Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(107,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.q (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.293 |
Dual form | 950.2.q.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | −0.633975 | − | 2.36603i | −0.366025 | − | 1.36603i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.22474 | + | 2.12132i | 0.500000 | + | 0.866025i | ||||
\(7\) | 0.775255 | − | 0.775255i | 0.293019 | − | 0.293019i | −0.545253 | − | 0.838272i | \(-0.683566\pi\) |
0.838272 | + | 0.545253i | \(0.183566\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.59808 | + | 1.50000i | −0.866025 | + | 0.500000i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44949 | −0.437038 | −0.218519 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218519 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(12\) | −1.73205 | − | 1.73205i | −0.500000 | − | 0.500000i | ||||
\(13\) | 4.73205 | + | 1.26795i | 1.31243 | + | 0.351666i | 0.846139 | − | 0.532963i | \(-0.178921\pi\) |
0.466296 | + | 0.884629i | \(0.345588\pi\) | |||||||
\(14\) | −0.548188 | + | 0.949490i | −0.146509 | + | 0.253762i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −0.732051 | − | 2.73205i | −0.177548 | − | 0.662620i | −0.996104 | − | 0.0881917i | \(-0.971891\pi\) |
0.818555 | − | 0.574428i | \(-0.194775\pi\) | |||||||
\(18\) | 2.12132 | − | 2.12132i | 0.500000 | − | 0.500000i | ||||
\(19\) | 2.98735 | − | 3.17423i | 0.685344 | − | 0.728219i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.32577 | − | 1.34278i | −0.507524 | − | 0.293019i | ||||
\(22\) | 1.40010 | − | 0.375156i | 0.298502 | − | 0.0799834i | ||||
\(23\) | 1.34486 | − | 5.01910i | 0.280423 | − | 1.04655i | −0.671696 | − | 0.740827i | \(-0.734434\pi\) |
0.952119 | − | 0.305727i | \(-0.0988995\pi\) | |||||||
\(24\) | 2.12132 | + | 1.22474i | 0.433013 | + | 0.250000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.89898 | −0.960769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.283763 | − | 1.05902i | 0.0536262 | − | 0.200136i | ||||
\(29\) | −3.85337 | − | 6.67423i | −0.715553 | − | 1.23937i | −0.962746 | − | 0.270408i | \(-0.912841\pi\) |
0.247193 | − | 0.968966i | \(-0.420492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.778539i | − | 0.139830i | −0.997553 | − | 0.0699149i | \(-0.977727\pi\) | ||
0.997553 | − | 0.0699149i | \(-0.0222728\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 0.918940 | + | 3.42953i | 0.159967 | + | 0.597004i | ||||
\(34\) | 1.41421 | + | 2.44949i | 0.242536 | + | 0.420084i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.50000 | + | 2.59808i | −0.250000 | + | 0.433013i | ||||
\(37\) | 3.85337 | + | 3.85337i | 0.633490 | + | 0.633490i | 0.948942 | − | 0.315451i | \(-0.102156\pi\) |
−0.315451 | + | 0.948942i | \(0.602156\pi\) | |||||||
\(38\) | −2.06400 | + | 3.83926i | −0.334825 | + | 0.622810i | ||||
\(39\) | − | 12.0000i | − | 1.92154i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 0.866025i | −0.234261 | − | 0.135250i | 0.378275 | − | 0.925693i | \(-0.376517\pi\) |
−0.612536 | + | 0.790443i | \(0.709851\pi\) | |||||||
\(42\) | 2.59405 | + | 0.695075i | 0.400271 | + | 0.107252i | ||||
\(43\) | −10.1762 | + | 2.72670i | −1.55185 | + | 0.415818i | −0.930074 | − | 0.367373i | \(-0.880257\pi\) |
−0.621781 | + | 0.783191i | \(0.713591\pi\) | |||||||
\(44\) | −1.25529 | + | 0.724745i | −0.189243 | + | 0.109259i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.19615i | 0.766131i | ||||||||
\(47\) | 6.69213 | + | 1.79315i | 0.976148 | + | 0.261558i | 0.711421 | − | 0.702766i | \(-0.248052\pi\) |
0.264726 | + | 0.964324i | \(0.414718\pi\) | |||||||
\(48\) | −2.36603 | − | 0.633975i | −0.341506 | − | 0.0915064i | ||||
\(49\) | 5.79796i | 0.828280i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | + | 3.46410i | −0.840168 | + | 0.485071i | ||||
\(52\) | 4.73205 | − | 1.26795i | 0.656217 | − | 0.175833i | ||||
\(53\) | −4.20030 | − | 1.12547i | −0.576955 | − | 0.154595i | −0.0414708 | − | 0.999140i | \(-0.513204\pi\) |
−0.535485 | + | 0.844545i | \(0.679871\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.09638i | 0.146509i | ||||||||
\(57\) | −9.40422 | − | 5.05575i | −1.24562 | − | 0.669651i | ||||
\(58\) | 5.44949 | + | 5.44949i | 0.715553 | + | 0.715553i | ||||
\(59\) | −1.73205 | + | 3.00000i | −0.225494 | + | 0.390567i | −0.956467 | − | 0.291839i | \(-0.905733\pi\) |
0.730974 | + | 0.682406i | \(0.239066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | + | 6.92820i | 0.512148 | + | 0.887066i | 0.999901 | + | 0.0140840i | \(0.00448323\pi\) |
−0.487753 | + | 0.872982i | \(0.662183\pi\) | |||||||
\(62\) | 0.201501 | + | 0.752011i | 0.0255906 | + | 0.0955055i | ||||
\(63\) | −0.851289 | + | 3.17705i | −0.107252 | + | 0.400271i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.77526 | − | 3.07483i | −0.218519 | − | 0.378486i | ||||
\(67\) | 3.73980 | − | 13.9571i | 0.456890 | − | 1.70514i | −0.225583 | − | 0.974224i | \(-0.572429\pi\) |
0.682472 | − | 0.730911i | \(-0.260905\pi\) | |||||||
\(68\) | −2.00000 | − | 2.00000i | −0.242536 | − | 0.242536i | ||||
\(69\) | −12.7279 | −1.53226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 1.73205i | −0.356034 | − | 0.205557i | 0.311305 | − | 0.950310i | \(-0.399234\pi\) |
−0.667340 | + | 0.744753i | \(0.732567\pi\) | |||||||
\(72\) | 0.776457 | − | 2.89778i | 0.0915064 | − | 0.341506i | ||||
\(73\) | −8.81017 | + | 2.36068i | −1.03115 | + | 0.276296i | −0.734442 | − | 0.678671i | \(-0.762556\pi\) |
−0.296710 | + | 0.954968i | \(0.595889\pi\) | |||||||
\(74\) | −4.71940 | − | 2.72474i | −0.548619 | − | 0.316745i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | − | 4.24264i | 0.114708 | − | 0.486664i | ||||
\(77\) | −1.12372 | + | 1.12372i | −0.128060 | + | 0.128060i | ||||
\(78\) | 3.10583 | + | 11.5911i | 0.351666 | + | 1.31243i | ||||
\(79\) | 2.51059 | − | 4.34847i | 0.282463 | − | 0.489241i | −0.689527 | − | 0.724260i | \(-0.742182\pi\) |
0.971991 | + | 0.235019i | \(0.0755151\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 1.67303 | + | 0.448288i | 0.184756 | + | 0.0495051i | ||||
\(83\) | −12.3485 | − | 12.3485i | −1.35542 | − | 1.35542i | −0.879474 | − | 0.475946i | \(-0.842106\pi\) |
−0.475946 | − | 0.879474i | \(-0.657894\pi\) | |||||||
\(84\) | −2.68556 | −0.293019 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.12372 | − | 5.26758i | 0.983836 | − | 0.568018i | ||||
\(87\) | −13.3485 | + | 13.3485i | −1.43111 | + | 1.43111i | ||||
\(88\) | 1.02494 | − | 1.02494i | 0.109259 | − | 0.109259i | ||||
\(89\) | −6.84072 | − | 11.8485i | −0.725115 | − | 1.25594i | −0.958927 | − | 0.283653i | \(-0.908453\pi\) |
0.233812 | − | 0.972282i | \(-0.424880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.65153 | − | 2.68556i | 0.487613 | − | 0.281523i | ||||
\(92\) | −1.34486 | − | 5.01910i | −0.140212 | − | 0.523277i | ||||
\(93\) | −1.84204 | + | 0.493574i | −0.191011 | + | 0.0511812i | ||||
\(94\) | −6.92820 | −0.714590 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.44949 | 0.250000 | ||||||||
\(97\) | −13.9571 | + | 3.73980i | −1.41713 | + | 0.379719i | −0.884466 | − | 0.466606i | \(-0.845477\pi\) |
−0.532667 | + | 0.846325i | \(0.678810\pi\) | |||||||
\(98\) | −1.50062 | − | 5.60040i | −0.151586 | − | 0.565726i | ||||
\(99\) | 3.76588 | − | 2.17423i | 0.378486 | − | 0.218519i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.34847 | + | 10.9959i | 0.631696 | + | 1.09413i | 0.987205 | + | 0.159457i | \(0.0509744\pi\) |
−0.355509 | + | 0.934673i | \(0.615692\pi\) | |||||||
\(102\) | 4.89898 | − | 4.89898i | 0.485071 | − | 0.485071i | ||||
\(103\) | −1.34278 | + | 1.34278i | −0.132308 | + | 0.132308i | −0.770160 | − | 0.637851i | \(-0.779823\pi\) |
0.637851 | + | 0.770160i | \(0.279823\pi\) | |||||||
\(104\) | −4.24264 | + | 2.44949i | −0.416025 | + | 0.240192i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.34847 | 0.422361 | ||||||||
\(107\) | 8.66025 | + | 8.66025i | 0.837218 | + | 0.837218i | 0.988492 | − | 0.151274i | \(-0.0483374\pi\) |
−0.151274 | + | 0.988492i | \(0.548337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.67423 | − | 11.5601i | 0.633490 | − | 1.09724i | ||||
\(112\) | −0.283763 | − | 1.05902i | −0.0268131 | − | 0.100068i | ||||
\(113\) | 12.9029 | − | 12.9029i | 1.21380 | − | 1.21380i | 0.244036 | − | 0.969766i | \(-0.421528\pi\) |
0.969766 | − | 0.244036i | \(-0.0784715\pi\) | |||||||
\(114\) | 10.3923 | + | 2.44949i | 0.973329 | + | 0.229416i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.67423 | − | 3.85337i | −0.619687 | − | 0.357777i | ||||
\(117\) | −14.1962 | + | 3.80385i | −1.31243 | + | 0.351666i | ||||
\(118\) | 0.896575 | − | 3.34607i | 0.0825365 | − | 0.308030i | ||||
\(119\) | −2.68556 | − | 1.55051i | −0.246185 | − | 0.142135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.89898 | −0.808998 | ||||||||
\(122\) | −5.65685 | − | 5.65685i | −0.512148 | − | 0.512148i | ||||
\(123\) | −1.09808 | + | 4.09808i | −0.0990102 | + | 0.369511i | ||||
\(124\) | −0.389270 | − | 0.674235i | −0.0349574 | − | 0.0605481i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 3.28913i | − | 0.293019i | ||||||
\(127\) | 3.59732 | − | 13.4254i | 0.319211 | − | 1.19131i | −0.600794 | − | 0.799404i | \(-0.705149\pi\) |
0.920005 | − | 0.391907i | \(-0.128184\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 12.9029 | + | 22.3485i | 1.13604 | + | 1.96767i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.62372 | + | 6.27647i | −0.316606 | + | 0.548378i | −0.979778 | − | 0.200089i | \(-0.935877\pi\) |
0.663171 | + | 0.748468i | \(0.269210\pi\) | |||||||
\(132\) | 2.51059 | + | 2.51059i | 0.218519 | + | 0.218519i | ||||
\(133\) | −0.144887 | − | 4.77680i | −0.0125633 | − | 0.414201i | ||||
\(134\) | 14.4495i | 1.24825i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.44949 | + | 1.41421i | 0.210042 | + | 0.121268i | ||||
\(137\) | 2.73205 | + | 0.732051i | 0.233415 | + | 0.0625433i | 0.373630 | − | 0.927578i | \(-0.378113\pi\) |
−0.140215 | + | 0.990121i | \(0.544780\pi\) | |||||||
\(138\) | 12.2942 | − | 3.29423i | 1.04655 | − | 0.280423i | ||||
\(139\) | 14.6349 | − | 8.44949i | 1.24132 | − | 0.716676i | 0.271957 | − | 0.962309i | \(-0.412329\pi\) |
0.969363 | + | 0.245633i | \(0.0789958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 16.9706i | − | 1.42918i | ||||||
\(142\) | 3.34607 | + | 0.896575i | 0.280796 | + | 0.0752389i | ||||
\(143\) | −6.85906 | − | 1.83788i | −0.573583 | − | 0.153691i | ||||
\(144\) | 3.00000i | 0.250000i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.89898 | − | 4.56048i | 0.653724 | − | 0.377428i | ||||
\(147\) | 13.7181 | − | 3.67576i | 1.13145 | − | 0.303171i | ||||
\(148\) | 5.26380 | + | 1.41043i | 0.432682 | + | 0.115937i | ||||
\(149\) | 5.58542 | + | 3.22474i | 0.457576 | + | 0.264181i | 0.711024 | − | 0.703167i | \(-0.248232\pi\) |
−0.253449 | + | 0.967349i | \(0.581565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.48528i | − | 0.690522i | −0.938507 | − | 0.345261i | \(-0.887790\pi\) | ||
0.938507 | − | 0.345261i | \(-0.112210\pi\) | |||||||
\(152\) | 0.132150 | + | 4.35690i | 0.0107188 | + | 0.353391i | ||||
\(153\) | 6.00000 | + | 6.00000i | 0.485071 | + | 0.485071i | ||||
\(154\) | 0.794593 | − | 1.37628i | 0.0640301 | − | 0.110903i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.00000 | − | 10.3923i | −0.480384 | − | 0.832050i | ||||
\(157\) | 1.71089 | + | 6.38512i | 0.136544 | + | 0.509588i | 0.999987 | + | 0.00514190i | \(0.00163673\pi\) |
−0.863443 | + | 0.504446i | \(0.831697\pi\) | |||||||
\(158\) | −1.29958 | + | 4.85009i | −0.103389 | + | 0.385852i | ||||
\(159\) | 10.6515i | 0.844721i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.84847 | − | 4.93369i | −0.224491 | − | 0.388830i | ||||
\(162\) | 2.32937 | − | 8.69333i | 0.183013 | − | 0.683013i | ||||
\(163\) | 9.34847 | + | 9.34847i | 0.732229 | + | 0.732229i | 0.971061 | − | 0.238832i | \(-0.0767646\pi\) |
−0.238832 | + | 0.971061i | \(0.576765\pi\) | |||||||
\(164\) | −1.73205 | −0.135250 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.1237 | + | 8.73169i | 1.17383 | + | 0.677710i | ||||
\(167\) | 1.47448 | − | 5.50282i | 0.114098 | − | 0.425821i | −0.885119 | − | 0.465364i | \(-0.845923\pi\) |
0.999218 | + | 0.0395428i | \(0.0125902\pi\) | |||||||
\(168\) | 2.59405 | − | 0.695075i | 0.200136 | − | 0.0536262i | ||||
\(169\) | 9.52628 | + | 5.50000i | 0.732791 | + | 0.423077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 12.7279i | −0.229416 | + | 0.973329i | ||||
\(172\) | −7.44949 | + | 7.44949i | −0.568018 | + | 0.568018i | ||||
\(173\) | 0.142483 | + | 0.531752i | 0.0108327 | + | 0.0404284i | 0.971131 | − | 0.238548i | \(-0.0766715\pi\) |
−0.960298 | + | 0.278977i | \(0.910005\pi\) | |||||||
\(174\) | 9.43879 | − | 16.3485i | 0.715553 | − | 1.23937i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.724745 | + | 1.25529i | −0.0546297 | + | 0.0946214i | ||||
\(177\) | 8.19615 | + | 2.19615i | 0.616061 | + | 0.165073i | ||||
\(178\) | 9.67423 | + | 9.67423i | 0.725115 | + | 0.725115i | ||||
\(179\) | 2.51059 | 0.187650 | 0.0938251 | − | 0.995589i | \(-0.470091\pi\) | ||||
0.0938251 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6742 | − | 10.7816i | 1.38804 | − | 0.801388i | 0.394950 | − | 0.918703i | \(-0.370762\pi\) |
0.993095 | + | 0.117314i | \(0.0374285\pi\) | |||||||
\(182\) | −3.79796 | + | 3.79796i | −0.281523 | + | 0.281523i | ||||
\(183\) | 13.8564 | − | 13.8564i | 1.02430 | − | 1.02430i | ||||
\(184\) | 2.59808 | + | 4.50000i | 0.191533 | + | 0.331744i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.65153 | − | 0.953512i | 0.121096 | − | 0.0699149i | ||||
\(187\) | 1.06110 | + | 3.96008i | 0.0775953 | + | 0.289590i | ||||
\(188\) | 6.69213 | − | 1.79315i | 0.488074 | − | 0.130779i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2474 | −1.17562 | −0.587812 | − | 0.808998i | \(-0.700011\pi\) | ||||
−0.587812 | + | 0.808998i | \(0.700011\pi\) | |||||||
\(192\) | −2.36603 | + | 0.633975i | −0.170753 | + | 0.0457532i | ||||
\(193\) | 3.45484 | + | 12.8936i | 0.248685 | + | 0.928104i | 0.971496 | + | 0.237058i | \(0.0761831\pi\) |
−0.722811 | + | 0.691046i | \(0.757150\pi\) | |||||||
\(194\) | 12.5136 | − | 7.22474i | 0.898426 | − | 0.518706i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.89898 | + | 5.02118i | 0.207070 | + | 0.358656i | ||||
\(197\) | −5.32577 | + | 5.32577i | −0.379445 | + | 0.379445i | −0.870902 | − | 0.491457i | \(-0.836465\pi\) |
0.491457 | + | 0.870902i | \(0.336465\pi\) | |||||||
\(198\) | −3.07483 | + | 3.07483i | −0.218519 | + | 0.218519i | ||||
\(199\) | −8.48528 | + | 4.89898i | −0.601506 | + | 0.347279i | −0.769634 | − | 0.638486i | \(-0.779561\pi\) |
0.168128 | + | 0.985765i | \(0.446228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −35.3939 | −2.49649 | ||||||||
\(202\) | −8.97809 | − | 8.97809i | −0.631696 | − | 0.631696i | ||||
\(203\) | −8.16158 | − | 2.18689i | −0.572831 | − | 0.153490i | ||||
\(204\) | −3.46410 | + | 6.00000i | −0.242536 | + | 0.420084i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.949490 | − | 1.64456i | 0.0661541 | − | 0.114582i | ||||
\(207\) | 4.03459 | + | 15.0573i | 0.280423 | + | 1.04655i | ||||
\(208\) | 3.46410 | − | 3.46410i | 0.240192 | − | 0.240192i | ||||
\(209\) | −4.33013 | + | 4.60102i | −0.299521 | + | 0.318259i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8258 | + | 9.13701i | 1.08949 | + | 0.629018i | 0.933441 | − | 0.358731i | \(-0.116791\pi\) |
0.156050 | + | 0.987749i | \(0.450124\pi\) | |||||||
\(212\) | −4.20030 | + | 1.12547i | −0.288478 | + | 0.0772974i | ||||
\(213\) | −2.19615 | + | 8.19615i | −0.150478 | + | 0.561591i | ||||
\(214\) | −10.6066 | − | 6.12372i | −0.725052 | − | 0.418609i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.603566 | − | 0.603566i | −0.0409728 | − | 0.0409728i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1708 | + | 19.3485i | 0.754856 | + | 1.30745i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.8564i | − | 0.932083i | ||||||
\(222\) | −3.45484 | + | 12.8936i | −0.231874 | + | 0.865364i | ||||
\(223\) | −3.02739 | − | 11.2984i | −0.202729 | − | 0.756595i | −0.990130 | − | 0.140154i | \(-0.955240\pi\) |
0.787401 | − | 0.616442i | \(-0.211426\pi\) | |||||||
\(224\) | 0.548188 | + | 0.949490i | 0.0366274 | + | 0.0634405i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.12372 | + | 15.8028i | −0.606901 | + | 1.05118i | ||||
\(227\) | 10.9959 | + | 10.9959i | 0.729822 | + | 0.729822i | 0.970584 | − | 0.240762i | \(-0.0773975\pi\) |
−0.240762 | + | 0.970584i | \(0.577397\pi\) | |||||||
\(228\) | −10.6722 | + | 0.323701i | −0.706782 | + | 0.0214376i | ||||
\(229\) | − | 15.5505i | − | 1.02761i | −0.857908 | − | 0.513803i | \(-0.828236\pi\) | ||
0.857908 | − | 0.513803i | \(-0.171764\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.37117 | + | 1.94635i | 0.221807 | + | 0.128060i | ||||
\(232\) | 7.44414 | + | 1.99465i | 0.488732 | + | 0.130955i | ||||
\(233\) | −3.34607 | + | 0.896575i | −0.219208 | + | 0.0587366i | −0.366751 | − | 0.930319i | \(-0.619530\pi\) |
0.147543 | + | 0.989056i | \(0.452863\pi\) | |||||||
\(234\) | 12.7279 | − | 7.34847i | 0.832050 | − | 0.480384i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.46410i | 0.225494i | ||||||||
\(237\) | −11.8802 | − | 3.18330i | −0.771704 | − | 0.206778i | ||||
\(238\) | 2.99536 | + | 0.802603i | 0.194160 | + | 0.0520250i | ||||
\(239\) | − | 13.7980i | − | 0.892516i | −0.894904 | − | 0.446258i | \(-0.852756\pi\) | ||
0.894904 | − | 0.446258i | \(-0.147244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.6969 | − | 13.6814i | 1.52645 | − | 0.881299i | 0.526947 | − | 0.849898i | \(-0.323337\pi\) |
0.999507 | − | 0.0314005i | \(-0.00999675\pi\) | |||||||
\(242\) | 8.59575 | − | 2.30323i | 0.552556 | − | 0.148057i | ||||
\(243\) | 21.2942 | + | 5.70577i | 1.36603 | + | 0.366025i | ||||
\(244\) | 6.92820 | + | 4.00000i | 0.443533 | + | 0.256074i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 4.24264i | − | 0.270501i | ||||||
\(247\) | 18.1610 | − | 11.2328i | 1.15556 | − | 0.714728i | ||||
\(248\) | 0.550510 | + | 0.550510i | 0.0349574 | + | 0.0349574i | ||||
\(249\) | −21.3882 | + | 37.0454i | −1.35542 | + | 2.34766i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.449490 | + | 0.778539i | 0.0283715 | + | 0.0491410i | 0.879863 | − | 0.475228i | \(-0.157635\pi\) |
−0.851491 | + | 0.524369i | \(0.824301\pi\) | |||||||
\(252\) | 0.851289 | + | 3.17705i | 0.0536262 | + | 0.200136i | ||||
\(253\) | −1.94937 | + | 7.27513i | −0.122556 | + | 0.457384i | ||||
\(254\) | 13.8990i | 0.872100i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 2.47185 | − | 9.22508i | 0.154190 | − | 0.575445i | −0.844983 | − | 0.534793i | \(-0.820390\pi\) |
0.999173 | − | 0.0406523i | \(-0.0129436\pi\) | |||||||
\(258\) | −18.2474 | − | 18.2474i | −1.13604 | − | 1.13604i | ||||
\(259\) | 5.97469 | 0.371249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0227 | + | 11.5601i | 1.23937 | + | 0.715553i | ||||
\(262\) | 1.87578 | − | 7.00050i | 0.115886 | − | 0.432492i | ||||
\(263\) | 22.3634 | − | 5.99227i | 1.37899 | − | 0.369499i | 0.508235 | − | 0.861218i | \(-0.330298\pi\) |
0.870754 | + | 0.491720i | \(0.163631\pi\) | |||||||
\(264\) | −3.07483 | − | 1.77526i | −0.189243 | − | 0.109259i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.37628 | + | 4.57653i | 0.0843849 | + | 0.280605i | ||||
\(267\) | −23.6969 | + | 23.6969i | −1.45023 | + | 1.45023i | ||||
\(268\) | −3.73980 | − | 13.9571i | −0.228445 | − | 0.852568i | ||||
\(269\) | −3.46410 | + | 6.00000i | −0.211210 | + | 0.365826i | −0.952093 | − | 0.305807i | \(-0.901074\pi\) |
0.740883 | + | 0.671634i | \(0.234407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65153 | + | 2.86054i | −0.100323 | + | 0.173765i | −0.911818 | − | 0.410595i | \(-0.865321\pi\) |
0.811495 | + | 0.584360i | \(0.198654\pi\) | |||||||
\(272\) | −2.73205 | − | 0.732051i | −0.165655 | − | 0.0443871i | ||||
\(273\) | −9.30306 | − | 9.30306i | −0.563047 | − | 0.563047i | ||||
\(274\) | −2.82843 | −0.170872 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −11.0227 | + | 6.36396i | −0.663489 | + | 0.383065i | ||||
\(277\) | −13.7980 | + | 13.7980i | −0.829039 | + | 0.829039i | −0.987384 | − | 0.158345i | \(-0.949384\pi\) |
0.158345 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(278\) | −11.9494 | + | 11.9494i | −0.716676 | + | 0.716676i | ||||
\(279\) | 1.16781 | + | 2.02270i | 0.0699149 | + | 0.121096i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5000 | + | 6.06218i | −0.626377 | + | 0.361639i | −0.779348 | − | 0.626592i | \(-0.784449\pi\) |
0.152970 | + | 0.988231i | \(0.451116\pi\) | |||||||
\(282\) | 4.39230 | + | 16.3923i | 0.261558 | + | 0.976148i | ||||
\(283\) | 0.614014 | − | 0.164525i | 0.0364994 | − | 0.00977998i | −0.240523 | − | 0.970643i | \(-0.577319\pi\) |
0.277023 | + | 0.960863i | \(0.410652\pi\) | |||||||
\(284\) | −3.46410 | −0.205557 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.10102 | 0.419892 | ||||||||
\(287\) | −1.83427 | + | 0.491492i | −0.108274 | + | 0.0290119i | ||||
\(288\) | −0.776457 | − | 2.89778i | −0.0457532 | − | 0.170753i | ||||
\(289\) | 7.79423 | − | 4.50000i | 0.458484 | − | 0.264706i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.6969 | + | 30.6520i | 1.03741 | + | 1.79685i | ||||
\(292\) | −6.44949 | + | 6.44949i | −0.377428 | + | 0.377428i | ||||
\(293\) | −19.2669 | + | 19.2669i | −1.12558 | + | 1.12558i | −0.134695 | + | 0.990887i | \(0.543005\pi\) |
−0.990887 | + | 0.134695i | \(0.956995\pi\) | |||||||
\(294\) | −12.2993 | + | 7.10102i | −0.717311 | + | 0.414140i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.44949 | −0.316745 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.22973 | − | 1.66925i | −0.360878 | − | 0.0966971i | ||||
\(299\) | 12.7279 | − | 22.0454i | 0.736075 | − | 1.27492i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.77526 | + | 10.0030i | −0.332880 | + | 0.576565i | ||||
\(302\) | 2.19615 | + | 8.19615i | 0.126374 | + | 0.471636i | ||||
\(303\) | 21.9917 | − | 21.9917i | 1.26339 | − | 1.26339i | ||||
\(304\) | −1.25529 | − | 4.17423i | −0.0719961 | − | 0.239409i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.34847 | − | 4.24264i | −0.420084 | − | 0.242536i | ||||
\(307\) | 12.8936 | − | 3.45484i | 0.735878 | − | 0.197178i | 0.128633 | − | 0.991692i | \(-0.458941\pi\) |
0.607245 | + | 0.794514i | \(0.292274\pi\) | |||||||
\(308\) | −0.411312 | + | 1.53504i | −0.0234367 | + | 0.0874668i | ||||
\(309\) | 4.02834 | + | 2.32577i | 0.229164 | + | 0.132308i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.7980 | 1.46287 | 0.731434 | − | 0.681912i | \(-0.238851\pi\) | ||||
0.731434 | + | 0.681912i | \(0.238851\pi\) | |||||||
\(312\) | 8.48528 | + | 8.48528i | 0.480384 | + | 0.480384i | ||||
\(313\) | −7.70315 | + | 28.7486i | −0.435408 | + | 1.62496i | 0.304680 | + | 0.952455i | \(0.401450\pi\) |
−0.740088 | + | 0.672510i | \(0.765216\pi\) | |||||||
\(314\) | −3.30518 | − | 5.72474i | −0.186522 | − | 0.323066i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 5.02118i | − | 0.282463i | ||||||
\(317\) | −3.94633 | + | 14.7279i | −0.221648 | + | 0.827202i | 0.762072 | + | 0.647492i | \(0.224182\pi\) |
−0.983720 | + | 0.179709i | \(0.942484\pi\) | |||||||
\(318\) | −2.75682 | − | 10.2886i | −0.154595 | − | 0.576955i | ||||
\(319\) | 5.58542 | + | 9.67423i | 0.312724 | + | 0.541653i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0000 | − | 25.9808i | 0.837218 | − | 1.45010i | ||||
\(322\) | 4.02834 | + | 4.02834i | 0.224491 | + | 0.224491i | ||||
\(323\) | −10.8591 | − | 5.83788i | −0.604214 | − | 0.324828i | ||||
\(324\) | 9.00000i | 0.500000i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.4495 | − | 6.61037i | −0.634129 | − | 0.366114i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.67303 | − | 0.448288i | 0.0923778 | − | 0.0247525i | ||||
\(329\) | 6.57826 | − | 3.79796i | 0.362671 | − | 0.209388i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.06767i | 0.223579i | 0.993732 | + | 0.111790i | \(0.0356583\pi\) | ||||
−0.993732 | + | 0.111790i | \(0.964342\pi\) | |||||||
\(332\) | −16.8683 | − | 4.51985i | −0.925769 | − | 0.248059i | ||||
\(333\) | −15.7914 | − | 4.23130i | −0.865364 | − | 0.231874i | ||||
\(334\) | 5.69694i | 0.311723i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.32577 | + | 1.34278i | −0.126881 | + | 0.0732547i | ||||
\(337\) | 17.3867 | − | 4.65874i | 0.947112 | − | 0.253778i | 0.247976 | − | 0.968766i | \(-0.420235\pi\) |
0.699136 | + | 0.714988i | \(0.253568\pi\) | |||||||
\(338\) | −10.6252 | − | 2.84701i | −0.577934 | − | 0.154857i | ||||
\(339\) | −38.7087 | − | 22.3485i | −2.10237 | − | 1.21380i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12848i | 0.0611109i | ||||||||
\(342\) | −0.396451 | − | 13.0707i | −0.0214376 | − | 0.706782i | ||||
\(343\) | 9.92168 | + | 9.92168i | 0.535721 | + | 0.535721i | ||||
\(344\) | 5.26758 | − | 9.12372i | 0.284009 | − | 0.491918i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.275255 | − | 0.476756i | −0.0147978 | − | 0.0256306i | ||||
\(347\) | −2.43463 | − | 9.08616i | −0.130698 | − | 0.487771i | 0.869281 | − | 0.494319i | \(-0.164582\pi\) |
−0.999979 | + | 0.00654796i | \(0.997916\pi\) | |||||||
\(348\) | −4.88588 | + | 18.2343i | −0.261911 | + | 0.977464i | ||||
\(349\) | − | 19.1010i | − | 1.02245i | −0.859446 | − | 0.511227i | \(-0.829191\pi\) | ||
0.859446 | − | 0.511227i | \(-0.170809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.375156 | − | 1.40010i | 0.0199959 | − | 0.0746256i | ||||
\(353\) | 1.65153 | + | 1.65153i | 0.0879021 | + | 0.0879021i | 0.749691 | − | 0.661788i | \(-0.230202\pi\) |
−0.661788 | + | 0.749691i | \(0.730202\pi\) | |||||||
\(354\) | −8.48528 | −0.450988 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.8485 | − | 6.84072i | −0.627968 | − | 0.362557i | ||||
\(357\) | −1.96597 | + | 7.33709i | −0.104050 | + | 0.388320i | ||||
\(358\) | −2.42504 | + | 0.649788i | −0.128168 | + | 0.0343424i | ||||
\(359\) | 20.6096 | + | 11.8990i | 1.08774 | + | 0.628004i | 0.932973 | − | 0.359948i | \(-0.117205\pi\) |
0.154763 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.15153 | − | 18.9651i | −0.0606069 | − | 0.998162i | ||||
\(362\) | −15.2474 | + | 15.2474i | −0.801388 | + | 0.801388i | ||||
\(363\) | 5.64173 | + | 21.0552i | 0.296114 | + | 1.10511i | ||||
\(364\) | 2.68556 | − | 4.65153i | 0.140762 | − | 0.243806i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.79796 | + | 16.9706i | −0.512148 | + | 0.887066i | ||||
\(367\) | 14.6123 | + | 3.91535i | 0.762755 | + | 0.204380i | 0.619169 | − | 0.785258i | \(-0.287470\pi\) |
0.143587 | + | 0.989638i | \(0.454136\pi\) | |||||||
\(368\) | −3.67423 | − | 3.67423i | −0.191533 | − | 0.191533i | ||||
\(369\) | 5.19615 | 0.270501 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.12883 | + | 2.38378i | −0.214358 | + | 0.123760i | ||||
\(372\) | −1.34847 | + | 1.34847i | −0.0699149 | + | 0.0699149i | ||||
\(373\) | 25.4165 | − | 25.4165i | 1.31602 | − | 1.31602i | 0.399118 | − | 0.916900i | \(-0.369316\pi\) |
0.916900 | − | 0.399118i | \(-0.130684\pi\) | |||||||
\(374\) | −2.04989 | − | 3.55051i | −0.105997 | − | 0.183593i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | −9.77176 | − | 36.4687i | −0.503271 | − | 1.87823i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.9199 | −1.48552 | −0.742759 | − | 0.669559i | \(-0.766483\pi\) | ||||
−0.742759 | + | 0.669559i | \(0.766483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.0454 | −1.74420 | ||||||||
\(382\) | 15.6938 | − | 4.20515i | 0.802966 | − | 0.215154i | ||||
\(383\) | −2.53590 | − | 9.46410i | −0.129578 | − | 0.483593i | 0.870383 | − | 0.492375i | \(-0.163871\pi\) |
−0.999961 | + | 0.00878215i | \(0.997205\pi\) | |||||||
\(384\) | 2.12132 | − | 1.22474i | 0.108253 | − | 0.0625000i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.67423 | − | 11.5601i | −0.339710 | − | 0.588394i | ||||
\(387\) | 22.3485 | − | 22.3485i | 1.13604 | − | 1.13604i | ||||
\(388\) | −10.2173 | + | 10.2173i | −0.518706 | + | 0.518706i | ||||
\(389\) | −2.51059 | + | 1.44949i | −0.127292 | + | 0.0734920i | −0.562294 | − | 0.826937i | \(-0.690081\pi\) |
0.435002 | + | 0.900430i | \(0.356748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6969 | −0.743256 | ||||||||
\(392\) | −4.09978 | − | 4.09978i | −0.207070 | − | 0.207070i | ||||
\(393\) | 17.1476 | + | 4.59470i | 0.864984 | + | 0.231772i | ||||
\(394\) | 3.76588 | − | 6.52270i | 0.189723 | − | 0.328609i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.17423 | − | 3.76588i | 0.109259 | − | 0.189243i | ||||
\(397\) | −2.11389 | − | 7.88915i | −0.106093 | − | 0.395945i | 0.892374 | − | 0.451297i | \(-0.149039\pi\) |
−0.998467 | + | 0.0553522i | \(0.982372\pi\) | |||||||
\(398\) | 6.92820 | − | 6.92820i | 0.347279 | − | 0.347279i | ||||
\(399\) | −11.2102 | + | 3.37117i | −0.561210 | + | 0.168770i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | − | 8.66025i | −0.749064 | − | 0.432472i | 0.0762914 | − | 0.997086i | \(-0.475692\pi\) |
−0.825356 | + | 0.564613i | \(0.809025\pi\) | |||||||
\(402\) | 34.1879 | − | 9.16061i | 1.70514 | − | 0.456890i | ||||
\(403\) | 0.987148 | − | 3.68409i | 0.0491733 | − | 0.183517i | ||||
\(404\) | 10.9959 | + | 6.34847i | 0.547065 | + | 0.315848i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.44949 | 0.419341 | ||||||||
\(407\) | −5.58542 | − | 5.58542i | −0.276859 | − | 0.276859i | ||||
\(408\) | 1.79315 | − | 6.69213i | 0.0887742 | − | 0.331310i | ||||
\(409\) | −7.79423 | − | 13.5000i | −0.385400 | − | 0.667532i | 0.606425 | − | 0.795141i | \(-0.292603\pi\) |
−0.991825 | + | 0.127609i | \(0.959270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.92820i | − | 0.341743i | ||||||
\(412\) | −0.491492 | + | 1.83427i | −0.0242141 | + | 0.0903682i | ||||
\(413\) | 0.982984 | + | 3.66855i | 0.0483695 | + | 0.180517i | ||||
\(414\) | −7.79423 | − | 13.5000i | −0.383065 | − | 0.663489i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.44949 | + | 4.24264i | −0.120096 | + | 0.208013i | ||||
\(417\) | −29.2699 | − | 29.2699i | −1.43335 | − | 1.43335i | ||||
\(418\) | 2.99175 | − | 5.56496i | 0.146331 | − | 0.272191i | ||||
\(419\) | 8.34847i | 0.407849i | 0.978987 | + | 0.203925i | \(0.0653698\pi\) | ||||
−0.978987 | + | 0.203925i | \(0.934630\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.32577 | + | 4.80688i | 0.405773 | + | 0.234273i | 0.688972 | − | 0.724788i | \(-0.258062\pi\) |
−0.283199 | + | 0.959061i | \(0.591396\pi\) | |||||||
\(422\) | −17.6513 | − | 4.72966i | −0.859254 | − | 0.230236i | ||||
\(423\) | −20.0764 | + | 5.37945i | −0.976148 | + | 0.261558i | ||||
\(424\) | 3.76588 | − | 2.17423i | 0.182888 | − | 0.105590i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 8.48528i | − | 0.411113i | ||||||
\(427\) | 8.47215 | + | 2.27010i | 0.409996 | + | 0.109858i | ||||
\(428\) | 11.8301 | + | 3.16987i | 0.571831 | + | 0.153222i | ||||
\(429\) | 17.3939i | 0.839784i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.0227 | − | 11.5601i | 0.964460 | − | 0.556831i | 0.0669170 | − | 0.997759i | \(-0.478684\pi\) |
0.897543 | + | 0.440927i | \(0.145350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6892 | + | 5.00775i | 0.898145 | + | 0.240657i | 0.678219 | − | 0.734859i | \(-0.262752\pi\) |
0.219926 | + | 0.975517i | \(0.429419\pi\) | |||||||
\(434\) | 0.739215 | + | 0.426786i | 0.0354834 | + | 0.0204864i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.9142 | − | 19.2627i | −0.569935 | − | 0.921460i | ||||
\(438\) | −15.7980 | − | 15.7980i | −0.754856 | − | 0.754856i | ||||
\(439\) | 5.41045 | − | 9.37117i | 0.258227 | − | 0.447262i | −0.707540 | − | 0.706673i | \(-0.750195\pi\) |
0.965767 | + | 0.259411i | \(0.0835285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.69694 | − | 15.0635i | −0.414140 | − | 0.717311i | ||||
\(442\) | 3.58630 | + | 13.3843i | 0.170583 | + | 0.636624i | ||||
\(443\) | 0.806003 | − | 3.00804i | 0.0382944 | − | 0.142916i | −0.944132 | − | 0.329568i | \(-0.893097\pi\) |
0.982426 | + | 0.186652i | \(0.0597635\pi\) | |||||||
\(444\) | − | 13.3485i | − | 0.633490i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.84847 | + | 10.1298i | 0.276933 | + | 0.479662i | ||||
\(447\) | 4.08881 | − | 15.2597i | 0.193394 | − | 0.721757i | ||||
\(448\) | −0.775255 | − | 0.775255i | −0.0366274 | − | 0.0366274i | ||||
\(449\) | 8.66025 | 0.408703 | 0.204351 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204351 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17423 | + | 1.25529i | 0.102381 | + | 0.0591095i | ||||
\(452\) | 4.72279 | − | 17.6257i | 0.222141 | − | 0.829042i | ||||
\(453\) | −20.0764 | + | 5.37945i | −0.943271 | + | 0.252749i | ||||
\(454\) | −13.4671 | − | 7.77526i | −0.632044 | − | 0.364911i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.2247 | − | 3.07483i | 0.478818 | − | 0.143992i | ||||
\(457\) | 19.2474 | − | 19.2474i | 0.900358 | − | 0.900358i | −0.0951092 | − | 0.995467i | \(-0.530320\pi\) |
0.995467 | + | 0.0951092i | \(0.0303200\pi\) | |||||||
\(458\) | 4.02477 | + | 15.0206i | 0.188065 | + | 0.701868i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.10102 | − | 14.0314i | 0.377302 | − | 0.653506i | −0.613367 | − | 0.789798i | \(-0.710185\pi\) |
0.990669 | + | 0.136292i | \(0.0435185\pi\) | |||||||
\(462\) | −3.76005 | − | 1.00750i | −0.174934 | − | 0.0468733i | ||||
\(463\) | 11.2247 | + | 11.2247i | 0.521658 | + | 0.521658i | 0.918072 | − | 0.396414i | \(-0.129745\pi\) |
−0.396414 | + | 0.918072i | \(0.629745\pi\) | |||||||
\(464\) | −7.70674 | −0.357777 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 1.73205i | 0.138972 | − | 0.0802357i | ||||
\(467\) | −23.4495 | + | 23.4495i | −1.08511 | + | 1.08511i | −0.0890893 | + | 0.996024i | \(0.528396\pi\) |
−0.996024 | + | 0.0890893i | \(0.971604\pi\) | |||||||
\(468\) | −10.3923 | + | 10.3923i | −0.480384 | + | 0.480384i | ||||
\(469\) | −7.92104 | − | 13.7196i | −0.365760 | − | 0.633514i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.0227 | − | 8.09601i | 0.646132 | − | 0.373045i | ||||
\(472\) | −0.896575 | − | 3.34607i | −0.0412682 | − | 0.154015i | ||||
\(473\) | 14.7503 | − | 3.95233i | 0.678219 | − | 0.181728i | ||||
\(474\) | 12.2993 | 0.564927 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.10102 | −0.142135 | ||||||||
\(477\) | 12.6009 | − | 3.37640i | 0.576955 | − | 0.154595i | ||||
\(478\) | 3.57117 | + | 13.3278i | 0.163342 | + | 0.609600i | ||||
\(479\) | −23.7238 | + | 13.6969i | −1.08397 | + | 0.625829i | −0.931964 | − | 0.362551i | \(-0.881906\pi\) |
−0.152004 | + | 0.988380i | \(0.548573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3485 | + | 23.1202i | 0.608638 | + | 1.05419i | ||||
\(482\) | −19.3485 | + | 19.3485i | −0.881299 | + | 0.881299i | ||||
\(483\) | −9.86739 | + | 9.86739i | −0.448982 | + | 0.448982i | ||||
\(484\) | −7.70674 | + | 4.44949i | −0.350306 | + | 0.202250i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −1.00000 | ||||||||
\(487\) | −16.4063 | − | 16.4063i | −0.743441 | − | 0.743441i | 0.229797 | − | 0.973239i | \(-0.426194\pi\) |
−0.973239 | + | 0.229797i | \(0.926194\pi\) | |||||||
\(488\) | −7.72741 | − | 2.07055i | −0.349803 | − | 0.0937295i | ||||
\(489\) | 16.1920 | − | 28.0454i | 0.732229 | − | 1.26826i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.1742 | + | 17.6223i | −0.459157 | + | 0.795283i | −0.998917 | − | 0.0465362i | \(-0.985182\pi\) |
0.539760 | + | 0.841819i | \(0.318515\pi\) | |||||||
\(492\) | 1.09808 | + | 4.09808i | 0.0495051 | + | 0.184756i | ||||
\(493\) | −15.4135 | + | 15.4135i | −0.694188 | + | 0.694188i | ||||
\(494\) | −14.6349 | + | 15.5505i | −0.658457 | + | 0.699651i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.674235 | − | 0.389270i | −0.0302740 | − | 0.0174787i | ||||
\(497\) | −3.66855 | + | 0.982984i | −0.164557 | + | 0.0440929i | ||||
\(498\) | 11.0713 | − | 41.3188i | 0.496118 | − | 1.85154i | ||||
\(499\) | 18.4008 | + | 10.6237i | 0.823734 | + | 0.475583i | 0.851703 | − | 0.524026i | \(-0.175570\pi\) |
−0.0279682 | + | 0.999609i | \(0.508904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.9546 | −0.623445 | ||||||||
\(502\) | −0.635674 | − | 0.635674i | −0.0283715 | − | 0.0283715i | ||||
\(503\) | −1.08977 | + | 4.06706i | −0.0485903 | + | 0.181341i | −0.985956 | − | 0.167006i | \(-0.946590\pi\) |
0.937366 | + | 0.348347i | \(0.113257\pi\) | |||||||
\(504\) | −1.64456 | − | 2.84847i | −0.0732547 | − | 0.126881i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 7.53177i | − | 0.334828i | ||||||
\(507\) | 6.97372 | − | 26.0263i | 0.309714 | − | 1.15587i | ||||
\(508\) | −3.59732 | − | 13.4254i | −0.159605 | − | 0.595655i | ||||
\(509\) | 10.7816 | + | 18.6742i | 0.477885 | + | 0.827721i | 0.999679 | − | 0.0253508i | \(-0.00807027\pi\) |
−0.521794 | + | 0.853072i | \(0.674737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00000 | + | 8.66025i | −0.221187 | + | 0.383107i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.55051i | 0.421255i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 22.3485 | + | 12.9029i | 0.983836 | + | 0.568018i | ||||
\(517\) | −9.70017 | − | 2.59915i | −0.426613 | − | 0.114311i | ||||
\(518\) | −5.77111 | + | 1.54636i | −0.253568 | + | 0.0679433i | ||||
\(519\) | 1.16781 | − | 0.674235i | 0.0512611 | − | 0.0295956i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.8481i | 1.57054i | 0.619156 | + | 0.785268i | \(0.287475\pi\) | ||||
−0.619156 | + | 0.785268i | \(0.712525\pi\) | |||||||
\(522\) | −22.3324 | − | 5.98396i | −0.977464 | − | 0.261911i | ||||
\(523\) | −0.824487 | − | 0.220921i | −0.0360523 | − | 0.00966019i | 0.240748 | − | 0.970588i | \(-0.422607\pi\) |
−0.276800 | + | 0.960928i | \(0.589274\pi\) | |||||||
\(524\) | 7.24745i | 0.316606i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0505 | + | 11.5762i | −0.874244 | + | 0.504745i | ||||
\(527\) | −2.12701 | + | 0.569930i | −0.0926539 | + | 0.0248265i | ||||
\(528\) | 3.42953 | + | 0.918940i | 0.149251 | + | 0.0399917i | ||||
\(529\) | −3.46410 | − | 2.00000i | −0.150613 | − | 0.0869565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 10.3923i | − | 0.450988i | ||||||
\(532\) | −2.51387 | − | 4.06438i | −0.108990 | − | 0.176213i | ||||
\(533\) | −6.00000 | − | 6.00000i | −0.259889 | − | 0.259889i | ||||
\(534\) | 16.7563 | − | 29.0227i | 0.725115 | − | 1.25594i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.22474 | + | 12.5136i | 0.312061 | + | 0.540506i | ||||
\(537\) | −1.59165 | − | 5.94012i | −0.0686848 | − | 0.256335i | ||||
\(538\) | 1.79315 | − | 6.69213i | 0.0773082 | − | 0.288518i | ||||
\(539\) | − | 8.40408i | − | 0.361989i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.22474 | + | 12.5136i | 0.310616 | + | 0.538003i | 0.978496 | − | 0.206266i | \(-0.0661313\pi\) |
−0.667880 | + | 0.744269i | \(0.732798\pi\) | |||||||
\(542\) | 0.854895 | − | 3.19051i | 0.0367209 | − | 0.137044i | ||||
\(543\) | −37.3485 | − | 37.3485i | −1.60278 | − | 1.60278i | ||||
\(544\) | 2.82843 | 0.121268 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.3939 | + | 6.57826i | 0.487613 | + | 0.281523i | ||||
\(547\) | −4.65874 | + | 17.3867i | −0.199193 | + | 0.743400i | 0.791948 | + | 0.610589i | \(0.209067\pi\) |
−0.991141 | + | 0.132811i | \(0.957600\pi\) | |||||||
\(548\) | 2.73205 | − | 0.732051i | 0.116707 | − | 0.0312717i | ||||
\(549\) | −20.7846 | − | 12.0000i | −0.887066 | − | 0.512148i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.6969 | − | 7.70674i | −1.39294 | − | 0.328318i | ||||
\(552\) | 9.00000 | − | 9.00000i | 0.383065 | − | 0.383065i | ||||
\(553\) | −1.42483 | − | 5.31752i | −0.0605897 | − | 0.226124i | ||||
\(554\) | 9.75663 | − | 16.8990i | 0.414520 | − | 0.717969i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.44949 | − | 14.6349i | 0.358338 | − | 0.620660i | ||||
\(557\) | 40.3978 | + | 10.8245i | 1.71171 | + | 0.458651i | 0.975842 | − | 0.218477i | \(-0.0701087\pi\) |
0.735866 | + | 0.677127i | \(0.236775\pi\) | |||||||
\(558\) | −1.65153 | − | 1.65153i | −0.0699149 | − | 0.0699149i | ||||
\(559\) | −51.6116 | −2.18294 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.69694 | − | 5.02118i | 0.367185 | − | 0.211994i | ||||
\(562\) | 8.57321 | − | 8.57321i | 0.361639 | − | 0.361639i | ||||
\(563\) | 16.9706 | − | 16.9706i | 0.715224 | − | 0.715224i | −0.252399 | − | 0.967623i | \(-0.581220\pi\) |
0.967623 | + | 0.252399i | \(0.0812196\pi\) | |||||||
\(564\) | −8.48528 | − | 14.6969i | −0.357295 | − | 0.618853i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.550510 | + | 0.317837i | −0.0231397 | + | 0.0133597i | ||||
\(567\) | 2.55387 | + | 9.53116i | 0.107252 | + | 0.400271i | ||||
\(568\) | 3.34607 | − | 0.896575i | 0.140398 | − | 0.0376195i | ||||
\(569\) | 15.2385 | 0.638832 | 0.319416 | − | 0.947615i | \(-0.396513\pi\) | ||||
0.319416 | + | 0.947615i | \(0.396513\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.0000 | −0.502184 | −0.251092 | − | 0.967963i | \(-0.580790\pi\) | ||||
−0.251092 | + | 0.967963i | \(0.580790\pi\) | |||||||
\(572\) | −6.85906 | + | 1.83788i | −0.286792 | + | 0.0768456i | ||||
\(573\) | 10.3005 | + | 38.4419i | 0.430308 | + | 1.60593i | ||||
\(574\) | 1.64456 | − | 0.949490i | 0.0686428 | − | 0.0396309i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −5.24745 | + | 5.24745i | −0.218454 | + | 0.218454i | −0.807847 | − | 0.589393i | \(-0.799367\pi\) |
0.589393 | + | 0.807847i | \(0.299367\pi\) | |||||||
\(578\) | −6.36396 | + | 6.36396i | −0.264706 | + | 0.264706i | ||||
\(579\) | 28.3164 | − | 16.3485i | 1.17679 | − | 0.679419i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.1464 | −0.794328 | ||||||||
\(582\) | −25.0273 | − | 25.0273i | −1.03741 | − | 1.03741i | ||||
\(583\) | 6.08829 | + | 1.63135i | 0.252151 | + | 0.0675637i | ||||
\(584\) | 4.56048 | − | 7.89898i | 0.188714 | − | 0.326862i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.6237 | − | 23.5970i | 0.562791 | − | 0.974782i | ||||
\(587\) | 3.58630 | + | 13.3843i | 0.148023 | + | 0.552428i | 0.999602 | + | 0.0282024i | \(0.00897830\pi\) |
−0.851580 | + | 0.524225i | \(0.824355\pi\) | |||||||
\(588\) | 10.0424 | − | 10.0424i | 0.414140 | − | 0.414140i | ||||
\(589\) | −2.47127 | − | 2.32577i | −0.101827 | − | 0.0958315i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.9773 | + | 9.22450i | 0.657218 | + | 0.379445i | ||||
\(592\) | 5.26380 | − | 1.41043i | 0.216341 | − | 0.0579684i | ||||
\(593\) | 10.6147 | − | 39.6147i | 0.435895 | − | 1.62678i | −0.303020 | − | 0.952984i | \(-0.597995\pi\) |
0.738915 | − | 0.673798i | \(-0.235338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.44949 | 0.264181 | ||||||||
\(597\) | 16.9706 | + | 16.9706i | 0.694559 | + | 0.694559i | ||||
\(598\) | −6.58846 | + | 24.5885i | −0.269422 | + | 1.00550i | ||||
\(599\) | 14.6349 | + | 25.3485i | 0.597968 | + | 1.03571i | 0.993121 | + | 0.117095i | \(0.0373582\pi\) |
−0.395153 | + | 0.918615i | \(0.629308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.174973i | 0.00713728i | 0.999994 | + | 0.00356864i | \(0.00113594\pi\) | ||||
−0.999994 | + | 0.00356864i | \(0.998864\pi\) | |||||||
\(602\) | 2.98949 | − | 11.1569i | 0.121843 | − | 0.454723i | ||||
\(603\) | 11.2194 | + | 41.8714i | 0.456890 | + | 1.70514i | ||||
\(604\) | −4.24264 | − | 7.34847i | −0.172631 | − | 0.299005i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.5505 | + | 26.9343i | −0.631696 | + | 1.09413i | ||||
\(607\) | 1.34278 | + | 1.34278i | 0.0545018 | + | 0.0545018i | 0.733832 | − | 0.679331i | \(-0.237730\pi\) |
−0.679331 | + | 0.733832i | \(0.737730\pi\) | |||||||
\(608\) | 2.29289 | + | 3.70711i | 0.0929891 | + | 0.150343i | ||||
\(609\) | 20.6969i | 0.838682i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3939 | + | 16.9706i | 1.18915 | + | 0.686555i | ||||
\(612\) | 8.19615 | + | 2.19615i | 0.331310 | + | 0.0887742i | ||||
\(613\) | −43.1918 | + | 11.5732i | −1.74450 | + | 0.467438i | −0.983439 | − | 0.181240i | \(-0.941989\pi\) |
−0.761063 | + | 0.648678i | \(0.775322\pi\) | |||||||
\(614\) | −11.5601 | + | 6.67423i | −0.466528 | + | 0.269350i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1.58919i | − | 0.0640301i | ||||||
\(617\) | 31.4806 | + | 8.43520i | 1.26736 | + | 0.339589i | 0.829020 | − | 0.559220i | \(-0.188899\pi\) |
0.438342 | + | 0.898808i | \(0.355566\pi\) | |||||||
\(618\) | −4.49303 | − | 1.20390i | −0.180736 | − | 0.0484282i | ||||
\(619\) | 19.0454i | 0.765500i | 0.923852 | + | 0.382750i | \(0.125023\pi\) | ||||
−0.923852 | + | 0.382750i | \(0.874977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −24.9189 | + | 6.67700i | −0.999157 | + | 0.267723i | ||||
\(623\) | −14.4889 | − | 3.88229i | −0.580485 | − | 0.155540i | ||||
\(624\) | −10.3923 | − | 6.00000i | −0.416025 | − | 0.240192i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 29.7627i | − | 1.18956i | ||||||
\(627\) | 13.6313 | + | 7.32826i | 0.544383 | + | 0.292663i | ||||
\(628\) | 4.67423 | + | 4.67423i | 0.186522 | + | 0.186522i | ||||
\(629\) | 7.70674 | − | 13.3485i | 0.307288 | − | 0.532238i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | − | 1.73205i | −0.0398094 | − | 0.0689519i | 0.845434 | − | 0.534080i | \(-0.179342\pi\) |
−0.885244 | + | 0.465128i | \(0.846008\pi\) | |||||||
\(632\) | 1.29958 | + | 4.85009i | 0.0516944 | + | 0.192926i | ||||
\(633\) | 11.5853 | − | 43.2368i | 0.460473 | − | 1.71851i | ||||
\(634\) | − | 15.2474i | − | 0.605554i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.32577 | + | 9.22450i | 0.211180 | + | 0.365775i | ||||
\(637\) | −7.35152 | + | 27.4362i | −0.291278 | + | 1.08706i | ||||
\(638\) | −7.89898 | − | 7.89898i | −0.312724 | − | 0.312724i | ||||
\(639\) | 10.3923 | 0.411113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.3485 | − | 12.9029i | −0.882711 | − | 0.509634i | −0.0111600 | − | 0.999938i | \(-0.503552\pi\) |
−0.871551 | + | 0.490304i | \(0.836886\pi\) | |||||||
\(642\) | −7.76457 | + | 28.9778i | −0.306443 | + | 1.14366i | ||||
\(643\) | 29.5006 | − | 7.90465i | 1.16339 | − | 0.311729i | 0.375070 | − | 0.926996i | \(-0.377619\pi\) |
0.788319 | + | 0.615267i | \(0.210952\pi\) | |||||||
\(644\) | −4.93369 | − | 2.84847i | −0.194415 | − | 0.112245i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | + | 2.82843i | 0.472134 | + | 0.111283i | ||||
\(647\) | 10.3258 | − | 10.3258i | 0.405948 | − | 0.405948i | −0.474375 | − | 0.880323i | \(-0.657326\pi\) |
0.880323 | + | 0.474375i | \(0.157326\pi\) | |||||||
\(648\) | −2.32937 | − | 8.69333i | −0.0915064 | − | 0.341506i | ||||
\(649\) | 2.51059 | − | 4.34847i | 0.0985493 | − | 0.170692i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.04541 | + | 1.81070i | −0.0409728 | + | 0.0709669i | ||||
\(652\) | 12.7702 | + | 3.42178i | 0.500121 | + | 0.134007i | ||||
\(653\) | 10.0227 | + | 10.0227i | 0.392219 | + | 0.392219i | 0.875478 | − | 0.483259i | \(-0.160547\pi\) |
−0.483259 | + | 0.875478i | \(0.660547\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | + | 0.866025i | −0.0585652 | + | 0.0338126i | ||||
\(657\) | 19.3485 | − | 19.3485i | 0.754856 | − | 0.754856i | ||||
\(658\) | −5.37113 | + | 5.37113i | −0.209388 | + | 0.209388i | ||||
\(659\) | −1.43027 | − | 2.47730i | −0.0557153 | − | 0.0965018i | 0.836823 | − | 0.547474i | \(-0.184411\pi\) |
−0.892538 | + | 0.450972i | \(0.851077\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0681 | + | 19.0919i | −1.28620 | + | 0.742588i | −0.977974 | − | 0.208725i | \(-0.933069\pi\) |
−0.308226 | + | 0.951313i | \(0.599735\pi\) | |||||||
\(662\) | −1.05279 | − | 3.92907i | −0.0409178 | − | 0.152707i | ||||
\(663\) | −32.7846 | + | 8.78461i | −1.27325 | + | 0.341166i | ||||
\(664\) | 17.4634 | 0.677710 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.3485 | 0.633490 | ||||||||
\(667\) | −38.6809 | + | 10.3645i | −1.49773 | + | 0.401316i | ||||
\(668\) | −1.47448 | − | 5.50282i | −0.0570492 | − | 0.212910i | ||||
\(669\) | −24.8130 | + | 14.3258i | −0.959324 | + | 0.553866i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.79796 | − | 10.0424i | −0.223828 | − | 0.387681i | ||||
\(672\) | 1.89898 | − | 1.89898i | 0.0732547 | − | 0.0732547i | ||||
\(673\) | 3.11416 | − | 3.11416i | 0.120042 | − | 0.120042i | −0.644534 | − | 0.764576i | \(-0.722949\pi\) |
0.764576 | + | 0.644534i | \(0.222949\pi\) | |||||||
\(674\) | −15.5885 | + | 9.00000i | −0.600445 | + | 0.346667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | 9.22450 | + | 9.22450i | 0.354526 | + | 0.354526i | 0.861791 | − | 0.507264i | \(-0.169343\pi\) |
−0.507264 | + | 0.861791i | \(0.669343\pi\) | |||||||
\(678\) | 43.1739 | + | 11.5684i | 1.65808 | + | 0.444282i | ||||
\(679\) | −7.92104 | + | 13.7196i | −0.303982 | + | 0.526512i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.0454 | − | 32.9876i | 0.729822 | − | 1.26409i | ||||
\(682\) | −0.292073 | − | 1.09003i | −0.0111841 | − | 0.0417395i | ||||
\(683\) | −25.8058 | + | 25.8058i | −0.987431 | + | 0.987431i | −0.999922 | − | 0.0124909i | \(-0.996024\pi\) |
0.0124909 | + | 0.999922i | \(0.496024\pi\) | |||||||
\(684\) | 3.76588 | + | 12.5227i | 0.143992 | + | 0.478818i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.1515 | − | 7.01569i | −0.463948 | − | 0.267860i | ||||
\(687\) | −36.7929 | + | 9.85863i | −1.40374 | + | 0.376130i | ||||
\(688\) | −2.72670 | + | 10.1762i | −0.103955 | + | 0.387964i | ||||
\(689\) | −18.4490 | − | 10.6515i | −0.702851 | − | 0.405791i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.55051 | 0.249193 | 0.124597 | − | 0.992207i | \(-0.460236\pi\) | ||||
0.124597 | + | 0.992207i | \(0.460236\pi\) | |||||||
\(692\) | 0.389270 | + | 0.389270i | 0.0147978 | + | 0.0147978i | ||||
\(693\) | 1.23393 | − | 4.60511i | 0.0468733 | − | 0.174934i | ||||
\(694\) | 4.70334 | + | 8.14643i | 0.178536 | + | 0.309234i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 18.8776i | − | 0.715553i | ||||||
\(697\) | −1.26795 | + | 4.73205i | −0.0480270 | + | 0.179239i | ||||
\(698\) | 4.94371 | + | 18.4502i | 0.187122 | + | 0.698349i | ||||
\(699\) | 4.24264 | + | 7.34847i | 0.160471 | + | 0.277945i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.67423 | + | 8.09601i | −0.176543 | + | 0.305782i | −0.940694 | − | 0.339255i | \(-0.889825\pi\) |
0.764151 | + | 0.645038i | \(0.223158\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.7429 | − | 0.720152i | 0.895479 | − | 0.0271611i | ||||
\(704\) | 1.44949i | 0.0546297i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.02270 | − | 1.16781i | −0.0761255 | − | 0.0439511i | ||||
\(707\) | 13.4463 | + | 3.60292i | 0.505700 | + | 0.135502i | ||||
\(708\) | 8.19615 | − | 2.19615i | 0.308030 | − | 0.0825365i | ||||
\(709\) | −23.1202 | + | 13.3485i | −0.868298 | + | 0.501312i | −0.866782 | − | 0.498687i | \(-0.833816\pi\) |
−0.00151596 | + | 0.999999i | \(0.500483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.0635i | 0.564927i | ||||||||
\(712\) | 13.2153 | + | 3.54102i | 0.495262 | + | 0.132705i | ||||
\(713\) | −3.90756 | − | 1.04703i | −0.146339 | − | 0.0392115i | ||||
\(714\) | − | 7.59592i | − | 0.284270i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.17423 | − | 1.25529i | 0.0812550 | − | 0.0469126i | ||||
\(717\) | −32.6463 | + | 8.74756i | −1.21920 | + | 0.326683i | ||||
\(718\) | −22.9871 | − | 6.15937i | −0.857870 | − | 0.229865i | ||||
\(719\) | −22.7310 | − | 13.1237i | −0.847722 | − | 0.489432i | 0.0121598 | − | 0.999926i | \(-0.496129\pi\) |
−0.859881 | + | 0.510494i | \(0.829463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.08200i | 0.0775376i | ||||||||
\(722\) | 6.02082 | + | 18.0208i | 0.224072 | + | 0.670665i | ||||
\(723\) | −47.3939 | − | 47.3939i | −1.76260 | − | 1.76260i | ||||
\(724\) | 10.7816 | − | 18.6742i | 0.400694 | − | 0.694022i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.8990 | − | 18.8776i | −0.404499 | − | 0.700613i | ||||
\(727\) | −5.45340 | − | 20.3524i | −0.202256 | − | 0.754828i | −0.990269 | − | 0.139170i | \(-0.955557\pi\) |
0.788013 | − | 0.615659i | \(-0.211110\pi\) | |||||||
\(728\) | −1.39015 | + | 5.18811i | −0.0515224 | + | 0.192284i | ||||
\(729\) | − | 27.0000i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.8990 | + | 25.8058i | 0.551059 | + | 0.954462i | ||||
\(732\) | 5.07180 | − | 18.9282i | 0.187459 | − | 0.699607i | ||||
\(733\) | −12.0227 | − | 12.0227i | −0.444069 | − | 0.444069i | 0.449308 | − | 0.893377i | \(-0.351671\pi\) |
−0.893377 | + | 0.449308i | \(0.851671\pi\) | |||||||
\(734\) | −15.1278 | −0.558376 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.50000 | + | 2.59808i | 0.165872 | + | 0.0957664i | ||||
\(737\) | −5.42081 | + | 20.2307i | −0.199678 | + | 0.745208i | ||||
\(738\) | −5.01910 | + | 1.34486i | −0.184756 | + | 0.0495051i | ||||
\(739\) | 38.4069 | + | 22.1742i | 1.41282 | + | 0.815692i | 0.995653 | − | 0.0931373i | \(-0.0296895\pi\) |
0.417167 | + | 0.908830i | \(0.363023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.0908 | − | 35.8481i | −1.39930 | − | 1.31691i | ||||
\(742\) | 3.37117 | − | 3.37117i | 0.123760 | − | 0.123760i | ||||
\(743\) | 12.7579 | + | 47.6132i | 0.468043 | + | 1.74676i | 0.646598 | + | 0.762831i | \(0.276191\pi\) |
−0.178555 | + | 0.983930i | \(0.557142\pi\) | |||||||
\(744\) | 0.953512 | − | 1.65153i | 0.0349574 | − | 0.0605481i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.9722 | + | 31.1288i | −0.658009 | + | 1.13970i | ||||
\(747\) | 50.6050 | + | 13.5596i | 1.85154 | + | 0.496118i | ||||
\(748\) | 2.89898 | + | 2.89898i | 0.105997 | + | 0.105997i | ||||
\(749\) | 13.4278 | 0.490642 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.0227 | + | 21.9524i | −1.38747 | + | 0.801055i | −0.993029 | − | 0.117867i | \(-0.962394\pi\) |
−0.394439 | + | 0.918922i | \(0.629061\pi\) | |||||||
\(752\) | 4.89898 | − | 4.89898i | 0.178647 | − | 0.178647i | ||||
\(753\) | 1.55708 | − | 1.55708i | 0.0567431 | − | 0.0567431i | ||||
\(754\) | 18.8776 | + | 32.6969i | 0.687481 | + | 1.19075i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.172835 | − | 0.645028i | −0.00628179 | − | 0.0234440i | 0.962714 | − | 0.270522i | \(-0.0871963\pi\) |
−0.968996 | + | 0.247078i | \(0.920530\pi\) | |||||||
\(758\) | 27.9345 | − | 7.48503i | 1.01463 | − | 0.271869i | ||||
\(759\) | 18.4490 | 0.669656 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.79796 | −0.318926 | −0.159463 | − | 0.987204i | \(-0.550976\pi\) | ||||
−0.159463 | + | 0.987204i | \(0.550976\pi\) | |||||||
\(762\) | 32.8853 | − | 8.81160i | 1.19131 | − | 0.319211i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.0707 | + | 8.12372i | −0.509060 | + | 0.293906i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.89898 | + | 8.48528i | 0.177007 | + | 0.306586i | ||||
\(767\) | −12.0000 | + | 12.0000i | −0.433295 | + | 0.433295i | ||||
\(768\) | −1.73205 | + | 1.73205i | −0.0625000 | + | 0.0625000i | ||||
\(769\) | 37.7552 | − | 21.7980i | 1.36149 | − | 0.786055i | 0.371665 | − | 0.928367i | \(-0.378787\pi\) |
0.989822 | + | 0.142313i | \(0.0454538\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.3939 | −0.842510 | ||||||||
\(772\) | 9.43879 | + | 9.43879i | 0.339710 | + | 0.339710i | ||||
\(773\) | −7.39081 | − | 1.98036i | −0.265829 | − | 0.0712287i | 0.123443 | − | 0.992352i | \(-0.460607\pi\) |
−0.389272 | + | 0.921123i | \(0.627273\pi\) | |||||||
\(774\) | −15.8028 | + | 27.3712i | −0.568018 | + | 0.983836i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.22474 | − | 12.5136i | 0.259353 | − | 0.449213i | ||||
\(777\) | −3.78780 | − | 14.1363i | −0.135887 | − | 0.507136i | ||||
\(778\) | 2.04989 | − | 2.04989i | 0.0734920 | − | 0.0734920i | ||||
\(779\) | −7.22999 | + | 2.17423i | −0.259041 | + | 0.0779000i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.34847 | + | 2.51059i | 0.155600 | + | 0.0898360i | ||||
\(782\) | 14.1962 | − | 3.80385i | 0.507653 | − | 0.136025i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.02118 | + | 2.89898i | 0.179328 | + | 0.103535i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.7526 | −0.633213 | ||||||||
\(787\) | −16.3670 | − | 16.3670i | −0.583420 | − | 0.583420i | 0.352421 | − | 0.935842i | \(-0.385358\pi\) |
−0.935842 | + | 0.352421i | \(0.885358\pi\) | |||||||
\(788\) | −1.94937 | + | 7.27513i | −0.0694433 | + | 0.259166i | ||||
\(789\) | −28.3557 | − | 49.1135i | −1.00949 | − | 1.74849i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 20.0061i | − | 0.711334i | ||||||
\(792\) | −1.12547 | + | 4.20030i | −0.0399917 | + | 0.149251i | ||||
\(793\) | 10.1436 | + | 37.8564i | 0.360210 | + | 1.34432i | ||||
\(794\) | 4.08372 | + | 7.07321i | 0.144926 | + | 0.251019i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.89898 | + | 8.48528i | −0.173640 | + | 0.300753i | ||||
\(797\) | −9.65309 | − | 9.65309i | −0.341930 | − | 0.341930i | 0.515163 | − | 0.857093i | \(-0.327732\pi\) |
−0.857093 | + | 0.515163i | \(0.827732\pi\) | |||||||
\(798\) | 9.95567 | − | 6.15771i | 0.352427 | − | 0.217981i | ||||
\(799\) | − | 19.5959i | − | 0.693254i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.5454 | + | 20.5222i | 1.25594 | + | 0.725115i | ||||
\(802\) | 16.7303 | + | 4.48288i | 0.590768 | + | 0.158296i | ||||
\(803\) | 12.7702 | − | 3.42178i | 0.450652 | − | 0.120752i | ||||
\(804\) | −30.6520 | + | 17.6969i | −1.08101 | + | 0.624123i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.81405i | 0.134344i | ||||||||
\(807\) | 16.3923 | + | 4.39230i | 0.577036 | + | 0.154616i | ||||
\(808\) | −12.2643 | − | 3.28621i | −0.431457 | − | 0.115608i | ||||
\(809\) | 18.2020i | 0.639950i | 0.947426 | + | 0.319975i | \(0.103674\pi\) | ||||
−0.947426 | + | 0.319975i | \(0.896326\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.52270 | − | 3.76588i | 0.229043 | − | 0.132238i | −0.381087 | − | 0.924539i | \(-0.624450\pi\) |
0.610131 | + | 0.792301i | \(0.291117\pi\) | |||||||
\(812\) | −8.16158 | + | 2.18689i | −0.286415 | + | 0.0767448i | ||||
\(813\) | 7.81513 | + | 2.09406i | 0.274088 | + | 0.0734418i | ||||
\(814\) | 6.84072 | + | 3.94949i | 0.239767 | + | 0.138430i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.92820i | 0.242536i | ||||||||
\(817\) | −21.7446 | + | 40.4472i | −0.760748 | + | 1.41507i | ||||
\(818\) | 11.0227 | + | 11.0227i | 0.385400 | + | 0.385400i | ||||
\(819\) | −8.05669 | + | 13.9546i | −0.281523 | + | 0.487613i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.24745 | + | 2.16064i | 0.0435363 | + | 0.0754070i | 0.886972 | − | 0.461822i | \(-0.152804\pi\) |
−0.843436 | + | 0.537229i | \(0.819471\pi\) | |||||||
\(822\) | 1.79315 | + | 6.69213i | 0.0625433 | + | 0.233415i | ||||
\(823\) | −3.21197 | + | 11.9872i | −0.111962 | + | 0.417848i | −0.999042 | − | 0.0437682i | \(-0.986064\pi\) |
0.887080 | + | 0.461616i | \(0.152730\pi\) | |||||||
\(824\) | − | 1.89898i | − | 0.0661541i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.89898 | − | 3.28913i | −0.0660739 | − | 0.114443i | ||||
\(827\) | −9.22465 | + | 34.4269i | −0.320773 | + | 1.19714i | 0.597721 | + | 0.801704i | \(0.296073\pi\) |
−0.918494 | + | 0.395436i | \(0.870594\pi\) | |||||||
\(828\) | 11.0227 | + | 11.0227i | 0.383065 | + | 0.383065i | ||||
\(829\) | 41.5692 | 1.44376 | 0.721879 | − | 0.692019i | \(-0.243279\pi\) | ||||
0.721879 | + | 0.692019i | \(0.243279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.3939 | + | 23.8988i | 1.43594 | + | 0.829039i | ||||
\(832\) | 1.26795 | − | 4.73205i | 0.0439582 | − | 0.164054i | ||||
\(833\) | 15.8403 | − | 4.24440i | 0.548835 | − | 0.147060i | ||||
\(834\) | 35.8481 | + | 20.6969i | 1.24132 | + | 0.716676i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.44949 | + | 6.14966i | −0.0501317 | + | 0.212691i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.16074 | − | 8.06400i | −0.0746416 | − | 0.278566i | ||||
\(839\) | −7.49245 | + | 12.9773i | −0.258668 | + | 0.448026i | −0.965885 | − | 0.258970i | \(-0.916617\pi\) |
0.707217 | + | 0.706996i | \(0.249950\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1969 | + | 26.3219i | −0.524032 | + | 0.907651i | ||||
\(842\) | −9.28618 | − | 2.48823i | −0.320023 | − | 0.0857499i | ||||
\(843\) | 21.0000 | + | 21.0000i | 0.723278 | + | 0.723278i | ||||
\(844\) | 18.2740 | 0.629018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18.0000 | − | 10.3923i | 0.618853 | − | 0.357295i | ||||
\(847\) | −6.89898 | + | 6.89898i | −0.237052 | + | 0.237052i | ||||
\(848\) | −3.07483 | + | 3.07483i | −0.105590 | + | 0.105590i | ||||
\(849\) | −0.778539 | − | 1.34847i | −0.0267194 | − | 0.0462793i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5227 | − | 14.1582i | 0.840627 | − | 0.485336i | ||||
\(852\) | 2.19615 | + | 8.19615i | 0.0752389 | + | 0.280796i | ||||
\(853\) | −29.2246 | + | 7.83070i | −1.00063 | + | 0.268118i | −0.721710 | − | 0.692196i | \(-0.756643\pi\) |
−0.278921 | + | 0.960314i | \(0.589977\pi\) | |||||||
\(854\) | −8.77101 | −0.300138 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.2474 | −0.418609 | ||||||||
\(857\) | 37.3784 | − | 10.0155i | 1.27682 | − | 0.342123i | 0.444181 | − | 0.895937i | \(-0.353495\pi\) |
0.832640 | + | 0.553814i | \(0.186828\pi\) | |||||||
\(858\) | −4.50187 | − | 16.8012i | −0.153691 | − | 0.573583i | ||||
\(859\) | −8.35847 | + | 4.82577i | −0.285187 | + | 0.164653i | −0.635769 | − | 0.771879i | \(-0.719317\pi\) |
0.350582 | + | 0.936532i | \(0.385984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.32577 | + | 4.02834i | 0.0792619 | + | 0.137286i | ||||
\(862\) | −16.3485 | + | 16.3485i | −0.556831 | + | 0.556831i | ||||
\(863\) | 21.7774 | − | 21.7774i | 0.741313 | − | 0.741313i | −0.231518 | − | 0.972831i | \(-0.574369\pi\) |
0.972831 | + | 0.231518i | \(0.0743692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.3485 | −0.657488 | ||||||||
\(867\) | −15.5885 | − | 15.5885i | −0.529412 | − | 0.529412i | ||||
\(868\) | −0.824487 | − | 0.220921i | −0.0279849 | − | 0.00749854i | ||||
\(869\) | −3.63907 | + | 6.30306i | −0.123447 | + | 0.213817i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3939 | − | 61.3040i | 1.19928 | − | 2.07721i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.6520 | − | 30.6520i | 1.03741 | − | 1.03741i | ||||
\(874\) | 16.4938 | + | 15.5227i | 0.557911 | + | 0.525063i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.3485 | + | 11.1708i | 0.653724 | + | 0.377428i | ||||
\(877\) | −17.3329 | + | 4.64435i | −0.585292 | + | 0.156829i | −0.539301 | − | 0.842113i | \(-0.681311\pi\) |
−0.0459914 | + | 0.998942i | \(0.514645\pi\) | |||||||
\(878\) | −2.80065 | + | 10.4522i | −0.0945175 | + | 0.352744i | ||||
\(879\) | 57.8006 | + | 33.3712i | 1.94956 | + | 1.12558i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.2929 | 1.52596 | 0.762978 | − | 0.646425i | \(-0.223737\pi\) | ||||
0.762978 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(882\) | 12.2993 | + | 12.2993i | 0.414140 | + | 0.414140i | ||||
\(883\) | 5.16133 | − | 19.2624i | 0.173693 | − | 0.648230i | −0.823078 | − | 0.567928i | \(-0.807745\pi\) |
0.996771 | − | 0.0803014i | \(-0.0255883\pi\) | |||||||
\(884\) | −6.92820 | − | 12.0000i | −0.233021 | − | 0.403604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.11416i | 0.104622i | ||||||||
\(887\) | 1.42483 | − | 5.31752i | 0.0478410 | − | 0.178545i | −0.937871 | − | 0.346984i | \(-0.887206\pi\) |
0.985712 | + | 0.168439i | \(0.0538726\pi\) | |||||||
\(888\) | 3.45484 | + | 12.8936i | 0.115937 | + | 0.432682i | ||||
\(889\) | −7.61926 | − | 13.1969i | −0.255542 | − | 0.442611i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.52270 | − | 11.2977i | 0.218519 | − | 0.378486i | ||||
\(892\) | −8.27098 | − | 8.27098i | −0.276933 | − | 0.276933i | ||||
\(893\) | 25.6836 | − | 15.8856i | 0.859469 | − | 0.531592i | ||||
\(894\) | 15.7980i | 0.528363i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.949490 | + | 0.548188i | 0.0317202 | + | 0.0183137i | ||||
\(897\) | −60.2292 | − | 16.1384i | −2.01099 | − | 0.538844i | ||||
\(898\) | −8.36516 | + | 2.24144i | −0.279149 | + | 0.0747978i | ||||
\(899\) | −5.19615 | + | 3.00000i | −0.173301 | + | 0.100056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.2993i | 0.409750i | ||||||||
\(902\) | −2.42504 | − | 0.649788i | −0.0807451 | − | 0.0216356i | ||||
\(903\) | 27.3288 | + | 7.32273i | 0.909446 | + | 0.243685i | ||||
\(904\) | 18.2474i | 0.606901i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.0000 | − | 10.3923i | 0.598010 | − | 0.345261i | ||||
\(907\) | 18.1037 | − | 4.85088i | 0.601124 | − | 0.161071i | 0.0545918 | − | 0.998509i | \(-0.482614\pi\) |
0.546532 | + | 0.837438i | \(0.315948\pi\) | |||||||
\(908\) | 15.0206 | + | 4.02477i | 0.498477 | + | 0.133567i | ||||
\(909\) | −32.9876 | − | 19.0454i | −1.09413 | − | 0.631696i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 39.6622i | − | 1.31407i | −0.753861 | − | 0.657034i | \(-0.771811\pi\) | ||
0.753861 | − | 0.657034i | \(-0.228189\pi\) | |||||||
\(912\) | −9.08052 | + | 5.61642i | −0.300686 | + | 0.185978i | ||||
\(913\) | 17.8990 | + | 17.8990i | 0.592370 | + | 0.592370i | ||||
\(914\) | −13.6100 | + | 23.5732i | −0.450179 | + | 0.779733i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.77526 | − | 13.4671i | −0.256902 | − | 0.444967i | ||||
\(917\) | 2.05656 | + | 7.67518i | 0.0679135 | + | 0.253457i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.0908i | − | 1.12455i | −0.826950 | − | 0.562276i | \(-0.809926\pi\) | ||
0.826950 | − | 0.562276i | \(-0.190074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.3485 | − | 28.3164i | −0.538700 | − | 0.933056i | ||||
\(922\) | −4.19340 | + | 15.6500i | −0.138102 | + | 0.515404i | ||||
\(923\) | −12.0000 | − | 12.0000i | −0.394985 | − | 0.394985i | ||||
\(924\) | 3.89270 | 0.128060 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.7474 | − | 7.93709i | −0.451769 | − | 0.260829i | ||||
\(927\) | 1.47448 | − | 5.50282i | 0.0484282 | − | 0.180736i | ||||
\(928\) | 7.44414 | − | 1.99465i | 0.244366 | − | 0.0654776i | ||||
\(929\) | 41.9103 | + | 24.1969i | 1.37503 | + | 0.793876i | 0.991557 | − | 0.129675i | \(-0.0413933\pi\) |
0.383477 | + | 0.923551i | \(0.374727\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4041 | + | 17.3205i | 0.603169 | + | 0.567657i | ||||
\(932\) | −2.44949 | + | 2.44949i | −0.0802357 | + | 0.0802357i | ||||
\(933\) | −16.3553 | − | 61.0386i | −0.535447 | − | 1.99831i | ||||
\(934\) | 16.5813 | − | 28.7196i | 0.542556 | − | 0.939735i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.34847 | − | 12.7279i | 0.240192 | − | 0.416025i | ||||
\(937\) | −49.7909 | − | 13.3414i | −1.62660 | − | 0.435846i | −0.673668 | − | 0.739034i | \(-0.735282\pi\) |
−0.952931 | + | 0.303188i | \(0.901949\pi\) | |||||||
\(938\) | 11.2020 | + | 11.2020i | 0.365760 | + | 0.365760i | ||||
\(939\) | 72.9034 | 2.37911 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.62883 | − | 4.98186i | 0.281292 | − | 0.162404i | −0.352716 | − | 0.935730i | \(-0.614742\pi\) |
0.634008 | + | 0.773326i | \(0.281409\pi\) | |||||||
\(942\) | −11.4495 | + | 11.4495i | −0.373045 | + | 0.373045i | ||||
\(943\) | −6.36396 | + | 6.36396i | −0.207239 | + | 0.207239i | ||||
\(944\) | 1.73205 | + | 3.00000i | 0.0563735 | + | 0.0976417i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.2247 | + | 7.63531i | −0.429974 | + | 0.248245i | ||||
\(947\) | −2.92820 | − | 10.9282i | −0.0951538 | − | 0.355119i | 0.901889 | − | 0.431968i | \(-0.142181\pi\) |
−0.997043 | + | 0.0768492i | \(0.975514\pi\) | |||||||
\(948\) | −11.8802 | + | 3.18330i | −0.385852 | + | 0.103389i | ||||
\(949\) | −44.6834 | −1.45048 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.3485 | 1.21111 | ||||||||
\(952\) | 2.99536 | − | 0.802603i | 0.0970800 | − | 0.0260125i | ||||
\(953\) | 1.96597 | + | 7.33709i | 0.0636840 | + | 0.237672i | 0.990430 | − | 0.138017i | \(-0.0440728\pi\) |
−0.926746 | + | 0.375689i | \(0.877406\pi\) | |||||||
\(954\) | −11.2977 | + | 6.52270i | −0.365775 | + | 0.211180i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.89898 | − | 11.9494i | −0.223129 | − | 0.386471i | ||||
\(957\) | 19.3485 | − | 19.3485i | 0.625447 | − | 0.625447i | ||||
\(958\) | 19.3704 | − | 19.3704i | 0.625829 | − | 0.625829i | ||||
\(959\) | 2.68556 | − | 1.55051i | 0.0867213 | − | 0.0500686i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.3939 | 0.980448 | ||||||||
\(962\) | −18.8776 | − | 18.8776i | −0.608638 | − | 0.608638i | ||||
\(963\) | −35.4904 | − | 9.50962i | −1.14366 | − | 0.306443i | ||||
\(964\) | 13.6814 | − | 23.6969i | 0.440649 | − | 0.763227i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.97730 | − | 12.0850i | 0.224491 | − | 0.388830i | ||||
\(967\) | 0.732051 | + | 2.73205i | 0.0235412 | + | 0.0878568i | 0.976697 | − | 0.214623i | \(-0.0688522\pi\) |
−0.953156 | + | 0.302480i | \(0.902186\pi\) | |||||||
\(968\) | 6.29253 | − | 6.29253i | 0.202250 | − | 0.202250i | ||||
\(969\) | −6.92820 | + | 29.3939i | −0.222566 | + | 0.944267i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.0454 | + | 9.26382i | 0.514922 | + | 0.297290i | 0.734854 | − | 0.678225i | \(-0.237250\pi\) |
−0.219933 | + | 0.975515i | \(0.570584\pi\) | |||||||
\(972\) | 21.2942 | − | 5.70577i | 0.683013 | − | 0.183013i | ||||
\(973\) | 4.79531 | − | 17.8963i | 0.153730 | − | 0.573730i | ||||
\(974\) | 20.0936 | + | 11.6010i | 0.643839 | + | 0.371721i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | 25.6308 | + | 25.6308i | 0.820002 | + | 0.820002i | 0.986108 | − | 0.166106i | \(-0.0531192\pi\) |
−0.166106 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(978\) | −8.38161 | + | 31.2806i | −0.268014 | + | 1.00024i | ||||
\(979\) | 9.91555 | + | 17.1742i | 0.316902 | + | 0.548891i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.26657 | − | 19.6551i | 0.168063 | − | 0.627220i | ||||
\(983\) | −10.2220 | − | 38.1491i | −0.326032 | − | 1.21677i | −0.913270 | − | 0.407354i | \(-0.866451\pi\) |
0.587238 | − | 0.809414i | \(-0.300215\pi\) | |||||||
\(984\) | −2.12132 | − | 3.67423i | −0.0676252 | − | 0.117130i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.8990 | − | 18.8776i | 0.347094 | − | 0.601185i | ||||
\(987\) | −13.1565 | − | 13.1565i | −0.418777 | − | 0.418777i | ||||
\(988\) | 10.1115 | − | 18.8084i | 0.321690 | − | 0.598376i | ||||
\(989\) | 54.7423i | 1.74071i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0227 | − | 23.6845i | −1.30313 | − | 0.752362i | −0.322190 | − | 0.946675i | \(-0.604419\pi\) |
−0.980940 | + | 0.194313i | \(0.937752\pi\) | |||||||
\(992\) | 0.752011 | + | 0.201501i | 0.0238764 | + | 0.00639765i | ||||
\(993\) | 9.62421 | − | 2.57880i | 0.305415 | − | 0.0818357i | ||||
\(994\) | 3.28913 | − | 1.89898i | 0.104325 | − | 0.0602320i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 42.7764i | 1.35542i | ||||||||
\(997\) | 39.5078 | + | 10.5861i | 1.25122 | + | 0.335264i | 0.822809 | − | 0.568318i | \(-0.192406\pi\) |
0.428414 | + | 0.903582i | \(0.359072\pi\) | |||||||
\(998\) | −20.5235 | − | 5.49924i | −0.649659 | − | 0.174076i | ||||
\(999\) | 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 | 950.2.q.a.293.1 | 8 | ||
5.2 | odd | 4 | inner | 950.2.q.a.407.1 | 8 | ||
5.3 | odd | 4 | 190.2.m.a.27.2 | ✓ | 8 | ||
5.4 | even | 2 | 190.2.m.a.103.2 | yes | 8 | ||
19.12 | odd | 6 | inner | 950.2.q.a.943.1 | 8 | ||
95.12 | even | 12 | inner | 950.2.q.a.107.1 | 8 | ||
95.69 | odd | 6 | 190.2.m.a.183.2 | yes | 8 | ||
95.88 | even | 12 | 190.2.m.a.107.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.m.a.27.2 | ✓ | 8 | 5.3 | odd | 4 | ||
190.2.m.a.103.2 | yes | 8 | 5.4 | even | 2 | ||
190.2.m.a.107.2 | yes | 8 | 95.88 | even | 12 | ||
190.2.m.a.183.2 | yes | 8 | 95.69 | odd | 6 | ||
950.2.q.a.107.1 | 8 | 95.12 | even | 12 | inner | ||
950.2.q.a.293.1 | 8 | 1.1 | even | 1 | trivial | ||
950.2.q.a.407.1 | 8 | 5.2 | odd | 4 | inner | ||
950.2.q.a.943.1 | 8 | 19.12 | odd | 6 | inner |