Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(101,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.l (of order \(4\), 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(0.719139 - 1.21772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.101 |
Dual form | 400.2.l.f.301.3 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.719139 | + | 1.21772i | −0.508508 | + | 0.861057i | ||||
\(3\) | 1.66783 | − | 1.66783i | 0.962922 | − | 0.962922i | −0.0364144 | − | 0.999337i | \(-0.511594\pi\) |
0.999337 | + | 0.0364144i | \(0.0115936\pi\) | |||||||
\(4\) | −0.965679 | − | 1.75142i | −0.482839 | − | 0.875709i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.831547 | + | 3.23035i | 0.339478 | + | 1.31879i | ||||
\(7\) | − | 1.87372i | − | 0.708198i | −0.935208 | − | 0.354099i | \(-0.884788\pi\) | ||
0.935208 | − | 0.354099i | \(-0.115212\pi\) | |||||||
\(8\) | 2.82719 | + | 0.0835873i | 0.999563 | + | 0.0295526i | ||||
\(9\) | − | 2.56332i | − | 0.854439i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.29695 | − | 3.29695i | −0.994068 | − | 0.994068i | 0.00591443 | − | 0.999983i | \(-0.498117\pi\) |
−0.999983 | + | 0.00591443i | \(0.998117\pi\) | |||||||
\(12\) | −4.53166 | − | 1.31048i | −1.30818 | − | 0.378303i | ||||
\(13\) | 1.90022 | − | 1.90022i | 0.527027 | − | 0.527027i | −0.392658 | − | 0.919685i | \(-0.628444\pi\) |
0.919685 | + | 0.392658i | \(0.128444\pi\) | |||||||
\(14\) | 2.28166 | + | 1.34746i | 0.609799 | + | 0.360124i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.13493 | + | 3.38261i | −0.533732 | + | 0.845653i | ||||
\(17\) | 2.57148 | 0.623675 | 0.311838 | − | 0.950135i | \(-0.399056\pi\) | ||||
0.311838 | + | 0.950135i | \(0.399056\pi\) | |||||||
\(18\) | 3.12140 | + | 1.84338i | 0.735721 | + | 0.434489i | ||||
\(19\) | −5.76636 | + | 5.76636i | −1.32289 | + | 1.32289i | −0.411472 | + | 0.911422i | \(0.634985\pi\) |
−0.911422 | + | 0.411472i | \(0.865015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.12504 | − | 3.12504i | −0.681940 | − | 0.681940i | ||||
\(22\) | 6.38572 | − | 1.64379i | 1.36144 | − | 0.350458i | ||||
\(23\) | − | 7.58574i | − | 1.58174i | −0.611987 | − | 0.790868i | \(-0.709629\pi\) | ||
0.611987 | − | 0.790868i | \(-0.290371\pi\) | |||||||
\(24\) | 4.85469 | − | 4.57587i | 0.990959 | − | 0.934045i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.947414 | + | 3.68046i | 0.185803 | + | 0.721798i | ||||
\(27\) | 0.728312 | + | 0.728312i | 0.140164 | + | 0.140164i | ||||
\(28\) | −3.28166 | + | 1.80941i | −0.620175 | + | 0.341946i | ||||
\(29\) | 6.45786 | − | 6.45786i | 1.19919 | − | 1.19919i | 0.224787 | − | 0.974408i | \(-0.427831\pi\) |
0.974408 | − | 0.224787i | \(-0.0721685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.799135 | −0.143529 | −0.0717644 | − | 0.997422i | \(-0.522863\pi\) | ||||
−0.0717644 | + | 0.997422i | \(0.522863\pi\) | |||||||
\(32\) | −2.58376 | − | 5.03231i | −0.456749 | − | 0.889596i | ||||
\(33\) | −10.9975 | −1.91442 | ||||||||
\(34\) | −1.84925 | + | 3.13134i | −0.317144 | + | 0.537020i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.48944 | + | 2.47534i | −0.748240 | + | 0.412557i | ||||
\(37\) | 2.69652 | + | 2.69652i | 0.443305 | + | 0.443305i | 0.893121 | − | 0.449816i | \(-0.148511\pi\) |
−0.449816 | + | 0.893121i | \(0.648511\pi\) | |||||||
\(38\) | −2.87499 | − | 11.1686i | −0.466386 | − | 1.81179i | ||||
\(39\) | − | 6.33850i | − | 1.01497i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.946984i | 0.147894i | 0.997262 | + | 0.0739471i | \(0.0235596\pi\) | ||||
−0.997262 | + | 0.0739471i | \(0.976440\pi\) | |||||||
\(42\) | 6.05276 | − | 1.55808i | 0.933961 | − | 0.240417i | ||||
\(43\) | 0.829986 | + | 0.829986i | 0.126572 | + | 0.126572i | 0.767555 | − | 0.640983i | \(-0.221473\pi\) |
−0.640983 | + | 0.767555i | \(0.721473\pi\) | |||||||
\(44\) | −2.59054 | + | 8.95813i | −0.390539 | + | 1.35049i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.23730 | + | 5.45520i | 1.36197 | + | 0.804325i | ||||
\(47\) | 1.52421 | 0.222329 | 0.111165 | − | 0.993802i | \(-0.464542\pi\) | ||||
0.111165 | + | 0.993802i | \(0.464542\pi\) | |||||||
\(48\) | 2.08093 | + | 9.20233i | 0.300356 | + | 1.32824i | ||||
\(49\) | 3.48919 | 0.498456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.28879 | − | 4.28879i | 0.600551 | − | 0.600551i | ||||
\(52\) | −5.16309 | − | 1.49308i | −0.715992 | − | 0.207053i | ||||
\(53\) | 6.97225 | + | 6.97225i | 0.957712 | + | 0.957712i | 0.999141 | − | 0.0414296i | \(-0.0131912\pi\) |
−0.0414296 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(54\) | −1.41064 | + | 0.363122i | −0.191963 | + | 0.0494147i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.156619 | − | 5.29735i | 0.0209291 | − | 0.707889i | ||||
\(57\) | 19.2346i | 2.54769i | ||||||||
\(58\) | 3.21976 | + | 12.5080i | 0.422775 | + | 1.64238i | ||||
\(59\) | 6.84418 | + | 6.84418i | 0.891036 | + | 0.891036i | 0.994621 | − | 0.103585i | \(-0.0330313\pi\) |
−0.103585 | + | 0.994621i | \(0.533031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.87247 | + | 6.87247i | −0.879930 | + | 0.879930i | −0.993527 | − | 0.113597i | \(-0.963763\pi\) |
0.113597 | + | 0.993527i | \(0.463763\pi\) | |||||||
\(62\) | 0.574689 | − | 0.973121i | 0.0729856 | − | 0.123587i | ||||
\(63\) | −4.80293 | −0.605112 | ||||||||
\(64\) | 7.98603 | + | 0.472635i | 0.998253 | + | 0.0590793i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.90874 | − | 13.3919i | 0.973498 | − | 1.64843i | ||||
\(67\) | −3.73647 | + | 3.73647i | −0.456483 | + | 0.456483i | −0.897499 | − | 0.441016i | \(-0.854618\pi\) |
0.441016 | + | 0.897499i | \(0.354618\pi\) | |||||||
\(68\) | −2.48322 | − | 4.50373i | −0.301135 | − | 0.546158i | ||||
\(69\) | −12.6517 | − | 12.6517i | −1.52309 | − | 1.52309i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.34417i | − | 1.10895i | −0.832201 | − | 0.554475i | \(-0.812919\pi\) | ||
0.832201 | − | 0.554475i | \(-0.187081\pi\) | |||||||
\(72\) | 0.214261 | − | 7.24699i | 0.0252509 | − | 0.854066i | ||||
\(73\) | − | 0.886316i | − | 0.103735i | −0.998654 | − | 0.0518677i | \(-0.983483\pi\) | ||
0.998654 | − | 0.0518677i | \(-0.0165174\pi\) | |||||||
\(74\) | −5.22277 | + | 1.34443i | −0.607135 | + | 0.156287i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.6678 | + | 4.53086i | 1.79722 | + | 0.519725i | ||||
\(77\) | −6.17755 | + | 6.17755i | −0.703997 | + | 0.703997i | ||||
\(78\) | 7.71851 | + | 4.55826i | 0.873949 | + | 0.516122i | ||||
\(79\) | 3.07575 | 0.346049 | 0.173024 | − | 0.984918i | \(-0.444646\pi\) | ||||
0.173024 | + | 0.984918i | \(0.444646\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1194 | 1.12437 | ||||||||
\(82\) | −1.15316 | − | 0.681013i | −0.127345 | − | 0.0752053i | ||||
\(83\) | −0.989393 | + | 0.989393i | −0.108600 | + | 0.108600i | −0.759319 | − | 0.650719i | \(-0.774468\pi\) |
0.650719 | + | 0.759319i | \(0.274468\pi\) | |||||||
\(84\) | −2.45547 | + | 8.49104i | −0.267913 | + | 0.926448i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.60756 | + | 0.413814i | −0.173348 | + | 0.0446227i | ||||
\(87\) | − | 21.5412i | − | 2.30946i | ||||||
\(88\) | −9.04553 | − | 9.59670i | −0.964257 | − | 1.02301i | ||||
\(89\) | 10.0942i | 1.06998i | 0.844859 | + | 0.534990i | \(0.179684\pi\) | ||||
−0.844859 | + | 0.534990i | \(0.820316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56048 | − | 3.56048i | −0.373239 | − | 0.373239i | ||||
\(92\) | −13.2858 | + | 7.32539i | −1.38514 | + | 0.763725i | ||||
\(93\) | −1.33282 | + | 1.33282i | −0.138207 | + | 0.138207i | ||||
\(94\) | −1.09612 | + | 1.85606i | −0.113056 | + | 0.191438i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.7023 | − | 4.08377i | −1.29643 | − | 0.416798i | ||||
\(97\) | −7.16829 | −0.727830 | −0.363915 | − | 0.931432i | \(-0.618560\pi\) | ||||
−0.363915 | + | 0.931432i | \(0.618560\pi\) | |||||||
\(98\) | −2.50921 | + | 4.24885i | −0.253469 | + | 0.429199i | ||||
\(99\) | −8.45113 | + | 8.45113i | −0.849371 | + | 0.849371i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05091 | − | 1.05091i | −0.104570 | − | 0.104570i | 0.652886 | − | 0.757456i | \(-0.273558\pi\) |
−0.757456 | + | 0.652886i | \(0.773558\pi\) | |||||||
\(102\) | 2.13831 | + | 8.30678i | 0.211724 | + | 0.822493i | ||||
\(103\) | 8.20690i | 0.808649i | 0.914616 | + | 0.404325i | \(0.132493\pi\) | ||||
−0.914616 | + | 0.404325i | \(0.867507\pi\) | |||||||
\(104\) | 5.53113 | − | 5.21346i | 0.542372 | − | 0.511222i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.5043 | + | 3.47622i | −1.31165 | + | 0.337641i | ||||
\(107\) | −2.85743 | − | 2.85743i | −0.276238 | − | 0.276238i | 0.555367 | − | 0.831605i | \(-0.312578\pi\) |
−0.831605 | + | 0.555367i | \(0.812578\pi\) | |||||||
\(108\) | 0.572264 | − | 1.97889i | 0.0550661 | − | 0.190419i | ||||
\(109\) | −11.3735 | + | 11.3735i | −1.08939 | + | 1.08939i | −0.0937940 | + | 0.995592i | \(0.529900\pi\) |
−0.995592 | + | 0.0937940i | \(0.970100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.99467 | 0.853736 | ||||||||
\(112\) | 6.33806 | + | 4.00025i | 0.598890 | + | 0.377988i | ||||
\(113\) | −3.54221 | −0.333223 | −0.166611 | − | 0.986023i | \(-0.553283\pi\) | ||||
−0.166611 | + | 0.986023i | \(0.553283\pi\) | |||||||
\(114\) | −23.4224 | − | 13.8324i | −2.19371 | − | 1.29552i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.5466 | − | 5.07419i | −1.62916 | − | 0.471127i | ||||
\(117\) | −4.87088 | − | 4.87088i | −0.450313 | − | 0.450313i | ||||
\(118\) | −13.2562 | + | 3.41237i | −1.22033 | + | 0.314134i | ||||
\(119\) | − | 4.81822i | − | 0.441685i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7398i | 0.976343i | ||||||||
\(122\) | −3.42648 | − | 13.3110i | −0.310219 | − | 1.20512i | ||||
\(123\) | 1.57941 | + | 1.57941i | 0.142411 | + | 0.142411i | ||||
\(124\) | 0.771707 | + | 1.39962i | 0.0693014 | + | 0.125689i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.45397 | − | 5.84862i | 0.307704 | − | 0.521036i | ||||
\(127\) | 18.0693 | 1.60339 | 0.801693 | − | 0.597735i | \(-0.203933\pi\) | ||||
0.801693 | + | 0.597735i | \(0.203933\pi\) | |||||||
\(128\) | −6.31860 | + | 9.38485i | −0.558490 | + | 0.829511i | ||||
\(129\) | 2.76855 | 0.243757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39614 | + | 6.39614i | −0.558834 | + | 0.558834i | −0.928975 | − | 0.370142i | \(-0.879309\pi\) |
0.370142 | + | 0.928975i | \(0.379309\pi\) | |||||||
\(132\) | 10.6201 | + | 19.2612i | 0.924358 | + | 1.67648i | ||||
\(133\) | 10.8045 | + | 10.8045i | 0.936871 | + | 0.936871i | ||||
\(134\) | −1.86293 | − | 7.23702i | −0.160933 | − | 0.625183i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.27006 | + | 0.214943i | 0.623403 | + | 0.0184312i | ||||
\(137\) | − | 10.7357i | − | 0.917212i | −0.888640 | − | 0.458606i | \(-0.848349\pi\) | ||
0.888640 | − | 0.458606i | \(-0.151651\pi\) | |||||||
\(138\) | 24.5046 | − | 6.30790i | 2.08597 | − | 0.536964i | ||||
\(139\) | −2.31086 | − | 2.31086i | −0.196005 | − | 0.196005i | 0.602280 | − | 0.798285i | \(-0.294259\pi\) |
−0.798285 | + | 0.602280i | \(0.794259\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54213 | − | 2.54213i | 0.214086 | − | 0.214086i | ||||
\(142\) | 11.3786 | + | 6.71976i | 0.954869 | + | 0.563909i | ||||
\(143\) | −12.5299 | −1.04780 | ||||||||
\(144\) | 8.67071 | + | 5.47250i | 0.722559 | + | 0.456042i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.07928 | + | 0.637384i | 0.0893221 | + | 0.0527503i | ||||
\(147\) | 5.81938 | − | 5.81938i | 0.479974 | − | 0.479974i | ||||
\(148\) | 2.11876 | − | 7.32670i | 0.174161 | − | 0.602251i | ||||
\(149\) | 1.38743 | + | 1.38743i | 0.113663 | + | 0.113663i | 0.761651 | − | 0.647988i | \(-0.224389\pi\) |
−0.647988 | + | 0.761651i | \(0.724389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.68590i | − | 0.462712i | −0.972869 | − | 0.231356i | \(-0.925684\pi\) | ||
0.972869 | − | 0.231356i | \(-0.0743163\pi\) | |||||||
\(152\) | −16.7846 | + | 15.8206i | −1.36141 | + | 1.28322i | ||||
\(153\) | − | 6.59152i | − | 0.532892i | ||||||
\(154\) | −3.08000 | − | 11.9650i | −0.248194 | − | 0.964170i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.1014 | + | 6.12096i | −0.888820 | + | 0.490069i | ||||
\(157\) | −2.48874 | + | 2.48874i | −0.198623 | + | 0.198623i | −0.799409 | − | 0.600787i | \(-0.794854\pi\) |
0.600787 | + | 0.799409i | \(0.294854\pi\) | |||||||
\(158\) | −2.21189 | + | 3.74540i | −0.175969 | + | 0.297968i | ||||
\(159\) | 23.2571 | 1.84440 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2135 | −1.12018 | ||||||||
\(162\) | −7.27722 | + | 12.3225i | −0.571753 | + | 0.968149i | ||||
\(163\) | 12.7091 | − | 12.7091i | 0.995451 | − | 0.995451i | −0.00453842 | − | 0.999990i | \(-0.501445\pi\) |
0.999990 | + | 0.00453842i | \(0.00144463\pi\) | |||||||
\(164\) | 1.65857 | − | 0.914483i | 0.129512 | − | 0.0714091i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.493292 | − | 1.91631i | −0.0382868 | − | 0.148735i | ||||
\(167\) | − | 5.00982i | − | 0.387672i | −0.981034 | − | 0.193836i | \(-0.937907\pi\) | ||
0.981034 | − | 0.193836i | \(-0.0620929\pi\) | |||||||
\(168\) | −8.57387 | − | 9.09630i | −0.661489 | − | 0.701795i | ||||
\(169\) | 5.77830i | 0.444485i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.7810 | + | 14.7810i | 1.13033 | + | 1.13033i | ||||
\(172\) | 0.652152 | − | 2.25515i | 0.0497261 | − | 0.171954i | ||||
\(173\) | 6.19546 | − | 6.19546i | 0.471032 | − | 0.471032i | −0.431216 | − | 0.902249i | \(-0.641915\pi\) |
0.902249 | + | 0.431216i | \(0.141915\pi\) | |||||||
\(174\) | 26.2312 | + | 15.4911i | 1.98858 | + | 1.17438i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.1911 | − | 4.11356i | 1.37120 | − | 0.310071i | ||||
\(177\) | 22.8299 | 1.71600 | ||||||||
\(178\) | −12.2919 | − | 7.25911i | −0.921313 | − | 0.544093i | ||||
\(179\) | −5.51628 | + | 5.51628i | −0.412306 | + | 0.412306i | −0.882541 | − | 0.470235i | \(-0.844169\pi\) |
0.470235 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.8993 | + | 11.8993i | 0.884470 | + | 0.884470i | 0.993985 | − | 0.109515i | \(-0.0349298\pi\) |
−0.109515 | + | 0.993985i | \(0.534930\pi\) | |||||||
\(182\) | 6.89614 | − | 1.77518i | 0.511176 | − | 0.131585i | ||||
\(183\) | 22.9242i | 1.69461i | ||||||||
\(184\) | 0.634072 | − | 21.4463i | 0.0467444 | − | 1.58105i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.664518 | − | 2.58149i | −0.0487248 | − | 0.189284i | ||||
\(187\) | −8.47804 | − | 8.47804i | −0.619976 | − | 0.619976i | ||||
\(188\) | −1.47190 | − | 2.66954i | −0.107349 | − | 0.194696i | ||||
\(189\) | 1.36465 | − | 1.36465i | 0.0992637 | − | 0.0992637i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1278 | 0.805180 | 0.402590 | − | 0.915380i | \(-0.368110\pi\) | ||||
0.402590 | + | 0.915380i | \(0.368110\pi\) | |||||||
\(192\) | 14.1076 | − | 12.5311i | 1.01813 | − | 0.904352i | ||||
\(193\) | 20.7821 | 1.49593 | 0.747965 | − | 0.663738i | \(-0.231031\pi\) | ||||
0.747965 | + | 0.663738i | \(0.231031\pi\) | |||||||
\(194\) | 5.15500 | − | 8.72896i | 0.370107 | − | 0.626703i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.36944 | − | 6.11103i | −0.240674 | − | 0.436502i | ||||
\(197\) | −14.0309 | − | 14.0309i | −0.999663 | − | 0.999663i | 0.000337236 | − | 1.00000i | \(-0.499893\pi\) |
−1.00000 | 0.000337236i | \(0.999893\pi\) | ||||||||
\(198\) | −4.21357 | − | 16.3686i | −0.299445 | − | 1.16327i | ||||
\(199\) | − | 3.24727i | − | 0.230193i | −0.993354 | − | 0.115096i | \(-0.963282\pi\) | ||
0.993354 | − | 0.115096i | \(-0.0367177\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.4636i | 0.879115i | ||||||||
\(202\) | 2.03547 | − | 0.523964i | 0.143215 | − | 0.0368660i | ||||
\(203\) | −12.1002 | − | 12.1002i | −0.849267 | − | 0.849267i | ||||
\(204\) | −11.6531 | − | 3.36987i | −0.815877 | − | 0.235938i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.99369 | − | 5.90190i | −0.696294 | − | 0.411205i | ||||
\(207\) | −19.4447 | −1.35150 | ||||||||
\(208\) | 2.37088 | + | 10.4846i | 0.164391 | + | 0.726974i | ||||
\(209\) | 38.0228 | 2.63009 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1821 | + | 10.1821i | −0.700964 | + | 0.700964i | −0.964617 | − | 0.263654i | \(-0.915072\pi\) |
0.263654 | + | 0.964617i | \(0.415072\pi\) | |||||||
\(212\) | 5.47837 | − | 18.9443i | 0.376256 | − | 1.30110i | ||||
\(213\) | −15.5845 | − | 15.5845i | −1.06783 | − | 1.06783i | ||||
\(214\) | 5.53443 | − | 1.42466i | 0.378326 | − | 0.0973876i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.99820 | + | 2.11996i | 0.135960 | + | 0.144245i | ||||
\(217\) | 1.49735i | 0.101647i | ||||||||
\(218\) | −5.67061 | − | 22.0289i | −0.384062 | − | 1.49198i | ||||
\(219\) | −1.47822 | − | 1.47822i | −0.0998892 | − | 0.0998892i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88638 | − | 4.88638i | 0.328694 | − | 0.328694i | ||||
\(222\) | −6.46842 | + | 10.9530i | −0.434132 | + | 0.735116i | ||||
\(223\) | 24.0469 | 1.61030 | 0.805151 | − | 0.593070i | \(-0.202084\pi\) | ||||
0.805151 | + | 0.593070i | \(0.202084\pi\) | |||||||
\(224\) | −9.42912 | + | 4.84124i | −0.630010 | + | 0.323469i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.54734 | − | 4.31341i | 0.169446 | − | 0.286924i | ||||
\(227\) | −11.9863 | + | 11.9863i | −0.795562 | + | 0.795562i | −0.982392 | − | 0.186830i | \(-0.940179\pi\) |
0.186830 | + | 0.982392i | \(0.440179\pi\) | |||||||
\(228\) | 33.6879 | − | 18.5745i | 2.23103 | − | 1.23012i | ||||
\(229\) | −20.1972 | − | 20.1972i | −1.33467 | − | 1.33467i | −0.901140 | − | 0.433529i | \(-0.857268\pi\) |
−0.433529 | − | 0.901140i | \(-0.642732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.6062i | 1.35579i | ||||||||
\(232\) | 18.7974 | − | 17.7178i | 1.23411 | − | 1.16323i | ||||
\(233\) | 10.0655i | 0.659410i | 0.944084 | + | 0.329705i | \(0.106949\pi\) | ||||
−0.944084 | + | 0.329705i | \(0.893051\pi\) | |||||||
\(234\) | 9.43419 | − | 2.42852i | 0.616733 | − | 0.158757i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.37774 | − | 18.5963i | 0.350061 | − | 1.21052i | ||||
\(237\) | 5.12983 | − | 5.12983i | 0.333218 | − | 0.333218i | ||||
\(238\) | 5.86724 | + | 3.46497i | 0.380316 | + | 0.224601i | ||||
\(239\) | 0.992801 | 0.0642189 | 0.0321095 | − | 0.999484i | \(-0.489777\pi\) | ||||
0.0321095 | + | 0.999484i | \(0.489777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1229 | 0.909738 | 0.454869 | − | 0.890558i | \(-0.349686\pi\) | ||||
0.454869 | + | 0.890558i | \(0.349686\pi\) | |||||||
\(242\) | −13.0780 | − | 7.72339i | −0.840687 | − | 0.496478i | ||||
\(243\) | 14.6924 | − | 14.6924i | 0.942520 | − | 0.942520i | ||||
\(244\) | 18.6732 | + | 5.39997i | 1.19543 | + | 0.345698i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.05909 | + | 0.787462i | −0.195041 | + | 0.0502068i | ||||
\(247\) | 21.9148i | 1.39440i | ||||||||
\(248\) | −2.25931 | − | 0.0667975i | −0.143466 | − | 0.00424165i | ||||
\(249\) | 3.30028i | 0.209147i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.56681 | + | 1.56681i | 0.0988961 | + | 0.0988961i | 0.754824 | − | 0.655928i | \(-0.227722\pi\) |
−0.655928 | + | 0.754824i | \(0.727722\pi\) | |||||||
\(252\) | 4.63809 | + | 8.41193i | 0.292172 | + | 0.529902i | ||||
\(253\) | −25.0098 | + | 25.0098i | −1.57235 | + | 1.57235i | ||||
\(254\) | −12.9943 | + | 22.0033i | −0.815335 | + | 1.38061i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.88415 | − | 14.4433i | −0.430260 | − | 0.902705i | ||||
\(257\) | 10.2593 | 0.639960 | 0.319980 | − | 0.947424i | \(-0.396324\pi\) | ||||
0.319980 | + | 0.947424i | \(0.396324\pi\) | |||||||
\(258\) | −1.99097 | + | 3.37132i | −0.123953 | + | 0.209889i | ||||
\(259\) | 5.05251 | − | 5.05251i | 0.313948 | − | 0.313948i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.5535 | − | 16.5535i | −1.02464 | − | 1.02464i | ||||
\(262\) | −3.18899 | − | 12.3884i | −0.197016 | − | 0.765359i | ||||
\(263\) | 19.0630i | 1.17548i | 0.809051 | + | 0.587739i | \(0.199982\pi\) | ||||
−0.809051 | + | 0.587739i | \(0.800018\pi\) | |||||||
\(264\) | −31.0921 | − | 0.919252i | −1.91358 | − | 0.0565761i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.9268 | + | 5.38692i | −1.28311 | + | 0.330293i | ||||
\(267\) | 16.8354 | + | 16.8354i | 1.03031 | + | 1.03031i | ||||
\(268\) | 10.1524 | + | 2.93589i | 0.620154 | + | 0.179338i | ||||
\(269\) | 3.48459 | − | 3.48459i | 0.212459 | − | 0.212459i | −0.592852 | − | 0.805311i | \(-0.701998\pi\) |
0.805311 | + | 0.592852i | \(0.201998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.0045 | −1.82264 | −0.911322 | − | 0.411695i | \(-0.864937\pi\) | ||||
−0.911322 | + | 0.411695i | \(0.864937\pi\) | |||||||
\(272\) | −5.48992 | + | 8.69832i | −0.332876 | + | 0.527413i | ||||
\(273\) | −11.8765 | −0.718801 | ||||||||
\(274\) | 13.0731 | + | 7.72045i | 0.789772 | + | 0.466409i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.94096 | + | 34.3760i | −0.598375 | + | 2.06919i | ||||
\(277\) | −8.43732 | − | 8.43732i | −0.506949 | − | 0.506949i | 0.406639 | − | 0.913589i | \(-0.366701\pi\) |
−0.913589 | + | 0.406639i | \(0.866701\pi\) | |||||||
\(278\) | 4.47581 | − | 1.15215i | 0.268441 | − | 0.0691014i | ||||
\(279\) | 2.04844i | 0.122637i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.44714i | − | 0.384604i | −0.981336 | − | 0.192302i | \(-0.938405\pi\) | ||
0.981336 | − | 0.192302i | \(-0.0615954\pi\) | |||||||
\(282\) | 1.26746 | + | 4.92375i | 0.0754759 | + | 0.293205i | ||||
\(283\) | −2.61000 | − | 2.61000i | −0.155148 | − | 0.155148i | 0.625264 | − | 0.780413i | \(-0.284991\pi\) |
−0.780413 | + | 0.625264i | \(0.784991\pi\) | |||||||
\(284\) | −16.3656 | + | 9.02347i | −0.971117 | + | 0.535444i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.01073 | − | 15.2579i | 0.532815 | − | 0.902217i | ||||
\(287\) | 1.77438 | 0.104738 | ||||||||
\(288\) | −12.8994 | + | 6.62300i | −0.760105 | + | 0.390264i | ||||
\(289\) | −10.3875 | −0.611029 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.9555 | + | 11.9555i | −0.700844 | + | 0.700844i | ||||
\(292\) | −1.55231 | + | 0.855896i | −0.0908420 | + | 0.0500875i | ||||
\(293\) | 7.52428 | + | 7.52428i | 0.439573 | + | 0.439573i | 0.891868 | − | 0.452295i | \(-0.149395\pi\) |
−0.452295 | + | 0.891868i | \(0.649395\pi\) | |||||||
\(294\) | 2.90143 | + | 11.2713i | 0.169215 | + | 0.657356i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.39818 | + | 7.84897i | 0.430010 | + | 0.456212i | ||||
\(297\) | − | 4.80242i | − | 0.278665i | ||||||
\(298\) | −2.68726 | + | 0.691746i | −0.155669 | + | 0.0400718i | ||||
\(299\) | −14.4146 | − | 14.4146i | −0.833618 | − | 0.833618i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55516 | − | 1.55516i | 0.0896377 | − | 0.0896377i | ||||
\(302\) | 6.92383 | + | 4.08895i | 0.398422 | + | 0.235293i | ||||
\(303\) | −3.50549 | −0.201385 | ||||||||
\(304\) | −7.19460 | − | 31.8162i | −0.412639 | − | 1.82478i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.02661 | + | 4.74021i | 0.458851 | + | 0.270980i | ||||
\(307\) | −12.7130 | + | 12.7130i | −0.725571 | + | 0.725571i | −0.969734 | − | 0.244163i | \(-0.921487\pi\) |
0.244163 | + | 0.969734i | \(0.421487\pi\) | |||||||
\(308\) | 16.7850 | + | 4.85394i | 0.956414 | + | 0.276579i | ||||
\(309\) | 13.6877 | + | 13.6877i | 0.778667 | + | 0.778667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.9313i | − | 0.676563i | −0.941045 | − | 0.338281i | \(-0.890154\pi\) | ||
0.941045 | − | 0.338281i | \(-0.109846\pi\) | |||||||
\(312\) | 0.529818 | − | 17.9202i | 0.0299951 | − | 1.01453i | ||||
\(313\) | − | 34.3458i | − | 1.94134i | −0.240414 | − | 0.970670i | \(-0.577283\pi\) | ||
0.240414 | − | 0.970670i | \(-0.422717\pi\) | |||||||
\(314\) | −1.24083 | − | 4.82033i | −0.0700244 | − | 0.272027i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.97019 | − | 5.38692i | −0.167086 | − | 0.303038i | ||||
\(317\) | 17.1112 | − | 17.1112i | 0.961060 | − | 0.961060i | −0.0382097 | − | 0.999270i | \(-0.512165\pi\) |
0.999270 | + | 0.0382097i | \(0.0121655\pi\) | |||||||
\(318\) | −16.7251 | + | 28.3206i | −0.937894 | + | 1.58814i | ||||
\(319\) | −42.5825 | −2.38416 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.53141 | −0.531992 | ||||||||
\(322\) | 10.2215 | − | 17.3081i | 0.569622 | − | 0.964541i | ||||
\(323\) | −14.8281 | + | 14.8281i | −0.825056 | + | 0.825056i | ||||
\(324\) | −9.77205 | − | 17.7232i | −0.542891 | − | 0.984623i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.33649 | + | 24.6157i | 0.350946 | + | 1.36334i | ||||
\(327\) | 37.9382i | 2.09799i | ||||||||
\(328\) | −0.0791559 | + | 2.67731i | −0.00437065 | + | 0.147830i | ||||
\(329\) | − | 2.85594i | − | 0.157453i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.80246 | + | 9.80246i | 0.538792 | + | 0.538792i | 0.923174 | − | 0.384382i | \(-0.125585\pi\) |
−0.384382 | + | 0.923174i | \(0.625585\pi\) | |||||||
\(332\) | 2.68828 | + | 0.777405i | 0.147538 | + | 0.0426656i | ||||
\(333\) | 6.91203 | − | 6.91203i | 0.378777 | − | 0.378777i | ||||
\(334\) | 6.10056 | + | 3.60276i | 0.333808 | + | 0.197134i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.2425 | − | 3.89906i | 0.940658 | − | 0.212711i | ||||
\(337\) | −6.07501 | −0.330927 | −0.165463 | − | 0.986216i | \(-0.552912\pi\) | ||||
−0.165463 | + | 0.986216i | \(0.552912\pi\) | |||||||
\(338\) | −7.03635 | − | 4.15540i | −0.382727 | − | 0.226024i | ||||
\(339\) | −5.90780 | + | 5.90780i | −0.320868 | + | 0.320868i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.63471 | + | 2.63471i | 0.142677 | + | 0.142677i | ||||
\(342\) | −28.6287 | + | 7.36952i | −1.54806 | + | 0.398498i | ||||
\(343\) | − | 19.6538i | − | 1.06120i | ||||||
\(344\) | 2.27715 | + | 2.41590i | 0.122776 | + | 0.130257i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.08894 | + | 11.9997i | 0.166062 | + | 0.645110i | ||||
\(347\) | −5.77231 | − | 5.77231i | −0.309874 | − | 0.309874i | 0.534987 | − | 0.844860i | \(-0.320317\pi\) |
−0.844860 | + | 0.534987i | \(0.820317\pi\) | |||||||
\(348\) | −37.7277 | + | 20.8019i | −2.02242 | + | 1.11510i | ||||
\(349\) | −7.58851 | + | 7.58851i | −0.406203 | + | 0.406203i | −0.880412 | − | 0.474209i | \(-0.842734\pi\) |
0.474209 | + | 0.880412i | \(0.342734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.76791 | 0.147740 | ||||||||
\(352\) | −8.07275 | + | 25.1098i | −0.430279 | + | 1.33836i | ||||
\(353\) | 16.2285 | 0.863753 | 0.431877 | − | 0.901933i | \(-0.357852\pi\) | ||||
0.431877 | + | 0.901933i | \(0.357852\pi\) | |||||||
\(354\) | −16.4178 | + | 27.8003i | −0.872598 | + | 1.47757i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 17.6791 | − | 9.74772i | 0.936990 | − | 0.516628i | ||||
\(357\) | −8.03597 | − | 8.03597i | −0.425309 | − | 0.425309i | ||||
\(358\) | −2.75031 | − | 10.6843i | −0.145358 | − | 0.564680i | ||||
\(359\) | − | 6.77298i | − | 0.357464i | −0.983898 | − | 0.178732i | \(-0.942800\pi\) | ||
0.983898 | − | 0.178732i | \(-0.0571996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 47.5019i | − | 2.50010i | ||||||
\(362\) | −23.0473 | + | 5.93277i | −1.21134 | + | 0.311819i | ||||
\(363\) | 17.9121 | + | 17.9121i | 0.940142 | + | 0.940142i | ||||
\(364\) | −2.79761 | + | 9.67416i | −0.146634 | + | 0.507064i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −27.9153 | − | 16.4857i | −1.45915 | − | 0.861722i | ||||
\(367\) | 6.35705 | 0.331835 | 0.165918 | − | 0.986140i | \(-0.446941\pi\) | ||||
0.165918 | + | 0.986140i | \(0.446941\pi\) | |||||||
\(368\) | 25.6596 | + | 16.1950i | 1.33760 | + | 0.844224i | ||||
\(369\) | 2.42742 | 0.126367 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0640 | − | 13.0640i | 0.678250 | − | 0.678250i | ||||
\(372\) | 3.62140 | + | 1.04725i | 0.187761 | + | 0.0542974i | ||||
\(373\) | −9.20937 | − | 9.20937i | −0.476843 | − | 0.476843i | 0.427278 | − | 0.904121i | \(-0.359473\pi\) |
−0.904121 | + | 0.427278i | \(0.859473\pi\) | |||||||
\(374\) | 16.4208 | − | 4.22698i | 0.849097 | − | 0.218572i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.30925 | + | 0.127405i | 0.222232 | + | 0.00657041i | ||||
\(377\) | − | 24.5428i | − | 1.26402i | ||||||
\(378\) | 0.680387 | + | 2.64313i | 0.0349954 | + | 0.135948i | ||||
\(379\) | 5.41600 | + | 5.41600i | 0.278201 | + | 0.278201i | 0.832391 | − | 0.554189i | \(-0.186972\pi\) |
−0.554189 | + | 0.832391i | \(0.686972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.1365 | − | 30.1365i | 1.54394 | − | 1.54394i | ||||
\(382\) | −8.00244 | + | 13.5505i | −0.409440 | + | 0.693306i | ||||
\(383\) | −28.1626 | −1.43904 | −0.719520 | − | 0.694472i | \(-0.755638\pi\) | ||||
−0.719520 | + | 0.694472i | \(0.755638\pi\) | |||||||
\(384\) | 5.11398 | + | 26.1907i | 0.260972 | + | 1.33654i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9452 | + | 25.3068i | −0.760693 | + | 1.28808i | ||||
\(387\) | 2.12752 | − | 2.12752i | 0.108148 | − | 0.108148i | ||||
\(388\) | 6.92227 | + | 12.5547i | 0.351425 | + | 0.637367i | ||||
\(389\) | 9.59783 | + | 9.59783i | 0.486629 | + | 0.486629i | 0.907241 | − | 0.420611i | \(-0.138184\pi\) |
−0.420611 | + | 0.907241i | \(0.638184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.5066i | − | 0.986490i | ||||||
\(392\) | 9.86461 | + | 0.291652i | 0.498238 | + | 0.0147307i | ||||
\(393\) | 21.3354i | 1.07623i | ||||||||
\(394\) | 27.1759 | − | 6.99554i | 1.36910 | − | 0.352430i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 22.9625 | + | 6.64039i | 1.15391 | + | 0.333692i | ||||
\(397\) | −10.4884 | + | 10.4884i | −0.526399 | + | 0.526399i | −0.919497 | − | 0.393098i | \(-0.871403\pi\) |
0.393098 | + | 0.919497i | \(0.371403\pi\) | |||||||
\(398\) | 3.95426 | + | 2.33524i | 0.198209 | + | 0.117055i | ||||
\(399\) | 36.0402 | 1.80427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.44221 | −0.121958 | −0.0609791 | − | 0.998139i | \(-0.519422\pi\) | ||||
−0.0609791 | + | 0.998139i | \(0.519422\pi\) | |||||||
\(402\) | −15.1772 | − | 8.96306i | −0.756969 | − | 0.447037i | ||||
\(403\) | −1.51853 | + | 1.51853i | −0.0756436 | + | 0.0756436i | ||||
\(404\) | −0.825743 | + | 2.85543i | −0.0410823 | + | 0.142063i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.4364 | − | 6.03292i | 1.16313 | − | 0.299409i | ||||
\(407\) | − | 17.7806i | − | 0.881350i | ||||||
\(408\) | 12.4837 | − | 11.7667i | 0.618036 | − | 0.582541i | ||||
\(409\) | 24.6628i | 1.21950i | 0.792596 | + | 0.609748i | \(0.208729\pi\) | ||||
−0.792596 | + | 0.609748i | \(0.791271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.9053 | − | 17.9053i | −0.883204 | − | 0.883204i | ||||
\(412\) | 14.3737 | − | 7.92522i | 0.708142 | − | 0.390448i | ||||
\(413\) | 12.8240 | − | 12.8240i | 0.631030 | − | 0.631030i | ||||
\(414\) | 13.9834 | − | 23.6781i | 0.687247 | − | 1.16372i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −14.4722 | − | 4.65279i | −0.709560 | − | 0.228122i | ||||
\(417\) | −7.70826 | −0.377475 | ||||||||
\(418\) | −27.3437 | + | 46.3011i | −1.33742 | + | 2.26466i | ||||
\(419\) | 19.1661 | − | 19.1661i | 0.936326 | − | 0.936326i | −0.0617649 | − | 0.998091i | \(-0.519673\pi\) |
0.998091 | + | 0.0617649i | \(0.0196729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.43469 | − | 7.43469i | −0.362345 | − | 0.362345i | 0.502331 | − | 0.864676i | \(-0.332476\pi\) |
−0.864676 | + | 0.502331i | \(0.832476\pi\) | |||||||
\(422\) | −5.07659 | − | 19.7213i | −0.247124 | − | 0.960016i | ||||
\(423\) | − | 3.90704i | − | 0.189967i | ||||||
\(424\) | 19.1291 | + | 20.2947i | 0.928991 | + | 0.985596i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 30.1850 | − | 7.77012i | 1.46247 | − | 0.376464i | ||||
\(427\) | 12.8771 | + | 12.8771i | 0.623164 | + | 0.623164i | ||||
\(428\) | −2.24519 | + | 7.76391i | −0.108526 | + | 0.375283i | ||||
\(429\) | −20.8977 | + | 20.8977i | −1.00895 | + | 1.00895i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.5647 | 1.08690 | 0.543451 | − | 0.839441i | \(-0.317117\pi\) | ||||
0.543451 | + | 0.839441i | \(0.317117\pi\) | |||||||
\(432\) | −4.01849 | + | 0.908704i | −0.193340 | + | 0.0437201i | ||||
\(433\) | −26.4811 | −1.27260 | −0.636301 | − | 0.771441i | \(-0.719536\pi\) | ||||
−0.636301 | + | 0.771441i | \(0.719536\pi\) | |||||||
\(434\) | −1.82335 | − | 1.07680i | −0.0875237 | − | 0.0516882i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.9030 | + | 8.93662i | 1.47998 | + | 0.427986i | ||||
\(437\) | 43.7421 | + | 43.7421i | 2.09247 | + | 2.09247i | ||||
\(438\) | 2.86311 | − | 0.737013i | 0.136805 | − | 0.0352159i | ||||
\(439\) | 0.765288i | 0.0365252i | 0.999833 | + | 0.0182626i | \(0.00581349\pi\) | ||||
−0.999833 | + | 0.0182626i | \(0.994187\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 8.94390i | − | 0.425900i | ||||||
\(442\) | 2.43625 | + | 9.46423i | 0.115881 | + | 0.450167i | ||||
\(443\) | −20.2685 | − | 20.2685i | −0.962985 | − | 0.962985i | 0.0363537 | − | 0.999339i | \(-0.488426\pi\) |
−0.999339 | + | 0.0363537i | \(0.988426\pi\) | |||||||
\(444\) | −8.68596 | − | 15.7534i | −0.412218 | − | 0.747625i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.2931 | + | 29.2824i | −0.818851 | + | 1.38656i | ||||
\(447\) | 4.62800 | 0.218897 | ||||||||
\(448\) | 0.885583 | − | 14.9635i | 0.0418399 | − | 0.706961i | ||||
\(449\) | −35.2717 | −1.66457 | −0.832287 | − | 0.554345i | \(-0.812969\pi\) | ||||
−0.832287 | + | 0.554345i | \(0.812969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.12216 | − | 3.12216i | 0.147017 | − | 0.147017i | ||||
\(452\) | 3.42063 | + | 6.20388i | 0.160893 | + | 0.291806i | ||||
\(453\) | −9.48312 | − | 9.48312i | −0.445556 | − | 0.445556i | ||||
\(454\) | −5.97615 | − | 23.2158i | −0.280475 | − | 1.08957i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.60777 | + | 54.3800i | −0.0752908 | + | 2.54658i | ||||
\(457\) | − | 9.01188i | − | 0.421558i | −0.977534 | − | 0.210779i | \(-0.932400\pi\) | ||
0.977534 | − | 0.210779i | \(-0.0676000\pi\) | |||||||
\(458\) | 39.1191 | − | 10.0699i | 1.82792 | − | 0.470537i | ||||
\(459\) | 1.87284 | + | 1.87284i | 0.0874167 | + | 0.0874167i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8247 | + | 22.8247i | −1.06305 | + | 1.06305i | −0.0651807 | + | 0.997873i | \(0.520762\pi\) |
−0.997873 | + | 0.0651807i | \(0.979238\pi\) | |||||||
\(462\) | −25.0926 | − | 14.8187i | −1.16741 | − | 0.689429i | ||||
\(463\) | −3.72721 | −0.173218 | −0.0866090 | − | 0.996242i | \(-0.527603\pi\) | ||||
−0.0866090 | + | 0.996242i | \(0.527603\pi\) | |||||||
\(464\) | 8.05738 | + | 35.6315i | 0.374054 | + | 1.65415i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.2569 | − | 7.23846i | −0.567790 | − | 0.335315i | ||||
\(467\) | 3.23477 | − | 3.23477i | 0.149687 | − | 0.149687i | −0.628291 | − | 0.777978i | \(-0.716245\pi\) |
0.777978 | + | 0.628291i | \(0.216245\pi\) | |||||||
\(468\) | −3.82724 | + | 13.2346i | −0.176914 | + | 0.611771i | ||||
\(469\) | 7.00109 | + | 7.00109i | 0.323280 | + | 0.323280i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.30158i | 0.382517i | ||||||||
\(472\) | 18.7777 | + | 19.9219i | 0.864314 | + | 0.916979i | ||||
\(473\) | − | 5.47284i | − | 0.251642i | ||||||
\(474\) | 2.55763 | + | 9.93575i | 0.117476 | + | 0.456364i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.43871 | + | 4.65285i | −0.386788 | + | 0.213263i | ||||
\(477\) | 17.8721 | − | 17.8721i | 0.818307 | − | 0.818307i | ||||
\(478\) | −0.713961 | + | 1.20895i | −0.0326558 | + | 0.0552962i | ||||
\(479\) | −11.0636 | −0.505508 | −0.252754 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252754 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.2480 | 0.467267 | ||||||||
\(482\) | −10.1563 | + | 17.1978i | −0.462609 | + | 0.783336i | ||||
\(483\) | −23.7057 | + | 23.7057i | −1.07865 | + | 1.07865i | ||||
\(484\) | 18.8098 | − | 10.3712i | 0.854992 | − | 0.471417i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.32536 | + | 28.4572i | 0.332285 | + | 1.29084i | ||||
\(487\) | 6.68176i | 0.302779i | 0.988474 | + | 0.151390i | \(0.0483748\pi\) | ||||
−0.988474 | + | 0.151390i | \(0.951625\pi\) | |||||||
\(488\) | −20.0042 | + | 18.8553i | −0.905550 | + | 0.853541i | ||||
\(489\) | − | 42.3932i | − | 1.91708i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.4274 | − | 18.4274i | −0.831618 | − | 0.831618i | 0.156120 | − | 0.987738i | \(-0.450101\pi\) |
−0.987738 | + | 0.156120i | \(0.950101\pi\) | |||||||
\(492\) | 1.24100 | − | 4.29141i | 0.0559488 | − | 0.193472i | ||||
\(493\) | 16.6063 | − | 16.6063i | 0.747908 | − | 0.747908i | ||||
\(494\) | −26.6860 | − | 15.7597i | −1.20066 | − | 0.709065i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.70610 | − | 2.70316i | 0.0766060 | − | 0.121376i | ||||
\(497\) | −17.5083 | −0.785356 | ||||||||
\(498\) | −4.01881 | − | 2.37336i | −0.180087 | − | 0.106353i | ||||
\(499\) | 8.84615 | − | 8.84615i | 0.396008 | − | 0.396008i | −0.480814 | − | 0.876822i | \(-0.659659\pi\) |
0.876822 | + | 0.480814i | \(0.159659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.35554 | − | 8.35554i | −0.373298 | − | 0.373298i | ||||
\(502\) | −3.03469 | + | 0.781180i | −0.135445 | + | 0.0348658i | ||||
\(503\) | − | 16.8746i | − | 0.752401i | −0.926538 | − | 0.376201i | \(-0.877230\pi\) | ||
0.926538 | − | 0.376201i | \(-0.122770\pi\) | |||||||
\(504\) | −13.5788 | − | 0.401464i | −0.604848 | − | 0.0178826i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.4694 | − | 48.4405i | −0.554332 | − | 2.15344i | ||||
\(507\) | 9.63723 | + | 9.63723i | 0.428004 | + | 0.428004i | ||||
\(508\) | −17.4491 | − | 31.6468i | −0.774178 | − | 1.40410i | ||||
\(509\) | 20.5691 | − | 20.5691i | 0.911707 | − | 0.911707i | −0.0846994 | − | 0.996407i | \(-0.526993\pi\) |
0.996407 | + | 0.0846994i | \(0.0269930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.66070 | −0.0734652 | ||||||||
\(512\) | 22.5385 | + | 2.00376i | 0.996071 | + | 0.0885545i | ||||
\(513\) | −8.39943 | −0.370844 | ||||||||
\(514\) | −7.37788 | + | 12.4930i | −0.325425 | + | 0.551042i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.67353 | − | 4.84889i | −0.117696 | − | 0.213460i | ||||
\(517\) | −5.02526 | − | 5.02526i | −0.221011 | − | 0.221011i | ||||
\(518\) | 2.51908 | + | 9.78599i | 0.110682 | + | 0.429972i | ||||
\(519\) | − | 20.6660i | − | 0.907135i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6708i | 0.555118i | 0.960709 | + | 0.277559i | \(0.0895253\pi\) | ||||
−0.960709 | + | 0.277559i | \(0.910475\pi\) | |||||||
\(522\) | 32.0619 | − | 8.25327i | 1.40331 | − | 0.361236i | ||||
\(523\) | 27.8509 | + | 27.8509i | 1.21784 | + | 1.21784i | 0.968388 | + | 0.249448i | \(0.0802491\pi\) |
0.249448 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(524\) | 17.3789 | + | 5.02570i | 0.759202 | + | 0.219549i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.2134 | − | 13.7090i | −1.01215 | − | 0.597740i | ||||
\(527\) | −2.05496 | −0.0895154 | ||||||||
\(528\) | 23.4789 | − | 37.2003i | 1.02179 | − | 1.61894i | ||||
\(529\) | −34.5435 | −1.50189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.5438 | − | 17.5438i | 0.761336 | − | 0.761336i | ||||
\(532\) | 8.48954 | − | 29.3569i | 0.368068 | − | 1.27278i | ||||
\(533\) | 1.79948 | + | 1.79948i | 0.0779442 | + | 0.0779442i | ||||
\(534\) | −32.6077 | + | 8.39377i | −1.41107 | + | 0.363234i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.8760 | + | 10.2514i | −0.469774 | + | 0.442793i | ||||
\(537\) | 18.4005i | 0.794038i | ||||||||
\(538\) | 1.73734 | + | 6.74915i | 0.0749023 | + | 0.290976i | ||||
\(539\) | −11.5037 | − | 11.5037i | −0.495499 | − | 0.495499i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.4122 | + | 23.4122i | −1.00657 | + | 1.00657i | −0.00659048 | + | 0.999978i | \(0.502098\pi\) |
−0.999978 | + | 0.00659048i | \(0.997902\pi\) | |||||||
\(542\) | 21.5774 | − | 36.5370i | 0.926829 | − | 1.56940i | ||||
\(543\) | 39.6921 | 1.70335 | ||||||||
\(544\) | −6.64409 | − | 12.9405i | −0.284863 | − | 0.554819i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.54089 | − | 14.4623i | 0.365516 | − | 0.618929i | ||||
\(547\) | −17.3745 | + | 17.3745i | −0.742878 | + | 0.742878i | −0.973131 | − | 0.230253i | \(-0.926045\pi\) |
0.230253 | + | 0.973131i | \(0.426045\pi\) | |||||||
\(548\) | −18.8027 | + | 10.3672i | −0.803211 | + | 0.442866i | ||||
\(549\) | 17.6163 | + | 17.6163i | 0.751846 | + | 0.751846i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 74.4767i | 3.17282i | ||||||||
\(552\) | −34.7113 | − | 36.8264i | −1.47741 | − | 1.56744i | ||||
\(553\) | − | 5.76308i | − | 0.245071i | ||||||
\(554\) | 16.3419 | − | 4.20668i | 0.694300 | − | 0.178725i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.81574 | + | 6.27884i | −0.0770043 | + | 0.266282i | ||||
\(557\) | −22.8889 | + | 22.8889i | −0.969832 | + | 0.969832i | −0.999558 | − | 0.0297261i | \(-0.990536\pi\) |
0.0297261 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(558\) | −2.49442 | − | 1.47311i | −0.105597 | − | 0.0623617i | ||||
\(559\) | 3.15432 | 0.133413 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.2799 | −1.19398 | ||||||||
\(562\) | 7.85081 | + | 4.63639i | 0.331166 | + | 0.195574i | ||||
\(563\) | −19.2489 | + | 19.2489i | −0.811246 | + | 0.811246i | −0.984821 | − | 0.173574i | \(-0.944468\pi\) |
0.173574 | + | 0.984821i | \(0.444468\pi\) | |||||||
\(564\) | −6.90721 | − | 1.99745i | −0.290846 | − | 0.0841079i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.05520 | − | 1.30129i | 0.212486 | − | 0.0546975i | ||||
\(567\) | − | 18.9608i | − | 0.796278i | ||||||
\(568\) | 0.781054 | − | 26.4178i | 0.0327723 | − | 1.10846i | ||||
\(569\) | 34.4274i | 1.44327i | 0.692273 | + | 0.721635i | \(0.256609\pi\) | ||||
−0.692273 | + | 0.721635i | \(0.743391\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.85059 | + | 5.85059i | 0.244840 | + | 0.244840i | 0.818849 | − | 0.574009i | \(-0.194613\pi\) |
−0.574009 | + | 0.818849i | \(0.694613\pi\) | |||||||
\(572\) | 12.0998 | + | 21.9451i | 0.505920 | + | 0.917569i | ||||
\(573\) | 18.5593 | − | 18.5593i | 0.775326 | − | 0.775326i | ||||
\(574\) | −1.27603 | + | 2.16070i | −0.0532603 | + | 0.0901857i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.21151 | − | 20.4707i | 0.0504797 | − | 0.852947i | ||||
\(577\) | −32.5042 | −1.35317 | −0.676585 | − | 0.736365i | \(-0.736541\pi\) | ||||
−0.676585 | + | 0.736365i | \(0.736541\pi\) | |||||||
\(578\) | 7.47005 | − | 12.6491i | 0.310713 | − | 0.526131i | ||||
\(579\) | 34.6611 | − | 34.6611i | 1.44047 | − | 1.44047i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.85384 | + | 1.85384i | 0.0769103 | + | 0.0769103i | ||||
\(582\) | −5.96077 | − | 23.1561i | −0.247082 | − | 0.959851i | ||||
\(583\) | − | 45.9743i | − | 1.90406i | ||||||
\(584\) | 0.0740848 | − | 2.50578i | 0.00306565 | − | 0.103690i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5735 | + | 3.75146i | −0.602024 | + | 0.154971i | ||||
\(587\) | 14.7519 | + | 14.7519i | 0.608875 | + | 0.608875i | 0.942652 | − | 0.333777i | \(-0.108323\pi\) |
−0.333777 | + | 0.942652i | \(0.608323\pi\) | |||||||
\(588\) | −15.8118 | − | 4.57251i | −0.652068 | − | 0.188567i | ||||
\(589\) | 4.60810 | − | 4.60810i | 0.189873 | − | 0.189873i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −46.8024 | −1.92520 | ||||||||
\(592\) | −14.8782 | + | 3.36440i | −0.611488 | + | 0.138276i | ||||
\(593\) | 20.5310 | 0.843108 | 0.421554 | − | 0.906803i | \(-0.361485\pi\) | ||||
0.421554 | + | 0.906803i | \(0.361485\pi\) | |||||||
\(594\) | 5.84800 | + | 3.45361i | 0.239946 | + | 0.141703i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.09016 | − | 3.76979i | 0.0446547 | − | 0.154416i | ||||
\(597\) | −5.41590 | − | 5.41590i | −0.221658 | − | 0.221658i | ||||
\(598\) | 27.9190 | − | 7.18683i | 1.14169 | − | 0.293891i | ||||
\(599\) | 12.3998i | 0.506644i | 0.967382 | + | 0.253322i | \(0.0815232\pi\) | ||||
−0.967382 | + | 0.253322i | \(0.918477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3980i | 0.505723i | 0.967502 | + | 0.252862i | \(0.0813718\pi\) | ||||
−0.967502 | + | 0.252862i | \(0.918628\pi\) | |||||||
\(602\) | 0.775370 | + | 3.01212i | 0.0316017 | + | 0.122765i | ||||
\(603\) | 9.57777 | + | 9.57777i | 0.390037 | + | 0.390037i | ||||
\(604\) | −9.95839 | + | 5.49076i | −0.405201 | + | 0.223416i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.52093 | − | 4.26870i | 0.102406 | − | 0.173404i | ||||
\(607\) | −4.90398 | −0.199046 | −0.0995232 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995232 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(608\) | 43.9171 | + | 14.1192i | 1.78107 | + | 0.572610i | ||||
\(609\) | −40.3621 | −1.63556 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.89635 | − | 2.89635i | 0.117174 | − | 0.117174i | ||||
\(612\) | −11.5445 | + | 6.36529i | −0.466659 | + | 0.257301i | ||||
\(613\) | 0.408547 | + | 0.408547i | 0.0165011 | + | 0.0165011i | 0.715309 | − | 0.698808i | \(-0.246286\pi\) |
−0.698808 | + | 0.715309i | \(0.746286\pi\) | |||||||
\(614\) | −6.33846 | − | 24.6233i | −0.255800 | − | 0.993717i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.9815 | + | 16.9487i | −0.724494 | + | 0.682884i | ||||
\(617\) | 6.17186i | 0.248470i | 0.992253 | + | 0.124235i | \(0.0396476\pi\) | ||||
−0.992253 | + | 0.124235i | \(0.960352\pi\) | |||||||
\(618\) | −26.5111 | + | 6.82442i | −1.06643 | + | 0.274518i | ||||
\(619\) | 18.5138 | + | 18.5138i | 0.744132 | + | 0.744132i | 0.973370 | − | 0.229238i | \(-0.0736234\pi\) |
−0.229238 | + | 0.973370i | \(0.573623\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.52479 | − | 5.52479i | 0.221702 | − | 0.221702i | ||||
\(622\) | 14.5290 | + | 8.58027i | 0.582559 | + | 0.344037i | ||||
\(623\) | 18.9136 | 0.757757 | ||||||||
\(624\) | 21.4407 | + | 13.5323i | 0.858315 | + | 0.541724i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 41.8236 | + | 24.6994i | 1.67161 | + | 0.987187i | ||||
\(627\) | 63.4156 | − | 63.4156i | 2.53258 | − | 2.53258i | ||||
\(628\) | 6.76214 | + | 1.95550i | 0.269839 | + | 0.0780329i | ||||
\(629\) | 6.93404 | + | 6.93404i | 0.276478 | + | 0.276478i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.7940i | − | 0.827795i | −0.910323 | − | 0.413897i | \(-0.864167\pi\) | ||
0.910323 | − | 0.413897i | \(-0.135833\pi\) | |||||||
\(632\) | 8.69574 | + | 0.257094i | 0.345898 | + | 0.0102266i | ||||
\(633\) | 33.9640i | 1.34995i | ||||||||
\(634\) | 8.53130 | + | 33.1419i | 0.338821 | + | 1.31623i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22.4588 | − | 40.7328i | −0.890551 | − | 1.61516i | ||||
\(637\) | 6.63024 | − | 6.63024i | 0.262700 | − | 0.262700i | ||||
\(638\) | 30.6227 | − | 51.8535i | 1.21237 | − | 2.05290i | ||||
\(639\) | −23.9521 | −0.947530 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.1179 | 0.636620 | 0.318310 | − | 0.947987i | \(-0.396885\pi\) | ||||
0.318310 | + | 0.947987i | \(0.396885\pi\) | |||||||
\(642\) | 6.85441 | − | 11.6066i | 0.270522 | − | 0.458075i | ||||
\(643\) | −10.3733 | + | 10.3733i | −0.409082 | + | 0.409082i | −0.881419 | − | 0.472336i | \(-0.843411\pi\) |
0.472336 | + | 0.881419i | \(0.343411\pi\) | |||||||
\(644\) | 13.7257 | + | 24.8938i | 0.540868 | + | 0.980954i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.39298 | − | 28.7199i | −0.290873 | − | 1.12997i | ||||
\(647\) | 32.5724i | 1.28055i | 0.768145 | + | 0.640276i | \(0.221180\pi\) | ||||
−0.768145 | + | 0.640276i | \(0.778820\pi\) | |||||||
\(648\) | 28.6094 | + | 0.845850i | 1.12388 | + | 0.0332281i | ||||
\(649\) | − | 45.1298i | − | 1.77150i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.49733 | + | 2.49733i | 0.0978780 | + | 0.0978780i | ||||
\(652\) | −34.5318 | − | 9.98601i | −1.35237 | − | 0.391083i | ||||
\(653\) | −4.31962 | + | 4.31962i | −0.169040 | + | 0.169040i | −0.786557 | − | 0.617517i | \(-0.788139\pi\) |
0.617517 | + | 0.786557i | \(0.288139\pi\) | |||||||
\(654\) | −46.1981 | − | 27.2828i | −1.80649 | − | 1.06684i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.20328 | − | 2.02174i | −0.125067 | − | 0.0789359i | ||||
\(657\) | −2.27191 | −0.0886356 | ||||||||
\(658\) | 3.47774 | + | 2.05382i | 0.135576 | + | 0.0800662i | ||||
\(659\) | −4.19711 | + | 4.19711i | −0.163496 | + | 0.163496i | −0.784114 | − | 0.620617i | \(-0.786882\pi\) |
0.620617 | + | 0.784114i | \(0.286882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2310 | + | 21.2310i | 0.825790 | + | 0.825790i | 0.986931 | − | 0.161141i | \(-0.0515175\pi\) |
−0.161141 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(662\) | −18.9860 | + | 4.88731i | −0.737911 | + | 0.189951i | ||||
\(663\) | − | 16.2993i | − | 0.633013i | ||||||
\(664\) | −2.87990 | + | 2.71450i | −0.111762 | + | 0.105343i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.44620 | + | 13.3876i | 0.133538 | + | 0.518760i | ||||
\(667\) | −48.9877 | − | 48.9877i | −1.89681 | − | 1.89681i | ||||
\(668\) | −8.77429 | + | 4.83788i | −0.339488 | + | 0.187183i | ||||
\(669\) | 40.1062 | − | 40.1062i | 1.55060 | − | 1.55060i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 45.3164 | 1.74942 | ||||||||
\(672\) | −7.65182 | + | 23.8005i | −0.295175 | + | 0.918126i | ||||
\(673\) | 6.08317 | 0.234489 | 0.117244 | − | 0.993103i | \(-0.462594\pi\) | ||||
0.117244 | + | 0.993103i | \(0.462594\pi\) | |||||||
\(674\) | 4.36877 | − | 7.39765i | 0.168279 | − | 0.284947i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.1202 | − | 5.57998i | 0.389239 | − | 0.214615i | ||||
\(677\) | 8.42443 | + | 8.42443i | 0.323777 | + | 0.323777i | 0.850214 | − | 0.526437i | \(-0.176472\pi\) |
−0.526437 | + | 0.850214i | \(0.676472\pi\) | |||||||
\(678\) | −2.94551 | − | 11.4426i | −0.113122 | − | 0.439449i | ||||
\(679\) | 13.4313i | 0.515447i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.9824i | 1.53213i | ||||||||
\(682\) | −5.10305 | + | 1.31361i | −0.195406 | + | 0.0503008i | ||||
\(683\) | −14.7609 | − | 14.7609i | −0.564812 | − | 0.564812i | 0.365859 | − | 0.930670i | \(-0.380775\pi\) |
−0.930670 | + | 0.365859i | \(0.880775\pi\) | |||||||
\(684\) | 11.6140 | − | 40.1615i | 0.444073 | − | 1.53561i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 23.9328 | + | 14.1338i | 0.913757 | + | 0.539630i | ||||
\(687\) | −67.3710 | −2.57036 | ||||||||
\(688\) | −4.57948 | + | 1.03556i | −0.174591 | + | 0.0394804i | ||||
\(689\) | 26.4977 | 1.00948 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.06268 | + | 4.06268i | −0.154552 | + | 0.154552i | −0.780147 | − | 0.625596i | \(-0.784856\pi\) |
0.625596 | + | 0.780147i | \(0.284856\pi\) | |||||||
\(692\) | −16.8337 | − | 4.86802i | −0.639920 | − | 0.185054i | ||||
\(693\) | 15.8350 | + | 15.8350i | 0.601523 | + | 0.601523i | ||||
\(694\) | 11.1801 | − | 2.87796i | 0.424392 | − | 0.109246i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.80057 | − | 60.9012i | 0.0682506 | − | 2.30845i | ||||
\(697\) | 2.43515i | 0.0922379i | ||||||||
\(698\) | −3.78348 | − | 14.6979i | −0.143207 | − | 0.556322i | ||||
\(699\) | 16.7875 | + | 16.7875i | 0.634961 | + | 0.634961i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1049 | − | 11.1049i | 0.419428 | − | 0.419428i | −0.465578 | − | 0.885007i | \(-0.654154\pi\) |
0.885007 | + | 0.465578i | \(0.154154\pi\) | |||||||
\(702\) | −1.99051 | + | 3.37054i | −0.0751271 | + | 0.127213i | ||||
\(703\) | −31.0982 | −1.17289 | ||||||||
\(704\) | −24.7713 | − | 27.8878i | −0.933603 | − | 1.05106i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11.6705 | + | 19.7617i | −0.439225 | + | 0.743741i | ||||
\(707\) | −1.96911 | + | 1.96911i | −0.0740561 | + | 0.0740561i | ||||
\(708\) | −22.0463 | − | 39.9846i | −0.828551 | − | 1.50271i | ||||
\(709\) | 13.0114 | + | 13.0114i | 0.488652 | + | 0.488652i | 0.907881 | − | 0.419229i | \(-0.137700\pi\) |
−0.419229 | + | 0.907881i | \(0.637700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 7.88412i | − | 0.295678i | ||||||
\(712\) | −0.843744 | + | 28.5381i | −0.0316206 | + | 1.06951i | ||||
\(713\) | 6.06203i | 0.227025i | ||||||||
\(714\) | 15.5645 | − | 4.00658i | 0.582488 | − | 0.149942i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.9883 | + | 4.33436i | 0.560138 | + | 0.161983i | ||||
\(717\) | 1.65582 | − | 1.65582i | 0.0618378 | − | 0.0618378i | ||||
\(718\) | 8.24759 | + | 4.87071i | 0.307797 | + | 0.181773i | ||||
\(719\) | −50.0570 | −1.86681 | −0.933406 | − | 0.358821i | \(-0.883179\pi\) | ||||
−0.933406 | + | 0.358821i | \(0.883179\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3774 | 0.572684 | ||||||||
\(722\) | 57.8439 | + | 34.1604i | 2.15273 | + | 1.27132i | ||||
\(723\) | 23.5547 | − | 23.5547i | 0.876007 | − | 0.876007i | ||||
\(724\) | 9.34977 | − | 32.3316i | 0.347481 | − | 1.20160i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.6932 | + | 8.93062i | −1.28759 | + | 0.331447i | ||||
\(727\) | − | 27.7141i | − | 1.02786i | −0.857832 | − | 0.513930i | \(-0.828189\pi\) | ||
0.857832 | − | 0.513930i | \(-0.171811\pi\) | |||||||
\(728\) | −9.76854 | − | 10.3638i | −0.362046 | − | 0.384107i | ||||
\(729\) | − | 18.6509i | − | 0.690775i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.13429 | + | 2.13429i | 0.0789396 | + | 0.0789396i | ||||
\(732\) | 40.1499 | − | 22.1374i | 1.48398 | − | 0.818224i | ||||
\(733\) | −16.8860 | + | 16.8860i | −0.623698 | + | 0.623698i | −0.946475 | − | 0.322777i | \(-0.895384\pi\) |
0.322777 | + | 0.946475i | \(0.395384\pi\) | |||||||
\(734\) | −4.57160 | + | 7.74110i | −0.168741 | + | 0.285729i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.1738 | + | 19.5998i | −1.40711 | + | 0.722457i | ||||
\(737\) | 24.6379 | 0.907550 | ||||||||
\(738\) | −1.74565 | + | 2.95592i | −0.0642584 | + | 0.108809i | ||||
\(739\) | −23.6286 | + | 23.6286i | −0.869193 | + | 0.869193i | −0.992383 | − | 0.123190i | \(-0.960688\pi\) |
0.123190 | + | 0.992383i | \(0.460688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.5501 | + | 36.5501i | 1.34270 | + | 1.34270i | ||||
\(742\) | 6.51345 | + | 25.3031i | 0.239116 | + | 0.928907i | ||||
\(743\) | 6.53356i | 0.239693i | 0.992792 | + | 0.119846i | \(0.0382402\pi\) | ||||
−0.992792 | + | 0.119846i | \(0.961760\pi\) | |||||||
\(744\) | −3.87955 | + | 3.65673i | −0.142231 | + | 0.134062i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.8372 | − | 4.59161i | 0.653068 | − | 0.168111i | ||||
\(747\) | 2.53613 | + | 2.53613i | 0.0927921 | + | 0.0927921i | ||||
\(748\) | −6.66153 | + | 23.0356i | −0.243570 | + | 0.842267i | ||||
\(749\) | −5.35401 | + | 5.35401i | −0.195631 | + | 0.195631i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.8483 | −0.833746 | −0.416873 | − | 0.908965i | \(-0.636874\pi\) | ||||
−0.416873 | + | 0.908965i | \(0.636874\pi\) | |||||||
\(752\) | −3.25409 | + | 5.15583i | −0.118664 | + | 0.188014i | ||||
\(753\) | 5.22634 | 0.190459 | ||||||||
\(754\) | 29.8862 | + | 17.6496i | 1.08839 | + | 0.642762i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.70789 | − | 1.07226i | −0.134855 | − | 0.0389977i | ||||
\(757\) | 24.0190 | + | 24.0190i | 0.872985 | + | 0.872985i | 0.992797 | − | 0.119811i | \(-0.0382290\pi\) |
−0.119811 | + | 0.992797i | \(0.538229\pi\) | |||||||
\(758\) | −10.4900 | + | 2.70031i | −0.381015 | + | 0.0980797i | ||||
\(759\) | 83.4243i | 3.02811i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.51772i | − | 0.200017i | −0.994987 | − | 0.100009i | \(-0.968113\pi\) | ||
0.994987 | − | 0.100009i | \(-0.0318871\pi\) | |||||||
\(762\) | 15.0254 | + | 58.3700i | 0.544314 | + | 2.11452i | ||||
\(763\) | 21.3107 | + | 21.3107i | 0.771501 | + | 0.771501i | ||||
\(764\) | −10.7459 | − | 19.4894i | −0.388772 | − | 0.705103i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.2528 | − | 34.2941i | 0.731763 | − | 1.23910i | ||||
\(767\) | 26.0109 | 0.939200 | ||||||||
\(768\) | −35.5706 | − | 12.6073i | −1.28354 | − | 0.454928i | ||||
\(769\) | 14.0124 | 0.505299 | 0.252649 | − | 0.967558i | \(-0.418698\pi\) | ||||
0.252649 | + | 0.967558i | \(0.418698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.1108 | − | 17.1108i | 0.616231 | − | 0.616231i | ||||
\(772\) | −20.0689 | − | 36.3982i | −0.722294 | − | 1.31000i | ||||
\(773\) | −0.753043 | − | 0.753043i | −0.0270851 | − | 0.0270851i | 0.693435 | − | 0.720520i | \(-0.256097\pi\) |
−0.720520 | + | 0.693435i | \(0.756097\pi\) | |||||||
\(774\) | 1.06074 | + | 4.12070i | 0.0381274 | + | 0.148115i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.2661 | − | 0.599178i | −0.727512 | − | 0.0215092i | ||||
\(777\) | − | 16.8535i | − | 0.604614i | ||||||
\(778\) | −18.5896 | + | 4.78529i | −0.666471 | + | 0.171561i | ||||
\(779\) | −5.46066 | − | 5.46066i | −0.195648 | − | 0.195648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.8073 | + | 30.8073i | −1.10237 | + | 1.10237i | ||||
\(782\) | 23.7535 | + | 14.0279i | 0.849424 | + | 0.501638i | ||||
\(783\) | 9.40668 | 0.336167 | ||||||||
\(784\) | −7.44917 | + | 11.8026i | −0.266042 | + | 0.421521i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.9805 | − | 15.3431i | −0.926693 | − | 0.547270i | ||||
\(787\) | 29.2752 | − | 29.2752i | 1.04355 | − | 1.04355i | 0.0445395 | − | 0.999008i | \(-0.485818\pi\) |
0.999008 | − | 0.0445395i | \(-0.0141821\pi\) | |||||||
\(788\) | −11.0247 | + | 38.1234i | −0.392737 | + | 1.35809i | ||||
\(789\) | 31.7939 | + | 31.7939i | 1.13189 | + | 1.13189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.63709i | 0.235988i | ||||||||
\(792\) | −24.5994 | + | 23.1866i | −0.874101 | + | 0.823899i | ||||
\(793\) | 26.1185i | 0.927494i | ||||||||
\(794\) | −5.22932 | − | 20.3146i | −0.185581 | − | 0.720937i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.68733 | + | 3.13582i | −0.201582 | + | 0.111146i | ||||
\(797\) | 6.09658 | − | 6.09658i | 0.215952 | − | 0.215952i | −0.590838 | − | 0.806790i | \(-0.701203\pi\) |
0.806790 | + | 0.590838i | \(0.201203\pi\) | |||||||
\(798\) | −25.9179 | + | 43.8869i | −0.917485 | + | 1.55358i | ||||
\(799\) | 3.91948 | 0.138661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25.8745 | 0.914232 | ||||||||
\(802\) | 1.75629 | − | 2.97393i | 0.0620167 | − | 0.105013i | ||||
\(803\) | −2.92214 | + | 2.92214i | −0.103120 | + | 0.103120i | ||||
\(804\) | 21.8290 | − | 12.0358i | 0.769849 | − | 0.424471i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.757111 | − | 2.94119i | −0.0266681 | − | 0.103599i | ||||
\(807\) | − | 11.6234i | − | 0.409163i | ||||||
\(808\) | −2.88329 | − | 3.05897i | −0.101434 | − | 0.107614i | ||||
\(809\) | − | 31.5083i | − | 1.10777i | −0.832592 | − | 0.553886i | \(-0.813144\pi\) | ||
0.832592 | − | 0.553886i | \(-0.186856\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.2317 | + | 20.2317i | 0.710431 | + | 0.710431i | 0.966625 | − | 0.256194i | \(-0.0824686\pi\) |
−0.256194 | + | 0.966625i | \(0.582469\pi\) | |||||||
\(812\) | −9.50760 | + | 32.8774i | −0.333651 | + | 1.15377i | ||||
\(813\) | −50.0424 | + | 50.0424i | −1.75506 | + | 1.75506i | ||||
\(814\) | 21.6517 | + | 12.7867i | 0.758893 | + | 0.448174i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.35106 | + | 23.6636i | 0.187325 | + | 0.828391i | ||||
\(817\) | −9.57200 | −0.334882 | ||||||||
\(818\) | −30.0323 | − | 17.7359i | −1.05006 | − | 0.620123i | ||||
\(819\) | −9.12664 | + | 9.12664i | −0.318910 | + | 0.318910i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1821 | − | 19.1821i | −0.669459 | − | 0.669459i | 0.288132 | − | 0.957591i | \(-0.406966\pi\) |
−0.957591 | + | 0.288132i | \(0.906966\pi\) | |||||||
\(822\) | 34.6800 | − | 8.92723i | 1.20961 | − | 0.311373i | ||||
\(823\) | 11.4746i | 0.399979i | 0.979798 | + | 0.199989i | \(0.0640907\pi\) | ||||
−0.979798 | + | 0.199989i | \(0.935909\pi\) | |||||||
\(824\) | −0.685992 | + | 23.2025i | −0.0238977 | + | 0.808296i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.39381 | + | 24.8383i | 0.222469 | + | 0.864236i | ||||
\(827\) | −17.7573 | − | 17.7573i | −0.617482 | − | 0.617482i | 0.327403 | − | 0.944885i | \(-0.393827\pi\) |
−0.944885 | + | 0.327403i | \(0.893827\pi\) | |||||||
\(828\) | 18.7773 | + | 34.0557i | 0.652556 | + | 1.18352i | ||||
\(829\) | −20.0071 | + | 20.0071i | −0.694876 | + | 0.694876i | −0.963301 | − | 0.268424i | \(-0.913497\pi\) |
0.268424 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.1440 | −0.976306 | ||||||||
\(832\) | 16.0733 | − | 14.2771i | 0.557243 | − | 0.494970i | ||||
\(833\) | 8.97238 | 0.310874 | ||||||||
\(834\) | 5.54331 | − | 9.38649i | 0.191949 | − | 0.325028i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −36.7178 | − | 66.5939i | −1.26991 | − | 2.30320i | ||||
\(837\) | −0.582020 | − | 0.582020i | −0.0201175 | − | 0.0201175i | ||||
\(838\) | 9.55584 | + | 37.1220i | 0.330101 | + | 1.28236i | ||||
\(839\) | 20.3936i | 0.704065i | 0.935988 | + | 0.352033i | \(0.114509\pi\) | ||||
−0.935988 | + | 0.352033i | \(0.885491\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 54.4079i | − | 1.87614i | ||||||
\(842\) | 14.3999 | − | 3.70679i | 0.496255 | − | 0.127744i | ||||
\(843\) | −10.7527 | − | 10.7527i | −0.370344 | − | 0.370344i | ||||
\(844\) | 27.6657 | + | 8.00047i | 0.952293 | + | 0.275387i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.75768 | + | 2.80971i | 0.163572 | + | 0.0965997i | ||||
\(847\) | 20.1233 | 0.691444 | ||||||||
\(848\) | −38.4697 | + | 8.69917i | −1.32105 | + | 0.298731i | ||||
\(849\) | −8.70608 | −0.298792 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.4551 | − | 20.4551i | 0.701191 | − | 0.701191i | ||||
\(852\) | −12.2453 | + | 42.3446i | −0.419519 | + | 1.45070i | ||||
\(853\) | −37.4481 | − | 37.4481i | −1.28220 | − | 1.28220i | −0.939414 | − | 0.342784i | \(-0.888630\pi\) |
−0.342784 | − | 0.939414i | \(-0.611370\pi\) | |||||||
\(854\) | −24.9410 | + | 6.42024i | −0.853464 | + | 0.219696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.83965 | − | 8.31734i | −0.267954 | − | 0.284281i | ||||
\(857\) | − | 12.7258i | − | 0.434706i | −0.976093 | − | 0.217353i | \(-0.930258\pi\) | ||
0.976093 | − | 0.217353i | \(-0.0697422\pi\) | |||||||
\(858\) | −10.4192 | − | 40.4759i | −0.355705 | − | 1.38183i | ||||
\(859\) | 17.4318 | + | 17.4318i | 0.594766 | + | 0.594766i | 0.938915 | − | 0.344149i | \(-0.111833\pi\) |
−0.344149 | + | 0.938915i | \(0.611833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.95936 | − | 2.95936i | 0.100855 | − | 0.100855i | ||||
\(862\) | −16.2271 | + | 27.4774i | −0.552699 | + | 0.935885i | ||||
\(863\) | 33.6976 | 1.14708 | 0.573540 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573540 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(864\) | 1.78331 | − | 5.54688i | 0.0606694 | − | 0.188709i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.0436 | − | 32.2466i | 0.647128 | − | 1.09578i | ||||
\(867\) | −17.3246 | + | 17.3246i | −0.588374 | + | 0.588374i | ||||
\(868\) | 2.62249 | − | 1.44596i | 0.0890130 | − | 0.0490791i | ||||
\(869\) | −10.1406 | − | 10.1406i | −0.343996 | − | 0.343996i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.2003i | 0.481158i | ||||||||
\(872\) | −33.1058 | + | 31.2044i | −1.12110 | + | 1.05672i | ||||
\(873\) | 18.3746i | 0.621886i | ||||||||
\(874\) | −84.7223 | + | 21.8090i | −2.86577 | + | 0.737699i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.16150 | + | 4.01648i | −0.0392434 | + | 0.135704i | ||||
\(877\) | 21.8386 | − | 21.8386i | 0.737436 | − | 0.737436i | −0.234645 | − | 0.972081i | \(-0.575393\pi\) |
0.972081 | + | 0.234645i | \(0.0753927\pi\) | |||||||
\(878\) | −0.931906 | − | 0.550349i | −0.0314503 | − | 0.0185734i | ||||
\(879\) | 25.0985 | 0.846550 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.3274 | −1.32497 | −0.662487 | − | 0.749073i | \(-0.730499\pi\) | ||||
−0.662487 | + | 0.749073i | \(0.730499\pi\) | |||||||
\(882\) | 10.8912 | + | 6.43191i | 0.366724 | + | 0.216574i | ||||
\(883\) | 6.80206 | − | 6.80206i | 0.228907 | − | 0.228907i | −0.583329 | − | 0.812236i | \(-0.698250\pi\) |
0.812236 | + | 0.583329i | \(0.198250\pi\) | |||||||
\(884\) | −13.2768 | − | 3.83942i | −0.446546 | − | 0.129134i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.2572 | − | 10.1055i | 1.31887 | − | 0.339500i | ||||
\(887\) | − | 29.4190i | − | 0.987793i | −0.869521 | − | 0.493897i | \(-0.835572\pi\) | ||
0.869521 | − | 0.493897i | \(-0.164428\pi\) | |||||||
\(888\) | 25.4297 | + | 0.751840i | 0.853363 | + | 0.0252301i | ||||
\(889\) | − | 33.8566i | − | 1.13552i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.3630 | − | 33.3630i | −1.11770 | − | 1.11770i | ||||
\(892\) | −23.2216 | − | 42.1162i | −0.777517 | − | 1.41016i | ||||
\(893\) | −8.78917 | + | 8.78917i | −0.294118 | + | 0.294118i | ||||
\(894\) | −3.32818 | + | 5.63561i | −0.111311 | + | 0.188483i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 17.5845 | + | 11.8393i | 0.587458 | + | 0.395522i | ||||
\(897\) | −48.0822 | −1.60542 | ||||||||
\(898\) | 25.3652 | − | 42.9510i | 0.846449 | − | 1.43329i | ||||
\(899\) | −5.16070 | + | 5.16070i | −0.172119 | + | 0.172119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9290 | + | 17.9290i | 0.597301 | + | 0.597301i | ||||
\(902\) | 1.55665 | + | 6.04718i | 0.0518307 | + | 0.201349i | ||||
\(903\) | − | 5.18748i | − | 0.172628i | ||||||
\(904\) | −10.0145 | − | 0.296084i | −0.333077 | − | 0.00984759i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.3675 | − | 4.72810i | 0.610218 | − | 0.157081i | ||||
\(907\) | −16.6137 | − | 16.6137i | −0.551649 | − | 0.551649i | 0.375267 | − | 0.926917i | \(-0.377551\pi\) |
−0.926917 | + | 0.375267i | \(0.877551\pi\) | |||||||
\(908\) | 32.5681 | + | 9.41814i | 1.08081 | + | 0.312552i | ||||
\(909\) | −2.69382 | + | 2.69382i | −0.0893485 | + | 0.0893485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7299 | 1.34944 | 0.674721 | − | 0.738073i | \(-0.264264\pi\) | ||||
0.674721 | + | 0.738073i | \(0.264264\pi\) | |||||||
\(912\) | −65.0633 | − | 41.0646i | −2.15446 | − | 1.35978i | ||||
\(913\) | 6.52396 | 0.215912 | ||||||||
\(914\) | 10.9739 | + | 6.48079i | 0.362985 | + | 0.214365i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15.8697 | + | 54.8777i | −0.524351 | + | 1.81321i | ||||
\(917\) | 11.9846 | + | 11.9846i | 0.395765 | + | 0.395765i | ||||
\(918\) | −3.62742 | + | 0.933760i | −0.119723 | + | 0.0308187i | ||||
\(919\) | 35.6125i | 1.17475i | 0.809316 | + | 0.587373i | \(0.199838\pi\) | ||||
−0.809316 | + | 0.587373i | \(0.800162\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.4064i | 1.39734i | ||||||||
\(922\) | −11.3800 | − | 44.2083i | −0.374779 | − | 1.45592i | ||||
\(923\) | −17.7560 | − | 17.7560i | −0.584446 | − | 0.584446i | ||||
\(924\) | 36.0901 | − | 19.8990i | 1.18728 | − | 0.654628i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.68038 | − | 4.53869i | 0.0880828 | − | 0.149151i | ||||
\(927\) | 21.0369 | 0.690942 | ||||||||
\(928\) | −49.1836 | − | 15.8124i | −1.61453 | − | 0.519067i | ||||
\(929\) | −0.570971 | −0.0187329 | −0.00936647 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936647 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.1199 | + | 20.1199i | −0.659404 | + | 0.659404i | ||||
\(932\) | 17.6288 | − | 9.72000i | 0.577451 | − | 0.318389i | ||||
\(933\) | −19.8994 | − | 19.8994i | −0.651477 | − | 0.651477i | ||||
\(934\) | 1.61279 | + | 6.26529i | 0.0527722 | + | 0.205007i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.3638 | − | 14.1780i | −0.436808 | − | 0.463424i | ||||
\(937\) | 21.3585i | 0.697750i | 0.937169 | + | 0.348875i | \(0.113436\pi\) | ||||
−0.937169 | + | 0.348875i | \(0.886564\pi\) | |||||||
\(938\) | −13.5601 | + | 3.49060i | −0.442753 | + | 0.113972i | ||||
\(939\) | −57.2830 | − | 57.2830i | −1.86936 | − | 1.86936i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.6914 | − | 33.6914i | 1.09831 | − | 1.09831i | 0.103700 | − | 0.994609i | \(-0.466932\pi\) |
0.994609 | − | 0.103700i | \(-0.0330681\pi\) | |||||||
\(942\) | −10.1090 | − | 5.96999i | −0.329369 | − | 0.194513i | ||||
\(943\) | 7.18358 | 0.233929 | ||||||||
\(944\) | −37.7630 | + | 8.53937i | −1.22908 | + | 0.277933i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.66438 | + | 3.93573i | 0.216678 | + | 0.127962i | ||||
\(947\) | −0.421834 | + | 0.421834i | −0.0137078 | + | 0.0137078i | −0.713927 | − | 0.700220i | \(-0.753085\pi\) |
0.700220 | + | 0.713927i | \(0.253085\pi\) | |||||||
\(948\) | −13.9382 | − | 4.03071i | −0.452693 | − | 0.130911i | ||||
\(949\) | −1.68420 | − | 1.68420i | −0.0546714 | − | 0.0546714i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 57.0771i | − | 1.85085i | ||||||
\(952\) | 0.402742 | − | 13.6220i | 0.0130529 | − | 0.441492i | ||||
\(953\) | 27.7261i | 0.898137i | 0.893497 | + | 0.449069i | \(0.148244\pi\) | ||||
−0.893497 | + | 0.449069i | \(0.851756\pi\) | |||||||
\(954\) | 8.91067 | + | 34.6157i | 0.288493 | + | 1.12072i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.958726 | − | 1.73881i | −0.0310074 | − | 0.0562371i | ||||
\(957\) | −71.0204 | + | 71.0204i | −2.29576 | + | 2.29576i | ||||
\(958\) | 7.95625 | − | 13.4723i | 0.257055 | − | 0.435271i | ||||
\(959\) | −20.1156 | −0.649567 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3614 | −0.979399 | ||||||||
\(962\) | −7.36972 | + | 12.4792i | −0.237609 | + | 0.402344i | ||||
\(963\) | −7.32450 | + | 7.32450i | −0.236029 | + | 0.236029i | ||||
\(964\) | −13.6382 | − | 24.7352i | −0.439257 | − | 0.796666i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −11.8192 | − | 45.9147i | −0.380277 | − | 1.47728i | ||||
\(967\) | 41.9640i | 1.34947i | 0.738060 | + | 0.674735i | \(0.235742\pi\) | ||||
−0.738060 | + | 0.674735i | \(0.764258\pi\) | |||||||
\(968\) | −0.897709 | + | 30.3634i | −0.0288534 | + | 0.975916i | ||||
\(969\) | 49.4614i | 1.58893i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0549 | + | 30.0549i | 0.964508 | + | 0.964508i | 0.999391 | − | 0.0348833i | \(-0.0111059\pi\) |
−0.0348833 | + | 0.999391i | \(0.511106\pi\) | |||||||
\(972\) | −39.9208 | − | 11.5444i | −1.28046 | − | 0.370287i | ||||
\(973\) | −4.32990 | + | 4.32990i | −0.138810 | + | 0.138810i | ||||
\(974\) | −8.13651 | − | 4.80511i | −0.260710 | − | 0.153966i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.57468 | − | 37.9192i | −0.274469 | − | 1.21376i | ||||
\(977\) | 44.3389 | 1.41853 | 0.709263 | − | 0.704944i | \(-0.249028\pi\) | ||||
0.709263 | + | 0.704944i | \(0.249028\pi\) | |||||||
\(978\) | 51.6229 | + | 30.4866i | 1.65072 | + | 0.974853i | ||||
\(979\) | 33.2800 | − | 33.2800i | 1.06363 | − | 1.06363i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.1539 | + | 29.1539i | 0.930814 | + | 0.930814i | ||||
\(982\) | 35.6913 | − | 9.18755i | 1.13896 | − | 0.293186i | ||||
\(983\) | 27.0764i | 0.863604i | 0.901968 | + | 0.431802i | \(0.142122\pi\) | ||||
−0.901968 | + | 0.431802i | \(0.857878\pi\) | |||||||
\(984\) | 4.33327 | + | 4.59731i | 0.138140 | + | 0.146557i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.27955 | + | 32.1639i | 0.263674 | + | 1.02431i | ||||
\(987\) | −4.76323 | − | 4.76323i | −0.151615 | − | 0.151615i | ||||
\(988\) | 38.3819 | − | 21.1626i | 1.22109 | − | 0.673272i | ||||
\(989\) | 6.29606 | − | 6.29606i | 0.200203 | − | 0.200203i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.3780 | 0.615564 | 0.307782 | − | 0.951457i | \(-0.400413\pi\) | ||||
0.307782 | + | 0.951457i | \(0.400413\pi\) | |||||||
\(992\) | 2.06477 | + | 4.02150i | 0.0655567 | + | 0.127683i | ||||
\(993\) | 32.6977 | 1.03763 | ||||||||
\(994\) | 12.5909 | − | 21.3202i | 0.399360 | − | 0.676236i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.78017 | − | 3.18701i | 0.183152 | − | 0.100984i | ||||
\(997\) | 8.69453 | + | 8.69453i | 0.275359 | + | 0.275359i | 0.831253 | − | 0.555894i | \(-0.187624\pi\) |
−0.555894 | + | 0.831253i | \(0.687624\pi\) | |||||||
\(998\) | 4.41051 | + | 17.1337i | 0.139612 | + | 0.542359i | ||||
\(999\) | 3.92782i | 0.124271i |
(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 | 400.2.l.f.101.3 | ✓ | 12 | |
4.3 | odd | 2 | 1600.2.l.g.1201.1 | 12 | |||
5.2 | odd | 4 | 400.2.q.e.149.2 | 12 | |||
5.3 | odd | 4 | 400.2.q.f.149.5 | 12 | |||
5.4 | even | 2 | 400.2.l.g.101.4 | yes | 12 | ||
16.3 | odd | 4 | 1600.2.l.g.401.1 | 12 | |||
16.13 | even | 4 | inner | 400.2.l.f.301.3 | yes | 12 | |
20.3 | even | 4 | 1600.2.q.f.49.1 | 12 | |||
20.7 | even | 4 | 1600.2.q.e.49.6 | 12 | |||
20.19 | odd | 2 | 1600.2.l.f.1201.6 | 12 | |||
80.3 | even | 4 | 1600.2.q.e.849.6 | 12 | |||
80.13 | odd | 4 | 400.2.q.e.349.2 | 12 | |||
80.19 | odd | 4 | 1600.2.l.f.401.6 | 12 | |||
80.29 | even | 4 | 400.2.l.g.301.4 | yes | 12 | ||
80.67 | even | 4 | 1600.2.q.f.849.1 | 12 | |||
80.77 | odd | 4 | 400.2.q.f.349.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
400.2.l.f.301.3 | yes | 12 | 16.13 | even | 4 | inner | |
400.2.l.g.101.4 | yes | 12 | 5.4 | even | 2 | ||
400.2.l.g.301.4 | yes | 12 | 80.29 | even | 4 | ||
400.2.q.e.149.2 | 12 | 5.2 | odd | 4 | |||
400.2.q.e.349.2 | 12 | 80.13 | odd | 4 | |||
400.2.q.f.149.5 | 12 | 5.3 | odd | 4 | |||
400.2.q.f.349.5 | 12 | 80.77 | odd | 4 | |||
1600.2.l.f.401.6 | 12 | 80.19 | odd | 4 | |||
1600.2.l.f.1201.6 | 12 | 20.19 | odd | 2 | |||
1600.2.l.g.401.1 | 12 | 16.3 | odd | 4 | |||
1600.2.l.g.1201.1 | 12 | 4.3 | odd | 2 | |||
1600.2.q.e.49.6 | 12 | 20.7 | even | 4 | |||
1600.2.q.e.849.6 | 12 | 80.3 | even | 4 | |||
1600.2.q.f.49.1 | 12 | 20.3 | even | 4 | |||
1600.2.q.f.849.1 | 12 | 80.67 | even | 4 |