Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(49,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.50712647503417344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 13x^{10} + 119x^{8} - 552x^{6} + 1863x^{4} - 2450x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-2.17114 - 1.25351i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.49 |
Dual form | 475.2.j.b.349.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.17114 | − | 1.25351i | −1.53523 | − | 0.886365i | −0.999108 | − | 0.0422238i | \(-0.986556\pi\) |
−0.536121 | − | 0.844141i | \(-0.680111\pi\) | |||||||
\(3\) | −1.05818 | − | 0.610938i | −0.610938 | − | 0.352725i | 0.162394 | − | 0.986726i | \(-0.448078\pi\) |
−0.773333 | + | 0.634001i | \(0.781412\pi\) | |||||||
\(4\) | 2.14257 | + | 3.71104i | 1.07129 | + | 1.85552i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.53163 | + | 2.65287i | 0.625287 | + | 1.08303i | ||||
\(7\) | 0.221876i | 0.0838613i | 0.999121 | + | 0.0419307i | \(0.0133509\pi\) | ||||
−0.999121 | + | 0.0419307i | \(0.986649\pi\) | |||||||
\(8\) | − | 5.72889i | − | 2.02547i | ||||||
\(9\) | −0.753509 | − | 1.30512i | −0.251170 | − | 0.435039i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.778124 | −0.234613 | −0.117307 | − | 0.993096i | \(-0.537426\pi\) | ||||
−0.117307 | + | 0.993096i | \(0.537426\pi\) | |||||||
\(12\) | − | 5.23591i | − | 1.51148i | ||||||
\(13\) | −4.33013 | + | 2.50000i | −1.20096 | + | 0.693375i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | 0.278124 | − | 0.481725i | 0.0743317 | − | 0.128746i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.89608 | + | 5.01616i | −0.724020 | + | 1.25404i | ||||
\(17\) | 6.12912 | + | 3.53865i | 1.48653 | + | 0.858249i | 0.999882 | − | 0.0153485i | \(-0.00488578\pi\) |
0.486649 | + | 0.873598i | \(0.338219\pi\) | |||||||
\(18\) | 3.77812i | 0.890512i | ||||||||
\(19\) | −1.33281 | + | 4.15013i | −0.305769 | + | 0.952106i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.135553 | − | 0.234784i | 0.0295800 | − | 0.0512341i | ||||
\(22\) | 1.68942 | + | 0.975385i | 0.360185 | + | 0.207953i | ||||
\(23\) | 6.99515 | − | 4.03865i | 1.45859 | − | 0.842117i | 0.459647 | − | 0.888101i | \(-0.347976\pi\) |
0.998942 | + | 0.0459843i | \(0.0146424\pi\) | |||||||
\(24\) | −3.50000 | + | 6.06218i | −0.714435 | + | 1.23744i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.5351 | 2.45833 | ||||||||
\(27\) | 5.50702i | 1.05983i | ||||||||
\(28\) | −0.823392 | + | 0.475385i | −0.155606 | + | 0.0898394i | ||||
\(29\) | 0.110938 | + | 0.192150i | 0.0206007 | + | 0.0356814i | 0.876142 | − | 0.482053i | \(-0.160109\pi\) |
−0.855541 | + | 0.517735i | \(0.826775\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50702 | 0.450274 | 0.225137 | − | 0.974327i | \(-0.427717\pi\) | ||||
0.225137 | + | 0.974327i | \(0.427717\pi\) | |||||||
\(32\) | 2.65287 | − | 1.53163i | 0.468965 | − | 0.270757i | ||||
\(33\) | 0.823392 | + | 0.475385i | 0.143334 | + | 0.0827540i | ||||
\(34\) | −8.87147 | − | 15.3658i | −1.52144 | − | 2.63522i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.22889 | − | 5.59261i | 0.538149 | − | 0.932102i | ||||
\(37\) | 1.90466i | 0.313124i | 0.987668 | + | 0.156562i | \(0.0500410\pi\) | ||||
−0.987668 | + | 0.156562i | \(0.949959\pi\) | |||||||
\(38\) | 8.09596 | − | 7.33983i | 1.31334 | − | 1.19068i | ||||
\(39\) | 6.10938 | 0.978284 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.61796 | − | 6.26648i | 0.565030 | − | 0.978661i | −0.432017 | − | 0.901865i | \(-0.642198\pi\) |
0.997047 | − | 0.0767950i | \(-0.0244687\pi\) | |||||||
\(42\) | −0.588608 | + | 0.339833i | −0.0908242 | + | 0.0524374i | ||||
\(43\) | −6.32128 | − | 3.64959i | −0.963985 | − | 0.556557i | −0.0665881 | − | 0.997781i | \(-0.521211\pi\) |
−0.897397 | + | 0.441223i | \(0.854545\pi\) | |||||||
\(44\) | −1.66719 | − | 2.88765i | −0.251338 | − | 0.435330i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.2500 | −2.98569 | ||||||||
\(47\) | 2.41808 | − | 1.39608i | 0.352714 | − | 0.203639i | −0.313166 | − | 0.949698i | \(-0.601390\pi\) |
0.665880 | + | 0.746059i | \(0.268056\pi\) | |||||||
\(48\) | 6.12912 | − | 3.53865i | 0.884663 | − | 0.510760i | ||||
\(49\) | 6.95077 | 0.992967 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.32379 | − | 7.48903i | −0.605452 | − | 1.04867i | ||||
\(52\) | −18.5552 | − | 10.7129i | −2.57314 | − | 1.48561i | ||||
\(53\) | 3.79361 | − | 2.19024i | 0.521093 | − | 0.300853i | −0.216289 | − | 0.976329i | \(-0.569395\pi\) |
0.737382 | + | 0.675476i | \(0.236062\pi\) | |||||||
\(54\) | 6.90310 | − | 11.9565i | 0.939393 | − | 1.62708i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.27111 | 0.169859 | ||||||||
\(57\) | 3.94583 | − | 3.57730i | 0.522637 | − | 0.473825i | ||||
\(58\) | − | 0.556248i | − | 0.0730389i | ||||||
\(59\) | −1.39608 | + | 2.41808i | −0.181754 | + | 0.314808i | −0.942478 | − | 0.334268i | \(-0.891511\pi\) |
0.760724 | + | 0.649076i | \(0.224844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.29216 | + | 10.8983i | 0.805629 | + | 1.39539i | 0.915866 | + | 0.401484i | \(0.131506\pi\) |
−0.110237 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(62\) | −5.44309 | − | 3.14257i | −0.691274 | − | 0.399107i | ||||
\(63\) | 0.289574 | − | 0.167186i | 0.0364829 | − | 0.0210634i | ||||
\(64\) | 3.90466 | 0.488082 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.19180 | − | 2.06426i | −0.146700 | − | 0.254093i | ||||
\(67\) | 9.15414 | − | 5.28514i | 1.11836 | − | 0.645683i | 0.177375 | − | 0.984143i | \(-0.443239\pi\) |
0.940981 | + | 0.338460i | \(0.109906\pi\) | |||||||
\(68\) | 30.3273i | 3.67772i | ||||||||
\(69\) | −9.86946 | −1.18814 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.92070 | − | 8.52289i | 0.583979 | − | 1.01148i | −0.411023 | − | 0.911625i | \(-0.634828\pi\) |
0.995002 | − | 0.0998563i | \(-0.0318383\pi\) | |||||||
\(72\) | −7.47687 | + | 4.31678i | −0.881158 | + | 0.508737i | ||||
\(73\) | 12.1913 | + | 7.03865i | 1.42688 | + | 0.823812i | 0.996874 | − | 0.0790121i | \(-0.0251766\pi\) |
0.430010 | + | 0.902824i | \(0.358510\pi\) | |||||||
\(74\) | 2.38750 | − | 4.13528i | 0.277542 | − | 0.480716i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.2570 | + | 3.94583i | −2.09422 | + | 0.452617i | ||||
\(77\) | − | 0.172647i | − | 0.0196750i | ||||||
\(78\) | −13.2643 | − | 7.65817i | −1.50189 | − | 0.867117i | ||||
\(79\) | 0.792161 | − | 1.37206i | 0.0891251 | − | 0.154369i | −0.818016 | − | 0.575195i | \(-0.804926\pi\) |
0.907142 | + | 0.420826i | \(0.138260\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.10392 | − | 1.91204i | 0.122658 | − | 0.212449i | ||||
\(82\) | −15.7102 | + | 9.07028i | −1.73490 | + | 1.00165i | ||||
\(83\) | − | 9.52106i | − | 1.04507i | −0.852617 | − | 0.522536i | \(-0.824986\pi\) | ||
0.852617 | − | 0.522536i | \(-0.175014\pi\) | |||||||
\(84\) | 1.16172 | 0.126755 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.14959 | + | 15.8476i | 0.986626 | + | 1.70889i | ||||
\(87\) | − | 0.271105i | − | 0.0290655i | ||||||
\(88\) | 4.45779i | 0.475202i | ||||||||
\(89\) | 1.57028 | + | 2.71981i | 0.166450 | + | 0.288300i | 0.937169 | − | 0.348875i | \(-0.113436\pi\) |
−0.770719 | + | 0.637175i | \(0.780103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.554690 | − | 0.960752i | −0.0581474 | − | 0.100714i | ||||
\(92\) | 29.9752 | + | 17.3062i | 3.12513 | + | 1.80430i | ||||
\(93\) | −2.65287 | − | 1.53163i | −0.275089 | − | 0.158823i | ||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.74293 | −0.382011 | ||||||||
\(97\) | −5.51004 | − | 3.18122i | −0.559460 | − | 0.323004i | 0.193469 | − | 0.981106i | \(-0.438026\pi\) |
−0.752929 | + | 0.658102i | \(0.771359\pi\) | |||||||
\(98\) | −15.0911 | − | 8.71286i | −1.52443 | − | 0.880131i | ||||
\(99\) | 0.586324 | + | 1.01554i | 0.0589277 | + | 0.102066i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.69726 | + | 6.40385i | 0.367891 | + | 0.637206i | 0.989236 | − | 0.146331i | \(-0.0467465\pi\) |
−0.621344 | + | 0.783538i | \(0.713413\pi\) | |||||||
\(102\) | 21.6797i | 2.14661i | ||||||||
\(103\) | 12.2038i | 1.20248i | 0.799069 | + | 0.601240i | \(0.205326\pi\) | ||||
−0.799069 | + | 0.601240i | \(0.794674\pi\) | |||||||
\(104\) | 14.3222 | + | 24.8068i | 1.40441 | + | 2.43251i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.9820 | −1.06666 | ||||||||
\(107\) | 1.63355i | 0.157921i | 0.996878 | + | 0.0789607i | \(0.0251602\pi\) | ||||
−0.996878 | + | 0.0789607i | \(0.974840\pi\) | |||||||
\(108\) | −20.4368 | + | 11.7992i | −1.96653 | + | 1.13538i | ||||
\(109\) | −3.80820 | + | 6.59600i | −0.364759 | + | 0.631782i | −0.988738 | − | 0.149660i | \(-0.952182\pi\) |
0.623978 | + | 0.781442i | \(0.285515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.16363 | − | 2.01546i | 0.110447 | − | 0.191299i | ||||
\(112\) | −1.11297 | − | 0.642571i | −0.105165 | − | 0.0607173i | ||||
\(113\) | 12.4890i | 1.17486i | 0.809273 | + | 0.587432i | \(0.199861\pi\) | ||||
−0.809273 | + | 0.587432i | \(0.800139\pi\) | |||||||
\(114\) | −13.0511 | + | 2.82070i | −1.22235 | + | 0.264183i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.475385 | + | 0.823392i | −0.0441384 | + | 0.0764500i | ||||
\(117\) | 6.52558 | + | 3.76755i | 0.603290 | + | 0.348310i | ||||
\(118\) | 6.06218 | − | 3.50000i | 0.558069 | − | 0.322201i | ||||
\(119\) | −0.785142 | + | 1.35991i | −0.0719739 | + | 0.124662i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3945 | −0.944957 | ||||||||
\(122\) | − | 31.5491i | − | 2.85632i | ||||||
\(123\) | −7.65687 | + | 4.42070i | −0.690397 | + | 0.398601i | ||||
\(124\) | 5.37147 | + | 9.30365i | 0.482372 | + | 0.835493i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.838276 | −0.0746795 | ||||||||
\(127\) | 11.2948 | − | 6.52106i | 1.00225 | − | 0.578650i | 0.0933378 | − | 0.995635i | \(-0.470246\pi\) |
0.908914 | + | 0.416984i | \(0.136913\pi\) | |||||||
\(128\) | −13.7833 | − | 7.95779i | −1.21828 | − | 0.703376i | ||||
\(129\) | 4.45935 | + | 7.72382i | 0.392624 | + | 0.680044i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.55469 | + | 6.15690i | −0.310575 | + | 0.537931i | −0.978487 | − | 0.206309i | \(-0.933855\pi\) |
0.667912 | + | 0.744240i | \(0.267188\pi\) | |||||||
\(132\) | 4.07419i | 0.354613i | ||||||||
\(133\) | −0.920816 | − | 0.295720i | −0.0798448 | − | 0.0256422i | ||||
\(134\) | −26.4999 | −2.28924 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.2726 | − | 35.1131i | 1.73836 | − | 3.01092i | ||||
\(137\) | −4.69880 | + | 2.71286i | −0.401446 | + | 0.231775i | −0.687108 | − | 0.726556i | \(-0.741120\pi\) |
0.285662 | + | 0.958331i | \(0.407787\pi\) | |||||||
\(138\) | 21.4280 | + | 12.3715i | 1.82407 | + | 1.05313i | ||||
\(139\) | 1.78514 | + | 3.09196i | 0.151414 | + | 0.262256i | 0.931747 | − | 0.363107i | \(-0.118284\pi\) |
−0.780334 | + | 0.625363i | \(0.784951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.41168 | −0.287315 | ||||||||
\(142\) | −21.3671 | + | 12.3363i | −1.79308 | + | 1.03524i | ||||
\(143\) | 3.36938 | − | 1.94531i | 0.281761 | − | 0.162675i | ||||
\(144\) | 8.72889 | 0.727408 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.6460 | − | 30.5638i | −1.46040 | − | 2.52948i | ||||
\(147\) | −7.35514 | − | 4.24649i | −0.606642 | − | 0.350245i | ||||
\(148\) | −7.06826 | + | 4.08086i | −0.581007 | + | 0.335445i | ||||
\(149\) | −0.468367 | + | 0.811235i | −0.0383701 | + | 0.0664590i | −0.884573 | − | 0.466402i | \(-0.845550\pi\) |
0.846203 | + | 0.532861i | \(0.178883\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.971925 | −0.0790942 | −0.0395471 | − | 0.999218i | \(-0.512592\pi\) | ||||
−0.0395471 | + | 0.999218i | \(0.512592\pi\) | |||||||
\(152\) | 23.7757 | + | 7.63555i | 1.92846 | + | 0.619325i | ||||
\(153\) | − | 10.6656i | − | 0.862265i | ||||||
\(154\) | −0.216415 | + | 0.374841i | −0.0174392 | + | 0.0302056i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.0898 | + | 22.6722i | 1.04802 | + | 1.81523i | ||||
\(157\) | 2.35114 | + | 1.35743i | 0.187641 | + | 0.108335i | 0.590878 | − | 0.806761i | \(-0.298782\pi\) |
−0.403237 | + | 0.915096i | \(0.632115\pi\) | |||||||
\(158\) | −3.43979 | + | 1.98596i | −0.273655 | + | 0.157995i | ||||
\(159\) | −5.35241 | −0.424474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.896081 | + | 1.55206i | 0.0706210 | + | 0.122319i | ||||
\(162\) | −4.79353 | + | 2.76755i | −0.376615 | + | 0.217439i | ||||
\(163\) | − | 3.20384i | − | 0.250944i | −0.992097 | − | 0.125472i | \(-0.959956\pi\) | ||
0.992097 | − | 0.125472i | \(-0.0400445\pi\) | |||||||
\(164\) | 31.0069 | 2.42123 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.9347 | + | 20.6716i | −0.926315 | + | 1.60442i | ||||
\(167\) | −8.85240 | + | 5.11094i | −0.685020 | + | 0.395496i | −0.801744 | − | 0.597668i | \(-0.796094\pi\) |
0.116724 | + | 0.993164i | \(0.462761\pi\) | |||||||
\(168\) | −1.34505 | − | 0.776567i | −0.103773 | − | 0.0599134i | ||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.42070 | − | 1.38769i | 0.491003 | − | 0.106119i | ||||
\(172\) | − | 31.2780i | − | 2.38493i | ||||||
\(173\) | 2.30850 | + | 1.33281i | 0.175512 | + | 0.101332i | 0.585182 | − | 0.810902i | \(-0.301023\pi\) |
−0.409670 | + | 0.912234i | \(0.634356\pi\) | |||||||
\(174\) | −0.339833 | + | 0.588608i | −0.0257627 | + | 0.0446222i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.25351 | − | 3.90319i | 0.169865 | − | 0.294214i | ||||
\(177\) | 2.95460 | − | 1.70584i | 0.222081 | − | 0.128219i | ||||
\(178\) | − | 7.87347i | − | 0.590141i | ||||||
\(179\) | 12.9367 | 0.966937 | 0.483468 | − | 0.875362i | \(-0.339377\pi\) | ||||
0.483468 | + | 0.875362i | \(0.339377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.30620 | + | 16.1188i | 0.691724 | + | 1.19810i | 0.971273 | + | 0.237970i | \(0.0764820\pi\) |
−0.279548 | + | 0.960132i | \(0.590185\pi\) | |||||||
\(182\) | 2.78124i | 0.206159i | ||||||||
\(183\) | − | 15.3765i | − | 1.13666i | ||||||
\(184\) | −23.1370 | − | 40.0745i | −1.70568 | − | 2.95433i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.83983 | + | 6.65079i | 0.281550 | + | 0.487659i | ||||
\(187\) | −4.76922 | − | 2.75351i | −0.348760 | − | 0.201357i | ||||
\(188\) | 10.3618 | + | 5.98240i | 0.755714 | + | 0.436312i | ||||
\(189\) | −1.22188 | −0.0888784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.0421 | −1.66727 | −0.833634 | − | 0.552317i | \(-0.813744\pi\) | ||||
−0.833634 | + | 0.552317i | \(0.813744\pi\) | |||||||
\(192\) | −4.13181 | − | 2.38550i | −0.298188 | − | 0.172159i | ||||
\(193\) | 14.7894 | + | 8.53865i | 1.06456 | + | 0.614626i | 0.926691 | − | 0.375824i | \(-0.122640\pi\) |
0.137872 | + | 0.990450i | \(0.455974\pi\) | |||||||
\(194\) | 7.97539 | + | 13.8138i | 0.572599 | + | 0.991771i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.8925 | + | 25.7946i | 1.06375 | + | 1.84247i | ||||
\(197\) | 8.82024i | 0.628416i | 0.949354 | + | 0.314208i | \(0.101739\pi\) | ||||
−0.949354 | + | 0.314208i | \(0.898261\pi\) | |||||||
\(198\) | − | 2.93985i | − | 0.208926i | ||||||
\(199\) | −1.42771 | − | 2.47287i | −0.101208 | − | 0.175297i | 0.810975 | − | 0.585081i | \(-0.198937\pi\) |
−0.912183 | + | 0.409784i | \(0.865604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9156 | −0.910995 | ||||||||
\(202\) | − | 18.5382i | − | 1.30434i | ||||||
\(203\) | −0.0426336 | + | 0.0246145i | −0.00299229 | + | 0.00172760i | ||||
\(204\) | 18.5281 | − | 32.0916i | 1.29722 | − | 2.24686i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.2976 | − | 26.4963i | 1.06584 | − | 1.84608i | ||||
\(207\) | −10.5418 | − | 6.08632i | −0.732707 | − | 0.423029i | ||||
\(208\) | − | 28.9608i | − | 2.00807i | ||||||
\(209\) | 1.03709 | − | 3.22932i | 0.0717373 | − | 0.223377i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44375 | − | 11.1609i | 0.443606 | − | 0.768348i | −0.554348 | − | 0.832285i | \(-0.687032\pi\) |
0.997954 | + | 0.0639367i | \(0.0203656\pi\) | |||||||
\(212\) | 16.2562 | + | 9.38550i | 1.11648 | + | 0.644599i | ||||
\(213\) | −10.4139 | + | 6.01248i | −0.713550 | + | 0.411968i | ||||
\(214\) | 2.04767 | − | 3.54667i | 0.139976 | − | 0.242445i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 31.5491 | 2.14665 | ||||||||
\(217\) | 0.556248i | 0.0377606i | ||||||||
\(218\) | 16.5363 | − | 9.54723i | 1.11998 | − | 0.646620i | ||||
\(219\) | −8.60036 | − | 14.8963i | −0.581159 | − | 1.00660i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.3865 | −2.38035 | ||||||||
\(222\) | −5.05280 | + | 2.91724i | −0.339122 | + | 0.195792i | ||||
\(223\) | −17.9334 | − | 10.3539i | −1.20091 | − | 0.693346i | −0.240153 | − | 0.970735i | \(-0.577198\pi\) |
−0.960758 | + | 0.277389i | \(0.910531\pi\) | |||||||
\(224\) | 0.339833 | + | 0.588608i | 0.0227060 | + | 0.0393280i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.6551 | − | 27.1153i | 1.04136 | − | 1.80369i | ||||
\(227\) | − | 4.00000i | − | 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | 21.7297 | + | 6.97850i | 1.43909 | + | 0.462162i | ||||
\(229\) | −3.53910 | −0.233870 | −0.116935 | − | 0.993140i | \(-0.537307\pi\) | ||||
−0.116935 | + | 0.993140i | \(0.537307\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.105477 | + | 0.182691i | −0.00693986 | + | 0.0120202i | ||||
\(232\) | 1.10081 | − | 0.635553i | 0.0722717 | − | 0.0417261i | ||||
\(233\) | 17.1344 | + | 9.89252i | 1.12251 | + | 0.648081i | 0.942040 | − | 0.335500i | \(-0.108905\pi\) |
0.180468 | + | 0.983581i | \(0.442239\pi\) | |||||||
\(234\) | −9.44531 | − | 16.3598i | −0.617459 | − | 1.06947i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.9648 | −0.778843 | ||||||||
\(237\) | −1.67649 | + | 0.967923i | −0.108900 | + | 0.0628733i | ||||
\(238\) | 3.40931 | − | 1.96837i | 0.220993 | − | 0.127590i | ||||
\(239\) | −23.7741 | −1.53782 | −0.768910 | − | 0.639357i | \(-0.779201\pi\) | ||||
−0.768910 | + | 0.639357i | \(0.779201\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.27111 | + | 3.93367i | 0.146295 | + | 0.253390i | 0.929855 | − | 0.367926i | \(-0.119932\pi\) |
−0.783561 | + | 0.621315i | \(0.786599\pi\) | |||||||
\(242\) | 22.5680 | + | 13.0296i | 1.45072 | + | 0.837576i | ||||
\(243\) | 11.9714 | − | 6.91168i | 0.767964 | − | 0.443384i | ||||
\(244\) | −26.9628 | + | 46.7010i | −1.72612 | + | 2.98972i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.1655 | 1.41322 | ||||||||
\(247\) | −4.60408 | − | 21.3026i | −0.292950 | − | 1.35545i | ||||
\(248\) | − | 14.3624i | − | 0.912016i | ||||||
\(249\) | −5.81678 | + | 10.0750i | −0.368623 | + | 0.638474i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.75151 | + | 16.8901i | 0.615510 | + | 1.06609i | 0.990295 | + | 0.138982i | \(0.0443832\pi\) |
−0.374785 | + | 0.927112i | \(0.622284\pi\) | |||||||
\(252\) | 1.24087 | + | 0.716415i | 0.0781673 | + | 0.0451299i | ||||
\(253\) | −5.44309 | + | 3.14257i | −0.342204 | + | 0.197572i | ||||
\(254\) | −32.6968 | −2.05158 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0457 | + | 27.7919i | 1.00285 | + | 1.73699i | ||||
\(257\) | −1.52774 | + | 0.882043i | −0.0952980 | + | 0.0550203i | −0.546892 | − | 0.837203i | \(-0.684189\pi\) |
0.451594 | + | 0.892224i | \(0.350856\pi\) | |||||||
\(258\) | − | 22.3593i | − | 1.39203i | ||||||
\(259\) | −0.422598 | −0.0262590 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.167186 | − | 0.289574i | 0.0103485 | − | 0.0179242i | ||||
\(262\) | 15.4355 | − | 8.91168i | 0.953607 | − | 0.550565i | ||||
\(263\) | 5.60477 | + | 3.23591i | 0.345605 | + | 0.199535i | 0.662748 | − | 0.748843i | \(-0.269390\pi\) |
−0.317143 | + | 0.948378i | \(0.602724\pi\) | |||||||
\(264\) | 2.72343 | − | 4.71713i | 0.167616 | − | 0.290319i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.62853 | + | 1.79630i | 0.0998518 | + | 0.110138i | ||||
\(267\) | − | 3.83739i | − | 0.234844i | ||||||
\(268\) | 39.2268 | + | 22.6476i | 2.39616 | + | 1.38342i | ||||
\(269\) | 14.2429 | − | 24.6695i | 0.868407 | − | 1.50412i | 0.00478280 | − | 0.999989i | \(-0.498478\pi\) |
0.863624 | − | 0.504136i | \(-0.168189\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.246491 | − | 0.426934i | 0.0149732 | − | 0.0259344i | −0.858442 | − | 0.512911i | \(-0.828567\pi\) |
0.873415 | + | 0.486977i | \(0.161900\pi\) | |||||||
\(272\) | −35.5009 | + | 20.4964i | −2.15256 | + | 1.24278i | ||||
\(273\) | 1.35553i | 0.0820402i | ||||||||
\(274\) | 13.6024 | 0.821749 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −21.1460 | − | 36.6260i | −1.27284 | − | 2.20463i | ||||
\(277\) | 8.78905i | 0.528083i | 0.964511 | + | 0.264041i | \(0.0850555\pi\) | ||||
−0.964511 | + | 0.264041i | \(0.914944\pi\) | |||||||
\(278\) | − | 8.95077i | − | 0.536832i | ||||||
\(279\) | −1.88906 | − | 3.27195i | −0.113095 | − | 0.195887i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.37147 | + | 4.10750i | 0.141470 | + | 0.245033i | 0.928050 | − | 0.372455i | \(-0.121484\pi\) |
−0.786581 | + | 0.617488i | \(0.788151\pi\) | |||||||
\(282\) | 7.40723 | + | 4.27657i | 0.441094 | + | 0.254666i | ||||
\(283\) | −14.6094 | − | 8.43473i | −0.868438 | − | 0.501393i | −0.00160901 | − | 0.999999i | \(-0.500512\pi\) |
−0.866829 | + | 0.498606i | \(0.833845\pi\) | |||||||
\(284\) | 42.1718 | 2.50243 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.75385 | −0.576758 | ||||||||
\(287\) | 1.39038 | + | 0.802738i | 0.0820717 | + | 0.0473841i | ||||
\(288\) | −3.99792 | − | 2.30820i | −0.235580 | − | 0.136012i | ||||
\(289\) | 16.5441 | + | 28.6552i | 0.973183 | + | 1.68560i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.88706 | + | 6.73259i | 0.227864 | + | 0.394671i | ||||
\(292\) | 60.3233i | 3.53015i | ||||||||
\(293\) | 11.6336i | 0.679639i | 0.940491 | + | 0.339820i | \(0.110366\pi\) | ||||
−0.940491 | + | 0.339820i | \(0.889634\pi\) | |||||||
\(294\) | 10.6460 | + | 18.4395i | 0.620889 | + | 1.07541i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.9116 | 0.634223 | ||||||||
\(297\) | − | 4.28514i | − | 0.248649i | ||||||
\(298\) | 2.03378 | − | 1.17420i | 0.117814 | − | 0.0680198i | ||||
\(299\) | −20.1933 | + | 34.9758i | −1.16781 | + | 2.02270i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.809757 | − | 1.40254i | 0.0466736 | − | 0.0808411i | ||||
\(302\) | 2.11019 | + | 1.21832i | 0.121428 | + | 0.0701063i | ||||
\(303\) | − | 9.03519i | − | 0.519058i | ||||||
\(304\) | −16.9578 | − | 18.7047i | −0.972596 | − | 1.07279i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.3695 | + | 23.1566i | −0.764281 | + | 1.32377i | ||||
\(307\) | 5.10143 | + | 2.94531i | 0.291154 | + | 0.168098i | 0.638462 | − | 0.769653i | \(-0.279571\pi\) |
−0.347308 | + | 0.937751i | \(0.612904\pi\) | |||||||
\(308\) | 0.640701 | − | 0.369909i | 0.0365073 | − | 0.0210775i | ||||
\(309\) | 7.45579 | − | 12.9138i | 0.424145 | − | 0.734641i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.8202 | 0.840378 | 0.420189 | − | 0.907437i | \(-0.361964\pi\) | ||||
0.420189 | + | 0.907437i | \(0.361964\pi\) | |||||||
\(312\) | − | 35.0000i | − | 1.98148i | ||||||
\(313\) | −5.10489 | + | 2.94731i | −0.288546 | + | 0.166592i | −0.637286 | − | 0.770628i | \(-0.719943\pi\) |
0.348740 | + | 0.937219i | \(0.386610\pi\) | |||||||
\(314\) | −3.40310 | − | 5.89434i | −0.192048 | − | 0.332637i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.78905 | 0.381914 | ||||||||
\(317\) | 3.60146 | − | 2.07930i | 0.202278 | − | 0.116785i | −0.395439 | − | 0.918492i | \(-0.629408\pi\) |
0.597718 | + | 0.801707i | \(0.296074\pi\) | |||||||
\(318\) | 11.6208 | + | 6.70930i | 0.651665 | + | 0.376239i | ||||
\(319\) | −0.0863236 | − | 0.149517i | −0.00483319 | − | 0.00837133i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.997999 | − | 1.72858i | 0.0557029 | − | 0.0964802i | ||||
\(322\) | − | 4.49298i | − | 0.250384i | ||||||
\(323\) | −22.8549 | + | 20.7203i | −1.27168 | + | 1.15291i | ||||
\(324\) | 9.46090 | 0.525606 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.01604 | + | 6.95598i | −0.222428 | + | 0.385256i | ||||
\(327\) | 8.05949 | − | 4.65315i | 0.445691 | − | 0.257320i | ||||
\(328\) | −35.9000 | − | 20.7269i | −1.98225 | − | 1.14445i | ||||
\(329\) | 0.309757 | + | 0.536515i | 0.0170775 | + | 0.0295790i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6797 | 0.587008 | 0.293504 | − | 0.955958i | \(-0.405179\pi\) | ||||
0.293504 | + | 0.955958i | \(0.405179\pi\) | |||||||
\(332\) | 35.3330 | − | 20.3995i | 1.93915 | − | 1.11957i | ||||
\(333\) | 2.48580 | − | 1.43518i | 0.136221 | − | 0.0786472i | ||||
\(334\) | 25.6264 | 1.40222 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.785142 | + | 1.35991i | 0.0428330 | + | 0.0741890i | ||||
\(337\) | −22.8157 | − | 13.1726i | −1.24285 | − | 0.717560i | −0.273177 | − | 0.961964i | \(-0.588074\pi\) |
−0.969673 | + | 0.244404i | \(0.921408\pi\) | |||||||
\(338\) | −26.0537 | + | 15.0421i | −1.41713 | + | 0.818183i | ||||
\(339\) | 7.62999 | − | 13.2155i | 0.414404 | − | 0.717769i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.95077 | −0.105640 | ||||||||
\(342\) | −15.6797 | − | 5.03554i | −0.847862 | − | 0.272291i | ||||
\(343\) | 3.09534i | 0.167133i | ||||||||
\(344\) | −20.9081 | + | 36.2139i | −1.12729 | + | 1.95252i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.34139 | − | 5.78746i | −0.179634 | − | 0.311136i | ||||
\(347\) | −14.6215 | − | 8.44175i | −0.784925 | − | 0.453177i | 0.0532476 | − | 0.998581i | \(-0.483043\pi\) |
−0.838173 | + | 0.545404i | \(0.816376\pi\) | |||||||
\(348\) | 1.00608 | − | 0.580862i | 0.0539317 | − | 0.0311375i | ||||
\(349\) | −4.61640 | −0.247110 | −0.123555 | − | 0.992338i | \(-0.539430\pi\) | ||||
−0.123555 | + | 0.992338i | \(0.539430\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.7675 | − | 23.8461i | −0.734857 | − | 1.27281i | ||||
\(352\) | −2.06426 | + | 1.19180i | −0.110025 | + | 0.0635232i | ||||
\(353\) | − | 24.9508i | − | 1.32800i | −0.747735 | − | 0.663998i | \(-0.768858\pi\) | ||
0.747735 | − | 0.663998i | \(-0.231142\pi\) | |||||||
\(354\) | −8.55313 | −0.454594 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.72889 | + | 11.6548i | −0.356631 | + | 0.617703i | ||||
\(357\) | 1.66164 | − | 0.959347i | 0.0879432 | − | 0.0507740i | ||||
\(358\) | −28.0875 | − | 16.2163i | −1.48447 | − | 0.857059i | ||||
\(359\) | 5.90110 | − | 10.2210i | 0.311448 | − | 0.539444i | −0.667228 | − | 0.744854i | \(-0.732519\pi\) |
0.978676 | + | 0.205410i | \(0.0658527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4472 | − | 11.0627i | −0.813011 | − | 0.582248i | ||||
\(362\) | − | 46.6616i | − | 2.45248i | ||||||
\(363\) | 10.9992 | + | 6.35041i | 0.577310 | + | 0.333310i | ||||
\(364\) | 2.37693 | − | 4.11696i | 0.124585 | − | 0.215787i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.2746 | + | 33.3845i | −1.00750 | + | 1.74504i | ||||
\(367\) | −22.7183 | + | 13.1164i | −1.18588 | + | 0.684670i | −0.957368 | − | 0.288870i | \(-0.906721\pi\) |
−0.228516 | + | 0.973540i | \(0.573387\pi\) | |||||||
\(368\) | 46.7850i | 2.43884i | ||||||||
\(369\) | −10.9047 | −0.567674 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.485963 | + | 0.841712i | 0.0252299 | + | 0.0436995i | ||||
\(372\) | − | 13.1265i | − | 0.680579i | ||||||
\(373\) | 11.9960i | 0.621129i | 0.950552 | + | 0.310565i | \(0.100518\pi\) | ||||
−0.950552 | + | 0.310565i | \(0.899482\pi\) | |||||||
\(374\) | 6.90310 | + | 11.9565i | 0.356951 | + | 0.618257i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.99800 | − | 13.8529i | −0.412465 | − | 0.714411i | ||||
\(377\) | −0.960752 | − | 0.554690i | −0.0494812 | − | 0.0285680i | ||||
\(378\) | 2.65287 | + | 1.53163i | 0.136449 | + | 0.0787787i | ||||
\(379\) | −0.313217 | −0.0160889 | −0.00804444 | − | 0.999968i | \(-0.502561\pi\) | ||||
−0.00804444 | + | 0.999968i | \(0.502561\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.9358 | −0.816418 | ||||||||
\(382\) | 50.0277 | + | 28.8835i | 2.55964 | + | 1.47781i | ||||
\(383\) | −26.0572 | − | 15.0441i | −1.33146 | − | 0.768718i | −0.345936 | − | 0.938258i | \(-0.612439\pi\) |
−0.985523 | + | 0.169540i | \(0.945772\pi\) | |||||||
\(384\) | 9.72343 | + | 16.8415i | 0.496197 | + | 0.859438i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −21.4066 | − | 37.0772i | −1.08957 | − | 1.88718i | ||||
\(387\) | 11.0000i | 0.559161i | ||||||||
\(388\) | − | 27.2640i | − | 1.38412i | ||||||
\(389\) | −17.8609 | − | 30.9360i | −0.905583 | − | 1.56852i | −0.820133 | − | 0.572173i | \(-0.806100\pi\) |
−0.0854503 | − | 0.996342i | \(-0.527233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.1655 | 2.89099 | ||||||||
\(392\) | − | 39.8202i | − | 2.01123i | ||||||
\(393\) | 7.52297 | − | 4.34339i | 0.379484 | − | 0.219095i | ||||
\(394\) | 11.0562 | − | 19.1500i | 0.557006 | − | 0.964762i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.51248 | + | 4.35174i | −0.126257 | + | 0.218683i | ||||
\(397\) | 8.27326 | + | 4.77657i | 0.415223 | + | 0.239729i | 0.693031 | − | 0.720907i | \(-0.256275\pi\) |
−0.277809 | + | 0.960636i | \(0.589608\pi\) | |||||||
\(398\) | 7.15861i | 0.358829i | ||||||||
\(399\) | 0.793718 | + | 0.875485i | 0.0397356 | + | 0.0438291i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4418 | + | 26.7459i | −0.771124 | + | 1.33563i | 0.165823 | + | 0.986156i | \(0.446972\pi\) |
−0.936947 | + | 0.349471i | \(0.886361\pi\) | |||||||
\(402\) | 28.0416 | + | 16.1898i | 1.39859 | + | 0.807474i | ||||
\(403\) | −10.8557 | + | 6.26755i | −0.540761 | + | 0.312209i | ||||
\(404\) | −15.8433 | + | 27.4414i | −0.788233 | + | 1.36526i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.123418 | 0.00612514 | ||||||||
\(407\) | − | 1.48206i | − | 0.0734629i | ||||||
\(408\) | −42.9039 | + | 24.7706i | −2.12406 | + | 1.22633i | ||||
\(409\) | 15.7816 | + | 27.3345i | 0.780349 | + | 1.35160i | 0.931738 | + | 0.363130i | \(0.118292\pi\) |
−0.151389 | + | 0.988474i | \(0.548375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.62955 | 0.327012 | ||||||||
\(412\) | −45.2890 | + | 26.1476i | −2.23123 | + | 1.28820i | ||||
\(413\) | −0.536515 | − | 0.309757i | −0.0264002 | − | 0.0152421i | ||||
\(414\) | 15.2585 | + | 26.4285i | 0.749916 | + | 1.29889i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.65817 | + | 13.2643i | −0.375472 | + | 0.650337i | ||||
\(417\) | − | 4.36245i | − | 0.213630i | ||||||
\(418\) | −6.29966 | + | 5.71130i | −0.308126 | + | 0.279349i | ||||
\(419\) | 26.5070 | 1.29495 | 0.647476 | − | 0.762086i | \(-0.275824\pi\) | ||||
0.647476 | + | 0.762086i | \(0.275824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1180 | − | 17.5248i | 0.493119 | − | 0.854107i | −0.506850 | − | 0.862035i | \(-0.669190\pi\) |
0.999969 | + | 0.00792731i | \(0.00252337\pi\) | |||||||
\(422\) | −27.9806 | + | 16.1546i | −1.36207 | + | 0.786394i | ||||
\(423\) | −3.64410 | − | 2.10392i | −0.177182 | − | 0.102296i | ||||
\(424\) | −12.5477 | − | 21.7332i | −0.609369 | − | 1.05546i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 30.1468 | 1.46062 | ||||||||
\(427\) | −2.41808 | + | 1.39608i | −0.117019 | + | 0.0675611i | ||||
\(428\) | −6.06218 | + | 3.50000i | −0.293026 | + | 0.169179i | ||||
\(429\) | −4.75385 | −0.229518 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.73045 | + | 9.92543i | 0.276026 | + | 0.478091i | 0.970394 | − | 0.241529i | \(-0.0776490\pi\) |
−0.694367 | + | 0.719621i | \(0.744316\pi\) | |||||||
\(432\) | −27.6241 | − | 15.9488i | −1.32906 | − | 0.767336i | ||||
\(433\) | 22.4706 | − | 12.9734i | 1.07987 | − | 0.623461i | 0.149006 | − | 0.988836i | \(-0.452393\pi\) |
0.930860 | + | 0.365375i | \(0.119059\pi\) | |||||||
\(434\) | 0.697262 | − | 1.20769i | 0.0334696 | − | 0.0579711i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −32.6374 | −1.56305 | ||||||||
\(437\) | 7.43771 | + | 34.4136i | 0.355794 | + | 1.64622i | ||||
\(438\) | 43.1225i | 2.06047i | ||||||||
\(439\) | 12.6562 | − | 21.9211i | 0.604046 | − | 1.04624i | −0.388156 | − | 0.921594i | \(-0.626888\pi\) |
0.992202 | − | 0.124644i | \(-0.0397789\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.23747 | − | 9.07157i | −0.249403 | − | 0.431979i | ||||
\(442\) | 76.8291 | + | 44.3573i | 3.65439 | + | 2.10986i | ||||
\(443\) | 17.3421 | − | 10.0125i | 0.823949 | − | 0.475707i | −0.0278272 | − | 0.999613i | \(-0.508859\pi\) |
0.851776 | + | 0.523905i | \(0.175525\pi\) | |||||||
\(444\) | 9.97262 | 0.473279 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.9573 | + | 44.9594i | 1.22912 | + | 2.12889i | ||||
\(447\) | 0.991229 | − | 0.572286i | 0.0468835 | − | 0.0270682i | ||||
\(448\) | 0.866350i | 0.0409312i | ||||||||
\(449\) | −19.7601 | −0.932536 | −0.466268 | − | 0.884644i | \(-0.654402\pi\) | ||||
−0.466268 | + | 0.884644i | \(0.654402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.81522 | + | 4.87610i | −0.132563 | + | 0.229607i | ||||
\(452\) | −46.3471 | + | 26.7585i | −2.17999 | + | 1.25862i | ||||
\(453\) | 1.02847 | + | 0.593786i | 0.0483216 | + | 0.0278985i | ||||
\(454\) | −5.01404 | + | 8.68457i | −0.235320 | + | 0.407587i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −20.4940 | − | 22.6052i | −0.959719 | − | 1.05859i | ||||
\(457\) | 34.4647i | 1.61219i | 0.591785 | + | 0.806096i | \(0.298423\pi\) | ||||
−0.591785 | + | 0.806096i | \(0.701577\pi\) | |||||||
\(458\) | 7.68388 | + | 4.43629i | 0.359044 | + | 0.207294i | ||||
\(459\) | −19.4874 | + | 33.7532i | −0.909595 | + | 1.57546i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.96637 | − | 6.86995i | 0.184732 | − | 0.319965i | −0.758754 | − | 0.651377i | \(-0.774192\pi\) |
0.943486 | + | 0.331412i | \(0.107525\pi\) | |||||||
\(462\) | 0.458010 | − | 0.264432i | 0.0213085 | − | 0.0123025i | ||||
\(463\) | 9.25395i | 0.430068i | 0.976607 | + | 0.215034i | \(0.0689862\pi\) | ||||
−0.976607 | + | 0.215034i | \(0.931014\pi\) | |||||||
\(464\) | −1.28514 | −0.0596612 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.8007 | − | 42.9561i | −1.14887 | − | 1.98990i | ||||
\(467\) | − | 9.47183i | − | 0.438304i | −0.975691 | − | 0.219152i | \(-0.929671\pi\) | ||
0.975691 | − | 0.219152i | \(-0.0703290\pi\) | |||||||
\(468\) | 32.2889i | 1.49256i | ||||||||
\(469\) | 1.17265 | + | 2.03108i | 0.0541478 | + | 0.0937868i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.65861 | − | 2.87280i | −0.0764247 | − | 0.132371i | ||||
\(472\) | 13.8529 | + | 7.99800i | 0.637633 | + | 0.368138i | ||||
\(473\) | 4.91873 | + | 2.83983i | 0.226164 | + | 0.130576i | ||||
\(474\) | 4.85320 | 0.222915 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.72889 | −0.308418 | ||||||||
\(477\) | −5.71704 | − | 3.30074i | −0.261765 | − | 0.151130i | ||||
\(478\) | 51.6170 | + | 29.8011i | 2.36091 | + | 1.36307i | ||||
\(479\) | −17.3574 | − | 30.0639i | −0.793081 | − | 1.37366i | −0.924050 | − | 0.382270i | \(-0.875142\pi\) |
0.130969 | − | 0.991386i | \(-0.458191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.76164 | − | 8.24740i | −0.217112 | − | 0.376049i | ||||
\(482\) | − | 11.3874i | − | 0.518682i | ||||||
\(483\) | − | 2.18980i | − | 0.0996393i | ||||||
\(484\) | −22.2710 | − | 38.5745i | −1.01232 | − | 1.75339i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.6554 | −1.57200 | ||||||||
\(487\) | 28.5070i | 1.29178i | 0.763432 | + | 0.645888i | \(0.223513\pi\) | ||||
−0.763432 | + | 0.645888i | \(0.776487\pi\) | |||||||
\(488\) | 62.4355 | − | 36.0471i | 2.82632 | − | 1.63178i | ||||
\(489\) | −1.95735 | + | 3.39022i | −0.0885142 | + | 0.153311i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5949 | − | 27.0112i | 0.703788 | − | 1.21900i | −0.263339 | − | 0.964703i | \(-0.584824\pi\) |
0.967127 | − | 0.254293i | \(-0.0818428\pi\) | |||||||
\(492\) | −32.8108 | − | 18.9433i | −1.47922 | − | 0.854030i | ||||
\(493\) | 1.57028i | 0.0707221i | ||||||||
\(494\) | −16.7070 | + | 52.0223i | −0.751681 | + | 2.34059i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.26053 | + | 12.5756i | −0.326007 | + | 0.564661i | ||||
\(497\) | 1.89103 | + | 1.09178i | 0.0848242 | + | 0.0489732i | ||||
\(498\) | 25.2581 | − | 14.5828i | 1.13184 | − | 0.653469i | ||||
\(499\) | 8.09334 | − | 14.0181i | 0.362308 | − | 0.627535i | −0.626032 | − | 0.779797i | \(-0.715322\pi\) |
0.988340 | + | 0.152262i | \(0.0486556\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.4899 | 0.558006 | ||||||||
\(502\) | − | 48.8944i | − | 2.18226i | ||||||
\(503\) | 14.9146 | − | 8.61094i | 0.665008 | − | 0.383943i | −0.129174 | − | 0.991622i | \(-0.541233\pi\) |
0.794183 | + | 0.607679i | \(0.207899\pi\) | |||||||
\(504\) | −0.957790 | − | 1.65894i | −0.0426633 | − | 0.0738951i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.7570 | 0.700483 | ||||||||
\(507\) | −12.6981 | + | 7.33126i | −0.563943 | + | 0.325593i | ||||
\(508\) | 48.3998 | + | 27.9437i | 2.14740 | + | 1.23980i | ||||
\(509\) | −18.2956 | − | 31.6889i | −0.810939 | − | 1.40459i | −0.912207 | − | 0.409729i | \(-0.865623\pi\) |
0.101268 | − | 0.994859i | \(-0.467710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.56171 | + | 2.70496i | −0.0690859 | + | 0.119660i | ||||
\(512\) | − | 48.6224i | − | 2.14883i | ||||||
\(513\) | −22.8549 | − | 7.33983i | −1.00907 | − | 0.324062i | ||||
\(514\) | 4.42260 | 0.195072 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −19.1089 | + | 33.0976i | −0.841224 | + | 1.45704i | ||||
\(517\) | −1.88157 | + | 1.08632i | −0.0827512 | + | 0.0477765i | ||||
\(518\) | 0.917520 | + | 0.529730i | 0.0403135 | + | 0.0232750i | ||||
\(519\) | −1.62853 | − | 2.82070i | −0.0714847 | − | 0.123815i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.63667 | −0.159325 | −0.0796626 | − | 0.996822i | \(-0.525384\pi\) | ||||
−0.0796626 | + | 0.996822i | \(0.525384\pi\) | |||||||
\(522\) | −0.725968 | + | 0.419138i | −0.0317748 | + | 0.0183452i | ||||
\(523\) | −30.8507 | + | 17.8117i | −1.34901 | + | 0.778850i | −0.988109 | − | 0.153756i | \(-0.950863\pi\) |
−0.360898 | + | 0.932605i | \(0.617530\pi\) | |||||||
\(524\) | −30.4647 | −1.33086 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.11250 | − | 14.0513i | −0.353722 | − | 0.612664i | ||||
\(527\) | 15.3658 | + | 8.87147i | 0.669346 | + | 0.386447i | ||||
\(528\) | −4.76922 | + | 2.75351i | −0.207554 | + | 0.119831i | ||||
\(529\) | 21.1214 | − | 36.5834i | 0.918322 | − | 1.59058i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.20784 | 0.182605 | ||||||||
\(532\) | −0.875485 | − | 4.05079i | −0.0379571 | − | 0.175624i | ||||
\(533\) | 36.1796i | 1.56711i | ||||||||
\(534\) | −4.81020 | + | 8.33151i | −0.208158 | + | 0.360540i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −30.2780 | − | 52.4431i | −1.30781 | − | 2.26520i | ||||
\(537\) | −13.6893 | − | 7.90354i | −0.590739 | − | 0.341063i | ||||
\(538\) | −61.8469 | + | 35.7073i | −2.66641 | + | 1.53945i | ||||
\(539\) | −5.40856 | −0.232963 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58632 | − | 2.74759i | −0.0682014 | − | 0.118128i | 0.829908 | − | 0.557900i | \(-0.188393\pi\) |
−0.898110 | + | 0.439772i | \(0.855059\pi\) | |||||||
\(542\) | −1.07033 | + | 0.617957i | −0.0459747 | + | 0.0265435i | ||||
\(543\) | − | 22.7420i | − | 0.975955i | ||||||
\(544\) | 21.6797 | 0.929508 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.69916 | − | 2.94304i | 0.0727175 | − | 0.125950i | ||||
\(547\) | 24.5782 | − | 14.1902i | 1.05089 | − | 0.606731i | 0.127991 | − | 0.991775i | \(-0.459147\pi\) |
0.922898 | + | 0.385044i | \(0.125814\pi\) | |||||||
\(548\) | −20.1350 | − | 11.6250i | −0.860127 | − | 0.496594i | ||||
\(549\) | 9.48240 | − | 16.4240i | 0.404699 | − | 0.700959i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.945310 | + | 0.204307i | −0.0402715 | + | 0.00870377i | ||||
\(552\) | 56.5411i | 2.40655i | ||||||||
\(553\) | 0.304428 | + | 0.175762i | 0.0129456 | + | 0.00747415i | ||||
\(554\) | 11.0172 | − | 19.0823i | 0.468074 | − | 0.810728i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.64959 | + | 13.2495i | −0.324415 | + | 0.561903i | ||||
\(557\) | −1.84510 | + | 1.06527i | −0.0781793 | + | 0.0451368i | −0.538580 | − | 0.842574i | \(-0.681039\pi\) |
0.460401 | + | 0.887711i | \(0.347706\pi\) | |||||||
\(558\) | 9.47183i | 0.400974i | ||||||||
\(559\) | 36.4959 | 1.54361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.36445 | + | 5.82739i | 0.142047 | + | 0.246033i | ||||
\(562\) | − | 11.8906i | − | 0.501575i | ||||||
\(563\) | − | 20.2609i | − | 0.853894i | −0.904277 | − | 0.426947i | \(-0.859589\pi\) | ||
0.904277 | − | 0.426947i | \(-0.140411\pi\) | |||||||
\(564\) | −7.30976 | − | 12.6609i | −0.307796 | − | 0.533119i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 21.1460 | + | 36.6260i | 0.888834 | + | 1.53951i | ||||
\(567\) | 0.424237 | + | 0.244933i | 0.0178163 | + | 0.0102862i | ||||
\(568\) | −48.8268 | − | 28.1901i | −2.04873 | − | 1.18283i | ||||
\(569\) | 34.7530 | 1.45692 | 0.728460 | − | 0.685088i | \(-0.240236\pi\) | ||||
0.728460 | + | 0.685088i | \(0.240236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0702 | 1.34210 | 0.671048 | − | 0.741414i | \(-0.265845\pi\) | ||||
0.671048 | + | 0.741414i | \(0.265845\pi\) | |||||||
\(572\) | 14.4383 | + | 8.33593i | 0.603694 | + | 0.348543i | ||||
\(573\) | 24.3826 | + | 14.0773i | 1.01860 | + | 0.588088i | ||||
\(574\) | −2.01248 | − | 3.48572i | −0.0839993 | − | 0.145491i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.94220 | − | 5.09603i | −0.122591 | − | 0.212335i | ||||
\(577\) | − | 30.2740i | − | 1.26032i | −0.776464 | − | 0.630162i | \(-0.782988\pi\) | ||
0.776464 | − | 0.630162i | \(-0.217012\pi\) | |||||||
\(578\) | − | 82.9528i | − | 3.45038i | ||||||
\(579\) | −10.4332 | − | 18.0708i | −0.433588 | − | 0.750996i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.11250 | 0.0876411 | ||||||||
\(582\) | − | 19.4899i | − | 0.807881i | ||||||
\(583\) | −2.95190 | + | 1.70428i | −0.122255 | + | 0.0705841i | ||||
\(584\) | 40.3237 | − | 69.8427i | 1.66861 | − | 2.89011i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5828 | − | 25.2581i | 0.602408 | − | 1.04340i | ||||
\(587\) | 2.16168 | + | 1.24805i | 0.0892222 | + | 0.0515125i | 0.543947 | − | 0.839119i | \(-0.316929\pi\) |
−0.454725 | + | 0.890632i | \(0.650262\pi\) | |||||||
\(588\) | − | 36.3936i | − | 1.50085i | ||||||
\(589\) | −3.34139 | + | 10.4045i | −0.137680 | + | 0.428708i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.38862 | − | 9.33336i | 0.221658 | − | 0.383923i | ||||
\(592\) | −9.55406 | − | 5.51604i | −0.392669 | − | 0.226708i | ||||
\(593\) | −8.62901 | + | 4.98196i | −0.354351 | + | 0.204585i | −0.666600 | − | 0.745416i | \(-0.732251\pi\) |
0.312249 | + | 0.950000i | \(0.398918\pi\) | |||||||
\(594\) | −5.37147 | + | 9.30365i | −0.220394 | + | 0.381733i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.01404 | −0.164421 | ||||||||
\(597\) | 3.48898i | 0.142794i | ||||||||
\(598\) | 87.6849 | − | 50.6249i | 3.58570 | − | 2.07021i | ||||
\(599\) | 16.0351 | + | 27.7736i | 0.655176 | + | 1.13480i | 0.981850 | + | 0.189661i | \(0.0607389\pi\) |
−0.326673 | + | 0.945137i | \(0.605928\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.68278 | 0.150224 | 0.0751119 | − | 0.997175i | \(-0.476069\pi\) | ||||
0.0751119 | + | 0.997175i | \(0.476069\pi\) | |||||||
\(602\) | −3.51619 | + | 2.03008i | −0.143309 | + | 0.0827397i | ||||
\(603\) | −13.7955 | − | 7.96481i | −0.561794 | − | 0.324352i | ||||
\(604\) | −2.08242 | − | 3.60686i | −0.0847324 | − | 0.146761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.3257 | + | 19.6167i | −0.460075 | + | 0.796873i | ||||
\(607\) | 20.4850i | 0.831460i | 0.909488 | + | 0.415730i | \(0.136474\pi\) | ||||
−0.909488 | + | 0.415730i | \(0.863526\pi\) | |||||||
\(608\) | 2.82070 | + | 13.0511i | 0.114395 | + | 0.529293i | ||||
\(609\) | 0.0601518 | 0.00243747 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.98040 | + | 12.0904i | −0.282397 | + | 0.489126i | ||||
\(612\) | 39.5806 | − | 22.8519i | 1.59995 | − | 0.923732i | ||||
\(613\) | −9.27664 | − | 5.35587i | −0.374680 | − | 0.216322i | 0.300821 | − | 0.953681i | \(-0.402739\pi\) |
−0.675501 | + | 0.737359i | \(0.736073\pi\) | |||||||
\(614\) | −7.38395 | − | 12.7894i | −0.297992 | − | 0.516137i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.989077 | −0.0398511 | ||||||||
\(617\) | 15.3564 | − | 8.86600i | 0.618224 | − | 0.356932i | −0.157953 | − | 0.987447i | \(-0.550489\pi\) |
0.776177 | + | 0.630515i | \(0.217156\pi\) | |||||||
\(618\) | −32.3751 | + | 18.6918i | −1.30232 | + | 0.751894i | ||||
\(619\) | 13.2780 | 0.533689 | 0.266844 | − | 0.963740i | \(-0.414019\pi\) | ||||
0.266844 | + | 0.963740i | \(0.414019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.2409 | + | 38.5224i | 0.892498 | + | 1.54585i | ||||
\(622\) | −32.1768 | − | 18.5773i | −1.29017 | − | 0.744882i | ||||
\(623\) | −0.603462 | + | 0.348409i | −0.0241772 | + | 0.0139587i | ||||
\(624\) | −17.6933 | + | 30.6456i | −0.708297 | + | 1.22681i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.7779 | 0.590645 | ||||||||
\(627\) | −3.07034 | + | 2.78359i | −0.122618 | + | 0.111166i | ||||
\(628\) | 11.6336i | 0.464229i | ||||||||
\(629\) | −6.73992 | + | 11.6739i | −0.268738 | + | 0.465468i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.03208 | − | 3.51966i | −0.0808957 | − | 0.140115i | 0.822739 | − | 0.568419i | \(-0.192445\pi\) |
−0.903635 | + | 0.428304i | \(0.859111\pi\) | |||||||
\(632\) | −7.86041 | − | 4.53821i | −0.312670 | − | 0.180520i | ||||
\(633\) | −13.6372 | + | 7.87347i | −0.542032 | + | 0.312942i | ||||
\(634\) | −10.4257 | −0.414058 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.4679 | − | 19.8630i | −0.454733 | − | 0.787620i | ||||
\(637\) | −30.0977 | + | 17.3769i | −1.19252 | + | 0.688499i | ||||
\(638\) | 0.432830i | 0.0171359i | ||||||||
\(639\) | −14.8312 | −0.586712 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.49254 | + | 4.31720i | −0.0984493 | + | 0.170519i | −0.911043 | − | 0.412311i | \(-0.864722\pi\) |
0.812594 | + | 0.582831i | \(0.198055\pi\) | |||||||
\(642\) | −4.33359 | + | 2.50200i | −0.171033 | + | 0.0987461i | ||||
\(643\) | 5.08927 | + | 2.93829i | 0.200701 | + | 0.115875i | 0.596983 | − | 0.802254i | \(-0.296366\pi\) |
−0.396281 | + | 0.918129i | \(0.629700\pi\) | |||||||
\(644\) | −3.83983 | + | 6.65079i | −0.151311 | + | 0.262078i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 75.5943 | − | 16.3380i | 2.97422 | − | 0.642809i | ||||
\(647\) | − | 16.9757i | − | 0.667385i | −0.942682 | − | 0.333692i | \(-0.891705\pi\) | ||
0.942682 | − | 0.333692i | \(-0.108295\pi\) | |||||||
\(648\) | −10.9539 | − | 6.32424i | −0.430310 | − | 0.248440i | ||||
\(649\) | 1.08632 | − | 1.88157i | 0.0426419 | − | 0.0738580i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.339833 | − | 0.588608i | 0.0133191 | − | 0.0230694i | ||||
\(652\) | 11.8896 | − | 6.86445i | 0.465632 | − | 0.268833i | ||||
\(653\) | 24.6797i | 0.965790i | 0.875678 | + | 0.482895i | \(0.160415\pi\) | ||||
−0.875678 | + | 0.482895i | \(0.839585\pi\) | |||||||
\(654\) | −23.3311 | −0.912317 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.9558 | + | 36.2965i | 0.818186 | + | 1.41714i | ||||
\(657\) | − | 21.2148i | − | 0.827667i | ||||||
\(658\) | − | 1.55313i | − | 0.0605474i | ||||||
\(659\) | 0.943308 | + | 1.63386i | 0.0367461 | + | 0.0636461i | 0.883814 | − | 0.467839i | \(-0.154967\pi\) |
−0.847067 | + | 0.531485i | \(0.821634\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3749 | − | 38.7545i | −0.870284 | − | 1.50738i | −0.861703 | − | 0.507413i | \(-0.830602\pi\) |
−0.00858048 | − | 0.999963i | \(-0.502731\pi\) | |||||||
\(662\) | −23.1871 | − | 13.3871i | −0.901191 | − | 0.520303i | ||||
\(663\) | 37.4452 | + | 21.6190i | 1.45425 | + | 0.839611i | ||||
\(664\) | −54.5451 | −2.11676 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.19603 | −0.278840 | ||||||||
\(667\) | 1.55206 | + | 0.896081i | 0.0600959 | + | 0.0346964i | ||||
\(668\) | −37.9338 | − | 21.9011i | −1.46770 | − | 0.847379i | ||||
\(669\) | 12.6511 | + | 21.9124i | 0.489122 | + | 0.847183i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.89608 | − | 8.48026i | −0.189011 | − | 0.327377i | ||||
\(672\) | − | 0.830467i | − | 0.0320360i | ||||||
\(673\) | 25.4046i | 0.979274i | 0.871926 | + | 0.489637i | \(0.162871\pi\) | ||||
−0.871926 | + | 0.489637i | \(0.837129\pi\) | |||||||
\(674\) | 33.0241 | + | 57.1994i | 1.27204 | + | 2.20324i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 51.4217 | 1.97776 | ||||||||
\(677\) | 3.86946i | 0.148716i | 0.997232 | + | 0.0743578i | \(0.0236907\pi\) | ||||
−0.997232 | + | 0.0743578i | \(0.976309\pi\) | |||||||
\(678\) | −33.1316 | + | 19.1285i | −1.27241 | + | 0.734627i | ||||
\(679\) | 0.705838 | − | 1.22255i | 0.0270876 | − | 0.0469170i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.44375 | + | 4.23270i | −0.0936448 | + | 0.162198i | ||||
\(682\) | 4.23540 | + | 2.44531i | 0.162182 | + | 0.0936357i | ||||
\(683\) | − | 48.5171i | − | 1.85645i | −0.372015 | − | 0.928227i | \(-0.621333\pi\) | ||
0.372015 | − | 0.928227i | \(-0.378667\pi\) | |||||||
\(684\) | 18.9066 | + | 20.8543i | 0.722910 | + | 0.797382i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.88004 | − | 6.72043i | 0.148141 | − | 0.256587i | ||||
\(687\) | 3.74499 | + | 2.16217i | 0.142880 | + | 0.0824919i | ||||
\(688\) | 36.6138 | − | 21.1390i | 1.39589 | − | 0.805917i | ||||
\(689\) | −10.9512 | + | 18.9681i | −0.417208 | + | 0.722626i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −47.6374 | −1.81221 | −0.906105 | − | 0.423052i | \(-0.860959\pi\) | ||||
−0.906105 | + | 0.423052i | \(0.860959\pi\) | |||||||
\(692\) | 11.4226i | 0.434222i | ||||||||
\(693\) | −0.225325 | + | 0.130091i | −0.00855937 | + | 0.00494176i | ||||
\(694\) | 21.1636 | + | 36.6565i | 0.803360 | + | 1.39146i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.55313 | −0.0588714 | ||||||||
\(697\) | 44.3498 | − | 25.6054i | 1.67987 | − | 0.969873i | ||||
\(698\) | 10.0229 | + | 5.78670i | 0.379371 | + | 0.219030i | ||||
\(699\) | −12.0874 | − | 20.9361i | −0.457189 | − | 0.791874i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.2766 | + | 24.7277i | −0.539218 | + | 0.933954i | 0.459728 | + | 0.888060i | \(0.347947\pi\) |
−0.998946 | + | 0.0458939i | \(0.985386\pi\) | |||||||
\(702\) | 69.0310i | 2.60541i | ||||||||
\(703\) | −7.90458 | − | 2.53855i | −0.298127 | − | 0.0957434i | ||||
\(704\) | −3.03831 | −0.114510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.2760 | + | 54.1717i | −1.17709 | + | 2.03878i | ||||
\(707\) | −1.42086 | + | 0.820334i | −0.0534370 | + | 0.0308518i | ||||
\(708\) | 12.6609 | + | 7.30976i | 0.475825 | + | 0.274717i | ||||
\(709\) | 9.74137 | + | 16.8726i | 0.365845 | + | 0.633662i | 0.988911 | − | 0.148507i | \(-0.0474467\pi\) |
−0.623066 | + | 0.782169i | \(0.714113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.38760 | −0.0895421 | ||||||||
\(712\) | 15.5815 | − | 8.99600i | 0.583942 | − | 0.337139i | ||||
\(713\) | 17.5370 | − | 10.1250i | 0.656765 | − | 0.379183i | ||||
\(714\) | −4.81020 | −0.180017 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.7179 | + | 48.0088i | 1.03587 | + | 1.79417i | ||||
\(717\) | 25.1572 | + | 14.5245i | 0.939513 | + | 0.542428i | ||||
\(718\) | −25.6242 | + | 14.7942i | −0.956288 | + | 0.552113i | ||||
\(719\) | 2.05313 | − | 3.55613i | 0.0765689 | − | 0.132621i | −0.825199 | − | 0.564843i | \(-0.808937\pi\) |
0.901767 | + | 0.432221i | \(0.142270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.70774 | −0.100842 | ||||||||
\(722\) | 19.6709 | + | 43.3819i | 0.732074 | + | 1.61451i | ||||
\(723\) | − | 5.55002i | − | 0.206407i | ||||||
\(724\) | −39.8784 | + | 69.0714i | −1.48207 | + | 2.56702i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15.9206 | − | 27.5753i | −0.590869 | − | 1.02341i | ||||
\(727\) | −10.7488 | − | 6.20584i | −0.398652 | − | 0.230162i | 0.287250 | − | 0.957856i | \(-0.407259\pi\) |
−0.685902 | + | 0.727694i | \(0.740592\pi\) | |||||||
\(728\) | −5.50405 | + | 3.17776i | −0.203994 | + | 0.117776i | ||||
\(729\) | −23.5139 | −0.870887 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.8293 | − | 44.7376i | −0.955330 | − | 1.65468i | ||||
\(732\) | 57.0628 | − | 32.9452i | 2.10910 | − | 1.21769i | ||||
\(733\) | − | 16.3985i | − | 0.605693i | −0.953039 | − | 0.302847i | \(-0.902063\pi\) | ||
0.953039 | − | 0.302847i | \(-0.0979370\pi\) | |||||||
\(734\) | 65.7661 | 2.42747 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.3715 | − | 21.4280i | 0.456018 | − | 0.789847i | ||||
\(737\) | −7.12305 | + | 4.11250i | −0.262381 | + | 0.151486i | ||||
\(738\) | 23.6756 | + | 13.6691i | 0.871509 | + | 0.503166i | ||||
\(739\) | −23.1018 | + | 40.0135i | −0.849814 | + | 1.47192i | 0.0315597 | + | 0.999502i | \(0.489953\pi\) |
−0.881374 | + | 0.472419i | \(0.843381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.14267 | + | 25.3547i | −0.299128 | + | 0.931430i | ||||
\(742\) | − | 2.43664i | − | 0.0894517i | ||||||
\(743\) | 21.4888 | + | 12.4066i | 0.788347 | + | 0.455153i | 0.839380 | − | 0.543544i | \(-0.182918\pi\) |
−0.0510331 | + | 0.998697i | \(0.516251\pi\) | |||||||
\(744\) | −8.77457 | + | 15.1980i | −0.321691 | + | 0.557185i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 15.0371 | − | 26.0450i | 0.550547 | − | 0.953576i | ||||
\(747\) | −12.4261 | + | 7.17420i | −0.454647 | + | 0.262490i | ||||
\(748\) | − | 23.5984i | − | 0.862841i | ||||||
\(749\) | −0.362446 | −0.0132435 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.26955 | + | 9.12712i | 0.192289 | + | 0.333054i | 0.946008 | − | 0.324142i | \(-0.105076\pi\) |
−0.753720 | + | 0.657196i | \(0.771742\pi\) | |||||||
\(752\) | 16.1726i | 0.589756i | ||||||||
\(753\) | − | 23.8303i | − | 0.868423i | ||||||
\(754\) | 1.39062 | + | 2.40862i | 0.0506434 | + | 0.0877169i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.61796 | − | 4.53443i | −0.0952142 | − | 0.164916i | ||||
\(757\) | −5.36652 | − | 3.09836i | −0.195049 | − | 0.112612i | 0.399295 | − | 0.916823i | \(-0.369255\pi\) |
−0.594344 | + | 0.804211i | \(0.702588\pi\) | |||||||
\(758\) | 0.680039 | + | 0.392621i | 0.0247001 | + | 0.0142606i | ||||
\(759\) | 7.67967 | 0.278754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6084 | 1.29080 | 0.645402 | − | 0.763843i | \(-0.276690\pi\) | ||||
0.645402 | + | 0.763843i | \(0.276690\pi\) | |||||||
\(762\) | 34.5990 | + | 19.9757i | 1.25339 | + | 0.723644i | ||||
\(763\) | −1.46349 | − | 0.844949i | −0.0529820 | − | 0.0305892i | ||||
\(764\) | −49.3694 | − | 85.5103i | −1.78612 | − | 3.09365i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.7159 | + | 65.3258i | 1.36273 | + | 2.36032i | ||||
\(767\) | − | 13.9608i | − | 0.504095i | ||||||
\(768\) | − | 39.2116i | − | 1.41493i | ||||||
\(769\) | −0.0777477 | − | 0.134663i | −0.00280365 | − | 0.00485607i | 0.864620 | − | 0.502426i | \(-0.167559\pi\) |
−0.867424 | + | 0.497570i | \(0.834226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.15550 | 0.0776283 | ||||||||
\(772\) | 73.1787i | 2.63376i | ||||||||
\(773\) | −4.40653 | + | 2.54411i | −0.158492 | + | 0.0915054i | −0.577148 | − | 0.816639i | \(-0.695835\pi\) |
0.418656 | + | 0.908145i | \(0.362501\pi\) | |||||||
\(774\) | 13.7886 | − | 23.8826i | 0.495621 | − | 0.858441i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.2249 | + | 31.5664i | −0.654236 | + | 1.13317i | ||||
\(777\) | 0.447183 | + | 0.258181i | 0.0160426 | + | 0.00926220i | ||||
\(778\) | 89.5552i | 3.21071i | ||||||||
\(779\) | 21.1847 | + | 23.3671i | 0.759020 | + | 0.837212i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.82891 | + | 6.63187i | −0.137009 | + | 0.237307i | ||||
\(782\) | −124.114 | − | 71.6575i | −4.43832 | − | 2.56247i | ||||
\(783\) | −1.05818 | + | 0.610938i | −0.0378161 | + | 0.0218331i | ||||
\(784\) | −20.1300 | + | 34.8662i | −0.718928 | + | 1.24522i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.7779 | −0.776793 | ||||||||
\(787\) | 22.5070i | 0.802289i | 0.916015 | + | 0.401144i | \(0.131387\pi\) | ||||
−0.916015 | + | 0.401144i | \(0.868613\pi\) | |||||||
\(788\) | −32.7323 | + | 18.8980i | −1.16604 | + | 0.673213i | ||||
\(789\) | −3.95389 | − | 6.84833i | −0.140762 | − | 0.243807i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.77101 | −0.0985257 | ||||||||
\(792\) | 5.81793 | − | 3.35899i | 0.206731 | − | 0.119356i | ||||
\(793\) | −54.4917 | − | 31.4608i | −1.93506 | − | 1.11721i | ||||
\(794\) | −11.9749 | − | 20.7412i | −0.424975 | − | 0.736078i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.11796 | − | 10.5966i | 0.216845 | − | 0.375587i | ||||
\(797\) | − | 29.2219i | − | 1.03509i | −0.855655 | − | 0.517546i | \(-0.826846\pi\) | ||
0.855655 | − | 0.517546i | \(-0.173154\pi\) | |||||||
\(798\) | −0.625847 | − | 2.89574i | −0.0221547 | − | 0.102508i | ||||
\(799\) | 19.7610 | 0.699093 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.36645 | − | 4.09881i | 0.0836144 | − | 0.144824i | ||||
\(802\) | 67.0525 | − | 38.7128i | 2.36770 | − | 1.36699i | ||||
\(803\) | −9.48634 | − | 5.47694i | −0.334766 | − | 0.193277i | ||||
\(804\) | −27.6725 | − | 47.9303i | −0.975936 | − | 1.69037i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 31.4257 | 1.10692 | ||||||||
\(807\) | −30.1431 | + | 17.4031i | −1.06109 | + | 0.612618i | ||||
\(808\) | 36.6870 | − | 21.1812i | 1.29064 | − | 0.745153i | ||||
\(809\) | −25.8664 | −0.909412 | −0.454706 | − | 0.890641i | \(-0.650256\pi\) | ||||
−0.454706 | + | 0.890641i | \(0.650256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.84841 | + | 17.0579i | 0.345824 | + | 0.598985i | 0.985503 | − | 0.169657i | \(-0.0542660\pi\) |
−0.639679 | + | 0.768642i | \(0.720933\pi\) | |||||||
\(812\) | −0.182691 | − | 0.105477i | −0.00641120 | − | 0.00370151i | ||||
\(813\) | −0.521661 | + | 0.301181i | −0.0182954 | + | 0.0105629i | ||||
\(814\) | −1.85777 | + | 3.21776i | −0.0651150 | + | 0.112782i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 50.0882 | 1.75344 | ||||||||
\(817\) | 23.5714 | − | 21.3699i | 0.824658 | − | 0.747638i | ||||
\(818\) | − | 79.1295i | − | 2.76670i | ||||||
\(819\) | −0.835929 | + | 1.44787i | −0.0292097 | + | 0.0505927i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.04021 | − | 3.53375i | −0.0712038 | − | 0.123329i | 0.828225 | − | 0.560395i | \(-0.189351\pi\) |
−0.899429 | + | 0.437067i | \(0.856017\pi\) | |||||||
\(822\) | −14.3937 | − | 8.31020i | −0.502038 | − | 0.289852i | ||||
\(823\) | 9.18538 | − | 5.30318i | 0.320182 | − | 0.184857i | −0.331292 | − | 0.943528i | \(-0.607484\pi\) |
0.651474 | + | 0.758671i | \(0.274151\pi\) | |||||||
\(824\) | 69.9145 | 2.43559 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.776567 | + | 1.34505i | 0.0270202 | + | 0.0468004i | ||||
\(827\) | −13.3407 | + | 7.70228i | −0.463903 | + | 0.267834i | −0.713684 | − | 0.700468i | \(-0.752975\pi\) |
0.249781 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(828\) | − | 52.1615i | − | 1.81274i | ||||||
\(829\) | −21.2350 | −0.737523 | −0.368761 | − | 0.929524i | \(-0.620218\pi\) | ||||
−0.368761 | + | 0.929524i | \(0.620218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.36956 | − | 9.30036i | 0.186268 | − | 0.322626i | ||||
\(832\) | −16.9077 | + | 9.76164i | −0.586168 | + | 0.338424i | ||||
\(833\) | 42.6021 | + | 24.5964i | 1.47608 | + | 0.852213i | ||||
\(834\) | −5.46837 | + | 9.47149i | −0.189354 | + | 0.327971i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 14.2062 | − | 3.07034i | 0.491331 | − | 0.106190i | ||||
\(837\) | 13.8062i | 0.477212i | ||||||||
\(838\) | −57.5505 | − | 33.2268i | −1.98805 | − | 1.14780i | ||||
\(839\) | −3.04567 | + | 5.27526i | −0.105148 | + | 0.182122i | −0.913799 | − | 0.406167i | \(-0.866865\pi\) |
0.808651 | + | 0.588289i | \(0.200198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4754 | − | 25.0721i | 0.499151 | − | 0.864555i | ||||
\(842\) | −43.9350 | + | 25.3659i | −1.51410 | + | 0.874167i | ||||
\(843\) | − | 5.79528i | − | 0.199600i | ||||||
\(844\) | 55.2248 | 1.90092 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.27457 | + | 9.13582i | 0.181343 | + | 0.314096i | ||||
\(847\) | − | 2.30630i | − | 0.0792453i | ||||||
\(848\) | 25.3725i | 0.871295i | ||||||||
\(849\) | 10.3062 | + | 17.8509i | 0.353708 | + | 0.612640i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.69224 | + | 13.3234i | 0.263687 | + | 0.456719i | ||||
\(852\) | −44.6251 | − | 25.7643i | −1.52883 | − | 0.882672i | ||||
\(853\) | 30.2804 | + | 17.4824i | 1.03678 | + | 0.598586i | 0.918920 | − | 0.394444i | \(-0.129063\pi\) |
0.117862 | + | 0.993030i | \(0.462396\pi\) | |||||||
\(854\) | 7.00000 | 0.239535 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.35844 | 0.319865 | ||||||||
\(857\) | 3.59530 | + | 2.07575i | 0.122813 | + | 0.0709061i | 0.560148 | − | 0.828393i | \(-0.310744\pi\) |
−0.437335 | + | 0.899299i | \(0.644078\pi\) | |||||||
\(858\) | 10.3213 | + | 5.95900i | 0.352363 | + | 0.203437i | ||||
\(859\) | 14.1245 | + | 24.4644i | 0.481923 | + | 0.834715i | 0.999785 | − | 0.0207495i | \(-0.00660523\pi\) |
−0.517862 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.980847 | − | 1.69888i | −0.0334272 | − | 0.0578976i | ||||
\(862\) | − | 28.7327i | − | 0.978640i | ||||||
\(863\) | 51.8272i | 1.76422i | 0.471046 | + | 0.882108i | \(0.343876\pi\) | ||||
−0.471046 | + | 0.882108i | \(0.656124\pi\) | |||||||
\(864\) | 8.43473 | + | 14.6094i | 0.286955 | + | 0.497021i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −65.0490 | −2.21046 | ||||||||
\(867\) | − | 40.4297i | − | 1.37307i | ||||||
\(868\) | −2.06426 | + | 1.19180i | −0.0700655 | + | 0.0404523i | ||||
\(869\) | −0.616399 | + | 1.06764i | −0.0209099 | + | 0.0362170i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.4257 | + | 45.7707i | −0.895401 | + | 1.55088i | ||||
\(872\) | 37.7878 | + | 21.8168i | 1.27966 | + | 0.738809i | ||||
\(873\) | 9.58832i | 0.324516i | ||||||||
\(874\) | 26.9894 | − | 84.0400i | 0.912931 | − | 2.84270i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 36.8538 | − | 63.8326i | 1.24517 | − | 2.15670i | ||||
\(877\) | −40.8763 | − | 23.5999i | −1.38029 | − | 0.796913i | −0.388099 | − | 0.921618i | \(-0.626868\pi\) |
−0.992194 | + | 0.124705i | \(0.960202\pi\) | |||||||
\(878\) | −54.9567 | + | 31.7292i | −1.85470 | + | 1.07081i | ||||
\(879\) | 7.10738 | − | 12.3103i | 0.239726 | − | 0.415218i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.8935 | −1.14190 | −0.570951 | − | 0.820984i | \(-0.693425\pi\) | ||||
−0.570951 | + | 0.820984i | \(0.693425\pi\) | |||||||
\(882\) | 26.2609i | 0.884250i | ||||||||
\(883\) | 18.2439 | − | 10.5331i | 0.613954 | − | 0.354467i | −0.160557 | − | 0.987027i | \(-0.551329\pi\) |
0.774512 | + | 0.632560i | \(0.217996\pi\) | |||||||
\(884\) | −75.8181 | − | 131.321i | −2.55004 | − | 4.41680i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −50.2029 | −1.68660 | ||||||||
\(887\) | −6.24816 | + | 3.60738i | −0.209793 | + | 0.121124i | −0.601215 | − | 0.799087i | \(-0.705317\pi\) |
0.391422 | + | 0.920211i | \(0.371983\pi\) | |||||||
\(888\) | −11.5464 | − | 6.66630i | −0.387471 | − | 0.223706i | ||||
\(889\) | 1.44687 | + | 2.50605i | 0.0485264 | + | 0.0840501i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.858986 | + | 1.48781i | −0.0287771 | + | 0.0498434i | ||||
\(892\) | − | 88.7356i | − | 2.97109i | ||||||
\(893\) | 2.57107 | + | 11.8961i | 0.0860374 | + | 0.398087i | ||||
\(894\) | −2.86946 | −0.0959693 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.76564 | − | 3.05818i | 0.0589860 | − | 0.102167i | ||||
\(897\) | 42.7360 | − | 24.6737i | 1.42691 | − | 0.823830i | ||||
\(898\) | 42.9019 | + | 24.7694i | 1.43166 | + | 0.826567i | ||||
\(899\) | 0.278124 | + | 0.481725i | 0.00927595 | + | 0.0160664i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.0020 | 1.03283 | ||||||||
\(902\) | 12.2245 | − | 7.05780i | 0.407031 | − | 0.234999i | ||||
\(903\) | −1.71373 | + | 0.989423i | −0.0570294 | + | 0.0329259i | ||||
\(904\) | 71.5480 | 2.37965 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.48863 | − | 2.57839i | −0.0494565 | − | 0.0856612i | ||||
\(907\) | 1.01208 | + | 0.584322i | 0.0336054 | + | 0.0194021i | 0.516709 | − | 0.856161i | \(-0.327157\pi\) |
−0.483103 | + | 0.875563i | \(0.660490\pi\) | |||||||
\(908\) | 14.8442 | − | 8.57028i | 0.492621 | − | 0.284415i | ||||
\(909\) | 5.57184 | − | 9.65071i | 0.184806 | − | 0.320094i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3313 | −0.408553 | −0.204276 | − | 0.978913i | \(-0.565484\pi\) | ||||
−0.204276 | + | 0.978913i | \(0.565484\pi\) | |||||||
\(912\) | 6.51689 | + | 30.1530i | 0.215796 | + | 0.998467i | ||||
\(913\) | 7.40856i | 0.245188i | ||||||||
\(914\) | 43.2018 | − | 74.8278i | 1.42899 | − | 2.47508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.58276 | − | 13.1337i | −0.250542 | − | 0.433951i | ||||
\(917\) | −1.36607 | − | 0.788701i | −0.0451116 | − | 0.0260452i | ||||
\(918\) | 84.6199 | − | 48.8553i | 2.79287 | − | 1.61247i | ||||
\(919\) | −52.8895 | −1.74466 | −0.872332 | − | 0.488913i | \(-0.837393\pi\) | ||||
−0.872332 | + | 0.488913i | \(0.837393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.59880 | − | 6.23331i | −0.118585 | − | 0.205395i | ||||
\(922\) | −17.2231 | + | 9.94375i | −0.567212 | + | 0.327480i | ||||
\(923\) | 49.2070i | 1.61967i | ||||||||
\(924\) | −0.903965 | −0.0297383 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.5999 | − | 20.0916i | 0.381197 | − | 0.660252i | ||||
\(927\) | 15.9274 | − | 9.19570i | 0.523125 | − | 0.302027i | ||||
\(928\) | 0.588608 | + | 0.339833i | 0.0193220 | + | 0.0111556i | ||||
\(929\) | 0.695704 | − | 1.20500i | 0.0228253 | − | 0.0395346i | −0.854387 | − | 0.519637i | \(-0.826067\pi\) |
0.877212 | + | 0.480102i | \(0.159401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.26409 | + | 28.8466i | −0.303618 | + | 0.945410i | ||||
\(932\) | 84.7817i | 2.77712i | ||||||||
\(933\) | −15.6824 | − | 9.05425i | −0.513419 | − | 0.296423i | ||||
\(934\) | −11.8730 | + | 20.5647i | −0.388497 | + | 0.672897i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 21.5839 | − | 37.3844i | 0.705491 | − | 1.22195i | ||||
\(937\) | 28.8987 | − | 16.6847i | 0.944080 | − | 0.545065i | 0.0528430 | − | 0.998603i | \(-0.483172\pi\) |
0.891237 | + | 0.453538i | \(0.149838\pi\) | |||||||
\(938\) | − | 5.87970i | − | 0.191979i | ||||||
\(939\) | 7.20250 | 0.235045 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.6616 | − | 30.5908i | −0.575753 | − | 0.997233i | −0.995959 | − | 0.0898043i | \(-0.971376\pi\) |
0.420207 | − | 0.907428i | \(-0.361958\pi\) | |||||||
\(942\) | 8.31633i | 0.270961i | ||||||||
\(943\) | − | 58.4467i | − | 1.90329i | ||||||
\(944\) | −8.08632 | − | 14.0059i | −0.263187 | − | 0.455854i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.11951 | − | 12.3314i | −0.231475 | − | 0.400927i | ||||
\(947\) | 11.4810 | + | 6.62853i | 0.373081 | + | 0.215398i | 0.674804 | − | 0.737997i | \(-0.264228\pi\) |
−0.301723 | + | 0.953396i | \(0.597562\pi\) | |||||||
\(948\) | −7.18400 | − | 4.14769i | −0.233326 | − | 0.134711i | ||||
\(949\) | −70.3865 | −2.28484 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.08131 | −0.164773 | ||||||||
\(952\) | 7.79076 | + | 4.49800i | 0.252500 | + | 0.145781i | ||||
\(953\) | −15.8225 | − | 9.13511i | −0.512540 | − | 0.295915i | 0.221337 | − | 0.975197i | \(-0.428958\pi\) |
−0.733877 | + | 0.679282i | \(0.762291\pi\) | |||||||
\(954\) | 8.27501 | + | 14.3327i | 0.267913 | + | 0.464039i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −50.9377 | − | 88.2268i | −1.64744 | − | 2.85346i | ||||
\(957\) | 0.210953i | 0.00681916i | ||||||||
\(958\) | 87.0308i | 2.81184i | ||||||||
\(959\) | −0.601918 | − | 1.04255i | −0.0194369 | − | 0.0336658i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7149 | −0.797253 | ||||||||
\(962\) | 23.8750i | 0.769762i | ||||||||
\(963\) | 2.13197 | − | 1.23090i | 0.0687019 | − | 0.0396651i | ||||
\(964\) | −9.73201 | + | 16.8563i | −0.313447 | + | 0.542906i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.74493 | + | 4.75436i | −0.0883168 | + | 0.152969i | ||||
\(967\) | −39.0686 | − | 22.5562i | −1.25636 | − | 0.725360i | −0.283995 | − | 0.958826i | \(-0.591660\pi\) |
−0.972365 | + | 0.233466i | \(0.924993\pi\) | |||||||
\(968\) | 59.5491i | 1.91398i | ||||||||
\(969\) | 36.8433 | − | 7.96283i | 1.18358 | − | 0.255803i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.80118 | + | 13.5120i | −0.250352 | + | 0.433622i | −0.963623 | − | 0.267266i | \(-0.913880\pi\) |
0.713271 | + | 0.700888i | \(0.247213\pi\) | |||||||
\(972\) | 51.2990 | + | 29.6175i | 1.64542 | + | 0.949982i | ||||
\(973\) | −0.686032 | + | 0.396081i | −0.0219932 | + | 0.0126978i | ||||
\(974\) | 35.7338 | − | 61.8928i | 1.14499 | − | 1.98317i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −72.8904 | −2.33317 | ||||||||
\(977\) | − | 26.2319i | − | 0.839233i | −0.907701 | − | 0.419617i | \(-0.862165\pi\) | ||
0.907701 | − | 0.419617i | \(-0.137835\pi\) | |||||||
\(978\) | 8.49935 | − | 4.90710i | 0.271779 | − | 0.156912i | ||||
\(979\) | −1.22188 | − | 2.11635i | −0.0390513 | − | 0.0676389i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4781 | 0.366466 | ||||||||
\(982\) | −67.7175 | + | 39.0967i | −2.16095 | + | 1.24763i | ||||
\(983\) | 29.7404 | + | 17.1706i | 0.948572 | + | 0.547659i | 0.892637 | − | 0.450776i | \(-0.148853\pi\) |
0.0559353 | + | 0.998434i | \(0.482186\pi\) | |||||||
\(984\) | 25.3257 | + | 43.8654i | 0.807354 | + | 1.39838i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.96837 | − | 3.40931i | 0.0626856 | − | 0.108575i | ||||
\(987\) | − | 0.756969i | − | 0.0240946i | ||||||
\(988\) | 69.1904 | − | 62.7284i | 2.20124 | − | 1.99565i | ||||
\(989\) | −58.9577 | −1.87475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.65159 | + | 2.86064i | −0.0524645 | + | 0.0908712i | −0.891065 | − | 0.453876i | \(-0.850041\pi\) |
0.838600 | + | 0.544747i | \(0.183374\pi\) | |||||||
\(992\) | 6.65079 | − | 3.83983i | 0.211163 | − | 0.121915i | ||||
\(993\) | −11.3010 | − | 6.52461i | −0.358625 | − | 0.207052i | ||||
\(994\) | −2.73713 | − | 4.74084i | −0.0868163 | − | 0.150370i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −49.8514 | −1.57960 | ||||||||
\(997\) | −8.50727 | + | 4.91168i | −0.269428 | + | 0.155554i | −0.628628 | − | 0.777706i | \(-0.716383\pi\) |
0.359200 | + | 0.933261i | \(0.383050\pi\) | |||||||
\(998\) | −35.1436 | + | 20.2902i | −1.11245 | + | 0.642274i | ||||
\(999\) | −10.4890 | −0.331857 |
(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 | 475.2.j.b.49.1 | 12 | ||
5.2 | odd | 4 | 95.2.e.b.11.3 | ✓ | 6 | ||
5.3 | odd | 4 | 475.2.e.d.201.1 | 6 | |||
5.4 | even | 2 | inner | 475.2.j.b.49.6 | 12 | ||
15.2 | even | 4 | 855.2.k.g.676.1 | 6 | |||
19.7 | even | 3 | inner | 475.2.j.b.349.6 | 12 | ||
20.7 | even | 4 | 1520.2.q.j.961.2 | 6 | |||
95.7 | odd | 12 | 95.2.e.b.26.3 | yes | 6 | ||
95.8 | even | 12 | 9025.2.a.ba.1.1 | 3 | |||
95.27 | even | 12 | 1805.2.a.g.1.3 | 3 | |||
95.64 | even | 6 | inner | 475.2.j.b.349.1 | 12 | ||
95.68 | odd | 12 | 9025.2.a.z.1.3 | 3 | |||
95.83 | odd | 12 | 475.2.e.d.26.1 | 6 | |||
95.87 | odd | 12 | 1805.2.a.h.1.1 | 3 | |||
285.197 | even | 12 | 855.2.k.g.406.1 | 6 | |||
380.7 | even | 12 | 1520.2.q.j.881.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.b.11.3 | ✓ | 6 | 5.2 | odd | 4 | ||
95.2.e.b.26.3 | yes | 6 | 95.7 | odd | 12 | ||
475.2.e.d.26.1 | 6 | 95.83 | odd | 12 | |||
475.2.e.d.201.1 | 6 | 5.3 | odd | 4 | |||
475.2.j.b.49.1 | 12 | 1.1 | even | 1 | trivial | ||
475.2.j.b.49.6 | 12 | 5.4 | even | 2 | inner | ||
475.2.j.b.349.1 | 12 | 95.64 | even | 6 | inner | ||
475.2.j.b.349.6 | 12 | 19.7 | even | 3 | inner | ||
855.2.k.g.406.1 | 6 | 285.197 | even | 12 | |||
855.2.k.g.676.1 | 6 | 15.2 | even | 4 | |||
1520.2.q.j.881.2 | 6 | 380.7 | even | 12 | |||
1520.2.q.j.961.2 | 6 | 20.7 | even | 4 | |||
1805.2.a.g.1.3 | 3 | 95.27 | even | 12 | |||
1805.2.a.h.1.1 | 3 | 95.87 | odd | 12 | |||
9025.2.a.z.1.3 | 3 | 95.68 | odd | 12 | |||
9025.2.a.ba.1.1 | 3 | 95.8 | even | 12 |