Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,2,Mod(149,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.ba (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: | \(6.38803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 549.10 | ||
Character | \(\chi\) | \(=\) | 800.549 |
Dual form | 800.2.ba.f.749.10 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.315126 | + | 1.37866i | 0.222827 | + | 0.974858i | ||||
\(3\) | −3.12667 | + | 1.29511i | −1.80518 | + | 0.747731i | −0.820913 | + | 0.571053i | \(0.806535\pi\) |
−0.984269 | + | 0.176678i | \(0.943465\pi\) | |||||||
\(4\) | −1.80139 | + | 0.868900i | −0.900696 | + | 0.434450i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.77080 | − | 3.90248i | −1.13118 | − | 1.59318i | ||||
\(7\) | 1.02642 | − | 1.02642i | 0.387952 | − | 0.387952i | −0.486004 | − | 0.873956i | \(-0.661546\pi\) |
0.873956 | + | 0.486004i | \(0.161546\pi\) | |||||||
\(8\) | −1.76558 | − | 2.20969i | −0.624227 | − | 0.781243i | ||||
\(9\) | 5.97742 | − | 5.97742i | 1.99247 | − | 1.99247i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.473788 | − | 1.14383i | 0.142853 | − | 0.344876i | −0.836218 | − | 0.548397i | \(-0.815238\pi\) |
0.979071 | + | 0.203520i | \(0.0652383\pi\) | |||||||
\(12\) | 4.50703 | − | 5.04976i | 1.30107 | − | 1.45774i | ||||
\(13\) | 2.14423 | + | 5.17663i | 0.594703 | + | 1.43574i | 0.878915 | + | 0.476979i | \(0.158268\pi\) |
−0.284212 | + | 0.958761i | \(0.591732\pi\) | |||||||
\(14\) | 1.73854 | + | 1.09164i | 0.464645 | + | 0.291752i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49002 | − | 3.13046i | 0.622506 | − | 0.782615i | ||||
\(17\) | 4.22533 | 1.02479 | 0.512396 | − | 0.858749i | \(-0.328758\pi\) | ||||
0.512396 | + | 0.858749i | \(0.328758\pi\) | |||||||
\(18\) | 10.1245 | + | 6.35718i | 2.38636 | + | 1.49840i | ||||
\(19\) | 3.63519 | − | 1.50574i | 0.833969 | − | 0.345441i | 0.0754966 | − | 0.997146i | \(-0.475946\pi\) |
0.758473 | + | 0.651705i | \(0.225946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.87996 | + | 4.53862i | −0.410240 | + | 0.990408i | ||||
\(22\) | 1.72625 | + | 0.292743i | 0.368037 | + | 0.0624130i | ||||
\(23\) | −5.53379 | − | 5.53379i | −1.15388 | − | 1.15388i | −0.985769 | − | 0.168107i | \(-0.946235\pi\) |
−0.168107 | − | 0.985769i | \(-0.553765\pi\) | |||||||
\(24\) | 8.38217 | + | 4.62234i | 1.71100 | + | 0.943532i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.46110 | + | 4.58745i | −1.26713 | + | 0.899673i | ||||
\(27\) | −7.06268 | + | 17.0508i | −1.35921 | + | 3.28143i | ||||
\(28\) | −0.957132 | + | 2.74085i | −0.180881 | + | 0.517973i | ||||
\(29\) | −0.848854 | − | 2.04932i | −0.157628 | − | 0.380548i | 0.825259 | − | 0.564754i | \(-0.191029\pi\) |
−0.982888 | + | 0.184205i | \(0.941029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.964876 | −0.173297 | −0.0866484 | − | 0.996239i | \(-0.527616\pi\) | ||||
−0.0866484 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(32\) | 5.10050 | + | 2.44640i | 0.901650 | + | 0.432467i | ||||
\(33\) | 4.18997i | 0.729380i | ||||||||
\(34\) | 1.33151 | + | 5.82528i | 0.228352 | + | 0.999027i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.57389 | + | 15.9615i | −0.928982 | + | 2.66024i | ||||
\(37\) | 0.998488 | − | 2.41056i | 0.164150 | − | 0.396294i | −0.820306 | − | 0.571925i | \(-0.806197\pi\) |
0.984456 | + | 0.175631i | \(0.0561967\pi\) | |||||||
\(38\) | 3.22145 | + | 4.53718i | 0.522588 | + | 0.736028i | ||||
\(39\) | −13.4086 | − | 13.4086i | −2.14709 | − | 2.14709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.62808 | − | 4.62808i | 0.722785 | − | 0.722785i | −0.246387 | − | 0.969172i | \(-0.579243\pi\) |
0.969172 | + | 0.246387i | \(0.0792434\pi\) | |||||||
\(42\) | −6.84962 | − | 1.16158i | −1.05692 | − | 0.179236i | ||||
\(43\) | 0.951273 | + | 0.394030i | 0.145068 | + | 0.0600890i | 0.454036 | − | 0.890983i | \(-0.349984\pi\) |
−0.308968 | + | 0.951072i | \(0.599984\pi\) | |||||||
\(44\) | 0.140393 | + | 2.47215i | 0.0211650 | + | 0.372691i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.88536 | − | 9.37304i | 0.867750 | − | 1.38198i | ||||
\(47\) | 2.36232 | 0.344580 | 0.172290 | − | 0.985046i | \(-0.444883\pi\) | ||||
0.172290 | + | 0.985046i | \(0.444883\pi\) | |||||||
\(48\) | −3.73119 | + | 13.0128i | −0.538551 | + | 1.87823i | ||||
\(49\) | 4.89290i | 0.698986i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.2112 | + | 5.47226i | −1.84994 | + | 0.766269i | ||||
\(52\) | −8.36058 | − | 7.46202i | −1.15940 | − | 1.03480i | ||||
\(53\) | 3.65259 | + | 1.51295i | 0.501722 | + | 0.207820i | 0.619167 | − | 0.785259i | \(-0.287470\pi\) |
−0.117445 | + | 0.993079i | \(0.537470\pi\) | |||||||
\(54\) | −25.7329 | − | 4.36386i | −3.50180 | − | 0.593847i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.08032 | − | 0.455844i | −0.545255 | − | 0.0609147i | ||||
\(57\) | −9.41592 | + | 9.41592i | −1.24717 | + | 1.24717i | ||||
\(58\) | 2.55781 | − | 1.81607i | 0.335857 | − | 0.238462i | ||||
\(59\) | 0.648566 | + | 0.268645i | 0.0844361 | + | 0.0349746i | 0.424502 | − | 0.905427i | \(-0.360449\pi\) |
−0.340066 | + | 0.940402i | \(0.610449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01738 | + | 7.28461i | 0.386336 | + | 0.932698i | 0.990709 | + | 0.135997i | \(0.0434237\pi\) |
−0.604373 | + | 0.796701i | \(0.706576\pi\) | |||||||
\(62\) | −0.304057 | − | 1.33023i | −0.0386153 | − | 0.168940i | ||||
\(63\) | − | 12.2708i | − | 1.54597i | ||||||
\(64\) | −1.76545 | + | 7.80277i | −0.220681 | + | 0.975346i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.77653 | + | 1.32037i | −0.711042 | + | 0.162526i | ||||
\(67\) | 1.65215 | − | 0.684344i | 0.201843 | − | 0.0836059i | −0.279472 | − | 0.960154i | \(-0.590159\pi\) |
0.481315 | + | 0.876548i | \(0.340159\pi\) | |||||||
\(68\) | −7.61147 | + | 3.67139i | −0.923027 | + | 0.445222i | ||||
\(69\) | 24.4692 | + | 10.1355i | 2.94574 | + | 1.22017i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.24109 | + | 6.24109i | 0.740681 | + | 0.740681i | 0.972709 | − | 0.232028i | \(-0.0745362\pi\) |
−0.232028 | + | 0.972709i | \(0.574536\pi\) | |||||||
\(72\) | −23.7619 | − | 2.65462i | −2.80036 | − | 0.312850i | ||||
\(73\) | −5.70275 | − | 5.70275i | −0.667457 | − | 0.667457i | 0.289670 | − | 0.957127i | \(-0.406454\pi\) |
−0.957127 | + | 0.289670i | \(0.906454\pi\) | |||||||
\(74\) | 3.63799 | + | 0.616942i | 0.422908 | + | 0.0717181i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.24006 | + | 5.87105i | −0.601076 | + | 0.673456i | ||||
\(77\) | −0.687743 | − | 1.66036i | −0.0783756 | − | 0.189216i | ||||
\(78\) | 14.2605 | − | 22.7113i | 1.61468 | − | 2.57154i | ||||
\(79\) | 14.9022i | 1.67663i | 0.545186 | + | 0.838315i | \(0.316459\pi\) | ||||
−0.545186 | + | 0.838315i | \(0.683541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 37.0991i | − | 4.12212i | ||||||
\(82\) | 7.83896 | + | 4.92211i | 0.865669 | + | 0.543556i | ||||
\(83\) | 1.38975 | + | 3.35516i | 0.152545 | + | 0.368277i | 0.981616 | − | 0.190867i | \(-0.0611299\pi\) |
−0.829071 | + | 0.559144i | \(0.811130\pi\) | |||||||
\(84\) | −0.557068 | − | 9.80933i | −0.0607811 | − | 1.07029i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.243462 | + | 1.43565i | −0.0262532 | + | 0.154810i | ||||
\(87\) | 5.30817 | + | 5.30817i | 0.569096 | + | 0.569096i | ||||
\(88\) | −3.36401 | + | 0.972592i | −0.358605 | + | 0.103679i | ||||
\(89\) | 9.90375 | + | 9.90375i | 1.04980 | + | 1.04980i | 0.998693 | + | 0.0511025i | \(0.0162735\pi\) |
0.0511025 | + | 0.998693i | \(0.483726\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.51432 | + | 3.11253i | 0.787715 | + | 0.326282i | ||||
\(92\) | 14.7768 | + | 5.16021i | 1.54059 | + | 0.537989i | ||||
\(93\) | 3.01685 | − | 1.24962i | 0.312832 | − | 0.129579i | ||||
\(94\) | 0.744427 | + | 3.25683i | 0.0767818 | + | 0.335916i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.1159 | − | 1.04338i | −1.95101 | − | 0.106490i | ||||
\(97\) | − | 13.1798i | − | 1.33820i | −0.743171 | − | 0.669101i | \(-0.766679\pi\) | ||
0.743171 | − | 0.669101i | \(-0.233321\pi\) | |||||||
\(98\) | −6.74564 | + | 1.54188i | −0.681412 | + | 0.155753i | ||||
\(99\) | −4.00510 | − | 9.66916i | −0.402528 | − | 0.971787i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.67079 | + | 1.52049i | 0.365257 | + | 0.151295i | 0.557761 | − | 0.830002i | \(-0.311661\pi\) |
−0.192503 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(102\) | −11.7076 | − | 16.4893i | −1.15922 | − | 1.63268i | ||||
\(103\) | 5.18393 | − | 5.18393i | 0.510788 | − | 0.510788i | −0.403980 | − | 0.914768i | \(-0.632374\pi\) |
0.914768 | + | 0.403980i | \(0.132374\pi\) | |||||||
\(104\) | 7.65294 | − | 13.8779i | 0.750432 | − | 1.36084i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.934818 | + | 5.51244i | −0.0907975 | + | 0.535415i | ||||
\(107\) | 10.3254 | + | 4.27693i | 0.998197 | + | 0.413467i | 0.821136 | − | 0.570733i | \(-0.193341\pi\) |
0.177061 | + | 0.984200i | \(0.443341\pi\) | |||||||
\(108\) | −2.09281 | − | 36.8520i | −0.201381 | − | 3.54608i | ||||
\(109\) | −12.7925 | + | 5.29882i | −1.22530 | + | 0.507534i | −0.899090 | − | 0.437764i | \(-0.855771\pi\) |
−0.326207 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.83018i | 0.838123i | ||||||||
\(112\) | −0.657360 | − | 5.76901i | −0.0621146 | − | 0.545120i | ||||
\(113\) | 6.33910 | 0.596332 | 0.298166 | − | 0.954514i | \(-0.403625\pi\) | ||||
0.298166 | + | 0.954514i | \(0.403625\pi\) | |||||||
\(114\) | −15.9485 | − | 10.0141i | −1.49372 | − | 0.937909i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.30977 | + | 2.95405i | 0.307305 | + | 0.274277i | ||||
\(117\) | 43.7599 | + | 18.1259i | 4.04561 | + | 1.67574i | ||||
\(118\) | −0.165989 | + | 0.978807i | −0.0152806 | + | 0.0901065i | ||||
\(119\) | 4.33698 | − | 4.33698i | 0.397571 | − | 0.397571i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.69431 | + | 6.69431i | 0.608574 | + | 0.608574i | ||||
\(122\) | −9.09212 | + | 6.45550i | −0.823162 | + | 0.584454i | ||||
\(123\) | −8.47660 | + | 20.4643i | −0.764310 | + | 1.84521i | ||||
\(124\) | 1.73812 | − | 0.838381i | 0.156088 | − | 0.0752888i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 16.9172 | − | 3.86683i | 1.50710 | − | 0.344484i | ||||
\(127\) | 11.3243i | 1.00487i | 0.864615 | + | 0.502435i | \(0.167562\pi\) | ||||
−0.864615 | + | 0.502435i | \(0.832438\pi\) | |||||||
\(128\) | −11.3137 | + | 0.0249011i | −0.999998 | + | 0.00220097i | ||||
\(129\) | −3.48462 | −0.306804 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.92584 | − | 7.06361i | −0.255632 | − | 0.617151i | 0.743008 | − | 0.669282i | \(-0.233398\pi\) |
−0.998640 | + | 0.0521319i | \(0.983398\pi\) | |||||||
\(132\) | −3.64067 | − | 7.54778i | −0.316879 | − | 0.656950i | ||||
\(133\) | 2.18571 | − | 5.27678i | 0.189526 | − | 0.457555i | ||||
\(134\) | 1.46411 | + | 2.06210i | 0.126480 | + | 0.178138i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.46016 | − | 9.33666i | −0.639703 | − | 0.800612i | ||||
\(137\) | −9.25823 | − | 9.25823i | −0.790984 | − | 0.790984i | 0.190670 | − | 0.981654i | \(-0.438934\pi\) |
−0.981654 | + | 0.190670i | \(0.938934\pi\) | |||||||
\(138\) | −6.26247 | + | 36.9286i | −0.533097 | + | 3.14357i | ||||
\(139\) | 0.956760 | − | 2.30982i | 0.0811513 | − | 0.195917i | −0.878096 | − | 0.478485i | \(-0.841186\pi\) |
0.959247 | + | 0.282568i | \(0.0911863\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.38619 | + | 3.05946i | −0.622029 | + | 0.257653i | ||||
\(142\) | −6.63759 | + | 10.5710i | −0.557014 | + | 0.887102i | ||||
\(143\) | 6.93708 | 0.580108 | ||||||||
\(144\) | −3.82816 | − | 33.5960i | −0.319013 | − | 2.79967i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.06506 | − | 9.65922i | 0.501948 | − | 0.799403i | ||||
\(147\) | −6.33684 | − | 15.2985i | −0.522654 | − | 1.26180i | ||||
\(148\) | 0.295872 | + | 5.20996i | 0.0243205 | + | 0.428256i | ||||
\(149\) | 7.06329 | − | 17.0523i | 0.578647 | − | 1.39698i | −0.315380 | − | 0.948965i | \(-0.602132\pi\) |
0.894027 | − | 0.448012i | \(-0.147868\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2469 | − | 13.2469i | 1.07802 | − | 1.07802i | 0.0813322 | − | 0.996687i | \(-0.474083\pi\) |
0.996687 | − | 0.0813322i | \(-0.0259175\pi\) | |||||||
\(152\) | −9.74545 | − | 5.37412i | −0.790460 | − | 0.435899i | ||||
\(153\) | 25.2566 | − | 25.2566i | 2.04187 | − | 2.04187i | ||||
\(154\) | 2.07234 | − | 1.47138i | 0.166994 | − | 0.118568i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 35.8049 | + | 12.5034i | 2.86668 | + | 1.00107i | ||||
\(157\) | 10.5325 | − | 4.36271i | 0.840586 | − | 0.348182i | 0.0795017 | − | 0.996835i | \(-0.474667\pi\) |
0.761085 | + | 0.648652i | \(0.224667\pi\) | |||||||
\(158\) | −20.5451 | + | 4.69607i | −1.63448 | + | 0.373599i | ||||
\(159\) | −13.3799 | −1.06109 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.3600 | −0.895297 | ||||||||
\(162\) | 51.1469 | − | 11.6909i | 4.01848 | − | 0.918522i | ||||
\(163\) | −11.9523 | + | 4.95082i | −0.936179 | + | 0.387778i | −0.798019 | − | 0.602632i | \(-0.794119\pi\) |
−0.138160 | + | 0.990410i | \(0.544119\pi\) | |||||||
\(164\) | −4.31564 | + | 12.3583i | −0.336995 | + | 0.965023i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.18767 | + | 2.97329i | −0.325026 | + | 0.230772i | ||||
\(167\) | 6.45942 | − | 6.45942i | 0.499845 | − | 0.499845i | −0.411545 | − | 0.911390i | \(-0.635011\pi\) |
0.911390 | + | 0.411545i | \(0.135011\pi\) | |||||||
\(168\) | 13.3482 | − | 3.85918i | 1.02983 | − | 0.297742i | ||||
\(169\) | −13.0074 | + | 13.0074i | −1.00057 | + | 1.00057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.7286 | − | 30.7295i | 0.973379 | − | 2.34995i | ||||
\(172\) | −2.05599 | + | 0.116759i | −0.156768 | + | 0.00890278i | ||||
\(173\) | −4.83167 | − | 11.6647i | −0.367345 | − | 0.886849i | −0.994183 | − | 0.107700i | \(-0.965651\pi\) |
0.626838 | − | 0.779149i | \(-0.284349\pi\) | |||||||
\(174\) | −5.64541 | + | 8.99089i | −0.427977 | + | 0.681598i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.40096 | − | 4.33133i | −0.180979 | − | 0.326486i | ||||
\(177\) | −2.37577 | −0.178574 | ||||||||
\(178\) | −10.5330 | + | 16.7748i | −0.789478 | + | 1.25733i | ||||
\(179\) | −1.39173 | + | 0.576474i | −0.104023 | + | 0.0430877i | −0.434088 | − | 0.900870i | \(-0.642929\pi\) |
0.330065 | + | 0.943958i | \(0.392929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.941575 | + | 2.27316i | −0.0699867 | + | 0.168963i | −0.955002 | − | 0.296599i | \(-0.904148\pi\) |
0.885016 | + | 0.465562i | \(0.154148\pi\) | |||||||
\(182\) | −1.92316 | + | 11.3405i | −0.142554 | + | 0.840615i | ||||
\(183\) | −18.8687 | − | 18.8687i | −1.39481 | − | 1.39481i | ||||
\(184\) | −2.45760 | + | 21.9983i | −0.181177 | + | 1.62174i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.67348 | + | 3.76541i | 0.196029 | + | 0.276093i | ||||
\(187\) | 2.00191 | − | 4.83304i | 0.146394 | − | 0.353427i | ||||
\(188\) | −4.25546 | + | 2.05262i | −0.310362 | + | 0.149703i | ||||
\(189\) | 10.2521 | + | 24.7507i | 0.745729 | + | 1.80035i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0923 | 1.09204 | 0.546020 | − | 0.837772i | \(-0.316142\pi\) | ||||
0.546020 | + | 0.837772i | \(0.316142\pi\) | |||||||
\(192\) | −4.58545 | − | 26.6831i | −0.330926 | − | 1.92569i | ||||
\(193\) | − | 2.95918i | − | 0.213007i | −0.994312 | − | 0.106503i | \(-0.966035\pi\) | ||
0.994312 | − | 0.106503i | \(-0.0339655\pi\) | |||||||
\(194\) | 18.1704 | − | 4.15328i | 1.30456 | − | 0.298188i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.25145 | − | 8.81404i | −0.303675 | − | 0.629574i | ||||
\(197\) | −5.14189 | + | 12.4136i | −0.366344 | + | 0.884433i | 0.627998 | + | 0.778215i | \(0.283874\pi\) |
−0.994343 | + | 0.106219i | \(0.966126\pi\) | |||||||
\(198\) | 12.0684 | − | 8.56866i | 0.857660 | − | 0.608948i | ||||
\(199\) | −7.68494 | − | 7.68494i | −0.544771 | − | 0.544771i | 0.380153 | − | 0.924924i | \(-0.375871\pi\) |
−0.924924 | + | 0.380153i | \(0.875871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.27943 | + | 4.27943i | −0.301848 | + | 0.301848i | ||||
\(202\) | −0.939476 | + | 5.53991i | −0.0661013 | + | 0.389787i | ||||
\(203\) | −2.97475 | − | 1.23218i | −0.208787 | − | 0.0864823i | ||||
\(204\) | 19.0437 | − | 21.3369i | 1.33333 | − | 1.49388i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.78045 | + | 5.51327i | 0.611763 | + | 0.384128i | ||||
\(207\) | −66.1556 | −4.59813 | ||||||||
\(208\) | 21.5444 | + | 6.17751i | 1.49384 | + | 0.428333i | ||||
\(209\) | − | 4.87143i | − | 0.336964i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.07097 | + | 1.27204i | −0.211414 | + | 0.0875707i | −0.485877 | − | 0.874027i | \(-0.661500\pi\) |
0.274463 | + | 0.961598i | \(0.411500\pi\) | |||||||
\(212\) | −7.89435 | + | 0.448317i | −0.542186 | + | 0.0307906i | ||||
\(213\) | −27.5967 | − | 11.4309i | −1.89089 | − | 0.783234i | ||||
\(214\) | −2.64262 | + | 15.5830i | −0.180646 | + | 1.06523i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 50.1467 | − | 14.4983i | 3.41205 | − | 0.986482i | ||||
\(217\) | −0.990373 | + | 0.990373i | −0.0672309 | + | 0.0672309i | ||||
\(218\) | −11.3365 | − | 15.9666i | −0.767804 | − | 1.08140i | ||||
\(219\) | 25.2163 | + | 10.4449i | 1.70396 | + | 0.705803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.06009 | + | 21.8730i | 0.609447 | + | 1.47134i | ||||
\(222\) | −12.1738 | + | 2.78262i | −0.817051 | + | 0.186757i | ||||
\(223\) | 23.3670i | 1.56477i | 0.622796 | + | 0.782384i | \(0.285996\pi\) | ||||
−0.622796 | + | 0.782384i | \(0.714004\pi\) | |||||||
\(224\) | 7.74633 | − | 2.72423i | 0.517573 | − | 0.182021i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.99761 | + | 8.73945i | 0.132879 | + | 0.581339i | ||||
\(227\) | 10.1954 | − | 4.22308i | 0.676693 | − | 0.280295i | −0.0177508 | − | 0.999842i | \(-0.505651\pi\) |
0.694444 | + | 0.719547i | \(0.255651\pi\) | |||||||
\(228\) | 8.78027 | − | 25.1433i | 0.581487 | − | 1.66515i | ||||
\(229\) | −16.7615 | − | 6.94283i | −1.10763 | − | 0.458795i | −0.247509 | − | 0.968886i | \(-0.579612\pi\) |
−0.860121 | + | 0.510090i | \(0.829612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.30069 | + | 4.30069i | 0.282965 | + | 0.282965i | ||||
\(232\) | −3.02963 | + | 5.49394i | −0.198905 | + | 0.360695i | ||||
\(233\) | 19.1508 | + | 19.1508i | 1.25461 | + | 1.25461i | 0.953631 | + | 0.300978i | \(0.0973131\pi\) |
0.300978 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(234\) | −11.1996 | + | 66.0419i | −0.732141 | + | 4.31729i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.40175 | + | 0.0796047i | −0.0912460 | + | 0.00518183i | ||||
\(237\) | −19.3000 | − | 46.5943i | −1.25367 | − | 3.02662i | ||||
\(238\) | 7.34591 | + | 4.61252i | 0.476165 | + | 0.298985i | ||||
\(239\) | − | 19.5640i | − | 1.26549i | −0.774360 | − | 0.632745i | \(-0.781928\pi\) | ||
0.774360 | − | 0.632745i | \(-0.218072\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.63126i | 0.298325i | 0.988813 | + | 0.149163i | \(0.0476578\pi\) | ||||
−0.988813 | + | 0.149163i | \(0.952342\pi\) | |||||||
\(242\) | −7.11961 | + | 11.3387i | −0.457666 | + | 0.728880i | ||||
\(243\) | 26.8593 | + | 64.8441i | 1.72302 | + | 4.15975i | ||||
\(244\) | −11.7651 | − | 10.5006i | −0.753182 | − | 0.672233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.8845 | − | 5.23750i | −1.96912 | − | 0.333931i | ||||
\(247\) | 15.5894 | + | 15.5894i | 0.991928 | + | 0.991928i | ||||
\(248\) | 1.70357 | + | 2.13208i | 0.108177 | + | 0.135387i | ||||
\(249\) | −8.69060 | − | 8.69060i | −0.550744 | − | 0.550744i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7556 | + | 4.45513i | 0.678890 | + | 0.281205i | 0.695363 | − | 0.718659i | \(-0.255244\pi\) |
−0.0164729 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(252\) | 10.6621 | + | 22.1044i | 0.671647 | + | 1.39245i | ||||
\(253\) | −8.95154 | + | 3.70785i | −0.562779 | + | 0.233111i | ||||
\(254\) | −15.6123 | + | 3.56858i | −0.979605 | + | 0.223913i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.59956 | − | 15.5898i | −0.224973 | − | 0.974365i | ||||
\(257\) | − | 4.04829i | − | 0.252525i | −0.991997 | − | 0.126263i | \(-0.959702\pi\) | ||
0.991997 | − | 0.126263i | \(-0.0402982\pi\) | |||||||
\(258\) | −1.09809 | − | 4.80410i | −0.0683644 | − | 0.299090i | ||||
\(259\) | −1.44939 | − | 3.49914i | −0.0900607 | − | 0.217426i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.3236 | − | 7.17567i | −1.07230 | − | 0.444163i | ||||
\(262\) | 8.81629 | − | 6.25966i | 0.544672 | − | 0.386723i | ||||
\(263\) | 1.60540 | − | 1.60540i | 0.0989933 | − | 0.0989933i | −0.655876 | − | 0.754869i | \(-0.727700\pi\) |
0.754869 | + | 0.655876i | \(0.227700\pi\) | |||||||
\(264\) | 9.25853 | − | 7.39773i | 0.569823 | − | 0.455299i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.96365 | + | 1.35050i | 0.488283 | + | 0.0828046i | ||||
\(267\) | −43.7922 | − | 18.1393i | −2.68004 | − | 1.11011i | ||||
\(268\) | −2.38155 | + | 2.66833i | −0.145476 | + | 0.162994i | ||||
\(269\) | −3.38365 | + | 1.40155i | −0.206305 | + | 0.0854542i | −0.483443 | − | 0.875376i | \(-0.660614\pi\) |
0.277138 | + | 0.960830i | \(0.410614\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.4256i | 1.36226i | 0.732165 | + | 0.681128i | \(0.238510\pi\) | ||||
−0.732165 | + | 0.681128i | \(0.761490\pi\) | |||||||
\(272\) | 10.5212 | − | 13.2272i | 0.637940 | − | 0.802018i | ||||
\(273\) | −27.5258 | −1.66594 | ||||||||
\(274\) | 9.84642 | − | 15.6814i | 0.594844 | − | 0.947350i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −52.8853 | + | 3.00334i | −3.18332 | + | 0.180780i | ||||
\(277\) | −5.32210 | − | 2.20449i | −0.319774 | − | 0.132455i | 0.217022 | − | 0.976167i | \(-0.430366\pi\) |
−0.536796 | + | 0.843712i | \(0.680366\pi\) | |||||||
\(278\) | 3.48595 | + | 0.591160i | 0.209074 | + | 0.0354554i | ||||
\(279\) | −5.76747 | + | 5.76747i | −0.345289 | + | 0.345289i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81582 | + | 1.81582i | 0.108323 | + | 0.108323i | 0.759191 | − | 0.650868i | \(-0.225595\pi\) |
−0.650868 | + | 0.759191i | \(0.725595\pi\) | |||||||
\(282\) | −6.54552 | − | 9.21891i | −0.389780 | − | 0.548978i | ||||
\(283\) | 6.30082 | − | 15.2115i | 0.374545 | − | 0.904232i | −0.618423 | − | 0.785846i | \(-0.712228\pi\) |
0.992968 | − | 0.118386i | \(-0.0377720\pi\) | |||||||
\(284\) | −16.6655 | − | 5.81976i | −0.988917 | − | 0.345339i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.18605 | + | 9.56386i | 0.129264 | + | 0.565523i | ||||
\(287\) | − | 9.50075i | − | 0.560812i | ||||||
\(288\) | 45.1110 | − | 15.8647i | 2.65819 | − | 0.934835i | ||||
\(289\) | 0.853410 | 0.0502006 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.0692 | + | 41.2087i | 1.00062 | + | 2.41570i | ||||
\(292\) | 15.2280 | + | 5.31777i | 0.891152 | + | 0.311199i | ||||
\(293\) | −6.53752 | + | 15.7830i | −0.381926 | + | 0.922051i | 0.609667 | + | 0.792658i | \(0.291303\pi\) |
−0.991593 | + | 0.129394i | \(0.958697\pi\) | |||||||
\(294\) | 19.0945 | − | 13.5573i | 1.11361 | − | 0.790676i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.08951 | + | 2.04970i | −0.412069 | + | 0.119136i | ||||
\(297\) | 16.1569 | + | 16.1569i | 0.937521 | + | 0.937521i | ||||
\(298\) | 25.7351 | + | 4.36424i | 1.49079 | + | 0.252814i | ||||
\(299\) | 16.7807 | − | 40.5122i | 0.970452 | − | 2.34288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38085 | − | 0.571968i | 0.0795910 | − | 0.0329677i | ||||
\(302\) | 22.4374 | + | 14.0885i | 1.29113 | + | 0.810703i | ||||
\(303\) | −13.4465 | −0.772484 | ||||||||
\(304\) | 4.33803 | − | 15.1292i | 0.248803 | − | 0.867716i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 42.7792 | + | 26.8612i | 2.44552 | + | 1.53555i | ||||
\(307\) | −0.203315 | − | 0.490845i | −0.0116038 | − | 0.0280140i | 0.917971 | − | 0.396646i | \(-0.129826\pi\) |
−0.929575 | + | 0.368632i | \(0.879826\pi\) | |||||||
\(308\) | 2.68158 | + | 2.39338i | 0.152797 | + | 0.136375i | ||||
\(309\) | −9.49467 | + | 22.9222i | −0.540133 | + | 1.30400i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.66343 | − | 2.66343i | 0.151029 | − | 0.151029i | −0.627548 | − | 0.778578i | \(-0.715942\pi\) |
0.778578 | + | 0.627548i | \(0.215942\pi\) | |||||||
\(312\) | −5.95487 | + | 53.3028i | −0.337128 | + | 3.01768i | ||||
\(313\) | 13.7553 | − | 13.7553i | 0.777493 | − | 0.777493i | −0.201911 | − | 0.979404i | \(-0.564715\pi\) |
0.979404 | + | 0.201911i | \(0.0647150\pi\) | |||||||
\(314\) | 9.33375 | + | 13.1459i | 0.526734 | + | 0.741868i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.9485 | − | 26.8447i | −0.728413 | − | 1.51013i | ||||
\(317\) | −20.0122 | + | 8.28931i | −1.12399 | + | 0.465574i | −0.865736 | − | 0.500502i | \(-0.833149\pi\) |
−0.258259 | + | 0.966076i | \(0.583149\pi\) | |||||||
\(318\) | −4.21634 | − | 18.4462i | −0.236440 | − | 1.03441i | ||||
\(319\) | −2.74624 | −0.153760 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −37.8233 | −2.11109 | ||||||||
\(322\) | −3.57984 | − | 15.6616i | −0.199497 | − | 0.872787i | ||||
\(323\) | 15.3599 | − | 6.36227i | 0.854646 | − | 0.354006i | ||||
\(324\) | 32.2354 | + | 66.8300i | 1.79086 | + | 3.71278i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.5920 | − | 14.9180i | −0.586635 | − | 0.826234i | ||||
\(327\) | 33.1353 | − | 33.1353i | 1.83238 | − | 1.83238i | ||||
\(328\) | −18.3979 | − | 2.05537i | −1.01585 | − | 0.113489i | ||||
\(329\) | 2.42474 | − | 2.42474i | 0.133680 | − | 0.133680i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.45036 | + | 8.32990i | −0.189649 | + | 0.457853i | −0.989892 | − | 0.141823i | \(-0.954704\pi\) |
0.800243 | + | 0.599675i | \(0.204704\pi\) | |||||||
\(332\) | −5.41879 | − | 4.83641i | −0.297395 | − | 0.265432i | ||||
\(333\) | −8.44057 | − | 20.3773i | −0.462540 | − | 1.11667i | ||||
\(334\) | 10.9409 | + | 6.86980i | 0.598657 | + | 0.375899i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.52683 | + | 17.1864i | 0.519731 | + | 0.937595i | ||||
\(337\) | −12.2658 | −0.668162 | −0.334081 | − | 0.942544i | \(-0.608426\pi\) | ||||
−0.334081 | + | 0.942544i | \(0.608426\pi\) | |||||||
\(338\) | −22.0318 | − | 13.8338i | −1.19837 | − | 0.752460i | ||||
\(339\) | −19.8203 | + | 8.20982i | −1.07649 | + | 0.445896i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.457147 | + | 1.10365i | −0.0247559 | + | 0.0597660i | ||||
\(342\) | 46.3766 | + | 7.86470i | 2.50776 | + | 0.425274i | ||||
\(343\) | 12.2072 | + | 12.2072i | 0.659125 | + | 0.659125i | ||||
\(344\) | −0.808865 | − | 2.79771i | −0.0436111 | − | 0.150842i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.5590 | − | 10.3371i | 0.782698 | − | 0.555724i | ||||
\(347\) | −6.72820 | + | 16.2433i | −0.361189 | + | 0.871987i | 0.633938 | + | 0.773384i | \(0.281437\pi\) |
−0.995127 | + | 0.0986033i | \(0.968563\pi\) | |||||||
\(348\) | −14.1744 | − | 4.94982i | −0.759826 | − | 0.265338i | ||||
\(349\) | 10.6274 | + | 25.6568i | 0.568871 | + | 1.37338i | 0.902507 | + | 0.430675i | \(0.141725\pi\) |
−0.333636 | + | 0.942702i | \(0.608275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −103.410 | −5.51961 | ||||||||
\(352\) | 5.21481 | − | 4.67501i | 0.277951 | − | 0.249179i | ||||
\(353\) | − | 21.9232i | − | 1.16686i | −0.812165 | − | 0.583428i | \(-0.801711\pi\) | ||
0.812165 | − | 0.583428i | \(-0.198289\pi\) | |||||||
\(354\) | −0.748667 | − | 3.27538i | −0.0397912 | − | 0.174084i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.4459 | − | 9.23516i | −1.40163 | − | 0.489463i | ||||
\(357\) | −7.94344 | + | 19.1772i | −0.420412 | + | 1.01496i | ||||
\(358\) | −1.23333 | − | 1.73706i | −0.0651835 | − | 0.0918064i | ||||
\(359\) | −4.02137 | − | 4.02137i | −0.212240 | − | 0.212240i | 0.592978 | − | 0.805218i | \(-0.297952\pi\) |
−0.805218 | + | 0.592978i | \(0.797952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.48770 | + | 2.48770i | −0.130931 | + | 0.130931i | ||||
\(362\) | −3.43063 | − | 0.581777i | −0.180310 | − | 0.0305775i | ||||
\(363\) | −29.6007 | − | 12.2610i | −1.55364 | − | 0.643537i | ||||
\(364\) | −16.2407 | + | 0.922305i | −0.851245 | + | 0.0483419i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 20.0675 | − | 31.9595i | 1.04894 | − | 1.67055i | ||||
\(367\) | 28.1923 | 1.47163 | 0.735814 | − | 0.677183i | \(-0.236800\pi\) | ||||
0.735814 | + | 0.677183i | \(0.236800\pi\) | |||||||
\(368\) | −31.1026 | + | 3.54404i | −1.62133 | + | 0.184746i | ||||
\(369\) | − | 55.3280i | − | 2.88026i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.30204 | − | 2.19618i | 0.275268 | − | 0.114020i | ||||
\(372\) | −4.34873 | + | 4.87239i | −0.225471 | + | 0.252622i | ||||
\(373\) | 1.14096 | + | 0.472600i | 0.0590765 | + | 0.0244703i | 0.412026 | − | 0.911172i | \(-0.364821\pi\) |
−0.352950 | + | 0.935642i | \(0.614821\pi\) | |||||||
\(374\) | 7.29396 | + | 1.23693i | 0.377162 | + | 0.0639604i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.17087 | − | 5.21999i | −0.215096 | − | 0.269201i | ||||
\(377\) | 8.78842 | − | 8.78842i | 0.452627 | − | 0.452627i | ||||
\(378\) | −30.8920 | + | 21.9337i | −1.58891 | + | 1.12815i | ||||
\(379\) | 6.22454 | + | 2.57829i | 0.319733 | + | 0.132438i | 0.536777 | − | 0.843724i | \(-0.319642\pi\) |
−0.217044 | + | 0.976162i | \(0.569642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.6662 | − | 35.4073i | −0.751372 | − | 1.81397i | ||||
\(382\) | 4.75597 | + | 20.8071i | 0.243337 | + | 1.06458i | ||||
\(383\) | − | 6.12827i | − | 0.313140i | −0.987667 | − | 0.156570i | \(-0.949956\pi\) | ||
0.987667 | − | 0.156570i | \(-0.0500437\pi\) | |||||||
\(384\) | 35.3419 | − | 14.7303i | 1.80353 | − | 0.751702i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.07970 | − | 0.932514i | 0.207651 | − | 0.0474637i | ||||
\(387\) | 8.04144 | − | 3.33087i | 0.408769 | − | 0.169318i | ||||
\(388\) | 11.4519 | + | 23.7419i | 0.581382 | + | 1.20531i | ||||
\(389\) | −15.9683 | − | 6.61427i | −0.809623 | − | 0.335357i | −0.0608194 | − | 0.998149i | \(-0.519371\pi\) |
−0.748804 | + | 0.662792i | \(0.769371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.3821 | − | 23.3821i | −1.18248 | − | 1.18248i | ||||
\(392\) | 10.8118 | − | 8.63882i | 0.546078 | − | 0.436326i | ||||
\(393\) | 18.2963 | + | 18.2963i | 0.922925 | + | 0.922925i | ||||
\(394\) | −18.7345 | − | 3.17705i | −0.943828 | − | 0.160058i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.6163 | + | 13.9379i | 0.784748 | + | 0.700407i | ||||
\(397\) | −6.14033 | − | 14.8241i | −0.308174 | − | 0.743999i | −0.999764 | − | 0.0217084i | \(-0.993089\pi\) |
0.691590 | − | 0.722290i | \(-0.256911\pi\) | |||||||
\(398\) | 8.17318 | − | 13.0166i | 0.409684 | − | 0.652464i | ||||
\(399\) | 19.3295i | 0.967684i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 27.3193i | − | 1.36426i | −0.731230 | − | 0.682131i | \(-0.761053\pi\) | ||
0.731230 | − | 0.682131i | \(-0.238947\pi\) | |||||||
\(402\) | −7.24843 | − | 4.55131i | −0.361519 | − | 0.226999i | ||||
\(403\) | −2.06892 | − | 4.99481i | −0.103060 | − | 0.248809i | ||||
\(404\) | −7.93369 | + | 0.450551i | −0.394716 | + | 0.0224158i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.761338 | − | 4.48946i | 0.0377846 | − | 0.222808i | ||||
\(407\) | −2.28419 | − | 2.28419i | −0.113223 | − | 0.113223i | ||||
\(408\) | 35.4174 | + | 19.5309i | 1.75342 | + | 0.966925i | ||||
\(409\) | 2.23691 | + | 2.23691i | 0.110608 | + | 0.110608i | 0.760245 | − | 0.649637i | \(-0.225079\pi\) |
−0.649637 | + | 0.760245i | \(0.725079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 40.9378 | + | 16.9570i | 2.01931 | + | 0.836427i | ||||
\(412\) | −4.83397 | + | 13.8426i | −0.238152 | + | 0.681976i | ||||
\(413\) | 0.941448 | − | 0.389961i | 0.0463256 | − | 0.0191887i | ||||
\(414\) | −20.8473 | − | 91.2059i | −1.02459 | − | 4.48253i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.72747 | + | 31.6491i | −0.0846960 | + | 1.55172i | ||||
\(417\) | 8.46115i | 0.414344i | ||||||||
\(418\) | 6.71603 | − | 1.53511i | 0.328492 | − | 0.0750848i | ||||
\(419\) | −3.88329 | − | 9.37508i | −0.189711 | − | 0.458003i | 0.800193 | − | 0.599743i | \(-0.204730\pi\) |
−0.989904 | + | 0.141740i | \(0.954730\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.20171 | + | 1.32619i | 0.156042 | + | 0.0646347i | 0.459337 | − | 0.888262i | \(-0.348087\pi\) |
−0.303295 | + | 0.952897i | \(0.598087\pi\) | |||||||
\(422\) | −2.72144 | − | 3.83296i | −0.132478 | − | 0.186586i | ||||
\(423\) | 14.1206 | − | 14.1206i | 0.686566 | − | 0.686566i | ||||
\(424\) | −3.10579 | − | 10.7423i | −0.150830 | − | 0.521693i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.06290 | − | 41.6485i | 0.342199 | − | 2.01788i | ||||
\(427\) | 10.5742 | + | 4.37998i | 0.511722 | + | 0.211962i | ||||
\(428\) | −22.3164 | + | 1.26734i | −1.07870 | + | 0.0612591i | ||||
\(429\) | −21.6899 | + | 8.98427i | −1.04720 | + | 0.433765i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 27.4030i | − | 1.31996i | −0.751285 | − | 0.659978i | \(-0.770566\pi\) | ||
0.751285 | − | 0.659978i | \(-0.229434\pi\) | |||||||
\(432\) | 35.7907 | + | 64.5664i | 1.72198 | + | 3.10645i | ||||
\(433\) | 31.7483 | 1.52573 | 0.762864 | − | 0.646560i | \(-0.223793\pi\) | ||||
0.762864 | + | 0.646560i | \(0.223793\pi\) | |||||||
\(434\) | −1.67748 | − | 1.05329i | −0.0805214 | − | 0.0505597i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.4401 | − | 20.6606i | 0.883121 | − | 0.989465i | ||||
\(437\) | −28.4489 | − | 11.7839i | −1.36089 | − | 0.563701i | ||||
\(438\) | −6.45368 | + | 38.0561i | −0.308369 | + | 1.81839i | ||||
\(439\) | −7.15702 | + | 7.15702i | −0.341586 | + | 0.341586i | −0.856963 | − | 0.515377i | \(-0.827652\pi\) |
0.515377 | + | 0.856963i | \(0.327652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 29.2469 | + | 29.2469i | 1.39271 | + | 1.39271i | ||||
\(442\) | −27.3003 | + | 19.3835i | −1.29854 | + | 0.921979i | ||||
\(443\) | 2.48722 | − | 6.00467i | 0.118171 | − | 0.285290i | −0.853715 | − | 0.520740i | \(-0.825656\pi\) |
0.971887 | + | 0.235449i | \(0.0756562\pi\) | |||||||
\(444\) | −7.67255 | − | 15.9066i | −0.364123 | − | 0.754894i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −32.2150 | + | 7.36353i | −1.52543 | + | 0.348673i | ||||
\(447\) | 62.4645i | 2.95447i | ||||||||
\(448\) | 6.19685 | + | 9.82106i | 0.292774 | + | 0.464001i | ||||
\(449\) | −8.48000 | −0.400196 | −0.200098 | − | 0.979776i | \(-0.564126\pi\) | ||||
−0.200098 | + | 0.979776i | \(0.564126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.10099 | − | 7.48645i | −0.146020 | − | 0.352523i | ||||
\(452\) | −11.4192 | + | 5.50805i | −0.537114 | + | 0.259077i | ||||
\(453\) | −24.2625 | + | 58.5749i | −1.13995 | + | 2.75209i | ||||
\(454\) | 9.03501 | + | 12.7252i | 0.424034 | + | 0.597222i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 37.4308 | + | 4.18169i | 1.75286 | + | 0.195826i | ||||
\(457\) | 17.8416 | + | 17.8416i | 0.834593 | + | 0.834593i | 0.988141 | − | 0.153548i | \(-0.0490701\pi\) |
−0.153548 | + | 0.988141i | \(0.549070\pi\) | |||||||
\(458\) | 4.28981 | − | 25.2962i | 0.200450 | − | 1.18201i | ||||
\(459\) | −29.8421 | + | 72.0453i | −1.39291 | + | 3.36279i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.54536 | + | 1.05432i | −0.118549 | + | 0.0491047i | −0.441170 | − | 0.897424i | \(-0.645436\pi\) |
0.322620 | + | 0.946528i | \(0.395436\pi\) | |||||||
\(462\) | −4.57392 | + | 7.28443i | −0.212798 | + | 0.338903i | ||||
\(463\) | −26.6297 | −1.23759 | −0.618793 | − | 0.785554i | \(-0.712378\pi\) | ||||
−0.618793 | + | 0.785554i | \(0.712378\pi\) | |||||||
\(464\) | −8.52897 | − | 2.44554i | −0.395947 | − | 0.113531i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.3675 | + | 32.4373i | −0.943504 | + | 1.50263i | ||||
\(467\) | −2.41096 | − | 5.82058i | −0.111566 | − | 0.269344i | 0.858228 | − | 0.513268i | \(-0.171565\pi\) |
−0.969794 | + | 0.243924i | \(0.921565\pi\) | |||||||
\(468\) | −94.5784 | + | 5.37107i | −4.37189 | + | 0.248278i | ||||
\(469\) | 0.993383 | − | 2.39824i | 0.0458702 | − | 0.110740i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.2815 | + | 27.2815i | −1.25706 | + | 1.25706i | ||||
\(472\) | −0.551474 | − | 1.90744i | −0.0253836 | − | 0.0877972i | ||||
\(473\) | 0.901403 | − | 0.901403i | 0.0414466 | − | 0.0414466i | ||||
\(474\) | 58.1556 | − | 41.2911i | 2.67118 | − | 1.89656i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.04420 | + | 11.5810i | −0.185366 | + | 0.530815i | ||||
\(477\) | 30.8766 | − | 12.7895i | 1.41374 | − | 0.585592i | ||||
\(478\) | 26.9721 | − | 6.16512i | 1.23367 | − | 0.281986i | ||||
\(479\) | −8.91801 | −0.407474 | −0.203737 | − | 0.979026i | \(-0.565309\pi\) | ||||
−0.203737 | + | 0.979026i | \(0.565309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.6196 | 0.666596 | ||||||||
\(482\) | −6.38492 | + | 1.45943i | −0.290825 | + | 0.0664751i | ||||
\(483\) | 35.5191 | − | 14.7125i | 1.61617 | − | 0.669441i | ||||
\(484\) | −17.8758 | − | 6.24239i | −0.812535 | − | 0.283745i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −80.9337 | + | 57.4638i | −3.67123 | + | 2.60661i | ||||
\(487\) | −14.5675 | + | 14.5675i | −0.660115 | + | 0.660115i | −0.955407 | − | 0.295292i | \(-0.904583\pi\) |
0.295292 | + | 0.955407i | \(0.404583\pi\) | |||||||
\(488\) | 10.7693 | − | 19.5290i | 0.487502 | − | 0.884038i | ||||
\(489\) | 30.9591 | − | 30.9591i | 1.40002 | − | 1.40002i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.1115 | − | 29.2397i | 0.546584 | − | 1.31957i | −0.373420 | − | 0.927662i | \(-0.621815\pi\) |
0.920004 | − | 0.391908i | \(-0.128185\pi\) | |||||||
\(492\) | −2.51178 | − | 44.2296i | −0.113240 | − | 1.99402i | ||||
\(493\) | −3.58669 | − | 8.65904i | −0.161536 | − | 0.389983i | ||||
\(494\) | −16.5798 | + | 26.4050i | −0.745960 | + | 1.18802i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.40256 | + | 3.02051i | −0.107878 | + | 0.135625i | ||||
\(497\) | 12.8120 | 0.574697 | ||||||||
\(498\) | 9.24273 | − | 14.7200i | 0.414176 | − | 0.659618i | ||||
\(499\) | 10.0229 | − | 4.15164i | 0.448689 | − | 0.185853i | −0.146885 | − | 0.989154i | \(-0.546925\pi\) |
0.595574 | + | 0.803301i | \(0.296925\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8308 | + | 28.5621i | −0.528562 | + | 1.27606i | ||||
\(502\) | −2.75272 | + | 16.2323i | −0.122860 | + | 0.724481i | ||||
\(503\) | 15.5986 | + | 15.5986i | 0.695505 | + | 0.695505i | 0.963438 | − | 0.267932i | \(-0.0863404\pi\) |
−0.267932 | + | 0.963438i | \(0.586340\pi\) | |||||||
\(504\) | −27.1145 | + | 21.6650i | −1.20778 | + | 0.965036i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.93271 | − | 11.1727i | −0.352652 | − | 0.496686i | ||||
\(507\) | 23.8239 | − | 57.5159i | 1.05806 | − | 2.55437i | ||||
\(508\) | −9.83969 | − | 20.3995i | −0.436566 | − | 0.905082i | ||||
\(509\) | −1.06698 | − | 2.57591i | −0.0472930 | − | 0.114175i | 0.898468 | − | 0.439040i | \(-0.144681\pi\) |
−0.945761 | + | 0.324864i | \(0.894681\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7069 | −0.517883 | ||||||||
\(512\) | 20.3587 | − | 9.87532i | 0.899737 | − | 0.436432i | ||||
\(513\) | 72.6175i | 3.20614i | ||||||||
\(514\) | 5.58120 | − | 1.27572i | 0.246176 | − | 0.0562696i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.27717 | − | 3.02779i | 0.276337 | − | 0.133291i | ||||
\(517\) | 1.11924 | − | 2.70208i | 0.0492241 | − | 0.118837i | ||||
\(518\) | 4.36737 | − | 3.10088i | 0.191891 | − | 0.136245i | ||||
\(519\) | 30.2140 | + | 30.2140i | 1.32625 | + | 1.32625i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9781 | + | 11.9781i | −0.524771 | + | 0.524771i | −0.919009 | − | 0.394238i | \(-0.871009\pi\) |
0.394238 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(522\) | 4.43368 | − | 26.1445i | 0.194057 | − | 1.14431i | ||||
\(523\) | 10.7057 | + | 4.43446i | 0.468129 | + | 0.193905i | 0.604263 | − | 0.796785i | \(-0.293468\pi\) |
−0.136134 | + | 0.990690i | \(0.543468\pi\) | |||||||
\(524\) | 11.4082 | + | 10.1821i | 0.498368 | + | 0.444805i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.71920 | + | 1.70739i | 0.118563 | + | 0.0744459i | ||||
\(527\) | −4.07692 | −0.177593 | ||||||||
\(528\) | 13.1165 | + | 10.4331i | 0.570824 | + | 0.454043i | ||||
\(529\) | 38.2457i | 1.66286i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.48256 | − | 2.27095i | 0.237923 | − | 0.0985508i | ||||
\(532\) | 0.647670 | + | 11.4047i | 0.0280801 | + | 0.494457i | ||||
\(533\) | 33.8816 | + | 14.0342i | 1.46757 | + | 0.607889i | ||||
\(534\) | 11.2079 | − | 66.0906i | 0.485011 | − | 2.86002i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.42920 | − | 2.44248i | −0.191312 | − | 0.105499i | ||||
\(537\) | 3.60488 | − | 3.60488i | 0.155562 | − | 0.155562i | ||||
\(538\) | −2.99853 | − | 4.22323i | −0.129276 | − | 0.182076i | ||||
\(539\) | 5.59663 | + | 2.31820i | 0.241064 | + | 0.0998519i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.28137 | + | 19.9930i | 0.356044 | + | 0.859566i | 0.995848 | + | 0.0910282i | \(0.0290153\pi\) |
−0.639804 | + | 0.768538i | \(0.720985\pi\) | |||||||
\(542\) | −30.9172 | + | 7.06687i | −1.32801 | + | 0.303548i | ||||
\(543\) | − | 8.32686i | − | 0.357340i | ||||||
\(544\) | 21.5513 | + | 10.3369i | 0.924004 | + | 0.443189i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.67410 | − | 37.9487i | −0.371217 | − | 1.62405i | ||||
\(547\) | 29.4527 | − | 12.1997i | 1.25931 | − | 0.521623i | 0.349611 | − | 0.936895i | \(-0.386314\pi\) |
0.909697 | + | 0.415272i | \(0.136314\pi\) | |||||||
\(548\) | 24.7222 | + | 8.63322i | 1.05608 | + | 0.368793i | ||||
\(549\) | 61.5793 | + | 25.5070i | 2.62814 | + | 1.08861i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.17149 | − | 6.17149i | −0.262914 | − | 0.262914i | ||||
\(552\) | −20.8061 | − | 71.9643i | −0.885566 | − | 3.06300i | ||||
\(553\) | 15.2960 | + | 15.2960i | 0.650453 | + | 0.650453i | ||||
\(554\) | 1.36210 | − | 8.03205i | 0.0578701 | − | 0.341249i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.283507 | + | 4.99222i | 0.0120234 | + | 0.211717i | ||||
\(557\) | −0.454492 | − | 1.09724i | −0.0192574 | − | 0.0464916i | 0.913958 | − | 0.405808i | \(-0.133010\pi\) |
−0.933216 | + | 0.359316i | \(0.883010\pi\) | |||||||
\(558\) | −9.76884 | − | 6.13389i | −0.413548 | − | 0.259668i | ||||
\(559\) | 5.76928i | 0.244015i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.7040i | 0.747464i | ||||||||
\(562\) | −1.93118 | + | 3.07561i | −0.0814621 | + | 0.129737i | ||||
\(563\) | −16.2116 | − | 39.1382i | −0.683236 | − | 1.64948i | −0.757982 | − | 0.652275i | \(-0.773815\pi\) |
0.0747465 | − | 0.997203i | \(-0.476185\pi\) | |||||||
\(564\) | 10.6471 | − | 11.9291i | 0.448322 | − | 0.502308i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.9570 | + | 3.89313i | 0.964956 | + | 0.163641i | ||||
\(567\) | −38.0794 | − | 38.0794i | −1.59919 | − | 1.59919i | ||||
\(568\) | 2.77172 | − | 24.8100i | 0.116299 | − | 1.04100i | ||||
\(569\) | −4.33822 | − | 4.33822i | −0.181868 | − | 0.181868i | 0.610301 | − | 0.792169i | \(-0.291048\pi\) |
−0.792169 | + | 0.610301i | \(0.791048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.2465 | − | 15.4280i | −1.55872 | − | 0.645643i | −0.573853 | − | 0.818958i | \(-0.694552\pi\) |
−0.984866 | + | 0.173316i | \(0.944552\pi\) | |||||||
\(572\) | −12.4964 | + | 6.02763i | −0.522501 | + | 0.252028i | ||||
\(573\) | −47.1886 | + | 19.5462i | −1.97133 | + | 0.816553i | ||||
\(574\) | 13.0983 | − | 2.99393i | 0.546712 | − | 0.124964i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 36.0876 | + | 57.1933i | 1.50365 | + | 2.38305i | ||||
\(577\) | 4.17488i | 0.173802i | 0.996217 | + | 0.0869012i | \(0.0276965\pi\) | ||||
−0.996217 | + | 0.0869012i | \(0.972304\pi\) | |||||||
\(578\) | 0.268931 | + | 1.17656i | 0.0111861 | + | 0.0489384i | ||||
\(579\) | 3.83246 | + | 9.25238i | 0.159272 | + | 0.384516i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.87030 | + | 2.01735i | 0.202054 | + | 0.0836936i | ||||
\(582\) | −51.4338 | + | 36.5185i | −2.13200 | + | 1.51374i | ||||
\(583\) | 3.46111 | − | 3.46111i | 0.143344 | − | 0.143344i | ||||
\(584\) | −2.53264 | + | 22.6700i | −0.104801 | + | 0.938090i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.8195 | − | 4.03938i | −0.983973 | − | 0.166865i | ||||
\(587\) | −17.3964 | − | 7.20581i | −0.718024 | − | 0.297415i | −0.00640387 | − | 0.999979i | \(-0.502038\pi\) |
−0.711621 | + | 0.702564i | \(0.752038\pi\) | |||||||
\(588\) | 24.7080 | + | 22.0525i | 1.01894 | + | 0.909429i | ||||
\(589\) | −3.50751 | + | 1.45286i | −0.144524 | + | 0.0598639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 45.4725i | − | 1.87049i | ||||||
\(592\) | −5.05991 | − | 9.12809i | −0.207961 | − | 0.375162i | ||||
\(593\) | 9.27068 | 0.380701 | 0.190351 | − | 0.981716i | \(-0.439038\pi\) | ||||
0.190351 | + | 0.981716i | \(0.439038\pi\) | |||||||
\(594\) | −17.1834 | + | 27.3664i | −0.705045 | + | 1.12286i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.09299 | + | 36.8551i | 0.0857322 | + | 1.50965i | ||||
\(597\) | 33.9811 | + | 14.0754i | 1.39075 | + | 0.576069i | ||||
\(598\) | 61.1404 | + | 10.3684i | 2.50022 | + | 0.423995i | ||||
\(599\) | −22.3629 | + | 22.3629i | −0.913723 | + | 0.913723i | −0.996563 | − | 0.0828402i | \(-0.973601\pi\) |
0.0828402 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9624 | + | 25.9624i | 1.05903 | + | 1.05903i | 0.998145 | + | 0.0608851i | \(0.0193923\pi\) |
0.0608851 | + | 0.998145i | \(0.480608\pi\) | |||||||
\(602\) | 1.22369 | + | 1.72348i | 0.0498739 | + | 0.0702438i | ||||
\(603\) | 5.78500 | − | 13.9662i | 0.235583 | − | 0.568749i | ||||
\(604\) | −12.3526 | + | 35.3732i | −0.502622 | + | 1.43931i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.23735 | − | 18.5382i | −0.172131 | − | 0.753062i | ||||
\(607\) | 3.46490i | 0.140636i | 0.997525 | + | 0.0703179i | \(0.0224014\pi\) | ||||
−0.997525 | + | 0.0703179i | \(0.977599\pi\) | |||||||
\(608\) | 22.2249 | + | 1.21308i | 0.901340 | + | 0.0491968i | ||||
\(609\) | 10.8969 | 0.441564 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.06536 | + | 12.2289i | 0.204923 | + | 0.494727i | ||||
\(612\) | −23.5515 | + | 67.4424i | −0.952014 | + | 2.72620i | ||||
\(613\) | 13.7592 | − | 33.2177i | 0.555730 | − | 1.34165i | −0.357388 | − | 0.933956i | \(-0.616333\pi\) |
0.913118 | − | 0.407695i | \(-0.133667\pi\) | |||||||
\(614\) | 0.612638 | − | 0.434979i | 0.0247241 | − | 0.0175543i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.45461 | + | 4.45120i | −0.0988991 | + | 0.179344i | ||||
\(617\) | −30.4580 | − | 30.4580i | −1.22619 | − | 1.22619i | −0.965393 | − | 0.260799i | \(-0.916014\pi\) |
−0.260799 | − | 0.965393i | \(-0.583986\pi\) | |||||||
\(618\) | −34.5938 | − | 5.86654i | −1.39157 | − | 0.235987i | ||||
\(619\) | −4.97518 | + | 12.0112i | −0.199969 | + | 0.482769i | −0.991773 | − | 0.128006i | \(-0.959142\pi\) |
0.791804 | + | 0.610775i | \(0.209142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 133.439 | − | 55.2723i | 5.35473 | − | 2.21800i | ||||
\(622\) | 4.51127 | + | 2.83264i | 0.180885 | + | 0.113578i | ||||
\(623\) | 20.3309 | 0.814541 | ||||||||
\(624\) | −75.3628 | + | 8.58735i | −3.01693 | + | 0.343769i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.2984 | + | 14.6292i | 0.931192 | + | 0.584699i | ||||
\(627\) | 6.30902 | + | 15.2313i | 0.251958 | + | 0.608281i | ||||
\(628\) | −15.1824 | + | 17.0107i | −0.605845 | + | 0.678799i | ||||
\(629\) | 4.21894 | − | 10.1854i | 0.168220 | − | 0.406119i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.07552 | + | 7.07552i | −0.281672 | + | 0.281672i | −0.833776 | − | 0.552103i | \(-0.813825\pi\) |
0.552103 | + | 0.833776i | \(0.313825\pi\) | |||||||
\(632\) | 32.9293 | − | 26.3111i | 1.30986 | − | 1.04660i | ||||
\(633\) | 7.95447 | − | 7.95447i | 0.316162 | − | 0.316162i | ||||
\(634\) | −17.7345 | − | 24.9777i | −0.704325 | − | 0.991993i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 24.1024 | − | 11.6258i | 0.955721 | − | 0.460992i | ||||
\(637\) | −25.3288 | + | 10.4915i | −1.00356 | + | 0.415689i | ||||
\(638\) | −0.865410 | − | 3.78612i | −0.0342619 | − | 0.149894i | ||||
\(639\) | 74.6112 | 2.95157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.8007 | −1.17706 | −0.588528 | − | 0.808477i | \(-0.700292\pi\) | ||||
−0.588528 | + | 0.808477i | \(0.700292\pi\) | |||||||
\(642\) | −11.9191 | − | 52.1453i | −0.470409 | − | 2.05801i | ||||
\(643\) | −13.5899 | + | 5.62912i | −0.535933 | + | 0.221991i | −0.634200 | − | 0.773169i | \(-0.718670\pi\) |
0.0982665 | + | 0.995160i | \(0.468670\pi\) | |||||||
\(644\) | 20.4639 | − | 9.87075i | 0.806390 | − | 0.388962i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.6117 | + | 19.1711i | 0.535544 | + | 0.754276i | ||||
\(647\) | −29.5002 | + | 29.5002i | −1.15977 | + | 1.15977i | −0.175247 | + | 0.984525i | \(0.556072\pi\) |
−0.984525 | + | 0.175247i | \(0.943928\pi\) | |||||||
\(648\) | −81.9775 | + | 65.5014i | −3.22038 | + | 2.57314i | ||||
\(649\) | 0.614566 | − | 0.614566i | 0.0241238 | − | 0.0241238i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.81393 | − | 4.37921i | 0.0710934 | − | 0.171635i | ||||
\(652\) | 17.2291 | − | 19.3037i | 0.674742 | − | 0.755993i | ||||
\(653\) | 12.9516 | + | 31.2680i | 0.506836 | + | 1.22361i | 0.945695 | + | 0.325054i | \(0.105383\pi\) |
−0.438859 | + | 0.898556i | \(0.644617\pi\) | |||||||
\(654\) | 56.1239 | + | 35.2404i | 2.19462 | + | 1.37801i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.96399 | − | 26.0121i | −0.115724 | − | 1.01560i | ||||
\(657\) | −68.1755 | −2.65978 | ||||||||
\(658\) | 4.10699 | + | 2.57879i | 0.160107 | + | 0.100532i | ||||
\(659\) | 38.4825 | − | 15.9400i | 1.49907 | − | 0.620933i | 0.525799 | − | 0.850609i | \(-0.323767\pi\) |
0.973267 | + | 0.229676i | \(0.0737666\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.78263 | − | 18.7889i | 0.302709 | − | 0.730805i | −0.697194 | − | 0.716883i | \(-0.745568\pi\) |
0.999903 | − | 0.0139222i | \(-0.00443172\pi\) | |||||||
\(662\) | −12.5714 | − | 2.13189i | −0.488600 | − | 0.0828584i | ||||
\(663\) | −56.6558 | − | 56.6558i | −2.20033 | − | 2.20033i | ||||
\(664\) | 4.96014 | − | 8.99474i | 0.192491 | − | 0.349063i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 25.4335 | − | 18.0581i | 0.985529 | − | 0.699736i | ||||
\(667\) | −6.64311 | + | 16.0379i | −0.257222 | + | 0.620989i | ||||
\(668\) | −6.02335 | + | 17.2485i | −0.233051 | + | 0.667366i | ||||
\(669\) | −30.2627 | − | 73.0607i | −1.17003 | − | 2.82469i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.76192 | 0.376855 | ||||||||
\(672\) | −20.6920 | + | 18.5501i | −0.798212 | + | 0.715586i | ||||
\(673\) | − | 33.3993i | − | 1.28745i | −0.765257 | − | 0.643725i | \(-0.777388\pi\) | ||
0.765257 | − | 0.643725i | \(-0.222612\pi\) | |||||||
\(674\) | −3.86527 | − | 16.9104i | −0.148885 | − | 0.651363i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.1293 | − | 34.7336i | 0.466512 | − | 1.33591i | ||||
\(677\) | −0.788676 | + | 1.90403i | −0.0303113 | + | 0.0731779i | −0.938310 | − | 0.345794i | \(-0.887610\pi\) |
0.907999 | + | 0.418972i | \(0.137610\pi\) | |||||||
\(678\) | −17.5644 | − | 24.7382i | −0.674557 | − | 0.950065i | ||||
\(679\) | −13.5280 | − | 13.5280i | −0.519158 | − | 0.519158i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.4083 | + | 26.4083i | −1.01197 | + | 1.01197i | ||||
\(682\) | −1.66561 | − | 0.282460i | −0.0637796 | − | 0.0108160i | ||||
\(683\) | 5.16393 | + | 2.13897i | 0.197592 | + | 0.0818454i | 0.479285 | − | 0.877659i | \(-0.340896\pi\) |
−0.281693 | + | 0.959505i | \(0.590896\pi\) | |||||||
\(684\) | 3.77173 | + | 66.4158i | 0.144216 | + | 2.53947i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.9827 | + | 20.6763i | −0.495682 | + | 0.789425i | ||||
\(687\) | 61.3993 | 2.34253 | ||||||||
\(688\) | 3.60219 | − | 1.99678i | 0.137332 | − | 0.0761264i | ||||
\(689\) | 22.1522i | 0.843933i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8310 | + | 9.04271i | −0.830492 | + | 0.344001i | −0.757097 | − | 0.653302i | \(-0.773383\pi\) |
−0.0733946 | + | 0.997303i | \(0.523383\pi\) | |||||||
\(692\) | 18.8392 | + | 16.8144i | 0.716158 | + | 0.639188i | ||||
\(693\) | −14.0356 | − | 5.81374i | −0.533168 | − | 0.220846i | ||||
\(694\) | −24.5142 | − | 4.15720i | −0.930546 | − | 0.157805i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.35740 | − | 21.1014i | 0.0893571 | − | 0.799847i | ||||
\(697\) | 19.5552 | − | 19.5552i | 0.740705 | − | 0.740705i | ||||
\(698\) | −32.0230 | + | 22.7367i | −1.21209 | + | 0.860595i | ||||
\(699\) | −84.6804 | − | 35.0758i | −3.20291 | − | 1.32669i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.38145 | − | 22.6488i | −0.354332 | − | 0.855434i | −0.996075 | − | 0.0885139i | \(-0.971788\pi\) |
0.641743 | − | 0.766920i | \(-0.278212\pi\) | |||||||
\(702\) | −32.5871 | − | 142.567i | −1.22992 | − | 5.38084i | ||||
\(703\) | − | 10.2663i | − | 0.387202i | ||||||
\(704\) | 8.08856 | + | 5.71623i | 0.304849 | + | 0.215438i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.2246 | − | 6.90857i | 1.13752 | − | 0.260007i | ||||
\(707\) | 5.32846 | − | 2.20712i | 0.200397 | − | 0.0830073i | ||||
\(708\) | 4.27970 | − | 2.06431i | 0.160841 | − | 0.0775816i | ||||
\(709\) | −34.4885 | − | 14.2856i | −1.29524 | − | 0.536506i | −0.374698 | − | 0.927147i | \(-0.622254\pi\) |
−0.920543 | + | 0.390640i | \(0.872254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 89.0769 | + | 89.0769i | 3.34064 | + | 3.34064i | ||||
\(712\) | 4.39834 | − | 39.3701i | 0.164835 | − | 1.47546i | ||||
\(713\) | 5.33942 | + | 5.33942i | 0.199963 | + | 0.199963i | ||||
\(714\) | −28.9419 | − | 4.90807i | −1.08312 | − | 0.183680i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.00615 | − | 2.24773i | 0.0749735 | − | 0.0840017i | ||||
\(717\) | 25.3375 | + | 61.1701i | 0.946246 | + | 2.28444i | ||||
\(718\) | 4.27686 | − | 6.81133i | 0.159611 | − | 0.254197i | ||||
\(719\) | 47.1132i | 1.75702i | 0.477719 | + | 0.878512i | \(0.341464\pi\) | ||||
−0.477719 | + | 0.878512i | \(0.658536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.6418i | − | 0.396322i | ||||||
\(722\) | −4.21362 | − | 2.64575i | −0.156815 | − | 0.0984645i | ||||
\(723\) | −5.99798 | − | 14.4804i | −0.223067 | − | 0.538532i | ||||
\(724\) | −0.279007 | − | 4.91299i | −0.0103692 | − | 0.182590i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.57580 | − | 44.6730i | 0.281164 | − | 1.65797i | ||||
\(727\) | 32.2735 | + | 32.2735i | 1.19696 | + | 1.19696i | 0.975073 | + | 0.221885i | \(0.0712210\pi\) |
0.221885 | + | 0.975073i | \(0.428779\pi\) | |||||||
\(728\) | −6.38941 | − | 22.0997i | −0.236807 | − | 0.819071i | ||||
\(729\) | −89.2611 | − | 89.2611i | −3.30597 | − | 3.30597i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.01944 | + | 1.66491i | 0.148664 | + | 0.0615788i | ||||
\(732\) | 50.3849 | + | 17.5949i | 1.86228 | + | 0.650326i | ||||
\(733\) | −38.8138 | + | 16.0772i | −1.43362 | + | 0.593825i | −0.958243 | − | 0.285956i | \(-0.907689\pi\) |
−0.475378 | + | 0.879782i | \(0.657689\pi\) | |||||||
\(734\) | 8.88413 | + | 38.8676i | 0.327919 | + | 1.43463i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.6872 | − | 41.7630i | −0.541379 | − | 1.53940i | ||||
\(737\) | − | 2.21401i | − | 0.0815541i | ||||||
\(738\) | 76.2783 | − | 17.4353i | 2.80784 | − | 0.641801i | ||||
\(739\) | 3.96376 | + | 9.56937i | 0.145809 | + | 0.352015i | 0.979864 | − | 0.199667i | \(-0.0639861\pi\) |
−0.834054 | + | 0.551682i | \(0.813986\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −68.9327 | − | 28.5529i | −2.53231 | − | 1.04892i | ||||
\(742\) | 4.69858 | + | 6.61762i | 0.172490 | + | 0.242941i | ||||
\(743\) | 27.5088 | − | 27.5088i | 1.00920 | − | 1.00920i | 0.00924260 | − | 0.999957i | \(-0.497058\pi\) |
0.999957 | − | 0.00924260i | \(-0.00294205\pi\) | |||||||
\(744\) | −8.08775 | − | 4.45999i | −0.296511 | − | 0.163511i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.292008 | + | 1.72192i | −0.0106912 | + | 0.0630439i | ||||
\(747\) | 28.3624 | + | 11.7481i | 1.03773 | + | 0.429840i | ||||
\(748\) | 0.593205 | + | 10.4457i | 0.0216897 | + | 0.381931i | ||||
\(749\) | 14.9882 | − | 6.20833i | 0.547658 | − | 0.226847i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 29.6365i | − | 1.08145i | −0.841199 | − | 0.540726i | \(-0.818149\pi\) | ||
0.841199 | − | 0.540726i | \(-0.181851\pi\) | |||||||
\(752\) | 5.88223 | − | 7.39515i | 0.214503 | − | 0.269673i | ||||
\(753\) | −39.3992 | −1.43579 | ||||||||
\(754\) | 14.8857 | + | 9.34676i | 0.542104 | + | 0.340389i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −39.9739 | − | 35.6777i | −1.45384 | − | 1.29758i | ||||
\(757\) | −48.4128 | − | 20.0533i | −1.75959 | − | 0.728848i | −0.996595 | − | 0.0824488i | \(-0.973726\pi\) |
−0.762999 | − | 0.646399i | \(-0.776274\pi\) | |||||||
\(758\) | −1.59306 | + | 9.39399i | −0.0578627 | + | 0.341205i | ||||
\(759\) | 23.1864 | − | 23.1864i | 0.841614 | − | 0.841614i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.0239 | − | 31.0239i | −1.12461 | − | 1.12461i | −0.991039 | − | 0.133576i | \(-0.957354\pi\) |
−0.133576 | − | 0.991039i | \(-0.542646\pi\) | |||||||
\(762\) | 44.1929 | − | 31.3774i | 1.60094 | − | 1.13668i | ||||
\(763\) | −7.69168 | + | 18.5694i | −0.278457 | + | 0.672256i | ||||
\(764\) | −27.1872 | + | 13.1137i | −0.983597 | + | 0.474437i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.44878 | − | 1.93118i | 0.305267 | − | 0.0697762i | ||||
\(767\) | 3.93343i | 0.142028i | ||||||||
\(768\) | 31.4452 | + | 44.0824i | 1.13468 | + | 1.59069i | ||||
\(769\) | 9.26292 | 0.334029 | 0.167015 | − | 0.985954i | \(-0.446587\pi\) | ||||
0.167015 | + | 0.985954i | \(0.446587\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.24297 | + | 12.6576i | 0.188821 | + | 0.455854i | ||||
\(772\) | 2.57124 | + | 5.33065i | 0.0925408 | + | 0.191854i | ||||
\(773\) | 8.47782 | − | 20.4673i | 0.304926 | − | 0.736156i | −0.694928 | − | 0.719079i | \(-0.744564\pi\) |
0.999854 | − | 0.0170771i | \(-0.00543608\pi\) | |||||||
\(774\) | 7.12620 | + | 10.0367i | 0.256146 | + | 0.360763i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29.1232 | + | 23.2699i | −1.04546 | + | 0.835342i | ||||
\(777\) | 9.06352 | + | 9.06352i | 0.325152 | + | 0.325152i | ||||
\(778\) | 4.08680 | − | 24.0991i | 0.146519 | − | 0.863994i | ||||
\(779\) | 9.85524 | − | 23.7927i | 0.353101 | − | 0.852460i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0957 | − | 4.18176i | 0.361251 | − | 0.149635i | ||||
\(782\) | 24.8676 | − | 39.6042i | 0.889264 | − | 1.41624i | ||||
\(783\) | 40.9377 | 1.46299 | ||||||||
\(784\) | 15.3170 | + | 12.1834i | 0.547037 | + | 0.435123i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.4587 | + | 30.9899i | −0.694068 | + | 1.10537i | ||||
\(787\) | 9.46364 | + | 22.8472i | 0.337342 | + | 0.814416i | 0.997969 | + | 0.0637018i | \(0.0202906\pi\) |
−0.660627 | + | 0.750715i | \(0.729709\pi\) | |||||||
\(788\) | −1.52364 | − | 26.8296i | −0.0542775 | − | 0.955764i | ||||
\(789\) | −2.94039 | + | 7.09872i | −0.104681 | + | 0.252721i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.50661 | − | 6.50661i | 0.231348 | − | 0.231348i | ||||
\(792\) | −14.2945 | + | 25.9217i | −0.507934 | + | 0.921088i | ||||
\(793\) | −31.2398 | + | 31.2398i | −1.10936 | + | 1.10936i | ||||
\(794\) | 18.5023 | − | 13.1369i | 0.656623 | − | 0.466210i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5210 | + | 7.16614i | 0.727349 | + | 0.253997i | ||||
\(797\) | −26.0050 | + | 10.7716i | −0.921145 | + | 0.381551i | −0.792313 | − | 0.610115i | \(-0.791123\pi\) |
−0.128833 | + | 0.991666i | \(0.541123\pi\) | |||||||
\(798\) | −26.6487 | + | 6.09121i | −0.943355 | + | 0.215627i | ||||
\(799\) | 9.98158 | 0.353123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 118.398 | 4.18338 | ||||||||
\(802\) | 37.6640 | − | 8.60902i | 1.32996 | − | 0.303995i | ||||
\(803\) | −9.22485 | + | 3.82106i | −0.325538 | + | 0.134842i | ||||
\(804\) | 3.99053 | − | 11.4273i | 0.140735 | − | 0.403011i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.23416 | − | 4.42632i | 0.219589 | − | 0.155911i | ||||
\(807\) | 8.76438 | − | 8.76438i | 0.308521 | − | 0.308521i | ||||
\(808\) | −3.12126 | − | 10.7959i | −0.109806 | − | 0.379797i | ||||
\(809\) | 24.2885 | − | 24.2885i | 0.853938 | − | 0.853938i | −0.136678 | − | 0.990616i | \(-0.543643\pi\) |
0.990616 | + | 0.136678i | \(0.0436426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8336 | − | 30.9831i | 0.450649 | − | 1.08796i | −0.521426 | − | 0.853296i | \(-0.674600\pi\) |
0.972076 | − | 0.234667i | \(-0.0754001\pi\) | |||||||
\(812\) | 6.42934 | − | 0.365120i | 0.225626 | − | 0.0128132i | ||||
\(813\) | −29.0435 | − | 70.1173i | −1.01860 | − | 2.45912i | ||||
\(814\) | 2.42931 | − | 3.86893i | 0.0851473 | − | 0.135606i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −15.7655 | + | 54.9832i | −0.551904 | + | 1.92480i | ||||
\(817\) | 4.05136 | 0.141739 | ||||||||
\(818\) | −2.37903 | + | 3.78885i | −0.0831808 | + | 0.132474i | ||||
\(819\) | 63.5212 | − | 26.3113i | 2.21961 | − | 0.919393i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.76592 | + | 9.09173i | −0.131431 | + | 0.317304i | −0.975871 | − | 0.218347i | \(-0.929934\pi\) |
0.844440 | + | 0.535651i | \(0.179934\pi\) | |||||||
\(822\) | −10.4773 | + | 61.7828i | −0.365439 | + | 2.15492i | ||||
\(823\) | 9.16017 | + | 9.16017i | 0.319304 | + | 0.319304i | 0.848500 | − | 0.529196i | \(-0.177506\pi\) |
−0.529196 | + | 0.848500i | \(0.677506\pi\) | |||||||
\(824\) | −20.6075 | − | 2.30223i | −0.717897 | − | 0.0802018i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.834296 | + | 1.17505i | 0.0290289 | + | 0.0408851i | ||||
\(827\) | 16.5936 | − | 40.0605i | 0.577017 | − | 1.39304i | −0.318461 | − | 0.947936i | \(-0.603166\pi\) |
0.895478 | − | 0.445106i | \(-0.146834\pi\) | |||||||
\(828\) | 119.172 | − | 57.4827i | 4.14152 | − | 1.99766i | ||||
\(829\) | −9.71946 | − | 23.4648i | −0.337571 | − | 0.814968i | −0.997948 | − | 0.0640336i | \(-0.979604\pi\) |
0.660377 | − | 0.750934i | \(-0.270396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.4955 | 0.676291 | ||||||||
\(832\) | −44.1776 | + | 7.59186i | −1.53158 | + | 0.263200i | ||||
\(833\) | 20.6741i | 0.716316i | ||||||||
\(834\) | −11.6650 | + | 2.66633i | −0.403927 | + | 0.0923273i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.23278 | + | 8.77535i | 0.146394 | + | 0.303502i | ||||
\(837\) | 6.81461 | − | 16.4519i | 0.235547 | − | 0.568662i | ||||
\(838\) | 11.7013 | − | 8.30805i | 0.404215 | − | 0.286997i | ||||
\(839\) | −32.2653 | − | 32.2653i | −1.11392 | − | 1.11392i | −0.992615 | − | 0.121307i | \(-0.961292\pi\) |
−0.121307 | − | 0.992615i | \(-0.538708\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0270 | − | 17.0270i | 0.587136 | − | 0.587136i | ||||
\(842\) | −0.819424 | + | 4.83198i | −0.0282392 | + | 0.166521i | ||||
\(843\) | −8.02915 | − | 3.32578i | −0.276539 | − | 0.114546i | ||||
\(844\) | 4.42675 | − | 4.95980i | 0.152375 | − | 0.170723i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 23.9172 | + | 15.0177i | 0.822290 | + | 0.516319i | ||||
\(847\) | 13.7424 | 0.472195 | ||||||||
\(848\) | 13.8313 | − | 7.66700i | 0.474968 | − | 0.263286i | ||||
\(849\) | 55.7216i | 1.91236i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8650 | + | 7.81413i | −0.646683 | + | 0.267865i | ||||
\(852\) | 59.6448 | − | 3.38721i | 2.04340 | − | 0.116044i | ||||
\(853\) | −4.41898 | − | 1.83040i | −0.151303 | − | 0.0626718i | 0.305747 | − | 0.952113i | \(-0.401094\pi\) |
−0.457050 | + | 0.889441i | \(0.651094\pi\) | |||||||
\(854\) | −2.70629 | + | 15.9585i | −0.0926073 | + | 0.546087i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.77968 | − | 30.3673i | −0.300083 | − | 1.03793i | ||||
\(857\) | 13.7258 | − | 13.7258i | 0.468864 | − | 0.468864i | −0.432683 | − | 0.901546i | \(-0.642433\pi\) |
0.901546 | + | 0.432683i | \(0.142433\pi\) | |||||||
\(858\) | −19.2213 | − | 27.0718i | −0.656204 | − | 0.924217i | ||||
\(859\) | 35.3096 | + | 14.6257i | 1.20475 | + | 0.499023i | 0.892530 | − | 0.450988i | \(-0.148928\pi\) |
0.312217 | + | 0.950011i | \(0.398928\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.3045 | + | 29.7057i | 0.419336 | + | 1.01237i | ||||
\(862\) | 37.7793 | − | 8.63538i | 1.28677 | − | 0.294122i | ||||
\(863\) | 52.6541i | 1.79237i | 0.443685 | + | 0.896183i | \(0.353671\pi\) | ||||
−0.443685 | + | 0.896183i | \(0.646329\pi\) | |||||||
\(864\) | −77.7363 | + | 69.6896i | −2.64464 | + | 2.37089i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.0047 | + | 43.7701i | 0.339974 | + | 1.48737i | ||||
\(867\) | −2.66833 | + | 1.10526i | −0.0906212 | + | 0.0375365i | ||||
\(868\) | 0.923514 | − | 2.64458i | 0.0313461 | − | 0.0897630i | ||||
\(869\) | 17.0455 | + | 7.06050i | 0.578231 | + | 0.239511i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.08520 | + | 7.08520i | 0.240073 | + | 0.240073i | ||||
\(872\) | 34.2949 | + | 18.9119i | 1.16137 | + | 0.640438i | ||||
\(873\) | −78.7810 | − | 78.7810i | −2.66633 | − | 2.66633i | ||||
\(874\) | 7.28100 | − | 42.9346i | 0.246283 | − | 1.45229i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −54.5000 | + | 3.09504i | −1.84138 | + | 0.104572i | ||||
\(877\) | 12.2342 | + | 29.5360i | 0.413120 | + | 0.997359i | 0.984295 | + | 0.176531i | \(0.0564876\pi\) |
−0.571175 | + | 0.820828i | \(0.693512\pi\) | |||||||
\(878\) | −12.1224 | − | 7.61172i | −0.409113 | − | 0.256883i | ||||
\(879\) | − | 57.8149i | − | 1.95005i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.17260i | 0.275342i | 0.990478 | + | 0.137671i | \(0.0439617\pi\) | ||||
−0.990478 | + | 0.137671i | \(0.956038\pi\) | |||||||
\(882\) | −31.1051 | + | 49.5380i | −1.04736 | + | 1.66803i | ||||
\(883\) | −4.83737 | − | 11.6784i | −0.162790 | − | 0.393011i | 0.821345 | − | 0.570432i | \(-0.193224\pi\) |
−0.984135 | + | 0.177422i | \(0.943224\pi\) | |||||||
\(884\) | −35.3262 | − | 31.5295i | −1.18815 | − | 1.06045i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.06216 | + | 1.53679i | 0.304449 | + | 0.0516295i | ||||
\(887\) | −24.8109 | − | 24.8109i | −0.833067 | − | 0.833067i | 0.154868 | − | 0.987935i | \(-0.450505\pi\) |
−0.987935 | + | 0.154868i | \(0.950505\pi\) | |||||||
\(888\) | 19.5119 | − | 15.5904i | 0.654778 | − | 0.523179i | ||||
\(889\) | 11.6236 | + | 11.6236i | 0.389841 | + | 0.389841i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −42.4349 | − | 17.5771i | −1.42162 | − | 0.588855i | ||||
\(892\) | −20.3036 | − | 42.0931i | −0.679814 | − | 1.40938i | ||||
\(893\) | 8.58748 | − | 3.55705i | 0.287369 | − | 0.119032i | ||||
\(894\) | −86.1172 | + | 19.6842i | −2.88019 | + | 0.658337i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.5871 | + | 11.6382i | −0.387097 | + | 0.388805i | ||||
\(897\) | 148.401i | 4.95496i | ||||||||
\(898\) | −2.67227 | − | 11.6910i | −0.0891747 | − | 0.390134i | ||||
\(899\) | 0.819039 | + | 1.97734i | 0.0273165 | + | 0.0659478i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4334 | + | 6.39272i | 0.514161 | + | 0.212972i | ||||
\(902\) | 9.34405 | − | 6.63437i | 0.311123 | − | 0.220900i | ||||
\(903\) | −3.57671 | + | 3.57671i | −0.119025 | + | 0.119025i | ||||
\(904\) | −11.1922 | − | 14.0074i | −0.372247 | − | 0.465881i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −88.4005 | − | 14.9912i | −2.93691 | − | 0.498051i | ||||
\(907\) | −32.3281 | − | 13.3908i | −1.07344 | − | 0.444633i | −0.225236 | − | 0.974304i | \(-0.572315\pi\) |
−0.848203 | + | 0.529672i | \(0.822315\pi\) | |||||||
\(908\) | −14.6965 | + | 16.4662i | −0.487720 | + | 0.546450i | ||||
\(909\) | 31.0305 | − | 12.8533i | 1.02922 | − | 0.426315i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2045i | 0.636273i | 0.948045 | + | 0.318137i | \(0.103057\pi\) | ||||
−0.948045 | + | 0.318137i | \(0.896943\pi\) | |||||||
\(912\) | 6.03030 | + | 52.9220i | 0.199683 | + | 1.75242i | ||||
\(913\) | 4.49617 | 0.148802 | ||||||||
\(914\) | −18.9751 | + | 30.2197i | −0.627639 | + | 0.999579i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.2266 | − | 2.05730i | 1.19696 | − | 0.0679750i | ||||
\(917\) | −10.2534 | − | 4.24711i | −0.338598 | − | 0.140252i | ||||
\(918\) | −108.730 | − | 18.4388i | −3.58862 | − | 0.608570i | ||||
\(919\) | 7.47911 | − | 7.47911i | 0.246713 | − | 0.246713i | −0.572907 | − | 0.819620i | \(-0.694184\pi\) |
0.819620 | + | 0.572907i | \(0.194184\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.27140 | + | 1.27140i | 0.0418939 | + | 0.0418939i | ||||
\(922\) | −2.25566 | − | 3.17693i | −0.0742861 | − | 0.104627i | ||||
\(923\) | −18.9255 | + | 45.6902i | −0.622940 | + | 1.50391i | ||||
\(924\) | −11.4841 | − | 4.01036i | −0.377799 | − | 0.131931i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.39169 | − | 36.7132i | −0.275768 | − | 1.20647i | ||||
\(927\) | − | 61.9731i | − | 2.03546i | ||||||
\(928\) | 0.683866 | − | 12.5292i | 0.0224490 | − | 0.411290i | ||||
\(929\) | −33.1810 | −1.08863 | −0.544317 | − | 0.838880i | \(-0.683211\pi\) | ||||
−0.544317 | + | 0.838880i | \(0.683211\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.36746 | + | 17.7866i | 0.241459 | + | 0.582933i | ||||
\(932\) | −51.1382 | − | 17.8579i | −1.67509 | − | 0.584956i | ||||
\(933\) | −4.87822 | + | 11.7771i | −0.159706 | + | 0.385564i | ||||
\(934\) | 7.26482 | − | 5.15810i | 0.237712 | − | 0.168778i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −37.2089 | − | 128.699i | −1.21621 | − | 4.20665i | ||||
\(937\) | −4.34060 | − | 4.34060i | −0.141801 | − | 0.141801i | 0.632643 | − | 0.774444i | \(-0.281970\pi\) |
−0.774444 | + | 0.632643i | \(0.781970\pi\) | |||||||
\(938\) | 3.61939 | + | 0.613788i | 0.118177 | + | 0.0200409i | ||||
\(939\) | −25.1936 | + | 60.8227i | −0.822161 | + | 1.98487i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2850 | + | 10.8876i | −0.856866 | + | 0.354925i | −0.767481 | − | 0.641072i | \(-0.778490\pi\) |
−0.0893847 | + | 0.995997i | \(0.528490\pi\) | |||||||
\(942\) | −46.2089 | − | 29.0147i | −1.50557 | − | 0.945351i | ||||
\(943\) | −51.2217 | −1.66801 | ||||||||
\(944\) | 2.45593 | − | 1.36138i | 0.0799336 | − | 0.0443091i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.52678 | + | 0.958671i | 0.0496400 | + | 0.0311691i | ||||
\(947\) | 14.7887 | + | 35.7030i | 0.480567 | + | 1.16019i | 0.959340 | + | 0.282252i | \(0.0910816\pi\) |
−0.478773 | + | 0.877939i | \(0.658918\pi\) | |||||||
\(948\) | 75.2526 | + | 67.1648i | 2.44409 | + | 2.18141i | ||||
\(949\) | 17.2930 | − | 41.7491i | 0.561356 | − | 1.35523i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.8358 | − | 51.8358i | 1.68089 | − | 1.68089i | ||||
\(952\) | −17.2407 | − | 1.92609i | −0.558774 | − | 0.0624250i | ||||
\(953\) | −16.4270 | + | 16.4270i | −0.532122 | + | 0.532122i | −0.921204 | − | 0.389081i | \(-0.872793\pi\) |
0.389081 | + | 0.921204i | \(0.372793\pi\) | |||||||
\(954\) | 27.3624 | + | 38.5380i | 0.885889 | + | 1.24771i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.9992 | + | 35.2424i | 0.549793 | + | 1.13982i | ||||
\(957\) | 8.58657 | − | 3.55667i | 0.277564 | − | 0.114971i | ||||
\(958\) | −2.81029 | − | 12.2949i | −0.0907965 | − | 0.397229i | ||||
\(959\) | −19.0058 | −0.613728 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0690 | −0.969968 | ||||||||
\(962\) | 4.60701 | + | 20.1554i | 0.148536 | + | 0.649837i | ||||
\(963\) | 87.2845 | − | 36.1544i | 2.81270 | − | 1.16506i | ||||
\(964\) | −4.02410 | − | 8.34271i | −0.129608 | − | 0.268701i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 31.4764 | + | 44.3324i | 1.01274 | + | 1.42637i | ||||
\(967\) | −6.93584 | + | 6.93584i | −0.223042 | + | 0.223042i | −0.809778 | − | 0.586736i | \(-0.800412\pi\) |
0.586736 | + | 0.809778i | \(0.300412\pi\) | |||||||
\(968\) | 2.97300 | − | 26.6117i | 0.0955558 | − | 0.855332i | ||||
\(969\) | −39.7854 | + | 39.7854i | −1.27809 | + | 1.27809i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.4706 | − | 34.9351i | 0.464383 | − | 1.12112i | −0.502197 | − | 0.864753i | \(-0.667475\pi\) |
0.966580 | − | 0.256366i | \(-0.0825253\pi\) | |||||||
\(972\) | −104.727 | − | 93.4715i | −3.35913 | − | 2.99810i | ||||
\(973\) | −1.38882 | − | 3.35290i | −0.0445234 | − | 0.107489i | ||||
\(974\) | −24.6741 | − | 15.4930i | −0.790610 | − | 0.496427i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.3175 | + | 8.69305i | 0.970440 | + | 0.278258i | ||||
\(977\) | −21.7591 | −0.696134 | −0.348067 | − | 0.937470i | \(-0.613162\pi\) | ||||
−0.348067 | + | 0.937470i | \(0.613162\pi\) | |||||||
\(978\) | 52.4380 | + | 32.9260i | 1.67678 | + | 1.05286i | ||||
\(979\) | 16.0205 | − | 6.63589i | 0.512016 | − | 0.212084i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −44.7928 | + | 108.139i | −1.43012 | + | 3.45262i | ||||
\(982\) | 44.1282 | + | 7.48341i | 1.40819 | + | 0.238805i | ||||
\(983\) | 31.8111 | + | 31.8111i | 1.01462 | + | 1.01462i | 0.999892 | + | 0.0147254i | \(0.00468739\pi\) |
0.0147254 | + | 0.999892i | \(0.495313\pi\) | |||||||
\(984\) | 60.1859 | − | 17.4008i | 1.91866 | − | 0.554716i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.8076 | − | 7.67350i | 0.344184 | − | 0.244374i | ||||
\(987\) | −4.44106 | + | 10.7217i | −0.141361 | + | 0.341275i | ||||
\(988\) | −41.6282 | − | 14.5370i | −1.32437 | − | 0.462482i | ||||
\(989\) | −3.08366 | − | 7.44463i | −0.0980548 | − | 0.236725i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.60717 | −0.146352 | −0.0731758 | − | 0.997319i | \(-0.523313\pi\) | ||||
−0.0731758 | + | 0.997319i | \(0.523313\pi\) | |||||||
\(992\) | −4.92135 | − | 2.36047i | −0.156253 | − | 0.0749451i | ||||
\(993\) | − | 30.5134i | − | 0.968313i | ||||||
\(994\) | 4.03739 | + | 17.6634i | 0.128058 | + | 0.560248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 23.2064 | + | 8.10391i | 0.735324 | + | 0.256782i | ||||
\(997\) | 12.3407 | − | 29.7932i | 0.390835 | − | 0.943559i | −0.598924 | − | 0.800806i | \(-0.704405\pi\) |
0.989758 | − | 0.142752i | \(-0.0455953\pi\) | |||||||
\(998\) | 8.88218 | + | 12.5099i | 0.281160 | + | 0.395995i | ||||
\(999\) | 34.0501 | + | 34.0501i | 1.07730 | + | 1.07730i |
(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 | 800.2.ba.f.549.10 | 64 | ||
5.2 | odd | 4 | 800.2.y.d.101.2 | ✓ | 64 | ||
5.3 | odd | 4 | 800.2.y.e.101.15 | yes | 64 | ||
5.4 | even | 2 | 800.2.ba.h.549.7 | 64 | |||
32.13 | even | 8 | 800.2.ba.h.749.7 | 64 | |||
160.13 | odd | 8 | 800.2.y.e.301.15 | yes | 64 | ||
160.77 | odd | 8 | 800.2.y.d.301.2 | yes | 64 | ||
160.109 | even | 8 | inner | 800.2.ba.f.749.10 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
800.2.y.d.101.2 | ✓ | 64 | 5.2 | odd | 4 | ||
800.2.y.d.301.2 | yes | 64 | 160.77 | odd | 8 | ||
800.2.y.e.101.15 | yes | 64 | 5.3 | odd | 4 | ||
800.2.y.e.301.15 | yes | 64 | 160.13 | odd | 8 | ||
800.2.ba.f.549.10 | 64 | 1.1 | even | 1 | trivial | ||
800.2.ba.f.749.10 | 64 | 160.109 | even | 8 | inner | ||
800.2.ba.h.549.7 | 64 | 5.4 | even | 2 | |||
800.2.ba.h.749.7 | 64 | 32.13 | even | 8 |