Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(95,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, 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("768.95");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(6.13251087523\) |
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 | 479.3 | ||
Character | \(\chi\) | \(=\) | 768.479 |
Dual form | 768.2.o.b.287.3 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 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 | \(-0.759843\pi\) |
0.0309186 | − | 0.999522i | \(-0.490157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.838552 | − | 0.838552i | −0.316943 | − | 0.316943i | 0.530649 | − | 0.847592i | \(-0.321948\pi\) |
−0.847592 | + | 0.530649i | \(0.821948\pi\) | |||||||
\(8\) | 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 | 0.649326 | − | 0.760510i | \(-0.275051\pi\) |
−0.0786194 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(14\) | 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 | 0.384421 | − | 0.923158i | \(-0.374401\pi\) |
−0.923158 | + | 0.384421i | \(0.874401\pi\) | |||||||
\(24\) | 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 | 0.0310857 | − | 0.999517i | \(-0.490104\pi\) |
−0.684784 | + | 0.728746i | \(0.740104\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.63408i | 1.37112i | 0.728015 | + | 0.685561i | \(0.240443\pi\) | ||||
−0.728015 | + | 0.685561i | \(0.759557\pi\) | |||||||
\(32\) | 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 | −0.429781 | − | 0.902933i | \(-0.641409\pi\) |
0.334570 | + | 0.942371i | \(0.391409\pi\) | |||||||
\(38\) | 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 | \(-0.856693\pi\) | ||
0.900354 | − | 0.435158i | \(-0.143307\pi\) | |||||||
\(48\) | 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 | −0.329677 | − | 0.944094i | \(-0.606940\pi\) |
0.434459 | + | 0.900692i | \(0.356940\pi\) | |||||||
\(54\) | 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 | \(0.273129\pi\) |
−0.997361 | + | 0.0725992i | \(0.976871\pi\) | |||||||
\(62\) | 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 | \(0.577523\pi\) |
−0.970489 | + | 0.241145i | \(0.922477\pi\) | |||||||
\(72\) | 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 | \(-0.724753\pi\) | ||||
−0.648857 | + | 0.760910i | \(0.724753\pi\) | |||||||
\(80\) | 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 | 0.822687 | − | 0.568494i | \(-0.192474\pi\) |
−0.983714 | + | 0.179742i | \(0.942474\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.29846 | − | 4.29846i | −0.423540 | − | 0.423540i | 0.462881 | − | 0.886421i | \(-0.346816\pi\) |
−0.886421 | + | 0.462881i | \(0.846816\pi\) | |||||||
\(104\) | 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 | −0.300859 | − | 0.953669i | \(-0.597273\pi\) |
−0.887085 | + | 0.461606i | \(0.847273\pi\) | |||||||
\(110\) | 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 | \(0.0102335\pi\) | ||||
−0.999483 | + | 0.0321441i | \(0.989766\pi\) | |||||||
\(128\) | 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 | −0.595423 | − | 0.803412i | \(-0.703016\pi\) |
0.147070 | + | 0.989126i | \(0.453016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.81381 | + | 5.81381i | −0.473121 | + | 0.473121i | −0.902923 | − | 0.429802i | \(-0.858583\pi\) |
0.429802 | + | 0.902923i | \(0.358583\pi\) | |||||||
\(152\) | 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 | −0.730247 | − | 0.683183i | \(-0.760595\pi\) |
0.999446 | + | 0.0332797i | \(0.0105952\pi\) | |||||||
\(158\) | 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 | −0.397157 | − | 0.917751i | \(-0.630003\pi\) |
0.917751 | + | 0.397157i | \(0.130003\pi\) | |||||||
\(168\) | 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 | −0.934017 | − | 0.357228i | \(-0.883722\pi\) |
0.913048 | + | 0.407852i | \(0.133722\pi\) | |||||||
\(174\) | 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 | 0.991489 | − | 0.130190i | \(-0.0415587\pi\) |
−0.793147 | + | 0.609030i | \(0.791559\pi\) | |||||||
\(182\) | 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 | \(-0.518702\pi\) | ||||
−0.0587210 | + | 0.998274i | \(0.518702\pi\) | |||||||
\(192\) | 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 | 0.949346 | − | 0.314234i | \(-0.101748\pi\) |
−0.893486 | + | 0.449092i | \(0.851748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.78498 | − | 8.78498i | −0.622751 | − | 0.622751i | 0.323483 | − | 0.946234i | \(-0.395146\pi\) |
−0.946234 | + | 0.323483i | \(0.895146\pi\) | |||||||
\(200\) | 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 | \(-0.815170\pi\) | ||
0.836101 | − | 0.548576i | \(-0.184830\pi\) | |||||||
\(224\) | 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 | 0.0215864 | − | 0.999767i | \(-0.493128\pi\) |
0.722206 | + | 0.691678i | \(0.243128\pi\) | |||||||
\(230\) | 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 | \(-0.787829\pi\) | ||
0.785956 | − | 0.618283i | \(-0.212171\pi\) | |||||||
\(240\) | 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 | −0.952264 | − | 0.305276i | \(-0.901251\pi\) |
0.305276 | + | 0.952264i | \(0.401251\pi\) | |||||||
\(264\) | 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 | \(0.253983\pi\) |
−0.999922 | + | 0.0125138i | \(0.996017\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.03570 | 0.427388 | 0.213694 | − | 0.976901i | \(-0.431450\pi\) | ||||
0.213694 | + | 0.976901i | \(0.431450\pi\) | |||||||
\(272\) | 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 | \(-0.860632\pi\) |
0.340606 | − | 0.940206i | \(-0.389368\pi\) | |||||||
\(278\) | 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 | 0.997109 | − | 0.0759896i | \(-0.0242116\pi\) |
−0.758795 | + | 0.651329i | \(0.774212\pi\) | |||||||
\(294\) | 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 | \(0.0667638\pi\) |
0.208210 | + | 0.978084i | \(0.433236\pi\) | |||||||
\(312\) | 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 | 0.396191 | − | 0.918168i | \(-0.370332\pi\) |
−0.369094 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(318\) | 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 | \(0.532761\pi\) |
−0.630716 | + | 0.776014i | \(0.717239\pi\) | |||||||
\(350\) | 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 | −0.778689 | − | 0.627410i | \(-0.784115\pi\) |
0.627410 | + | 0.778689i | \(0.284115\pi\) | |||||||
\(360\) | 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 | \(-0.773276\pi\) | ||||
−0.756878 | + | 0.653557i | \(0.773276\pi\) | |||||||
\(368\) | 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 | \(-0.954141\pi\) |
0.598261 | − | 0.801302i | \(-0.295859\pi\) | |||||||
\(374\) | 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 | \(-0.654195\pi\) | ||||
−0.465694 | + | 0.884946i | \(0.654195\pi\) | |||||||
\(384\) | 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 | 0.941706 | − | 0.336436i | \(-0.109221\pi\) |
−0.903783 | + | 0.427991i | \(0.859221\pi\) | |||||||
\(390\) | 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 | 0.561670 | − | 0.827361i | \(-0.310159\pi\) |
−0.187872 | + | 0.982193i | \(0.560159\pi\) | |||||||
\(398\) | 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 | −0.733179 | − | 0.680036i | \(-0.761964\pi\) |
−0.0375773 | + | 0.999294i | \(0.511964\pi\) | |||||||
\(422\) | 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 | \(0.170625\pi\) | ||||
−0.859742 | + | 0.510729i | \(0.829375\pi\) | |||||||
\(432\) | 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 | \(-0.422002\pi\) |
0.970128 | − | 0.242594i | \(-0.0779983\pi\) | |||||||
\(440\) | 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 | \(0.295762\pi\) |
−0.989684 | + | 0.143270i | \(0.954238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1790 | 1.12369 | 0.561847 | − | 0.827241i | \(-0.310091\pi\) | ||||
0.561847 | + | 0.827241i | \(0.310091\pi\) | |||||||
\(464\) | 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 | \(-0.681951\pi\) | ||||
−0.540991 | + | 0.841028i | \(0.681951\pi\) | |||||||
\(480\) | 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 | 0.967565 | − | 0.252623i | \(-0.0812931\pi\) |
−0.252623 | + | 0.967565i | \(0.581293\pi\) | |||||||
\(488\) | 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 | 0.476802 | − | 0.879011i | \(-0.341796\pi\) |
−0.879011 | + | 0.476802i | \(0.841796\pi\) | |||||||
\(504\) | 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 | 0.668873 | − | 0.743376i | \(-0.266777\pi\) |
−0.0526815 | + | 0.998611i | \(0.516777\pi\) | |||||||
\(510\) | 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 | \(0.338501\pi\) |
−0.961597 | + | 0.274466i | \(0.911499\pi\) | |||||||
\(542\) | 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 | \(-0.734611\pi\) |
0.998832 | − | 0.0483277i | \(-0.0153892\pi\) | |||||||
\(558\) | 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 | 0.204028 | − | 0.978965i | \(-0.434597\pi\) |
−0.978965 | + | 0.204028i | \(0.934597\pi\) | |||||||
\(600\) | 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 | \(0.0570054\pi\) | ||||
−0.984007 | + | 0.178132i | \(0.942995\pi\) | |||||||
\(608\) | 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 | −0.298564 | − | 0.954389i | \(-0.596508\pi\) |
0.463738 | + | 0.885972i | \(0.346508\pi\) | |||||||
\(614\) | 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 | −0.391907 | − | 0.920005i | \(-0.628185\pi\) |
0.920005 | + | 0.391907i | \(0.128185\pi\) | |||||||
\(632\) | 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 | −0.0675491 | − | 0.997716i | \(-0.521518\pi\) |
0.997716 | + | 0.0675491i | \(0.0215179\pi\) | |||||||
\(648\) | 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 | \(0.338906\pi\) |
−0.961247 | + | 0.275689i | \(0.911094\pi\) | |||||||
\(654\) | 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 | 0.871704 | − | 0.490033i | \(-0.163015\pi\) |
−0.962893 | + | 0.269882i | \(0.913015\pi\) | |||||||
\(662\) | 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 | \(0.285369\pi\) |
0.110886 | + | 0.993833i | \(0.464631\pi\) | |||||||
\(678\) | 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 | 0.192182 | − | 0.981359i | \(-0.438444\pi\) |
−0.558033 | + | 0.829819i | \(0.688444\pi\) | |||||||
\(702\) | 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 | 0.474904 | − | 0.880038i | \(-0.342483\pi\) |
0.958088 | + | 0.286473i | \(0.0924827\pi\) | |||||||
\(710\) | 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 | \(-0.664519\pi\) | ||
0.494147 | − | 0.869378i | \(-0.335481\pi\) | |||||||
\(720\) | 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 | −0.998013 | − | 0.0630153i | \(-0.979928\pi\) |
0.0630153 | + | 0.998013i | \(0.479928\pi\) | |||||||
\(728\) | 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 | −0.876860 | − | 0.480747i | \(-0.840366\pi\) |
0.959973 | + | 0.280094i | \(0.0903657\pi\) | |||||||
\(734\) | 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 | −0.364139 | − | 0.931345i | \(-0.618637\pi\) |
0.931345 | + | 0.364139i | \(0.118637\pi\) | |||||||
\(744\) | 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 | \(-0.282627\pi\) | ||||
0.631043 | + | 0.775748i | \(0.282627\pi\) | |||||||
\(752\) | 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 | 0.998048 | − | 0.0624455i | \(-0.0198900\pi\) |
−0.749882 | + | 0.661571i | \(0.769890\pi\) | |||||||
\(758\) | 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 | \(-0.956290\pi\) |
0.603657 | − | 0.797244i | \(-0.293710\pi\) | |||||||
\(774\) | 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 | 0.365089 | − | 0.930973i | \(-0.381039\pi\) |
−0.400141 | + | 0.916454i | \(0.631039\pi\) | |||||||
\(798\) | 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 | 0.217155 | − | 0.976137i | \(-0.430322\pi\) |
0.843785 | + | 0.536682i | \(0.180322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.58486 | + | 7.58486i | −0.264392 | + | 0.264392i | −0.826835 | − | 0.562444i | \(-0.809861\pi\) |
0.562444 | + | 0.826835i | \(0.309861\pi\) | |||||||
\(824\) | 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 | −0.893397 | − | 0.449268i | \(-0.851685\pi\) |
0.949407 | + | 0.314047i | \(0.101685\pi\) | |||||||
\(830\) | 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 | −0.902940 | − | 0.429767i | \(-0.858596\pi\) |
0.429767 | + | 0.902940i | \(0.358596\pi\) | |||||||
\(840\) | 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 | \(0.0870124\pi\) |
−0.489957 | + | 0.871746i | \(0.662988\pi\) | |||||||
\(854\) | 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 | \(-0.276979\pi\) | ||||
0.644708 | + | 0.764429i | \(0.276979\pi\) | |||||||
\(864\) | 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 | 0.227397 | − | 0.973802i | \(-0.426979\pi\) |
−0.527789 | + | 0.849376i | \(0.676979\pi\) | |||||||
\(878\) | 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 | 0.450885 | − | 0.892582i | \(-0.351109\pi\) |
−0.892582 | + | 0.450885i | \(0.851109\pi\) | |||||||
\(888\) | 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 | \(0.336218\pi\) | ||||
−0.492132 | + | 0.870520i | \(0.663782\pi\) | |||||||
\(912\) | 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 | \(0.522685\pi\) |
−0.997462 | + | 0.0712063i | \(0.977315\pi\) | |||||||
\(920\) | 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 | \(0.360463\pi\) |
−0.940387 | + | 0.340105i | \(0.889537\pi\) | |||||||
\(942\) | 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 | 0.985571 | − | 0.169265i | \(-0.0541395\pi\) |
−0.169265 | + | 0.985571i | \(0.554139\pi\) | |||||||
\(968\) | 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 | 0.964424 | − | 0.264361i | \(-0.0851611\pi\) |
−0.264361 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(984\) | 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 | \(-0.830304\pi\) | ||
0.861229 | − | 0.508218i | \(-0.169696\pi\) | |||||||
\(992\) | 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 | −0.797635 | − | 0.603140i | \(-0.793916\pi\) |
−0.137529 | + | 0.990498i | \(0.543916\pi\) | |||||||
\(998\) | 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 | 768.2.o.b.479.3 | 56 | ||
3.2 | odd | 2 | inner | 768.2.o.b.479.6 | 56 | ||
4.3 | odd | 2 | 768.2.o.a.479.12 | 56 | |||
8.3 | odd | 2 | 384.2.o.a.239.3 | 56 | |||
8.5 | even | 2 | 96.2.o.a.83.2 | yes | 56 | ||
12.11 | even | 2 | 768.2.o.a.479.9 | 56 | |||
24.5 | odd | 2 | 96.2.o.a.83.13 | yes | 56 | ||
24.11 | even | 2 | 384.2.o.a.239.6 | 56 | |||
32.5 | even | 8 | 768.2.o.a.287.9 | 56 | |||
32.11 | odd | 8 | 96.2.o.a.59.13 | yes | 56 | ||
32.21 | even | 8 | 384.2.o.a.143.6 | 56 | |||
32.27 | odd | 8 | inner | 768.2.o.b.287.6 | 56 | ||
96.5 | odd | 8 | 768.2.o.a.287.12 | 56 | |||
96.11 | even | 8 | 96.2.o.a.59.2 | ✓ | 56 | ||
96.53 | odd | 8 | 384.2.o.a.143.3 | 56 | |||
96.59 | even | 8 | inner | 768.2.o.b.287.3 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.2.o.a.59.2 | ✓ | 56 | 96.11 | even | 8 | ||
96.2.o.a.59.13 | yes | 56 | 32.11 | odd | 8 | ||
96.2.o.a.83.2 | yes | 56 | 8.5 | even | 2 | ||
96.2.o.a.83.13 | yes | 56 | 24.5 | odd | 2 | ||
384.2.o.a.143.3 | 56 | 96.53 | odd | 8 | |||
384.2.o.a.143.6 | 56 | 32.21 | even | 8 | |||
384.2.o.a.239.3 | 56 | 8.3 | odd | 2 | |||
384.2.o.a.239.6 | 56 | 24.11 | even | 2 | |||
768.2.o.a.287.9 | 56 | 32.5 | even | 8 | |||
768.2.o.a.287.12 | 56 | 96.5 | odd | 8 | |||
768.2.o.a.479.9 | 56 | 12.11 | even | 2 | |||
768.2.o.a.479.12 | 56 | 4.3 | odd | 2 | |||
768.2.o.b.287.3 | 56 | 96.59 | even | 8 | inner | ||
768.2.o.b.287.6 | 56 | 32.27 | odd | 8 | inner | ||
768.2.o.b.479.3 | 56 | 1.1 | even | 1 | trivial | ||
768.2.o.b.479.6 | 56 | 3.2 | odd | 2 | inner |