Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −0.447974 | −0.258638 | −0.129319 | − | 0.991603i | \(-0.541279\pi\) | ||||
−0.129319 | + | 0.991603i | \(0.541279\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.48474 | 1.11121 | 0.555605 | − | 0.831447i | \(-0.312487\pi\) | ||||
0.555605 | + | 0.831447i | \(0.312487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20909 | 1.21292 | 0.606461 | − | 0.795113i | \(-0.292589\pi\) | ||||
0.606461 | + | 0.795113i | \(0.292589\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79932 | −0.933106 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.332333 | −0.100202 | −0.0501011 | − | 0.998744i | \(-0.515954\pi\) | ||||
−0.0501011 | + | 0.998744i | \(0.515954\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.86212 | −1.34851 | −0.674254 | − | 0.738499i | \(-0.735535\pi\) | ||||
−0.674254 | + | 0.738499i | \(0.735535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.11310 | −0.287401 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.61386 | −1.11903 | −0.559513 | − | 0.828822i | \(-0.689012\pi\) | ||||
−0.559513 | + | 0.828822i | \(0.689012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.39401 | −1.69630 | −0.848151 | − | 0.529754i | \(-0.822284\pi\) | ||||
−0.848151 | + | 0.529754i | \(0.822284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.43759 | −0.313708 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.99857 | 1.25079 | 0.625395 | − | 0.780309i | \(-0.284938\pi\) | ||||
0.625395 | + | 0.780309i | \(0.284938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.17393 | 0.234786 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.59794 | 0.499975 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.23188 | 1.52862 | 0.764310 | − | 0.644848i | \(-0.223080\pi\) | ||||
0.764310 | + | 0.644848i | \(0.223080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.16322 | 1.28655 | 0.643276 | − | 0.765634i | \(-0.277575\pi\) | ||||
0.643276 | + | 0.765634i | \(0.277575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.148877 | 0.0259161 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.97375 | 1.34781 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.58586 | −0.918309 | −0.459155 | − | 0.888356i | \(-0.651848\pi\) | ||||
−0.459155 | + | 0.888356i | \(0.651848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.17810 | 0.348776 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.18131 | −0.496837 | −0.248418 | − | 0.968653i | \(-0.579911\pi\) | ||||
−0.248418 | + | 0.968653i | \(0.579911\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29032 | 0.501769 | 0.250884 | − | 0.968017i | \(-0.419279\pi\) | ||||
0.250884 | + | 0.968017i | \(0.419279\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.95558 | −1.03688 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.99363 | −1.45772 | −0.728861 | − | 0.684662i | \(-0.759950\pi\) | ||||
−0.728861 | + | 0.684662i | \(0.759950\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.29825 | 0.471179 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.06689 | 0.289423 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.53894 | −0.348750 | −0.174375 | − | 0.984679i | \(-0.555790\pi\) | ||||
−0.174375 | + | 0.984679i | \(0.555790\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.825761 | −0.111346 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.31233 | 0.438728 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.30087 | −0.690115 | −0.345057 | − | 0.938582i | \(-0.612141\pi\) | ||||
−0.345057 | + | 0.938582i | \(0.612141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.55552 | 1.09542 | 0.547711 | − | 0.836668i | \(-0.315499\pi\) | ||||
0.547711 | + | 0.836668i | \(0.315499\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.98326 | −1.13178 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.0811 | −1.49848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.87268 | −0.717462 | −0.358731 | − | 0.933441i | \(-0.616790\pi\) | ||||
−0.358731 | + | 0.933441i | \(0.616790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.68721 | −0.323502 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6528 | −1.62029 | −0.810147 | − | 0.586226i | \(-0.800613\pi\) | ||||
−0.810147 | + | 0.586226i | \(0.800613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.82965 | −0.331185 | −0.165593 | − | 0.986194i | \(-0.552954\pi\) | ||||
−0.165593 | + | 0.986194i | \(0.552954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.525891 | −0.0607246 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.06649 | −0.121537 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.1660 | −1.81881 | −0.909407 | − | 0.415907i | \(-0.863464\pi\) | ||||
−0.909407 | + | 0.415907i | \(0.863464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.23415 | 0.803794 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0448 | 1.43185 | 0.715927 | − | 0.698175i | \(-0.246004\pi\) | ||||
0.715927 | + | 0.698175i | \(0.246004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.4642 | −1.24347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.68767 | −0.395359 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.60233 | 0.699845 | 0.349923 | − | 0.936779i | \(-0.386208\pi\) | ||||
0.349923 | + | 0.936779i | \(0.386208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.6030 | −1.63564 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.20894 | −0.332751 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.3722 | −1.88495 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8090 | 1.30055 | 0.650277 | − | 0.759697i | \(-0.274653\pi\) | ||||
0.650277 | + | 0.759697i | \(0.274653\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.930306 | 0.0934993 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.8727 | −1.57940 | −0.789699 | − | 0.613495i | \(-0.789763\pi\) | ||||
−0.789699 | + | 0.613495i | \(0.789763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.96888 | −0.686664 | −0.343332 | − | 0.939214i | \(-0.611556\pi\) | ||||
−0.343332 | + | 0.939214i | \(0.611556\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.57203 | −0.348595 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −20.1653 | −1.94945 | −0.974725 | − | 0.223408i | \(-0.928282\pi\) | ||||
−0.974725 | + | 0.223408i | \(0.928282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.23463 | 0.405604 | 0.202802 | − | 0.979220i | \(-0.434995\pi\) | ||||
0.202802 | + | 0.979220i | \(0.434995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.50232 | 0.237510 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7102 | −1.28974 | −0.644871 | − | 0.764291i | \(-0.723089\pi\) | ||||
−0.644871 | + | 0.764291i | \(0.723089\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.9049 | 1.38989 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.6106 | 1.25830 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.8063 | −1.35729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8896 | −0.989960 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.42514 | 0.128501 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.50679 | −0.850313 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.35585 | 0.563990 | 0.281995 | − | 0.959416i | \(-0.409004\pi\) | ||||
0.281995 | + | 0.959416i | \(0.409004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.47398 | −0.129777 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.70378 | −0.673082 | −0.336541 | − | 0.941669i | \(-0.609257\pi\) | ||||
−0.336541 | + | 0.941669i | \(0.609257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.7280 | −2.05748 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.45522 | 0.555577 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.49056 | −0.639962 | −0.319981 | − | 0.947424i | \(-0.603677\pi\) | ||||
−0.319981 | + | 0.947424i | \(0.603677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.23746 | 0.529054 | 0.264527 | − | 0.964378i | \(-0.414784\pi\) | ||||
0.264527 | + | 0.964378i | \(0.414784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.47689 | 0.377022 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.61584 | 0.135124 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.4541 | 1.69862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.47753 | −0.121865 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.46677 | 0.447855 | 0.223928 | − | 0.974606i | \(-0.428112\pi\) | ||||
0.223928 | + | 0.974606i | \(0.428112\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.74213 | 0.467288 | 0.233644 | − | 0.972322i | \(-0.424935\pi\) | ||||
0.233644 | + | 0.972322i | \(0.424935\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.9157 | 1.04417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.7987 | 1.42963 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.05111 | 0.403122 | 0.201561 | − | 0.979476i | \(-0.435399\pi\) | ||||
0.201561 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.13738 | 0.0901999 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.2500 | 1.51711 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.48335 | 0.194511 | 0.0972554 | − | 0.995259i | \(-0.468994\pi\) | ||||
0.0972554 | + | 0.995259i | \(0.468994\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.369920 | 0.0287982 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6806 | −1.05864 | −0.529318 | − | 0.848423i | \(-0.677552\pi\) | ||||
−0.529318 | + | 0.848423i | \(0.677552\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6402 | 0.818476 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.6982 | 1.58283 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.89798 | 0.220330 | 0.110165 | − | 0.993913i | \(-0.464862\pi\) | ||||
0.110165 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.76725 | 0.284777 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.37465 | 0.178490 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.37568 | −0.476541 | −0.238271 | − | 0.971199i | \(-0.576580\pi\) | ||||
−0.238271 | + | 0.971199i | \(0.576580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.982308 | 0.0730144 | 0.0365072 | − | 0.999333i | \(-0.488377\pi\) | ||||
0.0365072 | + | 0.999333i | \(0.488377\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.83265 | −0.283318 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.8794 | −1.02043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.53334 | 0.112129 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.33704 | 0.606430 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.9651 | −0.938121 | −0.469060 | − | 0.883166i | \(-0.655407\pi\) | ||||
−0.469060 | + | 0.883166i | \(0.655407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8917 | −0.927965 | −0.463983 | − | 0.885844i | \(-0.653580\pi\) | ||||
−0.463983 | + | 0.885844i | \(0.653580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.41202 | 0.387563 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5782 | 1.75113 | 0.875564 | − | 0.483103i | \(-0.160490\pi\) | ||||
0.875564 | + | 0.483103i | \(0.160490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.1065 | −1.56709 | −0.783543 | − | 0.621338i | \(-0.786590\pi\) | ||||
−0.783543 | + | 0.621338i | \(0.786590\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.63081 | 0.185563 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.4168 | 1.85410 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.90472 | −0.552090 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.7919 | −1.16712 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.45727 | 0.169973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9156 | 1.30221 | 0.651103 | − | 0.758989i | \(-0.274307\pi\) | ||||
0.651103 | + | 0.758989i | \(0.274307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.11612 | 0.419070 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.17559 | 0.557570 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.9874 | 1.56049 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.26761 | 0.0856571 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4331 | 1.50902 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.30269 | −0.622954 | −0.311477 | − | 0.950254i | \(-0.600824\pi\) | ||||
−0.311477 | + | 0.950254i | \(0.600824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.28621 | −0.219080 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.5996 | −0.703521 | −0.351760 | − | 0.936090i | \(-0.614417\pi\) | ||||
−0.351760 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.5095 | 0.694484 | 0.347242 | − | 0.937775i | \(-0.387118\pi\) | ||||
0.347242 | + | 0.937775i | \(0.387118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.477758 | 0.0314342 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1138 | 0.990138 | 0.495069 | − | 0.868854i | \(-0.335143\pi\) | ||||
0.495069 | + | 0.868854i | \(0.335143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.8316 | −1.61983 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.24194 | 0.470415 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.41488 | 0.608998 | 0.304499 | − | 0.952513i | \(-0.401511\pi\) | ||||
0.304499 | + | 0.952513i | \(0.401511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.2390 | 1.62578 | 0.812892 | − | 0.582414i | \(-0.197892\pi\) | ||||
0.812892 | + | 0.582414i | \(0.197892\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0345 | −0.707866 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.19529 | 0.523578 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 35.9506 | 2.28748 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.84374 | −0.370332 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.1843 | 1.27402 | 0.637012 | − | 0.770854i | \(-0.280170\pi\) | ||||
0.637012 | + | 0.770854i | \(0.280170\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.99352 | −0.125332 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.13568 | 0.321609 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7762 | −0.921711 | −0.460856 | − | 0.887475i | \(-0.652457\pi\) | ||||
−0.460856 | + | 0.887475i | \(0.652457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.9255 | −1.11384 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −23.0436 | −1.42637 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.3298 | −1.37692 | −0.688458 | − | 0.725276i | \(-0.741712\pi\) | ||||
−0.688458 | + | 0.725276i | \(0.741712\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.30859 | −0.387534 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.95767 | −0.181007 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.74236 | 0.167205 | 0.0836023 | − | 0.996499i | \(-0.473357\pi\) | ||||
0.0836023 | + | 0.996499i | \(0.473357\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3192 | −1.29505 | −0.647525 | − | 0.762044i | \(-0.724196\pi\) | ||||
−0.647525 | + | 0.762044i | \(0.724196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.98973 | 0.423037 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.390136 | −0.0235261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.644053 | −0.0386974 | −0.0193487 | − | 0.999813i | \(-0.506159\pi\) | ||||
−0.0193487 | + | 0.999813i | \(0.506159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.0521 | −1.20049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.38031 | −0.440272 | −0.220136 | − | 0.975469i | \(-0.570650\pi\) | ||||
−0.220136 | + | 0.975469i | \(0.570650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.22725 | −0.429615 | −0.214808 | − | 0.976656i | \(-0.568912\pi\) | ||||
−0.214808 | + | 0.976656i | \(0.568912\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.23027 | 0.487519 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.2091 | −0.602624 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.28771 | 0.252218 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.73809 | −0.336373 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.9084 | −1.92253 | −0.961265 | − | 0.275626i | \(-0.911115\pi\) | ||||
−0.961265 | + | 0.275626i | \(0.911115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.1713 | −0.766862 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.863383 | −0.0500986 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.1658 | −1.68670 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5589 | 0.608606 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.11058 | 0.408492 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.2582 | 1.21724 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.389674 | 0.0222398 | 0.0111199 | − | 0.999938i | \(-0.496460\pi\) | ||||
0.0111199 | + | 0.999938i | \(0.496460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.12188 | 0.177598 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.0938662 | 0.00532267 | 0.00266133 | − | 0.999996i | \(-0.499153\pi\) | ||||
0.00266133 | + | 0.999996i | \(0.499153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.20154 | 0.520102 | 0.260051 | − | 0.965595i | \(-0.416261\pi\) | ||||
0.260051 | + | 0.965595i | \(0.416261\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −22.3211 | −1.25765 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.962046 | 0.0540339 | 0.0270170 | − | 0.999635i | \(-0.491399\pi\) | ||||
0.0270170 | + | 0.999635i | \(0.491399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73572 | −0.153171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.03352 | 0.504202 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 34.1150 | 1.89821 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.70779 | −0.316611 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.89700 | −0.104905 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −32.0705 | −1.76810 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.2189 | −1.77091 | −0.885455 | − | 0.464725i | \(-0.846153\pi\) | ||||
−0.885455 | + | 0.464725i | \(0.846153\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.6366 | 0.856880 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.5921 | −0.797250 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5432 | −1.55485 | −0.777425 | − | 0.628976i | \(-0.783474\pi\) | ||||
−0.777425 | + | 0.628976i | \(0.783474\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.14179 | 0.333576 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.38058 | −0.128915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.8792 | −0.641419 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.67701 | −0.359478 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.10425 | −0.381376 | −0.190688 | − | 0.981651i | \(-0.561072\pi\) | ||||
−0.190688 | + | 0.981651i | \(0.561072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.2532 | −1.08413 | −0.542065 | − | 0.840336i | \(-0.682358\pi\) | ||||
−0.542065 | + | 0.840336i | \(0.682358\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.6315 | −0.674220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3628 | 0.924130 | 0.462065 | − | 0.886846i | \(-0.347109\pi\) | ||||
0.462065 | + | 0.886846i | \(0.347109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.9238 | −1.80049 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.63283 | 0.351047 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.05041 | −0.108217 | −0.0541083 | − | 0.998535i | \(-0.517232\pi\) | ||||
−0.0541083 | + | 0.998535i | \(0.517232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.6714 | 1.87744 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.87824 | 0.256041 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.03094 | −0.368016 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.16599 | −0.321862 | −0.160931 | − | 0.986966i | \(-0.551450\pi\) | ||||
−0.160931 | + | 0.986966i | \(0.551450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.90550 | 0.463602 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.14767 | −0.423006 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.30418 | 0.171084 | 0.0855419 | − | 0.996335i | \(-0.472738\pi\) | ||||
0.0855419 | + | 0.996335i | \(0.472738\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.25879 | 0.219923 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −40.0244 | −2.06136 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.91790 | 0.509448 | 0.254724 | − | 0.967014i | \(-0.418015\pi\) | ||||
0.254724 | + | 0.967014i | \(0.418015\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.84726 | −0.145869 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.6968 | 1.36414 | 0.682072 | − | 0.731285i | \(-0.261079\pi\) | ||||
0.682072 | + | 0.731285i | \(0.261079\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.64994 | −0.135053 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.21065 | −0.468204 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5226 | 1.09124 | 0.545620 | − | 0.838033i | \(-0.316294\pi\) | ||||
0.545620 | + | 0.838033i | \(0.316294\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.6766 | −1.39967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.45109 | 0.174085 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −40.1682 | −2.02108 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.5816 | −1.33409 | −0.667047 | − | 0.745016i | \(-0.732442\pi\) | ||||
−0.667047 | + | 0.745016i | \(0.732442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.6295 | 0.532143 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5167 | 1.57387 | 0.786934 | − | 0.617037i | \(-0.211667\pi\) | ||||
0.786934 | + | 0.617037i | \(0.211667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.8284 | −1.73493 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.9750 | 0.893183 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85637 | 0.0920166 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7098 | −0.776797 | −0.388399 | − | 0.921491i | \(-0.626972\pi\) | ||||
−0.388399 | + | 0.921491i | \(0.626972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.35558 | 0.165518 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0110 | −0.837055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.4130 | 1.59109 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.79422 | −0.136834 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.7265 | −0.719436 | −0.359718 | − | 0.933061i | \(-0.617127\pi\) | ||||
−0.359718 | + | 0.933061i | \(0.617127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.5655 | 0.904828 | 0.452414 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452414 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.9754 | 1.36021 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.41635 | −0.262732 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.4554 | 1.32866 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.723856 | −0.0349481 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.88531 | 0.427990 | 0.213995 | − | 0.976835i | \(-0.431352\pi\) | ||||
0.213995 | + | 0.976835i | \(0.431352\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.3929 | 1.17225 | 0.586123 | − | 0.810222i | \(-0.300653\pi\) | ||||
0.586123 | + | 0.810222i | \(0.300653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.16289 | −0.439327 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −44.3535 | −2.12172 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7205 | 1.13212 | 0.566058 | − | 0.824365i | \(-0.308468\pi\) | ||||
0.566058 | + | 0.824365i | \(0.308468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.23285 | −0.439660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.9712 | 1.70904 | 0.854521 | − | 0.519417i | \(-0.173851\pi\) | ||||
0.854521 | + | 0.519417i | \(0.173851\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.4051 | 0.777675 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.44897 | −0.115832 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.95175 | 0.422459 | 0.211230 | − | 0.977436i | \(-0.432253\pi\) | ||||
0.211230 | + | 0.977436i | \(0.432253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.05725 | 0.0497841 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.57233 | −0.120858 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −38.7693 | −1.81753 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2645 | −0.994713 | −0.497357 | − | 0.867546i | \(-0.665696\pi\) | ||||
−0.497357 | + | 0.867546i | \(0.665696\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.9866 | −0.559485 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.06005 | 0.0959462 | 0.0479731 | − | 0.998849i | \(-0.484724\pi\) | ||||
0.0479731 | + | 0.998849i | \(0.484724\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.69056 | 0.217989 | 0.108994 | − | 0.994042i | \(-0.465237\pi\) | ||||
0.108994 | + | 0.994042i | \(0.465237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.97338 | −0.369756 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.8156 | 1.56480 | 0.782401 | − | 0.622775i | \(-0.213995\pi\) | ||||
0.782401 | + | 0.622775i | \(0.213995\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.8459 | −0.870225 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.26276 | −0.104263 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.09348 | −0.0502783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.68006 | −0.398268 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.10729 | 0.325421 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.1794 | 1.69877 | 0.849385 | − | 0.527773i | \(-0.176973\pi\) | ||||
0.849385 | + | 0.527773i | \(0.176973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.1591 | 1.23835 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.62348 | −0.392382 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.8270 | 1.44519 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5261 | 0.476982 | 0.238491 | − | 0.971145i | \(-0.423347\pi\) | ||||
0.238491 | + | 0.971145i | \(0.423347\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.11248 | −0.0503079 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.4399 | 1.77990 | 0.889948 | − | 0.456062i | \(-0.150740\pi\) | ||||
0.889948 | + | 0.456062i | \(0.150740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.9807 | −1.71057 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.31157 | 0.103897 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.8132 | −1.96529 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.30276 | 0.147852 | 0.0739259 | − | 0.997264i | \(-0.476447\pi\) | ||||
0.0739259 | + | 0.997264i | \(0.476447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.12855 | 0.273804 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.7041 | 0.878564 | 0.439282 | − | 0.898349i | \(-0.355233\pi\) | ||||
0.439282 | + | 0.898349i | \(0.355233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −39.4396 | −1.75504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.76653 | −0.211689 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.71119 | −0.253144 | −0.126572 | − | 0.991957i | \(-0.540398\pi\) | ||||
−0.126572 | + | 0.991957i | \(0.540398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.08059 | −0.401702 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.2092 | −0.848109 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.3159 | −0.763028 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.32121 | 0.146067 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.29822 | −0.0569856 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3375 | −1.46054 | −0.730272 | − | 0.683157i | \(-0.760607\pi\) | ||||
−0.730272 | + | 0.683157i | \(0.760607\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.2348 | −0.928531 | −0.464266 | − | 0.885696i | \(-0.653682\pi\) | ||||
−0.464266 | + | 0.885696i | \(0.653682\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.68763 | −0.0736542 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.0501 | −1.43969 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.9829 | 0.564474 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.8388 | 0.643950 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.4679 | 0.669989 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −50.1054 | −2.16625 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.85614 | 0.123252 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.09612 | −0.0472131 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4053 | −0.877291 | −0.438646 | − | 0.898660i | \(-0.644542\pi\) | ||||
−0.438646 | + | 0.898660i | \(0.644542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.440049 | −0.0188843 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5219 | 0.450711 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.7335 | −0.458933 | −0.229466 | − | 0.973317i | \(-0.573698\pi\) | ||||
−0.229466 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.9496 | −1.02215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.8666 | −2.59300 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.8781 | −2.20608 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.21761 | 0.263923 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.1020 | 1.06361 | 0.531804 | − | 0.846868i | \(-0.321514\pi\) | ||||
0.531804 | + | 0.846868i | \(0.321514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.9979 | −0.676640 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.686896 | −0.0290008 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.1743 | −1.27169 | −0.635847 | − | 0.771815i | \(-0.719349\pi\) | ||||
−0.635847 | + | 0.771815i | \(0.719349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.0662 | −1.43317 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2150 | 0.974939 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.8452 | 1.62848 | 0.814238 | − | 0.580531i | \(-0.197155\pi\) | ||||
0.814238 | + | 0.580531i | \(0.197155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.495491 | 0.0207357 | 0.0103678 | − | 0.999946i | \(-0.496700\pi\) | ||||
0.0103678 | + | 0.999946i | \(0.496700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.80802 | 0.242634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.04191 | 0.293668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.1553 | 1.92147 | 0.960735 | − | 0.277466i | \(-0.0894946\pi\) | ||||
0.960735 | + | 0.277466i | \(0.0894946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.77515 | 0.240007 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.8620 | 1.73673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.843772 | 0.0349455 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.8188 | 1.39824 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3829 | 0.800018 | 0.400009 | − | 0.916511i | \(-0.369007\pi\) | ||||
0.400009 | + | 0.916511i | \(0.369007\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.9650 | −2.18238 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.0104 | −0.452908 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.7561 | 0.482764 | 0.241382 | − | 0.970430i | \(-0.422399\pi\) | ||||
0.241382 | + | 0.970430i | \(0.422399\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.7898 | −1.50823 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.90312 | 0.405308 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.54616 | 0.144892 | 0.0724461 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724461 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2053 | −0.457074 | −0.228537 | − | 0.973535i | \(-0.573394\pi\) | ||||
−0.228537 | + | 0.973535i | \(0.573394\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.4395 | 0.669468 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.0577 | −1.10005 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.5933 | −0.754681 | −0.377340 | − | 0.926075i | \(-0.623161\pi\) | ||||
−0.377340 | + | 0.926075i | \(0.623161\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.8341 | −0.479540 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.5902 | 1.96575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8757 | 1.73173 | 0.865866 | − | 0.500276i | \(-0.166768\pi\) | ||||
0.865866 | + | 0.500276i | \(0.166768\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.54111 | 0.142791 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.797878 | −0.0321214 | −0.0160607 | − | 0.999871i | \(-0.505112\pi\) | ||||
−0.0160607 | + | 0.999871i | \(0.505112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.2811 | −0.734780 | −0.367390 | − | 0.930067i | \(-0.619749\pi\) | ||||
−0.367390 | + | 0.930067i | \(0.619749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.5840 | 0.625363 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.1875 | 0.848857 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.4915 | −1.17966 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.10080 | −0.0439615 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.7724 | 1.02761 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.7225 | −1.78037 | −0.890187 | − | 0.455596i | \(-0.849426\pi\) | ||||
−0.890187 | + | 0.455596i | \(0.849426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.47372 | −0.336800 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.7926 | 0.626711 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0365 | −0.635388 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.2187 | 1.51191 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4267 | −0.727812 | −0.363906 | − | 0.931436i | \(-0.618557\pi\) | ||||
−0.363906 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.41011 | 0.213354 | 0.106677 | − | 0.994294i | \(-0.465979\pi\) | ||||
0.106677 | + | 0.994294i | \(0.465979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.66245 | −0.144209 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.34078 | 0.367224 | 0.183612 | − | 0.982999i | \(-0.441221\pi\) | ||||
0.183612 | + | 0.982999i | \(0.441221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.76165 | 0.0691510 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.2978 | −0.403601 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.12144 | 0.278683 | 0.139342 | − | 0.990244i | \(-0.455501\pi\) | ||||
0.139342 | + | 0.990244i | \(0.455501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.1419 | −0.747935 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.92109 | 0.309031 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.3122 | −1.10289 | −0.551443 | − | 0.834213i | \(-0.685922\pi\) | ||||
−0.551443 | + | 0.834213i | \(0.685922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6088 | −0.490425 | −0.245213 | − | 0.969469i | \(-0.578858\pi\) | ||||
−0.245213 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.0495 | −0.390289 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −58.9580 | −2.28629 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 49.3795 | 1.91198 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.16736 | 0.161120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.84328 | −0.109764 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.5804 | 1.06314 | 0.531572 | − | 0.847013i | \(-0.321601\pi\) | ||||
0.531572 | + | 0.847013i | \(0.321601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.04981 | 0.117387 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.4276 | 0.554496 | 0.277248 | − | 0.960798i | \(-0.410578\pi\) | ||||
0.277248 | + | 0.960798i | \(0.410578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.1052 | 1.57747 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.74835 | 0.181957 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.8825 | 1.33474 | 0.667371 | − | 0.744726i | \(-0.267420\pi\) | ||||
0.667371 | + | 0.744726i | \(0.267420\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.6121 | −0.711132 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.70796 | −0.179620 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.3446 | 0.470292 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6552 | −1.47051 | −0.735257 | − | 0.677789i | \(-0.762938\pi\) | ||||
−0.735257 | + | 0.677789i | \(0.762938\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.98544 | 0.113407 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.4985 | 0.587890 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6781 | 0.555973 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.77059 | −0.256087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.35833 | 0.126842 | 0.0634211 | − | 0.997987i | \(-0.479799\pi\) | ||||
0.0634211 | + | 0.997987i | \(0.479799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.3019 | 1.55773 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.1239 | 0.418950 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −50.9370 | −1.91568 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.7796 | −0.930618 | −0.465309 | − | 0.885148i | \(-0.654057\pi\) | ||||
−0.465309 | + | 0.885148i | \(0.654057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.2537 | 1.69715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.9691 | 1.60921 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01495 | 0.150151 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.21762 | −0.157510 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.8983 | −1.89819 | −0.949094 | − | 0.314993i | \(-0.897998\pi\) | ||||
−0.949094 | + | 0.314993i | \(0.897998\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3638 | −0.832870 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.3064 | −0.420490 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.66365 | 0.358899 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4972 | −1.35361 | −0.676804 | − | 0.736163i | \(-0.736636\pi\) | ||||
−0.676804 | + | 0.736163i | \(0.736636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.7592 | −0.620713 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.1811 | −0.561492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.8000 | 0.731331 | 0.365666 | − | 0.930746i | \(-0.380841\pi\) | ||||
0.365666 | + | 0.930746i | \(0.380841\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.67128 | −0.135417 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.95168 | 0.0718912 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2545 | −0.855430 | −0.427715 | − | 0.903914i | \(-0.640681\pi\) | ||||
−0.427715 | + | 0.903914i | \(0.640681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.1049 | −0.591629 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5523 | 0.864052 | 0.432026 | − | 0.901861i | \(-0.357799\pi\) | ||||
0.432026 | + | 0.901861i | \(0.357799\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5835 | 0.497661 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.5166 | −1.33607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −64.7121 | −2.36453 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.04206 | −0.329511 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.2677 | 0.519255 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.8167 | −0.393139 | −0.196570 | − | 0.980490i | \(-0.562980\pi\) | ||||
−0.196570 | + | 0.980490i | \(0.562980\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.893047 | 0.0324156 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.49964 | 0.308112 | 0.154056 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154056 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5893 | 0.491965 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 32.0921 | 1.16029 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.7735 | 0.930626 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8173 | 0.390082 | 0.195041 | − | 0.980795i | \(-0.437516\pi\) | ||||
0.195041 | + | 0.980795i | \(0.437516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.61934 | 0.238390 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9068 | 0.536159 | 0.268079 | − | 0.963397i | \(-0.413611\pi\) | ||||
0.268079 | + | 0.963397i | \(0.413611\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.40913 | 0.302065 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.03017 | 0.288081 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.5226 | 0.842786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.53729 | 0.162357 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.3860 | 0.764272 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.5507 | 0.447953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3524 | −1.01066 | −0.505328 | − | 0.862928i | \(-0.668628\pi\) | ||||
−0.505328 | + | 0.862928i | \(0.668628\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.0032 | 0.356123 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.9971 | −1.56436 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.5979 | −1.47719 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.82609 | 0.100231 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6015 | 0.446369 | 0.223185 | − | 0.974776i | \(-0.428355\pi\) | ||||
0.223185 | + | 0.974776i | \(0.428355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.1092 | 1.63123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.4820 | −0.653030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.940386 | 0.0331855 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 47.8311 | 1.68583 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.22851 | −0.0432455 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5487 | −0.511505 | −0.255752 | − | 0.966742i | \(-0.582323\pi\) | ||||
−0.255752 | + | 0.966742i | \(0.582323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.97636 | −0.350317 | −0.175159 | − | 0.984540i | \(-0.556044\pi\) | ||||
−0.175159 | + | 0.984540i | \(0.556044\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.55045 | 0.334949 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.17047 | 0.216142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.3287 | −0.851152 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43.6777 | 1.52622 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.6090 | −1.66157 | −0.830784 | − | 0.556596i | \(-0.812107\pi\) | ||||
−0.830784 | + | 0.556596i | \(0.812107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.5601 | 1.62298 | 0.811491 | − | 0.584365i | \(-0.198656\pi\) | ||||
0.811491 | + | 0.584365i | \(0.198656\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.174771 | 0.00608474 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8537 | 1.10766 | 0.553831 | − | 0.832629i | \(-0.313165\pi\) | ||||
0.553831 | + | 0.832629i | \(0.313165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.9049 | 1.24703 | 0.623515 | − | 0.781811i | \(-0.285704\pi\) | ||||
0.623515 | + | 0.781811i | \(0.285704\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.288519 | 0.0100086 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.2177 | −0.527261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.9927 | −1.17637 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.6097 | 0.643244 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.7051 | −1.71601 | −0.858005 | − | 0.513641i | \(-0.828296\pi\) | ||||
−0.858005 | + | 0.513641i | \(0.828296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.7638 | 1.33668 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.30619 | 0.113871 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26.4381 | 0.909498 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.9455 | −1.20074 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.23762 | 0.111115 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.5072 | −1.14861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.6447 | 0.741100 | 0.370550 | − | 0.928812i | \(-0.379169\pi\) | ||||
0.370550 | + | 0.928812i | \(0.379169\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 51.4296 | 1.75886 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.20395 | 0.177764 | 0.0888818 | − | 0.996042i | \(-0.471671\pi\) | ||||
0.0888818 | + | 0.996042i | \(0.471671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.2358 | 1.64578 | 0.822891 | − | 0.568199i | \(-0.192360\pi\) | ||||
0.822891 | + | 0.568199i | \(0.192360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.57341 | 0.155861 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.2075 | 0.381507 | 0.190754 | − | 0.981638i | \(-0.438907\pi\) | ||||
0.190754 | + | 0.981638i | \(0.438907\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.20073 | 0.244832 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.92078 | −0.0652333 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.37249 | 0.182249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.5536 | 0.967503 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.8564 | −1.21356 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.5081 | −1.03136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.0904 | −0.881012 | −0.440506 | − | 0.897750i | \(-0.645201\pi\) | ||||
−0.440506 | + | 0.897750i | \(0.645201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.7421 | 0.497239 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.32074 | −0.314024 | −0.157012 | − | 0.987597i | \(-0.550186\pi\) | ||||
−0.157012 | + | 0.987597i | \(0.550186\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.1390 | 0.980605 | 0.490303 | − | 0.871552i | \(-0.336886\pi\) | ||||
0.490303 | + | 0.871552i | \(0.336886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.90039 | 0.198340 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.43141 | −0.283099 | −0.141550 | − | 0.989931i | \(-0.545208\pi\) | ||||
−0.141550 | + | 0.989931i | \(0.545208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.3965 | 0.684076 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.40415 | −0.0805419 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 73.8931 | 2.47274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.8419 | −0.529537 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.0655 | 0.436245 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 58.9668 | 1.96665 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.7143 | 0.390260 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.73013 | −0.157409 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.44078 | 0.0811343 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.4252 | 0.711411 | 0.355706 | − | 0.934598i | \(-0.384241\pi\) | ||||
0.355706 | + | 0.934598i | \(0.384241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.4329 | 1.47375 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.5613 | −0.349913 | −0.174956 | − | 0.984576i | \(-0.555978\pi\) | ||||
−0.174956 | + | 0.984576i | \(0.555978\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.33522 | −0.143475 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.52314 | −0.314825 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.7221 | −0.816396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.1784 | −0.962506 | −0.481253 | − | 0.876582i | \(-0.659818\pi\) | ||||
−0.481253 | + | 0.876582i | \(0.659818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.174564 | −0.00575207 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 66.3817 | 2.18498 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.55741 | −0.215606 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.5081 | 0.640731 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.0488 | −1.87171 | −0.935855 | − | 0.352386i | \(-0.885371\pi\) | ||||
−0.935855 | + | 0.352386i | \(0.885371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3873 | −0.799262 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.0420496 | −0.00137664 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.80995 | 0.124599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.79456 | 0.254637 | 0.127319 | − | 0.991862i | \(-0.459363\pi\) | ||||
0.127319 | + | 0.991862i | \(0.459363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.12205 | −0.134518 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.8670 | 1.49522 | 0.747611 | − | 0.664137i | \(-0.231201\pi\) | ||||
0.747611 | + | 0.664137i | \(0.231201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0833 | −0.621438 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.7154 | 0.673871 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.76210 | −0.219739 | −0.109869 | − | 0.993946i | \(-0.535043\pi\) | ||||
−0.109869 | + | 0.993946i | \(0.535043\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.7581 | 0.446606 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.430972 | −0.0139752 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.4991 | 0.566852 | 0.283426 | − | 0.958994i | \(-0.408529\pi\) | ||||
0.283426 | + | 0.958994i | \(0.408529\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.2149 | −1.04245 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.22553 | 0.0396159 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.0379 | −0.776223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.3118 | 0.655218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 56.4490 | 1.81904 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.0325 | −1.03116 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2725 | 0.491129 | 0.245565 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245565 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.2826 | −0.490948 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.8574 | 1.53582 | 0.767909 | − | 0.640560i | \(-0.221298\pi\) | ||||
0.767909 | + | 0.640560i | \(0.221298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0166 | 0.641702 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.55694 | 0.0818877 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.7857 | −1.49681 | −0.748403 | − | 0.663244i | \(-0.769179\pi\) | ||||
−0.748403 | + | 0.663244i | \(0.769179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.19417 | −0.0701260 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.8541 | −0.378471 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.2822 | −0.455530 | −0.227765 | − | 0.973716i | \(-0.573142\pi\) | ||||
−0.227765 | + | 0.973716i | \(0.573142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 61.0705 | 1.94587 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.3667 | 0.457298 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7372 | 0.627607 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.3109 | −1.02639 | −0.513195 | − | 0.858272i | \(-0.671538\pi\) | ||||
−0.513195 | + | 0.858272i | \(0.671538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.4332 | 0.458025 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.9288 | −1.74136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −56.2135 | −1.78030 | −0.890150 | − | 0.455669i | \(-0.849400\pi\) | ||||
−0.890150 | + | 0.455669i | \(0.849400\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.5118 | −0.459131 |
(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 | 6008.2.a.b.1.22 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.22 | ✓ | 44 | 1.1 | even | 1 | trivial |