Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.b.2591.8 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 4.38134i | − 1.95940i | −0.200480 | − | 0.979698i | \(-0.564250\pi\) | ||||
0.200480 | − | 0.979698i | \(-0.435750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.31079 | 0.696729 | 0.348365 | − | 0.937359i | \(-0.386737\pi\) | ||||
0.348365 | + | 0.937359i | \(0.386737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73205 | −1.31243 | −0.656217 | − | 0.754572i | \(-0.727845\pi\) | ||||
−0.656217 | + | 0.754572i | \(0.727845\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.27792i | − 1.28008i | −0.768340 | − | 0.640041i | \(-0.778917\pi\) | ||||
0.768340 | − | 0.640041i | \(-0.221083\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.00000i | − 1.14708i | −0.819178 | − | 0.573539i | \(-0.805570\pi\) | ||||
0.819178 | − | 0.573539i | \(-0.194430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.517638 | 0.107935 | 0.0539675 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539675 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.1962 | −2.83923 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.24264i | 0.787839i | 0.919145 | + | 0.393919i | \(0.128881\pi\) | ||||
−0.919145 | + | 0.393919i | \(0.871119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 3.53590i | − 0.635066i | −0.948247 | − | 0.317533i | \(-0.897146\pi\) | ||||
0.948247 | − | 0.317533i | \(-0.102854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.38134 | −0.740582 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.46410 | −0.733894 | −0.366947 | − | 0.930242i | \(-0.619597\pi\) | ||||
−0.366947 | + | 0.930242i | \(0.619597\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.45189i | 1.00762i | 0.863816 | + | 0.503808i | \(0.168068\pi\) | ||||
−0.863816 | + | 0.503808i | \(0.831932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.26795i | − 0.193360i | −0.995315 | − | 0.0966802i | \(-0.969178\pi\) | ||||
0.995315 | − | 0.0966802i | \(-0.0308224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.10634 | −1.18243 | −0.591216 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591216 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.93426i | 0.815133i | 0.913176 | + | 0.407566i | \(0.133622\pi\) | ||||
−0.913176 | + | 0.407566i | \(0.866378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 10.1244i | − 1.36517i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.31319 | −0.821908 | −0.410954 | − | 0.911656i | \(-0.634804\pi\) | ||||
−0.410954 | + | 0.911656i | \(0.634804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.7327i | 2.57158i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.66025i | 1.18019i | 0.807335 | + | 0.590094i | \(0.200909\pi\) | ||||
−0.807335 | + | 0.590094i | \(0.799091\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4877 | −1.48202 | −0.741008 | − | 0.671496i | \(-0.765652\pi\) | ||||
−0.741008 | + | 0.671496i | \(0.765652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1962 | 1.19337 | 0.596685 | − | 0.802476i | \(-0.296484\pi\) | ||||
0.596685 | + | 0.802476i | \(0.296484\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.31079i | − 0.263339i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 12.1962i | − 1.37217i | −0.727519 | − | 0.686087i | \(-0.759327\pi\) | ||||
0.727519 | − | 0.686087i | \(-0.240673\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.6269 | 1.93480 | 0.967402 | − | 0.253246i | \(-0.0814982\pi\) | ||||
0.967402 | + | 0.253246i | \(0.0814982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −23.1244 | −2.50819 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 0.517638i | − 0.0548695i | −0.999624 | − | 0.0274348i | \(-0.991266\pi\) | ||||
0.999624 | − | 0.0274348i | \(-0.00873385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.73205i | 0.496054i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.9067 | −2.24758 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.928203 | 0.0942448 | 0.0471224 | − | 0.998889i | \(-0.484995\pi\) | ||||
0.0471224 | + | 0.998889i | \(0.484995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 10.1769i | − 1.01264i | −0.862346 | − | 0.506320i | \(-0.831006\pi\) | ||||
0.862346 | − | 0.506320i | \(-0.168994\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.4641i | − 1.03106i | −0.856872 | − | 0.515529i | \(-0.827595\pi\) | ||||
0.856872 | − | 0.515529i | \(-0.172405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7632 | 1.33054 | 0.665269 | − | 0.746603i | \(-0.268317\pi\) | ||||
0.665269 | + | 0.746603i | \(0.268317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5885 | 1.30154 | 0.650769 | − | 0.759276i | \(-0.274447\pi\) | ||||
0.650769 | + | 0.759276i | \(0.274447\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 8.48528i | − 0.798228i | −0.916901 | − | 0.399114i | \(-0.869318\pi\) | ||||
0.916901 | − | 0.399114i | \(-0.130682\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.26795i | − 0.211487i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.27792 | −0.483826 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.66025 | −0.514569 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 40.2915i | 3.60378i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.339746i | 0.0301476i | 0.999886 | + | 0.0150738i | \(0.00479832\pi\) | ||||
−0.999886 | + | 0.0150738i | \(0.995202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.41421 | 0.123560 | 0.0617802 | − | 0.998090i | \(-0.480322\pi\) | ||||
0.0617802 | + | 0.998090i | \(0.480322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | −0.433555 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.31319i | 0.539372i | 0.962948 | + | 0.269686i | \(0.0869200\pi\) | ||||
−0.962948 | + | 0.269686i | \(0.913080\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.3205i | 1.97802i | 0.147850 | + | 0.989010i | \(0.452765\pi\) | ||||
−0.147850 | + | 0.989010i | \(0.547235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.9348 | −0.914411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.5885 | 1.54369 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 19.7990i | − 1.62200i | −0.585049 | − | 0.810998i | \(-0.698925\pi\) | ||||
0.585049 | − | 0.810998i | \(-0.301075\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.07180i | 0.0872216i | 0.999049 | + | 0.0436108i | \(0.0138862\pi\) | ||||
−0.999049 | + | 0.0436108i | \(0.986114\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.4920 | −1.24435 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.26795 | 0.260811 | 0.130405 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130405 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.517638i | − 0.0407956i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 20.0526i | − 1.57064i | −0.619092 | − | 0.785319i | \(-0.712499\pi\) | ||||
0.619092 | − | 0.785319i | \(-0.287501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.20788 | −0.635145 | −0.317572 | − | 0.948234i | \(-0.602868\pi\) | ||||
−0.317572 | + | 0.948234i | \(0.602868\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.39230 | 0.722485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.7298i | 0.891801i | 0.895083 | + | 0.445900i | \(0.147116\pi\) | ||||
−0.895083 | + | 0.445900i | \(0.852884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.1962i | 1.07313i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.17209 | −0.162350 | −0.0811748 | − | 0.996700i | \(-0.525867\pi\) | ||||
−0.0811748 | + | 0.996700i | \(0.525867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7846 | −1.24759 | −0.623795 | − | 0.781588i | \(-0.714410\pi\) | ||||
−0.623795 | + | 0.781588i | \(0.714410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.5588i | 1.43799i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.1962i | − 0.891871i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1087 | −0.876158 | −0.438079 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438079 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.3205 | −1.82261 | −0.911305 | − | 0.411732i | \(-0.864924\pi\) | ||||
−0.911305 | + | 0.411732i | \(0.864924\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.37945i | − 0.383270i | −0.981466 | − | 0.191635i | \(-0.938621\pi\) | ||||
0.981466 | − | 0.191635i | \(-0.0613790\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 17.7321i | − 1.25699i | −0.777813 | − | 0.628496i | \(-0.783671\pi\) | ||||
0.777813 | − | 0.628496i | \(-0.216329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.24264 | 0.297775 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.2679 | 1.97432 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 11.5539i | − 0.799203i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.4641i | 1.47765i | 0.673898 | + | 0.738825i | \(0.264619\pi\) | ||||
−0.673898 | + | 0.738825i | \(0.735381\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.55532 | −0.378870 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.53590 | −0.240032 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.9754i | 1.68003i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.124356i | − 0.00832747i | −0.999991 | − | 0.00416374i | \(-0.998675\pi\) | ||||
0.999991 | − | 0.00416374i | \(-0.00132536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.6274 | 1.50183 | 0.750917 | − | 0.660396i | \(-0.229612\pi\) | ||||
0.750917 | + | 0.660396i | \(0.229612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.535898 | 0.0354132 | 0.0177066 | − | 0.999843i | \(-0.494364\pi\) | ||||
0.0177066 | + | 0.999843i | \(0.494364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.757875i | 0.0496500i | 0.999692 | + | 0.0248250i | \(0.00790286\pi\) | ||||
−0.999692 | + | 0.0248250i | \(0.992097\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.5167i | 2.31685i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.62587 | −0.493277 | −0.246638 | − | 0.969108i | \(-0.579326\pi\) | ||||
−0.246638 | + | 0.969108i | \(0.579326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.1962 | 1.81627 | 0.908137 | − | 0.418673i | \(-0.137505\pi\) | ||||
0.908137 | + | 0.418673i | \(0.137505\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.38134i | 0.279914i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.6603i | 1.50547i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3538 | −1.28472 | −0.642360 | − | 0.766403i | \(-0.722045\pi\) | ||||
−0.642360 | + | 0.766403i | \(0.722045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.19615 | 0.0752015 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.9719i | 0.684411i | 0.939625 | + | 0.342205i | \(0.111174\pi\) | ||||
−0.939625 | + | 0.342205i | \(0.888826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.46410i | 0.277386i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.96764 | 0.491306 | 0.245653 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245653 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.0000 | 1.59717 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6288i | 1.01388i | 0.861983 | + | 0.506938i | \(0.169223\pi\) | ||||
−0.861983 | + | 0.506938i | \(0.830777\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8564i | 0.963208i | 0.876389 | + | 0.481604i | \(0.159946\pi\) | ||||
−0.876389 | + | 0.481604i | \(0.840054\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.8043 | −1.97817 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.92820 | 0.356191 | 0.178096 | − | 0.984013i | \(-0.443006\pi\) | ||||
0.178096 | + | 0.984013i | \(0.443006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.6985i | 1.77166i | 0.464007 | + | 0.885832i | \(0.346411\pi\) | ||||
−0.464007 | + | 0.885832i | \(0.653589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 24.5359i | − 1.45851i | −0.684243 | − | 0.729254i | \(-0.739867\pi\) | ||||
0.684243 | − | 0.729254i | \(-0.260133\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.45189 | 0.380843 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8564 | −0.638612 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.7680i | 1.27170i | 0.771812 | + | 0.635850i | \(0.219350\pi\) | ||||
−0.771812 | + | 0.635850i | \(0.780650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6603i | 1.61044i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.44949 | −0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.26795 | −0.0730834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 39.1175i | − 2.23986i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.00000i | − 0.513657i | −0.966457 | − | 0.256829i | \(-0.917322\pi\) | ||||
0.966457 | − | 0.256829i | \(-0.0826776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.27792 | 0.299283 | 0.149642 | − | 0.988740i | \(-0.452188\pi\) | ||||
0.149642 | + | 0.988740i | \(0.452188\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.05256 | −0.455158 | −0.227579 | − | 0.973760i | \(-0.573081\pi\) | ||||
−0.227579 | + | 0.973760i | \(0.573081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 2.72689i | − 0.153157i | −0.997064 | − | 0.0765787i | \(-0.975600\pi\) | ||||
0.997064 | − | 0.0765787i | \(-0.0243997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.80385i | 0.548910i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.3896 | −1.46836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 67.1769 | 3.72630 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.10634i | 0.446917i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.7846i | 0.922566i | 0.887253 | + | 0.461283i | \(0.152611\pi\) | ||||
−0.887253 | + | 0.461283i | \(0.847389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 42.3249 | 2.31245 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.53590 | −0.301560 | −0.150780 | − | 0.988567i | \(-0.548178\pi\) | ||||
−0.150780 | + | 0.988567i | \(0.548178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 8.17072i | − 0.442469i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.5278 | 1.15567 | 0.577836 | − | 0.816153i | \(-0.303897\pi\) | ||||
0.577836 | + | 0.816153i | \(0.303897\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.5359 | −1.09926 | −0.549631 | − | 0.835408i | \(-0.685232\pi\) | ||||
−0.549631 | + | 0.835408i | \(0.685232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.52245i | 0.453604i | 0.973941 | + | 0.226802i | \(0.0728270\pi\) | ||||
−0.973941 | + | 0.226802i | \(0.927173\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 54.7128i | 2.90385i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.1112 | −0.850314 | −0.425157 | − | 0.905120i | \(-0.639781\pi\) | ||||
−0.425157 | + | 0.905120i | \(0.639781\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 44.6728i | − 2.33828i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 30.5167i | − 1.59296i | −0.604667 | − | 0.796478i | \(-0.706694\pi\) | ||||
0.604667 | − | 0.796478i | \(-0.293306\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.93426 | 0.308091 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.66025 | 0.241299 | 0.120649 | − | 0.992695i | \(-0.461502\pi\) | ||||
0.120649 | + | 0.992695i | \(0.461502\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 20.0764i | − 1.03399i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.1962i | 1.44834i | 0.689622 | + | 0.724170i | \(0.257777\pi\) | ||||
−0.689622 | + | 0.724170i | \(0.742223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.82843 | 0.144526 | 0.0722629 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722629 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1244 | −0.515985 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.4206i | 1.23817i | 0.785323 | + | 0.619086i | \(0.212497\pi\) | ||||
−0.785323 | + | 0.619086i | \(0.787503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 2.73205i | − 0.138166i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −53.4355 | −2.68863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.92820 | 0.247339 | 0.123670 | − | 0.992323i | \(-0.460534\pi\) | ||||
0.123670 | + | 0.992323i | \(0.460534\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.41902i | 0.470363i | 0.971951 | + | 0.235182i | \(0.0755685\pi\) | ||||
−0.971951 | + | 0.235182i | \(0.924431\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.7321i | 0.833483i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.3156 | −0.511325 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.41154 | 0.168690 | 0.0843450 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843450 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.31319i | 0.310652i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 77.2295i | − 3.79105i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −37.8792 | −1.85052 | −0.925259 | − | 0.379336i | \(-0.876152\pi\) | ||||
−0.925259 | + | 0.379336i | \(0.876152\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.3205 | −0.990361 | −0.495180 | − | 0.868790i | \(-0.664898\pi\) | ||||
−0.495180 | + | 0.868790i | \(0.664898\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 74.9261i | 3.63445i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 8.92820i | − 0.432066i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.79126 | 0.134450 | 0.0672252 | − | 0.997738i | \(-0.478585\pi\) | ||||
0.0672252 | + | 0.997738i | \(0.478585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.7321 | −1.38077 | −0.690387 | − | 0.723440i | \(-0.742560\pi\) | ||||
−0.690387 | + | 0.723440i | \(0.742560\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 2.58819i | − 0.123810i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 38.2487i | − 1.82551i | −0.408506 | − | 0.912756i | \(-0.633950\pi\) | ||||
0.408506 | − | 0.912756i | \(-0.366050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.0077 | −0.808062 | −0.404031 | − | 0.914745i | \(-0.632391\pi\) | ||||
−0.404031 | + | 0.914745i | \(0.632391\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.26795 | −0.107511 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 9.31749i | − 0.439719i | −0.975532 | − | 0.219860i | \(-0.929440\pi\) | ||||
0.975532 | − | 0.219860i | \(-0.0705599\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.9090i | 0.702036i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.7327 | 0.971965 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.1769 | 1.69228 | 0.846142 | − | 0.532957i | \(-0.178919\pi\) | ||||
0.846142 | + | 0.532957i | \(0.178919\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.8671i | 0.832156i | 0.909329 | + | 0.416078i | \(0.136596\pi\) | ||||
−0.909329 | + | 0.416078i | \(0.863404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 36.2487i | − 1.68462i | −0.538993 | − | 0.842310i | \(-0.681195\pi\) | ||||
0.538993 | − | 0.842310i | \(-0.318805\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0101 | 0.972233 | 0.486116 | − | 0.873894i | \(-0.338413\pi\) | ||||
0.486116 | + | 0.873894i | \(0.338413\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.66025 | 0.446069 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 2.92996i | − 0.134720i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 70.9808i | 3.25682i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.28221 | −0.378424 | −0.189212 | − | 0.981936i | \(-0.560593\pi\) | ||||
−0.189212 | + | 0.981936i | \(0.560593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.1244 | 0.963188 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.06678i | − 0.184663i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 14.5885i | − 0.661066i | −0.943794 | − | 0.330533i | \(-0.892771\pi\) | ||||
0.943794 | − | 0.330533i | \(-0.107229\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3209 | −1.05246 | −0.526229 | − | 0.850343i | \(-0.676395\pi\) | ||||
−0.526229 | + | 0.850343i | \(0.676395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3923 | 1.00850 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4877i | 0.560149i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16.3397i | − 0.731467i | −0.930720 | − | 0.365734i | \(-0.880818\pi\) | ||||
0.930720 | − | 0.365734i | \(-0.119182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.5211 | −0.647463 | −0.323731 | − | 0.946149i | \(-0.604937\pi\) | ||||
−0.323731 | + | 0.946149i | \(0.604937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −44.5885 | −1.98416 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.2886i | 1.38684i | 0.720533 | + | 0.693421i | \(0.243897\pi\) | ||||
−0.720533 | + | 0.693421i | \(0.756103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 10.1962i | − 0.451051i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −45.8468 | −2.02025 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.7321 | −0.823835 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 11.9329i | − 0.522789i | −0.965232 | − | 0.261395i | \(-0.915818\pi\) | ||||
0.965232 | − | 0.261395i | \(-0.0841824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 11.3397i | − 0.495852i | −0.968779 | − | 0.247926i | \(-0.920251\pi\) | ||||
0.968779 | − | 0.247926i | \(-0.0797491\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.6622 | −0.812937 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7321 | −0.988350 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 30.5307i | − 1.32243i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 60.3013i | − 2.60705i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.31079 | −0.0995327 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1051 | −1.85323 | −0.926617 | − | 0.376007i | \(-0.877297\pi\) | ||||
−0.926617 | + | 0.376007i | \(0.877297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 59.5357i | − 2.55023i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.0000i | − 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.2132 | 0.903713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1962 | −0.518633 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.23835i | 0.0524705i | 0.999656 | + | 0.0262352i | \(0.00835190\pi\) | ||||
−0.999656 | + | 0.0262352i | \(0.991648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000i | 0.253773i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.2934 | −1.65602 | −0.828009 | − | 0.560715i | \(-0.810526\pi\) | ||||
−0.828009 | + | 0.560715i | \(0.810526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.1769 | −1.56404 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.7744i | 1.87704i | 0.345226 | + | 0.938519i | \(0.387802\pi\) | ||||
−0.345226 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 46.2487i | − 1.93545i | −0.252012 | − | 0.967724i | \(-0.581092\pi\) | ||||
0.252012 | − | 0.967724i | \(-0.418908\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.34847 | −0.306452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.60770 | −0.233451 | −0.116726 | − | 0.993164i | \(-0.537240\pi\) | ||||
−0.116726 | + | 0.993164i | \(0.537240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 17.6269i | − 0.731287i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.7128i | 0.567927i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.0096 | 0.660788 | 0.330394 | − | 0.943843i | \(-0.392818\pi\) | ||||
0.330394 | + | 0.943843i | \(0.392818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6795 | −0.728471 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.1397i | 0.416389i | 0.978087 | + | 0.208194i | \(0.0667587\pi\) | ||||
−0.978087 | + | 0.208194i | \(0.933241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.1244i | 0.948006i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.6999 | −0.968350 | −0.484175 | − | 0.874971i | \(-0.660880\pi\) | ||||
−0.484175 | + | 0.874971i | \(0.660880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.3397 | −1.23758 | −0.618792 | − | 0.785555i | \(-0.712378\pi\) | ||||
−0.618792 | + | 0.785555i | \(0.712378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.7995i | 1.00824i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 39.1769i | − 1.59014i | −0.606516 | − | 0.795071i | \(-0.707434\pi\) | ||||
0.606516 | − | 0.795071i | \(-0.292566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.3596 | 1.55186 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5885 | −1.19507 | −0.597533 | − | 0.801844i | \(-0.703852\pi\) | ||||
−0.597533 | + | 0.801844i | \(0.703852\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 18.9396i | − 0.762479i | −0.924476 | − | 0.381239i | \(-0.875497\pi\) | ||||
0.924476 | − | 0.381239i | \(-0.124503\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 28.6603i | − 1.15195i | −0.817466 | − | 0.575976i | \(-0.804622\pi\) | ||||
0.817466 | − | 0.575976i | \(-0.195378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.517638 | −0.0207387 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 105.550 | 4.22200 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.5612i | 0.939445i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0526i | 0.639042i | 0.947579 | + | 0.319521i | \(0.103522\pi\) | ||||
−0.947579 | + | 0.319521i | \(0.896478\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.48854 | 0.0590710 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.73205 | 0.187491 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 2.07055i | − 0.0817819i | −0.999164 | − | 0.0408910i | \(-0.986980\pi\) | ||||
0.999164 | − | 0.0408910i | \(-0.0130196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 22.8564i | − 0.901369i | −0.892683 | − | 0.450684i | \(-0.851180\pi\) | ||||
0.892683 | − | 0.450684i | \(-0.148820\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.3249 | 1.66396 | 0.831981 | − | 0.554804i | \(-0.187207\pi\) | ||||
0.831981 | + | 0.554804i | \(0.187207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5885 | −0.572647 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.48099i | − 0.214488i | −0.994233 | − | 0.107244i | \(-0.965797\pi\) | ||||
0.994233 | − | 0.107244i | \(-0.0342025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6.19615i | − 0.242104i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.7351 | 0.963544 | 0.481772 | − | 0.876297i | \(-0.339993\pi\) | ||||
0.481772 | + | 0.876297i | \(0.339993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.26795 | −0.204899 | −0.102450 | − | 0.994738i | \(-0.532668\pi\) | ||||
−0.102450 | + | 0.994738i | \(0.532668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.9067i | 0.849506i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.19615i | 0.0850354i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.6312 | 0.796458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.9282 | −0.498346 | −0.249173 | − | 0.968459i | \(-0.580159\pi\) | ||||
−0.249173 | + | 0.968459i | \(0.580159\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 39.1547i | − 1.50484i | −0.658686 | − | 0.752418i | \(-0.728887\pi\) | ||||
0.658686 | − | 0.752418i | \(-0.271113\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 0.928203i | − 0.0356212i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.41662 | 0.207261 | 0.103631 | − | 0.994616i | \(-0.466954\pi\) | ||||
0.103631 | + | 0.994616i | \(0.466954\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.6603 | 1.05684 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 28.0812i | − 1.06981i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 4.67949i | − 0.178016i | −0.996031 | − | 0.0890081i | \(-0.971630\pi\) | ||||
0.996031 | − | 0.0890081i | \(-0.0283697\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 102.175 | 3.87572 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.0526 | 1.28983 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4505i | 0.470250i | 0.971965 | + | 0.235125i | \(0.0755499\pi\) | ||||
−0.971965 | + | 0.235125i | \(0.924450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.3205i | 0.841834i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.1769 | −0.382742 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.6603 | 0.625689 | 0.312844 | − | 0.949804i | \(-0.398718\pi\) | ||||
0.312844 | + | 0.949804i | \(0.398718\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.83032i | − 0.0685459i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 47.9090i | 1.79169i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.2982 | 1.76392 | 0.881962 | − | 0.471320i | \(-0.156222\pi\) | ||||
0.881962 | + | 0.471320i | \(0.156222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4641 | −0.389704 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 60.2292i | − 2.23686i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 5.07180i | − 0.188103i | −0.995567 | − | 0.0940513i | \(-0.970018\pi\) | ||||
0.995567 | − | 0.0940513i | \(-0.0299818\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.69213 | −0.247517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8038 | −0.953087 | −0.476543 | − | 0.879151i | \(-0.658111\pi\) | ||||
−0.476543 | + | 0.879151i | \(0.658111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.3228i | 0.822271i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.9282i | 0.549143i | 0.961567 | + | 0.274571i | \(0.0885360\pi\) | ||||
−0.961567 | + | 0.274571i | \(0.911464\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.8004 | 0.506286 | 0.253143 | − | 0.967429i | \(-0.418536\pi\) | ||||
0.253143 | + | 0.967429i | \(0.418536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −86.7461 | −3.17813 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 13.7632i | − 0.502896i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 13.6603i | − 0.498470i | −0.968443 | − | 0.249235i | \(-0.919821\pi\) | ||||
0.968443 | − | 0.249235i | \(-0.0801791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.69591 | 0.170902 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.6410 | −0.604828 | −0.302414 | − | 0.953177i | \(-0.597793\pi\) | ||||
−0.302414 | + | 0.953177i | \(0.597793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 0.859411i | − 0.0311536i | −0.999879 | − | 0.0155768i | \(-0.995042\pi\) | ||||
0.999879 | − | 0.0155768i | \(-0.00495845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 13.5885i | − 0.491935i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.8744 | 1.07870 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6603 | 0.636845 | 0.318423 | − | 0.947949i | \(-0.396847\pi\) | ||||
0.318423 | + | 0.947949i | \(0.396847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 23.9773i | − 0.862402i | −0.902256 | − | 0.431201i | \(-0.858090\pi\) | ||||
0.902256 | − | 0.431201i | \(-0.141910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.1962i | 1.80310i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.2595 | 1.15582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.8564 | −1.03256 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 14.3180i | − 0.511031i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.32051i | − 0.260948i | −0.991452 | − | 0.130474i | \(-0.958350\pi\) | ||||
0.991452 | − | 0.130474i | \(-0.0416499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48528 | −0.301702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.2487 | −1.50030 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.20599i | 0.326093i | 0.986618 | + | 0.163046i | \(0.0521320\pi\) | ||||
−0.986618 | + | 0.163046i | \(0.947868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.7846i | 1.51361i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.5612 | 0.831455 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.26795 | −0.0799347 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 28.1827i | − 0.990852i | −0.868650 | − | 0.495426i | \(-0.835012\pi\) | ||||
0.868650 | − | 0.495426i | \(-0.164988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 44.6603i | − 1.56823i | −0.620613 | − | 0.784117i | \(-0.713116\pi\) | ||||
0.620613 | − | 0.784117i | \(-0.286884\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −87.8571 | −3.07750 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.33975 | −0.221800 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.8129i | 1.35458i | 0.735716 | + | 0.677290i | \(0.236846\pi\) | ||||
−0.735716 | + | 0.677290i | \(0.763154\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 7.07180i | − 0.246507i | −0.992375 | − | 0.123254i | \(-0.960667\pi\) | ||||
0.992375 | − | 0.123254i | \(-0.0393329\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.85752 | 0.0645924 | 0.0322962 | − | 0.999478i | \(-0.489718\pi\) | ||||
0.0322962 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.1962 | 1.25714 | 0.628572 | − | 0.777751i | \(-0.283640\pi\) | ||||
0.628572 | + | 0.777751i | \(0.283640\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.27792i | 0.182869i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.9615i | 1.24450i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −55.5061 | −1.91628 | −0.958141 | − | 0.286297i | \(-0.907576\pi\) | ||||
−0.958141 | + | 0.286297i | \(0.907576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | 0.379310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 41.1509i | − 1.41563i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.66025i | 0.194489i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.31079 | −0.0792128 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0000 | 0.616308 | 0.308154 | − | 0.951336i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 46.8821i | − 1.60146i | −0.599025 | − | 0.800731i | \(-0.704445\pi\) | ||||
0.599025 | − | 0.800731i | \(-0.295555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 55.1051i | − 1.88016i | −0.340951 | − | 0.940081i | \(-0.610749\pi\) | ||||
0.340951 | − | 0.940081i | \(-0.389251\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.93855 | 0.304272 | 0.152136 | − | 0.988360i | \(-0.451385\pi\) | ||||
0.152136 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.3923 | 1.74739 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 28.1827i | − 0.956034i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 45.7128i | − 1.54892i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.2915 | 1.36210 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.1436 | −0.612666 | −0.306333 | − | 0.951924i | \(-0.599102\pi\) | ||||
−0.306333 | + | 0.951924i | \(0.599102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.04197i | 0.270941i | 0.990781 | + | 0.135470i | \(0.0432546\pi\) | ||||
−0.990781 | + | 0.135470i | \(0.956745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3923i | 0.349729i | 0.984593 | + | 0.174864i | \(0.0559487\pi\) | ||||
−0.984593 | + | 0.174864i | \(0.944051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.1533 | −1.51610 | −0.758050 | − | 0.652197i | \(-0.773848\pi\) | ||||
−0.758050 | + | 0.652197i | \(0.773848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.339746 | 0.0113947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40.5317i | 1.35634i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.51666i | 0.318107i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15.0015 | 0.500330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.3205 | 1.04344 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 73.5391i | 2.44452i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.9282i | 0.960545i | 0.877119 | + | 0.480273i | \(0.159462\pi\) | ||||
−0.877119 | + | 0.480273i | \(0.840538\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.30942 | 0.275303 | 0.137652 | − | 0.990481i | \(-0.456045\pi\) | ||||
0.137652 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40.7321 | 1.34803 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.41421i | − 0.0467014i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 29.7128i | − 0.980135i | −0.871684 | − | 0.490068i | \(-0.836972\pi\) | ||||
0.871684 | − | 0.490068i | \(-0.163028\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 59.0924 | 1.94505 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.3731 | 2.08369 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 8.93855i | − 0.293264i | −0.989191 | − | 0.146632i | \(-0.953157\pi\) | ||||
0.989191 | − | 0.146632i | \(-0.0468434\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000i | 0.163868i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −53.4355 | −1.74753 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.5692 | −1.68469 | −0.842346 | − | 0.538936i | \(-0.818826\pi\) | ||||
−0.842346 | + | 0.538936i | \(0.818826\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 9.00292i | − 0.293487i | −0.989175 | − | 0.146743i | \(-0.953121\pi\) | ||||
0.989175 | − | 0.146743i | \(-0.0468792\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.33975i | 0.108757i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.2209 | 1.24201 | 0.621007 | − | 0.783805i | \(-0.286724\pi\) | ||||
0.621007 | + | 0.783805i | \(0.286724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48.2487 | −1.56622 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.2800i | 0.818899i | 0.912333 | + | 0.409449i | \(0.134279\pi\) | ||||
−0.912333 | + | 0.409449i | \(0.865721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53.0526i | 1.71674i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.31319 | 0.203864 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.4974 | 0.596691 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 110.938i | 3.57121i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 24.2487i | − 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.5317 | −1.30072 | −0.650362 | − | 0.759624i | \(-0.725383\pi\) | ||||
−0.650362 | + | 0.759624i | \(0.725383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.3205 | 0.747621 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 46.9192i | − 1.50108i | −0.660825 | − | 0.750540i | \(-0.729794\pi\) | ||||
0.660825 | − | 0.750540i | \(-0.270206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1.19615i | − 0.0382292i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.42280 | −0.236751 | −0.118375 | − | 0.992969i | \(-0.537769\pi\) | ||||
−0.118375 | + | 0.992969i | \(0.537769\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.5692 | −0.750978 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 0.656339i | − 0.0208704i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.8372i | 1.48783i | 0.668273 | + | 0.743916i | \(0.267034\pi\) | ||||
−0.668273 | + | 0.743916i | \(0.732966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −77.6902 | −2.46294 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.9282 | −0.916165 | −0.458083 | − | 0.888910i | \(-0.651464\pi\) | ||||
−0.458083 | + | 0.888910i | \(0.651464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.h.b.2591.1 | ✓ | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.b.2591.7 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.b.2591.2 | yes | 8 | |
12.11 | even | 2 | inner | 6048.2.h.b.2591.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.b.2591.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.b.2591.2 | yes | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.b.2591.7 | yes | 8 | 3.2 | odd | 2 | inner | |
6048.2.h.b.2591.8 | yes | 8 | 12.11 | even | 2 | inner |