Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(47,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.o (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 239.3 | ||
Character | \(\chi\) | \(=\) | 384.239 |
Dual form | 384.2.o.a.143.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −1.44423 | + | 0.956131i | −0.833829 | + | 0.552022i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56013 | + | 3.76650i | 0.697713 | + | 1.68443i | 0.728631 | + | 0.684906i | \(0.240157\pi\) |
−0.0309186 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.838552 | + | 0.838552i | 0.316943 | + | 0.316943i | 0.847592 | − | 0.530649i | \(-0.178052\pi\) |
−0.530649 | + | 0.847592i | \(0.678052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.17163 | − | 2.76175i | 0.390542 | − | 0.920585i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.249049 | + | 0.601256i | 0.0750910 | + | 0.181286i | 0.956968 | − | 0.290194i | \(-0.0937200\pi\) |
−0.881877 | + | 0.471480i | \(0.843720\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.05771 | − | 0.852332i | −0.570706 | − | 0.236394i | 0.0786194 | − | 0.996905i | \(-0.474949\pi\) |
−0.649326 | + | 0.760510i | \(0.724949\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.85446 | − | 3.94801i | −1.51162 | − | 1.01937i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23677 | −0.785032 | −0.392516 | − | 0.919745i | \(-0.628395\pi\) | ||||
−0.392516 | + | 0.919745i | \(0.628395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.47818 | + | 3.56865i | −0.339119 | + | 0.818705i | 0.658682 | + | 0.752421i | \(0.271114\pi\) |
−0.997801 | + | 0.0662838i | \(0.978886\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.01283 | − | 0.409300i | −0.439236 | − | 0.0893166i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.58369 | + | 2.58369i | 0.538737 | + | 0.538737i | 0.923158 | − | 0.384421i | \(-0.125599\pi\) |
−0.384421 | + | 0.923158i | \(0.625599\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.21694 | + | 8.21694i | −1.64339 | + | 1.64339i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.948494 | + | 5.10885i | 0.182538 | + | 0.983199i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.52027 | + | 1.45815i | 0.653698 | + | 0.270771i | 0.684784 | − | 0.728746i | \(-0.259896\pi\) |
−0.0310857 | + | 0.999517i | \(0.509896\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.63408i | − | 1.37112i | −0.728015 | − | 0.685561i | \(-0.759557\pi\) | ||
0.728015 | − | 0.685561i | \(-0.240443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.934564 | − | 0.630232i | −0.162687 | − | 0.109709i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.85015 | + | 4.46665i | −0.312732 | + | 0.755002i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.579146 | − | 0.239890i | 0.0952110 | − | 0.0394377i | −0.334570 | − | 0.942371i | \(-0.608591\pi\) |
0.429781 | + | 0.902933i | \(0.358591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.78676 | − | 0.736474i | 0.606367 | − | 0.117930i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54554 | + | 3.54554i | −0.553720 | + | 0.553720i | −0.927512 | − | 0.373792i | \(-0.878057\pi\) |
0.373792 | + | 0.927512i | \(0.378057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.19595 | − | 1.32381i | 0.487378 | − | 0.201879i | −0.125442 | − | 0.992101i | \(-0.540035\pi\) |
0.612820 | + | 0.790222i | \(0.290035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.2300 | + | 0.104223i | 1.82315 | + | 0.0155366i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.96658i | 0.870315i | 0.900354 | + | 0.435158i | \(0.143307\pi\) | ||||
−0.900354 | + | 0.435158i | \(0.856693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.59366i | − | 0.799095i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.67465 | − | 3.09477i | 0.654582 | − | 0.433355i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.762825 | + | 0.315973i | −0.104782 | + | 0.0434022i | −0.434459 | − | 0.900692i | \(-0.643060\pi\) |
0.329677 | + | 0.944094i | \(0.393060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.87608 | + | 1.87608i | −0.252971 | + | 0.252971i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.27725 | − | 6.56731i | −0.169176 | − | 0.869862i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.86827 | + | 2.43072i | −0.763984 | + | 0.316452i | −0.730433 | − | 0.682985i | \(-0.760682\pi\) |
−0.0335508 | + | 0.999437i | \(0.510682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.68247 | − | 6.47607i | 0.343456 | − | 0.829175i | −0.653906 | − | 0.756576i | \(-0.726871\pi\) |
0.997361 | − | 0.0725992i | \(-0.0231294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.29834 | − | 1.33340i | 0.415552 | − | 0.167993i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.08011i | − | 1.12625i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.78575 | − | 1.98232i | −0.584673 | − | 0.242179i | 0.0706842 | − | 0.997499i | \(-0.477482\pi\) |
−0.655357 | + | 0.755319i | \(0.727482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.20180 | − | 1.26111i | −0.746609 | − | 0.151820i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.2094 | − | 10.2094i | 1.21163 | − | 1.21163i | 0.241145 | − | 0.970489i | \(-0.422477\pi\) |
0.970489 | − | 0.241145i | \(-0.0775229\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.09458 | + | 8.09458i | 0.947399 | + | 0.947399i | 0.998684 | − | 0.0512851i | \(-0.0163317\pi\) |
−0.0512851 | + | 0.998684i | \(0.516332\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.01072 | − | 19.7237i | 0.463118 | − | 2.27749i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.295345 | + | 0.713025i | −0.0336576 | + | 0.0812567i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5343 | 1.29771 | 0.648857 | − | 0.760910i | \(-0.275247\pi\) | ||||
0.648857 | + | 0.760910i | \(0.275247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.25458 | − | 6.47149i | −0.694953 | − | 0.719055i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.998651 | − | 0.413655i | −0.109616 | − | 0.0454045i | 0.327201 | − | 0.944955i | \(-0.393894\pi\) |
−0.436818 | + | 0.899550i | \(0.643894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.04979 | − | 12.1913i | −0.547727 | − | 1.32233i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.47828 | + | 1.25994i | −0.694544 | + | 0.135080i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4124 | + | 10.4124i | 1.10372 | + | 1.10372i | 0.993958 | + | 0.109759i | \(0.0350078\pi\) |
0.109759 | + | 0.993958i | \(0.464992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.01077 | − | 2.44022i | −0.105958 | − | 0.255805i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.29918 | + | 11.0254i | 0.756890 | + | 1.14328i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15.7475 | −1.61566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.21596 | 0.935739 | 0.467870 | − | 0.883797i | \(-0.345022\pi\) | ||||
0.467870 | + | 0.883797i | \(0.345022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.95232 | + | 0.0166374i | 0.196215 | + | 0.00167212i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61830 | + | 3.90691i | 0.161026 | + | 0.388752i | 0.983714 | − | 0.179742i | \(-0.0575262\pi\) |
−0.822687 | + | 0.568494i | \(0.807526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.29846 | + | 4.29846i | 0.423540 | + | 0.423540i | 0.886421 | − | 0.462881i | \(-0.153184\pi\) |
−0.462881 | + | 0.886421i | \(0.653184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.59866 | − | 8.21988i | −0.156013 | − | 0.802178i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82811 | + | 6.82767i | 0.273404 | + | 0.660055i | 0.999624 | − | 0.0274065i | \(-0.00872486\pi\) |
−0.726221 | + | 0.687462i | \(0.758725\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4025 | + | 5.13729i | 1.18794 | + | 0.492063i | 0.887085 | − | 0.461606i | \(-0.152727\pi\) |
0.300859 | + | 0.953669i | \(0.402727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.607056 | + | 0.900196i | −0.0576192 | + | 0.0854429i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.42949 | 0.322619 | 0.161310 | − | 0.986904i | \(-0.448428\pi\) | ||||
0.161310 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.70056 | + | 13.7624i | −0.531580 | + | 1.28335i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.76480 | + | 4.68428i | −0.440506 | + | 0.433062i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.71420 | − | 2.71420i | −0.248810 | − | 0.248810i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.47869 | − | 7.47869i | 0.679881 | − | 0.679881i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.73059 | − | 8.51059i | 0.156042 | − | 0.767374i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.9361 | − | 10.3289i | −2.23035 | − | 0.923842i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.724490i | − | 0.0642881i | −0.999483 | − | 0.0321441i | \(-0.989766\pi\) | ||
0.999483 | − | 0.0321441i | \(-0.0102335\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.34997 | + | 4.96764i | −0.294949 | + | 0.437376i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.44273 | − | 3.48306i | 0.126052 | − | 0.304317i | −0.848238 | − | 0.529616i | \(-0.822336\pi\) |
0.974290 | + | 0.225299i | \(0.0723360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.23204 | + | 1.75297i | −0.366964 | + | 0.152001i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.7627 | + | 11.5430i | −1.52877 | + | 0.993462i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.20990 | − | 2.20990i | 0.188805 | − | 0.188805i | −0.606375 | − | 0.795179i | \(-0.707377\pi\) |
0.795179 | + | 0.606375i | \(0.207377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.01991 | + | 1.66510i | −0.340964 | + | 0.141232i | −0.546594 | − | 0.837398i | \(-0.684076\pi\) |
0.205629 | + | 0.978630i | \(0.434076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70483 | − | 8.61714i | −0.480434 | − | 0.725694i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1.44948i | − | 0.121212i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.5340i | 1.29003i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.34827 | + | 8.07856i | 0.441118 | + | 0.666308i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.47285 | − | 2.26693i | 0.448353 | − | 0.185714i | −0.147070 | − | 0.989126i | \(-0.546984\pi\) |
0.595423 | + | 0.803412i | \(0.296984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.81381 | − | 5.81381i | 0.473121 | − | 0.473121i | −0.429802 | − | 0.902923i | \(-0.641417\pi\) |
0.902923 | + | 0.429802i | \(0.141417\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.79229 | + | 8.93916i | −0.306588 | + | 0.722688i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.7537 | − | 11.9102i | 2.30956 | − | 0.956649i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.37305 | + | 8.14326i | −0.269199 | + | 0.649903i | −0.999446 | − | 0.0332797i | \(-0.989405\pi\) |
0.730247 | + | 0.683183i | \(0.239405\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.799588 | − | 1.18570i | 0.0634114 | − | 0.0940321i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33312i | 0.341498i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8401 | − | 5.73275i | −1.08404 | − | 0.449024i | −0.232114 | − | 0.972688i | \(-0.574564\pi\) |
−0.851924 | + | 0.523665i | \(0.824564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.915722 | − | 4.50328i | 0.0712889 | − | 0.350580i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.72756 | + | 6.72756i | −0.520594 | + | 0.520594i | −0.917751 | − | 0.397157i | \(-0.869997\pi\) |
0.397157 | + | 0.917751i | \(0.369997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.68468 | − | 5.68468i | −0.437283 | − | 0.437283i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.12386 | + | 8.26352i | 0.621247 | + | 0.631927i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.275804 | − | 0.665850i | 0.0209690 | − | 0.0506236i | −0.913048 | − | 0.407852i | \(-0.866278\pi\) |
0.934017 | + | 0.357228i | \(0.116278\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.7807 | −1.04172 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.15107 | − | 9.12136i | 0.462343 | − | 0.685603i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.9198 | − | 4.93735i | −0.890928 | − | 0.369035i | −0.110203 | − | 0.993909i | \(-0.535150\pi\) |
−0.780725 | + | 0.624875i | \(0.785150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.66842 | − | 6.44214i | −0.198342 | − | 0.478841i | 0.793147 | − | 0.609030i | \(-0.208441\pi\) |
−0.991489 | + | 0.130190i | \(0.958441\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.31784 | + | 11.9178i | 0.171340 | + | 0.880986i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.80709 | + | 1.80709i | 0.132860 | + | 0.132860i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.806113 | − | 1.94613i | −0.0589488 | − | 0.142315i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.48867 | + | 5.07940i | −0.253764 | + | 0.369472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.62308 | 0.117442 | 0.0587210 | − | 0.998274i | \(-0.481298\pi\) | ||||
0.0587210 | + | 0.998274i | \(0.481298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.3575 | −0.745548 | −0.372774 | − | 0.927922i | \(-0.621593\pi\) | ||||
−0.372774 | + | 0.927922i | \(0.621593\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.68177 | + | 13.1138i | 0.621715 | + | 0.939099i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.784033 | − | 1.89282i | −0.0558601 | − | 0.134858i | 0.893486 | − | 0.449092i | \(-0.148252\pi\) |
−0.949346 | + | 0.314234i | \(0.898252\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.78498 | + | 8.78498i | 0.622751 | + | 0.622751i | 0.946234 | − | 0.323483i | \(-0.104854\pi\) |
−0.323483 | + | 0.946234i | \(0.604854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.80711 | − | 1.71287i | 0.621206 | − | 0.120816i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.72920 | + | 4.17466i | 0.121366 | + | 0.293004i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.8858 | − | 7.82274i | −1.31904 | − | 0.546364i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.1626 | − | 4.10840i | 0.706353 | − | 0.285553i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.51382 | −0.173884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.81540 | − | 23.6965i | 0.675720 | − | 1.63133i | −0.0960096 | − | 0.995380i | \(-0.530608\pi\) |
0.771729 | − | 0.635951i | \(-0.219392\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.98325 | + | 24.5063i | −0.341447 | + | 1.67915i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.97223 | + | 9.97223i | 0.680100 | + | 0.680100i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.40157 | − | 6.40157i | 0.434567 | − | 0.434567i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.4300 | − | 3.95099i | −1.31295 | − | 0.266983i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.66034 | + | 2.75880i | 0.448023 | + | 0.185577i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.3840i | 1.09715i | 0.836101 | + | 0.548576i | \(0.184830\pi\) | ||||
−0.836101 | + | 0.548576i | \(0.815170\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0660 | + | 32.3204i | 0.871065 | + | 2.15469i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.61652 | − | 23.2163i | 0.638271 | − | 1.54092i | −0.190710 | − | 0.981646i | \(-0.561079\pi\) |
0.828981 | − | 0.559276i | \(-0.188921\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2556 | + | 4.66223i | −0.743792 | + | 0.308089i | −0.722206 | − | 0.691678i | \(-0.756872\pi\) |
−0.0215864 | + | 0.999767i | \(0.506872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.255198 | − | 1.31216i | −0.0167908 | − | 0.0863340i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5410 | + | 13.5410i | −0.887101 | + | 0.887101i | −0.994244 | − | 0.107143i | \(-0.965830\pi\) |
0.107143 | + | 0.994244i | \(0.465830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.4731 | + | 9.30866i | −1.46598 | + | 0.607230i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.6583 | + | 11.0283i | −1.08207 | + | 0.716367i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1168i | 1.23657i | 0.785956 | + | 0.618283i | \(0.212171\pi\) | ||||
−0.785956 | + | 0.618283i | \(0.787829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1.71219i | − | 0.110292i | −0.998478 | − | 0.0551460i | \(-0.982438\pi\) | ||
0.998478 | − | 0.0551460i | \(-0.0175624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2207 | + | 3.36616i | 0.976407 | + | 0.215939i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.0685 | − | 8.72686i | 1.34602 | − | 0.557539i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.08335 | − | 6.08335i | 0.387075 | − | 0.387075i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.83780 | − | 0.357427i | 0.116466 | − | 0.0226510i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.5253 | + | 10.5729i | −1.61115 | + | 0.667358i | −0.992936 | − | 0.118655i | \(-0.962142\pi\) |
−0.618210 | + | 0.786013i | \(0.712142\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.909996 | + | 2.19693i | −0.0572110 | + | 0.138120i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.9495 | + | 12.7788i | 1.18667 | + | 0.800239i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 21.5264i | − | 1.34278i | −0.741104 | − | 0.671391i | \(-0.765697\pi\) | ||
0.741104 | − | 0.671391i | \(-0.234303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.686804 | + | 0.284483i | 0.0426759 | + | 0.0176769i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.15149 | − | 8.01373i | 0.504564 | − | 0.496037i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4924 | − | 10.4924i | 0.646988 | − | 0.646988i | −0.305276 | − | 0.952264i | \(-0.598749\pi\) |
0.952264 | + | 0.305276i | \(0.0987488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.38022 | − | 2.38022i | −0.146216 | − | 0.146216i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.9937 | − | 5.08235i | −1.52959 | − | 0.311035i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.94856 | − | 11.9469i | 0.301719 | − | 0.728414i | −0.698203 | − | 0.715900i | \(-0.746017\pi\) |
0.999922 | − | 0.0125138i | \(-0.00398337\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.03570 | −0.427388 | −0.213694 | − | 0.976901i | \(-0.568550\pi\) | ||||
−0.213694 | + | 0.976901i | \(0.568550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.79296 | + | 2.55782i | 0.229561 | + | 0.154806i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.98690 | − | 2.89407i | −0.421326 | − | 0.174519i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.40456 | + | 22.7046i | 0.565065 | + | 1.36419i | 0.905671 | + | 0.423982i | \(0.139368\pi\) |
−0.340606 | + | 0.940206i | \(0.610632\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.0835 | − | 8.94430i | −1.26223 | − | 0.535481i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.7076 | − | 13.7076i | −0.817727 | − | 0.817727i | 0.168051 | − | 0.985778i | \(-0.446253\pi\) |
−0.985778 | + | 0.168051i | \(0.946253\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3422 | + | 27.3825i | 0.674224 | + | 1.62772i | 0.774358 | + | 0.632747i | \(0.218073\pi\) |
−0.100134 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 22.7431 | − | 15.0567i | 1.34718 | − | 0.891879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.94623 | −0.350995 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.52333 | −0.383725 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.3100 | + | 8.81167i | −0.780247 | + | 0.516549i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.07927 | − | 9.84823i | −0.238314 | − | 0.575340i | 0.758795 | − | 0.651329i | \(-0.225788\pi\) |
−0.997109 | + | 0.0759896i | \(0.975788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.3106 | − | 18.3106i | −1.06608 | − | 1.06608i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.83551 | + | 1.84264i | −0.164533 | + | 0.106921i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.11433 | − | 7.51865i | −0.180106 | − | 0.434815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.79005 | + | 1.56989i | 0.218455 | + | 0.0904871i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.07272 | − | 4.09520i | −0.348869 | − | 0.235263i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.5771 | 1.63632 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.04114 | − | 19.4130i | 0.458932 | − | 1.10796i | −0.509898 | − | 0.860235i | \(-0.670317\pi\) |
0.968830 | − | 0.247725i | \(-0.0796830\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.3179 | − | 2.09809i | −0.586963 | − | 0.119356i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9205 | − | 20.9205i | −1.18629 | − | 1.18629i | −0.978084 | − | 0.208210i | \(-0.933236\pi\) |
−0.208210 | − | 0.978084i | \(-0.566764\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.91198 | + | 8.91198i | −0.503735 | + | 0.503735i | −0.912596 | − | 0.408861i | \(-0.865926\pi\) |
0.408861 | + | 0.912596i | \(0.365926\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.1681 | + | 10.3429i | 0.572909 | + | 0.582757i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.482452 | − | 0.199838i | −0.0270972 | − | 0.0112240i | 0.369094 | − | 0.929392i | \(-0.379668\pi\) |
−0.396191 | + | 0.918168i | \(0.629668\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.47974i | 0.138839i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.6126 | − | 7.15671i | −0.592337 | − | 0.399448i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.78454 | − | 11.5509i | 0.266219 | − | 0.642710i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.9116 | − | 9.90452i | 1.32638 | − | 0.549404i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.8240 | + | 4.43897i | −1.26217 | + | 0.245476i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.00329 | + | 5.00329i | −0.275840 | + | 0.275840i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.5132 | − | 8.08262i | 1.07254 | − | 0.444261i | 0.224654 | − | 0.974439i | \(-0.427875\pi\) |
0.847887 | + | 0.530177i | \(0.177875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0160256 | − | 1.88052i | 0.000878196 | − | 0.103052i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 21.1182i | − | 1.15381i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.2626i | 0.559037i | 0.960140 | + | 0.279519i | \(0.0901749\pi\) | ||||
−0.960140 | + | 0.279519i | \(0.909825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.95299 | + | 3.27904i | −0.269009 | + | 0.178093i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.59004 | − | 1.90126i | 0.248565 | − | 0.102959i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.5604 | − | 10.5604i | 0.570210 | − | 0.570210i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.92568 | − | 25.3266i | −0.265190 | − | 1.36354i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.24383 | − | 1.75785i | 0.227821 | − | 0.0943665i | −0.265853 | − | 0.964014i | \(-0.585654\pi\) |
0.493674 | + | 0.869647i | \(0.335654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.7021 | − | 33.0798i | 0.733457 | − | 1.77072i | 0.102741 | − | 0.994708i | \(-0.467239\pi\) |
0.630716 | − | 0.776014i | \(-0.282761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.40271 | − | 11.3210i | 0.128247 | − | 0.604269i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.53983i | − | 0.241631i | −0.992675 | − | 0.120815i | \(-0.961449\pi\) | ||
0.992675 | − | 0.120815i | \(-0.0385509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.3817 | + | 22.5257i | 2.88628 | + | 1.19554i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.51507 | + | 1.32481i | 0.344814 | + | 0.0701164i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.86633 | − | 2.86633i | 0.151279 | − | 0.151279i | −0.627410 | − | 0.778689i | \(-0.715885\pi\) |
0.778689 | + | 0.627410i | \(0.215885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.88477 | + | 2.88477i | 0.151830 | + | 0.151830i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.65038 | + | 17.9516i | −0.191595 | + | 0.942214i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8596 | + | 43.1168i | −0.934813 | + | 2.25684i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.9994 | 1.51376 | 0.756878 | − | 0.653557i | \(-0.226724\pi\) | ||||
0.756878 | + | 0.653557i | \(0.226724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.63786 | + | 13.9460i | 0.293495 | + | 0.725997i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.904628 | − | 0.374709i | −0.0469659 | − | 0.0194539i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.55879 | + | 18.2485i | 0.391379 | + | 0.944873i | 0.989640 | + | 0.143572i | \(0.0458587\pi\) |
−0.598261 | + | 0.801302i | \(0.704141\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 45.8893 | − | 8.92486i | 2.36971 | − | 0.460878i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00088 | − | 6.00088i | −0.309061 | − | 0.309061i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.21366 | − | 17.4153i | −0.370541 | − | 0.894564i | −0.993659 | − | 0.112437i | \(-0.964134\pi\) |
0.623118 | − | 0.782128i | \(-0.285866\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.692708 | + | 1.04633i | 0.0354885 | + | 0.0536053i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.2276 | 0.931388 | 0.465694 | − | 0.884946i | \(-0.345805\pi\) | ||||
0.465694 | + | 0.884946i | \(0.345805\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.14638 | −0.160354 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0884355 | − | 10.3775i | 0.00449543 | − | 0.527515i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.747968 | − | 1.80575i | −0.0379235 | − | 0.0915554i | 0.903783 | − | 0.427991i | \(-0.140779\pi\) |
−0.941706 | + | 0.336436i | \(0.890779\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.36281 | − | 8.36281i | −0.422926 | − | 0.422926i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.24662 | + | 6.40980i | 0.0628837 | + | 0.323332i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.9951 | + | 43.4440i | 0.905432 | + | 2.18591i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.44786 | − | 3.08500i | −0.373797 | − | 0.154832i | 0.187872 | − | 0.982193i | \(-0.439841\pi\) |
−0.561670 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.43599 | − | 6.57807i | 0.222077 | − | 0.329316i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.1951 | −1.65768 | −0.828842 | − | 0.559482i | \(-0.811000\pi\) | ||||
−0.828842 | + | 0.559482i | \(0.811000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.50677 | + | 15.7087i | −0.324125 | + | 0.782508i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.6169 | − | 33.6542i | 0.726318 | − | 1.67229i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.288471 | + | 0.288471i | 0.0142990 | + | 0.0142990i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3278 | − | 24.3278i | 1.20293 | − | 1.20293i | 0.229664 | − | 0.973270i | \(-0.426237\pi\) |
0.973270 | − | 0.229664i | \(-0.0737629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.07866 | + | 5.30457i | −0.0532064 | + | 0.261655i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.95913 | − | 2.88257i | −0.342436 | − | 0.141842i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.40677i | − | 0.216320i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.21364 | − | 6.24836i | 0.206343 | − | 0.305983i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.96150 | + | 21.6350i | −0.437798 | + | 1.05694i | 0.538910 | + | 0.842363i | \(0.318836\pi\) |
−0.976708 | + | 0.214574i | \(0.931164\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.8146 | − | 6.55062i | 0.770756 | − | 0.319258i | 0.0375773 | − | 0.999294i | \(-0.488036\pi\) |
0.733179 | + | 0.680036i | \(0.238036\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.4782 | + | 6.99061i | 0.801199 | + | 0.339895i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.5963 | − | 26.5963i | 1.29011 | − | 1.29011i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.67991 | − | 3.18112i | 0.371657 | − | 0.153945i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.38590 | + | 2.09340i | 0.0669117 | + | 0.101070i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 21.2060i | − | 1.02146i | −0.859742 | − | 0.510729i | \(-0.829375\pi\) | ||
0.859742 | − | 0.510729i | \(-0.170625\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.73016i | − | 0.371488i | −0.982598 | − | 0.185744i | \(-0.940531\pi\) | ||
0.982598 | − | 0.185744i | \(-0.0594695\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.8525 | − | 22.4347i | −0.712124 | − | 1.07566i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.0395 | + | 5.40113i | −0.623763 | + | 0.258371i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4093 | + | 25.4093i | −1.21272 | + | 1.21272i | −0.242594 | + | 0.970128i | \(0.577998\pi\) |
−0.970128 | + | 0.242594i | \(0.922002\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.4483 | − | 6.55369i | −0.735634 | − | 0.312080i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.74325 | + | 1.96472i | −0.225359 | + | 0.0933467i | −0.492506 | − | 0.870309i | \(-0.663919\pi\) |
0.267147 | + | 0.963656i | \(0.413919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.9736 | + | 55.4632i | −1.08905 | + | 2.62921i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.73660 | + | 8.50674i | −0.271332 | + | 0.402355i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.4003i | − | 0.632399i | −0.948693 | − | 0.316199i | \(-0.897593\pi\) | ||
0.948693 | − | 0.316199i | \(-0.102407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.01479 | − | 1.24877i | −0.141961 | − | 0.0588021i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.83774 | + | 13.9553i | −0.133329 | + | 0.655676i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.61414 | − | 7.61414i | 0.356957 | − | 0.356957i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.8591 | − | 21.8591i | −1.02253 | − | 1.02253i | −0.999740 | − | 0.0227865i | \(-0.992746\pi\) |
−0.0227865 | − | 0.999740i | \(-0.507254\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.07006 | − | 16.5362i | −0.143298 | − | 0.771842i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.39897 | − | 20.2769i | 0.391179 | − | 0.944389i | −0.598505 | − | 0.801119i | \(-0.704238\pi\) |
0.989684 | − | 0.143270i | \(-0.0457618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.1790 | −1.12369 | −0.561847 | − | 0.827241i | \(-0.689909\pi\) | ||||
−0.561847 | + | 0.827241i | \(0.689909\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −30.1394 | + | 44.6934i | −1.39768 | + | 2.07261i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.1546 | − | 9.17674i | −1.02519 | − | 0.424649i | −0.194218 | − | 0.980958i | \(-0.562217\pi\) |
−0.830975 | + | 0.556309i | \(0.812217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.35082 | − | 5.67538i | −0.108551 | − | 0.262065i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.91455 | − | 14.9859i | −0.134295 | − | 0.690512i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.59190 | + | 1.59190i | 0.0731954 | + | 0.0731954i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.1772 | − | 41.4695i | −0.788146 | − | 1.90275i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0211082 | + | 2.47694i | −0.000966478 | + | 0.113411i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.6803 | 1.08198 | 0.540991 | − | 0.841028i | \(-0.318049\pi\) | ||||
0.540991 | + | 0.841028i | \(0.318049\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.39618 | −0.0636603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.14303 | − | 6.25804i | −0.188514 | − | 0.284751i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3781 | + | 34.7119i | 0.652877 | + | 1.57619i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7774 | − | 15.7774i | −0.714942 | − | 0.714942i | 0.252623 | − | 0.967565i | \(-0.418707\pi\) |
−0.967565 | + | 0.252623i | \(0.918707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.4696 | − | 4.95349i | 1.15177 | − | 0.224005i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.45911 | − | 3.52259i | −0.0658486 | − | 0.158972i | 0.887530 | − | 0.460751i | \(-0.152420\pi\) |
−0.953378 | + | 0.301778i | \(0.902420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.3943 | − | 4.71968i | −0.513174 | − | 0.212564i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.98321 | + | 7.37934i | 0.134085 | + | 0.331677i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.1222 | 0.768037 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0066 | + | 28.9865i | −0.537490 | + | 1.29761i | 0.388980 | + | 0.921246i | \(0.372827\pi\) |
−0.926470 | + | 0.376369i | \(0.877173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.28375 | − | 16.1486i | 0.146707 | − | 0.721466i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.02060 | + | 9.02060i | 0.402208 | + | 0.402208i | 0.879011 | − | 0.476802i | \(-0.158204\pi\) |
−0.476802 | + | 0.879011i | \(0.658204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.1906 | + | 12.1906i | −0.542475 | + | 0.542475i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.6453 | + | 2.77471i | 0.606010 | + | 0.123229i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9019 | − | 5.75836i | −0.616192 | − | 0.255235i | 0.0526815 | − | 0.998611i | \(-0.483223\pi\) |
−0.668873 | + | 0.743376i | \(0.733223\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5754i | 0.600543i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.6338 | − | 4.16698i | −0.866852 | − | 0.183977i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.48396 | + | 22.8963i | −0.417913 | + | 1.00893i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.58745 | + | 1.48597i | −0.157776 | + | 0.0653528i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.238314 | + | 1.22535i | 0.0104608 | + | 0.0537868i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.3052 | + | 24.3052i | −1.06483 | + | 1.06483i | −0.0670849 | + | 0.997747i | \(0.521370\pi\) |
−0.997747 | + | 0.0670849i | \(0.978630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.5224 | + | 4.77273i | −0.503839 | + | 0.208697i | −0.620102 | − | 0.784522i | \(-0.712909\pi\) |
0.116262 | + | 0.993219i | \(0.462909\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.9025 | − | 13.1761i | 0.868616 | − | 0.575053i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.7098i | 1.07637i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.64908i | − | 0.419525i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.162381 | + | 19.0546i | −0.00704675 | + | 0.826900i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3177 | − | 4.27372i | 0.446908 | − | 0.185115i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.3041 | + | 21.3041i | −0.921058 | + | 0.921058i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.9357 | − | 4.26621i | 0.946597 | − | 0.184101i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.36323 | − | 1.39309i | 0.144864 | − | 0.0600048i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.0650 | − | 26.7133i | 0.475722 | − | 1.14849i | −0.485875 | − | 0.874028i | \(-0.661499\pi\) |
0.961597 | − | 0.274466i | \(-0.0885010\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0134 | + | 6.75260i | 0.429714 | + | 0.289782i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 54.7288i | 2.34433i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.80786 | − | 2.40569i | −0.248326 | − | 0.102860i | 0.255049 | − | 0.966928i | \(-0.417909\pi\) |
−0.503375 | + | 0.864068i | \(0.667909\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.7424 | − | 14.9959i | −0.629192 | − | 0.640008i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4072 | + | 10.4072i | −0.443363 | + | 0.443363i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.67214 | + | 9.67214i | 0.411301 | + | 0.411301i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.33767 | − | 0.882047i | −0.184124 | − | 0.0374408i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.71096 | + | 18.6159i | −0.326724 | + | 0.788781i | 0.672108 | + | 0.740453i | \(0.265389\pi\) |
−0.998832 | + | 0.0483277i | \(0.984611\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.70467 | −0.325873 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.02497 | + | 2.03992i | 0.127714 | + | 0.0861253i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.4466 | + | 4.74136i | 0.482419 | + | 0.199824i | 0.610620 | − | 0.791924i | \(-0.290920\pi\) |
−0.128201 | + | 0.991748i | \(0.540920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.35046 | + | 12.9172i | 0.225096 | + | 0.543429i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.181895 | − | 10.6715i | 0.00763889 | − | 0.448160i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.9002 | + | 27.9002i | 1.16964 | + | 1.16964i | 0.982295 | + | 0.187343i | \(0.0599874\pi\) |
0.187343 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.45224 | + | 22.8197i | 0.395564 | + | 0.954976i | 0.988705 | + | 0.149877i | \(0.0478878\pi\) |
−0.593141 | + | 0.805099i | \(0.702112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.34411 | + | 1.55188i | −0.0979266 | + | 0.0648307i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −42.4601 | −1.77071 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6076 | −0.691383 | −0.345691 | − | 0.938348i | \(-0.612356\pi\) | ||||
−0.345691 | + | 0.938348i | \(0.612356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9586 | − | 9.90310i | 0.621659 | − | 0.411559i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.490550 | − | 1.18429i | −0.0203514 | − | 0.0491327i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.379961 | − | 0.379961i | −0.0157364 | − | 0.0157364i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.0770 | − | 10.6385i | −1.03681 | − | 0.439848i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.82661 | − | 14.0667i | −0.240490 | − | 0.580594i | 0.756842 | − | 0.653598i | \(-0.226741\pi\) |
−0.997332 | + | 0.0730041i | \(0.976741\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.2434 | + | 11.2846i | 1.12254 | + | 0.464973i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.94212 | + | 1.98404i | 0.121022 | + | 0.0816126i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.760076 | 0.0312126 | 0.0156063 | − | 0.999878i | \(-0.495032\pi\) | ||||
0.0156063 | + | 0.999878i | \(0.495032\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.98850 | − | 14.4575i | 0.245505 | − | 0.592701i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.0872 | − | 4.28798i | −0.863041 | − | 0.175495i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.9662 | + | 18.9662i | 0.774937 | + | 0.774937i | 0.978965 | − | 0.204028i | \(-0.0654033\pi\) |
−0.204028 | + | 0.978965i | \(0.565403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3756 | + | 15.3756i | −0.627183 | + | 0.627183i | −0.947358 | − | 0.320175i | \(-0.896258\pi\) |
0.320175 | + | 0.947358i | \(0.396258\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.0818 | + | 10.8945i | −0.451286 | + | 0.443660i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.8362 | + | 16.5007i | 1.61957 | + | 0.670849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.77741i | − | 0.356264i | −0.984007 | − | 0.178132i | \(-0.942995\pi\) | ||
0.984007 | − | 0.178132i | \(-0.0570054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.48890 | − | 4.37585i | −0.262943 | − | 0.177318i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.08551 | − | 12.2775i | 0.205738 | − | 0.496695i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.08951 | + | 1.69393i | −0.165174 | + | 0.0684172i | −0.463738 | − | 0.885972i | \(-0.653492\pi\) |
0.298564 | + | 0.954389i | \(0.403492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.7550 | − | 6.75939i | 1.40146 | − | 0.272565i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3859 | + | 10.3859i | −0.418123 | + | 0.418123i | −0.884556 | − | 0.466434i | \(-0.845539\pi\) |
0.466434 | + | 0.884556i | \(0.345539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6486 | − | 8.55293i | 0.829937 | − | 0.343771i | 0.0730593 | − | 0.997328i | \(-0.476724\pi\) |
0.756878 | + | 0.653556i | \(0.226724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.7491 | + | 15.6503i | −0.431346 | + | 0.628025i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.4628i | 0.699630i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 51.9336i | − | 2.07734i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.63054 | − | 2.40354i | 0.144990 | − | 0.0959880i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.87456 | + | 0.776468i | −0.0747436 | + | 0.0309598i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2657 | + | 13.2657i | −0.528098 | + | 0.528098i | −0.920005 | − | 0.391907i | \(-0.871815\pi\) |
0.391907 | + | 0.920005i | \(0.371815\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.48118 | + | 43.6081i | 0.337097 | + | 1.73326i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.72879 | − | 1.13030i | 0.108289 | − | 0.0448546i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.76766 | + | 11.5101i | −0.188901 | + | 0.456048i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.2343 | − | 40.1575i | −0.642218 | − | 1.58861i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.60149i | − | 0.142250i | −0.997467 | − | 0.0711252i | \(-0.977341\pi\) | ||
0.997467 | − | 0.0711252i | \(-0.0226590\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.5202 | − | 6.84287i | −0.651492 | − | 0.269857i | 0.0323617 | − | 0.999476i | \(-0.489697\pi\) |
−0.683853 | + | 0.729620i | \(0.739697\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.9370 | − | 4.86748i | −0.942518 | − | 0.191657i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.6599 | + | 23.6599i | −0.930167 | + | 0.930167i | −0.997716 | − | 0.0675491i | \(-0.978482\pi\) |
0.0675491 | + | 0.997716i | \(0.478482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.92297 | − | 2.92297i | −0.114737 | − | 0.114737i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.12463 | + | 15.3661i | −0.122464 | + | 0.602246i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.1760 | − | 29.3955i | 0.476484 | − | 1.15033i | −0.484763 | − | 0.874646i | \(-0.661094\pi\) |
0.961247 | − | 0.275689i | \(-0.0889058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.3698 | 0.600547 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.8391 | − | 12.8714i | 1.24216 | − | 0.502162i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6508 | + | 17.2523i | 1.62248 | + | 0.672055i | 0.994360 | − | 0.106059i | \(-0.0338233\pi\) |
0.628123 | + | 0.778114i | \(0.283823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.34448 | + | 5.66007i | 0.0911896 | + | 0.220151i | 0.962893 | − | 0.269882i | \(-0.0869847\pi\) |
−0.871704 | + | 0.490033i | \(0.836985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.2569 | + | 2.38380i | −0.476017 | + | 0.0925790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.2051 | − | 13.2051i | −0.512071 | − | 0.512071i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.32790 | + | 12.8627i | 0.206297 | + | 0.498046i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.6652 | − | 23.6623i | −0.605652 | − | 0.914837i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.56184 | 0.176108 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.2206 | 1.74313 | 0.871563 | − | 0.490283i | \(-0.163107\pi\) | ||||
0.871563 | + | 0.490283i | \(0.163107\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −49.7728 | − | 34.1854i | −1.91576 | − | 1.31580i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.1300 | − | 46.1838i | −0.735224 | − | 1.77499i | −0.624338 | − | 0.781155i | \(-0.714631\pi\) |
−0.110886 | − | 0.993833i | \(-0.535369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.72806 | + | 7.72806i | 0.296576 | + | 0.296576i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.30935 | + | 42.7245i | 0.318415 | + | 1.63721i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.1282 | − | 34.1085i | −0.540600 | − | 1.30512i | −0.924300 | − | 0.381666i | \(-0.875350\pi\) |
0.383700 | − | 0.923458i | \(-0.374650\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7713 | + | 4.87584i | 0.449759 | + | 0.186296i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.7981 | − | 17.4952i | 0.450124 | − | 0.667484i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.83899 | 0.0700599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.84991 | − | 4.46608i | 0.0703740 | − | 0.169898i | −0.884779 | − | 0.466011i | \(-0.845691\pi\) |
0.955153 | + | 0.296113i | \(0.0956906\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.62317 | + | 1.65107i | 0.0616590 | + | 0.0627189i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.5432 | − | 12.5432i | −0.475791 | − | 0.475791i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4761 | − | 11.4761i | 0.434688 | − | 0.434688i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.60942 | − | 32.5034i | 0.249991 | − | 1.22939i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.68643 | + | 4.01225i | 0.365851 | + | 0.151541i | 0.558033 | − | 0.829819i | \(-0.311556\pi\) |
−0.192182 | + | 0.981359i | \(0.561556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.42137i | 0.0913238i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.5561 | − | 34.9311i | 0.887175 | − | 1.31558i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.91912 | + | 4.63317i | −0.0721761 | + | 0.174248i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.1564 | + | 15.8049i | −1.43299 | + | 0.593565i | −0.958088 | − | 0.286473i | \(-0.907517\pi\) |
−0.474904 | + | 0.880038i | \(0.657517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5139 | − | 31.8550i | 0.506812 | − | 1.19466i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.7241 | − | 19.7241i | 0.738674 | − | 0.738674i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.45948 | − | 2.26139i | 0.204173 | − | 0.0845711i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.2782 | − | 27.6092i | −0.682612 | − | 1.03108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.6233i | 1.73876i | 0.494147 | + | 0.869378i | \(0.335481\pi\) | ||||
−0.494147 | + | 0.869378i | \(0.664519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.20896i | 0.268476i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.63708 | + | 2.47281i | 0.0608837 | + | 0.0919647i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.9074 | + | 16.9444i | −1.51926 | + | 0.629298i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2103 | − | 25.2103i | 0.934997 | − | 0.934997i | −0.0630153 | − | 0.998013i | \(-0.520072\pi\) |
0.998013 | + | 0.0630153i | \(0.0200717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.2007 | + | 9.69143i | −0.933360 | + | 0.358942i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.3446 | + | 4.28486i | −0.382608 | + | 0.158481i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.25020 | + | 5.43246i | −0.0831129 | + | 0.200652i | −0.959973 | − | 0.280094i | \(-0.909634\pi\) |
0.876860 | + | 0.480747i | \(0.159634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.0838 | + | 32.7479i | −0.814575 | + | 1.20792i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.37116i | − | 0.124178i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5170 | − | 4.35630i | −0.386876 | − | 0.160249i | 0.180763 | − | 0.983527i | \(-0.442143\pi\) |
−0.567639 | + | 0.823277i | \(0.692143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.96931 | + | 14.6023i | −0.109080 | + | 0.536428i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.4609 | + | 15.4609i | −0.567205 | + | 0.567205i | −0.931345 | − | 0.364139i | \(-0.881363\pi\) |
0.364139 | + | 0.931345i | \(0.381363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0768 | + | 17.0768i | 0.625644 | + | 0.625644i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.31246 | + | 2.27338i | −0.0846085 | + | 0.0831787i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.35383 | + | 8.09687i | −0.122546 | + | 0.295853i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.5867 | −1.26209 | −0.631043 | − | 0.775748i | \(-0.717373\pi\) | ||||
−0.631043 | + | 0.775748i | \(0.717373\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.7555 | − | 39.6754i | 0.975023 | − | 1.44585i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.9680 | + | 12.8274i | 1.12704 | + | 0.466836i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.82795 | − | 16.4841i | −0.248166 | − | 0.599126i | 0.749882 | − | 0.661571i | \(-0.230110\pi\) |
−0.998048 | + | 0.0624455i | \(0.980110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.786300 | − | 4.04295i | −0.0285409 | − | 0.146750i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6555 | − | 10.6555i | −0.386261 | − | 0.386261i | 0.487090 | − | 0.873352i | \(-0.338058\pi\) |
−0.873352 | + | 0.487090i | \(0.838058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.09226 | + | 14.7080i | 0.220555 | + | 0.532466i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −39.5858 | − | 0.337346i | −1.43123 | − | 0.0121968i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.1470 | 0.510818 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.53950 | 0.163699 | 0.0818493 | − | 0.996645i | \(-0.473917\pi\) | ||||
0.0818493 | + | 0.996645i | \(0.473917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.5821 | + | 31.0892i | 0.741245 | + | 1.11965i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.7578 | + | 25.9715i | 0.386929 | + | 0.934130i | 0.990587 | + | 0.136886i | \(0.0437095\pi\) |
−0.603657 | + | 0.797244i | \(0.706290\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.7288 | + | 62.7288i | 2.25328 | + | 2.25328i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.26391 | + | 0.245814i | −0.0453425 | + | 0.00881851i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.41183 | − | 17.8938i | −0.265557 | − | 0.641110i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.68111 | + | 3.59583i | 0.310635 | + | 0.128669i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.11049 | + | 19.3676i | −0.146897 | + | 0.692141i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.9340 | −1.28254 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2001 | − | 43.9390i | 0.648764 | − | 1.56626i | −0.165786 | − | 0.986162i | \(-0.553016\pi\) |
0.814550 | − | 0.580093i | \(-0.196984\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.12137 | + | 25.1855i | −0.182325 | + | 0.896629i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.87581 | + | 2.87581i | 0.102252 | + | 0.102252i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.0395 | + | 11.0395i | −0.392025 | + | 0.392025i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.71340 | + | 1.16179i | 0.202633 | + | 0.0412046i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.989560 | + | 0.409889i | 0.0350520 | + | 0.0145190i | 0.400141 | − | 0.916454i | \(-0.368961\pi\) |
−0.365089 | + | 0.930973i | \(0.618961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 19.3124i | − | 0.683225i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.9561 | − | 16.5571i | 1.44711 | − | 0.585017i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.85097 | + | 6.88286i | −0.100609 | + | 0.242891i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.3207 | + | 6.76024i | −0.575228 | + | 0.238267i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.27590 | + | 21.9856i | 0.150519 | + | 0.773928i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.4456 | − | 16.4456i | 0.578196 | − | 0.578196i | −0.356210 | − | 0.934406i | \(-0.615931\pi\) |
0.934406 | + | 0.356210i | \(0.115931\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7926 | − | 12.7547i | 1.08127 | − | 0.447878i | 0.230317 | − | 0.973116i | \(-0.426024\pi\) |
0.850956 | + | 0.525238i | \(0.176024\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.1612 | − | 6.72705i | 0.356369 | − | 0.235928i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 61.0725i | − | 2.13927i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.3621i | 0.467480i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.92354 | − | 0.0675235i | −0.276871 | − | 0.00235946i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.3992 | + | 12.5918i | −1.06094 | + | 0.439455i | −0.843785 | − | 0.536682i | \(-0.819678\pi\) |
−0.217155 | + | 0.976137i | \(0.569678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.58486 | − | 7.58486i | 0.264392 | − | 0.264392i | −0.562444 | − | 0.826835i | \(-0.690139\pi\) |
0.826835 | + | 0.562444i | \(0.190139\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.8578 | − | 2.50068i | 0.447652 | − | 0.0870624i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.9305 | − | 14.4687i | 1.21465 | − | 0.503126i | 0.318947 | − | 0.947773i | \(-0.396671\pi\) |
0.895706 | + | 0.444647i | \(0.146671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.61267 | + | 3.89332i | −0.0560102 | + | 0.135221i | −0.949407 | − | 0.314047i | \(-0.898315\pi\) |
0.893397 | + | 0.449268i | \(0.148315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.2910 | − | 23.7988i | −1.22423 | − | 0.825571i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.1054i | 0.627315i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.8352 | − | 14.8434i | −1.24013 | − | 0.513678i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.0014 | − | 7.24088i | 1.34809 | − | 0.250282i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.7057 | − | 13.7057i | 0.473173 | − | 0.473173i | −0.429767 | − | 0.902940i | \(-0.641404\pi\) |
0.902940 | + | 0.429767i | \(0.141404\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.2400 | − | 10.2400i | −0.353102 | − | 0.353102i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.9033 | + | 6.69074i | 1.13325 | + | 0.230441i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.5425 | − | 30.2802i | 0.431474 | − | 1.04167i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.5425 | 0.430967 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.5621 | − | 28.7021i | −1.46073 | − | 0.985055i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.11614 | + | 0.876532i | 0.0725402 | + | 0.0300471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.8120 | − | 33.3450i | −0.472913 | − | 1.14171i | −0.962870 | − | 0.269966i | \(-0.912988\pi\) |
0.489957 | − | 0.871746i | \(-0.337012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.4502 | + | 43.4907i | −0.630983 | + | 1.48735i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.4023 | + | 24.4023i | 0.833565 | + | 0.833565i | 0.988003 | − | 0.154438i | \(-0.0493565\pi\) |
−0.154438 | + | 0.988003i | \(0.549357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.51555 | − | 3.65886i | −0.0517099 | − | 0.124839i | 0.895914 | − | 0.444228i | \(-0.146522\pi\) |
−0.947623 | + | 0.319390i | \(0.896522\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.58776 | − | 5.68538i | 0.292670 | − | 0.193757i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.8790 | −1.28942 | −0.644708 | − | 0.764429i | \(-0.723021\pi\) | ||||
−0.644708 | + | 0.764429i | \(0.723021\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.93821 | 0.0999021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.42122 | − | 6.23716i | 0.319961 | − | 0.211825i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.87261 | + | 6.93509i | 0.0974466 | + | 0.235257i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.15810 | + | 8.15810i | 0.276427 | + | 0.276427i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.7977 | − | 25.4522i | 0.365446 | − | 0.861427i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.2489 | − | 29.5715i | −0.414089 | − | 0.999699i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.89587 | + | 3.68479i | 0.300392 | + | 0.124426i | 0.527789 | − | 0.849376i | \(-0.323021\pi\) |
−0.227397 | + | 0.973802i | \(0.573021\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.3076 | + | 10.3228i | 0.516313 | + | 0.348181i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.66239 | −0.291843 | −0.145922 | − | 0.989296i | \(-0.546615\pi\) | ||||
−0.145922 | + | 0.989296i | \(0.546615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.6679 | + | 25.7547i | −0.359005 | + | 0.866715i | 0.636435 | + | 0.771330i | \(0.280408\pi\) |
−0.995440 | + | 0.0953849i | \(0.969592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.9521 | + | 8.93746i | 1.47743 | + | 0.300429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.1549 | + | 13.1549i | 0.441698 | + | 0.441698i | 0.892582 | − | 0.450885i | \(-0.148891\pi\) |
−0.450885 | + | 0.892582i | \(0.648891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.607523 | − | 0.607523i | 0.0203757 | − | 0.0203757i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.33333 | − | 5.37232i | 0.0781696 | − | 0.179980i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.2927 | − | 8.81971i | −0.712532 | − | 0.295140i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 52.5988i | − | 1.75818i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.6866 | + | 7.88099i | 0.390205 | + | 0.263139i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1316 | − | 26.8741i | 0.371260 | − | 0.896300i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.46909 | − | 1.02273i | 0.0822573 | − | 0.0340721i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.97475 | + | 1.35650i | −0.232105 | + | 0.0451414i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.1012 | − | 20.1012i | 0.668187 | − | 0.668187i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0939 | + | 9.98004i | −0.800026 | + | 0.331382i | −0.744967 | − | 0.667101i | \(-0.767535\pi\) |
−0.0550594 | + | 0.998483i | \(0.517535\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.6860 | + | 0.108108i | 0.420767 | + | 0.00358573i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52.5495i | − | 1.74104i | −0.492132 | − | 0.870520i | \(-0.663782\pi\) | ||
0.492132 | − | 0.870520i | \(-0.336218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 0.703466i | − | 0.0232813i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.2720 | + | 27.3234i | −1.36441 | + | 0.903285i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.13053 | − | 1.71092i | 0.136402 | − | 0.0564997i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.3967 | − | 32.3967i | 1.06867 | − | 1.06867i | 0.0712063 | − | 0.997462i | \(-0.477315\pi\) |
0.997462 | − | 0.0712063i | \(-0.0226849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.94810 | + | 35.7253i | 0.228948 | + | 1.17719i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.7098 | + | 12.3062i | −0.977911 | + | 0.405064i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.78764 | + | 6.72996i | −0.0916571 | + | 0.221280i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.9075 | − | 6.83510i | 0.555315 | − | 0.224494i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45.9891i | 1.50885i | 0.656385 | + | 0.754426i | \(0.272085\pi\) | ||||
−0.656385 | + | 0.754426i | \(0.727915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.9618 | + | 8.26846i | 0.654223 | + | 0.270988i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50.2169 | + | 10.2114i | 1.64403 | + | 0.334306i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.07244 | − | 6.07244i | 0.198590 | − | 0.198590i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.7725 | − | 19.7725i | −0.645940 | − | 0.645940i | 0.306069 | − | 0.952009i | \(-0.400986\pi\) |
−0.952009 | + | 0.306069i | \(0.900986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.34997 | − | 21.3920i | 0.141956 | − | 0.698102i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.8263 | − | 38.2081i | 0.515924 | − | 1.24555i | −0.424464 | − | 0.905445i | \(-0.639537\pi\) |
0.940387 | − | 0.340105i | \(-0.110463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.3211 | −0.596619 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.5743 | − | 5.21554i | −0.799403 | − | 0.169661i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.7644 | − | 12.3288i | −0.967213 | − | 0.400633i | −0.157539 | − | 0.987513i | \(-0.550356\pi\) |
−0.809674 | + | 0.586880i | \(0.800356\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.75704 | − | 23.5556i | −0.316727 | − | 0.764646i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.887846 | − | 0.172674i | 0.0287904 | − | 0.00559934i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.6032 | − | 12.6032i | −0.408259 | − | 0.408259i | 0.472872 | − | 0.881131i | \(-0.343217\pi\) |
−0.881131 | + | 0.472872i | \(0.843217\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.53222 | + | 6.11333i | 0.0819408 | + | 0.197823i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.37095 | − | 3.58132i | −0.0766420 | − | 0.115768i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.70623 | 0.119681 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2792 | −0.879975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.1698 | + | 0.188929i | 0.714413 | + | 0.00608815i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.1590 | − | 39.0114i | −0.520178 | − | 1.25582i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3843 | − | 25.3843i | −0.816305 | − | 0.816305i | 0.169265 | − | 0.985571i | \(-0.445861\pi\) |
−0.985571 | + | 0.169265i | \(0.945861\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.13418 | + | 21.2569i | 0.132809 | + | 0.682869i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.40697 | + | 5.81095i | 0.0772435 | + | 0.186482i | 0.957784 | − | 0.287488i | \(-0.0928203\pi\) |
−0.880541 | + | 0.473971i | \(0.842820\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.76718 | − | 1.97463i | −0.152829 | − | 0.0633037i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.0640 | + | 37.1671i | −0.802690 | + | 1.19030i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9584 | 0.766497 | 0.383249 | − | 0.923645i | \(-0.374805\pi\) | ||||
0.383249 | + | 0.923645i | \(0.374805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.66735 | + | 8.85376i | −0.117209 | + | 0.282967i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.7190 | − | 28.2337i | 0.916928 | − | 0.901432i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.9489 | − | 21.9489i | −0.700063 | − | 0.700063i | 0.264361 | − | 0.964424i | \(-0.414839\pi\) |
−0.964424 | + | 0.264361i | \(0.914839\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.90611 | − | 5.90611i | 0.188184 | − | 0.188184i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.44212 | − | 12.0097i | 0.0777336 | − | 0.382274i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.6777 | + | 4.83705i | 0.371328 | + | 0.153809i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.9976i | 1.01644i | 0.861229 | + | 0.508218i | \(0.169696\pi\) | ||||
−0.861229 | + | 0.508218i | \(0.830304\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.4536 | + | 30.3304i | −0.649074 | + | 0.962505i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.3829 | + | 46.7944i | −0.614478 | + | 1.48348i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.5281 | − | 12.2309i | 0.935164 | − | 0.387358i | 0.137529 | − | 0.990498i | \(-0.456084\pi\) |
0.797635 | + | 0.603140i | \(0.206084\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77488 | + | 2.73123i | 0.0561547 | + | 0.0864124i |
(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 | 384.2.o.a.239.3 | 56 | ||
3.2 | odd | 2 | inner | 384.2.o.a.239.6 | 56 | ||
4.3 | odd | 2 | 96.2.o.a.83.2 | yes | 56 | ||
8.3 | odd | 2 | 768.2.o.b.479.3 | 56 | |||
8.5 | even | 2 | 768.2.o.a.479.12 | 56 | |||
12.11 | even | 2 | 96.2.o.a.83.13 | yes | 56 | ||
24.5 | odd | 2 | 768.2.o.a.479.9 | 56 | |||
24.11 | even | 2 | 768.2.o.b.479.6 | 56 | |||
32.5 | even | 8 | 96.2.o.a.59.13 | yes | 56 | ||
32.11 | odd | 8 | 768.2.o.a.287.9 | 56 | |||
32.21 | even | 8 | 768.2.o.b.287.6 | 56 | |||
32.27 | odd | 8 | inner | 384.2.o.a.143.6 | 56 | ||
96.5 | odd | 8 | 96.2.o.a.59.2 | ✓ | 56 | ||
96.11 | even | 8 | 768.2.o.a.287.12 | 56 | |||
96.53 | odd | 8 | 768.2.o.b.287.3 | 56 | |||
96.59 | even | 8 | inner | 384.2.o.a.143.3 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.59.2 | ✓ | 56 | 96.5 | odd | 8 | ||
96.2.o.a.59.13 | yes | 56 | 32.5 | even | 8 | ||
96.2.o.a.83.2 | yes | 56 | 4.3 | odd | 2 | ||
96.2.o.a.83.13 | yes | 56 | 12.11 | even | 2 | ||
384.2.o.a.143.3 | 56 | 96.59 | even | 8 | inner | ||
384.2.o.a.143.6 | 56 | 32.27 | odd | 8 | inner | ||
384.2.o.a.239.3 | 56 | 1.1 | even | 1 | trivial | ||
384.2.o.a.239.6 | 56 | 3.2 | odd | 2 | inner | ||
768.2.o.a.287.9 | 56 | 32.11 | odd | 8 | |||
768.2.o.a.287.12 | 56 | 96.11 | even | 8 | |||
768.2.o.a.479.9 | 56 | 24.5 | odd | 2 | |||
768.2.o.a.479.12 | 56 | 8.5 | even | 2 | |||
768.2.o.b.287.3 | 56 | 96.53 | odd | 8 | |||
768.2.o.b.287.6 | 56 | 32.21 | even | 8 | |||
768.2.o.b.479.3 | 56 | 8.3 | odd | 2 | |||
768.2.o.b.479.6 | 56 | 24.11 | even | 2 |