Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(1.32001 - 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.2.c.f.199.5 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.12489i | − 1.50252i | −0.660006 | − | 0.751260i | \(-0.729446\pi\) | ||||
0.660006 | − | 0.751260i | \(-0.270554\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −2.51514 | −1.25757 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.12489 | −0.867481 | ||||||||
\(7\) | − 3.64002i | − 1.37580i | −0.725806 | − | 0.687900i | \(-0.758533\pi\) | ||||
0.725806 | − | 0.687900i | \(-0.241467\pi\) | |||||||
\(8\) | 1.09461i | 0.387003i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.51514i | 0.726058i | ||||||||
\(13\) | 1.51514i | 0.420224i | 0.977677 | + | 0.210112i | \(0.0673828\pi\) | ||||
−0.977677 | + | 0.210112i | \(0.932617\pi\) | |||||||
\(14\) | −7.73463 | −2.06717 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70436 | −0.676089 | ||||||||
\(17\) | − 1.15516i | − 0.280168i | −0.990140 | − | 0.140084i | \(-0.955263\pi\) | ||||
0.990140 | − | 0.140084i | \(-0.0447372\pi\) | |||||||
\(18\) | 2.12489i | 0.500840i | ||||||||
\(19\) | −2.60975 | −0.598717 | −0.299359 | − | 0.954141i | \(-0.596773\pi\) | ||||
−0.299359 | + | 0.954141i | \(0.596773\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.64002 | −0.794318 | ||||||||
\(22\) | − 2.12489i | − 0.453027i | ||||||||
\(23\) | − 5.73463i | − 1.19575i | −0.801588 | − | 0.597877i | \(-0.796011\pi\) | ||||
0.801588 | − | 0.597877i | \(-0.203989\pi\) | |||||||
\(24\) | 1.09461 | 0.223436 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.21949 | 0.631395 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 9.15516i | 1.73016i | ||||||||
\(29\) | −6.24977 | −1.16055 | −0.580277 | − | 0.814419i | \(-0.697056\pi\) | ||||
−0.580277 | + | 0.814419i | \(0.697056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.51514 | 0.990548 | 0.495274 | − | 0.868737i | \(-0.335068\pi\) | ||||
0.495274 | + | 0.868737i | \(0.335068\pi\) | |||||||
\(32\) | 7.93567i | 1.40284i | ||||||||
\(33\) | − 1.00000i | − 0.174078i | ||||||||
\(34\) | −2.45459 | −0.420958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.51514 | 0.419190 | ||||||||
\(37\) | − 0.454586i | − 0.0747335i | −0.999302 | − | 0.0373667i | \(-0.988103\pi\) | ||||
0.999302 | − | 0.0373667i | \(-0.0118970\pi\) | |||||||
\(38\) | 5.54541i | 0.899585i | ||||||||
\(39\) | 1.51514 | 0.242616 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12489 | 0.644199 | 0.322099 | − | 0.946706i | \(-0.395611\pi\) | ||||
0.322099 | + | 0.946706i | \(0.395611\pi\) | |||||||
\(42\) | 7.73463i | 1.19348i | ||||||||
\(43\) | 11.7044i | 1.78490i | 0.451149 | + | 0.892449i | \(0.351014\pi\) | ||||
−0.451149 | + | 0.892449i | \(0.648986\pi\) | |||||||
\(44\) | −2.51514 | −0.379171 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.1854 | −1.79664 | ||||||||
\(47\) | 3.48486i | 0.508319i | 0.967162 | + | 0.254160i | \(0.0817989\pi\) | ||||
−0.967162 | + | 0.254160i | \(0.918201\pi\) | |||||||
\(48\) | 2.70436i | 0.390340i | ||||||||
\(49\) | −6.24977 | −0.892824 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.15516 | −0.161755 | ||||||||
\(52\) | − 3.81078i | − 0.528460i | ||||||||
\(53\) | − 12.5601i | − 1.72526i | −0.505834 | − | 0.862631i | \(-0.668815\pi\) | ||||
0.505834 | − | 0.862631i | \(-0.331185\pi\) | |||||||
\(54\) | 2.12489 | 0.289160 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.98440 | 0.532438 | ||||||||
\(57\) | 2.60975i | 0.345669i | ||||||||
\(58\) | 13.2800i | 1.74376i | ||||||||
\(59\) | 7.73463 | 1.00696 | 0.503482 | − | 0.864006i | \(-0.332052\pi\) | ||||
0.503482 | + | 0.864006i | \(0.332052\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0147 | −1.53832 | −0.769161 | − | 0.639055i | \(-0.779326\pi\) | ||||
−0.769161 | + | 0.639055i | \(0.779326\pi\) | |||||||
\(62\) | − 11.7190i | − 1.48832i | ||||||||
\(63\) | 3.64002i | 0.458600i | ||||||||
\(64\) | 11.4537 | 1.43171 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.12489 | −0.261555 | ||||||||
\(67\) | 14.2645i | 1.74268i | 0.490680 | + | 0.871340i | \(0.336749\pi\) | ||||
−0.490680 | + | 0.871340i | \(0.663251\pi\) | |||||||
\(68\) | 2.90539i | 0.352330i | ||||||||
\(69\) | −5.73463 | −0.690369 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.51514 | 1.01056 | 0.505280 | − | 0.862955i | \(-0.331389\pi\) | ||||
0.505280 | + | 0.862955i | \(0.331389\pi\) | |||||||
\(72\) | − 1.09461i | − 0.129001i | ||||||||
\(73\) | − 9.21949i | − 1.07906i | −0.841966 | − | 0.539530i | \(-0.818602\pi\) | ||||
0.841966 | − | 0.539530i | \(-0.181398\pi\) | |||||||
\(74\) | −0.965943 | −0.112289 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.56387 | 0.752928 | ||||||||
\(77\) | − 3.64002i | − 0.414819i | ||||||||
\(78\) | − 3.21949i | − 0.364536i | ||||||||
\(79\) | −5.09461 | −0.573188 | −0.286594 | − | 0.958052i | \(-0.592523\pi\) | ||||
−0.286594 | + | 0.958052i | \(0.592523\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 8.76491i | − 0.967922i | ||||||||
\(83\) | − 14.7493i | − 1.61895i | −0.587156 | − | 0.809474i | \(-0.699753\pi\) | ||||
0.587156 | − | 0.809474i | \(-0.300247\pi\) | |||||||
\(84\) | 9.15516 | 0.998910 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.8704 | 2.68185 | ||||||||
\(87\) | 6.24977i | 0.670046i | ||||||||
\(88\) | 1.09461i | 0.116686i | ||||||||
\(89\) | 10.4995 | 1.11295 | 0.556475 | − | 0.830865i | \(-0.312154\pi\) | ||||
0.556475 | + | 0.830865i | \(0.312154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.51514 | 0.578144 | ||||||||
\(92\) | 14.4234i | 1.50374i | ||||||||
\(93\) | − 5.51514i | − 0.571893i | ||||||||
\(94\) | 7.40493 | 0.763760 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.93567 | 0.809931 | ||||||||
\(97\) | 6.77959i | 0.688363i | 0.938903 | + | 0.344181i | \(0.111844\pi\) | ||||
−0.938903 | + | 0.344181i | \(0.888156\pi\) | |||||||
\(98\) | 13.2800i | 1.34149i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.40493 | 0.736818 | 0.368409 | − | 0.929664i | \(-0.379903\pi\) | ||||
0.368409 | + | 0.929664i | \(0.379903\pi\) | |||||||
\(102\) | 2.45459i | 0.243040i | ||||||||
\(103\) | − 16.4995i | − 1.62575i | −0.582439 | − | 0.812874i | \(-0.697902\pi\) | ||||
0.582439 | − | 0.812874i | \(-0.302098\pi\) | |||||||
\(104\) | −1.65848 | −0.162628 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −26.6888 | −2.59224 | ||||||||
\(107\) | − 3.93945i | − 0.380841i | −0.981703 | − | 0.190420i | \(-0.939015\pi\) | ||||
0.981703 | − | 0.190420i | \(-0.0609851\pi\) | |||||||
\(108\) | − 2.51514i | − 0.242019i | ||||||||
\(109\) | −6.73463 | −0.645061 | −0.322530 | − | 0.946559i | \(-0.604533\pi\) | ||||
−0.322530 | + | 0.946559i | \(0.604533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.454586 | −0.0431474 | ||||||||
\(112\) | 9.84392i | 0.930163i | ||||||||
\(113\) | − 6.00000i | − 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 5.54541 | 0.519376 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 15.7190 | 1.45948 | ||||||||
\(117\) | − 1.51514i | − 0.140075i | ||||||||
\(118\) | − 16.4352i | − 1.51298i | ||||||||
\(119\) | −4.20482 | −0.385455 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 25.5298i | 2.31136i | ||||||||
\(123\) | − 4.12489i | − 0.371928i | ||||||||
\(124\) | −13.8713 | −1.24568 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.73463 | 0.689056 | ||||||||
\(127\) | − 8.06433i | − 0.715594i | −0.933799 | − | 0.357797i | \(-0.883528\pi\) | ||||
0.933799 | − | 0.357797i | \(-0.116472\pi\) | |||||||
\(128\) | − 8.46640i | − 0.748331i | ||||||||
\(129\) | 11.7044 | 1.03051 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.8099 | −1.11920 | −0.559602 | − | 0.828762i | \(-0.689046\pi\) | ||||
−0.559602 | + | 0.828762i | \(0.689046\pi\) | |||||||
\(132\) | 2.51514i | 0.218915i | ||||||||
\(133\) | 9.49954i | 0.823715i | ||||||||
\(134\) | 30.3103 | 2.61841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.26445 | 0.108426 | ||||||||
\(137\) | − 22.8099i | − 1.94878i | −0.224868 | − | 0.974389i | \(-0.572195\pi\) | ||||
0.224868 | − | 0.974389i | \(-0.427805\pi\) | |||||||
\(138\) | 12.1854i | 1.03729i | ||||||||
\(139\) | −7.59037 | −0.643807 | −0.321903 | − | 0.946773i | \(-0.604323\pi\) | ||||
−0.321903 | + | 0.946773i | \(0.604323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.48486 | 0.293478 | ||||||||
\(142\) | − 18.0937i | − 1.51839i | ||||||||
\(143\) | 1.51514i | 0.126702i | ||||||||
\(144\) | 2.70436 | 0.225363 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.5904 | −1.62131 | ||||||||
\(147\) | 6.24977i | 0.515472i | ||||||||
\(148\) | 1.14335i | 0.0939825i | ||||||||
\(149\) | 1.81456 | 0.148655 | 0.0743274 | − | 0.997234i | \(-0.476319\pi\) | ||||
0.0743274 | + | 0.997234i | \(0.476319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.3250 | 1.97954 | 0.989770 | − | 0.142670i | \(-0.0455687\pi\) | ||||
0.989770 | + | 0.142670i | \(0.0455687\pi\) | |||||||
\(152\) | − 2.85665i | − 0.231705i | ||||||||
\(153\) | 1.15516i | 0.0933893i | ||||||||
\(154\) | −7.73463 | −0.623274 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.81078 | −0.305107 | ||||||||
\(157\) | − 9.76491i | − 0.779325i | −0.920958 | − | 0.389662i | \(-0.872592\pi\) | ||||
0.920958 | − | 0.389662i | \(-0.127408\pi\) | |||||||
\(158\) | 10.8255i | 0.861227i | ||||||||
\(159\) | −12.5601 | −0.996080 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.8742 | −1.64512 | ||||||||
\(162\) | − 2.12489i | − 0.166947i | ||||||||
\(163\) | − 6.98440i | − 0.547061i | −0.961863 | − | 0.273530i | \(-0.911809\pi\) | ||||
0.961863 | − | 0.273530i | \(-0.0881914\pi\) | |||||||
\(164\) | −10.3747 | −0.810125 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.3406 | −2.43250 | ||||||||
\(167\) | 6.31032i | 0.488307i | 0.969737 | + | 0.244154i | \(0.0785102\pi\) | ||||
−0.969737 | + | 0.244154i | \(0.921490\pi\) | |||||||
\(168\) | − 3.98440i | − 0.307403i | ||||||||
\(169\) | 10.7044 | 0.823412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.60975 | 0.199572 | ||||||||
\(172\) | − 29.4381i | − 2.24463i | ||||||||
\(173\) | − 12.8448i | − 0.976575i | −0.872683 | − | 0.488287i | \(-0.837622\pi\) | ||||
0.872683 | − | 0.488287i | \(-0.162378\pi\) | |||||||
\(174\) | 13.2800 | 1.00676 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.70436 | −0.203849 | ||||||||
\(177\) | − 7.73463i | − 0.581371i | ||||||||
\(178\) | − 22.3103i | − 1.67223i | ||||||||
\(179\) | −13.4849 | −1.00791 | −0.503953 | − | 0.863731i | \(-0.668122\pi\) | ||||
−0.503953 | + | 0.863731i | \(0.668122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0899 | −1.71626 | −0.858130 | − | 0.513433i | \(-0.828374\pi\) | ||||
−0.858130 | + | 0.513433i | \(0.828374\pi\) | |||||||
\(182\) | − 11.7190i | − 0.868673i | ||||||||
\(183\) | 12.0147i | 0.888151i | ||||||||
\(184\) | 6.27718 | 0.462760 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −11.7190 | −0.859281 | ||||||||
\(187\) | − 1.15516i | − 0.0844738i | ||||||||
\(188\) | − 8.76491i | − 0.639247i | ||||||||
\(189\) | 3.64002 | 0.264773 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.98440 | −0.577731 | −0.288866 | − | 0.957370i | \(-0.593278\pi\) | ||||
−0.288866 | + | 0.957370i | \(0.593278\pi\) | |||||||
\(192\) | − 11.4537i | − 0.826597i | ||||||||
\(193\) | 11.7649i | 0.846857i | 0.905930 | + | 0.423428i | \(0.139173\pi\) | ||||
−0.905930 | + | 0.423428i | \(0.860827\pi\) | |||||||
\(194\) | 14.4058 | 1.03428 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 15.7190 | 1.12279 | ||||||||
\(197\) | 3.81456i | 0.271776i | 0.990724 | + | 0.135888i | \(0.0433888\pi\) | ||||
−0.990724 | + | 0.135888i | \(0.956611\pi\) | |||||||
\(198\) | 2.12489i | 0.151009i | ||||||||
\(199\) | 12.0752 | 0.855990 | 0.427995 | − | 0.903781i | \(-0.359220\pi\) | ||||
0.427995 | + | 0.903781i | \(0.359220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.2645 | 1.00614 | ||||||||
\(202\) | − 15.7346i | − 1.10708i | ||||||||
\(203\) | 22.7493i | 1.59669i | ||||||||
\(204\) | 2.90539 | 0.203418 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −35.0596 | −2.44272 | ||||||||
\(207\) | 5.73463i | 0.398585i | ||||||||
\(208\) | − 4.09747i | − 0.284109i | ||||||||
\(209\) | −2.60975 | −0.180520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2645 | 0.706634 | 0.353317 | − | 0.935504i | \(-0.385054\pi\) | ||||
0.353317 | + | 0.935504i | \(0.385054\pi\) | |||||||
\(212\) | 31.5904i | 2.16964i | ||||||||
\(213\) | − 8.51514i | − 0.583448i | ||||||||
\(214\) | −8.37088 | −0.572221 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.09461 | −0.0744787 | ||||||||
\(217\) | − 20.0752i | − 1.36280i | ||||||||
\(218\) | 14.3103i | 0.969217i | ||||||||
\(219\) | −9.21949 | −0.622996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75023 | 0.117733 | ||||||||
\(222\) | 0.965943i | 0.0648298i | ||||||||
\(223\) | 12.9239i | 0.865445i | 0.901527 | + | 0.432723i | \(0.142447\pi\) | ||||
−0.901527 | + | 0.432723i | \(0.857553\pi\) | |||||||
\(224\) | 28.8860 | 1.93003 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7493 | −0.848072 | ||||||||
\(227\) | − 22.8099i | − 1.51394i | −0.653447 | − | 0.756972i | \(-0.726678\pi\) | ||||
0.653447 | − | 0.756972i | \(-0.273322\pi\) | |||||||
\(228\) | − 6.56387i | − 0.434703i | ||||||||
\(229\) | −14.7796 | −0.976663 | −0.488331 | − | 0.872658i | \(-0.662394\pi\) | ||||
−0.488331 | + | 0.872658i | \(0.662394\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.64002 | −0.239496 | ||||||||
\(232\) | − 6.84106i | − 0.449137i | ||||||||
\(233\) | 4.96594i | 0.325330i | 0.986681 | + | 0.162665i | \(0.0520089\pi\) | ||||
−0.986681 | + | 0.162665i | \(0.947991\pi\) | |||||||
\(234\) | −3.21949 | −0.210465 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −19.4537 | −1.26633 | ||||||||
\(237\) | 5.09461i | 0.330930i | ||||||||
\(238\) | 8.93475i | 0.579154i | ||||||||
\(239\) | 14.9991 | 0.970210 | 0.485105 | − | 0.874456i | \(-0.338781\pi\) | ||||
0.485105 | + | 0.874456i | \(0.338781\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.04496 | 0.324974 | 0.162487 | − | 0.986711i | \(-0.448048\pi\) | ||||
0.162487 | + | 0.986711i | \(0.448048\pi\) | |||||||
\(242\) | − 2.12489i | − 0.136593i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 30.2186 | 1.93455 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.76491 | −0.558830 | ||||||||
\(247\) | − 3.95413i | − 0.251595i | ||||||||
\(248\) | 6.03692i | 0.383345i | ||||||||
\(249\) | −14.7493 | −0.934700 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.03028 | −0.191269 | −0.0956347 | − | 0.995417i | \(-0.530488\pi\) | ||||
−0.0956347 | + | 0.995417i | \(0.530488\pi\) | |||||||
\(252\) | − 9.15516i | − 0.576721i | ||||||||
\(253\) | − 5.73463i | − 0.360533i | ||||||||
\(254\) | −17.1358 | −1.07519 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.91721 | 0.307325 | ||||||||
\(257\) | 13.6509i | 0.851521i | 0.904836 | + | 0.425761i | \(0.139993\pi\) | ||||
−0.904836 | + | 0.425761i | \(0.860007\pi\) | |||||||
\(258\) | − 24.8704i | − 1.54836i | ||||||||
\(259\) | −1.65470 | −0.102818 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.24977 | 0.386851 | ||||||||
\(262\) | 27.2195i | 1.68163i | ||||||||
\(263\) | 12.5601i | 0.774489i | 0.921977 | + | 0.387244i | \(0.126573\pi\) | ||||
−0.921977 | + | 0.387244i | \(0.873427\pi\) | |||||||
\(264\) | 1.09461 | 0.0673685 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.1854 | 1.23765 | ||||||||
\(267\) | − 10.4995i | − 0.642562i | ||||||||
\(268\) | − 35.8771i | − 2.19154i | ||||||||
\(269\) | 24.6888 | 1.50530 | 0.752650 | − | 0.658421i | \(-0.228775\pi\) | ||||
0.752650 | + | 0.658421i | \(0.228775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.56479 | 0.459528 | 0.229764 | − | 0.973246i | \(-0.426205\pi\) | ||||
0.229764 | + | 0.973246i | \(0.426205\pi\) | |||||||
\(272\) | 3.12397i | 0.189418i | ||||||||
\(273\) | − 5.51514i | − 0.333791i | ||||||||
\(274\) | −48.4683 | −2.92808 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.4234 | 0.868186 | ||||||||
\(277\) | − 1.92477i | − 0.115648i | −0.998327 | − | 0.0578241i | \(-0.981584\pi\) | ||||
0.998327 | − | 0.0578241i | \(-0.0184162\pi\) | |||||||
\(278\) | 16.1287i | 0.967333i | ||||||||
\(279\) | −5.51514 | −0.330183 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.87511 | −0.111860 | −0.0559300 | − | 0.998435i | \(-0.517812\pi\) | ||||
−0.0559300 | + | 0.998435i | \(0.517812\pi\) | |||||||
\(282\) | − 7.40493i | − 0.440957i | ||||||||
\(283\) | 30.1396i | 1.79161i | 0.444446 | + | 0.895806i | \(0.353401\pi\) | ||||
−0.444446 | + | 0.895806i | \(0.646599\pi\) | |||||||
\(284\) | −21.4167 | −1.27085 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.21949 | 0.190373 | ||||||||
\(287\) | − 15.0147i | − 0.886289i | ||||||||
\(288\) | − 7.93567i | − 0.467614i | ||||||||
\(289\) | 15.6656 | 0.921506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.77959 | 0.397427 | ||||||||
\(292\) | 23.1883i | 1.35699i | ||||||||
\(293\) | − 29.1552i | − 1.70326i | −0.524141 | − | 0.851631i | \(-0.675614\pi\) | ||||
0.524141 | − | 0.851631i | \(-0.324386\pi\) | |||||||
\(294\) | 13.2800 | 0.774508 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.497594 | 0.0289221 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | − 3.85574i | − 0.223357i | ||||||||
\(299\) | 8.68876 | 0.502484 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6041 | 2.45566 | ||||||||
\(302\) | − 51.6878i | − 2.97430i | ||||||||
\(303\) | − 7.40493i | − 0.425402i | ||||||||
\(304\) | 7.05769 | 0.404786 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.45459 | 0.140319 | ||||||||
\(307\) | − 27.8548i | − 1.58976i | −0.606768 | − | 0.794879i | \(-0.707534\pi\) | ||||
0.606768 | − | 0.794879i | \(-0.292466\pi\) | |||||||
\(308\) | 9.15516i | 0.521664i | ||||||||
\(309\) | −16.4995 | −0.938626 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.9083 | 1.35571 | 0.677856 | − | 0.735194i | \(-0.262909\pi\) | ||||
0.677856 | + | 0.735194i | \(0.262909\pi\) | |||||||
\(312\) | 1.65848i | 0.0938932i | ||||||||
\(313\) | 28.3094i | 1.60014i | 0.599905 | + | 0.800071i | \(0.295205\pi\) | ||||
−0.599905 | + | 0.800071i | \(0.704795\pi\) | |||||||
\(314\) | −20.7493 | −1.17095 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.8136 | 0.720824 | ||||||||
\(317\) | 8.80986i | 0.494811i | 0.968912 | + | 0.247406i | \(0.0795780\pi\) | ||||
−0.968912 | + | 0.247406i | \(0.920422\pi\) | |||||||
\(318\) | 26.6888i | 1.49663i | ||||||||
\(319\) | −6.24977 | −0.349920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.93945 | −0.219879 | ||||||||
\(322\) | 44.3553i | 2.47182i | ||||||||
\(323\) | 3.01468i | 0.167741i | ||||||||
\(324\) | −2.51514 | −0.139730 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.8411 | −0.821970 | ||||||||
\(327\) | 6.73463i | 0.372426i | ||||||||
\(328\) | 4.51514i | 0.249307i | ||||||||
\(329\) | 12.6850 | 0.699346 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.2498 | 1.77261 | 0.886304 | − | 0.463104i | \(-0.153264\pi\) | ||||
0.886304 | + | 0.463104i | \(0.153264\pi\) | |||||||
\(332\) | 37.0966i | 2.03594i | ||||||||
\(333\) | 0.454586i | 0.0249112i | ||||||||
\(334\) | 13.4087 | 0.733692 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.84392 | 0.537030 | ||||||||
\(337\) | − 28.9844i | − 1.57888i | −0.613827 | − | 0.789441i | \(-0.710371\pi\) | ||||
0.613827 | − | 0.789441i | \(-0.289629\pi\) | |||||||
\(338\) | − 22.7455i | − 1.23719i | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.51514 | 0.298661 | ||||||||
\(342\) | − 5.54541i | − 0.299862i | ||||||||
\(343\) | − 2.73085i | − 0.147452i | ||||||||
\(344\) | −12.8117 | −0.690760 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.2938 | −1.46732 | ||||||||
\(347\) | 35.7190i | 1.91750i | 0.284253 | + | 0.958749i | \(0.408254\pi\) | ||||
−0.284253 | + | 0.958749i | \(0.591746\pi\) | |||||||
\(348\) | − 15.7190i | − 0.842629i | ||||||||
\(349\) | 23.2800 | 1.24615 | 0.623076 | − | 0.782161i | \(-0.285883\pi\) | ||||
0.623076 | + | 0.782161i | \(0.285883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51514 | −0.0808721 | ||||||||
\(352\) | 7.93567i | 0.422972i | ||||||||
\(353\) | − 9.75023i | − 0.518952i | −0.965750 | − | 0.259476i | \(-0.916450\pi\) | ||||
0.965750 | − | 0.259476i | \(-0.0835499\pi\) | |||||||
\(354\) | −16.4352 | −0.873521 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −26.4078 | −1.39961 | ||||||||
\(357\) | 4.20482i | 0.222542i | ||||||||
\(358\) | 28.6538i | 1.51440i | ||||||||
\(359\) | −33.9007 | −1.78921 | −0.894605 | − | 0.446858i | \(-0.852543\pi\) | ||||
−0.894605 | + | 0.446858i | \(0.852543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1892 | −0.641538 | ||||||||
\(362\) | 49.0634i | 2.57872i | ||||||||
\(363\) | − 1.00000i | − 0.0524864i | ||||||||
\(364\) | −13.8713 | −0.727055 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.5298 | 1.33446 | ||||||||
\(367\) | − 1.88601i | − 0.0984491i | −0.998788 | − | 0.0492245i | \(-0.984325\pi\) | ||||
0.998788 | − | 0.0492245i | \(-0.0156750\pi\) | |||||||
\(368\) | 15.5085i | 0.808436i | ||||||||
\(369\) | −4.12489 | −0.214733 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −45.7190 | −2.37361 | ||||||||
\(372\) | 13.8713i | 0.719195i | ||||||||
\(373\) | − 16.3250i | − 0.845277i | −0.906298 | − | 0.422638i | \(-0.861104\pi\) | ||||
0.906298 | − | 0.422638i | \(-0.138896\pi\) | |||||||
\(374\) | −2.45459 | −0.126924 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81456 | −0.196721 | ||||||||
\(377\) | − 9.46927i | − 0.487692i | ||||||||
\(378\) | − 7.73463i | − 0.397827i | ||||||||
\(379\) | 26.0440 | 1.33779 | 0.668896 | − | 0.743356i | \(-0.266767\pi\) | ||||
0.668896 | + | 0.743356i | \(0.266767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.06433 | −0.413148 | ||||||||
\(382\) | 16.9659i | 0.868053i | ||||||||
\(383\) | 12.4702i | 0.637197i | 0.947890 | + | 0.318598i | \(0.103212\pi\) | ||||
−0.947890 | + | 0.318598i | \(0.896788\pi\) | |||||||
\(384\) | −8.46640 | −0.432049 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.9991 | 1.27242 | ||||||||
\(387\) | − 11.7044i | − 0.594966i | ||||||||
\(388\) | − 17.0516i | − 0.865664i | ||||||||
\(389\) | 18.0899 | 0.917195 | 0.458597 | − | 0.888644i | \(-0.348352\pi\) | ||||
0.458597 | + | 0.888644i | \(0.348352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62443 | −0.335012 | ||||||||
\(392\) | − 6.84106i | − 0.345526i | ||||||||
\(393\) | 12.8099i | 0.646172i | ||||||||
\(394\) | 8.10551 | 0.408350 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.51514 | 0.126390 | ||||||||
\(397\) | 15.2342i | 0.764581i | 0.924042 | + | 0.382291i | \(0.124865\pi\) | ||||
−0.924042 | + | 0.382291i | \(0.875135\pi\) | |||||||
\(398\) | − 25.6585i | − 1.28614i | ||||||||
\(399\) | 9.49954 | 0.475572 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.74931 | 0.137294 | 0.0686471 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686471 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(402\) | − 30.3103i | − 1.51174i | ||||||||
\(403\) | 8.35620i | 0.416252i | ||||||||
\(404\) | −18.6244 | −0.926600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.3397 | 2.39906 | ||||||||
\(407\) | − 0.454586i | − 0.0225330i | ||||||||
\(408\) | − 1.26445i | − 0.0625996i | ||||||||
\(409\) | 3.98532 | 0.197061 | 0.0985307 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985307 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8099 | −1.12513 | ||||||||
\(412\) | 41.4986i | 2.04449i | ||||||||
\(413\) | − 28.1542i | − 1.38538i | ||||||||
\(414\) | 12.1854 | 0.598882 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.0236 | −0.589507 | ||||||||
\(417\) | 7.59037i | 0.371702i | ||||||||
\(418\) | 5.54541i | 0.271235i | ||||||||
\(419\) | 5.13578 | 0.250899 | 0.125450 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125450 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.94657 | −0.436029 | −0.218014 | − | 0.975946i | \(-0.569958\pi\) | ||||
−0.218014 | + | 0.975946i | \(0.569958\pi\) | |||||||
\(422\) | − 21.8108i | − 1.06173i | ||||||||
\(423\) | − 3.48486i | − 0.169440i | ||||||||
\(424\) | 13.7484 | 0.667681 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0937 | −0.876642 | ||||||||
\(427\) | 43.7337i | 2.11642i | ||||||||
\(428\) | 9.90826i | 0.478934i | ||||||||
\(429\) | 1.51514 | 0.0731516 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.7493 | 1.09580 | 0.547898 | − | 0.836545i | \(-0.315428\pi\) | ||||
0.547898 | + | 0.836545i | \(0.315428\pi\) | |||||||
\(432\) | − 2.70436i | − 0.130113i | ||||||||
\(433\) | 7.58325i | 0.364428i | 0.983259 | + | 0.182214i | \(0.0583263\pi\) | ||||
−0.983259 | + | 0.182214i | \(0.941674\pi\) | |||||||
\(434\) | −42.6576 | −2.04763 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9385 | 0.811209 | ||||||||
\(437\) | 14.9659i | 0.715918i | ||||||||
\(438\) | 19.5904i | 0.936064i | ||||||||
\(439\) | −17.3903 | −0.829991 | −0.414996 | − | 0.909823i | \(-0.636217\pi\) | ||||
−0.414996 | + | 0.909823i | \(0.636217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.24977 | 0.297608 | ||||||||
\(442\) | − 3.71904i | − 0.176897i | ||||||||
\(443\) | 10.6438i | 0.505702i | 0.967505 | + | 0.252851i | \(0.0813683\pi\) | ||||
−0.967505 | + | 0.252851i | \(0.918632\pi\) | |||||||
\(444\) | 1.14335 | 0.0542608 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 27.4617 | 1.30035 | ||||||||
\(447\) | − 1.81456i | − 0.0858259i | ||||||||
\(448\) | − 41.6916i | − 1.96974i | ||||||||
\(449\) | 26.9310 | 1.27095 | 0.635476 | − | 0.772121i | \(-0.280804\pi\) | ||||
0.635476 | + | 0.772121i | \(0.280804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.12489 | 0.194233 | ||||||||
\(452\) | 15.0908i | 0.709813i | ||||||||
\(453\) | − 24.3250i | − 1.14289i | ||||||||
\(454\) | −48.4683 | −2.27473 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.85665 | −0.133775 | ||||||||
\(457\) | 15.7796i | 0.738138i | 0.929402 | + | 0.369069i | \(0.120323\pi\) | ||||
−0.929402 | + | 0.369069i | \(0.879677\pi\) | |||||||
\(458\) | 31.4049i | 1.46746i | ||||||||
\(459\) | 1.15516 | 0.0539183 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.18922 | 0.381410 | 0.190705 | − | 0.981647i | \(-0.438923\pi\) | ||||
0.190705 | + | 0.981647i | \(0.438923\pi\) | |||||||
\(462\) | 7.73463i | 0.359848i | ||||||||
\(463\) | 16.0899i | 0.747762i | 0.927477 | + | 0.373881i | \(0.121973\pi\) | ||||
−0.927477 | + | 0.373881i | \(0.878027\pi\) | |||||||
\(464\) | 16.9016 | 0.784638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5521 | 0.488815 | ||||||||
\(467\) | 29.4693i | 1.36367i | 0.731504 | + | 0.681837i | \(0.238819\pi\) | ||||
−0.731504 | + | 0.681837i | \(0.761181\pi\) | |||||||
\(468\) | 3.81078i | 0.176153i | ||||||||
\(469\) | 51.9229 | 2.39758 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.76491 | −0.449943 | ||||||||
\(472\) | 8.46640i | 0.389698i | ||||||||
\(473\) | 11.7044i | 0.538167i | ||||||||
\(474\) | 10.8255 | 0.497230 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.5757 | 0.484736 | ||||||||
\(477\) | 12.5601i | 0.575087i | ||||||||
\(478\) | − 31.8713i | − 1.45776i | ||||||||
\(479\) | −32.2186 | −1.47210 | −0.736052 | − | 0.676925i | \(-0.763312\pi\) | ||||
−0.736052 | + | 0.676925i | \(0.763312\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.688760 | 0.0314048 | ||||||||
\(482\) | − 10.7200i | − 0.488280i | ||||||||
\(483\) | 20.8742i | 0.949809i | ||||||||
\(484\) | −2.51514 | −0.114324 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.12489 | −0.0963868 | ||||||||
\(487\) | 35.8936i | 1.62649i | 0.581919 | + | 0.813247i | \(0.302302\pi\) | ||||
−0.581919 | + | 0.813247i | \(0.697698\pi\) | |||||||
\(488\) | − 13.1514i | − 0.595335i | ||||||||
\(489\) | −6.98440 | −0.315846 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.15894 | −0.323079 | −0.161539 | − | 0.986866i | \(-0.551646\pi\) | ||||
−0.161539 | + | 0.986866i | \(0.551646\pi\) | |||||||
\(492\) | 10.3747i | 0.467726i | ||||||||
\(493\) | 7.21949i | 0.325150i | ||||||||
\(494\) | −8.40207 | −0.378027 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.9149 | −0.669699 | ||||||||
\(497\) | − 30.9953i | − 1.39033i | ||||||||
\(498\) | 31.3406i | 1.40441i | ||||||||
\(499\) | −27.0743 | −1.21201 | −0.606006 | − | 0.795460i | \(-0.707229\pi\) | ||||
−0.606006 | + | 0.795460i | \(0.707229\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.31032 | 0.281924 | ||||||||
\(502\) | 6.43899i | 0.287386i | ||||||||
\(503\) | 26.9991i | 1.20383i | 0.798560 | + | 0.601915i | \(0.205595\pi\) | ||||
−0.798560 | + | 0.601915i | \(0.794405\pi\) | |||||||
\(504\) | −3.98440 | −0.177479 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −12.1854 | −0.541709 | ||||||||
\(507\) | − 10.7044i | − 0.475397i | ||||||||
\(508\) | 20.2829i | 0.899909i | ||||||||
\(509\) | −15.5904 | −0.691031 | −0.345515 | − | 0.938413i | \(-0.612296\pi\) | ||||
−0.345515 | + | 0.938413i | \(0.612296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −33.5592 | −1.48457 | ||||||||
\(512\) | − 27.3813i | − 1.21009i | ||||||||
\(513\) | − 2.60975i | − 0.115223i | ||||||||
\(514\) | 29.0066 | 1.27943 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −29.4381 | −1.29594 | ||||||||
\(517\) | 3.48486i | 0.153264i | ||||||||
\(518\) | 3.51605i | 0.154487i | ||||||||
\(519\) | −12.8448 | −0.563826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1589 | 0.488882 | 0.244441 | − | 0.969664i | \(-0.421396\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421396\pi\) | |||||||
\(522\) | − 13.2800i | − 0.581252i | ||||||||
\(523\) | − 10.5786i | − 0.462568i | −0.972886 | − | 0.231284i | \(-0.925707\pi\) | ||||
0.972886 | − | 0.231284i | \(-0.0742926\pi\) | |||||||
\(524\) | 32.2186 | 1.40748 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.6888 | 1.16369 | ||||||||
\(527\) | − 6.37088i | − 0.277520i | ||||||||
\(528\) | 2.70436i | 0.117692i | ||||||||
\(529\) | −9.88601 | −0.429827 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.73463 | −0.335654 | ||||||||
\(532\) | − 23.8927i | − 1.03588i | ||||||||
\(533\) | 6.24977i | 0.270708i | ||||||||
\(534\) | −22.3103 | −0.965462 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.6140 | −0.674422 | ||||||||
\(537\) | 13.4849i | 0.581915i | ||||||||
\(538\) | − 52.4608i | − 2.26175i | ||||||||
\(539\) | −6.24977 | −0.269197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.2947 | −0.485598 | −0.242799 | − | 0.970077i | \(-0.578066\pi\) | ||||
−0.242799 | + | 0.970077i | \(0.578066\pi\) | |||||||
\(542\) | − 16.0743i | − 0.690451i | ||||||||
\(543\) | 23.0899i | 0.990883i | ||||||||
\(544\) | 9.16698 | 0.393031 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.7190 | −0.501528 | ||||||||
\(547\) | − 6.09369i | − 0.260547i | −0.991478 | − | 0.130274i | \(-0.958414\pi\) | ||||
0.991478 | − | 0.130274i | \(-0.0415856\pi\) | |||||||
\(548\) | 57.3700i | 2.45072i | ||||||||
\(549\) | 12.0147 | 0.512774 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.3103 | 0.694843 | ||||||||
\(552\) | − 6.27718i | − 0.267175i | ||||||||
\(553\) | 18.5445i | 0.788592i | ||||||||
\(554\) | −4.08991 | −0.173764 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0908 | 0.809631 | ||||||||
\(557\) | 5.90069i | 0.250020i | 0.992155 | + | 0.125010i | \(0.0398964\pi\) | ||||
−0.992155 | + | 0.125010i | \(0.960104\pi\) | |||||||
\(558\) | 11.7190i | 0.496106i | ||||||||
\(559\) | −17.7337 | −0.750056 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.15516 | −0.0487710 | ||||||||
\(562\) | 3.98440i | 0.168072i | ||||||||
\(563\) | 3.03028i | 0.127711i | 0.997959 | + | 0.0638555i | \(0.0203397\pi\) | ||||
−0.997959 | + | 0.0638555i | \(0.979660\pi\) | |||||||
\(564\) | −8.76491 | −0.369069 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 64.0431 | 2.69193 | ||||||||
\(567\) | − 3.64002i | − 0.152867i | ||||||||
\(568\) | 9.32075i | 0.391090i | ||||||||
\(569\) | −13.4049 | −0.561964 | −0.280982 | − | 0.959713i | \(-0.590660\pi\) | ||||
−0.280982 | + | 0.959713i | \(0.590660\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8851 | 1.12511 | 0.562553 | − | 0.826761i | \(-0.309819\pi\) | ||||
0.562553 | + | 0.826761i | \(0.309819\pi\) | |||||||
\(572\) | − 3.81078i | − 0.159337i | ||||||||
\(573\) | 7.98440i | 0.333553i | ||||||||
\(574\) | −31.9045 | −1.33167 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.4537 | −0.477236 | ||||||||
\(577\) | − 2.03028i | − 0.0845215i | −0.999107 | − | 0.0422607i | \(-0.986544\pi\) | ||||
0.999107 | − | 0.0422607i | \(-0.0134560\pi\) | |||||||
\(578\) | − 33.2876i | − 1.38458i | ||||||||
\(579\) | 11.7649 | 0.488933 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.6878 | −2.22735 | ||||||||
\(582\) | − 14.4058i | − 0.597142i | ||||||||
\(583\) | − 12.5601i | − 0.520186i | ||||||||
\(584\) | 10.0917 | 0.417599 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −61.9514 | −2.55919 | ||||||||
\(587\) | − 21.8245i | − 0.900795i | −0.892828 | − | 0.450398i | \(-0.851282\pi\) | ||||
0.892828 | − | 0.450398i | \(-0.148718\pi\) | |||||||
\(588\) | − 15.7190i | − 0.648242i | ||||||||
\(589\) | −14.3931 | −0.593058 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.81456 | 0.156910 | ||||||||
\(592\) | 1.22936i | 0.0505265i | ||||||||
\(593\) | 8.06811i | 0.331318i | 0.986183 | + | 0.165659i | \(0.0529751\pi\) | ||||
−0.986183 | + | 0.165659i | \(0.947025\pi\) | |||||||
\(594\) | 2.12489 | 0.0871851 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.56387 | −0.186944 | ||||||||
\(597\) | − 12.0752i | − 0.494206i | ||||||||
\(598\) | − 18.4626i | − 0.754993i | ||||||||
\(599\) | −7.61353 | −0.311080 | −0.155540 | − | 0.987830i | \(-0.549712\pi\) | ||||
−0.155540 | + | 0.987830i | \(0.549712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.57569 | 0.145855 | 0.0729277 | − | 0.997337i | \(-0.476766\pi\) | ||||
0.0729277 | + | 0.997337i | \(0.476766\pi\) | |||||||
\(602\) | − 90.5289i | − 3.68968i | ||||||||
\(603\) | − 14.2645i | − 0.580893i | ||||||||
\(604\) | −61.1807 | −2.48941 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.7346 | −0.639176 | ||||||||
\(607\) | − 17.5298i | − 0.711513i | −0.934579 | − | 0.355757i | \(-0.884223\pi\) | ||||
0.934579 | − | 0.355757i | \(-0.115777\pi\) | |||||||
\(608\) | − 20.7101i | − 0.839905i | ||||||||
\(609\) | 22.7493 | 0.921849 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.28005 | −0.213608 | ||||||||
\(612\) | − 2.90539i | − 0.117443i | ||||||||
\(613\) | 12.5601i | 0.507297i | 0.967296 | + | 0.253649i | \(0.0816307\pi\) | ||||
−0.967296 | + | 0.253649i | \(0.918369\pi\) | |||||||
\(614\) | −59.1883 | −2.38865 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.98440 | 0.160536 | ||||||||
\(617\) | − 15.9612i | − 0.642576i | −0.946982 | − | 0.321288i | \(-0.895884\pi\) | ||||
0.946982 | − | 0.321288i | \(-0.104116\pi\) | |||||||
\(618\) | 35.0596i | 1.41031i | ||||||||
\(619\) | 9.23417 | 0.371153 | 0.185576 | − | 0.982630i | \(-0.440585\pi\) | ||||
0.185576 | + | 0.982630i | \(0.440585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.73463 | 0.230123 | ||||||||
\(622\) | − 50.8023i | − 2.03699i | ||||||||
\(623\) | − 38.2186i | − 1.53119i | ||||||||
\(624\) | −4.09747 | −0.164030 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 60.1542 | 2.40425 | ||||||||
\(627\) | 2.60975i | 0.104223i | ||||||||
\(628\) | 24.5601i | 0.980054i | ||||||||
\(629\) | −0.525120 | −0.0209379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2342 | 1.16379 | 0.581897 | − | 0.813262i | \(-0.302311\pi\) | ||||
0.581897 | + | 0.813262i | \(0.302311\pi\) | |||||||
\(632\) | − 5.57661i | − 0.221826i | ||||||||
\(633\) | − 10.2645i | − 0.407975i | ||||||||
\(634\) | 18.7200 | 0.743464 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 31.5904 | 1.25264 | ||||||||
\(637\) | − 9.46927i | − 0.375186i | ||||||||
\(638\) | 13.2800i | 0.525762i | ||||||||
\(639\) | −8.51514 | −0.336854 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9612 | 0.551436 | 0.275718 | − | 0.961239i | \(-0.411084\pi\) | ||||
0.275718 | + | 0.961239i | \(0.411084\pi\) | |||||||
\(642\) | 8.37088i | 0.330372i | ||||||||
\(643\) | 12.6206i | 0.497710i | 0.968541 | + | 0.248855i | \(0.0800542\pi\) | ||||
−0.968541 | + | 0.248855i | \(0.919946\pi\) | |||||||
\(644\) | 52.5015 | 2.06885 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.40585 | 0.252035 | ||||||||
\(647\) | − 29.6429i | − 1.16538i | −0.812694 | − | 0.582691i | \(-0.802000\pi\) | ||||
0.812694 | − | 0.582691i | \(-0.198000\pi\) | |||||||
\(648\) | 1.09461i | 0.0430003i | ||||||||
\(649\) | 7.73463 | 0.303611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0752 | −0.786810 | ||||||||
\(652\) | 17.5667i | 0.687967i | ||||||||
\(653\) | 9.90069i | 0.387444i | 0.981056 | + | 0.193722i | \(0.0620560\pi\) | ||||
−0.981056 | + | 0.193722i | \(0.937944\pi\) | |||||||
\(654\) | 14.3103 | 0.559578 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.1552 | −0.435536 | ||||||||
\(657\) | 9.21949i | 0.359687i | ||||||||
\(658\) | − 26.9541i | − 1.05078i | ||||||||
\(659\) | 5.28005 | 0.205681 | 0.102841 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102841 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.8548 | −1.04453 | −0.522266 | − | 0.852783i | \(-0.674913\pi\) | ||||
−0.522266 | + | 0.852783i | \(0.674913\pi\) | |||||||
\(662\) | − 68.5271i | − 2.66338i | ||||||||
\(663\) | − 1.75023i | − 0.0679733i | ||||||||
\(664\) | 16.1447 | 0.626537 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.965943 | 0.0374295 | ||||||||
\(667\) | 35.8401i | 1.38774i | ||||||||
\(668\) | − 15.8713i | − 0.614080i | ||||||||
\(669\) | 12.9239 | 0.499665 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0147 | −0.463822 | ||||||||
\(672\) | − 28.8860i | − 1.11430i | ||||||||
\(673\) | − 3.81834i | − 0.147186i | −0.997288 | − | 0.0735932i | \(-0.976553\pi\) | ||||
0.997288 | − | 0.0735932i | \(-0.0234466\pi\) | |||||||
\(674\) | −61.5885 | −2.37230 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.9229 | −1.03550 | ||||||||
\(677\) | 15.6897i | 0.603003i | 0.953466 | + | 0.301502i | \(0.0974879\pi\) | ||||
−0.953466 | + | 0.301502i | \(0.902512\pi\) | |||||||
\(678\) | 12.7493i | 0.489634i | ||||||||
\(679\) | 24.6779 | 0.947049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.8099 | −0.874076 | ||||||||
\(682\) | − 11.7190i | − 0.448745i | ||||||||
\(683\) | − 15.6353i | − 0.598269i | −0.954211 | − | 0.299135i | \(-0.903302\pi\) | ||||
0.954211 | − | 0.299135i | \(-0.0966979\pi\) | |||||||
\(684\) | −6.56387 | −0.250976 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.80275 | −0.221550 | ||||||||
\(687\) | 14.7796i | 0.563876i | ||||||||
\(688\) | − 31.6528i | − 1.20675i | ||||||||
\(689\) | 19.0303 | 0.724996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.4305 | −1.19567 | −0.597836 | − | 0.801618i | \(-0.703973\pi\) | ||||
−0.597836 | + | 0.801618i | \(0.703973\pi\) | |||||||
\(692\) | 32.3065i | 1.22811i | ||||||||
\(693\) | 3.64002i | 0.138273i | ||||||||
\(694\) | 75.8989 | 2.88108 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.84106 | −0.259310 | ||||||||
\(697\) | − 4.76491i | − 0.180484i | ||||||||
\(698\) | − 49.4674i | − 1.87237i | ||||||||
\(699\) | 4.96594 | 0.187829 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.24507 | 0.122565 | 0.0612824 | − | 0.998120i | \(-0.480481\pi\) | ||||
0.0612824 | + | 0.998120i | \(0.480481\pi\) | |||||||
\(702\) | 3.21949i | 0.121512i | ||||||||
\(703\) | 1.18635i | 0.0447442i | ||||||||
\(704\) | 11.4537 | 0.431676 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.7181 | −0.779737 | ||||||||
\(707\) | − 26.9541i | − 1.01371i | ||||||||
\(708\) | 19.4537i | 0.731114i | ||||||||
\(709\) | 26.7190 | 1.00345 | 0.501727 | − | 0.865026i | \(-0.332698\pi\) | ||||
0.501727 | + | 0.865026i | \(0.332698\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.09461 | 0.191063 | ||||||||
\(712\) | 11.4929i | 0.430714i | ||||||||
\(713\) | − 31.6273i | − 1.18445i | ||||||||
\(714\) | 8.93475 | 0.334375 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 33.9163 | 1.26751 | ||||||||
\(717\) | − 14.9991i | − 0.560151i | ||||||||
\(718\) | 72.0351i | 2.68833i | ||||||||
\(719\) | 6.78807 | 0.253152 | 0.126576 | − | 0.991957i | \(-0.459601\pi\) | ||||
0.126576 | + | 0.991957i | \(0.459601\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.0587 | −2.23670 | ||||||||
\(722\) | 25.9007i | 0.963924i | ||||||||
\(723\) | − 5.04496i | − 0.187624i | ||||||||
\(724\) | 58.0743 | 2.15831 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.12489 | −0.0788619 | ||||||||
\(727\) | 19.9154i | 0.738620i | 0.929306 | + | 0.369310i | \(0.120406\pi\) | ||||
−0.929306 | + | 0.369310i | \(0.879594\pi\) | |||||||
\(728\) | 6.03692i | 0.223743i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.5204 | 0.500071 | ||||||||
\(732\) | − 30.2186i | − 1.11691i | ||||||||
\(733\) | − 31.3388i | − 1.15752i | −0.815497 | − | 0.578762i | \(-0.803536\pi\) | ||||
0.815497 | − | 0.578762i | \(-0.196464\pi\) | |||||||
\(734\) | −4.00756 | −0.147922 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.5081 | 1.67745 | ||||||||
\(737\) | 14.2645i | 0.525438i | ||||||||
\(738\) | 8.76491i | 0.322641i | ||||||||
\(739\) | 2.25355 | 0.0828982 | 0.0414491 | − | 0.999141i | \(-0.486803\pi\) | ||||
0.0414491 | + | 0.999141i | \(0.486803\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.95413 | −0.145259 | ||||||||
\(742\) | 97.1477i | 3.56640i | ||||||||
\(743\) | − 6.74931i | − 0.247608i | −0.992307 | − | 0.123804i | \(-0.960491\pi\) | ||||
0.992307 | − | 0.123804i | \(-0.0395095\pi\) | |||||||
\(744\) | 6.03692 | 0.221324 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.6888 | −1.27005 | ||||||||
\(747\) | 14.7493i | 0.539649i | ||||||||
\(748\) | 2.90539i | 0.106232i | ||||||||
\(749\) | −14.3397 | −0.523961 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.4390 | 0.818810 | 0.409405 | − | 0.912353i | \(-0.365736\pi\) | ||||
0.409405 | + | 0.912353i | \(0.365736\pi\) | |||||||
\(752\) | − 9.42431i | − 0.343669i | ||||||||
\(753\) | 3.03028i | 0.110429i | ||||||||
\(754\) | −20.1211 | −0.732767 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.15516 | −0.332970 | ||||||||
\(757\) | − 25.4158i | − 0.923754i | −0.886944 | − | 0.461877i | \(-0.847176\pi\) | ||||
0.886944 | − | 0.461877i | \(-0.152824\pi\) | |||||||
\(758\) | − 55.3406i | − 2.01006i | ||||||||
\(759\) | −5.73463 | −0.208154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.7493 | −1.11466 | −0.557331 | − | 0.830291i | \(-0.688174\pi\) | ||||
−0.557331 | + | 0.830291i | \(0.688174\pi\) | |||||||
\(762\) | 17.1358i | 0.620764i | ||||||||
\(763\) | 24.5142i | 0.887474i | ||||||||
\(764\) | 20.0819 | 0.726537 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.4977 | 0.957401 | ||||||||
\(767\) | 11.7190i | 0.423150i | ||||||||
\(768\) | − 4.91721i | − 0.177434i | ||||||||
\(769\) | 16.2956 | 0.587636 | 0.293818 | − | 0.955861i | \(-0.405074\pi\) | ||||
0.293818 | + | 0.955861i | \(0.405074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.6509 | 0.491626 | ||||||||
\(772\) | − 29.5904i | − 1.06498i | ||||||||
\(773\) | 48.7787i | 1.75445i | 0.480082 | + | 0.877223i | \(0.340607\pi\) | ||||
−0.480082 | + | 0.877223i | \(0.659393\pi\) | |||||||
\(774\) | −24.8704 | −0.893949 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.42100 | −0.266398 | ||||||||
\(777\) | 1.65470i | 0.0593621i | ||||||||
\(778\) | − 38.4390i | − 1.37810i | ||||||||
\(779\) | −10.7649 | −0.385693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.51514 | 0.304696 | ||||||||
\(782\) | 14.0761i | 0.503362i | ||||||||
\(783\) | − 6.24977i | − 0.223349i | ||||||||
\(784\) | 16.9016 | 0.603629 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.2195 | 0.970887 | ||||||||
\(787\) | 46.2001i | 1.64686i | 0.567421 | + | 0.823428i | \(0.307941\pi\) | ||||
−0.567421 | + | 0.823428i | \(0.692059\pi\) | |||||||
\(788\) | − 9.59415i | − 0.341777i | ||||||||
\(789\) | 12.5601 | 0.447151 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.8401 | −0.776546 | ||||||||
\(792\) | − 1.09461i | − 0.0388952i | ||||||||
\(793\) | − 18.2039i | − 0.646439i | ||||||||
\(794\) | 32.3709 | 1.14880 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.3709 | −1.07647 | ||||||||
\(797\) | − 36.3784i | − 1.28859i | −0.764777 | − | 0.644295i | \(-0.777151\pi\) | ||||
0.764777 | − | 0.644295i | \(-0.222849\pi\) | |||||||
\(798\) | − 20.1854i | − 0.714557i | ||||||||
\(799\) | 4.02558 | 0.142415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.4995 | −0.370983 | ||||||||
\(802\) | − 5.84197i | − 0.206287i | ||||||||
\(803\) | − 9.21949i | − 0.325349i | ||||||||
\(804\) | −35.8771 | −1.26529 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.7560 | 0.625427 | ||||||||
\(807\) | − 24.6888i | − 0.869086i | ||||||||
\(808\) | 8.10551i | 0.285151i | ||||||||
\(809\) | −11.3737 | −0.399879 | −0.199940 | − | 0.979808i | \(-0.564075\pi\) | ||||
−0.199940 | + | 0.979808i | \(0.564075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3903 | −0.470195 | −0.235098 | − | 0.971972i | \(-0.575541\pi\) | ||||
−0.235098 | + | 0.971972i | \(0.575541\pi\) | |||||||
\(812\) | − 57.2177i | − 2.00795i | ||||||||
\(813\) | − 7.56479i | − 0.265309i | ||||||||
\(814\) | −0.965943 | −0.0338563 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.12397 | 0.109361 | ||||||||
\(817\) | − 30.5454i | − 1.06865i | ||||||||
\(818\) | − 8.46835i | − 0.296089i | ||||||||
\(819\) | −5.51514 | −0.192715 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.0975 | 1.12021 | 0.560105 | − | 0.828422i | \(-0.310761\pi\) | ||||
0.560105 | + | 0.828422i | \(0.310761\pi\) | |||||||
\(822\) | 48.4683i | 1.69053i | ||||||||
\(823\) | 16.7952i | 0.585443i | 0.956198 | + | 0.292722i | \(0.0945609\pi\) | ||||
−0.956198 | + | 0.292722i | \(0.905439\pi\) | |||||||
\(824\) | 18.0606 | 0.629169 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −59.8245 | −2.08156 | ||||||||
\(827\) | 45.5904i | 1.58533i | 0.609656 | + | 0.792666i | \(0.291308\pi\) | ||||
−0.609656 | + | 0.792666i | \(0.708692\pi\) | |||||||
\(828\) | − 14.4234i | − 0.501248i | ||||||||
\(829\) | −12.9385 | −0.449374 | −0.224687 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224687 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.92477 | −0.0667695 | ||||||||
\(832\) | 17.3539i | 0.601638i | ||||||||
\(833\) | 7.21949i | 0.250141i | ||||||||
\(834\) | 16.1287 | 0.558490 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.56387 | 0.227016 | ||||||||
\(837\) | 5.51514i | 0.190631i | ||||||||
\(838\) | − 10.9130i | − 0.376982i | ||||||||
\(839\) | 1.59037 | 0.0549057 | 0.0274528 | − | 0.999623i | \(-0.491260\pi\) | ||||
0.0274528 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0596 | 0.346884 | ||||||||
\(842\) | 19.0104i | 0.655143i | ||||||||
\(843\) | 1.87511i | 0.0645824i | ||||||||
\(844\) | −25.8165 | −0.888641 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.40493 | −0.254587 | ||||||||
\(847\) | − 3.64002i | − 0.125073i | ||||||||
\(848\) | 33.9670i | 1.16643i | ||||||||
\(849\) | 30.1396 | 1.03439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.60688 | −0.0893628 | ||||||||
\(852\) | 21.4167i | 0.733726i | ||||||||
\(853\) | 10.5161i | 0.360063i | 0.983661 | + | 0.180031i | \(0.0576199\pi\) | ||||
−0.983661 | + | 0.180031i | \(0.942380\pi\) | |||||||
\(854\) | 92.9291 | 3.17997 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.31216 | 0.147386 | ||||||||
\(857\) | 57.4637i | 1.96292i | 0.191665 | + | 0.981460i | \(0.438611\pi\) | ||||
−0.191665 | + | 0.981460i | \(0.561389\pi\) | |||||||
\(858\) | − 3.21949i | − 0.109912i | ||||||||
\(859\) | −32.7181 | −1.11633 | −0.558164 | − | 0.829731i | \(-0.688494\pi\) | ||||
−0.558164 | + | 0.829731i | \(0.688494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0147 | −0.511699 | ||||||||
\(862\) | − 48.3397i | − 1.64646i | ||||||||
\(863\) | − 43.1807i | − 1.46989i | −0.678127 | − | 0.734945i | \(-0.737208\pi\) | ||||
0.678127 | − | 0.734945i | \(-0.262792\pi\) | |||||||
\(864\) | −7.93567 | −0.269977 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.1135 | 0.547560 | ||||||||
\(867\) | − 15.6656i | − 0.532032i | ||||||||
\(868\) | 50.4920i | 1.71381i | ||||||||
\(869\) | −5.09461 | −0.172823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.6126 | −0.732315 | ||||||||
\(872\) | − 7.37179i | − 0.249640i | ||||||||
\(873\) | − 6.77959i | − 0.229454i | ||||||||
\(874\) | 31.8009 | 1.07568 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.1883 | 0.783460 | ||||||||
\(877\) | 16.0752i | 0.542822i | 0.962464 | + | 0.271411i | \(0.0874903\pi\) | ||||
−0.962464 | + | 0.271411i | \(0.912510\pi\) | |||||||
\(878\) | 36.9523i | 1.24708i | ||||||||
\(879\) | −29.1552 | −0.983379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.2876 | 1.05411 | 0.527053 | − | 0.849832i | \(-0.323297\pi\) | ||||
0.527053 | + | 0.849832i | \(0.323297\pi\) | |||||||
\(882\) | − 13.2800i | − 0.447162i | ||||||||
\(883\) | 24.7640i | 0.833375i | 0.909050 | + | 0.416687i | \(0.136809\pi\) | ||||
−0.909050 | + | 0.416687i | \(0.863191\pi\) | |||||||
\(884\) | −4.40207 | −0.148058 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.6169 | 0.759828 | ||||||||
\(887\) | 26.3085i | 0.883353i | 0.897174 | + | 0.441676i | \(0.145616\pi\) | ||||
−0.897174 | + | 0.441676i | \(0.854384\pi\) | |||||||
\(888\) | − 0.497594i | − 0.0166982i | ||||||||
\(889\) | −29.3544 | −0.984514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | − 32.5053i | − 1.08836i | ||||||||
\(893\) | − 9.09461i | − 0.304339i | ||||||||
\(894\) | −3.85574 | −0.128955 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −30.8179 | −1.02955 | ||||||||
\(897\) | − 8.68876i | − 0.290109i | ||||||||
\(898\) | − 57.2252i | − 1.90963i | ||||||||
\(899\) | −34.4683 | −1.14958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.5089 | −0.483363 | ||||||||
\(902\) | − 8.76491i | − 0.291840i | ||||||||
\(903\) | − 42.6041i | − 1.41778i | ||||||||
\(904\) | 6.56766 | 0.218437 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −51.6878 | −1.71721 | ||||||||
\(907\) | 55.9301i | 1.85713i | 0.371174 | + | 0.928563i | \(0.378955\pi\) | ||||
−0.371174 | + | 0.928563i | \(0.621045\pi\) | |||||||
\(908\) | 57.3700i | 1.90389i | ||||||||
\(909\) | −7.40493 | −0.245606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3931 | −0.509997 | −0.254998 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254998 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(912\) | − 7.05769i | − 0.233703i | ||||||||
\(913\) | − 14.7493i | − 0.488131i | ||||||||
\(914\) | 33.5298 | 1.10907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37.1727 | 1.22822 | ||||||||
\(917\) | 46.6282i | 1.53980i | ||||||||
\(918\) | − 2.45459i | − 0.0810134i | ||||||||
\(919\) | 51.2598 | 1.69090 | 0.845452 | − | 0.534052i | \(-0.179331\pi\) | ||||
0.845452 | + | 0.534052i | \(0.179331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.8548 | −0.917848 | ||||||||
\(922\) | − 17.4012i | − 0.573076i | ||||||||
\(923\) | 12.9016i | 0.424662i | ||||||||
\(924\) | 9.15516 | 0.301183 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.1892 | 1.12353 | ||||||||
\(927\) | 16.4995i | 0.541916i | ||||||||
\(928\) | − 49.5961i | − 1.62807i | ||||||||
\(929\) | −14.8099 | −0.485896 | −0.242948 | − | 0.970039i | \(-0.578114\pi\) | ||||
−0.242948 | + | 0.970039i | \(0.578114\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3103 | 0.534549 | ||||||||
\(932\) | − 12.4900i | − 0.409125i | ||||||||
\(933\) | − 23.9083i | − 0.782721i | ||||||||
\(934\) | 62.6188 | 2.04895 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.65848 | 0.0542093 | ||||||||
\(937\) | − 27.2654i | − 0.890721i | −0.895351 | − | 0.445360i | \(-0.853076\pi\) | ||||
0.895351 | − | 0.445360i | \(-0.146924\pi\) | |||||||
\(938\) | − 110.330i | − 3.60241i | ||||||||
\(939\) | 28.3094 | 0.923843 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.5630 | −1.61571 | −0.807853 | − | 0.589384i | \(-0.799371\pi\) | ||||
−0.807853 | + | 0.589384i | \(0.799371\pi\) | |||||||
\(942\) | 20.7493i | 0.676049i | ||||||||
\(943\) | − 23.6547i | − 0.770303i | ||||||||
\(944\) | −20.9172 | −0.680797 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.8704 | 0.808607 | ||||||||
\(947\) | 13.9844i | 0.454432i | 0.973844 | + | 0.227216i | \(0.0729623\pi\) | ||||
−0.973844 | + | 0.227216i | \(0.927038\pi\) | |||||||
\(948\) | − 12.8136i | − 0.416168i | ||||||||
\(949\) | 13.9688 | 0.453447 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.80986 | 0.285679 | ||||||||
\(952\) | − 4.60263i | − 0.149172i | ||||||||
\(953\) | 17.1240i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894561\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(954\) | 26.6888 | 0.864081 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −37.7248 | −1.22011 | ||||||||
\(957\) | 6.24977i | 0.202026i | ||||||||
\(958\) | 68.4608i | 2.21187i | ||||||||
\(959\) | −83.0284 | −2.68113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.583252 | −0.0188146 | ||||||||
\(962\) | − 1.46354i | − 0.0471863i | ||||||||
\(963\) | 3.93945i | 0.126947i | ||||||||
\(964\) | −12.6888 | −0.408677 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 44.3553 | 1.42711 | ||||||||
\(967\) | − 1.90826i | − 0.0613653i | −0.999529 | − | 0.0306827i | \(-0.990232\pi\) | ||||
0.999529 | − | 0.0306827i | \(-0.00976813\pi\) | |||||||
\(968\) | 1.09461i | 0.0351821i | ||||||||
\(969\) | 3.01468 | 0.0968455 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.3856 | 1.00721 | 0.503605 | − | 0.863934i | \(-0.332007\pi\) | ||||
0.503605 | + | 0.863934i | \(0.332007\pi\) | |||||||
\(972\) | 2.51514i | 0.0806731i | ||||||||
\(973\) | 27.6291i | 0.885749i | ||||||||
\(974\) | 76.2697 | 2.44384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.4920 | 1.04004 | ||||||||
\(977\) | − 41.4693i | − 1.32672i | −0.748301 | − | 0.663360i | \(-0.769130\pi\) | ||||
0.748301 | − | 0.663360i | \(-0.230870\pi\) | |||||||
\(978\) | 14.8411i | 0.474565i | ||||||||
\(979\) | 10.4995 | 0.335567 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.73463 | 0.215020 | ||||||||
\(982\) | 15.2119i | 0.485432i | ||||||||
\(983\) | − 6.23601i | − 0.198898i | −0.995043 | − | 0.0994489i | \(-0.968292\pi\) | ||||
0.995043 | − | 0.0994489i | \(-0.0317080\pi\) | |||||||
\(984\) | 4.51514 | 0.143937 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.3406 | 0.488544 | ||||||||
\(987\) | − 12.6850i | − 0.403767i | ||||||||
\(988\) | 9.94518i | 0.316398i | ||||||||
\(989\) | 67.1202 | 2.13430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.2048 | 0.864189 | 0.432095 | − | 0.901828i | \(-0.357775\pi\) | ||||
0.432095 | + | 0.901828i | \(0.357775\pi\) | |||||||
\(992\) | 43.7663i | 1.38958i | ||||||||
\(993\) | − 32.2498i | − 1.02342i | ||||||||
\(994\) | −65.8615 | −2.08900 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 37.0966 | 1.17545 | ||||||||
\(997\) | − 28.0606i | − 0.888687i | −0.895857 | − | 0.444343i | \(-0.853437\pi\) | ||||
0.895857 | − | 0.444343i | \(-0.146563\pi\) | |||||||
\(998\) | 57.5298i | 1.82107i | ||||||||
\(999\) | 0.454586 | 0.0143825 |
(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 | 825.2.c.f.199.2 | 6 | ||
3.2 | odd | 2 | 2475.2.c.q.199.5 | 6 | |||
5.2 | odd | 4 | 825.2.a.i.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 825.2.a.m.1.1 | yes | 3 | ||
5.4 | even | 2 | inner | 825.2.c.f.199.5 | 6 | ||
15.2 | even | 4 | 2475.2.a.bd.1.1 | 3 | |||
15.8 | even | 4 | 2475.2.a.z.1.3 | 3 | |||
15.14 | odd | 2 | 2475.2.c.q.199.2 | 6 | |||
55.32 | even | 4 | 9075.2.a.cj.1.1 | 3 | |||
55.43 | even | 4 | 9075.2.a.cd.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.i.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
825.2.a.m.1.1 | yes | 3 | 5.3 | odd | 4 | ||
825.2.c.f.199.2 | 6 | 1.1 | even | 1 | trivial | ||
825.2.c.f.199.5 | 6 | 5.4 | even | 2 | inner | ||
2475.2.a.z.1.3 | 3 | 15.8 | even | 4 | |||
2475.2.a.bd.1.1 | 3 | 15.2 | even | 4 | |||
2475.2.c.q.199.2 | 6 | 15.14 | odd | 2 | |||
2475.2.c.q.199.5 | 6 | 3.2 | odd | 2 | |||
9075.2.a.cd.1.3 | 3 | 55.43 | even | 4 | |||
9075.2.a.cj.1.1 | 3 | 55.32 | even | 4 |