Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2112,3,Mod(769,2112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2112.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2112 = 2^{6} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2112.j (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: | \(57.5478318329\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.39744.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} + 12x^{2} + 4x + 22 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.1 | ||
Root | \(1.36603 - 3.21405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2112.769 |
Dual form | 2112.3.j.a.769.2 |
$q$-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 \(\left(\mathbb{Z}/2112\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(1409\) | \(1729\) | \(2047\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.19615 | 0.839230 | 0.419615 | − | 0.907702i | \(-0.362165\pi\) | ||||
0.419615 | + | 0.907702i | \(0.362165\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 6.42810i | − | 0.918300i | −0.888359 | − | 0.459150i | \(-0.848154\pi\) | ||
0.888359 | − | 0.459150i | \(-0.151846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.26795 | + | 10.5034i | −0.297086 | + | 0.954851i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.68899i | 0.591461i | 0.955271 | + | 0.295730i | \(0.0955630\pi\) | ||||
−0.955271 | + | 0.295730i | \(0.904437\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.26795 | −0.484530 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.15051i | 0.479442i | 0.970842 | + | 0.239721i | \(0.0770559\pi\) | ||||
−0.970842 | + | 0.239721i | \(0.922944\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 30.4181i | − | 1.60095i | −0.599364 | − | 0.800477i | \(-0.704580\pi\) | ||
0.599364 | − | 0.800477i | \(-0.295420\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1338i | 0.530181i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −31.6603 | −1.37653 | −0.688266 | − | 0.725458i | \(-0.741628\pi\) | ||||
−0.688266 | + | 0.725458i | \(0.741628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.39230 | −0.295692 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.88962i | 0.237573i | 0.992920 | + | 0.118787i | \(0.0379004\pi\) | ||||
−0.992920 | + | 0.118787i | \(0.962100\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 51.1769 | 1.65087 | 0.825434 | − | 0.564498i | \(-0.190930\pi\) | ||||
0.825434 | + | 0.564498i | \(0.190930\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.66025 | − | 18.1923i | 0.171523 | − | 0.551283i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 26.9733i | − | 0.770666i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.4641 | 0.526057 | 0.263028 | − | 0.964788i | \(-0.415279\pi\) | ||||
0.263028 | + | 0.964788i | \(0.415279\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 13.3177i | − | 0.341480i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 47.9800i | − | 1.17024i | −0.810945 | − | 0.585122i | \(-0.801047\pi\) | ||
0.810945 | − | 0.585122i | \(-0.198953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 81.8429i | − | 1.90332i | −0.307147 | − | 0.951662i | \(-0.599374\pi\) | ||
0.307147 | − | 0.951662i | \(-0.400626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.5885 | 0.279743 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 30.1962 | 0.642471 | 0.321236 | − | 0.946999i | \(-0.395902\pi\) | ||||
0.321236 | + | 0.946999i | \(0.395902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.67949 | 0.156724 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 14.1171i | − | 0.276806i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26.0526 | −0.491558 | −0.245779 | − | 0.969326i | \(-0.579044\pi\) | ||||
−0.245779 | + | 0.969326i | \(0.579044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.7128 | + | 44.0737i | −0.249324 | + | 0.801340i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 52.6857i | 0.924311i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −82.7461 | −1.40248 | −0.701238 | − | 0.712927i | \(-0.747369\pi\) | ||||
−0.701238 | + | 0.712927i | \(0.747369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 75.4148i | 1.23631i | 0.786057 | + | 0.618154i | \(0.212119\pi\) | ||||
−0.786057 | + | 0.618154i | \(0.787881\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 19.2843i | − | 0.306100i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 32.2642i | 0.496372i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.0000 | 0.507463 | 0.253731 | − | 0.967275i | \(-0.418342\pi\) | ||||
0.253731 | + | 0.967275i | \(0.418342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 54.8372 | 0.794742 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.7321 | −1.02440 | −0.512198 | − | 0.858868i | \(-0.671168\pi\) | ||||
−0.512198 | + | 0.858868i | \(0.671168\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 54.8696i | − | 0.751639i | −0.926693 | − | 0.375819i | \(-0.877361\pi\) | ||
0.926693 | − | 0.375819i | \(-0.122639\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.8038 | 0.170718 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 67.5167 | + | 21.0067i | 0.876840 | + | 0.272814i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 24.3279i | − | 0.307948i | −0.988075 | − | 0.153974i | \(-0.950793\pi\) | ||
0.988075 | − | 0.153974i | \(-0.0492071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.923034i | 0.0111209i | 0.999985 | + | 0.00556045i | \(0.00176995\pi\) | ||||
−0.999985 | + | 0.00556045i | \(0.998230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 34.2008i | 0.402362i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 11.9332i | − | 0.137163i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 44.8231 | 0.503630 | 0.251815 | − | 0.967775i | \(-0.418973\pi\) | ||||
0.251815 | + | 0.967775i | \(0.418973\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.4256 | 0.543139 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −88.6410 | −0.953129 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 127.639i | − | 1.34357i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −21.2539 | −0.219112 | −0.109556 | − | 0.993981i | \(-0.534943\pi\) | ||||
−0.109556 | + | 0.993981i | \(0.534943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.80385 | + | 31.5101i | −0.0990288 | + | 0.318284i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 52.3479i | − | 0.518296i | −0.965838 | − | 0.259148i | \(-0.916558\pi\) | ||
0.965838 | − | 0.259148i | \(-0.0834417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.74613 | −0.0460790 | −0.0230395 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230395 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 46.7191i | 0.444944i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 147.723i | − | 1.38059i | −0.723530 | − | 0.690293i | \(-0.757482\pi\) | ||
0.723530 | − | 0.690293i | \(-0.242518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.56847i | 0.0327383i | 0.999866 | + | 0.0163691i | \(0.00521069\pi\) | ||||
−0.999866 | + | 0.0163691i | \(0.994789\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33.7128 | −0.303719 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −62.3154 | −0.551463 | −0.275732 | − | 0.961235i | \(-0.588920\pi\) | ||||
−0.275732 | + | 0.961235i | \(0.588920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −132.851 | −1.15523 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.0670i | 0.197154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 52.3923 | 0.440271 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −99.6410 | − | 68.6489i | −0.823479 | − | 0.567346i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 83.1038i | 0.675641i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −135.923 | −1.08738 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 28.0200i | 0.220630i | 0.993897 | + | 0.110315i | \(0.0351860\pi\) | ||||
−0.993897 | + | 0.110315i | \(0.964814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 141.756i | 1.09888i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 113.184i | 0.864001i | 0.901873 | + | 0.432000i | \(0.142192\pi\) | ||||
−0.901873 | + | 0.432000i | \(0.857808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −195.531 | −1.47016 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −21.8038 | −0.161510 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −70.7846 | −0.516676 | −0.258338 | − | 0.966055i | \(-0.583175\pi\) | ||||
−0.258338 | + | 0.966055i | \(0.583175\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 130.499i | − | 0.938839i | −0.882975 | − | 0.469420i | \(-0.844463\pi\) | ||
0.882975 | − | 0.469420i | \(-0.155537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −52.3013 | −0.370931 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −80.7602 | − | 25.1272i | −0.564757 | − | 0.175715i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.9099i | 0.199379i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.3013 | −0.0904848 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 125.793i | − | 0.844248i | −0.906538 | − | 0.422124i | \(-0.861285\pi\) | ||
0.906538 | − | 0.422124i | \(-0.138715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 275.238i | − | 1.82277i | −0.411556 | − | 0.911384i | \(-0.635015\pi\) | ||
0.411556 | − | 0.911384i | \(-0.364985\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.4515i | 0.159814i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 214.746 | 1.38546 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 273.138 | 1.73974 | 0.869868 | − | 0.493285i | \(-0.164204\pi\) | ||||
0.869868 | + | 0.493285i | \(0.164204\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 45.1244 | 0.283801 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 203.515i | 1.26407i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −62.0666 | −0.380777 | −0.190388 | − | 0.981709i | \(-0.560975\pi\) | ||||
−0.190388 | + | 0.981709i | \(0.560975\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.7513 | − | 76.3379i | 0.143947 | − | 0.462654i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 47.9800i | − | 0.287305i | −0.989628 | − | 0.143653i | \(-0.954115\pi\) | ||
0.989628 | − | 0.143653i | \(-0.0458848\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 109.879 | 0.650174 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 91.2543i | − | 0.533651i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 143.017i | − | 0.826688i | −0.910575 | − | 0.413344i | \(-0.864361\pi\) | ||
0.910575 | − | 0.413344i | \(-0.135639\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 47.5185i | 0.271534i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 143.321 | 0.809720 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −36.6025 | −0.204483 | −0.102242 | − | 0.994760i | \(-0.532602\pi\) | ||||
−0.102242 | + | 0.994760i | \(0.532602\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 84.1718 | 0.465037 | 0.232519 | − | 0.972592i | \(-0.425303\pi\) | ||||
0.232519 | + | 0.972592i | \(0.425303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 130.622i | − | 0.713783i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 81.6743 | 0.441483 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −85.6077 | − | 26.6354i | −0.457795 | − | 0.142436i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 33.4014i | 0.176727i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 44.2346 | 0.231595 | 0.115797 | − | 0.993273i | \(-0.463058\pi\) | ||||
0.115797 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 136.127i | − | 0.705323i | −0.935751 | − | 0.352662i | \(-0.885277\pi\) | ||
0.935751 | − | 0.352662i | \(-0.114723\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 55.8832i | − | 0.286580i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.96659i | − | 0.0302872i | −0.999885 | − | 0.0151436i | \(-0.995179\pi\) | ||
0.999885 | − | 0.0151436i | \(-0.00482055\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −234.056 | −1.17616 | −0.588081 | − | 0.808802i | \(-0.700116\pi\) | ||||
−0.588081 | + | 0.808802i | \(0.700116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −58.8897 | −0.292984 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44.2872 | 0.218163 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 201.331i | − | 0.982105i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −94.9808 | −0.458844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 319.492 | + | 99.4048i | 1.52867 | + | 0.475621i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 167.469i | − | 0.793690i | −0.917886 | − | 0.396845i | \(-0.870105\pi\) | ||
0.917886 | − | 0.396845i | \(-0.129895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 125.976 | 0.591435 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 343.425i | − | 1.59733i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 328.970i | − | 1.51599i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 95.0370i | 0.433959i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −62.6692 | −0.283571 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 82.2872 | 0.369001 | 0.184500 | − | 0.982832i | \(-0.440933\pi\) | ||||
0.184500 | + | 0.982832i | \(0.440933\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.1769 | −0.0985641 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 40.9999i | − | 0.180616i | −0.995914 | − | 0.0903081i | \(-0.971215\pi\) | ||
0.995914 | − | 0.0903081i | \(-0.0287852\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −160.718 | −0.701825 | −0.350913 | − | 0.936408i | \(-0.614129\pi\) | ||||
−0.350913 | + | 0.936408i | \(0.614129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −116.942 | − | 36.3847i | −0.506244 | − | 0.157510i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 407.954i | − | 1.75087i | −0.483332 | − | 0.875437i | \(-0.660573\pi\) | ||
0.483332 | − | 0.875437i | \(-0.339427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 126.708 | 0.539182 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 42.1371i | 0.177794i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 202.254i | − | 0.846253i | −0.906071 | − | 0.423127i | \(-0.860933\pi\) | ||
0.906071 | − | 0.423127i | \(-0.139067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 26.8828i | − | 0.111547i | −0.998443 | − | 0.0557734i | \(-0.982238\pi\) | ||
0.998443 | − | 0.0557734i | \(-0.0177624\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 32.2243 | 0.131528 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 233.885 | 0.946901 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 1.59874i | − | 0.00642065i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −398.277 | −1.58676 | −0.793380 | − | 0.608726i | \(-0.791681\pi\) | ||||
−0.793380 | + | 0.608726i | \(0.791681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 103.464 | − | 332.539i | 0.408949 | − | 1.31438i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 59.2375i | − | 0.232304i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −337.818 | −1.31447 | −0.657233 | − | 0.753687i | \(-0.728273\pi\) | ||||
−0.657233 | + | 0.753687i | \(0.728273\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 125.117i | − | 0.483078i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.6689i | 0.0791910i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 134.529i | − | 0.511516i | −0.966741 | − | 0.255758i | \(-0.917675\pi\) | ||
0.966741 | − | 0.255758i | \(-0.0823250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −109.321 | −0.412530 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −77.6359 | −0.290771 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 341.870 | 1.27089 | 0.635447 | − | 0.772144i | \(-0.280816\pi\) | ||||
0.635447 | + | 0.772144i | \(0.280816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 213.298i | 0.787077i | 0.919308 | + | 0.393538i | \(0.128749\pi\) | ||||
−0.919308 | + | 0.393538i | \(0.871251\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −85.6077 | −0.313581 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.1577 | − | 77.6440i | 0.0878461 | − | 0.282342i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 84.5789i | 0.305339i | 0.988277 | + | 0.152669i | \(0.0487870\pi\) | ||||
−0.988277 | + | 0.152669i | \(0.951213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 153.531 | 0.550289 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 351.148i | 1.24964i | 0.780771 | + | 0.624818i | \(0.214827\pi\) | ||||
−0.780771 | + | 0.624818i | \(0.785173\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 285.943i | − | 1.01040i | −0.863002 | − | 0.505201i | \(-0.831419\pi\) | ||
0.863002 | − | 0.505201i | \(-0.168581\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 221.077i | 0.775710i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −308.420 | −1.07464 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 222.569 | 0.770136 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.8128 | 0.126504 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 393.927i | 1.34446i | 0.740342 | + | 0.672231i | \(0.234664\pi\) | ||||
−0.740342 | + | 0.672231i | \(0.765336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −347.215 | −1.17700 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9808 | − | 54.5770i | 0.0571743 | − | 0.183761i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 243.435i | − | 0.814165i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −526.095 | −1.74782 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 90.6691i | 0.299238i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 316.452i | 1.03755i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 58.2239i | 0.189654i | 0.995494 | + | 0.0948272i | \(0.0302299\pi\) | ||||
−0.995494 | + | 0.0948272i | \(0.969770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.22055 | 0.0266037 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 207.611 | 0.667561 | 0.333780 | − | 0.942651i | \(-0.391676\pi\) | ||||
0.333780 | + | 0.942651i | \(0.391676\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −376.697 | −1.20351 | −0.601753 | − | 0.798682i | \(-0.705531\pi\) | ||||
−0.601753 | + | 0.798682i | \(0.705531\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 80.9199i | − | 0.256889i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −246.809 | −0.778577 | −0.389289 | − | 0.921116i | \(-0.627279\pi\) | ||||
−0.389289 | + | 0.921116i | \(0.627279\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −72.3641 | − | 22.5149i | −0.226847 | − | 0.0705797i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 255.863i | 0.797082i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 247.923 | 0.767564 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 56.8394i | − | 0.174890i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 6.18078i | − | 0.0189015i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 194.104i | − | 0.589982i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −146.431 | −0.442389 | −0.221195 | − | 0.975230i | \(-0.570996\pi\) | ||||
−0.221195 | + | 0.975230i | \(0.570996\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 58.3923 | 0.175352 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 142.669 | 0.425878 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 354.007i | − | 1.05047i | −0.850958 | − | 0.525233i | \(-0.823978\pi\) | ||
0.850958 | − | 0.525233i | \(-0.176022\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 107.933 | 0.318387 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −167.244 | + | 537.529i | −0.490450 | + | 1.57633i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 364.342i | − | 1.06222i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 230.105 | 0.666971 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 529.807i | − | 1.52682i | −0.645913 | − | 0.763411i | \(-0.723523\pi\) | ||
0.645913 | − | 0.763411i | \(-0.276477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 342.873i | − | 0.982445i | −0.871034 | − | 0.491223i | \(-0.836550\pi\) | ||
0.871034 | − | 0.491223i | \(-0.163450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 39.9532i | − | 0.113827i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 191.990 | 0.543880 | 0.271940 | − | 0.962314i | \(-0.412335\pi\) | ||||
0.271940 | + | 0.962314i | \(0.412335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −305.195 | −0.859704 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −90.7461 | −0.254191 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 601.654i | 1.67592i | 0.545735 | + | 0.837958i | \(0.316250\pi\) | ||||
−0.545735 | + | 0.837958i | \(0.683750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −564.261 | −1.56305 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 172.583 | + | 118.903i | 0.475436 | + | 0.327557i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 230.241i | − | 0.630798i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −139.415 | −0.379878 | −0.189939 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189939 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 143.940i | − | 0.390081i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 167.469i | 0.451398i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 303.629i | − | 0.814019i | −0.913424 | − | 0.407009i | \(-0.866572\pi\) | ||
0.913424 | − | 0.407009i | \(-0.133428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 235.426 | 0.627802 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −52.9742 | −0.140515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −690.046 | −1.82070 | −0.910351 | − | 0.413837i | \(-0.864188\pi\) | ||||
−0.910351 | + | 0.413837i | \(0.864188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 48.5321i | − | 0.127381i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −53.2576 | −0.139054 | −0.0695269 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695269 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 283.310 | + | 88.1474i | 0.735871 | + | 0.228954i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 245.529i | − | 0.634441i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 587.027 | 1.50907 | 0.754533 | − | 0.656262i | \(-0.227863\pi\) | ||||
0.754533 | + | 0.656262i | \(0.227863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 258.047i | − | 0.659967i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 196.041i | − | 0.498831i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 102.083i | − | 0.258439i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −485.797 | −1.22367 | −0.611835 | − | 0.790985i | \(-0.709569\pi\) | ||||
−0.611835 | + | 0.790985i | \(0.709569\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 338.669 | 0.848795 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −166.469 | −0.415135 | −0.207568 | − | 0.978221i | \(-0.566555\pi\) | ||||
−0.207568 | + | 0.978221i | \(0.566555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 393.499i | 0.976424i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 37.7654 | 0.0932478 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −63.6077 | + | 204.438i | −0.156284 | + | 0.502306i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 270.161i | − | 0.660541i | −0.943886 | − | 0.330271i | \(-0.892860\pi\) | ||
0.943886 | − | 0.330271i | \(-0.107140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 122.603 | 0.298303 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 531.901i | 1.28790i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.87319i | 0.00933299i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 226.030i | 0.542039i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 356.631 | 0.851147 | 0.425574 | − | 0.904924i | \(-0.360072\pi\) | ||||
0.425574 | + | 0.904924i | \(0.360072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 462.238 | 1.09795 | 0.548977 | − | 0.835838i | \(-0.315018\pi\) | ||||
0.548977 | + | 0.835838i | \(0.315018\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 90.5885 | 0.214157 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 60.2510i | − | 0.141767i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 484.774 | 1.13530 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 139.881 | + | 43.5216i | 0.326062 | + | 0.101449i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 199.552i | 0.462997i | 0.972835 | + | 0.231498i | \(0.0743628\pi\) | ||||
−0.972835 | + | 0.231498i | \(0.925637\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −45.3693 | −0.104779 | −0.0523895 | − | 0.998627i | \(-0.516684\pi\) | ||||
−0.0523895 | + | 0.998627i | \(0.516684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 50.0734i | − | 0.115111i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 963.045i | 2.20376i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 484.630i | 1.10394i | 0.833864 | + | 0.551970i | \(0.186124\pi\) | ||||
−0.833864 | + | 0.551970i | \(0.813876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 23.0385 | 0.0522414 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −375.538 | −0.847716 | −0.423858 | − | 0.905729i | \(-0.639324\pi\) | ||||
−0.423858 | + | 0.905729i | \(0.639324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 188.084 | 0.422662 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 217.880i | 0.487427i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −385.636 | −0.858877 | −0.429439 | − | 0.903096i | \(-0.641289\pi\) | ||||
−0.429439 | + | 0.903096i | \(0.641289\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 503.951 | + | 156.796i | 1.11741 | + | 0.347664i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 476.726i | 1.05238i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 207.397 | 0.455819 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 378.368i | − | 0.827939i | −0.910291 | − | 0.413970i | \(-0.864142\pi\) | ||
0.910291 | − | 0.413970i | \(-0.135858\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 42.3513i | − | 0.0922686i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 224.522i | − | 0.487033i | −0.969897 | − | 0.243516i | \(-0.921699\pi\) | ||
0.969897 | − | 0.243516i | \(-0.0783010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −52.3820 | −0.113136 | −0.0565680 | − | 0.998399i | \(-0.518016\pi\) | ||||
−0.0565680 | + | 0.998399i | \(0.518016\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −371.951 | −0.799895 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −513.387 | −1.09933 | −0.549665 | − | 0.835385i | \(-0.685245\pi\) | ||||
−0.549665 | + | 0.835385i | \(0.685245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 218.556i | − | 0.466003i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −473.090 | −1.00444 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 859.626 | + | 267.459i | 1.81739 | + | 0.565451i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 224.860i | 0.473389i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −78.1577 | −0.163853 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 238.730i | − | 0.498392i | −0.968453 | − | 0.249196i | \(-0.919834\pi\) | ||
0.968453 | − | 0.249196i | \(-0.0801663\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 149.659i | 0.311142i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 352.499i | − | 0.729812i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −89.1845 | −0.183885 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 593.251 | 1.21817 | 0.609087 | − | 0.793103i | \(-0.291536\pi\) | ||||
0.609087 | + | 0.793103i | \(0.291536\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 107.503 | 0.219842 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 858.935i | 1.74936i | 0.484703 | + | 0.874679i | \(0.338928\pi\) | ||||
−0.484703 | + | 0.874679i | \(0.661072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −56.1539 | −0.113902 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −41.1384 | + | 132.221i | −0.0831080 | + | 0.267113i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 467.529i | 0.940702i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 803.692 | 1.61061 | 0.805303 | − | 0.592864i | \(-0.202003\pi\) | ||||
0.805303 | + | 0.592864i | \(0.202003\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 83.1038i | 0.165876i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 752.302i | 1.49563i | 0.663907 | + | 0.747815i | \(0.268897\pi\) | ||||
−0.663907 | + | 0.747815i | \(0.731103\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 219.660i | − | 0.434969i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −190.317 | −0.375378 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 249.268 | 0.489721 | 0.244860 | − | 0.969558i | \(-0.421258\pi\) | ||||
0.244860 | + | 0.969558i | \(0.421258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −352.708 | −0.690230 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 158.057i | 0.308104i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.9155 | −0.0386709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −98.6795 | + | 317.161i | −0.190869 | + | 0.613464i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 247.713i | 0.477288i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 475.864 | 0.913367 | 0.456683 | − | 0.889629i | \(-0.349037\pi\) | ||||
0.456683 | + | 0.889629i | \(0.349037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 362.833i | 0.693754i | 0.937911 | + | 0.346877i | \(0.112758\pi\) | ||||
−0.937911 | + | 0.346877i | \(0.887242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 82.3045i | − | 0.156770i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 417.118i | 0.791495i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 473.372 | 0.894843 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −248.238 | −0.467492 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 368.918 | 0.692154 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 619.867i | − | 1.15863i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 63.3975 | 0.118059 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.0962 | + | 80.6604i | −0.0465606 | + | 0.149648i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 830.667i | − | 1.53543i | −0.640792 | − | 0.767715i | \(-0.721394\pi\) | ||
0.640792 | − | 0.767715i | \(-0.278606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −145.790 | −0.268489 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.9739i | 0.0274750i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 456.091i | 0.833804i | 0.908952 | + | 0.416902i | \(0.136884\pi\) | ||||
−0.908952 | + | 0.416902i | \(0.863116\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 226.244i | 0.412103i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 209.569 | 0.380343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −156.382 | −0.282788 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −141.464 | −0.254890 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 338.810i | − | 0.608277i | −0.952628 | − | 0.304138i | \(-0.901631\pi\) | ||
0.952628 | − | 0.304138i | \(-0.0983686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 629.290 | 1.12574 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 148.277 | + | 46.1339i | 0.264308 | + | 0.0822352i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 447.041i | 0.794034i | 0.917811 | + | 0.397017i | \(0.129955\pi\) | ||||
−0.917811 | + | 0.397017i | \(0.870045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −261.485 | −0.462805 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 57.8529i | − | 0.102033i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 522.893i | 0.918969i | 0.888186 | + | 0.459485i | \(0.151966\pi\) | ||||
−0.888186 | + | 0.459485i | \(0.848034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 904.574i | 1.58419i | 0.610396 | + | 0.792096i | \(0.291010\pi\) | ||||
−0.610396 | + | 0.792096i | \(0.708990\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −76.6166 | −0.133711 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 234.042 | 0.407030 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 237.674 | 0.411914 | 0.205957 | − | 0.978561i | \(-0.433969\pi\) | ||||
0.205957 | + | 0.978561i | \(0.433969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 235.780i | 0.407219i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.93336 | 0.0102123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 85.1384 | − | 273.639i | 0.146035 | − | 0.469364i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 96.7925i | 0.165457i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 578.515 | 0.985546 | 0.492773 | − | 0.870158i | \(-0.335983\pi\) | ||||
0.492773 | + | 0.870158i | \(0.335983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1556.71i | − | 2.64296i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.3344i | 0.0174863i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 333.857i | 0.562997i | 0.959562 | + | 0.281499i | \(0.0908314\pi\) | ||||
−0.959562 | + | 0.281499i | \(0.909169\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 219.846 | 0.369489 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 405.397 | 0.679058 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −846.483 | −1.41316 | −0.706580 | − | 0.707633i | \(-0.749763\pi\) | ||||
−0.706580 | + | 0.707633i | \(0.749763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 455.011i | 0.757089i | 0.925583 | + | 0.378545i | \(0.123575\pi\) | ||||
−0.925583 | + | 0.378545i | \(0.876425\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 102.000 | 0.169154 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −418.109 | − | 288.061i | −0.691089 | − | 0.476134i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 726.557i | 1.19696i | 0.801137 | + | 0.598482i | \(0.204229\pi\) | ||||
−0.801137 | + | 0.598482i | \(0.795771\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −76.7077 | −0.125957 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 232.178i | 0.379997i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 574.532i | − | 0.937247i | −0.883398 | − | 0.468624i | \(-0.844750\pi\) | ||
0.883398 | − | 0.468624i | \(-0.155250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 348.716i | 0.567018i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −278.946 | −0.452101 | −0.226050 | − | 0.974116i | \(-0.572581\pi\) | ||||
−0.226050 | + | 0.974116i | \(0.572581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 593.061 | 0.958096 | 0.479048 | − | 0.877789i | \(-0.340982\pi\) | ||||
0.479048 | + | 0.877789i | \(0.340982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 164.512 | 0.264914 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 288.127i | − | 0.462484i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −385.546 | −0.616874 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −553.377 | − | 172.174i | −0.882579 | − | 0.274600i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 158.642i | 0.252214i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −361.664 | −0.573160 | −0.286580 | − | 0.958056i | \(-0.592518\pi\) | ||||
−0.286580 | + | 0.958056i | \(0.592518\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 290.064i | 0.458237i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 117.576i | 0.185159i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 59.0475i | 0.0926963i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −218.196 | −0.341465 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 784.382 | 1.22368 | 0.611842 | − | 0.790980i | \(-0.290429\pi\) | ||||
0.611842 | + | 0.790980i | \(0.290429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −362.764 | −0.564174 | −0.282087 | − | 0.959389i | \(-0.591027\pi\) | ||||
−0.282087 | + | 0.959389i | \(0.591027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 594.830i | 0.922217i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 921.727 | 1.42462 | 0.712308 | − | 0.701867i | \(-0.247650\pi\) | ||||
0.712308 | + | 0.701867i | \(0.247650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 270.410 | − | 869.112i | 0.416657 | − | 1.33916i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 569.794i | 0.875259i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.8653 | −0.0411414 | −0.0205707 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205707 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 474.938i | 0.725096i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 164.609i | − | 0.250546i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 320.820i | 0.486828i | 0.969922 | + | 0.243414i | \(0.0782674\pi\) | ||||
−0.969922 | + | 0.243414i | \(0.921733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −331.969 | −0.502222 | −0.251111 | − | 0.967958i | \(-0.580796\pi\) | ||||
−0.251111 | + | 0.967958i | \(0.580796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 108.546 | 0.163720 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −820.477 | −1.23380 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 218.127i | − | 0.327027i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −142.526 | −0.213043 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −792.109 | − | 246.452i | −1.18049 | − | 0.367290i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 797.019i | 1.18428i | 0.805836 | + | 0.592139i | \(0.201716\pi\) | ||||
−0.805836 | + | 0.592139i | \(0.798284\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 38.4115 | 0.0569060 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 534.175i | 0.789033i | 0.918889 | + | 0.394516i | \(0.129088\pi\) | ||||
−0.918889 | + | 0.394516i | \(0.870912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 136.622i | 0.201211i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 71.0139i | 0.104279i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 843.097 | 1.23440 | 0.617201 | − | 0.786805i | \(-0.288266\pi\) | ||||
0.617201 | + | 0.786805i | \(0.288266\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −297.023 | −0.433610 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 278.372 | 0.405199 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 200.318i | − | 0.290737i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 193.615 | 0.280196 | 0.140098 | − | 0.990138i | \(-0.455258\pi\) | ||||
0.140098 | + | 0.990138i | \(0.455258\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 202.550 | + | 63.0201i | 0.292280 | + | 0.0909382i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 547.592i | − | 0.787903i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 391.061 | 0.561064 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 706.597i | 1.01087i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 448.863i | 0.640318i | 0.947364 | + | 0.320159i | \(0.103736\pi\) | ||||
−0.947364 | + | 0.320159i | \(0.896264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 592.061i | − | 0.842192i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −219.464 | −0.311297 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −336.497 | −0.475951 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 311.031 | 0.438689 | 0.219345 | − | 0.975647i | \(-0.429608\pi\) | ||||
0.219345 | + | 0.975647i | \(0.429608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 72.9836i | − | 0.102649i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1620.27 | −2.27247 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −338.882 | − | 105.438i | −0.473961 | − | 0.147465i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 350.315i | 0.488584i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 486.014 | 0.675958 | 0.337979 | − | 0.941154i | \(-0.390257\pi\) | ||||
0.337979 | + | 0.941154i | \(0.390257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.5086i | 0.0423143i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.5623i | 0.0644016i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 50.9302i | − | 0.0702485i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.8616 | 0.0534547 | 0.0267273 | − | 0.999643i | \(-0.491491\pi\) | ||||
0.0267273 | + | 0.999643i | \(0.491491\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 667.061 | 0.912533 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 175.562i | − | 0.239511i | −0.992803 | − | 0.119756i | \(-0.961789\pi\) | ||
0.992803 | − | 0.119756i | \(-0.0382111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −55.8142 | −0.0759376 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −111.110 | + | 357.114i | −0.150760 | + | 0.484551i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 494.527i | 0.669184i | 0.942363 | + | 0.334592i | \(0.108598\pi\) | ||||
−0.942363 | + | 0.334592i | \(0.891402\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −405.100 | −0.546694 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1150.84i | 1.54892i | 0.632625 | + | 0.774458i | \(0.281977\pi\) | ||||
−0.632625 | + | 0.774458i | \(0.718023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 527.846i | − | 0.708519i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.76910i | 0.00370696i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −949.577 | −1.26779 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1343.73 | 1.78926 | 0.894628 | − | 0.446813i | \(-0.147441\pi\) | ||||
0.894628 | + | 0.446813i | \(0.147441\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 689.836 | 0.916117 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1154.94i | − | 1.52972i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1034.58 | −1.36669 | −0.683343 | − | 0.730097i | \(-0.739475\pi\) | ||||
−0.683343 | + | 0.730097i | \(0.739475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −179.205 | + | 575.974i | −0.236107 | + | 0.758859i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 798.527i | − | 1.04931i | −0.851314 | − | 0.524656i | \(-0.824194\pi\) | ||
0.851314 | − | 0.524656i | \(-0.175806\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.9385 | 0.0300636 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 102.602i | 0.134121i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 636.234i | − | 0.829510i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 261.311i | − | 0.339806i | −0.985461 | − | 0.169903i | \(-0.945655\pi\) | ||
0.985461 | − | 0.169903i | \(-0.0543455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 585.118 | 0.758908 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 327.734 | 0.423977 | 0.211989 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211989 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −378.315 | −0.488149 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 216.709i | 0.278905i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1459.46 | −1.87351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 237.685 | − | 763.931i | 0.304334 | − | 0.978144i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 35.7995i | − | 0.0457210i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1146.13 | 1.46004 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 289.388i | 0.367711i | 0.982953 | + | 0.183855i | \(0.0588578\pi\) | ||||
−0.982953 | + | 0.183855i | \(0.941142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 233.010i | 0.295324i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 400.570i | 0.506409i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −579.864 | −0.731228 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 189.349 | 0.238174 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −113.681 | −0.142636 | −0.0713180 | − | 0.997454i | \(-0.522721\pi\) | ||||
−0.0713180 | + | 0.997454i | \(0.522721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 246.114i | 0.308028i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 134.469 | 0.167877 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 576.315 | + | 179.311i | 0.717703 | + | 0.223302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 853.982i | 1.06085i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −592.137 | −0.733751 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 854.163i | − | 1.05583i | −0.849299 | − | 0.527913i | \(-0.822975\pi\) | ||
0.849299 | − | 0.527913i | \(-0.177025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 486.533i | − | 0.599917i | −0.953952 | − | 0.299959i | \(-0.903027\pi\) | ||
0.953952 | − | 0.299959i | \(-0.0969729\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 369.443i | − | 0.454419i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −260.441 | −0.319560 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2489.51 | −3.04713 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 148.277 | 0.181046 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 527.104i | − | 0.642027i | −0.947075 | − | 0.321014i | \(-0.895976\pi\) | ||
0.947075 | − | 0.321014i | \(-0.104024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −314.805 | −0.382509 | −0.191255 | − | 0.981540i | \(-0.561256\pi\) | ||||
−0.191255 | + | 0.981540i | \(0.561256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −41.8423 | + | 134.483i | −0.0507180 | + | 0.163010i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 111.652i | 0.135008i | 0.997719 | + | 0.0675040i | \(0.0215035\pi\) | ||||
−0.997719 | + | 0.0675040i | \(0.978496\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 695.395 | 0.838836 | 0.419418 | − | 0.907793i | \(-0.362234\pi\) | ||||
0.419418 | + | 0.907793i | \(0.362234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 146.495i | − | 0.176288i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 62.5918i | 0.0751402i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 201.331i | − | 0.241116i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −265.923 | −0.317710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −383.968 | −0.457650 | −0.228825 | − | 0.973468i | \(-0.573488\pi\) | ||||
−0.228825 | + | 0.973468i | \(0.573488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 793.533 | 0.943559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 608.205i | − | 0.721477i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 461.071 | 0.545646 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −441.282 | + | 640.503i | −0.520994 | + | 0.756202i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 495.269i | 0.583355i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −616.238 | −0.724134 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 570.527i | 0.668847i | 0.942423 | + | 0.334424i | \(0.108542\pi\) | ||||
−0.942423 | + | 0.334424i | \(0.891458\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 382.917i | − | 0.447856i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 315.553i | − | 0.368207i | −0.982907 | − | 0.184103i | \(-0.941062\pi\) | ||
0.982907 | − | 0.184103i | \(-0.0589382\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 107.923 | 0.125638 | 0.0628190 | − | 0.998025i | \(-0.479991\pi\) | ||||
0.0628190 | + | 0.998025i | \(0.479991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 534.200 | 0.620441 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1431.55 | 1.65881 | 0.829403 | − | 0.558651i | \(-0.188681\pi\) | ||||
0.829403 | + | 0.558651i | \(0.188681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 600.121i | − | 0.693782i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −385.501 | −0.444638 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 255.524 | + | 79.5022i | 0.294044 | + | 0.0914870i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 261.426i | 0.300144i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −63.7616 | −0.0730373 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 873.727i | 0.998546i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 567.758i | − | 0.647386i | −0.946162 | − | 0.323693i | \(-0.895075\pi\) | ||
0.946162 | − | 0.323693i | \(-0.104925\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 682.302i | − | 0.776225i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 488.641 | 0.554644 | 0.277322 | − | 0.960777i | \(-0.410553\pi\) | ||||
0.277322 | + | 0.960777i | \(0.410553\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −840.144 | −0.951465 | −0.475732 | − | 0.879590i | \(-0.657817\pi\) | ||||
−0.475732 | + | 0.879590i | \(0.657817\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 601.395 | 0.679542 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 981.439i | 1.10647i | 0.833025 | + | 0.553235i | \(0.186607\pi\) | ||||
−0.833025 | + | 0.553235i | \(0.813393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 180.115 | 0.202605 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.4115 | + | 94.5302i | −0.0330096 | + | 0.106095i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 918.510i | − | 1.02857i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −153.590 | −0.171609 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 421.642i | 0.470059i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 352.589i | 0.392202i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 212.342i | − | 0.235673i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 911.223 | 1.00911 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 353.198 | 0.390274 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −438.610 | −0.483583 | −0.241792 | − | 0.970328i | \(-0.577735\pi\) | ||||
−0.241792 | + | 0.970328i | \(0.577735\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 157.044i | − | 0.172765i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −170.042 | −0.186654 | −0.0933272 | − | 0.995635i | \(-0.529750\pi\) | ||||
−0.0933272 | + | 0.995635i | \(0.529750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.69496 | − | 3.01643i | −0.0106188 | − | 0.00330386i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 548.111i | − | 0.599029i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 727.559 | 0.793412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1089.73i | 1.18578i | 0.805285 | + | 0.592888i | \(0.202012\pi\) | ||||
−0.805285 | + | 0.592888i | \(0.797988\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 100.847i | − | 0.109497i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 559.236i | − | 0.605890i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −143.885 | −0.155551 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.2384 | −0.0153597 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 769.446 | 0.828252 | 0.414126 | − | 0.910220i | \(-0.364087\pi\) | ||||
0.414126 | + | 0.910220i | \(0.364087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 233.596i | − | 0.250908i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −359.594 | −0.385417 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −359.223 | − | 111.766i | −0.384196 | − | 0.119536i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1606.78i | − | 1.71481i | −0.514641 | − | 0.857406i | \(-0.672075\pi\) | ||
0.514641 | − | 0.857406i | \(-0.327925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 652.459 | 0.694844 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1279.34i | − | 1.35955i | −0.733419 | − | 0.679777i | \(-0.762077\pi\) | ||
0.733419 | − | 0.679777i | \(-0.237923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1519.06i | 1.61088i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 140.157i | 0.148315i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 985.800 | 1.04097 | 0.520486 | − | 0.853870i | \(-0.325751\pi\) | ||||
0.520486 | + | 0.853870i | \(0.325751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 421.892 | 0.444565 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 427.486 | 0.449512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 761.038i | − | 0.798571i | −0.916827 | − | 0.399285i | \(-0.869258\pi\) | ||
0.916827 | − | 0.399285i | \(-0.130742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 185.615 | 0.194362 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 125.338 | + | 38.9970i | 0.130970 | + | 0.0407492i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 455.011i | 0.474464i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1658.08 | 1.72537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 443.168i | − | 0.460195i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 571.211i | − | 0.591929i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 702.938i | − | 0.726926i | −0.931609 | − | 0.363463i | \(-0.881594\pi\) | ||
0.931609 | − | 0.363463i | \(-0.118406\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −429.415 | −0.443153 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1289.42 | 1.32793 | 0.663963 | − | 0.747766i | \(-0.268873\pi\) | ||||
0.663963 | + | 0.747766i | \(0.268873\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −838.859 | −0.862136 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 98.4487i | 0.100973i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −690.526 | −0.706782 | −0.353391 | − | 0.935476i | \(-0.614971\pi\) | ||||
−0.353391 | + | 0.935476i | \(0.614971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −146.480 | + | 470.793i | −0.149622 | + | 0.480892i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7054i | 0.0109128i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1080.40 | 1.09908 | 0.549540 | − | 0.835467i | \(-0.314803\pi\) | ||||
0.549540 | + | 0.835467i | \(0.314803\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25.0367i | − | 0.0254180i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 336.198i | 0.340626i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2591.17i | 2.61999i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −686.561 | −0.692796 | −0.346398 | − | 0.938088i | \(-0.612595\pi\) | ||||
−0.346398 | + | 0.938088i | \(0.612595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 253.626 | 0.255413 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −982.136 | −0.987071 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1413.50i | 1.41775i | 0.705333 | + | 0.708876i | \(0.250797\pi\) | ||||
−0.705333 | + | 0.708876i | \(0.749203\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −101.138 | −0.101240 |
(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 | 2112.3.j.a.769.1 | 4 | ||
4.3 | odd | 2 | 2112.3.j.d.769.4 | 4 | |||
8.3 | odd | 2 | 528.3.j.c.241.2 | 4 | |||
8.5 | even | 2 | 33.3.c.a.10.3 | yes | 4 | ||
11.10 | odd | 2 | inner | 2112.3.j.a.769.2 | 4 | ||
24.5 | odd | 2 | 99.3.c.b.10.2 | 4 | |||
24.11 | even | 2 | 1584.3.j.f.1297.4 | 4 | |||
40.13 | odd | 4 | 825.3.h.a.274.6 | 8 | |||
40.29 | even | 2 | 825.3.b.a.76.2 | 4 | |||
40.37 | odd | 4 | 825.3.h.a.274.3 | 8 | |||
44.43 | even | 2 | 2112.3.j.d.769.3 | 4 | |||
88.5 | even | 10 | 363.3.g.e.118.2 | 16 | |||
88.13 | odd | 10 | 363.3.g.e.40.2 | 16 | |||
88.21 | odd | 2 | 33.3.c.a.10.2 | ✓ | 4 | ||
88.29 | odd | 10 | 363.3.g.e.94.3 | 16 | |||
88.37 | even | 10 | 363.3.g.e.94.2 | 16 | |||
88.43 | even | 2 | 528.3.j.c.241.1 | 4 | |||
88.53 | even | 10 | 363.3.g.e.40.3 | 16 | |||
88.61 | odd | 10 | 363.3.g.e.118.3 | 16 | |||
88.69 | even | 10 | 363.3.g.e.112.3 | 16 | |||
88.85 | odd | 10 | 363.3.g.e.112.2 | 16 | |||
264.131 | odd | 2 | 1584.3.j.f.1297.3 | 4 | |||
264.197 | even | 2 | 99.3.c.b.10.3 | 4 | |||
440.109 | odd | 2 | 825.3.b.a.76.3 | 4 | |||
440.197 | even | 4 | 825.3.h.a.274.5 | 8 | |||
440.373 | even | 4 | 825.3.h.a.274.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.c.a.10.2 | ✓ | 4 | 88.21 | odd | 2 | ||
33.3.c.a.10.3 | yes | 4 | 8.5 | even | 2 | ||
99.3.c.b.10.2 | 4 | 24.5 | odd | 2 | |||
99.3.c.b.10.3 | 4 | 264.197 | even | 2 | |||
363.3.g.e.40.2 | 16 | 88.13 | odd | 10 | |||
363.3.g.e.40.3 | 16 | 88.53 | even | 10 | |||
363.3.g.e.94.2 | 16 | 88.37 | even | 10 | |||
363.3.g.e.94.3 | 16 | 88.29 | odd | 10 | |||
363.3.g.e.112.2 | 16 | 88.85 | odd | 10 | |||
363.3.g.e.112.3 | 16 | 88.69 | even | 10 | |||
363.3.g.e.118.2 | 16 | 88.5 | even | 10 | |||
363.3.g.e.118.3 | 16 | 88.61 | odd | 10 | |||
528.3.j.c.241.1 | 4 | 88.43 | even | 2 | |||
528.3.j.c.241.2 | 4 | 8.3 | odd | 2 | |||
825.3.b.a.76.2 | 4 | 40.29 | even | 2 | |||
825.3.b.a.76.3 | 4 | 440.109 | odd | 2 | |||
825.3.h.a.274.3 | 8 | 40.37 | odd | 4 | |||
825.3.h.a.274.4 | 8 | 440.373 | even | 4 | |||
825.3.h.a.274.5 | 8 | 440.197 | even | 4 | |||
825.3.h.a.274.6 | 8 | 40.13 | odd | 4 | |||
1584.3.j.f.1297.3 | 4 | 264.131 | odd | 2 | |||
1584.3.j.f.1297.4 | 4 | 24.11 | even | 2 | |||
2112.3.j.a.769.1 | 4 | 1.1 | even | 1 | trivial | ||
2112.3.j.a.769.2 | 4 | 11.10 | odd | 2 | inner | ||
2112.3.j.d.769.3 | 4 | 44.43 | even | 2 | |||
2112.3.j.d.769.4 | 4 | 4.3 | odd | 2 |