | 55.7567i | 0.732213 | + | 0.169473i | ||||
\(330\) | −24.6746 | + | 48.3407i | −0.0747714 | + | 0.146487i | ||||
\(331\) | −11.1043 | − | 19.2332i | −0.0335477 | − | 0.0581063i | 0.848764 | − | 0.528772i | \(-0.177347\pi\) |
−0.882312 | + | 0.470665i | \(0.844014\pi\) | |||||||
\(332\) | −2.64573 | − | 9.87401i | −0.00796908 | − | 0.0297410i | ||||
\(333\) | −14.8835 | + | 3.98802i | −0.0446952 | + | 0.0119760i | ||||
\(334\) | 368.647 | − | 212.839i | 1.10373 | − | 0.637241i | ||||
\(335\) | 80.1776 | + | 247.366i | 0.239336 | + | 0.738405i | ||||
\(336\) | 138.575 | + | 129.367i | 0.412426 | + | 0.385022i | ||||
\(337\) | 229.038 | − | 229.038i | 0.679638 | − | 0.679638i | −0.280280 | − | 0.959918i | \(-0.590427\pi\) |
0.959918 | + | 0.280280i | \(0.0904275\pi\) | |||||||
\(338\) | 38.7010 | − | 144.434i | 0.114500 | − | 0.427319i | ||||
\(339\) | 323.839 | + | 186.968i | 0.955277 | + | 0.551529i | ||||
\(340\) | −1.53359 | + | 7.18958i | −0.00451056 | + | 0.0211458i | ||||
\(341\) | 96.4717 | + | 167.094i | 0.282908 | + | 0.490011i | ||||
\(342\) | −120.848 | + | 120.848i | −0.353356 | + | 0.353356i | ||||
\(343\) | 341.180 | − | 35.2847i | 0.994695 | − | 0.102871i | ||||
\(344\) | 183.838i | 0.534412i | ||||||||
\(345\) | 4.94491 | + | 95.6694i | 0.0143331 | + | 0.277303i | ||||
\(346\) | 21.4801 | − | 37.2045i | 0.0620811 | − | 0.107528i | ||||
\(347\) | 161.490 | + | 602.689i | 0.465389 | + | 1.73686i | 0.655595 | + | 0.755112i | \(0.272418\pi\) |
−0.190206 | + | 0.981744i | \(0.560916\pi\) | |||||||
\(348\) | 0.834315 | − | 3.11370i | 0.00239746 | − | 0.00894743i | ||||
\(349\) | 121.709i | 0.348736i | 0.984681 | + | 0.174368i | \(0.0557882\pi\) | ||||
−0.984681 | + | 0.174368i | \(0.944212\pi\) | |||||||
\(350\) | −343.419 | − | 42.8611i | −0.981196 | − | 0.122460i | ||||
\(351\) | −81.2680 | −0.231533 | ||||||||
\(352\) | −4.35961 | − | 1.16815i | −0.0123853 | − | 0.00331862i | ||||
\(353\) | −47.2091 | + | 12.6496i | −0.133737 | + | 0.0358347i | −0.325067 | − | 0.945691i | \(-0.605387\pi\) |
0.191330 | + | 0.981526i | \(0.438720\pi\) | |||||||
\(354\) | 303.779 | + | 175.387i | 0.858133 | + | 0.495443i | ||||
\(355\) | −126.706 | + | 6.54912i | −0.356918 | + | 0.0184482i | ||||
\(356\) | 3.66878 | 0.0103056 | ||||||||
\(357\) | −106.006 | − | 169.855i | −0.296936 | − | 0.475785i | ||||
\(358\) | 172.441 | + | 172.441i | 0.481680 | + | 0.481680i | ||||
\(359\) | 439.021 | − | 253.469i | 1.22290 | − | 0.706042i | 0.257365 | − | 0.966314i | \(-0.417146\pi\) |
0.965535 | + | 0.260273i | \(0.0838125\pi\) | |||||||
\(360\) | −118.629 | − | 25.3045i | −0.329526 | − | 0.0702903i | ||||
\(361\) | 234.408 | − | 406.006i | 0.649328 | − | 1.12467i | ||||
\(362\) | 111.837 | + | 29.9667i | 0.308943 | + | 0.0827811i | ||||
\(363\) | −135.895 | − | 135.895i | −0.374366 | − | 0.374366i | ||||
\(364\) | −2.84464 | − | 9.32293i | −0.00781496 | − | 0.0256125i | ||||
\(365\) | 424.260 | − | 137.514i | 1.16236 | − | 0.376749i | ||||
\(366\) | −58.1670 | − | 100.748i | −0.158926 | − | 0.275268i | ||||
\(367\) | 85.7047 | + | 319.854i | 0.233528 | + | 0.871538i | 0.978807 | + | 0.204785i | \(0.0656496\pi\) |
−0.745279 | + | 0.666753i | \(0.767684\pi\) | |||||||
\(368\) | 167.067 | − | 44.7654i | 0.453985 | − | 0.121645i | ||||
\(369\) | 1.57309 | − | 0.908222i | 0.00426311 | − | 0.00246131i | ||||
\(370\) | −45.2349 | − | 23.0893i | −0.122257 | − | 0.0624035i | ||||
\(371\) | 421.600 | − | 128.640i | 1.13639 | − | 0.346739i | ||||
\(372\) | −6.63902 | + | 6.63902i | −0.0178468 | + | 0.0178468i | ||||
\(373\) | −55.0306 | + | 205.377i | −0.147535 | + | 0.550608i | 0.852094 | + | 0.523388i | \(0.175332\pi\) |
−0.999629 | + | 0.0272202i | \(0.991334\pi\) | |||||||
\(374\) | −89.6272 | − | 51.7463i | −0.239645 | − | 0.138359i | ||||
\(375\) | 197.978 | − | 87.6346i | 0.527941 | − | 0.233692i | ||||
\(376\) | 142.824 | + | 247.378i | 0.379850 | + | 0.657919i | ||||
\(377\) | 231.179 | − | 231.179i | 0.613208 | − | 0.613208i | ||||
\(378\) | 61.0229 | − | 38.0843i | 0.161436 | − | 0.100752i | ||||
\(379\) | 147.615i | 0.389487i | 0.980854 | + | 0.194743i | \(0.0623874\pi\) | ||||
−0.980854 | + | 0.194743i | \(0.937613\pi\) | |||||||
\(380\) | 12.8064 | − | 0.661932i | 0.0337011 | − | 0.00174193i | ||||
\(381\) | 52.5767 | − | 91.0655i | 0.137997 | − | 0.239017i | ||||
\(382\) | −142.039 | − | 530.096i | −0.371829 | − | 1.38769i | ||||
\(383\) | 12.2398 | − | 45.6796i | 0.0319578 | − | 0.119268i | −0.948104 | − | 0.317959i | \(-0.897002\pi\) |
0.980062 | + | 0.198691i | \(0.0636691\pi\) | |||||||
\(384\) | 214.014i | 0.557327i | ||||||||
\(385\) | −47.0023 | + | 100.462i | −0.122084 | + | 0.260941i | ||||
\(386\) | −739.965 | −1.91701 | ||||||||
\(387\) | 65.8774 | + | 17.6518i | 0.170226 | + | 0.0456119i | ||||
\(388\) | −0.211771 | + | 0.0567440i | −0.000545803 | + | 0.000146247i | ||||
\(389\) | −289.878 | − | 167.361i | −0.745187 | − | 0.430234i | 0.0787651 | − | 0.996893i | \(-0.474902\pi\) |
−0.823952 | + | 0.566659i | \(0.808236\pi\) | |||||||
\(390\) | −198.931 | − | 179.377i | −0.510080 | − | 0.459942i | ||||
\(391\) | −182.671 | −0.467190 | ||||||||
\(392\) | 298.757 | + | 260.289i | 0.762136 | + | 0.664003i | ||||
\(393\) | 0.815018 | + | 0.815018i | 0.00207384 | + | 0.00207384i | ||||
\(394\) | −234.907 | + | 135.624i | −0.596211 | + | 0.344223i | ||||
\(395\) | −32.2654 | + | 20.9205i | −0.0816846 | + | 0.0529632i | ||||
\(396\) | −0.423210 | + | 0.733022i | −0.00106871 | + | 0.00185107i | ||||
\(397\) | −450.996 | − | 120.844i | −1.13601 | − | 0.304393i | −0.358665 | − | 0.933466i | \(-0.616768\pi\) |
−0.777346 | + | 0.629073i | \(0.783434\pi\) | |||||||
\(398\) | 126.014 | + | 126.014i | 0.316618 | + | 0.316618i | ||||
\(399\) | −238.337 | + | 255.301i | −0.597336 | + | 0.639851i | ||||
\(400\) | −229.310 | − | 316.573i | −0.573275 | − | 0.791433i | ||||
\(401\) | −13.7234 | − | 23.7697i | −0.0342230 | − | 0.0592759i | 0.848407 | − | 0.529345i | \(-0.177562\pi\) |
−0.882630 | + | 0.470069i | \(0.844229\pi\) | |||||||
\(402\) | −46.1064 | − | 172.071i | −0.114693 | − | 0.428038i | ||||
\(403\) | −919.799 | + | 246.459i | −2.28238 | + | 0.611562i | ||||
\(404\) | −11.5886 | + | 6.69069i | −0.0286847 | + | 0.0165611i | ||||
\(405\) | −20.4584 | + | 40.0806i | −0.0505145 | + | 0.0989645i | ||||
\(406\) | −65.2526 | + | 281.926i | −0.160721 | + | 0.694398i | ||||
\(407\) | −11.5092 | + | 11.5092i | −0.0282780 | + | 0.0282780i | ||||
\(408\) | 59.8644 | − | 223.417i | 0.146726 | − | 0.547590i | ||||
\(409\) | −418.429 | − | 241.580i | −1.02305 | − | 0.590660i | −0.108066 | − | 0.994144i | \(-0.534466\pi\) |
−0.914987 | + | 0.403484i | \(0.867799\pi\) | |||||||
\(410\) | 5.85532 | + | 1.24898i | 0.0142813 | + | 0.00304630i | ||||
\(411\) | 72.7479 | + | 126.003i | 0.177002 | + | 0.306577i | ||||
\(412\) | 9.24647 | − | 9.24647i | 0.0224429 | − | 0.0224429i | ||||
\(413\) | 632.745 | + | 336.888i | 1.53207 | + | 0.815709i | ||||
\(414\) | − | 65.6274i | − | 0.158520i | ||||||
\(415\) | −426.349 | − | 384.441i | −1.02735 | − | 0.926365i | ||||
\(416\) | 11.1376 | − | 19.2910i | 0.0267732 | − | 0.0463725i | ||||
\(417\) | 80.2342 | + | 299.438i | 0.192408 | + | 0.718077i | ||||
\(418\) | −46.7248 | + | 174.379i | −0.111782 | + | 0.417175i | ||||
\(419\) | − | 666.615i | − | 1.59097i | −0.605975 | − | 0.795484i | \(-0.707217\pi\) | ||
0.605975 | − | 0.795484i | \(-0.292783\pi\) | |||||||
\(420\) | −5.31409 | − | 0.943999i | −0.0126526 | − | 0.00224762i | ||||
\(421\) | −468.859 | −1.11368 | −0.556840 | − | 0.830620i | \(-0.687986\pi\) | ||||
−0.556840 | + | 0.830620i | \(0.687986\pi\) | |||||||
\(422\) | 7.33465 | + | 1.96531i | 0.0173807 | + | 0.00465714i | ||||
\(423\) | 102.360 | − | 27.4274i | 0.241987 | − | 0.0648402i | ||||
\(424\) | 440.987 | + | 254.604i | 1.04006 | + | 0.600481i | ||||
\(425\) | 147.397 | + | 385.638i | 0.346817 | + | 0.907383i | ||||
\(426\) | 86.9179 | 0.204033 | ||||||||
\(427\) | −125.871 | − | 201.685i | −0.294780 | − | 0.472330i | ||||
\(428\) | 6.40256 | + | 6.40256i | 0.0149593 | + | 0.0149593i | ||||
\(429\) | −74.3442 | + | 42.9227i | −0.173297 | + | 0.100053i | ||||
\(430\) | 122.296 | + | 188.616i | 0.284409 | + | 0.438641i | ||||
\(431\) | −128.770 | + | 223.036i | −0.298769 | + | 0.517484i | −0.975855 | − | 0.218421i | \(-0.929910\pi\) |
0.677085 | + | 0.735905i | \(0.263243\pi\) | |||||||
\(432\) | 78.4783 | + | 21.0282i | 0.181663 | + | 0.0486764i | ||||
\(433\) | 25.8365 | + | 25.8365i | 0.0596685 | + | 0.0596685i | 0.736311 | − | 0.676643i | \(-0.236566\pi\) |
−0.676643 | + | 0.736311i | \(0.736566\pi\) | |||||||
\(434\) | 575.166 | − | 616.104i | 1.32527 | − | 1.41959i | ||||
\(435\) | −55.8185 | − | 172.212i | −0.128318 | − | 0.395891i | ||||
\(436\) | 5.37182 | + | 9.30426i | 0.0123207 | + | 0.0213400i | ||||
\(437\) | 82.4724 | + | 307.791i | 0.188724 | + | 0.704328i | ||||
\(438\) | −295.122 | + | 79.0776i | −0.673793 | + | 0.180542i | ||||
\(439\) | −65.8274 | + | 38.0054i | −0.149948 | + | 0.0865728i | −0.573097 | − | 0.819488i | \(-0.694258\pi\) |
0.423149 | + | 0.906060i | \(0.360925\pi\) | |||||||
\(440\) | −121.887 | + | 39.5068i | −0.277017 | + | 0.0897882i | ||||
\(441\) | 121.960 | − | 82.0659i | 0.276553 | − | 0.186090i | ||||
\(442\) | 361.172 | − | 361.172i | 0.817131 | − | 0.817131i | ||||
\(443\) | 69.5026 | − | 259.387i | 0.156891 | − | 0.585524i | −0.842045 | − | 0.539407i | \(-0.818649\pi\) |
0.998936 | − | 0.0461173i | \(-0.0146848\pi\) | |||||||
\(444\) | −0.685927 | − | 0.396020i | −0.00154488 | − | 0.000891938i | ||||
\(445\) | 172.877 | − | 112.091i | 0.388489 | − | 0.251891i | ||||
\(446\) | 96.2394 | + | 166.692i | 0.215783 | + | 0.373748i | ||||
\(447\) | 7.24953 | − | 7.24953i | 0.0162182 | − | 0.0162182i | ||||
\(448\) | 15.7133 | + | 457.253i | 0.0350744 | + | 1.02065i | ||||
\(449\) | − | 458.330i | − | 1.02078i | −0.859943 | − | 0.510390i | \(-0.829501\pi\) | ||
0.859943 | − | 0.510390i | \(-0.170499\pi\) | |||||||
\(450\) | −138.546 | + | 52.9546i | −0.307880 | + | 0.117677i | ||||
\(451\) | 0.959377 | − | 1.66169i | 0.00212722 | − | 0.00368446i | ||||
\(452\) | 4.97486 | + | 18.5664i | 0.0110063 | + | 0.0410762i | ||||
\(453\) | −37.6420 | + | 140.482i | −0.0830949 | + | 0.310115i | ||||
\(454\) | 278.332i | 0.613065i | ||||||||
\(455\) | −418.885 | − | 352.397i | −0.920627 | − | 0.774498i | ||||
\(456\) | −403.473 | −0.884808 | ||||||||
\(457\) | −569.001 | − | 152.463i | −1.24508 | − | 0.333618i | −0.424645 | − | 0.905360i | \(-0.639601\pi\) |
−0.820433 | + | 0.571742i | \(0.806268\pi\) | |||||||
\(458\) | −315.698 | + | 84.5909i | −0.689296 | + | 0.184696i | ||||
\(459\) | −74.3124 | − | 42.9043i | −0.161901 | − | 0.0934734i | ||||
\(460\) | −3.29758 | + | 3.65705i | −0.00716866 | + | 0.00795011i | ||||
\(461\) | −520.350 | −1.12874 | −0.564371 | − | 0.825521i | \(-0.690881\pi\) | ||||
−0.564371 | + | 0.825521i | \(0.690881\pi\) | |||||||
\(462\) | 35.7093 | − | 67.0696i | 0.0772929 | − | 0.145172i | ||||
\(463\) | −457.986 | − | 457.986i | −0.989171 | − | 0.989171i | 0.0107714 | − | 0.999942i | \(-0.496571\pi\) |
−0.999942 | + | 0.0107714i | \(0.996571\pi\) | |||||||
\(464\) | −283.062 | + | 163.426i | −0.610047 | + | 0.352211i | ||||
\(465\) | −109.998 | + | 515.680i | −0.236556 | + | 1.10899i | ||||
\(466\) | −262.508 | + | 454.677i | −0.563322 | + | 0.975702i | ||||
\(467\) | −137.951 | − | 36.9638i | −0.295398 | − | 0.0791516i | 0.108077 | − | 0.994143i | \(-0.465531\pi\) |
−0.403474 | + | 0.914991i | \(0.632198\pi\) | |||||||
\(468\) | −2.95387 | − | 2.95387i | −0.00631168 | − | 0.00631168i | ||||
\(469\) | −106.244 | − | 348.201i | −0.226534 | − | 0.742433i | ||||
\(470\) | 311.101 | + | 158.795i | 0.661917 | + | 0.337863i | ||||
\(471\) | −76.4859 | − | 132.477i | −0.162390 | − | 0.281269i | ||||
\(472\) | 214.330 | + | 799.891i | 0.454089 | + | 1.69468i | ||||
\(473\) | 69.5879 | − | 18.6460i | 0.147120 | − | 0.0394208i | ||||
\(474\) | 22.8143 | − | 13.1718i | 0.0481314 | − | 0.0277887i | ||||
\(475\) | 583.231 | − | 422.464i | 1.22786 | − | 0.889397i | ||||
\(476\) | 2.32073 | − | 10.0268i | 0.00487549 | − | 0.0210647i | ||||
\(477\) | 133.579 | − | 133.579i | 0.280040 | − | 0.280040i | ||||
\(478\) | 191.040 | − | 712.972i | 0.399666 | − | 1.49157i | ||||
\(479\) | 220.224 | + | 127.146i | 0.459758 | + | 0.265441i | 0.711942 | − | 0.702238i | \(-0.247816\pi\) |
−0.252185 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(480\) | −6.71033 | − | 10.3493i | −0.0139799 | − | 0.0215610i | ||||
\(481\) | −40.1650 | − | 69.5678i | −0.0835031 | − | 0.144632i | ||||
\(482\) | −542.051 | + | 542.051i | −1.12459 | + | 1.12459i | ||||
\(483\) | −4.60612 | − | 134.037i | −0.00953648 | − | 0.277509i | ||||
\(484\) | − | 9.87879i | − | 0.0204107i | ||||||
\(485\) | −8.24525 | + | 9.14406i | −0.0170005 | + | 0.0188537i | ||||
\(486\) | 15.4140 | − | 26.6978i | 0.0317160 | − | 0.0549338i | ||||
\(487\) | 50.6027 | + | 188.852i | 0.103907 | + | 0.387786i | 0.998219 | − | 0.0596581i | \(-0.0190011\pi\) |
−0.894312 | + | 0.447444i | \(0.852334\pi\) | |||||||
\(488\) | 71.0825 | − | 265.284i | 0.145661 | − | 0.543614i | ||||
\(489\) | − | 292.860i | − | 0.598896i | ||||||
\(490\) | 479.677 | + | 68.3092i | 0.978932 | + | 0.139407i | ||||
\(491\) | −627.569 | −1.27814 | −0.639072 | − | 0.769147i | \(-0.720681\pi\) | ||||
−0.639072 | + | 0.769147i | \(0.720681\pi\) | |||||||
\(492\) | 0.0901887 | + | 0.0241660i | 0.000183310 | + | 4.91179e-5i | ||||
\(493\) | 333.441 | − | 89.3452i | 0.676351 | − | 0.181228i | ||||
\(494\) | −771.616 | − | 445.493i | −1.56198 | − | 0.901807i | ||||
\(495\) | 2.45367 | + | 47.4712i | 0.00495690 | + | 0.0959014i | ||||
\(496\) | 951.997 | 1.91935 | ||||||||
\(497\) | 177.520 | − | 6.10042i | 0.357184 | − | 0.0122745i | ||||
\(498\) | 278.093 | + | 278.093i | 0.558421 | + | 0.558421i | ||||
\(499\) | 796.995 | − | 460.145i | 1.59718 | − | 0.922135i | 0.605157 | − | 0.796106i | \(-0.293110\pi\) |
0.992027 | − | 0.126029i | \(-0.0402231\pi\) | |||||||
\(500\) | 10.3812 | + | 4.01066i | 0.0207624 | + | 0.00802133i | ||||
\(501\) | 186.410 | − | 322.871i | 0.372076 | − | 0.644454i | ||||
\(502\) | 46.0729 | + | 12.3452i | 0.0917787 | + | 0.0245920i | ||||
\(503\) | 414.553 | + | 414.553i | 0.824162 | + | 0.824162i | 0.986702 | − | 0.162540i | \(-0.0519686\pi\) |
−0.162540 | + | 0.986702i | \(0.551969\pi\) | |||||||
\(504\) | 165.444 | + | 38.2925i | 0.328261 | + | 0.0759772i | ||||
\(505\) | −341.651 | + | 669.339i | −0.676537 | + | 1.32542i | ||||
\(506\) | −34.6619 | − | 60.0361i | −0.0685018 | − | 0.118649i | ||||
\(507\) | −33.8954 | − | 126.499i | −0.0668547 | − | 0.249505i | ||||
\(508\) | 5.22100 | − | 1.39896i | 0.0102775 | − | 0.00275386i | ||||
\(509\) | −722.536 | + | 417.156i | −1.41952 | + | 0.819561i | −0.996257 | − | 0.0864459i | \(-0.972449\pi\) |
−0.423264 | + | 0.906006i | \(0.639116\pi\) | |||||||
\(510\) | −87.2053 | − | 269.048i | −0.170991 | − | 0.527545i | ||||
\(511\) | −597.204 | + | 182.221i | −1.16870 | + | 0.356596i | ||||
\(512\) | −373.375 | + | 373.375i | −0.729248 | + | 0.729248i | ||||
\(513\) | −38.7408 | + | 144.583i | −0.0755182 | + | 0.281838i | ||||
\(514\) | 345.206 | + | 199.305i | 0.671607 | + | 0.387752i | ||||
\(515\) | 153.200 | − | 718.211i | 0.297475 | − | 1.39458i | ||||
\(516\) | 1.75287 | + | 3.03606i | 0.00339703 | + | 0.00588383i | ||||
\(517\) | 79.1536 | − | 79.1536i | 0.153102 | − | 0.153102i | ||||
\(518\) | 62.7606 | + | 33.4151i | 0.121159 | + | 0.0645079i | ||||
\(519\) | − | 37.6256i | − | 0.0724964i | ||||||
\(520\) | −32.6420 | − | 631.526i | −0.0627730 | − | 1.21447i | ||||
\(521\) | −222.489 | + | 385.363i | −0.427043 | + | 0.739660i | −0.996609 | − | 0.0822856i | \(-0.973778\pi\) |
0.569566 | + | 0.821946i | \(0.307111\pi\) | |||||||
\(522\) | 32.0986 | + | 119.794i | 0.0614915 | + | 0.229490i | ||||
\(523\) | 69.1669 | − | 258.134i | 0.132250 | − | 0.493565i | −0.867744 | − | 0.497012i | \(-0.834431\pi\) |
0.999994 | + | 0.00344695i | \(0.00109720\pi\) | |||||||
\(524\) | 0.0592473i | 0.000113067i | ||||||||
\(525\) | −279.249 | + | 117.878i | −0.531902 | + | 0.224530i | ||||
\(526\) | 320.734 | 0.609760 | ||||||||
\(527\) | −971.190 | − | 260.230i | −1.84287 | − | 0.493794i | ||||
\(528\) | 82.8985 | − | 22.2126i | 0.157005 | − | 0.0420693i | ||||
\(529\) | 352.160 | + | 203.319i | 0.665708 | + | 0.384347i | ||||
\(530\) | 621.821 | − | 32.1404i | 1.17325 | − | 0.0606422i | ||||
\(531\) | 307.217 | 0.578564 | ||||||||
\(532\) | −17.9423 | + | 0.616582i | −0.0337262 | + | 0.00115899i | ||||
\(533\) | 6.69613 | + | 6.69613i | 0.0125631 | + | 0.0125631i | ||||
\(534\) | −122.238 | + | 70.5744i | −0.228911 | + | 0.132162i | ||||
\(535\) | 497.313 | + | 106.081i | 0.929558 | + | 0.198282i | ||||
\(536\) | 210.278 | − | 364.213i | 0.392311 | − | 0.679502i | ||||
\(537\) | 206.309 | + | 55.2804i | 0.384188 | + | 0.102943i | ||||
\(538\) | −111.953 | − | 111.953i | −0.208092 | − | 0.208092i | ||||
\(539\) | 68.2251 | − | 139.489i | 0.126577 | − | 0.258792i | ||||
\(540\) | −2.20042 | + | 0.713214i | −0.00407486 | + | 0.00132077i | ||||
\(541\) | 97.3418 | + | 168.601i | 0.179929 | + | 0.311647i | 0.941856 | − | 0.336016i | \(-0.109080\pi\) |
−0.761927 | + | 0.647663i | \(0.775746\pi\) | |||||||
\(542\) | 236.063 | + | 880.999i | 0.435540 | + | 1.62546i | ||||
\(543\) | 97.9503 | − | 26.2457i | 0.180387 | − | 0.0483346i | ||||
\(544\) | 20.3688 | − | 11.7599i | 0.0374426 | − | 0.0216175i | ||||
\(545\) | 537.398 | + | 274.304i | 0.986052 | + | 0.503311i | ||||
\(546\) | 274.120 | + | 255.906i | 0.502051 | + | 0.468692i | ||||
\(547\) | 256.595 | − | 256.595i | 0.469095 | − | 0.469095i | −0.432526 | − | 0.901621i | \(-0.642378\pi\) |
0.901621 | + | 0.432526i | \(0.142378\pi\) | |||||||
\(548\) | −1.93568 | + | 7.22404i | −0.00353226 | + | 0.0131826i | ||||
\(549\) | −88.2380 | − | 50.9442i | −0.160725 | − | 0.0927946i | ||||
\(550\) | −98.7738 | + | 121.618i | −0.179589 | + | 0.221123i | ||||
\(551\) | −301.083 | − | 521.492i | −0.546431 | − | 0.946446i | ||||
\(552\) | 109.554 | − | 109.554i | 0.198468 | − | 0.198468i | ||||
\(553\) | 45.6712 | − | 28.5033i | 0.0825881 | − | 0.0515430i | ||||
\(554\) | − | 340.504i | − | 0.614629i | ||||||
\(555\) | −44.4213 | + | 2.29603i | −0.0800384 | + | 0.00413698i | ||||
\(556\) | −7.96745 | + | 13.8000i | −0.0143300 | + | 0.0248202i | ||||
\(557\) | −150.923 | − | 563.251i | −0.270957 | − | 1.01122i | −0.958503 | − | 0.285083i | \(-0.907979\pi\) |
0.687546 | − | 0.726141i | \(-0.258688\pi\) | |||||||
\(558\) | 93.4913 | − | 348.914i | 0.167547 | − | 0.625294i | ||||
\(559\) | 355.557i | 0.636059i | ||||||||
\(560\) | 313.323 | + | 448.687i | 0.559505 | + | 0.801227i | ||||
\(561\) | −90.6417 | −0.161572 | ||||||||
\(562\) | −77.2574 | − | 20.7010i | −0.137469 | − | 0.0368346i | ||||
\(563\) | −799.735 | + | 214.288i | −1.42049 | + | 0.380619i | −0.885657 | − | 0.464340i | \(-0.846292\pi\) |
−0.534831 | + | 0.844959i | \(0.679625\pi\) | |||||||
\(564\) | 4.71743 | + | 2.72361i | 0.00836423 | + | 0.00482909i | ||||
\(565\) | 801.678 | + | 722.878i | 1.41890 | + | 1.27943i | ||||
\(566\) | 301.219 | 0.532189 | ||||||||
\(567\) | 29.6076 | − | 55.6093i | 0.0522180 | − | 0.0980763i | ||||
\(568\) | 145.096 | + | 145.096i | 0.255450 | + | 0.255450i | ||||
\(569\) | −683.193 | + | 394.442i | −1.20069 | + | 0.693219i | −0.960709 | − | 0.277558i | \(-0.910475\pi\) |
−0.239982 | + | 0.970777i | \(0.577141\pi\) | |||||||
\(570\) | −413.959 | + | 268.406i | −0.726244 | + | 0.470887i | ||||
\(571\) | 272.727 | − | 472.377i | 0.477631 | − | 0.827281i | −0.522040 | − | 0.852921i | \(-0.674829\pi\) |
0.999671 | + | 0.0256398i | \(0.00816230\pi\) | |||||||
\(572\) | −4.26233 | − | 1.14209i | −0.00745162 | − | 0.00199666i | ||||
\(573\) | −339.871 | − | 339.871i | −0.593144 | − | 0.593144i | ||||
\(574\) | −8.16600 | − | 1.89005i | −0.0142265 | − | 0.00329277i | ||||
\(575\) | −43.6531 | + | 273.075i | −0.0759185 | + | 0.474914i | ||||
\(576\) | 98.0406 | + | 169.811i | 0.170209 | + | 0.294811i | ||||
\(577\) | −285.030 | − | 1063.75i | −0.493987 | − | 1.84358i | −0.535633 | − | 0.844451i | \(-0.679927\pi\) |
0.0416465 | − | 0.999132i | \(-0.486740\pi\) | |||||||
\(578\) | −31.1214 | + | 8.33894i | −0.0538432 | + | 0.0144272i | ||||
\(579\) | −561.255 | + | 324.041i | −0.969352 | + | 0.559656i | ||||
\(580\) | 4.23060 | − | 8.28829i | 0.00729413 | − | 0.0142901i | ||||
\(581\) | 587.494 | + | 548.457i | 1.01118 | + | 0.943989i | ||||
\(582\) | 5.96437 | − | 5.96437i | 0.0102481 | − | 0.0102481i | ||||
\(583\) | 51.6472 | − | 192.750i | 0.0885888 | − | 0.330618i | ||||
\(584\) | −624.666 | − | 360.651i | −1.06963 | − | 0.617553i | ||||
\(585\) | −229.439 | − | 48.9410i | −0.392203 | − | 0.0836599i | ||||
\(586\) | 149.027 | + | 258.122i | 0.254312 | + | 0.440482i | ||||
\(587\) | 161.386 | − | 161.386i | 0.274934 | − | 0.274934i | −0.556149 | − | 0.831083i | \(-0.687722\pi\) |
0.831083 | + | 0.556149i | \(0.187722\pi\) | |||||||
\(588\) | 7.41577 | + | 1.45003i | 0.0126118 | + | 0.00246604i | ||||
\(589\) | 1753.89i | 2.97774i | ||||||||
\(590\) | 752.019 | + | 678.100i | 1.27461 | + | 1.14932i | ||||
\(591\) | −118.783 | + | 205.738i | −0.200987 | + | 0.348119i | ||||
\(592\) | 20.7855 | + | 77.5725i | 0.0351106 | + | 0.131035i | ||||
\(593\) | 261.697 | − | 976.667i | 0.441310 | − | 1.64699i | −0.284188 | − | 0.958769i | \(-0.591724\pi\) |
0.725498 | − | 0.688224i | \(-0.241609\pi\) | |||||||
\(594\) | − | 32.5643i | − | 0.0548221i | ||||||
\(595\) | −196.991 | − | 543.380i | −0.331077 | − | 0.913244i | ||||
\(596\) | 0.527000 | 0.000884228 | ||||||||
\(597\) | 150.763 | + | 40.3969i | 0.252535 | + | 0.0676665i | ||||
\(598\) | 330.480 | − | 88.5519i | 0.552642 | − | 0.148080i | ||||
\(599\) | 999.469 | + | 577.044i | 1.66856 | + | 0.963345i | 0.968414 | + | 0.249349i | \(0.0802166\pi\) |
0.700149 | + | 0.713996i | \(0.253117\pi\) | |||||||
\(600\) | −319.680 | − | 142.881i | −0.532800 | − | 0.238135i | ||||
\(601\) | 586.294 | 0.975531 | 0.487766 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487766 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(602\) | −166.623 | − | 266.983i | −0.276783 | − | 0.443493i | ||||
\(603\) | −110.324 | − | 110.324i | −0.182958 | − | 0.182958i | ||||
\(604\) | −6.47431 | + | 3.73794i | −0.0107191 | + | 0.00618865i | ||||
\(605\) | −301.825 | − | 465.501i | −0.498884 | − | 0.769424i | ||||
\(606\) | 257.411 | − | 445.849i | 0.424770 | − | 0.735724i | ||||
\(607\) | −743.260 | − | 199.156i | −1.22448 | − | 0.328099i | −0.412053 | − | 0.911160i | \(-0.635188\pi\) |
−0.812428 | + | 0.583061i | \(0.801855\pi\) | |||||||
\(608\) | −29.0109 | − | 29.0109i | −0.0477153 | − | 0.0477153i | ||||
\(609\) | 73.9657 | + | 242.412i | 0.121454 | + | 0.398050i | ||||
\(610\) | −103.547 | − | 319.465i | −0.169749 | − | 0.523714i | ||||
\(611\) | 276.233 | + | 478.449i | 0.452099 | + | 0.783059i | ||||
\(612\) | −1.14160 | − | 4.26050i | −0.00186536 | − | 0.00696161i | ||||
\(613\) | −182.550 | + | 48.9141i | −0.297797 | + | 0.0797946i | −0.404624 | − | 0.914483i | \(-0.632598\pi\) |
0.106827 | + | 0.994278i | \(0.465931\pi\) | |||||||
\(614\) | −475.688 | + | 274.639i | −0.774736 | + | 0.447294i | ||||
\(615\) | 4.98814 | − | 1.61679i | 0.00811080 | − | 0.00262892i | ||||
\(616\) | 171.573 | − | 52.3509i | 0.278528 | − | 0.0849853i | ||||
\(617\) | 362.020 | − | 362.020i | 0.586742 | − | 0.586742i | −0.350006 | − | 0.936748i | \(-0.613820\pi\) |
0.936748 | + | 0.350006i | \(0.113820\pi\) | |||||||
\(618\) | −130.210 | + | 485.949i | −0.210695 | + | 0.786325i | ||||
\(619\) | −608.882 | − | 351.538i | −0.983654 | − | 0.567913i | −0.0802824 | − | 0.996772i | \(-0.525582\pi\) |
−0.903371 | + | 0.428859i | \(0.858916\pi\) | |||||||
\(620\) | −22.7417 | + | 14.7454i | −0.0366801 | + | 0.0237829i | ||||
\(621\) | −28.7391 | − | 49.7776i | −0.0462788 | − | 0.0801572i | ||||
\(622\) | −259.845 | + | 259.845i | −0.417757 | + | 0.417757i | ||||
\(623\) | −244.705 | + | 152.720i | −0.392786 | + | 0.245136i | ||||
\(624\) | 423.567i | 0.678794i | ||||||||
\(625\) | 611.713 | − | 128.188i | 0.978741 | − | 0.205100i | ||||
\(626\) | 542.449 | − | 939.549i | 0.866532 | − | 1.50088i | ||||
\(627\) | 40.9228 | + | 152.726i | 0.0652677 | + | 0.243582i | ||||
\(628\) | 2.03514 | − | 7.59524i | 0.00324066 | − | 0.0120943i | ||||
\(629\) | − | 84.8182i | − | 0.134846i | ||||||
\(630\) | 195.217 | − | 70.7718i | 0.309869 | − | 0.112336i | ||||
\(631\) | 259.497 | 0.411247 | 0.205623 | − | 0.978631i | \(-0.434078\pi\) | ||||
0.205623 | + | 0.978631i | \(0.434078\pi\) | |||||||
\(632\) | 60.0731 | + | 16.0965i | 0.0950523 | + | 0.0254692i | ||||
\(633\) | 6.42389 | − | 1.72128i | 0.0101483 | − | 0.00271923i | ||||
\(634\) | 83.6174 | + | 48.2765i | 0.131889 | + | 0.0761459i | ||||
\(635\) | 203.278 | − | 225.437i | 0.320122 | − | 0.355019i | ||||
\(636\) | 9.71046 | 0.0152680 | ||||||||
\(637\) | 577.822 | + | 503.421i | 0.907098 | + | 0.790300i | ||||
\(638\) | 92.6343 | + | 92.6343i | 0.145195 | + | 0.145195i | ||||
\(639\) | 65.9263 | − | 38.0626i | 0.103171 | − | 0.0595658i | ||||
\(640\) | −128.883 | + | 604.211i | −0.201379 | + | 0.944080i | ||||
\(641\) | −451.476 | + | 781.979i | −0.704330 | + | 1.21994i | 0.262602 | + | 0.964904i | \(0.415419\pi\) |
−0.966933 | + | 0.255032i | \(0.917914\pi\) | |||||||
\(642\) | −336.487 | − | 90.1615i | −0.524124 | − | 0.140438i | ||||
\(643\) | −359.258 | − | 359.258i | −0.558722 | − | 0.558722i | 0.370222 | − | 0.928944i | \(-0.379282\pi\) |
−0.928944 | + | 0.370222i | \(0.879282\pi\) | |||||||
\(644\) | 4.70445 | − | 5.03929i | 0.00730504 | − | 0.00782498i | ||||
\(645\) | 175.357 | + | 89.5078i | 0.271872 | + | 0.138772i | ||||
\(646\) | −470.383 | − | 814.728i | −0.728147 | − | 1.26119i | ||||
\(647\) | 184.661 | + | 689.165i | 0.285411 | + | 1.06517i | 0.948538 | + | 0.316663i | \(0.102562\pi\) |
−0.663127 | + | 0.748507i | \(0.730771\pi\) | |||||||
\(648\) | 70.2990 | − | 18.8366i | 0.108486 | − | 0.0290688i | ||||
\(649\) | 281.043 | − | 162.260i | 0.433041 | − | 0.250016i | ||||
\(650\) | −453.606 | − | 626.225i | −0.697855 | − | 0.963423i | ||||
\(651\) | 166.457 | − | 719.181i | 0.255694 | − | 1.10473i | ||||
\(652\) | 10.6446 | − | 10.6446i | 0.0163261 | − | 0.0163261i | ||||
\(653\) | 127.162 | − | 474.577i | 0.194736 | − | 0.726764i | −0.797599 | − | 0.603188i | \(-0.793897\pi\) |
0.992335 | − | 0.123576i | \(-0.0394364\pi\) | |||||||
\(654\) | −357.963 | − | 206.670i | −0.547344 | − | 0.316009i | ||||
\(655\) | 1.81017 | + | 2.79181i | 0.00276362 | + | 0.00426230i | ||||
\(656\) | −4.73364 | − | 8.19890i | −0.00721591 | − | 0.0124983i | ||||
\(657\) | −189.217 | + | 189.217i | −0.288002 | + | 0.288002i | ||||
\(658\) | −431.632 | − | 229.811i | −0.655976 | − | 0.349256i | ||||
\(659\) | − | 379.448i | − | 0.575793i | −0.957662 | − | 0.287897i | \(-0.907044\pi\) | ||
0.957662 | − | 0.287897i | \(-0.0929559\pi\) | |||||||
\(660\) | −1.63626 | + | 1.81463i | −0.00247918 | + | 0.00274944i | ||||
\(661\) | −404.533 | + | 700.672i | −0.612002 | + | 1.06002i | 0.378900 | + | 0.925437i | \(0.376302\pi\) |
−0.990903 | + | 0.134581i | \(0.957031\pi\) | |||||||
\(662\) | 11.3673 | + | 42.4235i | 0.0171712 | + | 0.0640838i | ||||
\(663\) | 115.783 | − | 432.107i | 0.174635 | − | 0.651745i | ||||
\(664\) | 928.465i | 1.39829i | ||||||||
\(665\) | −826.628 | + | 577.243i | −1.24305 | + | 0.868035i | ||||
\(666\) | 30.4722 | 0.0457540 | ||||||||
\(667\) | 223.353 | + | 59.8472i | 0.334862 | + | 0.0897260i | ||||
\(668\) | 18.5110 | − | 4.95999i | 0.0277110 | − | 0.00742514i | ||||
\(669\) | 145.993 | + | 84.2891i | 0.218226 | + | 0.125993i | ||||
\(670\) | −26.5449 | − | 513.564i | −0.0396192 | − | 0.766514i | ||||
\(671\) | −107.627 | −0.160398 | ||||||||
\(672\) | 9.14255 | + | 14.6492i | 0.0136050 | + | 0.0217995i | ||||
\(673\) | 536.016 | + | 536.016i | 0.796458 | + | 0.796458i | 0.982535 | − | 0.186077i | \(-0.0595775\pi\) |
−0.186077 | + | 0.982535i | \(0.559577\pi\) | |||||||
\(674\) | −554.747 | + | 320.283i | −0.823067 | + | 0.475198i | ||||
\(675\) | −81.8961 | + | 100.837i | −0.121328 | + | 0.149388i | ||||
\(676\) | 3.36589 | − | 5.82989i | 0.00497913 | − | 0.00862410i | ||||
\(677\) | −121.106 | − | 32.4502i | −0.178886 | − | 0.0479323i | 0.168264 | − | 0.985742i | \(-0.446184\pi\) |
−0.347150 | + | 0.937810i | \(0.612851\pi\) | |||||||
\(678\) | −522.908 | − | 522.908i | −0.771251 | − | 0.771251i | ||||
\(679\) | 11.7630 | − | 12.6002i | 0.0173240 | − | 0.0185570i | ||||
\(680\) | 303.557 | − | 594.708i | 0.446407 | − | 0.874570i | ||||
\(681\) | 121.885 | + | 211.111i | 0.178980 | + | 0.310002i | ||||
\(682\) | −98.7570 | − | 368.566i | −0.144805 | − | 0.540420i | ||||
\(683\) | 671.930 | − | 180.043i | 0.983792 | − | 0.263606i | 0.269151 | − | 0.963098i | \(-0.413257\pi\) |
0.714641 | + | 0.699492i | \(0.246590\pi\) | |||||||
\(684\) | −6.66330 | + | 3.84706i | −0.00974167 | + | 0.00562435i | ||||
\(685\) | 129.503 | + | 399.547i | 0.189056 | + | 0.583280i | ||||
\(686\) | −669.793 | − | 107.229i | −0.976375 | − | 0.156311i | ||||
\(687\) | −202.410 | + | 202.410i | −0.294628 | + | 0.294628i | ||||
\(688\) | 92.0009 | − | 343.352i | 0.133722 | − | 0.499058i | ||||
\(689\) | 852.906 | + | 492.425i | 1.23789 | + | 0.714696i | ||||
\(690\) | 39.5220 | − | 185.282i | 0.0572782 | − | 0.268524i | ||||
\(691\) | −320.368 | − | 554.894i | −0.463630 | − | 0.803030i | 0.535509 | − | 0.844530i | \(-0.320120\pi\) |
−0.999139 | + | 0.0414993i | \(0.986787\pi\) | |||||||
\(692\) | 1.36759 | − | 1.36759i | 0.00197628 | − | 0.00197628i | ||||
\(693\) | −2.28556 | − | 66.5091i | −0.00329807 | − | 0.0959728i | ||||
\(694\) | − | 1233.93i | − | 1.77800i | ||||||
\(695\) | 46.1933 | + | 893.703i | 0.0664652 | + | 1.28590i | ||||
\(696\) | −146.393 | + | 253.560i | −0.210334 | + | 0.364310i | ||||
\(697\) | 2.58789 | + | 9.65814i | 0.00371290 | + | 0.0138567i | ||||
\(698\) | 62.2960 | − | 232.492i | 0.0892493 | − | 0.333083i | ||||
\(699\) | 459.823i | 0.657830i | ||||||||
\(700\) | −14.4344 | − | 5.86537i | −0.0206206 | − | 0.00837910i | ||||
\(701\) | 271.882 | 0.387849 | 0.193924 | − | 0.981016i | \(-0.437878\pi\) | ||||
0.193924 | + | 0.981016i | \(0.437878\pi\) | |||||||
\(702\) | 155.241 | + | 41.5966i | 0.221141 | + | 0.0592544i | ||||
\(703\) | −142.914 | + | 38.2937i | −0.203291 | + | 0.0544718i | ||||
\(704\) | 179.376 | + | 103.563i | 0.254795 | + | 0.147106i | ||||
\(705\) | 305.505 | − | 15.7908i | 0.433341 | − | 0.0223983i | ||||
\(706\) | 96.6549 | 0.136905 | ||||||||
\(707\) | 494.441 | − | 928.664i | 0.699351 | − | 1.31353i | ||||
\(708\) | 11.1665 | + | 11.1665i | 0.0157719 | + | 0.0157719i | ||||
\(709\) | −208.885 | + | 120.600i | −0.294619 | + | 0.170099i | −0.640023 | − | 0.768356i | \(-0.721075\pi\) |
0.345404 | + | 0.938454i | \(0.387742\pi\) | |||||||
\(710\) | 245.390 | + | 52.3435i | 0.345620 | + | 0.0737233i | ||||
\(711\) | 11.5363 | − | 19.9814i | 0.0162254 | − | 0.0281032i | ||||
\(712\) | −321.870 | − | 86.2449i | −0.452065 | − | 0.121130i | ||||
\(713\) | −476.232 | − | 476.232i | −0.667926 | − | 0.667926i | ||||
\(714\) | 115.557 | + | 378.721i | 0.161844 | + | 0.530422i | ||||
\(715\) | −235.740 | + | 76.4095i | −0.329707 | + | 0.106866i | ||||
\(716\) | 5.48948 | + | 9.50805i | 0.00766687 | + | 0.0132794i | ||||
\(717\) | −167.318 | − | 624.440i | −0.233359 | − | 0.870907i | ||||
\(718\) | −968.368 | + | 259.474i | −1.34870 | + | 0.361384i | ||||
\(719\) | 1158.13 | − | 668.644i | 1.61075 | − | 0.929964i | 0.621548 | − | 0.783376i | \(-0.286504\pi\) |
0.989198 | − | 0.146589i | \(-0.0468293\pi\) | |||||||
\(720\) | 208.899 | + | 106.629i | 0.290138 | + | 0.148095i | ||||
\(721\) | −231.832 | + | 1001.64i | −0.321543 | + | 1.38923i | ||||
\(722\) | −655.585 | + | 655.585i | −0.908012 | + | 0.908012i | ||||
\(723\) | −173.768 | + | 648.511i | −0.240343 | + | 0.896973i | ||||
\(724\) | 4.51418 | + | 2.60626i | 0.00623505 | + | 0.00359981i | ||||
\(725\) | −53.8794 | − | 519.811i | −0.0743164 | − | 0.716981i | ||||
\(726\) | 190.033 | + | 329.147i | 0.261754 | + | 0.453371i | ||||
\(727\) | 711.809 | − | 711.809i | 0.979105 | − | 0.979105i | −0.0206810 | − | 0.999786i | \(-0.506583\pi\) |
0.999786 | + | 0.0206810i | \(0.00658344\pi\) | |||||||
\(728\) | 30.4056 | + | 884.794i | 0.0417659 | + | 1.21538i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | −880.820 | + | 45.5274i | −1.20660 | + | 0.0623663i | ||||
\(731\) | −187.711 | + | 325.126i | −0.256787 | + | 0.444768i | ||||
\(732\) | −1.35553 | − | 5.05889i | −0.00185181 | − | 0.00691105i | ||||
\(733\) | 77.9360 | − | 290.861i | 0.106325 | − | 0.396809i | −0.892167 | − | 0.451705i | \(-0.850816\pi\) |
0.998492 | + | 0.0548957i | \(0.0174826\pi\) | |||||||
\(734\) | − | 654.863i | − | 0.892184i | ||||||
\(735\) | 393.743 | − | 158.245i | 0.535705 | − | 0.215300i | ||||
\(736\) | 15.7546 | 0.0214057 | ||||||||
\(737\) | −159.193 | − | 42.6557i | −0.216001 | − | 0.0578774i | ||||
\(738\) | −3.46983 | + | 0.929738i | −0.00470166 | + | 0.00125981i | ||||
\(739\) | −233.165 | − | 134.618i | −0.315514 | − | 0.182162i | 0.333877 | − | 0.942617i | \(-0.391643\pi\) |
−0.649391 | + | 0.760454i | \(0.724976\pi\) | |||||||
\(740\) | −1.69805 | − | 1.53114i | −0.00229466 | − | 0.00206910i | ||||
\(741\) | −780.349 | −1.05310 | ||||||||
\(742\) | −871.197 | + | 29.9383i | −1.17412 | + | 0.0403482i | ||||
\(743\) | −490.075 | − | 490.075i | −0.659589 | − | 0.659589i | 0.295694 | − | 0.955283i | \(-0.404449\pi\) |
−0.955283 | + | 0.295694i | \(0.904449\pi\) | |||||||
\(744\) | 738.525 | − | 426.388i | 0.992641 | − | 0.573102i | ||||
\(745\) | 24.8329 | − | 16.1013i | 0.0333328 | − | 0.0216125i | ||||
\(746\) | 210.242 | − | 364.150i | 0.281826 | − | 0.488137i | ||||
\(747\) | 332.712 | + | 89.1498i | 0.445397 | + | 0.119344i | ||||
\(748\) | −3.29457 | − | 3.29457i | −0.00440451 | − | 0.00440451i | ||||
\(749\) | −693.567 | − | 160.528i | −0.925991 | − | 0.214324i | ||||
\(750\) | −423.038 | + | 66.0685i | −0.564051 | + | 0.0880913i | ||||
\(751\) | 497.864 | + | 862.326i | 0.662935 | + | 1.14824i | 0.979841 | + | 0.199780i | \(0.0640227\pi\) |
−0.316906 | + | 0.948457i | \(0.602644\pi\) | |||||||
\(752\) | −142.951 | − | 533.501i | −0.190095 | − | 0.709443i | ||||
\(753\) | 40.3519 | − | 10.8123i | 0.0535882 | − | 0.0143589i | ||||
\(754\) | −559.934 | + | 323.278i | −0.742618 | + | 0.428751i | ||||
\(755\) | −190.873 | + | 373.945i | −0.252812 | + | 0.495291i | ||||
\(756\) | 3.09740 | − | 0.945088i | 0.00409708 | − | 0.00125012i | ||||
\(757\) | −111.675 | + | 111.675i | −0.147523 | + | 0.147523i | −0.777010 | − | 0.629488i | \(-0.783265\pi\) |
0.629488 | + | 0.777010i | \(0.283265\pi\) | |||||||
\(758\) | 75.5562 | − | 281.980i | 0.0996784 | − | 0.372005i | ||||
\(759\) | −52.5813 | − | 30.3578i | −0.0692771 | − | 0.0399971i | ||||
\(760\) | −1139.10 | − | 242.978i | −1.49881 | − | 0.319708i | ||||
\(761\) | 290.882 | + | 503.823i | 0.382237 | + | 0.662054i | 0.991382 | − | 0.131005i | \(-0.0418204\pi\) |
−0.609145 | + | 0.793059i | \(0.708487\pi\) | |||||||
\(762\) | −147.045 | + | 147.045i | −0.192973 | + | 0.192973i | ||||
\(763\) | −745.605 | − | 396.977i | −0.977202 | − | 0.520284i | ||||
\(764\) | − | 24.7067i | − | 0.0323387i | ||||||
\(765\) | −183.964 | − | 165.881i | −0.240476 | − | 0.216838i | ||||
\(766\) | −46.7618 | + | 80.9938i | −0.0610467 | + | 0.105736i | ||||
\(767\) | 414.532 | + | 1547.06i | 0.540459 | + | 2.01702i | ||||
\(768\) | −7.65928 | + | 28.5848i | −0.00997302 | + | 0.0372198i | ||||
\(769\) | 26.5351i | 0.0345060i | 0.999851 | + | 0.0172530i | \(0.00549207\pi\) | ||||
−0.999851 | + | 0.0172530i | \(0.994508\pi\) | |||||||
\(770\) | 141.206 | − | 167.849i | 0.183385 | − | 0.217985i | ||||
\(771\) | 349.113 | 0.452806 | ||||||||
\(772\) | −32.1780 | − | 8.62208i | −0.0416814 | − | 0.0111685i | ||||
\(773\) | 361.326 | − | 96.8169i | 0.467433 | − | 0.125248i | −0.0174120 | − | 0.999848i | \(-0.505543\pi\) |
0.484845 | + | 0.874600i | \(0.338876\pi\) | |||||||
\(774\) | −116.806 | − | 67.4380i | −0.150912 | − | 0.0871293i | ||||
\(775\) | −621.103 | + | 1389.64i | −0.801423 | + | 1.79309i | ||||
\(776\) | 19.9131 | 0.0256612 | ||||||||
\(777\) | 62.2361 | − | 2.13872i | 0.0800980 | − | 0.00275253i | ||||
\(778\) | 468.071 | + | 468.071i | 0.601633 | + | 0.601633i | ||||
\(779\) | 15.1050 | − | 8.72090i | 0.0193903 | − | 0.0111950i | ||||
\(780\) | −6.56059 | − | 10.1183i | −0.00841102 | − | 0.0129722i | ||||
\(781\) | 40.2064 | − | 69.6395i | 0.0514806 | − | 0.0891671i | ||||
\(782\) | 348.945 | + | 93.4995i | 0.446221 | + | 0.119565i | ||||
\(783\) | 76.8056 | + | 76.8056i | 0.0980915 | + | 0.0980915i | ||||
\(784\) | −427.726 | − | 635.652i | −0.545569 | − | 0.810781i | ||||
\(785\) | −136.158 | − | 420.076i | −0.173449 | − | 0.535129i | ||||
\(786\) | −1.13971 | − | 1.97404i | −0.00145001 | − | 0.00251150i | ||||
\(787\) | −190.095 | − | 709.443i | −0.241544 | − | 0.901453i | −0.975089 | − | 0.221813i | \(-0.928803\pi\) |
0.733546 | − | 0.679640i | \(-0.237864\pi\) | |||||||
\(788\) | −11.7954 | + | 3.16058i | −0.0149688 | + | 0.00401089i | ||||
\(789\) | 243.273 | − | 140.454i | 0.308331 | − | 0.178015i | ||||
\(790\) | 72.3424 | − | 23.4480i | 0.0915727 | − | 0.0296811i | ||||
\(791\) | −1104.68 | − | 1031.28i | −1.39657 | − | 1.30377i | ||||
\(792\) | 54.3610 | − | 54.3610i | 0.0686376 | − | 0.0686376i | ||||
\(793\) | 137.479 | − | 513.080i | 0.173366 | − | 0.647012i | ||||
\(794\) | 799.654 | + | 461.680i | 1.00712 | + | 0.581461i | ||||
\(795\) | 457.570 | − | 296.682i | 0.575559 | − | 0.373185i | ||||
\(796\) | 4.01151 | + | 6.94814i | 0.00503958 | + | 0.00872882i | ||||
\(797\) | −246.070 | + | 246.070i | −0.308745 | + | 0.308745i | −0.844423 | − | 0.535677i | \(-0.820056\pi\) |
0.535677 | + | 0.844423i | \(0.320056\pi\) | |||||||
\(798\) | 585.953 | − | 365.691i | 0.734277 | − | 0.458260i | ||||
\(799\) | 583.333i | 0.730078i | ||||||||
\(800\) | −12.7123 | − | 33.2595i | −0.0158904 | − | 0.0415744i | ||||
\(801\) | −61.8110 | + | 107.060i | −0.0771673 | + | 0.133658i | ||||
\(802\) | 14.0485 | + | 52.4298i | 0.0175169 | + | 0.0653738i | ||||
\(803\) | −73.1592 | + | 273.034i | −0.0911073 | + | 0.340017i | ||||
\(804\) | − | 8.01991i | − | 0.00997501i | ||||||
\(805\) | 67.7152 | − | 381.192i | 0.0841182 | − | 0.473530i | ||||
\(806\) | 1883.18 | 2.33645 | ||||||||
\(807\) | −133.941 | − | 35.8895i | −0.165974 | − | 0.0444727i | ||||
\(808\) | 1173.98 | − | 314.567i | 1.45295 | − | 0.389315i | ||||
\(809\) | −524.873 | − | 303.035i | −0.648792 | − | 0.374580i | 0.139201 | − | 0.990264i | \(-0.455546\pi\) |
−0.787993 | + | 0.615684i | \(0.788880\pi\) | |||||||
\(810\) | 59.5953 | − | 66.0917i | 0.0735744 | − | 0.0815947i | ||||
\(811\) | 158.508 | 0.195448 | 0.0977240 | − | 0.995214i | \(-0.468844\pi\) | ||||
0.0977240 | + | 0.995214i | \(0.468844\pi\) | |||||||
\(812\) | −6.12257 | + | 11.4995i | −0.00754011 | + | 0.0141619i | ||||
\(813\) | 564.852 | + | 564.852i | 0.694775 | + | 0.694775i | ||||
\(814\) | 27.8760 | − | 16.0942i | 0.0342458 | − | 0.0197718i | ||||
\(815\) | 176.365 | − | 826.813i | 0.216399 | − | 1.01450i | ||||
\(816\) | −223.616 | + | 387.315i | −0.274040 | + | 0.474651i | ||||
\(817\) | 632.566 | + | 169.496i | 0.774255 | + | 0.207461i | ||||
\(818\) | 675.644 | + | 675.644i | 0.825970 | + | 0.825970i | ||||
\(819\) | 319.982 | + | 74.0609i | 0.390698 | + | 0.0904284i | ||||
\(820\) | 0.240071 | + | 0.122540i | 0.000292769 | + | 0.000149438i | ||||
\(821\) | 169.327 | + | 293.282i | 0.206244 | + | 0.357226i | 0.950529 | − | 0.310637i | \(-0.100542\pi\) |
−0.744284 | + | 0.667863i | \(0.767209\pi\) | |||||||
\(822\) | −74.4713 | − | 277.931i | −0.0905977 | − | 0.338115i | ||||
\(823\) | −575.604 | + | 154.233i | −0.699398 | + | 0.187403i | −0.590961 | − | 0.806700i | \(-0.701251\pi\) |
−0.108437 | + | 0.994103i | \(0.534585\pi\) | |||||||
\(824\) | −1028.58 | + | 593.850i | −1.24827 | + | 0.720692i | ||||
\(825\) | −21.6607 | + | 135.500i | −0.0262554 | + | 0.164243i | ||||
\(826\) | −1036.26 | − | 967.401i | −1.25455 | − | 1.17119i | ||||
\(827\) | 108.883 | − | 108.883i | 0.131660 | − | 0.131660i | −0.638206 | − | 0.769866i | \(-0.720323\pi\) |
0.769866 | + | 0.638206i | \(0.220323\pi\) | |||||||
\(828\) | 0.764691 | − | 2.85387i | 0.000923540 | − | 0.00344670i | ||||
\(829\) | −264.922 | − | 152.953i | −0.319568 | − | 0.184503i | 0.331632 | − | 0.943409i | \(-0.392401\pi\) |
−0.651200 | + | 0.758906i | \(0.725734\pi\) | |||||||
\(830\) | 617.651 | + | 952.596i | 0.744158 | + | 1.14771i | ||||
\(831\) | −149.111 | − | 258.269i | −0.179436 | − | 0.310793i | ||||
\(832\) | −722.832 | + | 722.832i | −0.868789 | + | 0.868789i | ||||
\(833\) | 262.593 | + | 765.387i | 0.315238 | + | 0.918832i | ||||
\(834\) | − | 613.064i | − | 0.735088i | ||||||
\(835\) | 720.718 | − | 799.283i | 0.863135 | − | 0.957225i | ||||
\(836\) | −4.06374 | + | 7.03860i | −0.00486093 | + | 0.00841938i | ||||
\(837\) | −81.8822 | − | 305.589i | −0.0978282 | − | 0.365100i | ||||
\(838\) | −341.204 | + | 1273.39i | −0.407164 | + | 1.51956i | ||||
\(839\) | 762.350i | 0.908641i | 0.890838 | + | 0.454321i | \(0.150118\pi\) | ||||
−0.890838 | + | 0.454321i | \(0.849882\pi\) | |||||||
\(840\) | 444.026 | + | 207.742i | 0.528603 | + | 0.247312i | ||||
\(841\) | 404.029 | 0.480415 | ||||||||
\(842\) | 895.629 | + | 239.983i | 1.06369 | + | 0.285016i | ||||
\(843\) | −67.6641 | + | 18.1305i | −0.0802658 | + | 0.0215072i | ||||
\(844\) | 0.296054 | + | 0.170927i | 0.000350775 | + | 0.000202520i | ||||
\(845\) | −19.5146 | − | 377.550i | −0.0230942 | − | 0.446804i | ||||
\(846\) | −209.571 | −0.247720 | ||||||||
\(847\) | 411.224 | + | 658.910i | 0.485507 | + | 0.777934i | ||||
\(848\) | −696.212 | − | 696.212i | −0.821005 | − | 0.821005i | ||||
\(849\) | 228.471 | − | 131.908i | 0.269106 | − | 0.155369i | ||||
\(850\) | −84.1759 | − | 812.102i | −0.0990305 | − | 0.955414i | ||||
\(851\) | 28.4074 | − | 49.2031i | 0.0333812 | − | 0.0578180i | ||||
\(852\) | 3.77970 | + | 1.01277i | 0.00443627 | + | 0.00118870i | ||||
\(853\) | 582.940 | + | 582.940i | 0.683400 | + | 0.683400i | 0.960765 | − | 0.277365i | \(-0.0894610\pi\) |
−0.277365 | + | 0.960765i | \(0.589461\pi\) | |||||||
\(854\) | 137.211 | + | 449.691i | 0.160669 | + | 0.526570i | ||||
\(855\) | −196.445 | + | 384.861i | −0.229760 | + | 0.450130i | ||||
\(856\) | −411.202 | − | 712.222i | −0.480376 | − | 0.832035i | ||||
\(857\) | −288.117 | − | 1075.27i | −0.336193 | − | 1.25469i | −0.902570 | − | 0.430543i | \(-0.858322\pi\) |
0.566377 | − | 0.824146i | \(-0.308345\pi\) | |||||||
\(858\) | 163.984 | − | 43.9395i | 0.191124 | − | 0.0512115i | ||||
\(859\) | 600.525 | − | 346.713i | 0.699097 | − | 0.403624i | −0.107914 | − | 0.994160i | \(-0.534417\pi\) |
0.807011 | + | 0.590536i | \(0.201084\pi\) | |||||||
\(860\) | 3.12039 | + | 9.62711i | 0.00362837 | + | 0.0111943i | ||||
\(861\) | −7.02149 | + | 2.14242i | −0.00815505 | + | 0.00248829i | ||||
\(862\) | 360.139 | − | 360.139i | 0.417795 | − | 0.417795i | ||||
\(863\) | −190.009 | + | 709.122i | −0.220172 | + | 0.821694i | 0.764109 | + | 0.645087i | \(0.223179\pi\) |
−0.984281 | + | 0.176607i | \(0.943488\pi\) | |||||||
\(864\) | 6.40911 | + | 3.70030i | 0.00741796 | + | 0.00428276i | ||||
\(865\) | 22.6588 | − | 106.226i | 0.0261952 | − | 0.122805i | ||||
\(866\) | −36.1294 | − | 62.5779i | −0.0417198 | − | 0.0722608i | ||||
\(867\) | −19.9535 | + | 19.9535i | −0.0230144 | + | 0.0230144i | ||||
\(868\) | 32.1905 | − | 20.0900i | 0.0370858 | − | 0.0231451i | ||||
\(869\) | − | 24.3720i | − | 0.0280461i | ||||||
\(870\) | 18.4801 | + | 357.536i | 0.0212415 | + | 0.410961i | ||||
\(871\) | 406.696 | − | 704.418i | 0.466930 | − | 0.808746i | ||||
\(872\) | −252.559 | − | 942.564i | −0.289632 | − | 1.08092i | ||||
\(873\) | 1.91203 | − | 7.13579i | 0.00219018 | − | 0.00817387i | ||||
\(874\) | − | 630.165i | − | 0.721013i | ||||||
\(875\) | −859.373 | + | 164.629i | −0.982141 | + | 0.188148i | ||||
\(876\) | −13.7550 | −0.0157021 | ||||||||
\(877\) | 1011.30 | + | 270.978i | 1.15314 | + | 0.308983i | 0.784223 | − | 0.620479i | \(-0.213062\pi\) |
0.368918 | + | 0.929462i | \(0.379728\pi\) | |||||||
\(878\) | 145.198 | − | 38.9058i | 0.165374 | − | 0.0443118i | ||||
\(879\) | 226.071 | + | 130.522i | 0.257191 | + | 0.148489i | ||||
\(880\) | 247.419 | − | 12.7885i | 0.281158 | − | 0.0145324i | ||||
\(881\) | −1628.97 | −1.84900 | −0.924501 | − | 0.381180i | \(-0.875518\pi\) | ||||
−0.924501 | + | 0.381180i | \(0.875518\pi\) | |||||||
\(882\) | −274.976 | + | 94.3404i | −0.311765 | + | 0.106962i | ||||
\(883\) | 363.615 | + | 363.615i | 0.411795 | + | 0.411795i | 0.882363 | − | 0.470569i | \(-0.155951\pi\) |
−0.470569 | + | 0.882363i | \(0.655951\pi\) | |||||||
\(884\) | 19.9143 | − | 11.4975i | 0.0225274 | − | 0.0130062i | ||||
\(885\) | 867.347 | + | 185.012i | 0.980053 | + | 0.209053i | ||||
\(886\) | −265.532 | + | 459.915i | −0.299698 | + | 0.519091i | ||||
\(887\) | −164.352 | − | 44.0381i | −0.185290 | − | 0.0496483i | 0.164981 | − | 0.986297i | \(-0.447244\pi\) |
−0.350271 | + | 0.936648i | \(0.613910\pi\) | |||||||
\(888\) | 50.8684 | + | 50.8684i | 0.0572843 | + | 0.0572843i | ||||
\(889\) | −290.003 | + | 310.644i | −0.326213 | + | 0.349431i | ||||
\(890\) | −387.609 | + | 125.634i | −0.435516 | + | 0.141162i | ||||
\(891\) | −14.2604 | − | 24.6997i | −0.0160049 | − | 0.0277213i | ||||
\(892\) | 2.24277 | + | 8.37011i | 0.00251431 | + | 0.00938353i | ||||
\(893\) | 982.883 | − | 263.363i | 1.10065 | − | 0.294919i | ||||
\(894\) | −17.5589 | + | 10.1376i | −0.0196408 | + | 0.0113396i | ||||
\(895\) | 549.169 | + | 280.313i | 0.613597 | + | 0.313198i | ||||
\(896\) | 195.034 | − | 842.650i | 0.217672 | − | 0.940457i | ||||
\(897\) | 211.887 | − | 211.887i | 0.236218 | − | 0.236218i | ||||
\(898\) | −234.594 | + | 875.516i | −0.261240 | + | 0.974962i | ||||
\(899\) | 1102.22 | + | 636.367i | 1.22605 | + | 0.707861i | ||||
\(900\) | −6.64183 | + | 0.688438i | −0.00737981 | + | 0.000764931i | ||||
\(901\) | 519.938 | + | 900.559i | 0.577068 | + | 0.999511i | ||||
\(902\) | −2.68316 | + | 2.68316i | −0.00297468 | + | 0.00297468i | ||||
\(903\) | −243.297 | − | 129.537i | −0.269432 | − | 0.143452i | ||||
\(904\) | − | 1745.82i | − | 1.93122i | ||||||
\(905\) | 292.342 | − | 15.1104i | 0.323030 | − | 0.0166966i | ||||
\(906\) | 143.810 | − | 249.086i | 0.158731 | − | 0.274929i | ||||
\(907\) | 333.960 | + | 1246.36i | 0.368203 | + | 1.37415i | 0.863027 | + | 0.505159i | \(0.168566\pi\) |
−0.494824 | + | 0.868993i | \(0.664767\pi\) | |||||||
\(908\) | −3.24312 | + | 12.1035i | −0.00357172 | + | 0.0133298i | ||||
\(909\) | − | 450.895i | − | 0.496034i | ||||||
\(910\) | 619.795 | + | 887.563i | 0.681093 | + | 0.975344i | ||||
\(911\) | −758.411 | −0.832504 | −0.416252 | − | 0.909249i | \(-0.636657\pi\) | ||||
−0.416252 | + | 0.909249i | \(0.636657\pi\) | |||||||
\(912\) | 753.562 | + | 201.916i | 0.826275 | + | 0.221400i | ||||
\(913\) | 351.451 | − | 94.1711i | 0.384941 | − | 0.103145i | ||||
\(914\) | 1008.89 | + | 582.480i | 1.10381 | + | 0.637287i | ||||
\(915\) | −218.437 | − | 196.966i | −0.238729 | − | 0.215264i | ||||
\(916\) | −14.7141 | −0.0160634 | ||||||||
\(917\) | −2.46628 | − | 3.95176i | −0.00268951 | − | 0.00430945i | ||||
\(918\) | 119.994 | + | 119.994i | 0.130712 | + | 0.130712i | ||||
\(919\) | −9.29930 | + | 5.36895i | −0.0101189 | + | 0.00584217i | −0.505051 | − | 0.863090i | \(-0.668526\pi\) |
0.494932 | + | 0.868932i | \(0.335193\pi\) | |||||||
\(920\) | 375.274 | − | 243.323i | 0.407906 | − | 0.264481i | ||||
\(921\) | −240.536 | + | 416.621i | −0.261168 | + | 0.452357i | ||||
\(922\) | 993.989 | + | 266.339i | 1.07808 | + | 0.288870i | ||||
\(923\) | 280.627 | + | 280.627i | 0.304038 | + | 0.304038i | ||||
\(924\) | 2.33435 | − | 2.50050i | 0.00252635 | − | 0.00270616i | ||||
\(925\) | −126.795 | − | 20.2691i | −0.137075 | − | 0.0219125i | ||||
\(926\) | 640.441 | + | 1109.28i | 0.691621 | + | 1.19792i | ||||
\(927\) | 114.041 | + | 425.607i | 0.123022 | + | 0.459123i | ||||
\(928\) | −28.7578 | + | 7.70563i | −0.0309890 | + | 0.00830348i | ||||
\(929\) | 764.432 | − | 441.345i | 0.822854 | − | 0.475075i | −0.0285454 | − | 0.999592i | \(-0.509088\pi\) |
0.851400 | + | 0.524517i | \(0.175754\pi\) | |||||||
\(930\) | 474.070 | − | 928.765i | 0.509753 | − | 0.998672i | ||||
\(931\) | 1171.08 | − | 788.011i | 1.25787 | − | 0.846413i | ||||
\(932\) | −16.7133 | + | 16.7133i | −0.0179327 | + | 0.0179327i | ||||
\(933\) | −83.2998 | + | 310.879i | −0.0892817 | + | 0.333204i | ||||
\(934\) | 244.598 | + | 141.219i | 0.261882 | + | 0.151198i | ||||
\(935\) | −255.903 | − | 54.5860i | −0.273693 | − | 0.0583808i | ||||
\(936\) | 189.711 | + | 328.588i | 0.202682 | + | 0.351056i | ||||
\(937\) | −861.453 | + | 861.453i | −0.919373 | + | 0.919373i | −0.996984 | − | 0.0776103i | \(-0.975271\pi\) |
0.0776103 | + | 0.996984i | \(0.475271\pi\) | |||||||
\(938\) | 24.7262 | + | 719.525i | 0.0263605 | + | 0.767084i | ||||
\(939\) | − | 950.183i | − | 1.01191i | ||||||
\(940\) | 11.6782 | + | 10.5303i | 0.0124236 | + | 0.0112025i | ||||
\(941\) | 253.129 | − | 438.432i | 0.269000 | − | 0.465921i | −0.699604 | − | 0.714531i | \(-0.746640\pi\) |
0.968604 | + | 0.248610i | \(0.0799736\pi\) | |||||||
\(942\) | 78.2978 | + | 292.211i | 0.0831187 | + | 0.310203i | ||||
\(943\) | −1.73348 | + | 6.46944i | −0.00183826 | + | 0.00686048i | ||||
\(944\) | − | 1601.21i | − | 1.69620i | ||||||
\(945\) | 117.078 | − | 139.168i | 0.123892 | − | 0.147268i | ||||
\(946\) | −142.473 | −0.150606 | ||||||||
\(947\) | −1135.56 | − | 304.272i | −1.19911 | − | 0.321301i | −0.396630 | − | 0.917978i | \(-0.629821\pi\) |
−0.802481 | + | 0.596677i | \(0.796487\pi\) | |||||||
\(948\) | 1.14558 | − | 0.306957i | 0.00120842 | − | 0.000323794i | ||||
\(949\) | −1208.16 | − | 697.529i | −1.27308 | − | 0.735014i | ||||
\(950\) | −1330.34 | + | 508.479i | −1.40036 | + | 0.535241i | ||||
\(951\) | 84.5638 | 0.0889209 | ||||||||
\(952\) | −439.311 | + | 825.118i | −0.461461 | + | 0.866721i | ||||
\(953\) | −363.579 | − | 363.579i | −0.381510 | − | 0.381510i | 0.490136 | − | 0.871646i | \(-0.336947\pi\) |
−0.871646 | + | 0.490136i | \(0.836947\pi\) | |||||||
\(954\) | −323.539 | + | 186.795i | −0.339139 | + | 0.195802i | ||||
\(955\) | −754.861 | − | 1164.21i | −0.790430 | − | 1.21907i | ||||
\(956\) | 16.6151 | − | 28.7782i | 0.0173798 | − | 0.0301027i | ||||
\(957\) | 110.828 | + | 29.6962i | 0.115808 | + | 0.0310305i | ||||
\(958\) | −355.600 | − | 355.600i | −0.371189 | − | 0.371189i | ||||
\(959\) | −171.606 | − | 562.416i | −0.178943 | − | 0.586461i | ||||
\(960\) | 174.528 | + | 538.459i | 0.181801 | + | 0.560895i | ||||
\(961\) | −1373.00 | − | 2378.11i | −1.42872 | − | 2.47462i | ||||
\(962\) | 41.1165 | + | 153.449i | 0.0427406 | + | 0.159510i | ||||
\(963\) | −294.705 | + | 78.9659i | −0.306028 | + | 0.0819999i | ||||
\(964\) | −29.8876 | + | 17.2556i | −0.0310037 | + | 0.0179000i | ||||
\(965\) | −1779.70 | + | 576.846i | −1.84425 | + | 0.597768i | ||||
\(966\) | −59.8073 | + | 258.399i | −0.0619123 | + | 0.267494i | ||||
\(967\) | −741.851 | + | 741.851i | −0.767168 | + | 0.767168i | −0.977607 | − | 0.210439i | \(-0.932511\pi\) |
0.210439 | + | 0.977607i | \(0.432511\pi\) | |||||||
\(968\) | −232.229 | + | 866.690i | −0.239906 | + | 0.895340i | ||||
\(969\) | −713.561 | − | 411.974i | −0.736389 | − | 0.425154i | ||||
\(970\) | 20.4307 | − | 13.2470i | 0.0210626 | − | 0.0136567i | ||||
\(971\) | 375.989 | + | 651.232i | 0.387218 | + | 0.670682i | 0.992074 | − | 0.125653i | \(-0.0401027\pi\) |
−0.604856 | + | 0.796335i | \(0.706769\pi\) | |||||||
\(972\) | 0.981375 | − | 0.981375i | 0.00100964 | − | 0.00100964i | ||||
\(973\) | −43.0285 | − | 1252.12i | −0.0442225 | − | 1.28686i | ||||
\(974\) | − | 386.651i | − | 0.396972i | ||||||
\(975\) | −618.287 | − | 276.344i | −0.634141 | − | 0.283430i | ||||
\(976\) | −265.520 | + | 459.895i | −0.272050 | + | 0.471204i | ||||
\(977\) | −248.716 | − | 928.222i | −0.254572 | − | 0.950074i | −0.968328 | − | 0.249680i | \(-0.919674\pi\) |
0.713757 | − | 0.700394i | \(-0.246992\pi\) | |||||||
\(978\) | −149.899 | + | 559.430i | −0.153271 | + | 0.572015i | ||||
\(979\) | 130.585i | 0.133386i | ||||||||
\(980\) | 20.0632 | + | 8.55969i | 0.0204727 | + | 0.00873437i | ||||
\(981\) | −362.014 | −0.369026 | ||||||||
\(982\) | 1198.80 | + | 321.218i | 1.22077 | + | 0.327106i | ||||
\(983\) | −1582.53 | + | 424.037i | −1.60989 | + | 0.431370i | −0.948011 | − | 0.318237i | \(-0.896909\pi\) |
−0.661883 | + | 0.749607i | \(0.730243\pi\) | |||||||
\(984\) | −7.34437 | − | 4.24028i | −0.00746379 | − | 0.00430922i | ||||
\(985\) | −459.252 | + | 509.315i | −0.466246 | + | 0.517071i | ||||
\(986\) | −682.680 | −0.692373 | ||||||||
\(987\) | −428.025 | + | 14.7089i | −0.433663 | + | 0.0149027i | ||||
\(988\) | −28.3635 | − | 28.3635i | −0.0287080 | − | 0.0287080i | ||||
\(989\) | −217.783 | + | 125.737i | −0.220205 | + | 0.127136i | ||||
\(990\) | 19.6108 | − | 91.9369i | 0.0198089 | − | 0.0928655i | ||||
\(991\) | −686.253 | + | 1188.63i | −0.692485 | + | 1.19942i | 0.278536 | + | 0.960426i | \(0.410151\pi\) |
−0.971021 | + | 0.238994i | \(0.923182\pi\) | |||||||
\(992\) | 83.7608 | + | 22.4436i | 0.0844363 | + | 0.0226246i | ||||
\(993\) | 27.1998 | + | 27.1998i | 0.0273916 | + | 0.0273916i | ||||
\(994\) | −342.228 | − | 79.2097i | −0.344293 | − | 0.0796879i | ||||
\(995\) | 401.313 | + | 204.842i | 0.403329 | + | 0.205872i | ||||
\(996\) | 8.85279 | + | 15.3335i | 0.00888835 | + | 0.0153951i | ||||
\(997\) | −145.327 | − | 542.368i | −0.145764 | − | 0.544000i | −0.999720 | − | 0.0236546i | \(-0.992470\pi\) |
0.853956 | − | 0.520346i | \(-0.174197\pi\) | |||||||
\(998\) | −1757.97 | + | 471.046i | −1.76149 | + | 0.471990i | ||||
\(999\) | 23.1128 | − | 13.3442i | 0.0231359 | − | 0.0133575i |
(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 | 105.3.v.a.88.5 | yes | 64 | |
3.2 | odd | 2 | 315.3.ca.b.298.12 | 64 | |||
5.2 | odd | 4 | inner | 105.3.v.a.67.12 | yes | 64 | |
7.2 | even | 3 | inner | 105.3.v.a.58.12 | yes | 64 | |
15.2 | even | 4 | 315.3.ca.b.172.5 | 64 | |||
21.2 | odd | 6 | 315.3.ca.b.163.5 | 64 | |||
35.2 | odd | 12 | inner | 105.3.v.a.37.5 | ✓ | 64 | |
105.2 | even | 12 | 315.3.ca.b.37.12 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.v.a.37.5 | ✓ | 64 | 35.2 | odd | 12 | inner | |
105.3.v.a.58.12 | yes | 64 | 7.2 | even | 3 | inner | |
105.3.v.a.67.12 | yes | 64 | 5.2 | odd | 4 | inner | |
105.3.v.a.88.5 | yes | 64 | 1.1 | even | 1 | trivial | |
315.3.ca.b.37.12 | 64 | 105.2 | even | 12 | |||
315.3.ca.b.163.5 | 64 | 21.2 | odd | 6 | |||
315.3.ca.b.172.5 | 64 | 15.2 | even | 4 | |||
315.3.ca.b.298.12 | 64 | 3.2 | odd | 2 |