Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6030,2,Mod(2411,6030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6030, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6030.2411");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.1497924188\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2411.2 | ||
Character | \(\chi\) | \(=\) | 6030.2411 |
Dual form | 6030.2.d.k.2411.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6030\mathbb{Z}\right)^\times\).
\(n\) | \(1207\) | \(3151\) | \(4691\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.69493i | − | 1.39655i | −0.715829 | − | 0.698276i | \(-0.753951\pi\) | ||
0.715829 | − | 0.698276i | \(-0.246049\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.10258 | −1.53849 | −0.769243 | − | 0.638957i | \(-0.779366\pi\) | ||||
−0.769243 | + | 0.638957i | \(0.779366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.05495i | − | 1.67934i | −0.543096 | − | 0.839671i | \(-0.682748\pi\) | ||
0.543096 | − | 0.839671i | \(-0.317252\pi\) | |||||||
\(14\) | 3.69493i | 0.987512i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.252749i | 0.0613006i | 0.999530 | + | 0.0306503i | \(0.00975782\pi\) | ||||
−0.999530 | + | 0.0306503i | \(0.990242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.17889 | 0.958703 | 0.479352 | − | 0.877623i | \(-0.340872\pi\) | ||||
0.479352 | + | 0.877623i | \(0.340872\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.10258 | 1.08787 | ||||||||
\(23\) | − | 5.65818i | − | 1.17981i | −0.807472 | − | 0.589907i | \(-0.799165\pi\) | ||
0.807472 | − | 0.589907i | \(-0.200835\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.05495i | 1.18747i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.69493i | − | 0.698276i | ||||||
\(29\) | 9.12065i | 1.69366i | 0.531862 | + | 0.846831i | \(0.321492\pi\) | ||||
−0.531862 | + | 0.846831i | \(0.678508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.22881i | − | 1.29833i | −0.760647 | − | 0.649166i | \(-0.775118\pi\) | ||
0.760647 | − | 0.649166i | \(-0.224882\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 0.252749i | − | 0.0433461i | ||||||
\(35\) | 3.69493i | 0.624557i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.83907 | −0.959937 | −0.479969 | − | 0.877286i | \(-0.659352\pi\) | ||||
−0.479969 | + | 0.877286i | \(0.659352\pi\) | |||||||
\(38\) | −4.17889 | −0.677906 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 9.99657 | 1.56120 | 0.780601 | − | 0.625029i | \(-0.214913\pi\) | ||||
0.780601 | + | 0.625029i | \(0.214913\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.80931i | − | 0.885911i | −0.896544 | − | 0.442955i | \(-0.853930\pi\) | ||
0.896544 | − | 0.442955i | \(-0.146070\pi\) | |||||||
\(44\) | −5.10258 | −0.769243 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.65818i | 0.834254i | ||||||||
\(47\) | − | 13.0372i | − | 1.90166i | −0.309706 | − | 0.950832i | \(-0.600231\pi\) | ||
0.309706 | − | 0.950832i | \(-0.399769\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65251 | −0.950358 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 6.05495i | − | 0.839671i | ||||||
\(53\) | 3.38087 | 0.464398 | 0.232199 | − | 0.972668i | \(-0.425408\pi\) | ||||
0.232199 | + | 0.972668i | \(0.425408\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.10258 | 0.688032 | ||||||||
\(56\) | 3.69493i | 0.493756i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 9.12065i | − | 1.19760i | ||||||
\(59\) | − | 11.2319i | − | 1.46226i | −0.682237 | − | 0.731131i | \(-0.738993\pi\) | ||
0.682237 | − | 0.731131i | \(-0.261007\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.77473i | 0.355268i | 0.984097 | + | 0.177634i | \(0.0568444\pi\) | ||||
−0.984097 | + | 0.177634i | \(0.943156\pi\) | |||||||
\(62\) | 7.22881i | 0.918059i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.05495i | 0.751024i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.06213 | − | 5.50005i | 0.740607 | − | 0.671938i | ||||
\(68\) | 0.252749i | 0.0306503i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 3.69493i | − | 0.441629i | ||||||
\(71\) | − | 8.07879i | − | 0.958776i | −0.877603 | − | 0.479388i | \(-0.840859\pi\) | ||
0.877603 | − | 0.479388i | \(-0.159141\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.89962 | 0.339374 | 0.169687 | − | 0.985498i | \(-0.445724\pi\) | ||||
0.169687 | + | 0.985498i | \(0.445724\pi\) | |||||||
\(74\) | 5.83907 | 0.678778 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.17889 | 0.479352 | ||||||||
\(77\) | 18.8537i | 2.14858i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.22636i | 0.925537i | 0.886479 | + | 0.462769i | \(0.153144\pi\) | ||||
−0.886479 | + | 0.462769i | \(0.846856\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.99657 | −1.10394 | ||||||||
\(83\) | − | 12.6131i | − | 1.38447i | −0.721671 | − | 0.692236i | \(-0.756626\pi\) | ||
0.721671 | − | 0.692236i | \(-0.243374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.252749i | − | 0.0274145i | ||||||
\(86\) | 5.80931i | 0.626433i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.10258 | 0.543937 | ||||||||
\(89\) | 2.69800i | 0.285988i | 0.989724 | + | 0.142994i | \(0.0456730\pi\) | ||||
−0.989724 | + | 0.142994i | \(0.954327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3726 | −2.34529 | ||||||||
\(92\) | − | 5.65818i | − | 0.589907i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.0372i | 1.34468i | ||||||||
\(95\) | −4.17889 | −0.428745 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.99115i | − | 0.405240i | −0.979257 | − | 0.202620i | \(-0.935054\pi\) | ||
0.979257 | − | 0.202620i | \(-0.0649456\pi\) | |||||||
\(98\) | 6.65251 | 0.672005 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.22506 | 0.121898 | 0.0609490 | − | 0.998141i | \(-0.480587\pi\) | ||||
0.0609490 | + | 0.998141i | \(0.480587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92251 | 0.583562 | 0.291781 | − | 0.956485i | \(-0.405752\pi\) | ||||
0.291781 | + | 0.956485i | \(0.405752\pi\) | |||||||
\(104\) | 6.05495i | 0.593737i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.38087 | −0.328379 | ||||||||
\(107\) | 7.10549i | 0.686914i | 0.939168 | + | 0.343457i | \(0.111598\pi\) | ||||
−0.939168 | + | 0.343457i | \(0.888402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.14887i | 0.301607i | 0.988564 | + | 0.150803i | \(0.0481861\pi\) | ||||
−0.988564 | + | 0.150803i | \(0.951814\pi\) | |||||||
\(110\) | −5.10258 | −0.486512 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 3.69493i | − | 0.349138i | ||||||
\(113\) | −2.07969 | −0.195641 | −0.0978203 | − | 0.995204i | \(-0.531187\pi\) | ||||
−0.0978203 | + | 0.995204i | \(0.531187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.65818i | 0.527628i | ||||||||
\(116\) | 9.12065i | 0.846831i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.2319i | 1.03398i | ||||||||
\(119\) | 0.933890 | 0.0856095 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.0363 | 1.36694 | ||||||||
\(122\) | − | 2.77473i | − | 0.251213i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 7.22881i | − | 0.649166i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.2156 | −0.906486 | −0.453243 | − | 0.891387i | \(-0.649733\pi\) | ||||
−0.453243 | + | 0.891387i | \(0.649733\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | − | 6.05495i | − | 0.531054i | ||||||
\(131\) | 17.2121i | 1.50383i | 0.659262 | + | 0.751913i | \(0.270869\pi\) | ||||
−0.659262 | + | 0.751913i | \(0.729131\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 15.4407i | − | 1.33888i | ||||||
\(134\) | −6.06213 | + | 5.50005i | −0.523688 | + | 0.475132i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 0.252749i | − | 0.0216730i | ||||||
\(137\) | −19.1870 | −1.63926 | −0.819628 | − | 0.572895i | \(-0.805820\pi\) | ||||
−0.819628 | + | 0.572895i | \(0.805820\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.43228i | 0.545579i | 0.962074 | + | 0.272790i | \(0.0879463\pi\) | ||||
−0.962074 | + | 0.272790i | \(0.912054\pi\) | |||||||
\(140\) | 3.69493i | 0.312279i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.07879i | 0.677957i | ||||||||
\(143\) | 30.8959i | 2.58364i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.12065i | − | 0.757429i | ||||||
\(146\) | −2.89962 | −0.239974 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.83907 | −0.479969 | ||||||||
\(149\) | − | 14.0925i | − | 1.15450i | −0.816566 | − | 0.577252i | \(-0.804125\pi\) | ||
0.816566 | − | 0.577252i | \(-0.195875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.8467 | −1.85924 | −0.929621 | − | 0.368517i | \(-0.879866\pi\) | ||||
−0.929621 | + | 0.368517i | \(0.879866\pi\) | |||||||
\(152\) | −4.17889 | −0.338953 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 18.8537i | − | 1.51927i | ||||||
\(155\) | 7.22881i | 0.580632i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.3930 | −1.54773 | −0.773865 | − | 0.633351i | \(-0.781679\pi\) | ||||
−0.773865 | + | 0.633351i | \(0.781679\pi\) | |||||||
\(158\) | − | 8.22636i | − | 0.654454i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −20.9066 | −1.64767 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.65798 | −0.756471 | −0.378236 | − | 0.925709i | \(-0.623469\pi\) | ||||
−0.378236 | + | 0.925709i | \(0.623469\pi\) | |||||||
\(164\) | 9.99657 | 0.780601 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6131i | 0.978970i | ||||||||
\(167\) | 17.3264i | 1.34075i | 0.742020 | + | 0.670377i | \(0.233868\pi\) | ||||
−0.742020 | + | 0.670377i | \(0.766132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.6624 | −1.82019 | ||||||||
\(170\) | 0.252749i | 0.0193850i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.80931i | − | 0.442955i | ||||||
\(173\) | − | 5.05361i | − | 0.384219i | −0.981373 | − | 0.192110i | \(-0.938467\pi\) | ||
0.981373 | − | 0.192110i | \(-0.0615329\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.69493i | − | 0.279310i | ||||||
\(176\) | −5.10258 | −0.384621 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.69800i | − | 0.202224i | ||||||
\(179\) | 22.7443 | 1.69999 | 0.849995 | − | 0.526792i | \(-0.176605\pi\) | ||||
0.849995 | + | 0.526792i | \(0.176605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.4253 | 1.36954 | 0.684770 | − | 0.728759i | \(-0.259903\pi\) | ||||
0.684770 | + | 0.728759i | \(0.259903\pi\) | |||||||
\(182\) | 22.3726 | 1.65837 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.65818i | 0.417127i | ||||||||
\(185\) | 5.83907 | 0.429297 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.28967i | − | 0.0943101i | ||||||
\(188\) | − | 13.0372i | − | 0.950832i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.17889 | 0.303169 | ||||||||
\(191\) | −20.9633 | −1.51685 | −0.758424 | − | 0.651761i | \(-0.774031\pi\) | ||||
−0.758424 | + | 0.651761i | \(0.774031\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.26799 | −0.523162 | −0.261581 | − | 0.965182i | \(-0.584244\pi\) | ||||
−0.261581 | + | 0.965182i | \(0.584244\pi\) | |||||||
\(194\) | 3.99115i | 0.286548i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.65251 | −0.475179 | ||||||||
\(197\) | 24.5976 | 1.75251 | 0.876253 | − | 0.481851i | \(-0.160035\pi\) | ||||
0.876253 | + | 0.481851i | \(0.160035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2070 | 1.14888 | 0.574441 | − | 0.818546i | \(-0.305220\pi\) | ||||
0.574441 | + | 0.818546i | \(0.305220\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.22506 | −0.0861949 | ||||||||
\(203\) | 33.7002 | 2.36529 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.99657 | −0.698191 | ||||||||
\(206\) | −5.92251 | −0.412641 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 6.05495i | − | 0.419835i | ||||||
\(209\) | −21.3231 | −1.47495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5763 | 1.62306 | 0.811529 | − | 0.584313i | \(-0.198636\pi\) | ||||
0.811529 | + | 0.584313i | \(0.198636\pi\) | |||||||
\(212\) | 3.38087 | 0.232199 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 7.10549i | − | 0.485722i | ||||||
\(215\) | 5.80931i | 0.396191i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.7099 | −1.81319 | ||||||||
\(218\) | − | 3.14887i | − | 0.213268i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.10258 | 0.344016 | ||||||||
\(221\) | 1.53038 | 0.102945 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.31407 | 0.0879965 | 0.0439983 | − | 0.999032i | \(-0.485990\pi\) | ||||
0.0439983 | + | 0.999032i | \(0.485990\pi\) | |||||||
\(224\) | 3.69493i | 0.246878i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.07969 | 0.138339 | ||||||||
\(227\) | 18.0703i | 1.19937i | 0.800238 | + | 0.599683i | \(0.204707\pi\) | ||||
−0.800238 | + | 0.599683i | \(0.795293\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.73041i | 0.643004i | 0.946909 | + | 0.321502i | \(0.104188\pi\) | ||||
−0.946909 | + | 0.321502i | \(0.895812\pi\) | |||||||
\(230\) | − | 5.65818i | − | 0.373090i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 9.12065i | − | 0.598800i | ||||||
\(233\) | −24.9008 | −1.63130 | −0.815652 | − | 0.578542i | \(-0.803622\pi\) | ||||
−0.815652 | + | 0.578542i | \(0.803622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.0372i | 0.850450i | ||||||||
\(236\) | − | 11.2319i | − | 0.731131i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.933890 | −0.0605351 | ||||||||
\(239\) | −21.1041 | −1.36511 | −0.682555 | − | 0.730834i | \(-0.739131\pi\) | ||||
−0.682555 | + | 0.730834i | \(0.739131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.7911 | 1.01719 | 0.508597 | − | 0.861005i | \(-0.330164\pi\) | ||||
0.508597 | + | 0.861005i | \(0.330164\pi\) | |||||||
\(242\) | −15.0363 | −0.966571 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.77473i | 0.177634i | ||||||||
\(245\) | 6.65251 | 0.425013 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 25.3030i | − | 1.60999i | ||||||
\(248\) | 7.22881i | 0.459030i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 2.85903 | 0.180461 | 0.0902303 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902303 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.8713i | 1.81513i | ||||||||
\(254\) | 10.2156 | 0.640982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.0214i | 1.31128i | 0.755074 | + | 0.655640i | \(0.227601\pi\) | ||||
−0.755074 | + | 0.655640i | \(0.772399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.5750i | 1.34060i | ||||||||
\(260\) | 6.05495i | 0.375512i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 17.2121i | − | 1.06337i | ||||||
\(263\) | 20.6299i | 1.27209i | 0.771650 | + | 0.636047i | \(0.219432\pi\) | ||||
−0.771650 | + | 0.636047i | \(0.780568\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.38087 | −0.207685 | ||||||||
\(266\) | 15.4407i | 0.946731i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.06213 | − | 5.50005i | 0.370304 | − | 0.335969i | ||||
\(269\) | − | 24.7520i | − | 1.50915i | −0.656212 | − | 0.754577i | \(-0.727842\pi\) | ||
0.656212 | − | 0.754577i | \(-0.272158\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.60242i | − | 0.401068i | −0.979687 | − | 0.200534i | \(-0.935732\pi\) | ||
0.979687 | − | 0.200534i | \(-0.0642678\pi\) | |||||||
\(272\) | 0.252749i | 0.0153252i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.1870 | 1.15913 | ||||||||
\(275\) | −5.10258 | −0.307697 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.3675 | 1.10360 | 0.551798 | − | 0.833978i | \(-0.313942\pi\) | ||||
0.551798 | + | 0.833978i | \(0.313942\pi\) | |||||||
\(278\) | − | 6.43228i | − | 0.385783i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 3.69493i | − | 0.220814i | ||||||
\(281\) | −25.3203 | −1.51048 | −0.755240 | − | 0.655448i | \(-0.772480\pi\) | ||||
−0.755240 | + | 0.655448i | \(0.772480\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0733 | 0.658237 | 0.329118 | − | 0.944289i | \(-0.393248\pi\) | ||||
0.329118 | + | 0.944289i | \(0.393248\pi\) | |||||||
\(284\) | − | 8.07879i | − | 0.479388i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 30.8959i | − | 1.82691i | ||||||
\(287\) | − | 36.9366i | − | 2.18030i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9361 | 0.996242 | ||||||||
\(290\) | 9.12065i | 0.535583i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.89962 | 0.169687 | ||||||||
\(293\) | 18.9742i | 1.10848i | 0.832356 | + | 0.554242i | \(0.186992\pi\) | ||||
−0.832356 | + | 0.554242i | \(0.813008\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2319i | 0.653944i | ||||||||
\(296\) | 5.83907 | 0.339389 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.0925i | 0.816358i | ||||||||
\(299\) | −34.2600 | −1.98131 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.4650 | −1.23722 | ||||||||
\(302\) | 22.8467 | 1.31468 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.17889 | 0.239676 | ||||||||
\(305\) | − | 2.77473i | − | 0.158881i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4969 | 0.998599 | 0.499299 | − | 0.866430i | \(-0.333591\pi\) | ||||
0.499299 | + | 0.866430i | \(0.333591\pi\) | |||||||
\(308\) | 18.8537i | 1.07429i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 7.22881i | − | 0.410569i | ||||||
\(311\) | −11.7799 | −0.667978 | −0.333989 | − | 0.942577i | \(-0.608395\pi\) | ||||
−0.333989 | + | 0.942577i | \(0.608395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4886i | 1.32766i | 0.747886 | + | 0.663828i | \(0.231069\pi\) | ||||
−0.747886 | + | 0.663828i | \(0.768931\pi\) | |||||||
\(314\) | 19.3930 | 1.09441 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.22636i | 0.462769i | ||||||||
\(317\) | − | 29.0150i | − | 1.62964i | −0.579711 | − | 0.814822i | \(-0.696835\pi\) | ||
0.579711 | − | 0.814822i | \(-0.303165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 46.5388i | − | 2.60567i | ||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 20.9066 | 1.16508 | ||||||||
\(323\) | 1.05621i | 0.0587691i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.05495i | − | 0.335868i | ||||||
\(326\) | 9.65798 | 0.534906 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.99657 | −0.551968 | ||||||||
\(329\) | −48.1714 | −2.65577 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2208i | 1.05647i | 0.849099 | + | 0.528234i | \(0.177146\pi\) | ||||
−0.849099 | + | 0.528234i | \(0.822854\pi\) | |||||||
\(332\) | − | 12.6131i | − | 0.692236i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 17.3264i | − | 0.948057i | ||||||
\(335\) | −6.06213 | + | 5.50005i | −0.331210 | + | 0.300500i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.60819i | 0.0876037i | 0.999040 | + | 0.0438018i | \(0.0139470\pi\) | ||||
−0.999040 | + | 0.0438018i | \(0.986053\pi\) | |||||||
\(338\) | 23.6624 | 1.28707 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 0.252749i | − | 0.0137072i | ||||||
\(341\) | 36.8856i | 1.99747i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.28396i | − | 0.0693275i | ||||||
\(344\) | 5.80931i | 0.313217i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.05361i | 0.271684i | ||||||||
\(347\) | −3.77771 | −0.202798 | −0.101399 | − | 0.994846i | \(-0.532332\pi\) | ||||
−0.101399 | + | 0.994846i | \(0.532332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3534 | −1.14302 | −0.571510 | − | 0.820595i | \(-0.693642\pi\) | ||||
−0.571510 | + | 0.820595i | \(0.693642\pi\) | |||||||
\(350\) | 3.69493i | 0.197502i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.10258 | 0.271968 | ||||||||
\(353\) | 21.9172 | 1.16653 | 0.583267 | − | 0.812280i | \(-0.301774\pi\) | ||||
0.583267 | + | 0.812280i | \(0.301774\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.07879i | 0.428778i | ||||||||
\(356\) | 2.69800i | 0.142994i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.7443 | −1.20207 | ||||||||
\(359\) | − | 29.2681i | − | 1.54471i | −0.635189 | − | 0.772357i | \(-0.719078\pi\) | ||
0.635189 | − | 0.772357i | \(-0.280922\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.53687 | −0.0808878 | ||||||||
\(362\) | −18.4253 | −0.968411 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.3726 | −1.17264 | ||||||||
\(365\) | −2.89962 | −0.151773 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.5770i | − | 1.33511i | −0.744560 | − | 0.667555i | \(-0.767341\pi\) | ||
0.744560 | − | 0.667555i | \(-0.232659\pi\) | |||||||
\(368\) | − | 5.65818i | − | 0.294953i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.83907 | −0.303559 | ||||||||
\(371\) | − | 12.4921i | − | 0.648556i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 17.3266i | − | 0.897138i | −0.893748 | − | 0.448569i | \(-0.851934\pi\) | ||
0.893748 | − | 0.448569i | \(-0.148066\pi\) | |||||||
\(374\) | 1.28967i | 0.0666873i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.0372i | 0.672340i | ||||||||
\(377\) | 55.2251 | 2.84424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.93843i | − | 0.407770i | −0.978995 | − | 0.203885i | \(-0.934643\pi\) | ||
0.978995 | − | 0.203885i | \(-0.0653568\pi\) | |||||||
\(380\) | −4.17889 | −0.214373 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.9633 | 1.07257 | ||||||||
\(383\) | −17.9184 | −0.915587 | −0.457793 | − | 0.889059i | \(-0.651360\pi\) | ||||
−0.457793 | + | 0.889059i | \(0.651360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 18.8537i | − | 0.960872i | ||||||
\(386\) | 7.26799 | 0.369931 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 3.99115i | − | 0.202620i | ||||||
\(389\) | 22.9267i | 1.16243i | 0.813750 | + | 0.581215i | \(0.197423\pi\) | ||||
−0.813750 | + | 0.581215i | \(0.802577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.43010 | 0.0723233 | ||||||||
\(392\) | 6.65251 | 0.336002 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.5976 | −1.23921 | ||||||||
\(395\) | − | 8.22636i | − | 0.413913i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.23403 | 0.413254 | 0.206627 | − | 0.978420i | \(-0.433751\pi\) | ||||
0.206627 | + | 0.978420i | \(0.433751\pi\) | |||||||
\(398\) | −16.2070 | −0.812382 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −4.68848 | −0.234132 | −0.117066 | − | 0.993124i | \(-0.537349\pi\) | ||||
−0.117066 | + | 0.993124i | \(0.537349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.7701 | −2.18034 | ||||||||
\(404\) | 1.22506 | 0.0609490 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.7002 | −1.67251 | ||||||||
\(407\) | 29.7943 | 1.47685 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6532i | 1.21902i | 0.792778 | + | 0.609511i | \(0.208634\pi\) | ||||
−0.792778 | + | 0.609511i | \(0.791366\pi\) | |||||||
\(410\) | 9.99657 | 0.493696 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.92251 | 0.291781 | ||||||||
\(413\) | −41.5009 | −2.04213 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.6131i | 0.619155i | ||||||||
\(416\) | 6.05495i | 0.296868i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.3231 | 1.04295 | ||||||||
\(419\) | 24.8106i | 1.21208i | 0.795436 | + | 0.606038i | \(0.207242\pi\) | ||||
−0.795436 | + | 0.606038i | \(0.792758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.25483 | −0.402316 | −0.201158 | − | 0.979559i | \(-0.564470\pi\) | ||||
−0.201158 | + | 0.979559i | \(0.564470\pi\) | |||||||
\(422\) | −23.5763 | −1.14767 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.38087 | −0.164189 | ||||||||
\(425\) | 0.252749i | 0.0122601i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.2525 | 0.496151 | ||||||||
\(428\) | 7.10549i | 0.343457i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 5.80931i | − | 0.280150i | ||||||
\(431\) | 3.92206i | 0.188919i | 0.995529 | + | 0.0944596i | \(0.0301123\pi\) | ||||
−0.995529 | + | 0.0944596i | \(0.969888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.5714i | − | 0.604141i | −0.953286 | − | 0.302070i | \(-0.902322\pi\) | ||
0.953286 | − | 0.302070i | \(-0.0976778\pi\) | |||||||
\(434\) | 26.7099 | 1.28212 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.14887i | 0.150803i | ||||||||
\(437\) | − | 23.6449i | − | 1.13109i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.7852 | −1.85112 | −0.925558 | − | 0.378606i | \(-0.876403\pi\) | ||||
−0.925558 | + | 0.378606i | \(0.876403\pi\) | |||||||
\(440\) | −5.10258 | −0.243256 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.53038 | −0.0727929 | ||||||||
\(443\) | −34.5708 | −1.64251 | −0.821255 | − | 0.570562i | \(-0.806726\pi\) | ||||
−0.821255 | + | 0.570562i | \(0.806726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.69800i | − | 0.127898i | ||||||
\(446\) | −1.31407 | −0.0622229 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.69493i | − | 0.174569i | ||||||
\(449\) | − | 34.8770i | − | 1.64595i | −0.568079 | − | 0.822974i | \(-0.692313\pi\) | ||
0.568079 | − | 0.822974i | \(-0.307687\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −51.0083 | −2.40189 | ||||||||
\(452\) | −2.07969 | −0.0978203 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 18.0703i | − | 0.848080i | ||||||
\(455\) | 22.3726 | 1.04884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.01076 | −0.0472816 | −0.0236408 | − | 0.999721i | \(-0.507526\pi\) | ||||
−0.0236408 | + | 0.999721i | \(0.507526\pi\) | |||||||
\(458\) | − | 9.73041i | − | 0.454672i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.65818i | 0.263814i | ||||||||
\(461\) | 19.6304i | 0.914279i | 0.889395 | + | 0.457139i | \(0.151126\pi\) | ||||
−0.889395 | + | 0.457139i | \(0.848874\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.70958i | − | 0.404769i | −0.979306 | − | 0.202384i | \(-0.935131\pi\) | ||
0.979306 | − | 0.202384i | \(-0.0648690\pi\) | |||||||
\(464\) | 9.12065i | 0.423415i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.9008 | 1.15351 | ||||||||
\(467\) | 23.3816i | 1.08197i | 0.841032 | + | 0.540985i | \(0.181949\pi\) | ||||
−0.841032 | + | 0.540985i | \(0.818051\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.3223 | − | 22.3992i | −0.938397 | − | 1.03430i | ||||
\(470\) | − | 13.0372i | − | 0.601359i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.2319i | 0.516988i | ||||||||
\(473\) | 29.6424i | 1.36296i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.17889 | 0.191741 | ||||||||
\(476\) | 0.933890 | 0.0428048 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21.1041 | 0.965279 | ||||||||
\(479\) | − | 14.5193i | − | 0.663406i | −0.943384 | − | 0.331703i | \(-0.892377\pi\) | ||
0.943384 | − | 0.331703i | \(-0.107623\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.3553i | 1.61206i | ||||||||
\(482\) | −15.7911 | −0.719264 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.0363 | 0.683469 | ||||||||
\(485\) | 3.99115i | 0.181229i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.5245i | − | 0.612853i | −0.951894 | − | 0.306426i | \(-0.900867\pi\) | ||
0.951894 | − | 0.306426i | \(-0.0991333\pi\) | |||||||
\(488\) | − | 2.77473i | − | 0.125606i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.65251 | −0.300530 | ||||||||
\(491\) | − | 17.6500i | − | 0.796532i | −0.917270 | − | 0.398266i | \(-0.869612\pi\) | ||
0.917270 | − | 0.398266i | \(-0.130388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.30523 | −0.103823 | ||||||||
\(494\) | 25.3030i | 1.13844i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 7.22881i | − | 0.324583i | ||||||
\(497\) | −29.8506 | −1.33898 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.0141i | 1.43315i | 0.697511 | + | 0.716574i | \(0.254291\pi\) | ||||
−0.697511 | + | 0.716574i | \(0.745709\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.85903 | −0.127605 | ||||||||
\(503\) | 17.0489 | 0.760173 | 0.380086 | − | 0.924951i | \(-0.375894\pi\) | ||||
0.380086 | + | 0.924951i | \(0.375894\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22506 | −0.0545144 | ||||||||
\(506\) | − | 28.8713i | − | 1.28349i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.2156 | −0.453243 | ||||||||
\(509\) | − | 23.2788i | − | 1.03182i | −0.856644 | − | 0.515908i | \(-0.827455\pi\) | ||
0.856644 | − | 0.515908i | \(-0.172545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 10.7139i | − | 0.473954i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 21.0214i | − | 0.927215i | ||||||
\(515\) | −5.92251 | −0.260977 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 66.5231i | 2.92568i | ||||||||
\(518\) | − | 21.5750i | − | 0.947949i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 6.05495i | − | 0.265527i | ||||||
\(521\) | −17.5382 | −0.768365 | −0.384182 | − | 0.923257i | \(-0.625517\pi\) | ||||
−0.384182 | + | 0.923257i | \(0.625517\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4608 | 0.719782 | 0.359891 | − | 0.932994i | \(-0.382814\pi\) | ||||
0.359891 | + | 0.932994i | \(0.382814\pi\) | |||||||
\(524\) | 17.2121i | 0.751913i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 20.6299i | − | 0.899506i | ||||||
\(527\) | 1.82707 | 0.0795886 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.01505 | −0.391959 | ||||||||
\(530\) | 3.38087 | 0.146855 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 15.4407i | − | 0.669440i | ||||||
\(533\) | − | 60.5288i | − | 2.62179i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.10549i | − | 0.307197i | ||||||
\(536\) | −6.06213 | + | 5.50005i | −0.261844 | + | 0.237566i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.7520i | 1.06713i | ||||||||
\(539\) | 33.9449 | 1.46211 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.12941i | − | 0.177537i | −0.996052 | − | 0.0887686i | \(-0.971707\pi\) | ||
0.996052 | − | 0.0887686i | \(-0.0282932\pi\) | |||||||
\(542\) | 6.60242i | 0.283598i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 0.252749i | − | 0.0108365i | ||||||
\(545\) | − | 3.14887i | − | 0.134883i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.5064i | 1.13333i | 0.823947 | + | 0.566666i | \(0.191767\pi\) | ||||
−0.823947 | + | 0.566666i | \(0.808233\pi\) | |||||||
\(548\) | −19.1870 | −0.819628 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.10258 | 0.217575 | ||||||||
\(551\) | 38.1142i | 1.62372i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.3958 | 1.29256 | ||||||||
\(554\) | −18.3675 | −0.780360 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.43228i | 0.272790i | ||||||||
\(557\) | − | 2.63483i | − | 0.111641i | −0.998441 | − | 0.0558207i | \(-0.982222\pi\) | ||
0.998441 | − | 0.0558207i | \(-0.0177775\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.1751 | −1.48775 | ||||||||
\(560\) | 3.69493i | 0.156139i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.3203 | 1.06807 | ||||||||
\(563\) | 38.2567 | 1.61233 | 0.806164 | − | 0.591692i | \(-0.201540\pi\) | ||||
0.806164 | + | 0.591692i | \(0.201540\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.07969 | 0.0874932 | ||||||||
\(566\) | −11.0733 | −0.465444 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.07879i | 0.338979i | ||||||||
\(569\) | 5.20352i | 0.218143i | 0.994034 | + | 0.109071i | \(0.0347877\pi\) | ||||
−0.994034 | + | 0.109071i | \(0.965212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.3913 | 0.434862 | 0.217431 | − | 0.976076i | \(-0.430232\pi\) | ||||
0.217431 | + | 0.976076i | \(0.430232\pi\) | |||||||
\(572\) | 30.8959i | 1.29182i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 36.9366i | 1.54171i | ||||||||
\(575\) | − | 5.65818i | − | 0.235963i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.2770i | 0.802512i | 0.915966 | + | 0.401256i | \(0.131426\pi\) | ||||
−0.915966 | + | 0.401256i | \(0.868574\pi\) | |||||||
\(578\) | −16.9361 | −0.704450 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 9.12065i | − | 0.378714i | ||||||
\(581\) | −46.6047 | −1.93349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.2511 | −0.714469 | ||||||||
\(584\) | −2.89962 | −0.119987 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 18.9742i | − | 0.783817i | ||||||
\(587\) | 2.17246 | 0.0896671 | 0.0448336 | − | 0.998994i | \(-0.485724\pi\) | ||||
0.0448336 | + | 0.998994i | \(0.485724\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.2084i | − | 1.24472i | ||||||
\(590\) | − | 11.2319i | − | 0.462408i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.83907 | −0.239984 | ||||||||
\(593\) | −5.74134 | −0.235769 | −0.117884 | − | 0.993027i | \(-0.537611\pi\) | ||||
−0.117884 | + | 0.993027i | \(0.537611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.933890 | −0.0382857 | ||||||||
\(596\) | − | 14.0925i | − | 0.577252i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 34.2600 | 1.40100 | ||||||||
\(599\) | 8.81011 | 0.359971 | 0.179986 | − | 0.983669i | \(-0.442395\pi\) | ||||
0.179986 | + | 0.983669i | \(0.442395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7296 | 0.478460 | 0.239230 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239230 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(602\) | 21.4650 | 0.874847 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.8467 | −0.929621 | ||||||||
\(605\) | −15.0363 | −0.611313 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7653 | 1.41108 | 0.705540 | − | 0.708670i | \(-0.250705\pi\) | ||||
0.705540 | + | 0.708670i | \(0.250705\pi\) | |||||||
\(608\) | −4.17889 | −0.169476 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.77473i | 0.112346i | ||||||||
\(611\) | −78.9394 | −3.19354 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.566756 | −0.0228911 | −0.0114455 | − | 0.999934i | \(-0.503643\pi\) | ||||
−0.0114455 | + | 0.999934i | \(0.503643\pi\) | |||||||
\(614\) | −17.4969 | −0.706116 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 18.8537i | − | 0.759636i | ||||||
\(617\) | − | 18.1445i | − | 0.730471i | −0.930915 | − | 0.365235i | \(-0.880989\pi\) | ||
0.930915 | − | 0.365235i | \(-0.119011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2328 | 0.692645 | 0.346323 | − | 0.938115i | \(-0.387430\pi\) | ||||
0.346323 | + | 0.938115i | \(0.387430\pi\) | |||||||
\(620\) | 7.22881i | 0.290316i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7799 | 0.472331 | ||||||||
\(623\) | 9.96894 | 0.399397 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − | 23.4886i | − | 0.938794i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.3930 | −0.773865 | ||||||||
\(629\) | − | 1.47582i | − | 0.0588448i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.6732i | 0.663749i | 0.943324 | + | 0.331874i | \(0.107681\pi\) | ||||
−0.943324 | + | 0.331874i | \(0.892319\pi\) | |||||||
\(632\) | − | 8.22636i | − | 0.327227i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.0150i | 1.15233i | ||||||||
\(635\) | 10.2156 | 0.405393 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.2806i | 1.59598i | ||||||||
\(638\) | 46.5388i | 1.84249i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 11.4261 | 0.451304 | 0.225652 | − | 0.974208i | \(-0.427549\pi\) | ||||
0.225652 | + | 0.974208i | \(0.427549\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.0283 | −1.49969 | −0.749845 | − | 0.661614i | \(-0.769872\pi\) | ||||
−0.749845 | + | 0.661614i | \(0.769872\pi\) | |||||||
\(644\) | −20.9066 | −0.823835 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 1.05621i | − | 0.0415560i | ||||||
\(647\) | 31.0064 | 1.21899 | 0.609493 | − | 0.792792i | \(-0.291373\pi\) | ||||
0.609493 | + | 0.792792i | \(0.291373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.3114i | 2.24967i | ||||||||
\(650\) | 6.05495i | 0.237495i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.65798 | −0.378236 | ||||||||
\(653\) | −27.1561 | −1.06270 | −0.531351 | − | 0.847152i | \(-0.678315\pi\) | ||||
−0.531351 | + | 0.847152i | \(0.678315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.2121i | − | 0.672531i | ||||||
\(656\) | 9.99657 | 0.390301 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 48.1714 | 1.87792 | ||||||||
\(659\) | − | 38.9300i | − | 1.51650i | −0.651964 | − | 0.758249i | \(-0.726055\pi\) | ||
0.651964 | − | 0.758249i | \(-0.273945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 45.9057i | − | 1.78553i | −0.450527 | − | 0.892763i | \(-0.648764\pi\) | ||
0.450527 | − | 0.892763i | \(-0.351236\pi\) | |||||||
\(662\) | − | 19.2208i | − | 0.747036i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.6131i | 0.489485i | ||||||||
\(665\) | 15.4407i | 0.598765i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.6063 | 1.99820 | ||||||||
\(668\) | 17.3264i | 0.670377i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.06213 | − | 5.50005i | 0.234201 | − | 0.212486i | ||||
\(671\) | − | 14.1583i | − | 0.546575i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.3170i | 0.744616i | 0.928109 | + | 0.372308i | \(0.121434\pi\) | ||||
−0.928109 | + | 0.372308i | \(0.878566\pi\) | |||||||
\(674\) | − | 1.60819i | − | 0.0619451i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.6624 | −0.910094 | ||||||||
\(677\) | 36.3806 | 1.39822 | 0.699110 | − | 0.715014i | \(-0.253580\pi\) | ||||
0.699110 | + | 0.715014i | \(0.253580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.7470 | −0.565939 | ||||||||
\(680\) | 0.252749i | 0.00969248i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 36.8856i | − | 1.41242i | ||||||
\(683\) | −13.5354 | −0.517918 | −0.258959 | − | 0.965888i | \(-0.583380\pi\) | ||||
−0.258959 | + | 0.965888i | \(0.583380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1870 | 0.733098 | ||||||||
\(686\) | 1.28396i | 0.0490219i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 5.80931i | − | 0.221478i | ||||||
\(689\) | − | 20.4710i | − | 0.779882i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.8320 | −1.36312 | −0.681558 | − | 0.731764i | \(-0.738697\pi\) | ||||
−0.681558 | + | 0.731764i | \(0.738697\pi\) | |||||||
\(692\) | − | 5.05361i | − | 0.192110i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.77771 | 0.143400 | ||||||||
\(695\) | − | 6.43228i | − | 0.243990i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.52662i | 0.0957027i | ||||||||
\(698\) | 21.3534 | 0.808237 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 3.69493i | − | 0.139655i | ||||||
\(701\) | 31.6230 | 1.19438 | 0.597192 | − | 0.802099i | \(-0.296283\pi\) | ||||
0.597192 | + | 0.802099i | \(0.296283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.4008 | −0.920295 | ||||||||
\(704\) | −5.10258 | −0.192311 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.9172 | −0.824864 | ||||||||
\(707\) | − | 4.52651i | − | 0.170237i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.65099 | −0.212228 | −0.106114 | − | 0.994354i | \(-0.533841\pi\) | ||||
−0.106114 | + | 0.994354i | \(0.533841\pi\) | |||||||
\(710\) | − | 8.07879i | − | 0.303192i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 2.69800i | − | 0.101112i | ||||||
\(713\) | −40.9019 | −1.53179 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 30.8959i | − | 1.15544i | ||||||
\(716\) | 22.7443 | 0.849995 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.2681i | 1.09228i | ||||||||
\(719\) | − | 15.4960i | − | 0.577904i | −0.957344 | − | 0.288952i | \(-0.906693\pi\) | ||
0.957344 | − | 0.288952i | \(-0.0933067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 21.8832i | − | 0.814975i | ||||||
\(722\) | 1.53687 | 0.0571963 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.4253 | 0.684770 | ||||||||
\(725\) | 9.12065i | 0.338732i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 30.3663i | − | 1.12622i | −0.826381 | − | 0.563111i | \(-0.809604\pi\) | ||
0.826381 | − | 0.563111i | \(-0.190396\pi\) | |||||||
\(728\) | 22.3726 | 0.829185 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.89962 | 0.107320 | ||||||||
\(731\) | 1.46830 | 0.0543069 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.88141i | − | 0.0694914i | −0.999396 | − | 0.0347457i | \(-0.988938\pi\) | ||
0.999396 | − | 0.0347457i | \(-0.0110621\pi\) | |||||||
\(734\) | 25.5770i | 0.944066i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.65818i | 0.208563i | ||||||||
\(737\) | −30.9325 | + | 28.0644i | −1.13941 | + | 1.03377i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.4545i | 1.12029i | 0.828395 | + | 0.560144i | \(0.189254\pi\) | ||||
−0.828395 | + | 0.560144i | \(0.810746\pi\) | |||||||
\(740\) | 5.83907 | 0.214649 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.4921i | 0.458598i | ||||||||
\(743\) | 8.21651i | 0.301434i | 0.988577 | + | 0.150717i | \(0.0481583\pi\) | ||||
−0.988577 | + | 0.150717i | \(0.951842\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0925i | 0.516310i | ||||||||
\(746\) | 17.3266i | 0.634373i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.28967i | − | 0.0471551i | ||||||
\(749\) | 26.2543 | 0.959311 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.45700 | 0.235619 | 0.117810 | − | 0.993036i | \(-0.462413\pi\) | ||||
0.117810 | + | 0.993036i | \(0.462413\pi\) | |||||||
\(752\) | − | 13.0372i | − | 0.475416i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −55.2251 | −2.01118 | ||||||||
\(755\) | 22.8467 | 0.831478 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.20766i | 0.189276i | 0.995512 | + | 0.0946379i | \(0.0301693\pi\) | ||||
−0.995512 | + | 0.0946379i | \(0.969831\pi\) | |||||||
\(758\) | 7.93843i | 0.288337i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.17889 | 0.151584 | ||||||||
\(761\) | − | 15.7464i | − | 0.570805i | −0.958408 | − | 0.285403i | \(-0.907873\pi\) | ||
0.958408 | − | 0.285403i | \(-0.0921273\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.6349 | 0.421210 | ||||||||
\(764\) | −20.9633 | −0.758424 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.9184 | 0.647418 | ||||||||
\(767\) | −68.0083 | −2.45564 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.6659i | 1.39433i | 0.716912 | + | 0.697164i | \(0.245555\pi\) | ||||
−0.716912 | + | 0.697164i | \(0.754445\pi\) | |||||||
\(770\) | 18.8537i | 0.679439i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.26799 | −0.261581 | ||||||||
\(773\) | 1.53017i | 0.0550362i | 0.999621 | + | 0.0275181i | \(0.00876039\pi\) | ||||
−0.999621 | + | 0.0275181i | \(0.991240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.22881i | − | 0.259666i | ||||||
\(776\) | 3.99115i | 0.143274i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 22.9267i | − | 0.821963i | ||||||
\(779\) | 41.7746 | 1.49673 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.2227i | 1.47506i | ||||||||
\(782\) | −1.43010 | −0.0511403 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.65251 | −0.237590 | ||||||||
\(785\) | 19.3930 | 0.692166 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.0785i | 1.03654i | 0.855218 | + | 0.518268i | \(0.173423\pi\) | ||||
−0.855218 | + | 0.518268i | \(0.826577\pi\) | |||||||
\(788\) | 24.5976 | 0.876253 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.22636i | 0.292681i | ||||||||
\(791\) | 7.68430i | 0.273222i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8009 | 0.596617 | ||||||||
\(794\) | −8.23403 | −0.292215 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.2070 | 0.574441 | ||||||||
\(797\) | 40.4456i | 1.43266i | 0.697763 | + | 0.716329i | \(0.254179\pi\) | ||||
−0.697763 | + | 0.716329i | \(0.745821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.29513 | 0.116573 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.68848 | 0.165556 | ||||||||
\(803\) | −14.7955 | −0.522123 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.9066 | 0.736861 | ||||||||
\(806\) | 43.7701 | 1.54174 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.22506 | −0.0430974 | ||||||||
\(809\) | −41.0065 | −1.44171 | −0.720857 | − | 0.693084i | \(-0.756251\pi\) | ||||
−0.720857 | + | 0.693084i | \(0.756251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 43.6942i | − | 1.53431i | −0.641462 | − | 0.767155i | \(-0.721672\pi\) | ||
0.641462 | − | 0.767155i | \(-0.278328\pi\) | |||||||
\(812\) | 33.7002 | 1.18264 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.7943 | −1.04429 | ||||||||
\(815\) | 9.65798 | 0.338304 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.2765i | − | 0.849326i | ||||||
\(818\) | − | 24.6532i | − | 0.861978i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.99657 | −0.349095 | ||||||||
\(821\) | − | 1.40258i | − | 0.0489503i | −0.999700 | − | 0.0244752i | \(-0.992209\pi\) | ||
0.999700 | − | 0.0244752i | \(-0.00779146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.9384 | −1.25273 | −0.626367 | − | 0.779528i | \(-0.715459\pi\) | ||||
−0.626367 | + | 0.779528i | \(0.715459\pi\) | |||||||
\(824\) | −5.92251 | −0.206320 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41.5009 | 1.44400 | ||||||||
\(827\) | − | 10.6722i | − | 0.371110i | −0.982634 | − | 0.185555i | \(-0.940592\pi\) | ||
0.982634 | − | 0.185555i | \(-0.0594084\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.9736 | −0.693711 | −0.346855 | − | 0.937919i | \(-0.612751\pi\) | ||||
−0.346855 | + | 0.937919i | \(0.612751\pi\) | |||||||
\(830\) | − | 12.6131i | − | 0.437808i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 6.05495i | − | 0.209918i | ||||||
\(833\) | − | 1.68141i | − | 0.0582575i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 17.3264i | − | 0.599604i | ||||||
\(836\) | −21.3231 | −0.737476 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 24.8106i | − | 0.857067i | ||||||
\(839\) | 8.04265i | 0.277663i | 0.990316 | + | 0.138832i | \(0.0443347\pi\) | ||||
−0.990316 | + | 0.138832i | \(0.955665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −54.1862 | −1.86849 | ||||||||
\(842\) | 8.25483 | 0.284480 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.5763 | 0.811529 | ||||||||
\(845\) | 23.6624 | 0.814013 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 55.5581i | − | 1.90900i | ||||||
\(848\) | 3.38087 | 0.116099 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 0.252749i | − | 0.00866922i | ||||||
\(851\) | 33.0385i | 1.13255i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.8493 | −1.12474 | −0.562369 | − | 0.826886i | \(-0.690110\pi\) | ||||
−0.562369 | + | 0.826886i | \(0.690110\pi\) | |||||||
\(854\) | −10.2525 | −0.350832 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 7.10549i | − | 0.242861i | ||||||
\(857\) | 8.10834 | 0.276975 | 0.138488 | − | 0.990364i | \(-0.455776\pi\) | ||||
0.138488 | + | 0.990364i | \(0.455776\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.2358 | 1.74814 | 0.874072 | − | 0.485796i | \(-0.161470\pi\) | ||||
0.874072 | + | 0.485796i | \(0.161470\pi\) | |||||||
\(860\) | 5.80931i | 0.198096i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 3.92206i | − | 0.133586i | ||||||
\(863\) | 17.6393i | 0.600450i | 0.953868 | + | 0.300225i | \(0.0970618\pi\) | ||||
−0.953868 | + | 0.300225i | \(0.902938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.05361i | 0.171828i | ||||||||
\(866\) | 12.5714i | 0.427192i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.7099 | −0.906594 | ||||||||
\(869\) | − | 41.9756i | − | 1.42393i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.3025 | − | 36.7059i | −1.12841 | − | 1.24373i | ||||
\(872\) | − | 3.14887i | − | 0.106634i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 23.6449i | 0.799802i | ||||||||
\(875\) | 3.69493i | 0.124911i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.7958 | −1.74902 | −0.874511 | − | 0.485006i | \(-0.838817\pi\) | ||||
−0.874511 | + | 0.485006i | \(0.838817\pi\) | |||||||
\(878\) | 38.7852 | 1.30894 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.10258 | 0.172008 | ||||||||
\(881\) | − | 26.1742i | − | 0.881830i | −0.897549 | − | 0.440915i | \(-0.854654\pi\) | ||
0.897549 | − | 0.440915i | \(-0.145346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.4097i | 0.451273i | 0.974212 | + | 0.225636i | \(0.0724461\pi\) | ||||
−0.974212 | + | 0.225636i | \(0.927554\pi\) | |||||||
\(884\) | 1.53038 | 0.0514723 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 34.5708 | 1.16143 | ||||||||
\(887\) | − | 15.8830i | − | 0.533298i | −0.963794 | − | 0.266649i | \(-0.914084\pi\) | ||
0.963794 | − | 0.266649i | \(-0.0859164\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.7458i | 1.26595i | ||||||||
\(890\) | 2.69800i | 0.0904373i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.31407 | 0.0439983 | ||||||||
\(893\) | − | 54.4809i | − | 1.82313i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.7443 | −0.760258 | ||||||||
\(896\) | 3.69493i | 0.123439i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 34.8770i | 1.16386i | ||||||||
\(899\) | 65.9314 | 2.19894 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.854510i | 0.0284679i | ||||||||
\(902\) | 51.0083 | 1.69839 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.07969 | 0.0691694 | ||||||||
\(905\) | −18.4253 | −0.612477 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.8398 | 1.09043 | 0.545213 | − | 0.838298i | \(-0.316449\pi\) | ||||
0.545213 | + | 0.838298i | \(0.316449\pi\) | |||||||
\(908\) | 18.0703i | 0.599683i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22.3726 | −0.741645 | ||||||||
\(911\) | 38.8299i | 1.28649i | 0.765659 | + | 0.643246i | \(0.222413\pi\) | ||||
−0.765659 | + | 0.643246i | \(0.777587\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64.3595i | 2.12999i | ||||||||
\(914\) | 1.01076 | 0.0334331 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.73041i | 0.321502i | ||||||||
\(917\) | 63.5974 | 2.10017 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.0194i | 0.561418i | 0.959793 | + | 0.280709i | \(0.0905696\pi\) | ||||
−0.959793 | + | 0.280709i | \(0.909430\pi\) | |||||||
\(920\) | − | 5.65818i | − | 0.186545i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 19.6304i | − | 0.646493i | ||||||
\(923\) | −48.9167 | −1.61011 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.83907 | −0.191987 | ||||||||
\(926\) | 8.70958i | 0.286215i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 9.12065i | − | 0.299400i | ||||||
\(929\) | −26.1858 | −0.859128 | −0.429564 | − | 0.903036i | \(-0.641333\pi\) | ||||
−0.429564 | + | 0.903036i | \(0.641333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.8001 | −0.911112 | ||||||||
\(932\) | −24.9008 | −0.815652 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 23.3816i | − | 0.765069i | ||||||
\(935\) | 1.28967i | 0.0421768i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.58651i | − | 0.0518290i | −0.999664 | − | 0.0259145i | \(-0.991750\pi\) | ||
0.999664 | − | 0.0259145i | \(-0.00824977\pi\) | |||||||
\(938\) | 20.3223 | + | 22.3992i | 0.663547 | + | 0.731358i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.0372i | 0.425225i | ||||||||
\(941\) | 18.2168 | 0.593852 | 0.296926 | − | 0.954901i | \(-0.404039\pi\) | ||||
0.296926 | + | 0.954901i | \(0.404039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 56.5625i | − | 1.84193i | ||||||
\(944\) | − | 11.2319i | − | 0.365566i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 29.6424i | − | 0.963759i | ||||||
\(947\) | − | 38.8832i | − | 1.26353i | −0.775158 | − | 0.631767i | \(-0.782330\pi\) | ||
0.775158 | − | 0.631767i | \(-0.217670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 17.5570i | − | 0.569925i | ||||||
\(950\) | −4.17889 | −0.135581 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.933890 | −0.0302675 | ||||||||
\(953\) | 35.5052i | 1.15013i | 0.818109 | + | 0.575063i | \(0.195022\pi\) | ||||
−0.818109 | + | 0.575063i | \(0.804978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.9633 | 0.678355 | ||||||||
\(956\) | −21.1041 | −0.682555 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.5193i | 0.469099i | ||||||||
\(959\) | 70.8947i | 2.28931i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.2557 | −0.685666 | ||||||||
\(962\) | − | 35.3553i | − | 1.13990i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.7911 | 0.508597 | ||||||||
\(965\) | 7.26799 | 0.233965 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.46649 | 0.207948 | 0.103974 | − | 0.994580i | \(-0.466844\pi\) | ||||
0.103974 | + | 0.994580i | \(0.466844\pi\) | |||||||
\(968\) | −15.0363 | −0.483285 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 3.99115i | − | 0.128148i | ||||||
\(971\) | − | 14.2357i | − | 0.456845i | −0.973562 | − | 0.228423i | \(-0.926643\pi\) | ||
0.973562 | − | 0.228423i | \(-0.0733568\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.7668 | 0.761930 | ||||||||
\(974\) | 13.5245i | 0.433352i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.77473i | 0.0888171i | ||||||||
\(977\) | 2.57587i | 0.0824093i | 0.999151 | + | 0.0412047i | \(0.0131196\pi\) | ||||
−0.999151 | + | 0.0412047i | \(0.986880\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.7668i | − | 0.439988i | ||||||
\(980\) | 6.65251 | 0.212507 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.6500i | 0.563233i | ||||||||
\(983\) | 48.3618 | 1.54250 | 0.771251 | − | 0.636531i | \(-0.219631\pi\) | ||||
0.771251 | + | 0.636531i | \(0.219631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.5976 | −0.783745 | ||||||||
\(986\) | 2.30523 | 0.0734136 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 25.3030i | − | 0.804995i | ||||||
\(989\) | −32.8701 | −1.04521 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.8339i | 1.01124i | 0.862757 | + | 0.505619i | \(0.168736\pi\) | ||||
−0.862757 | + | 0.505619i | \(0.831264\pi\) | |||||||
\(992\) | 7.22881i | 0.229515i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 29.8506 | 0.946802 | ||||||||
\(995\) | −16.2070 | −0.513796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.5571 | 1.28446 | 0.642228 | − | 0.766513i | \(-0.278010\pi\) | ||||
0.642228 | + | 0.766513i | \(0.278010\pi\) | |||||||
\(998\) | − | 32.0141i | − | 1.01339i | ||||||
\(999\) | 0 | 0 |
(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 | 6030.2.d.k.2411.2 | ✓ | 24 | |
3.2 | odd | 2 | 6030.2.d.l.2411.2 | yes | 24 | ||
67.66 | odd | 2 | 6030.2.d.l.2411.23 | yes | 24 | ||
201.200 | even | 2 | inner | 6030.2.d.k.2411.23 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6030.2.d.k.2411.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
6030.2.d.k.2411.23 | yes | 24 | 201.200 | even | 2 | inner | |
6030.2.d.l.2411.2 | yes | 24 | 3.2 | odd | 2 | ||
6030.2.d.l.2411.23 | yes | 24 | 67.66 | odd | 2 |