Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (of order \(6\), 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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 18 x^{13} + 143 x^{12} - 148 x^{11} + 172 x^{10} + 1612 x^{9} + \cdots + 97344 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.4 | ||
Root | \(1.15585 + 1.15585i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.i.127.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 3.62374i | 1.62059i | 0.586025 | + | 0.810293i | \(0.300692\pi\) | ||||
−0.586025 | + | 0.810293i | \(0.699308\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.81187 | − | 3.13825i | 0.572964 | − | 0.992402i | ||||
\(11\) | 1.74589 | + | 1.00799i | 0.526406 | + | 0.303920i | 0.739551 | − | 0.673100i | \(-0.235038\pi\) |
−0.213146 | + | 0.977020i | \(0.568371\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.59505 | + | 0.275040i | 0.997086 | + | 0.0762824i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.79054 | + | 6.56541i | 0.919341 | + | 1.59235i | 0.800418 | + | 0.599442i | \(0.204611\pi\) |
0.118923 | + | 0.992904i | \(0.462056\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.40547 | − | 1.38880i | 0.551853 | − | 0.318613i | −0.198016 | − | 0.980199i | \(-0.563450\pi\) |
0.749869 | + | 0.661586i | \(0.230116\pi\) | |||||||
\(20\) | −3.13825 | + | 1.81187i | −0.701734 | + | 0.405147i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00799 | − | 1.74589i | −0.214904 | − | 0.372225i | ||||
\(23\) | 3.95583 | − | 6.85169i | 0.824847 | − | 1.42868i | −0.0771895 | − | 0.997016i | \(-0.524595\pi\) |
0.902036 | − | 0.431660i | \(-0.142072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.13150 | −1.62630 | ||||||||
\(26\) | −2.97588 | − | 2.03571i | −0.583618 | − | 0.399236i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.866025 | − | 0.500000i | −0.163663 | − | 0.0944911i | ||||
\(29\) | −2.83454 | + | 4.90957i | −0.526361 | + | 0.911684i | 0.473167 | + | 0.880973i | \(0.343111\pi\) |
−0.999528 | + | 0.0307115i | \(0.990223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.83236i | − | 1.04752i | −0.851865 | − | 0.523762i | \(-0.824528\pi\) | ||
0.851865 | − | 0.523762i | \(-0.175472\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 7.58108i | − | 1.30014i | ||||||
\(35\) | −1.81187 | − | 3.13825i | −0.306262 | − | 0.530461i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.48866 | − | 0.859480i | −0.244735 | − | 0.141298i | 0.372616 | − | 0.927986i | \(-0.378461\pi\) |
−0.617351 | + | 0.786688i | \(0.711794\pi\) | |||||||
\(38\) | −2.77760 | −0.450586 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.62374 | 0.572964 | ||||||||
\(41\) | 10.0684 | + | 5.81297i | 1.57241 | + | 0.907834i | 0.995872 | + | 0.0907662i | \(0.0289316\pi\) |
0.576542 | + | 0.817068i | \(0.304402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63741 | + | 4.56813i | 0.402201 | + | 0.696633i | 0.993991 | − | 0.109459i | \(-0.0349119\pi\) |
−0.591790 | + | 0.806092i | \(0.701579\pi\) | |||||||
\(44\) | 2.01598i | 0.303920i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.85169 | + | 3.95583i | −1.01023 | + | 0.583255i | ||||
\(47\) | 5.63658i | 0.822180i | 0.911595 | + | 0.411090i | \(0.134852\pi\) | ||||
−0.911595 | + | 0.411090i | \(0.865148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 7.04209 | + | 4.06575i | 0.995901 | + | 0.574984i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.55933 | + | 3.25092i | 0.216240 | + | 0.450822i | ||||
\(53\) | −0.0731130 | −0.0100428 | −0.00502142 | − | 0.999987i | \(-0.501598\pi\) | ||||
−0.00502142 | + | 0.999987i | \(0.501598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.65269 | + | 6.32665i | −0.492529 | + | 0.853086i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.90957 | − | 2.83454i | 0.644658 | − | 0.372194i | ||||
\(59\) | −1.15686 | + | 0.667915i | −0.150611 | + | 0.0869551i | −0.573411 | − | 0.819268i | \(-0.694380\pi\) |
0.422801 | + | 0.906223i | \(0.361047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.187787 | + | 0.325257i | 0.0240437 | + | 0.0416449i | 0.877797 | − | 0.479033i | \(-0.159013\pi\) |
−0.853753 | + | 0.520678i | \(0.825679\pi\) | |||||||
\(62\) | −2.91618 | + | 5.05098i | −0.370356 | + | 0.641475i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.996674 | + | 13.0275i | −0.123622 | + | 1.61586i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3907 | − | 7.15378i | −1.51377 | − | 0.873973i | −0.999870 | − | 0.0161201i | \(-0.994869\pi\) |
−0.513895 | − | 0.857853i | \(-0.671798\pi\) | |||||||
\(68\) | −3.79054 | + | 6.56541i | −0.459670 | + | 0.796173i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.62374i | 0.433120i | ||||||||
\(71\) | −11.0728 | + | 6.39291i | −1.31410 | + | 0.758698i | −0.982773 | − | 0.184816i | \(-0.940831\pi\) |
−0.331331 | + | 0.943515i | \(0.607498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.80070i | − | 0.561880i | −0.959725 | − | 0.280940i | \(-0.909354\pi\) | ||
0.959725 | − | 0.280940i | \(-0.0906462\pi\) | |||||||
\(74\) | 0.859480 | + | 1.48866i | 0.0999125 | + | 0.173053i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.40547 | + | 1.38880i | 0.275927 | + | 0.159306i | ||||
\(77\) | −2.01598 | −0.229742 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1368 | 1.14048 | 0.570241 | − | 0.821477i | \(-0.306850\pi\) | ||||
0.570241 | + | 0.821477i | \(0.306850\pi\) | |||||||
\(80\) | −3.13825 | − | 1.81187i | −0.350867 | − | 0.202573i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.81297 | − | 10.0684i | −0.641935 | − | 1.11186i | ||||
\(83\) | − | 1.97093i | − | 0.216338i | −0.994133 | − | 0.108169i | \(-0.965501\pi\) | ||
0.994133 | − | 0.108169i | \(-0.0344987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.7913 | + | 13.7359i | −2.58053 | + | 1.48987i | ||||
\(86\) | − | 5.27482i | − | 0.568798i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00799 | − | 1.74589i | 0.107452 | − | 0.186112i | ||||
\(89\) | −11.8252 | − | 6.82727i | −1.25347 | − | 0.723689i | −0.281670 | − | 0.959511i | \(-0.590888\pi\) |
−0.971796 | + | 0.235823i | \(0.924222\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25092 | + | 1.55933i | −0.340789 | + | 0.163462i | ||||
\(92\) | 7.91165 | 0.824847 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.81829 | − | 4.88142i | 0.290684 | − | 0.503480i | ||||
\(95\) | 5.03265 | + | 8.71681i | 0.516339 | + | 0.894326i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6356 | + | 7.87254i | −1.38449 | + | 0.799336i | −0.992687 | − | 0.120714i | \(-0.961482\pi\) |
−0.391802 | + | 0.920049i | \(0.628148\pi\) | |||||||
\(98\) | −0.866025 | + | 0.500000i | −0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.06575 | − | 7.04209i | −0.406575 | − | 0.704209i | ||||
\(101\) | −0.160081 | + | 0.277268i | −0.0159286 | + | 0.0275892i | −0.873880 | − | 0.486142i | \(-0.838404\pi\) |
0.857951 | + | 0.513731i | \(0.171737\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.139970 | −0.0137917 | −0.00689583 | − | 0.999976i | \(-0.502195\pi\) | ||||
−0.00689583 | + | 0.999976i | \(0.502195\pi\) | |||||||
\(104\) | 0.275040 | − | 3.59505i | 0.0269699 | − | 0.352523i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0633177 | + | 0.0365565i | 0.00614996 | + | 0.00355068i | ||||
\(107\) | 0.690440 | − | 1.19588i | 0.0667474 | − | 0.115610i | −0.830720 | − | 0.556690i | \(-0.812071\pi\) |
0.897468 | + | 0.441080i | \(0.145405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.13642i | 0.300415i | 0.988655 | + | 0.150207i | \(0.0479941\pi\) | ||||
−0.988655 | + | 0.150207i | \(0.952006\pi\) | |||||||
\(110\) | 6.32665 | − | 3.65269i | 0.603223 | − | 0.348271i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 6.23703 | + | 10.8029i | 0.586731 | + | 1.01625i | 0.994657 | + | 0.103233i | \(0.0329186\pi\) |
−0.407927 | + | 0.913015i | \(0.633748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.8288 | + | 14.3349i | 2.31529 | + | 1.33674i | ||||
\(116\) | −5.66908 | −0.526361 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.33583 | 0.122973 | ||||||||
\(119\) | −6.56541 | − | 3.79054i | −0.601850 | − | 0.347478i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.46791 | − | 6.00660i | −0.315265 | − | 0.546055i | ||||
\(122\) | − | 0.375574i | − | 0.0340029i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.05098 | − | 2.91618i | 0.453591 | − | 0.261881i | ||||
\(125\) | − | 11.3477i | − | 1.01497i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04409 | + | 5.27252i | −0.270119 | + | 0.467861i | −0.968892 | − | 0.247483i | \(-0.920397\pi\) |
0.698773 | + | 0.715344i | \(0.253730\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.37690 | − | 10.7838i | 0.646997 | − | 0.945804i | ||||
\(131\) | −4.04885 | −0.353749 | −0.176875 | − | 0.984233i | \(-0.556599\pi\) | ||||
−0.176875 | + | 0.984233i | \(0.556599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.38880 | + | 2.40547i | −0.120424 | + | 0.208581i | ||||
\(134\) | 7.15378 | + | 12.3907i | 0.617992 | + | 1.07039i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.56541 | − | 3.79054i | 0.562979 | − | 0.325036i | ||||
\(137\) | −7.38057 | + | 4.26117i | −0.630565 | + | 0.364057i | −0.780971 | − | 0.624568i | \(-0.785275\pi\) |
0.150406 | + | 0.988624i | \(0.451942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.60631 | + | 16.6386i | 0.814797 | + | 1.41127i | 0.909474 | + | 0.415761i | \(0.136485\pi\) |
−0.0946772 | + | 0.995508i | \(0.530182\pi\) | |||||||
\(140\) | 1.81187 | − | 3.13825i | 0.153131 | − | 0.265231i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7858 | 1.07296 | ||||||||
\(143\) | 5.99932 | + | 4.10396i | 0.501688 | + | 0.343190i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.7910 | − | 10.2716i | −1.47746 | − | 0.853014i | ||||
\(146\) | −2.40035 | + | 4.15753i | −0.198655 | + | 0.344080i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.71896i | − | 0.141298i | ||||||
\(149\) | 0.132571 | − | 0.0765401i | 0.0108607 | − | 0.00627041i | −0.494560 | − | 0.869144i | \(-0.664671\pi\) |
0.505421 | + | 0.862873i | \(0.331337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7618i | 0.957159i | 0.878044 | + | 0.478580i | \(0.158848\pi\) | ||||
−0.878044 | + | 0.478580i | \(0.841152\pi\) | |||||||
\(152\) | −1.38880 | − | 2.40547i | −0.112647 | − | 0.195110i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.74589 | + | 1.00799i | 0.140688 | + | 0.0812261i | ||||
\(155\) | 21.1350 | 1.69760 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.5119 | 1.87645 | 0.938226 | − | 0.346024i | \(-0.112468\pi\) | ||||
0.938226 | + | 0.346024i | \(0.112468\pi\) | |||||||
\(158\) | −8.77875 | − | 5.06841i | −0.698400 | − | 0.403221i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.81187 | + | 3.13825i | 0.143241 | + | 0.248101i | ||||
\(161\) | 7.91165i | 0.623526i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0068 | − | 9.24154i | 1.25375 | − | 0.723853i | 0.281898 | − | 0.959444i | \(-0.409036\pi\) |
0.971852 | + | 0.235591i | \(0.0757026\pi\) | |||||||
\(164\) | 11.6259i | 0.907834i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.985464 | + | 1.70687i | −0.0764869 | + | 0.132479i | ||||
\(167\) | −11.5477 | − | 6.66706i | −0.893587 | − | 0.515912i | −0.0184727 | − | 0.999829i | \(-0.505880\pi\) |
−0.875114 | + | 0.483917i | \(0.839214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8487 | + | 1.97756i | 0.988362 | + | 0.152120i | ||||
\(170\) | 27.4719 | 2.10700 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.63741 | + | 4.56813i | −0.201101 | + | 0.348316i | ||||
\(173\) | −8.41536 | − | 14.5758i | −0.639808 | − | 1.10818i | −0.985475 | − | 0.169823i | \(-0.945681\pi\) |
0.345667 | − | 0.938357i | \(-0.387653\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.04209 | − | 4.06575i | 0.532332 | − | 0.307342i | ||||
\(176\) | −1.74589 | + | 1.00799i | −0.131601 | + | 0.0759801i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.82727 | + | 11.8252i | 0.511725 | + | 0.886334i | ||||
\(179\) | 5.44812 | − | 9.43642i | 0.407212 | − | 0.705311i | −0.587364 | − | 0.809323i | \(-0.699834\pi\) |
0.994576 | + | 0.104011i | \(0.0331678\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.4301 | 1.22124 | 0.610619 | − | 0.791924i | \(-0.290921\pi\) | ||||
0.610619 | + | 0.791924i | \(0.290921\pi\) | |||||||
\(182\) | 3.59505 | + | 0.275040i | 0.266483 | + | 0.0203873i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.85169 | − | 3.95583i | −0.505113 | − | 0.291627i | ||||
\(185\) | 3.11453 | − | 5.39453i | 0.228985 | − | 0.396613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.2833i | 1.11763i | ||||||||
\(188\) | −4.88142 | + | 2.81829i | −0.356014 | + | 0.205545i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 10.0653i | − | 0.730214i | ||||||
\(191\) | −3.49738 | − | 6.05765i | −0.253062 | − | 0.438316i | 0.711305 | − | 0.702883i | \(-0.248104\pi\) |
−0.964367 | + | 0.264567i | \(0.914771\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.67583 | + | 2.69959i | 0.336574 | + | 0.194321i | 0.658756 | − | 0.752357i | \(-0.271083\pi\) |
−0.322182 | + | 0.946678i | \(0.604416\pi\) | |||||||
\(194\) | 15.7451 | 1.13043 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.43204 | + | 1.98149i | 0.244523 | + | 0.141175i | 0.617254 | − | 0.786764i | \(-0.288245\pi\) |
−0.372731 | + | 0.927939i | \(0.621579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.7019 | − | 22.0004i | −0.900417 | − | 1.55957i | −0.826954 | − | 0.562270i | \(-0.809928\pi\) |
−0.0734626 | − | 0.997298i | \(-0.523405\pi\) | |||||||
\(200\) | 8.13150i | 0.574984i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.277268 | − | 0.160081i | 0.0195085 | − | 0.0112632i | ||||
\(203\) | − | 5.66908i | − | 0.397892i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.0647 | + | 36.4851i | −1.47122 | + | 2.54823i | ||||
\(206\) | 0.121218 | + | 0.0699850i | 0.00844563 | + | 0.00487609i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.03571 | + | 2.97588i | −0.141151 | + | 0.206340i | ||||
\(209\) | 5.59959 | 0.387331 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.10268 | + | 1.90990i | −0.0759118 | + | 0.131483i | −0.901482 | − | 0.432816i | \(-0.857520\pi\) |
0.825571 | + | 0.564299i | \(0.190853\pi\) | |||||||
\(212\) | −0.0365565 | − | 0.0633177i | −0.00251071 | − | 0.00434868i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.19588 | + | 0.690440i | −0.0817485 | + | 0.0471975i | ||||
\(215\) | −16.5537 | + | 9.55729i | −1.12895 | + | 0.651802i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.91618 | + | 5.05098i | 0.197963 | + | 0.342883i | ||||
\(218\) | 1.56821 | − | 2.71622i | 0.106213 | − | 0.183966i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.30539 | −0.492529 | ||||||||
\(221\) | 11.8214 | + | 24.6455i | 0.795194 | + | 1.65784i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.93739 | − | 4.58265i | −0.531527 | − | 0.306877i | 0.210111 | − | 0.977678i | \(-0.432617\pi\) |
−0.741638 | + | 0.670800i | \(0.765951\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.4741i | − | 0.829762i | ||||||
\(227\) | −8.63738 | + | 4.98679i | −0.573283 | + | 0.330985i | −0.758460 | − | 0.651720i | \(-0.774048\pi\) |
0.185176 | + | 0.982705i | \(0.440714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.30526i | − | 0.0862538i | −0.999070 | − | 0.0431269i | \(-0.986268\pi\) | ||
0.999070 | − | 0.0431269i | \(-0.0137320\pi\) | |||||||
\(230\) | −14.3349 | − | 24.8288i | −0.945215 | − | 1.63716i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.90957 | + | 2.83454i | 0.322329 | + | 0.186097i | ||||
\(233\) | −27.4165 | −1.79612 | −0.898058 | − | 0.439876i | \(-0.855022\pi\) | ||||
−0.898058 | + | 0.439876i | \(0.855022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.4255 | −1.33241 | ||||||||
\(236\) | −1.15686 | − | 0.667915i | −0.0753053 | − | 0.0434775i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.79054 | + | 6.56541i | 0.245704 | + | 0.425572i | ||||
\(239\) | − | 0.343121i | − | 0.0221946i | −0.999938 | − | 0.0110973i | \(-0.996468\pi\) | ||
0.999938 | − | 0.0110973i | \(-0.00353246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.39860 | − | 5.42628i | 0.605417 | − | 0.349538i | −0.165753 | − | 0.986167i | \(-0.553005\pi\) |
0.771170 | + | 0.636630i | \(0.219672\pi\) | |||||||
\(242\) | 6.93583i | 0.445852i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.187787 | + | 0.325257i | −0.0120218 | + | 0.0208224i | ||||
\(245\) | 3.13825 | + | 1.81187i | 0.200496 | + | 0.115756i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.02976 | − | 4.33120i | 0.574550 | − | 0.275588i | ||||
\(248\) | −5.83236 | −0.370356 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.67387 | + | 9.82744i | −0.358847 | + | 0.621542i | ||||
\(251\) | −2.26799 | − | 3.92828i | −0.143154 | − | 0.247951i | 0.785528 | − | 0.618826i | \(-0.212391\pi\) |
−0.928683 | + | 0.370875i | \(0.879058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8129 | − | 7.97487i | 0.868408 | − | 0.501376i | ||||
\(254\) | 5.27252 | − | 3.04409i | 0.330827 | − | 0.191003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 10.1494 | − | 17.5792i | 0.633101 | − | 1.09656i | −0.353813 | − | 0.935316i | \(-0.615115\pi\) |
0.986914 | − | 0.161247i | \(-0.0515515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.71896 | 0.106811 | ||||||||
\(260\) | −11.7805 | + | 5.65061i | −0.730595 | + | 0.350436i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.50640 | + | 2.02442i | 0.216626 | + | 0.125069i | ||||
\(263\) | 9.81314 | − | 16.9969i | 0.605104 | − | 1.04807i | −0.386931 | − | 0.922109i | \(-0.626465\pi\) |
0.992035 | − | 0.125962i | \(-0.0402019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.264942i | − | 0.0162753i | ||||||
\(266\) | 2.40547 | − | 1.38880i | 0.147489 | − | 0.0851528i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 14.3076i | − | 0.873973i | ||||||
\(269\) | 4.52417 | + | 7.83610i | 0.275844 | + | 0.477775i | 0.970348 | − | 0.241714i | \(-0.0777095\pi\) |
−0.694504 | + | 0.719489i | \(0.744376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6128 | + | 11.3234i | 1.19139 | + | 0.687850i | 0.958622 | − | 0.284682i | \(-0.0918880\pi\) |
0.232769 | + | 0.972532i | \(0.425221\pi\) | |||||||
\(272\) | −7.58108 | −0.459670 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.52235 | 0.514854 | ||||||||
\(275\) | −14.1967 | − | 8.19647i | −0.856093 | − | 0.494266i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5587 | − | 18.2881i | −0.634409 | − | 1.09883i | −0.986640 | − | 0.162915i | \(-0.947910\pi\) |
0.352231 | − | 0.935913i | \(-0.385423\pi\) | |||||||
\(278\) | − | 19.2126i | − | 1.15230i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.13825 | + | 1.81187i | −0.187546 | + | 0.108280i | ||||
\(281\) | 19.3644i | 1.15518i | 0.816325 | + | 0.577592i | \(0.196008\pi\) | ||||
−0.816325 | + | 0.577592i | \(0.803992\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.78361 | + | 4.82136i | −0.165469 | + | 0.286600i | −0.936822 | − | 0.349808i | \(-0.886247\pi\) |
0.771353 | + | 0.636407i | \(0.219580\pi\) | |||||||
\(284\) | −11.0728 | − | 6.39291i | −0.657052 | − | 0.379349i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.14358 | − | 6.55379i | −0.185884 | − | 0.387534i | ||||
\(287\) | −11.6259 | −0.686258 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.2364 | + | 35.0504i | −1.19038 | + | 2.06179i | ||||
\(290\) | 10.2716 | + | 17.7910i | 0.603172 | + | 1.04472i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.15753 | − | 2.40035i | 0.243301 | − | 0.140470i | ||||
\(293\) | 27.2323 | − | 15.7226i | 1.59093 | − | 0.918523i | 0.597781 | − | 0.801659i | \(-0.296049\pi\) |
0.993148 | − | 0.116864i | \(-0.0372841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.42035 | − | 4.19217i | −0.140918 | − | 0.244078i | ||||
\(296\) | −0.859480 | + | 1.48866i | −0.0499562 | + | 0.0865267i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.153080 | −0.00886770 | ||||||||
\(299\) | 16.1059 | − | 23.5441i | 0.931426 | − | 1.36159i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.56813 | − | 2.63741i | −0.263303 | − | 0.152018i | ||||
\(302\) | 5.88088 | − | 10.1860i | 0.338407 | − | 0.586138i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.77760i | 0.159306i | ||||||||
\(305\) | −1.17865 | + | 0.680492i | −0.0674891 | + | 0.0389648i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.6952i | − | 0.781626i | −0.920470 | − | 0.390813i | \(-0.872194\pi\) | ||
0.920470 | − | 0.390813i | \(-0.127806\pi\) | |||||||
\(308\) | −1.00799 | − | 1.74589i | −0.0574356 | − | 0.0994813i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.3034 | − | 10.5675i | −1.03956 | − | 0.600193i | ||||
\(311\) | 20.9665 | 1.18890 | 0.594451 | − | 0.804132i | \(-0.297369\pi\) | ||||
0.594451 | + | 0.804132i | \(0.297369\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2102 | −0.690163 | −0.345082 | − | 0.938573i | \(-0.612149\pi\) | ||||
−0.345082 | + | 0.938573i | \(0.612149\pi\) | |||||||
\(314\) | −20.3619 | − | 11.7559i | −1.14909 | − | 0.663426i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.06841 | + | 8.77875i | 0.285121 | + | 0.493843i | ||||
\(317\) | − | 12.5110i | − | 0.702686i | −0.936247 | − | 0.351343i | \(-0.885725\pi\) | ||
0.936247 | − | 0.351343i | \(-0.114275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.89759 | + | 5.71438i | −0.554159 | + | 0.319944i | ||||
\(320\) | − | 3.62374i | − | 0.202573i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.95583 | − | 6.85169i | 0.220450 | − | 0.381830i | ||||
\(323\) | 18.2361 | + | 10.5286i | 1.01468 | + | 0.585827i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −29.2331 | − | 2.23649i | −1.62156 | − | 0.124058i | ||||
\(326\) | −18.4831 | −1.02368 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.81297 | − | 10.0684i | 0.320968 | − | 0.555932i | ||||
\(329\) | −2.81829 | − | 4.88142i | −0.155377 | − | 0.269121i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.0473 | + | 10.9970i | −1.04693 | + | 0.604448i | −0.921790 | − | 0.387690i | \(-0.873273\pi\) |
−0.125145 | + | 0.992138i | \(0.539940\pi\) | |||||||
\(332\) | 1.70687 | − | 0.985464i | 0.0936769 | − | 0.0540844i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.66706 | + | 11.5477i | 0.364805 | + | 0.631861i | ||||
\(335\) | 25.9234 | − | 44.9007i | 1.41635 | − | 2.45319i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.58788 | 0.413338 | 0.206669 | − | 0.978411i | \(-0.433738\pi\) | ||||
0.206669 | + | 0.978411i | \(0.433738\pi\) | |||||||
\(338\) | −10.1385 | − | 8.13697i | −0.551463 | − | 0.442593i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.7913 | − | 13.7359i | −1.29027 | − | 0.744936i | ||||
\(341\) | 5.87896 | − | 10.1827i | 0.318364 | − | 0.551422i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 4.56813 | − | 2.63741i | 0.246297 | − | 0.142200i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.8307i | 0.904825i | ||||||||
\(347\) | −3.75725 | − | 6.50774i | −0.201700 | − | 0.349354i | 0.747377 | − | 0.664401i | \(-0.231313\pi\) |
−0.949076 | + | 0.315047i | \(0.897980\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.9831 | − | 11.5373i | −1.06967 | − | 0.617575i | −0.141580 | − | 0.989927i | \(-0.545218\pi\) |
−0.928092 | + | 0.372352i | \(0.878551\pi\) | |||||||
\(350\) | −8.13150 | −0.434647 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.01598 | 0.107452 | ||||||||
\(353\) | −30.2137 | − | 17.4439i | −1.60811 | − | 0.928443i | −0.989793 | − | 0.142515i | \(-0.954481\pi\) |
−0.618318 | − | 0.785928i | \(-0.712186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.1662 | − | 40.1251i | −1.22954 | − | 2.12962i | ||||
\(356\) | − | 13.6545i | − | 0.723689i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.43642 | + | 5.44812i | −0.498731 | + | 0.287942i | ||||
\(359\) | − | 4.29129i | − | 0.226486i | −0.993567 | − | 0.113243i | \(-0.963876\pi\) | ||
0.993567 | − | 0.113243i | \(-0.0361238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.64247 | + | 9.77304i | −0.296972 | + | 0.514371i | ||||
\(362\) | −14.2289 | − | 8.21504i | −0.747853 | − | 0.431773i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.97588 | − | 2.03571i | −0.155979 | − | 0.106700i | ||||
\(365\) | 17.3965 | 0.910575 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4286 | + | 21.5270i | −0.648767 | + | 1.12370i | 0.334650 | + | 0.942342i | \(0.391382\pi\) |
−0.983418 | + | 0.181356i | \(0.941951\pi\) | |||||||
\(368\) | 3.95583 | + | 6.85169i | 0.206212 | + | 0.357169i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.39453 | + | 3.11453i | −0.280448 | + | 0.161917i | ||||
\(371\) | 0.0633177 | − | 0.0365565i | 0.00328729 | − | 0.00189792i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.2705 | − | 29.9134i | −0.894233 | − | 1.54886i | −0.834750 | − | 0.550628i | \(-0.814388\pi\) |
−0.0594830 | − | 0.998229i | \(-0.518945\pi\) | |||||||
\(374\) | 7.64165 | − | 13.2357i | 0.395140 | − | 0.684403i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.63658 | 0.290684 | ||||||||
\(377\) | −11.5406 | + | 16.8705i | −0.594373 | + | 0.868876i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.5599 | + | 13.6023i | 1.21019 | + | 0.698704i | 0.962801 | − | 0.270211i | \(-0.0870936\pi\) |
0.247391 | + | 0.968916i | \(0.420427\pi\) | |||||||
\(380\) | −5.03265 | + | 8.71681i | −0.258170 | + | 0.447163i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.99477i | 0.357883i | ||||||||
\(383\) | −25.0615 | + | 14.4693i | −1.28058 | + | 0.739344i | −0.976955 | − | 0.213447i | \(-0.931531\pi\) |
−0.303627 | + | 0.952791i | \(0.598198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.30539i | − | 0.372317i | ||||||
\(386\) | −2.69959 | − | 4.67583i | −0.137406 | − | 0.237993i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.6356 | − | 7.87254i | −0.692245 | − | 0.399668i | ||||
\(389\) | 21.5418 | 1.09221 | 0.546106 | − | 0.837716i | \(-0.316109\pi\) | ||||
0.546106 | + | 0.837716i | \(0.316109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.9789 | 3.03326 | ||||||||
\(392\) | −0.866025 | − | 0.500000i | −0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.98149 | − | 3.43204i | −0.0998259 | − | 0.172904i | ||||
\(395\) | 36.7332i | 1.84825i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.96408 | − | 1.71131i | 0.148763 | − | 0.0858883i | −0.423771 | − | 0.905769i | \(-0.639294\pi\) |
0.572534 | + | 0.819881i | \(0.305960\pi\) | |||||||
\(398\) | 25.4039i | 1.27338i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.06575 | − | 7.04209i | 0.203288 | − | 0.352104i | ||||
\(401\) | 6.45616 | + | 3.72747i | 0.322405 | + | 0.186141i | 0.652464 | − | 0.757819i | \(-0.273735\pi\) |
−0.330059 | + | 0.943960i | \(0.607069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.60413 | − | 20.9676i | 0.0799076 | − | 1.04447i | ||||
\(404\) | −0.320161 | −0.0159286 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.83454 | + | 4.90957i | −0.140676 | + | 0.243658i | ||||
\(407\) | −1.73269 | − | 3.00111i | −0.0858864 | − | 0.148760i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.65842 | + | 3.26689i | −0.279791 | + | 0.161537i | −0.633329 | − | 0.773883i | \(-0.718312\pi\) |
0.353538 | + | 0.935420i | \(0.384979\pi\) | |||||||
\(410\) | 36.4851 | − | 21.0647i | 1.80187 | − | 1.04031i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.0699850 | − | 0.121218i | −0.00344791 | − | 0.00597196i | ||||
\(413\) | 0.667915 | − | 1.15686i | 0.0328659 | − | 0.0569255i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.14213 | 0.350594 | ||||||||
\(416\) | 3.25092 | − | 1.55933i | 0.159390 | − | 0.0764525i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.84938 | − | 2.79979i | −0.237191 | − | 0.136942i | ||||
\(419\) | −8.61309 | + | 14.9183i | −0.420777 | + | 0.728807i | −0.996016 | − | 0.0891785i | \(-0.971576\pi\) |
0.575239 | + | 0.817986i | \(0.304909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 2.95781i | − | 0.144155i | −0.997399 | − | 0.0720774i | \(-0.977037\pi\) | ||
0.997399 | − | 0.0720774i | \(-0.0229629\pi\) | |||||||
\(422\) | 1.90990 | − | 1.10268i | 0.0929726 | − | 0.0536777i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.0731130i | 0.00355068i | ||||||||
\(425\) | −30.8228 | − | 53.3866i | −1.49512 | − | 2.58963i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.325257 | − | 0.187787i | −0.0157403 | − | 0.00908765i | ||||
\(428\) | 1.38088 | 0.0667474 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.1146 | 0.921787 | ||||||||
\(431\) | −17.3358 | − | 10.0088i | −0.835037 | − | 0.482109i | 0.0205370 | − | 0.999789i | \(-0.493462\pi\) |
−0.855574 | + | 0.517680i | \(0.826796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.9433 | + | 29.3466i | 0.814241 | + | 1.41031i | 0.909872 | + | 0.414890i | \(0.136180\pi\) |
−0.0956311 | + | 0.995417i | \(0.530487\pi\) | |||||||
\(434\) | − | 5.83236i | − | 0.279962i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.71622 | + | 1.56821i | −0.130083 | + | 0.0751036i | ||||
\(437\) | − | 21.9754i | − | 1.05123i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.6418 | − | 23.6283i | 0.651089 | − | 1.12772i | −0.331770 | − | 0.943360i | \(-0.607646\pi\) |
0.982859 | − | 0.184359i | \(-0.0590209\pi\) | |||||||
\(440\) | 6.32665 | + | 3.65269i | 0.301611 | + | 0.174135i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.08510 | − | 27.2543i | 0.0991781 | − | 1.29636i | ||||
\(443\) | −3.73740 | −0.177569 | −0.0887845 | − | 0.996051i | \(-0.528298\pi\) | ||||
−0.0887845 | + | 0.996051i | \(0.528298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.7402 | − | 42.8514i | 1.17280 | − | 2.03135i | ||||
\(446\) | 4.58265 | + | 7.93739i | 0.216995 | + | 0.375846i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.866025 | − | 0.500000i | 0.0409159 | − | 0.0236228i | ||||
\(449\) | −2.67990 | + | 1.54724i | −0.126472 | + | 0.0730189i | −0.561901 | − | 0.827204i | \(-0.689930\pi\) |
0.435429 | + | 0.900223i | \(0.356597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.7188 | + | 20.2976i | 0.551818 | + | 0.955777i | ||||
\(452\) | −6.23703 | + | 10.8029i | −0.293365 | + | 0.508124i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.97359 | 0.468084 | ||||||||
\(455\) | −5.65061 | − | 11.7805i | −0.264905 | − | 0.552278i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4469 | + | 10.0730i | 0.816130 | + | 0.471193i | 0.849080 | − | 0.528264i | \(-0.177157\pi\) |
−0.0329500 | + | 0.999457i | \(0.510490\pi\) | |||||||
\(458\) | −0.652628 | + | 1.13039i | −0.0304953 | + | 0.0528194i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 28.6698i | 1.33674i | ||||||||
\(461\) | −25.0527 | + | 14.4642i | −1.16682 | + | 0.673665i | −0.952929 | − | 0.303192i | \(-0.901948\pi\) |
−0.213892 | + | 0.976857i | \(0.568614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.2704i | − | 1.26736i | −0.773594 | − | 0.633681i | \(-0.781543\pi\) | ||
0.773594 | − | 0.633681i | \(-0.218457\pi\) | |||||||
\(464\) | −2.83454 | − | 4.90957i | −0.131590 | − | 0.227921i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 23.7434 | + | 13.7083i | 1.09989 | + | 0.635023i | ||||
\(467\) | 15.5605 | 0.720055 | 0.360028 | − | 0.932942i | \(-0.382767\pi\) | ||||
0.360028 | + | 0.932942i | \(0.382767\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.3076 | 0.660661 | ||||||||
\(470\) | 17.6890 | + | 10.2128i | 0.815933 | + | 0.471079i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.667915 | + | 1.15686i | 0.0307433 | + | 0.0532489i | ||||
\(473\) | 10.6339i | 0.488949i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.5601 | + | 11.2930i | −0.897479 | + | 0.518160i | ||||
\(476\) | − | 7.58108i | − | 0.347478i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.171560 | + | 0.297151i | −0.00784699 | + | 0.0135914i | ||||
\(479\) | 32.3400 | + | 18.6715i | 1.47765 | + | 0.853122i | 0.999681 | − | 0.0252536i | \(-0.00803931\pi\) |
0.477970 | + | 0.878376i | \(0.341373\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.11542 | − | 3.49931i | −0.233243 | − | 0.159555i | ||||
\(482\) | −10.8526 | −0.494321 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.46791 | − | 6.00660i | 0.157632 | − | 0.273027i | ||||
\(485\) | −28.5281 | − | 49.4120i | −1.29539 | − | 2.24369i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6297 | − | 13.6426i | 1.07076 | − | 0.618205i | 0.142373 | − | 0.989813i | \(-0.454527\pi\) |
0.928390 | + | 0.371608i | \(0.121194\pi\) | |||||||
\(488\) | 0.325257 | − | 0.187787i | 0.0147237 | − | 0.00850072i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.81187 | − | 3.13825i | −0.0818520 | − | 0.141772i | ||||
\(491\) | −10.3161 | + | 17.8680i | −0.465559 | + | 0.806373i | −0.999227 | − | 0.0393220i | \(-0.987480\pi\) |
0.533667 | + | 0.845695i | \(0.320814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.9778 | −1.93562 | ||||||||
\(494\) | −9.98560 | − | 0.763951i | −0.449273 | − | 0.0343718i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.05098 | + | 2.91618i | 0.226796 | + | 0.130940i | ||||
\(497\) | 6.39291 | − | 11.0728i | 0.286761 | − | 0.496685i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9558i | 0.848580i | 0.905526 | + | 0.424290i | \(0.139476\pi\) | ||||
−0.905526 | + | 0.424290i | \(0.860524\pi\) | |||||||
\(500\) | 9.82744 | − | 5.67387i | 0.439496 | − | 0.253743i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.53598i | 0.202451i | ||||||||
\(503\) | −7.30193 | − | 12.6473i | −0.325577 | − | 0.563916i | 0.656052 | − | 0.754716i | \(-0.272225\pi\) |
−0.981629 | + | 0.190800i | \(0.938892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00475 | − | 0.580091i | −0.0447106 | − | 0.0258137i | ||||
\(506\) | −15.9497 | −0.709052 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.08818 | −0.270119 | ||||||||
\(509\) | −26.0537 | − | 15.0421i | −1.15481 | − | 0.666730i | −0.204756 | − | 0.978813i | \(-0.565640\pi\) |
−0.950055 | + | 0.312083i | \(0.898973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.40035 | + | 4.15753i | 0.106185 | + | 0.183918i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.5792 | + | 10.1494i | −0.775387 | + | 0.447670i | ||||
\(515\) | − | 0.507215i | − | 0.0223506i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.68161 | + | 9.84085i | −0.249877 | + | 0.432800i | ||||
\(518\) | −1.48866 | − | 0.859480i | −0.0654081 | − | 0.0377634i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.0275 | + | 0.996674i | 0.571294 | + | 0.0437070i | ||||
\(521\) | 3.62407 | 0.158773 | 0.0793867 | − | 0.996844i | \(-0.474704\pi\) | ||||
0.0793867 | + | 0.996844i | \(0.474704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0474 | − | 22.5988i | 0.570523 | − | 0.988174i | −0.425989 | − | 0.904728i | \(-0.640074\pi\) |
0.996512 | − | 0.0834464i | \(-0.0265927\pi\) | |||||||
\(524\) | −2.02442 | − | 3.50640i | −0.0884374 | − | 0.153178i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.9969 | + | 9.81314i | −0.741098 | + | 0.427873i | ||||
\(527\) | 38.2919 | − | 22.1078i | 1.66802 | − | 0.963031i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7971 | − | 34.2896i | −0.860745 | − | 1.49085i | ||||
\(530\) | −0.132471 | + | 0.229447i | −0.00575418 | + | 0.00996654i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.77760 | −0.120424 | ||||||||
\(533\) | 34.5974 | + | 23.6671i | 1.49858 | + | 1.02514i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.33355 | + | 2.50198i | 0.187356 | + | 0.108170i | ||||
\(536\) | −7.15378 | + | 12.3907i | −0.308996 | + | 0.535197i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.04835i | − | 0.390102i | ||||||
\(539\) | 1.74589 | − | 1.00799i | 0.0752008 | − | 0.0434172i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.1512i | 0.436436i | 0.975900 | + | 0.218218i | \(0.0700243\pi\) | ||||
−0.975900 | + | 0.218218i | \(0.929976\pi\) | |||||||
\(542\) | −11.3234 | − | 19.6128i | −0.486383 | − | 0.842441i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.56541 | + | 3.79054i | 0.281490 | + | 0.162518i | ||||
\(545\) | −11.3656 | −0.486848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9605 | 1.28102 | 0.640509 | − | 0.767950i | \(-0.278723\pi\) | ||||
0.640509 | + | 0.767950i | \(0.278723\pi\) | |||||||
\(548\) | −7.38057 | − | 4.26117i | −0.315282 | − | 0.182028i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.19647 | + | 14.1967i | 0.349499 | + | 0.605349i | ||||
\(551\) | 15.7464i | 0.670821i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.77875 | + | 5.06841i | −0.373310 | + | 0.215531i | ||||
\(554\) | 21.1173i | 0.897189i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.60631 | + | 16.6386i | −0.407398 | + | 0.705635i | ||||
\(557\) | 3.62112 | + | 2.09066i | 0.153432 | + | 0.0885839i | 0.574750 | − | 0.818329i | \(-0.305099\pi\) |
−0.421318 | + | 0.906913i | \(0.638433\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.22519 | + | 17.1480i | 0.347889 | + | 0.725284i | ||||
\(560\) | 3.62374 | 0.153131 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.68221 | − | 16.7701i | 0.408419 | − | 0.707403i | ||||
\(563\) | 13.4183 | + | 23.2412i | 0.565514 | + | 0.979498i | 0.997002 | + | 0.0773798i | \(0.0246554\pi\) |
−0.431488 | + | 0.902119i | \(0.642011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.1468 | + | 22.6014i | −1.64692 | + | 0.950848i | ||||
\(566\) | 4.82136 | − | 2.78361i | 0.202657 | − | 0.117004i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.39291 | + | 11.0728i | 0.268240 | + | 0.464606i | ||||
\(569\) | −7.77089 | + | 13.4596i | −0.325773 | + | 0.564255i | −0.981668 | − | 0.190597i | \(-0.938958\pi\) |
0.655896 | + | 0.754851i | \(0.272291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.3351 | 1.98091 | 0.990457 | − | 0.137825i | \(-0.0440112\pi\) | ||||
0.990457 | + | 0.137825i | \(0.0440112\pi\) | |||||||
\(572\) | −0.554475 | + | 7.24754i | −0.0231838 | + | 0.303035i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.0684 | + | 5.81297i | 0.420245 | + | 0.242629i | ||||
\(575\) | −32.1668 | + | 55.7145i | −1.34145 | + | 2.32346i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.85520i | − | 0.0772330i | −0.999254 | − | 0.0386165i | \(-0.987705\pi\) | ||
0.999254 | − | 0.0386165i | \(-0.0122951\pi\) | |||||||
\(578\) | 35.0504 | − | 20.2364i | 1.45791 | − | 0.841723i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 20.5433i | − | 0.853014i | ||||||
\(581\) | 0.985464 | + | 1.70687i | 0.0408839 | + | 0.0708131i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.127647 | − | 0.0736971i | −0.00528661 | − | 0.00305222i | ||||
\(584\) | −4.80070 | −0.198655 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.4452 | −1.29899 | ||||||||
\(587\) | −3.73652 | − | 2.15728i | −0.154223 | − | 0.0890405i | 0.420903 | − | 0.907106i | \(-0.361713\pi\) |
−0.575125 | + | 0.818065i | \(0.695047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.09999 | − | 14.0296i | −0.333754 | − | 0.578079i | ||||
\(590\) | 4.84070i | 0.199288i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.48866 | − | 0.859480i | 0.0611836 | − | 0.0353244i | ||||
\(593\) | 13.8068i | 0.566979i | 0.958975 | + | 0.283490i | \(0.0914921\pi\) | ||||
−0.958975 | + | 0.283490i | \(0.908508\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.7359 | − | 23.7913i | 0.563118 | − | 0.975350i | ||||
\(596\) | 0.132571 | + | 0.0765401i | 0.00543034 | + | 0.00313521i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.7202 | + | 12.3369i | −1.05178 | + | 0.504493i | ||||
\(599\) | 19.0317 | 0.777612 | 0.388806 | − | 0.921320i | \(-0.372888\pi\) | ||||
0.388806 | + | 0.921320i | \(0.372888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.20400 | − | 12.4777i | 0.293857 | − | 0.508975i | −0.680861 | − | 0.732412i | \(-0.738394\pi\) |
0.974718 | + | 0.223437i | \(0.0717277\pi\) | |||||||
\(602\) | 2.63741 | + | 4.56813i | 0.107493 | + | 0.186183i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.1860 | + | 5.88088i | −0.414462 | + | 0.239290i | ||||
\(605\) | 21.7664 | − | 12.5668i | 0.884929 | − | 0.510914i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1587 | − | 33.1839i | −0.777629 | − | 1.34689i | −0.933305 | − | 0.359085i | \(-0.883089\pi\) |
0.155676 | − | 0.987808i | \(-0.450244\pi\) | |||||||
\(608\) | 1.38880 | − | 2.40547i | 0.0563233 | − | 0.0975548i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.36098 | 0.0551046 | ||||||||
\(611\) | −1.55029 | + | 20.2638i | −0.0627178 | + | 0.819784i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.7425 | − | 14.2851i | −0.999339 | − | 0.576968i | −0.0912860 | − | 0.995825i | \(-0.529098\pi\) |
−0.908053 | + | 0.418856i | \(0.862431\pi\) | |||||||
\(614\) | −6.84760 | + | 11.8604i | −0.276346 | + | 0.478646i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.01598i | 0.0812261i | ||||||||
\(617\) | −2.64638 | + | 1.52789i | −0.106539 | + | 0.0615105i | −0.552323 | − | 0.833630i | \(-0.686258\pi\) |
0.445784 | + | 0.895141i | \(0.352925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.2175i | − | 1.61648i | −0.588856 | − | 0.808238i | \(-0.700421\pi\) | ||
0.588856 | − | 0.808238i | \(-0.299579\pi\) | |||||||
\(620\) | 10.5675 | + | 18.3034i | 0.424401 | + | 0.735083i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.1575 | − | 10.4833i | −0.728051 | − | 0.420341i | ||||
\(623\) | 13.6545 | 0.547057 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.463794 | 0.0185518 | ||||||||
\(626\) | 10.5744 | + | 6.10512i | 0.422637 | + | 0.244010i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.7559 | + | 20.3619i | 0.469113 | + | 0.812527i | ||||
\(629\) | − | 13.0316i | − | 0.519603i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.7571 | − | 7.94266i | 0.547661 | − | 0.316192i | −0.200517 | − | 0.979690i | \(-0.564262\pi\) |
0.748178 | + | 0.663498i | \(0.230929\pi\) | |||||||
\(632\) | − | 10.1368i | − | 0.403221i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.25548 | + | 10.8348i | −0.248437 | + | 0.430305i | ||||
\(635\) | −19.1063 | − | 11.0310i | −0.758208 | − | 0.437752i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.03571 | − | 2.97588i | 0.0806579 | − | 0.117909i | ||||
\(638\) | 11.4288 | 0.452469 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.81187 | + | 3.13825i | −0.0716205 | + | 0.124050i | ||||
\(641\) | 5.52325 | + | 9.56655i | 0.218155 | + | 0.377856i | 0.954244 | − | 0.299029i | \(-0.0966628\pi\) |
−0.736089 | + | 0.676885i | \(0.763329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.24600 | + | 0.719378i | −0.0491374 | + | 0.0283695i | −0.524367 | − | 0.851492i | \(-0.675698\pi\) |
0.475230 | + | 0.879862i | \(0.342365\pi\) | |||||||
\(644\) | −6.85169 | + | 3.95583i | −0.269995 | + | 0.155881i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.5286 | − | 18.2361i | −0.414242 | − | 0.717489i | ||||
\(647\) | 10.6562 | − | 18.4571i | 0.418940 | − | 0.725625i | −0.576894 | − | 0.816819i | \(-0.695735\pi\) |
0.995833 | + | 0.0911948i | \(0.0290686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.69301 | −0.105710 | ||||||||
\(650\) | 24.1984 | + | 16.5534i | 0.949138 | + | 0.649278i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.0068 | + | 9.24154i | 0.626875 | + | 0.361927i | ||||
\(653\) | 15.5822 | − | 26.9891i | 0.609778 | − | 1.05617i | −0.381499 | − | 0.924369i | \(-0.624592\pi\) |
0.991277 | − | 0.131797i | \(-0.0420746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14.6720i | − | 0.573281i | ||||||
\(656\) | −10.0684 | + | 5.81297i | −0.393104 | + | 0.226958i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.63658i | 0.219737i | ||||||||
\(659\) | −11.9888 | − | 20.7653i | −0.467019 | − | 0.808901i | 0.532271 | − | 0.846574i | \(-0.321339\pi\) |
−0.999290 | + | 0.0376733i | \(0.988005\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.12358 | − | 2.95810i | −0.199284 | − | 0.115057i | 0.397037 | − | 0.917802i | \(-0.370038\pi\) |
−0.596322 | + | 0.802746i | \(0.703372\pi\) | |||||||
\(662\) | 21.9939 | 0.854819 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.97093 | −0.0764869 | ||||||||
\(665\) | −8.71681 | − | 5.03265i | −0.338023 | − | 0.195158i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4259 | + | 38.8428i | 0.868335 | + | 1.50400i | ||||
\(668\) | − | 13.3341i | − | 0.515912i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −44.9007 | + | 25.9234i | −1.73467 | + | 1.00151i | ||||
\(671\) | 0.757150i | 0.0292294i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.01309 | + | 3.48677i | −0.0775987 | + | 0.134405i | −0.902213 | − | 0.431290i | \(-0.858059\pi\) |
0.824615 | + | 0.565695i | \(0.191392\pi\) | |||||||
\(674\) | −6.57130 | − | 3.79394i | −0.253117 | − | 0.146137i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.71173 | + | 12.1161i | 0.181221 | + | 0.466003i | ||||
\(677\) | 27.7397 | 1.06612 | 0.533061 | − | 0.846077i | \(-0.321042\pi\) | ||||
0.533061 | + | 0.846077i | \(0.321042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.87254 | − | 13.6356i | 0.302120 | − | 0.523288i | ||||
\(680\) | 13.7359 | + | 23.7913i | 0.526749 | + | 0.912356i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.1827 | + | 5.87896i | −0.389914 | + | 0.225117i | ||||
\(683\) | −40.8116 | + | 23.5626i | −1.56161 | + | 0.901597i | −0.564518 | + | 0.825421i | \(0.690938\pi\) |
−0.997094 | + | 0.0761765i | \(0.975729\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4414 | − | 26.7453i | −0.589985 | − | 1.02188i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.27482 | −0.201101 | ||||||||
\(689\) | −0.262844 | − | 0.0201090i | −0.0100136 | − | 0.000766092i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.13743 | + | 5.27550i | 0.347604 | + | 0.200689i | 0.663630 | − | 0.748061i | \(-0.269015\pi\) |
−0.316025 | + | 0.948751i | \(0.602348\pi\) | |||||||
\(692\) | 8.41536 | − | 14.5758i | 0.319904 | − | 0.554090i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.51449i | 0.285246i | ||||||||
\(695\) | −60.2940 | + | 34.8108i | −2.28708 | + | 1.32045i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 88.1372i | 3.33844i | ||||||||
\(698\) | 11.5373 | + | 19.9831i | 0.436691 | + | 0.756372i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.04209 | + | 4.06575i | 0.266166 | + | 0.153671i | ||||
\(701\) | 43.5823 | 1.64608 | 0.823041 | − | 0.567982i | \(-0.192276\pi\) | ||||
0.823041 | + | 0.567982i | \(0.192276\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.77458 | −0.180077 | ||||||||
\(704\) | −1.74589 | − | 1.00799i | −0.0658007 | − | 0.0379900i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.4439 | + | 30.2137i | 0.656508 | + | 1.13711i | ||||
\(707\) | − | 0.320161i | − | 0.0120409i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0192 | − | 9.82602i | 0.639168 | − | 0.369024i | −0.145126 | − | 0.989413i | \(-0.546359\pi\) |
0.784294 | + | 0.620389i | \(0.213025\pi\) | |||||||
\(710\) | 46.3325i | 1.73883i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.82727 | + | 11.8252i | −0.255863 | + | 0.443167i | ||||
\(713\) | −39.9616 | − | 23.0718i | −1.49657 | − | 0.864047i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.8717 | + | 21.7400i | −0.556170 | + | 0.813029i | ||||
\(716\) | 10.8962 | 0.407212 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.14565 | + | 3.71637i | −0.0800749 | + | 0.138694i | ||||
\(719\) | 24.2207 | + | 41.9514i | 0.903279 | + | 1.56452i | 0.823211 | + | 0.567736i | \(0.192180\pi\) |
0.0800679 | + | 0.996789i | \(0.474486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.121218 | − | 0.0699850i | 0.00451438 | − | 0.00260638i | ||||
\(722\) | 9.77304 | − | 5.64247i | 0.363715 | − | 0.209991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.21504 | + | 14.2289i | 0.305310 | + | 0.528812i | ||||
\(725\) | 23.0491 | − | 39.9222i | 0.856021 | − | 1.48267i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.0669 | −1.07803 | −0.539016 | − | 0.842295i | \(-0.681204\pi\) | ||||
−0.539016 | + | 0.842295i | \(0.681204\pi\) | |||||||
\(728\) | 1.55933 | + | 3.25092i | 0.0577927 | + | 0.120487i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.0658 | − | 8.69825i | −0.557611 | − | 0.321937i | ||||
\(731\) | −19.9944 | + | 34.6313i | −0.739520 | + | 1.28089i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 5.40128i | − | 0.199501i | −0.995012 | − | 0.0997505i | \(-0.968196\pi\) | ||
0.995012 | − | 0.0997505i | \(-0.0318045\pi\) | |||||||
\(734\) | 21.5270 | − | 12.4286i | 0.794575 | − | 0.458748i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.91165i | − | 0.291627i | ||||||
\(737\) | −14.4219 | − | 24.9794i | −0.531236 | − | 0.920128i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.0102 | + | 15.0170i | 0.956800 | + | 0.552409i | 0.895187 | − | 0.445691i | \(-0.147042\pi\) |
0.0616132 | + | 0.998100i | \(0.480375\pi\) | |||||||
\(740\) | 6.22906 | 0.228985 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.0731130 | −0.00268406 | ||||||||
\(743\) | −20.2184 | − | 11.6731i | −0.741742 | − | 0.428245i | 0.0809605 | − | 0.996717i | \(-0.474201\pi\) |
−0.822702 | + | 0.568473i | \(0.807535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.277362 | + | 0.480405i | 0.0101617 | + | 0.0176007i | ||||
\(746\) | 34.5410i | 1.26464i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −13.2357 | + | 7.64165i | −0.483946 | + | 0.279406i | ||||
\(749\) | 1.38088i | 0.0504563i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0773 | + | 29.5788i | −0.623160 | + | 1.07934i | 0.365734 | + | 0.930719i | \(0.380818\pi\) |
−0.988894 | + | 0.148625i | \(0.952515\pi\) | |||||||
\(752\) | −4.88142 | − | 2.81829i | −0.178007 | − | 0.102772i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.4297 | − | 8.83998i | 0.671172 | − | 0.321933i | ||||
\(755\) | −42.6216 | −1.55116 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.63731 | − | 16.6923i | 0.350274 | − | 0.606693i | −0.636023 | − | 0.771670i | \(-0.719422\pi\) |
0.986297 | + | 0.164977i | \(0.0527551\pi\) | |||||||
\(758\) | −13.6023 | − | 23.5599i | −0.494059 | − | 0.855735i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.71681 | − | 5.03265i | 0.316192 | − | 0.182553i | ||||
\(761\) | 19.3565 | − | 11.1755i | 0.701673 | − | 0.405111i | −0.106297 | − | 0.994334i | \(-0.533900\pi\) |
0.807970 | + | 0.589223i | \(0.200566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.56821 | − | 2.71622i | −0.0567730 | − | 0.0983338i | ||||
\(764\) | 3.49738 | − | 6.05765i | 0.126531 | − | 0.219158i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.9385 | 1.04559 | ||||||||
\(767\) | −4.34268 | + | 2.08300i | −0.156805 | + | 0.0752128i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.4214 | + | 20.4505i | 1.27733 | + | 0.737466i | 0.976356 | − | 0.216168i | \(-0.0693557\pi\) |
0.300972 | + | 0.953633i | \(0.402689\pi\) | |||||||
\(770\) | −3.65269 | + | 6.32665i | −0.131634 | + | 0.227997i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.39918i | 0.194321i | ||||||||
\(773\) | 12.5621 | − | 7.25272i | 0.451827 | − | 0.260862i | −0.256775 | − | 0.966471i | \(-0.582660\pi\) |
0.708601 | + | 0.705609i | \(0.249327\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.4259i | 1.70359i | ||||||||
\(776\) | 7.87254 | + | 13.6356i | 0.282608 | + | 0.489491i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.6557 | − | 10.7709i | −0.668841 | − | 0.386156i | ||||
\(779\) | 32.2922 | 1.15699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.7759 | −0.922335 | ||||||||
\(782\) | −51.9432 | − | 29.9894i | −1.85749 | − | 1.07242i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | 85.2009i | 3.04095i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5349 | − | 12.4332i | 0.767638 | − | 0.443196i | −0.0643934 | − | 0.997925i | \(-0.520511\pi\) |
0.832031 | + | 0.554729i | \(0.187178\pi\) | |||||||
\(788\) | 3.96298i | 0.141175i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.3666 | − | 31.8119i | 0.653455 | − | 1.13182i | ||||
\(791\) | −10.8029 | − | 6.23703i | −0.384105 | − | 0.221763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.585644 | + | 1.22096i | 0.0207968 | + | 0.0433576i | ||||
\(794\) | −3.42263 | −0.121464 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.7019 | − | 22.0004i | 0.450208 | − | 0.779784i | ||||
\(797\) | −15.0884 | − | 26.1339i | −0.534459 | − | 0.925711i | −0.999189 | − | 0.0402584i | \(-0.987182\pi\) |
0.464730 | − | 0.885453i | \(-0.346151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.0064 | + | 21.3657i | −1.30919 | + | 0.755863i | ||||
\(800\) | −7.04209 | + | 4.06575i | −0.248975 | + | 0.143746i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.72747 | − | 6.45616i | −0.131621 | − | 0.227975i | ||||
\(803\) | 4.83906 | − | 8.38150i | 0.170767 | − | 0.295777i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.6698 | −1.01048 | ||||||||
\(806\) | −11.8730 | + | 17.3564i | −0.418210 | + | 0.611354i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.277268 | + | 0.160081i | 0.00975425 | + | 0.00563162i | ||||
\(809\) | −8.60876 | + | 14.9108i | −0.302668 | + | 0.524236i | −0.976739 | − | 0.214430i | \(-0.931211\pi\) |
0.674071 | + | 0.738666i | \(0.264544\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.3694i | − | 1.24199i | −0.783816 | − | 0.620994i | \(-0.786729\pi\) | ||
0.783816 | − | 0.620994i | \(-0.213271\pi\) | |||||||
\(812\) | 4.90957 | − | 2.83454i | 0.172292 | − | 0.0994729i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.46539i | 0.121462i | ||||||||
\(815\) | 33.4889 | + | 58.0045i | 1.17307 | + | 2.03181i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6884 | + | 7.32567i | 0.443912 | + | 0.256293i | ||||
\(818\) | 6.53378 | 0.228448 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −42.1294 | −1.47122 | ||||||||
\(821\) | −11.9747 | − | 6.91361i | −0.417921 | − | 0.241287i | 0.276267 | − | 0.961081i | \(-0.410903\pi\) |
−0.694187 | + | 0.719794i | \(0.744236\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.36729 | − | 4.10027i | −0.0825187 | − | 0.142927i | 0.821813 | − | 0.569758i | \(-0.192963\pi\) |
−0.904331 | + | 0.426831i | \(0.859630\pi\) | |||||||
\(824\) | 0.139970i | 0.00487609i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.15686 | + | 0.667915i | −0.0402524 | + | 0.0232397i | ||||
\(827\) | − | 6.83301i | − | 0.237607i | −0.992918 | − | 0.118803i | \(-0.962094\pi\) | ||
0.992918 | − | 0.118803i | \(-0.0379058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7308 | − | 35.9069i | 0.720012 | − | 1.24710i | −0.240982 | − | 0.970530i | \(-0.577470\pi\) |
0.960994 | − | 0.276568i | \(-0.0891971\pi\) | |||||||
\(830\) | −6.18527 | − | 3.57107i | −0.214694 | − | 0.123954i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.59505 | − | 0.275040i | −0.124636 | − | 0.00953530i | ||||
\(833\) | 7.58108 | 0.262669 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.1597 | − | 41.8458i | 0.836081 | − | 1.44813i | ||||
\(836\) | 2.79979 | + | 4.84938i | 0.0968329 | + | 0.167719i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14.9183 | − | 8.61309i | 0.515344 | − | 0.297534i | ||||
\(839\) | 14.4872 | − | 8.36420i | 0.500154 | − | 0.288764i | −0.228623 | − | 0.973515i | \(-0.573422\pi\) |
0.728777 | + | 0.684751i | \(0.240089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.56925 | − | 2.71802i | −0.0541120 | − | 0.0937248i | ||||
\(842\) | −1.47891 | + | 2.56154i | −0.0509665 | + | 0.0882765i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.20537 | −0.0759118 | ||||||||
\(845\) | −7.16618 | + | 46.5604i | −0.246524 | + | 1.60173i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00660 | + | 3.46791i | 0.206389 | + | 0.119159i | ||||
\(848\) | 0.0365565 | − | 0.0633177i | 0.00125535 | − | 0.00217434i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 61.6456i | 2.11443i | ||||||||
\(851\) | −11.7778 | + | 6.79990i | −0.403737 | + | 0.233098i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.15821i | − | 0.313571i | −0.987633 | − | 0.156786i | \(-0.949887\pi\) | ||
0.987633 | − | 0.156786i | \(-0.0501132\pi\) | |||||||
\(854\) | 0.187787 | + | 0.325257i | 0.00642594 | + | 0.0111301i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.19588 | − | 0.690440i | −0.0408743 | − | 0.0235988i | ||||
\(857\) | −12.2690 | −0.419101 | −0.209550 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209550 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.3713 | 0.695059 | 0.347529 | − | 0.937669i | \(-0.387021\pi\) | ||||
0.347529 | + | 0.937669i | \(0.387021\pi\) | |||||||
\(860\) | −16.5537 | − | 9.55729i | −0.564477 | − | 0.325901i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.0088 | + | 17.3358i | 0.340903 | + | 0.590461i | ||||
\(863\) | 24.7314i | 0.841867i | 0.907092 | + | 0.420933i | \(0.138297\pi\) | ||||
−0.907092 | + | 0.420933i | \(0.861703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 52.8190 | − | 30.4951i | 1.79590 | − | 1.03686i | ||||
\(866\) | − | 33.8865i | − | 1.15151i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.91618 | + | 5.05098i | −0.0989817 | + | 0.171441i | ||||
\(869\) | 17.6978 | + | 10.2178i | 0.600356 | + | 0.346616i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.5776 | − | 29.1261i | −1.44269 | − | 0.986900i | ||||
\(872\) | 3.13642 | 0.106213 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.9877 | + | 19.0313i | −0.371665 | + | 0.643742i | ||||
\(875\) | 5.67387 | + | 9.82744i | 0.191812 | + | 0.332228i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.33998 | + | 4.23774i | −0.247854 | + | 0.143098i | −0.618781 | − | 0.785564i | \(-0.712373\pi\) |
0.370927 | + | 0.928662i | \(0.379040\pi\) | |||||||
\(878\) | −23.6283 | + | 13.6418i | −0.797418 | + | 0.460389i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.65269 | − | 6.32665i | −0.123132 | − | 0.213271i | ||||
\(881\) | −13.6050 | + | 23.5645i | −0.458363 | + | 0.793907i | −0.998875 | − | 0.0474291i | \(-0.984897\pi\) |
0.540512 | + | 0.841336i | \(0.318231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.2333 | −0.882822 | −0.441411 | − | 0.897305i | \(-0.645522\pi\) | ||||
−0.441411 | + | 0.897305i | \(0.645522\pi\) | |||||||
\(884\) | −15.4329 | + | 22.5604i | −0.519065 | + | 0.758788i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.23668 | + | 1.86870i | 0.108738 | + | 0.0627802i | ||||
\(887\) | 15.0711 | − | 26.1040i | 0.506039 | − | 0.876486i | −0.493936 | − | 0.869498i | \(-0.664442\pi\) |
0.999976 | − | 0.00698791i | \(-0.00222434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.08818i | − | 0.204191i | ||||||
\(890\) | −42.8514 | + | 24.7402i | −1.43638 | + | 0.829295i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 9.16531i | − | 0.306877i | ||||||
\(893\) | 7.82808 | + | 13.5586i | 0.261957 | + | 0.453722i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.1952 | + | 19.7426i | 1.14302 | + | 0.659922i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.09449 | 0.103264 | ||||||||
\(899\) | 28.6344 | + | 16.5321i | 0.955011 | + | 0.551376i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.277138 | − | 0.480016i | −0.00923279 | − | 0.0159917i | ||||
\(902\) | − | 23.4377i | − | 0.780389i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.8029 | − | 6.23703i | 0.359298 | − | 0.207441i | ||||
\(905\) | 59.5384i | 1.97912i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0936 | + | 46.9274i | −0.899627 | + | 1.55820i | −0.0716561 | + | 0.997429i | \(0.522828\pi\) |
−0.827971 | + | 0.560771i | \(0.810505\pi\) | |||||||
\(908\) | −8.63738 | − | 4.98679i | −0.286642 | − | 0.165493i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.996674 | + | 13.0275i | −0.0330394 | + | 0.431858i | ||||
\(911\) | 55.2798 | 1.83150 | 0.915750 | − | 0.401748i | \(-0.131597\pi\) | ||||
0.915750 | + | 0.401748i | \(0.131597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.98668 | − | 3.44102i | 0.0657494 | − | 0.113881i | ||||
\(914\) | −10.0730 | − | 17.4469i | −0.333184 | − | 0.577091i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.13039 | − | 0.652628i | 0.0373490 | − | 0.0215634i | ||||
\(917\) | 3.50640 | − | 2.02442i | 0.115792 | − | 0.0668524i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.1684 | + | 28.0046i | 0.533348 | + | 0.923786i | 0.999241 | + | 0.0389449i | \(0.0123997\pi\) |
−0.465893 | + | 0.884841i | \(0.654267\pi\) | |||||||
\(920\) | 14.3349 | − | 24.8288i | 0.472607 | − | 0.818580i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 28.9284 | 0.952706 | ||||||||
\(923\) | −41.5657 | + | 19.9373i | −1.36815 | + | 0.656245i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.1051 | + | 6.98886i | 0.398012 | + | 0.229792i | ||||
\(926\) | −13.6352 | + | 23.6168i | −0.448080 | + | 0.776098i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.66908i | 0.186097i | ||||||||
\(929\) | −10.7865 | + | 6.22758i | −0.353893 | + | 0.204320i | −0.666399 | − | 0.745596i | \(-0.732165\pi\) |
0.312505 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.77760i | − | 0.0910322i | ||||||
\(932\) | −13.7083 | − | 23.7434i | −0.449029 | − | 0.777741i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.4758 | − | 7.78026i | −0.440942 | − | 0.254578i | ||||
\(935\) | −55.3827 | −1.81121 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.10103 | −0.264649 | −0.132325 | − | 0.991206i | \(-0.542244\pi\) | ||||
−0.132325 | + | 0.991206i | \(0.542244\pi\) | |||||||
\(938\) | −12.3907 | − | 7.15378i | −0.404571 | − | 0.233579i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.2128 | − | 17.6890i | −0.333103 | − | 0.576952i | ||||
\(941\) | 20.3653i | 0.663891i | 0.943299 | + | 0.331946i | \(0.107705\pi\) | ||||
−0.943299 | + | 0.331946i | \(0.892295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 79.6574 | − | 45.9902i | 2.59400 | − | 1.49765i | ||||
\(944\) | − | 1.33583i | − | 0.0434775i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.31696 | − | 9.20925i | 0.172869 | − | 0.299419i | ||||
\(947\) | 42.8214 | + | 24.7229i | 1.39151 | + | 0.803387i | 0.993482 | − | 0.113987i | \(-0.0363622\pi\) |
0.398026 | + | 0.917374i | \(0.369695\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.32039 | − | 17.2588i | 0.0428615 | − | 0.560243i | ||||
\(950\) | 22.5861 | 0.732788 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.79054 | + | 6.56541i | −0.122852 | + | 0.212786i | ||||
\(953\) | 2.49143 | + | 4.31528i | 0.0807052 | + | 0.139786i | 0.903553 | − | 0.428476i | \(-0.140949\pi\) |
−0.822848 | + | 0.568262i | \(0.807616\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.9513 | − | 12.6736i | 0.710329 | − | 0.410108i | ||||
\(956\) | 0.297151 | − | 0.171560i | 0.00961056 | − | 0.00554866i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.6715 | − | 32.3400i | −0.603249 | − | 1.04486i | ||||
\(959\) | 4.26117 | − | 7.38057i | 0.137600 | − | 0.238331i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.01648 | −0.0973057 | ||||||||
\(962\) | 2.68043 | + | 5.58820i | 0.0864204 | + | 0.180171i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.39860 | + | 5.42628i | 0.302708 | + | 0.174769i | ||||
\(965\) | −9.78262 | + | 16.9440i | −0.314914 | + | 0.545446i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.1018i | 1.99706i | 0.0542196 | + | 0.998529i | \(0.482733\pi\) | ||||
−0.0542196 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(968\) | −6.00660 | + | 3.46791i | −0.193059 | + | 0.111463i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 57.0561i | 1.83196i | ||||||||
\(971\) | −7.97831 | − | 13.8188i | −0.256036 | − | 0.443467i | 0.709140 | − | 0.705067i | \(-0.249083\pi\) |
−0.965176 | + | 0.261600i | \(0.915750\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.6386 | − | 9.60631i | −0.533410 | − | 0.307964i | ||||
\(974\) | −27.2852 | −0.874274 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.375574 | −0.0120218 | ||||||||
\(977\) | 17.5849 | + | 10.1527i | 0.562592 | + | 0.324813i | 0.754185 | − | 0.656662i | \(-0.228032\pi\) |
−0.191593 | + | 0.981474i | \(0.561365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.7636 | − | 23.8393i | −0.439888 | − | 0.761908i | ||||
\(980\) | 3.62374i | 0.115756i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.8680 | − | 10.3161i | 0.570192 | − | 0.329200i | ||||
\(983\) | − | 18.3230i | − | 0.584413i | −0.956355 | − | 0.292207i | \(-0.905611\pi\) | ||
0.956355 | − | 0.292207i | \(-0.0943895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.18040 | + | 12.4368i | −0.228787 | + | 0.396270i | ||||
\(986\) | 37.2198 | + | 21.4889i | 1.18532 | + | 0.684345i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.26581 | + | 5.65440i | 0.262970 | + | 0.179890i | ||||
\(989\) | 41.7325 | 1.32702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5596 | − | 33.8783i | 0.621332 | − | 1.07618i | −0.367906 | − | 0.929863i | \(-0.619925\pi\) |
0.989238 | − | 0.146315i | \(-0.0467414\pi\) | |||||||
\(992\) | −2.91618 | − | 5.05098i | −0.0925889 | − | 0.160369i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.0728 | + | 6.39291i | −0.351209 | + | 0.202771i | ||||
\(995\) | 79.7238 | − | 46.0285i | 2.52741 | − | 1.45920i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.790573 | − | 1.36931i | −0.0250377 | − | 0.0433666i | 0.853235 | − | 0.521527i | \(-0.174637\pi\) |
−0.878273 | + | 0.478160i | \(0.841304\pi\) | |||||||
\(998\) | 9.47792 | − | 16.4162i | 0.300018 | − | 0.519647i | ||||
\(999\) | 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 | 1638.2.bj.i.1135.4 | yes | 16 | |
3.2 | odd | 2 | 1638.2.bj.h.1135.5 | yes | 16 | ||
13.10 | even | 6 | inner | 1638.2.bj.i.127.1 | yes | 16 | |
39.23 | odd | 6 | 1638.2.bj.h.127.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1638.2.bj.h.127.8 | ✓ | 16 | 39.23 | odd | 6 | ||
1638.2.bj.h.1135.5 | yes | 16 | 3.2 | odd | 2 | ||
1638.2.bj.i.127.1 | yes | 16 | 13.10 | even | 6 | inner | |
1638.2.bj.i.1135.4 | yes | 16 | 1.1 | even | 1 | trivial |