Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(181,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.t (of order \(4\), degree \(2\), 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: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 240) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 181.8 | ||
Root | \(-1.04932 - 0.948122i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.181 |
Dual form | 720.2.t.d.541.8 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.04932 | − | 0.948122i | 0.741978 | − | 0.670424i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.202128 | − | 1.98976i | 0.101064 | − | 0.994880i | ||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.740019i | − | 0.279701i | −0.990173 | − | 0.139850i | \(-0.955338\pi\) | ||
0.990173 | − | 0.139850i | \(-0.0446622\pi\) | |||||||
\(8\) | −1.67444 | − | 2.27953i | −0.592004 | − | 0.805935i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.41240 | + | 0.0715547i | 0.446641 | + | 0.0226276i | ||||
\(11\) | 3.83476 | + | 3.83476i | 1.15622 | + | 1.15622i | 0.985281 | + | 0.170943i | \(0.0546815\pi\) |
0.170943 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.31314 | − | 3.31314i | 0.918899 | − | 0.918899i | −0.0780503 | − | 0.996949i | \(-0.524869\pi\) |
0.996949 | + | 0.0780503i | \(0.0248695\pi\) | |||||||
\(14\) | −0.701629 | − | 0.776514i | −0.187518 | − | 0.207532i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.91829 | − | 0.804372i | −0.979572 | − | 0.201093i | ||||
\(17\) | −2.93893 | −0.712796 | −0.356398 | − | 0.934334i | \(-0.615995\pi\) | ||||
−0.356398 | + | 0.934334i | \(0.615995\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.02789 | − | 5.02789i | 1.15348 | − | 1.15348i | 0.167628 | − | 0.985850i | \(-0.446389\pi\) |
0.985850 | − | 0.167628i | \(-0.0536107\pi\) | |||||||
\(20\) | 1.54990 | − | 1.26405i | 0.346568 | − | 0.282649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.65970 | + | 0.388053i | 1.63305 | + | 0.0827332i | ||||
\(23\) | − | 5.45159i | − | 1.13673i | −0.822775 | − | 0.568367i | \(-0.807575\pi\) | ||
0.822775 | − | 0.568367i | \(-0.192425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0.335268 | − | 6.61779i | 0.0657515 | − | 1.29786i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.47246 | − | 0.149579i | −0.278269 | − | 0.0282677i | ||||
\(29\) | −2.64012 | + | 2.64012i | −0.490258 | + | 0.490258i | −0.908388 | − | 0.418129i | \(-0.862686\pi\) |
0.418129 | + | 0.908388i | \(0.362686\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.94837 | −1.06836 | −0.534179 | − | 0.845371i | \(-0.679379\pi\) | ||||
−0.534179 | + | 0.845371i | \(0.679379\pi\) | |||||||
\(32\) | −4.87417 | + | 2.87098i | −0.861639 | + | 0.507522i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.08387 | + | 2.78647i | −0.528879 | + | 0.477875i | ||||
\(35\) | 0.523272 | − | 0.523272i | 0.0884492 | − | 0.0884492i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.479352 | − | 0.479352i | −0.0788049 | − | 0.0788049i | 0.666606 | − | 0.745411i | \(-0.267747\pi\) |
−0.745411 | + | 0.666606i | \(0.767747\pi\) | |||||||
\(38\) | 0.508791 | − | 10.0429i | 0.0825368 | − | 1.62918i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.427863 | − | 2.79588i | 0.0676510 | − | 0.442067i | ||||
\(41\) | 10.1918i | 1.59169i | 0.605497 | + | 0.795847i | \(0.292974\pi\) | ||||
−0.605497 | + | 0.795847i | \(0.707026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.93728 | − | 4.93728i | −0.752929 | − | 0.752929i | 0.222096 | − | 0.975025i | \(-0.428710\pi\) |
−0.975025 | + | 0.222096i | \(0.928710\pi\) | |||||||
\(44\) | 8.40537 | − | 6.85514i | 1.26716 | − | 1.03345i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.16877 | − | 5.72044i | −0.762094 | − | 0.843432i | ||||
\(47\) | 8.15706 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.45237 | 0.921767 | ||||||||
\(50\) | 0.948122 | + | 1.04932i | 0.134085 | + | 0.148396i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.92267 | − | 7.26203i | −0.821327 | − | 1.00706i | ||||
\(53\) | 5.05247 | + | 5.05247i | 0.694010 | + | 0.694010i | 0.963112 | − | 0.269102i | \(-0.0867267\pi\) |
−0.269102 | + | 0.963112i | \(0.586727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.42317i | 0.731260i | ||||||||
\(56\) | −1.68689 | + | 1.23912i | −0.225421 | + | 0.165584i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.267163 | + | 5.27348i | −0.0350803 | + | 0.692442i | ||||
\(59\) | −3.83709 | − | 3.83709i | −0.499547 | − | 0.499547i | 0.411750 | − | 0.911297i | \(-0.364918\pi\) |
−0.911297 | + | 0.411750i | \(0.864918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.87697 | + | 4.87697i | −0.624432 | + | 0.624432i | −0.946662 | − | 0.322229i | \(-0.895568\pi\) |
0.322229 | + | 0.946662i | \(0.395568\pi\) | |||||||
\(62\) | −6.24172 | + | 5.63978i | −0.792699 | + | 0.716253i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.39250 | + | 7.63387i | −0.299063 | + | 0.954233i | ||||
\(65\) | 4.68548 | 0.581163 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.99222 | + | 3.99222i | −0.487728 | + | 0.487728i | −0.907588 | − | 0.419861i | \(-0.862079\pi\) |
0.419861 | + | 0.907588i | \(0.362079\pi\) | |||||||
\(68\) | −0.594040 | + | 5.84777i | −0.0720379 | + | 0.709146i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0529518 | − | 1.04520i | 0.00632895 | − | 0.124926i | ||||
\(71\) | − | 3.55343i | − | 0.421715i | −0.977517 | − | 0.210857i | \(-0.932374\pi\) | ||
0.977517 | − | 0.210857i | \(-0.0676255\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.1655i | 1.30683i | 0.757002 | + | 0.653413i | \(0.226663\pi\) | ||||
−0.757002 | + | 0.653413i | \(0.773337\pi\) | |||||||
\(74\) | −0.957475 | − | 0.0485073i | −0.111304 | − | 0.00563886i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.98803 | − | 11.0206i | −1.03100 | − | 1.26415i | ||||
\(77\) | 2.83780 | − | 2.83780i | 0.323397 | − | 0.323397i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7776 | 1.21258 | 0.606288 | − | 0.795245i | \(-0.292658\pi\) | ||||
0.606288 | + | 0.795245i | \(0.292658\pi\) | |||||||
\(80\) | −2.20187 | − | 3.33943i | −0.246177 | − | 0.373359i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.66309 | + | 10.6944i | 1.06711 | + | 1.18100i | ||||
\(83\) | −4.61002 | + | 4.61002i | −0.506016 | + | 0.506016i | −0.913301 | − | 0.407285i | \(-0.866475\pi\) |
0.407285 | + | 0.913301i | \(0.366475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.07814 | − | 2.07814i | −0.225406 | − | 0.225406i | ||||
\(86\) | −9.86192 | − | 0.499621i | −1.06344 | − | 0.0538756i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.32037 | − | 15.1625i | 0.247353 | − | 1.61633i | ||||
\(89\) | 2.62476i | 0.278224i | 0.990277 | + | 0.139112i | \(0.0444247\pi\) | ||||
−0.990277 | + | 0.139112i | \(0.955575\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.45179 | − | 2.45179i | −0.257017 | − | 0.257017i | ||||
\(92\) | −10.8473 | − | 1.10192i | −1.13091 | − | 0.114883i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.55934 | − | 7.73389i | 0.882828 | − | 0.797690i | ||||
\(95\) | 7.11052 | 0.729524 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.67846 | 0.170422 | 0.0852108 | − | 0.996363i | \(-0.472844\pi\) | ||||
0.0852108 | + | 0.996363i | \(0.472844\pi\) | |||||||
\(98\) | 6.77058 | − | 6.11764i | 0.683932 | − | 0.617975i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.98976 | + | 0.202128i | 0.198976 | + | 0.0202128i | ||||
\(101\) | −6.52161 | − | 6.52161i | −0.648925 | − | 0.648925i | 0.303808 | − | 0.952733i | \(-0.401742\pi\) |
−0.952733 | + | 0.303808i | \(0.901742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.302418i | 0.0297981i | 0.999889 | + | 0.0148991i | \(0.00474269\pi\) | ||||
−0.999889 | + | 0.0148991i | \(0.995257\pi\) | |||||||
\(104\) | −13.1000 | − | 2.00474i | −1.28456 | − | 0.196581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0920 | + | 0.511278i | 0.980222 | + | 0.0496597i | ||||
\(107\) | 1.20078 | + | 1.20078i | 0.116084 | + | 0.116084i | 0.762762 | − | 0.646679i | \(-0.223843\pi\) |
−0.646679 | + | 0.762762i | \(0.723843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.99992 | + | 6.99992i | −0.670471 | + | 0.670471i | −0.957825 | − | 0.287353i | \(-0.907225\pi\) |
0.287353 | + | 0.957825i | \(0.407225\pi\) | |||||||
\(110\) | 5.14183 | + | 5.69062i | 0.490254 | + | 0.542579i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.595251 | + | 2.89961i | −0.0562459 | + | 0.273987i | ||||
\(113\) | −15.1350 | −1.42378 | −0.711892 | − | 0.702289i | \(-0.752161\pi\) | ||||
−0.711892 | + | 0.702289i | \(0.752161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.85485 | − | 3.85485i | 0.359467 | − | 0.359467i | ||||
\(116\) | 4.71957 | + | 5.78685i | 0.438201 | + | 0.537296i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.66436 | − | 0.388289i | −0.705561 | − | 0.0357449i | ||||
\(119\) | 2.17486i | 0.199370i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.4108i | 1.67371i | ||||||||
\(122\) | −0.493518 | + | 9.74145i | −0.0446811 | + | 0.881950i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.20233 | + | 11.8358i | −0.107973 | + | 1.06289i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94547 | 0.793782 | 0.396891 | − | 0.917866i | \(-0.370089\pi\) | ||||
0.396891 | + | 0.917866i | \(0.370089\pi\) | |||||||
\(128\) | 4.72735 | + | 10.2787i | 0.417843 | + | 0.908519i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.91655 | − | 4.44241i | 0.431210 | − | 0.389625i | ||||
\(131\) | −9.63786 | + | 9.63786i | −0.842064 | + | 0.842064i | −0.989127 | − | 0.147063i | \(-0.953018\pi\) |
0.147063 | + | 0.989127i | \(0.453018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.72074 | − | 3.72074i | −0.322629 | − | 0.322629i | ||||
\(134\) | −0.403987 | + | 7.97422i | −0.0348992 | + | 0.688867i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.92106 | + | 6.69938i | 0.421978 | + | 0.574467i | ||||
\(137\) | 6.92180i | 0.591370i | 0.955286 | + | 0.295685i | \(0.0955478\pi\) | ||||
−0.955286 | + | 0.295685i | \(0.904452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50393 | + | 6.50393i | 0.551657 | + | 0.551657i | 0.926919 | − | 0.375262i | \(-0.122447\pi\) |
−0.375262 | + | 0.926919i | \(0.622447\pi\) | |||||||
\(140\) | −0.935419 | − | 1.14695i | −0.0790573 | − | 0.0969353i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.36909 | − | 3.72867i | −0.282728 | − | 0.312903i | ||||
\(143\) | 25.4102 | 2.12491 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.73370 | −0.310067 | ||||||||
\(146\) | 10.5863 | + | 11.7162i | 0.876127 | + | 0.969636i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.05068 | + | 0.856904i | −0.0863658 | + | 0.0704371i | ||||
\(149\) | 5.75043 | + | 5.75043i | 0.471094 | + | 0.471094i | 0.902268 | − | 0.431175i | \(-0.141901\pi\) |
−0.431175 | + | 0.902268i | \(0.641901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.185782i | 0.0151187i | 0.999971 | + | 0.00755935i | \(0.00240624\pi\) | ||||
−0.999971 | + | 0.00755935i | \(0.997594\pi\) | |||||||
\(152\) | −19.8801 | − | 3.04232i | −1.61249 | − | 0.246765i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.287167 | − | 5.66832i | 0.0231406 | − | 0.456767i | ||||
\(155\) | −4.20613 | − | 4.20613i | −0.337845 | − | 0.337845i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8717 | + | 11.8717i | −0.947462 | + | 0.947462i | −0.998687 | − | 0.0512256i | \(-0.983687\pi\) |
0.0512256 | + | 0.998687i | \(0.483687\pi\) | |||||||
\(158\) | 11.3091 | − | 10.2185i | 0.899705 | − | 0.812940i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.47664 | − | 1.41647i | −0.432967 | − | 0.111982i | ||||
\(161\) | −4.03428 | −0.317946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3813 | − | 11.3813i | 0.891454 | − | 0.891454i | −0.103206 | − | 0.994660i | \(-0.532910\pi\) |
0.994660 | + | 0.103206i | \(0.0329101\pi\) | |||||||
\(164\) | 20.2793 | + | 2.06005i | 1.58354 | + | 0.160863i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.466505 | + | 9.20823i | −0.0362078 | + | 0.714698i | ||||
\(167\) | − | 12.8924i | − | 0.997644i | −0.866705 | − | 0.498822i | \(-0.833766\pi\) | ||
0.866705 | − | 0.498822i | \(-0.166234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.95377i | − | 0.688751i | ||||||
\(170\) | −4.15095 | − | 0.210294i | −0.318364 | − | 0.0161288i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.8220 | + | 8.82604i | −0.825167 | + | 0.672980i | ||||
\(173\) | 12.1023 | − | 12.1023i | 0.920122 | − | 0.920122i | −0.0769156 | − | 0.997038i | \(-0.524507\pi\) |
0.997038 | + | 0.0769156i | \(0.0245072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.740019 | 0.0559402 | ||||||||
\(176\) | −11.9411 | − | 18.1103i | −0.900096 | − | 1.36511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.48859 | + | 2.75420i | 0.186528 | + | 0.206436i | ||||
\(179\) | −15.5558 | + | 15.5558i | −1.16269 | + | 1.16269i | −0.178809 | + | 0.983884i | \(0.557224\pi\) |
−0.983884 | + | 0.178809i | \(0.942776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5970 | + | 10.5970i | 0.787670 | + | 0.787670i | 0.981112 | − | 0.193442i | \(-0.0619651\pi\) |
−0.193442 | + | 0.981112i | \(0.561965\pi\) | |||||||
\(182\) | −4.89729 | − | 0.248105i | −0.363011 | − | 0.0183908i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.4270 | + | 9.12835i | −0.916134 | + | 0.672951i | ||||
\(185\) | − | 0.677905i | − | 0.0498406i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.2701 | − | 11.2701i | −0.824151 | − | 0.824151i | ||||
\(188\) | 1.64877 | − | 16.2306i | 0.120249 | − | 1.18374i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.46118 | − | 6.74164i | 0.541291 | − | 0.489090i | ||||
\(191\) | −8.84439 | −0.639958 | −0.319979 | − | 0.947425i | \(-0.603676\pi\) | ||||
−0.319979 | + | 0.947425i | \(0.603676\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0714 | 1.01289 | 0.506443 | − | 0.862274i | \(-0.330960\pi\) | ||||
0.506443 | + | 0.862274i | \(0.330960\pi\) | |||||||
\(194\) | 1.76123 | − | 1.59138i | 0.126449 | − | 0.114255i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.30420 | − | 12.8387i | 0.0931575 | − | 0.917048i | ||||
\(197\) | −8.15230 | − | 8.15230i | −0.580827 | − | 0.580827i | 0.354303 | − | 0.935131i | \(-0.384718\pi\) |
−0.935131 | + | 0.354303i | \(0.884718\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.3466i | − | 0.804340i | −0.915565 | − | 0.402170i | \(-0.868256\pi\) | ||
0.915565 | − | 0.402170i | \(-0.131744\pi\) | |||||||
\(200\) | 2.27953 | − | 1.67444i | 0.161187 | − | 0.118401i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.0265 | − | 0.659945i | −0.916543 | − | 0.0464336i | ||||
\(203\) | 1.95374 | + | 1.95374i | 0.137126 | + | 0.137126i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.20670 | + | 7.20670i | −0.503338 | + | 0.503338i | ||||
\(206\) | 0.286729 | + | 0.317332i | 0.0199774 | + | 0.0221096i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −15.6468 | + | 10.3168i | −1.08491 | + | 0.715344i | ||||
\(209\) | 38.5616 | 2.66736 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.6416 | + | 15.6416i | −1.07681 | + | 1.07681i | −0.0800209 | + | 0.996793i | \(0.525499\pi\) |
−0.996793 | + | 0.0800209i | \(0.974501\pi\) | |||||||
\(212\) | 11.0744 | − | 9.03196i | 0.760596 | − | 0.620317i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.39848 | + | 0.121511i | 0.163957 | + | 0.00830632i | ||||
\(215\) | − | 6.98237i | − | 0.476194i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.40191i | 0.298821i | ||||||||
\(218\) | −0.708347 | + | 13.9819i | −0.0479753 | + | 0.946975i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.7908 | + | 1.09617i | 0.727516 | + | 0.0739041i | ||||
\(221\) | −9.73708 | + | 9.73708i | −0.654987 | + | 0.654987i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2773 | −0.688219 | −0.344110 | − | 0.938929i | \(-0.611819\pi\) | ||||
−0.344110 | + | 0.938929i | \(0.611819\pi\) | |||||||
\(224\) | 2.12458 | + | 3.60698i | 0.141954 | + | 0.241001i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.8814 | + | 14.3499i | −1.05642 | + | 0.954539i | ||||
\(227\) | 13.8323 | − | 13.8323i | 0.918082 | − | 0.918082i | −0.0788077 | − | 0.996890i | \(-0.525111\pi\) |
0.996890 | + | 0.0788077i | \(0.0251113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3025 | − | 11.3025i | −0.746890 | − | 0.746890i | 0.227004 | − | 0.973894i | \(-0.427107\pi\) |
−0.973894 | + | 0.227004i | \(0.927107\pi\) | |||||||
\(230\) | 0.390086 | − | 7.69983i | 0.0257215 | − | 0.507712i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.4390 | + | 1.59751i | 0.685351 | + | 0.104882i | ||||
\(233\) | − | 0.638284i | − | 0.0418154i | −0.999781 | − | 0.0209077i | \(-0.993344\pi\) | ||
0.999781 | − | 0.0209077i | \(-0.00665561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.76791 | + | 5.76791i | 0.376257 | + | 0.376257i | ||||
\(236\) | −8.41048 | + | 6.85931i | −0.547475 | + | 0.446503i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.06204 | + | 2.28212i | 0.133662 | + | 0.147928i | ||||
\(239\) | −27.2255 | −1.76107 | −0.880534 | − | 0.473983i | \(-0.842816\pi\) | ||||
−0.880534 | + | 0.473983i | \(0.842816\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0821 | −0.907106 | −0.453553 | − | 0.891229i | \(-0.649844\pi\) | ||||
−0.453553 | + | 0.891229i | \(0.649844\pi\) | |||||||
\(242\) | 17.4557 | + | 19.3187i | 1.12209 | + | 1.24186i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.71823 | + | 10.6898i | 0.558128 | + | 0.684343i | ||||
\(245\) | 4.56252 | + | 4.56252i | 0.291488 | + | 0.291488i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 33.3162i | − | 2.11986i | ||||||
\(248\) | 9.96019 | + | 13.5595i | 0.632473 | + | 0.861028i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.0715547 | + | 1.41240i | −0.00452551 | + | 0.0893282i | ||||
\(251\) | −1.61761 | − | 1.61761i | −0.102103 | − | 0.102103i | 0.654210 | − | 0.756313i | \(-0.273001\pi\) |
−0.756313 | + | 0.654210i | \(0.773001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9055 | − | 20.9055i | 1.31432 | − | 1.31432i | ||||
\(254\) | 9.38663 | − | 8.48140i | 0.588969 | − | 0.532170i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.7060 | + | 6.30352i | 0.919123 | + | 0.393970i | ||||
\(257\) | −4.53176 | −0.282683 | −0.141342 | − | 0.989961i | \(-0.545142\pi\) | ||||
−0.141342 | + | 0.989961i | \(0.545142\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.354729 | + | 0.354729i | −0.0220418 | + | 0.0220418i | ||||
\(260\) | 0.947067 | − | 9.32299i | 0.0587346 | − | 0.578187i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.975289 | + | 19.2510i | −0.0602536 | + | 1.18933i | ||||
\(263\) | − | 8.25620i | − | 0.509099i | −0.967060 | − | 0.254550i | \(-0.918073\pi\) | ||
0.967060 | − | 0.254550i | \(-0.0819272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.14527i | 0.438931i | ||||||||
\(266\) | −7.43194 | − | 0.376515i | −0.455682 | − | 0.0230856i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.13662 | + | 8.75050i | 0.435939 | + | 0.534522i | ||||
\(269\) | 14.8352 | − | 14.8352i | 0.904520 | − | 0.904520i | −0.0913029 | − | 0.995823i | \(-0.529103\pi\) |
0.995823 | + | 0.0913029i | \(0.0291031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 32.0786 | 1.94864 | 0.974319 | − | 0.225172i | \(-0.0722944\pi\) | ||||
0.974319 | + | 0.225172i | \(0.0722944\pi\) | |||||||
\(272\) | 11.5156 | + | 2.36399i | 0.698235 | + | 0.143338i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.56272 | + | 7.26316i | 0.396468 | + | 0.438784i | ||||
\(275\) | −3.83476 | + | 3.83476i | −0.231245 | + | 0.231245i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6755 | − | 14.6755i | −0.881763 | − | 0.881763i | 0.111951 | − | 0.993714i | \(-0.464290\pi\) |
−0.993714 | + | 0.111951i | \(0.964290\pi\) | |||||||
\(278\) | 12.9912 | + | 0.658156i | 0.779161 | + | 0.0394736i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.06900 | − | 0.316626i | −0.123647 | − | 0.0189220i | ||||
\(281\) | 24.6456i | 1.47023i | 0.677942 | + | 0.735116i | \(0.262872\pi\) | ||||
−0.677942 | + | 0.735116i | \(0.737128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.116449 | − | 0.116449i | −0.00692219 | − | 0.00692219i | 0.703637 | − | 0.710559i | \(-0.251558\pi\) |
−0.710559 | + | 0.703637i | \(0.751558\pi\) | |||||||
\(284\) | −7.07047 | − | 0.718248i | −0.419555 | − | 0.0426202i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.6633 | − | 24.0920i | 1.57664 | − | 1.42459i | ||||
\(287\) | 7.54214 | 0.445198 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.36268 | −0.491923 | ||||||||
\(290\) | −3.91783 | + | 3.54000i | −0.230063 | + | 0.207876i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.2167 | + | 2.25686i | 1.30013 | + | 0.132073i | ||||
\(293\) | −21.5697 | − | 21.5697i | −1.26012 | − | 1.26012i | −0.951036 | − | 0.309079i | \(-0.899979\pi\) |
−0.309079 | − | 0.951036i | \(-0.600021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.42647i | − | 0.315941i | ||||||
\(296\) | −0.290050 | + | 1.89534i | −0.0168588 | + | 0.110164i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.4861 | + | 0.581907i | 0.665374 | + | 0.0337090i | ||||
\(299\) | −18.0619 | − | 18.0619i | −1.04454 | − | 1.04454i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.65368 | + | 3.65368i | −0.210595 | + | 0.210595i | ||||
\(302\) | 0.176144 | + | 0.194944i | 0.0101359 | + | 0.0112177i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −23.7450 | + | 15.6564i | −1.36187 | + | 0.897959i | ||||
\(305\) | −6.89708 | −0.394926 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7544 | − | 11.7544i | 0.670856 | − | 0.670856i | −0.287057 | − | 0.957913i | \(-0.592677\pi\) |
0.957913 | + | 0.287057i | \(0.0926770\pi\) | |||||||
\(308\) | −5.07294 | − | 6.22013i | −0.289057 | − | 0.354425i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.40149 | − | 0.425634i | −0.477173 | − | 0.0241744i | ||||
\(311\) | 15.8798i | 0.900462i | 0.892912 | + | 0.450231i | \(0.148658\pi\) | ||||
−0.892912 | + | 0.450231i | \(0.851342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.5435i | 1.83947i | 0.392542 | + | 0.919734i | \(0.371596\pi\) | ||||
−0.392542 | + | 0.919734i | \(0.628404\pi\) | |||||||
\(314\) | −1.20134 | + | 23.7129i | −0.0677953 | + | 1.33820i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.17846 | − | 21.4449i | 0.122548 | − | 1.20637i | ||||
\(317\) | −13.8078 | + | 13.8078i | −0.775523 | + | 0.775523i | −0.979066 | − | 0.203543i | \(-0.934754\pi\) |
0.203543 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.2485 | −1.13370 | ||||||||
\(320\) | −7.08971 | + | 3.70620i | −0.396327 | + | 0.207183i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.23323 | + | 3.82499i | −0.235909 | + | 0.213158i | ||||
\(323\) | −14.7766 | + | 14.7766i | −0.822194 | + | 0.822194i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.31314 | + | 3.31314i | 0.183780 | + | 0.183780i | ||||
\(326\) | 1.15172 | − | 22.7335i | 0.0637877 | − | 1.25909i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.2325 | − | 17.0656i | 1.28280 | − | 0.942289i | ||||
\(329\) | − | 6.03638i | − | 0.332796i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.85148 | − | 5.85148i | −0.321627 | − | 0.321627i | 0.527764 | − | 0.849391i | \(-0.323030\pi\) |
−0.849391 | + | 0.527764i | \(0.823030\pi\) | |||||||
\(332\) | 8.24102 | + | 10.1047i | 0.452285 | + | 0.554565i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2236 | − | 13.5282i | −0.668844 | − | 0.740230i | ||||
\(335\) | −5.64585 | −0.308466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.3223 | −1.05255 | −0.526276 | − | 0.850314i | \(-0.676412\pi\) | ||||
−0.526276 | + | 0.850314i | \(0.676412\pi\) | |||||||
\(338\) | −8.48927 | − | 9.39533i | −0.461755 | − | 0.511039i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.55505 | + | 3.71495i | −0.247032 | + | 0.201471i | ||||
\(341\) | −22.8106 | − | 22.8106i | −1.23526 | − | 1.23526i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.95501i | − | 0.537520i | ||||||
\(344\) | −2.98750 | + | 19.5219i | −0.161075 | + | 1.05255i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.22468 | − | 24.1736i | 0.0658390 | − | 1.29958i | ||||
\(347\) | −6.92151 | − | 6.92151i | −0.371566 | − | 0.371566i | 0.496481 | − | 0.868047i | \(-0.334625\pi\) |
−0.868047 | + | 0.496481i | \(0.834625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.2497 | − | 13.2497i | 0.709241 | − | 0.709241i | −0.257135 | − | 0.966376i | \(-0.582778\pi\) |
0.966376 | + | 0.257135i | \(0.0827784\pi\) | |||||||
\(350\) | 0.776514 | − | 0.701629i | 0.0415064 | − | 0.0375036i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.7008 | − | 7.68175i | −1.58306 | − | 0.409439i | ||||
\(353\) | 21.8789 | 1.16450 | 0.582249 | − | 0.813010i | \(-0.302173\pi\) | ||||
0.582249 | + | 0.813010i | \(0.302173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.51265 | − | 2.51265i | 0.133358 | − | 0.133358i | ||||
\(356\) | 5.22263 | + | 0.530537i | 0.276799 | + | 0.0281184i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.57414 | + | 31.0717i | −0.0831961 | + | 1.64219i | ||||
\(359\) | − | 6.94782i | − | 0.366692i | −0.983048 | − | 0.183346i | \(-0.941307\pi\) | ||
0.983048 | − | 0.183346i | \(-0.0586928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 31.5595i | − | 1.66102i | ||||||
\(362\) | 21.1669 | + | 1.07235i | 1.11251 | + | 0.0563615i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.37404 | + | 4.38289i | −0.281676 | + | 0.229726i | ||||
\(365\) | −7.89522 | + | 7.89522i | −0.413254 | + | 0.413254i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.0448 | 0.889730 | 0.444865 | − | 0.895598i | \(-0.353252\pi\) | ||||
0.444865 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(368\) | −4.38510 | + | 21.3609i | −0.228589 | + | 1.11351i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.642737 | − | 0.711337i | −0.0334143 | − | 0.0369807i | ||||
\(371\) | 3.73892 | − | 3.73892i | 0.194115 | − | 0.194115i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.3704 | − | 14.3704i | −0.744071 | − | 0.744071i | 0.229287 | − | 0.973359i | \(-0.426360\pi\) |
−0.973359 | + | 0.229287i | \(0.926360\pi\) | |||||||
\(374\) | −22.5113 | − | 1.14046i | −1.16403 | − | 0.0589719i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.6585 | − | 18.5943i | −0.704384 | − | 0.958926i | ||||
\(377\) | 17.4942i | 0.900996i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.97499 | + | 2.97499i | 0.152815 | + | 0.152815i | 0.779374 | − | 0.626559i | \(-0.215537\pi\) |
−0.626559 | + | 0.779374i | \(0.715537\pi\) | |||||||
\(380\) | 1.43723 | − | 14.1482i | 0.0737286 | − | 0.725788i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.28056 | + | 8.38557i | −0.474835 | + | 0.429043i | ||||
\(383\) | 20.4810 | 1.04653 | 0.523266 | − | 0.852170i | \(-0.324714\pi\) | ||||
0.523266 | + | 0.852170i | \(0.324714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.01325 | 0.204534 | ||||||||
\(386\) | 14.7654 | − | 13.3415i | 0.751539 | − | 0.679062i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.339263 | − | 3.33973i | 0.0172235 | − | 0.169549i | ||||
\(389\) | −11.8703 | − | 11.8703i | −0.601848 | − | 0.601848i | 0.338955 | − | 0.940803i | \(-0.389927\pi\) |
−0.940803 | + | 0.338955i | \(0.889927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0218i | 0.810259i | ||||||||
\(392\) | −10.8041 | − | 14.7084i | −0.545690 | − | 0.742885i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.2837 | − | 0.824960i | −0.820361 | − | 0.0415609i | ||||
\(395\) | 7.62092 | + | 7.62092i | 0.383450 | + | 0.383450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.1282 | − | 19.1282i | 0.960019 | − | 0.960019i | −0.0392118 | − | 0.999231i | \(-0.512485\pi\) |
0.999231 | + | 0.0392118i | \(0.0124847\pi\) | |||||||
\(398\) | −10.7580 | − | 11.9062i | −0.539249 | − | 0.596803i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.804372 | − | 3.91829i | 0.0402186 | − | 0.195914i | ||||
\(401\) | 16.0874 | 0.803368 | 0.401684 | − | 0.915778i | \(-0.368425\pi\) | ||||
0.401684 | + | 0.915778i | \(0.368425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.7078 | + | 19.7078i | −0.981714 | + | 0.981714i | ||||
\(404\) | −14.2946 | + | 11.6582i | −0.711185 | + | 0.580019i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.90248 | + | 0.197706i | 0.193677 | + | 0.00981198i | ||||
\(407\) | − | 3.67640i | − | 0.182232i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.4524i | − | 1.15964i | −0.814743 | − | 0.579822i | \(-0.803122\pi\) | ||
0.814743 | − | 0.579822i | \(-0.196878\pi\) | |||||||
\(410\) | −0.729272 | + | 14.3949i | −0.0360162 | + | 0.710916i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.601739 | + | 0.0611271i | 0.0296456 | + | 0.00301152i | ||||
\(413\) | −2.83952 | + | 2.83952i | −0.139724 | + | 0.139724i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.51956 | −0.320032 | ||||||||
\(416\) | −6.63684 | + | 25.6607i | −0.325398 | + | 1.25812i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 40.4633 | − | 36.5611i | 1.97912 | − | 1.78826i | ||||
\(419\) | 14.1654 | − | 14.1654i | 0.692027 | − | 0.692027i | −0.270651 | − | 0.962678i | \(-0.587239\pi\) |
0.962678 | + | 0.270651i | \(0.0872388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.2978 | + | 21.2978i | 1.03799 | + | 1.03799i | 0.999249 | + | 0.0387434i | \(0.0123355\pi\) |
0.0387434 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(422\) | −1.58283 | + | 31.2432i | −0.0770511 | + | 1.52089i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.05719 | − | 19.9773i | 0.148470 | − | 0.970184i | ||||
\(425\) | − | 2.93893i | − | 0.142559i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.60905 | + | 3.60905i | 0.174654 | + | 0.174654i | ||||
\(428\) | 2.63197 | − | 2.14655i | 0.127221 | − | 0.103757i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.62014 | − | 7.32671i | −0.319252 | − | 0.353326i | ||||
\(431\) | 21.0148 | 1.01225 | 0.506123 | − | 0.862462i | \(-0.331078\pi\) | ||||
0.506123 | + | 0.862462i | \(0.331078\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.2253 | 0.779738 | 0.389869 | − | 0.920870i | \(-0.372520\pi\) | ||||
0.389869 | + | 0.920870i | \(0.372520\pi\) | |||||||
\(434\) | 4.17355 | + | 4.61899i | 0.200337 | + | 0.221719i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.5133 | + | 15.3430i | 0.599278 | + | 0.734799i | ||||
\(437\) | −27.4100 | − | 27.4100i | −1.31120 | − | 1.31120i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.33967i | 0.159394i | 0.996819 | + | 0.0796970i | \(0.0253953\pi\) | ||||
−0.996819 | + | 0.0796970i | \(0.974605\pi\) | |||||||
\(440\) | 12.3623 | − | 9.08078i | 0.589348 | − | 0.432909i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.985330 | + | 19.4492i | −0.0468674 | + | 0.925105i | ||||
\(443\) | −13.4671 | − | 13.4671i | −0.639841 | − | 0.639841i | 0.310675 | − | 0.950516i | \(-0.399445\pi\) |
−0.950516 | + | 0.310675i | \(0.899445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.85598 | + | 1.85598i | −0.0879820 | + | 0.0879820i | ||||
\(446\) | −10.7841 | + | 9.74415i | −0.510644 | + | 0.461399i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.64921 | + | 1.77050i | 0.266900 | + | 0.0836482i | ||||
\(449\) | −19.2995 | −0.910799 | −0.455400 | − | 0.890287i | \(-0.650504\pi\) | ||||
−0.455400 | + | 0.890287i | \(0.650504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.0832 | + | 39.0832i | −1.84036 | + | 1.84036i | ||||
\(452\) | −3.05921 | + | 30.1151i | −0.143893 | + | 1.41649i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.39974 | − | 27.6292i | 0.0656931 | − | 1.29670i | ||||
\(455\) | − | 3.46735i | − | 0.162552i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.0222i | − | 0.983377i | −0.870771 | − | 0.491688i | \(-0.836380\pi\) | ||
0.870771 | − | 0.491688i | \(-0.163620\pi\) | |||||||
\(458\) | −22.5760 | − | 1.14374i | −1.05491 | − | 0.0534434i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.89106 | − | 8.44941i | −0.321297 | − | 0.393956i | ||||
\(461\) | 23.3056 | − | 23.3056i | 1.08545 | − | 1.08545i | 0.0894616 | − | 0.995990i | \(-0.471485\pi\) |
0.995990 | − | 0.0894616i | \(-0.0285146\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.65187 | −0.0767687 | −0.0383844 | − | 0.999263i | \(-0.512221\pi\) | ||||
−0.0383844 | + | 0.999263i | \(0.512221\pi\) | |||||||
\(464\) | 12.4684 | − | 8.22112i | 0.578831 | − | 0.381656i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.605171 | − | 0.669762i | −0.0280340 | − | 0.0310261i | ||||
\(467\) | 14.4723 | − | 14.4723i | 0.669699 | − | 0.669699i | −0.287948 | − | 0.957646i | \(-0.592973\pi\) |
0.957646 | + | 0.287948i | \(0.0929729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95432 | + | 2.95432i | 0.136418 | + | 0.136418i | ||||
\(470\) | 11.5211 | + | 0.583676i | 0.531427 | + | 0.0269230i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.32178 | + | 15.1717i | −0.106869 | + | 0.698336i | ||||
\(473\) | − | 37.8666i | − | 1.74111i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.02789 | + | 5.02789i | 0.230696 | + | 0.230696i | ||||
\(476\) | 4.32746 | + | 0.439601i | 0.198349 | + | 0.0201491i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.5681 | + | 25.8131i | −1.30667 | + | 1.18066i | ||||
\(479\) | −6.07727 | −0.277678 | −0.138839 | − | 0.990315i | \(-0.544337\pi\) | ||||
−0.138839 | + | 0.990315i | \(0.544337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.17632 | −0.144828 | ||||||||
\(482\) | −14.7765 | + | 13.3515i | −0.673053 | + | 0.608145i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 36.6331 | + | 3.72134i | 1.66514 | + | 0.169152i | ||||
\(485\) | 1.18685 | + | 1.18685i | 0.0538921 | + | 0.0538921i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.1863i | 0.461586i | 0.973003 | + | 0.230793i | \(0.0741320\pi\) | ||||
−0.973003 | + | 0.230793i | \(0.925868\pi\) | |||||||
\(488\) | 19.2834 | + | 2.95100i | 0.872918 | + | 0.133586i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.11334 | + | 0.461697i | 0.411699 | + | 0.0208574i | ||||
\(491\) | −8.75035 | − | 8.75035i | −0.394898 | − | 0.394898i | 0.481531 | − | 0.876429i | \(-0.340081\pi\) |
−0.876429 | + | 0.481531i | \(0.840081\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.75914 | − | 7.75914i | 0.349454 | − | 0.349454i | ||||
\(494\) | −31.5879 | − | 34.9592i | −1.42120 | − | 1.57289i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.3074 | + | 4.78470i | 1.04653 | + | 0.214840i | ||||
\(497\) | −2.62961 | −0.117954 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.8260 | + | 23.8260i | −1.06660 | + | 1.06660i | −0.0689808 | + | 0.997618i | \(0.521975\pi\) |
−0.997618 | + | 0.0689808i | \(0.978025\pi\) | |||||||
\(500\) | 1.26405 | + | 1.54990i | 0.0565299 | + | 0.0693136i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.23108 | − | 0.163692i | −0.144210 | − | 0.00730592i | ||||
\(503\) | 9.42267i | 0.420136i | 0.977687 | + | 0.210068i | \(0.0673685\pi\) | ||||
−0.977687 | + | 0.210068i | \(0.932631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.22295i | − | 0.410416i | ||||||
\(506\) | 2.11551 | − | 41.7575i | 0.0940457 | − | 1.85635i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.80813 | − | 17.7993i | 0.0802228 | − | 0.789718i | ||||
\(509\) | 16.3129 | − | 16.3129i | 0.723055 | − | 0.723055i | −0.246172 | − | 0.969226i | \(-0.579173\pi\) |
0.969226 | + | 0.246172i | \(0.0791727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.26270 | 0.365520 | ||||||||
\(512\) | 21.4077 | − | 7.32867i | 0.946097 | − | 0.323885i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.75525 | + | 4.29666i | −0.209745 | + | 0.189518i | ||||
\(515\) | −0.213842 | + | 0.213842i | −0.00942299 | + | 0.00942299i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.2804 | + | 31.2804i | 1.37571 | + | 1.37571i | ||||
\(518\) | −0.0358963 | + | 0.708550i | −0.00157719 | + | 0.0311319i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.84556 | − | 10.6807i | −0.344051 | − | 0.468380i | ||||
\(521\) | 10.7287i | 0.470033i | 0.971991 | + | 0.235016i | \(0.0755144\pi\) | ||||
−0.971991 | + | 0.235016i | \(0.924486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.3868 | − | 16.3868i | −0.716546 | − | 0.716546i | 0.251351 | − | 0.967896i | \(-0.419125\pi\) |
−0.967896 | + | 0.251351i | \(0.919125\pi\) | |||||||
\(524\) | 17.2289 | + | 21.1251i | 0.752650 | + | 0.922855i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.82789 | − | 8.66337i | −0.341312 | − | 0.377741i | ||||
\(527\) | 17.4819 | 0.761521 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.71979 | −0.292165 | ||||||||
\(530\) | 6.77459 | + | 7.49765i | 0.294269 | + | 0.325677i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.15544 | + | 6.65131i | −0.353583 | + | 0.288371i | ||||
\(533\) | 33.7669 | + | 33.7669i | 1.46261 | + | 1.46261i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.69816i | 0.0734177i | ||||||||
\(536\) | 15.7851 | + | 2.41565i | 0.681813 | + | 0.104340i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.50123 | − | 29.6325i | 0.0647227 | − | 1.27755i | ||||
\(539\) | 24.7433 | + | 24.7433i | 1.06577 | + | 1.06577i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4471 | − | 11.4471i | 0.492148 | − | 0.492148i | −0.416834 | − | 0.908983i | \(-0.636860\pi\) |
0.908983 | + | 0.416834i | \(0.136860\pi\) | |||||||
\(542\) | 33.6606 | − | 30.4145i | 1.44585 | − | 1.30641i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.3248 | − | 8.43760i | 0.614172 | − | 0.361759i | ||||
\(545\) | −9.89939 | −0.424043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.67749 | − | 9.67749i | 0.413780 | − | 0.413780i | −0.469273 | − | 0.883053i | \(-0.655484\pi\) |
0.883053 | + | 0.469273i | \(0.155484\pi\) | |||||||
\(548\) | 13.7727 | + | 1.39909i | 0.588342 | + | 0.0597662i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.388053 | + | 7.65970i | −0.0165466 | + | 0.326611i | ||||
\(551\) | 26.5485i | 1.13100i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.97564i | − | 0.339159i | ||||||
\(554\) | −29.3133 | − | 1.48506i | −1.24540 | − | 0.0630942i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.2559 | − | 11.6266i | 0.604585 | − | 0.493079i | ||||
\(557\) | −10.0484 | + | 10.0484i | −0.425762 | + | 0.425762i | −0.887182 | − | 0.461420i | \(-0.847340\pi\) |
0.461420 | + | 0.887182i | \(0.347340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.7158 | −1.38373 | ||||||||
\(560\) | −2.47124 | + | 1.62943i | −0.104429 | + | 0.0688558i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.3670 | + | 25.8610i | 0.985678 | + | 1.09088i | ||||
\(563\) | −8.44120 | + | 8.44120i | −0.355754 | + | 0.355754i | −0.862245 | − | 0.506491i | \(-0.830942\pi\) |
0.506491 | + | 0.862245i | \(0.330942\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7021 | − | 10.7021i | −0.450240 | − | 0.450240i | ||||
\(566\) | −0.232600 | − | 0.0117839i | −0.00977692 | − | 0.000495315i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.10015 | + | 5.95001i | −0.339875 | + | 0.249657i | ||||
\(569\) | − | 7.27300i | − | 0.304900i | −0.988311 | − | 0.152450i | \(-0.951284\pi\) | ||
0.988311 | − | 0.152450i | \(-0.0487163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.28045 | − | 5.28045i | −0.220980 | − | 0.220980i | 0.587931 | − | 0.808911i | \(-0.299943\pi\) |
−0.808911 | + | 0.587931i | \(0.799943\pi\) | |||||||
\(572\) | 5.13611 | − | 50.5602i | 0.214752 | − | 2.11403i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.91409 | − | 7.15087i | 0.330328 | − | 0.298472i | ||||
\(575\) | 5.45159 | 0.227347 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.0550 | 1.12631 | 0.563157 | − | 0.826350i | \(-0.309587\pi\) | ||||
0.563157 | + | 0.826350i | \(0.309587\pi\) | |||||||
\(578\) | −8.77510 | + | 7.92885i | −0.364996 | + | 0.329797i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.754684 | + | 7.42916i | −0.0313366 | + | 0.308479i | ||||
\(581\) | 3.41150 | + | 3.41150i | 0.141533 | + | 0.141533i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.7500i | 1.60486i | ||||||||
\(584\) | 25.4521 | − | 18.6960i | 1.05322 | − | 0.773646i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −43.0841 | − | 2.18272i | −1.77979 | − | 0.0901671i | ||||
\(587\) | 6.62135 | + | 6.62135i | 0.273292 | + | 0.273292i | 0.830424 | − | 0.557132i | \(-0.188098\pi\) |
−0.557132 | + | 0.830424i | \(0.688098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.9078 | + | 29.9078i | −1.23233 | + | 1.23233i | ||||
\(590\) | −5.14496 | − | 5.69408i | −0.211815 | − | 0.234422i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.49266 | + | 2.26381i | 0.0613480 | + | 0.0930422i | ||||
\(593\) | 9.02017 | 0.370414 | 0.185207 | − | 0.982700i | \(-0.440704\pi\) | ||||
0.185207 | + | 0.982700i | \(0.440704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.53786 | + | 1.53786i | −0.0630462 | + | 0.0630462i | ||||
\(596\) | 12.6043 | − | 10.2797i | 0.516292 | − | 0.421071i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −36.0774 | − | 1.82774i | −1.47532 | − | 0.0747420i | ||||
\(599\) | − | 7.68375i | − | 0.313950i | −0.987603 | − | 0.156975i | \(-0.949826\pi\) | ||
0.987603 | − | 0.156975i | \(-0.0501742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.7822i | 1.29642i | 0.761460 | + | 0.648212i | \(0.224483\pi\) | ||||
−0.761460 | + | 0.648212i | \(0.775517\pi\) | |||||||
\(602\) | −0.369729 | + | 7.29801i | −0.0150690 | + | 0.297445i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.369661 | + | 0.0375517i | 0.0150413 | + | 0.00152796i | ||||
\(605\) | −13.0184 | + | 13.0184i | −0.529273 | + | 0.529273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.7518 | 1.04524 | 0.522618 | − | 0.852567i | \(-0.324956\pi\) | ||||
0.522618 | + | 0.852567i | \(0.324956\pi\) | |||||||
\(608\) | −10.0718 | + | 38.9418i | −0.408466 | + | 1.57930i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.23722 | + | 6.53928i | −0.293026 | + | 0.264768i | ||||
\(611\) | 27.0255 | − | 27.0255i | 1.09333 | − | 1.09333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.4967 | − | 10.4967i | −0.423956 | − | 0.423956i | 0.462607 | − | 0.886563i | \(-0.346914\pi\) |
−0.886563 | + | 0.462607i | \(0.846914\pi\) | |||||||
\(614\) | 1.18947 | − | 23.4786i | 0.0480029 | − | 0.947519i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.2206 | − | 1.71712i | −0.452089 | − | 0.0691847i | ||||
\(617\) | 29.2461i | 1.17740i | 0.808351 | + | 0.588701i | \(0.200360\pi\) | ||||
−0.808351 | + | 0.588701i | \(0.799640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.9641 | + | 21.9641i | 0.882814 | + | 0.882814i | 0.993820 | − | 0.111006i | \(-0.0354073\pi\) |
−0.111006 | + | 0.993820i | \(0.535407\pi\) | |||||||
\(620\) | −9.21937 | + | 7.51902i | −0.370259 | + | 0.301971i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15.0560 | + | 16.6629i | 0.603691 | + | 0.668123i | ||||
\(623\) | 1.94237 | 0.0778194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 30.8552 | + | 34.1484i | 1.23322 | + | 1.36485i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.2222 | + | 26.0213i | 0.846856 | + | 1.03836i | ||||
\(629\) | 1.40878 | + | 1.40878i | 0.0561718 | + | 0.0561718i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 6.46257i | − | 0.257271i | −0.991692 | − | 0.128635i | \(-0.958940\pi\) | ||
0.991692 | − | 0.128635i | \(-0.0410597\pi\) | |||||||
\(632\) | −18.0465 | − | 24.5679i | −0.717850 | − | 0.977257i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.39726 | + | 27.5802i | −0.0554923 | + | 1.09535i | ||||
\(635\) | 6.32540 | + | 6.32540i | 0.251016 | + | 0.251016i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.3776 | − | 21.3776i | 0.847011 | − | 0.847011i | ||||
\(638\) | −21.2471 | + | 19.1980i | −0.841179 | + | 0.760058i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.92542 | + | 10.6109i | −0.155166 | + | 0.419432i | ||||
\(641\) | 5.56318 | 0.219732 | 0.109866 | − | 0.993946i | \(-0.464958\pi\) | ||||
0.109866 | + | 0.993946i | \(0.464958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.91681 | − | 2.91681i | 0.115028 | − | 0.115028i | −0.647250 | − | 0.762278i | \(-0.724081\pi\) |
0.762278 | + | 0.647250i | \(0.224081\pi\) | |||||||
\(644\) | −0.815440 | + | 8.02724i | −0.0321328 | + | 0.316318i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.49530 | + | 29.5154i | −0.0588318 | + | 1.16127i | ||||
\(647\) | 22.9740i | 0.903201i | 0.892220 | + | 0.451601i | \(0.149147\pi\) | ||||
−0.892220 | + | 0.451601i | \(0.850853\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.4287i | − | 1.15518i | ||||||
\(650\) | 6.61779 | + | 0.335268i | 0.259571 | + | 0.0131503i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.3456 | − | 24.9466i | −0.796796 | − | 0.976984i | ||||
\(653\) | −25.9783 | + | 25.9783i | −1.01661 | + | 1.01661i | −0.0167495 | + | 0.999860i | \(0.505332\pi\) |
−0.999860 | + | 0.0167495i | \(0.994668\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.6300 | −0.532568 | ||||||||
\(656\) | 8.19801 | − | 39.9345i | 0.320079 | − | 1.55918i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.72323 | − | 6.33407i | −0.223115 | − | 0.246928i | ||||
\(659\) | −28.1599 | + | 28.1599i | −1.09695 | + | 1.09695i | −0.102189 | + | 0.994765i | \(0.532585\pi\) |
−0.994765 | + | 0.102189i | \(0.967415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8805 | − | 24.8805i | −0.967741 | − | 0.967741i | 0.0317548 | − | 0.999496i | \(-0.489890\pi\) |
−0.999496 | + | 0.0317548i | \(0.989890\pi\) | |||||||
\(662\) | −11.6880 | − | 0.592133i | −0.454266 | − | 0.0230139i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.2279 | + | 2.78947i | 0.707379 | + | 0.108253i | ||||
\(665\) | − | 5.26192i | − | 0.204048i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3929 | + | 14.3929i | 0.557294 | + | 0.557294i | ||||
\(668\) | −25.6528 | − | 2.60591i | −0.992536 | − | 0.100826i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.92429 | + | 5.35296i | −0.228875 | + | 0.206803i | ||||
\(671\) | −37.4041 | −1.44397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.37152 | −0.168510 | −0.0842548 | − | 0.996444i | \(-0.526851\pi\) | ||||
−0.0842548 | + | 0.996444i | \(0.526851\pi\) | |||||||
\(674\) | −20.2752 | + | 18.3199i | −0.780970 | + | 0.705655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.8158 | − | 1.80981i | −0.685225 | − | 0.0696079i | ||||
\(677\) | 7.19018 | + | 7.19018i | 0.276341 | + | 0.276341i | 0.831646 | − | 0.555305i | \(-0.187399\pi\) |
−0.555305 | + | 0.831646i | \(0.687399\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.24209i | − | 0.0476671i | ||||||
\(680\) | −1.25746 | + | 8.21689i | −0.0482213 | + | 0.315103i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −45.5627 | − | 2.30828i | −1.74469 | − | 0.0883888i | ||||
\(683\) | −27.3182 | − | 27.3182i | −1.04530 | − | 1.04530i | −0.998924 | − | 0.0463792i | \(-0.985232\pi\) |
−0.0463792 | − | 0.998924i | \(-0.514768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.89445 | + | 4.89445i | −0.187007 | + | 0.187007i | ||||
\(686\) | −9.43857 | − | 10.4460i | −0.360366 | − | 0.398828i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.3743 | + | 23.3171i | 0.586139 | + | 0.888957i | ||||
\(689\) | 33.4791 | 1.27545 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7859 | − | 10.7859i | 0.410316 | − | 0.410316i | −0.471533 | − | 0.881849i | \(-0.656299\pi\) |
0.881849 | + | 0.471533i | \(0.156299\pi\) | |||||||
\(692\) | −21.6345 | − | 26.5269i | −0.822420 | − | 1.00840i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.8253 | − | 0.700412i | −0.524801 | − | 0.0265873i | ||||
\(695\) | 9.19795i | 0.348898i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 29.9530i | − | 1.13455i | ||||||
\(698\) | 1.34079 | − | 26.4655i | 0.0507495 | − | 1.00173i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.149579 | − | 1.47246i | 0.00565354 | − | 0.0556538i | ||||
\(701\) | 7.34496 | − | 7.34496i | 0.277415 | − | 0.277415i | −0.554661 | − | 0.832076i | \(-0.687152\pi\) |
0.832076 | + | 0.554661i | \(0.187152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.82026 | −0.181799 | ||||||||
\(704\) | −38.4487 | + | 20.0994i | −1.44909 | + | 0.757524i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.9579 | − | 20.7439i | 0.864033 | − | 0.780707i | ||||
\(707\) | −4.82612 | + | 4.82612i | −0.181505 | + | 0.181505i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8251 | + | 36.8251i | 1.38299 | + | 1.38299i | 0.839254 | + | 0.543740i | \(0.182992\pi\) |
0.543740 | + | 0.839254i | \(0.317008\pi\) | |||||||
\(710\) | 0.254265 | − | 5.01887i | 0.00954238 | − | 0.188355i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.98321 | − | 4.39500i | 0.224230 | − | 0.164709i | ||||
\(713\) | 32.4281i | 1.21444i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9677 | + | 17.9677i | 0.671955 | + | 0.671955i | ||||
\(716\) | 27.8080 | + | 34.0965i | 1.03923 | + | 1.27425i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.58738 | − | 7.29046i | −0.245839 | − | 0.272077i | ||||
\(719\) | −15.1515 | −0.565055 | −0.282527 | − | 0.959259i | \(-0.591173\pi\) | ||||
−0.282527 | + | 0.959259i | \(0.591173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.223795 | 0.00833456 | ||||||||
\(722\) | −29.9222 | − | 33.1158i | −1.11359 | − | 1.23244i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.2275 | − | 18.9436i | 0.863242 | − | 0.704032i | ||||
\(725\) | −2.64012 | − | 2.64012i | −0.0980517 | − | 0.0980517i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.4900i | 0.685756i | 0.939380 | + | 0.342878i | \(0.111402\pi\) | ||||
−0.939380 | + | 0.342878i | \(0.888598\pi\) | |||||||
\(728\) | −1.48355 | + | 9.69428i | −0.0549840 | + | 0.359294i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.798945 | + | 15.7702i | −0.0295703 | + | 0.583682i | ||||
\(731\) | 14.5103 | + | 14.5103i | 0.536684 | + | 0.536684i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.2992 | + | 10.2992i | −0.380409 | + | 0.380409i | −0.871250 | − | 0.490840i | \(-0.836690\pi\) |
0.490840 | + | 0.871250i | \(0.336690\pi\) | |||||||
\(734\) | 17.8854 | − | 16.1605i | 0.660161 | − | 0.596496i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.6514 | + | 26.5719i | 0.576917 | + | 0.979455i | ||||
\(737\) | −30.6184 | −1.12784 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4615 | − | 25.4615i | 0.936618 | − | 0.936618i | −0.0614897 | − | 0.998108i | \(-0.519585\pi\) |
0.998108 | + | 0.0614897i | \(0.0195851\pi\) | |||||||
\(740\) | −1.34887 | − | 0.137024i | −0.0495854 | − | 0.00503709i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.378355 | − | 7.46827i | 0.0138899 | − | 0.274169i | ||||
\(743\) | 46.0798i | 1.69050i | 0.534368 | + | 0.845252i | \(0.320550\pi\) | ||||
−0.534368 | + | 0.845252i | \(0.679450\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.13234i | 0.297946i | ||||||||
\(746\) | −28.7040 | − | 1.45419i | −1.05093 | − | 0.0532418i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −24.7028 | + | 20.1468i | −0.903224 | + | 0.736640i | ||||
\(749\) | 0.888598 | − | 0.888598i | 0.0324687 | − | 0.0324687i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.4699 | −0.600997 | −0.300498 | − | 0.953782i | \(-0.597153\pi\) | ||||
−0.300498 | + | 0.953782i | \(0.597153\pi\) | |||||||
\(752\) | −31.9617 | − | 6.56131i | −1.16552 | − | 0.239266i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.5866 | + | 18.3569i | 0.604049 | + | 0.668520i | ||||
\(755\) | −0.131367 | + | 0.131367i | −0.00478095 | + | 0.00478095i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.4819 | − | 21.4819i | −0.780772 | − | 0.780772i | 0.199189 | − | 0.979961i | \(-0.436169\pi\) |
−0.979961 | + | 0.199189i | \(0.936169\pi\) | |||||||
\(758\) | 5.94235 | + | 0.301050i | 0.215836 | + | 0.0109346i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.9061 | − | 16.2086i | −0.431881 | − | 0.587949i | ||||
\(761\) | − | 10.1316i | − | 0.367270i | −0.982994 | − | 0.183635i | \(-0.941214\pi\) | ||
0.982994 | − | 0.183635i | \(-0.0587865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.18008 | + | 5.18008i | 0.187531 | + | 0.187531i | ||||
\(764\) | −1.78770 | + | 17.5982i | −0.0646767 | + | 0.636681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.4911 | − | 19.4185i | 0.776504 | − | 0.701619i | ||||
\(767\) | −25.4256 | −0.918067 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2758 | 1.19996 | 0.599979 | − | 0.800016i | \(-0.295176\pi\) | ||||
0.599979 | + | 0.800016i | \(0.295176\pi\) | |||||||
\(770\) | 4.21117 | − | 3.80505i | 0.151760 | − | 0.137125i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.84423 | − | 27.9988i | 0.102366 | − | 1.00770i | ||||
\(773\) | −6.50648 | − | 6.50648i | −0.234022 | − | 0.234022i | 0.580347 | − | 0.814369i | \(-0.302917\pi\) |
−0.814369 | + | 0.580347i | \(0.802917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.94837i | − | 0.213672i | ||||||
\(776\) | −2.81048 | − | 3.82609i | −0.100890 | − | 0.137349i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.7102 | − | 1.20120i | −0.850052 | − | 0.0430651i | ||||
\(779\) | 51.2434 | + | 51.2434i | 1.83598 | + | 1.83598i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.6266 | − | 13.6266i | 0.487597 | − | 0.487597i | ||||
\(782\) | 15.1907 | + | 16.8120i | 0.543217 | + | 0.601195i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25.2823 | − | 5.19011i | −0.902938 | − | 0.185361i | ||||
\(785\) | −16.7891 | −0.599227 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.9368 | + | 25.9368i | −0.924547 | + | 0.924547i | −0.997347 | − | 0.0727995i | \(-0.976807\pi\) |
0.0727995 | + | 0.997347i | \(0.476807\pi\) | |||||||
\(788\) | −17.8689 | + | 14.5733i | −0.636554 | + | 0.519153i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.2223 | + | 0.771188i | 0.541586 | + | 0.0274376i | ||||
\(791\) | 11.2002i | 0.398234i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.3162i | 1.14758i | ||||||||
\(794\) | 1.93566 | − | 38.2075i | 0.0686938 | − | 1.35593i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.5770 | − | 2.29347i | −0.800222 | − | 0.0812898i | ||||
\(797\) | 1.54315 | − | 1.54315i | 0.0546611 | − | 0.0546611i | −0.679248 | − | 0.733909i | \(-0.737694\pi\) |
0.733909 | + | 0.679248i | \(0.237694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.9730 | −0.848105 | ||||||||
\(800\) | −2.87098 | − | 4.87417i | −0.101504 | − | 0.172328i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.8808 | − | 15.2529i | 0.596082 | − | 0.538597i | ||||
\(803\) | −42.8171 | + | 42.8171i | −1.51098 | + | 1.51098i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.85266 | − | 2.85266i | −0.100543 | − | 0.100543i | ||||
\(806\) | −1.99430 | + | 39.3651i | −0.0702462 | + | 1.38658i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.94616 | + | 25.7863i | −0.138825 | + | 0.907157i | ||||
\(809\) | − | 25.5155i | − | 0.897076i | −0.893764 | − | 0.448538i | \(-0.851945\pi\) | ||
0.893764 | − | 0.448538i | \(-0.148055\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.6605 | + | 10.6605i | 0.374342 | + | 0.374342i | 0.869056 | − | 0.494714i | \(-0.164727\pi\) |
−0.494714 | + | 0.869056i | \(0.664727\pi\) | |||||||
\(812\) | 4.28238 | − | 3.49257i | 0.150282 | − | 0.122565i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.48568 | − | 3.85770i | −0.122173 | − | 0.135212i | ||||
\(815\) | 16.0956 | 0.563805 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.6483 | −1.73697 | ||||||||
\(818\) | −22.2357 | − | 24.6089i | −0.777453 | − | 0.860431i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.8829 | + | 15.7963i | 0.449892 | + | 0.551630i | ||||
\(821\) | 34.9507 | + | 34.9507i | 1.21979 | + | 1.21979i | 0.967706 | + | 0.252081i | \(0.0811148\pi\) |
0.252081 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.6125i | 1.24137i | 0.784059 | + | 0.620686i | \(0.213146\pi\) | ||||
−0.784059 | + | 0.620686i | \(0.786854\pi\) | |||||||
\(824\) | 0.689370 | − | 0.506381i | 0.0240154 | − | 0.0176406i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.287341 | + | 5.67177i | −0.00999789 | + | 0.197346i | ||||
\(827\) | 15.2133 | + | 15.2133i | 0.529019 | + | 0.529019i | 0.920280 | − | 0.391261i | \(-0.127961\pi\) |
−0.391261 | + | 0.920280i | \(0.627961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.4188 | − | 24.4188i | 0.848101 | − | 0.848101i | −0.141795 | − | 0.989896i | \(-0.545287\pi\) |
0.989896 | + | 0.141795i | \(0.0452874\pi\) | |||||||
\(830\) | −6.84107 | + | 6.18134i | −0.237457 | + | 0.214557i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.3654 | + | 33.2187i | 0.602036 | + | 1.15165i | ||||
\(833\) | −18.9631 | −0.657032 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.11630 | − | 9.11630i | 0.315483 | − | 0.315483i | ||||
\(836\) | 7.79437 | − | 76.7282i | 0.269574 | − | 2.65370i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.43345 | − | 28.2946i | 0.0495178 | − | 0.977420i | ||||
\(839\) | − | 1.78206i | − | 0.0615236i | −0.999527 | − | 0.0307618i | \(-0.990207\pi\) | ||
0.999527 | − | 0.0307618i | \(-0.00979333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.0595i | 0.519293i | ||||||||
\(842\) | 42.5411 | + | 2.15520i | 1.46606 | + | 0.0742732i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 27.9615 | + | 34.2847i | 0.962474 | + | 1.18013i | ||||
\(845\) | 6.33127 | − | 6.33127i | 0.217802 | − | 0.217802i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6243 | 0.468138 | ||||||||
\(848\) | −15.7330 | − | 23.8611i | −0.540272 | − | 0.819394i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.78647 | − | 3.08387i | −0.0955750 | − | 0.105776i | ||||
\(851\) | −2.61323 | + | 2.61323i | −0.0895802 | + | 0.0895802i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.1759 | − | 20.1759i | −0.690809 | − | 0.690809i | 0.271601 | − | 0.962410i | \(-0.412447\pi\) |
−0.962410 | + | 0.271601i | \(0.912447\pi\) | |||||||
\(854\) | 7.20886 | + | 0.365213i | 0.246682 | + | 0.0124973i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.726577 | − | 4.74784i | 0.0248339 | − | 0.162278i | ||||
\(857\) | − | 40.0844i | − | 1.36926i | −0.728893 | − | 0.684628i | \(-0.759965\pi\) | ||
0.728893 | − | 0.684628i | \(-0.240035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.09121 | − | 3.09121i | −0.105471 | − | 0.105471i | 0.652402 | − | 0.757873i | \(-0.273761\pi\) |
−0.757873 | + | 0.652402i | \(0.773761\pi\) | |||||||
\(860\) | −13.8932 | − | 1.41133i | −0.473756 | − | 0.0481260i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.0511 | − | 19.9246i | 0.751064 | − | 0.678633i | ||||
\(863\) | −13.8844 | −0.472630 | −0.236315 | − | 0.971676i | \(-0.575940\pi\) | ||||
−0.236315 | + | 0.971676i | \(0.575940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.1153 | 0.581936 | ||||||||
\(866\) | 17.0255 | − | 15.3836i | 0.578549 | − | 0.522755i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.75874 | + | 0.889748i | 0.297291 | + | 0.0302000i | ||||
\(869\) | 41.3296 | + | 41.3296i | 1.40201 | + | 1.40201i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.4536i | 0.896345i | ||||||||
\(872\) | 27.6775 | + | 4.23558i | 0.937278 | + | 0.143435i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −54.7498 | − | 2.77372i | −1.85194 | − | 0.0938224i | ||||
\(875\) | 0.523272 | + | 0.523272i | 0.0176898 | + | 0.0176898i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3550 | + | 21.3550i | −0.721107 | + | 0.721107i | −0.968831 | − | 0.247724i | \(-0.920317\pi\) |
0.247724 | + | 0.968831i | \(0.420317\pi\) | |||||||
\(878\) | 3.16642 | + | 3.50437i | 0.106861 | + | 0.118267i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.36225 | − | 21.2496i | 0.147051 | − | 0.716322i | ||||
\(881\) | 25.1815 | 0.848387 | 0.424193 | − | 0.905572i | \(-0.360558\pi\) | ||||
0.424193 | + | 0.905572i | \(0.360558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.36865 | − | 4.36865i | 0.147017 | − | 0.147017i | −0.629767 | − | 0.776784i | \(-0.716850\pi\) |
0.776784 | + | 0.629767i | \(0.216850\pi\) | |||||||
\(884\) | 17.4063 | + | 21.3426i | 0.585438 | + | 0.717829i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.8997 | − | 1.36278i | −0.903713 | − | 0.0457836i | ||||
\(887\) | − | 36.7638i | − | 1.23441i | −0.786803 | − | 0.617204i | \(-0.788265\pi\) | ||
0.786803 | − | 0.617204i | \(-0.211735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.61982i | − | 0.222022i | ||||||
\(890\) | −0.187814 | + | 3.70721i | −0.00629552 | + | 0.124266i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.07733 | + | 20.4494i | −0.0695542 | + | 0.684696i | ||||
\(893\) | 41.0129 | − | 41.0129i | 1.37244 | − | 1.37244i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.9992 | −0.735351 | ||||||||
\(896\) | 7.60645 | − | 3.49833i | 0.254114 | − | 0.116871i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.2513 | + | 18.2983i | −0.675793 | + | 0.610622i | ||||
\(899\) | 15.7044 | − | 15.7044i | 0.523772 | − | 0.523772i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8489 | − | 14.8489i | −0.494687 | − | 0.494687i | ||||
\(902\) | −3.95497 | + | 78.0663i | −0.131686 | + | 2.59932i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.3427 | + | 34.5007i | 0.842886 | + | 1.14748i | ||||
\(905\) | 14.9864i | 0.498166i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5327 | − | 24.5327i | −0.814594 | − | 0.814594i | 0.170725 | − | 0.985319i | \(-0.445389\pi\) |
−0.985319 | + | 0.170725i | \(0.945389\pi\) | |||||||
\(908\) | −24.7271 | − | 30.3189i | −0.820596 | − | 1.00617i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.28747 | − | 3.63834i | −0.108979 | − | 0.120610i | ||||
\(911\) | 0.221626 | 0.00734279 | 0.00367139 | − | 0.999993i | \(-0.498831\pi\) | ||||
0.00367139 | + | 0.999993i | \(0.498831\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.3567 | −1.17014 | ||||||||
\(914\) | −19.9316 | − | 22.0589i | −0.659279 | − | 0.729644i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.7738 | + | 20.2047i | −0.818549 | + | 0.667582i | ||||
\(917\) | 7.13220 | + | 7.13220i | 0.235526 | + | 0.235526i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.8234i | − | 0.752874i | −0.926442 | − | 0.376437i | \(-0.877149\pi\) | ||
0.926442 | − | 0.376437i | \(-0.122851\pi\) | |||||||
\(920\) | −15.2420 | − | 2.33253i | −0.502513 | − | 0.0769012i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.35838 | − | 46.5516i | 0.0776692 | − | 1.53309i | ||||
\(923\) | −11.7730 | − | 11.7730i | −0.387513 | − | 0.387513i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.479352 | − | 0.479352i | 0.0157610 | − | 0.0157610i | ||||
\(926\) | −1.73333 | + | 1.56617i | −0.0569607 | + | 0.0514676i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.28866 | − | 20.4481i | 0.173609 | − | 0.671243i | ||||
\(929\) | −12.9959 | −0.426383 | −0.213191 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213191 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.4418 | − | 32.4418i | 1.06324 | − | 1.06324i | ||||
\(932\) | −1.27003 | − | 0.129015i | −0.0416013 | − | 0.00422603i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.46450 | − | 28.9075i | 0.0479201 | − | 0.945884i | ||||
\(935\) | − | 15.9383i | − | 0.521239i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7244i | 1.68976i | 0.534954 | + | 0.844881i | \(0.320329\pi\) | ||||
−0.534954 | + | 0.844881i | \(0.679671\pi\) | |||||||
\(938\) | 5.90107 | + | 0.298958i | 0.192677 | + | 0.00976133i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.6426 | − | 10.3109i | 0.412357 | − | 0.336305i | ||||
\(941\) | 11.9700 | − | 11.9700i | 0.390210 | − | 0.390210i | −0.484552 | − | 0.874762i | \(-0.661017\pi\) |
0.874762 | + | 0.484552i | \(0.161017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.5616 | 1.80933 | ||||||||
\(944\) | 11.9484 | + | 18.1213i | 0.388887 | + | 0.589798i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.9022 | − | 39.7340i | −1.16728 | − | 1.29186i | ||||
\(947\) | −3.97492 | + | 3.97492i | −0.129168 | + | 0.129168i | −0.768735 | − | 0.639567i | \(-0.779113\pi\) |
0.639567 | + | 0.768735i | \(0.279113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.9929 | + | 36.9929i | 1.20084 | + | 1.20084i | ||||
\(950\) | 10.0429 | + | 0.508791i | 0.325835 | + | 0.0165074i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.95767 | − | 3.64168i | 0.160679 | − | 0.118028i | ||||
\(953\) | − | 13.1913i | − | 0.427308i | −0.976909 | − | 0.213654i | \(-0.931463\pi\) | ||
0.976909 | − | 0.213654i | \(-0.0685365\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.25393 | − | 6.25393i | −0.202372 | − | 0.202372i | ||||
\(956\) | −5.50303 | + | 54.1721i | −0.177981 | + | 1.75205i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.37698 | + | 5.76200i | −0.206031 | + | 0.186162i | ||||
\(959\) | 5.12227 | 0.165407 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.38311 | 0.141391 | ||||||||
\(962\) | −3.33296 | + | 3.01154i | −0.107459 | + | 0.0970958i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.84638 | + | 28.0199i | −0.0916757 | + | 0.902461i | ||||
\(965\) | 9.95002 | + | 9.95002i | 0.320302 | + | 0.320302i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.07109i | − | 0.163075i | −0.996670 | − | 0.0815376i | \(-0.974017\pi\) | ||
0.996670 | − | 0.0815376i | \(-0.0259831\pi\) | |||||||
\(968\) | 41.9679 | − | 30.8278i | 1.34890 | − | 0.990842i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.37066 | + | 0.120102i | 0.0761173 | + | 0.00385623i | ||||
\(971\) | −2.07041 | − | 2.07041i | −0.0664427 | − | 0.0664427i | 0.673105 | − | 0.739547i | \(-0.264960\pi\) |
−0.739547 | + | 0.673105i | \(0.764960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.81304 | − | 4.81304i | 0.154299 | − | 0.154299i | ||||
\(974\) | 9.65787 | + | 10.6887i | 0.309458 | + | 0.342487i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23.0323 | − | 15.1865i | 0.737246 | − | 0.486108i | ||||
\(977\) | 6.93371 | 0.221829 | 0.110914 | − | 0.993830i | \(-0.464622\pi\) | ||||
0.110914 | + | 0.993830i | \(0.464622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.0653 | + | 10.0653i | −0.321689 | + | 0.321689i | ||||
\(980\) | 10.0005 | − | 8.15610i | 0.319455 | − | 0.260537i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.4783 | − | 0.885479i | −0.557754 | − | 0.0282568i | ||||
\(983\) | − | 49.6290i | − | 1.58292i | −0.611221 | − | 0.791460i | \(-0.709321\pi\) | ||
0.611221 | − | 0.791460i | \(-0.290679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 11.5291i | − | 0.367347i | ||||||
\(986\) | 0.785175 | − | 15.4984i | 0.0250051 | − | 0.493570i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −66.2913 | − | 6.73414i | −2.10901 | − | 0.214241i | ||||
\(989\) | −26.9160 | + | 26.9160i | −0.855880 | + | 0.855880i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.6664 | 1.51417 | 0.757086 | − | 0.653315i | \(-0.226622\pi\) | ||||
0.757086 | + | 0.653315i | \(0.226622\pi\) | |||||||
\(992\) | 28.9933 | − | 17.0776i | 0.920540 | − | 0.542215i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.75929 | + | 2.49319i | −0.0875193 | + | 0.0790791i | ||||
\(995\) | 8.02327 | − | 8.02327i | 0.254355 | − | 0.254355i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.46020 | + | 4.46020i | 0.141256 | + | 0.141256i | 0.774199 | − | 0.632943i | \(-0.218153\pi\) |
−0.632943 | + | 0.774199i | \(0.718153\pi\) | |||||||
\(998\) | −2.41104 | + | 47.5910i | −0.0763201 | + | 1.50647i | ||||
\(999\) | 0 | 0 |
(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 | 720.2.t.d.181.8 | 20 | ||
3.2 | odd | 2 | 240.2.s.c.181.3 | yes | 20 | ||
4.3 | odd | 2 | 2880.2.t.d.2161.8 | 20 | |||
12.11 | even | 2 | 960.2.s.c.241.8 | 20 | |||
16.3 | odd | 4 | 2880.2.t.d.721.8 | 20 | |||
16.13 | even | 4 | inner | 720.2.t.d.541.8 | 20 | ||
24.5 | odd | 2 | 1920.2.s.e.481.8 | 20 | |||
24.11 | even | 2 | 1920.2.s.f.481.3 | 20 | |||
48.5 | odd | 4 | 1920.2.s.e.1441.8 | 20 | |||
48.11 | even | 4 | 1920.2.s.f.1441.3 | 20 | |||
48.29 | odd | 4 | 240.2.s.c.61.3 | ✓ | 20 | ||
48.35 | even | 4 | 960.2.s.c.721.8 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.3 | ✓ | 20 | 48.29 | odd | 4 | ||
240.2.s.c.181.3 | yes | 20 | 3.2 | odd | 2 | ||
720.2.t.d.181.8 | 20 | 1.1 | even | 1 | trivial | ||
720.2.t.d.541.8 | 20 | 16.13 | even | 4 | inner | ||
960.2.s.c.241.8 | 20 | 12.11 | even | 2 | |||
960.2.s.c.721.8 | 20 | 48.35 | even | 4 | |||
1920.2.s.e.481.8 | 20 | 24.5 | odd | 2 | |||
1920.2.s.e.1441.8 | 20 | 48.5 | odd | 4 | |||
1920.2.s.f.481.3 | 20 | 24.11 | even | 2 | |||
1920.2.s.f.1441.3 | 20 | 48.11 | even | 4 | |||
2880.2.t.d.721.8 | 20 | 16.3 | odd | 4 | |||
2880.2.t.d.2161.8 | 20 | 4.3 | odd | 2 |