Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(235,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.235");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 8x^{8} + 7x^{7} + 41x^{6} + 18x^{5} + 58x^{4} + 28x^{3} + 64x^{2} + 16x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 235.4 | ||
Root | \(-0.606661 - 1.05077i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.235 |
Dual form | 819.2.j.h.352.4 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10666 | + | 1.91679i | 0.782527 | + | 1.35538i | 0.930465 | + | 0.366381i | \(0.119403\pi\) |
−0.147938 | + | 0.988997i | \(0.547263\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.44940 | + | 2.51043i | −0.724699 | + | 1.25521i | ||||
\(5\) | −1.06140 | − | 1.83839i | −0.474671 | − | 0.822155i | 0.524908 | − | 0.851159i | \(-0.324100\pi\) |
−0.999579 | + | 0.0290040i | \(0.990766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63169 | + | 0.272389i | 0.994686 | + | 0.102953i | ||||
\(8\) | −1.98932 | −0.703331 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.34921 | − | 4.06896i | 0.742887 | − | 1.28672i | ||||
\(11\) | 2.39448 | − | 4.14736i | 0.721962 | − | 1.25048i | −0.238250 | − | 0.971204i | \(-0.576574\pi\) |
0.960212 | − | 0.279272i | \(-0.0900930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 2.39028 | + | 5.34585i | 0.638829 | + | 1.42874i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.697291 | + | 1.20774i | 0.174323 | + | 0.301936i | ||||
\(17\) | −1.88914 | + | 3.27208i | −0.458183 | + | 0.793597i | −0.998865 | − | 0.0476304i | \(-0.984833\pi\) |
0.540682 | + | 0.841227i | \(0.318166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78362 | + | 3.08931i | 0.409190 | + | 0.708737i | 0.994799 | − | 0.101856i | \(-0.0324781\pi\) |
−0.585609 | + | 0.810593i | \(0.699145\pi\) | |||||||
\(20\) | 6.15355 | 1.37597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.5995 | 2.25982 | ||||||||
\(23\) | 2.23721 | + | 3.87497i | 0.466491 | + | 0.807987i | 0.999267 | − | 0.0382695i | \(-0.0121845\pi\) |
−0.532776 | + | 0.846256i | \(0.678851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.246870 | − | 0.427591i | 0.0493740 | − | 0.0855182i | ||||
\(26\) | 1.10666 | + | 1.91679i | 0.217034 | + | 0.375914i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.49818 | + | 6.21188i | −0.850076 | + | 1.17393i | ||||
\(29\) | 5.90107 | 1.09580 | 0.547901 | − | 0.836543i | \(-0.315427\pi\) | ||||
0.547901 | + | 0.836543i | \(0.315427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.88558 | − | 3.26592i | 0.338660 | − | 0.586577i | −0.645521 | − | 0.763743i | \(-0.723360\pi\) |
0.984181 | + | 0.177166i | \(0.0566929\pi\) | |||||||
\(32\) | −3.53265 | + | 6.11873i | −0.624490 | + | 1.08165i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.36254 | −1.43416 | ||||||||
\(35\) | −2.29251 | − | 5.12720i | −0.387505 | − | 0.866655i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.81285 | − | 4.87200i | −0.462429 | − | 0.800951i | 0.536652 | − | 0.843804i | \(-0.319689\pi\) |
−0.999081 | + | 0.0428524i | \(0.986355\pi\) | |||||||
\(38\) | −3.94772 | + | 6.83765i | −0.640404 | + | 1.10921i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.11146 | + | 3.65716i | 0.333851 | + | 0.578247i | ||||
\(41\) | −10.3948 | −1.62340 | −0.811698 | − | 0.584077i | \(-0.801457\pi\) | ||||
−0.811698 | + | 0.584077i | \(0.801457\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.40733 | 0.519613 | 0.259807 | − | 0.965661i | \(-0.416341\pi\) | ||||
0.259807 | + | 0.965661i | \(0.416341\pi\) | |||||||
\(44\) | 6.94110 | + | 12.0223i | 1.04641 | + | 1.81244i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.95168 | + | 8.57655i | −0.730085 | + | 1.26454i | ||||
\(47\) | −3.55438 | − | 6.15636i | −0.518459 | − | 0.897998i | −0.999770 | − | 0.0214479i | \(-0.993172\pi\) |
0.481311 | − | 0.876550i | \(-0.340161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.85161 | + | 1.43369i | 0.978801 | + | 0.204813i | ||||
\(50\) | 1.09280 | 0.154546 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.44940 | + | 2.51043i | −0.200995 | + | 0.348134i | ||||
\(53\) | −6.19003 | + | 10.7214i | −0.850266 | + | 1.47270i | 0.0307027 | + | 0.999529i | \(0.490226\pi\) |
−0.880968 | + | 0.473175i | \(0.843108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.1660 | −1.37078 | ||||||||
\(56\) | −5.23528 | − | 0.541869i | −0.699594 | − | 0.0724103i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.53049 | + | 11.3111i | 0.857495 | + | 1.48522i | ||||
\(59\) | 2.39448 | − | 4.14736i | 0.311734 | − | 0.539940i | −0.667003 | − | 0.745055i | \(-0.732423\pi\) |
0.978738 | + | 0.205115i | \(0.0657567\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60348 | − | 2.77732i | −0.205305 | − | 0.355599i | 0.744925 | − | 0.667148i | \(-0.232485\pi\) |
−0.950230 | + | 0.311550i | \(0.899152\pi\) | |||||||
\(62\) | 8.34680 | 1.06004 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8486 | −1.60608 | ||||||||
\(65\) | −1.06140 | − | 1.83839i | −0.131650 | − | 0.228025i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.44978 | − | 2.51109i | 0.177118 | − | 0.306778i | −0.763774 | − | 0.645484i | \(-0.776656\pi\) |
0.940892 | + | 0.338706i | \(0.109989\pi\) | |||||||
\(68\) | −5.47622 | − | 9.48510i | −0.664090 | − | 1.15024i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.29075 | − | 10.0683i | 0.871411 | − | 1.20340i | ||||
\(71\) | 2.53876 | 0.301295 | 0.150648 | − | 0.988588i | \(-0.451864\pi\) | ||||
0.150648 | + | 0.988588i | \(0.451864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.85035 | + | 6.66901i | −0.450650 | + | 0.780548i | −0.998426 | − | 0.0560762i | \(-0.982141\pi\) |
0.547777 | + | 0.836625i | \(0.315474\pi\) | |||||||
\(74\) | 6.22574 | − | 10.7833i | 0.723727 | − | 1.25353i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.3407 | −1.18616 | ||||||||
\(77\) | 7.43122 | − | 10.2623i | 0.846867 | − | 1.16950i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.58925 | + | 4.48471i | 0.291313 | + | 0.504569i | 0.974120 | − | 0.226029i | \(-0.0725745\pi\) |
−0.682807 | + | 0.730598i | \(0.739241\pi\) | |||||||
\(80\) | 1.48021 | − | 2.56379i | 0.165492 | − | 0.286641i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.5035 | − | 19.9247i | −1.27035 | − | 2.20032i | ||||
\(83\) | −3.46731 | −0.380587 | −0.190294 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190294 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.02051 | 0.869946 | ||||||||
\(86\) | 3.77076 | + | 6.53115i | 0.406612 | + | 0.704272i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.76338 | + | 8.25042i | −0.507778 | + | 0.879498i | ||||
\(89\) | 1.83216 | + | 3.17339i | 0.194209 | + | 0.336379i | 0.946641 | − | 0.322291i | \(-0.104453\pi\) |
−0.752432 | + | 0.658670i | \(0.771119\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.63169 | + | 0.272389i | 0.275876 | + | 0.0285541i | ||||
\(92\) | −12.9704 | −1.35226 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.86698 | − | 13.6260i | 0.811417 | − | 1.40542i | ||||
\(95\) | 3.78625 | − | 6.55798i | 0.388461 | − | 0.672835i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.40733 | −0.549031 | −0.274516 | − | 0.961583i | \(-0.588518\pi\) | ||||
−0.274516 | + | 0.961583i | \(0.588518\pi\) | |||||||
\(98\) | 4.83432 | + | 14.7197i | 0.488340 | + | 1.48692i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.715625 | + | 1.23950i | 0.0715625 | + | 0.123950i | ||||
\(101\) | 4.65862 | − | 8.06897i | 0.463550 | − | 0.802892i | −0.535585 | − | 0.844482i | \(-0.679909\pi\) |
0.999135 | + | 0.0415891i | \(0.0132420\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.65318 | − | 6.32749i | −0.359958 | − | 0.623466i | 0.627995 | − | 0.778217i | \(-0.283876\pi\) |
−0.987953 | + | 0.154751i | \(0.950542\pi\) | |||||||
\(104\) | −1.98932 | −0.195069 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.4011 | −2.66143 | ||||||||
\(107\) | 3.37365 | + | 5.84333i | 0.326143 | + | 0.564896i | 0.981743 | − | 0.190212i | \(-0.0609176\pi\) |
−0.655600 | + | 0.755108i | \(0.727584\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.08822 | + | 3.61691i | −0.200016 | + | 0.346437i | −0.948533 | − | 0.316678i | \(-0.897433\pi\) |
0.748518 | + | 0.663115i | \(0.230766\pi\) | |||||||
\(110\) | −11.2503 | − | 19.4861i | −1.07267 | − | 1.85792i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.50608 | + | 3.36834i | 0.142311 | + | 0.318278i | ||||
\(113\) | −5.90107 | −0.555126 | −0.277563 | − | 0.960707i | \(-0.589527\pi\) | ||||
−0.277563 | + | 0.960707i | \(0.589527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.74915 | − | 8.22577i | 0.442860 | − | 0.767057i | ||||
\(116\) | −8.55300 | + | 14.8142i | −0.794126 | + | 1.37547i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.5995 | 0.975763 | ||||||||
\(119\) | −5.86291 | + | 8.09654i | −0.537452 | + | 0.742208i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.96705 | − | 10.3352i | −0.542459 | − | 0.939567i | ||||
\(122\) | 3.54903 | − | 6.14709i | 0.321314 | − | 0.556532i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.46591 | + | 9.46724i | 0.490853 | + | 0.850183i | ||||
\(125\) | −11.6621 | −1.04309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5268 | −0.934100 | −0.467050 | − | 0.884231i | \(-0.654683\pi\) | ||||
−0.467050 | + | 0.884231i | \(0.654683\pi\) | |||||||
\(128\) | −7.15377 | − | 12.3907i | −0.632309 | − | 1.09519i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.34921 | − | 4.06896i | 0.206040 | − | 0.356871i | ||||
\(131\) | 2.71204 | + | 4.69740i | 0.236952 | + | 0.410413i | 0.959838 | − | 0.280554i | \(-0.0905182\pi\) |
−0.722886 | + | 0.690967i | \(0.757185\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.85243 | + | 8.61596i | 0.334048 | + | 0.747099i | ||||
\(134\) | 6.41765 | 0.554400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.75810 | − | 6.50922i | 0.322255 | − | 0.558161i | ||||
\(137\) | 11.1224 | − | 19.2645i | 0.950248 | − | 1.64588i | 0.205363 | − | 0.978686i | \(-0.434163\pi\) |
0.744886 | − | 0.667192i | \(-0.232504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 16.1942 | + | 1.67616i | 1.36866 | + | 0.141661i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.80955 | + | 4.86628i | 0.235772 | + | 0.408369i | ||||
\(143\) | 2.39448 | − | 4.14736i | 0.200236 | − | 0.346819i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.26338 | − | 10.8485i | −0.520146 | − | 0.900919i | ||||
\(146\) | −17.0441 | −1.41058 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.3077 | 1.34049 | ||||||||
\(149\) | 1.47736 | + | 2.55887i | 0.121030 | + | 0.209630i | 0.920174 | − | 0.391509i | \(-0.128047\pi\) |
−0.799144 | + | 0.601140i | \(0.794714\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.27736 | − | 16.0689i | 0.754981 | − | 1.30766i | −0.190403 | − | 0.981706i | \(-0.560980\pi\) |
0.945384 | − | 0.325959i | \(-0.105687\pi\) | |||||||
\(152\) | −3.54818 | − | 6.14564i | −0.287796 | − | 0.498477i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 27.8946 | + | 2.88719i | 2.24781 | + | 0.232656i | ||||
\(155\) | −8.00541 | −0.643010 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.89982 | − | 8.48673i | 0.391048 | − | 0.677315i | −0.601540 | − | 0.798843i | \(-0.705446\pi\) |
0.992588 | + | 0.121528i | \(0.0387793\pi\) | |||||||
\(158\) | −5.73084 | + | 9.92610i | −0.455921 | + | 0.789678i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.9982 | 1.18571 | ||||||||
\(161\) | 4.83216 | + | 10.8071i | 0.380828 | + | 0.851720i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.91709 | − | 11.9808i | −0.541788 | − | 0.938405i | −0.998801 | − | 0.0489451i | \(-0.984414\pi\) |
0.457013 | − | 0.889460i | \(-0.348919\pi\) | |||||||
\(164\) | 15.0662 | − | 26.0954i | 1.17647 | − | 2.03771i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.83714 | − | 6.64612i | −0.297820 | − | 0.515839i | ||||
\(167\) | −17.3534 | −1.34285 | −0.671424 | − | 0.741073i | \(-0.734317\pi\) | ||||
−0.671424 | + | 0.741073i | \(0.734317\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 8.87598 | + | 15.3737i | 0.680757 | + | 1.17911i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.93858 | + | 8.55387i | −0.376563 | + | 0.652226i | ||||
\(173\) | −1.48069 | − | 2.56463i | −0.112575 | − | 0.194985i | 0.804233 | − | 0.594314i | \(-0.202576\pi\) |
−0.916808 | + | 0.399329i | \(0.869243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.766156 | − | 1.05804i | 0.0579160 | − | 0.0799806i | ||||
\(176\) | 6.67859 | 0.503418 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.05516 | + | 7.02374i | −0.303947 | + | 0.526452i | ||||
\(179\) | −2.83444 | + | 4.90939i | −0.211856 | + | 0.366945i | −0.952295 | − | 0.305178i | \(-0.901284\pi\) |
0.740440 | + | 0.672123i | \(0.234617\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.17645 | 0.533421 | 0.266711 | − | 0.963777i | \(-0.414063\pi\) | ||||
0.266711 | + | 0.963777i | \(0.414063\pi\) | |||||||
\(182\) | 2.39028 | + | 5.34585i | 0.177179 | + | 0.396261i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.45054 | − | 7.70855i | −0.328098 | − | 0.568282i | ||||
\(185\) | −5.97110 | + | 10.3423i | −0.439004 | + | 0.760377i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.04700 | + | 15.6699i | 0.661582 | + | 1.14589i | ||||
\(188\) | 20.6068 | 1.50291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.7604 | 1.21593 | ||||||||
\(191\) | 5.94088 | + | 10.2899i | 0.429867 | + | 0.744552i | 0.996861 | − | 0.0791703i | \(-0.0252271\pi\) |
−0.566994 | + | 0.823722i | \(0.691894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.4851 | + | 19.8927i | −0.826714 | + | 1.43191i | 0.0738876 | + | 0.997267i | \(0.476459\pi\) |
−0.900602 | + | 0.434645i | \(0.856874\pi\) | |||||||
\(194\) | −5.98408 | − | 10.3647i | −0.429632 | − | 0.744145i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.5299 | + | 15.1225i | −0.966420 | + | 1.08018i | ||||
\(197\) | −16.9216 | −1.20561 | −0.602806 | − | 0.797888i | \(-0.705951\pi\) | ||||
−0.602806 | + | 0.797888i | \(0.705951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.02953 | + | 8.71140i | −0.356534 | + | 0.617535i | −0.987379 | − | 0.158374i | \(-0.949375\pi\) |
0.630845 | + | 0.775909i | \(0.282708\pi\) | |||||||
\(200\) | −0.491103 | + | 0.850616i | −0.0347262 | + | 0.0601476i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.6221 | 1.45096 | ||||||||
\(203\) | 15.5298 | + | 1.60739i | 1.08998 | + | 0.112817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.0330 | + | 19.1098i | 0.770580 | + | 1.33468i | ||||
\(206\) | 8.08566 | − | 14.0048i | 0.563355 | − | 0.975759i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.697291 | + | 1.20774i | 0.0483484 | + | 0.0837419i | ||||
\(209\) | 17.0833 | 1.18168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4609 | −1.68396 | −0.841978 | − | 0.539512i | \(-0.818609\pi\) | ||||
−0.841978 | + | 0.539512i | \(0.818609\pi\) | |||||||
\(212\) | −17.9436 | − | 31.0793i | −1.23237 | − | 2.13453i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.46697 | + | 12.9332i | −0.510431 | + | 0.884093i | ||||
\(215\) | −3.61654 | − | 6.26402i | −0.246646 | − | 0.427203i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.85187 | − | 8.08129i | 0.397251 | − | 0.548594i | ||||
\(218\) | −9.24382 | −0.626071 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.7345 | − | 25.5210i | 0.993402 | − | 1.72062i | ||||
\(221\) | −1.88914 | + | 3.27208i | −0.127077 | + | 0.220104i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −29.2625 | −1.95956 | −0.979780 | − | 0.200076i | \(-0.935881\pi\) | ||||
−0.979780 | + | 0.200076i | \(0.935881\pi\) | |||||||
\(224\) | −10.9635 | + | 15.1404i | −0.732531 | + | 1.01161i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.53049 | − | 11.3111i | −0.434401 | − | 0.752405i | ||||
\(227\) | −5.03685 | + | 8.72408i | −0.334307 | + | 0.579038i | −0.983352 | − | 0.181713i | \(-0.941836\pi\) |
0.649044 | + | 0.760751i | \(0.275169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.56997 | + | 9.64748i | 0.368074 | + | 0.637523i | 0.989264 | − | 0.146137i | \(-0.0466839\pi\) |
−0.621190 | + | 0.783660i | \(0.713351\pi\) | |||||||
\(230\) | 21.0228 | 1.38620 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.7391 | −0.770711 | ||||||||
\(233\) | −8.54166 | − | 14.7946i | −0.559583 | − | 0.969226i | −0.997531 | − | 0.0702257i | \(-0.977628\pi\) |
0.437948 | − | 0.899000i | \(-0.355705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.54522 | + | 13.0687i | −0.492196 | + | 0.852508i | ||||
\(236\) | 6.94110 | + | 12.0223i | 0.451827 | + | 0.782587i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.0076 | − | 2.27787i | −1.42654 | − | 0.147652i | ||||
\(239\) | −6.92142 | −0.447710 | −0.223855 | − | 0.974622i | \(-0.571864\pi\) | ||||
−0.223855 | + | 0.974622i | \(0.571864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.24812 | + | 5.62592i | −0.209230 | + | 0.362397i | −0.951472 | − | 0.307735i | \(-0.900429\pi\) |
0.742242 | + | 0.670132i | \(0.233762\pi\) | |||||||
\(242\) | 13.2070 | − | 22.8752i | 0.848978 | − | 1.47047i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.29634 | 0.595137 | ||||||||
\(245\) | −4.63660 | − | 14.1177i | −0.296221 | − | 0.901945i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.78362 | + | 3.08931i | 0.113489 | + | 0.196568i | ||||
\(248\) | −3.75103 | + | 6.49697i | −0.238190 | + | 0.412558i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.9060 | − | 22.3538i | −0.816246 | − | 1.41378i | ||||
\(251\) | 9.86804 | 0.622865 | 0.311433 | − | 0.950268i | \(-0.399191\pi\) | ||||
0.311433 | + | 0.950268i | \(0.399191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.4278 | 1.34716 | ||||||||
\(254\) | −11.6496 | − | 20.1776i | −0.730959 | − | 1.26606i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.98497 | − | 5.17012i | 0.186560 | − | 0.323132i | ||||
\(257\) | 3.43234 | + | 5.94499i | 0.214104 | + | 0.370838i | 0.952995 | − | 0.302986i | \(-0.0979836\pi\) |
−0.738891 | + | 0.673825i | \(0.764650\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.07547 | − | 13.5878i | −0.377511 | − | 0.844304i | ||||
\(260\) | 6.15355 | 0.381627 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.00262 | + | 10.3969i | −0.370843 | + | 0.642320i | ||||
\(263\) | −0.0632753 | + | 0.109596i | −0.00390172 | + | 0.00675798i | −0.867970 | − | 0.496617i | \(-0.834575\pi\) |
0.864068 | + | 0.503375i | \(0.167909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.2803 | 1.61439 | ||||||||
\(266\) | −12.2517 | + | 16.9193i | −0.751199 | + | 1.03739i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.20261 | + | 7.27913i | 0.256715 | + | 0.444643i | ||||
\(269\) | −2.12154 | + | 3.67462i | −0.129353 | + | 0.224045i | −0.923426 | − | 0.383777i | \(-0.874623\pi\) |
0.794073 | + | 0.607822i | \(0.207957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.783616 | − | 1.35726i | −0.0476013 | − | 0.0824479i | 0.841243 | − | 0.540657i | \(-0.181824\pi\) |
−0.888844 | + | 0.458209i | \(0.848491\pi\) | |||||||
\(272\) | −5.26911 | −0.319487 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 49.2348 | 2.97438 | ||||||||
\(275\) | −1.18225 | − | 2.04771i | −0.0712923 | − | 0.123482i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.37260 | − | 11.0377i | 0.382892 | − | 0.663189i | −0.608582 | − | 0.793491i | \(-0.708261\pi\) |
0.991474 | + | 0.130302i | \(0.0415947\pi\) | |||||||
\(278\) | −4.42664 | − | 7.66717i | −0.265492 | − | 0.459846i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.56054 | + | 10.1996i | 0.272545 | + | 0.609546i | ||||
\(281\) | −4.62986 | −0.276194 | −0.138097 | − | 0.990419i | \(-0.544099\pi\) | ||||
−0.138097 | + | 0.990419i | \(0.544099\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.82416 | + | 3.15954i | −0.108435 | + | 0.187815i | −0.915136 | − | 0.403144i | \(-0.867917\pi\) |
0.806701 | + | 0.590959i | \(0.201251\pi\) | |||||||
\(284\) | −3.67967 | + | 6.37338i | −0.218348 | + | 0.378190i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.5995 | 0.626762 | ||||||||
\(287\) | −27.3559 | − | 2.83143i | −1.61477 | − | 0.167134i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.36231 | + | 2.35959i | 0.0801360 | + | 0.138800i | ||||
\(290\) | 13.8629 | − | 24.0112i | 0.814057 | − | 1.40999i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1614 | − | 19.3321i | −0.653171 | − | 1.13132i | ||||
\(293\) | 21.0415 | 1.22926 | 0.614630 | − | 0.788816i | \(-0.289305\pi\) | ||||
0.614630 | + | 0.788816i | \(0.289305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1660 | −0.591886 | ||||||||
\(296\) | 5.59566 | + | 9.69196i | 0.325241 | + | 0.563334i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.26988 | + | 5.66359i | −0.189419 | + | 0.328083i | ||||
\(299\) | 2.23721 | + | 3.87497i | 0.129381 | + | 0.224095i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.96705 | + | 0.928120i | 0.516852 | + | 0.0534960i | ||||
\(302\) | 41.0676 | 2.36317 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.48740 | + | 4.30830i | −0.142662 | + | 0.247098i | ||||
\(305\) | −3.40387 | + | 5.89567i | −0.194905 | + | 0.337585i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.95861 | −0.283003 | −0.141502 | − | 0.989938i | \(-0.545193\pi\) | ||||
−0.141502 | + | 0.989938i | \(0.545193\pi\) | |||||||
\(308\) | 14.9921 | + | 33.5298i | 0.854253 | + | 1.91054i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.85927 | − | 15.3447i | −0.503173 | − | 0.871521i | ||||
\(311\) | −1.21079 | + | 2.09715i | −0.0686575 | + | 0.118918i | −0.898311 | − | 0.439361i | \(-0.855205\pi\) |
0.829653 | + | 0.558279i | \(0.188538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.98026 | − | 12.0902i | −0.394548 | − | 0.683377i | 0.598496 | − | 0.801126i | \(-0.295765\pi\) |
−0.993043 | + | 0.117749i | \(0.962432\pi\) | |||||||
\(314\) | 21.6897 | 1.22402 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.0114 | −0.844457 | ||||||||
\(317\) | 1.53431 | + | 2.65750i | 0.0861753 | + | 0.149260i | 0.905891 | − | 0.423510i | \(-0.139202\pi\) |
−0.819716 | + | 0.572770i | \(0.805869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.1300 | − | 24.4739i | 0.791127 | − | 1.37027i | ||||
\(320\) | 13.6375 | + | 23.6208i | 0.762359 | + | 1.32044i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.3674 | + | 21.2221i | −0.856394 | + | 1.18266i | ||||
\(323\) | −13.4780 | −0.749936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.246870 | − | 0.427591i | 0.0136939 | − | 0.0237185i | ||||
\(326\) | 15.3098 | − | 26.5173i | 0.847929 | − | 1.46866i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.6786 | 1.14179 | ||||||||
\(329\) | −7.67710 | − | 17.1698i | −0.423252 | − | 0.946603i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.80261 | − | 11.7825i | −0.373905 | − | 0.647623i | 0.616257 | − | 0.787545i | \(-0.288648\pi\) |
−0.990162 | + | 0.139922i | \(0.955315\pi\) | |||||||
\(332\) | 5.02551 | − | 8.70445i | 0.275811 | − | 0.477719i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.2044 | − | 33.2629i | −1.05082 | − | 1.82007i | ||||
\(335\) | −6.15516 | −0.336292 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.1646 | −1.91554 | −0.957769 | − | 0.287538i | \(-0.907163\pi\) | ||||
−0.957769 | + | 0.287538i | \(0.907163\pi\) | |||||||
\(338\) | 1.10666 | + | 1.91679i | 0.0601944 | + | 0.104260i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.6249 | + | 20.1349i | −0.630449 | + | 1.09197i | ||||
\(341\) | −9.02997 | − | 15.6404i | −0.489000 | − | 0.846973i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.6408 | + | 5.63933i | 0.952514 | + | 0.304495i | ||||
\(344\) | −6.77828 | −0.365460 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.27724 | − | 5.67635i | 0.176186 | − | 0.305162i | ||||
\(347\) | −2.73551 | + | 4.73804i | −0.146850 | + | 0.254351i | −0.930062 | − | 0.367404i | \(-0.880247\pi\) |
0.783212 | + | 0.621755i | \(0.213580\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.34196 | 0.232420 | 0.116210 | − | 0.993225i | \(-0.462925\pi\) | ||||
0.116210 | + | 0.993225i | \(0.462925\pi\) | |||||||
\(350\) | 2.87593 | + | 0.297668i | 0.153725 | + | 0.0159110i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9177 | + | 29.3023i | 0.901717 | + | 1.56182i | ||||
\(353\) | 13.7996 | − | 23.9016i | 0.734479 | − | 1.27216i | −0.220472 | − | 0.975393i | \(-0.570760\pi\) |
0.954951 | − | 0.296762i | \(-0.0959068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.69463 | − | 4.66724i | −0.143016 | − | 0.247712i | ||||
\(356\) | −10.6221 | −0.562971 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.5470 | −0.663132 | ||||||||
\(359\) | 3.31427 | + | 5.74049i | 0.174921 | + | 0.302971i | 0.940134 | − | 0.340806i | \(-0.110700\pi\) |
−0.765213 | + | 0.643777i | \(0.777366\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.13742 | − | 5.43418i | 0.165128 | − | 0.286009i | ||||
\(362\) | 7.94189 | + | 13.7558i | 0.417417 | + | 0.722987i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.49818 | + | 6.21188i | −0.235769 | + | 0.325591i | ||||
\(365\) | 16.3470 | 0.855643 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.6037 | + | 27.0264i | −0.814506 | + | 1.41077i | 0.0951768 | + | 0.995460i | \(0.469658\pi\) |
−0.909682 | + | 0.415305i | \(0.863675\pi\) | |||||||
\(368\) | −3.11998 | + | 5.40396i | −0.162640 | + | 0.281701i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.4319 | −1.37413 | ||||||||
\(371\) | −19.2107 | + | 26.5294i | −0.997368 | + | 1.37734i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.88730 | + | 13.6612i | 0.408389 | + | 0.707350i | 0.994709 | − | 0.102729i | \(-0.0327574\pi\) |
−0.586321 | + | 0.810079i | \(0.699424\pi\) | |||||||
\(374\) | −20.0239 | + | 34.6825i | −1.03541 | + | 1.79339i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.07080 | + | 12.2470i | 0.364649 | + | 0.631590i | ||||
\(377\) | 5.90107 | 0.303921 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.6512 | 1.62581 | 0.812907 | − | 0.582393i | \(-0.197884\pi\) | ||||
0.812907 | + | 0.582393i | \(0.197884\pi\) | |||||||
\(380\) | 10.9756 | + | 19.0102i | 0.563035 | + | 0.975205i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.1491 | + | 22.7749i | −0.672766 | + | 1.16526i | ||||
\(383\) | 6.19675 | + | 10.7331i | 0.316639 | + | 0.548435i | 0.979785 | − | 0.200055i | \(-0.0641122\pi\) |
−0.663145 | + | 0.748491i | \(0.730779\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.7537 | − | 2.76910i | −1.36350 | − | 0.141126i | ||||
\(386\) | −50.8404 | −2.58771 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.83737 | − | 13.5747i | 0.397882 | − | 0.689152i | ||||
\(389\) | −7.03705 | + | 12.1885i | −0.356792 | + | 0.617983i | −0.987423 | − | 0.158100i | \(-0.949463\pi\) |
0.630631 | + | 0.776083i | \(0.282796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.9056 | −0.854954 | ||||||||
\(392\) | −13.6300 | − | 2.85207i | −0.688421 | − | 0.144051i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.7265 | − | 32.4352i | −0.943425 | − | 1.63406i | ||||
\(395\) | 5.49644 | − | 9.52012i | 0.276556 | − | 0.479009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.48652 | + | 6.03884i | 0.174984 | + | 0.303081i | 0.940156 | − | 0.340745i | \(-0.110679\pi\) |
−0.765172 | + | 0.643826i | \(0.777346\pi\) | |||||||
\(398\) | −22.2639 | −1.11599 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.688560 | 0.0344280 | ||||||||
\(401\) | 1.36841 | + | 2.37016i | 0.0683352 | + | 0.118360i | 0.898169 | − | 0.439651i | \(-0.144898\pi\) |
−0.829833 | + | 0.558011i | \(0.811565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88558 | − | 3.26592i | 0.0939275 | − | 0.162687i | ||||
\(404\) | 13.5044 | + | 23.3903i | 0.671868 | + | 1.16371i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.1052 | + | 31.5463i | 0.700029 | + | 1.56561i | ||||
\(407\) | −26.9412 | −1.33543 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.2577 | − | 21.2309i | 0.606104 | − | 1.04980i | −0.385772 | − | 0.922594i | \(-0.626065\pi\) |
0.991876 | − | 0.127208i | \(-0.0406017\pi\) | |||||||
\(410\) | −24.4196 | + | 42.2961i | −1.20600 | + | 2.08885i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.1796 | 1.04345 | ||||||||
\(413\) | 7.43122 | − | 10.2623i | 0.365667 | − | 0.504977i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.68020 | + | 6.37429i | 0.180654 | + | 0.312902i | ||||
\(416\) | −3.53265 | + | 6.11873i | −0.173202 | + | 0.299995i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.9054 | + | 32.7452i | 0.924696 | + | 1.60162i | ||||
\(419\) | 3.01252 | 0.147171 | 0.0735856 | − | 0.997289i | \(-0.476556\pi\) | ||||
0.0735856 | + | 0.997289i | \(0.476556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −27.0699 | − | 46.8864i | −1.31774 | − | 2.28240i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.3140 | − | 21.3284i | 0.598018 | − | 1.03580i | ||||
\(425\) | 0.932742 | + | 1.61556i | 0.0452447 | + | 0.0783660i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.46337 | − | 7.74581i | −0.167604 | − | 0.374846i | ||||
\(428\) | −19.5590 | −0.945421 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00456 | − | 13.8643i | 0.386014 | − | 0.668596i | ||||
\(431\) | −9.39711 | + | 16.2763i | −0.452643 | + | 0.784001i | −0.998549 | − | 0.0538455i | \(-0.982852\pi\) |
0.545906 | + | 0.837846i | \(0.316185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.76911 | −0.373360 | −0.186680 | − | 0.982421i | \(-0.559773\pi\) | ||||
−0.186680 | + | 0.982421i | \(0.559773\pi\) | |||||||
\(434\) | 21.9662 | + | 2.27358i | 1.05441 | + | 0.109135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.05333 | − | 10.4847i | −0.289902 | − | 0.502125i | ||||
\(437\) | −7.98066 | + | 13.8229i | −0.381767 | + | 0.661240i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.9841 | + | 32.8814i | 0.906060 | + | 1.56934i | 0.819488 | + | 0.573096i | \(0.194258\pi\) |
0.0865713 | + | 0.996246i | \(0.472409\pi\) | |||||||
\(440\) | 20.2234 | 0.964112 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.36254 | −0.397766 | ||||||||
\(443\) | 17.8135 | + | 30.8539i | 0.846344 | + | 1.46591i | 0.884449 | + | 0.466637i | \(0.154535\pi\) |
−0.0381050 | + | 0.999274i | \(0.512132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.88930 | − | 6.73647i | 0.184371 | − | 0.319339i | ||||
\(446\) | −32.3837 | − | 56.0901i | −1.53341 | − | 2.65594i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.8136 | − | 3.49982i | −1.59754 | − | 0.165351i | ||||
\(449\) | 8.05285 | 0.380038 | 0.190019 | − | 0.981780i | \(-0.439145\pi\) | ||||
0.190019 | + | 0.981780i | \(0.439145\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.8901 | + | 43.1110i | −1.17203 | + | 2.03002i | ||||
\(452\) | 8.55300 | − | 14.8142i | 0.402299 | − | 0.696803i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.2963 | −1.04642 | ||||||||
\(455\) | −2.29251 | − | 5.12720i | −0.107475 | − | 0.240367i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.79881 | − | 13.5079i | −0.364813 | − | 0.631875i | 0.623933 | − | 0.781478i | \(-0.285534\pi\) |
−0.988746 | + | 0.149603i | \(0.952200\pi\) | |||||||
\(458\) | −12.3281 | + | 21.3530i | −0.576056 | + | 0.997759i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.7668 | + | 23.8448i | 0.641880 | + | 1.11177i | ||||
\(461\) | 25.6991 | 1.19692 | 0.598462 | − | 0.801151i | \(-0.295779\pi\) | ||||
0.598462 | + | 0.801151i | \(0.295779\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5209 | −0.953685 | −0.476842 | − | 0.878989i | \(-0.658219\pi\) | ||||
−0.476842 | + | 0.878989i | \(0.658219\pi\) | |||||||
\(464\) | 4.11476 | + | 7.12698i | 0.191023 | + | 0.330862i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.9054 | − | 32.7452i | 0.875778 | − | 1.51689i | ||||
\(467\) | 5.91241 | + | 10.2406i | 0.273594 | + | 0.473878i | 0.969779 | − | 0.243984i | \(-0.0784543\pi\) |
−0.696186 | + | 0.717862i | \(0.745121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.49936 | − | 6.21351i | 0.207761 | − | 0.286913i | ||||
\(470\) | −33.4000 | −1.54063 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.76338 | + | 8.25042i | −0.219253 | + | 0.379757i | ||||
\(473\) | 8.15878 | − | 14.1314i | 0.375141 | − | 0.649764i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.76128 | 0.0808133 | ||||||||
\(476\) | −11.8281 | − | 26.4535i | −0.542140 | − | 1.21250i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.65967 | − | 13.2669i | −0.350345 | − | 0.606816i | ||||
\(479\) | 11.3276 | − | 19.6200i | 0.517571 | − | 0.896459i | −0.482221 | − | 0.876050i | \(-0.660170\pi\) |
0.999792 | − | 0.0204092i | \(-0.00649690\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.81285 | − | 4.87200i | −0.128255 | − | 0.222144i | ||||
\(482\) | −14.3783 | −0.654913 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 34.5945 | 1.57248 | ||||||||
\(485\) | 5.73933 | + | 9.94081i | 0.260610 | + | 0.451389i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3584 | − | 28.3335i | 0.741268 | − | 1.28391i | −0.210650 | − | 0.977562i | \(-0.567558\pi\) |
0.951918 | − | 0.306353i | \(-0.0991087\pi\) | |||||||
\(488\) | 3.18984 | + | 5.52497i | 0.144397 | + | 0.250104i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 21.9295 | − | 24.5109i | 0.990675 | − | 1.10729i | ||||
\(491\) | −6.17281 | −0.278575 | −0.139288 | − | 0.990252i | \(-0.544481\pi\) | ||||
−0.139288 | + | 0.990252i | \(0.544481\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1479 | + | 19.3088i | −0.502078 | + | 0.869625i | ||||
\(494\) | −3.94772 | + | 6.83765i | −0.177616 | + | 0.307640i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.25919 | 0.236145 | ||||||||
\(497\) | 6.68123 | + | 0.691531i | 0.299694 | + | 0.0310194i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.31934 | + | 12.6775i | 0.327659 | + | 0.567521i | 0.982047 | − | 0.188637i | \(-0.0604071\pi\) |
−0.654388 | + | 0.756159i | \(0.727074\pi\) | |||||||
\(500\) | 16.9030 | − | 29.2768i | 0.755925 | − | 1.30930i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.9206 | + | 18.9150i | 0.487409 | + | 0.844218i | ||||
\(503\) | −12.7787 | −0.569774 | −0.284887 | − | 0.958561i | \(-0.591956\pi\) | ||||
−0.284887 | + | 0.958561i | \(0.591956\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.7786 | −0.880136 | ||||||||
\(506\) | 23.7134 | + | 41.0727i | 1.05419 | + | 1.82591i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.2575 | − | 26.4267i | 0.676941 | − | 1.17250i | ||||
\(509\) | 5.84263 | + | 10.1197i | 0.258970 | + | 0.448549i | 0.965966 | − | 0.258668i | \(-0.0832835\pi\) |
−0.706996 | + | 0.707217i | \(0.749950\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9495 | + | 16.5020i | −0.528615 | + | 0.730005i | ||||
\(512\) | −15.4017 | −0.680664 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.59688 | + | 13.1582i | −0.335084 | + | 0.580382i | ||||
\(515\) | −7.75495 | + | 13.4320i | −0.341724 | + | 0.591883i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −34.0435 | −1.49723 | ||||||||
\(518\) | 19.3215 | − | 26.6825i | 0.848937 | − | 1.17236i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.11146 | + | 3.65716i | 0.0925937 | + | 0.160377i | ||||
\(521\) | 4.23838 | − | 7.34108i | 0.185687 | − | 0.321619i | −0.758121 | − | 0.652114i | \(-0.773882\pi\) |
0.943808 | + | 0.330495i | \(0.107216\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3554 | − | 28.3284i | −0.715172 | − | 1.23871i | −0.962893 | − | 0.269883i | \(-0.913015\pi\) |
0.247721 | − | 0.968831i | \(-0.420318\pi\) | |||||||
\(524\) | −15.7233 | −0.686876 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.280097 | −0.0122128 | ||||||||
\(527\) | 7.12425 | + | 12.3396i | 0.310337 | + | 0.537520i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.48975 | − | 2.58032i | 0.0647716 | − | 0.112188i | ||||
\(530\) | 29.0834 | + | 50.3739i | 1.26330 | + | 2.18810i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −27.2135 | − | 2.81669i | −1.17985 | − | 0.122119i | ||||
\(533\) | −10.3948 | −0.450249 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.16156 | − | 12.4042i | 0.309621 | − | 0.536280i | ||||
\(536\) | −2.88407 | + | 4.99536i | −0.124573 | + | 0.215767i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.39131 | −0.404888 | ||||||||
\(539\) | 22.3520 | − | 24.9831i | 0.962771 | − | 1.07610i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0853 | + | 24.3964i | 0.605573 | + | 1.04888i | 0.991961 | + | 0.126547i | \(0.0403893\pi\) |
−0.386388 | + | 0.922336i | \(0.626277\pi\) | |||||||
\(542\) | 1.73440 | − | 3.00406i | 0.0744987 | − | 0.129035i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.3473 | − | 23.1182i | −0.572262 | − | 0.991187i | ||||
\(545\) | 8.86574 | 0.379767 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.5377 | −0.792615 | −0.396307 | − | 0.918118i | \(-0.629709\pi\) | ||||
−0.396307 | + | 0.918118i | \(0.629709\pi\) | |||||||
\(548\) | 32.2415 | + | 55.8438i | 1.37729 | + | 2.38553i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.61670 | − | 4.53225i | 0.111576 | − | 0.193256i | ||||
\(551\) | 10.5252 | + | 18.2303i | 0.448391 | + | 0.776635i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.59252 | + | 12.5077i | 0.237818 | + | 0.531880i | ||||
\(554\) | 28.2092 | 1.19850 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.79759 | − | 10.0417i | 0.245873 | − | 0.425864i | ||||
\(557\) | 2.00142 | − | 3.46655i | 0.0848027 | − | 0.146883i | −0.820504 | − | 0.571640i | \(-0.806307\pi\) |
0.905307 | + | 0.424758i | \(0.139641\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.40733 | 0.144115 | ||||||||
\(560\) | 4.59379 | − | 6.34392i | 0.194123 | − | 0.268079i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.12368 | − | 8.87448i | −0.216129 | − | 0.374347i | ||||
\(563\) | −8.93100 | + | 15.4689i | −0.376397 | + | 0.651938i | −0.990535 | − | 0.137260i | \(-0.956170\pi\) |
0.614138 | + | 0.789199i | \(0.289504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.26338 | + | 10.8485i | 0.263503 | + | 0.456400i | ||||
\(566\) | −8.07490 | −0.339413 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.05041 | −0.211910 | ||||||||
\(569\) | −18.7336 | − | 32.4475i | −0.785353 | − | 1.36027i | −0.928788 | − | 0.370612i | \(-0.879148\pi\) |
0.143434 | − | 0.989660i | \(-0.454185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.78514 | + | 15.2163i | −0.367646 | + | 0.636782i | −0.989197 | − | 0.146592i | \(-0.953170\pi\) |
0.621551 | + | 0.783374i | \(0.286503\pi\) | |||||||
\(572\) | 6.94110 | + | 12.0223i | 0.290222 | + | 0.502679i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.8465 | − | 55.5691i | −1.03707 | − | 2.31941i | ||||
\(575\) | 2.20920 | 0.0921301 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.1247 | − | 29.6608i | 0.712910 | − | 1.23480i | −0.250850 | − | 0.968026i | \(-0.580710\pi\) |
0.963760 | − | 0.266770i | \(-0.0859565\pi\) | |||||||
\(578\) | −3.01524 | + | 5.22254i | −0.125417 | + | 0.217229i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 36.3125 | 1.50780 | ||||||||
\(581\) | −9.12490 | − | 0.944459i | −0.378565 | − | 0.0391828i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.6438 | + | 51.3445i | 1.22772 | + | 2.12647i | ||||
\(584\) | 7.65959 | − | 13.2668i | 0.316956 | − | 0.548984i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.2859 | + | 40.3323i | 0.961930 | + | 1.66611i | ||||
\(587\) | 29.4494 | 1.21551 | 0.607754 | − | 0.794126i | \(-0.292071\pi\) | ||||
0.607754 | + | 0.794126i | \(0.292071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4526 | 0.554305 | ||||||||
\(590\) | −11.2503 | − | 19.4861i | −0.463167 | − | 0.802229i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.92275 | − | 6.79439i | 0.161224 | − | 0.279248i | ||||
\(593\) | −17.0001 | − | 29.4450i | −0.698109 | − | 1.20916i | −0.969121 | − | 0.246584i | \(-0.920692\pi\) |
0.271013 | − | 0.962576i | \(-0.412641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.1075 | + | 2.18470i | 0.865324 | + | 0.0895640i | ||||
\(596\) | −8.56514 | −0.350842 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.95168 | + | 8.57655i | −0.202489 | + | 0.350721i | ||||
\(599\) | 10.7209 | − | 18.5691i | 0.438043 | − | 0.758713i | −0.559495 | − | 0.828834i | \(-0.689005\pi\) |
0.997539 | + | 0.0701203i | \(0.0223383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4039 | 1.64811 | 0.824054 | − | 0.566511i | \(-0.191707\pi\) | ||||
0.824054 | + | 0.566511i | \(0.191707\pi\) | |||||||
\(602\) | 8.14447 | + | 18.2151i | 0.331944 | + | 0.742392i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 26.8931 | + | 46.5803i | 1.09427 | + | 1.89533i | ||||
\(605\) | −12.6668 | + | 21.9396i | −0.514980 | + | 0.891971i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.9456 | + | 38.0110i | 0.890746 | + | 1.54282i | 0.838983 | + | 0.544158i | \(0.183151\pi\) |
0.0517636 | + | 0.998659i | \(0.483516\pi\) | |||||||
\(608\) | −25.2036 | −1.02214 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.0677 | −0.610074 | ||||||||
\(611\) | −3.55438 | − | 6.15636i | −0.143795 | − | 0.249060i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.15777 | − | 12.3976i | 0.289100 | − | 0.500735i | −0.684496 | − | 0.729017i | \(-0.739977\pi\) |
0.973595 | + | 0.228282i | \(0.0733108\pi\) | |||||||
\(614\) | −5.48750 | − | 9.50464i | −0.221458 | − | 0.383576i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.7831 | + | 20.4151i | −0.595628 | + | 0.822547i | ||||
\(617\) | 36.9097 | 1.48593 | 0.742965 | − | 0.669330i | \(-0.233419\pi\) | ||||
0.742965 | + | 0.669330i | \(0.233419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.14646 | + | 12.3780i | −0.287240 | + | 0.497515i | −0.973150 | − | 0.230172i | \(-0.926071\pi\) |
0.685910 | + | 0.727687i | \(0.259405\pi\) | |||||||
\(620\) | 11.6030 | − | 20.0970i | 0.465988 | − | 0.807115i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.35973 | −0.214906 | ||||||||
\(623\) | 3.95728 | + | 8.85046i | 0.158545 | + | 0.354586i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1438 | + | 19.3016i | 0.445750 | + | 0.772062i | ||||
\(626\) | 15.4496 | − | 26.7594i | 0.617489 | − | 1.06952i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.2036 | + | 24.6013i | 0.566784 | + | 0.981698i | ||||
\(629\) | 21.2554 | 0.847510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0431064 | −0.00171604 | −0.000858019 | − | 1.00000i | \(-0.500273\pi\) | ||||
−0.000858019 | 1.00000i | \(0.500273\pi\) | ||||||||
\(632\) | −5.15084 | − | 8.92152i | −0.204890 | − | 0.354879i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.39592 | + | 5.88190i | −0.134869 | + | 0.233600i | ||||
\(635\) | 11.1731 | + | 19.3524i | 0.443390 | + | 0.767975i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.85161 | + | 1.43369i | 0.271471 | + | 0.0568048i | ||||
\(638\) | 62.5484 | 2.47632 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.1860 | + | 26.3029i | −0.600279 | + | 1.03971i | ||||
\(641\) | 21.3328 | − | 36.9494i | 0.842594 | − | 1.45942i | −0.0451008 | − | 0.998982i | \(-0.514361\pi\) |
0.887695 | − | 0.460433i | \(-0.152306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.49737 | −0.216795 | −0.108398 | − | 0.994108i | \(-0.534572\pi\) | ||||
−0.108398 | + | 0.994108i | \(0.534572\pi\) | |||||||
\(644\) | −34.1342 | − | 3.53301i | −1.34508 | − | 0.139220i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.9156 | − | 25.8345i | −0.586845 | − | 1.01645i | ||||
\(647\) | −19.0933 | + | 33.0706i | −0.750637 | + | 1.30014i | 0.196877 | + | 0.980428i | \(0.436920\pi\) |
−0.947514 | + | 0.319713i | \(0.896413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.4671 | − | 19.8615i | −0.450121 | − | 0.779633i | ||||
\(650\) | 1.09280 | 0.0428633 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 40.1024 | 1.57053 | ||||||||
\(653\) | 19.2510 | + | 33.3437i | 0.753349 | + | 1.30484i | 0.946191 | + | 0.323608i | \(0.104896\pi\) |
−0.192843 | + | 0.981230i | \(0.561771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.75711 | − | 9.97161i | 0.224949 | − | 0.389623i | ||||
\(656\) | −7.24820 | − | 12.5543i | −0.282995 | − | 0.490161i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 24.4151 | − | 33.7166i | 0.951798 | − | 1.31441i | ||||
\(659\) | −19.4843 | −0.759002 | −0.379501 | − | 0.925191i | \(-0.623904\pi\) | ||||
−0.379501 | + | 0.925191i | \(0.623904\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8334 | − | 36.0844i | 0.810324 | − | 1.40352i | −0.102314 | − | 0.994752i | \(-0.532625\pi\) |
0.912638 | − | 0.408770i | \(-0.134042\pi\) | |||||||
\(662\) | 15.0564 | − | 26.0784i | 0.585182 | − | 1.01356i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.89760 | 0.267679 | ||||||||
\(665\) | 11.7506 | − | 16.2273i | 0.455668 | − | 0.629266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.2020 | + | 22.8665i | 0.511182 | + | 0.885393i | ||||
\(668\) | 25.1520 | − | 43.5645i | 0.973160 | − | 1.68556i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.81168 | − | 11.7982i | −0.263158 | − | 0.455803i | ||||
\(671\) | −15.3580 | −0.592890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.3157 | −0.551830 | −0.275915 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275915 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(674\) | −38.9153 | − | 67.4033i | −1.49896 | − | 2.59628i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.44940 | + | 2.51043i | −0.0557460 | + | 0.0965550i | ||||
\(677\) | −14.7641 | − | 25.5721i | −0.567429 | − | 0.982815i | −0.996819 | − | 0.0796963i | \(-0.974605\pi\) |
0.429391 | − | 0.903119i | \(-0.358728\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2304 | − | 1.47290i | −0.546114 | − | 0.0565247i | ||||
\(680\) | −15.9554 | −0.611860 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.9862 | − | 34.6172i | 0.765312 | − | 1.32556i | ||||
\(683\) | 23.5349 | − | 40.7637i | 0.900539 | − | 1.55978i | 0.0737441 | − | 0.997277i | \(-0.476505\pi\) |
0.826795 | − | 0.562503i | \(-0.190161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −47.2210 | −1.80422 | ||||||||
\(686\) | 8.71296 | + | 40.0546i | 0.332662 | + | 1.52929i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.37590 | + | 4.11518i | 0.0905804 | + | 0.156890i | ||||
\(689\) | −6.19003 | + | 10.7214i | −0.235821 | + | 0.408454i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4334 | + | 26.7314i | 0.587113 | + | 1.01691i | 0.994608 | + | 0.103703i | \(0.0330690\pi\) |
−0.407495 | + | 0.913207i | \(0.633598\pi\) | |||||||
\(692\) | 8.58442 | 0.326331 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.1091 | −0.459656 | ||||||||
\(695\) | 4.24559 | + | 7.35358i | 0.161044 | + | 0.278937i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.6372 | − | 34.0127i | 0.743813 | − | 1.28832i | ||||
\(698\) | 4.80508 | + | 8.32264i | 0.181875 | + | 0.315017i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.54568 | + | 3.45691i | 0.0584211 | + | 0.130659i | ||||
\(701\) | −6.48958 | −0.245108 | −0.122554 | − | 0.992462i | \(-0.539108\pi\) | ||||
−0.122554 | + | 0.992462i | \(0.539108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0341 | − | 17.3795i | 0.378443 | − | 0.655482i | ||||
\(704\) | −30.7657 | + | 53.2878i | −1.15953 | + | 2.00836i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 61.0860 | 2.29900 | ||||||||
\(707\) | 14.4580 | − | 19.9661i | 0.543747 | − | 0.750902i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.68689 | + | 11.5820i | 0.251131 | + | 0.434972i | 0.963838 | − | 0.266490i | \(-0.0858641\pi\) |
−0.712706 | + | 0.701463i | \(0.752531\pi\) | |||||||
\(710\) | 5.96409 | − | 10.3301i | 0.223828 | − | 0.387682i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.64475 | − | 6.31290i | −0.136593 | − | 0.236586i | ||||
\(713\) | 16.8738 | 0.631929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.1660 | −0.380186 | ||||||||
\(716\) | −8.21645 | − | 14.2313i | −0.307063 | − | 0.531849i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.33555 | + | 12.7055i | −0.273760 | + | 0.474167i | ||||
\(719\) | −8.37048 | − | 14.4981i | −0.312166 | − | 0.540688i | 0.666665 | − | 0.745358i | \(-0.267721\pi\) |
−0.978831 | + | 0.204670i | \(0.934388\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.89050 | − | 17.6471i | −0.293858 | − | 0.657212i | ||||
\(722\) | 13.8883 | 0.516868 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.4015 | + | 18.0160i | −0.386570 | + | 0.669558i | ||||
\(725\) | 1.45680 | − | 2.52325i | 0.0541041 | − | 0.0937110i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.8138 | 1.43952 | 0.719761 | − | 0.694221i | \(-0.244251\pi\) | ||||
0.719761 | + | 0.694221i | \(0.244251\pi\) | |||||||
\(728\) | −5.23528 | − | 0.541869i | −0.194032 | − | 0.0200830i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.0906 | + | 31.3339i | 0.669564 | + | 1.15972i | ||||
\(731\) | −6.43692 | + | 11.1491i | −0.238078 | + | 0.412364i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.8639 | − | 32.6733i | −0.696756 | − | 1.20682i | −0.969585 | − | 0.244754i | \(-0.921293\pi\) |
0.272830 | − | 0.962062i | \(-0.412040\pi\) | |||||||
\(734\) | −69.0719 | −2.54949 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.6132 | −1.16528 | ||||||||
\(737\) | −6.94292 | − | 12.0255i | −0.255746 | − | 0.442965i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.61476 | − | 7.99300i | 0.169757 | − | 0.294027i | −0.768578 | − | 0.639757i | \(-0.779035\pi\) |
0.938334 | + | 0.345729i | \(0.112368\pi\) | |||||||
\(740\) | −17.3090 | − | 29.9801i | −0.636291 | − | 1.10209i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −72.1111 | − | 7.46375i | −2.64728 | − | 0.274003i | ||||
\(743\) | 3.56327 | 0.130724 | 0.0653619 | − | 0.997862i | \(-0.479180\pi\) | ||||
0.0653619 | + | 0.997862i | \(0.479180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.13614 | − | 5.43195i | 0.114899 | − | 0.199011i | ||||
\(746\) | −17.4571 | + | 30.2366i | −0.639151 | + | 1.10704i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −52.4508 | −1.91779 | ||||||||
\(749\) | 7.28674 | + | 16.2968i | 0.266252 | + | 0.595472i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6053 | − | 44.3496i | −0.934350 | − | 1.61834i | −0.775789 | − | 0.630992i | \(-0.782648\pi\) |
−0.158561 | − | 0.987349i | \(-0.550685\pi\) | |||||||
\(752\) | 4.95687 | − | 8.58555i | 0.180758 | − | 0.313083i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.53049 | + | 11.3111i | 0.237826 | + | 0.411927i | ||||
\(755\) | −39.3879 | −1.43347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.2305 | 0.917019 | 0.458509 | − | 0.888690i | \(-0.348384\pi\) | ||||
0.458509 | + | 0.888690i | \(0.348384\pi\) | |||||||
\(758\) | 35.0272 | + | 60.6688i | 1.27224 | + | 2.20359i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.53207 | + | 13.0459i | −0.273217 | + | 0.473226i | ||||
\(761\) | 1.82372 | + | 3.15878i | 0.0661099 | + | 0.114506i | 0.897186 | − | 0.441653i | \(-0.145608\pi\) |
−0.831076 | + | 0.556159i | \(0.812275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.48077 | + | 8.94978i | −0.234620 | + | 0.324004i | ||||
\(764\) | −34.4428 | −1.24610 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.7154 | + | 23.7558i | −0.495558 | + | 0.858331i | ||||
\(767\) | 2.39448 | − | 4.14736i | 0.0864596 | − | 0.149752i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.9882 | 0.792914 | 0.396457 | − | 0.918053i | \(-0.370240\pi\) | ||||
0.396457 | + | 0.918053i | \(0.370240\pi\) | |||||||
\(770\) | −24.2995 | − | 54.3458i | −0.875693 | − | 1.95849i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −33.2929 | − | 57.6650i | −1.19824 | − | 2.07541i | ||||
\(773\) | 10.9295 | − | 18.9305i | 0.393108 | − | 0.680882i | −0.599750 | − | 0.800187i | \(-0.704733\pi\) |
0.992858 | + | 0.119305i | \(0.0380667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.930986 | − | 1.61252i | −0.0334420 | − | 0.0579233i | ||||
\(776\) | 10.7569 | 0.386151 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.1505 | −1.11680 | ||||||||
\(779\) | −18.5404 | − | 32.1128i | −0.664277 | − | 1.15056i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.07900 | − | 10.5291i | 0.217524 | − | 0.376762i | ||||
\(782\) | −18.7088 | − | 32.4046i | −0.669025 | − | 1.15879i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.04603 | + | 9.27468i | 0.108787 | + | 0.331239i | ||||
\(785\) | −20.8026 | −0.742477 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.9336 | + | 34.5261i | −0.710557 | + | 1.23072i | 0.254091 | + | 0.967180i | \(0.418224\pi\) |
−0.964648 | + | 0.263541i | \(0.915109\pi\) | |||||||
\(788\) | 24.5261 | − | 42.4804i | 0.873706 | − | 1.51330i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.3308 | 0.865651 | ||||||||
\(791\) | −15.5298 | − | 1.60739i | −0.552176 | − | 0.0571521i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.60348 | − | 2.77732i | −0.0569414 | − | 0.0986254i | ||||
\(794\) | −7.71680 | + | 13.3659i | −0.273859 | + | 0.474338i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.5796 | − | 25.2526i | −0.516759 | − | 0.895053i | ||||
\(797\) | 40.1971 | 1.42385 | 0.711927 | − | 0.702253i | \(-0.247822\pi\) | ||||
0.711927 | + | 0.702253i | \(0.247822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.8589 | 0.950198 | ||||||||
\(800\) | 1.74421 | + | 3.02106i | 0.0616671 | + | 0.106811i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.02873 | + | 5.24592i | −0.106948 | + | 0.185240i | ||||
\(803\) | 18.4392 | + | 31.9376i | 0.650704 | + | 1.12705i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.7389 | − | 20.3541i | 0.519478 | − | 0.717387i | ||||
\(806\) | 8.34680 | 0.294003 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.26749 | + | 16.0518i | −0.326029 | + | 0.564699i | ||||
\(809\) | 1.26924 | − | 2.19840i | 0.0446243 | − | 0.0772915i | −0.842851 | − | 0.538148i | \(-0.819124\pi\) |
0.887475 | + | 0.460856i | \(0.152458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.7062 | −1.46450 | −0.732251 | − | 0.681035i | \(-0.761530\pi\) | ||||
−0.732251 | + | 0.681035i | \(0.761530\pi\) | |||||||
\(812\) | −26.5441 | + | 36.6567i | −0.931515 | + | 1.28640i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.8148 | − | 51.6407i | −1.04501 | − | 1.81001i | ||||
\(815\) | −14.6836 | + | 25.4327i | −0.514343 | + | 0.890868i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.07737 | + | 10.5263i | 0.212620 | + | 0.368269i | ||||
\(818\) | 54.2604 | 1.89717 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −63.9650 | −2.23375 | ||||||||
\(821\) | 15.9652 | + | 27.6525i | 0.557189 | + | 0.965079i | 0.997730 | + | 0.0673467i | \(0.0214534\pi\) |
−0.440541 | + | 0.897733i | \(0.645213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1266 | − | 29.6641i | 0.596995 | − | 1.03402i | −0.396267 | − | 0.918135i | \(-0.629695\pi\) |
0.993262 | − | 0.115890i | \(-0.0369720\pi\) | |||||||
\(824\) | 7.26734 | + | 12.5874i | 0.253170 | + | 0.438503i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 27.8946 | + | 2.88719i | 0.970578 | + | 0.100458i | ||||
\(827\) | −36.9755 | −1.28576 | −0.642882 | − | 0.765965i | \(-0.722261\pi\) | ||||
−0.642882 | + | 0.765965i | \(0.722261\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.99473 | − | 17.3114i | 0.347131 | − | 0.601249i | −0.638607 | − | 0.769533i | \(-0.720489\pi\) |
0.985739 | + | 0.168284i | \(0.0538225\pi\) | |||||||
\(830\) | −8.14547 | + | 14.1084i | −0.282733 | + | 0.489708i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.8486 | −0.445446 | ||||||||
\(833\) | −17.6348 | + | 19.7106i | −0.611009 | + | 0.682932i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.4189 | + | 31.9024i | 0.637412 | + | 1.10403i | ||||
\(836\) | −24.7605 | + | 42.8865i | −0.856360 | + | 1.48326i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.33384 | + | 5.77438i | 0.115166 | + | 0.199473i | ||||
\(839\) | −12.8147 | −0.442411 | −0.221206 | − | 0.975227i | \(-0.570999\pi\) | ||||
−0.221206 | + | 0.975227i | \(0.570999\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.82265 | 0.200781 | ||||||||
\(842\) | −11.0666 | − | 19.1679i | −0.381381 | − | 0.660571i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.4535 | − | 61.4073i | 1.22036 | − | 2.11373i | ||||
\(845\) | −1.06140 | − | 1.83839i | −0.0365132 | − | 0.0632427i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8882 | − | 28.8245i | −0.442845 | − | 0.990422i | ||||
\(848\) | −17.2650 | −0.592882 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.06446 | + | 3.57575i | −0.0708104 | + | 0.122647i | ||||
\(851\) | 12.5859 | − | 21.7994i | 0.431439 | − | 0.747274i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1839 | −1.03348 | −0.516739 | − | 0.856143i | \(-0.672854\pi\) | ||||
−0.516739 | + | 0.856143i | \(0.672854\pi\) | |||||||
\(854\) | 11.0143 | − | 15.2105i | 0.376903 | − | 0.520494i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.71127 | − | 11.6243i | −0.229386 | − | 0.397309i | ||||
\(857\) | −26.6164 | + | 46.1009i | −0.909197 | + | 1.57478i | −0.0940154 | + | 0.995571i | \(0.529970\pi\) |
−0.815182 | + | 0.579205i | \(0.803363\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.13597 | + | 10.6278i | 0.209357 | + | 0.362616i | 0.951512 | − | 0.307611i | \(-0.0995297\pi\) |
−0.742155 | + | 0.670228i | \(0.766196\pi\) | |||||||
\(860\) | 20.9672 | 0.714975 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.5977 | −1.41682 | ||||||||
\(863\) | 12.2226 | + | 21.1702i | 0.416064 | + | 0.720643i | 0.995539 | − | 0.0943460i | \(-0.0300760\pi\) |
−0.579476 | + | 0.814989i | \(0.696743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.14320 | + | 5.44418i | −0.106872 | + | 0.185108i | ||||
\(866\) | −8.59778 | − | 14.8918i | −0.292164 | − | 0.506043i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.8058 | + | 26.4037i | 0.400716 | + | 0.896200i | ||||
\(869\) | 24.7996 | 0.841268 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.44978 | − | 2.51109i | 0.0491238 | − | 0.0850850i | ||||
\(872\) | 4.15415 | − | 7.19519i | 0.140677 | − | 0.243660i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −35.3276 | −1.19497 | ||||||||
\(875\) | −30.6910 | − | 3.17663i | −1.03755 | − | 0.107390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4376 | + | 45.7913i | 0.892736 | + | 1.54626i | 0.836582 | + | 0.547842i | \(0.184550\pi\) |
0.0561539 | + | 0.998422i | \(0.482116\pi\) | |||||||
\(878\) | −42.0178 | + | 72.7770i | −1.41803 | + | 2.45611i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.08864 | − | 12.2779i | −0.238958 | − | 0.413887i | ||||
\(881\) | −55.0118 | −1.85339 | −0.926697 | − | 0.375809i | \(-0.877365\pi\) | ||||
−0.926697 | + | 0.375809i | \(0.877365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.1730 | 1.48654 | 0.743269 | − | 0.668992i | \(-0.233274\pi\) | ||||
0.743269 | + | 0.668992i | \(0.233274\pi\) | |||||||
\(884\) | −5.47622 | − | 9.48510i | −0.184185 | − | 0.319018i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.4270 | + | 68.2895i | −1.32457 | + | 2.29423i | ||||
\(887\) | −2.54330 | − | 4.40512i | −0.0853955 | − | 0.147909i | 0.820164 | − | 0.572128i | \(-0.193882\pi\) |
−0.905560 | + | 0.424219i | \(0.860549\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.7032 | − | 2.86738i | −0.929136 | − | 0.0961688i | ||||
\(890\) | 17.2165 | 0.577100 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42.4130 | − | 73.4614i | 1.42009 | − | 2.45967i | ||||
\(893\) | 12.6793 | − | 21.9612i | 0.424296 | − | 0.734903i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0339 | 0.402248 | ||||||||
\(896\) | −15.4514 | − | 34.5571i | −0.516196 | − | 1.15447i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.91178 | + | 15.4356i | 0.297390 | + | 0.515094i | ||||
\(899\) | 11.1270 | − | 19.2724i | 0.371105 | − | 0.642772i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.3876 | − | 40.5086i | −0.779155 | − | 1.34954i | ||||
\(902\) | −110.180 | −3.66859 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.7391 | 0.390437 | ||||||||
\(905\) | −7.61706 | − | 13.1931i | −0.253200 | − | 0.438555i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.06264 | − | 15.6969i | 0.300920 | − | 0.521209i | −0.675425 | − | 0.737429i | \(-0.736040\pi\) |
0.976345 | + | 0.216220i | \(0.0693730\pi\) | |||||||
\(908\) | −14.6008 | − | 25.2893i | −0.484544 | − | 0.839255i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.29075 | − | 10.0683i | 0.241686 | − | 0.333763i | ||||
\(911\) | 9.65804 | 0.319985 | 0.159993 | − | 0.987118i | \(-0.448853\pi\) | ||||
0.159993 | + | 0.987118i | \(0.448853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.30241 | + | 14.3802i | −0.274770 | + | 0.475915i | ||||
\(914\) | 17.2613 | − | 29.8974i | 0.570952 | − | 0.988918i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −32.2924 | −1.06697 | ||||||||
\(917\) | 5.85774 | + | 13.1008i | 0.193440 | + | 0.432628i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.8801 | − | 41.3616i | −0.787733 | − | 1.36439i | −0.927353 | − | 0.374188i | \(-0.877922\pi\) |
0.139620 | − | 0.990205i | \(-0.455412\pi\) | |||||||
\(920\) | −9.44758 | + | 16.3637i | −0.311477 | + | 0.539495i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.4401 | + | 49.2598i | 0.936626 | + | 1.62228i | ||||
\(923\) | 2.53876 | 0.0835643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.77763 | −0.0913279 | ||||||||
\(926\) | −22.7096 | − | 39.3342i | −0.746285 | − | 1.29260i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.8464 | + | 36.1071i | −0.684317 | + | 1.18527i | ||||
\(929\) | 16.9905 | + | 29.4285i | 0.557442 | + | 0.965517i | 0.997709 | + | 0.0676505i | \(0.0215503\pi\) |
−0.440267 | + | 0.897867i | \(0.645116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.79153 | + | 23.7239i | 0.255357 | + | 0.777520i | ||||
\(932\) | 49.5210 | 1.62212 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.0861 | + | 22.6657i | −0.428189 | + | 0.741645i | ||||
\(935\) | 19.2049 | − | 33.2639i | 0.628068 | − | 1.08785i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.7948 | −0.810012 | −0.405006 | − | 0.914314i | \(-0.632731\pi\) | ||||
−0.405006 | + | 0.914314i | \(0.632731\pi\) | |||||||
\(938\) | 16.8893 | + | 1.74810i | 0.551454 | + | 0.0570774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21.8720 | − | 37.8835i | −0.713387 | − | 1.23562i | ||||
\(941\) | −4.12098 | + | 7.13774i | −0.134340 | + | 0.232684i | −0.925345 | − | 0.379126i | \(-0.876225\pi\) |
0.791005 | + | 0.611810i | \(0.209558\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.2554 | − | 40.2796i | −0.757301 | − | 1.31168i | ||||
\(944\) | 6.67859 | 0.217370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.1160 | 1.17423 | ||||||||
\(947\) | 9.98643 | + | 17.2970i | 0.324515 | + | 0.562077i | 0.981414 | − | 0.191902i | \(-0.0614655\pi\) |
−0.656899 | + | 0.753979i | \(0.728132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.85035 | + | 6.66901i | −0.124988 | + | 0.216485i | ||||
\(950\) | 1.94914 | + | 3.37602i | 0.0632386 | + | 0.109532i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.6632 | − | 16.1066i | 0.378007 | − | 0.522018i | ||||
\(953\) | 21.5341 | 0.697557 | 0.348778 | − | 0.937205i | \(-0.386597\pi\) | ||||
0.348778 | + | 0.937205i | \(0.386597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6113 | − | 21.8434i | 0.408091 | − | 0.706835i | ||||
\(956\) | 10.0319 | − | 17.3757i | 0.324455 | − | 0.561972i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 50.1432 | 1.62005 | ||||||||
\(959\) | 34.5181 | − | 47.6686i | 1.11465 | − | 1.53930i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.38917 | + | 14.5305i | 0.270618 | + | 0.468725i | ||||
\(962\) | 6.22574 | − | 10.7833i | 0.200726 | − | 0.347667i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.41564 | − | 16.3084i | −0.303257 | − | 0.525257i | ||||
\(965\) | 48.7610 | 1.56967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.2887 | 1.39207 | 0.696036 | − | 0.718007i | \(-0.254945\pi\) | ||||
0.696036 | + | 0.718007i | \(0.254945\pi\) | |||||||
\(968\) | 11.8704 | + | 20.5601i | 0.381528 | + | 0.660827i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.7030 | + | 22.0022i | −0.407868 | + | 0.706449i | ||||
\(971\) | −26.3356 | − | 45.6147i | −0.845151 | − | 1.46384i | −0.885490 | − | 0.464658i | \(-0.846177\pi\) |
0.0403390 | − | 0.999186i | \(-0.487156\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5268 | − | 1.08956i | −0.337473 | − | 0.0349296i | ||||
\(974\) | 72.4127 | 2.32025 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.23619 | − | 3.87319i | 0.0715787 | − | 0.123978i | ||||
\(977\) | 7.70305 | − | 13.3421i | 0.246442 | − | 0.426851i | −0.716094 | − | 0.698004i | \(-0.754072\pi\) |
0.962536 | + | 0.271153i | \(0.0874051\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.5483 | 0.560845 | ||||||||
\(980\) | 42.1617 | + | 8.82227i | 1.34681 | + | 0.281817i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.83121 | − | 11.8320i | −0.217993 | − | 0.377575i | ||||
\(983\) | 3.79073 | − | 6.56574i | 0.120906 | − | 0.209415i | −0.799219 | − | 0.601039i | \(-0.794754\pi\) |
0.920125 | + | 0.391625i | \(0.128087\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.9605 | + | 31.1085i | 0.572270 | + | 0.991201i | ||||
\(986\) | −49.3480 | −1.57156 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.3407 | −0.328981 | ||||||||
\(989\) | 7.62293 | + | 13.2033i | 0.242395 | + | 0.419841i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50923 | − | 16.4705i | 0.302071 | − | 0.523202i | −0.674534 | − | 0.738244i | \(-0.735655\pi\) |
0.976605 | + | 0.215042i | \(0.0689888\pi\) | |||||||
\(992\) | 13.3222 | + | 23.0747i | 0.422980 | + | 0.732623i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.06834 | + | 13.5718i | 0.192476 | + | 0.430472i | ||||
\(995\) | 21.3533 | 0.676946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0499 | + | 39.9236i | −0.729998 | + | 1.26439i | 0.226885 | + | 0.973922i | \(0.427146\pi\) |
−0.956883 | + | 0.290473i | \(0.906187\pi\) | |||||||
\(998\) | −16.2001 | + | 28.0593i | −0.512804 | + | 0.888202i | ||||
\(999\) | 0 | 0 |
(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 | 819.2.j.h.235.4 | 10 | ||
3.2 | odd | 2 | 91.2.e.c.53.2 | ✓ | 10 | ||
7.2 | even | 3 | inner | 819.2.j.h.352.4 | 10 | ||
7.3 | odd | 6 | 5733.2.a.bm.1.2 | 5 | |||
7.4 | even | 3 | 5733.2.a.bl.1.2 | 5 | |||
12.11 | even | 2 | 1456.2.r.p.417.5 | 10 | |||
21.2 | odd | 6 | 91.2.e.c.79.2 | yes | 10 | ||
21.5 | even | 6 | 637.2.e.m.79.2 | 10 | |||
21.11 | odd | 6 | 637.2.a.l.1.4 | 5 | |||
21.17 | even | 6 | 637.2.a.k.1.4 | 5 | |||
21.20 | even | 2 | 637.2.e.m.508.2 | 10 | |||
39.38 | odd | 2 | 1183.2.e.f.508.4 | 10 | |||
84.23 | even | 6 | 1456.2.r.p.625.5 | 10 | |||
273.38 | even | 6 | 8281.2.a.bx.1.2 | 5 | |||
273.116 | odd | 6 | 8281.2.a.bw.1.2 | 5 | |||
273.233 | odd | 6 | 1183.2.e.f.170.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.2 | ✓ | 10 | 3.2 | odd | 2 | ||
91.2.e.c.79.2 | yes | 10 | 21.2 | odd | 6 | ||
637.2.a.k.1.4 | 5 | 21.17 | even | 6 | |||
637.2.a.l.1.4 | 5 | 21.11 | odd | 6 | |||
637.2.e.m.79.2 | 10 | 21.5 | even | 6 | |||
637.2.e.m.508.2 | 10 | 21.20 | even | 2 | |||
819.2.j.h.235.4 | 10 | 1.1 | even | 1 | trivial | ||
819.2.j.h.352.4 | 10 | 7.2 | even | 3 | inner | ||
1183.2.e.f.170.4 | 10 | 273.233 | odd | 6 | |||
1183.2.e.f.508.4 | 10 | 39.38 | odd | 2 | |||
1456.2.r.p.417.5 | 10 | 12.11 | even | 2 | |||
1456.2.r.p.625.5 | 10 | 84.23 | even | 6 | |||
5733.2.a.bl.1.2 | 5 | 7.4 | even | 3 | |||
5733.2.a.bm.1.2 | 5 | 7.3 | odd | 6 | |||
8281.2.a.bw.1.2 | 5 | 273.116 | odd | 6 | |||
8281.2.a.bx.1.2 | 5 | 273.38 | even | 6 |