Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(244,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.244");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.b (of order \(2\), degree \(1\), 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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.3 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.244 |
Dual form | 405.2.b.a.244.2 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.792287i | 0.560232i | 0.959966 | + | 0.280116i | \(0.0903729\pi\) | ||||
−0.959966 | + | 0.280116i | \(0.909627\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.37228 | 0.686141 | ||||||||
\(5\) | 0.686141 | + | 2.12819i | 0.306851 | + | 0.951757i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410i | 1.30931i | 0.755929 | + | 0.654654i | \(0.227186\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 2.67181i | 0.944629i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.68614 | + | 0.543620i | −0.533204 | + | 0.171908i | ||||
\(11\) | −4.37228 | −1.31829 | −0.659146 | − | 0.752015i | \(-0.729082\pi\) | ||||
−0.659146 | + | 0.752015i | \(0.729082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.84096i | − | 1.61999i | −0.586436 | − | 0.809996i | \(-0.699469\pi\) | ||
0.586436 | − | 0.809996i | \(-0.300531\pi\) | |||||||
\(14\) | −2.74456 | −0.733515 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.627719 | 0.156930 | ||||||||
\(17\) | 0.792287i | 0.192158i | 0.995374 | + | 0.0960789i | \(0.0306301\pi\) | ||||
−0.995374 | + | 0.0960789i | \(0.969370\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.372281 | 0.0854072 | 0.0427036 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427036 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(20\) | 0.941578 | + | 2.92048i | 0.210543 | + | 0.653039i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.46410i | − | 0.738549i | ||||||
\(23\) | − | 1.58457i | − | 0.330407i | −0.986260 | − | 0.165203i | \(-0.947172\pi\) | ||
0.986260 | − | 0.165203i | \(-0.0528280\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.05842 | + | 2.92048i | −0.811684 | + | 0.584096i | ||||
\(26\) | 4.62772 | 0.907570 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.75372i | 0.898369i | ||||||||
\(29\) | 5.74456 | 1.06674 | 0.533369 | − | 0.845883i | \(-0.320926\pi\) | ||||
0.533369 | + | 0.845883i | \(0.320926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.37228 | 1.14450 | 0.572248 | − | 0.820081i | \(-0.306072\pi\) | ||||
0.572248 | + | 0.820081i | \(0.306072\pi\) | |||||||
\(32\) | 5.84096i | 1.03255i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.627719 | −0.107653 | ||||||||
\(35\) | −7.37228 | + | 2.37686i | −1.24614 | + | 0.401763i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.37686i | − | 0.390754i | −0.980728 | − | 0.195377i | \(-0.937407\pi\) | ||
0.980728 | − | 0.195377i | \(-0.0625930\pi\) | |||||||
\(38\) | 0.294954i | 0.0478478i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.68614 | + | 1.83324i | −0.899058 | + | 0.289861i | ||||
\(41\) | 4.37228 | 0.682836 | 0.341418 | − | 0.939912i | \(-0.389093\pi\) | ||||
0.341418 | + | 0.939912i | \(0.389093\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.25544 | 0.185104 | ||||||||
\(47\) | 1.87953i | 0.274157i | 0.990560 | + | 0.137079i | \(0.0437713\pi\) | ||||
−0.990560 | + | 0.137079i | \(0.956229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | −2.31386 | − | 3.21543i | −0.327229 | − | 0.454731i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 8.01544i | − | 1.11154i | ||||||
\(53\) | − | 11.9769i | − | 1.64515i | −0.568656 | − | 0.822575i | \(-0.692536\pi\) | ||
0.568656 | − | 0.822575i | \(-0.307464\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.00000 | − | 9.30506i | −0.404520 | − | 1.25469i | ||||
\(56\) | −9.25544 | −1.23681 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.55134i | 0.597621i | ||||||||
\(59\) | −1.62772 | −0.211911 | −0.105955 | − | 0.994371i | \(-0.533790\pi\) | ||||
−0.105955 | + | 0.994371i | \(0.533790\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.37228 | 1.20000 | 0.599999 | − | 0.800001i | \(-0.295168\pi\) | ||||
0.599999 | + | 0.800001i | \(0.295168\pi\) | |||||||
\(62\) | 5.04868i | 0.641182i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.37228 | −0.421535 | ||||||||
\(65\) | 12.4307 | − | 4.00772i | 1.54184 | − | 0.497097i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6819i | 1.42717i | 0.700566 | + | 0.713587i | \(0.252931\pi\) | ||||
−0.700566 | + | 0.713587i | \(0.747069\pi\) | |||||||
\(68\) | 1.08724i | 0.131847i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.88316 | − | 5.84096i | −0.225080 | − | 0.698129i | ||||
\(71\) | 13.1168 | 1.55668 | 0.778341 | − | 0.627841i | \(-0.216061\pi\) | ||||
0.778341 | + | 0.627841i | \(0.216061\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.37686i | 0.278191i | 0.990279 | + | 0.139095i | \(0.0444194\pi\) | ||||
−0.990279 | + | 0.139095i | \(0.955581\pi\) | |||||||
\(74\) | 1.88316 | 0.218912 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.510875 | 0.0586013 | ||||||||
\(77\) | − | 15.1460i | − | 1.72605i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.74456 | −0.758823 | −0.379411 | − | 0.925228i | \(-0.623873\pi\) | ||||
−0.379411 | + | 0.925228i | \(0.623873\pi\) | |||||||
\(80\) | 0.430703 | + | 1.33591i | 0.0481541 | + | 0.149359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.46410i | 0.382546i | ||||||||
\(83\) | − | 11.9769i | − | 1.31463i | −0.753615 | − | 0.657317i | \(-0.771691\pi\) | ||
0.753615 | − | 0.657317i | \(-0.228309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.68614 | + | 0.543620i | −0.182888 | + | 0.0589639i | ||||
\(86\) | −2.74456 | −0.295954 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 11.6819i | − | 1.24530i | ||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.2337 | 2.12107 | ||||||||
\(92\) | − | 2.17448i | − | 0.226705i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.48913 | −0.153592 | ||||||||
\(95\) | 0.255437 | + | 0.792287i | 0.0262073 | + | 0.0812869i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.28962i | − | 0.130941i | −0.997855 | − | 0.0654706i | \(-0.979145\pi\) | ||
0.997855 | − | 0.0654706i | \(-0.0208548\pi\) | |||||||
\(98\) | − | 3.96143i | − | 0.400165i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.56930 | + | 4.00772i | −0.556930 | + | 0.400772i | ||||
\(101\) | −16.3723 | −1.62910 | −0.814551 | − | 0.580091i | \(-0.803017\pi\) | ||||
−0.814551 | + | 0.580091i | \(0.803017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.92820i | 0.682656i | 0.939944 | + | 0.341328i | \(0.110877\pi\) | ||||
−0.939944 | + | 0.341328i | \(0.889123\pi\) | |||||||
\(104\) | 15.6060 | 1.53029 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.48913 | 0.921665 | ||||||||
\(107\) | − | 13.2665i | − | 1.28252i | −0.767323 | − | 0.641260i | \(-0.778412\pi\) | ||
0.767323 | − | 0.641260i | \(-0.221588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.74456 | −0.933360 | −0.466680 | − | 0.884426i | \(-0.654550\pi\) | ||||
−0.466680 | + | 0.884426i | \(0.654550\pi\) | |||||||
\(110\) | 7.37228 | − | 2.37686i | 0.702919 | − | 0.226625i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.17448i | 0.205469i | ||||||||
\(113\) | − | 6.13592i | − | 0.577218i | −0.957447 | − | 0.288609i | \(-0.906807\pi\) | ||
0.957447 | − | 0.288609i | \(-0.0931928\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.37228 | − | 1.08724i | 0.314467 | − | 0.101386i | ||||
\(116\) | 7.88316 | 0.731933 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.28962i | − | 0.118719i | ||||||
\(119\) | −2.74456 | −0.251594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.11684 | 0.737895 | ||||||||
\(122\) | 7.42554i | 0.672276i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.74456 | 0.785285 | ||||||||
\(125\) | −9.00000 | − | 6.63325i | −0.804984 | − | 0.593296i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.3923i | − | 0.922168i | −0.887357 | − | 0.461084i | \(-0.847461\pi\) | ||
0.887357 | − | 0.461084i | \(-0.152539\pi\) | |||||||
\(128\) | 9.01011i | 0.796389i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.17527 | + | 9.84868i | 0.278489 | + | 0.863787i | ||||
\(131\) | 4.37228 | 0.382008 | 0.191004 | − | 0.981589i | \(-0.438826\pi\) | ||||
0.191004 | + | 0.981589i | \(0.438826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.28962i | 0.111824i | ||||||||
\(134\) | −9.25544 | −0.799548 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.11684 | −0.181518 | ||||||||
\(137\) | − | 14.3537i | − | 1.22632i | −0.789958 | − | 0.613161i | \(-0.789898\pi\) | ||
0.789958 | − | 0.613161i | \(-0.210102\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1168 | −0.942918 | −0.471459 | − | 0.881888i | \(-0.656273\pi\) | ||||
−0.471459 | + | 0.881888i | \(0.656273\pi\) | |||||||
\(140\) | −10.1168 | + | 3.26172i | −0.855029 | + | 0.275666i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.3923i | 0.872103i | ||||||||
\(143\) | 25.5383i | 2.13562i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.94158 | + | 12.2255i | 0.327330 | + | 1.01528i | ||||
\(146\) | −1.88316 | −0.155851 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 3.26172i | − | 0.268112i | ||||||
\(149\) | −10.6277 | −0.870657 | −0.435328 | − | 0.900272i | \(-0.643368\pi\) | ||||
−0.435328 | + | 0.900272i | \(0.643368\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.883156 | 0.0718702 | 0.0359351 | − | 0.999354i | \(-0.488559\pi\) | ||||
0.0359351 | + | 0.999354i | \(0.488559\pi\) | |||||||
\(152\) | 0.994667i | 0.0806781i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | 4.37228 | + | 13.5615i | 0.351190 | + | 1.08928i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.4795i | − | 0.916167i | −0.888909 | − | 0.458084i | \(-0.848536\pi\) | ||
0.888909 | − | 0.458084i | \(-0.151464\pi\) | |||||||
\(158\) | − | 5.34363i | − | 0.425116i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.4307 | + | 4.00772i | −0.982733 | + | 0.316838i | ||||
\(161\) | 5.48913 | 0.432604 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 15.1460i | − | 1.18633i | −0.805082 | − | 0.593164i | \(-0.797878\pi\) | ||
0.805082 | − | 0.593164i | \(-0.202122\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.48913 | 0.736499 | ||||||||
\(167\) | 13.5615i | 1.04942i | 0.851282 | + | 0.524708i | \(0.175826\pi\) | ||||
−0.851282 | + | 0.524708i | \(0.824174\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −21.1168 | −1.62437 | ||||||||
\(170\) | −0.430703 | − | 1.33591i | −0.0330334 | − | 0.102459i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.75372i | 0.362468i | ||||||||
\(173\) | 11.1846i | 0.850349i | 0.905111 | + | 0.425174i | \(0.139787\pi\) | ||||
−0.905111 | + | 0.425174i | \(0.860213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1168 | − | 14.0588i | −0.764762 | − | 1.06274i | ||||
\(176\) | −2.74456 | −0.206879 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.37686i | 0.178153i | ||||||||
\(179\) | 4.88316 | 0.364984 | 0.182492 | − | 0.983207i | \(-0.441584\pi\) | ||||
0.182492 | + | 0.983207i | \(0.441584\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.8614 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(182\) | 16.0309i | 1.18829i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.23369 | 0.312112 | ||||||||
\(185\) | 5.05842 | − | 1.63086i | 0.371903 | − | 0.119903i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.46410i | − | 0.253320i | ||||||
\(188\) | 2.57924i | 0.188110i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.627719 | + | 0.202380i | −0.0455395 | + | 0.0146822i | ||||
\(191\) | 7.62772 | 0.551922 | 0.275961 | − | 0.961169i | \(-0.411004\pi\) | ||||
0.275961 | + | 0.961169i | \(0.411004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 11.4795i | − | 0.826316i | −0.910659 | − | 0.413158i | \(-0.864426\pi\) | ||
0.910659 | − | 0.413158i | \(-0.135574\pi\) | |||||||
\(194\) | 1.02175 | 0.0733573 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.86141 | −0.490100 | ||||||||
\(197\) | 6.43087i | 0.458181i | 0.973405 | + | 0.229090i | \(0.0735751\pi\) | ||||
−0.973405 | + | 0.229090i | \(0.926425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −7.80298 | − | 10.8434i | −0.551754 | − | 0.766741i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 12.9715i | − | 0.912675i | ||||||
\(203\) | 19.8997i | 1.39669i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 9.30506i | 0.209529 | + | 0.649894i | ||||
\(206\) | −5.48913 | −0.382445 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.66648i | − | 0.254225i | ||||||
\(209\) | −1.62772 | −0.112592 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.86141 | −0.128145 | −0.0640723 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640723 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(212\) | − | 16.4356i | − | 1.12880i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.5109 | 0.718509 | ||||||||
\(215\) | −7.37228 | + | 2.37686i | −0.502785 | + | 0.162101i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0742i | 1.49850i | ||||||||
\(218\) | − | 7.72049i | − | 0.522898i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.11684 | − | 12.7692i | −0.277558 | − | 0.860897i | ||||
\(221\) | 4.62772 | 0.311294 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6101i | 1.24623i | 0.782132 | + | 0.623113i | \(0.214132\pi\) | ||||
−0.782132 | + | 0.623113i | \(0.785868\pi\) | |||||||
\(224\) | −20.2337 | −1.35192 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.86141 | 0.323376 | ||||||||
\(227\) | 13.5615i | 0.900105i | 0.893002 | + | 0.450053i | \(0.148595\pi\) | ||||
−0.893002 | + | 0.450053i | \(0.851405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.6060 | 1.16344 | 0.581718 | − | 0.813391i | \(-0.302381\pi\) | ||||
0.581718 | + | 0.813391i | \(0.302381\pi\) | |||||||
\(230\) | 0.861407 | + | 2.67181i | 0.0567995 | + | 0.176174i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.3484i | 1.00767i | ||||||||
\(233\) | − | 6.13592i | − | 0.401977i | −0.979594 | − | 0.200989i | \(-0.935585\pi\) | ||
0.979594 | − | 0.200989i | \(-0.0644154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.00000 | + | 1.28962i | −0.260931 | + | 0.0841256i | ||||
\(236\) | −2.23369 | −0.145401 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.17448i | − | 0.140951i | ||||||
\(239\) | −22.9783 | −1.48634 | −0.743170 | − | 0.669103i | \(-0.766679\pi\) | ||||
−0.743170 | + | 0.669103i | \(0.766679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.51087 | −0.0973240 | −0.0486620 | − | 0.998815i | \(-0.515496\pi\) | ||||
−0.0486620 | + | 0.998815i | \(0.515496\pi\) | |||||||
\(242\) | 6.43087i | 0.413392i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.8614 | 0.823367 | ||||||||
\(245\) | −3.43070 | − | 10.6410i | −0.219180 | − | 0.679827i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.17448i | − | 0.138359i | ||||||
\(248\) | 17.0256i | 1.08112i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.25544 | − | 7.13058i | 0.332383 | − | 0.450978i | ||||
\(251\) | −20.2337 | −1.27714 | −0.638570 | − | 0.769564i | \(-0.720474\pi\) | ||||
−0.638570 | + | 0.769564i | \(0.720474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92820i | 0.435572i | ||||||||
\(254\) | 8.23369 | 0.516628 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | 6.43087i | 0.401147i | 0.979679 | + | 0.200573i | \(0.0642805\pi\) | ||||
−0.979679 | + | 0.200573i | \(0.935720\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.23369 | 0.511616 | ||||||||
\(260\) | 17.0584 | − | 5.49972i | 1.05792 | − | 0.341078i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.46410i | 0.214013i | ||||||||
\(263\) | 26.5330i | 1.63609i | 0.575151 | + | 0.818047i | \(0.304943\pi\) | ||||
−0.575151 | + | 0.818047i | \(0.695057\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.4891 | − | 8.21782i | 1.56578 | − | 0.504817i | ||||
\(266\) | −1.02175 | −0.0626475 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.0309i | 0.979242i | ||||||||
\(269\) | 29.2337 | 1.78241 | 0.891205 | − | 0.453601i | \(-0.149861\pi\) | ||||
0.891205 | + | 0.453601i | \(0.149861\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.25544 | 0.319245 | 0.159623 | − | 0.987178i | \(-0.448972\pi\) | ||||
0.159623 | + | 0.987178i | \(0.448972\pi\) | |||||||
\(272\) | 0.497333i | 0.0301553i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.3723 | 0.687025 | ||||||||
\(275\) | 17.7446 | − | 12.7692i | 1.07004 | − | 0.770010i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 22.0742i | − | 1.32631i | −0.748481 | − | 0.663156i | \(-0.769217\pi\) | ||
0.748481 | − | 0.663156i | \(-0.230783\pi\) | |||||||
\(278\) | − | 8.80773i | − | 0.528253i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.35053 | − | 19.6974i | −0.379517 | − | 1.17714i | ||||
\(281\) | −1.37228 | −0.0818634 | −0.0409317 | − | 0.999162i | \(-0.513033\pi\) | ||||
−0.0409317 | + | 0.999162i | \(0.513033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7128i | 1.64736i | 0.567058 | + | 0.823678i | \(0.308082\pi\) | ||||
−0.567058 | + | 0.823678i | \(0.691918\pi\) | |||||||
\(284\) | 18.0000 | 1.06810 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2337 | −1.19644 | ||||||||
\(287\) | 15.1460i | 0.894042i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3723 | 0.963075 | ||||||||
\(290\) | −9.68614 | + | 3.12286i | −0.568790 | + | 0.183381i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.26172i | 0.190878i | ||||||||
\(293\) | 0.792287i | 0.0462859i | 0.999732 | + | 0.0231430i | \(0.00736729\pi\) | ||||
−0.999732 | + | 0.0231430i | \(0.992633\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.11684 | − | 3.46410i | −0.0650252 | − | 0.201688i | ||||
\(296\) | 6.35053 | 0.369117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 8.42020i | − | 0.487769i | ||||||
\(299\) | −9.25544 | −0.535256 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 0.699713i | 0.0402640i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.233688 | 0.0134029 | ||||||||
\(305\) | 6.43070 | + | 19.9460i | 0.368221 | + | 1.14211i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 15.1460i | − | 0.864429i | −0.901771 | − | 0.432215i | \(-0.857732\pi\) | ||
0.901771 | − | 0.432215i | \(-0.142268\pi\) | |||||||
\(308\) | − | 20.7846i | − | 1.18431i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.7446 | + | 3.46410i | −0.610250 | + | 0.196748i | ||||
\(311\) | −15.8614 | −0.899418 | −0.449709 | − | 0.893175i | \(-0.648472\pi\) | ||||
−0.449709 | + | 0.893175i | \(0.648472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.4511i | − | 1.38206i | −0.722827 | − | 0.691029i | \(-0.757158\pi\) | ||
0.722827 | − | 0.691029i | \(-0.242842\pi\) | |||||||
\(314\) | 9.09509 | 0.513266 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.25544 | −0.520659 | ||||||||
\(317\) | − | 29.4998i | − | 1.65687i | −0.560084 | − | 0.828436i | \(-0.689231\pi\) | ||
0.560084 | − | 0.828436i | \(-0.310769\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.1168 | −1.40627 | ||||||||
\(320\) | −2.31386 | − | 7.17687i | −0.129349 | − | 0.401199i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.34896i | 0.242358i | ||||||||
\(323\) | 0.294954i | 0.0164117i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0584 | + | 23.7051i | 0.946231 | + | 1.31492i | ||||
\(326\) | 12.0000 | 0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.6819i | 0.645026i | ||||||||
\(329\) | −6.51087 | −0.358956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.11684 | 0.501107 | 0.250554 | − | 0.968103i | \(-0.419387\pi\) | ||||
0.250554 | + | 0.968103i | \(0.419387\pi\) | |||||||
\(332\) | − | 16.4356i | − | 0.902023i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.7446 | −0.587916 | ||||||||
\(335\) | −24.8614 | + | 8.01544i | −1.35832 | + | 0.437930i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.92820i | 0.377403i | 0.982034 | + | 0.188702i | \(0.0604279\pi\) | ||||
−0.982034 | + | 0.188702i | \(0.939572\pi\) | |||||||
\(338\) | − | 16.7306i | − | 0.910025i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.31386 | + | 0.746000i | −0.125487 | + | 0.0404575i | ||||
\(341\) | −27.8614 | −1.50878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | −9.25544 | −0.499020 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.86141 | −0.476392 | ||||||||
\(347\) | − | 2.87419i | − | 0.154295i | −0.997020 | − | 0.0771474i | \(-0.975419\pi\) | ||
0.997020 | − | 0.0771474i | \(-0.0245812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6060 | 1.42418 | 0.712092 | − | 0.702086i | \(-0.247748\pi\) | ||||
0.712092 | + | 0.702086i | \(0.247748\pi\) | |||||||
\(350\) | 11.1386 | − | 8.01544i | 0.595383 | − | 0.428443i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 25.5383i | − | 1.36120i | ||||||
\(353\) | 1.87953i | 0.100037i | 0.998748 | + | 0.0500186i | \(0.0159281\pi\) | ||||
−0.998748 | + | 0.0500186i | \(0.984072\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | + | 27.9152i | 0.477670 | + | 1.48158i | ||||
\(356\) | 4.11684 | 0.218192 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.86886i | 0.204476i | ||||||||
\(359\) | 10.8832 | 0.574391 | 0.287196 | − | 0.957872i | \(-0.407277\pi\) | ||||
0.287196 | + | 0.957872i | \(0.407277\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8614 | −0.992706 | ||||||||
\(362\) | − | 10.9822i | − | 0.577212i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.7663 | 1.45535 | ||||||||
\(365\) | −5.05842 | + | 1.63086i | −0.264770 | + | 0.0853632i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 16.4356i | − | 0.857934i | −0.903320 | − | 0.428967i | \(-0.858878\pi\) | ||
0.903320 | − | 0.428967i | \(-0.141122\pi\) | |||||||
\(368\) | − | 0.994667i | − | 0.0518506i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.29211 | + | 4.00772i | 0.0671736 | + | 0.208352i | ||||
\(371\) | 41.4891 | 2.15401 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8.21782i | − | 0.425503i | −0.977106 | − | 0.212751i | \(-0.931758\pi\) | ||
0.977106 | − | 0.212751i | \(-0.0682424\pi\) | |||||||
\(374\) | 2.74456 | 0.141918 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02175 | −0.258977 | ||||||||
\(377\) | − | 33.5538i | − | 1.72811i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48913 | 0.0764912 | 0.0382456 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382456 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(380\) | 0.350532 | + | 1.08724i | 0.0179819 | + | 0.0557743i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.04334i | 0.309204i | ||||||||
\(383\) | − | 11.0920i | − | 0.566776i | −0.959005 | − | 0.283388i | \(-0.908542\pi\) | ||
0.959005 | − | 0.283388i | \(-0.0914584\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.2337 | − | 10.3923i | 1.64278 | − | 0.529641i | ||||
\(386\) | 9.09509 | 0.462928 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.76972i | − | 0.0898440i | ||||||
\(389\) | 0.510875 | 0.0259024 | 0.0129512 | − | 0.999916i | \(-0.495877\pi\) | ||||
0.0129512 | + | 0.999916i | \(0.495877\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25544 | 0.0634902 | ||||||||
\(392\) | − | 13.3591i | − | 0.674735i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.09509 | −0.256687 | ||||||||
\(395\) | −4.62772 | − | 14.3537i | −0.232846 | − | 0.722215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5229i | 0.879449i | 0.898133 | + | 0.439724i | \(0.144924\pi\) | ||||
−0.898133 | + | 0.439724i | \(0.855076\pi\) | |||||||
\(398\) | − | 12.6766i | − | 0.635420i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.54755 | + | 1.83324i | −0.127377 | + | 0.0916620i | ||||
\(401\) | 25.3723 | 1.26703 | 0.633516 | − | 0.773730i | \(-0.281611\pi\) | ||||
0.633516 | + | 0.773730i | \(0.281611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 37.2203i | − | 1.85407i | ||||||
\(404\) | −22.4674 | −1.11779 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.7663 | −0.782469 | ||||||||
\(407\) | 10.3923i | 0.515127i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8614 | −1.13042 | −0.565212 | − | 0.824946i | \(-0.691206\pi\) | ||||
−0.565212 | + | 0.824946i | \(0.691206\pi\) | |||||||
\(410\) | −7.37228 | + | 2.37686i | −0.364091 | + | 0.117385i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.50744i | 0.468398i | ||||||||
\(413\) | − | 5.63858i | − | 0.277457i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.4891 | − | 8.21782i | 1.25121 | − | 0.403397i | ||||
\(416\) | 34.1168 | 1.67272 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.28962i | − | 0.0630774i | ||||||
\(419\) | 17.4891 | 0.854400 | 0.427200 | − | 0.904157i | \(-0.359500\pi\) | ||||
0.427200 | + | 0.904157i | \(0.359500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.7446 | −1.05977 | −0.529883 | − | 0.848071i | \(-0.677764\pi\) | ||||
−0.529883 | + | 0.848071i | \(0.677764\pi\) | |||||||
\(422\) | − | 1.47477i | − | 0.0717906i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 32.0000 | 1.55406 | ||||||||
\(425\) | −2.31386 | − | 3.21543i | −0.112239 | − | 0.155972i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.4665i | 1.57117i | ||||||||
\(428\) | − | 18.2054i | − | 0.879990i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.88316 | − | 5.84096i | −0.0908138 | − | 0.281676i | ||||
\(431\) | −33.3505 | −1.60644 | −0.803219 | − | 0.595683i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595683i | \(0.796881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7692i | 0.613647i | 0.951766 | + | 0.306823i | \(0.0992661\pi\) | ||||
−0.951766 | + | 0.306823i | \(0.900734\pi\) | |||||||
\(434\) | −17.4891 | −0.839505 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.3723 | −0.640416 | ||||||||
\(437\) | − | 0.589907i | − | 0.0282191i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.8614 | −1.52066 | −0.760331 | − | 0.649536i | \(-0.774963\pi\) | ||||
−0.760331 | + | 0.649536i | \(0.774963\pi\) | |||||||
\(440\) | 24.8614 | − | 8.01544i | 1.18522 | − | 0.382121i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.66648i | 0.174397i | ||||||||
\(443\) | − | 21.4843i | − | 1.02075i | −0.859952 | − | 0.510375i | \(-0.829506\pi\) | ||
0.859952 | − | 0.510375i | \(-0.170494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.05842 | + | 6.38458i | 0.0975786 | + | 0.302658i | ||||
\(446\) | −14.7446 | −0.698175 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 11.6819i | − | 0.551919i | ||||||
\(449\) | 10.8832 | 0.513608 | 0.256804 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256804 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1168 | −0.900177 | ||||||||
\(452\) | − | 8.42020i | − | 0.396053i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.7446 | −0.504267 | ||||||||
\(455\) | 13.8832 | + | 43.0612i | 0.650852 | + | 2.01874i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9870i | 0.981730i | 0.871236 | + | 0.490865i | \(0.163319\pi\) | ||||
−0.871236 | + | 0.490865i | \(0.836681\pi\) | |||||||
\(458\) | 13.9490i | 0.651793i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.62772 | − | 1.49200i | 0.215768 | − | 0.0695649i | ||||
\(461\) | 24.0951 | 1.12222 | 0.561110 | − | 0.827741i | \(-0.310374\pi\) | ||||
0.561110 | + | 0.827741i | \(0.310374\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.8564i | − | 0.643962i | −0.946746 | − | 0.321981i | \(-0.895651\pi\) | ||
0.946746 | − | 0.321981i | \(-0.104349\pi\) | |||||||
\(464\) | 3.60597 | 0.167403 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.86141 | 0.225200 | ||||||||
\(467\) | 18.3152i | 0.847525i | 0.905773 | + | 0.423763i | \(0.139291\pi\) | ||||
−0.905773 | + | 0.423763i | \(0.860709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.4674 | −1.86861 | ||||||||
\(470\) | −1.02175 | − | 3.16915i | −0.0471298 | − | 0.146182i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 4.34896i | − | 0.200177i | ||||||
\(473\) | − | 15.1460i | − | 0.696415i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.51087 | + | 1.08724i | −0.0693237 | + | 0.0498860i | ||||
\(476\) | −3.76631 | −0.172629 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 18.2054i | − | 0.832694i | ||||||
\(479\) | −18.6060 | −0.850128 | −0.425064 | − | 0.905163i | \(-0.639748\pi\) | ||||
−0.425064 | + | 0.905163i | \(0.639748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8832 | −0.633017 | ||||||||
\(482\) | − | 1.19705i | − | 0.0545240i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1386 | 0.506300 | ||||||||
\(485\) | 2.74456 | − | 0.884861i | 0.124624 | − | 0.0401795i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.50744i | − | 0.430823i | −0.976523 | − | 0.215412i | \(-0.930891\pi\) | ||
0.976523 | − | 0.215412i | \(-0.0691093\pi\) | |||||||
\(488\) | 25.0410i | 1.13355i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.43070 | − | 2.71810i | 0.380860 | − | 0.122791i | ||||
\(491\) | −31.6277 | −1.42734 | −0.713669 | − | 0.700483i | \(-0.752968\pi\) | ||||
−0.713669 | + | 0.700483i | \(0.752968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.55134i | 0.204982i | ||||||||
\(494\) | 1.72281 | 0.0775130 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | 0.179605 | ||||||||
\(497\) | 45.4381i | 2.03818i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.3723 | 1.09105 | 0.545527 | − | 0.838094i | \(-0.316330\pi\) | ||||
0.545527 | + | 0.838094i | \(0.316330\pi\) | |||||||
\(500\) | −12.3505 | − | 9.10268i | −0.552333 | − | 0.407084i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 16.0309i | − | 0.715494i | ||||||
\(503\) | 3.16915i | 0.141305i | 0.997501 | + | 0.0706527i | \(0.0225082\pi\) | ||||
−0.997501 | + | 0.0706527i | \(0.977492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2337 | − | 34.8434i | −0.499893 | − | 1.55051i | ||||
\(506\) | −5.48913 | −0.244021 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 14.2612i | − | 0.632737i | ||||||
\(509\) | −0.510875 | −0.0226441 | −0.0113221 | − | 0.999936i | \(-0.503604\pi\) | ||||
−0.0113221 | + | 0.999936i | \(0.503604\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.23369 | −0.364237 | ||||||||
\(512\) | 7.02078i | 0.310277i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.09509 | −0.224735 | ||||||||
\(515\) | −14.7446 | + | 4.75372i | −0.649723 | + | 0.209474i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.21782i | − | 0.361419i | ||||||
\(518\) | 6.52344i | 0.286624i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.7079 | + | 33.2125i | 0.469572 | + | 1.45647i | ||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.75372i | 0.207866i | 0.994584 | + | 0.103933i | \(0.0331427\pi\) | ||||
−0.994584 | + | 0.103933i | \(0.966857\pi\) | |||||||
\(524\) | 6.00000 | 0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.0217 | −0.916592 | ||||||||
\(527\) | 5.04868i | 0.219924i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4891 | 0.890832 | ||||||||
\(530\) | 6.51087 | + | 20.1947i | 0.282814 | + | 0.877202i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.76972i | 0.0767272i | ||||||||
\(533\) | − | 25.5383i | − | 1.10619i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.2337 | − | 9.10268i | 1.22065 | − | 0.393543i | ||||
\(536\) | −31.2119 | −1.34815 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.1615i | 0.998562i | ||||||||
\(539\) | 21.8614 | 0.941637 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2337 | 0.826921 | 0.413460 | − | 0.910522i | \(-0.364320\pi\) | ||||
0.413460 | + | 0.910522i | \(0.364320\pi\) | |||||||
\(542\) | 4.16381i | 0.178851i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.62772 | −0.198412 | ||||||||
\(545\) | −6.68614 | − | 20.7383i | −0.286403 | − | 0.888332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.92820i | − | 0.296229i | −0.988970 | − | 0.148114i | \(-0.952680\pi\) | ||
0.988970 | − | 0.148114i | \(-0.0473203\pi\) | |||||||
\(548\) | − | 19.6974i | − | 0.841430i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.1168 | + | 14.0588i | 0.431384 | + | 0.599469i | ||||
\(551\) | 2.13859 | 0.0911071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 23.3639i | − | 0.993532i | ||||||
\(554\) | 17.4891 | 0.743042 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2554 | −0.646975 | ||||||||
\(557\) | 25.0410i | 1.06102i | 0.847678 | + | 0.530511i | \(0.178000\pi\) | ||||
−0.847678 | + | 0.530511i | \(0.822000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2337 | 0.855794 | ||||||||
\(560\) | −4.62772 | + | 1.49200i | −0.195557 | + | 0.0630485i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 1.08724i | − | 0.0458625i | ||||||
\(563\) | 32.1716i | 1.35587i | 0.735122 | + | 0.677935i | \(0.237125\pi\) | ||||
−0.735122 | + | 0.677935i | \(0.762875\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.0584 | − | 4.21010i | 0.549372 | − | 0.177120i | ||||
\(566\) | −21.9565 | −0.922901 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 35.0458i | 1.47049i | ||||||||
\(569\) | −20.4891 | −0.858949 | −0.429474 | − | 0.903079i | \(-0.641301\pi\) | ||||
−0.429474 | + | 0.903079i | \(0.641301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.13859 | 0.173195 | 0.0865974 | − | 0.996243i | \(-0.472401\pi\) | ||||
0.0865974 | + | 0.996243i | \(0.472401\pi\) | |||||||
\(572\) | 35.0458i | 1.46534i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | −0.500870 | ||||||||
\(575\) | 4.62772 | + | 6.43087i | 0.192989 | + | 0.268186i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4077i | 0.766325i | 0.923681 | + | 0.383162i | \(0.125165\pi\) | ||||
−0.923681 | + | 0.383162i | \(0.874835\pi\) | |||||||
\(578\) | 12.9715i | 0.539545i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.40895 | + | 16.7769i | 0.224595 | + | 0.696622i | ||||
\(581\) | 41.4891 | 1.72126 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.3663i | 2.16879i | ||||||||
\(584\) | −6.35053 | −0.262787 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.627719 | −0.0259308 | ||||||||
\(587\) | − | 16.7306i | − | 0.690546i | −0.938502 | − | 0.345273i | \(-0.887786\pi\) | ||
0.938502 | − | 0.345273i | \(-0.112214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.37228 | 0.0977481 | ||||||||
\(590\) | 2.74456 | − | 0.884861i | 0.112992 | − | 0.0364291i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.49200i | − | 0.0613208i | ||||||
\(593\) | 1.67715i | 0.0688722i | 0.999407 | + | 0.0344361i | \(0.0109635\pi\) | ||||
−0.999407 | + | 0.0344361i | \(0.989036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.88316 | − | 5.84096i | −0.0772019 | − | 0.239456i | ||||
\(596\) | −14.5842 | −0.597393 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 7.33296i | − | 0.299867i | ||||||
\(599\) | −1.62772 | −0.0665068 | −0.0332534 | − | 0.999447i | \(-0.510587\pi\) | ||||
−0.0332534 | + | 0.999447i | \(0.510587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9783 | −0.733348 | −0.366674 | − | 0.930349i | \(-0.619504\pi\) | ||||
−0.366674 | + | 0.930349i | \(0.619504\pi\) | |||||||
\(602\) | − | 9.50744i | − | 0.387494i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.21194 | 0.0493131 | ||||||||
\(605\) | 5.56930 | + | 17.2742i | 0.226424 | + | 0.702297i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 43.2636i | − | 1.75602i | −0.478647 | − | 0.878008i | \(-0.658872\pi\) | ||
0.478647 | − | 0.878008i | \(-0.341128\pi\) | |||||||
\(608\) | 2.17448i | 0.0881869i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.8030 | + | 5.09496i | −0.639844 | + | 0.206289i | ||||
\(611\) | 10.9783 | 0.444132 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.2921i | 1.22348i | 0.791057 | + | 0.611742i | \(0.209531\pi\) | ||||
−0.791057 | + | 0.611742i | \(0.790469\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 40.4674 | 1.63048 | ||||||||
\(617\) | 20.6920i | 0.833030i | 0.909129 | + | 0.416515i | \(0.136749\pi\) | ||||
−0.909129 | + | 0.416515i | \(0.863251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 6.00000 | + | 18.6101i | 0.240966 | + | 0.747401i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.5668i | − | 0.503882i | ||||||
\(623\) | 10.3923i | 0.416359i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.94158 | − | 23.7051i | 0.317663 | − | 0.948204i | ||||
\(626\) | 19.3723 | 0.774272 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 15.7532i | − | 0.628620i | ||||||
\(629\) | 1.88316 | 0.0750863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.37228 | 0.253677 | 0.126838 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126838 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(632\) | − | 18.0202i | − | 0.716806i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23.3723 | 0.928232 | ||||||||
\(635\) | 22.1168 | − | 7.13058i | 0.877680 | − | 0.282969i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.2048i | 1.15714i | ||||||||
\(638\) | − | 19.8997i | − | 0.787839i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.1753 | + | 6.18220i | −0.757969 | + | 0.244373i | ||||
\(641\) | 7.97825 | 0.315122 | 0.157561 | − | 0.987509i | \(-0.449637\pi\) | ||||
0.157561 | + | 0.987509i | \(0.449637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.28962i | 0.0508577i | 0.999677 | + | 0.0254288i | \(0.00809512\pi\) | ||||
−0.999677 | + | 0.0254288i | \(0.991905\pi\) | |||||||
\(644\) | 7.53262 | 0.296827 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.233688 | −0.00919433 | ||||||||
\(647\) | 28.7075i | 1.12861i | 0.825567 | + | 0.564304i | \(0.190855\pi\) | ||||
−0.825567 | + | 0.564304i | \(0.809145\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.11684 | 0.279361 | ||||||||
\(650\) | −18.7812 | + | 13.5152i | −0.736661 | + | 0.530108i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 20.7846i | − | 0.813988i | ||||||
\(653\) | − | 6.33830i | − | 0.248037i | −0.992280 | − | 0.124018i | \(-0.960422\pi\) | ||
0.992280 | − | 0.124018i | \(-0.0395782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.00000 | + | 9.30506i | 0.117220 | + | 0.363579i | ||||
\(656\) | 2.74456 | 0.107157 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 5.15848i | − | 0.201099i | ||||||
\(659\) | −21.2554 | −0.827994 | −0.413997 | − | 0.910278i | \(-0.635868\pi\) | ||||
−0.413997 | + | 0.910278i | \(0.635868\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.2337 | −0.592522 | −0.296261 | − | 0.955107i | \(-0.595740\pi\) | ||||
−0.296261 | + | 0.955107i | \(0.595740\pi\) | |||||||
\(662\) | 7.22316i | 0.280736i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.0000 | 1.24184 | ||||||||
\(665\) | −2.74456 | + | 0.884861i | −0.106430 | + | 0.0343134i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.10268i | − | 0.352457i | ||||||
\(668\) | 18.6101i | 0.720047i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.35053 | − | 19.6974i | −0.245342 | − | 0.760976i | ||||
\(671\) | −40.9783 | −1.58195 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5947i | 0.408395i | 0.978930 | + | 0.204198i | \(0.0654585\pi\) | ||||
−0.978930 | + | 0.204198i | \(0.934542\pi\) | |||||||
\(674\) | −5.48913 | −0.211433 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9783 | −1.11455 | ||||||||
\(677\) | 26.5330i | 1.01975i | 0.860250 | + | 0.509873i | \(0.170308\pi\) | ||||
−0.860250 | + | 0.509873i | \(0.829692\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.46738 | 0.171442 | ||||||||
\(680\) | −1.45245 | − | 4.50506i | −0.0556990 | − | 0.172761i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 22.0742i | − | 0.845266i | ||||||
\(683\) | − | 27.1229i | − | 1.03783i | −0.854826 | − | 0.518915i | \(-0.826336\pi\) | ||
0.854826 | − | 0.518915i | \(-0.173664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5475 | − | 9.84868i | 1.16716 | − | 0.376299i | ||||
\(686\) | −5.48913 | −0.209576 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.17448i | 0.0829013i | ||||||||
\(689\) | −69.9565 | −2.66513 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.7228 | 1.73938 | 0.869689 | − | 0.493600i | \(-0.164319\pi\) | ||||
0.869689 | + | 0.493600i | \(0.164319\pi\) | |||||||
\(692\) | 15.3484i | 0.583459i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.27719 | 0.0864408 | ||||||||
\(695\) | −7.62772 | − | 23.6588i | −0.289336 | − | 0.897430i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.46410i | 0.131212i | ||||||||
\(698\) | 21.0796i | 0.797873i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.8832 | − | 19.2926i | −0.524734 | − | 0.729192i | ||||
\(701\) | 17.2337 | 0.650907 | 0.325454 | − | 0.945558i | \(-0.394483\pi\) | ||||
0.325454 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.884861i | − | 0.0333732i | ||||||
\(704\) | 14.7446 | 0.555707 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.48913 | −0.0560440 | ||||||||
\(707\) | − | 56.7152i | − | 2.13300i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −52.3505 | −1.96607 | −0.983033 | − | 0.183430i | \(-0.941280\pi\) | ||||
−0.983033 | + | 0.183430i | \(0.941280\pi\) | |||||||
\(710\) | −22.1168 | + | 7.13058i | −0.830030 | + | 0.267606i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.01544i | 0.300391i | ||||||||
\(713\) | − | 10.0974i | − | 0.378149i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.3505 | + | 17.5229i | −2.03259 | + | 0.655319i | ||||
\(716\) | 6.70106 | 0.250431 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.62258i | 0.321792i | ||||||||
\(719\) | −10.8832 | −0.405873 | −0.202937 | − | 0.979192i | \(-0.565049\pi\) | ||||
−0.202937 | + | 0.979192i | \(0.565049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.0000 | −0.893807 | ||||||||
\(722\) | − | 14.9436i | − | 0.556145i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.0217 | −0.706938 | ||||||||
\(725\) | −23.3139 | + | 16.7769i | −0.865855 | + | 0.623078i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.9022i | 1.81368i | 0.421473 | + | 0.906841i | \(0.361513\pi\) | ||||
−0.421473 | + | 0.906841i | \(0.638487\pi\) | |||||||
\(728\) | 54.0607i | 2.00362i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.29211 | − | 4.00772i | −0.0478231 | − | 0.148332i | ||||
\(731\) | −2.74456 | −0.101511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4356i | 0.607064i | 0.952821 | + | 0.303532i | \(0.0981660\pi\) | ||||
−0.952821 | + | 0.303532i | \(0.901834\pi\) | |||||||
\(734\) | 13.0217 | 0.480642 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.25544 | 0.341160 | ||||||||
\(737\) | − | 51.0767i | − | 1.88143i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.62772 | −0.207019 | −0.103509 | − | 0.994628i | \(-0.533007\pi\) | ||||
−0.103509 | + | 0.994628i | \(0.533007\pi\) | |||||||
\(740\) | 6.94158 | − | 2.23800i | 0.255177 | − | 0.0822705i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.8713i | 1.20674i | ||||||||
\(743\) | − | 9.39764i | − | 0.344766i | −0.985030 | − | 0.172383i | \(-0.944853\pi\) | ||
0.985030 | − | 0.172383i | \(-0.0551467\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.29211 | − | 22.6179i | −0.267162 | − | 0.828654i | ||||
\(746\) | 6.51087 | 0.238380 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 4.75372i | − | 0.173813i | ||||||
\(749\) | 45.9565 | 1.67921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.7228 | 0.792677 | 0.396338 | − | 0.918105i | \(-0.370281\pi\) | ||||
0.396338 | + | 0.918105i | \(0.370281\pi\) | |||||||
\(752\) | 1.17981i | 0.0430234i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.5842 | 0.968140 | ||||||||
\(755\) | 0.605969 | + | 1.87953i | 0.0220535 | + | 0.0684030i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 41.5692i | − | 1.51086i | −0.655230 | − | 0.755429i | \(-0.727428\pi\) | ||
0.655230 | − | 0.755429i | \(-0.272572\pi\) | |||||||
\(758\) | 1.17981i | 0.0428528i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.11684 | + | 0.682481i | −0.0767860 | + | 0.0247562i | ||||
\(761\) | 32.4891 | 1.17773 | 0.588865 | − | 0.808231i | \(-0.299575\pi\) | ||||
0.588865 | + | 0.808231i | \(0.299575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 33.7562i | − | 1.22205i | ||||||
\(764\) | 10.4674 | 0.378696 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.78806 | 0.317526 | ||||||||
\(767\) | 9.50744i | 0.343294i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.4891 | 0.594613 | 0.297307 | − | 0.954782i | \(-0.403912\pi\) | ||||
0.297307 | + | 0.954782i | \(0.403912\pi\) | |||||||
\(770\) | 8.23369 | + | 25.5383i | 0.296722 | + | 0.920338i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 15.7532i | − | 0.566969i | ||||||
\(773\) | 21.5769i | 0.776067i | 0.921645 | + | 0.388034i | \(0.126846\pi\) | ||||
−0.921645 | + | 0.388034i | \(0.873154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.8614 | + | 18.6101i | −0.928969 | + | 0.668496i | ||||
\(776\) | 3.44563 | 0.123691 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.404759i | 0.0145113i | ||||||||
\(779\) | 1.62772 | 0.0583191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.3505 | −2.05216 | ||||||||
\(782\) | 0.994667i | 0.0355692i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.13859 | −0.112093 | ||||||||
\(785\) | 24.4307 | − | 7.87658i | 0.871969 | − | 0.281127i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.3205i | 0.617409i | 0.951158 | + | 0.308705i | \(0.0998955\pi\) | ||||
−0.951158 | + | 0.308705i | \(0.900105\pi\) | |||||||
\(788\) | 8.82496i | 0.314376i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.3723 | − | 3.66648i | 0.404608 | − | 0.130448i | ||||
\(791\) | 21.2554 | 0.755756 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 54.7431i | − | 1.94399i | ||||||
\(794\) | −13.8832 | −0.492695 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.9565 | −0.778228 | ||||||||
\(797\) | − | 25.6309i | − | 0.907893i | −0.891029 | − | 0.453947i | \(-0.850016\pi\) | ||
0.891029 | − | 0.453947i | \(-0.149984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.48913 | −0.0526815 | ||||||||
\(800\) | −17.0584 | − | 23.7051i | −0.603106 | − | 0.838102i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.1021i | 0.709831i | ||||||||
\(803\) | − | 10.3923i | − | 0.366736i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.76631 | + | 11.6819i | 0.132745 | + | 0.411734i | ||||
\(806\) | 29.4891 | 1.03871 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 43.7437i | − | 1.53890i | ||||||
\(809\) | −21.0000 | −0.738321 | −0.369160 | − | 0.929366i | \(-0.620355\pi\) | ||||
−0.369160 | + | 0.929366i | \(0.620355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8832 | 0.873766 | 0.436883 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436883 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(812\) | 27.3081i | 0.958325i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.23369 | −0.288591 | ||||||||
\(815\) | 32.2337 | − | 10.3923i | 1.12910 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.28962i | 0.0451181i | ||||||||
\(818\) | − | 18.1128i | − | 0.633299i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.11684 | + | 12.7692i | 0.143766 | + | 0.445919i | ||||
\(821\) | −40.7228 | −1.42124 | −0.710618 | − | 0.703578i | \(-0.751585\pi\) | ||||
−0.710618 | + | 0.703578i | \(0.751585\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.34896i | − | 0.151595i | −0.997123 | − | 0.0757977i | \(-0.975850\pi\) | ||
0.997123 | − | 0.0757977i | \(-0.0241503\pi\) | |||||||
\(824\) | −18.5109 | −0.644857 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.46738 | 0.155440 | ||||||||
\(827\) | − | 22.3692i | − | 0.777853i | −0.921269 | − | 0.388926i | \(-0.872846\pi\) | ||
0.921269 | − | 0.388926i | \(-0.127154\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3505 | 0.810997 | 0.405499 | − | 0.914096i | \(-0.367098\pi\) | ||||
0.405499 | + | 0.914096i | \(0.367098\pi\) | |||||||
\(830\) | 6.51087 | + | 20.1947i | 0.225996 | + | 0.700968i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.6974i | 0.682883i | ||||||||
\(833\) | − | 3.96143i | − | 0.137256i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.8614 | + | 9.30506i | −0.998790 | + | 0.322015i | ||||
\(836\) | −2.23369 | −0.0772537 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8564i | 0.478662i | ||||||||
\(839\) | 45.8614 | 1.58331 | 0.791656 | − | 0.610967i | \(-0.209219\pi\) | ||||
0.791656 | + | 0.610967i | \(0.209219\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00000 | 0.137931 | ||||||||
\(842\) | − | 17.2279i | − | 0.593714i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.55437 | −0.0879252 | ||||||||
\(845\) | −14.4891 | − | 44.9407i | −0.498441 | − | 1.54601i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.1176i | 0.966131i | ||||||||
\(848\) | − | 7.51811i | − | 0.258173i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.54755 | − | 1.83324i | 0.0873802 | − | 0.0628796i | ||||
\(851\) | −3.76631 | −0.129108 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.7971i | − | 0.369684i | −0.982768 | − | 0.184842i | \(-0.940823\pi\) | ||
0.982768 | − | 0.184842i | \(-0.0591774\pi\) | |||||||
\(854\) | −25.7228 | −0.880217 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.4456 | 1.21151 | ||||||||
\(857\) | − | 49.3995i | − | 1.68746i | −0.536772 | − | 0.843728i | \(-0.680356\pi\) | ||
0.536772 | − | 0.843728i | \(-0.319644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.3288 | −1.64896 | −0.824478 | − | 0.565893i | \(-0.808531\pi\) | ||||
−0.824478 | + | 0.565893i | \(0.808531\pi\) | |||||||
\(860\) | −10.1168 | + | 3.26172i | −0.344982 | + | 0.111224i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 26.4232i | − | 0.899978i | ||||||
\(863\) | − | 16.7306i | − | 0.569516i | −0.958599 | − | 0.284758i | \(-0.908087\pi\) | ||
0.958599 | − | 0.284758i | \(-0.0919133\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.8030 | + | 7.67420i | −0.809326 | + | 0.260931i | ||||
\(866\) | −10.1168 | −0.343784 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 30.2921i | 1.02818i | ||||||||
\(869\) | 29.4891 | 1.00035 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68.2337 | 2.31201 | ||||||||
\(872\) | − | 26.0357i | − | 0.881679i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.467376 | 0.0158092 | ||||||||
\(875\) | 22.9783 | − | 31.1769i | 0.776807 | − | 1.05397i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.08724i | − | 0.0367135i | −0.999832 | − | 0.0183568i | \(-0.994157\pi\) | ||
0.999832 | − | 0.0183568i | \(-0.00584346\pi\) | |||||||
\(878\) | − | 25.2434i | − | 0.851923i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.88316 | − | 5.84096i | −0.0634812 | − | 0.196899i | ||||
\(881\) | 10.8832 | 0.366663 | 0.183331 | − | 0.983051i | \(-0.441312\pi\) | ||||
0.183331 | + | 0.983051i | \(0.441312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 54.9455i | − | 1.84906i | −0.381104 | − | 0.924532i | \(-0.624456\pi\) | ||
0.381104 | − | 0.924532i | \(-0.375544\pi\) | |||||||
\(884\) | 6.35053 | 0.213592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.0217 | 0.571857 | ||||||||
\(887\) | 43.8535i | 1.47246i | 0.676733 | + | 0.736228i | \(0.263395\pi\) | ||||
−0.676733 | + | 0.736228i | \(0.736605\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000 | 1.20740 | ||||||||
\(890\) | −5.05842 | + | 1.63086i | −0.169559 | + | 0.0546666i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 25.5383i | 0.855087i | ||||||||
\(893\) | 0.699713i | 0.0234150i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.35053 | + | 10.3923i | 0.111996 | + | 0.347376i | ||||
\(896\) | −31.2119 | −1.04272 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.62258i | 0.287739i | ||||||||
\(899\) | 36.6060 | 1.22088 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.48913 | 0.316129 | ||||||||
\(902\) | − | 15.1460i | − | 0.504308i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.3940 | 0.545257 | ||||||||
\(905\) | −9.51087 | − | 29.4998i | −0.316152 | − | 0.980605i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 18.2054i | − | 0.604499i | −0.953229 | − | 0.302250i | \(-0.902262\pi\) | ||
0.953229 | − | 0.302250i | \(-0.0977376\pi\) | |||||||
\(908\) | 18.6101i | 0.617599i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −34.1168 | + | 10.9994i | −1.13096 | + | 0.364628i | ||||
\(911\) | −18.6060 | −0.616443 | −0.308222 | − | 0.951315i | \(-0.599734\pi\) | ||||
−0.308222 | + | 0.951315i | \(0.599734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.3663i | 1.73307i | ||||||||
\(914\) | −16.6277 | −0.549996 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.1603 | 0.798280 | ||||||||
\(917\) | 15.1460i | 0.500166i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.3505 | −1.82585 | −0.912923 | − | 0.408132i | \(-0.866180\pi\) | ||||
−0.912923 | + | 0.408132i | \(0.866180\pi\) | |||||||
\(920\) | 2.90491 | + | 9.01011i | 0.0957719 | + | 0.297055i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.0902i | 0.628703i | ||||||||
\(923\) | − | 76.6150i | − | 2.52181i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.94158 | + | 9.64630i | 0.228238 | + | 0.317169i | ||||
\(926\) | 10.9783 | 0.360768 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.5538i | 1.10146i | ||||||||
\(929\) | 3.51087 | 0.115188 | 0.0575940 | − | 0.998340i | \(-0.481657\pi\) | ||||
0.0575940 | + | 0.998340i | \(0.481657\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.86141 | −0.0610051 | ||||||||
\(932\) | − | 8.42020i | − | 0.275813i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.5109 | −0.474810 | ||||||||
\(935\) | 7.37228 | − | 2.37686i | 0.241099 | − | 0.0777317i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 22.2766i | − | 0.727745i | −0.931449 | − | 0.363873i | \(-0.881454\pi\) | ||
0.931449 | − | 0.363873i | \(-0.118546\pi\) | |||||||
\(938\) | − | 32.0618i | − | 1.04685i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.48913 | + | 1.76972i | −0.179036 | + | 0.0577220i | ||||
\(941\) | −6.86141 | −0.223675 | −0.111838 | − | 0.993726i | \(-0.535674\pi\) | ||||
−0.111838 | + | 0.993726i | \(0.535674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.92820i | − | 0.225613i | ||||||
\(944\) | −1.02175 | −0.0332551 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | − | 43.1538i | − | 1.40231i | −0.713009 | − | 0.701155i | \(-0.752668\pi\) | ||
0.713009 | − | 0.701155i | \(-0.247332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.8832 | 0.450666 | ||||||||
\(950\) | −0.861407 | − | 1.19705i | −0.0279477 | − | 0.0388373i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 7.33296i | − | 0.237663i | ||||||
\(953\) | 25.0410i | 0.811158i | 0.914060 | + | 0.405579i | \(0.132930\pi\) | ||||
−0.914060 | + | 0.405579i | \(0.867070\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.23369 | + | 16.2333i | 0.169358 | + | 0.525296i | ||||
\(956\) | −31.5326 | −1.01984 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 14.7413i | − | 0.476269i | ||||||
\(959\) | 49.7228 | 1.60563 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.60597 | 0.309870 | ||||||||
\(962\) | − | 10.9994i | − | 0.354636i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.07335 | −0.0667780 | ||||||||
\(965\) | 24.4307 | − | 7.87658i | 0.786452 | − | 0.253556i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.2636i | − | 1.39126i | −0.718399 | − | 0.695632i | \(-0.755125\pi\) | ||
0.718399 | − | 0.695632i | \(-0.244875\pi\) | |||||||
\(968\) | 21.6867i | 0.697037i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.701064 | + | 2.17448i | 0.0225098 | + | 0.0698184i | ||||
\(971\) | 41.5842 | 1.33450 | 0.667251 | − | 0.744833i | \(-0.267471\pi\) | ||||
0.667251 | + | 0.744833i | \(0.267471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 38.5099i | − | 1.23457i | ||||||
\(974\) | 7.53262 | 0.241361 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.88316 | 0.188315 | ||||||||
\(977\) | 28.3027i | 0.905484i | 0.891642 | + | 0.452742i | \(0.149554\pi\) | ||||
−0.891642 | + | 0.452742i | \(0.850446\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.1168 | −0.419216 | ||||||||
\(980\) | −4.70789 | − | 14.6024i | −0.150388 | − | 0.466457i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 25.0582i | − | 0.799640i | ||||||
\(983\) | 50.3770i | 1.60678i | 0.595456 | + | 0.803388i | \(0.296971\pi\) | ||||
−0.595456 | + | 0.803388i | \(0.703029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.6861 | + | 4.41248i | −0.436077 | + | 0.140593i | ||||
\(986\) | −3.60597 | −0.114837 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 2.98400i | − | 0.0949337i | ||||||
\(989\) | 5.48913 | 0.174544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.6060 | 1.22636 | 0.613180 | − | 0.789944i | \(-0.289890\pi\) | ||||
0.613180 | + | 0.789944i | \(0.289890\pi\) | |||||||
\(992\) | 37.2203i | 1.18174i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36.0000 | −1.14185 | ||||||||
\(995\) | −10.9783 | − | 34.0511i | −0.348034 | − | 1.07949i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 60.3817i | − | 1.91231i | −0.292864 | − | 0.956154i | \(-0.594608\pi\) | ||
0.292864 | − | 0.956154i | \(-0.405392\pi\) | |||||||
\(998\) | 19.3098i | 0.611242i | ||||||||
\(999\) | 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 | 405.2.b.a.244.3 | yes | 4 | |
3.2 | odd | 2 | 405.2.b.b.244.2 | yes | 4 | ||
5.2 | odd | 4 | 2025.2.a.w.1.2 | 4 | |||
5.3 | odd | 4 | 2025.2.a.w.1.3 | 4 | |||
5.4 | even | 2 | inner | 405.2.b.a.244.2 | ✓ | 4 | |
9.2 | odd | 6 | 405.2.j.d.109.1 | 4 | |||
9.4 | even | 3 | 405.2.j.e.379.1 | 4 | |||
9.5 | odd | 6 | 405.2.j.a.379.2 | 4 | |||
9.7 | even | 3 | 405.2.j.b.109.2 | 4 | |||
15.2 | even | 4 | 2025.2.a.x.1.3 | 4 | |||
15.8 | even | 4 | 2025.2.a.x.1.2 | 4 | |||
15.14 | odd | 2 | 405.2.b.b.244.3 | yes | 4 | ||
45.4 | even | 6 | 405.2.j.b.379.2 | 4 | |||
45.14 | odd | 6 | 405.2.j.d.379.1 | 4 | |||
45.29 | odd | 6 | 405.2.j.a.109.2 | 4 | |||
45.34 | even | 6 | 405.2.j.e.109.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.b.a.244.2 | ✓ | 4 | 5.4 | even | 2 | inner | |
405.2.b.a.244.3 | yes | 4 | 1.1 | even | 1 | trivial | |
405.2.b.b.244.2 | yes | 4 | 3.2 | odd | 2 | ||
405.2.b.b.244.3 | yes | 4 | 15.14 | odd | 2 | ||
405.2.j.a.109.2 | 4 | 45.29 | odd | 6 | |||
405.2.j.a.379.2 | 4 | 9.5 | odd | 6 | |||
405.2.j.b.109.2 | 4 | 9.7 | even | 3 | |||
405.2.j.b.379.2 | 4 | 45.4 | even | 6 | |||
405.2.j.d.109.1 | 4 | 9.2 | odd | 6 | |||
405.2.j.d.379.1 | 4 | 45.14 | odd | 6 | |||
405.2.j.e.109.1 | 4 | 45.34 | even | 6 | |||
405.2.j.e.379.1 | 4 | 9.4 | even | 3 | |||
2025.2.a.w.1.2 | 4 | 5.2 | odd | 4 | |||
2025.2.a.w.1.3 | 4 | 5.3 | odd | 4 | |||
2025.2.a.x.1.2 | 4 | 15.8 | even | 4 | |||
2025.2.a.x.1.3 | 4 | 15.2 | even | 4 |