Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 147.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.147 |
Dual form | 169.4.e.d.23.2 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.59808 | + | 1.50000i | 0.918559 | + | 0.530330i | 0.883175 | − | 0.469044i | \(-0.155401\pi\) |
0.0353837 | + | 0.999374i | \(0.488735\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.0962250 | − | 0.166667i | −0.813894 | − | 0.581013i | \(-0.802656\pi\) |
0.910119 | + | 0.414346i | \(0.135990\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.0625000 | + | 0.108253i | ||||
\(5\) | 9.00000i | 0.804984i | 0.915423 | + | 0.402492i | \(0.131856\pi\) | ||||
−0.915423 | + | 0.402492i | \(0.868144\pi\) | |||||||
\(6\) | 2.59808 | − | 1.50000i | 0.176777 | − | 0.102062i | ||||
\(7\) | 12.9904 | − | 7.50000i | 0.701415 | − | 0.404962i | −0.106459 | − | 0.994317i | \(-0.533951\pi\) |
0.807874 | + | 0.589355i | \(0.200618\pi\) | |||||||
\(8\) | − | 21.0000i | − | 0.928078i | ||||||
\(9\) | 13.0000 | + | 22.5167i | 0.481481 | + | 0.833950i | ||||
\(10\) | −13.5000 | + | 23.3827i | −0.426907 | + | 0.739425i | ||||
\(11\) | 41.5692 | + | 24.0000i | 1.13942 | + | 0.657843i | 0.946286 | − | 0.323330i | \(-0.104802\pi\) |
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(12\) | 1.00000 | 0.0240563 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 45.0000 | 0.859054 | ||||||||
\(15\) | 7.79423 | + | 4.50000i | 0.134164 | + | 0.0774597i | ||||
\(16\) | 35.5000 | − | 61.4878i | 0.554688 | − | 0.960747i | ||||
\(17\) | 22.5000 | + | 38.9711i | 0.321003 | + | 0.555994i | 0.980695 | − | 0.195542i | \(-0.0626467\pi\) |
−0.659692 | + | 0.751536i | \(0.729313\pi\) | |||||||
\(18\) | 78.0000i | 1.02138i | ||||||||
\(19\) | −5.19615 | + | 3.00000i | −0.0627410 | + | 0.0362235i | −0.531042 | − | 0.847345i | \(-0.678199\pi\) |
0.468301 | + | 0.883569i | \(0.344866\pi\) | |||||||
\(20\) | −7.79423 | + | 4.50000i | −0.0871421 | + | 0.0503115i | ||||
\(21\) | − | 15.0000i | − | 0.155870i | ||||||
\(22\) | 72.0000 | + | 124.708i | 0.697748 | + | 1.20853i | ||||
\(23\) | −81.0000 | + | 140.296i | −0.734333 | + | 1.27190i | 0.220682 | + | 0.975346i | \(0.429172\pi\) |
−0.955015 | + | 0.296557i | \(0.904162\pi\) | |||||||
\(24\) | −18.1865 | − | 10.5000i | −0.154680 | − | 0.0893043i | ||||
\(25\) | 44.0000 | 0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 12.9904 | + | 7.50000i | 0.0876768 | + | 0.0506202i | ||||
\(29\) | 72.0000 | − | 124.708i | 0.461037 | − | 0.798539i | −0.537976 | − | 0.842960i | \(-0.680811\pi\) |
0.999013 | + | 0.0444210i | \(0.0141443\pi\) | |||||||
\(30\) | 13.5000 | + | 23.3827i | 0.0821584 | + | 0.142302i | ||||
\(31\) | − | 264.000i | − | 1.52954i | −0.644302 | − | 0.764771i | \(-0.722852\pi\) | ||
0.644302 | − | 0.764771i | \(-0.277148\pi\) | |||||||
\(32\) | 38.9711 | − | 22.5000i | 0.215287 | − | 0.124296i | ||||
\(33\) | 41.5692 | − | 24.0000i | 0.219281 | − | 0.126602i | ||||
\(34\) | 135.000i | 0.680950i | ||||||||
\(35\) | 67.5000 | + | 116.913i | 0.325988 | + | 0.564628i | ||||
\(36\) | −13.0000 | + | 22.5167i | −0.0601852 | + | 0.104244i | ||||
\(37\) | −262.406 | − | 151.500i | −1.16593 | − | 0.673147i | −0.213208 | − | 0.977007i | \(-0.568391\pi\) |
−0.952717 | + | 0.303860i | \(0.901725\pi\) | |||||||
\(38\) | −18.0000 | −0.0768417 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 189.000 | 0.747088 | ||||||||
\(41\) | −166.277 | − | 96.0000i | −0.633368 | − | 0.365675i | 0.148687 | − | 0.988884i | \(-0.452495\pi\) |
−0.782055 | + | 0.623209i | \(0.785829\pi\) | |||||||
\(42\) | 22.5000 | − | 38.9711i | 0.0826625 | − | 0.143176i | ||||
\(43\) | 48.5000 | + | 84.0045i | 0.172004 | + | 0.297920i | 0.939120 | − | 0.343588i | \(-0.111642\pi\) |
−0.767116 | + | 0.641508i | \(0.778309\pi\) | |||||||
\(44\) | 48.0000i | 0.164461i | ||||||||
\(45\) | −202.650 | + | 117.000i | −0.671317 | + | 0.387585i | ||||
\(46\) | −420.888 | + | 243.000i | −1.34906 | + | 0.778878i | ||||
\(47\) | 111.000i | 0.344490i | 0.985054 | + | 0.172245i | \(0.0551020\pi\) | ||||
−0.985054 | + | 0.172245i | \(0.944898\pi\) | |||||||
\(48\) | −35.5000 | − | 61.4878i | −0.106750 | − | 0.184896i | ||||
\(49\) | −59.0000 | + | 102.191i | −0.172012 | + | 0.297933i | ||||
\(50\) | 114.315 | + | 66.0000i | 0.323333 | + | 0.186676i | ||||
\(51\) | 45.0000 | 0.123554 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −414.000 | −1.07297 | −0.536484 | − | 0.843911i | \(-0.680248\pi\) | ||||
−0.536484 | + | 0.843911i | \(0.680248\pi\) | |||||||
\(54\) | 137.698 | + | 79.5000i | 0.347006 | + | 0.200344i | ||||
\(55\) | −216.000 | + | 374.123i | −0.529553 | + | 0.917213i | ||||
\(56\) | −157.500 | − | 272.798i | −0.375836 | − | 0.650967i | ||||
\(57\) | 6.00000i | 0.0139424i | ||||||||
\(58\) | 374.123 | − | 216.000i | 0.846979 | − | 0.489003i | ||||
\(59\) | 452.065 | − | 261.000i | 0.997523 | − | 0.575920i | 0.0900089 | − | 0.995941i | \(-0.471310\pi\) |
0.907515 | + | 0.420021i | \(0.137977\pi\) | |||||||
\(60\) | 9.00000i | 0.0193649i | ||||||||
\(61\) | −188.000 | − | 325.626i | −0.394605 | − | 0.683477i | 0.598445 | − | 0.801164i | \(-0.295785\pi\) |
−0.993051 | + | 0.117687i | \(0.962452\pi\) | |||||||
\(62\) | 396.000 | − | 685.892i | 0.811162 | − | 1.40497i | ||||
\(63\) | 337.750 | + | 195.000i | 0.675436 | + | 0.389963i | ||||
\(64\) | −433.000 | −0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 144.000 | 0.268563 | ||||||||
\(67\) | −31.1769 | − | 18.0000i | −0.0568488 | − | 0.0328216i | 0.471306 | − | 0.881970i | \(-0.343783\pi\) |
−0.528155 | + | 0.849148i | \(0.677116\pi\) | |||||||
\(68\) | −22.5000 | + | 38.9711i | −0.0401254 | + | 0.0694992i | ||||
\(69\) | 81.0000 | + | 140.296i | 0.141323 | + | 0.244778i | ||||
\(70\) | 405.000i | 0.691525i | ||||||||
\(71\) | −309.171 | + | 178.500i | −0.516787 | + | 0.298367i | −0.735619 | − | 0.677396i | \(-0.763109\pi\) |
0.218832 | + | 0.975762i | \(0.429775\pi\) | |||||||
\(72\) | 472.850 | − | 273.000i | 0.773971 | − | 0.446852i | ||||
\(73\) | − | 1098.00i | − | 1.76043i | −0.474578 | − | 0.880214i | \(-0.657399\pi\) | ||
0.474578 | − | 0.880214i | \(-0.342601\pi\) | |||||||
\(74\) | −454.500 | − | 787.217i | −0.713980 | − | 1.23665i | ||||
\(75\) | 22.0000 | − | 38.1051i | 0.0338712 | − | 0.0586667i | ||||
\(76\) | −5.19615 | − | 3.00000i | −0.00784263 | − | 0.00452794i | ||||
\(77\) | 720.000 | 1.06561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −830.000 | −1.18205 | −0.591027 | − | 0.806652i | \(-0.701277\pi\) | ||||
−0.591027 | + | 0.806652i | \(0.701277\pi\) | |||||||
\(80\) | 553.390 | + | 319.500i | 0.773386 | + | 0.446515i | ||||
\(81\) | −324.500 | + | 562.050i | −0.445130 | + | 0.770988i | ||||
\(82\) | −288.000 | − | 498.831i | −0.387857 | − | 0.671788i | ||||
\(83\) | 438.000i | 0.579238i | 0.957142 | + | 0.289619i | \(0.0935286\pi\) | ||||
−0.957142 | + | 0.289619i | \(0.906471\pi\) | |||||||
\(84\) | 12.9904 | − | 7.50000i | 0.0168734 | − | 0.00974187i | ||||
\(85\) | −350.740 | + | 202.500i | −0.447566 | + | 0.258402i | ||||
\(86\) | 291.000i | 0.364876i | ||||||||
\(87\) | −72.0000 | − | 124.708i | −0.0887266 | − | 0.153679i | ||||
\(88\) | 504.000 | − | 872.954i | 0.610529 | − | 1.05747i | ||||
\(89\) | 379.319 | + | 219.000i | 0.451772 | + | 0.260831i | 0.708578 | − | 0.705632i | \(-0.249337\pi\) |
−0.256806 | + | 0.966463i | \(0.582670\pi\) | |||||||
\(90\) | −702.000 | −0.822192 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −162.000 | −0.183583 | ||||||||
\(93\) | −228.631 | − | 132.000i | −0.254924 | − | 0.147180i | ||||
\(94\) | −166.500 | + | 288.386i | −0.182693 | + | 0.316434i | ||||
\(95\) | −27.0000 | − | 46.7654i | −0.0291594 | − | 0.0505055i | ||||
\(96\) | − | 45.0000i | − | 0.0478416i | ||||||
\(97\) | 737.854 | − | 426.000i | 0.772347 | − | 0.445915i | −0.0613640 | − | 0.998115i | \(-0.519545\pi\) |
0.833711 | + | 0.552201i | \(0.186212\pi\) | |||||||
\(98\) | −306.573 | + | 177.000i | −0.316006 | + | 0.182446i | ||||
\(99\) | 1248.00i | 1.26696i | ||||||||
\(100\) | 22.0000 | + | 38.1051i | 0.0220000 | + | 0.0381051i | ||||
\(101\) | −198.000 | + | 342.946i | −0.195067 | + | 0.337865i | −0.946922 | − | 0.321462i | \(-0.895826\pi\) |
0.751856 | + | 0.659328i | \(0.229159\pi\) | |||||||
\(102\) | 116.913 | + | 67.5000i | 0.113492 | + | 0.0655245i | ||||
\(103\) | 182.000 | 0.174107 | 0.0870534 | − | 0.996204i | \(-0.472255\pi\) | ||||
0.0870534 | + | 0.996204i | \(0.472255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 135.000 | 0.125473 | ||||||||
\(106\) | −1075.60 | − | 621.000i | −0.985584 | − | 0.569027i | ||||
\(107\) | 306.000 | − | 530.008i | 0.276469 | − | 0.478858i | −0.694036 | − | 0.719940i | \(-0.744169\pi\) |
0.970505 | + | 0.241083i | \(0.0775025\pi\) | |||||||
\(108\) | 26.5000 | + | 45.8993i | 0.0236108 | + | 0.0408951i | ||||
\(109\) | − | 1083.00i | − | 0.951675i | −0.879533 | − | 0.475838i | \(-0.842145\pi\) | ||
0.879533 | − | 0.475838i | \(-0.157855\pi\) | |||||||
\(110\) | −1122.37 | + | 648.000i | −0.972852 | + | 0.561676i | ||||
\(111\) | −262.406 | + | 151.500i | −0.224382 | + | 0.129547i | ||||
\(112\) | − | 1065.00i | − | 0.898509i | ||||||
\(113\) | −45.0000 | − | 77.9423i | −0.0374623 | − | 0.0648867i | 0.846686 | − | 0.532092i | \(-0.178594\pi\) |
−0.884149 | + | 0.467206i | \(0.845261\pi\) | |||||||
\(114\) | −9.00000 | + | 15.5885i | −0.00739410 | + | 0.0128070i | ||||
\(115\) | −1262.67 | − | 729.000i | −1.02386 | − | 0.591127i | ||||
\(116\) | 144.000 | 0.115259 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1566.00 | 1.22171 | ||||||||
\(119\) | 584.567 | + | 337.500i | 0.450312 | + | 0.259988i | ||||
\(120\) | 94.5000 | − | 163.679i | 0.0718886 | − | 0.124515i | ||||
\(121\) | 486.500 | + | 842.643i | 0.365515 | + | 0.633090i | ||||
\(122\) | − | 1128.00i | − | 0.837085i | ||||||
\(123\) | −166.277 | + | 96.0000i | −0.121892 | + | 0.0703742i | ||||
\(124\) | 228.631 | − | 132.000i | 0.165578 | − | 0.0955964i | ||||
\(125\) | 1521.00i | 1.08834i | ||||||||
\(126\) | 585.000 | + | 1013.25i | 0.413619 | + | 0.716408i | ||||
\(127\) | −1043.00 | + | 1806.53i | −0.728750 | + | 1.26223i | 0.228661 | + | 0.973506i | \(0.426565\pi\) |
−0.957412 | + | 0.288726i | \(0.906768\pi\) | |||||||
\(128\) | −1436.74 | − | 829.500i | −0.992115 | − | 0.572798i | ||||
\(129\) | 97.0000 | 0.0662044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1467.00 | −0.978415 | −0.489208 | − | 0.872167i | \(-0.662714\pi\) | ||||
−0.489208 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(132\) | 41.5692 | + | 24.0000i | 0.0274101 | + | 0.0158252i | ||||
\(133\) | −45.0000 | + | 77.9423i | −0.0293383 | + | 0.0508154i | ||||
\(134\) | −54.0000 | − | 93.5307i | −0.0348126 | − | 0.0602972i | ||||
\(135\) | 477.000i | 0.304101i | ||||||||
\(136\) | 818.394 | − | 472.500i | 0.516005 | − | 0.297916i | ||||
\(137\) | −358.535 | + | 207.000i | −0.223589 | + | 0.129089i | −0.607611 | − | 0.794235i | \(-0.707872\pi\) |
0.384022 | + | 0.923324i | \(0.374539\pi\) | |||||||
\(138\) | 486.000i | 0.299790i | ||||||||
\(139\) | 1209.50 | + | 2094.92i | 0.738046 | + | 1.27833i | 0.953374 | + | 0.301792i | \(0.0975848\pi\) |
−0.215327 | + | 0.976542i | \(0.569082\pi\) | |||||||
\(140\) | −67.5000 | + | 116.913i | −0.0407485 | + | 0.0705785i | ||||
\(141\) | 96.1288 | + | 55.5000i | 0.0574149 | + | 0.0331485i | ||||
\(142\) | −1071.00 | −0.632932 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1846.00 | 1.06829 | ||||||||
\(145\) | 1122.37 | + | 648.000i | 0.642811 | + | 0.371127i | ||||
\(146\) | 1647.00 | − | 2852.69i | 0.933607 | − | 1.61706i | ||||
\(147\) | 59.0000 | + | 102.191i | 0.0331037 | + | 0.0573372i | ||||
\(148\) | − | 303.000i | − | 0.168287i | ||||||
\(149\) | 805.404 | − | 465.000i | 0.442827 | − | 0.255666i | −0.261969 | − | 0.965076i | \(-0.584372\pi\) |
0.704796 | + | 0.709410i | \(0.251038\pi\) | |||||||
\(150\) | 114.315 | − | 66.0000i | 0.0622254 | − | 0.0359258i | ||||
\(151\) | − | 1683.00i | − | 0.907024i | −0.891250 | − | 0.453512i | \(-0.850171\pi\) | ||
0.891250 | − | 0.453512i | \(-0.149829\pi\) | |||||||
\(152\) | 63.0000 | + | 109.119i | 0.0336183 | + | 0.0582285i | ||||
\(153\) | −585.000 | + | 1013.25i | −0.309114 | + | 0.535401i | ||||
\(154\) | 1870.61 | + | 1080.00i | 0.978821 | + | 0.565123i | ||||
\(155\) | 2376.00 | 1.23126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1874.00 | 0.952621 | 0.476310 | − | 0.879277i | \(-0.341974\pi\) | ||||
0.476310 | + | 0.879277i | \(0.341974\pi\) | |||||||
\(158\) | −2156.40 | − | 1245.00i | −1.08579 | − | 0.626879i | ||||
\(159\) | −207.000 | + | 358.535i | −0.103246 | + | 0.178828i | ||||
\(160\) | 202.500 | + | 350.740i | 0.100056 | + | 0.173303i | ||||
\(161\) | 2430.00i | 1.18951i | ||||||||
\(162\) | −1686.15 | + | 973.500i | −0.817757 | + | 0.472132i | ||||
\(163\) | −1034.03 | + | 597.000i | −0.496882 | + | 0.286875i | −0.727425 | − | 0.686187i | \(-0.759283\pi\) |
0.230543 | + | 0.973062i | \(0.425950\pi\) | |||||||
\(164\) | − | 192.000i | − | 0.0914188i | ||||||
\(165\) | 216.000 | + | 374.123i | 0.101913 | + | 0.176518i | ||||
\(166\) | −657.000 | + | 1137.96i | −0.307187 | + | 0.532064i | ||||
\(167\) | 2068.07 | + | 1194.00i | 0.958275 | + | 0.553260i | 0.895642 | − | 0.444776i | \(-0.146717\pi\) |
0.0626334 | + | 0.998037i | \(0.480050\pi\) | |||||||
\(168\) | −315.000 | −0.144659 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1215.00 | −0.548154 | ||||||||
\(171\) | −135.100 | − | 78.0000i | −0.0604173 | − | 0.0348819i | ||||
\(172\) | −48.5000 | + | 84.0045i | −0.0215005 | + | 0.0372400i | ||||
\(173\) | 783.000 | + | 1356.20i | 0.344106 | + | 0.596010i | 0.985191 | − | 0.171461i | \(-0.0548486\pi\) |
−0.641085 | + | 0.767470i | \(0.721515\pi\) | |||||||
\(174\) | − | 432.000i | − | 0.188217i | ||||||
\(175\) | 571.577 | − | 330.000i | 0.246898 | − | 0.142547i | ||||
\(176\) | 2951.41 | − | 1704.00i | 1.26404 | − | 0.729795i | ||||
\(177\) | − | 522.000i | − | 0.221672i | ||||||
\(178\) | 657.000 | + | 1137.96i | 0.276653 | + | 0.479177i | ||||
\(179\) | 328.500 | − | 568.979i | 0.137169 | − | 0.237584i | −0.789255 | − | 0.614066i | \(-0.789533\pi\) |
0.926424 | + | 0.376482i | \(0.122866\pi\) | |||||||
\(180\) | −202.650 | − | 117.000i | −0.0839146 | − | 0.0484481i | ||||
\(181\) | −1222.00 | −0.501826 | −0.250913 | − | 0.968010i | \(-0.580731\pi\) | ||||
−0.250913 | + | 0.968010i | \(0.580731\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −376.000 | −0.151884 | ||||||||
\(184\) | 2946.22 | + | 1701.00i | 1.18042 | + | 0.681518i | ||||
\(185\) | 1363.50 | − | 2361.65i | 0.541873 | − | 0.938552i | ||||
\(186\) | −396.000 | − | 685.892i | −0.156108 | − | 0.270387i | ||||
\(187\) | 2160.00i | 0.844678i | ||||||||
\(188\) | −96.1288 | + | 55.5000i | −0.0372921 | + | 0.0215306i | ||||
\(189\) | 688.490 | − | 397.500i | 0.264975 | − | 0.152983i | ||||
\(190\) | − | 162.000i | − | 0.0618564i | ||||||
\(191\) | −630.000 | − | 1091.19i | −0.238666 | − | 0.413382i | 0.721666 | − | 0.692242i | \(-0.243377\pi\) |
−0.960332 | + | 0.278860i | \(0.910043\pi\) | |||||||
\(192\) | −216.500 | + | 374.989i | −0.0813778 | + | 0.140951i | ||||
\(193\) | −296.181 | − | 171.000i | −0.110464 | − | 0.0637764i | 0.443750 | − | 0.896151i | \(-0.353648\pi\) |
−0.554214 | + | 0.832374i | \(0.686981\pi\) | |||||||
\(194\) | 2556.00 | 0.945928 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −118.000 | −0.0430029 | ||||||||
\(197\) | 70.1481 | + | 40.5000i | 0.0253698 | + | 0.0146472i | 0.512631 | − | 0.858609i | \(-0.328671\pi\) |
−0.487261 | + | 0.873256i | \(0.662004\pi\) | |||||||
\(198\) | −1872.00 | + | 3242.40i | −0.671905 | + | 1.16377i | ||||
\(199\) | −998.000 | − | 1728.59i | −0.355509 | − | 0.615760i | 0.631696 | − | 0.775216i | \(-0.282359\pi\) |
−0.987205 | + | 0.159456i | \(0.949026\pi\) | |||||||
\(200\) | − | 924.000i | − | 0.326683i | ||||||
\(201\) | −31.1769 | + | 18.0000i | −0.0109405 | + | 0.00631653i | ||||
\(202\) | −1028.84 | + | 594.000i | −0.358360 | + | 0.206899i | ||||
\(203\) | − | 2160.00i | − | 0.746809i | ||||||
\(204\) | 22.5000 | + | 38.9711i | 0.00772213 | + | 0.0133751i | ||||
\(205\) | 864.000 | − | 1496.49i | 0.294363 | − | 0.509851i | ||||
\(206\) | 472.850 | + | 273.000i | 0.159927 | + | 0.0923340i | ||||
\(207\) | −4212.00 | −1.41427 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −288.000 | −0.0953176 | ||||||||
\(210\) | 350.740 | + | 202.500i | 0.115254 | + | 0.0665420i | ||||
\(211\) | −1416.50 | + | 2453.45i | −0.462161 | + | 0.800486i | −0.999068 | − | 0.0431553i | \(-0.986259\pi\) |
0.536908 | + | 0.843641i | \(0.319592\pi\) | |||||||
\(212\) | −207.000 | − | 358.535i | −0.0670605 | − | 0.116152i | ||||
\(213\) | 357.000i | 0.114841i | ||||||||
\(214\) | 1590.02 | − | 918.000i | 0.507905 | − | 0.293239i | ||||
\(215\) | −756.040 | + | 436.500i | −0.239821 | + | 0.138461i | ||||
\(216\) | − | 1113.00i | − | 0.350602i | ||||||
\(217\) | −1980.00 | − | 3429.46i | −0.619406 | − | 1.07284i | ||||
\(218\) | 1624.50 | − | 2813.72i | 0.504702 | − | 0.874169i | ||||
\(219\) | −950.896 | − | 549.000i | −0.293405 | − | 0.169397i | ||||
\(220\) | −432.000 | −0.132388 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −909.000 | −0.274811 | ||||||||
\(223\) | −3037.15 | − | 1753.50i | −0.912030 | − | 0.526561i | −0.0309462 | − | 0.999521i | \(-0.509852\pi\) |
−0.881084 | + | 0.472960i | \(0.843185\pi\) | |||||||
\(224\) | 337.500 | − | 584.567i | 0.100670 | − | 0.174366i | ||||
\(225\) | 572.000 | + | 990.733i | 0.169481 | + | 0.293551i | ||||
\(226\) | − | 270.000i | − | 0.0794696i | ||||||
\(227\) | 197.454 | − | 114.000i | 0.0577333 | − | 0.0333324i | −0.470855 | − | 0.882210i | \(-0.656055\pi\) |
0.528589 | + | 0.848878i | \(0.322721\pi\) | |||||||
\(228\) | −5.19615 | + | 3.00000i | −0.00150931 | + | 0.000871403i | ||||
\(229\) | 5493.00i | 1.58510i | 0.609808 | + | 0.792549i | \(0.291247\pi\) | ||||
−0.609808 | + | 0.792549i | \(0.708753\pi\) | |||||||
\(230\) | −2187.00 | − | 3788.00i | −0.626985 | − | 1.08597i | ||||
\(231\) | 360.000 | − | 623.538i | 0.102538 | − | 0.177601i | ||||
\(232\) | −2618.86 | − | 1512.00i | −0.741106 | − | 0.427878i | ||||
\(233\) | 3627.00 | 1.01980 | 0.509898 | − | 0.860235i | \(-0.329683\pi\) | ||||
0.509898 | + | 0.860235i | \(0.329683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −999.000 | −0.277309 | ||||||||
\(236\) | 452.065 | + | 261.000i | 0.124690 | + | 0.0719901i | ||||
\(237\) | −415.000 | + | 718.801i | −0.113743 | + | 0.197009i | ||||
\(238\) | 1012.50 | + | 1753.70i | 0.275759 | + | 0.477628i | ||||
\(239\) | − | 6075.00i | − | 1.64418i | −0.569357 | − | 0.822090i | \(-0.692808\pi\) | ||
0.569357 | − | 0.822090i | \(-0.307192\pi\) | |||||||
\(240\) | 553.390 | − | 319.500i | 0.148838 | − | 0.0859318i | ||||
\(241\) | 181.865 | − | 105.000i | 0.0486099 | − | 0.0280649i | −0.475498 | − | 0.879717i | \(-0.657732\pi\) |
0.524108 | + | 0.851652i | \(0.324399\pi\) | |||||||
\(242\) | 2919.00i | 0.775374i | ||||||||
\(243\) | 1040.00 | + | 1801.33i | 0.274552 | + | 0.475537i | ||||
\(244\) | 188.000 | − | 325.626i | 0.0493257 | − | 0.0854346i | ||||
\(245\) | −919.719 | − | 531.000i | −0.239831 | − | 0.138467i | ||||
\(246\) | −576.000 | −0.149286 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5544.00 | −1.41953 | ||||||||
\(249\) | 379.319 | + | 219.000i | 0.0965397 | + | 0.0557372i | ||||
\(250\) | −2281.50 | + | 3951.67i | −0.577179 | + | 0.999703i | ||||
\(251\) | −3546.00 | − | 6141.85i | −0.891719 | − | 1.54450i | −0.837813 | − | 0.545957i | \(-0.816166\pi\) |
−0.0539061 | − | 0.998546i | \(-0.517167\pi\) | |||||||
\(252\) | 390.000i | 0.0974908i | ||||||||
\(253\) | −6734.21 | + | 3888.00i | −1.67342 | + | 0.966152i | ||||
\(254\) | −5419.59 | + | 3129.00i | −1.33880 | + | 0.772956i | ||||
\(255\) | 405.000i | 0.0994592i | ||||||||
\(256\) | −756.500 | − | 1310.30i | −0.184692 | − | 0.319897i | ||||
\(257\) | 2902.50 | − | 5027.28i | 0.704486 | − | 1.22021i | −0.262390 | − | 0.964962i | \(-0.584511\pi\) |
0.966877 | − | 0.255244i | \(-0.0821559\pi\) | |||||||
\(258\) | 252.013 | + | 145.500i | 0.0608127 | + | 0.0351102i | ||||
\(259\) | −4545.00 | −1.09040 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3744.00 | 0.887923 | ||||||||
\(262\) | −3811.38 | − | 2200.50i | −0.898732 | − | 0.518883i | ||||
\(263\) | −396.000 | + | 685.892i | −0.0928457 | + | 0.160813i | −0.908707 | − | 0.417434i | \(-0.862930\pi\) |
0.815862 | + | 0.578247i | \(0.196263\pi\) | |||||||
\(264\) | −504.000 | − | 872.954i | −0.117496 | − | 0.203510i | ||||
\(265\) | − | 3726.00i | − | 0.863722i | ||||||
\(266\) | −233.827 | + | 135.000i | −0.0538979 | + | 0.0311180i | ||||
\(267\) | 379.319 | − | 219.000i | 0.0869436 | − | 0.0501969i | ||||
\(268\) | − | 36.0000i | − | 0.00820541i | ||||||
\(269\) | −2736.00 | − | 4738.89i | −0.620137 | − | 1.07411i | −0.989460 | − | 0.144808i | \(-0.953744\pi\) |
0.369323 | − | 0.929301i | \(-0.379590\pi\) | |||||||
\(270\) | −715.500 | + | 1239.28i | −0.161274 | + | 0.279335i | ||||
\(271\) | −2018.71 | − | 1165.50i | −0.452500 | − | 0.261251i | 0.256385 | − | 0.966575i | \(-0.417468\pi\) |
−0.708886 | + | 0.705323i | \(0.750802\pi\) | |||||||
\(272\) | 3195.00 | 0.712225 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1242.00 | −0.273839 | ||||||||
\(275\) | 1829.05 | + | 1056.00i | 0.401075 | + | 0.231561i | ||||
\(276\) | −81.0000 | + | 140.296i | −0.0176653 | + | 0.0305972i | ||||
\(277\) | 692.000 | + | 1198.58i | 0.150102 | + | 0.259984i | 0.931265 | − | 0.364343i | \(-0.118706\pi\) |
−0.781163 | + | 0.624327i | \(0.785373\pi\) | |||||||
\(278\) | 7257.00i | 1.56563i | ||||||||
\(279\) | 5944.40 | − | 3432.00i | 1.27556 | − | 0.736446i | ||||
\(280\) | 2455.18 | − | 1417.50i | 0.524019 | − | 0.302542i | ||||
\(281\) | − | 4062.00i | − | 0.862344i | −0.902270 | − | 0.431172i | \(-0.858100\pi\) | ||
0.902270 | − | 0.431172i | \(-0.141900\pi\) | |||||||
\(282\) | 166.500 | + | 288.386i | 0.0351593 | + | 0.0608977i | ||||
\(283\) | 1882.00 | − | 3259.72i | 0.395312 | − | 0.684700i | −0.597829 | − | 0.801624i | \(-0.703970\pi\) |
0.993141 | + | 0.116923i | \(0.0373032\pi\) | |||||||
\(284\) | −309.171 | − | 178.500i | −0.0645983 | − | 0.0372959i | ||||
\(285\) | −54.0000 | −0.0112235 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2880.00 | −0.592338 | ||||||||
\(288\) | 1013.25 | + | 585.000i | 0.207314 | + | 0.119693i | ||||
\(289\) | 1444.00 | − | 2501.08i | 0.293914 | − | 0.509074i | ||||
\(290\) | 1944.00 | + | 3367.11i | 0.393640 | + | 0.681805i | ||||
\(291\) | − | 852.000i | − | 0.171633i | ||||||
\(292\) | 950.896 | − | 549.000i | 0.190572 | − | 0.110027i | ||||
\(293\) | 3660.69 | − | 2113.50i | 0.729897 | − | 0.421406i | −0.0884876 | − | 0.996077i | \(-0.528203\pi\) |
0.818384 | + | 0.574671i | \(0.194870\pi\) | |||||||
\(294\) | 354.000i | 0.0702235i | ||||||||
\(295\) | 2349.00 | + | 4068.59i | 0.463607 | + | 0.802991i | ||||
\(296\) | −3181.50 | + | 5510.52i | −0.624733 | + | 1.08207i | ||||
\(297\) | 2203.17 | + | 1272.00i | 0.430440 | + | 0.248515i | ||||
\(298\) | 2790.00 | 0.542350 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 44.0000 | 0.00846780 | ||||||||
\(301\) | 1260.07 | + | 727.500i | 0.241293 | + | 0.139310i | ||||
\(302\) | 2524.50 | − | 4372.56i | 0.481022 | − | 0.833155i | ||||
\(303\) | 198.000 | + | 342.946i | 0.0375406 | + | 0.0650222i | ||||
\(304\) | 426.000i | 0.0803710i | ||||||||
\(305\) | 2930.63 | − | 1692.00i | 0.550188 | − | 0.317651i | ||||
\(306\) | −3039.75 | + | 1755.00i | −0.567879 | + | 0.327865i | ||||
\(307\) | 306.000i | 0.0568871i | 0.999595 | + | 0.0284436i | \(0.00905509\pi\) | ||||
−0.999595 | + | 0.0284436i | \(0.990945\pi\) | |||||||
\(308\) | 360.000 | + | 623.538i | 0.0666003 | + | 0.115355i | ||||
\(309\) | 91.0000 | − | 157.617i | 0.0167534 | − | 0.0290178i | ||||
\(310\) | 6173.03 | + | 3564.00i | 1.13098 | + | 0.652973i | ||||
\(311\) | −2106.00 | −0.383988 | −0.191994 | − | 0.981396i | \(-0.561495\pi\) | ||||
−0.191994 | + | 0.981396i | \(0.561495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10051.0 | 1.81507 | 0.907534 | − | 0.419979i | \(-0.137963\pi\) | ||||
0.907534 | + | 0.419979i | \(0.137963\pi\) | |||||||
\(314\) | 4868.79 | + | 2811.00i | 0.875038 | + | 0.505204i | ||||
\(315\) | −1755.00 | + | 3039.75i | −0.313914 | + | 0.543716i | ||||
\(316\) | −415.000 | − | 718.801i | −0.0738784 | − | 0.127961i | ||||
\(317\) | 2154.00i | 0.381643i | 0.981625 | + | 0.190821i | \(0.0611151\pi\) | ||||
−0.981625 | + | 0.190821i | \(0.938885\pi\) | |||||||
\(318\) | −1075.60 | + | 621.000i | −0.189676 | + | 0.109509i | ||||
\(319\) | 5985.97 | − | 3456.00i | 1.05063 | − | 0.606579i | ||||
\(320\) | − | 3897.00i | − | 0.680778i | ||||||
\(321\) | −306.000 | − | 530.008i | −0.0532064 | − | 0.0921562i | ||||
\(322\) | −3645.00 | + | 6313.33i | −0.630832 | + | 1.09263i | ||||
\(323\) | −233.827 | − | 135.000i | −0.0402801 | − | 0.0232557i | ||||
\(324\) | −649.000 | −0.111283 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3582.00 | −0.608554 | ||||||||
\(327\) | −937.906 | − | 541.500i | −0.158613 | − | 0.0915750i | ||||
\(328\) | −2016.00 | + | 3491.81i | −0.339375 | + | 0.587815i | ||||
\(329\) | 832.500 | + | 1441.93i | 0.139505 | + | 0.241630i | ||||
\(330\) | 1296.00i | 0.216189i | ||||||||
\(331\) | −9327.09 | + | 5385.00i | −1.54883 | + | 0.894219i | −0.550601 | + | 0.834769i | \(0.685601\pi\) |
−0.998231 | + | 0.0594500i | \(0.981065\pi\) | |||||||
\(332\) | −379.319 | + | 219.000i | −0.0627043 | + | 0.0362024i | ||||
\(333\) | − | 7878.00i | − | 1.29643i | ||||||
\(334\) | 3582.00 | + | 6204.21i | 0.586821 | + | 1.01640i | ||||
\(335\) | 162.000 | − | 280.592i | 0.0264209 | − | 0.0457624i | ||||
\(336\) | −922.317 | − | 532.500i | −0.149752 | − | 0.0864591i | ||||
\(337\) | −2171.00 | −0.350926 | −0.175463 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175463 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −90.0000 | −0.0144193 | ||||||||
\(340\) | −350.740 | − | 202.500i | −0.0559458 | − | 0.0323003i | ||||
\(341\) | 6336.00 | − | 10974.3i | 1.00620 | − | 1.74279i | ||||
\(342\) | −234.000 | − | 405.300i | −0.0369979 | − | 0.0640822i | ||||
\(343\) | 6915.00i | 1.08856i | ||||||||
\(344\) | 1764.09 | − | 1018.50i | 0.276493 | − | 0.159633i | ||||
\(345\) | −1262.67 | + | 729.000i | −0.197042 | + | 0.113762i | ||||
\(346\) | 4698.00i | 0.729960i | ||||||||
\(347\) | 3523.50 | + | 6102.88i | 0.545105 | + | 0.944149i | 0.998600 | + | 0.0528907i | \(0.0168435\pi\) |
−0.453495 | + | 0.891259i | \(0.649823\pi\) | |||||||
\(348\) | 72.0000 | − | 124.708i | 0.0110908 | − | 0.0192099i | ||||
\(349\) | 5952.19 | + | 3436.50i | 0.912933 | + | 0.527082i | 0.881374 | − | 0.472420i | \(-0.156619\pi\) |
0.0315592 | + | 0.999502i | \(0.489953\pi\) | |||||||
\(350\) | 1980.00 | 0.302387 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2160.00 | 0.327069 | ||||||||
\(353\) | −8069.62 | − | 4659.00i | −1.21672 | − | 0.702475i | −0.252507 | − | 0.967595i | \(-0.581255\pi\) |
−0.964215 | + | 0.265121i | \(0.914588\pi\) | |||||||
\(354\) | 783.000 | − | 1356.20i | 0.117559 | − | 0.203619i | ||||
\(355\) | −1606.50 | − | 2782.54i | −0.240181 | − | 0.416005i | ||||
\(356\) | 438.000i | 0.0652077i | ||||||||
\(357\) | 584.567 | − | 337.500i | 0.0866627 | − | 0.0500347i | ||||
\(358\) | 1706.94 | − | 985.500i | 0.251995 | − | 0.145490i | ||||
\(359\) | 4128.00i | 0.606873i | 0.952852 | + | 0.303437i | \(0.0981341\pi\) | ||||
−0.952852 | + | 0.303437i | \(0.901866\pi\) | |||||||
\(360\) | 2457.00 | + | 4255.65i | 0.359709 | + | 0.623034i | ||||
\(361\) | −3411.50 | + | 5908.89i | −0.497376 | + | 0.861480i | ||||
\(362\) | −3174.85 | − | 1833.00i | −0.460957 | − | 0.266134i | ||||
\(363\) | 973.000 | 0.140687 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9882.00 | 1.41712 | ||||||||
\(366\) | −976.877 | − | 564.000i | −0.139514 | − | 0.0805485i | ||||
\(367\) | 1268.00 | − | 2196.24i | 0.180352 | − | 0.312378i | −0.761649 | − | 0.647990i | \(-0.775610\pi\) |
0.942000 | + | 0.335612i | \(0.108943\pi\) | |||||||
\(368\) | 5751.00 | + | 9961.02i | 0.814651 | + | 1.41102i | ||||
\(369\) | − | 4992.00i | − | 0.704263i | ||||||
\(370\) | 7084.95 | − | 4090.50i | 0.995484 | − | 0.574743i | ||||
\(371\) | −5378.02 | + | 3105.00i | −0.752595 | + | 0.434511i | ||||
\(372\) | − | 264.000i | − | 0.0367951i | ||||||
\(373\) | 46.0000 | + | 79.6743i | 0.00638550 | + | 0.0110600i | 0.869200 | − | 0.494460i | \(-0.164634\pi\) |
−0.862815 | + | 0.505520i | \(0.831301\pi\) | |||||||
\(374\) | −3240.00 | + | 5611.84i | −0.447958 | + | 0.775887i | ||||
\(375\) | 1317.22 | + | 760.500i | 0.181390 | + | 0.104725i | ||||
\(376\) | 2331.00 | 0.319713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2385.00 | 0.324527 | ||||||||
\(379\) | 8817.87 | + | 5091.00i | 1.19510 | + | 0.689992i | 0.959459 | − | 0.281847i | \(-0.0909472\pi\) |
0.235643 | + | 0.971840i | \(0.424281\pi\) | |||||||
\(380\) | 27.0000 | − | 46.7654i | 0.00364492 | − | 0.00631319i | ||||
\(381\) | 1043.00 | + | 1806.53i | 0.140248 | + | 0.242917i | ||||
\(382\) | − | 3780.00i | − | 0.506287i | ||||||
\(383\) | 501.429 | − | 289.500i | 0.0668977 | − | 0.0386234i | −0.466178 | − | 0.884691i | \(-0.654369\pi\) |
0.533076 | + | 0.846068i | \(0.321036\pi\) | |||||||
\(384\) | −1436.74 | + | 829.500i | −0.190933 | + | 0.110235i | ||||
\(385\) | 6480.00i | 0.857796i | ||||||||
\(386\) | −513.000 | − | 888.542i | −0.0676451 | − | 0.117165i | ||||
\(387\) | −1261.00 | + | 2184.12i | −0.165634 | + | 0.286886i | ||||
\(388\) | 737.854 | + | 426.000i | 0.0965434 | + | 0.0557394i | ||||
\(389\) | 2106.00 | 0.274495 | 0.137247 | − | 0.990537i | \(-0.456174\pi\) | ||||
0.137247 | + | 0.990537i | \(0.456174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7290.00 | −0.942893 | ||||||||
\(392\) | 2146.01 | + | 1239.00i | 0.276505 | + | 0.159640i | ||||
\(393\) | −733.500 | + | 1270.46i | −0.0941480 | + | 0.163069i | ||||
\(394\) | 121.500 | + | 210.444i | 0.0155357 | + | 0.0269087i | ||||
\(395\) | − | 7470.00i | − | 0.951535i | ||||||
\(396\) | −1080.80 | + | 624.000i | −0.137152 | + | 0.0791848i | ||||
\(397\) | −1709.53 | + | 987.000i | −0.216119 | + | 0.124776i | −0.604152 | − | 0.796869i | \(-0.706488\pi\) |
0.388033 | + | 0.921645i | \(0.373155\pi\) | |||||||
\(398\) | − | 5988.00i | − | 0.754149i | ||||||
\(399\) | 45.0000 | + | 77.9423i | 0.00564616 | + | 0.00977944i | ||||
\(400\) | 1562.00 | − | 2705.46i | 0.195250 | − | 0.338183i | ||||
\(401\) | −10293.6 | − | 5943.00i | −1.28189 | − | 0.740098i | −0.304694 | − | 0.952450i | \(-0.598554\pi\) |
−0.977193 | + | 0.212352i | \(0.931888\pi\) | |||||||
\(402\) | −108.000 | −0.0133994 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −396.000 | −0.0487667 | ||||||||
\(405\) | −5058.45 | − | 2920.50i | −0.620634 | − | 0.358323i | ||||
\(406\) | 3240.00 | − | 5611.84i | 0.396055 | − | 0.685988i | ||||
\(407\) | −7272.00 | − | 12595.5i | −0.885650 | − | 1.53399i | ||||
\(408\) | − | 945.000i | − | 0.114668i | ||||||
\(409\) | −1086.00 | + | 627.000i | −0.131293 | + | 0.0758023i | −0.564208 | − | 0.825633i | \(-0.690818\pi\) |
0.432915 | + | 0.901435i | \(0.357485\pi\) | |||||||
\(410\) | 4489.48 | − | 2592.00i | 0.540779 | − | 0.312219i | ||||
\(411\) | 414.000i | 0.0496864i | ||||||||
\(412\) | 91.0000 | + | 157.617i | 0.0108817 | + | 0.0188476i | ||||
\(413\) | 3915.00 | − | 6780.98i | 0.466452 | − | 0.807918i | ||||
\(414\) | −10943.1 | − | 6318.00i | −1.29909 | − | 0.750031i | ||||
\(415\) | −3942.00 | −0.466278 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2419.00 | 0.284074 | ||||||||
\(418\) | −748.246 | − | 432.000i | −0.0875548 | − | 0.0505498i | ||||
\(419\) | −2911.50 | + | 5042.87i | −0.339466 | + | 0.587972i | −0.984332 | − | 0.176323i | \(-0.943580\pi\) |
0.644867 | + | 0.764295i | \(0.276913\pi\) | |||||||
\(420\) | 67.5000 | + | 116.913i | 0.00784205 | + | 0.0135828i | ||||
\(421\) | 7341.00i | 0.849830i | 0.905233 | + | 0.424915i | \(0.139696\pi\) | ||||
−0.905233 | + | 0.424915i | \(0.860304\pi\) | |||||||
\(422\) | −7360.35 | + | 4249.50i | −0.849043 | + | 0.490195i | ||||
\(423\) | −2499.35 | + | 1443.00i | −0.287287 | + | 0.165865i | ||||
\(424\) | 8694.00i | 0.995797i | ||||||||
\(425\) | 990.000 | + | 1714.73i | 0.112993 | + | 0.195710i | ||||
\(426\) | −535.500 | + | 927.513i | −0.0609039 | + | 0.105489i | ||||
\(427\) | −4884.38 | − | 2820.00i | −0.553564 | − | 0.319600i | ||||
\(428\) | 612.000 | 0.0691171 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2619.00 | −0.293720 | ||||||||
\(431\) | −6482.20 | − | 3742.50i | −0.724447 | − | 0.418260i | 0.0919403 | − | 0.995765i | \(-0.470693\pi\) |
−0.816387 | + | 0.577505i | \(0.804026\pi\) | |||||||
\(432\) | 1881.50 | − | 3258.85i | 0.209546 | − | 0.362944i | ||||
\(433\) | 7601.50 | + | 13166.2i | 0.843660 | + | 1.46126i | 0.886780 | + | 0.462192i | \(0.152937\pi\) |
−0.0431199 | + | 0.999070i | \(0.513730\pi\) | |||||||
\(434\) | − | 11880.0i | − | 1.31396i | ||||||
\(435\) | 1122.37 | − | 648.000i | 0.123709 | − | 0.0714235i | ||||
\(436\) | 937.906 | − | 541.500i | 0.103022 | − | 0.0594797i | ||||
\(437\) | − | 972.000i | − | 0.106401i | ||||||
\(438\) | −1647.00 | − | 2852.69i | −0.179673 | − | 0.311202i | ||||
\(439\) | 881.000 | − | 1525.94i | 0.0957809 | − | 0.165897i | −0.814153 | − | 0.580650i | \(-0.802799\pi\) |
0.909934 | + | 0.414752i | \(0.136132\pi\) | |||||||
\(440\) | 7856.58 | + | 4536.00i | 0.851245 | + | 0.491467i | ||||
\(441\) | −3068.00 | −0.331282 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7317.00 | −0.784743 | −0.392372 | − | 0.919807i | \(-0.628345\pi\) | ||||
−0.392372 | + | 0.919807i | \(0.628345\pi\) | |||||||
\(444\) | −262.406 | − | 151.500i | −0.0280478 | − | 0.0161934i | ||||
\(445\) | −1971.00 | + | 3413.87i | −0.209965 | + | 0.363670i | ||||
\(446\) | −5260.50 | − | 9111.45i | −0.558502 | − | 0.967354i | ||||
\(447\) | − | 930.000i | − | 0.0984060i | ||||||
\(448\) | −5624.83 | + | 3247.50i | −0.593189 | + | 0.342478i | ||||
\(449\) | −4343.98 | + | 2508.00i | −0.456582 | + | 0.263608i | −0.710606 | − | 0.703590i | \(-0.751579\pi\) |
0.254024 | + | 0.967198i | \(0.418246\pi\) | |||||||
\(450\) | 3432.00i | 0.359525i | ||||||||
\(451\) | −4608.00 | − | 7981.29i | −0.481114 | − | 0.833313i | ||||
\(452\) | 45.0000 | − | 77.9423i | 0.00468279 | − | 0.00811083i | ||||
\(453\) | −1457.52 | − | 841.500i | −0.151171 | − | 0.0872784i | ||||
\(454\) | 684.000 | 0.0707086 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 126.000 | 0.0129397 | ||||||||
\(457\) | 8547.67 | + | 4935.00i | 0.874930 | + | 0.505141i | 0.868984 | − | 0.494841i | \(-0.164774\pi\) |
0.00594684 | + | 0.999982i | \(0.498107\pi\) | |||||||
\(458\) | −8239.50 | + | 14271.2i | −0.840626 | + | 1.45601i | ||||
\(459\) | 1192.50 | + | 2065.47i | 0.121266 | + | 0.210039i | ||||
\(460\) | − | 1458.00i | − | 0.147782i | ||||||
\(461\) | 12592.9 | − | 7270.50i | 1.27225 | − | 0.734536i | 0.296842 | − | 0.954927i | \(-0.404067\pi\) |
0.975412 | + | 0.220391i | \(0.0707334\pi\) | |||||||
\(462\) | 1870.61 | − | 1080.00i | 0.188374 | − | 0.108758i | ||||
\(463\) | − | 2112.00i | − | 0.211993i | −0.994366 | − | 0.105997i | \(-0.966197\pi\) | ||
0.994366 | − | 0.105997i | \(-0.0338033\pi\) | |||||||
\(464\) | −5112.00 | − | 8854.24i | −0.511463 | − | 0.885879i | ||||
\(465\) | 1188.00 | − | 2057.68i | 0.118478 | − | 0.205210i | ||||
\(466\) | 9423.22 | + | 5440.50i | 0.936743 | + | 0.540829i | ||||
\(467\) | 3276.00 | 0.324615 | 0.162307 | − | 0.986740i | \(-0.448106\pi\) | ||||
0.162307 | + | 0.986740i | \(0.448106\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −540.000 | −0.0531661 | ||||||||
\(470\) | −2595.48 | − | 1498.50i | −0.254724 | − | 0.147065i | ||||
\(471\) | 937.000 | − | 1622.93i | 0.0916660 | − | 0.158770i | ||||
\(472\) | −5481.00 | − | 9493.37i | −0.534499 | − | 0.925779i | ||||
\(473\) | 4656.00i | 0.452607i | ||||||||
\(474\) | −2156.40 | + | 1245.00i | −0.208960 | + | 0.120643i | ||||
\(475\) | −228.631 | + | 132.000i | −0.0220848 | + | 0.0127507i | ||||
\(476\) | 675.000i | 0.0649970i | ||||||||
\(477\) | −5382.00 | − | 9321.90i | −0.516614 | − | 0.894802i | ||||
\(478\) | 9112.50 | − | 15783.3i | 0.871958 | − | 1.51028i | ||||
\(479\) | 13382.7 | + | 7726.50i | 1.27656 | + | 0.737020i | 0.976214 | − | 0.216811i | \(-0.0695655\pi\) |
0.300343 | + | 0.953831i | \(0.402899\pi\) | |||||||
\(480\) | 405.000 | 0.0385117 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 630.000 | 0.0595347 | ||||||||
\(483\) | 2104.44 | + | 1215.00i | 0.198251 | + | 0.114460i | ||||
\(484\) | −486.500 | + | 842.643i | −0.0456893 | + | 0.0791362i | ||||
\(485\) | 3834.00 | + | 6640.68i | 0.358955 | + | 0.621728i | ||||
\(486\) | 6240.00i | 0.582412i | ||||||||
\(487\) | 3169.65 | − | 1830.00i | 0.294930 | − | 0.170278i | −0.345233 | − | 0.938517i | \(-0.612200\pi\) |
0.640163 | + | 0.768239i | \(0.278867\pi\) | |||||||
\(488\) | −6838.14 | + | 3948.00i | −0.634319 | + | 0.366225i | ||||
\(489\) | 1194.00i | 0.110418i | ||||||||
\(490\) | −1593.00 | − | 2759.16i | −0.146866 | − | 0.254380i | ||||
\(491\) | −373.500 | + | 646.921i | −0.0343296 | + | 0.0594606i | −0.882680 | − | 0.469975i | \(-0.844263\pi\) |
0.848350 | + | 0.529436i | \(0.177596\pi\) | |||||||
\(492\) | −166.277 | − | 96.0000i | −0.0152365 | − | 0.00879678i | ||||
\(493\) | 6480.00 | 0.591977 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11232.0 | −1.01988 | ||||||||
\(496\) | −16232.8 | − | 9372.00i | −1.46950 | − | 0.848418i | ||||
\(497\) | −2677.50 | + | 4637.57i | −0.241655 | + | 0.418558i | ||||
\(498\) | 657.000 | + | 1137.96i | 0.0591182 | + | 0.102396i | ||||
\(499\) | 15804.0i | 1.41780i | 0.705307 | + | 0.708902i | \(0.250809\pi\) | ||||
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(500\) | −1317.22 | + | 760.500i | −0.117816 | + | 0.0680212i | ||||
\(501\) | 2068.07 | − | 1194.00i | 0.184420 | − | 0.106475i | ||||
\(502\) | − | 21276.0i | − | 1.89162i | ||||||
\(503\) | 6039.00 | + | 10459.9i | 0.535319 | + | 0.927201i | 0.999148 | + | 0.0412754i | \(0.0131421\pi\) |
−0.463828 | + | 0.885925i | \(0.653525\pi\) | |||||||
\(504\) | 4095.00 | − | 7092.75i | 0.361916 | − | 0.626857i | ||||
\(505\) | −3086.51 | − | 1782.00i | −0.271976 | − | 0.157026i | ||||
\(506\) | −23328.0 | −2.04952 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2086.00 | −0.182188 | ||||||||
\(509\) | 13951.7 | + | 8055.00i | 1.21493 | + | 0.701437i | 0.963828 | − | 0.266525i | \(-0.0858754\pi\) |
0.251097 | + | 0.967962i | \(0.419209\pi\) | |||||||
\(510\) | −607.500 | + | 1052.22i | −0.0527462 | + | 0.0913591i | ||||
\(511\) | −8235.00 | − | 14263.4i | −0.712906 | − | 1.23479i | ||||
\(512\) | 8733.00i | 0.753804i | ||||||||
\(513\) | −275.396 | + | 159.000i | −0.0237018 | + | 0.0136843i | ||||
\(514\) | 15081.8 | − | 8707.50i | 1.29422 | − | 0.747221i | ||||
\(515\) | 1638.00i | 0.140153i | ||||||||
\(516\) | 48.5000 | + | 84.0045i | 0.00413778 | + | 0.00716684i | ||||
\(517\) | −2664.00 | + | 4614.18i | −0.226620 | + | 0.392518i | ||||
\(518\) | −11808.3 | − | 6817.50i | −1.00159 | − | 0.578270i | ||||
\(519\) | 1566.00 | 0.132447 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3915.00 | 0.329212 | 0.164606 | − | 0.986359i | \(-0.447365\pi\) | ||||
0.164606 | + | 0.986359i | \(0.447365\pi\) | |||||||
\(522\) | 9727.20 | + | 5616.00i | 0.815609 | + | 0.470892i | ||||
\(523\) | −8092.00 | + | 14015.8i | −0.676555 | + | 1.17183i | 0.299456 | + | 0.954110i | \(0.403195\pi\) |
−0.976012 | + | 0.217718i | \(0.930139\pi\) | |||||||
\(524\) | −733.500 | − | 1270.46i | −0.0611509 | − | 0.105917i | ||||
\(525\) | − | 660.000i | − | 0.0548662i | ||||||
\(526\) | −2057.68 | + | 1188.00i | −0.170568 | + | 0.0984777i | ||||
\(527\) | 10288.4 | − | 5940.00i | 0.850415 | − | 0.490988i | ||||
\(528\) | − | 3408.00i | − | 0.280898i | ||||||
\(529\) | −7038.50 | − | 12191.0i | −0.578491 | − | 1.00198i | ||||
\(530\) | 5589.00 | − | 9680.43i | 0.458058 | − | 0.793379i | ||||
\(531\) | 11753.7 | + | 6786.00i | 0.960578 | + | 0.554590i | ||||
\(532\) | −90.0000 | −0.00733458 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1314.00 | 0.106484 | ||||||||
\(535\) | 4770.07 | + | 2754.00i | 0.385473 | + | 0.222553i | ||||
\(536\) | −378.000 | + | 654.715i | −0.0304610 | + | 0.0527601i | ||||
\(537\) | −328.500 | − | 568.979i | −0.0263982 | − | 0.0457230i | ||||
\(538\) | − | 16416.0i | − | 1.31551i | ||||||
\(539\) | −4905.17 | + | 2832.00i | −0.391986 | + | 0.226313i | ||||
\(540\) | −413.094 | + | 238.500i | −0.0329199 | + | 0.0190063i | ||||
\(541\) | − | 7923.00i | − | 0.629642i | −0.949151 | − | 0.314821i | \(-0.898055\pi\) | ||
0.949151 | − | 0.314821i | \(-0.101945\pi\) | |||||||
\(542\) | −3496.50 | − | 6056.12i | −0.277099 | − | 0.479949i | ||||
\(543\) | −611.000 | + | 1058.28i | −0.0482882 | + | 0.0836377i | ||||
\(544\) | 1753.70 | + | 1012.50i | 0.138216 | + | 0.0797989i | ||||
\(545\) | 9747.00 | 0.766084 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14389.0 | −1.12473 | −0.562367 | − | 0.826888i | \(-0.690109\pi\) | ||||
−0.562367 | + | 0.826888i | \(0.690109\pi\) | |||||||
\(548\) | −358.535 | − | 207.000i | −0.0279486 | − | 0.0161361i | ||||
\(549\) | 4888.00 | − | 8466.26i | 0.379990 | − | 0.658163i | ||||
\(550\) | 3168.00 | + | 5487.14i | 0.245607 | + | 0.425404i | ||||
\(551\) | 864.000i | 0.0668015i | ||||||||
\(552\) | 2946.22 | − | 1701.00i | 0.227173 | − | 0.131158i | ||||
\(553\) | −10782.0 | + | 6225.00i | −0.829110 | + | 0.478687i | ||||
\(554\) | 4152.00i | 0.318414i | ||||||||
\(555\) | −1363.50 | − | 2361.65i | −0.104284 | − | 0.180624i | ||||
\(556\) | −1209.50 | + | 2094.92i | −0.0922558 | + | 0.159792i | ||||
\(557\) | 8991.94 | + | 5191.50i | 0.684023 | + | 0.394921i | 0.801369 | − | 0.598170i | \(-0.204105\pi\) |
−0.117346 | + | 0.993091i | \(0.537439\pi\) | |||||||
\(558\) | 20592.0 | 1.56224 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9585.00 | 0.723286 | ||||||||
\(561\) | 1870.61 | + | 1080.00i | 0.140780 | + | 0.0812792i | ||||
\(562\) | 6093.00 | − | 10553.4i | 0.457327 | − | 0.792113i | ||||
\(563\) | 8212.50 | + | 14224.5i | 0.614770 | + | 1.06481i | 0.990425 | + | 0.138053i | \(0.0440846\pi\) |
−0.375655 | + | 0.926760i | \(0.622582\pi\) | |||||||
\(564\) | 111.000i | 0.00828713i | ||||||||
\(565\) | 701.481 | − | 405.000i | 0.0522328 | − | 0.0301566i | ||||
\(566\) | 9779.16 | − | 5646.00i | 0.726234 | − | 0.419292i | ||||
\(567\) | 9735.00i | 0.721043i | ||||||||
\(568\) | 3748.50 | + | 6492.59i | 0.276908 | + | 0.479618i | ||||
\(569\) | −6106.50 | + | 10576.8i | −0.449908 | + | 0.779264i | −0.998380 | − | 0.0569054i | \(-0.981877\pi\) |
0.548471 | + | 0.836169i | \(0.315210\pi\) | |||||||
\(570\) | −140.296 | − | 81.0000i | −0.0103094 | − | 0.00595213i | ||||
\(571\) | −6383.00 | −0.467811 | −0.233906 | − | 0.972259i | \(-0.575151\pi\) | ||||
−0.233906 | + | 0.972259i | \(0.575151\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1260.00 | −0.0918626 | ||||||||
\(574\) | −7482.46 | − | 4320.00i | −0.544097 | − | 0.314135i | ||||
\(575\) | −3564.00 | + | 6173.03i | −0.258485 | + | 0.447710i | ||||
\(576\) | −5629.00 | − | 9749.71i | −0.407190 | − | 0.705274i | ||||
\(577\) | − | 6426.00i | − | 0.463636i | −0.972759 | − | 0.231818i | \(-0.925533\pi\) | ||
0.972759 | − | 0.231818i | \(-0.0744674\pi\) | |||||||
\(578\) | 7503.24 | − | 4332.00i | 0.539955 | − | 0.311743i | ||||
\(579\) | −296.181 | + | 171.000i | −0.0212588 | + | 0.0122738i | ||||
\(580\) | 1296.00i | 0.0927818i | ||||||||
\(581\) | 3285.00 | + | 5689.79i | 0.234569 | + | 0.406286i | ||||
\(582\) | 1278.00 | − | 2213.56i | 0.0910220 | − | 0.157655i | ||||
\(583\) | −17209.7 | − | 9936.00i | −1.22256 | − | 0.705844i | ||||
\(584\) | −23058.0 | −1.63381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12681.0 | 0.893937 | ||||||||
\(587\) | −18472.3 | − | 10665.0i | −1.29887 | − | 0.749901i | −0.318658 | − | 0.947870i | \(-0.603232\pi\) |
−0.980208 | + | 0.197969i | \(0.936565\pi\) | |||||||
\(588\) | −59.0000 | + | 102.191i | −0.00413796 | + | 0.00716715i | ||||
\(589\) | 792.000 | + | 1371.78i | 0.0554054 | + | 0.0959650i | ||||
\(590\) | 14094.0i | 0.983459i | ||||||||
\(591\) | 70.1481 | − | 40.5000i | 0.00488241 | − | 0.00281886i | ||||
\(592\) | −18630.8 | + | 10756.5i | −1.29345 | + | 0.746773i | ||||
\(593\) | 12084.0i | 0.836813i | 0.908260 | + | 0.418407i | \(0.137411\pi\) | ||||
−0.908260 | + | 0.418407i | \(0.862589\pi\) | |||||||
\(594\) | 3816.00 | + | 6609.51i | 0.263590 | + | 0.456551i | ||||
\(595\) | −3037.50 | + | 5261.10i | −0.209286 | + | 0.362495i | ||||
\(596\) | 805.404 | + | 465.000i | 0.0553534 | + | 0.0319583i | ||||
\(597\) | −1996.00 | −0.136836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2394.00 | 0.163299 | 0.0816496 | − | 0.996661i | \(-0.473981\pi\) | ||||
0.0816496 | + | 0.996661i | \(0.473981\pi\) | |||||||
\(600\) | −800.207 | − | 462.000i | −0.0544472 | − | 0.0314351i | ||||
\(601\) | 10985.5 | − | 19027.4i | 0.745604 | − | 1.29142i | −0.204308 | − | 0.978907i | \(-0.565495\pi\) |
0.949912 | − | 0.312517i | \(-0.101172\pi\) | |||||||
\(602\) | 2182.50 | + | 3780.20i | 0.147761 | + | 0.255929i | ||||
\(603\) | − | 936.000i | − | 0.0632121i | ||||||
\(604\) | 1457.52 | − | 841.500i | 0.0981882 | − | 0.0566890i | ||||
\(605\) | −7583.78 | + | 4378.50i | −0.509628 | + | 0.294234i | ||||
\(606\) | 1188.00i | 0.0796356i | ||||||||
\(607\) | 7703.00 | + | 13342.0i | 0.515083 | + | 0.892149i | 0.999847 | + | 0.0175043i | \(0.00557208\pi\) |
−0.484764 | + | 0.874645i | \(0.661095\pi\) | |||||||
\(608\) | −135.000 | + | 233.827i | −0.00900489 | + | 0.0155969i | ||||
\(609\) | −1870.61 | − | 1080.00i | −0.124468 | − | 0.0718618i | ||||
\(610\) | 10152.0 | 0.673840 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1170.00 | −0.0772785 | ||||||||
\(613\) | −8339.82 | − | 4815.00i | −0.549498 | − | 0.317253i | 0.199421 | − | 0.979914i | \(-0.436094\pi\) |
−0.748920 | + | 0.662661i | \(0.769427\pi\) | |||||||
\(614\) | −459.000 | + | 795.011i | −0.0301689 | + | 0.0522541i | ||||
\(615\) | −864.000 | − | 1496.49i | −0.0566502 | − | 0.0981209i | ||||
\(616\) | − | 15120.0i | − | 0.988965i | ||||||
\(617\) | −12772.1 | + | 7374.00i | −0.833366 | + | 0.481144i | −0.855004 | − | 0.518622i | \(-0.826445\pi\) |
0.0216375 | + | 0.999766i | \(0.493112\pi\) | |||||||
\(618\) | 472.850 | − | 273.000i | 0.0307780 | − | 0.0177697i | ||||
\(619\) | − | 3672.00i | − | 0.238433i | −0.992868 | − | 0.119217i | \(-0.961962\pi\) | ||
0.992868 | − | 0.119217i | \(-0.0380383\pi\) | |||||||
\(620\) | 1188.00 | + | 2057.68i | 0.0769536 | + | 0.133288i | ||||
\(621\) | −4293.00 | + | 7435.69i | −0.277411 | + | 0.480490i | ||||
\(622\) | −5471.55 | − | 3159.00i | −0.352716 | − | 0.203640i | ||||
\(623\) | 6570.00 | 0.422506 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 26113.3 | + | 15076.5i | 1.66725 | + | 0.962585i | ||||
\(627\) | −144.000 | + | 249.415i | −0.00917194 | + | 0.0158863i | ||||
\(628\) | 937.000 | + | 1622.93i | 0.0595388 | + | 0.103124i | ||||
\(629\) | − | 13635.0i | − | 0.864329i | ||||||
\(630\) | −9119.25 | + | 5265.00i | −0.576698 | + | 0.332957i | ||||
\(631\) | −17212.3 | + | 9937.50i | −1.08591 | + | 0.626950i | −0.932485 | − | 0.361210i | \(-0.882364\pi\) |
−0.153425 | + | 0.988160i | \(0.549030\pi\) | |||||||
\(632\) | 17430.0i | 1.09704i | ||||||||
\(633\) | 1416.50 | + | 2453.45i | 0.0889428 | + | 0.154054i | ||||
\(634\) | −3231.00 | + | 5596.26i | −0.202397 | + | 0.350561i | ||||
\(635\) | −16258.8 | − | 9387.00i | −1.01608 | − | 0.586633i | ||||
\(636\) | −414.000 | −0.0258116 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20736.0 | 1.28675 | ||||||||
\(639\) | −8038.45 | − | 4641.00i | −0.497646 | − | 0.287316i | ||||
\(640\) | 7465.50 | − | 12930.6i | 0.461093 | − | 0.798637i | ||||
\(641\) | −855.000 | − | 1480.90i | −0.0526840 | − | 0.0912514i | 0.838481 | − | 0.544931i | \(-0.183444\pi\) |
−0.891165 | + | 0.453680i | \(0.850111\pi\) | |||||||
\(642\) | − | 1836.00i | − | 0.112868i | ||||||
\(643\) | 14247.8 | − | 8226.00i | 0.873842 | − | 0.504513i | 0.00521887 | − | 0.999986i | \(-0.498339\pi\) |
0.868623 | + | 0.495474i | \(0.165005\pi\) | |||||||
\(644\) | −2104.44 | + | 1215.00i | −0.128768 | + | 0.0743443i | ||||
\(645\) | 873.000i | 0.0532936i | ||||||||
\(646\) | −405.000 | − | 701.481i | −0.0246664 | − | 0.0427235i | ||||
\(647\) | −12951.0 | + | 22431.8i | −0.786950 | + | 1.36304i | 0.140878 | + | 0.990027i | \(0.455007\pi\) |
−0.927827 | + | 0.373010i | \(0.878326\pi\) | |||||||
\(648\) | 11803.1 | + | 6814.50i | 0.715537 | + | 0.413115i | ||||
\(649\) | 25056.0 | 1.51546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3960.00 | −0.238410 | ||||||||
\(652\) | −1034.03 | − | 597.000i | −0.0621103 | − | 0.0358594i | ||||
\(653\) | −9054.00 | + | 15682.0i | −0.542589 | + | 0.939791i | 0.456166 | + | 0.889895i | \(0.349222\pi\) |
−0.998754 | + | 0.0498963i | \(0.984111\pi\) | |||||||
\(654\) | −1624.50 | − | 2813.72i | −0.0971299 | − | 0.168234i | ||||
\(655\) | − | 13203.0i | − | 0.787609i | ||||||
\(656\) | −11805.7 | + | 6816.00i | −0.702643 | + | 0.405671i | ||||
\(657\) | 24723.3 | − | 14274.0i | 1.46811 | − | 0.847613i | ||||
\(658\) | 4995.00i | 0.295935i | ||||||||
\(659\) | 16452.0 | + | 28495.7i | 0.972502 | + | 1.68442i | 0.687943 | + | 0.725765i | \(0.258514\pi\) |
0.284559 | + | 0.958658i | \(0.408153\pi\) | |||||||
\(660\) | −216.000 | + | 374.123i | −0.0127391 | + | 0.0220647i | ||||
\(661\) | −13265.8 | − | 7659.00i | −0.780604 | − | 0.450682i | 0.0560406 | − | 0.998428i | \(-0.482152\pi\) |
−0.836644 | + | 0.547747i | \(0.815486\pi\) | |||||||
\(662\) | −32310.0 | −1.89692 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9198.00 | 0.537578 | ||||||||
\(665\) | −701.481 | − | 405.000i | −0.0409056 | − | 0.0236169i | ||||
\(666\) | 11817.0 | − | 20467.6i | 0.687537 | − | 1.19085i | ||||
\(667\) | 11664.0 | + | 20202.6i | 0.677109 | + | 1.17279i | ||||
\(668\) | 2388.00i | 0.138315i | ||||||||
\(669\) | −3037.15 | + | 1753.50i | −0.175520 | + | 0.101337i | ||||
\(670\) | 841.777 | − | 486.000i | 0.0485383 | − | 0.0280236i | ||||
\(671\) | − | 18048.0i | − | 1.03835i | ||||||
\(672\) | −337.500 | − | 584.567i | −0.0193740 | − | 0.0335568i | ||||
\(673\) | 3864.50 | − | 6693.51i | 0.221346 | − | 0.383382i | −0.733871 | − | 0.679289i | \(-0.762288\pi\) |
0.955217 | + | 0.295907i | \(0.0956218\pi\) | |||||||
\(674\) | −5640.42 | − | 3256.50i | −0.322346 | − | 0.186106i | ||||
\(675\) | 2332.00 | 0.132976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19242.0 | 1.09236 | 0.546182 | − | 0.837667i | \(-0.316081\pi\) | ||||
0.546182 | + | 0.837667i | \(0.316081\pi\) | |||||||
\(678\) | −233.827 | − | 135.000i | −0.0132449 | − | 0.00764697i | ||||
\(679\) | 6390.00 | − | 11067.8i | 0.361157 | − | 0.625543i | ||||
\(680\) | 4252.50 | + | 7365.55i | 0.239818 | + | 0.415376i | ||||
\(681\) | − | 228.000i | − | 0.0128296i | ||||||
\(682\) | 32922.8 | − | 19008.0i | 1.84850 | − | 1.06723i | ||||
\(683\) | 19501.2 | − | 11259.0i | 1.09252 | − | 0.630767i | 0.158274 | − | 0.987395i | \(-0.449407\pi\) |
0.934246 | + | 0.356629i | \(0.116074\pi\) | |||||||
\(684\) | − | 156.000i | − | 0.00872048i | ||||||
\(685\) | −1863.00 | − | 3226.81i | −0.103915 | − | 0.179986i | ||||
\(686\) | −10372.5 | + | 17965.7i | −0.577294 | + | 0.999903i | ||||
\(687\) | 4757.08 | + | 2746.50i | 0.264183 | + | 0.152526i | ||||
\(688\) | 6887.00 | 0.381634 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4374.00 | −0.241327 | ||||||||
\(691\) | 7939.72 | + | 4584.00i | 0.437107 | + | 0.252364i | 0.702370 | − | 0.711812i | \(-0.252125\pi\) |
−0.265262 | + | 0.964176i | \(0.585459\pi\) | |||||||
\(692\) | −783.000 | + | 1356.20i | −0.0430133 | + | 0.0745012i | ||||
\(693\) | 9360.00 | + | 16212.0i | 0.513069 | + | 0.888662i | ||||
\(694\) | 21141.0i | 1.15634i | ||||||||
\(695\) | −18854.2 | + | 10885.5i | −1.02904 | + | 0.594116i | ||||
\(696\) | −2618.86 | + | 1512.00i | −0.142626 | + | 0.0823451i | ||||
\(697\) | − | 8640.00i | − | 0.469531i | ||||||
\(698\) | 10309.5 | + | 17856.6i | 0.559055 | + | 0.968312i | ||||
\(699\) | 1813.50 | − | 3141.07i | 0.0981300 | − | 0.169966i | ||||
\(700\) | 571.577 | + | 330.000i | 0.0308622 | + | 0.0178183i | ||||
\(701\) | 1170.00 | 0.0630389 | 0.0315195 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315195 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1818.00 | 0.0975351 | ||||||||
\(704\) | −17999.5 | − | 10392.0i | −0.963609 | − | 0.556340i | ||||
\(705\) | −499.500 | + | 865.159i | −0.0266841 | + | 0.0462181i | ||||
\(706\) | −13977.0 | − | 24208.9i | −0.745087 | − | 1.29053i | ||||
\(707\) | 5940.00i | 0.315978i | ||||||||
\(708\) | 452.065 | − | 261.000i | 0.0239967 | − | 0.0138545i | ||||
\(709\) | −1439.33 | + | 831.000i | −0.0762417 | + | 0.0440181i | −0.537636 | − | 0.843177i | \(-0.680683\pi\) |
0.461395 | + | 0.887195i | \(0.347349\pi\) | |||||||
\(710\) | − | 9639.00i | − | 0.509500i | ||||||
\(711\) | −10790.0 | − | 18688.8i | −0.569137 | − | 0.985775i | ||||
\(712\) | 4599.00 | − | 7965.70i | 0.242071 | − | 0.419280i | ||||
\(713\) | 37038.2 | + | 21384.0i | 1.94543 | + | 1.12319i | ||||
\(714\) | 2025.00 | 0.106140 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 657.000 | 0.0342922 | ||||||||
\(717\) | −5261.10 | − | 3037.50i | −0.274030 | − | 0.158211i | ||||
\(718\) | −6192.00 | + | 10724.9i | −0.321843 | + | 0.557449i | ||||
\(719\) | −15480.0 | − | 26812.1i | −0.802930 | − | 1.39072i | −0.917680 | − | 0.397321i | \(-0.869940\pi\) |
0.114750 | − | 0.993394i | \(-0.463393\pi\) | |||||||
\(720\) | 16614.0i | 0.859954i | ||||||||
\(721\) | 2364.25 | − | 1365.00i | 0.122121 | − | 0.0705066i | ||||
\(722\) | −17726.7 | + | 10234.5i | −0.913738 | + | 0.527547i | ||||
\(723\) | − | 210.000i | − | 0.0108022i | ||||||
\(724\) | −611.000 | − | 1058.28i | −0.0313641 | − | 0.0543243i | ||||
\(725\) | 3168.00 | − | 5487.14i | 0.162285 | − | 0.281086i | ||||
\(726\) | 2527.93 | + | 1459.50i | 0.129229 | + | 0.0746104i | ||||
\(727\) | −8372.00 | −0.427098 | −0.213549 | − | 0.976932i | \(-0.568502\pi\) | ||||
−0.213549 | + | 0.976932i | \(0.568502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 25674.2 | + | 14823.0i | 1.30170 | + | 0.751540i | ||||
\(731\) | −2182.50 | + | 3780.20i | −0.110428 | + | 0.191266i | ||||
\(732\) | −188.000 | − | 325.626i | −0.00949273 | − | 0.0164419i | ||||
\(733\) | 2739.00i | 0.138018i | 0.997616 | + | 0.0690091i | \(0.0219837\pi\) | ||||
−0.997616 | + | 0.0690091i | \(0.978016\pi\) | |||||||
\(734\) | 6588.72 | − | 3804.00i | 0.331327 | − | 0.191292i | ||||
\(735\) | −919.719 | + | 531.000i | −0.0461556 | + | 0.0266479i | ||||
\(736\) | 7290.00i | 0.365099i | ||||||||
\(737\) | −864.000 | − | 1496.49i | −0.0431830 | − | 0.0747951i | ||||
\(738\) | 7488.00 | − | 12969.6i | 0.373492 | − | 0.646907i | ||||
\(739\) | 5850.87 | + | 3378.00i | 0.291242 | + | 0.168148i | 0.638502 | − | 0.769620i | \(-0.279555\pi\) |
−0.347260 | + | 0.937769i | \(0.612888\pi\) | |||||||
\(740\) | 2727.00 | 0.135468 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18630.0 | −0.921737 | ||||||||
\(743\) | 25671.6 | + | 14821.5i | 1.26756 | + | 0.731828i | 0.974526 | − | 0.224273i | \(-0.0720008\pi\) |
0.293037 | + | 0.956101i | \(0.405334\pi\) | |||||||
\(744\) | −2772.00 | + | 4801.24i | −0.136595 | + | 0.236589i | ||||
\(745\) | 4185.00 | + | 7248.63i | 0.205807 | + | 0.356469i | ||||
\(746\) | 276.000i | 0.0135457i | ||||||||
\(747\) | −9862.30 | + | 5694.00i | −0.483056 | + | 0.278892i | ||||
\(748\) | −1870.61 | + | 1080.00i | −0.0914391 | + | 0.0527924i | ||||
\(749\) | − | 9180.00i | − | 0.447837i | ||||||
\(750\) | 2281.50 | + | 3951.67i | 0.111078 | + | 0.192393i | ||||
\(751\) | −9064.00 | + | 15699.3i | −0.440413 | + | 0.762817i | −0.997720 | − | 0.0674890i | \(-0.978501\pi\) |
0.557307 | + | 0.830306i | \(0.311835\pi\) | |||||||
\(752\) | 6825.15 | + | 3940.50i | 0.330967 | + | 0.191084i | ||||
\(753\) | −7092.00 | −0.343223 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15147.0 | 0.730140 | ||||||||
\(756\) | 688.490 | + | 397.500i | 0.0331219 | + | 0.0191229i | ||||
\(757\) | 3205.00 | − | 5551.22i | 0.153881 | − | 0.266529i | −0.778770 | − | 0.627309i | \(-0.784156\pi\) |
0.932651 | + | 0.360780i | \(0.117490\pi\) | |||||||
\(758\) | 15273.0 | + | 26453.6i | 0.731847 | + | 1.26760i | ||||
\(759\) | 7776.00i | 0.371872i | ||||||||
\(760\) | −982.073 | + | 567.000i | −0.0468731 | + | 0.0270622i | ||||
\(761\) | 24499.9 | − | 14145.0i | 1.16704 | − | 0.673792i | 0.214061 | − | 0.976820i | \(-0.431331\pi\) |
0.952982 | + | 0.303028i | \(0.0979976\pi\) | |||||||
\(762\) | 6258.00i | 0.297511i | ||||||||
\(763\) | −8122.50 | − | 14068.6i | −0.385392 | − | 0.667519i | ||||
\(764\) | 630.000 | − | 1091.19i | 0.0298332 | − | 0.0516727i | ||||
\(765\) | −9119.25 | − | 5265.00i | −0.430990 | − | 0.248832i | ||||
\(766\) | 1737.00 | 0.0819326 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1513.00 | −0.0710881 | ||||||||
\(769\) | −24214.1 | − | 13980.0i | −1.13548 | − | 0.655568i | −0.190170 | − | 0.981751i | \(-0.560904\pi\) |
−0.945307 | + | 0.326183i | \(0.894237\pi\) | |||||||
\(770\) | −9720.00 | + | 16835.5i | −0.454915 | + | 0.787936i | ||||
\(771\) | −2902.50 | − | 5027.28i | −0.135578 | − | 0.234829i | ||||
\(772\) | − | 342.000i | − | 0.0159441i | ||||||
\(773\) | 4892.18 | − | 2824.50i | 0.227632 | − | 0.131423i | −0.381847 | − | 0.924225i | \(-0.624712\pi\) |
0.609479 | + | 0.792802i | \(0.291379\pi\) | |||||||
\(774\) | −6552.35 | + | 3783.00i | −0.304288 | + | 0.175681i | ||||
\(775\) | − | 11616.0i | − | 0.538399i | ||||||
\(776\) | −8946.00 | − | 15494.9i | −0.413844 | − | 0.716798i | ||||
\(777\) | −2272.50 | + | 3936.09i | −0.104923 | + | 0.181733i | ||||
\(778\) | 5471.55 | + | 3159.00i | 0.252139 | + | 0.145573i | ||||
\(779\) | 1152.00 | 0.0529842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17136.0 | −0.785114 | ||||||||
\(782\) | −18940.0 | − | 10935.0i | −0.866102 | − | 0.500045i | ||||
\(783\) | 3816.00 | − | 6609.51i | 0.174167 | − | 0.301666i | ||||
\(784\) | 4189.00 | + | 7255.56i | 0.190825 | + | 0.330519i | ||||
\(785\) | 16866.0i | 0.766845i | ||||||||
\(786\) | −3811.38 | + | 2200.50i | −0.172961 | + | 0.0998591i | ||||
\(787\) | 654.715 | − | 378.000i | 0.0296545 | − | 0.0171210i | −0.485099 | − | 0.874459i | \(-0.661217\pi\) |
0.514754 | + | 0.857338i | \(0.327883\pi\) | |||||||
\(788\) | 81.0000i | 0.00366181i | ||||||||
\(789\) | 396.000 | + | 685.892i | 0.0178682 | + | 0.0309486i | ||||
\(790\) | 11205.0 | − | 19407.6i | 0.504628 | − | 0.874041i | ||||
\(791\) | −1169.13 | − | 675.000i | −0.0525533 | − | 0.0303416i | ||||
\(792\) | 26208.0 | 1.17583 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −5922.00 | −0.264690 | ||||||||
\(795\) | −3226.81 | − | 1863.00i | −0.143954 | − | 0.0831117i | ||||
\(796\) | 998.000 | − | 1728.59i | 0.0444387 | − | 0.0769700i | ||||
\(797\) | −15597.0 | − | 27014.8i | −0.693192 | − | 1.20064i | −0.970786 | − | 0.239945i | \(-0.922870\pi\) |
0.277594 | − | 0.960698i | \(-0.410463\pi\) | |||||||
\(798\) | 270.000i | 0.0119773i | ||||||||
\(799\) | −4325.80 | + | 2497.50i | −0.191534 | + | 0.110582i | ||||
\(800\) | 1714.73 | − | 990.000i | 0.0757811 | − | 0.0437522i | ||||
\(801\) | 11388.0i | 0.502341i | ||||||||
\(802\) | −17829.0 | − | 30880.7i | −0.784992 | − | 1.35965i | ||||
\(803\) | 26352.0 | − | 45643.0i | 1.15808 | − | 2.00586i | ||||
\(804\) | −31.1769 | − | 18.0000i | −0.00136757 | − | 0.000789566i | ||||
\(805\) | −21870.0 | −0.957536 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5472.00 | −0.238691 | ||||||||
\(808\) | 7201.87 | + | 4158.00i | 0.313565 | + | 0.181037i | ||||
\(809\) | −8527.50 | + | 14770.1i | −0.370594 | + | 0.641888i | −0.989657 | − | 0.143453i | \(-0.954179\pi\) |
0.619063 | + | 0.785342i | \(0.287513\pi\) | |||||||
\(810\) | −8761.50 | − | 15175.4i | −0.380059 | − | 0.658281i | ||||
\(811\) | − | 35520.0i | − | 1.53795i | −0.639280 | − | 0.768974i | \(-0.720768\pi\) | ||
0.639280 | − | 0.768974i | \(-0.279232\pi\) | |||||||
\(812\) | 1870.61 | − | 1080.00i | 0.0808445 | − | 0.0466756i | ||||
\(813\) | −2018.71 | + | 1165.50i | −0.0870837 | + | 0.0502778i | ||||
\(814\) | − | 43632.0i | − | 1.87875i | ||||||
\(815\) | −5373.00 | − | 9306.31i | −0.230930 | − | 0.399983i | ||||
\(816\) | 1597.50 | − | 2766.95i | 0.0685339 | − | 0.118704i | ||||
\(817\) | −504.027 | − | 291.000i | −0.0215834 | − | 0.0124612i | ||||
\(818\) | −3762.00 | −0.160801 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1728.00 | 0.0735907 | ||||||||
\(821\) | 948.298 | + | 547.500i | 0.0403116 | + | 0.0232739i | 0.520020 | − | 0.854154i | \(-0.325924\pi\) |
−0.479709 | + | 0.877428i | \(0.659258\pi\) | |||||||
\(822\) | −621.000 | + | 1075.60i | −0.0263502 | + | 0.0456399i | ||||
\(823\) | 1277.00 | + | 2211.83i | 0.0540868 | + | 0.0936811i | 0.891801 | − | 0.452428i | \(-0.149442\pi\) |
−0.837714 | + | 0.546109i | \(0.816109\pi\) | |||||||
\(824\) | − | 3822.00i | − | 0.161585i | ||||||
\(825\) | 1829.05 | − | 1056.00i | 0.0771869 | − | 0.0445639i | ||||
\(826\) | 20342.9 | − | 11745.0i | 0.856927 | − | 0.494747i | ||||
\(827\) | 21522.0i | 0.904950i | 0.891777 | + | 0.452475i | \(0.149459\pi\) | ||||
−0.891777 | + | 0.452475i | \(0.850541\pi\) | |||||||
\(828\) | −2106.00 | − | 3647.70i | −0.0883920 | − | 0.153099i | ||||
\(829\) | 6562.00 | − | 11365.7i | 0.274919 | − | 0.476173i | −0.695196 | − | 0.718820i | \(-0.744682\pi\) |
0.970115 | + | 0.242647i | \(0.0780157\pi\) | |||||||
\(830\) | −10241.6 | − | 5913.00i | −0.428303 | − | 0.247281i | ||||
\(831\) | 1384.00 | 0.0577743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5310.00 | −0.220865 | ||||||||
\(834\) | 6284.75 | + | 3628.50i | 0.260939 | + | 0.150653i | ||||
\(835\) | −10746.0 | + | 18612.6i | −0.445366 | + | 0.771397i | ||||
\(836\) | −144.000 | − | 249.415i | −0.00595735 | − | 0.0103184i | ||||
\(837\) | − | 13992.0i | − | 0.577819i | ||||||
\(838\) | −15128.6 | + | 8734.50i | −0.623638 | + | 0.360058i | ||||
\(839\) | −20285.8 | + | 11712.0i | −0.834735 | + | 0.481935i | −0.855471 | − | 0.517850i | \(-0.826732\pi\) |
0.0207360 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(840\) | − | 2835.00i | − | 0.116449i | ||||||
\(841\) | 1826.50 | + | 3163.59i | 0.0748903 | + | 0.129714i | ||||
\(842\) | −11011.5 | + | 19072.5i | −0.450690 | + | 0.780619i | ||||
\(843\) | −3517.80 | − | 2031.00i | −0.143724 | − | 0.0829791i | ||||
\(844\) | −2833.00 | −0.115540 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8658.00 | −0.351854 | ||||||||
\(847\) | 12639.6 | + | 7297.50i | 0.512755 | + | 0.296039i | ||||
\(848\) | −14697.0 | + | 25456.0i | −0.595162 | + | 1.03085i | ||||
\(849\) | −1882.00 | − | 3259.72i | −0.0760778 | − | 0.131771i | ||||
\(850\) | 5940.00i | 0.239694i | ||||||||
\(851\) | 42509.7 | − | 24543.0i | 1.71236 | − | 0.988629i | ||||
\(852\) | −309.171 | + | 178.500i | −0.0124320 | + | 0.00717759i | ||||
\(853\) | 31077.0i | 1.24743i | 0.781653 | + | 0.623714i | \(0.214377\pi\) | ||||
−0.781653 | + | 0.623714i | \(0.785623\pi\) | |||||||
\(854\) | −8460.00 | − | 14653.1i | −0.338987 | − | 0.587143i | ||||
\(855\) | 702.000 | − | 1215.90i | 0.0280794 | − | 0.0486350i | ||||
\(856\) | −11130.2 | − | 6426.00i | −0.444417 | − | 0.256584i | ||||
\(857\) | −19422.0 | −0.774146 | −0.387073 | − | 0.922049i | \(-0.626514\pi\) | ||||
−0.387073 | + | 0.922049i | \(0.626514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1744.00 | 0.0692718 | 0.0346359 | − | 0.999400i | \(-0.488973\pi\) | ||||
0.0346359 | + | 0.999400i | \(0.488973\pi\) | |||||||
\(860\) | −756.040 | − | 436.500i | −0.0299776 | − | 0.0173076i | ||||
\(861\) | −1440.00 | + | 2494.15i | −0.0569978 | + | 0.0987230i | ||||
\(862\) | −11227.5 | − | 19446.6i | −0.443631 | − | 0.768392i | ||||
\(863\) | − | 19179.0i | − | 0.756501i | −0.925703 | − | 0.378251i | \(-0.876526\pi\) | ||
0.925703 | − | 0.378251i | \(-0.123474\pi\) | |||||||
\(864\) | 2065.47 | − | 1192.50i | 0.0813296 | − | 0.0469556i | ||||
\(865\) | −12205.8 | + | 7047.00i | −0.479778 | + | 0.277000i | ||||
\(866\) | 45609.0i | 1.78967i | ||||||||
\(867\) | −1444.00 | − | 2501.08i | −0.0565638 | − | 0.0979714i | ||||
\(868\) | 1980.00 | − | 3429.46i | 0.0774258 | − | 0.134105i | ||||
\(869\) | −34502.5 | − | 19920.0i | −1.34685 | − | 0.777606i | ||||
\(870\) | 3888.00 | 0.151512 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22743.0 | −0.883228 | ||||||||
\(873\) | 19184.2 | + | 11076.0i | 0.743742 | + | 0.429400i | ||||
\(874\) | 1458.00 | − | 2525.33i | 0.0564274 | − | 0.0977352i | ||||
\(875\) | 11407.5 | + | 19758.4i | 0.440736 | + | 0.763377i | ||||
\(876\) | − | 1098.00i | − | 0.0423493i | ||||||
\(877\) | −25302.7 | + | 14608.5i | −0.974242 | + | 0.562479i | −0.900527 | − | 0.434800i | \(-0.856819\pi\) |
−0.0737152 | + | 0.997279i | \(0.523486\pi\) | |||||||
\(878\) | 4577.81 | − | 2643.00i | 0.175961 | − | 0.101591i | ||||
\(879\) | − | 4227.00i | − | 0.162199i | ||||||
\(880\) | 15336.0 | + | 26562.7i | 0.587473 | + | 1.01753i | ||||
\(881\) | 7816.50 | − | 13538.6i | 0.298916 | − | 0.517737i | −0.676973 | − | 0.736008i | \(-0.736708\pi\) |
0.975888 | + | 0.218271i | \(0.0700418\pi\) | |||||||
\(882\) | −7970.90 | − | 4602.00i | −0.304302 | − | 0.175689i | ||||
\(883\) | 30589.0 | 1.16580 | 0.582900 | − | 0.812544i | \(-0.301918\pi\) | ||||
0.582900 | + | 0.812544i | \(0.301918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4698.00 | 0.178442 | ||||||||
\(886\) | −19010.1 | − | 10975.5i | −0.720832 | − | 0.416173i | ||||
\(887\) | 12942.0 | − | 22416.2i | 0.489910 | − | 0.848548i | −0.510023 | − | 0.860161i | \(-0.670363\pi\) |
0.999933 | + | 0.0116124i | \(0.00369644\pi\) | |||||||
\(888\) | 3181.50 | + | 5510.52i | 0.120230 | + | 0.208244i | ||||
\(889\) | 31290.0i | 1.18046i | ||||||||
\(890\) | −10241.6 | + | 5913.00i | −0.385730 | + | 0.222701i | ||||
\(891\) | −26978.4 | + | 15576.0i | −1.01438 | + | 0.585652i | ||||
\(892\) | − | 3507.00i | − | 0.131640i | ||||||
\(893\) | −333.000 | − | 576.773i | −0.0124786 | − | 0.0216136i | ||||
\(894\) | 1395.00 | − | 2416.21i | 0.0521877 | − | 0.0903917i | ||||
\(895\) | 5120.81 | + | 2956.50i | 0.191251 | + | 0.110419i | ||||
\(896\) | −24885.0 | −0.927845 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15048.0 | −0.559196 | ||||||||
\(899\) | −32922.8 | − | 19008.0i | −1.22140 | − | 0.705175i | ||||
\(900\) | −572.000 | + | 990.733i | −0.0211852 | + | 0.0366938i | ||||
\(901\) | −9315.00 | − | 16134.1i | −0.344426 | − | 0.596563i | ||||
\(902\) | − | 27648.0i | − | 1.02060i | ||||||
\(903\) | 1260.07 | − | 727.500i | 0.0464368 | − | 0.0268103i | ||||
\(904\) | −1636.79 | + | 945.000i | −0.0602199 | + | 0.0347680i | ||||
\(905\) | − | 10998.0i | − | 0.403962i | ||||||
\(906\) | −2524.50 | − | 4372.56i | −0.0925727 | − | 0.160341i | ||||
\(907\) | 6152.50 | − | 10656.4i | 0.225237 | − | 0.390123i | −0.731153 | − | 0.682213i | \(-0.761018\pi\) |
0.956391 | + | 0.292091i | \(0.0943509\pi\) | |||||||
\(908\) | 197.454 | + | 114.000i | 0.00721667 | + | 0.00416655i | ||||
\(909\) | −10296.0 | −0.375684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29772.0 | 1.08276 | 0.541378 | − | 0.840779i | \(-0.317903\pi\) | ||||
0.541378 | + | 0.840779i | \(0.317903\pi\) | |||||||
\(912\) | 368.927 | + | 213.000i | 0.0133952 | + | 0.00773370i | ||||
\(913\) | −10512.0 | + | 18207.3i | −0.381048 | + | 0.659994i | ||||
\(914\) | 14805.0 | + | 25643.0i | 0.535783 | + | 0.928004i | ||||
\(915\) | − | 3384.00i | − | 0.122264i | ||||||
\(916\) | −4757.08 | + | 2746.50i | −0.171592 | + | 0.0990687i | ||||
\(917\) | −19056.9 | + | 11002.5i | −0.686275 | + | 0.396221i | ||||
\(918\) | 7155.00i | 0.257244i | ||||||||
\(919\) | −23822.0 | − | 41260.9i | −0.855076 | − | 1.48104i | −0.876574 | − | 0.481267i | \(-0.840177\pi\) |
0.0214976 | − | 0.999769i | \(-0.493157\pi\) | |||||||
\(920\) | −15309.0 | + | 26516.0i | −0.548612 | + | 0.950223i | ||||
\(921\) | 265.004 | + | 153.000i | 0.00948118 | + | 0.00547396i | ||||
\(922\) | 43623.0 | 1.55819 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 720.000 | 0.0256345 | ||||||||
\(925\) | −11545.9 | − | 6666.00i | −0.410406 | − | 0.236948i | ||||
\(926\) | 3168.00 | − | 5487.14i | 0.112427 | − | 0.194728i | ||||
\(927\) | 2366.00 | + | 4098.03i | 0.0838292 | + | 0.145196i | ||||
\(928\) | − | 6480.00i | − | 0.229220i | ||||||
\(929\) | −18986.7 | + | 10962.0i | −0.670543 | + | 0.387138i | −0.796282 | − | 0.604925i | \(-0.793203\pi\) |
0.125739 | + | 0.992063i | \(0.459870\pi\) | |||||||
\(930\) | 6173.03 | − | 3564.00i | 0.217658 | − | 0.125665i | ||||
\(931\) | − | 708.000i | − | 0.0249235i | ||||||
\(932\) | 1813.50 | + | 3141.07i | 0.0637373 | + | 0.110396i | ||||
\(933\) | −1053.00 | + | 1823.85i | −0.0369493 | + | 0.0639980i | ||||
\(934\) | 8511.30 | + | 4914.00i | 0.298178 | + | 0.172153i | ||||
\(935\) | −19440.0 | −0.679953 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32398.0 | 1.12956 | 0.564779 | − | 0.825242i | \(-0.308961\pi\) | ||||
0.564779 | + | 0.825242i | \(0.308961\pi\) | |||||||
\(938\) | −1402.96 | − | 810.000i | −0.0488361 | − | 0.0281956i | ||||
\(939\) | 5025.50 | − | 8704.42i | 0.174655 | − | 0.302511i | ||||
\(940\) | −499.500 | − | 865.159i | −0.0173318 | − | 0.0300196i | ||||
\(941\) | − | 2097.00i | − | 0.0726464i | −0.999340 | − | 0.0363232i | \(-0.988435\pi\) | ||
0.999340 | − | 0.0363232i | \(-0.0115646\pi\) | |||||||
\(942\) | 4868.79 | − | 2811.00i | 0.168401 | − | 0.0972265i | ||||
\(943\) | 26936.9 | − | 15552.0i | 0.930206 | − | 0.537055i | ||||
\(944\) | − | 37062.0i | − | 1.27782i | ||||||
\(945\) | 3577.50 | + | 6196.41i | 0.123149 | + | 0.213301i | ||||
\(946\) | −6984.00 | + | 12096.6i | −0.240031 | + | 0.415746i | ||||
\(947\) | 17334.4 | + | 10008.0i | 0.594816 | + | 0.343417i | 0.767000 | − | 0.641648i | \(-0.221749\pi\) |
−0.172183 | + | 0.985065i | \(0.555082\pi\) | |||||||
\(948\) | −830.000 | −0.0284358 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −792.000 | −0.0270483 | ||||||||
\(951\) | 1865.42 | + | 1077.00i | 0.0636071 | + | 0.0367236i | ||||
\(952\) | 7087.50 | − | 12275.9i | 0.241289 | − | 0.417925i | ||||
\(953\) | −12496.5 | − | 21644.6i | −0.424765 | − | 0.735715i | 0.571633 | − | 0.820509i | \(-0.306310\pi\) |
−0.996398 | + | 0.0847942i | \(0.972977\pi\) | |||||||
\(954\) | − | 32292.0i | − | 1.09590i | ||||||
\(955\) | 9820.73 | − | 5670.00i | 0.332766 | − | 0.192122i | ||||
\(956\) | 5261.10 | − | 3037.50i | 0.177988 | − | 0.102761i | ||||
\(957\) | − | 6912.00i | − | 0.233473i | ||||||
\(958\) | 23179.5 | + | 40148.1i | 0.781728 | + | 1.35399i | ||||
\(959\) | −3105.00 | + | 5378.02i | −0.104552 | + | 0.181090i | ||||
\(960\) | −3374.90 | − | 1948.50i | −0.113463 | − | 0.0655079i | ||||
\(961\) | −39905.0 | −1.33950 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15912.0 | 0.532458 | ||||||||
\(964\) | 181.865 | + | 105.000i | 0.00607623 | + | 0.00350811i | ||||
\(965\) | 1539.00 | − | 2665.63i | 0.0513390 | − | 0.0889218i | ||||
\(966\) | 3645.00 | + | 6313.33i | 0.121404 | + | 0.210277i | ||||
\(967\) | 40959.0i | 1.36210i | 0.732236 | + | 0.681051i | \(0.238477\pi\) | ||||
−0.732236 | + | 0.681051i | \(0.761523\pi\) | |||||||
\(968\) | 17695.5 | − | 10216.5i | 0.587557 | − | 0.339226i | ||||
\(969\) | −233.827 | + | 135.000i | −0.00775191 | + | 0.00447557i | ||||
\(970\) | 23004.0i | 0.761458i | ||||||||
\(971\) | 24466.5 | + | 42377.2i | 0.808617 | + | 1.40057i | 0.913822 | + | 0.406116i | \(0.133117\pi\) |
−0.105204 | + | 0.994451i | \(0.533550\pi\) | |||||||
\(972\) | −1040.00 | + | 1801.33i | −0.0343189 | + | 0.0594422i | ||||
\(973\) | 31423.7 | + | 18142.5i | 1.03535 | + | 0.597761i | ||||
\(974\) | 10980.0 | 0.361213 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26696.0 | −0.875531 | ||||||||
\(977\) | 41039.2 | + | 23694.0i | 1.34387 | + | 0.775884i | 0.987373 | − | 0.158413i | \(-0.0506377\pi\) |
0.356497 | + | 0.934297i | \(0.383971\pi\) | |||||||
\(978\) | −1791.00 | + | 3102.10i | −0.0585581 | + | 0.101426i | ||||
\(979\) | 10512.0 | + | 18207.3i | 0.343172 | + | 0.594391i | ||||
\(980\) | − | 1062.00i | − | 0.0346167i | ||||||
\(981\) | 24385.5 | − | 14079.0i | 0.793650 | − | 0.458214i | ||||
\(982\) | −1940.76 | + | 1120.50i | −0.0630674 | + | 0.0364120i | ||||
\(983\) | 16803.0i | 0.545201i | 0.962127 | + | 0.272600i | \(0.0878837\pi\) | ||||
−0.962127 | + | 0.272600i | \(0.912116\pi\) | |||||||
\(984\) | 2016.00 | + | 3491.81i | 0.0653127 | + | 0.113125i | ||||
\(985\) | −364.500 | + | 631.333i | −0.0117908 | + | 0.0204223i | ||||
\(986\) | 16835.5 | + | 9720.00i | 0.543765 | + | 0.313943i | ||||
\(987\) | 1665.00 | 0.0536956 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15714.0 | −0.505234 | ||||||||
\(990\) | −29181.6 | − | 16848.0i | −0.936820 | − | 0.540873i | ||||
\(991\) | 28763.0 | − | 49819.0i | 0.921985 | − | 1.59692i | 0.125644 | − | 0.992075i | \(-0.459900\pi\) |
0.796340 | − | 0.604849i | \(-0.206767\pi\) | |||||||
\(992\) | −5940.00 | − | 10288.4i | −0.190116 | − | 0.329291i | ||||
\(993\) | 10770.0i | 0.344185i | ||||||||
\(994\) | −13912.7 | + | 8032.50i | −0.443948 | + | 0.256313i | ||||
\(995\) | 15557.3 | − | 8982.00i | 0.495677 | − | 0.286179i | ||||
\(996\) | 438.000i | 0.0139343i | ||||||||
\(997\) | 12500.0 | + | 21650.6i | 0.397070 | + | 0.687746i | 0.993363 | − | 0.115021i | \(-0.0366936\pi\) |
−0.596293 | + | 0.802767i | \(0.703360\pi\) | |||||||
\(998\) | −23706.0 | + | 41060.0i | −0.751904 | + | 1.30234i | ||||
\(999\) | −13907.5 | − | 8029.50i | −0.440454 | − | 0.254296i |
(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 | 169.4.e.d.147.2 | 4 | ||
13.2 | odd | 12 | 169.4.c.c.146.1 | 2 | |||
13.3 | even | 3 | inner | 169.4.e.d.23.1 | 4 | ||
13.4 | even | 6 | 13.4.b.a.12.2 | yes | 2 | ||
13.5 | odd | 4 | 169.4.c.c.22.1 | 2 | |||
13.6 | odd | 12 | 169.4.a.b.1.1 | 1 | |||
13.7 | odd | 12 | 169.4.a.c.1.1 | 1 | |||
13.8 | odd | 4 | 169.4.c.b.22.1 | 2 | |||
13.9 | even | 3 | 13.4.b.a.12.1 | ✓ | 2 | ||
13.10 | even | 6 | inner | 169.4.e.d.23.2 | 4 | ||
13.11 | odd | 12 | 169.4.c.b.146.1 | 2 | |||
13.12 | even | 2 | inner | 169.4.e.d.147.1 | 4 | ||
39.17 | odd | 6 | 117.4.b.a.64.1 | 2 | |||
39.20 | even | 12 | 1521.4.a.d.1.1 | 1 | |||
39.32 | even | 12 | 1521.4.a.i.1.1 | 1 | |||
39.35 | odd | 6 | 117.4.b.a.64.2 | 2 | |||
52.35 | odd | 6 | 208.4.f.b.129.2 | 2 | |||
52.43 | odd | 6 | 208.4.f.b.129.1 | 2 | |||
65.4 | even | 6 | 325.4.c.b.51.1 | 2 | |||
65.9 | even | 6 | 325.4.c.b.51.2 | 2 | |||
65.17 | odd | 12 | 325.4.d.a.324.2 | 2 | |||
65.22 | odd | 12 | 325.4.d.b.324.2 | 2 | |||
65.43 | odd | 12 | 325.4.d.b.324.1 | 2 | |||
65.48 | odd | 12 | 325.4.d.a.324.1 | 2 | |||
104.35 | odd | 6 | 832.4.f.c.129.1 | 2 | |||
104.43 | odd | 6 | 832.4.f.c.129.2 | 2 | |||
104.61 | even | 6 | 832.4.f.e.129.1 | 2 | |||
104.69 | even | 6 | 832.4.f.e.129.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.b.a.12.1 | ✓ | 2 | 13.9 | even | 3 | ||
13.4.b.a.12.2 | yes | 2 | 13.4 | even | 6 | ||
117.4.b.a.64.1 | 2 | 39.17 | odd | 6 | |||
117.4.b.a.64.2 | 2 | 39.35 | odd | 6 | |||
169.4.a.b.1.1 | 1 | 13.6 | odd | 12 | |||
169.4.a.c.1.1 | 1 | 13.7 | odd | 12 | |||
169.4.c.b.22.1 | 2 | 13.8 | odd | 4 | |||
169.4.c.b.146.1 | 2 | 13.11 | odd | 12 | |||
169.4.c.c.22.1 | 2 | 13.5 | odd | 4 | |||
169.4.c.c.146.1 | 2 | 13.2 | odd | 12 | |||
169.4.e.d.23.1 | 4 | 13.3 | even | 3 | inner | ||
169.4.e.d.23.2 | 4 | 13.10 | even | 6 | inner | ||
169.4.e.d.147.1 | 4 | 13.12 | even | 2 | inner | ||
169.4.e.d.147.2 | 4 | 1.1 | even | 1 | trivial | ||
208.4.f.b.129.1 | 2 | 52.43 | odd | 6 | |||
208.4.f.b.129.2 | 2 | 52.35 | odd | 6 | |||
325.4.c.b.51.1 | 2 | 65.4 | even | 6 | |||
325.4.c.b.51.2 | 2 | 65.9 | even | 6 | |||
325.4.d.a.324.1 | 2 | 65.48 | odd | 12 | |||
325.4.d.a.324.2 | 2 | 65.17 | odd | 12 | |||
325.4.d.b.324.1 | 2 | 65.43 | odd | 12 | |||
325.4.d.b.324.2 | 2 | 65.22 | odd | 12 | |||
832.4.f.c.129.1 | 2 | 104.35 | odd | 6 | |||
832.4.f.c.129.2 | 2 | 104.43 | odd | 6 | |||
832.4.f.e.129.1 | 2 | 104.61 | even | 6 | |||
832.4.f.e.129.2 | 2 | 104.69 | even | 6 | |||
1521.4.a.d.1.1 | 1 | 39.20 | even | 12 | |||
1521.4.a.i.1.1 | 1 | 39.32 | even | 12 |