Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.t.1351.3 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | − 1.00000i | − 0.408248i | ||||||||
\(7\) | − 3.04892i | − 1.15238i | −0.817315 | − | 0.576191i | \(-0.804538\pi\) | ||||
0.817315 | − | 0.576191i | \(-0.195462\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | − 1.13706i | − 0.342837i | −0.985198 | − | 0.171419i | \(-0.945165\pi\) | ||||
0.985198 | − | 0.171419i | \(-0.0548351\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.04892 | 0.814857 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.69202 | −0.652911 | −0.326456 | − | 0.945213i | \(-0.605854\pi\) | ||||
−0.326456 | + | 0.945213i | \(0.605854\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.55496i | 0.356732i | 0.983964 | + | 0.178366i | \(0.0570811\pi\) | ||||
−0.983964 | + | 0.178366i | \(0.942919\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 3.04892i | 0.665328i | ||||||||
\(22\) | 1.13706 | 0.242423 | ||||||||
\(23\) | −5.40581 | −1.12719 | −0.563595 | − | 0.826051i | \(-0.690582\pi\) | ||||
−0.563595 | + | 0.826051i | \(0.690582\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.04892i | 0.576191i | ||||||||
\(29\) | −6.15883 | −1.14367 | −0.571833 | − | 0.820370i | \(-0.693768\pi\) | ||||
−0.571833 | + | 0.820370i | \(0.693768\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | − 0.246980i | − 0.0443588i | −0.999754 | − | 0.0221794i | \(-0.992939\pi\) | ||||
0.999754 | − | 0.0221794i | \(-0.00706051\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.13706i | 0.197937i | ||||||||
\(34\) | − 2.69202i | − 0.461678i | ||||||||
\(35\) | 3.04892 | 0.515361 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.554958i | 0.0912346i | 0.998959 | + | 0.0456173i | \(0.0145255\pi\) | ||||
−0.998959 | + | 0.0456173i | \(0.985475\pi\) | |||||||
\(38\) | −1.55496 | −0.252248 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 8.26875i | 1.29136i | 0.763607 | + | 0.645681i | \(0.223426\pi\) | ||||
−0.763607 | + | 0.645681i | \(0.776574\pi\) | |||||||
\(42\) | −3.04892 | −0.470458 | ||||||||
\(43\) | −2.03923 | −0.310979 | −0.155490 | − | 0.987838i | \(-0.549696\pi\) | ||||
−0.155490 | + | 0.987838i | \(0.549696\pi\) | |||||||
\(44\) | 1.13706i | 0.171419i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − 5.40581i | − 0.797044i | ||||||||
\(47\) | 6.70171i | 0.977545i | 0.872411 | + | 0.488772i | \(0.162555\pi\) | ||||
−0.872411 | + | 0.488772i | \(0.837445\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −2.29590 | −0.327985 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 2.69202 | 0.376958 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.77479 | 0.793229 | 0.396614 | − | 0.917985i | \(-0.370185\pi\) | ||||
0.396614 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 1.13706 | 0.153322 | ||||||||
\(56\) | −3.04892 | −0.407429 | ||||||||
\(57\) | − 1.55496i | − 0.205959i | ||||||||
\(58\) | − 6.15883i | − 0.808694i | ||||||||
\(59\) | − 1.36898i | − 0.178226i | −0.996022 | − | 0.0891128i | \(-0.971597\pi\) | ||||
0.996022 | − | 0.0891128i | \(-0.0284032\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 10.9487 | 1.40184 | 0.700918 | − | 0.713242i | \(-0.252774\pi\) | ||||
0.700918 | + | 0.713242i | \(0.252774\pi\) | |||||||
\(62\) | 0.246980 | 0.0313664 | ||||||||
\(63\) | − 3.04892i | − 0.384127i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.13706 | −0.139963 | ||||||||
\(67\) | − 2.47219i | − 0.302026i | −0.988532 | − | 0.151013i | \(-0.951746\pi\) | ||||
0.988532 | − | 0.151013i | \(-0.0482535\pi\) | |||||||
\(68\) | 2.69202 | 0.326456 | ||||||||
\(69\) | 5.40581 | 0.650783 | ||||||||
\(70\) | 3.04892i | 0.364415i | ||||||||
\(71\) | − 8.57002i | − 1.01707i | −0.861040 | − | 0.508537i | \(-0.830186\pi\) | ||||
0.861040 | − | 0.508537i | \(-0.169814\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 14.8334i | 1.73612i | 0.496461 | + | 0.868059i | \(0.334632\pi\) | ||||
−0.496461 | + | 0.868059i | \(0.665368\pi\) | |||||||
\(74\) | −0.554958 | −0.0645126 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | − 1.55496i | − 0.178366i | ||||||||
\(77\) | −3.46681 | −0.395080 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.33513 | 0.600249 | 0.300124 | − | 0.953900i | \(-0.402972\pi\) | ||||
0.300124 | + | 0.953900i | \(0.402972\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.26875 | −0.913131 | ||||||||
\(83\) | − 5.45473i | − 0.598734i | −0.954138 | − | 0.299367i | \(-0.903224\pi\) | ||||
0.954138 | − | 0.299367i | \(-0.0967756\pi\) | |||||||
\(84\) | − 3.04892i | − 0.332664i | ||||||||
\(85\) | − 2.69202i | − 0.291991i | ||||||||
\(86\) | − 2.03923i | − 0.219896i | ||||||||
\(87\) | 6.15883 | 0.660296 | ||||||||
\(88\) | −1.13706 | −0.121211 | ||||||||
\(89\) | − 16.8877i | − 1.79009i | −0.445974 | − | 0.895046i | \(-0.647143\pi\) | ||||
0.445974 | − | 0.895046i | \(-0.352857\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.40581 | 0.563595 | ||||||||
\(93\) | 0.246980i | 0.0256106i | ||||||||
\(94\) | −6.70171 | −0.691229 | ||||||||
\(95\) | −1.55496 | −0.159535 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 1.93900i | 0.196876i | 0.995143 | + | 0.0984379i | \(0.0313846\pi\) | ||||
−0.995143 | + | 0.0984379i | \(0.968615\pi\) | |||||||
\(98\) | − 2.29590i | − 0.231921i | ||||||||
\(99\) | − 1.13706i | − 0.114279i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 14.4940 | 1.44220 | 0.721101 | − | 0.692830i | \(-0.243636\pi\) | ||||
0.721101 | + | 0.692830i | \(0.243636\pi\) | |||||||
\(102\) | 2.69202i | 0.266550i | ||||||||
\(103\) | 16.1836 | 1.59462 | 0.797308 | − | 0.603572i | \(-0.206257\pi\) | ||||
0.797308 | + | 0.603572i | \(0.206257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.04892 | −0.297544 | ||||||||
\(106\) | 5.77479i | 0.560897i | ||||||||
\(107\) | 4.92931 | 0.476535 | 0.238267 | − | 0.971200i | \(-0.423421\pi\) | ||||
0.238267 | + | 0.971200i | \(0.423421\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 0.801938i | 0.0768117i | 0.999262 | + | 0.0384059i | \(0.0122280\pi\) | ||||
−0.999262 | + | 0.0384059i | \(0.987772\pi\) | |||||||
\(110\) | 1.13706i | 0.108415i | ||||||||
\(111\) | − 0.554958i | − 0.0526743i | ||||||||
\(112\) | − 3.04892i | − 0.288096i | ||||||||
\(113\) | −11.5211 | −1.08381 | −0.541907 | − | 0.840438i | \(-0.682298\pi\) | ||||
−0.541907 | + | 0.840438i | \(0.682298\pi\) | |||||||
\(114\) | 1.55496 | 0.145635 | ||||||||
\(115\) | − 5.40581i | − 0.504095i | ||||||||
\(116\) | 6.15883 | 0.571833 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.36898 | 0.126025 | ||||||||
\(119\) | 8.20775i | 0.752403i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 9.70709 | 0.882462 | ||||||||
\(122\) | 10.9487i | 0.991248i | ||||||||
\(123\) | − 8.26875i | − 0.745568i | ||||||||
\(124\) | 0.246980i | 0.0221794i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 3.04892 | 0.271619 | ||||||||
\(127\) | −6.22521 | −0.552398 | −0.276199 | − | 0.961100i | \(-0.589075\pi\) | ||||
−0.276199 | + | 0.961100i | \(0.589075\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 2.03923 | 0.179544 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.34481 | 0.292238 | 0.146119 | − | 0.989267i | \(-0.453322\pi\) | ||||
0.146119 | + | 0.989267i | \(0.453322\pi\) | |||||||
\(132\) | − 1.13706i | − 0.0989687i | ||||||||
\(133\) | 4.74094 | 0.411092 | ||||||||
\(134\) | 2.47219 | 0.213565 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | 2.69202i | 0.230839i | ||||||||
\(137\) | 9.53079i | 0.814271i | 0.913368 | + | 0.407135i | \(0.133472\pi\) | ||||
−0.913368 | + | 0.407135i | \(0.866528\pi\) | |||||||
\(138\) | 5.40581i | 0.460173i | ||||||||
\(139\) | 18.7017 | 1.58626 | 0.793129 | − | 0.609053i | \(-0.208451\pi\) | ||||
0.793129 | + | 0.609053i | \(0.208451\pi\) | |||||||
\(140\) | −3.04892 | −0.257681 | ||||||||
\(141\) | − 6.70171i | − 0.564386i | ||||||||
\(142\) | 8.57002 | 0.719180 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 6.15883i | − 0.511463i | ||||||||
\(146\) | −14.8334 | −1.22762 | ||||||||
\(147\) | 2.29590 | 0.189362 | ||||||||
\(148\) | − 0.554958i | − 0.0456173i | ||||||||
\(149\) | 16.4209i | 1.34525i | 0.739983 | + | 0.672625i | \(0.234833\pi\) | ||||
−0.739983 | + | 0.672625i | \(0.765167\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 9.26636i | 0.754085i | 0.926196 | + | 0.377043i | \(0.123059\pi\) | ||||
−0.926196 | + | 0.377043i | \(0.876941\pi\) | |||||||
\(152\) | 1.55496 | 0.126124 | ||||||||
\(153\) | −2.69202 | −0.217637 | ||||||||
\(154\) | − 3.46681i | − 0.279364i | ||||||||
\(155\) | 0.246980 | 0.0198379 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.0761 | 1.36282 | 0.681409 | − | 0.731903i | \(-0.261367\pi\) | ||||
0.681409 | + | 0.731903i | \(0.261367\pi\) | |||||||
\(158\) | 5.33513i | 0.424440i | ||||||||
\(159\) | −5.77479 | −0.457971 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 16.4819i | 1.29895i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 9.61894i | 0.753414i | 0.926333 | + | 0.376707i | \(0.122944\pi\) | ||||
−0.926333 | + | 0.376707i | \(0.877056\pi\) | |||||||
\(164\) | − 8.26875i | − 0.645681i | ||||||||
\(165\) | −1.13706 | −0.0885203 | ||||||||
\(166\) | 5.45473 | 0.423369 | ||||||||
\(167\) | − 21.8509i | − 1.69087i | −0.534078 | − | 0.845435i | \(-0.679341\pi\) | ||||
0.534078 | − | 0.845435i | \(-0.320659\pi\) | |||||||
\(168\) | 3.04892 | 0.235229 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2.69202 | 0.206469 | ||||||||
\(171\) | 1.55496i | 0.118911i | ||||||||
\(172\) | 2.03923 | 0.155490 | ||||||||
\(173\) | −16.6853 | −1.26856 | −0.634281 | − | 0.773103i | \(-0.718704\pi\) | ||||
−0.634281 | + | 0.773103i | \(0.718704\pi\) | |||||||
\(174\) | 6.15883i | 0.466900i | ||||||||
\(175\) | 3.04892i | 0.230476i | ||||||||
\(176\) | − 1.13706i | − 0.0857094i | ||||||||
\(177\) | 1.36898i | 0.102899i | ||||||||
\(178\) | 16.8877 | 1.26579 | ||||||||
\(179\) | 3.94438 | 0.294817 | 0.147408 | − | 0.989076i | \(-0.452907\pi\) | ||||
0.147408 | + | 0.989076i | \(0.452907\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | 20.5308 | 1.52604 | 0.763021 | − | 0.646374i | \(-0.223715\pi\) | ||||
0.763021 | + | 0.646374i | \(0.223715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9487 | −0.809350 | ||||||||
\(184\) | 5.40581i | 0.398522i | ||||||||
\(185\) | −0.554958 | −0.0408013 | ||||||||
\(186\) | −0.246980 | −0.0181094 | ||||||||
\(187\) | 3.06100i | 0.223842i | ||||||||
\(188\) | − 6.70171i | − 0.488772i | ||||||||
\(189\) | 3.04892i | 0.221776i | ||||||||
\(190\) | − 1.55496i | − 0.112809i | ||||||||
\(191\) | −6.66487 | −0.482253 | −0.241127 | − | 0.970494i | \(-0.577517\pi\) | ||||
−0.241127 | + | 0.970494i | \(0.577517\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 16.6558i | − 1.19891i | −0.800409 | − | 0.599455i | \(-0.795384\pi\) | ||||
0.800409 | − | 0.599455i | \(-0.204616\pi\) | |||||||
\(194\) | −1.93900 | −0.139212 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.29590 | 0.163993 | ||||||||
\(197\) | 19.4494i | 1.38571i | 0.721077 | + | 0.692855i | \(0.243647\pi\) | ||||
−0.721077 | + | 0.692855i | \(0.756353\pi\) | |||||||
\(198\) | 1.13706 | 0.0808076 | ||||||||
\(199\) | 21.6558 | 1.53514 | 0.767569 | − | 0.640967i | \(-0.221466\pi\) | ||||
0.767569 | + | 0.640967i | \(0.221466\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 2.47219i | 0.174375i | ||||||||
\(202\) | 14.4940i | 1.01979i | ||||||||
\(203\) | 18.7778i | 1.31794i | ||||||||
\(204\) | −2.69202 | −0.188479 | ||||||||
\(205\) | −8.26875 | −0.577515 | ||||||||
\(206\) | 16.1836i | 1.12756i | ||||||||
\(207\) | −5.40581 | −0.375730 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.76809 | 0.122301 | ||||||||
\(210\) | − 3.04892i | − 0.210395i | ||||||||
\(211\) | 12.1521 | 0.836587 | 0.418294 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418294 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(212\) | −5.77479 | −0.396614 | ||||||||
\(213\) | 8.57002i | 0.587208i | ||||||||
\(214\) | 4.92931i | 0.336961i | ||||||||
\(215\) | − 2.03923i | − 0.139074i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −0.753020 | −0.0511184 | ||||||||
\(218\) | −0.801938 | −0.0543141 | ||||||||
\(219\) | − 14.8334i | − 1.00235i | ||||||||
\(220\) | −1.13706 | −0.0766608 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.554958 | 0.0372464 | ||||||||
\(223\) | 1.11960i | 0.0749743i | 0.999297 | + | 0.0374871i | \(0.0119353\pi\) | ||||
−0.999297 | + | 0.0374871i | \(0.988065\pi\) | |||||||
\(224\) | 3.04892 | 0.203714 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 11.5211i | − 0.766373i | ||||||||
\(227\) | 4.06638i | 0.269895i | 0.990853 | + | 0.134947i | \(0.0430866\pi\) | ||||
−0.990853 | + | 0.134947i | \(0.956913\pi\) | |||||||
\(228\) | 1.55496i | 0.102980i | ||||||||
\(229\) | 16.5187i | 1.09159i | 0.837920 | + | 0.545794i | \(0.183772\pi\) | ||||
−0.837920 | + | 0.545794i | \(0.816228\pi\) | |||||||
\(230\) | 5.40581 | 0.356449 | ||||||||
\(231\) | 3.46681 | 0.228099 | ||||||||
\(232\) | 6.15883i | 0.404347i | ||||||||
\(233\) | 6.16421 | 0.403831 | 0.201915 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201915 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70171 | −0.437171 | ||||||||
\(236\) | 1.36898i | 0.0891128i | ||||||||
\(237\) | −5.33513 | −0.346554 | ||||||||
\(238\) | −8.20775 | −0.532029 | ||||||||
\(239\) | 18.1793i | 1.17592i | 0.808890 | + | 0.587960i | \(0.200069\pi\) | ||||
−0.808890 | + | 0.587960i | \(0.799931\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 9.21744i | 0.593747i | 0.954917 | + | 0.296874i | \(0.0959441\pi\) | ||||
−0.954917 | + | 0.296874i | \(0.904056\pi\) | |||||||
\(242\) | 9.70709i | 0.623995i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.9487 | −0.700918 | ||||||||
\(245\) | − 2.29590i | − 0.146679i | ||||||||
\(246\) | 8.26875 | 0.527196 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.246980 | −0.0156832 | ||||||||
\(249\) | 5.45473i | 0.345680i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −17.2054 | −1.08599 | −0.542996 | − | 0.839735i | \(-0.682710\pi\) | ||||
−0.542996 | + | 0.839735i | \(0.682710\pi\) | |||||||
\(252\) | 3.04892i | 0.192064i | ||||||||
\(253\) | 6.14675i | 0.386443i | ||||||||
\(254\) | − 6.22521i | − 0.390604i | ||||||||
\(255\) | 2.69202i | 0.168581i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.5157 | 1.21736 | 0.608679 | − | 0.793417i | \(-0.291700\pi\) | ||||
0.608679 | + | 0.793417i | \(0.291700\pi\) | |||||||
\(258\) | 2.03923i | 0.126957i | ||||||||
\(259\) | 1.69202 | 0.105137 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.15883 | −0.381222 | ||||||||
\(262\) | 3.34481i | 0.206643i | ||||||||
\(263\) | 12.8834 | 0.794423 | 0.397212 | − | 0.917727i | \(-0.369978\pi\) | ||||
0.397212 | + | 0.917727i | \(0.369978\pi\) | |||||||
\(264\) | 1.13706 | 0.0699814 | ||||||||
\(265\) | 5.77479i | 0.354743i | ||||||||
\(266\) | 4.74094i | 0.290686i | ||||||||
\(267\) | 16.8877i | 1.03351i | ||||||||
\(268\) | 2.47219i | 0.151013i | ||||||||
\(269\) | −30.9138 | −1.88485 | −0.942423 | − | 0.334423i | \(-0.891459\pi\) | ||||
−0.942423 | + | 0.334423i | \(0.891459\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 7.24027i | − 0.439815i | −0.975521 | − | 0.219908i | \(-0.929424\pi\) | ||||
0.975521 | − | 0.219908i | \(-0.0705756\pi\) | |||||||
\(272\) | −2.69202 | −0.163228 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.53079 | −0.575776 | ||||||||
\(275\) | 1.13706i | 0.0685675i | ||||||||
\(276\) | −5.40581 | −0.325392 | ||||||||
\(277\) | −12.2446 | −0.735706 | −0.367853 | − | 0.929884i | \(-0.619907\pi\) | ||||
−0.367853 | + | 0.929884i | \(0.619907\pi\) | |||||||
\(278\) | 18.7017i | 1.12165i | ||||||||
\(279\) | − 0.246980i | − 0.0147863i | ||||||||
\(280\) | − 3.04892i | − 0.182208i | ||||||||
\(281\) | 2.74632i | 0.163831i | 0.996639 | + | 0.0819157i | \(0.0261038\pi\) | ||||
−0.996639 | + | 0.0819157i | \(0.973896\pi\) | |||||||
\(282\) | 6.70171 | 0.399081 | ||||||||
\(283\) | −14.9312 | −0.887570 | −0.443785 | − | 0.896133i | \(-0.646365\pi\) | ||||
−0.443785 | + | 0.896133i | \(0.646365\pi\) | |||||||
\(284\) | 8.57002i | 0.508537i | ||||||||
\(285\) | 1.55496 | 0.0921078 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 25.2107 | 1.48814 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −9.75302 | −0.573707 | ||||||||
\(290\) | 6.15883 | 0.361659 | ||||||||
\(291\) | − 1.93900i | − 0.113666i | ||||||||
\(292\) | − 14.8334i | − 0.868059i | ||||||||
\(293\) | − 18.5810i | − 1.08552i | −0.839889 | − | 0.542758i | \(-0.817380\pi\) | ||||
0.839889 | − | 0.542758i | \(-0.182620\pi\) | |||||||
\(294\) | 2.29590i | 0.133899i | ||||||||
\(295\) | 1.36898 | 0.0797049 | ||||||||
\(296\) | 0.554958 | 0.0322563 | ||||||||
\(297\) | 1.13706i | 0.0659791i | ||||||||
\(298\) | −16.4209 | −0.951236 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 6.21744i | 0.358367i | ||||||||
\(302\) | −9.26636 | −0.533219 | ||||||||
\(303\) | −14.4940 | −0.832656 | ||||||||
\(304\) | 1.55496i | 0.0891830i | ||||||||
\(305\) | 10.9487i | 0.626920i | ||||||||
\(306\) | − 2.69202i | − 0.153893i | ||||||||
\(307\) | − 32.4359i | − 1.85122i | −0.378482 | − | 0.925609i | \(-0.623554\pi\) | ||||
0.378482 | − | 0.925609i | \(-0.376446\pi\) | |||||||
\(308\) | 3.46681 | 0.197540 | ||||||||
\(309\) | −16.1836 | −0.920652 | ||||||||
\(310\) | 0.246980i | 0.0140275i | ||||||||
\(311\) | 21.2771 | 1.20651 | 0.603257 | − | 0.797547i | \(-0.293869\pi\) | ||||
0.603257 | + | 0.797547i | \(0.293869\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7060 | −1.05733 | −0.528663 | − | 0.848832i | \(-0.677307\pi\) | ||||
−0.528663 | + | 0.848832i | \(0.677307\pi\) | |||||||
\(314\) | 17.0761i | 0.963658i | ||||||||
\(315\) | 3.04892 | 0.171787 | ||||||||
\(316\) | −5.33513 | −0.300124 | ||||||||
\(317\) | 17.4776i | 0.981638i | 0.871262 | + | 0.490819i | \(0.163302\pi\) | ||||
−0.871262 | + | 0.490819i | \(0.836698\pi\) | |||||||
\(318\) | − 5.77479i | − 0.323834i | ||||||||
\(319\) | 7.00298i | 0.392092i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | −4.92931 | −0.275127 | ||||||||
\(322\) | −16.4819 | −0.918499 | ||||||||
\(323\) | − 4.18598i | − 0.232914i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.61894 | −0.532744 | ||||||||
\(327\) | − 0.801938i | − 0.0443473i | ||||||||
\(328\) | 8.26875 | 0.456565 | ||||||||
\(329\) | 20.4330 | 1.12651 | ||||||||
\(330\) | − 1.13706i | − 0.0625933i | ||||||||
\(331\) | − 23.1890i | − 1.27458i | −0.770624 | − | 0.637290i | \(-0.780055\pi\) | ||||
0.770624 | − | 0.637290i | \(-0.219945\pi\) | |||||||
\(332\) | 5.45473i | 0.299367i | ||||||||
\(333\) | 0.554958i | 0.0304115i | ||||||||
\(334\) | 21.8509 | 1.19563 | ||||||||
\(335\) | 2.47219 | 0.135070 | ||||||||
\(336\) | 3.04892i | 0.166332i | ||||||||
\(337\) | 26.1400 | 1.42394 | 0.711970 | − | 0.702210i | \(-0.247803\pi\) | ||||
0.711970 | + | 0.702210i | \(0.247803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.5211 | 0.625741 | ||||||||
\(340\) | 2.69202i | 0.145995i | ||||||||
\(341\) | −0.280831 | −0.0152079 | ||||||||
\(342\) | −1.55496 | −0.0840825 | ||||||||
\(343\) | − 14.3424i | − 0.774418i | ||||||||
\(344\) | 2.03923i | 0.109948i | ||||||||
\(345\) | 5.40581i | 0.291039i | ||||||||
\(346\) | − 16.6853i | − 0.897008i | ||||||||
\(347\) | 15.2959 | 0.821127 | 0.410563 | − | 0.911832i | \(-0.365332\pi\) | ||||
0.410563 | + | 0.911832i | \(0.365332\pi\) | |||||||
\(348\) | −6.15883 | −0.330148 | ||||||||
\(349\) | 19.2107i | 1.02833i | 0.857692 | + | 0.514164i | \(0.171898\pi\) | ||||
−0.857692 | + | 0.514164i | \(0.828102\pi\) | |||||||
\(350\) | −3.04892 | −0.162971 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.13706 | 0.0606057 | ||||||||
\(353\) | − 5.35450i | − 0.284991i | −0.989795 | − | 0.142496i | \(-0.954487\pi\) | ||||
0.989795 | − | 0.142496i | \(-0.0455127\pi\) | |||||||
\(354\) | −1.36898 | −0.0727603 | ||||||||
\(355\) | 8.57002 | 0.454850 | ||||||||
\(356\) | 16.8877i | 0.895046i | ||||||||
\(357\) | − 8.20775i | − 0.434400i | ||||||||
\(358\) | 3.94438i | 0.208467i | ||||||||
\(359\) | − 8.49934i | − 0.448578i | −0.974523 | − | 0.224289i | \(-0.927994\pi\) | ||||
0.974523 | − | 0.224289i | \(-0.0720059\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 16.5821 | 0.872742 | ||||||||
\(362\) | 20.5308i | 1.07907i | ||||||||
\(363\) | −9.70709 | −0.509490 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.8334 | −0.776415 | ||||||||
\(366\) | − 10.9487i | − 0.572297i | ||||||||
\(367\) | 4.76032 | 0.248486 | 0.124243 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124243 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(368\) | −5.40581 | −0.281797 | ||||||||
\(369\) | 8.26875i | 0.430454i | ||||||||
\(370\) | − 0.554958i | − 0.0288509i | ||||||||
\(371\) | − 17.6069i | − 0.914103i | ||||||||
\(372\) | − 0.246980i | − 0.0128053i | ||||||||
\(373\) | −20.2064 | −1.04625 | −0.523124 | − | 0.852256i | \(-0.675234\pi\) | ||||
−0.523124 | + | 0.852256i | \(0.675234\pi\) | |||||||
\(374\) | −3.06100 | −0.158280 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 6.70171 | 0.345614 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.04892 | −0.156819 | ||||||||
\(379\) | 24.4088i | 1.25380i | 0.779101 | + | 0.626898i | \(0.215676\pi\) | ||||
−0.779101 | + | 0.626898i | \(0.784324\pi\) | |||||||
\(380\) | 1.55496 | 0.0797677 | ||||||||
\(381\) | 6.22521 | 0.318927 | ||||||||
\(382\) | − 6.66487i | − 0.341005i | ||||||||
\(383\) | 32.0237i | 1.63633i | 0.574981 | + | 0.818167i | \(0.305010\pi\) | ||||
−0.574981 | + | 0.818167i | \(0.694990\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 3.46681i | − 0.176685i | ||||||||
\(386\) | 16.6558 | 0.847757 | ||||||||
\(387\) | −2.03923 | −0.103660 | ||||||||
\(388\) | − 1.93900i | − 0.0984379i | ||||||||
\(389\) | −21.1879 | −1.07427 | −0.537135 | − | 0.843497i | \(-0.680493\pi\) | ||||
−0.537135 | + | 0.843497i | \(0.680493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5526 | 0.735955 | ||||||||
\(392\) | 2.29590i | 0.115960i | ||||||||
\(393\) | −3.34481 | −0.168724 | ||||||||
\(394\) | −19.4494 | −0.979844 | ||||||||
\(395\) | 5.33513i | 0.268439i | ||||||||
\(396\) | 1.13706i | 0.0571396i | ||||||||
\(397\) | − 10.9608i | − 0.550105i | −0.961429 | − | 0.275053i | \(-0.911305\pi\) | ||||
0.961429 | − | 0.275053i | \(-0.0886953\pi\) | |||||||
\(398\) | 21.6558i | 1.08551i | ||||||||
\(399\) | −4.74094 | −0.237344 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 29.2301i | 1.45968i | 0.683617 | + | 0.729841i | \(0.260406\pi\) | ||||
−0.683617 | + | 0.729841i | \(0.739594\pi\) | |||||||
\(402\) | −2.47219 | −0.123302 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.4940 | −0.721101 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −18.7778 | −0.931925 | ||||||||
\(407\) | 0.631023 | 0.0312786 | ||||||||
\(408\) | − 2.69202i | − 0.133275i | ||||||||
\(409\) | 36.3163i | 1.79573i | 0.440274 | + | 0.897864i | \(0.354881\pi\) | ||||
−0.440274 | + | 0.897864i | \(0.645119\pi\) | |||||||
\(410\) | − 8.26875i | − 0.408364i | ||||||||
\(411\) | − 9.53079i | − 0.470119i | ||||||||
\(412\) | −16.1836 | −0.797308 | ||||||||
\(413\) | −4.17390 | −0.205384 | ||||||||
\(414\) | − 5.40581i | − 0.265681i | ||||||||
\(415\) | 5.45473 | 0.267762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7017 | −0.915827 | ||||||||
\(418\) | 1.76809i | 0.0864799i | ||||||||
\(419\) | 11.0382 | 0.539250 | 0.269625 | − | 0.962965i | \(-0.413100\pi\) | ||||
0.269625 | + | 0.962965i | \(0.413100\pi\) | |||||||
\(420\) | 3.04892 | 0.148772 | ||||||||
\(421\) | 4.58642i | 0.223528i | 0.993735 | + | 0.111764i | \(0.0356501\pi\) | ||||
−0.993735 | + | 0.111764i | \(0.964350\pi\) | |||||||
\(422\) | 12.1521i | 0.591556i | ||||||||
\(423\) | 6.70171i | 0.325848i | ||||||||
\(424\) | − 5.77479i | − 0.280449i | ||||||||
\(425\) | 2.69202 | 0.130582 | ||||||||
\(426\) | −8.57002 | −0.415219 | ||||||||
\(427\) | − 33.3817i | − 1.61545i | ||||||||
\(428\) | −4.92931 | −0.238267 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.03923 | 0.0983403 | ||||||||
\(431\) | 19.3642i | 0.932740i | 0.884590 | + | 0.466370i | \(0.154439\pi\) | ||||
−0.884590 | + | 0.466370i | \(0.845561\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −4.41119 | −0.211988 | −0.105994 | − | 0.994367i | \(-0.533802\pi\) | ||||
−0.105994 | + | 0.994367i | \(0.533802\pi\) | |||||||
\(434\) | − 0.753020i | − 0.0361461i | ||||||||
\(435\) | 6.15883i | 0.295293i | ||||||||
\(436\) | − 0.801938i | − 0.0384059i | ||||||||
\(437\) | − 8.40581i | − 0.402105i | ||||||||
\(438\) | 14.8334 | 0.708767 | ||||||||
\(439\) | −39.5260 | −1.88647 | −0.943237 | − | 0.332121i | \(-0.892236\pi\) | ||||
−0.943237 | + | 0.332121i | \(0.892236\pi\) | |||||||
\(440\) | − 1.13706i | − 0.0542074i | ||||||||
\(441\) | −2.29590 | −0.109328 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.16182 | −0.340268 | −0.170134 | − | 0.985421i | \(-0.554420\pi\) | ||||
−0.170134 | + | 0.985421i | \(0.554420\pi\) | |||||||
\(444\) | 0.554958i | 0.0263371i | ||||||||
\(445\) | 16.8877 | 0.800553 | ||||||||
\(446\) | −1.11960 | −0.0530148 | ||||||||
\(447\) | − 16.4209i | − 0.776681i | ||||||||
\(448\) | 3.04892i | 0.144048i | ||||||||
\(449\) | 4.46011i | 0.210485i | 0.994447 | + | 0.105243i | \(0.0335620\pi\) | ||||
−0.994447 | + | 0.105243i | \(0.966438\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 9.40209 | 0.442727 | ||||||||
\(452\) | 11.5211 | 0.541907 | ||||||||
\(453\) | − 9.26636i | − 0.435371i | ||||||||
\(454\) | −4.06638 | −0.190844 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.55496 | −0.0728176 | ||||||||
\(457\) | − 8.04593i | − 0.376373i | −0.982133 | − | 0.188186i | \(-0.939739\pi\) | ||||
0.982133 | − | 0.188186i | \(-0.0602609\pi\) | |||||||
\(458\) | −16.5187 | −0.771869 | ||||||||
\(459\) | 2.69202 | 0.125653 | ||||||||
\(460\) | 5.40581i | 0.252047i | ||||||||
\(461\) | 4.00538i | 0.186549i | 0.995640 | + | 0.0932745i | \(0.0297334\pi\) | ||||
−0.995640 | + | 0.0932745i | \(0.970267\pi\) | |||||||
\(462\) | 3.46681i | 0.161291i | ||||||||
\(463\) | 37.6142i | 1.74808i | 0.485856 | + | 0.874039i | \(0.338508\pi\) | ||||
−0.485856 | + | 0.874039i | \(0.661492\pi\) | |||||||
\(464\) | −6.15883 | −0.285917 | ||||||||
\(465\) | −0.246980 | −0.0114534 | ||||||||
\(466\) | 6.16421i | 0.285552i | ||||||||
\(467\) | 32.8079 | 1.51817 | 0.759084 | − | 0.650992i | \(-0.225647\pi\) | ||||
0.759084 | + | 0.650992i | \(0.225647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.53750 | −0.348049 | ||||||||
\(470\) | − 6.70171i | − 0.309127i | ||||||||
\(471\) | −17.0761 | −0.786824 | ||||||||
\(472\) | −1.36898 | −0.0630123 | ||||||||
\(473\) | 2.31873i | 0.106615i | ||||||||
\(474\) | − 5.33513i | − 0.245050i | ||||||||
\(475\) | − 1.55496i | − 0.0713464i | ||||||||
\(476\) | − 8.20775i | − 0.376202i | ||||||||
\(477\) | 5.77479 | 0.264410 | ||||||||
\(478\) | −18.1793 | −0.831501 | ||||||||
\(479\) | 9.88530i | 0.451671i | 0.974165 | + | 0.225835i | \(0.0725112\pi\) | ||||
−0.974165 | + | 0.225835i | \(0.927489\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.21744 | −0.419843 | ||||||||
\(483\) | − 16.4819i | − 0.749951i | ||||||||
\(484\) | −9.70709 | −0.441231 | ||||||||
\(485\) | −1.93900 | −0.0880455 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | 20.2610i | 0.918113i | 0.888407 | + | 0.459056i | \(0.151812\pi\) | ||||
−0.888407 | + | 0.459056i | \(0.848188\pi\) | |||||||
\(488\) | − 10.9487i | − 0.495624i | ||||||||
\(489\) | − 9.61894i | − 0.434984i | ||||||||
\(490\) | 2.29590 | 0.103718 | ||||||||
\(491\) | 22.4940 | 1.01514 | 0.507569 | − | 0.861611i | \(-0.330544\pi\) | ||||
0.507569 | + | 0.861611i | \(0.330544\pi\) | |||||||
\(492\) | 8.26875i | 0.372784i | ||||||||
\(493\) | 16.5797 | 0.746713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.13706 | 0.0511072 | ||||||||
\(496\) | − 0.246980i | − 0.0110897i | ||||||||
\(497\) | −26.1293 | −1.17206 | ||||||||
\(498\) | −5.45473 | −0.244432 | ||||||||
\(499\) | − 15.2728i | − 0.683704i | −0.939754 | − | 0.341852i | \(-0.888946\pi\) | ||||
0.939754 | − | 0.341852i | \(-0.111054\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | 21.8509i | 0.976224i | ||||||||
\(502\) | − 17.2054i | − 0.767913i | ||||||||
\(503\) | −2.95838 | −0.131908 | −0.0659538 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659538 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(504\) | −3.04892 | −0.135810 | ||||||||
\(505\) | 14.4940i | 0.644973i | ||||||||
\(506\) | −6.14675 | −0.273256 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.22521 | 0.276199 | ||||||||
\(509\) | − 4.34614i | − 0.192639i | −0.995350 | − | 0.0963197i | \(-0.969293\pi\) | ||||
0.995350 | − | 0.0963197i | \(-0.0307071\pi\) | |||||||
\(510\) | −2.69202 | −0.119205 | ||||||||
\(511\) | 45.2258 | 2.00067 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 1.55496i | − 0.0686531i | ||||||||
\(514\) | 19.5157i | 0.860802i | ||||||||
\(515\) | 16.1836i | 0.713134i | ||||||||
\(516\) | −2.03923 | −0.0897720 | ||||||||
\(517\) | 7.62027 | 0.335139 | ||||||||
\(518\) | 1.69202i | 0.0743432i | ||||||||
\(519\) | 16.6853 | 0.732404 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.13228 | 0.400092 | 0.200046 | − | 0.979786i | \(-0.435891\pi\) | ||||
0.200046 | + | 0.979786i | \(0.435891\pi\) | |||||||
\(522\) | − 6.15883i | − 0.269565i | ||||||||
\(523\) | 10.2828 | 0.449633 | 0.224817 | − | 0.974401i | \(-0.427822\pi\) | ||||
0.224817 | + | 0.974401i | \(0.427822\pi\) | |||||||
\(524\) | −3.34481 | −0.146119 | ||||||||
\(525\) | − 3.04892i | − 0.133066i | ||||||||
\(526\) | 12.8834i | 0.561742i | ||||||||
\(527\) | 0.664874i | 0.0289624i | ||||||||
\(528\) | 1.13706i | 0.0494843i | ||||||||
\(529\) | 6.22282 | 0.270557 | ||||||||
\(530\) | −5.77479 | −0.250841 | ||||||||
\(531\) | − 1.36898i | − 0.0594086i | ||||||||
\(532\) | −4.74094 | −0.205546 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −16.8877 | −0.730802 | ||||||||
\(535\) | 4.92931i | 0.213113i | ||||||||
\(536\) | −2.47219 | −0.106782 | ||||||||
\(537\) | −3.94438 | −0.170212 | ||||||||
\(538\) | − 30.9138i | − 1.33279i | ||||||||
\(539\) | 2.61058i | 0.112446i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | − 1.47517i | − 0.0634226i | −0.999497 | − | 0.0317113i | \(-0.989904\pi\) | ||||
0.999497 | − | 0.0317113i | \(-0.0100957\pi\) | |||||||
\(542\) | 7.24027 | 0.310996 | ||||||||
\(543\) | −20.5308 | −0.881061 | ||||||||
\(544\) | − 2.69202i | − 0.115419i | ||||||||
\(545\) | −0.801938 | −0.0343512 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.82908 | −0.206477 | −0.103238 | − | 0.994657i | \(-0.532920\pi\) | ||||
−0.103238 | + | 0.994657i | \(0.532920\pi\) | |||||||
\(548\) | − 9.53079i | − 0.407135i | ||||||||
\(549\) | 10.9487 | 0.467279 | ||||||||
\(550\) | −1.13706 | −0.0484845 | ||||||||
\(551\) | − 9.57673i | − 0.407982i | ||||||||
\(552\) | − 5.40581i | − 0.230087i | ||||||||
\(553\) | − 16.2664i | − 0.691716i | ||||||||
\(554\) | − 12.2446i | − 0.520223i | ||||||||
\(555\) | 0.554958 | 0.0235567 | ||||||||
\(556\) | −18.7017 | −0.793129 | ||||||||
\(557\) | − 3.26145i | − 0.138192i | −0.997610 | − | 0.0690961i | \(-0.977988\pi\) | ||||
0.997610 | − | 0.0690961i | \(-0.0220115\pi\) | |||||||
\(558\) | 0.246980 | 0.0104555 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.04892 | 0.128840 | ||||||||
\(561\) | − 3.06100i | − 0.129235i | ||||||||
\(562\) | −2.74632 | −0.115846 | ||||||||
\(563\) | −18.1551 | −0.765147 | −0.382573 | − | 0.923925i | \(-0.624962\pi\) | ||||
−0.382573 | + | 0.923925i | \(0.624962\pi\) | |||||||
\(564\) | 6.70171i | 0.282193i | ||||||||
\(565\) | − 11.5211i | − 0.484697i | ||||||||
\(566\) | − 14.9312i | − 0.627606i | ||||||||
\(567\) | − 3.04892i | − 0.128042i | ||||||||
\(568\) | −8.57002 | −0.359590 | ||||||||
\(569\) | 39.2669 | 1.64616 | 0.823078 | − | 0.567928i | \(-0.192255\pi\) | ||||
0.823078 | + | 0.567928i | \(0.192255\pi\) | |||||||
\(570\) | 1.55496i | 0.0651300i | ||||||||
\(571\) | 36.8649 | 1.54275 | 0.771373 | − | 0.636383i | \(-0.219570\pi\) | ||||
0.771373 | + | 0.636383i | \(0.219570\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.66487 | 0.278429 | ||||||||
\(574\) | 25.2107i | 1.05228i | ||||||||
\(575\) | 5.40581 | 0.225438 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 20.3043i | − 0.845277i | −0.906298 | − | 0.422639i | \(-0.861104\pi\) | ||||
0.906298 | − | 0.422639i | \(-0.138896\pi\) | |||||||
\(578\) | − 9.75302i | − 0.405672i | ||||||||
\(579\) | 16.6558i | 0.692190i | ||||||||
\(580\) | 6.15883i | 0.255732i | ||||||||
\(581\) | −16.6310 | −0.689971 | ||||||||
\(582\) | 1.93900 | 0.0803742 | ||||||||
\(583\) | − 6.56630i | − 0.271948i | ||||||||
\(584\) | 14.8334 | 0.613810 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5810 | 0.767576 | ||||||||
\(587\) | 24.5472i | 1.01317i | 0.862190 | + | 0.506585i | \(0.169093\pi\) | ||||
−0.862190 | + | 0.506585i | \(0.830907\pi\) | |||||||
\(588\) | −2.29590 | −0.0946812 | ||||||||
\(589\) | 0.384043 | 0.0158242 | ||||||||
\(590\) | 1.36898i | 0.0563599i | ||||||||
\(591\) | − 19.4494i | − 0.800040i | ||||||||
\(592\) | 0.554958i | 0.0228086i | ||||||||
\(593\) | 24.0844i | 0.989029i | 0.869169 | + | 0.494514i | \(0.164654\pi\) | ||||
−0.869169 | + | 0.494514i | \(0.835346\pi\) | |||||||
\(594\) | −1.13706 | −0.0466543 | ||||||||
\(595\) | −8.20775 | −0.336485 | ||||||||
\(596\) | − 16.4209i | − 0.672625i | ||||||||
\(597\) | −21.6558 | −0.886312 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.84415 | 0.0753499 | 0.0376750 | − | 0.999290i | \(-0.488005\pi\) | ||||
0.0376750 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | −15.6770 | −0.639476 | −0.319738 | − | 0.947506i | \(-0.603595\pi\) | ||||
−0.319738 | + | 0.947506i | \(0.603595\pi\) | |||||||
\(602\) | −6.21744 | −0.253404 | ||||||||
\(603\) | − 2.47219i | − 0.100675i | ||||||||
\(604\) | − 9.26636i | − 0.377043i | ||||||||
\(605\) | 9.70709i | 0.394649i | ||||||||
\(606\) | − 14.4940i | − 0.588777i | ||||||||
\(607\) | −29.6866 | −1.20494 | −0.602472 | − | 0.798140i | \(-0.705817\pi\) | ||||
−0.602472 | + | 0.798140i | \(0.705817\pi\) | |||||||
\(608\) | −1.55496 | −0.0630619 | ||||||||
\(609\) | − 18.7778i | − 0.760914i | ||||||||
\(610\) | −10.9487 | −0.443299 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.69202 | 0.108819 | ||||||||
\(613\) | − 42.5163i | − 1.71722i | −0.512631 | − | 0.858609i | \(-0.671329\pi\) | ||||
0.512631 | − | 0.858609i | \(-0.328671\pi\) | |||||||
\(614\) | 32.4359 | 1.30901 | ||||||||
\(615\) | 8.26875 | 0.333428 | ||||||||
\(616\) | 3.46681i | 0.139682i | ||||||||
\(617\) | 27.3666i | 1.10174i | 0.834592 | + | 0.550869i | \(0.185703\pi\) | ||||
−0.834592 | + | 0.550869i | \(0.814297\pi\) | |||||||
\(618\) | − 16.1836i | − 0.650999i | ||||||||
\(619\) | − 27.9420i | − 1.12308i | −0.827449 | − | 0.561542i | \(-0.810208\pi\) | ||||
0.827449 | − | 0.561542i | \(-0.189792\pi\) | |||||||
\(620\) | −0.246980 | −0.00991894 | ||||||||
\(621\) | 5.40581 | 0.216928 | ||||||||
\(622\) | 21.2771i | 0.853134i | ||||||||
\(623\) | −51.4892 | −2.06287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 18.7060i | − 0.747643i | ||||||||
\(627\) | −1.76809 | −0.0706105 | ||||||||
\(628\) | −17.0761 | −0.681409 | ||||||||
\(629\) | − 1.49396i | − 0.0595681i | ||||||||
\(630\) | 3.04892i | 0.121472i | ||||||||
\(631\) | − 7.43594i | − 0.296020i | −0.988986 | − | 0.148010i | \(-0.952713\pi\) | ||||
0.988986 | − | 0.148010i | \(-0.0472868\pi\) | |||||||
\(632\) | − 5.33513i | − 0.212220i | ||||||||
\(633\) | −12.1521 | −0.483004 | ||||||||
\(634\) | −17.4776 | −0.694123 | ||||||||
\(635\) | − 6.22521i | − 0.247040i | ||||||||
\(636\) | 5.77479 | 0.228985 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.00298 | −0.277251 | ||||||||
\(639\) | − 8.57002i | − 0.339025i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 24.9444 | 0.985244 | 0.492622 | − | 0.870243i | \(-0.336039\pi\) | ||||
0.492622 | + | 0.870243i | \(0.336039\pi\) | |||||||
\(642\) | − 4.92931i | − 0.194544i | ||||||||
\(643\) | 30.1661i | 1.18964i | 0.803860 | + | 0.594818i | \(0.202776\pi\) | ||||
−0.803860 | + | 0.594818i | \(0.797224\pi\) | |||||||
\(644\) | − 16.4819i | − 0.649477i | ||||||||
\(645\) | 2.03923i | 0.0802946i | ||||||||
\(646\) | 4.18598 | 0.164695 | ||||||||
\(647\) | 44.4053 | 1.74575 | 0.872877 | − | 0.487940i | \(-0.162252\pi\) | ||||
0.872877 | + | 0.487940i | \(0.162252\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −1.55661 | −0.0611024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.753020 | 0.0295132 | ||||||||
\(652\) | − 9.61894i | − 0.376707i | ||||||||
\(653\) | −29.2573 | −1.14493 | −0.572463 | − | 0.819931i | \(-0.694012\pi\) | ||||
−0.572463 | + | 0.819931i | \(0.694012\pi\) | |||||||
\(654\) | 0.801938 | 0.0313582 | ||||||||
\(655\) | 3.34481i | 0.130693i | ||||||||
\(656\) | 8.26875i | 0.322840i | ||||||||
\(657\) | 14.8334i | 0.578706i | ||||||||
\(658\) | 20.4330i | 0.796560i | ||||||||
\(659\) | −11.4808 | −0.447229 | −0.223614 | − | 0.974678i | \(-0.571786\pi\) | ||||
−0.223614 | + | 0.974678i | \(0.571786\pi\) | |||||||
\(660\) | 1.13706 | 0.0442601 | ||||||||
\(661\) | − 26.1129i | − 1.01567i | −0.861453 | − | 0.507837i | \(-0.830445\pi\) | ||||
0.861453 | − | 0.507837i | \(-0.169555\pi\) | |||||||
\(662\) | 23.1890 | 0.901265 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.45473 | −0.211685 | ||||||||
\(665\) | 4.74094i | 0.183846i | ||||||||
\(666\) | −0.554958 | −0.0215042 | ||||||||
\(667\) | 33.2935 | 1.28913 | ||||||||
\(668\) | 21.8509i | 0.845435i | ||||||||
\(669\) | − 1.11960i | − 0.0432864i | ||||||||
\(670\) | 2.47219i | 0.0955090i | ||||||||
\(671\) | − 12.4494i | − 0.480602i | ||||||||
\(672\) | −3.04892 | −0.117615 | ||||||||
\(673\) | 12.4190 | 0.478716 | 0.239358 | − | 0.970931i | \(-0.423063\pi\) | ||||
0.239358 | + | 0.970931i | \(0.423063\pi\) | |||||||
\(674\) | 26.1400i | 1.00688i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7646 | 0.490585 | 0.245292 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245292 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(678\) | 11.5211i | 0.442465i | ||||||||
\(679\) | 5.91185 | 0.226876 | ||||||||
\(680\) | −2.69202 | −0.103234 | ||||||||
\(681\) | − 4.06638i | − 0.155824i | ||||||||
\(682\) | − 0.280831i | − 0.0107536i | ||||||||
\(683\) | − 31.6142i | − 1.20968i | −0.796346 | − | 0.604841i | \(-0.793237\pi\) | ||||
0.796346 | − | 0.604841i | \(-0.206763\pi\) | |||||||
\(684\) | − 1.55496i | − 0.0594553i | ||||||||
\(685\) | −9.53079 | −0.364153 | ||||||||
\(686\) | 14.3424 | 0.547596 | ||||||||
\(687\) | − 16.5187i | − 0.630228i | ||||||||
\(688\) | −2.03923 | −0.0777449 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −5.40581 | −0.205796 | ||||||||
\(691\) | 2.06962i | 0.0787322i | 0.999225 | + | 0.0393661i | \(0.0125339\pi\) | ||||
−0.999225 | + | 0.0393661i | \(0.987466\pi\) | |||||||
\(692\) | 16.6853 | 0.634281 | ||||||||
\(693\) | −3.46681 | −0.131693 | ||||||||
\(694\) | 15.2959i | 0.580624i | ||||||||
\(695\) | 18.7017i | 0.709396i | ||||||||
\(696\) | − 6.15883i | − 0.233450i | ||||||||
\(697\) | − 22.2597i | − 0.843144i | ||||||||
\(698\) | −19.2107 | −0.727137 | ||||||||
\(699\) | −6.16421 | −0.233152 | ||||||||
\(700\) | − 3.04892i | − 0.115238i | ||||||||
\(701\) | 23.0030 | 0.868811 | 0.434405 | − | 0.900717i | \(-0.356959\pi\) | ||||
0.434405 | + | 0.900717i | \(0.356959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.862937 | −0.0325463 | ||||||||
\(704\) | 1.13706i | 0.0428547i | ||||||||
\(705\) | 6.70171 | 0.252401 | ||||||||
\(706\) | 5.35450 | 0.201519 | ||||||||
\(707\) | − 44.1909i | − 1.66197i | ||||||||
\(708\) | − 1.36898i | − 0.0514493i | ||||||||
\(709\) | 32.4373i | 1.21821i | 0.793091 | + | 0.609104i | \(0.208471\pi\) | ||||
−0.793091 | + | 0.609104i | \(0.791529\pi\) | |||||||
\(710\) | 8.57002i | 0.321627i | ||||||||
\(711\) | 5.33513 | 0.200083 | ||||||||
\(712\) | −16.8877 | −0.632893 | ||||||||
\(713\) | 1.33513i | 0.0500008i | ||||||||
\(714\) | 8.20775 | 0.307167 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.94438 | −0.147408 | ||||||||
\(717\) | − 18.1793i | − 0.678917i | ||||||||
\(718\) | 8.49934 | 0.317192 | ||||||||
\(719\) | 13.7845 | 0.514074 | 0.257037 | − | 0.966402i | \(-0.417254\pi\) | ||||
0.257037 | + | 0.966402i | \(0.417254\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | − 49.3424i | − 1.83761i | ||||||||
\(722\) | 16.5821i | 0.617122i | ||||||||
\(723\) | − 9.21744i | − 0.342800i | ||||||||
\(724\) | −20.5308 | −0.763021 | ||||||||
\(725\) | 6.15883 | 0.228733 | ||||||||
\(726\) | − 9.70709i | − 0.360264i | ||||||||
\(727\) | −4.64848 | −0.172403 | −0.0862013 | − | 0.996278i | \(-0.527473\pi\) | ||||
−0.0862013 | + | 0.996278i | \(0.527473\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 14.8334i | − 0.549009i | ||||||||
\(731\) | 5.48965 | 0.203042 | ||||||||
\(732\) | 10.9487 | 0.404675 | ||||||||
\(733\) | − 27.4717i | − 1.01469i | −0.861743 | − | 0.507345i | \(-0.830627\pi\) | ||||
0.861743 | − | 0.507345i | \(-0.169373\pi\) | |||||||
\(734\) | 4.76032i | 0.175706i | ||||||||
\(735\) | 2.29590i | 0.0846854i | ||||||||
\(736\) | − 5.40581i | − 0.199261i | ||||||||
\(737\) | −2.81104 | −0.103546 | ||||||||
\(738\) | −8.26875 | −0.304377 | ||||||||
\(739\) | 48.0170i | 1.76633i | 0.469059 | + | 0.883167i | \(0.344593\pi\) | ||||
−0.469059 | + | 0.883167i | \(0.655407\pi\) | |||||||
\(740\) | 0.554958 | 0.0204007 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.6069 | 0.646368 | ||||||||
\(743\) | − 23.6517i | − 0.867698i | −0.900986 | − | 0.433849i | \(-0.857155\pi\) | ||||
0.900986 | − | 0.433849i | \(-0.142845\pi\) | |||||||
\(744\) | 0.246980 | 0.00905471 | ||||||||
\(745\) | −16.4209 | −0.601614 | ||||||||
\(746\) | − 20.2064i | − 0.739810i | ||||||||
\(747\) | − 5.45473i | − 0.199578i | ||||||||
\(748\) | − 3.06100i | − 0.111921i | ||||||||
\(749\) | − 15.0291i | − 0.549150i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 39.5133 | 1.44186 | 0.720931 | − | 0.693007i | \(-0.243714\pi\) | ||||
0.720931 | + | 0.693007i | \(0.243714\pi\) | |||||||
\(752\) | 6.70171i | 0.244386i | ||||||||
\(753\) | 17.2054 | 0.626998 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.26636 | −0.337237 | ||||||||
\(756\) | − 3.04892i | − 0.110888i | ||||||||
\(757\) | −11.2239 | −0.407939 | −0.203969 | − | 0.978977i | \(-0.565384\pi\) | ||||
−0.203969 | + | 0.978977i | \(0.565384\pi\) | |||||||
\(758\) | −24.4088 | −0.886567 | ||||||||
\(759\) | − 6.14675i | − 0.223113i | ||||||||
\(760\) | 1.55496i | 0.0564043i | ||||||||
\(761\) | 5.80864i | 0.210563i | 0.994442 | + | 0.105282i | \(0.0335744\pi\) | ||||
−0.994442 | + | 0.105282i | \(0.966426\pi\) | |||||||
\(762\) | 6.22521i | 0.225516i | ||||||||
\(763\) | 2.44504 | 0.0885165 | ||||||||
\(764\) | 6.66487 | 0.241127 | ||||||||
\(765\) | − 2.69202i | − 0.0973302i | ||||||||
\(766\) | −32.0237 | −1.15706 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | − 31.8316i | − 1.14788i | −0.818899 | − | 0.573938i | \(-0.805415\pi\) | ||||
0.818899 | − | 0.573938i | \(-0.194585\pi\) | |||||||
\(770\) | 3.46681 | 0.124935 | ||||||||
\(771\) | −19.5157 | −0.702842 | ||||||||
\(772\) | 16.6558i | 0.599455i | ||||||||
\(773\) | 39.7434i | 1.42947i | 0.699394 | + | 0.714736i | \(0.253453\pi\) | ||||
−0.699394 | + | 0.714736i | \(0.746547\pi\) | |||||||
\(774\) | − 2.03923i | − 0.0732986i | ||||||||
\(775\) | 0.246980i | 0.00887177i | ||||||||
\(776\) | 1.93900 | 0.0696061 | ||||||||
\(777\) | −1.69202 | −0.0607009 | ||||||||
\(778\) | − 21.1879i | − 0.759623i | ||||||||
\(779\) | −12.8576 | −0.460670 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.74466 | −0.348691 | ||||||||
\(782\) | 14.5526i | 0.520399i | ||||||||
\(783\) | 6.15883 | 0.220099 | ||||||||
\(784\) | −2.29590 | −0.0819963 | ||||||||
\(785\) | 17.0761i | 0.609471i | ||||||||
\(786\) | − 3.34481i | − 0.119306i | ||||||||
\(787\) | − 19.3183i | − 0.688622i | −0.938856 | − | 0.344311i | \(-0.888113\pi\) | ||||
0.938856 | − | 0.344311i | \(-0.111887\pi\) | |||||||
\(788\) | − 19.4494i | − 0.692855i | ||||||||
\(789\) | −12.8834 | −0.458660 | ||||||||
\(790\) | −5.33513 | −0.189815 | ||||||||
\(791\) | 35.1269i | 1.24897i | ||||||||
\(792\) | −1.13706 | −0.0404038 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 10.9608 | 0.388983 | ||||||||
\(795\) | − 5.77479i | − 0.204811i | ||||||||
\(796\) | −21.6558 | −0.767569 | ||||||||
\(797\) | −29.4946 | −1.04475 | −0.522375 | − | 0.852716i | \(-0.674954\pi\) | ||||
−0.522375 | + | 0.852716i | \(0.674954\pi\) | |||||||
\(798\) | − 4.74094i | − 0.167827i | ||||||||
\(799\) | − 18.0411i | − 0.638250i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | − 16.8877i | − 0.596697i | ||||||||
\(802\) | −29.2301 | −1.03215 | ||||||||
\(803\) | 16.8665 | 0.595206 | ||||||||
\(804\) | − 2.47219i | − 0.0871874i | ||||||||
\(805\) | −16.4819 | −0.580910 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.9138 | 1.08822 | ||||||||
\(808\) | − 14.4940i | − 0.509896i | ||||||||
\(809\) | 14.0901 | 0.495380 | 0.247690 | − | 0.968839i | \(-0.420329\pi\) | ||||
0.247690 | + | 0.968839i | \(0.420329\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | − 45.5060i | − 1.59793i | −0.601375 | − | 0.798967i | \(-0.705380\pi\) | ||||
0.601375 | − | 0.798967i | \(-0.294620\pi\) | |||||||
\(812\) | − 18.7778i | − 0.658971i | ||||||||
\(813\) | 7.24027i | 0.253928i | ||||||||
\(814\) | 0.631023i | 0.0221173i | ||||||||
\(815\) | −9.61894 | −0.336937 | ||||||||
\(816\) | 2.69202 | 0.0942396 | ||||||||
\(817\) | − 3.17092i | − 0.110936i | ||||||||
\(818\) | −36.3163 | −1.26977 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.26875 | 0.288757 | ||||||||
\(821\) | − 14.6853i | − 0.512521i | −0.966608 | − | 0.256261i | \(-0.917509\pi\) | ||||
0.966608 | − | 0.256261i | \(-0.0824905\pi\) | |||||||
\(822\) | 9.53079 | 0.332425 | ||||||||
\(823\) | 32.0551 | 1.11737 | 0.558686 | − | 0.829379i | \(-0.311306\pi\) | ||||
0.558686 | + | 0.829379i | \(0.311306\pi\) | |||||||
\(824\) | − 16.1836i | − 0.563782i | ||||||||
\(825\) | − 1.13706i | − 0.0395875i | ||||||||
\(826\) | − 4.17390i | − 0.145229i | ||||||||
\(827\) | − 8.09352i | − 0.281439i | −0.990049 | − | 0.140720i | \(-0.955058\pi\) | ||||
0.990049 | − | 0.140720i | \(-0.0449416\pi\) | |||||||
\(828\) | 5.40581 | 0.187865 | ||||||||
\(829\) | 23.8708 | 0.829068 | 0.414534 | − | 0.910034i | \(-0.363945\pi\) | ||||
0.414534 | + | 0.910034i | \(0.363945\pi\) | |||||||
\(830\) | 5.45473i | 0.189336i | ||||||||
\(831\) | 12.2446 | 0.424760 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.18060 | 0.214145 | ||||||||
\(834\) | − 18.7017i | − 0.647587i | ||||||||
\(835\) | 21.8509 | 0.756180 | ||||||||
\(836\) | −1.76809 | −0.0611505 | ||||||||
\(837\) | 0.246980i | 0.00853686i | ||||||||
\(838\) | 11.0382i | 0.381307i | ||||||||
\(839\) | 17.5569i | 0.606131i | 0.952970 | + | 0.303065i | \(0.0980100\pi\) | ||||
−0.952970 | + | 0.303065i | \(0.901990\pi\) | |||||||
\(840\) | 3.04892i | 0.105198i | ||||||||
\(841\) | 8.93123 | 0.307973 | ||||||||
\(842\) | −4.58642 | −0.158058 | ||||||||
\(843\) | − 2.74632i | − 0.0945881i | ||||||||
\(844\) | −12.1521 | −0.418294 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.70171 | −0.230410 | ||||||||
\(847\) | − 29.5961i | − 1.01693i | ||||||||
\(848\) | 5.77479 | 0.198307 | ||||||||
\(849\) | 14.9312 | 0.512439 | ||||||||
\(850\) | 2.69202i | 0.0923356i | ||||||||
\(851\) | − 3.00000i | − 0.102839i | ||||||||
\(852\) | − 8.57002i | − 0.293604i | ||||||||
\(853\) | 40.2892i | 1.37948i | 0.724059 | + | 0.689738i | \(0.242274\pi\) | ||||
−0.724059 | + | 0.689738i | \(0.757726\pi\) | |||||||
\(854\) | 33.3817 | 1.14230 | ||||||||
\(855\) | −1.55496 | −0.0531784 | ||||||||
\(856\) | − 4.92931i | − 0.168480i | ||||||||
\(857\) | −44.5913 | −1.52321 | −0.761605 | − | 0.648041i | \(-0.775588\pi\) | ||||
−0.761605 | + | 0.648041i | \(0.775588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.6467 | −1.38685 | −0.693423 | − | 0.720530i | \(-0.743898\pi\) | ||||
−0.693423 | + | 0.720530i | \(0.743898\pi\) | |||||||
\(860\) | 2.03923i | 0.0695371i | ||||||||
\(861\) | −25.2107 | −0.859180 | ||||||||
\(862\) | −19.3642 | −0.659547 | ||||||||
\(863\) | − 31.9748i | − 1.08843i | −0.838945 | − | 0.544217i | \(-0.816827\pi\) | ||||
0.838945 | − | 0.544217i | \(-0.183173\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 16.6853i | − 0.567318i | ||||||||
\(866\) | − 4.41119i | − 0.149898i | ||||||||
\(867\) | 9.75302 | 0.331230 | ||||||||
\(868\) | 0.753020 | 0.0255592 | ||||||||
\(869\) | − 6.06638i | − 0.205788i | ||||||||
\(870\) | −6.15883 | −0.208804 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.801938 | 0.0271570 | ||||||||
\(873\) | 1.93900i | 0.0656252i | ||||||||
\(874\) | 8.40581 | 0.284331 | ||||||||
\(875\) | −3.04892 | −0.103072 | ||||||||
\(876\) | 14.8334i | 0.501174i | ||||||||
\(877\) | − 39.2476i | − 1.32530i | −0.748931 | − | 0.662648i | \(-0.769433\pi\) | ||||
0.748931 | − | 0.662648i | \(-0.230567\pi\) | |||||||
\(878\) | − 39.5260i | − 1.33394i | ||||||||
\(879\) | 18.5810i | 0.626723i | ||||||||
\(880\) | 1.13706 | 0.0383304 | ||||||||
\(881\) | 24.3153 | 0.819202 | 0.409601 | − | 0.912265i | \(-0.365668\pi\) | ||||
0.409601 | + | 0.912265i | \(0.365668\pi\) | |||||||
\(882\) | − 2.29590i | − 0.0773069i | ||||||||
\(883\) | −51.8756 | −1.74575 | −0.872877 | − | 0.487941i | \(-0.837748\pi\) | ||||
−0.872877 | + | 0.487941i | \(0.837748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.36898 | −0.0460177 | ||||||||
\(886\) | − 7.16182i | − 0.240606i | ||||||||
\(887\) | −13.4383 | −0.451215 | −0.225608 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225608 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(888\) | −0.554958 | −0.0186232 | ||||||||
\(889\) | 18.9801i | 0.636574i | ||||||||
\(890\) | 16.8877i | 0.566077i | ||||||||
\(891\) | − 1.13706i | − 0.0380931i | ||||||||
\(892\) | − 1.11960i | − 0.0374871i | ||||||||
\(893\) | −10.4209 | −0.348721 | ||||||||
\(894\) | 16.4209 | 0.549196 | ||||||||
\(895\) | 3.94438i | 0.131846i | ||||||||
\(896\) | −3.04892 | −0.101857 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.46011 | −0.148836 | ||||||||
\(899\) | 1.52111i | 0.0507317i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −15.5459 | −0.517908 | ||||||||
\(902\) | 9.40209i | 0.313055i | ||||||||
\(903\) | − 6.21744i | − 0.206903i | ||||||||
\(904\) | 11.5211i | 0.383186i | ||||||||
\(905\) | 20.5308i | 0.682467i | ||||||||
\(906\) | 9.26636 | 0.307854 | ||||||||
\(907\) | 6.58881 | 0.218778 | 0.109389 | − | 0.993999i | \(-0.465111\pi\) | ||||
0.109389 | + | 0.993999i | \(0.465111\pi\) | |||||||
\(908\) | − 4.06638i | − 0.134947i | ||||||||
\(909\) | 14.4940 | 0.480734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51.2646 | 1.69847 | 0.849235 | − | 0.528015i | \(-0.177063\pi\) | ||||
0.849235 | + | 0.528015i | \(0.177063\pi\) | |||||||
\(912\) | − 1.55496i | − 0.0514898i | ||||||||
\(913\) | −6.20237 | −0.205269 | ||||||||
\(914\) | 8.04593 | 0.266136 | ||||||||
\(915\) | − 10.9487i | − 0.361953i | ||||||||
\(916\) | − 16.5187i | − 0.545794i | ||||||||
\(917\) | − 10.1981i | − 0.336770i | ||||||||
\(918\) | 2.69202i | 0.0888499i | ||||||||
\(919\) | 50.7066 | 1.67266 | 0.836328 | − | 0.548229i | \(-0.184698\pi\) | ||||
0.836328 | + | 0.548229i | \(0.184698\pi\) | |||||||
\(920\) | −5.40581 | −0.178224 | ||||||||
\(921\) | 32.4359i | 1.06880i | ||||||||
\(922\) | −4.00538 | −0.131910 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.46681 | −0.114050 | ||||||||
\(925\) | − 0.554958i | − 0.0182469i | ||||||||
\(926\) | −37.6142 | −1.23608 | ||||||||
\(927\) | 16.1836 | 0.531539 | ||||||||
\(928\) | − 6.15883i | − 0.202174i | ||||||||
\(929\) | − 18.2903i | − 0.600084i | −0.953926 | − | 0.300042i | \(-0.902999\pi\) | ||||
0.953926 | − | 0.300042i | \(-0.0970007\pi\) | |||||||
\(930\) | − 0.246980i | − 0.00809878i | ||||||||
\(931\) | − 3.57002i | − 0.117003i | ||||||||
\(932\) | −6.16421 | −0.201915 | ||||||||
\(933\) | −21.2771 | −0.696581 | ||||||||
\(934\) | 32.8079i | 1.07351i | ||||||||
\(935\) | −3.06100 | −0.100105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −59.6679 | −1.94926 | −0.974632 | − | 0.223814i | \(-0.928149\pi\) | ||||
−0.974632 | + | 0.223814i | \(0.928149\pi\) | |||||||
\(938\) | − 7.53750i | − 0.246108i | ||||||||
\(939\) | 18.7060 | 0.610448 | ||||||||
\(940\) | 6.70171 | 0.218586 | ||||||||
\(941\) | − 36.2513i | − 1.18176i | −0.806760 | − | 0.590879i | \(-0.798781\pi\) | ||||
0.806760 | − | 0.590879i | \(-0.201219\pi\) | |||||||
\(942\) | − 17.0761i | − 0.556368i | ||||||||
\(943\) | − 44.6993i | − 1.45561i | ||||||||
\(944\) | − 1.36898i | − 0.0445564i | ||||||||
\(945\) | −3.04892 | −0.0991813 | ||||||||
\(946\) | −2.31873 | −0.0753885 | ||||||||
\(947\) | − 7.02475i | − 0.228274i | −0.993465 | − | 0.114137i | \(-0.963590\pi\) | ||||
0.993465 | − | 0.114137i | \(-0.0364103\pi\) | |||||||
\(948\) | 5.33513 | 0.173277 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.55496 | 0.0504495 | ||||||||
\(951\) | − 17.4776i | − 0.566749i | ||||||||
\(952\) | 8.20775 | 0.266015 | ||||||||
\(953\) | −12.5730 | −0.407280 | −0.203640 | − | 0.979046i | \(-0.565277\pi\) | ||||
−0.203640 | + | 0.979046i | \(0.565277\pi\) | |||||||
\(954\) | 5.77479i | 0.186966i | ||||||||
\(955\) | − 6.66487i | − 0.215670i | ||||||||
\(956\) | − 18.1793i | − 0.587960i | ||||||||
\(957\) | − 7.00298i | − 0.226374i | ||||||||
\(958\) | −9.88530 | −0.319379 | ||||||||
\(959\) | 29.0586 | 0.938351 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 30.9390 | 0.998032 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.92931 | 0.158845 | ||||||||
\(964\) | − 9.21744i | − 0.296874i | ||||||||
\(965\) | 16.6558 | 0.536168 | ||||||||
\(966\) | 16.4819 | 0.530296 | ||||||||
\(967\) | − 23.1371i | − 0.744038i | −0.928225 | − | 0.372019i | \(-0.878666\pi\) | ||||
0.928225 | − | 0.372019i | \(-0.121334\pi\) | |||||||
\(968\) | − 9.70709i | − 0.311998i | ||||||||
\(969\) | 4.18598i | 0.134473i | ||||||||
\(970\) | − 1.93900i | − 0.0622576i | ||||||||
\(971\) | −26.5394 | −0.851690 | −0.425845 | − | 0.904796i | \(-0.640023\pi\) | ||||
−0.425845 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 57.0200i | − 1.82798i | ||||||||
\(974\) | −20.2610 | −0.649204 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9487 | 0.350459 | ||||||||
\(977\) | 19.5670i | 0.626005i | 0.949752 | + | 0.313003i | \(0.101335\pi\) | ||||
−0.949752 | + | 0.313003i | \(0.898665\pi\) | |||||||
\(978\) | 9.61894 | 0.307580 | ||||||||
\(979\) | −19.2024 | −0.613711 | ||||||||
\(980\) | 2.29590i | 0.0733397i | ||||||||
\(981\) | 0.801938i | 0.0256039i | ||||||||
\(982\) | 22.4940i | 0.717811i | ||||||||
\(983\) | 8.82610i | 0.281509i | 0.990045 | + | 0.140754i | \(0.0449528\pi\) | ||||
−0.990045 | + | 0.140754i | \(0.955047\pi\) | |||||||
\(984\) | −8.26875 | −0.263598 | ||||||||
\(985\) | −19.4494 | −0.619708 | ||||||||
\(986\) | 16.5797i | 0.528006i | ||||||||
\(987\) | −20.4330 | −0.650388 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0237 | 0.350533 | ||||||||
\(990\) | 1.13706i | 0.0361382i | ||||||||
\(991\) | 0.601483 | 0.0191067 | 0.00955336 | − | 0.999954i | \(-0.496959\pi\) | ||||
0.00955336 | + | 0.999954i | \(0.496959\pi\) | |||||||
\(992\) | 0.246980 | 0.00784161 | ||||||||
\(993\) | 23.1890i | 0.735880i | ||||||||
\(994\) | − 26.1293i | − 0.828771i | ||||||||
\(995\) | 21.6558i | 0.686534i | ||||||||
\(996\) | − 5.45473i | − 0.172840i | ||||||||
\(997\) | 13.4101 | 0.424703 | 0.212351 | − | 0.977193i | \(-0.431888\pi\) | ||||
0.212351 | + | 0.977193i | \(0.431888\pi\) | |||||||
\(998\) | 15.2728 | 0.483452 | ||||||||
\(999\) | − 0.554958i | − 0.0175581i |
(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 | 5070.2.b.t.1351.4 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bu.1.3 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bj.1.1 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.t.1351.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bj.1.1 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bu.1.3 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.t.1351.3 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.t.1351.4 | 6 | 1.1 | even | 1 | trivial |