Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,4,Mod(31,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.31");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.p (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: | \(6.60821392064\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.12258833328.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 29x^{4} - 20x^{3} + 808x^{2} - 672x + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(2.68858 + 4.65676i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.47 |
Dual form | 112.4.p.g.31.2 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.38417 | + | 4.12950i | 0.458834 | + | 0.794723i | 0.998900 | − | 0.0468996i | \(-0.0149341\pi\) |
−0.540066 | + | 0.841623i | \(0.681601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.6315 | + | 8.44749i | 1.30868 | + | 0.755566i | 0.981876 | − | 0.189526i | \(-0.0606952\pi\) |
0.326803 | + | 0.945092i | \(0.394029\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.89981 | − | 16.2417i | 0.480545 | − | 0.876970i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.13148 | − | 3.69182i | 0.0789436 | − | 0.136734i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −35.2840 | + | 20.3712i | −0.967138 | + | 0.558378i | −0.898363 | − | 0.439255i | \(-0.855243\pi\) |
−0.0687757 | + | 0.997632i | \(0.521909\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.7321i | 1.21036i | 0.796089 | + | 0.605179i | \(0.206899\pi\) | ||||
−0.796089 | + | 0.605179i | \(0.793101\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 80.5609i | 1.38672i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.377 | − | 61.4170i | 1.51767 | − | 0.876225i | 0.517882 | − | 0.855452i | \(-0.326721\pi\) |
0.999784 | − | 0.0207724i | \(-0.00661253\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −37.7473 | + | 65.3803i | −0.455780 | + | 0.789435i | −0.998733 | − | 0.0503288i | \(-0.983973\pi\) |
0.542952 | + | 0.839763i | \(0.317306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 88.2889 | − | 1.97120i | 0.917438 | − | 0.0204833i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −91.9414 | − | 53.0824i | −0.833526 | − | 0.481236i | 0.0215324 | − | 0.999768i | \(-0.493146\pi\) |
−0.855058 | + | 0.518532i | \(0.826479\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 80.2201 | + | 138.945i | 0.641760 | + | 1.11156i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 149.072 | 1.06255 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −146.703 | −0.939382 | −0.469691 | − | 0.882831i | \(-0.655635\pi\) | ||||
−0.469691 | + | 0.882831i | \(0.655635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.2956 | − | 36.8850i | −0.123381 | − | 0.213702i | 0.797718 | − | 0.603030i | \(-0.206040\pi\) |
−0.921099 | + | 0.389329i | \(0.872707\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −168.246 | − | 97.1369i | −0.887511 | − | 0.512405i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 267.419 | − | 162.459i | 1.29149 | − | 0.784589i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.4571 | + | 70.0738i | −0.179760 | + | 0.311353i | −0.941798 | − | 0.336179i | \(-0.890865\pi\) |
0.762039 | + | 0.647532i | \(0.224199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −234.275 | + | 135.259i | −0.961900 | + | 0.555353i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 53.8052i | − | 0.204950i | −0.994736 | − | 0.102475i | \(-0.967324\pi\) | ||
0.994736 | − | 0.102475i | \(-0.0326762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 341.166i | − | 1.20994i | −0.796249 | − | 0.604970i | \(-0.793185\pi\) | ||
0.796249 | − | 0.604970i | \(-0.206815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 62.3733 | − | 36.0112i | 0.206624 | − | 0.119294i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.06393 | + | 3.57482i | −0.00640542 | + | 0.0110945i | −0.869210 | − | 0.494442i | \(-0.835372\pi\) |
0.862805 | + | 0.505537i | \(0.168706\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −184.587 | − | 289.096i | −0.538153 | − | 0.842847i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 507.244 | + | 292.857i | 1.39271 | + | 0.804083i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −139.849 | − | 242.225i | −0.362447 | − | 0.627777i | 0.625916 | − | 0.779891i | \(-0.284725\pi\) |
−0.988363 | + | 0.152114i | \(0.951392\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −688.342 | −1.68756 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −359.984 | −0.836509 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −87.4155 | − | 151.408i | −0.192890 | − | 0.334096i | 0.753317 | − | 0.657658i | \(-0.228453\pi\) |
−0.946207 | + | 0.323562i | \(0.895119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −404.509 | − | 233.543i | −0.849050 | − | 0.490199i | 0.0112801 | − | 0.999936i | \(-0.496409\pi\) |
−0.860330 | + | 0.509737i | \(0.829743\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −40.9918 | − | 67.4754i | −0.0819759 | − | 0.134938i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −479.244 | + | 830.075i | −0.914506 | + | 1.58397i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 652.335 | − | 376.626i | 1.18948 | − | 0.686748i | 0.231294 | − | 0.972884i | \(-0.425704\pi\) |
0.958189 | + | 0.286136i | \(0.0923708\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 506.229i | − | 0.883230i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 669.583i | − | 1.11922i | −0.828755 | − | 0.559611i | \(-0.810950\pi\) | ||
0.828755 | − | 0.559611i | \(-0.189050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 723.802 | − | 417.887i | 1.16047 | − | 0.670000i | 0.209057 | − | 0.977904i | \(-0.432961\pi\) |
0.951418 | + | 0.307904i | \(0.0996274\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −382.516 | + | 662.538i | −0.588922 | + | 1.02004i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.8426 | + | 754.372i | 0.0249272 | + | 1.11648i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 958.008 | + | 553.106i | 1.36436 | + | 0.787713i | 0.990201 | − | 0.139652i | \(-0.0445983\pi\) |
0.374159 | + | 0.927365i | \(0.377932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 297.864 | + | 515.915i | 0.408592 | + | 0.707703i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −552.905 | −0.731195 | −0.365597 | − | 0.930773i | \(-0.619135\pi\) | ||||
−0.365597 | + | 0.930773i | \(0.619135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2075.28 | 2.64818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −349.765 | − | 605.811i | −0.431020 | − | 0.746548i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106.062 | + | 61.2347i | 0.126320 | + | 0.0729310i | 0.561829 | − | 0.827254i | \(-0.310098\pi\) |
−0.435508 | + | 0.900185i | \(0.643431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 921.427 | + | 504.906i | 1.06145 | + | 0.581632i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 101.545 | − | 175.880i | 0.113222 | − | 0.196107i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1104.60 | + | 637.740i | −1.19294 | + | 0.688744i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 291.203i | − | 0.304816i | −0.988318 | − | 0.152408i | \(-0.951297\pi\) | ||
0.988318 | − | 0.152408i | \(-0.0487028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 173.683i | 0.176321i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1168.30 | + | 674.520i | −1.15099 | + | 0.664527i | −0.949129 | − | 0.314887i | \(-0.898034\pi\) |
−0.201865 | + | 0.979413i | \(0.564700\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −989.035 | + | 1713.06i | −0.946141 | + | 1.63876i | −0.192690 | + | 0.981260i | \(0.561721\pi\) |
−0.753451 | + | 0.657504i | \(0.771612\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1308.45 | + | 716.977i | 1.21611 | + | 0.666379i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 732.931 | + | 423.158i | 0.662198 | + | 0.382320i | 0.793114 | − | 0.609073i | \(-0.208459\pi\) |
−0.130916 | + | 0.991393i | \(0.541792\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −463.538 | − | 802.872i | −0.407330 | − | 0.705516i | 0.587260 | − | 0.809398i | \(-0.300207\pi\) |
−0.994590 | + | 0.103883i | \(0.966873\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −385.826 | −0.329919 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −599.053 | −0.498709 | −0.249355 | − | 0.968412i | \(-0.580218\pi\) | ||||
−0.249355 | + | 0.968412i | \(0.580218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −896.825 | − | 1553.35i | −0.727212 | − | 1.25957i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 209.445 | + | 120.923i | 0.165497 | + | 0.0955500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −50.7787 | − | 2274.35i | −0.0391166 | − | 1.75201i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 164.473 | − | 284.876i | 0.123571 | − | 0.214031i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 222.189 | − | 128.281i | 0.162879 | − | 0.0940380i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 598.760i | 0.428438i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1833.90i | 1.28136i | 0.767810 | + | 0.640678i | \(0.221347\pi\) | ||||
−0.767810 | + | 0.640678i | \(0.778653\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1408.85 | − | 813.398i | 0.961567 | − | 0.555161i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −689.574 | + | 1194.38i | −0.459911 | + | 0.796589i | −0.998956 | − | 0.0456878i | \(-0.985452\pi\) |
0.539045 | + | 0.842277i | \(0.318785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 725.943 | + | 1194.95i | 0.473288 | + | 0.779064i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2181.15 | + | 1259.29i | 1.39054 | + | 0.802831i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −736.714 | − | 1276.03i | −0.459429 | − | 0.795754i | 0.539502 | − | 0.841984i | \(-0.318612\pi\) |
−0.998931 | + | 0.0462305i | \(0.985279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1929.87 | 1.17762 | 0.588811 | − | 0.808271i | \(-0.299596\pi\) | ||||
0.588811 | + | 0.808271i | \(0.299596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.6830 | −0.0117561 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1155.70 | − | 2001.74i | −0.675837 | − | 1.17058i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2146.48 | − | 1239.27i | −1.22935 | − | 0.709765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 753.739 | − | 1451.51i | 0.422907 | − | 0.814409i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1153.42 | + | 1997.78i | −0.634172 | + | 1.09842i | 0.352517 | + | 0.935805i | \(0.385326\pi\) |
−0.986690 | + | 0.162614i | \(0.948008\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 887.906 | − | 512.633i | 0.478522 | − | 0.276275i | −0.241278 | − | 0.970456i | \(-0.577567\pi\) |
0.719800 | + | 0.694181i | \(0.244233\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 523.636i | − | 0.276689i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 719.577i | − | 0.372889i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 66.6966 | − | 38.5073i | 0.0339043 | − | 0.0195746i | −0.482952 | − | 0.875647i | \(-0.660435\pi\) |
0.516856 | + | 0.856072i | \(0.327102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 666.846 | − | 1155.01i | 0.332606 | − | 0.576090i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1680.41 | + | 1020.86i | −0.822577 | + | 0.499722i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3366.71 | − | 1943.77i | −1.61780 | − | 0.934036i | −0.987489 | − | 0.157691i | \(-0.949595\pi\) |
−0.630308 | − | 0.776345i | \(-0.717072\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1641.12 | − | 2842.51i | −0.774311 | − | 1.34115i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −117.863 | −0.0546141 | −0.0273070 | − | 0.999627i | \(-0.508693\pi\) | ||||
−0.0273070 | + | 0.999627i | \(0.508693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1021.54 | −0.464969 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 160.915 | + | 278.713i | 0.0719618 | + | 0.124642i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2480.48 | − | 1432.11i | −1.09010 | − | 0.629370i | −0.156498 | − | 0.987678i | \(-0.550020\pi\) |
−0.933603 | + | 0.358308i | \(0.883354\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2970.65 | − | 66.3248i | 1.28320 | − | 0.0286496i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 416.826 | − | 721.965i | 0.177009 | − | 0.306589i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1195.93 | + | 690.471i | −0.499375 | + | 0.288314i | −0.728455 | − | 0.685093i | \(-0.759761\pi\) |
0.229081 | + | 0.973407i | \(0.426428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 204.817i | − | 0.0841103i | −0.999115 | − | 0.0420551i | \(-0.986609\pi\) | ||
0.999115 | − | 0.0420551i | \(-0.0133905\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2227.23i | − | 0.899680i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1183.89 | + | 683.522i | −0.470495 | + | 0.271641i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2502.28 | + | 4334.08i | −0.978528 | + | 1.69486i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1326.72 | − | 2421.19i | 0.510605 | − | 0.931829i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3609.38 | + | 2083.88i | 1.36736 | + | 0.789445i | 0.990590 | − | 0.136862i | \(-0.0437018\pi\) |
0.376769 | + | 0.926307i | \(0.377035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2392.97 | + | 4144.74i | 0.892485 | + | 1.54583i | 0.836887 | + | 0.547376i | \(0.184373\pi\) |
0.0555978 | + | 0.998453i | \(0.482294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4570.39 | −1.67842 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −377.368 | −0.136479 | −0.0682395 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682395 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 809.764 | + | 1402.55i | 0.288455 | + | 0.499620i | 0.973441 | − | 0.228937i | \(-0.0735249\pi\) |
−0.684986 | + | 0.728556i | \(0.740192\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3110.55 | + | 1795.88i | 1.09155 | + | 0.630206i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1305.63 | + | 2382.71i | −0.451415 | + | 0.823810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 454.519 | − | 787.249i | 0.154853 | − | 0.268214i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −391.942 | + | 226.288i | −0.131603 | + | 0.0759810i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3075.83i | − | 1.01799i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3010.54i | − | 0.982247i | −0.871090 | − | 0.491123i | \(-0.836586\pi\) | ||
0.871090 | − | 0.491123i | \(-0.163414\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2765.04 | − | 1596.40i | 0.889472 | − | 0.513537i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2882.00 | − | 4991.77i | 0.914189 | − | 1.58342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −788.603 | + | 17.6069i | −0.246700 | + | 0.00550798i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3451.33 | + | 1992.63i | 1.06493 | + | 0.614837i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3484.32 | + | 6035.02i | 1.06055 | + | 1.83692i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 879.692 | 0.264164 | 0.132082 | − | 0.991239i | \(-0.457834\pi\) | ||||
0.132082 | + | 0.991239i | \(0.457834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 683.948 | 0.202651 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −712.315 | − | 1233.77i | −0.208273 | − | 0.360740i | 0.742897 | − | 0.669405i | \(-0.233451\pi\) |
−0.951171 | + | 0.308665i | \(0.900118\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 206.746 | + | 119.365i | 0.0596602 | + | 0.0344448i | 0.529533 | − | 0.848289i | \(-0.322367\pi\) |
−0.469873 | + | 0.882734i | \(0.655700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3075.03 | + | 1868.10i | −0.875852 | + | 0.532087i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2920.86 | + | 5059.08i | −0.821253 | + | 1.42245i | 0.0834970 | + | 0.996508i | \(0.473391\pi\) |
−0.904750 | + | 0.425943i | \(0.859942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −60.3966 | + | 34.8700i | −0.0167653 | + | 0.00967943i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5274.80i | 1.44572i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2101.91i | 0.568876i | 0.958694 | + | 0.284438i | \(0.0918070\pi\) | ||||
−0.958694 | + | 0.284438i | \(0.908193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1883.76 | − | 1087.59i | 0.503501 | − | 0.290697i | −0.226657 | − | 0.973975i | \(-0.572780\pi\) |
0.730158 | + | 0.683278i | \(0.239446\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 592.161 | − | 1025.65i | 0.156326 | − | 0.270764i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −258.636 | − | 5789.20i | −0.0674435 | − | 1.50963i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3709.16 | − | 2141.49i | −0.955499 | − | 0.551658i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1318.22 | − | 2283.22i | −0.335497 | − | 0.581097i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2069.98 | −0.520542 | −0.260271 | − | 0.965536i | \(-0.583812\pi\) | ||||
−0.260271 | + | 0.965536i | \(0.583812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4325.41 | 1.07485 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4947.81 | + | 8569.87i | 1.21508 | + | 2.10457i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4498.76 | + | 2597.36i | 1.09192 | + | 0.630423i | 0.934088 | − | 0.357042i | \(-0.116215\pi\) |
0.157836 | + | 0.987465i | \(0.449548\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 778.057 | + | 1280.74i | 0.186665 | + | 0.307263i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −312.694 | + | 541.602i | −0.0741581 | + | 0.128446i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1580.24 | + | 912.352i | −0.370501 | + | 0.213909i | −0.673677 | − | 0.739026i | \(-0.735286\pi\) |
0.303176 | + | 0.952934i | \(0.401953\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 4725.48i | − | 1.09541i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 583.975i | 0.133853i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2162.50 | − | 1248.52i | 0.490148 | − | 0.282987i | −0.234488 | − | 0.972119i | \(-0.575341\pi\) |
0.724636 | + | 0.689132i | \(0.242008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −961.292 | + | 1665.01i | −0.215477 | + | 0.373217i | −0.953420 | − | 0.301646i | \(-0.902464\pi\) |
0.737943 | + | 0.674863i | \(0.235797\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 111.830 | + | 5008.82i | 0.0247922 | + | 1.11043i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5660.97 | − | 3268.36i | −1.24134 | − | 0.716689i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 942.717 | + | 1632.83i | 0.204485 | + | 0.354179i | 0.949969 | − | 0.312345i | \(-0.101115\pi\) |
−0.745483 | + | 0.666524i | \(0.767781\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −181.564 | −0.0389604 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2666.13 | −0.566006 | −0.283003 | − | 0.959119i | \(-0.591331\pi\) | ||||
−0.283003 | + | 0.959119i | \(0.591331\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1873.94 | + | 3245.75i | 0.393618 | + | 0.681766i | 0.992924 | − | 0.118754i | \(-0.0378899\pi\) |
−0.599306 | + | 0.800520i | \(0.704557\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5267.09 | − | 3040.96i | −1.09472 | − | 0.632038i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −873.889 | − | 478.856i | −0.179735 | − | 0.0984878i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5087.61 | − | 8811.99i | 1.03554 | − | 1.79361i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1202.52 | − | 694.276i | 0.242244 | − | 0.139860i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6486.41i | 1.29331i | 0.762782 | + | 0.646655i | \(0.223833\pi\) | ||||
−0.762782 | + | 0.646655i | \(0.776167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2953.76i | − | 0.582965i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5259.87 | + | 3036.78i | −1.02764 | + | 0.593307i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3011.48 | − | 5216.03i | 0.582469 | − | 1.00887i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5541.13 | − | 3036.32i | −1.06108 | − | 0.581430i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5570.86 | − | 3216.34i | −1.05623 | − | 0.609814i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3945.71 | − | 6834.17i | −0.740756 | − | 1.28303i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8884.08 | 1.65160 | 0.825800 | − | 0.563963i | \(-0.190724\pi\) | ||||
0.825800 | + | 0.563963i | \(0.190724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9432.11 | −1.73648 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3500.88 | − | 6063.71i | −0.638318 | − | 1.10560i | −0.985802 | − | 0.167913i | \(-0.946297\pi\) |
0.347484 | − | 0.937686i | \(-0.387036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4140.54 | + | 2390.54i | 0.747722 | + | 0.431697i | 0.824870 | − | 0.565322i | \(-0.191248\pi\) |
−0.0771483 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −29.7735 | − | 1333.54i | −0.00532555 | − | 0.238529i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1801.72 | − | 3120.66i | 0.319226 | − | 0.552915i | −0.661101 | − | 0.750297i | \(-0.729911\pi\) |
0.980327 | + | 0.197382i | \(0.0632439\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5176.27 | − | 2988.52i | 0.908512 | − | 0.524530i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4035.52i | 0.701685i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9273.31i | 1.59746i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7882.66 | + | 4551.06i | −1.34539 | + | 0.776760i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2210.31 | − | 3828.37i | 0.373793 | − | 0.647428i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 39.6927 | + | 65.3370i | 0.00665146 | + | 0.0109488i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2861.42 | − | 1652.04i | −0.475159 | − | 0.274333i | 0.243238 | − | 0.969967i | \(-0.421790\pi\) |
−0.718397 | + | 0.695633i | \(0.755124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 172.467 | + | 298.721i | 0.0283817 | + | 0.0491586i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12726.2 | 2.07554 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6650.35 | −1.07498 | −0.537489 | − | 0.843271i | \(-0.680627\pi\) | ||||
−0.537489 | + | 0.843271i | \(0.680627\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1428.24 | − | 2473.79i | −0.228825 | − | 0.396336i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1502.79 | + | 867.634i | 0.238652 | + | 0.137786i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6338.21 | + | 425.098i | −0.997758 | + | 0.0669188i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4276.37 | − | 7406.88i | 0.667339 | − | 1.15586i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 203.832 | − | 117.683i | 0.0315339 | − | 0.0182061i | −0.484150 | − | 0.874985i | \(-0.660871\pi\) |
0.515684 | + | 0.856779i | \(0.327538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2984.02i | − | 0.457681i | −0.973464 | − | 0.228841i | \(-0.926507\pi\) | ||
0.973464 | − | 0.228841i | \(-0.0734935\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8457.19i | 1.28607i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2118.54 | + | 1223.14i | −0.319429 | + | 0.184422i | −0.651138 | − | 0.758959i | \(-0.725708\pi\) |
0.331709 | + | 0.943382i | \(0.392375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5656.29 | − | 9796.98i | 0.845647 | − | 1.46470i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9270.88 | − | 5632.13i | 1.37442 | − | 0.834969i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4931.22 | − | 2847.04i | −0.724957 | − | 0.418554i | 0.0916173 | − | 0.995794i | \(-0.470796\pi\) |
−0.816574 | + | 0.577240i | \(0.804130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 579.782 | + | 1004.21i | 0.0845286 | + | 0.146408i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1568.53 | 0.226794 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14120.4 | 2.02492 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 168.161 | + | 291.263i | 0.0239180 | + | 0.0414272i | 0.877737 | − | 0.479143i | \(-0.159053\pi\) |
−0.853819 | + | 0.520571i | \(0.825719\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −198.639 | − | 114.684i | −0.0280237 | − | 0.0161795i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5178.78 | + | 115.625i | −0.724714 | + | 0.0161804i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4908.42 | + | 8501.64i | −0.681363 | + | 1.18016i | 0.293202 | + | 0.956051i | \(0.405279\pi\) |
−0.974565 | + | 0.224105i | \(0.928054\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2472.58 | + | 1427.54i | −0.340489 | + | 0.196582i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8322.78i | − | 1.13699i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3978.71i | 0.539242i | 0.962967 | + | 0.269621i | \(0.0868984\pi\) | ||||
−0.962967 | + | 0.269621i | \(0.913102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7573.09 | + | 4372.33i | −1.01832 | + | 0.587929i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1862.99 | + | 3226.80i | −0.248550 | + | 0.430501i | −0.963124 | − | 0.269059i | \(-0.913287\pi\) |
0.714574 | + | 0.699560i | \(0.246621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6126.12 | + | 11179.9i | −0.810950 | + | 1.47994i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1259.53 | − | 727.188i | −0.165440 | − | 0.0955169i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6346.89 | − | 10993.1i | −0.827250 | − | 1.43284i | −0.900187 | − | 0.435503i | \(-0.856571\pi\) |
0.0729372 | − | 0.997337i | \(-0.476763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13040.6 | −1.68669 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6576.24 | −0.844091 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9344.72 | + | 16185.5i | 1.19034 | + | 2.06173i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1794.63 | + | 1036.13i | 0.226877 | + | 0.130987i | 0.609130 | − | 0.793070i | \(-0.291519\pi\) |
−0.382254 | + | 0.924057i | \(0.624852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3203.79 | + | 5846.76i | −0.401980 | + | 0.733594i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4928.69 | − | 8536.75i | 0.613784 | − | 1.06310i | −0.376813 | − | 0.926289i | \(-0.622980\pi\) |
0.990597 | − | 0.136815i | \(-0.0436866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2092.57 | − | 1208.14i | 0.258656 | − | 0.149335i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10064.8i | 1.23487i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3296.64i | − | 0.401495i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1190.33 | − | 687.236i | 0.143907 | − | 0.0830847i | −0.426318 | − | 0.904573i | \(-0.640189\pi\) |
0.570225 | + | 0.821489i | \(0.306856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3512.90 | − | 6084.52i | 0.421603 | − | 0.730237i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3237.11 | + | 72.2738i | −0.385684 | + | 0.00861104i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8089.81 | − | 4670.66i | −0.956899 | − | 0.552466i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4601.14 | + | 7969.40i | 0.540332 | + | 0.935883i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11066.7 | 1.29032 | 0.645158 | − | 0.764049i | \(-0.276791\pi\) | ||||
0.645158 | + | 0.764049i | \(0.276791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15288.1 | 1.76982 | 0.884910 | − | 0.465761i | \(-0.154219\pi\) | ||||
0.884910 | + | 0.465761i | \(0.154219\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.79842 | + | 15.2393i | 0.00101133 | + | 0.00175168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17067.2 | + | 9853.76i | 1.94796 | + | 1.12465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7393.20 | + | 4491.43i | −0.837897 | + | 0.509029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5510.78 | − | 9544.95i | 0.620194 | − | 1.07421i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2265.08 | + | 1307.74i | −0.253143 | + | 0.146152i | −0.621203 | − | 0.783650i | \(-0.713356\pi\) |
0.368059 | + | 0.929802i | \(0.380022\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3152.43i | 0.349875i | 0.984580 | + | 0.174938i | \(0.0559723\pi\) | ||||
−0.984580 | + | 0.174938i | \(0.944028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 11818.5i | − | 1.30266i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6941.08 | − | 4007.43i | 0.759810 | − | 0.438676i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3470.23 | + | 6010.62i | −0.377278 | + | 0.653465i | −0.990665 | − | 0.136317i | \(-0.956473\pi\) |
0.613387 | + | 0.789783i | \(0.289807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1460.74 | + | 65.2592i | −0.157730 | + | 0.00704667i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10854.6 | + | 6266.93i | 1.16415 | + | 0.672123i | 0.952295 | − | 0.305177i | \(-0.0987158\pi\) |
0.211856 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1034.56 | + | 1791.91i | 0.110208 | + | 0.190887i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10999.8 | −1.16392 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8637.25 | 0.907833 | 0.453917 | − | 0.891044i | \(-0.350026\pi\) | ||||
0.453917 | + | 0.891044i | \(0.350026\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1096.08 | + | 1898.46i | 0.114440 | + | 0.198215i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4233.84 | + | 2444.41i | 0.439124 | + | 0.253528i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9216.66 | + | 15171.3i | 0.949634 | + | 1.56316i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8248.34 | + | 14286.5i | −0.844291 | + | 1.46236i | 0.0419444 | + | 0.999120i | \(0.486645\pi\) |
−0.886235 | + | 0.463235i | \(0.846689\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15857.9 | − | 9155.58i | 1.61260 | − | 0.931037i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6423.89i | 0.649003i | 0.945885 | + | 0.324501i | \(0.105197\pi\) | ||||
−0.945885 | + | 0.324501i | \(0.894803\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3390.22i | 0.340295i | 0.985419 | + | 0.170148i | \(0.0544245\pi\) | ||||
−0.985419 | + | 0.170148i | \(0.945576\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2971.49 | − | 1715.59i | 0.296343 | − | 0.171094i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −580.262 | + | 1005.04i | −0.0574975 | + | 0.0995886i | −0.893341 | − | 0.449379i | \(-0.851645\pi\) |
0.835844 | + | 0.548967i | \(0.184979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −311.388 | − | 13946.9i | −0.0306580 | − | 1.37315i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 318.032 | + | 183.616i | 0.0311128 | + | 0.0179630i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6949.97 | + | 12037.7i | 0.675603 | + | 1.17018i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12112.4 | −1.17001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1192.34 | −0.114451 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2042.46 | − | 3537.65i | −0.194828 | − | 0.337452i | 0.752016 | − | 0.659145i | \(-0.229081\pi\) |
−0.946844 | + | 0.321693i | \(0.895748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3975.43 | − | 2295.22i | −0.376849 | − | 0.217574i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8222.03 | − | 4505.35i | −0.774566 | − | 0.424431i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2459.93 | − | 4260.72i | 0.230309 | − | 0.398906i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6340.08 | − | 3660.44i | 0.589931 | − | 0.340597i | −0.175139 | − | 0.984544i | \(-0.556038\pi\) |
0.765070 | + | 0.643947i | \(0.222704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18537.1i | − | 1.71427i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.0507i | − | 0.00294588i | −0.999999 | − | 0.00147294i | \(-0.999531\pi\) | ||
0.999999 | − | 0.00147294i | \(-0.000468851\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15605.9 | + | 9010.07i | −1.42567 | + | 0.823110i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1467.19 | + | 2541.24i | −0.133222 | + | 0.230748i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10875.2 | − | 5959.16i | −0.981525 | − | 0.537837i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6513.95 | + | 3760.83i | 0.584378 | + | 0.337391i | 0.762871 | − | 0.646550i | \(-0.223789\pi\) |
−0.178493 | + | 0.983941i | \(0.557122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −281.006 | − | 486.717i | −0.0250588 | − | 0.0434031i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4599.64 | 0.407729 | 0.203865 | − | 0.978999i | \(-0.434650\pi\) | ||||
0.203865 | + | 0.978999i | \(0.434650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22792.0 | −2.00838 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2435.51 | − | 4218.43i | −0.213343 | − | 0.369521i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18006.2 | − | 10395.9i | −1.56800 | − | 0.905286i | −0.996402 | − | 0.0847525i | \(-0.972990\pi\) |
−0.571599 | − | 0.820533i | \(-0.693677\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −345.503 | − | 15474.9i | −0.0299103 | − | 1.33967i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5627.08 | + | 9746.39i | −0.484292 | + | 0.838818i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28942.1 | + | 16709.7i | −2.47639 | + | 1.42974i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 168.179i | − | 0.0143066i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 13657.5i | − | 1.15511i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16707.9 | − | 9646.31i | 1.40496 | − | 0.811156i | 0.410067 | − | 0.912055i | \(-0.365505\pi\) |
0.994897 | + | 0.100899i | \(0.0321718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8344.02 | − | 14452.3i | 0.697626 | − | 1.20832i | −0.271661 | − | 0.962393i | \(-0.587573\pi\) |
0.969287 | − | 0.245931i | \(-0.0790936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7356.43 | + | 12109.2i | 0.611544 | + | 1.00664i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4530.74 | − | 2615.82i | −0.374501 | − | 0.216218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −448.024 | − | 776.000i | −0.0368229 | − | 0.0637791i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −745.296 | −0.0609098 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3052.48 | 0.248063 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7149.24 | + | 12382.9i | 0.577736 | + | 1.00067i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5702.60 | − | 3292.40i | −0.458260 | − | 0.264576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12402.2 | + | 6440.22i | 0.991096 | + | 0.514657i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1525.67 | + | 2642.54i | −0.121245 | + | 0.210003i | −0.920259 | − | 0.391310i | \(-0.872022\pi\) |
0.799014 | + | 0.601313i | \(0.205355\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 845.794 | − | 488.320i | 0.0668444 | − | 0.0385926i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 15662.9i | − | 1.23106i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12022.3i | 0.939740i | 0.882736 | + | 0.469870i | \(0.155699\pi\) | ||||
−0.882736 | + | 0.469870i | \(0.844301\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1724.40 | + | 995.584i | −0.134054 | + | 0.0773962i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5537.65 | − | 9591.48i | 0.428152 | − | 0.741581i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17509.5 | − | 10637.2i | 1.34644 | − | 0.817971i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5645.21 | − | 3259.26i | −0.431758 | − | 0.249276i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5913.89 | − | 10243.2i | −0.449873 | − | 0.779204i | 0.548504 | − | 0.836148i | \(-0.315198\pi\) |
−0.998377 | + | 0.0569444i | \(0.981864\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19355.1 | 1.46446 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −23863.4 | −1.79593 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6841.32 | − | 11849.5i | −0.512127 | − | 0.887030i | −0.999901 | − | 0.0140600i | \(-0.995524\pi\) |
0.487774 | − | 0.872970i | \(-0.337809\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8765.03 | − | 5060.49i | −0.652650 | − | 0.376808i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11030.3 | − | 246.269i | 0.816981 | − | 0.0182405i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −816.737 | + | 1414.63i | −0.0601747 | + | 0.104226i | −0.894543 | − | 0.446981i | \(-0.852499\pi\) |
0.834369 | + | 0.551207i | \(0.185832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12962.1 | + | 7483.67i | −0.949995 | + | 0.548480i | −0.893079 | − | 0.449899i | \(-0.851460\pi\) |
−0.0569155 | + | 0.998379i | \(0.518127\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19873.3i | 1.44890i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 17033.1i | − | 1.23535i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11197.4 | − | 6464.81i | 0.807891 | − | 0.466436i | −0.0383317 | − | 0.999265i | \(-0.512204\pi\) |
0.846223 | + | 0.532829i | \(0.178871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11410.5 | + | 19763.5i | −0.819004 | + | 1.41856i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4920.75 | + | 8980.12i | −0.351372 | + | 0.641236i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9868.84 | + | 5697.78i | 0.701073 | + | 0.404765i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2042.99 | + | 3538.57i | 0.144389 | + | 0.250089i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7486.36 | −0.526397 | −0.263199 | − | 0.964742i | \(-0.584777\pi\) | ||||
−0.263199 | + | 0.964742i | \(0.584777\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3215.40 | 0.224938 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −899.710 | − | 1558.34i | −0.0626212 | − | 0.108463i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2294.33 | + | 1324.63i | 0.158882 | + | 0.0917304i | 0.577333 | − | 0.816509i | \(-0.304094\pi\) |
−0.418451 | + | 0.908239i | \(0.637427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18469.6 | − | 33706.1i | 1.27257 | − | 2.32238i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3861.23 | + | 6687.84i | −0.264706 | + | 0.458484i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15164.6 | − | 8755.28i | 1.03440 | − | 0.597213i | 0.116161 | − | 0.993230i | \(-0.462941\pi\) |
0.918243 | + | 0.396017i | \(0.129608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12124.7i | 0.822922i | 0.911427 | + | 0.411461i | \(0.134981\pi\) | ||||
−0.911427 | + | 0.411461i | \(0.865019\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3211.07i | − | 0.216857i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4812.96 | − | 2778.77i | 0.323429 | − | 0.186732i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5706.27 | + | 9883.55i | −0.381566 | + | 0.660891i | −0.991286 | − | 0.131725i | \(-0.957948\pi\) |
0.609721 | + | 0.792616i | \(0.291282\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12952.2 | + | 289.180i | −0.861825 | + | 0.0192417i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −202.807 | − | 117.091i | −0.0134283 | − | 0.00775285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3379.38 | − | 5853.26i | −0.222662 | − | 0.385662i | 0.732953 | − | 0.680279i | \(-0.238141\pi\) |
−0.955615 | + | 0.294617i | \(0.904808\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4334.60 | 0.284208 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9991.14 | −0.651909 | −0.325955 | − | 0.945385i | \(-0.605686\pi\) | ||||
−0.325955 | + | 0.945385i | \(0.605686\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10332.1 | − | 17895.6i | −0.670889 | − | 1.16201i | −0.977652 | − | 0.210228i | \(-0.932579\pi\) |
0.306764 | − | 0.951786i | \(-0.400754\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13705.9 | − | 7913.11i | −0.885667 | − | 0.511340i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1938.48 | − | 1177.64i | 0.124661 | − | 0.0757325i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4969.49 | − | 8607.41i | 0.318047 | − | 0.550874i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12701.7 | − | 7333.31i | 0.809020 | − | 0.467088i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9939.02i | 0.630039i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28295.8i | 1.78516i | 0.450887 | + | 0.892581i | \(0.351108\pi\) | ||||
−0.450887 | + | 0.892581i | \(0.648892\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12432.0 | − | 7177.63i | 0.780614 | − | 0.450688i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15491.8 | + | 26832.6i | −0.968149 | + | 1.67688i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16401.1 | − | 10472.0i | 1.02015 | − | 0.651359i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2471.98 | − | 1427.20i | −0.153036 | − | 0.0883554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8207.85 | + | 14216.4i | 0.505758 | + | 0.875998i | 0.999978 | + | 0.00666106i | \(0.00212030\pi\) |
−0.494220 | + | 0.869337i | \(0.664546\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14139.9 | −0.867220 | −0.433610 | − | 0.901101i | \(-0.642760\pi\) | ||||
−0.433610 | + | 0.901101i | \(0.642760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 27484.7 | 1.67784 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10974.5 | − | 19008.5i | −0.666853 | − | 1.15502i | −0.978779 | − | 0.204917i | \(-0.934308\pi\) |
0.311926 | − | 0.950106i | \(-0.399026\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6168.73 | + | 3561.52i | 0.373103 | + | 0.215411i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1952.87 | − | 3214.56i | −0.117571 | − | 0.193531i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2938.88 | + | 5090.29i | −0.176121 | + | 0.305051i | −0.940549 | − | 0.339659i | \(-0.889688\pi\) |
0.764427 | + | 0.644710i | \(0.223022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20179.0 | + | 11650.3i | −1.20375 | + | 0.694987i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3562.87i | − | 0.211569i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11002.0i | 0.650344i | 0.945655 | + | 0.325172i | \(0.105422\pi\) | ||||
−0.945655 | + | 0.325172i | \(0.894578\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3196.72 | − | 1845.63i | 0.188106 | − | 0.108603i | −0.402990 | − | 0.915205i | \(-0.632029\pi\) |
0.591095 | + | 0.806602i | \(0.298696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16614.4 | + | 28777.0i | −0.973229 | + | 1.68568i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 527.274 | + | 23616.3i | 0.0307471 | + | 1.37715i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13488.1 | + | 7787.35i | 0.782999 | + | 0.452065i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2097.33 | + | 3632.69i | 0.121207 | + | 0.209937i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19030.2 | 1.09487 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6819.19 | 0.390580 | 0.195290 | − | 0.980746i | \(-0.437435\pi\) | ||||
0.195290 | + | 0.980746i | \(0.437435\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11958.6 | + | 20712.9i | 0.681906 | + | 1.18110i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13683.4 | + | 7900.10i | 0.776802 | + | 0.448487i | 0.835296 | − | 0.549801i | \(-0.185296\pi\) |
−0.0584939 | + | 0.998288i | \(0.518630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4729.63 | − | 2591.65i | −0.267314 | − | 0.146478i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3396.56 | − | 5883.02i | 0.191126 | − | 0.331039i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18649.6 | + | 10767.3i | −1.04481 | + | 0.603222i | −0.921192 | − | 0.389108i | \(-0.872783\pi\) |
−0.123619 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 24893.5i | − | 1.38851i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1138.35i | 0.0632177i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13742.0 | − | 7933.92i | 0.759835 | − | 0.438691i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2019.27 | − | 3497.48i | 0.111167 | − | 0.192548i | −0.805074 | − | 0.593175i | \(-0.797874\pi\) |
0.916241 | + | 0.400627i | \(0.131208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2820.91 | + | 1545.75i | 0.154628 | + | 0.0847302i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28236.8 | + | 16302.6i | 1.54113 | + | 0.889771i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3304.56 | − | 5723.66i | −0.179582 | − | 0.311046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27855.3 | −1.50727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11823.9 | 0.637066 | 0.318533 | − | 0.947912i | \(-0.396810\pi\) | ||||
0.318533 | + | 0.947912i | \(0.396810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3054.29 | − | 5290.19i | −0.163862 | − | 0.283817i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −287.991 | − | 166.272i | −0.0153849 | − | 0.00888249i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 557.683 | + | 24978.3i | 0.0296659 | + | 1.32872i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13143.3 | + | 22764.8i | −0.696200 | + | 1.20585i | 0.273575 | + | 0.961851i | \(0.411794\pi\) |
−0.969775 | + | 0.244003i | \(0.921539\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4083.94 | − | 2357.87i | 0.215415 | − | 0.124370i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4521.68i | 0.237501i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 39051.1i | − | 2.04256i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8679.85 | + | 5011.32i | −0.452099 | + | 0.261020i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9614.97 | − | 16653.6i | 0.498717 | − | 0.863804i | −0.501282 | − | 0.865284i | \(-0.667138\pi\) |
0.999999 | + | 0.00148052i | \(0.000471263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19020.8 | + | 31309.5i | 0.982484 | + | 1.61724i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8982.42 | + | 5186.00i | 0.462047 | + | 0.266763i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11768.5 | − | 20383.7i | −0.602858 | − | 1.04418i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33771.2 | −1.72284 | −0.861419 | − | 0.507895i | \(-0.830424\pi\) | ||||
−0.861419 | + | 0.507895i | \(0.830424\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21731.9 | 1.10409 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20953.4 | − | 36292.4i | −1.06018 | − | 1.83628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1835.93 | + | 1059.97i | 0.0925125 | + | 0.0534121i | 0.545543 | − | 0.838083i | \(-0.316324\pi\) |
−0.453030 | + | 0.891495i | \(0.649657\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23289.9 | − | 14870.5i | 1.16879 | − | 0.746266i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15344.6 | + | 26577.7i | −0.766930 | + | 1.32836i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9238.36 | − | 5333.77i | 0.459863 | − | 0.265502i | −0.252124 | − | 0.967695i | \(-0.581129\pi\) |
0.711987 | + | 0.702193i | \(0.247796\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 20422.7i | − | 1.01248i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 26684.2i | − | 1.31756i | −0.752335 | − | 0.658781i | \(-0.771072\pi\) | ||
0.752335 | − | 0.658781i | \(-0.228928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33752.4 | + | 19487.0i | −1.65986 | + | 0.958318i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1178.50 | + | 2041.23i | −0.0577231 | + | 0.0999794i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13395.8 | − | 8138.03i | 0.653499 | − | 0.397006i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30415.3 | + | 17560.3i | 1.47785 | + | 0.853240i | 0.999687 | − | 0.0250284i | \(-0.00796761\pi\) |
0.478168 | + | 0.878268i | \(0.341301\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4935.19 | − | 8547.99i | −0.238842 | − | 0.413687i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17321.8 | 0.834975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10060.1 | 0.483011 | 0.241506 | − | 0.970399i | \(-0.422359\pi\) | ||||
0.241506 | + | 0.970399i | \(0.422359\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10312.5 | + | 17861.8i | 0.493176 | + | 0.854205i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31480.5 | − | 18175.3i | −1.49956 | − | 0.865774i | −0.499565 | − | 0.866276i | \(-0.666507\pi\) |
−1.00000 | 0.000502093i | \(0.999840\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17165.4 | + | 383.247i | −0.814456 | + | 0.0181841i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4423.41 | − | 7661.56i | 0.209057 | − | 0.362097i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8589.70 | − | 4959.27i | 0.404376 | − | 0.233466i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17664.9i | − | 0.828366i | −0.910194 | − | 0.414183i | \(-0.864067\pi\) | ||
0.910194 | − | 0.414183i | \(-0.135933\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24770.2i | 1.15704i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6848.89 | + | 3954.21i | −0.318677 | + | 0.183988i | −0.650803 | − | 0.759247i | \(-0.725568\pi\) |
0.332126 | + | 0.943235i | \(0.392234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3416.67 | − | 5917.84i | 0.158362 | − | 0.274290i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3433.78 | + | 6266.48i | −0.158541 | + | 0.289329i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3517.80 | + | 2031.00i | 0.161795 | + | 0.0934123i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13640.2 | + | 23625.5i | 0.624949 | + | 1.08244i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21869.4 | −0.998145 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1301.16 | 0.0591598 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5940.56 | + | 10289.4i | 0.269070 | + | 0.466043i | 0.968622 | − | 0.248539i | \(-0.0799503\pi\) |
−0.699552 | + | 0.714582i | \(0.746617\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7535.12 | − | 4350.40i | −0.339997 | − | 0.196297i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5331.46 | + | 9729.65i | −0.239652 | + | 0.437353i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13249.4 | − | 22948.7i | 0.593317 | − | 1.02766i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19513.9 | − | 11266.3i | 0.870549 | − | 0.502611i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10203.4i | 0.453480i | 0.973955 | + | 0.226740i | \(0.0728068\pi\) | ||||
−0.973955 | + | 0.226740i | \(0.927193\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 507.041i | 0.0224503i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 452.135 | − | 261.040i | 0.0199443 | − | 0.0115149i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17025.7 | + | 29489.5i | −0.748226 | + | 1.29597i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33210.6 | + | 741.482i | −1.45406 | + | 0.0324643i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10311.5 | + | 5953.36i | 0.449793 | + | 0.259688i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10471.1 | − | 18136.4i | −0.455059 | − | 0.788185i | 0.543633 | − | 0.839323i | \(-0.317048\pi\) |
−0.998692 | + | 0.0511383i | \(0.983715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5434.74 | −0.235314 | −0.117657 | − | 0.993054i | \(-0.537538\pi\) | ||||
−0.117657 | + | 0.993054i | \(0.537538\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9167.53 | −0.395473 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32839.9 | − | 56880.4i | −1.41145 | − | 2.44471i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22305.5 | + | 12878.1i | 0.955168 | + | 0.551467i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3828.02 | − | 2325.55i | 0.163323 | − | 0.0992203i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1066.43 | − | 1847.11i | 0.0453334 | − | 0.0785197i | −0.842468 | − | 0.538746i | \(-0.818898\pi\) |
0.887802 | + | 0.460226i | \(0.152232\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16591.2 | − | 9578.95i | 0.702714 | − | 0.405712i | −0.105643 | − | 0.994404i | \(-0.533690\pi\) |
0.808358 | + | 0.588692i | \(0.200357\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 31169.3i | − | 1.31536i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27208.2i | − | 1.14404i | −0.820239 | − | 0.572021i | \(-0.806160\pi\) | ||
0.820239 | − | 0.572021i | \(-0.193840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14900.9 | − | 8603.02i | 0.624281 | − | 0.360429i | −0.154253 | − | 0.988031i | \(-0.549297\pi\) |
0.778534 | + | 0.627603i | \(0.215964\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4495.19 | + | 7785.91i | −0.187649 | + | 0.325018i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37391.3 | − | 19416.6i | −1.55526 | − | 0.807617i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1724.52 | − | 995.650i | −0.0714723 | − | 0.0412645i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3174.58 | − | 5498.54i | −0.131099 | − | 0.227070i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9526.10 | −0.391988 | −0.195994 | − | 0.980605i | \(-0.562793\pi\) | ||||
−0.195994 | + | 0.980605i | \(0.562793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2867.21 | −0.117562 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6356.49 | − | 11009.8i | −0.259703 | − | 0.449818i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14946.6 | − | 8629.41i | −0.608495 | − | 0.351315i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3163.09 | − | 5206.66i | −0.128318 | − | 0.211220i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8935.56 | + | 15476.8i | −0.361210 | + | 0.625635i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7439.36 | − | 4295.12i | 0.299669 | − | 0.173014i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8447.62i | 0.339087i | 0.985523 | + | 0.169543i | \(0.0542293\pi\) | ||||
−0.985523 | + | 0.169543i | \(0.945771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5437.31i | 0.217488i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22211.6 | + | 12823.9i | −0.885337 | + | 0.511150i | −0.872414 | − | 0.488767i | \(-0.837447\pi\) |
−0.0129226 | + | 0.999916i | \(0.504114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3738.66 | + | 6475.54i | −0.148500 | + | 0.257209i | −0.930673 | − | 0.365852i | \(-0.880778\pi\) |
0.782173 | + | 0.623061i | \(0.214111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −106.061 | − | 4750.40i | −0.00419807 | − | 0.188029i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20094.6 | − | 11601.6i | −0.792616 | − | 0.457617i | 0.0482670 | − | 0.998834i | \(-0.484630\pi\) |
−0.840883 | + | 0.541218i | \(0.817964\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24195.4 | − | 41907.7i | −0.951062 | − | 1.64729i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48518.9 | 1.90056 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45069.8 | −1.75937 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21366.8 | + | 37008.3i | 0.831212 | + | 1.43970i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1075.07 | − | 620.691i | −0.0416788 | − | 0.0240633i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9724.89 | + | 5328.85i | 0.375727 | + | 0.205883i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6141.61 | + | 10637.6i | −0.236474 | + | 0.409584i | −0.959700 | − | 0.281027i | \(-0.909325\pi\) |
0.723226 | + | 0.690611i | \(0.242658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26785.6 | + | 15464.7i | −1.02782 | + | 0.593414i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44697.8i | 1.70931i | 0.519193 | + | 0.854657i | \(0.326233\pi\) | ||||
−0.519193 | + | 0.854657i | \(0.673767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9474.88i | − | 0.361104i | −0.983565 | − | 0.180552i | \(-0.942212\pi\) | ||
0.983565 | − | 0.180552i | \(-0.0577884\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12197.6 | − | 7042.27i | 0.463296 | − | 0.267484i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7502.29 | − | 12994.3i | 0.283993 | − | 0.491891i | −0.688371 | − | 0.725359i | \(-0.741674\pi\) |
0.972365 | + | 0.233468i | \(0.0750073\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29785.7 | + | 16321.4i | 1.12371 | + | 0.615749i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21019.6 | − | 12135.7i | −0.790330 | − | 0.456298i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −155.815 | − | 269.880i | −0.00583892 | − | 0.0101133i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23331.0 | −0.871361 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28719.5 | 1.06902 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3124.13 | + | 5411.15i | 0.115902 | + | 0.200747i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29753.5 | − | 17178.2i | −1.10015 | − | 0.635170i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −672.506 | − | 30121.2i | −0.0247836 | − | 1.11004i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1730.19 | − | 2996.78i | 0.0635509 | − | 0.110073i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24244.0 | − | 13997.3i | 0.887549 | − | 0.512427i | 0.0144093 | − | 0.999896i | \(-0.495413\pi\) |
0.873140 | + | 0.487469i | \(0.162080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5750.89i | 0.209840i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27683.1i | 1.00679i | 0.864057 | + | 0.503393i | \(0.167915\pi\) | ||||
−0.864057 | + | 0.503393i | \(0.832085\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19508.7 | − | 11263.3i | 0.707167 | − | 0.408283i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18814.5 | − | 32587.6i | 0.679767 | − | 1.17739i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13261.7 | + | 21829.6i | 0.477577 | + | 0.786125i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.0992 | + | 8.71755i | 0.000541978 | + | 0.000312911i | 0.500271 | − | 0.865869i | \(-0.333234\pi\) |
−0.499729 | + | 0.866182i | \(0.666567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21181.2 | + | 36686.8i | 0.757810 | + | 1.31256i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37986.9 | 1.35466 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12981.9 | −0.461451 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4216.21 | + | 7302.69i | 0.149383 | + | 0.258740i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36888.5 | + | 21297.6i | 1.30277 | + | 0.752155i | 0.980878 | − | 0.194621i | \(-0.0623478\pi\) |
0.321892 | + | 0.946776i | \(0.395681\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25868.8 | − | 1155.71i | 0.910652 | − | 0.0406839i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16693.4 | − | 28913.8i | 0.585764 | − | 1.01457i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −73224.1 | + | 42275.9i | −2.56116 | + | 1.47869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26316.4i | − | 0.917522i | −0.888560 | − | 0.458761i | \(-0.848293\pi\) | ||
0.888560 | − | 0.458761i | \(-0.151707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22797.8i | 0.792309i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25507.0 | − | 14726.5i | 0.883640 | − | 0.510170i | 0.0117829 | − | 0.999931i | \(-0.496249\pi\) |
0.871857 | + | 0.489761i | \(0.162916\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2856.11 | + | 4946.92i | −0.0986295 | + | 0.170831i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39864.8 | − | 24218.2i | 1.37228 | − | 0.833669i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18190.8 | − | 10502.5i | −0.624205 | − | 0.360385i | 0.154299 | − | 0.988024i | \(-0.450688\pi\) |
−0.778504 | + | 0.627639i | \(0.784021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23707.6 | + | 41062.8i | 0.810940 | + | 1.40459i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17182.4 | 0.585885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10707.4 | 0.363952 | 0.181976 | − | 0.983303i | \(-0.441751\pi\) | ||||
0.181976 | + | 0.983303i | \(0.441751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35207.0 | + | 60980.4i | 1.19296 | + | 2.06626i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24682.2 | + | 14250.3i | 0.833712 | + | 0.481344i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27281.5 | + | 609.104i | −0.918628 | + | 0.0205099i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13988.5 | − | 24228.8i | 0.469554 | − | 0.813292i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3124.45 | − | 1803.90i | 0.104552 | − | 0.0603634i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 80858.2i | 2.69733i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20353.4i | 0.676859i | 0.940992 | + | 0.338429i | \(0.109896\pi\) | ||||
−0.940992 | + | 0.338429i | \(0.890104\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38294.2 | + | 22109.1i | −1.26954 | + | 0.732970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27664.6 | − | 47916.6i | 0.914316 | − | 1.58364i | 0.106416 | − | 0.994322i | \(-0.466062\pi\) |
0.807900 | − | 0.589320i | \(-0.200604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17175.5 | − | 31344.4i | 0.565900 | − | 1.03274i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −37587.2 | − | 21701.0i | −1.23462 | − | 0.712808i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14962.5 | − | 25915.8i | −0.489963 | − | 0.848640i | 0.509971 | − | 0.860192i | \(-0.329656\pi\) |
−0.999933 | + | 0.0115516i | \(0.996323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4989.70 | −0.162892 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3952.08 | −0.128624 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2281.10 | − | 3950.97i | −0.0740139 | − | 0.128196i | 0.826643 | − | 0.562727i | \(-0.190248\pi\) |
−0.900657 | + | 0.434531i | \(0.856914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5521.45 | − | 3187.81i | −0.178607 | − | 0.103119i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −175.175 | + | 319.686i | −0.00564932 | + | 0.0103097i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18109.9 | + | 31367.3i | −0.582267 | + | 1.00852i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1060.34 | − | 612.186i | 0.0339886 | − | 0.0196233i | −0.482909 | − | 0.875670i | \(-0.660420\pi\) |
0.516898 | + | 0.856047i | \(0.327087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 15755.0i | − | 0.503493i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27361.9i | 0.871789i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39922.0 | − | 23049.0i | 1.26815 | − | 0.732165i | 0.293510 | − | 0.955956i | \(-0.405177\pi\) |
0.974637 | + | 0.223791i | \(0.0718433\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6031.03 | + | 10446.1i | −0.191004 | + | 0.330829i |
(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 | 112.4.p.g.47.2 | yes | 6 | |
4.3 | odd | 2 | 112.4.p.f.47.2 | yes | 6 | ||
7.2 | even | 3 | 784.4.f.g.783.3 | 6 | |||
7.3 | odd | 6 | 112.4.p.f.31.2 | ✓ | 6 | ||
7.5 | odd | 6 | 784.4.f.h.783.4 | 6 | |||
8.3 | odd | 2 | 448.4.p.g.383.2 | 6 | |||
8.5 | even | 2 | 448.4.p.f.383.2 | 6 | |||
28.3 | even | 6 | inner | 112.4.p.g.31.2 | yes | 6 | |
28.19 | even | 6 | 784.4.f.g.783.4 | 6 | |||
28.23 | odd | 6 | 784.4.f.h.783.3 | 6 | |||
56.3 | even | 6 | 448.4.p.f.255.2 | 6 | |||
56.45 | odd | 6 | 448.4.p.g.255.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.4.p.f.31.2 | ✓ | 6 | 7.3 | odd | 6 | ||
112.4.p.f.47.2 | yes | 6 | 4.3 | odd | 2 | ||
112.4.p.g.31.2 | yes | 6 | 28.3 | even | 6 | inner | |
112.4.p.g.47.2 | yes | 6 | 1.1 | even | 1 | trivial | |
448.4.p.f.255.2 | 6 | 56.3 | even | 6 | |||
448.4.p.f.383.2 | 6 | 8.5 | even | 2 | |||
448.4.p.g.255.2 | 6 | 56.45 | odd | 6 | |||
448.4.p.g.383.2 | 6 | 8.3 | odd | 2 | |||
784.4.f.g.783.3 | 6 | 7.2 | even | 3 | |||
784.4.f.g.783.4 | 6 | 28.19 | even | 6 | |||
784.4.f.h.783.3 | 6 | 28.23 | odd | 6 | |||
784.4.f.h.783.4 | 6 | 7.5 | odd | 6 |