Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.d.1011.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.662827 | − | 0.382683i | 0.382683 | − | 0.220942i | −0.296302 | − | 0.955094i | \(-0.595753\pi\) |
0.678985 | + | 0.734152i | \(0.262420\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 3.37695 | + | 1.94969i | 1.51022 | + | 0.871926i | 0.999929 | + | 0.0119244i | \(0.00379573\pi\) |
0.510291 | + | 0.860002i | \(0.329538\pi\) | |||||||
\(6\) | −0.765367 | −0.312460 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.20711 | + | 2.09077i | −0.402369 | + | 0.696923i | ||||
\(10\) | −1.94969 | − | 3.37695i | −0.616545 | − | 1.06789i | ||||
\(11\) | −2.97369 | + | 1.46874i | −0.896601 | + | 0.442840i | ||||
\(12\) | 0.662827 | + | 0.382683i | 0.191342 | + | 0.110471i | ||||
\(13\) | −1.81903 | −0.504507 | −0.252254 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252254 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.98445 | 0.770582 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.03803 | + | 5.26202i | 0.736830 | + | 1.27623i | 0.953916 | + | 0.300075i | \(0.0970116\pi\) |
−0.217085 | + | 0.976153i | \(0.569655\pi\) | |||||||
\(18\) | 2.09077 | − | 1.20711i | 0.492799 | − | 0.284518i | ||||
\(19\) | 3.41476 | − | 5.91454i | 0.783400 | − | 1.35689i | −0.146550 | − | 0.989203i | \(-0.546817\pi\) |
0.929950 | − | 0.367685i | \(-0.119850\pi\) | |||||||
\(20\) | 3.89937i | 0.871926i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.30966 | + | 0.214882i | 0.705621 | + | 0.0458130i | ||||
\(23\) | 2.18834 | − | 3.79031i | 0.456300 | − | 0.790334i | −0.542462 | − | 0.840080i | \(-0.682508\pi\) |
0.998762 | + | 0.0497460i | \(0.0158412\pi\) | |||||||
\(24\) | −0.382683 | − | 0.662827i | −0.0781149 | − | 0.135299i | ||||
\(25\) | 5.10255 | + | 8.83788i | 1.02051 | + | 1.76758i | ||||
\(26\) | 1.57532 | + | 0.909513i | 0.308946 | + | 0.178370i | ||||
\(27\) | 4.14386i | 0.797486i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.36112i | 1.73832i | 0.494534 | + | 0.869158i | \(0.335339\pi\) | ||||
−0.494534 | + | 0.869158i | \(0.664661\pi\) | |||||||
\(30\) | −2.58461 | − | 1.49222i | −0.471883 | − | 0.272442i | ||||
\(31\) | −6.82704 | + | 3.94159i | −1.22617 | + | 0.707931i | −0.966227 | − | 0.257693i | \(-0.917038\pi\) |
−0.259945 | + | 0.965623i | \(0.583704\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −1.40898 | + | 2.11150i | −0.245272 | + | 0.367565i | ||||
\(34\) | − | 6.07606i | − | 1.04204i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.41421 | −0.402369 | ||||||||
\(37\) | 2.30389 | − | 3.99045i | 0.378757 | − | 0.656026i | −0.612125 | − | 0.790761i | \(-0.709685\pi\) |
0.990882 | + | 0.134735i | \(0.0430183\pi\) | |||||||
\(38\) | −5.91454 | + | 3.41476i | −0.959465 | + | 0.553947i | ||||
\(39\) | −1.20570 | + | 0.696111i | −0.193067 | + | 0.111467i | ||||
\(40\) | 1.94969 | − | 3.37695i | 0.308272 | − | 0.533943i | ||||
\(41\) | 3.58235 | 0.559469 | 0.279734 | − | 0.960077i | \(-0.409754\pi\) | ||||
0.279734 | + | 0.960077i | \(0.409754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.25819i | − | 0.496869i | −0.968649 | − | 0.248435i | \(-0.920084\pi\) | ||
0.968649 | − | 0.248435i | \(-0.0799161\pi\) | |||||||
\(44\) | −2.75881 | − | 1.84092i | −0.415906 | − | 0.277529i | ||||
\(45\) | −8.15269 | + | 4.70696i | −1.21533 | + | 0.701672i | ||||
\(46\) | −3.79031 | + | 2.18834i | −0.558851 | + | 0.322653i | ||||
\(47\) | 0.176542 | + | 0.101927i | 0.0257513 | + | 0.0148675i | 0.512820 | − | 0.858496i | \(-0.328601\pi\) |
−0.487069 | + | 0.873363i | \(0.661934\pi\) | |||||||
\(48\) | 0.765367i | 0.110471i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 10.2051i | − | 1.44322i | ||||||
\(51\) | 4.02738 | + | 2.32521i | 0.563945 | + | 0.325594i | ||||
\(52\) | −0.909513 | − | 1.57532i | −0.126127 | − | 0.218458i | ||||
\(53\) | −2.49222 | − | 4.31666i | −0.342333 | − | 0.592939i | 0.642532 | − | 0.766259i | \(-0.277884\pi\) |
−0.984866 | + | 0.173320i | \(0.944551\pi\) | |||||||
\(54\) | 2.07193 | − | 3.58869i | 0.281954 | − | 0.488359i | ||||
\(55\) | −12.9056 | − | 0.837904i | −1.74019 | − | 0.112983i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.22709i | − | 0.692345i | ||||||
\(58\) | 4.68056 | − | 8.10697i | 0.614588 | − | 1.06450i | ||||
\(59\) | −4.50118 | + | 2.59876i | −0.586004 | + | 0.338330i | −0.763516 | − | 0.645789i | \(-0.776529\pi\) |
0.177512 | + | 0.984119i | \(0.443195\pi\) | |||||||
\(60\) | 1.49222 | + | 2.58461i | 0.192645 | + | 0.333672i | ||||
\(61\) | −4.49186 | + | 7.78013i | −0.575124 | + | 0.996143i | 0.420905 | + | 0.907105i | \(0.361713\pi\) |
−0.996028 | + | 0.0890385i | \(0.971621\pi\) | |||||||
\(62\) | 7.88318 | 1.00117 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −6.14277 | − | 3.54653i | −0.761917 | − | 0.439893i | ||||
\(66\) | 2.27596 | − | 1.12412i | 0.280152 | − | 0.138370i | ||||
\(67\) | 4.01676 | + | 6.95724i | 0.490726 | + | 0.849962i | 0.999943 | − | 0.0106761i | \(-0.00339837\pi\) |
−0.509217 | + | 0.860638i | \(0.670065\pi\) | |||||||
\(68\) | −3.03803 | + | 5.26202i | −0.368415 | + | 0.638114i | ||||
\(69\) | − | 3.34976i | − | 0.403264i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.86195 | 1.05172 | 0.525860 | − | 0.850571i | \(-0.323744\pi\) | ||||
0.525860 | + | 0.850571i | \(0.323744\pi\) | |||||||
\(72\) | 2.09077 | + | 1.20711i | 0.246400 | + | 0.142259i | ||||
\(73\) | −0.0278530 | − | 0.0482428i | −0.00325995 | − | 0.00564639i | 0.864391 | − | 0.502821i | \(-0.167704\pi\) |
−0.867651 | + | 0.497174i | \(0.834371\pi\) | |||||||
\(74\) | −3.99045 | + | 2.30389i | −0.463881 | + | 0.267822i | ||||
\(75\) | 6.76422 | + | 3.90532i | 0.781064 | + | 0.450948i | ||||
\(76\) | 6.82952 | 0.783400 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.39222 | 0.157638 | ||||||||
\(79\) | 7.34847 | + | 4.24264i | 0.826767 | + | 0.477334i | 0.852745 | − | 0.522328i | \(-0.174936\pi\) |
−0.0259772 | + | 0.999663i | \(0.508270\pi\) | |||||||
\(80\) | −3.37695 | + | 1.94969i | −0.377555 | + | 0.217982i | ||||
\(81\) | −2.03553 | − | 3.52565i | −0.226170 | − | 0.391739i | ||||
\(82\) | −3.10240 | − | 1.79117i | −0.342603 | − | 0.197802i | ||||
\(83\) | −10.4676 | −1.14897 | −0.574483 | − | 0.818517i | \(-0.694797\pi\) | ||||
−0.574483 | + | 0.818517i | \(0.694797\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.6928i | 2.56985i | ||||||||
\(86\) | −1.62910 | + | 2.82168i | −0.175670 | + | 0.304269i | ||||
\(87\) | 3.58235 | + | 6.20481i | 0.384068 | + | 0.665225i | ||||
\(88\) | 1.46874 | + | 2.97369i | 0.156568 | + | 0.316996i | ||||
\(89\) | −1.46160 | − | 0.843855i | −0.154929 | − | 0.0894484i | 0.420531 | − | 0.907278i | \(-0.361844\pi\) |
−0.575460 | + | 0.817830i | \(0.695177\pi\) | |||||||
\(90\) | 9.41392 | 0.992314 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.37667 | 0.456300 | ||||||||
\(93\) | −3.01676 | + | 5.22519i | −0.312824 | + | 0.541827i | ||||
\(94\) | −0.101927 | − | 0.176542i | −0.0105129 | − | 0.0182090i | ||||
\(95\) | 23.0630 | − | 13.3154i | 2.36621 | − | 1.36613i | ||||
\(96\) | 0.382683 | − | 0.662827i | 0.0390575 | − | 0.0676495i | ||||
\(97\) | − | 9.23880i | − | 0.938058i | −0.883183 | − | 0.469029i | \(-0.844604\pi\) | ||
0.883183 | − | 0.469029i | \(-0.155396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.518771 | − | 7.99022i | 0.0521384 | − | 0.803047i | ||||
\(100\) | −5.10255 | + | 8.83788i | −0.510255 | + | 0.883788i | ||||
\(101\) | −2.67283 | − | 4.62948i | −0.265957 | − | 0.460651i | 0.701857 | − | 0.712318i | \(-0.252355\pi\) |
−0.967814 | + | 0.251667i | \(0.919021\pi\) | |||||||
\(102\) | −2.32521 | − | 4.02738i | −0.230230 | − | 0.398770i | ||||
\(103\) | 3.67639 | + | 2.12256i | 0.362246 | + | 0.209143i | 0.670065 | − | 0.742302i | \(-0.266266\pi\) |
−0.307820 | + | 0.951445i | \(0.599599\pi\) | |||||||
\(104\) | 1.81903i | 0.178370i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.98445i | 0.484133i | ||||||||
\(107\) | 6.26883 | + | 3.61931i | 0.606031 | + | 0.349892i | 0.771411 | − | 0.636338i | \(-0.219552\pi\) |
−0.165379 | + | 0.986230i | \(0.552885\pi\) | |||||||
\(108\) | −3.58869 | + | 2.07193i | −0.345322 | + | 0.199372i | ||||
\(109\) | 5.19615 | − | 3.00000i | 0.497701 | − | 0.287348i | −0.230063 | − | 0.973176i | \(-0.573893\pi\) |
0.727764 | + | 0.685828i | \(0.240560\pi\) | |||||||
\(110\) | 10.7576 | + | 7.17844i | 1.02570 | + | 0.684437i | ||||
\(111\) | − | 3.52664i | − | 0.334734i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8400 | 1.58417 | 0.792085 | − | 0.610411i | \(-0.208996\pi\) | ||||
0.792085 | + | 0.610411i | \(0.208996\pi\) | |||||||
\(114\) | −2.61355 | + | 4.52679i | −0.244781 | + | 0.423973i | ||||
\(115\) | 14.7798 | − | 8.53314i | 1.37823 | − | 0.795719i | ||||
\(116\) | −8.10697 | + | 4.68056i | −0.752713 | + | 0.434579i | ||||
\(117\) | 2.19576 | − | 3.80317i | 0.202998 | − | 0.351603i | ||||
\(118\) | 5.19752 | 0.478470 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 2.98445i | − | 0.272442i | ||||||
\(121\) | 6.68563 | − | 8.73512i | 0.607785 | − | 0.794102i | ||||
\(122\) | 7.78013 | − | 4.49186i | 0.704380 | − | 0.406674i | ||||
\(123\) | 2.37448 | − | 1.37090i | 0.214099 | − | 0.123610i | ||||
\(124\) | −6.82704 | − | 3.94159i | −0.613086 | − | 0.353965i | ||||
\(125\) | 20.2966i | 1.81538i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.3300i | − | 1.53779i | −0.639375 | − | 0.768895i | \(-0.720807\pi\) | ||
0.639375 | − | 0.768895i | \(-0.279193\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −1.24686 | − | 2.15962i | −0.109780 | − | 0.190144i | ||||
\(130\) | 3.54653 | + | 6.14277i | 0.311051 | + | 0.538757i | ||||
\(131\) | 3.17776 | − | 5.50404i | 0.277642 | − | 0.480890i | −0.693156 | − | 0.720788i | \(-0.743780\pi\) |
0.970798 | + | 0.239897i | \(0.0771137\pi\) | |||||||
\(132\) | −2.53310 | − | 0.164463i | −0.220478 | − | 0.0143147i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 8.03353i | − | 0.693991i | ||||||
\(135\) | −8.07922 | + | 13.9936i | −0.695349 | + | 1.20438i | ||||
\(136\) | 5.26202 | − | 3.03803i | 0.451215 | − | 0.260509i | ||||
\(137\) | −0.674793 | − | 1.16878i | −0.0576515 | − | 0.0998553i | 0.835759 | − | 0.549096i | \(-0.185028\pi\) |
−0.893411 | + | 0.449241i | \(0.851695\pi\) | |||||||
\(138\) | −1.67488 | + | 2.90098i | −0.142575 | + | 0.246948i | ||||
\(139\) | 11.8957 | 1.00898 | 0.504491 | − | 0.863417i | \(-0.331680\pi\) | ||||
0.504491 | + | 0.863417i | \(0.331680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.156023 | 0.0131395 | ||||||||
\(142\) | −7.67468 | − | 4.43098i | −0.644045 | − | 0.371839i | ||||
\(143\) | 5.40922 | − | 2.67167i | 0.452341 | − | 0.223416i | ||||
\(144\) | −1.20711 | − | 2.09077i | −0.100592 | − | 0.174231i | ||||
\(145\) | −18.2512 | + | 31.6121i | −1.51568 | + | 2.62524i | ||||
\(146\) | 0.0557060i | 0.00461026i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.60778 | 0.378757 | ||||||||
\(149\) | 5.69557 | + | 3.28834i | 0.466599 | + | 0.269391i | 0.714815 | − | 0.699314i | \(-0.246511\pi\) |
−0.248216 | + | 0.968705i | \(0.579844\pi\) | |||||||
\(150\) | −3.90532 | − | 6.76422i | −0.318868 | − | 0.552296i | ||||
\(151\) | −7.48149 | + | 4.31944i | −0.608835 | + | 0.351511i | −0.772509 | − | 0.635003i | \(-0.780999\pi\) |
0.163674 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(152\) | −5.91454 | − | 3.41476i | −0.479733 | − | 0.276974i | ||||
\(153\) | −14.6689 | −1.18591 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −30.7395 | −2.46905 | ||||||||
\(156\) | −1.20570 | − | 0.696111i | −0.0965333 | − | 0.0557335i | ||||
\(157\) | −2.12168 | + | 1.22495i | −0.169329 | + | 0.0977619i | −0.582269 | − | 0.812996i | \(-0.697835\pi\) |
0.412941 | + | 0.910758i | \(0.364502\pi\) | |||||||
\(158\) | −4.24264 | − | 7.34847i | −0.337526 | − | 0.584613i | ||||
\(159\) | −3.30383 | − | 1.90747i | −0.262011 | − | 0.151272i | ||||
\(160\) | 3.89937 | 0.308272 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.07107i | 0.319853i | ||||||||
\(163\) | −1.14503 | + | 1.98325i | −0.0896854 | + | 0.155340i | −0.907378 | − | 0.420315i | \(-0.861920\pi\) |
0.817693 | + | 0.575655i | \(0.195253\pi\) | |||||||
\(164\) | 1.79117 | + | 3.10240i | 0.139867 | + | 0.242257i | ||||
\(165\) | −8.87482 | + | 4.38337i | −0.690904 | + | 0.341245i | ||||
\(166\) | 9.06519 | + | 5.23379i | 0.703595 | + | 0.406221i | ||||
\(167\) | 8.51406 | 0.658838 | 0.329419 | − | 0.944184i | \(-0.393147\pi\) | ||||
0.329419 | + | 0.944184i | \(0.393147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.69114 | −0.745473 | ||||||||
\(170\) | 11.8464 | − | 20.5186i | 0.908578 | − | 1.57370i | ||||
\(171\) | 8.24396 | + | 14.2790i | 0.630432 | + | 1.09194i | ||||
\(172\) | 2.82168 | − | 1.62910i | 0.215151 | − | 0.124217i | ||||
\(173\) | 11.9961 | − | 20.7778i | 0.912044 | − | 1.57971i | 0.100872 | − | 0.994899i | \(-0.467837\pi\) |
0.811172 | − | 0.584807i | \(-0.198830\pi\) | |||||||
\(174\) | − | 7.16469i | − | 0.543154i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.214882 | − | 3.30966i | 0.0161973 | − | 0.249475i | ||||
\(177\) | −1.98900 | + | 3.44506i | −0.149503 | + | 0.258946i | ||||
\(178\) | 0.843855 | + | 1.46160i | 0.0632496 | + | 0.109552i | ||||
\(179\) | −10.0792 | − | 17.4577i | −0.753357 | − | 1.30485i | −0.946187 | − | 0.323620i | \(-0.895100\pi\) |
0.192831 | − | 0.981232i | \(-0.438233\pi\) | |||||||
\(180\) | −8.15269 | − | 4.70696i | −0.607666 | − | 0.350836i | ||||
\(181\) | − | 11.1135i | − | 0.826062i | −0.910717 | − | 0.413031i | \(-0.864470\pi\) | ||
0.910717 | − | 0.413031i | \(-0.135530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.87584i | 0.508277i | ||||||||
\(184\) | −3.79031 | − | 2.18834i | −0.279425 | − | 0.161326i | ||||
\(185\) | 15.5603 | − | 8.98372i | 1.14401 | − | 0.660496i | ||||
\(186\) | 5.22519 | − | 3.01676i | 0.383129 | − | 0.221200i | ||||
\(187\) | −16.7627 | − | 11.1855i | −1.22581 | − | 0.817968i | ||||
\(188\) | 0.203854i | 0.0148675i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −26.6308 | −1.93200 | ||||||||
\(191\) | 12.2542 | − | 21.2249i | 0.886681 | − | 1.53578i | 0.0429063 | − | 0.999079i | \(-0.486338\pi\) |
0.843775 | − | 0.536698i | \(-0.180328\pi\) | |||||||
\(192\) | −0.662827 | + | 0.382683i | −0.0478354 | + | 0.0276178i | ||||
\(193\) | −10.9286 | + | 6.30966i | −0.786661 | + | 0.454179i | −0.838786 | − | 0.544462i | \(-0.816734\pi\) |
0.0521247 | + | 0.998641i | \(0.483401\pi\) | |||||||
\(194\) | −4.61940 | + | 8.00103i | −0.331653 | + | 0.574441i | ||||
\(195\) | −5.42879 | −0.388764 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2697i | 1.23042i | 0.788364 | + | 0.615209i | \(0.210928\pi\) | ||||
−0.788364 | + | 0.615209i | \(0.789072\pi\) | |||||||
\(198\) | −4.44438 | + | 6.66035i | −0.315848 | + | 0.473330i | ||||
\(199\) | −7.95279 | + | 4.59154i | −0.563758 | + | 0.325486i | −0.754653 | − | 0.656125i | \(-0.772195\pi\) |
0.190894 | + | 0.981611i | \(0.438861\pi\) | |||||||
\(200\) | 8.83788 | − | 5.10255i | 0.624932 | − | 0.360805i | ||||
\(201\) | 5.32484 | + | 3.07430i | 0.375585 | + | 0.216844i | ||||
\(202\) | 5.34567i | 0.376120i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.65041i | 0.325594i | ||||||||
\(205\) | 12.0974 | + | 6.98445i | 0.844921 | + | 0.487815i | ||||
\(206\) | −2.12256 | − | 3.67639i | −0.147886 | − | 0.256146i | ||||
\(207\) | 5.28311 | + | 9.15062i | 0.367202 | + | 0.636012i | ||||
\(208\) | 0.909513 | − | 1.57532i | 0.0630634 | − | 0.109229i | ||||
\(209\) | −1.46754 | + | 22.6034i | −0.101512 | + | 1.56351i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.12250i | 0.146119i | 0.997328 | + | 0.0730593i | \(0.0232762\pi\) | ||||
−0.997328 | + | 0.0730593i | \(0.976724\pi\) | |||||||
\(212\) | 2.49222 | − | 4.31666i | 0.171167 | − | 0.296469i | ||||
\(213\) | 5.87394 | − | 3.39132i | 0.402476 | − | 0.232370i | ||||
\(214\) | −3.61931 | − | 6.26883i | −0.247411 | − | 0.428529i | ||||
\(215\) | 6.35245 | − | 11.0028i | 0.433233 | − | 0.750382i | ||||
\(216\) | 4.14386 | 0.281954 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | −0.0369234 | − | 0.0213178i | −0.00249505 | − | 0.00144052i | ||||
\(220\) | −5.72714 | − | 11.5955i | −0.386124 | − | 0.781769i | ||||
\(221\) | −5.52625 | − | 9.57175i | −0.371736 | − | 0.643866i | ||||
\(222\) | −1.76332 | + | 3.05416i | −0.118346 | + | 0.204982i | ||||
\(223\) | 5.77586i | 0.386780i | 0.981122 | + | 0.193390i | \(0.0619483\pi\) | ||||
−0.981122 | + | 0.193390i | \(0.938052\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.6373 | −1.64249 | ||||||||
\(226\) | −14.5838 | − | 8.41998i | −0.970102 | − | 0.560089i | ||||
\(227\) | −0.605269 | − | 1.04836i | −0.0401731 | − | 0.0695819i | 0.845240 | − | 0.534387i | \(-0.179458\pi\) |
−0.885413 | + | 0.464805i | \(0.846124\pi\) | |||||||
\(228\) | 4.52679 | − | 2.61355i | 0.299794 | − | 0.173086i | ||||
\(229\) | −16.8020 | − | 9.70062i | −1.11031 | − | 0.641035i | −0.171397 | − | 0.985202i | \(-0.554828\pi\) |
−0.938909 | + | 0.344167i | \(0.888161\pi\) | |||||||
\(230\) | −17.0663 | −1.12532 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.36112 | 0.614588 | ||||||||
\(233\) | 17.0714 | + | 9.85619i | 1.11839 | + | 0.645700i | 0.940988 | − | 0.338439i | \(-0.109899\pi\) |
0.177397 | + | 0.984139i | \(0.443232\pi\) | |||||||
\(234\) | −3.80317 | + | 2.19576i | −0.248621 | + | 0.143541i | ||||
\(235\) | 0.397450 | + | 0.688404i | 0.0259268 | + | 0.0449065i | ||||
\(236\) | −4.50118 | − | 2.59876i | −0.293002 | − | 0.169165i | ||||
\(237\) | 6.49435 | 0.421854 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 11.6292i | − | 0.752229i | −0.926573 | − | 0.376115i | \(-0.877260\pi\) | ||
0.926573 | − | 0.376115i | \(-0.122740\pi\) | |||||||
\(240\) | −1.49222 | + | 2.58461i | −0.0963227 | + | 0.166836i | ||||
\(241\) | −13.6869 | − | 23.7064i | −0.881651 | − | 1.52706i | −0.849505 | − | 0.527581i | \(-0.823099\pi\) |
−0.0321456 | − | 0.999483i | \(-0.510234\pi\) | |||||||
\(242\) | −10.1575 | + | 4.22202i | −0.652948 | + | 0.271402i | ||||
\(243\) | −13.4645 | − | 7.77372i | −0.863747 | − | 0.498684i | ||||
\(244\) | −8.98372 | −0.575124 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.74181 | −0.174811 | ||||||||
\(247\) | −6.21154 | + | 10.7587i | −0.395231 | + | 0.684560i | ||||
\(248\) | 3.94159 | + | 6.82704i | 0.250291 | + | 0.433517i | ||||
\(249\) | −6.93819 | + | 4.00577i | −0.439690 | + | 0.253855i | ||||
\(250\) | 10.1483 | − | 17.5774i | 0.641835 | − | 1.11169i | ||||
\(251\) | − | 13.5021i | − | 0.852243i | −0.904666 | − | 0.426122i | \(-0.859880\pi\) | ||
0.904666 | − | 0.426122i | \(-0.140120\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.940467 | + | 14.4853i | −0.0591267 | + | 0.910682i | ||||
\(254\) | −8.66501 | + | 15.0082i | −0.543691 | + | 0.941701i | ||||
\(255\) | 9.06684 | + | 15.7042i | 0.567788 | + | 0.983437i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.43041 | − | 1.40320i | −0.151605 | − | 0.0875289i | 0.422279 | − | 0.906466i | \(-0.361230\pi\) |
−0.573883 | + | 0.818937i | \(0.694564\pi\) | |||||||
\(258\) | 2.49371i | 0.155252i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 7.09306i | − | 0.439893i | ||||||
\(261\) | −19.5720 | − | 11.2999i | −1.21147 | − | 0.699445i | ||||
\(262\) | −5.50404 | + | 3.17776i | −0.340041 | + | 0.196323i | ||||
\(263\) | −7.34847 | + | 4.24264i | −0.453126 | + | 0.261612i | −0.709150 | − | 0.705058i | \(-0.750921\pi\) |
0.256023 | + | 0.966671i | \(0.417588\pi\) | |||||||
\(264\) | 2.11150 | + | 1.40898i | 0.129954 | + | 0.0867167i | ||||
\(265\) | − | 19.4362i | − | 1.19396i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.29172 | −0.0790518 | ||||||||
\(268\) | −4.01676 | + | 6.95724i | −0.245363 | + | 0.424981i | ||||
\(269\) | 18.1498 | − | 10.4788i | 1.10662 | − | 0.638905i | 0.168665 | − | 0.985673i | \(-0.446054\pi\) |
0.937951 | + | 0.346768i | \(0.112721\pi\) | |||||||
\(270\) | 13.9936 | − | 8.07922i | 0.851625 | − | 0.491686i | ||||
\(271\) | −7.30660 | + | 12.6554i | −0.443844 | + | 0.768761i | −0.997971 | − | 0.0636717i | \(-0.979719\pi\) |
0.554127 | + | 0.832432i | \(0.313052\pi\) | |||||||
\(272\) | −6.07606 | −0.368415 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.34959i | 0.0815315i | ||||||||
\(275\) | −28.1539 | − | 18.7868i | −1.69774 | − | 1.13289i | ||||
\(276\) | 2.90098 | − | 1.67488i | 0.174618 | − | 0.100816i | ||||
\(277\) | 9.63380 | − | 5.56208i | 0.578839 | − | 0.334193i | −0.181833 | − | 0.983329i | \(-0.558203\pi\) |
0.760672 | + | 0.649136i | \(0.224870\pi\) | |||||||
\(278\) | −10.3020 | − | 5.94786i | −0.617873 | − | 0.356729i | ||||
\(279\) | − | 19.0317i | − | 1.13940i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.28929i | − | 0.434843i | −0.976078 | − | 0.217421i | \(-0.930235\pi\) | ||
0.976078 | − | 0.217421i | \(-0.0697646\pi\) | |||||||
\(282\) | −0.135120 | − | 0.0780114i | −0.00804626 | − | 0.00464551i | ||||
\(283\) | 8.00696 | + | 13.8685i | 0.475965 | + | 0.824395i | 0.999621 | − | 0.0275349i | \(-0.00876573\pi\) |
−0.523656 | + | 0.851930i | \(0.675432\pi\) | |||||||
\(284\) | 4.43098 | + | 7.67468i | 0.262930 | + | 0.455408i | ||||
\(285\) | 10.1912 | − | 17.6516i | 0.603674 | − | 1.04559i | ||||
\(286\) | −6.02035 | − | 0.390876i | −0.355991 | − | 0.0231130i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.41421i | 0.142259i | ||||||||
\(289\) | −9.95924 | + | 17.2499i | −0.585838 | + | 1.01470i | ||||
\(290\) | 31.6121 | − | 18.2512i | 1.85633 | − | 1.07175i | ||||
\(291\) | −3.53553 | − | 6.12372i | −0.207257 | − | 0.358979i | ||||
\(292\) | 0.0278530 | − | 0.0482428i | 0.00162997 | − | 0.00282320i | ||||
\(293\) | 14.2550 | 0.832783 | 0.416392 | − | 0.909185i | \(-0.363295\pi\) | ||||
0.416392 | + | 0.909185i | \(0.363295\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.2671 | −1.17999 | ||||||||
\(296\) | −3.99045 | − | 2.30389i | −0.231940 | − | 0.133911i | ||||
\(297\) | −6.08623 | − | 12.3225i | −0.353159 | − | 0.715027i | ||||
\(298\) | −3.28834 | − | 5.69557i | −0.190488 | − | 0.329935i | ||||
\(299\) | −3.98064 | + | 6.89467i | −0.230206 | + | 0.398729i | ||||
\(300\) | 7.81064i | 0.450948i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.63888 | 0.497112 | ||||||||
\(303\) | −3.54325 | − | 2.04570i | −0.203555 | − | 0.117522i | ||||
\(304\) | 3.41476 | + | 5.91454i | 0.195850 | + | 0.339222i | ||||
\(305\) | −30.3376 | + | 17.5154i | −1.73713 | + | 1.00293i | ||||
\(306\) | 12.7036 | + | 7.33445i | 0.726219 | + | 0.419283i | ||||
\(307\) | −6.75074 | −0.385285 | −0.192643 | − | 0.981269i | \(-0.561706\pi\) | ||||
−0.192643 | + | 0.981269i | \(0.561706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.24908 | 0.184834 | ||||||||
\(310\) | 26.6212 | + | 15.3697i | 1.51198 | + | 0.872942i | ||||
\(311\) | 15.4763 | − | 8.93526i | 0.877581 | − | 0.506672i | 0.00772127 | − | 0.999970i | \(-0.497542\pi\) |
0.869860 | + | 0.493298i | \(0.164209\pi\) | |||||||
\(312\) | 0.696111 | + | 1.20570i | 0.0394095 | + | 0.0682593i | ||||
\(313\) | 13.0188 | + | 7.51640i | 0.735865 | + | 0.424852i | 0.820564 | − | 0.571554i | \(-0.193659\pi\) |
−0.0846986 | + | 0.996407i | \(0.526993\pi\) | |||||||
\(314\) | 2.44991 | 0.138256 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.48528i | 0.477334i | ||||||||
\(317\) | −4.86597 | + | 8.42810i | −0.273300 | + | 0.473370i | −0.969705 | − | 0.244280i | \(-0.921449\pi\) |
0.696405 | + | 0.717649i | \(0.254782\pi\) | |||||||
\(318\) | 1.90747 | + | 3.30383i | 0.106965 | + | 0.185270i | ||||
\(319\) | −13.7490 | − | 27.8371i | −0.769797 | − | 1.55858i | ||||
\(320\) | −3.37695 | − | 1.94969i | −0.188778 | − | 0.108991i | ||||
\(321\) | 5.54020 | 0.309224 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.4966 | 2.30893 | ||||||||
\(324\) | 2.03553 | − | 3.52565i | 0.113085 | − | 0.195869i | ||||
\(325\) | −9.28167 | − | 16.0763i | −0.514854 | − | 0.891754i | ||||
\(326\) | 1.98325 | − | 1.14503i | 0.109842 | − | 0.0634172i | ||||
\(327\) | 2.29610 | − | 3.97696i | 0.126975 | − | 0.219927i | ||||
\(328\) | − | 3.58235i | − | 0.197802i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.87750 | + | 0.641304i | 0.543739 | + | 0.0353026i | ||||
\(331\) | −9.12993 | + | 15.8135i | −0.501826 | + | 0.869188i | 0.498172 | + | 0.867078i | \(0.334005\pi\) |
−0.999998 | + | 0.00210996i | \(0.999328\pi\) | |||||||
\(332\) | −5.23379 | − | 9.06519i | −0.287241 | − | 0.497517i | ||||
\(333\) | 5.56208 | + | 9.63380i | 0.304800 | + | 0.527929i | ||||
\(334\) | −7.37339 | − | 4.25703i | −0.403454 | − | 0.232934i | ||||
\(335\) | 31.3257i | 1.71151i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 29.6928i | − | 1.61747i | −0.588173 | − | 0.808735i | \(-0.700153\pi\) | ||
0.588173 | − | 0.808735i | \(-0.299847\pi\) | |||||||
\(338\) | 8.39278 | + | 4.84557i | 0.456507 | + | 0.263564i | ||||
\(339\) | 11.1620 | − | 6.44437i | 0.606236 | − | 0.350010i | ||||
\(340\) | −20.5186 | + | 11.8464i | −1.11278 | + | 0.642461i | ||||
\(341\) | 14.5123 | − | 21.7482i | 0.785886 | − | 1.17773i | ||||
\(342\) | − | 16.4879i | − | 0.891565i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.25819 | −0.175670 | ||||||||
\(345\) | 6.53098 | − | 11.3120i | 0.351616 | − | 0.609017i | ||||
\(346\) | −20.7778 | + | 11.9961i | −1.11702 | + | 0.644913i | ||||
\(347\) | 16.6981 | − | 9.64063i | 0.896399 | − | 0.517536i | 0.0203688 | − | 0.999793i | \(-0.493516\pi\) |
0.876030 | + | 0.482256i | \(0.160183\pi\) | |||||||
\(348\) | −3.58235 | + | 6.20481i | −0.192034 | + | 0.332613i | ||||
\(349\) | −23.9921 | −1.28427 | −0.642135 | − | 0.766592i | \(-0.721951\pi\) | ||||
−0.642135 | + | 0.766592i | \(0.721951\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 7.53779i | − | 0.402337i | ||||||
\(352\) | −1.84092 | + | 2.75881i | −0.0981214 | + | 0.147045i | ||||
\(353\) | −13.9844 | + | 8.07391i | −0.744316 | + | 0.429731i | −0.823636 | − | 0.567118i | \(-0.808058\pi\) |
0.0793204 | + | 0.996849i | \(0.474725\pi\) | |||||||
\(354\) | 3.44506 | − | 1.98900i | 0.183103 | − | 0.105714i | ||||
\(355\) | 29.9264 | + | 17.2780i | 1.58833 | + | 0.917022i | ||||
\(356\) | − | 1.68771i | − | 0.0894484i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.1584i | 1.06541i | ||||||||
\(359\) | −15.7145 | − | 9.07278i | −0.829381 | − | 0.478843i | 0.0242599 | − | 0.999706i | \(-0.492277\pi\) |
−0.853641 | + | 0.520862i | \(0.825610\pi\) | |||||||
\(360\) | 4.70696 | + | 8.15269i | 0.248078 | + | 0.429685i | ||||
\(361\) | −13.8212 | − | 23.9390i | −0.727431 | − | 1.25995i | ||||
\(362\) | −5.55676 | + | 9.62460i | −0.292057 | + | 0.505858i | ||||
\(363\) | 1.08864 | − | 8.34836i | 0.0571385 | − | 0.438175i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.217218i | − | 0.0113697i | ||||||
\(366\) | 3.43792 | − | 5.95465i | 0.179703 | − | 0.311255i | ||||
\(367\) | −4.25692 | + | 2.45773i | −0.222209 | + | 0.128293i | −0.606973 | − | 0.794723i | \(-0.707616\pi\) |
0.384763 | + | 0.923015i | \(0.374283\pi\) | |||||||
\(368\) | 2.18834 | + | 3.79031i | 0.114075 | + | 0.197584i | ||||
\(369\) | −4.32427 | + | 7.48986i | −0.225113 | + | 0.389907i | ||||
\(370\) | −17.9674 | −0.934083 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.03353 | −0.312824 | ||||||||
\(373\) | 1.96420 | + | 1.13403i | 0.101702 | + | 0.0587179i | 0.549989 | − | 0.835172i | \(-0.314632\pi\) |
−0.448286 | + | 0.893890i | \(0.647965\pi\) | |||||||
\(374\) | 8.92412 | + | 18.0683i | 0.461455 | + | 0.934289i | ||||
\(375\) | 7.76718 | + | 13.4531i | 0.401095 | + | 0.694718i | ||||
\(376\) | 0.101927 | − | 0.176542i | 0.00525647 | − | 0.00910448i | ||||
\(377\) | − | 17.0281i | − | 0.876993i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7984 | 0.760143 | 0.380072 | − | 0.924957i | \(-0.375899\pi\) | ||||
0.380072 | + | 0.924957i | \(0.375899\pi\) | |||||||
\(380\) | 23.0630 | + | 13.3154i | 1.18311 | + | 0.683067i | ||||
\(381\) | −6.63191 | − | 11.4868i | −0.339763 | − | 0.588487i | ||||
\(382\) | −21.2249 | + | 12.2542i | −1.08596 | + | 0.626978i | ||||
\(383\) | −6.29627 | − | 3.63515i | −0.321724 | − | 0.185748i | 0.330437 | − | 0.943828i | \(-0.392804\pi\) |
−0.652161 | + | 0.758081i | \(0.726137\pi\) | |||||||
\(384\) | 0.765367 | 0.0390575 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.6193 | 0.642306 | ||||||||
\(387\) | 6.81213 | + | 3.93298i | 0.346280 | + | 0.199925i | ||||
\(388\) | 8.00103 | − | 4.61940i | 0.406191 | − | 0.234514i | ||||
\(389\) | 17.5968 | + | 30.4786i | 0.892194 | + | 1.54533i | 0.837239 | + | 0.546837i | \(0.184168\pi\) |
0.0549549 | + | 0.998489i | \(0.482498\pi\) | |||||||
\(390\) | 4.70147 | + | 2.71440i | 0.238068 | + | 0.137449i | ||||
\(391\) | 26.5929 | 1.34486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.86431i | − | 0.245372i | ||||||
\(394\) | 8.63486 | − | 14.9560i | 0.435018 | − | 0.753473i | ||||
\(395\) | 16.5436 | + | 28.6544i | 0.832401 | + | 1.44176i | ||||
\(396\) | 7.17912 | − | 3.54584i | 0.360764 | − | 0.178185i | ||||
\(397\) | −16.3081 | − | 9.41550i | −0.818481 | − | 0.472550i | 0.0314111 | − | 0.999507i | \(-0.490000\pi\) |
−0.849893 | + | 0.526956i | \(0.823333\pi\) | |||||||
\(398\) | 9.18309 | 0.460307 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −10.2051 | −0.510255 | ||||||||
\(401\) | 3.55347 | − | 6.15480i | 0.177452 | − | 0.307356i | −0.763555 | − | 0.645743i | \(-0.776548\pi\) |
0.941007 | + | 0.338387i | \(0.109881\pi\) | |||||||
\(402\) | −3.07430 | − | 5.32484i | −0.153332 | − | 0.265579i | ||||
\(403\) | 12.4186 | − | 7.16986i | 0.618612 | − | 0.357156i | ||||
\(404\) | 2.67283 | − | 4.62948i | 0.132978 | − | 0.230325i | ||||
\(405\) | − | 15.8746i | − | 0.788816i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.990128 | + | 15.2502i | −0.0490788 | + | 0.755922i | ||||
\(408\) | 2.32521 | − | 4.02738i | 0.115115 | − | 0.199385i | ||||
\(409\) | −4.85705 | − | 8.41267i | −0.240166 | − | 0.415980i | 0.720595 | − | 0.693356i | \(-0.243869\pi\) |
−0.960761 | + | 0.277376i | \(0.910535\pi\) | |||||||
\(410\) | −6.98445 | − | 12.0974i | −0.344937 | − | 0.597449i | ||||
\(411\) | −0.894543 | − | 0.516465i | −0.0441245 | − | 0.0254753i | ||||
\(412\) | 4.24513i | 0.209143i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 10.5662i | − | 0.519301i | ||||||
\(415\) | −35.3485 | − | 20.4085i | −1.73519 | − | 1.00181i | ||||
\(416\) | −1.57532 | + | 0.909513i | −0.0772366 | + | 0.0445925i | ||||
\(417\) | 7.88481 | − | 4.55230i | 0.386121 | − | 0.222927i | ||||
\(418\) | 12.5726 | − | 18.8413i | 0.614947 | − | 0.921559i | ||||
\(419\) | 23.0474i | 1.12594i | 0.826478 | + | 0.562970i | \(0.190341\pi\) | ||||
−0.826478 | + | 0.562970i | \(0.809659\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.67074 | −0.0814270 | −0.0407135 | − | 0.999171i | \(-0.512963\pi\) | ||||
−0.0407135 | + | 0.999171i | \(0.512963\pi\) | |||||||
\(422\) | 1.06125 | − | 1.83814i | 0.0516608 | − | 0.0894790i | ||||
\(423\) | −0.426211 | + | 0.246073i | −0.0207231 | + | 0.0119645i | ||||
\(424\) | −4.31666 | + | 2.49222i | −0.209636 | + | 0.121033i | ||||
\(425\) | −31.0034 | + | 53.6994i | −1.50389 | + | 2.60481i | ||||
\(426\) | −6.78265 | −0.328620 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.23863i | 0.349892i | ||||||||
\(429\) | 2.56297 | − | 3.84087i | 0.123741 | − | 0.185439i | ||||
\(430\) | −11.0028 | + | 6.35245i | −0.530600 | + | 0.306342i | ||||
\(431\) | 33.6434 | − | 19.4240i | 1.62055 | − | 0.935623i | 0.633772 | − | 0.773520i | \(-0.281506\pi\) |
0.986774 | − | 0.162103i | \(-0.0518277\pi\) | |||||||
\(432\) | −3.58869 | − | 2.07193i | −0.172661 | − | 0.0996858i | ||||
\(433\) | 31.8479i | 1.53051i | 0.643726 | + | 0.765256i | \(0.277388\pi\) | ||||
−0.643726 | + | 0.765256i | \(0.722612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.9378i | 1.33951i | ||||||||
\(436\) | 5.19615 | + | 3.00000i | 0.248851 | + | 0.143674i | ||||
\(437\) | −14.9453 | − | 25.8860i | −0.714930 | − | 1.23830i | ||||
\(438\) | 0.0213178 | + | 0.0369234i | 0.00101860 | + | 0.00176427i | ||||
\(439\) | 6.02035 | − | 10.4276i | 0.287336 | − | 0.497680i | −0.685837 | − | 0.727755i | \(-0.740564\pi\) |
0.973173 | + | 0.230075i | \(0.0738971\pi\) | |||||||
\(440\) | −0.837904 | + | 12.9056i | −0.0399455 | + | 0.615249i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.0525i | 0.525714i | ||||||||
\(443\) | 15.2762 | − | 26.4591i | 0.725793 | − | 1.25711i | −0.232854 | − | 0.972512i | \(-0.574807\pi\) |
0.958647 | − | 0.284598i | \(-0.0918601\pi\) | |||||||
\(444\) | 3.05416 | − | 1.76332i | 0.144944 | − | 0.0836835i | ||||
\(445\) | −3.29050 | − | 5.69932i | −0.155985 | − | 0.270174i | ||||
\(446\) | 2.88793 | − | 5.00204i | 0.136748 | − | 0.236854i | ||||
\(447\) | 5.03357 | 0.238080 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7378 | 0.742712 | 0.371356 | − | 0.928490i | \(-0.378893\pi\) | ||||
0.371356 | + | 0.928490i | \(0.378893\pi\) | |||||||
\(450\) | 21.3365 | + | 12.3186i | 1.00581 | + | 0.580706i | ||||
\(451\) | −10.6528 | + | 5.26152i | −0.501620 | + | 0.247755i | ||||
\(452\) | 8.41998 | + | 14.5838i | 0.396043 | + | 0.685966i | ||||
\(453\) | −3.30596 | + | 5.72608i | −0.155327 | + | 0.269035i | ||||
\(454\) | 1.21054i | 0.0568134i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.22709 | −0.244781 | ||||||||
\(457\) | 14.8669 | + | 8.58340i | 0.695443 | + | 0.401514i | 0.805648 | − | 0.592395i | \(-0.201817\pi\) |
−0.110205 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(458\) | 9.70062 | + | 16.8020i | 0.453280 | + | 0.785105i | ||||
\(459\) | −21.8051 | + | 12.5892i | −1.01777 | + | 0.587612i | ||||
\(460\) | 14.7798 | + | 8.53314i | 0.689113 | + | 0.397860i | ||||
\(461\) | 0.312096 | 0.0145357 | 0.00726787 | − | 0.999974i | \(-0.497687\pi\) | ||||
0.00726787 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.9402 | −1.48439 | −0.742194 | − | 0.670185i | \(-0.766215\pi\) | ||||
−0.742194 | + | 0.670185i | \(0.766215\pi\) | |||||||
\(464\) | −8.10697 | − | 4.68056i | −0.376357 | − | 0.217290i | ||||
\(465\) | −20.3749 | + | 11.7635i | −0.944866 | + | 0.545518i | ||||
\(466\) | −9.85619 | − | 17.0714i | −0.456579 | − | 0.790818i | ||||
\(467\) | −16.3264 | − | 9.42604i | −0.755495 | − | 0.436185i | 0.0721810 | − | 0.997392i | \(-0.477004\pi\) |
−0.827676 | + | 0.561206i | \(0.810337\pi\) | |||||||
\(468\) | 4.39152 | 0.202998 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 0.794901i | − | 0.0366660i | ||||||
\(471\) | −0.937539 | + | 1.62386i | −0.0431995 | + | 0.0748237i | ||||
\(472\) | 2.59876 | + | 4.50118i | 0.119618 | + | 0.207184i | ||||
\(473\) | 4.78542 | + | 9.68884i | 0.220034 | + | 0.445493i | ||||
\(474\) | −5.62427 | − | 3.24718i | −0.258331 | − | 0.149148i | ||||
\(475\) | 69.6960 | 3.19787 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.0335 | 0.550977 | ||||||||
\(478\) | −5.81459 | + | 10.0712i | −0.265953 | + | 0.460645i | ||||
\(479\) | −14.5270 | − | 25.1615i | −0.663755 | − | 1.14966i | −0.979621 | − | 0.200854i | \(-0.935628\pi\) |
0.315866 | − | 0.948804i | \(-0.397705\pi\) | |||||||
\(480\) | 2.58461 | − | 1.49222i | 0.117971 | − | 0.0681104i | ||||
\(481\) | −4.19083 | + | 7.25874i | −0.191086 | + | 0.330970i | ||||
\(482\) | 27.3738i | 1.24684i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9077 | + | 1.42237i | 0.495802 | + | 0.0646532i | ||||
\(485\) | 18.0127 | − | 31.1990i | 0.817917 | − | 1.41667i | ||||
\(486\) | 7.77372 | + | 13.4645i | 0.352623 | + | 0.610761i | ||||
\(487\) | 16.5674 | + | 28.6956i | 0.750742 | + | 1.30032i | 0.947463 | + | 0.319864i | \(0.103637\pi\) |
−0.196721 | + | 0.980459i | \(0.563029\pi\) | |||||||
\(488\) | 7.78013 | + | 4.49186i | 0.352190 | + | 0.203337i | ||||
\(489\) | 1.75273i | 0.0792613i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 42.4151i | − | 1.91416i | −0.289817 | − | 0.957082i | \(-0.593594\pi\) | ||
0.289817 | − | 0.957082i | \(-0.406406\pi\) | |||||||
\(492\) | 2.37448 | + | 1.37090i | 0.107050 | + | 0.0618052i | ||||
\(493\) | −49.2584 | + | 28.4394i | −2.21849 | + | 1.28084i | ||||
\(494\) | 10.7587 | − | 6.21154i | 0.484057 | − | 0.279470i | ||||
\(495\) | 17.3303 | − | 25.9712i | 0.778938 | − | 1.16732i | ||||
\(496\) | − | 7.88318i | − | 0.353965i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.01154 | 0.359005 | ||||||||
\(499\) | −7.72103 | + | 13.3732i | −0.345641 | + | 0.598667i | −0.985470 | − | 0.169850i | \(-0.945672\pi\) |
0.639829 | + | 0.768517i | \(0.279005\pi\) | |||||||
\(500\) | −17.5774 | + | 10.1483i | −0.786085 | + | 0.453846i | ||||
\(501\) | 5.64335 | − | 3.25819i | 0.252126 | − | 0.145565i | ||||
\(502\) | −6.75103 | + | 11.6931i | −0.301313 | + | 0.521890i | ||||
\(503\) | −39.5816 | −1.76486 | −0.882429 | − | 0.470446i | \(-0.844093\pi\) | ||||
−0.882429 | + | 0.470446i | \(0.844093\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 20.8447i | − | 0.927579i | ||||||
\(506\) | 8.05711 | − | 12.0744i | 0.358182 | − | 0.536772i | ||||
\(507\) | −6.42355 | + | 3.70864i | −0.285280 | + | 0.164706i | ||||
\(508\) | 15.0082 | − | 8.66501i | 0.665883 | − | 0.384448i | ||||
\(509\) | −4.57165 | − | 2.63944i | −0.202635 | − | 0.116991i | 0.395249 | − | 0.918574i | \(-0.370658\pi\) |
−0.597884 | + | 0.801583i | \(0.703992\pi\) | |||||||
\(510\) | − | 18.1337i | − | 0.802973i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 24.5090 | + | 14.1503i | 1.08210 | + | 0.624751i | ||||
\(514\) | 1.40320 | + | 2.43041i | 0.0618923 | + | 0.107201i | ||||
\(515\) | 8.27667 | + | 14.3356i | 0.364714 | + | 0.631703i | ||||
\(516\) | 1.24686 | − | 2.15962i | 0.0548898 | − | 0.0950719i | ||||
\(517\) | −0.674685 | − | 0.0438044i | −0.0296726 | − | 0.00192652i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 18.3628i | − | 0.806037i | ||||||
\(520\) | −3.54653 | + | 6.14277i | −0.155526 | + | 0.269378i | ||||
\(521\) | −23.6500 | + | 13.6543i | −1.03613 | + | 0.598207i | −0.918733 | − | 0.394878i | \(-0.870787\pi\) |
−0.117392 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(522\) | 11.2999 | + | 19.5720i | 0.494582 | + | 0.856641i | ||||
\(523\) | −4.32645 | + | 7.49363i | −0.189182 | + | 0.327673i | −0.944978 | − | 0.327134i | \(-0.893917\pi\) |
0.755796 | + | 0.654808i | \(0.227250\pi\) | |||||||
\(524\) | 6.35552 | 0.277642 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.48528 | 0.369976 | ||||||||
\(527\) | −41.4815 | − | 23.9493i | −1.80696 | − | 1.04325i | ||||
\(528\) | −1.12412 | − | 2.27596i | −0.0489211 | − | 0.0990485i | ||||
\(529\) | 1.92237 | + | 3.32964i | 0.0835813 | + | 0.144767i | ||||
\(530\) | −9.71811 | + | 16.8323i | −0.422128 | + | 0.731147i | ||||
\(531\) | − | 12.5479i | − | 0.544533i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.51638 | −0.282256 | ||||||||
\(534\) | 1.11866 | + | 0.645859i | 0.0484092 | + | 0.0279490i | ||||
\(535\) | 14.1130 | + | 24.4445i | 0.610160 | + | 1.05683i | ||||
\(536\) | 6.95724 | − | 4.01676i | 0.300507 | − | 0.173498i | ||||
\(537\) | −13.3616 | − | 7.71430i | −0.576594 | − | 0.332897i | ||||
\(538\) | −20.9576 | −0.903548 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16.1584 | −0.695349 | ||||||||
\(541\) | 0.447200 | + | 0.258191i | 0.0192266 | + | 0.0111005i | 0.509583 | − | 0.860422i | \(-0.329800\pi\) |
−0.490356 | + | 0.871522i | \(0.663133\pi\) | |||||||
\(542\) | 12.6554 | − | 7.30660i | 0.543596 | − | 0.313845i | ||||
\(543\) | −4.25296 | − | 7.36635i | −0.182512 | − | 0.316120i | ||||
\(544\) | 5.26202 | + | 3.03803i | 0.225607 | + | 0.130254i | ||||
\(545\) | 23.3962 | 1.00218 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 28.0407i | − | 1.19894i | −0.800399 | − | 0.599468i | \(-0.795379\pi\) | ||
0.800399 | − | 0.599468i | \(-0.204621\pi\) | |||||||
\(548\) | 0.674793 | − | 1.16878i | 0.0288257 | − | 0.0499277i | ||||
\(549\) | −10.8443 | − | 18.7829i | −0.462824 | − | 0.801634i | ||||
\(550\) | 14.9886 | + | 30.3468i | 0.639116 | + | 1.29399i | ||||
\(551\) | 55.3667 | + | 31.9660i | 2.35870 | + | 1.36180i | ||||
\(552\) | −3.34976 | −0.142575 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −11.1242 | −0.472620 | ||||||||
\(555\) | 6.87584 | − | 11.9093i | 0.291863 | − | 0.505522i | ||||
\(556\) | 5.94786 | + | 10.3020i | 0.252246 | + | 0.436902i | ||||
\(557\) | −24.8942 | + | 14.3727i | −1.05480 | + | 0.608989i | −0.923989 | − | 0.382418i | \(-0.875091\pi\) |
−0.130811 | + | 0.991407i | \(0.541758\pi\) | |||||||
\(558\) | −9.51584 | + | 16.4819i | −0.402838 | + | 0.697735i | ||||
\(559\) | 5.92673i | 0.250674i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.3913 | − | 0.999289i | −0.649820 | − | 0.0421900i | ||||
\(562\) | −3.64465 | + | 6.31271i | −0.153740 | + | 0.266286i | ||||
\(563\) | 3.37537 | + | 5.84631i | 0.142255 | + | 0.246393i | 0.928345 | − | 0.371719i | \(-0.121231\pi\) |
−0.786090 | + | 0.618111i | \(0.787898\pi\) | |||||||
\(564\) | 0.0780114 | + | 0.135120i | 0.00328487 | + | 0.00568956i | ||||
\(565\) | 56.8678 | + | 32.8326i | 2.39245 | + | 1.38128i | ||||
\(566\) | − | 16.0139i | − | 0.673115i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8.86195i | − | 0.371839i | ||||||
\(569\) | 8.41827 | + | 4.86029i | 0.352912 | + | 0.203754i | 0.665967 | − | 0.745981i | \(-0.268019\pi\) |
−0.313055 | + | 0.949735i | \(0.601352\pi\) | |||||||
\(570\) | −17.6516 | + | 10.1912i | −0.739346 | + | 0.426862i | ||||
\(571\) | −17.6516 | + | 10.1912i | −0.738698 | + | 0.426487i | −0.821596 | − | 0.570071i | \(-0.806916\pi\) |
0.0828978 | + | 0.996558i | \(0.473582\pi\) | |||||||
\(572\) | 5.01834 | + | 3.34868i | 0.209827 | + | 0.140016i | ||||
\(573\) | − | 18.7579i | − | 0.783622i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.6644 | 1.86263 | ||||||||
\(576\) | 1.20711 | − | 2.09077i | 0.0502961 | − | 0.0871154i | ||||
\(577\) | 10.5781 | − | 6.10726i | 0.440371 | − | 0.254248i | −0.263384 | − | 0.964691i | \(-0.584839\pi\) |
0.703755 | + | 0.710443i | \(0.251505\pi\) | |||||||
\(578\) | 17.2499 | − | 9.95924i | 0.717502 | − | 0.414250i | ||||
\(579\) | −4.82920 | + | 8.36442i | −0.200695 | + | 0.347614i | ||||
\(580\) | −36.5025 | −1.51568 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.07107i | 0.293105i | ||||||||
\(583\) | 13.7511 | + | 9.17598i | 0.569514 | + | 0.380030i | ||||
\(584\) | −0.0482428 | + | 0.0278530i | −0.00199630 | + | 0.00115257i | ||||
\(585\) | 14.8300 | − | 8.56208i | 0.613143 | − | 0.353998i | ||||
\(586\) | −12.3451 | − | 7.12748i | −0.509973 | − | 0.294433i | ||||
\(587\) | 22.5689i | 0.931519i | 0.884911 | + | 0.465759i | \(0.154219\pi\) | ||||
−0.884911 | + | 0.465759i | \(0.845781\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.8384i | 2.21837i | ||||||||
\(590\) | 17.5518 | + | 10.1335i | 0.722596 | + | 0.417191i | ||||
\(591\) | 6.60884 | + | 11.4468i | 0.271851 | + | 0.470860i | ||||
\(592\) | 2.30389 | + | 3.99045i | 0.0946892 | + | 0.164007i | ||||
\(593\) | −18.3348 | + | 31.7568i | −0.752920 | + | 1.30410i | 0.193481 | + | 0.981104i | \(0.438022\pi\) |
−0.946402 | + | 0.322992i | \(0.895311\pi\) | |||||||
\(594\) | −0.890440 | + | 13.7148i | −0.0365352 | + | 0.562723i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.57668i | 0.269391i | ||||||||
\(597\) | −3.51422 | + | 6.08680i | −0.143827 | + | 0.249116i | ||||
\(598\) | 6.89467 | − | 3.98064i | 0.281944 | − | 0.162780i | ||||
\(599\) | −3.17279 | − | 5.49543i | −0.129637 | − | 0.224537i | 0.793899 | − | 0.608049i | \(-0.208048\pi\) |
−0.923536 | + | 0.383512i | \(0.874714\pi\) | |||||||
\(600\) | 3.90532 | − | 6.76422i | 0.159434 | − | 0.276148i | ||||
\(601\) | −1.60141 | −0.0653230 | −0.0326615 | − | 0.999466i | \(-0.510398\pi\) | ||||
−0.0326615 | + | 0.999466i | \(0.510398\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.3946 | −0.789811 | ||||||||
\(604\) | −7.48149 | − | 4.31944i | −0.304417 | − | 0.175755i | ||||
\(605\) | 39.6078 | − | 16.4632i | 1.61029 | − | 0.669325i | ||||
\(606\) | 2.04570 | + | 3.54325i | 0.0831008 | + | 0.143935i | ||||
\(607\) | −8.37216 | + | 14.5010i | −0.339815 | + | 0.588578i | −0.984398 | − | 0.175957i | \(-0.943698\pi\) |
0.644582 | + | 0.764535i | \(0.277031\pi\) | |||||||
\(608\) | − | 6.82952i | − | 0.276974i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 35.0309 | 1.41836 | ||||||||
\(611\) | −0.321135 | − | 0.185407i | −0.0129917 | − | 0.00750078i | ||||
\(612\) | −7.33445 | − | 12.7036i | −0.296478 | − | 0.513514i | ||||
\(613\) | 1.57905 | − | 0.911666i | 0.0637773 | − | 0.0368219i | −0.467772 | − | 0.883849i | \(-0.654943\pi\) |
0.531550 | + | 0.847027i | \(0.321610\pi\) | |||||||
\(614\) | 5.84631 | + | 3.37537i | 0.235938 | + | 0.136219i | ||||
\(615\) | 10.6913 | 0.431116 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.7616 | 1.88255 | 0.941276 | − | 0.337638i | \(-0.109628\pi\) | ||||
0.941276 | + | 0.337638i | \(0.109628\pi\) | |||||||
\(618\) | −2.81379 | − | 1.62454i | −0.113187 | − | 0.0653486i | ||||
\(619\) | −35.0519 | + | 20.2372i | −1.40885 | + | 0.813402i | −0.995278 | − | 0.0970680i | \(-0.969054\pi\) |
−0.413576 | + | 0.910470i | \(0.635720\pi\) | |||||||
\(620\) | −15.3697 | − | 26.6212i | −0.617263 | − | 1.06913i | ||||
\(621\) | 15.7065 | + | 9.06816i | 0.630281 | + | 0.363893i | ||||
\(622\) | −17.8705 | −0.716542 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 1.39222i | − | 0.0557335i | ||||||
\(625\) | −14.0593 | + | 24.3514i | −0.562371 | + | 0.974055i | ||||
\(626\) | −7.51640 | − | 13.0188i | −0.300416 | − | 0.520335i | ||||
\(627\) | 7.67721 | + | 15.5437i | 0.306598 | + | 0.620757i | ||||
\(628\) | −2.12168 | − | 1.22495i | −0.0846643 | − | 0.0488810i | ||||
\(629\) | 27.9971 | 1.11632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6619 | 0.504064 | 0.252032 | − | 0.967719i | \(-0.418901\pi\) | ||||
0.252032 | + | 0.967719i | \(0.418901\pi\) | |||||||
\(632\) | 4.24264 | − | 7.34847i | 0.168763 | − | 0.292306i | ||||
\(633\) | 0.812244 | + | 1.40685i | 0.0322838 | + | 0.0559172i | ||||
\(634\) | 8.42810 | − | 4.86597i | 0.334723 | − | 0.193252i | ||||
\(635\) | 33.7881 | − | 58.5227i | 1.34084 | − | 2.32240i | ||||
\(636\) | − | 3.81493i | − | 0.151272i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.01154 | + | 30.9821i | −0.0796374 | + | 1.22659i | ||||
\(639\) | −10.6973 | + | 18.5283i | −0.423180 | + | 0.732969i | ||||
\(640\) | 1.94969 | + | 3.37695i | 0.0770681 | + | 0.133486i | ||||
\(641\) | 0.653476 | + | 1.13185i | 0.0258107 | + | 0.0447055i | 0.878642 | − | 0.477481i | \(-0.158450\pi\) |
−0.852832 | + | 0.522186i | \(0.825117\pi\) | |||||||
\(642\) | −4.79796 | − | 2.77010i | −0.189360 | − | 0.109327i | ||||
\(643\) | − | 39.1745i | − | 1.54489i | −0.635081 | − | 0.772446i | \(-0.719033\pi\) | ||
0.635081 | − | 0.772446i | \(-0.280967\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 9.72391i | − | 0.382878i | ||||||
\(646\) | −35.9371 | − | 20.7483i | −1.41393 | − | 0.816330i | ||||
\(647\) | 14.3245 | − | 8.27023i | 0.563153 | − | 0.325136i | −0.191257 | − | 0.981540i | \(-0.561256\pi\) |
0.754410 | + | 0.656404i | \(0.227923\pi\) | |||||||
\(648\) | −3.52565 | + | 2.03553i | −0.138501 | + | 0.0799633i | ||||
\(649\) | 9.56822 | − | 14.3389i | 0.375586 | − | 0.562853i | ||||
\(650\) | 18.5633i | 0.728114i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.29005 | −0.0896854 | ||||||||
\(653\) | −17.3853 | + | 30.1122i | −0.680339 | + | 1.17838i | 0.294539 | + | 0.955639i | \(0.404834\pi\) |
−0.974878 | + | 0.222741i | \(0.928499\pi\) | |||||||
\(654\) | −3.97696 | + | 2.29610i | −0.155512 | + | 0.0897846i | ||||
\(655\) | 21.4623 | − | 12.3913i | 0.838602 | − | 0.484167i | ||||
\(656\) | −1.79117 | + | 3.10240i | −0.0699336 | + | 0.121128i | ||||
\(657\) | 0.134486 | 0.00524680 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.4888i | 0.876039i | 0.898966 | + | 0.438019i | \(0.144320\pi\) | ||||
−0.898966 | + | 0.438019i | \(0.855680\pi\) | |||||||
\(660\) | −8.23352 | − | 5.49414i | −0.320489 | − | 0.213859i | ||||
\(661\) | 22.7587 | − | 13.1398i | 0.885212 | − | 0.511077i | 0.0128383 | − | 0.999918i | \(-0.495913\pi\) |
0.872373 | + | 0.488840i | \(0.162580\pi\) | |||||||
\(662\) | 15.8135 | − | 9.12993i | 0.614609 | − | 0.354845i | ||||
\(663\) | −7.32590 | − | 4.22961i | −0.284514 | − | 0.164265i | ||||
\(664\) | 10.4676i | 0.406221i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 11.1242i | − | 0.431052i | ||||||
\(667\) | 35.4815 | + | 20.4853i | 1.37385 | + | 0.793193i | ||||
\(668\) | 4.25703 | + | 7.37339i | 0.164709 | + | 0.285285i | ||||
\(669\) | 2.21033 | + | 3.82840i | 0.0854562 | + | 0.148014i | ||||
\(670\) | 15.6629 | − | 27.1289i | 0.605109 | − | 1.04808i | ||||
\(671\) | 1.93044 | − | 29.7330i | 0.0745237 | − | 1.14783i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.77457i | − | 0.145499i | −0.997350 | − | 0.0727495i | \(-0.976823\pi\) | ||
0.997350 | − | 0.0727495i | \(-0.0231774\pi\) | |||||||
\(674\) | −14.8464 | + | 25.7147i | −0.571862 | + | 0.990494i | ||||
\(675\) | −36.6229 | + | 21.1442i | −1.40962 | + | 0.813843i | ||||
\(676\) | −4.84557 | − | 8.39278i | −0.186368 | − | 0.322799i | ||||
\(677\) | 15.7129 | − | 27.2155i | 0.603896 | − | 1.04598i | −0.388329 | − | 0.921521i | \(-0.626948\pi\) |
0.992225 | − | 0.124457i | \(-0.0397190\pi\) | |||||||
\(678\) | −12.8887 | −0.494989 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 23.6928 | 0.908578 | ||||||||
\(681\) | −0.802378 | − | 0.463253i | −0.0307472 | − | 0.0177519i | ||||
\(682\) | −23.4421 | + | 11.5783i | −0.897645 | + | 0.443356i | ||||
\(683\) | 9.95029 | + | 17.2344i | 0.380737 | + | 0.659456i | 0.991168 | − | 0.132614i | \(-0.0423369\pi\) |
−0.610431 | + | 0.792070i | \(0.709004\pi\) | |||||||
\(684\) | −8.24396 | + | 14.2790i | −0.315216 | + | 0.545970i | ||||
\(685\) | − | 5.26254i | − | 0.201071i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8491 | −0.566527 | ||||||||
\(688\) | 2.82168 | + | 1.62910i | 0.107575 | + | 0.0621087i | ||||
\(689\) | 4.53342 | + | 7.85212i | 0.172710 | + | 0.299142i | ||||
\(690\) | −11.3120 | + | 6.53098i | −0.430640 | + | 0.248630i | ||||
\(691\) | 24.7690 | + | 14.3004i | 0.942255 | + | 0.544011i | 0.890667 | − | 0.454657i | \(-0.150238\pi\) |
0.0515887 | + | 0.998668i | \(0.483572\pi\) | |||||||
\(692\) | 23.9921 | 0.912044 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.2813 | −0.731907 | ||||||||
\(695\) | 40.1713 | + | 23.1929i | 1.52379 | + | 0.879758i | ||||
\(696\) | 6.20481 | − | 3.58235i | 0.235193 | − | 0.135788i | ||||
\(697\) | 10.8833 | + | 18.8504i | 0.412233 | + | 0.714009i | ||||
\(698\) | 20.7778 | + | 11.9961i | 0.786451 | + | 0.454058i | ||||
\(699\) | 15.0872 | 0.570650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.2928i | − | 0.804218i | −0.915592 | − | 0.402109i | \(-0.868277\pi\) | ||
0.915592 | − | 0.402109i | \(-0.131723\pi\) | |||||||
\(702\) | −3.76889 | + | 6.52792i | −0.142248 | + | 0.246380i | ||||
\(703\) | −15.7345 | − | 27.2529i | −0.593436 | − | 1.02786i | ||||
\(704\) | 2.97369 | − | 1.46874i | 0.112075 | − | 0.0553550i | ||||
\(705\) | 0.526882 | + | 0.304195i | 0.0198435 | + | 0.0114567i | ||||
\(706\) | 16.1478 | 0.607731 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.97801 | −0.149503 | ||||||||
\(709\) | 8.43913 | − | 14.6170i | 0.316938 | − | 0.548953i | −0.662909 | − | 0.748700i | \(-0.730679\pi\) |
0.979848 | + | 0.199746i | \(0.0640118\pi\) | |||||||
\(710\) | −17.2780 | − | 29.9264i | −0.648433 | − | 1.12312i | ||||
\(711\) | −17.7408 | + | 10.2426i | −0.665331 | + | 0.384129i | ||||
\(712\) | −0.843855 | + | 1.46160i | −0.0316248 | + | 0.0547758i | ||||
\(713\) | 34.5021i | 1.29211i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.4756 | + | 1.52417i | 0.877937 | + | 0.0570007i | ||||
\(716\) | 10.0792 | − | 17.4577i | 0.376678 | − | 0.652426i | ||||
\(717\) | −4.45030 | − | 7.70814i | −0.166199 | − | 0.287866i | ||||
\(718\) | 9.07278 | + | 15.7145i | 0.338593 | + | 0.586461i | ||||
\(719\) | −31.3046 | − | 18.0737i | −1.16746 | − | 0.674036i | −0.214383 | − | 0.976750i | \(-0.568774\pi\) |
−0.953081 | + | 0.302714i | \(0.902107\pi\) | |||||||
\(720\) | − | 9.41392i | − | 0.350836i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 27.6424i | 1.02874i | ||||||||
\(723\) | −18.1441 | − | 10.4755i | −0.674786 | − | 0.389588i | ||||
\(724\) | 9.62460 | − | 5.55676i | 0.357695 | − | 0.206515i | ||||
\(725\) | −82.7324 | + | 47.7656i | −3.07261 | + | 1.77397i | ||||
\(726\) | −5.11696 | + | 6.68557i | −0.189908 | + | 0.248125i | ||||
\(727\) | 8.74172i | 0.324212i | 0.986773 | + | 0.162106i | \(0.0518287\pi\) | ||||
−0.986773 | + | 0.162106i | \(0.948171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.313708 | 0.0116188 | ||||||||
\(730\) | −0.108609 | + | 0.188117i | −0.00401981 | + | 0.00696251i | ||||
\(731\) | 17.1447 | − | 9.89848i | 0.634118 | − | 0.366108i | ||||
\(732\) | −5.95465 | + | 3.43792i | −0.220090 | + | 0.127069i | ||||
\(733\) | −6.73225 | + | 11.6606i | −0.248661 | + | 0.430694i | −0.963155 | − | 0.268948i | \(-0.913324\pi\) |
0.714493 | + | 0.699642i | \(0.246657\pi\) | |||||||
\(734\) | 4.91547 | 0.181433 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 4.37667i | − | 0.161326i | ||||||
\(737\) | −22.1629 | − | 14.7891i | −0.816382 | − | 0.544763i | ||||
\(738\) | 7.48986 | − | 4.32427i | 0.275706 | − | 0.159179i | ||||
\(739\) | 32.3387 | − | 18.6708i | 1.18960 | − | 0.686816i | 0.231384 | − | 0.972862i | \(-0.425675\pi\) |
0.958216 | + | 0.286047i | \(0.0923413\pi\) | |||||||
\(740\) | 15.5603 | + | 8.98372i | 0.572006 | + | 0.330248i | ||||
\(741\) | 9.50821i | 0.349293i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.5472i | − | 0.643746i | −0.946783 | − | 0.321873i | \(-0.895688\pi\) | ||
0.946783 | − | 0.321873i | \(-0.104312\pi\) | |||||||
\(744\) | 5.22519 | + | 3.01676i | 0.191565 | + | 0.110600i | ||||
\(745\) | 12.8225 | + | 22.2091i | 0.469778 | + | 0.813680i | ||||
\(746\) | −1.13403 | − | 1.96420i | −0.0415198 | − | 0.0719145i | ||||
\(747\) | 12.6355 | − | 21.8853i | 0.462308 | − | 0.800741i | ||||
\(748\) | 1.30563 | − | 20.1097i | 0.0477387 | − | 0.735282i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 15.5344i | − | 0.567235i | ||||||
\(751\) | 17.3623 | − | 30.0724i | 0.633561 | − | 1.09736i | −0.353258 | − | 0.935526i | \(-0.614926\pi\) |
0.986818 | − | 0.161833i | \(-0.0517406\pi\) | |||||||
\(752\) | −0.176542 | + | 0.101927i | −0.00643784 | + | 0.00371689i | ||||
\(753\) | −5.16702 | − | 8.94954i | −0.188297 | − | 0.326139i | ||||
\(754\) | −8.51406 | + | 14.7468i | −0.310064 | + | 0.537046i | ||||
\(755\) | −33.6862 | −1.22597 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0627 | 1.01996 | 0.509978 | − | 0.860187i | \(-0.329653\pi\) | ||||
0.509978 | + | 0.860187i | \(0.329653\pi\) | |||||||
\(758\) | −12.8158 | − | 7.39920i | −0.465491 | − | 0.268751i | ||||
\(759\) | 4.91991 | + | 9.96114i | 0.178581 | + | 0.361566i | ||||
\(760\) | −13.3154 | − | 23.0630i | −0.483001 | − | 0.836583i | ||||
\(761\) | −3.79149 | + | 6.56706i | −0.137442 | + | 0.238056i | −0.926527 | − | 0.376227i | \(-0.877221\pi\) |
0.789086 | + | 0.614283i | \(0.210555\pi\) | |||||||
\(762\) | 13.2638i | 0.480498i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.5084 | 0.886681 | ||||||||
\(765\) | −49.5362 | − | 28.5997i | −1.79099 | − | 1.03403i | ||||
\(766\) | 3.63515 | + | 6.29627i | 0.131343 | + | 0.227494i | ||||
\(767\) | 8.18777 | − | 4.72721i | 0.295643 | − | 0.170690i | ||||
\(768\) | −0.662827 | − | 0.382683i | −0.0239177 | − | 0.0138089i | ||||
\(769\) | −1.95786 | −0.0706022 | −0.0353011 | − | 0.999377i | \(-0.511239\pi\) | ||||
−0.0353011 | + | 0.999377i | \(0.511239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.14792 | −0.0773554 | ||||||||
\(772\) | −10.9286 | − | 6.30966i | −0.393331 | − | 0.227090i | ||||
\(773\) | −8.18023 | + | 4.72286i | −0.294223 | + | 0.169869i | −0.639845 | − | 0.768504i | \(-0.721001\pi\) |
0.345622 | + | 0.938374i | \(0.387668\pi\) | |||||||
\(774\) | −3.93298 | − | 6.81213i | −0.141368 | − | 0.244857i | ||||
\(775\) | −69.6706 | − | 40.2243i | −2.50264 | − | 1.44490i | ||||
\(776\) | −9.23880 | −0.331653 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 35.1936i | − | 1.26175i | ||||||
\(779\) | 12.2329 | − | 21.1879i | 0.438288 | − | 0.759136i | ||||
\(780\) | −2.71440 | − | 4.70147i | −0.0971910 | − | 0.168340i | ||||
\(781\) | −26.3527 | + | 13.0159i | −0.942973 | + | 0.465744i | ||||
\(782\) | −23.0301 | − | 13.2965i | −0.823556 | − | 0.475480i | ||||
\(783\) | −38.7912 | −1.38628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.55310 | −0.340965 | ||||||||
\(786\) | −2.43215 | + | 4.21261i | −0.0867520 | + | 0.150259i | ||||
\(787\) | 10.0436 | + | 17.3960i | 0.358016 | + | 0.620101i | 0.987629 | − | 0.156807i | \(-0.0501201\pi\) |
−0.629614 | + | 0.776908i | \(0.716787\pi\) | |||||||
\(788\) | −14.9560 | + | 8.63486i | −0.532786 | + | 0.307604i | ||||
\(789\) | −3.24718 | + | 5.62427i | −0.115603 | + | 0.200229i | ||||
\(790\) | − | 33.0873i | − | 1.17719i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.99022 | − | 0.518771i | −0.283920 | − | 0.0184337i | ||||
\(793\) | 8.17081 | − | 14.1523i | 0.290154 | − | 0.502561i | ||||
\(794\) | 9.41550 | + | 16.3081i | 0.334144 | + | 0.578754i | ||||
\(795\) | −7.43792 | − | 12.8829i | −0.263796 | − | 0.456908i | ||||
\(796\) | −7.95279 | − | 4.59154i | −0.281879 | − | 0.162743i | ||||
\(797\) | 36.2219i | 1.28304i | 0.767105 | + | 0.641522i | \(0.221697\pi\) | ||||
−0.767105 | + | 0.641522i | \(0.778303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.23863i | 0.0438194i | ||||||||
\(800\) | 8.83788 | + | 5.10255i | 0.312466 | + | 0.180402i | ||||
\(801\) | 3.52861 | − | 2.03725i | 0.124677 | − | 0.0719826i | ||||
\(802\) | −6.15480 | + | 3.55347i | −0.217333 | + | 0.125477i | ||||
\(803\) | 0.153682 | + | 0.102550i | 0.00542332 | + | 0.00361892i | ||||
\(804\) | 6.14859i | 0.216844i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.3397 | −0.505095 | ||||||||
\(807\) | 8.02014 | − | 13.8913i | 0.282322 | − | 0.488997i | ||||
\(808\) | −4.62948 | + | 2.67283i | −0.162865 | + | 0.0940299i | ||||
\(809\) | 0.169942 | − | 0.0981160i | 0.00597484 | − | 0.00344958i | −0.497010 | − | 0.867745i | \(-0.665569\pi\) |
0.502984 | + | 0.864295i | \(0.332235\pi\) | |||||||
\(810\) | −7.93730 | + | 13.7478i | −0.278888 | + | 0.483049i | ||||
\(811\) | 13.1515 | 0.461811 | 0.230905 | − | 0.972976i | \(-0.425831\pi\) | ||||
0.230905 | + | 0.972976i | \(0.425831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.1845i | 0.392256i | ||||||||
\(814\) | 8.48256 | − | 12.7120i | 0.297313 | − | 0.445554i | ||||
\(815\) | −7.73341 | + | 4.46489i | −0.270890 | + | 0.156398i | ||||
\(816\) | −4.02738 | + | 2.32521i | −0.140986 | + | 0.0813985i | ||||
\(817\) | −19.2707 | − | 11.1259i | −0.674196 | − | 0.389248i | ||||
\(818\) | 9.71411i | 0.339646i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.9689i | 0.487815i | ||||||||
\(821\) | −16.2662 | − | 9.39127i | −0.567693 | − | 0.327758i | 0.188535 | − | 0.982067i | \(-0.439626\pi\) |
−0.756227 | + | 0.654309i | \(0.772960\pi\) | |||||||
\(822\) | 0.516465 | + | 0.894543i | 0.0180138 | + | 0.0312008i | ||||
\(823\) | −18.1347 | − | 31.4103i | −0.632137 | − | 1.09489i | −0.987114 | − | 0.160019i | \(-0.948844\pi\) |
0.354977 | − | 0.934875i | \(-0.384489\pi\) | |||||||
\(824\) | 2.12256 | − | 3.67639i | 0.0739431 | − | 0.128073i | ||||
\(825\) | −25.8506 | − | 1.67837i | −0.900001 | − | 0.0584332i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26.5489i | − | 0.923196i | −0.887089 | − | 0.461598i | \(-0.847276\pi\) | ||
0.887089 | − | 0.461598i | \(-0.152724\pi\) | |||||||
\(828\) | −5.28311 | + | 9.15062i | −0.183601 | + | 0.318006i | ||||
\(829\) | −7.93057 | + | 4.57871i | −0.275440 | + | 0.159025i | −0.631357 | − | 0.775492i | \(-0.717502\pi\) |
0.355917 | + | 0.934517i | \(0.384168\pi\) | |||||||
\(830\) | 20.4085 | + | 35.3485i | 0.708389 | + | 1.22697i | ||||
\(831\) | 4.25703 | − | 7.37339i | 0.147675 | − | 0.255780i | ||||
\(832\) | 1.81903 | 0.0630634 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.10459 | −0.315266 | ||||||||
\(835\) | 28.7516 | + | 16.5997i | 0.994990 | + | 0.574458i | ||||
\(836\) | −20.3089 | + | 10.0308i | −0.702397 | + | 0.346921i | ||||
\(837\) | −16.3334 | − | 28.2903i | −0.564565 | − | 0.977855i | ||||
\(838\) | 11.5237 | − | 19.9596i | 0.398080 | − | 0.689494i | ||||
\(839\) | 42.3516i | 1.46214i | 0.682302 | + | 0.731070i | \(0.260979\pi\) | ||||
−0.682302 | + | 0.731070i | \(0.739021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −58.6306 | −2.02175 | ||||||||
\(842\) | 1.44690 | + | 0.835371i | 0.0498636 | + | 0.0287888i | ||||
\(843\) | −2.78949 | − | 4.83154i | −0.0960752 | − | 0.166407i | ||||
\(844\) | −1.83814 | + | 1.06125i | −0.0632712 | + | 0.0365297i | ||||
\(845\) | −32.7266 | − | 18.8947i | −1.12583 | − | 0.649997i | ||||
\(846\) | 0.492146 | 0.0169203 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.98445 | 0.171167 | ||||||||
\(849\) | 10.6145 | + | 6.12826i | 0.364287 | + | 0.210321i | ||||
\(850\) | 53.6994 | − | 31.0034i | 1.84188 | − | 1.06341i | ||||
\(851\) | −10.0834 | − | 17.4649i | −0.345653 | − | 0.598689i | ||||
\(852\) | 5.87394 | + | 3.39132i | 0.201238 | + | 0.116185i | ||||
\(853\) | −56.4552 | −1.93299 | −0.966495 | − | 0.256686i | \(-0.917369\pi\) | ||||
−0.966495 | + | 0.256686i | \(0.917369\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 64.2926i | 2.19876i | ||||||||
\(856\) | 3.61931 | − | 6.26883i | 0.123706 | − | 0.214264i | ||||
\(857\) | 18.0227 | + | 31.2163i | 0.615644 | + | 1.06633i | 0.990271 | + | 0.139151i | \(0.0444374\pi\) |
−0.374627 | + | 0.927176i | \(0.622229\pi\) | |||||||
\(858\) | −4.14003 | + | 2.04481i | −0.141338 | + | 0.0698085i | ||||
\(859\) | 0.0732103 | + | 0.0422680i | 0.00249790 | + | 0.00144217i | 0.501248 | − | 0.865303i | \(-0.332874\pi\) |
−0.498751 | + | 0.866746i | \(0.666208\pi\) | |||||||
\(860\) | 12.7049 | 0.433233 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.8481 | −1.32317 | ||||||||
\(863\) | −22.8620 | + | 39.5981i | −0.778230 | + | 1.34793i | 0.154731 | + | 0.987957i | \(0.450549\pi\) |
−0.932961 | + | 0.359977i | \(0.882784\pi\) | |||||||
\(864\) | 2.07193 | + | 3.58869i | 0.0704885 | + | 0.122090i | ||||
\(865\) | 81.0204 | − | 46.7771i | 2.75477 | − | 1.59047i | ||||
\(866\) | 15.9239 | − | 27.5811i | 0.541118 | − | 0.937244i | ||||
\(867\) | 15.2449i | 0.517745i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0834 | − | 1.82333i | −0.952663 | − | 0.0618523i | ||||
\(870\) | 13.9689 | − | 24.1948i | 0.473590 | − | 0.820282i | ||||
\(871\) | −7.30660 | − | 12.6554i | −0.247575 | − | 0.428812i | ||||
\(872\) | −3.00000 | − | 5.19615i | −0.101593 | − | 0.175964i | ||||
\(873\) | 19.3162 | + | 11.1522i | 0.653754 | + | 0.377445i | ||||
\(874\) | 29.8906i | 1.01106i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 0.0426355i | − | 0.00144052i | ||||||
\(877\) | −40.0453 | − | 23.1201i | −1.35223 | − | 0.780712i | −0.363671 | − | 0.931528i | \(-0.618477\pi\) |
−0.988562 | + | 0.150816i | \(0.951810\pi\) | |||||||
\(878\) | −10.4276 | + | 6.02035i | −0.351913 | + | 0.203177i | ||||
\(879\) | 9.44857 | − | 5.45513i | 0.318692 | − | 0.183997i | ||||
\(880\) | 7.17844 | − | 10.7576i | 0.241985 | − | 0.362639i | ||||
\(881\) | − | 37.2892i | − | 1.25630i | −0.778091 | − | 0.628152i | \(-0.783812\pi\) | ||
0.778091 | − | 0.628152i | \(-0.216188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.3548 | −0.819603 | −0.409801 | − | 0.912175i | \(-0.634402\pi\) | ||||
−0.409801 | + | 0.912175i | \(0.634402\pi\) | |||||||
\(884\) | 5.52625 | − | 9.57175i | 0.185868 | − | 0.321933i | ||||
\(885\) | −13.4336 | + | 7.75587i | −0.451564 | + | 0.260711i | ||||
\(886\) | −26.4591 | + | 15.2762i | −0.888911 | + | 0.513213i | ||||
\(887\) | −5.74396 | + | 9.94883i | −0.192863 | + | 0.334049i | −0.946198 | − | 0.323588i | \(-0.895111\pi\) |
0.753335 | + | 0.657637i | \(0.228444\pi\) | |||||||
\(888\) | −3.52664 | −0.118346 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.58101i | 0.220596i | ||||||||
\(891\) | 11.2313 | + | 7.49452i | 0.376262 | + | 0.251076i | ||||
\(892\) | −5.00204 | + | 2.88793i | −0.167481 | + | 0.0966951i | ||||
\(893\) | 1.20570 | − | 0.696111i | 0.0403472 | − | 0.0232945i | ||||
\(894\) | −4.35920 | − | 2.51679i | −0.145793 | − | 0.0841739i | ||||
\(895\) | − | 78.6053i | − | 2.62748i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.09330i | 0.203449i | ||||||||
\(898\) | −13.6293 | − | 7.86890i | −0.454817 | − | 0.262588i | ||||
\(899\) | −36.8977 | − | 63.9087i | −1.23061 | − | 2.13148i | ||||
\(900\) | −12.3186 | − | 21.3365i | −0.410621 | − | 0.711217i | ||||
\(901\) | 15.1429 | − | 26.2283i | 0.504483 | − | 0.873791i | ||||
\(902\) | 11.8563 | + | 0.769781i | 0.394773 | + | 0.0256309i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.8400i | − | 0.560089i | ||||||
\(905\) | 21.6679 | − | 37.5299i | 0.720265 | − | 1.24754i | ||||
\(906\) | 5.72608 | − | 3.30596i | 0.190236 | − | 0.109833i | ||||
\(907\) | 11.6507 | + | 20.1796i | 0.386854 | + | 0.670051i | 0.992025 | − | 0.126045i | \(-0.0402283\pi\) |
−0.605170 | + | 0.796096i | \(0.706895\pi\) | |||||||
\(908\) | 0.605269 | − | 1.04836i | 0.0200866 | − | 0.0347910i | ||||
\(909\) | 12.9056 | 0.428051 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6447 | −1.08157 | −0.540784 | − | 0.841161i | \(-0.681872\pi\) | ||||
−0.540784 | + | 0.841161i | \(0.681872\pi\) | |||||||
\(912\) | 4.52679 | + | 2.61355i | 0.149897 | + | 0.0865431i | ||||
\(913\) | 31.1273 | − | 15.3741i | 1.03016 | − | 0.508808i | ||||
\(914\) | −8.58340 | − | 14.8669i | −0.283914 | − | 0.491753i | ||||
\(915\) | −13.4057 | + | 23.2194i | −0.443180 | + | 0.767610i | ||||
\(916\) | − | 19.4012i | − | 0.641035i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 25.1783 | 0.831009 | ||||||||
\(919\) | 33.0701 | + | 19.0931i | 1.09088 | + | 0.629822i | 0.933812 | − | 0.357765i | \(-0.116461\pi\) |
0.157072 | + | 0.987587i | \(0.449795\pi\) | |||||||
\(920\) | −8.53314 | − | 14.7798i | −0.281329 | − | 0.487276i | ||||
\(921\) | −4.47458 | + | 2.58340i | −0.147442 | + | 0.0851258i | ||||
\(922\) | −0.270283 | − | 0.156048i | −0.00890129 | − | 0.00513916i | ||||
\(923\) | −16.1201 | −0.530600 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47.0228 | 1.54610 | ||||||||
\(926\) | 27.6610 | + | 15.9701i | 0.908998 | + | 0.524810i | ||||
\(927\) | −8.87559 | + | 5.12433i | −0.291513 | + | 0.168305i | ||||
\(928\) | 4.68056 | + | 8.10697i | 0.153647 | + | 0.266124i | ||||
\(929\) | 7.05212 | + | 4.07155i | 0.231373 | + | 0.133583i | 0.611205 | − | 0.791472i | \(-0.290685\pi\) |
−0.379832 | + | 0.925055i | \(0.624018\pi\) | |||||||
\(930\) | 23.5270 | 0.771479 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.7124i | 0.645700i | ||||||||
\(933\) | 6.83875 | − | 11.8451i | 0.223891 | − | 0.387790i | ||||
\(934\) | 9.42604 | + | 16.3264i | 0.308429 | + | 0.534216i | ||||
\(935\) | −34.7985 | − | 70.4550i | −1.13803 | − | 2.30412i | ||||
\(936\) | −3.80317 | − | 2.19576i | −0.124310 | − | 0.0717706i | ||||
\(937\) | 29.3997 | 0.960445 | 0.480222 | − | 0.877147i | \(-0.340556\pi\) | ||||
0.480222 | + | 0.877147i | \(0.340556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.5056 | 0.375471 | ||||||||
\(940\) | −0.397450 | + | 0.688404i | −0.0129634 | + | 0.0224533i | ||||
\(941\) | −12.5519 | − | 21.7406i | −0.409181 | − | 0.708722i | 0.585617 | − | 0.810588i | \(-0.300852\pi\) |
−0.994798 | + | 0.101866i | \(0.967519\pi\) | |||||||
\(942\) | 1.62386 | − | 0.937539i | 0.0529084 | − | 0.0305467i | ||||
\(943\) | 7.83938 | − | 13.5782i | 0.255285 | − | 0.442167i | ||||
\(944\) | − | 5.19752i | − | 0.169165i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.700126 | − | 10.7835i | 0.0227631 | − | 0.350602i | ||||
\(947\) | −29.0590 | + | 50.3316i | −0.944290 | + | 1.63556i | −0.187124 | + | 0.982336i | \(0.559917\pi\) |
−0.757166 | + | 0.653222i | \(0.773417\pi\) | |||||||
\(948\) | 3.24718 | + | 5.62427i | 0.105463 | + | 0.182668i | ||||
\(949\) | 0.0506653 | + | 0.0877549i | 0.00164467 | + | 0.00284864i | ||||
\(950\) | −60.3585 | − | 34.8480i | −1.95829 | − | 1.13062i | ||||
\(951\) | 7.44850i | 0.241534i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.3237i | 1.82450i | 0.409632 | + | 0.912251i | \(0.365657\pi\) | ||||
−0.409632 | + | 0.912251i | \(0.634343\pi\) | |||||||
\(954\) | −10.4213 | − | 6.01676i | −0.337403 | − | 0.194800i | ||||
\(955\) | 82.7636 | − | 47.7836i | 2.67817 | − | 1.54624i | ||||
\(956\) | 10.0712 | − | 5.81459i | 0.325725 | − | 0.188057i | ||||
\(957\) | −19.7660 | − | 13.1896i | −0.638944 | − | 0.426360i | ||||
\(958\) | 29.0540i | 0.938692i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.98445 | −0.0963227 | ||||||||
\(961\) | 15.5723 | − | 26.9720i | 0.502332 | − | 0.870064i | ||||
\(962\) | 7.25874 | − | 4.19083i | 0.234031 | − | 0.135118i | ||||
\(963\) | −15.1343 | + | 8.73779i | −0.487696 | + | 0.281571i | ||||
\(964\) | 13.6869 | − | 23.7064i | 0.440825 | − | 0.763532i | ||||
\(965\) | −49.2074 | −1.58404 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.3825i | − | 0.912721i | −0.889795 | − | 0.456360i | \(-0.849153\pi\) | ||
0.889795 | − | 0.456360i | \(-0.150847\pi\) | |||||||
\(968\) | −8.73512 | − | 6.68563i | −0.280757 | − | 0.214884i | ||||
\(969\) | 27.5051 | − | 15.8801i | 0.883590 | − | 0.510141i | ||||
\(970\) | −31.1990 | + | 18.0127i | −1.00174 | + | 0.578354i | ||||
\(971\) | 38.2269 | + | 22.0703i | 1.22676 | + | 0.708270i | 0.966351 | − | 0.257229i | \(-0.0828094\pi\) |
0.260409 | + | 0.965499i | \(0.416143\pi\) | |||||||
\(972\) | − | 15.5474i | − | 0.498684i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 33.1349i | − | 1.06171i | ||||||
\(975\) | −12.3043 | − | 7.10388i | −0.394053 | − | 0.227506i | ||||
\(976\) | −4.49186 | − | 7.78013i | −0.143781 | − | 0.249036i | ||||
\(977\) | 4.83203 | + | 8.36932i | 0.154590 | + | 0.267758i | 0.932910 | − | 0.360110i | \(-0.117261\pi\) |
−0.778319 | + | 0.627868i | \(0.783928\pi\) | |||||||
\(978\) | 0.876366 | − | 1.51791i | 0.0280231 | − | 0.0485374i | ||||
\(979\) | 5.58574 | + | 0.362658i | 0.178521 | + | 0.0115906i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4853i | 0.462479i | ||||||||
\(982\) | −21.2075 | + | 36.7325i | −0.676759 | + | 1.17218i | ||||
\(983\) | 23.1226 | − | 13.3498i | 0.737497 | − | 0.425794i | −0.0836616 | − | 0.996494i | \(-0.526661\pi\) |
0.821159 | + | 0.570700i | \(0.193328\pi\) | |||||||
\(984\) | −1.37090 | − | 2.37448i | −0.0437028 | − | 0.0756955i | ||||
\(985\) | −33.6705 | + | 58.3191i | −1.07283 | + | 1.85820i | ||||
\(986\) | 56.8787 | 1.81139 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.4231 | −0.395231 | ||||||||
\(989\) | −12.3496 | − | 7.13002i | −0.392693 | − | 0.226721i | ||||
\(990\) | −27.9940 | + | 13.8265i | −0.889709 | + | 0.439437i | ||||
\(991\) | 18.2219 | + | 31.5612i | 0.578837 | + | 1.00257i | 0.995613 | + | 0.0935654i | \(0.0298264\pi\) |
−0.416777 | + | 0.909009i | \(0.636840\pi\) | |||||||
\(992\) | −3.94159 | + | 6.82704i | −0.125146 | + | 0.216759i | ||||
\(993\) | 13.9755i | 0.443499i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.8083 | −1.13520 | ||||||||
\(996\) | −6.93819 | − | 4.00577i | −0.219845 | − | 0.126928i | ||||
\(997\) | 14.5129 | + | 25.1370i | 0.459627 | + | 0.796097i | 0.998941 | − | 0.0460077i | \(-0.0146499\pi\) |
−0.539314 | + | 0.842104i | \(0.681317\pi\) | |||||||
\(998\) | 13.3732 | − | 7.72103i | 0.423322 | − | 0.244405i | ||||
\(999\) | 16.5359 | + | 9.54699i | 0.523172 | + | 0.302053i |
(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 | 1078.2.i.d.901.2 | 32 | ||
7.2 | even | 3 | 1078.2.c.c.1077.13 | yes | 16 | ||
7.3 | odd | 6 | inner | 1078.2.i.d.1011.12 | 32 | ||
7.4 | even | 3 | inner | 1078.2.i.d.1011.11 | 32 | ||
7.5 | odd | 6 | 1078.2.c.c.1077.12 | yes | 16 | ||
7.6 | odd | 2 | inner | 1078.2.i.d.901.1 | 32 | ||
11.10 | odd | 2 | inner | 1078.2.i.d.901.12 | 32 | ||
77.10 | even | 6 | inner | 1078.2.i.d.1011.2 | 32 | ||
77.32 | odd | 6 | inner | 1078.2.i.d.1011.1 | 32 | ||
77.54 | even | 6 | 1078.2.c.c.1077.4 | ✓ | 16 | ||
77.65 | odd | 6 | 1078.2.c.c.1077.5 | yes | 16 | ||
77.76 | even | 2 | inner | 1078.2.i.d.901.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1078.2.c.c.1077.4 | ✓ | 16 | 77.54 | even | 6 | ||
1078.2.c.c.1077.5 | yes | 16 | 77.65 | odd | 6 | ||
1078.2.c.c.1077.12 | yes | 16 | 7.5 | odd | 6 | ||
1078.2.c.c.1077.13 | yes | 16 | 7.2 | even | 3 | ||
1078.2.i.d.901.1 | 32 | 7.6 | odd | 2 | inner | ||
1078.2.i.d.901.2 | 32 | 1.1 | even | 1 | trivial | ||
1078.2.i.d.901.11 | 32 | 77.76 | even | 2 | inner | ||
1078.2.i.d.901.12 | 32 | 11.10 | odd | 2 | inner | ||
1078.2.i.d.1011.1 | 32 | 77.32 | odd | 6 | inner | ||
1078.2.i.d.1011.2 | 32 | 77.10 | even | 6 | inner | ||
1078.2.i.d.1011.11 | 32 | 7.4 | even | 3 | inner | ||
1078.2.i.d.1011.12 | 32 | 7.3 | odd | 6 | inner |