Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,5,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (of order \(8\), degree \(4\), 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: | \(13.2313552747\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 47.5 | ||
Character | \(\chi\) | \(=\) | 128.47 |
Dual form | 128.5.h.a.79.5 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.03024 | + | 7.31565i | −0.336694 | + | 0.812850i | 0.661335 | + | 0.750091i | \(0.269990\pi\) |
−0.998029 | + | 0.0627598i | \(0.980010\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.4171 | + | 29.9775i | 0.496683 | + | 1.19910i | 0.951260 | + | 0.308391i | \(0.0997905\pi\) |
−0.454577 | + | 0.890708i | \(0.650209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 51.5981 | + | 51.5981i | 1.05302 | + | 1.05302i | 0.998513 | + | 0.0545102i | \(0.0173597\pi\) |
0.0545102 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.9392 | + | 12.9392i | 0.159743 | + | 0.159743i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −68.2659 | − | 164.808i | −0.564181 | − | 1.36205i | −0.906395 | − | 0.422431i | \(-0.861177\pi\) |
0.342214 | − | 0.939622i | \(-0.388823\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 25.9560 | − | 62.6632i | 0.153586 | − | 0.370788i | −0.828294 | − | 0.560293i | \(-0.810688\pi\) |
0.981880 | + | 0.189505i | \(0.0606883\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −256.932 | −1.14192 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 489.438i | 1.69356i | 0.531946 | + | 0.846778i | \(0.321461\pi\) | ||||
−0.531946 | + | 0.846778i | \(0.678539\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 164.710 | + | 68.2250i | 0.456260 | + | 0.188989i | 0.598963 | − | 0.800777i | \(-0.295580\pi\) |
−0.142704 | + | 0.989765i | \(0.545580\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −533.829 | + | 221.119i | −1.21050 | + | 0.501404i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −51.6300 | + | 51.6300i | −0.0975992 | + | 0.0975992i | −0.754220 | − | 0.656621i | \(-0.771985\pi\) |
0.656621 | + | 0.754220i | \(0.271985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −302.523 | + | 302.523i | −0.484037 | + | 0.484037i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −726.436 | + | 300.900i | −0.996483 | + | 0.412757i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −779.698 | − | 322.962i | −0.927108 | − | 0.384021i | −0.132528 | − | 0.991179i | \(-0.542309\pi\) |
−0.794581 | + | 0.607158i | \(0.792309\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.47504i | 0.00361607i | 0.999998 | + | 0.00180804i | \(0.000575516\pi\) | ||||
−0.999998 | + | 0.00180804i | \(0.999424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1412.54 | 1.29710 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −906.084 | + | 2187.48i | −0.739660 | + | 1.78570i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −375.072 | − | 905.504i | −0.273975 | − | 0.661435i | 0.725671 | − | 0.688042i | \(-0.241530\pi\) |
−0.999646 | + | 0.0266075i | \(0.991530\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 379.770 | + | 379.770i | 0.249684 | + | 0.249684i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1135.82 | − | 1135.82i | −0.675681 | − | 0.675681i | 0.283339 | − | 0.959020i | \(-0.408558\pi\) |
−0.959020 | + | 0.283339i | \(0.908558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 318.285 | + | 768.407i | 0.172139 | + | 0.415580i | 0.986279 | − | 0.165089i | \(-0.0527911\pi\) |
−0.814140 | + | 0.580669i | \(0.802791\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −227.218 | + | 548.552i | −0.112206 | + | 0.270890i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1860.54 | 0.842252 | 0.421126 | − | 0.907002i | \(-0.361635\pi\) | ||||
0.421126 | + | 0.907002i | \(0.361635\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2923.74i | 1.21772i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3580.56 | − | 1483.12i | −1.37661 | − | 0.570210i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2841.49 | − | 1176.98i | 1.01157 | − | 0.419004i | 0.185540 | − | 0.982637i | \(-0.440597\pi\) |
0.826025 | + | 0.563633i | \(0.190597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4092.88 | − | 4092.88i | 1.35302 | − | 1.35302i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −998.221 | + | 998.221i | −0.307240 | + | 0.307240i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2613.25 | − | 1082.44i | 0.750717 | − | 0.310957i | 0.0256828 | − | 0.999670i | \(-0.491824\pi\) |
0.725034 | + | 0.688713i | \(0.241824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1511.76 | − | 626.192i | −0.406278 | − | 0.168286i | 0.170179 | − | 0.985413i | \(-0.445565\pi\) |
−0.576458 | + | 0.817127i | \(0.695565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1335.28i | 0.336427i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2200.78 | 0.520895 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1325.18 | + | 3199.26i | −0.295205 | + | 0.712688i | 0.704790 | + | 0.709416i | \(0.251041\pi\) |
−0.999995 | + | 0.00327157i | \(0.998959\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −221.256 | − | 534.158i | −0.0464725 | − | 0.112195i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5659.31 | − | 5659.31i | −1.12266 | − | 1.12266i | −0.991341 | − | 0.131315i | \(-0.958080\pi\) |
−0.131315 | − | 0.991341i | \(-0.541920\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5143.36 | + | 5143.36i | 0.965163 | + | 0.965163i | 0.999413 | − | 0.0342500i | \(-0.0109042\pi\) |
−0.0342500 | + | 0.999413i | \(0.510904\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1296.44 | − | 3129.87i | −0.230477 | − | 0.556422i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4981.42 | − | 12026.2i | 0.840178 | − | 2.02837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5180.13 | 0.830016 | 0.415008 | − | 0.909818i | \(-0.363779\pi\) | ||||
0.415008 | + | 0.909818i | \(0.363779\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 4743.95i | − | 0.723053i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2002.61 | − | 829.509i | −0.290697 | − | 0.120411i | 0.232569 | − | 0.972580i | \(-0.425287\pi\) |
−0.523266 | + | 0.852169i | \(0.675287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14672.1 | + | 6077.38i | −2.03074 | + | 0.841160i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4725.35 | − | 4725.35i | 0.624303 | − | 0.624303i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2938.70 | − | 2938.70i | 0.371002 | − | 0.371002i | −0.496840 | − | 0.867842i | \(-0.665507\pi\) |
0.867842 | + | 0.496840i | \(0.165507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4572.59 | − | 1894.03i | 0.552178 | − | 0.228720i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.4222 | − | 10.5302i | −0.00293932 | − | 0.00121751i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5784.74i | 0.640968i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14104.1 | 1.49900 | 0.749499 | − | 0.662006i | \(-0.230295\pi\) | ||||
0.749499 | + | 0.662006i | \(0.230295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1249.19 | − | 3015.80i | 0.127455 | − | 0.307703i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4233.68 | + | 10221.0i | 0.415026 | + | 1.00196i | 0.983768 | + | 0.179446i | \(0.0574305\pi\) |
−0.568741 | + | 0.822516i | \(0.692570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 135.994 | + | 135.994i | 0.0128188 | + | 0.0128188i | 0.713487 | − | 0.700668i | \(-0.247115\pi\) |
−0.700668 | + | 0.713487i | \(0.747115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13257.2 | − | 13257.2i | −1.20247 | − | 1.20247i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4453.05 | + | 10750.6i | 0.388947 | + | 0.939001i | 0.990164 | + | 0.139915i | \(0.0446828\pi\) |
−0.601217 | + | 0.799086i | \(0.705317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5688.78 | − | 13733.9i | 0.478813 | − | 1.15596i | −0.481353 | − | 0.876527i | \(-0.659854\pi\) |
0.960166 | − | 0.279431i | \(-0.0901457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7760.91 | 0.629893 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17675.0i | 1.38421i | 0.721795 | + | 0.692107i | \(0.243317\pi\) | ||||
−0.721795 | + | 0.692107i | \(0.756683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2188.83 | − | 906.643i | −0.165507 | − | 0.0685552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1146.66 | − | 474.964i | 0.0837653 | − | 0.0346967i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25254.1 | + | 25254.1i | −1.78335 | + | 1.78335i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12148.8 | + | 12148.8i | −0.829782 | + | 0.829782i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11751.1 | − | 4867.45i | 0.776725 | − | 0.321730i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5910.59 | + | 2448.25i | 0.378278 | + | 0.156688i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13463.4i | 0.834730i | 0.908739 | + | 0.417365i | \(0.137046\pi\) | ||||
−0.908739 | + | 0.417365i | \(0.862954\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6585.88 | −0.395762 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2440.14 | + | 5891.02i | −0.142191 | + | 0.343279i | −0.978891 | − | 0.204382i | \(-0.934482\pi\) |
0.836700 | + | 0.547661i | \(0.184482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4978.43 | + | 12019.0i | 0.281442 | + | 0.679462i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18040.4 | − | 18040.4i | −0.989872 | − | 0.989872i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −24401.5 | − | 24401.5i | −1.30010 | − | 1.30010i | −0.928323 | − | 0.371776i | \(-0.878749\pi\) |
−0.371776 | − | 0.928323i | \(-0.621251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3377.01 | − | 8152.83i | −0.174785 | − | 0.421967i | 0.812074 | − | 0.583555i | \(-0.198339\pi\) |
−0.986858 | + | 0.161587i | \(0.948339\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5637.87 | + | 13611.0i | −0.283581 | + | 0.684625i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12099.3 | −0.591684 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 27383.6i | − | 1.30243i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21389.1 | − | 8859.64i | −0.989822 | − | 0.409998i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22044.4 | + | 9131.09i | −0.992946 | + | 0.411292i | −0.819206 | − | 0.573500i | \(-0.805585\pi\) |
−0.173740 | + | 0.984791i | \(0.555585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21912.5 | − | 21912.5i | 0.961031 | − | 0.961031i | −0.0382374 | − | 0.999269i | \(-0.512174\pi\) |
0.999269 | + | 0.0382374i | \(0.0121743\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6332.94 | + | 6332.94i | −0.270535 | + | 0.270535i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −104.173 | + | 43.1499i | −0.00433603 | + | 0.00179604i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 26287.6 | + | 10888.7i | 1.06648 | + | 0.441750i | 0.845747 | − | 0.533584i | \(-0.179155\pi\) |
0.220732 | + | 0.975334i | \(0.429155\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24353.9i | 0.963327i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5328.02 | −0.205548 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4953.52 | + | 11958.9i | −0.186440 | + | 0.450106i | −0.989269 | − | 0.146103i | \(-0.953327\pi\) |
0.802830 | + | 0.596209i | \(0.203327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17539.7 | + | 42344.5i | 0.644248 | + | 1.55535i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2732.66 | − | 2732.66i | −0.0979835 | − | 0.0979835i | 0.656416 | − | 0.754399i | \(-0.272072\pi\) |
−0.754399 | + | 0.656416i | \(0.772072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16942.7 | + | 16942.7i | 0.593211 | + | 0.593211i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1248.44 | + | 3013.99i | 0.0426948 | + | 0.103074i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10506.7 | + | 25365.4i | −0.351054 | + | 0.847519i | 0.645437 | + | 0.763814i | \(0.276675\pi\) |
−0.996491 | + | 0.0837050i | \(0.973325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31219.2 | −1.01940 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22397.7i | 0.714918i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 30976.8 | + | 12831.0i | 0.966786 | + | 0.400456i | 0.809515 | − | 0.587099i | \(-0.199730\pi\) |
0.157271 | + | 0.987555i | \(0.449730\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 31191.2 | − | 12919.8i | 0.952082 | − | 0.394365i | 0.148069 | − | 0.988977i | \(-0.452694\pi\) |
0.804013 | + | 0.594612i | \(0.202694\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9162.01 | − | 9162.01i | 0.273583 | − | 0.273583i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22487.4 | − | 22487.4i | 0.657047 | − | 0.657047i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 80663.5 | − | 33411.9i | 2.30671 | − | 0.955472i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −53008.6 | − | 21956.9i | −1.48396 | − | 0.614677i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10804.6i | 0.296170i | 0.988975 | + | 0.148085i | \(0.0473109\pi\) | ||||
−0.988975 | + | 0.148085i | \(0.952689\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19160.5 | 0.514388 | 0.257194 | − | 0.966360i | \(-0.417202\pi\) | ||||
0.257194 | + | 0.966360i | \(0.417202\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6668.91 | + | 16100.2i | −0.175382 | + | 0.423410i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22479.7 | − | 54270.7i | −0.579239 | − | 1.39841i | −0.893497 | − | 0.449068i | \(-0.851756\pi\) |
0.314259 | − | 0.949337i | \(-0.398244\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4494.51 | + | 4494.51i | 0.113495 | + | 0.113495i | 0.761574 | − | 0.648079i | \(-0.224427\pi\) |
−0.648079 | + | 0.761574i | \(0.724427\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19389.0 | − | 19389.0i | −0.479915 | − | 0.479915i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23566.8 | − | 56895.2i | −0.571884 | − | 1.38065i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19945.4 | − | 48152.5i | 0.474609 | − | 1.14581i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1336.10 | −0.0311817 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 31803.0i | − | 0.728074i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7136.71 | + | 2956.12i | 0.160300 | + | 0.0663983i | 0.461391 | − | 0.887197i | \(-0.347351\pi\) |
−0.301091 | + | 0.953595i | \(0.597351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 58550.6 | − | 24252.5i | 1.29054 | − | 0.534560i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19082.7 | + | 19082.7i | −0.412823 | + | 0.412823i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −179.306 | + | 179.306i | −0.00380781 | + | 0.00380781i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −53212.6 | + | 22041.4i | −1.10950 | + | 0.459569i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30669.8 | + | 12703.8i | 0.627951 | + | 0.260106i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24536.0i | − | 0.493394i | −0.969093 | − | 0.246697i | \(-0.920655\pi\) | ||
0.969093 | − | 0.246697i | \(-0.0793452\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7828.82 | −0.154643 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23630.9 | − | 57050.0i | 0.458594 | − | 1.10714i | −0.510373 | − | 0.859953i | \(-0.670493\pi\) |
0.968967 | − | 0.247190i | \(-0.0795072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15539.7 | − | 37516.1i | −0.296327 | − | 0.715396i | −0.999988 | − | 0.00486046i | \(-0.998453\pi\) |
0.703662 | − | 0.710535i | \(-0.251547\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 72884.6 | + | 72884.6i | 1.36588 | + | 1.36588i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1502.52 | + | 1502.52i | 0.0276764 | + | 0.0276764i | 0.720810 | − | 0.693133i | \(-0.243770\pi\) |
−0.693133 | + | 0.720810i | \(0.743770\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23102.4 | + | 55774.1i | 0.418332 | + | 1.00994i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15697.1 | + | 37896.0i | −0.279461 | + | 0.674679i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 47803.7 | 0.836885 | 0.418442 | − | 0.908243i | \(-0.362576\pi\) | ||||
0.418442 | + | 0.908243i | \(0.362576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28441.1i | 0.489679i | 0.969564 | + | 0.244840i | \(0.0787353\pi\) | ||||
−0.969564 | + | 0.244840i | \(0.921265\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −24136.2 | − | 9997.55i | −0.408749 | − | 0.169309i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −87646.2 | + | 36304.3i | −1.46016 | + | 0.604819i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8550.40 | − | 8550.40i | 0.140150 | − | 0.140150i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12136.8 | − | 12136.8i | 0.195752 | − | 0.195752i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −104181. | + | 43153.0i | −1.65364 | + | 0.684958i | −0.997565 | − | 0.0697419i | \(-0.977782\pi\) |
−0.656070 | + | 0.754700i | \(0.727782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12033.6 | + | 4984.49i | 0.187999 | + | 0.0778717i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 125752.i | − | 1.93390i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 58517.2 | 0.885967 | 0.442984 | − | 0.896530i | \(-0.353920\pi\) | ||||
0.442984 | + | 0.896530i | \(0.353920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27369.3 | − | 66075.3i | 0.408004 | − | 0.985008i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5909.82 | − | 14267.6i | −0.0867547 | − | 0.209444i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −72405.5 | − | 72405.5i | −1.04679 | − | 1.04679i | −0.998850 | − | 0.0479411i | \(-0.984734\pi\) |
−0.0479411 | − | 0.998850i | \(-0.515266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 70565.9 | + | 70565.9i | 1.00485 | + | 1.00485i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12593.6 | + | 30403.5i | 0.176655 | + | 0.426483i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3628.21 | − | 8759.27i | 0.0501404 | − | 0.121050i | −0.896825 | − | 0.442386i | \(-0.854132\pi\) |
0.946965 | + | 0.321337i | \(0.104132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 80438.8 | 1.09528 | 0.547642 | − | 0.836713i | \(-0.315526\pi\) | ||||
0.547642 | + | 0.836713i | \(0.315526\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 39190.8i | 0.525847i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 70510.3 | + | 29206.3i | 0.932368 | + | 0.386199i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42328.8 | − | 17533.2i | 0.551666 | − | 0.228508i | −0.0893965 | − | 0.995996i | \(-0.528494\pi\) |
0.641063 | + | 0.767488i | \(0.278494\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −44.9644 | + | 44.9644i | −0.000577644 | + | 0.000577644i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28015.2 | + | 28015.2i | −0.354798 | + | 0.354798i | −0.861891 | − | 0.507093i | \(-0.830720\pi\) |
0.507093 | + | 0.861891i | \(0.330720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −111649. | + | 46246.3i | −1.39406 | + | 0.577437i | −0.948202 | − | 0.317669i | \(-0.897100\pi\) |
−0.445854 | + | 0.895106i | \(0.647100\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −42319.1 | − | 17529.2i | −0.521011 | − | 0.215810i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 117212.i | − | 1.42302i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −156028. | −1.86813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −42738.8 | + | 103180.i | −0.504703 | + | 1.21846i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8654.24 | − | 20893.2i | −0.100808 | − | 0.243371i | 0.865427 | − | 0.501035i | \(-0.167047\pi\) |
−0.966235 | + | 0.257664i | \(0.917047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 64897.7 | + | 64897.7i | 0.745736 | + | 0.745736i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 99181.6 | + | 99181.6i | 1.12439 | + | 1.12439i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1895.20 | + | 4575.41i | 0.0211988 | + | 0.0511785i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23225.5 | + | 56071.3i | −0.256349 | + | 0.618881i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −87602.5 | −0.954182 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 53094.3i | − | 0.570753i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11997.1 | − | 4969.36i | −0.127292 | − | 0.0527259i | 0.318128 | − | 0.948048i | \(-0.396946\pi\) |
−0.445420 | + | 0.895322i | \(0.646946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1406.98 | + | 582.791i | −0.0147357 | + | 0.00610374i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7023.22 | − | 7023.22i | 0.0726132 | − | 0.0726132i | −0.669867 | − | 0.742481i | \(-0.733649\pi\) |
0.742481 | + | 0.669867i | \(0.233649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25821.6 | − | 25821.6i | 0.263569 | − | 0.263569i | −0.562933 | − | 0.826502i | \(-0.690327\pi\) |
0.826502 | + | 0.562933i | \(0.190327\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −40028.3 | + | 16580.3i | −0.403409 | + | 0.167098i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −49717.1 | − | 20593.5i | −0.494752 | − | 0.204933i | 0.121334 | − | 0.992612i | \(-0.461283\pi\) |
−0.616086 | + | 0.787679i | \(0.711283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 150548.i | 1.47943i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −92141.6 | −0.894223 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33391.9 | + | 80615.2i | −0.320063 | + | 0.772701i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11104.8 | + | 26809.3i | 0.105134 | + | 0.253816i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 83234.3 | + | 83234.3i | 0.778407 | + | 0.778407i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 96000.2 | + | 96000.2i | 0.886911 | + | 0.886911i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16857.0 | + | 40696.5i | 0.153860 | + | 0.371450i | 0.981949 | − | 0.189146i | \(-0.0605719\pi\) |
−0.828089 | + | 0.560596i | \(0.810572\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6863.38 | − | 16569.7i | 0.0618941 | − | 0.149426i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −112360. | −1.00121 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 39444.9i | − | 0.347321i | −0.984806 | − | 0.173660i | \(-0.944440\pi\) | ||
0.984806 | − | 0.173660i | \(-0.0555595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −129304. | − | 53559.7i | −1.12516 | − | 0.466056i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 572.717 | − | 237.227i | 0.00492528 | − | 0.00204012i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −26972.3 | + | 26972.3i | −0.229261 | + | 0.229261i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13265.4 | − | 13265.4i | 0.111450 | − | 0.111450i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 51393.3 | − | 21287.8i | 0.426823 | − | 0.176796i | −0.158922 | − | 0.987291i | \(-0.550802\pi\) |
0.585745 | + | 0.810495i | \(0.300802\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 44357.7 | + | 18373.6i | 0.364182 | + | 0.150849i | 0.557268 | − | 0.830333i | \(-0.311850\pi\) |
−0.193086 | + | 0.981182i | \(0.561850\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 53331.0i | 0.432878i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −231798. | −1.86020 | −0.930101 | − | 0.367303i | \(-0.880281\pi\) | ||||
−0.930101 | + | 0.367303i | \(0.880281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 99379.7 | − | 239924.i | 0.788571 | − | 1.90378i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −108224. | − | 261276.i | −0.849156 | − | 2.05004i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35078.5 | − | 35078.5i | −0.272177 | − | 0.272177i | 0.557799 | − | 0.829976i | \(-0.311646\pi\) |
−0.829976 | + | 0.557799i | \(0.811646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −69676.2 | − | 69676.2i | −0.534651 | − | 0.534651i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −52062.8 | − | 125691.i | −0.395106 | − | 0.953871i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −90319.3 | + | 218050.i | −0.677946 | + | 1.63671i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 154694. | 1.14853 | 0.574263 | − | 0.818671i | \(-0.305289\pi\) | ||||
0.574263 | + | 0.818671i | \(0.305289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 29393.2i | − | 0.215871i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 207346. | + | 85885.3i | 1.50642 | + | 0.623981i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 106468. | − | 44100.4i | 0.765245 | − | 0.316975i | 0.0343001 | − | 0.999412i | \(-0.489080\pi\) |
0.730945 | + | 0.682437i | \(0.239080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −35821.1 | + | 35821.1i | −0.254728 | + | 0.254728i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40475.6 | + | 40475.6i | −0.284781 | + | 0.284781i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −85313.9 | + | 35338.2i | −0.593939 | + | 0.246017i | −0.659344 | − | 0.751841i | \(-0.729166\pi\) |
0.0654054 | + | 0.997859i | \(0.479166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −98493.3 | − | 40797.3i | −0.678511 | − | 0.281048i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 102095.i | − | 0.695994i | −0.937496 | − | 0.347997i | \(-0.886862\pi\) | ||
0.937496 | − | 0.347997i | \(-0.113138\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 422370. | 2.84952 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5824.23 | + | 14060.9i | −0.0388881 | + | 0.0938842i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 76247.2 | + | 184077.i | 0.503877 | + | 1.21647i | 0.947356 | + | 0.320182i | \(0.103744\pi\) |
−0.443479 | + | 0.896285i | \(0.646256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25269.7 | − | 25269.7i | −0.165290 | − | 0.165290i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35702.4 | − | 35702.4i | −0.231160 | − | 0.231160i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 64322.0 | + | 155287.i | 0.412255 | + | 0.995271i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4363.53 | − | 10534.5i | 0.0276858 | − | 0.0668394i | −0.909432 | − | 0.415853i | \(-0.863483\pi\) |
0.937118 | + | 0.349013i | \(0.113483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −103013. | −0.647061 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 79631.3i | − | 0.495217i | −0.968860 | − | 0.247608i | \(-0.920355\pi\) | ||
0.968860 | − | 0.247608i | \(-0.0796446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 217.758 | + | 90.1981i | 0.00134080 | + | 0.000555376i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 142212. | − | 58905.9i | 0.867011 | − | 0.359128i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −123630. | + | 123630.i | −0.746338 | + | 0.746338i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 125746. | − | 125746.i | 0.751707 | − | 0.751707i | −0.223091 | − | 0.974798i | \(-0.571615\pi\) |
0.974798 | + | 0.223091i | \(0.0716146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 252456. | − | 104571.i | 1.49452 | − | 0.619051i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 190691. | + | 78986.6i | 1.11797 | + | 0.463077i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 70333.3i | − | 0.408380i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 69876.5 | 0.401845 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 70409.1 | − | 169983.i | 0.401052 | − | 0.968225i | −0.586359 | − | 0.810051i | \(-0.699439\pi\) |
0.987411 | − | 0.158174i | \(-0.0505607\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15986.4 | − | 38594.5i | −0.0901956 | − | 0.217751i | 0.872344 | − | 0.488893i | \(-0.162599\pi\) |
−0.962540 | + | 0.271141i | \(0.912599\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24073.9 | + | 24073.9i | 0.134544 | + | 0.134544i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −148066. | − | 148066.i | −0.819743 | − | 0.819743i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45693.8 | − | 110315.i | −0.250612 | − | 0.605030i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 36663.9 | − | 88514.6i | 0.199216 | − | 0.480950i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −246277. | −1.32578 | −0.662888 | − | 0.748719i | \(-0.730669\pi\) | ||||
−0.662888 | + | 0.748719i | \(0.730669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 240681.i | 1.28371i | 0.766828 | + | 0.641853i | \(0.221834\pi\) | ||||
−0.766828 | + | 0.641853i | \(0.778166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 200329. | + | 82979.0i | 1.05868 | + | 0.438520i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12026.4 | + | 4981.50i | −0.0629758 | + | 0.0260854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 267417. | − | 267417.i | 1.38759 | − | 1.38759i | 0.557220 | − | 0.830365i | \(-0.311868\pi\) |
0.830365 | − | 0.557220i | \(-0.188132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37830.9 | + | 37830.9i | −0.194522 | + | 0.194522i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 183796. | − | 76130.7i | 0.936544 | − | 0.387929i | 0.138387 | − | 0.990378i | \(-0.455808\pi\) |
0.798157 | + | 0.602449i | \(0.205808\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 124585. | + | 51604.8i | 0.629138 | + | 0.260597i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 188939.i | − | 0.945596i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −114159. | −0.566260 | −0.283130 | − | 0.959082i | \(-0.591373\pi\) | ||||
−0.283130 | + | 0.959082i | \(0.591373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −109655. | + | 264730.i | −0.539107 | + | 1.30152i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 93904.0 | + | 226704.i | 0.457602 | + | 1.10475i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 113556. | + | 113556.i | 0.548515 | + | 0.548515i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −262872. | − | 262872.i | −1.25867 | − | 1.25867i | −0.951728 | − | 0.306943i | \(-0.900694\pi\) |
−0.306943 | − | 0.951728i | \(-0.599306\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −147272. | − | 355545.i | −0.699027 | − | 1.68760i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33053.9 | + | 79799.1i | −0.155532 | + | 0.375488i | −0.982369 | − | 0.186955i | \(-0.940138\pi\) |
0.826836 | + | 0.562443i | \(0.190138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 105487. | 0.492080 | 0.246040 | − | 0.969260i | \(-0.420870\pi\) | ||||
0.246040 | + | 0.969260i | \(0.420870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 892.848i | − | 0.00412926i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −179694. | − | 74431.5i | −0.823946 | − | 0.341290i | −0.0694429 | − | 0.997586i | \(-0.522122\pi\) |
−0.754503 | + | 0.656296i | \(0.772122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −233452. | + | 96699.1i | −1.06133 | + | 0.439619i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −159316. | + | 159316.i | −0.718153 | + | 0.718153i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 104912. | − | 104912.i | 0.468924 | − | 0.468924i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −70468.1 | + | 29188.9i | −0.312324 | + | 0.129369i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 51995.9 | + | 21537.4i | 0.228524 | + | 0.0946578i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 265190.i | 1.15581i | 0.816105 | + | 0.577904i | \(0.196129\pi\) | ||||
−0.816105 | + | 0.577904i | \(0.803871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −66477.2 | −0.287331 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16145.2 | − | 38978.0i | 0.0692069 | − | 0.167080i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 175131. | + | 422804.i | 0.744526 | + | 1.79745i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −178867. | − | 178867.i | −0.754177 | − | 0.754177i | 0.221079 | − | 0.975256i | \(-0.429042\pi\) |
−0.975256 | + | 0.221079i | \(0.929042\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −72476.5 | − | 72476.5i | −0.303095 | − | 0.303095i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1535.66 | − | 3707.42i | −0.00636990 | − | 0.0153783i | 0.920663 | − | 0.390359i | \(-0.127649\pi\) |
−0.927032 | + | 0.374981i | \(0.877649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 158070. | − | 381614.i | 0.650361 | − | 1.57011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 105917. | 0.432271 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 584020.i | − | 2.36437i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −94336.4 | − | 39075.4i | −0.378860 | − | 0.156929i | 0.185123 | − | 0.982715i | \(-0.440732\pi\) |
−0.563983 | + | 0.825787i | \(0.690732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28271.8 | − | 11710.6i | 0.112636 | − | 0.0466555i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 122210. | − | 122210.i | 0.483027 | − | 0.483027i | −0.423070 | − | 0.906097i | \(-0.639048\pi\) |
0.906097 | + | 0.423070i | \(0.139048\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −253830. | + | 253830.i | −0.995315 | + | 0.995315i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −175288. | + | 72606.5i | −0.681923 | + | 0.282462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −146281. | − | 60591.4i | −0.564613 | − | 0.233871i | 0.0820732 | − | 0.996626i | \(-0.473846\pi\) |
−0.646687 | + | 0.762756i | \(0.723846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 530775.i | 2.03268i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −140180. | −0.532661 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2388.11 | + | 5765.41i | −0.00900410 | + | 0.0217378i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −127011. | − | 306632.i | −0.475183 | − | 1.14719i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −153727. | − | 153727.i | −0.570708 | − | 0.570708i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 160559. | + | 160559.i | 0.591508 | + | 0.591508i | 0.938039 | − | 0.346531i | \(-0.112640\pi\) |
−0.346531 | + | 0.938039i | \(0.612640\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 199672. | + | 482051.i | 0.729985 | + | 1.76234i | 0.642648 | + | 0.766162i | \(0.277836\pi\) |
0.0873373 | + | 0.996179i | \(0.472164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 94601.9 | − | 228389.i | 0.343227 | − | 0.828623i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1700.82 | −0.00612402 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 274510.i | 0.980949i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 47819.3 | + | 19807.4i | 0.169596 | + | 0.0702488i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −100655. | + | 41692.8i | −0.354309 | + | 0.146760i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −266982. | + | 266982.i | −0.932771 | + | 0.932771i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −187734. | + | 187734.i | −0.651022 | + | 0.651022i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 481857. | − | 199592.i | 1.65859 | − | 0.687012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11552.6 | − | 4785.24i | −0.0394717 | − | 0.0163497i | 0.362860 | − | 0.931844i | \(-0.381800\pi\) |
−0.402332 | + | 0.915494i | \(0.631800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 267334.i | 0.906681i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 482346. | 1.62393 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −131230. | + | 316817.i | −0.438589 | + | 1.05885i | 0.537847 | + | 0.843043i | \(0.319238\pi\) |
−0.976436 | + | 0.215806i | \(0.930762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11458.6 | − | 27663.5i | −0.0380177 | − | 0.0917829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −106390. | − | 106390.i | −0.350427 | − | 0.350427i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 267285. | + | 267285.i | 0.874026 | + | 0.874026i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 96367.8 | + | 232653.i | 0.312857 | + | 0.755304i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −98441.9 | + | 237660.i | −0.317300 | + | 0.766029i | 0.682096 | + | 0.731263i | \(0.261069\pi\) |
−0.999395 | + | 0.0347663i | \(0.988931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 56412.3 | 0.180530 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 691352.i | 2.19671i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −215850. | − | 89408.0i | −0.680981 | − | 0.282072i | 0.0152558 | − | 0.999884i | \(-0.495144\pi\) |
−0.696237 | + | 0.717812i | \(0.745144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −529853. | + | 219472.i | −1.65981 | + | 0.687516i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 244779. | − | 244779.i | 0.761391 | − | 0.761391i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 299019. | − | 299019.i | 0.923578 | − | 0.923578i | −0.0737022 | − | 0.997280i | \(-0.523481\pi\) |
0.997280 | + | 0.0737022i | \(0.0234814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 74877.7 | − | 31015.4i | 0.229657 | − | 0.0951272i | −0.264887 | − | 0.964279i | \(-0.585335\pi\) |
0.494545 | + | 0.869152i | \(0.335335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −79042.5 | − | 32740.5i | −0.240742 | − | 0.0997185i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 31238.5i | − | 0.0944832i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −169930. | −0.510410 | −0.255205 | − | 0.966887i | \(-0.582143\pi\) | ||||
−0.255205 | + | 0.966887i | \(0.582143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −58060.8 | + | 140171.i | −0.173191 | + | 0.418121i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60530.0 | − | 146132.i | −0.179316 | − | 0.432906i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −387953. | − | 387953.i | −1.14141 | − | 1.14141i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28476.4 | + | 28476.4i | 0.0832096 | + | 0.0832096i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 69704.8 | + | 168282.i | 0.202296 | + | 0.488385i | 0.992172 | − | 0.124882i | \(-0.0398552\pi\) |
−0.789876 | + | 0.613266i | \(0.789855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −237.085 | + | 572.374i | −0.000683397 | + | 0.00164987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 465145. | 1.33172 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 446782.i | − | 1.27053i | −0.772293 | − | 0.635267i | \(-0.780890\pi\) | ||
0.772293 | − | 0.635267i | \(-0.219110\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.07064e6 | − | 443472.i | −3.02418 | − | 1.25266i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −46499.8 | + | 19260.8i | −0.130467 | + | 0.0540414i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −123181. | + | 123181.i | −0.343312 | + | 0.343312i | −0.857611 | − | 0.514299i | \(-0.828052\pi\) |
0.514299 | + | 0.857611i | \(0.328052\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −268659. | + | 268659.i | −0.743794 | + | 0.743794i | −0.973306 | − | 0.229512i | \(-0.926287\pi\) |
0.229512 | + | 0.973306i | \(0.426287\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −58542.6 | + | 24249.1i | −0.161004 | + | 0.0666902i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −515044. | − | 213338.i | −1.40713 | − | 0.582852i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 374047.i | − | 1.01519i | −0.861595 | − | 0.507597i | \(-0.830534\pi\) | ||
0.861595 | − | 0.507597i | \(-0.169466\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 487639. | 1.31481 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48292.0 | − | 116587.i | 0.129358 | − | 0.312297i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 160688. | + | 387935.i | 0.427625 | + | 1.03238i | 0.980039 | + | 0.198807i | \(0.0637068\pi\) |
−0.552414 | + | 0.833570i | \(0.686293\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 291828. | + | 291828.i | 0.771572 | + | 0.771572i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −157953. | − | 157953.i | −0.414914 | − | 0.414914i | 0.468532 | − | 0.883446i | \(-0.344783\pi\) |
−0.883446 | + | 0.468532i | \(0.844783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −231148. | − | 558042.i | −0.603267 | − | 1.45642i | −0.870199 | − | 0.492700i | \(-0.836010\pi\) |
0.266932 | − | 0.963715i | \(-0.413990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21970.4 | − | 53041.3i | 0.0569712 | − | 0.137541i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 303263. | 0.781347 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 474980.i | 1.21595i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 232660. | + | 96370.8i | 0.591815 | + | 0.245138i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 443188. | − | 183574.i | 1.12018 | − | 0.463992i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 455364. | − | 455364.i | 1.14367 | − | 1.14367i | 0.155895 | − | 0.987774i | \(-0.450174\pi\) |
0.987774 | − | 0.155895i | \(-0.0498263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −43251.9 | + | 43251.9i | −0.107944 | + | 0.107944i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −403598. | + | 167176.i | −1.00092 | + | 0.414596i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 183211. | + | 75888.4i | 0.451515 | + | 0.187024i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 146454.i | − | 0.358674i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 294774. | 0.717418 | 0.358709 | − | 0.933449i | \(-0.383217\pi\) | ||||
0.358709 | + | 0.933449i | \(0.383217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −97454.5 | + | 235276.i | −0.235711 | + | 0.569057i | −0.996830 | − | 0.0795549i | \(-0.974650\pi\) |
0.761119 | + | 0.648612i | \(0.224650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −81777.4 | − | 197428.i | −0.196568 | − | 0.474558i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −435797. | − | 435797.i | −1.04106 | − | 1.04106i | −0.999120 | − | 0.0419402i | \(-0.986646\pi\) |
−0.0419402 | − | 0.999120i | \(-0.513354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −356791. | − | 356791.i | −0.847080 | − | 0.847080i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −768.399 | − | 1855.08i | −0.00181311 | − | 0.00437724i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 212867. | − | 513905.i | 0.499208 | − | 1.20519i | −0.450704 | − | 0.892674i | \(-0.648827\pi\) |
0.949911 | − | 0.312520i | \(-0.101173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −206897. | −0.482250 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 133102.i | 0.308357i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 590015. | + | 244392.i | 1.35860 | + | 0.562751i | 0.938674 | − | 0.344806i | \(-0.112055\pi\) |
0.419928 | + | 0.907557i | \(0.362055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −476292. | + | 197287.i | −1.09011 | + | 0.451538i | −0.854045 | − | 0.520199i | \(-0.825858\pi\) |
−0.236065 | + | 0.971737i | \(0.575858\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −185874. | + | 185874.i | −0.422854 | + | 0.422854i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −298482. | + | 298482.i | −0.674954 | + | 0.674954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 56930.3 | − | 23581.3i | 0.127965 | − | 0.0530049i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 179497. | + | 74349.9i | 0.401055 | + | 0.166122i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 291899.i | 0.648317i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −88432.6 | −0.195246 | −0.0976230 | − | 0.995223i | \(-0.531124\pi\) | ||||
−0.0976230 | + | 0.995223i | \(0.531124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 128735. | − | 310793.i | 0.282545 | − | 0.682124i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33417.8 | + | 80677.8i | 0.0729123 | + | 0.176026i | 0.956134 | − | 0.292930i | \(-0.0946303\pi\) |
−0.883222 | + | 0.468956i | \(0.844630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 727744. | + | 727744.i | 1.57848 | + | 1.57848i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 345751. | + | 345751.i | 0.745536 | + | 0.745536i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 71540.4 | + | 172714.i | 0.153359 | + | 0.370242i | 0.981822 | − | 0.189801i | \(-0.0607844\pi\) |
−0.828463 | + | 0.560043i | \(0.810784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 428501. | − | 1.03449e6i | 0.913210 | − | 2.20468i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 321544. | 0.681281 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 208606.i | − | 0.439430i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 405341. | + | 167898.i | 0.848915 | + | 0.351632i | 0.764362 | − | 0.644787i | \(-0.223054\pi\) |
0.0845525 | + | 0.996419i | \(0.473054\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 220065. | − | 91154.1i | 0.458232 | − | 0.189806i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 202469. | − | 202469.i | 0.419168 | − | 0.419168i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 555913. | − | 555913.i | 1.14430 | − | 1.14430i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15544.9 | + | 6438.92i | −0.0318152 | + | 0.0131783i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 612430. | + | 253677.i | 1.24629 | + | 0.516231i | 0.905676 | − | 0.423971i | \(-0.139364\pi\) |
0.340617 | + | 0.940202i | \(0.389364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 174735.i | − | 0.353564i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −478030. | −0.961783 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −308935. | + | 745836.i | −0.618057 | + | 1.49212i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −202534. | − | 488959.i | −0.402907 | − | 0.972703i | −0.986957 | − | 0.160985i | \(-0.948533\pi\) |
0.584050 | − | 0.811718i | \(-0.301467\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 67026.8 | + | 67026.8i | 0.132590 | + | 0.132590i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −179.416 | − | 179.416i | −0.000352926 | − | 0.000352926i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −150238. | − | 362707.i | −0.293879 | − | 0.709487i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −144857. | + | 349715.i | −0.281774 | + | 0.680262i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −459937. | −0.889694 | −0.444847 | − | 0.895607i | \(-0.646742\pi\) | ||||
−0.444847 | + | 0.895607i | \(0.646742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14034.1i | 0.0269969i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −208065. | − | 86183.3i | −0.398036 | − | 0.164872i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 333580. | − | 138173.i | 0.634635 | − | 0.262874i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 620411. | − | 620411.i | 1.17385 | − | 1.17385i | 0.192560 | − | 0.981285i | \(-0.438321\pi\) |
0.981285 | − | 0.192560i | \(-0.0616790\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 417990. | − | 417990.i | 0.786522 | − | 0.786522i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −376087. | + | 155781.i | −0.703808 | + | 0.291527i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −434533. | − | 179989.i | −0.808751 | − | 0.334996i | −0.0602955 | − | 0.998181i | \(-0.519204\pi\) |
−0.748456 | + | 0.663185i | \(0.769204\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 751200.i | − | 1.39053i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 617729. | 1.13727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 195326. | − | 471558.i | 0.357660 | − | 0.863469i | −0.637968 | − | 0.770063i | \(-0.720225\pi\) |
0.995628 | − | 0.0934055i | \(-0.0297753\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36642.0 | + | 88461.6i | 0.0667333 | + | 0.161108i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 126962. | + | 126962.i | 0.229982 | + | 0.229982i | 0.812685 | − | 0.582703i | \(-0.198005\pi\) |
−0.582703 | + | 0.812685i | \(0.698005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −547454. | − | 547454.i | −0.986359 | − | 0.986359i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15179.0 | − | 36645.5i | −0.0272021 | − | 0.0656718i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −324943. | + | 784481.i | −0.579220 | + | 1.39836i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −849371. | −1.50597 | −0.752987 | − | 0.658036i | \(-0.771388\pi\) | ||||
−0.752987 | + | 0.658036i | \(0.771388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 892914.i | − | 1.57478i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 928969. | + | 384792.i | 1.62970 | + | 0.675043i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −199956. | + | 82824.7i | −0.348934 | + | 0.144533i | −0.550265 | − | 0.834990i | \(-0.685473\pi\) |
0.201331 | + | 0.979523i | \(0.435473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −72929.6 | + | 72929.6i | −0.126596 | + | 0.126596i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −183793. | + | 183793.i | −0.317366 | + | 0.317366i | −0.847755 | − | 0.530389i | \(-0.822046\pi\) |
0.530389 | + | 0.847755i | \(0.322046\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.00218e6 | − | 415115.i | 1.72145 | − | 0.713049i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −268482. | − | 111209.i | −0.458768 | − | 0.190028i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 191850.i | − | 0.326116i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −267282. | −0.451979 | −0.225989 | − | 0.974130i | \(-0.572561\pi\) | ||||
−0.225989 | + | 0.974130i | \(0.572561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −177321. | + | 428092.i | −0.298300 | + | 0.720159i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41754.1 | + | 100803.i | 0.0698779 | + | 0.168700i | 0.954960 | − | 0.296735i | \(-0.0958978\pi\) |
−0.885082 | + | 0.465435i | \(0.845898\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1051.28 | − | 1051.28i | −0.00175031 | − | 0.00175031i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 400449. | + | 400449.i | 0.663292 | + | 0.663292i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −109589. | − | 264572.i | −0.180590 | − | 0.435982i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −546364. | + | 1.31904e6i | −0.895736 | + | 2.16250i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 663580. | 1.08235 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 923242.i | 1.49822i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −993710. | − | 411608.i | −1.60439 | − | 0.664561i | −0.612363 | − | 0.790577i | \(-0.709781\pi\) |
−0.992028 | + | 0.126016i | \(0.959781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 749100. | − | 310287.i | 1.20333 | − | 0.498437i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −911999. | + | 911999.i | −1.45761 | + | 1.45761i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −78478.5 | + | 78478.5i | −0.124797 | + | 0.124797i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −730067. | + | 302404.i | −1.15512 | + | 0.478468i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −700909. | − | 290326.i | −1.10343 | − | 0.457056i | −0.244760 | − | 0.969584i | \(-0.578709\pi\) |
−0.858671 | + | 0.512528i | \(0.828709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 910616.i | 1.42640i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 76049.1 | 0.118530 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 496553. | − | 1.19878e6i | 0.770077 | − | 1.85913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −66158.4 | − | 159721.i | −0.102092 | − | 0.246473i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 53085.4 | + | 53085.4i | 0.0815133 | + | 0.0815133i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 237940. | + | 237940.i | 0.363555 | + | 0.363555i | 0.865120 | − | 0.501565i | \(-0.167242\pi\) |
−0.501565 | + | 0.865120i | \(0.667242\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 245980. | + | 593849.i | 0.373989 | + | 0.902889i | 0.993066 | + | 0.117559i | \(0.0375069\pi\) |
−0.619077 | + | 0.785330i | \(0.712493\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −243749. | + | 588462.i | −0.368775 | + | 0.890302i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −420004. | −0.632322 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 148279.i | 0.222145i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 83673.0 | + | 34658.5i | 0.124743 | + | 0.0516704i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 867491. | − | 359327.i | 1.28700 | − | 0.533093i | 0.368910 | − | 0.929465i | \(-0.379731\pi\) |
0.918090 | + | 0.396372i | \(0.129731\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −891926. | + | 891926.i | −1.31683 | + | 1.31683i | −0.400557 | + | 0.916272i | \(0.631183\pi\) |
−0.916272 | + | 0.400557i | \(0.868817\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −427327. | + | 427327.i | −0.627845 | + | 0.627845i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 401413. | − | 166271.i | 0.586922 | − | 0.243111i | −0.0694040 | − | 0.997589i | \(-0.522110\pi\) |
0.656326 | + | 0.754478i | \(0.272110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 654720. | + | 271194.i | 0.952678 | + | 0.394612i | 0.804237 | − | 0.594309i | \(-0.202574\pi\) |
0.148441 | + | 0.988921i | \(0.452574\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 362793.i | 0.525359i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.43099e6 | −2.06227 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47986.6 | − | 115850.i | 0.0688251 | − | 0.166159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1045.64 | − | 2524.40i | −0.00149256 | − | 0.00360335i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −231028. | − | 231028.i | −0.328202 | − | 0.328202i | 0.523700 | − | 0.851903i | \(-0.324551\pi\) |
−0.851903 | + | 0.523700i | \(0.824551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3501.86 | + | 3501.86i | 0.00495116 | + | 0.00495116i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −120057. | − | 289843.i | −0.168940 | − | 0.407857i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −297521. | + | 718278.i | −0.416681 | + | 1.00596i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.25371e6 | −1.74756 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 956919.i | − | 1.32758i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 66116.1 | + | 27386.2i | 0.0912952 | + | 0.0378157i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −293641. | + | 121630.i | −0.403570 | + | 0.167164i | −0.575229 | − | 0.817992i | \(-0.695087\pi\) |
0.171659 | + | 0.985156i | \(0.445087\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −74850.0 | + | 74850.0i | −0.102390 | + | 0.102390i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 579802. | − | 579802.i | 0.789438 | − | 0.789438i | −0.191964 | − | 0.981402i | \(-0.561486\pi\) |
0.981402 | + | 0.191964i | \(0.0614857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52706.4 | + | 21831.7i | −0.0714294 | + | 0.0295870i | −0.418112 | − | 0.908395i | \(-0.637308\pi\) |
0.346683 | + | 0.937982i | \(0.387308\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 857485. | + | 355182.i | 1.15670 | + | 0.479120i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.04826e6i | − | 1.40750i | −0.710449 | − | 0.703748i | \(-0.751508\pi\) | ||
0.710449 | − | 0.703748i | \(-0.248492\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −890852. | −1.19062 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 472804. | − | 1.14145e6i | 0.628988 | − | 1.51851i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −353626. | − | 853729.i | −0.468279 | − | 1.13053i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 166080. | + | 166080.i | 0.218917 | + | 0.218917i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 182496. | + | 182496.i | 0.239455 | + | 0.239455i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 178651. | + | 431301.i | 0.233340 | + | 0.563332i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 367736. | − | 887793.i | 0.478120 | − | 1.15428i | −0.482369 | − | 0.875968i | \(-0.660224\pi\) |
0.960490 | − | 0.278316i | \(-0.0897763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 179072. | 0.231766 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 723917.i | − | 0.932689i | −0.884603 | − | 0.466344i | \(-0.845571\pi\) | ||
0.884603 | − | 0.466344i | \(-0.154429\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 412295. | + | 170778.i | 0.528794 | + | 0.219034i | 0.631075 | − | 0.775722i | \(-0.282614\pi\) |
−0.102281 | + | 0.994756i | \(0.532614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −671425. | + | 278113.i | −0.857257 | + | 0.355087i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 252860. | − | 252860.i | 0.321390 | − | 0.321390i | −0.527910 | − | 0.849300i | \(-0.677024\pi\) |
0.849300 | + | 0.527910i | \(0.177024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −694685. | + | 694685.i | −0.878991 | + | 0.878991i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −781843. | + | 323850.i | −0.984836 | + | 0.407932i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 306448. | + | 126935.i | 0.384286 | + | 0.159176i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.08793e6i | 1.35817i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −39215.0 | −0.0487380 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1122.31 | − | 2709.49i | 0.00138865 | − | 0.00335249i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 576059. | + | 1.39073e6i | 0.709607 | + | 1.71314i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −339819. | − | 339819.i | −0.416747 | − | 0.416747i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 774606. | + | 774606.i | 0.945766 | + | 0.945766i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24975.7 | + | 60296.7i | 0.0303601 | + | 0.0732958i | 0.938332 | − | 0.345734i | \(-0.112370\pi\) |
−0.907972 | + | 0.419030i | \(0.862370\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −77471.4 | + | 187033.i | −0.0937592 | + | 0.226355i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 620126. | 0.747211 | 0.373606 | − | 0.927588i | \(-0.378121\pi\) | ||||
0.373606 | + | 0.927588i | \(0.378121\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 386675.i | 0.463878i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 388419. | + | 160889.i | 0.463937 | + | 0.192169i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −429872. | + | 178059.i | −0.511212 | + | 0.211751i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −456978. | + | 456978.i | −0.541084 | + | 0.541084i | −0.923847 | − | 0.382763i | \(-0.874973\pi\) |
0.382763 | + | 0.923847i | \(0.374973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72708.3 | − | 72708.3i | 0.0857165 | − | 0.0857165i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −501523. | + | 207738.i | −0.588692 | + | 0.243844i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 387404. | + | 160468.i | 0.452773 | + | 0.187545i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3519.32i | 0.00409543i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.29711e6 | −1.50296 | −0.751479 | − | 0.659757i | \(-0.770659\pi\) | ||||
−0.751479 | + | 0.659757i | \(0.770659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −199472. | + | 481568.i | −0.230135 | + | 0.555595i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30097.4 | + | 72661.5i | 0.0345753 | + | 0.0834721i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.00321e6 | + | 2.00321e6i | 2.29141 | + | 2.29141i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 170416. | + | 170416.i | 0.194102 | + | 0.194102i | 0.797466 | − | 0.603364i | \(-0.206173\pi\) |
−0.603364 | + | 0.797466i | \(0.706173\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 110656. | + | 267147.i | 0.125500 | + | 0.302984i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −105038. | + | 253584.i | −0.118622 | + | 0.286380i | −0.972027 | − | 0.234869i | \(-0.924534\pi\) |
0.853405 | + | 0.521249i | \(0.174534\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 117285. | 0.131892 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 1.86170e6i | − | 2.08472i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.58561e6 | + | 656779.i | 1.76805 | + | 0.732351i | 0.995211 | + | 0.0977520i | \(0.0311652\pi\) |
0.772841 | + | 0.634599i | \(0.218835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 455800. | − | 188799.i | 0.506107 | − | 0.209636i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 301310. | − | 301310.i | 0.333160 | − | 0.333160i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 776606. | − | 776606.i | 0.855096 | − | 0.855096i | −0.135659 | − | 0.990756i | \(-0.543315\pi\) |
0.990756 | + | 0.135659i | \(0.0433153\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −323894. | + | 134161.i | −0.355137 | + | 0.147102i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.10136e6 | − | 456197.i | −1.20255 | − | 0.498114i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.51815e6i | − | 2.73807i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 923509. | 0.999987 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81485.6 | + | 196724.i | −0.0878675 | + | 0.212131i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 237917. | + | 574382.i | 0.255488 | + | 0.616802i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.23673e6 | − | 1.23673e6i | −1.32258 | − | 1.32258i | −0.911679 | − | 0.410902i | \(-0.865214\pi\) |
−0.410902 | − | 0.911679i | \(-0.634786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −488567. | − | 488567.i | −0.520327 | − | 0.520327i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −407205. | − | 983079.i | −0.431891 | − | 1.04268i | −0.978677 | − | 0.205405i | \(-0.934149\pi\) |
0.546786 | − | 0.837273i | \(-0.315851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 246423. | − | 594919.i | 0.260289 | − | 0.628394i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −229778. | −0.241713 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.17141e6i | 1.22721i | 0.789614 | + | 0.613604i | \(0.210281\pi\) | ||||
−0.789614 | + | 0.613604i | \(0.789719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −684936. | − | 283710.i | −0.714636 | − | 0.296012i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 251315. | − | 104098.i | 0.261144 | − | 0.108169i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −518176. | + | 518176.i | −0.536254 | + | 0.536254i | −0.922427 | − | 0.386173i | \(-0.873797\pi\) |
0.386173 | + | 0.922427i | \(0.373797\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.34777e6 | − | 1.34777e6i | 1.38913 | − | 1.38913i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −993208. | + | 411400.i | −1.01954 | + | 0.422309i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56105.9 | − | 23239.8i | −0.0573609 | − | 0.0237596i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 522347.i | − | 0.531878i | −0.963990 | − | 0.265939i | \(-0.914318\pi\) | ||
0.963990 | − | 0.265939i | \(-0.0856820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −348802. | −0.353737 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −78925.4 | + | 190543.i | −0.0797206 | + | 0.192463i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −646593. | − | 1.56101e6i | −0.650490 | − | 1.57042i | −0.812068 | − | 0.583563i | \(-0.801658\pi\) |
0.161578 | − | 0.986860i | \(-0.448342\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 544932. | + | 544932.i | 0.546023 | + | 0.546023i |
(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 | 128.5.h.a.47.5 | 60 | ||
4.3 | odd | 2 | 32.5.h.a.3.12 | ✓ | 60 | ||
32.11 | odd | 8 | inner | 128.5.h.a.79.5 | 60 | ||
32.21 | even | 8 | 32.5.h.a.11.12 | yes | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.5.h.a.3.12 | ✓ | 60 | 4.3 | odd | 2 | ||
32.5.h.a.11.12 | yes | 60 | 32.21 | even | 8 | ||
128.5.h.a.47.5 | 60 | 1.1 | even | 1 | trivial | ||
128.5.h.a.79.5 | 60 | 32.11 | odd | 8 | inner |