Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,4,Mod(55,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.55");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.g (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: | \(6.90322347067\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.3 | ||
Root | \(1.18088 - 2.04535i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.100 |
Dual form | 117.4.g.e.55.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18088 | − | 2.04535i | 0.417505 | − | 0.723139i | −0.578183 | − | 0.815907i | \(-0.696238\pi\) |
0.995688 | + | 0.0927678i | \(0.0295714\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.21104 | + | 2.09758i | 0.151380 | + | 0.262198i | ||||
\(5\) | −6.42208 | −0.574408 | −0.287204 | − | 0.957869i | \(-0.592726\pi\) | ||||
−0.287204 | + | 0.957869i | \(0.592726\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.7469 | + | 25.5424i | 0.796259 | + | 1.37916i | 0.922037 | + | 0.387102i | \(0.126524\pi\) |
−0.125778 | + | 0.992058i | \(0.540143\pi\) | |||||||
\(8\) | 24.6145 | 1.08782 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.58371 | + | 13.1354i | −0.239818 | + | 0.415377i | ||||
\(11\) | −0.312358 | + | 0.541019i | −0.00856176 | + | 0.0148294i | −0.870275 | − | 0.492567i | \(-0.836059\pi\) |
0.861713 | + | 0.507396i | \(0.169392\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.3948 | − | 15.0368i | 0.947146 | − | 0.320804i | ||||
\(14\) | 69.6575 | 1.32977 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 19.3785 | − | 33.5645i | 0.302788 | − | 0.524445i | ||||
\(17\) | 43.8645 | + | 75.9756i | 0.625807 | + | 1.08393i | 0.988384 | + | 0.151976i | \(0.0485635\pi\) |
−0.362577 | + | 0.931954i | \(0.618103\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −41.4009 | − | 71.7085i | −0.499896 | − | 0.865845i | 0.500104 | − | 0.865965i | \(-0.333295\pi\) |
−1.00000 | 0.000120110i | \(0.999962\pi\) | ||||||||
\(20\) | −7.77738 | − | 13.4708i | −0.0869538 | − | 0.150608i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.737715 | + | 1.27776i | 0.00714915 | + | 0.0123827i | ||||
\(23\) | −37.3989 | + | 64.7767i | −0.339052 | + | 0.587256i | −0.984255 | − | 0.176756i | \(-0.943440\pi\) |
0.645203 | + | 0.764012i | \(0.276773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −83.7569 | −0.670055 | ||||||||
\(26\) | 21.6695 | − | 108.559i | 0.163452 | − | 0.818855i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −35.7182 | + | 61.8657i | −0.241075 | + | 0.417554i | ||||
\(29\) | 113.165 | − | 196.007i | 0.724625 | − | 1.25509i | −0.234503 | − | 0.972115i | \(-0.575346\pi\) |
0.959128 | − | 0.282973i | \(-0.0913205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 173.660 | 1.00614 | 0.503070 | − | 0.864246i | \(-0.332204\pi\) | ||||
0.503070 | + | 0.864246i | \(0.332204\pi\) | |||||||
\(32\) | 52.6906 | + | 91.2627i | 0.291077 | + | 0.504160i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 207.195 | 1.04511 | ||||||||
\(35\) | −94.7059 | − | 164.035i | −0.457378 | − | 0.792201i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −56.0102 | + | 97.0124i | −0.248865 | + | 0.431047i | −0.963211 | − | 0.268745i | \(-0.913391\pi\) |
0.714346 | + | 0.699793i | \(0.246724\pi\) | |||||||
\(38\) | −195.558 | −0.834835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −158.076 | −0.624850 | ||||||||
\(41\) | −133.506 | + | 231.238i | −0.508538 | + | 0.880814i | 0.491413 | + | 0.870927i | \(0.336481\pi\) |
−0.999951 | + | 0.00988706i | \(0.996853\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −191.725 | − | 332.077i | −0.679948 | − | 1.17770i | −0.974996 | − | 0.222222i | \(-0.928669\pi\) |
0.295048 | − | 0.955483i | \(-0.404664\pi\) | |||||||
\(44\) | −1.51311 | −0.00518431 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 88.3272 | + | 152.987i | 0.283112 | + | 0.490364i | ||||
\(47\) | −337.380 | −1.04706 | −0.523530 | − | 0.852007i | \(-0.675385\pi\) | ||||
−0.523530 | + | 0.852007i | \(0.675385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −263.443 | + | 456.297i | −0.768057 | + | 1.33031i | ||||
\(50\) | −98.9070 | + | 171.312i | −0.279751 | + | 0.484543i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 85.3046 | + | 74.9115i | 0.227493 | + | 0.199776i | ||||
\(53\) | 146.354 | 0.379308 | 0.189654 | − | 0.981851i | \(-0.439263\pi\) | ||||
0.189654 | + | 0.981851i | \(0.439263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00598 | − | 3.47447i | 0.00491794 | − | 0.00851813i | ||||
\(56\) | 362.988 | + | 628.713i | 0.866183 | + | 1.50027i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −267.268 | − | 462.922i | −0.605069 | − | 1.04801i | ||||
\(59\) | −264.587 | − | 458.277i | −0.583834 | − | 1.01123i | −0.995020 | − | 0.0996790i | \(-0.968218\pi\) |
0.411185 | − | 0.911552i | \(-0.365115\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −101.636 | − | 176.038i | −0.213330 | − | 0.369499i | 0.739425 | − | 0.673239i | \(-0.235098\pi\) |
−0.952755 | + | 0.303741i | \(0.901764\pi\) | |||||||
\(62\) | 205.072 | − | 355.195i | 0.420068 | − | 0.727579i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 558.941 | 1.09168 | ||||||||
\(65\) | −285.107 | + | 96.5673i | −0.544048 | + | 0.184272i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −60.7484 | + | 105.219i | −0.110770 | + | 0.191859i | −0.916081 | − | 0.400993i | \(-0.868665\pi\) |
0.805311 | + | 0.592853i | \(0.201998\pi\) | |||||||
\(68\) | −106.243 | + | 184.019i | −0.189469 | + | 0.328170i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −447.346 | −0.763829 | ||||||||
\(71\) | −330.657 | − | 572.715i | −0.552701 | − | 0.957306i | −0.998078 | − | 0.0619630i | \(-0.980264\pi\) |
0.445378 | − | 0.895343i | \(-0.353069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 167.341 | 0.268299 | 0.134150 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134150 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(74\) | 132.283 | + | 229.120i | 0.207805 | + | 0.359928i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 100.276 | − | 173.684i | 0.151348 | − | 0.262143i | ||||
\(77\) | −18.4253 | −0.0272695 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −101.399 | −0.144408 | −0.0722042 | − | 0.997390i | \(-0.523003\pi\) | ||||
−0.0722042 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(80\) | −124.450 | + | 215.554i | −0.173924 | + | 0.301245i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 315.308 | + | 546.130i | 0.424634 | + | 0.735487i | ||||
\(83\) | 506.985 | 0.670468 | 0.335234 | − | 0.942135i | \(-0.391185\pi\) | ||||
0.335234 | + | 0.942135i | \(0.391185\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −281.702 | − | 487.921i | −0.359468 | − | 0.622618i | ||||
\(86\) | −905.617 | −1.13553 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.68852 | + | 13.3169i | −0.00931362 | + | 0.0161317i | ||||
\(89\) | 701.166 | − | 1214.45i | 0.835095 | − | 1.44643i | −0.0588586 | − | 0.998266i | \(-0.518746\pi\) |
0.893953 | − | 0.448160i | \(-0.147921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1038.76 | + | 912.204i | 1.19661 | + | 1.05082i | ||||
\(92\) | −181.166 | −0.205303 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −398.405 | + | 690.058i | −0.437153 | + | 0.757171i | ||||
\(95\) | 265.880 | + | 460.518i | 0.287144 | + | 0.497348i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −951.445 | − | 1647.95i | −0.995924 | − | 1.72499i | −0.576075 | − | 0.817397i | \(-0.695416\pi\) |
−0.419849 | − | 0.907594i | \(-0.637917\pi\) | |||||||
\(98\) | 622.191 | + | 1077.67i | 0.641334 | + | 1.11082i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −101.433 | − | 175.687i | −0.101433 | − | 0.175687i | ||||
\(101\) | 916.546 | − | 1587.50i | 0.902968 | − | 1.56399i | 0.0793462 | − | 0.996847i | \(-0.474717\pi\) |
0.823622 | − | 0.567139i | \(-0.191950\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1446.99 | 1.38423 | 0.692115 | − | 0.721787i | \(-0.256679\pi\) | ||||
0.692115 | + | 0.721787i | \(0.256679\pi\) | |||||||
\(104\) | 1092.75 | − | 370.122i | 1.03032 | − | 0.348976i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 172.827 | − | 299.345i | 0.158363 | − | 0.274292i | ||||
\(107\) | −184.643 | + | 319.811i | −0.166823 | + | 0.288947i | −0.937301 | − | 0.348520i | \(-0.886684\pi\) |
0.770478 | + | 0.637467i | \(0.220018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −815.694 | −0.716782 | −0.358391 | − | 0.933572i | \(-0.616675\pi\) | ||||
−0.358391 | + | 0.933572i | \(0.616675\pi\) | |||||||
\(110\) | −4.73766 | − | 8.20587i | −0.00410653 | − | 0.00711272i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1143.09 | 0.964392 | ||||||||
\(113\) | 895.282 | + | 1550.67i | 0.745319 | + | 1.29093i | 0.950045 | + | 0.312112i | \(0.101036\pi\) |
−0.204726 | + | 0.978819i | \(0.565630\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 240.178 | − | 416.001i | 0.194754 | − | 0.337324i | ||||
\(116\) | 548.187 | 0.438775 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1249.78 | −0.975014 | ||||||||
\(119\) | −1293.73 | + | 2240.81i | −0.996608 | + | 1.72618i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 665.305 | + | 1152.34i | 0.499853 | + | 0.865771i | ||||
\(122\) | −480.079 | −0.356265 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 210.309 | + | 364.266i | 0.152309 | + | 0.263807i | ||||
\(125\) | 1340.65 | 0.959293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 22.6450 | − | 39.2223i | 0.0158222 | − | 0.0274048i | −0.858006 | − | 0.513640i | \(-0.828297\pi\) |
0.873828 | + | 0.486235i | \(0.161630\pi\) | |||||||
\(128\) | 238.518 | − | 413.125i | 0.164705 | − | 0.285277i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −139.163 | + | 697.176i | −0.0938880 | + | 0.470357i | ||||
\(131\) | −1051.82 | −0.701511 | −0.350756 | − | 0.936467i | \(-0.614075\pi\) | ||||
−0.350756 | + | 0.936467i | \(0.614075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1221.07 | − | 2114.96i | 0.796093 | − | 1.37887i | ||||
\(134\) | 143.473 | + | 248.503i | 0.0924940 | + | 0.160204i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1079.70 | + | 1870.10i | 0.680763 | + | 1.17912i | ||||
\(137\) | −771.471 | − | 1336.23i | −0.481104 | − | 0.833296i | 0.518661 | − | 0.854980i | \(-0.326431\pi\) |
−0.999765 | + | 0.0216836i | \(0.993097\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9322 | − | 32.7915i | −0.0115526 | − | 0.0200097i | 0.860191 | − | 0.509971i | \(-0.170344\pi\) |
−0.871744 | + | 0.489962i | \(0.837011\pi\) | |||||||
\(140\) | 229.385 | − | 397.306i | 0.138475 | − | 0.239847i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1561.87 | −0.923020 | ||||||||
\(143\) | −5.73186 | + | 28.7153i | −0.00335190 | + | 0.0167923i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −726.752 | + | 1258.77i | −0.416231 | + | 0.720933i | ||||
\(146\) | 197.610 | − | 342.271i | 0.112016 | − | 0.194018i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −271.322 | −0.150693 | ||||||||
\(149\) | −911.199 | − | 1578.24i | −0.500995 | − | 0.867749i | −0.999999 | − | 0.00114972i | \(-0.999634\pi\) |
0.499004 | − | 0.866600i | \(-0.333699\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3239.36 | −1.74580 | −0.872900 | − | 0.487899i | \(-0.837763\pi\) | ||||
−0.872900 | + | 0.487899i | \(0.837763\pi\) | |||||||
\(152\) | −1019.06 | − | 1765.07i | −0.543795 | − | 0.941881i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.7580 | + | 37.6860i | −0.0113851 | + | 0.0197197i | ||||
\(155\) | −1115.26 | −0.577934 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 830.565 | 0.422206 | 0.211103 | − | 0.977464i | \(-0.432295\pi\) | ||||
0.211103 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(158\) | −119.740 | + | 207.396i | −0.0602912 | + | 0.104427i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −338.383 | − | 586.096i | −0.167197 | − | 0.289594i | ||||
\(161\) | −2206.07 | −1.07989 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1039.95 | + | 1801.25i | 0.499725 | + | 0.865550i | 1.00000 | 0.000317114i | \(-0.000100941\pi\) | |
−0.500275 | + | 0.865867i | \(0.666768\pi\) | |||||||
\(164\) | −646.721 | −0.307930 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 598.689 | − | 1036.96i | 0.279923 | − | 0.484842i | ||||
\(167\) | 42.9895 | − | 74.4600i | 0.0199199 | − | 0.0345023i | −0.855894 | − | 0.517152i | \(-0.826992\pi\) |
0.875814 | + | 0.482650i | \(0.160326\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1744.79 | − | 1335.11i | 0.794170 | − | 0.607696i | ||||
\(170\) | −1330.62 | −0.600319 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 464.373 | − | 804.317i | 0.205861 | − | 0.356562i | ||||
\(173\) | 1353.23 | + | 2343.87i | 0.594708 | + | 1.03006i | 0.993588 | + | 0.113061i | \(0.0360655\pi\) |
−0.398880 | + | 0.917003i | \(0.630601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1235.16 | − | 2139.35i | −0.533538 | − | 0.924114i | ||||
\(176\) | 12.1060 | + | 20.9682i | 0.00518480 | + | 0.00898035i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1655.99 | − | 2868.25i | −0.697312 | − | 1.20778i | ||||
\(179\) | −2201.05 | + | 3812.33i | −0.919074 | + | 1.59188i | −0.118250 | + | 0.992984i | \(0.537728\pi\) |
−0.800825 | + | 0.598899i | \(0.795605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1673.98 | −0.687435 | −0.343718 | − | 0.939073i | \(-0.611686\pi\) | ||||
−0.343718 | + | 0.939073i | \(0.611686\pi\) | |||||||
\(182\) | 3092.43 | − | 1047.42i | 1.25948 | − | 0.426594i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −920.553 | + | 1594.44i | −0.368826 | + | 0.638826i | ||||
\(185\) | 359.702 | − | 623.021i | 0.142950 | − | 0.247597i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −54.8057 | −0.0214320 | ||||||||
\(188\) | −408.580 | − | 707.681i | −0.158504 | − | 0.274537i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1255.89 | 0.479536 | ||||||||
\(191\) | −145.059 | − | 251.249i | −0.0549533 | − | 0.0951819i | 0.837240 | − | 0.546835i | \(-0.184168\pi\) |
−0.892193 | + | 0.451654i | \(0.850834\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −519.750 | + | 900.233i | −0.193847 | + | 0.335752i | −0.946522 | − | 0.322640i | \(-0.895430\pi\) |
0.752675 | + | 0.658392i | \(0.228763\pi\) | |||||||
\(194\) | −4494.18 | −1.66321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1276.16 | −0.465073 | ||||||||
\(197\) | 709.352 | − | 1228.63i | 0.256544 | − | 0.444348i | −0.708769 | − | 0.705440i | \(-0.750749\pi\) |
0.965314 | + | 0.261092i | \(0.0840827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1194.19 | + | 2068.40i | 0.425398 | + | 0.736810i | 0.996457 | − | 0.0840980i | \(-0.0268009\pi\) |
−0.571060 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(200\) | −2061.63 | −0.728897 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2164.66 | − | 3749.31i | −0.753987 | − | 1.30594i | ||||
\(203\) | 6675.32 | 2.30796 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 857.383 | − | 1485.03i | 0.292108 | − | 0.505946i | ||||
\(206\) | 1708.72 | − | 2959.59i | 0.577922 | − | 1.00099i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 355.601 | − | 1781.48i | 0.118541 | − | 0.593861i | ||||
\(209\) | 51.7276 | 0.0171200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2170.72 | + | 3759.81i | −0.708241 | + | 1.22671i | 0.257268 | + | 0.966340i | \(0.417178\pi\) |
−0.965509 | + | 0.260369i | \(0.916156\pi\) | |||||||
\(212\) | 177.241 | + | 306.990i | 0.0574195 | + | 0.0994536i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 436.083 | + | 755.317i | 0.139299 | + | 0.241273i | ||||
\(215\) | 1231.27 | + | 2132.63i | 0.390568 | + | 0.676483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2560.95 | + | 4435.70i | 0.801147 | + | 1.38763i | ||||
\(218\) | −963.237 | + | 1668.38i | −0.299260 | + | 0.518333i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.71730 | 0.00297791 | ||||||||
\(221\) | 3089.78 | + | 2713.34i | 0.940459 | + | 0.825878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2307.69 | + | 3997.03i | −0.692978 | + | 1.20027i | 0.277880 | + | 0.960616i | \(0.410368\pi\) |
−0.970858 | + | 0.239657i | \(0.922965\pi\) | |||||||
\(224\) | −1554.05 | + | 2691.69i | −0.463545 | + | 0.802884i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4228.89 | 1.24470 | ||||||||
\(227\) | −1081.72 | − | 1873.59i | −0.316283 | − | 0.547817i | 0.663427 | − | 0.748241i | \(-0.269101\pi\) |
−0.979709 | + | 0.200424i | \(0.935768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1859.48 | 0.536584 | 0.268292 | − | 0.963338i | \(-0.413541\pi\) | ||||
0.268292 | + | 0.963338i | \(0.413541\pi\) | |||||||
\(230\) | −567.244 | − | 982.496i | −0.162622 | − | 0.281669i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2785.49 | − | 4824.60i | 0.788259 | − | 1.36531i | ||||
\(233\) | −2866.87 | −0.806073 | −0.403037 | − | 0.915184i | \(-0.632045\pi\) | ||||
−0.403037 | + | 0.915184i | \(0.632045\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2166.68 | 0.601440 | ||||||||
\(236\) | 640.849 | − | 1109.98i | 0.176762 | − | 0.306160i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3055.49 | + | 5292.27i | 0.832177 | + | 1.44137i | ||||
\(239\) | −1893.55 | −0.512485 | −0.256242 | − | 0.966613i | \(-0.582484\pi\) | ||||
−0.256242 | + | 0.966613i | \(0.582484\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 906.788 | + | 1570.60i | 0.242371 | + | 0.419798i | 0.961389 | − | 0.275193i | \(-0.0887416\pi\) |
−0.719018 | + | 0.694991i | \(0.755408\pi\) | |||||||
\(242\) | 3142.58 | 0.834764 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 246.170 | − | 426.379i | 0.0645878 | − | 0.111869i | ||||
\(245\) | 1691.85 | − | 2930.38i | 0.441178 | − | 0.764142i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2916.25 | − | 2560.95i | −0.751241 | − | 0.659713i | ||||
\(248\) | 4274.56 | 1.09449 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1583.15 | − | 2742.10i | 0.400509 | − | 0.693703i | ||||
\(251\) | 2081.16 | + | 3604.67i | 0.523353 | + | 0.906474i | 0.999631 | + | 0.0271788i | \(0.00865235\pi\) |
−0.476278 | + | 0.879295i | \(0.658014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.3636 | − | 40.4670i | −0.00580577 | − | 0.0100559i | ||||
\(254\) | −53.4821 | − | 92.6337i | −0.0132117 | − | 0.0228833i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1672.44 | + | 2896.75i | 0.408310 | + | 0.707214i | ||||
\(257\) | 2992.65 | − | 5183.42i | 0.726368 | − | 1.25811i | −0.232041 | − | 0.972706i | \(-0.574540\pi\) |
0.958409 | − | 0.285400i | \(-0.0921263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3303.91 | −0.792645 | ||||||||
\(260\) | −547.833 | − | 481.087i | −0.130674 | − | 0.114753i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1242.07 | + | 2151.34i | −0.292884 | + | 0.507290i | ||||
\(263\) | 287.309 | − | 497.634i | 0.0673621 | − | 0.116675i | −0.830377 | − | 0.557202i | \(-0.811875\pi\) |
0.897739 | + | 0.440527i | \(0.145208\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −939.899 | −0.217877 | ||||||||
\(266\) | −2883.88 | − | 4995.03i | −0.664745 | − | 1.15137i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −294.275 | −0.0670734 | ||||||||
\(269\) | 3174.30 | + | 5498.06i | 0.719482 | + | 1.24618i | 0.961205 | + | 0.275835i | \(0.0889542\pi\) |
−0.241723 | + | 0.970345i | \(0.577712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1639.19 | − | 2839.16i | 0.367431 | − | 0.636408i | −0.621732 | − | 0.783230i | \(-0.713571\pi\) |
0.989163 | + | 0.146821i | \(0.0469042\pi\) | |||||||
\(272\) | 3400.11 | 0.757948 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3644.06 | −0.803452 | ||||||||
\(275\) | 26.1621 | − | 45.3141i | 0.00573685 | − | 0.00993652i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1976.09 | − | 3422.68i | −0.428633 | − | 0.742415i | 0.568119 | − | 0.822947i | \(-0.307671\pi\) |
−0.996752 | + | 0.0805318i | \(0.974338\pi\) | |||||||
\(278\) | −89.4267 | −0.0192930 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2331.14 | − | 4037.64i | −0.497543 | − | 0.861769i | ||||
\(281\) | 411.389 | 0.0873360 | 0.0436680 | − | 0.999046i | \(-0.486096\pi\) | ||||
0.0436680 | + | 0.999046i | \(0.486096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2936.39 | − | 5085.98i | 0.616785 | − | 1.06830i | −0.373283 | − | 0.927717i | \(-0.621768\pi\) |
0.990068 | − | 0.140586i | \(-0.0448987\pi\) | |||||||
\(284\) | 800.877 | − | 1387.16i | 0.167335 | − | 0.289834i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 51.9640 | + | 45.6330i | 0.0107437 | + | 0.00943474i | ||||
\(287\) | −7875.18 | −1.61971 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1391.70 | + | 2410.49i | −0.283268 | + | 0.490635i | ||||
\(290\) | 1716.42 | + | 2972.92i | 0.347556 | + | 0.601985i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 202.657 | + | 351.012i | 0.0406151 | + | 0.0703474i | ||||
\(293\) | −250.478 | − | 433.841i | −0.0499423 | − | 0.0865026i | 0.839974 | − | 0.542627i | \(-0.182570\pi\) |
−0.889916 | + | 0.456125i | \(0.849237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1699.20 | + | 2943.09i | 0.335359 | + | 0.580859i | ||||
\(296\) | −1378.66 | + | 2387.91i | −0.270720 | + | 0.468900i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4304.07 | −0.836671 | ||||||||
\(299\) | −686.281 | + | 3438.11i | −0.132738 | + | 0.664986i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5654.70 | − | 9794.24i | 1.08283 | − | 1.87552i | ||||
\(302\) | −3825.31 | + | 6625.62i | −0.728879 | + | 1.26246i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3209.14 | −0.605451 | ||||||||
\(305\) | 652.713 | + | 1130.53i | 0.122539 | + | 0.212243i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5975.57 | −1.11089 | −0.555446 | − | 0.831553i | \(-0.687452\pi\) | ||||
−0.555446 | + | 0.831553i | \(0.687452\pi\) | |||||||
\(308\) | −22.3137 | − | 38.6485i | −0.00412805 | − | 0.00715000i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1316.99 | + | 2281.09i | −0.241290 | + | 0.417927i | ||||
\(311\) | −44.4925 | −0.00811234 | −0.00405617 | − | 0.999992i | \(-0.501291\pi\) | ||||
−0.00405617 | + | 0.999992i | \(0.501291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9957.78 | 1.79823 | 0.899117 | − | 0.437709i | \(-0.144210\pi\) | ||||
0.899117 | + | 0.437709i | \(0.144210\pi\) | |||||||
\(314\) | 980.798 | − | 1698.79i | 0.176273 | − | 0.305313i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −122.798 | − | 212.692i | −0.0218605 | − | 0.0378636i | ||||
\(317\) | −7752.29 | −1.37354 | −0.686770 | − | 0.726875i | \(-0.740972\pi\) | ||||
−0.686770 | + | 0.726875i | \(0.740972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 70.6956 | + | 122.448i | 0.0124081 | + | 0.0214915i | ||||
\(320\) | −3589.56 | −0.627070 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2605.11 | + | 4512.18i | −0.450860 | + | 0.780913i | ||||
\(323\) | 3632.07 | − | 6290.92i | 0.625677 | − | 1.08370i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3718.37 | + | 1259.43i | −0.634640 | + | 0.214956i | ||||
\(326\) | 4912.23 | 0.834550 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3286.17 | + | 5691.81i | −0.553196 | + | 0.958163i | ||||
\(329\) | −4975.31 | − | 8617.49i | −0.833732 | − | 1.44407i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 669.427 | + | 1159.48i | 0.111163 | + | 0.192540i | 0.916240 | − | 0.400631i | \(-0.131209\pi\) |
−0.805076 | + | 0.593171i | \(0.797876\pi\) | |||||||
\(332\) | 613.979 | + | 1063.44i | 0.101495 | + | 0.175795i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −101.531 | − | 175.857i | −0.0166333 | − | 0.0288097i | ||||
\(335\) | 390.131 | − | 675.726i | 0.0636272 | − | 0.110206i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3788.95 | 0.612454 | 0.306227 | − | 0.951958i | \(-0.400933\pi\) | ||||
0.306227 | + | 0.951958i | \(0.400933\pi\) | |||||||
\(338\) | −670.368 | − | 5145.31i | −0.107879 | − | 0.828011i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 682.303 | − | 1181.78i | 0.108833 | − | 0.188504i | ||||
\(341\) | −54.2441 | + | 93.9536i | −0.00861432 | + | 0.0149204i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5423.53 | −0.853770 | ||||||||
\(344\) | −4719.21 | − | 8173.91i | −0.739659 | − | 1.28113i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6392.03 | 0.993173 | ||||||||
\(347\) | 3897.58 | + | 6750.80i | 0.602977 | + | 1.04439i | 0.992368 | + | 0.123314i | \(0.0393521\pi\) |
−0.389391 | + | 0.921072i | \(0.627315\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −67.2666 | + | 116.509i | −0.0103172 | + | 0.0178699i | −0.871138 | − | 0.491038i | \(-0.836617\pi\) |
0.860821 | + | 0.508908i | \(0.169951\pi\) | |||||||
\(350\) | −5834.29 | −0.891018 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −65.8332 | −0.00996853 | ||||||||
\(353\) | −1486.85 | + | 2575.31i | −0.224185 | + | 0.388300i | −0.956075 | − | 0.293124i | \(-0.905305\pi\) |
0.731890 | + | 0.681423i | \(0.238639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2123.50 | + | 3678.02i | 0.317476 | + | 0.549884i | ||||
\(356\) | 3396.56 | 0.505666 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5198.36 | + | 9003.82i | 0.767435 | + | 1.32924i | ||||
\(359\) | −8671.60 | −1.27485 | −0.637423 | − | 0.770514i | \(-0.719999\pi\) | ||||
−0.637423 | + | 0.770514i | \(0.719999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.42682 | − | 2.47133i | 0.000208022 | − | 0.000360304i | ||||
\(362\) | −1976.77 | + | 3423.86i | −0.287007 | + | 0.497111i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −655.440 | + | 3283.60i | −0.0943802 | + | 0.472823i | ||||
\(365\) | −1074.68 | −0.154113 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2257.16 | + | 3909.52i | −0.321043 | + | 0.556063i | −0.980704 | − | 0.195501i | \(-0.937367\pi\) |
0.659660 | + | 0.751564i | \(0.270700\pi\) | |||||||
\(368\) | 1449.46 | + | 2510.55i | 0.205322 | + | 0.355628i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −849.530 | − | 1471.43i | −0.119365 | − | 0.206746i | ||||
\(371\) | 2158.28 | + | 3738.24i | 0.302027 | + | 0.523126i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3285.30 | − | 5690.31i | −0.456049 | − | 0.789901i | 0.542699 | − | 0.839928i | \(-0.317403\pi\) |
−0.998748 | + | 0.0500270i | \(0.984069\pi\) | |||||||
\(374\) | −64.7190 | + | 112.097i | −0.00894797 | + | 0.0154983i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8304.42 | −1.13901 | ||||||||
\(377\) | 2076.61 | − | 10403.3i | 0.283689 | − | 1.42121i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2745.19 | − | 4754.81i | 0.372060 | − | 0.644427i | −0.617822 | − | 0.786318i | \(-0.711985\pi\) |
0.989882 | + | 0.141891i | \(0.0453181\pi\) | |||||||
\(380\) | −643.982 | + | 1115.41i | −0.0869357 | + | 0.150577i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −685.188 | −0.0917730 | ||||||||
\(383\) | 5093.63 | + | 8822.42i | 0.679562 | + | 1.17704i | 0.975113 | + | 0.221709i | \(0.0711635\pi\) |
−0.295551 | + | 0.955327i | \(0.595503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 118.328 | 0.0156638 | ||||||||
\(386\) | 1227.53 | + | 2126.14i | 0.161864 | + | 0.280356i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2304.47 | − | 3991.47i | 0.301526 | − | 0.522258i | ||||
\(389\) | −4883.97 | −0.636573 | −0.318287 | − | 0.947995i | \(-0.603107\pi\) | ||||
−0.318287 | + | 0.947995i | \(0.603107\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6561.94 | −0.848725 | ||||||||
\(392\) | −6484.52 | + | 11231.5i | −0.835504 | + | 1.44714i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1675.32 | − | 2901.74i | −0.214217 | − | 0.371035i | ||||
\(395\) | 651.192 | 0.0829494 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1057.52 | + | 1831.68i | 0.133691 | + | 0.231560i | 0.925097 | − | 0.379732i | \(-0.123984\pi\) |
−0.791406 | + | 0.611291i | \(0.790650\pi\) | |||||||
\(398\) | 5640.80 | 0.710422 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1623.08 | + | 2811.26i | −0.202885 | + | 0.351407i | ||||
\(401\) | −337.127 | + | 583.921i | −0.0419834 | + | 0.0727173i | −0.886254 | − | 0.463201i | \(-0.846701\pi\) |
0.844270 | + | 0.535918i | \(0.180034\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7709.61 | − | 2611.29i | 0.952960 | − | 0.322773i | ||||
\(404\) | 4439.89 | 0.546765 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7882.76 | − | 13653.3i | 0.963583 | − | 1.66897i | ||||
\(407\) | −34.9904 | − | 60.6051i | −0.00426145 | − | 0.00738105i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2336.67 | − | 4047.23i | −0.282496 | − | 0.489297i | 0.689503 | − | 0.724283i | \(-0.257829\pi\) |
−0.971999 | + | 0.234986i | \(0.924496\pi\) | |||||||
\(410\) | −2024.93 | − | 3507.29i | −0.243913 | − | 0.422470i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1752.35 | + | 3035.17i | 0.209544 | + | 0.362942i | ||||
\(413\) | 7803.67 | − | 13516.4i | 0.929767 | − | 1.61040i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3255.90 | −0.385122 | ||||||||
\(416\) | 3711.48 | + | 3259.29i | 0.437429 | + | 0.384134i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 61.0841 | − | 105.801i | 0.00714766 | − | 0.0123801i | ||||
\(419\) | −128.427 | + | 222.441i | −0.0149739 | + | 0.0259355i | −0.873415 | − | 0.486976i | \(-0.838100\pi\) |
0.858441 | + | 0.512912i | \(0.171433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8746.82 | −1.01257 | −0.506287 | − | 0.862365i | \(-0.668982\pi\) | ||||
−0.506287 | + | 0.862365i | \(0.668982\pi\) | |||||||
\(422\) | 5126.74 | + | 8879.77i | 0.591388 | + | 1.02431i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3602.43 | 0.412617 | ||||||||
\(425\) | −3673.96 | − | 6363.48i | −0.419325 | − | 0.726293i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2997.63 | − | 5192.05i | 0.339732 | − | 0.588433i | ||||
\(428\) | −894.439 | −0.101015 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5815.95 | 0.652255 | ||||||||
\(431\) | 4381.36 | − | 7588.74i | 0.489658 | − | 0.848113i | −0.510271 | − | 0.860014i | \(-0.670455\pi\) |
0.999929 | + | 0.0119008i | \(0.00378823\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3212.75 | − | 5564.64i | −0.356570 | − | 0.617597i | 0.630815 | − | 0.775933i | \(-0.282721\pi\) |
−0.987385 | + | 0.158336i | \(0.949387\pi\) | |||||||
\(434\) | 12096.7 | 1.33793 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −987.836 | − | 1710.98i | −0.108506 | − | 0.187939i | ||||
\(437\) | 6193.39 | 0.677963 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3410.14 | + | 5906.54i | −0.370745 | + | 0.642149i | −0.989680 | − | 0.143293i | \(-0.954231\pi\) |
0.618935 | + | 0.785442i | \(0.287564\pi\) | |||||||
\(440\) | 49.3763 | − | 85.5222i | 0.00534982 | − | 0.00926616i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9198.39 | − | 3115.55i | 0.989870 | − | 0.335275i | ||||
\(443\) | −5062.48 | −0.542948 | −0.271474 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271474 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4502.94 | + | 7799.32i | −0.479685 | + | 0.830839i | ||||
\(446\) | 5450.20 | + | 9440.03i | 0.578643 | + | 1.00224i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8242.65 | + | 14276.7i | 0.869261 | + | 1.50560i | ||||
\(449\) | −3295.41 | − | 5707.82i | −0.346370 | − | 0.599930i | 0.639232 | − | 0.769014i | \(-0.279252\pi\) |
−0.985602 | + | 0.169084i | \(0.945919\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −83.4029 | − | 144.458i | −0.00870796 | − | 0.0150826i | ||||
\(452\) | −2168.44 | + | 3755.85i | −0.225653 | + | 0.390842i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5109.52 | −0.528198 | ||||||||
\(455\) | −6671.01 | − | 5858.24i | −0.687344 | − | 0.603601i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1127.37 | − | 1952.67i | 0.115397 | − | 0.199873i | −0.802542 | − | 0.596596i | \(-0.796519\pi\) |
0.917938 | + | 0.396723i | \(0.129853\pi\) | |||||||
\(458\) | 2195.82 | − | 3803.28i | 0.224026 | − | 0.388025i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1163.46 | 0.117928 | ||||||||
\(461\) | 3679.40 | + | 6372.90i | 0.371728 | + | 0.643852i | 0.989831 | − | 0.142245i | \(-0.0454321\pi\) |
−0.618104 | + | 0.786097i | \(0.712099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11598.3 | 1.16419 | 0.582096 | − | 0.813120i | \(-0.302233\pi\) | ||||
0.582096 | + | 0.813120i | \(0.302233\pi\) | |||||||
\(464\) | −4385.91 | − | 7596.62i | −0.438816 | − | 0.760052i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3385.44 | + | 5863.75i | −0.336539 | + | 0.582903i | ||||
\(467\) | 302.150 | 0.0299397 | 0.0149698 | − | 0.999888i | \(-0.495235\pi\) | ||||
0.0149698 | + | 0.999888i | \(0.495235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3583.41 | −0.352807 | ||||||||
\(470\) | 2558.59 | − | 4431.61i | 0.251104 | − | 0.434925i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6512.66 | − | 11280.3i | −0.635105 | − | 1.10003i | ||||
\(473\) | 239.547 | 0.0232862 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3467.61 | + | 6006.08i | 0.334958 | + | 0.580164i | ||||
\(476\) | −6267.05 | −0.603466 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2236.06 | + | 3872.97i | −0.213965 | + | 0.370598i | ||||
\(479\) | −1573.07 | + | 2724.64i | −0.150053 | + | 0.259900i | −0.931247 | − | 0.364389i | \(-0.881278\pi\) |
0.781193 | + | 0.624289i | \(0.214611\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1027.80 | + | 5149.06i | −0.0974300 | + | 0.488101i | ||||
\(482\) | 4283.24 | 0.404764 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1611.42 | + | 2791.06i | −0.151335 | + | 0.262121i | ||||
\(485\) | 6110.25 | + | 10583.3i | 0.572067 | + | 0.990849i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1534.08 | − | 2657.10i | −0.142743 | − | 0.247238i | 0.785786 | − | 0.618499i | \(-0.212259\pi\) |
−0.928529 | + | 0.371261i | \(0.878926\pi\) | |||||||
\(488\) | −2501.71 | − | 4333.09i | −0.232064 | − | 0.401947i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3995.76 | − | 6920.85i | −0.368388 | − | 0.638066i | ||||
\(491\) | −50.2791 | + | 87.0859i | −0.00462131 | + | 0.00800435i | −0.868327 | − | 0.495992i | \(-0.834804\pi\) |
0.863706 | + | 0.503997i | \(0.168138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19855.7 | 1.81390 | ||||||||
\(494\) | −8681.77 | + | 2940.57i | −0.790711 | + | 0.267818i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3365.27 | − | 5828.82i | 0.304647 | − | 0.527665i | ||||
\(497\) | 9752.34 | − | 16891.6i | 0.880186 | − | 1.52453i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3616.55 | 0.324447 | 0.162223 | − | 0.986754i | \(-0.448133\pi\) | ||||
0.162223 | + | 0.986754i | \(0.448133\pi\) | |||||||
\(500\) | 1623.58 | + | 2812.13i | 0.145218 | + | 0.251524i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9830.40 | 0.874009 | ||||||||
\(503\) | −2686.32 | − | 4652.84i | −0.238125 | − | 0.412445i | 0.722051 | − | 0.691840i | \(-0.243200\pi\) |
−0.960176 | + | 0.279395i | \(0.909866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5886.13 | + | 10195.1i | −0.518672 | + | 0.898366i | ||||
\(506\) | −110.359 | −0.00969574 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 109.696 | 0.00958065 | ||||||||
\(509\) | −5657.37 | + | 9798.85i | −0.492649 | + | 0.853293i | −0.999964 | − | 0.00846746i | \(-0.997305\pi\) |
0.507315 | + | 0.861761i | \(0.330638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2467.77 | + | 4274.30i | 0.213636 | + | 0.370028i | ||||
\(512\) | 11716.1 | 1.01130 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7067.93 | − | 12242.0i | −0.606524 | − | 1.05053i | ||||
\(515\) | −9292.65 | −0.795113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 105.383 | − | 182.529i | 0.00896469 | − | 0.0155273i | ||||
\(518\) | −3901.52 | + | 6757.64i | −0.330933 | + | 0.573192i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7017.75 | + | 2376.95i | −0.591824 | + | 0.200454i | ||||
\(521\) | 18470.9 | 1.55321 | 0.776606 | − | 0.629986i | \(-0.216939\pi\) | ||||
0.776606 | + | 0.629986i | \(0.216939\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5445.51 | + | 9431.90i | −0.455288 | + | 0.788582i | −0.998705 | − | 0.0508814i | \(-0.983797\pi\) |
0.543417 | + | 0.839463i | \(0.317130\pi\) | |||||||
\(524\) | −1273.79 | − | 2206.28i | −0.106195 | − | 0.183935i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −678.556 | − | 1175.29i | −0.0562480 | − | 0.0974243i | ||||
\(527\) | 7617.53 | + | 13193.9i | 0.629649 | + | 1.09058i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3286.15 | + | 5691.78i | 0.270087 | + | 0.467805i | ||||
\(530\) | −1109.91 | + | 1922.42i | −0.0909648 | + | 0.157556i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5915.06 | 0.482050 | ||||||||
\(533\) | −2449.87 | + | 12273.3i | −0.199091 | + | 0.997400i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1185.79 | − | 2053.85i | 0.0958247 | − | 0.165973i | ||||
\(536\) | −1495.29 | + | 2589.92i | −0.120497 | + | 0.208708i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14993.9 | 1.20155 | ||||||||
\(539\) | −164.577 | − | 285.056i | −0.0131518 | − | 0.0227796i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13416.3 | −1.06620 | −0.533099 | − | 0.846053i | \(-0.678973\pi\) | ||||
−0.533099 | + | 0.846053i | \(0.678973\pi\) | |||||||
\(542\) | −3871.38 | − | 6705.42i | −0.306808 | − | 0.531407i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4622.50 | + | 8006.40i | −0.364316 | + | 0.631014i | ||||
\(545\) | 5238.45 | 0.411726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17849.0 | −1.39519 | −0.697593 | − | 0.716495i | \(-0.745745\pi\) | ||||
−0.697593 | + | 0.716495i | \(0.745745\pi\) | |||||||
\(548\) | 1868.56 | − | 3236.45i | 0.145659 | − | 0.252289i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −61.7887 | − | 107.021i | −0.00479033 | − | 0.00829709i | ||||
\(551\) | −18740.5 | −1.44895 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1495.32 | − | 2589.97i | −0.114987 | − | 0.199163i | ||||
\(554\) | −9334.09 | −0.715826 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 45.8553 | − | 79.4237i | 0.00349766 | − | 0.00605812i | ||||
\(557\) | −10065.7 | + | 17434.3i | −0.765703 | + | 1.32624i | 0.174172 | + | 0.984715i | \(0.444275\pi\) |
−0.939874 | + | 0.341521i | \(0.889058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13505.0 | − | 11859.6i | −1.02182 | − | 0.897328i | ||||
\(560\) | −7341.02 | −0.553955 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 485.801 | − | 841.433i | 0.0364632 | − | 0.0631561i | ||||
\(563\) | −11172.9 | − | 19352.0i | −0.836380 | − | 1.44865i | −0.892902 | − | 0.450251i | \(-0.851334\pi\) |
0.0565220 | − | 0.998401i | \(-0.481999\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5749.57 | − | 9958.55i | −0.428117 | − | 0.741521i | ||||
\(566\) | −6935.05 | − | 12011.9i | −0.515021 | − | 0.892043i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8138.94 | − | 14097.1i | −0.601237 | − | 1.04137i | ||||
\(569\) | −4227.86 | + | 7322.87i | −0.311496 | + | 0.539527i | −0.978686 | − | 0.205360i | \(-0.934163\pi\) |
0.667191 | + | 0.744887i | \(0.267497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12813.0 | 0.939069 | 0.469534 | − | 0.882914i | \(-0.344422\pi\) | ||||
0.469534 | + | 0.882914i | \(0.344422\pi\) | |||||||
\(572\) | −67.1741 | + | 22.7523i | −0.00491030 | + | 0.00166315i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9299.65 | + | 16107.5i | −0.676237 | + | 1.17128i | ||||
\(575\) | 3132.41 | − | 5425.50i | 0.227184 | − | 0.393494i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1971.59 | 0.142251 | 0.0711253 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711253 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(578\) | 3286.86 | + | 5693.01i | 0.236532 | + | 0.409685i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3520.50 | −0.252036 | ||||||||
\(581\) | 7476.47 | + | 12949.6i | 0.533866 | + | 0.924683i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.7149 | + | 79.1805i | −0.00324754 | + | 0.00562491i | ||||
\(584\) | 4119.02 | 0.291860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1183.14 | −0.0834046 | ||||||||
\(587\) | 4292.85 | − | 7435.43i | 0.301848 | − | 0.522816i | −0.674707 | − | 0.738086i | \(-0.735730\pi\) |
0.976555 | + | 0.215270i | \(0.0690632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7189.70 | − | 12452.9i | −0.502965 | − | 0.871161i | ||||
\(590\) | 8026.19 | 0.560056 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2170.78 | + | 3759.90i | 0.150707 | + | 0.261032i | ||||
\(593\) | 1746.73 | 0.120961 | 0.0604803 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604803 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8308.46 | − | 14390.7i | 0.572460 | − | 0.991530i | ||||
\(596\) | 2206.99 | − | 3822.63i | 0.151681 | − | 0.262720i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6221.70 | + | 5463.68i | 0.425459 | + | 0.373623i | ||||
\(599\) | −27531.1 | −1.87794 | −0.938972 | − | 0.343994i | \(-0.888220\pi\) | ||||
−0.938972 | + | 0.343994i | \(0.888220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8769.54 | − | 15189.3i | 0.595203 | − | 1.03092i | −0.398315 | − | 0.917249i | \(-0.630405\pi\) |
0.993518 | − | 0.113673i | \(-0.0362616\pi\) | |||||||
\(602\) | −13355.1 | − | 23131.7i | −0.904173 | − | 1.56607i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3923.00 | − | 6794.83i | −0.264279 | − | 0.457744i | ||||
\(605\) | −4272.64 | − | 7400.43i | −0.287120 | − | 0.497306i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11345.5 | + | 19651.1i | 0.758651 | + | 1.31402i | 0.943539 | + | 0.331263i | \(0.107475\pi\) |
−0.184887 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(608\) | 4362.88 | − | 7556.72i | 0.291016 | − | 0.504055i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3083.11 | 0.204642 | ||||||||
\(611\) | −14977.9 | + | 5073.10i | −0.991719 | + | 0.335901i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3607.65 | + | 6248.63i | −0.237702 | + | 0.411713i | −0.960055 | − | 0.279813i | \(-0.909728\pi\) |
0.722352 | + | 0.691525i | \(0.243061\pi\) | |||||||
\(614\) | −7056.44 | + | 12222.1i | −0.463802 | + | 0.803329i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −453.528 | −0.0296642 | ||||||||
\(617\) | −8435.22 | − | 14610.2i | −0.550387 | − | 0.953299i | −0.998246 | − | 0.0591947i | \(-0.981147\pi\) |
0.447859 | − | 0.894104i | \(-0.352187\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2244.53 | 0.145743 | 0.0728717 | − | 0.997341i | \(-0.476784\pi\) | ||||
0.0728717 | + | 0.997341i | \(0.476784\pi\) | |||||||
\(620\) | −1350.62 | − | 2339.35i | −0.0874876 | − | 0.151533i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −52.5403 | + | 91.0025i | −0.00338694 | + | 0.00586635i | ||||
\(623\) | 41360.1 | 2.65981 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1859.84 | 0.119030 | ||||||||
\(626\) | 11759.0 | − | 20367.1i | 0.750771 | − | 1.30037i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1005.85 | + | 1742.18i | 0.0639134 | + | 0.110701i | ||||
\(629\) | −9827.44 | −0.622966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1834.61 | + | 3177.63i | 0.115744 | + | 0.200475i | 0.918077 | − | 0.396402i | \(-0.129741\pi\) |
−0.802333 | + | 0.596877i | \(0.796408\pi\) | |||||||
\(632\) | −2495.88 | −0.157090 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9154.54 | + | 15856.1i | −0.573459 | + | 0.993260i | ||||
\(635\) | −145.428 | + | 251.889i | −0.00908840 | + | 0.0157416i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4834.27 | + | 24218.6i | −0.300692 | + | 1.50640i | ||||
\(638\) | 333.933 | 0.0207218 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1531.78 | + | 2653.12i | −0.0946077 | + | 0.163865i | ||||
\(641\) | 7339.30 | + | 12712.0i | 0.452239 | + | 0.783300i | 0.998525 | − | 0.0542983i | \(-0.0172922\pi\) |
−0.546286 | + | 0.837599i | \(0.683959\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2759.86 | − | 4780.22i | −0.169266 | − | 0.293178i | 0.768896 | − | 0.639374i | \(-0.220807\pi\) |
−0.938162 | + | 0.346196i | \(0.887473\pi\) | |||||||
\(644\) | −2671.64 | − | 4627.41i | −0.163474 | − | 0.283145i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8578.08 | − | 14857.7i | −0.522446 | − | 0.904902i | ||||
\(647\) | −5663.43 | + | 9809.35i | −0.344131 | + | 0.596052i | −0.985195 | − | 0.171435i | \(-0.945160\pi\) |
0.641065 | + | 0.767487i | \(0.278493\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 330.582 | 0.0199946 | ||||||||
\(650\) | −1814.97 | + | 9092.59i | −0.109522 | + | 0.548678i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2518.84 | + | 4362.76i | −0.151297 | + | 0.262054i | ||||
\(653\) | 1951.44 | − | 3380.00i | 0.116946 | − | 0.202557i | −0.801610 | − | 0.597848i | \(-0.796023\pi\) |
0.918556 | + | 0.395291i | \(0.129356\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6754.87 | 0.402954 | ||||||||
\(656\) | 5174.26 | + | 8962.09i | 0.307959 | + | 0.533400i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23501.0 | −1.39235 | ||||||||
\(659\) | 4011.23 | + | 6947.66i | 0.237110 | + | 0.410687i | 0.959884 | − | 0.280398i | \(-0.0904665\pi\) |
−0.722774 | + | 0.691085i | \(0.757133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2584.38 | − | 4476.27i | 0.152074 | − | 0.263399i | −0.779916 | − | 0.625884i | \(-0.784738\pi\) |
0.931990 | + | 0.362485i | \(0.118072\pi\) | |||||||
\(662\) | 3162.05 | 0.185645 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12479.2 | 0.729346 | ||||||||
\(665\) | −7841.82 | + | 13582.4i | −0.457282 | + | 0.792036i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8464.45 | + | 14660.9i | 0.491372 | + | 0.851081i | ||||
\(668\) | 208.248 | 0.0120619 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −921.396 | − | 1595.91i | −0.0531293 | − | 0.0920227i | ||||
\(671\) | 126.987 | 0.00730593 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3327.05 | − | 5762.62i | 0.190562 | − | 0.330063i | −0.754875 | − | 0.655869i | \(-0.772302\pi\) |
0.945437 | + | 0.325806i | \(0.105636\pi\) | |||||||
\(674\) | 4474.30 | − | 7749.71i | 0.255702 | − | 0.442890i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4913.51 | + | 2042.97i | 0.279558 | + | 0.116236i | ||||
\(677\) | 20649.4 | 1.17226 | 0.586130 | − | 0.810217i | \(-0.300651\pi\) | ||||
0.586130 | + | 0.810217i | \(0.300651\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28061.8 | − | 48604.4i | 1.58603 | − | 2.74708i | ||||
\(680\) | −6933.93 | − | 12009.9i | −0.391036 | − | 0.677294i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 128.112 | + | 221.896i | 0.00719304 | + | 0.0124587i | ||||
\(683\) | 14237.8 | + | 24660.6i | 0.797649 | + | 1.38157i | 0.921144 | + | 0.389223i | \(0.127256\pi\) |
−0.123495 | + | 0.992345i | \(0.539410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4954.45 | + | 8581.36i | 0.276350 | + | 0.478652i | ||||
\(686\) | −6404.54 | + | 11093.0i | −0.356453 | + | 0.617394i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −14861.3 | −0.823522 | ||||||||
\(689\) | 6497.37 | − | 2200.70i | 0.359260 | − | 0.121683i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5305.41 | + | 9189.24i | −0.292080 | + | 0.505897i | −0.974301 | − | 0.225248i | \(-0.927681\pi\) |
0.682221 | + | 0.731146i | \(0.261014\pi\) | |||||||
\(692\) | −3277.64 | + | 5677.03i | −0.180053 | + | 0.311862i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18410.3 | 1.00698 | ||||||||
\(695\) | 121.584 | + | 210.590i | 0.00663590 | + | 0.0114937i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23424.6 | −1.27299 | ||||||||
\(698\) | 158.868 | + | 275.167i | 0.00861495 | + | 0.0149215i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2991.65 | − | 5181.68i | 0.161534 | − | 0.279785i | ||||
\(701\) | 13518.9 | 0.728390 | 0.364195 | − | 0.931323i | \(-0.381344\pi\) | ||||
0.364195 | + | 0.931323i | \(0.381344\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9275.49 | 0.497627 | ||||||||
\(704\) | −174.589 | + | 302.398i | −0.00934671 | + | 0.0161890i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3511.60 | + | 6082.26i | 0.187196 | + | 0.324234i | ||||
\(707\) | 54064.9 | 2.87599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7422.69 | − | 12856.5i | −0.393180 | − | 0.681008i | 0.599687 | − | 0.800235i | \(-0.295292\pi\) |
−0.992867 | + | 0.119226i | \(0.961959\pi\) | |||||||
\(710\) | 10030.4 | 0.530190 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17258.8 | − | 29893.2i | 0.908430 | − | 1.57345i | ||||
\(713\) | −6494.70 | + | 11249.1i | −0.341134 | + | 0.590861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.8104 | − | 184.412i | 0.00192536 | − | 0.00964561i | ||||
\(716\) | −10662.2 | −0.556517 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10240.1 | + | 17736.4i | −0.532254 | + | 0.921891i | ||||
\(719\) | −17950.1 | − | 31090.4i | −0.931049 | − | 1.61262i | −0.781531 | − | 0.623866i | \(-0.785561\pi\) |
−0.149518 | − | 0.988759i | \(-0.547772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21338.6 | + | 36959.5i | 1.10221 | + | 1.90908i | ||||
\(722\) | −3.36981 | − | 5.83669i | −0.000173700 | − | 0.000300857i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2027.25 | − | 3511.30i | −0.104064 | − | 0.180244i | ||||
\(725\) | −9478.32 | + | 16416.9i | −0.485539 | + | 0.840978i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12951.4 | 0.660715 | 0.330357 | − | 0.943856i | \(-0.392831\pi\) | ||||
0.330357 | + | 0.943856i | \(0.392831\pi\) | |||||||
\(728\) | 25568.6 | + | 22453.4i | 1.30170 | + | 1.14310i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1269.07 | + | 2198.09i | −0.0643429 | + | 0.111445i | ||||
\(731\) | 16819.9 | − | 29132.8i | 0.851032 | − | 1.47403i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1105.36 | −0.0556989 | −0.0278494 | − | 0.999612i | \(-0.508866\pi\) | ||||
−0.0278494 | + | 0.999612i | \(0.508866\pi\) | |||||||
\(734\) | 5330.88 | + | 9233.35i | 0.268074 | + | 0.464318i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7882.27 | −0.394761 | ||||||||
\(737\) | −37.9504 | − | 65.7321i | −0.00189677 | − | 0.00328531i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6819.03 | + | 11810.9i | −0.339434 | + | 0.587917i | −0.984326 | − | 0.176356i | \(-0.943569\pi\) |
0.644892 | + | 0.764274i | \(0.276902\pi\) | |||||||
\(740\) | 1742.45 | 0.0865591 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10194.7 | 0.504391 | ||||||||
\(743\) | 5077.44 | − | 8794.38i | 0.250704 | − | 0.434232i | −0.713016 | − | 0.701148i | \(-0.752671\pi\) |
0.963720 | + | 0.266916i | \(0.0860045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5851.79 | + | 10135.6i | 0.287776 | + | 0.498442i | ||||
\(746\) | −15518.2 | −0.761611 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −66.3718 | − | 114.959i | −0.00324438 | − | 0.00561943i | ||||
\(749\) | −10891.7 | −0.531338 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13289.7 | + | 23018.5i | −0.645738 | + | 1.11845i | 0.338393 | + | 0.941005i | \(0.390117\pi\) |
−0.984131 | + | 0.177446i | \(0.943217\pi\) | |||||||
\(752\) | −6537.90 | + | 11324.0i | −0.317038 | + | 0.549126i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18826.1 | − | 16532.4i | −0.909294 | − | 0.798510i | ||||
\(755\) | 20803.5 | 1.00280 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6838.86 | − | 11845.3i | 0.328352 | − | 0.568723i | −0.653833 | − | 0.756639i | \(-0.726840\pi\) |
0.982185 | + | 0.187916i | \(0.0601734\pi\) | |||||||
\(758\) | −6483.48 | − | 11229.7i | −0.310674 | − | 0.538103i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6544.49 | + | 11335.4i | 0.312360 | + | 0.541024i | ||||
\(761\) | 8998.36 | + | 15585.6i | 0.428634 | + | 0.742415i | 0.996752 | − | 0.0805314i | \(-0.0256617\pi\) |
−0.568118 | + | 0.822947i | \(0.692328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12029.0 | − | 20834.8i | −0.570744 | − | 0.988558i | ||||
\(764\) | 351.343 | − | 608.544i | 0.0166376 | − | 0.0288172i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24059.9 | 1.13488 | ||||||||
\(767\) | −18637.3 | − | 16366.6i | −0.877383 | − | 0.770487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1497.52 | + | 2593.78i | −0.0702236 | + | 0.121631i | −0.898999 | − | 0.437950i | \(-0.855705\pi\) |
0.828776 | + | 0.559581i | \(0.189038\pi\) | |||||||
\(770\) | 139.732 | − | 242.023i | 0.00653972 | − | 0.0113271i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2517.75 | −0.117378 | ||||||||
\(773\) | −13027.7 | − | 22564.7i | −0.606177 | − | 1.04993i | −0.991864 | − | 0.127299i | \(-0.959369\pi\) |
0.385688 | − | 0.922629i | \(-0.373964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14545.3 | −0.674169 | ||||||||
\(776\) | −23419.3 | − | 40563.5i | −1.08338 | − | 1.87647i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5767.39 | + | 9989.41i | −0.265772 | + | 0.460331i | ||||
\(779\) | 22109.0 | 1.01686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 413.133 | 0.0189284 | ||||||||
\(782\) | −7748.87 | + | 13421.4i | −0.354346 | + | 0.613746i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10210.3 | + | 17684.7i | 0.465117 | + | 0.805607i | ||||
\(785\) | −5333.95 | −0.242518 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11496.0 | + | 19911.7i | 0.520697 | + | 0.901874i | 0.999710 | + | 0.0240662i | \(0.00766123\pi\) |
−0.479013 | + | 0.877808i | \(0.659005\pi\) | |||||||
\(788\) | 3436.21 | 0.155343 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 768.980 | − | 1331.91i | 0.0346318 | − | 0.0599840i | ||||
\(791\) | −26405.3 | + | 45735.4i | −1.18693 | + | 2.05583i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7159.15 | − | 6286.91i | −0.320591 | − | 0.281532i | ||||
\(794\) | 4995.22 | 0.223267 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2892.43 | + | 5009.84i | −0.128793 | + | 0.223077i | ||||
\(797\) | −12913.1 | − | 22366.2i | −0.573910 | − | 0.994042i | −0.996159 | − | 0.0875619i | \(-0.972092\pi\) |
0.422249 | − | 0.906480i | \(-0.361241\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14799.0 | − | 25632.6i | −0.655258 | − | 1.13494i | ||||
\(800\) | −4413.20 | − | 7643.89i | −0.195038 | − | 0.337815i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 796.214 | + | 1379.08i | 0.0350565 | + | 0.0607196i | ||||
\(803\) | −52.2704 | + | 90.5349i | −0.00229711 | + | 0.00397872i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14167.6 | 0.620299 | ||||||||
\(806\) | 3763.14 | − | 18852.4i | 0.164455 | − | 0.823882i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22560.3 | − | 39075.6i | 0.982263 | − | 1.70133i | ||||
\(809\) | −14247.9 | + | 24678.1i | −0.619195 | + | 1.07248i | 0.370438 | + | 0.928857i | \(0.379208\pi\) |
−0.989633 | + | 0.143620i | \(0.954126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6992.41 | 0.302758 | 0.151379 | − | 0.988476i | \(-0.451629\pi\) | ||||
0.151379 | + | 0.988476i | \(0.451629\pi\) | |||||||
\(812\) | 8084.07 | + | 14002.0i | 0.349378 | + | 0.605141i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −165.278 | −0.00711670 | ||||||||
\(815\) | −6678.64 | − | 11567.8i | −0.287046 | − | 0.497179i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15875.2 | + | 27496.6i | −0.679807 | + | 1.17746i | ||||
\(818\) | −11037.3 | −0.471773 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4153.29 | 0.176877 | ||||||||
\(821\) | 15756.3 | − | 27290.8i | 0.669793 | − | 1.16012i | −0.308168 | − | 0.951332i | \(-0.599716\pi\) |
0.977962 | − | 0.208784i | \(-0.0669507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19579.8 | − | 33913.2i | −0.829293 | − | 1.43638i | −0.898593 | − | 0.438782i | \(-0.855410\pi\) |
0.0693001 | − | 0.997596i | \(-0.477923\pi\) | |||||||
\(824\) | 35616.8 | 1.50579 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18430.4 | − | 31922.4i | −0.776364 | − | 1.34470i | ||||
\(827\) | 36557.6 | 1.53716 | 0.768581 | − | 0.639752i | \(-0.220963\pi\) | ||||
0.768581 | + | 0.639752i | \(0.220963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7337.59 | + | 12709.1i | −0.307413 | + | 0.532454i | −0.977796 | − | 0.209561i | \(-0.932797\pi\) |
0.670383 | + | 0.742015i | \(0.266130\pi\) | |||||||
\(830\) | −3844.83 | + | 6659.44i | −0.160790 | + | 0.278497i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 24814.0 | − | 8404.66i | 1.03398 | − | 0.350215i | ||||
\(833\) | −46223.3 | −1.92262 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −276.082 | + | 478.188i | −0.0114422 | + | 0.0198184i | ||||
\(836\) | 62.6441 | + | 108.503i | 0.00259162 | + | 0.00448881i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 303.313 | + | 525.354i | 0.0125033 | + | 0.0216564i | ||||
\(839\) | −4257.78 | − | 7374.69i | −0.175202 | − | 0.303459i | 0.765029 | − | 0.643996i | \(-0.222725\pi\) |
−0.940231 | + | 0.340536i | \(0.889391\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13417.9 | − | 23240.6i | −0.550164 | − | 0.952912i | ||||
\(842\) | −10329.0 | + | 17890.3i | −0.422755 | + | 0.732232i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10515.3 | −0.428854 | ||||||||
\(845\) | −11205.2 | + | 8574.17i | −0.456177 | + | 0.349066i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19622.4 | + | 33987.0i | −0.796025 | + | 1.37876i | ||||
\(848\) | 2836.12 | − | 4912.31i | 0.114850 | − | 0.198926i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17354.0 | −0.700281 | ||||||||
\(851\) | −4189.43 | − | 7256.31i | −0.168757 | − | 0.292295i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9645.93 | 0.387187 | 0.193593 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193593 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(854\) | −7079.69 | − | 12262.4i | −0.283679 | − | 0.491347i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4544.89 | + | 7871.97i | −0.181473 | + | 0.314321i | ||||
\(857\) | −36139.6 | −1.44050 | −0.720248 | − | 0.693717i | \(-0.755972\pi\) | ||||
−0.720248 | + | 0.693717i | \(0.755972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7108.04 | −0.282332 | −0.141166 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141166 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(860\) | −2982.24 | + | 5165.39i | −0.118248 | + | 0.204812i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10347.7 | − | 17922.8i | −0.408869 | − | 0.708182i | ||||
\(863\) | −16225.8 | −0.640016 | −0.320008 | − | 0.947415i | \(-0.603686\pi\) | ||||
−0.320008 | + | 0.947415i | \(0.603686\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8690.57 | − | 15052.5i | −0.341605 | − | 0.591677i | ||||
\(866\) | −15175.5 | −0.595478 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6202.83 | + | 10743.6i | −0.242555 | + | 0.420118i | ||||
\(869\) | 31.6727 | − | 54.8588i | 0.00123639 | − | 0.00214149i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1114.75 | + | 5584.64i | −0.0433661 | + | 0.217254i | ||||
\(872\) | −20077.9 | −0.779727 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7313.66 | − | 12667.6i | 0.283053 | − | 0.490262i | ||||
\(875\) | 19770.5 | + | 34243.5i | 0.763846 | + | 1.32302i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15491.5 | + | 26832.0i | 0.596477 | + | 1.03313i | 0.993337 | + | 0.115249i | \(0.0367667\pi\) |
−0.396860 | + | 0.917879i | \(0.629900\pi\) | |||||||
\(878\) | 8053.94 | + | 13949.8i | 0.309576 | + | 0.536201i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −77.7458 | − | 134.660i | −0.00297819 | − | 0.00515838i | ||||
\(881\) | −3835.38 | + | 6643.07i | −0.146671 | + | 0.254042i | −0.929995 | − | 0.367572i | \(-0.880189\pi\) |
0.783324 | + | 0.621614i | \(0.213523\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34340.6 | −1.30878 | −0.654390 | − | 0.756157i | \(-0.727075\pi\) | ||||
−0.654390 | + | 0.756157i | \(0.727075\pi\) | |||||||
\(884\) | −1949.60 | + | 9767.03i | −0.0741766 | + | 0.371607i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5978.19 | + | 10354.5i | −0.226683 | + | 0.392627i | ||||
\(887\) | −9604.17 | + | 16634.9i | −0.363559 | + | 0.629702i | −0.988544 | − | 0.150935i | \(-0.951772\pi\) |
0.624985 | + | 0.780637i | \(0.285105\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1335.78 | 0.0503943 | ||||||||
\(890\) | 10634.9 | + | 18420.1i | 0.400541 | + | 0.693758i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11178.8 | −0.419611 | ||||||||
\(893\) | 13967.8 | + | 24193.0i | 0.523422 | + | 0.906593i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14135.3 | − | 24483.1i | 0.527924 | − | 0.914390i | ||||
\(896\) | 14069.6 | 0.524591 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15566.0 | −0.578444 | ||||||||
\(899\) | 19652.2 | − | 34038.6i | 0.729074 | − | 1.26279i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6419.77 | + | 11119.4i | 0.237373 | + | 0.411143i | ||||
\(902\) | −393.956 | −0.0145425 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22036.9 | + | 38169.0i | 0.810770 | + | 1.40430i | ||||
\(905\) | 10750.4 | 0.394868 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23240.5 | − | 40253.7i | 0.850813 | − | 1.47365i | −0.0296621 | − | 0.999560i | \(-0.509443\pi\) |
0.880475 | − | 0.474092i | \(-0.157224\pi\) | |||||||
\(908\) | 2620.00 | − | 4537.98i | 0.0957576 | − | 0.165857i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19859.8 | + | 6726.63i | −0.723457 | + | 0.245039i | ||||
\(911\) | 34109.3 | 1.24050 | 0.620248 | − | 0.784406i | \(-0.287032\pi\) | ||||
0.620248 | + | 0.784406i | \(0.287032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −158.361 | + | 274.289i | −0.00574039 | + | 0.00994264i | ||||
\(914\) | −2662.59 | − | 4611.74i | −0.0963573 | − | 0.166896i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2251.90 | + | 3900.41i | 0.0812280 | + | 0.140691i | ||||
\(917\) | −15511.1 | − | 26866.0i | −0.558584 | − | 0.967497i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18766.8 | + | 32505.1i | 0.673623 | + | 1.16675i | 0.976869 | + | 0.213837i | \(0.0685962\pi\) |
−0.303246 | + | 0.952912i | \(0.598070\pi\) | |||||||
\(920\) | 5911.86 | − | 10239.6i | 0.211857 | − | 0.366947i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17379.7 | 0.620793 | ||||||||
\(923\) | −23291.2 | − | 20453.5i | −0.830596 | − | 0.729399i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4691.24 | − | 8125.46i | 0.166753 | − | 0.288825i | ||||
\(926\) | 13696.3 | − | 23722.6i | 0.486055 | − | 0.841872i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23850.8 | 0.843687 | ||||||||
\(929\) | 2483.37 | + | 4301.33i | 0.0877038 | + | 0.151907i | 0.906540 | − | 0.422120i | \(-0.138714\pi\) |
−0.818836 | + | 0.574027i | \(0.805380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 43627.2 | 1.53579 | ||||||||
\(932\) | −3471.89 | − | 6013.50i | −0.122023 | − | 0.211351i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 356.803 | − | 618.001i | 0.0124999 | − | 0.0216505i | ||||
\(935\) | 351.966 | 0.0123107 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5096.90 | −0.177704 | −0.0888519 | − | 0.996045i | \(-0.528320\pi\) | ||||
−0.0888519 | + | 0.996045i | \(0.528320\pi\) | |||||||
\(938\) | −4231.58 | + | 7329.31i | −0.147298 | + | 0.255128i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2623.93 | + | 4544.78i | 0.0910459 | + | 0.157696i | ||||
\(941\) | −54774.8 | −1.89756 | −0.948781 | − | 0.315933i | \(-0.897682\pi\) | ||||
−0.948781 | + | 0.315933i | \(0.897682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9985.91 | − | 17296.1i | −0.344842 | − | 0.597284i | ||||
\(944\) | −20509.1 | −0.707113 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 282.877 | − | 489.957i | 0.00972210 | − | 0.0168392i | ||||
\(947\) | −6884.24 | + | 11923.9i | −0.236228 | + | 0.409159i | −0.959629 | − | 0.281269i | \(-0.909245\pi\) |
0.723401 | + | 0.690428i | \(0.242578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7429.08 | − | 2516.28i | 0.254118 | − | 0.0860714i | ||||
\(950\) | 16379.4 | 0.559386 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −31844.6 | + | 55156.4i | −1.08413 | + | 1.87776i | ||||
\(953\) | 17933.3 | + | 31061.4i | 0.609566 | + | 1.05580i | 0.991312 | + | 0.131532i | \(0.0419897\pi\) |
−0.381746 | + | 0.924267i | \(0.624677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 931.578 | + | 1613.54i | 0.0315656 | + | 0.0546732i | ||||
\(956\) | −2293.17 | − | 3971.88i | −0.0775798 | − | 0.134372i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3715.23 | + | 6434.96i | 0.125296 | + | 0.217019i | ||||
\(959\) | 22753.7 | − | 39410.5i | 0.766167 | − | 1.32704i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 366.899 | 0.0123158 | ||||||||
\(962\) | 9317.89 | + | 8182.64i | 0.312288 | + | 0.274240i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2196.31 | + | 3804.12i | −0.0733801 | + | 0.127098i | ||||
\(965\) | 3337.87 | − | 5781.37i | 0.111347 | − | 0.192859i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24476.5 | −0.813972 | −0.406986 | − | 0.913434i | \(-0.633420\pi\) | ||||
−0.406986 | + | 0.913434i | \(0.633420\pi\) | |||||||
\(968\) | 16376.1 | + | 28364.3i | 0.543749 | + | 0.941800i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 28861.9 | 0.955362 | ||||||||
\(971\) | −4488.03 | − | 7773.50i | −0.148329 | − | 0.256914i | 0.782281 | − | 0.622926i | \(-0.214056\pi\) |
−0.930610 | + | 0.366012i | \(0.880723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 558.383 | − | 967.149i | 0.0183977 | − | 0.0318657i | ||||
\(974\) | −7246.26 | −0.238383 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7878.18 | −0.258376 | ||||||||
\(977\) | −21001.4 | + | 36375.5i | −0.687711 | + | 1.19115i | 0.284865 | + | 0.958568i | \(0.408051\pi\) |
−0.972576 | + | 0.232583i | \(0.925282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 438.029 | + | 758.688i | 0.0142998 | + | 0.0247679i | ||||
\(980\) | 8195.60 | 0.267142 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 118.747 | + | 205.676i | 0.00385884 | + | 0.00668370i | ||||
\(983\) | −43240.7 | −1.40301 | −0.701507 | − | 0.712662i | \(-0.747489\pi\) | ||||
−0.701507 | + | 0.712662i | \(0.747489\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4555.51 | + | 7890.38i | −0.147361 | + | 0.255237i | ||||
\(986\) | 23447.2 | − | 40611.7i | 0.757312 | − | 1.31170i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1840.10 | − | 9218.47i | 0.0592524 | − | 0.296841i | ||||
\(989\) | 28681.2 | 0.922152 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18958.3 | + | 32836.7i | −0.607698 | + | 1.05256i | 0.383921 | + | 0.923366i | \(0.374574\pi\) |
−0.991619 | + | 0.129198i | \(0.958760\pi\) | |||||||
\(992\) | 9150.26 | + | 15848.7i | 0.292864 | + | 0.507255i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23032.7 | − | 39893.8i | −0.734963 | − | 1.27299i | ||||
\(995\) | −7669.20 | − | 13283.5i | −0.244352 | − | 0.423230i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3317.43 | − | 5745.96i | −0.105380 | − | 0.182524i | 0.808513 | − | 0.588478i | \(-0.200273\pi\) |
−0.913893 | + | 0.405954i | \(0.866939\pi\) | |||||||
\(998\) | 4270.71 | − | 7397.09i | 0.135458 | − | 0.234620i | ||||
\(999\) | 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 | 117.4.g.e.100.3 | 8 | ||
3.2 | odd | 2 | 39.4.e.c.22.2 | yes | 8 | ||
12.11 | even | 2 | 624.4.q.i.529.3 | 8 | |||
13.3 | even | 3 | inner | 117.4.g.e.55.3 | 8 | ||
13.4 | even | 6 | 1521.4.a.bb.1.3 | 4 | |||
13.9 | even | 3 | 1521.4.a.v.1.2 | 4 | |||
39.17 | odd | 6 | 507.4.a.i.1.2 | 4 | |||
39.20 | even | 12 | 507.4.b.h.337.6 | 8 | |||
39.29 | odd | 6 | 39.4.e.c.16.2 | ✓ | 8 | ||
39.32 | even | 12 | 507.4.b.h.337.3 | 8 | |||
39.35 | odd | 6 | 507.4.a.m.1.3 | 4 | |||
156.107 | even | 6 | 624.4.q.i.289.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.2 | ✓ | 8 | 39.29 | odd | 6 | ||
39.4.e.c.22.2 | yes | 8 | 3.2 | odd | 2 | ||
117.4.g.e.55.3 | 8 | 13.3 | even | 3 | inner | ||
117.4.g.e.100.3 | 8 | 1.1 | even | 1 | trivial | ||
507.4.a.i.1.2 | 4 | 39.17 | odd | 6 | |||
507.4.a.m.1.3 | 4 | 39.35 | odd | 6 | |||
507.4.b.h.337.3 | 8 | 39.32 | even | 12 | |||
507.4.b.h.337.6 | 8 | 39.20 | even | 12 | |||
624.4.q.i.289.3 | 8 | 156.107 | even | 6 | |||
624.4.q.i.529.3 | 8 | 12.11 | even | 2 | |||
1521.4.a.v.1.2 | 4 | 13.9 | even | 3 | |||
1521.4.a.bb.1.3 | 4 | 13.4 | even | 6 |