Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(17,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.ci (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 560.257 |
Dual form | 560.2.ci.b.353.1 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.133975 | − | 0.500000i | 0.0773503 | − | 0.288675i | −0.916406 | − | 0.400251i | \(-0.868923\pi\) |
0.993756 | + | 0.111576i | \(0.0355897\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.133975 | − | 2.23205i | 0.0599153 | − | 0.998203i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.36603 | + | 1.36603i | 0.788675 | + | 0.455342i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36603 | − | 2.36603i | −0.411872 | − | 0.713384i | 0.583222 | − | 0.812313i | \(-0.301792\pi\) |
−0.995094 | + | 0.0989291i | \(0.968458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | − | 2.00000i | −0.554700 | − | 0.554700i | 0.373094 | − | 0.927794i | \(-0.378297\pi\) |
−0.927794 | + | 0.373094i | \(0.878297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.09808 | − | 0.366025i | −0.283522 | − | 0.0945074i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.73205 | + | 1.00000i | 0.905155 | + | 0.242536i | 0.681229 | − | 0.732070i | \(-0.261446\pi\) |
0.223926 | + | 0.974606i | \(0.428112\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.366025 | + | 0.633975i | −0.0839720 | + | 0.145444i | −0.904953 | − | 0.425512i | \(-0.860094\pi\) |
0.820981 | + | 0.570956i | \(0.193427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.767949 | − | 1.13397i | 0.167580 | − | 0.247454i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0358984 | − | 0.133975i | −0.00748533 | − | 0.0279356i | 0.962082 | − | 0.272760i | \(-0.0879364\pi\) |
−0.969567 | + | 0.244824i | \(0.921270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96410 | − | 0.598076i | −0.992820 | − | 0.119615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.09808 | − | 2.09808i | 0.403775 | − | 0.403775i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.00000i | − | 0.557086i | −0.960424 | − | 0.278543i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278543i | \(-0.0898515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.46410 | − | 3.73205i | 1.16099 | − | 0.670296i | 0.209447 | − | 0.977820i | \(-0.432834\pi\) |
0.951540 | + | 0.307524i | \(0.0995004\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.36603 | + | 0.366025i | −0.237795 | + | 0.0637168i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.26795 | − | 5.46410i | 0.383353 | − | 0.923602i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.73205 | + | 1.26795i | −0.777944 | + | 0.208450i | −0.625878 | − | 0.779921i | \(-0.715259\pi\) |
−0.152066 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.26795 | + | 0.732051i | −0.203034 | + | 0.117222i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.46410i | − | 1.00952i | −0.863259 | − | 0.504762i | \(-0.831580\pi\) | ||
0.863259 | − | 0.504762i | \(-0.168420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83013 | + | 2.83013i | −0.431590 | + | 0.431590i | −0.889169 | − | 0.457579i | \(-0.848717\pi\) |
0.457579 | + | 0.889169i | \(0.348717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.36603 | − | 5.09808i | 0.501777 | − | 0.759976i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.36603 | − | 8.83013i | −0.345120 | − | 1.28801i | −0.892472 | − | 0.451103i | \(-0.851031\pi\) |
0.547351 | − | 0.836903i | \(-0.315636\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | − | 1.73205i | 0.140028 | − | 0.242536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.83013 | + | 1.83013i | 0.938190 | + | 0.251387i | 0.695344 | − | 0.718677i | \(-0.255252\pi\) |
0.242846 | + | 0.970065i | \(0.421919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.46410 | + | 2.73205i | −0.736779 | + | 0.368390i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.267949 | + | 0.267949i | 0.0354907 | + | 0.0354907i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.09808 | + | 7.09808i | 0.533524 | + | 0.924091i | 0.999233 | + | 0.0391530i | \(0.0124660\pi\) |
−0.465709 | + | 0.884938i | \(0.654201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33013 | + | 0.767949i | 0.170305 | + | 0.0983258i | 0.582730 | − | 0.812666i | \(-0.301985\pi\) |
−0.412424 | + | 0.910992i | \(0.635318\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.73205 | + | 5.46410i | 0.596182 | + | 0.688412i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.73205 | + | 4.19615i | −0.586939 | + | 0.520469i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.86603 | + | 10.6962i | −0.350141 | + | 1.30674i | 0.536350 | + | 0.843996i | \(0.319803\pi\) |
−0.886490 | + | 0.462747i | \(0.846864\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0717968 | −0.00864332 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.26795 | −0.150478 | −0.0752389 | − | 0.997166i | \(-0.523972\pi\) | ||||
−0.0752389 | + | 0.997166i | \(0.523972\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.46410 | + | 12.9282i | −0.405442 | + | 1.51313i | 0.397796 | + | 0.917474i | \(0.369775\pi\) |
−0.803238 | + | 0.595658i | \(0.796891\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.964102 | + | 2.40192i | −0.111325 | + | 0.277350i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.36603 | − | 7.09808i | −0.155673 | − | 0.808901i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.83013 | − | 1.63397i | −0.318414 | − | 0.183837i | 0.332271 | − | 0.943184i | \(-0.392185\pi\) |
−0.650686 | + | 0.759347i | \(0.725518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.33013 | + | 5.76795i | 0.370014 | + | 0.640883i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.09808 | + | 2.09808i | 0.230294 | + | 0.230294i | 0.812815 | − | 0.582522i | \(-0.197934\pi\) |
−0.582522 | + | 0.812815i | \(0.697934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.73205 | − | 8.19615i | 0.296333 | − | 0.888998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | − | 0.401924i | −0.160817 | − | 0.0430908i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.330127 | + | 0.571797i | −0.0349934 | + | 0.0606103i | −0.882992 | − | 0.469389i | \(-0.844474\pi\) |
0.847998 | + | 0.529999i | \(0.177808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.26795 | − | 6.73205i | −0.342574 | − | 0.705711i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.00000 | − | 3.73205i | −0.103695 | − | 0.386996i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36603 | + | 0.901924i | 0.140151 | + | 0.0925354i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.92820 | + | 5.92820i | −0.601918 | + | 0.601918i | −0.940821 | − | 0.338903i | \(-0.889944\pi\) |
0.338903 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 7.46410i | − | 0.750170i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.16025 | − | 4.13397i | 0.712472 | − | 0.411346i | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.59808 | + | 1.23205i | −0.453062 | + | 0.121398i | −0.478132 | − | 0.878288i | \(-0.658686\pi\) |
0.0250698 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.42820 | − | 1.86603i | −0.236968 | − | 0.182105i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6962 | + | 3.40192i | −1.22738 | + | 0.328876i | −0.813560 | − | 0.581481i | \(-0.802474\pi\) |
−0.413823 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.76795 | + | 5.06218i | −0.839817 | + | 0.484869i | −0.857202 | − | 0.514980i | \(-0.827799\pi\) |
0.0173849 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.53590i | 0.240697i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.73205 | + | 7.73205i | −0.727370 | + | 0.727370i | −0.970095 | − | 0.242725i | \(-0.921959\pi\) |
0.242725 | + | 0.970095i | \(0.421959\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.303848 | + | 0.0621778i | −0.0283339 | + | 0.00579811i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | − | 7.46410i | −0.184900 | − | 0.690056i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.46410 | + | 5.73205i | 0.775903 | + | 0.525456i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.76795 | − | 3.06218i | 0.160723 | − | 0.278380i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.23205 | − | 0.866025i | −0.291424 | − | 0.0780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.464102 | − | 0.464102i | −0.0411824 | − | 0.0411824i | 0.686216 | − | 0.727398i | \(-0.259271\pi\) |
−0.727398 | + | 0.686216i | \(0.759271\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.03590 | + | 1.79423i | 0.0912058 | + | 0.157973i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3923 | + | 7.73205i | 1.17009 | + | 0.675552i | 0.953702 | − | 0.300755i | \(-0.0972385\pi\) |
0.216390 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.46410 | + | 1.26795i | −0.126954 | + | 0.109945i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.40192 | − | 4.96410i | −0.378857 | − | 0.427242i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.53590 | + | 13.1962i | −0.302092 | + | 1.12742i | 0.633327 | + | 0.773884i | \(0.281689\pi\) |
−0.935420 | + | 0.353539i | \(0.884978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.66025 | 0.480096 | 0.240048 | − | 0.970761i | \(-0.422837\pi\) | ||||
0.240048 | + | 0.970761i | \(0.422837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.73205 | −0.398511 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | + | 7.46410i | −0.167248 | + | 0.624180i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.69615 | − | 0.401924i | −0.556085 | − | 0.0333780i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.90192 | − | 2.16987i | 0.239347 | − | 0.178968i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.696152 | + | 0.401924i | 0.0570310 | + | 0.0329269i | 0.528244 | − | 0.849092i | \(-0.322850\pi\) |
−0.471213 | + | 0.882019i | \(0.656184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.92820 | + | 12.0000i | 0.563809 | + | 0.976546i | 0.997159 | + | 0.0753205i | \(0.0239980\pi\) |
−0.433350 | + | 0.901226i | \(0.642669\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.46410 | + | 7.46410i | 0.603437 | + | 0.603437i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.46410 | − | 14.9282i | −0.599531 | − | 1.19906i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.63397 | − | 1.24167i | −0.369831 | − | 0.0990960i | 0.0691164 | − | 0.997609i | \(-0.477982\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.83013 | − | 3.16987i | 0.145139 | − | 0.251387i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0262794 | − | 0.366025i | 0.00207111 | − | 0.0288468i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.63397 | + | 13.5622i | 0.284635 | + | 1.06227i | 0.949106 | + | 0.314958i | \(0.101990\pi\) |
−0.664471 | + | 0.747314i | \(0.731343\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.633975 | + | 3.09808i | 0.0493549 | + | 0.241185i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.7583 | + | 11.7583i | −0.909887 | + | 0.909887i | −0.996263 | − | 0.0863757i | \(-0.972471\pi\) |
0.0863757 | + | 0.996263i | \(0.472471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.73205 | + | 1.00000i | −0.132453 | + | 0.0764719i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.9282 | − | 5.33975i | 1.51511 | − | 0.405973i | 0.596984 | − | 0.802253i | \(-0.296366\pi\) |
0.918130 | + | 0.396280i | \(0.129699\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.8923 | − | 5.79423i | −0.898974 | − | 0.438003i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.09808 | − | 1.09808i | 0.308030 | − | 0.0825365i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.80385 | + | 3.92820i | −0.508543 | + | 0.293608i | −0.732235 | − | 0.681052i | \(-0.761523\pi\) |
0.223691 | + | 0.974660i | \(0.428189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.19615i | − | 0.0889093i | −0.999011 | − | 0.0444547i | \(-0.985845\pi\) | ||
0.999011 | − | 0.0444547i | \(-0.0141550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.562178 | − | 0.562178i | 0.0415574 | − | 0.0415574i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.19615 | + | 10.7321i | 0.161464 | + | 0.789036i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.73205 | − | 10.1962i | −0.199787 | − | 0.745617i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.06218 | − | 3.42820i | 0.513698 | − | 0.249365i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.63397 | − | 11.4904i | 0.480018 | − | 0.831415i | −0.519720 | − | 0.854337i | \(-0.673964\pi\) |
0.999737 | + | 0.0229220i | \(0.00729695\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.83013 | − | 2.09808i | −0.563625 | − | 0.151023i | −0.0342537 | − | 0.999413i | \(-0.510905\pi\) |
−0.529371 | + | 0.848390i | \(0.677572\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.46410 | + | 2.92820i | 0.104846 | + | 0.209693i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1244 | − | 10.1244i | −0.721330 | − | 0.721330i | 0.247546 | − | 0.968876i | \(-0.420376\pi\) |
−0.968876 | + | 0.247546i | \(0.920376\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.53590 | + | 9.58846i | 0.392429 | + | 0.679708i | 0.992769 | − | 0.120037i | \(-0.0383014\pi\) |
−0.600340 | + | 0.799745i | \(0.704968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.96410 | + | 2.86603i | 0.350141 | + | 0.202154i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.59808 | − | 7.50000i | 0.182349 | − | 0.526397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.4282 | − | 0.866025i | −1.00771 | − | 0.0604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0980762 | − | 0.366025i | 0.00681677 | − | 0.0254405i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.196152 | 0.0135037 | 0.00675184 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675184 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.169873 | + | 0.633975i | −0.0116395 | + | 0.0434392i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.93782 | + | 6.69615i | 0.404956 | + | 0.456674i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3923 | − | 3.73205i | 1.31644 | − | 0.253348i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 3.46410i | 0.405442 | + | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.46410 | − | 9.46410i | −0.367555 | − | 0.636624i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1244 | − | 18.1244i | −1.21370 | − | 1.21370i | −0.969802 | − | 0.243895i | \(-0.921575\pi\) |
−0.243895 | − | 0.969802i | \(-0.578425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.9282 | − | 8.19615i | −0.728547 | − | 0.546410i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.0263 | + | 5.09808i | 1.26282 | + | 0.338371i | 0.827275 | − | 0.561797i | \(-0.189890\pi\) |
0.435543 | + | 0.900168i | \(0.356556\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.19615 | + | 15.9282i | −0.607699 | + | 1.05257i | 0.383920 | + | 0.923366i | \(0.374574\pi\) |
−0.991619 | + | 0.129199i | \(0.958759\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.73205 | − | 0.267949i | −0.245551 | − | 0.0176298i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.73205 | − | 6.46410i | −0.113470 | − | 0.423477i | 0.885698 | − | 0.464263i | \(-0.153681\pi\) |
−0.999168 | + | 0.0407854i | \(0.987014\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.0263 | + | 4.09808i | −1.30637 | + | 0.267329i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.19615 | + | 1.19615i | −0.0776984 | + | 0.0776984i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2.39230i | − | 0.154745i | −0.997002 | − | 0.0773727i | \(-0.975347\pi\) | ||
0.997002 | − | 0.0773727i | \(-0.0246531\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.4641 | − | 12.3923i | 1.38262 | − | 0.798259i | 0.390155 | − | 0.920749i | \(-0.372422\pi\) |
0.992470 | + | 0.122491i | \(0.0390882\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.9282 | − | 3.19615i | 0.765195 | − | 0.205033i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.4019 | − | 11.6962i | 0.664555 | − | 0.747240i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | − | 0.535898i | 0.127257 | − | 0.0340984i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.33013 | − | 0.767949i | 0.0842934 | − | 0.0486668i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 21.8564i | − | 1.37956i | −0.724017 | − | 0.689782i | \(-0.757706\pi\) | ||
0.724017 | − | 0.689782i | \(-0.242294\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.267949 | + | 0.267949i | −0.0168458 | + | 0.0168458i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.73205 | − | 2.46410i | −0.233710 | − | 0.154308i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.732051 | − | 2.73205i | −0.0456641 | − | 0.170421i | 0.939328 | − | 0.343020i | \(-0.111450\pi\) |
−0.984992 | + | 0.172600i | \(0.944783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9282 | − | 0.928203i | −0.803319 | − | 0.0576757i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.09808 | − | 7.09808i | 0.253665 | − | 0.439360i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.1603 | + | 4.06218i | 0.934821 | + | 0.250485i | 0.693909 | − | 0.720062i | \(-0.255887\pi\) |
0.240912 | + | 0.970547i | \(0.422553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.00000 | − | 15.0000i | 0.307148 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.241670 | + | 0.241670i | 0.0147899 | + | 0.0147899i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4282 | + | 19.7942i | 0.696790 | + | 1.20688i | 0.969574 | + | 0.244800i | \(0.0787223\pi\) |
−0.272784 | + | 0.962075i | \(0.587944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.4186 | − | 10.6340i | −1.11885 | − | 0.645968i | −0.177742 | − | 0.984077i | \(-0.556879\pi\) |
−0.941107 | + | 0.338109i | \(0.890213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.80385 | + | 0.732051i | −0.230219 | + | 0.0443057i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.36603 | + | 12.5622i | 0.323584 | + | 0.757528i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.39230 | + | 5.19615i | −0.0836555 | + | 0.312207i | −0.995056 | − | 0.0993135i | \(-0.968335\pi\) |
0.911401 | + | 0.411520i | \(0.135002\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.3923 | 1.22086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.928203 | −0.0553720 | −0.0276860 | − | 0.999617i | \(-0.508814\pi\) | ||||
−0.0276860 | + | 0.999617i | \(0.508814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.509619 | − | 1.90192i | 0.0302937 | − | 0.113058i | −0.949123 | − | 0.314904i | \(-0.898028\pi\) |
0.979417 | + | 0.201847i | \(0.0646943\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.633975 | − | 0.562178i | 0.0375534 | − | 0.0333005i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.59808 | − | 16.1603i | 0.330444 | − | 0.953910i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.79423 | − | 1.03590i | −0.105543 | − | 0.0609352i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.16987 | + | 3.75833i | 0.127200 | + | 0.220317i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.39230 | − | 2.39230i | −0.139760 | − | 0.139760i | 0.633765 | − | 0.773525i | \(-0.281508\pi\) |
−0.773525 | + | 0.633765i | \(0.781508\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.3923 | − | 8.19615i | 0.954397 | − | 0.477198i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.83013 | − | 2.09808i | −0.454350 | − | 0.121743i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.196152 | + | 0.339746i | −0.0113438 | + | 0.0196480i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.52628 | + | 4.62436i | −0.549086 | + | 0.266543i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.10770 | − | 4.13397i | −0.0636354 | − | 0.237491i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.89230 | − | 2.86603i | 0.108353 | − | 0.164108i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.29423 | + | 6.29423i | −0.359231 | + | 0.359231i | −0.863529 | − | 0.504299i | \(-0.831751\pi\) |
0.504299 | + | 0.863529i | \(0.331751\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.46410i | 0.140178i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2224 | − | 7.63397i | 0.749775 | − | 0.432883i | −0.0758374 | − | 0.997120i | \(-0.524163\pi\) |
0.825613 | + | 0.564237i | \(0.190830\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.19615 | + | 1.39230i | −0.293704 | + | 0.0786977i | −0.402662 | − | 0.915349i | \(-0.631915\pi\) |
0.108958 | + | 0.994046i | \(0.465248\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.8301 | − | 9.83013i | 0.722896 | − | 0.553865i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.19615 | − | 2.46410i | 0.516507 | − | 0.138398i | 0.00885679 | − | 0.999961i | \(-0.497181\pi\) |
0.507651 | + | 0.861563i | \(0.330514\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.09808 | + | 4.09808i | −0.397416 | + | 0.229448i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.80385i | 0.379754i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | + | 2.00000i | −0.111283 | + | 0.111283i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.73205 | + | 11.1244i | 0.484367 | + | 0.617068i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.35641 | + | 5.06218i | 0.0750094 | + | 0.279939i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.73205 | − | 24.1244i | 0.0954911 | − | 1.33002i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.928203 | + | 1.60770i | −0.0510187 | + | 0.0883669i | −0.890407 | − | 0.455165i | \(-0.849580\pi\) |
0.839388 | + | 0.543532i | \(0.182913\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.9282 | − | 3.46410i | −0.708461 | − | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.4904 | + | 7.83013i | 1.28342 | + | 0.427806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.53590 | + | 9.53590i | 0.519453 | + | 0.519453i | 0.917406 | − | 0.397953i | \(-0.130279\pi\) |
−0.397953 | + | 0.917406i | \(0.630279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.83013 | + | 4.90192i | 0.153711 | + | 0.266236i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.6603 | − | 10.1962i | −0.956356 | − | 0.552153i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.00961894 | + | 0.160254i | −0.000517866 | + | 0.00862779i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.79423 | − | 29.0885i | 0.418416 | − | 1.56155i | −0.359477 | − | 0.933154i | \(-0.617045\pi\) |
0.777893 | − | 0.628396i | \(-0.216288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.26795 | 0.335516 | 0.167758 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167758 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.39230 | −0.447948 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.63397 | − | 13.5622i | 0.193417 | − | 0.721842i | −0.799254 | − | 0.600993i | \(-0.794772\pi\) |
0.992671 | − | 0.120849i | \(-0.0385615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.169873 | + | 2.83013i | −0.00901592 | + | 0.150208i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | − | 3.46410i | 0.211702 | − | 0.183340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.6603 | − | 17.1244i | −1.56541 | − | 0.903789i | −0.996693 | − | 0.0812542i | \(-0.974107\pi\) |
−0.568715 | − | 0.822535i | \(-0.692559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.23205 | + | 15.9904i | 0.485897 | + | 0.841599i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.29423 | − | 1.29423i | −0.0679294 | − | 0.0679294i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 28.3923 | + | 9.46410i | 1.48612 | + | 0.495374i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.500000 | − | 0.133975i | −0.0260998 | − | 0.00699342i | 0.245746 | − | 0.969334i | \(-0.420967\pi\) |
−0.271845 | + | 0.962341i | \(0.587634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.83013 | − | 15.2942i | 0.459678 | − | 0.796186i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4904 | + | 10.4904i | 0.804221 | + | 0.544633i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.07180 | + | 7.73205i | 0.107274 | + | 0.400350i | 0.998593 | − | 0.0530251i | \(-0.0168863\pi\) |
−0.891320 | + | 0.453376i | \(0.850220\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.23205 | + | 2.47372i | 0.270182 | + | 0.127742i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.00000 | + | 6.00000i | −0.309016 | + | 0.309016i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.33975i | − | 0.120185i | −0.998193 | − | 0.0600923i | \(-0.980860\pi\) | ||
0.998193 | − | 0.0600923i | \(-0.0191395\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.294229 | + | 0.169873i | −0.0150738 | + | 0.00870286i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.5526 | + | 8.18653i | −1.56116 | + | 0.418312i | −0.933031 | − | 0.359795i | \(-0.882847\pi\) |
−0.628131 | + | 0.778107i | \(0.716180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0263 | + | 2.09808i | −0.816775 | + | 0.106928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5622 | + | 2.83013i | −0.536906 | + | 0.143863i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.26795 | + | 2.46410i | −0.216394 | + | 0.124935i | −0.604279 | − | 0.796773i | \(-0.706539\pi\) |
0.387886 | + | 0.921707i | \(0.373206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.535898i | − | 0.0271015i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.66025 | − | 5.66025i | 0.285522 | − | 0.285522i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.02628 | + | 6.09808i | −0.202584 | + | 0.306828i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.973721 | − | 3.63397i | −0.0488696 | − | 0.182384i | 0.937177 | − | 0.348855i | \(-0.113429\pi\) |
−0.986046 | + | 0.166471i | \(0.946763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.437822 | + | 0.901924i | 0.0219185 | + | 0.0451527i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.50000 | + | 9.52628i | −0.274657 | + | 0.475720i | −0.970049 | − | 0.242911i | \(-0.921898\pi\) |
0.695392 | + | 0.718631i | \(0.255231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.3923 | − | 5.46410i | −1.01581 | − | 0.272186i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.3205 | − | 6.66025i | 0.661901 | − | 0.330951i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.46410 | + | 9.46410i | 0.469118 | + | 0.469118i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4282 | − | 18.0622i | −0.515641 | − | 0.893117i | −0.999835 | − | 0.0181564i | \(-0.994220\pi\) |
0.484194 | − | 0.874961i | \(-0.339113\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.12436 | + | 3.53590i | 0.302092 | + | 0.174413i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.09808 | + | 21.2942i | 0.201653 | + | 1.04782i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.96410 | − | 4.40192i | 0.243678 | − | 0.216082i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.758330 | − | 2.83013i | 0.0371356 | − | 0.138592i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.8564 | −1.16546 | −0.582731 | − | 0.812665i | \(-0.698016\pi\) | ||||
−0.582731 | + | 0.812665i | \(0.698016\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.3397 | −0.845088 | −0.422544 | − | 0.906343i | \(-0.638863\pi\) | ||||
−0.422544 | + | 0.906343i | \(0.638863\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.46410 | − | 24.1244i | 0.314295 | − | 1.17297i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.9282 | − | 7.19615i | −0.869646 | − | 0.349065i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.66025 | + | 3.07180i | 0.128739 | + | 0.148655i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.46410 | + | 2.00000i | 0.167248 | + | 0.0965609i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.09808 | + | 5.36603i | 0.149229 | + | 0.258472i | 0.930943 | − | 0.365165i | \(-0.118987\pi\) |
−0.781714 | + | 0.623637i | \(0.785654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5359 | − | 17.5359i | −0.842721 | − | 0.842721i | 0.146491 | − | 0.989212i | \(-0.453202\pi\) |
−0.989212 | + | 0.146491i | \(0.953202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.09808 | + | 3.29423i | −0.0526487 | + | 0.157946i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0980762 | + | 0.0262794i | 0.00469162 | + | 0.00125712i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.66025 | + | 2.87564i | −0.0792396 | + | 0.137247i | −0.902922 | − | 0.429804i | \(-0.858583\pi\) |
0.823682 | + | 0.567051i | \(0.191916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.09808 | + | 17.7583i | 0.338004 | + | 0.845635i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50000 | + | 13.0622i | 0.166290 | + | 0.620603i | 0.997872 | + | 0.0652010i | \(0.0207689\pi\) |
−0.831582 | + | 0.555402i | \(0.812564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.23205 | + | 0.813467i | 0.0584048 | + | 0.0385620i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.294229 | − | 0.294229i | 0.0139165 | − | 0.0139165i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 33.0526i | − | 1.55985i | −0.625875 | − | 0.779923i | \(-0.715258\pi\) | ||
0.625875 | − | 0.779923i | \(-0.284742\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.2942 | + | 8.83013i | −0.720177 | + | 0.415794i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820 | − | 1.85641i | 0.325515 | − | 0.0872216i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.4641 | + | 6.39230i | −0.724968 | + | 0.299676i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7321 | + | 3.14359i | −0.548802 | + | 0.147051i | −0.522557 | − | 0.852604i | \(-0.675022\pi\) |
−0.0262453 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.92820 | − | 5.73205i | 0.463409 | − | 0.267549i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.60770i | − | 0.261176i | −0.991437 | − | 0.130588i | \(-0.958313\pi\) | ||
0.991437 | − | 0.130588i | \(-0.0416866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.75833 | − | 4.75833i | 0.221138 | − | 0.221138i | −0.587839 | − | 0.808978i | \(-0.700021\pi\) |
0.808978 | + | 0.587839i | \(0.200021\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.46410 | + | 1.73205i | −0.392513 | + | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.64359 | − | 13.5981i | −0.168605 | − | 0.629244i | −0.997553 | − | 0.0699173i | \(-0.977726\pi\) |
0.828947 | − | 0.559327i | \(-0.188940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4282 | + | 24.2583i | −0.758584 | + | 1.12015i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.24167 | + | 2.15064i | −0.0572131 | + | 0.0990960i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.5622 | + | 2.83013i | 0.485649 | + | 0.130129i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.19615 | − | 2.92820i | 0.100766 | − | 0.134355i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.6603 | + | 13.6603i | 0.625460 | + | 0.625460i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.53590 | − | 11.3205i | −0.298633 | − | 0.517247i | 0.677191 | − | 0.735808i | \(-0.263197\pi\) |
−0.975823 | + | 0.218560i | \(0.929864\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 6.92820i | 0.547153 | + | 0.315899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.179492 | − | 0.0621778i | −0.00816717 | − | 0.00282919i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.4378 | + | 14.0263i | 0.564772 | + | 0.636901i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.29423 | + | 27.2224i | −0.330533 | + | 1.23357i | 0.578098 | + | 0.815967i | \(0.303795\pi\) |
−0.908631 | + | 0.417599i | \(0.862872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.26795 | 0.328668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.7128 | −1.70196 | −0.850978 | − | 0.525202i | \(-0.823990\pi\) | ||||
−0.850978 | + | 0.525202i | \(0.823990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.00000 | − | 11.1962i | 0.135113 | − | 0.504249i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.6603 | − | 1.00000i | −0.748823 | − | 0.0449467i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.16987 | − | 1.09808i | −0.142188 | − | 0.0492554i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.97372 | + | 5.75833i | 0.446485 | + | 0.257778i | 0.706345 | − | 0.707868i | \(-0.250343\pi\) |
−0.259860 | + | 0.965646i | \(0.583676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.30385 | + | 7.45448i | 0.192282 | + | 0.333042i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.6340 | + | 17.6340i | 0.786260 | + | 0.786260i | 0.980879 | − | 0.194619i | \(-0.0623470\pi\) |
−0.194619 | + | 0.980879i | \(0.562347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.26795 | − | 16.5359i | −0.367919 | − | 0.735838i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.50000 | − | 0.669873i | −0.111029 | − | 0.0297501i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.4545 | + | 33.6962i | −0.862305 | + | 1.49356i | 0.00739389 | + | 0.999973i | \(0.497646\pi\) |
−0.869699 | + | 0.493583i | \(0.835687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.8564 | + | 29.3205i | −0.878396 | + | 1.29706i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.562178 | + | 2.09808i | 0.0248208 | + | 0.0926323i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.13397 | + | 10.4282i | 0.0940342 | + | 0.459522i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.6603 | + | 17.6603i | −0.776697 | + | 0.776697i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.6795i | − | 0.468778i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.6603 | + | 11.9282i | −0.905142 | + | 0.522584i | −0.878865 | − | 0.477071i | \(-0.841699\pi\) |
−0.0262772 | + | 0.999655i | \(0.508365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.8827 | − | 11.4904i | 1.87513 | − | 0.502439i | 0.875307 | − | 0.483568i | \(-0.160659\pi\) |
0.999822 | − | 0.0188717i | \(-0.00600740\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.49038 | + | 5.16987i | −0.195976 | + | 0.225632i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.8564 | − | 7.46410i | 1.21344 | − | 0.325141i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.9019 | − | 11.4904i | 0.865301 | − | 0.499582i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.3923i | 0.971743i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9282 | + | 12.9282i | −0.559983 | + | 0.559983i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.89230 | + | 28.7942i | 0.254747 | + | 1.24488i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.05256 | + | 3.92820i | 0.0454213 | + | 0.169514i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.73205 | − | 18.9282i | 0.117678 | − | 0.815295i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3564 | + | 31.7942i | −0.789204 | + | 1.36694i | 0.137252 | + | 0.990536i | \(0.456173\pi\) |
−0.926455 | + | 0.376404i | \(0.877160\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.598076 | − | 0.160254i | −0.0256659 | − | 0.00687716i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1244 | + | 20.2487i | 0.433680 | + | 0.867359i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7583 | + | 16.7583i | 0.716534 | + | 0.716534i | 0.967894 | − | 0.251359i | \(-0.0808776\pi\) |
−0.251359 | + | 0.967894i | \(0.580878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.09808 | + | 3.63397i | 0.0895437 | + | 0.155094i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.90192 | + | 1.09808i | 0.0810247 | + | 0.0467796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.66025 | − | 6.53590i | −0.240698 | − | 0.277935i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.66025 | + | 0.339746i | 0.240264 | + | 0.0144214i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.36603 | − | 31.2224i | 0.354480 | − | 1.32294i | −0.526658 | − | 0.850077i | \(-0.676555\pi\) |
0.881138 | − | 0.472860i | \(-0.156778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3205 | 0.478806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.46410 | −0.230695 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.35641 | − | 23.7224i | 0.267891 | − | 0.999781i | −0.692567 | − | 0.721354i | \(-0.743520\pi\) |
0.960457 | − | 0.278427i | \(-0.0898132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.2224 | + | 18.2942i | 0.682483 | + | 0.769644i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.33013 | + | 17.3038i | 0.139852 | + | 0.726693i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.0526 | − | 14.4641i | −1.05026 | − | 0.606367i | −0.127536 | − | 0.991834i | \(-0.540707\pi\) |
−0.922722 | + | 0.385467i | \(0.874040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.02628 | − | 15.6340i | −0.377738 | − | 0.654261i | 0.612995 | − | 0.790087i | \(-0.289965\pi\) |
−0.990733 | + | 0.135826i | \(0.956631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.85641 | − | 4.85641i | −0.202879 | − | 0.202879i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0980762 | + | 0.686533i | 0.00409006 | + | 0.0286304i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63397 | + | 1.50962i | 0.234545 | + | 0.0628463i | 0.374177 | − | 0.927357i | \(-0.377925\pi\) |
−0.139632 | + | 0.990204i | \(0.544592\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.09808 | + | 3.63397i | −0.0871931 | + | 0.151023i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.42820 | + | 7.06218i | 0.142226 | + | 0.292989i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.00000 | − | 18.6603i | −0.207079 | − | 0.772829i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.9282 | + | 3.46410i | −0.699895 | + | 0.143223i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.7846 | + | 15.7846i | −0.651501 | + | 0.651501i | −0.953354 | − | 0.301854i | \(-0.902395\pi\) |
0.301854 | + | 0.953354i | \(0.402395\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.46410i | 0.225144i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.41858 | + | 3.70577i | −0.264025 | + | 0.152435i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7583 | − | 5.56218i | 0.852442 | − | 0.228411i | 0.193962 | − | 0.981009i | \(-0.437866\pi\) |
0.658481 | + | 0.752598i | \(0.271199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.9282 | − | 18.1244i | 0.571001 | − | 0.743026i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.53590 | − | 1.48334i | 0.226569 | − | 0.0607090i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3397 | − | 8.85641i | 0.626765 | − | 0.361863i | −0.152733 | − | 0.988267i | \(-0.548807\pi\) |
0.779498 | + | 0.626405i | \(0.215474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 41.1769i | − | 1.67964i | −0.542864 | − | 0.839821i | \(-0.682660\pi\) | ||
0.542864 | − | 0.839821i | \(-0.317340\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.3923 | + | 21.3923i | −0.871162 | + | 0.871162i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.59808 | − | 4.35641i | −0.268250 | − | 0.177113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.40192 | − | 12.6962i | −0.138080 | − | 0.515321i | −0.999966 | − | 0.00821951i | \(-0.997384\pi\) |
0.861886 | − | 0.507101i | \(-0.169283\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.40192 | − | 2.30385i | −0.137853 | − | 0.0933566i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.9282 | + | 22.3923i | −0.523019 | + | 0.905896i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3923 | + | 6.53590i | 0.985196 | + | 0.263982i | 0.715231 | − | 0.698888i | \(-0.246321\pi\) |
0.269965 | + | 0.962870i | \(0.412988\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.36603 | + | 7.09808i | −0.0954074 | + | 0.286222i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9090 | + | 33.9090i | 1.36512 | + | 1.36512i | 0.867249 | + | 0.497874i | \(0.165886\pi\) |
0.497874 | + | 0.867249i | \(0.334114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.09808 | − | 8.83013i | −0.204909 | − | 0.354913i | 0.745195 | − | 0.666847i | \(-0.232357\pi\) |
−0.950104 | + | 0.311934i | \(0.899023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.356406 | − | 0.205771i | −0.0143021 | − | 0.00825732i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.32051 | + | 1.14359i | −0.0529050 | + | 0.0458171i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2846 | + | 5.93782i | 0.971384 | + | 0.237513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.267949 | − | 1.00000i | 0.0107009 | − | 0.0399362i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.9282 | −0.754717 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.58846 | 0.182664 | 0.0913318 | − | 0.995821i | \(-0.470888\pi\) | ||||
0.0913318 | + | 0.995821i | \(0.470888\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0262794 | − | 0.0980762i | 0.00104451 | − | 0.00389818i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.09808 | + | 0.973721i | −0.0435758 | + | 0.0386409i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.33975 | − | 19.6603i | −0.0927041 | − | 0.778968i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.00000 | − | 1.73205i | −0.118678 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.33013 | − | 9.23205i | −0.210527 | − | 0.364644i | 0.741352 | − | 0.671116i | \(-0.234185\pi\) |
−0.951880 | + | 0.306472i | \(0.900851\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5359 | − | 17.5359i | −0.691548 | − | 0.691548i | 0.271024 | − | 0.962573i | \(-0.412638\pi\) |
−0.962573 | + | 0.271024i | \(0.912638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.14359 | − | 2.07180i | 0.163154 | − | 0.0815769i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.5526 | − | 10.5981i | −1.55497 | − | 0.416653i | −0.623904 | − | 0.781501i | \(-0.714454\pi\) |
−0.931067 | + | 0.364847i | \(0.881121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1962 | − | 19.3923i | 0.439487 | − | 0.761215i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.732051 | − | 10.1962i | 0.0286913 | − | 0.399619i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.26795 | − | 19.6603i | −0.206151 | − | 0.769365i | −0.989096 | − | 0.147274i | \(-0.952950\pi\) |
0.782945 | − | 0.622091i | \(-0.213717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.0526 | − | 28.8564i | 0.744445 | − | 1.12751i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −25.8564 | + | 25.8564i | −1.00875 | + | 1.00875i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.6603i | 1.07749i | 0.842469 | + | 0.538745i | \(0.181101\pi\) | ||||
−0.842469 | + | 0.538745i | \(0.818899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7224 | + | 24.0885i | −1.62281 | + | 0.936932i | −0.636652 | + | 0.771151i | \(0.719681\pi\) |
−0.986163 | + | 0.165781i | \(0.946985\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.46410 | + | 1.46410i | −0.212208 | + | 0.0568610i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.63397 | + | 3.43782i | 0.102141 | + | 0.133313i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.401924 | + | 0.107695i | −0.0155626 | + | 0.00416997i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4904 | + | 6.63397i | −0.444244 | + | 0.256484i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.19615i | − | 0.161991i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.39230 | − | 4.39230i | 0.169311 | − | 0.169311i | −0.617366 | − | 0.786676i | \(-0.711800\pi\) |
0.786676 | + | 0.617366i | \(0.211800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.6699 | + | 9.16025i | −0.449174 | + | 0.352578i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.92820 | − | 25.8564i | −0.266272 | − | 0.993742i | −0.961467 | − | 0.274921i | \(-0.911348\pi\) |
0.695194 | − | 0.718822i | \(-0.255318\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.9545 | + | 9.68653i | −0.765783 | + | 0.371735i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.09808 | − | 8.83013i | 0.195359 | − | 0.338371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.0622 | − | 4.57180i | −0.652866 | − | 0.174935i | −0.0828417 | − | 0.996563i | \(-0.526400\pi\) |
−0.570024 | + | 0.821628i | \(0.693066\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.9808 | + | 9.66025i | 1.10730 | + | 0.369099i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.73205 | + | 6.73205i | 0.256844 | + | 0.256844i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | − | 17.3205i | −0.380970 | − | 0.659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0263 | + | 25.4186i | 1.67484 | + | 0.966969i | 0.964867 | + | 0.262738i | \(0.0846255\pi\) |
0.709971 | + | 0.704231i | \(0.248708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.46410 | − | 18.6603i | 0.245551 | − | 0.708844i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.758330 | − | 12.6340i | 0.0287651 | − | 0.479234i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.46410 | − | 24.1244i | 0.244845 | − | 0.913775i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.46410 | −0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.2679 | −0.765510 | −0.382755 | − | 0.923850i | \(-0.625025\pi\) | ||||
−0.382755 | + | 0.923850i | \(0.625025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.928203 | − | 3.46410i | 0.0350078 | − | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.633975 | + | 10.5622i | −0.0238769 | + | 0.397795i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.4808 | − | 4.13397i | 0.807867 | − | 0.155474i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.9904 | + | 10.9641i | 0.713199 | + | 0.411765i | 0.812244 | − | 0.583317i | \(-0.198246\pi\) |
−0.0990456 | + | 0.995083i | \(0.531579\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.46410 | − | 7.73205i | −0.167417 | − | 0.289975i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.732051 | − | 0.732051i | −0.0274155 | − | 0.0274155i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3923 | + | 5.46410i | 0.613037 | + | 0.204346i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.19615 | − | 0.320508i | −0.0446711 | − | 0.0119696i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.2942 | + | 33.4186i | −0.719553 | + | 1.24630i | 0.241624 | + | 0.970370i | \(0.422320\pi\) |
−0.961177 | + | 0.275933i | \(0.911013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5622 | − | 0.901924i | −0.467840 | − | 0.0335894i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.32051 | − | 12.3923i | −0.123491 | − | 0.460875i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.79423 | + | 14.8923i | −0.0666360 | + | 0.553086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0981 | − | 10.0981i | 0.374517 | − | 0.374517i | −0.494602 | − | 0.869119i | \(-0.664686\pi\) |
0.869119 | + | 0.494602i | \(0.164686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.5885i | 0.503276i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.3923 | + | 7.73205i | −0.495332 | + | 0.285980i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.36603 | + | 1.16987i | −0.161263 | + | 0.0432102i | −0.338547 | − | 0.940949i | \(-0.609935\pi\) |
0.177284 | + | 0.984160i | \(0.443269\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.45448 | − | 6.76795i | −0.164306 | − | 0.249640i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.2224 | − | 7.83013i | 1.07642 | − | 0.288426i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.5622 | − | 11.2942i | 0.719606 | − | 0.415465i | −0.0950014 | − | 0.995477i | \(-0.530286\pi\) |
0.814608 | + | 0.580012i | \(0.196952\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1.07180i | − | 0.0393734i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.16987 | − | 6.16987i | 0.226351 | − | 0.226351i | −0.584816 | − | 0.811166i | \(-0.698833\pi\) |
0.811166 | + | 0.584816i | \(0.198833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.990381 | − | 1.50000i | 0.0362848 | − | 0.0549557i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.09808 | + | 7.83013i | 0.0767646 | + | 0.286489i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.6865 | − | 2.49038i | −1.26742 | − | 0.0909965i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.19615 | + | 5.53590i | −0.116629 | + | 0.202008i | −0.918430 | − | 0.395584i | \(-0.870542\pi\) |
0.801801 | + | 0.597592i | \(0.203876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.9282 | − | 2.92820i | −0.398246 | − | 0.106710i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.7128 | − | 13.8564i | 1.00857 | − | 0.504286i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7321 | + | 12.7321i | 0.462754 | + | 0.462754i | 0.899557 | − | 0.436803i | \(-0.143889\pi\) |
−0.436803 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0980762 | + | 0.169873i | 0.00355994 | + | 0.00616600i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.9282 | + | 14.3923i | 0.903647 | + | 0.521721i | 0.878382 | − | 0.477960i | \(-0.158624\pi\) |
0.0252651 | + | 0.999681i | \(0.491957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.3038 | + | 5.06218i | −0.952263 | + | 0.183263i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.6603 | − | 15.6603i | 0.638508 | − | 0.566198i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | − | 22.3923i | 0.216647 | − | 0.808539i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.1769 | 0.547294 | 0.273647 | − | 0.961830i | \(-0.411770\pi\) | ||||
0.273647 | + | 0.961830i | \(0.411770\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.46410 | −0.0527283 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.07180 | − | 15.1962i | 0.146452 | − | 0.546568i | −0.853234 | − | 0.521528i | \(-0.825362\pi\) |
0.999686 | − | 0.0250395i | \(-0.00797116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −34.3205 | + | 14.6603i | −1.23283 | + | 0.526612i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.19615 | + | 6.33975i | −0.0787865 | + | 0.227437i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.09808 | + | 2.36603i | 0.146829 | + | 0.0847717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.73205 | + | 3.00000i | 0.0619777 | + | 0.107348i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.29423 | − | 6.29423i | −0.224937 | − | 0.224937i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.39230 | + | 10.1769i | −0.121077 | + | 0.363230i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.1865 | − | 8.35641i | −1.11168 | − | 0.297874i | −0.344168 | − | 0.938908i | \(-0.611839\pi\) |
−0.767512 | + | 0.641034i | \(0.778506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.06218 | − | 7.03590i | 0.144617 | − | 0.250485i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.0263 | + | 12.6340i | −0.925388 | + | 0.449212i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.12436 | − | 4.19615i | −0.0399270 | − | 0.149010i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.83013 | − | 4.50962i | −0.242240 | − | 0.159940i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.5359 | − | 22.5359i | 0.798262 | − | 0.798262i | −0.184559 | − | 0.982821i | \(-0.559086\pi\) |
0.982821 | + | 0.184559i | \(0.0590857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 35.3205i | − | 1.24955i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.56218 | + | 0.901924i | −0.0551968 | + | 0.0318679i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.3205 | − | 9.46410i | 1.24643 | − | 0.333981i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.813467 | − | 0.107695i | −0.0286709 | − | 0.00379576i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.4282 | − | 3.06218i | 0.402292 | − | 0.107794i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.99038 | + | 2.30385i | −0.140294 | + | 0.0809990i | −0.568504 | − | 0.822680i | \(-0.692478\pi\) |
0.428210 | + | 0.903679i | \(0.359144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 42.9282i | − | 1.50741i | −0.657211 | − | 0.753707i | \(-0.728264\pi\) | ||
0.657211 | − | 0.753707i | \(-0.271736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.78461 | + | 7.78461i | −0.273018 | + | 0.273018i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.7583 | − | 6.29423i | 1.07742 | − | 0.220477i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.758330 | − | 2.83013i | −0.0265306 | − | 0.0990136i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.46410 | − | 20.3923i | 0.0511599 | − | 0.712565i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.6603 | − | 42.7128i | 0.860649 | − | 1.49069i | −0.0106549 | − | 0.999943i | \(-0.503392\pi\) |
0.871304 | − | 0.490744i | \(-0.163275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 53.3827 | + | 14.3038i | 1.86080 | + | 0.498601i | 0.999947 | − | 0.0102479i | \(-0.00326207\pi\) |
0.860856 | + | 0.508849i | \(0.169929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.00000 | − | 1.00000i | 0.243709 | − | 0.0348155i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.2224 | + | 33.2224i | 1.15526 | + | 1.15526i | 0.985483 | + | 0.169774i | \(0.0543038\pi\) |
0.169774 | + | 0.985483i | \(0.445696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.26795 | − | 12.5885i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.41154 | + | 1.39230i | 0.0836555 | + | 0.0482985i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.1962 | + | 21.6603i | 0.561163 | + | 0.750483i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.6699 | + | 27.8205i | 0.853736 | + | 0.962768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.73205 | − | 21.3923i | 0.198129 | − | 0.739426i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.87564 | −0.237374 | −0.118687 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118687 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.124356 | + | 0.464102i | −0.00428304 | + | 0.0159845i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1603 | − | 0.669873i | −0.383924 | − | 0.0230443i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.07180 | − | 6.12436i | 0.242990 | − | 0.210435i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.882686 | − | 0.509619i | −0.0302937 | − | 0.0174901i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.339746 | + | 0.588457i | 0.0116463 | + | 0.0201721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.1244 | − | 18.1244i | −0.620566 | − | 0.620566i | 0.325110 | − | 0.945676i | \(-0.394599\pi\) |
−0.945676 | + | 0.325110i | \(0.894599\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.00000 | + | 4.00000i | 0.0683986 | + | 0.136797i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0981 | − | 2.97372i | −0.379103 | − | 0.101580i | 0.0642351 | − | 0.997935i | \(-0.479539\pi\) |
−0.443338 | + | 0.896354i | \(0.646206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4641 | − | 30.2487i | 0.595867 | − | 1.03207i | −0.397556 | − | 0.917578i | \(-0.630142\pi\) |
0.993424 | − | 0.114495i | \(-0.0365250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.33013 | − | 4.96410i | −0.249810 | − | 0.169176i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.3827 | − | 49.9449i | −0.455552 | − | 1.70014i | −0.686460 | − | 0.727167i | \(-0.740836\pi\) |
0.230908 | − | 0.972976i | \(-0.425830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.24871 | − | 45.1962i | −0.314466 | − | 1.53672i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.758330 | + | 0.758330i | −0.0257542 | + | 0.0257542i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.92820i | 0.302869i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.1244 | − | 15.6603i | 0.919074 | − | 0.530627i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.1244 | + | 5.92820i | −0.748796 | + | 0.200639i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.5263 | + | 25.7679i | −0.491078 | + | 0.871116i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.1506 | + | 10.4904i | −1.32202 | + | 0.354235i | −0.849735 | − | 0.527209i | \(-0.823238\pi\) |
−0.472288 | + | 0.881444i | \(0.656572\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.51666 | + | 0.875644i | −0.0511557 | + | 0.0295348i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.1436i | 0.847109i | 0.905871 | + | 0.423555i | \(0.139218\pi\) | ||||
−0.905871 | + | 0.423555i | \(0.860782\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.07180 | + | 8.07180i | −0.271638 | + | 0.271638i | −0.829759 | − | 0.558122i | \(-0.811522\pi\) |
0.558122 | + | 0.829759i | \(0.311522\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.90192 | − | 9.29423i | −0.0639325 | − | 0.312422i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.91858 | − | 10.8923i | −0.0979965 | − | 0.365728i | 0.899460 | − | 0.437003i | \(-0.143960\pi\) |
−0.997457 | + | 0.0712748i | \(0.977293\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.758330 | − | 1.56218i | −0.0254336 | − | 0.0523938i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.09808 | − | 15.7583i | 0.304797 | − | 0.527924i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.46410 | + | 1.73205i | 0.216313 | + | 0.0579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.85641 | + | 15.7128i | 0.262611 | + | 0.525221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.143594 | + | 0.143594i | 0.00479445 | + | 0.00479445i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.1962 | − | 19.3923i | −0.373413 | − | 0.646770i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.6603 | + | 13.6603i | 0.788237 | + | 0.455089i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.03590 | + | 5.38269i | 0.0344725 | + | 0.179125i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.66987 | − | 0.160254i | −0.0887496 | − | 0.00532702i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.69615 | − | 32.4545i | 0.288751 | − | 1.07763i | −0.657304 | − | 0.753626i | \(-0.728303\pi\) |
0.946055 | − | 0.324007i | \(-0.105030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.5885 | 0.749212 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.51666 | 0.249038 | 0.124519 | − | 0.992217i | \(-0.460261\pi\) | ||||
0.124519 | + | 0.992217i | \(0.460261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09808 | − | 7.83013i | 0.0694362 | − | 0.259139i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.17949 | − | 1.33013i | −0.0389928 | − | 0.0439726i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.7846 | + | 30.9282i | 0.884506 | + | 1.02134i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6673 | + | 28.0981i | 1.60539 | + | 0.926870i | 0.990384 | + | 0.138344i | \(0.0441780\pi\) |
0.615002 | + | 0.788526i | \(0.289155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.30385 | + | 3.99038i | 0.0759144 | + | 0.131488i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.53590 | + | 2.53590i | 0.0834701 | + | 0.0834701i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.2487 | − | 3.46410i | 0.797293 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.5622 | − | 3.36603i | −0.412596 | − | 0.110555i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18.1603 | + | 31.4545i | −0.595819 | + | 1.03199i | 0.397612 | + | 0.917554i | \(0.369839\pi\) |
−0.993431 | + | 0.114435i | \(0.963494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.75833 | + | 1.90192i | −0.155948 | + | 0.0623330i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.04552 | − | 7.63397i | −0.0669672 | − | 0.249925i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.1244 | + | 4.73205i | −0.756247 | + | 0.154755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.0718 | − | 17.0718i | 0.557711 | − | 0.557711i | −0.370944 | − | 0.928655i | \(-0.620966\pi\) |
0.928655 | + | 0.370944i | \(0.120966\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.78461i | 0.0908723i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1962 | − | 20.3205i | 1.14736 | − | 0.662430i | 0.199119 | − | 0.979975i | \(-0.436192\pi\) |
0.948243 | + | 0.317546i | \(0.102859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.866025 | + | 0.232051i | −0.0282017 | + | 0.00755661i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.70577 | − | 16.2224i | −0.218139 | − | 0.527716i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.30385 | − | 0.349365i | 0.0423694 | − | 0.0113528i | −0.237572 | − | 0.971370i | \(-0.576352\pi\) |
0.279941 | + | 0.960017i | \(0.409685\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.7846 | − | 18.9282i | 1.06423 | − | 0.614435i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.92820i | − | 0.159808i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −37.8564 | + | 37.8564i | −1.22629 | + | 1.22629i | −0.260932 | + | 0.965357i | \(0.584030\pi\) |
−0.965357 | + | 0.260932i | \(0.915970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.7583 | − | 16.3468i | −0.801161 | − | 0.528970i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.09808 | + | 4.09808i | 0.0354958 | + | 0.132472i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.2679 | + | 29.9282i | −0.654486 | + | 0.966432i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3564 | − | 21.4019i | 0.398594 | − | 0.690385i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.6865 | − | 9.29423i | −1.11776 | − | 0.299502i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.73205 | + | 17.1962i | −0.184521 | + | 0.553564i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5622 | + | 13.5622i | 0.436130 | + | 0.436130i | 0.890707 | − | 0.454577i | \(-0.150210\pi\) |
−0.454577 | + | 0.890707i | \(0.650210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.732051 | + | 1.26795i | 0.0235169 | + | 0.0407324i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.0718 | − | 16.7846i | −0.932958 | − | 0.538644i | −0.0452124 | − | 0.998977i | \(-0.514396\pi\) |
−0.887746 | + | 0.460334i | \(0.847730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1506 | + | 4.90192i | 0.453649 | + | 0.157148i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.73205 | − | 2.87564i | 0.215598 | − | 0.0920943i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.150635 | + | 0.562178i | −0.00481924 | + | 0.0179857i | −0.968294 | − | 0.249815i | \(-0.919630\pi\) |
0.963474 | + | 0.267801i | \(0.0862969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.80385 | 0.0576512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.6603 | −0.883124 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.5000 | + | 54.1147i | −0.462478 | + | 1.72599i | 0.202639 | + | 0.979253i | \(0.435048\pi\) |
−0.665118 | + | 0.746739i | \(0.731619\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.9545 | + | 21.2417i | −0.763253 | + | 0.676816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.8301 | − | 4.09808i | −0.376557 | − | 0.130443i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.480762 | + | 0.277568i | 0.0152873 | + | 0.00882615i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.8564 | + | 27.4641i | 0.503695 | + | 0.872426i | 0.999991 | + | 0.00427229i | \(0.00135992\pi\) |
−0.496296 | + | 0.868154i | \(0.665307\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.679492 | + | 0.679492i | 0.0215630 | + | 0.0215630i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.1436 | − | 11.0718i | 0.701999 | − | 0.351000i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.8827 | − | 10.6865i | −1.26310 | − | 0.338446i | −0.435715 | − | 0.900085i | \(-0.643504\pi\) |
−0.827382 | + | 0.561639i | \(0.810171\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.26795 | + | 12.5885i | −0.229948 | + | 0.398281i |
(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 | 560.2.ci.b.257.1 | 4 | ||
4.3 | odd | 2 | 35.2.k.b.12.1 | yes | 4 | ||
5.3 | odd | 4 | 560.2.ci.a.33.1 | 4 | |||
7.3 | odd | 6 | 560.2.ci.a.17.1 | 4 | |||
12.11 | even | 2 | 315.2.bz.a.82.1 | 4 | |||
20.3 | even | 4 | 35.2.k.a.33.1 | yes | 4 | ||
20.7 | even | 4 | 175.2.o.b.68.1 | 4 | |||
20.19 | odd | 2 | 175.2.o.a.82.1 | 4 | |||
28.3 | even | 6 | 35.2.k.a.17.1 | ✓ | 4 | ||
28.11 | odd | 6 | 245.2.l.a.227.1 | 4 | |||
28.19 | even | 6 | 245.2.f.a.97.1 | 4 | |||
28.23 | odd | 6 | 245.2.f.b.97.1 | 4 | |||
28.27 | even | 2 | 245.2.l.b.117.1 | 4 | |||
35.3 | even | 12 | inner | 560.2.ci.b.353.1 | 4 | ||
60.23 | odd | 4 | 315.2.bz.b.208.1 | 4 | |||
84.59 | odd | 6 | 315.2.bz.b.262.1 | 4 | |||
140.3 | odd | 12 | 35.2.k.b.3.1 | yes | 4 | ||
140.23 | even | 12 | 245.2.f.a.48.1 | 4 | |||
140.59 | even | 6 | 175.2.o.b.157.1 | 4 | |||
140.83 | odd | 4 | 245.2.l.a.68.1 | 4 | |||
140.87 | odd | 12 | 175.2.o.a.143.1 | 4 | |||
140.103 | odd | 12 | 245.2.f.b.48.1 | 4 | |||
140.123 | even | 12 | 245.2.l.b.178.1 | 4 | |||
420.143 | even | 12 | 315.2.bz.a.73.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.k.a.17.1 | ✓ | 4 | 28.3 | even | 6 | ||
35.2.k.a.33.1 | yes | 4 | 20.3 | even | 4 | ||
35.2.k.b.3.1 | yes | 4 | 140.3 | odd | 12 | ||
35.2.k.b.12.1 | yes | 4 | 4.3 | odd | 2 | ||
175.2.o.a.82.1 | 4 | 20.19 | odd | 2 | |||
175.2.o.a.143.1 | 4 | 140.87 | odd | 12 | |||
175.2.o.b.68.1 | 4 | 20.7 | even | 4 | |||
175.2.o.b.157.1 | 4 | 140.59 | even | 6 | |||
245.2.f.a.48.1 | 4 | 140.23 | even | 12 | |||
245.2.f.a.97.1 | 4 | 28.19 | even | 6 | |||
245.2.f.b.48.1 | 4 | 140.103 | odd | 12 | |||
245.2.f.b.97.1 | 4 | 28.23 | odd | 6 | |||
245.2.l.a.68.1 | 4 | 140.83 | odd | 4 | |||
245.2.l.a.227.1 | 4 | 28.11 | odd | 6 | |||
245.2.l.b.117.1 | 4 | 28.27 | even | 2 | |||
245.2.l.b.178.1 | 4 | 140.123 | even | 12 | |||
315.2.bz.a.73.1 | 4 | 420.143 | even | 12 | |||
315.2.bz.a.82.1 | 4 | 12.11 | even | 2 | |||
315.2.bz.b.208.1 | 4 | 60.23 | odd | 4 | |||
315.2.bz.b.262.1 | 4 | 84.59 | odd | 6 | |||
560.2.ci.a.17.1 | 4 | 7.3 | odd | 6 | |||
560.2.ci.a.33.1 | 4 | 5.3 | odd | 4 | |||
560.2.ci.b.257.1 | 4 | 1.1 | even | 1 | trivial | ||
560.2.ci.b.353.1 | 4 | 35.3 | even | 12 | inner |