Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,2,Mod(5,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.i (of order \(9\), degree \(6\), 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: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} + \cdots + 4161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Root | \(-1.25236 + 0.642788i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.25 |
Dual form | 76.2.i.a.73.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −2.83638 | − | 1.03236i | −1.63758 | − | 0.596031i | −0.650969 | − | 0.759105i | \(-0.725637\pi\) |
−0.986614 | + | 0.163073i | \(0.947859\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.658711 | − | 3.73574i | −0.294585 | − | 1.67067i | −0.668886 | − | 0.743365i | \(-0.733228\pi\) |
0.374301 | − | 0.927307i | \(-0.377883\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0695116 | + | 0.120398i | −0.0262729 | + | 0.0455060i | −0.878863 | − | 0.477074i | \(-0.841697\pi\) |
0.852590 | + | 0.522580i | \(0.175031\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.68114 | + | 3.92794i | 1.56038 | + | 1.30931i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.350493 | − | 0.607072i | −0.105678 | − | 0.183039i | 0.808337 | − | 0.588720i | \(-0.200368\pi\) |
−0.914015 | + | 0.405681i | \(0.867034\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.47751 | + | 0.537771i | −0.409789 | + | 0.149151i | −0.538685 | − | 0.842507i | \(-0.681079\pi\) |
0.128896 | + | 0.991658i | \(0.458857\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.98826 | + | 11.2760i | −0.513366 | + | 2.91145i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.88131 | − | 2.41771i | 0.698820 | − | 0.586380i | −0.222617 | − | 0.974906i | \(-0.571460\pi\) |
0.921438 | + | 0.388526i | \(0.127016\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.28653 | − | 0.790990i | 0.983397 | − | 0.181466i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.321454 | − | 0.269732i | 0.0701471 | − | 0.0588604i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.02690 | − | 5.82385i | 0.214124 | − | 1.21436i | −0.668297 | − | 0.743895i | \(-0.732976\pi\) |
0.882421 | − | 0.470461i | \(-0.155912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.82337 | + | 3.21144i | −1.76467 | + | 0.642289i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.69482 | − | 8.13166i | −0.903518 | − | 1.56494i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.28209 | + | 4.43220i | 0.980860 | + | 0.823039i | 0.984219 | − | 0.176955i | \(-0.0566248\pi\) |
−0.00335912 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.43886 | − | 2.49217i | 0.258426 | − | 0.447608i | −0.707394 | − | 0.706819i | \(-0.750129\pi\) |
0.965821 | + | 0.259212i | \(0.0834627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.367416 | + | 2.08372i | 0.0639588 | + | 0.362729i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.495562 | + | 0.180370i | 0.0837653 | + | 0.0304881i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.33018 | −1.04067 | −0.520337 | − | 0.853961i | \(-0.674194\pi\) | ||||
−0.520337 | + | 0.853961i | \(0.674194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.74596 | 0.759961 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.40018 | − | 1.60154i | −0.687193 | − | 0.250118i | −0.0252602 | − | 0.999681i | \(-0.508041\pi\) |
−0.661933 | + | 0.749563i | \(0.730264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.935226 | + | 5.30393i | 0.142621 | + | 0.808842i | 0.969247 | + | 0.246091i | \(0.0791461\pi\) |
−0.826626 | + | 0.562751i | \(0.809743\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.5902 | − | 20.0749i | 1.72777 | − | 2.99259i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.42658 | − | 1.19704i | −0.208088 | − | 0.174607i | 0.532787 | − | 0.846249i | \(-0.321145\pi\) |
−0.740875 | + | 0.671643i | \(0.765589\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.49034 | + | 6.04544i | 0.498619 | + | 0.863634i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.6684 | + | 3.88299i | −1.49388 | + | 0.543727i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.551093 | − | 3.12541i | 0.0756985 | − | 0.429307i | −0.923280 | − | 0.384127i | \(-0.874503\pi\) |
0.998979 | − | 0.0451806i | \(-0.0143863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.03699 | + | 1.70923i | −0.274667 | + | 0.230473i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.9748 | − | 2.18168i | −1.71855 | − | 0.288971i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.81608 | − | 1.52387i | 0.236433 | − | 0.198391i | −0.516871 | − | 0.856063i | \(-0.672903\pi\) |
0.753304 | + | 0.657672i | \(0.228459\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.587398 | − | 3.33130i | 0.0752086 | − | 0.426529i | −0.923834 | − | 0.382792i | \(-0.874963\pi\) |
0.999043 | − | 0.0437370i | \(-0.0139264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.798308 | + | 0.290560i | −0.100577 | + | 0.0366072i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.98223 | + | 5.16537i | 0.369900 | + | 0.640685i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.61119 | + | 6.38655i | 0.929855 | + | 0.780241i | 0.975791 | − | 0.218704i | \(-0.0701828\pi\) |
−0.0459367 | + | 0.998944i | \(0.514627\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.92496 | + | 15.4585i | −1.07444 | + | 1.86098i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.375070 | + | 2.12713i | 0.0445127 | + | 0.252444i | 0.998942 | − | 0.0459940i | \(-0.0146455\pi\) |
−0.954429 | + | 0.298438i | \(0.903534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.6967 | + | 3.89330i | 1.25196 | + | 0.455676i | 0.881063 | − | 0.472998i | \(-0.156828\pi\) |
0.370896 | + | 0.928674i | \(0.379051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.3417 | 3.27262 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.0974533 | 0.0111058 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.36033 | + | 2.67894i | 0.828102 | + | 0.301404i | 0.721079 | − | 0.692852i | \(-0.243646\pi\) |
0.107022 | + | 0.994257i | \(0.465868\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.73811 | + | 9.85732i | 0.193123 | + | 1.09526i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.12849 | + | 8.88280i | −0.562925 | + | 0.975014i | 0.434315 | + | 0.900761i | \(0.356991\pi\) |
−0.997239 | + | 0.0742528i | \(0.976343\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9299 | − | 9.17125i | −1.18551 | − | 0.994761i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.4064 | − | 18.0244i | −1.11568 | − | 1.93242i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2044 | + | 4.44204i | −1.29366 | + | 0.470856i | −0.894928 | − | 0.446210i | \(-0.852773\pi\) |
−0.398737 | + | 0.917066i | \(0.630551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0379580 | − | 0.215271i | 0.00397908 | − | 0.0225665i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.65395 | + | 5.58333i | −0.689983 | + | 0.578964i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.77852 | − | 15.4923i | −0.592863 | − | 1.58948i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.581665 | + | 0.488075i | −0.0590591 | + | 0.0495565i | −0.671839 | − | 0.740697i | \(-0.734496\pi\) |
0.612780 | + | 0.790253i | \(0.290051\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.743835 | − | 4.21850i | 0.0747583 | − | 0.423975i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7847 | − | 4.28927i | 1.17262 | − | 0.426798i | 0.319029 | − | 0.947745i | \(-0.396643\pi\) |
0.853589 | + | 0.520947i | \(0.174421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.32365 | − | 7.48879i | −0.426022 | − | 0.737892i | 0.570493 | − | 0.821302i | \(-0.306752\pi\) |
−0.996515 | + | 0.0834102i | \(0.973419\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.21939 | − | 1.02319i | −0.119001 | − | 0.0998534i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.492451 | − | 0.852950i | 0.0476070 | − | 0.0824578i | −0.841240 | − | 0.540662i | \(-0.818174\pi\) |
0.888847 | + | 0.458204i | \(0.151507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.47482 | − | 14.0354i | −0.237044 | − | 1.34435i | −0.838265 | − | 0.545263i | \(-0.816430\pi\) |
0.601221 | − | 0.799083i | \(-0.294681\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.9548 | + | 6.53500i | 1.70419 | + | 0.620275i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.86600 | 0.269611 | 0.134805 | − | 0.990872i | \(-0.456959\pi\) | ||||
0.134805 | + | 0.990872i | \(0.456959\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.4328 | −2.09187 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.02878 | − | 3.28621i | −0.834711 | − | 0.303810i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0908016 | + | 0.514962i | 0.00832377 | + | 0.0472065i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.25431 | − | 9.10073i | 0.477664 | − | 0.827339i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.8272 | + | 9.08512i | 0.976258 | + | 0.819177i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.32575 | + | 14.4206i | 0.744677 | + | 1.28982i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8223 | − | 7.21472i | 1.75894 | − | 0.640203i | 0.759002 | − | 0.651089i | \(-0.225687\pi\) |
0.999941 | + | 0.0108860i | \(0.00346520\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82289 | − | 16.0094i | 0.248542 | − | 1.40955i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.87172 | + | 6.60516i | −0.687756 | + | 0.577096i | −0.918261 | − | 0.395975i | \(-0.870407\pi\) |
0.230505 | + | 0.973071i | \(0.425962\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.202730 | + | 0.571071i | −0.0175789 | + | 0.0495181i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.2852 | + | 22.8950i | −2.34834 | + | 1.97049i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.08375 | + | 11.8175i | −0.178027 | + | 1.00964i | 0.756565 | + | 0.653919i | \(0.226876\pi\) |
−0.934592 | + | 0.355722i | \(0.884235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.67258 | + | 3.52053i | −0.820417 | + | 0.298607i | −0.717920 | − | 0.696126i | \(-0.754906\pi\) |
−0.102497 | + | 0.994733i | \(0.532683\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.81054 | + | 4.86800i | 0.236690 | + | 0.409960i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.844324 | + | 0.708472i | 0.0706059 | + | 0.0592454i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.0782 | − | 22.6520i | 1.08608 | − | 1.88115i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.65886 | − | 20.7504i | −0.301777 | − | 1.71147i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.52238 | + | 1.28204i | 0.288565 | + | 0.105029i | 0.482247 | − | 0.876035i | \(-0.339821\pi\) |
−0.193682 | + | 0.981064i | \(0.562043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3866 | −1.08939 | −0.544693 | − | 0.838636i | \(-0.683354\pi\) | ||||
−0.544693 | + | 0.838636i | \(0.683354\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.9844 | 1.85818 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2579 | − | 3.73357i | −0.823934 | − | 0.299888i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.40711 | + | 7.98010i | 0.112299 | + | 0.636881i | 0.988052 | + | 0.154121i | \(0.0492546\pi\) |
−0.875753 | + | 0.482760i | \(0.839634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.78964 | + | 8.29590i | −0.379843 | + | 0.657908i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.629796 | + | 0.528461i | 0.0496349 | + | 0.0416486i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.12600 | + | 7.14644i | 0.323173 | + | 0.559753i | 0.981141 | − | 0.193294i | \(-0.0619170\pi\) |
−0.657968 | + | 0.753046i | \(0.728584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.54220 | − | 2.74514i | 0.587159 | − | 0.213709i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.04523 | + | 11.5991i | −0.158264 | + | 0.897562i | 0.797476 | + | 0.603351i | \(0.206168\pi\) |
−0.955740 | + | 0.294211i | \(0.904943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.06473 | + | 6.76711i | −0.620364 | + | 0.520547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.1728 | + | 13.1345i | 1.77207 | + | 1.00442i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.17235 | − | 6.01832i | 0.545304 | − | 0.457564i | −0.328043 | − | 0.944663i | \(-0.606389\pi\) |
0.873347 | + | 0.487098i | \(0.161945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.226676 | − | 1.28555i | 0.0171351 | − | 0.0971781i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.72425 | + | 2.44743i | −0.505426 | + | 0.183960i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.64499 | − | 8.04536i | −0.347183 | − | 0.601339i | 0.638565 | − | 0.769568i | \(-0.279528\pi\) |
−0.985748 | + | 0.168229i | \(0.946195\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.07659 | − | 1.74246i | −0.154351 | − | 0.129516i | 0.562342 | − | 0.826905i | \(-0.309901\pi\) |
−0.716693 | + | 0.697389i | \(0.754345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.10517 | + | 8.84242i | −0.377385 | + | 0.653650i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.16976 | + | 23.6479i | 0.306567 | + | 1.73863i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.47760 | − | 0.901773i | −0.181180 | − | 0.0659441i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.30538 | 0.0949522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8935 | −1.36709 | −0.683544 | − | 0.729910i | \(-0.739562\pi\) | ||||
−0.683544 | + | 0.729910i | \(0.739562\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0362 | + | 7.29258i | 1.44224 | + | 0.524931i | 0.940412 | − | 0.340037i | \(-0.110440\pi\) |
0.501825 | + | 0.864969i | \(0.332662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.12622 | − | 17.7297i | −0.223873 | − | 1.26965i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.29055 | + | 14.3597i | −0.590677 | + | 1.02308i | 0.403464 | + | 0.914996i | \(0.367806\pi\) |
−0.994141 | + | 0.108088i | \(0.965527\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.3943 | + | 10.4001i | 0.878610 | + | 0.737241i | 0.965893 | − | 0.258943i | \(-0.0833741\pi\) |
−0.0872832 | + | 0.996184i | \(0.527819\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.9950 | − | 25.9721i | −1.05767 | − | 1.83193i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.900793 | + | 0.327862i | −0.0632233 | + | 0.0230114i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.08447 | + | 17.4929i | −0.215428 | + | 1.22176i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 27.6828 | − | 23.2286i | 1.92409 | − | 1.61450i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.98259 | − | 2.32499i | −0.137138 | − | 0.160823i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1088 | − | 16.8733i | 1.38434 | − | 1.16160i | 0.416772 | − | 0.909011i | \(-0.363161\pi\) |
0.967573 | − | 0.252592i | \(-0.0812831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.13212 | − | 6.42055i | 0.0775713 | − | 0.439929i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.1981 | − | 6.98752i | 1.30930 | − | 0.476545i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.200035 | + | 0.346470i | 0.0135792 | + | 0.0235199i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.3207 | − | 22.0857i | −1.77859 | − | 1.49241i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.95700 | + | 5.12168i | −0.198910 | + | 0.344522i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.397301 | + | 2.25321i | 0.0266053 | + | 0.150886i | 0.995216 | − | 0.0976949i | \(-0.0311469\pi\) |
−0.968611 | + | 0.248581i | \(0.920036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −53.9178 | − | 19.6245i | −3.59452 | − | 1.30830i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.4671 | −1.15934 | −0.579668 | − | 0.814853i | \(-0.696818\pi\) | ||||
−0.579668 | + | 0.814853i | \(0.696818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.14952 | 0.538536 | 0.269268 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269268 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.276414 | − | 0.100607i | −0.0181867 | − | 0.00661943i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.69185 | − | 20.9375i | −0.241861 | − | 1.37166i | −0.827671 | − | 0.561214i | \(-0.810335\pi\) |
0.585810 | − | 0.810449i | \(-0.300777\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.53213 | + | 6.11783i | −0.230411 | + | 0.399083i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.1110 | − | 15.1970i | −1.17644 | − | 0.987149i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3725 | + | 17.9657i | 0.670941 | + | 1.16210i | 0.977638 | + | 0.210296i | \(0.0674429\pi\) |
−0.306697 | + | 0.951807i | \(0.599224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.7960 | + | 6.84119i | −1.21076 | + | 0.440680i | −0.866966 | − | 0.498367i | \(-0.833933\pi\) |
−0.343791 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.354850 | − | 2.01245i | 0.0227636 | − | 0.129099i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.2851 | − | 17.0212i | 1.29596 | − | 1.08744i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.90804 | + | 3.47387i | −0.375919 | + | 0.221037i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.7165 | − | 19.9005i | 1.50297 | − | 1.26115i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.27528 | + | 7.23245i | −0.0804948 | + | 0.456508i | 0.917743 | + | 0.397174i | \(0.130009\pi\) |
−0.998238 | + | 0.0593346i | \(0.981102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.89541 | + | 1.41781i | −0.244903 | + | 0.0891372i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.5332 | + | 37.2966i | 1.34846 | + | 2.33561i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7914 | + | 17.4460i | 1.29693 | + | 1.08825i | 0.990666 | + | 0.136308i | \(0.0435238\pi\) |
0.306265 | + | 0.951946i | \(0.400921\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.440021 | − | 0.762139i | 0.0273416 | − | 0.0473570i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.31677 | + | 41.4955i | 0.452897 | + | 2.56851i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.3152 | − | 7.39413i | −1.25269 | − | 0.455941i | −0.371379 | − | 0.928481i | \(-0.621115\pi\) |
−0.881309 | + | 0.472540i | \(0.843337\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0387 | −0.739532 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 39.2021 | 2.39913 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.63396 | − | 2.05060i | −0.343509 | − | 0.125027i | 0.164504 | − | 0.986376i | \(-0.447398\pi\) |
−0.508013 | + | 0.861349i | \(0.669620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.11091 | − | 23.3141i | −0.249720 | − | 1.41623i | −0.809271 | − | 0.587436i | \(-0.800137\pi\) |
0.559551 | − | 0.828796i | \(-0.310974\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.329899 | + | 0.571402i | −0.0199664 | + | 0.0345828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.04211 | + | 4.23083i | 0.304050 | + | 0.255129i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.74294 | + | 8.21502i | 0.284976 | + | 0.493593i | 0.972603 | − | 0.232471i | \(-0.0746811\pi\) |
−0.687628 | + | 0.726064i | \(0.741348\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.5246 | − | 6.01446i | 0.989302 | − | 0.360076i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.22110 | − | 23.9391i | 0.251810 | − | 1.42808i | −0.552321 | − | 0.833632i | \(-0.686258\pi\) |
0.804131 | − | 0.594453i | \(-0.202631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.94917 | + | 7.50925i | −0.531973 | + | 0.446378i | −0.868782 | − | 0.495195i | \(-0.835097\pi\) |
0.336809 | + | 0.941573i | \(0.390652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.396453 | + | 49.9075i | 0.0234839 | + | 2.95627i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.498685 | − | 0.418446i | 0.0294364 | − | 0.0247001i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.495374 | + | 2.80941i | −0.0291397 | + | 0.165259i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.15369 | − | 0.783879i | 0.126251 | − | 0.0459518i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.01571 | − | 12.1516i | −0.409862 | − | 0.709902i | 0.585012 | − | 0.811025i | \(-0.301090\pi\) |
−0.994874 | + | 0.101122i | \(0.967757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.88905 | − | 5.78060i | −0.401096 | − | 0.336559i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.29100 | + | 5.70018i | −0.190963 | + | 0.330758i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.61464 | + | 9.15705i | 0.0933768 | + | 0.529566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.703590 | − | 0.256086i | −0.0405543 | − | 0.0147605i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.8538 | −2.17464 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.8318 | −0.734746 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.522125 | + | 0.190038i | 0.0297993 | + | 0.0108460i | 0.356877 | − | 0.934151i | \(-0.383842\pi\) |
−0.327078 | + | 0.944998i | \(0.606064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.53241 | + | 25.7046i | 0.257840 | + | 1.46228i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.89478 | − | 13.6742i | 0.447672 | − | 0.775390i | −0.550562 | − | 0.834794i | \(-0.685587\pi\) |
0.998234 | + | 0.0594037i | \(0.0189199\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4399 | − | 14.6338i | −0.985763 | − | 0.827153i | −0.000814014 | − | 1.00000i | \(-0.500259\pi\) |
−0.984949 | + | 0.172846i | \(0.944704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61131 | + | 2.79087i | 0.0907871 | + | 0.157248i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.8284 | − | 6.48900i | 1.00134 | − | 0.364458i | 0.211240 | − | 0.977434i | \(-0.432250\pi\) |
0.790102 | + | 0.612976i | \(0.210028\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.839328 | − | 4.76006i | 0.0469933 | − | 0.266512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.27733 | + | 1.91090i | −0.127108 | + | 0.106656i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.4384 | − | 12.6427i | 0.580810 | − | 0.703456i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3096 | − | 9.48991i | 0.627345 | − | 0.526405i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.47001 | + | 42.3645i | −0.413092 | + | 2.34276i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.243285 | − | 0.0885485i | 0.0134127 | − | 0.00488184i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.38160 | + | 12.7853i | 0.405729 | + | 0.702744i | 0.994406 | − | 0.105625i | \(-0.0336843\pi\) |
−0.588677 | + | 0.808368i | \(0.700351\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −29.6324 | − | 24.8646i | −1.62385 | − | 1.36257i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.8449 | − | 32.6403i | 1.02961 | − | 1.78333i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.43116 | − | 8.11649i | −0.0779601 | − | 0.442134i | −0.998655 | − | 0.0518502i | \(-0.983488\pi\) |
0.920695 | − | 0.390283i | \(-0.127623\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.12906 | − | 2.95874i | −0.441510 | − | 0.160697i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.01724 | −0.109240 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.94364 | −0.104947 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 63.6278 | + | 23.1586i | 3.42561 | + | 1.24682i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.39699 | + | 19.2653i | 0.182360 | + | 1.03421i | 0.929301 | + | 0.369324i | \(0.120411\pi\) |
−0.746941 | + | 0.664891i | \(0.768478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.8829 | + | 22.3139i | −0.689607 | + | 1.19443i | 0.282358 | + | 0.959309i | \(0.408884\pi\) |
−0.971965 | + | 0.235126i | \(0.924450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3096 | + | 9.48991i | 0.603663 | + | 0.506534i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.712979 | + | 1.23492i | 0.0379480 | + | 0.0657279i | 0.884376 | − | 0.466776i | \(-0.154585\pi\) |
−0.846428 | + | 0.532504i | \(0.821251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.69934 | − | 2.80233i | 0.408638 | − | 0.148732i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.274076 | − | 1.55436i | 0.0145057 | − | 0.0822657i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.55106 | − | 6.33609i | 0.398530 | − | 0.334406i | −0.421395 | − | 0.906877i | \(-0.638460\pi\) |
0.819925 | + | 0.572471i | \(0.194015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7487 | − | 6.78120i | 0.934141 | − | 0.356905i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.2984 | + | 20.3888i | −1.27534 | + | 1.07013i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.49827 | − | 42.5248i | 0.392477 | − | 2.22585i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.7351 | + | 3.90726i | −0.560368 | + | 0.203957i | −0.606647 | − | 0.794971i | \(-0.707486\pi\) |
0.0462791 | + | 0.998929i | \(0.485264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.3071 | − | 24.7807i | −0.744799 | − | 1.29003i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.337984 | + | 0.283602i | 0.0175473 | + | 0.0147239i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.3194 | + | 23.0699i | −0.689653 | + | 1.19451i | 0.282297 | + | 0.959327i | \(0.408903\pi\) |
−0.971950 | + | 0.235187i | \(0.924430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.72773 | − | 49.4974i | −0.450698 | − | 2.55604i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.1879 | − | 3.70808i | −0.524702 | − | 0.190976i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.8016 | 1.01714 | 0.508569 | − | 0.861021i | \(-0.330174\pi\) | ||||
0.508569 | + | 0.861021i | \(0.330174\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −63.6716 | −3.26199 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.8435 | − | 6.13052i | −0.860661 | − | 0.313255i | −0.126282 | − | 0.991994i | \(-0.540304\pi\) |
−0.734379 | + | 0.678739i | \(0.762527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0641936 | − | 0.364060i | −0.00327161 | − | 0.0185542i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.4556 | + | 28.5019i | −0.836485 | + | 1.44884i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.4626 | − | 13.8137i | −0.834685 | − | 0.700384i | 0.121676 | − | 0.992570i | \(-0.461173\pi\) |
−0.956362 | + | 0.292186i | \(0.905617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.1215 | − | 19.2631i | −0.562440 | − | 0.974175i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.1461 | − | 10.6083i | 1.47022 | − | 0.535118i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.15949 | − | 29.2609i | 0.259602 | − | 1.47228i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.26129 | − | 3.57565i | 0.213868 | − | 0.179457i | −0.529560 | − | 0.848272i | \(-0.677643\pi\) |
0.743428 | + | 0.668816i | \(0.233199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.16457 | − | 1.41048i | 0.0583013 | − | 0.0706124i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.9884 | + | 23.4850i | −1.39767 | + | 1.17279i | −0.435550 | + | 0.900164i | \(0.643446\pi\) |
−0.962121 | + | 0.272621i | \(0.912109\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.785713 | + | 4.45600i | −0.0391391 | + | 0.221969i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 35.6794 | − | 12.9863i | 1.77293 | − | 0.645292i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.21868 | + | 3.84287i | 0.109976 | + | 0.190484i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.581665 | − | 0.488075i | −0.0287615 | − | 0.0241338i | 0.628294 | − | 0.777976i | \(-0.283754\pi\) |
−0.657055 | + | 0.753843i | \(0.728198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.1102 | − | 31.3678i | 0.893311 | − | 1.54726i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0572319 | + | 0.324578i | 0.00281620 | + | 0.0159714i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.5620 | + | 13.3075i | 1.79476 | + | 0.653238i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.0695 | 1.52148 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.2619 | 0.794446 | 0.397223 | − | 0.917722i | \(-0.369974\pi\) | ||||
0.397223 | + | 0.917722i | \(0.369974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1059 | − | 5.13414i | −0.687481 | − | 0.250223i | −0.0254245 | − | 0.999677i | \(-0.508094\pi\) |
−0.662056 | + | 0.749454i | \(0.730316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.97610 | − | 11.2070i | −0.0960814 | − | 0.544905i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.6585 | + | 30.5855i | −0.856565 | + | 1.48361i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.360250 | + | 0.302285i | 0.0174337 | + | 0.0146286i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.66342 | − | 2.88114i | −0.0803109 | − | 0.139103i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.41358 | + | 3.42626i | −0.453436 | + | 0.165037i | −0.558634 | − | 0.829414i | \(-0.688674\pi\) |
0.105198 | + | 0.994451i | \(0.466452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.711701 | − | 4.03626i | 0.0342022 | − | 0.193970i | −0.962919 | − | 0.269789i | \(-0.913046\pi\) |
0.997122 | + | 0.0758190i | \(0.0241571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −60.4796 | + | 50.7484i | −2.89977 | + | 2.43320i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.204761 | − | 25.7764i | −0.00979506 | − | 1.23305i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00981 | + | 3.36463i | −0.191378 | + | 0.160585i | −0.733442 | − | 0.679752i | \(-0.762087\pi\) |
0.542064 | + | 0.840337i | \(0.317643\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.40738 | + | 42.0094i | −0.352733 | + | 2.00045i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.8347 | − | 11.5869i | 1.51251 | − | 0.550509i | 0.553247 | − | 0.833017i | \(-0.313389\pi\) |
0.959265 | + | 0.282508i | \(0.0911665\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.6335 | + | 42.6664i | 1.16774 | + | 2.02258i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.66727 | − | 7.27271i | −0.409948 | − | 0.343987i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.545695 | − | 0.945172i | 0.0257530 | − | 0.0446054i | −0.852862 | − | 0.522137i | \(-0.825135\pi\) |
0.878615 | + | 0.477531i | \(0.158468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.569986 | + | 3.23255i | 0.0268396 | + | 0.152215i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.9694 | + | 13.8197i | 1.78396 | + | 0.649308i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.829198 | −0.0388734 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9280 | 0.791858 | 0.395929 | − | 0.918281i | \(-0.370423\pi\) | ||||
0.395929 | + | 0.918281i | \(0.370423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.1872 | − | 12.0792i | −1.54905 | − | 0.563806i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.62318 | + | 9.20551i | 0.0755991 | + | 0.428744i | 0.998992 | + | 0.0448876i | \(0.0142930\pi\) |
−0.923393 | + | 0.383856i | \(0.874596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.80227 | + | 6.58572i | −0.176706 | + | 0.306064i | −0.940750 | − | 0.339100i | \(-0.889878\pi\) |
0.764044 | + | 0.645164i | \(0.223211\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.2409 | + | 21.1796i | 1.17052 | + | 0.982181i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.7403 | + | 30.7272i | 0.820925 | + | 1.42188i | 0.904994 | + | 0.425424i | \(0.139875\pi\) |
−0.0840686 | + | 0.996460i | \(0.526792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.29799 | + | 0.472430i | −0.0599357 | + | 0.0218148i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.24722 | − | 24.0872i | 0.195702 | − | 1.10988i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.89208 | − | 2.42674i | 0.132978 | − | 0.111582i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.2814 | + | 20.7451i | −1.61882 | + | 0.951853i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.8561 | − | 12.4658i | 0.680216 | − | 0.570769i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.87224 | + | 27.6318i | −0.222618 | + | 1.26253i | 0.644568 | + | 0.764547i | \(0.277037\pi\) |
−0.867186 | + | 0.497984i | \(0.834074\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.35293 | − | 3.40419i | 0.426457 | − | 0.155218i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.24078 | − | 2.14909i | −0.0564573 | − | 0.0977870i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.20647 | + | 1.85145i | 0.100191 | + | 0.0840699i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5368 | + | 37.3029i | −0.975926 | + | 1.69035i | −0.299082 | + | 0.954228i | \(0.596680\pi\) |
−0.676844 | + | 0.736126i | \(0.736653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.32521 | − | 24.5295i | −0.195593 | − | 1.10926i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4166 | + | 6.33912i | 0.786000 | + | 0.286080i | 0.703672 | − | 0.710525i | \(-0.251542\pi\) |
0.0823275 | + | 0.996605i | \(0.473765\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.9351 | 1.16806 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.2492 | −0.730346 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.282173 | − | 0.102703i | −0.0126572 | − | 0.00460684i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.54046 | − | 42.7641i | −0.337557 | − | 1.91438i | −0.400361 | − | 0.916358i | \(-0.631115\pi\) |
0.0628031 | − | 0.998026i | \(-0.479996\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7754 | − | 30.7879i | 0.794146 | − | 1.37550i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.819590 | − | 0.687718i | −0.0365437 | − | 0.0306638i | 0.624333 | − | 0.781158i | \(-0.285371\pi\) |
−0.660877 | + | 0.750495i | \(0.729815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.7863 | − | 41.1990i | −1.05847 | − | 1.83333i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.8607 | − | 10.8684i | 1.32616 | − | 0.482682i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.01402 | − | 5.75077i | 0.0449455 | − | 0.254899i | −0.954053 | − | 0.299637i | \(-0.903134\pi\) |
0.998999 | + | 0.0447386i | \(0.0142455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.21229 | + | 1.01723i | −0.0536286 | + | 0.0449998i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −26.5565 | − | 31.1431i | −1.17250 | − | 1.37500i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.1281 | + | 21.0850i | −1.10728 | + | 0.929116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.226684 | + | 1.28559i | −0.00996957 | + | 0.0565402i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.5565 | + | 9.66579i | −1.16570 | + | 0.424281i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.78321 | + | 10.0168i | 0.253367 | + | 0.438844i | 0.964451 | − | 0.264263i | \(-0.0851287\pi\) |
−0.711084 | + | 0.703107i | \(0.751795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.87535 | + | 2.41270i | 0.125730 | + | 0.105500i | 0.703485 | − | 0.710710i | \(-0.251626\pi\) |
−0.577754 | + | 0.816211i | \(0.696071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.97008 | + | 3.41228i | −0.0859814 | + | 0.148924i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.87955 | − | 10.6595i | −0.0818745 | − | 0.464333i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2497 | − | 4.09457i | −0.489119 | − | 0.178025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.4870 | 0.628681 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.36259 | 0.318909 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.51078 | − | 1.27782i | −0.151784 | − | 0.0552450i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.86926 | + | 27.6150i | 0.210124 | + | 1.19167i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.44668 | − | 4.23777i | 0.105386 | − | 0.182534i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2927 | − | 9.47568i | −0.485510 | − | 0.407391i | 0.366904 | − | 0.930259i | \(-0.380418\pi\) |
−0.852414 | + | 0.522867i | \(0.824862\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.09114 | + | 7.08606i | 0.175568 | + | 0.304092i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.8023 | + | 18.4905i | −2.17613 | + | 0.792047i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.35734 | + | 7.69785i | −0.0580356 | + | 0.329136i | −0.999978 | − | 0.00663836i | \(-0.997887\pi\) |
0.941942 | + | 0.335775i | \(0.108998\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.8348 | − | 13.2870i | 0.675814 | − | 0.567076i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.1477 | + | 14.8207i | 1.11393 | + | 0.631382i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.834166 | + | 0.699949i | −0.0354724 | + | 0.0297648i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.5860 | − | 71.3790i | 0.534248 | − | 3.02987i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.775402 | + | 0.282223i | −0.0328549 | + | 0.0119582i | −0.358395 | − | 0.933570i | \(-0.616676\pi\) |
0.325540 | + | 0.945528i | \(0.394454\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.23411 | − | 7.33370i | −0.179084 | − | 0.310182i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.09645 | + | 5.11553i | 0.257393 | + | 0.215978i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.41715 | − | 4.18662i | 0.101871 | − | 0.176445i | −0.810585 | − | 0.585621i | \(-0.800851\pi\) |
0.912455 | + | 0.409176i | \(0.134184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.88787 | − | 10.7066i | −0.0794232 | − | 0.450431i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.30762 | − | 0.475933i | −0.0549147 | − | 0.0199873i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.7045 | −0.867977 | −0.433989 | − | 0.900918i | \(-0.642894\pi\) | ||||
−0.433989 | + | 0.900918i | \(0.642894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.15233 | −0.341164 | −0.170582 | − | 0.985343i | \(-0.554565\pi\) | ||||
−0.170582 | + | 0.985343i | \(0.554565\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 53.5891 | + | 19.5048i | 2.23872 | + | 0.814827i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64223 | + | 54.6838i | 0.402109 | + | 2.28047i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.61121 | − | 4.52275i | 0.108706 | − | 0.188285i | −0.806540 | − | 0.591179i | \(-0.798663\pi\) |
0.915246 | + | 0.402895i | \(0.131996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.3017 | − | 41.3690i | −2.04891 | − | 1.71924i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.712979 | − | 1.23492i | −0.0295793 | − | 0.0512329i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.09050 | + | 0.760879i | −0.0865796 | + | 0.0315124i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.32905 | + | 35.8938i | −0.261674 | + | 1.48403i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.74153 | − | 3.97861i | 0.195704 | − | 0.164215i | −0.539670 | − | 0.841877i | \(-0.681451\pi\) |
0.735374 | + | 0.677662i | \(0.237007\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.19642 | − | 11.8209i | 0.172910 | − | 0.487072i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.3394 | − | 32.1706i | 1.57707 | − | 1.32332i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.92199 | − | 16.5715i | 0.119992 | − | 0.680508i | −0.864165 | − | 0.503209i | \(-0.832153\pi\) |
0.984157 | − | 0.177300i | \(-0.0567361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.86395 | − | 0.678422i | 0.0764145 | − | 0.0278126i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.4184 | − | 42.2938i | −0.999377 | − | 1.73097i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.5345 | + | 22.2651i | 1.08417 | + | 0.909726i | 0.996260 | − | 0.0864028i | \(-0.0275372\pi\) |
0.0879086 | + | 0.996129i | \(0.471982\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0714 | − | 17.4442i | 0.410822 | − | 0.711564i | −0.584158 | − | 0.811640i | \(-0.698575\pi\) |
0.994980 | + | 0.100076i | \(0.0319085\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5430 | + | 59.7926i | 0.429346 | + | 2.43494i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.4590 | − | 13.6340i | −1.52293 | − | 0.554300i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9282 | 1.25534 | 0.627668 | − | 0.778481i | \(-0.284010\pi\) | ||||
0.627668 | + | 0.778481i | \(0.284010\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.89346 | 0.117249 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.75153 | + | 1.00147i | 0.111315 | + | 0.0405153i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.55289 | + | 8.80687i | 0.0627206 | + | 0.355706i | 0.999975 | + | 0.00706025i | \(0.00224737\pi\) |
−0.937254 | + | 0.348646i | \(0.886642\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 26.8076 | − | 46.4321i | 1.08099 | − | 1.87232i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.4246 | + | 13.7819i | 0.661230 | + | 0.554838i | 0.910455 | − | 0.413607i | \(-0.135731\pi\) |
−0.249225 | + | 0.968446i | \(0.580176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.7984 | − | 22.1675i | −0.514413 | − | 0.890989i | −0.999860 | − | 0.0167229i | \(-0.994677\pi\) |
0.485448 | − | 0.874266i | \(-0.338657\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −52.1787 | + | 18.9915i | −2.09386 | + | 0.762102i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.313537 | − | 1.77816i | 0.0125616 | − | 0.0712403i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4230 | − | 10.4241i | 0.496919 | − | 0.416965i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.22314 | + | 8.64129i | 0.128720 | + | 0.345100i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.2392 | + | 15.3045i | −0.727245 | + | 0.610231i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.493858 | + | 2.80081i | −0.0196602 | + | 0.111498i | −0.993059 | − | 0.117621i | \(-0.962473\pi\) |
0.973398 | + | 0.229119i | \(0.0735845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −74.4553 | + | 27.0995i | −2.95933 | + | 1.07711i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.0094 | − | 69.2984i | −1.58773 | − | 2.75002i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.40808 | − | 7.05522i | −0.333140 | − | 0.279538i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.59948 | + | 11.4306i | −0.261072 | + | 0.452189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.07050 | + | 45.7701i | 0.318765 | + | 1.80781i | 0.550283 | + | 0.834978i | \(0.314520\pi\) |
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.80807 | − | 3.20587i | −0.347356 | − | 0.126427i | 0.162450 | − | 0.986717i | \(-0.448061\pi\) |
−0.509806 | + | 0.860290i | \(0.670283\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −61.6665 | −2.42812 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.27319 | −0.207311 | −0.103655 | − | 0.994613i | \(-0.533054\pi\) | ||||
−0.103655 | + | 0.994613i | \(0.533054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.56162 | − | 0.568383i | −0.0612990 | − | 0.0223110i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.209693 | − | 1.18923i | −0.00821851 | − | 0.0466095i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.0269 | − | 36.4197i | 0.822848 | − | 1.42521i | −0.0807056 | − | 0.996738i | \(-0.525717\pi\) |
0.903553 | − | 0.428476i | \(-0.140949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.8603 | + | 25.0558i | 1.16674 | + | 0.979011i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.7803 | + | 60.2412i | 1.35691 | + | 2.35023i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31.5671 | − | 11.4895i | 1.22968 | − | 0.447567i | 0.356192 | − | 0.934413i | \(-0.384075\pi\) |
0.873488 | + | 0.486846i | \(0.161853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.70331 | + | 21.0025i | −0.144042 | + | 0.816903i | 0.824089 | + | 0.566460i | \(0.191687\pi\) |
−0.968131 | + | 0.250443i | \(0.919424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.6746 | − | 11.4743i | 0.531077 | − | 0.445626i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.26691 | + | 0.381176i | 0.0879071 | + | 0.0147814i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.2366 | − | 26.2107i | 1.20949 | − | 1.01488i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.19922 | − | 6.80110i | 0.0463644 | − | 0.262946i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.22822 | + | 0.811004i | −0.0860193 | + | 0.0313085i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.8335 | + | 29.1564i | 0.648882 | + | 1.12390i | 0.983390 | + | 0.181504i | \(0.0580964\pi\) |
−0.334508 | + | 0.942393i | \(0.608570\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 67.5385 | + | 56.6715i | 2.59956 | + | 2.18129i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2965 | + | 28.2264i | −0.626327 | + | 1.08483i | 0.361956 | + | 0.932195i | \(0.382109\pi\) |
−0.988283 | + | 0.152635i | \(0.951224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0183306 | − | 0.103958i | −0.000703464 | − | 0.00398954i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49.5434 | + | 18.0323i | 1.89851 | + | 0.691000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.1071 | −1.11375 | −0.556875 | − | 0.830596i | \(-0.688000\pi\) | ||||
−0.556875 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 45.5198 | 1.73922 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.1151 | − | 8.41321i | −0.881897 | − | 0.320984i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.866505 | + | 4.91419i | 0.0330112 | + | 0.187216i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.4572 | − | 30.2367i | 0.664102 | − | 1.15026i | −0.315425 | − | 0.948950i | \(-0.602147\pi\) |
0.979528 | − | 0.201309i | \(-0.0645195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.456192 | + | 0.382791i | 0.0173293 | + | 0.0145410i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.5232 | + | 33.8152i | 0.740558 | + | 1.28268i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.5503 | + | 6.02383i | −0.626889 | + | 0.228169i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.1435 | + | 63.1980i | −0.421486 | + | 2.39037i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.84929 | − | 1.55174i | 0.0698467 | − | 0.0586084i | −0.607196 | − | 0.794552i | \(-0.707706\pi\) |
0.677043 | + | 0.735944i | \(0.263261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.1345 | + | 5.00711i | −1.02340 | + | 0.188847i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.3342 | − | 13.7061i | 0.615183 | − | 0.516200i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.302753 | + | 1.71700i | −0.0113862 | + | 0.0645744i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00623 | + | 1.45815i | −0.150457 | + | 0.0547619i | −0.416151 | − | 0.909296i | \(-0.636621\pi\) |
0.265694 | + | 0.964057i | \(0.414399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.9320 | + | 41.4514i | 0.897519 | + | 1.55455i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.0365 | − | 10.9389i | −0.488220 | − | 0.409665i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.09050 | − | 3.62085i | 0.0781802 | − | 0.135412i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.8733 | − | 61.6656i | −0.406071 | − | 2.30294i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5194 | − | 10.0162i | −1.02630 | − | 0.373543i | −0.226630 | − | 0.973981i | \(-0.572771\pi\) |
−0.799671 | + | 0.600438i | \(0.794993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.20218 | 0.0447714 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 60.3751 | 2.24537 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −60.8396 | − | 22.1438i | −2.25953 | − | 0.822400i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.25564 | − | 41.1488i | −0.269097 | − | 1.52612i | −0.757110 | − | 0.653287i | \(-0.773389\pi\) |
0.488013 | − | 0.872836i | \(-0.337722\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.9300 | − | 20.6634i | 0.441852 | − | 0.765311i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.5180 | + | 13.0212i | 0.573955 | + | 0.481605i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.63173 | − | 2.82624i | −0.0602693 | − | 0.104390i | 0.834316 | − | 0.551286i | \(-0.185863\pi\) |
−0.894586 | + | 0.446896i | \(0.852529\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −75.1080 | + | 27.3371i | −2.77040 | + | 1.00834i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.20942 | − | 6.85898i | 0.0445496 | − | 0.252654i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.24786 | − | 2.72528i | 0.119474 | − | 0.100251i | −0.581093 | − | 0.813837i | \(-0.697375\pi\) |
0.700567 | + | 0.713586i | \(0.252930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.3437 | − | 3.75400i | 0.747344 | − | 0.137907i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.3449 | + | 10.3586i | −0.452889 | + | 0.380019i | −0.840507 | − | 0.541801i | \(-0.817742\pi\) |
0.387618 | + | 0.921820i | \(0.373298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.46914 | − | 14.0032i | 0.0904623 | − | 0.513037i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −58.8982 | + | 21.4372i | −2.15497 | + | 0.784346i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0684621 | + | 0.118580i | 0.00250155 | + | 0.00433281i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4072 | − | 22.1583i | −0.963614 | − | 0.808568i | 0.0179232 | − | 0.999839i | \(-0.494295\pi\) |
−0.981537 | + | 0.191271i | \(0.938739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.0836 | − | 19.1974i | 0.403910 | − | 0.699593i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.81790 | + | 50.0088i | 0.320916 | + | 1.82001i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.7846 | − | 8.65689i | −0.864466 | − | 0.314640i | −0.128542 | − | 0.991704i | \(-0.541030\pi\) |
−0.735924 | + | 0.677064i | \(0.763252\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.5125 | 0.454177 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.6889 | −0.496223 | −0.248111 | − | 0.968731i | \(-0.579810\pi\) | ||||
−0.248111 | + | 0.968731i | \(0.579810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.86186 | + | 0.677660i | 0.0674037 | + | 0.0245329i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −15.1401 | − | 85.8637i | −0.547391 | − | 3.10441i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.86379 | + | 3.22817i | −0.0672974 | + | 0.116563i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.4169 | + | 22.1664i | 0.952616 | + | 0.799340i | 0.979736 | − | 0.200292i | \(-0.0641891\pi\) |
−0.0271198 | + | 0.999632i | \(0.508634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.9617 | − | 70.9477i | −1.47520 | − | 2.55512i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.5996 | − | 16.5969i | 1.64010 | − | 0.596948i | 0.653045 | − | 0.757319i | \(-0.273491\pi\) |
0.987057 | + | 0.160371i | \(0.0512689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.69209 | + | 26.6102i | −0.168545 | + | 0.955866i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.03486 | + | 1.70745i | −0.0730003 | + | 0.0612545i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.1283 | − | 3.38453i | −0.721172 | − | 0.121263i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15986 | − | 0.973239i | 0.0415031 | − | 0.0348252i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2427 | − | 63.7606i | 0.401782 | − | 2.27862i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.8847 | − | 10.5132i | 1.03094 | − | 0.375231i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.4705 | − | 40.6521i | −0.836633 | − | 1.44909i | −0.892694 | − | 0.450663i | \(-0.851188\pi\) |
0.0560615 | − | 0.998427i | \(-0.482146\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 49.9882 | + | 41.9451i | 1.77963 | + | 1.49328i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.199220 | + | 0.345060i | −0.00708346 | + | 0.0122689i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.923588 | + | 5.23793i | 0.0327976 | + | 0.186004i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.1463 | + | 12.4282i | 1.21104 | + | 0.440784i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.6388 | 1.61661 | 0.808305 | − | 0.588764i | \(-0.200385\pi\) | ||||
0.808305 | + | 0.588764i | \(0.200385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.00452 | −0.247802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −74.5786 | − | 27.1444i | −2.63510 | − | 0.959100i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.38562 | − | 7.85826i | −0.0488976 | − | 0.277312i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.55934 | − | 2.70086i | 0.0549595 | − | 0.0951926i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8631 | + | 11.6325i | 0.488004 | + | 0.409484i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.7365 | − | 27.2565i | −0.553267 | − | 0.958286i | −0.998036 | − | 0.0626411i | \(-0.980048\pi\) |
0.444769 | − | 0.895645i | \(-0.353286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.7312 | + | 14.4610i | −1.39515 | + | 0.507793i | −0.926735 | − | 0.375716i | \(-0.877397\pi\) |
−0.468415 | + | 0.883509i | \(0.655175\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.4084 | + | 70.3715i | −0.435182 | + | 2.46804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.9794 | − | 20.1211i | 0.839962 | − | 0.704811i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.20423 | + | 21.9957i | 0.287030 | + | 0.769532i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.02326 | − | 0.858614i | 0.0357555 | − | 0.0300024i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.33917 | + | 18.9374i | −0.116538 | + | 0.660919i | 0.869440 | + | 0.494039i | \(0.164480\pi\) |
−0.985977 | + | 0.166879i | \(0.946631\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9230 | − | 9.07122i | 0.868760 | − | 0.316203i | 0.131095 | − | 0.991370i | \(-0.458151\pi\) |
0.737665 | + | 0.675167i | \(0.235928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.93358 | − | 17.2055i | −0.345843 | − | 0.599018i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.3929 | − | 11.2380i | −0.465718 | − | 0.390784i | 0.379512 | − | 0.925187i | \(-0.376092\pi\) |
−0.845230 | + | 0.534403i | \(0.820536\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.9372 | + | 22.4079i | −0.449328 | + | 0.778259i | −0.998342 | − | 0.0575537i | \(-0.981670\pi\) |
0.549014 | + | 0.835813i | \(0.315003\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.97194 | − | 28.1973i | −0.172475 | − | 0.978153i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.6728 | + | 8.98018i | 0.854863 | + | 0.311145i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44.6782 | 1.54615 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −27.0207 | −0.933972 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.2066 | + | 13.5421i | 1.28451 | + | 0.467524i | 0.891922 | − | 0.452189i | \(-0.149357\pi\) |
0.392591 | + | 0.919713i | \(0.371579\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.22029 | + | 18.2632i | 0.111044 | + | 0.629764i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.6863 | + | 63.5425i | −1.26354 | + | 2.18852i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.5925 | + | 25.6701i | 1.05241 | + | 0.883079i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.730471 | + | 1.26521i | 0.0250993 | + | 0.0434732i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 33.1354 | − | 12.0603i | 1.13720 | − | 0.413909i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.50047 | + | 36.8660i | −0.222833 | + | 1.26375i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.9929 | + | 20.1325i | −0.821502 | + | 0.689322i | −0.953323 | − | 0.301951i | \(-0.902362\pi\) |
0.131821 | + | 0.991274i | \(0.457918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.8029 | − | 95.2193i | 1.15603 | − | 3.25643i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.5482 | + | 10.5292i | −0.428637 | + | 0.359669i | −0.831437 | − | 0.555619i | \(-0.812481\pi\) |
0.402800 | + | 0.915288i | \(0.368037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.23449 | + | 35.3576i | −0.212718 | + | 1.20638i | 0.672105 | + | 0.740456i | \(0.265391\pi\) |
−0.884823 | + | 0.465928i | \(0.845721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.84644 | + | 0.672051i | −0.0629266 | + | 0.0229034i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3886 | − | 33.5820i | −0.659995 | − | 1.14314i | −0.980616 | − | 0.195938i | \(-0.937225\pi\) |
0.320621 | − | 0.947207i | \(-0.396108\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.2074 | − | 22.8297i | −0.925078 | − | 0.776233i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.30538 | − | 7.45713i | 0.146218 | − | 0.253258i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.953434 | − | 5.40720i | −0.0323430 | − | 0.183427i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6801 | − | 5.34313i | −0.497418 | − | 0.181045i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63998 | −0.157040 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.31494 | −0.0782594 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.6819 | − | 4.61584i | −0.428238 | − | 0.155866i | 0.118904 | − | 0.992906i | \(-0.462062\pi\) |
−0.547142 | + | 0.837040i | \(0.684284\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.35445 | + | 41.7091i | 0.248059 | + | 1.40681i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.03251 | − | 5.25246i | 0.102168 | − | 0.176960i | −0.810410 | − | 0.585864i | \(-0.800755\pi\) |
0.912578 | + | 0.408904i | \(0.134089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.42261 | − | 4.55011i | −0.182485 | − | 0.153123i | 0.546969 | − | 0.837153i | \(-0.315782\pi\) |
−0.729454 | + | 0.684029i | \(0.760226\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5723 | + | 23.5079i | 0.456228 | + | 0.790209i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.7141 | + | 15.5466i | −1.43420 | + | 0.522005i | −0.938132 | − | 0.346279i | \(-0.887445\pi\) |
−0.496066 | + | 0.868285i | \(0.665223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.509243 | + | 2.88806i | −0.0170795 | + | 0.0968625i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.37490 | − | 4.51008i | 0.180066 | − | 0.151093i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.06192 | − | 4.00275i | −0.236318 | − | 0.133947i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.9957 | + | 22.6520i | −0.902365 | + | 0.757174i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.87363 | − | 27.6397i | 0.162726 | − | 0.922864i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.6460 | − | 6.78659i | 0.621879 | − | 0.226345i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.96844 | − | 10.3376i | −0.198838 | − | 0.344397i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.73127 | + | 1.45271i | 0.0576132 | + | 0.0483432i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.14151 | + | 8.90536i | −0.170910 | + | 0.296024i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.82814 | − | 38.7243i | −0.226725 | − | 1.28582i | −0.859360 | − | 0.511370i | \(-0.829138\pi\) |
0.632636 | − | 0.774450i | \(-0.281973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.0136 | + | 26.2108i | 2.38854 | + | 0.869357i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.52856 | −0.315695 | −0.157848 | − | 0.987463i | \(-0.550455\pi\) | ||||
−0.157848 | + | 0.987463i | \(0.550455\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.18999 | 0.237954 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 36.3958 | + | 13.2470i | 1.20321 | + | 0.437932i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.248070 | − | 1.40687i | −0.00819198 | − | 0.0464590i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.36681 | − | 14.4917i | 0.275996 | − | 0.478039i | −0.694390 | − | 0.719599i | \(-0.744326\pi\) |
0.970386 | + | 0.241560i | \(0.0776591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.28476 | − | 1.07804i | −0.0423342 | − | 0.0355226i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.69808 | − | 2.94116i | −0.0558930 | − | 0.0968096i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55.8535 | − | 20.3290i | 1.83645 | − | 0.668414i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.17590 | − | 52.0391i | 0.301376 | − | 1.70919i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.66832 | − | 4.75629i | 0.185972 | − | 0.156049i | −0.545049 | − | 0.838404i | \(-0.683489\pi\) |
0.731020 | + | 0.682356i | \(0.239044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.7433 | + | 23.1531i | 0.647061 | + | 0.758813i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.5092 | + | 30.6348i | −1.19526 | + | 1.00294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.73676 | + | 9.84967i | −0.0567982 | + | 0.322119i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4994 | + | 9.64498i | −0.865697 | + | 0.315088i | −0.736423 | − | 0.676521i | \(-0.763487\pi\) |
−0.129273 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.3589 | + | 59.5113i | 1.12126 | + | 1.94208i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.9787 | + | 33.5461i | 1.30327 | + | 1.09357i | 0.989570 | + | 0.144050i | \(0.0460125\pi\) |
0.313698 | + | 0.949523i | \(0.398432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8457 | + | 23.9814i | −0.450877 | + | 0.780941i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.859867 | − | 4.87655i | −0.0279715 | − | 0.158634i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.1023 | − | 8.04458i | −0.718228 | − | 0.261414i | −0.0430549 | − | 0.999073i | \(-0.513709\pi\) |
−0.675174 | + | 0.737659i | \(0.735931\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.8983 | −0.581003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −57.2669 | −1.85701 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.1886 | − | 12.8076i | −1.13987 | − | 0.414879i | −0.298004 | − | 0.954565i | \(-0.596321\pi\) |
−0.841867 | + | 0.539686i | \(0.818543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4454 | + | 70.5812i | 0.402723 | + | 2.28395i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.29473 | + | 12.6348i | −0.235805 | + | 0.408426i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.27796 | − | 1.07234i | −0.0412675 | − | 0.0346275i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.3594 | + | 19.6750i | 0.366432 | + | 0.634678i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.65557 | − | 2.05846i | 0.182248 | − | 0.0663329i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0451 | − | 79.6537i | 0.452128 | − | 2.56414i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.3924 | + | 21.3068i | −0.816565 | + | 0.685179i | −0.952165 | − | 0.305585i | \(-0.901148\pi\) |
0.135600 | + | 0.990764i | \(0.456704\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −42.6591 | + | 25.0831i | −1.37041 | + | 0.805787i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.1983 | + | 10.2356i | −0.391462 | + | 0.328476i | −0.817182 | − | 0.576379i | \(-0.804465\pi\) |
0.425720 | + | 0.904855i | \(0.360021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.248493 | − | 1.40927i | 0.00796632 | − | 0.0451792i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −41.8753 | + | 15.2414i | −1.34108 | + | 0.488115i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.950197 | − | 1.64579i | −0.0303995 | − | 0.0526535i | 0.850425 | − | 0.526096i | \(-0.176345\pi\) |
−0.880825 | + | 0.473442i | \(0.843011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.97420 | + | 5.85205i | 0.222896 | + | 0.187032i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.5452 | − | 75.4225i | 1.39029 | − | 2.40805i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.74254 | − | 15.5537i | −0.0874733 | − | 0.496086i | −0.996795 | − | 0.0799929i | \(-0.974510\pi\) |
0.909322 | − | 0.416093i | \(-0.136601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.1050 | + | 21.5125i | 1.88324 | + | 0.685444i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.781461 | −0.0248742 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.8497 | 1.01276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.1131 | + | 13.1441i | 1.14717 | + | 0.417536i | 0.844498 | − | 0.535559i | \(-0.179899\pi\) |
0.302672 | + | 0.953095i | \(0.402121\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.73800 | − | 43.8844i | −0.245558 | − | 1.39263i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.6876 | − | 53.1525i | 0.972863 | − | 1.68505i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.30982 | + | 5.29457i | 0.199834 | + | 0.167681i | 0.737213 | − | 0.675660i | \(-0.236141\pi\) |
−0.537379 | + | 0.843341i | \(0.680586\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.7190 | + | 51.4749i | 0.940268 | + | 1.62859i |
(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 | 76.2.i.a.25.1 | ✓ | 12 | |
3.2 | odd | 2 | 684.2.bo.c.253.2 | 12 | |||
4.3 | odd | 2 | 304.2.u.e.177.2 | 12 | |||
19.4 | even | 9 | 1444.2.a.h.1.6 | 6 | |||
19.6 | even | 9 | 1444.2.e.g.653.1 | 12 | |||
19.9 | even | 9 | 1444.2.e.g.429.1 | 12 | |||
19.10 | odd | 18 | 1444.2.e.h.429.6 | 12 | |||
19.13 | odd | 18 | 1444.2.e.h.653.6 | 12 | |||
19.15 | odd | 18 | 1444.2.a.g.1.1 | 6 | |||
19.16 | even | 9 | inner | 76.2.i.a.73.1 | yes | 12 | |
57.35 | odd | 18 | 684.2.bo.c.73.2 | 12 | |||
76.15 | even | 18 | 5776.2.a.by.1.6 | 6 | |||
76.23 | odd | 18 | 5776.2.a.bw.1.1 | 6 | |||
76.35 | odd | 18 | 304.2.u.e.225.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.i.a.25.1 | ✓ | 12 | 1.1 | even | 1 | trivial | |
76.2.i.a.73.1 | yes | 12 | 19.16 | even | 9 | inner | |
304.2.u.e.177.2 | 12 | 4.3 | odd | 2 | |||
304.2.u.e.225.2 | 12 | 76.35 | odd | 18 | |||
684.2.bo.c.73.2 | 12 | 57.35 | odd | 18 | |||
684.2.bo.c.253.2 | 12 | 3.2 | odd | 2 | |||
1444.2.a.g.1.1 | 6 | 19.15 | odd | 18 | |||
1444.2.a.h.1.6 | 6 | 19.4 | even | 9 | |||
1444.2.e.g.429.1 | 12 | 19.9 | even | 9 | |||
1444.2.e.g.653.1 | 12 | 19.6 | even | 9 | |||
1444.2.e.h.429.6 | 12 | 19.10 | odd | 18 | |||
1444.2.e.h.653.6 | 12 | 19.13 | odd | 18 | |||
5776.2.a.bw.1.1 | 6 | 76.23 | odd | 18 | |||
5776.2.a.by.1.6 | 6 | 76.15 | even | 18 |