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: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.29 | ||
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 | ||||||||
\(3\) | 0.416230 | 0.240311 | 0.120155 | − | 0.992755i | \(-0.461661\pi\) | ||||
0.120155 | + | 0.992755i | \(0.461661\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.95581 | 1.76909 | 0.884545 | − | 0.466455i | \(-0.154469\pi\) | ||||
0.884545 | + | 0.466455i | \(0.154469\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.52758 | 0.955337 | 0.477669 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477669 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82675 | −0.942251 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.42008 | 1.03119 | 0.515596 | − | 0.856832i | \(-0.327570\pi\) | ||||
0.515596 | + | 0.856832i | \(0.327570\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.31267 | −0.918771 | −0.459385 | − | 0.888237i | \(-0.651930\pi\) | ||||
−0.459385 | + | 0.888237i | \(0.651930\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.64653 | 0.425131 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.23883 | −1.75567 | −0.877837 | − | 0.478959i | \(-0.841014\pi\) | ||||
−0.877837 | + | 0.478959i | \(0.841014\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.52109 | 1.03721 | 0.518604 | − | 0.855014i | \(-0.326452\pi\) | ||||
0.518604 | + | 0.855014i | \(0.326452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05206 | 0.229578 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.20387 | 1.50211 | 0.751055 | − | 0.660240i | \(-0.229545\pi\) | ||||
0.751055 | + | 0.660240i | \(0.229545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.6484 | 2.12968 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.42527 | −0.466744 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.29186 | 1.35406 | 0.677032 | − | 0.735953i | \(-0.263266\pi\) | ||||
0.677032 | + | 0.735953i | \(0.263266\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.45184 | −0.799573 | −0.399787 | − | 0.916608i | \(-0.630916\pi\) | ||||
−0.399787 | + | 0.916608i | \(0.630916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42354 | 0.247807 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.99863 | 1.69008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.53567 | −1.07446 | −0.537229 | − | 0.843436i | \(-0.680529\pi\) | ||||
−0.537229 | + | 0.843436i | \(0.680529\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.37884 | −0.220790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.03924 | 0.630823 | 0.315412 | − | 0.948955i | \(-0.397857\pi\) | ||||
0.315412 | + | 0.948955i | \(0.397857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.48256 | −1.44608 | −0.723038 | − | 0.690808i | \(-0.757255\pi\) | ||||
−0.723038 | + | 0.690808i | \(0.757255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.1821 | −1.66693 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.0683152 | −0.00996480 | −0.00498240 | − | 0.999988i | \(-0.501586\pi\) | ||||
−0.00498240 | + | 0.999988i | \(0.501586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.611316 | −0.0873308 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.01302 | −0.421907 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.07518 | 1.24657 | 0.623286 | − | 0.781994i | \(-0.285797\pi\) | ||||
0.623286 | + | 0.781994i | \(0.285797\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.5292 | 1.82427 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.88181 | 0.249252 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.40101 | 1.09372 | 0.546859 | − | 0.837225i | \(-0.315823\pi\) | ||||
0.546859 | + | 0.837225i | \(0.315823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.48581 | 0.446312 | 0.223156 | − | 0.974783i | \(-0.428364\pi\) | ||||
0.223156 | + | 0.974783i | \(0.428364\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.14486 | −0.900167 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.1043 | −1.62539 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.25056 | 0.885797 | 0.442899 | − | 0.896572i | \(-0.353950\pi\) | ||||
0.442899 | + | 0.896572i | \(0.353950\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.99847 | 0.360973 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.26703 | 0.387725 | 0.193862 | − | 0.981029i | \(-0.437898\pi\) | ||||
0.193862 | + | 0.981029i | \(0.437898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2983 | 1.32236 | 0.661182 | − | 0.750225i | \(-0.270055\pi\) | ||||
0.661182 | + | 0.750225i | \(0.270055\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.43219 | 0.511785 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.64454 | 0.985137 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5574 | 1.18780 | 0.593899 | − | 0.804540i | \(-0.297588\pi\) | ||||
0.593899 | + | 0.804540i | \(0.297588\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.47078 | 0.830087 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.52092 | 0.166942 | 0.0834712 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834712 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.6354 | −3.10595 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.03510 | 0.325396 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.80313 | −0.933130 | −0.466565 | − | 0.884487i | \(-0.654509\pi\) | ||||
−0.466565 | + | 0.884487i | \(0.654509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.37306 | −0.877736 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.85299 | −0.192146 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.8845 | 1.83492 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.44088 | −0.247833 | −0.123917 | − | 0.992293i | \(-0.539546\pi\) | ||||
−0.123917 | + | 0.992293i | \(0.539546\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.66772 | −0.971642 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.56249 | 0.951503 | 0.475752 | − | 0.879580i | \(-0.342176\pi\) | ||||
0.475752 | + | 0.879580i | \(0.342176\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1103 | −1.78446 | −0.892232 | − | 0.451578i | \(-0.850861\pi\) | ||||
−0.892232 | + | 0.451578i | \(0.850861\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.16174 | 0.406144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.61886 | 0.833217 | 0.416608 | − | 0.909086i | \(-0.363219\pi\) | ||||
0.416608 | + | 0.909086i | \(0.363219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.48252 | 0.716695 | 0.358348 | − | 0.933588i | \(-0.383340\pi\) | ||||
0.358348 | + | 0.933588i | \(0.383340\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.72035 | −0.258204 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.0448 | 1.88565 | 0.942826 | − | 0.333284i | \(-0.108157\pi\) | ||||
0.942826 | + | 0.333284i | \(0.108157\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.4971 | 2.65737 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.36411 | 0.865712 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.2968 | −1.67726 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.696945 | 0.0633587 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.68125 | 0.151594 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.3440 | 1.99851 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1367 | 1.78685 | 0.893423 | − | 0.449217i | \(-0.148297\pi\) | ||||
0.893423 | + | 0.449217i | \(0.148297\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.94693 | −0.347508 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.66923 | −0.320582 | −0.160291 | − | 0.987070i | \(-0.551243\pi\) | ||||
−0.160291 | + | 0.987070i | \(0.551243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4274 | 0.990884 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.59390 | −0.825712 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6612 | 0.996285 | 0.498143 | − | 0.867095i | \(-0.334016\pi\) | ||||
0.498143 | + | 0.867095i | \(0.334016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.78719 | 0.406045 | 0.203022 | − | 0.979174i | \(-0.434924\pi\) | ||||
0.203022 | + | 0.979174i | \(0.434924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0284349 | −0.00239465 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.3296 | −0.947430 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.8452 | 2.39546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.254448 | −0.0209865 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.28138 | −0.186898 | −0.0934492 | − | 0.995624i | \(-0.529789\pi\) | ||||
−0.0934492 | + | 0.995624i | \(0.529789\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6729 | −1.03130 | −0.515651 | − | 0.856799i | \(-0.672450\pi\) | ||||
−0.515651 | + | 0.856799i | \(0.672450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.4624 | 1.65429 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.6106 | −1.41452 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.94428 | 0.234979 | 0.117489 | − | 0.993074i | \(-0.462515\pi\) | ||||
0.117489 | + | 0.993074i | \(0.462515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.77737 | 0.299565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.2084 | 1.43502 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7301 | −0.918773 | −0.459387 | − | 0.888236i | \(-0.651931\pi\) | ||||
−0.459387 | + | 0.888236i | \(0.651931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.63125 | 0.438392 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.66363 | 0.283500 | 0.141750 | − | 0.989902i | \(-0.454727\pi\) | ||||
0.141750 | + | 0.989902i | \(0.454727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.02619 | −0.155861 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.7800 | −0.977310 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.7203 | −1.49930 | −0.749652 | − | 0.661832i | \(-0.769779\pi\) | ||||
−0.749652 | + | 0.661832i | \(0.769779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.9147 | 2.03456 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.49676 | 0.262832 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.3864 | −1.59850 | −0.799248 | − | 0.601002i | \(-0.794768\pi\) | ||||
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.5412 | −1.52681 | −0.763406 | − | 0.645919i | \(-0.776475\pi\) | ||||
−0.763406 | + | 0.645919i | \(0.776475\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.45090 | 0.107254 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.8538 | −1.90081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.7574 | −1.81044 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.13008 | −0.445898 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.33691 | −0.458523 | −0.229261 | − | 0.973365i | \(-0.573631\pi\) | ||||
−0.229261 | + | 0.973365i | \(0.573631\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00200 | −0.144107 | −0.0720536 | − | 0.997401i | \(-0.522955\pi\) | ||||
−0.0720536 | + | 0.997401i | \(0.522955\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.45441 | −0.390598 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.57793 | −0.611152 | −0.305576 | − | 0.952168i | \(-0.598849\pi\) | ||||
−0.305576 | + | 0.952168i | \(0.598849\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4115 | −0.808942 | −0.404471 | − | 0.914551i | \(-0.632544\pi\) | ||||
−0.404471 | + | 0.914551i | \(0.632544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.01790 | 0.212867 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4308 | 1.29359 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.9784 | 1.11598 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.3635 | −1.41536 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.4625 | 1.06956 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.1333 | −1.79909 | −0.899544 | − | 0.436831i | \(-0.856101\pi\) | ||||
−0.899544 | + | 0.436831i | \(0.856101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35984 | 0.0931744 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −37.5112 | −2.55824 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2524 | −0.763862 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.70269 | 0.317778 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.9799 | 1.61306 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3328 | 1.16069 | 0.580346 | − | 0.814370i | \(-0.302917\pi\) | ||||
0.580346 | + | 0.814370i | \(0.302917\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −30.1004 | −2.00669 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.144305 | −0.00957789 | −0.00478894 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478894 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5673 | −0.962637 | −0.481319 | − | 0.876546i | \(-0.659842\pi\) | ||||
−0.481319 | + | 0.876546i | \(0.659842\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.59812 | 0.236739 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.4715 | 1.21011 | 0.605055 | − | 0.796184i | \(-0.293151\pi\) | ||||
0.605055 | + | 0.796184i | \(0.293151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.270242 | −0.0176286 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.39430 | 0.285440 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.6859 | −1.59680 | −0.798400 | − | 0.602127i | \(-0.794320\pi\) | ||||
−0.798400 | + | 0.602127i | \(0.794320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.94882 | 0.254366 | 0.127183 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127183 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.3854 | 0.666223 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.41825 | −0.154496 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9769 | −0.952957 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.633052 | 0.0401180 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.4129 | −0.657259 | −0.328629 | − | 0.944459i | \(-0.606587\pi\) | ||||
−0.328629 | + | 0.944459i | \(0.606587\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.6378 | 1.54897 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.9189 | −0.746392 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.99666 | −0.124548 | −0.0622740 | − | 0.998059i | \(-0.519835\pi\) | ||||
−0.0622740 | + | 0.998059i | \(0.519835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.5195 | −1.02647 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.6123 | −1.27587 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.62185 | −0.284996 | −0.142498 | − | 0.989795i | \(-0.545513\pi\) | ||||
−0.142498 | + | 0.989795i | \(0.545513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.8997 | 2.20530 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.66413 | −0.224241 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.2497 | 0.868822 | 0.434411 | − | 0.900715i | \(-0.356957\pi\) | ||||
0.434411 | + | 0.900715i | \(0.356957\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.6060 | −1.31247 | −0.656235 | − | 0.754557i | \(-0.727852\pi\) | ||||
−0.656235 | + | 0.754557i | \(0.727852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.48512 | −0.210929 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 36.4184 | 2.19611 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.3677 | −0.863273 | −0.431637 | − | 0.902048i | \(-0.642064\pi\) | ||||
−0.431637 | + | 0.902048i | \(0.642064\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.5842 | 0.753398 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.43523 | 0.204929 | 0.102464 | − | 0.994737i | \(-0.467327\pi\) | ||||
0.102464 | + | 0.994737i | \(0.467327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.31349 | 0.196966 | 0.0984832 | − | 0.995139i | \(-0.468601\pi\) | ||||
0.0984832 | + | 0.995139i | \(0.468601\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.44409 | 0.440950 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.2095 | 0.602649 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.4007 | 2.08239 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.01597 | −0.0595570 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.90794 | 0.461987 | 0.230993 | − | 0.972955i | \(-0.425802\pi\) | ||||
0.230993 | + | 0.972955i | \(0.425802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.2328 | 1.93489 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.29462 | −0.481303 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8641 | −1.38009 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.9680 | −1.38149 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.98020 | 0.228656 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.7892 | 0.789566 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.4809 | 0.598175 | 0.299087 | − | 0.954226i | \(-0.403318\pi\) | ||||
0.299087 | + | 0.954226i | \(0.403318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.53807 | −0.428826 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.32281 | −0.245124 | −0.122562 | − | 0.992461i | \(-0.539111\pi\) | ||||
−0.122562 | + | 0.992461i | \(0.539111\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4570 | 0.930205 | 0.465103 | − | 0.885257i | \(-0.346017\pi\) | ||||
0.465103 | + | 0.885257i | \(0.346017\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.2637 | −1.59248 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.1651 | −1.35725 | −0.678623 | − | 0.734487i | \(-0.737423\pi\) | ||||
−0.678623 | + | 0.734487i | \(0.737423\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.9388 | 1.39630 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.58743 | 0.200231 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.7274 | −1.82100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −35.2747 | −1.95669 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.11445 | 0.172230 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.172672 | −0.00951974 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1035 | 0.720234 | 0.360117 | − | 0.932907i | \(-0.382737\pi\) | ||||
0.360117 | + | 0.932907i | \(0.382737\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 18.4747 | 1.01241 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.6818 | 1.56705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.16212 | 0.390146 | 0.195073 | − | 0.980789i | \(-0.437506\pi\) | ||||
0.195073 | + | 0.980789i | \(0.437506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.34324 | 0.453143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.2256 | −0.824514 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2382 | −1.03877 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8614 | 0.638594 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.74633 | −0.147431 | −0.0737154 | − | 0.997279i | \(-0.523486\pi\) | ||||
−0.0737154 | + | 0.997279i | \(0.523486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7346 | −1.16343 | −0.581715 | − | 0.813393i | \(-0.697618\pi\) | ||||
−0.581715 | + | 0.813393i | \(0.697618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.03414 | 0.428830 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.7124 | 1.74110 | 0.870551 | − | 0.492078i | \(-0.163762\pi\) | ||||
0.870551 | + | 0.492078i | \(0.163762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.9237 | 0.685920 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.61567 | −0.403064 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6087 | 0.876573 | 0.438287 | − | 0.898835i | \(-0.355585\pi\) | ||||
0.438287 | + | 0.898835i | \(0.355585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44023 | 0.0758015 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.290090 | 0.0152258 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.6938 | 2.33938 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.70718 | −0.193513 | −0.0967566 | − | 0.995308i | \(-0.530847\pi\) | ||||
−0.0967566 | + | 0.995308i | \(0.530847\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4179 | −0.594394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.9383 | 1.19090 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.39864 | −0.279531 | −0.139765 | − | 0.990185i | \(-0.544635\pi\) | ||||
−0.139765 | + | 0.990185i | \(0.544635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.30024 | 0.480262 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.1556 | −1.24407 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.09265 | −0.261592 | −0.130796 | − | 0.991409i | \(-0.541753\pi\) | ||||
−0.130796 | + | 0.991409i | \(0.541753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.38152 | 0.429398 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.8186 | 1.67695 | 0.838476 | − | 0.544938i | \(-0.183447\pi\) | ||||
0.838476 | + | 0.544938i | \(0.183447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.1961 | 1.74280 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.8048 | 1.36257 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.8011 | −1.81519 | −0.907594 | − | 0.419849i | \(-0.862083\pi\) | ||||
−0.907594 | + | 0.419849i | \(0.862083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.1476 | −2.63722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.52725 | −0.0770394 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.7629 | 2.10132 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.2770 | 1.67012 | 0.835061 | − | 0.550157i | \(-0.185432\pi\) | ||||
0.835061 | + | 0.550157i | \(0.185432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.75644 | 0.238120 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.2385 | −1.06060 | −0.530299 | − | 0.847811i | \(-0.677920\pi\) | ||||
−0.530299 | + | 0.847811i | \(0.677920\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.7475 | 0.734624 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.5530 | 1.46850 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.3525 | −1.10797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.5580 | 0.719849 | 0.359924 | − | 0.932981i | \(-0.382802\pi\) | ||||
0.359924 | + | 0.932981i | \(0.382802\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.85376 | 0.239418 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.2343 | 1.04487 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.01645 | 0.295336 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.99258 | 0.0975769 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.7092 | 1.30483 | 0.652416 | − | 0.757861i | \(-0.273756\pi\) | ||||
0.652416 | + | 0.757861i | \(0.273756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3395 | −1.33245 | −0.666223 | − | 0.745752i | \(-0.732090\pi\) | ||||
−0.666223 | + | 0.745752i | \(0.732090\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.193110 | 0.00938934 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −77.0820 | −3.73902 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.81067 | 0.426378 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.71573 | −0.227678 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.8344 | −1.24440 | −0.622199 | − | 0.782859i | \(-0.713761\pi\) | ||||
−0.622199 | + | 0.782859i | \(0.713761\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.10488 | 0.197268 | 0.0986340 | − | 0.995124i | \(-0.468553\pi\) | ||||
0.0986340 | + | 0.995124i | \(0.468553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0062 | 0.575656 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.5693 | 1.55800 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.5009 | −1.36027 | −0.680137 | − | 0.733085i | \(-0.738080\pi\) | ||||
−0.680137 | + | 0.733085i | \(0.738080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.72804 | 0.0822876 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.09069 | −0.0993316 | −0.0496658 | − | 0.998766i | \(-0.515816\pi\) | ||||
−0.0496658 | + | 0.998766i | \(0.515816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.8235 | −1.65079 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.949582 | −0.0449137 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.2633 | −0.956285 | −0.478143 | − | 0.878282i | \(-0.658690\pi\) | ||||
−0.478143 | + | 0.878282i | \(0.658690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.8145 | 0.650500 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.27483 | −0.247833 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.1222 | −1.55279 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.3056 | −0.715968 | −0.357984 | − | 0.933728i | \(-0.616536\pi\) | ||||
−0.357984 | + | 0.933728i | \(0.616536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.5561 | 0.819450 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.0225 | 1.67773 | 0.838867 | − | 0.544336i | \(-0.183218\pi\) | ||||
0.838867 | + | 0.544336i | \(0.183218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9678 | −1.06740 | −0.533702 | − | 0.845673i | \(-0.679200\pi\) | ||||
−0.533702 | + | 0.845673i | \(0.679200\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.33007 | −0.339924 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.03068 | 0.0476941 | 0.0238471 | − | 0.999716i | \(-0.492409\pi\) | ||||
0.0238471 | + | 0.999716i | \(0.492409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3264 | 0.846235 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.22550 | 0.0564679 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.4311 | −1.49118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.1423 | 2.20892 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.6533 | −1.17458 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.6486 | 1.72021 | 0.860103 | − | 0.510120i | \(-0.170399\pi\) | ||||
0.860103 | + | 0.510120i | \(0.170399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.6506 | 0.987180 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.57888 | 0.344851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.65563 | −0.438439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.2919 | 1.19140 | 0.595700 | − | 0.803207i | \(-0.296875\pi\) | ||||
0.595700 | + | 0.803207i | \(0.296875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.88243 | −0.220791 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.92374 | −0.131947 | −0.0659733 | − | 0.997821i | \(-0.521015\pi\) | ||||
−0.0659733 | + | 0.997821i | \(0.521015\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −52.7846 | −2.37730 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −38.2436 | −1.71892 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.25769 | 0.370408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.40783 | 0.242088 | 0.121044 | − | 0.992647i | \(-0.461376\pi\) | ||||
0.121044 | + | 0.992647i | \(0.461376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52491 | 0.0681282 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.6924 | 0.610513 | 0.305257 | − | 0.952270i | \(-0.401258\pi\) | ||||
0.305257 | + | 0.952270i | \(0.401258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.8273 | 1.68329 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.843362 | −0.0374550 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.1325 | 1.69020 | 0.845098 | − | 0.534612i | \(-0.179542\pi\) | ||||
0.845098 | + | 0.534612i | \(0.179542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.5574 | 1.26330 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.9649 | −0.484111 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −71.6409 | −3.15688 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.233643 | −0.0102756 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.20818 | −0.360299 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.2455 | −0.930781 | −0.465390 | − | 0.885105i | \(-0.654086\pi\) | ||||
−0.465390 | + | 0.885105i | \(0.654086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.96494 | 0.129648 | 0.0648238 | − | 0.997897i | \(-0.479351\pi\) | ||||
0.0648238 | + | 0.997897i | \(0.479351\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.2027 | 0.488927 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.2261 | 1.40379 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.8957 | 1.25633 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.7476 | −1.03056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.3807 | −0.579582 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.0945 | 1.47404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.90167 | −0.384136 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.09075 | −0.0900549 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.64629 | −0.0707795 | −0.0353898 | − | 0.999374i | \(-0.511267\pi\) | ||||
−0.0353898 | + | 0.999374i | \(0.511267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.54986 | −0.366910 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.5994 | 1.26790 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.8332 | −0.976279 | −0.488139 | − | 0.872766i | \(-0.662324\pi\) | ||||
−0.488139 | + | 0.872766i | \(0.662324\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.85351 | −0.420537 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.9671 | 1.40445 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.6847 | 1.13475 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.7612 | −0.456786 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.83084 | 0.119947 | 0.0599733 | − | 0.998200i | \(-0.480898\pi\) | ||||
0.0599733 | + | 0.998200i | \(0.480898\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.4126 | 1.32861 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3048 | −0.435068 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.2716 | −0.685766 | −0.342883 | − | 0.939378i | \(-0.611403\pi\) | ||||
−0.342883 | + | 0.939378i | \(0.611403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 79.2932 | 3.33589 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.8830 | 0.793013 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0818 | −1.13533 | −0.567664 | − | 0.823260i | \(-0.692153\pi\) | ||||
−0.567664 | + | 0.823260i | \(0.692153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.6590 | −1.28304 | −0.641520 | − | 0.767107i | \(-0.721696\pi\) | ||||
−0.641520 | + | 0.767107i | \(0.721696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.63761 | −0.110188 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 76.7097 | 3.19901 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.19730 | 0.0914749 | 0.0457374 | − | 0.998953i | \(-0.485436\pi\) | ||||
0.0457374 | + | 0.998953i | \(0.485436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.833293 | −0.0346305 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.84425 | 0.159486 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.0378 | 1.28546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 37.0426 | 1.53152 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.26846 | 0.176178 | 0.0880891 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880891 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1271 | −0.829324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.57040 | −0.146867 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2142 | −0.501578 | −0.250789 | − | 0.968042i | \(-0.580690\pi\) | ||||
−0.250789 | + | 0.968042i | \(0.580690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −72.3784 | −2.96723 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.74983 | −0.194398 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.3761 | −1.36371 | −0.681856 | − | 0.731487i | \(-0.738827\pi\) | ||||
−0.681856 | + | 0.731487i | \(0.738827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.8036 | 1.66441 | 0.832206 | − | 0.554466i | \(-0.187078\pi\) | ||||
0.832206 | + | 0.554466i | \(0.187078\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.4955 | −0.834643 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.75698 | 0.112087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.2049 | −1.18539 | −0.592695 | − | 0.805427i | \(-0.701936\pi\) | ||||
−0.592695 | + | 0.805427i | \(0.701936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.67146 | 0.310863 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.226306 | 0.00915536 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.8257 | −1.08348 | −0.541741 | − | 0.840546i | \(-0.682235\pi\) | ||||
−0.541741 | + | 0.840546i | \(0.682235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.65072 | 0.268183 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5959 | 0.547349 | 0.273675 | − | 0.961822i | \(-0.411761\pi\) | ||||
0.273675 | + | 0.961822i | \(0.411761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.7095 | −1.27451 | −0.637257 | − | 0.770651i | \(-0.719931\pi\) | ||||
−0.637257 | + | 0.770651i | \(0.719931\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.4713 | −0.701101 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.2507 | −0.891454 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 35.1464 | 1.40586 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.43595 | 0.257027 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47.3106 | 1.88640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.6540 | −1.37956 | −0.689778 | − | 0.724021i | \(-0.742292\pi\) | ||||
−0.689778 | + | 0.724021i | \(0.742292\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.8775 | −0.432340 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 79.6570 | 3.16109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.02509 | 0.0802370 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.23508 | −0.365334 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.3012 | −0.643857 | −0.321929 | − | 0.946764i | \(-0.604331\pi\) | ||||
−0.321929 | + | 0.946764i | \(0.604331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2511 | 0.404264 | 0.202132 | − | 0.979358i | \(-0.435213\pi\) | ||||
0.202132 | + | 0.979358i | \(0.435213\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.6133 | −0.614773 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.0119 | −1.10126 | −0.550630 | − | 0.834749i | \(-0.685612\pi\) | ||||
−0.550630 | + | 0.834749i | \(0.685612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.7321 | 1.12783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.68359 | −0.183564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.7086 | −1.67132 | −0.835659 | − | 0.549249i | \(-0.814914\pi\) | ||||
−0.835659 | + | 0.549249i | \(0.814914\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.5148 | −0.567139 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.9375 | −1.24600 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.5297 | −0.916586 | −0.458293 | − | 0.888801i | \(-0.651539\pi\) | ||||
−0.458293 | + | 0.888801i | \(0.651539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6562 | −1.19239 | −0.596194 | − | 0.802840i | \(-0.703321\pi\) | ||||
−0.596194 | + | 0.802840i | \(0.703321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.98116 | 0.387636 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 45.2047 | 1.75296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.5296 | 2.03395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.21445 | 0.278927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9217 | 0.460233 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.7867 | −1.68785 | −0.843926 | − | 0.536459i | \(-0.819762\pi\) | ||||
−0.843926 | + | 0.536459i | \(0.819762\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.8253 | −0.994015 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.6766 | 1.29430 | 0.647148 | − | 0.762364i | \(-0.275961\pi\) | ||||
0.647148 | + | 0.762364i | \(0.275961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.16952 | −0.236764 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.0600643 | −0.00230167 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.0664 | 0.729557 | 0.364778 | − | 0.931094i | \(-0.381145\pi\) | ||||
0.364778 | + | 0.931094i | \(0.381145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.1295 | 1.76252 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.06337 | −0.231332 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −30.0631 | −1.14531 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.3146 | 0.696722 | 0.348361 | − | 0.937361i | \(-0.386738\pi\) | ||||
0.348361 | + | 0.937361i | \(0.386738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −24.4360 | −0.928246 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.9372 | 0.718329 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29.2394 | −1.10752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.68841 | 0.290803 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.0765 | −0.682740 | −0.341370 | − | 0.939929i | \(-0.610891\pi\) | ||||
−0.341370 | + | 0.939929i | \(0.610891\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.5483 | −1.11444 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.112483 | −0.00423635 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.1700 | 0.909006 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.6654 | 0.926327 | 0.463164 | − | 0.886273i | \(-0.346714\pi\) | ||||
0.463164 | + | 0.886273i | \(0.346714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.8431 | −1.11920 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.0704 | −1.20105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.8177 | −1.67609 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.2750 | −0.383728 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.6829 | 0.435699 | 0.217849 | − | 0.975982i | \(-0.430096\pi\) | ||||
0.217849 | + | 0.975982i | \(0.430096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.7754 | −1.70476 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.64362 | 0.0611269 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 77.6467 | 2.88372 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9582 | 0.740210 | 0.370105 | − | 0.928990i | \(-0.379322\pi\) | ||||
0.370105 | + | 0.928990i | \(0.379322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.0896 | −0.669987 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68.6426 | 2.53884 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.0802 | −1.77588 | −0.887941 | − | 0.459957i | \(-0.847865\pi\) | ||||
−0.887941 | + | 0.459957i | \(0.847865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00655 | −0.0371271 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.7975 | 0.913428 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.9960 | −1.61842 | −0.809209 | − | 0.587521i | \(-0.800104\pi\) | ||||
−0.809209 | + | 0.587521i | \(0.800104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.23384 | −0.229006 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0686 | 0.589500 | 0.294750 | − | 0.955574i | \(-0.404764\pi\) | ||||
0.294750 | + | 0.955574i | \(0.404764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.02471 | −0.330640 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.29926 | −0.157302 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.7849 | 0.796003 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.33418 | −0.157946 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −50.1314 | −1.82447 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.40087 | −0.123607 | −0.0618034 | − | 0.998088i | \(-0.519685\pi\) | ||||
−0.0618034 | + | 0.998088i | \(0.519685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2550 | 0.372233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0807 | 0.546674 | 0.273337 | − | 0.961918i | \(-0.411873\pi\) | ||||
0.273337 | + | 0.961918i | \(0.411873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.9127 | 0.684685 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 80.9452 | 2.92658 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.8298 | −1.00488 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.8490 | 1.36487 | 0.682436 | − | 0.730946i | \(-0.260921\pi\) | ||||
0.682436 | + | 0.730946i | \(0.260921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.831069 | −0.0299302 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.68818 | −0.0607198 | −0.0303599 | − | 0.999539i | \(-0.509665\pi\) | ||||
−0.0303599 | + | 0.999539i | \(0.509665\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.4049 | −1.70283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.87590 | −0.246672 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.2618 | 0.654295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1735 | 0.399819 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.6847 | −0.632001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.6470 | 0.415699 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.1509 | 0.753949 | 0.376975 | − | 0.926224i | \(-0.376964\pi\) | ||||
0.376975 | + | 0.926224i | \(0.376964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.92376 | −0.0684875 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.6648 | 1.80143 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.5473 | −0.410058 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.9425 | 0.529957 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.5742 | 1.89770 | 0.948848 | − | 0.315733i | \(-0.102250\pi\) | ||||
0.948848 | + | 0.315733i | \(0.102250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.494522 | 0.0174949 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.8843 | 0.879242 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.6410 | 1.36361 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 72.0288 | 2.53868 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.93117 | 0.208787 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8424 | 1.01404 | 0.507022 | − | 0.861933i | \(-0.330746\pi\) | ||||
0.507022 | + | 0.861933i | \(0.330746\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4030 | −1.41874 | −0.709371 | − | 0.704835i | \(-0.751021\pi\) | ||||
−0.709371 | + | 0.704835i | \(0.751021\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.99307 | −0.315401 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.4021 | −1.62539 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.8715 | −1.49988 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.6686 | 0.827047 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.4957 | 1.76231 | 0.881157 | − | 0.472824i | \(-0.156765\pi\) | ||||
0.881157 | + | 0.472824i | \(0.156765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.2314 | 1.64638 | 0.823191 | − | 0.567764i | \(-0.192192\pi\) | ||||
0.823191 | + | 0.567764i | \(0.192192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.1584 | 0.527749 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.3757 | −0.499892 | −0.249946 | − | 0.968260i | \(-0.580413\pi\) | ||||
−0.249946 | + | 0.968260i | \(0.580413\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.41240 | −0.0490548 | −0.0245274 | − | 0.999699i | \(-0.507808\pi\) | ||||
−0.0245274 | + | 0.999699i | \(0.507808\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.98029 | −0.207454 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.42521 | 0.153325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.4926 | 0.501537 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7969 | 0.373196 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.522791 | −0.0180488 | −0.00902438 | − | 0.999959i | \(-0.502873\pi\) | ||||
−0.00902438 | + | 0.999959i | \(0.502873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1713 | 0.833492 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.42985 | 0.0492466 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.01521 | −0.275732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.76159 | 0.0605289 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.37918 | 0.0473332 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.0821 | −1.61395 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.31887 | −0.113636 | −0.0568180 | − | 0.998385i | \(-0.518095\pi\) | ||||
−0.0568180 | + | 0.998385i | \(0.518095\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −50.5552 | −1.72895 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.52657 | 0.154625 | 0.0773124 | − | 0.997007i | \(-0.475366\pi\) | ||||
0.0773124 | + | 0.997007i | \(0.475366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2237 | 0.451186 | 0.225593 | − | 0.974222i | \(-0.427568\pi\) | ||||
0.225593 | + | 0.974222i | \(0.427568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.24951 | 0.144823 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.4020 | 0.354089 | 0.177044 | − | 0.984203i | \(-0.443346\pi\) | ||||
0.177044 | + | 0.984203i | \(0.443346\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −78.0095 | −2.65240 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7348 | 0.500421 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.1071 | 1.22485 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0187 | −0.813844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.89975 | 0.233521 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 56.4763 | 1.90925 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.1045 | 1.08409 | 0.542047 | − | 0.840348i | \(-0.317650\pi\) | ||||
0.542047 | + | 0.840348i | \(0.317650\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.29152 | 0.111020 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.1835 | −1.55596 | −0.777981 | − | 0.628288i | \(-0.783756\pi\) | ||||
−0.777981 | + | 0.628288i | \(0.783756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.3369 | −0.516127 | −0.258063 | − | 0.966128i | \(-0.583084\pi\) | ||||
−0.258063 | + | 0.966128i | \(0.583084\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.8325 | 0.464974 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1206 | −0.910620 | −0.455310 | − | 0.890333i | \(-0.650472\pi\) | ||||
−0.455310 | + | 0.890333i | \(0.650472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.8973 | 1.70704 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 25.5507 | 0.855980 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.308859 | −0.0103356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −84.6005 | −2.82788 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.93295 | −0.331652 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.4622 | −1.08267 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −65.6937 | −2.18857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.97620 | −0.331987 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −81.2568 | −2.70107 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.8042 | 0.557976 | 0.278988 | − | 0.960295i | \(-0.410001\pi\) | ||||
0.278988 | + | 0.960295i | \(0.410001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.0308 | −0.896554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.9944 | 1.35820 | 0.679102 | − | 0.734044i | \(-0.262369\pi\) | ||||
0.679102 | + | 0.734044i | \(0.262369\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.20166 | 0.172150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.73947 | 0.189741 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.27430 | −0.306264 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.07414 | −0.0684197 | −0.0342098 | − | 0.999415i | \(-0.510891\pi\) | ||||
−0.0342098 | + | 0.999415i | \(0.510891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.36246 | 0.143748 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8226 | −0.356230 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −69.5944 | −2.28825 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 51.1934 | 1.68141 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.3153 | −0.994612 | −0.497306 | − | 0.867575i | \(-0.665677\pi\) | ||||
−0.497306 | + | 0.867575i | \(0.665677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.76381 | −0.0905803 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.79929 | −0.0589060 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −97.9354 | −3.20283 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0261 | −0.490881 | −0.245440 | − | 0.969412i | \(-0.578933\pi\) | ||||
−0.245440 | + | 0.969412i | \(0.578933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.84991 | 0.223538 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.7935 | −0.840843 | −0.420422 | − | 0.907329i | \(-0.638118\pi\) | ||||
−0.420422 | + | 0.907329i | \(0.638118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.0981 | 0.947566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.2494 | −0.788833 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.9193 | 1.55717 | 0.778584 | − | 0.627540i | \(-0.215938\pi\) | ||||
0.778584 | + | 0.627540i | \(0.215938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.4276 | −1.21495 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0582 | −0.326161 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.9750 | −1.48928 | −0.744638 | − | 0.667469i | \(-0.767378\pi\) | ||||
−0.744638 | + | 0.667469i | \(0.767378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.0676 | −0.811168 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.3803 | 0.335546 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 29.4747 | 0.951788 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1812 | −0.360683 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.3634 | −0.785099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.91952 | −0.254938 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.1328 | 1.32274 | 0.661371 | − | 0.750059i | \(-0.269975\pi\) | ||||
0.661371 | + | 0.750059i | \(0.269975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.6221 | −0.437606 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.13673 | −0.229028 | −0.114514 | − | 0.993422i | \(-0.536531\pi\) | ||||
−0.114514 | + | 0.993422i | \(0.536531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.1000 | 0.387909 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.6824 | −0.470213 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.7605 | −1.01611 | −0.508054 | − | 0.861325i | \(-0.669635\pi\) | ||||
−0.508054 | + | 0.861325i | \(0.669635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.1074 | −0.962237 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1512 | −0.675306 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0639 | 0.512359 | 0.256180 | − | 0.966629i | \(-0.417536\pi\) | ||||
0.256180 | + | 0.966629i | \(0.417536\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.9326 | −1.08118 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.0718715 | −0.00228770 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −68.3111 | −2.17217 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.7424 | −0.627138 | −0.313569 | − | 0.949565i | \(-0.601525\pi\) | ||||
−0.313569 | + | 0.949565i | \(0.601525\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.45408 | 0.173080 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.1418 | −1.43109 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.2962 | −0.389426 | −0.194713 | − | 0.980860i | \(-0.562378\pi\) | ||||
−0.194713 | + | 0.980860i | \(0.562378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.8508 | 0.501497 |
(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.e.1.29 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.29 | ✓ | 50 | 1.1 | even | 1 | trivial |