Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 158x^{6} + 8461x^{4} + 180672x^{2} + 1232100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.8 | ||
Root | \(-6.15149i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.e.895.1 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.9291i | 1.87195i | 0.352062 | + | 0.935977i | \(0.385481\pi\) | ||||
−0.352062 | + | 0.935977i | \(0.614519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.6950 | − | 5.46693i | 0.955440 | − | 0.295187i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 23.8516i | − | 0.653776i | −0.945063 | − | 0.326888i | \(-0.894000\pi\) | ||
0.945063 | − | 0.326888i | \(-0.106000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 74.6121i | 1.59182i | 0.605415 | + | 0.795910i | \(0.293007\pi\) | ||||
−0.605415 | + | 0.795910i | \(0.706993\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 62.7872i | − | 1.08077i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 68.6323i | 0.979164i | 0.871957 | + | 0.489582i | \(0.162851\pi\) | ||||
−0.871957 | + | 0.489582i | \(0.837149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −26.6585 | −0.321888 | −0.160944 | − | 0.986964i | \(-0.551454\pi\) | ||||
−0.160944 | + | 0.986964i | \(0.551454\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −53.0850 | + | 16.4008i | −0.551623 | + | 0.170426i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 74.6991i | − | 0.677210i | −0.940929 | − | 0.338605i | \(-0.890045\pi\) | ||
0.940929 | − | 0.338605i | \(-0.109955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −313.026 | −2.50421 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −128.393 | −0.822140 | −0.411070 | − | 0.911604i | \(-0.634845\pi\) | ||||
−0.411070 | + | 0.911604i | \(0.634845\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.201 | −1.22943 | −0.614717 | − | 0.788748i | \(-0.710730\pi\) | ||||
−0.614717 | + | 0.788748i | \(0.710730\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 71.5548i | 0.377458i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 114.418 | + | 370.340i | 0.552576 | + | 1.78854i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 329.440 | 1.46377 | 0.731887 | − | 0.681426i | \(-0.238640\pi\) | ||||
0.731887 | + | 0.681426i | \(0.238640\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 223.836i | − | 0.919038i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 182.595i | 0.695527i | 0.937582 | + | 0.347763i | \(0.113059\pi\) | ||||
−0.937582 | + | 0.347763i | \(0.886941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 260.938i | 0.925410i | 0.886512 | + | 0.462705i | \(0.153121\pi\) | ||||
−0.886512 | + | 0.462705i | \(0.846879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 188.362i | 0.623985i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 401.555 | 1.24623 | 0.623115 | − | 0.782130i | \(-0.285867\pi\) | ||||
0.623115 | + | 0.782130i | \(0.285867\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 283.225 | − | 193.475i | 0.825730 | − | 0.564066i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 205.897i | − | 0.565320i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 76.7726 | 0.198972 | 0.0994862 | − | 0.995039i | \(-0.468280\pi\) | ||||
0.0994862 | + | 0.995039i | \(0.468280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 499.192 | 1.22384 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 79.9755 | 0.185842 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −901.219 | −1.98862 | −0.994311 | − | 0.106518i | \(-0.966030\pi\) | ||||
−0.994311 | + | 0.106518i | \(0.966030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 271.635i | 0.570152i | 0.958505 | + | 0.285076i | \(0.0920189\pi\) | ||||
−0.958505 | + | 0.285076i | \(0.907981\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 159.255 | − | 49.2024i | 0.318480 | − | 0.0983956i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1561.56 | −2.97981 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 499.962i | 0.911644i | 0.890071 | + | 0.455822i | \(0.150655\pi\) | ||||
−0.890071 | + | 0.455822i | \(0.849345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 224.097i | 0.390988i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 299.147i | − | 0.500032i | −0.968242 | − | 0.250016i | \(-0.919564\pi\) | ||
0.968242 | − | 0.250016i | \(-0.0804358\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 452.227i | 0.725057i | 0.931973 | + | 0.362528i | \(0.118086\pi\) | ||||
−0.931973 | + | 0.362528i | \(0.881914\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 939.079 | 1.44581 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −130.395 | − | 422.054i | −0.192986 | − | 0.624643i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 347.233i | 0.494516i | 0.968950 | + | 0.247258i | \(0.0795295\pi\) | ||||
−0.968950 | + | 0.247258i | \(0.920470\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 775.624 | 1.02573 | 0.512866 | − | 0.858468i | \(-0.328584\pi\) | ||||
0.512866 | + | 0.858468i | \(0.328584\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1436.41 | −1.83295 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 385.180 | 0.474663 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.7979i | 0.0581188i | 0.999578 | + | 0.0290594i | \(0.00925119\pi\) | ||||
−0.999578 | + | 0.0290594i | \(0.990749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 407.899 | + | 1320.26i | 0.469884 | + | 1.52089i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 636.604 | 0.709814 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 557.938i | − | 0.602560i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1054.44i | − | 1.10373i | −0.833933 | − | 0.551865i | \(-0.813916\pi\) | ||
0.833933 | − | 0.551865i | \(-0.186084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 214.665i | − | 0.217925i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 615.627i | − | 0.606506i | −0.952910 | − | 0.303253i | \(-0.901927\pi\) | ||
0.952910 | − | 0.303253i | \(-0.0980728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −609.844 | −0.583396 | −0.291698 | − | 0.956511i | \(-0.594220\pi\) | ||||
−0.291698 | + | 0.956511i | \(0.594220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −343.254 | − | 1111.02i | −0.319030 | − | 1.03261i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1905.47i | − | 1.72157i | −0.508966 | − | 0.860787i | \(-0.669972\pi\) | ||
0.508966 | − | 0.860787i | \(-0.330028\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −152.454 | −0.133968 | −0.0669838 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669838 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −988.321 | −0.845110 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 928.079 | 0.772622 | 0.386311 | − | 0.922368i | \(-0.373749\pi\) | ||||
0.386311 | + | 0.922368i | \(0.373749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1563.38 | 1.26771 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 671.509i | 0.530607i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 375.208 | + | 1214.45i | 0.289036 | + | 0.935532i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 762.100 | 0.572577 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 547.786i | − | 0.401563i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3935.22i | − | 2.81581i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1115.88i | 0.779672i | 0.920884 | + | 0.389836i | \(0.127468\pi\) | ||||
−0.920884 | + | 0.389836i | \(0.872532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 782.814i | − | 0.534286i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −936.794 | −0.624795 | −0.312397 | − | 0.949952i | \(-0.601132\pi\) | ||||
−0.312397 | + | 0.949952i | \(0.601132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −471.722 | + | 145.740i | −0.307545 | + | 0.0950172i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 565.085i | − | 0.360258i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2044.46 | −1.27496 | −0.637481 | − | 0.770466i | \(-0.720024\pi\) | ||||
−0.637481 | + | 0.770466i | \(0.720024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2914.20 | −1.77827 | −0.889133 | − | 0.457650i | \(-0.848691\pi\) | ||||
−0.889133 | + | 0.457650i | \(0.848691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1204.66 | −0.719511 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1779.62 | 1.04069 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2687.16i | − | 1.53901i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −849.676 | + | 580.424i | −0.476735 | + | 0.325664i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3427.89 | −1.88472 | −0.942360 | − | 0.334600i | \(-0.891399\pi\) | ||||
−0.942360 | + | 0.334600i | \(0.891399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2984.28i | 1.60832i | 0.594410 | + | 0.804162i | \(0.297386\pi\) | ||||
−0.594410 | + | 0.804162i | \(0.702614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 617.691i | 0.326388i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4441.18i | − | 2.30144i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3074.64i | − | 1.56295i | −0.623938 | − | 0.781474i | \(-0.714468\pi\) | ||
0.623938 | − | 0.781474i | \(-0.285532\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −230.318 | −0.114877 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −408.375 | − | 1321.80i | −0.199904 | − | 0.647034i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 87.6924i | − | 0.0421386i | −0.999778 | − | 0.0210693i | \(-0.993293\pi\) | ||
0.999778 | − | 0.0210693i | \(-0.00670707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1497.58 | −0.706583 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −199.541 | −0.0924608 | −0.0462304 | − | 0.998931i | \(-0.514721\pi\) | ||||
−0.0462304 | + | 0.998931i | \(0.514721\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3369.96 | −1.53389 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −239.927 | −0.107296 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1698.44i | − | 0.746418i | −0.927747 | − | 0.373209i | \(-0.878257\pi\) | ||
0.927747 | − | 0.373209i | \(-0.121743\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5539.00 | + | 1711.29i | −2.39262 | + | 0.739209i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2703.66 | 1.14813 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 709.691i | 0.296340i | 0.988962 | + | 0.148170i | \(0.0473382\pi\) | ||||
−0.988962 | + | 0.148170i | \(0.952662\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4297.66i | 1.76488i | 0.470427 | + | 0.882439i | \(0.344100\pi\) | ||||
−0.470427 | + | 0.882439i | \(0.655900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 814.904i | − | 0.329177i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6894.88i | 2.74012i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1636.99 | 0.640153 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −477.765 | + | 147.607i | −0.183874 | + | 0.0568087i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3487.40i | − | 1.32115i | −0.750760 | − | 0.660575i | \(-0.770312\pi\) | ||
0.750760 | − | 0.660575i | \(-0.229688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −210.502 | −0.0785090 | −0.0392545 | − | 0.999229i | \(-0.512498\pi\) | ||||
−0.0392545 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4684.69 | 1.72040 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2245.04 | 0.811943 | 0.405972 | − | 0.913886i | \(-0.366933\pi\) | ||||
0.405972 | + | 0.913886i | \(0.366933\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −976.701 | −0.347922 | −0.173961 | − | 0.984753i | \(-0.555657\pi\) | ||||
−0.173961 | + | 0.984753i | \(0.555657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1499.89i | − | 0.526338i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2271.92 | + | 701.918i | −0.785505 | + | 0.242685i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3821.55 | −1.30199 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 672.292i | − | 0.225737i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 635.849i | 0.210443i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4470.74i | − | 1.45867i | −0.684159 | − | 0.729333i | \(-0.739831\pi\) | ||
0.684159 | − | 0.729333i | \(-0.260169\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 897.442i | 0.288693i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5461.19 | −1.73233 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3754.90 | + | 1160.09i | −1.17465 | + | 0.362913i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1356.68i | − | 0.418612i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5120.80 | −1.55865 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5256.06 | 1.57835 | 0.789174 | − | 0.614169i | \(-0.210509\pi\) | ||||
0.789174 | + | 0.614169i | \(0.210509\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2817.24 | −0.834737 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6251.50 | −1.82787 | −0.913935 | − | 0.405860i | \(-0.866972\pi\) | ||||
−0.913935 | + | 0.405860i | \(0.866972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3326.07i | 0.959794i | 0.877325 | + | 0.479897i | \(0.159326\pi\) | ||||
−0.877325 | + | 0.479897i | \(0.840674\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 391.186 | + | 1266.16i | 0.111420 | + | 0.360638i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1823.44 | −0.512695 | −0.256347 | − | 0.966585i | \(-0.582519\pi\) | ||||
−0.256347 | + | 0.966585i | \(0.582519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8404.17i | 2.33288i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1041.70i | − | 0.285509i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2536.33i | − | 0.686450i | −0.939253 | − | 0.343225i | \(-0.888481\pi\) | ||
0.939253 | − | 0.343225i | \(-0.111519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 959.148i | 0.256366i | 0.991751 | + | 0.128183i | \(0.0409144\pi\) | ||||
−0.991751 | + | 0.128183i | \(0.959086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4049.25 | + | 5927.64i | 1.05591 | + | 1.54573i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1989.05i | − | 0.512389i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2326.87 | −0.592207 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3386.13 | −0.851516 | −0.425758 | − | 0.904837i | \(-0.639992\pi\) | ||||
−0.425758 | + | 0.904837i | \(0.639992\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1781.69 | −0.442744 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4309.23 | 1.05825 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2333.34i | − | 0.566343i | −0.959069 | − | 0.283171i | \(-0.908614\pi\) | ||
0.959069 | − | 0.283171i | \(-0.0913865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5829.44 | − | 1801.03i | 1.39855 | − | 0.432087i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1155.54 | −0.274047 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5769.92i | 1.35281i | 0.736531 | + | 0.676404i | \(0.236463\pi\) | ||||
−0.736531 | + | 0.676404i | \(0.763537\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1606.78i | 0.372467i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 146.394i | − | 0.0335549i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 64.3624i | − | 0.0145883i | −0.999973 | − | 0.00729413i | \(-0.997678\pi\) | ||
0.999973 | − | 0.00729413i | \(-0.00232182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6269.92 | 1.40543 | 0.702713 | − | 0.711473i | \(-0.251972\pi\) | ||||
0.702713 | + | 0.711473i | \(0.251972\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1223.70 | − | 3960.78i | −0.271288 | − | 0.878085i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7466.18i | 1.63719i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5895.37 | −1.27877 | −0.639383 | − | 0.768888i | \(-0.720810\pi\) | ||||
−0.639383 | + | 0.768888i | \(0.720810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1909.81 | −0.409812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4455.82 | −0.945949 | −0.472974 | − | 0.881076i | \(-0.656820\pi\) | ||||
−0.472974 | + | 0.881076i | \(0.656820\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1357.37 | −0.285115 | −0.142557 | − | 0.989787i | \(-0.545533\pi\) | ||||
−0.142557 | + | 0.989787i | \(0.545533\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1673.81i | 0.347888i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 998.236 | + | 3231.02i | 0.205310 | + | 0.664534i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 202.606 | 0.0412388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3163.31i | 0.637239i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3600.78i | − | 0.717952i | −0.933347 | − | 0.358976i | \(-0.883126\pi\) | ||
0.933347 | − | 0.358976i | \(-0.116874\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 18861.7i | − | 3.72261i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 643.994i | 0.125819i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5573.46 | 1.07800 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1426.53 | + | 4617.29i | 0.273169 | + | 0.884174i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1846.88i | 0.350167i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5685.07 | −1.06730 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3344.04 | −0.621677 | −0.310838 | − | 0.950463i | \(-0.600610\pi\) | ||||
−0.310838 | + | 0.950463i | \(0.600610\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1829.53 | 0.336824 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 597.591 | 0.108959 | 0.0544795 | − | 0.998515i | \(-0.482650\pi\) | ||||
0.0544795 | + | 0.998515i | \(0.482650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6906.72i | − | 1.24726i | −0.781721 | − | 0.623628i | \(-0.785658\pi\) | ||
0.781721 | − | 0.623628i | \(-0.214342\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1029.76 | + | 3333.06i | 0.184192 | + | 0.596180i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6668.30 | 1.18148 | 0.590740 | − | 0.806862i | \(-0.298836\pi\) | ||||
0.590740 | + | 0.806862i | \(0.298836\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3062.39i | 0.537495i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5716.40i | 0.993951i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1829.64i | − | 0.315181i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 23355.5i | − | 3.98625i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 457.363 | 0.0773462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7105.51 | − | 2195.27i | 1.19070 | − | 0.367870i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1117.68i | − | 0.185599i | −0.995685 | − | 0.0927997i | \(-0.970418\pi\) | ||
0.995685 | − | 0.0927997i | \(-0.0295816\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2964.96 | 0.487925 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10463.8 | −1.70655 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −987.236 | −0.159579 | −0.0797896 | − | 0.996812i | \(-0.525425\pi\) | ||||
−0.0797896 | + | 0.996812i | \(0.525425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2784.24 | −0.446074 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5061.34i | 0.803774i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3953.95 | − | 4971.91i | 0.622430 | − | 0.782675i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4690.15 | −0.731911 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8322.10i | 1.28747i | 0.765247 | + | 0.643737i | \(0.222617\pi\) | ||||
−0.765247 | + | 0.643737i | \(0.777383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 878.983i | − | 0.134816i | −0.997725 | − | 0.0674081i | \(-0.978527\pi\) | ||
0.997725 | − | 0.0674081i | \(-0.0214730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 2014.53i | − | 0.306346i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4253.69i | 0.641362i | 0.947187 | + | 0.320681i | \(0.103912\pi\) | ||||
−0.947187 | + | 0.320681i | \(0.896088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6260.88 | 0.936036 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1125.62 | − | 3643.34i | −0.166875 | − | 0.540129i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2174.96i | − | 0.319750i | −0.987137 | − | 0.159875i | \(-0.948891\pi\) | ||
0.987137 | − | 0.159875i | \(-0.0511091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6148.32 | −0.896388 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2286.30 | −0.330578 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9464.69 | −1.35727 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3958.85 | 0.563080 | 0.281540 | − | 0.959549i | \(-0.409155\pi\) | ||||
0.281540 | + | 0.959549i | \(0.409155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1643.36i | 0.231842i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1358.49 | − | 419.711i | 0.190106 | − | 0.0587340i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11819.9 | 1.64078 | 0.820388 | − | 0.571807i | \(-0.193758\pi\) | ||||
0.820388 | + | 0.571807i | \(0.193758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11805.6i | 1.62571i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 9579.70i | − | 1.30870i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8146.54i | − | 1.10411i | −0.833806 | − | 0.552057i | \(-0.813843\pi\) | ||
0.833806 | − | 0.552057i | \(-0.186157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 3347.64i | − | 0.450144i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 781.310 | 0.104238 | 0.0521189 | − | 0.998641i | \(-0.483403\pi\) | ||||
0.0521189 | + | 0.998641i | \(0.483403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8833.20 | − | 2729.05i | 1.16930 | − | 0.361261i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2348.44i | 0.308470i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4647.45 | 0.605746 | 0.302873 | − | 0.953031i | \(-0.402054\pi\) | ||||
0.302873 | + | 0.953031i | \(0.402054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5126.77 | 0.663100 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2810.38 | 0.360725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7267.27 | −0.925711 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7571.92i | 0.957239i | 0.878022 | + | 0.478620i | \(0.158863\pi\) | ||||
−0.878022 | + | 0.478620i | \(0.841137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1415.17 | − | 437.221i | 0.177561 | − | 0.0548582i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4013.10 | 0.499762 | 0.249881 | − | 0.968277i | \(-0.419609\pi\) | ||||
0.249881 | + | 0.968277i | \(0.419609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15832.8i | − | 1.95704i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1695.26i | 0.207995i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 7857.68i | − | 0.956980i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5888.31i | − | 0.711879i | −0.934509 | − | 0.355939i | \(-0.884161\pi\) | ||
0.934509 | − | 0.355939i | \(-0.115839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6133.37 | 0.736100 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15947.1 | + | 4926.90i | −1.90001 | + | 0.587015i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16233.1i | 1.92012i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8742.59 | 1.02668 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8575.63 | −0.999873 | −0.499936 | − | 0.866062i | \(-0.666643\pi\) | ||||
−0.499936 | + | 0.866062i | \(0.666643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7655.57 | 0.886246 | 0.443123 | − | 0.896461i | \(-0.353871\pi\) | ||||
0.443123 | + | 0.896461i | \(0.353871\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3613.99 | 0.415410 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 21483.7i | − | 2.45203i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1485.01 | + | 4806.58i | 0.168301 | + | 0.544746i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5338.86 | −0.600845 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5829.43i | − | 0.651493i | −0.945457 | − | 0.325747i | \(-0.894384\pi\) | ||
0.945457 | − | 0.325747i | \(-0.105616\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10072.7i | 1.11793i | 0.829191 | + | 0.558965i | \(0.188801\pi\) | ||||
−0.829191 | + | 0.558965i | \(0.811199\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8061.47i | 0.888547i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1991.37i | 0.217986i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5808.36 | −0.631476 | −0.315738 | − | 0.948846i | \(-0.602252\pi\) | ||||
−0.315738 | + | 0.948846i | \(0.602252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2549.03 | − | 1741.27i | 0.275243 | − | 0.188022i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 8923.50i | − | 0.957039i | −0.878077 | − | 0.478520i | \(-0.841174\pi\) | ||
0.878077 | − | 0.478520i | \(-0.158826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1021.30 | −0.108796 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10283.7 | 1.08814 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14002.7 | 1.47178 | 0.735888 | − | 0.677103i | \(-0.236765\pi\) | ||||
0.735888 | + | 0.677103i | \(0.236765\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4355.19 | 0.454719 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 8952.83i | − | 0.928567i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27631.8 | + | 8536.96i | −2.84703 | + | 0.879602i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5652.19 | −0.578552 | −0.289276 | − | 0.957246i | \(-0.593415\pi\) | ||||
−0.289276 | + | 0.957246i | \(0.593415\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1853.07i | − | 0.188440i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4689.73i | − | 0.473801i | −0.971534 | − | 0.236901i | \(-0.923868\pi\) | ||
0.971534 | − | 0.236901i | \(-0.0761316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 252.859i | 0.0253809i | 0.999919 | + | 0.0126904i | \(0.00403960\pi\) | ||||
−0.999919 | + | 0.0126904i | \(0.995960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13323.5i | 1.32874i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5019.67 | 0.497393 | 0.248697 | − | 0.968581i | \(-0.419998\pi\) | ||||
0.248697 | + | 0.968581i | \(0.419998\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2733.26 | + | 8846.83i | 0.269105 | + | 0.871021i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9223.91i | 0.902368i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6223.79 | 0.605011 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8344.81 | 0.806076 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 690.954 | 0.0663241 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4266.51 | −0.406977 | −0.203488 | − | 0.979077i | \(-0.565228\pi\) | ||||
−0.203488 | + | 0.979077i | \(0.565228\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24580.2i | 2.33007i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1225.13 | + | 3965.40i | 0.115414 | + | 0.373565i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22068.4 | 2.06613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4599.91i | 0.428012i | 0.976832 | + | 0.214006i | \(0.0686512\pi\) | ||||
−0.976832 | + | 0.214006i | \(0.931349\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 263.077i | 0.0243288i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10713.6i | − | 0.984725i | −0.870390 | − | 0.492362i | \(-0.836133\pi\) | ||
0.870390 | − | 0.492362i | \(-0.163867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8811.94i | − | 0.805009i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4492.73 | 0.407946 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1635.42 | − | 5293.41i | −0.147603 | − | 0.477750i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5256.23i | − | 0.471545i | −0.971808 | − | 0.235773i | \(-0.924238\pi\) | ||
0.971808 | − | 0.235773i | \(-0.0757621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 598.623 | 0.0533823 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12369.0 | −1.09644 | −0.548219 | − | 0.836335i | \(-0.684694\pi\) | ||||
−0.548219 | + | 0.836335i | \(0.684694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12884.5 | 1.13535 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10109.9 | 0.885594 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15337.1i | 1.33557i | 0.744354 | + | 0.667785i | \(0.232758\pi\) | ||||
−0.744354 | + | 0.667785i | \(0.767242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2472.29 | + | 8002.15i | 0.214027 | + | 0.692748i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 719.780 | 0.0619475 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 12763.5i | − | 1.09209i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9577.73i | − | 0.814755i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5095.33i | 0.430945i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17351.3i | 1.45906i | 0.683947 | + | 0.729532i | \(0.260262\pi\) | ||||
−0.683947 | + | 0.729532i | \(0.739738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7260.17 | 0.607007 | 0.303504 | − | 0.952830i | \(-0.401844\pi\) | ||||
0.303504 | + | 0.952830i | \(0.401844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16617.0 | − | 5133.88i | 1.38138 | − | 0.426783i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 14563.9i | − | 1.20382i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6587.04 | 0.541386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8110.97 | −0.662874 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13623.8 | −1.10715 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39879.6 | 3.22271 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2129.07i | − | 0.171092i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4614.68 | − | 6755.38i | −0.368773 | − | 0.539842i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14127.5 | −1.12271 | −0.561357 | − | 0.827573i | \(-0.689721\pi\) | ||||
−0.561357 | + | 0.827573i | \(0.689721\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 12893.0i | − | 1.01895i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3190.73i | − | 0.250781i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10564.8i | 0.825810i | 0.910774 | + | 0.412905i | \(0.135486\pi\) | ||||
−0.910774 | + | 0.412905i | \(0.864514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2444.71i | 0.190051i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3422.78 | 0.264637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1898.30 | + | 6144.28i | 0.145975 | + | 0.472480i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 20684.6i | − | 1.58201i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15271.5 | −1.16171 | −0.580855 | − | 0.814007i | \(-0.697282\pi\) | ||||
−0.580855 | + | 0.814007i | \(0.697282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19469.1 | −1.47309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4910.97 | −0.369593 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11971.0 | 0.896124 | 0.448062 | − | 0.894003i | \(-0.352114\pi\) | ||||
0.448062 | + | 0.894003i | \(0.352114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19423.8i | 1.44631i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1433.29 | − | 442.822i | 0.106160 | − | 0.0327985i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9396.66 | 0.692317 | 0.346158 | − | 0.938176i | \(-0.387486\pi\) | ||||
0.346158 | + | 0.938176i | \(0.387486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15035.4i | 1.10194i | 0.834523 | + | 0.550972i | \(0.185743\pi\) | ||||
−0.834523 | + | 0.550972i | \(0.814257\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10462.2i | 0.762767i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23382.8i | 1.69588i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5019.96i | 0.362190i | 0.983466 | + | 0.181095i | \(0.0579642\pi\) | ||||
−0.983466 | + | 0.181095i | \(0.942036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 631.505 | 0.0453272 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13724.7 | − | 4240.29i | 0.980026 | − | 0.302783i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1831.15i | − | 0.130083i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14054.1 | −0.993271 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10231.3 | −0.719404 | −0.359702 | − | 0.933067i | \(-0.617122\pi\) | ||||
−0.359702 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5656.97 | 0.395741 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6735.13 | −0.468776 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4278.75i | 0.296302i | 0.988965 | + | 0.148151i | \(0.0473322\pi\) | ||||
−0.988965 | + | 0.148151i | \(0.952668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −25417.3 | + | 7852.76i | −1.75127 | + | 0.541062i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2930.10 | 0.200873 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 114.830i | − | 0.00783279i | −0.999992 | − | 0.00391639i | \(-0.998753\pi\) | ||
0.999992 | − | 0.00391639i | \(-0.00124663\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2048.91i | − | 0.139063i | −0.997580 | − | 0.0695315i | \(-0.977850\pi\) | ||
0.997580 | − | 0.0695315i | \(-0.0221504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4499.66i | 0.303881i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15950.1i | 1.07184i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1447.87 | −0.0968162 | −0.0484081 | − | 0.998828i | \(-0.515415\pi\) | ||||
−0.0484081 | + | 0.998828i | \(0.515415\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6815.76 | − | 2105.75i | 0.453512 | − | 0.140114i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29960.8i | 1.98377i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13450.7 | 0.886245 | 0.443123 | − | 0.896461i | \(-0.353871\pi\) | ||||
0.443123 | + | 0.896461i | \(0.353871\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11464.7 | 0.751706 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19623.3 | −1.28039 | −0.640197 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640197 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15910.6 | −1.03312 | −0.516561 | − | 0.856250i | \(-0.672788\pi\) | ||||
−0.516561 | + | 0.856250i | \(0.672788\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2016.88i | 0.130329i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 266.775 | + | 863.479i | 0.0171559 | + | 0.0555290i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 43232.2 | 2.76686 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1907.55i | − | 0.121499i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22610.2i | 1.43327i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20416.1i | 1.28804i | 0.765008 | + | 0.644021i | \(0.222735\pi\) | ||||
−0.765008 | + | 0.644021i | \(0.777265\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13412.2i | 0.842161i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23354.3 | −1.45951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14435.5 | + | 21132.0i | 0.897892 | + | 1.31441i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 2692.33i | − | 0.166677i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 699.877 | 0.0431256 | 0.0215628 | − | 0.999767i | \(-0.493136\pi\) | ||||
0.0215628 | + | 0.999767i | \(0.493136\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11449.1 | 0.702192 | 0.351096 | − | 0.936339i | \(-0.385809\pi\) | ||||
0.351096 | + | 0.936339i | \(0.385809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16383.6 | 1.00016 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20822.8 | −1.26527 | −0.632634 | − | 0.774451i | \(-0.718026\pi\) | ||||
−0.632634 | + | 0.774451i | \(0.718026\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21495.5i | 1.30011i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11264.7 | − | 3480.27i | 0.678185 | − | 0.209528i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13036.2 | 0.781236 | 0.390618 | − | 0.920553i | \(-0.372261\pi\) | ||||
0.390618 | + | 0.920553i | \(0.372261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 19606.2i | − | 1.16959i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4070.04i | 0.241686i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13602.0i | − | 0.804034i | −0.915632 | − | 0.402017i | \(-0.868309\pi\) | ||
0.915632 | − | 0.402017i | \(-0.131691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13817.6i | 0.813076i | 0.913634 | + | 0.406538i | \(0.133264\pi\) | ||||
−0.913634 | + | 0.406538i | \(0.866736\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15362.4 | 0.899889 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3050.21 | − | 9872.71i | −0.177868 | − | 0.575710i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9590.87i | 0.556762i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15768.2 | −0.911260 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6478.93 | 0.372752 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14766.4 | −0.845771 | −0.422886 | − | 0.906183i | \(-0.638983\pi\) | ||||
−0.422886 | + | 0.906183i | \(0.638983\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8451.71 | 0.481935 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 19480.1i | − | 1.10588i | −0.833222 | − | 0.552939i | \(-0.813506\pi\) | ||
0.833222 | − | 0.552939i | \(-0.186494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5764.54 | − | 18658.2i | −0.325806 | − | 1.05455i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18754.5 | 1.05532 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17335.1i | 0.971170i | 0.874189 | + | 0.485585i | \(0.161393\pi\) | ||||
−0.874189 | + | 0.485585i | \(0.838607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 42788.6i | − | 2.38667i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9978.20i | − | 0.554137i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5728.17i | 0.316728i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29783.9 | 1.63970 | 0.819850 | − | 0.572578i | \(-0.194057\pi\) | ||||
0.819850 | + | 0.572578i | \(0.194057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1173.56 | − | 3798.49i | −0.0643286 | − | 0.208214i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 60991.4i | − | 3.32883i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12531.9 | −0.681034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5470.33 | 0.296004 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23567.6 | 1.26981 | 0.634903 | − | 0.772592i | \(-0.281040\pi\) | ||||
0.634903 | + | 0.772592i | \(0.281040\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8782.39 | −0.471172 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 25212.5i | − | 1.34689i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3365.59 | − | 10893.5i | −0.179033 | − | 0.579480i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9637.20 | −0.510484 | −0.255242 | − | 0.966877i | \(-0.582155\pi\) | ||||
−0.255242 | + | 0.966877i | \(0.582155\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3125.10i | 0.164839i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15851.2i | 0.832586i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37245.8i | 1.94813i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7609.00i | 0.396322i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26050.6 | −1.35121 | −0.675606 | − | 0.737263i | \(-0.736118\pi\) | ||||
−0.675606 | + | 0.737263i | \(0.736118\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10791.2 | + | 3333.98i | −0.557399 | + | 0.172211i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2877.44i | − | 0.148013i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40190.5 | 2.05881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35153.8 | −1.79337 | −0.896685 | − | 0.442668i | \(-0.854032\pi\) | ||||
−0.896685 | + | 0.442668i | \(0.854032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17908.8 | −0.906128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12635.0i | 0.636677i | 0.947977 | + | 0.318338i | \(0.103125\pi\) | ||||
−0.947977 | + | 0.318338i | \(0.896875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12147.7 | − | 17782.9i | −0.609627 | − | 0.892426i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11924.9 | 0.596011 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24477.7i | − | 1.21844i | −0.793001 | − | 0.609220i | \(-0.791483\pi\) | ||
0.793001 | − | 0.609220i | \(-0.208517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5967.14i | 0.295828i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38742.2i | 1.91294i | 0.291833 | + | 0.956469i | \(0.405735\pi\) | ||||
−0.291833 | + | 0.956469i | \(0.594265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 71742.5i | − | 3.52811i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6980.62 | 0.341911 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10417.1 | − | 33717.2i | −0.508186 | − | 1.64486i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17887.8i | 0.869153i | 0.900635 | + | 0.434577i | \(0.143102\pi\) | ||||
−0.900635 | + | 0.434577i | \(0.856898\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10158.4 | 0.491623 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −62458.2 | −3.01071 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34118.1 | 1.63810 | 0.819052 | − | 0.573720i | \(-0.194500\pi\) | ||||
0.819052 | + | 0.573720i | \(0.194500\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5345.08 | 0.255618 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4807.40i | − | 0.228999i | −0.993423 | − | 0.114499i | \(-0.963474\pi\) | ||
0.993423 | − | 0.114499i | \(-0.0365264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2697.68 | + | 833.457i | −0.127998 | + | 0.0395454i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12927.7 | −0.610983 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 67241.8i | − | 3.16553i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25362.7i | − | 1.18934i | −0.803970 | − | 0.594670i | \(-0.797283\pi\) | ||
0.803970 | − | 0.594670i | \(-0.202717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7000.03i | 0.326978i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8758.34i | − | 0.407523i | −0.979021 | − | 0.203762i | \(-0.934683\pi\) | ||
0.979021 | − | 0.203762i | \(-0.0653167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 66424.6 | 3.07876 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17488.3 | + | 5403.08i | −0.807452 | + | 0.249465i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 4867.72i | − | 0.223882i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7135.15 | −0.326909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3466.62 | 0.158221 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 64349.3 | 2.92576 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13007.0 | −0.589137 | −0.294569 | − | 0.955630i | \(-0.595176\pi\) | ||||
−0.294569 | + | 0.955630i | \(0.595176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 17309.8i | − | 0.781044i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16422.3 | − | 5073.75i | 0.738194 | − | 0.228068i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20267.2 | −0.907580 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 4820.34i | − | 0.215044i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27449.5i | 1.21997i | 0.792415 | + | 0.609983i | \(0.208824\pi\) | ||||
−0.792415 | + | 0.609983i | \(0.791176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27559.6i | 1.22026i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 439.181i | 0.0193729i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10786.3 | 0.474025 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27664.1 | − | 8546.91i | 1.21122 | − | 0.374210i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 193.087i | 0.00842254i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11638.3 | −0.505788 | −0.252894 | − | 0.967494i | \(-0.581382\pi\) | ||||
−0.252894 | + | 0.967494i | \(0.581382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 732.648 | 0.0317222 | 0.0158611 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158611 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18809.8 | −0.811423 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1835.32 | 0.0788816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6956.21i | − | 0.297879i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3671.09 | + | 11882.3i | 0.156628 | + | 0.506963i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2380.21 | −0.101181 | −0.0505907 | − | 0.998719i | \(-0.516110\pi\) | ||||
−0.0505907 | + | 0.998719i | \(0.516110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19256.2i | 0.815588i | 0.913074 | + | 0.407794i | \(0.133702\pi\) | ||||
−0.913074 | + | 0.407794i | \(0.866298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 22398.5i | − | 0.945233i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8930.67i | 0.375514i | 0.982216 | + | 0.187757i | \(0.0601217\pi\) | ||||
−0.982216 | + | 0.187757i | \(0.939878\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 28554.2i | − | 1.19630i | −0.801386 | − | 0.598148i | \(-0.795903\pi\) | ||
0.801386 | − | 0.598148i | \(-0.204097\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17686.1 | 0.738296 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13278.6 | + | 19438.4i | 0.552313 | + | 0.808524i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4176.21i | − | 0.173082i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5729.43 | 0.236605 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5568.93 | −0.229155 | −0.114577 | − | 0.993414i | \(-0.536551\pi\) | ||||
−0.114577 | + | 0.993414i | \(0.536551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7904.13 | −0.324086 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13367.4 | 0.546144 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 70530.2i | − | 2.87138i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13485.4 | − | 4166.35i | 0.547063 | − | 0.169017i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4072.12 | 0.164611 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 24608.9i | − | 0.991283i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26913.6i | 1.08031i | 0.841566 | + | 0.540155i | \(0.181634\pi\) | ||||
−0.841566 | + | 0.540155i | \(0.818366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5021.44i | − | 0.200853i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18275.6i | 0.728452i | 0.931311 | + | 0.364226i | \(0.118666\pi\) | ||||
−0.931311 | + | 0.364226i | \(0.881334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25266.9 | 1.00360 | 0.501802 | − | 0.864982i | \(-0.332670\pi\) | ||||
0.501802 | + | 0.864982i | \(0.332670\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2994.71 | − | 9693.07i | −0.118536 | − | 0.383669i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30621.0i | 1.20782i | 0.797051 | + | 0.603912i | \(0.206392\pi\) | ||||
−0.797051 | + | 0.603912i | \(0.793608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35546.9 | 1.39726 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −607.818 | −0.0238092 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8282.07 | 0.323303 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37303.2 | −1.45117 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 9489.93i | − | 0.367910i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21513.6 | − | 69633.6i | −0.831190 | − | 2.69034i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26961.9 | 1.03813 | 0.519064 | − | 0.854735i | \(-0.326280\pi\) | ||||
0.519064 | + | 0.854735i | \(0.326280\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10802.3i | 0.414510i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34254.9i | 1.30996i | 0.755645 | + | 0.654982i | \(0.227324\pi\) | ||||
−0.755645 | + | 0.654982i | \(0.772676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35366.4i | 1.34788i | 0.738788 | + | 0.673938i | \(0.235398\pi\) | ||||
−0.738788 | + | 0.673938i | \(0.764602\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56585.0i | 2.14925i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38236.0 | 1.44739 | 0.723697 | − | 0.690118i | \(-0.242441\pi\) | ||||
0.723697 | + | 0.690118i | \(0.242441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6100.44 | + | 19745.5i | 0.230149 | + | 0.744929i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1931.98i | − | 0.0726417i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10704.9 | −0.401147 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14853.2 | −0.554734 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16720.4 | −0.622382 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27245.2 | 1.01077 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5269.08i | 0.194826i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4279.59 | − | 13851.9i | −0.157714 | − | 0.510478i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −89946.1 | −3.30377 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36703.5i | 1.34368i | 0.740695 | + | 0.671842i | \(0.234497\pi\) | ||||
−0.740695 | + | 0.671842i | \(0.765503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 5540.64i | − | 0.202169i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9583.16i | 0.348523i | 0.984699 | + | 0.174261i | \(0.0557538\pi\) | ||||
−0.984699 | + | 0.174261i | \(0.944246\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18499.9i | − | 0.670599i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 17055.2 | 0.616205 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16576.6 | + | 5121.39i | −0.596954 | + | 0.184431i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32765.0i | 1.17608i | 0.808832 | + | 0.588040i | \(0.200100\pi\) | ||||
−0.808832 | + | 0.588040i | \(0.799900\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10032.1 | 0.358925 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22320.0 | 0.795961 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −103123. | −3.66560 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5488.60 | −0.194465 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25650.6i | 0.905885i | 0.891540 | + | 0.452943i | \(0.149626\pi\) | ||||
−0.891540 | + | 0.452943i | \(0.850374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7550.36 | + | 5157.75i | −0.265793 | + | 0.181566i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1792.77 | −0.0629075 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 34260.7i | 1.19834i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14746.2i | 0.514129i | 0.966394 | + | 0.257064i | \(0.0827553\pi\) | ||||
−0.966394 | + | 0.257064i | \(0.917245\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20720.2i | 0.720103i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22330.7i | 0.773604i | 0.922163 | + | 0.386802i | \(0.126420\pi\) | ||||
−0.922163 | + | 0.386802i | \(0.873580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13639.7 | 0.471018 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3089.28 | − | 9999.17i | −0.106343 | − | 0.344204i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34804.7i | 1.19430i | 0.802130 | + | 0.597149i | \(0.203700\pi\) | ||||
−0.802130 | + | 0.597149i | \(0.796300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −33741.6 | −1.15416 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20004.9 | −0.682127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10582.9 | 0.359719 | 0.179860 | − | 0.983692i | \(-0.442436\pi\) | ||||
0.179860 | + | 0.983692i | \(0.442436\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 72988.2 | 2.47313 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 9187.17i | − | 0.310323i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −36176.7 | + | 11176.9i | −1.21815 | + | 0.376352i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15238.4 | 0.511509 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 17149.2i | − | 0.573858i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 4405.60i | − | 0.146965i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4491.20i | 0.149356i | 0.997208 | + | 0.0746780i | \(0.0237929\pi\) | ||||
−0.997208 | + | 0.0746780i | \(0.976207\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5488.91i | 0.181970i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28182.0 | 0.931413 | 0.465706 | − | 0.884939i | \(-0.345800\pi\) | ||||
0.465706 | + | 0.884939i | \(0.345800\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51566.7 | + | 15931.7i | −1.69902 | + | 0.524920i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 70066.6i | 2.30146i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −22874.1 | −0.749036 | −0.374518 | − | 0.927220i | \(-0.622192\pi\) | ||||
−0.374518 | + | 0.927220i | \(0.622192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1163.91 | 0.0379966 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1372.09 | −0.0446559 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 671.036 | 0.0217729 | 0.0108864 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108864 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46986.7i | 1.51992i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21316.5 | + | 6585.82i | −0.687449 | + | 0.212390i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19491.8 | 0.626698 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 11573.2i | − | 0.370975i | −0.982647 | − | 0.185487i | \(-0.940614\pi\) | ||
0.982647 | − | 0.185487i | \(-0.0593864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3353.05i | 0.107156i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 20441.5i | − | 0.651294i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33269.8i | 1.05684i | 0.848984 | + | 0.528419i | \(0.177215\pi\) | ||||
−0.848984 | + | 0.528419i | \(0.822785\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8894.89 | −0.281703 |
(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 | 1344.4.b.e.895.8 | 8 | ||
4.3 | odd | 2 | 1344.4.b.f.895.8 | 8 | |||
7.6 | odd | 2 | 1344.4.b.f.895.1 | 8 | |||
8.3 | odd | 2 | 336.4.b.e.223.1 | ✓ | 8 | ||
8.5 | even | 2 | 336.4.b.f.223.1 | yes | 8 | ||
24.5 | odd | 2 | 1008.4.b.k.559.8 | 8 | |||
24.11 | even | 2 | 1008.4.b.i.559.8 | 8 | |||
28.27 | even | 2 | inner | 1344.4.b.e.895.1 | 8 | ||
56.13 | odd | 2 | 336.4.b.e.223.8 | yes | 8 | ||
56.27 | even | 2 | 336.4.b.f.223.8 | yes | 8 | ||
168.83 | odd | 2 | 1008.4.b.k.559.1 | 8 | |||
168.125 | even | 2 | 1008.4.b.i.559.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.b.e.223.1 | ✓ | 8 | 8.3 | odd | 2 | ||
336.4.b.e.223.8 | yes | 8 | 56.13 | odd | 2 | ||
336.4.b.f.223.1 | yes | 8 | 8.5 | even | 2 | ||
336.4.b.f.223.8 | yes | 8 | 56.27 | even | 2 | ||
1008.4.b.i.559.1 | 8 | 168.125 | even | 2 | |||
1008.4.b.i.559.8 | 8 | 24.11 | even | 2 | |||
1008.4.b.k.559.1 | 8 | 168.83 | odd | 2 | |||
1008.4.b.k.559.8 | 8 | 24.5 | odd | 2 | |||
1344.4.b.e.895.1 | 8 | 28.27 | even | 2 | inner | ||
1344.4.b.e.895.8 | 8 | 1.1 | even | 1 | trivial | ||
1344.4.b.f.895.1 | 8 | 7.6 | odd | 2 | |||
1344.4.b.f.895.8 | 8 | 4.3 | odd | 2 |