Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(113,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.ba (of order \(10\), degree \(4\), 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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 113.2 | ||
Character | \(\chi\) | \(=\) | 1148.113 |
Dual form | 1148.2.ba.a.701.19 |
$q$-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 \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).
\(n\) | \(493\) | \(575\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.81622i | − | 1.62594i | −0.582303 | − | 0.812972i | \(-0.697848\pi\) | ||
0.582303 | − | 0.812972i | \(-0.302152\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.10836 | + | 3.41119i | 0.495676 | + | 1.52553i | 0.815901 | + | 0.578191i | \(0.196241\pi\) |
−0.320226 | + | 0.947341i | \(0.603759\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.587785 | + | 0.809017i | 0.222162 | + | 0.305780i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.93108 | −1.64369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.213839 | − | 0.0694806i | −0.0644750 | − | 0.0209492i | 0.276602 | − | 0.960985i | \(-0.410792\pi\) |
−0.341077 | + | 0.940035i | \(0.610792\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.07430 | + | 4.23140i | −0.852656 | + | 1.17358i | 0.130615 | + | 0.991433i | \(0.458305\pi\) |
−0.983271 | + | 0.182147i | \(0.941695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.60667 | − | 3.12140i | 2.48043 | − | 0.805941i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00515 | − | 0.976434i | −0.728857 | − | 0.236820i | −0.0789980 | − | 0.996875i | \(-0.525172\pi\) |
−0.649859 | + | 0.760055i | \(0.725172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.68046 | + | 3.68934i | 0.614941 | + | 0.846393i | 0.996972 | − | 0.0777561i | \(-0.0247755\pi\) |
−0.382032 | + | 0.924149i | \(0.624776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.27837 | − | 1.65533i | 0.497181 | − | 0.361223i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.82515 | + | 2.77914i | 0.797600 | + | 0.579490i | 0.910209 | − | 0.414149i | \(-0.135921\pi\) |
−0.112609 | + | 0.993639i | \(0.535921\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.36269 | + | 4.62277i | −1.27254 | + | 0.924553i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.43835i | 1.04661i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.396882 | + | 0.128955i | −0.0736991 | + | 0.0239463i | −0.345635 | − | 0.938369i | \(-0.612336\pi\) |
0.271935 | + | 0.962316i | \(0.412336\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.43283 | + | 4.40979i | −0.257343 | + | 0.792021i | 0.736016 | + | 0.676964i | \(0.236705\pi\) |
−0.993359 | + | 0.115057i | \(0.963295\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.195673 | + | 0.602218i | −0.0340622 | + | 0.104833i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.10823 | + | 2.90174i | −0.356357 | + | 0.490483i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.846662 | + | 2.60576i | 0.139190 | + | 0.428384i | 0.996218 | − | 0.0868860i | \(-0.0276916\pi\) |
−0.857028 | + | 0.515270i | \(0.827692\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.9166 | + | 8.65788i | 1.90818 | + | 1.38637i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.14062 | + | 4.88418i | 0.646657 | + | 0.762781i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.388402 | + | 0.282190i | 0.0592307 | + | 0.0430336i | 0.617007 | − | 0.786958i | \(-0.288345\pi\) |
−0.557776 | + | 0.829992i | \(0.688345\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.46544 | − | 16.8209i | −0.814739 | − | 2.50751i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.40935 | + | 6.06894i | −0.643169 | + | 0.885247i | −0.998780 | − | 0.0493877i | \(-0.984273\pi\) |
0.355610 | + | 0.934634i | \(0.384273\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.309017 | + | 0.951057i | −0.0441453 | + | 0.135865i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.74985 | + | 8.46317i | −0.385056 | + | 1.18508i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.20312 | + | 0.390916i | −0.165261 | + | 0.0536964i | −0.390479 | − | 0.920612i | \(-0.627691\pi\) |
0.225218 | + | 0.974308i | \(0.427691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.806457i | − | 0.108743i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3900 | − | 7.54877i | 1.37619 | − | 0.999859i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.96171 | − | 6.51107i | −1.16672 | − | 0.847668i | −0.176104 | − | 0.984372i | \(-0.556349\pi\) |
−0.990612 | + | 0.136703i | \(0.956349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89239 | − | 7.18725i | 1.26659 | − | 0.920232i | 0.267530 | − | 0.963550i | \(-0.413793\pi\) |
0.999061 | + | 0.0433171i | \(0.0137926\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.89842 | − | 3.98933i | −0.365166 | − | 0.502608i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17.8416 | − | 5.79708i | −2.21298 | − | 0.719039i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70062 | + | 2.17716i | −0.818612 | + | 0.265983i | −0.688241 | − | 0.725482i | \(-0.741617\pi\) |
−0.130371 | + | 0.991465i | \(0.541617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.82666 | − | 10.7725i | 0.942219 | − | 1.29685i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1052 | + | 3.60829i | 1.31794 | + | 0.428226i | 0.881788 | − | 0.471646i | \(-0.156340\pi\) |
0.436155 | + | 0.899871i | \(0.356340\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.44830 | −0.403593 | −0.201796 | − | 0.979428i | \(-0.564678\pi\) | ||||
−0.201796 | + | 0.979428i | \(0.564678\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.0187 | + | 17.9187i | 1.50327 | + | 2.06908i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0694806 | − | 0.213839i | −0.00791805 | − | 0.0243693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.1848i | − | 1.37090i | −0.728119 | − | 0.685450i | \(-0.759605\pi\) | ||
0.728119 | − | 0.685450i | \(-0.240395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.522330 | 0.0580367 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1285 | 1.66057 | 0.830284 | − | 0.557341i | \(-0.188178\pi\) | ||||
0.830284 | + | 0.557341i | \(0.188178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 11.3334i | − | 1.22928i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.363165 | + | 1.11771i | 0.0389353 | + | 0.119831i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.68737 | + | 6.45161i | 0.496860 | + | 0.683870i | 0.981635 | − | 0.190769i | \(-0.0610983\pi\) |
−0.484774 | + | 0.874639i | \(0.661098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.23030 | −0.548285 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4189 | + | 4.03515i | 1.28778 | + | 0.418426i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.61413 | + | 13.2327i | −0.986389 | + | 1.35765i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.28078 | − | 2.36567i | 0.739252 | − | 0.240197i | 0.0849018 | − | 0.996389i | \(-0.472942\pi\) |
0.654350 | + | 0.756192i | \(0.272942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.05446 | + | 0.342615i | 0.105977 | + | 0.0344341i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.70889 | + | 7.85762i | 0.568056 | + | 0.781862i | 0.992323 | − | 0.123675i | \(-0.0394681\pi\) |
−0.424267 | + | 0.905537i | \(0.639468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.78404 | − | 5.65544i | 0.766984 | − | 0.557247i | −0.134060 | − | 0.990973i | \(-0.542802\pi\) |
0.901045 | + | 0.433727i | \(0.142802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.17192 | + | 5.93725i | 0.797498 | + | 0.579416i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.43447 | − | 3.22183i | 0.428696 | − | 0.311466i | −0.352431 | − | 0.935838i | \(-0.614645\pi\) |
0.781127 | + | 0.624372i | \(0.214645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.3127i | − | 1.37091i | −0.728115 | − | 0.685455i | \(-0.759603\pi\) | ||
0.728115 | − | 0.685455i | \(-0.240397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.33838 | − | 2.38439i | 0.696529 | − | 0.226316i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.56698 | + | 10.9780i | −0.335554 | + | 1.03273i | 0.630895 | + | 0.775868i | \(0.282688\pi\) |
−0.966449 | + | 0.256860i | \(0.917312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.24051 | + | 16.1286i | −0.488680 | + | 1.50400i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.1596 | − | 20.8654i | 1.40151 | − | 1.92901i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.976434 | − | 3.00515i | −0.0895095 | − | 0.275482i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85829 | − | 6.43592i | −0.805299 | − | 0.585084i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.7549 | − | 11.6609i | 1.24024 | − | 1.05143i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.31266 | − | 6.03950i | −0.743507 | − | 0.540189i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64540 | + | 8.14171i | 0.234742 | + | 0.722460i | 0.997156 | + | 0.0753706i | \(0.0240140\pi\) |
−0.762414 | + | 0.647089i | \(0.775986\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.794709 | − | 1.09382i | 0.0699702 | − | 0.0963058i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.682712 | − | 2.10117i | 0.0596489 | − | 0.183580i | −0.916792 | − | 0.399365i | \(-0.869231\pi\) |
0.976441 | + | 0.215784i | \(0.0692308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.40920 | + | 4.33708i | −0.122193 | + | 0.376073i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.5513 | + | 6.02767i | −1.59664 | + | 0.518780i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.43989i | − | 0.464761i | −0.972625 | − | 0.232381i | \(-0.925349\pi\) | ||
0.972625 | − | 0.232381i | \(-0.0746515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.07087 | + | 5.13729i | −0.599743 | + | 0.435739i | −0.845788 | − | 0.533520i | \(-0.820869\pi\) |
0.246045 | + | 0.969259i | \(0.420869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0915 | + | 12.4177i | 1.43936 | + | 1.04576i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.951406 | − | 0.691237i | 0.0795606 | − | 0.0578041i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.879779 | − | 1.21091i | −0.0730617 | − | 0.100561i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.67838 | + | 0.870259i | 0.220909 | + | 0.0717778i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5188 | + | 3.41778i | −0.861737 | + | 0.279995i | −0.706354 | − | 0.707859i | \(-0.749661\pi\) |
−0.155383 | + | 0.987854i | \(0.549661\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0773 | − | 16.6229i | 0.982834 | − | 1.35275i | 0.0475449 | − | 0.998869i | \(-0.484860\pi\) |
0.935289 | − | 0.353885i | \(-0.115140\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.8187 | + | 4.81488i | 1.19802 | + | 0.389260i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.6307 | −1.33581 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.77240 | − | 13.4506i | −0.779922 | − | 1.07347i | −0.995290 | − | 0.0969381i | \(-0.969095\pi\) |
0.215368 | − | 0.976533i | \(-0.430905\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.10090 | + | 3.38824i | 0.0873074 | + | 0.268705i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.72815i | 0.372630i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.7104 | 1.30886 | 0.654428 | − | 0.756124i | \(-0.272909\pi\) | ||||
0.654428 | + | 0.756124i | \(0.272909\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.27116 | −0.176810 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.98742i | 0.463321i | 0.972797 | + | 0.231660i | \(0.0744158\pi\) | ||||
−0.972797 | + | 0.231660i | \(0.925584\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.43627 | − | 13.6534i | −0.341252 | − | 1.05026i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.2176 | − | 18.1925i | −1.01077 | − | 1.39121i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.3113 | −1.54424 | −0.772120 | − | 0.635477i | \(-0.780804\pi\) | ||||
−0.772120 | + | 0.635477i | \(0.780804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.47979 | − | 2.43033i | −0.565419 | − | 0.183716i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.3366 | + | 25.2381i | −1.37826 | + | 1.89701i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.4093 | + | 7.28123i | −1.67495 | + | 0.544225i | −0.983921 | − | 0.178602i | \(-0.942843\pi\) |
−0.691029 | + | 0.722827i | \(0.742843\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8254 | − | 4.16721i | −0.953302 | − | 0.309747i | −0.209245 | − | 0.977863i | \(-0.567101\pi\) |
−0.744057 | + | 0.668117i | \(0.767101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.2408 | − | 27.8591i | −1.49625 | − | 2.05941i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.95034 | + | 5.77626i | −0.584521 | + | 0.424679i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.574777 | + | 0.417600i | 0.0420319 | + | 0.0305379i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.39972 | + | 3.19658i | −0.320032 | + | 0.232517i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.7883i | − | 1.79362i | −0.442416 | − | 0.896810i | \(-0.645879\pi\) | ||
0.442416 | − | 0.896810i | \(-0.354121\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.55539 | + | 2.77982i | −0.615831 | + | 0.200095i | −0.600288 | − | 0.799784i | \(-0.704947\pi\) |
−0.0155423 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.3258 | + | 50.2458i | −1.16912 | + | 3.59818i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.18408 | + | 12.8773i | −0.298103 | + | 0.917468i | 0.684058 | + | 0.729428i | \(0.260214\pi\) |
−0.982161 | + | 0.188040i | \(0.939786\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.74535 | − | 3.77865i | 0.194613 | − | 0.267861i | −0.700548 | − | 0.713606i | \(-0.747061\pi\) |
0.895160 | + | 0.445744i | \(0.147061\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.13137 | + | 18.8704i | 0.432474 | + | 1.33102i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.337608 | − | 0.245286i | −0.0236954 | − | 0.0172157i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0716 | + | 19.5379i | −0.843115 | + | 1.36459i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.8622 | − | 13.7042i | −1.31101 | − | 0.952505i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.316851 | − | 0.975167i | −0.0219170 | − | 0.0674537i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.81663 | + | 8.00590i | −0.400433 | + | 0.551149i | −0.960853 | − | 0.277060i | \(-0.910640\pi\) |
0.560420 | + | 0.828209i | \(0.310640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1617 | − | 31.2746i | 0.696271 | − | 2.14290i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.532115 | + | 1.63768i | −0.0362900 | + | 0.111689i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.40979 | + | 1.43283i | −0.299356 | + | 0.0972666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.71116i | 0.656219i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.3704 | − | 9.71418i | 0.899392 | − | 0.653446i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.2615 | + | 11.0881i | 1.02198 | + | 0.742515i | 0.966689 | − | 0.255955i | \(-0.0823900\pi\) |
0.0552953 | + | 0.998470i | \(0.482390\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 31.3750 | − | 22.7952i | 2.09166 | − | 1.51968i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2478 | + | 15.4812i | 0.746542 | + | 1.02753i | 0.998215 | + | 0.0597145i | \(0.0190190\pi\) |
−0.251674 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8359 | − | 3.84572i | −0.782139 | − | 0.254132i | −0.109386 | − | 0.993999i | \(-0.534888\pi\) |
−0.672753 | + | 0.739867i | \(0.734888\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.602218 | + | 0.195673i | −0.0396230 | + | 0.0128743i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.79638 | − | 9.35441i | 0.445246 | − | 0.612828i | −0.526122 | − | 0.850409i | \(-0.676355\pi\) |
0.971368 | + | 0.237581i | \(0.0763545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.5895 | − | 8.31454i | −1.66928 | − | 0.542381i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.3151 | −2.22901 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.84320 | − | 5.28971i | −0.248596 | − | 0.342163i | 0.666423 | − | 0.745574i | \(-0.267824\pi\) |
−0.915019 | + | 0.403411i | \(0.867824\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.15022 | + | 25.0838i | 0.525002 | + | 1.61579i | 0.764312 | + | 0.644847i | \(0.223079\pi\) |
−0.239310 | + | 0.970943i | \(0.576921\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8441i | 0.952247i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.58674 | −0.229149 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.8516 | −1.51764 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 42.6051i | − | 2.69999i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.18170 | + | 22.1030i | 0.453305 | + | 1.39513i | 0.873114 | + | 0.487516i | \(0.162097\pi\) |
−0.419810 | + | 0.907612i | \(0.637903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.624872 | − | 0.860063i | −0.0392854 | − | 0.0540717i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.9174 | −1.99874 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3030 | + | 4.32241i | 0.829819 | + | 0.269625i | 0.692969 | − | 0.720967i | \(-0.256302\pi\) |
0.136850 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.61045 | + | 2.21659i | −0.100068 | + | 0.137732i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.95706 | − | 0.635887i | 0.121139 | − | 0.0393604i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.95221 | − | 1.93399i | −0.367029 | − | 0.119255i | 0.119695 | − | 0.992811i | \(-0.461808\pi\) |
−0.486724 | + | 0.873556i | \(0.661808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.66698 | − | 3.67078i | −0.163831 | − | 0.225495i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.1692 | − | 13.2007i | 1.11193 | − | 0.807867i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.4003 | + | 12.6421i | 1.06092 | + | 0.770800i | 0.974258 | − | 0.225438i | \(-0.0723812\pi\) |
0.0866582 | + | 0.996238i | \(0.472381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.50412 | + | 5.45207i | −0.455843 | + | 0.331189i | −0.791898 | − | 0.610653i | \(-0.790907\pi\) |
0.336055 | + | 0.941842i | \(0.390907\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14.7297i | 0.891480i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.68179 | − | 0.546446i | 0.101416 | − | 0.0329519i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.06768 | + | 18.6744i | −0.364572 | + | 1.12204i | 0.585677 | + | 0.810545i | \(0.300829\pi\) |
−0.950249 | + | 0.311492i | \(0.899171\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.06539 | − | 21.7450i | 0.422994 | − | 1.30184i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6892 | − | 24.3470i | 1.05525 | − | 1.45242i | 0.171076 | − | 0.985258i | \(-0.445276\pi\) |
0.884170 | − | 0.467164i | \(-0.154724\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.18655 | − | 22.1179i | −0.427196 | − | 1.31477i | −0.900876 | − | 0.434077i | \(-0.857074\pi\) |
0.473679 | − | 0.880697i | \(-0.342926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 37.2662 | + | 27.0755i | 2.20746 | + | 1.60381i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.51759 | + | 6.22069i | −0.0895804 | + | 0.367195i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.67576 | − | 4.12368i | −0.333868 | − | 0.242569i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.66224 | − | 20.5043i | −0.390548 | − | 1.20198i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.62647 | + | 3.61503i | −0.153440 | + | 0.211192i | −0.878816 | − | 0.477161i | \(-0.841666\pi\) |
0.725376 | + | 0.688353i | \(0.241666\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2777 | − | 37.7868i | 0.714833 | − | 2.20003i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.377860 | − | 1.16293i | 0.0219257 | − | 0.0674802i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.5193 | + | 7.64189i | −1.36016 | + | 0.441942i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.480091i | 0.0276720i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.1288 | − | 16.0775i | 1.27126 | − | 0.923628i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 35.4815 | + | 25.7788i | 2.03166 | + | 1.47609i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4056 | + | 9.01318i | −0.708023 | + | 0.514409i | −0.882535 | − | 0.470246i | \(-0.844165\pi\) |
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.9269 | − | 21.9215i | −0.906052 | − | 1.24707i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.99483 | + | 3.24752i | 0.566755 | + | 0.184150i | 0.578358 | − | 0.815783i | \(-0.303694\pi\) |
−0.0116035 | + | 0.999933i | \(0.503694\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.2840 | − | 8.86510i | 1.54218 | − | 0.501085i | 0.590204 | − | 0.807254i | \(-0.299047\pi\) |
0.951977 | + | 0.306169i | \(0.0990473\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3959 | − | 14.3087i | 0.585741 | − | 0.806204i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.2729 | + | 4.63755i | 0.801647 | + | 0.260471i | 0.681056 | − | 0.732231i | \(-0.261521\pi\) |
0.120591 | + | 0.992702i | \(0.461521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0938288 | 0.00525341 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.07338 | − | 12.4884i | −0.506426 | − | 0.697036i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.45281 | − | 13.7043i | −0.247761 | − | 0.762530i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 41.1349i | − | 2.28175i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −40.3077 | −2.22902 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.50163 | −0.413578 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.5738i | − | 1.46063i | −0.683112 | − | 0.730313i | \(-0.739374\pi\) | ||
0.683112 | − | 0.730313i | \(-0.260626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.17496 | − | 12.8492i | −0.228787 | − | 0.704132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.8535 | − | 20.4440i | −0.811532 | − | 1.11698i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.3291 | −1.43424 | −0.717119 | − | 0.696951i | \(-0.754540\pi\) | ||||
−0.717119 | + | 0.696951i | \(0.754540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.9166 | + | 10.0454i | 1.67916 | + | 0.545591i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.612789 | − | 0.843432i | 0.0331844 | − | 0.0456744i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.951057 | + | 0.309017i | −0.0513522 | + | 0.0166853i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 45.4218 | + | 14.7584i | 2.44543 | + | 0.794567i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3889 | + | 15.6755i | 0.611388 | + | 0.841503i | 0.996691 | − | 0.0812871i | \(-0.0259031\pi\) |
−0.385303 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.87461 | − | 7.17432i | 0.528576 | − | 0.384033i | −0.291249 | − | 0.956647i | \(-0.594071\pi\) |
0.819825 | + | 0.572615i | \(0.194071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.0119 | − | 16.7191i | −1.22828 | − | 0.892399i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.11741 | − | 1.53839i | 0.112698 | − | 0.0818801i | −0.530009 | − | 0.847992i | \(-0.677811\pi\) |
0.642707 | + | 0.766112i | \(0.277811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41.8813i | 2.22283i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.46317 | + | 2.74985i | −0.447918 | + | 0.145538i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.03472 | − | 3.18454i | 0.0546104 | − | 0.168074i | −0.920031 | − | 0.391845i | \(-0.871837\pi\) |
0.974642 | + | 0.223771i | \(0.0718369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.555034 | + | 1.70822i | −0.0292123 | + | 0.0899063i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.1250 | + | 24.9469i | −0.951314 | + | 1.30937i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.82197 | − | 11.7628i | −0.200051 | − | 0.615694i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.6390 | + | 15.7217i | 1.12955 | + | 0.820665i | 0.985629 | − | 0.168925i | \(-0.0540294\pi\) |
0.143919 | + | 0.989589i | \(0.454029\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.4178 | − | 24.0843i | −1.06291 | − | 1.25378i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.02343 | − | 0.743566i | −0.0531339 | − | 0.0386040i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0333 | + | 33.9570i | 0.571282 | + | 1.75823i | 0.648504 | + | 0.761211i | \(0.275395\pi\) |
−0.0772217 | + | 0.997014i | \(0.524605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.0085 | + | 23.4103i | −0.878318 | + | 1.20890i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.674472 | − | 2.07581i | 0.0347371 | − | 0.106910i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.83014 | − | 21.0210i | 0.350841 | − | 1.07978i | −0.607541 | − | 0.794288i | \(-0.707844\pi\) |
0.958382 | − | 0.285489i | \(-0.0921560\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.9288 | − | 7.45003i | 1.17468 | − | 0.381677i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 1.35520i | − | 0.0692474i | −0.999400 | − | 0.0346237i | \(-0.988977\pi\) | ||
0.999400 | − | 0.0346237i | \(-0.0110233\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.652438 | − | 0.474024i | 0.0332513 | − | 0.0241585i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.91524 | − | 1.39150i | −0.0973571 | − | 0.0707341i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7815 | − | 14.3721i | 1.00296 | − | 0.728693i | 0.0402387 | − | 0.999190i | \(-0.487188\pi\) |
0.962721 | + | 0.270497i | \(0.0871882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.78153 | − | 12.0867i | −0.444101 | − | 0.611253i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.91736 | − | 1.92267i | −0.298491 | − | 0.0969857i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.5648 | − | 13.5052i | 2.09135 | − | 0.679522i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.70117 | − | 5.09423i | 0.185756 | − | 0.255672i | −0.705975 | − | 0.708237i | \(-0.749491\pi\) |
0.891731 | + | 0.452565i | \(0.149491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.2142 | + | 3.96862i | 0.611473 | + | 0.198680i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2022 | 1.20860 | 0.604301 | − | 0.796756i | \(-0.293453\pi\) | ||||
0.604301 | + | 0.796756i | \(0.293453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.2547 | − | 19.6199i | −0.710075 | − | 0.977334i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.578932 | + | 1.78177i | 0.0287674 | + | 0.0885369i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.616040i | − | 0.0305360i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7138 | −0.727549 | −0.363774 | − | 0.931487i | \(-0.618512\pi\) | ||||
−0.363774 | + | 0.931487i | \(0.618512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.3199 | −0.755676 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.0773i | − | 0.545078i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7679 | + | 51.6062i | 0.823103 | + | 2.53325i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.4677 | + | 19.9131i | 0.708487 | + | 0.975149i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.8648 | 0.677342 | 0.338671 | − | 0.940905i | \(-0.390023\pi\) | ||||
0.338671 | + | 0.940905i | \(0.390023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75433 | − | 1.86970i | −0.280449 | − | 0.0911234i | 0.165415 | − | 0.986224i | \(-0.447104\pi\) |
−0.445864 | + | 0.895101i | \(0.647104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.7429 | − | 29.9265i | 1.05717 | − | 1.45507i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.6347 | − | 7.67938i | 1.14645 | − | 0.372505i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.6292 | + | 3.77856i | 0.562777 | + | 0.182857i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.94667 | − | 2.67937i | −0.0939863 | − | 0.129361i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.11074 | + | 3.71317i | −0.246176 | + | 0.178857i | −0.704030 | − | 0.710170i | \(-0.748618\pi\) |
0.457855 | + | 0.889027i | \(0.348618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.8183 | − | 20.9377i | −1.38492 | − | 1.00620i | −0.996401 | − | 0.0847597i | \(-0.972988\pi\) |
−0.388516 | − | 0.921442i | \(-0.627012\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.41019 | + | 2.47765i | −0.163506 | + | 0.118794i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.5617i | 1.03143i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.11777 | − | 2.96254i | 0.435168 | − | 0.141395i | −0.0832374 | − | 0.996530i | \(-0.526526\pi\) |
0.518405 | + | 0.855135i | \(0.326526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.52379 | − | 4.68974i | 0.0725614 | − | 0.223321i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0918636 | − | 0.282727i | 0.00436457 | − | 0.0134328i | −0.948851 | − | 0.315726i | \(-0.897752\pi\) |
0.953215 | + | 0.302293i | \(0.0977521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8124 | + | 23.1403i | −0.796984 | + | 1.09695i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.62521 | + | 29.6233i | 0.455257 | + | 1.40114i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.8419 | − | 13.6894i | −0.889203 | − | 0.646044i | 0.0464672 | − | 0.998920i | \(-0.485204\pi\) |
−0.935670 | + | 0.352876i | \(0.885204\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.546072 | − | 1.33212i | −0.0257135 | − | 0.0627272i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −46.8138 | − | 34.0122i | −2.19950 | − | 1.59803i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.79708 | − | 17.8416i | −0.271771 | − | 0.836426i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9801 | − | 20.6184i | 0.700741 | − | 0.964487i | −0.299206 | − | 0.954189i | \(-0.596722\pi\) |
0.999947 | − | 0.0102988i | \(-0.00327828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.31019 | − | 16.3431i | 0.247858 | − | 0.762830i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.53726 | + | 20.1196i | −0.304471 | + | 0.937064i | 0.675404 | + | 0.737448i | \(0.263969\pi\) |
−0.979874 | + | 0.199616i | \(0.936031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.94406 | − | 3.23102i | 0.462140 | − | 0.150158i | −0.0686878 | − | 0.997638i | \(-0.521881\pi\) |
0.530827 | + | 0.847480i | \(0.321881\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 46.8358i | 2.17196i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.4593 | + | 17.7707i | −1.13184 | + | 0.822330i | −0.985962 | − | 0.166972i | \(-0.946601\pi\) |
−0.145879 | + | 0.989302i | \(0.546601\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.69989 | − | 4.14121i | −0.263197 | − | 0.191223i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.8797 | + | 27.5212i | −1.74540 | + | 1.26811i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0634488 | − | 0.0873298i | −0.00291738 | − | 0.00401543i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.1099 | − | 11.0830i | −1.56507 | − | 0.508522i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.93266 | − | 1.92764i | 0.271638 | − | 0.0882605i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.5030 | − | 26.8435i | 0.891114 | − | 1.22651i | −0.0821029 | − | 0.996624i | \(-0.526164\pi\) |
0.973217 | − | 0.229889i | \(-0.0738364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.6289 | − | 4.42830i | −0.621425 | − | 0.201913i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.3155 | 0.605876 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.1395 | + | 22.2141i | 0.732858 | + | 1.00869i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.89232 | − | 8.90163i | −0.131063 | − | 0.403371i | 0.863894 | − | 0.503674i | \(-0.168019\pi\) |
−0.994957 | + | 0.100303i | \(0.968019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 47.0600i | − | 2.12813i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9066 | 0.582466 | 0.291233 | − | 0.956652i | \(-0.405935\pi\) | ||||
0.291233 | + | 0.956652i | \(0.405935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.31861 | 0.0593871 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.97671i | 0.178740i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.60829 | + | 11.1052i | 0.161854 | + | 0.498136i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.10437 | − | 5.64918i | −0.183737 | − | 0.252892i | 0.707206 | − | 0.707008i | \(-0.249955\pi\) |
−0.890943 | + | 0.454115i | \(0.849955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.8619 | 0.753334 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.0672 | + | 13.3435i | 1.83110 | + | 0.594959i | 0.999198 | + | 0.0400303i | \(0.0127454\pi\) |
0.831898 | + | 0.554929i | \(0.187255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.4763 | + | 28.1832i | −0.911185 | + | 1.25414i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −38.4511 | + | 12.4935i | −1.70767 | + | 0.554856i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8407 | + | 5.47188i | 0.746452 | + | 0.242537i | 0.657454 | − | 0.753495i | \(-0.271633\pi\) |
0.0889982 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.02686 | − | 2.78973i | −0.0896629 | − | 0.123410i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0639 | + | 14.5773i | −0.885844 | + | 0.643604i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.9193 | + | 20.2846i | 1.23027 | + | 0.893846i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36457 | − | 0.991415i | 0.0600135 | − | 0.0436024i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.2011i | 2.51085i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.13142 | − | 0.367619i | 0.0495682 | − | 0.0161057i | −0.284128 | − | 0.958786i | \(-0.591704\pi\) |
0.333696 | + | 0.942681i | \(0.391704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.72967 | − | 11.4787i | 0.163087 | − | 0.501930i | −0.835803 | − | 0.549029i | \(-0.814998\pi\) |
0.998890 | + | 0.0470989i | \(0.0149976\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.84434 | + | 21.0647i | −0.298712 | + | 0.919340i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.61173 | − | 11.8530i | 0.375133 | − | 0.516326i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.199190 | − | 0.613043i | −0.00866043 | − | 0.0266541i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44.1909 | + | 32.1066i | 1.91772 | + | 1.39331i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.3964 | + | 2.50524i | −1.44656 | + | 0.108514i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.9053 | + | 11.5559i | 0.687646 | + | 0.499604i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.5055 | + | 63.1095i | 0.884879 | + | 2.72338i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.132160 | − | 0.181903i | 0.00569253 | − | 0.00783510i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.68004 | + | 11.3260i | −0.158217 | + | 0.486943i | −0.998473 | − | 0.0552481i | \(-0.982405\pi\) |
0.840255 | + | 0.542191i | \(0.182405\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.7358 | + | 36.1190i | −0.503631 | + | 1.55002i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 48.8235 | − | 15.8637i | 2.09137 | − | 0.679527i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.3251i | 1.04007i | 0.854146 | + | 0.520033i | \(0.174080\pi\) | ||||
−0.854146 | + | 0.520033i | \(0.825920\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −48.7802 | + | 35.4409i | −2.08189 | + | 1.51258i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53959 | − | 1.11857i | −0.0655885 | − | 0.0476529i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.85774 | − | 7.16207i | 0.419194 | − | 0.304562i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.2672 | + | 22.3899i | 0.690504 | + | 0.950398i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.6344 | − | 12.2282i | −1.59462 | − | 0.518124i | −0.628852 | − | 0.777525i | \(-0.716475\pi\) |
−0.965770 | + | 0.259401i | \(0.916475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.38812 | + | 0.775948i | −0.101007 | + | 0.0328191i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.17605 | − | 1.61870i | 0.0496530 | − | 0.0683415i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.1783 | − | 9.48062i | −1.22972 | − | 0.399560i | −0.379107 | − | 0.925353i | \(-0.623769\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.4018 | −1.74179 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.307018 | + | 0.422574i | 0.0128935 | + | 0.0177464i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.12477 | + | 25.0055i | 0.340608 | + | 1.04828i | 0.963893 | + | 0.266290i | \(0.0857977\pi\) |
−0.623285 | + | 0.781995i | \(0.714202\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.5365i | 1.44531i | 0.691211 | + | 0.722653i | \(0.257078\pi\) | ||||
−0.691211 | + | 0.722653i | \(0.742922\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −69.8093 | −2.91633 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.1856 | −1.55075 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.1300i | − | 1.00455i | −0.864709 | − | 0.502273i | \(-0.832497\pi\) | ||
0.864709 | − | 0.502273i | \(-0.167503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.82856 | + | 24.0938i | 0.325344 | + | 1.00131i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.89230 | + | 12.2392i | 0.368915 | + | 0.507768i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.284435 | 0.0117801 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 87.9783 | + | 28.5859i | 3.63746 | + | 1.18188i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.0777 | + | 18.0000i | −0.539776 | + | 0.742938i | −0.988581 | − | 0.150692i | \(-0.951850\pi\) |
0.448804 | + | 0.893630i | \(0.351850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1098 | + | 6.53409i | −0.828612 | + | 0.269232i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.2652 | + | 11.7833i | 1.49175 | + | 0.484700i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.8651 | − | 16.3309i | −0.487241 | − | 0.670630i | 0.492635 | − | 0.870236i | \(-0.336034\pi\) |
−0.979876 | + | 0.199606i | \(0.936034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.16892 | − | 6.66161i | 0.375889 | − | 0.273099i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.6415 | − | 7.73150i | −0.435527 | − | 0.316429i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7519 | − | 8.53827i | 0.480170 | − | 0.348864i | −0.321221 | − | 0.947004i | \(-0.604093\pi\) |
0.801392 | + | 0.598140i | \(0.204093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 32.6497i | − | 1.33181i | −0.746037 | − | 0.665905i | \(-0.768046\pi\) | ||
0.746037 | − | 0.665905i | \(-0.231954\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33.0413 | − | 10.7358i | 1.34555 | − | 0.437195i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1360 | − | 37.3507i | 0.493398 | − | 1.51852i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.36027 | − | 16.4972i | 0.217566 | − | 0.669601i | −0.781395 | − | 0.624037i | \(-0.785492\pi\) |
0.998961 | − | 0.0455639i | \(-0.0145085\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.690780 | + | 0.950777i | −0.0279918 | + | 0.0385274i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.1245 | − | 37.3155i | −0.490506 | − | 1.50962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.33601 | − | 6.78301i | −0.377078 | − | 0.273963i | 0.383062 | − | 0.923723i | \(-0.374870\pi\) |
−0.760140 | + | 0.649760i | \(0.774870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 55.0231 | + | 33.9962i | 2.21874 | + | 1.37086i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8528 | − | 15.1504i | −0.839501 | − | 0.609933i | 0.0827305 | − | 0.996572i | \(-0.473636\pi\) |
−0.922231 | + | 0.386639i | \(0.873636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.35463 | + | 4.16914i | 0.0544474 | + | 0.167572i | 0.974582 | − | 0.224030i | \(-0.0719212\pi\) |
−0.920135 | + | 0.391601i | \(0.871921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.1139 | + | 20.8025i | −0.606501 | + | 0.834777i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.46430 | + | 7.58433i | −0.0987300 | + | 0.303860i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.763206 | + | 2.34891i | −0.0305282 | + | 0.0939563i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.74628 | + | 0.892321i | −0.109676 | + | 0.0356359i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.65742i | − | 0.345194i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8654 | − | 26.0577i | 1.42778 | − | 1.03734i | 0.437354 | − | 0.899289i | \(-0.355916\pi\) |
0.990425 | − | 0.138053i | \(-0.0440843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.5464 | + | 16.3809i | 0.896137 | + | 0.651082i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.8409 | + | 18.0480i | −0.985781 | + | 0.716212i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.07430 | − | 4.23140i | −0.121808 | − | 0.167654i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −54.7606 | − | 17.7928i | −2.16630 | − | 0.703872i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5795 | − | 5.06209i | 0.615353 | − | 0.199940i | 0.0152771 | − | 0.999883i | \(-0.495137\pi\) |
0.600076 | + | 0.799943i | \(0.295137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.76286 | − | 2.42637i | 0.0695205 | − | 0.0956867i | −0.772841 | − | 0.634600i | \(-0.781165\pi\) |
0.842361 | + | 0.538913i | \(0.181165\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.61207 | + | 1.49855i | 0.181600 | + | 0.0590055i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.5087 | 1.82845 | 0.914223 | − | 0.405211i | \(-0.132802\pi\) | ||||
0.914223 | + | 0.405211i | \(0.132802\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.46397 | + | 2.01499i | 0.0574660 | + | 0.0790952i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.03515 | + | 12.4189i | 0.158150 | + | 0.486736i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.17878i | 0.359193i | 0.983740 | + | 0.179597i | \(0.0574792\pi\) | ||||
−0.983740 | + | 0.179597i | \(0.942521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.92420 | 0.309624 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.0038 | 0.663383 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 37.4362i | − | 1.45831i | −0.684349 | − | 0.729154i | \(-0.739914\pi\) | ||
0.684349 | − | 0.729154i | \(-0.260086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.78564 | − | 11.6510i | −0.147244 | − | 0.453172i | 0.850048 | − | 0.526705i | \(-0.176573\pi\) |
−0.997293 | + | 0.0735330i | \(0.976573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.3572 | − | 37.6540i | −1.06247 | − | 1.46236i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.3565 | −0.634279 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.87652 | − | 0.609717i | −0.0726590 | − | 0.0236084i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.2265 | − | 42.9796i | 1.20729 | − | 1.66169i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.61476 | + | 0.849586i | −0.100942 | + | 0.0327979i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.86293 | − | 0.605304i | −0.0718108 | − | 0.0233328i | 0.272891 | − | 0.962045i | \(-0.412020\pi\) |
−0.344702 | + | 0.938712i | \(0.612020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.1402 | − | 34.6025i | −0.967648 | − | 1.33185i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.8596 | + | 10.0696i | −0.532668 | + | 0.387006i | −0.821355 | − | 0.570418i | \(-0.806781\pi\) |
0.288687 | + | 0.957424i | \(0.406781\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.19341 | + | 4.49977i | 0.237681 | + | 0.172685i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 43.5986 | − | 31.6762i | 1.67070 | − | 1.21384i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.3586i | − | 0.587680i | −0.955855 | − | 0.293840i | \(-0.905067\pi\) | ||
0.955855 | − | 0.293840i | \(-0.0949333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5565 | − | 6.02938i | 0.709008 | − | 0.230371i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.8304 | + | 33.3325i | −0.413205 | + | 1.27171i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.04461 | − | 6.29266i | 0.0778934 | − | 0.239731i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1798 | − | 16.7641i | 0.463342 | − | 0.637735i | −0.511856 | − | 0.859071i | \(-0.671042\pi\) |
0.975198 | + | 0.221336i | \(0.0710418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.342615 | + | 1.05446i | 0.0130149 | + | 0.0400556i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −25.3614 | − | 18.4261i | −0.962012 | − | 0.698943i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.67413 | − | 18.7208i | −0.290679 | − | 0.709100i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.3441 | − | 19.1401i | −0.996424 | − | 0.723945i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.35289 | − | 7.24147i | −0.0888676 | − | 0.273506i | 0.896739 | − | 0.442559i | \(-0.145929\pi\) |
−0.985607 | + | 0.169053i | \(0.945929\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.34409 | + | 10.1083i | −0.276987 | + | 0.381241i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.4155 | + | 72.0656i | −0.881881 | + | 2.71415i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.00134 | + | 9.23718i | −0.112877 | + | 0.347400i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.4560 | − | 14.7696i | 1.70714 | − | 0.554682i | 0.717284 | − | 0.696780i | \(-0.245385\pi\) |
0.989853 | + | 0.142098i | \(0.0453848\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 60.0844i | 2.25334i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.7362 | + | 12.8861i | −0.664225 | + | 0.482588i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.41245 | + | 2.47929i | 0.127618 | + | 0.0927201i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.8970 | + | 10.8233i | −0.556337 | + | 0.404203i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.56657 | − | 10.4145i | −0.282185 | − | 0.388395i | 0.644271 | − | 0.764797i | \(-0.277161\pi\) |
−0.926456 | + | 0.376403i | \(0.877161\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.15069 | + | 2.97324i | 0.340789 | + | 0.110729i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 70.6415 | − | 22.9528i | 2.62718 | − | 0.853624i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.92911 | − | 2.65519i | 0.0716453 | − | 0.0986113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.9096 | − | 11.3428i | −1.29472 | − | 0.420681i | −0.420981 | − | 0.907069i | \(-0.638314\pi\) |
−0.873743 | + | 0.486388i | \(0.838314\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.3711 | 1.60634 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.891666 | − | 1.22727i | −0.0329795 | − | 0.0453924i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.00841 | − | 18.4920i | −0.221926 | − | 0.683017i | −0.998589 | − | 0.0531013i | \(-0.983089\pi\) |
0.776663 | − | 0.629916i | \(-0.216911\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.1010i | 0.372583i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.58413 | 0.0583521 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.9961 | 0.735569 | 0.367784 | − | 0.929911i | \(-0.380116\pi\) | ||||
0.367784 | + | 0.929911i | \(0.380116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 67.1714i | 2.46760i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.4902 | + | 47.6740i | 0.568281 | + | 1.74899i | 0.657996 | + | 0.753021i | \(0.271404\pi\) |
−0.0897153 | + | 0.995967i | \(0.528596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3174 | − | 32.0937i | −0.854284 | − | 1.17582i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −74.5999 | −2.72947 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.21303 | + | 1.69382i | 0.190480 | + | 0.0618907i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5232 | − | 17.2368i | 0.456980 | − | 0.628979i | −0.516899 | − | 0.856046i | \(-0.672914\pi\) |
0.973879 | + | 0.227068i | \(0.0729138\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62.2468 | − | 20.2252i | 2.26840 | − | 0.737048i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 70.0900 | + | 22.7736i | 2.55084 | + | 0.828817i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.08626 | − | 4.24787i | −0.112172 | − | 0.154391i | 0.749240 | − | 0.662299i | \(-0.230419\pi\) |
−0.861412 | + | 0.507908i | \(0.830419\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.42212 | + | 1.75978i | −0.0879176 | + | 0.0638758i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.4646 | + | 15.5949i | 0.778090 | + | 0.565315i | 0.904405 | − | 0.426675i | \(-0.140315\pi\) |
−0.126315 | + | 0.991990i | \(0.540315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.5792 | − | 8.41281i | 0.419196 | − | 0.304564i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 55.8860i | 2.02056i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 55.1019 | − | 17.9037i | 1.98961 | − | 0.646465i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4719 | + | 32.2292i | −0.377626 | + | 1.16221i | 0.564063 | + | 0.825731i | \(0.309237\pi\) |
−0.941690 | + | 0.336483i | \(0.890763\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.1729 | − | 37.4642i | 0.438395 | − | 1.34924i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.8034 | + | 18.9987i | −0.496473 | + | 0.683337i | −0.981565 | − | 0.191126i | \(-0.938786\pi\) |
0.485092 | + | 0.874463i | \(0.338786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.2688 | − | 34.6817i | −0.404786 | − | 1.24580i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.24240 | + | 4.53537i | 0.223945 | + | 0.162706i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.92062 | + | 28.3680i | −0.247957 | + | 1.01639i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.12402 | − | 1.54319i | −0.0760034 | − | 0.0552197i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.701301 | − | 2.15838i | −0.0250625 | − | 0.0771343i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 35.0511 | − | 48.2437i | 1.25103 | − | 1.72189i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.24017 | − | 19.2053i | 0.222438 | − | 0.684594i | −0.776104 | − | 0.630606i | \(-0.782807\pi\) |
0.998542 | − | 0.0539884i | \(-0.0171934\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.44654 | + | 16.7627i | −0.193902 | + | 0.596769i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9780 | + | 3.56698i | −0.390334 | + | 0.126827i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.9544i | 2.27109i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.3377 | + | 7.51080i | −0.366641 | + | 0.266381i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.41203 | − | 1.75244i | −0.0854385 | − | 0.0620747i | 0.544246 | − | 0.838926i | \(-0.316816\pi\) |
−0.629684 | + | 0.776851i | \(0.716816\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.1767 | − | 13.9327i | 0.678422 | − | 0.492903i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.1138 | − | 31.8134i | −0.816687 | − | 1.12407i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.737382 | + | 0.239590i | 0.0260216 | + | 0.00845494i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.1286 | + | 5.24051i | −0.568460 | + | 0.184704i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35.6028 | − | 49.0031i | 1.25328 | − | 1.72499i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.85232 | + | 0.926774i | 0.100282 | + | 0.0325836i | 0.358728 | − | 0.933442i | \(-0.383210\pi\) |
−0.258446 | + | 0.966026i | \(0.583210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6202 | 0.443156 | 0.221578 | − | 0.975143i | \(-0.428879\pi\) | ||||
0.221578 | + | 0.975143i | \(0.428879\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3542 | + | 21.1332i | 0.538495 | + | 0.741175i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.5212 | + | 57.0023i | 0.648768 | + | 1.99670i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.18935i | 0.0765955i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 25.7911 | 0.901213 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.3732 | −1.23453 | −0.617267 | − | 0.786754i | \(-0.711760\pi\) | ||||
−0.617267 | + | 0.786754i | \(0.711760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 21.0341i | − | 0.733203i | −0.930378 | − | 0.366602i | \(-0.880521\pi\) | ||
0.930378 | − | 0.366602i | \(-0.119479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.53891 | − | 4.73628i | −0.0535780 | − | 0.164896i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.8384 | − | 16.2941i | −0.411661 | − | 0.566603i | 0.551962 | − | 0.833870i | \(-0.313879\pi\) |
−0.963623 | + | 0.267267i | \(0.913879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.6755 | 1.48218 | 0.741091 | − | 0.671405i | \(-0.234309\pi\) | ||||
0.741091 | + | 0.671405i | \(0.234309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.5912 | + | 17.0879i | 1.82437 | + | 0.592773i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.85729 | − | 2.55634i | 0.0643512 | − | 0.0885718i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.4243 | + | 6.63625i | −0.706811 | + | 0.229657i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.9820 | − | 7.79221i | −0.828938 | − | 0.269338i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.4428 | + | 39.1482i | 0.981955 | + | 1.35155i | 0.935769 | + | 0.352612i | \(0.114707\pi\) |
0.0461856 | + | 0.998933i | \(0.485293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.3206 | + | 16.9434i | −0.804159 | + | 0.584256i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −68.5666 | − | 49.8165i | −2.36156 | − | 1.71577i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 41.6575 | − | 30.2660i | 1.43306 | − | 1.04118i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.9494i | − | 0.376227i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −62.2889 | + | 20.2389i | −2.13775 | + | 0.694597i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00315 | + | 12.3204i | −0.137226 | + | 0.422339i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.2637 | + | 46.9769i | −0.522620 | + | 1.60846i | 0.246355 | + | 0.969180i | \(0.420767\pi\) |
−0.768975 | + | 0.639279i | \(0.779233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47.4081 | − | 65.2516i | 1.62132 | − | 2.23156i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.2874 | + | 47.0498i | 0.522208 | + | 1.60719i | 0.769773 | + | 0.638318i | \(0.220370\pi\) |
−0.247565 | + | 0.968871i | \(0.579630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7120 | − | 14.3216i | −0.672564 | − | 0.488647i | 0.198318 | − | 0.980138i | \(-0.436452\pi\) |
−0.870883 | + | 0.491491i | \(0.836452\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.5188 | + | 4.27386i | 0.597039 | + | 0.145653i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.33000 | − | 5.32556i | −0.249516 | − | 0.181284i | 0.455996 | − | 0.889982i | \(-0.349283\pi\) |
−0.705512 | + | 0.708698i | \(0.749283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.5123 | − | 69.2858i | −0.765442 | − | 2.35579i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.6132 | + | 15.9842i | −0.394404 | + | 0.542851i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.846610 | + | 2.60560i | −0.0287193 | + | 0.0883888i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.3872 | − | 35.0463i | 0.385842 | − | 1.18750i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.9022 | + | 11.6653i | −1.21510 | + | 0.394811i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 10.2750i | − | 0.347359i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.1004 | − | 10.2445i | 0.476136 | − | 0.345933i | −0.323692 | − | 0.946163i | \(-0.604924\pi\) |
0.799828 | + | 0.600230i | \(0.204924\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1807 | + | 7.39671i | 0.343386 | + | 0.249485i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.8614 | − | 19.5160i | 0.904984 | − | 0.657510i | −0.0347569 | − | 0.999396i | \(-0.511066\pi\) |
0.939741 | + | 0.341886i | \(0.111066\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.7369 | + | 21.6599i | 0.529588 | + | 0.728915i | 0.987068 | − | 0.160305i | \(-0.0512477\pi\) |
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −106.416 | − | 34.5766i | −3.57713 | − | 1.16228i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.6502 | − | 3.78538i | 0.391176 | − | 0.127101i | −0.106824 | − | 0.994278i | \(-0.534068\pi\) |
0.498000 | + | 0.867177i | \(0.334068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.03185 | + | 6.92575i | −0.168763 | + | 0.232282i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.111695 | − | 0.0362918i | −0.00374192 | − | 0.00121582i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.2095 | −1.14478 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.6754 | − | 68.3723i | −1.66046 | − | 2.28543i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.5212 | + | 66.2355i | 0.718572 | + | 2.21154i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1.93493i | − | 0.0645337i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.99725 | 0.133168 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.35204 | 0.0449931 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 48.3686i | − | 1.60783i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.4776 | − | 47.6352i | −0.513926 | − | 1.58170i | −0.785227 | − | 0.619207i | \(-0.787454\pi\) |
0.271301 | − | 0.962494i | \(-0.412546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.1510 | − | 38.7466i | −0.933711 | − | 1.28514i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.3036 | −1.40158 | −0.700790 | − | 0.713367i | \(-0.747169\pi\) | ||||
−0.700790 | + | 0.713367i | \(0.747169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.23507 | − | 1.05114i | −0.107065 | − | 0.0347876i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 72.5987 | − | 99.9235i | 2.40004 | − | 3.30337i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.10117 | − | 0.682712i | 0.0693868 | − | 0.0225451i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.7521 | + | 4.79326i | 0.486628 | + | 0.158115i | 0.542047 | − | 0.840348i | \(-0.317650\pi\) |
−0.0554192 | + | 0.998463i | \(0.517650\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.3831 | + | 34.9368i | 0.836400 | + | 1.15121i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.4088 | + | 35.8976i | −1.62631 | + | 1.18158i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.4329 | − | 12.6657i | −0.573189 | − | 0.416446i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.3837 | + | 27.8874i | −1.26069 | + | 0.915943i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.644184i | 0.0211350i | 0.999944 | + | 0.0105675i | \(0.00336380\pi\) | ||||
−0.999944 | + | 0.0105675i | \(0.996636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.33708 | + | 1.40920i | −0.142142 | + | 0.0461848i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.14571 | − | 28.1476i | 0.299417 | − | 0.921512i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.787452 | + | 2.42353i | −0.0257524 | + | 0.0792579i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.5107 | + | 47.4998i | −1.12741 | + | 1.55175i | −0.334525 | + | 0.942387i | \(0.608576\pi\) |
−0.792889 | + | 0.609365i | \(0.791424\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.9660 | − | 76.8376i | −0.814736 | − | 2.50750i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.3822 | + | 11.1758i | 0.501446 | + | 0.364322i | 0.809569 | − | 0.587025i | \(-0.199701\pi\) |
−0.308123 | + | 0.951347i | \(0.599701\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.26471 | + | 30.1901i | 0.0737492 | + | 0.983125i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.7807 | − | 11.4653i | −0.513345 | − | 0.372967i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.36525 | − | 4.20181i | −0.0443647 | − | 0.136540i | 0.926421 | − | 0.376490i | \(-0.122869\pi\) |
−0.970785 | + | 0.239950i | \(0.922869\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.6011 | − | 14.5911i | 0.344126 | − | 0.473648i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.0604 | − | 40.1957i | 0.423511 | − | 1.30343i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.67452 | + | 17.4644i | −0.183816 | + | 0.565727i | −0.999926 | − | 0.0121696i | \(-0.996126\pi\) |
0.816110 | + | 0.577896i | \(0.196126\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84.5578 | − | 27.4745i | 2.73623 | − | 0.889054i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.264242i | − | 0.00854174i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.40096 | − | 3.19749i | 0.142114 | − | 0.103252i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.68630 | + | 5.58443i | 0.247945 | + | 0.180143i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −21.8667 | + | 15.8871i | −0.704646 | + | 0.511955i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.9650 | − | 26.1031i | −0.610504 | − | 0.840287i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6199 | + | 3.45061i | 0.341512 | + | 0.110964i | 0.474752 | − | 0.880120i | \(-0.342538\pi\) |
−0.133239 | + | 0.991084i | \(0.542538\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.5944 | + | 12.5401i | −1.23983 | + | 0.402845i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.5001 | − | 26.8395i | 0.625787 | − | 0.861322i | −0.371971 | − | 0.928244i | \(-0.621318\pi\) |
0.997758 | + | 0.0669224i | \(0.0213180\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.31230 | − | 2.70083i | −0.266480 | − | 0.0865847i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −115.845 | −3.71000 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.6750 | − | 22.9512i | −0.533482 | − | 0.734275i | 0.454174 | − | 0.890913i | \(-0.349934\pi\) |
−0.987656 | + | 0.156638i | \(0.949934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.554082 | − | 1.70529i | −0.0177086 | − | 0.0545013i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 70.5772i | 2.25336i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.4078 | 0.587119 | 0.293559 | − | 0.955941i | \(-0.405160\pi\) | ||||
0.293559 | + | 0.955941i | \(0.405160\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.5644 | −1.54739 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.1262i | 0.672455i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.701450 | + | 2.15884i | 0.0223048 | + | 0.0686472i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1531 | − | 29.1147i | −0.671950 | − | 0.924860i | 0.327852 | − | 0.944729i | \(-0.393675\pi\) |
−0.999803 | + | 0.0198687i | \(0.993675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −74.8375 | −2.37490 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.9325 | + | 5.17680i | 0.505096 | + | 0.164116i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.4321 | − | 33.6280i | 0.773774 | − | 1.06501i | −0.222168 | − | 0.975008i | \(-0.571313\pi\) |
0.995942 | − | 0.0899996i | \(-0.0286866\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.1710 | + | 4.60445i | −0.448352 | + | 0.145678i |
(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 | 1148.2.ba.a.113.2 | ✓ | 80 | |
41.4 | even | 10 | inner | 1148.2.ba.a.701.19 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.ba.a.113.2 | ✓ | 80 | 1.1 | even | 1 | trivial | |
1148.2.ba.a.701.19 | yes | 80 | 41.4 | even | 10 | inner |