Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(289,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.q (of order \(3\), degree \(2\), not 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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.529 |
Dual form | 624.4.q.b.289.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.00000 | −0.804984 | −0.402492 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402492 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.0539949 | + | 0.0935220i | 0.891760 | − | 0.452510i | \(-0.149471\pi\) |
−0.837765 | + | 0.546032i | \(0.816138\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0000 | − | 25.9808i | 0.411152 | − | 0.712136i | −0.583864 | − | 0.811851i | \(-0.698460\pi\) |
0.995016 | + | 0.0997155i | \(0.0317933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.5000 | + | 33.7750i | 0.693375 | + | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.5000 | + | 23.3827i | −0.232379 | + | 0.402492i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 55.5000 | + | 96.1288i | 0.791807 | + | 1.37145i | 0.924847 | + | 0.380340i | \(0.124193\pi\) |
−0.133039 | + | 0.991111i | \(0.542474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.0000 | − | 39.8372i | −0.277714 | − | 0.481014i | 0.693102 | − | 0.720839i | \(-0.256243\pi\) |
−0.970816 | + | 0.239825i | \(0.922910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | 0.0623480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.0271975 | + | 0.0471075i | −0.879304 | − | 0.476261i | \(-0.841992\pi\) |
0.852106 | + | 0.523369i | \(0.175325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.5000 | − | 90.9327i | 0.336173 | − | 0.582268i | −0.647537 | − | 0.762034i | \(-0.724201\pi\) |
0.983709 | + | 0.179766i | \(0.0575341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 100.000 | 0.579372 | 0.289686 | − | 0.957122i | \(-0.406449\pi\) | ||||
0.289686 | + | 0.957122i | \(0.406449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −45.0000 | − | 77.9423i | −0.237379 | − | 0.411152i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.00000 | − | 15.5885i | −0.0434651 | − | 0.0752837i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.50000 | + | 14.7224i | −0.0377673 | + | 0.0654149i | −0.884291 | − | 0.466936i | \(-0.845358\pi\) |
0.846524 | + | 0.532351i | \(0.178691\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 136.500 | − | 33.7750i | 0.560449 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 115.500 | − | 200.052i | 0.439953 | − | 0.762021i | −0.557732 | − | 0.830021i | \(-0.688328\pi\) |
0.997685 | + | 0.0680000i | \(0.0216618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −257.000 | − | 445.137i | −0.911445 | − | 1.57867i | −0.812024 | − | 0.583623i | \(-0.801634\pi\) |
−0.0994205 | − | 0.995046i | \(-0.531699\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 40.5000 | + | 70.1481i | 0.134164 | + | 0.232379i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 162.000 | 0.502769 | 0.251384 | − | 0.967887i | \(-0.419114\pi\) | ||||
0.251384 | + | 0.967887i | \(0.419114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 169.500 | − | 293.583i | 0.494169 | − | 0.855926i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 333.000 | 0.914301 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 639.000 | 1.65610 | 0.828051 | − | 0.560653i | \(-0.189450\pi\) | ||||
0.828051 | + | 0.560653i | \(0.189450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | + | 233.827i | −0.330971 | + | 0.573258i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −138.000 | −0.320676 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 300.000 | + | 519.615i | 0.661978 | + | 1.14658i | 0.980095 | + | 0.198527i | \(0.0636159\pi\) |
−0.318118 | + | 0.948051i | \(0.603051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −116.500 | − | 201.784i | −0.244529 | − | 0.423537i | 0.717470 | − | 0.696590i | \(-0.245300\pi\) |
−0.961999 | + | 0.273052i | \(0.911967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.00000 | − | 15.5885i | 0.0179983 | − | 0.0311740i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −292.500 | − | 303.975i | −0.558156 | − | 0.580053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 463.000 | − | 801.940i | 0.844246 | − | 1.46228i | −0.0420292 | − | 0.999116i | \(-0.513382\pi\) |
0.886275 | − | 0.463160i | \(-0.153284\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.00000 | + | 15.5885i | 0.0157025 | + | 0.0271975i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −465.000 | − | 805.404i | −0.777258 | − | 1.34625i | −0.933516 | − | 0.358535i | \(-0.883276\pi\) |
0.156258 | − | 0.987716i | \(-0.450057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −253.000 | −0.405636 | −0.202818 | − | 0.979216i | \(-0.565010\pi\) | ||||
−0.202818 | + | 0.979216i | \(0.565010\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −66.0000 | + | 114.315i | −0.101614 | + | 0.176000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 60.0000 | 0.0888004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1324.00 | 1.88559 | 0.942795 | − | 0.333373i | \(-0.108187\pi\) | ||||
0.942795 | + | 0.333373i | \(0.108187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −810.000 | −1.07119 | −0.535597 | − | 0.844474i | \(-0.679913\pi\) | ||||
−0.535597 | + | 0.844474i | \(0.679913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −499.500 | − | 865.159i | −0.637393 | − | 1.10400i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −157.500 | − | 272.798i | −0.194089 | − | 0.336173i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −249.000 | + | 431.281i | −0.296561 | + | 0.513659i | −0.975347 | − | 0.220677i | \(-0.929173\pi\) |
0.678786 | + | 0.734336i | \(0.262507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.0000 | + | 90.0666i | −0.0299510 | + | 0.103753i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 150.000 | − | 259.808i | 0.167250 | − | 0.289686i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 207.000 | + | 358.535i | 0.223555 | + | 0.387209i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −679.000 | − | 1176.06i | −0.710742 | − | 1.23104i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −270.000 | −0.274101 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 178.500 | − | 309.171i | 0.175856 | − | 0.304591i | −0.764601 | − | 0.644503i | \(-0.777064\pi\) |
0.940457 | + | 0.339913i | \(0.110397\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1118.00 | −1.06951 | −0.534756 | − | 0.845006i | \(-0.679597\pi\) | ||||
−0.534756 | + | 0.845006i | \(0.679597\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −54.0000 | −0.0501891 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 357.000 | − | 618.342i | 0.322547 | − | 0.558667i | −0.658466 | − | 0.752610i | \(-0.728794\pi\) |
0.981013 | + | 0.193943i | \(0.0621277\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2006.00 | 1.76275 | 0.881376 | − | 0.472416i | \(-0.156618\pi\) | ||||
0.881376 | + | 0.472416i | \(0.156618\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 25.5000 | + | 44.1673i | 0.0218050 | + | 0.0377673i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 559.500 | + | 969.082i | 0.465782 | + | 0.806758i | 0.999236 | − | 0.0390710i | \(-0.0124399\pi\) |
−0.533455 | + | 0.845829i | \(0.679107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.0000 | − | 46.7654i | 0.0218936 | − | 0.0379208i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | − | 405.300i | 0.0924500 | − | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −111.000 | + | 192.258i | −0.0855072 | + | 0.148103i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.500 | + | 373.257i | 0.161908 | + | 0.280433i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −346.500 | − | 600.156i | −0.254007 | − | 0.439953i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −302.000 | + | 523.079i | −0.211009 | + | 0.365479i | −0.952031 | − | 0.306003i | \(-0.901008\pi\) |
0.741021 | + | 0.671481i | \(0.234342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1542.00 | −1.05245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1584.00 | 1.05645 | 0.528224 | − | 0.849105i | \(-0.322858\pi\) | ||||
0.528224 | + | 0.849105i | \(0.322858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 46.0000 | − | 79.6743i | 0.0299903 | − | 0.0519447i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 243.000 | 0.154919 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −358.500 | − | 620.940i | −0.223567 | − | 0.387230i | 0.732321 | − | 0.680959i | \(-0.238437\pi\) |
−0.955889 | + | 0.293729i | \(0.905104\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −410.000 | − | 710.141i | −0.250185 | − | 0.433334i | 0.713391 | − | 0.700766i | \(-0.247158\pi\) |
−0.963577 | + | 0.267432i | \(0.913825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 243.000 | − | 420.888i | 0.145137 | − | 0.251384i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1365.00 | − | 337.750i | 0.798231 | − | 0.197511i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −472.500 | + | 818.394i | −0.270614 | + | 0.468717i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −508.500 | − | 880.748i | −0.285309 | − | 0.494169i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 874.500 | + | 1514.68i | 0.480818 | + | 0.832801i | 0.999758 | − | 0.0220100i | \(-0.00700656\pi\) |
−0.518940 | + | 0.854811i | \(0.673673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 370.000 | 0.199405 | 0.0997026 | − | 0.995017i | \(-0.468211\pi\) | ||||
0.0997026 | + | 0.995017i | \(0.468211\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 499.500 | − | 865.159i | 0.263936 | − | 0.457150i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −900.000 | −0.466385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2611.00 | −1.32726 | −0.663632 | − | 0.748059i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748059i | \(0.730986\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 958.500 | − | 1660.17i | 0.478075 | − | 0.828051i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.00587411 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −818.000 | − | 1416.82i | −0.393072 | − | 0.680820i | 0.599781 | − | 0.800164i | \(-0.295254\pi\) |
−0.992853 | + | 0.119344i | \(0.961921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 405.000 | + | 701.481i | 0.191086 | + | 0.330971i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 132.000 | − | 228.631i | 0.0611645 | − | 0.105940i | −0.833822 | − | 0.552034i | \(-0.813852\pi\) |
0.894986 | + | 0.446094i | \(0.147185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −84.5000 | + | 2195.37i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −207.000 | + | 358.535i | −0.0925713 | + | 0.160338i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −705.000 | − | 1221.10i | −0.309827 | − | 0.536637i | 0.668497 | − | 0.743715i | \(-0.266938\pi\) |
−0.978324 | + | 0.207078i | \(0.933605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −44.0000 | − | 76.2102i | −0.0190062 | − | 0.0329197i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1800.00 | 0.764386 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −237.000 | + | 410.496i | −0.0989621 | + | 0.171407i | −0.911255 | − | 0.411842i | \(-0.864886\pi\) |
0.812293 | + | 0.583249i | \(0.198219\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2249.00 | 0.923574 | 0.461787 | − | 0.886991i | \(-0.347208\pi\) | ||||
0.461787 | + | 0.886991i | \(0.347208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −699.000 | −0.282358 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 76.5000 | − | 132.502i | 0.0304021 | − | 0.0526580i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3330.00 | 1.30221 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27.0000 | − | 46.7654i | −0.0103913 | − | 0.0179983i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1722.00 | + | 2982.59i | 0.652354 | + | 1.12991i | 0.982550 | + | 0.185997i | \(0.0595516\pi\) |
−0.330197 | + | 0.943912i | \(0.607115\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2136.50 | − | 3700.53i | 0.796832 | − | 1.38015i | −0.124837 | − | 0.992177i | \(-0.539841\pi\) |
0.921669 | − | 0.387977i | \(-0.126826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1228.50 | + | 303.975i | −0.451152 | + | 0.111631i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 993.000 | − | 1719.93i | 0.359129 | − | 0.622029i | −0.628687 | − | 0.777658i | \(-0.716407\pi\) |
0.987815 | + | 0.155630i | \(0.0497406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1193.00 | − | 2066.34i | −0.424973 | − | 0.736074i | 0.571445 | − | 0.820640i | \(-0.306383\pi\) |
−0.996418 | + | 0.0845661i | \(0.973050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1389.00 | − | 2405.82i | −0.487425 | − | 0.844246i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 210.000 | 0.0726065 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1039.50 | + | 1800.47i | −0.354155 | + | 0.613415i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 54.0000 | 0.0181317 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1380.00 | −0.456730 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −800.000 | + | 1385.64i | −0.261016 | + | 0.452092i | −0.966512 | − | 0.256621i | \(-0.917391\pi\) |
0.705497 | + | 0.708713i | \(0.250724\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2790.00 | −0.897501 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2313.00 | + | 4006.23i | 0.733699 | + | 1.27080i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 100.000 | + | 173.205i | 0.0312831 | + | 0.0541840i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −379.500 | + | 657.313i | −0.117097 | + | 0.202818i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1443.00 | + | 4998.70i | −0.439216 | + | 1.52149i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1916.00 | + | 3318.61i | −0.575358 | + | 0.996549i | 0.420645 | + | 0.907226i | \(0.361804\pi\) |
−0.996003 | + | 0.0893239i | \(0.971529\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 198.000 | + | 342.946i | 0.0586667 | + | 0.101614i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −699.000 | − | 1210.70i | −0.204380 | − | 0.353997i | 0.745555 | − | 0.666444i | \(-0.232184\pi\) |
−0.949935 | + | 0.312448i | \(0.898851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4466.00 | 1.28874 | 0.644370 | − | 0.764714i | \(-0.277120\pi\) | ||||
0.644370 | + | 0.764714i | \(0.277120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 90.0000 | − | 155.885i | 0.0256345 | − | 0.0444002i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1638.00 | −0.460553 | −0.230277 | − | 0.973125i | \(-0.573963\pi\) | ||||
−0.230277 | + | 0.973125i | \(0.573963\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1458.00 | −0.404721 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1986.00 | − | 3439.85i | 0.544323 | − | 0.942795i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 594.000 | 0.160764 | 0.0803821 | − | 0.996764i | \(-0.474386\pi\) | ||||
0.0803821 | + | 0.996764i | \(0.474386\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1151.50 | − | 1994.46i | −0.307779 | − | 0.533088i | 0.670098 | − | 0.742273i | \(-0.266252\pi\) |
−0.977876 | + | 0.209185i | \(0.932919\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1525.50 | + | 2642.24i | −0.397798 | + | 0.689007i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 598.000 | − | 2071.53i | 0.154048 | − | 0.533638i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1215.00 | + | 2104.44i | −0.309227 | + | 0.535597i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3162.00 | + | 5476.74i | 0.795154 | + | 1.37725i | 0.922741 | + | 0.385420i | \(0.125943\pi\) |
−0.127587 | + | 0.991827i | \(0.540723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 90.0000 | + | 155.885i | 0.0223646 | + | 0.0387367i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2997.00 | −0.735998 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3916.50 | + | 6783.58i | −0.950601 | + | 1.64649i | −0.206474 | + | 0.978452i | \(0.566199\pi\) |
−0.744127 | + | 0.668038i | \(0.767134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.0000 | −0.00815698 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −945.000 | −0.224115 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1515.00 | + | 2624.06i | −0.355205 | + | 0.615233i | −0.987153 | − | 0.159778i | \(-0.948922\pi\) |
0.631948 | + | 0.775011i | \(0.282256\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5751.00 | −1.33314 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 747.000 | + | 1293.84i | 0.171220 | + | 0.296561i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 267.000 | + | 462.458i | 0.0605178 | + | 0.104820i | 0.894697 | − | 0.446674i | \(-0.147391\pi\) |
−0.834179 | + | 0.551493i | \(0.814058\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1844.00 | + | 3193.90i | −0.413340 | + | 0.715925i | −0.995253 | − | 0.0973259i | \(-0.968971\pi\) |
0.581913 | + | 0.813251i | \(0.302304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 195.000 | + | 202.650i | 0.0432305 | + | 0.0449265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −660.000 | + | 1143.15i | −0.144725 | + | 0.250672i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −932.500 | − | 1615.14i | −0.202269 | − | 0.350340i | 0.746990 | − | 0.664835i | \(-0.231498\pi\) |
−0.949259 | + | 0.314495i | \(0.898165\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −450.000 | − | 779.423i | −0.0965620 | − | 0.167250i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2997.00 | 0.636249 | 0.318125 | − | 0.948049i | \(-0.396947\pi\) | ||||
0.318125 | + | 0.948049i | \(0.396947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2057.00 | + | 3562.83i | −0.432071 | + | 0.748368i | −0.997051 | − | 0.0767359i | \(-0.975550\pi\) |
0.564981 | + | 0.825104i | \(0.308884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1242.00 | 0.258139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 462.000 | 0.0950209 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3704.00 | + | 6415.52i | −0.753918 | + | 1.30582i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4074.00 | −0.820695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2332.50 | + | 4040.01i | 0.465072 | + | 0.805528i | 0.999205 | − | 0.0398722i | \(-0.0126951\pi\) |
−0.534133 | + | 0.845401i | \(0.679362\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2700.00 | − | 4676.54i | −0.532882 | − | 0.922978i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −405.000 | + | 701.481i | −0.0791262 | + | 0.137051i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −273.000 | + | 67.5500i | −0.0528027 | + | 0.0130653i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 514.000 | − | 890.274i | 0.0984268 | − | 0.170480i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −535.500 | − | 927.513i | −0.101530 | − | 0.175856i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1048.50 | + | 1816.06i | 0.196842 | + | 0.340941i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1502.00 | −0.279230 | −0.139615 | − | 0.990206i | \(-0.544587\pi\) | ||||
−0.139615 | + | 0.990206i | \(0.544587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1677.00 | + | 2904.65i | −0.308742 | + | 0.534756i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2106.00 | −0.383988 | −0.191994 | − | 0.981396i | \(-0.561495\pi\) | ||||
−0.191994 | + | 0.981396i | \(0.561495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3898.00 | −0.703923 | −0.351962 | − | 0.936014i | \(-0.614485\pi\) | ||||
−0.351962 | + | 0.936014i | \(0.614485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −81.0000 | + | 140.296i | −0.0144884 | + | 0.0250946i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9351.00 | 1.65680 | 0.828398 | − | 0.560140i | \(-0.189253\pi\) | ||||
0.828398 | + | 0.560140i | \(0.189253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1575.00 | − | 2727.98i | −0.276436 | − | 0.478801i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1071.00 | − | 1855.03i | −0.186222 | − | 0.322547i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2553.00 | − | 4421.93i | 0.439792 | − | 0.761742i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1430.00 | − | 1486.10i | −0.244068 | − | 0.253643i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3009.00 | − | 5211.74i | 0.508863 | − | 0.881376i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 162.000 | + | 280.592i | 0.0271470 | + | 0.0470199i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4586.00 | − | 7943.19i | −0.761539 | − | 1.31902i | −0.942057 | − | 0.335452i | \(-0.891111\pi\) |
0.180518 | − | 0.983572i | \(-0.442222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 153.000 | 0.0251782 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4167.00 | + | 7217.46i | −0.679605 | + | 1.17711i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11089.0 | −1.79245 | −0.896226 | − | 0.443598i | \(-0.853702\pi\) | ||||
−0.896226 | + | 0.443598i | \(0.853702\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3357.00 | 0.537838 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1500.00 | − | 2598.08i | 0.238210 | − | 0.412592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1364.00 | 0.214720 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −81.0000 | − | 140.296i | −0.0126403 | − | 0.0218936i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4881.00 | + | 8454.14i | 0.755118 | + | 1.30790i | 0.945316 | + | 0.326156i | \(0.105754\pi\) |
−0.190198 | + | 0.981746i | \(0.560913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4145.00 | − | 7179.35i | 0.635750 | − | 1.10115i | −0.350606 | − | 0.936523i | \(-0.614024\pi\) |
0.986356 | − | 0.164628i | \(-0.0526424\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −877.500 | − | 911.925i | −0.133440 | − | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6202.50 | + | 10743.0i | −0.935200 | + | 1.61981i | −0.160924 | + | 0.986967i | \(0.551448\pi\) |
−0.774276 | + | 0.632848i | \(0.781886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4185.00 | + | 7248.63i | 0.625681 | + | 1.08371i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 333.000 | + | 576.773i | 0.0493676 | + | 0.0855072i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1098.00 | 0.161421 | 0.0807106 | − | 0.996738i | \(-0.474281\pi\) | ||||
0.0807106 | + | 0.996738i | \(0.474281\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2371.50 | − | 4107.56i | 0.345750 | − | 0.598857i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1293.00 | 0.186956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2277.00 | 0.326530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2867.00 | + | 4965.79i | −0.407783 | + | 0.706300i | −0.994641 | − | 0.103390i | \(-0.967031\pi\) |
0.586858 | + | 0.809690i | \(0.300365\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2079.00 | −0.293302 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 639.000 | + | 1106.78i | 0.0894211 | + | 0.154882i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4485.50 | + | 7769.11i | 0.622655 | + | 1.07847i | 0.988989 | + | 0.147987i | \(0.0472794\pi\) |
−0.366334 | + | 0.930483i | \(0.619387\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2281.50 | − | 3951.67i | 0.314176 | − | 0.544170i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4777.50 | − | 1182.12i | 0.652663 | − | 0.161492i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3622.00 | − | 6273.49i | 0.490896 | − | 0.850257i | −0.509049 | − | 0.860738i | \(-0.670003\pi\) |
0.999945 | + | 0.0104805i | \(0.00333611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 906.000 | + | 1569.24i | 0.121826 | + | 0.211009i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3156.00 | − | 5466.35i | −0.421055 | − | 0.729289i | 0.574988 | − | 0.818162i | \(-0.305007\pi\) |
−0.996043 | + | 0.0888732i | \(0.971673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −540.000 | −0.0714830 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2313.00 | + | 4006.23i | −0.303815 | + | 0.526223i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3627.00 | 0.472741 | 0.236370 | − | 0.971663i | \(-0.424042\pi\) | ||||
0.236370 | + | 0.971663i | \(0.424042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −666.000 | −0.0861408 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2376.00 | − | 4115.35i | 0.304970 | − | 0.528224i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11916.0 | −1.51787 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1949.00 | + | 3375.77i | 0.246392 | + | 0.426763i | 0.962522 | − | 0.271204i | \(-0.0874217\pi\) |
−0.716130 | + | 0.697967i | \(0.754088\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −138.000 | − | 239.023i | −0.0173149 | − | 0.0299903i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2851.50 | − | 4938.94i | 0.355105 | − | 0.615060i | −0.632031 | − | 0.774943i | \(-0.717778\pi\) |
0.987136 | + | 0.159883i | \(0.0511118\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3250.00 | + | 3377.50i | 0.401722 | + | 0.417482i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 364.500 | − | 631.333i | 0.0447214 | − | 0.0774597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 255.000 | + | 441.673i | 0.0310562 | + | 0.0537909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3155.50 | − | 5465.49i | −0.381490 | − | 0.660760i | 0.609785 | − | 0.792567i | \(-0.291256\pi\) |
−0.991275 | + | 0.131806i | \(0.957922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2151.00 | −0.258153 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −600.000 | + | 1039.23i | −0.0714869 | + | 0.123819i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7290.00 | 0.862294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2460.00 | −0.288889 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1164.00 | + | 2016.11i | −0.135716 | + | 0.235067i | −0.925871 | − | 0.377840i | \(-0.876667\pi\) |
0.790155 | + | 0.612908i | \(0.210000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2045.00 | 0.236739 | 0.118370 | − | 0.992970i | \(-0.462233\pi\) | ||||
0.118370 | + | 0.992970i | \(0.462233\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −729.000 | − | 1262.67i | −0.0837948 | − | 0.145137i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2442.00 | − | 4229.67i | −0.278716 | − | 0.482751i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 233.000 | − | 403.568i | 0.0264067 | − | 0.0457377i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1170.00 | − | 4053.00i | 0.131674 | − | 0.456132i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2517.00 | − | 4359.57i | 0.281298 | − | 0.487223i | −0.690406 | − | 0.723422i | \(-0.742568\pi\) |
0.971705 | + | 0.236199i | \(0.0759016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2141.50 | − | 3709.19i | −0.237676 | − | 0.411668i | 0.722371 | − | 0.691506i | \(-0.243052\pi\) |
−0.960047 | + | 0.279838i | \(0.909719\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1417.50 | + | 2455.18i | 0.156239 | + | 0.270614i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 276.000 | 0.0302125 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −653.000 | + | 1131.03i | −0.0709931 | + | 0.122964i | −0.899337 | − | 0.437257i | \(-0.855950\pi\) |
0.828344 | + | 0.560220i | \(0.189284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3051.00 | −0.329446 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5796.00 | 0.621617 | 0.310808 | − | 0.950473i | \(-0.399400\pi\) | ||||
0.310808 | + | 0.950473i | \(0.399400\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2241.00 | − | 3881.53i | 0.238727 | − | 0.413488i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5247.00 | 0.555200 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1353.00 | − | 2343.46i | −0.142209 | − | 0.246314i | 0.786119 | − | 0.618075i | \(-0.212087\pi\) |
−0.928328 | + | 0.371761i | \(0.878754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3465.00 | − | 6001.56i | −0.361775 | − | 0.626612i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 555.000 | − | 961.288i | 0.0575633 | − | 0.0997026i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 234.000 | − | 810.600i | 0.0241101 | − | 0.0835198i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 414.500 | − | 717.935i | 0.0424278 | − | 0.0734871i | −0.844032 | − | 0.536293i | \(-0.819824\pi\) |
0.886459 | + | 0.462806i | \(0.153157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1498.50 | − | 2595.48i | −0.152383 | − | 0.263936i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2746.50 | + | 4757.08i | 0.277478 | + | 0.480606i | 0.970757 | − | 0.240063i | \(-0.0771682\pi\) |
−0.693279 | + | 0.720669i | \(0.743835\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15346.0 | 1.54037 | 0.770183 | − | 0.637823i | \(-0.220165\pi\) | ||||
0.770183 | + | 0.637823i | \(0.220165\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1350.00 | + | 2338.27i | −0.134634 | + | 0.233193i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9594.00 | 0.950658 | 0.475329 | − | 0.879808i | \(-0.342329\pi\) | ||||
0.475329 | + | 0.879808i | \(0.342329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1852.00 | 0.182340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3916.50 | + | 6783.58i | −0.383148 | + | 0.663632i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15420.0 | −1.49897 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1012.00 | + | 1752.84i | 0.0977553 | + | 0.169317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2875.50 | − | 4980.51i | −0.276017 | − | 0.478075i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6420.00 | + | 11119.8i | −0.612395 | + | 1.06070i | 0.378440 | + | 0.925626i | \(0.376461\pi\) |
−0.990836 | + | 0.135074i | \(0.956873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −773.500 | + | 191.392i | −0.0733234 | + | 0.0181428i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.0000 | + | 31.1769i | −0.00169571 | + | 0.00293706i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6111.00 | + | 10584.6i | 0.572137 | + | 0.990970i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7043.00 | − | 12198.8i | −0.655336 | − | 1.13508i | −0.981809 | − | 0.189869i | \(-0.939194\pi\) |
0.326473 | − | 0.945207i | \(-0.394140\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4908.00 | −0.453880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5847.00 | − | 10127.3i | 0.537416 | − | 0.930832i | −0.461626 | − | 0.887075i | \(-0.652734\pi\) |
0.999042 | − | 0.0437577i | \(-0.0139329\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11655.0 | 1.06474 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2430.00 | 0.220647 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 930.000 | − | 1610.81i | 0.0839360 | − | 0.145381i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3688.00 | 0.330857 | 0.165428 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165428 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −396.000 | − | 685.892i | −0.0353133 | − | 0.0611645i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2373.00 | − | 4110.16i | −0.210352 | − | 0.364340i | 0.741473 | − | 0.670983i | \(-0.234128\pi\) |
−0.951825 | + | 0.306643i | \(0.900794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1606.50 | + | 2782.54i | −0.141561 | + | 0.245191i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5577.00 | + | 3512.60i | 0.488527 | + | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7252.50 | − | 12561.7i | 0.631555 | − | 1.09389i | −0.355679 | − | 0.934608i | \(-0.615750\pi\) |
0.987234 | − | 0.159277i | \(-0.0509163\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −253.000 | − | 438.209i | −0.0219023 | − | 0.0379358i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 621.000 | + | 1075.60i | 0.0534460 | + | 0.0925713i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10062.0 | 0.860941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2430.00 | − | 4208.88i | 0.206714 | − | 0.358040i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4230.00 | −0.357758 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5085.00 | 0.427597 | 0.213798 | − | 0.976878i | \(-0.431416\pi\) | ||||
0.213798 | + | 0.976878i | \(0.431416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5441.00 | + | 9424.09i | −0.454911 | + | 0.787929i | −0.998683 | − | 0.0513043i | \(-0.983662\pi\) |
0.543772 | + | 0.839233i | \(0.316996\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −264.000 | −0.0219465 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5550.00 | + | 9612.88i | 0.458751 | + | 0.794580i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6065.50 | + | 10505.8i | 0.498521 | + | 0.863463i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2700.00 | − | 4676.54i | 0.220659 | − | 0.382193i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10510.5 | − | 2600.67i | 0.854147 | − | 0.211347i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3213.00 | + | 5565.08i | −0.259645 | + | 0.449718i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 711.000 | + | 1231.49i | 0.0571358 | + | 0.0989621i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5085.00 | − | 8807.48i | −0.406357 | − | 0.703831i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4699.00 | −0.373430 | −0.186715 | − | 0.982414i | \(-0.559784\pi\) | ||||
−0.186715 | + | 0.982414i | \(0.559784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3373.50 | − | 5843.07i | 0.266613 | − | 0.461787i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18054.0 | −1.41899 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8270.00 | −0.646434 | −0.323217 | − | 0.946325i | \(-0.604764\pi\) | ||||
−0.323217 | + | 0.946325i | \(0.604764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1048.50 | + | 1816.06i | −0.0815098 | + | 0.141179i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4830.00 | −0.373439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1324.00 | + | 2293.24i | 0.101812 | + | 0.176344i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −229.500 | − | 397.506i | −0.0175527 | − | 0.0304021i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11392.5 | − | 19732.4i | 0.866635 | − | 1.50106i | 0.00122056 | − | 0.999999i | \(-0.499611\pi\) |
0.865414 | − | 0.501057i | \(-0.167055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6682.00 | − | 23147.1i | 0.505579 | − | 1.75138i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4995.00 | − | 8651.59i | 0.375916 | − | 0.651106i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5964.00 | − | 10330.0i | −0.446452 | − | 0.773278i | 0.551700 | − | 0.834043i | \(-0.313979\pi\) |
−0.998152 | + | 0.0607647i | \(0.980646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5035.50 | − | 8721.74i | −0.374947 | − | 0.649427i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −162.000 | −0.0119989 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3981.00 | − | 6895.29i | 0.293308 | − | 0.508024i | −0.681282 | − | 0.732021i | \(-0.738577\pi\) |
0.974590 | + | 0.223997i | \(0.0719106\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20618.0 | −1.51110 | −0.755549 | − | 0.655093i | \(-0.772630\pi\) | ||||
−0.755549 | + | 0.655093i | \(0.772630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10332.0 | 0.753273 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 132.000 | − | 228.631i | 0.00957353 | − | 0.0165818i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3493.00 | −0.252020 | −0.126010 | − | 0.992029i | \(-0.540217\pi\) | ||||
−0.126010 | + | 0.992029i | \(0.540217\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6409.50 | − | 11101.6i | −0.460051 | − | 0.796832i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −810.000 | − | 1402.96i | −0.0578390 | − | 0.100180i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9585.00 | − | 16601.7i | 0.680909 | − | 1.17937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1053.00 | + | 3647.70i | −0.0744208 | + | 0.257801i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5208.00 | − | 9020.52i | 0.366196 | − | 0.634270i | −0.622771 | − | 0.782404i | \(-0.713993\pi\) |
0.988967 | + | 0.148134i | \(0.0473266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2300.00 | − | 3983.72i | −0.160900 | − | 0.278686i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2979.00 | − | 5159.78i | −0.207343 | − | 0.359129i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2061.00 | 0.142724 | 0.0713618 | − | 0.997450i | \(-0.477266\pi\) | ||||
0.0713618 | + | 0.997450i | \(0.477266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 999.000 | − | 1730.32i | 0.0688319 | − | 0.119220i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7158.00 | −0.490716 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12456.0 | −0.849647 | −0.424823 | − | 0.905276i | \(-0.639664\pi\) | ||||
−0.424823 | + | 0.905276i | \(0.639664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 390.500 | − | 676.366i | 0.0265039 | − | 0.0459061i | −0.852469 | − | 0.522777i | \(-0.824896\pi\) |
0.878973 | + | 0.476871i | \(0.158229\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8334.00 | −0.562830 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1939.50 | − | 3359.31i | −0.130334 | − | 0.225745i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9652.00 | + | 16717.8i | 0.645408 | + | 1.11788i | 0.984207 | + | 0.177021i | \(0.0566459\pi\) |
−0.338799 | + | 0.940859i | \(0.610021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 315.000 | − | 545.596i | 0.0209597 | − | 0.0363032i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5265.00 | + | 5471.55i | 0.348607 | + | 0.362283i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6020.50 | + | 10427.8i | −0.396681 | + | 0.687072i | −0.993314 | − | 0.115442i | \(-0.963172\pi\) |
0.596633 | + | 0.802514i | \(0.296505\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3118.50 | + | 5401.40i | 0.204472 | + | 0.354155i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4858.50 | − | 8415.17i | −0.317011 | − | 0.549079i | 0.662852 | − | 0.748751i | \(-0.269346\pi\) |
−0.979863 | + | 0.199671i | \(0.936013\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21040.0 | 1.36619 | 0.683093 | − | 0.730332i | \(-0.260634\pi\) | ||||
0.683093 | + | 0.730332i | \(0.260634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 81.0000 | − | 140.296i | 0.00523417 | − | 0.00906584i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −996.000 | −0.0640512 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2070.00 | + | 3585.35i | −0.131847 | + | 0.228365i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1887.00 | −0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2534.00 | − | 4389.02i | −0.159868 | − | 0.276900i | 0.774953 | − | 0.632019i | \(-0.217774\pi\) |
−0.934821 | + | 0.355119i | \(0.884440\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2400.00 | + | 4156.92i | 0.150697 | + | 0.261016i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2718.00 | − | 4707.71i | 0.169859 | − | 0.294205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15424.5 | − | 3816.57i | 0.959405 | − | 0.237391i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4185.00 | + | 7248.63i | −0.259086 | + | 0.448750i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5092.50 | − | 8820.47i | −0.313794 | − | 0.543506i | 0.665387 | − | 0.746499i | \(-0.268267\pi\) |
−0.979180 | + | 0.202992i | \(0.934933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12964.0 | + | 22454.3i | 0.795101 | + | 1.37716i | 0.922775 | + | 0.385340i | \(0.125916\pi\) |
−0.127673 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13878.0 | 0.847203 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11580.0 | − | 20057.1i | 0.703643 | − | 1.21874i | −0.263537 | − | 0.964649i | \(-0.584889\pi\) |
0.967179 | − | 0.254095i | \(-0.0817777\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18000.0 | 1.08869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 600.000 | 0.0361227 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8313.00 | + | 14398.5i | −0.498182 | + | 0.862876i | −0.999998 | − | 0.00209801i | \(-0.999332\pi\) |
0.501816 | + | 0.864974i | \(0.332666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14256.0 | −0.850424 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1138.50 | + | 1971.94i | 0.0676060 | + | 0.117097i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7404.00 | − | 12824.1i | −0.437661 | − | 0.758052i | 0.559847 | − | 0.828596i | \(-0.310860\pi\) |
−0.997509 | + | 0.0705440i | \(0.977526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2426.50 | + | 4202.82i | −0.142784 | + | 0.247308i | −0.928544 | − | 0.371223i | \(-0.878939\pi\) |
0.785760 | + | 0.618531i | \(0.212272\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10822.5 | + | 11247.1i | 0.633953 | + | 0.658824i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −414.000 | + | 717.069i | −0.0241417 | + | 0.0418147i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 315.000 | + | 545.596i | 0.0182861 | + | 0.0316725i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5748.00 | + | 9955.83i | 0.332183 | + | 0.575358i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6990.00 | −0.402155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8082.50 | − | 13999.3i | 0.462938 | − | 0.801833i | −0.536168 | − | 0.844112i | \(-0.680128\pi\) |
0.999106 | + | 0.0422789i | \(0.0134618\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1188.00 | 0.0677424 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25686.0 | −1.45819 | −0.729094 | − | 0.684414i | \(-0.760058\pi\) | ||||
−0.729094 | + | 0.684414i | \(0.760058\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1358.00 | − | 2352.12i | 0.0767530 | − | 0.132940i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4194.00 | −0.235998 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9528.00 | − | 16503.0i | −0.533790 | − | 0.924552i | −0.999221 | − | 0.0394675i | \(-0.987434\pi\) |
0.465431 | − | 0.885084i | \(-0.345900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3226.50 | + | 5588.46i | 0.179968 | + | 0.311714i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6699.00 | − | 11603.0i | 0.372027 | − | 0.644370i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20767.5 | + | 21582.2i | 1.14830 | + | 1.19335i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8195.00 | + | 14194.2i | −0.451161 | + | 0.781434i | −0.998458 | − | 0.0555040i | \(-0.982323\pi\) |
0.547297 | + | 0.836938i | \(0.315657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −270.000 | − | 467.654i | −0.0148001 | − | 0.0256345i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3690.00 | + | 6391.27i | 0.201395 | + | 0.348827i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25641.0 | 1.39343 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2457.00 | + | 4255.65i | −0.132950 | + | 0.230277i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27846.0 | −1.50033 | −0.750163 | − | 0.661253i | \(-0.770025\pi\) | ||||
−0.750163 | + | 0.661253i | \(0.770025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 782.000 | 0.0419540 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2187.00 | + | 3788.00i | −0.116833 | + | 0.202360i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 714.000 | 0.0379812 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6141.50 | + | 10637.4i | 0.325316 | + | 0.563463i | 0.981576 | − | 0.191071i | \(-0.0611961\pi\) |
−0.656260 | + | 0.754534i | \(0.727863\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5958.00 | − | 10319.6i | −0.314265 | − | 0.544323i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −300.000 | + | 519.615i | −0.0157575 | + | 0.0272928i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12285.0 | + | 3039.75i | −0.642564 | + | 0.158993i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 891.000 | − | 1543.26i | 0.0464087 | − | 0.0803821i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12756.0 | + | 22094.0i | 0.661639 | + | 1.14599i | 0.980185 | + | 0.198085i | \(0.0634722\pi\) |
−0.318546 | + | 0.947908i | \(0.603194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1118.00 | − | 1936.43i | −0.0577483 | − | 0.100023i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6909.00 | −0.355392 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2310.00 | + | 4001.04i | −0.118333 | + | 0.204958i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6110.00 | −0.311702 | −0.155851 | − | 0.987781i | \(-0.549812\pi\) | ||||
−0.155851 | + | 0.987781i | \(0.549812\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28527.0 | − | 49410.2i | 1.44338 | − | 2.50000i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27127.0 | −1.36693 | −0.683464 | − | 0.729984i | \(-0.739527\pi\) | ||||
−0.683464 | + | 0.729984i | \(0.739527\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4576.50 | + | 7926.73i | 0.229669 | + | 0.397798i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13890.0 | − | 24058.2i | −0.694226 | − | 1.20244i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −440.000 | + | 762.102i | −0.0219021 | + | 0.0379356i | −0.876769 | − | 0.480912i | \(-0.840306\pi\) |
0.854867 | + | 0.518848i | \(0.173639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4485.00 | − | 4660.95i | −0.222349 | − | 0.231072i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10938.0 | + | 18945.2i | −0.540076 | + | 0.935439i | 0.458823 | + | 0.888528i | \(0.348271\pi\) |
−0.998899 | + | 0.0469111i | \(0.985062\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7870.50 | − | 13632.1i | −0.387051 | − | 0.670392i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3645.00 | + | 6313.33i | 0.178532 | + | 0.309227i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1428.00 | 0.0696635 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5899.00 | − | 10217.4i | 0.286628 | − | 0.496454i | −0.686375 | − | 0.727248i | \(-0.740799\pi\) |
0.973003 | + | 0.230794i | \(0.0741323\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18972.0 | 0.918165 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3330.00 | −0.160518 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4037.00 | − | 6992.29i | 0.193827 | − | 0.335719i | −0.752688 | − | 0.658377i | \(-0.771243\pi\) |
0.946515 | + | 0.322658i | \(0.104577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 540.000 | 0.0258245 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9777.00 | − | 16934.3i | −0.465724 | − | 0.806658i | 0.533510 | − | 0.845794i | \(-0.320873\pi\) |
−0.999234 | + | 0.0391362i | \(0.987539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2006.00 | + | 3474.49i | 0.0951797 | + | 0.164856i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4495.50 | + | 7786.43i | −0.212464 | + | 0.367999i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7800.00 | + | 27020.0i | −0.367199 | + | 1.27201i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7015.00 | + | 12150.3i | −0.328956 | + | 0.569769i | −0.982305 | − | 0.187288i | \(-0.940030\pi\) |
0.653349 | + | 0.757057i | \(0.273364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11749.5 | + | 20350.7i | 0.548830 | + | 0.950601i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18021.0 | − | 31213.3i | −0.838513 | − | 1.45235i | −0.891138 | − | 0.453732i | \(-0.850092\pi\) |
0.0526253 | − | 0.998614i | \(-0.483241\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4400.00 | −0.203939 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −51.0000 | + | 88.3346i | −0.00235472 | + | 0.00407849i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10626.0 | −0.488724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27900.0 | −1.27828 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1417.50 | + | 2455.18i | −0.0646964 | + | 0.112058i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23499.0 | 1.06843 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14314.0 | + | 24792.6i | 0.648334 | + | 1.12295i | 0.983521 | + | 0.180796i | \(0.0578674\pi\) |
−0.335186 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4545.00 | + | 7872.17i | 0.205078 | + | 0.355205i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1119.00 | + | 1938.16i | −0.0502997 | + | 0.0871216i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3029.00 | − | 10492.8i | 0.135641 | − | 0.469873i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8626.50 | + | 14941.5i | −0.384843 | + | 0.666568i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18717.0 | + | 32418.8i | 0.831857 | + | 1.44082i | 0.896564 | + | 0.442915i | \(0.146055\pi\) |
−0.0647067 | + | 0.997904i | \(0.520611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8991.00 | + | 15572.9i | 0.398096 | + | 0.689523i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4482.00 | 0.197707 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3795.00 | + | 6573.13i | −0.166778 | + | 0.288868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 108.000 | 0.00472857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1602.00 | 0.0698799 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18784.5 | + | 32535.7i | −0.816351 | + | 1.41396i | 0.0920030 | + | 0.995759i | \(0.470673\pi\) |
−0.908354 | + | 0.418202i | \(0.862660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5516.00 | −0.238832 | −0.119416 | − | 0.992844i | \(-0.538102\pi\) | ||||
−0.119416 | + | 0.992844i | \(0.538102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5532.00 | + | 9581.71i | 0.238642 | + | 0.413340i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7362.00 | + | 12751.4i | 0.316417 | + | 0.548050i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11822.0 | + | 20476.3i | −0.506242 | + | 0.876836i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 819.000 | − | 202.650i | 0.0349428 | − | 0.00864611i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4389.00 | + | 7601.97i | −0.186574 | + | 0.323155i | −0.944106 | − | 0.329643i | \(-0.893072\pi\) |
0.757532 | + | 0.652798i | \(0.226405\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1544.00 | − | 2674.29i | −0.0653955 | − | 0.113268i | 0.831474 | − | 0.555564i | \(-0.187498\pi\) |
−0.896869 | + | 0.442296i | \(0.854164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1980.00 | + | 3429.46i | 0.0835573 | + | 0.144725i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13176.0 | −0.554020 | −0.277010 | − | 0.960867i | \(-0.589343\pi\) | ||||
−0.277010 | + | 0.960867i | \(0.589343\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1179.50 | − | 2042.95i | 0.0494158 | − | 0.0855907i | −0.840259 | − | 0.542185i | \(-0.817597\pi\) |
0.889675 | + | 0.456594i | \(0.150931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5595.00 | −0.233560 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37629.0 | 1.56515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1188.00 | + | 2057.68i | −0.0492364 | + | 0.0852800i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2700.00 | −0.111500 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1338.00 | − | 2317.48i | −0.0550571 | − | 0.0953617i | 0.837183 | − | 0.546922i | \(-0.184201\pi\) |
−0.892240 | + | 0.451561i | \(0.850867\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6682.00 | + | 11573.6i | 0.273976 | + | 0.474540i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4495.50 | − | 7786.43i | 0.183669 | − | 0.318125i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 760.500 | − | 19758.4i | 0.0309609 | − | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −431.000 | + | 746.514i | −0.0174845 | + | 0.0302840i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6171.00 | + | 10688.5i | 0.249456 | + | 0.432071i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.0000 | − | 88.3346i | −0.00205436 | − | 0.00355825i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2477.00 | 0.0994266 | 0.0497133 | − | 0.998764i | \(-0.484169\pi\) | ||||
0.0497133 | + | 0.998764i | \(0.484169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1863.00 | − | 3226.81i | 0.0745184 | − | 0.129070i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17199.0 | −0.685539 | −0.342769 | − | 0.939420i | \(-0.611365\pi\) | ||||
−0.342769 | + | 0.939420i | \(0.611365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24338.0 | −0.966708 | −0.483354 | − | 0.875425i | \(-0.660582\pi\) | ||||
−0.483354 | + | 0.875425i | \(0.660582\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 693.000 | − | 1200.31i | 0.0274302 | − | 0.0475104i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25146.0 | −0.991865 | −0.495933 | − | 0.868361i | \(-0.665174\pi\) | ||||
−0.495933 | + | 0.868361i | \(0.665174\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6345.00 | + | 10989.9i | 0.249406 | + | 0.431984i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11112.0 | + | 19246.5i | 0.435275 | + | 0.753918i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19860.0 | − | 34398.5i | 0.775264 | − | 1.34280i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42133.0 | − | 10425.2i | 1.63906 | − | 0.405562i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6111.00 | + | 10584.6i | −0.236914 | + | 0.410347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1521.00 | + | 2634.45i | 0.0587648 | + | 0.101784i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9044.50 | − | 15665.5i | −0.348245 | − | 0.603178i | 0.637693 | − | 0.770291i | \(-0.279889\pi\) |
−0.985938 | + | 0.167113i | \(0.946556\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13995.0 | 0.537019 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7549.50 | − | 13076.1i | 0.288705 | − | 0.500052i | −0.684796 | − | 0.728735i | \(-0.740109\pi\) |
0.973501 | + | 0.228683i | \(0.0734420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33488.0 | −1.27629 | −0.638143 | − | 0.769918i | \(-0.720297\pi\) | ||||
−0.638143 | + | 0.769918i | \(0.720297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16200.0 | −0.615319 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19884.0 | + | 34440.1i | −0.752694 | + | 1.30370i | 0.193819 | + | 0.981037i | \(0.437913\pi\) |
−0.946513 | + | 0.322667i | \(0.895421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1208.00 | −0.0455737 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1215.00 | + | 2104.44i | 0.0456835 | + | 0.0791262i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3726.00 | − | 6453.62i | −0.139626 | − | 0.241839i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2133.00 | − | 3694.46i | 0.0796629 | − | 0.137980i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −234.000 | + | 810.600i | −0.00871018 | + | 0.0301730i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5250.00 | − | 9093.27i | 0.194769 | − | 0.337350i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35464.5 | + | 61426.3i | 1.31131 | + | 2.27126i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1542.00 | − | 2670.82i | −0.0568267 | − | 0.0984268i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20241.0 | −0.743463 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16078.0 | − | 27847.9i | 0.588601 | − | 1.01949i | −0.405815 | − | 0.913955i | \(-0.633012\pi\) |
0.994416 | − | 0.105532i | \(-0.0336545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3213.00 | −0.117237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11520.0 | −0.418962 | −0.209481 | − | 0.977813i | \(-0.567177\pi\) | ||||
−0.209481 | + | 0.977813i | \(0.567177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12150.0 | + | 21044.4i | −0.440423 | + | 0.762835i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6291.00 | 0.227294 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1584.00 | + | 2743.57i | 0.0570428 | + | 0.0988011i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2476.00 | + | 4288.56i | 0.0888745 | + | 0.153935i | 0.907036 | − | 0.421054i | \(-0.138340\pi\) |
−0.818161 | + | 0.574989i | \(0.805006\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2253.00 | + | 3902.31i | −0.0806068 | + | 0.139615i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12090.0 | − | 41881.0i | 0.431145 | − | 1.49353i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 374.000 | − | 647.787i | 0.0132941 | − | 0.0230261i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5031.00 | + | 8713.95i | 0.178252 | + | 0.308742i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4390.50 | − | 7604.57i | −0.155057 | − | 0.268566i | 0.778023 | − | 0.628236i | \(-0.216223\pi\) |
−0.933080 | + | 0.359670i | \(0.882889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15594.0 | −0.548950 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3159.00 | + | 5471.55i | −0.110848 | + | 0.191994i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29970.0 | −1.04826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50039.0 | 1.74461 | 0.872307 | − | 0.488959i | \(-0.162623\pi\) | ||||
0.872307 | + | 0.488959i | \(0.162623\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5847.00 | + | 10127.3i | −0.203205 | + | 0.351962i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50670.0 | −1.75536 | −0.877681 | − | 0.479246i | \(-0.840910\pi\) | ||||
−0.877681 | + | 0.479246i | \(0.840910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 693.000 | + | 1200.31i | 0.0239313 | + | 0.0414502i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 243.000 | + | 420.888i | 0.00836486 | + | 0.0144884i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21192.0 | − | 36705.6i | 0.727188 | − | 1.25953i | −0.230878 | − | 0.972983i | \(-0.574160\pi\) |
0.958067 | − | 0.286545i | \(-0.0925067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8222.50 | − | 8545.07i | −0.281258 | − | 0.292292i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14026.5 | − | 24294.6i | 0.478276 | − | 0.828398i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25269.0 | + | 43767.2i | 0.858912 | + | 1.48768i | 0.872968 | + | 0.487778i | \(0.162192\pi\) |
−0.0140556 | + | 0.999901i | \(0.504474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15498.0 | − | 26843.3i | −0.525135 | − | 0.909560i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9450.00 | −0.319201 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 717.000 | − | 1241.88i | 0.0241430 | − | 0.0418169i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19791.0 | −0.664328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6426.00 | −0.215031 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19228.5 | + | 33304.7i | −0.641438 | + | 1.11100i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6886.00 | 0.228996 | 0.114498 | − | 0.993423i | \(-0.463474\pi\) | ||||
0.114498 | + | 0.993423i | \(0.463474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7659.00 | − | 13265.8i | −0.253914 | − | 0.439792i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4530.00 | + | 7846.19i | 0.149716 | + | 0.259316i | 0.931123 | − | 0.364706i | \(-0.118831\pi\) |
−0.781406 | + | 0.624023i | \(0.785497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 820.000 | − | 1420.28i | 0.0270175 | − | 0.0467956i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6006.00 | + | 1486.10i | −0.197278 | + | 0.0488136i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14155.5 | − | 24518.0i | 0.463536 | − | 0.802868i | −0.535598 | − | 0.844473i | \(-0.679914\pi\) |
0.999134 | + | 0.0416052i | \(0.0132472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7470.00 | + | 12938.4i | 0.243863 | + | 0.422384i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9027.00 | − | 15635.2i | −0.293792 | − | 0.508863i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4284.00 | −0.139001 | −0.0695007 | − | 0.997582i | \(-0.522141\pi\) | ||||
−0.0695007 | + | 0.997582i | \(0.522141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8937.00 | + | 15479.3i | −0.289093 | + | 0.500724i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 972.000 | 0.0313466 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3084.00 | 0.0991562 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1229.00 | + | 2128.69i | −0.0393950 | + | 0.0682342i | −0.885051 | − | 0.465495i | \(-0.845876\pi\) |
0.845656 | + | 0.533729i | \(0.179210\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27516.0 | −0.879349 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10737.0 | + | 18597.0i | 0.342096 | + | 0.592528i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12050.5 | − | 20872.1i | −0.382792 | − | 0.663014i | 0.608669 | − | 0.793425i | \(-0.291704\pi\) |
−0.991460 | + | 0.130410i | \(0.958371\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 229.500 | − | 397.506i | 0.00726833 | − | 0.0125891i |
(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 | 624.4.q.b.529.1 | 2 | ||
4.3 | odd | 2 | 39.4.e.a.22.1 | yes | 2 | ||
12.11 | even | 2 | 117.4.g.b.100.1 | 2 | |||
13.3 | even | 3 | inner | 624.4.q.b.289.1 | 2 | ||
52.3 | odd | 6 | 39.4.e.a.16.1 | ✓ | 2 | ||
52.7 | even | 12 | 507.4.b.c.337.2 | 2 | |||
52.19 | even | 12 | 507.4.b.c.337.1 | 2 | |||
52.35 | odd | 6 | 507.4.a.e.1.1 | 1 | |||
52.43 | odd | 6 | 507.4.a.a.1.1 | 1 | |||
156.35 | even | 6 | 1521.4.a.c.1.1 | 1 | |||
156.95 | even | 6 | 1521.4.a.j.1.1 | 1 | |||
156.107 | even | 6 | 117.4.g.b.55.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.a.16.1 | ✓ | 2 | 52.3 | odd | 6 | ||
39.4.e.a.22.1 | yes | 2 | 4.3 | odd | 2 | ||
117.4.g.b.55.1 | 2 | 156.107 | even | 6 | |||
117.4.g.b.100.1 | 2 | 12.11 | even | 2 | |||
507.4.a.a.1.1 | 1 | 52.43 | odd | 6 | |||
507.4.a.e.1.1 | 1 | 52.35 | odd | 6 | |||
507.4.b.c.337.1 | 2 | 52.19 | even | 12 | |||
507.4.b.c.337.2 | 2 | 52.7 | even | 12 | |||
624.4.q.b.289.1 | 2 | 13.3 | even | 3 | inner | ||
624.4.q.b.529.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.c.1.1 | 1 | 156.35 | even | 6 | |||
1521.4.a.j.1.1 | 1 | 156.95 | even | 6 |