Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,2,Mod(45,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.g (of order \(6\), 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: | \(2.57118294509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 45.4 | ||
Root | \(0.768626 + 1.33130i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.45 |
Dual form | 322.2.g.a.229.4 |
$q$-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 \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).
\(n\) | \(185\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.508912 | − | 0.293820i | −0.293820 | − | 0.169637i | 0.345843 | − | 0.938292i | \(-0.387593\pi\) |
−0.639663 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.863449 | + | 1.49554i | 0.386146 | + | 0.668825i | 0.991927 | − | 0.126806i | \(-0.0404727\pi\) |
−0.605781 | + | 0.795631i | \(0.707139\pi\) | |||||||
\(6\) | 0.587641i | 0.239903i | ||||||||
\(7\) | −1.63208 | − | 2.08239i | −0.616866 | − | 0.787068i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.32734 | − | 2.29902i | −0.442446 | − | 0.766340i | ||||
\(10\) | 0.863449 | − | 1.49554i | 0.273047 | − | 0.472930i | ||||
\(11\) | 3.46919 | + | 2.00294i | 1.04600 | + | 0.603908i | 0.921527 | − | 0.388315i | \(-0.126943\pi\) |
0.124472 | + | 0.992223i | \(0.460276\pi\) | |||||||
\(12\) | 0.508912 | − | 0.293820i | 0.146910 | − | 0.0848187i | ||||
\(13\) | − | 5.60127i | − | 1.55351i | −0.629802 | − | 0.776756i | \(-0.716864\pi\) | ||
0.629802 | − | 0.776756i | \(-0.283136\pi\) | |||||||
\(14\) | −0.987361 | + | 2.45461i | −0.263883 | + | 0.656023i | ||||
\(15\) | − | 1.01480i | − | 0.262019i | ||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.91929 | − | 5.05637i | 0.708033 | − | 1.22635i | −0.257553 | − | 0.966264i | \(-0.582916\pi\) |
0.965586 | − | 0.260085i | \(-0.0837505\pi\) | |||||||
\(18\) | −1.32734 | + | 2.29902i | −0.312857 | + | 0.541884i | ||||
\(19\) | 0.863449 | + | 1.49554i | 0.198089 | + | 0.343100i | 0.947909 | − | 0.318542i | \(-0.103193\pi\) |
−0.749820 | + | 0.661642i | \(0.769860\pi\) | |||||||
\(20\) | −1.72690 | −0.386146 | ||||||||
\(21\) | 0.218735 | + | 1.53929i | 0.0477319 | + | 0.335900i | ||||
\(22\) | − | 4.00587i | − | 0.854054i | ||||||
\(23\) | 2.15076 | − | 4.28652i | 0.448464 | − | 0.893801i | ||||
\(24\) | −0.508912 | − | 0.293820i | −0.103881 | − | 0.0599758i | ||||
\(25\) | 1.00891 | − | 1.74749i | 0.201782 | − | 0.349497i | ||||
\(26\) | −4.85084 | + | 2.80063i | −0.951328 | + | 0.549249i | ||||
\(27\) | 3.32292i | 0.639496i | ||||||||
\(28\) | 2.61944 | − | 0.372226i | 0.495027 | − | 0.0703441i | ||||
\(29\) | −9.71950 | −1.80487 | −0.902433 | − | 0.430830i | \(-0.858221\pi\) | ||||
−0.902433 | + | 0.430830i | \(0.858221\pi\) | |||||||
\(30\) | −0.878839 | + | 0.507398i | −0.160453 | + | 0.0926378i | ||||
\(31\) | 3.47311 | + | 2.00520i | 0.623788 | + | 0.360144i | 0.778342 | − | 0.627840i | \(-0.216061\pi\) |
−0.154554 | + | 0.987984i | \(0.549394\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.17701 | − | 2.03864i | −0.204891 | − | 0.354881i | ||||
\(34\) | −5.83859 | −1.00131 | ||||||||
\(35\) | 1.70507 | − | 4.23886i | 0.288210 | − | 0.716499i | ||||
\(36\) | 2.65468 | 0.442446 | ||||||||
\(37\) | −7.43623 | + | 4.29331i | −1.22251 | + | 0.705816i | −0.965452 | − | 0.260581i | \(-0.916086\pi\) |
−0.257057 | + | 0.966396i | \(0.582753\pi\) | |||||||
\(38\) | 0.863449 | − | 1.49554i | 0.140070 | − | 0.242608i | ||||
\(39\) | −1.64577 | + | 2.85055i | −0.263534 | + | 0.456453i | ||||
\(40\) | 0.863449 | + | 1.49554i | 0.136523 | + | 0.236465i | ||||
\(41\) | − | 5.60127i | − | 0.874771i | −0.899274 | − | 0.437385i | \(-0.855905\pi\) | ||
0.899274 | − | 0.437385i | \(-0.144095\pi\) | |||||||
\(42\) | 1.22369 | − | 0.959074i | 0.188820 | − | 0.147988i | ||||
\(43\) | 3.11579i | 0.475153i | 0.971369 | + | 0.237577i | \(0.0763531\pi\) | ||||
−0.971369 | + | 0.237577i | \(0.923647\pi\) | |||||||
\(44\) | −3.46919 | + | 2.00294i | −0.522999 | + | 0.301954i | ||||
\(45\) | 2.29218 | − | 3.97017i | 0.341698 | − | 0.591838i | ||||
\(46\) | −4.78761 | + | 0.280648i | −0.705895 | + | 0.0413792i | ||||
\(47\) | 6.35084 | − | 3.66666i | 0.926365 | − | 0.534837i | 0.0407049 | − | 0.999171i | \(-0.487040\pi\) |
0.885660 | + | 0.464334i | \(0.153706\pi\) | |||||||
\(48\) | 0.587641i | 0.0848187i | ||||||||
\(49\) | −1.67266 | + | 6.79722i | −0.238952 | + | 0.971031i | ||||
\(50\) | −2.01782 | −0.285363 | ||||||||
\(51\) | −2.97133 | + | 1.71550i | −0.416069 | + | 0.240218i | ||||
\(52\) | 4.85084 | + | 2.80063i | 0.672690 | + | 0.388378i | ||||
\(53\) | 2.09249 | + | 1.20810i | 0.287425 | + | 0.165945i | 0.636780 | − | 0.771045i | \(-0.280266\pi\) |
−0.349355 | + | 0.936991i | \(0.613599\pi\) | |||||||
\(54\) | 2.87773 | − | 1.66146i | 0.391610 | − | 0.226096i | ||||
\(55\) | 6.91773i | 0.932786i | ||||||||
\(56\) | −1.63208 | − | 2.08239i | −0.218095 | − | 0.278271i | ||||
\(57\) | − | 1.01480i | − | 0.134413i | ||||||
\(58\) | 4.85975 | + | 8.41733i | 0.638116 | + | 1.10525i | ||||
\(59\) | 5.45528 | + | 3.14961i | 0.710217 | + | 0.410044i | 0.811141 | − | 0.584850i | \(-0.198847\pi\) |
−0.100924 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(60\) | 0.878839 | + | 0.507398i | 0.113458 | + | 0.0655048i | ||||
\(61\) | 1.19240 | + | 2.06529i | 0.152671 | + | 0.264433i | 0.932208 | − | 0.361922i | \(-0.117879\pi\) |
−0.779538 | + | 0.626355i | \(0.784546\pi\) | |||||||
\(62\) | − | 4.01040i | − | 0.509321i | ||||||
\(63\) | −2.62113 | + | 6.51620i | −0.330231 | + | 0.820964i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.37690 | − | 4.83641i | 1.03903 | − | 0.599882i | ||||
\(66\) | −1.17701 | + | 2.03864i | −0.144879 | + | 0.250939i | ||||
\(67\) | 9.25574 | + | 5.34380i | 1.13077 | + | 0.652850i | 0.944128 | − | 0.329579i | \(-0.106907\pi\) |
0.186641 | + | 0.982428i | \(0.440240\pi\) | |||||||
\(68\) | 2.91929 | + | 5.05637i | 0.354016 | + | 0.613174i | ||||
\(69\) | −2.35401 | + | 1.54952i | −0.283390 | + | 0.186541i | ||||
\(70\) | −4.52350 | + | 0.642796i | −0.540662 | + | 0.0768288i | ||||
\(71\) | 11.7373 | 1.39296 | 0.696482 | − | 0.717574i | \(-0.254748\pi\) | ||||
0.696482 | + | 0.717574i | \(0.254748\pi\) | |||||||
\(72\) | −1.32734 | − | 2.29902i | −0.156428 | − | 0.270942i | ||||
\(73\) | 3.47311 | + | 2.00520i | 0.406496 | + | 0.234691i | 0.689283 | − | 0.724492i | \(-0.257926\pi\) |
−0.282787 | + | 0.959183i | \(0.591259\pi\) | |||||||
\(74\) | 7.43623 | + | 4.29331i | 0.864444 | + | 0.499087i | ||||
\(75\) | −1.02689 | + | 0.592878i | −0.118576 | + | 0.0684596i | ||||
\(76\) | −1.72690 | −0.198089 | ||||||||
\(77\) | −1.49109 | − | 10.4931i | −0.169925 | − | 1.19580i | ||||
\(78\) | 3.29153 | 0.372693 | ||||||||
\(79\) | −8.75788 | + | 5.05637i | −0.985339 | + | 0.568886i | −0.903878 | − | 0.427791i | \(-0.859292\pi\) |
−0.0814611 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(80\) | 0.863449 | − | 1.49554i | 0.0965365 | − | 0.167206i | ||||
\(81\) | −3.00568 | + | 5.20598i | −0.333964 | + | 0.578443i | ||||
\(82\) | −4.85084 | + | 2.80063i | −0.535686 | + | 0.309278i | ||||
\(83\) | −14.8417 | −1.62909 | −0.814543 | − | 0.580103i | \(-0.803012\pi\) | ||||
−0.814543 | + | 0.580103i | \(0.803012\pi\) | |||||||
\(84\) | −1.44243 | − | 0.580214i | −0.157382 | − | 0.0633065i | ||||
\(85\) | 10.0826 | 1.09362 | ||||||||
\(86\) | 2.69835 | − | 1.55789i | 0.290971 | − | 0.167992i | ||||
\(87\) | 4.94637 | + | 2.85579i | 0.530306 | + | 0.306173i | ||||
\(88\) | 3.46919 | + | 2.00294i | 0.369816 | + | 0.213514i | ||||
\(89\) | −7.80182 | − | 13.5131i | −0.826991 | − | 1.43239i | −0.900388 | − | 0.435088i | \(-0.856717\pi\) |
0.0733966 | − | 0.997303i | \(-0.476616\pi\) | |||||||
\(90\) | −4.58436 | −0.483234 | ||||||||
\(91\) | −11.6640 | + | 9.14169i | −1.22272 | + | 0.958309i | ||||
\(92\) | 2.63685 | + | 4.00587i | 0.274911 | + | 0.417641i | ||||
\(93\) | −1.17834 | − | 2.04094i | −0.122188 | − | 0.211635i | ||||
\(94\) | −6.35084 | − | 3.66666i | −0.655039 | − | 0.378187i | ||||
\(95\) | −1.49109 | + | 2.58264i | −0.152982 | + | 0.264973i | ||||
\(96\) | 0.508912 | − | 0.293820i | 0.0519406 | − | 0.0299879i | ||||
\(97\) | 15.4996 | 1.57374 | 0.786872 | − | 0.617117i | \(-0.211699\pi\) | ||||
0.786872 | + | 0.617117i | \(0.211699\pi\) | |||||||
\(98\) | 6.72290 | − | 1.95004i | 0.679115 | − | 0.196984i | ||||
\(99\) | − | 10.6343i | − | 1.06879i | ||||||
\(100\) | 1.00891 | + | 1.74749i | 0.100891 | + | 0.174749i | ||||
\(101\) | 1.47326 | + | 0.850590i | 0.146595 | + | 0.0846368i | 0.571504 | − | 0.820600i | \(-0.306360\pi\) |
−0.424908 | + | 0.905236i | \(0.639694\pi\) | |||||||
\(102\) | 2.97133 | + | 1.71550i | 0.294205 | + | 0.169859i | ||||
\(103\) | −3.14024 | − | 5.43905i | −0.309417 | − | 0.535926i | 0.668818 | − | 0.743426i | \(-0.266801\pi\) |
−0.978235 | + | 0.207500i | \(0.933467\pi\) | |||||||
\(104\) | − | 5.60127i | − | 0.549249i | ||||||
\(105\) | −2.11320 | + | 1.65622i | −0.206227 | + | 0.161631i | ||||
\(106\) | − | 2.41620i | − | 0.234682i | ||||||
\(107\) | −9.14774 | + | 5.28145i | −0.884345 | + | 0.510577i | −0.872089 | − | 0.489348i | \(-0.837235\pi\) |
−0.0122565 | + | 0.999925i | \(0.503901\pi\) | |||||||
\(108\) | −2.87773 | − | 1.66146i | −0.276910 | − | 0.159874i | ||||
\(109\) | 0.770835 | + | 0.445042i | 0.0738326 | + | 0.0426273i | 0.536462 | − | 0.843925i | \(-0.319761\pi\) |
−0.462629 | + | 0.886552i | \(0.653094\pi\) | |||||||
\(110\) | 5.99093 | − | 3.45886i | 0.571213 | − | 0.329790i | ||||
\(111\) | 5.04585 | 0.478931 | ||||||||
\(112\) | −0.987361 | + | 2.45461i | −0.0932969 | + | 0.231939i | ||||
\(113\) | 20.5509i | 1.93327i | 0.256162 | + | 0.966634i | \(0.417542\pi\) | ||||
−0.256162 | + | 0.966634i | \(0.582458\pi\) | |||||||
\(114\) | −0.878839 | + | 0.507398i | −0.0823108 | + | 0.0475222i | ||||
\(115\) | 8.26772 | − | 0.484650i | 0.770969 | − | 0.0451938i | ||||
\(116\) | 4.85975 | − | 8.41733i | 0.451216 | − | 0.781530i | ||||
\(117\) | −12.8774 | + | 7.43478i | −1.19052 | + | 0.687346i | ||||
\(118\) | − | 6.29922i | − | 0.579890i | ||||||
\(119\) | −15.2938 | + | 2.17327i | −1.40198 | + | 0.199224i | ||||
\(120\) | − | 1.01480i | − | 0.0926378i | ||||||
\(121\) | 2.52350 | + | 4.37083i | 0.229409 | + | 0.397348i | ||||
\(122\) | 1.19240 | − | 2.06529i | 0.107955 | − | 0.186983i | ||||
\(123\) | −1.64577 | + | 2.85055i | −0.148394 | + | 0.257026i | ||||
\(124\) | −3.47311 | + | 2.00520i | −0.311894 | + | 0.180072i | ||||
\(125\) | 12.1191 | 1.08396 | ||||||||
\(126\) | 6.95376 | − | 0.988140i | 0.619490 | − | 0.0880305i | ||||
\(127\) | −16.7195 | −1.48362 | −0.741808 | − | 0.670612i | \(-0.766031\pi\) | ||||
−0.741808 | + | 0.670612i | \(0.766031\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0.915482 | − | 1.58566i | 0.0806037 | − | 0.139610i | ||||
\(130\) | −8.37690 | − | 4.83641i | −0.734703 | − | 0.424181i | ||||
\(131\) | 5.41948 | − | 3.12894i | 0.473502 | − | 0.273376i | −0.244203 | − | 0.969724i | \(-0.578526\pi\) |
0.717704 | + | 0.696348i | \(0.245193\pi\) | |||||||
\(132\) | 2.35401 | 0.204891 | ||||||||
\(133\) | 1.70507 | − | 4.23886i | 0.147849 | − | 0.367556i | ||||
\(134\) | − | 10.6876i | − | 0.923269i | ||||||
\(135\) | −4.96955 | + | 2.86917i | −0.427711 | + | 0.246939i | ||||
\(136\) | 2.91929 | − | 5.05637i | 0.250327 | − | 0.433580i | ||||
\(137\) | 6.55739 | + | 3.78591i | 0.560236 | + | 0.323452i | 0.753240 | − | 0.657746i | \(-0.228490\pi\) |
−0.193004 | + | 0.981198i | \(0.561823\pi\) | |||||||
\(138\) | 2.51893 | + | 1.26387i | 0.214426 | + | 0.107588i | ||||
\(139\) | 11.0200i | 0.934705i | 0.884071 | + | 0.467352i | \(0.154792\pi\) | ||||
−0.884071 | + | 0.467352i | \(0.845208\pi\) | |||||||
\(140\) | 2.81843 | + | 3.59607i | 0.238201 | + | 0.303923i | ||||
\(141\) | −4.30936 | −0.362913 | ||||||||
\(142\) | −5.86866 | − | 10.1648i | −0.492487 | − | 0.853013i | ||||
\(143\) | 11.2190 | − | 19.4318i | 0.938178 | − | 1.62497i | ||||
\(144\) | −1.32734 | + | 2.29902i | −0.110612 | + | 0.191585i | ||||
\(145\) | −8.39229 | − | 14.5359i | −0.696942 | − | 1.20714i | ||||
\(146\) | − | 4.01040i | − | 0.331903i | ||||||
\(147\) | 2.84840 | − | 2.96772i | 0.234932 | − | 0.244774i | ||||
\(148\) | − | 8.58662i | − | 0.705816i | ||||||
\(149\) | 6.93837 | − | 4.00587i | 0.568414 | − | 0.328174i | −0.188102 | − | 0.982150i | \(-0.560234\pi\) |
0.756515 | + | 0.653976i | \(0.226900\pi\) | |||||||
\(150\) | 1.02689 | + | 0.592878i | 0.0838456 | + | 0.0484083i | ||||
\(151\) | −5.15468 | + | 8.92816i | −0.419482 | + | 0.726564i | −0.995887 | − | 0.0906000i | \(-0.971122\pi\) |
0.576406 | + | 0.817164i | \(0.304455\pi\) | |||||||
\(152\) | 0.863449 | + | 1.49554i | 0.0700350 | + | 0.121304i | ||||
\(153\) | −15.4996 | −1.25307 | ||||||||
\(154\) | −8.34177 | + | 6.53788i | −0.672199 | + | 0.526838i | ||||
\(155\) | 6.92555i | 0.556273i | ||||||||
\(156\) | −1.64577 | − | 2.85055i | −0.131767 | − | 0.228227i | ||||
\(157\) | 4.04427 | − | 7.00488i | 0.322768 | − | 0.559050i | −0.658290 | − | 0.752764i | \(-0.728720\pi\) |
0.981058 | + | 0.193714i | \(0.0620534\pi\) | |||||||
\(158\) | 8.75788 | + | 5.05637i | 0.696740 | + | 0.402263i | ||||
\(159\) | −0.709928 | − | 1.22963i | −0.0563010 | − | 0.0975161i | ||||
\(160\) | −1.72690 | −0.136523 | ||||||||
\(161\) | −12.4364 | + | 2.51721i | −0.980124 | + | 0.198384i | ||||
\(162\) | 6.01135 | 0.472296 | ||||||||
\(163\) | 0.672661 | + | 1.16508i | 0.0526869 | + | 0.0912563i | 0.891166 | − | 0.453677i | \(-0.149888\pi\) |
−0.838479 | + | 0.544934i | \(0.816555\pi\) | |||||||
\(164\) | 4.85084 | + | 2.80063i | 0.378787 | + | 0.218693i | ||||
\(165\) | 2.03257 | − | 3.52051i | 0.158235 | − | 0.274072i | ||||
\(166\) | 7.42084 | + | 12.8533i | 0.575969 | + | 0.997607i | ||||
\(167\) | − | 17.0172i | − | 1.31683i | −0.752655 | − | 0.658415i | \(-0.771227\pi\) | ||
0.752655 | − | 0.658415i | \(-0.228773\pi\) | |||||||
\(168\) | 0.218735 | + | 1.53929i | 0.0168758 | + | 0.118759i | ||||
\(169\) | −18.3742 | −1.41340 | ||||||||
\(170\) | −5.04132 | − | 8.73183i | −0.386652 | − | 0.669701i | ||||
\(171\) | 2.29218 | − | 3.97017i | 0.175287 | − | 0.303607i | ||||
\(172\) | −2.69835 | − | 1.55789i | −0.205747 | − | 0.118788i | ||||
\(173\) | 4.41072 | − | 2.54653i | 0.335341 | − | 0.193609i | −0.322869 | − | 0.946444i | \(-0.604647\pi\) |
0.658210 | + | 0.752834i | \(0.271314\pi\) | |||||||
\(174\) | − | 5.71158i | − | 0.432993i | ||||||
\(175\) | −5.28556 | + | 0.751086i | −0.399551 | + | 0.0567768i | ||||
\(176\) | − | 4.00587i | − | 0.301954i | ||||||
\(177\) | −1.85084 | − | 3.20575i | −0.139118 | − | 0.240959i | ||||
\(178\) | −7.80182 | + | 13.5131i | −0.584771 | + | 1.01285i | ||||
\(179\) | −3.82734 | + | 6.62915i | −0.286069 | + | 0.495486i | −0.972868 | − | 0.231362i | \(-0.925682\pi\) |
0.686799 | + | 0.726847i | \(0.259015\pi\) | |||||||
\(180\) | 2.29218 | + | 3.97017i | 0.170849 | + | 0.295919i | ||||
\(181\) | −10.9152 | −0.811322 | −0.405661 | − | 0.914024i | \(-0.632959\pi\) | ||||
−0.405661 | + | 0.914024i | \(0.632959\pi\) | |||||||
\(182\) | 13.7489 | + | 5.53047i | 1.01914 | + | 0.409946i | ||||
\(183\) | − | 1.40140i | − | 0.103595i | ||||||
\(184\) | 2.15076 | − | 4.28652i | 0.158556 | − | 0.316006i | ||||
\(185\) | −12.8416 | − | 7.41411i | −0.944134 | − | 0.545096i | ||||
\(186\) | −1.17834 | + | 2.04094i | −0.0863998 | + | 0.149649i | ||||
\(187\) | 20.2551 | − | 11.6943i | 1.48120 | − | 0.855173i | ||||
\(188\) | 7.33332i | 0.534837i | ||||||||
\(189\) | 6.91960 | − | 5.42326i | 0.503327 | − | 0.394484i | ||||
\(190\) | 2.98218 | 0.216350 | ||||||||
\(191\) | 8.64988 | − | 4.99401i | 0.625883 | − | 0.361354i | −0.153273 | − | 0.988184i | \(-0.548981\pi\) |
0.779156 | + | 0.626830i | \(0.215648\pi\) | |||||||
\(192\) | −0.508912 | − | 0.293820i | −0.0367276 | − | 0.0212047i | ||||
\(193\) | 10.3150 | − | 17.8662i | 0.742492 | − | 1.28603i | −0.208865 | − | 0.977944i | \(-0.566977\pi\) |
0.951357 | − | 0.308090i | \(-0.0996897\pi\) | |||||||
\(194\) | −7.74979 | − | 13.4230i | −0.556402 | − | 0.963717i | ||||
\(195\) | −5.68414 | −0.407050 | ||||||||
\(196\) | −5.05024 | − | 4.84718i | −0.360731 | − | 0.346227i | ||||
\(197\) | 5.41662 | 0.385918 | 0.192959 | − | 0.981207i | \(-0.438192\pi\) | ||||
0.192959 | + | 0.981207i | \(0.438192\pi\) | |||||||
\(198\) | −9.20957 | + | 5.31715i | −0.654496 | + | 0.377873i | ||||
\(199\) | 3.50583 | − | 6.07227i | 0.248522 | − | 0.430452i | −0.714594 | − | 0.699539i | \(-0.753389\pi\) |
0.963116 | + | 0.269087i | \(0.0867220\pi\) | |||||||
\(200\) | 1.00891 | − | 1.74749i | 0.0713408 | − | 0.123566i | ||||
\(201\) | −3.14024 | − | 5.43905i | −0.221495 | − | 0.383641i | ||||
\(202\) | − | 1.70118i | − | 0.119695i | ||||||
\(203\) | 15.8630 | + | 20.2398i | 1.11336 | + | 1.42055i | ||||
\(204\) | − | 3.43099i | − | 0.240218i | ||||||
\(205\) | 8.37690 | − | 4.83641i | 0.585068 | − | 0.337789i | ||||
\(206\) | −3.14024 | + | 5.43905i | −0.218791 | + | 0.378957i | ||||
\(207\) | −12.7096 | + | 0.745029i | −0.883376 | + | 0.0517831i | ||||
\(208\) | −4.85084 | + | 2.80063i | −0.336345 | + | 0.194189i | ||||
\(209\) | 6.91773i | 0.478509i | ||||||||
\(210\) | 2.49093 | + | 1.00197i | 0.171890 | + | 0.0691425i | ||||
\(211\) | 3.97539 | 0.273677 | 0.136838 | − | 0.990593i | \(-0.456306\pi\) | ||||
0.136838 | + | 0.990593i | \(0.456306\pi\) | |||||||
\(212\) | −2.09249 | + | 1.20810i | −0.143713 | + | 0.0829726i | ||||
\(213\) | −5.97326 | − | 3.44867i | −0.409281 | − | 0.236299i | ||||
\(214\) | 9.14774 | + | 5.28145i | 0.625326 | + | 0.361032i | ||||
\(215\) | −4.65978 | + | 2.69032i | −0.317794 | + | 0.183479i | ||||
\(216\) | 3.32292i | 0.226096i | ||||||||
\(217\) | −1.49277 | − | 10.5050i | −0.101336 | − | 0.713124i | ||||
\(218\) | − | 0.890083i | − | 0.0602841i | ||||||
\(219\) | −1.17834 | − | 2.04094i | −0.0796246 | − | 0.137914i | ||||
\(220\) | −5.99093 | − | 3.45886i | −0.403908 | − | 0.233197i | ||||
\(221\) | −28.3221 | − | 16.3517i | −1.90515 | − | 1.09994i | ||||
\(222\) | −2.52292 | − | 4.36983i | −0.169328 | − | 0.293284i | ||||
\(223\) | 11.2439i | 0.752946i | 0.926428 | + | 0.376473i | \(0.122863\pi\) | ||||
−0.926428 | + | 0.376473i | \(0.877137\pi\) | |||||||
\(224\) | 2.61944 | − | 0.372226i | 0.175018 | − | 0.0248704i | ||||
\(225\) | −5.35667 | −0.357112 | ||||||||
\(226\) | 17.7976 | − | 10.2755i | 1.18388 | − | 0.683513i | ||||
\(227\) | −7.19990 | + | 12.4706i | −0.477874 | + | 0.827702i | −0.999678 | − | 0.0253633i | \(-0.991926\pi\) |
0.521804 | + | 0.853065i | \(0.325259\pi\) | |||||||
\(228\) | 0.878839 | + | 0.507398i | 0.0582025 | + | 0.0336032i | ||||
\(229\) | 10.6537 | + | 18.4527i | 0.704016 | + | 1.21939i | 0.967046 | + | 0.254603i | \(0.0819449\pi\) |
−0.263030 | + | 0.964788i | \(0.584722\pi\) | |||||||
\(230\) | −4.55358 | − | 6.91773i | −0.300254 | − | 0.456142i | ||||
\(231\) | −2.32426 | + | 5.77819i | −0.152925 | + | 0.380177i | ||||
\(232\) | −9.71950 | −0.638116 | ||||||||
\(233\) | 3.74697 | + | 6.48995i | 0.245472 | + | 0.425171i | 0.962264 | − | 0.272116i | \(-0.0877236\pi\) |
−0.716792 | + | 0.697287i | \(0.754390\pi\) | |||||||
\(234\) | 12.8774 | + | 7.43478i | 0.841823 | + | 0.486027i | ||||
\(235\) | 10.9672 | + | 6.33194i | 0.715424 | + | 0.413051i | ||||
\(236\) | −5.45528 | + | 3.14961i | −0.355109 | + | 0.205022i | ||||
\(237\) | 5.94265 | 0.386017 | ||||||||
\(238\) | 9.52902 | + | 12.1582i | 0.617674 | + | 0.788099i | ||||
\(239\) | −8.53607 | −0.552152 | −0.276076 | − | 0.961136i | \(-0.589034\pi\) | ||||
−0.276076 | + | 0.961136i | \(0.589034\pi\) | |||||||
\(240\) | −0.878839 | + | 0.507398i | −0.0567288 | + | 0.0327524i | ||||
\(241\) | −14.1595 | + | 24.5250i | −0.912095 | + | 1.57979i | −0.100995 | + | 0.994887i | \(0.532203\pi\) |
−0.811100 | + | 0.584908i | \(0.801131\pi\) | |||||||
\(242\) | 2.52350 | − | 4.37083i | 0.162217 | − | 0.280968i | ||||
\(243\) | 11.6924 | − | 6.75064i | 0.750071 | − | 0.433054i | ||||
\(244\) | −2.38479 | −0.152671 | ||||||||
\(245\) | −11.6098 | + | 3.36753i | −0.741720 | + | 0.215143i | ||||
\(246\) | 3.29153 | 0.209860 | ||||||||
\(247\) | 8.37690 | − | 4.83641i | 0.533010 | − | 0.307733i | ||||
\(248\) | 3.47311 | + | 2.00520i | 0.220542 | + | 0.127330i | ||||
\(249\) | 7.55311 | + | 4.36079i | 0.478659 | + | 0.276354i | ||||
\(250\) | −6.05953 | − | 10.4954i | −0.383238 | − | 0.663789i | ||||
\(251\) | 22.9918 | 1.45123 | 0.725614 | − | 0.688102i | \(-0.241556\pi\) | ||||
0.725614 | + | 0.688102i | \(0.241556\pi\) | |||||||
\(252\) | −4.33263 | − | 5.52806i | −0.272930 | − | 0.348235i | ||||
\(253\) | 16.0470 | − | 10.5629i | 1.00887 | − | 0.664084i | ||||
\(254\) | 8.35975 | + | 14.4795i | 0.524537 | + | 0.908525i | ||||
\(255\) | −5.13118 | − | 2.96249i | −0.321327 | − | 0.185518i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 24.3952 | − | 14.0846i | 1.52173 | − | 0.878573i | 0.522063 | − | 0.852907i | \(-0.325163\pi\) |
0.999671 | − | 0.0256659i | \(-0.00817062\pi\) | |||||||
\(258\) | −1.83096 | −0.113991 | ||||||||
\(259\) | 21.0768 | + | 8.47810i | 1.30965 | + | 0.526803i | ||||
\(260\) | 9.67281i | 0.599882i | ||||||||
\(261\) | 12.9011 | + | 22.3453i | 0.798556 | + | 1.38314i | ||||
\(262\) | −5.41948 | − | 3.12894i | −0.334816 | − | 0.193306i | ||||
\(263\) | 4.84588 | + | 2.79777i | 0.298810 | + | 0.172518i | 0.641908 | − | 0.766782i | \(-0.278143\pi\) |
−0.343098 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(264\) | −1.17701 | − | 2.03864i | −0.0724397 | − | 0.125469i | ||||
\(265\) | 4.17253i | 0.256316i | ||||||||
\(266\) | −4.52350 | + | 0.642796i | −0.277354 | + | 0.0394123i | ||||
\(267\) | 9.16934i | 0.561154i | ||||||||
\(268\) | −9.25574 | + | 5.34380i | −0.565384 | + | 0.326425i | ||||
\(269\) | −7.02689 | − | 4.05698i | −0.428437 | − | 0.247358i | 0.270243 | − | 0.962792i | \(-0.412896\pi\) |
−0.698681 | + | 0.715434i | \(0.746229\pi\) | |||||||
\(270\) | 4.96955 | + | 2.86917i | 0.302437 | + | 0.174612i | ||||
\(271\) | −9.30596 | + | 5.37280i | −0.565297 | + | 0.326374i | −0.755269 | − | 0.655415i | \(-0.772494\pi\) |
0.189972 | + | 0.981790i | \(0.439160\pi\) | |||||||
\(272\) | −5.83859 | −0.354016 | ||||||||
\(273\) | 8.62196 | − | 1.22519i | 0.521825 | − | 0.0741521i | ||||
\(274\) | − | 7.57182i | − | 0.457431i | ||||||
\(275\) | 7.00021 | − | 4.04157i | 0.422128 | − | 0.243716i | ||||
\(276\) | −0.164920 | − | 2.81340i | −0.00992702 | − | 0.169347i | ||||
\(277\) | −3.43136 | + | 5.94330i | −0.206171 | + | 0.357098i | −0.950505 | − | 0.310709i | \(-0.899434\pi\) |
0.744334 | + | 0.667807i | \(0.232767\pi\) | |||||||
\(278\) | 9.54360 | − | 5.51000i | 0.572387 | − | 0.330468i | ||||
\(279\) | − | 10.6463i | − | 0.637378i | ||||||
\(280\) | 1.70507 | − | 4.23886i | 0.101898 | − | 0.253321i | ||||
\(281\) | 4.76100i | 0.284017i | 0.989865 | + | 0.142009i | \(0.0453561\pi\) | ||||
−0.989865 | + | 0.142009i | \(0.954644\pi\) | |||||||
\(282\) | 2.15468 | + | 3.73201i | 0.128309 | + | 0.222238i | ||||
\(283\) | −4.69823 | + | 8.13756i | −0.279280 | + | 0.483728i | −0.971206 | − | 0.238241i | \(-0.923429\pi\) |
0.691926 | + | 0.721969i | \(0.256763\pi\) | |||||||
\(284\) | −5.86866 | + | 10.1648i | −0.348241 | + | 0.603171i | ||||
\(285\) | 1.51766 | − | 0.876224i | 0.0898987 | − | 0.0519030i | ||||
\(286\) | −22.4379 | −1.32678 | ||||||||
\(287\) | −11.6640 | + | 9.14169i | −0.688504 | + | 0.539617i | ||||
\(288\) | 2.65468 | 0.156428 | ||||||||
\(289\) | −8.54456 | − | 14.7996i | −0.502621 | − | 0.870565i | ||||
\(290\) | −8.39229 | + | 14.5359i | −0.492812 | + | 0.853576i | ||||
\(291\) | −7.88792 | − | 4.55409i | −0.462398 | − | 0.266966i | ||||
\(292\) | −3.47311 | + | 2.00520i | −0.203248 | + | 0.117345i | ||||
\(293\) | 10.7608 | 0.628651 | 0.314325 | − | 0.949315i | \(-0.398222\pi\) | ||||
0.314325 | + | 0.949315i | \(0.398222\pi\) | |||||||
\(294\) | −3.99432 | − | 0.982924i | −0.232954 | − | 0.0573253i | ||||
\(295\) | 10.8781i | 0.633348i | ||||||||
\(296\) | −7.43623 | + | 4.29331i | −0.432222 | + | 0.249544i | ||||
\(297\) | −6.65559 | + | 11.5278i | −0.386197 | + | 0.668912i | ||||
\(298\) | −6.93837 | − | 4.00587i | −0.401929 | − | 0.232054i | ||||
\(299\) | −24.0099 | − | 12.0470i | −1.38853 | − | 0.696694i | ||||
\(300\) | − | 1.18576i | − | 0.0684596i | ||||||
\(301\) | 6.48827 | − | 5.08520i | 0.373978 | − | 0.293106i | ||||
\(302\) | 10.3094 | 0.593237 | ||||||||
\(303\) | −0.499841 | − | 0.865750i | −0.0287151 | − | 0.0497361i | ||||
\(304\) | 0.863449 | − | 1.49554i | 0.0495222 | − | 0.0857750i | ||||
\(305\) | −2.05915 | + | 3.56655i | −0.117906 | + | 0.204220i | ||||
\(306\) | 7.74979 | + | 13.4230i | 0.443026 | + | 0.767343i | ||||
\(307\) | − | 16.7244i | − | 0.954510i | −0.878765 | − | 0.477255i | \(-0.841632\pi\) | ||
0.878765 | − | 0.477255i | \(-0.158368\pi\) | |||||||
\(308\) | 9.83286 | + | 3.95524i | 0.560279 | + | 0.225371i | ||||
\(309\) | 3.69066i | 0.209955i | ||||||||
\(310\) | 5.99770 | − | 3.46277i | 0.340646 | − | 0.196672i | ||||
\(311\) | 18.8865 | + | 10.9041i | 1.07095 | + | 0.618316i | 0.928442 | − | 0.371477i | \(-0.121149\pi\) |
0.142512 | + | 0.989793i | \(0.454482\pi\) | |||||||
\(312\) | −1.64577 | + | 2.85055i | −0.0931732 | + | 0.161381i | ||||
\(313\) | 0.144647 | + | 0.250536i | 0.00817593 | + | 0.0141611i | 0.870084 | − | 0.492903i | \(-0.164064\pi\) |
−0.861908 | + | 0.507064i | \(0.830731\pi\) | |||||||
\(314\) | −8.08854 | −0.456462 | ||||||||
\(315\) | −12.0084 | + | 1.70642i | −0.676599 | + | 0.0961457i | ||||
\(316\) | − | 10.1127i | − | 0.568886i | ||||||
\(317\) | 2.35651 | + | 4.08160i | 0.132355 | + | 0.229246i | 0.924584 | − | 0.380978i | \(-0.124413\pi\) |
−0.792229 | + | 0.610224i | \(0.791079\pi\) | |||||||
\(318\) | −0.709928 | + | 1.22963i | −0.0398108 | + | 0.0689543i | ||||
\(319\) | −33.7188 | − | 19.4675i | −1.88789 | − | 1.08997i | ||||
\(320\) | 0.863449 | + | 1.49554i | 0.0482683 | + | 0.0836031i | ||||
\(321\) | 6.20719 | 0.346452 | ||||||||
\(322\) | 8.39816 | + | 9.51162i | 0.468011 | + | 0.530062i | ||||
\(323\) | 10.0826 | 0.561013 | ||||||||
\(324\) | −3.00568 | − | 5.20598i | −0.166982 | − | 0.289221i | ||||
\(325\) | −9.78814 | − | 5.65118i | −0.542948 | − | 0.313471i | ||||
\(326\) | 0.672661 | − | 1.16508i | 0.0372552 | − | 0.0645280i | ||||
\(327\) | −0.261525 | − | 0.452974i | −0.0144623 | − | 0.0250495i | ||||
\(328\) | − | 5.60127i | − | 0.309278i | ||||||
\(329\) | −18.0004 | − | 7.24063i | −0.992397 | − | 0.399189i | ||||
\(330\) | −4.06514 | −0.223779 | ||||||||
\(331\) | 5.64237 | + | 9.77287i | 0.310133 | + | 0.537166i | 0.978391 | − | 0.206764i | \(-0.0662932\pi\) |
−0.668258 | + | 0.743929i | \(0.732960\pi\) | |||||||
\(332\) | 7.42084 | − | 12.8533i | 0.407271 | − | 0.705415i | ||||
\(333\) | 19.7408 | + | 11.3974i | 1.08179 | + | 0.624571i | ||||
\(334\) | −14.7373 | + | 8.50860i | −0.806391 | + | 0.465570i | ||||
\(335\) | 18.4564i | 1.00838i | ||||||||
\(336\) | 1.22369 | − | 0.959074i | 0.0667580 | − | 0.0523218i | ||||
\(337\) | 8.65802i | 0.471632i | 0.971798 | + | 0.235816i | \(0.0757763\pi\) | ||||
−0.971798 | + | 0.235816i | \(0.924224\pi\) | |||||||
\(338\) | 9.18709 | + | 15.9125i | 0.499712 | + | 0.865526i | ||||
\(339\) | 6.03828 | − | 10.4586i | 0.327954 | − | 0.568034i | ||||
\(340\) | −5.04132 | + | 8.73183i | −0.273404 | + | 0.473550i | ||||
\(341\) | 8.03257 | + | 13.9128i | 0.434988 | + | 0.753421i | ||||
\(342\) | −4.58436 | −0.247894 | ||||||||
\(343\) | 16.8843 | − | 7.61045i | 0.911669 | − | 0.410926i | ||||
\(344\) | 3.11579i | 0.167992i | ||||||||
\(345\) | −4.34994 | − | 2.18258i | −0.234193 | − | 0.117506i | ||||
\(346\) | −4.41072 | − | 2.54653i | −0.237122 | − | 0.136902i | ||||
\(347\) | 15.5647 | − | 26.9588i | 0.835555 | − | 1.44722i | −0.0580229 | − | 0.998315i | \(-0.518480\pi\) |
0.893578 | − | 0.448908i | \(-0.148187\pi\) | |||||||
\(348\) | −4.94637 | + | 2.85579i | −0.265153 | + | 0.153086i | ||||
\(349\) | − | 3.74843i | − | 0.200649i | −0.994955 | − | 0.100324i | \(-0.968012\pi\) | ||
0.994955 | − | 0.100324i | \(-0.0319881\pi\) | |||||||
\(350\) | 3.29324 | + | 4.20189i | 0.176031 | + | 0.224600i | ||||
\(351\) | 18.6126 | 0.993465 | ||||||||
\(352\) | −3.46919 | + | 2.00294i | −0.184908 | + | 0.106757i | ||||
\(353\) | −1.18215 | − | 0.682515i | −0.0629195 | − | 0.0363266i | 0.468210 | − | 0.883617i | \(-0.344899\pi\) |
−0.531130 | + | 0.847291i | \(0.678232\pi\) | |||||||
\(354\) | −1.85084 | + | 3.20575i | −0.0983710 | + | 0.170383i | ||||
\(355\) | 10.1346 | + | 17.5536i | 0.537888 | + | 0.931649i | ||||
\(356\) | 15.6036 | 0.826991 | ||||||||
\(357\) | 8.42176 | + | 3.38763i | 0.445727 | + | 0.179292i | ||||
\(358\) | 7.65468 | 0.404562 | ||||||||
\(359\) | −2.92323 | + | 1.68773i | −0.154282 | + | 0.0890749i | −0.575154 | − | 0.818045i | \(-0.695058\pi\) |
0.420871 | + | 0.907120i | \(0.361724\pi\) | |||||||
\(360\) | 2.29218 | − | 3.97017i | 0.120808 | − | 0.209246i | ||||
\(361\) | 8.00891 | − | 13.8718i | 0.421522 | − | 0.730097i | ||||
\(362\) | 5.45761 | + | 9.45285i | 0.286846 | + | 0.496831i | ||||
\(363\) | − | 2.96582i | − | 0.155665i | ||||||
\(364\) | −2.08494 | − | 14.6722i | −0.109280 | − | 0.769030i | ||||
\(365\) | 6.92555i | 0.362500i | ||||||||
\(366\) | −1.21365 | + | 0.700701i | −0.0634385 | + | 0.0366262i | ||||
\(367\) | −6.79372 | + | 11.7671i | −0.354630 | + | 0.614236i | −0.987054 | − | 0.160385i | \(-0.948726\pi\) |
0.632425 | + | 0.774622i | \(0.282060\pi\) | |||||||
\(368\) | −4.78761 | + | 0.280648i | −0.249572 | + | 0.0146298i | ||||
\(369\) | −12.8774 | + | 7.43478i | −0.670371 | + | 0.387039i | ||||
\(370\) | 14.8282i | 0.770882i | ||||||||
\(371\) | −0.899371 | − | 6.32908i | −0.0466930 | − | 0.328589i | ||||
\(372\) | 2.35667 | 0.122188 | ||||||||
\(373\) | 9.92344 | − | 5.72930i | 0.513816 | − | 0.296652i | −0.220585 | − | 0.975368i | \(-0.570797\pi\) |
0.734401 | + | 0.678716i | \(0.237463\pi\) | |||||||
\(374\) | −20.2551 | − | 11.6943i | −1.04737 | − | 0.604699i | ||||
\(375\) | −6.16754 | − | 3.56083i | −0.318490 | − | 0.183880i | ||||
\(376\) | 6.35084 | − | 3.66666i | 0.327519 | − | 0.189093i | ||||
\(377\) | 54.4415i | 2.80388i | ||||||||
\(378\) | −8.15648 | − | 3.28092i | −0.419524 | − | 0.168752i | ||||
\(379\) | − | 3.50239i | − | 0.179906i | −0.995946 | − | 0.0899529i | \(-0.971328\pi\) | ||
0.995946 | − | 0.0899529i | \(-0.0286717\pi\) | |||||||
\(380\) | −1.49109 | − | 2.58264i | −0.0764912 | − | 0.132487i | ||||
\(381\) | 8.50875 | + | 4.91253i | 0.435917 | + | 0.251677i | ||||
\(382\) | −8.64988 | − | 4.99401i | −0.442566 | − | 0.255516i | ||||
\(383\) | −8.13077 | − | 14.0829i | −0.415463 | − | 0.719603i | 0.580014 | − | 0.814606i | \(-0.303047\pi\) |
−0.995477 | + | 0.0950037i | \(0.969714\pi\) | |||||||
\(384\) | 0.587641i | 0.0299879i | ||||||||
\(385\) | 14.4054 | − | 11.2903i | 0.734166 | − | 0.575405i | ||||
\(386\) | −20.6301 | −1.05004 | ||||||||
\(387\) | 7.16325 | − | 4.13571i | 0.364129 | − | 0.210230i | ||||
\(388\) | −7.74979 | + | 13.4230i | −0.393436 | + | 0.681451i | ||||
\(389\) | −16.3502 | − | 9.43980i | −0.828989 | − | 0.478617i | 0.0245176 | − | 0.999699i | \(-0.492195\pi\) |
−0.853506 | + | 0.521083i | \(0.825528\pi\) | |||||||
\(390\) | 2.84207 | + | 4.92261i | 0.143914 | + | 0.249266i | ||||
\(391\) | −15.3955 | − | 23.3886i | −0.778584 | − | 1.18281i | ||||
\(392\) | −1.67266 | + | 6.79722i | −0.0844821 | + | 0.343311i | ||||
\(393\) | −3.67738 | −0.185499 | ||||||||
\(394\) | −2.70831 | − | 4.69093i | −0.136443 | − | 0.236326i | ||||
\(395\) | −15.1240 | − | 8.73183i | −0.760969 | − | 0.439346i | ||||
\(396\) | 9.20957 | + | 5.31715i | 0.462798 | + | 0.267197i | ||||
\(397\) | −23.1989 | + | 13.3939i | −1.16432 | + | 0.672219i | −0.952335 | − | 0.305055i | \(-0.901325\pi\) |
−0.211982 | + | 0.977273i | \(0.567992\pi\) | |||||||
\(398\) | −7.01166 | −0.351463 | ||||||||
\(399\) | −2.11320 | + | 1.65622i | −0.105792 | + | 0.0829149i | ||||
\(400\) | −2.01782 | −0.100891 | ||||||||
\(401\) | −3.02637 | + | 1.74728i | −0.151130 | + | 0.0872548i | −0.573658 | − | 0.819095i | \(-0.694476\pi\) |
0.422528 | + | 0.906350i | \(0.361143\pi\) | |||||||
\(402\) | −3.14024 | + | 5.43905i | −0.156621 | + | 0.271275i | ||||
\(403\) | 11.2316 | − | 19.4538i | 0.559488 | − | 0.969062i | ||||
\(404\) | −1.47326 | + | 0.850590i | −0.0732976 | + | 0.0423184i | ||||
\(405\) | −10.3810 | −0.515836 | ||||||||
\(406\) | 9.59666 | − | 23.8576i | 0.476274 | − | 1.18403i | ||||
\(407\) | −34.3969 | −1.70499 | ||||||||
\(408\) | −2.97133 | + | 1.71550i | −0.147103 | + | 0.0849297i | ||||
\(409\) | 19.8178 | + | 11.4418i | 0.979930 | + | 0.565763i | 0.902249 | − | 0.431216i | \(-0.141915\pi\) |
0.0776807 | + | 0.996978i | \(0.475249\pi\) | |||||||
\(410\) | −8.37690 | − | 4.83641i | −0.413706 | − | 0.238853i | ||||
\(411\) | −2.22476 | − | 3.85339i | −0.109739 | − | 0.190074i | ||||
\(412\) | 6.28048 | 0.309417 | ||||||||
\(413\) | −2.34473 | − | 16.5004i | −0.115377 | − | 0.811932i | ||||
\(414\) | 7.00000 | + | 10.6343i | 0.344031 | + | 0.522647i | ||||
\(415\) | −12.8150 | − | 22.1963i | −0.629065 | − | 1.08957i | ||||
\(416\) | 4.85084 | + | 2.80063i | 0.237832 | + | 0.137312i | ||||
\(417\) | 3.23790 | − | 5.60821i | 0.158561 | − | 0.274635i | ||||
\(418\) | 5.99093 | − | 3.45886i | 0.293026 | − | 0.169179i | ||||
\(419\) | 13.9192 | 0.680000 | 0.340000 | − | 0.940425i | \(-0.389573\pi\) | ||||
0.340000 | + | 0.940425i | \(0.389573\pi\) | |||||||
\(420\) | −0.377733 | − | 2.65819i | −0.0184315 | − | 0.129707i | ||||
\(421\) | − | 17.4351i | − | 0.849736i | −0.905255 | − | 0.424868i | \(-0.860320\pi\) | ||
0.905255 | − | 0.424868i | \(-0.139680\pi\) | |||||||
\(422\) | −1.98769 | − | 3.44279i | −0.0967594 | − | 0.167592i | ||||
\(423\) | −16.8594 | − | 9.73380i | −0.819734 | − | 0.473273i | ||||
\(424\) | 2.09249 | + | 1.20810i | 0.101620 | + | 0.0586705i | ||||
\(425\) | −5.89062 | − | 10.2029i | −0.285737 | − | 0.494911i | ||||
\(426\) | 6.89733i | 0.334177i | ||||||||
\(427\) | 2.35465 | − | 5.85374i | 0.113950 | − | 0.283282i | ||||
\(428\) | − | 10.5629i | − | 0.510577i | ||||||
\(429\) | −11.4189 | + | 6.59273i | −0.551312 | + | 0.318300i | ||||
\(430\) | 4.65978 | + | 2.69032i | 0.224714 | + | 0.129739i | ||||
\(431\) | 26.0665 | + | 15.0495i | 1.25558 | + | 0.724909i | 0.972212 | − | 0.234102i | \(-0.0752149\pi\) |
0.283368 | + | 0.959011i | \(0.408548\pi\) | |||||||
\(432\) | 2.87773 | − | 1.66146i | 0.138455 | − | 0.0799370i | ||||
\(433\) | 29.5615 | 1.42064 | 0.710319 | − | 0.703880i | \(-0.248551\pi\) | ||||
0.710319 | + | 0.703880i | \(0.248551\pi\) | |||||||
\(434\) | −8.35119 | + | 6.54527i | −0.400870 | + | 0.314183i | ||||
\(435\) | 9.86331i | 0.472909i | ||||||||
\(436\) | −0.770835 | + | 0.445042i | −0.0369163 | + | 0.0213136i | ||||
\(437\) | 8.26772 | − | 0.484650i | 0.395499 | − | 0.0231839i | ||||
\(438\) | −1.17834 | + | 2.04094i | −0.0563031 | + | 0.0975198i | ||||
\(439\) | −13.2106 | + | 7.62714i | −0.630507 | + | 0.364023i | −0.780948 | − | 0.624596i | \(-0.785264\pi\) |
0.150441 | + | 0.988619i | \(0.451931\pi\) | |||||||
\(440\) | 6.91773i | 0.329790i | ||||||||
\(441\) | 17.8471 | − | 5.17674i | 0.849863 | − | 0.246511i | ||||
\(442\) | 32.7035i | 1.55555i | ||||||||
\(443\) | −4.24072 | − | 7.34514i | −0.201483 | − | 0.348978i | 0.747524 | − | 0.664235i | \(-0.231243\pi\) |
−0.949006 | + | 0.315257i | \(0.897909\pi\) | |||||||
\(444\) | −2.52292 | + | 4.36983i | −0.119733 | + | 0.207383i | ||||
\(445\) | 13.4729 | − | 23.3358i | 0.638679 | − | 1.10622i | ||||
\(446\) | 9.73748 | − | 5.62194i | 0.461083 | − | 0.266207i | ||||
\(447\) | −4.70803 | −0.222682 | ||||||||
\(448\) | −1.63208 | − | 2.08239i | −0.0771083 | − | 0.0983835i | ||||
\(449\) | −4.82792 | −0.227843 | −0.113922 | − | 0.993490i | \(-0.536341\pi\) | ||||
−0.113922 | + | 0.993490i | \(0.536341\pi\) | |||||||
\(450\) | 2.67834 | + | 4.63901i | 0.126258 | + | 0.218685i | ||||
\(451\) | 11.2190 | − | 19.4318i | 0.528281 | − | 0.915009i | ||||
\(452\) | −17.7976 | − | 10.2755i | −0.837129 | − | 0.483317i | ||||
\(453\) | 5.24655 | − | 3.02910i | 0.246505 | − | 0.142320i | ||||
\(454\) | 14.3998 | 0.675816 | ||||||||
\(455\) | −23.7430 | − | 9.55056i | −1.11309 | − | 0.447737i | ||||
\(456\) | − | 1.01480i | − | 0.0475222i | ||||||
\(457\) | 8.59484 | − | 4.96223i | 0.402049 | − | 0.232123i | −0.285318 | − | 0.958433i | \(-0.592099\pi\) |
0.687368 | + | 0.726309i | \(0.258766\pi\) | |||||||
\(458\) | 10.6537 | − | 18.4527i | 0.497814 | − | 0.862240i | ||||
\(459\) | 16.8019 | + | 9.70058i | 0.784246 | + | 0.452784i | ||||
\(460\) | −3.71414 | + | 7.40238i | −0.173173 | + | 0.345138i | ||||
\(461\) | − | 24.1817i | − | 1.12625i | −0.826370 | − | 0.563127i | \(-0.809598\pi\) | ||
0.826370 | − | 0.563127i | \(-0.190402\pi\) | |||||||
\(462\) | 6.16619 | − | 0.876224i | 0.286877 | − | 0.0407656i | ||||
\(463\) | −11.4928 | −0.534115 | −0.267058 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267058 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(464\) | 4.85975 | + | 8.41733i | 0.225608 | + | 0.390765i | ||||
\(465\) | 2.03487 | − | 3.52449i | 0.0943647 | − | 0.163444i | ||||
\(466\) | 3.74697 | − | 6.48995i | 0.173575 | − | 0.300641i | ||||
\(467\) | −0.441887 | − | 0.765371i | −0.0204481 | − | 0.0354172i | 0.855620 | − | 0.517604i | \(-0.173176\pi\) |
−0.876068 | + | 0.482187i | \(0.839843\pi\) | |||||||
\(468\) | − | 14.8696i | − | 0.687346i | ||||||
\(469\) | −3.97820 | − | 27.9955i | −0.183696 | − | 1.29271i | ||||
\(470\) | − | 12.6639i | − | 0.584142i | ||||||
\(471\) | −4.11635 | + | 2.37658i | −0.189672 | + | 0.109507i | ||||
\(472\) | 5.45528 | + | 3.14961i | 0.251100 | + | 0.144972i | ||||
\(473\) | −6.24072 | + | 10.8092i | −0.286949 | + | 0.497010i | ||||
\(474\) | −2.97133 | − | 5.14649i | −0.136478 | − | 0.236386i | ||||
\(475\) | 3.48458 | 0.159883 | ||||||||
\(476\) | 5.76480 | − | 14.3315i | 0.264229 | − | 0.656882i | ||||
\(477\) | − | 6.41423i | − | 0.293687i | ||||||
\(478\) | 4.26803 | + | 7.39245i | 0.195215 | + | 0.338123i | ||||
\(479\) | 1.87154 | − | 3.24161i | 0.0855131 | − | 0.148113i | −0.820097 | − | 0.572225i | \(-0.806080\pi\) |
0.905610 | + | 0.424112i | \(0.139414\pi\) | |||||||
\(480\) | 0.878839 | + | 0.507398i | 0.0401133 | + | 0.0231594i | ||||
\(481\) | 24.0480 | + | 41.6523i | 1.09649 | + | 1.89918i | ||||
\(482\) | 28.3190 | 1.28990 | ||||||||
\(483\) | 7.06863 | + | 2.37302i | 0.321634 | + | 0.107976i | ||||
\(484\) | −5.04700 | −0.229409 | ||||||||
\(485\) | 13.3831 | + | 23.1802i | 0.607695 | + | 1.05256i | ||||
\(486\) | −11.6924 | − | 6.75064i | −0.530380 | − | 0.306215i | ||||
\(487\) | −15.4635 | + | 26.7835i | −0.700716 | + | 1.21368i | 0.267499 | + | 0.963558i | \(0.413803\pi\) |
−0.968215 | + | 0.250118i | \(0.919531\pi\) | |||||||
\(488\) | 1.19240 | + | 2.06529i | 0.0539773 | + | 0.0934913i | ||||
\(489\) | − | 0.790566i | − | 0.0357506i | ||||||
\(490\) | 8.72124 | + | 8.37058i | 0.393985 | + | 0.378144i | ||||
\(491\) | 7.43932 | 0.335732 | 0.167866 | − | 0.985810i | \(-0.446312\pi\) | ||||
0.167866 | + | 0.985810i | \(0.446312\pi\) | |||||||
\(492\) | −1.64577 | − | 2.85055i | −0.0741969 | − | 0.128513i | ||||
\(493\) | −28.3741 | + | 49.1454i | −1.27790 | + | 2.21340i | ||||
\(494\) | −8.37690 | − | 4.83641i | −0.376895 | − | 0.217600i | ||||
\(495\) | 15.9040 | − | 9.18217i | 0.714831 | − | 0.412708i | ||||
\(496\) | − | 4.01040i | − | 0.180072i | ||||||
\(497\) | −19.1562 | − | 24.4416i | −0.859273 | − | 1.09636i | ||||
\(498\) | − | 8.72158i | − | 0.390823i | ||||||
\(499\) | 6.40771 | + | 11.0985i | 0.286848 | + | 0.496836i | 0.973056 | − | 0.230570i | \(-0.0740591\pi\) |
−0.686207 | + | 0.727406i | \(0.740726\pi\) | |||||||
\(500\) | −6.05953 | + | 10.4954i | −0.270991 | + | 0.469369i | ||||
\(501\) | −5.00000 | + | 8.66025i | −0.223384 | + | 0.386912i | ||||
\(502\) | −11.4959 | − | 19.9115i | −0.513087 | − | 0.888692i | ||||
\(503\) | −1.59205 | −0.0709861 | −0.0354930 | − | 0.999370i | \(-0.511300\pi\) | ||||
−0.0354930 | + | 0.999370i | \(0.511300\pi\) | |||||||
\(504\) | −2.62113 | + | 6.51620i | −0.116754 | + | 0.290255i | ||||
\(505\) | 2.93776i | 0.130729i | ||||||||
\(506\) | −17.1712 | − | 8.61566i | −0.763355 | − | 0.383013i | ||||
\(507\) | 9.35084 | + | 5.39871i | 0.415285 | + | 0.239765i | ||||
\(508\) | 8.35975 | − | 14.4795i | 0.370904 | − | 0.642424i | ||||
\(509\) | 0.851794 | − | 0.491784i | 0.0377551 | − | 0.0217979i | −0.481004 | − | 0.876719i | \(-0.659728\pi\) |
0.518759 | + | 0.854921i | \(0.326394\pi\) | |||||||
\(510\) | 5.92497i | 0.262362i | ||||||||
\(511\) | −1.49277 | − | 10.5050i | −0.0660364 | − | 0.464713i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.96955 | + | 2.86917i | −0.219411 | + | 0.126677i | ||||
\(514\) | −24.3952 | − | 14.0846i | −1.07603 | − | 0.621245i | ||||
\(515\) | 5.42287 | − | 9.39269i | 0.238960 | − | 0.413891i | ||||
\(516\) | 0.915482 | + | 1.58566i | 0.0403018 | + | 0.0698048i | ||||
\(517\) | 29.3763 | 1.29197 | ||||||||
\(518\) | −3.19616 | − | 22.4921i | −0.140431 | − | 0.988246i | ||||
\(519\) | −2.99289 | −0.131373 | ||||||||
\(520\) | 8.37690 | − | 4.83641i | 0.367351 | − | 0.212090i | ||||
\(521\) | −4.51786 | + | 7.82517i | −0.197931 | + | 0.342827i | −0.947857 | − | 0.318695i | \(-0.896756\pi\) |
0.749926 | + | 0.661521i | \(0.230089\pi\) | |||||||
\(522\) | 12.9011 | − | 22.3453i | 0.564665 | − | 0.978028i | ||||
\(523\) | 2.74946 | + | 4.76220i | 0.120225 | + | 0.208236i | 0.919856 | − | 0.392255i | \(-0.128305\pi\) |
−0.799631 | + | 0.600492i | \(0.794972\pi\) | |||||||
\(524\) | 6.25787i | 0.273376i | ||||||||
\(525\) | 2.91057 | + | 1.17077i | 0.127028 | + | 0.0510966i | ||||
\(526\) | − | 5.59554i | − | 0.243977i | ||||||
\(527\) | 20.2780 | − | 11.7075i | 0.883325 | − | 0.509988i | ||||
\(528\) | −1.17701 | + | 2.03864i | −0.0512226 | + | 0.0887202i | ||||
\(529\) | −13.7485 | − | 18.4385i | −0.597760 | − | 0.801675i | ||||
\(530\) | 3.61351 | − | 2.08626i | 0.156961 | − | 0.0906215i | ||||
\(531\) | − | 16.7224i | − | 0.725690i | ||||||
\(532\) | 2.81843 | + | 3.59607i | 0.122194 | + | 0.155909i | ||||
\(533\) | −31.3742 | −1.35897 | ||||||||
\(534\) | 7.94088 | − | 4.58467i | 0.343635 | − | 0.198398i | ||||
\(535\) | −15.7972 | − | 9.12052i | −0.682973 | − | 0.394315i | ||||
\(536\) | 9.25574 | + | 5.34380i | 0.399787 | + | 0.230817i | ||||
\(537\) | 3.89556 | − | 2.24910i | 0.168106 | − | 0.0970559i | ||||
\(538\) | 8.11396i | 0.349818i | ||||||||
\(539\) | −19.4172 | + | 20.2306i | −0.836356 | + | 0.871393i | ||||
\(540\) | − | 5.73834i | − | 0.246939i | ||||||
\(541\) | −1.91963 | − | 3.32490i | −0.0825315 | − | 0.142949i | 0.821805 | − | 0.569769i | \(-0.192967\pi\) |
−0.904337 | + | 0.426820i | \(0.859634\pi\) | |||||||
\(542\) | 9.30596 | + | 5.37280i | 0.399725 | + | 0.230781i | ||||
\(543\) | 5.55488 | + | 3.20711i | 0.238383 | + | 0.137630i | ||||
\(544\) | 2.91929 | + | 5.05637i | 0.125164 | + | 0.216790i | ||||
\(545\) | 1.53708i | 0.0658414i | ||||||||
\(546\) | −5.37203 | − | 6.85424i | −0.229902 | − | 0.293334i | ||||
\(547\) | 28.7241 | 1.22815 | 0.614076 | − | 0.789247i | \(-0.289529\pi\) | ||||
0.614076 | + | 0.789247i | \(0.289529\pi\) | |||||||
\(548\) | −6.55739 | + | 3.78591i | −0.280118 | + | 0.161726i | ||||
\(549\) | 3.16543 | − | 5.48268i | 0.135097 | − | 0.233995i | ||||
\(550\) | −7.00021 | − | 4.04157i | −0.298490 | − | 0.172333i | ||||
\(551\) | −8.39229 | − | 14.5359i | −0.357524 | − | 0.619249i | ||||
\(552\) | −2.35401 | + | 1.54952i | −0.100193 | + | 0.0659521i | ||||
\(553\) | 24.8228 | + | 9.98492i | 1.05557 | + | 0.424602i | ||||
\(554\) | 6.86273 | 0.291569 | ||||||||
\(555\) | 4.35683 | + | 7.54625i | 0.184937 | + | 0.320321i | ||||
\(556\) | −9.54360 | − | 5.51000i | −0.404739 | − | 0.233676i | ||||
\(557\) | −38.8444 | − | 22.4268i | −1.64589 | − | 0.950255i | −0.978681 | − | 0.205384i | \(-0.934156\pi\) |
−0.667209 | − | 0.744871i | \(-0.732511\pi\) | |||||||
\(558\) | −9.21998 | + | 5.32316i | −0.390313 | + | 0.225347i | ||||
\(559\) | 17.4524 | 0.738156 | ||||||||
\(560\) | −4.52350 | + | 0.642796i | −0.191153 | + | 0.0271631i | ||||
\(561\) | −13.7441 | −0.580277 | ||||||||
\(562\) | 4.12314 | − | 2.38050i | 0.173924 | − | 0.100415i | ||||
\(563\) | −2.20937 | + | 3.82673i | −0.0931137 | + | 0.161278i | −0.908820 | − | 0.417189i | \(-0.863015\pi\) |
0.815706 | + | 0.578467i | \(0.196349\pi\) | |||||||
\(564\) | 2.15468 | − | 3.73201i | 0.0907283 | − | 0.157146i | ||||
\(565\) | −30.7347 | + | 17.7447i | −1.29302 | + | 0.746524i | ||||
\(566\) | 9.39645 | 0.394962 | ||||||||
\(567\) | 15.7464 | − | 2.23758i | 0.661285 | − | 0.0939695i | ||||
\(568\) | 11.7373 | 0.492487 | ||||||||
\(569\) | 1.59671 | − | 0.921863i | 0.0669377 | − | 0.0386465i | −0.466158 | − | 0.884702i | \(-0.654362\pi\) |
0.533095 | + | 0.846055i | \(0.321029\pi\) | |||||||
\(570\) | −1.51766 | − | 0.876224i | −0.0635680 | − | 0.0367010i | ||||
\(571\) | 5.07756 | + | 2.93153i | 0.212489 | + | 0.122681i | 0.602468 | − | 0.798143i | \(-0.294184\pi\) |
−0.389979 | + | 0.920824i | \(0.627518\pi\) | |||||||
\(572\) | 11.2190 | + | 19.4318i | 0.469089 | + | 0.812486i | ||||
\(573\) | −5.86937 | −0.245196 | ||||||||
\(574\) | 13.7489 | + | 5.53047i | 0.573869 | + | 0.230838i | ||||
\(575\) | −5.32071 | − | 8.08314i | −0.221889 | − | 0.337090i | ||||
\(576\) | −1.32734 | − | 2.29902i | −0.0553058 | − | 0.0957924i | ||||
\(577\) | −28.5416 | − | 16.4785i | −1.18820 | − | 0.686009i | −0.230304 | − | 0.973119i | \(-0.573972\pi\) |
−0.957898 | + | 0.287110i | \(0.907305\pi\) | |||||||
\(578\) | −8.54456 | + | 14.7996i | −0.355407 | + | 0.615583i | ||||
\(579\) | −10.4989 | + | 6.06153i | −0.436319 | + | 0.251909i | ||||
\(580\) | 16.7846 | 0.696942 | ||||||||
\(581\) | 24.2227 | + | 30.9061i | 1.00493 | + | 1.28220i | ||||
\(582\) | 9.10818i | 0.377546i | ||||||||
\(583\) | 4.83949 | + | 8.38224i | 0.200431 | + | 0.347157i | ||||
\(584\) | 3.47311 | + | 2.00520i | 0.143718 | + | 0.0829757i | ||||
\(585\) | −22.2380 | − | 12.8391i | −0.919427 | − | 0.530832i | ||||
\(586\) | −5.38038 | − | 9.31910i | −0.222262 | − | 0.384968i | ||||
\(587\) | 26.6670i | 1.10066i | 0.834946 | + | 0.550331i | \(0.185499\pi\) | ||||
−0.834946 | + | 0.550331i | \(0.814501\pi\) | |||||||
\(588\) | 1.14593 | + | 3.95065i | 0.0472572 | + | 0.162922i | ||||
\(589\) | 6.92555i | 0.285362i | ||||||||
\(590\) | 9.42071 | − | 5.43905i | 0.387845 | − | 0.223922i | ||||
\(591\) | −2.75658 | − | 1.59151i | −0.113391 | − | 0.0654661i | ||||
\(592\) | 7.43623 | + | 4.29331i | 0.305627 | + | 0.176454i | ||||
\(593\) | 15.9371 | − | 9.20131i | 0.654460 | − | 0.377853i | −0.135703 | − | 0.990750i | \(-0.543329\pi\) |
0.790163 | + | 0.612897i | \(0.209996\pi\) | |||||||
\(594\) | 13.3112 | 0.546165 | ||||||||
\(595\) | −16.4556 | − | 20.9960i | −0.674615 | − | 0.860750i | ||||
\(596\) | 8.01174i | 0.328174i | ||||||||
\(597\) | −3.56832 | + | 2.06017i | −0.146041 | + | 0.0843171i | ||||
\(598\) | 1.57198 | + | 26.8167i | 0.0642831 | + | 1.09662i | ||||
\(599\) | −8.29477 | + | 14.3670i | −0.338915 | + | 0.587018i | −0.984229 | − | 0.176899i | \(-0.943393\pi\) |
0.645314 | + | 0.763918i | \(0.276727\pi\) | |||||||
\(600\) | −1.02689 | + | 0.592878i | −0.0419228 | + | 0.0242041i | ||||
\(601\) | 19.4387i | 0.792921i | 0.918052 | + | 0.396460i | \(0.129762\pi\) | ||||
−0.918052 | + | 0.396460i | \(0.870238\pi\) | |||||||
\(602\) | −7.64805 | − | 3.07641i | −0.311711 | − | 0.125385i | ||||
\(603\) | − | 28.3722i | − | 1.15540i | ||||||
\(604\) | −5.15468 | − | 8.92816i | −0.209741 | − | 0.363282i | ||||
\(605\) | −4.35783 | + | 7.54798i | −0.177171 | + | 0.306869i | ||||
\(606\) | −0.499841 | + | 0.865750i | −0.0203047 | + | 0.0351687i | ||||
\(607\) | −12.4276 | + | 7.17507i | −0.504420 | + | 0.291227i | −0.730537 | − | 0.682873i | \(-0.760730\pi\) |
0.226117 | + | 0.974100i | \(0.427397\pi\) | |||||||
\(608\) | −1.72690 | −0.0700350 | ||||||||
\(609\) | −2.12600 | − | 14.9611i | −0.0861497 | − | 0.606255i | ||||
\(610\) | 4.11829 | 0.166745 | ||||||||
\(611\) | −20.5379 | − | 35.5727i | −0.830876 | − | 1.43912i | ||||
\(612\) | 7.74979 | − | 13.4230i | 0.313267 | − | 0.542594i | ||||
\(613\) | −17.0749 | − | 9.85818i | −0.689648 | − | 0.398168i | 0.113832 | − | 0.993500i | \(-0.463687\pi\) |
−0.803480 | + | 0.595332i | \(0.797021\pi\) | |||||||
\(614\) | −14.4837 | + | 8.36218i | −0.584515 | + | 0.337470i | ||||
\(615\) | −5.68414 | −0.229207 | ||||||||
\(616\) | −1.49109 | − | 10.4931i | −0.0600777 | − | 0.422780i | ||||
\(617\) | 27.5354i | 1.10853i | 0.832339 | + | 0.554267i | \(0.187001\pi\) | ||||
−0.832339 | + | 0.554267i | \(0.812999\pi\) | |||||||
\(618\) | 3.19621 | − | 1.84533i | 0.128570 | − | 0.0742301i | ||||
\(619\) | 13.6801 | − | 23.6946i | 0.549848 | − | 0.952365i | −0.448436 | − | 0.893815i | \(-0.648019\pi\) |
0.998284 | − | 0.0585501i | \(-0.0186478\pi\) | |||||||
\(620\) | −5.99770 | − | 3.46277i | −0.240873 | − | 0.139068i | ||||
\(621\) | 14.2438 | + | 7.14680i | 0.571582 | + | 0.286791i | ||||
\(622\) | − | 21.8082i | − | 0.874431i | ||||||
\(623\) | −15.4064 | + | 38.3009i | −0.617246 | + | 1.53449i | ||||
\(624\) | 3.29153 | 0.131767 | ||||||||
\(625\) | 5.41963 | + | 9.38708i | 0.216785 | + | 0.375483i | ||||
\(626\) | 0.144647 | − | 0.250536i | 0.00578126 | − | 0.0100134i | ||||
\(627\) | 2.03257 | − | 3.52051i | 0.0811730 | − | 0.140596i | ||||
\(628\) | 4.04427 | + | 7.00488i | 0.161384 | + | 0.279525i | ||||
\(629\) | 50.1337i | 1.99896i | ||||||||
\(630\) | 7.48202 | + | 9.54640i | 0.298091 | + | 0.380338i | ||||
\(631\) | − | 5.14760i | − | 0.204923i | −0.994737 | − | 0.102461i | \(-0.967328\pi\) | ||
0.994737 | − | 0.102461i | \(-0.0326718\pi\) | |||||||
\(632\) | −8.75788 | + | 5.05637i | −0.348370 | + | 0.201131i | ||||
\(633\) | −2.02312 | − | 1.16805i | −0.0804118 | − | 0.0464258i | ||||
\(634\) | 2.35651 | − | 4.08160i | 0.0935891 | − | 0.162101i | ||||
\(635\) | −14.4364 | − | 25.0046i | −0.572892 | − | 0.992279i | ||||
\(636\) | 1.41986 | 0.0563010 | ||||||||
\(637\) | 38.0730 | + | 9.36902i | 1.50851 | + | 0.371214i | ||||
\(638\) | 38.9351i | 1.54145i | ||||||||
\(639\) | −15.5794 | − | 26.9843i | −0.616312 | − | 1.06748i | ||||
\(640\) | 0.863449 | − | 1.49554i | 0.0341308 | − | 0.0591163i | ||||
\(641\) | −6.10570 | − | 3.52513i | −0.241161 | − | 0.139234i | 0.374549 | − | 0.927207i | \(-0.377797\pi\) |
−0.615710 | + | 0.787973i | \(0.711131\pi\) | |||||||
\(642\) | −3.10360 | − | 5.37558i | −0.122489 | − | 0.212157i | ||||
\(643\) | −32.0178 | −1.26266 | −0.631329 | − | 0.775515i | \(-0.717490\pi\) | ||||
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(644\) | 4.03822 | − | 12.0288i | 0.159128 | − | 0.474002i | ||||
\(645\) | 3.16189 | 0.124499 | ||||||||
\(646\) | −5.04132 | − | 8.73183i | −0.198348 | − | 0.343549i | ||||
\(647\) | 15.5852 | + | 8.99811i | 0.612717 | + | 0.353752i | 0.774028 | − | 0.633151i | \(-0.218239\pi\) |
−0.161311 | + | 0.986904i | \(0.551572\pi\) | |||||||
\(648\) | −3.00568 | + | 5.20598i | −0.118074 | + | 0.204510i | ||||
\(649\) | 12.6169 | + | 21.8532i | 0.495258 | + | 0.857811i | ||||
\(650\) | 11.3024i | 0.443315i | ||||||||
\(651\) | −2.32689 | + | 5.78472i | −0.0911979 | + | 0.226721i | ||||
\(652\) | −1.34532 | −0.0526869 | ||||||||
\(653\) | −8.72841 | − | 15.1181i | −0.341569 | − | 0.591615i | 0.643155 | − | 0.765736i | \(-0.277625\pi\) |
−0.984724 | + | 0.174121i | \(0.944292\pi\) | |||||||
\(654\) | −0.261525 | + | 0.452974i | −0.0102264 | + | 0.0177127i | ||||
\(655\) | 9.35888 | + | 5.40335i | 0.365682 | + | 0.211126i | ||||
\(656\) | −4.85084 | + | 2.80063i | −0.189393 | + | 0.109346i | ||||
\(657\) | − | 10.6463i | − | 0.415352i | ||||||
\(658\) | 2.72965 | + | 19.2092i | 0.106413 | + | 0.748851i | ||||
\(659\) | 25.2564i | 0.983849i | 0.870638 | + | 0.491924i | \(0.163706\pi\) | ||||
−0.870638 | + | 0.491924i | \(0.836294\pi\) | |||||||
\(660\) | 2.03257 | + | 3.52051i | 0.0791177 | + | 0.137036i | ||||
\(661\) | −4.76959 | + | 8.26117i | −0.185515 | + | 0.321322i | −0.943750 | − | 0.330660i | \(-0.892729\pi\) |
0.758235 | + | 0.651982i | \(0.226062\pi\) | |||||||
\(662\) | 5.64237 | − | 9.77287i | 0.219297 | − | 0.379834i | ||||
\(663\) | 9.60895 | + | 16.6432i | 0.373181 | + | 0.646368i | ||||
\(664\) | −14.8417 | −0.575969 | ||||||||
\(665\) | 7.81162 | − | 1.11004i | 0.302922 | − | 0.0430456i | ||||
\(666\) | − | 22.7947i | − | 0.883277i | ||||||
\(667\) | −20.9043 | + | 41.6628i | −0.809418 | + | 1.61319i | ||||
\(668\) | 14.7373 | + | 8.50860i | 0.570204 | + | 0.329208i | ||||
\(669\) | 3.30368 | − | 5.72214i | 0.127728 | − | 0.221231i | ||||
\(670\) | 15.9837 | − | 9.22821i | 0.617505 | − | 0.356517i | ||||
\(671\) | 9.55317i | 0.368796i | ||||||||
\(672\) | −1.44243 | − | 0.580214i | −0.0556429 | − | 0.0223822i | ||||
\(673\) | 27.5879 | 1.06344 | 0.531719 | − | 0.846921i | \(-0.321546\pi\) | ||||
0.531719 | + | 0.846921i | \(0.321546\pi\) | |||||||
\(674\) | 7.49806 | − | 4.32901i | 0.288815 | − | 0.166747i | ||||
\(675\) | 5.80676 | + | 3.35253i | 0.223502 | + | 0.129039i | ||||
\(676\) | 9.18709 | − | 15.9125i | 0.353350 | − | 0.612019i | ||||
\(677\) | 8.61324 | + | 14.9186i | 0.331034 | + | 0.573367i | 0.982715 | − | 0.185126i | \(-0.0592693\pi\) |
−0.651681 | + | 0.758493i | \(0.725936\pi\) | |||||||
\(678\) | −12.0766 | −0.463797 | ||||||||
\(679\) | −25.2965 | − | 32.2761i | −0.970789 | − | 1.23864i | ||||
\(680\) | 10.0826 | 0.386652 | ||||||||
\(681\) | 7.32823 | − | 4.23095i | 0.280818 | − | 0.162130i | ||||
\(682\) | 8.03257 | − | 13.9128i | 0.307583 | − | 0.532749i | ||||
\(683\) | 3.48865 | − | 6.04252i | 0.133489 | − | 0.231210i | −0.791530 | − | 0.611130i | \(-0.790715\pi\) |
0.925019 | + | 0.379920i | \(0.124048\pi\) | |||||||
\(684\) | 2.29218 | + | 3.97017i | 0.0876437 | + | 0.151803i | ||||
\(685\) | 13.0758i | 0.499599i | ||||||||
\(686\) | −15.0330 | − | 10.8170i | −0.573963 | − | 0.412997i | ||||
\(687\) | − | 12.5211i | − | 0.477709i | ||||||
\(688\) | 2.69835 | − | 1.55789i | 0.102874 | − | 0.0593941i | ||||
\(689\) | 6.76688 | − | 11.7206i | 0.257798 | − | 0.446519i | ||||
\(690\) | 0.284800 | + | 4.85845i | 0.0108422 | + | 0.184958i | ||||
\(691\) | −1.84914 | + | 1.06760i | −0.0703444 | + | 0.0406134i | −0.534760 | − | 0.845004i | \(-0.679598\pi\) |
0.464415 | + | 0.885618i | \(0.346265\pi\) | |||||||
\(692\) | 5.09306i | 0.193609i | ||||||||
\(693\) | −22.1447 | + | 17.3560i | −0.841208 | + | 0.659299i | ||||
\(694\) | −31.1293 | −1.18165 | ||||||||
\(695\) | −16.4808 | + | 9.51521i | −0.625153 | + | 0.360933i | ||||
\(696\) | 4.94637 | + | 2.85579i | 0.187492 | + | 0.108248i | ||||
\(697\) | −28.3221 | − | 16.3517i | −1.07277 | − | 0.619366i | ||||
\(698\) | −3.24624 | + | 1.87422i | −0.122872 | + | 0.0709401i | ||||
\(699\) | − | 4.40375i | − | 0.166565i | ||||||
\(700\) | 1.99232 | − | 4.95297i | 0.0753027 | − | 0.187205i | ||||
\(701\) | 15.7616i | 0.595307i | 0.954674 | + | 0.297653i | \(0.0962040\pi\) | ||||
−0.954674 | + | 0.297653i | \(0.903796\pi\) | |||||||
\(702\) | −9.30628 | − | 16.1189i | −0.351243 | − | 0.608370i | ||||
\(703\) | −12.8416 | − | 7.41411i | −0.484330 | − | 0.279628i | ||||
\(704\) | 3.46919 | + | 2.00294i | 0.130750 | + | 0.0754885i | ||||
\(705\) | −3.72091 | − | 6.44480i | −0.140138 | − | 0.242725i | ||||
\(706\) | 1.36503i | 0.0513736i | ||||||||
\(707\) | −0.633223 | − | 4.45613i | −0.0238148 | − | 0.167590i | ||||
\(708\) | 3.70168 | 0.139118 | ||||||||
\(709\) | −39.5534 | + | 22.8362i | −1.48546 | + | 0.857630i | −0.999863 | − | 0.0165529i | \(-0.994731\pi\) |
−0.485596 | + | 0.874183i | \(0.661397\pi\) | |||||||
\(710\) | 10.1346 | − | 17.5536i | 0.380344 | − | 0.658775i | ||||
\(711\) | 23.2494 | + | 13.4230i | 0.871919 | + | 0.503403i | ||||
\(712\) | −7.80182 | − | 13.5131i | −0.292386 | − | 0.506427i | ||||
\(713\) | 16.0651 | − | 10.5748i | 0.601644 | − | 0.396031i | ||||
\(714\) | −1.27710 | − | 8.98727i | −0.0477944 | − | 0.336340i | ||||
\(715\) | 38.7480 | 1.44909 | ||||||||
\(716\) | −3.82734 | − | 6.62915i | −0.143034 | − | 0.247743i | ||||
\(717\) | 4.34411 | + | 2.50807i | 0.162234 | + | 0.0936656i | ||||
\(718\) | 2.92323 | + | 1.68773i | 0.109094 | + | 0.0629855i | ||||
\(719\) | 6.28093 | − | 3.62630i | 0.234239 | − | 0.135238i | −0.378287 | − | 0.925688i | \(-0.623487\pi\) |
0.612526 | + | 0.790450i | \(0.290153\pi\) | |||||||
\(720\) | −4.58436 | −0.170849 | ||||||||
\(721\) | −6.20110 | + | 15.4161i | −0.230941 | + | 0.574127i | ||||
\(722\) | −16.0178 | −0.596122 | ||||||||
\(723\) | 14.4119 | − | 8.32071i | 0.535984 | − | 0.309451i | ||||
\(724\) | 5.45761 | − | 9.45285i | 0.202830 | − | 0.351313i | ||||
\(725\) | −9.80612 | + | 16.9847i | −0.364190 | + | 0.630796i | ||||
\(726\) | −2.56848 | + | 1.48291i | −0.0953252 | + | 0.0550360i | ||||
\(727\) | 12.5073 | 0.463869 | 0.231934 | − | 0.972731i | \(-0.425495\pi\) | ||||
0.231934 | + | 0.972731i | \(0.425495\pi\) | |||||||
\(728\) | −11.6640 | + | 9.14169i | −0.432296 | + | 0.338813i | ||||
\(729\) | 10.1002 | 0.374080 | ||||||||
\(730\) | 5.99770 | − | 3.46277i | 0.221985 | − | 0.128163i | ||||
\(731\) | 15.7546 | + | 9.09590i | 0.582703 | + | 0.336424i | ||||
\(732\) | 1.21365 | + | 0.700701i | 0.0448578 | + | 0.0258987i | ||||
\(733\) | 9.64817 | + | 16.7111i | 0.356363 | + | 0.617240i | 0.987350 | − | 0.158554i | \(-0.0506832\pi\) |
−0.630987 | + | 0.775793i | \(0.717350\pi\) | |||||||
\(734\) | 13.5874 | 0.501522 | ||||||||
\(735\) | 6.89779 | + | 1.69741i | 0.254429 | + | 0.0626099i | ||||
\(736\) | 2.63685 | + | 4.00587i | 0.0971957 | + | 0.147658i | ||||
\(737\) | 21.4066 | + | 37.0773i | 0.788522 | + | 1.36576i | ||||
\(738\) | 12.8774 | + | 7.43478i | 0.474024 | + | 0.273678i | ||||
\(739\) | −24.6924 | + | 42.7686i | −0.908326 | + | 1.57327i | −0.0919375 | + | 0.995765i | \(0.529306\pi\) |
−0.816389 | + | 0.577503i | \(0.804027\pi\) | |||||||
\(740\) | 12.8416 | − | 7.41411i | 0.472067 | − | 0.272548i | ||||
\(741\) | −5.68414 | −0.208812 | ||||||||
\(742\) | −5.03146 | + | 3.94342i | −0.184711 | + | 0.144767i | ||||
\(743\) | − | 26.0648i | − | 0.956225i | −0.878299 | − | 0.478113i | \(-0.841321\pi\) | ||
0.878299 | − | 0.478113i | \(-0.158679\pi\) | |||||||
\(744\) | −1.17834 | − | 2.04094i | −0.0431999 | − | 0.0748244i | ||||
\(745\) | 11.9819 | + | 6.91773i | 0.438981 | + | 0.253446i | ||||
\(746\) | −9.92344 | − | 5.72930i | −0.363323 | − | 0.209765i | ||||
\(747\) | 19.6999 | + | 34.1213i | 0.720783 | + | 1.24843i | ||||
\(748\) | 23.3886i | 0.855173i | ||||||||
\(749\) | 25.9278 | + | 10.4294i | 0.947382 | + | 0.381082i | ||||
\(750\) | 7.12166i | 0.260046i | ||||||||
\(751\) | −39.4984 | + | 22.8044i | −1.44132 | + | 0.832144i | −0.997938 | − | 0.0641908i | \(-0.979553\pi\) |
−0.443378 | + | 0.896335i | \(0.646220\pi\) | |||||||
\(752\) | −6.35084 | − | 3.66666i | −0.231591 | − | 0.133709i | ||||
\(753\) | −11.7008 | − | 6.75545i | −0.426400 | − | 0.246182i | ||||
\(754\) | 47.1477 | − | 27.2208i | 1.71702 | − | 0.991321i | ||||
\(755\) | −17.8032 | −0.647925 | ||||||||
\(756\) | 1.23688 | + | 8.70418i | 0.0449848 | + | 0.316568i | ||||
\(757\) | − | 48.0863i | − | 1.74773i | −0.486172 | − | 0.873863i | \(-0.661607\pi\) | ||
0.486172 | − | 0.873863i | \(-0.338393\pi\) | |||||||
\(758\) | −3.03316 | + | 1.75120i | −0.110169 | + | 0.0636063i | ||||
\(759\) | −11.2701 | + | 0.660648i | −0.409079 | + | 0.0239800i | ||||
\(760\) | −1.49109 | + | 2.58264i | −0.0540874 | + | 0.0936822i | ||||
\(761\) | −16.8605 | + | 9.73444i | −0.611194 | + | 0.352873i | −0.773433 | − | 0.633878i | \(-0.781462\pi\) |
0.162238 | + | 0.986752i | \(0.448129\pi\) | |||||||
\(762\) | − | 9.82506i | − | 0.355924i | ||||||
\(763\) | −0.331312 | − | 2.33152i | −0.0119943 | − | 0.0844066i | ||||
\(764\) | 9.98802i | 0.361354i | ||||||||
\(765\) | −13.3831 | − | 23.1802i | −0.483867 | − | 0.838082i | ||||
\(766\) | −8.13077 | + | 14.0829i | −0.293777 | + | 0.508836i | ||||
\(767\) | 17.6418 | − | 30.5565i | 0.637008 | − | 1.10333i | ||||
\(768\) | 0.508912 | − | 0.293820i | 0.0183638 | − | 0.0106023i | ||||
\(769\) | 14.2164 | 0.512657 | 0.256329 | − | 0.966590i | \(-0.417487\pi\) | ||||
0.256329 | + | 0.966590i | \(0.417487\pi\) | |||||||
\(770\) | −16.9803 | − | 6.83030i | −0.611929 | − | 0.246147i | ||||
\(771\) | −16.5534 | −0.596155 | ||||||||
\(772\) | 10.3150 | + | 17.8662i | 0.371246 | + | 0.643017i | ||||
\(773\) | −6.81004 | + | 11.7953i | −0.244940 | + | 0.424249i | −0.962115 | − | 0.272645i | \(-0.912102\pi\) |
0.717175 | + | 0.696894i | \(0.245435\pi\) | |||||||
\(774\) | −7.16325 | − | 4.13571i | −0.257478 | − | 0.148655i | ||||
\(775\) | 7.00811 | − | 4.04614i | 0.251739 | − | 0.145342i | ||||
\(776\) | 15.4996 | 0.556402 | ||||||||
\(777\) | −8.23520 | − | 10.5074i | −0.295436 | − | 0.376951i | ||||
\(778\) | 18.8796i | 0.676866i | ||||||||
\(779\) | 8.37690 | − | 4.83641i | 0.300134 | − | 0.173282i | ||||
\(780\) | 2.84207 | − | 4.92261i | 0.101762 | − | 0.176258i | ||||
\(781\) | 40.7190 | + | 23.5091i | 1.45704 | + | 0.841222i | ||||
\(782\) | −12.5574 | + | 25.0272i | −0.449051 | + | 0.894971i | ||||
\(783\) | − | 32.2971i | − | 1.15421i | ||||||
\(784\) | 6.72290 | − | 1.95004i | 0.240103 | − | 0.0696444i | ||||
\(785\) | 13.9681 | 0.498542 | ||||||||
\(786\) | 1.83869 | + | 3.18470i | 0.0655839 | + | 0.113595i | ||||
\(787\) | −19.3595 | + | 33.5317i | −0.690093 | + | 1.19528i | 0.281714 | + | 0.959498i | \(0.409097\pi\) |
−0.971807 | + | 0.235778i | \(0.924236\pi\) | |||||||
\(788\) | −2.70831 | + | 4.69093i | −0.0964795 | + | 0.167107i | ||||
\(789\) | −1.64408 | − | 2.84764i | −0.0585310 | − | 0.101379i | ||||
\(790\) | 17.4637i | 0.621329i | ||||||||
\(791\) | 42.7949 | − | 33.5406i | 1.52161 | − | 1.19257i | ||||
\(792\) | − | 10.6343i | − | 0.377873i | ||||||
\(793\) | 11.5682 | − | 6.67893i | 0.410800 | − | 0.237176i | ||||
\(794\) | 23.1989 | + | 13.3939i | 0.823297 | + | 0.475331i | ||||
\(795\) | 1.22597 | − | 2.12345i | 0.0434808 | − | 0.0753110i | ||||
\(796\) | 3.50583 | + | 6.07227i | 0.124261 | + | 0.215226i | ||||
\(797\) | 3.41129 | 0.120834 | 0.0604170 | − | 0.998173i | \(-0.480757\pi\) | ||||
0.0604170 | + | 0.998173i | \(0.480757\pi\) | |||||||
\(798\) | 2.49093 | + | 1.00197i | 0.0881779 | + | 0.0354694i | ||||
\(799\) | − | 42.8162i | − | 1.51473i | ||||||
\(800\) | 1.00891 | + | 1.74749i | 0.0356704 | + | 0.0617830i | ||||
\(801\) | −20.7113 | + | 35.8731i | −0.731799 | + | 1.26751i | ||||
\(802\) | 3.02637 | + | 1.74728i | 0.106865 | + | 0.0616985i | ||||
\(803\) | 8.03257 | + | 13.9128i | 0.283463 | + | 0.490972i | ||||
\(804\) | 6.28048 | 0.221495 | ||||||||
\(805\) | −14.5028 | − | 16.4256i | −0.511155 | − | 0.578926i | ||||
\(806\) | −22.4633 | −0.791236 | ||||||||
\(807\) | 2.38405 | + | 4.12929i | 0.0839224 | + | 0.145358i | ||||
\(808\) | 1.47326 | + | 0.850590i | 0.0518293 | + | 0.0299236i | ||||
\(809\) | 9.17552 | − | 15.8925i | 0.322594 | − | 0.558749i | −0.658428 | − | 0.752643i | \(-0.728778\pi\) |
0.981022 | + | 0.193894i | \(0.0621118\pi\) | |||||||
\(810\) | 5.19049 | + | 8.99020i | 0.182375 | + | 0.315883i | ||||
\(811\) | 35.8682i | 1.25950i | 0.776796 | + | 0.629752i | \(0.216844\pi\) | ||||
−0.776796 | + | 0.629752i | \(0.783156\pi\) | |||||||
\(812\) | −25.4596 | + | 3.61785i | −0.893457 | + | 0.126962i | ||||
\(813\) | 6.31455 | 0.221461 | ||||||||
\(814\) | 17.1984 | + | 29.7886i | 0.602805 | + | 1.04409i | ||||
\(815\) | −1.16162 | + | 2.01198i | −0.0406897 | + | 0.0704766i | ||||
\(816\) | 2.97133 | + | 1.71550i | 0.104017 | + | 0.0600544i | ||||
\(817\) | −4.65978 | + | 2.69032i | −0.163025 | + | 0.0941225i | ||||
\(818\) | − | 22.8837i | − | 0.800109i | ||||||
\(819\) | 36.4990 | + | 14.6816i | 1.27538 | + | 0.513018i | ||||
\(820\) | 9.67281i | 0.337789i | ||||||||
\(821\) | 2.19048 | + | 3.79403i | 0.0764484 | + | 0.132413i | 0.901715 | − | 0.432330i | \(-0.142309\pi\) |
−0.825267 | + | 0.564743i | \(0.808975\pi\) | |||||||
\(822\) | −2.22476 | + | 3.85339i | −0.0775973 | + | 0.134402i | ||||
\(823\) | 8.31445 | − | 14.4011i | 0.289824 | − | 0.501989i | −0.683944 | − | 0.729535i | \(-0.739737\pi\) |
0.973767 | + | 0.227545i | \(0.0730700\pi\) | |||||||
\(824\) | −3.14024 | − | 5.43905i | −0.109395 | − | 0.189478i | ||||
\(825\) | −4.74998 | −0.165373 | ||||||||
\(826\) | −13.1174 | + | 10.2808i | −0.456413 | + | 0.357715i | ||||
\(827\) | − | 9.43925i | − | 0.328235i | −0.986441 | − | 0.164118i | \(-0.947522\pi\) | ||
0.986441 | − | 0.164118i | \(-0.0524776\pi\) | |||||||
\(828\) | 5.70957 | − | 11.3793i | 0.198421 | − | 0.395459i | ||||
\(829\) | 19.9373 | + | 11.5108i | 0.692451 | + | 0.399787i | 0.804530 | − | 0.593913i | \(-0.202418\pi\) |
−0.112079 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(830\) | −12.8150 | + | 22.1963i | −0.444816 | + | 0.770444i | ||||
\(831\) | 3.49252 | − | 2.01641i | 0.121154 | − | 0.0699485i | ||||
\(832\) | − | 5.60127i | − | 0.194189i | ||||||
\(833\) | 29.4862 | + | 28.3007i | 1.02164 | + | 0.980560i | ||||
\(834\) | −6.47580 | −0.224239 | ||||||||
\(835\) | 25.4499 | − | 14.6935i | 0.880729 | − | 0.508489i | ||||
\(836\) | −5.99093 | − | 3.45886i | −0.207201 | − | 0.119627i | ||||
\(837\) | −6.66311 | + | 11.5409i | −0.230311 | + | 0.398910i | ||||
\(838\) | −6.95962 | − | 12.0544i | −0.240416 | − | 0.416413i | ||||
\(839\) | −19.7349 | −0.681326 | −0.340663 | − | 0.940186i | \(-0.610651\pi\) | ||||
−0.340663 | + | 0.940186i | \(0.610651\pi\) | |||||||
\(840\) | −2.11320 | + | 1.65622i | −0.0729122 | + | 0.0571451i | ||||
\(841\) | 65.4687 | 2.25754 | ||||||||
\(842\) | −15.0993 | + | 8.71757i | −0.520355 | + | 0.300427i | ||||
\(843\) | 1.39888 | − | 2.42293i | 0.0481799 | − | 0.0834500i | ||||
\(844\) | −1.98769 | + | 3.44279i | −0.0684192 | + | 0.118506i | ||||
\(845\) | −15.8652 | − | 27.4793i | −0.545778 | − | 0.945316i | ||||
\(846\) | 19.4676i | 0.669310i | ||||||||
\(847\) | 4.98321 | − | 12.3884i | 0.171225 | − | 0.425671i | ||||
\(848\) | − | 2.41620i | − | 0.0829726i | ||||||
\(849\) | 4.78197 | − | 2.76087i | 0.164117 | − | 0.0947528i | ||||
\(850\) | −5.89062 | + | 10.2029i | −0.202047 | + | 0.349955i | ||||
\(851\) | 2.40981 | + | 41.1094i | 0.0826074 | + | 1.40921i | ||||
\(852\) | 5.97326 | − | 3.44867i | 0.204641 | − | 0.118149i | ||||
\(853\) | − | 52.6163i | − | 1.80155i | −0.434289 | − | 0.900774i | \(-0.643000\pi\) | ||
0.434289 | − | 0.900774i | \(-0.357000\pi\) | |||||||
\(854\) | −6.24681 | + | 0.887681i | −0.213762 | + | 0.0303758i | ||||
\(855\) | 7.91672 | 0.270746 | ||||||||
\(856\) | −9.14774 | + | 5.28145i | −0.312663 | + | 0.180516i | ||||
\(857\) | −12.8671 | − | 7.42883i | −0.439532 | − | 0.253764i | 0.263867 | − | 0.964559i | \(-0.415002\pi\) |
−0.703399 | + | 0.710795i | \(0.748335\pi\) | |||||||
\(858\) | 11.4189 | + | 6.59273i | 0.389836 | + | 0.225072i | ||||
\(859\) | 22.5159 | − | 12.9996i | 0.768233 | − | 0.443540i | −0.0640109 | − | 0.997949i | \(-0.520389\pi\) |
0.832244 | + | 0.554410i | \(0.187056\pi\) | |||||||
\(860\) | − | 5.38065i | − | 0.183479i | ||||||
\(861\) | 8.62196 | − | 1.22519i | 0.293836 | − | 0.0417545i | ||||
\(862\) | − | 30.0990i | − | 1.02518i | ||||||
\(863\) | 10.4134 | + | 18.0365i | 0.354476 | + | 0.613970i | 0.987028 | − | 0.160548i | \(-0.0513261\pi\) |
−0.632552 | + | 0.774518i | \(0.717993\pi\) | |||||||
\(864\) | −2.87773 | − | 1.66146i | −0.0979025 | − | 0.0565240i | ||||
\(865\) | 7.61687 | + | 4.39760i | 0.258981 | + | 0.149523i | ||||
\(866\) | −14.7808 | − | 25.6010i | −0.502271 | − | 0.869959i | ||||
\(867\) | 10.0423i | 0.341053i | ||||||||
\(868\) | 9.84397 | + | 3.95971i | 0.334126 | + | 0.134401i | ||||
\(869\) | −40.5103 | −1.37422 | ||||||||
\(870\) | 8.54188 | − | 4.93165i | 0.289597 | − | 0.167199i | ||||
\(871\) | 29.9321 | − | 51.8439i | 1.01421 | − | 1.75666i | ||||
\(872\) | 0.770835 | + | 0.445042i | 0.0261038 | + | 0.0150710i | ||||
\(873\) | −20.5732 | − | 35.6338i | −0.696297 | − | 1.20602i | ||||
\(874\) | −4.55358 | − | 6.91773i | −0.154027 | − | 0.233996i | ||||
\(875\) | −19.7792 | − | 25.2366i | −0.668660 | − | 0.853152i | ||||
\(876\) | 2.35667 | 0.0796246 | ||||||||
\(877\) | −21.9447 | − | 38.0093i | −0.741019 | − | 1.28348i | −0.952032 | − | 0.305999i | \(-0.901009\pi\) |
0.211013 | − | 0.977483i | \(-0.432324\pi\) | |||||||
\(878\) | 13.2106 | + | 7.62714i | 0.445836 | + | 0.257403i | ||||
\(879\) | −5.47628 | − | 3.16173i | −0.184710 | − | 0.106643i | ||||
\(880\) | 5.99093 | − | 3.45886i | 0.201954 | − | 0.116598i | ||||
\(881\) | −32.5912 | −1.09803 | −0.549013 | − | 0.835814i | \(-0.684996\pi\) | ||||
−0.549013 | + | 0.835814i | \(0.684996\pi\) | |||||||
\(882\) | −13.4067 | − | 12.8677i | −0.451429 | − | 0.433278i | ||||
\(883\) | −43.1588 | −1.45241 | −0.726205 | − | 0.687478i | \(-0.758718\pi\) | ||||
−0.726205 | + | 0.687478i | \(0.758718\pi\) | |||||||
\(884\) | 28.3221 | − | 16.3517i | 0.952574 | − | 0.549969i | ||||
\(885\) | 3.19621 | − | 5.53600i | 0.107439 | − | 0.186090i | ||||
\(886\) | −4.24072 | + | 7.34514i | −0.142470 | + | 0.246765i | ||||
\(887\) | −41.7550 | + | 24.1073i | −1.40200 | + | 0.809442i | −0.994597 | − | 0.103808i | \(-0.966897\pi\) |
−0.407398 | + | 0.913251i | \(0.633564\pi\) | |||||||
\(888\) | 5.04585 | 0.169328 | ||||||||
\(889\) | 27.2875 | + | 34.8165i | 0.915193 | + | 1.16771i | ||||
\(890\) | −26.9459 | −0.903228 | ||||||||
\(891\) | −20.8545 | + | 12.0403i | −0.698652 | + | 0.403367i | ||||
\(892\) | −9.73748 | − | 5.62194i | −0.326035 | − | 0.188236i | ||||
\(893\) | 10.9672 | + | 6.33194i | 0.367005 | + | 0.211890i | ||||
\(894\) | 2.35401 | + | 4.07727i | 0.0787300 | + | 0.136364i | ||||
\(895\) | −13.2188 | −0.441857 | ||||||||
\(896\) | −0.987361 | + | 2.45461i | −0.0329854 | + | 0.0820028i | ||||
\(897\) | 8.67929 | + | 13.1855i | 0.289793 | + | 0.440249i | ||||
\(898\) | 2.41396 | + | 4.18110i | 0.0805548 | + | 0.139525i | ||||
\(899\) | −33.7569 | − | 19.4895i | −1.12585 | − | 0.650012i | ||||
\(900\) | 2.67834 | − | 4.63901i | 0.0892779 | − | 0.154634i | ||||
\(901\) | 12.2172 | − | 7.05359i | 0.407013 | − | 0.234989i | ||||
\(902\) | −22.4379 | −0.747102 | ||||||||
\(903\) | −4.79609 | + | 0.681532i | −0.159604 | + | 0.0226800i | ||||
\(904\) | 20.5509i | 0.683513i | ||||||||
\(905\) | −9.42473 | − | 16.3241i | −0.313289 | − | 0.542632i | ||||
\(906\) | −5.24655 | − | 3.02910i | −0.174305 | − | 0.100635i | ||||
\(907\) | 4.14576 | + | 2.39355i | 0.137658 | + | 0.0794766i | 0.567247 | − | 0.823548i | \(-0.308008\pi\) |
−0.429590 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(908\) | −7.19990 | − | 12.4706i | −0.238937 | − | 0.413851i | ||||
\(909\) | − | 4.51608i | − | 0.149789i | ||||||
\(910\) | 3.60047 | + | 25.3373i | 0.119354 | + | 0.839924i | ||||
\(911\) | − | 12.5267i | − | 0.415028i | −0.978232 | − | 0.207514i | \(-0.933463\pi\) | ||
0.978232 | − | 0.207514i | \(-0.0665373\pi\) | |||||||
\(912\) | −0.878839 | + | 0.507398i | −0.0291013 | + | 0.0168016i | ||||
\(913\) | −51.4885 | − | 29.7269i | −1.70402 | − | 0.983818i | ||||
\(914\) | −8.59484 | − | 4.96223i | −0.284292 | − | 0.164136i | ||||
\(915\) | 2.09585 | − | 1.21004i | 0.0692866 | − | 0.0400027i | ||||
\(916\) | −21.3074 | −0.704016 | ||||||||
\(917\) | −15.3606 | − | 6.17878i | −0.507253 | − | 0.204041i | ||||
\(918\) | − | 19.4012i | − | 0.640334i | ||||||
\(919\) | 22.5796 | − | 13.0363i | 0.744832 | − | 0.430029i | −0.0789917 | − | 0.996875i | \(-0.525170\pi\) |
0.823823 | + | 0.566846i | \(0.191837\pi\) | |||||||
\(920\) | 8.26772 | − | 0.484650i | 0.272579 | − | 0.0159784i | ||||
\(921\) | −4.91396 | + | 8.51123i | −0.161920 | + | 0.280454i | ||||
\(922\) | −20.9420 | + | 12.0909i | −0.689687 | + | 0.398191i | ||||
\(923\) | − | 65.7439i | − | 2.16399i | ||||||
\(924\) | −3.84193 | − | 4.90196i | −0.126390 | − | 0.161263i | ||||
\(925\) | 17.3263i | 0.569685i | ||||||||
\(926\) | 5.74640 | + | 9.95305i | 0.188838 | + | 0.327077i | ||||
\(927\) | −8.33632 | + | 14.4389i | −0.273801 | + | 0.474237i | ||||
\(928\) | 4.85975 | − | 8.41733i | 0.159529 | − | 0.276313i | ||||
\(929\) | 30.1479 | − | 17.4059i | 0.989120 | − | 0.571069i | 0.0841089 | − | 0.996457i | \(-0.473196\pi\) |
0.905011 | + | 0.425388i | \(0.139862\pi\) | |||||||
\(930\) | −4.06973 | −0.133452 | ||||||||
\(931\) | −11.6098 | + | 3.36753i | −0.380494 | + | 0.110366i | ||||
\(932\) | −7.49395 | −0.245472 | ||||||||
\(933\) | −6.40771 | − | 11.0985i | −0.209779 | − | 0.363348i | ||||
\(934\) | −0.441887 | + | 0.765371i | −0.0144590 | + | 0.0250437i | ||||
\(935\) | 34.9786 | + | 20.1949i | 1.14392 | + | 0.660443i | ||||
\(936\) | −12.8774 | + | 7.43478i | −0.420911 | + | 0.243013i | ||||
\(937\) | −51.8954 | −1.69535 | −0.847675 | − | 0.530516i | \(-0.821998\pi\) | ||||
−0.847675 | + | 0.530516i | \(0.821998\pi\) | |||||||
\(938\) | −22.2557 | + | 17.4430i | −0.726675 | + | 0.569534i | ||||
\(939\) | − | 0.170001i | − | 0.00554777i | ||||||
\(940\) | −10.9672 | + | 6.33194i | −0.357712 | + | 0.206525i | ||||
\(941\) | 9.23148 | − | 15.9894i | 0.300938 | − | 0.521239i | −0.675411 | − | 0.737442i | \(-0.736034\pi\) |
0.976349 | + | 0.216202i | \(0.0693671\pi\) | |||||||
\(942\) | 4.11635 | + | 2.37658i | 0.134118 | + | 0.0774331i | ||||
\(943\) | −24.0099 | − | 12.0470i | −0.781871 | − | 0.392303i | ||||
\(944\) | − | 6.29922i | − | 0.205022i | ||||||
\(945\) | 14.0854 | + | 5.66582i | 0.458198 | + | 0.184309i | ||||
\(946\) | 12.4814 | 0.405807 | ||||||||
\(947\) | 7.30936 | + | 12.6602i | 0.237522 | + | 0.411400i | 0.960003 | − | 0.279991i | \(-0.0903314\pi\) |
−0.722481 | + | 0.691391i | \(0.756998\pi\) | |||||||
\(948\) | −2.97133 | + | 5.14649i | −0.0965042 | + | 0.167150i | ||||
\(949\) | 11.2316 | − | 19.4538i | 0.364595 | − | 0.631497i | ||||
\(950\) | −1.74229 | − | 3.01773i | −0.0565273 | − | 0.0979081i | ||||
\(951\) | − | 2.76957i | − | 0.0898094i | ||||||
\(952\) | −15.2938 | + | 2.17327i | −0.495675 | + | 0.0704362i | ||||
\(953\) | 8.39051i | 0.271795i | 0.990723 | + | 0.135898i | \(0.0433918\pi\) | ||||
−0.990723 | + | 0.135898i | \(0.956608\pi\) | |||||||
\(954\) | −5.55488 | + | 3.20711i | −0.179846 | + | 0.103834i | ||||
\(955\) | 14.9375 | + | 8.62415i | 0.483365 | + | 0.279071i | ||||
\(956\) | 4.26803 | − | 7.39245i | 0.138038 | − | 0.239089i | ||||
\(957\) | 11.4399 | + | 19.8145i | 0.369800 | + | 0.640512i | ||||
\(958\) | −3.74309 | −0.120934 | ||||||||
\(959\) | −2.81843 | − | 19.8339i | −0.0910118 | − | 0.640470i | ||||
\(960\) | − | 1.01480i | − | 0.0327524i | ||||||
\(961\) | −7.45836 | − | 12.9183i | −0.240592 | − | 0.416718i | ||||
\(962\) | 24.0480 | − | 41.6523i | 0.775338 | − | 1.34292i | ||||
\(963\) | 24.2843 | + | 14.0205i | 0.782551 | + | 0.451806i | ||||
\(964\) | −14.1595 | − | 24.5250i | −0.456047 | − | 0.789897i | ||||
\(965\) | 35.6260 | 1.14684 | ||||||||
\(966\) | −1.47922 | − | 7.30813i | −0.0475930 | − | 0.235135i | ||||
\(967\) | 9.30511 | 0.299232 | 0.149616 | − | 0.988744i | \(-0.452196\pi\) | ||||
0.149616 | + | 0.988744i | \(0.452196\pi\) | |||||||
\(968\) | 2.52350 | + | 4.37083i | 0.0811083 | + | 0.140484i | ||||
\(969\) | −5.13118 | − | 2.96249i | −0.164837 | − | 0.0951688i | ||||
\(970\) | 13.3831 | − | 23.1802i | 0.429705 | − | 0.744271i | ||||
\(971\) | −29.3514 | − | 50.8381i | −0.941931 | − | 1.63147i | −0.761782 | − | 0.647834i | \(-0.775675\pi\) |
−0.180149 | − | 0.983639i | \(-0.557658\pi\) | |||||||
\(972\) | 13.5013i | 0.433054i | ||||||||
\(973\) | 22.9479 | − | 17.9855i | 0.735676 | − | 0.576588i | ||||
\(974\) | 30.9269 | 0.990962 | ||||||||
\(975\) | 3.32087 | + | 5.75191i | 0.106353 | + | 0.184209i | ||||
\(976\) | 1.19240 | − | 2.06529i | 0.0381677 | − | 0.0661084i | ||||
\(977\) | 3.52423 | + | 2.03471i | 0.112750 | + | 0.0650963i | 0.555315 | − | 0.831640i | \(-0.312598\pi\) |
−0.442564 | + | 0.896737i | \(0.645931\pi\) | |||||||
\(978\) | −0.684650 | + | 0.395283i | −0.0218927 | + | 0.0126398i | ||||
\(979\) | − | 62.5062i | − | 1.99771i | ||||||
\(980\) | 2.88851 | − | 11.7381i | 0.0922702 | − | 0.374960i | ||||
\(981\) | − | 2.36289i | − | 0.0754411i | ||||||
\(982\) | −3.71966 | − | 6.44264i | −0.118699 | − | 0.205593i | ||||
\(983\) | 17.4483 | − | 30.2214i | 0.556516 | − | 0.963914i | −0.441268 | − | 0.897375i | \(-0.645471\pi\) |
0.997784 | − | 0.0665382i | \(-0.0211954\pi\) | |||||||
\(984\) | −1.64577 | + | 2.85055i | −0.0524651 | + | 0.0908722i | ||||
\(985\) | 4.67697 | + | 8.10075i | 0.149021 | + | 0.258111i | ||||
\(986\) | 56.7482 | 1.80723 | ||||||||
\(987\) | 7.03319 | + | 8.97374i | 0.223869 | + | 0.285637i | ||||
\(988\) | 9.67281i | 0.307733i | ||||||||
\(989\) | 13.3559 | + | 6.70131i | 0.424692 | + | 0.213089i | ||||
\(990\) | −15.9040 | − | 9.18217i | −0.505462 | − | 0.291829i | ||||
\(991\) | −26.3316 | + | 45.6076i | −0.836450 | + | 1.44877i | 0.0563939 | + | 0.998409i | \(0.482040\pi\) |
−0.892844 | + | 0.450366i | \(0.851294\pi\) | |||||||
\(992\) | −3.47311 | + | 2.00520i | −0.110271 | + | 0.0636651i | ||||
\(993\) | − | 6.63138i | − | 0.210440i | ||||||
\(994\) | −11.5890 | + | 28.8106i | −0.367580 | + | 0.913816i | ||||
\(995\) | 12.1084 | 0.383863 | ||||||||
\(996\) | −7.55311 | + | 4.36079i | −0.239329 | + | 0.138177i | ||||
\(997\) | −29.0078 | − | 16.7477i | −0.918686 | − | 0.530404i | −0.0354705 | − | 0.999371i | \(-0.511293\pi\) |
−0.883216 | + | 0.468967i | \(0.844626\pi\) | |||||||
\(998\) | 6.40771 | − | 11.0985i | 0.202832 | − | 0.351316i | ||||
\(999\) | −14.2663 | − | 24.7100i | −0.451366 | − | 0.781790i |
(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 | 322.2.g.a.45.4 | yes | 16 | |
7.3 | odd | 6 | 2254.2.c.c.2253.8 | 16 | |||
7.4 | even | 3 | 2254.2.c.c.2253.9 | 16 | |||
7.5 | odd | 6 | inner | 322.2.g.a.229.3 | yes | 16 | |
23.22 | odd | 2 | inner | 322.2.g.a.45.3 | ✓ | 16 | |
161.45 | even | 6 | 2254.2.c.c.2253.7 | 16 | |||
161.68 | even | 6 | inner | 322.2.g.a.229.4 | yes | 16 | |
161.137 | odd | 6 | 2254.2.c.c.2253.10 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.a.45.3 | ✓ | 16 | 23.22 | odd | 2 | inner | |
322.2.g.a.45.4 | yes | 16 | 1.1 | even | 1 | trivial | |
322.2.g.a.229.3 | yes | 16 | 7.5 | odd | 6 | inner | |
322.2.g.a.229.4 | yes | 16 | 161.68 | even | 6 | inner | |
2254.2.c.c.2253.7 | 16 | 161.45 | even | 6 | |||
2254.2.c.c.2253.8 | 16 | 7.3 | odd | 6 | |||
2254.2.c.c.2253.9 | 16 | 7.4 | even | 3 | |||
2254.2.c.c.2253.10 | 16 | 161.137 | odd | 6 |